diff --git a/-PGcTRLh1u4.txt b/-PGcTRLh1u4.txt new file mode 100644 index 0000000000000000000000000000000000000000..4e2ec3e39c243858294921556b43b3a7e08904de --- /dev/null +++ b/-PGcTRLh1u4.txt @@ -0,0 +1,2080 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I'd like to do two problems that ask us + + align:start position:0% +I'd like to do two problems that ask us + + + align:start position:0% +I'd like to do two problems that ask us +to determine the flux of a vector field + + align:start position:0% +to determine the flux of a vector field + + + align:start position:0% +to determine the flux of a vector field +along a surface so the first one is I'd + + align:start position:0% +along a surface so the first one is I'd + + + align:start position:0% +along a surface so the first one is I'd +like you to find the outward flux of the + + align:start position:0% +like you to find the outward flux of the + + + align:start position:0% +like you to find the outward flux of the +vector Z comma X comma y through the + + align:start position:0% +vector Z comma X comma y through the + + + align:start position:0% +vector Z comma X comma y through the +piece of the cylinder that's shown so + + align:start position:0% +piece of the cylinder that's shown so + + + align:start position:0% +piece of the cylinder that's shown so +it's just shading the cylindrical part + + align:start position:0% +it's just shading the cylindrical part + + + align:start position:0% +it's just shading the cylindrical part +so it's a cylinder of radius a and + + align:start position:0% +so it's a cylinder of radius a and + + + align:start position:0% +so it's a cylinder of radius a and +you're taking the piece in the first + + align:start position:0% +you're taking the piece in the first + + + align:start position:0% +you're taking the piece in the first +octant up to height H so that's the + + align:start position:0% +octant up to height H so that's the + + + align:start position:0% +octant up to height H so that's the +first question I'd like you to answer is + + align:start position:0% +first question I'd like you to answer is + + + align:start position:0% +first question I'd like you to answer is +the flux of this Vector field through + + align:start position:0% +the flux of this Vector field through + + + align:start position:0% +the flux of this Vector field through +that piece of the cylinder the outward + + align:start position:0% +that piece of the cylinder the outward + + + align:start position:0% +that piece of the cylinder the outward +flux and then I'd also like you to find + + align:start position:0% +flux and then I'd also like you to find + + + align:start position:0% +flux and then I'd also like you to find +the outward flux of this Vector field uh + + align:start position:0% +the outward flux of this Vector field uh + + + align:start position:0% +the outward flux of this Vector field uh +XZ comma YZ comma z s through the piece + + align:start position:0% +XZ comma YZ comma z s through the piece + + + align:start position:0% +XZ comma YZ comma z s through the piece +of the sphere of radius a in the first + + align:start position:0% +of the sphere of radius a in the first + + + align:start position:0% +of the sphere of radius a in the first +Octan so again it'll be in the first + + align:start position:0% +Octan so again it'll be in the first + + + align:start position:0% +Octan so again it'll be in the first +octant like this one is in the first + + align:start position:0% +octant like this one is in the first + + + align:start position:0% +octant like this one is in the first +Octan it'll be the piece of the sphere + + align:start position:0% +Octan it'll be the piece of the sphere + + + align:start position:0% +Octan it'll be the piece of the sphere +that sits in the same part of + + align:start position:0% +that sits in the same part of + + + align:start position:0% +that sits in the same part of +three-dimensional space as the piece of + + align:start position:0% +three-dimensional space as the piece of + + + align:start position:0% +three-dimensional space as the piece of +the cylinder we're looking at at here so + + align:start position:0% +the cylinder we're looking at at here so + + + align:start position:0% +the cylinder we're looking at at here so +what I'd like you to do again just find + + align:start position:0% +what I'd like you to do again just find + + + align:start position:0% +what I'd like you to do again just find +the flux in both cases the outward flux + + align:start position:0% +the flux in both cases the outward flux + + + align:start position:0% +the flux in both cases the outward flux +of the vector listed through the the + + align:start position:0% +of the vector listed through the the + + + align:start position:0% +of the vector listed through the the +surface that is listed and then when you + + align:start position:0% +surface that is listed and then when you + + + align:start position:0% +surface that is listed and then when you +feel comfortable and confident with your + + align:start position:0% +feel comfortable and confident with your + + + align:start position:0% +feel comfortable and confident with your +answer you can bring the video back up + + align:start position:0% +answer you can bring the video back up + + + align:start position:0% +answer you can bring the video back up +and I'll show you how I did + + align:start position:0% + + + + align:start position:0% + +it okay welcome back so again what we're + + align:start position:0% +it okay welcome back so again what we're + + + align:start position:0% +it okay welcome back so again what we're +trying to do is determine flux of a + + align:start position:0% +trying to do is determine flux of a + + + align:start position:0% +trying to do is determine flux of a +vector field through a surface so I am + + align:start position:0% +vector field through a surface so I am + + + align:start position:0% +vector field through a surface so I am +going to determine first what the normal + + align:start position:0% +going to determine first what the normal + + + align:start position:0% +going to determine first what the normal +is here and then what f.n is here and + + align:start position:0% +is here and then what f.n is here and + + + align:start position:0% +is here and then what f.n is here and +then using the fact that I know f.n and + + align:start position:0% +then using the fact that I know f.n and + + + align:start position:0% +then using the fact that I know f.n and +I know DS in a good parameterization I'm + + align:start position:0% +I know DS in a good parameterization I'm + + + align:start position:0% +I know DS in a good parameterization I'm +going to be able to calculate the + + align:start position:0% +going to be able to calculate the + + + align:start position:0% +going to be able to calculate the +integral quite simply so let's point out + + align:start position:0% +integral quite simply so let's point out + + + align:start position:0% +integral quite simply so let's point out +first that the normal at any point on + + align:start position:0% +first that the normal at any point on + + + align:start position:0% +first that the normal at any point on +this surface the normal at any point is + + align:start position:0% +this surface the normal at any point is + + + align:start position:0% +this surface the normal at any point is +going to be equal to X comma y comma 0 / + + align:start position:0% +going to be equal to X comma y comma 0 / + + + align:start position:0% +going to be equal to X comma y comma 0 / +a where a is again the radius because + + align:start position:0% +a where a is again the radius because + + + align:start position:0% +a where a is again the radius because +the normal I know there's no Z component + + align:start position:0% +the normal I know there's no Z component + + + align:start position:0% +the normal I know there's no Z component +and I actually know it's the same as the + + align:start position:0% +and I actually know it's the same as the + + + align:start position:0% +and I actually know it's the same as the +normal would be on a circle of radius a + + align:start position:0% +normal would be on a circle of radius a + + + align:start position:0% +normal would be on a circle of radius a +and so this this Vector X comma y has + + align:start position:0% +and so this this Vector X comma y has + + + align:start position:0% +and so this this Vector X comma y has +length a obviously so that's why I'm + + align:start position:0% +length a obviously so that's why I'm + + + align:start position:0% +length a obviously so that's why I'm +dividing by a so when I look at the + + align:start position:0% +dividing by a so when I look at the + + + align:start position:0% +dividing by a so when I look at the +normal and I dot it with f let's see + + align:start position:0% +normal and I dot it with f let's see + + + align:start position:0% +normal and I dot it with f let's see +what I + + align:start position:0% + + + + align:start position:0% + +get F dotted with the normal is going to + + align:start position:0% +get F dotted with the normal is going to + + + align:start position:0% +get F dotted with the normal is going to +be + + align:start position:0% +be + + + align:start position:0% +be +XZ plus + + align:start position:0% +XZ plus + + + align:start position:0% +XZ plus +XY + + align:start position:0% +XY + + + align:start position:0% +XY +ID + + align:start position:0% +ID + + + align:start position:0% +ID +a right so I just took X started with x + + align:start position:0% +a right so I just took X started with x + + + align:start position:0% +a right so I just took X started with x +* z y * Z 0 * y I add those up and I + + align:start position:0% +* z y * Z 0 * y I add those up and I + + + align:start position:0% +* z y * Z 0 * y I add those up and I +still have to divide by my a so that's + + align:start position:0% +still have to divide by my a so that's + + + align:start position:0% +still have to divide by my a so that's +actually the vector dotted with the + + align:start position:0% +actually the vector dotted with the + + + align:start position:0% +actually the vector dotted with the +normal now what's a natural + + align:start position:0% +normal now what's a natural + + + align:start position:0% +normal now what's a natural +parameterization to use here is + + align:start position:0% +parameterization to use here is + + + align:start position:0% +parameterization to use here is +obviously the cylindrical coordinates + + align:start position:0% +obviously the cylindrical coordinates + + + align:start position:0% +obviously the cylindrical coordinates +because I'm on a cylinder so what I'm + + align:start position:0% +because I'm on a cylinder so what I'm + + + align:start position:0% +because I'm on a cylinder so what I'm +interested in the radius is fixed but + + align:start position:0% +interested in the radius is fixed but + + + align:start position:0% +interested in the radius is fixed but +what I'm interested in is changes in + + align:start position:0% +what I'm interested in is changes in + + + align:start position:0% +what I'm interested in is changes in +Theta and changes in the height so I'm + + align:start position:0% +Theta and changes in the height so I'm + + + align:start position:0% +Theta and changes in the height so I'm +going to be interested in in D Theta and + + align:start position:0% +going to be interested in in D Theta and + + + align:start position:0% +going to be interested in in D Theta and +DZ and I need to understand what DS in + + align:start position:0% +DZ and I need to understand what DS in + + + align:start position:0% +DZ and I need to understand what DS in +this case is and it's just a d Theta DZ + + align:start position:0% +this case is and it's just a d Theta DZ + + + align:start position:0% +this case is and it's just a d Theta DZ +so let me write down what I'm going to + + align:start position:0% +so let me write down what I'm going to + + + align:start position:0% +so let me write down what I'm going to +need to completely determine the rest of + + align:start position:0% +need to completely determine the rest of + + + align:start position:0% +need to completely determine the rest of +number one is I'm + + align:start position:0% +number one is I'm + + + align:start position:0% +number one is I'm +integrating over the surface and I'll + + align:start position:0% +integrating over the surface and I'll + + + align:start position:0% +integrating over the surface and I'll +put the bounds + + align:start position:0% +put the bounds + + + align:start position:0% +put the bounds +momentarily um actually I should also + + align:start position:0% +momentarily um actually I should also + + + align:start position:0% +momentarily um actually I should also +point out I'm going to write X and Y in + + align:start position:0% +point out I'm going to write X and Y in + + + align:start position:0% +point out I'm going to write X and Y in +terms of theta because now I know what + + align:start position:0% +terms of theta because now I know what + + + align:start position:0% +terms of theta because now I know what +they are X in terms of theta is a cosine + + align:start position:0% +they are X in terms of theta is a cosine + + + align:start position:0% +they are X in terms of theta is a cosine +Theta and Y in terms of theta is a sin + + align:start position:0% +Theta and Y in terms of theta is a sin + + + align:start position:0% +Theta and Y in terms of theta is a sin +Theta so when I simplify the expression + + align:start position:0% +Theta so when I simplify the expression + + + align:start position:0% +Theta so when I simplify the expression +f.n I get Z * cosine Theta for my first + + align:start position:0% +f.n I get Z * cosine Theta for my first + + + align:start position:0% +f.n I get Z * cosine Theta for my first +component and I get a * cosine Theta sin + + align:start position:0% +component and I get a * cosine Theta sin + + + align:start position:0% +component and I get a * cosine Theta sin +Theta for my second + + align:start position:0% + + + + align:start position:0% + +component so let me maybe point out + + align:start position:0% +component so let me maybe point out + + + align:start position:0% +component so let me maybe point out +again how I got that let me come over + + align:start position:0% +again how I got that let me come over + + + align:start position:0% +again how I got that let me come over +here x is a cosine Theta so I get Z * a + + align:start position:0% +here x is a cosine Theta so I get Z * a + + + align:start position:0% +here x is a cosine Theta so I get Z * a +cosine Theta / a so I get Z * cosine + + align:start position:0% +cosine Theta / a so I get Z * cosine + + + align:start position:0% +cosine Theta / a so I get Z * cosine +Theta + + align:start position:0% +Theta + + + align:start position:0% +Theta +X again is a cosine Theta Y is a sin + + align:start position:0% +X again is a cosine Theta Y is a sin + + + align:start position:0% +X again is a cosine Theta Y is a sin +Theta so I get a^ 2 cosine Theta sin + + align:start position:0% +Theta so I get a^ 2 cosine Theta sin + + + align:start position:0% +Theta so I get a^ 2 cosine Theta sin +Theta and I divide by a I get a single a + + align:start position:0% +Theta and I divide by a I get a single a + + + align:start position:0% +Theta and I divide by a I get a single a +cosine Theta sin Theta and then my DS as + + align:start position:0% +cosine Theta sin Theta and then my DS as + + + align:start position:0% +cosine Theta sin Theta and then my DS as +I mentioned before is a d Theta + + align:start position:0% +I mentioned before is a d Theta + + + align:start position:0% +I mentioned before is a d Theta +DZ right and so now I just have to + + align:start position:0% +DZ right and so now I just have to + + + align:start position:0% +DZ right and so now I just have to +figure out the bounds in Theta and the + + align:start position:0% +figure out the bounds in Theta and the + + + align:start position:0% +figure out the bounds in Theta and the +bounds in Z well the bounds in Z are + + align:start position:0% +bounds in Z well the bounds in Z are + + + align:start position:0% +bounds in Z well the bounds in Z are +very easy the bounds in Z are simply + + align:start position:0% +very easy the bounds in Z are simply + + + align:start position:0% +very easy the bounds in Z are simply +zero to H and so I'm going to put those + + align:start position:0% +zero to H and so I'm going to put those + + + align:start position:0% +zero to H and so I'm going to put those +here + + align:start position:0% +here + + + align:start position:0% +here +on the outside and then the bounds in + + align:start position:0% +on the outside and then the bounds in + + + align:start position:0% +on the outside and then the bounds in +Theta if I look at my picture maybe it's + + align:start position:0% +Theta if I look at my picture maybe it's + + + align:start position:0% +Theta if I look at my picture maybe it's +helpful to come over and look at my + + align:start position:0% +helpful to come over and look at my + + + align:start position:0% +helpful to come over and look at my +picture this direction in the X + + align:start position:0% +picture this direction in the X + + + align:start position:0% +picture this direction in the X +direction is theta equals 0 when I swing + + align:start position:0% +direction is theta equals 0 when I swing + + + align:start position:0% +direction is theta equals 0 when I swing +around to the Y Direction I'm at Theta + + align:start position:0% +around to the Y Direction I'm at Theta + + + align:start position:0% +around to the Y Direction I'm at Theta +equal Pi / + + align:start position:0% +equal Pi / + + + align:start position:0% +equal Pi / +2 so I need to go from zero to pi over 2 + + align:start position:0% +2 so I need to go from zero to pi over 2 + + + align:start position:0% +2 so I need to go from zero to pi over 2 +right so let me come back over + + align:start position:0% + + + + align:start position:0% + +here okay so now really I have a couple + + align:start position:0% +here okay so now really I have a couple + + + align:start position:0% +here okay so now really I have a couple +constant that are letters but everything + + align:start position:0% +constant that are letters but everything + + + align:start position:0% +constant that are letters but everything +now I'm ready to integrate so a is just + + align:start position:0% +now I'm ready to integrate so a is just + + + align:start position:0% +now I'm ready to integrate so a is just +a constant and H is a constant and z and + + align:start position:0% +a constant and H is a constant and z and + + + align:start position:0% +a constant and H is a constant and z and +Theta are my variables and I can + + align:start position:0% +Theta are my variables and I can + + + align:start position:0% +Theta are my variables and I can +actually do this integration quite + + align:start position:0% +actually do this integration quite + + + align:start position:0% +actually do this integration quite +simply I'm not going to do it because I + + align:start position:0% +simply I'm not going to do it because I + + + align:start position:0% +simply I'm not going to do it because I +I know this is at this point something + + align:start position:0% +I know this is at this point something + + + align:start position:0% +I know this is at this point something +we already know how to do but I'll give + + align:start position:0% +we already know how to do but I'll give + + + align:start position:0% +we already know how to do but I'll give +you the answer so let me write down the + + align:start position:0% +you the answer so let me write down the + + + align:start position:0% +you the answer so let me write down the +answer you get a h^ 2/ 2 plus a^2 h/ 2 + + align:start position:0% +answer you get a h^ 2/ 2 plus a^2 h/ 2 + + + align:start position:0% +answer you get a h^ 2/ 2 plus a^2 h/ 2 +so that's the solution you actually get + + align:start position:0% +so that's the solution you actually get + + + align:start position:0% +so that's the solution you actually get +so again I mean you you have to you + + align:start position:0% +so again I mean you you have to you + + + align:start position:0% +so again I mean you you have to you +integrate in D Theta first so you have + + align:start position:0% +integrate in D Theta first so you have + + + align:start position:0% +integrate in D Theta first so you have +to deal with this you have to deal with + + align:start position:0% +to deal with this you have to deal with + + + align:start position:0% +to deal with this you have to deal with +this this uses a good trig identity you + + align:start position:0% +this this uses a good trig identity you + + + align:start position:0% +this this uses a good trig identity you +can use the fact that 2 sin Theta cosine + + align:start position:0% +can use the fact that 2 sin Theta cosine + + + align:start position:0% +can use the fact that 2 sin Theta cosine +Theta is sin 2 Theta that I'll give you + + align:start position:0% +Theta is sin 2 Theta that I'll give you + + + align:start position:0% +Theta is sin 2 Theta that I'll give you +that little hint and then you can figure + + align:start position:0% +that little hint and then you can figure + + + align:start position:0% +that little hint and then you can figure +it out from there and then you integrate + + align:start position:0% +it out from there and then you integrate + + + align:start position:0% +it out from there and then you integrate +in Z and you you integrate you evaluate + + align:start position:0% +in Z and you you integrate you evaluate + + + align:start position:0% +in Z and you you integrate you evaluate +from Z to H so that's that's the + + align:start position:0% +from Z to H so that's that's the + + + align:start position:0% +from Z to H so that's that's the +solution to number one so now let's look + + align:start position:0% +solution to number one so now let's look + + + align:start position:0% +solution to number one so now let's look +at number + + align:start position:0% +at number + + + align:start position:0% +at number +two and number two we have to again + + align:start position:0% +two and number two we have to again + + + align:start position:0% +two and number two we have to again +figure out we have our Vector field + + align:start position:0% +figure out we have our Vector field + + + align:start position:0% +figure out we have our Vector field +and we know our surface is a piece of a + + align:start position:0% +and we know our surface is a piece of a + + + align:start position:0% +and we know our surface is a piece of a +sphere and so if we're going to + + align:start position:0% +sphere and so if we're going to + + + align:start position:0% +sphere and so if we're going to +parameterize the surface of a sphere we + + align:start position:0% +parameterize the surface of a sphere we + + + align:start position:0% +parameterize the surface of a sphere we +know we want to use D Theta and D Fe + + align:start position:0% +know we want to use D Theta and D Fe + + + align:start position:0% +know we want to use D Theta and D Fe +okay and let me point out first that the + + align:start position:0% +okay and let me point out first that the + + + align:start position:0% +okay and let me point out first that the +normal here again the normal is going to + + align:start position:0% +normal here again the normal is going to + + + align:start position:0% +normal here again the normal is going to +be in some ways similar to what we saw + + align:start position:0% +be in some ways similar to what we saw + + + align:start position:0% +be in some ways similar to what we saw +in the cylinder but now instead of X + + align:start position:0% +in the cylinder but now instead of X + + + align:start position:0% +in the cylinder but now instead of X +comma y comma 0 because it's a sphere + + align:start position:0% +comma y comma 0 because it's a sphere + + + align:start position:0% +comma y comma 0 because it's a sphere +it's going to be X comma y comma Z / a + + align:start position:0% +it's going to be X comma y comma Z / a + + + align:start position:0% +it's going to be X comma y comma Z / a +so again as before let me just point out + + align:start position:0% +so again as before let me just point out + + + align:start position:0% +so again as before let me just point out +the normal that I'm going to be using is + + align:start position:0% +the normal that I'm going to be using is + + + align:start position:0% +the normal that I'm going to be using is +X comma y comma + + align:start position:0% +X comma y comma + + + align:start position:0% +X comma y comma +Z all divided by a so I'm going to dot f + + align:start position:0% +Z all divided by a so I'm going to dot f + + + align:start position:0% +Z all divided by a so I'm going to dot f +with n and look at the surface integral + + align:start position:0% +with n and look at the surface integral + + + align:start position:0% +with n and look at the surface integral +with with respect to DS capital D + + align:start position:0% +with with respect to DS capital D + + + align:start position:0% +with with respect to DS capital D +capital S there and I'll see what I get + + align:start position:0% +capital S there and I'll see what I get + + + align:start position:0% +capital S there and I'll see what I get +so again I know how I'm going to + + align:start position:0% +so again I know how I'm going to + + + align:start position:0% +so again I know how I'm going to +parameterize the sphere I already + + align:start position:0% +parameterize the sphere I already + + + align:start position:0% +parameterize the sphere I already +mentioned it but let me say it again + + align:start position:0% +mentioned it but let me say it again + + + align:start position:0% +mentioned it but let me say it again +it's going to be in Theta and Z sorry + + align:start position:0% +it's going to be in Theta and Z sorry + + + align:start position:0% +it's going to be in Theta and Z sorry +Theta and d and Fe right because we have + + align:start position:0% +Theta and d and Fe right because we have + + + align:start position:0% +Theta and d and Fe right because we have +a constant radius we're on a sphere of + + align:start position:0% +a constant radius we're on a sphere of + + + align:start position:0% +a constant radius we're on a sphere of +radius a so I don't need to change row + + align:start position:0% +radius a so I don't need to change row + + + align:start position:0% +radius a so I don't need to change row +it's a it's a two-dimensional thing so + + align:start position:0% +it's a it's a two-dimensional thing so + + + align:start position:0% +it's a it's a two-dimensional thing so +Theta is varying and Fe is varying so + + align:start position:0% +Theta is varying and Fe is varying so + + + align:start position:0% +Theta is varying and Fe is varying so +let's see what we get first let me do a + + align:start position:0% +let's see what we get first let me do a + + + align:start position:0% +let's see what we get first let me do a +little work and see what we get when we + + align:start position:0% +little work and see what we get when we + + + align:start position:0% +little work and see what we get when we +get look at F dotted with n so let me + + align:start position:0% +get look at F dotted with n so let me + + + align:start position:0% +get look at F dotted with n so let me +first point out that F dotted with + + align:start position:0% +first point out that F dotted with + + + align:start position:0% +first point out that F dotted with +n looks like it's X2 + + align:start position:0% +n looks like it's X2 + + + align:start position:0% +n looks like it's X2 +Z Plus Y 2 Z Plus just to make this + + align:start position:0% +Z Plus Y 2 Z Plus just to make this + + + align:start position:0% +Z Plus Y 2 Z Plus just to make this +obvious z^ 2 Z all divided by + + align:start position:0% +obvious z^ 2 Z all divided by + + + align:start position:0% +obvious z^ 2 Z all divided by +a x^2 + y^2 + z^2 is a s + + align:start position:0% +a x^2 + y^2 + z^2 is a s + + + align:start position:0% +a x^2 + y^2 + z^2 is a s +right so it's actually a 2 * Z / a so + + align:start position:0% +right so it's actually a 2 * Z / a so + + + align:start position:0% +right so it's actually a 2 * Z / a so +it's just a * + + align:start position:0% +it's just a * + + + align:start position:0% +it's just a * +Z right so so far all I did was I dotted + + align:start position:0% +Z right so so far all I did was I dotted + + + align:start position:0% +Z right so so far all I did was I dotted +f with the normal and I knew the fact + + align:start position:0% +f with the normal and I knew the fact + + + align:start position:0% +f with the normal and I knew the fact +that x2+ y^2 + z^2 was a s because I was + + align:start position:0% +that x2+ y^2 + z^2 was a s because I was + + + align:start position:0% +that x2+ y^2 + z^2 was a s because I was +on a sphere of radius a so a 2 * z/ a is + + align:start position:0% +on a sphere of radius a so a 2 * z/ a is + + + align:start position:0% +on a sphere of radius a so a 2 * z/ a is +a * Z and now if I want to use the right + + align:start position:0% +a * Z and now if I want to use the right + + + align:start position:0% +a * Z and now if I want to use the right +coordinates think about Theta and f z is + + align:start position:0% +coordinates think about Theta and f z is + + + align:start position:0% +coordinates think about Theta and f z is +a cosine F so f.n in the the coordinates + + align:start position:0% +a cosine F so f.n in the the coordinates + + + align:start position:0% +a cosine F so f.n in the the coordinates +I'm interested in is going to be a^ 2 + + align:start position:0% +I'm interested in is going to be a^ 2 + + + align:start position:0% +I'm interested in is going to be a^ 2 +cosine F so let me get out of the way so + + align:start position:0% +cosine F so let me get out of the way so + + + align:start position:0% +cosine F so let me get out of the way so +you can see that so that's what our + + align:start position:0% +you can see that so that's what our + + + align:start position:0% +you can see that so that's what our +that's what our f.n will + + align:start position:0% +that's what our f.n will + + + align:start position:0% +that's what our f.n will +be and now if we're going to figure out + + align:start position:0% +be and now if we're going to figure out + + + align:start position:0% +be and now if we're going to figure out +the Flux Of course it's the integral of + + align:start position:0% +the Flux Of course it's the integral of + + + align:start position:0% +the Flux Of course it's the integral of +f.n DS and let's remind ourselves what + + align:start position:0% +f.n DS and let's remind ourselves what + + + align:start position:0% +f.n DS and let's remind ourselves what +DS is DS is going to be a + + align:start position:0% +DS is DS is going to be a + + + align:start position:0% +DS is DS is going to be a +s sin + + align:start position:0% +s sin + + + align:start position:0% +s sin +Fe D Theta D Fe you saw this in lecture + + align:start position:0% +Fe D Theta D Fe you saw this in lecture + + + align:start position:0% +Fe D Theta D Fe you saw this in lecture +actually also so this should look + + align:start position:0% +actually also so this should look + + + align:start position:0% +actually also so this should look +familiar and so now I just have to + + align:start position:0% +familiar and so now I just have to + + + align:start position:0% +familiar and so now I just have to +integrate f.n DS over the right + + align:start position:0% +integrate f.n DS over the right + + + align:start position:0% +integrate f.n DS over the right +components over the right bounds for + + align:start position:0% +components over the right bounds for + + + align:start position:0% +components over the right bounds for +Theta and Fe so let's determine what + + align:start position:0% +Theta and Fe so let's determine what + + + align:start position:0% +Theta and Fe so let's determine what +those are I'll put everything together + + align:start position:0% +those are I'll put everything together + + + align:start position:0% +those are I'll put everything together +and we'll determine what those are so + + align:start position:0% +and we'll determine what those are so + + + align:start position:0% +and we'll determine what those are so +I've got f. NDS that's going to be a to + + align:start position:0% +I've got f. NDS that's going to be a to + + + align:start position:0% +I've got f. NDS that's going to be a to +the + + align:start position:0% + + + + align:start position:0% + +4th sin + + align:start position:0% +4th sin + + + align:start position:0% +4th sin +Fe cosine + + align:start position:0% +Fe cosine + + + align:start position:0% +Fe cosine +Fe D Theta D + + align:start position:0% +Fe D Theta D + + + align:start position:0% +Fe D Theta D +Fe and let's think about what is the + + align:start position:0% +Fe and let's think about what is the + + + align:start position:0% +Fe and let's think about what is the +picture that I need in terms of the + + align:start position:0% +picture that I need in terms of the + + + align:start position:0% +picture that I need in terms of the +first octant of a sphere maybe I should + + align:start position:0% +first octant of a sphere maybe I should + + + align:start position:0% +first octant of a sphere maybe I should +draw a quick picture over here so we can + + align:start position:0% +draw a quick picture over here so we can + + + align:start position:0% +draw a quick picture over here so we can +remember what that looks + + align:start position:0% +remember what that looks + + + align:start position:0% +remember what that looks +like so it's going to + + align:start position:0% + + + + align:start position:0% + +be this is not going to be the greatest + + align:start position:0% +be this is not going to be the greatest + + + align:start position:0% +be this is not going to be the greatest +drawing ever but it's something like + + align:start position:0% +drawing ever but it's something like + + + align:start position:0% +drawing ever but it's something like +this and so I've got circles coming sort + + align:start position:0% +this and so I've got circles coming sort + + + align:start position:0% +this and so I've got circles coming sort +of pieces of a circle at each level I've + + align:start position:0% +of pieces of a circle at each level I've + + + align:start position:0% +of pieces of a circle at each level I've +got a piece of a circle right so Theta + + align:start position:0% +got a piece of a circle right so Theta + + + align:start position:0% +got a piece of a circle right so Theta +if this is the X Direction This is the y + + align:start position:0% +if this is the X Direction This is the y + + + align:start position:0% +if this is the X Direction This is the y +direction this is the Z Direction + + align:start position:0% +direction this is the Z Direction + + + align:start position:0% +direction this is the Z Direction +Theta is going from 0 again to Pi / 2 + + align:start position:0% +Theta is going from 0 again to Pi / 2 + + + align:start position:0% +Theta is going from 0 again to Pi / 2 +and F is going from 0 to Pi / + + align:start position:0% +and F is going from 0 to Pi / + + + align:start position:0% +and F is going from 0 to Pi / + + align:start position:0% + + + align:start position:0% +right so they're both going from 0 to pi + + align:start position:0% +right so they're both going from 0 to pi + + + align:start position:0% +right so they're both going from 0 to pi +over + + align:start position:0% + + + + align:start position:0% + +two so hopefully you were able to get + + align:start position:0% +two so hopefully you were able to get + + + align:start position:0% +two so hopefully you were able to get +this far at least in the calculation or + + align:start position:0% +this far at least in the calculation or + + + align:start position:0% +this far at least in the calculation or +into terms of figuring out the flux of f + + align:start position:0% +into terms of figuring out the flux of f + + + align:start position:0% +into terms of figuring out the flux of f +through that piece of the surface piece + + align:start position:0% +through that piece of the surface piece + + + align:start position:0% +through that piece of the surface piece +of the sphere and I'm just again going + + align:start position:0% +of the sphere and I'm just again going + + + align:start position:0% +of the sphere and I'm just again going +to write down the solution and then you + + align:start position:0% +to write down the solution and then you + + + align:start position:0% +to write down the solution and then you +can check your your answer against the + + align:start position:0% +can check your your answer against the + + + align:start position:0% +can check your your answer against the +solution and I got a 4 over 4 * pi so + + align:start position:0% +solution and I got a 4 over 4 * pi so + + + align:start position:0% +solution and I got a 4 over 4 * pi so +this whole solution is a 4 / 4 * pi so + + align:start position:0% +this whole solution is a 4 / 4 * pi so + + + align:start position:0% +this whole solution is a 4 / 4 * pi so +you can check your solution there again + + align:start position:0% +you can check your solution there again + + + align:start position:0% +you can check your solution there again +I want to point out what we did in both + + align:start position:0% +I want to point out what we did in both + + + align:start position:0% +I want to point out what we did in both +of these problems is we were trying to + + align:start position:0% +of these problems is we were trying to + + + align:start position:0% +of these problems is we were trying to +compute the flux of a certain Vector + + align:start position:0% +compute the flux of a certain Vector + + + align:start position:0% +compute the flux of a certain Vector +field through a surface and if you'll + + align:start position:0% +field through a surface and if you'll + + + align:start position:0% +field through a surface and if you'll +notice what I actually did in in this + + align:start position:0% +notice what I actually did in in this + + + align:start position:0% +notice what I actually did in in this +case is I kept the parameterization in + + align:start position:0% +case is I kept the parameterization in + + + align:start position:0% +case is I kept the parameterization in +terms of X Y and Z or I kept it in terms + + align:start position:0% +terms of X Y and Z or I kept it in terms + + + align:start position:0% +terms of X Y and Z or I kept it in terms +of the X y z variables first and then I + + align:start position:0% +of the X y z variables first and then I + + + align:start position:0% +of the X y z variables first and then I +put it in the parameterization of theta + + align:start position:0% +put it in the parameterization of theta + + + align:start position:0% +put it in the parameterization of theta +and Fe after and that made it a little + + align:start position:0% +and Fe after and that made it a little + + + align:start position:0% +and Fe after and that made it a little +easier to hang on to and figure out what + + align:start position:0% +easier to hang on to and figure out what + + + align:start position:0% +easier to hang on to and figure out what +it was because notice that X Y and Z + + align:start position:0% +it was because notice that X Y and Z + + + align:start position:0% +it was because notice that X Y and Z +become very complicated in Theta and V I + + align:start position:0% +become very complicated in Theta and V I + + + align:start position:0% +become very complicated in Theta and V I +have to write a lot more down I guess + + align:start position:0% +have to write a lot more down I guess + + + align:start position:0% +have to write a lot more down I guess +and then simplify things more care more + + align:start position:0% +and then simplify things more care more + + + align:start position:0% +and then simplify things more care more +carefully this way it was very obvious + + align:start position:0% +carefully this way it was very obvious + + + align:start position:0% +carefully this way it was very obvious +that I got an a^2 time Z in the + + align:start position:0% +that I got an a^2 time Z in the + + + align:start position:0% +that I got an a^2 time Z in the +numerator so sometimes it's a little + + align:start position:0% +numerator so sometimes it's a little + + + align:start position:0% +numerator so sometimes it's a little +easier to to compute the f.n in the + + align:start position:0% +easier to to compute the f.n in the + + + align:start position:0% +easier to to compute the f.n in the +initial XYZ variables and then change it + + align:start position:0% +initial XYZ variables and then change it + + + align:start position:0% +initial XYZ variables and then change it +to the appropriate parameterization for + + align:start position:0% +to the appropriate parameterization for + + + align:start position:0% +to the appropriate parameterization for +the surface you're looking at so that's + + align:start position:0% +the surface you're looking at so that's + + + align:start position:0% +the surface you're looking at so that's +what we did actually in both cases is we + + align:start position:0% +what we did actually in both cases is we + + + align:start position:0% +what we did actually in both cases is we +computed f.n we put it in the right + + align:start position:0% +computed f.n we put it in the right + + + align:start position:0% +computed f.n we put it in the right +parameterization and then we had to + + align:start position:0% +parameterization and then we had to + + + align:start position:0% +parameterization and then we had to +figure out what DS was we had to make + + align:start position:0% +figure out what DS was we had to make + + + align:start position:0% +figure out what DS was we had to make +sure we knew DS and then we just had to + + align:start position:0% +sure we knew DS and then we just had to + + + align:start position:0% +sure we knew DS and then we just had to +integrate over the appropriate bounds + + align:start position:0% +integrate over the appropriate bounds + + + align:start position:0% +integrate over the appropriate bounds +for our parameters and that's giving us + + align:start position:0% +for our parameters and that's giving us + + + align:start position:0% +for our parameters and that's giving us +the flux across the surface so I think + + align:start position:0% +the flux across the surface so I think + + + align:start position:0% +the flux across the surface so I think +that's where I'll + + align:start position:0% +that's where I'll + + + align:start position:0% +that's where I'll +sto \ No newline at end of file diff --git a/02NyrrxEGqM.txt b/02NyrrxEGqM.txt new file mode 100644 index 0000000000000000000000000000000000000000..698c91af77d6c6bb952a54d6945053a207900b1a --- /dev/null +++ b/02NyrrxEGqM.txt @@ -0,0 +1,323 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free to make a donation or to view + + align:start position:0% +for free to make a donation or to view + + + align:start position:0% +for free to make a donation or to view +additional materials from hundreds of + + align:start position:0% +additional materials from hundreds of + + + align:start position:0% +additional materials from hundreds of +MIT courses visit MIT opencourseware at + + align:start position:0% +MIT courses visit MIT opencourseware at + + + align:start position:0% +MIT courses visit MIT opencourseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so for today we're just going to break + + align:start position:0% +so for today we're just going to break + + + align:start position:0% +so for today we're just going to break +you guys up into groups so kenneth and + + align:start position:0% +you guys up into groups so kenneth and + + + align:start position:0% +you guys up into groups so kenneth and +andrea you guys could work together + + align:start position:0% +andrea you guys could work together + + + align:start position:0% +andrea you guys could work together +today for the rest of class Paul Yulia + + align:start position:0% +today for the rest of class Paul Yulia + + + align:start position:0% +today for the rest of class Paul Yulia +and David and since we have an odd + + align:start position:0% +and David and since we have an odd + + + align:start position:0% +and David and since we have an odd +number there's going to be a group of + + align:start position:0% +number there's going to be a group of + + + align:start position:0% +number there's going to be a group of +three then Nathan and Joshua you guys + + align:start position:0% +three then Nathan and Joshua you guys + + + align:start position:0% +three then Nathan and Joshua you guys +can film each other and I know that + + align:start position:0% +can film each other and I know that + + + align:start position:0% +can film each other and I know that +you're going to be a little bit limited + + align:start position:0% +you're going to be a little bit limited + + + align:start position:0% +you're going to be a little bit limited +with locations today so if you wanted to + + align:start position:0% +with locations today so if you wanted to + + + align:start position:0% +with locations today so if you wanted to +film on location you might not be able + + align:start position:0% +film on location you might not be able + + + align:start position:0% +film on location you might not be able +to do that for today but just get + + align:start position:0% +to do that for today but just get + + + align:start position:0% +to do that for today but just get +comfortable with like the movements of + + align:start position:0% +comfortable with like the movements of + + + align:start position:0% +comfortable with like the movements of +the camera incorporating the stuff Chris + + align:start position:0% +the camera incorporating the stuff Chris + + + align:start position:0% +the camera incorporating the stuff Chris +talked about earlier that's what we want + + align:start position:0% +talked about earlier that's what we want + + + align:start position:0% +talked about earlier that's what we want +you guys to do today and bike go team + + align:start position:0% + + + + align:start position:0% + +funny + + align:start position:0% +funny + + + align:start position:0% +funny +Sally + + align:start position:0% + + + + align:start position:0% + +in a year 2009 famous astrophysicist + + align:start position:0% +in a year 2009 famous astrophysicist + + + align:start position:0% +in a year 2009 famous astrophysicist +Stephen Hawking can actually go solo + + align:start position:0% +Stephen Hawking can actually go solo + + + align:start position:0% +Stephen Hawking can actually go solo +artist + + align:start position:0% + + + + align:start position:0% + +ok + + align:start position:0% + + + + align:start position:0% + +but also charging you rent not contain + + align:start position:0% +but also charging you rent not contain + + + align:start position:0% +but also charging you rent not contain +the travelin this through all sorts + + align:start position:0% +the travelin this through all sorts + + + align:start position:0% +the travelin this through all sorts +of wine orders even litza absolutely no + + align:start position:0% +of wine orders even litza absolutely no + + + align:start position:0% +of wine orders even litza absolutely no +one came + + align:start position:0% + + + + align:start position:0% + +just going for me that was home I mean + + align:start position:0% +just going for me that was home I mean + + + align:start position:0% +just going for me that was home I mean +this could be a different way yeah half + + align:start position:0% +this could be a different way yeah half + + + align:start position:0% +this could be a different way yeah half +a second of a shock response on the + + align:start position:0% +a second of a shock response on the + + + align:start position:0% +a second of a shock response on the +couch or where they are och sorry we are + + align:start position:0% +couch or where they are och sorry we are + + + align:start position:0% +couch or where they are och sorry we are +you should get my snacks and water grab + + align:start position:0% +you should get my snacks and water grab + + + align:start position:0% +you should get my snacks and water grab +one and one and so like I'm kind of like + + align:start position:0% +one and one and so like I'm kind of like + + + align:start position:0% +one and one and so like I'm kind of like +okay effectiveness \ No newline at end of file diff --git a/08Ih9GGB5-c.txt b/08Ih9GGB5-c.txt new file mode 100644 index 0000000000000000000000000000000000000000..86df97cd74cced332b1bae2061a74d47b1f2b155 --- /dev/null +++ b/08Ih9GGB5-c.txt @@ -0,0 +1,101 @@ +Our last example involves +a company called D2Hawkeye, + +a medical software +company founded in 2001. + +The company combined +data with analytics + +to improve quality and cost +management in health care. + +In 2009, the company was +analyzing 20 million people + +monthly. + +It is impossible for humans to +sift through patient records + +and assess quality and +cost without algorithms. + +This motivated the approach +that D2Hawkeye took. + +Let us discuss the data +that D2Hawkeye utilized. + +Health care industry +is data rich, + +but data may be hard to assess. + +It is often unstructured +and unavailable. + +The company used insurance +data regarding procedures, + +prescriptions, and diagnosis. + +It further defined +new risk factors + +based on doctor's insights. + +For example, obesity +and depression. + +Finally, it used +demographic information, + +like gender and age. + +What were the analytics used? + +The goal was to predict +future heath care costs, + +and identify high-risk +patients to be + +prioritized for intervention. + +The company created +interpretable models + +for doctors to +analyze and verify. + +This led to significant +improvements + +over just using +historical costs. + +So what is the edge? + +The analytics used led to +substantial improvement + +in D2Hawkeye's +ability to identify + +patients who need +more attention. + +The approach allowed +expert knowledge + +to identify new variables and +refine existing variables. + +Further, it allowed the +ability to make predictions + +for millions of patients +without manually + +reading patient's files. \ No newline at end of file diff --git a/0fChZwU1zEc.txt b/0fChZwU1zEc.txt new file mode 100644 index 0000000000000000000000000000000000000000..c362df751239304028369a578e4fe461cc495b8d --- /dev/null +++ b/0fChZwU1zEc.txt @@ -0,0 +1,4876 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high-quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +HONG LIU: So let me first +just remind you briefly + +what we did in last lecture-- + +AUDIENCE: [INAUDIBLE]. + +HONG LIU: --which was ages ago. + +[LAUGHTER] + +So we, say, quote unquote, +derived the AdS duality. + +And then we also +described a little bit + +to the geometry of the +Anti-de Sitter spacetime. + +So there are two things +I want you to remember + +about Anti-de Sitter spacetime. + +You said, there's two +ways to think about it. + +One is so-called +the Poincare patch, + +is that, say, we have a +coordinate z or R. It depends + +on your choice. + +So for each constant-- +z is equal to 0. + +Add to the boundary of AdS. + +So AdS have a boundary, +symmetric, yeah, so R squared. + +So z goes from 0 to infinity. + +And at z equal to 0, the +overall [? prefect ?] blows up. + +So the spacetime become +bigger and bigger. + +So this is what we will +normally call the AdS boundary. + +And then when z become bigger, +then you go to the interior. + +And then at each consonant z +the spacetime is [INAUDIBLE] + +Minkowski space, say, our D +dimension in Minkowski space. + +So this give you +an AdS d plus 1. + +OK, so this gave +you an AdS d plus 1. + +And so of each z [INAUDIBLE], +it's an AdS space. + +So this is so-called +the Poincare patch. + +And another way +to think about AdS + +is so-called the global AdS. + +In the global AdS, AdS +is just essentially + +a [? sort ?] in the cylinder. + +And it is a time direction, +which we call tau. + +And then there's a radial +direction we call rho. + +And then there's some +angular direction. + +And then the boundary of +the surface-- for example, + +you can write in this +global case as 1 over, + +say R squared cosine squared +rho, say, minus dt squared + +plus d rho squared plus sine +squared rho [? d ?] omega + +squared d minus 1 squared. + +OK? + +And this rho, and +the angular direction + +is this omega d minus +1, so d tau squared. + +OK? + +And then when [? rho ?] goes +to pi over 2, then the, again, + +the overall +[? prefactor ?] blows up. + +So at the rho power over +2, so this is the boundary. + +So the boundary here is S3 +times R. So SD minus 1 times + +the time. + +So it's just really a cylinder. + +So here, the boundary +is the R1 d minus 1, + +just the Minkowski +spacetime, OK? + +So this is two way I want you to +think about the Anti-de Sitter + +spacetime. + +And also, yeah-- so +before we continue, + +do you have any questions? + +Yes? + +AUDIENCE: Just a short one. + +So you draw a cylinder, But +the spatial part of that metric + +is not precisely a cylinder. + +HONG LIU: Hm? + +AUDIENCE: I mean, the +spatial part of the metric + +is not precisely [INAUDIBLE]. + +HONG LIU: You mean the boundary? + +AUDIENCE: No, I mean the +sine squared rho term. + +That's a cylinder. + +HONG LIU: Oh, I'm just +saying the topology. + +I'm saying the topology is +[? a sorted ?] cylinder. + +Yeah, the topology is +[? a sorted ?] cylinder, yeah. + +Any other questions? + +OK, good. + +So also, let me remind you +this original definition + +of the Anti-de Sitter spacetime. + +So Anti-de Sitter +spacetime can also + +be defined as a hyperboloid. + +Hyperboloid in the d plus +2 dimensional Minkowski + +spacetime. + +OK, so this is the +AdS d plus 1 can also + +be defined as +hyperboloids in the d plus + +2 dimensional +Minkowski spacetime. + +It's 2 time. + +So it's a 2,d +signature with 2 time. + +OK? + +So now, let's talk +a little bit more + +about the-- the last time we +talked about geometry of AdS. + +Now, we talk about little +bit the symmetries of AdS. + +So let's just further +that discussion, so d + +plus 1 dimension of AdS, +Anti-de Sitter spacetime. + +So I assume all of +you are familiar of is + +the concept called isometry. + +If not, it's very +easy to understand. + +So isometry refers to +the class of coordinate + +transformations, which +leaves the metric invariant. + +OK? + +And it's, say, if it's a +Minkowski spacetime, then + +the isometry will the +Lorentz transformation + +plus the translations, OK? + +So that's the isometries. + +And so for this +AdS, by definition, + +the isometry would be SO(d,2), +because this is hyperbole + +for AdS, because the AdS +is defined as a hyperboloid + +in this d plus 2 dimensional +Minkowski spacetime with + +signature (2,d). + +And this hyperboloid preserves +the Lorentz transformation. + +So the AdS, the symmetry +will be SO(d,2). + +Just the Lorentz symmetry +of this embedded Minkowski + +spacetime. + +There's no translation +because this equation + +breaks the translation. + +OK? + +Because this equation +breaks the translation. + +So yeah, so you can see +immediately just from there. + +But what we will +be useful later is + +to understand how +this is refracted + +in the so-called Poincare patch. + +OK? + +So let's talk about how +this symmetry is realized + +in the Poincare +patch, which I will + +use these z coordinates, which +I will use these z coordinates. + +So first, they are translations, +which we can translate, say, + +x mu to some constant. + +So by x mu, I always +refer to using + +these Poincare coordinates. + +The x mu always refer +to t and the vector x. + +OK? + +So this is the-- +so first, obvious, + +there's a translation in +the t and x direction, + +because that's independent +here [? in the ?] x. + +And then this also +Lorentz transformation + +in the x direction, because of +the dependence on the t and x + +is just the Minkowski metric, +because each is [INAUDIBLE] + +that Minkowski metric. + +OK? + +So this has d generators. + +So this have 1/2 +d times d minus 1, + +because this is the +Lorentz transformation + +in the d dimension. + +And then, also, there's scaling. + +So that metric, it's invariant +under such a scaling. + +So just scale x +mu and z together. + +And clearly, the +metric does not change. + +So if you scale +z and x together, + +then all the scaling cancels. + +No, of course, this does +not change the metric. + +OK? + +So there's also scaling, +so this have one generator. + +So the last isometry +in the-- it's + +called special conformal +transformation. + +The last image of +this space, which + +is called the special +conformal transformation, + +it's a little bit +more complicated. + +Let me just first write it down. + +Then I will try to give you +some intuition about it. + +So the [? free ?] parameter, +so the parameter for this + +transformation of +[? actor ?] b mu. + +OK? + +So I will introduce. + +So the transformation +is the following. + +z go to z prime equal to-- and +the x mu goes to x mu prime. + +OK? + +So b mu is just an arbitrary +constant vector, just constant + +vector. + +And so b mu squared, +so b squared is just + +your standard b mu b mu. + +Under the A square, it's defined +to be z square plus x mu x mu. + +OK? + +So you can check +yourself, requires + +a little bit of effort. + +You plug this transformation +into this expression. + +And then you can show +that this is invariant. + +OK? + +So this have d +parameters, because b. + +So the transformation +parameters, + +they are the d parameters. + +So they are d parameters here. + +OK? + +Because of the b mu. + +So this transformation +can be understood + +in a slightly easier +way, as follows. + +It's as you will also +do this in your p + +set, is that you can check. + +So to understand this Special +Conformal Transformation, + +so I called SCT. + +First, you can check the +following is isometry, + +something we call inversion. + +It said if z goes to z divided +by A, so A is this quantity. + +Oh, A, I think I'm having +some notation error, myself. + +So I should call it +A, rather, A squared. + +Sorry. + +It doesn't matter. + +I can also call it A +squared, but let me just + +call it A. I think that one +would be [? A2. ?] Yeah, + +that is [? A2. ?] So, +yeah, I could just + +call everything A squared. + +But to be consistent with my +notation on the [? notes, ?] + +just let me call it A. + +So you can also check that +the following discrete + +transformation is +also isometry, so when + +z equal to z divided +by A, and x mu + +goes to x mu divided by A. OK? + +You can check this is isometry. + +So if you plug this +into this metric, + +you find this [? leaves ?] +the metric invariant. + +And this thing is +much easier to check. + +But as you will +do in your p set, + +and you can check yourself, +this discrete transformation + +actually is not +part of the SO(d,2). + +It's, in fact, +part of the O(d,2). + +So if you calculate its +determinant, say the Jacobean, + +actually find the +minus 1, rather than 1. + +OK? + +So this is not a proper +Lorentz transformation. + +It's not a proper +transformation, + +what we normally call the +proper transformation. + +But however, if +you do this twice, + +the minus 1 times +minus 1 equal to 1, + +then you get the +proper transformation. + +But, of course, if +you do this twice, + +you just go back to itself. + +You can check. + +This is inverse of itself. + +So this is like a +[? z2 ?] transformation. + +But you can do +[? a slightly ?] [? trick ?]. + +Then you can show that +this special conformal + +transformation is +given by an inversion. + +You first do an inversion, and +then you follow the [? bad ?] + +translation in b mu. + +And then invert it back. + +OK? + +So even though you can check +that I squared is equal to 1, + +well, now in the middle, you +have added the translation + +in b mu, a constant. + +And this is a symmetry. + +And, of course, the whole +thing will be a symmetry. + +But now, this is a +proper transformation, + +because I have act I twice, OK? + +So you can now check this +transformation is precisely-- + +if you do this, it's precisely +just that transformation. + +OK? + +So if you add all +of them together, + +d will have d minus 1 d. + +Then you can show actually +they form this symmetry group. + +They form this symmetry group. + +So altogether, you +have d plus 1/2 d times + +d minus 1 plus 1 plus d. + +Then that give you 1/2 d. + +You can check yourself, +like 1/2 d plus 1 and d + +plus 2, which is precisely the +number generated for that one. + +OK? + +Yes? + +AUDIENCE: So the total here +that dimension, the d plus 1-- + +HONG LIU: Yeah. + +AUDIENCE: Why like +even translation, + +it only has a d +dimensional invariant. + +HONG LIU: No, because this +depend on z, so the translation + +[? in ?] z is not invariant. + +AUDIENCE: Oh, OK. + +Yeah, so that would be-- + +HONG LOU: Because +this depend on z. + +AUDIENCE: Yeah. + +HONG LIU: So if you translate +z, this is not the isometry + +[? under ?] the metric changes. + +So only the translation +t and x is a symmetry. + +So that's why we only +do the translation x mu. + +AUDIENCE: I have some questions. + +HONG LIU: Yes? + +AUDIENCE: So +conversion is isometry. + +HONG LIU: Yeah. + +AUDIENCE: Yes? + +OK, so but inversion, +there's a [? release ?] not + +in the SO(d,2)? + +HONG LIU: Yeah, right. + +AUDIENCE: So that +means the symmetry, + +isometry [? work ?] [? with ?] +[INAUDIBLE] [? SO? ?] + +HONG LIU: Yeah, yeah. + +It's the standard story. + +You have O. You can +have an O symmetry. + +There's a discrete +part, which is O/ When + +you're transformation, +you're changing the Jacobean, + +whether your Jacobean +is 1 or minus 1. + +You just actually +[? exactly ?] the standards + +of the transformation in +the Minkowski spacetime. + +In the Minkowski +spacetime, you can also + +can see the [? site ?] +transmissions. + +AUDIENCE: OK. + +HONG LIU: Yeah, +just the same thing, + +because this is just the +transformation in the Minkowski + +spacetime of this +embedded space. + +AUDIENCE: So in the +[INAUDIBLE] metric, + +we also have a, like a-- +determine [INAUDIBLE] + +transformation. + +HONG LOU: Exactly the same as +the standard Minkowski space. + +AUDIENCE: OK. + +AUDIENCE: But discrete part +just like a [INAUDIBLE]? + +HONG LIU: Oh, no, it depends. + +Yeah, in the old dimension, +yeah, in the 3 plus 1 + +dimension, just the +[? parity. ?] That's right. + +In the 2 plus 1 dimension, +if we invert all directions, + +then it's not. + +Right? + +Yes? + +AUDIENCE: Is there +an easy way to see + +the special conformal +symmetry of the system? + +HONG LIU: Hm? + +AUDIENCE: Is there +an easy way to see + +a symmetry from the metric? + +HONG LIU: Yeah, you +just plug this in. + +[LAUGHTER] + +AUDIENCE: Well, I +mean, how do you + +know that there is such +symmetry, [? complicated ?] + +symmetries? + +HONG LIU: No, just say +another way to understand + +is to do this one. + +So this inversion is a much +simpler transformation, + +which you can easily +check [? its ?] isometry. + +And then this procedure will +guarantee this is isometry. + +[? because ?] each +step is isometry. + +Good? + +OK, so after talking +about the-- so + +that concludes our very quick +review about the geometry + +and properties of +Anti-de Sitter spacetime. + +AUDIENCE: But maybe one +more quick question. + +So since you said the isometry +[? bigger, ?] and so if you why + +you only answer on the [? SO? ?] + +HONG LIU: It's the same thing. + +In Minkowski space, +we can also separate + +the discrete transformations and +consider the continuous part. + +AUDIENCE: Oh. + +HONG LIU: Yeah, so it's +just exactly the same thing. + +AUDIENCE: OK. + +HONG LIU: Yeah. + +Certainly here, we can +consider the inversion too. + +We just here, I'm +considering the part, which + +connect to the [? identity ?]. + +AUDIENCE: OK. + +HONG LIU: Any other question? + +AUDIENCE: So is it true +that in some dimensions + +the inversions +[INAUDIBLE] isometry? + +HONG LIU: I think-- no, I +think actually more dimensions. + +This is not. + +In more dimension, +this is [INAUDIBLE]. + +Yeah, it-- + +AUDIENCE: [INAUDIBLE]. + +HONG LIU: Inversion is always +isometry in any dimension. + +AUDIENCE: But it's just that +the determinant [INAUDIBLE]. + +HONG LIU: No, it's always +minus 1, any dimension. + +AUDIENCE: Oh, OK. + +HONG LIU: Yeah. + +Other questions? + +Good. + +So after talk about Anti-de +Sitter spacetime, now + +we can talk a little bit +about the string theory + +in Anti-de Sitter spacetime. + +OK? + +We can talk about string theory. + +Now, let's talk a little bit +more about a string [INAUDIBLE] + +the distance [INAUDIBLE]. + +This discussion is very +easy and essentially trivial + +because we know very little +about this string theory + +in Anti-de Sitter spacetime. + +[LAUGHTER] + +And so there's not +much to talk about. + +But there are a few general +statements we can say. + +So there are a few general +statements we can say. + +First is that both +AdS 5-- so we have + +said that AdS 5 is the +maximally symmetric space + +of negative curvature. + +And we all know from your +really kindergarten years, + +that S5 is the maximal symmetric +space of positive curvature. + +So this combined +together is really + +a maximally symmetric space OK? + +So this AdS 5 times +S5, so AdS 5 times + +S5 is a homogeneous space, +homogeneous spacetime, + +maximally symmetric +homogeneous spacetime. + +So whatever string +theory in this space, + +it's-- so the only scale in +this space is the curvature, + +curvature radius, and which +is the same everywhere. + +OK? + +It's homogeneous. + +It's the same everywhere. + +So essentially, R, so this R +will be just a single parameter + +to characterize the curvature +of this spacetime, so + +single number, +which characterize + +the curvature of the spacetime. + +So even the space +is not homogeneous, + +and you have to specify +which place, which curvature, + +et cetera. + +But this is the maximally +symmetric space, homogeneous. + +So a single number captures +the curvature everywhere. + +So that means that in string +theory on this spacetime, + +it's really just characterized +by the following dimensionless + +parameter, so alpha prime +divided by R squared. + +I mean, alpha prime is +a dimensional parameter. + +But in the end, it's given by +the following dimensionless + +parameter. + +And only for any +physical process can + +only this +dimensionless parameter + +goes in, not separate +of them, because there's + +no other scales. + +i is the only scale, and alpha +prime is the only [? other ?] + +scale. + +And so for any physics, the +only dimension parameter + +can come in is this one. + +And, of course, there's +another dimensionless parameter + +is the gs, is what we +call the string coupling. + +So essentially, the +series is specified + +by these two parameters. + +OK? + +And depend on what +you want, you can also + +construct the Newton constant. + +The Newton constant +can be expressed + +in terms of gs and 1/2 prime. + +So in type IIB +string, the relation, + +so we are talking about type +IIB string, the relation + +between the Newton +constant and the, + +say, alpha prime and the gs +is given by the following. + +So instead of a considering +these two parameters, + +you can exchange gs +by Newton constant. + +So you can alternatively +consider, say, + +gn to the R to the power 8, or +alpha prime to the R squared, + +or just characterized by these +two dimensionless numbers. + +After your choice, sometimes +this is more convenient, + +and sometimes, this +is more convenient. + +So if you talk +about string theory, + +work with the string theory +[? parse ?] [? integral, ?] et + +cetera, then this +is more convenient. + +But if you think +about the gravity, + +then the Newton constant +appears naturally. + +And then this become +more [? natural. ?] OK? + +So the fact of the theory +is controlled by these two + +dimensionless parameters. + +AUDIENCE: The R is a constant R? + +HONG LIU: Yeah, same R. It's +just the curvature radius + +over the spacetime. + +The whole spacetime, it's just +controlled by the single R. + +AUDIENCE: Yeah, yeah. + +HONG LIU: Yeah, yeah, also, +implicit in the discussion + +here, which is in the metric +where I wrote last time, + +is that the +curvature radius here + +is exactly the same as +the curvature radius here. + +And so the single +curvature radius + +characterizes the whole thing. + +OK? + +OK, good. + +So this means that whatever +quantum gravitational theory + +or string theory +in this spacetime, + +you can consider q limit, +based on this 2 dimensionless + +parameter. + +So first is so-called the +classical gravity limits. + +So this is the limit, which +the string coupling goes to 0. + +So that means-- remember, +the string coupling controls + +the [? loop ?] [? corrections ?] +over the strings. + +And also, essentially, it's the +fluctuation over the spacetime. + +And so the string coupling is 0. + +And also, the alpha prime +divided by R squared goes to 0. + +OK? + +So this alpha prime divided +by R squared goes to 0. + +So this is can be considered +as a point particle limit. + +Because alpha prime +essentially characterize + +so the [? sides ?] of a string. + +And when the side of the +string is much smaller + +than the curvature radius, +and then essentially, + +it's a point particle limit. + +So this is the standard +classical gravity limit. + +So in this region, we +have classical gravity. + +And you cannot tell that +those particles are strings. + +They're just like +ordinary particles. + +OK? + +So similarly, so g string +[? to ?] [? 0 ?] can also be + +considered as the limit. + +The Newton constant goes to 0. + +It's the same thing. + +OK? + +It's same thing. + +And so in this region, +[? you ?] get classical gravity. + +And more specifically, +in our case, + +we get to have to be super +gravity, which we briefly + +mentioned before. + +So there's a lot of the region +is called the classical string + +limit. + +In this case, the alpha +prime divided by R + +squared can be arbitrary. + +Does not have to be small. + +So in this region, than the +string [? G ?] [? fact ?] will + +be important. + +So you should be +able-- then that means + +that the spacetime +curvature radius is + +comparable to the string sides. + +Then in this case, you can +no longer treat the string + +as a point particle. + +But we still take +g string goes to 0. + +So that means that the +quantum fluctuation is small. + +The spacetime quantum +fluctuation is small. + +So in this case, you still +have a classical theory. + +But it's a classical +string theory, rather than + +a classical gravity theory. + +OK? + +Any questions regarding this? + +So there's another-- +something else? + +AUDIENCE: No. + +HONG LIU: So there's one +feature in this spacetime. + +So this is altogether 10 +dimensional spacetime. + +There's one feature +of this spacetime. + +It said S5 is a compact +space with a finite volume. + +And AdS 5 is uncompact OK? + +So normally, when you +have a compact space, + +so it's convenient-- +so S5 is compact. + +So it's actually convenient +inside your situation + +to express whatever, say, 10 +dimensional field in terms + +of-- yeah, it may be to +not express, to expand, + +but in 10 dimensional +fields, in terms + +of harmonics, [? inverse ?] 5. + +OK? + +Because there's a discrete +set of harmonics on S5, + +you can always expand some +10 dimensional field on it. + +So for example, if you +have a scalar field, + +so supposing if you have a +10 dimensional scalar field, + +say we have x mu. + +We have z. + +So this is AdS5 part. + +And them let me call it +omega 5, which is S5 part. + +Then you can always, say, so you +can expand these scalar fields + +in terms of spherical +harmonics on S5. + +OK? + +Then what you get is you +get a tau field in AdS 5. + +And then this are +spherical harmonics in S5. + +OK? + +And in particular, when you do +this expansion, than the higher + +harmonics, they will +develop a mass, because + +of the curvature of the S5. + +So the lowest mode +will be independent, + +say, of the +coordinate on the S5, + +where the higher mode will +depend on the coordinate of S5. + +And because of those +dependence, because + +of the curvature of [? base ?] +5, they will develop a mass. + +So the lowest mode +would be massless, + +then they will be followed +by tau of massive modes, + +controlled by the +[? size ?] of AdS 5. + +OK? + +So you can do this for any +field, any particular [? the ?] + +metric. + +So when you do +this, essentially, + +only the massless graviton in 5 +dimension will [? mediate ?] no + +[? range, ?] say, gravitation +[? interactions ?] in AdS 5. + +So essentially, so the +gravity, so at a long distance, + +the gravity is +essentially 5 dimensional. + +OK? + +It's the same in 5 dimen-- +because you can always + +reduce on S5. + +So there's a slightly +tricky thing here. + +But it's only-- it's +that the size of S5, + +the curvature radius +of S5 is actually + +the same as the curvature +radius of AdS 5. + +So there's not really a +hierarchy here in terms + +of the curvature radius. + +But there's still an +important difference. + +These have infinite volume. + +These only have a finite volume. + +So these are compact. + +These are uncompact. + +OK? + +AUDIENCE: But why the +gravity [? doesn't-- ?] + +HONG LIU: Hm? + +AUDIENCE: But why +the gravity doesn't + +say this string [? S5? ?] + +HONG LIU: No, it-- [INAUDIBLE] +[? this thing ?] radius-- + +this [? thing ?] S5. + +But just as I said, +this is a compact part. + +You can always do a reduction. + +And then the higher graviton +mode will develop a mass. + +AUDIENCE: Oh. + +HONG LIU: Yeah, we +develop a mass, yeah, + +even though that +mass is not very big. + +Yes? + +AUDIENCE: So if we applied +this to the real world, then + +what would estimate for R? + +HONG LIU: Sorry? + +AUDIENCE: What's the +estimate of this radius, + +this curvature for if +it's should be comparables + +are of the original worlds? + +HONG LIU: [INAUDIBLE] +the size of the universe. + +AUDIENCE: But then +doesn't it mean + +that we only should worry about +the mass of this compact mode? + +HONG LIU: Yeah. + +AUDIENCE: Only on distances +much longer than ours? + +HONG LIU: Yeah, yeah. + +I mean, just saying, +at very large distance, + +essentially is 5 dimensions. + +But it's still-- you can +talk about the distance + +scale, et cetera. + +But here, R is the only scale. + +It doesn't matter how +large is R. Everything + +matches against R. R +provides your units. + +AUDIENCE: Yes, but when +we talk about distances + +shorter than R then-- + +HONG LIU: Yeah, if you talk +about a distance shorter + +than R, it doesn't matter. + +It's like a 10 dimensional. + +It's like a 10 +dimension [INAUDIBLE]. + +But AdS is uncompact, you can +go as much distance as you want. + +I'm just saying, the +story is slightly tricky + +because they have the +same curvature radius. + +But I'm trying to +describe it in the spirit. + +And also, mathematically, +you can always, + +because S5 is uncompact, +you can always + +do dimensional reduction on it. + +And this provides +a convenient way + +to organize fields, in terms +of 5 dimensional fields. + +AUDIENCE: OK. + +HONG LIU: OK. + +So one thing we will +often use is, indeed, + +just consider the dimensional +reduction of the gravity + +to 5 dimension. + +So if you have, say, +say suppose this is + +Einstein-Hilbert action in 10d. + +So this is AdS 5 part. + +This is the S5 part. + +So you have some 10 +dimensional, so curvature. + +So R is a [? rich ?] +scalar in 10d. + +OK. + +Now, suppose the metric, +suppose this considered + +the lowest mode for the metric, +which have low S5 dependence. + +And then you can just reduce +this to a 5 dimensional theory. + +Gravity, so the +volume of the S5 part, + +we are just +[? factorize. ?] Then + +you have a 5 dimensional scalar. + +OK? + +And this b5 is just +the volume of S5. + +OK? + +5. + +And now, we can absorb this b5 +into downstairs, then define + +or you factor your 5 +dimension Newton constant. + +5 [INAUDIBLE] Newton +constant, which + +we are call G5, which is +defined to be GN divided + +by the volume of the 5 sphere. + +OK? + +And the volume of the 5 sphere +is, essentially, just pi q. + +OK? + +And then, of course, there's +R to the power [? of 5th. ?] + +So this is the quantity +we will often use. + +OK? + +So of the dimensional +reduction, in the end, + +you get the action [? we will ?] +have the form 14 pi G5, + +so 5 dimensional Newton +constant, say, [? d5x ?], + +just AdS part. + +And then you have the +gravity part of the action. + +And then you plus many, +many matter fields. + +So this is, the essentially will +be the structure of your action + +when you do the +dimensional reduction. + +OK? + +AUDIENCE: Shall we have +matter fields in the S5? + +HONG LIU: No, you +reduce everything on S5. + +And once you have done that, +then S5 will disappear. + +AUDIENCE: But when +we do, say, the R + +is [? always ?] a constant, so +we can do the integral easily + +in S5. + +But if we don't have +some mass [INAUDIBLE]. + +HONG LIU: Yeah, so +no, it doesn't matter. + +So you can take-- this is a +standard story for [INAUDIBLE] + +reduct-- a standard story. + +When you expand around in this, +so this will go into here. + +Then the only dependence +on the S5 part + +will depend on those things. + +AUDIENCE: Uh-huh. + +HONG LIU: Then you just +can't integrate those things. + +AUDIENCE: Oh. + +HONG LIU: You can +always integrate them. + +AUDIENCE: Oh, OK. + +HONG LIU: And they just give you +some integrals, some numbers. + +It would just give +you some numbers. + +And in the end, you can +always write the action + +in terms of 5 +dimensional action. + +AUDIENCE: But that solution +is a classical solution + +for the [INAUDIBLE] equation. + +HONG LIU: No, no, no. + +This is not a +classical solution. + +I'm just doing an expansion. + +It's just like doing +a Fornier transform. + +AUDIENCE: Oh, OK. + +HONG LIU: This is expand +in terms-- in some basis. + +No, have not done anything. + +This just a +mathematical rewriting, + +AUDIENCE: Mm-hm, OK. + +HONG LIU: Yes? + +AUDIENCE: But I think in terms +of expression for G Newton + +into the affected-- don't we +have that this G5 is like G + +squared alpha for the +[INAUDIBLE] [? divided by ?] + +[? R to the 5th y ?] can put +[? a use it ?] to this alpha R + +squared combination? + +HONG LIU: Sorry-- + +AUDIENCE: Express G5 in +terms of GS and alpha prime. + +HONG LIU: Yeah? + +AUDIENCE: And [INAUDIBLE]. + +Why don't it look like only +combinations of R prime over R + +squared and GS? + +HONG LIU: Sorry, I don't +understand what you're asking. + +No, G5 is a +dimensional parameter. + +5 dimension Newton +constant had dimensions 3. + +So whatever dimension here, +some [? other ?] dimension + +there would be +compensated by R5. + +But you always have +3 dimension left. + +So this is a dimension +3 number, yeah. + +Any other questions? + +Good. + +OK, so then this +concludes our discussion + +about string theory +in AdS 5 times S5. + +As I said, there's not +much to talk about it. + +And so now, let's look +at the other object, + +which is the N equal +to 4 super-Yang-Mills + +theory, which is the other +side of the equation, + +of the duality equation. + +OK? + +So in this case, we have +a lot to talk about it. + +We, in principle, have +a lot to talk about it, + +but we won't have time. + +So we will also not +talk much about it. + +So we are only mentioning +a few essential things, OK? + +So the field content, say, of +a N equal to 4 super-Yang-Mills + +theory, which we +already learned, + +which we already learned +from the [INAUDIBLE] theory + +on the D3-brane is that you +should have a gauge field. + +And then you have a 6 scalar +field, because 1 into 6 + +transverse direction +over the D3-brane. + +OK, you have 6 scalar fields. + +And then when you include +the super symmetric center, + +in the super string, +then they actually also + +the massless of fermions. + +So this is 3 plus 1 dimension. + +OK? + +So this is 3 plus 1 dimension. + +So in 3 plus 1 dimension, you +can represent the fermions + +conveniently by two components, +for example, two component Weyl + +fermions. + +They it turns out there +are 4 such Weyl fermions. + +So A will go to 1 to 4. + +So alpha is a spinor indices. + +And A just neighbor +different spinors. + +So altogether, you +have four spinors. + +OK? + +And so this is, essentially, +the field content + +of the N equal to 4 +super-Yang-Mills theory. + +So we would not worry +about the fermions. + +So but I'm just mention +here for completeness. + +So if you have a +U(N) gauge theory, + +if you have a U(N) +guage theory, say, + +for the N D3-brane, +then all this, + +all this field is in the +of the [INAUDIBLE] of U(N). + +In other words, each of +them is an N by N matrix, + +is N by N Hermitian matrix. + +OK? + +So each of them +can be represented + +by Hermitian matrices. + +So altogether, yeah, yeah-- +so let me not write it. + +Let me just say it in words. + +So altogether, you +have 8 [INAUDIBLE]. + +You have 8 bosonic +degrees of freedom. + +Because for the +photon, you have 2. + +For photon, you have 2 +[INAUDIBLE] degrees of freedom. + +And here, 6 scalar field, +you have 8 [INAUDIBLE] + +degrees of freedom. + +And for the fermion, +you can also + +count that the 4 Weyl spinors +actually have 8 [INAUDIBLE] + +degrees of freedom. + +So altogether, you +have 8 N square. + +Each of them is +an N by N matrix. + +So you have 8 N squared, say, +[INAUDIBLE] bosonic degrees + +of freedom, and eight 8 N +squared for mionic [INAUDIBLE] + +degrees of freedom. + +OK, for the-- + +AUDIENCE: Why would +we have 8 fermions? + +HONG LIU: Hm? + +AUDIENCE: We have 8 fermions? + +HONG LIU: No, we +have 4 fermions, + +but each fermion have +some spinor component. + +AUDIENCE: Oh, OK, OK. + +HONG LIU: Yeah. + +AUDIENCE: Where did +the number come from? + +HONG LIU: Sorry? + +AUDIENCE: Where did 4 fermions? + +HONG LIU: That come +from a calculation. + +This I cannot explain here. + +This, I can only +quote this fact. + +It's just that if you work out +the theory on the D3-brane, + +then [INAUDIBLE] there's +4 Weyl fermions, yeah, + +which we did not go through +that, because we did not + +do super string. + +Yeah. + +AUDIENCE: Should this come +from the fact that it's where + +[INAUDIBLE]? + +Symmetry? + +HONG LIU: Yeah, it's come +from the super symmetry. + +Yeah, come form the string +theory, super string theory. + +So in our discussion, we +only discussed bosonic part. + +We never had time to discuss +for mionic part, et cetera. + +So let me now mention one +important point, which + +I think is-- I hope +is self-obvious, + +self-evident to you. + +It's that this U(N)-- actually, +there's a U(1) which decouples, + +which U(1) decouples, +just actually, + +let me just write down the +Yang-Mills theory first. + +So let me write down the +Yang-Mills theory first. + +So you can write down the +Yang-Mills theory, which we are + +actually wrote it down before. + +Let me only write +down the bosonic part. + +So essentially, just given +by Yang-Mills coupling trace. + +And this is a covariant +derivative acting + +on the scalar, standard +covariant derivatives. + +And the I and the +j are all summed. + +OK? + +So I and the j are all summed. + +So this is the Lagrangian, +then plus the fermionic part. + +So this is the bosonic part, +then plus the fermionic part. + +OK? + +Yes? + +AUDIENCE: Are fermions +coupled through 5 fields? + +HONG LIU: Yeah, +they're all coupled. + +They're all coupled. + +AUDIENCE: How do they couple? + +HONG LIU: Standard +[INAUDIBLE] coupling. + +Yeah, so the key, so they couple +through a particular coupling. + +The hosting, it just can show +to have a single coupling. + +In principle, if you +have so many fields, + +you can have many, many +different possible couplings. + +You can have one +coupling between them, + +one coupling between +them, et cetera. + +You can have different +components, but + +and self-couplings, et cetera. + +And under the key of N +equal to 4 super-Yang-Mills + +theory is that every coupling, +they equal up to some constant, + +up to some constant +factors, which is precisely + +give you the supersymmetry. + +Anyway, so I think +it's obvious to you + +that you have a U(N) +Yang-Mills theory that the U(1) + +part decouples. + +OK? + +OK, you unplug the couples. + +So U(N), you can +always decompose it + +into SU(N) times U(1). + +Under the U(1) +part, [INAUDIBLE]. + +So each A, each field +is N by N matrix. + +And the U(1) part +is the part which + +is proportional to +the identity matrix. + +And the SU(N) part is +the part which given + +by N by N trace this matrix. + +And so the U(1) part is +proportional to the identity + +matrix. + +So but you can immediately +see from here, anything which + +is proportional to +the identity matrix + +all the commentators +will vanish. + +OK? + +So essentially, U(1) +part is a free theory. + +So U(1) part is a free theory. + +Yeah, if this is +not clear to you, + +you can easily convince +yourself afterwards. + +And this is also +where-- this is also + +physically clear from +the point of view, + +thinking that this is +coming from the D-branes. + +Coming from the D-brane, +you have, essentially, you + +have N D-brane together. + +And this Yang-Mills +theory essentially + +describes the low energy +dynamics of D-branes, brains, + +so how all these N D-branes +interact with each other. + +But no matter know how +they [? co-communicate ?] + +[? interact ?] with each other, +there's always a center of mass + +motion. + +Does not depend on their +internal structure. + +And that central mass motion +essentially is just this U(1). + +And the central mass +motion always decouple. + +OK? + +So U(1) decouples. + +And you can do the +check from here. + +A U(1) decouples. + +OK? + +AUDIENCE: Yeah. + +HONG LIU: Good. + +So now let me-- so the +interacting part is just SU(N). + +OK? + +The interacting +part is just SU(N). + +So now, let me say a +few words regarding + +the properties of the theory. + +So first, it's that this theory +has N equal to 4 supersymmetry. + +OK? + +So this is another +important remark. + +This is just explain the +name, just explains the name. + +So in supersymmetric +theories, so you + +have a transformation between +boson and the fermion. + +OK? + +You have some-- the theory is +invariant on the transformation + +between boson and fermion. + +So on the [? side of ?] +transformation, + +the [? conserved ?] charge, so +for [INAUDIBLE] transformation, + +then you have loss of charge. + +[? For ?] [? such ?] [? as ?] +transformation and loss + +of charge can be +described by a spinor. + +OK? + +So normally, we say N +equal to 1 supersymmetry + +if the super charge is +given by a single Weyl + +spinor in 4 dimension. + +So N equal to 4 means +that the total number + +of such [? conserved ?] charge +is actually given by the 4 Weyl + +spinors in the 4 dimension. + +So it doesn't +matter, so these have + +a number of supersymmetries. + +OK? + +And also, if you know a +little bit of supersymmetry, + +then this is actually +the maximally allowed, + +the supersymmetry +in 4 dimensions, + +for [INAUDIBLE] field theory. + +So this is actually maximum +allowed supersymmetry. + +But this will not +be important for us. + +OK? + +But this will be. + +But the next point will +be very important for us. + +It's that because of this +theory is so symmetric, + +so G Yang-Mills coupling, its +dimensionless, classically. + +OK? + +Because this is a 4 dimension, +the Yang-Mills coupling + +is dimensionless, classically. + +And the same thing with +our own QCD, our own QCD + +coupling this +dimensionless, classically. + +But then quantum mechanically, +then the coupling actually + +changes with the scale, OK, +because over the quantum + +corrections, et cetera. + +So generic coupling +changes with scale. + +But N equal to 4 +super-Yang-Mills theory + +is special. + +But this actually, this +Yang-Mills coupling + +does not change with the scale, +even at the quantum level. + +So the quantum +level, this remains, + +so dimensionless coupling. + +So using the technical +term, for those of you who + +have studied the QC +Yang-Mills theory, + +is that the beta function at +the quantum mechanical level, + +the beta function +for G Yang-Mills + +is actually 0, which means +you can really treat this G + +Yang-Mills as a parameter, as +a dimensionless parameter, even + +quantum mechanically. + +OK? + +So this is a genuine parameter. + +In contrasting our QCD, +there's no such parameter. + +OK? + +In QCD, we only have a scale. + +There's no parameter. + +Good? + +So any questions +regarding these? + +AUDIENCE: But you +said you wouldn't + +know the coupling [INAUDIBLE] +coupling because of + +[INAUDIBLE]? + +HONG LIU: Yeah. + +AUDIENCE: That means +this is not [INAUDIBLE]? + +HONG LIU: No, it's not. + +No, in the-- + +AUDIENCE: It's not [INAUDIBLE]. + +HONG LIU: In QCD, the Yang-Mills +coupling is not the parameter. + +It's not the +dimensionless parameter. + +AUDIENCE: OK. + +HONG LIU: It translates +into a scale. + +AUDIENCE: Yes. + +HONG LIU: It translates +into a scale. + +AUDIENCE: So-- + +HONG LIU: It translates +into a mass scale. + +AUDIENCE: Yes, but can we +find a massless parameter + +in [INAUDIBLE] like this? + +HONG LIU: No, because the beta +function is nonzero there. + +AUDIENCE: Ah. + +HONG LIU: Yeah, yeah because the +beta function is nonzero there. + +OK? + +And also because of this, +the beta function is 0. + +This theory is actually +conformally invariant, + +theory is actually +conformally invariant. + +OK? + +So which we'll normally call, +say, it's a conformal field + +theory, because it's a CFT. + +So one way to understand this +is because of the beta function + +is 0, essentially, the +theory does not have a scale. + +So theory classical scale, +invariant quantum mechanically + +remains scale invariant. + +And then you can show +that there actually + +is a little bit more generous +conformally invariant. + +So let me say a little +bit about the-- are people + +familiar with the concept of +the conformally invariant, + +or conformal? + +AUDIENCE: No. + +HONG LIU: No? + +OK. + +Yeah, so let me say a few +words about the conformal. + +So conformally invariant +means that the theory + +were under the conformal +transformations. + +OK? + +So let me say a few words on +the conformal transformations. + +So conformal transformations +are the following. + +Say, suppose your +spacetime metric + +is given by some G mu mu. + +So the conformal +transformations are those + +coordinate transformations. + +OK? + +You go from x to x prime. + +So that under such a +transformation, your metric, + +the transformed metric is +related to the original one + +only by an overall scale factor. + +OK? + +So if lambda is +equal to 1, then this + +is what we called +earlier isometry, which + +leave the metric invariant, +will be isometry. + +And if you leave +the metric invariant + +after your overall +scale factor, then this + +is called the conformal +transformation. + +OK? + +And for the Minkowski spacetime, +for Minkowski spacetime, + +actually, I can just +even use this thing here. + +Yeah, maybe let me-- +yeah, let me erase here. + +So for Minkowski +spacetime, say if the G mu + +mu is equal to [INAUDIBLE] +mu mu-- suppose this + +is a d dimensional +Minkowski spacetime-- OK? + +Then you can show-- +you can just work + +how to solve this +equation, work out + +all possible such +transformations. + +OK? + +And you can show that +conformal transformations + +are the following. + +First, they are the +standard isometry, + +which is the translation, +because the translation does + +not give you lambda 1. + +And then you have a +Lorentz transformation, + +which also give you lambda 1. + +OK? + +And they you can have a scaling. + +Of course, if you +scale your coordinate + +with some factor, +then, of course, + +the metric will only +change by overall factor. + +So this is a translation. + +So this is s Lorentz symmetry. + +And this is scaling. + +And then we also +have something what + +we call a special +conformal transformation. + +So this is for-- OK? + +And the b, again, is +some constant parameter. + +OK? + +And also for the +discrete transformation, + +also, you can have a discrete. + +Also you can have a discrete +transformations inversion. + +You [? said ?] x prime mu equal +to x mu divided by x squared. + +OK? + +So these are all +the transformations. + +In general dimension, which +leave you metric invariant, + +leave the Minkowski +metric invariant number + +up to overall factor. + +And the conformal +invariant theory + +is a theory which +[? involves ?] transformations. + +OK? + +And so obviously, +a Yang-Mills theory + +are always invariant on the +translation on the Lorentz + +transformation. + +But when the beta +function is 0, the system + +does not have a scale. + +Then it's invariant +on the scaling. + +But typically, in general, +4 dimensional theory, + +any theory invariant +on the scaling + +is also invariant on +this special conformal + +transformations. + +So actually, the N equal +to 4 super-Yang-Mills + +theory is actually +conformal theory, + +OK, conformally +invariant theory. + +So now, as part +of your p set, you + +can actually see that this +conformal transformations + +in fact [? have ?] 1 +to 1 correspondence + +with these isometries +of the AdS. + +OK? + +And this we will see later. + +This is a part, important part +of the relation between AdS. + +This is an important part +of this duality relation. + +It's that the symmetry +have to be the same. + +So you compare the two. + +You can see that, indeed, they +1 to 1 correspond to each other. + +So the conformal transformation +add together give you SO(d,2). + +OK? + +So this is the conformal group, +so-called the conformal group + +in d dimension. + +Then you get to the +[? SO(d,2). ?] OK? + +And but in this theory, +there's actually also + +global symmetry, because the +N equal to 4 super-Yang-Mills + +theory come from the D3-brane, +which is a transverse space, + +is the [? rotation of ?] +invariant. + +So this actually our SO(6) +symmetry rotates different phi + +i's. + +So actually, there's also +global SO(6) symmetry, + +which rotates phi i, +OK, and the fermions. + +OK? + +And then when you include +in the supersymmetry + +then you get a huge +symmetry group. + +It's normally called a +super conformal symmetry. + +Anyway, let me just +write some notation down. + +It doesn't matter. + +So if you include the symmetry, +the full symmetry group + +is what we normally call it. + +So this is a super group, so +[? SU(2,2|4) ?] Doesn't matter. + +So the bottom line is that the +N equal to 4 super-Yang-Mills + +theory is the most symmetric +4 dimensional theory. + +OK? + +And almost-- no theory +has more symmetries than N + +equal to 4 +super-Yang-Mills theory. + +Any questions? + +AUDIENCE: [INAUDIBLE]. + +HONG LIU: Yes? + +AUDIENCE: So How do you know +that the [? flows are ?] + +[INAUDIBLE]? + +[? HONG LIU: Though ?] you can +classify it by solving this + +equation. + +You can classify it by +solving this equation. + +AUDIENCE: But what's +the q [INAUDIBLE]? + +HONG LIU: No, this +is just a notation. + +AUDIENCE: A notation? + +HONG LIU: Yeah. + +Any other questions? + +So I can say a few words about +the conformal field theories. + +But it's getting +a little bit late, + +and I want to talk +about other things. + +So let me just say it in words. + +And then you can try to +read it in other places. + +Because even if I just write +a couple formulas here, + +it still won't +change you very much. + +[LAUGHTER] + +I won't teach you too much. + +So important thing about +this conformal field theory + +is that each operator, say +each local operator-- yeah, + +you can classify local operators +by how they transform, say, + +under these +conformal symmetries. + +And then you can +associate, say, a dimension + +to each operator, +related to how they + +transform in these +conformal transformations. + +And then you can also show +that the symmetry actually + +dictates the 2-point function +and the 3-point function + +of such operators. + +And essentially, the structure +of the 2-point function + +and 3-point function +are completely fixed. + +But not higher point +function, but only + +2 and 3-point functions. + +Yeah, so that's essentially it. + +Not much known, many things +are known about conformal field + +theory in 1 plus 1 dimension. + +And but higher +dimensions, yeah, other + +than what I said, not much. + +Not too much more +is known, yeah. + +So any questions regarding this? + +OK, so let me just summarize, +then we can have a break. + +So we can summarize. + +So let me just summarize what +we have done so far, and also, + +with an important refinement. + +So what we said is we +started with two picture. + +One is D-brane with +some open strings, + +and then some closed strings +can interact with it. + +And then when we go to +the low energy limit, + +then we get N equal +to 4 super-Yang-Mills + +theory with, now, I say SU(N) +plus a decoupled U(1), and then + +plus what we discussed last +time, a decoupled the gravitons + +in the low energy limit. + +So let me just write +E equal to 0 limit. + +On the other side, we have this +[? pure, ?] [? geometric ?] + +picture of the curved spacetime +produced by those D-branes. + +So those curved +spacetime at infinity + +behaves like just 10 +dimensional Minkowski spacetime. + +And then when you go to +the close to the brane, + +then the space deforms +into the AdS 5 times S5. + +OK, form into AdS 5 times S 5. + +Under the low energy limit, +because 1 into-- we can see + +the string theory in the +[? very ?] [? much ?] + +[? tongue ?] this +[? throat. ?] OK? + +So the low energy limit +is the string theory. + +The one here when you're +take E equal to 0, + +we get string theory +in AdS 5 times S5, + +then plus decoupled graviton. + +Here, also, here, when we look +at the geometry of the brane, + +essentially, we have fixed +the location of the brane. + +So essentially, we have fixed +to the center of mass motion. + +But in principle, +you can allow, also, + +the brane to move anywhere. + +So here, essentially, there's +also a decoupled center + +of mass motion. + +OK? + +So now, let's get rid of +this decoupled graviton. + +Let's get rid of +this decoupled U(1), + +or decoupled center +of mass motion. + +Then what we get is the +fully interacting part. + +OK? + +So the fully interacting +part is so small + +refinement than what +we said last time. + +We said N equal to 4 +super-Yang-Mill theory + +with [? stage ?] group SU(N) +should be the same as the type + +IIB string in AdS 5 times S5. + +OK? + +So, now, other side, +now, this is SU(N). + +And more precisely, this is AdS +prime S5 in the Poincare patch. + +OK? + +Yes? + +AUDIENCE: The N +just to recall, is + +the that N comes from the +amount of flux on the S5. + +Is that correct? + +HONG LIU: Yeah, that's right. + +That's right. + +So the N here related to +the flux on the AdS 5, + +it's also related, +as we will see, + +related the Newton +Constant, et cetera. + +Yeah, we will see that, yeah. + +OK? + +So now, we can look at +this geometric picture. + +OK? + +We can look at this +geometric picture. + +Then we observer +something interesting. + +So this SU(N) group, let +me say, [INAUDIBLE] R 1,3. + +OK? + +On the 3, approximate +dimensional-- yeah, + +let me write it better-- +this SU(N) on the space, + +on the Minkowski space, R 1,3. + +So now, let's note. + +Make a simple observation +based on the geometry of AdS + +is that this R 1,3 is actually +the boundary of AdS 5. + +OK? + +It's essentially the +boundary manifold of AdS 5. + +And the right hand +side, no matter + +whether you do field +theory or string theory, + +you can always do +dimensional reduction on S5. + +You can always +decompose everything + +on S5 in terms harmonics. + +So essentially, the +right hand side, + +because S5 is a compact +space, the right hand side + +is a 5 dimensional +gravity theory. + +OK? + +So we actually now here see a +5 dimensional gravity theory. + +Now, it's equivalent that your +4 dimensional theory [? lives ?] + +on its boundary. + +OK? + +So this really can be considered +[? actually ?] realization + +of holographic principle. + +So actually, there are two +ways to think about it. + +One way is to think from this-- +so previously, we motivated. + +Long time ago, we +motivated the duality using + +two perspec-- [INAUDIBLE]. + +One is the +holographic principle. + +Some gravity theory should be +[INAUDIBLE] to the [? theory ?] + +living on this boundary. + +And also, motivated that the +Yang-Mills theory in the gauge + +group SU(N) or U(N), when you +do the [? large N ?] expansion, + +then behaves like +a string theory. + +OK? + +So this could also be considered +as an explicit example + +of that relation. + +That this is a Yang-Mill +male theory, and then + +turned out to be [INAUDIBLE] +to a string theory. + +OK? + +So now, if you look +at this statement, + +you say, is this a coincidence? + +Because I don't really see +somehow in this picture + +not so much somehow how why this +Yang-Mills theory is actually + +should be considered as living +on the boundary of AdS 5 times + +S5, because the boundary +of AdS 5 times S5, + +somewhere around here. + +Yeah, I don't see some +Yang-Mills theory living + +on there, OK? + +So is this really +just some coincidence + +that just happened to be that? + +But actually, there's a +very important prediction + +one can make if you +take this point of view. + +Now, I can erase here. + +Maybe I will do it here. + +Yeah, but if you take +this point of view, + +then there's a very important +prediction you can make. + +Then there's a very +important prediction + +you can make, and then +check whether that + +has any chance of working. + +So if you believe this +picture, then we can have + +a [? non-trivial ?] prediction, +because AdS also have + +[? a lot ?] of description +in terms of the global AdS. + +Then let's say, what +happens if we put the string + +theory in this global +AdS, which certainly, we + +should be able to do, +because these two only differ + +by some global structure. + +OK? + +And this is one part of that. + +They only differ by +some global structure. + +So if this is really true, +if this is not a coincidence, + +then we can make a non-trivial +prediction is that N equal to 4 + +is a type IIB string in +global AdS 5 times S5. + +So now, the AdS 5 we +take to be the global, + +to take to be the cylinder. + +That should be equal to the N +equals to 4 super-Yang-Mills + +theory, which now, should +live on the boundary + +of that cylinder, which +is our S3 times R. OK? + +So this realization +will give you + +a powerful prediction, which +in principle, you can check. + +OK? + +And, of course, if +this is a coincidence, + +then there's no reason +why this to be true. + +Because from the +brane point of view, + +we cannot really do the sphere. + +OK? + +AUDIENCE: Why is [INAUDIBLE]? + +Oh. + +HONG LIU: So any +questions about this? + +AUDIENCE: One question +[? on that. ?] + +so when we derive the +right hand picture, + +we impose that there's +some charge on the D-brane. + +But on the left +hand side, it seems + +that we-- [INAUDIBLE] a +the charge [INAUDIBLE]? + +HONG LIU: No, the +charge is just reflected + +in open string dynamics. + +AUDIENCE: OK. + +So by your right hand side, +we will have the charge. + +HONG LIU: No, you +essentially have a charge. + +But in that +description, you don't + +need to introduce a charge. + +Whatever charge-- + +AUDIENCE: If we impose charge +if the left hand side will never + +be changed? + +HONG LIU: No, no. + +Just there from the side, +you just talk about strings. + +AUDIENCE: Uh-huh. + +HONG LIU: You don't talk +about the whatever charge. + +The charge is a +gravity description. + +AUDIENCE: Uh-huh. + +HONG LIU: The charge don't +even arise in this picture. + +I just have some strings. + +I have some open strings. + +I have some closed strings. + +They interact with each other. + +AUDIENCE: OK. + +And did this picture +go to low energy means + +it will appear as a charge of +the super-Yang-Mills theory. + +HONG LIU: No, no, no, no, no. + +No, no. + +This goes [? in ?] [? order. ?] +You just super-Yang-Mills + +theory. + +Yeah. + +Good? + +Any other questions? + +Yes? + +AUDIENCE: Is this true? + +HONG LIU: Yeah, this is true. + +AUDIENCE: OK. + +[LAUGHTER] + +HONG LIU: And the yeah. + +So that means this +is not a fantasy. + +Yeah, this tells +this is a fantasy. + +This is actually a +powerful realization. + +This is a powerful +realization, yeah. + +So let me before +conclude-- Let me + +just quickly mention something +just in terms of semantics. + +So I always say, type IIB +string in AdS 5 times S5. + +So you may ask, does this +make sense to say such things? + +Because if we think +this is really + +as a quantum +gravitational theory, + +so if you have a +finite string coupling, + +then everything fluctuates. + +And then why we specify +a rigid spacetime here? + +OK? + +Why do we specify a +rigid spacetime here? + +So the way you should understand +the statement is the following, + +is that indeed, if you, +say, consider the finite G + +Newton, the finite +G string, then + +the spacetime can +fluctuate a lot, + +will typical be a deviate +from AdS 5 times S5. + +But this AdS 5 +times S5 specifies + +it's asymptotic geometry of AdS. + +It's asymptotic geometry. + +It's the geometry of AdS very +far away near the boundary. + +And essentially, this +can be considered + +as specifying the +boundary condition + +for gravity, the boundary +condition for the quantum + +gravity. + +So this, essentially, specify +the boundary condition. + +Good, so let's have a +couple minutes break. + +Then we will talk more +about the duality. + +OK, good. + +So let's start again. + +[SIDE CONVERSATION] + +So now, let's move +to a new chapter. + +So now, have we +established the duality. + +So let's try to +understand the duality. + +So let me call it +the duality toolbox. + +And then we can try to use it. + +So first, let me say some +general aspect on the duality. + +Oh, I erased. + +Oh, I should keep +that figure there. + +Anyway, so the first +important thing + +is so-called IR/UV connection. + +So here, we see the equivalents, +say, from the AdS 5 gravity. + +So we have some +AdS 5 gravity to go + +to N equal to 4 super-Yang-Mills +theory in d equal to 4. + +So from this direction, we +may consider as a realization + +of the holographic principle. + +OK? + +We can consider this direction +as a holographic principle. + +And then you may ask, from +the field perspective, + +if we think from this +angle, why somehow, + +this description of the field +theory have one more dimension. + +So this is a 4 +dimensional theory. + +This is a 5 dimensional theory. + +OK? + +What does this actual +dimension does? + +What does this x +dimension do, OK? + +How do we understand +from the field theory + +perspective somehow this +increase of one dimension? + +OK? + +So the answer turns out-- the +answer is actually very simple. + +And it's already nice in a way. + +The answer is already +in the way which + +we take the low energy limit. + +OK? + +So remember, when we take +the low energy limit-- so + +let me draw this figure +again-- in the gravity side, + +and this is going +to R goes to 0. + +OK? + +So by studying the red shift +due to the curved spacetime, + +we show that if you want +to go to low energies, + +then you want to go to +smaller and smaller R. OK? + +So you want to go to +smaller and smaller R + +if you want to go to [? lower ?] +and [? lower ?] emerges. + +OK? + +So smaller r, and then +give you smaller energy. + +So we use this +argument to decouple + +this, the other factor. + +We say, if you want +to go to low energy, + +you take r go to 0 limit. + +Then there are infinite +distance between them. + +But the nice thing +about infinities + +is that after you +go to infinity, + +there's still infinite left. + +OK? + +So the same argument +also applies in AdS, + +in the AdS part, after you +decouple the other stuff. + +And the AdS part of this +argument still applies. + +Still, the same thing happens. + +The same red shift +argument applies. + +So if you want to +go to low energies, + +you want to go to smaller r. + +OK? + +And so this immediately tells +us that this actual dimension, + +this r direction, it's precisely +the direction, which external + +to the N equal to 4 +super-Yang-Mills theory, + +transverse to the N equal to +4 super-Yang-Mills theory. + +So this [? immediate ?] +[? here is ?] this actual + +dimension, this r, or in +this coordinate z-- remember, + +in this z, z related to that +thing just by R squared divided + +by r, so that r +related to that z. + +So that the r goes to +0 limit, it tells you + +that that r dimension, +r can be considered, + +this actual dimension +can be considered + +as representing the energy +scale of the Yang-Mills theory, + +OK, or the energy scale +of the boundary theory. + +So if you want to +go to low energy, + +you go down [? farthest ?] +[? route. ?] OK? + +This is a very, very +important point. + +And this nice into many +phenomenon between AdS + +and the CFT and +the disconnection. + +Very important, and if you +have a good understanding, + +it will give you lots +of good intuitions + +in you understand the relation. + +So let me just to elaborate +the argument again, + +now using this metric. + +OK? + +OK, so now, we'll go over +this red shift argument again, + +and to use this metric. + +OK? + +So again, so the key thing +is that the x mu, which + +you t go to x appear +in this metric, + +is defining the boundary unit. + +OK? + +So this defines-- so this +defined in the boundary unit. + +So this is the unit we use +in the Yang-Mills theory. + +OK? + +So those coordinates are +defined in the boundary units. + +So now, if we want to talk +about energies in some bulk, + +say, the local proper +time, and the length, + +and the total proper length +at some, say, at some z, + +OK, so at some +location z in the bulk + +is related by the +standard relation, + +which we can read from there. + +It say d tau should be equal to +R, so this local proper time. + +Local proper time should be +equal to R divided by z dt. + +And the dl, so +local length scale, + +should be a proper length, +should be related R z times dx. + +OK? + +OK, just because of this. + +You can just read it from here. + +Locally, you can always write +this as a Minkowski metric + +in d plus 1 dimension. + +And then for the local +observer, and this + +is the local time, local proper +time and local proper length. + +OK? + +And then this tells +you that you can easily + +invert this relation. + +This tells you the energy +we observe in the Yang-Mills + +theory, was just energy +we measure in terms of t + +should be related to the energy, +which we measure locally, + +so all these relation, +local energy. + +And length scale, now +d in Yang-Mills theory, + +is related to the local +length scale by this relation. + +OK? + +So this is an inverse of +that because of the tau + +and the [? energy. ?] This +is just the same as that. + +OK? + +Good? + +So now, let's consider +the same bulk process. + +OK? + +So let's consider the +same bulk process. + +Say, for example, +this process we + +are sitting in this +classroom, say, supposing we + +[? leaving ?] AdS. + +Let's imagine that happens +at different values of z, + +OK say, for the same bulk +process, at different z. + +OK. + +Then, of course, the E +local, the local energy scale + +and the local length +scale would be the same. + +OK? + +So if we consider +the different process + +at different z, the +same physical process + +at different z, in terms of a +local observers, it's the same. + +So E local and the d +local does not change. + +OK? + +But if you translate into +the Yang-Mills scale, + +then you find now that the +corresponding Yang-Mills energy + +scale now proportional +to 1 over z, + +OK, because now, we +have fixed E local. + +OK? + +We have fixed E local. + +We are changing z. + +So now, you find at a different +location, now corresponding + +to a different energy scale +in the Yang-Mills theory. + +Say, the d Yang-Mills we +will [? portion it ?] to z. + +OK? + +And in particular, for +the same process as z + +equal to 0, if we move this +process close to the boundary-- + +z equal to 0 means close +to the boundary-- then + +the Yang-Mills energy, the +corresponding Yang-Mills + +energy, actually +goes to infinity. + +Under the corresponding +Yang-Mills scale, + +actually goes-- distance +scale goes to 0. + +So that means this is +a mapped to some UV + +process in the +Yang-Mills theory. + +OK? + +And but if you take the +z goes to infinity, which + +means you go to interior, +far away from the boundary-- + +so you go to infinity, far +away from the boundary, + +go to interior-- then +this E Yang-Mills, + +then the corresponding +Yang-Mills energy scale + +will go to 0. + +And the corresponding +Yang-Mills length scale + +will go to infinity. + +OK? + +So this would corresponding +to the IR process. + +So this will be a +low-energy process, + +and [? much ?] distance +in the Yang-Mills theory. + +So there, of course, +[? those run ?] into the IR + +process in the Yang-Mills. + +OK? + +And [? this-- ?] + +So normally, if you think +about the perspective + +from AdS point of view, +when you go to the boundary, + +means you've got +a long distance. + +So from AdS point of view, +this is going to the IR. + +OK? + +And then when you go to the +infinity, z go to infinity. + +You are going to the +interior in the bulk. + +So roughly, it's not precisely-- +[? if you ?] [? risk, ?] you + +can think of this actually +going to the short distance + +in the-- not really the +short distance, just-- yeah, + +this name is not very proper, +but let's just call it the UV. + +Just go into the +interior of the bulk. + +So now, since you see an +[? opposite ?] process going + +on, in the AdS will go to IR. + +Then from the Yang-Mills +theory, corresponding + +to going to the UV, but in +the AdS, you go to interior. + +And then from the +Yang-Mills theory, + +corresponding to go +to the IR low energy. + +OK? + +So here, we have something +like IR-UV connection. + +OK? + +In particular, I already +said in particular once. + +[LAUGHS] So but I +don't have other words. + +So in particular-- + +[LAUGHTER] + +--if you really consider the +typical gravity process, OK, + +so if you consider the +typical gravity process, + +so not consider string +theory, just consider gravity. + +Typical gravity process, +a classical gravity + +processes, then essentially, +the curvature radius + +defines your scale. + +OK? + +So that means that the +typical gravity processes, + +the E local is of order 1 +over the curvature scale. + +And the typical length +scale in the bulk, + +you can also see that it's +also the curvature radius. + +So in these cases, if you +plug this into this relation, + +then you can see that for +the typical bulk process, + +you can really identify the +E Yang-Mills, essentially, + +just with the radial +direction, OK, + +because this product will be 1. + +This product will be of order 1. + +And then you can really just +identify the z, the inverse + +z with the Yang-Mills energy. + +OK? + +So let me just say this +in the little bit slide + +today, in the picture. + +Maybe I'll do it here, +maybe just do it here. + +So think about this +in the picture. + +So suppose this is a boundary. + +So this is the picture. + +This is the picture, which +on the back page of the class + +it said, if you consider +some process here, + +which we draw a +cow, which I don't + +know how to draw a cow here. + +[LAUGHTER] + +And at some distance, +say, here, some value + +of z here, and similar process +as some other value of z, + +then the corresponding +boundary image of them, + +so this will corresponding +to a bigger guy. + +And this guy will corresponding +slightly small guy. + +OK? + +Yeah, I hope you +understand the picture. + +Yeah, [? so ?] the +further away, the same + +process in the interior, +they corresponding + +to a process with a larger +distance and a lower energy + +from the field +theory perspective. + +OK? + +So now, let me +make some remarks. + +Yeah, I did not +show it very well. + +Is this clear what I +mean by this picture? + +OK, good. + +Yeah, a more fancy +picture is just + +in the web page of the class. + +So now, let me +make some remarks. + +The first remarks is that +the AdS, if you, say, + +calculate the volume +of AdS, so calculate + +the determinant of this guy, +square root of the determinant + +of the metric, +and then integrate + +over the [? O ?] space. + +Then you find it's divergent. + +And particularly, +it's divergent because + +of the infinite distance +in going to the boundary. + +OK? + +So often, we will, say, put +some cut-off, IR cut-off, + +near the boundary, +say, rather than + +let z go all the +way to z equal to 0. + +We, say, we stop the space at +z equal to some [? epsilon. ?] + +OK? + +That's the procedure +we often do, just + +as a mathematical convenience. + +Because if you go all +the way to z equal to 0, + +then this factor blows up. + +And then many things +become tricky to do. + +And then we often, in order +to get the finite answer, + +we always put the z-- +put the boundary at z + +equal to some epsilon. + +And epsilon's some +small parameter. + +OK? + +So and for example, this is +what you will do in your p set, + +in one of the p set problem. + +OK, when we try +to-- when you will + +check this holographic bound. + +And that's the trick +[? you're ?] [? ready ?] + +to use. + +So putting the IR +cut-off in AdS, at some z + +equal to epsilon, then +from this IR-UV picture, + +then translate in the boundary. + +In the boundary, we introduce +a short distance cut-off, + +or UV cut-off, say, at +some short distance scale, + +say, [? data ?] x say or order +epsilon, or energy cut-off, + +or UV energy cut-off +at, say, energy, say, + +of order 1 over epsilon. + +OK? + +So this just a [? natural-- ?] +the reason this + +goes 1 into a UV cut-off +because of this relation, + +because of this relation. + +When you cut-off +the space at some z, + +then you can no longer +go to infinite energy. + +You can no longer go to +infinite distance scale, OK? + +And essentially, equivalently +providing a short distance + +cut-off from that relation. + +OK? + +Is it clear? + +And you will use +this in your p set. + +OK? + +So the second remark is that +here, we are considering, + +so N equal to 4 super-Yang-Mills +theory, as we said, + +it's a conformal theory. + +Or it's a scale +invariant theory. + +A feature for scale +invariant theory + +is that there's no scale. + +There's no scale means you can +have arbitrarily low energy + +excitations. + +OK? + +So for conformal theory, +say, in R(1,3), there exists, + +because of the scale invariants, +there exist arbitrarily low + +energy excitations. + +OK? + +So from this IR-UV, +then this corresponding + +to-- then this just +map to the z equal + +to infinity region in the bulk. + +OK? + +So this map to the z equal to +infinity region in the bulk. + +So it's a very good +thing that this z + +equal to infinity region. + +OK? + +It's a very good thing, this +z equal to infinity region, + +because otherwise, those +modes have nothing to map to. + +So on the other +hand, even the theory + +have a gap, on the +other hand, if, say, + +if the corresponding bulk +spacetime, say, "ends" + +at the finite proper distance, +OK, so important thing + +is the following. + +So let's take any point here. + +Take any point here. + +So this is some +reference scale, say. + +Choose it as a reference +scale in the field theory, + +because of this [? UV ?] +[? R ?] connection. + +So now, we want to consider +arbitrary low energy scale + +compared to this scale. + +Then what you want +to do, then you just + +you go to z equal to infinity. + +And this, what is +actually hidden here + +when you do this +argument, is actually + +the proper distance going to z +equal to infinity is infinite. + +And because when you do +this proper distance, yeah, + +essentially, there's infinite +proper distance [? in ?] + +go to z equal to infinity. + +And then you can go to +infinite low energy scales. + +OK? + +But now, if you look +at the global AdS, + +then take some interior point. + +Then actually, you +can easily check. + +When you go to the most interior +point, it's just ro equal to 0. + +OK? + +And that is finite +proper distance away. + +So in some sense, +the spacetime ends + +at the finite proper distance +in the radial direction. + +OK? + +In this case, if you apply +this, this will tell you that + +the theory cannot have arbitrary +low energy excitations. + +OK? + +Is this clear? + +Let me just say it again. + +In this theory, in the +Poincare patch, in the bulk, + +we can go to z +equal to infinity. + +And that's infinite +proper distance away. + +And using this UV +IR argument, that + +translates to infinite low +energy process in the field + +theory. + +But now, let's consider what's +happening in the global AdS. + +Just from the geometry, +we see something dramatic + +happens, because now, +this is a cylinder. + +And look at the metric. + +You take finite +distance from some point + +to go to the most center +point, which is rho 0. + +So you no longer have +infinite distance to go to. + +So if this argument +is consistent, + +then this must be +due to a theory + +without arbitrary low +energy excitation. + +OK? + +But this is, indeed, the +case, because according + +to what I erased, +just before we break, + +we say for the gravity theory +in the global AdS, that + +should be due to a +Yang-Mills theory, + +and the boundary +over here, which + +is S times R. For any field +theory [? under ?] S-- again, + +this is a compact +manifold-- then + +there's a mass gap +from the vacuum. + +And so this theory +actually have a mass gap. + +OK? + +So that means if the +corresponding bulk space that + +ends this on finite proper +distance, the boundary theory + +must have a mass +gap, and vice versa. + +If the fields theory +have a mass gap, + +which you cannot go to +arbitrary low energies, + +and then the bulk spacetime +have to be end somewhere. + +Otherwise, these +statements will not apply. + +OK? + +So consistency check +of that statement + +is that this has to be true. + +OK? + +So in the p set, +you should think + +through these for the +process over the field theory + +on the cylinder. + +OK? + +OK, I think I will stop here. + +Do you have any +questions regarding this? + +Yes? + +AUDIENCE: I was somewhat +under the impression + +that the global AdS +and the Poincare patch + +were just different +coordinates for presentation + +with the same thing, sort of? + +So how -- would that be correct? + +HONG LIU: Hm? + +AUDIENCE: I was +under the impression + +that the global AdS +and the Poincare patch + +are just different coordinate +charts on the same sort + +of structure or [INAUDIBLE]. + +HONG LIU: Yeah. + +AUDIENCE: So why do we have +infinite distance in one + +and finite distance in another? + +Is that? + +HONG LIU: Figured out. + +Figured it out. + +And this is geometry. + +You can just look at them. + +It depend on how you +slice the spacetime. + +Yeah, it's very easy to see. + +Just see how you map one point +to the other point, et cetera. + +Yeah. + +AUDIENCE: OK. + +HONG LIU: But the important +thing, the important thing + +is that the-- yeah, +I'll give you a hint. + +So this z equal to +infinity can be considered + +as a coordinate singularity +of that [? thing. ?] + +so even though here +it's completely smooth, + +but in here is like a coordinate +singularity because of this. + +AUDIENCE: OK. + +HONG LIU: Yeah, yeah, yeah. + +Yeah, so that's why, actually, +to talk about theory on R3 + +and the theory on S3 is heading +[? on 2 ?] because the physics + +are very different. + +Because here, yeah, +because here, you always + +have a mass gap. + +And here, you don't. + +And so that refract the +geometry very different. + +The way you view the +geometry are very different. + +AUDIENCE: So the +[INAUDIBLE] 5 [INAUDIBLE]? + +HONG LIU: Hm? + +AUDIENCE: The [INAUDIBLE]? + +HONG LIU: Yeah, +yeah. [INAUDIBLE] + +AUDIENCE: But if you +change this [INAUDIBLE], + +then it's still N equal 4 +super-Yang-Mills [INAUDIBLE]. + +HONG LIU: Yeah, it +would be something else. + +AUDIENCE: Then yeah. + +HONG LIU: Yeah, yeah. + +[APPLAUSE] \ No newline at end of file diff --git a/0wxS1iBHG9U.txt b/0wxS1iBHG9U.txt new file mode 100644 index 0000000000000000000000000000000000000000..4f89ea77b9d96311ee09bdfeacb3414b4b92375c --- /dev/null +++ b/0wxS1iBHG9U.txt @@ -0,0 +1,8331 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi everybody today we're going to talk + + align:start position:0% +hi everybody today we're going to talk + + + align:start position:0% +hi everybody today we're going to talk +about semantic localization so first I'm + + align:start position:0% +about semantic localization so first I'm + + + align:start position:0% +about semantic localization so first I'm +going to talk about you know what is + + align:start position:0% +going to talk about you know what is + + + align:start position:0% +going to talk about you know what is +semantic localization and what is the + + align:start position:0% +semantic localization and what is the + + + align:start position:0% +semantic localization and what is the +motivation for it then we'll go through + + align:start position:0% +motivation for it then we'll go through + + + align:start position:0% +motivation for it then we'll go through +an algorithm that will allow us to + + align:start position:0% +an algorithm that will allow us to + + + align:start position:0% +an algorithm that will allow us to +localize and then we'll go into how to + + align:start position:0% +localize and then we'll go into how to + + + align:start position:0% +localize and then we'll go into how to +actually add semantic information into + + align:start position:0% +actually add semantic information into + + + align:start position:0% +actually add semantic information into +this algorithm so our sort of focus when + + align:start position:0% +this algorithm so our sort of focus when + + + align:start position:0% +this algorithm so our sort of focus when +we were coming up with this was the + + align:start position:0% +we were coming up with this was the + + + align:start position:0% +we were coming up with this was the +orienteering grand challenge so in + + align:start position:0% +orienteering grand challenge so in + + + align:start position:0% +orienteering grand challenge so in +orienteering basically you have a map + + align:start position:0% +orienteering basically you have a map + + + align:start position:0% +orienteering basically you have a map +and you have a compass and you have to + + align:start position:0% +and you have a compass and you have to + + + align:start position:0% +and you have a compass and you have to +go around to various checkpoints so as + + align:start position:0% +go around to various checkpoints so as + + + align:start position:0% +go around to various checkpoints so as +you can imagine this is sort of + + align:start position:0% +you can imagine this is sort of + + + align:start position:0% +you can imagine this is sort of +difficult because you don't know where + + align:start position:0% +difficult because you don't know where + + + align:start position:0% +difficult because you don't know where +you are on this map except what you can + + align:start position:0% +you are on this map except what you can + + + align:start position:0% +you are on this map except what you can +tell from your compass and so we weren't + + align:start position:0% +tell from your compass and so we weren't + + + align:start position:0% +tell from your compass and so we weren't +sure how to do this either so we asked + + align:start position:0% +sure how to do this either so we asked + + + align:start position:0% +sure how to do this either so we asked +some orienteering experts so basically + + align:start position:0% +some orienteering experts so basically + + + align:start position:0% +some orienteering experts so basically +the key ideas are if you are + + align:start position:0% +the key ideas are if you are + + + align:start position:0% +the key ideas are if you are +disorientated that's fine you just need + + align:start position:0% +disorientated that's fine you just need + + + align:start position:0% +disorientated that's fine you just need +to sort of find you know a reference + + align:start position:0% +to sort of find you know a reference + + + align:start position:0% +to sort of find you know a reference +point so that you can figure out where + + align:start position:0% +point so that you can figure out where + + + align:start position:0% +point so that you can figure out where +you are you can think about where you + + align:start position:0% +you are you can think about where you + + + align:start position:0% +you are you can think about where you +last you wherever you are and you know + + align:start position:0% +last you wherever you are and you know + + + align:start position:0% +last you wherever you are and you know +sort of estimate what your movement has + + align:start position:0% +sort of estimate what your movement has + + + align:start position:0% +sort of estimate what your movement has +been since you were there and that can + + align:start position:0% +been since you were there and that can + + + align:start position:0% +been since you were there and that can +give you some options as to where you + + align:start position:0% +give you some options as to where you + + + align:start position:0% +give you some options as to where you +are and you can look around for features + + align:start position:0% +are and you can look around for features + + + align:start position:0% +are and you can look around for features +that you can identify uniquely on the + + align:start position:0% +that you can identify uniquely on the + + + align:start position:0% +that you can identify uniquely on the +map and if you sort of this is an + + align:start position:0% +map and if you sort of this is an + + + align:start position:0% +map and if you sort of this is an +example of an orienteering map um + + align:start position:0% +example of an orienteering map um + + + align:start position:0% +example of an orienteering map um +if you just sort of have what's over + + align:start position:0% +if you just sort of have what's over + + + align:start position:0% +if you just sort of have what's over +here it's not very useful you can't + + align:start position:0% +here it's not very useful you can't + + + align:start position:0% +here it's not very useful you can't +actually you know tell what those things + + align:start position:0% +actually you know tell what those things + + + align:start position:0% +actually you know tell what those things +are you might guess that Green is grass + + align:start position:0% +are you might guess that Green is grass + + + align:start position:0% +are you might guess that Green is grass +but you don't actually know what they + + align:start position:0% +but you don't actually know what they + + + align:start position:0% +but you don't actually know what they +are this map isn't useful until you + + align:start position:0% +are this map isn't useful until you + + + align:start position:0% +are this map isn't useful until you +actually have a legend to go along with + + align:start position:0% +actually have a legend to go along with + + + align:start position:0% +actually have a legend to go along with +it so that you can say you know you have + + align:start position:0% +it so that you can say you know you have + + + align:start position:0% +it so that you can say you know you have +roads or footpaths or pits or different + + align:start position:0% +roads or footpaths or pits or different + + + align:start position:0% +roads or footpaths or pits or different +things on the map that you can actually + + align:start position:0% +things on the map that you can actually + + + align:start position:0% +things on the map that you can actually +identify so this is sort of the + + align:start position:0% +identify so this is sort of the + + + align:start position:0% +identify so this is sort of the +difference between how robots typically + + align:start position:0% +difference between how robots typically + + + align:start position:0% +difference between how robots typically +localized and how human is localized + + align:start position:0% +localized and how human is localized + + + align:start position:0% +localized and how human is localized +here's think about places in terms of + + align:start position:0% +here's think about places in terms of + + + align:start position:0% +here's think about places in terms of +features in terms of what you can do + + align:start position:0% +features in terms of what you can do + + + align:start position:0% +features in terms of what you can do +with them things like that whereas + + align:start position:0% +with them things like that whereas + + + align:start position:0% +with them things like that whereas +robots might measure distances with + + align:start position:0% +robots might measure distances with + + + align:start position:0% +robots might measure distances with +laser scanners to form you know a + + align:start position:0% +laser scanners to form you know a + + + align:start position:0% +laser scanners to form you know a +perfect map of the entire space whereas + + align:start position:0% +perfect map of the entire space whereas + + + align:start position:0% +perfect map of the entire space whereas +humans might think about you know + + align:start position:0% +humans might think about you know + + + align:start position:0% +humans might think about you know +obstructions such as rooms and their + + align:start position:0% +obstructions such as rooms and their + + + align:start position:0% +obstructions such as rooms and their +relative location to each other so we + + align:start position:0% +relative location to each other so we + + + align:start position:0% +relative location to each other so we +can sort of define semantic information + + align:start position:0% +can sort of define semantic information + + + align:start position:0% +can sort of define semantic information +as signs and symbols that contain + + align:start position:0% +as signs and symbols that contain + + + align:start position:0% +as signs and symbols that contain +meaningful concepts for humans basically + + align:start position:0% +meaningful concepts for humans basically + + + align:start position:0% +meaningful concepts for humans basically +different sorts of abstractions and why + + align:start position:0% +different sorts of abstractions and why + + + align:start position:0% +different sorts of abstractions and why +might we want the semantic information + + align:start position:0% +might we want the semantic information + + + align:start position:0% +might we want the semantic information +well one very important application + + align:start position:0% +well one very important application + + + align:start position:0% +well one very important application +would be improving human robot + + align:start position:0% +would be improving human robot + + + align:start position:0% +would be improving human robot +interaction so say you want a robot that + + align:start position:0% +interaction so say you want a robot that + + + align:start position:0% +interaction so say you want a robot that +can make coffee it has to understand + + align:start position:0% +can make coffee it has to understand + + + align:start position:0% +can make coffee it has to understand +commands like go to the kitchen like get + + align:start position:0% +commands like go to the kitchen like get + + + align:start position:0% +commands like go to the kitchen like get +a mug turn on the coffee maker this is + + align:start position:0% +a mug turn on the coffee maker this is + + + align:start position:0% +a mug turn on the coffee maker this is +sort of the language that humans think + + align:start position:0% +sort of the language that humans think + + + align:start position:0% +sort of the language that humans think +in and it's very useful if iRobot can + + align:start position:0% +in and it's very useful if iRobot can + + + align:start position:0% +in and it's very useful if iRobot can +actually understand these sorts this + + align:start position:0% +actually understand these sorts this + + + align:start position:0% +actually understand these sorts this +sort of language as well you know what a + + align:start position:0% +sort of language as well you know what a + + + align:start position:0% +sort of language as well you know what a +coffee maker is what it does and where + + align:start position:0% +coffee maker is what it does and where + + + align:start position:0% +coffee maker is what it does and where +it is and additionally you can sort of + + align:start position:0% +it is and additionally you can sort of + + + align:start position:0% +it is and additionally you can sort of +get some performance and memory benefits + + align:start position:0% +get some performance and memory benefits + + + align:start position:0% +get some performance and memory benefits +you're not starting this fold map you + + align:start position:0% +you're not starting this fold map you + + + align:start position:0% +you're not starting this fold map you +know with the distance to every single + + align:start position:0% +know with the distance to every single + + + align:start position:0% +know with the distance to every single +surface you're just storing locations of + + align:start position:0% +surface you're just storing locations of + + + align:start position:0% +surface you're just storing locations of +key information and this means that your + + align:start position:0% +key information and this means that your + + + align:start position:0% +key information and this means that your +search space is a lot smaller too so you + + align:start position:0% +search space is a lot smaller too so you + + + align:start position:0% +search space is a lot smaller too so you +can prune everything that's not related + + align:start position:0% +can prune everything that's not related + + + align:start position:0% +can prune everything that's not related +to kitchens or coffee makers and sort of + + align:start position:0% +to kitchens or coffee makers and sort of + + + align:start position:0% +to kitchens or coffee makers and sort of +get a performance benefit that way + + align:start position:0% +get a performance benefit that way + + + align:start position:0% +get a performance benefit that way +finally the fact that you can use simply + + align:start position:0% +finally the fact that you can use simply + + + align:start position:0% +finally the fact that you can use simply +a camera instead of a complicated laser + + align:start position:0% +a camera instead of a complicated laser + + + align:start position:0% +a camera instead of a complicated laser +scanner means that this is a lot cheaper + + align:start position:0% +scanner means that this is a lot cheaper + + + align:start position:0% +scanner means that this is a lot cheaper +and more accessible for robots to have + + align:start position:0% + + + + align:start position:0% + +so we talked about what semantic + + align:start position:0% +so we talked about what semantic + + + align:start position:0% +so we talked about what semantic +information is so now let's define what + + align:start position:0% +information is so now let's define what + + + align:start position:0% +information is so now let's define what +semantic localization is so basically + + align:start position:0% +semantic localization is so basically + + + align:start position:0% +semantic localization is so basically +it's localizing based on semantic + + align:start position:0% +it's localizing based on semantic + + + align:start position:0% +it's localizing based on semantic +information rather than metric + + align:start position:0% +information rather than metric + + + align:start position:0% +information rather than metric +information like distances so for our + + align:start position:0% +information like distances so for our + + + align:start position:0% +information like distances so for our +grand challenge we have a map with + + align:start position:0% +grand challenge we have a map with + + + align:start position:0% +grand challenge we have a map with +labeled objects and their coordinates + + align:start position:0% +labeled objects and their coordinates + + + align:start position:0% +labeled objects and their coordinates +this is our semantic information and we + + align:start position:0% +this is our semantic information and we + + + align:start position:0% +this is our semantic information and we +want to basically look around and say + + align:start position:0% +want to basically look around and say + + + align:start position:0% +want to basically look around and say +what can we see in our field of view and + + align:start position:0% +what can we see in our field of view and + + + align:start position:0% +what can we see in our field of view and +from that we want to figure out where + + align:start position:0% +from that we want to figure out where + + + align:start position:0% +from that we want to figure out where +could we be on this map and it's + + align:start position:0% +could we be on this map and it's + + + align:start position:0% +could we be on this map and it's +important to note that map building is + + align:start position:0% +important to note that map building is + + + align:start position:0% +important to note that map building is +actually a very different and hard + + align:start position:0% +actually a very different and hard + + + align:start position:0% +actually a very different and hard +problem with a lot of other research hi + + align:start position:0% +problem with a lot of other research hi + + + align:start position:0% +problem with a lot of other research hi +in our case we've been given a map and + + align:start position:0% +in our case we've been given a map and + + + align:start position:0% +in our case we've been given a map and +we're simply talking about the problem + + align:start position:0% +we're simply talking about the problem + + + align:start position:0% +we're simply talking about the problem +of localizing based on that map and now + + align:start position:0% +of localizing based on that map and now + + + align:start position:0% +of localizing based on that map and now +I'm gonna let Matt tell you about + + align:start position:0% +I'm gonna let Matt tell you about + + + align:start position:0% +I'm gonna let Matt tell you about +particle filters which is an algorithm + + align:start position:0% +particle filters which is an algorithm + + + align:start position:0% +particle filters which is an algorithm +for localization okay so my name is Matt + + align:start position:0% +for localization okay so my name is Matt + + + align:start position:0% +for localization okay so my name is Matt +geo and now we're going to talk about + + align:start position:0% +geo and now we're going to talk about + + + align:start position:0% +geo and now we're going to talk about +particle filters so this is a tool the + + align:start position:0% +particle filters so this is a tool the + + + align:start position:0% +particle filters so this is a tool the +rent each you're going to use + + align:start position:0% +rent each you're going to use + + + align:start position:0% +rent each you're going to use +specifically for state estimation using + + align:start position:0% +specifically for state estimation using + + + align:start position:0% +specifically for state estimation using +a given map and measurements so so what + + align:start position:0% +a given map and measurements so so what + + + align:start position:0% +a given map and measurements so so what +is localization we just went over it + + align:start position:0% +is localization we just went over it + + + align:start position:0% +is localization we just went over it +specifically it's the question of where + + align:start position:0% +specifically it's the question of where + + + align:start position:0% +specifically it's the question of where +am I for any system to work the the + + align:start position:0% +am I for any system to work the the + + + align:start position:0% +am I for any system to work the the +robot needs to know where it is on a map + + align:start position:0% +robot needs to know where it is on a map + + + align:start position:0% +robot needs to know where it is on a map +this isn't that so simple of an answer + + align:start position:0% +this isn't that so simple of an answer + + + align:start position:0% +this isn't that so simple of an answer +metric globalization and as we said + + align:start position:0% +metric globalization and as we said + + + align:start position:0% +metric globalization and as we said +before it is quantitative so how many + + align:start position:0% +before it is quantitative so how many + + + align:start position:0% +before it is quantitative so how many +meters are you from this wall or from + + align:start position:0% +meters are you from this wall or from + + + align:start position:0% +meters are you from this wall or from +your origin + + align:start position:0% +your origin + + + align:start position:0% +your origin +what's your orientation and degrees and + + align:start position:0% +what's your orientation and degrees and + + + align:start position:0% +what's your orientation and degrees and +use some examples of that you can + + align:start position:0% +use some examples of that you can + + + align:start position:0% +use some examples of that you can +convert between coordinate frames really + + align:start position:0% +convert between coordinate frames really + + + align:start position:0% +convert between coordinate frames really +easily if you have metric so the + + align:start position:0% +easily if you have metric so the + + + align:start position:0% +easily if you have metric so the +localization is well in our case + + align:start position:0% +localization is well in our case + + + align:start position:0% +localization is well in our case +mathematically the problem statement is + + align:start position:0% +mathematically the problem statement is + + + align:start position:0% +mathematically the problem statement is +you have a control you you're going to + + align:start position:0% +you have a control you you're going to + + + align:start position:0% +you have a control you you're going to +observe something about your state it + + align:start position:0% +observe something about your state it + + + align:start position:0% +observe something about your state it +might be a camera image it might be + + align:start position:0% +might be a camera image it might be + + + align:start position:0% +might be a camera image it might be +laser scans and then essentially on your + + align:start position:0% +laser scans and then essentially on your + + + align:start position:0% +laser scans and then essentially on your +map you're gonna use probability to + + align:start position:0% +map you're gonna use probability to + + + align:start position:0% +map you're gonna use probability to +figure out where you are + + align:start position:0% +figure out where you are + + + align:start position:0% +figure out where you are +so this equation specifically is taking + + align:start position:0% +so this equation specifically is taking + + + align:start position:0% +so this equation specifically is taking +into account the probability of the + + align:start position:0% +into account the probability of the + + + align:start position:0% +into account the probability of the +position there being in a position at + + align:start position:0% +position there being in a position at + + + align:start position:0% +position there being in a position at +your current time based off your + + align:start position:0% +your current time based off your + + + align:start position:0% +your current time based off your +previous position the observation that + + align:start position:0% +previous position the observation that + + + align:start position:0% +previous position the observation that +you're taking right now the command + + align:start position:0% +you're taking right now the command + + + align:start position:0% +you're taking right now the command +variable you gave it and then your map + + align:start position:0% +variable you gave it and then your map + + + align:start position:0% +variable you gave it and then your map +like I said so that is that's built on + + align:start position:0% +like I said so that is that's built on + + + align:start position:0% +like I said so that is that's built on +the observation noise actuation and then + + align:start position:0% +the observation noise actuation and then + + + align:start position:0% +the observation noise actuation and then +the belief we're specifically looking at + + align:start position:0% +the belief we're specifically looking at + + + align:start position:0% +the belief we're specifically looking at +belief here for the particle filter so + + align:start position:0% +belief here for the particle filter so + + + align:start position:0% +belief here for the particle filter so +I'm in our case we're approximating by a + + align:start position:0% +I'm in our case we're approximating by a + + + align:start position:0% +I'm in our case we're approximating by a +set of points alternative particles so + + align:start position:0% +set of points alternative particles so + + + align:start position:0% +set of points alternative particles so +we're going to look at an example here + + align:start position:0% +we're going to look at an example here + + + align:start position:0% +we're going to look at an example here +I actually personally click on anything + + align:start position:0% +I actually personally click on anything + + + align:start position:0% +I actually personally click on anything +okay + + align:start position:0% +okay + + + align:start position:0% +okay +here's a quick demo right there so a + + align:start position:0% +here's a quick demo right there so a + + + align:start position:0% +here's a quick demo right there so a +quick YouTube demo of a particle filter + + align:start position:0% +quick YouTube demo of a particle filter + + + align:start position:0% +quick YouTube demo of a particle filter +in action so I'm just going to show it + + align:start position:0% +in action so I'm just going to show it + + + align:start position:0% +in action so I'm just going to show it +first so pause the red dot here is our + + align:start position:0% +first so pause the red dot here is our + + + align:start position:0% +first so pause the red dot here is our +actual robot position and it's trying to + + align:start position:0% +actual robot position and it's trying to + + + align:start position:0% +actual robot position and it's trying to +localize itself in a maze there's black + + align:start position:0% +localize itself in a maze there's black + + + align:start position:0% +localize itself in a maze there's black +walls throughout here and it's it looks + + align:start position:0% +walls throughout here and it's it looks + + + align:start position:0% +walls throughout here and it's it looks +like a rigged world but that initial + + align:start position:0% +like a rigged world but that initial + + + align:start position:0% +like a rigged world but that initial +distribution we had was completely + + align:start position:0% +distribution we had was completely + + + align:start position:0% +distribution we had was completely +random across all the walls so extinct + + align:start position:0% +random across all the walls so extinct + + + align:start position:0% +random across all the walls so extinct +mean observations of probably probably + + align:start position:0% +mean observations of probably probably + + + align:start position:0% +mean observations of probably probably +laser rangefinders + + align:start position:0% +laser rangefinders + + + align:start position:0% +laser rangefinders +so it's essentially knows that there are + + align:start position:0% +so it's essentially knows that there are + + + align:start position:0% +so it's essentially knows that there are +walls around it and it knows that + + align:start position:0% +walls around it and it knows that + + + align:start position:0% +walls around it and it knows that +there's not a wall in front of it so + + align:start position:0% +there's not a wall in front of it so + + + align:start position:0% +there's not a wall in front of it so +that centers all of these guesses on the + + align:start position:0% +that centers all of these guesses on the + + + align:start position:0% +that centers all of these guesses on the +center hallways obviously it got rid of + + align:start position:0% +center hallways obviously it got rid of + + + align:start position:0% +center hallways obviously it got rid of +things that were close to the walls + + align:start position:0% +things that were close to the walls + + + align:start position:0% +things that were close to the walls +there's a little probability that it's + + align:start position:0% +there's a little probability that it's + + + align:start position:0% +there's a little probability that it's +right up against the wall because the + + align:start position:0% +right up against the wall because the + + + align:start position:0% +right up against the wall because the +observations is taking and we're going + + align:start position:0% +observations is taking and we're going + + + align:start position:0% +observations is taking and we're going +to revisit this example at the end of + + align:start position:0% +to revisit this example at the end of + + + align:start position:0% +to revisit this example at the end of +the presentation particle filters so the + + align:start position:0% +the presentation particle filters so the + + + align:start position:0% +the presentation particle filters so the +method that we're going to teach you as + + align:start position:0% +method that we're going to teach you as + + + align:start position:0% +method that we're going to teach you as +four easy steps one is now repeated so + + align:start position:0% +four easy steps one is now repeated so + + + align:start position:0% +four easy steps one is now repeated so +the initialization step is your first + + align:start position:0% +the initialization step is your first + + + align:start position:0% +the initialization step is your first +sample of particles if you don't know + + align:start position:0% +sample of particles if you don't know + + + align:start position:0% +sample of particles if you don't know +anything about your state at the start + + align:start position:0% +anything about your state at the start + + + align:start position:0% +anything about your state at the start +then you can sample just a distribution + + align:start position:0% +then you can sample just a distribution + + + align:start position:0% +then you can sample just a distribution +over entire space and then the repeated + + align:start position:0% +over entire space and then the repeated + + + align:start position:0% +over entire space and then the repeated +steps are updating weights resampling + + align:start position:0% +steps are updating weights resampling + + + align:start position:0% +steps are updating weights resampling +and then propagating with dynamics and + + align:start position:0% +and then propagating with dynamics and + + + align:start position:0% +and then propagating with dynamics and +so we're going to show you a toy example + + align:start position:0% +so we're going to show you a toy example + + + align:start position:0% +so we're going to show you a toy example +this is a really simple example just to + + align:start position:0% +this is a really simple example just to + + + align:start position:0% +this is a really simple example just to +get idea across we're focusing on just + + align:start position:0% +get idea across we're focusing on just + + + align:start position:0% +get idea across we're focusing on just +one dimension we've an aircraft constant + + align:start position:0% +one dimension we've an aircraft constant + + + align:start position:0% +one dimension we've an aircraft constant +altitude so take that variable out the + + align:start position:0% +altitude so take that variable out the + + + align:start position:0% +altitude so take that variable out the +only thing we're trying to localize to + + align:start position:0% +only thing we're trying to localize to + + + align:start position:0% +only thing we're trying to localize to +is a distance x over a map the sensor is + + align:start position:0% +is a distance x over a map the sensor is + + + align:start position:0% +is a distance x over a map the sensor is +is just a rangefinder down to the ground + + align:start position:0% +is just a rangefinder down to the ground + + + align:start position:0% +is just a rangefinder down to the ground +at this constant altitude and the map is + + align:start position:0% +at this constant altitude and the map is + + + align:start position:0% +at this constant altitude and the map is +a NOAA mapping of next location to + + align:start position:0% +a NOAA mapping of next location to + + + align:start position:0% +a NOAA mapping of next location to +ground altitudes and we're about to see + + align:start position:0% +ground altitudes and we're about to see + + + align:start position:0% +ground altitudes and we're about to see +you with that means the goal here is + + align:start position:0% +you with that means the goal here is + + + align:start position:0% +you with that means the goal here is +determining where you are in the + + align:start position:0% +determining where you are in the + + + align:start position:0% +determining where you are in the +mountains so your radar playing as you + + align:start position:0% +mountains so your radar playing as you + + + align:start position:0% +mountains so your radar playing as you +see we know the map below and we know + + align:start position:0% +see we know the map below and we know + + + align:start position:0% +see we know the map below and we know +that it has to be flying at this + + align:start position:0% +that it has to be flying at this + + + align:start position:0% +that it has to be flying at this +altitude + + align:start position:0% +altitude + + + align:start position:0% +altitude +so with that rangefinder you can measure + + align:start position:0% +so with that rangefinder you can measure + + + align:start position:0% +so with that rangefinder you can measure +different depths down to the mountain so + + align:start position:0% +different depths down to the mountain so + + + align:start position:0% +different depths down to the mountain so +here we have long distances and medium + + align:start position:0% +here we have long distances and medium + + + align:start position:0% +here we have long distances and medium +distance and a short distance if it's + + align:start position:0% +distance and a short distance if it's + + + align:start position:0% +distance and a short distance if it's +directly on top of the mountain constant + + align:start position:0% +directly on top of the mountain constant + + + align:start position:0% +directly on top of the mountain constant +altitude unknown X that's what we're + + align:start position:0% +altitude unknown X that's what we're + + + align:start position:0% +altitude unknown X that's what we're +solving for and then we actually have no + + align:start position:0% +solving for and then we actually have no + + + align:start position:0% +solving for and then we actually have no +easy velocity forward so we know how + + align:start position:0% +easy velocity forward so we know how + + + align:start position:0% +easy velocity forward so we know how +fast the plane wants to be traveling but + + align:start position:0% +fast the plane wants to be traveling but + + + align:start position:0% +fast the plane wants to be traveling but +in this direction but obviously there's + + align:start position:0% +in this direction but obviously there's + + + align:start position:0% +in this direction but obviously there's +some noise it could be trip a little + + align:start position:0% +some noise it could be trip a little + + + align:start position:0% +some noise it could be trip a little +faster a little slower + + align:start position:0% +faster a little slower + + + align:start position:0% +faster a little slower +so the first step sampling areas will + + align:start position:0% +so the first step sampling areas will + + + align:start position:0% +so the first step sampling areas will +believe here is that we don't know where + + align:start position:0% +believe here is that we don't know where + + + align:start position:0% +believe here is that we don't know where +it is and with respect to these + + align:start position:0% +it is and with respect to these + + + align:start position:0% +it is and with respect to these +mountains so we're gonna actually sample + + align:start position:0% +mountains so we're gonna actually sample + + + align:start position:0% +mountains so we're gonna actually sample +with the uniform distribution well this + + align:start position:0% +with the uniform distribution well this + + + align:start position:0% +with the uniform distribution well this +is his uniform as that you get it so + + align:start position:0% +is his uniform as that you get it so + + + align:start position:0% +is his uniform as that you get it so +over this range those are our initial + + align:start position:0% +over this range those are our initial + + + align:start position:0% +over this range those are our initial +particles essentially guesses for what + + align:start position:0% +particles essentially guesses for what + + + align:start position:0% +particles essentially guesses for what +the X location is we're gonna update + + align:start position:0% +the X location is we're gonna update + + + align:start position:0% +the X location is we're gonna update +these weights based on the observation + + align:start position:0% +these weights based on the observation + + + align:start position:0% +these weights based on the observation +so we get our first observation from our + + align:start position:0% +so we get our first observation from our + + + align:start position:0% +so we get our first observation from our +rangefinder and it's this length so it's + + align:start position:0% +rangefinder and it's this length so it's + + + align:start position:0% +rangefinder and it's this length so it's +a long length it's I guess green in this + + align:start position:0% +a long length it's I guess green in this + + + align:start position:0% +a long length it's I guess green in this +case this is our measured value here are + + align:start position:0% +case this is our measured value here are + + + align:start position:0% +case this is our measured value here are +all the values that we expect to see of + + align:start position:0% +all the values that we expect to see of + + + align:start position:0% +all the values that we expect to see of +these particles so this is pretty easy + + align:start position:0% +these particles so this is pretty easy + + + align:start position:0% +these particles so this is pretty easy +to calculate based on the map that you + + align:start position:0% +to calculate based on the map that you + + + align:start position:0% +to calculate based on the map that you +have the position of each particle maps + + align:start position:0% +have the position of each particle maps + + + align:start position:0% +have the position of each particle maps +directly to a range finder measurement + + align:start position:0% +directly to a range finder measurement + + + align:start position:0% +directly to a range finder measurement +so we're gonna compare them so the + + align:start position:0% +so we're gonna compare them so the + + + align:start position:0% +so we're gonna compare them so the +likelihood of getting these so measuring + + align:start position:0% +likelihood of getting these so measuring + + + align:start position:0% +likelihood of getting these so measuring +the likelihood of each of these + + align:start position:0% +the likelihood of each of these + + + align:start position:0% +the likelihood of each of these +occurring and we're actually waiting the + + align:start position:0% +occurring and we're actually waiting the + + + align:start position:0% +occurring and we're actually waiting the +particles so based on what we measure + + align:start position:0% +particles so based on what we measure + + + align:start position:0% +particles so based on what we measure +these are most likely so they get a + + align:start position:0% +these are most likely so they get a + + + align:start position:0% +these are most likely so they get a +larger week and we are most likely not + + align:start position:0% +larger week and we are most likely not + + + align:start position:0% +larger week and we are most likely not +on top of a mountain at this point so + + align:start position:0% +on top of a mountain at this point so + + + align:start position:0% +on top of a mountain at this point so +they get smaller weights so we're going + + align:start position:0% +they get smaller weights so we're going + + + align:start position:0% +they get smaller weights so we're going +to resample given that so we're gonna + + align:start position:0% +to resample given that so we're gonna + + + align:start position:0% +to resample given that so we're gonna +keep the same number of samples the + + align:start position:0% +keep the same number of samples the + + + align:start position:0% +keep the same number of samples the +entire time that's just how this + + align:start position:0% +entire time that's just how this + + + align:start position:0% +entire time that's just how this +particle filter works except we're gonna + + align:start position:0% +particle filter works except we're gonna + + + align:start position:0% +particle filter works except we're gonna +resembled + + align:start position:0% +resembled + + + align:start position:0% +resembled +across our new distribution + + align:start position:0% + + + + align:start position:0% + +so this is the these are the weeks if + + align:start position:0% +so this is the these are the weeks if + + + align:start position:0% +so this is the these are the weeks if +you just came up with and we're gonna + + align:start position:0% +you just came up with and we're gonna + + + align:start position:0% +you just came up with and we're gonna +resample over them so now it's more + + align:start position:0% +resample over them so now it's more + + + align:start position:0% +resample over them so now it's more +likely that's here or here or way over + + align:start position:0% +likely that's here or here or way over + + + align:start position:0% +likely that's here or here or way over +there and in the final step is + + align:start position:0% +there and in the final step is + + + align:start position:0% +there and in the final step is +propagating so this whole time that + + align:start position:0% +propagating so this whole time that + + + align:start position:0% +propagating so this whole time that +we've been filtering and updating our + + align:start position:0% +we've been filtering and updating our + + + align:start position:0% +we've been filtering and updating our +weights the plane has been moving + + align:start position:0% +weights the plane has been moving + + + align:start position:0% +weights the plane has been moving +forward so we need to take that into + + align:start position:0% +forward so we need to take that into + + + align:start position:0% +forward so we need to take that into +account so we have a forward velocity it + + align:start position:0% +account so we have a forward velocity it + + + align:start position:0% +account so we have a forward velocity it +might be traveling let's say this range + + align:start position:0% +might be traveling let's say this range + + + align:start position:0% +might be traveling let's say this range +is zero meters per second to five meters + + align:start position:0% +is zero meters per second to five meters + + + align:start position:0% +is zero meters per second to five meters +per second to 10 meters per second that + + align:start position:0% +per second to 10 meters per second that + + + align:start position:0% +per second to 10 meters per second that +you can see on this plot so we're most + + align:start position:0% +you can see on this plot so we're most + + + align:start position:0% +you can see on this plot so we're most +likely moving 5 meters per second so + + align:start position:0% +likely moving 5 meters per second so + + + align:start position:0% +likely moving 5 meters per second so +essentially this is your change in time + + align:start position:0% +essentially this is your change in time + + + align:start position:0% +essentially this is your change in time +between sensor measurements obviously if + + align:start position:0% +between sensor measurements obviously if + + + align:start position:0% +between sensor measurements obviously if +you're only getting sensor measurements + + align:start position:0% +you're only getting sensor measurements + + + align:start position:0% +you're only getting sensor measurements +at 10 Hertz then you can't propagate in + + align:start position:0% +at 10 Hertz then you can't propagate in + + + align:start position:0% +at 10 Hertz then you can't propagate in +between each of those so here here we + + align:start position:0% +between each of those so here here we + + + align:start position:0% +between each of those so here here we +are using our new sample particles + + align:start position:0% +are using our new sample particles + + + align:start position:0% +are using our new sample particles +propagating them forward for example + + align:start position:0% +propagating them forward for example + + + align:start position:0% +propagating them forward for example +this one moving there is a low + + align:start position:0% +this one moving there is a low + + + align:start position:0% +this one moving there is a low +likelihood that's a large distance and + + align:start position:0% +likelihood that's a large distance and + + + align:start position:0% +likelihood that's a large distance and +these moving at a shorter distance is + + align:start position:0% +these moving at a shorter distance is + + + align:start position:0% +these moving at a shorter distance is +more likely given our model so we have + + align:start position:0% +more likely given our model so we have + + + align:start position:0% +more likely given our model so we have +those new ones the new weights are now + + align:start position:0% +those new ones the new weights are now + + + align:start position:0% +those new ones the new weights are now +basing the probability of the + + align:start position:0% +basing the probability of the + + + align:start position:0% +basing the probability of the +transitioning to that point how likely + + align:start position:0% +transitioning to that point how likely + + + align:start position:0% +transitioning to that point how likely +is it for the plane to move that far + + align:start position:0% +is it for the plane to move that far + + + align:start position:0% +is it for the plane to move that far +essentially and then we repeat so we're + + align:start position:0% +essentially and then we repeat so we're + + + align:start position:0% +essentially and then we repeat so we're +repeating it the steps again we're going + + align:start position:0% +repeating it the steps again we're going + + + align:start position:0% +repeating it the steps again we're going +to get a measurement in my rangefinder + + align:start position:0% +to get a measurement in my rangefinder + + + align:start position:0% +to get a measurement in my rangefinder +we're going to compare it to the map to + + align:start position:0% +we're going to compare it to the map to + + + align:start position:0% +we're going to compare it to the map to +our particles keep the ones that are + + align:start position:0% +our particles keep the ones that are + + + align:start position:0% +our particles keep the ones that are +most likely and weight them more and + + align:start position:0% +most likely and weight them more and + + + align:start position:0% +most likely and weight them more and +then propagate again so as an example + + align:start position:0% +then propagate again so as an example + + + align:start position:0% +then propagate again so as an example +here's time step two when we're + + align:start position:0% +here's time step two when we're + + + align:start position:0% +here's time step two when we're +measuring the uphill of this mountain + + align:start position:0% +measuring the uphill of this mountain + + + align:start position:0% +measuring the uphill of this mountain +time step three now we're halfway up the + + align:start position:0% +time step three now we're halfway up the + + + align:start position:0% +time step three now we're halfway up the +mountain so positions that we've kept + + align:start position:0% +mountain so positions that we've kept + + + align:start position:0% +mountain so positions that we've kept +are at similar Heights so here and here + + align:start position:0% +are at similar Heights so here and here + + + align:start position:0% +are at similar Heights so here and here +and then we can slowly get down with two + + align:start position:0% +and then we can slowly get down with two + + + align:start position:0% +and then we can slowly get down with two +differentiating it so now that we're on + + align:start position:0% +differentiating it so now that we're on + + + align:start position:0% +differentiating it so now that we're on +top of a mountain the only pattern that + + align:start position:0% +top of a mountain the only pattern that + + + align:start position:0% +top of a mountain the only pattern that +matches that is here and maybe over + + align:start position:0% +matches that is here and maybe over + + + align:start position:0% +matches that is here and maybe over +there and then eventually we get down to + + align:start position:0% +there and then eventually we get down to + + + align:start position:0% +there and then eventually we get down to +these two and then eventually as this + + align:start position:0% +these two and then eventually as this + + + align:start position:0% +these two and then eventually as this +mountain drops off it's a unique + + align:start position:0% +mountain drops off it's a unique + + + align:start position:0% +mountain drops off it's a unique +position where it goes farther than that + + align:start position:0% +position where it goes farther than that + + + align:start position:0% +position where it goes farther than that +one did so in the end our particle + + align:start position:0% +one did so in the end our particle + + + align:start position:0% +one did so in the end our particle +filter thinks that we're right around + + align:start position:0% +filter thinks that we're right around + + + align:start position:0% +filter thinks that we're right around +here or here and then finally there's a + + align:start position:0% +here or here and then finally there's a + + + align:start position:0% +here or here and then finally there's a +pretty high chance that we're + + align:start position:0% +pretty high chance that we're + + + align:start position:0% +pretty high chance that we're +over that Valley so we're to look at + + align:start position:0% +over that Valley so we're to look at + + + align:start position:0% +over that Valley so we're to look at +this again now that you know how to do + + align:start position:0% +this again now that you know how to do + + + align:start position:0% +this again now that you know how to do +the filter and this will make a little + + align:start position:0% +the filter and this will make a little + + + align:start position:0% +the filter and this will make a little +more sense now so they started with the + + align:start position:0% +more sense now so they started with the + + + align:start position:0% +more sense now so they started with the +uniform distribution they have no clue + + align:start position:0% +uniform distribution they have no clue + + + align:start position:0% +uniform distribution they have no clue +where they were at the beginning and as + + align:start position:0% +where they were at the beginning and as + + + align:start position:0% +where they were at the beginning and as +the robot moves forward they are + + align:start position:0% +the robot moves forward they are + + + align:start position:0% +the robot moves forward they are +resampling and the measurements are + + align:start position:0% +resampling and the measurements are + + + align:start position:0% +resampling and the measurements are +changing obviously because it's seeing + + align:start position:0% +changing obviously because it's seeing + + + align:start position:0% +changing obviously because it's seeing +these two walls and eventually it sees + + align:start position:0% +these two walls and eventually it sees + + + align:start position:0% +these two walls and eventually it sees +that there's a doorway to the left and + + align:start position:0% +that there's a doorway to the left and + + + align:start position:0% +that there's a doorway to the left and +you can keep going forward as well so + + align:start position:0% +you can keep going forward as well so + + + align:start position:0% +you can keep going forward as well so +eventually that geometry doesn't line up + + align:start position:0% +eventually that geometry doesn't line up + + + align:start position:0% +eventually that geometry doesn't line up +with with any other spot on the map here + + align:start position:0% +with with any other spot on the map here + + + align:start position:0% +with with any other spot on the map here +we see it knows it's in this hallway + + align:start position:0% +we see it knows it's in this hallway + + + align:start position:0% +we see it knows it's in this hallway +I think this top hallway is the only one + + align:start position:0% +I think this top hallway is the only one + + + align:start position:0% +I think this top hallway is the only one +on this map that's that long but it + + align:start position:0% +on this map that's that long but it + + + align:start position:0% +on this map that's that long but it +still doesn't know which direction it's + + align:start position:0% +still doesn't know which direction it's + + + align:start position:0% +still doesn't know which direction it's +going + + align:start position:0% +going + + + align:start position:0% +going +it hasn't been able to differentiate + + align:start position:0% +it hasn't been able to differentiate + + + align:start position:0% +it hasn't been able to differentiate +that yet but it's about two so the only + + align:start position:0% +that yet but it's about two so the only + + + align:start position:0% +that yet but it's about two so the only +remaining particles are here and here it + + align:start position:0% +remaining particles are here and here it + + + align:start position:0% +remaining particles are here and here it +knows it's in the middle of the hallway + + align:start position:0% +knows it's in the middle of the hallway + + + align:start position:0% +knows it's in the middle of the hallway +and it knows it's moved about two blocks + + align:start position:0% +and it knows it's moved about two blocks + + + align:start position:0% +and it knows it's moved about two blocks +now without seeing a wall and directly + + align:start position:0% +now without seeing a wall and directly + + + align:start position:0% +now without seeing a wall and directly +in front of it which that doesn't occur + + align:start position:0% +in front of it which that doesn't occur + + + align:start position:0% +in front of it which that doesn't occur +anywhere else without having another + + align:start position:0% +anywhere else without having another + + + align:start position:0% +anywhere else without having another +turn off so it's about to solve itself + + align:start position:0% +turn off so it's about to solve itself + + + align:start position:0% +turn off so it's about to solve itself +because eventually it sees this wall + + align:start position:0% +because eventually it sees this wall + + + align:start position:0% +because eventually it sees this wall +over here and those observations don't + + align:start position:0% +over here and those observations don't + + + align:start position:0% +over here and those observations don't +match up with what it's actually seen so + + align:start position:0% +match up with what it's actually seen so + + + align:start position:0% +match up with what it's actually seen so +there we go + + align:start position:0% +there we go + + + align:start position:0% +there we go +here's a sick particle filter + + align:start position:0% +here's a sick particle filter + + + align:start position:0% +here's a sick particle filter +successfully working for a little robot + + align:start position:0% +successfully working for a little robot + + + align:start position:0% +successfully working for a little robot +with a rangefinder + + align:start position:0% + + + + align:start position:0% + +I want to park there okay so I'm David + + align:start position:0% +I want to park there okay so I'm David + + + align:start position:0% +I want to park there okay so I'm David +Stingley and now after we've got an idea + + align:start position:0% +Stingley and now after we've got an idea + + + align:start position:0% +Stingley and now after we've got an idea +why we want to use semantic localization + + align:start position:0% +why we want to use semantic localization + + + align:start position:0% +why we want to use semantic localization +and how to use particle filters to get + + align:start position:0% +and how to use particle filters to get + + + align:start position:0% +and how to use particle filters to get +an idea of our guesses for initial + + align:start position:0% +an idea of our guesses for initial + + + align:start position:0% +an idea of our guesses for initial +positions we're going to talk about how + + align:start position:0% +positions we're going to talk about how + + + align:start position:0% +positions we're going to talk about how +we can use these two to actually + + align:start position:0% +we can use these two to actually + + + align:start position:0% +we can use these two to actually +implement semantic localization onto a + + align:start position:0% +implement semantic localization onto a + + + align:start position:0% +implement semantic localization onto a +robot so hardening back to the + + align:start position:0% +robot so hardening back to the + + + align:start position:0% +robot so hardening back to the +implementation idea we have three + + align:start position:0% +implementation idea we have three + + + align:start position:0% +implementation idea we have three +important parts we have a belief + + align:start position:0% +important parts we have a belief + + + align:start position:0% +important parts we have a belief +representation we have the actuation + + align:start position:0% +representation we have the actuation + + + align:start position:0% +representation we have the actuation +model so once we have the location how + + align:start position:0% +model so once we have the location how + + + align:start position:0% +model so once we have the location how +are we going to move as we said before + + align:start position:0% +are we going to move as we said before + + + align:start position:0% +are we going to move as we said before +you know if you don't exactly know how + + align:start position:0% +you know if you don't exactly know how + + + align:start position:0% +you know if you don't exactly know how +fast you're moving there's a probability + + align:start position:0% +fast you're moving there's a probability + + + align:start position:0% +fast you're moving there's a probability +you move to a bunch of different + + align:start position:0% +you move to a bunch of different + + + align:start position:0% +you move to a bunch of different +locations and then finally we have an + + align:start position:0% +locations and then finally we have an + + + align:start position:0% +locations and then finally we have an +observation model which is the + + align:start position:0% +observation model which is the + + + align:start position:0% +observation model which is the +probability that you see some certain + + align:start position:0% +probability that you see some certain + + + align:start position:0% +probability that you see some certain +observation given your in this newly + + align:start position:0% +observation given your in this newly + + + align:start position:0% +observation given your in this newly +simulated position if we continuously + + align:start position:0% +simulated position if we continuously + + + align:start position:0% +simulated position if we continuously +solve for our most probable X then + + align:start position:0% +solve for our most probable X then + + + align:start position:0% +solve for our most probable X then +that's our location so that particle + + align:start position:0% +that's our location so that particle + + + align:start position:0% +that's our location so that particle +that is the most probable is the place + + align:start position:0% +that is the most probable is the place + + + align:start position:0% +that is the most probable is the place +that we guessed we're going to be so + + align:start position:0% +that we guessed we're going to be so + + + align:start position:0% +that we guessed we're going to be so +let's look at like a pseudocode for what + + align:start position:0% +let's look at like a pseudocode for what + + + align:start position:0% +let's look at like a pseudocode for what +a semantic localization would look like + + align:start position:0% +a semantic localization would look like + + + align:start position:0% +a semantic localization would look like +so as long as our robots moving we're + + align:start position:0% +so as long as our robots moving we're + + + align:start position:0% +so as long as our robots moving we're +going to make observations and those + + align:start position:0% +going to make observations and those + + + align:start position:0% +going to make observations and those +observations are going to be that Z 1 + + align:start position:0% +observations are going to be that Z 1 + + + align:start position:0% +observations are going to be that Z 1 +then for those observations we're going + + align:start position:0% +then for those observations we're going + + + align:start position:0% +then for those observations we're going +to start our particle filter and guess a + + align:start position:0% +to start our particle filter and guess a + + + align:start position:0% +to start our particle filter and guess a +certain number of probable locations + + align:start position:0% +certain number of probable locations + + + align:start position:0% +certain number of probable locations +we're going to use our actuation to + + align:start position:0% +we're going to use our actuation to + + + align:start position:0% +we're going to use our actuation to +update it and then we're going to + + align:start position:0% +update it and then we're going to + + + align:start position:0% +update it and then we're going to +simulate observations at that location + + align:start position:0% +simulate observations at that location + + + align:start position:0% +simulate observations at that location +and compare what we expect to see for + + align:start position:0% +and compare what we expect to see for + + + align:start position:0% +and compare what we expect to see for +that particle on our map versus what we + + align:start position:0% +that particle on our map versus what we + + + align:start position:0% +that particle on our map versus what we +actually saw when we made our + + align:start position:0% +actually saw when we made our + + + align:start position:0% +actually saw when we made our +observation this is going to be our + + align:start position:0% +observation this is going to be our + + + align:start position:0% +observation this is going to be our +update and this is what we're going to + + align:start position:0% +update and this is what we're going to + + + align:start position:0% +update and this is what we're going to +focus on understanding since a lot of + + align:start position:0% +focus on understanding since a lot of + + + align:start position:0% +focus on understanding since a lot of +the rest of this is covered by a + + align:start position:0% +the rest of this is covered by a + + + align:start position:0% +the rest of this is covered by a +particle filter so what kind of models + + align:start position:0% +particle filter so what kind of models + + + align:start position:0% +particle filter so what kind of models +can we pick because we need to define + + align:start position:0% +can we pick because we need to define + + + align:start position:0% +can we pick because we need to define +what our observation looks like and you + + align:start position:0% +what our observation looks like and you + + + align:start position:0% +what our observation looks like and you +get a lot of choices in metric + + align:start position:0% +get a lot of choices in metric + + + align:start position:0% +get a lot of choices in metric +localization you use a label laser scan + + align:start position:0% +localization you use a label laser scan + + + align:start position:0% +localization you use a label laser scan +we have perfect information about the + + align:start position:0% +we have perfect information about the + + + align:start position:0% +we have perfect information about the +environment and so you can see + + align:start position:0% +environment and so you can see + + + align:start position:0% +environment and so you can see +everything it might be nice to use a + + align:start position:0% +everything it might be nice to use a + + + align:start position:0% +everything it might be nice to use a +scene with objects at specific locations + + align:start position:0% +scene with objects at specific locations + + + align:start position:0% +scene with objects at specific locations +but that requires once again a lot of + + align:start position:0% +but that requires once again a lot of + + + align:start position:0% +but that requires once again a lot of +information now you need to know where + + align:start position:0% +information now you need to know where + + + align:start position:0% +information now you need to know where +the objects are you need to have an idea + + align:start position:0% +the objects are you need to have an idea + + + align:start position:0% +the objects are you need to have an idea +of exact specific locations and + + align:start position:0% +of exact specific locations and + + + align:start position:0% +of exact specific locations and +orientations the respect to each other + + align:start position:0% +orientations the respect to each other + + + align:start position:0% +orientations the respect to each other +maybe it might be nice just to use like + + align:start position:0% +maybe it might be nice just to use like + + + align:start position:0% +maybe it might be nice just to use like +a bag of objects I see four things in my + + align:start position:0% +a bag of objects I see four things in my + + + align:start position:0% +a bag of objects I see four things in my +tea + + align:start position:0% +tea + + + align:start position:0% +tea +paint versus three these are all choices + + align:start position:0% +paint versus three these are all choices + + + align:start position:0% +paint versus three these are all choices +and we're going to take a look just + + align:start position:0% +and we're going to take a look just + + + align:start position:0% +and we're going to take a look just +really quickly at what the but the + + align:start position:0% +really quickly at what the but the + + + align:start position:0% +really quickly at what the but the +effects of these are as we stated before + + align:start position:0% +effects of these are as we stated before + + + align:start position:0% +effects of these are as we stated before +there's a lot of choices and observation + + align:start position:0% +there's a lot of choices and observation + + + align:start position:0% +there's a lot of choices and observation +it can get really complicated really + + align:start position:0% +it can get really complicated really + + + align:start position:0% +it can get really complicated really +quickly so just to impress that upon you + + align:start position:0% +quickly so just to impress that upon you + + + align:start position:0% +quickly so just to impress that upon you +imagine if you used laser scanners when + + align:start position:0% +imagine if you used laser scanners when + + + align:start position:0% +imagine if you used laser scanners when +you have three objects here for instance + + align:start position:0% +you have three objects here for instance + + + align:start position:0% +you have three objects here for instance +a house a couple of trees and a mailbox + + align:start position:0% +a house a couple of trees and a mailbox + + + align:start position:0% +a house a couple of trees and a mailbox +you check each line for an intersection + + align:start position:0% +you check each line for an intersection + + + align:start position:0% +you check each line for an intersection +and then you'd have to figure out what + + align:start position:0% +and then you'd have to figure out what + + + align:start position:0% +and then you'd have to figure out what +counts is your detection since you're + + align:start position:0% +counts is your detection since you're + + + align:start position:0% +counts is your detection since you're +going to have to differentiate what's in + + align:start position:0% +going to have to differentiate what's in + + + align:start position:0% +going to have to differentiate what's in +your scene the problem with that might + + align:start position:0% +your scene the problem with that might + + + align:start position:0% +your scene the problem with that might +be is that well you saw an entire wall + + align:start position:0% +be is that well you saw an entire wall + + + align:start position:0% +be is that well you saw an entire wall +for instance where do you want the house + + align:start position:0% +for instance where do you want the house + + + align:start position:0% +for instance where do you want the house +to be so let's say we assume that + + align:start position:0% +to be so let's say we assume that + + + align:start position:0% +to be so let's say we assume that +objects were point at some point you + + align:start position:0% +objects were point at some point you + + + align:start position:0% +objects were point at some point you +either completely seed or you completely + + align:start position:0% +either completely seed or you completely + + + align:start position:0% +either completely seed or you completely +don't that way you don't have to have to + + align:start position:0% +don't that way you don't have to have to + + + align:start position:0% +don't that way you don't have to have to +see an object um you just check to see + + align:start position:0% +see an object um you just check to see + + + align:start position:0% +see an object um you just check to see +if whatever you want your center mass to + + align:start position:0% +if whatever you want your center mass to + + + align:start position:0% +if whatever you want your center mass to +be intersects with your current view + + align:start position:0% +be intersects with your current view + + + align:start position:0% +be intersects with your current view +plane if it does then you're good the + + align:start position:0% +plane if it does then you're good the + + + align:start position:0% +plane if it does then you're good the +issue with that is that for instance + + align:start position:0% +issue with that is that for instance + + + align:start position:0% +issue with that is that for instance +something center view isn't inside the + + align:start position:0% +something center view isn't inside the + + + align:start position:0% +something center view isn't inside the +scene anymore you just completely ignore + + align:start position:0% +scene anymore you just completely ignore + + + align:start position:0% +scene anymore you just completely ignore +it we have the exact opposite problem + + align:start position:0% +it we have the exact opposite problem + + + align:start position:0% +it we have the exact opposite problem +sue might want to make it a bit more + + align:start position:0% +sue might want to make it a bit more + + + align:start position:0% +sue might want to make it a bit more +complex and have polygons parts of + + align:start position:0% +complex and have polygons parts of + + + align:start position:0% +complex and have polygons parts of +objects do you see some percentage of + + align:start position:0% +objects do you see some percentage of + + + align:start position:0% +objects do you see some percentage of +something how much of its in the view + + align:start position:0% +something how much of its in the view + + + align:start position:0% +something how much of its in the view +plane it adds in a lot of chance for + + align:start position:0% +plane it adds in a lot of chance for + + + align:start position:0% +plane it adds in a lot of chance for +arrows and that's I guess the big point + + align:start position:0% +arrows and that's I guess the big point + + + align:start position:0% +arrows and that's I guess the big point +here to remember is that depending on + + align:start position:0% +here to remember is that depending on + + + align:start position:0% +here to remember is that depending on +how to characterize their observations + + align:start position:0% +how to characterize their observations + + + align:start position:0% +how to characterize their observations +we have different ways to get things + + align:start position:0% +we have different ways to get things + + + align:start position:0% +we have different ways to get things +wrong so let's say for instance for an + + align:start position:0% +wrong so let's say for instance for an + + + align:start position:0% +wrong so let's say for instance for an +observation like distance and bearing to + + align:start position:0% +observation like distance and bearing to + + + align:start position:0% +observation like distance and bearing to +some new scenic object what can be wrong + + align:start position:0% +some new scenic object what can be wrong + + + align:start position:0% +some new scenic object what can be wrong +well you have noise inside of your + + align:start position:0% +well you have noise inside of your + + + align:start position:0% +well you have noise inside of your +sensors your sensors might have + + align:start position:0% +sensors your sensors might have + + + align:start position:0% +sensors your sensors might have +limitations you can't necessarily see to + + align:start position:0% +limitations you can't necessarily see to + + + align:start position:0% +limitations you can't necessarily see to +infinity so an object might be too far + + align:start position:0% +infinity so an object might be too far + + + align:start position:0% +infinity so an object might be too far +away for you to identify correctly it + + align:start position:0% +away for you to identify correctly it + + + align:start position:0% +away for you to identify correctly it +might be rotated in a way that you can't + + align:start position:0% +might be rotated in a way that you can't + + + align:start position:0% +might be rotated in a way that you can't +necessarily interpret it correctly how + + align:start position:0% +necessarily interpret it correctly how + + + align:start position:0% +necessarily interpret it correctly how +about if you want to have your + + align:start position:0% +about if you want to have your + + + align:start position:0% +about if you want to have your +observations be classes of objects so + + align:start position:0% +observations be classes of objects so + + + align:start position:0% +observations be classes of objects so +instead of just everything being an + + align:start position:0% +instead of just everything being an + + + align:start position:0% +instead of just everything being an +obstruction now you have different types + + align:start position:0% +obstruction now you have different types + + + align:start position:0% +obstruction now you have different types +of instructions trees are different from + + align:start position:0% +of instructions trees are different from + + + align:start position:0% +of instructions trees are different from +mailboxes of course in which case you + + align:start position:0% +mailboxes of course in which case you + + + align:start position:0% +mailboxes of course in which case you +have a classification error what if you + + align:start position:0% +have a classification error what if you + + + align:start position:0% +have a classification error what if you +see the tree you just think it's a + + align:start position:0% +see the tree you just think it's a + + + align:start position:0% +see the tree you just think it's a +really really big mailbox or do you see + + align:start position:0% +really really big mailbox or do you see + + + align:start position:0% +really really big mailbox or do you see +a mailbox do you think it's a really + + align:start position:0% +a mailbox do you think it's a really + + + align:start position:0% +a mailbox do you think it's a really +small tree with a funny little metal top + + align:start position:0% +small tree with a funny little metal top + + + align:start position:0% +small tree with a funny little metal top +these kind of errors can then make your + + align:start position:0% +these kind of errors can then make your + + + align:start position:0% +these kind of errors can then make your +scenes looking + + align:start position:0% +scenes looking + + + align:start position:0% +scenes looking +if you decide to have sets of objects + + align:start position:0% +if you decide to have sets of objects + + + align:start position:0% +if you decide to have sets of objects +well what permutations matter if you + + align:start position:0% +well what permutations matter if you + + + align:start position:0% +well what permutations matter if you +don't have a way of differentiating + + align:start position:0% +don't have a way of differentiating + + + align:start position:0% +don't have a way of differentiating +elements in the set then you don't know + + align:start position:0% +elements in the set then you don't know + + + align:start position:0% +elements in the set then you don't know +that two trees in a mailbox with the + + align:start position:0% +that two trees in a mailbox with the + + + align:start position:0% +that two trees in a mailbox with the +trees on the left and the mailboxes on + + align:start position:0% +trees on the left and the mailboxes on + + + align:start position:0% +trees on the left and the mailboxes on +the right or vice versa aren't the same + + align:start position:0% +the right or vice versa aren't the same + + + align:start position:0% +the right or vice versa aren't the same +thing + + align:start position:0% +thing + + + align:start position:0% +thing +so with that in mind we're going to + + align:start position:0% +so with that in mind we're going to + + + align:start position:0% +so with that in mind we're going to +start talking about how we're going to + + align:start position:0% +start talking about how we're going to + + + align:start position:0% +start talking about how we're going to +solve this question of given in some + + align:start position:0% +solve this question of given in some + + + align:start position:0% +solve this question of given in some +position and your synthetic view how + + align:start position:0% +position and your synthetic view how + + + align:start position:0% +position and your synthetic view how +likely is it that it's your actual + + align:start position:0% +likely is it that it's your actual + + + align:start position:0% +likely is it that it's your actual +observation and for that which is going + + align:start position:0% +observation and for that which is going + + + align:start position:0% +observation and for that which is going +to change what this probability + + align:start position:0% +to change what this probability + + + align:start position:0% +to change what this probability +statement looks like to make it a little + + align:start position:0% +statement looks like to make it a little + + + align:start position:0% +statement looks like to make it a little +more concrete in this case Z is the set + + align:start position:0% +more concrete in this case Z is the set + + + align:start position:0% +more concrete in this case Z is the set +of observed objects that you have so + + align:start position:0% +of observed objects that you have so + + + align:start position:0% +of observed objects that you have so +we're going to say that there are + + align:start position:0% +we're going to say that there are + + + align:start position:0% +we're going to say that there are +objects in the scene and we put them + + align:start position:0% +objects in the scene and we put them + + + align:start position:0% +objects in the scene and we put them +inside of this value Z so for instance + + align:start position:0% +inside of this value Z so for instance + + + align:start position:0% +inside of this value Z so for instance +you see a house and you see a mailbox + + align:start position:0% +you see a house and you see a mailbox + + + align:start position:0% +you see a house and you see a mailbox +that would be see your set of objects is + + align:start position:0% +that would be see your set of objects is + + + align:start position:0% +that would be see your set of objects is +just two things we're going to use the + + align:start position:0% +just two things we're going to use the + + + align:start position:0% +just two things we're going to use the +bag of objects approximation Y of X is + + align:start position:0% +bag of objects approximation Y of X is + + + align:start position:0% +bag of objects approximation Y of X is +going to be the set of objects you + + align:start position:0% +going to be the set of objects you + + + align:start position:0% +going to be the set of objects you +expect to see given your map for the + + align:start position:0% +expect to see given your map for the + + + align:start position:0% +expect to see given your map for the +position that you're at so given a + + align:start position:0% +position that you're at so given a + + + align:start position:0% +position that you're at so given a +position X Y is the set of objects that + + align:start position:0% +position X Y is the set of objects that + + + align:start position:0% +position X Y is the set of objects that +you would see so you might be in a + + align:start position:0% +you would see so you might be in a + + + align:start position:0% +you would see so you might be in a +position where you can see a house in a + + align:start position:0% +position where you can see a house in a + + + align:start position:0% +position where you can see a house in a +mailbox then Y is a house in a mailbox + + align:start position:0% +mailbox then Y is a house in a mailbox + + + align:start position:0% +mailbox then Y is a house in a mailbox +and X is just going to be your position + + align:start position:0% +and X is just going to be your position + + + align:start position:0% +and X is just going to be your position +that's the element that we're getting + + align:start position:0% +that's the element that we're getting + + + align:start position:0% +that's the element that we're getting +from our particle filter so in our + + align:start position:0% +from our particle filter so in our + + + align:start position:0% +from our particle filter so in our +example as you can tell by how much I + + align:start position:0% +example as you can tell by how much I + + + align:start position:0% +example as you can tell by how much I +talk about it we're going to use just + + align:start position:0% +talk about it we're going to use just + + + align:start position:0% +talk about it we're going to use just +two things trees and mail boxes because + + align:start position:0% +two things trees and mail boxes because + + + align:start position:0% +two things trees and mail boxes because +I like them so here's my map there's + + align:start position:0% +I like them so here's my map there's + + + align:start position:0% +I like them so here's my map there's +gonna be a long road and off to the side + + align:start position:0% +gonna be a long road and off to the side + + + align:start position:0% +gonna be a long road and off to the side +we have trees and mailboxes and let's + + align:start position:0% +we have trees and mailboxes and let's + + + align:start position:0% +we have trees and mailboxes and let's +say you get your robot wants to be a + + align:start position:0% +say you get your robot wants to be a + + + align:start position:0% +say you get your robot wants to be a +paper delivery boy so we need to be able + + align:start position:0% +paper delivery boy so we need to be able + + + align:start position:0% +paper delivery boy so we need to be able +to figure out where the mailboxes are + + align:start position:0% +to figure out where the mailboxes are + + + align:start position:0% +to figure out where the mailboxes are +and how far down the street he is + + align:start position:0% +and how far down the street he is + + + align:start position:0% +and how far down the street he is +because if he were to throw the paper + + align:start position:0% +because if he were to throw the paper + + + align:start position:0% +because if he were to throw the paper +wrong he'd throw paper into a tree so in + + align:start position:0% +wrong he'd throw paper into a tree so in + + + align:start position:0% +wrong he'd throw paper into a tree so in +this world our robots gonna be here + + align:start position:0% +this world our robots gonna be here + + + align:start position:0% +this world our robots gonna be here +represented by orange hexagons and it + + align:start position:0% +represented by orange hexagons and it + + + align:start position:0% +represented by orange hexagons and it +has this field of view so given this + + align:start position:0% +has this field of view so given this + + + align:start position:0% +has this field of view so given this +field of view what does Z look like or + + align:start position:0% +field of view what does Z look like or + + + align:start position:0% +field of view what does Z look like or +our actual observation 23 in one mailbox + + align:start position:0% +our actual observation 23 in one mailbox + + + align:start position:0% +our actual observation 23 in one mailbox +well for this case what we're gonna say + + align:start position:0% +well for this case what we're gonna say + + + align:start position:0% +well for this case what we're gonna say +is we're going to assume that as long as + + align:start position:0% +is we're going to assume that as long as + + + align:start position:0% +is we're going to assume that as long as +something intersects with our field of + + align:start position:0% +something intersects with our field of + + + align:start position:0% +something intersects with our field of +view we're going to see it so + + align:start position:0% +view we're going to see it so + + + align:start position:0% +view we're going to see it so +simplifying that we're just going + + align:start position:0% +simplifying that we're just going + + + align:start position:0% +simplifying that we're just going +see both trees endless mailbox once + + align:start position:0% +see both trees endless mailbox once + + + align:start position:0% +see both trees endless mailbox once +again we talked about how difficult it + + align:start position:0% +again we talked about how difficult it + + + align:start position:0% +again we talked about how difficult it +is to do this observations so for a + + align:start position:0% +is to do this observations so for a + + + align:start position:0% +is to do this observations so for a +simplifying assumption let's say that we + + align:start position:0% +simplifying assumption let's say that we + + + align:start position:0% +simplifying assumption let's say that we +just completely see the tree so that's + + align:start position:0% +just completely see the tree so that's + + + align:start position:0% +just completely see the tree so that's +great for our actual robot position but + + align:start position:0% +great for our actual robot position but + + + align:start position:0% +great for our actual robot position but +when we start spawning particles we need + + align:start position:0% +when we start spawning particles we need + + + align:start position:0% +when we start spawning particles we need +to figure out what we're going to say + + align:start position:0% +to figure out what we're going to say + + + align:start position:0% +to figure out what we're going to say +they synthetically do so saving spawn a + + align:start position:0% +they synthetically do so saving spawn a + + + align:start position:0% +they synthetically do so saving spawn a +particle here I mean this bottle on the + + align:start position:0% +particle here I mean this bottle on the + + + align:start position:0% +particle here I mean this bottle on the +neuter just slightly off with rohui + + align:start position:0% +neuter just slightly off with rohui + + + align:start position:0% +neuter just slightly off with rohui +Eevee ated a little bit we're further + + align:start position:0% +Eevee ated a little bit we're further + + + align:start position:0% +Eevee ated a little bit we're further +forward than the actual position we've + + align:start position:0% +forward than the actual position we've + + + align:start position:0% +forward than the actual position we've +drove into somebody's house another + + align:start position:0% +drove into somebody's house another + + + align:start position:0% +drove into somebody's house another +guy's house in the woods then what is + + align:start position:0% +guy's house in the woods then what is + + + align:start position:0% +guy's house in the woods then what is +each of our synthetic observations for + + align:start position:0% +each of our synthetic observations for + + + align:start position:0% +each of our synthetic observations for +these given points determining this is + + align:start position:0% +these given points determining this is + + + align:start position:0% +these given points determining this is +going to determine how we actually get + + align:start position:0% +going to determine how we actually get + + + align:start position:0% +going to determine how we actually get +that probability calculation so what do + + align:start position:0% +that probability calculation so what do + + + align:start position:0% +that probability calculation so what do +we need to consider here well the first + + align:start position:0% +we need to consider here well the first + + + align:start position:0% +we need to consider here well the first +thing we need to consider is + + align:start position:0% +thing we need to consider is + + + align:start position:0% +thing we need to consider is +classification like we said before with + + align:start position:0% +classification like we said before with + + + align:start position:0% +classification like we said before with +this set of objects approximation it's + + align:start position:0% +this set of objects approximation it's + + + align:start position:0% +this set of objects approximation it's +important that you understand if you + + align:start position:0% +important that you understand if you + + + align:start position:0% +important that you understand if you +classify things correctly or not past + + align:start position:0% +classify things correctly or not past + + + align:start position:0% +classify things correctly or not past +that we like we asked before we said + + align:start position:0% +that we like we asked before we said + + + align:start position:0% +that we like we asked before we said +wait why didn't I just see a tree a + + align:start position:0% +wait why didn't I just see a tree a + + + align:start position:0% +wait why didn't I just see a tree a +mailbox well we need to know if we saw + + align:start position:0% +mailbox well we need to know if we saw + + + align:start position:0% +mailbox well we need to know if we saw +everything inside were filled with you + + align:start position:0% +everything inside were filled with you + + + align:start position:0% +everything inside were filled with you +maybe we did miss something + + align:start position:0% +maybe we did miss something + + + align:start position:0% +maybe we did miss something +maybe instead that old scene saw just + + align:start position:0% +maybe instead that old scene saw just + + + align:start position:0% +maybe instead that old scene saw just +1/3 one mailbox even though the other + + align:start position:0% +1/3 one mailbox even though the other + + + align:start position:0% +1/3 one mailbox even though the other +tree intersected it and noise can happen + + align:start position:0% +tree intersected it and noise can happen + + + align:start position:0% +tree intersected it and noise can happen +in Reverse so we can accidentally see a + + align:start position:0% +in Reverse so we can accidentally see a + + + align:start position:0% +in Reverse so we can accidentally see a +tree when there actually isn't one + + align:start position:0% +tree when there actually isn't one + + + align:start position:0% +tree when there actually isn't one +and finally we could see things overlap + + align:start position:0% +and finally we could see things overlap + + + align:start position:0% +and finally we could see things overlap +you can kind of ignore this before but + + align:start position:0% +you can kind of ignore this before but + + + align:start position:0% +you can kind of ignore this before but +what if two trees were right on top of + + align:start position:0% +what if two trees were right on top of + + + align:start position:0% +what if two trees were right on top of +each other it might make it kind of + + align:start position:0% +each other it might make it kind of + + + align:start position:0% +each other it might make it kind of +difficult for you to successfully see + + align:start position:0% +difficult for you to successfully see + + + align:start position:0% +difficult for you to successfully see +that there are two trees there instead + + align:start position:0% +that there are two trees there instead + + + align:start position:0% +that there are two trees there instead +of one so to start with we're going to + + align:start position:0% +of one so to start with we're going to + + + align:start position:0% +of one so to start with we're going to +strike this assumption it'll become more + + align:start position:0% +strike this assumption it'll become more + + + align:start position:0% +strike this assumption it'll become more +evident later why this is important but + + align:start position:0% +evident later why this is important but + + + align:start position:0% +evident later why this is important but +for now we're just going to assume that + + align:start position:0% +for now we're just going to assume that + + + align:start position:0% +for now we're just going to assume that +every observation + + align:start position:0% +every observation + + + align:start position:0% +every observation +corresponds to only one object being + + align:start position:0% +corresponds to only one object being + + + align:start position:0% +corresponds to only one object being +seen otherwise you could end up + + align:start position:0% +seen otherwise you could end up + + + align:start position:0% +seen otherwise you could end up +infinitely expanding your scene think + + align:start position:0% +infinitely expanding your scene think + + + align:start position:0% +infinitely expanding your scene think +about it you see a tree there might be a + + align:start position:0% +about it you see a tree there might be a + + + align:start position:0% +about it you see a tree there might be a +probability that that trees - trees well + + align:start position:0% +probability that that trees - trees well + + + align:start position:0% +probability that that trees - trees well +you saw two trees then so maybe there's + + align:start position:0% +you saw two trees then so maybe there's + + + align:start position:0% +you saw two trees then so maybe there's +probably that each of those two trees is + + align:start position:0% +probably that each of those two trees is + + + align:start position:0% +probably that each of those two trees is +also two trees and you keep going and + + align:start position:0% +also two trees and you keep going and + + + align:start position:0% +also two trees and you keep going and +you keep going into the entire forest is + + align:start position:0% +you keep going into the entire forest is + + + align:start position:0% +you keep going into the entire forest is +behind one tree be kind of bad for doing + + align:start position:0% +behind one tree be kind of bad for doing + + + align:start position:0% +behind one tree be kind of bad for doing +a probability calculation because you + + align:start position:0% +a probability calculation because you + + + align:start position:0% +a probability calculation because you +don't actually have to cut that off at + + align:start position:0% +don't actually have to cut that off at + + + align:start position:0% +don't actually have to cut that off at +some points that your algorithm actually + + align:start position:0% +some points that your algorithm actually + + + align:start position:0% +some points that your algorithm actually +finishes so for our purposes we're just + + align:start position:0% +finishes so for our purposes we're just + + + align:start position:0% +finishes so for our purposes we're just +going to cut it off at the start and say + + align:start position:0% +going to cut it off at the start and say + + + align:start position:0% +going to cut it off at the start and say +that everything's just one object + + align:start position:0% +that everything's just one object + + + align:start position:0% +that everything's just one object +it's just error so now we need to talk + + align:start position:0% +it's just error so now we need to talk + + + align:start position:0% +it's just error so now we need to talk +about if we classify correctly + + align:start position:0% +about if we classify correctly + + + align:start position:0% +about if we classify correctly +okay if we can solve this equation + + align:start position:0% +okay if we can solve this equation + + + align:start position:0% +okay if we can solve this equation +what's the probability that our + + align:start position:0% +what's the probability that our + + + align:start position:0% +what's the probability that our +classifications right so for now we're + + align:start position:0% +classifications right so for now we're + + + align:start position:0% +classifications right so for now we're +going to make two simplifying + + align:start position:0% +going to make two simplifying + + + align:start position:0% +going to make two simplifying +assumptions they're going to remove the + + align:start position:0% +assumptions they're going to remove the + + + align:start position:0% +assumptions they're going to remove the +two of the problems that we had before + + align:start position:0% +two of the problems that we had before + + + align:start position:0% +two of the problems that we had before +and don't worry we'll relax them later + + align:start position:0% +and don't worry we'll relax them later + + + align:start position:0% +and don't worry we'll relax them later +for our first assumption we're going to + + align:start position:0% +for our first assumption we're going to + + + align:start position:0% +for our first assumption we're going to +assume that we see everything inside of + + align:start position:0% +assume that we see everything inside of + + + align:start position:0% +assume that we see everything inside of +our field of view so that means we're + + align:start position:0% +our field of view so that means we're + + + align:start position:0% +our field of view so that means we're +not going to have any missed detections + + align:start position:0% +not going to have any missed detections + + + align:start position:0% +not going to have any missed detections +and we're going to assume that we never + + align:start position:0% +and we're going to assume that we never + + + align:start position:0% +and we're going to assume that we never +see something that doesn't exist so we + + align:start position:0% +see something that doesn't exist so we + + + align:start position:0% +see something that doesn't exist so we +have no false detection everything + + align:start position:0% +have no false detection everything + + + align:start position:0% +have no false detection everything +that's in the scene we see successfully + + align:start position:0% +that's in the scene we see successfully + + + align:start position:0% +that's in the scene we see successfully +it's not in the scene we don't see it so + + align:start position:0% +it's not in the scene we don't see it so + + + align:start position:0% +it's not in the scene we don't see it so +given that and I'm spawn a robot here + + align:start position:0% +given that and I'm spawn a robot here + + + align:start position:0% +given that and I'm spawn a robot here +and it has this field of view what is + + align:start position:0% +and it has this field of view what is + + + align:start position:0% +and it has this field of view what is +this robot see retrieve yes it happens + + align:start position:0% +this robot see retrieve yes it happens + + + align:start position:0% +this robot see retrieve yes it happens +to see three trees so remember our + + align:start position:0% +to see three trees so remember our + + + align:start position:0% +to see three trees so remember our +assumptions we're going to say here that + + align:start position:0% +assumptions we're going to say here that + + + align:start position:0% +assumptions we're going to say here that +our eyeful observation for wherever a + + align:start position:0% +our eyeful observation for wherever a + + + align:start position:0% +our eyeful observation for wherever a +robot is is one mailbox and two trees + + align:start position:0% +robot is is one mailbox and two trees + + + align:start position:0% +robot is is one mailbox and two trees +and we can see that this synthetic robot + + align:start position:0% +and we can see that this synthetic robot + + + align:start position:0% +and we can see that this synthetic robot +that we made soft three trees so what + + align:start position:0% +that we made soft three trees so what + + + align:start position:0% +that we made soft three trees so what +are some other forms of why we can make + + align:start position:0% +are some other forms of why we can make + + + align:start position:0% +are some other forms of why we can make +that would also map to this that what is + + align:start position:0% +that would also map to this that what is + + + align:start position:0% +that would also map to this that what is +the sorry what's the way that we can + + align:start position:0% +the sorry what's the way that we can + + + align:start position:0% +the sorry what's the way that we can +take our Y and transform it so that it + + align:start position:0% +take our Y and transform it so that it + + + align:start position:0% +take our Y and transform it so that it +Maps this Z what kind of action we have + + align:start position:0% +Maps this Z what kind of action we have + + + align:start position:0% +Maps this Z what kind of action we have +to take on this if you were thinking + + align:start position:0% +to take on this if you were thinking + + + align:start position:0% +to take on this if you were thinking +that you have two misclassify one of + + align:start position:0% +that you have two misclassify one of + + + align:start position:0% +that you have two misclassify one of +these trees you're correct and remember + + align:start position:0% +these trees you're correct and remember + + + align:start position:0% +these trees you're correct and remember +this is just a set of objects so this + + align:start position:0% +this is just a set of objects so this + + + align:start position:0% +this is just a set of objects so this +doesn't have to be the first tree that + + align:start position:0% +doesn't have to be the first tree that + + + align:start position:0% +doesn't have to be the first tree that +got misclassified there's three of them + + align:start position:0% +got misclassified there's three of them + + + align:start position:0% +got misclassified there's three of them +we could have any permutation of these + + align:start position:0% +we could have any permutation of these + + + align:start position:0% +we could have any permutation of these +trees getting misclassified so it + + align:start position:0% +trees getting misclassified so it + + + align:start position:0% +trees getting misclassified so it +becomes important and we're going to + + align:start position:0% +becomes important and we're going to + + + align:start position:0% +becomes important and we're going to +introduce this concept of this operator + + align:start position:0% +introduce this concept of this operator + + + align:start position:0% +introduce this concept of this operator +fee and what he's going to do is it's + + align:start position:0% +fee and what he's going to do is it's + + + align:start position:0% +fee and what he's going to do is it's +going to be a map a way to map the + + align:start position:0% +going to be a map a way to map the + + + align:start position:0% +going to be a map a way to map the +permutations that we could have with + + align:start position:0% +permutations that we could have with + + + align:start position:0% +permutations that we could have with +misclassifications for y to look like + + align:start position:0% +misclassifications for y to look like + + + align:start position:0% +misclassifications for y to look like +see that way we don't have to try and + + align:start position:0% +see that way we don't have to try and + + + align:start position:0% +see that way we don't have to try and +write all the permutations down it's + + align:start position:0% +write all the permutations down it's + + + align:start position:0% +write all the permutations down it's +possible to do this essentially with a + + align:start position:0% +possible to do this essentially with a + + + align:start position:0% +possible to do this essentially with a +matrix like a permutation matrix that + + align:start position:0% +matrix like a permutation matrix that + + + align:start position:0% +matrix like a permutation matrix that +just reorder the elements that you have + + align:start position:0% +just reorder the elements that you have + + + align:start position:0% +just reorder the elements that you have +so what does this probably look like now + + align:start position:0% +so what does this probably look like now + + + align:start position:0% +so what does this probably look like now +we're going to use the lowercase Z Y I + + align:start position:0% +we're going to use the lowercase Z Y I + + + align:start position:0% +we're going to use the lowercase Z Y I +to represent each individual element + + align:start position:0% +to represent each individual element + + + align:start position:0% +to represent each individual element +they're sets so for some element is in + + align:start position:0% +they're sets so for some element is in + + + align:start position:0% +they're sets so for some element is in +the actual observations II with Republic + + align:start position:0% +the actual observations II with Republic + + + align:start position:0% +the actual observations II with Republic +that some elements in our synthetic + + align:start position:0% +that some elements in our synthetic + + + align:start position:0% +that some elements in our synthetic +observation matches it well for that we + + align:start position:0% +observation matches it well for that we + + + align:start position:0% +observation matches it well for that we +need to pick well there's some + + align:start position:0% +need to pick well there's some + + + align:start position:0% +need to pick well there's some +probability being wrong or + + align:start position:0% +probability being wrong or + + + align:start position:0% +probability being wrong or +misclassifying or classifying correctly + + align:start position:0% +misclassifying or classifying correctly + + + align:start position:0% +misclassifying or classifying correctly +so we're going to use C to represent + + align:start position:0% +so we're going to use C to represent + + + align:start position:0% +so we're going to use C to represent +like a classification matrix so there's + + align:start position:0% +like a classification matrix so there's + + + align:start position:0% +like a classification matrix so there's +some probability that would cost by + + align:start position:0% +some probability that would cost by + + + align:start position:0% +some probability that would cost by +correctly usually a higher probability + + align:start position:0% +correctly usually a higher probability + + + align:start position:0% +correctly usually a higher probability +and then some small probability that an + + align:start position:0% +and then some small probability that an + + + align:start position:0% +and then some small probability that an +object becomes another type of object so + + align:start position:0% +object becomes another type of object so + + + align:start position:0% +object becomes another type of object so +how often we miss classify is + + align:start position:0% +how often we miss classify is + + + align:start position:0% +how often we miss classify is +represented here but we can add another + + align:start position:0% +represented here but we can add another + + + align:start position:0% +represented here but we can add another +term let's say that our classification + + align:start position:0% +term let's say that our classification + + + align:start position:0% +term let's say that our classification +engine gave like the weighted values of + + align:start position:0% +engine gave like the weighted values of + + + align:start position:0% +engine gave like the weighted values of +things + + align:start position:0% +things + + + align:start position:0% +things +it's common for neural nets and other + + align:start position:0% +it's common for neural nets and other + + + align:start position:0% +it's common for neural nets and other +types of systems that observed images to + + align:start position:0% +types of systems that observed images to + + + align:start position:0% +types of systems that observed images to +kind of give weights to their + + align:start position:0% +kind of give weights to their + + + align:start position:0% +kind of give weights to their +classification so you might want to use + + align:start position:0% +classification so you might want to use + + + align:start position:0% +classification so you might want to use +those weights to represent our + + align:start position:0% +those weights to represent our + + + align:start position:0% +those weights to represent our +confidence and there's a probability + + align:start position:0% +confidence and there's a probability + + + align:start position:0% +confidence and there's a probability +that that confidence determines that our + + align:start position:0% +that that confidence determines that our + + + align:start position:0% +that that confidence determines that our +classification might just be wrong out + + align:start position:0% +classification might just be wrong out + + + align:start position:0% +classification might just be wrong out +of the get-go in that case we want to + + align:start position:0% +of the get-go in that case we want to + + + align:start position:0% +of the get-go in that case we want to +know what's it probably that that score + + align:start position:0% +know what's it probably that that score + + + align:start position:0% +know what's it probably that that score +is likely to be that type of object and + + align:start position:0% +is likely to be that type of object and + + + align:start position:0% +is likely to be that type of object and +then we could have other things for + + align:start position:0% +then we could have other things for + + + align:start position:0% +then we could have other things for +instance let's say that our + + align:start position:0% +instance let's say that our + + + align:start position:0% +instance let's say that our +classification engine was way better at + + align:start position:0% +classification engine was way better at + + + align:start position:0% +classification engine was way better at +identifying mailboxes from the front and + + align:start position:0% +identifying mailboxes from the front and + + + align:start position:0% +identifying mailboxes from the front and +if we turn a mailbox to the side it gets + + align:start position:0% +if we turn a mailbox to the side it gets + + + align:start position:0% +if we turn a mailbox to the side it gets +poor observations and it tells us if it + + align:start position:0% +poor observations and it tells us if it + + + align:start position:0% +poor observations and it tells us if it +thinks the mailbox is on the side so it + + align:start position:0% +thinks the mailbox is on the side so it + + + align:start position:0% +thinks the mailbox is on the side so it +doesn't really know in that case maybe + + align:start position:0% +doesn't really know in that case maybe + + + align:start position:0% +doesn't really know in that case maybe +having the bearing of the object inside + + align:start position:0% +having the bearing of the object inside + + + align:start position:0% +having the bearing of the object inside +of our synthetic view allows us to + + align:start position:0% +of our synthetic view allows us to + + + align:start position:0% +of our synthetic view allows us to +determine another probability for miss + + align:start position:0% +determine another probability for miss + + + align:start position:0% +determine another probability for miss +classification the important thing to + + align:start position:0% +classification the important thing to + + + align:start position:0% +classification the important thing to +notice here is that we can keep adding + + align:start position:0% +notice here is that we can keep adding + + + align:start position:0% +notice here is that we can keep adding +more terms to this the more specific + + align:start position:0% +more terms to this the more specific + + + align:start position:0% +more terms to this the more specific +your classification can get the more + + align:start position:0% +your classification can get the more + + + align:start position:0% +your classification can get the more +terms you can introduce into it to help + + align:start position:0% +terms you can introduce into it to help + + + align:start position:0% +terms you can introduce into it to help +add some confusion to it and make the + + align:start position:0% +add some confusion to it and make the + + + align:start position:0% +add some confusion to it and make the +probabilities of misclassifications + + align:start position:0% +probabilities of misclassifications + + + align:start position:0% +probabilities of misclassifications +smaller and smaller and smaller so with + + align:start position:0% +smaller and smaller and smaller so with + + + align:start position:0% +smaller and smaller and smaller so with +that in mind we're going to look at what + + align:start position:0% +that in mind we're going to look at what + + + align:start position:0% +that in mind we're going to look at what +the probability for these entire sexes + + align:start position:0% +the probability for these entire sexes + + + align:start position:0% +the probability for these entire sexes +is going to look like and what it really + + align:start position:0% +is going to look like and what it really + + + align:start position:0% +is going to look like and what it really +is going to be czar just going to be a + + align:start position:0% +is going to be czar just going to be a + + + align:start position:0% +is going to be czar just going to be a +product over all these classifications + + align:start position:0% +product over all these classifications + + + align:start position:0% +product over all these classifications +for some selection of feet so you're + + align:start position:0% +for some selection of feet so you're + + + align:start position:0% +for some selection of feet so you're +going to have to take all the different + + align:start position:0% +going to have to take all the different + + + align:start position:0% +going to have to take all the different +permutations that you could possibly + + align:start position:0% +permutations that you could possibly + + + align:start position:0% +permutations that you could possibly +have and for each of them they're going + + align:start position:0% +have and for each of them they're going + + + align:start position:0% +have and for each of them they're going +to multiply all of these probabilities + + align:start position:0% +to multiply all of these probabilities + + + align:start position:0% +to multiply all of these probabilities +by each other that's in the end is going + + align:start position:0% +by each other that's in the end is going + + + align:start position:0% +by each other that's in the end is going +to give you that entire probability so + + align:start position:0% +to give you that entire probability so + + + align:start position:0% +to give you that entire probability so +as all the permutations that you have + + align:start position:0% +as all the permutations that you have + + + align:start position:0% +as all the permutations that you have +and then just the probability of each of + + align:start position:0% +and then just the probability of each of + + + align:start position:0% +and then just the probability of each of +those objects being classified is that + + align:start position:0% +those objects being classified is that + + + align:start position:0% +those objects being classified is that +type + + align:start position:0% +type + + + align:start position:0% +type +so you just map one set to the other set + + align:start position:0% +so you just map one set to the other set + + + align:start position:0% +so you just map one set to the other set +so now let's take a look at another + + align:start position:0% +so now let's take a look at another + + + align:start position:0% +so now let's take a look at another +scene so we spawned a particle of faith + + align:start position:0% +scene so we spawned a particle of faith + + + align:start position:0% +scene so we spawned a particle of faith +robot here and it has this field of view + + align:start position:0% +robot here and it has this field of view + + + align:start position:0% +robot here and it has this field of view +what does this field of you look like if + + align:start position:0% +what does this field of you look like if + + + align:start position:0% +what does this field of you look like if +you said it looked like two mailboxes + + align:start position:0% +you said it looked like two mailboxes + + + align:start position:0% +you said it looked like two mailboxes +and two trees you're right and so we're + + align:start position:0% +and two trees you're right and so we're + + + align:start position:0% +and two trees you're right and so we're +gonna assume that we have the same + + align:start position:0% +gonna assume that we have the same + + + align:start position:0% +gonna assume that we have the same +actual observation we still see a mail a + + align:start position:0% +actual observation we still see a mail a + + + align:start position:0% +actual observation we still see a mail a +mailbox and two trees and we're going to + + align:start position:0% +mailbox and two trees and we're going to + + + align:start position:0% +mailbox and two trees and we're going to +remove our old assumption we're going to + + align:start position:0% +remove our old assumption we're going to + + + align:start position:0% +remove our old assumption we're going to +say that it might be possible that we + + align:start position:0% +say that it might be possible that we + + + align:start position:0% +say that it might be possible that we +don't see everything in a synthetic + + align:start position:0% +don't see everything in a synthetic + + + align:start position:0% +don't see everything in a synthetic +robots field in which case how do we map + + align:start position:0% +robots field in which case how do we map + + + align:start position:0% +robots field in which case how do we map +this synthetic observation to the actual + + align:start position:0% +this synthetic observation to the actual + + + align:start position:0% +this synthetic observation to the actual +observation well we just added a + + align:start position:0% +observation well we just added a + + + align:start position:0% +observation well we just added a +probability that we missed identifying + + align:start position:0% +probability that we missed identifying + + + align:start position:0% +probability that we missed identifying +an object if we just didn't see one of + + align:start position:0% +an object if we just didn't see one of + + + align:start position:0% +an object if we just didn't see one of +these mailboxes looks exactly like this + + align:start position:0% +these mailboxes looks exactly like this + + + align:start position:0% +these mailboxes looks exactly like this +so for that we want to capture what's + + align:start position:0% +so for that we want to capture what's + + + align:start position:0% +so for that we want to capture what's +the probability that we see nothing so + + align:start position:0% +the probability that we see nothing so + + + align:start position:0% +the probability that we see nothing so +say the other synthetic view was some + + align:start position:0% +say the other synthetic view was some + + + align:start position:0% +say the other synthetic view was some +number of objects the probability we + + align:start position:0% +number of objects the probability we + + + align:start position:0% +number of objects the probability we +just missed all of them so the + + align:start position:0% +just missed all of them so the + + + align:start position:0% +just missed all of them so the +probability that we missed all of them + + align:start position:0% +probability that we missed all of them + + + align:start position:0% +probability that we missed all of them +we're going to add an assumption here + + align:start position:0% +we're going to add an assumption here + + + align:start position:0% +we're going to add an assumption here +which is that we're going to say that + + align:start position:0% +which is that we're going to say that + + + align:start position:0% +which is that we're going to say that +there exists some probability that we + + align:start position:0% +there exists some probability that we + + + align:start position:0% +there exists some probability that we +see an object for a given synthetic view + + align:start position:0% +see an object for a given synthetic view + + + align:start position:0% +see an object for a given synthetic view +here and that we don't see it with a + + align:start position:0% +here and that we don't see it with a + + + align:start position:0% +here and that we don't see it with a +probability one minus that probability + + align:start position:0% +probability one minus that probability + + + align:start position:0% +probability one minus that probability +so essentially there's just two states + + align:start position:0% +so essentially there's just two states + + + align:start position:0% +so essentially there's just two states +either we see the object or we don't see + + align:start position:0% +either we see the object or we don't see + + + align:start position:0% +either we see the object or we don't see +the object and we're going to say that + + align:start position:0% +the object and we're going to say that + + + align:start position:0% +the object and we're going to say that +probability of identifying objects is + + align:start position:0% +probability of identifying objects is + + + align:start position:0% +probability of identifying objects is +independent so if we see one object then + + align:start position:0% +independent so if we see one object then + + + align:start position:0% +independent so if we see one object then +there does not change our chances of + + align:start position:0% +there does not change our chances of + + + align:start position:0% +there does not change our chances of +seeing the next object both of these + + align:start position:0% +seeing the next object both of these + + + align:start position:0% +seeing the next object both of these +assumptions help simplify the map here + + align:start position:0% +assumptions help simplify the map here + + + align:start position:0% +assumptions help simplify the map here +in reality these might be strongly + + align:start position:0% +in reality these might be strongly + + + align:start position:0% +in reality these might be strongly +interlinked for instance if your robots + + align:start position:0% +interlinked for instance if your robots + + + align:start position:0% +interlinked for instance if your robots +camera is broken the probability that it + + align:start position:0% +camera is broken the probability that it + + + align:start position:0% +camera is broken the probability that it +sees doesn't see one object directly + + align:start position:0% +sees doesn't see one object directly + + + align:start position:0% +sees doesn't see one object directly +correlates the other ones because it + + align:start position:0% +correlates the other ones because it + + + align:start position:0% +correlates the other ones because it +won't see any of the objects + + align:start position:0% +won't see any of the objects + + + align:start position:0% +won't see any of the objects +successfully it has a camera anymore if + + align:start position:0% +successfully it has a camera anymore if + + + align:start position:0% +successfully it has a camera anymore if +your robot drives into a wall and can't + + align:start position:0% +your robot drives into a wall and can't + + + align:start position:0% +your robot drives into a wall and can't +see anything because it's staring + + align:start position:0% +see anything because it's staring + + + align:start position:0% +see anything because it's staring +straight at the wall the same kind of + + align:start position:0% +straight at the wall the same kind of + + + align:start position:0% +straight at the wall the same kind of +idea holds but the purposes of making us + + align:start position:0% +idea holds but the purposes of making us + + + align:start position:0% +idea holds but the purposes of making us +that you don't have a lot of covariances + + align:start position:0% +that you don't have a lot of covariances + + + align:start position:0% +that you don't have a lot of covariances +in a really really big conditional + + align:start position:0% +in a really really big conditional + + + align:start position:0% +in a really really big conditional +statement of a lot of probabilities of + + align:start position:0% +statement of a lot of probabilities of + + + align:start position:0% +statement of a lot of probabilities of +seeing things we make these assumptions + + align:start position:0% +seeing things we make these assumptions + + + align:start position:0% +seeing things we make these assumptions +Sora items can be independent + + align:start position:0% +Sora items can be independent + + + align:start position:0% +Sora items can be independent +independence means we can multiply our + + align:start position:0% +independence means we can multiply our + + + align:start position:0% +independence means we can multiply our +probabilities successfully so if we just + + align:start position:0% +probabilities successfully so if we just + + + align:start position:0% +probabilities successfully so if we just +don't want to see any of the objects we + + align:start position:0% +don't want to see any of the objects we + + + align:start position:0% +don't want to see any of the objects we +just take one - the + + align:start position:0% +just take one - the + + + align:start position:0% +just take one - the +you've seen the object for all the + + align:start position:0% +you've seen the object for all the + + + align:start position:0% +you've seen the object for all the +objects in the scene alright so what + + align:start position:0% +objects in the scene alright so what + + + align:start position:0% +objects in the scene alright so what +goes in hand-in-hand with not seeing + + align:start position:0% +goes in hand-in-hand with not seeing + + + align:start position:0% +goes in hand-in-hand with not seeing +anything think about it if you had a + + align:start position:0% +anything think about it if you had a + + + align:start position:0% +anything think about it if you had a +robot far off in the distance over here + + align:start position:0% +robot far off in the distance over here + + + align:start position:0% +robot far off in the distance over here +what can I see just two trees so now + + align:start position:0% +what can I see just two trees so now + + + align:start position:0% +what can I see just two trees so now +we're going to remove the idea that we + + align:start position:0% +we're going to remove the idea that we + + + align:start position:0% +we're going to remove the idea that we +can't see things that don't exist so to + + align:start position:0% +can't see things that don't exist so to + + + align:start position:0% +can't see things that don't exist so to +make two trees map to two trees in the + + align:start position:0% +make two trees map to two trees in the + + + align:start position:0% +make two trees map to two trees in the +mailbox we just made up a mailbox out of + + align:start position:0% +mailbox we just made up a mailbox out of + + + align:start position:0% +mailbox we just made up a mailbox out of +some noise so what's the probability + + align:start position:0% +some noise so what's the probability + + + align:start position:0% +some noise so what's the probability +that we see a full scene when we can't + + align:start position:0% +that we see a full scene when we can't + + + align:start position:0% +that we see a full scene when we can't +see anything and if you're thinking it's + + align:start position:0% +see anything and if you're thinking it's + + + align:start position:0% +see anything and if you're thinking it's +gonna map to a very similar formula + + align:start position:0% +gonna map to a very similar formula + + + align:start position:0% +gonna map to a very similar formula +you're kinda bright but we need to + + align:start position:0% +you're kinda bright but we need to + + + align:start position:0% +you're kinda bright but we need to +figure out a way to capture our noise + + align:start position:0% +figure out a way to capture our noise + + + align:start position:0% +figure out a way to capture our noise +statement specifically we're going to + + align:start position:0% +statement specifically we're going to + + + align:start position:0% +statement specifically we're going to +use noises of Poisson variable which + + align:start position:0% +use noises of Poisson variable which + + + align:start position:0% +use noises of Poisson variable which +means that there's always some + + align:start position:0% +means that there's always some + + + align:start position:0% +means that there's always some +probability of seeing an object out of + + align:start position:0% +probability of seeing an object out of + + + align:start position:0% +probability of seeing an object out of +nothing and it's going to be spatially + + align:start position:0% +nothing and it's going to be spatially + + + align:start position:0% +nothing and it's going to be spatially +coordinated and according to this factor + + align:start position:0% +coordinated and according to this factor + + + align:start position:0% +coordinated and according to this factor +KC will get to on the next slide you + + align:start position:0% +KC will get to on the next slide you + + + align:start position:0% +KC will get to on the next slide you +could choose a lot of different things + + align:start position:0% +could choose a lot of different things + + + align:start position:0% +could choose a lot of different things +to represent door noise in this case a + + align:start position:0% +to represent door noise in this case a + + + align:start position:0% +to represent door noise in this case a +Poisson variable was just chosen by the + + align:start position:0% +Poisson variable was just chosen by the + + + align:start position:0% +Poisson variable was just chosen by the +specific method that we used and + + align:start position:0% +specific method that we used and + + + align:start position:0% +specific method that we used and +implemented from another paper but with + + align:start position:0% +implemented from another paper but with + + + align:start position:0% +implemented from another paper but with +testing you could find that different + + align:start position:0% +testing you could find that different + + + align:start position:0% +testing you could find that different +detention distributions map to your + + align:start position:0% +detention distributions map to your + + + align:start position:0% +detention distributions map to your +noise for your particular sensor better + + align:start position:0% +noise for your particular sensor better + + + align:start position:0% +noise for your particular sensor better +so with a Poisson variable what we're + + align:start position:0% +so with a Poisson variable what we're + + + align:start position:0% +so with a Poisson variable what we're +going to have is we're just going to + + align:start position:0% +going to have is we're just going to + + + align:start position:0% +going to have is we're just going to +have the product of all of our Poisson + + align:start position:0% +have the product of all of our Poisson + + + align:start position:0% +have the product of all of our Poisson +variables times this KZ factor for the + + align:start position:0% +variables times this KZ factor for the + + + align:start position:0% +variables times this KZ factor for the +given scene that we want to map to + + align:start position:0% +given scene that we want to map to + + + align:start position:0% +given scene that we want to map to +essentially it's just the product of all + + align:start position:0% +essentially it's just the product of all + + + align:start position:0% +essentially it's just the product of all +these independent Poisson variables for + + align:start position:0% +these independent Poisson variables for + + + align:start position:0% +these independent Poisson variables for +each of our different objects that we + + align:start position:0% +each of our different objects that we + + + align:start position:0% +each of our different objects that we +want to create so with that in mind + + align:start position:0% +want to create so with that in mind + + + align:start position:0% +want to create so with that in mind +what's this KZ factor that we're + + align:start position:0% +what's this KZ factor that we're + + + align:start position:0% +what's this KZ factor that we're +multiplying everything by what it's + + align:start position:0% +multiplying everything by what it's + + + align:start position:0% +multiplying everything by what it's +actually going to be is it's going to be + + align:start position:0% +actually going to be is it's going to be + + + align:start position:0% +actually going to be is it's going to be +a set of uniform distributions these + + align:start position:0% +a set of uniform distributions these + + + align:start position:0% +a set of uniform distributions these +uniform distributions are going to be + + align:start position:0% +uniform distributions are going to be + + + align:start position:0% +uniform distributions are going to be +uniform over all the classifications we + + align:start position:0% +uniform over all the classifications we + + + align:start position:0% +uniform over all the classifications we +could get for an object we spawn from + + align:start position:0% +could get for an object we spawn from + + + align:start position:0% +could get for an object we spawn from +the noise and all possible scores and + + align:start position:0% +the noise and all possible scores and + + + align:start position:0% +the noise and all possible scores and +all these possible bearings for the + + align:start position:0% +all these possible bearings for the + + + align:start position:0% +all these possible bearings for the +synthetic object and if you remember a + + align:start position:0% +synthetic object and if you remember a + + + align:start position:0% +synthetic object and if you remember a +few slides ago where you rewind the + + align:start position:0% +few slides ago where you rewind the + + + align:start position:0% +few slides ago where you rewind the +video you'll notice that these map + + align:start position:0% +video you'll notice that these map + + + align:start position:0% +video you'll notice that these map +directly to the categories that we put + + align:start position:0% +directly to the categories that we put + + + align:start position:0% +directly to the categories that we put +in that classification engine in fact + + align:start position:0% +in that classification engine in fact + + + align:start position:0% +in that classification engine in fact +they should so if you added more things + + align:start position:0% +they should so if you added more things + + + align:start position:0% +they should so if you added more things +or took them out you change this uniform + + align:start position:0% +or took them out you change this uniform + + + align:start position:0% +or took them out you change this uniform +distribution the idea is that when you + + align:start position:0% +distribution the idea is that when you + + + align:start position:0% +distribution the idea is that when you +synthetically create an object out of + + align:start position:0% +synthetically create an object out of + + + align:start position:0% +synthetically create an object out of +you might get any of those types of + + align:start position:0% +you might get any of those types of + + + align:start position:0% +you might get any of those types of +objects she might get but if you needed + + align:start position:0% +objects she might get but if you needed + + + align:start position:0% +objects she might get but if you needed +to create a tree synthetically from + + align:start position:0% +to create a tree synthetically from + + + align:start position:0% +to create a tree synthetically from +seeing it in the noise you might get a + + align:start position:0% +seeing it in the noise you might get a + + + align:start position:0% +seeing it in the noise you might get a +tree or you might get a mailbox either + + align:start position:0% +tree or you might get a mailbox either + + + align:start position:0% +tree or you might get a mailbox either +one of them might show up if you had a + + align:start position:0% +one of them might show up if you had a + + + align:start position:0% +one of them might show up if you had a +different or more intelligent + + align:start position:0% +different or more intelligent + + + align:start position:0% +different or more intelligent +distribution for how you might miss + + align:start position:0% +distribution for how you might miss + + + align:start position:0% +distribution for how you might miss +classify things for instance let's say + + align:start position:0% +classify things for instance let's say + + + align:start position:0% +classify things for instance let's say +your noise whenever it shows up always + + align:start position:0% +your noise whenever it shows up always + + + align:start position:0% +your noise whenever it shows up always +identifies trees + + align:start position:0% +identifies trees + + + align:start position:0% +identifies trees +whenever you accidentally seen always + + align:start position:0% +whenever you accidentally seen always + + + align:start position:0% +whenever you accidentally seen always +the Sun object it's always a tree but + + align:start position:0% +the Sun object it's always a tree but + + + align:start position:0% +the Sun object it's always a tree but +you might only want to have a + + align:start position:0% +you might only want to have a + + + align:start position:0% +you might only want to have a +probability of seeing trees over here + + align:start position:0% +probability of seeing trees over here + + + align:start position:0% +probability of seeing trees over here +and it would change your distribution + + align:start position:0% +and it would change your distribution + + + align:start position:0% +and it would change your distribution +but for simplicity sake we're going to + + align:start position:0% +but for simplicity sake we're going to + + + align:start position:0% +but for simplicity sake we're going to +assume that it's equally probable that + + align:start position:0% +assume that it's equally probable that + + + align:start position:0% +assume that it's equally probable that +any type of object shows up out of nice + + align:start position:0% +any type of object shows up out of nice + + + align:start position:0% +any type of object shows up out of nice +so now we're going to put it all + + align:start position:0% +so now we're going to put it all + + + align:start position:0% +so now we're going to put it all +together since we've relaxed our + + align:start position:0% +together since we've relaxed our + + + align:start position:0% +together since we've relaxed our +assumptions right so we have a lot of + + align:start position:0% +assumptions right so we have a lot of + + + align:start position:0% +assumptions right so we have a lot of +different things that can potentially + + align:start position:0% +different things that can potentially + + + align:start position:0% +different things that can potentially +map to this actual scene we have scenes + + align:start position:0% +map to this actual scene we have scenes + + + align:start position:0% +map to this actual scene we have scenes +that black objects we have scenes that + + align:start position:0% +that black objects we have scenes that + + + align:start position:0% +that black objects we have scenes that +we have scenes that black objects and + + align:start position:0% +we have scenes that black objects and + + + align:start position:0% +we have scenes that black objects and +therefore need to add the object in and + + align:start position:0% +therefore need to add the object in and + + + align:start position:0% +therefore need to add the object in and +when they lack objects and have to add + + align:start position:0% +when they lack objects and have to add + + + align:start position:0% +when they lack objects and have to add +the object in there's a chance they add + + align:start position:0% +the object in there's a chance they add + + + align:start position:0% +the object in there's a chance they add +in a different object and then maybe + + align:start position:0% +in a different object and then maybe + + + align:start position:0% +in a different object and then maybe +they just miss classify something like + + align:start position:0% +they just miss classify something like + + + align:start position:0% +they just miss classify something like +our misspecification idea but wait I + + align:start position:0% +our misspecification idea but wait I + + + align:start position:0% +our misspecification idea but wait I +guess we could make this more + + align:start position:0% +guess we could make this more + + + align:start position:0% +guess we could make this more +complicated but if one of them just + + align:start position:0% +complicated but if one of them just + + + align:start position:0% +complicated but if one of them just +wasn't seen so we take one of these out + + align:start position:0% +wasn't seen so we take one of these out + + + align:start position:0% +wasn't seen so we take one of these out +and then we just see two things from + + align:start position:0% +and then we just see two things from + + + align:start position:0% +and then we just see two things from +noise as you can see these keep getting + + align:start position:0% +noise as you can see these keep getting + + + align:start position:0% +noise as you can see these keep getting +more complicated but if you think about + + align:start position:0% +more complicated but if you think about + + + align:start position:0% +more complicated but if you think about +it with our previous probabilities every + + align:start position:0% +it with our previous probabilities every + + + align:start position:0% +it with our previous probabilities every +single one of these is going to add a + + align:start position:0% +single one of these is going to add a + + + align:start position:0% +single one of these is going to add a +lot of turn probability terms to be + + align:start position:0% +lot of turn probability terms to be + + + align:start position:0% +lot of turn probability terms to be +multiplied by each other you can keep + + align:start position:0% +multiplied by each other you can keep + + + align:start position:0% +multiplied by each other you can keep +getting as complicated as you want it to + + align:start position:0% +getting as complicated as you want it to + + + align:start position:0% +getting as complicated as you want it to +if we add it if we removed our first + + align:start position:0% +if we add it if we removed our first + + + align:start position:0% +if we add it if we removed our first +assumption we'd be adding in + + align:start position:0% +assumption we'd be adding in + + + align:start position:0% +assumption we'd be adding in +probabilities of two objects becoming + + align:start position:0% +probabilities of two objects becoming + + + align:start position:0% +probabilities of two objects becoming +one object g-d is sort of like higher + + align:start position:0% +one object g-d is sort of like higher + + + align:start position:0% +one object g-d is sort of like higher +power turns when you're doing + + align:start position:0% +power turns when you're doing + + + align:start position:0% +power turns when you're doing +approximations the goal is to make sure + + align:start position:0% +approximations the goal is to make sure + + + align:start position:0% +approximations the goal is to make sure +that any particle you spawn could + + align:start position:0% +that any particle you spawn could + + + align:start position:0% +that any particle you spawn could +potentially be what you've actually seen + + align:start position:0% +potentially be what you've actually seen + + + align:start position:0% +potentially be what you've actually seen +but we want the ones that are very low + + align:start position:0% +but we want the ones that are very low + + + align:start position:0% +but we want the ones that are very low +probability to really be very low + + align:start position:0% +probability to really be very low + + + align:start position:0% +probability to really be very low +probability so we make sure that these + + align:start position:0% +probability so we make sure that these + + + align:start position:0% +probability so we make sure that these +incredibly complicated transformations + + align:start position:0% +incredibly complicated transformations + + + align:start position:0% +incredibly complicated transformations +are going to be so insignificant that + + align:start position:0% +are going to be so insignificant that + + + align:start position:0% +are going to be so insignificant that +they'll usually return to almost zero so + + align:start position:0% +they'll usually return to almost zero so + + + align:start position:0% +they'll usually return to almost zero so +if you wanted to solve this we need to + + align:start position:0% +if you wanted to solve this we need to + + + align:start position:0% +if you wanted to solve this we need to +start by using a little assumption which + + align:start position:0% +start by using a little assumption which + + + align:start position:0% +start by using a little assumption which +is the fact that we now have to fold in + + align:start position:0% +is the fact that we now have to fold in + + + align:start position:0% +is the fact that we now have to fold in +the idea that we + + align:start position:0% +the idea that we + + + align:start position:0% +the idea that we +some miss detection and some false + + align:start position:0% +some miss detection and some false + + + align:start position:0% +some miss detection and some false +detection so false protections would + + align:start position:0% +detection so false protections would + + + align:start position:0% +detection so false protections would +increase the number of objects we've + + align:start position:0% +increase the number of objects we've + + + align:start position:0% +increase the number of objects we've +seen over the number of objects that are + + align:start position:0% +seen over the number of objects that are + + + align:start position:0% +seen over the number of objects that are +actually they at present and miss + + align:start position:0% +actually they at present and miss + + + align:start position:0% +actually they at present and miss +detection to reduce the number of + + align:start position:0% +detection to reduce the number of + + + align:start position:0% +detection to reduce the number of +objects that are actually present notice + + align:start position:0% +objects that are actually present notice + + + align:start position:0% +objects that are actually present notice +that this always has to be the same size + + align:start position:0% +that this always has to be the same size + + + align:start position:0% +that this always has to be the same size +as the number of expected objects + + align:start position:0% +as the number of expected objects + + + align:start position:0% +as the number of expected objects +because you're trying to map whatever + + align:start position:0% +because you're trying to map whatever + + + align:start position:0% +because you're trying to map whatever +your synthetic scene is to the actual + + align:start position:0% +your synthetic scene is to the actual + + + align:start position:0% +your synthetic scene is to the actual +thing that you observed when you do this + + align:start position:0% +thing that you observed when you do this + + + align:start position:0% +thing that you observed when you do this +it really turns into a large number of + + align:start position:0% +it really turns into a large number of + + + align:start position:0% +it really turns into a large number of +multiplications so fish should look + + align:start position:0% +multiplications so fish should look + + + align:start position:0% +multiplications so fish should look +familiar this is our term for + + align:start position:0% +familiar this is our term for + + + align:start position:0% +familiar this is our term for +successfully classifying all of our + + align:start position:0% +successfully classifying all of our + + + align:start position:0% +successfully classifying all of our +objects and we're going to multiply it + + align:start position:0% +objects and we're going to multiply it + + + align:start position:0% +objects and we're going to multiply it +by the probability that we actually + + align:start position:0% +by the probability that we actually + + + align:start position:0% +by the probability that we actually +identify it since we could now miss + + align:start position:0% +identify it since we could now miss + + + align:start position:0% +identify it since we could now miss +things then we have to multiply that by + + align:start position:0% +things then we have to multiply that by + + + align:start position:0% +things then we have to multiply that by +the probability that for whatever + + align:start position:0% +the probability that for whatever + + + align:start position:0% +the probability that for whatever +objects we didn't see that we actually + + align:start position:0% +objects we didn't see that we actually + + + align:start position:0% +objects we didn't see that we actually +missed them and then finally we have to + + align:start position:0% +missed them and then finally we have to + + + align:start position:0% +missed them and then finally we have to +add in the noise because the noise is + + align:start position:0% +add in the noise because the noise is + + + align:start position:0% +add in the noise because the noise is +going to make the objects that were + + align:start position:0% +going to make the objects that were + + + align:start position:0% +going to make the objects that were +missing show up so that we have a + + align:start position:0% +missing show up so that we have a + + + align:start position:0% +missing show up so that we have a +classification of the same size as the + + align:start position:0% +classification of the same size as the + + + align:start position:0% +classification of the same size as the +thing that we want to see now one thing + + align:start position:0% +thing that we want to see now one thing + + + align:start position:0% +thing that we want to see now one thing +you should note is that we added in a + + align:start position:0% +you should note is that we added in a + + + align:start position:0% +you should note is that we added in a +way down here at KC that's because we + + align:start position:0% +way down here at KC that's because we + + + align:start position:0% +way down here at KC that's because we +have to map these false detection x' + + align:start position:0% +have to map these false detection x' + + + align:start position:0% +have to map these false detection x' +that added to the number of objects that + + align:start position:0% +that added to the number of objects that + + + align:start position:0% +that added to the number of objects that +we can see as well as the actual + + align:start position:0% +we can see as well as the actual + + + align:start position:0% +we can see as well as the actual +protections essentially we have to take + + align:start position:0% +protections essentially we have to take + + + align:start position:0% +protections essentially we have to take +all the objects that are seen here real + + align:start position:0% +all the objects that are seen here real + + + align:start position:0% +all the objects that are seen here real +or not and map them to all the objects + + align:start position:0% +or not and map them to all the objects + + + align:start position:0% +or not and map them to all the objects +we expect to see because they're going + + align:start position:0% +we expect to see because they're going + + + align:start position:0% +we expect to see because they're going +to be one to one so let's take a look at + + align:start position:0% +to be one to one so let's take a look at + + + align:start position:0% +to be one to one so let's take a look at +a little video that shows what semantic + + align:start position:0% +a little video that shows what semantic + + + align:start position:0% +a little video that shows what semantic +localization can do so in this video for + + align:start position:0% +localization can do so in this video for + + + align:start position:0% +localization can do so in this video for +a little heads up we have essentially a + + align:start position:0% +a little heads up we have essentially a + + + align:start position:0% +a little heads up we have essentially a +scene where they have mapped out two + + align:start position:0% +scene where they have mapped out two + + + align:start position:0% +scene where they have mapped out two +things inside of the suburban area + + align:start position:0% +things inside of the suburban area + + + align:start position:0% +things inside of the suburban area +they've mapped out cars and windows on + + align:start position:0% +they've mapped out cars and windows on + + + align:start position:0% +they've mapped out cars and windows on +the path of a robot as it drives around + + align:start position:0% +the path of a robot as it drives around + + + align:start position:0% +the path of a robot as it drives around +an area and they're attempted to use + + align:start position:0% +an area and they're attempted to use + + + align:start position:0% +an area and they're attempted to use +just the information of the cars and + + align:start position:0% +just the information of the cars and + + + align:start position:0% +just the information of the cars and +windows visible in the scene in order to + + align:start position:0% +windows visible in the scene in order to + + + align:start position:0% +windows visible in the scene in order to +localize how they believe the robot to + + align:start position:0% +localize how they believe the robot to + + + align:start position:0% +localize how they believe the robot to +be during its journey these are the + + align:start position:0% +be during its journey these are the + + + align:start position:0% +be during its journey these are the +video extensions of the paper look so + + align:start position:0% +video extensions of the paper look so + + + align:start position:0% +video extensions of the paper look so +gonna mute that it's on so this is a few + + align:start position:0% +gonna mute that it's on so this is a few + + + align:start position:0% +gonna mute that it's on so this is a few +steps into the process and then it + + align:start position:0% +steps into the process and then it + + + align:start position:0% +steps into the process and then it +resets it spawns a number of points for + + align:start position:0% +resets it spawns a number of points for + + + align:start position:0% +resets it spawns a number of points for +potential locations and then it very + + align:start position:0% +potential locations and then it very + + + align:start position:0% +potential locations and then it very +quickly localizes and finds its + + align:start position:0% +quickly localizes and finds its + + + align:start position:0% +quickly localizes and finds its +protective rotation these are all the + + align:start position:0% +protective rotation these are all the + + + align:start position:0% +protective rotation these are all the +identity + + align:start position:0% +identity + + + align:start position:0% +identity +that are happening inside the scenes you + + align:start position:0% +that are happening inside the scenes you + + + align:start position:0% +that are happening inside the scenes you +can see the bounding boxes for cars and + + align:start position:0% +can see the bounding boxes for cars and + + + align:start position:0% +can see the bounding boxes for cars and +windows showing up the cars up right in + + align:start position:0% +windows showing up the cars up right in + + + align:start position:0% +windows showing up the cars up right in +the windows green it expands out its + + align:start position:0% +the windows green it expands out its + + + align:start position:0% +the windows green it expands out its +distribution of particles and then + + align:start position:0% +distribution of particles and then + + + align:start position:0% +distribution of particles and then +shortly thereafter it gets a couple of + + align:start position:0% +shortly thereafter it gets a couple of + + + align:start position:0% +shortly thereafter it gets a couple of +approximations and then it settles in on + + align:start position:0% +approximations and then it settles in on + + + align:start position:0% +approximations and then it settles in on +a location it happens to use kind of + + align:start position:0% +a location it happens to use kind of + + + align:start position:0% +a location it happens to use kind of +like a central wait for where it is for + + align:start position:0% +like a central wait for where it is for + + + align:start position:0% +like a central wait for where it is for +the set of particles and then it draws + + align:start position:0% +the set of particles and then it draws + + + align:start position:0% +the set of particles and then it draws +the car as being in that location if you + + align:start position:0% +the car as being in that location if you + + + align:start position:0% +the car as being in that location if you +let it keep running it occasionally + + align:start position:0% +let it keep running it occasionally + + + align:start position:0% +let it keep running it occasionally +expands back out to make sure it doesn't + + align:start position:0% +expands back out to make sure it doesn't + + + align:start position:0% +expands back out to make sure it doesn't +fall into the local minima and then + + align:start position:0% +fall into the local minima and then + + + align:start position:0% +fall into the local minima and then +compresses once again where its + + align:start position:0% +compresses once again where its + + + align:start position:0% +compresses once again where its +strongest belief is notice that it has a + + align:start position:0% +strongest belief is notice that it has a + + + align:start position:0% +strongest belief is notice that it has a +couple of seconds of having a very very + + align:start position:0% +couple of seconds of having a very very + + + align:start position:0% +couple of seconds of having a very very +spread distribution that very quickly + + align:start position:0% +spread distribution that very quickly + + + align:start position:0% +spread distribution that very quickly +converges into a singular point that's + + align:start position:0% +converges into a singular point that's + + + align:start position:0% +converges into a singular point that's +because a lot of these locations become + + align:start position:0% +because a lot of these locations become + + + align:start position:0% +because a lot of these locations become +very very low probability after you've + + align:start position:0% +very very low probability after you've + + + align:start position:0% +very very low probability after you've +seen a couple of scenes into the future + + align:start position:0% +seen a couple of scenes into the future + + + align:start position:0% +seen a couple of scenes into the future +and we're gonna pause this I welcome you + + align:start position:0% +and we're gonna pause this I welcome you + + + align:start position:0% +and we're gonna pause this I welcome you +to go see the video to see the video + + align:start position:0% +to go see the video to see the video + + + align:start position:0% +to go see the video to see the video +yourself if you want to you can check + + align:start position:0% +yourself if you want to you can check + + + align:start position:0% +yourself if you want to you can check +the title it's pretty easy to find on + + align:start position:0% +the title it's pretty easy to find on + + + align:start position:0% +the title it's pretty easy to find on +YouTube because it's pretty much the + + align:start position:0% +YouTube because it's pretty much the + + + align:start position:0% +YouTube because it's pretty much the +only one oh no really the other side so + + align:start position:0% +only one oh no really the other side so + + + align:start position:0% +only one oh no really the other side so +why did semantic localization too useful + + align:start position:0% +why did semantic localization too useful + + + align:start position:0% +why did semantic localization too useful +in this manner in the example that was + + align:start position:0% +in this manner in the example that was + + + align:start position:0% +in this manner in the example that was +just shown it was kind of done on post + + align:start position:0% +just shown it was kind of done on post + + + align:start position:0% +just shown it was kind of done on post +processed data they took a scene they + + align:start position:0% +processed data they took a scene they + + + align:start position:0% +processed data they took a scene they +drove around it already then they get + + align:start position:0% +drove around it already then they get + + + align:start position:0% +drove around it already then they get +the identification on the video feed and + + align:start position:0% +the identification on the video feed and + + + align:start position:0% +the identification on the video feed and +use that to do a localization well I + + align:start position:0% +use that to do a localization well I + + + align:start position:0% +use that to do a localization well I +talked about it before but people kind + + align:start position:0% +talked about it before but people kind + + + align:start position:0% +talked about it before but people kind +of used sparse information to do a lot + + align:start position:0% +of used sparse information to do a lot + + + align:start position:0% +of used sparse information to do a lot +of their work you can't walk into a room + + align:start position:0% +of their work you can't walk into a room + + + align:start position:0% +of their work you can't walk into a room +people won't walk into a room and + + align:start position:0% +people won't walk into a room and + + + align:start position:0% +people won't walk into a room and +produce an exact laser scan map of the + + align:start position:0% +produce an exact laser scan map of the + + + align:start position:0% +produce an exact laser scan map of the +entire area themselves but they can + + align:start position:0% +entire area themselves but they can + + + align:start position:0% +entire area themselves but they can +store important information like scenic + + align:start position:0% +store important information like scenic + + + align:start position:0% +store important information like scenic +objects and tables that they find with + + align:start position:0% +objects and tables that they find with + + + align:start position:0% +objects and tables that they find with +their shins and use those to move around + + align:start position:0% +their shins and use those to move around + + + align:start position:0% +their shins and use those to move around +um robots stored that perfect map if + + align:start position:0% +um robots stored that perfect map if + + + align:start position:0% +um robots stored that perfect map if +they can manage to make it but they + + align:start position:0% +they can manage to make it but they + + + align:start position:0% +they can manage to make it but they +don't really have a good understanding + + align:start position:0% +don't really have a good understanding + + + align:start position:0% +don't really have a good understanding +of what that map might mean to a human + + align:start position:0% +of what that map might mean to a human + + + align:start position:0% +of what that map might mean to a human +so that means there that we're actually + + align:start position:0% +so that means there that we're actually + + + align:start position:0% +so that means there that we're actually +kind of like better at doing tasks with + + align:start position:0% +kind of like better at doing tasks with + + + align:start position:0% +kind of like better at doing tasks with +the environment if we wanted to go + + align:start position:0% +the environment if we wanted to go + + + align:start position:0% +the environment if we wanted to go +directly to a location we don't have to + + align:start position:0% +directly to a location we don't have to + + + align:start position:0% +directly to a location we don't have to +look around and figure it out on the + + align:start position:0% +look around and figure it out on the + + + align:start position:0% +look around and figure it out on the +wall where how what our distance from + + align:start position:0% +wall where how what our distance from + + + align:start position:0% +wall where how what our distance from +the wall is before we can then localize + + align:start position:0% +the wall is before we can then localize + + + align:start position:0% +the wall is before we can then localize +and move ourselves back over the tape we + + align:start position:0% +and move ourselves back over the tape we + + + align:start position:0% +and move ourselves back over the tape we +just say oh I want to go to the table + + align:start position:0% +just say oh I want to go to the table + + + align:start position:0% +just say oh I want to go to the table +would you look over + + align:start position:0% +would you look over + + + align:start position:0% +would you look over +oh there's the table table got it so how + + align:start position:0% +oh there's the table table got it so how + + + align:start position:0% +oh there's the table table got it so how +can we make robots think a little more + + align:start position:0% +can we make robots think a little more + + + align:start position:0% +can we make robots think a little more +like humans so it's easier for us to + + align:start position:0% +like humans so it's easier for us to + + + align:start position:0% +like humans so it's easier for us to +give them instructions well if we can + + align:start position:0% +give them instructions well if we can + + + align:start position:0% +give them instructions well if we can +make the robot use a map that has just + + align:start position:0% +make the robot use a map that has just + + + align:start position:0% +make the robot use a map that has just +scenic objects like we use a map that + + align:start position:0% +scenic objects like we use a map that + + + align:start position:0% +scenic objects like we use a map that +just has scenic objects then orders to + + align:start position:0% +just has scenic objects then orders to + + + align:start position:0% +just has scenic objects then orders to +move between scenic optics are as simple + + align:start position:0% +move between scenic optics are as simple + + + align:start position:0% +move between scenic optics are as simple +as turning finding the object and saying + + align:start position:0% +as turning finding the object and saying + + + align:start position:0% +as turning finding the object and saying +oh well I know where the object is so I + + align:start position:0% +oh well I know where the object is so I + + + align:start position:0% +oh well I know where the object is so I +know roughly where I need to be and then + + align:start position:0% +know roughly where I need to be and then + + + align:start position:0% +know roughly where I need to be and then +you start moving in process towards it + + align:start position:0% +you start moving in process towards it + + + align:start position:0% +you start moving in process towards it +inclusion semantic localization has a + + align:start position:0% +inclusion semantic localization has a + + + align:start position:0% +inclusion semantic localization has a +lot of I'm going to leave the references + + align:start position:0% +lot of I'm going to leave the references + + + align:start position:0% +lot of I'm going to leave the references +slide up while I talks that if you + + align:start position:0% +slide up while I talks that if you + + + align:start position:0% +slide up while I talks that if you +wanted to go and camp take a chance to + + align:start position:0% +wanted to go and camp take a chance to + + + align:start position:0% +wanted to go and camp take a chance to +go see any of these papers you + + align:start position:0% +go see any of these papers you + + + align:start position:0% +go see any of these papers you +definitely can most of the work in the + + align:start position:0% +definitely can most of the work in the + + + align:start position:0% +definitely can most of the work in the +slide comes directly from these sources + + align:start position:0% +slide comes directly from these sources + + + align:start position:0% +slide comes directly from these sources +semantic localization offers us the + + align:start position:0% +semantic localization offers us the + + + align:start position:0% +semantic localization offers us the +opportunity to take robots use sparser + + align:start position:0% +opportunity to take robots use sparser + + + align:start position:0% +opportunity to take robots use sparser +information to potentially localize and + + align:start position:0% +information to potentially localize and + + + align:start position:0% +information to potentially localize and +find ourselves inside of spaces and also + + align:start position:0% +find ourselves inside of spaces and also + + + align:start position:0% +find ourselves inside of spaces and also +business a chance to have really + + align:start position:0% +business a chance to have really + + + align:start position:0% +business a chance to have really +tweakable factors for how you might + + align:start position:0% +tweakable factors for how you might + + + align:start position:0% +tweakable factors for how you might +understand where you are in a space + + align:start position:0% +understand where you are in a space + + + align:start position:0% +understand where you are in a space +intuitively if you think certain things + + align:start position:0% +intuitively if you think certain things + + + align:start position:0% +intuitively if you think certain things +are important you can add them in as + + align:start position:0% +are important you can add them in as + + + align:start position:0% +are important you can add them in as +probabilistic factors if you don't + + align:start position:0% +probabilistic factors if you don't + + + align:start position:0% +probabilistic factors if you don't +remove them just as well thank you and + + align:start position:0% +remove them just as well thank you and + + + align:start position:0% +remove them just as well thank you and +this is essentially the conclusion our + + align:start position:0% +this is essentially the conclusion our + + + align:start position:0% +this is essentially the conclusion our +presentation I definitely recommend + + align:start position:0% +presentation I definitely recommend + + + align:start position:0% +presentation I definitely recommend +taking if you wanted to use something + + align:start position:0% +taking if you wanted to use something + + + align:start position:0% +taking if you wanted to use something +like this taking a look at this + + align:start position:0% +like this taking a look at this + + + align:start position:0% +like this taking a look at this +particular paper here notice how it says + + align:start position:0% +particular paper here notice how it says + + + align:start position:0% +particular paper here notice how it says +via the matrix permanent uhm as I said + + align:start position:0% +via the matrix permanent uhm as I said + + + align:start position:0% +via the matrix permanent uhm as I said +before a lot of these operations are a + + align:start position:0% +before a lot of these operations are a + + + align:start position:0% +before a lot of these operations are a +series of multiplications and some + + align:start position:0% +series of multiplications and some + + + align:start position:0% +series of multiplications and some +permutations + + align:start position:0% +permutations + + + align:start position:0% +permutations +there's permutation matrices there's + + align:start position:0% +there's permutation matrices there's + + + align:start position:0% +there's permutation matrices there's +matrix multiplication and there's a lot + + align:start position:0% +matrix multiplication and there's a lot + + + align:start position:0% +matrix multiplication and there's a lot +of ways to makes matrix multiplication + + align:start position:0% +of ways to makes matrix multiplication + + + align:start position:0% +of ways to makes matrix multiplication +faster those paper details how you can + + align:start position:0% +faster those paper details how you can + + + align:start position:0% +faster those paper details how you can +take the math that was shown before + + align:start position:0% +take the math that was shown before + + + align:start position:0% +take the math that was shown before +that's pretty inefficient and turn it + + align:start position:0% +that's pretty inefficient and turn it + + + align:start position:0% +that's pretty inefficient and turn it +into something that you can do an + + align:start position:0% +into something that you can do an + + + align:start position:0% +into something that you can do an +estimate of very quickly + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/1UdGbyj8924.txt b/1UdGbyj8924.txt new file mode 100644 index 0000000000000000000000000000000000000000..264d86fc628a0376877e61d09a0a5aa69d0cab9f --- /dev/null +++ b/1UdGbyj8924.txt @@ -0,0 +1,731 @@ +align:start position:0% + +when solving physics problems we have + + align:start position:0% +when solving physics problems we have + + + align:start position:0% +when solving physics problems we have +fundamental principles for instance we + + align:start position:0% +fundamental principles for instance we + + + align:start position:0% +fundamental principles for instance we +have Newton's second law and we also + + align:start position:0% +have Newton's second law and we also + + + align:start position:0% +have Newton's second law and we also +have an energy principle work + + align:start position:0% +have an energy principle work + + + align:start position:0% +have an energy principle work +non-conservative equals the change in + + align:start position:0% +non-conservative equals the change in + + + align:start position:0% +non-conservative equals the change in +kinetic energy plus the change in + + align:start position:0% +kinetic energy plus the change in + + + align:start position:0% +kinetic energy plus the change in +potential energy and many times students + + align:start position:0% +potential energy and many times students + + + align:start position:0% +potential energy and many times students +are challenged by do I use this law do I + + align:start position:0% +are challenged by do I use this law do I + + + align:start position:0% +are challenged by do I use this law do I +use that law why do I use one or the + + align:start position:0% +use that law why do I use one or the + + + align:start position:0% +use that law why do I use one or the +other do I use both at the same time can + + align:start position:0% +other do I use both at the same time can + + + align:start position:0% +other do I use both at the same time can +I get the same answers etc now I want to + + align:start position:0% +I get the same answers etc now I want to + + + align:start position:0% +I get the same answers etc now I want to +illustrate a particular category of + + align:start position:0% +illustrate a particular category of + + + align:start position:0% +illustrate a particular category of +problems where we have some type of + + align:start position:0% +problems where we have some type of + + + align:start position:0% +problems where we have some type of +circular motion and why we need to use + + align:start position:0% +circular motion and why we need to use + + + align:start position:0% +circular motion and why we need to use +both of these laws so let's consider + + align:start position:0% +both of these laws so let's consider + + + align:start position:0% +both of these laws so let's consider +let's go back to our dome example at MIT + + align:start position:0% +let's go back to our dome example at MIT + + + align:start position:0% +let's go back to our dome example at MIT +and let's say we have an object that's + + align:start position:0% +and let's say we have an object that's + + + align:start position:0% +and let's say we have an object that's +on the dome and now let's write out a + + align:start position:0% +on the dome and now let's write out a + + + align:start position:0% +on the dome and now let's write out a +Freebody diagram for this object so we + + align:start position:0% +Freebody diagram for this object so we + + + align:start position:0% +Freebody diagram for this object so we +have our gravitational force we have a + + align:start position:0% +have our gravitational force we have a + + + align:start position:0% +have our gravitational force we have a +normal force and here let's just assume + + align:start position:0% +normal force and here let's just assume + + + align:start position:0% +normal force and here let's just assume +that our dome is frictionless for + + align:start position:0% +that our dome is frictionless for + + + align:start position:0% +that our dome is frictionless for +simplicity so what you see here and is + + align:start position:0% +simplicity so what you see here and is + + + align:start position:0% +simplicity so what you see here and is +that the object is displacing in a + + align:start position:0% +that the object is displacing in a + + + align:start position:0% +that the object is displacing in a +direction now here if I choose R hat and + + align:start position:0% +direction now here if I choose R hat and + + + align:start position:0% +direction now here if I choose R hat and +theta hat and if I choose a coordinate + + align:start position:0% +theta hat and if I choose a coordinate + + + align:start position:0% +theta hat and if I choose a coordinate +system where I take my positive angle + + align:start position:0% +system where I take my positive angle + + + align:start position:0% +system where I take my positive angle +theta this way that the normal force and + + align:start position:0% +theta this way that the normal force and + + + align:start position:0% +theta this way that the normal force and +the displacement are perpendicular now + + align:start position:0% +the displacement are perpendicular now + + + align:start position:0% +the displacement are perpendicular now +what that means is that the work done by + + align:start position:0% +what that means is that the work done by + + + align:start position:0% +what that means is that the work done by +the normal force F normal dot d s is + + align:start position:0% +the normal force F normal dot d s is + + + align:start position:0% +the normal force F normal dot d s is +zero because while we're calling F + + align:start position:0% +zero because while we're calling F + + + align:start position:0% +zero because while we're calling F +normal equal to the normal force and + + align:start position:0% +normal equal to the normal force and + + + align:start position:0% +normal equal to the normal force and +that the normal force is perpendicular + + align:start position:0% +that the normal force is perpendicular + + + align:start position:0% +that the normal force is perpendicular +to the displacement so what that means + + align:start position:0% +to the displacement so what that means + + + align:start position:0% +to the displacement so what that means +is all information about the normal + + align:start position:0% +is all information about the normal + + + align:start position:0% +is all information about the normal +force is not included in the energy + + align:start position:0% +force is not included in the energy + + + align:start position:0% +force is not included in the energy +principle in fact the energy principle + + align:start position:0% +principle in fact the energy principle + + + align:start position:0% +principle in fact the energy principle +is the work that's done is just the + + align:start position:0% +is the work that's done is just the + + + align:start position:0% +is the work that's done is just the +amount this is angle theta so this is + + align:start position:0% +amount this is angle theta so this is + + + align:start position:0% +amount this is angle theta so this is +angle theta + + align:start position:0% +angle theta + + + align:start position:0% +angle theta +so the actual work done by the + + align:start position:0% +so the actual work done by the + + + align:start position:0% +so the actual work done by the +gravitational force gene is the + + align:start position:0% +gravitational force gene is the + + + align:start position:0% +gravitational force gene is the +component of G mg sine theta times the + + align:start position:0% +component of G mg sine theta times the + + + align:start position:0% +component of G mg sine theta times the +displacement D s so the only work that's + + align:start position:0% +displacement D s so the only work that's + + + align:start position:0% +displacement D s so the only work that's +appearing here and this is conservative + + align:start position:0% +appearing here and this is conservative + + + align:start position:0% +appearing here and this is conservative +and so when we integrated this work and + + align:start position:0% +and so when we integrated this work and + + + align:start position:0% +and so when we integrated this work and +got that the work done by the + + align:start position:0% +got that the work done by the + + + align:start position:0% +got that the work done by the +gravitational force is minus the change + + align:start position:0% +gravitational force is minus the change + + + align:start position:0% +gravitational force is minus the change +in potential energy that's showing up + + align:start position:0% +in potential energy that's showing up + + + align:start position:0% +in potential energy that's showing up +here so the part of the force that's in + + align:start position:0% +here so the part of the force that's in + + + align:start position:0% +here so the part of the force that's in +the direction of the motion is giving us + + align:start position:0% +the direction of the motion is giving us + + + align:start position:0% +the direction of the motion is giving us +the energy condition but we're losing + + align:start position:0% +the energy condition but we're losing + + + align:start position:0% +the energy condition but we're losing +all information about the forces in the + + align:start position:0% +all information about the forces in the + + + align:start position:0% +all information about the forces in the +radial direction so we also because also + + align:start position:0% +radial direction so we also because also + + + align:start position:0% +radial direction so we also because also +what we need is Newton's second law in + + align:start position:0% +what we need is Newton's second law in + + + align:start position:0% +what we need is Newton's second law in +the direction perpendicular to the + + align:start position:0% +the direction perpendicular to the + + + align:start position:0% +the direction perpendicular to the +displacement displacement is in the + + align:start position:0% +displacement displacement is in the + + + align:start position:0% +displacement displacement is in the +theta hat direction so we need Newton's + + align:start position:0% +theta hat direction so we need Newton's + + + align:start position:0% +theta hat direction so we need Newton's +second law in the radial direction and + + align:start position:0% +second law in the radial direction and + + + align:start position:0% +second law in the radial direction and +that we have our hat is we have a normal + + align:start position:0% +that we have our hat is we have a normal + + + align:start position:0% +that we have our hat is we have a normal +force minus mg cosine theta and the + + align:start position:0% +force minus mg cosine theta and the + + + align:start position:0% +force minus mg cosine theta and the +object is undergoing circular motion so + + align:start position:0% +object is undergoing circular motion so + + + align:start position:0% +object is undergoing circular motion so +it's equal to minus M V squared over R + + align:start position:0% +it's equal to minus M V squared over R + + + align:start position:0% +it's equal to minus M V squared over R +where R is the radius of the dome this + + align:start position:0% +where R is the radius of the dome this + + + align:start position:0% +where R is the radius of the dome this +equation is not an all included in the + + align:start position:0% +equation is not an all included in the + + + align:start position:0% +equation is not an all included in the +energy condition you may say well what + + align:start position:0% +energy condition you may say well what + + + align:start position:0% +energy condition you may say well what +about the tangential Newton's second law + + align:start position:0% +about the tangential Newton's second law + + + align:start position:0% +about the tangential Newton's second law +which is mg sine theta equals M R d + + align:start position:0% +which is mg sine theta equals M R d + + + align:start position:0% +which is mg sine theta equals M R d +squared theta DT squared but it's + + align:start position:0% +squared theta DT squared but it's + + + align:start position:0% +squared theta DT squared but it's +precisely this equation that's + + align:start position:0% +precisely this equation that's + + + align:start position:0% +precisely this equation that's +integrated + + align:start position:0% + + + + align:start position:0% + +with respect to the displacement and + + align:start position:0% +with respect to the displacement and + + + align:start position:0% +with respect to the displacement and +that gives us our energy principle so in + + align:start position:0% +that gives us our energy principle so in + + + align:start position:0% +that gives us our energy principle so in +summary the energy principle is the + + align:start position:0% +summary the energy principle is the + + + align:start position:0% +summary the energy principle is the +integration of Newton's second law in + + align:start position:0% +integration of Newton's second law in + + + align:start position:0% +integration of Newton's second law in +the direction of motion and we're + + align:start position:0% +the direction of motion and we're + + + align:start position:0% +the direction of motion and we're +completely missing the application of + + align:start position:0% +completely missing the application of + + + align:start position:0% +completely missing the application of +Newton's second law in the direction + + align:start position:0% +Newton's second law in the direction + + + align:start position:0% +Newton's second law in the direction +perpendicular to the motion energy does + + align:start position:0% +perpendicular to the motion energy does + + + align:start position:0% +perpendicular to the motion energy does +not account for that and that's why we + + align:start position:0% +not account for that and that's why we + + + align:start position:0% +not account for that and that's why we +needed separately to apply both of the + + align:start position:0% +needed separately to apply both of the + + + align:start position:0% +needed separately to apply both of the +principles of energy and Newton's second + + align:start position:0% +principles of energy and Newton's second + + + align:start position:0% +principles of energy and Newton's second +law in the radial direction in order to + + align:start position:0% +law in the radial direction in order to + + + align:start position:0% +law in the radial direction in order to +figure out how to solve this problem now + + align:start position:0% +figure out how to solve this problem now + + + align:start position:0% +figure out how to solve this problem now +this idea is true in general when you + + align:start position:0% +this idea is true in general when you + + + align:start position:0% +this idea is true in general when you +have circular motion you need the energy + + align:start position:0% +have circular motion you need the energy + + + align:start position:0% +have circular motion you need the energy +equation which is the tangentially + + align:start position:0% +equation which is the tangentially + + + align:start position:0% +equation which is the tangentially +integrated in Newton's second law in the + + align:start position:0% +integrated in Newton's second law in the + + + align:start position:0% +integrated in Newton's second law in the +tangential direction and you need + + align:start position:0% +tangential direction and you need + + + align:start position:0% +tangential direction and you need +Newton's second law in the direction + + align:start position:0% +Newton's second law in the direction + + + align:start position:0% +Newton's second law in the direction +perpendicular to that circular motion \ No newline at end of file diff --git a/1dW_izzvfOk.txt b/1dW_izzvfOk.txt new file mode 100644 index 0000000000000000000000000000000000000000..480c6521f699f72037c77a74c325db9b3d61df80 --- /dev/null +++ b/1dW_izzvfOk.txt @@ -0,0 +1,2227 @@ +align:start position:0% + +so what is the wave function that we + + align:start position:0% +so what is the wave function that we + + + align:start position:0% +so what is the wave function that we +have we must have a wave function now + + align:start position:0% +have we must have a wave function now + + + align:start position:0% +have we must have a wave function now +that is symmetric and built with e to + + align:start position:0% +that is symmetric and built with e to + + + align:start position:0% +that is symmetric and built with e to +the KX Capa X and e to the minus Kaa X + + align:start position:0% +the KX Capa X and e to the minus Kaa X + + + align:start position:0% +the KX Capa X and e to the minus Kaa X +this is the only possibility e to the + + align:start position:0% +this is the only possibility e to the + + + align:start position:0% +this is the only possibility e to the +minus of + + align:start position:0% +minus of + + + align:start position:0% +minus of +Kappa absolute value of x this is p of X + + align:start position:0% +Kappa absolute value of x this is p of X + + + align:start position:0% +Kappa absolute value of x this is p of X +for X different from zero this is uh as + + align:start position:0% +for X different from zero this is uh as + + + align:start position:0% +for X different from zero this is uh as +you can quickly see this is e to the + + align:start position:0% +you can quickly see this is e to the + + + align:start position:0% +you can quickly see this is e to the +minus Kaa X when X is positive a e to + + align:start position:0% +minus Kaa X when X is positive a e to + + + align:start position:0% +minus Kaa X when X is positive a e to +the Capa X when X is negative and both + + align:start position:0% +the Capa X when X is negative and both + + + align:start position:0% +the Capa X when X is negative and both +of them Decay the first exponential + + align:start position:0% +of them Decay the first exponential + + + align:start position:0% +of them Decay the first exponential +negative is the standard decaying + + align:start position:0% +negative is the standard decaying + + + align:start position:0% +negative is the standard decaying +exponential to the right the one with + + align:start position:0% +exponential to the right the one with + + + align:start position:0% +exponential to the right the one with +positive well here x is negative as you + + align:start position:0% +positive well here x is negative as you + + + align:start position:0% +positive well here x is negative as you +go all the way to the left this one + + align:start position:0% +go all the way to the left this one + + + align:start position:0% +go all the way to the left this one +decays as well and this thing Plus it is + + align:start position:0% +decays as well and this thing Plus it is + + + align:start position:0% +decays as well and this thing Plus it is +a decaying exponential with amplitude a + + align:start position:0% +a decaying exponential with amplitude a + + + align:start position:0% +a decaying exponential with amplitude a +like that and a decaying exponential + + align:start position:0% +like that and a decaying exponential + + + align:start position:0% +like that and a decaying exponential +with amplitude a and a singularity there + + align:start position:0% +with amplitude a and a singularity there + + + align:start position:0% +with amplitude a and a singularity there +which is what you would have + + align:start position:0% +which is what you would have + + + align:start position:0% +which is what you would have +expected so this seems to be on the + + align:start position:0% +expected so this seems to be on the + + + align:start position:0% +expected so this seems to be on the +right track it's a continuous wave + + align:start position:0% +right track it's a continuous wave + + + align:start position:0% +right track it's a continuous wave +function the wave function cannot fail + + align:start position:0% +function the wave function cannot fail + + + align:start position:0% +function the wave function cannot fail +to be continuous that's complete + + align:start position:0% +to be continuous that's complete + + + align:start position:0% +to be continuous that's complete +disaster the sharing equation could not + + align:start position:0% +disaster the sharing equation could not + + + align:start position:0% +disaster the sharing equation could not +be satisfied so so this is our + + align:start position:0% +be satisfied so so this is our + + + align:start position:0% +be satisfied so so this is our +discontinuous wave + + align:start position:0% +discontinuous wave + + + align:start position:0% +discontinuous wave +function so at this + + align:start position:0% +function so at this + + + align:start position:0% +function so at this +moment you really haven't yet used the + + align:start position:0% +moment you really haven't yet used the + + + align:start position:0% +moment you really haven't yet used the +Delta function the Delta function with + + align:start position:0% +Delta function the Delta function with + + + align:start position:0% +Delta function the Delta function with +intensity Alpha down I I should have + + align:start position:0% +intensity Alpha down I I should have + + + align:start position:0% +intensity Alpha down I I should have +made a comment that it's uh very nice + + align:start position:0% +made a comment that it's uh very nice + + + align:start position:0% +made a comment that it's uh very nice +that Alpha appeared here in the + + align:start position:0% +that Alpha appeared here in the + + + align:start position:0% +that Alpha appeared here in the +numerator if it would have appeared in + + align:start position:0% +numerator if it would have appeared in + + + align:start position:0% +numerator if it would have appeared in +the denominator I would be telling you + + align:start position:0% +the denominator I would be telling you + + + align:start position:0% +the denominator I would be telling you +that I think this problem is not going + + align:start position:0% +that I think this problem is not going + + + align:start position:0% +that I think this problem is not going +to have a solution + + align:start position:0% +to have a solution + + + align:start position:0% +to have a solution +ution why because if it appears in the + + align:start position:0% +ution why because if it appears in the + + + align:start position:0% +ution why because if it appears in the +numerator it means that as the Delta + + align:start position:0% +numerator it means that as the Delta + + + align:start position:0% +numerator it means that as the Delta +function potential is becoming stronger + + align:start position:0% +function potential is becoming stronger + + + align:start position:0% +function potential is becoming stronger +and stronger the bound state is getting + + align:start position:0% +and stronger the bound state is getting + + + align:start position:0% +and stronger the bound state is getting +deeper and deeper which is what you + + align:start position:0% +deeper and deeper which is what you + + + align:start position:0% +deeper and deeper which is what you +would expect but if it would be in the + + align:start position:0% +would expect but if it would be in the + + + align:start position:0% +would expect but if it would be in the +numerator in the denominator as the + + align:start position:0% +numerator in the denominator as the + + + align:start position:0% +numerator in the denominator as the +potential gets deeper and deeper the + + align:start position:0% +potential gets deeper and deeper the + + + align:start position:0% +potential gets deeper and deeper the +bound is going up that makes no sense + + align:start position:0% +bound is going up that makes no sense + + + align:start position:0% +bound is going up that makes no sense +whatsoever so it's good that it appeared + + align:start position:0% +whatsoever so it's good that it appeared + + + align:start position:0% +whatsoever so it's good that it appeared +there it's a sign that things are in + + align:start position:0% +there it's a sign that things are in + + + align:start position:0% +there it's a sign that things are in +good in reasonable condition so now we + + align:start position:0% +good in reasonable condition so now we + + + align:start position:0% +good in reasonable condition so now we +really have to face the Delta function + + align:start position:0% +really have to face the Delta function + + + align:start position:0% +really have to face the Delta function +and this is a procedure you're going to + + align:start position:0% +and this is a procedure you're going to + + + align:start position:0% +and this is a procedure you're going to +do many times in this course so look at + + align:start position:0% +do many times in this course so look at + + + align:start position:0% +do many times in this course so look at +it and do it again and again until + + align:start position:0% +it and do it again and again until + + + align:start position:0% +it and do it again and again until +you're very comfortable with it it's the + + align:start position:0% +you're very comfortable with it it's the + + + align:start position:0% +you're very comfortable with it it's the +issue of + + align:start position:0% +issue of + + + align:start position:0% +issue of +discovering what kind of + + align:start position:0% +discovering what kind of + + + align:start position:0% +discovering what kind of +discontinuity you can have with a Delta + + align:start position:0% +discontinuity you can have with a Delta + + + align:start position:0% +discontinuity you can have with a Delta +function and it's a continuity in the + + align:start position:0% +function and it's a continuity in the + + + align:start position:0% +function and it's a continuity in the +derivative so let's quantify it so here + + align:start position:0% +derivative so let's quantify it so here + + + align:start position:0% +derivative so let's quantify it so here +it is we begin with a shinger equation + + align:start position:0% + + + + align:start position:0% + +again but I will write now the potential + + align:start position:0% +again but I will write now the potential + + + align:start position:0% +again but I will write now the potential +term as + + align:start position:0% +term as + + + align:start position:0% +term as +well the potential is plus v of + + align:start position:0% + + + + align:start position:0% + +x s of x equals e of + + align:start position:0% +x s of x equals e of + + + align:start position:0% +x s of x equals e of +X and the idea is to integrate this + + align:start position:0% +X and the idea is to integrate this + + + align:start position:0% +X and the idea is to integrate this +equation from minus Epsilon to + + align:start position:0% + + + + align:start position:0% + +Epsilon and that's Epsilon is supposed + + align:start position:0% +Epsilon and that's Epsilon is supposed + + + align:start position:0% +Epsilon and that's Epsilon is supposed +to be a small positive number so you + + align:start position:0% +to be a small positive number so you + + + align:start position:0% +to be a small positive number so you +integrate from minus Epsilon to Epsilon + + align:start position:0% +integrate from minus Epsilon to Epsilon + + + align:start position:0% +integrate from minus Epsilon to Epsilon +the differential + + align:start position:0% +the differential + + + align:start position:0% +the differential +equation and see what it does to you in + + align:start position:0% +equation and see what it does to you in + + + align:start position:0% +equation and see what it does to you in +the limit as Epsilon goes to + + align:start position:0% +the limit as Epsilon goes to + + + align:start position:0% +the limit as Epsilon goes to +zero that's what we're going to try to + + align:start position:0% +zero that's what we're going to try to + + + align:start position:0% +zero that's what we're going to try to +do + + align:start position:0% +do + + + align:start position:0% +do +so what do we get if you integrate uh + + align:start position:0% +so what do we get if you integrate uh + + + align:start position:0% +so what do we get if you integrate uh +this you get min - h^2 over 2 m and now + + align:start position:0% +this you get min - h^2 over 2 m and now + + + align:start position:0% +this you get min - h^2 over 2 m and now +you have to integrate the second + + align:start position:0% +you have to integrate the second + + + align:start position:0% +you have to integrate the second +derivative with respect to X which is + + align:start position:0% +derivative with respect to X which is + + + align:start position:0% +derivative with respect to X which is +the first derivative and therefore this + + align:start position:0% +the first derivative and therefore this + + + align:start position:0% +the first derivative and therefore this +is the first + + align:start position:0% +is the first + + + align:start position:0% +is the first +derivative at X = Epsilon minus the + + align:start position:0% +derivative at X = Epsilon minus the + + + align:start position:0% +derivative at X = Epsilon minus the +first + + align:start position:0% + + + + align:start position:0% + +derivative at X = minus + + align:start position:0% + + + + align:start position:0% + +Epsilon this is from the first term + + align:start position:0% +Epsilon this is from the first term + + + align:start position:0% +Epsilon this is from the first term +because you + + align:start position:0% +because you + + + align:start position:0% +because you +integrate DX D + + align:start position:0% +integrate DX D + + + align:start position:0% +integrate DX D +second dx^ 2 SI is the same thing as DX + + align:start position:0% +second dx^ 2 SI is the same thing as DX + + + align:start position:0% +second dx^ 2 SI is the same thing as DX +D + + align:start position:0% +D + + + align:start position:0% +D +DX of thei + + align:start position:0% +DX of thei + + + align:start position:0% +DX of thei +DX between a and b and the integral of a + + align:start position:0% +DX between a and b and the integral of a + + + align:start position:0% +DX between a and b and the integral of a +total derivative is + + align:start position:0% +total derivative is + + + align:start position:0% +total derivative is +d d x at b a + + align:start position:0% +d d x at b a + + + align:start position:0% +d d x at b a +I think people write it like this A to + + align:start position:0% +I think people write it like this A to + + + align:start position:0% +I think people write it like this A to +B evaluated at the top minus the + + align:start position:0% +B evaluated at the top minus the + + + align:start position:0% +B evaluated at the top minus the +evaluation at the + + align:start position:0% +evaluation at the + + + align:start position:0% +evaluation at the +bottom now the next + + align:start position:0% +bottom now the next + + + align:start position:0% +bottom now the next +term is the + + align:start position:0% +term is the + + + align:start position:0% +term is the +integral of s * V of X so I'll write it + + align:start position:0% +integral of s * V of X so I'll write it + + + align:start position:0% +integral of s * V of X so I'll write it +plus the integral from minus Epsilon to + + align:start position:0% +plus the integral from minus Epsilon to + + + align:start position:0% +plus the integral from minus Epsilon to +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +DX minus Alpha Delta of + + align:start position:0% +DX minus Alpha Delta of + + + align:start position:0% +DX minus Alpha Delta of +x p + + align:start position:0% +x p + + + align:start position:0% +x p +X that's the potential now we use the + + align:start position:0% +X that's the potential now we use the + + + align:start position:0% +X that's the potential now we use the +Delta function and on the right hand + + align:start position:0% +Delta function and on the right hand + + + align:start position:0% +Delta function and on the right hand +side this would be e * the integral from + + align:start position:0% +side this would be e * the integral from + + + align:start position:0% +side this would be e * the integral from +minus Epsilon to + + align:start position:0% +minus Epsilon to + + + align:start position:0% +minus Epsilon to +Epsilon of s of + + align:start position:0% +Epsilon of s of + + + align:start position:0% +Epsilon of s of +X + + align:start position:0% +X + + + align:start position:0% +X +DX so that's the differential equation + + align:start position:0% +DX so that's the differential equation + + + align:start position:0% +DX so that's the differential equation +integrated and + + align:start position:0% +integrated and + + + align:start position:0% +integrated and +now we're going to do two things things + + align:start position:0% +now we're going to do two things things + + + align:start position:0% +now we're going to do two things things +we're going to do some of these + + align:start position:0% +we're going to do some of these + + + align:start position:0% +we're going to do some of these +integrals um and uh take the limit as + + align:start position:0% +integrals um and uh take the limit as + + + align:start position:0% +integrals um and uh take the limit as +Epsilon goes to zero + + align:start position:0% +Epsilon goes to zero + + + align:start position:0% +Epsilon goes to zero +so I'll write this - h^ + + align:start position:0% +so I'll write this - h^ + + + align:start position:0% +so I'll write this - h^ +2/ 2 m limit as Epsilon goes to zero of + + align:start position:0% +2/ 2 m limit as Epsilon goes to zero of + + + align:start position:0% +2/ 2 m limit as Epsilon goes to zero of +D DX at Epsilon minus + + align:start position:0% +D DX at Epsilon minus + + + align:start position:0% +D DX at Epsilon minus +D the X at minus + + align:start position:0% +D the X at minus + + + align:start position:0% +D the X at minus +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +plus let's think of this integral we can + + align:start position:0% +plus let's think of this integral we can + + + align:start position:0% +plus let's think of this integral we can +do this integral it's a Delta function + + align:start position:0% +do this integral it's a Delta function + + + align:start position:0% +do this integral it's a Delta function +so it picks the value of the wave + + align:start position:0% +so it picks the value of the wave + + + align:start position:0% +so it picks the value of the wave +function at zero because zero is inside + + align:start position:0% +function at zero because zero is inside + + + align:start position:0% +function at zero because zero is inside +the interval of integration that's why + + align:start position:0% +the interval of integration that's why + + + align:start position:0% +the interval of integration that's why +we integrate it from minus Epsilon to + + align:start position:0% +we integrate it from minus Epsilon to + + + align:start position:0% +we integrate it from minus Epsilon to +Epsilon to have the Delta function + + align:start position:0% +Epsilon to have the Delta function + + + align:start position:0% +Epsilon to have the Delta function +inside so you get an alpha out a of zero + + align:start position:0% +inside so you get an alpha out a of zero + + + align:start position:0% +inside so you get an alpha out a of zero +and that's what this integral is it's + + align:start position:0% +and that's what this integral is it's + + + align:start position:0% +and that's what this integral is it's +independent of the value of Epsilon as + + align:start position:0% +independent of the value of Epsilon as + + + align:start position:0% +independent of the value of Epsilon as +long as Epsilon is different from zero + + align:start position:0% +long as Epsilon is different from zero + + + align:start position:0% +long as Epsilon is different from zero +so this gives you + + align:start position:0% + + + + align:start position:0% + +minus + + align:start position:0% +minus + + + align:start position:0% +minus +Alpha P of + + align:start position:0% + + + + align:start position:0% + +zero and now the last + + align:start position:0% +zero and now the last + + + align:start position:0% +zero and now the last +term is an integral from minus Epsilon + + align:start position:0% +term is an integral from minus Epsilon + + + align:start position:0% +term is an integral from minus Epsilon +to Epsilon of the wave + + align:start position:0% +to Epsilon of the wave + + + align:start position:0% +to Epsilon of the wave +function now the wave function is + + align:start position:0% +function now the wave function is + + + align:start position:0% +function now the wave function is +continuous it should be be continuous + + align:start position:0% +continuous it should be be continuous + + + align:start position:0% +continuous it should be be continuous +that means it's finite and this + + align:start position:0% +that means it's finite and this + + + align:start position:0% +that means it's finite and this +integral as of any function that is not + + align:start position:0% +integral as of any function that is not + + + align:start position:0% +integral as of any function that is not +Divergent from Epsilon to minus Epsilon + + align:start position:0% +Divergent from Epsilon to minus Epsilon + + + align:start position:0% +Divergent from Epsilon to minus Epsilon +to Epsilon as Epsilon goes to zero is + + align:start position:0% +to Epsilon as Epsilon goes to zero is + + + align:start position:0% +to Epsilon as Epsilon goes to zero is +zero any integral of a function that + + align:start position:0% +zero any integral of a function that + + + align:start position:0% +zero any integral of a function that +doesn't diverge as the limits of + + align:start position:0% +doesn't diverge as the limits of + + + align:start position:0% +doesn't diverge as the limits of +integration go to zero the area under + + align:start position:0% +integration go to zero the area under + + + align:start position:0% +integration go to zero the area under +the function is zero so this is zero the + + align:start position:0% +the function is zero so this is zero the + + + align:start position:0% +the function is zero so this is zero the +limit and this thing goes to zero so we + + align:start position:0% +limit and this thing goes to zero so we + + + align:start position:0% +limit and this thing goes to zero so we +put a zero + + align:start position:0% +put a zero + + + align:start position:0% +put a zero +here so at this moment we got really + + align:start position:0% +here so at this moment we got really + + + align:start position:0% +here so at this moment we got really +what we um Wanted um I'll write it um + + align:start position:0% +what we um Wanted um I'll write it um + + + align:start position:0% +what we um Wanted um I'll write it um +this + + align:start position:0% +this + + + align:start position:0% +this +way I'll go + + align:start position:0% +way I'll go + + + align:start position:0% +way I'll go +here and I'll say - h^2 / 2 m and what + + align:start position:0% +here and I'll say - h^2 / 2 m and what + + + align:start position:0% +here and I'll say - h^2 / 2 m and what +is + + align:start position:0% +is + + + align:start position:0% +is +this this expression says calculate the + + align:start position:0% +this this expression says calculate the + + + align:start position:0% +this this expression says calculate the +derivative of the function a little bit + + align:start position:0% +derivative of the function a little bit + + + align:start position:0% +derivative of the function a little bit +to the right of zero and subtract the + + align:start position:0% +to the right of zero and subtract the + + + align:start position:0% +to the right of zero and subtract the +derivative of the function a little bit + + align:start position:0% +derivative of the function a little bit + + + align:start position:0% +derivative of the function a little bit +to the left of zero this is nothing but + + align:start position:0% +to the left of zero this is nothing but + + + align:start position:0% +to the left of zero this is nothing but +the + + align:start position:0% +the + + + align:start position:0% +the +discontinuity in P Prime you're + + align:start position:0% +discontinuity in P Prime you're + + + align:start position:0% +discontinuity in P Prime you're +evaluating for any Epsilon greater than + + align:start position:0% +evaluating for any Epsilon greater than + + + align:start position:0% +evaluating for any Epsilon greater than +zero the P prime a little to the right a + + align:start position:0% +zero the P prime a little to the right a + + + align:start position:0% +zero the P prime a little to the right a +little to the left and taking the + + align:start position:0% +little to the left and taking the + + + align:start position:0% +little to the left and taking the +difference so this is what we should + + align:start position:0% +difference so this is what we should + + + align:start position:0% +difference so this is what we should +call the the + + align:start position:0% +call the the + + + align:start position:0% +call the the +discontinuity Delta at Zer at xal 0 this + + align:start position:0% +discontinuity Delta at Zer at xal 0 this + + + align:start position:0% +discontinuity Delta at Zer at xal 0 this +and this is for + + align:start position:0% +and this is for + + + align:start position:0% +and this is for +discontinuity + + align:start position:0% +discontinuity + + + align:start position:0% +discontinuity +nuity of P + + align:start position:0% +nuity of P + + + align:start position:0% +nuity of P +Prime at xal + + align:start position:0% +Prime at xal + + + align:start position:0% +Prime at xal +0 minus Alpha P of 0 = + + align:start position:0% +0 minus Alpha P of 0 = + + + align:start position:0% +0 minus Alpha P of 0 = +0 and from + + align:start position:0% +0 and from + + + align:start position:0% +0 and from +here we discovered the Delta 0o P Prime + + align:start position:0% +here we discovered the Delta 0o P Prime + + + align:start position:0% +here we discovered the Delta 0o P Prime +is equal to - 2 m alpha over h^ + + align:start position:0% +is equal to - 2 m alpha over h^ + + + align:start position:0% +is equal to - 2 m alpha over h^ +2 of + + align:start position:0% + + + + align:start position:0% + +Z this is the + + align:start position:0% +Z this is the + + + align:start position:0% +Z this is the +discontinuity condition produced by the + + align:start position:0% +discontinuity condition produced by the + + + align:start position:0% +discontinuity condition produced by the +Delta + + align:start position:0% + + + + align:start position:0% + +function this whole + + align:start position:0% +function this whole + + + align:start position:0% +function this whole +quantity is what we call delta0 of P + + align:start position:0% +quantity is what we call delta0 of P + + + align:start position:0% +quantity is what we call delta0 of P +Prime + + align:start position:0% + + + + align:start position:0% + +and what it says is that yes the wave + + align:start position:0% +and what it says is that yes the wave + + + align:start position:0% +and what it says is that yes the wave +function can have a discontinuous first + + align:start position:0% +function can have a discontinuous first + + + align:start position:0% +function can have a discontinuous first +derivative if the wave function doesn't + + align:start position:0% +derivative if the wave function doesn't + + + align:start position:0% +derivative if the wave function doesn't +vanish there once the wave function + + align:start position:0% +vanish there once the wave function + + + align:start position:0% +vanish there once the wave function +doesn't vanish at that point is the + + align:start position:0% +doesn't vanish at that point is the + + + align:start position:0% +doesn't vanish at that point is the +discontinuity is in fact even + + align:start position:0% +discontinuity is in fact even + + + align:start position:0% +discontinuity is in fact even +proportional to the value of the wave + + align:start position:0% +proportional to the value of the wave + + + align:start position:0% +proportional to the value of the wave +function at that point and here are the + + align:start position:0% +function at that point and here are the + + + align:start position:0% +function at that point and here are the +constants of + + align:start position:0% +constants of + + + align:start position:0% +constants of +proportionality + + align:start position:0% +proportionality + + + align:start position:0% +proportionality +now I don't think it's worth to memorize + + align:start position:0% +now I don't think it's worth to memorize + + + align:start position:0% +now I don't think it's worth to memorize +this equation or anything like that + + align:start position:0% +this equation or anything like that + + + align:start position:0% +this equation or anything like that +because it basically can be derived in a + + align:start position:0% +because it basically can be derived in a + + + align:start position:0% +because it basically can be derived in a +few lines this may have looked like an + + align:start position:0% +few lines this may have looked like an + + + align:start position:0% +few lines this may have looked like an +interesting or + + align:start position:0% +interesting or + + + align:start position:0% +interesting or +somewhat intricate derivation but after + + align:start position:0% +somewhat intricate derivation but after + + + align:start position:0% +somewhat intricate derivation but after +you've done it a couple of times this is + + align:start position:0% +you've done it a couple of times this is + + + align:start position:0% +you've done it a couple of times this is +something you'll do in a minute or so + + align:start position:0% +something you'll do in a minute or so + + + align:start position:0% +something you'll do in a minute or so +and uh you just integrate and find the + + align:start position:0% +and uh you just integrate and find the + + + align:start position:0% +and uh you just integrate and find the +discontinuity in the derivative that's a + + align:start position:0% +discontinuity in the derivative that's a + + + align:start position:0% +discontinuity in the derivative that's a +formula there and that's a formula for a + + align:start position:0% + + + + align:start position:0% + +potential minus Alpha Delta of X so if + + align:start position:0% +potential minus Alpha Delta of X so if + + + align:start position:0% +potential minus Alpha Delta of X so if +somebody gives you a different potential + + align:start position:0% +somebody gives you a different potential + + + align:start position:0% +somebody gives you a different potential +well you have to change the alpha + + align:start position:0% +well you have to change the alpha + + + align:start position:0% +well you have to change the alpha +accordingly so let's wrap this + + align:start position:0% +accordingly so let's wrap this + + + align:start position:0% +accordingly so let's wrap this +up so we go to our case here is + + align:start position:0% +up so we go to our case here is + + + align:start position:0% +up so we go to our case here is +our situation so let's apply this uh so + + align:start position:0% +our situation so let's apply this uh so + + + align:start position:0% +our situation so let's apply this uh so +what is the value + + align:start position:0% +what is the value + + + align:start position:0% +what is the value +apply this equation to our wave function + + align:start position:0% +apply this equation to our wave function + + + align:start position:0% +apply this equation to our wave function +so what is the derivative at Epsilon + + align:start position:0% +so what is the derivative at Epsilon + + + align:start position:0% +so what is the derivative at Epsilon +it's minus Kaa a e to the minus Kaa + + align:start position:0% +it's minus Kaa a e to the minus Kaa + + + align:start position:0% +it's minus Kaa a e to the minus Kaa +Epsilon that's the derivative of Si on + + align:start position:0% +Epsilon that's the derivative of Si on + + + align:start position:0% +Epsilon that's the derivative of Si on +the positive side I differentiated the + + align:start position:0% +the positive side I differentiated the + + + align:start position:0% +the positive side I differentiated the +top line of this equation minus the + + align:start position:0% +top line of this equation minus the + + + align:start position:0% +top line of this equation minus the +derivative on the left + + align:start position:0% +derivative on the left + + + align:start position:0% +derivative on the left +side this one the derivative so this is + + align:start position:0% +side this one the derivative so this is + + + align:start position:0% +side this one the derivative so this is +Kappa a e to the Kappa + + align:start position:0% +Kappa a e to the Kappa + + + align:start position:0% +Kappa a e to the Kappa +Epsilon no Kappa minus + + align:start position:0% +Epsilon no Kappa minus + + + align:start position:0% +Epsilon no Kappa minus +Epsilon + + align:start position:0% + + + + align:start position:0% + +again so that's the left hand side the + + align:start position:0% +again so that's the left hand side the + + + align:start position:0% +again so that's the left hand side the +right hand side would be minus 2 m alpha + + align:start position:0% +right hand side would be minus 2 m alpha + + + align:start position:0% +right hand side would be minus 2 m alpha +h² p at zero well p at zero is + + align:start position:0% +h² p at zero well p at zero is + + + align:start position:0% +h² p at zero well p at zero is +a so that's what it gives us and we + + align:start position:0% +a so that's what it gives us and we + + + align:start position:0% +a so that's what it gives us and we +should take the limit as Epsilon goes to + + align:start position:0% +should take the limit as Epsilon goes to + + + align:start position:0% +should take the limit as Epsilon goes to +zero so if + + align:start position:0% +zero so if + + + align:start position:0% +zero so if +I this is going to one both of + + align:start position:0% +I this is going to one both of + + + align:start position:0% +I this is going to one both of +them so the left hand side is - 2 Kaa a + + align:start position:0% +them so the left hand side is - 2 Kaa a + + + align:start position:0% +them so the left hand side is - 2 Kaa a +and the right hand side is 2 + + align:start position:0% +and the right hand side is 2 + + + align:start position:0% +and the right hand side is 2 +m um + + align:start position:0% +m um + + + align:start position:0% +m um +Alpha over h^2 + + align:start position:0% +Alpha over h^2 + + + align:start position:0% +Alpha over h^2 +a so the twoos it's also minus I'm + + align:start position:0% +a so the twoos it's also minus I'm + + + align:start position:0% +a so the twoos it's also minus I'm +sorry so the twos + + align:start position:0% +sorry so the twos + + + align:start position:0% +sorry so the twos +cancel the a cancels you never should + + align:start position:0% +cancel the a cancels you never should + + + align:start position:0% +cancel the a cancels you never should +have expected to determine a unless you + + align:start position:0% +have expected to determine a unless you + + + align:start position:0% +have expected to determine a unless you +try to normalize the wave function + + align:start position:0% +try to normalize the wave function + + + align:start position:0% +try to normalize the wave function +solving for energy against States will + + align:start position:0% +solving for energy against States will + + + align:start position:0% +solving for energy against States will +never determine a the Shing equation is + + align:start position:0% +never determine a the Shing equation is + + + align:start position:0% +never determine a the Shing equation is +linear so a drops out the minus two + + align:start position:0% +linear so a drops out the minus two + + + align:start position:0% +linear so a drops out the minus two +drops out and + + align:start position:0% +drops out and + + + align:start position:0% +drops out and +Kappa is equal to + + align:start position:0% +Kappa is equal to + + + align:start position:0% +Kappa is equal to +m alpha over + + align:start position:0% + + + + align:start position:0% + +H2 + + align:start position:0% +H2 + + + align:start position:0% +H2 +so that's it that's great because Kappa + + align:start position:0% +so that's it that's great because Kappa + + + align:start position:0% +so that's it that's great because Kappa +is a just another name for the + + align:start position:0% +is a just another name for the + + + align:start position:0% +is a just another name for the +energy so I have Kaa m alpha over H2 so + + align:start position:0% +energy so I have Kaa m alpha over H2 so + + + align:start position:0% +energy so I have Kaa m alpha over H2 so +that's another name for the energy so + + align:start position:0% +that's another name for the energy so + + + align:start position:0% +that's another name for the energy so +let's go to the + + align:start position:0% +let's go to the + + + align:start position:0% +let's go to the +energy the energy is H bar^ squ Kaa + + align:start position:0% +energy the energy is H bar^ squ Kaa + + + align:start position:0% +energy the energy is H bar^ squ Kaa +minus I'm sorry minus h bar^ 2 Kaa 2/ 2 + + align:start position:0% +minus I'm sorry minus h bar^ 2 Kaa 2/ 2 + + + align:start position:0% +minus I'm sorry minus h bar^ 2 Kaa 2/ 2 +m so it's + + align:start position:0% +m so it's + + + align:start position:0% +m so it's +uh minus H bar squ Kappa squ would be m^ + + align:start position:0% +uh minus H bar squ Kappa squ would be m^ + + + align:start position:0% +uh minus H bar squ Kappa squ would be m^ +S Alpha squar H to the + + align:start position:0% +S Alpha squar H to the + + + align:start position:0% +S Alpha squar H to the +4th and there's a 2 + + align:start position:0% + + + + align:start position:0% + +m all these constants + + align:start position:0% +m all these constants + + + align:start position:0% +m all these constants +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +so Final + + align:start position:0% +so Final + + + align:start position:0% +so Final +Answer + + align:start position:0% +Answer + + + align:start position:0% +Answer +e the bound State energy is + + align:start position:0% +e the bound State energy is + + + align:start position:0% +e the bound State energy is +minus m + + align:start position:0% +minus m + + + align:start position:0% +minus m +alpha squar or minus m alpha + + align:start position:0% +alpha squar or minus m alpha + + + align:start position:0% +alpha squar or minus m alpha +squar M cancels the over H + + align:start position:0% +squar M cancels the over H + + + align:start position:0% +squar M cancels the over H +2ar minus + + align:start position:0% + + + + align:start position:0% + +12 so back + + align:start position:0% +12 so back + + + align:start position:0% +12 so back +here the units worked out everything is + + align:start position:0% +here the units worked out everything is + + + align:start position:0% +here the units worked out everything is +good and the number was determined this + + align:start position:0% +good and the number was determined this + + + align:start position:0% +good and the number was determined this +minus + + align:start position:0% +minus + + + align:start position:0% +minus +one2 that's your bound State energy for + + align:start position:0% +one2 that's your bound State energy for + + + align:start position:0% +one2 that's your bound State energy for +this problem + + align:start position:0% +this problem + + + align:start position:0% +this problem +so uh this problem is instructive + + align:start position:0% +so uh this problem is instructive + + + align:start position:0% +so uh this problem is instructive +because you basically learn that in + + align:start position:0% +because you basically learn that in + + + align:start position:0% +because you basically learn that in +Delta functions with one Delta function + + align:start position:0% +Delta functions with one Delta function + + + align:start position:0% +Delta functions with one Delta function +you get a bound state if you have two + + align:start position:0% +you get a bound state if you have two + + + align:start position:0% +you get a bound state if you have two +Delta functions you may get more bound + + align:start position:0% +Delta functions you may get more bound + + + align:start position:0% +Delta functions you may get more bound +States three four people study those + + align:start position:0% +States three four people study those + + + align:start position:0% +States three four people study those +problems and you will investigate the + + align:start position:0% +problems and you will investigate the + + + align:start position:0% +problems and you will investigate the +two Delta function case \ No newline at end of file diff --git a/20GlFVyxqHY.txt b/20GlFVyxqHY.txt new file mode 100644 index 0000000000000000000000000000000000000000..c9b13467a2807c7c60bde563f7ca0ac3ed743e47 --- /dev/null +++ b/20GlFVyxqHY.txt @@ -0,0 +1,198 @@ +[MUSIC PLAYING] + +PROFESSOR: Hello, everyone. + +In our last demo, +we demonstrated + +how the electrical +conductivity of silicon + +can be changed by over +six orders of magnitude + +by adding dopants +that can increase + +the number of free or mobile +charges in the material. + +Today, we'll show how we can use +light to break electronic bonds + +and silicon, and create +free mobile charges. + +The principles +we'll be using today + +can be applied to +everything from sun screen, + +to of course, solar cells. + +We'll use the undoped, or +intrinsic silicon sample + +from our last demo, and measure +how the conductivity changes + +when we shine light on it. + +Our set up is identical +to that of last time. + +We'll take a piece of +silicon with metal contacts. + +We'll use an ohmmeter that we +connect to our sample via metal + +wires to measure +its conductivity. + +The measured resistance +will be determined + +by the conductivity and the +size and shape of our sample. + +Finally, we represent +the connectivity + +in terms of our measured +values and relate it + +to the number of +free, mobile charges, + +and the material +properties of silicon. + +We'll first measure the +conductivity of our sample + +in the dark, and then +shine light on our sample + +and see how the +conductivity changes. + +Our ohmmeter is hooked +up to our sample, + +and we measure a resistance +of around 120,000 ohms, which + +is equivalent to a conductivity +of around 0.0002 inverse ohm + +centimeters. + +Now, let's flip on the light. + +We can see that we measure +a slightly lower resistance + +of around 40,000 ohms, +but what is light + +doing to affect the +conductivity so much. + +Let's zoom in to the atomic +level and explore why. + +We see here a 2D representation +of a pure silicon crystal where + +all the valence electrons +form rigid covalent bonds, + +are immobile, and don't allow +the flow of electricity. + +This material +structure is identical + +to our intrinsic sample +when in the dark, + +which has a very +low conductivity. + +When light hits our sample, +photons of sufficient energy + +can break these covalent bonds, +injecting the formally immobile + +electron, giving enough +energy to move around. + +The mobile electron leaves +behind a mobile hole, + +which can move +through the crystal + +by swapping positions with +neighboring covalently bonded + +electrons. + +This explains why +the light increases + +the conductivity of our sample. + +Again, our conductivity +is determined primarily + +by the number of mobile charges. + +Light creates additional +pairs of mobile electrons, + +and holes, thus increasing +n and our conductivity. + +We've demonstrated that +light is able to generate + +fee carriers in our +ultra-pure sample. + +The same effect still +happens in dope silicon, + +but the light induced +change in conductivity + +only creates a small +relative change + +that we can't measure +using our ohm meter. + +Generating these +extra mobile charges + +by breaking covalent +bonds with light + +is the source of the +electricity that we eventually + +collect in our solar cell. + +In the next video, we'll explain +how these light generated + +mobile charges will be collected +and converted into electricity. + +I'm Joe Sullivan, +thanks for watching. + +[MUSIC PLAYING] \ No newline at end of file diff --git a/2KbvJ3iapbc.txt b/2KbvJ3iapbc.txt new file mode 100644 index 0000000000000000000000000000000000000000..fbb3a6089af8e7cda577341d05fd67681e40e47f --- /dev/null +++ b/2KbvJ3iapbc.txt @@ -0,0 +1,16816 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so really + + align:start position:0% +ocw.mit.edu so really + + + align:start position:0% +ocw.mit.edu so really +what my + + align:start position:0% +what my + + + align:start position:0% +what my +main concern it has been for quite a few + + align:start position:0% +main concern it has been for quite a few + + + align:start position:0% +main concern it has been for quite a few +years uh is + + align:start position:0% +years uh is + + + align:start position:0% +years uh is +to make some theory of + + align:start position:0% + + + + align:start position:0% + +how uh what makes people able to solve + + align:start position:0% +how uh what makes people able to solve + + + align:start position:0% +how uh what makes people able to solve +so many kinds of problems I guess if you + + align:start position:0% +so many kinds of problems I guess if you + + + align:start position:0% +so many kinds of problems I guess if you +ran through the spectrum of all the + + align:start position:0% + + + + align:start position:0% + +animals you'd find lots of problems that + + align:start position:0% +animals you'd find lots of problems that + + + align:start position:0% +animals you'd find lots of problems that +some animals can solve and people can't + + align:start position:0% +some animals can solve and people can't + + + align:start position:0% +some animals can solve and people can't +like uh how many of you could build a + + align:start position:0% +like uh how many of you could build a + + + align:start position:0% +like uh how many of you could build a +beaver + + align:start position:0% +beaver + + + align:start position:0% +beaver +dam + + align:start position:0% +dam + + + align:start position:0% +dam +and or a termite + + align:start position:0% +and or a termite + + + align:start position:0% +and or a termite +Nest so there are all sorts of things + + align:start position:0% +Nest so there are all sorts of things + + + align:start position:0% +Nest so there are all sorts of things +that Evolution manages to + + align:start position:0% +that Evolution manages to + + + align:start position:0% +that Evolution manages to +produce but maybe the most impressive + + align:start position:0% +produce but maybe the most impressive + + + align:start position:0% +produce but maybe the most impressive +one is the what the human infant can + + align:start position:0% +one is the what the human infant can + + + align:start position:0% +one is the what the human infant can +do um just by hanging around for 10 or + + align:start position:0% +do um just by hanging around for 10 or + + + align:start position:0% +do um just by hanging around for 10 or +20 or 30 years and uh watching what + + align:start position:0% +20 or 30 years and uh watching what + + + align:start position:0% +20 or 30 years and uh watching what +other humans can + + align:start position:0% +other humans can + + + align:start position:0% +other humans can +do so we can solve all sorts of problems + + align:start position:0% +do so we can solve all sorts of problems + + + align:start position:0% +do so we can solve all sorts of problems +and uh my quarrel with + + align:start position:0% +and uh my quarrel with + + + align:start position:0% +and uh my quarrel with +the rest of the most of the artificial + + align:start position:0% +the rest of the most of the artificial + + + align:start position:0% +the rest of the most of the artificial +intelligence Community has been that + + align:start position:0% +intelligence Community has been that + + + align:start position:0% +intelligence Community has been that +uh the great success of Science in the + + align:start position:0% +uh the great success of Science in the + + + align:start position:0% +uh the great success of Science in the +last 500 years + + align:start position:0% +last 500 years + + + align:start position:0% +last 500 years +really has been in physics and it's been + + align:start position:0% +really has been in physics and it's been + + + align:start position:0% +really has been in physics and it's been +uh rewarded by finding little sets of + + align:start position:0% +uh rewarded by finding little sets of + + + align:start position:0% +uh rewarded by finding little sets of +rules like Newton's three laws and + + align:start position:0% +rules like Newton's three laws and + + + align:start position:0% +rules like Newton's three laws and +Maxwell's four + + align:start position:0% +Maxwell's four + + + align:start position:0% +Maxwell's four +laws and uh Einstein's one law or + + align:start position:0% + + + + align:start position:0% + +two that + + align:start position:0% +two that + + + align:start position:0% +two that +explained a huge range of everyday + + align:start position:0% +explained a huge range of everyday + + + align:start position:0% +explained a huge range of everyday +phenomena of course in the 19 20s and + + align:start position:0% +phenomena of course in the 19 20s and + + + align:start position:0% +phenomena of course in the 19 20s and +30s that apple cart got upset + + align:start position:0% +30s that apple cart got upset + + + align:start position:0% +30s that apple cart got upset +because actually uh Einstein himself who + + align:start position:0% +because actually uh Einstein himself who + + + align:start position:0% +because actually uh Einstein himself who +had discovered the first Quantum + + align:start position:0% +had discovered the first Quantum + + + align:start position:0% +had discovered the first Quantum +phenomenon namely the uh quantization of + + align:start position:0% +phenomenon namely the uh quantization of + + + align:start position:0% +phenomenon namely the uh quantization of +photons + + align:start position:0% +photons + + + align:start position:0% +photons +uh had produced various uh scientific + + align:start position:0% +uh had produced various uh scientific + + + align:start position:0% +uh had produced various uh scientific +laboratory observations that were + + align:start position:0% +laboratory observations that were + + + align:start position:0% +laboratory observations that were +inexplicable uh in terms of either + + align:start position:0% +inexplicable uh in terms of either + + + align:start position:0% +inexplicable uh in terms of either +Maxwell or Newton or Einstein's earlier + + align:start position:0% +Maxwell or Newton or Einstein's earlier + + + align:start position:0% +Maxwell or Newton or Einstein's earlier +formulations + + align:start position:0% +formulations + + + align:start position:0% +formulations +so + + align:start position:0% +so + + + align:start position:0% +so +uh my picture of the history is that in + + align:start position:0% +uh my picture of the history is that in + + + align:start position:0% +uh my picture of the history is that in +the 19th century and a little bit + + align:start position:0% +the 19th century and a little bit + + + align:start position:0% +the 19th century and a little bit +earlier going back to lock and Spinosa + + align:start position:0% +earlier going back to lock and Spinosa + + + align:start position:0% +earlier going back to lock and Spinosa +and Hume and a few of those philosophers + + align:start position:0% +and Hume and a few of those philosophers + + + align:start position:0% +and Hume and a few of those philosophers +even Emanuel count they had some pretty + + align:start position:0% +even Emanuel count they had some pretty + + + align:start position:0% +even Emanuel count they had some pretty +good psychological ideas and as I + + align:start position:0% +good psychological ideas and as I + + + align:start position:0% +good psychological ideas and as I +mentioned the other day uh I suspect + + align:start position:0% +mentioned the other day uh I suspect + + + align:start position:0% +mentioned the other day uh I suspect +that + + align:start position:0% +that + + + align:start position:0% +that +Aristotle uh was more like a modern + + align:start position:0% +Aristotle uh was more like a modern + + + align:start position:0% +Aristotle uh was more like a modern +cognitive psychologist and had even + + align:start position:0% +cognitive psychologist and had even + + + align:start position:0% +cognitive psychologist and had even +better ideas but uh we've probably lost + + align:start position:0% +better ideas but uh we've probably lost + + + align:start position:0% +better ideas but uh we've probably lost +a lot of them because there are no tape + + align:start position:0% +a lot of them because there are no tape + + + align:start position:0% +a lot of them because there are no tape +recorders who knows what Aristotle and + + align:start position:0% +recorders who knows what Aristotle and + + + align:start position:0% +recorders who knows what Aristotle and +Plato Plato said that their students + + align:start position:0% +Plato Plato said that their students + + + align:start position:0% +Plato Plato said that their students +didn't write down because it sounded + + align:start position:0% + + + + align:start position:0% + +silly + + align:start position:0% +silly + + + align:start position:0% +silly +uh so uh + + align:start position:0% + + + + align:start position:0% + +the idea that + + align:start position:0% +the idea that + + + align:start position:0% +the idea that +uh we developed around here mostly uh SE + + align:start position:0% +uh we developed around here mostly uh SE + + + align:start position:0% +uh we developed around here mostly uh SE +more paper and uh a lot of students Pat + + align:start position:0% +more paper and uh a lot of students Pat + + + align:start position:0% +more paper and uh a lot of students Pat +Winston + + align:start position:0% +Winston + + + align:start position:0% +Winston +was one of the great stars of that + + align:start position:0% +was one of the great stars of that + + + align:start position:0% +was one of the great stars of that +period was the idea + + align:start position:0% +period was the idea + + + align:start position:0% +period was the idea +that uh to get anything like + + align:start position:0% +that uh to get anything like + + + align:start position:0% +that uh to get anything like +human uh intellectual abilities you're + + align:start position:0% +human uh intellectual abilities you're + + + align:start position:0% +human uh intellectual abilities you're +going to have to have all sorts of high + + align:start position:0% +going to have to have all sorts of high + + + align:start position:0% +going to have to have all sorts of high +level + + align:start position:0% +level + + + align:start position:0% +level +representations so one has to say the + + align:start position:0% +representations so one has to say the + + + align:start position:0% +representations so one has to say the +old conditioned reflex of stimulus + + align:start position:0% +old conditioned reflex of stimulus + + + align:start position:0% +old conditioned reflex of stimulus +versus stimulus producing a + + align:start position:0% +versus stimulus producing a + + + align:start position:0% +versus stimulus producing a +response uh isn't good enough you the + + align:start position:0% +response uh isn't good enough you the + + + align:start position:0% +response uh isn't good enough you the +stimulus has to be represented by some + + align:start position:0% +stimulus has to be represented by some + + + align:start position:0% +stimulus has to be represented by some +kind of semantic structure somewhere in + + align:start position:0% +kind of semantic structure somewhere in + + + align:start position:0% +kind of semantic structure somewhere in +the brain or + + align:start position:0% +the brain or + + + align:start position:0% +the brain or +mind and so far as I know it's only in + + align:start position:0% +mind and so far as I know it's only in + + + align:start position:0% +mind and so far as I know it's only in +the theories + + align:start position:0% +the theories + + + align:start position:0% +the theories +of not even modern artificial + + align:start position:0% +of not even modern artificial + + + align:start position:0% +of not even modern artificial +intelligence but the the AI of the 60s + + align:start position:0% +intelligence but the the AI of the 60s + + + align:start position:0% +intelligence but the the AI of the 60s +and 70s and + + align:start position:0% +and 70s and + + + align:start position:0% +and 70s and +80s that people thought about what the + + align:start position:0% +80s that people thought about what the + + + align:start position:0% +80s that people thought about what the +what could be the internal + + align:start position:0% +what could be the internal + + + align:start position:0% +what could be the internal +representation of the kinds of things + + align:start position:0% +representation of the kinds of things + + + align:start position:0% +representation of the kinds of things +that that we think + + align:start position:0% +that that we think + + + align:start position:0% +that that we think +about um + + align:start position:0% +about um + + + align:start position:0% +about um +and uh even more important if one of + + align:start position:0% +and uh even more important if one of + + + align:start position:0% +and uh even more important if one of +those representations you see something + + align:start position:0% +those representations you see something + + + align:start position:0% +those representations you see something +or you remember some incident and your + + align:start position:0% +or you remember some incident and your + + + align:start position:0% +or you remember some incident and your +brain represents it in some way and if + + align:start position:0% +brain represents it in some way and if + + + align:start position:0% +brain represents it in some way and if +that way doesn't work you take a breath + + align:start position:0% +that way doesn't work you take a breath + + + align:start position:0% +that way doesn't work you take a breath +and you uh sort of stumble around and + + align:start position:0% +and you uh sort of stumble around and + + + align:start position:0% +and you uh sort of stumble around and +find another way to represent it maybe + + align:start position:0% +find another way to represent it maybe + + + align:start position:0% +find another way to represent it maybe +when the original event first happened + + align:start position:0% +when the original event first happened + + + align:start position:0% +when the original event first happened +uh you represented it in three or four + + align:start position:0% +uh you represented it in three or four + + + align:start position:0% +uh you represented it in three or four +ways and so we're beginning to + + align:start position:0% +ways and so we're beginning to + + + align:start position:0% +ways and so we're beginning to +see uh did anybody hear fi's + + align:start position:0% +see uh did anybody hear fi's + + + align:start position:0% +see uh did anybody hear fi's +talk uh the Watson guy was up + + align:start position:0% +talk uh the Watson guy was up + + + align:start position:0% +talk uh the Watson guy was up +here a couple of days ago I missed it + + align:start position:0% +here a couple of days ago I missed it + + + align:start position:0% +here a couple of days ago I missed it +but + + align:start position:0% +but + + + align:start position:0% +but +um they haven't made a technical + + align:start position:0% +um they haven't made a technical + + + align:start position:0% +um they haven't made a technical +publication as far as I know of how this + + align:start position:0% +publication as far as I know of how this + + + align:start position:0% +publication as far as I know of how this +Watson program works but it sounds like + + align:start position:0% +Watson program works but it sounds like + + + align:start position:0% +Watson program works but it sounds like +it's something of a interesting Society + + align:start position:0% +it's something of a interesting Society + + + align:start position:0% +it's something of a interesting Society +of Mind likee structure and it' be nice + + align:start position:0% +of Mind likee structure and it' be nice + + + align:start position:0% +of Mind likee structure and it' be nice +if they would has anybody read any long + + align:start position:0% +if they would has anybody read any long + + + align:start position:0% +if they would has anybody read any long +paper on it there have been a lot of + + align:start position:0% +paper on it there have been a lot of + + + align:start position:0% +paper on it there have been a lot of +press reports have you seen anything + + align:start position:0% +press reports have you seen anything + + + align:start position:0% +press reports have you seen anything +Pat Uh so anyway they seem to have + + align:start position:0% +Pat Uh so anyway they seem to have + + + align:start position:0% +Pat Uh so anyway they seem to have +uh done some sorts of Common Sense + + align:start position:0% +uh done some sorts of Common Sense + + + align:start position:0% +uh done some sorts of Common Sense +reasoning as I said the other day I + + align:start position:0% +reasoning as I said the other day I + + + align:start position:0% +reasoning as I said the other day I +doubt that Watson could understand why + + align:start position:0% +doubt that Watson could understand why + + + align:start position:0% +doubt that Watson could understand why +you can pull something with a string but + + align:start position:0% +you can pull something with a string but + + + align:start position:0% +you can pull something with a string but +you can't + + align:start position:0% +you can't + + + align:start position:0% +you can't +push and uh actually I don't know if any + + align:start position:0% +push and uh actually I don't know if any + + + align:start position:0% +push and uh actually I don't know if any +existing program can understand that yet + + align:start position:0% +existing program can understand that yet + + + align:start position:0% +existing program can understand that yet +uh I saw some amazing demonstrations + + align:start position:0% +uh I saw some amazing demonstrations + + + align:start position:0% +uh I saw some amazing demonstrations +Yesterday + + align:start position:0% +Yesterday + + + align:start position:0% +Yesterday +by um or Monday by + + align:start position:0% +by um or Monday by + + + align:start position:0% +by um or Monday by +uh W Steve Wolfram of uh his Wolfram + + align:start position:0% +uh W Steve Wolfram of uh his Wolfram + + + align:start position:0% +uh W Steve Wolfram of uh his Wolfram +Alpha which doesn't do much Common Sense + + align:start position:0% +Alpha which doesn't do much Common Sense + + + align:start position:0% +Alpha which doesn't do much Common Sense +reasoning but it has what it does do is + + align:start position:0% +reasoning but it has what it does do is + + + align:start position:0% +reasoning but it has what it does do is +uh if you put in a sentence it finds + + align:start position:0% +uh if you put in a sentence it finds + + + align:start position:0% +uh if you put in a sentence it finds +five or 10 different representations + + align:start position:0% +five or 10 different representations + + + align:start position:0% +five or 10 different representations +anything he can find that's sort of + + align:start position:0% +anything he can find that's sort of + + + align:start position:0% +anything he can find that's sort of +mathematical and so when you ask it a + + align:start position:0% +mathematical and so when you ask it a + + + align:start position:0% +mathematical and so when you ask it a +question it gives you 10 answers and + + align:start position:0% +question it gives you 10 answers and + + + align:start position:0% +question it gives you 10 answers and +it's much better than previous systems + + align:start position:0% +it's much better than previous systems + + + align:start position:0% +it's much better than previous systems +because it doesn't U well Google gives + + align:start position:0% +because it doesn't U well Google gives + + + align:start position:0% +because it doesn't U well Google gives +you uh a quarter million answers but + + align:start position:0% +you uh a quarter million answers but + + + align:start position:0% +you uh a quarter million answers but +that's too many and + + align:start position:0% + + + + align:start position:0% + +anyway I'm just going to talk a little + + align:start position:0% +anyway I'm just going to talk a little + + + align:start position:0% +anyway I'm just going to talk a little +bit more and + + align:start position:0% +bit more and + + + align:start position:0% +bit more and +just everybody should be trying to think + + align:start position:0% +just everybody should be trying to think + + + align:start position:0% +just everybody should be trying to think +of a question that the rest of the + + align:start position:0% +of a question that the rest of the + + + align:start position:0% +of a question that the rest of the +class might + + align:start position:0% +class might + + + align:start position:0% +class might +answer so there are lots of different + + align:start position:0% +answer so there are lots of different + + + align:start position:0% +answer so there are lots of different +kinds of problems that people can solve + + align:start position:0% +kinds of problems that people can solve + + + align:start position:0% +kinds of problems that people can solve +going back to the first one like which + + align:start position:0% +going back to the first one like which + + + align:start position:0% +going back to the first one like which +moving object out there is my mother or + + align:start position:0% +moving object out there is my mother or + + + align:start position:0% +moving object out there is my mother or +and which might be a Potential + + align:start position:0% +and which might be a Potential + + + align:start position:0% +and which might be a Potential +Threat so there a lot of kinds of + + align:start position:0% +Threat so there a lot of kinds of + + + align:start position:0% +Threat so there a lot of kinds of +problems that we + + align:start position:0% +problems that we + + + align:start position:0% +problems that we +solve and I've never seen any discussion + + align:start position:0% +solve and I've never seen any discussion + + + align:start position:0% +solve and I've never seen any discussion +in psychology books + + align:start position:0% + + + + align:start position:0% + +of what are the activities princip + + align:start position:0% +of what are the activities princip + + + align:start position:0% +of what are the activities princip +activities of Common Sense + + align:start position:0% +activities of Common Sense + + + align:start position:0% +activities of Common Sense +thinking + + align:start position:0% +thinking + + + align:start position:0% +thinking +somehow + + align:start position:0% + + + + align:start position:0% + +uh they don't have or people don't + + align:start position:0% +uh they don't have or people don't + + + align:start position:0% +uh they don't have or people don't +before computers there really wasn't any + + align:start position:0% +before computers there really wasn't any + + + align:start position:0% +before computers there really wasn't any +way to think about high Lev thinking + + align:start position:0% +way to think about high Lev thinking + + + align:start position:0% +way to think about high Lev thinking +because there weren't any technical + + align:start position:0% +because there weren't any technical + + + align:start position:0% +because there weren't any technical +technically usable ways to describe + + align:start position:0% +technically usable ways to describe + + + align:start position:0% +technically usable ways to describe +complicated processes the idea of a + + align:start position:0% +complicated processes the idea of a + + + align:start position:0% +complicated processes the idea of a +conditional uh expression ression was + + align:start position:0% +conditional uh expression ression was + + + align:start position:0% +conditional uh expression ression was +was barely on the threshold of of + + align:start position:0% +was barely on the threshold of of + + + align:start position:0% +was barely on the threshold of of +psychology so what kinds of problems do + + align:start position:0% +psychology so what kinds of problems do + + + align:start position:0% +psychology so what kinds of problems do +we have and if you take some particular + + align:start position:0% +we have and if you take some particular + + + align:start position:0% +we have and if you take some particular +problem like + + align:start position:0% +problem like + + + align:start position:0% +problem like +uh I find these days I can't get the top + + align:start position:0% +uh I find these days I can't get the top + + + align:start position:0% +uh I find these days I can't get the top +off bottles so how do I solve that and + + align:start position:0% +off bottles so how do I solve that and + + + align:start position:0% +off bottles so how do I solve that and +uh there lots of answers uh one is you + + align:start position:0% +uh there lots of answers uh one is you + + + align:start position:0% +uh there lots of answers uh one is you +look for somebody who looks really + + align:start position:0% +look for somebody who looks really + + + align:start position:0% +look for somebody who looks really +strong + + align:start position:0% +strong + + + align:start position:0% +strong +or you reach into your pocket + + align:start position:0% + + + + align:start position:0% + +and you probably have one of + + align:start position:0% +and you probably have one of + + + align:start position:0% +and you probably have one of +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +these and so on there must be some way + + align:start position:0% +these and so on there must be some way + + + align:start position:0% +these and so on there must be some way +to put it on the floor and step on it + + align:start position:0% +to put it on the floor and step on it + + + align:start position:0% +to put it on the floor and step on it +and kick it with the other foot but + + align:start position:0% +and kick it with the other foot but + + + align:start position:0% +and kick it with the other foot but +uh so there are lots of uh problems that + + align:start position:0% +uh so there are lots of uh problems that + + + align:start position:0% +uh so there are lots of uh problems that +we're facing every day and uh if you + + align:start position:0% +we're facing every day and uh if you + + + align:start position:0% +we're facing every day and uh if you +look in traditional cognitive psychology + + align:start position:0% +look in traditional cognitive psychology + + + align:start position:0% +look in traditional cognitive psychology +you're well what's the worst Theory the + + align:start position:0% +you're well what's the worst Theory the + + + align:start position:0% +you're well what's the worst Theory the +worst and the best theory was got + + align:start position:0% +worst and the best theory was got + + + align:start position:0% +worst and the best theory was got +popular in in the 1980s it was called + + align:start position:0% +popular in in the 1980s it was called + + + align:start position:0% +popular in in the 1980s it was called +rule-based systems and you just have a + + align:start position:0% +rule-based systems and you just have a + + + align:start position:0% +rule-based systems and you just have a +big Library which says if you have a + + align:start position:0% +big Library which says if you have a + + + align:start position:0% +big Library which says if you have a +soda bottle and you can't get the cap + + align:start position:0% +soda bottle and you can't get the cap + + + align:start position:0% +soda bottle and you can't get the cap +off then do this or that or the other + + align:start position:0% +off then do this or that or the other + + + align:start position:0% +off then do this or that or the other +and so some people uh decided Well + + align:start position:0% +and so some people uh decided Well + + + align:start position:0% +and so some people uh decided Well +that's really all you need + + align:start position:0% +that's really all you need + + + align:start position:0% +that's really all you need +Rod Brooks in the + + align:start position:0% +Rod Brooks in the + + + align:start position:0% +Rod Brooks in the +1980s uh sort of said we don't need + + align:start position:0% +1980s uh sort of said we don't need + + + align:start position:0% +1980s uh sort of said we don't need +those fancy theories that people like + + align:start position:0% +those fancy theories that people like + + + align:start position:0% +those fancy theories that people like +Minsky and paper and Winston are working + + align:start position:0% +Minsky and paper and Winston are working + + + align:start position:0% +Minsky and paper and Winston are working +on why not just say for each situation + + align:start position:0% +on why not just say for each situation + + + align:start position:0% +on why not just say for each situation +in the outer world uh have a rule that + + align:start position:0% +in the outer world uh have a rule that + + + align:start position:0% +in the outer world uh have a rule that +says how to deal with that situation + + align:start position:0% +says how to deal with that situation + + + align:start position:0% +says how to deal with that situation +let's make a hierarchy of them and he + + align:start position:0% +let's make a hierarchy of them and he + + + align:start position:0% +let's make a hierarchy of them and he +described a system that sort of looked + + align:start position:0% +described a system that sort of looked + + + align:start position:0% +described a system that sort of looked +like the priority interrupt system in a + + align:start position:0% +like the priority interrupt system in a + + + align:start position:0% +like the priority interrupt system in a +computer computer and + + align:start position:0% +computer computer and + + + align:start position:0% +computer computer and +uh and he won all sorts of prizes for + + align:start position:0% +uh and he won all sorts of prizes for + + + align:start position:0% +uh and he won all sorts of prizes for +this really bad idea that's spread + + align:start position:0% +this really bad idea that's spread + + + align:start position:0% +this really bad idea that's spread +around the world and but it solved a lot + + align:start position:0% +around the world and but it solved a lot + + + align:start position:0% +around the world and but it solved a lot +of problems uh there are things about + + align:start position:0% +of problems uh there are things about + + + align:start position:0% +of problems uh there are things about +priority interrup that aren't obvious + + align:start position:0% +priority interrup that aren't obvious + + + align:start position:0% +priority interrup that aren't obvious +like suppose you + + align:start position:0% +like suppose you + + + align:start position:0% +like suppose you +have uh in the first computers there was + + align:start position:0% +have uh in the first computers there was + + + align:start position:0% +have uh in the first computers there was +some problem because uh what should you + + align:start position:0% +some problem because uh what should you + + + align:start position:0% +some problem because uh what should you +do if there's several signals coming + + align:start position:0% +do if there's several signals coming + + + align:start position:0% +do if there's several signals coming +into the computer and you want to + + align:start position:0% +into the computer and you want to + + + align:start position:0% +into the computer and you want to +respond to them and some of the signals + + align:start position:0% +respond to them and some of the signals + + + align:start position:0% +respond to them and some of the signals +are very fast and very + + align:start position:0% +are very fast and very + + + align:start position:0% +are very fast and very +short then you might think well I should + + align:start position:0% +short then you might think well I should + + + align:start position:0% +short then you might think well I should +give the highest priority to the signal + + align:start position:0% +give the highest priority to the signal + + + align:start position:0% +give the highest priority to the signal +that's going to be there the the + + align:start position:0% +that's going to be there the the + + + align:start position:0% +that's going to be there the the +shortest time something like that the + + align:start position:0% +shortest time something like that the + + + align:start position:0% +shortest time something like that the +funny part is that when you made such a + + align:start position:0% +funny part is that when you made such a + + + align:start position:0% +funny part is that when you made such a +system the result was that if if you had + + align:start position:0% +system the result was that if if you had + + + align:start position:0% +system the result was that if if you had +a computer that was responding to some + + align:start position:0% +a computer that was responding to some + + + align:start position:0% +a computer that was responding to some +signal that's coming in at a uh I'm + + align:start position:0% +signal that's coming in at a uh I'm + + + align:start position:0% +signal that's coming in at a uh I'm +talking about the days when computers + + align:start position:0% +talking about the days when computers + + + align:start position:0% +talking about the days when computers +were only working at a few kilohertz few + + align:start position:0% +were only working at a few kilohertz few + + + align:start position:0% +were only working at a few kilohertz few +thousand operations a second God that's + + align:start position:0% +thousand operations a second God that's + + + align:start position:0% +thousand operations a second God that's +slow million times shorter than what you + + align:start position:0% +slow million times shorter than what you + + + align:start position:0% +slow million times shorter than what you +have in your + + align:start position:0% +have in your + + + align:start position:0% +have in your +pocket and + + align:start position:0% +pocket and + + + align:start position:0% +pocket and +uh if you give priority to the signals + + align:start position:0% +uh if you give priority to the signals + + + align:start position:0% +uh if you give priority to the signals +that have to be reacted to very fast + + align:start position:0% +that have to be reacted to very fast + + + align:start position:0% +that have to be reacted to very fast +then what happens if you type to those + + align:start position:0% +then what happens if you type to those + + + align:start position:0% +then what happens if you type to those +computers it would never see them + + align:start position:0% +computers it would never see them + + + align:start position:0% +computers it would never see them +because it's always I saw this happening + + align:start position:0% +because it's always I saw this happening + + + align:start position:0% +because it's always I saw this happening +once and finally somebody realized that + + align:start position:0% +once and finally somebody realized that + + + align:start position:0% +once and finally somebody realized that +uh you should give the highest priority + + align:start position:0% +uh you should give the highest priority + + + align:start position:0% +uh you should give the highest priority +to the uh to the inputs that come in + + align:start position:0% +to the uh to the inputs that come in + + + align:start position:0% +to the uh to the inputs that come in +most least + + align:start position:0% +most least + + + align:start position:0% +most least +frequently because there's always + + align:start position:0% +frequently because there's always + + + align:start position:0% +frequently because there's always +otherwise if there's something coming in + + align:start position:0% +otherwise if there's something coming in + + + align:start position:0% +otherwise if there's something coming in +very frequently you'll just always be + + align:start position:0% +very frequently you'll just always be + + + align:start position:0% +very frequently you'll just always be +responding to it any of you run into + + align:start position:0% +responding to it any of you run into + + + align:start position:0% +responding to it any of you run into +this + + align:start position:0% +this + + + align:start position:0% +this +um took me while to figure out why uh + + align:start position:0% +um took me while to figure out why uh + + + align:start position:0% +um took me while to figure out why uh +anyway there are lots of kinds of + + align:start position:0% +anyway there are lots of kinds of + + + align:start position:0% +anyway there are lots of kinds of +problems + + align:start position:0% + + + + align:start position:0% + +and um the other day I was complaining + + align:start position:0% +and um the other day I was complaining + + + align:start position:0% +and um the other day I was complaining +that we didn't have enough ways to just + + align:start position:0% +that we didn't have enough ways to just + + + align:start position:0% +that we didn't have enough ways to just +we had hundreds of words for + + align:start position:0% +we had hundreds of words for + + + align:start position:0% +we had hundreds of words for +emotions and + + align:start position:0% +emotions and + + + align:start position:0% +emotions and +uh here's a couple of dozen they're in + + align:start position:0% +uh here's a couple of dozen they're in + + + align:start position:0% +uh here's a couple of dozen they're in +chapters seven and8 actually most of + + align:start position:0% +chapters seven and8 actually most of + + + align:start position:0% +chapters seven and8 actually most of +these so here's a bunch of uh words for + + align:start position:0% +these so here's a bunch of uh words for + + + align:start position:0% +these so here's a bunch of uh words for +describing ways to think but they're not + + align:start position:0% +describing ways to think but they're not + + + align:start position:0% +describing ways to think but they're not +very technical so you can talk about + + align:start position:0% +very technical so you can talk about + + + align:start position:0% +very technical so you can talk about +remorse and sorrow and blah blah blah + + align:start position:0% +remorse and sorrow and blah blah blah + + + align:start position:0% +remorse and sorrow and blah blah blah +hundreds and hundreds of words for for + + align:start position:0% +hundreds and hundreds of words for for + + + align:start position:0% +hundreds and hundreds of words for for +feelings and it's a lot of effort to + + align:start position:0% +feelings and it's a lot of effort to + + + align:start position:0% +feelings and it's a lot of effort to +find a dozen words for uh for + + align:start position:0% +find a dozen words for uh for + + + align:start position:0% +find a dozen words for uh for +intellectual + + align:start position:0% +intellectual + + + align:start position:0% +intellectual +for what should I call them problem + + align:start position:0% +for what should I call them problem + + + align:start position:0% +for what should I call them problem +solving + + align:start position:0% +solving + + + align:start position:0% +solving +processes so it's curious ious to me + + align:start position:0% +processes so it's curious ious to me + + + align:start position:0% +processes so it's curious ious to me +that the the great field called + + align:start position:0% +that the the great field called + + + align:start position:0% +that the the great field called +cognitive psychology + + align:start position:0% +cognitive psychology + + + align:start position:0% +cognitive psychology +has not focused in that direction anyway + + align:start position:0% +has not focused in that direction anyway + + + align:start position:0% +has not focused in that direction anyway +here's about 20 or 30 of them and you'll + + align:start position:0% +here's about 20 or 30 of them and you'll + + + align:start position:0% +here's about 20 or 30 of them and you'll +find them scattered through chapters + + align:start position:0% +find them scattered through chapters + + + align:start position:0% +find them scattered through chapters +seven and + + align:start position:0% + + + + align:start position:0% + +8 here's my favorite one and I don't + + align:start position:0% +8 here's my favorite one and I don't + + + align:start position:0% +8 here's my favorite one and I don't +know of any proper name for it but uh if + + align:start position:0% +know of any proper name for it but uh if + + + align:start position:0% +know of any proper name for it but uh if +you're trying to solve a problem and + + align:start position:0% +you're trying to solve a problem and + + + align:start position:0% +you're trying to solve a problem and +you're + + align:start position:0% +you're + + + align:start position:0% +you're +stuck and the example that comes to mind + + align:start position:0% +stuck and the example that comes to mind + + + align:start position:0% +stuck and the example that comes to mind +my mind is uh if I'm trying to remember + + align:start position:0% +my mind is uh if I'm trying to remember + + + align:start position:0% +my mind is uh if I'm trying to remember +someone's name I can tell when it's + + align:start position:0% +someone's name I can tell when it's + + + align:start position:0% +someone's name I can tell when it's +hopeless + + align:start position:0% +hopeless + + + align:start position:0% +hopeless +and the reason + + align:start position:0% + + + + align:start position:0% + +is that for somehow or other I know that + + align:start position:0% +is that for somehow or other I know that + + + align:start position:0% +is that for somehow or other I know that +there's a huge tree of + + align:start position:0% +there's a huge tree of + + + align:start position:0% +there's a huge tree of +choices that's one way to represent + + align:start position:0% +choices that's one way to represent + + + align:start position:0% +choices that's one way to represent +what's going on and you know I might + + align:start position:0% +what's going on and you know I might + + + align:start position:0% +what's going on and you know I might +know that I'm sure that that letter that + + align:start position:0% +know that I'm sure that that letter that + + + align:start position:0% +know that I'm sure that that letter that +name has a z in it so you search around + + align:start position:0% +name has a z in it so you search around + + + align:start position:0% +name has a z in it so you search around +and uh try everything you can but of + + align:start position:0% +and uh try everything you can but of + + + align:start position:0% +and uh try everything you can but of +course it doesn't have a z + + align:start position:0% +course it doesn't have a z + + + align:start position:0% +course it doesn't have a z +it's uh so + + align:start position:0% +it's uh so + + + align:start position:0% +it's uh so +you're so the way to the way to solve + + align:start position:0% +you're so the way to the way to solve + + + align:start position:0% +you're so the way to the way to solve +that problem is to uh give + + align:start position:0% +that problem is to uh give + + + align:start position:0% +that problem is to uh give +up and then a couple of minutes + + align:start position:0% +up and then a couple of minutes + + + align:start position:0% +up and then a couple of minutes +later + + align:start position:0% +later + + + align:start position:0% +later +uh the name occurs to you and you have + + align:start position:0% +uh the name occurs to you and you have + + + align:start position:0% +uh the name occurs to you and you have +no idea how it happened and + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so forth so anyway the long story is + + align:start position:0% +so forth so anyway the long story is + + + align:start position:0% +so forth so anyway the long story is +that uh PT and I and lots of lots of uh + + align:start position:0% +that uh PT and I and lots of lots of uh + + + align:start position:0% +that uh PT and I and lots of lots of uh +really great students in the 60s and + + align:start position:0% +really great students in the 60s and + + + align:start position:0% +really great students in the 60s and +70s uh spent a lot of time making little + + align:start position:0% +70s uh spent a lot of time making little + + + align:start position:0% +70s uh spent a lot of time making little +models of problem solvers that didn't + + align:start position:0% +models of problem solvers that didn't + + + align:start position:0% +models of problem solvers that didn't +work and uh we discover that uh you + + align:start position:0% +work and uh we discover that uh you + + + align:start position:0% +work and uh we discover that uh you +needed something else and we put that in + + align:start position:0% +needed something else and we put that in + + + align:start position:0% +needed something else and we put that in +uh other people people would come say + + align:start position:0% +uh other people people would come say + + + align:start position:0% +uh other people people would come say +that's hopeless uh you're putting in + + align:start position:0% +that's hopeless uh you're putting in + + + align:start position:0% +that's hopeless uh you're putting in +more things than you + + align:start position:0% +more things than you + + + align:start position:0% +more things than you +need + + align:start position:0% +need + + + align:start position:0% +need +and my conclusion is that uh wow it's + + align:start position:0% +and my conclusion is that uh wow it's + + + align:start position:0% +and my conclusion is that uh wow it's +the opposite of physics in physics + + align:start position:0% +the opposite of physics in physics + + + align:start position:0% +the opposite of physics in physics +you're always trying to find you don't + + align:start position:0% +you're always trying to find you don't + + + align:start position:0% +you're always trying to find you don't +want to what is it called aam's + + align:start position:0% +want to what is it called aam's + + + align:start position:0% +want to what is it called aam's +razor never have more structure than you + + align:start position:0% +razor never have more structure than you + + + align:start position:0% +razor never have more structure than you +need because because what uh well it'll + + align:start position:0% +need because because what uh well it'll + + + align:start position:0% +need because because what uh well it'll +waste your time but my feeling was I + + align:start position:0% +waste your time but my feeling was I + + + align:start position:0% +waste your time but my feeling was I +never have less than you'll need but you + + align:start position:0% +never have less than you'll need but you + + + align:start position:0% +never have less than you'll need but you +don't know how many you'll need so what + + align:start position:0% +don't know how many you'll need so what + + + align:start position:0% +don't know how many you'll need so what +I did I had four of these and then I + + align:start position:0% +I did I had four of these and then I + + + align:start position:0% +I did I had four of these and then I +forced myself to put in two more and + + align:start position:0% +forced myself to put in two more and + + + align:start position:0% +forced myself to put in two more and +people ask what's the difference between + + align:start position:0% +people ask what's the difference between + + + align:start position:0% +people ask what's the difference between +self- models and self-conscious + + align:start position:0% +self- models and self-conscious + + + align:start position:0% +self- models and self-conscious +processes and I don't care uh or what's + + align:start position:0% +processes and I don't care uh or what's + + + align:start position:0% +processes and I don't care uh or what's +the difference between self-conscious + + align:start position:0% +the difference between self-conscious + + + align:start position:0% +the difference between self-conscious +and reflective I don't care and the + + align:start position:0% +and reflective I don't care and the + + + align:start position:0% +and reflective I don't care and the +reason is that wow it's nice to have a + + align:start position:0% +reason is that wow it's nice to have a + + + align:start position:0% +reason is that wow it's nice to have a +box that isn't full yet + + align:start position:0% +box that isn't full yet + + + align:start position:0% +box that isn't full yet +so + + align:start position:0% +so + + + align:start position:0% +so +uh if you find something that your + + align:start position:0% +uh if you find something that your + + + align:start position:0% +uh if you find something that your +previous Theory going back to Brooks + + align:start position:0% +previous Theory going back to Brooks + + + align:start position:0% +previous Theory going back to Brooks +uh he was so successful getting simple + + align:start position:0% +uh he was so successful getting simple + + + align:start position:0% +uh he was so successful getting simple +robots to work that he concluded that + + align:start position:0% +robots to work that he concluded that + + + align:start position:0% +robots to work that he concluded that +the things didn't need any internal + + align:start position:0% +the things didn't need any internal + + + align:start position:0% +the things didn't need any internal +representations at all and for some + + align:start position:0% +representations at all and for some + + + align:start position:0% +representations at all and for some +mysterious reason the artificial + + align:start position:0% +mysterious reason the artificial + + + align:start position:0% +mysterious reason the artificial +intelligence Society gave him their + + align:start position:0% +intelligence Society gave him their + + + align:start position:0% +intelligence Society gave him their +annual big prize for for this very wrong + + align:start position:0% +annual big prize for for this very wrong + + + align:start position:0% +annual big prize for for this very wrong +idea and it caused AI research to sort + + align:start position:0% +idea and it caused AI research to sort + + + align:start position:0% +idea and it caused AI research to sort +of half collapse in places like Japan + + align:start position:0% +of half collapse in places like Japan + + + align:start position:0% +of half collapse in places like Japan +who said oh rule-based systems is all we + + align:start position:0% +who said oh rule-based systems is all we + + + align:start position:0% +who said oh rule-based systems is all we +need uh anybody want to defend + + align:start position:0% +need uh anybody want to defend + + + align:start position:0% +need uh anybody want to defend +him the odd thing is if you talk to + + align:start position:0% +him the odd thing is if you talk to + + + align:start position:0% +him the odd thing is if you talk to +Brooks he's one of the best philosophers + + align:start position:0% +Brooks he's one of the best philosophers + + + align:start position:0% +Brooks he's one of the best philosophers +you'll ever meet and he says oh yes of + + align:start position:0% +you'll ever meet and he says oh yes of + + + align:start position:0% +you'll ever meet and he says oh yes of +course that's wrong uh but it helps + + align:start position:0% +course that's wrong uh but it helps + + + align:start position:0% +course that's wrong uh but it helps +people do research and get things done + + align:start position:0% +people do research and get things done + + + align:start position:0% +people do research and get things done +and as as I think I mentioned the other + + align:start position:0% +and as as I think I mentioned the other + + + align:start position:0% +and as as I think I mentioned the other +day + + align:start position:0% +day + + + align:start position:0% +day +when + + align:start position:0% +when + + + align:start position:0% +when +the Three Mile Island thing happened + + align:start position:0% +the Three Mile Island thing happened + + + align:start position:0% +the Three Mile Island thing happened +there was no way to get into the reactor + + align:start position:0% +there was no way to get into the reactor + + + align:start position:0% +there was no way to get into the reactor +that was + + align:start position:0% +that was + + + align:start position:0% +that was +1980 and 30 years later when + + align:start position:0% +1980 and 30 years later when + + + align:start position:0% +1980 and 30 years later when +the what's how do you pronounce it + + align:start position:0% +the what's how do you pronounce it + + + align:start position:0% +the what's how do you pronounce it +Fukushima uh accident happened there was + + align:start position:0% +Fukushima uh accident happened there was + + + align:start position:0% +Fukushima uh accident happened there was +no robot that could go in and open a + + align:start position:0% +no robot that could go in and open a + + + align:start position:0% +no robot that could go in and open a +door + + align:start position:0% +door + + + align:start position:0% +door +and + + align:start position:0% + + + + align:start position:0% + +uh I don't know who to blame for that + + align:start position:0% +uh I don't know who to blame for that + + + align:start position:0% +uh I don't know who to blame for that +maybe + + align:start position:0% + + + + align:start position:0% + +us but my picture of the history is that + + align:start position:0% +us but my picture of the history is that + + + align:start position:0% +us but my picture of the history is that +the places that did research on + + align:start position:0% +the places that did research on + + + align:start position:0% +the places that did research on +robotics there were quite a few + + align:start position:0% +robotics there were quite a few + + + align:start position:0% +robotics there were quite a few +places and for example Carnegie melon + + align:start position:0% +places and for example Carnegie melon + + + align:start position:0% +places and for example Carnegie melon +was very impressive in getting the Sony + + align:start position:0% +was very impressive in getting the Sony + + + align:start position:0% +was very impressive in getting the Sony +dogs to play soccer + + align:start position:0% +dogs to play soccer + + + align:start position:0% +dogs to play soccer +and they're still at it and I think I + + align:start position:0% +and they're still at it and I think I + + + align:start position:0% +and they're still at it and I think I +mentioned that Sony still has a stock of + + align:start position:0% +mentioned that Sony still has a stock of + + + align:start position:0% +mentioned that Sony still has a stock of +uh what's it called + + align:start position:0% +uh what's it called + + + align:start position:0% +uh what's it called +fibos say it again fibos fibo fibo AO oh + + align:start position:0% +fibos say it again fibos fibo fibo AO oh + + + align:start position:0% +fibos say it again fibos fibo fibo AO oh +right I ibows right + + align:start position:0% +right I ibows right + + + align:start position:0% +right I ibows right +um but the trouble is they're always + + align:start position:0% +um but the trouble is they're always + + + align:start position:0% +um but the trouble is they're always +broken and uh we had a there was a robot + + align:start position:0% +broken and uh we had a there was a robot + + + align:start position:0% +broken and uh we had a there was a robot +here called Cog that Brooks made and it + + align:start position:0% +here called Cog that Brooks made and it + + + align:start position:0% +here called Cog that Brooks made and it +sometimes worked but usually it wasn't + + align:start position:0% +sometimes worked but usually it wasn't + + + align:start position:0% +sometimes worked but usually it wasn't +working and so only one student at a + + align:start position:0% +working and so only one student at a + + + align:start position:0% +working and so only one student at a +time could experiment with the robot + + align:start position:0% +time could experiment with the robot + + + align:start position:0% +time could experiment with the robot +what was that wonderful project of + + align:start position:0% +what was that wonderful project of + + + align:start position:0% +what was that wonderful project of +trying to make a walking machine for + + align:start position:0% +trying to make a walking machine for + + + align:start position:0% +trying to make a walking machine for +four years in + + align:start position:0% +four years in + + + align:start position:0% +four years in +uh there was a project to make a robot + + align:start position:0% +uh there was a project to make a robot + + + align:start position:0% +uh there was a project to make a robot +walk and there was only one of it so + + align:start position:0% +walk and there was only one of it so + + + align:start position:0% +walk and there was only one of it so +first only one student at a time can do + + align:start position:0% +first only one student at a time can do + + + align:start position:0% +first only one student at a time can do +research on it and most of the time it's + + align:start position:0% +research on it and most of the time it's + + + align:start position:0% +research on it and most of the time it's +something's broken and you're fixing it + + align:start position:0% +something's broken and you're fixing it + + + align:start position:0% +something's broken and you're fixing it +and so you end up that uh you sort of + + align:start position:0% +and so you end up that uh you sort of + + + align:start position:0% +and so you end up that uh you sort of +get five or 10 hours a week on your + + align:start position:0% +get five or 10 hours a week on your + + + align:start position:0% +get five or 10 hours a week on your +laboratory physical robot at the same + + align:start position:0% +laboratory physical robot at the same + + + align:start position:0% +laboratory physical robot at the same +time uh Ed fredkin had a student who + + align:start position:0% +time uh Ed fredkin had a student who + + + align:start position:0% +time uh Ed fredkin had a student who +tried to make a walking robot and it was + + align:start position:0% +tried to make a walking robot and it was + + + align:start position:0% +tried to make a walking robot and it was +a stick figure on the + + align:start position:0% +a stick figure on the + + + align:start position:0% +a stick figure on the +screen and uh i' forgot the student's + + align:start position:0% +screen and uh i' forgot the student's + + + align:start position:0% +screen and uh i' forgot the student's +name but anyway + + align:start position:0% +name but anyway + + + align:start position:0% +name but anyway +uh he simulated gravity and a few other + + align:start position:0% +uh he simulated gravity and a few other + + + align:start position:0% +uh he simulated gravity and a few other +things and in a couple of weeks he had a + + align:start position:0% +things and in a couple of weeks he had a + + + align:start position:0% +things and in a couple of weeks he had a +pretty good robot that could walk and go + + align:start position:0% +pretty good robot that could walk and go + + + align:start position:0% +pretty good robot that could walk and go +around turns and bank and uh if you put + + align:start position:0% +around turns and bank and uh if you put + + + align:start position:0% +around turns and bank and uh if you put +if you simulated an oily floor it could + + align:start position:0% +if you simulated an oily floor it could + + + align:start position:0% +if you simulated an oily floor it could +slip and fall which we considered the + + align:start position:0% +slip and fall which we considered the + + + align:start position:0% +slip and fall which we considered the +high point of the demo + + align:start position:0% + + + + align:start position:0% + +actually so + + align:start position:0% +actually so + + + align:start position:0% +actually so +there + + align:start position:0% + + + + align:start position:0% + +let me + + align:start position:0% + + + + align:start position:0% + +find so anyway I've sort of asked you to + + align:start position:0% +find so anyway I've sort of asked you to + + + align:start position:0% +find so anyway I've sort of asked you to +read my two books for this + + align:start position:0% +read my two books for this + + + align:start position:0% +read my two books for this +course but that those are not the only + + align:start position:0% +course but that those are not the only + + + align:start position:0% +course but that those are not the only +good uh texts about artificial + + align:start position:0% +good uh texts about artificial + + + align:start position:0% +good uh texts about artificial +intelligence and if you want to dig + + align:start position:0% +intelligence and if you want to dig + + + align:start position:0% +intelligence and if you want to dig +deeper uh it might be a good idea + + align:start position:0% +deeper uh it might be a good idea + + + align:start position:0% +deeper uh it might be a good idea +to + + align:start position:0% +to + + + align:start position:0% +to +go to the web and type in Aaron + + align:start position:0% + + + + align:start position:0% + +slowman s l m + + align:start position:0% +slowman s l m + + + align:start position:0% +slowman s l m +an and you'll get to his website which + + align:start position:0% +an and you'll get to his website which + + + align:start position:0% +an and you'll get to his website which +is something like + + align:start position:0% +is something like + + + align:start position:0% +is something like +that and uh slowman is a sort + + align:start position:0% +that and uh slowman is a sort + + + align:start position:0% +that and uh slowman is a sort +of philosopher who can + + align:start position:0% +of philosopher who can + + + align:start position:0% +of philosopher who can +program um there are a handful of them + + align:start position:0% +program um there are a handful of them + + + align:start position:0% +program um there are a handful of them +in the + + align:start position:0% +in the + + + align:start position:0% +in the +world and uh he has lots of interesting + + align:start position:0% +world and uh he has lots of interesting + + + align:start position:0% +world and uh he has lots of interesting +ideas that nobody's gotten to carry + + align:start position:0% +ideas that nobody's gotten to carry + + + align:start position:0% +ideas that nobody's gotten to carry +out and + + align:start position:0% +out and + + + align:start position:0% +out and +uh so I + + align:start position:0% + + + + align:start position:0% + +recommend who else + + align:start position:0% +recommend who else + + + align:start position:0% +recommend who else +is Pat do you ever recommend anyone + + align:start position:0% +is Pat do you ever recommend anyone + + + align:start position:0% +is Pat do you ever recommend anyone +else + + align:start position:0% + + + + align:start position:0% + +no + + align:start position:0% + + + + align:start position:0% + +what I'm trying to + + align:start position:0% +what I'm trying to + + + align:start position:0% +what I'm trying to +think + + align:start position:0% + + + + align:start position:0% + +I mean if you're looking for lot for + + align:start position:0% +I mean if you're looking for lot for + + + align:start position:0% +I mean if you're looking for lot for +philosophers uh Dan Dennett has a lot of + + align:start position:0% +philosophers uh Dan Dennett has a lot of + + + align:start position:0% +philosophers uh Dan Dennett has a lot of +ideas but but slowman is the + + align:start position:0% +ideas but but slowman is the + + + align:start position:0% +ideas but but slowman is the +only person I'd say is a sort of real + + align:start position:0% +only person I'd say is a sort of real + + + align:start position:0% +only person I'd say is a sort of real +professional + + align:start position:0% +professional + + + align:start position:0% +professional +philosopher who uh tries to program at + + align:start position:0% +philosopher who uh tries to program at + + + align:start position:0% +philosopher who uh tries to program at +least some of his ideas and uh he has + + align:start position:0% +least some of his ideas and uh he has + + + align:start position:0% +least some of his ideas and uh he has +successful students who have made larger + + align:start position:0% +successful students who have made larger + + + align:start position:0% +successful students who have made larger +systems work so um if you get tired of + + align:start position:0% +systems work so um if you get tired of + + + align:start position:0% +systems work so um if you get tired of +me and you ought + + align:start position:0% +me and you ought + + + align:start position:0% +me and you ought +to uh + + align:start position:0% +to uh + + + align:start position:0% +to uh +then go look at this guy and see who he + + align:start position:0% +then go look at this guy and see who he + + + align:start position:0% +then go look at this guy and see who he +recommends so okay + + align:start position:0% +recommends so okay + + + align:start position:0% +recommends so okay +any who has a good question to + + align:start position:0% +any who has a good question to + + + align:start position:0% +any who has a good question to +ask Mar you were talking about how we + + align:start position:0% +ask Mar you were talking about how we + + + align:start position:0% +ask Mar you were talking about how we +have a lot of words for emotions why do + + align:start position:0% +have a lot of words for emotions why do + + + align:start position:0% +have a lot of words for emotions why do +we only have one word for + + align:start position:0% +we only have one word for + + + align:start position:0% +we only have one word for +cause it's a mystery but + + align:start position:0% +cause it's a mystery but + + + align:start position:0% +cause it's a mystery but +uh I spent uh most of the couple of days + + align:start position:0% +uh I spent uh most of the couple of days + + + align:start position:0% +uh I spent uh most of the couple of days +making this list + + align:start position:0% + + + + align:start position:0% + +bigger but these aren't you + + align:start position:0% +bigger but these aren't you + + + align:start position:0% +bigger but these aren't you +know these are things that you do when + + align:start position:0% +know these are things that you do when + + + align:start position:0% +know these are things that you do when +you're thinking you make + + align:start position:0% +you're thinking you make + + + align:start position:0% +you're thinking you make +analogies + + align:start position:0% +analogies + + + align:start position:0% +analogies +uh if you have multiple goals you uh try + + align:start position:0% +uh if you have multiple goals you uh try + + + align:start position:0% +uh if you have multiple goals you uh try +to pick the most important one or uh in + + align:start position:0% +to pick the most important one or uh in + + + align:start position:0% +to pick the most important one or uh in +some cases uh if you have several go + + align:start position:0% +some cases uh if you have several go + + + align:start position:0% +some cases uh if you have several go +goals maybe you should try to achieve + + align:start position:0% +goals maybe you should try to achieve + + + align:start position:0% +goals maybe you should try to achieve +the easiest one and there's a chance + + align:start position:0% +the easiest one and there's a chance + + + align:start position:0% +the easiest one and there's a chance +that it'll lead you into what to do + + align:start position:0% +that it'll lead you into what to do + + + align:start position:0% +that it'll lead you into what to do +about the harder ones + + align:start position:0% +about the harder ones + + + align:start position:0% +about the harder ones +but + + align:start position:0% + + + + align:start position:0% + +uh a lot of people think that mostly in + + align:start position:0% +uh a lot of people think that mostly in + + + align:start position:0% +uh a lot of people think that mostly in +England that logic is a good way to do + + align:start position:0% +England that logic is a good way to do + + + align:start position:0% +England that logic is a good way to do +reasoning and that's completely + + align:start position:0% +reasoning and that's completely + + + align:start position:0% +reasoning and that's completely +wrong uh because in + + align:start position:0% +wrong uh because in + + + align:start position:0% +wrong uh because in +logic first of all you can't do analogy + + align:start position:0% +logic first of all you can't do analogy + + + align:start position:0% +logic first of all you can't do analogy +at all except at a very high level it + + align:start position:0% +at all except at a very high level it + + + align:start position:0% +at all except at a very high level it +takes four or five nested quantifiers to + + align:start position:0% +takes four or five nested quantifiers to + + + align:start position:0% +takes four or five nested quantifiers to +say a is to be as c as to which of the + + align:start position:0% +say a is to be as c as to which of the + + + align:start position:0% +say a is to be as c as to which of the +following five + + align:start position:0% +following five + + + align:start position:0% +following five +or uh so I've never seen anyone do + + align:start position:0% +or uh so I've never seen anyone do + + + align:start position:0% +or uh so I've never seen anyone do +analogical + + align:start position:0% +analogical + + + align:start position:0% +analogical +thinking uh using formal logic first + + align:start position:0% +thinking uh using formal logic first + + + align:start position:0% +thinking uh using formal logic first +order or higher order predicate + + align:start position:0% +order or higher order predicate + + + align:start position:0% +order or higher order predicate +calculus um what's logic good for it's + + align:start position:0% +calculus um what's logic good for it's + + + align:start position:0% +calculus um what's logic good for it's +great after you've solved a + + align:start position:0% +great after you've solved a + + + align:start position:0% +great after you've solved a +problem because then you can formalize + + align:start position:0% +problem because then you can formalize + + + align:start position:0% +problem because then you can formalize +what you did and see if some of the + + align:start position:0% +what you did and see if some of the + + + align:start position:0% +what you did and see if some of the +things you did weren't necessary in + + align:start position:0% +things you did weren't necessary in + + + align:start position:0% +things you did weren't necessary in +other words after you've got the + + align:start position:0% +other words after you've got the + + + align:start position:0% +other words after you've got the +solution to a problem which you got by + + align:start position:0% +solution to a problem which you got by + + + align:start position:0% +solution to a problem which you got by +going through a big search you finally + + align:start position:0% +going through a big search you finally + + + align:start position:0% +going through a big search you finally +found a path from A to Z and now you + + align:start position:0% +found a path from A to Z and now you + + + align:start position:0% +found a path from A to Z and now you +can uh see if the assumptions that you + + align:start position:0% +can uh see if the assumptions that you + + + align:start position:0% +can uh see if the assumptions that you +had to make to bridge all these various + + align:start position:0% +had to make to bridge all these various + + + align:start position:0% +had to make to bridge all these various +little gaps were all essential or not so + + align:start position:0% +little gaps were all essential or not so + + + align:start position:0% +little gaps were all essential or not so +so um yes like what kind of example + + align:start position:0% +so um yes like what kind of example + + + align:start position:0% +so um yes like what kind of example +would you say that logic can do + + align:start position:0% +would you say that logic can do + + + align:start position:0% +would you say that logic can do +analogies like like water is for Bott as + + align:start position:0% +analogies like like water is for Bott as + + + align:start position:0% +analogies like like water is for Bott as +like containment or like why + + align:start position:0% +like containment or like why + + + align:start position:0% +like containment or like why +why don't see well because you have to + + align:start position:0% +why don't see well because you have to + + + align:start position:0% +why don't see well because you have to +make a list of + + align:start position:0% +make a list of + + + align:start position:0% +make a list of +hypotheses and then let me see if I can + + align:start position:0% +hypotheses and then let me see if I can + + + align:start position:0% +hypotheses and then let me see if I can +find + + align:start position:0% +find + + + align:start position:0% +find +Evans the trouble is + + align:start position:0% +Evans the trouble is + + + align:start position:0% +Evans the trouble is +darn Evan's name is in a + + align:start position:0% +darn Evan's name is in a + + + align:start position:0% +darn Evan's name is in a +picture and word can't look inside its + + align:start position:0% +picture and word can't look inside its + + + align:start position:0% +picture and word can't look inside its +pictures can power can PowerPoint find + + align:start position:0% +pictures can power can PowerPoint find + + + align:start position:0% +pictures can power can PowerPoint find +words in its + + align:start position:0% + + + + align:start position:0% + +illustrations why don't I use + + align:start position:0% +illustrations why don't I use + + + align:start position:0% +illustrations why don't I use +PowerPoint because I've discovered that + + align:start position:0% +PowerPoint because I've discovered that + + + align:start position:0% +PowerPoint because I've discovered that +PowerPoint can't read pictures made by + + align:start position:0% +PowerPoint can't read pictures made by + + + align:start position:0% +PowerPoint can't read pictures made by +other programs in the Microsoft Word + + align:start position:0% +other programs in the Microsoft Word + + + align:start position:0% +other programs in the Microsoft Word +Suite + + align:start position:0% + + + + align:start position:0% + +the drawing program in word is pretty + + align:start position:0% +the drawing program in word is pretty + + + align:start position:0% +the drawing program in word is pretty +good and then there's an operation in + + align:start position:0% +good and then there's an operation in + + + align:start position:0% +good and then there's an operation in +word which will make a + + align:start position:0% +word which will make a + + + align:start position:0% +word which will make a +PowerPoint out of what you + + align:start position:0% +PowerPoint out of what you + + + align:start position:0% +PowerPoint out of what you +drew and + + align:start position:0% + + + + align:start position:0% + +it it's 25 years since Microsoft hasn't + + align:start position:0% +it it's 25 years since Microsoft hasn't + + + align:start position:0% +it it's 25 years since Microsoft hasn't +fixed the fatal errors that it makes + + align:start position:0% +fixed the fatal errors that it makes + + + align:start position:0% +fixed the fatal errors that it makes +when you do + + align:start position:0% +when you do + + + align:start position:0% +when you do +that in other words I don't think that + + align:start position:0% +that in other words I don't think that + + + align:start position:0% +that in other words I don't think that +the PowerPoint and word people + + align:start position:0% +the PowerPoint and word people + + + align:start position:0% +the PowerPoint and word people +communicate and they both make a lot of + + align:start position:0% +communicate and they both make a lot of + + + align:start position:0% +communicate and they both make a lot of +money so that might be the might be the + + align:start position:0% + + + + align:start position:0% + +reason where was + + align:start position:0% + + + + align:start position:0% + +I well you can do anything in logic if + + align:start position:0% +I well you can do anything in logic if + + + align:start position:0% +I well you can do anything in logic if +you try hard enough but but uh a is to B + + align:start position:0% +you try hard enough but but uh a is to B + + + align:start position:0% +you try hard enough but but uh a is to B +as C is to X is a four-part relation and + + align:start position:0% +as C is to X is a four-part relation and + + + align:start position:0% +as C is to X is a four-part relation and +you'd need a whole pile of quantifi + + align:start position:0% + + + + align:start position:0% + +and how would you know what to do next + + align:start position:0% +and how would you know what to do next + + + align:start position:0% +and how would you know what to do next +yes talk a bit about um the situation in + + align:start position:0% +yes talk a bit about um the situation in + + + align:start position:0% +yes talk a bit about um the situation in +which we are able to perform some sort + + align:start position:0% +which we are able to perform some sort + + + align:start position:0% +which we are able to perform some sort +of action like really fluently and + + align:start position:0% +of action like really fluently and + + + align:start position:0% +of action like really fluently and +really well but we cannot describe what + + align:start position:0% +really well but we cannot describe what + + + align:start position:0% +really well but we cannot describe what +we're doing um and the example I give is + + align:start position:0% +we're doing um and the example I give is + + + align:start position:0% +we're doing um and the example I give is +um say I'm like an expert African + + align:start position:0% +um say I'm like an expert African + + + align:start position:0% +um say I'm like an expert African +drummer from Africa and I can make these + + align:start position:0% +drummer from Africa and I can make these + + + align:start position:0% +drummer from Africa and I can make these +like really complicated rhythms but if + + align:start position:0% +like really complicated rhythms but if + + + align:start position:0% +like really complicated rhythms but if +you ask me what did you just do like I + + align:start position:0% +you ask me what did you just do like I + + + align:start position:0% +you ask me what did you just do like I +have no idea how to describe + + align:start position:0% +have no idea how to describe + + + align:start position:0% +have no idea how to describe +and in that case do you think the person + + align:start position:0% +and in that case do you think the person + + + align:start position:0% +and in that case do you think the person +is capable of like or I guess do you + + align:start position:0% +is capable of like or I guess do you + + + align:start position:0% +is capable of like or I guess do you +think the person we can say that the + + align:start position:0% +think the person we can say that the + + + align:start position:0% +think the person we can say that the +person understands this even though they + + align:start position:0% +person understands this even though they + + + align:start position:0% +person understands this even though they +cannot explain + + align:start position:0% +cannot explain + + + align:start position:0% +cannot explain +it + + align:start position:0% +it + + + align:start position:0% +it +well but if you take an extreme form of + + align:start position:0% +well but if you take an extreme form of + + + align:start position:0% +well but if you take an extreme form of +that uh you can't explain why you use + + align:start position:0% +that uh you can't explain why you use + + + align:start position:0% +that uh you can't explain why you use +just any particular word for + + align:start position:0% +just any particular word for + + + align:start position:0% +just any particular word for +anything there's no + + align:start position:0% +anything there's no + + + align:start position:0% +anything there's no +reason it's remarkable how well people + + align:start position:0% +reason it's remarkable how well people + + + align:start position:0% +reason it's remarkable how well people +can do in everyday life to uh tell + + align:start position:0% +can do in everyday life to uh tell + + + align:start position:0% +can do in everyday life to uh tell +people how they got an idea but when you + + align:start position:0% +people how they got an idea but when you + + + align:start position:0% +people how they got an idea but when you +look at it it doesn't say how you would + + align:start position:0% +look at it it doesn't say how you would + + + align:start position:0% +look at it it doesn't say how you would +program a machine to do it so there's + + align:start position:0% +program a machine to do it so there's + + + align:start position:0% +program a machine to do it so there's +something very peculiar + + align:start position:0% +something very peculiar + + + align:start position:0% +something very peculiar +about the idea + + align:start position:0% + + + + align:start position:0% + +that goes back to + + align:start position:0% +that goes back to + + + align:start position:0% +that goes back to +this this idea that people have free + + align:start position:0% +this this idea that people have free + + + align:start position:0% +this this idea that people have free +will and so forth suppose I say + + align:start position:0% +will and so forth suppose I say + + + align:start position:0% +will and so forth suppose I say +uh look at this and say + + align:start position:0% +uh look at this and say + + + align:start position:0% +uh look at this and say +say this has a constriction at this + + align:start position:0% +say this has a constriction at this + + + align:start position:0% +say this has a constriction at this +point why did I say + + align:start position:0% +point why did I say + + + align:start position:0% +point why did I say +constriction uh how do you get any how + + align:start position:0% +constriction uh how do you get any how + + + align:start position:0% +constriction uh how do you get any how +do you decide what word to use for + + align:start position:0% +do you decide what word to use for + + + align:start position:0% +do you decide what word to use for +something you have no + + align:start position:0% +something you have no + + + align:start position:0% +something you have no +idea + + align:start position:0% +idea + + + align:start position:0% +idea +uh so it's it's a very general question + + align:start position:0% +uh so it's it's a very general question + + + align:start position:0% +uh so it's it's a very general question +it's not clear that the different parts + + align:start position:0% +it's not clear that the different parts + + + align:start position:0% +it's not clear that the different parts +of the that the the frontal loes which + + align:start position:0% +of the that the the frontal loes which + + + align:start position:0% +of the that the the frontal loes which +might have something to do with making + + align:start position:0% +might have something to do with making + + + align:start position:0% +might have something to do with making +plans and analyzing certain kinds of + + align:start position:0% +plans and analyzing certain kinds of + + + align:start position:0% +plans and analyzing certain kinds of +situations have any access to what + + align:start position:0% +situations have any access to what + + + align:start position:0% +situations have any access to what +happens in the broker or what's + + align:start position:0% +happens in the broker or what's + + + align:start position:0% +happens in the broker or what's +the what's the speech production + + align:start position:0% + + + + align:start position:0% + +area broker and + + align:start position:0% +area broker and + + + align:start position:0% +area broker and +uh I'm trying to find the name of the + + align:start position:0% +uh I'm trying to find the name of the + + + align:start position:0% +uh I'm trying to find the name of the +other one it's connected by a cable + + align:start position:0% +other one it's connected by a cable + + + align:start position:0% +other one it's connected by a cable +that's about a quarter inch thick + + align:start position:0% +that's about a quarter inch thick + + + align:start position:0% +that's about a quarter inch thick +there's also verik yeah we have no idea + + align:start position:0% +there's also verik yeah we have no idea + + + align:start position:0% +there's also verik yeah we have no idea +how those + + align:start position:0% +how those + + + align:start position:0% +how those +work as far as I've never + + align:start position:0% +work as far as I've never + + + align:start position:0% +work as far as I've never +seen any + + align:start position:0% +seen any + + + align:start position:0% +seen any +publication in + + align:start position:0% +publication in + + + align:start position:0% +publication in +Neuroscience that says here's a theory + + align:start position:0% +Neuroscience that says here's a theory + + + align:start position:0% +Neuroscience that says here's a theory +of what happens in W's area have any of + + align:start position:0% +of what happens in W's area have any of + + + align:start position:0% +of what happens in W's area have any of +you ever seen + + align:start position:0% +you ever seen + + + align:start position:0% +you ever seen +one what do those people think + + align:start position:0% +one what do those people think + + + align:start position:0% +one what do those people think +about but they'll tell you + + align:start position:0% +about but they'll tell you + + + align:start position:0% +about but they'll tell you +about I was reading something which said + + align:start position:0% +about I was reading something which said + + + align:start position:0% +about I was reading something which said +it's going to be very hard to understand + + align:start position:0% +it's going to be very hard to understand + + + align:start position:0% +it's going to be very hard to understand +these areas because each neuron is + + align:start position:0% +these areas because each neuron is + + + align:start position:0% +these areas because each neuron is +connected to 100,000 Little Fibers well + + align:start position:0% +connected to 100,000 Little Fibers well + + + align:start position:0% +connected to 100,000 Little Fibers well +some of them are and I bet they don't do + + align:start position:0% +some of them are and I bet they don't do + + + align:start position:0% +some of them are and I bet they don't do +much except sort of set the bias for uh + + align:start position:0% +much except sort of set the bias for uh + + + align:start position:0% +much except sort of set the bias for uh +some + + align:start position:0% +some + + + align:start position:0% +some +large collection of other neurons + + align:start position:0% + + + + align:start position:0% + +but but we if you ask somebody how did + + align:start position:0% +but but we if you ask somebody how did + + + align:start position:0% +but but we if you ask somebody how did +you think of such a word they will tell + + align:start position:0% +you think of such a word they will tell + + + align:start position:0% +you think of such a word they will tell +you some story or anecdote but they + + align:start position:0% +you some story or anecdote but they + + + align:start position:0% +you some story or anecdote but they +won't be able to describe some sort of + + align:start position:0% +won't be able to describe some sort of + + + align:start position:0% +won't be able to describe some sort of +procedure which is say in terms of a + + align:start position:0% +procedure which is say in terms of a + + + align:start position:0% +procedure which is say in terms of a +language like lisp and say I consed this + + align:start position:0% +language like lisp and say I consed this + + + align:start position:0% +language like lisp and say I consed this +and that and I took the cter of this and + + align:start position:0% +and that and I took the cter of this and + + + align:start position:0% +and that and I took the cter of this and +the car of that and I uh put them in + + align:start position:0% +the car of that and I uh put them in + + + align:start position:0% +the car of that and I uh put them in +this register and then I swapped that + + align:start position:0% +this register and then I swapped that + + + align:start position:0% +this register and then I swapped that +with you don't see theories of how the + + align:start position:0% +with you don't see theories of how the + + + align:start position:0% +with you don't see theories of how the +mind works in Psychology + + align:start position:0% +mind works in Psychology + + + align:start position:0% +mind works in Psychology +today the only parts are they know a + + align:start position:0% +today the only parts are they know a + + + align:start position:0% +today the only parts are they know a +little bit about some aspects of vision + + align:start position:0% +little bit about some aspects of vision + + + align:start position:0% +little bit about some aspects of vision +because you can track the paths of + + align:start position:0% +because you can track the paths of + + + align:start position:0% +because you can track the paths of +images from the retina to the what call + + align:start position:0% +images from the retina to the what call + + + align:start position:0% +images from the retina to the what call +to the primary visual cortex and people + + align:start position:0% +to the primary visual cortex and people + + + align:start position:0% +to the primary visual cortex and people +have been able to figure out what what + + align:start position:0% +have been able to figure out what what + + + align:start position:0% +have been able to figure out what what +some of those cortical columns do and uh + + align:start position:0% +some of those cortical columns do and uh + + + align:start position:0% +some of those cortical columns do and uh +if you go back to an animal like the + + align:start position:0% +if you go back to an animal like the + + + align:start position:0% +if you go back to an animal like the +Frog then researchers like bitsy and + + align:start position:0% +Frog then researchers like bitsy and + + + align:start position:0% +Frog then researchers like bitsy and +others have figured out how the + + align:start position:0% +others have figured out how the + + + align:start position:0% +others have figured out how the +equivalent of the cerebellum in the + + align:start position:0% +equivalent of the cerebellum in the + + + align:start position:0% +equivalent of the cerebellum in the +Frog uh they've got almost the whole + + align:start position:0% +Frog uh they've got almost the whole + + + align:start position:0% +Frog uh they've got almost the whole +Circuit of how when the Frog sees a fly + + align:start position:0% +Circuit of how when the Frog sees a fly + + + align:start position:0% +Circuit of how when the Frog sees a fly +it manages to turn its head that way and + + align:start position:0% +it manages to turn its head that way and + + + align:start position:0% +it manages to turn its head that way and +stick its tongue out and catch it but in + + align:start position:0% +stick its tongue out and catch it but in + + + align:start position:0% +stick its tongue out and catch it but in +the case of a human I've never seen any + + align:start position:0% +the case of a human I've never seen any + + + align:start position:0% +the case of a human I've never seen any +theory of how any person thinks of + + align:start position:0% +theory of how any person thinks of + + + align:start position:0% +theory of how any person thinks of +anything + + align:start position:0% +anything + + + align:start position:0% +anything +so there's artificial intelligence which + + align:start position:0% +so there's artificial intelligence which + + + align:start position:0% +so there's artificial intelligence which +has high level theories of semantic + + align:start position:0% +has high level theories of semantic + + + align:start position:0% +has high level theories of semantic +representations and there's NE + + align:start position:0% +representations and there's NE + + + align:start position:0% +representations and there's NE +Neuroscience which has good theories of + + align:start position:0% +Neuroscience which has good theories of + + + align:start position:0% +Neuroscience which has good theories of +loc some parts of locomotion and some + + align:start position:0% +loc some parts of locomotion and some + + + align:start position:0% +loc some parts of locomotion and some +parts of sensory + + align:start position:0% +parts of sensory + + + align:start position:0% +parts of sensory +systems and to this day there's nothing + + align:start position:0% +systems and to this day there's nothing + + + align:start position:0% +systems and to this day there's nothing +much in between uh + + align:start position:0% +much in between uh + + + align:start position:0% +much in between uh +so + + align:start position:0% +so + + + align:start position:0% +so +uh David here has decided to go from one + + align:start position:0% +uh David here has decided to go from one + + + align:start position:0% +uh David here has decided to go from one +to the other and um former student of + + align:start position:0% +to the other and um former student of + + + align:start position:0% +to the other and um former student of +mine Bob Hearn has done a little bit on + + align:start position:0% +mine Bob Hearn has done a little bit on + + + align:start position:0% +mine Bob Hearn has done a little bit on +both and I bet there are 20 or 30 people + + align:start position:0% +both and I bet there are 20 or 30 people + + + align:start position:0% +both and I bet there are 20 or 30 people +around the country who have trying to + + align:start position:0% +around the country who have trying to + + + align:start position:0% +around the country who have trying to +bridge the gap between symbolic + + align:start position:0% +bridge the gap between symbolic + + + align:start position:0% +bridge the gap between symbolic +artificial intelligence and uh mappings + + align:start position:0% +artificial intelligence and uh mappings + + + align:start position:0% +artificial intelligence and uh mappings +of the nervous + + align:start position:0% +of the nervous + + + align:start position:0% +of the nervous +system but it's it's very rare and uh I + + align:start position:0% +system but it's it's very rare and uh I + + + align:start position:0% +system but it's it's very rare and uh I +don't know who you could ask to get + + align:start position:0% +don't know who you could ask to get + + + align:start position:0% +don't know who you could ask to get +support to work on a problem like that + + align:start position:0% +support to work on a problem like that + + + align:start position:0% +support to work on a problem like that +for five years yeah so presumably to + + align:start position:0% +for five years yeah so presumably to + + + align:start position:0% +for five years yeah so presumably to +build a humanlike artificial + + align:start position:0% +build a humanlike artificial + + + align:start position:0% +build a humanlike artificial +intelligence we need to like we need to + + align:start position:0% +intelligence we need to like we need to + + + align:start position:0% +intelligence we need to like we need to +perfectly model our own intelligence + + align:start position:0% +perfectly model our own intelligence + + + align:start position:0% +perfectly model our own intelligence +which means that we're the system we + + align:start position:0% +which means that we're the system we + + + align:start position:0% +which means that we're the system we +ourselves are the system that we're + + align:start position:0% +ourselves are the system that we're + + + align:start position:0% +ourselves are the system that we're +trying to understand well it doesn't + + align:start position:0% +trying to understand well it doesn't + + + align:start position:0% +trying to understand well it doesn't +have to be exact I mean people are + + align:start position:0% +have to be exact I mean people are + + + align:start position:0% +have to be exact I mean people are +different and + + align:start position:0% +different and + + + align:start position:0% +different and +uh typical person has looks like they + + align:start position:0% +uh typical person has looks like they + + + align:start position:0% +uh typical person has looks like they +have 400 different brain centers doing + + align:start position:0% +have 400 different brain centers doing + + + align:start position:0% +have 400 different brain centers doing +slightly different things or very + + align:start position:0% +slightly different things or very + + + align:start position:0% +slightly different things or very +different + + align:start position:0% +different + + + align:start position:0% +different +things and we have these examples in + + align:start position:0% +things and we have these examples in + + + align:start position:0% +things and we have these examples in +many cases if you lose a lot of your + + align:start position:0% +many cases if you lose a lot of your + + + align:start position:0% +many cases if you lose a lot of your +brain uh you're very badly damaged and + + align:start position:0% +brain uh you're very badly damaged and + + + align:start position:0% +brain uh you're very badly damaged and +in other cases + + align:start position:0% +in other cases + + + align:start position:0% +in other cases +uh you recover and uh + + align:start position:0% +uh you recover and uh + + + align:start position:0% +uh you recover and uh +become just about as smart as you were + + align:start position:0% +become just about as smart as you were + + + align:start position:0% +become just about as smart as you were +probably a few cases where you got rid + + align:start position:0% +probably a few cases where you got rid + + + align:start position:0% +probably a few cases where you got rid +of something that was holding you back + + align:start position:0% +of something that was holding you back + + + align:start position:0% +of something that was holding you back +but it's hard to prove that so we don't + + align:start position:0% +but it's hard to prove that so we don't + + + align:start position:0% +but it's hard to prove that so we don't +need to we don't need a theory of how + + align:start position:0% +need to we don't need a theory of how + + + align:start position:0% +need to we don't need a theory of how +people work yet and the nice thing about + + align:start position:0% +people work yet and the nice thing about + + + align:start position:0% +people work yet and the nice thing about +AI is + + align:start position:0% +AI is + + + align:start position:0% +AI is +that we could get we could eventually + + align:start position:0% +that we could get we could eventually + + + align:start position:0% +that we could get we could eventually +get models which are pretty good at + + align:start position:0% +get models which are pretty good at + + + align:start position:0% +get models which are pretty good at +solving what people call everyday Common + + align:start position:0% +solving what people call everyday Common + + + align:start position:0% +solving what people call everyday Common +Sense + + align:start position:0% +Sense + + + align:start position:0% +Sense +problems and probably in many respects + + align:start position:0% +problems and probably in many respects + + + align:start position:0% +problems and probably in many respects +they're not the way the human mind works + + align:start position:0% +they're not the way the human mind works + + + align:start position:0% +they're not the way the human mind works +it doesn't matter but once you've + + align:start position:0% +it doesn't matter but once you've + + + align:start position:0% +it doesn't matter but once you've +got if I had a program which was pretty + + align:start position:0% +got if I had a program which was pretty + + + align:start position:0% +got if I had a program which was pretty +good at understanding why you can pull + + align:start position:0% +good at understanding why you can pull + + + align:start position:0% +good at understanding why you can pull +with a string but not + + align:start position:0% +with a string but not + + + align:start position:0% +with a string but not +push uh then there's a fair chance you + + align:start position:0% +push uh then there's a fair chance you + + + align:start position:0% +push uh then there's a fair chance you +could say well that seems to resemble + + align:start position:0% +could say well that seems to resemble + + + align:start position:0% +could say well that seems to resemble +what people do I'll do this a few + + align:start position:0% +what people do I'll do this a few + + + align:start position:0% +what people do I'll do this a few +psychological experiments and see what's + + align:start position:0% +psychological experiments and see what's + + + align:start position:0% +psychological experiments and see what's +wrong with that theory and how to change + + align:start position:0% +wrong with that theory and how to change + + + align:start position:0% +wrong with that theory and how to change +it so at some point + + align:start position:0% +it so at some point + + + align:start position:0% +it so at some point +uh there'll be people making AI systems + + align:start position:0% +uh there'll be people making AI systems + + + align:start position:0% +uh there'll be people making AI systems +comparing them to particular people and + + align:start position:0% +comparing them to particular people and + + + align:start position:0% +comparing them to particular people and +trying to make them fit the trouble is + + align:start position:0% +trying to make them fit the trouble is + + + align:start position:0% +trying to make them fit the trouble is +nowadays it takes a few months to if you + + align:start position:0% +nowadays it takes a few months to if you + + + align:start position:0% +nowadays it takes a few months to if you +get a really good new idea to program + + align:start position:0% +get a really good new idea to program + + + align:start position:0% +get a really good new idea to program +it um I think there's something wrong + + align:start position:0% +it um I think there's something wrong + + + align:start position:0% +it um I think there's something wrong +with programming languages and what we + + align:start position:0% +with programming languages and what we + + + align:start position:0% +with programming languages and what we +need is + + align:start position:0% +need is + + + align:start position:0% +need is +a we need a programming language which + + align:start position:0% +a we need a programming language which + + + align:start position:0% +a we need a programming language which +uh where the instructions describe goals + + align:start position:0% +uh where the instructions describe goals + + + align:start position:0% +uh where the instructions describe goals +and then subg goals and then finally you + + align:start position:0% +and then subg goals and then finally you + + + align:start position:0% +and then subg goals and then finally you +might say well let's represent this + + align:start position:0% +might say well let's represent this + + + align:start position:0% +might say well let's represent this +concept by a number or a semantic + + align:start position:0% +concept by a number or a semantic + + + align:start position:0% +concept by a number or a semantic +network of some sort but + + align:start position:0% +network of some sort but + + + align:start position:0% +network of some sort but +uh yes that idea of having a program + + align:start position:0% +uh yes that idea of having a program + + + align:start position:0% +uh yes that idea of having a program +language where you define goals is there + + align:start position:0% +language where you define goals is there + + + align:start position:0% +language where you define goals is there +a goal oriented language so there + + align:start position:0% +a goal oriented language so there + + + align:start position:0% +a goal oriented language so there +there's kind of one if you think about + + align:start position:0% +there's kind of one if you think about + + + align:start position:0% +there's kind of one if you think about +it if you squint hard enough um + + align:start position:0% +it if you squint hard enough um + + + align:start position:0% +it if you squint hard enough um +something like SQL um where you you tell + + align:start position:0% +something like SQL um where you you tell + + + align:start position:0% +something like SQL um where you you tell +the computer you know I want to find you + + align:start position:0% +the computer you know I want to find you + + + align:start position:0% +the computer you know I want to find you +the the top 10 people in my database + + align:start position:0% +the the top 10 people in my database + + + align:start position:0% +the the top 10 people in my database +with this typ value and then you don't + + align:start position:0% +with this typ value and then you don't + + + align:start position:0% +with this typ value and then you don't +worry about how the system goes about + + align:start position:0% +worry about how the system goes about + + + align:start position:0% +worry about how the system goes about +doing that in a sense that's defining + + align:start position:0% +doing that in a sense that's defining + + + align:start position:0% +doing that in a sense that's defining +the goes you got s a little bit uhhuh + + align:start position:0% +the goes you got s a little bit uhhuh + + + align:start position:0% +the goes you got s a little bit uhhuh +what's it called SQL + + align:start position:0% +what's it called SQL + + + align:start position:0% +what's it called SQL +sqls at a + + align:start position:0% + + + + align:start position:0% + +datab oh right yes I guess uh database + + align:start position:0% +datab oh right yes I guess uh database + + + align:start position:0% +datab oh right yes I guess uh database +query languages are on the track but uh + + align:start position:0% +query languages are on the track but uh + + + align:start position:0% +query languages are on the track but uh +wol Alpha + + align:start position:0% +wol Alpha + + + align:start position:0% +wol Alpha +seems to be better than I thought well + + align:start position:0% +seems to be better than I thought well + + + align:start position:0% +seems to be better than I thought well +he was running + + align:start position:0% +he was running + + + align:start position:0% +he was running +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +it and he Steve wlr was giving this demo + + align:start position:0% +it and he Steve wlr was giving this demo + + + align:start position:0% +it and he Steve wlr was giving this demo +at meeting we were at uh on Monday and + + align:start position:0% +at meeting we were at uh on Monday and + + + align:start position:0% +at meeting we were at uh on Monday and +he'd say well maybe I'll just say this + + align:start position:0% +he'd say well maybe I'll just say this + + + align:start position:0% +he'd say well maybe I'll just say this +and and it always worked + + align:start position:0% +and and it always worked + + + align:start position:0% +and and it always worked +so so maybe either the language is + + align:start position:0% +so so maybe either the language is + + + align:start position:0% +so so maybe either the language is +better than I thought or Wolfram is + + align:start position:0% +better than I thought or Wolfram is + + + align:start position:0% +better than I thought or Wolfram is +better than I thought at + + align:start position:0% + + + + align:start position:0% + +something remarkable + + align:start position:0% + + + + align:start position:0% + +guy yes so I like this example of uh you + + align:start position:0% +guy yes so I like this example of uh you + + + align:start position:0% +guy yes so I like this example of uh you +only remember a name after you can + + align:start position:0% +only remember a name after you can + + + align:start position:0% +only remember a name after you can +remember a name after you've given up + + align:start position:0% +remember a name after you've given up + + + align:start position:0% +remember a name after you've given up +consciously trying to think about it do + + align:start position:0% +consciously trying to think about it do + + + align:start position:0% +consciously trying to think about it do +you think this is a matter of us being + + align:start position:0% +you think this is a matter of us being + + + align:start position:0% +you think this is a matter of us being +able to set up background processes and + + align:start position:0% +able to set up background processes and + + + align:start position:0% +able to set up background processes and +then either there's some delay like we + + align:start position:0% +then either there's some delay like we + + + align:start position:0% +then either there's some delay like we +give up there's some delay or we don't + + align:start position:0% +give up there's some delay or we don't + + + align:start position:0% +give up there's some delay or we don't +have the ability to correctly terminate + + align:start position:0% +have the ability to correctly terminate + + + align:start position:0% +have the ability to correctly terminate +processes do you think this only works + + align:start position:0% +processes do you think this only works + + + align:start position:0% +processes do you think this only works +for memory or could it work for other + + align:start position:0% +for memory or could it work for other + + + align:start position:0% +for memory or could it work for other +things like could I start an arithmetic + + align:start position:0% +things like could I start an arithmetic + + + align:start position:0% +things like could I start an arithmetic +operation and then give up and then + + align:start position:0% +operation and then give up and then + + + align:start position:0% +operation and then give up and then +it'll come to me + + align:start position:0% +it'll come to me + + + align:start position:0% +it'll come to me +later well there's a lot of nice + + align:start position:0% +later well there's a lot of nice + + + align:start position:0% +later well there's a lot of nice +questions + + align:start position:0% +questions + + + align:start position:0% +questions +about things like that how many + + align:start position:0% +about things like that how many + + + align:start position:0% +about things like that how many +processes can you run at once in your + + align:start position:0% +processes can you run at once in your + + + align:start position:0% +processes can you run at once in your +brain and uh I was having a sort of + + align:start position:0% +brain and uh I was having a sort of + + + align:start position:0% +brain and uh I was having a sort of +argument the other day about uh + + align:start position:0% + + + + align:start position:0% + +music + + align:start position:0% +music + + + align:start position:0% +music +and I was wondering + + align:start position:0% +and I was wondering + + + align:start position:0% +and I was wondering +if I see a big difference between Bach + + align:start position:0% +if I see a big difference between Bach + + + align:start position:0% +if I see a big difference between Bach +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +the and uh the composers who do + + align:start position:0% +the and uh the composers who do + + + align:start position:0% +the and uh the composers who do +Counterpoint Counterpoint you usually + + align:start position:0% +Counterpoint Counterpoint you usually + + + align:start position:0% +Counterpoint Counterpoint you usually +have several versions of a very similar + + align:start position:0% +have several versions of a very similar + + + align:start position:0% +have several versions of a very similar +idea maybe there's one theme and you + + align:start position:0% +idea maybe there's one theme and you + + + align:start position:0% +idea maybe there's one theme and you +have it playing and then another voice + + align:start position:0% +have it playing and then another voice + + + align:start position:0% +have it playing and then another voice +comes in and it has that theme upside + + align:start position:0% +comes in and it has that theme upside + + + align:start position:0% +comes in and it has that theme upside +down or a variation of it or in some + + align:start position:0% +down or a variation of it or in some + + + align:start position:0% +down or a variation of it or in some +cases exactly the same and then it's + + align:start position:0% +cases exactly the same and then it's + + + align:start position:0% +cases exactly the same and then it's +called a + + align:start position:0% +called a + + + align:start position:0% +called a +Canon um so the T to force in classical + + align:start position:0% +Canon um so the T to force in classical + + + align:start position:0% +Canon um so the T to force in classical +music is when you have two or three or + + align:start position:0% +music is when you have two or three or + + + align:start position:0% +music is when you have two or three or +four versions of the same thought going + + align:start position:0% +four versions of the same thought going + + + align:start position:0% +four versions of the same thought going +on at once in different times and my + + align:start position:0% +on at once in different times and my + + + align:start position:0% +on at once in different times and my +feeling was that in uh popular music or + + align:start position:0% +feeling was that in uh popular music or + + + align:start position:0% +feeling was that in uh popular music or +reg uh if if you take it a typical + + align:start position:0% +reg uh if if you take it a typical + + + align:start position:0% +reg uh if if you take it a typical +band then there might be four people and + + align:start position:0% +band then there might be four people and + + + align:start position:0% +band then there might be four people and +they're doing different things at the + + align:start position:0% +they're doing different things at the + + + align:start position:0% +they're doing different things at the +same time uh usually not the same U + + align:start position:0% +same time uh usually not the same U + + + align:start position:0% +same time uh usually not the same U +musical Tunes but there's a rhythm and + + align:start position:0% +musical Tunes but there's a rhythm and + + + align:start position:0% +musical Tunes but there's a rhythm and +there's uh a Tony and there's various + + align:start position:0% +there's uh a Tony and there's various + + + align:start position:0% +there's uh a Tony and there's various +instruments doing different things but + + align:start position:0% +instruments doing different things but + + + align:start position:0% +instruments doing different things but +there you don't have several doing the + + align:start position:0% +there you don't have several doing the + + + align:start position:0% +there you don't have several doing the +same thing I might might be wrong and um + + align:start position:0% +same thing I might might be wrong and um + + + align:start position:0% +same thing I might might be wrong and um +somebody said well some some popular + + align:start position:0% +somebody said well some some popular + + + align:start position:0% +somebody said well some some popular +music has a lot of CounterPoint I'm I'm + + align:start position:0% +music has a lot of CounterPoint I'm I'm + + + align:start position:0% +music has a lot of CounterPoint I'm I'm +just not familiar with it but I think + + align:start position:0% +just not familiar with it but I think + + + align:start position:0% +just not familiar with it but I think +that's if you're trying to solve a hard + + align:start position:0% +that's if you're trying to solve a hard + + + align:start position:0% +that's if you're trying to solve a hard +problem it's fairly easy to look at the + + align:start position:0% +problem it's fairly easy to look at the + + + align:start position:0% +problem it's fairly easy to look at the +problem in several different ways but + + align:start position:0% +problem in several different ways but + + + align:start position:0% +problem in several different ways but +what's hard is to look it in several + + align:start position:0% +what's hard is to look it in several + + + align:start position:0% +what's hard is to look it in several +almost the same ways that are slightly + + align:start position:0% +almost the same ways that are slightly + + + align:start position:0% +almost the same ways that are slightly +different because probably uh if you + + align:start position:0% +different because probably uh if you + + + align:start position:0% +different because probably uh if you +believe that the brain is made of Agents + + align:start position:0% +believe that the brain is made of Agents + + + align:start position:0% +believe that the brain is made of Agents +or resources or whatever uh you probably + + align:start position:0% +or resources or whatever uh you probably + + + align:start position:0% +or resources or whatever uh you probably +don't have duplicate copies of ones that + + align:start position:0% +don't have duplicate copies of ones that + + + align:start position:0% +don't have duplicate copies of ones that +do important things because that would + + align:start position:0% +do important things because that would + + + align:start position:0% +do important things because that would +take up too much real + + align:start position:0% +take up too much real + + + align:start position:0% +take up too much real +estate anyway I might be completely + + align:start position:0% +estate anyway I might be completely + + + align:start position:0% +estate anyway I might be completely +wrong about uh Jazz somebody + + align:start position:0% +wrong about uh Jazz somebody + + + align:start position:0% +wrong about uh Jazz somebody +um maybe they + + align:start position:0% +um maybe they + + + align:start position:0% +um maybe they +have just as complicated overlapping + + align:start position:0% +have just as complicated overlapping + + + align:start position:0% +have just as complicated overlapping +things uh as Bach and uh the + + align:start position:0% +things uh as Bach and uh the + + + align:start position:0% +things uh as Bach and uh the +contrapuntal composers did + + align:start position:0% + + + + align:start position:0% + +but yeah what is the goal of artificial + + align:start position:0% +but yeah what is the goal of artificial + + + align:start position:0% +but yeah what is the goal of artificial +intelligence is it some sort of + + align:start position:0% +intelligence is it some sort of + + + align:start position:0% +intelligence is it some sort of +application or is it more + + align:start position:0% +application or is it more + + + align:start position:0% +application or is it more +philosophical oh uh everyone has + + align:start position:0% +philosophical oh uh everyone has + + + align:start position:0% +philosophical oh uh everyone has +different goals or ones in your + + align:start position:0% +different goals or ones in your + + + align:start position:0% +different goals or ones in your +opinion uh I think we're going to need + + align:start position:0% +opinion uh I think we're going to need + + + align:start position:0% +opinion uh I think we're going to need +it because uh the disaster that we're + + align:start position:0% +it because uh the disaster that we're + + + align:start position:0% +it because uh the disaster that we're +working our way toward is that people + + align:start position:0% +working our way toward is that people + + + align:start position:0% +working our way toward is that people +are going to live longer and uh they'll + + align:start position:0% +are going to live longer and uh they'll + + + align:start position:0% +are going to live longer and uh they'll +become slightly less able and so you'll + + align:start position:0% +become slightly less able and so you'll + + + align:start position:0% +become slightly less able and so you'll +have uh billions of 200 year old people + + align:start position:0% +have uh billions of 200 year old people + + + align:start position:0% +have uh billions of 200 year old people +who can barely get around and there + + align:start position:0% +who can barely get around and there + + + align:start position:0% +who can barely get around and there +won't be enough + + align:start position:0% +won't be enough + + + align:start position:0% +won't be enough +uh people to import from underdeveloped + + align:start position:0% +uh people to import from underdeveloped + + + align:start position:0% +uh people to import from underdeveloped +countries + + align:start position:0% +countries + + + align:start position:0% +countries +to or they won't be able to afford them + + align:start position:0% +to or they won't be able to afford them + + + align:start position:0% +to or they won't be able to afford them +so we're going to have to have machines + + align:start position:0% +so we're going to have to have machines + + + align:start position:0% +so we're going to have to have machines +that take care of + + align:start position:0% +that take care of + + + align:start position:0% +that take care of +us of course that's just a Trent because + + align:start position:0% +us of course that's just a Trent because + + + align:start position:0% +us of course that's just a Trent because +at some point then you'll download your + + align:start position:0% +at some point then you'll download your + + + align:start position:0% +at some point then you'll download your +brain into a machine and fix everything + + align:start position:0% +brain into a machine and fix everything + + + align:start position:0% +brain into a machine and fix everything +that's wrong so we'll need robots for a + + align:start position:0% +that's wrong so we'll need robots for a + + + align:start position:0% +that's wrong so we'll need robots for a +few hundred years years or a few decades + + align:start position:0% +few hundred years years or a few decades + + + align:start position:0% +few hundred years years or a few decades +and uh then we'll be them and we won't + + align:start position:0% +and uh then we'll be them and we won't + + + align:start position:0% +and uh then we'll be them and we won't +need them + + align:start position:0% +need them + + + align:start position:0% +need them +anymore but it's an important problem + + align:start position:0% +anymore but it's an important problem + + + align:start position:0% +anymore but it's an important problem +what's going to happen in in the next + + align:start position:0% +what's going to happen in in the next + + + align:start position:0% +what's going to happen in in the next + + align:start position:0% + + + align:start position:0% +years you're going to + + align:start position:0% +years you're going to + + + align:start position:0% +years you're going to +have 20 billion 2 200 year olds and + + align:start position:0% +have 20 billion 2 200 year olds and + + + align:start position:0% +have 20 billion 2 200 year olds and +nobody to take care of them unless we + + align:start position:0% +nobody to take care of them unless we + + + align:start position:0% +nobody to take care of them unless we +get + + align:start position:0% + + + + align:start position:0% + +AI + + align:start position:0% +AI + + + align:start position:0% +AI +nobody seems particularly sad about + + align:start position:0% + + + + align:start position:0% + +that how + + align:start position:0% +that how + + + align:start position:0% +that how +long oh another + + align:start position:0% +long oh another + + + align:start position:0% +long oh another +anecdote I was once giving a lecture and + + align:start position:0% +anecdote I was once giving a lecture and + + + align:start position:0% +anecdote I was once giving a lecture and +talking about people living a long + + align:start position:0% +talking about people living a long + + + align:start position:0% +talking about people living a long +time and nobody in the audience seemed + + align:start position:0% +time and nobody in the audience seemed + + + align:start position:0% +time and nobody in the audience seemed +interested and I'd say well suppose you + + align:start position:0% +interested and I'd say well suppose you + + + align:start position:0% +interested and I'd say well suppose you +could live 400 years and most of the + + align:start position:0% +could live 400 years and most of the + + + align:start position:0% +could live 400 years and most of the +people I then I asked what what was the + + align:start position:0% +people I then I asked what what was the + + + align:start position:0% +people I then I asked what what was the +trouble and said wouldn't it be + + align:start position:0% +trouble and said wouldn't it be + + + align:start position:0% +trouble and said wouldn't it be +boring so then I tried it again in a + + align:start position:0% +boring so then I tried it again in a + + + align:start position:0% +boring so then I tried it again in a +couple of other lectures and uh if you + + align:start position:0% +couple of other lectures and uh if you + + + align:start position:0% +couple of other lectures and uh if you +ask a bunch of scientists how would you + + align:start position:0% +ask a bunch of scientists how would you + + + align:start position:0% +ask a bunch of scientists how would you +like to live 400 + + align:start position:0% +like to live 400 + + + align:start position:0% +like to live 400 +years everyone says + + align:start position:0% +years everyone says + + + align:start position:0% +years everyone says +yay and you ask them why and they say + + align:start position:0% +yay and you ask them why and they say + + + align:start position:0% +yay and you ask them why and they say +well I'm working on a problem that I + + align:start position:0% +well I'm working on a problem that I + + + align:start position:0% +well I'm working on a problem that I +might not have time to solve but if I if + + align:start position:0% +might not have time to solve but if I if + + + align:start position:0% +might not have time to solve but if I if +I had 400 years I bet I could get + + align:start position:0% +I had 400 years I bet I could get + + + align:start position:0% +I had 400 years I bet I could get +somewhere on it and the other people + + align:start position:0% +somewhere on it and the other people + + + align:start position:0% +somewhere on it and the other people +don't have any goal that's my + + align:start position:0% +don't have any goal that's my + + + align:start position:0% +don't have any goal that's my +coldblooded view of + + align:start position:0% +coldblooded view of + + + align:start position:0% +coldblooded view of +the typical + + align:start position:0% + + + + align:start position:0% + +non-scientist there's nothing for them + + align:start position:0% +non-scientist there's nothing for them + + + align:start position:0% +non-scientist there's nothing for them +to do in the long + + align:start position:0% +to do in the long + + + align:start position:0% +to do in the long +run who who can think of what should + + align:start position:0% +run who who can think of what should + + + align:start position:0% +run who who can think of what should +people do what's your + + align:start position:0% +people do what's your + + + align:start position:0% +people do what's your +goal how many of you want to live 400 + + align:start position:0% +goal how many of you want to live 400 + + + align:start position:0% +goal how many of you want to live 400 +years wow must be scientists + + align:start position:0% + + + + align:start position:0% + +here try it on some crowd and let me + + align:start position:0% +here try it on some crowd and let me + + + align:start position:0% +here try it on some crowd and let me +know what + + align:start position:0% +know what + + + align:start position:0% +know what +happens are people really afraid yeah I + + align:start position:0% +happens are people really afraid yeah I + + + align:start position:0% +happens are people really afraid yeah I +think I think maybe the differentiating + + align:start position:0% +think I think maybe the differentiating + + + align:start position:0% +think I think maybe the differentiating +factor whether or not your 400 years is + + align:start position:0% +factor whether or not your 400 years is + + + align:start position:0% +factor whether or not your 400 years is +just going to be the repetition of 100 + + align:start position:0% +just going to be the repetition of 100 + + + align:start position:0% +just going to be the repetition of 100 +years experience or if it'll start to + + align:start position:0% +years experience or if it'll start to + + + align:start position:0% +years experience or if it'll start to +like take off you'll start to learn + + align:start position:0% +like take off you'll start to learn + + + align:start position:0% +like take off you'll start to learn +better progress + + align:start position:0% +better progress + + + align:start position:0% +better progress +right I've seen + + align:start position:0% + + + + align:start position:0% + +30 issues of the big bang and I don't + + align:start position:0% +30 issues of the big bang and I don't + + + align:start position:0% +30 issues of the big bang and I don't +look forward to the next next one + + align:start position:0% +look forward to the next next one + + + align:start position:0% +look forward to the next next one +anymore because they're all the they're + + align:start position:0% +anymore because they're all the they're + + + align:start position:0% +anymore because they're all the they're +getting to be all the same although it's + + align:start position:0% +getting to be all the same although it's + + + align:start position:0% +getting to be all the same although it's +the only thing on TV that has + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +scientists seriously I hardly read + + align:start position:0% +scientists seriously I hardly read + + + align:start position:0% +scientists seriously I hardly read +anything except journals and science + + align:start position:0% +anything except journals and science + + + align:start position:0% +anything except journals and science +fiction + + align:start position:0% +fiction + + + align:start position:0% +fiction +because yeah what's the motivation to + + align:start position:0% +because yeah what's the motivation to + + + align:start position:0% +because yeah what's the motivation to +have robots take care of us as we age as + + align:start position:0% +have robots take care of us as we age as + + + align:start position:0% +have robots take care of us as we age as +opposed to our own cognitive abilities + + align:start position:0% +opposed to our own cognitive abilities + + + align:start position:0% +opposed to our own cognitive abilities +or own or a prosthetic body or something + + align:start position:0% +or own or a prosthetic body or something + + + align:start position:0% +or own or a prosthetic body or something +or + + align:start position:0% +or + + + align:start position:0% +or +cyborg why + + align:start position:0% +cyborg why + + + align:start position:0% +cyborg why +have the joy of living if you can't do + + align:start position:0% +have the joy of living if you can't do + + + align:start position:0% +have the joy of living if you can't do +anything somebody takes care of I can't + + align:start position:0% +anything somebody takes care of I can't + + + align:start position:0% +anything somebody takes care of I can't +think of any advantage except that uh + + align:start position:0% +think of any advantage except that uh + + + align:start position:0% +think of any advantage except that uh +medicine has isn't getting you know the + + align:start position:0% +medicine has isn't getting you know the + + + align:start position:0% +medicine has isn't getting you know the +the age of unhandy cap people went up + + align:start position:0% +the age of unhandy cap people went up + + + align:start position:0% +the age of unhandy cap people went up +one year every four since the late 19 + + align:start position:0% +one year every four since the late 19 + + + align:start position:0% +one year every four since the late 19 +1940s so lifespan is so that's 60 years + + align:start position:0% +1940s so lifespan is so that's 60 years + + + align:start position:0% +1940s so lifespan is so that's 60 years +so people are living 15 years longer on + + align:start position:0% +so people are living 15 years longer on + + + align:start position:0% +so people are living 15 years longer on +the average than uh they did when I was + + align:start position:0% +the average than uh they did when I was + + + align:start position:0% +the average than uh they did when I was +born or even more than that but it's + + align:start position:0% +born or even more than that but it's + + + align:start position:0% +born or even more than that but it's +leveled off + + align:start position:0% +leveled off + + + align:start position:0% +leveled off +lately now I suspect that you only have + + align:start position:0% +lately now I suspect that you only have + + + align:start position:0% +lately now I suspect that you only have +to fix a dozen genes or who knows nobody + + align:start position:0% +to fix a dozen genes or who knows nobody + + + align:start position:0% +to fix a dozen genes or who knows nobody +really has a good estimate but you can + + align:start position:0% +really has a good estimate but you can + + + align:start position:0% +really has a good estimate but you can +probably double the lifespan if you + + align:start position:0% +probably double the lifespan if you + + + align:start position:0% +probably double the lifespan if you +could uh fix + + align:start position:0% +could uh fix + + + align:start position:0% +could uh fix +nobody knows but maybe there's just a + + align:start position:0% +nobody knows but maybe there's just a + + + align:start position:0% +nobody knows but maybe there's just a +dozen processes that that would fix a + + align:start position:0% +dozen processes that that would fix a + + + align:start position:0% +dozen processes that that would fix a +lot of things and then you could live + + align:start position:0% +lot of things and then you could live + + + align:start position:0% +lot of things and then you could live +longer without + + align:start position:0% +longer without + + + align:start position:0% +longer without +deteriorating and uh lots of people + + align:start position:0% +deteriorating and uh lots of people + + + align:start position:0% +deteriorating and uh lots of people +might get bored + + align:start position:0% +might get bored + + + align:start position:0% +might get bored +but they'll self- + + align:start position:0% +but they'll self- + + + align:start position:0% +but they'll self- +select I don't + + align:start position:0% +select I don't + + + align:start position:0% +select I don't +know what's your + + align:start position:0% +know what's your + + + align:start position:0% +know what's your +answer um + + align:start position:0% +answer um + + + align:start position:0% +answer um +I I feel that + + align:start position:0% +I I feel that + + + align:start position:0% +I I feel that +creating I feel that AI is + + align:start position:0% +creating I feel that AI is + + + align:start position:0% +creating I feel that AI is +more um as the goal is not to help take + + align:start position:0% +more um as the goal is not to help take + + + align:start position:0% +more um as the goal is not to help take +care of people but to complement what we + + align:start position:0% +care of people but to complement what we + + + align:start position:0% +care of people but to complement what we +already have entertain us you could also + + align:start position:0% +already have entertain us you could also + + + align:start position:0% +already have entertain us you could also +look at them as our descendants and we + + align:start position:0% +look at them as our descendants and we + + + align:start position:0% +look at them as our descendants and we +um they we will have them replace us + + align:start position:0% +um they we will have them replace us + + + align:start position:0% +um they we will have them replace us +and uh just as a lot of people consider + + align:start position:0% +and uh just as a lot of people consider + + + align:start position:0% +and uh just as a lot of people consider +their children to be + + align:start position:0% +their children to be + + + align:start position:0% +their children to be +the next generation of them and I know a + + align:start position:0% +the next generation of them and I know a + + + align:start position:0% +the next generation of them and I know a +lot of people who don't so it's it's not + + align:start position:0% +lot of people who don't so it's it's not + + + align:start position:0% +lot of people who don't so it's it's not +a + + align:start position:0% +a + + + align:start position:0% +a +universal + + align:start position:0% + + + + align:start position:0% + +but what's the point of anything I don't + + align:start position:0% +but what's the point of anything I don't + + + align:start position:0% +but what's the point of anything I don't +want to get + + align:start position:0% +want to get + + + align:start position:0% +want to get +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +in we might be the only intelligent life + + align:start position:0% +in we might be the only intelligent life + + + align:start position:0% +in we might be the only intelligent life +in the universe and um in that case it's + + align:start position:0% +in the universe and um in that case it's + + + align:start position:0% +in the universe and um in that case it's +very important that we solve all our + + align:start position:0% +very important that we solve all our + + + align:start position:0% +very important that we solve all our +problems and make sure that something + + align:start position:0% +problems and make sure that something + + + align:start position:0% +problems and make sure that something +intelligent + + align:start position:0% +intelligent + + + align:start position:0% +intelligent +persists I think Carl San had some + + align:start position:0% +persists I think Carl San had some + + + align:start position:0% +persists I think Carl San had some +argument of that + + align:start position:0% +argument of that + + + align:start position:0% +argument of that +sort + + align:start position:0% +sort + + + align:start position:0% +sort +uh if you were sure that there were lots + + align:start position:0% +uh if you were sure that there were lots + + + align:start position:0% +uh if you were sure that there were lots +of others uh then then it wouldn't seem + + align:start position:0% +of others uh then then it wouldn't seem + + + align:start position:0% +of others uh then then it wouldn't seem +so + + align:start position:0% + + + + align:start position:0% + +important who's the new Carl San + + align:start position:0% + + + + align:start position:0% + +is there any who's the who's the + + align:start position:0% +is there any who's the who's the + + + align:start position:0% +is there any who's the who's the +no is there a public + + align:start position:0% +no is there a public + + + align:start position:0% +no is there a public +scientist + + align:start position:0% + + + + align:start position:0% + +who oh + + align:start position:0% + + + + align:start position:0% + +Tyson Brian Green he's he's very good uh + + align:start position:0% +Tyson Brian Green he's he's very good uh + + + align:start position:0% +Tyson Brian Green he's he's very good uh +Tyson is the uh + + align:start position:0% + + + + align:start position:0% + +astrophysicist Brian Green is a great + + align:start position:0% +astrophysicist Brian Green is a great + + + align:start position:0% +astrophysicist Brian Green is a great +actor it's quite + + align:start position:0% + + + + align:start position:0% + +impressive yeah when would you say a + + align:start position:0% +impressive yeah when would you say a + + + align:start position:0% +impressive yeah when would you say a +machine has a sense of self like we + + align:start position:0% +machine has a sense of self like we + + + align:start position:0% +machine has a sense of self like we +think there's something that's like a + + align:start position:0% +think there's something that's like a + + + align:start position:0% +think there's something that's like a +self inside us because partly because + + align:start position:0% +self inside us because partly because + + + align:start position:0% +self inside us because partly because +there's some processes we don't like sh + + align:start position:0% +there's some processes we don't like sh + + + align:start position:0% +there's some processes we don't like sh +from + + align:start position:0% + + + + align:start position:0% + +us but what would say machine + + align:start position:0% +us but what would say machine + + + align:start position:0% +us but what would say machine +well I think that's a funny question + + align:start position:0% +well I think that's a funny question + + + align:start position:0% +well I think that's a funny question +because uh if we're programming it we + + align:start position:0% +because uh if we're programming it we + + + align:start position:0% +because uh if we're programming it we +can make sure that the machine has a + + align:start position:0% +can make sure that the machine has a + + + align:start position:0% +can make sure that the machine has a +very good uh abstract but correct model + + align:start position:0% +very good uh abstract but correct model + + + align:start position:0% +very good uh abstract but correct model +of how it works which people don't so + + align:start position:0% +of how it works which people don't so + + + align:start position:0% +of how it works which people don't so +people have a sense of self but it's + + align:start position:0% +people have a sense of self but it's + + + align:start position:0% +people have a sense of self but it's +only a sense of self and it's it's just + + align:start position:0% +only a sense of self and it's it's just + + + align:start position:0% +only a sense of self and it's it's just +plain wrong in almost every every + + align:start position:0% +plain wrong in almost every every + + + align:start position:0% +plain wrong in almost every every +respect and uh so it's a it's it's a + + align:start position:0% +respect and uh so it's a it's it's a + + + align:start position:0% +respect and uh so it's a it's it's a +really funny question + + align:start position:0% +really funny question + + + align:start position:0% +really funny question +because when you make a machine that + + align:start position:0% +because when you make a machine that + + + align:start position:0% +because when you make a machine that +really has a good useful representation + + align:start position:0% +really has a good useful representation + + + align:start position:0% +really has a good useful representation +of what it is and how it works it might + + align:start position:0% +of what it is and how it works it might + + + align:start position:0% +of what it is and how it works it might +be quite different have different + + align:start position:0% +be quite different have different + + + align:start position:0% +be quite different have different +attitudes than a person does like it + + align:start position:0% +attitudes than a person does like it + + + align:start position:0% +attitudes than a person does like it +might not consider itself very valuable + + align:start position:0% +might not consider itself very valuable + + + align:start position:0% +might not consider itself very valuable +and say could say oh I could make + + align:start position:0% +and say could say oh I could make + + + align:start position:0% +and say could say oh I could make +something that's even better than me and + + align:start position:0% +something that's even better than me and + + + align:start position:0% +something that's even better than me and +jump into + + align:start position:0% +jump into + + + align:start position:0% +jump into +that and so it wouldn't have the it + + align:start position:0% +that and so it wouldn't have the it + + + align:start position:0% +that and so it wouldn't have the it +might not have any + + align:start position:0% +might not have any + + + align:start position:0% +might not have any +self-protective reaction + + align:start position:0% +self-protective reaction + + + align:start position:0% +self-protective reaction +because if you could improve yourself + + align:start position:0% +because if you could improve yourself + + + align:start position:0% +because if you could improve yourself +then you don't want not to whereas we're + + align:start position:0% +then you don't want not to whereas we're + + + align:start position:0% +then you don't want not to whereas we're +in a state where there's nothing much we + + align:start position:0% +in a state where there's nothing much we + + + align:start position:0% +in a state where there's nothing much we +can do except try to keep living and uh + + align:start position:0% +can do except try to keep living and uh + + + align:start position:0% +can do except try to keep living and uh +we don't have any + + align:start position:0% +we don't have any + + + align:start position:0% +we don't have any +alternative + + align:start position:0% +alternative + + + align:start position:0% +alternative +if stupid thing to + + align:start position:0% + + + + align:start position:0% + +say I can't imagine getting tired of + + align:start position:0% +say I can't imagine getting tired of + + + align:start position:0% +say I can't imagine getting tired of +living but lots of people + + align:start position:0% + + + + align:start position:0% + +do + + align:start position:0% +do + + + align:start position:0% +do +yeah do you think about creative + + align:start position:0% +yeah do you think about creative + + + align:start position:0% +yeah do you think about creative +thinking as a way of thinking and where + + align:start position:0% +thinking as a way of thinking and where + + + align:start position:0% +thinking as a way of thinking and where +does this creativity come from or + + align:start position:0% +does this creativity come from or + + + align:start position:0% +does this creativity come from or +anything + + align:start position:0% +anything + + + align:start position:0% +anything +that I had a little section about that + + align:start position:0% +that I had a little section about that + + + align:start position:0% +that I had a little section about that +somewhere that I wrote which was the + + align:start position:0% +somewhere that I wrote which was the + + + align:start position:0% +somewhere that I wrote which was the +difference between artists and + + align:start position:0% +difference between artists and + + + align:start position:0% +difference between artists and +scientists and + + align:start position:0% +scientists and + + + align:start position:0% +scientists and +engineers + + align:start position:0% + + + + align:start position:0% + +and Engineers are in have a very nice + + align:start position:0% +and Engineers are in have a very nice + + + align:start position:0% +and Engineers are in have a very nice +situation because they know what they + + align:start position:0% +situation because they know what they + + + align:start position:0% +situation because they know what they +want cuz somebody's ordered them to make + + align:start position:0% +want cuz somebody's ordered them to make + + + align:start position:0% +want cuz somebody's ordered them to make +a in the last month three times I've + + align:start position:0% +a in the last month three times I've + + + align:start position:0% +a in the last month three times I've +walked + + align:start position:0% +walked + + + align:start position:0% +walked +away from uh my computer + + align:start position:0% +away from uh my computer + + + align:start position:0% +away from uh my computer +and how many of you have a Mac with the + + align:start position:0% +and how many of you have a Mac with the + + + align:start position:0% +and how many of you have a Mac with the +magnetic + + align:start position:0% + + + + align:start position:0% + +thing and three times I pulled it with + + align:start position:0% +thing and three times I pulled it with + + + align:start position:0% +thing and three times I pulled it with +by tripping on this and it fell to the + + align:start position:0% +by tripping on this and it fell to the + + + align:start position:0% +by tripping on this and it fell to the +floor and didn't didn't + + align:start position:0% +floor and didn't didn't + + + align:start position:0% +floor and didn't didn't +break and I've had Max for 20 odd years + + align:start position:0% +break and I've had Max for 20 odd years + + + align:start position:0% +break and I've had Max for 20 odd years +or since 198 when did they + + align:start position:0% +or since 198 when did they + + + align:start position:0% +or since 198 when did they +start + + align:start position:0% +start + + + align:start position:0% +start +oo 30 years and uh they used they have + + align:start position:0% +oo 30 years and uh they used they have + + + align:start position:0% +oo 30 years and uh they used they have +the regular Jack power supply in the old + + align:start position:0% +the regular Jack power supply in the old + + + align:start position:0% +the regular Jack power supply in the old +days and I don't remember and usually + + align:start position:0% +days and I don't remember and usually + + + align:start position:0% +days and I don't remember and usually +when you pull the cord it comes out + + align:start position:0% +when you pull the cord it comes out + + + align:start position:0% +when you pull the cord it comes out +here's this cord that Steve Jobs and + + align:start position:0% +here's this cord that Steve Jobs and + + + align:start position:0% +here's this cord that Steve Jobs and +everybody designed very carefully so + + align:start position:0% +everybody designed very carefully so + + + align:start position:0% +everybody designed very carefully so +that when you pull it nothing bad would + + align:start position:0% + + + + align:start position:0% + +happen but it + + align:start position:0% + + + + align:start position:0% + +does how do you account for that it used + + align:start position:0% +does how do you account for that it used + + + align:start position:0% +does how do you account for that it used +to be better when the like plugs were + + align:start position:0% +to be better when the like plugs were + + + align:start position:0% +to be better when the like plugs were +perpendicular to and now it's kind + + align:start position:0% +perpendicular to and now it's kind + + + align:start position:0% +perpendicular to and now it's kind +of well it's quite a wide + + align:start position:0% +of well it's quite a wide + + + align:start position:0% +of well it's quite a wide +angle so it works at like a certain + + align:start position:0% +angle so it works at like a certain + + + align:start position:0% +angle so it works at like a certain +angle and the cable now instead of + + align:start position:0% +angle and the cable now instead of + + + align:start position:0% +angle and the cable now instead of +naturally lying in that area actually + + align:start position:0% +naturally lying in that area actually + + + align:start position:0% +naturally lying in that area actually +naturally lies in the area where it + + align:start position:0% +naturally lies in the area where it + + + align:start position:0% +naturally lies in the area where it +doesn't work well what it needs is a + + align:start position:0% +doesn't work well what it needs is a + + + align:start position:0% +doesn't work well what it needs is a +little ramp so that it would slide + + align:start position:0% +little ramp so that it would slide + + + align:start position:0% +little ramp so that it would slide +out I mean it would only take a minute + + align:start position:0% +out I mean it would only take a minute + + + align:start position:0% +out I mean it would only take a minute +to file it down so so that it would + + align:start position:0% +to file it down so so that it would + + + align:start position:0% +to file it down so so that it would +slide out right but they + + align:start position:0% +slide out right but they + + + align:start position:0% +slide out right but they +didn't I forget why I mentioned that + + align:start position:0% + + + + align:start position:0% + +but Engineers creativity right so what's + + align:start position:0% +but Engineers creativity right so what's + + + align:start position:0% +but Engineers creativity right so what's +the difference between an artist and + + align:start position:0% +the difference between an artist and + + + align:start position:0% +the difference between an artist and +engineer well when you do a painting + + align:start position:0% +engineer well when you do a painting + + + align:start position:0% +engineer well when you do a painting +it seems to me if you're already good at + + align:start position:0% +it seems to me if you're already good at + + + align:start position:0% +it seems to me if you're already good at +painting the 9/10 of the problem is what + + align:start position:0% +painting the 9/10 of the problem is what + + + align:start position:0% +painting the 9/10 of the problem is what +should I + + align:start position:0% +should I + + + align:start position:0% +should I +paint so you can think of an artist as + + align:start position:0% +paint so you can think of an artist as + + + align:start position:0% +paint so you can think of an artist as +10% skill and 90% trying to figure out + + align:start position:0% +10% skill and 90% trying to figure out + + + align:start position:0% +10% skill and 90% trying to figure out +what the problem is to solve whereas for + + align:start position:0% +what the problem is to solve whereas for + + + align:start position:0% +what the problem is to solve whereas for +the + + align:start position:0% +the + + + align:start position:0% +the +engineer uh somebody's told him what to + + align:start position:0% +engineer uh somebody's told him what to + + + align:start position:0% +engineer uh somebody's told him what to +do uh make a better cable connector and + + align:start position:0% +do uh make a better cable connector and + + + align:start position:0% +do uh make a better cable connector and +so he's going to spend 90% of his time + + align:start position:0% +so he's going to spend 90% of his time + + + align:start position:0% +so he's going to spend 90% of his time +actually solving the problem and only + + align:start position:0% +actually solving the problem and only + + + align:start position:0% +actually solving the problem and only +10% of the time trying to decide what + + align:start position:0% +10% of the time trying to decide what + + + align:start position:0% +10% of the time trying to decide what +problem to solve so I don't see any + + align:start position:0% +problem to solve so I don't see any + + + align:start position:0% +problem to solve so I don't see any +difference between artists and + + align:start position:0% +difference between artists and + + + align:start position:0% +difference between artists and +Engineers except + + align:start position:0% +Engineers except + + + align:start position:0% +Engineers except +that um the artist has more problems to + + align:start position:0% +that um the artist has more problems to + + + align:start position:0% +that um the artist has more problems to +solve than it could possibly solve and + + align:start position:0% +solve than it could possibly solve and + + + align:start position:0% +solve than it could possibly solve and +usually ends up by picking a really dumb + + align:start position:0% +usually ends up by picking a really dumb + + + align:start position:0% +usually ends up by picking a really dumb +one like let's have a saint and Three + + align:start position:0% +one like let's have a saint and Three + + + align:start position:0% +one like let's have a saint and Three +Angels where will I put the third + + align:start position:0% +Angels where will I put the third + + + align:start position:0% +Angels where will I put the third +Angel that's the engineering part + + align:start position:0% + + + + align:start position:0% + +just just + + align:start position:0% + + + + align:start position:0% + +improvising so the to me the media lab + + align:start position:0% +improvising so the to me the media lab + + + align:start position:0% +improvising so the to me the media lab +makes sense the artists and or semi + + align:start position:0% +makes sense the artists and or semi + + + align:start position:0% +makes sense the artists and or semi +artists and the scientists are doing + + align:start position:0% +artists and the scientists are doing + + + align:start position:0% +artists and the scientists are doing +almost the same thing and if you look at + + align:start position:0% +almost the same thing and if you look at + + + align:start position:0% +almost the same thing and if you look at +the more Arty people they're a little + + align:start position:0% +the more Arty people they're a little + + + align:start position:0% +the more Arty people they're a little +more concerned with human social + + align:start position:0% +more concerned with human social + + + align:start position:0% +more concerned with human social +relations and this and that and others + + align:start position:0% +relations and this and that and others + + + align:start position:0% +relations and this and that and others +are more more concerned with very + + align:start position:0% +are more more concerned with very + + + align:start position:0% +are more more concerned with very +technical specific aspects of signal + + align:start position:0% +technical specific aspects of signal + + + align:start position:0% +technical specific aspects of signal +processing or semantic + + align:start position:0% +processing or semantic + + + align:start position:0% +processing or semantic +representations so on but so I don't see + + align:start position:0% +representations so on but so I don't see + + + align:start position:0% +representations so on but so I don't see +much difference between the Arts and the + + align:start position:0% +much difference between the Arts and the + + + align:start position:0% +much difference between the Arts and the +sciences and then of course the Great + + align:start position:0% +sciences and then of course the Great + + + align:start position:0% +sciences and then of course the Great +Moments are when you run into people + + align:start position:0% +Moments are when you run into people + + + align:start position:0% +Moments are when you run into people +like Leonardo and Michelangelo who uh + + align:start position:0% +like Leonardo and Michelangelo who uh + + + align:start position:0% +like Leonardo and Michelangelo who uh +get some idea that requires a great new + + align:start position:0% +get some idea that requires a great new + + + align:start position:0% +get some idea that requires a great new +technical innovation that nobody has + + align:start position:0% +technical innovation that nobody has + + + align:start position:0% +technical innovation that nobody has +ever done + + align:start position:0% +ever done + + + align:start position:0% +ever done +and it's hard to separate them I think + + align:start position:0% +and it's hard to separate them I think + + + align:start position:0% +and it's hard to separate them I think +there's some place where + + align:start position:0% +there's some place where + + + align:start position:0% +there's some place where +Leonardo uh realizes that the lens in + + align:start position:0% +Leonardo uh realizes that the lens in + + + align:start position:0% +Leonardo uh realizes that the lens in +the eye would mean that the image is + + align:start position:0% +the eye would mean that the image is + + + align:start position:0% +the eye would mean that the image is +upside down on the retina and he + + align:start position:0% +upside down on the retina and he + + + align:start position:0% +upside down on the retina and he +couldn't stand that so there's a diagram + + align:start position:0% +couldn't stand that so there's a diagram + + + align:start position:0% +couldn't stand that so there's a diagram +he has where the corny is curved enough + + align:start position:0% +he has where the corny is curved enough + + + align:start position:0% +he has where the corny is curved enough +to invert the image and then the lens + + align:start position:0% +to invert the image and then the lens + + + align:start position:0% +to invert the image and then the lens +inverts it back + + align:start position:0% + + + + align:start position:0% + +again which is contrary to fact + + align:start position:0% +again which is contrary to fact + + + align:start position:0% +again which is contrary to fact +but he has a sketch showing that he was + + align:start position:0% +but he has a sketch showing that he was + + + align:start position:0% +but he has a sketch showing that he was +worried about + + align:start position:0% +worried about + + + align:start position:0% +worried about +if if the image were upside down on the + + align:start position:0% +if if the image were upside down on the + + + align:start position:0% +if if the image were upside down on the +retina wouldn't things look upside down + + align:start position:0% + + + + align:start position:0% + +but yeah I have related question did you + + align:start position:0% +but yeah I have related question did you + + + align:start position:0% +but yeah I have related question did you +ever heard + + align:start position:0% + + + + align:start position:0% + +about temporal memory and like temporal + + align:start position:0% +about temporal memory and like temporal + + + align:start position:0% +about temporal memory and like temporal +temporal + + align:start position:0% +temporal + + + align:start position:0% +temporal +memory like there's a system + + align:start position:0% +memory like there's a system + + + align:start position:0% +memory like there's a system +thaty to create that TR toate how our + + align:start position:0% +thaty to create that TR toate how our + + + align:start position:0% +thaty to create that TR toate how our +brain requirs + + align:start position:0% +brain requirs + + + align:start position:0% +brain requirs +stuff they have a company called LMA and + + align:start position:0% +stuff they have a company called LMA and + + + align:start position:0% +stuff they have a company called LMA and +they going to release a at the end of + + align:start position:0% +they going to release a at the end of + + + align:start position:0% +they going to release a at the end of +this year on it and there's like some + + align:start position:0% +this year on it and there's like some + + + align:start position:0% +this year on it and there's like some +research they have + + align:start position:0% +research they have + + + align:start position:0% +research they have +paper well I'm not sure + + align:start position:0% +paper well I'm not sure + + + align:start position:0% +paper well I'm not sure +what this is Hawkins project I don't + + align:start position:0% +what this is Hawkins project I don't + + + align:start position:0% +what this is Hawkins project I don't +yeah I haven't heard about 10 years ago + + align:start position:0% +yeah I haven't heard about 10 years ago + + + align:start position:0% +yeah I haven't heard about 10 years ago +he said Hawkins Yeahs yeah well he he + + align:start position:0% +he said Hawkins Yeahs yeah well he he + + + align:start position:0% +he said Hawkins Yeahs yeah well he he +was talking about 10 years ago how great + + align:start position:0% +was talking about 10 years ago how great + + + align:start position:0% +was talking about 10 years ago how great +it was and I haven't heard a word of any + + align:start position:0% +it was and I haven't heard a word of any + + + align:start position:0% +it was and I haven't heard a word of any +progress is there + + align:start position:0% +progress is there + + + align:start position:0% +progress is there +some have anybody heard + + align:start position:0% +some have anybody heard + + + align:start position:0% +some have anybody heard +of there's a couple of books about it + + align:start position:0% +of there's a couple of books about it + + + align:start position:0% +of there's a couple of books about it +but I've never seen any claim of that it + + align:start position:0% +but I've never seen any claim of that it + + + align:start position:0% +but I've never seen any claim of that it +works they wrote it for ious review of + + align:start position:0% +works they wrote it for ious review of + + + align:start position:0% +works they wrote it for ious review of +The Society of + + align:start position:0% +The Society of + + + align:start position:0% +The Society of +Mind in which came out in + + align:start position:0% +Mind in which came out in + + + align:start position:0% +Mind in which came out in +1986 and + + align:start position:0% +1986 and + + + align:start position:0% +1986 and +uh the Hawkins group existed then and + + align:start position:0% +uh the Hawkins group existed then and + + + align:start position:0% +uh the Hawkins group existed then and +had this talk about a hierarchical + + align:start position:0% +had this talk about a hierarchical + + + align:start position:0% +had this talk about a hierarchical +memory + + align:start position:0% + + + + align:start position:0% + +system but you + + align:start position:0% +system but you + + + align:start position:0% +system but you +have as far as I can tell it's all Bluff + + align:start position:0% +have as far as I can tell it's all Bluff + + + align:start position:0% +have as far as I can tell it's all Bluff +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +happened I've never seen a report that + + align:start position:0% +happened I've never seen a report that + + + align:start position:0% +happened I've never seen a report that +they have a machine which solved the + + align:start position:0% +they have a machine which solved the + + + align:start position:0% +they have a machine which solved the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +let me know if you find one because + + align:start position:0% + + + + align:start position:0% + +uh oh + + align:start position:0% +uh oh + + + align:start position:0% +uh oh +well Hawkins got really mad at me for + + align:start position:0% +well Hawkins got really mad at me for + + + align:start position:0% +well Hawkins got really mad at me for +pointing this + + align:start position:0% +pointing this + + + align:start position:0% +pointing this +out but I was really mad at him for + + align:start position:0% +out but I was really mad at him for + + + align:start position:0% +out but I was really mad at him for +having four of his assistants write a + + align:start position:0% +having four of his assistants write a + + + align:start position:0% +having four of his assistants write a +bad book review of my book + + align:start position:0% +bad book review of my book + + + align:start position:0% +bad book review of my book +so I hope we were + + align:start position:0% + + + + align:start position:0% + +even uh + + align:start position:0% +even uh + + + align:start position:0% +even uh +if anybody can find out whether I forget + + align:start position:0% +if anybody can find out whether I forget + + + align:start position:0% +if anybody can find out whether I forget +what it's called do you remember its + + align:start position:0% + + + + align:start position:0% + +name was the name of this compy uhhuh + + align:start position:0% +name was the name of this compy uhhuh + + + align:start position:0% +name was the name of this compy uhhuh +well let's find out if it can do + + align:start position:0% +well let's find out if it can do + + + align:start position:0% +well let's find out if it can do +anything + + align:start position:0% +anything + + + align:start position:0% +anything +yet Hawkins is wealthy enough to support + + align:start position:0% +yet Hawkins is wealthy enough to support + + + align:start position:0% +yet Hawkins is wealthy enough to support +it for a long time so it should be good + + align:start position:0% +it for a long time so it should be good + + + align:start position:0% +it for a long time so it should be good +by + + align:start position:0% + + + + align:start position:0% + +now yes do you think when going to solve + + align:start position:0% +now yes do you think when going to solve + + + align:start position:0% +now yes do you think when going to solve +a problem people first start out with + + align:start position:0% +a problem people first start out with + + + align:start position:0% +a problem people first start out with +some sort of um classification in their + + align:start position:0% +some sort of um classification in their + + + align:start position:0% +some sort of um classification in their +head of the kind of problem it is or is + + align:start position:0% +head of the kind of problem it is or is + + + align:start position:0% +head of the kind of problem it is or is +that not necessary yes that's + + align:start position:0% +that not necessary yes that's + + + align:start position:0% +that not necessary yes that's +uh + + align:start position:0% + + + + align:start position:0% + +well there's this huge book called human + + align:start position:0% +well there's this huge book called human + + + align:start position:0% +well there's this huge book called human +problem + + align:start position:0% +problem + + + align:start position:0% +problem +solving which was I don't know how many + + align:start position:0% +solving which was I don't know how many + + + align:start position:0% +solving which was I don't know how many +of you know the names of new and Simon + + align:start position:0% +of you know the names of new and Simon + + + align:start position:0% +of you know the names of new and Simon +originally was new Shaw and + + align:start position:0% +originally was new Shaw and + + + align:start position:0% +originally was new Shaw and +Simon and in the believe it or not in + + align:start position:0% +Simon and in the believe it or not in + + + align:start position:0% +Simon and in the believe it or not in +the late + + align:start position:0% +the late + + + align:start position:0% +the late +1950s they did some of the first really + + align:start position:0% +1950s they did some of the first really + + + align:start position:0% +1950s they did some of the first really +productive AI + + align:start position:0% +productive AI + + + align:start position:0% +productive AI +research + + align:start position:0% +research + + + align:start position:0% +research +and uh then I think in + + align:start position:0% +and uh then I think in + + + align:start position:0% +and uh then I think in +1970 so that's uh sort of after 12 years + + align:start position:0% +1970 so that's uh sort of after 12 years + + + align:start position:0% +1970 so that's uh sort of after 12 years +of uh discovering interesting things + + align:start position:0% +of uh discovering interesting things + + + align:start position:0% +of uh discovering interesting things +their main Discovery was the gadget that + + align:start position:0% +their main Discovery was the gadget that + + + align:start position:0% +their main Discovery was the gadget that +they called GPS which is not global + + align:start position:0% +they called GPS which is not global + + + align:start position:0% +they called GPS which is not global +positioning satellite but General + + align:start position:0% +positioning satellite but General + + + align:start position:0% +positioning satellite but General +Problem + + align:start position:0% +Problem + + + align:start position:0% +Problem +Solver and uh you can look it up in the + + align:start position:0% +Solver and uh you can look it up in the + + + align:start position:0% +Solver and uh you can look it up in the +index of my book and there's a sort of + + align:start position:0% +index of my book and there's a sort of + + + align:start position:0% +index of my book and there's a sort of +one or two page description but if you + + align:start position:0% +one or two page description but if you + + + align:start position:0% +one or two page description but if you +ever get some Spare Time U search the + + align:start position:0% +ever get some Spare Time U search the + + + align:start position:0% +ever get some Spare Time U search the +web for their early early paper by newel + + align:start position:0% +web for their early early paper by newel + + + align:start position:0% +web for their early early paper by newel +and Simon on how GPS worked cuz it's + + align:start position:0% +and Simon on how GPS worked cuz it's + + + align:start position:0% +and Simon on how GPS worked cuz it's +really fascinating what it did is it + + align:start position:0% +really fascinating what it did is it + + + align:start position:0% +really fascinating what it did is it +looked at a problem and found some + + align:start position:0% +looked at a problem and found some + + + align:start position:0% +looked at a problem and found some +features of it and then looked up in a + + align:start position:0% +features of it and then looked up in a + + + align:start position:0% +features of it and then looked up in a +table saying that if there's this + + align:start position:0% +table saying that if there's this + + + align:start position:0% +table saying that if there's this +difference between what you have and + + align:start position:0% +difference between what you have and + + + align:start position:0% +difference between what you have and +what you want use such and such a method + + align:start position:0% +what you want use such and such a method + + + align:start position:0% +what you want use such and such a method +so it was sort what I called it I + + align:start position:0% +so it was sort what I called it I + + + align:start position:0% +so it was sort what I called it I +renamed it A Difference Engine as a sort + + align:start position:0% +renamed it A Difference Engine as a sort + + + align:start position:0% +renamed it A Difference Engine as a sort +of joke because the first computer in + + align:start position:0% +of joke because the first computer in + + + align:start position:0% +of joke because the first computer in +history + + align:start position:0% +history + + + align:start position:0% +history +was uh the one called The Difference + + align:start position:0% +was uh the one called The Difference + + + align:start position:0% +was uh the one called The Difference +Engine but it was + + align:start position:0% +Engine but it was + + + align:start position:0% +Engine but it was +for predicting tides and things anyway + + align:start position:0% +for predicting tides and things anyway + + + align:start position:0% +for predicting tides and things anyway +uh they did some beautiful work and + + align:start position:0% +uh they did some beautiful work and + + + align:start position:0% +uh they did some beautiful work and +there's this big book which I think is + + align:start position:0% +there's this big book which I think is + + + align:start position:0% +there's this big book which I think is +about 1970 called human problem + + align:start position:0% +about 1970 called human problem + + + align:start position:0% +about 1970 called human problem +solving + + align:start position:0% +solving + + + align:start position:0% +solving +and what they did is uh got some people + + align:start position:0% +and what they did is uh got some people + + + align:start position:0% +and what they did is uh got some people +to solve problems and they trained the + + align:start position:0% +to solve problems and they trained the + + + align:start position:0% +to solve problems and they trained the +people to talk while they're solving the + + align:start position:0% +people to talk while they're solving the + + + align:start position:0% +people to talk while they're solving the +problem so some of them were little + + align:start position:0% +problem so some of them were little + + + align:start position:0% +problem so some of them were little +cryptograms like + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if each letter stands + + align:start position:0% +if each letter stands + + + align:start position:0% +if each letter stands +for for a + + align:start position:0% + + + + align:start position:0% + +digit I've forgotten + + align:start position:0% +digit I've forgotten + + + align:start position:0% +digit I've forgotten +it pat do you remember the name one of + + align:start position:0% +it pat do you remember the name one of + + + align:start position:0% +it pat do you remember the name one of +those + + align:start position:0% +those + + + align:start position:0% +those +problems John plus + + align:start position:0% +problems John plus + + + align:start position:0% +problems John plus +Joe John plus Jane equals Robert or + + align:start position:0% +Joe John plus Jane equals Robert or + + + align:start position:0% +Joe John plus Jane equals Robert or +something that I'm sure that has no + + align:start position:0% +something that I'm sure that has no + + + align:start position:0% +something that I'm sure that has no +solution but uh those are called Crypt + + align:start position:0% +solution but uh those are called Crypt + + + align:start position:0% +solution but uh those are called Crypt +arithmetic and uh so they had dozens or + + align:start position:0% +arithmetic and uh so they had dozens or + + + align:start position:0% +arithmetic and uh so they had dozens or +hundreds of people who would be trying + + align:start position:0% +hundreds of people who would be trying + + + align:start position:0% +hundreds of people who would be trying +to talk aloud while they're solving + + align:start position:0% +to talk aloud while they're solving + + + align:start position:0% +to talk aloud while they're solving +little puzzles like that and then uh + + align:start position:0% +little puzzles like that and then uh + + + align:start position:0% +little puzzles like that and then uh +what they did was uh look at exactly + + align:start position:0% +what they did was uh look at exactly + + + align:start position:0% +what they did was uh look at exactly +what the people said and how long they + + align:start position:0% +what the people said and how long they + + + align:start position:0% +what the people said and how long they +took and uh in some cases where they + + align:start position:0% +took and uh in some cases where they + + + align:start position:0% +took and uh in some cases where they +moved their eyes they had an eye + + align:start position:0% +moved their eyes they had an eye + + + align:start position:0% +moved their eyes they had an eye +tracking machine and then they wrote + + align:start position:0% +tracking machine and then they wrote + + + align:start position:0% +tracking machine and then they wrote +programs uh that showed how this guy + + align:start position:0% +programs uh that showed how this guy + + + align:start position:0% +programs uh that showed how this guy +solved a couple of these cryptarithmetic + + align:start position:0% +solved a couple of these cryptarithmetic + + + align:start position:0% +solved a couple of these cryptarithmetic +problems then they ran the program on on + + align:start position:0% +problems then they ran the program on on + + + align:start position:0% +problems then they ran the program on on +a new one and in some rare cases it + + align:start position:0% +a new one and in some rare cases it + + + align:start position:0% +a new one and in some rare cases it +actually solved the uh the other problem + + align:start position:0% +actually solved the uh the other problem + + + align:start position:0% +actually solved the uh the other problem +so this is a book which uh looks at + + align:start position:0% +so this is a book which uh looks at + + + align:start position:0% +so this is a book which uh looks at +human behavior and makes a theory of + + align:start position:0% +human behavior and makes a theory of + + + align:start position:0% +human behavior and makes a theory of +what it's doing and the output is a + + align:start position:0% +what it's doing and the output is a + + + align:start position:0% +what it's doing and the output is a +rule-based system so it's uh it's not a + + align:start position:0% +rule-based system so it's uh it's not a + + + align:start position:0% +rule-based system so it's uh it's not a +very exciting Theory but but uh there + + align:start position:0% +very exciting Theory but but uh there + + + align:start position:0% +very exciting Theory but but uh there +have never been anything like it in pych + + align:start position:0% +have never been anything like it in pych + + + align:start position:0% +have never been anything like it in pych +you know it was like Pavlov discovering + + align:start position:0% +you know it was like Pavlov discovering + + + align:start position:0% +you know it was like Pavlov discovering +conditioned reflexes for rat s or dogs + + align:start position:0% +conditioned reflexes for rat s or dogs + + + align:start position:0% +conditioned reflexes for rat s or dogs +and nle and Simon are discovering some + + align:start position:0% +and nle and Simon are discovering some + + + align:start position:0% +and nle and Simon are discovering some +rather higher + + align:start position:0% +rather higher + + + align:start position:0% +rather higher +level + + align:start position:0% +level + + + align:start position:0% +level +um almost a Rodney Brooks likee system + + align:start position:0% +um almost a Rodney Brooks likee system + + + align:start position:0% +um almost a Rodney Brooks likee system +for how humans solve some problems that + + align:start position:0% +for how humans solve some problems that + + + align:start position:0% +for how humans solve some problems that +most people find pretty hard you um + + align:start position:0% + + + + align:start position:0% + +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +uh what there hasn't been is + + align:start position:0% +uh what there hasn't been is + + + align:start position:0% +uh what there hasn't been is +much I don't of any followup they spent + + align:start position:0% +much I don't of any followup they spent + + + align:start position:0% +much I don't of any followup they spent +years perfecting those experiments and + + align:start position:0% +years perfecting those experiments and + + + align:start position:0% +years perfecting those experiments and +writing + + align:start position:0% +writing + + + align:start position:0% +writing +about + + align:start position:0% + + + + align:start position:0% + +results anybody know anything like that + + align:start position:0% +results anybody know anything like that + + + align:start position:0% +results anybody know anything like that +what psychologist are trying to + + align:start position:0% +what psychologist are trying to + + + align:start position:0% +what psychologist are trying to +make real models of real people + + align:start position:0% +make real models of real people + + + align:start position:0% +make real models of real people +solving + + align:start position:0% + + + + align:start position:0% + +problems + + align:start position:0% + + + + align:start position:0% + +it has a green light it has a green + + align:start position:0% +it has a green light it has a green + + + align:start position:0% +it has a green light it has a green +light but the switch was up boo oh it + + align:start position:0% + + + + align:start position:0% + +does yes did that particular study um + + align:start position:0% +does yes did that particular study um + + + align:start position:0% +does yes did that particular study um +try to see when a person gave up on a + + align:start position:0% +try to see when a person gave up on a + + + align:start position:0% +try to see when a person gave up on a +particular problem solving method how + + align:start position:0% +particular problem solving method how + + + align:start position:0% +particular problem solving method how +they switch another which one they + + align:start position:0% +they switch another which one they + + + align:start position:0% +they switch another which one they +switch to based + + align:start position:0% +switch to based + + + align:start position:0% +switch to based +on it has it has + + align:start position:0% +on it has it has + + + align:start position:0% +on it has it has +inexplicable points at which the person + + align:start position:0% +inexplicable points at which the person + + + align:start position:0% +inexplicable points at which the person +suddenly gives up on that representation + + align:start position:0% +suddenly gives up on that representation + + + align:start position:0% +suddenly gives up on that representation +and he says oh well I + + align:start position:0% +and he says oh well I + + + align:start position:0% +and he says oh well I +guess I guess R must be + + align:start position:0% + + + + align:start position:0% + +three did I erase + + align:start position:0% +three did I erase + + + align:start position:0% +three did I erase +well yes it's got episodes and they + + align:start position:0% +well yes it's got episodes and they + + + align:start position:0% +well yes it's got episodes and they +can't account for + + align:start position:0% +can't account for + + + align:start position:0% +can't account for +the these little jerks in the + + align:start position:0% +the these little jerks in the + + + align:start position:0% +the these little jerks in the +script where the model + + align:start position:0% +script where the model + + + align:start position:0% +script where the model +changes and + + align:start position:0% + + + + align:start position:0% + +sorry and they announced those to be + + align:start position:0% +sorry and they announced those to be + + + align:start position:0% +sorry and they announced those to be +Mysteries and say Here's a place where + + align:start position:0% +Mysteries and say Here's a place where + + + align:start position:0% +Mysteries and say Here's a place where +the person has decided the strategy + + align:start position:0% +the person has decided the strategy + + + align:start position:0% +the person has decided the strategy +isn't working and starts over or is + + align:start position:0% +isn't working and starts over or is + + + align:start position:0% +isn't working and starts over or is +changing + + align:start position:0% +changing + + + align:start position:0% +changing +something the amazing part is that their + + align:start position:0% +something the amazing part is that their + + + align:start position:0% +something the amazing part is that their +model sometimes fits what the person + + align:start position:0% +model sometimes fits what the person + + + align:start position:0% +model sometimes fits what the person +says for 50 or even a 100 steps the guy + + align:start position:0% +says for 50 or even a 100 steps the guy + + + align:start position:0% +says for 50 or even a 100 steps the guy +saying oh I think two must be Z must be + + align:start position:0% +saying oh I think two must be Z must be + + + align:start position:0% +saying oh I think two must be Z must be +two and and P must be seven and that + + align:start position:0% +two and and P must be seven and that + + + align:start position:0% +two and and P must be seven and that +means P plus Z is nine and I wonder + + align:start position:0% +means P plus Z is nine and I wonder + + + align:start position:0% +means P plus Z is nine and I wonder +what's nine and uh so their model fits + + align:start position:0% +what's nine and uh so their model fits + + + align:start position:0% +what's nine and uh so their model fits +for very + + align:start position:0% +for very + + + align:start position:0% +for very +long uh strings maybe two minutes of the + + align:start position:0% +long uh strings maybe two minutes of the + + + align:start position:0% +long uh strings maybe two minutes of the +person + + align:start position:0% +person + + + align:start position:0% +person +mumbling uh to + + align:start position:0% +mumbling uh to + + + align:start position:0% +mumbling uh to +themselves and then it breaks and then + + align:start position:0% +themselves and then it breaks and then + + + align:start position:0% +themselves and then it breaks and then +there's another + + align:start position:0% +there's another + + + align:start position:0% +there's another +sequence so new actually + + align:start position:0% +sequence so new actually + + + align:start position:0% +sequence so new actually +spent more than a year here after doing + + align:start position:0% +spent more than a year here after doing + + + align:start position:0% +spent more than a year here after doing +it + + align:start position:0% +it + + + align:start position:0% +it +verbally + + align:start position:0% +verbally + + + align:start position:0% +verbally +uh at tracking the person's eye motions + + align:start position:0% +uh at tracking the person's eye motions + + + align:start position:0% +uh at tracking the person's eye motions +and trying to correlate the person's eye + + align:start position:0% +and trying to correlate the person's eye + + + align:start position:0% +and trying to correlate the person's eye +motions with what the person was talking + + align:start position:0% +motions with what the person was talking + + + align:start position:0% +motions with what the person was talking +about and guess + + align:start position:0% +about and guess + + + align:start position:0% +about and guess +what + + align:start position:0% + + + + align:start position:0% + +none it was almost as though you look at + + align:start position:0% +none it was almost as though you look at + + + align:start position:0% +none it was almost as though you look at +something and then to think about it you + + align:start position:0% +something and then to think about it you + + + align:start position:0% +something and then to think about it you +look away it was uh new was quite + + align:start position:0% +look away it was uh new was quite + + + align:start position:0% +look away it was uh new was quite +distressed because he spent about a year + + align:start position:0% +distressed because he spent about a year + + + align:start position:0% +distressed because he spent about a year +crawling over this data trying to figure + + align:start position:0% +crawling over this data trying to figure + + + align:start position:0% +crawling over this data trying to figure +out what kinds of mental events caused + + align:start position:0% +out what kinds of mental events caused + + + align:start position:0% +out what kinds of mental events caused +the eyes to change what they were + + align:start position:0% +the eyes to change what they were + + + align:start position:0% +the eyes to change what they were +looking at but when the problem got hard + + align:start position:0% +looking at but when the problem got hard + + + align:start position:0% +looking at but when the problem got hard +you would look at a blank part of the + + align:start position:0% +you would look at a blank part of the + + + align:start position:0% +you would look at a blank part of the +thing more more often than uh the place + + align:start position:0% +thing more more often than uh the place + + + align:start position:0% +thing more more often than uh the place +where the problem turned + + align:start position:0% +where the problem turned + + + align:start position:0% +where the problem turned +up so conclusion + + align:start position:0% +up so conclusion + + + align:start position:0% +up so conclusion +it that didn't + + align:start position:0% +it that didn't + + + align:start position:0% +it that didn't +work when I was a very young student in + + align:start position:0% +work when I was a very young student in + + + align:start position:0% +work when I was a very young student in +college I had + + align:start position:0% +college I had + + + align:start position:0% +college I had +a friend named Marcus singer + + align:start position:0% +a friend named Marcus singer + + + align:start position:0% +a friend named Marcus singer +who was trying to figure out how the + + align:start position:0% +who was trying to figure out how the + + + align:start position:0% +who was trying to figure out how the +nerve in the forelimb of a frog + + align:start position:0% +nerve in the forelimb of a frog + + + align:start position:0% +nerve in the forelimb of a frog +worked and so he was operating on + + align:start position:0% +worked and so he was operating on + + + align:start position:0% +worked and so he was operating on +tadpoles + + align:start position:0% +tadpoles + + + align:start position:0% +tadpoles +and he spent about six weeks prep moving + + align:start position:0% +and he spent about six weeks prep moving + + + align:start position:0% +and he spent about six weeks prep moving +this sciatic nerve from the leg up to + + align:start position:0% +this sciatic nerve from the leg up to + + + align:start position:0% +this sciatic nerve from the leg up to +the arm of this tadp + + align:start position:0% +the arm of this tadp + + + align:start position:0% +the arm of this tadp +and then they all got some fungus and + + align:start position:0% + + + + align:start position:0% + +died so I said what are you going to do + + align:start position:0% +died so I said what are you going to do + + + align:start position:0% +died so I said what are you going to do +and he said + + align:start position:0% +and he said + + + align:start position:0% +and he said +well I guess I'll have to do it + + align:start position:0% +well I guess I'll have to do it + + + align:start position:0% +well I guess I'll have to do it +again and I switch from biology to + + align:start position:0% +again and I switch from biology to + + + align:start position:0% +again and I switch from biology to +[Laughter] + + align:start position:0% + + + + align:start position:0% + +mathematics but in fact he discovered + + align:start position:0% +mathematics but in fact he discovered + + + align:start position:0% +mathematics but in fact he discovered +the growth hormone that he thought came + + align:start position:0% +the growth hormone that he thought came + + + align:start position:0% +the growth hormone that he thought came +from the nerve and made the if you cut + + align:start position:0% +from the nerve and made the if you cut + + + align:start position:0% +from the nerve and made the if you cut +off the limb Bud of a tadpole it'll grow + + align:start position:0% +off the limb Bud of a tadpole it'll grow + + + align:start position:0% +off the limb Bud of a tadpole it'll grow +another one and grow a whole it was a + + align:start position:0% +another one and grow a whole it was a + + + align:start position:0% +another one and grow a whole it was a +nud I'm sorry it's salamander it'll grow + + align:start position:0% +nud I'm sorry it's salamander it'll grow + + + align:start position:0% +nud I'm sorry it's salamander it'll grow +a new + + align:start position:0% +a new + + + align:start position:0% +a new +hand if you wait till it's got a + + align:start position:0% +hand if you wait till it's got a + + + align:start position:0% +hand if you wait till it's got a +substantial hand it won't grow a new one + + align:start position:0% +substantial hand it won't grow a new one + + + align:start position:0% +substantial hand it won't grow a new one +but uh he discovered the hormone that + + align:start position:0% +but uh he discovered the hormone that + + + align:start position:0% +but uh he discovered the hormone that +makes it do that yeah oh yeah um + + align:start position:0% +makes it do that yeah oh yeah um + + + align:start position:0% +makes it do that yeah oh yeah um +questions from the homework that kind of + + align:start position:0% +questions from the homework that kind of + + + align:start position:0% +questions from the homework that kind of +relates to problem solving thing um a + + align:start position:0% +relates to problem solving thing um a + + + align:start position:0% +relates to problem solving thing um a +common theme is having multiple ways to + + align:start position:0% +common theme is having multiple ways to + + + align:start position:0% +common theme is having multiple ways to +react to the same problem but how do we + + align:start position:0% +react to the same problem but how do we + + + align:start position:0% +react to the same problem but how do we +choose which option to add as possible + + align:start position:0% +choose which option to add as possible + + + align:start position:0% +choose which option to add as possible +reactions to the same problem oh so we + + align:start position:0% +reactions to the same problem oh so we + + + align:start position:0% +reactions to the same problem oh so we +have a whole lot of if then and we have + + align:start position:0% +have a whole lot of if then and we have + + + align:start position:0% +have a whole lot of if then and we have +to choose which + + align:start position:0% +to choose which + + + align:start position:0% +to choose which +if I don't think I have a good theory of + + align:start position:0% + + + + align:start position:0% + +that yes if you have a huge rule-based + + align:start position:0% +that yes if you have a huge rule-based + + + align:start position:0% +that yes if you have a huge rule-based +system and they're what does Randy Davis + + align:start position:0% +system and they're what does Randy Davis + + + align:start position:0% +system and they're what does Randy Davis +do what if you have a rule-based system + + align:start position:0% +do what if you have a rule-based system + + + align:start position:0% +do what if you have a rule-based system +and a whole lot of rules fit ifs fit the + + align:start position:0% +and a whole lot of rules fit ifs fit the + + + align:start position:0% +and a whole lot of rules fit ifs fit the +condition do you just take the one + + align:start position:0% +condition do you just take the one + + + align:start position:0% +condition do you just take the one +that's most often + + align:start position:0% +that's most often + + + align:start position:0% +that's most often +worked or if nothing seems to be working + + align:start position:0% +worked or if nothing seems to be working + + + align:start position:0% +worked or if nothing seems to be working +do + + align:start position:0% +do + + + align:start position:0% +do +you you certainly don't want to keep + + align:start position:0% +you you certainly don't want to keep + + + align:start position:0% +you you certainly don't want to keep +trying the same + + align:start position:0% + + + + align:start position:0% + +one I think I mentioned Doug lett's rule + + align:start position:0% +one I think I mentioned Doug lett's rule + + + align:start position:0% +one I think I mentioned Doug lett's rule +so people will assign probabilities to + + align:start position:0% +so people will assign probabilities to + + + align:start position:0% +so people will assign probabilities to +things to uh behaviors and then uh pick + + align:start position:0% +things to uh behaviors and then uh pick + + + align:start position:0% +things to uh behaviors and then uh pick +the way to react in proportional to the + + align:start position:0% +the way to react in proportional to the + + + align:start position:0% +the way to react in proportional to the +probability that that thing has worked + + align:start position:0% +probability that that thing has worked + + + align:start position:0% +probability that that thing has worked +in the past and Doug + + align:start position:0% +in the past and Doug + + + align:start position:0% +in the past and Doug +lenet thought of doing that but instead + + align:start position:0% +lenet thought of doing that but instead + + + align:start position:0% +lenet thought of doing that but instead +he just put the things in a list and + + align:start position:0% +he just put the things in a list and + + + align:start position:0% +he just put the things in a list and +whenever a + + align:start position:0% +whenever a + + + align:start position:0% +whenever a +hypothesis worked better than another + + align:start position:0% +hypothesis worked better than another + + + align:start position:0% +hypothesis worked better than another +one he would raise it push it toward the + + align:start position:0% +one he would raise it push it toward the + + + align:start position:0% +one he would raise it push it toward the +front of the list and then whenever + + align:start position:0% +front of the list and then whenever + + + align:start position:0% +front of the list and then whenever +there was a choice it would + + align:start position:0% +there was a choice it would + + + align:start position:0% +there was a choice it would +pick if all the rules that fit it would + + align:start position:0% +pick if all the rules that fit it would + + + align:start position:0% +pick if all the rules that fit it would +pick the one at the top of the list and + + align:start position:0% +pick the one at the top of the list and + + + align:start position:0% +pick the one at the top of the list and +if that didn't work it would get + + align:start position:0% +if that didn't work it would get + + + align:start position:0% +if that didn't work it would get +demoted + + align:start position:0% +demoted + + + align:start position:0% +demoted +so uh that's when I became an anti- + + align:start position:0% +so uh that's when I became an anti- + + + align:start position:0% +so uh that's when I became an anti- +probability + + align:start position:0% +probability + + + align:start position:0% +probability +person that is if just sorting the + + align:start position:0% +person that is if just sorting the + + + align:start position:0% +person that is if just sorting the +things on a list worked pretty + + align:start position:0% +things on a list worked pretty + + + align:start position:0% +things on a list worked pretty +well uh our probability is going to do + + align:start position:0% +well uh our probability is going to do + + + align:start position:0% +well uh our probability is going to do +much better no because if you do + + align:start position:0% +much better no because if you do + + + align:start position:0% +much better no because if you do +probability + + align:start position:0% +probability + + + align:start position:0% +probability +matching you're worse off + + align:start position:0% +matching you're worse off + + + align:start position:0% +matching you're worse off +than than + + align:start position:0% + + + + align:start position:0% + +what Ray solomonov discovered that if + + align:start position:0% +what Ray solomonov discovered that if + + + align:start position:0% +what Ray solomonov discovered that if +you have a set of probabilities that + + align:start position:0% +you have a set of probabilities that + + + align:start position:0% +you have a set of probabilities that +something will + + align:start position:0% +something will + + + align:start position:0% +something will +work and you have no memory so that each + + align:start position:0% +work and you have no memory so that each + + + align:start position:0% +work and you have no memory so that each +time you come and uh try + + align:start position:0% +time you come and uh try + + + align:start position:0% +time you come and uh try +the I think I mentioned that the other + + align:start position:0% +the I think I mentioned that the other + + + align:start position:0% +the I think I mentioned that the other +day but it's worth emphasizing because + + align:start position:0% +day but it's worth emphasizing because + + + align:start position:0% +day but it's worth emphasizing because +nobody in the world seems to know + + align:start position:0% + + + + align:start position:0% + +it suppose you have a list of things P + + align:start position:0% +it suppose you have a list of things P + + + align:start position:0% +it suppose you have a list of things P +equals this or that or + + align:start position:0% + + + + align:start position:0% + +that and + + align:start position:0% +that and + + + align:start position:0% +that and +uh in other words suppose there's a 100 + + align:start position:0% +uh in other words suppose there's a 100 + + + align:start position:0% +uh in other words suppose there's a 100 +boxes here + + align:start position:0% +boxes here + + + align:start position:0% +boxes here +and one of them has a + + align:start position:0% +and one of them has a + + + align:start position:0% +and one of them has a +gold brick in + + align:start position:0% +gold brick in + + + align:start position:0% +gold brick in +it and the others don't and so for each + + align:start position:0% +it and the others don't and so for each + + + align:start position:0% +it and the others don't and so for each +box suppose the probability is + + align:start position:0% +box suppose the probability is + + + align:start position:0% +box suppose the probability is +0.9 that this one has the gold + + align:start position:0% +0.9 that this one has the gold + + + align:start position:0% +0.9 that this one has the gold +brick and this one has + + align:start position:0% +brick and this one has + + + align:start position:0% +brick and this one has +0.01 and this has + + align:start position:0% +0.01 and this has + + + align:start position:0% +0.01 and this has +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +0.01 let's see how many of them so + + align:start position:0% +0.01 let's see how many of them so + + + align:start position:0% +0.01 let's see how many of them so +there's 10 of these that + + align:start position:0% + + + + align:start position:0% + +makes now what should you do suppose + + align:start position:0% +makes now what should you do suppose + + + align:start position:0% +makes now what should you do suppose +you're allowed + + align:start position:0% +you're allowed + + + align:start position:0% +you're allowed +to uh keep choosing a box and you want + + align:start position:0% +to uh keep choosing a box and you want + + + align:start position:0% +to uh keep choosing a box and you want +to get your gold brick as soon as + + align:start position:0% +to get your gold brick as soon as + + + align:start position:0% +to get your gold brick as soon as +possible what's the smart thing to do + + align:start position:0% +possible what's the smart thing to do + + + align:start position:0% +possible what's the smart thing to do +should you but you have no + + align:start position:0% + + + + align:start position:0% + +memory or maybe the gold brick is + + align:start position:0% +memory or maybe the gold brick is + + + align:start position:0% +memory or maybe the gold brick is +decreasing in value I don't care but so + + align:start position:0% +decreasing in value I don't care but so + + + align:start position:0% +decreasing in value I don't care but so +should you keep trying 0. + + align:start position:0% +should you keep trying 0. + + + align:start position:0% +should you keep trying 0. +n if you have no memory well of course + + align:start position:0% +n if you have no memory well of course + + + align:start position:0% +n if you have no memory well of course +not because if you don't get it the + + align:start position:0% +not because if you don't get it the + + + align:start position:0% +not because if you don't get it the +first time you'll never get + + align:start position:0% +first time you'll never get + + + align:start position:0% +first time you'll never get +it whereas if you tried them at + + align:start position:0% +it whereas if you tried them at + + + align:start position:0% +it whereas if you tried them at +random each time then you'd have 0.9 + + align:start position:0% +random each time then you'd have 0.9 + + + align:start position:0% +random each time then you'd have 0.9 +chance of getting it so in in two trials + + align:start position:0% +chance of getting it so in in two trials + + + align:start position:0% +chance of getting it so in in two trials +you'd + + align:start position:0% +you'd + + + align:start position:0% +you'd +have what am I saying you know 100 + + align:start position:0% +have what am I saying you know 100 + + + align:start position:0% +have what am I saying you know 100 +trials you're pretty sure to get it but + + align:start position:0% +trials you're pretty sure to get it but + + + align:start position:0% +trials you're pretty sure to get it but +in e00 Trials + + align:start position:0% +in e00 Trials + + + align:start position:0% +in e00 Trials +uh almost certain so if you don't have + + align:start position:0% +uh almost certain so if you don't have + + + align:start position:0% +uh almost certain so if you don't have +any + + align:start position:0% +any + + + align:start position:0% +any +memory then probability matching is not + + align:start position:0% +memory then probability matching is not + + + align:start position:0% +memory then probability matching is not +a good + + align:start position:0% +a good + + + align:start position:0% +a good +idea certainly picking the highest + + align:start position:0% +idea certainly picking the highest + + + align:start position:0% +idea certainly picking the highest +probability is not a good idea because + + align:start position:0% +probability is not a good idea because + + + align:start position:0% +probability is not a good idea because +if you don't get it the first trial + + align:start position:0% +if you don't get it the first trial + + + align:start position:0% +if you don't get it the first trial +you'll never get it if you keep using + + align:start position:0% +you'll never get it if you keep using + + + align:start position:0% +you'll never get it if you keep using +the + + align:start position:0% +the + + + align:start position:0% +the +probabilities um + + align:start position:0% +probabilities um + + + align:start position:0% +probabilities um +at what am I saying anyway what do you + + align:start position:0% +at what am I saying anyway what do you + + + align:start position:0% +at what am I saying anyway what do you +think is the best thing to do it's to + + align:start position:0% +think is the best thing to do it's to + + + align:start position:0% +think is the best thing to do it's to +take the square roots of those + + align:start position:0% +take the square roots of those + + + align:start position:0% +take the square roots of those +probabilities and then divide them by + + align:start position:0% +probabilities and then divide them by + + + align:start position:0% +probabilities and then divide them by +the sum of the square roots so it adds + + align:start position:0% +the sum of the square roots so it adds + + + align:start position:0% +the sum of the square roots so it adds +up to + + align:start position:0% +up to + + + align:start position:0% +up to +one and uh so a lot of psychologists + + align:start position:0% +one and uh so a lot of psychologists + + + align:start position:0% +one and uh so a lot of psychologists +design experiments until they get the + + align:start position:0% +design experiments until they get the + + + align:start position:0% +design experiments until they get the +rat to match the + + align:start position:0% +rat to match the + + + align:start position:0% +rat to match the +probability and then they publish it + + align:start position:0% +probability and then they publish it + + + align:start position:0% +probability and then they publish it +sort of like the uh + + align:start position:0% + + + + align:start position:0% + +but if the animal is optimal and doesn't + + align:start position:0% +but if the animal is optimal and doesn't + + + align:start position:0% +but if the animal is optimal and doesn't +have much memory then it shouldn't match + + align:start position:0% +have much memory then it shouldn't match + + + align:start position:0% +have much memory then it shouldn't match +the probability of the unknown it should + + align:start position:0% +the probability of the unknown it should + + + align:start position:0% +the probability of the unknown it should +uh end of + + align:start position:0% + + + + align:start position:0% + +story every now and then I + + align:start position:0% +story every now and then I + + + align:start position:0% +story every now and then I +search uh every few years to see if + + align:start position:0% +search uh every few years to see if + + + align:start position:0% +search uh every few years to see if +anybody has noticed this thing which + + align:start position:0% +anybody has noticed this thing which + + + align:start position:0% +anybody has noticed this thing which +uh and I've never found it on the + + align:start position:0% + + + + align:start position:0% + +web yeah so earlier in the course class + + align:start position:0% +web yeah so earlier in the course class + + + align:start position:0% +web yeah so earlier in the course class +you mentioned that their rule base + + align:start position:0% +you mentioned that their rule base + + + align:start position:0% +you mentioned that their rule base +methods didn't work and that several + + align:start position:0% +methods didn't work and that several + + + align:start position:0% +methods didn't work and that several +other methods were tried in6 and80s + + align:start position:0% +other methods were tried in6 and80s + + + align:start position:0% +other methods were tried in6 and80s +could you go into a bit about what these + + align:start position:0% +could you go into a bit about what these + + + align:start position:0% +could you go into a bit about what these +other methods were that have been tried + + align:start position:0% +other methods were that have been tried + + + align:start position:0% +other methods were that have been tried +I didn't didn't don't mean to say they + + align:start position:0% +I didn't didn't don't mean to say they + + + align:start position:0% +I didn't didn't don't mean to say they +don't work rule-based methods are great + + align:start position:0% +don't work rule-based methods are great + + + align:start position:0% +don't work rule-based methods are great +for some kinds of problems so most + + align:start position:0% + + + + align:start position:0% + +uh most systems uh make money and you + + align:start position:0% +uh most systems uh make money and you + + + align:start position:0% +uh most systems uh make money and you +know if if you're trying to + + align:start position:0% + + + + align:start position:0% + +uh make hotel reservations and things + + align:start position:0% +uh make hotel reservations and things + + + align:start position:0% +uh make hotel reservations and things +um this business is a rule-based system + + align:start position:0% +um this business is a rule-based system + + + align:start position:0% +um this business is a rule-based system +uh it has a nice history a couple of AI + + align:start position:0% +uh it has a nice history a couple of AI + + + align:start position:0% +uh it has a nice history a couple of AI +researchers really notably Ed Fen bam + + align:start position:0% +researchers really notably Ed Fen bam + + + align:start position:0% +researchers really notably Ed Fen bam +who was a student of new and + + align:start position:0% + + + + align:start position:0% + +Simon started a company for making + + align:start position:0% +Simon started a company for making + + + align:start position:0% +Simon started a company for making +rule-based + + align:start position:0% +rule-based + + + align:start position:0% +rule-based +systems and Company did pretty well for + + align:start position:0% +systems and Company did pretty well for + + + align:start position:0% +systems and Company did pretty well for +a while + + align:start position:0% +a while + + + align:start position:0% +a while +until uh and they maintained that only + + align:start position:0% +until uh and they maintained that only + + + align:start position:0% +until uh and they maintained that only +an expert in artificial intelligence uh + + align:start position:0% +an expert in artificial intelligence uh + + + align:start position:0% +an expert in artificial intelligence uh +could be really good at making + + align:start position:0% +could be really good at making + + + align:start position:0% +could be really good at making +rule-based systems and so they had a lot + + align:start position:0% +rule-based systems and so they had a lot + + + align:start position:0% +rule-based systems and so they had a lot +of customers and quite a bit of success + + align:start position:0% +of customers and quite a bit of success + + + align:start position:0% +of customers and quite a bit of success +for a year or + + align:start position:0% +for a year or + + + align:start position:0% +for a year or +two and then some people at Arthur D + + align:start position:0% +two and then some people at Arthur D + + + align:start position:0% +two and then some people at Arthur D +little said oh we can do that and they + + align:start position:0% +little said oh we can do that and they + + + align:start position:0% +little said oh we can do that and they +made some systems that worked fine and + + align:start position:0% +made some systems that worked fine and + + + align:start position:0% +made some systems that worked fine and +uh the market disappeared because it + + align:start position:0% +uh the market disappeared because it + + + align:start position:0% +uh the market disappeared because it +turned out that you didn't have to be + + align:start position:0% +turned out that you didn't have to be + + + align:start position:0% +turned out that you didn't have to be +good at anything in particular to make + + align:start position:0% +good at anything in particular to make + + + align:start position:0% +good at anything in particular to make +rule-based systems work + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +but for doing harder problems like + + align:start position:0% +but for doing harder problems like + + + align:start position:0% +but for doing harder problems like +translating from one language to + + align:start position:0% +translating from one language to + + + align:start position:0% +translating from one language to +another uh you really needed to have + + align:start position:0% +another uh you really needed to have + + + align:start position:0% +another uh you really needed to have +more structure and you couldn't just + + align:start position:0% +more structure and you couldn't just + + + align:start position:0% +more structure and you couldn't just +take the probabilities of words being in + + align:start position:0% +take the probabilities of words being in + + + align:start position:0% +take the probabilities of words being in +a sentence but you had to look for + + align:start position:0% +a sentence but you had to look for + + + align:start position:0% +a sentence but you had to look for +diagrams and trigrams + + align:start position:0% +diagrams and trigrams + + + align:start position:0% +diagrams and trigrams +and have some grammar Theory and so + + align:start position:0% +and have some grammar Theory and so + + + align:start position:0% +and have some grammar Theory and so +forth + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +but generally if you have + + align:start position:0% +but generally if you have + + + align:start position:0% +but generally if you have +a + + align:start position:0% +a + + + align:start position:0% +a +ordinary data processing problem try a + + align:start position:0% +ordinary data processing problem try a + + + align:start position:0% +ordinary data processing problem try a +rule-based system first + + align:start position:0% +rule-based system first + + + align:start position:0% +rule-based system first +because if you understand what's going + + align:start position:0% +because if you understand what's going + + + align:start position:0% +because if you understand what's going +on it's good chance you'll get things to + + align:start position:0% +on it's good chance you'll get things to + + + align:start position:0% +on it's good chance you'll get things to +work I'm sure that's what the + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +Hawkins thing started out in + + align:start position:0% + + + + align:start position:0% + +I don't have any + + align:start position:0% + + + + align:start position:0% + +questions sure + + align:start position:0% +questions sure + + + align:start position:0% +questions sure +um uh computers or machines can use + + align:start position:0% +um uh computers or machines can use + + + align:start position:0% +um uh computers or machines can use +relatively few electronic components to + + align:start position:0% +relatively few electronic components to + + + align:start position:0% +relatively few electronic components to +run a batch of different types of + + align:start position:0% +run a batch of different types of + + + align:start position:0% +run a batch of different types of +thought operations all that changes is + + align:start position:0% +thought operations all that changes is + + + align:start position:0% +thought operations all that changes is +data over which the operation runs in + + align:start position:0% +data over which the operation runs in + + + align:start position:0% +data over which the operation runs in +the critic selector model are resources + + align:start position:0% +the critic selector model are resources + + + align:start position:0% +the critic selector model are resources +different bundles of data or different + + align:start position:0% +different bundles of data or different + + + align:start position:0% +different bundles of data or different +physical parts of the brain which model + + align:start position:0% +physical parts of the brain which model + + + align:start position:0% +physical parts of the brain which model +um the uh critics leor + + align:start position:0% +um the uh critics leor + + + align:start position:0% +um the uh critics leor +model oh + + align:start position:0% + + + + align:start position:0% + +actually + + align:start position:0% +actually + + + align:start position:0% +actually +I've never seen + + align:start position:0% + + + + align:start position:0% + +a I've never seen a large scale theory + + align:start position:0% +a I've never seen a large scale theory + + + align:start position:0% +a I've never seen a large scale theory +of how the + + align:start position:0% +of how the + + + align:start position:0% +of how the +brain connects + + align:start position:0% +brain connects + + + align:start position:0% +brain connects +its there doesn't seem to be a a global + + align:start position:0% +its there doesn't seem to be a a global + + + align:start position:0% +its there doesn't seem to be a a global +model anywhere anybody read any + + align:start position:0% +model anywhere anybody read any + + + align:start position:0% +model anywhere anybody read any +uh Neuroscience books + + align:start position:0% + + + + align:start position:0% + +lately I + + align:start position:0% +lately I + + + align:start position:0% +lately I +mean I + + align:start position:0% +mean I + + + align:start position:0% +mean I +I just don't know of + + align:start position:0% +I just don't know of + + + align:start position:0% +I just don't know of +any any big + + align:start position:0% + + + + align:start position:0% + +diagrams here's this wonderful + + align:start position:0% +diagrams here's this wonderful + + + align:start position:0% +diagrams here's this wonderful +behavioral diagram + + align:start position:0% + + + + align:start position:0% + +so how many of you have run across the + + align:start position:0% +so how many of you have run across the + + + align:start position:0% +so how many of you have run across the +word + + align:start position:0% + + + + align:start position:0% + +ethology just a + + align:start position:0% +ethology just a + + + align:start position:0% +ethology just a +few there's a branch of the psychology + + align:start position:0% +few there's a branch of the psychology + + + align:start position:0% +few there's a branch of the psychology +of + + align:start position:0% +of + + + align:start position:0% +of +animals which is + + align:start position:0% + + + + align:start position:0% + +thanks which is called + + align:start position:0% +thanks which is called + + + align:start position:0% +thanks which is called +ethology and it's the study of + + align:start position:0% +ethology and it's the study of + + + align:start position:0% +ethology and it's the study of +instinctive + + align:start position:0% +instinctive + + + align:start position:0% +instinctive +Behavior + + align:start position:0% +Behavior + + + align:start position:0% +Behavior +Uh so these and the most famous people + + align:start position:0% +Uh so these and the most famous people + + + align:start position:0% +Uh so these and the most famous people +in that + + align:start position:0% + + + + align:start position:0% + +field who well tinbergen niiko tinbergen + + align:start position:0% +field who well tinbergen niiko tinbergen + + + align:start position:0% +field who well tinbergen niiko tinbergen +and Conrad lorence are the most + + align:start position:0% +and Conrad lorence are the most + + + align:start position:0% +and Conrad lorence are the most +famous I've just lost the name of + + align:start position:0% +famous I've just lost the name of + + + align:start position:0% +famous I've just lost the name of +the guy around the + + align:start position:0% +the guy around the + + + align:start position:0% +the guy around the +1900 who wrote uh a lot about the + + align:start position:0% +1900 who wrote uh a lot about the + + + align:start position:0% +1900 who wrote uh a lot about the +behavior of + + align:start position:0% +behavior of + + + align:start position:0% +behavior of +ants + + align:start position:0% +ants + + + align:start position:0% +ants +anybody ring a + + align:start position:0% +anybody ring a + + + align:start position:0% +anybody ring a +bell so he was the sort of the first + + align:start position:0% +bell so he was the sort of the first + + + align:start position:0% +bell so he was the sort of the first +ethologist and these people don't study + + align:start position:0% +ethologist and these people don't study + + + align:start position:0% +ethologist and these people don't study +learning because it's hard to I don't + + align:start position:0% +learning because it's hard to I don't + + + align:start position:0% +learning because it's hard to I don't +know why but uh so they're studying + + align:start position:0% +know why but uh so they're studying + + + align:start position:0% +know why but uh so they're studying +instinctive Behavior which is what are + + align:start position:0% +instinctive Behavior which is what are + + + align:start position:0% +instinctive Behavior which is what are +the things that all fish do of of a + + align:start position:0% +the things that all fish do of of a + + + align:start position:0% +the things that all fish do of of a +certain species and uh you get these big + + align:start position:0% +certain species and uh you get these big + + + align:start position:0% +certain species and uh you get these big +diagrams + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +uh this is from a little book which you + + align:start position:0% +uh this is from a little book which you + + + align:start position:0% +uh this is from a little book which you +really should read called the study of + + align:start position:0% + + + + align:start position:0% + +instinct + + align:start position:0% + + + + align:start position:0% + +and it's a beautiful + + align:start position:0% +and it's a beautiful + + + align:start position:0% +and it's a beautiful +book and if that's not + + align:start position:0% +book and if that's not + + + align:start position:0% +book and if that's not +enough then there's a TW + + align:start position:0% +enough then there's a TW + + + align:start position:0% +enough then there's a TW +volume similar Book By Conrad + + align:start position:0% +volume similar Book By Conrad + + + align:start position:0% +volume similar Book By Conrad +Laurence who + + align:start position:0% +Laurence who + + + align:start position:0% +Laurence who +uh was Austrian + + align:start position:0% +uh was Austrian + + + align:start position:0% +uh was Austrian +researcher um they were + + align:start position:0% +researcher um they were + + + align:start position:0% +researcher um they were +they did a lot of stuff together these + + align:start position:0% +they did a lot of stuff together these + + + align:start position:0% +they did a lot of stuff together these +two people and it's full of diagrams + + align:start position:0% +two people and it's full of diagrams + + + align:start position:0% +two people and it's full of diagrams +showing the main behaviors that they + + align:start position:0% +showing the main behaviors that they + + + align:start position:0% +showing the main behaviors that they +were able to observe of various uh + + align:start position:0% +were able to observe of various uh + + + align:start position:0% +were able to observe of various uh +lowcost + + align:start position:0% +lowcost + + + align:start position:0% +lowcost +animals uh I think I mentioned that I + + align:start position:0% +animals uh I think I mentioned that I + + + align:start position:0% +animals uh I think I mentioned that I +had some fish and I watched the fish + + align:start position:0% +had some fish and I watched the fish + + + align:start position:0% +had some fish and I watched the fish +tanks what they were doing for a very + + align:start position:0% +tanks what they were doing for a very + + + align:start position:0% +tanks what they were doing for a very +long time + + align:start position:0% +long time + + + align:start position:0% +long time +and came to no conclusions at all and + + align:start position:0% +and came to no conclusions at all and + + + align:start position:0% +and came to no conclusions at all and +when I finally read tinbergen and + + align:start position:0% +when I finally read tinbergen and + + + align:start position:0% +when I finally read tinbergen and +Laurence I realized + + align:start position:0% +Laurence I realized + + + align:start position:0% +Laurence I realized +I just it never occurred to me to to + + align:start position:0% +I just it never occurred to me to to + + + align:start position:0% +I just it never occurred to me to to +guess what to look + + align:start position:0% + + + + align:start position:0% + +for my favorite one + + align:start position:0% +for my favorite one + + + align:start position:0% +for my favorite one +was that whenever a fire engine went + + align:start position:0% +was that whenever a fire engine went + + + align:start position:0% +was that whenever a fire engine went +by loreno's stickle backs the male + + align:start position:0% +by loreno's stickle backs the male + + + align:start position:0% +by loreno's stickle backs the male +stickle backs would go crazy and look + + align:start position:0% +stickle backs would go crazy and look + + + align:start position:0% +stickle backs would go crazy and look +for a female because when the female's + + align:start position:0% +for a female because when the female's + + + align:start position:0% +for a female because when the female's +in heat or whatever it's called + + align:start position:0% +in heat or whatever it's called + + + align:start position:0% +in heat or whatever it's called +estrus Uh the lower abdomen turns + + align:start position:0% +estrus Uh the lower abdomen turns + + + align:start position:0% +estrus Uh the lower abdomen turns +red I think fire engines have turned + + align:start position:0% +red I think fire engines have turned + + + align:start position:0% +red I think fire engines have turned +yellow recently so no one I don't know + + align:start position:0% +yellow recently so no one I don't know + + + align:start position:0% +yellow recently so no one I don't know +what the sticklebacks do about + + align:start position:0% + + + + align:start position:0% + +that so if you're just in + + align:start position:0% +that so if you're just in + + + align:start position:0% +that so if you're just in +AI you really should look at at at least + + align:start position:0% +AI you really should look at at at least + + + align:start position:0% +AI you really should look at at at least +one of these people + + align:start position:0% +one of these people + + + align:start position:0% +one of these people +because it's the first appearance of + + align:start position:0% +because it's the first appearance of + + + align:start position:0% +because it's the first appearance of +rule-based systems in great detail in + + align:start position:0% +rule-based systems in great detail in + + + align:start position:0% +rule-based systems in great detail in +Psychology didn't get in there weren't + + align:start position:0% +Psychology didn't get in there weren't + + + align:start position:0% +Psychology didn't get in there weren't +any computers + + align:start position:0% + + + + align:start position:0% + +yet there must be 20 Questions + + align:start position:0% + + + + align:start position:0% + +left yeah + + align:start position:0% +left yeah + + + align:start position:0% +left yeah +uh while we're on the topic of ethology + + align:start position:0% +uh while we're on the topic of ethology + + + align:start position:0% +uh while we're on the topic of ethology +so I know that uh early on people were + + align:start position:0% +so I know that uh early on people were + + + align:start position:0% +so I know that uh early on people were +kind + + align:start position:0% +kind + + + align:start position:0% +kind +of they're careful not to apply ethology + + align:start position:0% +of they're careful not to apply ethology + + + align:start position:0% +of they're careful not to apply ethology +to + + align:start position:0% +to + + + align:start position:0% +to +humans um until about what 60 EO Wilson + + align:start position:0% +humans um until about what 60 EO Wilson + + + align:start position:0% +humans um until about what 60 EO Wilson +with uh + + align:start position:0% +with uh + + + align:start position:0% +with uh +sociobiology so I was wondering about + + align:start position:0% +sociobiology so I was wondering about + + + align:start position:0% +sociobiology so I was wondering about +your opinion on that and maybe even have + + align:start position:0% +your opinion on that and maybe even have + + + align:start position:0% +your opinion on that and maybe even have +anecdotes about the time I pretty + + align:start position:0% +anecdotes about the time I pretty + + + align:start position:0% +anecdotes about the time I pretty +controversial around this area + + align:start position:0% +controversial around this area + + + align:start position:0% +controversial around this area +especially oh I don't know uh + + align:start position:0% +especially oh I don't know uh + + + align:start position:0% +especially oh I don't know uh +I sort of grew up with Ed Wilson because + + align:start position:0% +I sort of grew up with Ed Wilson because + + + align:start position:0% +I sort of grew up with Ed Wilson because +we had the same fellowship at Harvard + + align:start position:0% +we had the same fellowship at Harvard + + + align:start position:0% +we had the same fellowship at Harvard +for three years but he was almost never + + align:start position:0% +for three years but he was almost never + + + align:start position:0% +for three years but he was almost never +there because he was out in the jungle + + align:start position:0% +there because he was out in the jungle + + + align:start position:0% +there because he was out in the jungle +in some little telephone booth watching + + align:start position:0% +in some little telephone booth watching + + + align:start position:0% +in some little telephone booth watching +the birds or be + + align:start position:0% + + + + align:start position:0% + +or he also had a 26-year-old + + align:start position:0% +or he also had a 26-year-old + + + align:start position:0% +or he also had a 26-year-old +aunt aunt not aunt + + align:start position:0% + + + + align:start position:0% + +aunt + + align:start position:0% + + + + align:start position:0% + +ant I'm not sure what the controversy + + align:start position:0% +ant I'm not sure what the controversy + + + align:start position:0% +ant I'm not sure what the controversy +would have been but of + + align:start position:0% + + + + align:start position:0% + +course there would be humanists who + + align:start position:0% +course there would be humanists who + + + align:start position:0% +course there would be humanists who +would say people aren't animals + + align:start position:0% + + + + align:start position:0% + +but but then what the devil are + + align:start position:0% + + + + align:start position:0% + +they why aren't they better than they + + align:start position:0% + + + + align:start position:0% + +you've got to read this it's a fairly + + align:start position:0% +you've got to read this it's a fairly + + + align:start position:0% +you've got to read this it's a fairly +short book and you'll never see an + + align:start position:0% +short book and you'll never see an + + + align:start position:0% +short book and you'll never see an +animal as the same again because uh I + + align:start position:0% +animal as the same again because uh I + + + align:start position:0% +animal as the same again because uh I +swear you start to notice all these + + align:start position:0% +swear you start to notice all these + + + align:start position:0% +swear you start to notice all these +little things you're probably wrong but + + align:start position:0% +little things you're probably wrong but + + + align:start position:0% +little things you're probably wrong but +you start picking up little pieces of + + align:start position:0% +you start picking up little pieces of + + + align:start position:0% +you start picking up little pieces of +behavior and trying to figure + + align:start position:0% +behavior and trying to figure + + + align:start position:0% +behavior and trying to figure +out what what part of the Instinct + + align:start position:0% +out what what part of the Instinct + + + align:start position:0% +out what what part of the Instinct +system is it + + align:start position:0% + + + + align:start position:0% + +lorence was particularly I think in + + align:start position:0% +lorence was particularly I think in + + + align:start position:0% +lorence was particularly I think in +chapter two of + + align:start position:0% +chapter two of + + + align:start position:0% +chapter two of +the emotion machine I have some quotes + + align:start position:0% +the emotion machine I have some quotes + + + align:start position:0% +the emotion machine I have some quotes +from these guys and + + align:start position:0% +from these guys and + + + align:start position:0% +from these guys and +uh lorence was particularly interested + + align:start position:0% +uh lorence was particularly interested + + + align:start position:0% +uh lorence was particularly interested +in in how uh animals got attached to + + align:start position:0% +in in how uh animals got attached to + + + align:start position:0% +in in how uh animals got attached to +their parents that is for those animals + + align:start position:0% +their parents that is for those animals + + + align:start position:0% +their parents that is for those animals +that do get attached attaching their bre + + align:start position:0% +that do get attached attaching their bre + + + align:start position:0% +that do get attached attaching their bre +like alligator babies live in the + + align:start position:0% +like alligator babies live in the + + + align:start position:0% +like alligator babies live in the +alligator's mouth uh for quite a + + align:start position:0% +alligator's mouth uh for quite a + + + align:start position:0% +alligator's mouth uh for quite a +while it's a good safe + + align:start position:0% + + + + align:start position:0% + +place and + + align:start position:0% +place and + + + align:start position:0% +place and +um lorence would + + align:start position:0% + + + + align:start position:0% + +uh catch birds just when they're + + align:start position:0% +uh catch birds just when they're + + + align:start position:0% +uh catch birds just when they're +hatching and within the first day or so + + align:start position:0% +hatching and within the first day or so + + + align:start position:0% +hatching and within the first day or so +some baby birds get attached to whatever + + align:start position:0% +some baby birds get attached to whatever + + + align:start position:0% +some baby birds get attached to whatever +large moving object is + + align:start position:0% +large moving object is + + + align:start position:0% +large moving object is +nearby and he that was often Conrad + + align:start position:0% +nearby and he that was often Conrad + + + align:start position:0% +nearby and he that was often Conrad +lorence rather than the + + align:start position:0% +lorence rather than the + + + align:start position:0% +lorence rather than the +bird's mother who's supposed to be + + align:start position:0% +bird's mother who's supposed to be + + + align:start position:0% +bird's mother who's supposed to be +sitting on the egg when it hatches and + + align:start position:0% +sitting on the egg when it hatches and + + + align:start position:0% +sitting on the egg when it hatches and +the bird gets attached to the mother + + align:start position:0% +the bird gets attached to the mother + + + align:start position:0% +the bird gets attached to the mother +most most birds do because uh they have + + align:start position:0% +most most birds do because uh they have + + + align:start position:0% +most most birds do because uh they have +to stay around and get + + align:start position:0% +to stay around and get + + + align:start position:0% +to stay around and get +fed uh + + align:start position:0% +fed uh + + + align:start position:0% +fed uh +so it is said that wherever lorence went + + align:start position:0% +so it is said that wherever lorence went + + + align:start position:0% +so it is said that wherever lorence went +in + + align:start position:0% +in + + + align:start position:0% +in +Vienna uh there would some ducks or + + align:start position:0% +Vienna uh there would some ducks or + + + align:start position:0% +Vienna uh there would some ducks or +whatever birds that had gotten imprinted + + align:start position:0% +whatever birds that had gotten imprinted + + + align:start position:0% +whatever birds that had gotten imprinted +on him would come out of the sky and + + align:start position:0% +on him would come out of the sky and + + + align:start position:0% +on him would come out of the sky and +land on his shoulder + + align:start position:0% +land on his shoulder + + + align:start position:0% +land on his shoulder +and and on no one else and he has + + align:start position:0% +and and on no one else and he has + + + align:start position:0% +and and on no one else and he has +various theories of how they recognize + + align:start position:0% +various theories of how they recognize + + + align:start position:0% +various theories of how they recognize +him + + align:start position:0% +him + + + align:start position:0% +him +but but you could do that + + align:start position:0% + + + + align:start position:0% + +too anyway that was quite a field this + + align:start position:0% +too anyway that was quite a field this + + + align:start position:0% +too anyway that was quite a field this +thing called + + align:start position:0% +thing called + + + align:start position:0% +thing called +ethology and between 1920 and 1950 1930 + + align:start position:0% +ethology and between 1920 and 1950 1930 + + + align:start position:0% +ethology and between 1920 and 1950 1930 +I guess 1950 there were lots of people + + align:start position:0% +I guess 1950 there were lots of people + + + align:start position:0% +I guess 1950 there were lots of people +studying the behavior of animals and Ed + + align:start position:0% +studying the behavior of animals and Ed + + + align:start position:0% +studying the behavior of animals and Ed +Wilson is probably + + align:start position:0% +Wilson is probably + + + align:start position:0% +Wilson is probably +the most uh well-known successor to Len + + align:start position:0% +the most uh well-known successor to Len + + + align:start position:0% +the most uh well-known successor to Len +and + + align:start position:0% +and + + + align:start position:0% +and +tinbergen and I think he just wrote a + + align:start position:0% +tinbergen and I think he just wrote a + + + align:start position:0% +tinbergen and I think he just wrote a +book is that anybody anybody seen + + align:start position:0% +book is that anybody anybody seen + + + align:start position:0% +book is that anybody anybody seen +it he has a huge book called + + align:start position:0% +it he has a huge book called + + + align:start position:0% +it he has a huge book called +sociobiology which is too heavy to + + align:start position:0% + + + + align:start position:0% + +read I've run out of + + align:start position:0% +read I've run out of + + + align:start position:0% +read I've run out of +things + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +ideas that + + align:start position:0% +ideas that + + + align:start position:0% +ideas that +book had Machinery from it um what would + + align:start position:0% +book had Machinery from it um what would + + + align:start position:0% +book had Machinery from it um what would +the initial state of the machine be if + + align:start position:0% +the initial state of the machine be if + + + align:start position:0% +the initial state of the machine be if +we would to start something is that + + align:start position:0% +we would to start something is that + + + align:start position:0% +we would to start something is that +dictated by the goals given to it by + + align:start position:0% +dictated by the goals given to it by + + + align:start position:0% +dictated by the goals given to it by +State I mean from different agents the + + align:start position:0% +State I mean from different agents the + + + align:start position:0% +State I mean from different agents the +resources they have access to what would + + align:start position:0% +resources they have access to what would + + + align:start position:0% +resources they have access to what would +that initial State look + + align:start position:0% +that initial State look + + + align:start position:0% +that initial State look +like he's asking if you were if you made + + align:start position:0% +like he's asking if you were if you made + + + align:start position:0% +like he's asking if you were if you made +a model of the program to Society of + + align:start position:0% +a model of the program to Society of + + + align:start position:0% +a model of the program to Society of +Mind architecture what would you put in + + align:start position:0% +Mind architecture what would you put in + + + align:start position:0% +Mind architecture what would you put in +it to start with I never thought about + + align:start position:0% +it to start with I never thought about + + + align:start position:0% +it to start with I never thought about +that it's great question I guess it + + align:start position:0% +that it's great question I guess it + + + align:start position:0% +that it's great question I guess it +depends whether you want it to be a + + align:start position:0% +depends whether you want it to be a + + + align:start position:0% +depends whether you want it to be a +person or a marad + + align:start position:0% +person or a marad + + + align:start position:0% +person or a marad +or chicken or + + align:start position:0% + + + + align:start position:0% + +something are there some animals that + + align:start position:0% +something are there some animals that + + + align:start position:0% +something are there some animals that +don't learn anything must + + align:start position:0% +don't learn anything must + + + align:start position:0% +don't learn anything must +be what do the + + align:start position:0% +be what do the + + + align:start position:0% +be what do the +uh ones at Sydney brener study they + + align:start position:0% +uh ones at Sydney brener study they + + + align:start position:0% +uh ones at Sydney brener study they +learn + + align:start position:0% +learn + + + align:start position:0% +learn +I me very simple associations the little + + align:start position:0% + + + + align:start position:0% + +worms there was a rumor that if you fed + + align:start position:0% +worms there was a rumor that if you fed + + + align:start position:0% +worms there was a rumor that if you fed +them + + align:start position:0% +them + + + align:start position:0% +them +RNA was it them or was it some slightly + + align:start position:0% +RNA was it them or was it some slightly + + + align:start position:0% +RNA was it them or was it some slightly +higher + + align:start position:0% +higher + + + align:start position:0% +higher +animal it was worms what R interference + + align:start position:0% +animal it was worms what R interference + + + align:start position:0% +animal it was worms what R interference +that talking about yeah there was one + + align:start position:0% +that talking about yeah there was one + + + align:start position:0% +that talking about yeah there was one +that if you Tau a worm to turn left when + + align:start position:0% +that if you Tau a worm to turn left when + + + align:start position:0% +that if you Tau a worm to turn left when +there was a bright light + + align:start position:0% +there was a bright light + + + align:start position:0% +there was a bright light +or right and put some of its RNA into + + align:start position:0% +or right and put some of its RNA into + + + align:start position:0% +or right and put some of its RNA into +another + + align:start position:0% +another + + + align:start position:0% +another +worm uh that worm would uh copy that + + align:start position:0% +worm uh that worm would uh copy that + + + align:start position:0% +worm uh that worm would uh copy that +reaction even though it hadn't been + + align:start position:0% +reaction even though it hadn't been + + + align:start position:0% +reaction even though it hadn't been +trained and this was that wasn't worms + + align:start position:0% +trained and this was that wasn't worms + + + align:start position:0% +trained and this was that wasn't worms +that was slugs slugs I think it was yes + + align:start position:0% +that was slugs slugs I think it was yes + + + align:start position:0% +that was slugs slugs I think it was yes +or something some little snail like + + align:start position:0% +or something some little snail like + + + align:start position:0% +or something some little snail like +thing uh and nobody was ever able to + + align:start position:0% +thing uh and nobody was ever able to + + + align:start position:0% +thing uh and nobody was ever able to +replicate it so it's that rumors spread + + align:start position:0% +replicate it so it's that rumors spread + + + align:start position:0% +replicate it so it's that rumors spread +around the world quite happily + + align:start position:0% +around the world quite happily + + + align:start position:0% +around the world quite happily +and + + align:start position:0% +and + + + align:start position:0% +and +uh there was a great science fiction + + align:start position:0% +uh there was a great science fiction + + + align:start position:0% +uh there was a great science fiction +story trying to + + align:start position:0% +story trying to + + + align:start position:0% +story trying to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +remember in which + + align:start position:0% +remember in which + + + align:start position:0% +remember in which +uh somebody got to eat some of an + + align:start position:0% +uh somebody got to eat some of an + + + align:start position:0% +uh somebody got to eat some of an +alien's RNA and got magical + + align:start position:0% + + + + align:start position:0% + +powers I think it's Larry nien who + + align:start position:0% +powers I think it's Larry nien who + + + align:start position:0% +powers I think it's Larry nien who +is wonderful wonderful at taking little + + align:start position:0% +is wonderful wonderful at taking little + + + align:start position:0% +is wonderful wonderful at taking little +scientific ideas and making a novel out + + align:start position:0% +scientific ideas and making a novel out + + + align:start position:0% +scientific ideas and making a novel out +of + + align:start position:0% +of + + + align:start position:0% +of +them and his wife Marilyn was + + align:start position:0% + + + + align:start position:0% + +a undergraduate + + align:start position:0% +a undergraduate + + + align:start position:0% +a undergraduate +here + + align:start position:0% + + + + align:start position:0% + +so she introduced me to Larry nien + + align:start position:0% + + + + align:start position:0% + +and I once got to write an artic I once + + align:start position:0% +and I once got to write an artic I once + + + align:start position:0% +and I once got to write an artic I once +gave a lecture and he wrote it up + + align:start position:0% +gave a lecture and he wrote it up + + + align:start position:0% +gave a lecture and he wrote it up +it was one of the big Thrills + + align:start position:0% +it was one of the big Thrills + + + align:start position:0% +it was one of the big Thrills +because nian is one of my heroes imagine + + align:start position:0% +because nian is one of my heroes imagine + + + align:start position:0% +because nian is one of my heroes imagine +writing a book with a good idea in every + + align:start position:0% + + + + align:start position:0% + +paragraph verer vingi and Larry nien and + + align:start position:0% +paragraph verer vingi and Larry nien and + + + align:start position:0% +paragraph verer vingi and Larry nien and +Frederick + + align:start position:0% +Frederick + + + align:start position:0% +Frederick +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +pole seem to be able to do that or at + + align:start position:0% +pole seem to be able to do that or at + + + align:start position:0% +pole seem to be able to do that or at +least on every page I don't know about + + align:start position:0% +least on every page I don't know about + + + align:start position:0% +least on every page I don't know about +every + + align:start position:0% +every + + + align:start position:0% +every +paragraph + + align:start position:0% +paragraph + + + align:start position:0% +paragraph +yeah to follow up on that question it + + align:start position:0% +yeah to follow up on that question it + + + align:start position:0% +yeah to follow up on that question it +seems to me that you are you almost were + + align:start position:0% +seems to me that you are you almost were + + + align:start position:0% +seems to me that you are you almost were +saying that um if this machiner exists + + align:start position:0% +saying that um if this machiner exists + + + align:start position:0% +saying that um if this machiner exists +the difference between um you know these + + align:start position:0% +the difference between um you know these + + + align:start position:0% +the difference between um you know these +sort of animals would be the start State + + align:start position:0% +sort of animals would be the start State + + + align:start position:0% +sort of animals would be the start State +and depending on the start State we + + align:start position:0% +and depending on the start State we + + + align:start position:0% +and depending on the start State we +could either create like a chicken or a + + align:start position:0% +could either create like a chicken or a + + + align:start position:0% +could either create like a chicken or a +human well no I don't think + + align:start position:0% + + + + align:start position:0% + +that I don't think that most animals + + align:start position:0% +that I don't think that most animals + + + align:start position:0% +that I don't think that most animals +have + + align:start position:0% +have + + + align:start position:0% +have +Scripts they some might + + align:start position:0% +Scripts they some might + + + align:start position:0% +Scripts they some might +but but + + align:start position:0% +but but + + + align:start position:0% +but but +uh you know I'd say + + align:start position:0% + + + + align:start position:0% + +that I don't know where most animals are + + align:start position:0% +that I don't know where most animals are + + + align:start position:0% +that I don't know where most animals are +but + + align:start position:0% +but + + + align:start position:0% +but +but I sort of make these six levels and + + align:start position:0% +but I sort of make these six levels and + + + align:start position:0% +but I sort of make these six levels and +I'd say that none of the animals have + + align:start position:0% +I'd say that none of the animals have + + + align:start position:0% +I'd say that none of the animals have +this top self-reflected layer except for + + align:start position:0% +this top self-reflected layer except for + + + align:start position:0% +this top self-reflected layer except for +all we know dolphins and uh chimpanzees + + align:start position:0% +all we know dolphins and uh chimpanzees + + + align:start position:0% +all we know dolphins and uh chimpanzees +and whatever it would be nice to know + + align:start position:0% +and whatever it would be nice to know + + + align:start position:0% +and whatever it would be nice to know +more about octopuses + + align:start position:0% +more about octopuses + + + align:start position:0% +more about octopuses +because uh they do so much wonderful + + align:start position:0% +because uh they do so much wonderful + + + align:start position:0% +because uh they do so much wonderful +things with their eight + + align:start position:0% +things with their eight + + + align:start position:0% +things with their eight +legs what kind + + align:start position:0% +legs what kind + + + align:start position:0% +legs what kind +of how does it + + align:start position:0% +of how does it + + + align:start position:0% +of how does it +manage have you seen pictures of an + + align:start position:0% +manage have you seen pictures of an + + + align:start position:0% +manage have you seen pictures of an +octopus picking up a shell and walking + + align:start position:0% +octopus picking up a shell and walking + + + align:start position:0% +octopus picking up a shell and walking +to some quiet place and it's got there's + + align:start position:0% +to some quiet place and it's got there's + + + align:start position:0% +to some quiet place and it's got there's +some movies of this on the + + align:start position:0% +some movies of this on the + + + align:start position:0% +some movies of this on the +web and then it drops the shell and + + align:start position:0% +web and then it drops the shell and + + + align:start position:0% +web and then it drops the shell and +climbs under it and + + align:start position:0% + + + + align:start position:0% + +disappears it's hard to imagine + + align:start position:0% +disappears it's hard to imagine + + + align:start position:0% +disappears it's hard to imagine +programming a robot to do + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +yeah so uh I've noticed both in your + + align:start position:0% +yeah so uh I've noticed both in your + + + align:start position:0% +yeah so uh I've noticed both in your +books and in the lecture a lot of your + + align:start position:0% +books and in the lecture a lot of your + + + align:start position:0% +books and in the lecture a lot of your +models and diagram seem have very + + align:start position:0% +models and diagram seem have very + + + align:start position:0% +models and diagram seem have very +hierarchical structure to them uh but as + + align:start position:0% +hierarchical structure to them uh but as + + + align:start position:0% +hierarchical structure to them uh but as +you mentioned in your bu and other + + align:start position:0% +you mentioned in your bu and other + + + align:start position:0% +you mentioned in your bu and other +places + + align:start position:0% +places + + + align:start position:0% +places +uh passing between levels feedback and + + align:start position:0% +uh passing between levels feedback and + + + align:start position:0% +uh passing between levels feedback and +self- reference are all very important + + align:start position:0% +self- reference are all very important + + + align:start position:0% +self- reference are all very important +to intelligence so I'm curious if you + + align:start position:0% +to intelligence so I'm curious if you + + + align:start position:0% +to intelligence so I'm curious if you +could discuss some of the uses of these + + align:start position:0% +could discuss some of the uses of these + + + align:start position:0% +could discuss some of the uses of these +very hierarchical models why you've + + align:start position:0% +very hierarchical models why you've + + + align:start position:0% +very hierarchical models why you've +represented so many things in that way + + align:start position:0% +represented so many things in that way + + + align:start position:0% +represented so many things in that way +and some of the limitations there well + + align:start position:0% +and some of the limitations there well + + + align:start position:0% +and some of the limitations there well +it's probably very hard to debug things + + align:start position:0% +it's probably very hard to debug things + + + align:start position:0% +it's probably very hard to debug things +that + + align:start position:0% +that + + + align:start position:0% +that +aren't so uh so we need a sort of meta + + align:start position:0% +aren't so uh so we need a sort of meta + + + align:start position:0% +aren't so uh so we need a sort of meta +Theory one thing is + + align:start position:0% + + + + align:start position:0% + +that for example it looks like that all + + align:start position:0% +that for example it looks like that all + + + align:start position:0% +that for example it looks like that all +neurons are almost the same now there's + + align:start position:0% +neurons are almost the same now there's + + + align:start position:0% +neurons are almost the same now there's +lots of difference in in geometric + + align:start position:0% +lots of difference in in geometric + + + align:start position:0% +lots of difference in in geometric +features of them but they all use the + + align:start position:0% +features of them but they all use the + + + align:start position:0% +features of them but they all use the +same uh one or two transmitters + + align:start position:0% +same uh one or two transmitters + + + align:start position:0% +same uh one or two transmitters +and + + align:start position:0% +and + + + align:start position:0% +and +uh every now and then you run across + + align:start position:0% +uh every now and then you run across + + + align:start position:0% +uh every now and then you run across +people saying oh neurons are incredibly + + align:start position:0% +people saying oh neurons are incredibly + + + align:start position:0% +people saying oh neurons are incredibly +complicated they have 100,000 connection + + align:start position:0% +complicated they have 100,000 connection + + + align:start position:0% +complicated they have 100,000 connection +you can find it if you just + + align:start position:0% +you can find it if you just + + + align:start position:0% +you can find it if you just +just look up neuron on the web and get + + align:start position:0% +just look up neuron on the web and get + + + align:start position:0% +just look up neuron on the web and get +these essays explaining that nobody will + + align:start position:0% +these essays explaining that nobody will + + + align:start position:0% +these essays explaining that nobody will +ever understand them because typically a + + align:start position:0% +ever understand them because typically a + + + align:start position:0% +ever understand them because typically a +neuron is connected to 100,000 others + + align:start position:0% +neuron is connected to 100,000 others + + + align:start position:0% +neuron is connected to 100,000 others +and blah blah blah so it must be + + align:start position:0% +and blah blah blah so it must be + + + align:start position:0% +and blah blah blah so it must be +something inside the neuron that figures + + align:start position:0% +something inside the neuron that figures + + + align:start position:0% +something inside the neuron that figures +out all this stuff uh as far as I can + + align:start position:0% +out all this stuff uh as far as I can + + + align:start position:0% +out all this stuff uh as far as I can +see it's it looks almost the opposite + + align:start position:0% +see it's it looks almost the opposite + + + align:start position:0% +see it's it looks almost the opposite +namely probably the neuron hasn't + + align:start position:0% +namely probably the neuron hasn't + + + align:start position:0% +namely probably the neuron hasn't +changed for half a billion years very + + align:start position:0% +changed for half a billion years very + + + align:start position:0% +changed for half a billion years very +much + + align:start position:0% +much + + + align:start position:0% +much +except in sort of superficial ways in + + align:start position:0% +except in sort of superficial ways in + + + align:start position:0% +except in sort of superficial ways in +which it grows because if you change any + + align:start position:0% +which it grows because if you change any + + + align:start position:0% +which it grows because if you change any +of the genes controlling its metabolism + + align:start position:0% +of the genes controlling its metabolism + + + align:start position:0% +of the genes controlling its metabolism +or the way it propagates + + align:start position:0% +or the way it propagates + + + align:start position:0% +or the way it propagates +impulses then + + align:start position:0% +impulses then + + + align:start position:0% +impulses then +uh then the animal would die in + + align:start position:0% +uh then the animal would die in + + + align:start position:0% +uh then the animal would die in +in before it was + + align:start position:0% +in before it was + + + align:start position:0% +in before it was +born and uh so you can't make + + align:start position:0% +born and uh so you can't make + + + align:start position:0% +born and uh so you can't make +that's why the embryology of all mammals + + align:start position:0% +that's why the embryology of all mammals + + + align:start position:0% +that's why the embryology of all mammals +is almost identical you can't make a + + align:start position:0% +is almost identical you can't make a + + + align:start position:0% +is almost identical you can't make a +change at that level at the after the + + align:start position:0% +change at that level at the after the + + + align:start position:0% +change at that level at the after the +first before + + align:start position:0% +first before + + + align:start position:0% +first before +the you can't make changes before the + + align:start position:0% +the you can't make changes before the + + + align:start position:0% +the you can't make changes before the +first + + align:start position:0% +first + + + align:start position:0% +first +uh generations of cell divisions or + + align:start position:0% +uh generations of cell divisions or + + + align:start position:0% +uh generations of cell divisions or +everything would be clobbered the + + align:start position:0% +everything would be clobbered the + + + align:start position:0% +everything would be clobbered the +architecture would be all screwed up so + + align:start position:0% +architecture would be all screwed up so + + + align:start position:0% +architecture would be all screwed up so +I suspect that the people who say well + + align:start position:0% +I suspect that the people who say well + + + align:start position:0% +I suspect that the people who say well +maybe the important memories of a neuron + + align:start position:0% +maybe the important memories of a neuron + + + align:start position:0% +maybe the important memories of a neuron +are inside it because there's so many + + align:start position:0% +are inside it because there's so many + + + align:start position:0% +are inside it because there's so many +fibers and things I bet it's it's sort + + align:start position:0% +fibers and things I bet it's it's sort + + + align:start position:0% +fibers and things I bet it's it's sort +of like saying the important memory in a + + align:start position:0% +of like saying the important memory in a + + + align:start position:0% +of like saying the important memory in a +computer is in the Arsenic and + + align:start position:0% +computer is in the Arsenic and + + + align:start position:0% +computer is in the Arsenic and +phosphorus atoms of the + + align:start position:0% +phosphorus atoms of the + + + align:start position:0% +phosphorus atoms of the +semiconductor so I think things have to + + align:start position:0% +semiconductor so I think things have to + + + align:start position:0% +semiconductor so I think things have to +be hierarchical in in evolution because + + align:start position:0% +be hierarchical in in evolution because + + + align:start position:0% +be hierarchical in in evolution because +if you're building later stuff on + + align:start position:0% +if you're building later stuff on + + + align:start position:0% +if you're building later stuff on +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +stuff then it's very hard to make any + + align:start position:0% +stuff then it's very hard to make any + + + align:start position:0% +stuff then it's very hard to make any +changes in the the earlier + + align:start position:0% +changes in the the earlier + + + align:start position:0% +changes in the the earlier +stuff so as far as I know the neurons in + + align:start position:0% +stuff so as far as I know the neurons in + + + align:start position:0% +stuff so as far as I know the neurons in +C anemones are almost identical to the + + align:start position:0% +C anemones are almost identical to the + + + align:start position:0% +C anemones are almost identical to the +neurons in mammals + + align:start position:0% +neurons in mammals + + + align:start position:0% +neurons in mammals +except for the later stages of growth + + align:start position:0% +except for the later stages of growth + + + align:start position:0% +except for the later stages of growth +and the way the fibers ramify + + align:start position:0% + + + + align:start position:0% + +and who knows but but + + align:start position:0% +and who knows but but + + + align:start position:0% +and who knows but but +uh there are many people who want to + + align:start position:0% +uh there are many people who want to + + + align:start position:0% +uh there are many people who want to +find the secret of the brain in what's + + align:start position:0% +find the secret of the brain in what's + + + align:start position:0% +find the secret of the brain in what's +in inside the neurons rather than + + align:start position:0% +in inside the neurons rather than + + + align:start position:0% +in inside the neurons rather than +outside and + + align:start position:0% +outside and + + + align:start position:0% +outside and +U be be nice to get a textbook on + + align:start position:0% +U be be nice to get a textbook on + + + align:start position:0% +U be be nice to get a textbook on +neurology from 50 years in the future + + align:start position:0% +neurology from 50 years in the future + + + align:start position:0% +neurology from 50 years in the future +see how much of that stuff + + align:start position:0% + + + + align:start position:0% + +mattered where at our time + + align:start position:0% +mattered where at our time + + + align:start position:0% +mattered where at our time +machines did you most systems have a + + align:start position:0% +machines did you most systems have a + + + align:start position:0% +machines did you most systems have a +state that they prefer to be in right + + align:start position:0% +state that they prefer to be in right + + + align:start position:0% +state that they prefer to be in right +like a state that they're comfort do you + + align:start position:0% +like a state that they're comfort do you + + + align:start position:0% +like a state that they're comfort do you +think the mind has such a state or would + + align:start position:0% +think the mind has such a state or would + + + align:start position:0% +think the mind has such a state or would +it tend to certain like + + align:start position:0% +it tend to certain like + + + align:start position:0% +it tend to certain like +places that's an interesting I don't how + + align:start position:0% +places that's an interesting I don't how + + + align:start position:0% +places that's an interesting I don't how +does that apply to living + + align:start position:0% + + + + align:start position:0% + +things I mean this bottle would rather + + align:start position:0% +things I mean this bottle would rather + + + align:start position:0% +things I mean this bottle would rather +be here than here but I'm not sure what + + align:start position:0% +be here than here but I'm not sure what + + + align:start position:0% +be here than here but I'm not sure what +you mean well okay so + + align:start position:0% +you mean well okay so + + + align:start position:0% +you mean well okay so +apparently + + align:start position:0% +apparently + + + align:start position:0% +apparently +in Professor ten bom's class he shows + + align:start position:0% +in Professor ten bom's class he shows + + + align:start position:0% +in Professor ten bom's class he shows +this like example of a + + align:start position:0% +this like example of a + + + align:start position:0% +this like example of a +number game he'll give you a sequence of + + align:start position:0% +number game he'll give you a sequence of + + + align:start position:0% +number game he'll give you a sequence of +numbers and he'll ask you to find a + + align:start position:0% +numbers and he'll ask you to find a + + + align:start position:0% +numbers and he'll ask you to find a +pattern in it so for example if you had + + align:start position:0% +pattern in it so for example if you had + + + align:start position:0% +pattern in it so for example if you had +a pattern like 10 40 50 and 55 he kind + + align:start position:0% +a pattern like 10 40 50 and 55 he kind + + + align:start position:0% +a pattern like 10 40 50 and 55 he kind +of asked the class to come up with like + + align:start position:0% +of asked the class to come up with like + + + align:start position:0% +of asked the class to come up with like +different things that could be + + align:start position:0% +different things that could be + + + align:start position:0% +different things that could be +describing the sequence and um you know + + align:start position:0% +describing the sequence and um you know + + + align:start position:0% +describing the sequence and um you know +between a choice of oh this sequence is + + align:start position:0% +between a choice of oh this sequence is + + + align:start position:0% +between a choice of oh this sequence is +a sequence of the multiples of five + + align:start position:0% +a sequence of the multiples of five + + + align:start position:0% +a sequence of the multiples of five +versus a sequence of the multiples of 10 + + align:start position:0% +versus a sequence of the multiples of 10 + + + align:start position:0% +versus a sequence of the multiples of 10 +or multiples of 11 um you know know he + + align:start position:0% +or multiples of 11 um you know know he + + + align:start position:0% +or multiples of 11 um you know know he +says something like he phrases it like + + align:start position:0% +says something like he phrases it like + + + align:start position:0% +says something like he phrases it like +the multiples of five would have a + + align:start position:0% +the multiples of five would have a + + + align:start position:0% +the multiples of five would have a +higher prior probability but so so that + + align:start position:0% +higher prior probability but so so that + + + align:start position:0% +higher prior probability but so so that +got me thinking like why would that be + + align:start position:0% +got me thinking like why would that be + + + align:start position:0% +got me thinking like why would that be +would would our minds have a preference + + align:start position:0% +would would our minds have a preference + + + align:start position:0% +would would our minds have a preference +for having as few categories as possible + + align:start position:0% +for having as few categories as possible + + + align:start position:0% +for having as few categories as possible +in trying to view the world around us + + align:start position:0% +in trying to view the world around us + + + align:start position:0% +in trying to view the world around us +like trying to categorize things in as + + align:start position:0% +like trying to categorize things in as + + + align:start position:0% +like trying to categorize things in as +few things as possible + + align:start position:0% +few things as possible + + + align:start position:0% +few things as possible +is sounds very strange to me but uh + + align:start position:0% + + + + align:start position:0% + +certainly if you're going to generate + + align:start position:0% +certainly if you're going to generate + + + align:start position:0% +certainly if you're going to generate +hypothesis you have to + + align:start position:0% + + + + align:start position:0% + +have the way you do it depends on what + + align:start position:0% +have the way you do it depends on what + + + align:start position:0% +have the way you do it depends on what +what this per if what does this problem + + align:start position:0% +what this per if what does this problem + + + align:start position:0% +what this per if what does this problem +remind you of so I don't I don't see how + + align:start position:0% +remind you of so I don't I don't see how + + + align:start position:0% +remind you of so I don't I don't see how +you could make + + align:start position:0% + + + + align:start position:0% + +a a + + align:start position:0% + + + + align:start position:0% + +general if you look at the history of + + align:start position:0% +general if you look at the history of + + + align:start position:0% +general if you look at the history of +psychology + + align:start position:0% +psychology + + + align:start position:0% +psychology +there are so many efforts to find four + + align:start position:0% +there are so many efforts to find four + + + align:start position:0% +there are so many efforts to find four +laws three laws of motion like + + align:start position:0% +laws three laws of motion like + + + align:start position:0% +laws three laws of motion like +Newton's is he trying to do + + align:start position:0% + + + + align:start position:0% + +that I mean you're here you're talking + + align:start position:0% +that I mean you're here you're talking + + + align:start position:0% +that I mean you're here you're talking +about people with language and high + + align:start position:0% +about people with language and high + + + align:start position:0% +about people with language and high +level semantics + + align:start position:0% + + + + align:start position:0% + +and let's ask him what he meant + + align:start position:0% + + + + align:start position:0% + +Prof yeah this more of a social question + + align:start position:0% +Prof yeah this more of a social question + + + align:start position:0% +Prof yeah this more of a social question +but there's always this debate about how + + align:start position:0% +but there's always this debate about how + + + align:start position:0% +but there's always this debate about how +if AI gets to the point where it can + + align:start position:0% +if AI gets to the point where it can + + + align:start position:0% +if AI gets to the point where it can +take care of humans will it ever destroy + + align:start position:0% +take care of humans will it ever destroy + + + align:start position:0% +take care of humans will it ever destroy +humanity and how would do you think + + align:start position:0% +humanity and how would do you think + + + align:start position:0% +humanity and how would do you think +that's something that we should fear and + + align:start position:0% +that's something that we should fear and + + + align:start position:0% +that's something that we should fear and +if so is there some way we can prevent + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% + + + + align:start position:0% + +if you judge by the + + align:start position:0% +if you judge by the + + + align:start position:0% +if you judge by the +recent by what's happened in AI since + + align:start position:0% +recent by what's happened in AI since + + + align:start position:0% +recent by what's happened in AI since +1980 it's hard to imagine anything to + + align:start position:0% +1980 it's hard to imagine anything to + + + align:start position:0% +1980 it's hard to imagine anything to +fear + + align:start position:0% +fear + + + align:start position:0% +fear +but but + + align:start position:0% + + + + align:start position:0% + +uh funny you should mention that I'm + + align:start position:0% +uh funny you should mention that I'm + + + align:start position:0% +uh funny you should mention that I'm +just trying to organize a conference + + align:start position:0% +just trying to organize a conference + + + align:start position:0% +just trying to organize a conference +sometime next year about + + align:start position:0% +sometime next year about + + + align:start position:0% +sometime next year about +disasters and there's a nice book about + + align:start position:0% +disasters and there's a nice book about + + + align:start position:0% +disasters and there's a nice book about +disasters + + align:start position:0% + + + + align:start position:0% + +by what's his name the Royal the + + align:start position:0% +by what's his name the Royal the + + + align:start position:0% +by what's his name the Royal the +astronomer + + align:start position:0% +astronomer + + + align:start position:0% +astronomer +Royal what Martin Martin + + align:start position:0% +Royal what Martin Martin + + + align:start position:0% +Royal what Martin Martin +Ree um so he has a nice book which I + + align:start position:0% +Ree um so he has a nice book which I + + + align:start position:0% +Ree um so he has a nice book which I +just ordered from Amazon and it came the + + align:start position:0% +just ordered from Amazon and it came the + + + align:start position:0% +just ordered from Amazon and it came the +next + + align:start position:0% +next + + + align:start position:0% +next +day and it has about 10 + + align:start position:0% +day and it has about 10 + + + align:start position:0% +day and it has about 10 +disasters uh + + align:start position:0% +disasters uh + + + align:start position:0% +disasters uh +like a big meteor coming and hitting the + + align:start position:0% +like a big meteor coming and hitting the + + + align:start position:0% +like a big meteor coming and hitting the +earth I forget the other 10 but I have + + align:start position:0% +earth I forget the other 10 but I have + + + align:start position:0% +earth I forget the other 10 but I have +it in here + + align:start position:0% +it in here + + + align:start position:0% +it in here +somewhere so I generated another list of + + align:start position:0% +somewhere so I generated another list of + + + align:start position:0% +somewhere so I generated another list of +10 to go with it + + align:start position:0% +10 to go with it + + + align:start position:0% +10 to go with it +and so there are lots of bad things that + + align:start position:0% +and so there are lots of bad things that + + + align:start position:0% +and so there are lots of bad things that +could + + align:start position:0% + + + + align:start position:0% + +happen + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% + + + + align:start position:0% + +I think right now that's not on the top + + align:start position:0% +I think right now that's not on the top + + + align:start position:0% +I think right now that's not on the top +of the list of disasters eventually uh + + align:start position:0% +of the list of disasters eventually uh + + + align:start position:0% +of the list of disasters eventually uh +some hacker ought to be able to stop the + + align:start position:0% +some hacker ought to be able to stop the + + + align:start position:0% +some hacker ought to be able to stop the +uh net firm working because it's not + + align:start position:0% +uh net firm working because it's not + + + align:start position:0% +uh net firm working because it's not +very + + align:start position:0% +very + + + align:start position:0% +very +secure and uh while you're at it you + + align:start position:0% +secure and uh while you're at it you + + + align:start position:0% +secure and uh while you're at it you +could probably knock out all of the uh + + align:start position:0% +could probably knock out all of the uh + + + align:start position:0% +could probably knock out all of the uh +navigation + + align:start position:0% +navigation + + + align:start position:0% +navigation +satellites + + align:start position:0% +satellites + + + align:start position:0% +satellites +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +maybe set off a few nuclear + + align:start position:0% + + + + align:start position:0% + +reactors + + align:start position:0% +reactors + + + align:start position:0% +reactors +but I don't think AI is the principal + + align:start position:0% +but I don't think AI is the principal + + + align:start position:0% +but I don't think AI is the principal +thing to worry about but it should very + + align:start position:0% +thing to worry about but it should very + + + align:start position:0% +thing to worry about but it should very +suddenly get to be a problem and there + + align:start position:0% +suddenly get to be a problem and there + + + align:start position:0% +suddenly get to be a problem and there +are lots of good science fiction + + align:start position:0% +are lots of good science fiction + + + align:start position:0% +are lots of good science fiction +stories my favorite is the Colossus + + align:start position:0% +stories my favorite is the Colossus + + + align:start position:0% +stories my favorite is the Colossus +series by DF Jones anybody know there + + align:start position:0% +series by DF Jones anybody know there + + + align:start position:0% +series by DF Jones anybody know there +was a movie called The Forbidden project + + align:start position:0% +was a movie called The Forbidden project + + + align:start position:0% +was a movie called The Forbidden project +and it's about somebody who builds an + + align:start position:0% +and it's about somebody who builds an + + + align:start position:0% +and it's about somebody who builds an +AI and it's trained to do some + + align:start position:0% +AI and it's trained to do some + + + align:start position:0% +AI and it's trained to do some +learning + + align:start position:0% +learning + + + align:start position:0% +learning +and uh it's also the early days of the + + align:start position:0% +and uh it's also the early days of the + + + align:start position:0% +and uh it's also the early days of the +web and it's starts talking to another + + align:start position:0% +web and it's starts talking to another + + + align:start position:0% +web and it's starts talking to another +computer in + + align:start position:0% +computer in + + + align:start position:0% +computer in +Russia and suddenly it gets faster and + + align:start position:0% +Russia and suddenly it gets faster and + + + align:start position:0% +Russia and suddenly it gets faster and +faster and takes over all the computers + + align:start position:0% +faster and takes over all the computers + + + align:start position:0% +faster and takes over all the computers +in the world and gets control of all the + + align:start position:0% +in the world and gets control of all the + + + align:start position:0% +in the world and gets control of all the +missiles because they're linked to the + + align:start position:0% +missiles because they're linked to the + + + align:start position:0% +missiles because they're linked to the +network and it says we will I will + + align:start position:0% +network and it says we will I will + + + align:start position:0% +network and it says we will I will +destroy all the cities in the world + + align:start position:0% +destroy all the cities in the world + + + align:start position:0% +destroy all the cities in the world +unless you clear off some Island and + + align:start position:0% +unless you clear off some Island and + + + align:start position:0% +unless you clear off some Island and +start building the following + + align:start position:0% + + + + align:start position:0% + +machine I think it's Sardinia or + + align:start position:0% +machine I think it's Sardinia or + + + align:start position:0% +machine I think it's Sardinia or +someplace so they get bulldozers + + align:start position:0% + + + + align:start position:0% + +and and it starts building another + + align:start position:0% +and and it starts building another + + + align:start position:0% +and and it starts building another +machine which it calls Colossus + + align:start position:0% +machine which it calls Colossus + + + align:start position:0% +machine which it calls Colossus +2 and they ask what's it going to + + align:start position:0% +2 and they ask what's it going to + + + align:start position:0% +2 and they ask what's it going to +do and Colossus says well you + + align:start position:0% +do and Colossus says well you + + + align:start position:0% +do and Colossus says well you +see I have detected that there's a + + align:start position:0% +see I have detected that there's a + + + align:start position:0% +see I have detected that there's a +really bad AI out in space and it's + + align:start position:0% +really bad AI out in space and it's + + + align:start position:0% +really bad AI out in space and it's +coming this way and I have to make + + align:start position:0% +coming this way and I have to make + + + align:start position:0% +coming this way and I have to make +myself smarter than it really + + align:start position:0% +myself smarter than it really + + + align:start position:0% +myself smarter than it really +quick anyway + + align:start position:0% +quick anyway + + + align:start position:0% +quick anyway +uh see if you can order the sequel to + + align:start position:0% +uh see if you can order the sequel to + + + align:start position:0% +uh see if you can order the sequel to +Colossus that's that's the second + + align:start position:0% +Colossus that's that's the second + + + align:start position:0% +Colossus that's that's the second +volume where the Invader actually + + align:start position:0% +volume where the Invader actually + + + align:start position:0% +volume where the Invader actually +arrives and I forget what happens and + + align:start position:0% +arrives and I forget what happens and + + + align:start position:0% +arrives and I forget what happens and +then there's a third one which was an + + align:start position:0% +then there's a third one which was an + + + align:start position:0% +then there's a third one which was an +anticlimax + + align:start position:0% +anticlimax + + + align:start position:0% +anticlimax +because I guess DF Jones couldn't think + + align:start position:0% +because I guess DF Jones couldn't think + + + align:start position:0% +because I guess DF Jones couldn't think +of anything worse that could + + align:start position:0% +of anything worse that could + + + align:start position:0% +of anything worse that could +happen but but but Martin Reese + + align:start position:0% + + + + align:start position:0% + +can yeah um going back to her question + + align:start position:0% +can yeah um going back to her question + + + align:start position:0% +can yeah um going back to her question +about the + + align:start position:0% +about the + + + align:start position:0% +about the +example mind has a state that it prefers + + align:start position:0% +example mind has a state that it prefers + + + align:start position:0% +example mind has a state that it prefers +to be in would that example be more of a + + align:start position:0% +to be in would that example be more of a + + + align:start position:0% +to be in would that example be more of a +pattern recognition example so instead + + align:start position:0% +pattern recognition example so instead + + + align:start position:0% +pattern recognition example so instead +of 1040 50 55 what if it was + + align:start position:0% +of 1040 50 55 what if it was + + + align:start position:0% +of 1040 50 55 what if it was +linguistical like good fine great and + + align:start position:0% +linguistical like good fine great and + + + align:start position:0% +linguistical like good fine great and +you have to come up with a word that um + + align:start position:0% +you have to come up with a word that um + + + align:start position:0% +you have to come up with a word that um +that could potentially fit in that + + align:start position:0% +that could potentially fit in that + + + align:start position:0% +that could potentially fit in that +pattern and then that pattern could be + + align:start position:0% +pattern and then that pattern could be + + + align:start position:0% +pattern and then that pattern could be +waste answering how are you let's do an + + align:start position:0% +waste answering how are you let's do an + + + align:start position:0% +waste answering how are you let's do an +experiment how many of you have a + + align:start position:0% +experiment how many of you have a + + + align:start position:0% +experiment how many of you have a +resting + + align:start position:0% + + + + align:start position:0% + +state sometimes when I have nothing else + + align:start position:0% +state sometimes when I have nothing else + + + align:start position:0% +state sometimes when I have nothing else +to + + align:start position:0% +to + + + align:start position:0% +to +do I try to think of Twinkle Twinkle + + align:start position:0% +do I try to think of Twinkle Twinkle + + + align:start position:0% +do I try to think of Twinkle Twinkle +Little + + align:start position:0% +Little + + + align:start position:0% +Little +Star + + align:start position:0% +Star + + + align:start position:0% +Star +happening with the second one starting + + align:start position:0% +happening with the second one starting + + + align:start position:0% +happening with the second one starting +in the second measure and then the third + + align:start position:0% +in the second measure and then the third + + + align:start position:0% +in the second measure and then the third +one starts up on the third measure and + + align:start position:0% +one starts up on the third measure and + + + align:start position:0% +one starts up on the third measure and +when that happens I start losing the + + align:start position:0% +when that happens I start losing the + + + align:start position:0% +when that happens I start losing the +first one and ever since I was a + + align:start position:0% +first one and ever since I was a + + + align:start position:0% +first one and ever since I was a +baby uh when I have nothing else to do + + align:start position:0% +baby uh when I have nothing else to do + + + align:start position:0% +baby uh when I have nothing else to do +which is almost + + align:start position:0% +which is almost + + + align:start position:0% +which is almost +never + + align:start position:0% +never + + + align:start position:0% +never +uh I try to think of three versions of + + align:start position:0% +uh I try to think of three versions of + + + align:start position:0% +uh I try to think of three versions of +the same tune at once and usually + + align:start position:0% +the same tune at once and usually + + + align:start position:0% +the same tune at once and usually +fail what do you do when you have + + align:start position:0% +fail what do you do when you have + + + align:start position:0% +fail what do you do when you have +nothing else to do any + + align:start position:0% +nothing else to do any + + + align:start position:0% +nothing else to do any +volunteers what's yours try not to think + + align:start position:0% +volunteers what's yours try not to think + + + align:start position:0% +volunteers what's yours try not to think +anything at all see how I'm okay you + + align:start position:0% +anything at all see how I'm okay you + + + align:start position:0% +anything at all see how I'm okay you +tried not to or two not to isn't that a + + align:start position:0% +tried not to or two not to isn't that a + + + align:start position:0% +tried not to or two not to isn't that a +sort of uh Buddhist thing yes + + align:start position:0% +sort of uh Buddhist thing yes + + + align:start position:0% +sort of uh Buddhist thing yes +sir do you ever succeed how do you get + + align:start position:0% +sir do you ever succeed how do you get + + + align:start position:0% +sir do you ever succeed how do you get +out of it you have to you have to think + + align:start position:0% +out of it you have to you have to think + + + align:start position:0% +out of it you have to you have to think +well enough of this + + align:start position:0% +well enough of this + + + align:start position:0% +well enough of this +nothingness if you succeeded wouldn't + + align:start position:0% +nothingness if you succeeded wouldn't + + + align:start position:0% +nothingness if you succeeded wouldn't +you be + + align:start position:0% + + + + align:start position:0% + +dead or stuck eventually some simulus + + align:start position:0% +dead or stuck eventually some simulus + + + align:start position:0% +dead or stuck eventually some simulus +will appear that is too interesting to + + align:start position:0% +will appear that is too interesting to + + + align:start position:0% +will appear that is too interesting to +ignore right the threshold goes down + + align:start position:0% +ignore right the threshold goes down + + + align:start position:0% +ignore right the threshold goes down +till right even the most boring thing is + + align:start position:0% +till right even the most boring thing is + + + align:start position:0% +till right even the most boring thing is +fascinating + + align:start position:0% + + + + align:start position:0% + +yeah make a good short + + align:start position:0% +yeah make a good short + + + align:start position:0% +yeah make a good short +story yep there was actually a a movie + + align:start position:0% +story yep there was actually a a movie + + + align:start position:0% +story yep there was actually a a movie +that really got to me when I was little + + align:start position:0% +that really got to me when I was little + + + align:start position:0% +that really got to me when I was little +these aliens were trying to infiltrate + + align:start position:0% +these aliens were trying to infiltrate + + + align:start position:0% +these aliens were trying to infiltrate +people's brains and like their thoughts + + align:start position:0% +people's brains and like their thoughts + + + align:start position:0% +people's brains and like their thoughts +and to keep the aliens from infiltrating + + align:start position:0% +and to keep the aliens from infiltrating + + + align:start position:0% +and to keep the aliens from infiltrating +your thoughts you had to think of a wall + + align:start position:0% +your thoughts you had to think of a wall + + + align:start position:0% +your thoughts you had to think of a wall +which like didn't make any sense at all + + align:start position:0% +which like didn't make any sense at all + + + align:start position:0% +which like didn't make any sense at all +but but + + align:start position:0% +but but + + + align:start position:0% +but but +now but now whenever I try to think of + + align:start position:0% +now but now whenever I try to think of + + + align:start position:0% +now but now whenever I try to think of +nothing I just end up thinking of a + + align:start position:0% + + + + align:start position:0% + +wall there are these awful psychoses + + align:start position:0% + + + + align:start position:0% + +and about + + align:start position:0% +and about + + + align:start position:0% +and about +every about every five + + align:start position:0% +every about every five + + + align:start position:0% +every about every five +years I get an email from + + align:start position:0% +years I get an email from + + + align:start position:0% +years I get an email from +someone who says + + align:start position:0% +someone who says + + + align:start position:0% +someone who says +that please help me there are some + + align:start position:0% +that please help me there are some + + + align:start position:0% +that please help me there are some +people who are putting these terrible + + align:start position:0% +people who are putting these terrible + + + align:start position:0% +people who are putting these terrible +ideas in my head have you ever gotten + + align:start position:0% +ideas in my head have you ever gotten + + + align:start position:0% +ideas in my head have you ever gotten +one + + align:start position:0% +one + + + align:start position:0% +one +Pat and + + align:start position:0% +Pat and + + + align:start position:0% +Pat and +uh they're sort of scary because the you + + align:start position:0% +uh they're sort of scary because the you + + + align:start position:0% +uh they're sort of scary because the you +realize that maybe the person will + + align:start position:0% +realize that maybe the person will + + + align:start position:0% +realize that maybe the person will +suddenly figure out that it's you who's + + align:start position:0% +suddenly figure out that it's you who's + + + align:start position:0% +suddenly figure out that it's you who's +doing it if + + align:start position:0% +doing it if + + + align:start position:0% +doing it if +[Music] + + align:start position:0% + + + + align:start position:0% + +they + + align:start position:0% +they + + + align:start position:0% +they +put a couple of them together once I + + align:start position:0% +put a couple of them together once I + + + align:start position:0% +put a couple of them together once I +think they + + align:start position:0% + + + + align:start position:0% + +married I remember there was + + align:start position:0% + + + + align:start position:0% + +once one of them came to + + align:start position:0% +once one of them came to + + + align:start position:0% +once one of them came to +visit actually showed up and he came to + + align:start position:0% +visit actually showed up and he came to + + + align:start position:0% +visit actually showed up and he came to +visit Norbert weiner who was famous + + align:start position:0% +visit Norbert weiner who was famous + + + align:start position:0% +visit Norbert weiner who was famous +for I mean he's the cybernetics person + + align:start position:0% +for I mean he's the cybernetics person + + + align:start position:0% +for I mean he's the cybernetics person +of the world that was + + align:start position:0% + + + + align:start position:0% + +and this person came in and he got + + align:start position:0% +and this person came in and he got + + + align:start position:0% +and this person came in and he got +between Weiner and the door and started + + align:start position:0% +between Weiner and the door and started + + + align:start position:0% +between Weiner and the door and started +explaining that somebody was putting + + align:start position:0% +explaining that somebody was putting + + + align:start position:0% +explaining that somebody was putting +dirty words in his head and making the + + align:start position:0% +dirty words in his head and making the + + + align:start position:0% +dirty words in his head and making the +grass on their lawn + + align:start position:0% +grass on their lawn + + + align:start position:0% +grass on their lawn +die and he was sure it was someone in + + align:start position:0% +die and he was sure it was someone in + + + align:start position:0% +die and he was sure it was someone in +the government and + + align:start position:0% +the government and + + + align:start position:0% +the government and +uh this was getting pretty scary and I + + align:start position:0% +uh this was getting pretty scary and I + + + align:start position:0% +uh this was getting pretty scary and I +was near the door + + align:start position:0% + + + + align:start position:0% + +so I went and got + + align:start position:0% + + + + align:start position:0% + +lein it's a true story go nearby + + align:start position:0% +lein it's a true story go nearby + + + align:start position:0% +lein it's a true story go nearby +and I got lein to come in and lein + + align:start position:0% +and I got lein to come in and lein + + + align:start position:0% +and I got lein to come in and lein +actually took this guy down and took him + + align:start position:0% +actually took this guy down and took him + + + align:start position:0% +actually took this guy down and took him +by the arm and went somewhere and I + + align:start position:0% +by the arm and went somewhere and I + + + align:start position:0% +by the arm and went somewhere and I +don't know what happened but weer was + + align:start position:0% +don't know what happened but weer was + + + align:start position:0% +don't know what happened but weer was +really + + align:start position:0% +really + + + align:start position:0% +really +scared because the guy kept keeping him + + align:start position:0% +scared because the guy kept keeping him + + + align:start position:0% +scared because the guy kept keeping him +from going out letvin was big + + align:start position:0% +from going out letvin was big + + + align:start position:0% +from going out letvin was big +weer is not very + + align:start position:0% + + + + align:start position:0% + +big anyway + + align:start position:0% +big anyway + + + align:start position:0% +big anyway +uh that keeps happening every every few + + align:start position:0% +uh that keeps happening every every few + + + align:start position:0% +uh that keeps happening every every few +years I get one and I don't answer + + align:start position:0% +years I get one and I don't answer + + + align:start position:0% +years I get one and I don't answer +them it's probably doesn't he's probably + + align:start position:0% +them it's probably doesn't he's probably + + + align:start position:0% +them it's probably doesn't he's probably +sending it to several people and uh I'm + + align:start position:0% +sending it to several people and uh I'm + + + align:start position:0% +sending it to several people and uh I'm +sure one of them is much better at it + + align:start position:0% +sure one of them is much better at it + + + align:start position:0% +sure one of them is much better at it +than we + + align:start position:0% +than we + + + align:start position:0% +than we +are how many of you have ever had to + + align:start position:0% +are how many of you have ever had to + + + align:start position:0% +are how many of you have ever had to +deal with + + align:start position:0% +deal with + + + align:start position:0% +deal with +a obsessed person how did they find + + align:start position:0% +a obsessed person how did they find + + + align:start position:0% +a obsessed person how did they find +you I don't know they found a number of + + align:start position:0% +you I don't know they found a number of + + + align:start position:0% +you I don't know they found a number of +people in the media lab + + align:start position:0% + + + + align:start position:0% + +actually don't answer + + align:start position:0% +actually don't answer + + + align:start position:0% +actually don't answer +anything but if they actually come then + + align:start position:0% +anything but if they actually come then + + + align:start position:0% +anything but if they actually come then +it's not clear what to + + align:start position:0% + + + + align:start position:0% + +do + + align:start position:0% + + + + align:start position:0% + +last + + align:start position:0% + + + + align:start position:0% + +question thanks for + + align:start position:0% + + + + align:start position:0% + +coming \ No newline at end of file diff --git a/2pfdTSZ-GUM.txt b/2pfdTSZ-GUM.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d94c503014530ffe41876fc5686c3e99dcbd9bf --- /dev/null +++ b/2pfdTSZ-GUM.txt @@ -0,0 +1,12091 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right so let's go ahead + + align:start position:0% +ocw.mit.edu all right so let's go ahead + + + align:start position:0% +ocw.mit.edu all right so let's go ahead +and get started um a couple quick + + align:start position:0% +and get started um a couple quick + + + align:start position:0% +and get started um a couple quick +announcements before we jump into the + + align:start position:0% +announcements before we jump into the + + + align:start position:0% +announcements before we jump into the +day um we had a couple questions about + + align:start position:0% +day um we had a couple questions about + + + align:start position:0% +day um we had a couple questions about +what happens if one of my team members + + align:start position:0% +what happens if one of my team members + + + align:start position:0% +what happens if one of my team members +dropped out of the class for this first + + align:start position:0% +dropped out of the class for this first + + + align:start position:0% +dropped out of the class for this first +project um has anybody had + + align:start position:0% +project um has anybody had + + + align:start position:0% +project um has anybody had +that okay so if somebody drops out of + + align:start position:0% +that okay so if somebody drops out of + + + align:start position:0% +that okay so if somebody drops out of +your team at any point in the next you + + align:start position:0% +your team at any point in the next you + + + align:start position:0% +your team at any point in the next you +know first two projects that's okay um + + align:start position:0% +know first two projects that's okay um + + + align:start position:0% +know first two projects that's okay um +you're not going to be um penalized for + + align:start position:0% +you're not going to be um penalized for + + + align:start position:0% +you're not going to be um penalized for +having fewer people you're not going to + + align:start position:0% +having fewer people you're not going to + + + align:start position:0% +having fewer people you're not going to +be um propped for having fewer people + + align:start position:0% +be um propped for having fewer people + + + align:start position:0% +be um propped for having fewer people +it's basically we're not necessarily + + align:start position:0% +it's basically we're not necessarily + + + align:start position:0% +it's basically we're not necessarily +grading the quality of the games for + + align:start position:0% +grading the quality of the games for + + + align:start position:0% +grading the quality of the games for +this first project right now u double + + align:start position:0% +this first project right now u double + + + align:start position:0% +this first project right now u double +check check the project one assignment + + align:start position:0% +check check the project one assignment + + + align:start position:0% +check check the project one assignment +to see what the grading rubric is for + + align:start position:0% +to see what the grading rubric is for + + + align:start position:0% +to see what the grading rubric is for +that what we are checking is are you + + align:start position:0% +that what we are checking is are you + + + align:start position:0% +that what we are checking is are you +doing iteration have you tested the game + + align:start position:0% +doing iteration have you tested the game + + + align:start position:0% +doing iteration have you tested the game +multiple times do you have multiple + + align:start position:0% +multiple times do you have multiple + + + align:start position:0% +multiple times do you have multiple +versions of the game so that's basically + + align:start position:0% +versions of the game so that's basically + + + align:start position:0% +versions of the game so that's basically +reflected in your design change log that + + align:start position:0% +reflected in your design change log that + + + align:start position:0% +reflected in your design change log that +you're doing for this this class there's + + align:start position:0% +you're doing for this this class there's + + + align:start position:0% +you're doing for this this class there's +also a um an individual write up so + + align:start position:0% +also a um an individual write up so + + + align:start position:0% +also a um an individual write up so +we're asking you to write a onepage + + align:start position:0% +we're asking you to write a onepage + + + align:start position:0% +we're asking you to write a onepage +paper about your experience with the + + align:start position:0% +paper about your experience with the + + + align:start position:0% +paper about your experience with the +requirements for that are in the + + align:start position:0% +requirements for that are in the + + + align:start position:0% +requirements for that are in the +assignment um we want to + + align:start position:0% +assignment um we want to + + + align:start position:0% +assignment um we want to +know what happened when your teammate + + align:start position:0% +know what happened when your teammate + + + align:start position:0% +know what happened when your teammate +dropped out did it feel different if you + + align:start position:0% +dropped out did it feel different if you + + + align:start position:0% +dropped out did it feel different if you +had two people versus three people do + + align:start position:0% +had two people versus three people do + + + align:start position:0% +had two people versus three people do +you feel like you had fewer ideas that's + + align:start position:0% +you feel like you had fewer ideas that's + + + align:start position:0% +you feel like you had fewer ideas that's +actually a really interesting thing for + + align:start position:0% +actually a really interesting thing for + + + align:start position:0% +actually a really interesting thing for +you to understand about when you're + + align:start position:0% +you to understand about when you're + + + align:start position:0% +you to understand about when you're +coming together and working on group + + align:start position:0% +coming together and working on group + + + align:start position:0% +coming together and working on group +projects and you're doing collaborative + + align:start position:0% +projects and you're doing collaborative + + + align:start position:0% +projects and you're doing collaborative +projects what does team size do to the + + align:start position:0% +projects what does team size do to the + + + align:start position:0% +projects what does team size do to the +kind of um ideas you have the number of + + align:start position:0% +kind of um ideas you have the number of + + + align:start position:0% +kind of um ideas you have the number of +ideas you have and the quality of ideas + + align:start position:0% +ideas you have and the quality of ideas + + + align:start position:0% +ideas you have and the quality of ideas +you have um in the later all the later + + align:start position:0% +you have um in the later all the later + + + align:start position:0% +you have um in the later all the later +projects your teams are going to be big + + align:start position:0% +projects your teams are going to be big + + + align:start position:0% +projects your teams are going to be big +enough that dropping one member isn't + + align:start position:0% +enough that dropping one member isn't + + + align:start position:0% +enough that dropping one member isn't +going to be a huge difference dropping + + align:start position:0% +going to be a huge difference dropping + + + align:start position:0% +going to be a huge difference dropping +two might so if that happens just let us + + align:start position:0% +two might so if that happens just let us + + + align:start position:0% +two might so if that happens just let us +know about it we'll talk you through it + + align:start position:0% +know about it we'll talk you through it + + + align:start position:0% +know about it we'll talk you through it +it'll be okay you'll get through it + + align:start position:0% +it'll be okay you'll get through it + + + align:start position:0% +it'll be okay you'll get through it +um if I may this is actually part of the + + align:start position:0% +um if I may this is actually part of the + + + align:start position:0% +um if I may this is actually part of the +experience of working on a team + + align:start position:0% +experience of working on a team + + + align:start position:0% +experience of working on a team +sometimes you lose people and it's + + align:start position:0% +sometimes you lose people and it's + + + align:start position:0% +sometimes you lose people and it's +sometimes that's a problem um I like to + + align:start position:0% +sometimes that's a problem um I like to + + + align:start position:0% +sometimes that's a problem um I like to +call it the hit by a bus test you know + + align:start position:0% +call it the hit by a bus test you know + + + align:start position:0% +call it the hit by a bus test you know +if your team can't stand losing one + + align:start position:0% +if your team can't stand losing one + + + align:start position:0% +if your team can't stand losing one +person any one person then you have to + + align:start position:0% +person any one person then you have to + + + align:start position:0% +person any one person then you have to +plan around that and make sure that you + + align:start position:0% +plan around that and make sure that you + + + align:start position:0% +plan around that and make sure that you +can handle it um other people like to + + align:start position:0% +can handle it um other people like to + + + align:start position:0% +can handle it um other people like to +call it the winning the lottery test + + align:start position:0% +call it the winning the lottery test + + + align:start position:0% +call it the winning the lottery test +because that's nicer but basically one + + align:start position:0% +because that's nicer but basically one + + + align:start position:0% +because that's nicer but basically one +person who gets taken out of the + + align:start position:0% +person who gets taken out of the + + + align:start position:0% +person who gets taken out of the +equation you do have to adapt to that + + align:start position:0% +equation you do have to adapt to that + + + align:start position:0% +equation you do have to adapt to that +and be ready for it to happen again on + + align:start position:0% +and be ready for it to happen again on + + + align:start position:0% +and be ready for it to happen again on +this project It's + + align:start position:0% +this project It's + + + align:start position:0% +this project It's +relatively the teamk is easier because + + align:start position:0% +relatively the teamk is easier because + + + align:start position:0% +relatively the teamk is easier because +you're it's a simpler deliverable and a + + align:start position:0% +you're it's a simpler deliverable and a + + + align:start position:0% +you're it's a simpler deliverable and a +simpler project but things are going to + + align:start position:0% +simpler project but things are going to + + + align:start position:0% +simpler project but things are going to +come up throughout the semester somebody + + align:start position:0% +come up throughout the semester somebody + + + align:start position:0% +come up throughout the semester somebody +falling sick um somebody going away for + + align:start position:0% +falling sick um somebody going away for + + + align:start position:0% +falling sick um somebody going away for +interviews especially seniors going for + + align:start position:0% +interviews especially seniors going for + + + align:start position:0% +interviews especially seniors going for +job interviews those are things you're + + align:start position:0% +job interviews those are things you're + + + align:start position:0% +job interviews those are things you're +going to need to plan for to react to um + + align:start position:0% +going to need to plan for to react to um + + + align:start position:0% +going to need to plan for to react to um +and have alternate plans just in case + + align:start position:0% +and have alternate plans just in case + + + align:start position:0% +and have alternate plans just in case +something like that happens during the + + align:start position:0% +something like that happens during the + + + align:start position:0% +something like that happens during the +project so just be aware of that + + align:start position:0% +project so just be aware of that + + + align:start position:0% +project so just be aware of that +throughout throughout the class all + + align:start position:0% +throughout throughout the class all + + + align:start position:0% +throughout throughout the class all +right so what are we doing today today + + align:start position:0% +right so what are we doing today today + + + align:start position:0% +right so what are we doing today today +is a very very busy day that's going to + + align:start position:0% +is a very very busy day that's going to + + + align:start position:0% +is a very very busy day that's going to +involve lots of movement on your part um + + align:start position:0% +involve lots of movement on your part um + + + align:start position:0% +involve lots of movement on your part um +we're going to do a workshop on on + + align:start position:0% +we're going to do a workshop on on + + + align:start position:0% +we're going to do a workshop on on +Version Control that Drew is going to + + align:start position:0% +Version Control that Drew is going to + + + align:start position:0% +Version Control that Drew is going to +going to walk you through um we're going + + align:start position:0% +going to walk you through um we're going + + + align:start position:0% +going to walk you through um we're going +to go into um discussion groups and talk + + align:start position:0% +to go into um discussion groups and talk + + + align:start position:0% +to go into um discussion groups and talk +about the game engine tutorials that you + + align:start position:0% +about the game engine tutorials that you + + + align:start position:0% +about the game engine tutorials that you +had that you all completed um before + + align:start position:0% +had that you all completed um before + + + align:start position:0% +had that you all completed um before +today um and there'll be a mechanism for + + align:start position:0% +today um and there'll be a mechanism for + + + align:start position:0% +today um and there'll be a mechanism for +talking about that um basically people + + align:start position:0% +talking about that um basically people + + + align:start position:0% +talking about that um basically people +talking about forming groups in the same + + align:start position:0% +talking about forming groups in the same + + + align:start position:0% +talking about forming groups in the same +project and then later on forming groups + + align:start position:0% +project and then later on forming groups + + + align:start position:0% +project and then later on forming groups +where we can have people compare you + + align:start position:0% +where we can have people compare you + + + align:start position:0% +where we can have people compare you +know somebody who worked on Unity + + align:start position:0% +know somebody who worked on Unity + + + align:start position:0% +know somebody who worked on Unity +talking to somebody who worked on flixel + + align:start position:0% +talking to somebody who worked on flixel + + + align:start position:0% +talking to somebody who worked on flixel +things like that um after that we're + + align:start position:0% +things like that um after that we're + + + align:start position:0% +things like that um after that we're +going to have project One play test so + + align:start position:0% +going to have project One play test so + + + align:start position:0% +going to have project One play test so +this is going to be an informal play + + align:start position:0% +this is going to be an informal play + + + align:start position:0% +this is going to be an informal play +test basically it's a check can you play + + align:start position:0% +test basically it's a check can you play + + + align:start position:0% +test basically it's a check can you play +your game today if you can't then play + + align:start position:0% +your game today if you can't then play + + + align:start position:0% +your game today if you can't then play +what you got because you're going to be + + align:start position:0% +what you got because you're going to be + + + align:start position:0% +what you got because you're going to be +forced to play it um maybe you have some + + align:start position:0% +forced to play it um maybe you have some + + + align:start position:0% +forced to play it um maybe you have some +rules written down great just act them + + align:start position:0% +rules written down great just act them + + + align:start position:0% +rules written down great just act them +out in that 15-minute block we give you + + align:start position:0% +out in that 15-minute block we give you + + + align:start position:0% +out in that 15-minute block we give you +to act out those rules and maybe within + + align:start position:0% +to act out those rules and maybe within + + + align:start position:0% +to act out those rules and maybe within +that 15-minute block come up with a few + + align:start position:0% +that 15-minute block come up with a few + + + align:start position:0% +that 15-minute block come up with a few +different rules or a few different + + align:start position:0% +different rules or a few different + + + align:start position:0% +different rules or a few different +pieces um so that's going to happen um + + align:start position:0% +pieces um so that's going to happen um + + + align:start position:0% +pieces um so that's going to happen um +we'll go through the how that's going to + + align:start position:0% +we'll go through the how that's going to + + + align:start position:0% +we'll go through the how that's going to +work later and then at the end of the + + align:start position:0% +work later and then at the end of the + + + align:start position:0% +work later and then at the end of the +day we're going to do another Workshop + + align:start position:0% +day we're going to do another Workshop + + + align:start position:0% +day we're going to do another Workshop +um Sarah's going to us on that um + + align:start position:0% +um Sarah's going to us on that um + + + align:start position:0% +um Sarah's going to us on that um +talking about vision statements so this + + align:start position:0% +talking about vision statements so this + + + align:start position:0% +talking about vision statements so this +is a tool that we used to help large + + align:start position:0% +is a tool that we used to help large + + + align:start position:0% +is a tool that we used to help large +teams understand what it is we're + + align:start position:0% +teams understand what it is we're + + + align:start position:0% +teams understand what it is we're +actually + + align:start position:0% +actually + + + align:start position:0% +actually +creating so with that I'm going to + + align:start position:0% +creating so with that I'm going to + + + align:start position:0% +creating so with that I'm going to +switch slides and bring it over to Drew + + align:start position:0% +switch slides and bring it over to Drew + + + align:start position:0% +switch slides and bring it over to Drew +so the first thing I see a lot of + + align:start position:0% +so the first thing I see a lot of + + + align:start position:0% +so the first thing I see a lot of +laptops which is pretty awesome how many + + align:start position:0% +laptops which is pretty awesome how many + + + align:start position:0% +laptops which is pretty awesome how many +of you brought a computer that you could + + align:start position:0% +of you brought a computer that you could + + + align:start position:0% +of you brought a computer that you could +actually that actually has the code you + + align:start position:0% +actually that actually has the code you + + + align:start position:0% +actually that actually has the code you +used for your tutorials on it that is + + align:start position:0% +used for your tutorials on it that is + + + align:start position:0% +used for your tutorials on it that is +more than half awesome so you get the + + align:start position:0% +more than half awesome so you get the + + + align:start position:0% +more than half awesome so you get the +short version of the presentation not + + align:start position:0% +short version of the presentation not + + + align:start position:0% +short version of the presentation not +the long one um so uh as soon as we get + + align:start position:0% +the long one um so uh as soon as we get + + + align:start position:0% +the long one um so uh as soon as we get +it up there and going uh let's see any + + align:start position:0% +it up there and going uh let's see any + + + align:start position:0% +it up there and going uh let's see any +other question who here has used Version + + align:start position:0% +other question who here has used Version + + + align:start position:0% +other question who here has used Version +Control or Source control before most of + + align:start position:0% +Control or Source control before most of + + + align:start position:0% +Control or Source control before most of +you fascinating who here feels confident + + align:start position:0% +you fascinating who here feels confident + + + align:start position:0% +you fascinating who here feels confident +that you know why you used Version + + align:start position:0% +that you know why you used Version + + + align:start position:0% +that you know why you used Version +Control and that it was awesome and + + align:start position:0% +Control and that it was awesome and + + + align:start position:0% +Control and that it was awesome and +you're cool and you're good at + + align:start position:0% +you're cool and you're good at + + + align:start position:0% +you're cool and you're good at +this okay the hands went up and started + + align:start position:0% +this okay the hands went up and started + + + align:start position:0% +this okay the hands went up and started +to come down slowly which makes sense + + align:start position:0% +to come down slowly which makes sense + + + align:start position:0% +to come down slowly which makes sense +that's what they should have + + align:start position:0% +that's what they should have + + + align:start position:0% +that's what they should have +done all right so I'm not actually going + + align:start position:0% +done all right so I'm not actually going + + + align:start position:0% +done all right so I'm not actually going +to talk about the nitty-gritty details + + align:start position:0% +to talk about the nitty-gritty details + + + align:start position:0% +to talk about the nitty-gritty details +of exactly which commands you type + + align:start position:0% +of exactly which commands you type + + + align:start position:0% +of exactly which commands you type +because there's a bunch of different + + align:start position:0% +because there's a bunch of different + + + align:start position:0% +because there's a bunch of different +version Control Systems they all work + + align:start position:0% +version Control Systems they all work + + + align:start position:0% +version Control Systems they all work +very + + align:start position:0% +very + + + align:start position:0% +very +similarly um but you're going to + + align:start position:0% +similarly um but you're going to + + + align:start position:0% +similarly um but you're going to +basically need to read the documentation + + align:start position:0% +basically need to read the documentation + + + align:start position:0% +basically need to read the documentation +on the particular one that you're using + + align:start position:0% +on the particular one that you're using + + + align:start position:0% +on the particular one that you're using +I would recommend today if you're + + align:start position:0% +I would recommend today if you're + + + align:start position:0% +I would recommend today if you're +familiar with one that you stick with + + align:start position:0% +familiar with one that you stick with + + + align:start position:0% +familiar with one that you stick with +that if possible but um but don't worry + + align:start position:0% +that if possible but um but don't worry + + + align:start position:0% +that if possible but um but don't worry +about it if you + + align:start position:0% +about it if you + + + align:start position:0% +about it if you +can't um so let's see I give a high + + align:start position:0% +can't um so let's see I give a high + + + align:start position:0% +can't um so let's see I give a high +level description of what is revision + + align:start position:0% +level description of what is revision + + + align:start position:0% +level description of what is revision +control um I'm going to use different + + align:start position:0% +control um I'm going to use different + + + align:start position:0% +control um I'm going to use different +words for it Source control revision + + align:start position:0% +words for it Source control revision + + + align:start position:0% +words for it Source control revision +control or sort of the big ones um the + + align:start position:0% +control or sort of the big ones um the + + + align:start position:0% +control or sort of the big ones um the +basic notion is that and this is a very + + align:start position:0% +basic notion is that and this is a very + + + align:start position:0% +basic notion is that and this is a very +simple notion that you've got one copy + + align:start position:0% +simple notion that you've got one copy + + + align:start position:0% +simple notion that you've got one copy +of The Source on your local machine and + + align:start position:0% +of The Source on your local machine and + + + align:start position:0% +of The Source on your local machine and +you've got one copy of the source + + align:start position:0% +you've got one copy of the source + + + align:start position:0% +you've got one copy of the source +somewhere else and that copy out there + + align:start position:0% +somewhere else and that copy out there + + + align:start position:0% +somewhere else and that copy out there +is the perfect copy that's the true copy + + align:start position:0% +is the perfect copy that's the true copy + + + align:start position:0% +is the perfect copy that's the true copy +of what you're working on that's the + + align:start position:0% +of what you're working on that's the + + + align:start position:0% +of what you're working on that's the +platonic ideal of your project and your + + align:start position:0% +platonic ideal of your project and your + + + align:start position:0% +platonic ideal of your project and your +job is to copy files down from it change + + align:start position:0% +job is to copy files down from it change + + + align:start position:0% +job is to copy files down from it change +them and copy them back up to that one + + align:start position:0% +them and copy them back up to that one + + + align:start position:0% +them and copy them back up to that one +um not much going on there + + align:start position:0% +um not much going on there + + + align:start position:0% +um not much going on there +right all right I'll get into more + + align:start position:0% +right all right I'll get into more + + + align:start position:0% +right all right I'll get into more +details on that so um we started there's + + align:start position:0% +details on that so um we started there's + + + align:start position:0% +details on that so um we started there's +a whole bunch of words that go along + + align:start position:0% +a whole bunch of words that go along + + + align:start position:0% +a whole bunch of words that go along +with this topic uh revision control + + align:start position:0% +with this topic uh revision control + + + align:start position:0% +with this topic uh revision control +system uh RCS is what is often used as a + + align:start position:0% +system uh RCS is what is often used as a + + + align:start position:0% +system uh RCS is what is often used as a +generic term it's also a specific piece + + align:start position:0% +generic term it's also a specific piece + + + align:start position:0% +generic term it's also a specific piece +of software that you probably won't use + + align:start position:0% +of software that you probably won't use + + + align:start position:0% +of software that you probably won't use +because it's really + + align:start position:0% +because it's really + + + align:start position:0% +because it's really +old um Source control Version Control + + align:start position:0% +old um Source control Version Control + + + align:start position:0% +old um Source control Version Control +and you also see SCM as a common uh TLA + + align:start position:0% +and you also see SCM as a common uh TLA + + + align:start position:0% +and you also see SCM as a common uh TLA +for Source Control + + align:start position:0% +for Source Control + + + align:start position:0% +for Source Control +Management um CVS the concurrent version + + align:start position:0% +Management um CVS the concurrent version + + + align:start position:0% +Management um CVS the concurrent version +system is also older but one you might + + align:start position:0% +system is also older but one you might + + + align:start position:0% +system is also older but one you might +actually see used it's mostly command + + align:start position:0% +actually see used it's mostly command + + + align:start position:0% +actually see used it's mostly command +line only + + align:start position:0% +line only + + + align:start position:0% +line only +um SVN is a more recent open source + + align:start position:0% +um SVN is a more recent open source + + + align:start position:0% +um SVN is a more recent open source +version of CVS I CS may have been too + + align:start position:0% +version of CVS I CS may have been too + + + align:start position:0% +version of CVS I CS may have been too +I'm not sure on that one SVN is more + + align:start position:0% +I'm not sure on that one SVN is more + + + align:start position:0% +I'm not sure on that one SVN is more +usable and I hardly recommend it + + align:start position:0% +usable and I hardly recommend it + + + align:start position:0% +usable and I hardly recommend it +perforce is one that's used quite often + + align:start position:0% +perforce is one that's used quite often + + + align:start position:0% +perforce is one that's used quite often +in the games + + align:start position:0% +in the games + + + align:start position:0% +in the games +industry and then you're going to see + + align:start position:0% +industry and then you're going to see + + + align:start position:0% +industry and then you're going to see +git and Mercurial which are often + + align:start position:0% +git and Mercurial which are often + + + align:start position:0% +git and Mercurial which are often +mentioned in the same breadth they're + + align:start position:0% +mentioned in the same breadth they're + + + align:start position:0% +mentioned in the same breadth they're +both what's called distributed Source + + align:start position:0% +both what's called distributed Source + + + align:start position:0% +both what's called distributed Source +control we'll get to that but their + + align:start position:0% +control we'll get to that but their + + + align:start position:0% +control we'll get to that but their +interface is very similar um to all of + + align:start position:0% +interface is very similar um to all of + + + align:start position:0% +interface is very similar um to all of +the above actually all they almost all + + align:start position:0% +the above actually all they almost all + + + align:start position:0% +the above actually all they almost all +have a command line interface where you + + align:start position:0% +have a command line interface where you + + + align:start position:0% +have a command line interface where you +can do everything for the command line + + align:start position:0% +can do everything for the command line + + + align:start position:0% +can do everything for the command line +and most of them have a gooey you can + + align:start position:0% +and most of them have a gooey you can + + + align:start position:0% +and most of them have a gooey you can +use as well but you're going to see a + + align:start position:0% +use as well but you're going to see a + + + align:start position:0% +use as well but you're going to see a +bunch of different words used to talk + + align:start position:0% +bunch of different words used to talk + + + align:start position:0% +bunch of different words used to talk +about this stuff so again its most basic + + align:start position:0% +about this stuff so again its most basic + + + align:start position:0% +about this stuff so again its most basic +form you've got a server you got your + + align:start position:0% +form you've got a server you got your + + + align:start position:0% +form you've got a server you got your +local you copy stuff back and forth + + align:start position:0% +local you copy stuff back and forth + + + align:start position:0% +local you copy stuff back and forth +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +basic and it's a little bit easier to + + align:start position:0% +basic and it's a little bit easier to + + + align:start position:0% +basic and it's a little bit easier to +see why you might want that when you got + + align:start position:0% +see why you might want that when you got + + + align:start position:0% +see why you might want that when you got +more than one person on the team um it's + + align:start position:0% +more than one person on the team um it's + + + align:start position:0% +more than one person on the team um it's +a really good way to make sure your + + align:start position:0% +a really good way to make sure your + + + align:start position:0% +a really good way to make sure your +files are + + align:start position:0% + + + + align:start position:0% + +synchronized it's even more important + + align:start position:0% +synchronized it's even more important + + + align:start position:0% +synchronized it's even more important +the bigger your team so what's really + + align:start position:0% +the bigger your team so what's really + + + align:start position:0% +the bigger your team so what's really +really important is that that server + + align:start position:0% +really important is that that server + + + align:start position:0% +really important is that that server +copy of your code is useful so you want + + align:start position:0% +copy of your code is useful so you want + + + align:start position:0% +copy of your code is useful so you want +to make sure that you are only you know + + align:start position:0% +to make sure that you are only you know + + + align:start position:0% +to make sure that you are only you know +contributing to that Central suppository + + align:start position:0% +contributing to that Central suppository + + + align:start position:0% +contributing to that Central suppository +of repository of code the useful + + align:start position:0% + + + + align:start position:0% + +pieces + + align:start position:0% +pieces + + + align:start position:0% +pieces +now what we really want to do is that + + align:start position:0% +now what we really want to do is that + + + align:start position:0% +now what we really want to do is that +Central version of the code is sort of + + align:start position:0% +Central version of the code is sort of + + + align:start position:0% +Central version of the code is sort of +what's considered as I mentioned the the + + align:start position:0% +what's considered as I mentioned the the + + + align:start position:0% +what's considered as I mentioned the the +ideal version of your code is the + + align:start position:0% +ideal version of your code is the + + + align:start position:0% +ideal version of your code is the +authoritative it's the one you can + + align:start position:0% +authoritative it's the one you can + + + align:start position:0% +authoritative it's the one you can +trust so that actually becomes a little + + align:start position:0% +trust so that actually becomes a little + + + align:start position:0% +trust so that actually becomes a little +bit more than a backup system right so a + + align:start position:0% +bit more than a backup system right so a + + + align:start position:0% +bit more than a backup system right so a +backup system is quite useful if you + + align:start position:0% +backup system is quite useful if you + + + align:start position:0% +backup system is quite useful if you +lose something or you you make a mistake + + align:start position:0% +lose something or you you make a mistake + + + align:start position:0% +lose something or you you make a mistake +you want to be able to revert to a + + align:start position:0% +you want to be able to revert to a + + + align:start position:0% +you want to be able to revert to a +previous version of your your code and + + align:start position:0% +previous version of your your code and + + + align:start position:0% +previous version of your your code and +that is certainly one of the things that + + align:start position:0% +that is certainly one of the things that + + + align:start position:0% +that is certainly one of the things that +Source control does for you um but and + + align:start position:0% +Source control does for you um but and + + + align:start position:0% +Source control does for you um but and +we also talk about how it's a way to + + align:start position:0% +we also talk about how it's a way to + + + align:start position:0% +we also talk about how it's a way to +share your code but it's actually more + + align:start position:0% +share your code but it's actually more + + + align:start position:0% +share your code but it's actually more +important than that so the history of + + align:start position:0% +important than that so the history of + + + align:start position:0% +important than that so the history of +your project is one of the big things + + align:start position:0% +your project is one of the big things + + + align:start position:0% +your project is one of the big things +you get out of it when you submit your + + align:start position:0% +you get out of it when you submit your + + + align:start position:0% +you get out of it when you submit your +files which is can be source code files + + align:start position:0% +files which is can be source code files + + + align:start position:0% +files which is can be source code files +it could be images it could be anything + + align:start position:0% +it could be images it could be anything + + + align:start position:0% +it could be images it could be anything +when you submit them you should conclude + + align:start position:0% +when you submit them you should conclude + + + align:start position:0% +when you submit them you should conclude +a comment about what the heck you've + + align:start position:0% +a comment about what the heck you've + + + align:start position:0% +a comment about what the heck you've +done and it's really this is one of the + + align:start position:0% +done and it's really this is one of the + + + align:start position:0% +done and it's really this is one of the +things I find new programmers have the + + align:start position:0% +things I find new programmers have the + + + align:start position:0% +things I find new programmers have the +hardest time with in fact I know plenty + + align:start position:0% +hardest time with in fact I know plenty + + + align:start position:0% +hardest time with in fact I know plenty +of old programmers that can't do it but + + align:start position:0% +of old programmers that can't do it but + + + align:start position:0% +of old programmers that can't do it but +really it's use and the reason is it's + + align:start position:0% +really it's use and the reason is it's + + + align:start position:0% +really it's use and the reason is it's +useful is all because of this um we're + + align:start position:0% +useful is all because of this um we're + + + align:start position:0% +useful is all because of this um we're +going to talk about different methods of + + align:start position:0% +going to talk about different methods of + + + align:start position:0% +going to talk about different methods of +communication throughout this course and + + align:start position:0% +communication throughout this course and + + + align:start position:0% +communication throughout this course and +um I've talked about um or I will talk + + align:start position:0% +um I've talked about um or I will talk + + + align:start position:0% +um I've talked about um or I will talk +about the fact that your source code is + + align:start position:0% +about the fact that your source code is + + + align:start position:0% +about the fact that your source code is +a way to communicate with other people + + align:start position:0% +a way to communicate with other people + + + align:start position:0% +a way to communicate with other people +but it turns out your comment log in + + align:start position:0% +but it turns out your comment log in + + + align:start position:0% +but it turns out your comment log in +your version control system is also a + + align:start position:0% +your version control system is also a + + + align:start position:0% +your version control system is also a +great way to commun with your team so + + align:start position:0% +great way to commun with your team so + + + align:start position:0% +great way to commun with your team so +for example if you submit a whole bunch + + align:start position:0% +for example if you submit a whole bunch + + + align:start position:0% +for example if you submit a whole bunch +of files and it's not obvious what that + + align:start position:0% +of files and it's not obvious what that + + + align:start position:0% +of files and it's not obvious what that +did to your game that comment can tell + + align:start position:0% +did to your game that comment can tell + + + align:start position:0% +did to your game that comment can tell +everyone else on your team what just + + align:start position:0% +everyone else on your team what just + + + align:start position:0% +everyone else on your team what just +happened maybe you rewrote the entire AI + + align:start position:0% +happened maybe you rewrote the entire AI + + + align:start position:0% +happened maybe you rewrote the entire AI +so that the bad guys now run away from + + align:start position:0% +so that the bad guys now run away from + + + align:start position:0% +so that the bad guys now run away from +the player and it may be that someone + + align:start position:0% +the player and it may be that someone + + + align:start position:0% +the player and it may be that someone +else on your team is trying to figure + + align:start position:0% +else on your team is trying to figure + + + align:start position:0% +else on your team is trying to figure +out why are the bad guys AI broken now + + align:start position:0% +out why are the bad guys AI broken now + + + align:start position:0% +out why are the bad guys AI broken now +and the answer is it's not broken + + align:start position:0% +and the answer is it's not broken + + + align:start position:0% +and the answer is it's not broken +they're just doing something different + + align:start position:0% +they're just doing something different + + + align:start position:0% +they're just doing something different +and when they do get that code from the + + align:start position:0% +and when they do get that code from the + + + align:start position:0% +and when they do get that code from the +server they're going to see that comment + + align:start position:0% +server they're going to see that comment + + + align:start position:0% +server they're going to see that comment +and say oh I get it the AI changed so if + + align:start position:0% +and say oh I get it the AI changed so if + + + align:start position:0% +and say oh I get it the AI changed so if +you fail to report that in a scrum or + + align:start position:0% +you fail to report that in a scrum or + + + align:start position:0% +you fail to report that in a scrum or +maybe you don't have a scrum because you + + align:start position:0% +maybe you don't have a scrum because you + + + align:start position:0% +maybe you don't have a scrum because you +did in the middle of the night this is + + align:start position:0% +did in the middle of the night this is + + + align:start position:0% +did in the middle of the night this is +one a great way to communicate with your + + align:start position:0% +one a great way to communicate with your + + + align:start position:0% +one a great way to communicate with your +team even more than that that history is + + align:start position:0% +team even more than that that history is + + + align:start position:0% +team even more than that that history is +also really useful let's say you check + + align:start position:0% +also really useful let's say you check + + + align:start position:0% +also really useful let's say you check +in this code that causes bad guys to run + + align:start position:0% +in this code that causes bad guys to run + + + align:start position:0% +in this code that causes bad guys to run +away and then a couple days later you + + align:start position:0% +away and then a couple days later you + + + align:start position:0% +away and then a couple days later you +find out that there's some problem in + + align:start position:0% +find out that there's some problem in + + + align:start position:0% +find out that there's some problem in +the AI where things actually crash + + align:start position:0% +the AI where things actually crash + + + align:start position:0% +the AI where things actually crash +horribly if the game sits there for an + + align:start position:0% +horribly if the game sits there for an + + + align:start position:0% +horribly if the game sits there for an +hour well where do you begin looking for + + align:start position:0% +hour well where do you begin looking for + + + align:start position:0% +hour well where do you begin looking for +that bug you may not know that it's in + + align:start position:0% +that bug you may not know that it's in + + + align:start position:0% +that bug you may not know that it's in +the AI you may just um um have some + + align:start position:0% +the AI you may just um um have some + + + align:start position:0% +the AI you may just um um have some +little bit of Clues but you can know you + + align:start position:0% +little bit of Clues but you can know you + + + align:start position:0% +little bit of Clues but you can know you +know that it changed in the last two + + align:start position:0% +know that it changed in the last two + + + align:start position:0% +know that it changed in the last two +days this Behavior started so you can + + align:start position:0% +days this Behavior started so you can + + + align:start position:0% +days this Behavior started so you can +look at the log and say what happened in + + align:start position:0% +look at the log and say what happened in + + + align:start position:0% +look at the log and say what happened in +the last two days and if someone further + + align:start position:0% +the last two days and if someone further + + + align:start position:0% +the last two days and if someone further +discovers that well it's crashing + + align:start position:0% +discovers that well it's crashing + + + align:start position:0% +discovers that well it's crashing +somewhere in AI then you have a hint + + align:start position:0% +somewhere in AI then you have a hint + + + align:start position:0% +somewhere in AI then you have a hint +that it's in the AI system but more than + + align:start position:0% +that it's in the AI system but more than + + + align:start position:0% +that it's in the AI system but more than +that you can go to the exact last change + + align:start position:0% +that you can go to the exact last change + + + align:start position:0% +that you can go to the exact last change +in the AI system and look at those files + + align:start position:0% +in the AI system and look at those files + + + align:start position:0% +in the AI system and look at those files +and that's probably where your bug is + + align:start position:0% +and that's probably where your bug is + + + align:start position:0% +and that's probably where your bug is +that's pretty + + align:start position:0% +that's pretty + + + align:start position:0% +that's pretty +handy and let's say that you do + + align:start position:0% +handy and let's say that you do + + + align:start position:0% +handy and let's say that you do +something really really horrible you + + align:start position:0% +something really really horrible you + + + align:start position:0% +something really really horrible you +also get an undo button out of all this + + align:start position:0% +also get an undo button out of all this + + + align:start position:0% +also get an undo button out of all this +right you can say you know what that + + align:start position:0% +right you can say you know what that + + + align:start position:0% +right you can say you know what that +version two days ago let's go back to + + align:start position:0% +version two days ago let's go back to + + + align:start position:0% +version two days ago let's go back to +that that's better than what we have + + align:start position:0% +that that's better than what we have + + + align:start position:0% +that that's better than what we have +right now you don't often do that but + + align:start position:0% +right now you don't often do that but + + + align:start position:0% +right now you don't often do that but +it's really nice to have that kind of + + align:start position:0% +it's really nice to have that kind of + + + align:start position:0% +it's really nice to have that kind of +security especially when you're working + + align:start position:0% +security especially when you're working + + + align:start position:0% +security especially when you're working +in your local version let's say you're + + align:start position:0% +in your local version let's say you're + + + align:start position:0% +in your local version let's say you're +trying out to find a bug you need to + + align:start position:0% +trying out to find a bug you need to + + + align:start position:0% +trying out to find a bug you need to +change 15 files and putting your debug + + align:start position:0% +change 15 files and putting your debug + + + align:start position:0% +change 15 files and putting your debug +statements everywhere to figure out what + + align:start position:0% +statements everywhere to figure out what + + + align:start position:0% +statements everywhere to figure out what +the heck's going on and then you find + + align:start position:0% +the heck's going on and then you find + + + align:start position:0% +the heck's going on and then you find +the bug finally and you realize it's a + + align:start position:0% +the bug finally and you realize it's a + + + align:start position:0% +the bug finally and you realize it's a +oneline + + align:start position:0% +oneline + + + align:start position:0% +oneline +change well it's easier just to revert + + align:start position:0% +change well it's easier just to revert + + + align:start position:0% +change well it's easier just to revert +back to the server version and make that + + align:start position:0% +back to the server version and make that + + + align:start position:0% +back to the server version and make that +oneline change than to make sure you've + + align:start position:0% +oneline change than to make sure you've + + + align:start position:0% +oneline change than to make sure you've +undo every little piece let the computer + + align:start position:0% +undo every little piece let the computer + + + align:start position:0% +undo every little piece let the computer +be your memory let the computer be your + + align:start position:0% +be your memory let the computer be your + + + align:start position:0% +be your memory let the computer be your +undo button you don't need to rely on + + align:start position:0% +undo button you don't need to rely on + + + align:start position:0% +undo button you don't need to rely on +knowing which files you changed it will + + align:start position:0% +knowing which files you changed it will + + + align:start position:0% +knowing which files you changed it will +tell + + align:start position:0% +tell + + + align:start position:0% +tell +you and this is the cool thing that is + + align:start position:0% +you and this is the cool thing that is + + + align:start position:0% +you and this is the cool thing that is +kind of scary but pretty awesome is you + + align:start position:0% +kind of scary but pretty awesome is you + + + align:start position:0% +kind of scary but pretty awesome is you +can actually simultaneously edit the + + align:start position:0% +can actually simultaneously edit the + + + align:start position:0% +can actually simultaneously edit the +same files if they are text files um + + align:start position:0% +same files if they are text files um + + + align:start position:0% +same files if they are text files um +this involves a merge process afterwards + + align:start position:0% +this involves a merge process afterwards + + + align:start position:0% +this involves a merge process afterwards +which is a little bit frightening the + + align:start position:0% +which is a little bit frightening the + + + align:start position:0% +which is a little bit frightening the +first several times you do it but + + align:start position:0% +first several times you do it but + + + align:start position:0% +first several times you do it but +actually the tools are pretty good um as + + align:start position:0% +actually the tools are pretty good um as + + + align:start position:0% +actually the tools are pretty good um as +long as you're not modifying the same + + align:start position:0% +long as you're not modifying the same + + + align:start position:0% +long as you're not modifying the same +line of the file it's pretty good about + + align:start position:0% +line of the file it's pretty good about + + + align:start position:0% +line of the file it's pretty good about +figuring what should happen but you do + + align:start position:0% +figuring what should happen but you do + + + align:start position:0% +figuring what should happen but you do +need to manually check it with your eyes + + align:start position:0% +need to manually check it with your eyes + + + align:start position:0% +need to manually check it with your eyes +to verify it didn't do anything stupid + + align:start position:0% +to verify it didn't do anything stupid + + + align:start position:0% +to verify it didn't do anything stupid +but it's actually pretty common to be + + align:start position:0% +but it's actually pretty common to be + + + align:start position:0% +but it's actually pretty common to be +able to work with the same file with two + + align:start position:0% +able to work with the same file with two + + + align:start position:0% +able to work with the same file with two +different people and actually have it + + align:start position:0% +different people and actually have it + + + align:start position:0% +different people and actually have it +work out okay the exception to that is + + align:start position:0% +work out okay the exception to that is + + + align:start position:0% +work out okay the exception to that is +extremely complicated text files or + + align:start position:0% +extremely complicated text files or + + + align:start position:0% +extremely complicated text files or +binary files you can't merge changes to + + align:start position:0% +binary files you can't merge changes to + + + align:start position:0% +binary files you can't merge changes to +a PNG or GIF that doesn't make sense um + + align:start position:0% +a PNG or GIF that doesn't make sense um + + + align:start position:0% +a PNG or GIF that doesn't make sense um +at least on the file level and uh if a + + align:start position:0% +at least on the file level and uh if a + + + align:start position:0% +at least on the file level and uh if a +lot of the um data files in unity + + align:start position:0% +lot of the um data files in unity + + + align:start position:0% +lot of the um data files in unity +especially the scene files and prefab + + align:start position:0% +especially the scene files and prefab + + + align:start position:0% +especially the scene files and prefab +files are going to be too complicated + + align:start position:0% +files are going to be too complicated + + + align:start position:0% +files are going to be too complicated +probably for you to actually manage it + + align:start position:0% +probably for you to actually manage it + + + align:start position:0% +probably for you to actually manage it +to emerge so for those you need be a + + align:start position:0% +to emerge so for those you need be a + + + align:start position:0% +to emerge so for those you need be a +little more careful about it but it's + + align:start position:0% +little more careful about it but it's + + + align:start position:0% +little more careful about it but it's +actually a really useful tool to to to + + align:start position:0% +actually a really useful tool to to to + + + align:start position:0% +actually a really useful tool to to to +to lean on + + align:start position:0% +to lean on + + + align:start position:0% +to lean on +that so we're going to talk about the + + align:start position:0% +that so we're going to talk about the + + + align:start position:0% +that so we're going to talk about the +various operations very very + + align:start position:0% +various operations very very + + + align:start position:0% +various operations very very +quickly um when you copy things from the + + align:start position:0% +quickly um when you copy things from the + + + align:start position:0% +quickly um when you copy things from the +server different Source Control Systems + + align:start position:0% +server different Source Control Systems + + + align:start position:0% +server different Source Control Systems +will call it different things um you're + + align:start position:0% +will call it different things um you're + + + align:start position:0% +will call it different things um you're +going to see the term get to mean pull + + align:start position:0% +going to see the term get to mean pull + + + align:start position:0% +going to see the term get to mean pull +the files down from the server uh update + + align:start position:0% +the files down from the server uh update + + + align:start position:0% +the files down from the server uh update +pull and check out in different systems + + align:start position:0% +pull and check out in different systems + + + align:start position:0% +pull and check out in different systems +will all mean that same thing copy files + + align:start position:0% +will all mean that same thing copy files + + + align:start position:0% +will all mean that same thing copy files +from the server um I also have in there + + align:start position:0% +from the server um I also have in there + + + align:start position:0% +from the server um I also have in there +the word revert which is kind of a fancy + + align:start position:0% +the word revert which is kind of a fancy + + + align:start position:0% +the word revert which is kind of a fancy +special case when I said you can undo + + align:start position:0% +special case when I said you can undo + + + align:start position:0% +special case when I said you can undo +your changes you got a whole bunch of + + align:start position:0% +your changes you got a whole bunch of + + + align:start position:0% +your changes you got a whole bunch of +files changed and you don't like those + + align:start position:0% +files changed and you don't like those + + + align:start position:0% +files changed and you don't like those +changes you can revert to the server + + align:start position:0% +changes you can revert to the server + + + align:start position:0% +changes you can revert to the server +version which is you know under the + + align:start position:0% +version which is you know under the + + + align:start position:0% +version which is you know under the +covers which really going on there is + + align:start position:0% +covers which really going on there is + + + align:start position:0% +covers which really going on there is +you're copying down from the server but + + align:start position:0% +you're copying down from the server but + + + align:start position:0% +you're copying down from the server but +it'll call that revert because it's + + align:start position:0% +it'll call that revert because it's + + + align:start position:0% +it'll call that revert because it's +going to ask you wait a minute you + + align:start position:0% +going to ask you wait a minute you + + + align:start position:0% +going to ask you wait a minute you +change that file are you sure you really + + align:start position:0% +change that file are you sure you really + + + align:start position:0% +change that file are you sure you really +want to wipe that out and at that point + + align:start position:0% +want to wipe that out and at that point + + + align:start position:0% +want to wipe that out and at that point +you should say yes or no depending on + + align:start position:0% +you should say yes or no depending on + + + align:start position:0% +you should say yes or no depending on +how sure you are that you really want to + + align:start position:0% +how sure you are that you really want to + + + align:start position:0% +how sure you are that you really want to +do that + + align:start position:0% +do that + + + align:start position:0% +do that +similarly when you have decided that + + align:start position:0% +similarly when you have decided that + + + align:start position:0% +similarly when you have decided that +You' finished with your changes locally + + align:start position:0% +You' finished with your changes locally + + + align:start position:0% +You' finished with your changes locally +and you want to copy them out to the + + align:start position:0% +and you want to copy them out to the + + + align:start position:0% +and you want to copy them out to the +server for everyone else to see um + + align:start position:0% +server for everyone else to see um + + + align:start position:0% +server for everyone else to see um +that's going to be called submit commit + + align:start position:0% +that's going to be called submit commit + + + align:start position:0% +that's going to be called submit commit +put push or checkin generally speaking + + align:start position:0% +put push or checkin generally speaking + + + align:start position:0% +put push or checkin generally speaking +people talk about that copying up to the + + align:start position:0% +people talk about that copying up to the + + + align:start position:0% +people talk about that copying up to the +server um directionally and the reason + + align:start position:0% +server um directionally and the reason + + + align:start position:0% +server um directionally and the reason +you they have used some fancy words like + + align:start position:0% +you they have used some fancy words like + + + align:start position:0% +you they have used some fancy words like +um commit is they want you to sort of + + align:start position:0% +um commit is they want you to sort of + + + align:start position:0% +um commit is they want you to sort of +realize that this is not just I'm not + + align:start position:0% +realize that this is not just I'm not + + + align:start position:0% +realize that this is not just I'm not +just copying a file you're copying a + + align:start position:0% +just copying a file you're copying a + + + align:start position:0% +just copying a file you're copying a +file for everyone to see so you want to + + align:start position:0% +file for everyone to see so you want to + + + align:start position:0% +file for everyone to see so you want to +be sure that you're your changes are + + align:start position:0% +be sure that you're your changes are + + + align:start position:0% +be sure that you're your changes are +good um this one's easier if you want to + + align:start position:0% +good um this one's easier if you want to + + + align:start position:0% +good um this one's easier if you want to +find out the status of what's going on + + align:start position:0% +find out the status of what's going on + + + align:start position:0% +find out the status of what's going on +almost all the s Source controls use the + + align:start position:0% +almost all the s Source controls use the + + + align:start position:0% +almost all the s Source controls use the +word status for that um but basically + + align:start position:0% +word status for that um but basically + + + align:start position:0% +word status for that um but basically +what you can do is you can say things + + align:start position:0% +what you can do is you can say things + + + align:start position:0% +what you can do is you can say things +like so I've changed a bunch of files + + align:start position:0% +like so I've changed a bunch of files + + + align:start position:0% +like so I've changed a bunch of files +and I forget what I've changed I'm sure + + align:start position:0% +and I forget what I've changed I'm sure + + + align:start position:0% +and I forget what I've changed I'm sure +there's a lot of them you can actually + + align:start position:0% +there's a lot of them you can actually + + + align:start position:0% +there's a lot of them you can actually +ask your Source control system what did + + align:start position:0% +ask your Source control system what did + + + align:start position:0% +ask your Source control system what did +I change and you'll say well these files + + align:start position:0% +I change and you'll say well these files + + + align:start position:0% +I change and you'll say well these files +five files have changed and in fact you + + align:start position:0% +five files have changed and in fact you + + + align:start position:0% +five files have changed and in fact you +can even get more information from that + + align:start position:0% +can even get more information from that + + + align:start position:0% +can even get more information from that +um if you want to you know compare what + + align:start position:0% +um if you want to you know compare what + + + align:start position:0% +um if you want to you know compare what +these actual changes are and diff is the + + align:start position:0% +these actual changes are and diff is the + + + align:start position:0% +these actual changes are and diff is the +term for + + align:start position:0% +term for + + + align:start position:0% +term for +that um locking files so no one else can + + align:start position:0% +that um locking files so no one else can + + + align:start position:0% +that um locking files so no one else can +change them is not often used in source + + align:start position:0% +change them is not often used in source + + + align:start position:0% +change them is not often used in source +code but um it's very useful for as I + + align:start position:0% +code but um it's very useful for as I + + + align:start position:0% +code but um it's very useful for as I +was talking about there are some files + + align:start position:0% +was talking about there are some files + + + align:start position:0% +was talking about there are some files +that are so complicated that it can't + + align:start position:0% +that are so complicated that it can't + + + align:start position:0% +that are so complicated that it can't +automatically merge them for you and the + + align:start position:0% +automatically merge them for you and the + + + align:start position:0% +automatically merge them for you and the +binary files as well you may find that + + align:start position:0% +binary files as well you may find that + + + align:start position:0% +binary files as well you may find that +some Source Control Systems don't + + align:start position:0% +some Source Control Systems don't + + + align:start position:0% +some Source Control Systems don't +automatically lock these for you and so + + align:start position:0% +automatically lock these for you and so + + + align:start position:0% +automatically lock these for you and so +in that case you might want to make as + + align:start position:0% +in that case you might want to make as + + + align:start position:0% +in that case you might want to make as +your team policy that you want to lock + + align:start position:0% +your team policy that you want to lock + + + align:start position:0% +your team policy that you want to lock +the file so that no one else messes with + + align:start position:0% +the file so that no one else messes with + + + align:start position:0% +the file so that no one else messes with +it so again I'll go back to Unity as an + + align:start position:0% +it so again I'll go back to Unity as an + + + align:start position:0% +it so again I'll go back to Unity as an +example if you're changing the main + + align:start position:0% +example if you're changing the main + + + align:start position:0% +example if you're changing the main +scene file for your game and it's this + + align:start position:0% +scene file for your game and it's this + + + align:start position:0% +scene file for your game and it's this +complicated gigantic XML thing um you + + align:start position:0% +complicated gigantic XML thing um you + + + align:start position:0% +complicated gigantic XML thing um you +might lock that file so no one else + + align:start position:0% +might lock that file so no one else + + + align:start position:0% +might lock that file so no one else +changes it while you're working on + + align:start position:0% +changes it while you're working on + + + align:start position:0% +changes it while you're working on +it and then finally um merge is the last + + align:start position:0% +it and then finally um merge is the last + + + align:start position:0% +it and then finally um merge is the last +thing that you'll do when I talk about + + align:start position:0% +thing that you'll do when I talk about + + + align:start position:0% +thing that you'll do when I talk about +if you're changing one code file and + + align:start position:0% +if you're changing one code file and + + + align:start position:0% +if you're changing one code file and +someone else changes a code file while + + align:start position:0% +someone else changes a code file while + + + align:start position:0% +someone else changes a code file while +you're working on it and checks it in + + align:start position:0% +you're working on it and checks it in + + + align:start position:0% +you're working on it and checks it in +before you do you're going to have to + + align:start position:0% +before you do you're going to have to + + + align:start position:0% +before you do you're going to have to +include their changes into your version + + align:start position:0% +include their changes into your version + + + align:start position:0% +include their changes into your version +and that's called a merge most of them + + align:start position:0% +and that's called a merge most of them + + + align:start position:0% +and that's called a merge most of them +have tools that do it for you + + align:start position:0% +have tools that do it for you + + + align:start position:0% +have tools that do it for you +automatically but if there's a conflict + + align:start position:0% +automatically but if there's a conflict + + + align:start position:0% +automatically but if there's a conflict +it will then have force you to do what's + + align:start position:0% +it will then have force you to do what's + + + align:start position:0% +it will then have force you to do what's +called resolve which is to say hey this + + align:start position:0% +called resolve which is to say hey this + + + align:start position:0% +called resolve which is to say hey this +file changed more than I can figure out + + align:start position:0% +file changed more than I can figure out + + + align:start position:0% +file changed more than I can figure out +automatically so a human needs to + + align:start position:0% +automatically so a human needs to + + + align:start position:0% +automatically so a human needs to +interfere with it and at that point + + align:start position:0% +interfere with it and at that point + + + align:start position:0% +interfere with it and at that point +that's called resolve um and that's the + + align:start position:0% +that's called resolve um and that's the + + + align:start position:0% +that's called resolve um and that's the +process is called to you'll you'll have + + align:start position:0% +process is called to you'll you'll have + + + align:start position:0% +process is called to you'll you'll have +to go through that manually a couple + + align:start position:0% +to go through that manually a couple + + + align:start position:0% +to go through that manually a couple +times all right so we talked about how + + align:start position:0% +times all right so we talked about how + + + align:start position:0% +times all right so we talked about how +there's an authoritative server that's + + align:start position:0% +there's an authoritative server that's + + + align:start position:0% +there's an authoritative server that's +true for per force and + + align:start position:0% +true for per force and + + + align:start position:0% +true for per force and +subversion um and basically there's the + + align:start position:0% +subversion um and basically there's the + + + align:start position:0% +subversion um and basically there's the +one server that's going to be taken care + + align:start position:0% +one server that's going to be taken care + + + align:start position:0% +one server that's going to be taken care +of you but it's not always true + + align:start position:0% +of you but it's not always true + + + align:start position:0% +of you but it's not always true +especially if you're looking at um git + + align:start position:0% +especially if you're looking at um git + + + align:start position:0% +especially if you're looking at um git +and Mercurial which are using use what's + + align:start position:0% +and Mercurial which are using use what's + + + align:start position:0% +and Mercurial which are using use what's +called distributed Source control there + + align:start position:0% +called distributed Source control there + + + align:start position:0% +called distributed Source control there +actually is no difference between your + + align:start position:0% +actually is no difference between your + + + align:start position:0% +actually is no difference between your +version of the code and the server's + + align:start position:0% +version of the code and the server's + + + align:start position:0% +version of the code and the server's +version of the code or your teammate's + + align:start position:0% +version of the code or your teammate's + + + align:start position:0% +version of the code or your teammate's +version of the code it's just a bunch of + + align:start position:0% +version of the code it's just a bunch of + + + align:start position:0% +version of the code it's just a bunch of +lists of changes and you can send them + + align:start position:0% +lists of changes and you can send them + + + align:start position:0% +lists of changes and you can send them +left and right and upwards and downwards + + align:start position:0% +left and right and upwards and downwards + + + align:start position:0% +left and right and upwards and downwards +it doesn't + + align:start position:0% +it doesn't + + + align:start position:0% +it doesn't +matter um but if you actually do this + + align:start position:0% +matter um but if you actually do this + + + align:start position:0% +matter um but if you actually do this +you're in trouble uh unless you're + + align:start position:0% +you're in trouble uh unless you're + + + align:start position:0% +you're in trouble uh unless you're +really careful about it so whenever you + + align:start position:0% +really careful about it so whenever you + + + align:start position:0% +really careful about it so whenever you +do a sideways shift you send some code + + align:start position:0% +do a sideways shift you send some code + + + align:start position:0% +do a sideways shift you send some code +to your teammate but you don't send it + + align:start position:0% +to your teammate but you don't send it + + + align:start position:0% +to your teammate but you don't send it +to the server you want to make sure you + + align:start position:0% +to the server you want to make sure you + + + align:start position:0% +to the server you want to make sure you +know what you're doing and be very + + align:start position:0% +know what you're doing and be very + + + align:start position:0% +know what you're doing and be very +careful with it so I recommend if if + + align:start position:0% +careful with it so I recommend if if + + + align:start position:0% +careful with it so I recommend if if +you're using a distributed Source + + align:start position:0% +you're using a distributed Source + + + align:start position:0% +you're using a distributed Source +control system until you're really + + align:start position:0% +control system until you're really + + + align:start position:0% +control system until you're really +comfortable with what's going on there + + align:start position:0% +comfortable with what's going on there + + + align:start position:0% +comfortable with what's going on there +that you mostly treat it like a standard + + align:start position:0% +that you mostly treat it like a standard + + + align:start position:0% +that you mostly treat it like a standard +server-based system until you're really + + align:start position:0% +server-based system until you're really + + + align:start position:0% +server-based system until you're really +make sure if you do any other kinds of + + align:start position:0% +make sure if you do any other kinds of + + + align:start position:0% +make sure if you do any other kinds of +cross submits that you know what you're + + align:start position:0% +cross submits that you know what you're + + + align:start position:0% +cross submits that you know what you're +doing and you think about it a little + + align:start position:0% +doing and you think about it a little + + + align:start position:0% +doing and you think about it a little +bit um the cool thing about these + + align:start position:0% +bit um the cool thing about these + + + align:start position:0% +bit um the cool thing about these +systems though is that if I make a + + align:start position:0% +systems though is that if I make a + + + align:start position:0% +systems though is that if I make a +change and I send it to my + + align:start position:0% +change and I send it to my + + + align:start position:0% +change and I send it to my +teammate and both of us submit it to the + + align:start position:0% +teammate and both of us submit it to the + + + align:start position:0% +teammate and both of us submit it to the +central server it actually keeps track + + align:start position:0% +central server it actually keeps track + + + align:start position:0% +central server it actually keeps track +of that it says oh it's the same change + + align:start position:0% +of that it says oh it's the same change + + + align:start position:0% +of that it says oh it's the same change +I don't need to apply it twice it's + + align:start position:0% +I don't need to apply it twice it's + + + align:start position:0% +I don't need to apply it twice it's +actually really a really very clever + + align:start position:0% +actually really a really very clever + + + align:start position:0% +actually really a really very clever +technology it's very very cool and very + + align:start position:0% +technology it's very very cool and very + + + align:start position:0% +technology it's very very cool and very +powerful but like many powerful + + align:start position:0% +powerful but like many powerful + + + align:start position:0% +powerful but like many powerful +Technologies it can be very confusing so + + align:start position:0% +Technologies it can be very confusing so + + + align:start position:0% +Technologies it can be very confusing so +as I say start out here and if you're + + align:start position:0% +as I say start out here and if you're + + + align:start position:0% +as I say start out here and if you're +feeling really cocky go + + align:start position:0% +feeling really cocky go + + + align:start position:0% +feeling really cocky go +there all right um couple quick rules + + align:start position:0% +there all right um couple quick rules + + + align:start position:0% +there all right um couple quick rules +about this they're not going to apply to + + align:start position:0% +about this they're not going to apply to + + + align:start position:0% +about this they're not going to apply to +you yet because you're not yet writing + + align:start position:0% +you yet because you're not yet writing + + + align:start position:0% +you yet because you're not yet writing +code in teams but um the policy is for + + align:start position:0% +code in teams but um the policy is for + + + align:start position:0% +code in teams but um the policy is for +most teams never ever ever break the + + align:start position:0% +most teams never ever ever break the + + + align:start position:0% +most teams never ever ever break the +build and when I say break the build I + + align:start position:0% +build and when I say break the build I + + + align:start position:0% +build and when I say break the build I +mean you want it to be the case that + + align:start position:0% +mean you want it to be the case that + + + align:start position:0% +mean you want it to be the case that +that one canonical copy the perfect copy + + align:start position:0% +that one canonical copy the perfect copy + + + align:start position:0% +that one canonical copy the perfect copy +of your project can anybody could go to + + align:start position:0% +of your project can anybody could go to + + + align:start position:0% +of your project can anybody could go to +an empty machine run a get get all the + + align:start position:0% +an empty machine run a get get all the + + + align:start position:0% +an empty machine run a get get all the +files hit the build button for whatever + + align:start position:0% +files hit the build button for whatever + + + align:start position:0% +files hit the build button for whatever +environment you're using and have it + + align:start position:0% +environment you're using and have it + + + align:start position:0% +environment you're using and have it +build and work perfectly that is the + + align:start position:0% +build and work perfectly that is the + + + align:start position:0% +build and work perfectly that is the +goal that's what you always want and if + + align:start position:0% +goal that's what you always want and if + + + align:start position:0% +goal that's what you always want and if +you ever submit something to the server + + align:start position:0% +you ever submit something to the server + + + align:start position:0% +you ever submit something to the server +that makes that impossible it's highly + + align:start position:0% +that makes that impossible it's highly + + + align:start position:0% +that makes that impossible it's highly +likely that you have just made everyone + + align:start position:0% +likely that you have just made everyone + + + align:start position:0% +likely that you have just made everyone +else on your team have to wait and + + align:start position:0% +else on your team have to wait and + + + align:start position:0% +else on your team have to wait and +that's a big pain because they're going + + align:start position:0% +that's a big pain because they're going + + + align:start position:0% +that's a big pain because they're going +to be sitting there wishing they could + + align:start position:0% +to be sitting there wishing they could + + + align:start position:0% +to be sitting there wishing they could +get work done but they did a get to make + + align:start position:0% +get work done but they did a get to make + + + align:start position:0% +get work done but they did a get to make +sure they could do the merge and then + + align:start position:0% +sure they could do the merge and then + + + align:start position:0% +sure they could do the merge and then +all all of a sudden they can't get any + + align:start position:0% +all all of a sudden they can't get any + + + align:start position:0% +all all of a sudden they can't get any +work done at all so you want to make + + align:start position:0% +work done at all so you want to make + + + align:start position:0% +work done at all so you want to make +100% sure that you can always always + + align:start position:0% +100% sure that you can always always + + + align:start position:0% +100% sure that you can always always +always do that + + align:start position:0% +always do that + + + align:start position:0% +always do that +build another thing and this is me sort + + align:start position:0% +build another thing and this is me sort + + + align:start position:0% +build another thing and this is me sort +of stepping aside to my um coding hat um + + align:start position:0% +of stepping aside to my um coding hat um + + + align:start position:0% +of stepping aside to my um coding hat um +you should always have zero errors and + + align:start position:0% +you should always have zero errors and + + + align:start position:0% +you should always have zero errors and +zero warnings if it all humanly possible + + align:start position:0% +zero warnings if it all humanly possible + + + align:start position:0% +zero warnings if it all humanly possible +in your project um a lot of times I see + + align:start position:0% +in your project um a lot of times I see + + + align:start position:0% +in your project um a lot of times I see +programmers who are just starting out + + align:start position:0% +programmers who are just starting out + + + align:start position:0% +programmers who are just starting out +who think that warnings are you know + + align:start position:0% +who think that warnings are you know + + + align:start position:0% +who think that warnings are you know +optional and it's true unfortunately + + align:start position:0% +optional and it's true unfortunately + + + align:start position:0% +optional and it's true unfortunately +most of them are kind of optional but + + align:start position:0% +most of them are kind of optional but + + + align:start position:0% +most of them are kind of optional but +there's two problems with with leaving + + align:start position:0% +there's two problems with with leaving + + + align:start position:0% +there's two problems with with leaving +them in your in your build problem + + align:start position:0% +them in your in your build problem + + + align:start position:0% +them in your in your build problem +number one is you some of them are + + align:start position:0% +number one is you some of them are + + + align:start position:0% +number one is you some of them are +optional but they do in fact highlight + + align:start position:0% +optional but they do in fact highlight + + + align:start position:0% +optional but they do in fact highlight +an issue that you should think about and + + align:start position:0% +an issue that you should think about and + + + align:start position:0% +an issue that you should think about and +if you leave it there on the screen and + + align:start position:0% +if you leave it there on the screen and + + + align:start position:0% +if you leave it there on the screen and +ignore it you might be ignoring an + + align:start position:0% +ignore it you might be ignoring an + + + align:start position:0% +ignore it you might be ignoring an +important tool that'll help you find a + + align:start position:0% +important tool that'll help you find a + + + align:start position:0% +important tool that'll help you find a +bug but the second one I think it's even + + align:start position:0% +bug but the second one I think it's even + + + align:start position:0% +bug but the second one I think it's even +more important actually is that as soon + + align:start position:0% +more important actually is that as soon + + + align:start position:0% +more important actually is that as soon +as you get used to seeing warnings in + + align:start position:0% +as you get used to seeing warnings in + + + align:start position:0% +as you get used to seeing warnings in +your build every time you start ignoring + + align:start position:0% +your build every time you start ignoring + + + align:start position:0% +your build every time you start ignoring +all the warnings so let's say there are + + align:start position:0% +all the warnings so let's say there are + + + align:start position:0% +all the warnings so let's say there are +five warnings that pop up in your build + + align:start position:0% +five warnings that pop up in your build + + + align:start position:0% +five warnings that pop up in your build +every time you build it and this has + + align:start position:0% +every time you build it and this has + + + align:start position:0% +every time you build it and this has +been true for a week and a half now and + + align:start position:0% +been true for a week and a half now and + + + align:start position:0% +been true for a week and a half now and +you're writing some code and you add two + + align:start position:0% +you're writing some code and you add two + + + align:start position:0% +you're writing some code and you add two +warnings and don't notice because there + + align:start position:0% +warnings and don't notice because there + + + align:start position:0% +warnings and don't notice because there +are warnings 5 to seven I didn't noce + + align:start position:0% +are warnings 5 to seven I didn't noce + + + align:start position:0% +are warnings 5 to seven I didn't noce +you didn't notice the difference but one + + align:start position:0% +you didn't notice the difference but one + + + align:start position:0% +you didn't notice the difference but one +of the two warnings that you added might + + align:start position:0% +of the two warnings that you added might + + + align:start position:0% +of the two warnings that you added might +be really important so if you can get + + align:start position:0% +be really important so if you can get + + + align:start position:0% +be really important so if you can get +down to zero warnings as soon as you add + + align:start position:0% +down to zero warnings as soon as you add + + + align:start position:0% +down to zero warnings as soon as you add +one warning it will instantly hit your + + align:start position:0% +one warning it will instantly hit your + + + align:start position:0% +one warning it will instantly hit your +brain and your brain will say oh wait a + + align:start position:0% +brain and your brain will say oh wait a + + + align:start position:0% +brain and your brain will say oh wait a +minute I did something that the computer + + align:start position:0% +minute I did something that the computer + + + align:start position:0% +minute I did something that the computer +says is a little bit risky and in + + align:start position:0% +says is a little bit risky and in + + + align:start position:0% +says is a little bit risky and in +computer science you want to avoid a + + align:start position:0% +computer science you want to avoid a + + + align:start position:0% +computer science you want to avoid a +little bit risky because it's going to + + align:start position:0% +little bit risky because it's going to + + + align:start position:0% +little bit risky because it's going to +come back and bite you and I promise + + align:start position:0% +come back and bite you and I promise + + + align:start position:0% +come back and bite you and I promise +it's easier to fix a bug 10 minutes + + align:start position:0% +it's easier to fix a bug 10 minutes + + + align:start position:0% +it's easier to fix a bug 10 minutes +after your it than a day after you wrote + + align:start position:0% +after your it than a day after you wrote + + + align:start position:0% +after your it than a day after you wrote +it and a week after you wrote it it's + + align:start position:0% +it and a week after you wrote it it's + + + align:start position:0% +it and a week after you wrote it it's +even harder we in this class won't get + + align:start position:0% +even harder we in this class won't get + + + align:start position:0% +even harder we in this class won't get +to a year after you wrote it but + + align:start position:0% +to a year after you wrote it but + + + align:start position:0% +to a year after you wrote it but +sometime your career you probably will + + align:start position:0% +sometime your career you probably will + + + align:start position:0% +sometime your career you probably will +and you won't enjoy it avoid bugs the + + align:start position:0% +and you won't enjoy it avoid bugs the + + + align:start position:0% +and you won't enjoy it avoid bugs the +first time if you can oh so therefore I + + align:start position:0% +first time if you can oh so therefore I + + + align:start position:0% +first time if you can oh so therefore I +call use a check build um on a team you + + align:start position:0% +call use a check build um on a team you + + + align:start position:0% +call use a check build um on a team you +might say to someone s sitting on your + + align:start position:0% +might say to someone s sitting on your + + + align:start position:0% +might say to someone s sitting on your +team next to you hey can you do a get + + align:start position:0% +team next to you hey can you do a get + + + align:start position:0% +team next to you hey can you do a get +and build and make sure I didn't mess it + + align:start position:0% +and build and make sure I didn't mess it + + + align:start position:0% +and build and make sure I didn't mess it +up that's one easy way to do it but + + align:start position:0% +up that's one easy way to do it but + + + align:start position:0% +up that's one easy way to do it but +actually you don't need to do that um + + align:start position:0% +actually you don't need to do that um + + + align:start position:0% +actually you don't need to do that um +all these Source Control Systems you can + + align:start position:0% +all these Source Control Systems you can + + + align:start position:0% +all these Source Control Systems you can +have more than one they call them + + align:start position:0% +have more than one they call them + + + align:start position:0% +have more than one they call them +workspace might be your local version of + + align:start position:0% +workspace might be your local version of + + + align:start position:0% +workspace might be your local version of +the code you can have two workspaces one + + align:start position:0% +the code you can have two workspaces one + + + align:start position:0% +the code you can have two workspaces one +where you're doing your work you check + + align:start position:0% +where you're doing your work you check + + + align:start position:0% +where you're doing your work you check +it all into the central server and then + + align:start position:0% +it all into the central server and then + + + align:start position:0% +it all into the central server and then +you second one you go to the second + + align:start position:0% +you second one you go to the second + + + align:start position:0% +you second one you go to the second +workspace you pull the code down you do + + align:start position:0% +workspace you pull the code down you do + + + align:start position:0% +workspace you pull the code down you do +a build you verify that everything still + + align:start position:0% +a build you verify that everything still + + + align:start position:0% +a build you verify that everything still +works and that's sort of a safety way + + align:start position:0% +works and that's sort of a safety way + + + align:start position:0% +works and that's sort of a safety way +that you can in a couple minutes verify + + align:start position:0% +that you can in a couple minutes verify + + + align:start position:0% +that you can in a couple minutes verify +that you aren't about to make the entire + + align:start position:0% +that you aren't about to make the entire + + + align:start position:0% +that you aren't about to make the entire +team wait and lose + + align:start position:0% + + + + align:start position:0% + +time all right couple little tips that + + align:start position:0% +time all right couple little tips that + + + align:start position:0% +time all right couple little tips that +again you probably won't need for a + + align:start position:0% +again you probably won't need for a + + + align:start position:0% +again you probably won't need for a +little bit but I'm going to talk about + + align:start position:0% +little bit but I'm going to talk about + + + align:start position:0% +little bit but I'm going to talk about +it very quickly now so you don't forget + + align:start position:0% +it very quickly now so you don't forget + + + align:start position:0% +it very quickly now so you don't forget +um all these things I'm talking about + + align:start position:0% +um all these things I'm talking about + + + align:start position:0% +um all these things I'm talking about +are things you're probably going to have + + align:start position:0% +are things you're probably going to have + + + align:start position:0% +are things you're probably going to have +to look up the details on how to do them + + align:start position:0% +to look up the details on how to do them + + + align:start position:0% +to look up the details on how to do them +but I want you to at least have heard + + align:start position:0% +but I want you to at least have heard + + + align:start position:0% +but I want you to at least have heard +the words so that when you see them on + + align:start position:0% +the words so that when you see them on + + + align:start position:0% +the words so that when you see them on +the screen they'll look familiar to you + + align:start position:0% +the screen they'll look familiar to you + + + align:start position:0% +the screen they'll look familiar to you +and you know what what you can find um + + align:start position:0% +and you know what what you can find um + + + align:start position:0% +and you know what what you can find um +um ignore unneeded files is a really + + align:start position:0% +um ignore unneeded files is a really + + + align:start position:0% +um ignore unneeded files is a really +powerful thing almost all these systems + + align:start position:0% +powerful thing almost all these systems + + + align:start position:0% +powerful thing almost all these systems +can ignore types of files for example if + + align:start position:0% +can ignore types of files for example if + + + align:start position:0% +can ignore types of files for example if +you're working in C there might be some + + align:start position:0% +you're working in C there might be some + + + align:start position:0% +you're working in C there might be some +object files or whatever and you don't + + align:start position:0% +object files or whatever and you don't + + + align:start position:0% +object files or whatever and you don't +want to check those in um it doesn't + + align:start position:0% +want to check those in um it doesn't + + + align:start position:0% +want to check those in um it doesn't +help you to check them in in particular + + align:start position:0% +help you to check them in in particular + + + align:start position:0% +help you to check them in in particular +if you're using perforce checking them + + align:start position:0% +if you're using perforce checking them + + + align:start position:0% +if you're using perforce checking them +in is actually problematic because when + + align:start position:0% +in is actually problematic because when + + + align:start position:0% +in is actually problematic because when +one one of the things that perforce does + + align:start position:0% +one one of the things that perforce does + + + align:start position:0% +one one of the things that perforce does +that the other systems don't do is that + + align:start position:0% +that the other systems don't do is that + + + align:start position:0% +that the other systems don't do is that +perforce uses the readon flag as a way + + align:start position:0% +perforce uses the readon flag as a way + + + align:start position:0% +perforce uses the readon flag as a way +to on your local machine to tell you + + align:start position:0% +to on your local machine to tell you + + + align:start position:0% +to on your local machine to tell you +whether or not you have a file checked + + align:start position:0% +whether or not you have a file checked + + + align:start position:0% +whether or not you have a file checked +out for changes so if a file is readon + + align:start position:0% +out for changes so if a file is readon + + + align:start position:0% +out for changes so if a file is readon +it's saying you haven't checked you + + align:start position:0% +it's saying you haven't checked you + + + align:start position:0% +it's saying you haven't checked you +haven't told me that you're going to + + align:start position:0% +haven't told me that you're going to + + + align:start position:0% +haven't told me that you're going to +change this file so I'm not going to let + + align:start position:0% +change this file so I'm not going to let + + + align:start position:0% +change this file so I'm not going to let +you if you try to do a build on a bunch + + align:start position:0% +you if you try to do a build on a bunch + + + align:start position:0% +you if you try to do a build on a bunch +of readon files your build environment + + align:start position:0% +of readon files your build environment + + + align:start position:0% +of readon files your build environment +has two choices it can ignore that which + + align:start position:0% +has two choices it can ignore that which + + + align:start position:0% +has two choices it can ignore that which +is kind of scary or it can + + align:start position:0% +is kind of scary or it can + + + align:start position:0% +is kind of scary or it can +just fail so that's kind of annoying but + + align:start position:0% +just fail so that's kind of annoying but + + + align:start position:0% +just fail so that's kind of annoying but +more of the point there's no reason to + + align:start position:0% +more of the point there's no reason to + + + align:start position:0% +more of the point there's no reason to +check in these gigantic product files + + align:start position:0% +check in these gigantic product files + + + align:start position:0% +check in these gigantic product files +that are all part of your build when you + + align:start position:0% +that are all part of your build when you + + + align:start position:0% +that are all part of your build when you +can actually rebuild everything from the + + align:start position:0% +can actually rebuild everything from the + + + align:start position:0% +can actually rebuild everything from the +bare Source um the only things you want + + align:start position:0% +bare Source um the only things you want + + + align:start position:0% +bare Source um the only things you want +to actually check in are the the + + align:start position:0% +to actually check in are the the + + + align:start position:0% +to actually check in are the the +original source files for your project + + align:start position:0% +original source files for your project + + + align:start position:0% +original source files for your project +whether that be art audio code whatever + + align:start position:0% +whether that be art audio code whatever + + + align:start position:0% +whether that be art audio code whatever +but you want to be able to rebuild the + + align:start position:0% +but you want to be able to rebuild the + + + align:start position:0% +but you want to be able to rebuild the +entire thing and all the intermediate + + align:start position:0% +entire thing and all the intermediate + + + align:start position:0% +entire thing and all the intermediate +files that or the final result files + + align:start position:0% +files that or the final result files + + + align:start position:0% +files that or the final result files +generally speaking you don't want to + + align:start position:0% +generally speaking you don't want to + + + align:start position:0% +generally speaking you don't want to +check those into Source control unless + + align:start position:0% +check those into Source control unless + + + align:start position:0% +check those into Source control unless +you got a special build folder or + + align:start position:0% +you got a special build folder or + + + align:start position:0% +you got a special build folder or +something you want to have one folder + + align:start position:0% +something you want to have one folder + + + align:start position:0% +something you want to have one folder +which is purely pull down the project + + align:start position:0% +which is purely pull down the project + + + align:start position:0% +which is purely pull down the project +and build it and it contains all the + + align:start position:0% +and build it and it contains all the + + + align:start position:0% +and build it and it contains all the +information necessary to regenerate + + align:start position:0% +information necessary to regenerate + + + align:start position:0% +information necessary to regenerate +everything that you can so if you can + + align:start position:0% +everything that you can so if you can + + + align:start position:0% +everything that you can so if you can +ignore all the files that you don't want + + align:start position:0% +ignore all the files that you don't want + + + align:start position:0% +ignore all the files that you don't want +to check in that's good this is + + align:start position:0% +to check in that's good this is + + + align:start position:0% +to check in that's good this is +particularly a problem with unity um you + + align:start position:0% +particularly a problem with unity um you + + + align:start position:0% +particularly a problem with unity um you +don't want to check in anything but the + + align:start position:0% +don't want to check in anything but the + + + align:start position:0% +don't want to check in anything but the +asset folder and the project settings + + align:start position:0% +asset folder and the project settings + + + align:start position:0% +asset folder and the project settings +folder there's a bunch of other gigantic + + align:start position:0% +folder there's a bunch of other gigantic + + + align:start position:0% +folder there's a bunch of other gigantic +folders in unity that look important and + + align:start position:0% +folders in unity that look important and + + + align:start position:0% +folders in unity that look important and +they are important but Unity will + + align:start position:0% +they are important but Unity will + + + align:start position:0% +they are important but Unity will +regenerate them for you and you don't + + align:start position:0% +regenerate them for you and you don't + + + align:start position:0% +regenerate them for you and you don't +want to check them + + align:start position:0% +want to check them + + + align:start position:0% +want to check them +in and then finally um I talked about + + align:start position:0% +in and then finally um I talked about + + + align:start position:0% +in and then finally um I talked about +locking before locking lock your binary + + align:start position:0% +locking before locking lock your binary + + + align:start position:0% +locking before locking lock your binary +files in your in your big text files + + align:start position:0% +files in your in your big text files + + + align:start position:0% +files in your in your big text files +that don't merge well just to avoid + + align:start position:0% +that don't merge well just to avoid + + + align:start position:0% +that don't merge well just to avoid +headaches you're going to if you don't + + align:start position:0% +headaches you're going to if you don't + + + align:start position:0% +headaches you're going to if you don't +do that and you know more than one + + align:start position:0% +do that and you know more than one + + + align:start position:0% +do that and you know more than one +person touches that file eventually you + + align:start position:0% +person touches that file eventually you + + + align:start position:0% +person touches that file eventually you +get in a situation where you lose your + + align:start position:0% +get in a situation where you lose your + + + align:start position:0% +get in a situation where you lose your +changes because someone else checked in + + align:start position:0% +changes because someone else checked in + + + align:start position:0% +changes because someone else checked in +something over you um similarly with a + + align:start position:0% +something over you um similarly with a + + + align:start position:0% +something over you um similarly with a +merge you to be careful if you don't do + + align:start position:0% +merge you to be careful if you don't do + + + align:start position:0% +merge you to be careful if you don't do +if someone has checked in even a text + + align:start position:0% +if someone has checked in even a text + + + align:start position:0% +if someone has checked in even a text +file and you do get it down from the + + align:start position:0% +file and you do get it down from the + + + align:start position:0% +file and you do get it down from the +server and has to merge with your + + align:start position:0% +server and has to merge with your + + + align:start position:0% +server and has to merge with your +changes and you don't do that and you + + align:start position:0% +changes and you don't do that and you + + + align:start position:0% +changes and you don't do that and you +just say nah forget their changes use + + align:start position:0% +just say nah forget their changes use + + + align:start position:0% +just say nah forget their changes use +mine that's going to be a problem + + align:start position:0% +mine that's going to be a problem + + + align:start position:0% +mine that's going to be a problem +because someone just lost some work + + align:start position:0% +because someone just lost some work + + + align:start position:0% +because someone just lost some work +there luckily Source control you can + + align:start position:0% +there luckily Source control you can + + + align:start position:0% +there luckily Source control you can +recover from that but it won't be smooth + + align:start position:0% +recover from that but it won't be smooth + + + align:start position:0% +recover from that but it won't be smooth +teamwork you no one will be happy that + + align:start position:0% +teamwork you no one will be happy that + + + align:start position:0% +teamwork you no one will be happy that +you wiped out their + + align:start position:0% +you wiped out their + + + align:start position:0% +you wiped out their +changes + + align:start position:0% +changes + + + align:start position:0% +changes +all right that is the quick version and + + align:start position:0% +all right that is the quick version and + + + align:start position:0% +all right that is the quick version and +now we're going to go on to a workshop + + align:start position:0% +now we're going to go on to a workshop + + + align:start position:0% +now we're going to go on to a workshop +so you should be sitting near people who + + align:start position:0% +so you should be sitting near people who + + + align:start position:0% +so you should be sitting near people who +use the game engine that you used + + align:start position:0% +use the game engine that you used + + + align:start position:0% +use the game engine that you used +hopefully most of you actually did this + + align:start position:0% +hopefully most of you actually did this + + + align:start position:0% +hopefully most of you actually did this +thing so what we want to do is team up + + align:start position:0% +thing so what we want to do is team up + + + align:start position:0% +thing so what we want to do is team up +in pairs with people ideally who used + + align:start position:0% +in pairs with people ideally who used + + + align:start position:0% +in pairs with people ideally who used +your engine if there's only three of you + + align:start position:0% +your engine if there's only three of you + + + align:start position:0% +your engine if there's only three of you +who used your engine I guess you're a + + align:start position:0% +who used your engine I guess you're a + + + align:start position:0% +who used your engine I guess you're a +triplet um and what we want to do is + + align:start position:0% +triplet um and what we want to do is + + + align:start position:0% +triplet um and what we want to do is +ideally two ways but one way we'll do um + + align:start position:0% +ideally two ways but one way we'll do um + + + align:start position:0% +ideally two ways but one way we'll do um +one of you should say yes I've got + + align:start position:0% +one of you should say yes I've got + + + align:start position:0% +one of you should say yes I've got +working code it's pretty cool run it see + + align:start position:0% +working code it's pretty cool run it see + + + align:start position:0% +working code it's pretty cool run it see +that showen see it works and then pick a + + align:start position:0% +that showen see it works and then pick a + + + align:start position:0% +that showen see it works and then pick a +source control engine of your choice I + + align:start position:0% +source control engine of your choice I + + + align:start position:0% +source control engine of your choice I +recommend GitHub if you because it's + + align:start position:0% +recommend GitHub if you because it's + + + align:start position:0% +recommend GitHub if you because it's +easy to get something set up check in + + align:start position:0% +easy to get something set up check in + + + align:start position:0% +easy to get something set up check in +your code have the other people check it + + align:start position:0% +your code have the other people check it + + + align:start position:0% +your code have the other people check it +out and see if they can build it and + + align:start position:0% +out and see if they can build it and + + + align:start position:0% +out and see if they can build it and +then if you succeed at that Swap and do + + align:start position:0% +then if you succeed at that Swap and do + + + align:start position:0% +then if you succeed at that Swap and do +do the other way around actually you can + + align:start position:0% +do the other way around actually you can + + + align:start position:0% +do the other way around actually you can +do this simultaneously everyone can + + align:start position:0% +do this simultaneously everyone can + + + align:start position:0% +do this simultaneously everyone can +start checking in to new projects and + + align:start position:0% +start checking in to new projects and + + + align:start position:0% +start checking in to new projects and +then pull + + align:start position:0% + + + + align:start position:0% + +down + + align:start position:0% + + + + align:start position:0% + +well I'll take that as a cue that I can + + align:start position:0% +well I'll take that as a cue that I can + + + align:start position:0% +well I'll take that as a cue that I can +start talking a little bit but not for + + align:start position:0% +start talking a little bit but not for + + + align:start position:0% +start talking a little bit but not for +long I promise so the next step we want + + align:start position:0% +long I promise so the next step we want + + + align:start position:0% +long I promise so the next step we want +to do is discuss the game engines that + + align:start position:0% +to do is discuss the game engines that + + + align:start position:0% +to do is discuss the game engines that +you did the tutorials for you've + + align:start position:0% +you did the tutorials for you've + + + align:start position:0% +you did the tutorials for you've +probably done a little bit that already + + align:start position:0% +probably done a little bit that already + + + align:start position:0% +probably done a little bit that already +because you've been hanging out with + + align:start position:0% +because you've been hanging out with + + + align:start position:0% +because you've been hanging out with +people near you who use them but I want + + align:start position:0% +people near you who use them but I want + + + align:start position:0% +people near you who use them but I want +you to try to get into groups of five to + + align:start position:0% +you to try to get into groups of five to + + + align:start position:0% +you to try to get into groups of five to +six people um if you can't that's fine + + align:start position:0% +six people um if you can't that's fine + + + align:start position:0% +six people um if you can't that's fine +but try to balance it out there about + + align:start position:0% +but try to balance it out there about + + + align:start position:0% +but try to balance it out there about +probably should be about two groups per + + align:start position:0% +probably should be about two groups per + + + align:start position:0% +probably should be about two groups per +G engine um and talk about what your + + align:start position:0% +G engine um and talk about what your + + + align:start position:0% +G engine um and talk about what your +experiences were with the with the + + align:start position:0% +experiences were with the with the + + + align:start position:0% +experiences were with the with the +tutorials so you know things like what + + align:start position:0% +tutorials so you know things like what + + + align:start position:0% +tutorials so you know things like what +was easier easy what was hard what was + + align:start position:0% +was easier easy what was hard what was + + + align:start position:0% +was easier easy what was hard what was +more difficult than you expected um + + align:start position:0% +more difficult than you expected um + + + align:start position:0% +more difficult than you expected um +compare your experiences on different + + align:start position:0% +compare your experiences on different + + + align:start position:0% +compare your experiences on different +operating systems if you happen to have + + align:start position:0% +operating systems if you happen to have + + + align:start position:0% +operating systems if you happen to have +that experience um compare your + + align:start position:0% +that experience um compare your + + + align:start position:0% +that experience um compare your +experiences if you use different + + align:start position:0% +experiences if you use different + + + align:start position:0% +experiences if you use different +tutorials or the same tutorial but + + align:start position:0% +tutorials or the same tutorial but + + + align:start position:0% +tutorials or the same tutorial but +basically want you to sort of get an + + align:start position:0% +basically want you to sort of get an + + + align:start position:0% +basically want you to sort of get an +idea of what other people's experiences + + align:start position:0% +idea of what other people's experiences + + + align:start position:0% +idea of what other people's experiences +were like compared to your own and the + + align:start position:0% +were like compared to your own and the + + + align:start position:0% +were like compared to your own and the +main reason for this is that you want to + + align:start position:0% +main reason for this is that you want to + + + align:start position:0% +main reason for this is that you want to +sort of figure out something about a + + align:start position:0% +sort of figure out something about a + + + align:start position:0% +sort of figure out something about a +little bit more about your game engine + + align:start position:0% +little bit more about your game engine + + + align:start position:0% +little bit more about your game engine +because after this we're going to + + align:start position:0% +because after this we're going to + + + align:start position:0% +because after this we're going to +shuffle and get into groups where we've + + align:start position:0% +shuffle and get into groups where we've + + + align:start position:0% +shuffle and get into groups where we've +mixed up the game engines so for example + + align:start position:0% +mixed up the game engines so for example + + + align:start position:0% +mixed up the game engines so for example +if you use Hax flixel you'll be in a + + align:start position:0% +if you use Hax flixel you'll be in a + + + align:start position:0% +if you use Hax flixel you'll be in a +group with someone who used flixel and + + align:start position:0% +group with someone who used flixel and + + + align:start position:0% +group with someone who used flixel and +someone who used unity and you want to + + align:start position:0% +someone who used unity and you want to + + + align:start position:0% +someone who used unity and you want to +be sort of compare and contrast those + + align:start position:0% +be sort of compare and contrast those + + + align:start position:0% +be sort of compare and contrast those +engines and so think of this first sort + + align:start position:0% +engines and so think of this first sort + + + align:start position:0% +engines and so think of this first sort +of discussion as a way to to get figure + + align:start position:0% +of discussion as a way to to get figure + + + align:start position:0% +of discussion as a way to to get figure +out how to talk about your game engine + + align:start position:0% +out how to talk about your game engine + + + align:start position:0% +out how to talk about your game engine +and maybe learn a little more about + + align:start position:0% +and maybe learn a little more about + + + align:start position:0% +and maybe learn a little more about +other people's experiences with it all + + align:start position:0% +other people's experiences with it all + + + align:start position:0% +other people's experiences with it all +right so I believe that we're already + + align:start position:0% +right so I believe that we're already + + + align:start position:0% +right so I believe that we're already +seated mostly near each other um in the + + align:start position:0% +seated mostly near each other um in the + + + align:start position:0% +seated mostly near each other um in the +game engines I think that um um that's + + align:start position:0% +game engines I think that um um that's + + + align:start position:0% +game engines I think that um um that's +all I need to say really so split up to + + align:start position:0% +all I need to say really so split up to + + + align:start position:0% +all I need to say really so split up to +groups of five or six in your game + + align:start position:0% +groups of five or six in your game + + + align:start position:0% +groups of five or six in your game +engine and if you need help with that + + align:start position:0% +engine and if you need help with that + + + align:start position:0% +engine and if you need help with that +we'll + + align:start position:0% +we'll + + + align:start position:0% +we'll +help + + align:start position:0% +help + + + align:start position:0% +help +um 15 15 minutes of that and then we'll + + align:start position:0% +um 15 15 minutes of that and then we'll + + + align:start position:0% +um 15 15 minutes of that and then we'll +swap into do multiple we'll help you + + align:start position:0% +swap into do multiple we'll help you + + + align:start position:0% +swap into do multiple we'll help you +with that part + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +twoo all right uh your attention + + align:start position:0% +twoo all right uh your attention + + + align:start position:0% +twoo all right uh your attention +please may I have your attention + + align:start position:0% + + + + align:start position:0% + +please all right so I think a lot of you + + align:start position:0% +please all right so I think a lot of you + + + align:start position:0% +please all right so I think a lot of you +uh I see quite a few groups are sort of + + align:start position:0% +uh I see quite a few groups are sort of + + + align:start position:0% +uh I see quite a few groups are sort of +winding around on their discussion uh + + align:start position:0% +winding around on their discussion uh + + + align:start position:0% +winding around on their discussion uh +within the same game engine now what + + align:start position:0% +within the same game engine now what + + + align:start position:0% +within the same game engine now what +we're going to do is um ask you to + + align:start position:0% +we're going to do is um ask you to + + + align:start position:0% +we're going to do is um ask you to +gather back in your original + + align:start position:0% +gather back in your original + + + align:start position:0% +gather back in your original +brainstorming groups uh which is + + align:start position:0% +brainstorming groups uh which is + + + align:start position:0% +brainstorming groups uh which is +probably going to be pretty close to the + + align:start position:0% +probably going to be pretty close to the + + + align:start position:0% +probably going to be pretty close to the +the uh a combination of the teams that + + align:start position:0% +the uh a combination of the teams that + + + align:start position:0% +the uh a combination of the teams that +you are currently in so remember when we + + align:start position:0% +you are currently in so remember when we + + + align:start position:0% +you are currently in so remember when we +did brainstorming on Monday okay those + + align:start position:0% +did brainstorming on Monday okay those + + + align:start position:0% +did brainstorming on Monday okay those +people uh you are going to gather with + + align:start position:0% +people uh you are going to gather with + + + align:start position:0% +people uh you are going to gather with +with them and hopefully you're going to + + align:start position:0% +with them and hopefully you're going to + + + align:start position:0% +with them and hopefully you're going to +get a good spread of different game + + align:start position:0% +get a good spread of different game + + + align:start position:0% +get a good spread of different game +engines within that discussion group and + + align:start position:0% +engines within that discussion group and + + + align:start position:0% +engines within that discussion group and +what we want you to do is share your + + align:start position:0% +what we want you to do is share your + + + align:start position:0% +what we want you to do is share your +experience having used that game engine + + align:start position:0% +experience having used that game engine + + + align:start position:0% +experience having used that game engine +first take a quick survey around of + + align:start position:0% +first take a quick survey around of + + + align:start position:0% +first take a quick survey around of +which game engines are being represented + + align:start position:0% +which game engines are being represented + + + align:start position:0% +which game engines are being represented +have a talk and uh uh so so so that you + + align:start position:0% +have a talk and uh uh so so so that you + + + align:start position:0% +have a talk and uh uh so so so that you +you know which game engines you're + + align:start position:0% +you know which game engines you're + + + align:start position:0% +you know which game engines you're +discussing then talk about you know what + + align:start position:0% +discussing then talk about you know what + + + align:start position:0% +discussing then talk about you know what +what what you found good what you found + + align:start position:0% +what what you found good what you found + + + align:start position:0% +what what you found good what you found +terrible about those game engines and + + align:start position:0% +terrible about those game engines and + + + align:start position:0% +terrible about those game engines and +what you recommend it for okay as a + + align:start position:0% +what you recommend it for okay as a + + + align:start position:0% +what you recommend it for okay as a +primary motivator for this project 2 + + align:start position:0% +primary motivator for this project 2 + + + align:start position:0% +primary motivator for this project 2 +starts next Monday and you're going to + + align:start position:0% +starts next Monday and you're going to + + + align:start position:0% +starts next Monday and you're going to +choose an engine and make a game in it + + align:start position:0% +choose an engine and make a game in it + + + align:start position:0% +choose an engine and make a game in it +and you're going to be committed to that + + align:start position:0% +and you're going to be committed to that + + + align:start position:0% +and you're going to be committed to that +engine for about 2 and a half weeks so + + align:start position:0% +engine for about 2 and a half weeks so + + + align:start position:0% +engine for about 2 and a half weeks so +that's the whole reason why we're + + align:start position:0% +that's the whole reason why we're + + + align:start position:0% +that's the whole reason why we're +talking about all this + + align:start position:0% + + + + align:start position:0% + +stuff this might not need to be said but + + align:start position:0% +stuff this might not need to be said but + + + align:start position:0% +stuff this might not need to be said but +if half of you used one game engine do + + align:start position:0% +if half of you used one game engine do + + + align:start position:0% +if half of you used one game engine do +some + + align:start position:0% + + + + align:start position:0% + +swapping + + align:start position:0% + + + + align:start position:0% + +I would like to see if we can put a + + align:start position:0% +I would like to see if we can put a + + + align:start position:0% +I would like to see if we can put a +final couple of sort of uh details as to + + align:start position:0% +final couple of sort of uh details as to + + + align:start position:0% +final couple of sort of uh details as to +what we discovered here um I if you were + + align:start position:0% +what we discovered here um I if you were + + + align:start position:0% +what we discovered here um I if you were +to try to describe the experience of + + align:start position:0% +to try to describe the experience of + + + align:start position:0% +to try to describe the experience of +hacks in a sentence like thumbs up + + align:start position:0% +hacks in a sentence like thumbs up + + + align:start position:0% +hacks in a sentence like thumbs up +thumbs down what was the hardest + + align:start position:0% +thumbs down what was the hardest + + + align:start position:0% +thumbs down what was the hardest +thing + + align:start position:0% +thing + + + align:start position:0% +thing +anybody please a lot of resources out + + align:start position:0% +anybody please a lot of resources out + + + align:start position:0% +anybody please a lot of resources out +there for not a lot of resources so you + + align:start position:0% +there for not a lot of resources so you + + + align:start position:0% +there for not a lot of resources so you +couldn't find help when you got got + + align:start position:0% +couldn't find help when you got got + + + align:start position:0% +couldn't find help when you got got +stuck yeah okay I've heard that the + + align:start position:0% +stuck yeah okay I've heard that the + + + align:start position:0% +stuck yeah okay I've heard that the +install process is + + align:start position:0% +install process is + + + align:start position:0% +install process is +painful um uh let's see what else have I + + align:start position:0% +painful um uh let's see what else have I + + + align:start position:0% +painful um uh let's see what else have I +heard anything else anything to + + align:start position:0% +heard anything else anything to + + + align:start position:0% +heard anything else anything to +recommend + + align:start position:0% +recommend + + + align:start position:0% +recommend +it you got up rning once you got up and + + align:start position:0% +it you got up rning once you got up and + + + align:start position:0% +it you got up rning once you got up and +running it was easy all right cool um + + align:start position:0% +running it was easy all right cool um + + + align:start position:0% +running it was easy all right cool um +personally I was on a window or on a Mac + + align:start position:0% +personally I was on a window or on a Mac + + + align:start position:0% +personally I was on a window or on a Mac +and I found the installation really + + align:start position:0% +and I found the installation really + + + align:start position:0% +and I found the installation really +simple it was just a + + align:start position:0% +simple it was just a + + + align:start position:0% +simple it was just a +couple + + align:start position:0% +couple + + + align:start position:0% +couple +okays all right calls and uh it seemed + + align:start position:0% +okays all right calls and uh it seemed + + + align:start position:0% +okays all right calls and uh it seemed +like it was really useful for a simple + + align:start position:0% +like it was really useful for a simple + + + align:start position:0% +like it was really useful for a simple +game I'm not sure how difficult it would + + align:start position:0% +game I'm not sure how difficult it would + + + align:start position:0% +game I'm not sure how difficult it would +get when we trying to build something + + align:start position:0% +get when we trying to build something + + + align:start position:0% +get when we trying to build something +bigger but for getting like a very + + align:start position:0% +bigger but for getting like a very + + + align:start position:0% +bigger but for getting like a very +simple game running fast all right so it + + align:start position:0% +simple game running fast all right so it + + + align:start position:0% +simple game running fast all right so it +sounds like this some mixed experience + + align:start position:0% +sounds like this some mixed experience + + + align:start position:0% +sounds like this some mixed experience +on the install mac may be the difference + + align:start position:0% +on the install mac may be the difference + + + align:start position:0% +on the install mac may be the difference +I don't know like I I was also on a Mac + + align:start position:0% +I don't know like I I was also on a Mac + + + align:start position:0% +I don't know like I I was also on a Mac +and once I figur out how like to install + + align:start position:0% +and once I figur out how like to install + + + align:start position:0% +and once I figur out how like to install +on a Mac it was like extremely simple + + align:start position:0% +on a Mac it was like extremely simple + + + align:start position:0% +on a Mac it was like extremely simple +but like the thing was the tutorial was + + align:start position:0% +but like the thing was the tutorial was + + + align:start position:0% +but like the thing was the tutorial was +just for Windows like inst FL + + align:start position:0% +just for Windows like inst FL + + + align:start position:0% +just for Windows like inst FL +that like + + align:start position:0% +that like + + + align:start position:0% +that like +okay okay all right so the main thing I + + align:start position:0% +okay okay all right so the main thing I + + + align:start position:0% +okay okay all right so the main thing I +have heard then then is that the support + + align:start position:0% +have heard then then is that the support + + + align:start position:0% +have heard then then is that the support +is limited the install may or may not be + + align:start position:0% +is limited the install may or may not be + + + align:start position:0% +is limited the install may or may not be +hard but if you get stuck the support + + align:start position:0% +hard but if you get stuck the support + + + align:start position:0% +hard but if you get stuck the support +isn't going to help you through it at + + align:start position:0% +isn't going to help you through it at + + + align:start position:0% +isn't going to help you through it at +least in that experience um okay um the + + align:start position:0% +least in that experience um okay um the + + + align:start position:0% +least in that experience um okay um the +main reason why I think hack flixel + + align:start position:0% +main reason why I think hack flixel + + + align:start position:0% +main reason why I think hack flixel +might be interesting is because I + + align:start position:0% +might be interesting is because I + + + align:start position:0% +might be interesting is because I +actually know that flixel is interesting + + align:start position:0% +actually know that flixel is interesting + + + align:start position:0% +actually know that flixel is interesting +but you guys may have a different + + align:start position:0% +but you guys may have a different + + + align:start position:0% +but you guys may have a different +opinion on that so flixel and any other + + align:start position:0% +opinion on that so flixel and any other + + + align:start position:0% +opinion on that so flixel and any other +big picture takeaway for + + align:start position:0% +big picture takeaway for + + + align:start position:0% +big picture takeaway for +flexel you're all going to disagree with + + align:start position:0% +flexel you're all going to disagree with + + + align:start position:0% +flexel you're all going to disagree with +me now which is fine but say + + align:start position:0% +me now which is fine but say + + + align:start position:0% +me now which is fine but say +something I think support is also + + align:start position:0% +something I think support is also + + + align:start position:0% +something I think support is also +okay one of the problems I've seen with + + align:start position:0% +okay one of the problems I've seen with + + + align:start position:0% +okay one of the problems I've seen with +Fel is that in in fact has evolved over + + align:start position:0% +Fel is that in in fact has evolved over + + + align:start position:0% +Fel is that in in fact has evolved over +about five or six years now and so if + + align:start position:0% +about five or six years now and so if + + + align:start position:0% +about five or six years now and so if +you look for a bug in flixel and try to + + align:start position:0% +you look for a bug in flixel and try to + + + align:start position:0% +you look for a bug in flixel and try to +figure out what was going wrong it'll + + align:start position:0% +figure out what was going wrong it'll + + + align:start position:0% +figure out what was going wrong it'll +say well in flixel 4 you want to do this + + align:start position:0% +say well in flixel 4 you want to do this + + + align:start position:0% +say well in flixel 4 you want to do this +and flex it's it does it being a little + + align:start position:0% +and flex it's it does it being a little + + + align:start position:0% +and flex it's it does it being a little +bit more complicated there too so in + + align:start position:0% +bit more complicated there too so in + + + align:start position:0% +bit more complicated there too so in +addition to there not being as much + + align:start position:0% +addition to there not being as much + + + align:start position:0% +addition to there not being as much +support as there is for say Unity um + + align:start position:0% +support as there is for say Unity um + + + align:start position:0% +support as there is for say Unity um +it's fragmented support um that and and + + align:start position:0% +it's fragmented support um that and and + + + align:start position:0% +it's fragmented support um that and and +then of course flash is is one of those + + align:start position:0% +then of course flash is is one of those + + + align:start position:0% +then of course flash is is one of those +technologies that people considering to + + align:start position:0% +technologies that people considering to + + + align:start position:0% +technologies that people considering to +be aging um um I will say however that + + align:start position:0% +be aging um um I will say however that + + + align:start position:0% +be aging um um I will say however that +for in my experience for 2D stuff flixel + + align:start position:0% +for in my experience for 2D stuff flixel + + + align:start position:0% +for in my experience for 2D stuff flixel +is really really easy to pick up once + + align:start position:0% +is really really easy to pick up once + + + align:start position:0% +is really really easy to pick up once +you get going and it can really do the + + align:start position:0% +you get going and it can really do the + + + align:start position:0% +you get going and it can really do the +2D stuff pretty well on the other hand + + align:start position:0% +2D stuff pretty well on the other hand + + + align:start position:0% +2D stuff pretty well on the other hand +we have a new Contender there um phaser + + align:start position:0% +we have a new Contender there um phaser + + + align:start position:0% +we have a new Contender there um phaser +which I heard the tutorial was really + + align:start position:0% +which I heard the tutorial was really + + + align:start position:0% +which I heard the tutorial was really +really good for phaser um did anyone + + align:start position:0% +really good for phaser um did anyone + + + align:start position:0% +really good for phaser um did anyone +have any that was my Takeaway on phaser + + align:start position:0% +have any that was my Takeaway on phaser + + + align:start position:0% +have any that was my Takeaway on phaser +um tutorial was good it handled St stuff + + align:start position:0% +um tutorial was good it handled St stuff + + + align:start position:0% +um tutorial was good it handled St stuff +pretty well we haven't gone in depth on + + align:start position:0% +pretty well we haven't gone in depth on + + + align:start position:0% +pretty well we haven't gone in depth on +collisions definely good for very + + align:start position:0% +collisions definely good for very + + + align:start position:0% +collisions definely good for very +intuitive + + align:start position:0% + + + + align:start position:0% + +okay does anybody know if it supports + + align:start position:0% +okay does anybody know if it supports + + + align:start position:0% +okay does anybody know if it supports +typescript did it it does support + + align:start position:0% +typescript did it it does support + + + align:start position:0% +typescript did it it does support +typescript did anyone use typescript for + + align:start position:0% +typescript did anyone use typescript for + + + align:start position:0% +typescript did anyone use typescript for +phaser no oh you did right I just talked + + align:start position:0% +phaser no oh you did right I just talked + + + align:start position:0% +phaser no oh you did right I just talked +to you about that um in fact you were + + align:start position:0% +to you about that um in fact you were + + + align:start position:0% +to you about that um in fact you were +able to use a debugger with phaser + + align:start position:0% +able to use a debugger with phaser + + + align:start position:0% +able to use a debugger with phaser +through Visual Studio right that + + align:start position:0% +through Visual Studio right that + + + align:start position:0% +through Visual Studio right that +actually I find pretty encouraging + + align:start position:0% +actually I find pretty encouraging + + + align:start position:0% +actually I find pretty encouraging +someone's put some thought into that um + + align:start position:0% +someone's put some thought into that um + + + align:start position:0% +someone's put some thought into that um +um how about support were there a lot of + + align:start position:0% +um how about support were there a lot of + + + align:start position:0% +um how about support were there a lot of +people using phaser enough that you can + + align:start position:0% +people using phaser enough that you can + + + align:start position:0% +people using phaser enough that you can +get some help for + + align:start position:0% +get some help for + + + align:start position:0% +get some help for +churches yeah Okay cool so it sounds + + align:start position:0% +churches yeah Okay cool so it sounds + + + align:start position:0% +churches yeah Okay cool so it sounds +like phaser is a I haven't heard about + + align:start position:0% +like phaser is a I haven't heard about + + + align:start position:0% +like phaser is a I haven't heard about +many of the HTML5 engines that I would + + align:start position:0% +many of the HTML5 engines that I would + + + align:start position:0% +many of the HTML5 engines that I would +actually want to recommend but it sounds + + align:start position:0% +actually want to recommend but it sounds + + + align:start position:0% +actually want to recommend but it sounds +like so far your experience of the + + align:start position:0% +like so far your experience of the + + + align:start position:0% +like so far your experience of the +phaser have been pretty positive which + + align:start position:0% +phaser have been pretty positive which + + + align:start position:0% +phaser have been pretty positive which +is pretty cool I have a question about + + align:start position:0% +is pretty cool I have a question about + + + align:start position:0% +is pretty cool I have a question about +pher what about the install process any + + align:start position:0% +pher what about the install process any + + + align:start position:0% +pher what about the install process any +thoughts on + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +so you just copied and it works yeah so + + align:start position:0% +so you just copied and it works yeah so + + + align:start position:0% +so you just copied and it works yeah so +has like verion control pretty much you + + align:start position:0% +has like verion control pretty much you + + + align:start position:0% +has like verion control pretty much you +have to everything from get uh the + + align:start position:0% +have to everything from get uh the + + + align:start position:0% +have to everything from get uh the +second tutorial of making the game is + + align:start position:0% +second tutorial of making the game is + + + align:start position:0% +second tutorial of making the game is +great but uh as a couple of us noticed + + align:start position:0% +great but uh as a couple of us noticed + + + align:start position:0% +great but uh as a couple of us noticed +the first tutorial about installation + + align:start position:0% +the first tutorial about installation + + + align:start position:0% +the first tutorial about installation +like setting up a web server and then + + align:start position:0% +like setting up a web server and then + + + align:start position:0% +like setting up a web server and then +choos your ID was a little bit more OB + + align:start position:0% +choos your ID was a little bit more OB + + + align:start position:0% +choos your ID was a little bit more OB +OB like why are they telling us to do + + align:start position:0% +OB like why are they telling us to do + + + align:start position:0% +OB like why are they telling us to do +these + + align:start position:0% +these + + + align:start position:0% +these +things oh right right yeah because I do + + align:start position:0% +things oh right right yeah because I do + + + align:start position:0% +things oh right right yeah because I do +think that that it was there's somebody + + align:start position:0% +think that that it was there's somebody + + + align:start position:0% +think that that it was there's somebody +said if you st a web server this is how + + align:start position:0% +said if you st a web server this is how + + + align:start position:0% +said if you st a web server this is how +I would do it and I think the answer is + + align:start position:0% +I would do it and I think the answer is + + + align:start position:0% +I would do it and I think the answer is +there are easier ways to do it than + + align:start position:0% +there are easier ways to do it than + + + align:start position:0% +there are easier ways to do it than +they've suggested especially with an if + + align:start position:0% +they've suggested especially with an if + + + align:start position:0% +they've suggested especially with an if +you're an MIT student you can copy it to + + align:start position:0% +you're an MIT student you can copy it to + + + align:start position:0% +you're an MIT student you can copy it to +your web locker and L you've installed + + align:start position:0% +your web locker and L you've installed + + + align:start position:0% +your web locker and L you've installed +it um is a fine way to do it + + align:start position:0% + + + + align:start position:0% + +um cool all right um all right and then + + align:start position:0% +um cool all right um all right and then + + + align:start position:0% +um cool all right um all right and then +we had I split Unity into sort of + + align:start position:0% +we had I split Unity into sort of + + + align:start position:0% +we had I split Unity into sort of +concentrate on 2D concentrate on 3D but + + align:start position:0% +concentrate on 2D concentrate on 3D but + + + align:start position:0% +concentrate on 2D concentrate on 3D but +fundamentally that some of the there is + + align:start position:0% +fundamentally that some of the there is + + + align:start position:0% +fundamentally that some of the there is +a difference between those two um that + + align:start position:0% +a difference between those two um that + + + align:start position:0% +a difference between those two um that +Unity pretty much and I heard someone + + align:start position:0% +Unity pretty much and I heard someone + + + align:start position:0% +Unity pretty much and I heard someone +even saying that that Unity is designed + + align:start position:0% +even saying that that Unity is designed + + + align:start position:0% +even saying that that Unity is designed +for 3D games and they've kind of pasted + + align:start position:0% +for 3D games and they've kind of pasted + + + align:start position:0% +for 3D games and they've kind of pasted +2D on top of it um which I think is an + + align:start position:0% +2D on top of it um which I think is an + + + align:start position:0% +2D on top of it um which I think is an +accurate criticism um um about the + + align:start position:0% +accurate criticism um um about the + + + align:start position:0% +accurate criticism um um about the +usability on that do anyone experience + + align:start position:0% +usability on that do anyone experience + + + align:start position:0% +usability on that do anyone experience +the trying to use the 2D was that a + + align:start position:0% + + + + align:start position:0% + +problem like are you going still need to + + align:start position:0% +problem like are you going still need to + + + align:start position:0% +problem like are you going still need to +to to think in 3D to make it work yeah + + align:start position:0% +to to think in 3D to make it work yeah + + + align:start position:0% +to to think in 3D to make it work yeah +only thing was the initial Le was pretty + + align:start position:0% +only thing was the initial Le was pretty + + + align:start position:0% +only thing was the initial Le was pretty +like took a while to + + align:start position:0% + + + + align:start position:0% + +get sure it definitely doesn't feel + + align:start position:0% +get sure it definitely doesn't feel + + + align:start position:0% +get sure it definitely doesn't feel +lacking like it's like Photoshop in the + + align:start position:0% +lacking like it's like Photoshop in the + + + align:start position:0% +lacking like it's like Photoshop in the +sense that there's like all these + + align:start position:0% +sense that there's like all these + + + align:start position:0% +sense that there's like all these +features and you maybe use like not even + + align:start position:0% +features and you maybe use like not even + + + align:start position:0% +features and you maybe use like not even +10% of them but they're there if you + + align:start position:0% +10% of them but they're there if you + + + align:start position:0% +10% of them but they're there if you +need them which may or may not be a good + + align:start position:0% +need them which may or may not be a good + + + align:start position:0% +need them which may or may not be a good +thing that can be very intimidating sort + + align:start position:0% +thing that can be very intimidating sort + + + align:start position:0% +thing that can be very intimidating sort +of hard to work sure I'll agree with + + align:start position:0% +of hard to work sure I'll agree with + + + align:start position:0% +of hard to work sure I'll agree with +that 100% there's too much there perhaps + + align:start position:0% +that 100% there's too much there perhaps + + + align:start position:0% +that 100% there's too much there perhaps +if you're trying to do a quick project + + align:start position:0% +if you're trying to do a quick project + + + align:start position:0% +if you're trying to do a quick project +you might be tempted to use more than + + align:start position:0% +you might be tempted to use more than + + + align:start position:0% +you might be tempted to use more than +you should um also you need to get lost + + align:start position:0% +you should um also you need to get lost + + + align:start position:0% +you should um also you need to get lost +in the features some of the videos they + + align:start position:0% +in the features some of the videos they + + + align:start position:0% +in the features some of the videos they +demonstrate how you can actually have 3D + + align:start position:0% +demonstrate how you can actually have 3D + + + align:start position:0% +demonstrate how you can actually have 3D +objects in the 2D environment when + + align:start position:0% +objects in the 2D environment when + + + align:start position:0% +objects in the 2D environment when +you're developing 2D games which I guess + + align:start position:0% +you're developing 2D games which I guess + + + align:start position:0% +you're developing 2D games which I guess +they were like excited about and they + + align:start position:0% +they were like excited about and they + + + align:start position:0% +they were like excited about and they +were sh hey you can do this cool thing + + align:start position:0% +were sh hey you can do this cool thing + + + align:start position:0% +were sh hey you can do this cool thing +but um I think it has the opposite + + align:start position:0% +but um I think it has the opposite + + + align:start position:0% +but um I think it has the opposite +effect in that it intimidates people + + align:start position:0% +effect in that it intimidates people + + + align:start position:0% +effect in that it intimidates people +there's like a lot of options that were + + align:start position:0% +there's like a lot of options that were + + + align:start position:0% +there's like a lot of options that were +built originally for 3D and you're + + align:start position:0% +built originally for 3D and you're + + + align:start position:0% +built originally for 3D and you're +looking through menus and looking + + align:start position:0% +looking through menus and looking + + + align:start position:0% +looking through menus and looking +through all the + + align:start position:0% +through all the + + + align:start position:0% +through all the +uh you know drop down things most of + + align:start position:0% +uh you know drop down things most of + + + align:start position:0% +uh you know drop down things most of +them are things that you can't touch or + + align:start position:0% +them are things that you can't touch or + + + align:start position:0% +them are things that you can't touch or +that you can't use um because they're + + align:start position:0% +that you can't use um because they're + + + align:start position:0% +that you can't use um because they're +meant for 3D and there's no way you can + + align:start position:0% +meant for 3D and there's no way you can + + + align:start position:0% +meant for 3D and there's no way you can +restrict the UI to be only 2D um so I + + align:start position:0% +restrict the UI to be only 2D um so I + + + align:start position:0% +restrict the UI to be only 2D um so I +feel like they should + + align:start position:0% +feel like they should + + + align:start position:0% +feel like they should +instead make it make it into a + + align:start position:0% +instead make it make it into a + + + align:start position:0% +instead make it make it into a +standalone Unity 2D um software that + + align:start position:0% +standalone Unity 2D um software that + + + align:start position:0% +standalone Unity 2D um software that +which which would be easier I understand + + align:start position:0% +which which would be easier I understand + + + align:start position:0% +which which would be easier I understand +why they don't turn into Standalone + + align:start position:0% +why they don't turn into Standalone + + + align:start position:0% +why they don't turn into Standalone +Unity 2D software but I think your point + + align:start position:0% +Unity 2D software but I think your point + + + align:start position:0% +Unity 2D software but I think your point +is well taken I think that it would help + + align:start position:0% +is well taken I think that it would help + + + align:start position:0% +is well taken I think that it would help +with their uptake if they were to try to + + align:start position:0% +with their uptake if they were to try to + + + align:start position:0% +with their uptake if they were to try to +limit their feature set oddly enough + + align:start position:0% +limit their feature set oddly enough + + + align:start position:0% +limit their feature set oddly enough +this is not the first time this has + + align:start position:0% +this is not the first time this has + + + align:start position:0% +this is not the first time this has +happened actually way back when there + + align:start position:0% +happened actually way back when there + + + align:start position:0% +happened actually way back when there +was + + align:start position:0% +was + + + align:start position:0% +was +torque uh which was a game engine a 3D + + align:start position:0% +torque uh which was a game engine a 3D + + + align:start position:0% +torque uh which was a game engine a 3D +game engine it was really cheap Indie + + align:start position:0% +game engine it was really cheap Indie + + + align:start position:0% +game engine it was really cheap Indie +one of the first indie game engines for + + align:start position:0% +one of the first indie game engines for + + + align:start position:0% +one of the first indie game engines for +like a hundred bucks for you know use it + + align:start position:0% +like a hundred bucks for you know use it + + + align:start position:0% +like a hundred bucks for you know use it +all you want uh and they started with + + align:start position:0% +all you want uh and they started with + + + align:start position:0% +all you want uh and they started with +their big fancy torque 3D package and + + align:start position:0% +their big fancy torque 3D package and + + + align:start position:0% +their big fancy torque 3D package and +everyone said wow this is awesome and a + + align:start position:0% +everyone said wow this is awesome and a + + + align:start position:0% +everyone said wow this is awesome and a +bunch of people bought it and they never + + align:start position:0% +bunch of people bought it and they never + + + align:start position:0% +bunch of people bought it and they never +made any games because 3D is as we've + + align:start position:0% +made any games because 3D is as we've + + + align:start position:0% +made any games because 3D is as we've +mentioned more than three times as hard + + align:start position:0% +mentioned more than three times as hard + + + align:start position:0% +mentioned more than three times as hard +as 2D and so they came up with torque 2D + + align:start position:0% +as 2D and so they came up with torque 2D + + + align:start position:0% +as 2D and so they came up with torque 2D +and that did a lot better again because + + align:start position:0% +and that did a lot better again because + + + align:start position:0% +and that did a lot better again because +developers 3D is an extra hurdle to jump + + align:start position:0% +developers 3D is an extra hurdle to jump + + + align:start position:0% +developers 3D is an extra hurdle to jump +over and when you're all developers have + + align:start position:0% +over and when you're all developers have + + + align:start position:0% +over and when you're all developers have +to deal with a short time frame and that + + align:start position:0% +to deal with a short time frame and that + + + align:start position:0% +to deal with a short time frame and that +3D King can get in your way so I think + + align:start position:0% +3D King can get in your way so I think + + + align:start position:0% +3D King can get in your way so I think +the takeaway for for me on Unity is + + align:start position:0% +the takeaway for for me on Unity is + + + align:start position:0% +the takeaway for for me on Unity is +always is basically the same which is + + align:start position:0% +always is basically the same which is + + + align:start position:0% +always is basically the same which is +it's a lot you can do a lot with it but + + align:start position:0% +it's a lot you can do a lot with it but + + + align:start position:0% +it's a lot you can do a lot with it but +it's got a learning curve it's going to + + align:start position:0% +it's got a learning curve it's going to + + + align:start position:0% +it's got a learning curve it's going to +be a little bit harder for you so you + + align:start position:0% +be a little bit harder for you so you + + + align:start position:0% +be a little bit harder for you so you +might want to think twice about doing + + align:start position:0% +might want to think twice about doing + + + align:start position:0% +might want to think twice about doing +that especially if you're conc + + align:start position:0% +that especially if you're conc + + + align:start position:0% +that especially if you're conc +concentrating on a 2d game which you + + align:start position:0% +concentrating on a 2d game which you + + + align:start position:0% +concentrating on a 2d game which you +probably should be doing if you can this + + align:start position:0% +probably should be doing if you can this + + + align:start position:0% +probably should be doing if you can this +this semester um Unity also do a couple + + align:start position:0% +this semester um Unity also do a couple + + + align:start position:0% +this semester um Unity also do a couple +things that are a little bit different I + + align:start position:0% +things that are a little bit different I + + + align:start position:0% +things that are a little bit different I +think most the flixel certainly and it + + align:start position:0% +think most the flixel certainly and it + + + align:start position:0% +think most the flixel certainly and it +sounds like phaser has a little flexal + + align:start position:0% +sounds like phaser has a little flexal + + + align:start position:0% +sounds like phaser has a little flexal +blood in it um is they're both designed + + align:start position:0% +blood in it um is they're both designed + + + align:start position:0% +blood in it um is they're both designed +for 2D very simple straightforward + + align:start position:0% +for 2D very simple straightforward + + + align:start position:0% +for 2D very simple straightforward +implementations uh of in an + + align:start position:0% +implementations uh of in an + + + align:start position:0% +implementations uh of in an +object-oriented kind of way uh Unity has + + align:start position:0% +object-oriented kind of way uh Unity has + + + align:start position:0% +object-oriented kind of way uh Unity has +this crazy component system where you + + align:start position:0% +this crazy component system where you + + + align:start position:0% +this crazy component system where you +got one object but you can staple + + align:start position:0% +got one object but you can staple + + + align:start position:0% +got one object but you can staple +anything you want to to it and it's + + align:start position:0% +anything you want to to it and it's + + + align:start position:0% +anything you want to to it and it's +really really powerful but also it takes + + align:start position:0% +really really powerful but also it takes + + + align:start position:0% +really really powerful but also it takes +a while to get your brain around it um + + align:start position:0% +a while to get your brain around it um + + + align:start position:0% +a while to get your brain around it um +so long story short I would say that if + + align:start position:0% +so long story short I would say that if + + + align:start position:0% +so long story short I would say that if +you can do what you want to do without + + align:start position:0% +you can do what you want to do without + + + align:start position:0% +you can do what you want to do without +taking on a big engine like Unity I kind + + align:start position:0% +taking on a big engine like Unity I kind + + + align:start position:0% +taking on a big engine like Unity I kind +of recommend that but obviously if you + + align:start position:0% +of recommend that but obviously if you + + + align:start position:0% +of recommend that but obviously if you +need to do it and we'll kind of raise an + + align:start position:0% +need to do it and we'll kind of raise an + + + align:start position:0% +need to do it and we'll kind of raise an +eyebrow at you if you tell us that you + + align:start position:0% +eyebrow at you if you tell us that you + + + align:start position:0% +eyebrow at you if you tell us that you +do need to do it but if you do need to + + align:start position:0% +do need to do it but if you do need to + + + align:start position:0% +do need to do it but if you do need to +do it it's worth considering because I + + align:start position:0% +do it it's worth considering because I + + + align:start position:0% +do it it's worth considering because I +think it is a very powerful and useful + + align:start position:0% +think it is a very powerful and useful + + + align:start position:0% +think it is a very powerful and useful +friendly engine which + + align:start position:0% + + + + align:start position:0% + +oneel good question but I was going to + + align:start position:0% +oneel good question but I was going to + + + align:start position:0% +oneel good question but I was going to +guess at this point + + align:start position:0% +guess at this point + + + align:start position:0% +guess at this point +um in our experience we have not used + + align:start position:0% +um in our experience we have not used + + + align:start position:0% +um in our experience we have not used +phaser in a class before you know so + + align:start position:0% +phaser in a class before you know so + + + align:start position:0% +phaser in a class before you know so +flixel is the one I know flixel is + + align:start position:0% +flixel is the one I know flixel is + + + align:start position:0% +flixel is the one I know flixel is +faster than Unity it sounds like from + + align:start position:0% +faster than Unity it sounds like from + + + align:start position:0% +faster than Unity it sounds like from +the feedback we're getting here that + + align:start position:0% +the feedback we're getting here that + + + align:start position:0% +the feedback we're getting here that +phaser might be a good Contender so I + + align:start position:0% +phaser might be a good Contender so I + + + align:start position:0% +phaser might be a good Contender so I +would recommend in Project two you might + + align:start position:0% +would recommend in Project two you might + + + align:start position:0% +would recommend in Project two you might +want to take a look at those two engines + + align:start position:0% +want to take a look at those two engines + + + align:start position:0% +want to take a look at those two engines +as your first go-to things um and and + + align:start position:0% +as your first go-to things um and and + + + align:start position:0% +as your first go-to things um and and +check it out um because they not good + + align:start position:0% +check it out um because they not good + + + align:start position:0% +check it out um because they not good +options um I would go there first though + + align:start position:0% +options um I would go there first though + + + align:start position:0% +options um I would go there first though +rather than going straight to Unity + + align:start position:0% +rather than going straight to Unity + + + align:start position:0% +rather than going straight to Unity +unless you've got a team that really + + align:start position:0% +unless you've got a team that really + + + align:start position:0% +unless you've got a team that really +wants to take it + + align:start position:0% +wants to take it + + + align:start position:0% +wants to take it +on lied to these options uh yes you're + + align:start position:0% +on lied to these options uh yes you're + + + align:start position:0% +on lied to these options uh yes you're +limited to these + + align:start position:0% +limited to these + + + align:start position:0% +limited to these +options + + align:start position:0% +options + + + align:start position:0% +options +um so let's see I think our next step + + align:start position:0% +um so let's see I think our next step + + + align:start position:0% +um so let's see I think our next step +then is + + align:start position:0% +then is + + + align:start position:0% +then is +something else yes it is all right so + + align:start position:0% +something else yes it is all right so + + + align:start position:0% +something else yes it is all right so +congratulations you've gotten through + + align:start position:0% +congratulations you've gotten through + + + align:start position:0% +congratulations you've gotten through +the first two-thirds of class + + align:start position:0% +the first two-thirds of class + + + align:start position:0% +the first two-thirds of class +today + + align:start position:0% +today + + + align:start position:0% +today +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +yay um and that was our game engine + + align:start position:0% +yay um and that was our game engine + + + align:start position:0% +yay um and that was our game engine +tutorial so um keep all these thoughts + + align:start position:0% +tutorial so um keep all these thoughts + + + align:start position:0% +tutorial so um keep all these thoughts +in mind as you start a project two next + + align:start position:0% +in mind as you start a project two next + + + align:start position:0% +in mind as you start a project two next +week uh the remainder of class is going + + align:start position:0% +week uh the remainder of class is going + + + align:start position:0% +week uh the remainder of class is going +to be devoted to finishing up project + + align:start position:0% +to be devoted to finishing up project + + + align:start position:0% +to be devoted to finishing up project +we're doing more work on Project one um + + align:start position:0% +we're doing more work on Project one um + + + align:start position:0% +we're doing more work on Project one um +we're going to do two activities as we + + align:start position:0% +we're going to do two activities as we + + + align:start position:0% +we're going to do two activities as we +mentioned in the beginning of class um + + align:start position:0% +mentioned in the beginning of class um + + + align:start position:0% +mentioned in the beginning of class um +we're going to start off with a play + + align:start position:0% +we're going to start off with a play + + + align:start position:0% +we're going to start off with a play +test so um if you have something + + align:start position:0% +test so um if you have something + + + align:start position:0% +test so um if you have something +testable great you're ahead of the game + + align:start position:0% +testable great you're ahead of the game + + + align:start position:0% +testable great you're ahead of the game +if you don't have something testable + + align:start position:0% +if you don't have something testable + + + align:start position:0% +if you don't have something testable +we're going to give you a little bit of + + align:start position:0% +we're going to give you a little bit of + + + align:start position:0% +we're going to give you a little bit of +time to get you to to something testable + + align:start position:0% +time to get you to to something testable + + + align:start position:0% +time to get you to to something testable +what do we mean by testable it means + + align:start position:0% +what do we mean by testable it means + + + align:start position:0% +what do we mean by testable it means +somebody else that is not on your team + + align:start position:0% +somebody else that is not on your team + + + align:start position:0% +somebody else that is not on your team +with a little bit of guidance by + + align:start position:0% +with a little bit of guidance by + + + align:start position:0% +with a little bit of guidance by +somebody on the team can make things + + align:start position:0% +somebody on the team can make things + + + align:start position:0% +somebody on the team can make things +happen in the game that gives you + + align:start position:0% +happen in the game that gives you + + + align:start position:0% +happen in the game that gives you +feedback that says that was cool that's + + align:start position:0% +feedback that says that was cool that's + + + align:start position:0% +feedback that says that was cool that's +what we were going for or that's really + + align:start position:0% +what we were going for or that's really + + + align:start position:0% +what we were going for or that's really +broken that's awful let's not go that + + align:start position:0% +broken that's awful let's not go that + + + align:start position:0% +broken that's awful let's not go that +direction that's all we were asking for + + align:start position:0% +direction that's all we were asking for + + + align:start position:0% +direction that's all we were asking for +you to do for for class today + + align:start position:0% +you to do for for class today + + + align:start position:0% +you to do for for class today +um so at 3:00 we are going to start the + + align:start position:0% +um so at 3:00 we are going to start the + + + align:start position:0% +um so at 3:00 we are going to start the +play test it is 2:47 right now um ignore + + align:start position:0% +play test it is 2:47 right now um ignore + + + align:start position:0% +play test it is 2:47 right now um ignore +that first part basically what we're + + align:start position:0% +that first part basically what we're + + + align:start position:0% +that first part basically what we're +going to do is set up in your teams + + align:start position:0% +going to do is set up in your teams + + + align:start position:0% +going to do is set up in your teams +every team should have have their gam + + align:start position:0% +every team should have have their gam + + + align:start position:0% +every team should have have their gam +set up and ready to play at 3:00 the + + align:start position:0% +set up and ready to play at 3:00 the + + + align:start position:0% +set up and ready to play at 3:00 the +team that is closest to them you're + + align:start position:0% +team that is closest to them you're + + + align:start position:0% +team that is closest to them you're +going to first one team is going to play + + align:start position:0% +going to first one team is going to play + + + align:start position:0% +going to first one team is going to play +the other person the other team's game + + align:start position:0% +the other person the other team's game + + + align:start position:0% +the other person the other team's game +and have 15 minutes to do that and then + + align:start position:0% +and have 15 minutes to do that and then + + + align:start position:0% +and have 15 minutes to do that and then +swap um if you followed project one's + + align:start position:0% +swap um if you followed project one's + + + align:start position:0% +swap um if you followed project one's +examples correctly and you have a 5 + + align:start position:0% +examples correctly and you have a 5 + + + align:start position:0% +examples correctly and you have a 5 +minute game play game so your game can + + align:start position:0% +minute game play game so your game can + + + align:start position:0% +minute game play game so your game can +be played in 5 minutes or less you can + + align:start position:0% +be played in 5 minutes or less you can + + + align:start position:0% +be played in 5 minutes or less you can +get three tests done today awesome um + + align:start position:0% +get three tests done today awesome um + + + align:start position:0% +get three tests done today awesome um +but if you only get one or two that's + + align:start position:0% +but if you only get one or two that's + + + align:start position:0% +but if you only get one or two that's +okay you've got the whole weekend to + + align:start position:0% +okay you've got the whole weekend to + + + align:start position:0% +okay you've got the whole weekend to +finish up on that too so come back into + + align:start position:0% +finish up on that too so come back into + + + align:start position:0% +finish up on that too so come back into +this room 3:00 with your game set up and + + align:start position:0% +this room 3:00 with your game set up and + + + align:start position:0% +this room 3:00 with your game set up and +we'll start the play + + align:start position:0% + + + + align:start position:0% + +test does everybody have a playable + + align:start position:0% + + + + align:start position:0% + +game yes thumbs up if you're ready to + + align:start position:0% + + + + align:start position:0% + +go okay all right so we are not just + + align:start position:0% +go okay all right so we are not just + + + align:start position:0% +go okay all right so we are not just +playing our games we are play testing + + align:start position:0% +playing our games we are play testing + + + align:start position:0% +playing our games we are play testing +our games and we're following uh The + + align:start position:0% +our games and we're following uh The + + + align:start position:0% +our games and we're following uh The +Wizard of Oz method that Philip + + align:start position:0% +Wizard of Oz method that Philip + + + align:start position:0% +Wizard of Oz method that Philip +mentioned on Monday uh by that what we + + align:start position:0% +mentioned on Monday uh by that what we + + + align:start position:0% +mentioned on Monday uh by that what we +mean is all of your games probably have + + align:start position:0% +mean is all of your games probably have + + + align:start position:0% +mean is all of your games probably have +some kind of computer that's doing + + align:start position:0% +some kind of computer that's doing + + + align:start position:0% +some kind of computer that's doing +something in the game that the player is + + align:start position:0% +something in the game that the player is + + + align:start position:0% +something in the game that the player is +interacting with the with the computer + + align:start position:0% +interacting with the with the computer + + + align:start position:0% +interacting with the with the computer +um what that means is there some + + align:start position:0% +um what that means is there some + + + align:start position:0% +um what that means is there some +constrained communication between the + + align:start position:0% +constrained communication between the + + + align:start position:0% +constrained communication between the +computer and the + + align:start position:0% +computer and the + + + align:start position:0% +computer and the +player this is the time where you want + + align:start position:0% +player this is the time where you want + + + align:start position:0% +player this is the time where you want +to think about what are the things that + + align:start position:0% +to think about what are the things that + + + align:start position:0% +to think about what are the things that +the player knows versus what are the + + align:start position:0% +the player knows versus what are the + + + align:start position:0% +the player knows versus what are the +things that the computer is doing + + align:start position:0% +things that the computer is doing + + + align:start position:0% +things that the computer is doing +there's going to be a little bit of a + + align:start position:0% +there's going to be a little bit of a + + + align:start position:0% +there's going to be a little bit of a +difference going on there um don't let + + align:start position:0% +difference going on there um don't let + + + align:start position:0% +difference going on there um don't let +the player know what the computer is + + align:start position:0% +the player know what the computer is + + + align:start position:0% +the player know what the computer is +thinking unless it's actually part of + + align:start position:0% +thinking unless it's actually part of + + + align:start position:0% +thinking unless it's actually part of +the game it's something that the the + + align:start position:0% +the game it's something that the the + + + align:start position:0% +the game it's something that the the +computer is like if you could imagine + + align:start position:0% +computer is like if you could imagine + + + align:start position:0% +computer is like if you could imagine +the computer saying here's a screen with + + align:start position:0% +the computer saying here's a screen with + + + align:start position:0% +the computer saying here's a screen with +an icon on it that says some stuff + + align:start position:0% +an icon on it that says some stuff + + + align:start position:0% +an icon on it that says some stuff +that's something the player knows if + + align:start position:0% +that's something the player knows if + + + align:start position:0% +that's something the player knows if +it's just some calculation going on in + + align:start position:0% +it's just some calculation going on in + + + align:start position:0% +it's just some calculation going on in +the background that is not something the + + align:start position:0% +the background that is not something the + + + align:start position:0% +the background that is not something the +player knows so just think about it that + + align:start position:0% +player knows so just think about it that + + + align:start position:0% +player knows so just think about it that +way when you're doing this um so how + + align:start position:0% +way when you're doing this um so how + + + align:start position:0% +way when you're doing this um so how +many teams do we have over + + align:start position:0% +many teams do we have over + + + align:start position:0% +many teams do we have over +here + + align:start position:0% +here + + + align:start position:0% +here +one four okay so pair how many teams do + + align:start position:0% +one four okay so pair how many teams do + + + align:start position:0% +one four okay so pair how many teams do +we have in + + align:start position:0% +we have in + + + align:start position:0% +we have in +here one two three four five six is that + + align:start position:0% +here one two three four five six is that + + + align:start position:0% +here one two three four five six is that +right so pair to your closest and then + + align:start position:0% +right so pair to your closest and then + + + align:start position:0% +right so pair to your closest and then +pair and how many teams over here one + + align:start position:0% +pair and how many teams over here one + + + align:start position:0% +pair and how many teams over here one +two is that the three total all right + + align:start position:0% +two is that the three total all right + + + align:start position:0% +two is that the three total all right +instructors will test the back + + align:start position:0% +instructors will test the back + + + align:start position:0% +instructors will test the back +one okay so you got 15 minutes to play + + align:start position:0% +one okay so you got 15 minutes to play + + + align:start position:0% +one okay so you got 15 minutes to play +one game I'm going to come back in at at + + align:start position:0% +one game I'm going to come back in at at + + + align:start position:0% +one game I'm going to come back in at at +3:15 and then tell you to + + align:start position:0% + + + + align:start position:0% + +switch + + align:start position:0% +switch + + + align:start position:0% +switch +okay so we're going to do we're going to + + align:start position:0% +okay so we're going to do we're going to + + + align:start position:0% +okay so we're going to do we're going to +bit we're going to do the uh the the + + align:start position:0% +bit we're going to do the uh the the + + + align:start position:0% +bit we're going to do the uh the the +shift from the very fun play testing and + + align:start position:0% +shift from the very fun play testing and + + + align:start position:0% +shift from the very fun play testing and +working on games to talking a little bit + + align:start position:0% +working on games to talking a little bit + + + align:start position:0% +working on games to talking a little bit +about project management as I said we're + + align:start position:0% +about project management as I said we're + + + align:start position:0% +about project management as I said we're +kind of trying and get the project + + align:start position:0% +kind of trying and get the project + + + align:start position:0% +kind of trying and get the project +management in bit by bit um hopefully at + + align:start position:0% +management in bit by bit um hopefully at + + + align:start position:0% +management in bit by bit um hopefully at +the point at which they becomes helpful + + align:start position:0% +the point at which they becomes helpful + + + align:start position:0% +the point at which they becomes helpful +in each of your projects so the first + + align:start position:0% +in each of your projects so the first + + + align:start position:0% +in each of your projects so the first +thing we're going to talk about here is + + align:start position:0% +thing we're going to talk about here is + + + align:start position:0% +thing we're going to talk about here is +vision + + align:start position:0% +vision + + + align:start position:0% +vision +statements + + align:start position:0% +statements + + + align:start position:0% +statements +um why are we talking about vision + + align:start position:0% +um why are we talking about vision + + + align:start position:0% +um why are we talking about vision +statements I'd rather be play testing + + align:start position:0% +statements I'd rather be play testing + + + align:start position:0% +statements I'd rather be play testing +someone else's game um the very short + + align:start position:0% +someone else's game um the very short + + + align:start position:0% +someone else's game um the very short +answer is because it's good for you and + + align:start position:0% +answer is because it's good for you and + + + align:start position:0% +answer is because it's good for you and +because it's good for your project um + + align:start position:0% +because it's good for your project um + + + align:start position:0% +because it's good for your project um +the longer answer is because a vision + + align:start position:0% +the longer answer is because a vision + + + align:start position:0% +the longer answer is because a vision +statement is really one of the shortest + + align:start position:0% +statement is really one of the shortest + + + align:start position:0% +statement is really one of the shortest +and simplest ways to understand to make + + align:start position:0% +and simplest ways to understand to make + + + align:start position:0% +and simplest ways to understand to make +sure that you the people on your team + + align:start position:0% +sure that you the people on your team + + + align:start position:0% +sure that you the people on your team +and the person you are making the game + + align:start position:0% +and the person you are making the game + + + align:start position:0% +and the person you are making the game +for assuming you were making the game + + align:start position:0% +for assuming you were making the game + + + align:start position:0% +for assuming you were making the game +for a client or an instructor or someone + + align:start position:0% +for a client or an instructor or someone + + + align:start position:0% +for a client or an instructor or someone +else who might be interested in it are + + align:start position:0% +else who might be interested in it are + + + align:start position:0% +else who might be interested in it are +all on the same page and understand that + + align:start position:0% +all on the same page and understand that + + + align:start position:0% +all on the same page and understand that +what understand what they expect to get + + align:start position:0% +what understand what they expect to get + + + align:start position:0% +what understand what they expect to get +at the end of the project + + align:start position:0% +at the end of the project + + + align:start position:0% +at the end of the project +um it can't + + align:start position:0% +um it can't + + + align:start position:0% +um it can't +guarantee that you all believe you're + + align:start position:0% +guarantee that you all believe you're + + + align:start position:0% +guarantee that you all believe you're +getting the same thing but you can at + + align:start position:0% +getting the same thing but you can at + + + align:start position:0% +getting the same thing but you can at +least get started by being on the same + + align:start position:0% +least get started by being on the same + + + align:start position:0% +least get started by being on the same +page um another very common early design + + align:start position:0% +page um another very common early design + + + align:start position:0% +page um another very common early design +document for for for games is is the + + align:start position:0% +document for for for games is is the + + + align:start position:0% +document for for for games is is the +design doc has anybody here heard of + + align:start position:0% +design doc has anybody here heard of + + + align:start position:0% +design doc has anybody here heard of +heard of design documents I + + align:start position:0% +heard of design documents I + + + align:start position:0% +heard of design documents I +assume yeah do you know what they are + + align:start position:0% +assume yeah do you know what they are + + + align:start position:0% +assume yeah do you know what they are +does anyone not know what I mean when I + + align:start position:0% +does anyone not know what I mean when I + + + align:start position:0% +does anyone not know what I mean when I +say a design doc + + align:start position:0% + + + + align:start position:0% + +okay um traditionally and this is + + align:start position:0% +okay um traditionally and this is + + + align:start position:0% +okay um traditionally and this is +actually going further and further back + + align:start position:0% +actually going further and further back + + + align:start position:0% +actually going further and further back +into the history of game development for + + align:start position:0% +into the history of game development for + + + align:start position:0% +into the history of game development for +which I am thankful um traditionally a + + align:start position:0% +which I am thankful um traditionally a + + + align:start position:0% +which I am thankful um traditionally a +game design dock was a was a document + + align:start position:0% +game design dock was a was a document + + + align:start position:0% +game design dock was a was a document +usually um a big word page that might + + align:start position:0% +usually um a big word page that might + + + align:start position:0% +usually um a big word page that might +occasionally get printed out that pretty + + align:start position:0% +occasionally get printed out that pretty + + + align:start position:0% +occasionally get printed out that pretty +much described the game from start to + + align:start position:0% +much described the game from start to + + + align:start position:0% +much described the game from start to +finish everything that was going to + + align:start position:0% +finish everything that was going to + + + align:start position:0% +finish everything that was going to +happen in it all the mechanics all the + + align:start position:0% +happen in it all the mechanics all the + + + align:start position:0% +happen in it all the mechanics all the +characters all the stories every all the + + align:start position:0% +characters all the stories every all the + + + align:start position:0% +characters all the stories every all the +interactions everything that's going to + + align:start position:0% +interactions everything that's going to + + + align:start position:0% +interactions everything that's going to +happen it was traditionally a very big + + align:start position:0% +happen it was traditionally a very big + + + align:start position:0% +happen it was traditionally a very big +long file + + align:start position:0% +long file + + + align:start position:0% +long file +that a either someone spent a lot of + + align:start position:0% +that a either someone spent a lot of + + + align:start position:0% +that a either someone spent a lot of +time maintaining and nobody spent any + + align:start position:0% +time maintaining and nobody spent any + + + align:start position:0% +time maintaining and nobody spent any +time reading or B nobody spent any time + + align:start position:0% +time reading or B nobody spent any time + + + align:start position:0% +time reading or B nobody spent any time +maintaining and nobody spent any time + + align:start position:0% +maintaining and nobody spent any time + + + align:start position:0% +maintaining and nobody spent any time +reading so it was not what I would call + + align:start position:0% +reading so it was not what I would call + + + align:start position:0% +reading so it was not what I would call +a very useful investment of time but a + + align:start position:0% +a very useful investment of time but a + + + align:start position:0% +a very useful investment of time but a +lot of time tended to get invested in it + + align:start position:0% +lot of time tended to get invested in it + + + align:start position:0% +lot of time tended to get invested in it +so you may ask + + align:start position:0% +so you may ask + + + align:start position:0% +so you may ask +why at least partially because people + + align:start position:0% +why at least partially because people + + + align:start position:0% +why at least partially because people +feel better when things are written down + + align:start position:0% +feel better when things are written down + + + align:start position:0% +feel better when things are written down +they'd like to have a place they can go + + align:start position:0% +they'd like to have a place they can go + + + align:start position:0% +they'd like to have a place they can go +to look at to say am I doing what I + + align:start position:0% +to look at to say am I doing what I + + + align:start position:0% +to look at to say am I doing what I +think we're supposed to be doing I'd + + align:start position:0% +think we're supposed to be doing I'd + + + align:start position:0% +think we're supposed to be doing I'd +like to go check the documents and see + + align:start position:0% +like to go check the documents and see + + + align:start position:0% +like to go check the documents and see +if that's + + align:start position:0% +if that's + + + align:start position:0% +if that's +true um unfortunately a really long a + + align:start position:0% +true um unfortunately a really long a + + + align:start position:0% +true um unfortunately a really long a +really long document that tries to + + align:start position:0% +really long document that tries to + + + align:start position:0% +really long document that tries to +detail everything is not the right way + + align:start position:0% +detail everything is not the right way + + + align:start position:0% +detail everything is not the right way +to try and do this on a game games + + align:start position:0% +to try and do this on a game games + + + align:start position:0% +to try and do this on a game games +change too fast um and the thing you're + + align:start position:0% +change too fast um and the thing you're + + + align:start position:0% +change too fast um and the thing you're +trying to get to the end product of game + + align:start position:0% +trying to get to the end product of game + + + align:start position:0% +trying to get to the end product of game +is not written it's not something that's + + align:start position:0% +is not written it's not something that's + + + align:start position:0% +is not written it's not something that's +going to be something you look at it's + + align:start position:0% +going to be something you look at it's + + + align:start position:0% +going to be something you look at it's +something that happens in action um so + + align:start position:0% +something that happens in action um so + + + align:start position:0% +something that happens in action um so +our proposed substitute and if someone + + align:start position:0% +our proposed substitute and if someone + + + align:start position:0% +our proposed substitute and if someone +comes up with a better solution I would + + align:start position:0% +comes up with a better solution I would + + + align:start position:0% +comes up with a better solution I would +love to hear it um because this vision + + align:start position:0% +love to hear it um because this vision + + + align:start position:0% +love to hear it um because this vision +statements are also not the perfect + + align:start position:0% +statements are also not the perfect + + + align:start position:0% +statements are also not the perfect +they're not the perfect thing they're + + align:start position:0% +they're not the perfect thing they're + + + align:start position:0% +they're not the perfect thing they're +just better than anything else I've seen + + align:start position:0% +just better than anything else I've seen + + + align:start position:0% +just better than anything else I've seen +um our solution to this is a vision + + align:start position:0% +um our solution to this is a vision + + + align:start position:0% +um our solution to this is a vision +statement um we tend to think that in + + align:start position:0% +statement um we tend to think that in + + + align:start position:0% +statement um we tend to think that in +between a prototype and a vision + + align:start position:0% +between a prototype and a vision + + + align:start position:0% +between a prototype and a vision +statement and really good project + + align:start position:0% +statement and really good project + + + align:start position:0% +statement and really good project +communication that's about the that and + + align:start position:0% +communication that's about the that and + + + align:start position:0% +communication that's about the that and +really good communication on your + + align:start position:0% +really good communication on your + + + align:start position:0% +really good communication on your +project that's most of the design + + align:start position:0% +project that's most of the design + + + align:start position:0% +project that's most of the design +documentation you need + + align:start position:0% + + + + align:start position:0% + +um so so all right so we're going to + + align:start position:0% +um so so all right so we're going to + + + align:start position:0% +um so so all right so we're going to +talk about vision statements and then + + align:start position:0% +talk about vision statements and then + + + align:start position:0% +talk about vision statements and then +we're going to make one so there you go + + align:start position:0% +we're going to make one so there you go + + + align:start position:0% +we're going to make one so there you go +I forgot I forgot that I include the + + align:start position:0% +I forgot I forgot that I include the + + + align:start position:0% +I forgot I forgot that I include the +animation on the slides I did not time + + align:start position:0% +animation on the slides I did not time + + + align:start position:0% +animation on the slides I did not time +it right oh well that's what I get for + + align:start position:0% +it right oh well that's what I get for + + + align:start position:0% +it right oh well that's what I get for +trying to be fancy um so if a vision + + align:start position:0% +trying to be fancy um so if a vision + + + align:start position:0% +trying to be fancy um so if a vision +statement is going to define the project + + align:start position:0% +statement is going to define the project + + + align:start position:0% +statement is going to define the project +so vision statements defines the project + + align:start position:0% +so vision statements defines the project + + + align:start position:0% +so vision statements defines the project +or the game if it's for game for the + + align:start position:0% +or the game if it's for game for the + + + align:start position:0% +or the game if it's for game for the +team for the client and its investors + + align:start position:0% +team for the client and its investors + + + align:start position:0% +team for the client and its investors +what do you think it ought to include to + + align:start position:0% +what do you think it ought to include to + + + align:start position:0% +what do you think it ought to include to +do + + align:start position:0% +do + + + align:start position:0% +do +that + + align:start position:0% +that + + + align:start position:0% +that +I see my chalkboards have already been + + align:start position:0% +I see my chalkboards have already been + + + align:start position:0% +I see my chalkboards have already been +used and the chalk has been hidden there + + align:start position:0% +used and the chalk has been hidden there + + + align:start position:0% +used and the chalk has been hidden there +it is all right any ideas any + + align:start position:0% +it is all right any ideas any + + + align:start position:0% +it is all right any ideas any +suggestions what would you like to have + + align:start position:0% +suggestions what would you like to have + + + align:start position:0% +suggestions what would you like to have +in such a document you're the ones using + + align:start position:0% +in such a document you're the ones using + + + align:start position:0% +in such a document you're the ones using +it goals + + align:start position:0% + + + + align:start position:0% + +okay goals scope I heard + + align:start position:0% +okay goals scope I heard + + + align:start position:0% +okay goals scope I heard +ideas what kind of + + align:start position:0% + + + + align:start position:0% + +ideas the game goals ideas goals ideas + + align:start position:0% +ideas the game goals ideas goals ideas + + + align:start position:0% +ideas the game goals ideas goals ideas +the game so got goals got ideas got + + align:start position:0% +the game so got goals got ideas got + + + align:start position:0% +the game so got goals got ideas got +scope I heard + + align:start position:0% +scope I heard + + + align:start position:0% +scope I heard +game theme theme okay theme that sounds + + align:start position:0% +game theme theme okay theme that sounds + + + align:start position:0% +game theme theme okay theme that sounds +like a really good + + align:start position:0% + + + + align:start position:0% + +idea core mechanics core + + align:start position:0% +idea core mechanics core + + + align:start position:0% +idea core mechanics core +mechanics + + align:start position:0% + + + + align:start position:0% + +yeah anything else story + + align:start position:0% + + + + align:start position:0% + +story the audience + + align:start position:0% +story the audience + + + align:start position:0% +story the audience +audience + + align:start position:0% + + + + align:start position:0% + +anything else you think you really + + align:start position:0% +anything else you think you really + + + align:start position:0% +anything else you think you really +need characters + + align:start position:0% + + + + align:start position:0% + +characters okay I think this is actually + + align:start position:0% +characters okay I think this is actually + + + align:start position:0% +characters okay I think this is actually +a pretty darn good + + align:start position:0% +a pretty darn good + + + align:start position:0% +a pretty darn good +list um the tricky part with the vision + + align:start position:0% +list um the tricky part with the vision + + + align:start position:0% +list um the tricky part with the vision +statement is trying to get most of that + + align:start position:0% +statement is trying to get most of that + + + align:start position:0% +statement is trying to get most of that +in on one page or + + align:start position:0% + + + + align:start position:0% + +less um the other thing that your vision + + align:start position:0% +less um the other thing that your vision + + + align:start position:0% +less um the other thing that your vision +statement may want to include that is + + align:start position:0% +statement may want to include that is + + + align:start position:0% +statement may want to include that is +less relevant to the vision part of the + + align:start position:0% +less relevant to the vision part of the + + + align:start position:0% +less relevant to the vision part of the +statement and more relevant to the team + + align:start position:0% +statement and more relevant to the team + + + align:start position:0% +statement and more relevant to the team +is who's working on the game what's the + + align:start position:0% +is who's working on the game what's the + + + align:start position:0% +is who's working on the game what's the +name of the game um what is each person + + align:start position:0% +name of the game um what is each person + + + align:start position:0% +name of the game um what is each person +on the team going to contribute to the + + align:start position:0% +on the team going to contribute to the + + + align:start position:0% +on the team going to contribute to the +game so that the vision statement + + align:start position:0% +game so that the vision statement + + + align:start position:0% +game so that the vision statement +becomes both a contract about what the + + align:start position:0% +becomes both a contract about what the + + + align:start position:0% +becomes both a contract about what the +game is going to be and what the team is + + align:start position:0% +game is going to be and what the team is + + + align:start position:0% +game is going to be and what the team is +going to do to get it + + align:start position:0% + + + + align:start position:0% + +done so surprise surprise we actually + + align:start position:0% +done so surprise surprise we actually + + + align:start position:0% +done so surprise surprise we actually +have a format for this actually we have + + align:start position:0% +have a format for this actually we have + + + align:start position:0% +have a format for this actually we have +two different formats to help you get + + align:start position:0% +two different formats to help you get + + + align:start position:0% +two different formats to help you get +all of these things crammed in on one + + align:start position:0% +all of these things crammed in on one + + + align:start position:0% +all of these things crammed in on one +page and hopefully express it well + + align:start position:0% +page and hopefully express it well + + + align:start position:0% +page and hopefully express it well +enough that you will understand and be + + align:start position:0% +enough that you will understand and be + + + align:start position:0% +enough that you will understand and be +able to use it um we have we have what + + align:start position:0% +able to use it um we have we have what + + + align:start position:0% +able to use it um we have we have what +we call the backof the Box vision + + align:start position:0% +we call the backof the Box vision + + + align:start position:0% +we call the backof the Box vision +statement and a highle design Dock and + + align:start position:0% +statement and a highle design Dock and + + + align:start position:0% +statement and a highle design Dock and +you guys are welcome to choose to use + + align:start position:0% +you guys are welcome to choose to use + + + align:start position:0% +you guys are welcome to choose to use +either one of those two Frameworks + + align:start position:0% +either one of those two Frameworks + + + align:start position:0% +either one of those two Frameworks +they're up on Sellar they can be + + align:start position:0% +they're up on Sellar they can be + + + align:start position:0% +they're up on Sellar they can be +downloaded and once I finish talking at + + align:start position:0% +downloaded and once I finish talking at + + + align:start position:0% +downloaded and once I finish talking at +you I will pull them up so you can see + + align:start position:0% +you I will pull them up so you can see + + + align:start position:0% +you I will pull them up so you can see +them up on the screen and actually see + + align:start position:0% +them up on the screen and actually see + + + align:start position:0% +them up on the screen and actually see +what the files look like um the idea + + align:start position:0% +what the files look like um the idea + + + align:start position:0% +what the files look like um the idea +behind the back of the vision box vision + + align:start position:0% +behind the back of the vision box vision + + + align:start position:0% +behind the back of the vision box vision +statement is it takes sort of a + + align:start position:0% +statement is it takes sort of a + + + align:start position:0% +statement is it takes sort of a +marketing pitch approach instead of + + align:start position:0% +marketing pitch approach instead of + + + align:start position:0% +marketing pitch approach instead of +actually saying here's the goals here's + + align:start position:0% +actually saying here's the goals here's + + + align:start position:0% +actually saying here's the goals here's +the theme here's the cork mechanic + + align:start position:0% +the theme here's the cork mechanic + + + align:start position:0% +the theme here's the cork mechanic +here's the scope the team comes together + + align:start position:0% +here's the scope the team comes together + + + align:start position:0% +here's the scope the team comes together +and tries to find three or four or five + + align:start position:0% +and tries to find three or four or five + + + align:start position:0% +and tries to find three or four or five +bullet points that would go on the back + + align:start position:0% +bullet points that would go on the back + + + align:start position:0% +bullet points that would go on the back +of the box that capture those ideas + + align:start position:0% +of the box that capture those ideas + + + align:start position:0% +of the box that capture those ideas +within the bullet points right you've + + align:start position:0% +within the bullet points right you've + + + align:start position:0% +within the bullet points right you've +all seen the Box okay maybe you haven't + + align:start position:0% +all seen the Box okay maybe you haven't + + + align:start position:0% +all seen the Box okay maybe you haven't +seen the box back of a game box these + + align:start position:0% +seen the box back of a game box these + + + align:start position:0% +seen the box back of a game box these +days because half the game are being so + + align:start position:0% +days because half the game are being so + + + align:start position:0% +days because half the game are being so +downloaded um from Steam but they still + + align:start position:0% +downloaded um from Steam but they still + + + align:start position:0% +downloaded um from Steam but they still +have the little marketing pitches where + + align:start position:0% +have the little marketing pitches where + + + align:start position:0% +have the little marketing pitches where +you know it says you know fire 38 + + align:start position:0% +you know it says you know fire 38 + + + align:start position:0% +you know it says you know fire 38 +different guns form teams with your + + align:start position:0% +different guns form teams with your + + + align:start position:0% +different guns form teams with your +friends and backstab them you know that + + align:start position:0% +friends and backstab them you know that + + + align:start position:0% +friends and backstab them you know that +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +thing um you know but if you're if that + + align:start position:0% +thing um you know but if you're if that + + + align:start position:0% +thing um you know but if you're if that +is the way your team thinks and your + + align:start position:0% +is the way your team thinks and your + + + align:start position:0% +is the way your team thinks and your +team envisions the game that can be a + + align:start position:0% +team envisions the game that can be a + + + align:start position:0% +team envisions the game that can be a +very good way to formulate and + + align:start position:0% +very good way to formulate and + + + align:start position:0% +very good way to formulate and +encapsulate all of those ideas + + align:start position:0% +encapsulate all of those ideas + + + align:start position:0% +encapsulate all of those ideas +especially if you can kind of really + + align:start position:0% +especially if you can kind of really + + + align:start position:0% +especially if you can kind of really +drill down to what are the four things + + align:start position:0% +drill down to what are the four things + + + align:start position:0% +drill down to what are the four things +you want people to say about your game + + align:start position:0% +you want people to say about your game + + + align:start position:0% +you want people to say about your game +and then every time you make a decision + + align:start position:0% +and then every time you make a decision + + + align:start position:0% +and then every time you make a decision +about your game every time you add a + + align:start position:0% +about your game every time you add a + + + align:start position:0% +about your game every time you add a +mechanic every time you add a story a + + align:start position:0% +mechanic every time you add a story a + + + align:start position:0% +mechanic every time you add a story a +character a setting you make a change of + + align:start position:0% +character a setting you make a change of + + + align:start position:0% +character a setting you make a change of +the way the game works you can go back + + align:start position:0% +the way the game works you can go back + + + align:start position:0% +the way the game works you can go back +read those four or five bullet points + + align:start position:0% +read those four or five bullet points + + + align:start position:0% +read those four or five bullet points +and say is this change actually + + align:start position:0% +and say is this change actually + + + align:start position:0% +and say is this change actually +enhancing and working with that pitch + + align:start position:0% +enhancing and working with that pitch + + + align:start position:0% +enhancing and working with that pitch +and if it is it's probably a good change + + align:start position:0% +and if it is it's probably a good change + + + align:start position:0% +and if it is it's probably a good change +and if it isn't it probably is a bad + + align:start position:0% +and if it isn't it probably is a bad + + + align:start position:0% +and if it isn't it probably is a bad +change it gives you something to to high + + align:start position:0% +change it gives you something to to high + + + align:start position:0% +change it gives you something to to high +have a core of your game + + align:start position:0% +have a core of your game + + + align:start position:0% +have a core of your game +around some people don't think like that + + align:start position:0% +around some people don't think like that + + + align:start position:0% +around some people don't think like that +some people don't think in terms of + + align:start position:0% +some people don't think in terms of + + + align:start position:0% +some people don't think in terms of +marketing pitches they'd much rather + + align:start position:0% +marketing pitches they'd much rather + + + align:start position:0% +marketing pitches they'd much rather +have sort of a better spelled out this + + align:start position:0% +have sort of a better spelled out this + + + align:start position:0% +have sort of a better spelled out this +is my goal this is the setting this is + + align:start position:0% +is my goal this is the setting this is + + + align:start position:0% +is my goal this is the setting this is +the mechanics um a highlevel design dock + + align:start position:0% +the mechanics um a highlevel design dock + + + align:start position:0% +the mechanics um a highlevel design dock +is the solution for those people and in + + align:start position:0% +is the solution for those people and in + + + align:start position:0% +is the solution for those people and in +it asks for a goal statement for your + + align:start position:0% +it asks for a goal statement for your + + + align:start position:0% +it asks for a goal statement for your +game as a short paragraph written out + + align:start position:0% +game as a short paragraph written out + + + align:start position:0% +game as a short paragraph written out +rather than as pitch um it's got a + + align:start position:0% +rather than as pitch um it's got a + + + align:start position:0% +rather than as pitch um it's got a +little less bang but it's often more + + align:start position:0% +little less bang but it's often more + + + align:start position:0% +little less bang but it's often more +precise + + align:start position:0% +precise + + + align:start position:0% +precise +and it's a and and both of them are + + align:start position:0% +and it's a and and both of them are + + + align:start position:0% +and it's a and and both of them are +equally effective what really depends on + + align:start position:0% +equally effective what really depends on + + + align:start position:0% +equally effective what really depends on +is which one resonates with the team + + align:start position:0% +is which one resonates with the team + + + align:start position:0% +is which one resonates with the team +which one the team thinks works well for + + align:start position:0% +which one the team thinks works well for + + + align:start position:0% +which one the team thinks works well for +them that's why we have both of them + + align:start position:0% +them that's why we have both of them + + + align:start position:0% +them that's why we have both of them +they're really covering the same + + align:start position:0% +they're really covering the same + + + align:start position:0% +they're really covering the same +information um you don't you don't save + + align:start position:0% +information um you don't you don't save + + + align:start position:0% +information um you don't you don't save +anything by choosing one format over the + + align:start position:0% +anything by choosing one format over the + + + align:start position:0% +anything by choosing one format over the +other it's just how are you presenting + + align:start position:0% +other it's just how are you presenting + + + align:start position:0% +other it's just how are you presenting +it to yourself and to your team um both + + align:start position:0% +it to yourself and to your team um both + + + align:start position:0% +it to yourself and to your team um both +documents also ask for a little bit of + + align:start position:0% +documents also ask for a little bit of + + + align:start position:0% +documents also ask for a little bit of +gameplay um a risk assessment what are + + align:start position:0% +gameplay um a risk assessment what are + + + align:start position:0% +gameplay um a risk assessment what are +the big risks on your game they may be + + align:start position:0% +the big risks on your game they may be + + + align:start position:0% +the big risks on your game they may be +related to your team hey we're trying an + + align:start position:0% +related to your team hey we're trying an + + + align:start position:0% +related to your team hey we're trying an +engine we've never tried before we may + + align:start position:0% +engine we've never tried before we may + + + align:start position:0% +engine we've never tried before we may +not be able to get it to run um it may + + align:start position:0% +not be able to get it to run um it may + + + align:start position:0% +not be able to get it to run um it may +be related to the gameplay we are going + + align:start position:0% +be related to the gameplay we are going + + + align:start position:0% +be related to the gameplay we are going +to try and do a mechanic no one has ever + + align:start position:0% +to try and do a mechanic no one has ever + + + align:start position:0% +to try and do a mechanic no one has ever +managed to do before whatever your + + align:start position:0% +managed to do before whatever your + + + align:start position:0% +managed to do before whatever your +whatever your big risk is just one just + + align:start position:0% +whatever your big risk is just one just + + + align:start position:0% +whatever your big risk is just one just +one or two sentences of it and then some + + align:start position:0% +one or two sentences of it and then some + + + align:start position:0% +one or two sentences of it and then some +space for your team members to put in + + align:start position:0% +space for your team members to put in + + + align:start position:0% +space for your team members to put in +your names what they're going to do + + align:start position:0% +your names what they're going to do + + + align:start position:0% +your names what they're going to do +stuff like that it's really pretty + + align:start position:0% +stuff like that it's really pretty + + + align:start position:0% +stuff like that it's really pretty +simple + + align:start position:0% +simple + + + align:start position:0% +simple +um and the next step is in fact to do + + align:start position:0% +um and the next step is in fact to do + + + align:start position:0% +um and the next step is in fact to do +exactly that so um as a threers team + + align:start position:0% +exactly that so um as a threers team + + + align:start position:0% +exactly that so um as a threers team +um go ahead and decide which format + + align:start position:0% +um go ahead and decide which format + + + align:start position:0% +um go ahead and decide which format +you're just going to use create your + + align:start position:0% +you're just going to use create your + + + align:start position:0% +you're just going to use create your +vision document decide who's going to + + align:start position:0% +vision document decide who's going to + + + align:start position:0% +vision document decide who's going to +upload it for + + align:start position:0% +upload it for + + + align:start position:0% +upload it for +Monday um make sure you've got your + + align:start position:0% +Monday um make sure you've got your + + + align:start position:0% +Monday um make sure you've got your +people's names on it so we know who did + + align:start position:0% +people's names on it so we know who did + + + align:start position:0% +people's names on it so we know who did +what because if you're only uploading + + align:start position:0% +what because if you're only uploading + + + align:start position:0% +what because if you're only uploading +one document that means we're only + + align:start position:0% +one document that means we're only + + + align:start position:0% +one document that means we're only +getting one document for every three + + align:start position:0% +getting one document for every three + + + align:start position:0% +getting one document for every three +people in class and we would like to + + align:start position:0% +people in class and we would like to + + + align:start position:0% +people in class and we would like to +give credit to everyone for having + + align:start position:0% +give credit to everyone for having + + + align:start position:0% +give credit to everyone for having +worked on them um and you're going to + + align:start position:0% +worked on them um and you're going to + + + align:start position:0% +worked on them um and you're going to +have till the end of class so about 20 + + align:start position:0% +have till the end of class so about 20 + + + align:start position:0% +have till the end of class so about 20 +minutes um let me see if I can find the + + align:start position:0% +minutes um let me see if I can find the + + + align:start position:0% +minutes um let me see if I can find the +find where Rick has hidden the forms are + + align:start position:0% +find where Rick has hidden the forms are + + + align:start position:0% +find where Rick has hidden the forms are +they Sor y look atalar I'm not looking + + align:start position:0% +they Sor y look atalar I'm not looking + + + align:start position:0% +they Sor y look atalar I'm not looking +your + + align:start position:0% +your + + + align:start position:0% +your +calendar oh no I am looking at your + + align:start position:0% +calendar oh no I am looking at your + + + align:start position:0% +calendar oh no I am looking at your +calendar I'm + + align:start position:0% +calendar I'm + + + align:start position:0% +calendar I'm +sorry oh I'm not looking at the calendar + + align:start position:0% +sorry oh I'm not looking at the calendar + + + align:start position:0% +sorry oh I'm not looking at the calendar +you're looking at the + + align:start position:0% +you're looking at the + + + align:start position:0% +you're looking at the +calendar I'm + + align:start position:0% +calendar I'm + + + align:start position:0% +calendar I'm +sorry um I don't know how well they're + + align:start position:0% +sorry um I don't know how well they're + + + align:start position:0% +sorry um I don't know how well they're +going to fit but well we'll do them one + + align:start position:0% +going to fit but well we'll do them one + + + align:start position:0% +going to fit but well we'll do them one +at a time we just do them one one at a + + align:start position:0% +at a time we just do them one one at a + + + align:start position:0% +at a time we just do them one one at a +kind to clarify the upload Happ before + + align:start position:0% +kind to clarify the upload Happ before + + + align:start position:0% +kind to clarify the upload Happ before +Monday not before the class right yeah + + align:start position:0% +Monday not before the class right yeah + + + align:start position:0% +Monday not before the class right yeah +yeah the upload yeah this the Turnin for + + align:start position:0% +yeah the upload yeah this the Turnin for + + + align:start position:0% +yeah the upload yeah this the Turnin for +this the Turnin date is for Monday + + align:start position:0% +this the Turnin date is for Monday + + + align:start position:0% +this the Turnin date is for Monday +before start of class on Monday and the + + align:start position:0% +before start of class on Monday and the + + + align:start position:0% +before start of class on Monday and the +other thing is you're not actually + + align:start position:0% +other thing is you're not actually + + + align:start position:0% +other thing is you're not actually +writing the vision DOC for the Prototype + + align:start position:0% +writing the vision DOC for the Prototype + + + align:start position:0% +writing the vision DOC for the Prototype +you just + + align:start position:0% +you just + + + align:start position:0% +you just +made the Prototype you made is the core + + align:start position:0% +made the Prototype you made is the core + + + align:start position:0% +made the Prototype you made is the core +is sort of the core Mechanics for the + + align:start position:0% +is sort of the core Mechanics for the + + + align:start position:0% +is sort of the core Mechanics for the +game you and vision being made with it + + align:start position:0% +game you and vision being made with it + + + align:start position:0% +game you and vision being made with it +for project two okay so this is your + + align:start position:0% +for project two okay so this is your + + + align:start position:0% +for project two okay so this is your +vision document your sort of pitchy + + align:start position:0% +vision document your sort of pitchy + + + align:start position:0% +vision document your sort of pitchy +document for project + + align:start position:0% +document for project + + + align:start position:0% +document for project +2 with the game that will be made for + + align:start position:0% +2 with the game that will be made for + + + align:start position:0% +2 with the game that will be made for +project 2 okay + + align:start position:0% +project 2 okay + + + align:start position:0% +project 2 okay +um all right anyway so here's the highle + + align:start position:0% +um all right anyway so here's the highle + + + align:start position:0% +um all right anyway so here's the highle +design document I think that there's + + align:start position:0% +design document I think that there's + + + align:start position:0% +design document I think that there's +both an an RTF format and a Word format + + align:start position:0% +both an an RTF format and a Word format + + + align:start position:0% +both an an RTF format and a Word format +up there um when you upload them we much + + align:start position:0% +up there um when you upload them we much + + + align:start position:0% +up there um when you upload them we much +prefer it to be in PDF that way it's + + align:start position:0% +prefer it to be in PDF that way it's + + + align:start position:0% +prefer it to be in PDF that way it's +easy for us to read so oh I love trying + + align:start position:0% +easy for us to read so oh I love trying + + + align:start position:0% +easy for us to read so oh I love trying +to do this while not being able to see + + align:start position:0% +to do this while not being able to see + + + align:start position:0% +to do this while not being able to see +what I'm doing on the + + align:start position:0% + + + + align:start position:0% + +screen look on Stellar I like mice I + + align:start position:0% +screen look on Stellar I like mice I + + + align:start position:0% +screen look on Stellar I like mice I +much prefer mice I hate touchpads I also + + align:start position:0% +much prefer mice I hate touchpads I also + + + align:start position:0% +much prefer mice I hate touchpads I also +make mine kind of wonky yeah oh + + align:start position:0% +make mine kind of wonky yeah oh + + + align:start position:0% +make mine kind of wonky yeah oh +thanks thanks okay yeah I'm trying to + + align:start position:0% +thanks thanks okay yeah I'm trying to + + + align:start position:0% +thanks thanks okay yeah I'm trying to +scroll okay so this is the this is + + align:start position:0% +scroll okay so this is the this is + + + align:start position:0% +scroll okay so this is the this is +basically the high level design Dock and + + align:start position:0% +basically the high level design Dock and + + + align:start position:0% +basically the high level design Dock and +what it's got Vision breakdown major + + align:start position:0% +what it's got Vision breakdown major + + + align:start position:0% +what it's got Vision breakdown major +game play Concepts um 30 seconds of game + + align:start position:0% +game play Concepts um 30 seconds of game + + + align:start position:0% +game play Concepts um 30 seconds of game +play and then your risks and the team + + align:start position:0% +play and then your risks and the team + + + align:start position:0% +play and then your risks and the team +responsibility and breakdown um let's go + + align:start position:0% +responsibility and breakdown um let's go + + + align:start position:0% +responsibility and breakdown um let's go +ahead and jump over to the vision + + align:start position:0% + + + + align:start position:0% + +document oh that's yep so and here's the + + align:start position:0% +document oh that's yep so and here's the + + + align:start position:0% +document oh that's yep so and here's the +here's the vision statement one + + align:start position:0% +here's the vision statement one + + + align:start position:0% +here's the vision statement one +basically all of that goal and stuff + + align:start position:0% +basically all of that goal and stuff + + + align:start position:0% +basically all of that goal and stuff +needs to be conveyed in your back of the + + align:start position:0% +needs to be conveyed in your back of the + + + align:start position:0% +needs to be conveyed in your back of the +box advertisement and then the rest of + + align:start position:0% +box advertisement and then the rest of + + + align:start position:0% +box advertisement and then the rest of +it pretty much the same any + + align:start position:0% + + + + align:start position:0% + +questions okay there's no + + align:start position:0% +questions okay there's no + + + align:start position:0% +questions okay there's no +questions + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% +go + + + align:start position:0% +go +okay before you leave just want to make + + align:start position:0% +okay before you leave just want to make + + + align:start position:0% +okay before you leave just want to make +sure we all understand what is due + + align:start position:0% +sure we all understand what is due + + + align:start position:0% +sure we all understand what is due +tomorrow because all of our projects are + + align:start position:0% +tomorrow because all of our projects are + + + align:start position:0% +tomorrow because all of our projects are +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +complex Monday Monday thank you you're + + align:start position:0% +complex Monday Monday thank you you're + + + align:start position:0% +complex Monday Monday thank you you're +awake all right so for project one on + + align:start position:0% +awake all right so for project one on + + + align:start position:0% +awake all right so for project one on +Monday before class starts so before 1M + + align:start position:0% +Monday before class starts so before 1M + + + align:start position:0% +Monday before class starts so before 1M +turn into Stellar the following three + + align:start position:0% +turn into Stellar the following three + + + align:start position:0% +turn into Stellar the following three +things an in individual postmortem so + + align:start position:0% +things an in individual postmortem so + + + align:start position:0% +things an in individual postmortem so +this is a onepage write up of your + + align:start position:0% +this is a onepage write up of your + + + align:start position:0% +this is a onepage write up of your +experiences working on this project the + + align:start position:0% +experiences working on this project the + + + align:start position:0% +experiences working on this project the +specification are in that project one + + align:start position:0% +specification are in that project one + + + align:start position:0% +specification are in that project one +assignment that's so we can kind of know + + align:start position:0% +assignment that's so we can kind of know + + + align:start position:0% +assignment that's so we can kind of know +what you got out of this project the + + align:start position:0% +what you got out of this project the + + + align:start position:0% +what you got out of this project the +design change log you made some changes + + align:start position:0% +design change log you made some changes + + + align:start position:0% +design change log you made some changes +today so on your change log you should + + align:start position:0% +today so on your change log you should + + + align:start position:0% +today so on your change log you should +at least have one entry on it at the end + + align:start position:0% +at least have one entry on it at the end + + + align:start position:0% +at least have one entry on it at the end +of the day now you've got two entries on + + align:start position:0% +of the day now you've got two entries on + + + align:start position:0% +of the day now you've got two entries on +it hopefully test your game this weekend + + align:start position:0% +it hopefully test your game this weekend + + + align:start position:0% +it hopefully test your game this weekend +make some changes to the Prototype this + + align:start position:0% +make some changes to the Prototype this + + + align:start position:0% +make some changes to the Prototype this +weekend add them to the to the change + + align:start position:0% +weekend add them to the to the change + + + align:start position:0% +weekend add them to the to the change +log only one per team so appoint one + + align:start position:0% +log only one per team so appoint one + + + align:start position:0% +log only one per team so appoint one +person to to submit all the team + + align:start position:0% +person to to submit all the team + + + align:start position:0% +person to to submit all the team +documents submit it make sure all of + + align:start position:0% +documents submit it make sure all of + + + align:start position:0% +documents submit it make sure all of +your names are on it the vision document + + align:start position:0% +your names are on it the vision document + + + align:start position:0% +your names are on it the vision document +which you've just been right working on + + align:start position:0% +which you've just been right working on + + + align:start position:0% +which you've just been right working on +one per team and again um it's a little + + align:start position:0% +one per team and again um it's a little + + + align:start position:0% +one per team and again um it's a little +weird for project one because you're + + align:start position:0% +weird for project one because you're + + + align:start position:0% +weird for project one because you're +talking about what it would be like for + + align:start position:0% +talking about what it would be like for + + + align:start position:0% +talking about what it would be like for +project two so under team roles and + + align:start position:0% +project two so under team roles and + + + align:start position:0% +project two so under team roles and +responsibilities it's a project two is a + + align:start position:0% +responsibilities it's a project two is a + + + align:start position:0% +responsibilities it's a project two is a +six-person project if you can know if + + align:start position:0% +six-person project if you can know if + + + align:start position:0% +six-person project if you can know if +you have an idea of what are the complex + + align:start position:0% +you have an idea of what are the complex + + + align:start position:0% +you have an idea of what are the complex +things are going to be needed for + + align:start position:0% +things are going to be needed for + + + align:start position:0% +things are going to be needed for +project two that those mystery three + + align:start position:0% +project two that those mystery three + + + align:start position:0% +project two that those mystery three +people would be working on put them down + + align:start position:0% +people would be working on put them down + + + align:start position:0% +people would be working on put them down +or in your case four people um so + + align:start position:0% +or in your case four people um so + + + align:start position:0% +or in your case four people um so +imagine that you are working on this + + align:start position:0% +imagine that you are working on this + + + align:start position:0% +imagine that you are working on this +project for project two question yeah so + + align:start position:0% +project for project two question yeah so + + + align:start position:0% +project for project two question yeah so +Vis Vision + + align:start position:0% + + + + align:start position:0% + +St can hold on one second I can't hear + + align:start position:0% +St can hold on one second I can't hear + + + align:start position:0% +St can hold on one second I can't hear +that we have to on uhuh are we assuming + + align:start position:0% +that we have to on uhuh are we assuming + + + align:start position:0% +that we have to on uhuh are we assuming +that for the team responsibility + + align:start position:0% +that for the team responsibility + + + align:start position:0% +that for the team responsibility +breakdown are we assuming that we'll be + + align:start position:0% +breakdown are we assuming that we'll be + + + align:start position:0% +breakdown are we assuming that we'll be +working on this for assume you are + + align:start position:0% +working on this for assume you are + + + align:start position:0% +working on this for assume you are +working on this as yes responsibility + + align:start position:0% +working on this as yes responsibility + + + align:start position:0% +working on this as yes responsibility +exactly right yep now what we're doing + + align:start position:0% +exactly right yep now what we're doing + + + align:start position:0% +exactly right yep now what we're doing +in class one minute to pitch your game + + align:start position:0% +in class one minute to pitch your game + + + align:start position:0% +in class one minute to pitch your game +as a project two Contender um you're + + align:start position:0% +as a project two Contender um you're + + + align:start position:0% +as a project two Contender um you're +going to come up here and just give us a + + align:start position:0% +going to come up here and just give us a + + + align:start position:0% +going to come up here and just give us a +quick elevator pitch what is the game + + align:start position:0% +quick elevator pitch what is the game + + + align:start position:0% +quick elevator pitch what is the game +why is the game exciting how does the + + align:start position:0% +why is the game exciting how does the + + + align:start position:0% +why is the game exciting how does the +game do what it's going to do um based + + align:start position:0% +game do what it's going to do um based + + + align:start position:0% +game do what it's going to do um based +on this Vision document and then you're + + align:start position:0% +on this Vision document and then you're + + + align:start position:0% +on this Vision document and then you're +going to give us a demonstration of the + + align:start position:0% +going to give us a demonstration of the + + + align:start position:0% +going to give us a demonstration of the +Prototype and that's actually going to + + align:start position:0% +Prototype and that's actually going to + + + align:start position:0% +Prototype and that's actually going to +happen in this big basically how we did + + align:start position:0% +happen in this big basically how we did + + + align:start position:0% +happen in this big basically how we did +play testing today you'll be + + align:start position:0% +play testing today you'll be + + + align:start position:0% +play testing today you'll be +demonstrating the game and more people + + align:start position:0% +demonstrating the game and more people + + + align:start position:0% +demonstrating the game and more people +will play their game so that we can + + align:start position:0% +will play their game so that we can + + + align:start position:0% +will play their game so that we can +figure out which games we want to work + + align:start position:0% +figure out which games we want to work + + + align:start position:0% +figure out which games we want to work +on question there and then question + + align:start position:0% + + + + align:start position:0% + +there has to be paper this project one + + align:start position:0% +there has to be paper this project one + + + align:start position:0% +there has to be paper this project one +is paper project one is non- + + align:start position:0% +is paper project one is non- + + + align:start position:0% +is paper project one is non- +digital we know which projects Everybody + + align:start position:0% +digital we know which projects Everybody + + + align:start position:0% +digital we know which projects Everybody +by the end of class on Monday all of the + + align:start position:0% +by the end of class on Monday all of the + + + align:start position:0% +by the end of class on Monday all of the +teams will be formed for project two all + + align:start position:0% +teams will be formed for project two all + + + align:start position:0% +teams will be formed for project two all +right so project two again it's a single + + align:start position:0% +right so project two again it's a single + + + align:start position:0% +right so project two again it's a single +player game project two some of you have + + align:start position:0% +player game project two some of you have + + + align:start position:0% +player game project two some of you have +made multiplayer games that's okay + + align:start position:0% +made multiplayer games that's okay + + + align:start position:0% +made multiplayer games that's okay +imagine what the game is going to be + + align:start position:0% +imagine what the game is going to be + + + align:start position:0% +imagine what the game is going to be +like for a single player are those other + + align:start position:0% +like for a single player are those other + + + align:start position:0% +like for a single player are those other +players AI make them the AI but project + + align:start position:0% +players AI make them the AI but project + + + align:start position:0% +players AI make them the AI but project +2 as a digital game is only a single + + align:start position:0% +2 as a digital game is only a single + + + align:start position:0% +2 as a digital game is only a single +player game do not turn in a multiplayer + + align:start position:0% +player game do not turn in a multiplayer + + + align:start position:0% +player game do not turn in a multiplayer +game for project 2 for project 4 we're + + align:start position:0% +game for project 2 for project 4 we're + + + align:start position:0% +game for project 2 for project 4 we're +going to relax that but for two and + + align:start position:0% +going to relax that but for two and + + + align:start position:0% +going to relax that but for two and +three just to make sure we're getting + + align:start position:0% +three just to make sure we're getting + + + align:start position:0% +three just to make sure we're getting +some games in here let's make them + + align:start position:0% +some games in here let's make them + + + align:start position:0% +some games in here let's make them +single player again five minutes of game + + align:start position:0% +single player again five minutes of game + + + align:start position:0% +single player again five minutes of game +play I'm again planning for Randomness + + align:start position:0% +play I'm again planning for Randomness + + + align:start position:0% +play I'm again planning for Randomness +if your game right now if project one + + align:start position:0% +if your game right now if project one + + + align:start position:0% +if your game right now if project one +doesn't quite fit that planning for + + align:start position:0% +doesn't quite fit that planning for + + + align:start position:0% +doesn't quite fit that planning for +Randomness theme that's okay um in Your + + align:start position:0% +Randomness theme that's okay um in Your + + + align:start position:0% +Randomness theme that's okay um in Your +Vision document what are you gonna what + + align:start position:0% +Vision document what are you gonna what + + + align:start position:0% +Vision document what are you gonna what +would you do for project two to kind of + + align:start position:0% +would you do for project two to kind of + + + align:start position:0% +would you do for project two to kind of +beef that up to make it to make that um + + align:start position:0% +beef that up to make it to make that um + + + align:start position:0% +beef that up to make it to make that um +really a pop out and again project two + + align:start position:0% +really a pop out and again project two + + + align:start position:0% +really a pop out and again project two +those four um engines that we that we um + + align:start position:0% +those four um engines that we that we um + + + align:start position:0% +those four um engines that we that we um +worked on today not Photon phaser I re I + + align:start position:0% +worked on today not Photon phaser I re I + + + align:start position:0% +worked on today not Photon phaser I re I +miswrote that those are the game engines + + align:start position:0% +miswrote that those are the game engines + + + align:start position:0% +miswrote that those are the game engines +we're working for for project too so I + + align:start position:0% +we're working for for project too so I + + + align:start position:0% +we're working for for project too so I +kept you a little too late sorry if you + + align:start position:0% +kept you a little too late sorry if you + + + align:start position:0% +kept you a little too late sorry if you +want to keep working in the room I don't + + align:start position:0% +want to keep working in the room I don't + + + align:start position:0% +want to keep working in the room I don't +think anybody has it afterwards so feel + + align:start position:0% +think anybody has it afterwards so feel + + + align:start position:0% +think anybody has it afterwards so feel +free to work feel free to + + align:start position:0% +free to work feel free to + + + align:start position:0% +free to work feel free to +leave \ No newline at end of file diff --git a/2q--tAPkVXI.txt b/2q--tAPkVXI.txt new file mode 100644 index 0000000000000000000000000000000000000000..cdee74a99c57664a58ec23abadbfa7c5a0b8b88d --- /dev/null +++ b/2q--tAPkVXI.txt @@ -0,0 +1,2156 @@ +OPERATOR: The following content +is provided under a + +Creative Commons license. + +You're support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare course at + +ocw.mit.edu. + +PROFESSOR: All right. + +Today's lecture, mostly I want +to talk about what computer + +scientists do. + +We've sort of been teaching you +computer science in the + +small, I want to pull back and +think in the large about, what + +do people do once they learn +about computer science? + +And then I'll wrap up with a +quick overview of what I think + +we've accomplished this term. + +So what does a computer +scientist do? + +What they really do is, +almost everything. + +Graduates of our department, +other departments, have done + +things like animation for movies +you've all seen, they + +keep airplanes from falling +out of the sky, they help + +surgeons do a better job of +brain surgery, that's + +something Professor Grimson +has worked on. + +All sorts of exciting things. + +Mostly what they have in common, +and it's incredibly + +varied, what you can do with +computer science, but it all + +involves thinking +computationally. + +And if I had to use a single +phrase to describe 6.00, + +that's the phrase I would use. + +The semester is really about +computational thinking. + +I think this will be a +fundamental skill used by + +everyone in the world by the +middle of the current century. + +And it'll be like the, it will +become one of the three r's, + +reading writing arithmetic. + +And I haven't quite figured I +how to put an r in the front + +of it, but sooner or later. + +So what is it? + +Well, the process is the process +that we've sort of + +been advocating throughout +the semester. + +You identify or invent +useful abstractions. + +Sometimes they're out there, +and we can just pluck them. + +Sometimes you have to invent +them ourselves. + +We then formulate a solution to +a problem as some sort of a + +computational experiment. + +Typically using those +abstractions. + +Then comes the part that many +you get bogged down in, but + +it'll get easier for +you as you go on. + +Is to design and construct +a sufficiently efficient + +implementation of +the experiment. + +And I want to emphasize the +word sufficiently here, in + +that it only has to be +fast enough to run + +it and get an answer. + +And it doesn't have to be +the fastest possible. + +We then need to validate the +experimental setup, convince + +ourselves that the code is +right, and then run the + +experiment, and then evaluate +the results, and + +then repeat as needed. + +And that's, of course, +the key. + +By now you've all learned that +these experiments rarely are + +done the first time +you run them. + +But of course, this is true of +experiments in biology and + +physics and chemistry +and everything else. + +But this is the basic process. + +And I think, it's a view that's +not universally held, + +but I think is the correct view +of what computational + +thinking is all about. + +It's an experimental +discipline. + +So the two a's are abstraction, +choosing the + +right abstraction, and operating +in terms of multiple + +layers of abstraction +simultaneously. + +And that's a little +bit tricky. + +Something that you've +worked on this term. + +You invent some beautiful, high +level of abstraction. + +But then you have to think about +it, and implement it + +using the rather low level +abstractions provided by the + +programming language. + +So we'll do a simulation of, +well, the stock market, we've + +looked at it just recently. + +And you've got this abstraction +of a stock, and at + +one level, when we're thinking +about the market, we think of + +a stock abstractly, as something +that has a price + +that moves up and down. + +But then at the same time, we +say, well, is the movement + +Gaussian, or uniform, and we're +operating at a somewhat + +different level. + +And then at a lower level, we're +asking questions like, + +well, how should we +represent it? is? + +It a dictionary, is it a list, +that sort of thing. + +And we always bounce back and +forth and spend a lot of time + +thinking about how the +layers relate. + +Now the other thing that's +important, and it really + +distinguishes, I think, +computing from a lot of other + +disciplines. + +Is, we don't just write elegant +descriptions of + +abstractions on paper, the +way you say, would do in + +mathematics. + +But we have to then automate +those attractions. + +And we always think in terms of, +how can we mechanize the + +abstractions? + +And that's the computational +part, in many ways. + +How can we do that? + +Well, we can do it because we +have precise and exacting + +notations in which to express +these models. + +So I'll say a few words about +the model of stocks, or a few + +words about the model of a +drunk wandering around a + +field, but I can't get away +with just the words. + +Eventually I have to convert +the words to code. + +And that's sort of the +acid test of truth. + +Have I really understood +what the words mean? + +Because if I don't, I can't +actually convert it to code. + +And that's both the cursing +and the bless of being a + +computer scientist. It's +the curse because, you + +can't fake it, right? + +And that's one of the reasons +that many students end up + +spending a lot of time in +a course like 6.00. + +Because they know whether or +not their program works. + +When you write a proof in math, +you can delude we into + +thinking it's a solid proof, +when it isn't. + +When you write an essay, you +can delude yourself into + +thinking it's brilliant, +when it isn't. + +But here, you look at what it +does, and it either did what + +you thought it would +do or didn't. + +And so that means you sometimes +have to work extra + +hard, but the blessing is, when +it's done, you really + +know you've done it. + +And you've got something +useful. + +And that's because there's a +machine that will execute your + +descriptions. + +And that's what makes it fun. + +So some examples of +computational thinking. + +How difficult is this problem? + +That's what we talked about +when we talked about + +complexity. + +And we talked about, for many +problems, for all problems, + +there's an intrinsic difficulty +of solving the + +problem with the computation. + +Independent of how efficient +your particular solution is. + +And then the question is, +how can I best solve it? + +Theoretical computer science has +given us precise meaning + +to these and related +questions. + +Thinking recursively, another +good example. + +Where we take a seemingly +difficult problem, and + +reformulate it into one which +we know how to solve. + +Very often, it's a smaller +instance of + +the original problem. + +And we say, gosh, this +is hard to solve. + +But then we think, well suppose +the list only had two + +elements in it, would I +know how to sort it? + +Yeah. + +Well, then we can build up and +say, therefore I can use that + +idea to sort a list +of any size. + +As part of this thinking +recursively we learn about + +reduction, we learned how to, +say, reduce the problem of + +deciding what courses to take to +an optimization problem in + +terms of the knapsack problem. + +Once we did that, we could say, +oh, we know how to solve + +all knapsack problems, dynamic +programming has been around a + +long time, we'll just do that. + +So we do a lot of these +reductions, in betting, + +transformations, transforming +one problem into another, and + +simulations. + +So some other examples, choosing +an appropriate + +representation, modeling the +relevant abstracts of a + +problem to make it practical. + +And this is the essence of +abstraction that computer + +scientists learn, is how to +figure out what's relevant and + +ignore what is irrelevant, +or less relevant. + +Focus on the important things. + +That's an enormous +skill in not only + +computing, but in life. + +We worry about worst-case +scenarios, damage containment, + +error correction, all of this +we talked about, we talked + +about debugging, defensive +programming, making sure the + +types were right, but again +these are very general things + +that we think about. + +And we think about the fact, +sometimes, it's kind of a nice + +idea, the fact that there exists +really hard problems is + +actually a good thing. + +Because that's what let's us do +things like use encryption + +to get privacy of our data, +or privacy for our + +communications, privacy +of our phone calls. + +Because we have learned +that some problems are + +intrinsically difficult to +solve, and that's what coding + +is all about. + +Or encryption is all about. + +That's a nice thing. + +I now want to talk more +specifically about what one + +group of computer +scientists does. + +And that's my research group. + +Which consists of mostly +graduate students, but every + +year I try and incorporate a +few undergraduates in it. + +We work in the area of medicine, +it's also the area + +in which Professor Grimson +does most of his work. + +The goal is pretty simple: we +want to help people live + +longer and better lives. + +Right? + +I don't think any of you will +think that's a worthless goal. + +But, a second goal is, +we want to have fun + +while we're doing it. + +Because life is way too short to +do anything that's not fun + +for very long. + +So we push the frontiers of +computer science, electrical + +engineering, and medicine. + +Working in close collaboration +with physicians, and here + +you've got logos of some +of the hospitals + +with which we work. + +It is, of course, fairly +technical work. + +We use machine learning, +clustering, data mining, + +algorithm design, signal +processing. + +And everything we do ends up, +eventually, getting translated + +to code which we then run. + +And so we worry a lot +about software + +systems and the quality. + +We do write systems that, for +example, inject electrical + +signals into people's brains. + +And it's kind of important, +when you do that, that the + +software does what it's +intended to do. + +At least if you like +the people. + +So some specific activities, and +this is only a sampling. + +We work on extracting clinically +useful information + +from electrical signals +in the human body. + +Mostly the heart, the brain, +and connected anatomy. + +For those of you who've never +studied anatomy, I've labeled + +the heart and the brain in +the diagram for you. + +The two major projects in this +area we've been working on, is + +predicting adverse cardiac +events and detecting and + +responding to epileptic +seizures. + +And I want to say a few words +about each of those. + +We'll skip this. + +So example one, treating +epilepsy. + +I suspect most of you are +surprised by the fact that one + +percent of the world's +population has epilepsy. + +This is true in almost every +part of the world. + +It's true in the United +States, it's true in + +underdeveloped countries +in Central Africa. + +It seems to be one of the few +diseases that's invariant to + +economic situations. + +One of the reasons that people +are surprised by this number + +is, most folks who +have epilepsy try + +to keep it a secret. + +There's a long history, getting +back to witches, + +people with epilepsy were deemed +to be witches, were + +burned at the stake, things +of that nature. + +People who have epilepsy are not +allowed by the FAA to work + +on maintenance of aircraft. + +It's a ridiculous restriction, +but it's in the law, so I know + +someone with epilepsy who's kept +it a secret because he + +doesn't want to lose his job. + +That's a different sermon. + +It's characterized by recurrent +seizures, generated + +by abnormal electrical activity +in the brain. + +It's really less a disease +than a description of + +symptoms, because there are lots +of independent, different + +causes of it. + +It can be inherited, that's +a significant fraction. + +Or it can be acquired, typically +by some sort of + +insult to the brain. + +People who have strokes or +serious infections will + +develop epilepsy. + +Hemorrhages, and increasingly +head injuries. + +Turns out to be an illness +that is of now great + +interested the Defense +Department because people are + +coming back from Iraq +with epilepsy. + +So those of you who don't have +a strong stomach, you might + +want to avert your eyes. + +Here's one manifestation +of it. + +On the left is an EEG, and +that's, in this case, a + +recording of the electrical +activity in the surface of + +this girl's brain. + +You can see she's wearing what +looks like a very funny + +looking shower cap. + +That's where the +electrodes are. + +And it's recording the +electrical activity in the + +brain, on the right is +obviously a video. + +Well, pretty frightening. + +Not all seizures are quite +that frightening. + +In fact, most of them are not. + +Sometimes people have what are +called absence seizures, where + +they just sort of black out +for a period of time. + +Still not a good thing if +you're, say, driving a car + +when that happens. + +The key issue here, is that the +onset of the seizure seems + +unpredictable. + +And in particular, it seems +unpredictable to the person + +who has the seizure. + +And that's the real risk. + +Seizures are typically +self-limiting. + +They will correct themselves +over time. + +Eventually this girl will return +to, quote, normal. + +The seizure itself will probably +be over in a minute + +or two, and for about an hour +she'll be confused, and then + +she'll be OK again. + +But, because they're +unpredictable, even people who + +have as few as, say, two a year, +it dominates their life. + +So, if you're that girl, and +even if you're going to have + +one of those a year, you're +never going to be + +allowed on a bicycle. + +Because if that happens when +you're on a bicycle, it's + +really bad. + +If you're an adult, and you +have one or two year, you + +should never drive a car. + +Imagine if you've been driving +a car when that happened. + +Almost everybody with +epilepsy eventually + +suffers a serious injury. + +They have a seizure while +they're on a flight of stairs, + +and they fall down and +fracture their skull. + +They get intra-cranial +hematomas, they get burns if + +they're cooking at the stove, +they drown in the bathtub. + +And it's the unpredictability +that's bad. + +Death is high, two to three +times out of the general + +population. + +Typically by accident related +to the seizure. + +And then there's something +called sudden unexplained + +death in epilepsy patients, +SUDEP, which is estimated to + +be one per 100 patients +per year. + +Just will die, and +no one knows why. + +Frequently it will be at night, +while they're in bed, + +and the conjecture is, they +have a seizure, and end up + +face down in the pillow, +smother, that kind of thing. + +So you can imagine, if you're +a parent, you have a child + +with this, you don't +sleep much. + +Really very sad. + +So we want to do something +about that. + +And our idea is to detect +the seizure early. + +There are two onset times, +electrographic and clinical. + +Electrographic is when the brain +first starts looking + +suspicious, and clinical is when +there's a overt physical + +symptom, that stiffness you +saw in that young girl. + +Probably it went by too fast for +any of you to notice, but + +if you'd looked carefully at +the EEG on the left of that + +picture, you would have seen it +going abnormal before she + +had any clinical symptoms. +Because the symptoms are + +caused by the electrical +activity in the brain, by + +definition, it proceeds the +symptoms, or at least doesn't + +follow them. + +So our idea was to try +and detect the + +electrographic onset. + +If you could do this, you +could provide warning. + +So you could tell somebody, sit +down before you fall down. + +Get out of the bathtub. + +Back away from the stove. + +Just an oral warning would +be tremendously useful. + +You could summon help. + +You could tell a parent, come +quick, your child is having a + +seizure right now in +bed or elsewhere. + +There are fast-acting drugs, +Ativan, which if you inhale at + +the start of a seizure, can +stop it, reduce it. + +And our particular interest +is neural stimulation. + +There is reason to believe, it's +yet to be proved, that if + +you apply the correct electrical +stimulation at the + +very beginning of a seizure, +you can block it. + +Or at least ameliorate +it greatly. + +So, here's a picture +of an EEG. + +And I'll just point +out, seizures can + +be tricky to find. + +You might think this is a +seizure, but it isn't. + +That's blinking your eyes. + +Oh well. + +Here is the seizure, but in +fact, it's begun about here. + +Where things don't look +particularly ominous. + +So it's pretty subtle +to detect. + +One of the problems is, EEG +varies across patients. + +And epileptics have abnormal +baselines. + +Yeah? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Highly variable +in patients, but + +that's kind of typical. + +But that would be plenty of +time to back away from the + +stove, or get off a bicycle. + +Not so much time to get off the +Mass Turnpike, if you're + +driving a car. + +But it would be great, +if you can give 10 + +or 15 seconds warning. + +In fact, if you could give five +seconds warning, it would + +be tremendously useful. + +And for the treatments, it's +even different, right? + +Yes, you're exactly right, +in that particular case. + +The problem is, one of the +things I've discovered in + +medicine, my work, is that +almost all healthy people look + +alike, and all sick people +look different. + +So, EEG, if you have epilepsy, +your quote, normal EEG, when + +you're not having a seizure, +looks weird compared to people + +who don't have epilepsy. + +People have been building +seizure detectors for about 40 + +years now, and they don't +work very well. + +Every EEG that gets shipped +comes with a seizure detector, + +and the first thing most +hospitals do is, turn it off. + +Because it just doesn't work. + +The good news is, that even +though each epileptics brain + +signals look different, once +you've learned what an + +individual's signal looks like, +it's pretty consistent. + +Both the interictal, between +seizure, and the + +start of the seizure. + +Well, that tells a computer +scientist, let's use machine + +learning to figure out what that +patient's EEG looks like. + +And build a highly specific +detector that will work great + +for one person, and not at +all for anybody else. + +And then we'll just install +it, and you know, everyone + +gets their own. + +So instead of one size fits all, +it's design a detector to + +fit the patient. + +We have been working on this +now for about six years. + +We've done, we've looked at +about 80 patients now, more. + +And, highly successful. + +And I'm not going to weigh you +down with all the statistical + +tests and everything, but we've +done the kind of things + +I talked about in class. + +Looking at the data, doing the +statistics, and suffice it to + +say, it works great. + +For nine out of 10 patients, +roughly. + +And for the tenth, we +just have to say, + +sorry, we can't do it. + +But, you know, you can't help +everybody all the time. + +We're currently, what you see +here, is a picture of a neural + +stimulator. + +The stimulator itself gets +implanted under the clavicle, + +and then a wire runs up and +wraps around the left vagus + +nerve, which is the longest +nerve in the human body. + +It runs all away from +the head, down + +into the lower intestine. + +Latin for wanderer. + +Does amazing things, like +control whether + +you're hungry or not. + +Its main, one of its main +functions, is it controls the + +parasympathetic nervous +system for the heart. + +And it's the nerve that +the brain uses to tell + +the heart, slow down. + +But, in addition to transmitting +down from the + +brain, you can transmit +up the nerve. + +And in fact, the left one, for +reasons I don't understand, + +translates much better up +than the right one does. + +Which transmits much +better down. + +So use the left one. + +And the notion is, if at the +start of a seizure, we put a + +current on that wire, we +stimulate the brain and we + +stop the seizure. + +That's the theory. + +It's been shown to stop +seizures in rats. + +But I don't much care +about helping rats. + +People purport to have shown it +stops seizures in adults, + +or in people. + +The level of evidence is, +honestly, ambiguous. + +Because what they've done is, +they've implanted it, and they + +give the patient a magnet. + +And say, when you're having a +seizure, swipe the magnet + +across, sorry about that, swipe +the magnet across the + +stimulator, it will turn it +on and stop your seizure. + +Well, could you imagine that +little girl trying to swipe a + +magnet across her chest? + +Not likely. + +So most people don't +do it successfully. + +Some people report, I thought I +was about to have a seizure, + +I swiped the magnet and +I didn't have it. + +Well, how do we know? + +Did they really stop it, or +did they just imagine they + +were going to have one? + +So it's pretty ambiguous, but +we're now in the process of + +doing some real tests +at Beth Israel + +Deaconness Medical Center. + +And we've been admitting +patients, and controlling the + +stimulator, and so far +I'm optimistic. + +All right, one more example. + +Predicting death. + +Well, that's kind of +ominous sounding. + +About one and a quarter million +Americans have an + +acute coronary syndrome +each year. + +That's to say, some sort +of a cardiac event. + +A heart attack, or an arrhythmia +of some sort, + +various kinds of things, +unstable angina. + +And of that one and a quarter +million people, 15 percent to + +20 percent of them will die of a +cardiac-related event within + +the next 4 years. + +Pretty high. + +In fact, about 5% within the +next 90 days, there about. + +So what do you do? + +The key thing, we +have treatments. + +We actually know how to treat +most of these things. + +But we don't know who to +give the treatments to? + +So, for example, who gets an +implanted defibrillator? + +Who should be treated +aggressively with statins? + +We think we've found a new way +to decide who should get which + +of these kinds of treatments. + +Something called morphological +variability, which I'll talk + +about only briefly. + +We've tested it on a fairly +large database. + +We have a database with +about 8,000 patients. + +We've looked at 2 days for each +patient, each day has 24 + +hours, each hour has 60 minutes, +each minute has, on + +average, 70 heartbeats. + +That's a lot of heartbeats. + +Over a billion. + +So a lot of the techniques we've +talked about this term, + +about how do you deal with big +things, I live with every day. + +Actually, more accurately, my +students live with every day, + +and I commiserate. + +But the tests are pretty +convincing. + +As an example, they're implanted +defibrillators, + +they, too, go under +the clavicle. + +Fortunately we have +two clavicles. + +And then they connect to the +heart, and they notice, they + +have a sensor, they notice the +heart is beating very badly, + +and they shock the heart. + +So you've all seen medical +shows, where people put + +paddles on, say, clear, the +patient goes boom boom, and + +then they say, sinus +rhythm restored. + +Well, this does the same +thing, but you + +walk around with it. + +Now, you don't want to turn on +all the time, because as you + +can see, it delivers +quite a jolt. + +Interestingly, this is an +article from this fall, from + +the New York Times, 90 percent +of the people who get one + +implanted, and the device itself +costs about $50,000, + +let alone the cost +of implanting it. + +90 percent receive negative +medical benefit. + +How do I know that they received +medical benefit? + +Well, I know that 90% of them +are never turned on. + +Remember, there's a sensor +that decides whether + +to apply the shock. + +90 percent of them, the sensor +never says, turn on. + +So 90 percent of them can +deliver no benefit because + +they're never used. + +On the other hand, clearly +having the surgery to implant + +this, is some risk. + +So that's why the benefit +is not only + +neutral, but negative. + +You've had fairly serious +surgery, you've risked + +infection, and, in fact, this +year several people died. + +I think three or four died +when leads broke + +off on these things. + +So, clearly we're putting in too +many of them, if only 10 + +percent are used. + +On the other hand, roughly +every one minute and 50 + +seconds, somebody in +this country dies a + +sudden cardiac death. + +More often once every +two minutes. + +100 of them during the course +of this lecture. + +If these people all had +defibrillators implanted, many + +of them would not die. + +So, we have a therapy, we just +don't know who to give it to. + +So, what does this look like? + +Again, this is pretty +strong stuff. + +That's what sudden cardiac +death looks like. + +An apparently healthy guy, +suddenly he's dead. + +It's things like this that +remind us why we can do real + +useful things with our +talents or skills. + +So how do you identify +high risk cases? + +Lots of different ways, I won't +go through them, but + +we're focusing again +on the electrical + +signals in the heart. + +We're trying to evaluate the +shape of the heartbeat and + +what's going on. + +I won't go through details, +the only thing I wanted to + +point out is, we use +dynamic programming + +to actually do this. + +So the key idea in our method +depends upon dynamic + +programming. + +We've evaluated it +several times. + +Here's one evaluation. + +We took the 25 percent of the +population that we thought was + +at the highest risk. + +And you'll notice that within, +actually the first 30 days, + +4.19 percent of those +people were dead. + +This is a retrospective +study, by the way. + +The ECG had been recorded, and +we knew, we had follow-ups on + +them, and of the people we said +were not, the other 3/4 + +of the population, a very +small fraction died. + +So this is called a Kaplan +Meier curve, and it + +shows a huge gap. + +And in fact, roughly speaking, +if we think you were at high + +risk, you were 8 1/2 times more +likely to die within a + +month, within 90 days. + +And the good news is, we don't +do this just so we can say, + +make your will. + +Get your affairs in order. + +We actually do this so that we +can say, all right, this is a + +person who should maybe get a +defibrillator, maybe should + +have their arteries +cleaned out. + +Maybe should take +a blood thinner. + +Once we know who's at risk, we +can do something about it. + +All right, all I want to do is +just give you a flavor of the + +kinds of things you've been +learning, are really useful, + +and can be used to really do +things that are worth doing. + +So wrapping up the term, +what have you learned? + +Well, you know, I think +we'll start with this. + +If you think what you could do +in September, and what you can + +do now, you've really come +a long way, right? + +So try and go back and do +problem set number one, and + +see how long it takes you now, +and how long it took you then. + +You'll discover that you really +are at a place you were + +not in September. + +We covered five major topics. + +Learning a language for +expressing computations, + +that's Python. + +I already talked about the + +importance of having a notation. + +Learning about the process +of writing and debugging + +programs. But more generally, +learning about the process of + +moving from some relatively +ambiguous problem statement. + +As you've all noticed in the +current problem set, we left a + +lot of things unspecified. + +You know, and the email was +flying back and forth, and + +often the answer was, +you figure it out. + +Because that's one of the things +we want you to learn. + +To go from some problem +statement to a computational + +formulation. + +As a tool to that, you learned +a basic set of recipes, bunch + +of different algorithms. And +you learned how to use + +simulations to deal with +problems that did not have + +nice closed form solutions. + +Why Python? + +Well, believe it or not, it's +an easy language to learn, + +compared to other languages. + +Simple syntax, it's +interpretive, which helps with + +the debugging, you don't have to +worry about managing memory + +as you would in a language +like C. It's modern. + +It supports, in a fairly elegant +way, object-oriented + +programming and classes, and +it's increasingly popular. + +It's used increasing in other +subjects at MIT and other + +universities, increasing in +industry, and a large and + +ever-growing set of libraries. + +We talked about writing, +testing, and debugging + +programs. And if I had one +message I want you to remember + +about all of this, +it's be slow. + +Slow down, take it one step at +a time, take your time and be + +methodical, systematic, +and careful. + +Understand the problem first. +Then think about the overall + +structure of the solution, and +the algorithms independently + +of how you're going +to code it up. + +So you might say, well, I'm +going to use dynamic + +programming. + +And that's an independent +decision from Python or Java + +or C++ , or anything else +to implement it. + +And in fact, it's pretty easy to +translate a well-organized + +program from one language +to another. + +Break it into small parts, and +we talked about unit testing + +and the importance of that. + +Nobody can build anything +big in one fell swoop. + +So, break it into small parts, +identify useful abstractions, + +both functional and data, code +and unit test each part, and + +first worry about +functionality. + +Are you getting the +correct answer? + +And then efficiency. + +And a piece of that is, learn +to use pseudo code to help + +yourself out. + +As I said earlier, be systematic +when debugging. + +Think about the scientific +method. + +It's not just something that +we use to torture middle + +school students. + +And when you write a program +and it doesn't work, ask + +yourself, why it did +what it did? + +Focus on understanding why the +program is doing what it's + +doing, rather than why +it's not doing what + +you wanted it to? + +Because as soon as you know +why it's doing what it's + +doing, you'll know +how to fix it. + +But if you skip that step, +you'll waste an + +awful lot of time. + +Going from problem statement +to computation. + +We said a lot of this, you +break the problem into a + +series of smaller problems. +Ideally, reducing it to a + +problem you already have code +to solve, or somebody else's + +code to solve. + +My first instinct when I have to +solve a problem is, I type, + +I go to Google, and I type, I +think about, oh this is really + +an x problem, a shortest +path problem. + +I type Python shortest path, +and I see what code + +pops up on my screen. + +But I can't do that until I've +realized, oh, it's really a + +shortest path, or it's +really a knapsack. + +If I type Python select +courses, I won't + +get anything useful. + +Think about what kind of output +you'd like to see. + +I often start thinking about +a program by first asking + +myself, what's the output +going to look like? + +And I'll actually write +the output down. + +And then I'll see if I can't +write a program to generate + +that kind of output. + +Often you can take a problem +formulated as an optimization + +problem, a lot of thing reduce +to finding the minimum or + +maximum values, satisfying +some set of constraints. + +So when you're given something +like, how do I find the + +directions from here to +Providence, think about it as + +an optimization problem. + +And also, think about whether +you really have to solve it. + +It's very often the case that an +approximate solution is all + +you really need. + +And they're a lot faster. + +So, we think about approximation +formally, in the + +sense of, say, Newton Raphson, +we looked at, successive + +approximation. + +But more informally, an +approximation can be, solve a + +simpler problem. + +That you don't really need to +solve the problem you thought + +needed to solve, if you solve +something simpler, it + +will do just fine. + +So you don't find the best +solution, you just find a + +pretty good solution. + +Or you simplify the assumptions +and say, well, I'm + +going to find directions, and +to make my problem a little + +simpler, I'm not going to allow +myself to take any roads + +except highways to get from +city a to city b. + +It may not be the shortest, but +it's an easier problem to + +solve because are so +many fewer roads. + +We talked about algorithms, we +talked about big o notation, + +orders of growth, that's +very important. + +We talked a little bit about +amortized analysis, that you + +might want to, say, sort +something first if you were + +going to do a lot +of searching. + +We looked at a bunch of +kinds of algorithms. + +I've listed them here. + +I'm, by the way, going to send +you a list with all this stuff + +on it, among other things, +so don't feel you need to + +transcribe it. + +But a lot of, surprisingly large +number of algorithms, to + +cover in one semester, when +you think about it. + +Exhaustive enumeration, +successive approximation, + +greedy, divide and conquer, +decision trees, dynamic + +programming. + +Quite a lot. + +Specific algorithms and +specific optimization + +problems. We spent a lot +of time on simulation. + +It's important, but maybe not as +important as all that time, + +relative to the semester, but +it gave me an excuse to talk + +about some things that +I wanted to cover. + +So it gave me a framework to +talk a little bit about + +probability and statistics. + +And it's my view, personally, +that every MIT student should + +be made to take such a course. + +Since they're not, I tried +to sneak it in here. + +But it's all, it's important +stuff to know. + +It gave me an excuse to build +some interesting programs. So, + +what I hope you noticed, is as I +went through these things, I + +actually tried to develop the +programs incrementally, to + +talk about the abstractions, +to talk about how + +I would test them. + +And so, just as important as the +simulation itself, was the + +process of building +the simulation. + +And so I just shows that as a +mechanism to go through some + +case studies of building some +interesting programs. It let + +us talk about random choice. + +Much of the world is, or +at least appears to be, + +stochastic. + +And therefore, we have to model +randomness in programs. + +And even we don't have to, it +can be used to solve problems + +that are not inherently +random, like finding + +the value of pi. + +It let us look at the issue +of assessing the + +quality of an answer. + +We look at things, said, do we +believe that that answer is + +right or not? + +And building models of, at least +parts of, the world. + +Some pervasive themes that +we talked about. + +The power of abstraction, +systematic problem solving, + +these will be useful even if +you never again write a + +program in your whole life. + +What next? + +Well, many of you, almost all of +you, have worked very hard + +this semester. + +I hope you feel that you've +got a return on your + +investment. + +Only you know that. + +As I said earlier, take a look +at the problem sets, and see + +whether you think you've +learned anything. + +I'd like you to remember after +you leave this course, that + +you've got a skill you can use +to solve problems. And when + +you sit down, and there's some +issue that you don't know, + +just knock out a program +to get your answer. + +I do it all the time, and +it's very useful. + +If you want to take more +courses, there are + +others you can take. + +6.01, the first course +for Course 6 majors, + +you will find easy. + +Experience says, people who +take 6.00 first don't + +understand what all the +fuss is about 6.01. + +You'll also find it fun +and interesting. + +6.034, the introduction to +AI, is now using Python. + +You know everything you need +to know to take that. + +6.005, which is software +engineering, you know + +everything you need +to take that. + +And, for many of you, you can +take 6.006, which is a really + +interesting kind of +algorithms course. + +More advanced algorithms, +particularly those you who + +like math would find +6.006 really fun. + +So if you want to take +more courses, there + +are courses to take. + +Thank you all, good luck with +the rest of the semester. \ No newline at end of file diff --git a/3AF4I5hhIkM.txt b/3AF4I5hhIkM.txt new file mode 100644 index 0000000000000000000000000000000000000000..c6692eaa07b49a443503958795c6273661d588b8 --- /dev/null +++ b/3AF4I5hhIkM.txt @@ -0,0 +1,7747 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu let's finish this discussion + + align:start position:0% +ocw.mit.edu let's finish this discussion + + + align:start position:0% +ocw.mit.edu let's finish this discussion +of this spatial organization of the + + align:start position:0% +of this spatial organization of the + + + align:start position:0% +of this spatial organization of the +motor the descending Pathways of the + + align:start position:0% +motor the descending Pathways of the + + + align:start position:0% +motor the descending Pathways of the +motor + + align:start position:0% +motor + + + align:start position:0% +motor +system the + + align:start position:0% +system the + + + align:start position:0% +system the +uh we we had talked about + + align:start position:0% +uh we we had talked about + + + align:start position:0% +uh we we had talked about +these pathway shown in these diagrams + + align:start position:0% +these pathway shown in these diagrams + + + align:start position:0% +these pathway shown in these diagrams +and gone over them a little + + align:start position:0% +and gone over them a little + + + align:start position:0% +and gone over them a little +bit + + align:start position:0% + + + + align:start position:0% + +uh I just mentioned the the bilateral + + align:start position:0% +uh I just mentioned the the bilateral + + + align:start position:0% +uh I just mentioned the the bilateral +lesions of the medial + + align:start position:0% +lesions of the medial + + + align:start position:0% +lesions of the medial +Pathways they had to be bilateral + + align:start position:0% +Pathways they had to be bilateral + + + align:start position:0% +Pathways they had to be bilateral +because those Pathways tend to + + align:start position:0% +because those Pathways tend to + + + align:start position:0% +because those Pathways tend to +distribute on both both sides so the + + align:start position:0% +distribute on both both sides so the + + + align:start position:0% +distribute on both both sides so the +only way to really + + align:start position:0% +only way to really + + + align:start position:0% +only way to really +eliminate the medial Pathways in + + align:start position:0% +eliminate the medial Pathways in + + + align:start position:0% +eliminate the medial Pathways in +a in a way that would really impact + + align:start position:0% +a in a way that would really impact + + + align:start position:0% +a in a way that would really impact +function is to get rid of them on both + + align:start position:0% +function is to get rid of them on both + + + align:start position:0% +function is to get rid of them on both +sides and they really can't control + + align:start position:0% +sides and they really can't control + + + align:start position:0% +sides and they really can't control +their body axis well at all so they + + align:start position:0% +their body axis well at all so they + + + align:start position:0% +their body axis well at all so they +can't write they can't walk straight + + align:start position:0% +can't write they can't walk straight + + + align:start position:0% +can't write they can't walk straight +uh they can't even Orient their heads + + align:start position:0% +uh they can't even Orient their heads + + + align:start position:0% +uh they can't even Orient their heads +very well because the tectum is pretty + + align:start position:0% +very well because the tectum is pretty + + + align:start position:0% +very well because the tectum is pretty +dominant in + + align:start position:0% +dominant in + + + align:start position:0% +dominant in +the after the cord is removed remember + + align:start position:0% +the after the cord is removed remember + + + align:start position:0% +the after the cord is removed remember +that was critical to these experiments + + align:start position:0% +that was critical to these experiments + + + align:start position:0% +that was critical to these experiments +they had to remove the paramal tract + + align:start position:0% +they had to remove the paramal tract + + + align:start position:0% +they had to remove the paramal tract +first actually the cortex was intact + + align:start position:0% +first actually the cortex was intact + + + align:start position:0% +first actually the cortex was intact +it's still connected to the U the brain + + align:start position:0% +it's still connected to the U the brain + + + align:start position:0% +it's still connected to the U the brain +stem except the lower most brain stem + + align:start position:0% +stem except the lower most brain stem + + + align:start position:0% +stem except the lower most brain stem +and that means they have normal eye + + align:start position:0% +and that means they have normal eye + + + align:start position:0% +and that means they have normal eye +movements so you can tell that the + + align:start position:0% +movements so you can tell that the + + + align:start position:0% +movements so you can tell that the +monkey knows where he wants to walk and + + align:start position:0% +monkey knows where he wants to walk and + + + align:start position:0% +monkey knows where he wants to walk and +yet he can't steer himself well because + + align:start position:0% +yet he can't steer himself well because + + + align:start position:0% +yet he can't steer himself well because +he doesn't have good control of the + + align:start position:0% +he doesn't have good control of the + + + align:start position:0% +he doesn't have good control of the +axial + + align:start position:0% +axial + + + align:start position:0% +axial +muscles uh below his + + align:start position:0% + + + + align:start position:0% + +head he does is able to control his + + align:start position:0% +head he does is able to control his + + + align:start position:0% +head he does is able to control his +hands though the only way they could + + align:start position:0% +hands though the only way they could + + + align:start position:0% +hands though the only way they could +test that was to strap him in a chair so + + align:start position:0% +test that was to strap him in a chair so + + + align:start position:0% +test that was to strap him in a chair so +he doesn't have to struggle to try to + + align:start position:0% +he doesn't have to struggle to try to + + + align:start position:0% +he doesn't have to struggle to try to +balance so then his arms are just + + align:start position:0% +balance so then his arms are just + + + align:start position:0% +balance so then his arms are just +dangling and they can present things to + + align:start position:0% +dangling and they can present things to + + + align:start position:0% +dangling and they can present things to +him and he'll use his vision to guide + + align:start position:0% +him and he'll use his vision to guide + + + align:start position:0% +him and he'll use his vision to guide +his + + align:start position:0% +his + + + align:start position:0% +his +hand um to grasp food objects he does + + align:start position:0% +hand um to grasp food objects he does + + + align:start position:0% +hand um to grasp food objects he does +that pretty + + align:start position:0% +that pretty + + + align:start position:0% +that pretty +well all right + + align:start position:0% + + + + align:start position:0% + +uh and then the other leion that is + + align:start position:0% +uh and then the other leion that is + + + align:start position:0% +uh and then the other leion that is +instead of cutting the medial Pathways + + align:start position:0% +instead of cutting the medial Pathways + + + align:start position:0% +instead of cutting the medial Pathways +they can go in and cut the lateral + + align:start position:0% +they can go in and cut the lateral + + + align:start position:0% +they can go in and cut the lateral +Pathways just on one side because they + + align:start position:0% +Pathways just on one side because they + + + align:start position:0% +Pathways just on one side because they +don't tend to distribute + + align:start position:0% +don't tend to distribute + + + align:start position:0% +don't tend to distribute +bilaterally and then they got very great + + align:start position:0% +bilaterally and then they got very great + + + align:start position:0% +bilaterally and then they got very great +differences in control of the two + + align:start position:0% +differences in control of the two + + + align:start position:0% +differences in control of the two +hands okay so if they if they cut the + + align:start position:0% +hands okay so if they if they cut the + + + align:start position:0% +hands okay so if they if they cut the +pathways on the left + + align:start position:0% +pathways on the left + + + align:start position:0% +pathways on the left +side he would reach with his right hand + + align:start position:0% +side he would reach with his right hand + + + align:start position:0% +side he would reach with his right hand +and grasp things not with single digits + + align:start position:0% +and grasp things not with single digits + + + align:start position:0% +and grasp things not with single digits +but with using the whole hand so he + + align:start position:0% +but with using the whole hand so he + + + align:start position:0% +but with using the whole hand so he +could grasp things but with this hand he + + align:start position:0% +could grasp things but with this hand he + + + align:start position:0% +could grasp things but with this hand he +knows exactly what he wants to do he + + align:start position:0% +knows exactly what he wants to do he + + + align:start position:0% +knows exactly what he wants to do he +would + + align:start position:0% +would + + + align:start position:0% +would +reach the hand just wouldn't grasp he + + align:start position:0% +reach the hand just wouldn't grasp he + + + align:start position:0% +reach the hand just wouldn't grasp he +has control of his arm muscles + + align:start position:0% +has control of his arm muscles + + + align:start position:0% +has control of his arm muscles +but he can't do that + + align:start position:0% +but he can't do that + + + align:start position:0% +but he can't do that +so very selective types of paralysis now + + align:start position:0% +so very selective types of paralysis now + + + align:start position:0% +so very selective types of paralysis now +one of the most interesting parts of + + align:start position:0% +one of the most interesting parts of + + + align:start position:0% +one of the most interesting parts of +that lesion is that if they let the + + align:start position:0% +that lesion is that if they let the + + + align:start position:0% +that lesion is that if they let the +monkey + + align:start position:0% +monkey + + + align:start position:0% +monkey +go okay so he can run and climb his cage + + align:start position:0% +go okay so he can run and climb his cage + + + align:start position:0% +go okay so he can run and climb his cage +and + + align:start position:0% +and + + + align:start position:0% +and +everything while he's doing that he's + + align:start position:0% +everything while he's doing that he's + + + align:start position:0% +everything while he's doing that he's +got good control of the hands so what's + + align:start position:0% +got good control of the hands so what's + + + align:start position:0% +got good control of the hands so what's +going + + align:start position:0% +going + + + align:start position:0% +going +on when the whole body is involved that + + align:start position:0% +on when the whole body is involved that + + + align:start position:0% +on when the whole body is involved that +system for axial muscle control is + + align:start position:0% +system for axial muscle control is + + + align:start position:0% +system for axial muscle control is +really a whole body control system and + + align:start position:0% +really a whole body control system and + + + align:start position:0% +really a whole body control system and +controls things like a Locomotion and cl + + align:start position:0% +controls things like a Locomotion and cl + + + align:start position:0% +controls things like a Locomotion and cl +timing and so in those movements he can + + align:start position:0% +timing and so in those movements he can + + + align:start position:0% +timing and so in those movements he can +control his grasping but when you ask + + align:start position:0% +control his grasping but when you ask + + + align:start position:0% +control his grasping but when you ask +him to grasp as a individual movement + + align:start position:0% +him to grasp as a individual movement + + + align:start position:0% +him to grasp as a individual movement +separate from other movements then he + + align:start position:0% +separate from other movements then he + + + align:start position:0% +separate from other movements then he +can't do + + align:start position:0% + + + + align:start position:0% + +it it's a good lesson on what paralysis + + align:start position:0% +it it's a good lesson on what paralysis + + + align:start position:0% +it it's a good lesson on what paralysis +means when it's due to a central + + align:start position:0% +means when it's due to a central + + + align:start position:0% +means when it's due to a central +lesion if it's due to a lesion that + + align:start position:0% +lesion if it's due to a lesion that + + + align:start position:0% +lesion if it's due to a lesion that +affects the motor neurons or the axons + + align:start position:0% +affects the motor neurons or the axons + + + align:start position:0% +affects the motor neurons or the axons +from motor neurons then you get a + + align:start position:0% +from motor neurons then you get a + + + align:start position:0% +from motor neurons then you get a +flaccid paralysis the muscles are just + + align:start position:0% +flaccid paralysis the muscles are just + + + align:start position:0% +flaccid paralysis the muscles are just +totally relaxed they're not getting + + align:start position:0% +totally relaxed they're not getting + + + align:start position:0% +totally relaxed they're not getting +their input anymore we're just talking + + align:start position:0% +their input anymore we're just talking + + + align:start position:0% +their input anymore we're just talking +about Central lesions + + align:start position:0% +about Central lesions + + + align:start position:0% +about Central lesions +here okay so those experiments made + + align:start position:0% +here okay so those experiments made + + + align:start position:0% +here okay so those experiments made +clear two very different things one is + + align:start position:0% +clear two very different things one is + + + align:start position:0% +clear two very different things one is +the spatial layout of the motor pathways + + align:start position:0% +the spatial layout of the motor pathways + + + align:start position:0% +the spatial layout of the motor pathways +the descending + + align:start position:0% +the descending + + + align:start position:0% +the descending +Pathways and the other point was the + + align:start position:0% +Pathways and the other point was the + + + align:start position:0% +Pathways and the other point was the +quantitative dominance of the cortical + + align:start position:0% +quantitative dominance of the cortical + + + align:start position:0% +quantitative dominance of the cortical +Pathways and monkeys and of course + + align:start position:0% +Pathways and monkeys and of course + + + align:start position:0% +Pathways and monkeys and of course +humans all of those things describe in + + align:start position:0% +humans all of those things describe in + + + align:start position:0% +humans all of those things describe in +monkeys if you you can find clinical + + align:start position:0% +monkeys if you you can find clinical + + + align:start position:0% +monkeys if you you can find clinical +cases that match parts of + + align:start position:0% +cases that match parts of + + + align:start position:0% +cases that match parts of +them but of course the monkeys gave the + + align:start position:0% +them but of course the monkeys gave the + + + align:start position:0% +them but of course the monkeys gave the +advantage of being able to control the + + align:start position:0% +advantage of being able to control the + + + align:start position:0% +advantage of being able to control the +lesion much + + align:start position:0% + + + + align:start position:0% + +better okay what's the major symptoms if + + align:start position:0% +better okay what's the major symptoms if + + + align:start position:0% +better okay what's the major symptoms if +you just cut all these + + align:start position:0% +you just cut all these + + + align:start position:0% +you just cut all these +pathies you can do say someone a person + + align:start position:0% +pathies you can do say someone a person + + + align:start position:0% +pathies you can do say someone a person +or a monkey has a transected spinal cord + + align:start position:0% +or a monkey has a transected spinal cord + + + align:start position:0% +or a monkey has a transected spinal cord +they die if the lesion is above before + + align:start position:0% +they die if the lesion is above before + + + align:start position:0% +they die if the lesion is above before +why is + + align:start position:0% +why is + + + align:start position:0% +why is +that they stop + + align:start position:0% +that they stop + + + align:start position:0% +that they stop +breathing okay so you've got to have + + align:start position:0% +breathing okay so you've got to have + + + align:start position:0% +breathing okay so you've got to have +intact spinal cord down to the fourth + + align:start position:0% +intact spinal cord down to the fourth + + + align:start position:0% +intact spinal cord down to the fourth +cervical level to get control of the + + align:start position:0% +cervical level to get control of the + + + align:start position:0% +cervical level to get control of the +diaphragm for + + align:start position:0% +diaphragm for + + + align:start position:0% +diaphragm for +breathing okay + + align:start position:0% + + + + align:start position:0% + +so but what happens to them then say + + align:start position:0% +so but what happens to them then say + + + align:start position:0% +so but what happens to them then say +around C4 C5 you get a spinal transction + + align:start position:0% +around C4 C5 you get a spinal transction + + + align:start position:0% +around C4 C5 you get a spinal transction +say the there's an auto accident the + + align:start position:0% +say the there's an auto accident the + + + align:start position:0% +say the there's an auto accident the +neck is + + align:start position:0% +neck is + + + align:start position:0% +neck is +broken if his breathing survives he will + + align:start position:0% +broken if his breathing survives he will + + + align:start position:0% +broken if his breathing survives he will +live but he + + align:start position:0% +live but he + + + align:start position:0% +live but he +becomes + + align:start position:0% + + + + align:start position:0% + +what what's the + + align:start position:0% +what what's the + + + align:start position:0% +what what's the +term quadriplegic or the actual + + align:start position:0% +term quadriplegic or the actual + + + align:start position:0% +term quadriplegic or the actual +grammatically correct word is + + align:start position:0% +grammatically correct word is + + + align:start position:0% +grammatically correct word is +tetraplegic but we often mix Latin and + + align:start position:0% +tetraplegic but we often mix Latin and + + + align:start position:0% +tetraplegic but we often mix Latin and +Greek in these words so quadriplegic is + + align:start position:0% +Greek in these words so quadriplegic is + + + align:start position:0% +Greek in these words so quadriplegic is +actually more commonly + + align:start position:0% +actually more commonly + + + align:start position:0% +actually more commonly +used oh okay and + + align:start position:0% +used oh okay and + + + align:start position:0% +used oh okay and +if so you get a brain that's + + align:start position:0% +if so you get a brain that's + + + align:start position:0% +if so you get a brain that's +disconnected from the major motor output + + align:start position:0% +disconnected from the major motor output + + + align:start position:0% +disconnected from the major motor output +below the + + align:start position:0% +below the + + + align:start position:0% +below the +head loses control of all four + + align:start position:0% +head loses control of all four + + + align:start position:0% +head loses control of all four +limbs he does eventually recover reflex + + align:start position:0% +limbs he does eventually recover reflex + + + align:start position:0% +limbs he does eventually recover reflex +reflex control of course the spinal + + align:start position:0% +reflex control of course the spinal + + + align:start position:0% +reflex control of course the spinal +reflex pathways are intact he loses the + + align:start position:0% +reflex pathways are intact he loses the + + + align:start position:0% +reflex pathways are intact he loses the +spinal reflex for a well that's as we + + align:start position:0% +spinal reflex for a well that's as we + + + align:start position:0% +spinal reflex for a well that's as we +know a diasis effect you remove moove so + + align:start position:0% +know a diasis effect you remove moove so + + + align:start position:0% +know a diasis effect you remove moove so +much excitatory input from those neurons + + align:start position:0% +much excitatory input from those neurons + + + align:start position:0% +much excitatory input from those neurons +in the reflex Pathways that they they + + align:start position:0% +in the reflex Pathways that they they + + + align:start position:0% +in the reflex Pathways that they they +don't even function the reflexes don't + + align:start position:0% +don't even function the reflexes don't + + + align:start position:0% +don't even function the reflexes don't +function but they come back and often + + align:start position:0% +function but they come back and often + + + align:start position:0% +function but they come back and often +they become even + + align:start position:0% +they become even + + + align:start position:0% +they become even +hyperactive because of sprouting and + + align:start position:0% +hyperactive because of sprouting and + + + align:start position:0% +hyperactive because of sprouting and +denervations super + + align:start position:0% + + + + align:start position:0% + +sensitivity which are the major reasons + + align:start position:0% +sensitivity which are the major reasons + + + align:start position:0% +sensitivity which are the major reasons +you get recovery of the + + align:start position:0% + + + + align:start position:0% + +reflexes they can think + + align:start position:0% +reflexes they can think + + + align:start position:0% +reflexes they can think +that they want to move they're able to + + align:start position:0% +that they want to move they're able to + + + align:start position:0% +that they want to move they're able to +move in their minds okay and we know + + align:start position:0% +move in their minds okay and we know + + + align:start position:0% +move in their minds okay and we know +that because you can record with imaging + + align:start position:0% +that because you can record with imaging + + + align:start position:0% +that because you can record with imaging +methods and that's what this figure is + + align:start position:0% +methods and that's what this figure is + + + align:start position:0% +methods and that's what this figure is +about it's in the book + + align:start position:0% + + + + align:start position:0% + +uh it + + align:start position:0% + + + + align:start position:0% + +shows here patience + + align:start position:0% +shows here patience + + + align:start position:0% +shows here patience +with I forgot now if one of these is a + + align:start position:0% +with I forgot now if one of these is a + + + align:start position:0% +with I forgot now if one of these is a +control that should should be this + + align:start position:0% +control that should should be this + + + align:start position:0% +control that should should be this +should be the control but anyway you can + + align:start position:0% +should be the control but anyway you can + + + align:start position:0% +should be the control but anyway you can +see that in the + + align:start position:0% +see that in the + + + align:start position:0% +see that in the +patients uh they are able to activate + + align:start position:0% +patients uh they are able to activate + + + align:start position:0% +patients uh they are able to activate +parts of the motor cortex if they're + + align:start position:0% +parts of the motor cortex if they're + + + align:start position:0% +parts of the motor cortex if they're +trying to move you ask them to try to + + align:start position:0% +trying to move you ask them to try to + + + align:start position:0% +trying to move you ask them to try to +move your right forearm and the right + + align:start position:0% +move your right forearm and the right + + + align:start position:0% +move your right forearm and the right +forearm area of the cortex will increase + + align:start position:0% +forearm area of the cortex will increase + + + align:start position:0% +forearm area of the cortex will increase +in its + + align:start position:0% +in its + + + align:start position:0% +in its +activity and similarly for other body + + align:start position:0% +activity and similarly for other body + + + align:start position:0% +activity and similarly for other body +parts so they're able to + + align:start position:0% +parts so they're able to + + + align:start position:0% +parts so they're able to +map those areas just + + align:start position:0% +map those areas just + + + align:start position:0% +map those areas just +by + + align:start position:0% +by + + + align:start position:0% +by +getting the voluntary intention to move + + align:start position:0% +getting the voluntary intention to move + + + align:start position:0% +getting the voluntary intention to move +but they don't move because there's no + + align:start position:0% +but they don't move because there's no + + + align:start position:0% +but they don't move because there's no +way for these descending Pathways to + + align:start position:0% +way for these descending Pathways to + + + align:start position:0% +way for these descending Pathways to +activate the motor neurons okay so of + + align:start position:0% +activate the motor neurons okay so of + + + align:start position:0% +activate the motor neurons okay so of +course this big question remains is + + align:start position:0% +course this big question remains is + + + align:start position:0% +course this big question remains is +there any way to uh get those long + + align:start position:0% +there any way to uh get those long + + + align:start position:0% +there any way to uh get those long +Pathways to + + align:start position:0% +Pathways to + + + align:start position:0% +Pathways to +reconnect and people have worked on + + align:start position:0% +reconnect and people have worked on + + + align:start position:0% +reconnect and people have worked on +various ways to give such people some + + align:start position:0% +various ways to give such people some + + + align:start position:0% +various ways to give such people some +movement by artificial means and there + + align:start position:0% +movement by artificial means and there + + + align:start position:0% +movement by artificial means and there +are ways that are being developed as you + + align:start position:0% +are ways that are being developed as you + + + align:start position:0% +are ways that are being developed as you +know and get even some speaking ability + + align:start position:0% +know and get even some speaking ability + + + align:start position:0% +know and get even some speaking ability +and people that have lost these + + align:start position:0% +and people that have lost these + + + align:start position:0% +and people that have lost these +movements + + align:start position:0% +movements + + + align:start position:0% +movements +but because of the det deterioration of + + align:start position:0% +but because of the det deterioration of + + + align:start position:0% +but because of the det deterioration of +bodily functions that occurs in these + + align:start position:0% +bodily functions that occurs in these + + + align:start position:0% +bodily functions that occurs in these +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +people uh they usually don't live real + + align:start position:0% +people uh they usually don't live real + + + align:start position:0% +people uh they usually don't live real +long lives after + + align:start position:0% + + + + align:start position:0% + +that can you think of famous + + align:start position:0% +that can you think of famous + + + align:start position:0% +that can you think of famous +actor that this happened to due to a + + align:start position:0% +actor that this happened to due to a + + + align:start position:0% +actor that this happened to due to a +horse + + align:start position:0% +horse + + + align:start position:0% +horse +accident not all that long + + align:start position:0% +accident not all that long + + + align:start position:0% +accident not all that long +ago Christoper re guy that played + + align:start position:0% +ago Christoper re guy that played + + + align:start position:0% +ago Christoper re guy that played +Superman in the Superman whole long + + align:start position:0% +Superman in the Superman whole long + + + align:start position:0% +Superman in the Superman whole long +series of Superman movies so he's very + + align:start position:0% +series of Superman movies so he's very + + + align:start position:0% +series of Superman movies so he's very +well + + align:start position:0% +well + + + align:start position:0% +well +known from both uh films and + + align:start position:0% + + + + align:start position:0% + +TV and they established the Reeves found + + align:start position:0% +TV and they established the Reeves found + + + align:start position:0% +TV and they established the Reeves found +established a foundation to support work + + align:start position:0% +established a foundation to support work + + + align:start position:0% +established a foundation to support work +on + + align:start position:0% + + + + align:start position:0% + +regeneration I met them I talked mostly + + align:start position:0% +regeneration I met them I talked mostly + + + align:start position:0% +regeneration I met them I talked mostly +to his Steve Christopher Reed's wife + + align:start position:0% +to his Steve Christopher Reed's wife + + + align:start position:0% +to his Steve Christopher Reed's wife +about the I was still pretty early on in + + align:start position:0% +about the I was still pretty early on in + + + align:start position:0% +about the I was still pretty early on in +the research on + + align:start position:0% +the research on + + + align:start position:0% +the research on +regeneration it was after that that we + + align:start position:0% +regeneration it was after that that we + + + align:start position:0% +regeneration it was after that that we +developed these two methods of + + align:start position:0% +developed these two methods of + + + align:start position:0% +developed these two methods of +getting some uh Vision back in animals + + align:start position:0% +getting some uh Vision back in animals + + + align:start position:0% +getting some uh Vision back in animals +using the visual system as a model which + + align:start position:0% +using the visual system as a model which + + + align:start position:0% +using the visual system as a model which +is easier to work with than the spinal + + align:start position:0% +is easier to work with than the spinal + + + align:start position:0% +is easier to work with than the spinal +cord but now it is starting to be done + + align:start position:0% +cord but now it is starting to be done + + + align:start position:0% +cord but now it is starting to be done +similar things with spinal cord as + + align:start position:0% +similar things with spinal cord as + + + align:start position:0% +similar things with spinal cord as +well although as I was saying to some of + + align:start position:0% +well although as I was saying to some of + + + align:start position:0% +well although as I was saying to some of +you who talk to me after the class the + + align:start position:0% +you who talk to me after the class the + + + align:start position:0% +you who talk to me after the class the +uh these things are very slow to move + + align:start position:0% +uh these things are very slow to move + + + align:start position:0% +uh these things are very slow to move +into the to regular clinical + + align:start position:0% +into the to regular clinical + + + align:start position:0% +into the to regular clinical +practice all + + align:start position:0% +practice all + + + align:start position:0% +practice all +right a couple more topics here + + align:start position:0% +right a couple more topics here + + + align:start position:0% +right a couple more topics here +and these Pathways first of + + align:start position:0% +and these Pathways first of + + + align:start position:0% +and these Pathways first of +all what do we mean by the sensory motor + + align:start position:0% +all what do we mean by the sensory motor + + + align:start position:0% +all what do we mean by the sensory motor +imag amalgam + + align:start position:0% +imag amalgam + + + align:start position:0% +imag amalgam +hypothesis by amalgam we mean + + align:start position:0% +hypothesis by amalgam we mean + + + align:start position:0% +hypothesis by amalgam we mean +amalgamation of the primary sensory area + + align:start position:0% +amalgamation of the primary sensory area + + + align:start position:0% +amalgamation of the primary sensory area +and the primary motor area there are + + align:start position:0% +and the primary motor area there are + + + align:start position:0% +and the primary motor area there are +animals especially the Virginia posum + + align:start position:0% +animals especially the Virginia posum + + + align:start position:0% +animals especially the Virginia posum +when you can't really separate them that + + align:start position:0% +when you can't really separate them that + + + align:start position:0% +when you can't really separate them that +is if you map primary smat sensory + + align:start position:0% +is if you map primary smat sensory + + + align:start position:0% +is if you map primary smat sensory +cortex and then you use the method of + + align:start position:0% +cortex and then you use the method of + + + align:start position:0% +cortex and then you use the method of +stimulation to find where the low + + align:start position:0% +stimulation to find where the low + + + align:start position:0% +stimulation to find where the low +threshold areas are in the cortex for + + align:start position:0% +threshold areas are in the cortex for + + + align:start position:0% +threshold areas are in the cortex for +getting movement you find it just + + align:start position:0% +getting movement you find it just + + + align:start position:0% +getting movement you find it just +overlaps with S1 sensory area + + align:start position:0% +overlaps with S1 sensory area + + + align:start position:0% +overlaps with S1 sensory area +one so they well how do you + + align:start position:0% +one so they well how do you + + + align:start position:0% +one so they well how do you +know is there any purely anatomical + + align:start position:0% +know is there any purely anatomical + + + align:start position:0% +know is there any purely anatomical +method not using + + align:start position:0% +method not using + + + align:start position:0% +method not using +stimulation to map + + align:start position:0% + + + + align:start position:0% + +those then there's a couple other topics + + align:start position:0% +those then there's a couple other topics + + + align:start position:0% +those then there's a couple other topics +here I'll go over so that that's this + + align:start position:0% +here I'll go over so that that's this + + + align:start position:0% +here I'll go over so that that's this +question and + + align:start position:0% +question and + + + align:start position:0% +question and +basically this is my figure about that + + align:start position:0% +basically this is my figure about that + + + align:start position:0% +basically this is my figure about that +uh you do it by mapping the projections + + align:start position:0% +uh you do it by mapping the projections + + + align:start position:0% +uh you do it by mapping the projections +of the thalamic nuclei that project to + + align:start position:0% +of the thalamic nuclei that project to + + + align:start position:0% +of the thalamic nuclei that project to +these areas so if you take a human a + + align:start position:0% +these areas so if you take a human a + + + align:start position:0% +these areas so if you take a human a +monkey or another primate like the + + align:start position:0% +monkey or another primate like the + + + align:start position:0% +monkey or another primate like the +galago you'll find that the vental + + align:start position:0% +galago you'll find that the vental + + + align:start position:0% +galago you'll find that the vental +posterior nucleus that gets the input + + align:start position:0% +posterior nucleus that gets the input + + + align:start position:0% +posterior nucleus that gets the input +from + + align:start position:0% +from + + + align:start position:0% +from +spinothalamic tract from medial and from + + align:start position:0% +spinothalamic tract from medial and from + + + align:start position:0% +spinothalamic tract from medial and from +the medial liscus the smos sensory input + + align:start position:0% +the medial liscus the smos sensory input + + + align:start position:0% +the medial liscus the smos sensory input +it projects the primary CA sensory + + align:start position:0% +it projects the primary CA sensory + + + align:start position:0% +it projects the primary CA sensory +cortex it also projects to a second CA + + align:start position:0% +cortex it also projects to a second CA + + + align:start position:0% +cortex it also projects to a second CA +sensory area but we don't show that here + + align:start position:0% +sensory area but we don't show that here + + + align:start position:0% +sensory area but we don't show that here +okay and then the nucleus just in front + + align:start position:0% +okay and then the nucleus just in front + + + align:start position:0% +okay and then the nucleus just in front +of it the vental lateral nucleus and + + align:start position:0% +of it the vental lateral nucleus and + + + align:start position:0% +of it the vental lateral nucleus and +there's one more the vental anterior + + align:start position:0% +there's one more the vental anterior + + + align:start position:0% +there's one more the vental anterior +nucleus the ventrolateral nucleus is the + + align:start position:0% +nucleus the ventrolateral nucleus is the + + + align:start position:0% +nucleus the ventrolateral nucleus is the +provides the primary input to motor one + + align:start position:0% +provides the primary input to motor one + + + align:start position:0% +provides the primary input to motor one +motor cortex just in front of the + + align:start position:0% +motor cortex just in front of the + + + align:start position:0% +motor cortex just in front of the +primary SM sensory cortex and these two + + align:start position:0% +primary SM sensory cortex and these two + + + align:start position:0% +primary SM sensory cortex and these two +areas are quite + + align:start position:0% +areas are quite + + + align:start position:0% +areas are quite +separate + + align:start position:0% +separate + + + align:start position:0% +separate +in these large + + align:start position:0% +in these large + + + align:start position:0% +in these large +primates okay even some of the smaller + + align:start position:0% +primates okay even some of the smaller + + + align:start position:0% +primates okay even some of the smaller +ones okay + + align:start position:0% +ones okay + + + align:start position:0% +ones okay +okay but if you look at the rat you'll + + align:start position:0% +okay but if you look at the rat you'll + + + align:start position:0% +okay but if you look at the rat you'll +find well it's pretty similar but + + align:start position:0% +find well it's pretty similar but + + + align:start position:0% +find well it's pretty similar but +there's an area there behind lib + + align:start position:0% +there's an area there behind lib + + + align:start position:0% +there's an area there behind lib +representation where the two areas do + + align:start position:0% +representation where the two areas do + + + align:start position:0% +representation where the two areas do +overlap okay in meaning that the VP and + + align:start position:0% +overlap okay in meaning that the VP and + + + align:start position:0% +overlap okay in meaning that the VP and +the VL both project to that + + align:start position:0% +the VL both project to that + + + align:start position:0% +the VL both project to that +area if you look at the Virginia possum + + align:start position:0% +area if you look at the Virginia possum + + + align:start position:0% +area if you look at the Virginia possum +they overlap almost + + align:start position:0% + + + + align:start position:0% + +completely the area + + align:start position:0% +completely the area + + + align:start position:0% +completely the area +where the ventral pure I nucleus + + align:start position:0% +where the ventral pure I nucleus + + + align:start position:0% +where the ventral pure I nucleus +projects overlaps completely with areas + + align:start position:0% +projects overlaps completely with areas + + + align:start position:0% +projects overlaps completely with areas +that the ventrolateral nucleus + + align:start position:0% +that the ventrolateral nucleus + + + align:start position:0% +that the ventrolateral nucleus +projects so there's an amalgamation they + + align:start position:0% +projects so there's an amalgamation they + + + align:start position:0% +projects so there's an amalgamation they +do have a separate vental posterior + + align:start position:0% +do have a separate vental posterior + + + align:start position:0% +do have a separate vental posterior +nucleus and vent lateral + + align:start position:0% +nucleus and vent lateral + + + align:start position:0% +nucleus and vent lateral +nucleus there they're seg they're seg + + align:start position:0% +nucleus there they're seg they're seg + + + align:start position:0% +nucleus there they're seg they're seg +they're SE no they're segregated in the + + align:start position:0% +they're SE no they're segregated in the + + + align:start position:0% +they're SE no they're segregated in the +thalamus but in the + + align:start position:0% +thalamus but in the + + + align:start position:0% +thalamus but in the +cortex it's the same area they just + + align:start position:0% +cortex it's the same area they just + + + align:start position:0% +cortex it's the same area they just +project an overlapping way + + align:start position:0% +project an overlapping way + + + align:start position:0% +project an overlapping way +yes in the brush tailed pum pretty + + align:start position:0% +yes in the brush tailed pum pretty + + + align:start position:0% +yes in the brush tailed pum pretty +similar to in some ways to the Virginia + + align:start position:0% +similar to in some ways to the Virginia + + + align:start position:0% +similar to in some ways to the Virginia +posum but notice that there's a large + + align:start position:0% +posum but notice that there's a large + + + align:start position:0% +posum but notice that there's a large +area where they are overlapping but + + align:start position:0% +area where they are overlapping but + + + align:start position:0% +area where they are overlapping but +there's also a pretty sizable area where + + align:start position:0% +there's also a pretty sizable area where + + + align:start position:0% +there's also a pretty sizable area where +there's a a c meta sensory area that's + + align:start position:0% +there's a a c meta sensory area that's + + + align:start position:0% +there's a a c meta sensory area that's +not part of the motor cortex and there's + + align:start position:0% +not part of the motor cortex and there's + + + align:start position:0% +not part of the motor cortex and there's +a small area of motor cortex that's + + align:start position:0% +a small area of motor cortex that's + + + align:start position:0% +a small area of motor cortex that's +separate from this s sensory area so you + + align:start position:0% +separate from this s sensory area so you + + + align:start position:0% +separate from this s sensory area so you +get these + + align:start position:0% +get these + + + align:start position:0% +get these +differences so we're pretty sure that + + align:start position:0% +differences so we're pretty sure that + + + align:start position:0% +differences so we're pretty sure that +the motor cortex primary motor cortex + + align:start position:0% +the motor cortex primary motor cortex + + + align:start position:0% +the motor cortex primary motor cortex +evolved out of C sensory areas and was + + align:start position:0% +evolved out of C sensory areas and was + + + align:start position:0% +evolved out of C sensory areas and was +probably a separate cat sensory area + + align:start position:0% +probably a separate cat sensory area + + + align:start position:0% +probably a separate cat sensory area +that became specialized in its + + align:start position:0% +that became specialized in its + + + align:start position:0% +that became specialized in its +descending projections all the cortical + + align:start position:0% +descending projections all the cortical + + + align:start position:0% +descending projections all the cortical +areas have descending + + align:start position:0% +areas have descending + + + align:start position:0% +areas have descending +projections see and most of them do + + align:start position:0% +projections see and most of them do + + + align:start position:0% +projections see and most of them do +control movement even the visual cortex + + align:start position:0% +control movement even the visual cortex + + + align:start position:0% +control movement even the visual cortex +controls movement IT projects directly + + align:start position:0% +controls movement IT projects directly + + + align:start position:0% +controls movement IT projects directly +to the tectum for example so it can + + align:start position:0% +to the tectum for example so it can + + + align:start position:0% +to the tectum for example so it can +control + + align:start position:0% +control + + + align:start position:0% +control +eye and head movement quite apart from + + align:start position:0% +eye and head movement quite apart from + + + align:start position:0% +eye and head movement quite apart from +you don't need motor + + align:start position:0% +you don't need motor + + + align:start position:0% +you don't need motor +cortex to get movement from the visual + + align:start position:0% +cortex to get movement from the visual + + + align:start position:0% +cortex to get movement from the visual +curve + + align:start position:0% +curve + + + align:start position:0% +curve +cortex don't think of motor motor cortex + + align:start position:0% +cortex don't think of motor motor cortex + + + align:start position:0% +cortex don't think of motor motor cortex +are not motor NS it's just a specialized + + align:start position:0% +are not motor NS it's just a specialized + + + align:start position:0% +are not motor NS it's just a specialized +CTIC sensory area that's develop these + + align:start position:0% +CTIC sensory area that's develop these + + + align:start position:0% +CTIC sensory area that's develop these +long direct connections to the spinal + + align:start position:0% +long direct connections to the spinal + + + align:start position:0% +long direct connections to the spinal +cord all right uh the last thing is this + + align:start position:0% +cord all right uh the last thing is this + + + align:start position:0% +cord all right uh the last thing is this +correlation + + align:start position:0% +correlation + + + align:start position:0% +correlation +of cortical projections with manual + + align:start position:0% + + + + align:start position:0% + +dexterity and the first thing we look at + + align:start position:0% +dexterity and the first thing we look at + + + align:start position:0% +dexterity and the first thing we look at +is just comparing the volume of + + align:start position:0% +is just comparing the volume of + + + align:start position:0% +is just comparing the volume of +neocortex in various + + align:start position:0% +neocortex in various + + + align:start position:0% +neocortex in various +animals + + align:start position:0% +animals + + + align:start position:0% +animals +with the projections to the cord + + align:start position:0% +with the projections to the cord + + + align:start position:0% +with the projections to the cord +either how far down in the cord they + + align:start position:0% +either how far down in the cord they + + + align:start position:0% +either how far down in the cord they +project do they go all the way down to + + align:start position:0% +project do they go all the way down to + + + align:start position:0% +project do they go all the way down to +the Lamy where the motor neurons + + align:start position:0% +the Lamy where the motor neurons + + + align:start position:0% +the Lamy where the motor neurons +are or are they only more + + align:start position:0% + + + + align:start position:0% + +dorsal and uh sorry these are layer 10 + + align:start position:0% +dorsal and uh sorry these are layer 10 + + + align:start position:0% +dorsal and uh sorry these are layer 10 +here is where the 10 and nine + + align:start position:0% +here is where the 10 and nine + + + align:start position:0% +here is where the 10 and nine +are where the motor neurons are eight + + align:start position:0% +are where the motor neurons are eight + + + align:start position:0% +are where the motor neurons are eight +there are the the axial neurons these + + align:start position:0% +there are the the axial neurons these + + + align:start position:0% +there are the the axial neurons these +are these don't contain any motor + + align:start position:0% +are these don't contain any motor + + + align:start position:0% +are these don't contain any motor +neurons at all and you can see there are + + align:start position:0% +neurons at all and you can see there are + + + align:start position:0% +neurons at all and you can see there are +animals where there are no cortical + + align:start position:0% +animals where there are no cortical + + + align:start position:0% +animals where there are no cortical +accents going to the areas of motor + + align:start position:0% +accents going to the areas of motor + + + align:start position:0% +accents going to the areas of motor +neurons and there's a number of animals + + align:start position:0% +neurons and there's a number of animals + + + align:start position:0% +neurons and there's a number of animals +though where they do go there they are + + align:start position:0% +though where they do go there they are + + + align:start position:0% +though where they do go there they are +the ones with + + align:start position:0% +the ones with + + + align:start position:0% +the ones with +greater that spinal projections + + align:start position:0% +greater that spinal projections + + + align:start position:0% +greater that spinal projections +correlated as other said show with their + + align:start position:0% +correlated as other said show with their + + + align:start position:0% +correlated as other said show with their +dexterity let's see this one well this + + align:start position:0% +dexterity let's see this one well this + + + align:start position:0% +dexterity let's see this one well this +one just is another measure of + + align:start position:0% +one just is another measure of + + + align:start position:0% +one just is another measure of +penetration in the cord but here they're + + align:start position:0% +penetration in the cord but here they're + + + align:start position:0% +penetration in the cord but here they're +looking at something different how far + + align:start position:0% +looking at something different how far + + + align:start position:0% +looking at something different how far +down the cord the accents of paramal + + align:start position:0% +down the cord the accents of paramal + + + align:start position:0% +down the cord the accents of paramal +tract + + align:start position:0% +tract + + + align:start position:0% +tract +go this is the codl cord cidial area + + align:start position:0% +go this is the codl cord cidial area + + + align:start position:0% +go this is the codl cord cidial area +this is the sacal area lower lumbar so + + align:start position:0% +this is the sacal area lower lumbar so + + + align:start position:0% +this is the sacal area lower lumbar so +these are the areas furthest down the + + align:start position:0% +these are the areas furthest down the + + + align:start position:0% +these are the areas furthest down the +court so you need the longest accents + + align:start position:0% +court so you need the longest accents + + + align:start position:0% +court so you need the longest accents +from + + align:start position:0% +from + + + align:start position:0% +from +cortex and you can see if you're an + + align:start position:0% +cortex and you can see if you're an + + + align:start position:0% +cortex and you can see if you're an +armadillo or + + align:start position:0% +armadillo or + + + align:start position:0% +armadillo or +Treo + + align:start position:0% +Treo + + + align:start position:0% +Treo +the paramal tract never projects to the + + align:start position:0% +the paramal tract never projects to the + + + align:start position:0% +the paramal tract never projects to the +codl most + + align:start position:0% + + + + align:start position:0% + +cord whereas if you're these animals + + align:start position:0% +cord whereas if you're these animals + + + align:start position:0% +cord whereas if you're these animals +with + + align:start position:0% +with + + + align:start position:0% +with +the greater dexterity like humans and + + align:start position:0% +the greater dexterity like humans and + + + align:start position:0% +the greater dexterity like humans and +monkeys these are other monkeys goes all + + align:start position:0% +monkeys these are other monkeys goes all + + + align:start position:0% +monkeys these are other monkeys goes all +the way down to the cidal cord and then + + align:start position:0% +the way down to the cidal cord and then + + + align:start position:0% +the way down to the cidal cord and then +the correlations with de dexterity + + align:start position:0% +the correlations with de dexterity + + + align:start position:0% +the correlations with de dexterity +they're not perfect but if you have some + + align:start position:0% +they're not perfect but if you have some + + + align:start position:0% +they're not perfect but if you have some +index of measuring how dextrous they are + + align:start position:0% +index of measuring how dextrous they are + + + align:start position:0% +index of measuring how dextrous they are +with their hands you'll find that there + + align:start position:0% +with their hands you'll find that there + + + align:start position:0% +with their hands you'll find that there +is a correlation with the deepest spinal + + align:start position:0% +is a correlation with the deepest spinal + + + align:start position:0% +is a correlation with the deepest spinal +Amina that you find the accents + + align:start position:0% +Amina that you find the accents + + + align:start position:0% +Amina that you find the accents +terminating in the lowest final segment + + align:start position:0% +terminating in the lowest final segment + + + align:start position:0% +terminating in the lowest final segment +where they go okay the animals with the + + align:start position:0% +where they go okay the animals with the + + + align:start position:0% +where they go okay the animals with the +greatest dexterity this group here are + + align:start position:0% +greatest dexterity this group here are + + + align:start position:0% +greatest dexterity this group here are +the ones that have the most penetration + + align:start position:0% +the ones that have the most penetration + + + align:start position:0% +the ones that have the most penetration +in the + + align:start position:0% +in the + + + align:start position:0% +in the +court and in + + align:start position:0% +court and in + + + align:start position:0% +court and in +general the larger the cortex + + align:start position:0% + + + + align:start position:0% + +is as the cortex grows it becomes not + + align:start position:0% +is as the cortex grows it becomes not + + + align:start position:0% +is as the cortex grows it becomes not +just bigger + + align:start position:0% +just bigger + + + align:start position:0% +just bigger +has it does the spinal cord doesn't grow + + align:start position:0% +has it does the spinal cord doesn't grow + + + align:start position:0% +has it does the spinal cord doesn't grow +at the same + + align:start position:0% +at the same + + + align:start position:0% +at the same +rate so the + + align:start position:0% +rate so the + + + align:start position:0% +rate so the +cord the neocortex is relatively much + + align:start position:0% +cord the neocortex is relatively much + + + align:start position:0% +cord the neocortex is relatively much +larger than the cord in these animals + + align:start position:0% +larger than the cord in these animals + + + align:start position:0% +larger than the cord in these animals +with the highest + + align:start position:0% +with the highest + + + align:start position:0% +with the highest +dexterity okay with + + align:start position:0% +dexterity okay with + + + align:start position:0% +dexterity okay with +humans having the greatest relative + + align:start position:0% +humans having the greatest relative + + + align:start position:0% +humans having the greatest relative +size of the + + align:start position:0% +size of the + + + align:start position:0% +size of the +neocortex and what do we call that rule + + align:start position:0% +neocortex and what do we call that rule + + + align:start position:0% +neocortex and what do we call that rule +that the larger a structure the more + + align:start position:0% +that the larger a structure the more + + + align:start position:0% +that the larger a structure the more +connected it is + + align:start position:0% +connected it is + + + align:start position:0% +connected it is +is it was first enunciated by Deacon so + + align:start position:0% +is it was first enunciated by Deacon so + + + align:start position:0% +is it was first enunciated by Deacon so +we call it deon's rule it's a general + + align:start position:0% +we call it deon's rule it's a general + + + align:start position:0% +we call it deon's rule it's a general +rule in compare in comparative + + align:start position:0% +rule in compare in comparative + + + align:start position:0% +rule in compare in comparative +neurology that when a structure grows + + align:start position:0% +neurology that when a structure grows + + + align:start position:0% +neurology that when a structure grows +really big it has more connections so + + align:start position:0% +really big it has more connections so + + + align:start position:0% +really big it has more connections so +similarly the optic tectum becomes very + + align:start position:0% +similarly the optic tectum becomes very + + + align:start position:0% +similarly the optic tectum becomes very +big in some species and if you look in + + align:start position:0% +big in some species and if you look in + + + align:start position:0% +big in some species and if you look in +those species according to this rule + + align:start position:0% +those species according to this rule + + + align:start position:0% +those species according to this rule +you're going to find more connections so + + align:start position:0% +you're going to find more connections so + + + align:start position:0% +you're going to find more connections so +when the tectum grew very big you have + + align:start position:0% +when the tectum grew very big you have + + + align:start position:0% +when the tectum grew very big you have +more projections even to the thalamus + + align:start position:0% +more projections even to the thalamus + + + align:start position:0% +more projections even to the thalamus +you know from the tectum and to the core + + align:start position:0% + + + + align:start position:0% + +yes yeah there are there are some + + align:start position:0% +yes yeah there are there are some + + + align:start position:0% +yes yeah there are there are some +exceptions but it's it's been looked at + + align:start position:0% +exceptions but it's it's been looked at + + + align:start position:0% +exceptions but it's it's been looked at +in for it's it's not been looked at for + + align:start position:0% +in for it's it's not been looked at for + + + align:start position:0% +in for it's it's not been looked at for +all structures you know like is it and + + align:start position:0% +all structures you know like is it and + + + align:start position:0% +all structures you know like is it and +it it seems to hold when the differences + + align:start position:0% +it it seems to hold when the differences + + + align:start position:0% +it it seems to hold when the differences +in size are very big now when they're + + align:start position:0% +in size are very big now when they're + + + align:start position:0% +in size are very big now when they're +not so big it's not a perfect + + align:start position:0% +not so big it's not a perfect + + + align:start position:0% +not so big it's not a perfect +correlation all right good + + align:start position:0% +correlation all right good + + + align:start position:0% +correlation all right good +question and this just shows various + + align:start position:0% +question and this just shows various + + + align:start position:0% +question and this just shows various +studies I've just included a bunch of + + align:start position:0% +studies I've just included a bunch of + + + align:start position:0% +studies I've just included a bunch of +them here where they're + + align:start position:0% +them here where they're + + + align:start position:0% +them here where they're +showing where the corticospinal neurons + + align:start position:0% +showing where the corticospinal neurons + + + align:start position:0% +showing where the corticospinal neurons +are in the cortex they're + + align:start position:0% +are in the cortex they're + + + align:start position:0% +are in the cortex they're +basically + + align:start position:0% +basically + + + align:start position:0% +basically +in the motor areas and the ca sensory + + align:start position:0% +in the motor areas and the ca sensory + + + align:start position:0% +in the motor areas and the ca sensory +areas both okay ca sensory areas tend + + align:start position:0% +areas both okay ca sensory areas tend + + + align:start position:0% +areas both okay ca sensory areas tend +not to project to the motor neurons they + + align:start position:0% +not to project to the motor neurons they + + + align:start position:0% +not to project to the motor neurons they +project to the dorsal horn and the motor + + align:start position:0% +project to the dorsal horn and the motor + + + align:start position:0% +project to the dorsal horn and the motor +areas project more to the ventral horn + + align:start position:0% +areas project more to the ventral horn + + + align:start position:0% +areas project more to the ventral horn +than intermediate layers of the + + align:start position:0% + + + + align:start position:0% + +cord it looks like animals like Reese's + + align:start position:0% +cord it looks like animals like Reese's + + + align:start position:0% +cord it looks like animals like Reese's +monkey here have more but that's look at + + align:start position:0% +monkey here have more but that's look at + + + align:start position:0% +monkey here have more but that's look at +the + + align:start position:0% +the + + + align:start position:0% +the +scale here the smaller + + align:start position:0% +scale here the smaller + + + align:start position:0% +scale here the smaller +animals they all represent 1 + + align:start position:0% +animals they all represent 1 + + + align:start position:0% +animals they all represent 1 +cm so to really + + align:start position:0% +cm so to really + + + align:start position:0% +cm so to really +compare the rees's monkey here with one + + align:start position:0% +compare the rees's monkey here with one + + + align:start position:0% +compare the rees's monkey here with one +of these you would have to blow this up + + align:start position:0% +of these you would have to blow this up + + + align:start position:0% +of these you would have to blow this up +so the brain was bigger than the page + + align:start position:0% +so the brain was bigger than the page + + + align:start position:0% +so the brain was bigger than the page +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +because to make the scale + + align:start position:0% +because to make the scale + + + align:start position:0% +because to make the scale +match so you can't really see any + + align:start position:0% +match so you can't really see any + + + align:start position:0% +match so you can't really see any +indication of Deacon + + align:start position:0% +indication of Deacon + + + align:start position:0% +indication of Deacon +rule but in fact then if you measure if + + align:start position:0% +rule but in fact then if you measure if + + + align:start position:0% +rule but in fact then if you measure if +you count number of cortical spinal + + align:start position:0% +you count number of cortical spinal + + + align:start position:0% +you count number of cortical spinal +neurons it's very strongly correlated + + align:start position:0% +neurons it's very strongly correlated + + + align:start position:0% +neurons it's very strongly correlated +with the total size of the + + align:start position:0% +with the total size of the + + + align:start position:0% +with the total size of the +neocortex + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% + + + + align:start position:0% + +I have a figure in the book that I + + align:start position:0% +I have a figure in the book that I + + + align:start position:0% +I have a figure in the book that I +didn't put in these slides but it's + + align:start position:0% +didn't put in these slides but it's + + + align:start position:0% +didn't put in these slides but it's +fairly recent work that shows that + + align:start position:0% +fairly recent work that shows that + + + align:start position:0% +fairly recent work that shows that +there's really two separate motor + + align:start position:0% +there's really two separate motor + + + align:start position:0% +there's really two separate motor +regions in the motor + + align:start position:0% +regions in the motor + + + align:start position:0% +regions in the motor +CeX they say the more coddle region is + + align:start position:0% +CeX they say the more coddle region is + + + align:start position:0% +CeX they say the more coddle region is +newer how is it different from the older + + align:start position:0% +newer how is it different from the older + + + align:start position:0% +newer how is it different from the older +regions they're both motor cortex and + + align:start position:0% +regions they're both motor cortex and + + + align:start position:0% +regions they're both motor cortex and +you can stimulate both areas and get + + align:start position:0% +you can stimulate both areas and get + + + align:start position:0% +you can stimulate both areas and get +movement of the same body parts so + + align:start position:0% +movement of the same body parts so + + + align:start position:0% +movement of the same body parts so +what's + + align:start position:0% + + + + align:start position:0% + +different did you read + + align:start position:0% +different did you read + + + align:start position:0% +different did you read +it you got to read it if you expect to + + align:start position:0% +it you got to read it if you expect to + + + align:start position:0% +it you got to read it if you expect to +do + + align:start position:0% + + + + align:start position:0% + +well you got to read it more than once + + align:start position:0% +well you got to read it more than once + + + align:start position:0% +well you got to read it more than once +actually what's the difference the + + align:start position:0% +actually what's the difference the + + + align:start position:0% +actually what's the difference the +difference is does the area contain + + align:start position:0% +difference is does the area contain + + + align:start position:0% +difference is does the area contain +neurons that project direct to motor + + align:start position:0% +neurons that project direct to motor + + + align:start position:0% +neurons that project direct to motor +neurons rather than just to the inter + + align:start position:0% +neurons rather than just to the inter + + + align:start position:0% +neurons rather than just to the inter +neurons remember I said the dominant + + align:start position:0% +neurons remember I said the dominant + + + align:start position:0% +neurons remember I said the dominant +connection to the cord isn't directly to + + align:start position:0% +connection to the cord isn't directly to + + + align:start position:0% +connection to the cord isn't directly to +motor neurons even for motor + + align:start position:0% +motor neurons even for motor + + + align:start position:0% +motor neurons even for motor +cortex the dominant connection is to the + + align:start position:0% +cortex the dominant connection is to the + + + align:start position:0% +cortex the dominant connection is to the +inter Nur that connect to the motor + + align:start position:0% +inter Nur that connect to the motor + + + align:start position:0% +inter Nur that connect to the motor +neurons okay but there is an area it's + + align:start position:0% +neurons okay but there is an area it's + + + align:start position:0% +neurons okay but there is an area it's +the more coddle + + align:start position:0% +the more coddle + + + align:start position:0% +the more coddle +area + + align:start position:0% +area + + + align:start position:0% +area +okay in the motor the strip of motor + + align:start position:0% +okay in the motor the strip of motor + + + align:start position:0% +okay in the motor the strip of motor +cortex we're talking + + align:start position:0% +cortex we're talking + + + align:start position:0% +cortex we're talking +about this strip here there you see it + + align:start position:0% +about this strip here there you see it + + + align:start position:0% +about this strip here there you see it +in the + + align:start position:0% + + + + align:start position:0% + +so you don't see any indication of that + + align:start position:0% +so you don't see any indication of that + + + align:start position:0% +so you don't see any indication of that +in these + + align:start position:0% +in these + + + align:start position:0% +in these +pictures like in the maret + + align:start position:0% +pictures like in the maret + + + align:start position:0% +pictures like in the maret +here but this would this would be a CET + + align:start position:0% +here but this would this would be a CET + + + align:start position:0% +here but this would this would be a CET +sensory area this would be the motor + + align:start position:0% +sensory area this would be the motor + + + align:start position:0% +sensory area this would be the motor +area there's a more rostal area and a + + align:start position:0% +area there's a more rostal area and a + + + align:start position:0% +area there's a more rostal area and a +more codal area Okay the more coddle + + align:start position:0% +more codal area Okay the more coddle + + + align:start position:0% +more codal area Okay the more coddle +area would contain the ones direct to + + align:start position:0% +area would contain the ones direct to + + + align:start position:0% +area would contain the ones direct to +the motor + + align:start position:0% +the motor + + + align:start position:0% +the motor +neurons and that will vary a bit in size + + align:start position:0% +neurons and that will vary a bit in size + + + align:start position:0% +neurons and that will vary a bit in size +in different species + + align:start position:0% + + + + align:start position:0% + +okay these are maps of that show all of + + align:start position:0% +okay these are maps of that show all of + + + align:start position:0% +okay these are maps of that show all of +the + + align:start position:0% +the + + + align:start position:0% +the +neurons but so like I mean so they're + + align:start position:0% +neurons but so like I mean so they're + + + align:start position:0% +neurons but so like I mean so they're +like that's rodents and everything else + + align:start position:0% +like that's rodents and everything else + + + align:start position:0% +like that's rodents and everything else +not or it just yeah the there aren't so + + align:start position:0% +not or it just yeah the there aren't so + + + align:start position:0% +not or it just yeah the there aren't so +many studies that can really that have + + align:start position:0% +many studies that can really that have + + + align:start position:0% +many studies that can really that have +mapped exactly how many neurons there + + align:start position:0% +mapped exactly how many neurons there + + + align:start position:0% +mapped exactly how many neurons there +it's not easy to study you see when you + + align:start position:0% +it's not easy to study you see when you + + + align:start position:0% +it's not easy to study you see when you +just study projections you know you can + + align:start position:0% +just study projections you know you can + + + align:start position:0% +just study projections you know you can +look to see if there are accents that + + align:start position:0% +look to see if there are accents that + + + align:start position:0% +look to see if there are accents that +appear to be right in the motor neuron + + align:start position:0% +appear to be right in the motor neuron + + + align:start position:0% +appear to be right in the motor neuron +area and that's about the only way we + + align:start position:0% +area and that's about the only way we + + + align:start position:0% +area and that's about the only way we +have of mapping it and you do find them + + align:start position:0% +have of mapping it and you do find them + + + align:start position:0% +have of mapping it and you do find them +even in in all these + + align:start position:0% + + + + align:start position:0% + +species all right uh but there is it + + align:start position:0% +species all right uh but there is it + + + align:start position:0% +species all right uh but there is it +there's appears to be a lot more of them + + align:start position:0% +there's appears to be a lot more of them + + + align:start position:0% +there's appears to be a lot more of them +in the in the large + + align:start position:0% +in the in the large + + + align:start position:0% +in the in the large +primat okay uh I have a last question + + align:start position:0% +primat okay uh I have a last question + + + align:start position:0% +primat okay uh I have a last question +here does anybody want to try to answer + + align:start position:0% +here does anybody want to try to answer + + + align:start position:0% +here does anybody want to try to answer +it what's the highest level of motor + + align:start position:0% + + + + align:start position:0% + +control to answer it you've got to + + align:start position:0% +control to answer it you've got to + + + align:start position:0% +control to answer it you've got to +Define what you mean by + + align:start position:0% +Define what you mean by + + + align:start position:0% +Define what you mean by +higher perhaps the more interesting + + align:start position:0% +higher perhaps the more interesting + + + align:start position:0% +higher perhaps the more interesting +question is one uh that's certainly an + + align:start position:0% +question is one uh that's certainly an + + + align:start position:0% +question is one uh that's certainly an +interesting question does movement began + + align:start position:0% +interesting question does movement began + + + align:start position:0% +interesting question does movement began +with activity in the motor + + align:start position:0% +with activity in the motor + + + align:start position:0% +with activity in the motor +cortex probably not right what makes us + + align:start position:0% +cortex probably not right what makes us + + + align:start position:0% +cortex probably not right what makes us +want to + + align:start position:0% +want to + + + align:start position:0% +want to +move some motivation + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +okay that's one way you could start and + + align:start position:0% +okay that's one way you could start and + + + align:start position:0% +okay that's one way you could start and +you so where would you find endogenous + + align:start position:0% + + + + align:start position:0% + +activity where would you find activity + + align:start position:0% +activity where would you find activity + + + align:start position:0% +activity where would you find activity +that's varying over + + align:start position:0% +that's varying over + + + align:start position:0% +that's varying over +time that's not originating outside the + + align:start position:0% + + + + align:start position:0% + +organism + + align:start position:0% +organism + + + align:start position:0% +organism +anybody probably the activity that + + align:start position:0% +anybody probably the activity that + + + align:start position:0% +anybody probably the activity that +corresponds to changing changing + + align:start position:0% +corresponds to changing changing + + + align:start position:0% +corresponds to changing changing +activity with changing motivational + + align:start position:0% +activity with changing motivational + + + align:start position:0% +activity with changing motivational +levels okay yes we do get a little + + align:start position:0% +levels okay yes we do get a little + + + align:start position:0% +levels okay yes we do get a little +hungrier when we see good food that's + + align:start position:0% +hungrier when we see good food that's + + + align:start position:0% +hungrier when we see good food that's +true that's a sensory effect but we also + + align:start position:0% +true that's a sensory effect but we also + + + align:start position:0% +true that's a sensory effect but we also +get hungrier just because we haven't + + align:start position:0% +get hungrier just because we haven't + + + align:start position:0% +get hungrier just because we haven't +eaten for a long time that comes from + + align:start position:0% +eaten for a long time that comes from + + + align:start position:0% +eaten for a long time that comes from +internal stimula within our bodies so in + + align:start position:0% +internal stimula within our bodies so in + + + align:start position:0% +internal stimula within our bodies so in +a sense it's endogenous to the organism + + align:start position:0% +a sense it's endogenous to the organism + + + align:start position:0% +a sense it's endogenous to the organism +okay it doesn't mean there's no stimuli + + align:start position:0% +okay it doesn't mean there's no stimuli + + + align:start position:0% +okay it doesn't mean there's no stimuli +it's coming from somewhere okay + + align:start position:0% + + + + align:start position:0% + +so I answer the question + + align:start position:0% + + + + align:start position:0% + +here I asked that last question why is + + align:start position:0% +here I asked that last question why is + + + align:start position:0% +here I asked that last question why is +motor cortex become so dominant in + + align:start position:0% +motor cortex become so dominant in + + + align:start position:0% +motor cortex become so dominant in +humans and in monkeys and + + align:start position:0% +humans and in monkeys and + + + align:start position:0% +humans and in monkeys and +AES I don't think it's only because of + + align:start position:0% +AES I don't think it's only because of + + + align:start position:0% +AES I don't think it's only because of +the stotal connections I don't and all + + align:start position:0% +the stotal connections I don't and all + + + align:start position:0% +the stotal connections I don't and all +of these areas project heavily to the + + align:start position:0% +of these areas project heavily to the + + + align:start position:0% +of these areas project heavily to the +Corpus + + align:start position:0% +Corpus + + + align:start position:0% +Corpus +trium important for learning of + + align:start position:0% +trium important for learning of + + + align:start position:0% +trium important for learning of +habits I don't think it's because of the + + align:start position:0% +habits I don't think it's because of the + + + align:start position:0% +habits I don't think it's because of the +direct projections to motor neurons + + align:start position:0% +direct projections to motor neurons + + + align:start position:0% +direct projections to motor neurons +either I think it's because of its close + + align:start position:0% +either I think it's because of its close + + + align:start position:0% +either I think it's because of its close +connections from the prefrontal areas of + + align:start position:0% + + + + align:start position:0% + +Cortex + + align:start position:0% +Cortex + + + align:start position:0% +Cortex +that contains neurons whose firing is + + align:start position:0% +that contains neurons whose firing is + + + align:start position:0% +that contains neurons whose firing is +anticipating what's about to happen so + + align:start position:0% +anticipating what's about to happen so + + + align:start position:0% +anticipating what's about to happen so +in the frontal eye Fields there part of + + align:start position:0% +in the frontal eye Fields there part of + + + align:start position:0% +in the frontal eye Fields there part of +the prefrontal cortex AAL part the + + align:start position:0% +the prefrontal cortex AAL part the + + + align:start position:0% +the prefrontal cortex AAL part the +prefrontal cortex you have neurons that + + align:start position:0% +prefrontal cortex you have neurons that + + + align:start position:0% +prefrontal cortex you have neurons that +fire in anticipation of where you expect + + align:start position:0% +fire in anticipation of where you expect + + + align:start position:0% +fire in anticipation of where you expect +something to be so we move we say we + + align:start position:0% +something to be so we move we say we + + + align:start position:0% +something to be so we move we say we +well I move voluntarily to there well + + align:start position:0% +well I move voluntarily to there well + + + align:start position:0% +well I move voluntarily to there well +you were expecting something there so + + align:start position:0% +you were expecting something there so + + + align:start position:0% +you were expecting something there so +you move your eyes + + align:start position:0% +you move your eyes + + + align:start position:0% +you move your eyes +there we call it + + align:start position:0% +there we call it + + + align:start position:0% +there we call it +voluntary okay that reaches that kind of + + align:start position:0% +voluntary okay that reaches that kind of + + + align:start position:0% +voluntary okay that reaches that kind of +activity from various parts of the + + align:start position:0% +activity from various parts of the + + + align:start position:0% +activity from various parts of the +prefrontal cortex reaches motor + + align:start position:0% +prefrontal cortex reaches motor + + + align:start position:0% +prefrontal cortex reaches motor +cortex that's how it exerts its + + align:start position:0% +cortex that's how it exerts its + + + align:start position:0% +cortex that's how it exerts its +influence the prefrontal cortex does not + + align:start position:0% +influence the prefrontal cortex does not + + + align:start position:0% +influence the prefrontal cortex does not +project directly to the spinal cord and + + align:start position:0% +project directly to the spinal cord and + + + align:start position:0% +project directly to the spinal cord and +control these movements it goes through + + align:start position:0% +control these movements it goes through + + + align:start position:0% +control these movements it goes through +motor cortex and I think one reason the + + align:start position:0% +motor cortex and I think one reason the + + + align:start position:0% +motor cortex and I think one reason the +motor cortex became so dominant is + + align:start position:0% +motor cortex became so dominant is + + + align:start position:0% +motor cortex became so dominant is +because it's getting that input from the + + align:start position:0% +because it's getting that input from the + + + align:start position:0% +because it's getting that input from the +prefrontal areas and it's most dominant + + align:start position:0% +prefrontal areas and it's most dominant + + + align:start position:0% +prefrontal areas and it's most dominant +in the animals with the larger + + align:start position:0% +in the animals with the larger + + + align:start position:0% +in the animals with the larger +prefrontal cortex + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +it's hard to call them motor deficits + + align:start position:0% +it's hard to call them motor deficits + + + align:start position:0% +it's hard to call them motor deficits +but you have incredible changes in the + + align:start position:0% +but you have incredible changes in the + + + align:start position:0% +but you have incredible changes in the +way they + + align:start position:0% + + + + align:start position:0% + +behave probably the most dramatic are + + align:start position:0% +behave probably the most dramatic are + + + align:start position:0% +behave probably the most dramatic are +they lose normal + + align:start position:0% +they lose normal + + + align:start position:0% +they lose normal +inhibitions they it's almost like a + + align:start position:0% +inhibitions they it's almost like a + + + align:start position:0% +inhibitions they it's almost like a +release of AC because there are other + + align:start position:0% +release of AC because there are other + + + align:start position:0% +release of AC because there are other +influences too on motor + + align:start position:0% +influences too on motor + + + align:start position:0% +influences too on motor +cortex and mo movement doesn't all go + + align:start position:0% +cortex and mo movement doesn't all go + + + align:start position:0% +cortex and mo movement doesn't all go +through motor cortex but what we call + + align:start position:0% +through motor cortex but what we call + + + align:start position:0% +through motor cortex but what we call +voluntary movement does go through motor + + align:start position:0% +voluntary movement does go through motor + + + align:start position:0% +voluntary movement does go through motor +cortex it doesn't originate + + align:start position:0% +cortex it doesn't originate + + + align:start position:0% +cortex it doesn't originate +there it originates usually in the lyic + + align:start position:0% +there it originates usually in the lyic + + + align:start position:0% +there it originates usually in the lyic +system but it's these association areas + + align:start position:0% +system but it's these association areas + + + align:start position:0% +system but it's these association areas +that include the prefrontal areas + + align:start position:0% +that include the prefrontal areas + + + align:start position:0% +that include the prefrontal areas +prefrontal association areas that seem + + align:start position:0% +prefrontal association areas that seem + + + align:start position:0% +prefrontal association areas that seem +to be where expected things control our + + align:start position:0% +to be where expected things control our + + + align:start position:0% +to be where expected things control our +movements all right let's + + align:start position:0% +movements all right let's + + + align:start position:0% +movements all right let's +uh say a little bit about temporal + + align:start position:0% +uh say a little bit about temporal + + + align:start position:0% +uh say a little bit about temporal +patterns and about brain States if we + + align:start position:0% +patterns and about brain States if we + + + align:start position:0% +patterns and about brain States if we +don't have time we can say a little bit + + align:start position:0% +don't have time we can say a little bit + + + align:start position:0% +don't have time we can say a little bit +about brain States on Monday but I'm + + align:start position:0% +about brain States on Monday but I'm + + + align:start position:0% +about brain States on Monday but I'm +going to spend a lot of that hour just + + align:start position:0% +going to spend a lot of that hour just + + + align:start position:0% +going to spend a lot of that hour just +reviewing to help you get ready for the + + align:start position:0% +reviewing to help you get ready for the + + + align:start position:0% +reviewing to help you get ready for the +midterm but let's just talk briefly + + align:start position:0% +midterm but let's just talk briefly + + + align:start position:0% +midterm but let's just talk briefly +about temporal patterns and this is an + + align:start position:0% +about temporal patterns and this is an + + + align:start position:0% +about temporal patterns and this is an +interesting area + + align:start position:0% + + + + align:start position:0% + +because the explanations have been + + align:start position:0% +because the explanations have been + + + align:start position:0% +because the explanations have been +generated as much from Theory as from + + align:start position:0% +generated as much from Theory as from + + + align:start position:0% +generated as much from Theory as from +actual experiments there are experiments + + align:start position:0% +actual experiments there are experiments + + + align:start position:0% +actual experiments there are experiments +Rel + + align:start position:0% +Rel + + + align:start position:0% +Rel +uh related to + + align:start position:0% +uh related to + + + align:start position:0% +uh related to +this + + align:start position:0% +this + + + align:start position:0% +this +uh we usually start by talking about + + align:start position:0% +uh we usually start by talking about + + + align:start position:0% +uh we usually start by talking about +rhythmic output and timing the simplest + + align:start position:0% +rhythmic output and timing the simplest + + + align:start position:0% +rhythmic output and timing the simplest +kind of temporal pattern is a rhythmic + + align:start position:0% +kind of temporal pattern is a rhythmic + + + align:start position:0% +kind of temporal pattern is a rhythmic +pattern uh and there are various ways + + align:start position:0% +pattern uh and there are various ways + + + align:start position:0% +pattern uh and there are various ways +that we can talk about how P Temple + + align:start position:0% +that we can talk about how P Temple + + + align:start position:0% +that we can talk about how P Temple +patterns are generated we can talk just + + align:start position:0% +patterns are generated we can talk just + + + align:start position:0% +patterns are generated we can talk just +about reflex types of connections that + + align:start position:0% +about reflex types of connections that + + + align:start position:0% +about reflex types of connections that +go from input to Output so the Rhythm + + align:start position:0% +go from input to Output so the Rhythm + + + align:start position:0% +go from input to Output so the Rhythm +depends on the in the + + align:start position:0% + + + + align:start position:0% + +inputs and on the timing of those + + align:start position:0% +inputs and on the timing of those + + + align:start position:0% +inputs and on the timing of those +Pathways it takes time + + align:start position:0% +Pathways it takes time + + + align:start position:0% +Pathways it takes time +for input to travel activity to travel + + align:start position:0% +for input to travel activity to travel + + + align:start position:0% +for input to travel activity to travel +through the central nervous + + align:start position:0% +through the central nervous + + + align:start position:0% +through the central nervous +system and then of course you can have + + align:start position:0% +system and then of course you can have + + + align:start position:0% +system and then of course you can have +feedback connections of various sorts + + align:start position:0% +feedback connections of various sorts + + + align:start position:0% +feedback connections of various sorts +that will generate temporal patterns and + + align:start position:0% +that will generate temporal patterns and + + + align:start position:0% +that will generate temporal patterns and +you can also have endogenous activity + + align:start position:0% +you can also have endogenous activity + + + align:start position:0% +you can also have endogenous activity +activity + + align:start position:0% +activity + + + align:start position:0% +activity +originating in the nervous system and + + align:start position:0% +originating in the nervous system and + + + align:start position:0% +originating in the nervous system and +even in single + + align:start position:0% +even in single + + + align:start position:0% +even in single +cells + + align:start position:0% +cells + + + align:start position:0% +cells +uh so first of all how can how can the + + align:start position:0% +uh so first of all how can how can the + + + align:start position:0% +uh so first of all how can how can the +concept of + + align:start position:0% +concept of + + + align:start position:0% +concept of +reflexes or more generally stimulus + + align:start position:0% +reflexes or more generally stimulus + + + align:start position:0% +reflexes or more generally stimulus +response + + align:start position:0% +response + + + align:start position:0% +response +connections of the sort that underlies + + align:start position:0% +connections of the sort that underlies + + + align:start position:0% +connections of the sort that underlies +fixed action patterns innate behavior be + + align:start position:0% +fixed action patterns innate behavior be + + + align:start position:0% +fixed action patterns innate behavior be +used to + + align:start position:0% +used to + + + align:start position:0% +used to +explain sequences that are longer than a + + align:start position:0% +explain sequences that are longer than a + + + align:start position:0% +explain sequences that are longer than a +single refle + + align:start position:0% + + + + align:start position:0% + +if we start with + + align:start position:0% +if we start with + + + align:start position:0% +if we start with +just a single + + align:start position:0% +just a single + + + align:start position:0% +just a single +reflex then we're we have to talk about + + align:start position:0% +reflex then we're we have to talk about + + + align:start position:0% +reflex then we're we have to talk about +conduction time various things that + + align:start position:0% +conduction time various things that + + + align:start position:0% +conduction time various things that +affect conduction + + align:start position:0% +affect conduction + + + align:start position:0% +affect conduction +time if we talk about beyond the single + + align:start position:0% +time if we talk about beyond the single + + + align:start position:0% +time if we talk about beyond the single +reflex then the only way we can use that + + align:start position:0% +reflex then the only way we can use that + + + align:start position:0% +reflex then the only way we can use that +model is to talk about some kind of + + align:start position:0% +model is to talk about some kind of + + + align:start position:0% +model is to talk about some kind of +chaining so let's start by that and uh I + + align:start position:0% +chaining so let's start by that and uh I + + + align:start position:0% +chaining so let's start by that and uh I +mentioned the startle reflex there's a a + + align:start position:0% +mentioned the startle reflex there's a a + + + align:start position:0% +mentioned the startle reflex there's a a +very loud + + align:start position:0% +very loud + + + align:start position:0% +very loud +noise louder than I could produce here + + align:start position:0% +noise louder than I could produce here + + + align:start position:0% +noise louder than I could produce here +CU I don't have a good amplifier + + align:start position:0% +CU I don't have a good amplifier + + + align:start position:0% +CU I don't have a good amplifier +here you get this sequence of movements + + align:start position:0% +here you get this sequence of movements + + + align:start position:0% +here you get this sequence of movements +that are always the same the eyes blink + + align:start position:0% +that are always the same the eyes blink + + + align:start position:0% +that are always the same the eyes blink +first and then you get contraction of + + align:start position:0% +first and then you get contraction of + + + align:start position:0% +first and then you get contraction of +other facial + + align:start position:0% +other facial + + + align:start position:0% +other facial +muscles then you get neck flexion then + + align:start position:0% +muscles then you get neck flexion then + + + align:start position:0% +muscles then you get neck flexion then +you get arm flexion you see this in + + align:start position:0% +you get arm flexion you see this in + + + align:start position:0% +you get arm flexion you see this in +around explosions okay and with the loud + + align:start position:0% +around explosions okay and with the loud + + + align:start position:0% +around explosions okay and with the loud +EXP expion you even get leg flexion okay + + align:start position:0% +EXP expion you even get leg flexion okay + + + align:start position:0% +EXP expion you even get leg flexion okay +but it's always in that + + align:start position:0% +but it's always in that + + + align:start position:0% +but it's always in that +sequence and you can explain that + + align:start position:0% +sequence and you can explain that + + + align:start position:0% +sequence and you can explain that +timing by the length of Pathways the + + align:start position:0% +timing by the length of Pathways the + + + align:start position:0% +timing by the length of Pathways the +fiber size which makes changes + + align:start position:0% +fiber size which makes changes + + + align:start position:0% +fiber size which makes changes +conduction time can explain it by + + align:start position:0% +conduction time can explain it by + + + align:start position:0% +conduction time can explain it by +synaptic blaze in the pathway you can + + align:start position:0% +synaptic blaze in the pathway you can + + + align:start position:0% +synaptic blaze in the pathway you can +explain it by temporal summation + + align:start position:0% + + + + align:start position:0% + +TS okay and uh staral reflex has been a + + align:start position:0% +TS okay and uh staral reflex has been a + + + align:start position:0% +TS okay and uh staral reflex has been a +reflex that's been studied in this way + + align:start position:0% +reflex that's been studied in this way + + + align:start position:0% +reflex that's been studied in this way +and they you get this you can explain it + + align:start position:0% +and they you get this you can explain it + + + align:start position:0% +and they you get this you can explain it +just in terms of these timing through + + align:start position:0% +just in terms of these timing through + + + align:start position:0% +just in terms of these timing through +the stimulus to response + + align:start position:0% + + + + align:start position:0% + +pathway but when we get to + + align:start position:0% +pathway but when we get to + + + align:start position:0% +pathway but when we get to +chaining it's been very difficult to + + align:start position:0% +chaining it's been very difficult to + + + align:start position:0% +chaining it's been very difficult to +prove there's any real chaining of + + align:start position:0% +prove there's any real chaining of + + + align:start position:0% +prove there's any real chaining of +reflexes but when it comes to fixed + + align:start position:0% +reflexes but when it comes to fixed + + + align:start position:0% +reflexes but when it comes to fixed +action patterns it's much + + align:start position:0% +action patterns it's much + + + align:start position:0% +action patterns it's much +easier so + + align:start position:0% +easier so + + + align:start position:0% +easier so +and then we'll talk about the swallowing + + align:start position:0% +and then we'll talk about the swallowing + + + align:start position:0% +and then we'll talk about the swallowing +reflex so-called swallowing reflex it + + align:start position:0% +reflex so-called swallowing reflex it + + + align:start position:0% +reflex so-called swallowing reflex it +turns out it's not a reflex in the usual + + align:start position:0% +turns out it's not a reflex in the usual + + + align:start position:0% +turns out it's not a reflex in the usual +sense I like Timber Timber's exam + + align:start position:0% +sense I like Timber Timber's exam + + + align:start position:0% +sense I like Timber Timber's exam +Timber's example of fix action patterns + + align:start position:0% +Timber's example of fix action patterns + + + align:start position:0% +Timber's example of fix action patterns +where you have a whole sequence of + + align:start position:0% +where you have a whole sequence of + + + align:start position:0% +where you have a whole sequence of +movements but it actually involves two + + align:start position:0% +movements but it actually involves two + + + align:start position:0% +movements but it actually involves two +different animals so for example starts + + align:start position:0% +different animals so for example starts + + + align:start position:0% +different animals so for example starts +with a female the female appears she's + + align:start position:0% +with a female the female appears she's + + + align:start position:0% +with a female the female appears she's +got the swollen belly which is the key + + align:start position:0% +got the swollen belly which is the key + + + align:start position:0% +got the swollen belly which is the key +stimulus for triggering the + + align:start position:0% +stimulus for triggering the + + + align:start position:0% +stimulus for triggering the +male response which is if he's in a + + align:start position:0% +male response which is if he's in a + + + align:start position:0% +male response which is if he's in a +courtship mood he will start this they + + align:start position:0% +courtship mood he will start this they + + + align:start position:0% +courtship mood he will start this they +call it the zigzag dance a particular + + align:start position:0% +call it the zigzag dance a particular + + + align:start position:0% +call it the zigzag dance a particular +way he moves to get the + + align:start position:0% +way he moves to get the + + + align:start position:0% +way he moves to get the +female to approach + + align:start position:0% +female to approach + + + align:start position:0% +female to approach +him and when she does then he swims + + align:start position:0% +him and when she does then he swims + + + align:start position:0% +him and when she does then he swims +toward his nest and she follows him so + + align:start position:0% +toward his nest and she follows him so + + + align:start position:0% +toward his nest and she follows him so +that's her next + + align:start position:0% +that's her next + + + align:start position:0% +that's her next +response she follows him and then when + + align:start position:0% +response she follows him and then when + + + align:start position:0% +response she follows him and then when +he gets to the nest he adopts a + + align:start position:0% +he gets to the nest he adopts a + + + align:start position:0% +he gets to the nest he adopts a +particular posture that causes her to + + align:start position:0% +particular posture that causes her to + + + align:start position:0% +particular posture that causes her to +enter the nest he doesn't enter it first + + align:start position:0% +enter the nest he doesn't enter it first + + + align:start position:0% +enter the nest he doesn't enter it first +he he changes his posture + + align:start position:0% +he he changes his posture + + + align:start position:0% +he he changes his posture +she enters the + + align:start position:0% +she enters the + + + align:start position:0% +she enters the +nest and then the + + align:start position:0% +nest and then the + + + align:start position:0% +nest and then the +male stimulates her very specific way he + + align:start position:0% +male stimulates her very specific way he + + + align:start position:0% +male stimulates her very specific way he +trembles puts his snout at her tail it + + align:start position:0% +trembles puts his snout at her tail it + + + align:start position:0% +trembles puts his snout at her tail it +causes her to spawn it's just an innate + + align:start position:0% +causes her to spawn it's just an innate + + + align:start position:0% +causes her to spawn it's just an innate +response and when she + + align:start position:0% +response and when she + + + align:start position:0% +response and when she +spawns + + align:start position:0% +spawns + + + align:start position:0% +spawns +actually I left out she she swims out of + + align:start position:0% +actually I left out she she swims out of + + + align:start position:0% +actually I left out she she swims out of +the + + align:start position:0% +the + + + align:start position:0% +the +nest and as she swims out of the nest + + align:start position:0% +nest and as she swims out of the nest + + + align:start position:0% +nest and as she swims out of the nest +he's right behind her but he pauses in + + align:start position:0% +he's right behind her but he pauses in + + + align:start position:0% +he's right behind her but he pauses in +the nest and fertilizes the + + align:start position:0% +the nest and fertilizes the + + + align:start position:0% +the nest and fertilizes the +eggs + + align:start position:0% +eggs + + + align:start position:0% +eggs +okay they don't have sexual intercourse + + align:start position:0% +okay they don't have sexual intercourse + + + align:start position:0% +okay they don't have sexual intercourse +this is the way they fertilize okay and + + align:start position:0% +this is the way they fertilize okay and + + + align:start position:0% +this is the way they fertilize okay and +it's a sequence of fixed action patterns + + align:start position:0% +it's a sequence of fixed action patterns + + + align:start position:0% +it's a sequence of fixed action patterns +each step is a necessary stimulus for + + align:start position:0% +each step is a necessary stimulus for + + + align:start position:0% +each step is a necessary stimulus for +triggering the next step and in the + + align:start position:0% +triggering the next step and in the + + + align:start position:0% +triggering the next step and in the +book I use that se quence of fixed + + align:start position:0% +book I use that se quence of fixed + + + align:start position:0% +book I use that se quence of fixed +action patterns + + align:start position:0% +action patterns + + + align:start position:0% +action patterns +explanation for a behavior which I've + + align:start position:0% +explanation for a behavior which I've + + + align:start position:0% +explanation for a behavior which I've +observed many times with Syrian hamsters + + align:start position:0% +observed many times with Syrian hamsters + + + align:start position:0% +observed many times with Syrian hamsters +they when they forage for food shows the + + align:start position:0% +they when they forage for food shows the + + + align:start position:0% +they when they forage for food shows the +same thing one fixed action pattern + + align:start position:0% +same thing one fixed action pattern + + + align:start position:0% +same thing one fixed action pattern +follows + + align:start position:0% +follows + + + align:start position:0% +follows +another because one fixed action pattern + + align:start position:0% +another because one fixed action pattern + + + align:start position:0% +another because one fixed action pattern +leads to a stimulus that then triggers + + align:start position:0% +leads to a stimulus that then triggers + + + align:start position:0% +leads to a stimulus that then triggers +the next fixed action pattern and so on + + align:start position:0% +the next fixed action pattern and so on + + + align:start position:0% +the next fixed action pattern and so on +and that ends with their pushing the + + align:start position:0% +and that ends with their pushing the + + + align:start position:0% +and that ends with their pushing the +seeds out of their pouch back in their + + align:start position:0% +seeds out of their pouch back in their + + + align:start position:0% +seeds out of their pouch back in their +nest area they push it onto a food + + align:start position:0% +nest area they push it onto a food + + + align:start position:0% +nest area they push it onto a food +okay + + align:start position:0% + + + + align:start position:0% + +so so then I I ask you here to name a + + align:start position:0% +so so then I I ask you here to name a + + + align:start position:0% +so so then I I ask you here to name a +movement pattern in an animal or human + + align:start position:0% +movement pattern in an animal or human + + + align:start position:0% +movement pattern in an animal or human +that's largely under the control of the + + align:start position:0% +that's largely under the control of the + + + align:start position:0% +that's largely under the control of the +hind brain and spinal cord that is + + align:start position:0% +hind brain and spinal cord that is + + + align:start position:0% +hind brain and spinal cord that is +centrally generated once it's + + align:start position:0% + + + + align:start position:0% + +trigger and I want to know how it's + + align:start position:0% +trigger and I want to know how it's + + + align:start position:0% +trigger and I want to know how it's +different from a reflex even though it + + align:start position:0% +different from a reflex even though it + + + align:start position:0% +different from a reflex even though it +might be called a reflex in clinical + + align:start position:0% + + + + align:start position:0% + +neurology like swallowing exactly we + + align:start position:0% +neurology like swallowing exactly we + + + align:start position:0% +neurology like swallowing exactly we +call it the swallowing reflex why do we + + align:start position:0% +call it the swallowing reflex why do we + + + align:start position:0% +call it the swallowing reflex why do we +call it the swallowing + + align:start position:0% +call it the swallowing + + + align:start position:0% +call it the swallowing +reflex you know how swallowing is + + align:start position:0% +reflex you know how swallowing is + + + align:start position:0% +reflex you know how swallowing is +triggered it's triggered by a you + + align:start position:0% +triggered it's triggered by a you + + + align:start position:0% +triggered it's triggered by a you +actually you think you trigger it + + align:start position:0% +actually you think you trigger it + + + align:start position:0% +actually you think you trigger it +voluntarily but you're not triggering it + + align:start position:0% +voluntarily but you're not triggering it + + + align:start position:0% +voluntarily but you're not triggering it +directly what you're doing is moving the + + align:start position:0% +directly what you're doing is moving the + + + align:start position:0% +directly what you're doing is moving the +back of your tongue so you stimulate the + + align:start position:0% +back of your tongue so you stimulate the + + + align:start position:0% +back of your tongue so you stimulate the +area behind a row of pil called the + + align:start position:0% +area behind a row of pil called the + + + align:start position:0% +area behind a row of pil called the +circumvallate pil in back of the + + align:start position:0% +circumvallate pil in back of the + + + align:start position:0% +circumvallate pil in back of the +tongue and so a doctor stimulates it if + + align:start position:0% +tongue and so a doctor stimulates it if + + + align:start position:0% +tongue and so a doctor stimulates it if +he slides a stick you can trigger it + + align:start position:0% +he slides a stick you can trigger it + + + align:start position:0% +he slides a stick you can trigger it +very easily with your finger what do you + + align:start position:0% +very easily with your finger what do you + + + align:start position:0% +very easily with your finger what do you +what do you get when as soon as you get + + align:start position:0% +what do you get when as soon as you get + + + align:start position:0% +what do you get when as soon as you get +beyond that place on your tongue you + + align:start position:0% +beyond that place on your tongue you + + + align:start position:0% +beyond that place on your tongue you +start gagging what you're doing is + + align:start position:0% +start gagging what you're doing is + + + align:start position:0% +start gagging what you're doing is +trying to swallow okay you can't swallow + + align:start position:0% +trying to swallow okay you can't swallow + + + align:start position:0% +trying to swallow okay you can't swallow +CU your fingers in your throat and + + align:start position:0% +CU your fingers in your throat and + + + align:start position:0% +CU your fingers in your throat and +similarly with a stick you know so he's + + align:start position:0% +similarly with a stick you know so he's + + + align:start position:0% +similarly with a stick you know so he's +simply triggering what he calls the + + align:start position:0% +simply triggering what he calls the + + + align:start position:0% +simply triggering what he calls the +swallowing + + align:start position:0% +swallowing + + + align:start position:0% +swallowing +reflex or the gag reflex he will call it + + align:start position:0% + + + + align:start position:0% + +okay but + + align:start position:0% + + + + align:start position:0% + +that we'll come back to the other one + + align:start position:0% +that we'll come back to the other one + + + align:start position:0% +that we'll come back to the other one +other one + + align:start position:0% +other one + + + align:start position:0% +other one +there so it's called reflex swallowing + + align:start position:0% +there so it's called reflex swallowing + + + align:start position:0% +there so it's called reflex swallowing +or reflex + + align:start position:0% +or reflex + + + align:start position:0% +or reflex +deglutition the name used in by + + align:start position:0% +deglutition the name used in by + + + align:start position:0% +deglutition the name used in by +neurologists it actually involves about + + align:start position:0% +neurologists it actually involves about + + + align:start position:0% +neurologists it actually involves about +20 muscles controlled by neurons all the + + align:start position:0% +20 muscles controlled by neurons all the + + + align:start position:0% +20 muscles controlled by neurons all the +way from the midbrain to the cervical + + align:start position:0% +way from the midbrain to the cervical + + + align:start position:0% +way from the midbrain to the cervical +spinal cord levels mostly in the + + align:start position:0% +spinal cord levels mostly in the + + + align:start position:0% +spinal cord levels mostly in the +hindbrain and upper uppermost spinal + + align:start position:0% +hindbrain and upper uppermost spinal + + + align:start position:0% +hindbrain and upper uppermost spinal +cord many experiments have been done to + + align:start position:0% +cord many experiments have been done to + + + align:start position:0% +cord many experiments have been done to +eliminate uh after one muscle contracts + + align:start position:0% +eliminate uh after one muscle contracts + + + align:start position:0% +eliminate uh after one muscle contracts +to see which stimuli that causes and you + + align:start position:0% +to see which stimuli that causes and you + + + align:start position:0% +to see which stimuli that causes and you +can eliminate all the sources of + + align:start position:0% +can eliminate all the sources of + + + align:start position:0% +can eliminate all the sources of +appropri reception you can even take out + + align:start position:0% +appropri reception you can even take out + + + align:start position:0% +appropri reception you can even take out +some of the + + align:start position:0% +some of the + + + align:start position:0% +some of the +muscles involved in the sequence of + + align:start position:0% +muscles involved in the sequence of + + + align:start position:0% +muscles involved in the sequence of +movements involved in + + align:start position:0% +movements involved in + + + align:start position:0% +movements involved in +swallowing and the pattern will continue + + align:start position:0% +swallowing and the pattern will continue + + + align:start position:0% +swallowing and the pattern will continue +exactly even when some of the elements + + align:start position:0% +exactly even when some of the elements + + + align:start position:0% +exactly even when some of the elements +are missing + + align:start position:0% + + + + align:start position:0% + +okay and those experiments show that + + align:start position:0% +okay and those experiments show that + + + align:start position:0% +okay and those experiments show that +it's centrally programmed once it's + + align:start position:0% +it's centrally programmed once it's + + + align:start position:0% +it's centrally programmed once it's +triggered by the key stimulus it's a c + + align:start position:0% +triggered by the key stimulus it's a c + + + align:start position:0% +triggered by the key stimulus it's a c +centrally programmed movement it's a + + align:start position:0% +centrally programmed movement it's a + + + align:start position:0% +centrally programmed movement it's a +fixed action pattern in the ethological + + align:start position:0% +fixed action pattern in the ethological + + + align:start position:0% +fixed action pattern in the ethological +sense it even has a motivation that + + align:start position:0% +sense it even has a motivation that + + + align:start position:0% +sense it even has a motivation that +builds up we don't pay a lot of + + align:start position:0% +builds up we don't pay a lot of + + + align:start position:0% +builds up we don't pay a lot of +attention to that but we swallow + + align:start position:0% +attention to that but we swallow + + + align:start position:0% +attention to that but we swallow +occasionally keep our throat lubricated + + align:start position:0% +occasionally keep our throat lubricated + + + align:start position:0% +occasionally keep our throat lubricated +we don't even think about it now that + + align:start position:0% +we don't even think about it now that + + + align:start position:0% +we don't even think about it now that +you're thinking about it you will + + align:start position:0% +you're thinking about it you will + + + align:start position:0% +you're thinking about it you will +probably SW + + align:start position:0% +probably SW + + + align:start position:0% +probably SW +swow I'm doing it myself okay + + align:start position:0% + + + + align:start position:0% + +uh I mention + + align:start position:0% +uh I mention + + + align:start position:0% +uh I mention +here name a movement pattern that's + + align:start position:0% +here name a movement pattern that's + + + align:start position:0% +here name a movement pattern that's +largely under the control of the spinal + + align:start position:0% +largely under the control of the spinal + + + align:start position:0% +largely under the control of the spinal +cord and completely so in many species + + align:start position:0% +cord and completely so in many species + + + align:start position:0% +cord and completely so in many species +we talked about that one + + align:start position:0% +we talked about that one + + + align:start position:0% +we talked about that one +earlier the pattern a pattern that's + + align:start position:0% +earlier the pattern a pattern that's + + + align:start position:0% +earlier the pattern a pattern that's +almost completely deter + + align:start position:0% +almost completely deter + + + align:start position:0% +almost completely deter +probably completely in the spinal + + align:start position:0% +probably completely in the spinal + + + align:start position:0% +probably completely in the spinal +cord in mammals it requires + + align:start position:0% +cord in mammals it requires + + + align:start position:0% +cord in mammals it requires +some external input to get it started or + + align:start position:0% +some external input to get it started or + + + align:start position:0% +some external input to get it started or +some input from the brain but it doesn't + + align:start position:0% +some input from the brain but it doesn't + + + align:start position:0% +some input from the brain but it doesn't +require any pattern in those + + align:start position:0% +require any pattern in those + + + align:start position:0% +require any pattern in those +inputs we're just talking about the + + align:start position:0% +inputs we're just talking about the + + + align:start position:0% +inputs we're just talking about the +movements of locomotion okay it's a + + align:start position:0% +movements of locomotion okay it's a + + + align:start position:0% +movements of locomotion okay it's a +spinal generated pattern + + align:start position:0% +spinal generated pattern + + + align:start position:0% +spinal generated pattern +okay it's again it is + + align:start position:0% +okay it's again it is + + + align:start position:0% +okay it's again it is +a it's a fixed action pattern that's + + align:start position:0% +a it's a fixed action pattern that's + + + align:start position:0% +a it's a fixed action pattern that's +wired in by our genetics okay this + + align:start position:0% +wired in by our genetics okay this + + + align:start position:0% +wired in by our genetics okay this +problem of how patterns are generated + + align:start position:0% +problem of how patterns are generated + + + align:start position:0% +problem of how patterns are generated +was what Carl Ashley called the problem + + align:start position:0% +was what Carl Ashley called the problem + + + align:start position:0% +was what Carl Ashley called the problem +of Serial order in Behavior how is a + + align:start position:0% +of Serial order in Behavior how is a + + + align:start position:0% +of Serial order in Behavior how is a +sequence an ordered sequence he used to + + align:start position:0% +sequence an ordered sequence he used to + + + align:start position:0% +sequence an ordered sequence he used to +say how do we do this you know and he + + align:start position:0% +say how do we do this you know and he + + + align:start position:0% +say how do we do this you know and he +would move his hand like this toyer used + + align:start position:0% +would move his hand like this toyer used + + + align:start position:0% +would move his hand like this toyer used +to do that + + align:start position:0% +to do that + + + align:start position:0% +to do that +how do we do + + align:start position:0% + + + + align:start position:0% + +that and he + + align:start position:0% +that and he + + + align:start position:0% +that and he +argued the key part of his argument + + align:start position:0% +argued the key part of his argument + + + align:start position:0% +argued the key part of his argument +was that many of our movements are + + align:start position:0% +was that many of our movements are + + + align:start position:0% +was that many of our movements are +simply too fast to for each movement to + + align:start position:0% +simply too fast to for each movement to + + + align:start position:0% +simply too fast to for each movement to +be separately triggered by a reflex + + align:start position:0% +be separately triggered by a reflex + + + align:start position:0% +be separately triggered by a reflex +they're too fast our our reaction times + + align:start position:0% +they're too fast our our reaction times + + + align:start position:0% +they're too fast our our reaction times +when you measure them for reflexes + + align:start position:0% +when you measure them for reflexes + + + align:start position:0% +when you measure them for reflexes +simply aren't that fast he talks about + + align:start position:0% +simply aren't that fast he talks about + + + align:start position:0% +simply aren't that fast he talks about +the finger Strokes of a m musician can + + align:start position:0% +the finger Strokes of a m musician can + + + align:start position:0% +the finger Strokes of a m musician can +reach 16 per second + + align:start position:0% + + + + align:start position:0% + +in passages which call for a definite + + align:start position:0% +in passages which call for a definite + + + align:start position:0% +in passages which call for a definite +and changing order of successive finger + + align:start position:0% +and changing order of successive finger + + + align:start position:0% +and changing order of successive finger +movements so there has to be Central + + align:start position:0% +movements so there has to be Central + + + align:start position:0% +movements so there has to be Central +generation of movements like that and + + align:start position:0% +generation of movements like that and + + + align:start position:0% +generation of movements like that and +there's now a lot of + + align:start position:0% +there's now a lot of + + + align:start position:0% +there's now a lot of +evidence for various centrally generated + + align:start position:0% +evidence for various centrally generated + + + align:start position:0% +evidence for various centrally generated +patterns like grooming in mice we + + align:start position:0% +patterns like grooming in mice we + + + align:start position:0% +patterns like grooming in mice we +mentioned last time John pentrest + + align:start position:0% +mentioned last time John pentrest + + + align:start position:0% +mentioned last time John pentrest +experiments he asked whether when the + + align:start position:0% +experiments he asked whether when the + + + align:start position:0% +experiments he asked whether when the +when the mouse starts grooming + + align:start position:0% +when the mouse starts grooming + + + align:start position:0% +when the mouse starts grooming +well he he's generating stimuli right so + + align:start position:0% +well he he's generating stimuli right so + + + align:start position:0% +well he he's generating stimuli right so +is each stimulus triggering The Next + + align:start position:0% +is each stimulus triggering The Next + + + align:start position:0% +is each stimulus triggering The Next +Movement so he did things like amputate + + align:start position:0% +Movement so he did things like amputate + + + align:start position:0% +Movement so he did things like amputate +the arm and Trigger The + + align:start position:0% +the arm and Trigger The + + + align:start position:0% +the arm and Trigger The +Grooming the mouse Grooms as if the arm + + align:start position:0% +Grooming the mouse Grooms as if the arm + + + align:start position:0% +Grooming the mouse Grooms as if the arm +were there he's not producing any + + align:start position:0% + + + + align:start position:0% + +stimuli you can get rid of any source of + + align:start position:0% +stimuli you can get rid of any source of + + + align:start position:0% +stimuli you can get rid of any source of +the stimulus and yet the movement goes + + align:start position:0% +the stimulus and yet the movement goes + + + align:start position:0% +the stimulus and yet the movement goes +off in the proper order egg rolling in + + align:start position:0% +off in the proper order egg rolling in + + + align:start position:0% +off in the proper order egg rolling in +guls it's the same way they they can + + align:start position:0% +guls it's the same way they they can + + + align:start position:0% +guls it's the same way they they can +they will roll an egg back into the + + align:start position:0% +they will roll an egg back into the + + + align:start position:0% +they will roll an egg back into the +nest remove the egg in the middle of it + + align:start position:0% +nest remove the egg in the middle of it + + + align:start position:0% +nest remove the egg in the middle of it +and he keeps doing it he just does it as + + align:start position:0% +and he keeps doing it he just does it as + + + align:start position:0% +and he keeps doing it he just does it as +if the egg were there you know we call + + align:start position:0% +if the egg were there you know we call + + + align:start position:0% +if the egg were there you know we call +those invacuo movement patterns movement + + align:start position:0% +those invacuo movement patterns movement + + + align:start position:0% +those invacuo movement patterns movement +patterns inate Behavior without any + + align:start position:0% +patterns inate Behavior without any + + + align:start position:0% +patterns inate Behavior without any +stimulus that's any normal stimulus + + align:start position:0% +stimulus that's any normal stimulus + + + align:start position:0% +stimulus that's any normal stimulus +okay and Locomotion has been studied a + + align:start position:0% +okay and Locomotion has been studied a + + + align:start position:0% +okay and Locomotion has been studied a +lot we know that the fin movements in + + align:start position:0% +lot we know that the fin movements in + + + align:start position:0% +lot we know that the fin movements in +fish are centrally generated they've + + align:start position:0% +fish are centrally generated they've + + + align:start position:0% +fish are centrally generated they've +even + + align:start position:0% +even + + + align:start position:0% +even +neurons that are generating those + + align:start position:0% +neurons that are generating those + + + align:start position:0% +neurons that are generating those +movements + + align:start position:0% +movements + + + align:start position:0% +movements +U and I mentioned Locomotion in mammals + + align:start position:0% +U and I mentioned Locomotion in mammals + + + align:start position:0% +U and I mentioned Locomotion in mammals +it does require some activation but it + + align:start position:0% +it does require some activation but it + + + align:start position:0% +it does require some activation but it +doesn't require patterned + + align:start position:0% + + + + align:start position:0% + +Activation so how are they generated + + align:start position:0% +Activation so how are they generated + + + align:start position:0% +Activation so how are they generated +then if it's not by + + align:start position:0% +then if it's not by + + + align:start position:0% +then if it's not by +reflexes and there's basically two kinds + + align:start position:0% +reflexes and there's basically two kinds + + + align:start position:0% +reflexes and there's basically two kinds +of pattern either there's got to be + + align:start position:0% +of pattern either there's got to be + + + align:start position:0% +of pattern either there's got to be +feedback in neural circuits or there's + + align:start position:0% +feedback in neural circuits or there's + + + align:start position:0% +feedback in neural circuits or there's +got to be endogenous activity okay or + + align:start position:0% +got to be endogenous activity okay or + + + align:start position:0% +got to be endogenous activity okay or +they could be various combinations of + + align:start position:0% +they could be various combinations of + + + align:start position:0% +they could be various combinations of +those kinds of mechanisms those are the + + align:start position:0% +those kinds of mechanisms those are the + + + align:start position:0% +those kinds of mechanisms those are the +kinds we know about so with feedback you + + align:start position:0% +kinds we know about so with feedback you + + + align:start position:0% +kinds we know about so with feedback you +can talk about self-re exciting loops + + align:start position:0% +can talk about self-re exciting loops + + + align:start position:0% +can talk about self-re exciting loops +and I put in this little diagram just to + + align:start position:0% +and I put in this little diagram just to + + + align:start position:0% +and I put in this little diagram just to +illustrate that here we have you have + + align:start position:0% +illustrate that here we have you have + + + align:start position:0% +illustrate that here we have you have +make certain assumptions about how these + + align:start position:0% +make certain assumptions about how these + + + align:start position:0% +make certain assumptions about how these +neurons are firing simplifying + + align:start position:0% +neurons are firing simplifying + + + align:start position:0% +neurons are firing simplifying +assumptions and now you can have a + + align:start position:0% +assumptions and now you can have a + + + align:start position:0% +assumptions and now you can have a +steady input + + align:start position:0% +steady input + + + align:start position:0% +steady input +here doesn't generate any pattern output + + align:start position:0% +here doesn't generate any pattern output + + + align:start position:0% +here doesn't generate any pattern output +but with one pulse coming in from + + align:start position:0% +but with one pulse coming in from + + + align:start position:0% +but with one pulse coming in from +another source you could start the + + align:start position:0% +another source you could start the + + + align:start position:0% +another source you could start the +feedback + + align:start position:0% +feedback + + + align:start position:0% +feedback +circuit and get a the output here to be + + align:start position:0% +circuit and get a the output here to be + + + align:start position:0% +circuit and get a the output here to be +a series of + + align:start position:0% +a series of + + + align:start position:0% +a series of +pulses how would you stop it well you'd + + align:start position:0% +pulses how would you stop it well you'd + + + align:start position:0% +pulses how would you stop it well you'd +have either by fatigue or by inhibitory + + align:start position:0% +have either by fatigue or by inhibitory + + + align:start position:0% +have either by fatigue or by inhibitory +input very simple way you can have a + + align:start position:0% +input very simple way you can have a + + + align:start position:0% +input very simple way you can have a +feedback circuit generating a + + align:start position:0% +feedback circuit generating a + + + align:start position:0% +feedback circuit generating a +pattern the system that's been studied + + align:start position:0% +pattern the system that's been studied + + + align:start position:0% +pattern the system that's been studied +the most that is controlled by such + + align:start position:0% +the most that is controlled by such + + + align:start position:0% +the most that is controlled by such +circuits is breathing okay been a number + + align:start position:0% +circuits is breathing okay been a number + + + align:start position:0% +circuits is breathing okay been a number +of studies there's a guy here at MIT in + + align:start position:0% +of studies there's a guy here at MIT in + + + align:start position:0% +of studies there's a guy here at MIT in +engineering named pun that has studied + + align:start position:0% +engineering named pun that has studied + + + align:start position:0% +engineering named pun that has studied +breathing a lot it's actually pretty + + align:start position:0% +breathing a lot it's actually pretty + + + align:start position:0% +breathing a lot it's actually pretty +complex but the basic story always + + align:start position:0% +complex but the basic story always + + + align:start position:0% +complex but the basic story always +involves + + align:start position:0% +involves + + + align:start position:0% +involves +these feedback + + align:start position:0% +these feedback + + + align:start position:0% +these feedback +circuits and there's many examples in + + align:start position:0% +circuits and there's many examples in + + + align:start position:0% +circuits and there's many examples in +their anatomical studies of the brain + + align:start position:0% +their anatomical studies of the brain + + + align:start position:0% +their anatomical studies of the brain +that show these + + align:start position:0% +that show these + + + align:start position:0% +that show these +Loops anatomists love to talk about + + align:start position:0% +Loops anatomists love to talk about + + + align:start position:0% +Loops anatomists love to talk about +loops they all doesn't mean they always + + align:start position:0% +loops they all doesn't mean they always + + + align:start position:0% +loops they all doesn't mean they always +know what they do okay but there's + + align:start position:0% +know what they do okay but there's + + + align:start position:0% +know what they do okay but there's +certainly the ner nervous system is full + + align:start position:0% +certainly the ner nervous system is full + + + align:start position:0% +certainly the ner nervous system is full +of connections like this and then we + + align:start position:0% +of connections like this and then we + + + align:start position:0% +of connections like this and then we +have endogenous + + align:start position:0% +have endogenous + + + align:start position:0% +have endogenous +activity uh how can a neuron a single + + align:start position:0% +activity uh how can a neuron a single + + + align:start position:0% +activity uh how can a neuron a single +neuron generate a temporal pattern this + + align:start position:0% +neuron generate a temporal pattern this + + + align:start position:0% +neuron generate a temporal pattern this +for example is an example I I took this + + align:start position:0% +for example is an example I I took this + + + align:start position:0% +for example is an example I I took this +from Felix trost's work he studied big + + align:start position:0% +from Felix trost's work he studied big + + + align:start position:0% +from Felix trost's work he studied big +neurons in the abdominal gang of apesia + + align:start position:0% +neurons in the abdominal gang of apesia + + + align:start position:0% +neurons in the abdominal gang of apesia +because he could identify the same + + align:start position:0% +because he could identify the same + + + align:start position:0% +because he could identify the same +neuron in one animal after the other and + + align:start position:0% +neuron in one animal after the other and + + + align:start position:0% +neuron in one animal after the other and +he found that they generated r + + align:start position:0% +he found that they generated r + + + align:start position:0% +he found that they generated r +activity just + + align:start position:0% +activity just + + + align:start position:0% +activity just +the they had a membrane potential that + + align:start position:0% +the they had a membrane potential that + + + align:start position:0% +the they had a membrane potential that +oscillated even if you block the action + + align:start position:0% +oscillated even if you block the action + + + align:start position:0% +oscillated even if you block the action +potentials they still generate how does + + align:start position:0% +potentials they still generate how does + + + align:start position:0% +potentials they still generate how does +it do that what in the membrane is + + align:start position:0% +it do that what in the membrane is + + + align:start position:0% +it do that what in the membrane is +causing that they call they find + + align:start position:0% +causing that they call they find + + + align:start position:0% +causing that they call they find +specific areas in the membrane they call + + align:start position:0% +specific areas in the membrane they call + + + align:start position:0% +specific areas in the membrane they call +a pacemaker + + align:start position:0% +a pacemaker + + + align:start position:0% +a pacemaker +Locus that generates these changes + + align:start position:0% +Locus that generates these changes + + + align:start position:0% +Locus that generates these changes +particular types of molecules they use + + align:start position:0% +particular types of molecules they use + + + align:start position:0% +particular types of molecules they use +energy and they o they cause the + + align:start position:0% +energy and they o they cause the + + + align:start position:0% +energy and they o they cause the +membrane potential to oscillate and of + + align:start position:0% +membrane potential to oscillate and of + + + align:start position:0% +membrane potential to oscillate and of +course if you don't block the action + + align:start position:0% +course if you don't block the action + + + align:start position:0% +course if you don't block the action +potentials when the depolarization is + + align:start position:0% +potentials when the depolarization is + + + align:start position:0% +potentials when the depolarization is +enough you will Trigger action + + align:start position:0% +enough you will Trigger action + + + align:start position:0% +enough you will Trigger action +potentials so some of those neurons then + + align:start position:0% +potentials so some of those neurons then + + + align:start position:0% +potentials so some of those neurons then +deize enough with every cycle to + + align:start position:0% +deize enough with every cycle to + + + align:start position:0% +deize enough with every cycle to +generate Action potentials and that's + + align:start position:0% +generate Action potentials and that's + + + align:start position:0% +generate Action potentials and that's +true of some of the very slow + + align:start position:0% +true of some of the very slow + + + align:start position:0% +true of some of the very slow +oscillators are have endogenous activity + + align:start position:0% +oscillators are have endogenous activity + + + align:start position:0% +oscillators are have endogenous activity +like this like the endogenous clock + + align:start position:0% +like this like the endogenous clock + + + align:start position:0% +like this like the endogenous clock +single neurons in the supermatic nucleus + + align:start position:0% +single neurons in the supermatic nucleus + + + align:start position:0% +single neurons in the supermatic nucleus +will oscillate like this in this case + + align:start position:0% +will oscillate like this in this case + + + align:start position:0% +will oscillate like this in this case +case that in the aesia abdominal gangion + + align:start position:0% +case that in the aesia abdominal gangion + + + align:start position:0% +case that in the aesia abdominal gangion +the Rhythm was 40 + + align:start position:0% +the Rhythm was 40 + + + align:start position:0% +the Rhythm was 40 +seconds + + align:start position:0% +seconds + + + align:start position:0% +seconds +but he claims that in that neuron + + align:start position:0% +but he claims that in that neuron + + + align:start position:0% +but he claims that in that neuron +there's also circadian rhythm that + + align:start position:0% +there's also circadian rhythm that + + + align:start position:0% +there's also circadian rhythm that +changes over 24 hours I'm not convinced + + align:start position:0% +changes over 24 hours I'm not convinced + + + align:start position:0% +changes over 24 hours I'm not convinced +he recorded from them uh long enough to + + align:start position:0% +he recorded from them uh long enough to + + + align:start position:0% +he recorded from them uh long enough to +be sure about that because other things + + align:start position:0% +be sure about that because other things + + + align:start position:0% +be sure about that because other things +could have been changing but there's + + align:start position:0% +could have been changing but there's + + + align:start position:0% +could have been changing but there's +definitely good + + align:start position:0% + + + + align:start position:0% + +evidence all right that just means I + + align:start position:0% +evidence all right that just means I + + + align:start position:0% +evidence all right that just means I +have to stop + + align:start position:0% +have to stop + + + align:start position:0% +have to stop +that's your startle refle + + align:start position:0% +that's your startle refle + + + align:start position:0% +that's your startle refle +so okay yeah the startle can I'd like + + align:start position:0% +so okay yeah the startle can I'd like + + + align:start position:0% +so okay yeah the startle can I'd like +you to read the rest of this and read + + align:start position:0% +you to read the rest of this and read + + + align:start position:0% +you to read the rest of this and read +what I say about overall state of the + + align:start position:0% +what I say about overall state of the + + + align:start position:0% +what I say about overall state of the +brain and its control and we'll have a + + align:start position:0% +brain and its control and we'll have a + + + align:start position:0% +brain and its control and we'll have a +chance to discuss that a little bit on + + align:start position:0% +chance to discuss that a little bit on + + + align:start position:0% +chance to discuss that a little bit on +Monday and then we'll best spend the + + align:start position:0% +Monday and then we'll best spend the + + + align:start position:0% +Monday and then we'll best spend the +rest of the time reviewing + + align:start position:0% +rest of the time reviewing + + + align:start position:0% +rest of the time reviewing +okay \ No newline at end of file diff --git a/3PzuSPQPEU4.txt b/3PzuSPQPEU4.txt new file mode 100644 index 0000000000000000000000000000000000000000..993acea5ba588c1c5618c6e58fa2e1506c0d7052 --- /dev/null +++ b/3PzuSPQPEU4.txt @@ -0,0 +1,16819 @@ +align:start position:0% + +okay why don't i get started um + + align:start position:0% +okay why don't i get started um + + + align:start position:0% +okay why don't i get started um +so + + align:start position:0% + + + + align:start position:0% + +okay what would what have we been doing + + align:start position:0% +okay what would what have we been doing + + + align:start position:0% +okay what would what have we been doing +um so last time we considered a bunch of + + align:start position:0% +um so last time we considered a bunch of + + + align:start position:0% +um so last time we considered a bunch of +uh procedures for testing properties of + + align:start position:0% +uh procedures for testing properties of + + + align:start position:0% +uh procedures for testing properties of +various automata and grammars + + align:start position:0% +various automata and grammars + + + align:start position:0% +various automata and grammars +the acceptance problem for dfas + + align:start position:0% +the acceptance problem for dfas + + + align:start position:0% +the acceptance problem for dfas +for anaphase + + align:start position:0% + + + + align:start position:0% + +the acceptance problem which is really + + align:start position:0% +the acceptance problem which is really + + + align:start position:0% +the acceptance problem which is really +the generation problem for context-free + + align:start position:0% +the generation problem for context-free + + + align:start position:0% +the generation problem for context-free +grammars + + align:start position:0% +grammars + + + align:start position:0% +grammars +and emptiness problems for dfas and and + + align:start position:0% +and emptiness problems for dfas and and + + + align:start position:0% +and emptiness problems for dfas and and +and context-free grammars + + align:start position:0% +and context-free grammars + + + align:start position:0% +and context-free grammars +and also um + + align:start position:0% +and also um + + + align:start position:0% +and also um +we looked we we showed that atm is + + align:start position:0% +we looked we we showed that atm is + + + align:start position:0% +we looked we we showed that atm is +turning recognizable like there's a + + align:start position:0% +turning recognizable like there's a + + + align:start position:0% +turning recognizable like there's a +question here in the chat already about + + align:start position:0% +question here in the chat already about + + + align:start position:0% +question here in the chat already about +that yes we did show that that was the + + align:start position:0% +that yes we did show that that was the + + + align:start position:0% +that yes we did show that that was the +universal turing machine that we + + align:start position:0% +universal turing machine that we + + + align:start position:0% +universal turing machine that we +presented at the end that's what shows + + align:start position:0% +presented at the end that's what shows + + + align:start position:0% +presented at the end that's what shows +that atm is turning recognizable + + align:start position:0% +that atm is turning recognizable + + + align:start position:0% +that atm is turning recognizable +um + + align:start position:0% +um + + + align:start position:0% +um +we mentioned that uh it's not atm is not + + align:start position:0% +we mentioned that uh it's not atm is not + + + align:start position:0% +we mentioned that uh it's not atm is not +decidable uh which we promised we will + + align:start position:0% +decidable uh which we promised we will + + + align:start position:0% +decidable uh which we promised we will +prove today and we will do so okay so + + align:start position:0% +prove today and we will do so okay so + + + align:start position:0% +prove today and we will do so okay so +that is the plan + + align:start position:0% +that is the plan + + + align:start position:0% +that is the plan +um proving atm is undecidable + + align:start position:0% +um proving atm is undecidable + + + align:start position:0% +um proving atm is undecidable +and we'll introduce the method for doing + + align:start position:0% +and we'll introduce the method for doing + + + align:start position:0% +and we'll introduce the method for doing +that called the diagonalization method + + align:start position:0% +that called the diagonalization method + + + align:start position:0% +that called the diagonalization method +i will also show the complement of atm + + align:start position:0% +i will also show the complement of atm + + + align:start position:0% +i will also show the complement of atm +is + + align:start position:0% +is + + + align:start position:0% +is +uh turing on rec unrecognizable even + + align:start position:0% +uh turing on rec unrecognizable even + + + align:start position:0% +uh turing on rec unrecognizable even +though atm itself is recognizable the + + align:start position:0% +though atm itself is recognizable the + + + align:start position:0% +though atm itself is recognizable the +complement is not + + align:start position:0% +complement is not + + + align:start position:0% +complement is not +and + + align:start position:0% +and + + + align:start position:0% +and +then we will introduce another method + + align:start position:0% +then we will introduce another method + + + align:start position:0% +then we will introduce another method +called the reducibility method for + + align:start position:0% +called the reducibility method for + + + align:start position:0% +called the reducibility method for +showing other problems are not decidable + + align:start position:0% +showing other problems are not decidable + + + align:start position:0% +showing other problems are not decidable +and give a one example of another + + align:start position:0% +and give a one example of another + + + align:start position:0% +and give a one example of another +problem which is not decidable assuming + + align:start position:0% +problem which is not decidable assuming + + + align:start position:0% +problem which is not decidable assuming +we have time to get to it if not we will + + align:start position:0% +we have time to get to it if not we will + + + align:start position:0% +we have time to get to it if not we will +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh delay that part until uh next + + align:start position:0% +uh delay that part until uh next + + + align:start position:0% +uh delay that part until uh next +tuesday's lecture + + align:start position:0% +tuesday's lecture + + + align:start position:0% +tuesday's lecture +all right acceptance problem for uh + + align:start position:0% +all right acceptance problem for uh + + + align:start position:0% +all right acceptance problem for uh +touring machines uh so just um + + align:start position:0% +touring machines uh so just um + + + align:start position:0% +touring machines uh so just um +as i mentioned we showed that atm um + + align:start position:0% +as i mentioned we showed that atm um + + + align:start position:0% +as i mentioned we showed that atm um +which is the language of turing machines + + align:start position:0% +which is the language of turing machines + + + align:start position:0% +which is the language of turing machines +and inputs where the machine accepts the + + align:start position:0% +and inputs where the machine accepts the + + + align:start position:0% +and inputs where the machine accepts the +input + + align:start position:0% +input + + + align:start position:0% +input +um + + align:start position:0% +um + + + align:start position:0% +um +we showed that was recognizable we + + align:start position:0% +we showed that was recognizable we + + + align:start position:0% +we showed that was recognizable we +claimed it was decidable today we're + + align:start position:0% +claimed it was decidable today we're + + + align:start position:0% +claimed it was decidable today we're +going to prove it's not decidable + + align:start position:0% +going to prove it's not decidable + + + align:start position:0% +going to prove it's not decidable +all right now the method + + align:start position:0% +all right now the method + + + align:start position:0% +all right now the method +uh that + + align:start position:0% +uh that + + + align:start position:0% +uh that +uh we're going to use um which is really + + align:start position:0% +uh we're going to use um which is really + + + align:start position:0% +uh we're going to use um which is really +the only method out there um for proving + + align:start position:0% +the only method out there um for proving + + + align:start position:0% +the only method out there um for proving +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +some pro you know a problem was + + align:start position:0% +some pro you know a problem was + + + align:start position:0% +some pro you know a problem was +undecidable is the decoder + + align:start position:0% +undecidable is the decoder + + + align:start position:0% +undecidable is the decoder +diagonalization method i mean ultimately + + align:start position:0% +diagonalization method i mean ultimately + + + align:start position:0% +diagonalization method i mean ultimately +we're going to show the reducibility + + align:start position:0% +we're going to show the reducibility + + + align:start position:0% +we're going to show the reducibility +method as well but it really depends on + + align:start position:0% +method as well but it really depends on + + + align:start position:0% +method as well but it really depends on +having already shown some other problem + + align:start position:0% +having already shown some other problem + + + align:start position:0% +having already shown some other problem +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +via + + align:start position:0% +via + + + align:start position:0% +via +the diagonalization method so ultimately + + align:start position:0% +the diagonalization method so ultimately + + + align:start position:0% +the diagonalization method so ultimately +everything hinges on the diagonalization + + align:start position:0% +everything hinges on the diagonalization + + + align:start position:0% +everything hinges on the diagonalization +method which is really all we have um + + align:start position:0% +method which is really all we have um + + + align:start position:0% +method which is really all we have um +and uh so + + align:start position:0% +and uh so + + + align:start position:0% +and uh so +to + + align:start position:0% +to + + + align:start position:0% +to +uh introduce the diagonalization method + + align:start position:0% +uh introduce the diagonalization method + + + align:start position:0% +uh introduce the diagonalization method +i'm going to + + align:start position:0% +i'm going to + + + align:start position:0% +i'm going to +make a bit of a + + align:start position:0% +make a bit of a + + + align:start position:0% +make a bit of a +digression into a + + align:start position:0% +digression into a + + + align:start position:0% +digression into a +uh branch of mathematics called set + + align:start position:0% +uh branch of mathematics called set + + + align:start position:0% +uh branch of mathematics called set +theory or + + align:start position:0% +theory or + + + align:start position:0% +theory or +it's part of mathematical logic where + + align:start position:0% +it's part of mathematical logic where + + + align:start position:0% +it's part of mathematical logic where +the method of diagonalization was first + + align:start position:0% +the method of diagonalization was first + + + align:start position:0% +the method of diagonalization was first +uh + + align:start position:0% +uh + + + align:start position:0% +uh +conceived of uh back in the late 19th + + align:start position:0% +conceived of uh back in the late 19th + + + align:start position:0% +conceived of uh back in the late 19th +century by a mathematician called georg + + align:start position:0% +century by a mathematician called georg + + + align:start position:0% +century by a mathematician called georg +cantor + + align:start position:0% +cantor + + + align:start position:0% +cantor +and cantor was considering the problem + + align:start position:0% +and cantor was considering the problem + + + align:start position:0% +and cantor was considering the problem +of how do you compare + + align:start position:0% +of how do you compare + + + align:start position:0% +of how do you compare +the relative sizes of infinite sets + + align:start position:0% +the relative sizes of infinite sets + + + align:start position:0% +the relative sizes of infinite sets +you know for finite sets um + + align:start position:0% +you know for finite sets um + + + align:start position:0% +you know for finite sets um +the + + align:start position:0% +the + + + align:start position:0% +the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the problem of comparing somebody said + + align:start position:0% +the problem of comparing somebody said + + + align:start position:0% +the problem of comparing somebody said +that the cantor went crazy that is that + + align:start position:0% +that the cantor went crazy that is that + + + align:start position:0% +that the cantor went crazy that is that +is true um + + align:start position:0% +is true um + + + align:start position:0% +is true um +and maybe i i i don't know why he went + + align:start position:0% +and maybe i i i don't know why he went + + + align:start position:0% +and maybe i i i don't know why he went +crazy but + + align:start position:0% +crazy but + + + align:start position:0% +crazy but +um he um he did go uh he had some mental + + align:start position:0% +um he um he did go uh he had some mental + + + align:start position:0% +um he um he did go uh he had some mental +problems unfortunately um + + align:start position:0% +problems unfortunately um + + + align:start position:0% +problems unfortunately um +and so + + align:start position:0% +and so + + + align:start position:0% +and so +so how do we compare the sizes of sets + + align:start position:0% +so how do we compare the sizes of sets + + + align:start position:0% +so how do we compare the sizes of sets +in general if they're finite sets we can + + align:start position:0% +in general if they're finite sets we can + + + align:start position:0% +in general if they're finite sets we can +just count them up + + align:start position:0% +just count them up + + + align:start position:0% +just count them up +we can say oh this set has + + align:start position:0% +we can say oh this set has + + + align:start position:0% +we can say oh this set has +uh 11 elements and the other set has uh + + align:start position:0% +uh 11 elements and the other set has uh + + + align:start position:0% +uh 11 elements and the other set has uh +10 elements so the 11 one with 11 is + + align:start position:0% +10 elements so the 11 one with 11 is + + + align:start position:0% +10 elements so the 11 one with 11 is +bigger or if they both have 11 they're + + align:start position:0% +bigger or if they both have 11 they're + + + align:start position:0% +bigger or if they both have 11 they're +the same size well that's not going to + + align:start position:0% +the same size well that's not going to + + + align:start position:0% +the same size well that's not going to +work for infinite sets because you can't + + align:start position:0% +work for infinite sets because you can't + + + align:start position:0% +work for infinite sets because you can't +count them up um + + align:start position:0% +count them up um + + + align:start position:0% +count them up um +and so he had cantor had the following + + align:start position:0% +and so he had cantor had the following + + + align:start position:0% +and so he had cantor had the following +idea for comparing the sizes of infinite + + align:start position:0% +idea for comparing the sizes of infinite + + + align:start position:0% +idea for comparing the sizes of infinite +sets + + align:start position:0% +sets + + + align:start position:0% +sets +um and that was + + align:start position:0% +um and that was + + + align:start position:0% +um and that was +basically um to see whether you can have + + align:start position:0% +basically um to see whether you can have + + + align:start position:0% +basically um to see whether you can have +a function + + align:start position:0% +a function + + + align:start position:0% +a function +that would map + + align:start position:0% +that would map + + + align:start position:0% +that would map +from one set to the other set with + + align:start position:0% +from one set to the other set with + + + align:start position:0% +from one set to the other set with +certain properties + + align:start position:0% +certain properties + + + align:start position:0% +certain properties +and those properties are um called + + align:start position:0% +and those properties are um called + + + align:start position:0% +and those properties are um called +traditionally well i mean + + align:start position:0% +traditionally well i mean + + + align:start position:0% +traditionally well i mean +in the past have been called the + + align:start position:0% +in the past have been called the + + + align:start position:0% +in the past have been called the +one-to-one and onto properties for the + + align:start position:0% +one-to-one and onto properties for the + + + align:start position:0% +one-to-one and onto properties for the +function i'll tell you what that means + + align:start position:0% +function i'll tell you what that means + + + align:start position:0% +function i'll tell you what that means +um but the concept is very simple um so + + align:start position:0% +um but the concept is very simple um so + + + align:start position:0% +um but the concept is very simple um so +a one-to-one function is one a function + + align:start position:0% +a one-to-one function is one a function + + + align:start position:0% +a one-to-one function is one a function +that's mapping from a to b those are the + + align:start position:0% +that's mapping from a to b those are the + + + align:start position:0% +that's mapping from a to b those are the +two sets whose sizes we're trying to + + align:start position:0% +two sets whose sizes we're trying to + + + align:start position:0% +two sets whose sizes we're trying to +compare + + align:start position:0% +compare + + + align:start position:0% +compare +and + + align:start position:0% +and + + + align:start position:0% +and +uh the function being one to one just + + align:start position:0% +uh the function being one to one just + + + align:start position:0% +uh the function being one to one just +means that there are no collisions if + + align:start position:0% +means that there are no collisions if + + + align:start position:0% +means that there are no collisions if +you have two different elements of a + + align:start position:0% +you have two different elements of a + + + align:start position:0% +you have two different elements of a +they're never going to map onto the same + + align:start position:0% +they're never going to map onto the same + + + align:start position:0% +they're never going to map onto the same +element of b + + align:start position:0% +element of b + + + align:start position:0% +element of b +so two different elements of a always + + align:start position:0% +so two different elements of a always + + + align:start position:0% +so two different elements of a always +map onto two different elements of b + + align:start position:0% +map onto two different elements of b + + + align:start position:0% +map onto two different elements of b +so that's the one-to-one property it's + + align:start position:0% +so that's the one-to-one property it's + + + align:start position:0% +so that's the one-to-one property it's +also called injective um + + align:start position:0% +also called injective um + + + align:start position:0% +also called injective um +and um the other property is called onto + + align:start position:0% +and um the other property is called onto + + + align:start position:0% +and um the other property is called onto +or surjective um which is that the range + + align:start position:0% +or surjective um which is that the range + + + align:start position:0% +or surjective um which is that the range +of f has to be all of b so you're not + + align:start position:0% +of f has to be all of b so you're not + + + align:start position:0% +of f has to be all of b so you're not +allowed to miss any elements b you have + + align:start position:0% +allowed to miss any elements b you have + + + align:start position:0% +allowed to miss any elements b you have +to hit everything + + align:start position:0% +to hit everything + + + align:start position:0% +to hit everything +um + + align:start position:0% +um + + + align:start position:0% +um +and when you have the both of those + + align:start position:0% +and when you have the both of those + + + align:start position:0% +and when you have the both of those +properties it the function is called the + + align:start position:0% +properties it the function is called the + + + align:start position:0% +properties it the function is called the +one-to-one correspondence or a bijection + + align:start position:0% +one-to-one correspondence or a bijection + + + align:start position:0% +one-to-one correspondence or a bijection +also + + align:start position:0% +also + + + align:start position:0% +also +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +now uh another way of looking at i don't + + align:start position:0% +now uh another way of looking at i don't + + + align:start position:0% +now uh another way of looking at i don't +want to make this overly more + + align:start position:0% +want to make this overly more + + + align:start position:0% +want to make this overly more +complicated than it needs to be it just + + align:start position:0% +complicated than it needs to be it just + + + align:start position:0% +complicated than it needs to be it just +simply means that two sets are + + align:start position:0% +simply means that two sets are + + + align:start position:0% +simply means that two sets are +considered to be the same size if we can + + align:start position:0% +considered to be the same size if we can + + + align:start position:0% +considered to be the same size if we can +match up the elements with one set with + + align:start position:0% +match up the elements with one set with + + + align:start position:0% +match up the elements with one set with +elements of the other set you just pair + + align:start position:0% +elements of the other set you just pair + + + align:start position:0% +elements of the other set you just pair +them up + + align:start position:0% +them up + + + align:start position:0% +them up +you know for example well + + align:start position:0% +you know for example well + + + align:start position:0% +you know for example well +if you look have finite sets um that + + align:start position:0% +if you look have finite sets um that + + + align:start position:0% +if you look have finite sets um that +into that idea that informal idea just + + align:start position:0% +into that idea that informal idea just + + + align:start position:0% +into that idea that informal idea just +works exactly as you would expect you + + align:start position:0% +works exactly as you would expect you + + + align:start position:0% +works exactly as you would expect you +know for example if we have two sets + + align:start position:0% +know for example if we have two sets + + + align:start position:0% +know for example if we have two sets +here's a set of puppies here's a set of + + align:start position:0% +here's a set of puppies here's a set of + + + align:start position:0% +here's a set of puppies here's a set of +kittens + + align:start position:0% +kittens + + + align:start position:0% +kittens +um + + align:start position:0% +um + + + align:start position:0% +um +now we want to show that those two sets + + align:start position:0% +now we want to show that those two sets + + + align:start position:0% +now we want to show that those two sets +have the same size we could count them + + align:start position:0% +have the same size we could count them + + + align:start position:0% +have the same size we could count them +up as i mentioned and see that there are + + align:start position:0% +up as i mentioned and see that there are + + + align:start position:0% +up as i mentioned and see that there are +six elements in both + + align:start position:0% +six elements in both + + + align:start position:0% +six elements in both +but it's counting up does not work for + + align:start position:0% +but it's counting up does not work for + + + align:start position:0% +but it's counting up does not work for +infinite sets + + align:start position:0% +infinite sets + + + align:start position:0% +infinite sets +so + + align:start position:0% +so + + + align:start position:0% +so +um we can just match up the elements of + + align:start position:0% +um we can just match up the elements of + + + align:start position:0% +um we can just match up the elements of +the the puppies with the kittens + + align:start position:0% +the the puppies with the kittens + + + align:start position:0% +the the puppies with the kittens +and then we know they're we have the + + align:start position:0% +and then we know they're we have the + + + align:start position:0% +and then we know they're we have the +same number of puppies as kittens + + align:start position:0% +same number of puppies as kittens + + + align:start position:0% +same number of puppies as kittens +okay now that has the advantage of it + + align:start position:0% +okay now that has the advantage of it + + + align:start position:0% +okay now that has the advantage of it +making sense when you have infinite sets + + align:start position:0% +making sense when you have infinite sets + + + align:start position:0% +making sense when you have infinite sets +so we're just going to extend that idea + + align:start position:0% +so we're just going to extend that idea + + + align:start position:0% +so we're just going to extend that idea +and apply it to infinite sets too and + + align:start position:0% +and apply it to infinite sets too and + + + align:start position:0% +and apply it to infinite sets too and +then we'll have a notion of what it + + align:start position:0% +then we'll have a notion of what it + + + align:start position:0% +then we'll have a notion of what it +means for two infinite sets to have the + + align:start position:0% +means for two infinite sets to have the + + + align:start position:0% +means for two infinite sets to have the +same size + + align:start position:0% +same size + + + align:start position:0% +same size +and you might wonder what do you get you + + align:start position:0% +and you might wonder what do you get you + + + align:start position:0% +and you might wonder what do you get you +know are all infinite sets of the same + + align:start position:0% +know are all infinite sets of the same + + + align:start position:0% +know are all infinite sets of the same +size when you use this notion or or not + + align:start position:0% +size when you use this notion or or not + + + align:start position:0% +size when you use this notion or or not +what happens um well some strange things + + align:start position:0% +what happens um well some strange things + + + align:start position:0% +what happens um well some strange things +do happen but there actually are quite + + align:start position:0% +do happen but there actually are quite + + + align:start position:0% +do happen but there actually are quite +some interesting um + + align:start position:0% +some interesting um + + + align:start position:0% +some interesting um +uh structure there that uh that emerges + + align:start position:0% +uh structure there that uh that emerges + + + align:start position:0% +uh structure there that uh that emerges +so if um + + align:start position:0% +so if um + + + align:start position:0% +so if um +so anyway + + align:start position:0% +so anyway + + + align:start position:0% +so anyway +i don't want to rush on uh questions on + + align:start position:0% +i don't want to rush on uh questions on + + + align:start position:0% +i don't want to rush on uh questions on +any of this if you want to uh + + align:start position:0% +any of this if you want to uh + + + align:start position:0% +any of this if you want to uh +quick question this hopefully was not + + align:start position:0% +quick question this hopefully was not + + + align:start position:0% +quick question this hopefully was not +too hard but i want to make sure + + align:start position:0% +too hard but i want to make sure + + + align:start position:0% +too hard but i want to make sure +everybody's together with me on it so we + + align:start position:0% +everybody's together with me on it so we + + + align:start position:0% +everybody's together with me on it so we +can pop in uh + + align:start position:0% +can pop in uh + + + align:start position:0% +can pop in uh +i'll give a few seconds for a chat if + + align:start position:0% +i'll give a few seconds for a chat if + + + align:start position:0% +i'll give a few seconds for a chat if +you have any uh questions + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +the rain the range of the set is all of + + align:start position:0% +the rain the range of the set is all of + + + align:start position:0% +the rain the range of the set is all of +the elements that you hit as you look at + + align:start position:0% +the elements that you hit as you look at + + + align:start position:0% +the elements that you hit as you look at +the different possible elements of a so + + align:start position:0% +the different possible elements of a so + + + align:start position:0% +the different possible elements of a so +all of the things that f hits the + + align:start position:0% +all of the things that f hits the + + + align:start position:0% +all of the things that f hits the +standard notion of range of a function + + align:start position:0% +standard notion of range of a function + + + align:start position:0% +standard notion of range of a function +um + + align:start position:0% +um + + + align:start position:0% +um +so the range of s f has to be equal to b + + align:start position:0% +so the range of s f has to be equal to b + + + align:start position:0% +so the range of s f has to be equal to b +you have to hit everything + + align:start position:0% + + + + align:start position:0% + +um right uh + + align:start position:0% +um right uh + + + align:start position:0% +um right uh +can you think of a one-to-one + + align:start position:0% +can you think of a one-to-one + + + align:start position:0% +can you think of a one-to-one +correspondent says relabeling yeah i'm + + align:start position:0% +correspondent says relabeling yeah i'm + + + align:start position:0% +correspondent says relabeling yeah i'm +not sure that's helpful but yes you can + + align:start position:0% +not sure that's helpful but yes you can + + + align:start position:0% +not sure that's helpful but yes you can +think of as a re-labeling of the + + align:start position:0% +think of as a re-labeling of the + + + align:start position:0% +think of as a re-labeling of the +elements in a sense but uh yeah + + align:start position:0% +elements in a sense but uh yeah + + + align:start position:0% +elements in a sense but uh yeah +i just think of it as a matching up + + align:start position:0% +i just think of it as a matching up + + + align:start position:0% +i just think of it as a matching up +um all right so let's move on um + + align:start position:0% +um all right so let's move on um + + + align:start position:0% +um all right so let's move on um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +coming out of this notion of sets of + + align:start position:0% +coming out of this notion of sets of + + + align:start position:0% +coming out of this notion of sets of +being of the same size there was this + + align:start position:0% +being of the same size there was this + + + align:start position:0% +being of the same size there was this +notion of countable sets as we'll see in + + align:start position:0% +notion of countable sets as we'll see in + + + align:start position:0% +notion of countable sets as we'll see in +a minute um + + align:start position:0% +a minute um + + + align:start position:0% +a minute um +so + + align:start position:0% +so + + + align:start position:0% +so +let's do an example + + align:start position:0% +let's do an example + + + align:start position:0% +let's do an example +let's take the set of natural numbers + + align:start position:0% +let's take the set of natural numbers + + + align:start position:0% +let's take the set of natural numbers +you know one two three four dot dot dot + + align:start position:0% +you know one two three four dot dot dot + + + align:start position:0% +you know one two three four dot dot dot +and the set of integers + + align:start position:0% +and the set of integers + + + align:start position:0% +and the set of integers +which includes the natural numbers but + + align:start position:0% +which includes the natural numbers but + + + align:start position:0% +which includes the natural numbers but +but also the negative numbers in zero um + + align:start position:0% +but also the negative numbers in zero um + + + align:start position:0% +but also the negative numbers in zero um +so the + + align:start position:0% +so the + + + align:start position:0% +so the +natural numbers are typically referred + + align:start position:0% +natural numbers are typically referred + + + align:start position:0% +natural numbers are typically referred +to as n the + + align:start position:0% +to as n the + + + align:start position:0% +to as n the +integers are typically referred to as z + + align:start position:0% +integers are typically referred to as z + + + align:start position:0% +integers are typically referred to as z +and + + align:start position:0% +and + + + align:start position:0% +and +how do we + + align:start position:0% +how do we + + + align:start position:0% +how do we +what do we think of the relative sizes + + align:start position:0% +what do we think of the relative sizes + + + align:start position:0% +what do we think of the relative sizes +of um + + align:start position:0% +of um + + + align:start position:0% +of um +n and z + + align:start position:0% +n and z + + + align:start position:0% +n and z +well n is a subset of z it's a proper + + align:start position:0% +well n is a subset of z it's a proper + + + align:start position:0% +well n is a subset of z it's a proper +subset of c so you might at first glance + + align:start position:0% +subset of c so you might at first glance + + + align:start position:0% +subset of c so you might at first glance +think that z is larger and they're not + + align:start position:0% +think that z is larger and they're not + + + align:start position:0% +think that z is larger and they're not +really going to be of the same size + + align:start position:0% +really going to be of the same size + + + align:start position:0% +really going to be of the same size +but it actually it turns out that + + align:start position:0% +but it actually it turns out that + + + align:start position:0% +but it actually it turns out that +there's a very simple way + + align:start position:0% +there's a very simple way + + + align:start position:0% +there's a very simple way +you know the arithmetic and the + + align:start position:0% +you know the arithmetic and the + + + align:start position:0% +you know the arithmetic and the +properties of infinite sensor can be a + + align:start position:0% +properties of infinite sensor can be a + + + align:start position:0% +properties of infinite sensor can be a +little bit surprising and there is a way + + align:start position:0% +little bit surprising and there is a way + + + align:start position:0% +little bit surprising and there is a way +of matching up all of the elements of z + + align:start position:0% +of matching up all of the elements of z + + + align:start position:0% +of matching up all of the elements of z +with elements their own elements of n um + + align:start position:0% +with elements their own elements of n um + + + align:start position:0% +with elements their own elements of n um +and so you can show that as uh + + align:start position:0% +and so you can show that as uh + + + align:start position:0% +and so you can show that as uh +following that definition that these two + + align:start position:0% +following that definition that these two + + + align:start position:0% +following that definition that these two +sets are in fact of the same size so + + align:start position:0% +sets are in fact of the same size so + + + align:start position:0% +sets are in fact of the same size so +let's just quickly go that goes make + + align:start position:0% +let's just quickly go that goes make + + + align:start position:0% +let's just quickly go that goes make +sure you see that + + align:start position:0% +sure you see that + + + align:start position:0% +sure you see that +um + + align:start position:0% +um + + + align:start position:0% +um +so here is n + + align:start position:0% +so here is n + + + align:start position:0% +so here is n +here is z i'm going to write down a + + align:start position:0% +here is z i'm going to write down a + + + align:start position:0% +here is z i'm going to write down a +table which shows how they match up and + + align:start position:0% +table which shows how they match up and + + + align:start position:0% +table which shows how they match up and +here's the function f of n that i'm + + align:start position:0% +here's the function f of n that i'm + + + align:start position:0% +here's the function f of n that i'm +going to be describing that's the um the + + align:start position:0% +going to be describing that's the um the + + + align:start position:0% +going to be describing that's the um the +one-to-one correspondence + + align:start position:0% +one-to-one correspondence + + + align:start position:0% +one-to-one correspondence +and so here are the natural numbers + + align:start position:0% +and so here are the natural numbers + + + align:start position:0% +and so here are the natural numbers +dot one through seven dot dot dot and + + align:start position:0% +dot one through seven dot dot dot and + + + align:start position:0% +dot one through seven dot dot dot and +here are the elements of z that i'm + + align:start position:0% +here are the elements of z that i'm + + + align:start position:0% +here are the elements of z that i'm +gonna be matching up this is how the + + align:start position:0% +gonna be matching up this is how the + + + align:start position:0% +gonna be matching up this is how the +function is working so one i'm gonna you + + align:start position:0% +function is working so one i'm gonna you + + + align:start position:0% +function is working so one i'm gonna you +know f of one is gonna be zero f of two + + align:start position:0% +know f of one is gonna be zero f of two + + + align:start position:0% +know f of one is gonna be zero f of two +is gonna be minus one f of three is + + align:start position:0% +is gonna be minus one f of three is + + + align:start position:0% +is gonna be minus one f of three is +gonna be one + + align:start position:0% +gonna be one + + + align:start position:0% +gonna be one +um and i'm just giving you a way to + + align:start position:0% +um and i'm just giving you a way to + + + align:start position:0% +um and i'm just giving you a way to +match up each of the natural numbers + + align:start position:0% +match up each of the natural numbers + + + align:start position:0% +match up each of the natural numbers +with with integers + + align:start position:0% +with with integers + + + align:start position:0% +with with integers +so that every single integer has its own + + align:start position:0% +so that every single integer has its own + + + align:start position:0% +so that every single integer has its own +natural number and vice versa um + + align:start position:0% +natural number and vice versa um + + + align:start position:0% +natural number and vice versa um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so four goes to minus two five goes to + + align:start position:0% +so four goes to minus two five goes to + + + align:start position:0% +so four goes to minus two five goes to +two six goes to minus three seven goes + + align:start position:0% +two six goes to minus three seven goes + + + align:start position:0% +two six goes to minus three seven goes +to three and then minus four and then + + align:start position:0% +to three and then minus four and then + + + align:start position:0% +to three and then minus four and then +four minus five then five and so on + + align:start position:0% +four minus five then five and so on + + + align:start position:0% +four minus five then five and so on +you're clearly going to cover all of the + + align:start position:0% +you're clearly going to cover all of the + + + align:start position:0% +you're clearly going to cover all of the +integers in this way and each of the + + align:start position:0% +integers in this way and each of the + + + align:start position:0% +integers in this way and each of the +natural numbers is going to have its own + + align:start position:0% +natural numbers is going to have its own + + + align:start position:0% +natural numbers is going to have its own +integer and there's never going to be + + align:start position:0% +integer and there's never going to be + + + align:start position:0% +integer and there's never going to be +any collisions there's never going to be + + align:start position:0% +any collisions there's never going to be + + + align:start position:0% +any collisions there's never going to be +two natural numbers assigned to the same + + align:start position:0% +two natural numbers assigned to the same + + + align:start position:0% +two natural numbers assigned to the same +integer so this is meets the uh the + + align:start position:0% +integer so this is meets the uh the + + + align:start position:0% +integer so this is meets the uh the +conditions of a one-to-one + + align:start position:0% +conditions of a one-to-one + + + align:start position:0% +conditions of a one-to-one +correspondence and shows that the + + align:start position:0% +correspondence and shows that the + + + align:start position:0% +correspondence and shows that the +natural numbers and the um and the + + align:start position:0% +natural numbers and the um and the + + + align:start position:0% +natural numbers and the um and the +integers have the same size + + align:start position:0% +integers have the same size + + + align:start position:0% +integers have the same size +uh following this definition um + + align:start position:0% +uh following this definition um + + + align:start position:0% +uh following this definition um +okay let's do one that's slightly + + align:start position:0% +okay let's do one that's slightly + + + align:start position:0% +okay let's do one that's slightly +more + + align:start position:0% +more + + + align:start position:0% +more +complicated um and perhaps slightly more + + align:start position:0% +complicated um and perhaps slightly more + + + align:start position:0% +complicated um and perhaps slightly more +surprising + + align:start position:0% +surprising + + + align:start position:0% +surprising +which is that if you consider all of the + + align:start position:0% +which is that if you consider all of the + + + align:start position:0% +which is that if you consider all of the +rational numbers + + align:start position:0% +rational numbers + + + align:start position:0% +rational numbers +and um then they have the same that is a + + align:start position:0% +and um then they have the same that is a + + + align:start position:0% +and um then they have the same that is a +collection even though the rational + + align:start position:0% +collection even though the rational + + + align:start position:0% +collection even though the rational +numbers seem to be much richer and + + align:start position:0% +numbers seem to be much richer and + + + align:start position:0% +numbers seem to be much richer and +more numerous than the integers from + + align:start position:0% +more numerous than the integers from + + + align:start position:0% +more numerous than the integers from +this perspective they have the same size + + align:start position:0% +this perspective they have the same size + + + align:start position:0% +this perspective they have the same size +and for the simplicity of my uh + + align:start position:0% +and for the simplicity of my uh + + + align:start position:0% +and for the simplicity of my uh +my presentation i'm going to consider + + align:start position:0% +my presentation i'm going to consider + + + align:start position:0% +my presentation i'm going to consider +only the positive rational numbers which + + align:start position:0% +only the positive rational numbers which + + + align:start position:0% +only the positive rational numbers which +i'm going to write as q plus + + align:start position:0% +i'm going to write as q plus + + + align:start position:0% +i'm going to write as q plus +so those are all of the positive + + align:start position:0% +so those are all of the positive + + + align:start position:0% +so those are all of the positive +rational numbers that can be expressed + + align:start position:0% +rational numbers that can be expressed + + + align:start position:0% +rational numbers that can be expressed +as a ratio of two natural numbers + + align:start position:0% +as a ratio of two natural numbers + + + align:start position:0% +as a ratio of two natural numbers +and um i'm going to show that there is a + + align:start position:0% +and um i'm going to show that there is a + + + align:start position:0% +and um i'm going to show that there is a +one-to-one correspondence between the + + align:start position:0% +one-to-one correspondence between the + + + align:start position:0% +one-to-one correspondence between the +rations between these positive rational + + align:start position:0% +rations between these positive rational + + + align:start position:0% +rations between these positive rational +numbers and and the natural numbers + + align:start position:0% +numbers and and the natural numbers + + + align:start position:0% +numbers and and the natural numbers +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% +um + + + align:start position:0% +um +here i'm going to again make a table + + align:start position:0% +here i'm going to again make a table + + + align:start position:0% +here i'm going to again make a table +just as i did up uh up above um + + align:start position:0% +just as i did up uh up above um + + + align:start position:0% +just as i did up uh up above um +so comparing the natural numbers and the + + align:start position:0% +so comparing the natural numbers and the + + + align:start position:0% +so comparing the natural numbers and the +positive rational numbers + + align:start position:0% +positive rational numbers + + + align:start position:0% +positive rational numbers +and + + align:start position:0% +and + + + align:start position:0% +and +to do that i'm going to write down over + + align:start position:0% +to do that i'm going to write down over + + + align:start position:0% +to do that i'm going to write down over +here on the side just to help you see + + align:start position:0% +here on the side just to help you see + + + align:start position:0% +here on the side just to help you see +how i'm getting this table + + align:start position:0% +how i'm getting this table + + + align:start position:0% +how i'm getting this table +a table a separate table that can that + + align:start position:0% +a table a separate table that can that + + + align:start position:0% +a table a separate table that can that +has all of the rational number positive + + align:start position:0% +has all of the rational number positive + + + align:start position:0% +has all of the rational number positive +rational numbers appearing you know in + + align:start position:0% +rational numbers appearing you know in + + + align:start position:0% +rational numbers appearing you know in +kind of a nicely organized way um here + + align:start position:0% +kind of a nicely organized way um here + + + align:start position:0% +kind of a nicely organized way um here +are all the rational numbers here that + + align:start position:0% +are all the rational numbers here that + + + align:start position:0% +are all the rational numbers here that +have one as a numerator that have two as + + align:start position:0% +have one as a numerator that have two as + + + align:start position:0% +have one as a numerator that have two as +a numerator and and so on and going + + align:start position:0% +a numerator and and so on and going + + + align:start position:0% +a numerator and and so on and going +through across the columns the different + + align:start position:0% +through across the columns the different + + + align:start position:0% +through across the columns the different +denominators + + align:start position:0% +denominators + + + align:start position:0% +denominators +um so it's the the numbers inside here + + align:start position:0% +um so it's the the numbers inside here + + + align:start position:0% +um so it's the the numbers inside here +represent all of the different rational + + align:start position:0% +represent all of the different rational + + + align:start position:0% +represent all of the different rational +numbers and so whatever rational number + + align:start position:0% +numbers and so whatever rational number + + + align:start position:0% +numbers and so whatever rational number +you have + + align:start position:0% +you have + + + align:start position:0% +you have +m over n + + align:start position:0% +m over n + + + align:start position:0% +m over n +um + + align:start position:0% +um + + + align:start position:0% +um +that's going to appear down the nth row + + align:start position:0% +that's going to appear down the nth row + + + align:start position:0% +that's going to appear down the nth row +in the nth column + + align:start position:0% +in the nth column + + + align:start position:0% +in the nth column +that number is going to appear so + + align:start position:0% +that number is going to appear so + + + align:start position:0% +that number is going to appear so +they're all going to show up + + align:start position:0% +they're all going to show up + + + align:start position:0% +they're all going to show up +and i'm going to use this + + align:start position:0% +and i'm going to use this + + + align:start position:0% +and i'm going to use this +table here to fill out this function + + align:start position:0% +table here to fill out this function + + + align:start position:0% +table here to fill out this function +um + + align:start position:0% +um + + + align:start position:0% +um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +here are all the natural numbers and the + + align:start position:0% +here are all the natural numbers and the + + + align:start position:0% +here are all the natural numbers and the +way i'm going to assign + + align:start position:0% +way i'm going to assign + + + align:start position:0% +way i'm going to assign +the + + align:start position:0% +the + + + align:start position:0% +the +rational numbers to appear over here is + + align:start position:0% +rational numbers to appear over here is + + + align:start position:0% +rational numbers to appear over here is +i'm just going to work my way in from + + align:start position:0% +i'm just going to work my way in from + + + align:start position:0% +i'm just going to work my way in from +the corner + + align:start position:0% +the corner + + + align:start position:0% +the corner +and i'm going to do that by kind of + + align:start position:0% +and i'm going to do that by kind of + + + align:start position:0% +and i'm going to do that by kind of +doing layers so first i'll take the one + + align:start position:0% +doing layers so first i'll take the one + + + align:start position:0% +doing layers so first i'll take the one +in this + + align:start position:0% +in this + + + align:start position:0% +in this +this number here in this corner then + + align:start position:0% +this number here in this corner then + + + align:start position:0% +this number here in this corner then +i'll do these three that surround it and + + align:start position:0% +i'll do these three that surround it and + + + align:start position:0% +i'll do these three that surround it and +then these guys that's around that and + + align:start position:0% +then these guys that's around that and + + + align:start position:0% +then these guys that's around that and +these guys sort of in shells going + + align:start position:0% +these guys sort of in shells going + + + align:start position:0% +these guys sort of in shells going +around the previous ones that i've + + align:start position:0% +around the previous ones that i've + + + align:start position:0% +around the previous ones that i've +already covered + + align:start position:0% +already covered + + + align:start position:0% +already covered +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +let me illustrate that + + align:start position:0% +let me illustrate that + + + align:start position:0% +let me illustrate that +so here's one over one my first rational + + align:start position:0% +so here's one over one my first rational + + + align:start position:0% +so here's one over one my first rational +number that i'm going to enter then to + + align:start position:0% +number that i'm going to enter then to + + + align:start position:0% +number that i'm going to enter then to +the table + + align:start position:0% +the table + + + align:start position:0% +the table +appearing right over there so next i'm + + align:start position:0% +appearing right over there so next i'm + + + align:start position:0% +appearing right over there so next i'm +going to go 2 over 1 + + align:start position:0% +going to go 2 over 1 + + + align:start position:0% +going to go 2 over 1 +that's going to appear in the table over + + align:start position:0% +that's going to appear in the table over + + + align:start position:0% +that's going to appear in the table over +there + + align:start position:0% +there + + + align:start position:0% +there +now we have 2 over 2. now that's + + align:start position:0% +now we have 2 over 2. now that's + + + align:start position:0% +now we have 2 over 2. now that's +actually a little bit uh problematic + + align:start position:0% +actually a little bit uh problematic + + + align:start position:0% +actually a little bit uh problematic +because 2 over 2 has already been done + + align:start position:0% +because 2 over 2 has already been done + + + align:start position:0% +because 2 over 2 has already been done +um and if we put that in + + align:start position:0% +um and if we put that in + + + align:start position:0% +um and if we put that in +uh because 2 over 2 equals 1 over 1 + + align:start position:0% +uh because 2 over 2 equals 1 over 1 + + + align:start position:0% +uh because 2 over 2 equals 1 over 1 +they're both the equal to the rational + + align:start position:0% +they're both the equal to the rational + + + align:start position:0% +they're both the equal to the rational +number one + + align:start position:0% +number one + + + align:start position:0% +number one +so if we put two over two in this table + + align:start position:0% +so if we put two over two in this table + + + align:start position:0% +so if we put two over two in this table +over here then we would no longer have + + align:start position:0% +over here then we would no longer have + + + align:start position:0% +over here then we would no longer have +the one-to-one property because both one + + align:start position:0% +the one-to-one property because both one + + + align:start position:0% +the one-to-one property because both one +and three would be mapping to the same + + align:start position:0% +and three would be mapping to the same + + + align:start position:0% +and three would be mapping to the same +point um so we're just going to simply + + align:start position:0% +point um so we're just going to simply + + + align:start position:0% +point um so we're just going to simply +skip over two over two + + align:start position:0% +skip over two over two + + + align:start position:0% +skip over two over two +um + + align:start position:0% +um + + + align:start position:0% +um +i'll show that as kind of graying it out + + align:start position:0% +i'll show that as kind of graying it out + + + align:start position:0% +i'll show that as kind of graying it out +so we're not gonna + + align:start position:0% +so we're not gonna + + + align:start position:0% +so we're not gonna +we're not gonna add that one onto the + + align:start position:0% +we're not gonna add that one onto the + + + align:start position:0% +we're not gonna add that one onto the +table onto my function + + align:start position:0% +table onto my function + + + align:start position:0% +table onto my function +um + + align:start position:0% +um + + + align:start position:0% +um +so but so we'll skip over that we'll go + + align:start position:0% +so but so we'll skip over that we'll go + + + align:start position:0% +so but so we'll skip over that we'll go +to one over two which is um has not been + + align:start position:0% +to one over two which is um has not been + + + align:start position:0% +to one over two which is um has not been +seen before + + align:start position:0% +seen before + + + align:start position:0% +seen before +and then we're just going to continue + + align:start position:0% +and then we're just going to continue + + + align:start position:0% +and then we're just going to continue +doing the same thing now going to this + + align:start position:0% +doing the same thing now going to this + + + align:start position:0% +doing the same thing now going to this +next shell out here + + align:start position:0% +next shell out here + + + align:start position:0% +next shell out here +three over one + + align:start position:0% +three over one + + + align:start position:0% +three over one +three over two + + align:start position:0% +three over two + + + align:start position:0% +three over two +three over three + + align:start position:0% +three over three + + + align:start position:0% +three over three +same thing i'm going to skip over that + + align:start position:0% +same thing i'm going to skip over that + + + align:start position:0% +same thing i'm going to skip over that +one + + align:start position:0% +one + + + align:start position:0% +one +2 over 3 + + align:start position:0% +2 over 3 + + + align:start position:0% +2 over 3 +1 over 3. i hope you're getting the idea + + align:start position:0% +1 over 3. i hope you're getting the idea + + + align:start position:0% +1 over 3. i hope you're getting the idea +um so i'm not going to fill this + + align:start position:0% +um so i'm not going to fill this + + + align:start position:0% +um so i'm not going to fill this +together i ran out of room to + + align:start position:0% +together i ran out of room to + + + align:start position:0% +together i ran out of room to +put fill out this table some more but + + align:start position:0% +put fill out this table some more but + + + align:start position:0% +put fill out this table some more but +just to look at how the process is going + + align:start position:0% +just to look at how the process is going + + + align:start position:0% +just to look at how the process is going +to continue here i would get 4 over 1. + + align:start position:0% +to continue here i would get 4 over 1. + + + align:start position:0% +to continue here i would get 4 over 1. +now 4 over 2 + + align:start position:0% +now 4 over 2 + + + align:start position:0% +now 4 over 2 +again is the number we've previously + + align:start position:0% +again is the number we've previously + + + align:start position:0% +again is the number we've previously +seen because that's the that's the + + align:start position:0% +seen because that's the that's the + + + align:start position:0% +seen because that's the that's the +rational number 2. we saw that up here + + align:start position:0% +rational number 2. we saw that up here + + + align:start position:0% +rational number 2. we saw that up here +when we had 2 over 1 so we're going to + + align:start position:0% +when we had 2 over 1 so we're going to + + + align:start position:0% +when we had 2 over 1 so we're going to +have to skip that one + + align:start position:0% +have to skip that one + + + align:start position:0% +have to skip that one +4 over 3 four over four + + align:start position:0% +4 over 3 four over four + + + align:start position:0% +4 over 3 four over four +that was going to skip + + align:start position:0% +that was going to skip + + + align:start position:0% +that was going to skip +three or four and so on + + align:start position:0% +three or four and so on + + + align:start position:0% +three or four and so on +okay so by uh following this procedure + + align:start position:0% +okay so by uh following this procedure + + + align:start position:0% +okay so by uh following this procedure +i'm going to be able to define this + + align:start position:0% +i'm going to be able to define this + + + align:start position:0% +i'm going to be able to define this +function now this function is not + + align:start position:0% +function now this function is not + + + align:start position:0% +function now this function is not +particularly nice in terms of having a + + align:start position:0% +particularly nice in terms of having a + + + align:start position:0% +particularly nice in terms of having a +an elegant closed form but it is a + + align:start position:0% +an elegant closed form but it is a + + + align:start position:0% +an elegant closed form but it is a +the total legitimate function in the + + align:start position:0% +the total legitimate function in the + + + align:start position:0% +the total legitimate function in the +sense of being a mapping from + + align:start position:0% +sense of being a mapping from + + + align:start position:0% +sense of being a mapping from +natural numbers to + + align:start position:0% +natural numbers to + + + align:start position:0% +natural numbers to +the positive rational numbers + + align:start position:0% +the positive rational numbers + + + align:start position:0% +the positive rational numbers +and it has the one-to-one correspondence + + align:start position:0% +and it has the one-to-one correspondence + + + align:start position:0% +and it has the one-to-one correspondence +property + + align:start position:0% +property + + + align:start position:0% +property +so it pairs up each of the + + align:start position:0% +so it pairs up each of the + + + align:start position:0% +so it pairs up each of the +natural numbers with each of the um + + align:start position:0% +natural numbers with each of the um + + + align:start position:0% +natural numbers with each of the um +uh positive rational numbers um they + + align:start position:0% +uh positive rational numbers um they + + + align:start position:0% +uh positive rational numbers um they +each get their own + + align:start position:0% +each get their own + + + align:start position:0% +each get their own +mate in a sense and so that shows that + + align:start position:0% +mate in a sense and so that shows that + + + align:start position:0% +mate in a sense and so that shows that +the rational numbers despite the fact + + align:start position:0% +the rational numbers despite the fact + + + align:start position:0% +the rational numbers despite the fact +that they're dense and they have all + + align:start position:0% +that they're dense and they have all + + + align:start position:0% +that they're dense and they have all +sorts of very sort of more much bigger + + align:start position:0% +sorts of very sort of more much bigger + + + align:start position:0% +sorts of very sort of more much bigger +seaming they really and from this + + align:start position:0% +seaming they really and from this + + + align:start position:0% +seaming they really and from this +perspective of the sizes of the sets + + align:start position:0% +perspective of the sizes of the sets + + + align:start position:0% +perspective of the sizes of the sets +they have the same size as the + + align:start position:0% +they have the same size as the + + + align:start position:0% +they have the same size as the +natural numbers do and so with that it + + align:start position:0% +natural numbers do and so with that it + + + align:start position:0% +natural numbers do and so with that it +suggested + + align:start position:0% +suggested + + + align:start position:0% +suggested +the following definition that a set is + + align:start position:0% +the following definition that a set is + + + align:start position:0% +the following definition that a set is +countable + + align:start position:0% +countable + + + align:start position:0% +countable +if it has the same size as the natural + + align:start position:0% +if it has the same size as the natural + + + align:start position:0% +if it has the same size as the natural +numbers or it's finite + + align:start position:0% +numbers or it's finite + + + align:start position:0% +numbers or it's finite +from this perspective we're going to be + + align:start position:0% +from this perspective we're going to be + + + align:start position:0% +from this perspective we're going to be +focusing on infinite sets uh but yeah + + align:start position:0% +focusing on infinite sets uh but yeah + + + align:start position:0% +focusing on infinite sets uh but yeah +countable or countably infinite + + align:start position:0% +countable or countably infinite + + + align:start position:0% +countable or countably infinite +sometimes people say uh if it has the + + align:start position:0% +sometimes people say uh if it has the + + + align:start position:0% +sometimes people say uh if it has the +same size as the natural numbers or + + align:start position:0% +same size as the natural numbers or + + + align:start position:0% +same size as the natural numbers or +otherwise you have to include the finite + + align:start position:0% +otherwise you have to include the finite + + + align:start position:0% +otherwise you have to include the finite +sets as well and countable means you can + + align:start position:0% +sets as well and countable means you can + + + align:start position:0% +sets as well and countable means you can +just sort of go through the the sets the + + align:start position:0% +just sort of go through the the sets the + + + align:start position:0% +just sort of go through the the sets the +the elements of the set kind of + + align:start position:0% +the elements of the set kind of + + + align:start position:0% +the elements of the set kind of +as a list + + align:start position:0% +as a list + + + align:start position:0% +as a list +so you can count them the first one the + + align:start position:0% +so you can count them the first one the + + + align:start position:0% +so you can count them the first one the +second one the third one the fourth one + + align:start position:0% +second one the third one the fourth one + + + align:start position:0% +second one the third one the fourth one +dot dot dot and once you can do that and + + align:start position:0% +dot dot dot and once you can do that and + + + align:start position:0% +dot dot dot and once you can do that and +that counting is going to hit everything + + align:start position:0% +that counting is going to hit everything + + + align:start position:0% +that counting is going to hit everything +then you know um you can match them you + + align:start position:0% +then you know um you can match them you + + + align:start position:0% +then you know um you can match them you +can pair them up with the natural + + align:start position:0% +can pair them up with the natural + + + align:start position:0% +can pair them up with the natural +numbers and so therefore you have a + + align:start position:0% +numbers and so therefore you have a + + + align:start position:0% +numbers and so therefore you have a +countable set okay um + + align:start position:0% +countable set okay um + + + align:start position:0% +countable set okay um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so as we've shown + + align:start position:0% +so as we've shown + + + align:start position:0% +so as we've shown +both z + + align:start position:0% +both z + + + align:start position:0% +both z +the integers and the positive rational + + align:start position:0% +the integers and the positive rational + + + align:start position:0% +the integers and the positive rational +numbers are countable sets + + align:start position:0% +numbers are countable sets + + + align:start position:0% +numbers are countable sets +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +you might think that well since we're + + align:start position:0% +you might think that well since we're + + + align:start position:0% +you might think that well since we're +allowing ourselves to do something as + + align:start position:0% +allowing ourselves to do something as + + + align:start position:0% +allowing ourselves to do something as +arbitrary in a way as this kind of a + + align:start position:0% +arbitrary in a way as this kind of a + + + align:start position:0% +arbitrary in a way as this kind of a +function + + align:start position:0% +function + + + align:start position:0% +function +to match up the natural numbers with + + align:start position:0% +to match up the natural numbers with + + + align:start position:0% +to match up the natural numbers with +whatever set you're trying to um + + align:start position:0% +whatever set you're trying to um + + + align:start position:0% +whatever set you're trying to um +to measure + + align:start position:0% +to measure + + + align:start position:0% +to measure +that every set is going to be countable + + align:start position:0% +that every set is going to be countable + + + align:start position:0% +that every set is going to be countable +if you think about it that way because + + align:start position:0% +if you think about it that way because + + + align:start position:0% +if you think about it that way because +it seems like you're allowing two too + + align:start position:0% +it seems like you're allowing two too + + + align:start position:0% +it seems like you're allowing two too +too many possibilities and that all the + + align:start position:0% +too many possibilities and that all the + + + align:start position:0% +too many possibilities and that all the +infinite sets are going to end up being + + align:start position:0% +infinite sets are going to end up being + + + align:start position:0% +infinite sets are going to end up being +the same size as the natural numbers + + align:start position:0% +the same size as the natural numbers + + + align:start position:0% +the same size as the natural numbers +well that isn't in fact is not true + + align:start position:0% +well that isn't in fact is not true + + + align:start position:0% +well that isn't in fact is not true +um + + align:start position:0% +um + + + align:start position:0% +um +and i don't know i i i + + align:start position:0% +and i don't know i i i + + + align:start position:0% +and i don't know i i i +can't or as the one who discovered that + + align:start position:0% +can't or as the one who discovered that + + + align:start position:0% +can't or as the one who discovered that +um i don't know if that was surprising + + align:start position:0% +um i don't know if that was surprising + + + align:start position:0% +um i don't know if that was surprising +or not um but uh it is kind of uh + + align:start position:0% +or not um but uh it is kind of uh + + + align:start position:0% +or not um but uh it is kind of uh +interesting i think that there are + + align:start position:0% +interesting i think that there are + + + align:start position:0% +interesting i think that there are +different sizes of infinities um + + align:start position:0% +different sizes of infinities um + + + align:start position:0% +different sizes of infinities um +and uh so uh we're gonna now take a look + + align:start position:0% +and uh so uh we're gonna now take a look + + + align:start position:0% +and uh so uh we're gonna now take a look +and see uh that but i want to again um + + align:start position:0% +and see uh that but i want to again um + + + align:start position:0% +and see uh that but i want to again um +i want to uh stop and make sure we're + + align:start position:0% +i want to uh stop and make sure we're + + + align:start position:0% +i want to uh stop and make sure we're +all together can we always find a closed + + align:start position:0% +all together can we always find a closed + + + align:start position:0% +all together can we always find a closed +formula for f somebody's asking me um + + align:start position:0% +formula for f somebody's asking me um + + + align:start position:0% +formula for f somebody's asking me um +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +for this particular f uh + + align:start position:0% + + + + align:start position:0% + +you probably could but it would probably + + align:start position:0% +you probably could but it would probably + + + align:start position:0% +you probably could but it would probably +be very messy um + + align:start position:0% +be very messy um + + + align:start position:0% +be very messy um +um but in general that's not a + + align:start position:0% +um but in general that's not a + + + align:start position:0% +um but in general that's not a +requirement + + align:start position:0% +requirement + + + align:start position:0% +requirement +having a closed form for the for the + + align:start position:0% +having a closed form for the for the + + + align:start position:0% +having a closed form for the for the +mapping function any function is allowed + + align:start position:0% +mapping function any function is allowed + + + align:start position:0% +mapping function any function is allowed +as long as it's a one-to-one + + align:start position:0% +as long as it's a one-to-one + + + align:start position:0% +as long as it's a one-to-one +correspondence + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +are we all together on this is this are + + align:start position:0% +are we all together on this is this are + + + align:start position:0% +are we all together on this is this are +we comfortable with the notion of + + align:start position:0% +we comfortable with the notion of + + + align:start position:0% +we comfortable with the notion of +some infinite sets + + align:start position:0% +some infinite sets + + + align:start position:0% +some infinite sets +having the same size as the natural + + align:start position:0% +having the same size as the natural + + + align:start position:0% +having the same size as the natural +numbers and therefore we're going to + + align:start position:0% +numbers and therefore we're going to + + + align:start position:0% +numbers and therefore we're going to +call them countable sets and we're going + + align:start position:0% +call them countable sets and we're going + + + align:start position:0% +call them countable sets and we're going +to show some other sets are going to + + align:start position:0% +to show some other sets are going to + + + align:start position:0% +to show some other sets are going to +have um more elements they're going to + + align:start position:0% +have um more elements they're going to + + + align:start position:0% +have um more elements they're going to +be uncountable they're going to be + + align:start position:0% +be uncountable they're going to be + + + align:start position:0% +be uncountable they're going to be +beyond + + align:start position:0% +beyond + + + align:start position:0% +beyond +strictly speaking strictly larger sets + + align:start position:0% +strictly speaking strictly larger sets + + + align:start position:0% +strictly speaking strictly larger sets +in the sense that we won't be able to + + align:start position:0% +in the sense that we won't be able to + + + align:start position:0% +in the sense that we won't be able to +put them into a one-to-one + + align:start position:0% +put them into a one-to-one + + + align:start position:0% +put them into a one-to-one +correspondence with the integers um so + + align:start position:0% +correspondence with the integers um so + + + align:start position:0% +correspondence with the integers um so +then the smallest infinity yes n is the + + align:start position:0% +then the smallest infinity yes n is the + + + align:start position:0% +then the smallest infinity yes n is the +smallest um + + align:start position:0% +smallest um + + + align:start position:0% +smallest um +smallest one so + + align:start position:0% +smallest one so + + + align:start position:0% +smallest one so +any infinity is going to have um + + align:start position:0% +any infinity is going to have um + + + align:start position:0% +any infinity is going to have um +you know you can always i don't think + + align:start position:0% +you know you can always i don't think + + + align:start position:0% +you know you can always i don't think +you even need it you need a special + + align:start position:0% +you even need it you need a special + + + align:start position:0% +you even need it you need a special +you know you can always + + align:start position:0% +you know you can always + + + align:start position:0% +you know you can always +and whenever you have an + + align:start position:0% +and whenever you have an + + + align:start position:0% +and whenever you have an +internet collection you can always find + + align:start position:0% +internet collection you can always find + + + align:start position:0% +internet collection you can always find +a subset which is going to be + + align:start position:0% +a subset which is going to be + + + align:start position:0% +a subset which is going to be +a countable subset uh so it's uh + + align:start position:0% +a countable subset uh so it's uh + + + align:start position:0% +a countable subset uh so it's uh +and is going to be the smallest of the + + align:start position:0% +and is going to be the smallest of the + + + align:start position:0% +and is going to be the smallest of the +infinities but there are bigger ones + + align:start position:0% +infinities but there are bigger ones + + + align:start position:0% +infinities but there are bigger ones +all right why don't we move on + + align:start position:0% + + + + align:start position:0% + +okay so um + + align:start position:0% +okay so um + + + align:start position:0% +okay so um +the example of a set that we will show + + align:start position:0% +the example of a set that we will show + + + align:start position:0% +the example of a set that we will show +is not countable an uncountable set as + + align:start position:0% +is not countable an uncountable set as + + + align:start position:0% +is not countable an uncountable set as +we call it um is the + + align:start position:0% +we call it um is the + + + align:start position:0% +we call it um is the +uh set of real numbers which you i + + align:start position:0% +uh set of real numbers which you i + + + align:start position:0% +uh set of real numbers which you i +you know + + align:start position:0% +you know + + + align:start position:0% +you know +we all know what these are i hope uh + + align:start position:0% +we all know what these are i hope uh + + + align:start position:0% +we all know what these are i hope uh +these are all of the numbers that you + + align:start position:0% +these are all of the numbers that you + + + align:start position:0% +these are all of the numbers that you +can express by possibly infinite decimal + + align:start position:0% +can express by possibly infinite decimal + + + align:start position:0% +can express by possibly infinite decimal +representations like pi or e square root + + align:start position:0% +representations like pi or e square root + + + align:start position:0% +representations like pi or e square root +of two + + align:start position:0% +of two + + + align:start position:0% +of two +um or on any of the other familiar ones + + align:start position:0% +um or on any of the other familiar ones + + + align:start position:0% +um or on any of the other familiar ones +you know um rational numbers are also + + align:start position:0% +you know um rational numbers are also + + + align:start position:0% +you know um rational numbers are also +members of uh + + align:start position:0% +members of uh + + + align:start position:0% +members of uh +are also count as real numbers and + + align:start position:0% +are also count as real numbers and + + + align:start position:0% +are also count as real numbers and +integers too um + + align:start position:0% +integers too um + + + align:start position:0% +integers too um +and so + + align:start position:0% +and so + + + align:start position:0% +and so +uh but you know there are these + + align:start position:0% +uh but you know there are these + + + align:start position:0% +uh but you know there are these +additional numbers that you can get by + + align:start position:0% +additional numbers that you can get by + + + align:start position:0% +additional numbers that you can get by +uh + + align:start position:0% +uh + + + align:start position:0% +uh +decimal expansions which may not be + + align:start position:0% +decimal expansions which may not be + + + align:start position:0% +decimal expansions which may not be +rational + + align:start position:0% +rational + + + align:start position:0% +rational +um + + align:start position:0% +um + + + align:start position:0% +um +and that collection even though in some + + align:start position:0% +and that collection even though in some + + + align:start position:0% +and that collection even though in some +ways it looks somewhat similar to the + + align:start position:0% +ways it looks somewhat similar to the + + + align:start position:0% +ways it looks somewhat similar to the +rational numbers um the real numbers i + + align:start position:0% +rational numbers um the real numbers i + + + align:start position:0% +rational numbers um the real numbers i +hope i said that right the real numbers + + align:start position:0% +hope i said that right the real numbers + + + align:start position:0% +hope i said that right the real numbers +um uh the the uh which is the set i'm + + align:start position:0% +um uh the the uh which is the set i'm + + + align:start position:0% +um uh the the uh which is the set i'm +considering here the ones with the + + align:start position:0% +considering here the ones with the + + + align:start position:0% +considering here the ones with the +infinite decimal expansions they + + align:start position:0% +infinite decimal expansions they + + + align:start position:0% +infinite decimal expansions they +actually are much larger + + align:start position:0% +actually are much larger + + + align:start position:0% +actually are much larger +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +the theorem is and this was discovered + + align:start position:0% +the theorem is and this was discovered + + + align:start position:0% +the theorem is and this was discovered +by kantor um that uh r is an uncountable + + align:start position:0% +by kantor um that uh r is an uncountable + + + align:start position:0% +by kantor um that uh r is an uncountable +set + + align:start position:0% +set + + + align:start position:0% +set +and the reason why i'm introducing this + + align:start position:0% +and the reason why i'm introducing this + + + align:start position:0% +and the reason why i'm introducing this +is um besides that i think it's + + align:start position:0% +is um besides that i think it's + + + align:start position:0% +is um besides that i think it's +interesting um + + align:start position:0% +interesting um + + + align:start position:0% +interesting um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and has some some relation uh to uh the + + align:start position:0% +and has some some relation uh to uh the + + + align:start position:0% +and has some some relation uh to uh the +kinds of things we're doing but it's + + align:start position:0% +kinds of things we're doing but it's + + + align:start position:0% +kinds of things we're doing but it's +really for the purposes right now is to + + align:start position:0% +really for the purposes right now is to + + + align:start position:0% +really for the purposes right now is to +introduce this method called + + align:start position:0% +introduce this method called + + + align:start position:0% +introduce this method called +diagonalization + + align:start position:0% +diagonalization + + + align:start position:0% +diagonalization +um + + align:start position:0% +um + + + align:start position:0% +um +okay uh that's we're gonna use later on + + align:start position:0% +okay uh that's we're gonna use later on + + + align:start position:0% +okay uh that's we're gonna use later on +again but this is the first time it + + align:start position:0% +again but this is the first time it + + + align:start position:0% +again but this is the first time it +appeared + + align:start position:0% +appeared + + + align:start position:0% +appeared +so we're going to + + align:start position:0% +so we're going to + + + align:start position:0% +so we're going to +use a proof by contradiction in order to + + align:start position:0% +use a proof by contradiction in order to + + + align:start position:0% +use a proof by contradiction in order to +show that r the collection of real + + align:start position:0% +show that r the collection of real + + + align:start position:0% +show that r the collection of real +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +is uncountable and we'll assume for + + align:start position:0% +is uncountable and we'll assume for + + + align:start position:0% +is uncountable and we'll assume for +contradiction that r is countable + + align:start position:0% +contradiction that r is countable + + + align:start position:0% +contradiction that r is countable +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +if we assume that r is countable it + + align:start position:0% +if we assume that r is countable it + + + align:start position:0% +if we assume that r is countable it +means we have by definition a one to one + + align:start position:0% +means we have by definition a one to one + + + align:start position:0% +means we have by definition a one to one +correspondence from the natural numbers + + align:start position:0% +correspondence from the natural numbers + + + align:start position:0% +correspondence from the natural numbers +to the real numbers + + align:start position:0% +to the real numbers + + + align:start position:0% +to the real numbers +okay so we can match up + + align:start position:0% +okay so we can match up + + + align:start position:0% +okay so we can match up +all of the natural numbers with + + align:start position:0% +all of the natural numbers with + + + align:start position:0% +all of the natural numbers with +uh the real numbers in a one-to-one and + + align:start position:0% +uh the real numbers in a one-to-one and + + + align:start position:0% +uh the real numbers in a one-to-one and +onto fashion so we can pair up the + + align:start position:0% +onto fashion so we can pair up the + + + align:start position:0% +onto fashion so we can pair up the +natural numbers with the real numbers + + align:start position:0% +natural numbers with the real numbers + + + align:start position:0% +natural numbers with the real numbers +and we will cover all of the real + + align:start position:0% +and we will cover all of the real + + + align:start position:0% +and we will cover all of the real +numbers by doing that and we can make a + + align:start position:0% +numbers by doing that and we can make a + + + align:start position:0% +numbers by doing that and we can make a +table + + align:start position:0% +table + + + align:start position:0% +table +just like i did before + + align:start position:0% +just like i did before + + + align:start position:0% +just like i did before +here it is + + align:start position:0% +here it is + + + align:start position:0% +here it is +um + + align:start position:0% +um + + + align:start position:0% +um +and you can fill this out with all of + + align:start position:0% +and you can fill this out with all of + + + align:start position:0% +and you can fill this out with all of +the real numbers + + align:start position:0% +the real numbers + + + align:start position:0% +the real numbers +and um + + align:start position:0% +and um + + + align:start position:0% +and um +that was what the assumption means and + + align:start position:0% +that was what the assumption means and + + + align:start position:0% +that was what the assumption means and +i'm going to show you that that's + + align:start position:0% +i'm going to show you that that's + + + align:start position:0% +i'm going to show you that that's +impossible something is going to go + + align:start position:0% +impossible something is going to go + + + align:start position:0% +impossible something is going to go +terribly wrong if you do that + + align:start position:0% +terribly wrong if you do that + + + align:start position:0% +terribly wrong if you do that +um now uh + + align:start position:0% +um now uh + + + align:start position:0% +um now uh +you might disagree you might be + + align:start position:0% +you might disagree you might be + + + align:start position:0% +you might disagree you might be +surprised you might think well + + align:start position:0% +surprised you might think well + + + align:start position:0% +surprised you might think well +uh professor sipser is wrong um you know + + align:start position:0% +uh professor sipser is wrong um you know + + + align:start position:0% +uh professor sipser is wrong um you know +that i'm gonna work on this overnight + + align:start position:0% +that i'm gonna work on this overnight + + + align:start position:0% +that i'm gonna work on this overnight +and forget the rest of my classes and + + align:start position:0% +and forget the rest of my classes and + + + align:start position:0% +and forget the rest of my classes and +i'm gonna come up with a list of + + align:start position:0% +i'm gonna come up with a list of + + + align:start position:0% +i'm gonna come up with a list of +uh all the real numbers i'm gonna fill + + align:start position:0% +uh all the real numbers i'm gonna fill + + + align:start position:0% +uh all the real numbers i'm gonna fill +them out here and show that that's + + align:start position:0% +them out here and show that that's + + + align:start position:0% +them out here and show that that's +impossible um so let's say + + align:start position:0% +impossible um so let's say + + + align:start position:0% +impossible um so let's say +hypothetically just for my example's + + align:start position:0% +hypothetically just for my example's + + + align:start position:0% +hypothetically just for my example's +sake um here is the list that you came + + align:start position:0% +sake um here is the list that you came + + + align:start position:0% +sake um here is the list that you came +up with um + + align:start position:0% +up with um + + + align:start position:0% +up with um +so you know you had to match up + + align:start position:0% +so you know you had to match up + + + align:start position:0% +so you know you had to match up +something with the one let's say e had + + align:start position:0% +something with the one let's say e had + + + align:start position:0% +something with the one let's say e had +to that was a special case so you're + + align:start position:0% +to that was a special case so you're + + + align:start position:0% +to that was a special case so you're +gonna stick that with one and then pi + + align:start position:0% +gonna stick that with one and then pi + + + align:start position:0% +gonna stick that with one and then pi +came out to be the number that you you + + align:start position:0% +came out to be the number that you you + + + align:start position:0% +came out to be the number that you you +connected up with uh two you wanna see + + align:start position:0% +connected up with uh two you wanna see + + + align:start position:0% +connected up with uh two you wanna see +what i'm doing here i'm making a list + + align:start position:0% +what i'm doing here i'm making a list + + + align:start position:0% +what i'm doing here i'm making a list +i'm trying to make my one my + + align:start position:0% +i'm trying to make my one my + + + align:start position:0% +i'm trying to make my one my +correspondence my matching up between + + align:start position:0% +correspondence my matching up between + + + align:start position:0% +correspondence my matching up between +the natural numbers and my real numbers + + align:start position:0% +the natural numbers and my real numbers + + + align:start position:0% +the natural numbers and my real numbers +that i'm hypothesizing to exist for a + + align:start position:0% +that i'm hypothesizing to exist for a + + + align:start position:0% +that i'm hypothesizing to exist for a +contradiction + + align:start position:0% +contradiction + + + align:start position:0% +contradiction +so three + + align:start position:0% +so three + + + align:start position:0% +so three +i i don't know three is gets connected + + align:start position:0% +i i don't know three is gets connected + + + align:start position:0% +i i don't know three is gets connected +to zero i'm making this up obviously uh + + align:start position:0% +to zero i'm making this up obviously uh + + + align:start position:0% +to zero i'm making this up obviously uh +not on the spot i wrote the slide you + + align:start position:0% +not on the spot i wrote the slide you + + + align:start position:0% +not on the spot i wrote the slide you +know uh yesterday but uh here's a square + + align:start position:0% +know uh yesterday but uh here's a square + + + align:start position:0% +know uh yesterday but uh here's a square +root of two showing up for whatever + + align:start position:0% +root of two showing up for whatever + + + align:start position:0% +root of two showing up for whatever +reason here is one seventh + + align:start position:0% +reason here is one seventh + + + align:start position:0% +reason here is one seventh +here is some other number which i'll be + + align:start position:0% +here is some other number which i'll be + + + align:start position:0% +here is some other number which i'll be +interested if you recognize that one + + align:start position:0% +interested if you recognize that one + + + align:start position:0% +interested if you recognize that one +that's a that's a subtle one um + + align:start position:0% +that's a that's a subtle one um + + + align:start position:0% +that's a that's a subtle one um +this is one point two three four one + + align:start position:0% +this is one point two three four one + + + align:start position:0% +this is one point two three four one +point yeah some some familiar looking + + align:start position:0% +point yeah some some familiar looking + + + align:start position:0% +point yeah some some familiar looking +sequence here and whatever it is + + align:start position:0% +sequence here and whatever it is + + + align:start position:0% +sequence here and whatever it is +whatever it is this is what you came up + + align:start position:0% +whatever it is this is what you came up + + + align:start position:0% +whatever it is this is what you came up +with you claim that this is to work as + + align:start position:0% +with you claim that this is to work as + + + align:start position:0% +with you claim that this is to work as +uh very good you somebody got it + + align:start position:0% +uh very good you somebody got it + + + align:start position:0% +uh very good you somebody got it +it's i to the eighth power but let's not + + align:start position:0% +it's i to the eighth power but let's not + + + align:start position:0% +it's i to the eighth power but let's not +get hung up on that please um + + align:start position:0% +get hung up on that please um + + + align:start position:0% +get hung up on that please um +i to the either power oddly enough can + + align:start position:0% +i to the either power oddly enough can + + + align:start position:0% +i to the either power oddly enough can +be seen as a real number under you know + + align:start position:0% +be seen as a real number under you know + + + align:start position:0% +be seen as a real number under you know +if you define the uh + + align:start position:0% +if you define the uh + + + align:start position:0% +if you define the uh +imaginary exponentiation + + align:start position:0% +imaginary exponentiation + + + align:start position:0% +imaginary exponentiation +uh which is weird but anyway + + align:start position:0% +uh which is weird but anyway + + + align:start position:0% +uh which is weird but anyway +let's uh let's not get too distracted um + + align:start position:0% +let's uh let's not get too distracted um + + + align:start position:0% +let's uh let's not get too distracted um +so here's my list of numbers my real + + align:start position:0% +so here's my list of numbers my real + + + align:start position:0% +so here's my list of numbers my real +numbers that i've matched up in my table + + align:start position:0% +numbers that i've matched up in my table + + + align:start position:0% +numbers that i've matched up in my table +here with the natural numbers + + align:start position:0% +here with the natural numbers + + + align:start position:0% +here with the natural numbers +now something's go i claim something + + align:start position:0% +now something's go i claim something + + + align:start position:0% +now something's go i claim something +goes wrong what goes wrong i'm going to + + align:start position:0% +goes wrong what goes wrong i'm going to + + + align:start position:0% +goes wrong what goes wrong i'm going to +show you that you actually + + align:start position:0% +show you that you actually + + + align:start position:0% +show you that you actually +uh did not + + align:start position:0% +uh did not + + + align:start position:0% +uh did not +do as you claimed + + align:start position:0% +do as you claimed + + + align:start position:0% +do as you claimed +that there's actually um at least one + + align:start position:0% +that there's actually um at least one + + + align:start position:0% +that there's actually um at least one +number that's missing from this list and + + align:start position:0% +number that's missing from this list and + + + align:start position:0% +number that's missing from this list and +i'll exhibit that number i'm going to + + align:start position:0% +i'll exhibit that number i'm going to + + + align:start position:0% +i'll exhibit that number i'm going to +show you what that number is i'm going + + align:start position:0% +show you what that number is i'm going + + + align:start position:0% +show you what that number is i'm going +to explicitly come up with a number and + + align:start position:0% +to explicitly come up with a number and + + + align:start position:0% +to explicitly come up with a number and +show you that there's that number it's + + align:start position:0% +show you that there's that number it's + + + align:start position:0% +show you that there's that number it's +missing from the list um so here + + align:start position:0% +missing from the list um so here + + + align:start position:0% +missing from the list um so here +it's going to be a number x + + align:start position:0% +it's going to be a number x + + + align:start position:0% +it's going to be a number x +x is the x is the one that's missing + + align:start position:0% +x is the x is the one that's missing + + + align:start position:0% +x is the x is the one that's missing +so how am i going to get x + + align:start position:0% +so how am i going to get x + + + align:start position:0% +so how am i going to get x +so x well i'm going to start it off with + + align:start position:0% +so x well i'm going to start it off with + + + align:start position:0% +so x well i'm going to start it off with +zero point and then i'm going to fill + + align:start position:0% +zero point and then i'm going to fill + + + align:start position:0% +zero point and then i'm going to fill +out the rest of the places and how am i + + align:start position:0% +out the rest of the places and how am i + + + align:start position:0% +out the rest of the places and how am i +going to get those places i'm going to + + align:start position:0% +going to get those places i'm going to + + + align:start position:0% +going to get those places i'm going to +look at the table here + + align:start position:0% + + + + align:start position:0% + +so i want to look at to get my first + + align:start position:0% +so i want to look at to get my first + + + align:start position:0% +so i want to look at to get my first +digit after the decimal point of x + + align:start position:0% +digit after the decimal point of x + + + align:start position:0% +digit after the decimal point of x +i'm going to look at the first digit + + align:start position:0% +i'm going to look at the first digit + + + align:start position:0% +i'm going to look at the first digit +after the decimal point of the very + + align:start position:0% +after the decimal point of the very + + + align:start position:0% +after the decimal point of the very +first number + + align:start position:0% +first number + + + align:start position:0% +first number +so i take the first number look at the + + align:start position:0% +so i take the first number look at the + + + align:start position:0% +so i take the first number look at the +first digit after the decimal point + + align:start position:0% +first digit after the decimal point + + + align:start position:0% +first digit after the decimal point +and which happens to be a 7 + + align:start position:0% +and which happens to be a 7 + + + align:start position:0% +and which happens to be a 7 +and the number i'm going to put in for x + + align:start position:0% +and the number i'm going to put in for x + + + align:start position:0% +and the number i'm going to put in for x +is not going to be 7 it's going to be + + align:start position:0% +is not going to be 7 it's going to be + + + align:start position:0% +is not going to be 7 it's going to be +anything except 7. + + align:start position:0% +anything except 7. + + + align:start position:0% +anything except 7. +let's say + + align:start position:0% +let's say + + + align:start position:0% +let's say +8. um + + align:start position:0% +8. um + + + align:start position:0% +8. um +for my next digit of x + + align:start position:0% +for my next digit of x + + + align:start position:0% +for my next digit of x +i'm going to look at + + align:start position:0% +i'm going to look at + + + align:start position:0% +i'm going to look at +so my second digit of x i'm going to + + align:start position:0% +so my second digit of x i'm going to + + + align:start position:0% +so my second digit of x i'm going to +after the decimal everything's going to + + align:start position:0% +after the decimal everything's going to + + + align:start position:0% +after the decimal everything's going to +be after the decimal point now uh so i'm + + align:start position:0% +be after the decimal point now uh so i'm + + + align:start position:0% +be after the decimal point now uh so i'm +not going to keep saying that i'm going + + align:start position:0% +not going to keep saying that i'm going + + + align:start position:0% +not going to keep saying that i'm going +to look at the second digit of the + + align:start position:0% +to look at the second digit of the + + + align:start position:0% +to look at the second digit of the +second number uh which is a four + + align:start position:0% +second number uh which is a four + + + align:start position:0% +second number uh which is a four +uh after the decimal point um + + align:start position:0% +uh after the decimal point um + + + align:start position:0% +uh after the decimal point um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +there it is + + align:start position:0% +there it is + + + align:start position:0% +there it is +and for the second digit of x i'm going + + align:start position:0% +and for the second digit of x i'm going + + + align:start position:0% +and for the second digit of x i'm going +to use something which is + + align:start position:0% +to use something which is + + + align:start position:0% +to use something which is +anything besides four five + + align:start position:0% +anything besides four five + + + align:start position:0% +anything besides four five +i have some flexibility here um so i + + align:start position:0% +i have some flexibility here um so i + + + align:start position:0% +i have some flexibility here um so i +could have used six i could have used + + align:start position:0% +could have used six i could have used + + + align:start position:0% +could have used six i could have used +seven + + align:start position:0% +seven + + + align:start position:0% +seven +i'm going for those of you who have seen + + align:start position:0% +i'm going for those of you who have seen + + + align:start position:0% +i'm going for those of you who have seen +this before who are gonna nitpick on me + + align:start position:0% +this before who are gonna nitpick on me + + + align:start position:0% +this before who are gonna nitpick on me +i'm gonna stay away from nine and zero + + align:start position:0% +i'm gonna stay away from nine and zero + + + align:start position:0% +i'm gonna stay away from nine and zero +just because there are some little um + + align:start position:0% +just because there are some little um + + + align:start position:0% +just because there are some little um +edge cases that arise there which i + + align:start position:0% +edge cases that arise there which i + + + align:start position:0% +edge cases that arise there which i +don't want to get into because i don't + + align:start position:0% +don't want to get into because i don't + + + align:start position:0% +don't want to get into because i don't +think it's interesting for this argument + + align:start position:0% +think it's interesting for this argument + + + align:start position:0% +think it's interesting for this argument +um but since i have some flexibility i'm + + align:start position:0% +um but since i have some flexibility i'm + + + align:start position:0% +um but since i have some flexibility i'm +going to avoid zeros and nines probably + + align:start position:0% +going to avoid zeros and nines probably + + + align:start position:0% +going to avoid zeros and nines probably +just nine is all i really need and then + + align:start position:0% +just nine is all i really need and then + + + align:start position:0% +just nine is all i really need and then +um + + align:start position:0% +um + + + align:start position:0% +um +the argument is just going to work fine + + align:start position:0% +the argument is just going to work fine + + + align:start position:0% +the argument is just going to work fine +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so uh the next digit is a zero + + align:start position:0% +so uh the next digit is a zero + + + align:start position:0% +so uh the next digit is a zero +uh for the third digit of the third + + align:start position:0% +uh for the third digit of the third + + + align:start position:0% +uh for the third digit of the third +number is a zero the third digit of x is + + align:start position:0% +number is a zero the third digit of x is + + + align:start position:0% +number is a zero the third digit of x is +going to be anything except for zero be + + align:start position:0% +going to be anything except for zero be + + + align:start position:0% +going to be anything except for zero be +a one + + align:start position:0% +a one + + + align:start position:0% +a one +then i have a two here + + align:start position:0% + + + + align:start position:0% + +anything except a two + + align:start position:0% +anything except a two + + + align:start position:0% +anything except a two +six + + align:start position:0% +six + + + align:start position:0% +six +uh then five anything except a five a + + align:start position:0% +uh then five anything except a five a + + + align:start position:0% +uh then five anything except a five a +one a nine anything except a nine an + + align:start position:0% +one a nine anything except a nine an + + + align:start position:0% +one a nine anything except a nine an +eight + + align:start position:0% +eight + + + align:start position:0% +eight +and so on there's an eight + + align:start position:0% +and so on there's an eight + + + align:start position:0% +and so on there's an eight +there's a two and dot dot dot i'm just + + align:start position:0% +there's a two and dot dot dot i'm just + + + align:start position:0% +there's a two and dot dot dot i'm just +gonna keep doing that + + align:start position:0% +gonna keep doing that + + + align:start position:0% +gonna keep doing that +and i'm gonna say + + align:start position:0% +and i'm gonna say + + + align:start position:0% +and i'm gonna say +you missed that number whatever it is + + align:start position:0% +you missed that number whatever it is + + + align:start position:0% +you missed that number whatever it is +but that number it's a that's a number + + align:start position:0% +but that number it's a that's a number + + + align:start position:0% +but that number it's a that's a number +after i'm all done it's going to be the + + align:start position:0% +after i'm all done it's going to be the + + + align:start position:0% +after i'm all done it's going to be the +decimal representation of something + + align:start position:0% +decimal representation of something + + + align:start position:0% +decimal representation of something +and that number uh i claim + + align:start position:0% +and that number uh i claim + + + align:start position:0% +and that number uh i claim +is absent from the table + + align:start position:0% +is absent from the table + + + align:start position:0% +is absent from the table +and you might say well + + align:start position:0% +and you might say well + + + align:start position:0% +and you might say well +you know it's really there + + align:start position:0% +you know it's really there + + + align:start position:0% +you know it's really there +um it's just on the + + align:start position:0% +um it's just on the + + + align:start position:0% +um it's just on the +um + + align:start position:0% +um + + + align:start position:0% +um +23rd row + + align:start position:0% +23rd row + + + align:start position:0% +23rd row +you just didn't get to it on your slide + + align:start position:0% +you just didn't get to it on your slide + + + align:start position:0% +you just didn't get to it on your slide +but it's there well i'm going to say i + + align:start position:0% +but it's there well i'm going to say i + + + align:start position:0% +but it's there well i'm going to say i +know it's not in the 23rd row because it + + align:start position:0% +know it's not in the 23rd row because it + + + align:start position:0% +know it's not in the 23rd row because it +differs from the number in the 23rd row + + align:start position:0% +differs from the number in the 23rd row + + + align:start position:0% +differs from the number in the 23rd row +at the 23rd digit + + align:start position:0% +at the 23rd digit + + + align:start position:0% +at the 23rd digit +because i constructed it that way + + align:start position:0% +because i constructed it that way + + + align:start position:0% +because i constructed it that way +this number is designed + + align:start position:0% +this number is designed + + + align:start position:0% +this number is designed +explicitly to be different from each of + + align:start position:0% +explicitly to be different from each of + + + align:start position:0% +explicitly to be different from each of +the numbers that's on the list + + align:start position:0% + + + + align:start position:0% + +okay so it can't be on the list because + + align:start position:0% +okay so it can't be on the list because + + + align:start position:0% +okay so it can't be on the list because +it's been constructed to be different + + align:start position:0% +it's been constructed to be different + + + align:start position:0% +it's been constructed to be different +from each of them in at least one place + + align:start position:0% +from each of them in at least one place + + + align:start position:0% +from each of them in at least one place +so it's i think this is a beautiful + + align:start position:0% +so it's i think this is a beautiful + + + align:start position:0% +so it's i think this is a beautiful +argument and it shows that + + align:start position:0% +argument and it shows that + + + align:start position:0% +argument and it shows that +uh no matter how you try to come up with + + align:start position:0% +uh no matter how you try to come up with + + + align:start position:0% +uh no matter how you try to come up with +a one-to-one correspondence you're going + + align:start position:0% +a one-to-one correspondence you're going + + + align:start position:0% +a one-to-one correspondence you're going +to fail you know you might say oh you + + align:start position:0% +to fail you know you might say oh you + + + align:start position:0% +to fail you know you might say oh you +know like + + align:start position:0% +know like + + + align:start position:0% +know like +you know just one number you know it did + + align:start position:0% +you know just one number you know it did + + + align:start position:0% +you know just one number you know it did +so much hard work and missing just one + + align:start position:0% +so much hard work and missing just one + + + align:start position:0% +so much hard work and missing just one +number can i get partial credit + + align:start position:0% +number can i get partial credit + + + align:start position:0% +number can i get partial credit +you know and put this one on the list + + align:start position:0% +you know and put this one on the list + + + align:start position:0% +you know and put this one on the list +now i fix it no obviously there are many + + align:start position:0% +now i fix it no obviously there are many + + + align:start position:0% +now i fix it no obviously there are many +many numbers that are missing if you put + + align:start position:0% +many numbers that are missing if you put + + + align:start position:0% +many numbers that are missing if you put +this one on the list i'm going to + + align:start position:0% +this one on the list i'm going to + + + align:start position:0% +this one on the list i'm going to +construct another number that was + + align:start position:0% +construct another number that was + + + align:start position:0% +construct another number that was +missing + + align:start position:0% +missing + + + align:start position:0% +missing +so + + align:start position:0% +so + + + align:start position:0% +so +um this is uh + + align:start position:0% +um this is uh + + + align:start position:0% +um this is uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +there's just not no possibility of + + align:start position:0% +there's just not no possibility of + + + align:start position:0% +there's just not no possibility of +fixing this and in fact you know the um + + align:start position:0% +fixing this and in fact you know the um + + + align:start position:0% +fixing this and in fact you know the um +the real numbers are + + align:start position:0% +the real numbers are + + + align:start position:0% +the real numbers are +are uncountable cannot be matched up + + align:start position:0% +are uncountable cannot be matched up + + + align:start position:0% +are uncountable cannot be matched up +with the natural numbers and there's + + align:start position:0% +with the natural numbers and there's + + + align:start position:0% +with the natural numbers and there's +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +it can't even come it doesn't even come + + align:start position:0% +it can't even come it doesn't even come + + + align:start position:0% +it can't even come it doesn't even come +close um + + align:start position:0% +close um + + + align:start position:0% +close um +so um + + align:start position:0% +so um + + + align:start position:0% +so um +here's summary what i just said + + align:start position:0% +here's summary what i just said + + + align:start position:0% +here's summary what i just said +um f is not a one-to-one correspondence + + align:start position:0% +um f is not a one-to-one correspondence + + + align:start position:0% +um f is not a one-to-one correspondence +no matter what you try to do you can't + + align:start position:0% +no matter what you try to do you can't + + + align:start position:0% +no matter what you try to do you can't +come up with a one-to-one correspondence + + align:start position:0% +come up with a one-to-one correspondence + + + align:start position:0% +come up with a one-to-one correspondence +so that's the contradiction + + align:start position:0% +so that's the contradiction + + + align:start position:0% +so that's the contradiction +okay so that proves that + + align:start position:0% +okay so that proves that + + + align:start position:0% +okay so that proves that +r is uncountable + + align:start position:0% +r is uncountable + + + align:start position:0% +r is uncountable +okay and that's why by the way we call + + align:start position:0% +okay and that's why by the way we call + + + align:start position:0% +okay and that's why by the way we call +this a diagonalization because we're + + align:start position:0% +this a diagonalization because we're + + + align:start position:0% +this a diagonalization because we're +going down this diagonal here that's + + align:start position:0% +going down this diagonal here that's + + + align:start position:0% +going down this diagonal here that's +where the term that's where the name has + + align:start position:0% +where the term that's where the name has + + + align:start position:0% +where the term that's where the name has +come from + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so i i'm happy to + + align:start position:0% + + + + align:start position:0% + +okay that's it uh + + align:start position:0% +okay that's it uh + + + align:start position:0% +okay that's it uh +somebody's asking me + + align:start position:0% +somebody's asking me + + + align:start position:0% +somebody's asking me +i'm actually i have a + + align:start position:0% +i'm actually i have a + + + align:start position:0% +i'm actually i have a +um + + align:start position:0% +um + + + align:start position:0% +um +is it here i can't remember it's here i + + align:start position:0% +is it here i can't remember it's here i + + + align:start position:0% +is it here i can't remember it's here i +have a uh check-in coming about this and + + align:start position:0% +have a uh check-in coming about this and + + + align:start position:0% +have a uh check-in coming about this and +somebody is kind of um anticipating that + + align:start position:0% +somebody is kind of um anticipating that + + + align:start position:0% +somebody is kind of um anticipating that +by asking uh the the actual rather + + align:start position:0% +by asking uh the the actual rather + + + align:start position:0% +by asking uh the the actual rather +famous question about there being a + + align:start position:0% +famous question about there being a + + + align:start position:0% +famous question about there being a +possible infinity in between + + align:start position:0% +possible infinity in between + + + align:start position:0% +possible infinity in between +the natural numbers and the real numbers + + align:start position:0% +the natural numbers and the real numbers + + + align:start position:0% +the natural numbers and the real numbers +we know the real numbers now are bigger + + align:start position:0% +we know the real numbers now are bigger + + + align:start position:0% +we know the real numbers now are bigger +than the natural numbers but is there + + align:start position:0% +than the natural numbers but is there + + + align:start position:0% +than the natural numbers but is there +something that's in between i mean this + + align:start position:0% +something that's in between i mean this + + + align:start position:0% +something that's in between i mean this +is a very very famous problem um + + align:start position:0% +is a very very famous problem um + + + align:start position:0% +is a very very famous problem um +uh which i'll talk about you know when + + align:start position:0% +uh which i'll talk about you know when + + + align:start position:0% +uh which i'll talk about you know when +we get to our check-in which is coming + + align:start position:0% +we get to our check-in which is coming + + + align:start position:0% +we get to our check-in which is coming +up + + align:start position:0% +up + + + align:start position:0% +up +um + + align:start position:0% + + + + align:start position:0% + +well somebody is objecting just the way + + align:start position:0% +well somebody is objecting just the way + + + align:start position:0% +well somebody is objecting just the way +i've defined x using this procedure that + + align:start position:0% +i've defined x using this procedure that + + + align:start position:0% +i've defined x using this procedure that +really really can't in a sense state + + align:start position:0% +really really can't in a sense state + + + align:start position:0% +really really can't in a sense state +you know but it x is a number x is the + + align:start position:0% +you know but it x is a number x is the + + + align:start position:0% +you know but it x is a number x is the +result of + + align:start position:0% +result of + + + align:start position:0% +result of +what what this procedure is it's you + + align:start position:0% +what what this procedure is it's you + + + align:start position:0% +what what this procedure is it's you +know following this procedure we're + + align:start position:0% +know following this procedure we're + + + align:start position:0% +know following this procedure we're +converging on some particular value and + + align:start position:0% +converging on some particular value and + + + align:start position:0% +converging on some particular value and +so that is the value um if you want you + + align:start position:0% +so that is the value um if you want you + + + align:start position:0% +so that is the value um if you want you +know we can make a more precise way of + + align:start position:0% +know we can make a more precise way of + + + align:start position:0% +know we can make a more precise way of +determining i mean i so i we don't have + + align:start position:0% +determining i mean i so i we don't have + + + align:start position:0% +determining i mean i so i we don't have +the flexibility of choosing the way i + + align:start position:0% +the flexibility of choosing the way i + + + align:start position:0% +the flexibility of choosing the way i +did in my example we can make a precise + + align:start position:0% +did in my example we can make a precise + + + align:start position:0% +did in my example we can make a precise +procedure for coming up with these + + align:start position:0% +procedure for coming up with these + + + align:start position:0% +procedure for coming up with these +digits but + + align:start position:0% +digits but + + + align:start position:0% +digits but +i don't think there's anybody thinks + + align:start position:0% +i don't think there's anybody thinks + + + align:start position:0% +i don't think there's anybody thinks +there's anything + + align:start position:0% +there's anything + + + align:start position:0% +there's anything +that's um + + align:start position:0% + + + + align:start position:0% + +there's any shortcoming in this argument + + align:start position:0% +there's any shortcoming in this argument + + + align:start position:0% +there's any shortcoming in this argument +in terms of the way we're defining x + + align:start position:0% +in terms of the way we're defining x + + + align:start position:0% +in terms of the way we're defining x +it's i i think it's worth understanding + + align:start position:0% +it's i i think it's worth understanding + + + align:start position:0% +it's i i think it's worth understanding +this + + align:start position:0% +this + + + align:start position:0% +this +because it's really going to set the + + align:start position:0% +because it's really going to set the + + + align:start position:0% +because it's really going to set the +groundwork for our proof that atm is + + align:start position:0% +groundwork for our proof that atm is + + + align:start position:0% +groundwork for our proof that atm is +undecidable which is a little i think + + align:start position:0% +undecidable which is a little i think + + + align:start position:0% +undecidable which is a little i think +perhaps slightly more abstract in a way + + align:start position:0% +perhaps slightly more abstract in a way + + + align:start position:0% +perhaps slightly more abstract in a way +um in the way it sort of comes across + + align:start position:0% +um in the way it sort of comes across + + + align:start position:0% +um in the way it sort of comes across +i'm going to try to can make connect the + + align:start position:0% +i'm going to try to can make connect the + + + align:start position:0% +i'm going to try to can make connect the +two + + align:start position:0% +two + + + align:start position:0% +two +but uh i think it's helpful to + + align:start position:0% +but uh i think it's helpful to + + + align:start position:0% +but uh i think it's helpful to +understand at least this argument + + align:start position:0% +understand at least this argument + + + align:start position:0% +understand at least this argument +because this argument is kind of + + align:start position:0% +because this argument is kind of + + + align:start position:0% +because this argument is kind of +diagonalization in its kind of most + + align:start position:0% +diagonalization in its kind of most + + + align:start position:0% +diagonalization in its kind of most +raw form + + align:start position:0% + + + + align:start position:0% + +all right i think we're good um so let + + align:start position:0% +all right i think we're good um so let + + + align:start position:0% +all right i think we're good um so let +why don't we continue then um + + align:start position:0% +why don't we continue then um + + + align:start position:0% +why don't we continue then um +so there are a number of corollaries + + align:start position:0% +so there are a number of corollaries + + + align:start position:0% +so there are a number of corollaries +that follow from the statement that the + + align:start position:0% +that follow from the statement that the + + + align:start position:0% +that follow from the statement that the +real numbers is uncountable um + + align:start position:0% +real numbers is uncountable um + + + align:start position:0% +real numbers is uncountable um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +first of all if you let script l be the + + align:start position:0% +first of all if you let script l be the + + + align:start position:0% +first of all if you let script l be the +collection of all languages if you want + + align:start position:0% +collection of all languages if you want + + + align:start position:0% +collection of all languages if you want +to consider over some particular + + align:start position:0% +to consider over some particular + + + align:start position:0% +to consider over some particular +alphabet that's fine but that's not + + align:start position:0% +alphabet that's fine but that's not + + + align:start position:0% +alphabet that's fine but that's not +going to be really uh + + align:start position:0% +going to be really uh + + + align:start position:0% +going to be really uh +you know important for this uh + + align:start position:0% +you know important for this uh + + + align:start position:0% +you know important for this uh +point that i'm trying going to make so + + align:start position:0% +point that i'm trying going to make so + + + align:start position:0% +point that i'm trying going to make so +uh l + + align:start position:0% +uh l + + + align:start position:0% +uh l +uh script l is the collection of all + + align:start position:0% +uh script l is the collection of all + + + align:start position:0% +uh script l is the collection of all +languages um so every subset + + align:start position:0% +languages um so every subset + + + align:start position:0% +languages um so every subset +of sigma star + + align:start position:0% +of sigma star + + + align:start position:0% +of sigma star +every subset of sigma star is a language + + align:start position:0% +every subset of sigma star is a language + + + align:start position:0% +every subset of sigma star is a language +um so look at all those possible subsets + + align:start position:0% +um so look at all those possible subsets + + + align:start position:0% +um so look at all those possible subsets +um so that includes you know 0 to the k + + align:start position:0% +um so that includes you know 0 to the k + + + align:start position:0% +um so that includes you know 0 to the k +1 to the k plus every other language you + + align:start position:0% +1 to the k plus every other language you + + + align:start position:0% +1 to the k plus every other language you +can ever think of and more all possible + + align:start position:0% +can ever think of and more all possible + + + align:start position:0% +can ever think of and more all possible +languages + + align:start position:0% +languages + + + align:start position:0% +languages +um so that + + align:start position:0% +um so that + + + align:start position:0% +um so that +the collection of all languages is + + align:start position:0% +the collection of all languages is + + + align:start position:0% +the collection of all languages is +uncountable + + align:start position:0% +uncountable + + + align:start position:0% +uncountable +there's uncountably many different + + align:start position:0% +there's uncountably many different + + + align:start position:0% +there's uncountably many different +languages out there + + align:start position:0% +languages out there + + + align:start position:0% +languages out there +i don't want to belabor this point you + + align:start position:0% +i don't want to belabor this point you + + + align:start position:0% +i don't want to belabor this point you +can just take this if you don't quite + + align:start position:0% +can just take this if you don't quite + + + align:start position:0% +can just take this if you don't quite +follow the the quick argument i'm going + + align:start position:0% +follow the the quick argument i'm going + + + align:start position:0% +follow the the quick argument i'm going +to make here but um + + align:start position:0% +to make here but um + + + align:start position:0% +to make here but um +uh you can make a correspondence + + align:start position:0% +uh you can make a correspondence + + + align:start position:0% +uh you can make a correspondence +one-to-one correspondence from all + + align:start position:0% +one-to-one correspondence from all + + + align:start position:0% +one-to-one correspondence from all +languages to the reals + + align:start position:0% +languages to the reals + + + align:start position:0% +languages to the reals +so that each language gets its own real + + align:start position:0% +so that each language gets its own real + + + align:start position:0% +so that each language gets its own real +number + + align:start position:0% +number + + + align:start position:0% +number +and the way i'm going to think about + + align:start position:0% +and the way i'm going to think about + + + align:start position:0% +and the way i'm going to think about +that let's put the real numbers into + + align:start position:0% +that let's put the real numbers into + + + align:start position:0% +that let's put the real numbers into +binary form + + align:start position:0% +binary form + + + align:start position:0% +binary form +and if you imagine here being sigma star + + align:start position:0% +and if you imagine here being sigma star + + + align:start position:0% +and if you imagine here being sigma star +all of the possible strings of sigma + + align:start position:0% +all of the possible strings of sigma + + + align:start position:0% +all of the possible strings of sigma +star + + align:start position:0% +star + + + align:start position:0% +star +you know written out in their standard + + align:start position:0% +you know written out in their standard + + + align:start position:0% +you know written out in their standard +order + + align:start position:0% +order + + + align:start position:0% +order +um and now if you have a language here a + + align:start position:0% +um and now if you have a language here a + + + align:start position:0% +um and now if you have a language here a +it's just some arbitrary language so + + align:start position:0% +it's just some arbitrary language so + + + align:start position:0% +it's just some arbitrary language so +that's going to have some of the strings + + align:start position:0% +that's going to have some of the strings + + + align:start position:0% +that's going to have some of the strings +of um of sigma star appearing like zero + + align:start position:0% +of um of sigma star appearing like zero + + + align:start position:0% +of um of sigma star appearing like zero +is appearing but one is not appearing + + align:start position:0% +is appearing but one is not appearing + + + align:start position:0% +is appearing but one is not appearing +zero zero is appearing in zero one but + + align:start position:0% +zero zero is appearing in zero one but + + + align:start position:0% +zero zero is appearing in zero one but +not these three + + align:start position:0% + + + + align:start position:0% + +um and i'm gonna associate to a + + align:start position:0% +um and i'm gonna associate to a + + + align:start position:0% +um and i'm gonna associate to a +my language + + align:start position:0% +my language + + + align:start position:0% +my language +some real number in binary by putting in + + align:start position:0% +some real number in binary by putting in + + + align:start position:0% +some real number in binary by putting in +a zero in the decimal representation or + + align:start position:0% +a zero in the decimal representation or + + + align:start position:0% +a zero in the decimal representation or +the binary representation i should say + + align:start position:0% +the binary representation i should say + + + align:start position:0% +the binary representation i should say +um + + align:start position:0% +um + + + align:start position:0% +um +for that + + align:start position:0% +for that + + + align:start position:0% +for that +string + + align:start position:0% +string + + + align:start position:0% +string +if it's not there and a one if it is + + align:start position:0% +if it's not there and a one if it is + + + align:start position:0% +if it's not there and a one if it is +there + + align:start position:0% + + + + align:start position:0% + +um and so a real number because there's + + align:start position:0% +um and so a real number because there's + + + align:start position:0% +um and so a real number because there's +infinite many infinitely many yes no + + align:start position:0% +infinite many infinitely many yes no + + + align:start position:0% +infinite many infinitely many yes no +choices + + align:start position:0% +choices + + + align:start position:0% +choices +in the binary representation can + + align:start position:0% +in the binary representation can + + + align:start position:0% +in the binary representation can +represent a language because of each of + + align:start position:0% +represent a language because of each of + + + align:start position:0% +represent a language because of each of +the yes no choices of a string being + + align:start position:0% +the yes no choices of a string being + + + align:start position:0% +the yes no choices of a string being +present or not i'm going to put a one + + align:start position:0% +present or not i'm going to put a one + + + align:start position:0% +present or not i'm going to put a one +for when the string is present the zero + + align:start position:0% +for when the string is present the zero + + + align:start position:0% +for when the string is present the zero +when it's not present so each + + align:start position:0% +when it's not present so each + + + align:start position:0% +when it's not present so each +uh language has its own real number and + + align:start position:0% +uh language has its own real number and + + + align:start position:0% +uh language has its own real number and +each real number is going to be + + align:start position:0% +each real number is going to be + + + align:start position:0% +each real number is going to be +associated to its own uh language here + + align:start position:0% +associated to its own uh language here + + + align:start position:0% +associated to its own uh language here +i'm restricting myself to real numbers + + align:start position:0% +i'm restricting myself to real numbers + + + align:start position:0% +i'm restricting myself to real numbers +between zero and 1 + + align:start position:0% +between zero and 1 + + + align:start position:0% +between zero and 1 +that's not going to be an essential + + align:start position:0% +that's not going to be an essential + + + align:start position:0% +that's not going to be an essential +point so let's not get hung up on that + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the + + align:start position:0% +the + + + align:start position:0% +the +the fact that + + align:start position:0% +the fact that + + + align:start position:0% +the fact that +the + + align:start position:0% +the + + + align:start position:0% +the +the languages can be + + align:start position:0% +the languages can be + + + align:start position:0% +the languages can be +uh + + align:start position:0% + + + + align:start position:0% + +put into one-to-one correspondence with + + align:start position:0% +put into one-to-one correspondence with + + + align:start position:0% +put into one-to-one correspondence with +the real numbers + + align:start position:0% +the real numbers + + + align:start position:0% +the real numbers +um + + align:start position:0% +um + + + align:start position:0% +um +shows that the collection of all + + align:start position:0% +shows that the collection of all + + + align:start position:0% +shows that the collection of all +languages is also uncountable + + align:start position:0% +languages is also uncountable + + + align:start position:0% +languages is also uncountable +now another + + align:start position:0% +now another + + + align:start position:0% +now another +observation here another point worth + + align:start position:0% +observation here another point worth + + + align:start position:0% +observation here another point worth +noting is that if you look at sigma star + + align:start position:0% +noting is that if you look at sigma star + + + align:start position:0% +noting is that if you look at sigma star +itself + + align:start position:0% +itself + + + align:start position:0% +itself +the strings + + align:start position:0% +the strings + + + align:start position:0% +the strings +uh all possible strings that's a + + align:start position:0% +uh all possible strings that's a + + + align:start position:0% +uh all possible strings that's a +countable set + + align:start position:0% +countable set + + + align:start position:0% +countable set +the collection of all possible languages + + align:start position:0% +the collection of all possible languages + + + align:start position:0% +the collection of all possible languages +is uncountable but the collection of all + + align:start position:0% +is uncountable but the collection of all + + + align:start position:0% +is uncountable but the collection of all +possible finite strings + + align:start position:0% +possible finite strings + + + align:start position:0% +possible finite strings +is countable because i can just list + + align:start position:0% +is countable because i can just list + + + align:start position:0% +is countable because i can just list +them + + align:start position:0% +them + + + align:start position:0% +them +here is my list of all possible strings + + align:start position:0% +here is my list of all possible strings + + + align:start position:0% +here is my list of all possible strings +which you can put into a table if you + + align:start position:0% +which you can put into a table if you + + + align:start position:0% +which you can put into a table if you +like to think of it matching up with the + + align:start position:0% +like to think of it matching up with the + + + align:start position:0% +like to think of it matching up with the +natural numbers in that way + + align:start position:0% +natural numbers in that way + + + align:start position:0% +natural numbers in that way +now i'm get i'm trying to make a point + + align:start position:0% +now i'm get i'm trying to make a point + + + align:start position:0% +now i'm get i'm trying to make a point +here which is that + + align:start position:0% +here which is that + + + align:start position:0% +here which is that +if you take am which is all possible + + align:start position:0% +if you take am which is all possible + + + align:start position:0% +if you take am which is all possible +turing machines script m is all possible + + align:start position:0% +turing machines script m is all possible + + + align:start position:0% +turing machines script m is all possible +turing machines the collection of all + + align:start position:0% +turing machines the collection of all + + + align:start position:0% +turing machines the collection of all +possible turing machines is countable + + align:start position:0% +possible turing machines is countable + + + align:start position:0% +possible turing machines is countable +there are only countably many different + + align:start position:0% +there are only countably many different + + + align:start position:0% +there are only countably many different +turing machines + + align:start position:0% +turing machines + + + align:start position:0% +turing machines +and you can argue that in all sorts of + + align:start position:0% +and you can argue that in all sorts of + + + align:start position:0% +and you can argue that in all sorts of +messy different ways but i think the + + align:start position:0% +messy different ways but i think the + + + align:start position:0% +messy different ways but i think the +most simple way to see that + + align:start position:0% +most simple way to see that + + + align:start position:0% +most simple way to see that +is to think about each turing machine as + + align:start position:0% +is to think about each turing machine as + + + align:start position:0% +is to think about each turing machine as +having a description + + align:start position:0% +having a description + + + align:start position:0% +having a description +which is a string + + align:start position:0% +which is a string + + + align:start position:0% +which is a string +so the collection of all descriptions of + + align:start position:0% +so the collection of all descriptions of + + + align:start position:0% +so the collection of all descriptions of +turing machines is just a subset of + + align:start position:0% +turing machines is just a subset of + + + align:start position:0% +turing machines is just a subset of +sigma star which we already know is + + align:start position:0% +sigma star which we already know is + + + align:start position:0% +sigma star which we already know is +countable + + align:start position:0% +countable + + + align:start position:0% +countable +and the subset of any countable set is + + align:start position:0% +and the subset of any countable set is + + + align:start position:0% +and the subset of any countable set is +going to be countable + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +anyway + + align:start position:0% + + + + align:start position:0% + +i think it's worth + + align:start position:0% +i think it's worth + + + align:start position:0% +i think it's worth +remembering + + align:start position:0% +remembering + + + align:start position:0% +remembering +that + + align:start position:0% +that + + + align:start position:0% +that +the collection of all turing machines is + + align:start position:0% +the collection of all turing machines is + + + align:start position:0% +the collection of all turing machines is +countable + + align:start position:0% +countable + + + align:start position:0% +countable +um whereas the collection of languages + + align:start position:0% +um whereas the collection of languages + + + align:start position:0% +um whereas the collection of languages +is uncountable and that tells you right + + align:start position:0% +is uncountable and that tells you right + + + align:start position:0% +is uncountable and that tells you right +there + + align:start position:0% +there + + + align:start position:0% +there +that some language is not decided + + align:start position:0% + + + + align:start position:0% + +because there are more languages than + + align:start position:0% +because there are more languages than + + + align:start position:0% +because there are more languages than +touring machines + + align:start position:0% +touring machines + + + align:start position:0% +touring machines +we have uncountably many language only + + align:start position:0% +we have uncountably many language only + + + align:start position:0% +we have uncountably many language only +countably many turing machines so that's + + align:start position:0% +countably many turing machines so that's + + + align:start position:0% +countably many turing machines so that's +fewer turing machines than languages + + align:start position:0% +fewer turing machines than languages + + + align:start position:0% +fewer turing machines than languages +there's no way to map all the languages + + align:start position:0% +there's no way to map all the languages + + + align:start position:0% +there's no way to map all the languages +onto turing machines so there's going to + + align:start position:0% +onto turing machines so there's going to + + + align:start position:0% +onto turing machines so there's going to +always be some languages that got + + align:start position:0% +always be some languages that got + + + align:start position:0% +always be some languages that got +unmapped + + align:start position:0% +unmapped + + + align:start position:0% +unmapped +um and so in particular there are going + + align:start position:0% +um and so in particular there are going + + + align:start position:0% +um and so in particular there are going +to be some languages which are + + align:start position:0% +to be some languages which are + + + align:start position:0% +to be some languages which are +undecidable there are going to be some + + align:start position:0% +undecidable there are going to be some + + + align:start position:0% +undecidable there are going to be some +languages which are not touring + + align:start position:0% +languages which are not touring + + + align:start position:0% +languages which are not touring +recognizable + + align:start position:0% +recognizable + + + align:start position:0% +recognizable +and anything based on some automata kind + + align:start position:0% +and anything based on some automata kind + + + align:start position:0% +and anything based on some automata kind +of um + + align:start position:0% +of um + + + align:start position:0% +of um +definite definition process is going to + + align:start position:0% +definite definition process is going to + + + align:start position:0% +definite definition process is going to +be some languages that you're not going + + align:start position:0% +be some languages that you're not going + + + align:start position:0% +be some languages that you're not going +to be not going to be defining + + align:start position:0% +to be not going to be defining + + + align:start position:0% +to be not going to be defining +um + + align:start position:0% +um + + + align:start position:0% +um +okay now what this corollary shows you + + align:start position:0% +okay now what this corollary shows you + + + align:start position:0% +okay now what this corollary shows you +that there is some language out there + + align:start position:0% +that there is some language out there + + + align:start position:0% +that there is some language out there +which is not decidable what we're going + + align:start position:0% +which is not decidable what we're going + + + align:start position:0% +which is not decidable what we're going +to show next is that there is a specific + + align:start position:0% +to show next is that there is a specific + + + align:start position:0% +to show next is that there is a specific +language atm which is not decidable + + align:start position:0% +language atm which is not decidable + + + align:start position:0% +language atm which is not decidable +okay and but first i think we have a + + align:start position:0% +okay and but first i think we have a + + + align:start position:0% +okay and but first i think we have a +check-in coming up + + align:start position:0% +check-in coming up + + + align:start position:0% +check-in coming up +and + + align:start position:0% +and + + + align:start position:0% +and +let me give you a little bit of + + align:start position:0% +let me give you a little bit of + + + align:start position:0% +let me give you a little bit of +background here because this is relevant + + align:start position:0% +background here because this is relevant + + + align:start position:0% +background here because this is relevant +to this question that i got + + align:start position:0% +to this question that i got + + + align:start position:0% +to this question that i got +about intermediate sized sets so + + align:start position:0% +about intermediate sized sets so + + + align:start position:0% +about intermediate sized sets so +the question of whether there is a set + + align:start position:0% +the question of whether there is a set + + + align:start position:0% +the question of whether there is a set +of size between the natural numbers and + + align:start position:0% +of size between the natural numbers and + + + align:start position:0% +of size between the natural numbers and +the real knit numbers + + align:start position:0% +the real knit numbers + + + align:start position:0% +the real knit numbers +strictly in between so bigger than the + + align:start position:0% +strictly in between so bigger than the + + + align:start position:0% +strictly in between so bigger than the +natural numbers not the same size as the + + align:start position:0% +natural numbers not the same size as the + + + align:start position:0% +natural numbers not the same size as the +natural numbers but not the same size as + + align:start position:0% +natural numbers but not the same size as + + + align:start position:0% +natural numbers but not the same size as +the real numbers either + + align:start position:0% +the real numbers either + + + align:start position:0% +the real numbers either +um but in between uh in size + + align:start position:0% +um but in between uh in size + + + align:start position:0% +um but in between uh in size +um + + align:start position:0% +um + + + align:start position:0% +um +that was hilbert's question number one + + align:start position:0% +that was hilbert's question number one + + + align:start position:0% +that was hilbert's question number one +out of his list of 23 that i talked + + align:start position:0% +out of his list of 23 that i talked + + + align:start position:0% +out of his list of 23 that i talked +about a few lectures back + + align:start position:0% +about a few lectures back + + + align:start position:0% +about a few lectures back +it's interesting that he put it as + + align:start position:0% +it's interesting that he put it as + + + align:start position:0% +it's interesting that he put it as +number one in that very privileged + + align:start position:0% +number one in that very privileged + + + align:start position:0% +number one in that very privileged +special place + + align:start position:0% +special place + + + align:start position:0% +special place +because i know hilbert was very + + align:start position:0% +because i know hilbert was very + + + align:start position:0% +because i know hilbert was very +he felt that the understanding infinity + + align:start position:0% +he felt that the understanding infinity + + + align:start position:0% +he felt that the understanding infinity +was a really central issue in + + align:start position:0% +was a really central issue in + + + align:start position:0% +was a really central issue in +mathematics and that if we can't answer + + align:start position:0% +mathematics and that if we can't answer + + + align:start position:0% +mathematics and that if we can't answer +a question like this we don't really + + align:start position:0% +a question like this we don't really + + + align:start position:0% +a question like this we don't really +understand infinity um + + align:start position:0% +understand infinity um + + + align:start position:0% +understand infinity um +uh you want to understand what kind of + + align:start position:0% +uh you want to understand what kind of + + + align:start position:0% +uh you want to understand what kind of +sizes of infinities are there um we know + + align:start position:0% +sizes of infinities are there um we know + + + align:start position:0% +sizes of infinities are there um we know +there's the real numbers bigger than the + + align:start position:0% +there's the real numbers bigger than the + + + align:start position:0% +there's the real numbers bigger than the +than the natural numbers is there + + align:start position:0% +than the natural numbers is there + + + align:start position:0% +than the natural numbers is there +something in between so fundamental + + align:start position:0% +something in between so fundamental + + + align:start position:0% +something in between so fundamental +really um + + align:start position:0% +really um + + + align:start position:0% +really um +but uh it was shown uh during the course + + align:start position:0% +but uh it was shown uh during the course + + + align:start position:0% +but uh it was shown uh during the course +of the 20th century really in two + + align:start position:0% +of the 20th century really in two + + + align:start position:0% +of the 20th century really in two +separate steps one in the 1930s by + + align:start position:0% +separate steps one in the 1930s by + + + align:start position:0% +separate steps one in the 1930s by +girdle one in the early 1970s by cohen + + align:start position:0% +girdle one in the early 1970s by cohen + + + align:start position:0% +girdle one in the early 1970s by cohen +that we can't answer this question by + + align:start position:0% +that we can't answer this question by + + + align:start position:0% +that we can't answer this question by +using the standard axioms of mathematics + + align:start position:0% +using the standard axioms of mathematics + + + align:start position:0% +using the standard axioms of mathematics +you know it's + + align:start position:0% +you know it's + + + align:start position:0% +you know it's +the the answer can go either way + + align:start position:0% +the the answer can go either way + + + align:start position:0% +the the answer can go either way +and it's both of them are consistent + + align:start position:0% +and it's both of them are consistent + + + align:start position:0% +and it's both of them are consistent +with the axis of mathematics so you're + + align:start position:0% +with the axis of mathematics so you're + + + align:start position:0% +with the axis of mathematics so you're +never going to be able to prove + + align:start position:0% +never going to be able to prove + + + align:start position:0% +never going to be able to prove +that there is a set whose size is in + + align:start position:0% +that there is a set whose size is in + + + align:start position:0% +that there is a set whose size is in +between + + align:start position:0% +between + + + align:start position:0% +between +or that you or that there is no such set + + align:start position:0% +or that you or that there is no such set + + + align:start position:0% +or that you or that there is no such set +it's just impossible to prove either + + align:start position:0% +it's just impossible to prove either + + + align:start position:0% +it's just impossible to prove either +direct either way + + align:start position:0% +direct either way + + + align:start position:0% +direct either way +using the standard axiom in mathematics + + align:start position:0% +using the standard axiom in mathematics + + + align:start position:0% +using the standard axiom in mathematics +which actually is kind of remarkable um + + align:start position:0% +which actually is kind of remarkable um + + + align:start position:0% +which actually is kind of remarkable um +and so my question for you is and this + + align:start position:0% +and so my question for you is and this + + + align:start position:0% +and so my question for you is and this +is really a philosophical question not + + align:start position:0% +is really a philosophical question not + + + align:start position:0% +is really a philosophical question not +one that um is directly and you need to + + align:start position:0% +one that um is directly and you need to + + + align:start position:0% +one that um is directly and you need to +know about material in the course just i + + align:start position:0% +know about material in the course just i + + + align:start position:0% +know about material in the course just i +think it's just a matter of your own + + align:start position:0% +think it's just a matter of your own + + + align:start position:0% +think it's just a matter of your own +interest i hope you find it interesting + + align:start position:0% +interest i hope you find it interesting + + + align:start position:0% +interest i hope you find it interesting +if you don't you pick a wren you can + + align:start position:0% +if you don't you pick a wren you can + + + align:start position:0% +if you don't you pick a wren you can +just answer it randomly um + + align:start position:0% +just answer it randomly um + + + align:start position:0% +just answer it randomly um +but um + + align:start position:0% + + + + align:start position:0% + +what's going on here that we can't + + align:start position:0% +what's going on here that we can't + + + align:start position:0% +what's going on here that we can't +answer that question about whether there + + align:start position:0% +answer that question about whether there + + + align:start position:0% +answer that question about whether there +is a set of intermediate sides is it + + align:start position:0% +is a set of intermediate sides is it + + + align:start position:0% +is a set of intermediate sides is it +because our axioms for mathematics are + + align:start position:0% +because our axioms for mathematics are + + + align:start position:0% +because our axioms for mathematics are +inadequate + + align:start position:0% +inadequate + + + align:start position:0% +inadequate +or + + align:start position:0% +or + + + align:start position:0% +or +maybe there is no such thing as a + + align:start position:0% +maybe there is no such thing as a + + + align:start position:0% +maybe there is no such thing as a +mathematical reality you can talk about + + align:start position:0% +mathematical reality you can talk about + + + align:start position:0% +mathematical reality you can talk about +you know you know what's what's real + + align:start position:0% +you know you know what's what's real + + + align:start position:0% +you know you know what's what's real +here what what what's the reality either + + align:start position:0% +here what what what's the reality either + + + align:start position:0% +here what what what's the reality either +there is a set in between or not + + align:start position:0% +there is a set in between or not + + + align:start position:0% +there is a set in between or not +if you imagine all of these things have + + align:start position:0% +if you imagine all of these things have + + + align:start position:0% +if you imagine all of these things have +their own reality to them well then + + align:start position:0% +their own reality to them well then + + + align:start position:0% +their own reality to them well then +there's going to be an answer and then + + align:start position:0% +there's going to be an answer and then + + + align:start position:0% +there's going to be an answer and then +you would expect well maybe we could + + align:start position:0% +you would expect well maybe we could + + + align:start position:0% +you would expect well maybe we could +find better axioms which will actually + + align:start position:0% +find better axioms which will actually + + + align:start position:0% +find better axioms which will actually +give us that answer or you can say well + + align:start position:0% +give us that answer or you can say well + + + align:start position:0% +give us that answer or you can say well +there is no reality + + align:start position:0% +there is no reality + + + align:start position:0% +there is no reality +and um + + align:start position:0% +and um + + + align:start position:0% +and um +you know it + + align:start position:0% +you know it + + + align:start position:0% +you know it +infinite sets are kind of human + + align:start position:0% +infinite sets are kind of human + + + align:start position:0% +infinite sets are kind of human +constructs anyway so we can make them + + align:start position:0% +constructs anyway so we can make them + + + align:start position:0% +constructs anyway so we can make them +kind of play out any way we like + + align:start position:0% +kind of play out any way we like + + + align:start position:0% +kind of play out any way we like +mathematicians argue about that to this + + align:start position:0% +mathematicians argue about that to this + + + align:start position:0% +mathematicians argue about that to this +day um + + align:start position:0% +day um + + + align:start position:0% +day um +and um it is as i say really it's a + + align:start position:0% +and um it is as i say really it's a + + + align:start position:0% +and um it is as i say really it's a +philosophical question but just out of + + align:start position:0% +philosophical question but just out of + + + align:start position:0% +philosophical question but just out of +curiosity let's see how you guys end up + + align:start position:0% +curiosity let's see how you guys end up + + + align:start position:0% +curiosity let's see how you guys end up +uh deciding on that one um so here's the + + align:start position:0% +uh deciding on that one um so here's the + + + align:start position:0% +uh deciding on that one um so here's the +poll + + align:start position:0% +poll + + + align:start position:0% +poll +five seconds to go please vote + + align:start position:0% +five seconds to go please vote + + + align:start position:0% +five seconds to go please vote +and uh we're going to end the polling + + align:start position:0% +and uh we're going to end the polling + + + align:start position:0% +and uh we're going to end the polling +one two three now + + align:start position:0% + + + + align:start position:0% + +all right here we go + + align:start position:0% +all right here we go + + + align:start position:0% +all right here we go +so there's no right answer + + align:start position:0% +so there's no right answer + + + align:start position:0% +so there's no right answer +um + + align:start position:0% +um + + + align:start position:0% +um +i think if most mathematicians were + + align:start position:0% +i think if most mathematicians were + + + align:start position:0% +i think if most mathematicians were +to um + + align:start position:0% +to um + + + align:start position:0% +to um +i think the instinct of most logicians + + align:start position:0% +i think the instinct of most logicians + + + align:start position:0% +i think the instinct of most logicians +especially i'm not sure our general + + align:start position:0% +especially i'm not sure our general + + + align:start position:0% +especially i'm not sure our general +mathematicians really even care about + + align:start position:0% +mathematicians really even care about + + + align:start position:0% +mathematicians really even care about +this question but logicians um + + align:start position:0% +this question but logicians um + + + align:start position:0% +this question but logicians um +would probably have an instinct that + + align:start position:0% +would probably have an instinct that + + + align:start position:0% +would probably have an instinct that +probably there are sets in between + + align:start position:0% +probably there are sets in between + + + align:start position:0% +probably there are sets in between +there's no reason that there shouldn't + + align:start position:0% +there's no reason that there shouldn't + + + align:start position:0% +there's no reason that there shouldn't +be + + align:start position:0% +be + + + align:start position:0% +be +um + + align:start position:0% +um + + + align:start position:0% +um +you know it seems kind of strange that + + align:start position:0% +you know it seems kind of strange that + + + align:start position:0% +you know it seems kind of strange that +there should be this sort of jump uh + + align:start position:0% +there should be this sort of jump uh + + + align:start position:0% +there should be this sort of jump uh +from the + + align:start position:0% +from the + + + align:start position:0% +from the +natural numbers to the real numbers and + + align:start position:0% +natural numbers to the real numbers and + + + align:start position:0% +natural numbers to the real numbers and +why nothing in between um + + align:start position:0% +why nothing in between um + + + align:start position:0% +why nothing in between um +but um + + align:start position:0% +but um + + + align:start position:0% +but um +it's uh + + align:start position:0% +it's uh + + + align:start position:0% +it's uh +i don't think that question is really + + align:start position:0% +i don't think that question is really + + + align:start position:0% +i don't think that question is really +settled + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +all right let's continue on i think we + + align:start position:0% +all right let's continue on i think we + + + align:start position:0% +all right let's continue on i think we +are + + align:start position:0% +are + + + align:start position:0% +are +um okay so we're gonna + + align:start position:0% +um okay so we're gonna + + + align:start position:0% +um okay so we're gonna +um + + align:start position:0% + + + + align:start position:0% + +a coffee break is coming in case you're + + align:start position:0% +a coffee break is coming in case you're + + + align:start position:0% +a coffee break is coming in case you're +wondering so this is on my last slide + + align:start position:0% +wondering so this is on my last slide + + + align:start position:0% +wondering so this is on my last slide +before then but this is an important + + align:start position:0% +before then but this is an important + + + align:start position:0% +before then but this is an important +slide so please uh hold hold out + + align:start position:0% +slide so please uh hold hold out + + + align:start position:0% +slide so please uh hold hold out +um + + align:start position:0% +um + + + align:start position:0% +um +so here is our + + align:start position:0% +so here is our + + + align:start position:0% +so here is our +uh promised theorem of the day + + align:start position:0% +uh promised theorem of the day + + + align:start position:0% +uh promised theorem of the day +i'm going to show that atm is not + + align:start position:0% +i'm going to show that atm is not + + + align:start position:0% +i'm going to show that atm is not +decidable the acceptance problem for + + align:start position:0% +decidable the acceptance problem for + + + align:start position:0% +decidable the acceptance problem for +turing machines + + align:start position:0% +turing machines + + + align:start position:0% +turing machines +and it's all going to be contained on + + align:start position:0% +and it's all going to be contained on + + + align:start position:0% +and it's all going to be contained on +this one slide we're going to give a + + align:start position:0% +this one slide we're going to give a + + + align:start position:0% +this one slide we're going to give a +proof by contradiction using + + align:start position:0% +proof by contradiction using + + + align:start position:0% +proof by contradiction using +diagonalization + + align:start position:0% +diagonalization + + + align:start position:0% +diagonalization +and we're going to assume some turing + + align:start position:0% +and we're going to assume some turing + + + align:start position:0% +and we're going to assume some turing +machine h decides atm + + align:start position:0% +machine h decides atm + + + align:start position:0% +machine h decides atm +and we're going to get a contradiction + + align:start position:0% +and we're going to get a contradiction + + + align:start position:0% +and we're going to get a contradiction +so let's first of all make sure we + + align:start position:0% +so let's first of all make sure we + + + align:start position:0% +so let's first of all make sure we +understand what h is doing + + align:start position:0% +understand what h is doing + + + align:start position:0% +understand what h is doing +so h gets an input a turing machine and + + align:start position:0% +so h gets an input a turing machine and + + + align:start position:0% +so h gets an input a turing machine and +an + + align:start position:0% +an + + + align:start position:0% +an +input and h is going to be a decider so + + align:start position:0% +input and h is going to be a decider so + + + align:start position:0% +input and h is going to be a decider so +it always halts + + align:start position:0% +it always halts + + + align:start position:0% +it always halts +with an accept or a reject + + align:start position:0% +with an accept or a reject + + + align:start position:0% +with an accept or a reject +it's supposed to accept if m accepts w + + align:start position:0% +it's supposed to accept if m accepts w + + + align:start position:0% +it's supposed to accept if m accepts w +and reject if it doesn't so in other + + align:start position:0% +and reject if it doesn't so in other + + + align:start position:0% +and reject if it doesn't so in other +words it's going to reject if m rejects + + align:start position:0% +words it's going to reject if m rejects + + + align:start position:0% +words it's going to reject if m rejects +w either by whole by halting or by + + align:start position:0% +w either by whole by halting or by + + + align:start position:0% +w either by whole by halting or by +looping + + align:start position:0% + + + + align:start position:0% + +that's the job of h + + align:start position:0% +that's the job of h + + + align:start position:0% +that's the job of h +and we're assuming we can do that + + align:start position:0% +and we're assuming we can do that + + + align:start position:0% +and we're assuming we can do that +but we will see a contradiction occur + + align:start position:0% + + + + align:start position:0% + +so the way we're going to do that + + align:start position:0% +so the way we're going to do that + + + align:start position:0% +so the way we're going to do that +is is really kind of just one step here + + align:start position:0% +is is really kind of just one step here + + + align:start position:0% +is is really kind of just one step here +in a way and we're going to use h to + + align:start position:0% +in a way and we're going to use h to + + + align:start position:0% +in a way and we're going to use h to +construct another turing machine d + + align:start position:0% +construct another turing machine d + + + align:start position:0% +construct another turing machine d +h is going to be a subroutine to d + + align:start position:0% +h is going to be a subroutine to d + + + align:start position:0% +h is going to be a subroutine to d +we've already seen us doing that in the + + align:start position:0% +we've already seen us doing that in the + + + align:start position:0% +we've already seen us doing that in the +past + + align:start position:0% + + + + align:start position:0% + +d is going to do something a little + + align:start position:0% +d is going to do something a little + + + align:start position:0% +d is going to do something a little +strange + + align:start position:0% +strange + + + align:start position:0% +strange +just to just to warn you um + + align:start position:0% +just to just to warn you um + + + align:start position:0% +just to just to warn you um +these input is just a turing machine no + + align:start position:0% +these input is just a turing machine no + + + align:start position:0% +these input is just a turing machine no +in no w + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +what + + align:start position:0% +what + + + align:start position:0% +what +d is going to do + + align:start position:0% +d is going to do + + + align:start position:0% +d is going to do +using its subroutine h + + align:start position:0% +using its subroutine h + + + align:start position:0% +using its subroutine h +is going to simulate h + + align:start position:0% +is going to simulate h + + + align:start position:0% +is going to simulate h +on input + + align:start position:0% +on input + + + align:start position:0% +on input +m comma the description of m now what is + + align:start position:0% +m comma the description of m now what is + + + align:start position:0% +m comma the description of m now what is +that + + align:start position:0% + + + + align:start position:0% + +well the description of m is just some + + align:start position:0% +well the description of m is just some + + + align:start position:0% +well the description of m is just some +string + + align:start position:0% +string + + + align:start position:0% +string +so what h is trying what it's asking h + + align:start position:0% +so what h is trying what it's asking h + + + align:start position:0% +so what h is trying what it's asking h +uh to tell to answer is does m + + align:start position:0% +uh to tell to answer is does m + + + align:start position:0% +uh to tell to answer is does m +accept + + align:start position:0% + + + + align:start position:0% + +the string representing m's own + + align:start position:0% +the string representing m's own + + + align:start position:0% +the string representing m's own +description + + align:start position:0% +description + + + align:start position:0% +description +it's as if we're feeding m into itself + + align:start position:0% +it's as if we're feeding m into itself + + + align:start position:0% +it's as if we're feeding m into itself +which seems like a totally twisted thing + + align:start position:0% +which seems like a totally twisted thing + + + align:start position:0% +which seems like a totally twisted thing +to do + + align:start position:0% +to do + + + align:start position:0% +to do +um + + align:start position:0% + + + + align:start position:0% + +you might say + + align:start position:0% +you might say + + + align:start position:0% +you might say +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +why would you ever feed a program into + + align:start position:0% +why would you ever feed a program into + + + align:start position:0% +why would you ever feed a program into +itself + + align:start position:0% + + + + align:start position:0% + +somebody's written cannibalism here + + align:start position:0% +somebody's written cannibalism here + + + align:start position:0% +somebody's written cannibalism here +yeah kind of uh i said it's it's worse + + align:start position:0% +yeah kind of uh i said it's it's worse + + + align:start position:0% +yeah kind of uh i said it's it's worse +because it's + + align:start position:0% +because it's + + + align:start position:0% +because it's +not eating somebody else it's eating + + align:start position:0% +not eating somebody else it's eating + + + align:start position:0% +not eating somebody else it's eating +himself + + align:start position:0% +himself + + + align:start position:0% +himself +okay but + + align:start position:0% +okay but + + + align:start position:0% +okay but +um + + align:start position:0% +um + + + align:start position:0% +um +i claim + + align:start position:0% +i claim + + + align:start position:0% +i claim +that we actually there are actual cases + + align:start position:0% +that we actually there are actual cases + + + align:start position:0% +that we actually there are actual cases +in practice + + align:start position:0% +in practice + + + align:start position:0% +in practice +where we do this + + align:start position:0% +where we do this + + + align:start position:0% +where we do this +we feed programs into themselves + + align:start position:0% + + + + align:start position:0% + +and uh the example that i know of where + + align:start position:0% +and uh the example that i know of where + + + align:start position:0% +and uh the example that i know of where +this is done + + align:start position:0% +this is done + + + align:start position:0% +this is done +is when you're making a compiler + + align:start position:0% +is when you're making a compiler + + + align:start position:0% +is when you're making a compiler +you might want to make a compiler and + + align:start position:0% +you might want to make a compiler and + + + align:start position:0% +you might want to make a compiler and +then written in the same language that + + align:start position:0% +then written in the same language that + + + align:start position:0% +then written in the same language that +it's compiling and then you feed the + + align:start position:0% +it's compiling and then you feed the + + + align:start position:0% +it's compiling and then you feed the +compiler into itself + + align:start position:0% +compiler into itself + + + align:start position:0% +compiler into itself +they may say why even bother because + + align:start position:0% +they may say why even bother because + + + align:start position:0% +they may say why even bother because +it's already obviously if once it's + + align:start position:0% +it's already obviously if once it's + + + align:start position:0% +it's already obviously if once it's +running you don't need to + + align:start position:0% + + + + align:start position:0% + +compile it again um but actually you + + align:start position:0% +compile it again um but actually you + + + align:start position:0% +compile it again um but actually you +know an example where this was really + + align:start position:0% +know an example where this was really + + + align:start position:0% +know an example where this was really +used + + align:start position:0% +used + + + align:start position:0% +used +was when there was an optimizing + + align:start position:0% +was when there was an optimizing + + + align:start position:0% +was when there was an optimizing +compiler i think for c uh written on + + align:start position:0% +compiler i think for c uh written on + + + align:start position:0% +compiler i think for c uh written on +early unix machines + + align:start position:0% +early unix machines + + + align:start position:0% +early unix machines +and the optimizing compiler for c was + + align:start position:0% +and the optimizing compiler for c was + + + align:start position:0% +and the optimizing compiler for c was +written in c + + align:start position:0% +written in c + + + align:start position:0% +written in c +so you would feed the optimizing + + align:start position:0% +so you would feed the optimizing + + + align:start position:0% +so you would feed the optimizing +compiler + + align:start position:0% +compiler + + + align:start position:0% +compiler +into the regular compiler first of all + + align:start position:0% +into the regular compiler first of all + + + align:start position:0% +into the regular compiler first of all +now you had the um + + align:start position:0% +now you had the um + + + align:start position:0% +now you had the um +compiler running + + align:start position:0% +compiler running + + + align:start position:0% +compiler running +but it was unoptimized + + align:start position:0% +but it was unoptimized + + + align:start position:0% +but it was unoptimized +so but now that it's the optimizing + + align:start position:0% +so but now that it's the optimizing + + + align:start position:0% +so but now that it's the optimizing +compiler is running + + align:start position:0% +compiler is running + + + align:start position:0% +compiler is running +you can feed the optimizing compiler + + align:start position:0% +you can feed the optimizing compiler + + + align:start position:0% +you can feed the optimizing compiler +into that which is itself now you have + + align:start position:0% +into that which is itself now you have + + + align:start position:0% +into that which is itself now you have +an optimized optimizing compiler + + align:start position:0% +an optimized optimizing compiler + + + align:start position:0% +an optimized optimizing compiler +so it really makes + + align:start position:0% +so it really makes + + + align:start position:0% +so it really makes +some there is a at least one case where + + align:start position:0% +some there is a at least one case where + + + align:start position:0% +some there is a at least one case where +this has actually been done uh in + + align:start position:0% +this has actually been done uh in + + + align:start position:0% +this has actually been done uh in +practice + + align:start position:0% +practice + + + align:start position:0% +practice +um not that we really care this is a + + align:start position:0% +um not that we really care this is a + + + align:start position:0% +um not that we really care this is a +theory class but just for fun to observe + + align:start position:0% +theory class but just for fun to observe + + + align:start position:0% +theory class but just for fun to observe +that + + align:start position:0% +that + + + align:start position:0% +that +so here h is trying to say well does n a + + align:start position:0% +so here h is trying to say well does n a + + + align:start position:0% +so here h is trying to say well does n a +m end up accepting when it's fed + + align:start position:0% +m end up accepting when it's fed + + + align:start position:0% +m end up accepting when it's fed +the description of itself + + align:start position:0% +the description of itself + + + align:start position:0% +the description of itself +you know at least mathematically + + align:start position:0% +you know at least mathematically + + + align:start position:0% +you know at least mathematically +speaking that's a reasonable uh thing to + + align:start position:0% +speaking that's a reasonable uh thing to + + + align:start position:0% +speaking that's a reasonable uh thing to +ask + + align:start position:0% +ask + + + align:start position:0% +ask +and then what + + align:start position:0% +and then what + + + align:start position:0% +and then what +d is going to do when it gets the answer + + align:start position:0% +d is going to do when it gets the answer + + + align:start position:0% +d is going to do when it gets the answer +back from h + + align:start position:0% +back from h + + + align:start position:0% +back from h +h as a decider don't forget + + align:start position:0% +h as a decider don't forget + + + align:start position:0% +h as a decider don't forget +is d is going to do the opposite + + align:start position:0% +is d is going to do the opposite + + + align:start position:0% +is d is going to do the opposite +whatever h does it's going to accept if + + align:start position:0% +whatever h does it's going to accept if + + + align:start position:0% +whatever h does it's going to accept if +h rejects and rejective h accepts + + align:start position:0% +h rejects and rejective h accepts + + + align:start position:0% +h rejects and rejective h accepts +um so let's in summary let's pull this + + align:start position:0% +um so let's in summary let's pull this + + + align:start position:0% +um so let's in summary let's pull this +together some + + align:start position:0% +together some + + + align:start position:0% +together some +you know it's easy to understand in the + + align:start position:0% +you know it's easy to understand in the + + + align:start position:0% +you know it's easy to understand in the +end what is d doing + + align:start position:0% +end what is d doing + + + align:start position:0% +end what is d doing +d is going to accept d is also going to + + align:start position:0% +d is going to accept d is also going to + + + align:start position:0% +d is going to accept d is also going to +be decided by the way so d d is always + + align:start position:0% +be decided by the way so d d is always + + + align:start position:0% +be decided by the way so d d is always +going to either accept or reject + + align:start position:0% +going to either accept or reject + + + align:start position:0% +going to either accept or reject +just the opposite of what h tells it to + + align:start position:0% +just the opposite of what h tells it to + + + align:start position:0% +just the opposite of what h tells it to +do so d is going to accept + + align:start position:0% +do so d is going to accept + + + align:start position:0% +do so d is going to accept +m + + align:start position:0% +m + + + align:start position:0% +m +exactly when m doesn't accept m because + + align:start position:0% +exactly when m doesn't accept m because + + + align:start position:0% +exactly when m doesn't accept m because +you know when m doesn't accept m + + align:start position:0% +you know when m doesn't accept m + + + align:start position:0% +you know when m doesn't accept m +h is going to reject + + align:start position:0% +h is going to reject + + + align:start position:0% +h is going to reject +um and so then d is going to accept so d + + align:start position:0% +um and so then d is going to accept so d + + + align:start position:0% +um and so then d is going to accept so d +accepts m if and only if m doesn't + + align:start position:0% +accepts m if and only if m doesn't + + + align:start position:0% +accepts m if and only if m doesn't +accept that that's exactly the condition + + align:start position:0% +accept that that's exactly the condition + + + align:start position:0% +accept that that's exactly the condition +in which d accepts it + + align:start position:0% +in which d accepts it + + + align:start position:0% +in which d accepts it +i think it's important to just step back + + align:start position:0% +i think it's important to just step back + + + align:start position:0% +i think it's important to just step back +and make sure you understand this line + + align:start position:0% +and make sure you understand this line + + + align:start position:0% +and make sure you understand this line +because we have only one line left + + align:start position:0% +because we have only one line left + + + align:start position:0% +because we have only one line left +to get our contradiction + + align:start position:0% + + + + align:start position:0% + +right are we together d accepts m if and + + align:start position:0% +right are we together d accepts m if and + + + align:start position:0% +right are we together d accepts m if and +only if m doesn't accept m that's just + + align:start position:0% +only if m doesn't accept m that's just + + + align:start position:0% +only if m doesn't accept m that's just +by the that way we've defined setup d + + align:start position:0% +by the that way we've defined setup d + + + align:start position:0% +by the that way we've defined setup d +now + + align:start position:0% +now + + + align:start position:0% +now +what we're going to do is feed in + + align:start position:0% +what we're going to do is feed in + + + align:start position:0% +what we're going to do is feed in +instead of m to d and not some arbitrary + + align:start position:0% +instead of m to d and not some arbitrary + + + align:start position:0% +instead of m to d and not some arbitrary +fee + + align:start position:0% +fee + + + align:start position:0% +fee +we're going to use feed in d into d + + align:start position:0% +we're going to use feed in d into d + + + align:start position:0% +we're going to use feed in d into d +and that is going to be our + + align:start position:0% +and that is going to be our + + + align:start position:0% +and that is going to be our +contradiction because d is now going to + + align:start position:0% +contradiction because d is now going to + + + align:start position:0% +contradiction because d is now going to +accept d if and only if d doesn't accept + + align:start position:0% +accept d if and only if d doesn't accept + + + align:start position:0% +accept d if and only if d doesn't accept +e and that's certainly impossible + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's our contradiction which proves + + align:start position:0% +that's our contradiction which proves + + + align:start position:0% +that's our contradiction which proves +that h cannot exist and therefore atm is + + align:start position:0% +that h cannot exist and therefore atm is + + + align:start position:0% +that h cannot exist and therefore atm is +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +okay so we're done + + align:start position:0% +okay so we're done + + + align:start position:0% +okay so we're done +except for the one point which is that + + align:start position:0% +except for the one point which is that + + + align:start position:0% +except for the one point which is that +um + + align:start position:0% +um + + + align:start position:0% +um +why is this a + + align:start position:0% +why is this a + + + align:start position:0% +why is this a +diagonalization + + align:start position:0% +diagonalization + + + align:start position:0% +diagonalization +and i think you can get that from the + + align:start position:0% +and i think you can get that from the + + + align:start position:0% +and i think you can get that from the +following picture + + align:start position:0% + + + + align:start position:0% + +if you imagine here writing down all + + align:start position:0% +if you imagine here writing down all + + + align:start position:0% +if you imagine here writing down all +possible time i'm making i'm going to + + align:start position:0% +possible time i'm making i'm going to + + + align:start position:0% +possible time i'm making i'm going to +make a table here here is a list of all + + align:start position:0% +make a table here here is a list of all + + + align:start position:0% +make a table here here is a list of all +turing machines + + align:start position:0% +turing machines + + + align:start position:0% +turing machines +okay uh including d which is a machine + + align:start position:0% +okay uh including d which is a machine + + + align:start position:0% +okay uh including d which is a machine +which i + + align:start position:0% +which i + + + align:start position:0% +which i +built + + align:start position:0% +built + + + align:start position:0% +built +under the assumption that h exists so d + + align:start position:0% +under the assumption that h exists so d + + + align:start position:0% +under the assumption that h exists so d +appears here somewhere but here are the + + align:start position:0% +appears here somewhere but here are the + + + align:start position:0% +appears here somewhere but here are the +all the other turing machines and here + + align:start position:0% +all the other turing machines and here + + + align:start position:0% +all the other turing machines and here +are all these descriptions of the turing + + align:start position:0% +are all these descriptions of the turing + + + align:start position:0% +are all these descriptions of the turing +machines along the uh labeling all of + + align:start position:0% +machines along the uh labeling all of + + + align:start position:0% +machines along the uh labeling all of +the columns + + align:start position:0% +the columns + + + align:start position:0% +the columns +okay so these are the rows labeled these + + align:start position:0% +okay so these are the rows labeled these + + + align:start position:0% +okay so these are the rows labeled these +are the column labels and inside i'm + + align:start position:0% +are the column labels and inside i'm + + + align:start position:0% +are the column labels and inside i'm +going to tell you + + align:start position:0% +going to tell you + + + align:start position:0% +going to tell you +uh the answer for whether a given + + align:start position:0% +uh the answer for whether a given + + + align:start position:0% +uh the answer for whether a given +machine + + align:start position:0% +machine + + + align:start position:0% +machine +accepts a given input + + align:start position:0% + + + + align:start position:0% + +so for example m1 accepts its own + + align:start position:0% +so for example m1 accepts its own + + + align:start position:0% +so for example m1 accepts its own +description but rejects the description + + align:start position:0% +description but rejects the description + + + align:start position:0% +description but rejects the description +of m2 but accepts the description of m3 + + align:start position:0% +of m2 but accepts the description of m3 + + + align:start position:0% +of m2 but accepts the description of m3 +i don't know you know i'm obviously + + align:start position:0% +i don't know you know i'm obviously + + + align:start position:0% +i don't know you know i'm obviously +making this up i don't know what m1 is + + align:start position:0% +making this up i don't know what m1 is + + + align:start position:0% +making this up i don't know what m1 is +but just hypothetically that's what the + + align:start position:0% +but just hypothetically that's what the + + + align:start position:0% +but just hypothetically that's what the +machine m1 does + + align:start position:0% +machine m1 does + + + align:start position:0% +machine m1 does +um so i'm just filling out this table + + align:start position:0% +um so i'm just filling out this table + + + align:start position:0% +um so i'm just filling out this table +and you know this is + + align:start position:0% +and you know this is + + + align:start position:0% +and you know this is +d + + align:start position:0% +d + + + align:start position:0% +d +uh h could get the answer to any of the + + align:start position:0% +uh h could get the answer to any of the + + + align:start position:0% +uh h could get the answer to any of the +elements in this table because it can + + align:start position:0% +elements in this table because it can + + + align:start position:0% +elements in this table because it can +test whether m4 + + align:start position:0% +test whether m4 + + + align:start position:0% +test whether m4 +um accepts the description of m3 so it + + align:start position:0% +um accepts the description of m3 so it + + + align:start position:0% +um accepts the description of m3 so it +could h could fill out this table + + align:start position:0% +could h could fill out this table + + + align:start position:0% +could h could fill out this table +so maybe m2 is a machine that always + + align:start position:0% +so maybe m2 is a machine that always + + + align:start position:0% +so maybe m2 is a machine that always +rejects it's a very unfriendly rejecting + + align:start position:0% +rejects it's a very unfriendly rejecting + + + align:start position:0% +rejects it's a very unfriendly rejecting +machine + + align:start position:0% +machine + + + align:start position:0% +machine +m3 is a very friendly machine it accepts + + align:start position:0% +m3 is a very friendly machine it accepts + + + align:start position:0% +m3 is a very friendly machine it accepts +all inputs and for its reject sum and + + align:start position:0% +all inputs and for its reject sum and + + + align:start position:0% +all inputs and for its reject sum and +accepts other dot dot dot + + align:start position:0% +accepts other dot dot dot + + + align:start position:0% +accepts other dot dot dot +now i want to look and see what does d + + align:start position:0% +now i want to look and see what does d + + + align:start position:0% +now i want to look and see what does d +do + + align:start position:0% +do + + + align:start position:0% +do +um + + align:start position:0% +um + + + align:start position:0% +um +now based on the information i've + + align:start position:0% +now based on the information i've + + + align:start position:0% +now based on the information i've +already given you we can understand what + + align:start position:0% +already given you we can understand what + + + align:start position:0% +already given you we can understand what +d does + + align:start position:0% +d does + + + align:start position:0% +d does +so for example what does d do when i + + align:start position:0% +so for example what does d do when i + + + align:start position:0% +so for example what does d do when i +feed it the description of m1 + + align:start position:0% +feed it the description of m1 + + + align:start position:0% +feed it the description of m1 +what does d do + + align:start position:0% +what does d do + + + align:start position:0% +what does d do +well we can look over here d accepts m + + align:start position:0% +well we can look over here d accepts m + + + align:start position:0% +well we can look over here d accepts m +if and only if m doesn't accept m so d + + align:start position:0% +if and only if m doesn't accept m so d + + + align:start position:0% +if and only if m doesn't accept m so d +is going to accept + + align:start position:0% +is going to accept + + + align:start position:0% +is going to accept +um + + align:start position:0% +um + + + align:start position:0% +um +m1 if and only if m1 does not accept m1 + + align:start position:0% +m1 if and only if m1 does not accept m1 + + + align:start position:0% +m1 if and only if m1 does not accept m1 +well m1 does accept m1 + + align:start position:0% +well m1 does accept m1 + + + align:start position:0% +well m1 does accept m1 +so d + + align:start position:0% +so d + + + align:start position:0% +so d +does the opposite d rejects + + align:start position:0% +does the opposite d rejects + + + align:start position:0% +does the opposite d rejects +so okay i'm highlighting here + + align:start position:0% +so okay i'm highlighting here + + + align:start position:0% +so okay i'm highlighting here +d rejects because it's going to d is + + align:start position:0% +d rejects because it's going to d is + + + align:start position:0% +d rejects because it's going to d is +going to do the opposite of what the + + align:start position:0% +going to do the opposite of what the + + + align:start position:0% +going to do the opposite of what the +machine does on its own it on input + + align:start position:0% +machine does on its own it on input + + + align:start position:0% +machine does on its own it on input +um so m2 on so d on m2 you have to look + + align:start position:0% +um so m2 on so d on m2 you have to look + + + align:start position:0% +um so m2 on so d on m2 you have to look +what m2 does on m2 it rejects so d does + + align:start position:0% +what m2 does on m2 it rejects so d does + + + align:start position:0% +what m2 does on m2 it rejects so d does +the opposite of that it accepts + + align:start position:0% +the opposite of that it accepts + + + align:start position:0% +the opposite of that it accepts +and similarly + + align:start position:0% +and similarly + + + align:start position:0% +and similarly +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know all each one of these things + + align:start position:0% +you know all each one of these things + + + align:start position:0% +you know all each one of these things +these answer is going to be the opposite + + align:start position:0% +these answer is going to be the opposite + + + align:start position:0% +these answer is going to be the opposite +of what the machine does on its own + + align:start position:0% +of what the machine does on its own + + + align:start position:0% +of what the machine does on its own +description + + align:start position:0% +description + + + align:start position:0% +description +um just by virtue of the definition of + + align:start position:0% +um just by virtue of the definition of + + + align:start position:0% +um just by virtue of the definition of +date + + align:start position:0% +date + + + align:start position:0% +date +okay and so on so far so good + + align:start position:0% +okay and so on so far so good + + + align:start position:0% +okay and so on so far so good +but the problem is what happens when d + + align:start position:0% +but the problem is what happens when d + + + align:start position:0% +but the problem is what happens when d +is fed itself + + align:start position:0% +is fed itself + + + align:start position:0% +is fed itself +because as you can see + + align:start position:0% +because as you can see + + + align:start position:0% +because as you can see +you know um we're we're heading for + + align:start position:0% +you know um we're we're heading for + + + align:start position:0% +you know um we're we're heading for +we're heading for trouble because this + + align:start position:0% +we're heading for trouble because this + + + align:start position:0% +we're heading for trouble because this +is a diagonal down here + + align:start position:0% +is a diagonal down here + + + align:start position:0% +is a diagonal down here +d is just one of the rows that diagonal + + align:start position:0% +d is just one of the rows that diagonal + + + align:start position:0% +d is just one of the rows that diagonal +is going to + + align:start position:0% +is going to + + + align:start position:0% +is going to +intersect that row at this point + + align:start position:0% +intersect that row at this point + + + align:start position:0% +intersect that row at this point +and d is defined to be going to be doing + + align:start position:0% +and d is defined to be going to be doing + + + align:start position:0% +and d is defined to be going to be doing +the opposite of what that element is but + + align:start position:0% +the opposite of what that element is but + + + align:start position:0% +the opposite of what that element is but +it can't be the opposite of itself + + align:start position:0% +it can't be the opposite of itself + + + align:start position:0% +it can't be the opposite of itself +okay and so that's that's the + + align:start position:0% +okay and so that's that's the + + + align:start position:0% +okay and so that's that's the +contradiction + + align:start position:0% +contradiction + + + align:start position:0% +contradiction +so i think you know where um + + align:start position:0% +so i think you know where um + + + align:start position:0% +so i think you know where um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i i'm gonna call us give us a little + + align:start position:0% +i i'm gonna call us give us a little + + + align:start position:0% +i i'm gonna call us give us a little +break here um and then you can also text + + align:start position:0% +break here um and then you can also text + + + align:start position:0% +break here um and then you can also text +me in the meantime we'll be happy to + + align:start position:0% +me in the meantime we'll be happy to + + + align:start position:0% +me in the meantime we'll be happy to +answer some questions during during that + + align:start position:0% +answer some questions during during that + + + align:start position:0% +answer some questions during during that +a little over four minutes to go so + + align:start position:0% +a little over four minutes to go so + + + align:start position:0% +a little over four minutes to go so +let's see let me see if i can + + align:start position:0% +let's see let me see if i can + + + align:start position:0% +let's see let me see if i can +answer your questions + + align:start position:0% +answer your questions + + + align:start position:0% +answer your questions +okay what's so special about atm that + + align:start position:0% +okay what's so special about atm that + + + align:start position:0% +okay what's so special about atm that +enables us to do this why can't we do + + align:start position:0% +enables us to do this why can't we do + + + align:start position:0% +enables us to do this why can't we do +this on adfa for example + + align:start position:0% +this on adfa for example + + + align:start position:0% +this on adfa for example +um so that's a good question i i i + + align:start position:0% +um so that's a good question i i i + + + align:start position:0% +um so that's a good question i i i +and + + align:start position:0% +and + + + align:start position:0% +and +the answer is that um + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% + + + + align:start position:0% + +you know in a sense + + align:start position:0% +you know in a sense + + + align:start position:0% +you know in a sense +you know we can do this on dfa i mean i + + align:start position:0% +you know we can do this on dfa i mean i + + + align:start position:0% +you know we can do this on dfa i mean i +i think this is perhaps a bit bit of a + + align:start position:0% +i think this is perhaps a bit bit of a + + + align:start position:0% +i think this is perhaps a bit bit of a +stretch but you know dfas could not + + align:start position:0% +stretch but you know dfas could not + + + align:start position:0% +stretch but you know dfas could not +answer adfa i mean we could prove that + + align:start position:0% +answer adfa i mean we could prove that + + + align:start position:0% +answer adfa i mean we could prove that +in other ways as well you know by uh + + align:start position:0% +in other ways as well you know by uh + + + align:start position:0% +in other ways as well you know by uh +because + + align:start position:0% +because + + + align:start position:0% +because +you know we could use things like the + + align:start position:0% +you know we could use things like the + + + align:start position:0% +you know we could use things like the +pumping lima and it's not clear even how + + align:start position:0% +pumping lima and it's not clear even how + + + align:start position:0% +pumping lima and it's not clear even how +you formulate adf8 + + align:start position:0% +you formulate adf8 + + + align:start position:0% +you formulate adf8 +but what's important here is that the + + align:start position:0% +but what's important here is that the + + + align:start position:0% +but what's important here is that the +um it's really the model talking about + + align:start position:0% +um it's really the model talking about + + + align:start position:0% +um it's really the model talking about +itself + + align:start position:0% +itself + + + align:start position:0% +itself +um that really is where the problem + + align:start position:0% +um that really is where the problem + + + align:start position:0% +um that really is where the problem +comes up + + align:start position:0% +comes up + + + align:start position:0% +comes up +so if you try to push this argument + + align:start position:0% +so if you try to push this argument + + + align:start position:0% +so if you try to push this argument +through to show that adfa is not + + align:start position:0% +through to show that adfa is not + + + align:start position:0% +through to show that adfa is not +decidable by touring machines you're + + align:start position:0% +decidable by touring machines you're + + + align:start position:0% +decidable by touring machines you're +gonna fail + + align:start position:0% +gonna fail + + + align:start position:0% +gonna fail +um + + align:start position:0% +um + + + align:start position:0% +um +because you know we're starting off with + + align:start position:0% +because you know we're starting off with + + + align:start position:0% +because you know we're starting off with +a turing machine and um i mean + + align:start position:0% +a turing machine and um i mean + + + align:start position:0% +a turing machine and um i mean +i think i'm gonna confuse myself if i + + align:start position:0% +i think i'm gonna confuse myself if i + + + align:start position:0% +i think i'm gonna confuse myself if i +try to just repeat it but um you're you + + align:start position:0% +try to just repeat it but um you're you + + + align:start position:0% +try to just repeat it but um you're you +won't get a contradiction because the + + align:start position:0% +won't get a contradiction because the + + + align:start position:0% +won't get a contradiction because the +turing machine is not a find out + + align:start position:0% +turing machine is not a find out + + + align:start position:0% +turing machine is not a find out +automaton + + align:start position:0% +automaton + + + align:start position:0% +automaton +um + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% + + + + align:start position:0% + +will this argument get into self loops i + + align:start position:0% +will this argument get into self loops i + + + align:start position:0% +will this argument get into self loops i +don't see why there was there is some + + align:start position:0% +don't see why there was there is some + + + align:start position:0% +don't see why there was there is some +self-reference perhaps we're going to + + align:start position:0% +self-reference perhaps we're going to + + + align:start position:0% +self-reference perhaps we're going to +talk about that a little later because + + align:start position:0% +talk about that a little later because + + + align:start position:0% +talk about that a little later because +we're going to come back and revisit + + align:start position:0% +we're going to come back and revisit + + + align:start position:0% +we're going to come back and revisit +this argument um + + align:start position:0% +this argument um + + + align:start position:0% +this argument um +you know in a + + align:start position:0% +you know in a + + + align:start position:0% +you know in a +in a week or so when we talk about the + + align:start position:0% +in a week or so when we talk about the + + + align:start position:0% +in a week or so when we talk about the +recursion theorem which talks about + + align:start position:0% +recursion theorem which talks about + + + align:start position:0% +recursion theorem which talks about +machines that can refer to themselves + + align:start position:0% +machines that can refer to themselves + + + align:start position:0% +machines that can refer to themselves +but this is a little bit of a head + + align:start position:0% +but this is a little bit of a head + + + align:start position:0% +but this is a little bit of a head +getting ahead of ourselves so + + align:start position:0% +getting ahead of ourselves so + + + align:start position:0% +getting ahead of ourselves so +uh somebody's commenting on this + + align:start position:0% +uh somebody's commenting on this + + + align:start position:0% +uh somebody's commenting on this +reminding them of the barber paradox if + + align:start position:0% +reminding them of the barber paradox if + + + align:start position:0% +reminding them of the barber paradox if +you remember that the + + align:start position:0% +you remember that the + + + align:start position:0% +you remember that the +which has some similarity you know the + + align:start position:0% +which has some similarity you know the + + + align:start position:0% +which has some similarity you know the +there's a town in which uh there is a + + align:start position:0% +there's a town in which uh there is a + + + align:start position:0% +there's a town in which uh there is a +barber which shaves every man who + + align:start position:0% +barber which shaves every man who + + + align:start position:0% +barber which shaves every man who +doesn't shave themselves + + align:start position:0% +doesn't shave themselves + + + align:start position:0% +doesn't shave themselves +which seems you know he's a very good + + align:start position:0% +which seems you know he's a very good + + + align:start position:0% +which seems you know he's a very good +barber so there's some people who shave + + align:start position:0% +barber so there's some people who shave + + + align:start position:0% +barber so there's some people who shave +themselves + + align:start position:0% +themselves + + + align:start position:0% +themselves +and + + align:start position:0% +and + + + align:start position:0% +and +all the rest the barber shavers uh the + + align:start position:0% +all the rest the barber shavers uh the + + + align:start position:0% +all the rest the barber shavers uh the +question is does the barber shave + + align:start position:0% +question is does the barber shave + + + align:start position:0% +question is does the barber shave +himself because he shaves only those men + + align:start position:0% +himself because he shaves only those men + + + align:start position:0% +himself because he shaves only those men +who don't shave themselves so you got a + + align:start position:0% +who don't shave themselves so you got a + + + align:start position:0% +who don't shave themselves so you got a +same kind of a contradiction there is a + + align:start position:0% +same kind of a contradiction there is a + + + align:start position:0% +same kind of a contradiction there is a +there is a relationship there + + align:start position:0% +there is a relationship there + + + align:start position:0% +there is a relationship there +um + + align:start position:0% +um + + + align:start position:0% +um +so somebody wants to know where did we + + align:start position:0% +so somebody wants to know where did we + + + align:start position:0% +so somebody wants to know where did we +use the decidability so we used the + + align:start position:0% +use the decidability so we used the + + + align:start position:0% +use the decidability so we used the +decidability to come up with h + + align:start position:0% +decidability to come up with h + + + align:start position:0% +decidability to come up with h +um + + align:start position:0% +um + + + align:start position:0% +um +you know once we know that atm is + + align:start position:0% +you know once we know that atm is + + + align:start position:0% +you know once we know that atm is +decidable then we have that h function + + align:start position:0% +decidable then we have that h function + + + align:start position:0% +decidable then we have that h function +and then we can build d + + align:start position:0% +and then we can build d + + + align:start position:0% +and then we can build d +um so that's where that's the the the + + align:start position:0% +um so that's where that's the the the + + + align:start position:0% +um so that's where that's the the the +chain of that's the chain of reasoning + + align:start position:0% +chain of that's the chain of reasoning + + + align:start position:0% +chain of that's the chain of reasoning +um + + align:start position:0% +um + + + align:start position:0% +um +so you assume atm is decidable then you + + align:start position:0% +so you assume atm is decidable then you + + + align:start position:0% +so you assume atm is decidable then you +have the decider + + align:start position:0% +have the decider + + + align:start position:0% +have the decider +and then + + align:start position:0% +and then + + + align:start position:0% +and then +called h and then you can build d um + + align:start position:0% +called h and then you can build d um + + + align:start position:0% +called h and then you can build d um +somebody wants to see the previous slide + + align:start position:0% +somebody wants to see the previous slide + + + align:start position:0% +somebody wants to see the previous slide +well + + align:start position:0% +well + + + align:start position:0% +well +uh what part of this one do you want + + align:start position:0% +uh what part of this one do you want + + + align:start position:0% +uh what part of this one do you want +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so i'll leave that up there why can't we + + align:start position:0% +so i'll leave that up there why can't we + + + align:start position:0% +so i'll leave that up there why can't we +why can't we apply the proof that all + + align:start position:0% +why can't we apply the proof that all + + + align:start position:0% +why can't we apply the proof that all +touring machines are countable to all + + align:start position:0% +touring machines are countable to all + + + align:start position:0% +touring machines are countable to all +languages well because turing machines + + align:start position:0% +languages well because turing machines + + + align:start position:0% +languages well because turing machines +have descriptions + + align:start position:0% +have descriptions + + + align:start position:0% +have descriptions +languages general languages don't have + + align:start position:0% +languages general languages don't have + + + align:start position:0% +languages general languages don't have +descriptions + + align:start position:0% +descriptions + + + align:start position:0% +descriptions +and so that's uh why okay the candle has + + align:start position:0% +and so that's uh why okay the candle has + + + align:start position:0% +and so that's uh why okay the candle has +burned to the to the bottom and it's + + align:start position:0% +burned to the to the bottom and it's + + + align:start position:0% +burned to the to the bottom and it's +time to move on um + + align:start position:0% +time to move on um + + + align:start position:0% +time to move on um +so now let's look at the + + align:start position:0% +so now let's look at the + + + align:start position:0% +so now let's look at the +uh acceptance problem for kuwatama + + align:start position:0% +uh acceptance problem for kuwatama + + + align:start position:0% +uh acceptance problem for kuwatama +i'll give you a q automaton an input + + align:start position:0% +i'll give you a q automaton an input + + + align:start position:0% +i'll give you a q automaton an input +and i want to know does it accept the + + align:start position:0% +and i want to know does it accept the + + + align:start position:0% +and i want to know does it accept the +input is that going to be decidable + + align:start position:0% +input is that going to be decidable + + + align:start position:0% +input is that going to be decidable +and you have you have your choices it's + + align:start position:0% +and you have you have your choices it's + + + align:start position:0% +and you have you have your choices it's +either yes + + align:start position:0% +either yes + + + align:start position:0% +either yes +it is decidable because these are + + align:start position:0% +it is decidable because these are + + + align:start position:0% +it is decidable because these are +similar to put down automata and apda is + + align:start position:0% +similar to put down automata and apda is + + + align:start position:0% +similar to put down automata and apda is +decidable + + align:start position:0% +decidable + + + align:start position:0% +decidable +or no because yes would con contradicts + + align:start position:0% +or no because yes would con contradicts + + + align:start position:0% +or no because yes would con contradicts +results that we know at this point or we + + align:start position:0% +results that we know at this point or we + + + align:start position:0% +results that we know at this point or we +don't have enough information to answer + + align:start position:0% +don't have enough information to answer + + + align:start position:0% +don't have enough information to answer +the question + + align:start position:0% +the question + + + align:start position:0% +the question +okay let's put that up + + align:start position:0% + + + + align:start position:0% + +one second + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +that's it ready going gone + + align:start position:0% + + + + align:start position:0% + +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +yes the answer is uh well no + + align:start position:0% +yes the answer is uh well no + + + align:start position:0% +yes the answer is uh well no +the answer is the indeed the answer is b + + align:start position:0% +the answer is the indeed the answer is b + + + align:start position:0% +the answer is the indeed the answer is b +um + + align:start position:0% +um + + + align:start position:0% +um +uh true that uh cubitamina are similar + + align:start position:0% +uh true that uh cubitamina are similar + + + align:start position:0% +uh true that uh cubitamina are similar +to push on automata but all these atomic + + align:start position:0% +to push on automata but all these atomic + + + align:start position:0% +to push on automata but all these atomic +are kind of similar to each other and + + align:start position:0% +are kind of similar to each other and + + + align:start position:0% +are kind of similar to each other and +that's not going to be good enough + + align:start position:0% +that's not going to be good enough + + + align:start position:0% +that's not going to be good enough +uh + + align:start position:0% +uh + + + align:start position:0% +uh +well the homework has asked you to do is + + align:start position:0% +well the homework has asked you to do is + + + align:start position:0% +well the homework has asked you to do is +to show that you can simulate turing + + align:start position:0% +to show that you can simulate turing + + + align:start position:0% +to show that you can simulate turing +machines with q automata + + align:start position:0% +machines with q automata + + + align:start position:0% +machines with q automata +so if you can answer the question about + + align:start position:0% +so if you can answer the question about + + + align:start position:0% +so if you can answer the question about +whether the queue automata uh will + + align:start position:0% +whether the queue automata uh will + + + align:start position:0% +whether the queue automata uh will +accept their input that would allow you + + align:start position:0% +accept their input that would allow you + + + align:start position:0% +accept their input that would allow you +to be able to answer questions about + + align:start position:0% +to be able to answer questions about + + + align:start position:0% +to be able to answer questions about +whether turing machines accept their + + align:start position:0% +whether turing machines accept their + + + align:start position:0% +whether turing machines accept their +input and we just proved that's not + + align:start position:0% +input and we just proved that's not + + + align:start position:0% +input and we just proved that's not +possible + + align:start position:0% +possible + + + align:start position:0% +possible +so um + + align:start position:0% +so um + + + align:start position:0% +so um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it would get it be a contradiction if we + + align:start position:0% +it would get it be a contradiction if we + + + align:start position:0% +it would get it be a contradiction if we +could answer + + align:start position:0% +could answer + + + align:start position:0% +could answer +uh if we could decide a qa + + align:start position:0% +uh if we could decide a qa + + + align:start position:0% +uh if we could decide a qa +now we have an example of an undecidable + + align:start position:0% +now we have an example of an undecidable + + + align:start position:0% +now we have an example of an undecidable +language let's look at an example of an + + align:start position:0% +language let's look at an example of an + + + align:start position:0% +language let's look at an example of an +unrecognizable language + + align:start position:0% +unrecognizable language + + + align:start position:0% +unrecognizable language +now atm is not going to serve + + align:start position:0% +now atm is not going to serve + + + align:start position:0% +now atm is not going to serve +that purpose because atm + + align:start position:0% +that purpose because atm + + + align:start position:0% +that purpose because atm +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +is + + align:start position:0% +is + + + align:start position:0% +is +um + + align:start position:0% +um + + + align:start position:0% +um +recognizable is turning recognizable as + + align:start position:0% +recognizable is turning recognizable as + + + align:start position:0% +recognizable is turning recognizable as +we pointed out by the universal turing + + align:start position:0% +we pointed out by the universal turing + + + align:start position:0% +we pointed out by the universal turing +machine + + align:start position:0% +machine + + + align:start position:0% +machine +so uh atm is undecidable however how + + align:start position:0% +so uh atm is undecidable however how + + + align:start position:0% +so uh atm is undecidable however how +about an unrecognizable language + + align:start position:0% +about an unrecognizable language + + + align:start position:0% +about an unrecognizable language +for that we will see that the complement + + align:start position:0% +for that we will see that the complement + + + align:start position:0% +for that we will see that the complement +of atm + + align:start position:0% +of atm + + + align:start position:0% +of atm +will serve so the complement of atm + + align:start position:0% +will serve so the complement of atm + + + align:start position:0% +will serve so the complement of atm +is + + align:start position:0% +is + + + align:start position:0% +is +neither decidable nor even recognizable + + align:start position:0% +neither decidable nor even recognizable + + + align:start position:0% +neither decidable nor even recognizable +that's not turing recognizable + + align:start position:0% +that's not turing recognizable + + + align:start position:0% +that's not turing recognizable +and that's going to follow from a pretty + + align:start position:0% +and that's going to follow from a pretty + + + align:start position:0% +and that's going to follow from a pretty +basic theorem that connects + + align:start position:0% +basic theorem that connects + + + align:start position:0% +basic theorem that connects +recognizability and decidability that i + + align:start position:0% +recognizability and decidability that i + + + align:start position:0% +recognizability and decidability that i +put up here on the screen + + align:start position:0% +put up here on the screen + + + align:start position:0% +put up here on the screen +which is that if you have a language + + align:start position:0% +which is that if you have a language + + + align:start position:0% +which is that if you have a language +where it and its complement are both + + align:start position:0% +where it and its complement are both + + + align:start position:0% +where it and its complement are both +recognizable then the language turnout + + align:start position:0% +recognizable then the language turnout + + + align:start position:0% +recognizable then the language turnout +turns out to be decidable in fact the + + align:start position:0% +turns out to be decidable in fact the + + + align:start position:0% +turns out to be decidable in fact the +language and its complement are decided + + align:start position:0% +language and its complement are decided + + + align:start position:0% +language and its complement are decided +but but being decidable is closed under + + align:start position:0% +but but being decidable is closed under + + + align:start position:0% +but but being decidable is closed under +complement so that's something you + + align:start position:0% +complement so that's something you + + + align:start position:0% +complement so that's something you +should be aware of + + align:start position:0% +should be aware of + + + align:start position:0% +should be aware of +um + + align:start position:0% +um + + + align:start position:0% +um +but being uh okay + + align:start position:0% +but being uh okay + + + align:start position:0% +but being uh okay +we'll get to that in a minute but + + align:start position:0% +we'll get to that in a minute but + + + align:start position:0% +we'll get to that in a minute but +uh if um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so anyway so we have a language and it's + + align:start position:0% +so anyway so we have a language and it's + + + align:start position:0% +so anyway so we have a language and it's +complement both recognizable how do we + + align:start position:0% +complement both recognizable how do we + + + align:start position:0% +complement both recognizable how do we +know the language is decidable so first + + align:start position:0% +know the language is decidable so first + + + align:start position:0% +know the language is decidable so first +of all let's take the two turing + + align:start position:0% +of all let's take the two turing + + + align:start position:0% +of all let's take the two turing +machines m1 and m2 that recognizes a and + + align:start position:0% +machines m1 and m2 that recognizes a and + + + align:start position:0% +machines m1 and m2 that recognizes a and +a complement + + align:start position:0% + + + + align:start position:0% + +and we're going to put those together + + align:start position:0% +and we're going to put those together + + + align:start position:0% +and we're going to put those together +to get a decider for a + + align:start position:0% +to get a decider for a + + + align:start position:0% +to get a decider for a +um + + align:start position:0% +um + + + align:start position:0% +um +and that's going to work like this + + align:start position:0% +and that's going to work like this + + + align:start position:0% +and that's going to work like this +it's going to be called t + + align:start position:0% +it's going to be called t + + + align:start position:0% +it's going to be called t +so t says on input w what it's going to + + align:start position:0% +so t says on input w what it's going to + + + align:start position:0% +so t says on input w what it's going to +do + + align:start position:0% +do + + + align:start position:0% +do +it's going to feed w into m1 and m2 both + + align:start position:0% + + + + align:start position:0% + +um a is a language by the way yes a is + + align:start position:0% +um a is a language by the way yes a is + + + align:start position:0% +um a is a language by the way yes a is +when i'm telling you when i say it's + + align:start position:0% +when i'm telling you when i say it's + + + align:start position:0% +when i'm telling you when i say it's +touring recognizable you know turing + + align:start position:0% +touring recognizable you know turing + + + align:start position:0% +touring recognizable you know turing +recognizable only applies to languages + + align:start position:0% +recognizable only applies to languages + + + align:start position:0% +recognizable only applies to languages +so so yes a um is often this symbol i'm + + align:start position:0% +so so yes a um is often this symbol i'm + + + align:start position:0% +so so yes a um is often this symbol i'm +going to use for languages sometimes for + + align:start position:0% +going to use for languages sometimes for + + + align:start position:0% +going to use for languages sometimes for +an automaton but + + align:start position:0% +an automaton but + + + align:start position:0% +an automaton but +a is typically going to be a language + + align:start position:0% +a is typically going to be a language + + + align:start position:0% +a is typically going to be a language +so um + + align:start position:0% +so um + + + align:start position:0% +so um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +if uh so + + align:start position:0% +if uh so + + + align:start position:0% +if uh so +now i'm trying to make t + + align:start position:0% +now i'm trying to make t + + + align:start position:0% +now i'm trying to make t +be a decider for a + + align:start position:0% +be a decider for a + + + align:start position:0% +be a decider for a +from the recognizers for a and a + + align:start position:0% +from the recognizers for a and a + + + align:start position:0% +from the recognizers for a and a +complement + + align:start position:0% +complement + + + align:start position:0% +complement +so i'm gonna + + align:start position:0% +so i'm gonna + + + align:start position:0% +so i'm gonna +take an input to t + + align:start position:0% +take an input to t + + + align:start position:0% +take an input to t +and feed it into both recognizers m1 and + + align:start position:0% +and feed it into both recognizers m1 and + + + align:start position:0% +and feed it into both recognizers m1 and +m2 + + align:start position:0% + + + + align:start position:0% + +okay i'm going to run them in parallel + + align:start position:0% +okay i'm going to run them in parallel + + + align:start position:0% +okay i'm going to run them in parallel +what's nice + + align:start position:0% +what's nice + + + align:start position:0% +what's nice +is that because + + align:start position:0% +is that because + + + align:start position:0% +is that because +um + + align:start position:0% +um + + + align:start position:0% +um +m2 is a + + align:start position:0% +m2 is a + + + align:start position:0% +m2 is a +recognizes the complement of what m1 + + align:start position:0% +recognizes the complement of what m1 + + + align:start position:0% +recognizes the complement of what m1 +recognizes + + align:start position:0% +recognizes + + + align:start position:0% +recognizes +every string is going to be accepted + + align:start position:0% +every string is going to be accepted + + + align:start position:0% +every string is going to be accepted +either by m1 or by m2 + + align:start position:0% +either by m1 or by m2 + + + align:start position:0% +either by m1 or by m2 +because every string is either an a or + + align:start position:0% +because every string is either an a or + + + align:start position:0% +because every string is either an a or +an a complement + + align:start position:0% +an a complement + + + align:start position:0% +an a complement +so if i run m1 and m2 on w until one of + + align:start position:0% +so if i run m1 and m2 on w until one of + + + align:start position:0% +so if i run m1 and m2 on w until one of +them holds one of them accepts i know + + align:start position:0% +them holds one of them accepts i know + + + align:start position:0% +them holds one of them accepts i know +i'm not going to run forever because + + align:start position:0% +i'm not going to run forever because + + + align:start position:0% +i'm not going to run forever because +eventually one of the other ones have to + + align:start position:0% +eventually one of the other ones have to + + + align:start position:0% +eventually one of the other ones have to +accept + + align:start position:0% + + + + align:start position:0% + +so and then i got my answer because if + + align:start position:0% +so and then i got my answer because if + + + align:start position:0% +so and then i got my answer because if +m1 accepts that i know i'm in the + + align:start position:0% +m1 accepts that i know i'm in the + + + align:start position:0% +m1 accepts that i know i'm in the +language but if m2 accepts i know i'm in + + align:start position:0% +language but if m2 accepts i know i'm in + + + align:start position:0% +language but if m2 accepts i know i'm in +the complement of the language no matter + + align:start position:0% +the complement of the language no matter + + + align:start position:0% +the complement of the language no matter +the language so if m1 accepts then t + + align:start position:0% +the language so if m1 accepts then t + + + align:start position:0% +the language so if m1 accepts then t +should accept if m2 accepts then t + + align:start position:0% +should accept if m2 accepts then t + + + align:start position:0% +should accept if m2 accepts then t +should reject + + align:start position:0% +should reject + + + align:start position:0% +should reject +um + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +so that proves that + + align:start position:0% + + + + align:start position:0% + +nice little theorem uh written at the + + align:start position:0% +nice little theorem uh written at the + + + align:start position:0% +nice little theorem uh written at the +top in blue + + align:start position:0% +top in blue + + + align:start position:0% +top in blue +um so i got my decider for a + + align:start position:0% +um so i got my decider for a + + + align:start position:0% +um so i got my decider for a +built out of the recognizers for a and a + + align:start position:0% +built out of the recognizers for a and a + + + align:start position:0% +built out of the recognizers for a and a +complement + + align:start position:0% +complement + + + align:start position:0% +complement +now immediately it follows that + + align:start position:0% +now immediately it follows that + + + align:start position:0% +now immediately it follows that +the complement of atm is not touring + + align:start position:0% +the complement of atm is not touring + + + align:start position:0% +the complement of atm is not touring +recognizable + + align:start position:0% +recognizable + + + align:start position:0% +recognizable +because + + align:start position:0% +because + + + align:start position:0% +because +we know + + align:start position:0% +we know + + + align:start position:0% +we know +that atm itself + + align:start position:0% +that atm itself + + + align:start position:0% +that atm itself +is recognizable but it's undecidable + + align:start position:0% +is recognizable but it's undecidable + + + align:start position:0% +is recognizable but it's undecidable +if its complement were also on recognize + + align:start position:0% +if its complement were also on recognize + + + align:start position:0% +if its complement were also on recognize +if the complement was also recognizable + + align:start position:0% +if the complement was also recognizable + + + align:start position:0% +if the complement was also recognizable +then atm would be decidable but it isn't + + align:start position:0% +then atm would be decidable but it isn't + + + align:start position:0% +then atm would be decidable but it isn't +so when something is + + align:start position:0% +so when something is + + + align:start position:0% +so when something is +undecidable either it or its complement + + align:start position:0% +undecidable either it or its complement + + + align:start position:0% +undecidable either it or its complement +have to be unrecognizable and in the + + align:start position:0% +have to be unrecognizable and in the + + + align:start position:0% +have to be unrecognizable and in the +case for atm it has to be the compliment + + align:start position:0% +case for atm it has to be the compliment + + + align:start position:0% +case for atm it has to be the compliment +because we already showed that it is + + align:start position:0% +because we already showed that it is + + + align:start position:0% +because we already showed that it is +itself is recognizable + + align:start position:0% +itself is recognizable + + + align:start position:0% +itself is recognizable +um + + align:start position:0% +um + + + align:start position:0% +um +so that's the proof of that so here is a + + align:start position:0% +so that's the proof of that so here is a + + + align:start position:0% +so that's the proof of that so here is a +little picture of the way the world + + align:start position:0% +little picture of the way the world + + + align:start position:0% +little picture of the way the world +looks right now if you have here in the + + align:start position:0% +looks right now if you have here in the + + + align:start position:0% +looks right now if you have here in the +middle of the decidable languages see + + align:start position:0% +middle of the decidable languages see + + + align:start position:0% +middle of the decidable languages see +these are all languages here this venn + + align:start position:0% +these are all languages here this venn + + + align:start position:0% +these are all languages here this venn +diagram of languages kind of we showed + + align:start position:0% +diagram of languages kind of we showed + + + align:start position:0% +diagram of languages kind of we showed +earlier you know like the regular the + + align:start position:0% +earlier you know like the regular the + + + align:start position:0% +earlier you know like the regular the +context free decidable recognizable + + align:start position:0% +context free decidable recognizable + + + align:start position:0% +context free decidable recognizable +here i've got the recognizable and what + + align:start position:0% +here i've got the recognizable and what + + + align:start position:0% +here i've got the recognizable and what +i'm calling the co + + align:start position:0% +i'm calling the co + + + align:start position:0% +i'm calling the co +co code touring recognizable + + align:start position:0% +co code touring recognizable + + + align:start position:0% +co code touring recognizable +this is the collection of all + + align:start position:0% +this is the collection of all + + + align:start position:0% +this is the collection of all +complements + + align:start position:0% +complements + + + align:start position:0% +complements +of recognizable languages so atm + + align:start position:0% +of recognizable languages so atm + + + align:start position:0% +of recognizable languages so atm +bar atm complement is the complement of + + align:start position:0% +bar atm complement is the complement of + + + align:start position:0% +bar atm complement is the complement of +a recognizable language this uh + + align:start position:0% +a recognizable language this uh + + + align:start position:0% +a recognizable language this uh +region here is are all the complements + + align:start position:0% +region here is are all the complements + + + align:start position:0% +region here is are all the complements +of the recognizable languages or the + + align:start position:0% +of the recognizable languages or the + + + align:start position:0% +of the recognizable languages or the +so-called + + align:start position:0% +so-called + + + align:start position:0% +so-called +co-turing recognizable languages + + align:start position:0% +co-turing recognizable languages + + + align:start position:0% +co-turing recognizable languages +complement of + + align:start position:0% +complement of + + + align:start position:0% +complement of +so atm is on this side atm complement is + + align:start position:0% +so atm is on this side atm complement is + + + align:start position:0% +so atm is on this side atm complement is +on that side but if something's in both + + align:start position:0% +on that side but if something's in both + + + align:start position:0% +on that side but if something's in both +by virtue of this theorem here then it's + + align:start position:0% +by virtue of this theorem here then it's + + + align:start position:0% +by virtue of this theorem here then it's +decidable + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +last check-in for the day + + align:start position:0% +last check-in for the day + + + align:start position:0% +last check-in for the day +um from what we've learned so far + + align:start position:0% +um from what we've learned so far + + + align:start position:0% +um from what we've learned so far +um which closure properties can we prove + + align:start position:0% +um which closure properties can we prove + + + align:start position:0% +um which closure properties can we prove +for the class of + + align:start position:0% +for the class of + + + align:start position:0% +for the class of +the touring recognizable languages + + align:start position:0% +the touring recognizable languages + + + align:start position:0% +the touring recognizable languages +choose all that apply + + align:start position:0% + + + + align:start position:0% + +well as i say + + align:start position:0% +well as i say + + + align:start position:0% +well as i say +you don't have to get it right let's + + align:start position:0% +you don't have to get it right let's + + + align:start position:0% +you don't have to get it right let's +let's not spend too much more time on + + align:start position:0% +let's not spend too much more time on + + + align:start position:0% +let's not spend too much more time on +this because we'll we'll we'll talk a + + align:start position:0% +this because we'll we'll we'll talk a + + + align:start position:0% +this because we'll we'll we'll talk a +little bit about it + + align:start position:0% +little bit about it + + + align:start position:0% +little bit about it +um + + align:start position:0% +um + + + align:start position:0% +um +almost all it's closed under almost all + + align:start position:0% +almost all it's closed under almost all + + + align:start position:0% +almost all it's closed under almost all +of them but not all of them + + align:start position:0% + + + + align:start position:0% + +because you know + + align:start position:0% +because you know + + + align:start position:0% +because you know +are we done here i think we're done + + align:start position:0% +are we done here i think we're done + + + align:start position:0% +are we done here i think we're done +five seconds + + align:start position:0% + + + + align:start position:0% + +okay here we go ending polling + + align:start position:0% + + + + align:start position:0% + +i'm not sure what the meaning of + + align:start position:0% +i'm not sure what the meaning of + + + align:start position:0% +i'm not sure what the meaning of +the leading answer is here uh everybody + + align:start position:0% +the leading answer is here uh everybody + + + align:start position:0% +the leading answer is here uh everybody +likes union i guess they're closed under + + align:start position:0% +likes union i guess they're closed under + + + align:start position:0% +likes union i guess they're closed under +all of these operations except + + align:start position:0% +all of these operations except + + + align:start position:0% +all of these operations except +complement so + + align:start position:0% +complement so + + + align:start position:0% +complement so +um + + align:start position:0% + + + + align:start position:0% + +but we just proved it's not closing the + + align:start position:0% +but we just proved it's not closing the + + + align:start position:0% +but we just proved it's not closing the +confidence i'm a little + + align:start position:0% +confidence i'm a little + + + align:start position:0% +confidence i'm a little +you know a little puzzled by why we have + + align:start position:0% +you know a little puzzled by why we have + + + align:start position:0% +you know a little puzzled by why we have +so many votes for closure under + + align:start position:0% +so many votes for closure under + + + align:start position:0% +so many votes for closure under +compliment + + align:start position:0% +compliment + + + align:start position:0% +compliment +uh we have here atm + + align:start position:0% +uh we have here atm + + + align:start position:0% +uh we have here atm +is touring recognizable but atm + + align:start position:0% +is touring recognizable but atm + + + align:start position:0% +is touring recognizable but atm +complement is not touring recognizable + + align:start position:0% +complement is not touring recognizable + + + align:start position:0% +complement is not touring recognizable +so right here on the slide + + align:start position:0% +so right here on the slide + + + align:start position:0% +so right here on the slide +so i'm not trying to make you feel bad + + align:start position:0% +so i'm not trying to make you feel bad + + + align:start position:0% +so i'm not trying to make you feel bad +but uh + + align:start position:0% +but uh + + + align:start position:0% +but uh +um i'm trying to + + align:start position:0% +um i'm trying to + + + align:start position:0% +um i'm trying to +just point out that you + + align:start position:0% +just point out that you + + + align:start position:0% +just point out that you +think please um + + align:start position:0% +think please um + + + align:start position:0% +think please um +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +now closure under union and intersection + + align:start position:0% +now closure under union and intersection + + + align:start position:0% +now closure under union and intersection +i mean you could kind of get those + + align:start position:0% +i mean you could kind of get those + + + align:start position:0% +i mean you could kind of get those +answers just by running things in + + align:start position:0% +answers just by running things in + + + align:start position:0% +answers just by running things in +parallel the way we did the proof here + + align:start position:0% +parallel the way we did the proof here + + + align:start position:0% +parallel the way we did the proof here +you just run both machines + + align:start position:0% +you just run both machines + + + align:start position:0% +you just run both machines +and + + align:start position:0% + + + + align:start position:0% + +if they both + + align:start position:0% +if they both + + + align:start position:0% +if they both +give i mean it's a little tricky i + + align:start position:0% +give i mean it's a little tricky i + + + align:start position:0% +give i mean it's a little tricky i +suppose you know if if if either one of + + align:start position:0% +suppose you know if if if either one of + + + align:start position:0% +suppose you know if if if either one of +them accept um + + align:start position:0% +them accept um + + + align:start position:0% +them accept um +then you can accept or if they both + + align:start position:0% +then you can accept or if they both + + + align:start position:0% +then you can accept or if they both +accept you just wait until they both + + align:start position:0% +accept you just wait until they both + + + align:start position:0% +accept you just wait until they both +have accepted otherwise you just keep + + align:start position:0% +have accepted otherwise you just keep + + + align:start position:0% +have accepted otherwise you just keep +running um so the first two are pretty + + align:start position:0% +running um so the first two are pretty + + + align:start position:0% +running um so the first two are pretty +straightforward um closure under + + align:start position:0% +straightforward um closure under + + + align:start position:0% +straightforward um closure under +concatenation is also going to be + + align:start position:0% +concatenation is also going to be + + + align:start position:0% +concatenation is also going to be +similar you just try every possible way + + align:start position:0% +similar you just try every possible way + + + align:start position:0% +similar you just try every possible way +of cutting uh the string up into two + + align:start position:0% +of cutting uh the string up into two + + + align:start position:0% +of cutting uh the string up into two +pieces + + align:start position:0% +pieces + + + align:start position:0% +pieces +and run in parallel on and if you ever + + align:start position:0% +and run in parallel on and if you ever + + + align:start position:0% +and run in parallel on and if you ever +find a way + + align:start position:0% +find a way + + + align:start position:0% +find a way +of cutting it up and you run those two + + align:start position:0% +of cutting it up and you run those two + + + align:start position:0% +of cutting it up and you run those two +and those two sides in parallel and if + + align:start position:0% +and those two sides in parallel and if + + + align:start position:0% +and those two sides in parallel and if +they both um accept + + align:start position:0% +they both um accept + + + align:start position:0% +they both um accept +um then uh then you can accept and star + + align:start position:0% +um then uh then you can accept and star + + + align:start position:0% +um then uh then you can accept and star +is again very similar so there these are + + align:start position:0% +is again very similar so there these are + + + align:start position:0% +is again very similar so there these are +not too bad um but i admit you know it's + + align:start position:0% +not too bad um but i admit you know it's + + + align:start position:0% +not too bad um but i admit you know it's +not a whole lot of time to i have to + + align:start position:0% +not a whole lot of time to i have to + + + align:start position:0% +not a whole lot of time to i have to +contend with something uh that you're + + align:start position:0% +contend with something uh that you're + + + align:start position:0% +contend with something uh that you're +just getting uh used to + + align:start position:0% +just getting uh used to + + + align:start position:0% +just getting uh used to +so let's um + + align:start position:0% +so let's um + + + align:start position:0% +so let's um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +let's talk about the very last topic of + + align:start position:0% +let's talk about the very last topic of + + + align:start position:0% +let's talk about the very last topic of +the day which is really going to be + + align:start position:0% +the day which is really going to be + + + align:start position:0% +the day which is really going to be +setting ourselves up + + align:start position:0% +setting ourselves up + + + align:start position:0% +setting ourselves up +for um tuesday's lecture next week um + + align:start position:0% +for um tuesday's lecture next week um + + + align:start position:0% +for um tuesday's lecture next week um +and that's + + align:start position:0% +and that's + + + align:start position:0% +and that's +how we are going to be showing other + + align:start position:0% +how we are going to be showing other + + + align:start position:0% +how we are going to be showing other +languages are undecidable which is + + align:start position:0% +languages are undecidable which is + + + align:start position:0% +languages are undecidable which is +something that + + align:start position:0% +something that + + + align:start position:0% +something that +um i'm going to be expecting you guys to + + align:start position:0% +um i'm going to be expecting you guys to + + + align:start position:0% +um i'm going to be expecting you guys to +be able to do um + + align:start position:0% +be able to do um + + + align:start position:0% +be able to do um +this is um + + align:start position:0% +this is um + + + align:start position:0% +this is um +the standard procedure for showing + + align:start position:0% +the standard procedure for showing + + + align:start position:0% +the standard procedure for showing +languages are undecidable using what's + + align:start position:0% +languages are undecidable using what's + + + align:start position:0% +languages are undecidable using what's +called the reducibility method + + align:start position:0% +called the reducibility method + + + align:start position:0% +called the reducibility method +um + + align:start position:0% +um + + + align:start position:0% +um +and what that does is it + + align:start position:0% +and what that does is it + + + align:start position:0% +and what that does is it +takes as a starting point a language + + align:start position:0% +takes as a starting point a language + + + align:start position:0% +takes as a starting point a language +that we already know is undecidable + + align:start position:0% +that we already know is undecidable + + + align:start position:0% +that we already know is undecidable +typically atm + + align:start position:0% +typically atm + + + align:start position:0% +typically atm +or it could be another one that you've + + align:start position:0% +or it could be another one that you've + + + align:start position:0% +or it could be another one that you've +previously shown to be undecidable and + + align:start position:0% +previously shown to be undecidable and + + + align:start position:0% +previously shown to be undecidable and +leverages that information to show other + + align:start position:0% +leverages that information to show other + + + align:start position:0% +leverages that information to show other +languages are undecided + + align:start position:0% +languages are undecided + + + align:start position:0% +languages are undecided +and um + + align:start position:0% +and um + + + align:start position:0% +and um +it's using what's called reducibility + + align:start position:0% +it's using what's called reducibility + + + align:start position:0% +it's using what's called reducibility +we're going to go into this + + align:start position:0% +we're going to go into this + + + align:start position:0% +we're going to go into this +more carefully next time + + align:start position:0% +more carefully next time + + + align:start position:0% +more carefully next time +but basically reducibility is a way of + + align:start position:0% +but basically reducibility is a way of + + + align:start position:0% +but basically reducibility is a way of +using one problem to solve another + + align:start position:0% +using one problem to solve another + + + align:start position:0% +using one problem to solve another +problem + + align:start position:0% +problem + + + align:start position:0% +problem +and so we're going to show for example + + align:start position:0% +and so we're going to show for example + + + align:start position:0% +and so we're going to show for example +uh let's take a look at the problem + + align:start position:0% +uh let's take a look at the problem + + + align:start position:0% +uh let's take a look at the problem +called the holding the halting problem + + align:start position:0% +called the holding the halting problem + + + align:start position:0% +called the holding the halting problem +which is like the famous problem for + + align:start position:0% +which is like the famous problem for + + + align:start position:0% +which is like the famous problem for +turing machines um + + align:start position:0% +turing machines um + + + align:start position:0% +turing machines um +uh you just want to know whether it + + align:start position:0% +uh you just want to know whether it + + + align:start position:0% +uh you just want to know whether it +holds not necessarily whether it accepts + + align:start position:0% +holds not necessarily whether it accepts + + + align:start position:0% +holds not necessarily whether it accepts +so it's very similar but not exactly the + + align:start position:0% +so it's very similar but not exactly the + + + align:start position:0% +so it's very similar but not exactly the +same + + align:start position:0% + + + + align:start position:0% + +and we're going to show that + + align:start position:0% +and we're going to show that + + + align:start position:0% +and we're going to show that +this halting problem is similarly + + align:start position:0% +this halting problem is similarly + + + align:start position:0% +this halting problem is similarly +undecidable now we could go back and do + + align:start position:0% +undecidable now we could go back and do + + + align:start position:0% +undecidable now we could go back and do +the whole diagonalization but that seems + + align:start position:0% +the whole diagonalization but that seems + + + align:start position:0% +the whole diagonalization but that seems +like + + align:start position:0% +like + + + align:start position:0% +like +well that's more work than necessary now + + align:start position:0% +well that's more work than necessary now + + + align:start position:0% +well that's more work than necessary now +that we already know atm is undecidable + + align:start position:0% +that we already know atm is undecidable + + + align:start position:0% +that we already know atm is undecidable +because we're going to show that we can + + align:start position:0% +because we're going to show that we can + + + align:start position:0% +because we're going to show that we can +reduce the atm + + align:start position:0% +reduce the atm + + + align:start position:0% +reduce the atm +problem to the hold holding problem um + + align:start position:0% +problem to the hold holding problem um + + + align:start position:0% +problem to the hold holding problem um +and we'll explain what that means again + + align:start position:0% +and we'll explain what that means again + + + align:start position:0% +and we'll explain what that means again +uh later but um the idea is and as as + + align:start position:0% +uh later but um the idea is and as as + + + align:start position:0% +uh later but um the idea is and as as +we'll show in an illustration uh shortly + + align:start position:0% +we'll show in an illustration uh shortly + + + align:start position:0% +we'll show in an illustration uh shortly +that + + align:start position:0% +that + + + align:start position:0% +that +by proving by contradiction um + + align:start position:0% +by proving by contradiction um + + + align:start position:0% +by proving by contradiction um +if the whole thing if halt tm + + align:start position:0% +if the whole thing if halt tm + + + align:start position:0% +if the whole thing if halt tm +were decidable then atm would be + + align:start position:0% +were decidable then atm would be + + + align:start position:0% +were decidable then atm would be +decidable + + align:start position:0% +decidable + + + align:start position:0% +decidable +and we know atm is not decidable and so + + align:start position:0% +and we know atm is not decidable and so + + + align:start position:0% +and we know atm is not decidable and so +um + + align:start position:0% +um + + + align:start position:0% +um +that's our contradiction + + align:start position:0% +that's our contradiction + + + align:start position:0% +that's our contradiction +now + + align:start position:0% +now + + + align:start position:0% +now +uh + + align:start position:0% + + + + align:start position:0% + +the way we're going to show that if + + align:start position:0% +the way we're going to show that if + + + align:start position:0% +the way we're going to show that if +whole team is decidable than atm is + + align:start position:0% +whole team is decidable than atm is + + + align:start position:0% +whole team is decidable than atm is +decidable + + align:start position:0% +decidable + + + align:start position:0% +decidable +is use a decider for whole tm to decide + + align:start position:0% +is use a decider for whole tm to decide + + + align:start position:0% +is use a decider for whole tm to decide +atm with a suitable + + align:start position:0% +atm with a suitable + + + align:start position:0% +atm with a suitable +um + + align:start position:0% +um + + + align:start position:0% +um +you know uh + + align:start position:0% +you know uh + + + align:start position:0% +you know uh +uh + + align:start position:0% + + + + align:start position:0% + +modification + + align:start position:0% +modification + + + align:start position:0% +modification +so basically we're gonna turn + + align:start position:0% + + + + align:start position:0% + +and hold tm decider into an atm decider + + align:start position:0% +and hold tm decider into an atm decider + + + align:start position:0% +and hold tm decider into an atm decider +and that's + + align:start position:0% +and that's + + + align:start position:0% +and that's +how we're going to reduce the problem of + + align:start position:0% +how we're going to reduce the problem of + + + align:start position:0% +how we're going to reduce the problem of +solving atm to the problem of solving + + align:start position:0% +solving atm to the problem of solving + + + align:start position:0% +solving atm to the problem of solving +halt tm + + align:start position:0% +halt tm + + + align:start position:0% +halt tm +let's just do an example like you know + + align:start position:0% +let's just do an example like you know + + + align:start position:0% +let's just do an example like you know +if you've seen it before obviously this + + align:start position:0% +if you've seen it before obviously this + + + align:start position:0% +if you've seen it before obviously this +is not going to be hard but for the many + + align:start position:0% +is not going to be hard but for the many + + + align:start position:0% +is not going to be hard but for the many +of you who have not seen it before i it + + align:start position:0% +of you who have not seen it before i it + + + align:start position:0% +of you who have not seen it before i it +i'm partly doing it this time just so we + + align:start position:0% +i'm partly doing it this time just so we + + + align:start position:0% +i'm partly doing it this time just so we +can do it again next time and maybe + + align:start position:0% +can do it again next time and maybe + + + align:start position:0% +can do it again next time and maybe +it'll sink in by virtue of repetition + + align:start position:0% +it'll sink in by virtue of repetition + + + align:start position:0% +it'll sink in by virtue of repetition +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +so again so as i just said we're going + + align:start position:0% +so again so as i just said we're going + + + align:start position:0% +so again so as i just said we're going +to assume the whole tm problem is + + align:start position:0% +to assume the whole tm problem is + + + align:start position:0% +to assume the whole tm problem is +decidable and use that to show that atm + + align:start position:0% +decidable and use that to show that atm + + + align:start position:0% +decidable and use that to show that atm +is decidable which we know is false we + + align:start position:0% +is decidable which we know is false we + + + align:start position:0% +is decidable which we know is false we +showed it just earlier that it's not + + align:start position:0% +showed it just earlier that it's not + + + align:start position:0% +showed it just earlier that it's not +so assume we have a decider for whole + + align:start position:0% +so assume we have a decider for whole + + + align:start position:0% +so assume we have a decider for whole +team we'll call it r + + align:start position:0% +team we'll call it r + + + align:start position:0% +team we'll call it r +and we're going to construct from our + + align:start position:0% +and we're going to construct from our + + + align:start position:0% +and we're going to construct from our +decider for atm we'll call s + + align:start position:0% + + + + align:start position:0% + +okay so we're again typical proof by + + align:start position:0% +okay so we're again typical proof by + + + align:start position:0% +okay so we're again typical proof by +contradiction we're assuming the + + align:start position:0% +contradiction we're assuming the + + + align:start position:0% +contradiction we're assuming the +opposite of what we're trying to prove + + align:start position:0% +opposite of what we're trying to prove + + + align:start position:0% +opposite of what we're trying to prove +and then we're going to get something + + align:start position:0% +and then we're going to get something + + + align:start position:0% +and then we're going to get something +crazy + + align:start position:0% +crazy + + + align:start position:0% +crazy +okay so here my job now is i'm assuming + + align:start position:0% +okay so here my job now is i'm assuming + + + align:start position:0% +okay so here my job now is i'm assuming +i have r which is a whole tm decider so + + align:start position:0% +i have r which is a whole tm decider so + + + align:start position:0% +i have r which is a whole tm decider so +now i'm assuming i know how to + + align:start position:0% + + + + align:start position:0% + +decide + + align:start position:0% +decide + + + align:start position:0% +decide +if a turing machine and an input + + align:start position:0% +if a turing machine and an input + + + align:start position:0% +if a turing machine and an input +eventually halts + + align:start position:0% +eventually halts + + + align:start position:0% +eventually halts +not necessarily except just whether it + + align:start position:0% +not necessarily except just whether it + + + align:start position:0% +not necessarily except just whether it +holds + + align:start position:0% +holds + + + align:start position:0% +holds +you know it's conceivable you know you + + align:start position:0% +you know it's conceivable you know you + + + align:start position:0% +you know it's conceivable you know you +have to bear with me here it's + + align:start position:0% +have to bear with me here it's + + + align:start position:0% +have to bear with me here it's +conceivable that you could find a way to + + align:start position:0% +conceivable that you could find a way to + + + align:start position:0% +conceivable that you could find a way to +test whether + + align:start position:0% +test whether + + + align:start position:0% +test whether +you know turing machines halt on their + + align:start position:0% +you know turing machines halt on their + + + align:start position:0% +you know turing machines halt on their +input even though we now know that + + align:start position:0% +input even though we now know that + + + align:start position:0% +input even though we now know that +testing whether they accept their input + + align:start position:0% +testing whether they accept their input + + + align:start position:0% +testing whether they accept their input +is not decidable + + align:start position:0% + + + + align:start position:0% + +so you have to kind of be open-minded to + + align:start position:0% +so you have to kind of be open-minded to + + + align:start position:0% +so you have to kind of be open-minded to +the possibility that we can + + align:start position:0% +the possibility that we can + + + align:start position:0% +the possibility that we can +that the whole problem is decidable and + + align:start position:0% +that the whole problem is decidable and + + + align:start position:0% +that the whole problem is decidable and +we're going to show that that's can't be + + align:start position:0% +we're going to show that that's can't be + + + align:start position:0% +we're going to show that that's can't be +so we're going to show that + + align:start position:0% +so we're going to show that + + + align:start position:0% +so we're going to show that +if we could decide the whole thing + + align:start position:0% +if we could decide the whole thing + + + align:start position:0% +if we could decide the whole thing +problem then we can use that to decide + + align:start position:0% +problem then we can use that to decide + + + align:start position:0% +problem then we can use that to decide +the uh the acceptance problem + + align:start position:0% +the uh the acceptance problem + + + align:start position:0% +the uh the acceptance problem +okay so how do we how do we going to do + + align:start position:0% +okay so how do we how do we going to do + + + align:start position:0% +okay so how do we how do we going to do +that so imagine now we can solve the + + align:start position:0% +that so imagine now we can solve the + + + align:start position:0% +that so imagine now we can solve the +halting problem + + align:start position:0% +halting problem + + + align:start position:0% +halting problem +so to solve the atm + + align:start position:0% +so to solve the atm + + + align:start position:0% +so to solve the atm +which is what my job is + + align:start position:0% +which is what my job is + + + align:start position:0% +which is what my job is +to do + + align:start position:0% +to do + + + align:start position:0% +to do +so s is supposed to solve atm + + align:start position:0% +so s is supposed to solve atm + + + align:start position:0% +so s is supposed to solve atm +i'm constructing two + + align:start position:0% +i'm constructing two + + + align:start position:0% +i'm constructing two +machine as the site atm + + align:start position:0% +machine as the site atm + + + align:start position:0% +machine as the site atm +i'm going to use first i'm given an mnw + + align:start position:0% +i'm going to use first i'm given an mnw + + + align:start position:0% +i'm going to use first i'm given an mnw +i'm going to feed it into r since that's + + align:start position:0% +i'm going to feed it into r since that's + + + align:start position:0% +i'm going to feed it into r since that's +really all i got + + align:start position:0% +really all i got + + + align:start position:0% +really all i got +see if r + + align:start position:0% +see if r + + + align:start position:0% +see if r +tells me + + align:start position:0% +tells me + + + align:start position:0% +tells me +what happens + + align:start position:0% +what happens + + + align:start position:0% +what happens +does m on w at least hold + + align:start position:0% + + + + align:start position:0% + +well if r says no it doesn't hold + + align:start position:0% +well if r says no it doesn't hold + + + align:start position:0% +well if r says no it doesn't hold +well then then i'm actually done + + align:start position:0% +well then then i'm actually done + + + align:start position:0% +well then then i'm actually done +because if it m doesn't even hold on w + + align:start position:0% +because if it m doesn't even hold on w + + + align:start position:0% +because if it m doesn't even hold on w +then it couldn't be accepting w so at + + align:start position:0% +then it couldn't be accepting w so at + + + align:start position:0% +then it couldn't be accepting w so at +that point i know that m doesn't accept + + align:start position:0% +that point i know that m doesn't accept + + + align:start position:0% +that point i know that m doesn't accept +w and i can reject right + + align:start position:0% +w and i can reject right + + + align:start position:0% +w and i can reject right +off + + align:start position:0% +off + + + align:start position:0% +off +so our you can see how it could + + align:start position:0% +so our you can see how it could + + + align:start position:0% +so our you can see how it could +potentially be helpful but it's going to + + align:start position:0% +potentially be helpful but it's going to + + + align:start position:0% +potentially be helpful but it's going to +be helpful in either way because if r if + + align:start position:0% +be helpful in either way because if r if + + + align:start position:0% +be helpful in either way because if r if +r says m + + align:start position:0% +r says m + + + align:start position:0% +r says m +does hold + + align:start position:0% +does hold + + + align:start position:0% +does hold +well then i'm also good + + align:start position:0% +well then i'm also good + + + align:start position:0% +well then i'm also good +because i don't know the answer yet but + + align:start position:0% +because i don't know the answer yet but + + + align:start position:0% +because i don't know the answer yet but +what i do know is i can now simulate m + + align:start position:0% +what i do know is i can now simulate m + + + align:start position:0% +what i do know is i can now simulate m +on w + + align:start position:0% +on w + + + align:start position:0% +on w +until it holds because r has told me it + + align:start position:0% +until it holds because r has told me it + + + align:start position:0% +until it holds because r has told me it +holds so i don't have to worry about + + align:start position:0% +holds so i don't have to worry about + + + align:start position:0% +holds so i don't have to worry about +getting into a loop + + align:start position:0% +getting into a loop + + + align:start position:0% +getting into a loop +um + + align:start position:0% +um + + + align:start position:0% +um +uh so s can be confident in being a + + align:start position:0% +uh so s can be confident in being a + + + align:start position:0% +uh so s can be confident in being a +decider for whatever it's doing um + + align:start position:0% +decider for whatever it's doing um + + + align:start position:0% +decider for whatever it's doing um +because i'm running uh now m on w with a + + align:start position:0% +because i'm running uh now m on w with a + + + align:start position:0% +because i'm running uh now m on w with a +guarantee that it holds + + align:start position:0% +guarantee that it holds + + + align:start position:0% +guarantee that it holds +um + + align:start position:0% +um + + + align:start position:0% +um +and now that going to tell me now + + align:start position:0% +and now that going to tell me now + + + align:start position:0% +and now that going to tell me now +eventually the simulation of m w is + + align:start position:0% +eventually the simulation of m w is + + + align:start position:0% +eventually the simulation of m w is +going to end up at an acceptor reject + + align:start position:0% +going to end up at an acceptor reject + + + align:start position:0% +going to end up at an acceptor reject +and that's going to be the answer i need + + align:start position:0% +and that's going to be the answer i need + + + align:start position:0% +and that's going to be the answer i need +so if m is accepted then accept and as m + + align:start position:0% +so if m is accepted then accept and as m + + + align:start position:0% +so if m is accepted then accept and as m +is rejected then reject + + align:start position:0% +is rejected then reject + + + align:start position:0% +is rejected then reject +and that's how s solves the atm using r + + align:start position:0% +and that's how s solves the atm using r + + + align:start position:0% +and that's how s solves the atm using r +which which solves whole tia + + align:start position:0% +which which solves whole tia + + + align:start position:0% +which which solves whole tia +but s can't exist + + align:start position:0% +but s can't exist + + + align:start position:0% +but s can't exist +and so therefore r can't exist and + + align:start position:0% +and so therefore r can't exist and + + + align:start position:0% +and so therefore r can't exist and +therefore whole tm can't be decidable + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that quickly + + align:start position:0% +so that quickly + + + align:start position:0% +so that quickly +um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +i'm not sure which diagram you wanted me + + align:start position:0% +i'm not sure which diagram you wanted me + + + align:start position:0% +i'm not sure which diagram you wanted me +to show but anyway maybe we can do that + + align:start position:0% +to show but anyway maybe we can do that + + + align:start position:0% +to show but anyway maybe we can do that +we're basically at the end of the hour + + align:start position:0% +we're basically at the end of the hour + + + align:start position:0% +we're basically at the end of the hour +or end of that 90 minutes so let's do a + + align:start position:0% +or end of that 90 minutes so let's do a + + + align:start position:0% +or end of that 90 minutes so let's do a +quick review and if you stick around i'm + + align:start position:0% +quick review and if you stick around i'm + + + align:start position:0% +quick review and if you stick around i'm +happy to go back and look at any of the + + align:start position:0% +happy to go back and look at any of the + + + align:start position:0% +happy to go back and look at any of the +other slides uh that you might have + + align:start position:0% +other slides uh that you might have + + + align:start position:0% +other slides uh that you might have +missed something on + + align:start position:0% +missed something on + + + align:start position:0% +missed something on +okay so just to recap we showed that + + align:start position:0% +okay so just to recap we showed that + + + align:start position:0% +okay so just to recap we showed that +uh the natural numbers of the real + + align:start position:0% +uh the natural numbers of the real + + + align:start position:0% +uh the natural numbers of the real +numbers are not the same size using that + + align:start position:0% +numbers are not the same size using that + + + align:start position:0% +numbers are not the same size using that +definition of one-to-one correspondence + + align:start position:0% +definition of one-to-one correspondence + + + align:start position:0% +definition of one-to-one correspondence +to introduce the diagonalization method + + align:start position:0% +to introduce the diagonalization method + + + align:start position:0% +to introduce the diagonalization method +we use the diagonalization method to + + align:start position:0% +we use the diagonalization method to + + + align:start position:0% +we use the diagonalization method to +show that atm is undecidable + + align:start position:0% +show that atm is undecidable + + + align:start position:0% +show that atm is undecidable +we also showed that little theorem that + + align:start position:0% +we also showed that little theorem that + + + align:start position:0% +we also showed that little theorem that +if the language and its complement are + + align:start position:0% +if the language and its complement are + + + align:start position:0% +if the language and its complement are +recognizable then the language is + + align:start position:0% +recognizable then the language is + + + align:start position:0% +recognizable then the language is +decidable + + align:start position:0% +decidable + + + align:start position:0% +decidable +and from that we conclude that atm + + align:start position:0% +and from that we conclude that atm + + + align:start position:0% +and from that we conclude that atm +complement is not recognizable + + align:start position:0% +complement is not recognizable + + + align:start position:0% +complement is not recognizable +and then we showed at least by virtue of + + align:start position:0% +and then we showed at least by virtue of + + + align:start position:0% +and then we showed at least by virtue of +an introduction to the method the + + align:start position:0% +an introduction to the method the + + + align:start position:0% +an introduction to the method the +reducibility method to show that whole + + align:start position:0% +reducibility method to show that whole + + + align:start position:0% +reducibility method to show that whole +tm is undecided + + align:start position:0% +tm is undecided + + + align:start position:0% +tm is undecided +okay and that's that that was today's + + align:start position:0% +okay and that's that that was today's + + + align:start position:0% +okay and that's that that was today's +lecture and we're and we're uh + + align:start position:0% +lecture and we're and we're uh + + + align:start position:0% +lecture and we're and we're uh +at the end of the hour so why don't i um + + align:start position:0% +at the end of the hour so why don't i um + + + align:start position:0% +at the end of the hour so why don't i um +you know we are finished uh you can uh + + align:start position:0% +you know we are finished uh you can uh + + + align:start position:0% +you know we are finished uh you can uh +log out um and if you want i will stick + + align:start position:0% +log out um and if you want i will stick + + + align:start position:0% +log out um and if you want i will stick +around + + align:start position:0% +around + + + align:start position:0% +around +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay this is kind of a good question + + align:start position:0% +okay this is kind of a good question + + + align:start position:0% +okay this is kind of a good question +here + + align:start position:0% +here + + + align:start position:0% +here +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so i'm getting a question about the + + align:start position:0% +so i'm getting a question about the + + + align:start position:0% +so i'm getting a question about the +atm complement + + align:start position:0% + + + + align:start position:0% + +which is uh you know since we have a + + align:start position:0% +which is uh you know since we have a + + + align:start position:0% +which is uh you know since we have a +a recognizer for atm + + align:start position:0% +a recognizer for atm + + + align:start position:0% +a recognizer for atm +uh if i'm doing justice to this uh + + align:start position:0% +uh if i'm doing justice to this uh + + + align:start position:0% +uh if i'm doing justice to this uh +question uh we have a co we have a + + align:start position:0% +question uh we have a co we have a + + + align:start position:0% +question uh we have a co we have a +recognizer for atm so why can't we just + + align:start position:0% +recognizer for atm so why can't we just + + + align:start position:0% +recognizer for atm so why can't we just +invert the answer + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% +you know + + + align:start position:0% +you know +flip flip the answer around and now we + + align:start position:0% +flip flip the answer around and now we + + + align:start position:0% +flip flip the answer around and now we +have a recognizer for + + align:start position:0% +have a recognizer for + + + align:start position:0% +have a recognizer for +the complement of atm atm complement + + align:start position:0% +the complement of atm atm complement + + + align:start position:0% +the complement of atm atm complement +so why doesn't that work + + align:start position:0% +so why doesn't that work + + + align:start position:0% +so why doesn't that work +well the reason that doesn't work + + align:start position:0% +well the reason that doesn't work + + + align:start position:0% +well the reason that doesn't work +is because + + align:start position:0% +is because + + + align:start position:0% +is because +the recognizer for atm + + align:start position:0% +the recognizer for atm + + + align:start position:0% +the recognizer for atm +might be rejecting some things by + + align:start position:0% +might be rejecting some things by + + + align:start position:0% +might be rejecting some things by +looping + + align:start position:0% +looping + + + align:start position:0% +looping +and now if you just flip + + align:start position:0% +and now if you just flip + + + align:start position:0% +and now if you just flip +the accepting and rejecting + + align:start position:0% +the accepting and rejecting + + + align:start position:0% +the accepting and rejecting +um + + align:start position:0% +um + + + align:start position:0% +um +when it hits one of those uh holding + + align:start position:0% +when it hits one of those uh holding + + + align:start position:0% +when it hits one of those uh holding +states it's going to give the reverse + + align:start position:0% +states it's going to give the reverse + + + align:start position:0% +states it's going to give the reverse +answer + + align:start position:0% +answer + + + align:start position:0% +answer +but the uh when it uh + + align:start position:0% +but the uh when it uh + + + align:start position:0% +but the uh when it uh +rejects by looping it'll continue to + + align:start position:0% +rejects by looping it'll continue to + + + align:start position:0% +rejects by looping it'll continue to +reject by looping so you won't get the + + align:start position:0% +reject by looping so you won't get the + + + align:start position:0% +reject by looping so you won't get the +complementary language coming out + + align:start position:0% + + + + align:start position:0% + +so you know if we want you know if we + + align:start position:0% +so you know if we want you know if we + + + align:start position:0% +so you know if we want you know if we +would be helpful i can go back + + align:start position:0% +would be helpful i can go back + + + align:start position:0% +would be helpful i can go back +to that uh slide here + + align:start position:0% +to that uh slide here + + + align:start position:0% +to that uh slide here +um + + align:start position:0% + + + + align:start position:0% + +which proves that atm complement is + + align:start position:0% +which proves that atm complement is + + + align:start position:0% +which proves that atm complement is +unrecognizable + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +maybe we should start with the bottom + + align:start position:0% +maybe we should start with the bottom + + + align:start position:0% +maybe we should start with the bottom +we know that atm + + align:start position:0% +we know that atm + + + align:start position:0% +we know that atm +is recognizable and undecidable + + align:start position:0% +is recognizable and undecidable + + + align:start position:0% +is recognizable and undecidable +right we already proved those two facts + + align:start position:0% +right we already proved those two facts + + + align:start position:0% +right we already proved those two facts +atm is recognizable + + align:start position:0% +atm is recognizable + + + align:start position:0% +atm is recognizable +from the um universal turing machine + + align:start position:0% +from the um universal turing machine + + + align:start position:0% +from the um universal turing machine +and it's undecidable by the + + align:start position:0% +and it's undecidable by the + + + align:start position:0% +and it's undecidable by the +diagonalization argument + + align:start position:0% +diagonalization argument + + + align:start position:0% +diagonalization argument +those two things together + + align:start position:0% +those two things together + + + align:start position:0% +those two things together +tell us that the complement has to be + + align:start position:0% +tell us that the complement has to be + + + align:start position:0% +tell us that the complement has to be +unrecognizable + + align:start position:0% +unrecognizable + + + align:start position:0% +unrecognizable +because + + align:start position:0% +because + + + align:start position:0% +because +if a language and its complement are + + align:start position:0% +if a language and its complement are + + + align:start position:0% +if a language and its complement are +both recognizable and we already know + + align:start position:0% +both recognizable and we already know + + + align:start position:0% +both recognizable and we already know +the language itself is recognizable + + align:start position:0% +the language itself is recognizable + + + align:start position:0% +the language itself is recognizable +so now if the complement is also + + align:start position:0% +so now if the complement is also + + + align:start position:0% +so now if the complement is also +recognizable the language is going to be + + align:start position:0% +recognizable the language is going to be + + + align:start position:0% +recognizable the language is going to be +decidable by the upper theorem + + align:start position:0% + + + + align:start position:0% + +so it must be the case that either the + + align:start position:0% +so it must be the case that either the + + + align:start position:0% +so it must be the case that either the +language itself is unrecognizable or its + + align:start position:0% +language itself is unrecognizable or its + + + align:start position:0% +language itself is unrecognizable or its +complement is unrecognizable + + align:start position:0% +complement is unrecognizable + + + align:start position:0% +complement is unrecognizable +we know the language is recognizable + + align:start position:0% +we know the language is recognizable + + + align:start position:0% +we know the language is recognizable +that's what the universal turing machine + + align:start position:0% +that's what the universal turing machine + + + align:start position:0% +that's what the universal turing machine +told us so the only thing left is for + + align:start position:0% +told us so the only thing left is for + + + align:start position:0% +told us so the only thing left is for +the complement to be unrecognizable + + align:start position:0% + + + + align:start position:0% + +you should review that if you didn't get + + align:start position:0% +you should review that if you didn't get + + + align:start position:0% +you should review that if you didn't get +it um because + + align:start position:0% +it um because + + + align:start position:0% +it um because +this is a kind of + + align:start position:0% +this is a kind of + + + align:start position:0% +this is a kind of +you know + + align:start position:0% +you know + + + align:start position:0% +you know +kind of reasoning we + + align:start position:0% +kind of reasoning we + + + align:start position:0% +kind of reasoning we +you know we're going to be building on + + align:start position:0% +you know we're going to be building on + + + align:start position:0% +you know we're going to be building on +things like that so i think it's good + + align:start position:0% +things like that so i think it's good + + + align:start position:0% +things like that so i think it's good +good to make sure you understand + + align:start position:0% +good to make sure you understand + + + align:start position:0% +good to make sure you understand +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +okay the diagram on the right so this is + + align:start position:0% +okay the diagram on the right so this is + + + align:start position:0% +okay the diagram on the right so this is +just a venn diagram here + + align:start position:0% +just a venn diagram here + + + align:start position:0% +just a venn diagram here +kind of threw this in at the last minute + + align:start position:0% +kind of threw this in at the last minute + + + align:start position:0% +kind of threw this in at the last minute +here i was worried about it being + + align:start position:0% +here i was worried about it being + + + align:start position:0% +here i was worried about it being +confusing + + align:start position:0% +confusing + + + align:start position:0% +confusing +you know that part is um + + align:start position:0% + + + + align:start position:0% + +you know so you know i'm trying to show + + align:start position:0% +you know so you know i'm trying to show + + + align:start position:0% +you know so you know i'm trying to show +that the three classes that we've + + align:start position:0% +that the three classes that we've + + + align:start position:0% +that the three classes that we've +already talked about + + align:start position:0% +already talked about + + + align:start position:0% +already talked about +the languages which are decidable the + + align:start position:0% +the languages which are decidable the + + + align:start position:0% +the languages which are decidable the +languages which are touring recognizable + + align:start position:0% +languages which are touring recognizable + + + align:start position:0% +languages which are touring recognizable +and the languages whose compliments are + + align:start position:0% +and the languages whose compliments are + + + align:start position:0% +and the languages whose compliments are +going recognizable those are three + + align:start position:0% +going recognizable those are three + + + align:start position:0% +going recognizable those are three +separate classes of languages + + align:start position:0% +separate classes of languages + + + align:start position:0% +separate classes of languages +and + + align:start position:0% +and + + + align:start position:0% +and +those come up here in those three + + align:start position:0% +those come up here in those three + + + align:start position:0% +those come up here in those three +regions + + align:start position:0% +regions + + + align:start position:0% +regions +these are the decidable ones + + align:start position:0% +these are the decidable ones + + + align:start position:0% +these are the decidable ones +here are the recognizable ones + + align:start position:0% +here are the recognizable ones + + + align:start position:0% +here are the recognizable ones +and here are the ones whose compliments + + align:start position:0% +and here are the ones whose compliments + + + align:start position:0% +and here are the ones whose compliments +are recognizable + + align:start position:0% + + + + align:start position:0% + +now if a language + + align:start position:0% +now if a language + + + align:start position:0% +now if a language +is in both + + align:start position:0% +is in both + + + align:start position:0% +is in both +recognizable and its complement is + + align:start position:0% +recognizable and its complement is + + + align:start position:0% +recognizable and its complement is +recognizable so it's in both of these + + align:start position:0% +recognizable so it's in both of these + + + align:start position:0% +recognizable so it's in both of these +bigger regions here + + align:start position:0% +bigger regions here + + + align:start position:0% +bigger regions here +then this theorem tells you it's + + align:start position:0% +then this theorem tells you it's + + + align:start position:0% +then this theorem tells you it's +decidable + + align:start position:0% + + + + align:start position:0% + +so that's why + + align:start position:0% +so that's why + + + align:start position:0% +so that's why +the intersection of these two regions is + + align:start position:0% +the intersection of these two regions is + + + align:start position:0% +the intersection of these two regions is +marked as being decidable because that + + align:start position:0% +marked as being decidable because that + + + align:start position:0% +marked as being decidable because that +means you're in both + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but we know that atm is sitting out here + + align:start position:0% +but we know that atm is sitting out here + + + align:start position:0% +but we know that atm is sitting out here +as recognizable but not decidable so atm + + align:start position:0% +as recognizable but not decidable so atm + + + align:start position:0% +as recognizable but not decidable so atm +is in the recognizable side but it's not + + align:start position:0% +is in the recognizable side but it's not + + + align:start position:0% +is in the recognizable side but it's not +on the complement of recognizable atm + + align:start position:0% +on the complement of recognizable atm + + + align:start position:0% +on the complement of recognizable atm +itself um + + align:start position:0% +itself um + + + align:start position:0% +itself um +the complement of atm is the complement + + align:start position:0% +the complement of atm is the complement + + + align:start position:0% +the complement of atm is the complement +of a recognizable but itself is not + + align:start position:0% +of a recognizable but itself is not + + + align:start position:0% +of a recognizable but itself is not +recognizable um + + align:start position:0% +recognizable um + + + align:start position:0% +recognizable um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +not decidable so you get this side of + + align:start position:0% +not decidable so you get this side of + + + align:start position:0% +not decidable so you get this side of +nice + + align:start position:0% +nice + + + align:start position:0% +nice +you know + + align:start position:0% +you know + + + align:start position:0% +you know +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +i hope it's you think it's nice but it's + + align:start position:0% +i hope it's you think it's nice but it's + + + align:start position:0% +i hope it's you think it's nice but it's +a sort of uh trying to summarize things + + align:start position:0% +a sort of uh trying to summarize things + + + align:start position:0% +a sort of uh trying to summarize things +in this in this field diagram + + align:start position:0% + + + + align:start position:0% + +so i think i'm going to then uh + + align:start position:0% +so i think i'm going to then uh + + + align:start position:0% +so i think i'm going to then uh +sign off + + align:start position:0% +sign off + + + align:start position:0% +sign off +and um + + align:start position:0% +and um + + + align:start position:0% +and um +i'll see you all on + + align:start position:0% +i'll see you all on + + + align:start position:0% +i'll see you all on +tuesday and have a good weekend bye-bye \ No newline at end of file diff --git a/3V5y9uq5au0.txt b/3V5y9uq5au0.txt new file mode 100644 index 0000000000000000000000000000000000000000..e1b3b24da26a39b1c7ba4b71c2a4542a72695859 --- /dev/null +++ b/3V5y9uq5au0.txt @@ -0,0 +1,979 @@ +align:start position:0% + +we want to look at this pulley system we + + align:start position:0% +we want to look at this pulley system we + + + align:start position:0% +we want to look at this pulley system we +want to find out what this force here is + + align:start position:0% +want to find out what this force here is + + + align:start position:0% +want to find out what this force here is +for example with which this block is + + align:start position:0% +for example with which this block is + + + align:start position:0% +for example with which this block is +being poked now we have two massless + + align:start position:0% +being poked now we have two massless + + + align:start position:0% +being poked now we have two massless +polizia and two moving parts and one key + + align:start position:0% +polizia and two moving parts and one key + + + align:start position:0% +polizia and two moving parts and one key +component of this problem is to derive + + align:start position:0% +component of this problem is to derive + + + align:start position:0% +component of this problem is to derive +the acceleration constraint how we're + + align:start position:0% +the acceleration constraint how we're + + + align:start position:0% +the acceleration constraint how we're +going to do that well we have to look at + + align:start position:0% +going to do that well we have to look at + + + align:start position:0% +going to do that well we have to look at +this string here first of all it's a + + align:start position:0% +this string here first of all it's a + + + align:start position:0% +this string here first of all it's a +fixed string length and that will help + + align:start position:0% +fixed string length and that will help + + + align:start position:0% +fixed string length and that will help +us ultimately this is just a distance + + align:start position:0% +us ultimately this is just a distance + + + align:start position:0% +us ultimately this is just a distance +that connects all of these objects and + + align:start position:0% +that connects all of these objects and + + + align:start position:0% +that connects all of these objects and +if we eventually differentiate that + + align:start position:0% +if we eventually differentiate that + + + align:start position:0% +if we eventually differentiate that +twice we get to an acceleration so the + + align:start position:0% +twice we get to an acceleration so the + + + align:start position:0% +twice we get to an acceleration so the +first thing we're going to do is to + + align:start position:0% +first thing we're going to do is to + + + align:start position:0% +first thing we're going to do is to +derive the to figure out what the string + + align:start position:0% +derive the to figure out what the string + + + align:start position:0% +derive the to figure out what the string +length is and we then derive the + + align:start position:0% +length is and we then derive the + + + align:start position:0% +length is and we then derive the +acceleration condition let's begin by + + align:start position:0% +acceleration condition let's begin by + + + align:start position:0% +acceleration condition let's begin by +first identifying the fixed length in + + align:start position:0% +first identifying the fixed length in + + + align:start position:0% +first identifying the fixed length in +this problem so we have a little + + align:start position:0% +this problem so we have a little + + + align:start position:0% +this problem so we have a little +distance here we call it SB and we have + + align:start position:0% +distance here we call it SB and we have + + + align:start position:0% +distance here we call it SB and we have +a distance here that's fixed as a and we + + align:start position:0% +a distance here that's fixed as a and we + + + align:start position:0% +a distance here that's fixed as a and we +furthermore know that this block here is + + align:start position:0% +furthermore know that this block here is + + + align:start position:0% +furthermore know that this block here is +fixed to the ground and we can choose a + + align:start position:0% +fixed to the ground and we can choose a + + + align:start position:0% +fixed to the ground and we can choose a +coordinate system origin let's say we do + + align:start position:0% +coordinate system origin let's say we do + + + align:start position:0% +coordinate system origin let's say we do +that here we know that we have the + + align:start position:0% +that here we know that we have the + + + align:start position:0% +that here we know that we have the +distance D here - to this little block + + align:start position:0% +distance D here - to this little block + + + align:start position:0% +distance D here - to this little block +the moving parts block 1 and block 2 so + + align:start position:0% +the moving parts block 1 and block 2 so + + + align:start position:0% +the moving parts block 1 and block 2 so +we have to assign position functions and + + align:start position:0% +we have to assign position functions and + + + align:start position:0% +we have to assign position functions and +actually this one here is x1 it goes up + + align:start position:0% +actually this one here is x1 it goes up + + + align:start position:0% +actually this one here is x1 it goes up +to here because we want to measure the + + align:start position:0% +to here because we want to measure the + + + align:start position:0% +to here because we want to measure the +string length ultimately and we we know + + align:start position:0% +string length ultimately and we we know + + + align:start position:0% +string length ultimately and we we know +this portion here so we can subtract it + + align:start position:0% +this portion here so we can subtract it + + + align:start position:0% +this portion here so we can subtract it +and then of course we need also x1 that + + align:start position:0% +and then of course we need also x1 that + + + align:start position:0% +and then of course we need also x1 that +goes here x2 + + align:start position:0% +goes here x2 + + + align:start position:0% +goes here x2 +so now we can we can tell you up the + + align:start position:0% +so now we can we can tell you up the + + + align:start position:0% +so now we can we can tell you up the +length let's start with this portion + + align:start position:0% +length let's start with this portion + + + align:start position:0% +length let's start with this portion +here that is D minus si minus X 2 e + + align:start position:0% +here that is D minus si minus X 2 e + + + align:start position:0% +here that is D minus si minus X 2 e +minus s a minus X 2 and then we have a + + align:start position:0% +minus s a minus X 2 and then we have a + + + align:start position:0% +minus s a minus X 2 and then we have a +half circle here PI R and we know + + align:start position:0% +half circle here PI R and we know + + + align:start position:0% +half circle here PI R and we know +actually that there's another half + + align:start position:0% +actually that there's another half + + + align:start position:0% +actually that there's another half +circle gonna come there so we can just + + align:start position:0% +circle gonna come there so we can just + + + align:start position:0% +circle gonna come there so we can just +write 2 PI R immediately and then we + + align:start position:0% +write 2 PI R immediately and then we + + + align:start position:0% +write 2 PI R immediately and then we +have this part here that one is X 1 + + align:start position:0% +have this part here that one is X 1 + + + align:start position:0% +have this part here that one is X 1 +minus s B and then minus si minus X 2 + + align:start position:0% + + + + align:start position:0% + +and then finally we have this portion + + align:start position:0% +and then finally we have this portion + + + align:start position:0% +and then finally we have this portion +and that is X 1 minus SB minus X 2 + + align:start position:0% + + + + align:start position:0% + +okay so the next step is that we need to + + align:start position:0% +okay so the next step is that we need to + + + align:start position:0% +okay so the next step is that we need to +simplify this a little bit so we have 1 + + align:start position:0% +simplify this a little bit so we have 1 + + + align:start position:0% +simplify this a little bit so we have 1 +X 1 and another 1 here 2 X 1 plus X 2 X + + align:start position:0% +X 1 and another 1 here 2 X 1 plus X 2 X + + + align:start position:0% +X 1 and another 1 here 2 X 1 plus X 2 X +2 X 2 actually 3 minus 3 X 2 and then we + + align:start position:0% +2 X 2 actually 3 minus 3 X 2 and then we + + + align:start position:0% +2 X 2 actually 3 minus 3 X 2 and then we +have all sorts of constants we have D we + + align:start position:0% +have all sorts of constants we have D we + + + align:start position:0% +have all sorts of constants we have D we +have s a as be the 2pi r but as you will + + align:start position:0% +have s a as be the 2pi r but as you will + + + align:start position:0% +have s a as be the 2pi r but as you will +see if we differentiate this L here if + + align:start position:0% +see if we differentiate this L here if + + + align:start position:0% +see if we differentiate this L here if +that will actually all fall away so + + align:start position:0% +that will actually all fall away so + + + align:start position:0% +that will actually all fall away so +we're going to make a life easy and just + + align:start position:0% +we're going to make a life easy and just + + + align:start position:0% +we're going to make a life easy and just +add a constant here and so we want to + + align:start position:0% +add a constant here and so we want to + + + align:start position:0% +add a constant here and so we want to +now do the second derivative here of our + + align:start position:0% +now do the second derivative here of our + + + align:start position:0% +now do the second derivative here of our +string length there is respect to time + + align:start position:0% +string length there is respect to time + + + align:start position:0% +string length there is respect to time +because these are all position functions + + align:start position:0% +because these are all position functions + + + align:start position:0% +because these are all position functions +so we can differentiate those and what's + + align:start position:0% +so we can differentiate those and what's + + + align:start position:0% +so we can differentiate those and what's +important of course here's the string + + align:start position:0% +important of course here's the string + + + align:start position:0% +important of course here's the string +length is not changing with time so + + align:start position:0% +length is not changing with time so + + + align:start position:0% +length is not changing with time so +actually we know that a derivative will + + align:start position:0% +actually we know that a derivative will + + + align:start position:0% +actually we know that a derivative will +be 0 and we can just write this up here + + align:start position:0% +be 0 and we can just write this up here + + + align:start position:0% +be 0 and we can just write this up here +because x differentiate it twice is 8 so + + align:start position:0% +because x differentiate it twice is 8 so + + + align:start position:0% +because x differentiate it twice is 8 so +2 a 1 minus 3 a 2 and we immediately see + + align:start position:0% +2 a 1 minus 3 a 2 and we immediately see + + + align:start position:0% +2 a 1 minus 3 a 2 and we immediately see +from that that a 1 equals 3 a 2 so this + + align:start position:0% +from that that a 1 equals 3 a 2 so this + + + align:start position:0% +from that that a 1 equals 3 a 2 so this +is our constraint condition that we will + + align:start position:0% +is our constraint condition that we will + + + align:start position:0% +is our constraint condition that we will +need later for now we need to continue + + align:start position:0% +need later for now we need to continue + + + align:start position:0% +need later for now we need to continue +with setting up Freebody diagrams of all + + align:start position:0% +with setting up Freebody diagrams of all + + + align:start position:0% +with setting up Freebody diagrams of all +four objects let's start that with + + align:start position:0% +four objects let's start that with + + + align:start position:0% +four objects let's start that with +object won + + align:start position:0% +object won + + + align:start position:0% +object won +what's acting on object 1 well we have F + + align:start position:0% +what's acting on object 1 well we have F + + + align:start position:0% +what's acting on object 1 well we have F +here we write it as magnitude we have F + + align:start position:0% +here we write it as magnitude we have F + + + align:start position:0% +here we write it as magnitude we have F +and then we have here a tension that + + align:start position:0% +and then we have here a tension that + + + align:start position:0% +and then we have here a tension that +goes to the pulley B that one is + + align:start position:0% +goes to the pulley B that one is + + + align:start position:0% +goes to the pulley B that one is +different from the tension in the string + + align:start position:0% +different from the tension in the string + + + align:start position:0% +different from the tension in the string +so we're going to call this TB + + align:start position:0% +so we're going to call this TB + + + align:start position:0% +so we're going to call this TB +then we have object to oh and of course + + align:start position:0% +then we have object to oh and of course + + + align:start position:0% +then we have object to oh and of course +I had goes in this direction because it + + align:start position:0% +I had goes in this direction because it + + + align:start position:0% +I had goes in this direction because it +follows the motion of the object we have + + align:start position:0% +follows the motion of the object we have + + + align:start position:0% +follows the motion of the object we have +here kind of the reverse now we have + + align:start position:0% +here kind of the reverse now we have + + + align:start position:0% +here kind of the reverse now we have +attention of this string here that's + + align:start position:0% +attention of this string here that's + + + align:start position:0% +attention of this string here that's +attached to pulley a but it's different + + align:start position:0% +attached to pulley a but it's different + + + align:start position:0% +attached to pulley a but it's different +from the string tension that's a + + align:start position:0% +from the string tension that's a + + + align:start position:0% +from the string tension that's a +specific one TA and we also have a T + + align:start position:0% +specific one TA and we also have a T + + + align:start position:0% +specific one TA and we also have a T +from the string here so add T and then + + align:start position:0% +from the string here so add T and then + + + align:start position:0% +from the string here so add T and then +if we look at pulley a we have to string + + align:start position:0% +if we look at pulley a we have to string + + + align:start position:0% +if we look at pulley a we have to string +tensions T and T and here we can have a + + align:start position:0% +tensions T and T and here we can have a + + + align:start position:0% +tensions T and T and here we can have a +TA and could he be TB and 2t over here + + align:start position:0% +TA and could he be TB and 2t over here + + + align:start position:0% +TA and could he be TB and 2t over here +so that means we can write down our + + align:start position:0% +so that means we can write down our + + + align:start position:0% +so that means we can write down our +equations of motions using Newton's + + align:start position:0% +equations of motions using Newton's + + + align:start position:0% +equations of motions using Newton's +second law F equals MA and since this is + + align:start position:0% +second law F equals MA and since this is + + + align:start position:0% +second law F equals MA and since this is +just going in the I hat direction we can + + align:start position:0% +just going in the I hat direction we can + + + align:start position:0% +just going in the I hat direction we can +just write it down four equations + + align:start position:0% +just write it down four equations + + + align:start position:0% +just write it down four equations +following the for Freebody diagrams here + + align:start position:0% +following the for Freebody diagrams here + + + align:start position:0% +following the for Freebody diagrams here +so we have F minus TB equals m1 a1 a1 we + + align:start position:0% +so we have F minus TB equals m1 a1 a1 we + + + align:start position:0% +so we have F minus TB equals m1 a1 a1 we +have + + align:start position:0% + + + + align:start position:0% + +ta T plus ta equals M - a - then we have + + align:start position:0% +ta T plus ta equals M - a - then we have + + + align:start position:0% +ta T plus ta equals M - a - then we have +to t minus ta equals 0 that is 0 because + + align:start position:0% +to t minus ta equals 0 that is 0 because + + + align:start position:0% +to t minus ta equals 0 that is 0 because +we are dealing with two massless pulleys + + align:start position:0% +we are dealing with two massless pulleys + + + align:start position:0% +we are dealing with two massless pulleys +there that means M is 0 and so our + + align:start position:0% +there that means M is 0 and so our + + + align:start position:0% +there that means M is 0 and so our +acceleration term is 0 so the M is 0 + + align:start position:0% +acceleration term is 0 so the M is 0 + + + align:start position:0% +acceleration term is 0 so the M is 0 +here and finally we have TB minus 2 T + + align:start position:0% +here and finally we have TB minus 2 T + + + align:start position:0% +here and finally we have TB minus 2 T +naught 2 pi 2 T and that one is also 0 + + align:start position:0% +naught 2 pi 2 T and that one is also 0 + + + align:start position:0% +naught 2 pi 2 T and that one is also 0 +because it is a massless pulley so here + + align:start position:0% +because it is a massless pulley so here + + + align:start position:0% +because it is a massless pulley so here +we have our four equations of motion + + align:start position:0% +we have our four equations of motion + + + align:start position:0% +we have our four equations of motion +that fully govern this this pulley + + align:start position:0% +that fully govern this this pulley + + + align:start position:0% +that fully govern this this pulley +system and we can use it then for + + align:start position:0% +system and we can use it then for + + + align:start position:0% +system and we can use it then for +example to find this pulling force here + + align:start position:0% +example to find this pulling force here + + + align:start position:0% +example to find this pulling force here +we know what TB is from the equation + + align:start position:0% +we know what TB is from the equation + + + align:start position:0% +we know what TB is from the equation +down here so 2 T we know what T a is + + align:start position:0% +down here so 2 T we know what T a is + + + align:start position:0% +down here so 2 T we know what T a is +it's also 2 T and we can then solve this + + align:start position:0% +it's also 2 T and we can then solve this + + + align:start position:0% +it's also 2 T and we can then solve this +for F the only sticky part is that we + + align:start position:0% +for F the only sticky part is that we + + + align:start position:0% +for F the only sticky part is that we +have this a 1 and the a 2 in here but + + align:start position:0% +have this a 1 and the a 2 in here but + + + align:start position:0% +have this a 1 and the a 2 in here but +for that we derived this constraint + + align:start position:0% +for that we derived this constraint + + + align:start position:0% +for that we derived this constraint +condition so with that one we can fully + + align:start position:0% +condition so with that one we can fully + + + align:start position:0% +condition so with that one we can fully +solve this otherwise we would have one + + align:start position:0% +solve this otherwise we would have one + + + align:start position:0% +solve this otherwise we would have one +too many unknowns alternatively if one + + align:start position:0% +too many unknowns alternatively if one + + + align:start position:0% +too many unknowns alternatively if one +were to be interested in one of these + + align:start position:0% +were to be interested in one of these + + + align:start position:0% +were to be interested in one of these +accelerations then this equation system + + align:start position:0% +accelerations then this equation system + + + align:start position:0% +accelerations then this equation system +can also be solved for a 1 or a 2 \ No newline at end of file diff --git a/4VztgBcVH5Q.txt b/4VztgBcVH5Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..b9fa91081ceb2b72fa9dee65bcc842c2ef5a0877 --- /dev/null +++ b/4VztgBcVH5Q.txt @@ -0,0 +1,9731 @@ +align:start position:0% + +before diving into this I'd like to + + align:start position:0% +before diving into this I'd like to + + + align:start position:0% +before diving into this I'd like to +remind you of what we talked about + + align:start position:0% +remind you of what we talked about + + + align:start position:0% +remind you of what we talked about +earlier in the course uh which is sort + + align:start position:0% +earlier in the course uh which is sort + + + align:start position:0% +earlier in the course uh which is sort +of switching loss if I took for example + + align:start position:0% +of switching loss if I took for example + + + align:start position:0% +of switching loss if I took for example +let me just take my friendly + + align:start position:0% +let me just take my friendly + + + align:start position:0% +let me just take my friendly +neighborhood Buck converter here right + + align:start position:0% +neighborhood Buck converter here right + + + align:start position:0% +neighborhood Buck converter here right +so I have + + align:start position:0% +so I have + + + align:start position:0% +so I have +VN and I might have a switch + + align:start position:0% + + + + align:start position:0% + +okay and maybe I have an a diode and + + align:start position:0% +okay and maybe I have an a diode and + + + align:start position:0% +okay and maybe I have an a diode and +I'll think of these as + + align:start position:0% +I'll think of these as + + + align:start position:0% +I'll think of these as +ideal um + + align:start position:0% +ideal um + + + align:start position:0% +ideal um +and actually perhaps let me just leave + + align:start position:0% +and actually perhaps let me just leave + + + align:start position:0% +and actually perhaps let me just leave +myself a little more room here I'll have + + align:start position:0% +myself a little more room here I'll have + + + align:start position:0% +myself a little more room here I'll have +a + + align:start position:0% +a + + + align:start position:0% +a +diode right and maybe for the moment + + align:start position:0% +diode right and maybe for the moment + + + align:start position:0% +diode right and maybe for the moment +I'll think of this as sort of ID this + + align:start position:0% +I'll think of this as sort of ID this + + + align:start position:0% +I'll think of this as sort of ID this +almost constant current into the output + + align:start position:0% +almost constant current into the output + + + align:start position:0% +almost constant current into the output +that I'm controlling by PW my + + align:start position:0% +that I'm controlling by PW my + + + align:start position:0% +that I'm controlling by PW my +converter and we can say okay well I'm + + align:start position:0% +converter and we can say okay well I'm + + + align:start position:0% +converter and we can say okay well I'm +interested in the losses in the switch + + align:start position:0% +interested in the losses in the switch + + + align:start position:0% +interested in the losses in the switch +in the diode let's focus on the switch + + align:start position:0% +in the diode let's focus on the switch + + + align:start position:0% +in the diode let's focus on the switch +here so I might have some switch voltage + + align:start position:0% +here so I might have some switch voltage + + + align:start position:0% +here so I might have some switch voltage +that I'll call V + + align:start position:0% + + + + align:start position:0% + +switch and I might have some switch + + align:start position:0% +switch and I might have some switch + + + align:start position:0% +switch and I might have some switch +current that I'll call I + + align:start position:0% + + + + align:start position:0% + +switch right and I might say well you + + align:start position:0% +switch right and I might say well you + + + align:start position:0% +switch right and I might say well you +know when my switch is on I have I + + align:start position:0% +know when my switch is on I have I + + + align:start position:0% +know when my switch is on I have I +switch squared r on for the switch and + + align:start position:0% +switch squared r on for the switch and + + + align:start position:0% +switch squared r on for the switch and +that's how I figure out my conduct + + align:start position:0% +that's how I figure out my conduct + + + align:start position:0% +that's how I figure out my conduct +uction loss in my switch we also said + + align:start position:0% +uction loss in my switch we also said + + + align:start position:0% +uction loss in my switch we also said +you have to worry about switching losses + + align:start position:0% +you have to worry about switching losses + + + align:start position:0% +you have to worry about switching losses +in the + + align:start position:0% +in the + + + align:start position:0% +in the +device and we might + + align:start position:0% +device and we might + + + align:start position:0% +device and we might +approximate uh switching loss this way + + align:start position:0% +approximate uh switching loss this way + + + align:start position:0% +approximate uh switching loss this way +uh we might say okay let me just focus + + align:start position:0% +uh we might say okay let me just focus + + + align:start position:0% +uh we might say okay let me just focus +in on the tiny part of the time cycle + + align:start position:0% +in on the tiny part of the time cycle + + + align:start position:0% +in on the tiny part of the time cycle +when I'm say turning this device on and + + align:start position:0% +when I'm say turning this device on and + + + align:start position:0% +when I'm say turning this device on and +off and turning this device on and off + + align:start position:0% +off and turning this device on and off + + + align:start position:0% +off and turning this device on and off +I'm switching between the two devices in + + align:start position:0% +I'm switching between the two devices in + + + align:start position:0% +I'm switching between the two devices in +an ideal world that happens instantly + + align:start position:0% +an ideal world that happens instantly + + + align:start position:0% +an ideal world that happens instantly +but in the real world it doesn't it can + + align:start position:0% +but in the real world it doesn't it can + + + align:start position:0% +but in the real world it doesn't it can +take you know depending upon my + + align:start position:0% +take you know depending upon my + + + align:start position:0% +take you know depending upon my +switching frequency maybe a percent of + + align:start position:0% +switching frequency maybe a percent of + + + align:start position:0% +switching frequency maybe a percent of +the cycle or something like that okay so + + align:start position:0% +the cycle or something like that okay so + + + align:start position:0% +the cycle or something like that okay so +let's just think what happens when I + + align:start position:0% +let's just think what happens when I + + + align:start position:0% +let's just think what happens when I +turn this uh switch off right suppose + + align:start position:0% +turn this uh switch off right suppose + + + align:start position:0% +turn this uh switch off right suppose +this switch is carrying ID I would like + + align:start position:0% +this switch is carrying ID I would like + + + align:start position:0% +this switch is carrying ID I would like +to turn him off okay and I can worry + + align:start position:0% +to turn him off okay and I can worry + + + align:start position:0% +to turn him off okay and I can worry +about what does vs switch do and I + + align:start position:0% +about what does vs switch do and I + + + align:start position:0% +about what does vs switch do and I +switch do and if I just thought of this + + align:start position:0% +switch do and if I just thought of this + + + align:start position:0% +switch do and if I just thought of this +switch as an ideal current Source or + + align:start position:0% +switch as an ideal current Source or + + + align:start position:0% +switch as an ideal current Source or +ramping from carrying High current down + + align:start position:0% +ramping from carrying High current down + + + align:start position:0% +ramping from carrying High current down +to zero + + align:start position:0% +to zero + + + align:start position:0% +to zero +uh maybe that would do something like + + align:start position:0% +uh maybe that would do something like + + + align:start position:0% +uh maybe that would do something like +this so here's I + + align:start position:0% + + + + align:start position:0% + +switch right and at some point it's + + align:start position:0% +switch right and at some point it's + + + align:start position:0% +switch right and at some point it's +going to fall from high current down to + + align:start position:0% +going to fall from high current down to + + + align:start position:0% +going to fall from high current down to +zero the question is does the switch + + align:start position:0% +zero the question is does the switch + + + align:start position:0% +zero the question is does the switch +voltage rise before or after the switch + + align:start position:0% +voltage rise before or after the switch + + + align:start position:0% +voltage rise before or after the switch +current + + align:start position:0% +current + + + align:start position:0% +current +Falls okay and to the extent that we can + + align:start position:0% +Falls okay and to the extent that we can + + + align:start position:0% +Falls okay and to the extent that we can +think of this diode as being ideal right + + align:start position:0% +think of this diode as being ideal right + + + align:start position:0% +think of this diode as being ideal right +the diode cannot carry any + + align:start position:0% +the diode cannot carry any + + + align:start position:0% +the diode cannot carry any +current um until the diode has zero + + align:start position:0% +current um until the diode has zero + + + align:start position:0% +current um until the diode has zero +volts on him right so he's not going to + + align:start position:0% +volts on him right so he's not going to + + + align:start position:0% +volts on him right so he's not going to +carry any current until he has zero + + align:start position:0% +carry any current until he has zero + + + align:start position:0% +carry any current until he has zero +volts on him that means that the switch + + align:start position:0% +volts on him that means that the switch + + + align:start position:0% +volts on him that means that the switch +voltage must go up to VN before this + + align:start position:0% +voltage must go up to VN before this + + + align:start position:0% +voltage must go up to VN before this +diode can start picking up current right + + align:start position:0% +diode can start picking up current right + + + align:start position:0% +diode can start picking up current right +so I might expect then that the switch + + align:start position:0% +so I might expect then that the switch + + + align:start position:0% +so I might expect then that the switch +voltage if I'm going to have my + + align:start position:0% +voltage if I'm going to have my + + + align:start position:0% +voltage if I'm going to have my +switching start here the switch voltage + + align:start position:0% +switching start here the switch voltage + + + align:start position:0% +switching start here the switch voltage +has to rise from Z to VN at which point + + align:start position:0% +has to rise from Z to VN at which point + + + align:start position:0% +has to rise from Z to VN at which point +the current in the switch can start + + align:start position:0% +the current in the switch can start + + + align:start position:0% +the current in the switch can start +falling okay so I'm going to have some + + align:start position:0% +falling okay so I'm going to have some + + + align:start position:0% +falling okay so I'm going to have some +switching + + align:start position:0% +switching + + + align:start position:0% +switching +transition okay and I'm a approximating + + align:start position:0% +transition okay and I'm a approximating + + + align:start position:0% +transition okay and I'm a approximating +these transitions as linear what do they + + align:start position:0% +these transitions as linear what do they + + + align:start position:0% +these transitions as linear what do they +actually look like that depends upon the + + align:start position:0% +actually look like that depends upon the + + + align:start position:0% +actually look like that depends upon the +device and the device driver and a lot + + align:start position:0% +device and the device driver and a lot + + + align:start position:0% +device and the device driver and a lot +of other things but approximating them + + align:start position:0% +of other things but approximating them + + + align:start position:0% +of other things but approximating them +as linear is often not a bad + + align:start position:0% +as linear is often not a bad + + + align:start position:0% +as linear is often not a bad +idea and I might say that this time + + align:start position:0% +idea and I might say that this time + + + align:start position:0% +idea and I might say that this time +period uh takes some say time + + align:start position:0% +period uh takes some say time + + + align:start position:0% +period uh takes some say time +tall okay and in fact if you look in + + align:start position:0% +tall okay and in fact if you look in + + + align:start position:0% +tall okay and in fact if you look in +data sheets you can find expressions for + + align:start position:0% +data sheets you can find expressions for + + + align:start position:0% +data sheets you can find expressions for +tall for under some nominal Drive + + align:start position:0% +tall for under some nominal Drive + + + align:start position:0% +tall for under some nominal Drive +conditions it'll give you some + + align:start position:0% +conditions it'll give you some + + + align:start position:0% +conditions it'll give you some +approximate notion of how long that will + + align:start position:0% +approximate notion of how long that will + + + align:start position:0% +approximate notion of how long that will +take and but we can control it by the + + align:start position:0% +take and but we can control it by the + + + align:start position:0% +take and but we can control it by the +driver we choose and other things okay + + align:start position:0% +driver we choose and other things okay + + + align:start position:0% +driver we choose and other things okay +but here's the point during this time + + align:start position:0% +but here's the point during this time + + + align:start position:0% +but here's the point during this time +period the switching transition when the + + align:start position:0% +period the switching transition when the + + + align:start position:0% +period the switching transition when the +the voltage on the switch is + + align:start position:0% +the voltage on the switch is + + + align:start position:0% +the voltage on the switch is +rising and the current on the switch is + + align:start position:0% +rising and the current on the switch is + + + align:start position:0% +rising and the current on the switch is +falling I have a big overlap in voltage + + align:start position:0% +falling I have a big overlap in voltage + + + align:start position:0% +falling I have a big overlap in voltage +and current on that switch so right so I + + align:start position:0% +and current on that switch so right so I + + + align:start position:0% +and current on that switch so right so I +if I looked at the power in the switch + + align:start position:0% +if I looked at the power in the switch + + + align:start position:0% +if I looked at the power in the switch +power dissipating the switch Yeah I had + + align:start position:0% +power dissipating the switch Yeah I had + + + align:start position:0% +power dissipating the switch Yeah I had +some i squ r going on here it wasn't + + align:start position:0% +some i squ r going on here it wasn't + + + align:start position:0% +some i squ r going on here it wasn't +zero but it was pretty darn small here I + + align:start position:0% +zero but it was pretty darn small here I + + + align:start position:0% +zero but it was pretty darn small here I +may have you know if this is 100 volts + + align:start position:0% +may have you know if this is 100 volts + + + align:start position:0% +may have you know if this is 100 volts +and 100 amps maybe that's like five + + align:start position:0% +and 100 amps maybe that's like five + + + align:start position:0% +and 100 amps maybe that's like five +kilowatts Peak dissipation it's 5 + + align:start position:0% +kilowatts Peak dissipation it's 5 + + + align:start position:0% +kilowatts Peak dissipation it's 5 +kilowatts for a very short period of + + align:start position:0% +kilowatts for a very short period of + + + align:start position:0% +kilowatts for a very short period of +time that that just goes actually I + + align:start position:0% +time that that just goes actually I + + + align:start position:0% +time that that just goes actually I +haven't drawn that very well that just + + align:start position:0% +haven't drawn that very well that just + + + align:start position:0% +haven't drawn that very well that just +sort of goes over this + + align:start position:0% +sort of goes over this + + + align:start position:0% +sort of goes over this +duration okay but I get a big pulse of + + align:start position:0% +duration okay but I get a big pulse of + + + align:start position:0% +duration okay but I get a big pulse of +power in the + + align:start position:0% +power in the + + + align:start position:0% +power in the +switch + + align:start position:0% +switch + + + align:start position:0% +switch +okay and you know this is taking place + + align:start position:0% +okay and you know this is taking place + + + align:start position:0% +okay and you know this is taking place +over a very short time period right + + align:start position:0% +over a very short time period right + + + align:start position:0% +over a very short time period right +maybe if I have uh if I was switching to + + align:start position:0% +maybe if I have uh if I was switching to + + + align:start position:0% +maybe if I have uh if I was switching to +megahertz that would be a microsc period + + align:start position:0% +megahertz that would be a microsc period + + + align:start position:0% +megahertz that would be a microsc period +and maybe this takes 10 + + align:start position:0% +and maybe this takes 10 + + + align:start position:0% +and maybe this takes 10 +NCS so maybe that's a percent of the + + align:start position:0% +NCS so maybe that's a percent of the + + + align:start position:0% +NCS so maybe that's a percent of the +cycle but on on the other hand this is a + + align:start position:0% +cycle but on on the other hand this is a + + + align:start position:0% +cycle but on on the other hand this is a +pretty big instantaneous power so I + + align:start position:0% +pretty big instantaneous power so I + + + align:start position:0% +pretty big instantaneous power so I +actually have to care about figuring out + + align:start position:0% +actually have to care about figuring out + + + align:start position:0% +actually have to care about figuring out +that power dissipation right if I waited + + align:start position:0% +that power dissipation right if I waited + + + align:start position:0% +that power dissipation right if I waited +for the other transition this is when I + + align:start position:0% +for the other transition this is when I + + + align:start position:0% +for the other transition this is when I +went from the switch conducting the + + align:start position:0% +went from the switch conducting the + + + align:start position:0% +went from the switch conducting the +switch turns off and the diode turns on + + align:start position:0% +switch turns off and the diode turns on + + + align:start position:0% +switch turns off and the diode turns on +if I waited in the other direction and I + + align:start position:0% +if I waited in the other direction and I + + + align:start position:0% +if I waited in the other direction and I +said what is the switch Lo + + align:start position:0% +said what is the switch Lo + + + align:start position:0% +said what is the switch Lo +what's going to happen here sort of the + + align:start position:0% +what's going to happen here sort of the + + + align:start position:0% +what's going to happen here sort of the +opposite before the switch can pick up + + align:start position:0% +opposite before the switch can pick up + + + align:start position:0% +opposite before the switch can pick up +any + + align:start position:0% +any + + + align:start position:0% +any +current + + align:start position:0% +current + + + align:start position:0% +current +um or for the switch to pick up current + + align:start position:0% +um or for the switch to pick up current + + + align:start position:0% +um or for the switch to pick up current +as long as the DI is carrying any + + align:start position:0% +as long as the DI is carrying any + + + align:start position:0% +as long as the DI is carrying any +current the switch voltage has to stay + + align:start position:0% +current the switch voltage has to stay + + + align:start position:0% +current the switch voltage has to stay +high right and so the switch current + + align:start position:0% +high right and so the switch current + + + align:start position:0% +high right and so the switch current +will come up before the switch voltage + + align:start position:0% +will come up before the switch voltage + + + align:start position:0% +will come up before the switch voltage +collapses and if I looked at the other + + align:start position:0% +collapses and if I looked at the other + + + align:start position:0% +collapses and if I looked at the other +transition I would see something like + + align:start position:0% +transition I would see something like + + + align:start position:0% +transition I would see something like +this later at the other end of the cycle + + align:start position:0% +this later at the other end of the cycle + + + align:start position:0% +this later at the other end of the cycle +I would see something like the switch + + align:start position:0% +I would see something like the switch + + + align:start position:0% +I would see something like the switch +current + + align:start position:0% +current + + + align:start position:0% +current +Rises and then after the switch current + + align:start position:0% +Rises and then after the switch current + + + align:start position:0% +Rises and then after the switch current +Rises the switch voltage can + + align:start position:0% +Rises the switch voltage can + + + align:start position:0% +Rises the switch voltage can +fall right and I might call this time + + align:start position:0% +fall right and I might call this time + + + align:start position:0% +fall right and I might call this time +period uh t + + align:start position:0% + + + + align:start position:0% + +Rise okay and again I will get a power + + align:start position:0% +Rise okay and again I will get a power + + + align:start position:0% +Rise okay and again I will get a power +pulsation a big Power pulsation during + + align:start position:0% +pulsation a big Power pulsation during + + + align:start position:0% +pulsation a big Power pulsation during +that time period and then if I use the + + align:start position:0% +that time period and then if I use the + + + align:start position:0% +that time period and then if I use the +simplified model what I'd get is a + + align:start position:0% +simplified model what I'd get is a + + + align:start position:0% +simplified model what I'd get is a +switching loss that was equal to sort of + + align:start position:0% +switching loss that was equal to sort of + + + align:start position:0% +switching loss that was equal to sort of +uh V + + align:start position:0% +uh V + + + align:start position:0% +uh V +in because that's the peak voltage times + + align:start position:0% +in because that's the peak voltage times + + + align:start position:0% +in because that's the peak voltage times +ID that's the peak current time TR + + + align:start position:0% +ID that's the peak current time TR + + + + align:start position:0% +ID that's the peak current time TR + +TF over two times the switching + + align:start position:0% +TF over two times the switching + + + align:start position:0% +TF over two times the switching +frequency okay this is the area under + + align:start position:0% +frequency okay this is the area under + + + align:start position:0% +frequency okay this is the area under +each of + + align:start position:0% +each of + + + align:start position:0% +each of +these times + + align:start position:0% +these times + + + align:start position:0% +these times +TR and I'd get this total power + + align:start position:0% +TR and I'd get this total power + + + align:start position:0% +TR and I'd get this total power +dissipation okay any questions about + + align:start position:0% +dissipation okay any questions about + + + align:start position:0% +dissipation okay any questions about +that + + align:start position:0% + + + + align:start position:0% + +so I care about this because you know + + align:start position:0% +so I care about this because you know + + + align:start position:0% +so I care about this because you know +we're motivated to turn up our switching + + align:start position:0% +we're motivated to turn up our switching + + + align:start position:0% +we're motivated to turn up our switching +frequency sort of until it hurts right + + align:start position:0% +frequency sort of until it hurts right + + + align:start position:0% +frequency sort of until it hurts right +if I have a low switching frequency I + + align:start position:0% +if I have a low switching frequency I + + + align:start position:0% +if I have a low switching frequency I +have big components I want my components + + align:start position:0% +have big components I want my components + + + align:start position:0% +have big components I want my components +to be small so I'm going to keep turning + + align:start position:0% +to be small so I'm going to keep turning + + + align:start position:0% +to be small so I'm going to keep turning +up my switching frequency until + + align:start position:0% +up my switching frequency until + + + align:start position:0% +up my switching frequency until +something tells me that I shouldn't and + + align:start position:0% +something tells me that I shouldn't and + + + align:start position:0% +something tells me that I shouldn't and +here you have it you get frequency + + align:start position:0% +here you have it you get frequency + + + align:start position:0% +here you have it you get frequency +dependent losses and one of those losses + + align:start position:0% +dependent losses and one of those losses + + + align:start position:0% +dependent losses and one of those losses +is the switching frequency this is + + align:start position:0% +is the switching frequency this is + + + align:start position:0% +is the switching frequency this is +proportional to how many times seconds I + + align:start position:0% +proportional to how many times seconds I + + + align:start position:0% +proportional to how many times seconds I +switch okay and we can control that to + + align:start position:0% +switch okay and we can control that to + + + align:start position:0% +switch okay and we can control that to +some extent by you know making t fall + + align:start position:0% +some extent by you know making t fall + + + align:start position:0% +some extent by you know making t fall +and t Rise short but that also has Emi + + align:start position:0% +and t Rise short but that also has Emi + + + align:start position:0% +and t Rise short but that also has Emi +implications right so we can't do that + + align:start position:0% +implications right so we can't do that + + + align:start position:0% +implications right so we can't do that +arbitrarily so we're sort of stuck with + + align:start position:0% +arbitrarily so we're sort of stuck with + + + align:start position:0% +arbitrarily so we're sort of stuck with +some amount of switching loss and I'm + + align:start position:0% +some amount of switching loss and I'm + + + align:start position:0% +some amount of switching loss and I'm +going to pick my switching frequency in + + align:start position:0% +going to pick my switching frequency in + + + align:start position:0% +going to pick my switching frequency in +part to balance the switching loss + + align:start position:0% +part to balance the switching loss + + + align:start position:0% +part to balance the switching loss +against the conduction + + align:start position:0% +against the conduction + + + align:start position:0% +against the conduction +loss okay um or get my total loss + + align:start position:0% +loss okay um or get my total loss + + + align:start position:0% +loss okay um or get my total loss +down and this is a good way to um + + align:start position:0% +down and this is a good way to um + + + align:start position:0% +down and this is a good way to um +proceed right you figure out some + + align:start position:0% +proceed right you figure out some + + + align:start position:0% +proceed right you figure out some +balance between the size of the device + + align:start position:0% +balance between the size of the device + + + align:start position:0% +balance between the size of the device +you're going to use is Ron how fast you + + align:start position:0% +you're going to use is Ron how fast you + + + align:start position:0% +you're going to use is Ron how fast you +can switch it and get some total + + align:start position:0% +can switch it and get some total + + + align:start position:0% +can switch it and get some total +loss we also did however talk about um + + align:start position:0% +loss we also did however talk about um + + + align:start position:0% +loss we also did however talk about um +how might I slow up these kind of um + + align:start position:0% +how might I slow up these kind of um + + + align:start position:0% +how might I slow up these kind of um +Transitions okay we said sometimes those + + align:start position:0% +Transitions okay we said sometimes those + + + align:start position:0% +Transitions okay we said sometimes those +transitions can cause a lot of Emi + + align:start position:0% +transitions can cause a lot of Emi + + + align:start position:0% +transitions can cause a lot of Emi +right and one of the tricks that we + + align:start position:0% +right and one of the tricks that we + + + align:start position:0% +right and one of the tricks that we +showed earlier in the term was we said + + align:start position:0% +showed earlier in the term was we said + + + align:start position:0% +showed earlier in the term was we said +okay well I could come in + + align:start position:0% +okay well I could come in + + + align:start position:0% +okay well I could come in +here and if I put essentially a circuit + + align:start position:0% +here and if I put essentially a circuit + + + align:start position:0% +here and if I put essentially a circuit +that looked like did something like + + align:start position:0% +that looked like did something like + + + align:start position:0% +that looked like did something like +this okay I'll put a capacitor across + + align:start position:0% +this okay I'll put a capacitor across + + + align:start position:0% +this okay I'll put a capacitor across +the device ideally but what I will do is + + align:start position:0% +the device ideally but what I will do is + + + align:start position:0% +the device ideally but what I will do is +I will make it so that um instead of + + align:start position:0% +I will make it so that um instead of + + + align:start position:0% +I will make it so that um instead of +putting it directly across the device + + align:start position:0% +putting it directly across the device + + + align:start position:0% +putting it directly across the device +I'll do it so that in the for direction + + align:start position:0% +I'll do it so that in the for direction + + + align:start position:0% +I'll do it so that in the for direction +it looks directly across the device + + align:start position:0% +it looks directly across the device + + + align:start position:0% +it looks directly across the device +and in the reverse Direction I have a + + align:start position:0% +and in the reverse Direction I have a + + + align:start position:0% +and in the reverse Direction I have a +resistor here okay if I did that okay + + align:start position:0% +resistor here okay if I did that okay + + + align:start position:0% +resistor here okay if I did that okay +what that would do is when I turn the + + align:start position:0% +what that would do is when I turn the + + + align:start position:0% +what that would do is when I turn the +transistor off I have another path for + + align:start position:0% +transistor off I have another path for + + + align:start position:0% +transistor off I have another path for +current to go through and I can + + align:start position:0% +current to go through and I can + + + align:start position:0% +current to go through and I can +charge um the I can charge up this + + align:start position:0% +charge um the I can charge up this + + + align:start position:0% +charge um the I can charge up this +capacitance so voltage doesn't need to + + align:start position:0% +capacitance so voltage doesn't need to + + + align:start position:0% +capacitance so voltage doesn't need to +rise so + + align:start position:0% +rise so + + + align:start position:0% +rise so +quickly right so if I do this + + align:start position:0% +quickly right so if I do this + + + align:start position:0% +quickly right so if I do this +um if I put this kind of circuit in I + + align:start position:0% +um if I put this kind of circuit in I + + + align:start position:0% +um if I put this kind of circuit in I +can sort of delay the voltage rise on + + align:start position:0% +can sort of delay the voltage rise on + + + align:start position:0% +can sort of delay the voltage rise on +the device + + align:start position:0% +the device + + + align:start position:0% +the device +okay it might do something like this so + + align:start position:0% +okay it might do something like this so + + + align:start position:0% +okay it might do something like this so +I kind of push this out here and I + + align:start position:0% +I kind of push this out here and I + + + align:start position:0% +I kind of push this out here and I +reduce the vi overlap and I also instead + + align:start position:0% +reduce the vi overlap and I also instead + + + align:start position:0% +reduce the vi overlap and I also instead +of a fast rise I get a slow + + align:start position:0% +of a fast rise I get a slow + + + align:start position:0% +of a fast rise I get a slow +rise + + align:start position:0% +rise + + + align:start position:0% +rise +okay and that + + align:start position:0% +okay and that + + + align:start position:0% +okay and that +works and it does return reduce the loss + + align:start position:0% +works and it does return reduce the loss + + + align:start position:0% +works and it does return reduce the loss +at turnoff that's very nice the penalty + + align:start position:0% +at turnoff that's very nice the penalty + + + align:start position:0% +at turnoff that's very nice the penalty +I pay is I put a bunch of energy in this + + align:start position:0% +I pay is I put a bunch of energy in this + + + align:start position:0% +I pay is I put a bunch of energy in this +capacitor okay and when I go to turn the + + align:start position:0% +capacitor okay and when I go to turn the + + + align:start position:0% +capacitor okay and when I go to turn the +switch back on that energy ultimately + + align:start position:0% +switch back on that energy ultimately + + + align:start position:0% +switch back on that energy ultimately +gets dumped into this resistor and in + + align:start position:0% +gets dumped into this resistor and in + + + align:start position:0% +gets dumped into this resistor and in +turn in in practice typically I make the + + align:start position:0% +turn in in practice typically I make the + + + align:start position:0% +turn in in practice typically I make the +efficiency of the converter worse not + + align:start position:0% +efficiency of the converter worse not + + + align:start position:0% +efficiency of the converter worse not +better right I've reduced the loss in + + align:start position:0% +better right I've reduced the loss in + + + align:start position:0% +better right I've reduced the loss in +the device but I've offset that more + + align:start position:0% +the device but I've offset that more + + + align:start position:0% +the device but I've offset that more +than offset with that with loss in the + + align:start position:0% +than offset with that with loss in the + + + align:start position:0% +than offset with that with loss in the +resistor I get + + align:start position:0% +resistor I get + + + align:start position:0% +resistor I get +here okay I could do if I had a device + + align:start position:0% +here okay I could do if I had a device + + + align:start position:0% +here okay I could do if I had a device +that needed it I could do the same kind + + align:start position:0% +that needed it I could do the same kind + + + align:start position:0% +that needed it I could do the same kind +of thing at turn on I could come in here + + align:start position:0% +of thing at turn on I could come in here + + + align:start position:0% +of thing at turn on I could come in here +and I could say okay uh let me add an + + align:start position:0% +and I could say okay uh let me add an + + + align:start position:0% +and I could say okay uh let me add an +inductor here and then I will add a uh + + align:start position:0% +inductor here and then I will add a uh + + + align:start position:0% +inductor here and then I will add a uh +resistor and a + + align:start position:0% +resistor and a + + + align:start position:0% +resistor and a +diode okay so when I go to turn the + + align:start position:0% +diode okay so when I go to turn the + + + align:start position:0% +diode okay so when I go to turn the +device on this will will hold the + + align:start position:0% +device on this will will hold the + + + align:start position:0% +device on this will will hold the +voltage and keep the current from rising + + align:start position:0% +voltage and keep the current from rising + + + align:start position:0% +voltage and keep the current from rising +very quickly so instead of the current + + align:start position:0% +very quickly so instead of the current + + + align:start position:0% +very quickly so instead of the current +Rising like this you know the current + + align:start position:0% +Rising like this you know the current + + + align:start position:0% +Rising like this you know the current +Rising might do + + align:start position:0% + + + + align:start position:0% + +this and I will again reduce the overlap + + align:start position:0% +this and I will again reduce the overlap + + + align:start position:0% +this and I will again reduce the overlap +between the voltage and current by + + align:start position:0% +between the voltage and current by + + + align:start position:0% +between the voltage and current by +delaying the current rod + + align:start position:0% +delaying the current rod + + + align:start position:0% +delaying the current rod +but I store a bunch of energy in this + + align:start position:0% +but I store a bunch of energy in this + + + align:start position:0% +but I store a bunch of energy in this +inductor when I go to turn the switch + + align:start position:0% +inductor when I go to turn the switch + + + align:start position:0% +inductor when I go to turn the switch +off that current will circulate in here + + align:start position:0% +off that current will circulate in here + + + align:start position:0% +off that current will circulate in here +and dissipate in the resistor okay so + + align:start position:0% +and dissipate in the resistor okay so + + + align:start position:0% +and dissipate in the resistor okay so +again I've uh reduced the overlap at the + + align:start position:0% +again I've uh reduced the overlap at the + + + align:start position:0% +again I've uh reduced the overlap at the +switching transition but I've lost + + align:start position:0% +switching transition but I've lost + + + align:start position:0% +switching transition but I've lost +energy in the process unbalance but I + + align:start position:0% +energy in the process unbalance but I + + + align:start position:0% +energy in the process unbalance but I +might want to do it for reasons of + + align:start position:0% +might want to do it for reasons of + + + align:start position:0% +might want to do it for reasons of +changing say the DTs or the DVDs over + + align:start position:0% +changing say the DTs or the DVDs over + + + align:start position:0% +changing say the DTs or the DVDs over +here okay so that's all a little bit of + + align:start position:0% +here okay so that's all a little bit of + + + align:start position:0% +here okay so that's all a little bit of +a review any questions about that + + align:start position:0% + + + + align:start position:0% + +um are we expected to look into SN of + + align:start position:0% +um are we expected to look into SN of + + + align:start position:0% +um are we expected to look into SN of +the project uh that's a very good + + align:start position:0% +the project uh that's a very good + + + align:start position:0% +the project uh that's a very good +question so no right why because the + + align:start position:0% +question so no right why because the + + + align:start position:0% +question so no right why because the +devices that you're using mosfets and + + align:start position:0% +devices that you're using mosfets and + + + align:start position:0% +devices that you're using mosfets and +chaky diodes tend not to be very + + align:start position:0% +chaky diodes tend not to be very + + + align:start position:0% +chaky diodes tend not to be very +susceptible to failure of having a like + + align:start position:0% +susceptible to failure of having a like + + + align:start position:0% +susceptible to failure of having a like +a a safe operating area limitation or + + align:start position:0% +a a safe operating area limitation or + + + align:start position:0% +a a safe operating area limitation or +dvdt or DT limit in their + + align:start position:0% +dvdt or DT limit in their + + + align:start position:0% +dvdt or DT limit in their +operation if I were working with + + align:start position:0% +operation if I were working with + + + align:start position:0% +operation if I were working with +giant gate turnoff + + align:start position:0% +giant gate turnoff + + + align:start position:0% +giant gate turnoff +thyr uh then that would be a different + + align:start position:0% +thyr uh then that would be a different + + + align:start position:0% +thyr uh then that would be a different +story and I would have to put snubbers + + align:start position:0% +story and I would have to put snubbers + + + align:start position:0% +story and I would have to put snubbers +on them but for the kind of converter + + align:start position:0% +on them but for the kind of converter + + + align:start position:0% +on them but for the kind of converter +you're designing in the design project + + align:start position:0% +you're designing in the design project + + + align:start position:0% +you're designing in the design project +pretty much you can get away without + + align:start position:0% +pretty much you can get away without + + + align:start position:0% +pretty much you can get away without +snubbers in the real world if you were + + align:start position:0% +snubbers in the real world if you were + + + align:start position:0% +snubbers in the real world if you were +to build one you might build it and then + + align:start position:0% +to build one you might build it and then + + + align:start position:0% +to build one you might build it and then +say Oh you know I'm getting a little bit + + align:start position:0% +say Oh you know I'm getting a little bit + + + align:start position:0% +say Oh you know I'm getting a little bit +too much Emi and I associate with that + + align:start position:0% +too much Emi and I associate with that + + + align:start position:0% +too much Emi and I associate with that +with the slew rate of the voltage for + + align:start position:0% +with the slew rate of the voltage for + + + align:start position:0% +with the slew rate of the voltage for +example and then I might go in throw in + + align:start position:0% +example and then I might go in throw in + + + align:start position:0% +example and then I might go in throw in +a small snubber to slow down the voltage + + align:start position:0% +a small snubber to slow down the voltage + + + align:start position:0% +a small snubber to slow down the voltage +transition so sometimes people will + + align:start position:0% +transition so sometimes people will + + + align:start position:0% +transition so sometimes people will +leave provision to put a snubber in if + + align:start position:0% +leave provision to put a snubber in if + + + align:start position:0% +leave provision to put a snubber in if +they need it in practice but it's not + + align:start position:0% +they need it in practice but it's not + + + align:start position:0% +they need it in practice but it's not +something you would necessarily have to + + align:start position:0% +something you would necessarily have to + + + align:start position:0% +something you would necessarily have to +design up front unless the types of + + align:start position:0% +design up front unless the types of + + + align:start position:0% +design up front unless the types of +devices you were + + align:start position:0% +devices you were + + + align:start position:0% +devices you were +using required it and that would be + + align:start position:0% +using required it and that would be + + + align:start position:0% +using required it and that would be +typically very high power devices that + + align:start position:0% +typically very high power devices that + + + align:start position:0% +typically very high power devices that +are a bit more fragile for mosfets and + + align:start position:0% +are a bit more fragile for mosfets and + + + align:start position:0% +are a bit more fragile for mosfets and +Shi doodes and stuff CH typically you + + align:start position:0% +Shi doodes and stuff CH typically you + + + align:start position:0% +Shi doodes and stuff CH typically you +don't have to worry about it excellent + + align:start position:0% +don't have to worry about it excellent + + + align:start position:0% +don't have to worry about it excellent +question okay so that brings me to the + + align:start position:0% +question okay so that brings me to the + + + align:start position:0% +question okay so that brings me to the +topic I wanted to tell you about today + + align:start position:0% +topic I wanted to tell you about today + + + align:start position:0% +topic I wanted to tell you about today +and I only really wanted to give you a + + align:start position:0% +and I only really wanted to give you a + + + align:start position:0% +and I only really wanted to give you a +flavor of + + align:start position:0% +flavor of + + + align:start position:0% +flavor of +today but I want to give you a notion of + + align:start position:0% +today but I want to give you a notion of + + + align:start position:0% +today but I want to give you a notion of +how this + + align:start position:0% +how this + + + align:start position:0% +how this +works this kind of poses a question I + + align:start position:0% +works this kind of poses a question I + + + align:start position:0% +works this kind of poses a question I +said putting the inductor the capacitor + + align:start position:0% +said putting the inductor the capacitor + + + align:start position:0% +said putting the inductor the capacitor +in parallel with the device here sort of + + align:start position:0% +in parallel with the device here sort of + + + align:start position:0% +in parallel with the device here sort of +does reduce the overlap but I burn a + + align:start position:0% +does reduce the overlap but I burn a + + + align:start position:0% +does reduce the overlap but I burn a +bunch of energy and likewise putting the + + align:start position:0% +bunch of energy and likewise putting the + + + align:start position:0% +bunch of energy and likewise putting the +inductor in series reduces the overlap + + align:start position:0% +inductor in series reduces the overlap + + + align:start position:0% +inductor in series reduces the overlap +but I burn a bunch of + + align:start position:0% +but I burn a bunch of + + + align:start position:0% +but I burn a bunch of +energy could I do that without burning a + + align:start position:0% +energy could I do that without burning a + + + align:start position:0% +energy could I do that without burning a +bunch of energy right could I somehow + + align:start position:0% +bunch of energy right could I somehow + + + align:start position:0% +bunch of energy right could I somehow +get that energy back + + align:start position:0% +get that energy back + + + align:start position:0% +get that energy back +and what would be the benefit of that + + align:start position:0% +and what would be the benefit of that + + + align:start position:0% +and what would be the benefit of that +this loss if I only thought about the + + align:start position:0% +this loss if I only thought about the + + + align:start position:0% +this loss if I only thought about the +overlaps this loss would be greatly + + align:start position:0% +overlaps this loss would be greatly + + + align:start position:0% +overlaps this loss would be greatly +reduced and that would either let me a + + align:start position:0% +reduced and that would either let me a + + + align:start position:0% +reduced and that would either let me a +get rid of that loss and get a very high + + align:start position:0% +get rid of that loss and get a very high + + + align:start position:0% +get rid of that loss and get a very high +efficiency converter or B crank up the + + align:start position:0% +efficiency converter or B crank up the + + + align:start position:0% +efficiency converter or B crank up the +switching frequency and make my + + align:start position:0% +switching frequency and make my + + + align:start position:0% +switching frequency and make my +component smaller or some combination + + align:start position:0% +component smaller or some combination + + + align:start position:0% +component smaller or some combination +thereof okay as you make things smaller + + align:start position:0% +thereof okay as you make things smaller + + + align:start position:0% +thereof okay as you make things smaller +it has to get more efficient in order to + + align:start position:0% +it has to get more efficient in order to + + + align:start position:0% +it has to get more efficient in order to +to meet thermal requirements but + + align:start position:0% +to meet thermal requirements but + + + align:start position:0% +to meet thermal requirements but +nonetheless + + align:start position:0% +nonetheless + + + align:start position:0% +nonetheless +what that would do is um let me either + + align:start position:0% +what that would do is um let me either + + + align:start position:0% +what that would do is um let me either +get to higher efficiencies or higher + + align:start position:0% +get to higher efficiencies or higher + + + align:start position:0% +get to higher efficiencies or higher +switching frequencies okay and people do + + align:start position:0% +switching frequencies okay and people do + + + align:start position:0% +switching frequencies okay and people do +this they come up with circuits either + + align:start position:0% +this they come up with circuits either + + + align:start position:0% +this they come up with circuits either +changes in the circuit design or changes + + align:start position:0% +changes in the circuit design or changes + + + align:start position:0% +changes in the circuit design or changes +in the control that will let people sort + + align:start position:0% +in the control that will let people sort + + + align:start position:0% +in the control that will let people sort +of get this so-called soft switching + + align:start position:0% +of get this so-called soft switching + + + align:start position:0% +of get this so-called soft switching +this kind of a pink and yellow + + align:start position:0% +this kind of a pink and yellow + + + align:start position:0% +this kind of a pink and yellow +transition we would consider hard + + align:start position:0% +transition we would consider hard + + + align:start position:0% +transition we would consider hard +switched a soft switch transitions one + + align:start position:0% +switched a soft switch transitions one + + + align:start position:0% +switched a soft switch transitions one +in which you reduce the voltage and + + align:start position:0% +in which you reduce the voltage and + + + align:start position:0% +in which you reduce the voltage and +current overlap at the switching + + align:start position:0% +current overlap at the switching + + + align:start position:0% +current overlap at the switching +transition and get much lower switching + + align:start position:0% +transition and get much lower switching + + + align:start position:0% +transition and get much lower switching +loss okay now I say that many many very + + align:start position:0% +loss okay now I say that many many very + + + align:start position:0% +loss okay now I say that many many very +high performance converters do this this + + align:start position:0% +high performance converters do this this + + + align:start position:0% +high performance converters do this this +is a very common thing at the high + + align:start position:0% +is a very common thing at the high + + + align:start position:0% +is a very common thing at the high +performance end of the Spectrum in fact + + align:start position:0% +performance end of the Spectrum in fact + + + align:start position:0% +performance end of the Spectrum in fact +uh if you looked at the power converter + + align:start position:0% +uh if you looked at the power converter + + + align:start position:0% +uh if you looked at the power converter +that's in this little miniaturized + + align:start position:0% +that's in this little miniaturized + + + align:start position:0% +that's in this little miniaturized +laptop adapter which is a very small and + + align:start position:0% +laptop adapter which is a very small and + + + align:start position:0% +laptop adapter which is a very small and +B you know exceeds 95% endend efficiency + + align:start position:0% +B you know exceeds 95% endend efficiency + + + align:start position:0% +B you know exceeds 95% endend efficiency +so so they can make it small without it + + align:start position:0% +so so they can make it small without it + + + align:start position:0% +so so they can make it small without it +getting hot that will that you that + + align:start position:0% +getting hot that will that you that + + + align:start position:0% +getting hot that will that you that +design uses soft switching techniques + + align:start position:0% +design uses soft switching techniques + + + align:start position:0% +design uses soft switching techniques +and turns up the frequency uh to make it + + align:start position:0% +and turns up the frequency uh to make it + + + align:start position:0% +and turns up the frequency uh to make it +small and uses part of that benefit to + + align:start position:0% +small and uses part of that benefit to + + + align:start position:0% +small and uses part of that benefit to +make it efficient + + align:start position:0% +make it efficient + + + align:start position:0% +make it efficient +okay um so what I want to do is show you + + align:start position:0% +okay um so what I want to do is show you + + + align:start position:0% +okay um so what I want to do is show you +the kind of category of techniques that + + align:start position:0% +the kind of category of techniques that + + + align:start position:0% +the kind of category of techniques that +you might use there I will say though + + align:start position:0% +you might use there I will say though + + + align:start position:0% +you might use there I will say though +that while this is very very common in + + align:start position:0% +that while this is very very common in + + + align:start position:0% +that while this is very very common in +the high performance end of the spectrum + + align:start position:0% +the high performance end of the spectrum + + + align:start position:0% +the high performance end of the spectrum +where you're trying it for great + + align:start position:0% +where you're trying it for great + + + align:start position:0% +where you're trying it for great +miniaturization or really fast response + + align:start position:0% +miniaturization or really fast response + + + align:start position:0% +miniaturization or really fast response +on something like that perhaps the + + align:start position:0% +on something like that perhaps the + + + align:start position:0% +on something like that perhaps the +majority of power converters designed in + + align:start position:0% +majority of power converters designed in + + + align:start position:0% +majority of power converters designed in +the world don't do this right they just + + align:start position:0% +the world don't do this right they just + + + align:start position:0% +the world don't do this right they just +kind of get an Optimum they live they + + align:start position:0% +kind of get an Optimum they live they + + + align:start position:0% +kind of get an Optimum they live they +try to get good devices live with the + + align:start position:0% +try to get good devices live with the + + + align:start position:0% +try to get good devices live with the +switching + + align:start position:0% +switching + + + align:start position:0% +switching +loss make the design trade-offs all the + + align:start position:0% +loss make the design trade-offs all the + + + align:start position:0% +loss make the design trade-offs all the +stuff I showed you so far in the term is + + align:start position:0% +stuff I showed you so far in the term is + + + align:start position:0% +stuff I showed you so far in the term is +you know the majority of things that's + + align:start position:0% +you know the majority of things that's + + + align:start position:0% +you know the majority of things that's +the way they're defi designed + + align:start position:0% +the way they're defi designed + + + align:start position:0% +the way they're defi designed +nonetheless when you're really trying to + + align:start position:0% +nonetheless when you're really trying to + + + align:start position:0% +nonetheless when you're really trying to +push the boundaries or for whatever + + align:start position:0% +push the boundaries or for whatever + + + align:start position:0% +push the boundaries or for whatever +reason you want to go to very high + + align:start position:0% +reason you want to go to very high + + + align:start position:0% +reason you want to go to very high +frequencies suddenly you have to use the + + align:start position:0% +frequencies suddenly you have to use the + + + align:start position:0% +frequencies suddenly you have to use the +these other kinds of techniques okay any + + align:start position:0% +these other kinds of techniques okay any + + + align:start position:0% +these other kinds of techniques okay any +questions about + + align:start position:0% + + + + align:start position:0% + +that okay so let's think about what we + + align:start position:0% +that okay so let's think about what we + + + align:start position:0% +that okay so let's think about what we +might do to build so-called soft + + align:start position:0% +might do to build so-called soft + + + align:start position:0% +might do to build so-called soft +switched + + align:start position:0% + + + + align:start position:0% + +converters and how soft is soft well + + align:start position:0% +converters and how soft is soft well + + + align:start position:0% +converters and how soft is soft well +that's you know that's there's all + + align:start position:0% +that's you know that's there's all + + + align:start position:0% +that's you know that's there's all +degrees of softness but but we'll uh + + align:start position:0% +degrees of softness but but we'll uh + + + align:start position:0% +degrees of softness but but we'll uh +talk about it now there's two flavors + + align:start position:0% +talk about it now there's two flavors + + + align:start position:0% +talk about it now there's two flavors +um there's one that I'll call zero + + align:start position:0% +um there's one that I'll call zero + + + align:start position:0% +um there's one that I'll call zero +voltage switching + + align:start position:0% +voltage switching + + + align:start position:0% +voltage switching +zvs and one that I'll call zero current + + align:start position:0% +zvs and one that I'll call zero current + + + align:start position:0% +zvs and one that I'll call zero current +switching + + align:start position:0% +switching + + + align:start position:0% +switching +zcs okay so you'll see these acronyms + + align:start position:0% +zcs okay so you'll see these acronyms + + + align:start position:0% +zcs okay so you'll see these acronyms +used + + align:start position:0% +used + + + align:start position:0% +used +everywhere um and essentially I'll I'll + + align:start position:0% +everywhere um and essentially I'll I'll + + + align:start position:0% +everywhere um and essentially I'll I'll +describe what they mean you also have + + align:start position:0% +describe what they mean you also have + + + align:start position:0% +describe what they mean you also have +kind of in any if I think about a given + + align:start position:0% +kind of in any if I think about a given + + + align:start position:0% +kind of in any if I think about a given +switch right like here I'll think about + + align:start position:0% +switch right like here I'll think about + + + align:start position:0% +switch right like here I'll think about +the active switch here he has two + + align:start position:0% +the active switch here he has two + + + align:start position:0% +the active switch here he has two +transitions he has a turn on transition + + align:start position:0% +transitions he has a turn on transition + + + align:start position:0% +transitions he has a turn on transition +and a turnoff transition I got to think + + align:start position:0% +and a turnoff transition I got to think + + + align:start position:0% +and a turnoff transition I got to think +about both of those because both of + + align:start position:0% +about both of those because both of + + + align:start position:0% +about both of those because both of +those give me some loss okay so I might + + align:start position:0% +those give me some loss okay so I might + + + align:start position:0% +those give me some loss okay so I might +think about turn + + align:start position:0% + + + + align:start position:0% + +off and I might think about turn + + align:start position:0% +off and I might think about turn + + + align:start position:0% +off and I might think about turn +on Okay so let's think about these four + + align:start position:0% +on Okay so let's think about these four + + + align:start position:0% +on Okay so let's think about these four +possibilities + + align:start position:0% +possibilities + + + align:start position:0% +possibilities +okay what is zvs turnoff zvs turnoff if + + align:start position:0% +okay what is zvs turnoff zvs turnoff if + + + align:start position:0% +okay what is zvs turnoff zvs turnoff if +I thought about uh say the turnoff I had + + align:start position:0% +I thought about uh say the turnoff I had + + + align:start position:0% +I thought about uh say the turnoff I had +here right I had something where the um + + align:start position:0% +here right I had something where the um + + + align:start position:0% +here right I had something where the um +current was + + align:start position:0% +current was + + + align:start position:0% +current was +falling like + + align:start position:0% +falling like + + + align:start position:0% +falling like +this at turn + + align:start position:0% +this at turn + + + align:start position:0% +this at turn +off and uh under a hard switch + + align:start position:0% +off and uh under a hard switch + + + align:start position:0% +off and uh under a hard switch +transition so this is I + + align:start position:0% +transition so this is I + + + align:start position:0% +transition so this is I +switch under a hard switch transition we + + align:start position:0% +switch under a hard switch transition we + + + align:start position:0% +switch under a hard switch transition we +expect kind of V switch to rise before + + align:start position:0% +expect kind of V switch to rise before + + + align:start position:0% +expect kind of V switch to rise before +the current Falls like + + align:start position:0% +the current Falls like + + + align:start position:0% +the current Falls like +this and that would be a hard switch + + align:start position:0% +this and that would be a hard switch + + + align:start position:0% +this and that would be a hard switch +transition what what we do in a zero + + align:start position:0% +transition what what we do in a zero + + + align:start position:0% +transition what what we do in a zero +voltage turn off is we typically do + + align:start position:0% +voltage turn off is we typically do + + + align:start position:0% +voltage turn off is we typically do +something to delay the the current rise + + align:start position:0% +something to delay the the current rise + + + align:start position:0% +something to delay the the current rise +the voltage rise on the switch you know + + align:start position:0% +the voltage rise on the switch you know + + + align:start position:0% +the voltage rise on the switch you know +maybe it does something like that right + + align:start position:0% +maybe it does something like that right + + + align:start position:0% +maybe it does something like that right +well that ought to look pretty familiar + + align:start position:0% +well that ought to look pretty familiar + + + align:start position:0% +well that ought to look pretty familiar +to you right that's sort of what the + + align:start position:0% +to you right that's sort of what the + + + align:start position:0% +to you right that's sort of what the +snubber did over here right so I might + + align:start position:0% +snubber did over here right so I might + + + align:start position:0% +snubber did over here right so I might +get this kind of + + align:start position:0% +get this kind of + + + align:start position:0% +get this kind of +behavior by taking a my by taking my + + align:start position:0% +behavior by taking a my by taking my + + + align:start position:0% +behavior by taking a my by taking my +switch + + align:start position:0% +switch + + + align:start position:0% +switch +that I'm going to try to turn off and + + align:start position:0% +that I'm going to try to turn off and + + + align:start position:0% +that I'm going to try to turn off and +just put a capacitor across + + align:start position:0% +just put a capacitor across + + + align:start position:0% +just put a capacitor across +him + + align:start position:0% +him + + + align:start position:0% +him +right and so if I put an external + + align:start position:0% +right and so if I put an external + + + align:start position:0% +right and so if I put an external +capacitor across the switch when he + + align:start position:0% +capacitor across the switch when he + + + align:start position:0% +capacitor across the switch when he +turns off it'll delay the rise in the + + align:start position:0% +turns off it'll delay the rise in the + + + align:start position:0% +turns off it'll delay the rise in the +switch and I'll reduce the overlap okay + + align:start position:0% +switch and I'll reduce the overlap okay + + + align:start position:0% +switch and I'll reduce the overlap okay +so it's no different than what this + + align:start position:0% +so it's no different than what this + + + align:start position:0% +so it's no different than what this +number does but now that I've put energy + + align:start position:0% +number does but now that I've put energy + + + align:start position:0% +number does but now that I've put energy +in this capacitor we got to figure out a + + align:start position:0% +in this capacitor we got to figure out a + + + align:start position:0% +in this capacitor we got to figure out a +way to get that energy back without + + align:start position:0% +way to get that energy back without + + + align:start position:0% +way to get that energy back without +dissipating it so I can't turn I can't + + align:start position:0% +dissipating it so I can't turn I can't + + + align:start position:0% +dissipating it so I can't turn I can't +just turn on the switch because I dump + + align:start position:0% +just turn on the switch because I dump + + + align:start position:0% +just turn on the switch because I dump +that energy and lose it okay + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% +what + + + align:start position:0% +what +about + + align:start position:0% +about + + + align:start position:0% +about +um zero voltage turn + + align:start position:0% +um zero voltage turn + + + align:start position:0% +um zero voltage turn +on Okay what would zero voltage turn on + + align:start position:0% +on Okay what would zero voltage turn on + + + align:start position:0% +on Okay what would zero voltage turn on +look like well we said okay um what we + + align:start position:0% +look like well we said okay um what we + + + align:start position:0% +look like well we said okay um what we +expect normally at turn on is you know + + align:start position:0% +expect normally at turn on is you know + + + align:start position:0% +expect normally at turn on is you know +the current in the switch is going to + + align:start position:0% +the current in the switch is going to + + + align:start position:0% +the current in the switch is going to +rise at the turn on + + align:start position:0% +rise at the turn on + + + align:start position:0% +rise at the turn on +transition + + align:start position:0% +transition + + + align:start position:0% +transition +right and + + align:start position:0% +right and + + + align:start position:0% +right and +usually after the current + + align:start position:0% +usually after the current + + + align:start position:0% +usually after the current +Rises here's the switch + + align:start position:0% +Rises here's the switch + + + align:start position:0% +Rises here's the switch +voltage the switch voltage Falls right + + align:start position:0% +voltage the switch voltage Falls right + + + align:start position:0% +voltage the switch voltage Falls right +so that's what I would get and I'd have + + align:start position:0% +so that's what I would get and I'd have + + + align:start position:0% +so that's what I would get and I'd have +this overlap period right well what if I + + align:start position:0% +this overlap period right well what if I + + + align:start position:0% +this overlap period right well what if I +could be somehow super clever in my + + align:start position:0% +could be somehow super clever in my + + + align:start position:0% +could be somehow super clever in my +circuit through magical means and just + + align:start position:0% +circuit through magical means and just + + + align:start position:0% +circuit through magical means and just +happen to work it so that instead of the + + align:start position:0% +happen to work it so that instead of the + + + align:start position:0% +happen to work it so that instead of the +voltage falling because I'm turning the + + align:start position:0% +voltage falling because I'm turning the + + + align:start position:0% +voltage falling because I'm turning the +switch on I do something else in the + + align:start position:0% +switch on I do something else in the + + + align:start position:0% +switch on I do something else in the +circuit to make the voltage go to zero + + align:start position:0% +circuit to make the voltage go to zero + + + align:start position:0% +circuit to make the voltage go to zero +before I try to turn the switch on maybe + + align:start position:0% +before I try to turn the switch on maybe + + + align:start position:0% +before I try to turn the switch on maybe +I have a + + align:start position:0% +I have a + + + align:start position:0% +I have a +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +where somehow through natural action of + + align:start position:0% +where somehow through natural action of + + + align:start position:0% +where somehow through natural action of +the circuit the voltage goes to zero and + + align:start position:0% +the circuit the voltage goes to zero and + + + align:start position:0% +the circuit the voltage goes to zero and +then I can turn the switch on with no + + align:start position:0% +then I can turn the switch on with no + + + align:start position:0% +then I can turn the switch on with no +voltage across it and then I get no + + align:start position:0% +voltage across it and then I get no + + + align:start position:0% +voltage across it and then I get no +overlap okay so zero voltage switching + + align:start position:0% +overlap okay so zero voltage switching + + + align:start position:0% +overlap okay so zero voltage switching +either on or off is sort of + + align:start position:0% +either on or off is sort of + + + align:start position:0% +either on or off is sort of +arranging the switching operation such + + align:start position:0% +arranging the switching operation such + + + align:start position:0% +arranging the switching operation such +that I don't I move the voltage around + + align:start position:0% +that I don't I move the voltage around + + + align:start position:0% +that I don't I move the voltage around +in a way that gives me little overlap + + align:start position:0% +in a way that gives me little overlap + + + align:start position:0% +in a way that gives me little overlap +between voltage and current at the + + align:start position:0% +between voltage and current at the + + + align:start position:0% +between voltage and current at the +transition + + align:start position:0% +transition + + + align:start position:0% +transition +and we'll talk about how you might do + + align:start position:0% +and we'll talk about how you might do + + + align:start position:0% +and we'll talk about how you might do +that but that's the idea any + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +so what would a zeroc current turn on + + align:start position:0% +so what would a zeroc current turn on + + + align:start position:0% +so what would a zeroc current turn on +look like well we said okay for turn on + + align:start position:0% +look like well we said okay for turn on + + + align:start position:0% +look like well we said okay for turn on +right + + align:start position:0% +right + + + align:start position:0% +right +usually what happens is I have my switch + + align:start position:0% +usually what happens is I have my switch + + + align:start position:0% +usually what happens is I have my switch +current and he he's Rising because this + + align:start position:0% +current and he he's Rising because this + + + align:start position:0% +current and he he's Rising because this +is turn on so here's I switch this + + align:start position:0% +is turn on so here's I switch this + + + align:start position:0% +is turn on so here's I switch this +current's going to go from zero and then + + align:start position:0% +current's going to go from zero and then + + + align:start position:0% +current's going to go from zero and then +I'm going to turn them on it's going to + + align:start position:0% +I'm going to turn them on it's going to + + + align:start position:0% +I'm going to turn them on it's going to +be something and normally um what + + align:start position:0% +be something and normally um what + + + align:start position:0% +be something and normally um what +happens is the + + align:start position:0% +happens is the + + + align:start position:0% +happens is the +um the voltage + + align:start position:0% +um the voltage + + + align:start position:0% +um the voltage +Falls after the current + + align:start position:0% + + + + align:start position:0% + +Rises + + align:start position:0% +Rises + + + align:start position:0% +Rises +right so + + align:start position:0% + + + + align:start position:0% + +um what if I could + + align:start position:0% +um what if I could + + + align:start position:0% +um what if I could +do what if I could do this + + align:start position:0% +do what if I could do this + + + align:start position:0% +do what if I could do this +um what if I + + align:start position:0% +um what if I + + + align:start position:0% +um what if I +coulds what am I + + align:start position:0% + + + + align:start position:0% + +doing what if I could do this what if I + + align:start position:0% +doing what if I could do this what if I + + + align:start position:0% +doing what if I could do this what if I +could say all right instead of having + + align:start position:0% +could say all right instead of having + + + align:start position:0% +could say all right instead of having +the switch current rise early I did some + + align:start position:0% +the switch current rise early I did some + + + align:start position:0% +the switch current rise early I did some +magic + + align:start position:0% +magic + + + align:start position:0% +magic +game such that he didn't rise until + + align:start position:0% + + + + align:start position:0% + +later okay I somehow delay the switch + + align:start position:0% +later okay I somehow delay the switch + + + align:start position:0% +later okay I somehow delay the switch +current rise until after the voltage has + + align:start position:0% +current rise until after the voltage has + + + align:start position:0% +current rise until after the voltage has +fallen okay I would then have little + + align:start position:0% +fallen okay I would then have little + + + align:start position:0% +fallen okay I would then have little +overlap and that would be good well this + + align:start position:0% +overlap and that would be good well this + + + align:start position:0% +overlap and that would be good well this +is very similar to the notion of if I + + align:start position:0% +is very similar to the notion of if I + + + align:start position:0% +is very similar to the notion of if I +had my + + align:start position:0% +had my + + + align:start position:0% +had my +switch you know maybe I could go put a + + align:start position:0% +switch you know maybe I could go put a + + + align:start position:0% +switch you know maybe I could go put a +inductor in series with the + + align:start position:0% +inductor in series with the + + + align:start position:0% +inductor in series with the +switch right so even after I turn the + + align:start position:0% +switch right so even after I turn the + + + align:start position:0% +switch right so even after I turn the +switch on the voltage doesn't appear + + align:start position:0% +switch on the voltage doesn't appear + + + align:start position:0% +switch on the voltage doesn't appear +across the + + align:start position:0% +across the + + + align:start position:0% +across the +switch it could this is V switch it + + align:start position:0% +switch it could this is V switch it + + + align:start position:0% +switch it could this is V switch it +could appear across this inductor and + + align:start position:0% +could appear across this inductor and + + + align:start position:0% +could appear across this inductor and +the current in the inductor will be + + align:start position:0% +the current in the inductor will be + + + align:start position:0% +the current in the inductor will be +delayed in its rise right so in some + + align:start position:0% +delayed in its rise right so in some + + + align:start position:0% +delayed in its rise right so in some +sense this number sort of helps give me + + align:start position:0% +sense this number sort of helps give me + + + align:start position:0% +sense this number sort of helps give me +zero current turn on except that I'm + + align:start position:0% +zero current turn on except that I'm + + + align:start position:0% +zero current turn on except that I'm +dumping the energy so I can play this + + align:start position:0% +dumping the energy so I can play this + + + align:start position:0% +dumping the energy so I can play this +same game except that then I got to + + align:start position:0% +same game except that then I got to + + + align:start position:0% +same game except that then I got to +figure out how to recover the energy in + + align:start position:0% +figure out how to recover the energy in + + + align:start position:0% +figure out how to recover the energy in +this + + align:start position:0% +this + + + align:start position:0% +this +inductor okay and you can kind of + + align:start position:0% +inductor okay and you can kind of + + + align:start position:0% +inductor okay and you can kind of +see that these two zero voltage turn off + + align:start position:0% +see that these two zero voltage turn off + + + align:start position:0% +see that these two zero voltage turn off +and zero current turn on are are kind of + + align:start position:0% +and zero current turn on are are kind of + + + align:start position:0% +and zero current turn on are are kind of +duel of one another right I'm just sort + + align:start position:0% +duel of one another right I'm just sort + + + align:start position:0% +duel of one another right I'm just sort +of swapping voltage and current + + align:start position:0% +of swapping voltage and current + + + align:start position:0% +of swapping voltage and current +waveforms and I'm swapping the role of + + align:start position:0% +waveforms and I'm swapping the role of + + + align:start position:0% +waveforms and I'm swapping the role of +the capacitor and zero voltage turnoff + + align:start position:0% +the capacitor and zero voltage turnoff + + + align:start position:0% +the capacitor and zero voltage turnoff +and the inductor and zero current turn + + align:start position:0% +and the inductor and zero current turn + + + align:start position:0% +and the inductor and zero current turn +on there are other ways to get zvs turn + + align:start position:0% +on there are other ways to get zvs turn + + + align:start position:0% +on there are other ways to get zvs turn +off or zcs turn on but I'm showing you a + + align:start position:0% +off or zcs turn on but I'm showing you a + + + align:start position:0% +off or zcs turn on but I'm showing you a +common way to do + + align:start position:0% +common way to do + + + align:start position:0% +common way to do +it what's the last one well we + + align:start position:0% +it what's the last one well we + + + align:start position:0% +it what's the last one well we +said you know I want to do zero current + + align:start position:0% +said you know I want to do zero current + + + align:start position:0% +said you know I want to do zero current +turnoff and we said what usually happens + + align:start position:0% +turnoff and we said what usually happens + + + align:start position:0% +turnoff and we said what usually happens +is that um my switch voltage + + align:start position:0% + + + + align:start position:0% + +Rises and then my switch current can + + align:start position:0% +Rises and then my switch current can + + + align:start position:0% +Rises and then my switch current can +fall only after that happens right well + + align:start position:0% +fall only after that happens right well + + + align:start position:0% +fall only after that happens right well +what if I were really + + align:start position:0% +what if I were really + + + align:start position:0% +what if I were really +clever and said okay here's I + + align:start position:0% +clever and said okay here's I + + + align:start position:0% +clever and said okay here's I +switch what if I were really clever and + + align:start position:0% +switch what if I were really clever and + + + align:start position:0% +switch what if I were really clever and +made the somehow I could make + + align:start position:0% +made the somehow I could make + + + align:start position:0% +made the somehow I could make +the current go to zero before the time I + + align:start position:0% +the current go to zero before the time I + + + align:start position:0% +the current go to zero before the time I +wanted to turn off if the current were + + align:start position:0% +wanted to turn off if the current were + + + align:start position:0% +wanted to turn off if the current were +naturally zero when I was going to turn + + align:start position:0% +naturally zero when I was going to turn + + + align:start position:0% +naturally zero when I was going to turn +off I can turn off the switch with no + + align:start position:0% +off I can turn off the switch with no + + + align:start position:0% +off I can turn off the switch with no +overlap in voltage and current I'm + + align:start position:0% +overlap in voltage and current I'm + + + align:start position:0% +overlap in voltage and current I'm +done all right I've got to come up with + + align:start position:0% +done all right I've got to come up with + + + align:start position:0% +done all right I've got to come up with +some magical circuit means to do this + + align:start position:0% +some magical circuit means to do this + + + align:start position:0% +some magical circuit means to do this +we've kind of got ideas for how we might + + align:start position:0% +we've kind of got ideas for how we might + + + align:start position:0% +we've kind of got ideas for how we might +do these two we got to figure out how we + + align:start position:0% +do these two we got to figure out how we + + + align:start position:0% +do these two we got to figure out how we +might do these two guys but that's the + + align:start position:0% +might do these two guys but that's the + + + align:start position:0% +might do these two guys but that's the +basic concept I'm either going to + + align:start position:0% +basic concept I'm either going to + + + align:start position:0% +basic concept I'm either going to +manipulate the voltage to make the + + align:start position:0% +manipulate the voltage to make the + + + align:start position:0% +manipulate the voltage to make the +voltage and current overlap small or I'm + + align:start position:0% +voltage and current overlap small or I'm + + + align:start position:0% +voltage and current overlap small or I'm +going to manipulate the current to make + + align:start position:0% +going to manipulate the current to make + + + align:start position:0% +going to manipulate the current to make +the voltage and current overlap small or + + align:start position:0% +the voltage and current overlap small or + + + align:start position:0% +the voltage and current overlap small or +both for that matter right but I'm + + align:start position:0% +both for that matter right but I'm + + + align:start position:0% +both for that matter right but I'm +trying to create this kind of magical + + align:start position:0% +trying to create this kind of magical + + + align:start position:0% +trying to create this kind of magical +opportunity to change my switch + + align:start position:0% +opportunity to change my switch + + + align:start position:0% +opportunity to change my switch +configurations at low + + align:start position:0% +configurations at low + + + align:start position:0% +configurations at low +loss + + align:start position:0% +loss + + + align:start position:0% +loss +and we that's not for free if I just go + + align:start position:0% +and we that's not for free if I just go + + + align:start position:0% +and we that's not for free if I just go +design a buck converter I don't get that + + align:start position:0% +design a buck converter I don't get that + + + align:start position:0% +design a buck converter I don't get that +for + + align:start position:0% +for + + + align:start position:0% +for +free um but maybe I can do something + + align:start position:0% +free um but maybe I can do something + + + align:start position:0% +free um but maybe I can do something +more complicated that make that makes + + align:start position:0% +more complicated that make that makes + + + align:start position:0% +more complicated that make that makes +that + + align:start position:0% +that + + + align:start position:0% +that +work so does everybody first of all get + + align:start position:0% +work so does everybody first of all get + + + align:start position:0% +work so does everybody first of all get +the premise of soft switching + + align:start position:0% + + + + align:start position:0% + +okay let me show you a few + + align:start position:0% +okay let me show you a few + + + align:start position:0% +okay let me show you a few +examples of different ways people do + + align:start position:0% +examples of different ways people do + + + align:start position:0% +examples of different ways people do +this and I'm going to show you examples + + align:start position:0% +this and I'm going to show you examples + + + align:start position:0% +this and I'm going to show you examples +in DC todc converters today we'll talk + + align:start position:0% +in DC todc converters today we'll talk + + + align:start position:0% +in DC todc converters today we'll talk +about more ideas of doing soft switching + + align:start position:0% +about more ideas of doing soft switching + + + align:start position:0% +about more ideas of doing soft switching +and other kind of converters next class + + align:start position:0% +and other kind of converters next class + + + align:start position:0% +and other kind of converters next class +um but here is + + align:start position:0% +um but here is + + + align:start position:0% +um but here is +the first example I'd like to show you + + align:start position:0% +the first example I'd like to show you + + + align:start position:0% +the first example I'd like to show you +now this circuit and I'm showing you an + + align:start position:0% +now this circuit and I'm showing you an + + + align:start position:0% +now this circuit and I'm showing you an +actual circuit because I wanted to show + + align:start position:0% +actual circuit because I wanted to show + + + align:start position:0% +actual circuit because I wanted to show +you the real circuit and the switching + + align:start position:0% +you the real circuit and the switching + + + align:start position:0% +you the real circuit and the switching +waveforms from it is a version of a buck + + align:start position:0% +waveforms from it is a version of a buck + + + align:start position:0% +waveforms from it is a version of a buck +converter and you could do this same + + align:start position:0% +converter and you could do this same + + + align:start position:0% +converter and you could do this same +technique in a regular Buck converter + + align:start position:0% +technique in a regular Buck converter + + + align:start position:0% +technique in a regular Buck converter +it's just that this version of the + + align:start position:0% +it's just that this version of the + + + align:start position:0% +it's just that this version of the +circuit I'm showing you here is what we + + align:start position:0% +circuit I'm showing you here is what we + + + align:start position:0% +circuit I'm showing you here is what we +would call an inverted Buck converter or + + align:start position:0% +would call an inverted Buck converter or + + + align:start position:0% +would call an inverted Buck converter or +a common positive Buck converter that is + + align:start position:0% +a common positive Buck converter that is + + + align:start position:0% +a common positive Buck converter that is +the switch is ground referenced and the + + align:start position:0% +the switch is ground referenced and the + + + align:start position:0% +the switch is ground referenced and the +input and output share a common positive + + align:start position:0% +input and output share a common positive + + + align:start position:0% +input and output share a common positive +terminal instead of a common negative + + align:start position:0% +terminal instead of a common negative + + + align:start position:0% +terminal instead of a common negative +terminal which they normally would okay + + align:start position:0% +terminal which they normally would okay + + + align:start position:0% +terminal which they normally would okay +but you could see that this is still a + + align:start position:0% +but you could see that this is still a + + + align:start position:0% +but you could see that this is still a +buck converter right when the switch is + + align:start position:0% +buck converter right when the switch is + + + align:start position:0% +buck converter right when the switch is +on I get V in minus V out across the + + align:start position:0% +on I get V in minus V out across the + + + align:start position:0% +on I get V in minus V out across the +inductor and when the switch is off I + + align:start position:0% +inductor and when the switch is off I + + + align:start position:0% +inductor and when the switch is off I +get minus V out across the inductor it's + + align:start position:0% +get minus V out across the inductor it's + + + align:start position:0% +get minus V out across the inductor it's +it is a buck + + align:start position:0% +it is a buck + + + align:start position:0% +it is a buck +converter + + align:start position:0% +converter + + + align:start position:0% +converter +okay but how are we going to run this + + align:start position:0% +okay but how are we going to run this + + + align:start position:0% +okay but how are we going to run this +Buck converter well let me tell you how + + align:start position:0% +Buck converter well let me tell you how + + + align:start position:0% +Buck converter well let me tell you how +we're going to run this Buck converter + + align:start position:0% +we're going to run this Buck converter + + + align:start position:0% +we're going to run this Buck converter +and the one thing you can't see in this + + align:start position:0% +and the one thing you can't see in this + + + align:start position:0% +and the one thing you can't see in this +picture okay first of all is there any + + align:start position:0% +picture okay first of all is there any + + + align:start position:0% +picture okay first of all is there any +question as to why this thing's a buck + + align:start position:0% + + + + align:start position:0% + +converter okay so here's the circuit + + align:start position:0% +converter okay so here's the circuit + + + align:start position:0% +converter okay so here's the circuit +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and it looks like this so this is my + + align:start position:0% +and it looks like this so this is my + + + align:start position:0% +and it looks like this so this is my +buck Bas this is my basic Buck converter + + align:start position:0% +buck Bas this is my basic Buck converter + + + align:start position:0% +buck Bas this is my basic Buck converter +if I drew this for you and put it on + + align:start position:0% +if I drew this for you and put it on + + + align:start position:0% +if I drew this for you and put it on +exam and say what kind of converter that + + align:start position:0% +exam and say what kind of converter that + + + align:start position:0% +exam and say what kind of converter that +is you tell me it's a buck converter + + align:start position:0% +is you tell me it's a buck converter + + + align:start position:0% +is you tell me it's a buck converter +right here's here is missing something + + align:start position:0% +right here's here is missing something + + + align:start position:0% +right here's here is missing something +here I'm missing my output + + align:start position:0% + + + + align:start position:0% + +voltage so you know here we + + align:start position:0% +voltage so you know here we + + + align:start position:0% +voltage so you know here we +go here's my output capacitor and my + + align:start position:0% +go here's my output capacitor and my + + + align:start position:0% +go here's my output capacitor and my +output resistor for example here's V + + align:start position:0% +output resistor for example here's V + + + align:start position:0% +output resistor for example here's V +out and here here's + + align:start position:0% +out and here here's + + + align:start position:0% +out and here here's +I okay that's a buck converter okay + + align:start position:0% +I okay that's a buck converter okay + + + align:start position:0% +I okay that's a buck converter okay +and we're going to have to do some + + align:start position:0% +and we're going to have to do some + + + align:start position:0% +and we're going to have to do some +work to get soft switching in this + + align:start position:0% +work to get soft switching in this + + + align:start position:0% +work to get soft switching in this +converter but let me tell you the one + + align:start position:0% +converter but let me tell you the one + + + align:start position:0% +converter but let me tell you the one +thing that's missing in the circuit + + align:start position:0% +thing that's missing in the circuit + + + align:start position:0% +thing that's missing in the circuit +diagram picture and that is that there's + + align:start position:0% +diagram picture and that is that there's + + + align:start position:0% +diagram picture and that is that there's +a capacitance here an effective + + align:start position:0% +a capacitance here an effective + + + align:start position:0% +a capacitance here an effective +capacitance here okay across the device + + align:start position:0% +capacitance here okay across the device + + + align:start position:0% +capacitance here okay across the device +where does that capacitance come from + + align:start position:0% +where does that capacitance come from + + + align:start position:0% +where does that capacitance come from +well it comes from the fact that this + + align:start position:0% +well it comes from the fact that this + + + align:start position:0% +well it comes from the fact that this +switch has + + align:start position:0% +switch has + + + align:start position:0% +switch has +capacitance and so that's in parallel + + align:start position:0% +capacitance and so that's in parallel + + + align:start position:0% +capacitance and so that's in parallel +with the device the diode also has some + + align:start position:0% +with the device the diode also has some + + + align:start position:0% +with the device the diode also has some +capacitance and that's connected between + + align:start position:0% +capacitance and that's connected between + + + align:start position:0% +capacitance and that's connected between +this node and a fixed potential so from + + align:start position:0% +this node and a fixed potential so from + + + align:start position:0% +this node and a fixed potential so from +an AC perspective it also looks like + + align:start position:0% +an AC perspective it also looks like + + + align:start position:0% +an AC perspective it also looks like +capacitance sitting here right so what + + align:start position:0% +capacitance sitting here right so what + + + align:start position:0% +capacitance sitting here right so what +we're going to do is we're going to use + + align:start position:0% +we're going to do is we're going to use + + + align:start position:0% +we're going to do is we're going to use +the net capacitance at this node to help + + align:start position:0% +the net capacitance at this node to help + + + align:start position:0% +the net capacitance at this node to help +give us zero voltage + + align:start position:0% +give us zero voltage + + + align:start position:0% +give us zero voltage +switching okay + + align:start position:0% +switching okay + + + align:start position:0% +switching okay +and I'll remind you that a capacitor + + align:start position:0% +and I'll remind you that a capacitor + + + align:start position:0% +and I'll remind you that a capacitor +across the device is just what we need + + align:start position:0% +across the device is just what we need + + + align:start position:0% +across the device is just what we need +to get zero voltage turn + + align:start position:0% +to get zero voltage turn + + + align:start position:0% +to get zero voltage turn +off right so we're going to we're going + + align:start position:0% +off right so we're going to we're going + + + align:start position:0% +off right so we're going to we're going +to do this trick because I've put a + + align:start position:0% +to do this trick because I've put a + + + align:start position:0% +to do this trick because I've put a +capacitor across the device so if I see + + align:start position:0% +capacitor across the device so if I see + + + align:start position:0% +capacitor across the device so if I see +a design with a capacitor across the + + align:start position:0% +a design with a capacitor across the + + + align:start position:0% +a design with a capacitor across the +device I think yeah I'm probably doing + + align:start position:0% +device I think yeah I'm probably doing + + + align:start position:0% +device I think yeah I'm probably doing +zero voltage switching so how does this + + align:start position:0% +zero voltage switching so how does this + + + align:start position:0% +zero voltage switching so how does this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +work okay well I'm going to turn let's + + align:start position:0% +work okay well I'm going to turn let's + + + align:start position:0% +work okay well I'm going to turn let's +assume the switch is + + align:start position:0% +assume the switch is + + + align:start position:0% +assume the switch is +on okay I'm in I'm in my normal State + + align:start position:0% +on okay I'm in I'm in my normal State + + + align:start position:0% +on okay I'm in I'm in my normal State +when the switch is on the inductor + + align:start position:0% +when the switch is on the inductor + + + align:start position:0% +when the switch is on the inductor +currents going to + + align:start position:0% +currents going to + + + align:start position:0% +currents going to +rise okay we're going to let the + + align:start position:0% +rise okay we're going to let the + + + align:start position:0% +rise okay we're going to let the +inductor current rise and we're actually + + align:start position:0% +inductor current rise and we're actually + + + align:start position:0% +inductor current rise and we're actually +going to have a large Ripple ratio in + + align:start position:0% +going to have a large Ripple ratio in + + + align:start position:0% +going to have a large Ripple ratio in +this inductor current and eventually the + + align:start position:0% +this inductor current and eventually the + + + align:start position:0% +this inductor current and eventually the +inductor current is going to get up to + + align:start position:0% +inductor current is going to get up to + + + align:start position:0% +inductor current is going to get up to +some level where I tell the switch to + + align:start position:0% +some level where I tell the switch to + + + align:start position:0% +some level where I tell the switch to +turn off okay now what + + align:start position:0% +turn off okay now what + + + align:start position:0% +turn off okay now what +happens when uh this inductor current + + align:start position:0% + + + + align:start position:0% + +I is + + align:start position:0% +I is + + + align:start position:0% +I is +big and I turn off well if this + + align:start position:0% +big and I turn off well if this + + + align:start position:0% +big and I turn off well if this +capacitor sitting across the switch even + + align:start position:0% +capacitor sitting across the switch even + + + align:start position:0% +capacitor sitting across the switch even +though is big and coming here this + + align:start position:0% +though is big and coming here this + + + align:start position:0% +though is big and coming here this +capacitor delays the rise and voltage on + + align:start position:0% +capacitor delays the rise and voltage on + + + align:start position:0% +capacitor delays the rise and voltage on +the switch and I can turn off the switch + + align:start position:0% +the switch and I can turn off the switch + + + align:start position:0% +the switch and I can turn off the switch +under approximately zero voltage because + + align:start position:0% +under approximately zero voltage because + + + align:start position:0% +under approximately zero voltage because +of the capacitance of this node all + + align:start position:0% +of the capacitance of this node all + + + align:start position:0% +of the capacitance of this node all +right so that's + + align:start position:0% +right so that's + + + align:start position:0% +right so that's +exactly this picture + + align:start position:0% +exactly this picture + + + align:start position:0% +exactly this picture +here okay so what happens + + align:start position:0% +here okay so what happens + + + align:start position:0% +here okay so what happens +eventually this inductor charges up this + + align:start position:0% +eventually this inductor charges up this + + + align:start position:0% +eventually this inductor charges up this +capacitor until the diode turns + + align:start position:0% +capacitor until the diode turns + + + align:start position:0% +capacitor until the diode turns +on right so I get a z Z voltage + + align:start position:0% +on right so I get a z Z voltage + + + align:start position:0% +on right so I get a z Z voltage +transition you can see that in this + + align:start position:0% +transition you can see that in this + + + align:start position:0% +transition you can see that in this +operating diagram here right the voltage + + align:start position:0% +operating diagram here right the voltage + + + align:start position:0% +operating diagram here right the voltage +across the switch goes up until hit it + + align:start position:0% +across the switch goes up until hit it + + + align:start position:0% +across the switch goes up until hit it +hits + + align:start position:0% +hits + + + align:start position:0% +hits +VN which is exactly the condition in + + align:start position:0% +VN which is exactly the condition in + + + align:start position:0% +VN which is exactly the condition in +which the diode's on and the inductor is + + align:start position:0% +which the diode's on and the inductor is + + + align:start position:0% +which the diode's on and the inductor is +going to circulate current its current + + align:start position:0% +going to circulate current its current + + + align:start position:0% +going to circulate current its current +into the output does that make sense + + align:start position:0% +into the output does that make sense + + + align:start position:0% +into the output does that make sense +everybody now what I have to do in this + + align:start position:0% +everybody now what I have to do in this + + + align:start position:0% +everybody now what I have to do in this +circuit is somehow ensure that this + + align:start position:0% +circuit is somehow ensure that this + + + align:start position:0% +circuit is somehow ensure that this +voltage across the switch be switch + + align:start position:0% +voltage across the switch be switch + + + align:start position:0% +voltage across the switch be switch +which I I guess I should have kept my + + align:start position:0% +which I I guess I should have kept my + + + align:start position:0% +which I I guess I should have kept my +color scheme consistent V + + align:start position:0% +color scheme consistent V + + + align:start position:0% +color scheme consistent V +switch + + align:start position:0% +switch + + + align:start position:0% +switch +um is going to get back down to zero how + + align:start position:0% +um is going to get back down to zero how + + + align:start position:0% +um is going to get back down to zero how +does that work in this circuit what + + align:start position:0% +does that work in this circuit what + + + align:start position:0% +does that work in this circuit what +magic do I do in the circuit well in + + align:start position:0% +magic do I do in the circuit well in + + + align:start position:0% +magic do I do in the circuit well in +this circuit what we're going to do is + + align:start position:0% +this circuit what we're going to do is + + + align:start position:0% +this circuit what we're going to do is +we're going to let the diode conduct and + + align:start position:0% +we're going to let the diode conduct and + + + align:start position:0% +we're going to let the diode conduct and +because there's a negative voltage + + align:start position:0% +because there's a negative voltage + + + align:start position:0% +because there's a negative voltage +across the inductor the inductor current + + align:start position:0% +across the inductor the inductor current + + + align:start position:0% +across the inductor the inductor current +is going to ramp + + align:start position:0% +is going to ramp + + + align:start position:0% +is going to ramp +down until the inductor current hits + + align:start position:0% +down until the inductor current hits + + + align:start position:0% +down until the inductor current hits +zero okay once the inductor current hits + + align:start position:0% +zero okay once the inductor current hits + + + align:start position:0% +zero okay once the inductor current hits +zero + + align:start position:0% +zero + + + align:start position:0% +zero +the switch is off the diode is off and + + align:start position:0% +the switch is off the diode is off and + + + align:start position:0% +the switch is off the diode is off and +all I essentially have is a resonance if + + align:start position:0% +all I essentially have is a resonance if + + + align:start position:0% +all I essentially have is a resonance if +I think about V out as being constant I + + align:start position:0% +I think about V out as being constant I + + + align:start position:0% +I think about V out as being constant I +have a resonance between the buck + + align:start position:0% +have a resonance between the buck + + + align:start position:0% +have a resonance between the buck +inductor and the capacitance at the + + align:start position:0% +inductor and the capacitance at the + + + align:start position:0% +inductor and the capacitance at the +switch okay so both devices are now + + align:start position:0% +switch okay so both devices are now + + + align:start position:0% +switch okay so both devices are now +off by the way this diode is turned off + + align:start position:0% +off by the way this diode is turned off + + + align:start position:0% +off by the way this diode is turned off +at zero current naturally because the + + align:start position:0% +at zero current naturally because the + + + align:start position:0% +at zero current naturally because the +current ramp down to zero + + align:start position:0% +current ramp down to zero + + + align:start position:0% +current ramp down to zero +okay but what's going to happen then the + + align:start position:0% +okay but what's going to happen then the + + + align:start position:0% +okay but what's going to happen then the +inductor and the capacitor are going to + + align:start position:0% +inductor and the capacitor are going to + + + align:start position:0% +inductor and the capacitor are going to +ring with each other and the voltage + + align:start position:0% +ring with each other and the voltage + + + align:start position:0% +ring with each other and the voltage +across the transistor is going to ring + + align:start position:0% +across the transistor is going to ring + + + align:start position:0% +across the transistor is going to ring +down how far is it going to ring down + + align:start position:0% +down how far is it going to ring down + + + align:start position:0% +down how far is it going to ring down +that makes for a great homework problem + + align:start position:0% +that makes for a great homework problem + + + align:start position:0% +that makes for a great homework problem +but it's going to ring down to V in + + align:start position:0% +but it's going to ring down to V in + + + align:start position:0% +but it's going to ring down to V in +minus 2v out okay so if the output + + align:start position:0% +minus 2v out okay so if the output + + + align:start position:0% +minus 2v out okay so if the output +voltage V out was exactly half the input + + align:start position:0% +voltage V out was exactly half the input + + + align:start position:0% +voltage V out was exactly half the input +voltage this node would ring exactly + + align:start position:0% +voltage this node would ring exactly + + + align:start position:0% +voltage this node would ring exactly +down to + + align:start position:0% +down to + + + align:start position:0% +down to +zero if it was a little bit bigger it + + align:start position:0% +zero if it was a little bit bigger it + + + align:start position:0% +zero if it was a little bit bigger it +wouldn't quite get to zero if it was a + + align:start position:0% +wouldn't quite get to zero if it was a + + + align:start position:0% +wouldn't quite get to zero if it was a +little bit less it would ring all the + + align:start position:0% +little bit less it would ring all the + + + align:start position:0% +little bit less it would ring all the +way into zero and the the + + align:start position:0% +way into zero and the the + + + align:start position:0% +way into zero and the the +internal body diode of this mosfet would + + align:start position:0% +internal body diode of this mosfet would + + + align:start position:0% +internal body diode of this mosfet would +turn on right because don't forget + + align:start position:0% +turn on right because don't forget + + + align:start position:0% +turn on right because don't forget +there's a free diode right there + + align:start position:0% +there's a free diode right there + + + align:start position:0% +there's a free diode right there +right so what that means is this circuit + + align:start position:0% +right so what that means is this circuit + + + align:start position:0% +right so what that means is this circuit +as long as I let the inductor current + + align:start position:0% +as long as I let the inductor current + + + align:start position:0% +as long as I let the inductor current +get all the way down to zero and then + + align:start position:0% +get all the way down to zero and then + + + align:start position:0% +get all the way down to zero and then +turn the diode turns off this voltage + + align:start position:0% +turn the diode turns off this voltage + + + align:start position:0% +turn the diode turns off this voltage +can ring all the way down to zero and I + + align:start position:0% +can ring all the way down to zero and I + + + align:start position:0% +can ring all the way down to zero and I +get the opportunity to turn on the + + align:start position:0% +get the opportunity to turn on the + + + align:start position:0% +get the opportunity to turn on the +switch when he already has zero voltage + + align:start position:0% +switch when he already has zero voltage + + + align:start position:0% +switch when he already has zero voltage +across him the resonance between the + + align:start position:0% +across him the resonance between the + + + align:start position:0% +across him the resonance between the +buck inductor in the capacitor at that + + align:start position:0% +buck inductor in the capacitor at that + + + align:start position:0% +buck inductor in the capacitor at that +node give me a + + align:start position:0% +node give me a + + + align:start position:0% +node give me a +free zero voltage switching + + align:start position:0% +free zero voltage switching + + + align:start position:0% +free zero voltage switching +opportunity the current in the device is + + align:start position:0% +opportunity the current in the device is + + + align:start position:0% +opportunity the current in the device is +zero the voltage is naturally rung down + + align:start position:0% +zero the voltage is naturally rung down + + + align:start position:0% +zero the voltage is naturally rung down +to zero and I can turn them on for free + + align:start position:0% +to zero and I can turn them on for free + + + align:start position:0% +to zero and I can turn them on for free +okay so I've got zero voltage turn off + + align:start position:0% +okay so I've got zero voltage turn off + + + align:start position:0% +okay so I've got zero voltage turn off +of the switch zero voltage turn on of + + align:start position:0% +of the switch zero voltage turn on of + + + align:start position:0% +of the switch zero voltage turn on of +the + + align:start position:0% +the + + + align:start position:0% +the +switch any questions about + + align:start position:0% +switch any questions about + + + align:start position:0% +switch any questions about +that these are actually real waveforms + + align:start position:0% +that these are actually real waveforms + + + align:start position:0% +that these are actually real waveforms +the green is the inductor current + + align:start position:0% +the green is the inductor current + + + align:start position:0% +the green is the inductor current +ringing up and down with this high + + align:start position:0% +ringing up and down with this high + + + align:start position:0% +ringing up and down with this high +ringing the the blue waveform is + + align:start position:0% +ringing the the blue waveform is + + + align:start position:0% +ringing the the blue waveform is +actually the drain voltage of the + + align:start position:0% +actually the drain voltage of the + + + align:start position:0% +actually the drain voltage of the +transistor so you can see where it's on + + align:start position:0% +transistor so you can see where it's on + + + align:start position:0% +transistor so you can see where it's on +this is the Gate Drive turning off the + + align:start position:0% +this is the Gate Drive turning off the + + + align:start position:0% +this is the Gate Drive turning off the +voltage goes up then it eventually Rings + + align:start position:0% +voltage goes up then it eventually Rings + + + align:start position:0% +voltage goes up then it eventually Rings +down so I can turn them on again for + + align:start position:0% +down so I can turn them on again for + + + align:start position:0% +down so I can turn them on again for +free okay in this example this was + + align:start position:0% +free okay in this example this was + + + align:start position:0% +free okay in this example this was +coming from 100 volts in to 35 volts out + + align:start position:0% +coming from 100 volts in to 35 volts out + + + align:start position:0% +coming from 100 volts in to 35 volts out +the in this snapshot and it was it was + + align:start position:0% +the in this snapshot and it was it was + + + align:start position:0% +the in this snapshot and it was it was +running at about 8 + + align:start position:0% +running at about 8 + + + align:start position:0% +running at about 8 +MHz right so if you do your calculations + + align:start position:0% +MHz right so if you do your calculations + + + align:start position:0% +MHz right so if you do your calculations +for 100 vol volts input and running at 8 + + align:start position:0% +for 100 vol volts input and running at 8 + + + align:start position:0% +for 100 vol volts input and running at 8 +mehz you try to do that hard switch + + align:start position:0% +mehz you try to do that hard switch + + + align:start position:0% +mehz you try to do that hard switch +you're going to be very unhappy okay so + + align:start position:0% +you're going to be very unhappy okay so + + + align:start position:0% +you're going to be very unhappy okay so +one of the things is by Soft switching + + align:start position:0% +one of the things is by Soft switching + + + align:start position:0% +one of the things is by Soft switching +this thing we get to get to very high + + align:start position:0% +this thing we get to get to very high + + + align:start position:0% +this thing we get to get to very high +frequencies while main maintaining high + + align:start position:0% +frequencies while main maintaining high + + + align:start position:0% +frequencies while main maintaining high +efficiency the efficiency of that + + align:start position:0% +efficiency the efficiency of that + + + align:start position:0% +efficiency the efficiency of that +converter at that point is about + + align:start position:0% +converter at that point is about + + + align:start position:0% +converter at that point is about +97% yeah about how large is the + + align:start position:0% +97% yeah about how large is the + + + align:start position:0% +97% yeah about how large is the +parasitic capacitance across the + + align:start position:0% +parasitic capacitance across the + + + align:start position:0% +parasitic capacitance across the +transistor and do you choose a + + align:start position:0% +transistor and do you choose a + + + align:start position:0% +transistor and do you choose a +transistor based on par cap that's an + + align:start position:0% +transistor based on par cap that's an + + + align:start position:0% +transistor based on par cap that's an +excellent question + + align:start position:0% +excellent question + + + align:start position:0% +excellent question +um in this + + align:start position:0% +um in this + + + align:start position:0% +um in this +design you have to the switching + + align:start position:0% +design you have to the switching + + + align:start position:0% +design you have to the switching +frequency is going to be determined by + + align:start position:0% +frequency is going to be determined by + + + align:start position:0% +frequency is going to be determined by +the inductance value and by the net + + align:start position:0% +the inductance value and by the net + + + align:start position:0% +the inductance value and by the net +capacitance if all the net capacitance + + align:start position:0% +capacitance if all the net capacitance + + + align:start position:0% +capacitance if all the net capacitance +is provided by the switch in the trans + + align:start position:0% +is provided by the switch in the trans + + + align:start position:0% +is provided by the switch in the trans +in the diode then you very much care you + + align:start position:0% +in the diode then you very much care you + + + align:start position:0% +in the diode then you very much care you +can't throw a random switch in there you + + align:start position:0% +can't throw a random switch in there you + + + align:start position:0% +can't throw a random switch in there you +need one with the right capacitance + + align:start position:0% +need one with the right capacitance + + + align:start position:0% +need one with the right capacitance +that'll get you at the right frequency + + align:start position:0% +that'll get you at the right frequency + + + align:start position:0% +that'll get you at the right frequency +and everything else if you added you + + align:start position:0% +and everything else if you added you + + + align:start position:0% +and everything else if you added you +could and people often do add external + + align:start position:0% +could and people often do add external + + + align:start position:0% +could and people often do add external +capacitance so that then that's the + + align:start position:0% +capacitance so that then that's the + + + align:start position:0% +capacitance so that then that's the +controlled capacitance and the device + + align:start position:0% +controlled capacitance and the device + + + align:start position:0% +controlled capacitance and the device +capacitance doesn't matter as much but + + align:start position:0% +capacitance doesn't matter as much but + + + align:start position:0% +capacitance doesn't matter as much but +when you're doing this game yes you care + + align:start position:0% +when you're doing this game yes you care + + + align:start position:0% +when you're doing this game yes you care +much more about what the parasitics look + + align:start position:0% +much more about what the parasitics look + + + align:start position:0% +much more about what the parasitics look +like because you're actually using the + + align:start position:0% +like because you're actually using the + + + align:start position:0% +like because you're actually using the +parasitics here okay and I should say by + + align:start position:0% +parasitics here okay and I should say by + + + align:start position:0% +parasitics here okay and I should say by +the way I'm pretending that the device + + align:start position:0% +the way I'm pretending that the device + + + align:start position:0% +the way I'm pretending that the device +capacitance is a lossless capacitance + + align:start position:0% +capacitance is a lossless capacitance + + + align:start position:0% +capacitance is a lossless capacitance +were that it were so but you actually + + align:start position:0% +were that it were so but you actually + + + align:start position:0% +were that it were so but you actually +get some loss in that capacitance so + + align:start position:0% +get some loss in that capacitance so + + + align:start position:0% +get some loss in that capacitance so +sometimes you would like to use a + + align:start position:0% +sometimes you would like to use a + + + align:start position:0% +sometimes you would like to use a +highquality external + + align:start position:0% +highquality external + + + align:start position:0% +highquality external +capacitor um so that that ring down is + + align:start position:0% +capacitor um so that that ring down is + + + align:start position:0% +capacitor um so that that ring down is +less lossy than it would other otherwise + + align:start position:0% +less lossy than it would other otherwise + + + align:start position:0% +less lossy than it would other otherwise +be but in this case we pushed up the + + align:start position:0% +be but in this case we pushed up the + + + align:start position:0% +be but in this case we pushed up the +switching frequency so far that we could + + align:start position:0% +switching frequency so far that we could + + + align:start position:0% +switching frequency so far that we could +just do it with the device + + align:start position:0% +just do it with the device + + + align:start position:0% +just do it with the device +capacitance + + align:start position:0% +capacitance + + + align:start position:0% +capacitance +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um now the fact that this inductor is + + align:start position:0% +um now the fact that this inductor is + + + align:start position:0% +um now the fact that this inductor is +resonating with the capacitor also means + + align:start position:0% +resonating with the capacitor also means + + + align:start position:0% +resonating with the capacitor also means +you got to be very careful about how you + + align:start position:0% +you got to be very careful about how you + + + align:start position:0% +you got to be very careful about how you +size that inductor it's not can't pick + + align:start position:0% +size that inductor it's not can't pick + + + align:start position:0% +size that inductor it's not can't pick +any inductance value you got to pick the + + align:start position:0% +any inductance value you got to pick the + + + align:start position:0% +any inductance value you got to pick the +right one but it turns out to be an + + align:start position:0% +right one but it turns out to be an + + + align:start position:0% +right one but it turns out to be an +extremely small inductor because it has + + align:start position:0% +extremely small inductor because it has + + + align:start position:0% +extremely small inductor because it has +a lot of Ripple in it okay um how do we + + align:start position:0% +a lot of Ripple in it okay um how do we + + + align:start position:0% +a lot of Ripple in it okay um how do we +control Power in this converter well + + align:start position:0% +control Power in this converter well + + + align:start position:0% +control Power in this converter well +basically we can turn on this the switch + + align:start position:0% +basically we can turn on this the switch + + + align:start position:0% +basically we can turn on this the switch +until the inductor current hits the + + align:start position:0% +until the inductor current hits the + + + align:start position:0% +until the inductor current hits the +current I want it's sort of like Peak + + align:start position:0% +current I want it's sort of like Peak + + + align:start position:0% +current I want it's sort of like Peak +current control if you will but with + + align:start position:0% +current control if you will but with + + + align:start position:0% +current control if you will but with +high Ripple so this is a variable + + align:start position:0% +high Ripple so this is a variable + + + align:start position:0% +high Ripple so this is a variable +frequency converter in fact over its + + align:start position:0% +frequency converter in fact over its + + + align:start position:0% +frequency converter in fact over its +operating range this converter varies + + align:start position:0% +operating range this converter varies + + + align:start position:0% +operating range this converter varies +between like 5 and 10 megahertz so it's + + align:start position:0% +between like 5 and 10 megahertz so it's + + + align:start position:0% +between like 5 and 10 megahertz so it's +not fixed frequency pwm so if you're + + align:start position:0% +not fixed frequency pwm so if you're + + + align:start position:0% +not fixed frequency pwm so if you're +going to do this game in this design + + align:start position:0% +going to do this game in this design + + + align:start position:0% +going to do this game in this design +you've had to sort of design the whole + + align:start position:0% +you've had to sort of design the whole + + + align:start position:0% +you've had to sort of design the whole +converter and its operation its control + + align:start position:0% +converter and its operation its control + + + align:start position:0% +converter and its operation its control +all around getting soft switching so + + align:start position:0% +all around getting soft switching so + + + align:start position:0% +all around getting soft switching so +it's not like I can say I want my + + align:start position:0% +it's not like I can say I want my + + + align:start position:0% +it's not like I can say I want my +switching frequency to be this and you + + align:start position:0% +switching frequency to be this and you + + + align:start position:0% +switching frequency to be this and you +know just go design it with pwm no it + + align:start position:0% +know just go design it with pwm no it + + + align:start position:0% +know just go design it with pwm no it +the whole thing is designed around the + + align:start position:0% +the whole thing is designed around the + + + align:start position:0% +the whole thing is designed around the +soft switched + + align:start position:0% +soft switched + + + align:start position:0% +soft switched +operation any questions about + + align:start position:0% +operation any questions about + + + align:start position:0% +operation any questions about +that where might you do this I'll show + + align:start position:0% +that where might you do this I'll show + + + align:start position:0% +that where might you do this I'll show +you one more example oh I should say it + + align:start position:0% +you one more example oh I should say it + + + align:start position:0% +you one more example oh I should say it +has a limited zero voltage switching + + align:start position:0% +has a limited zero voltage switching + + + align:start position:0% +has a limited zero voltage switching +range right technically we need the + + align:start position:0% +range right technically we need the + + + align:start position:0% +range right technically we need the +output voltage to be greater than half + + align:start position:0% +output voltage to be greater than half + + + align:start position:0% +output voltage to be greater than half +the input + + align:start position:0% +the input + + + align:start position:0% +the input +voltage which is you know limits your + + align:start position:0% +voltage which is you know limits your + + + align:start position:0% +voltage which is you know limits your +buck conversion ratio that you can get + + align:start position:0% +buck conversion ratio that you can get + + + align:start position:0% +buck conversion ratio that you can get +with this converter maybe you can get + + align:start position:0% +with this converter maybe you can get + + + align:start position:0% +with this converter maybe you can get +down to a third of the input voltage + + align:start position:0% +down to a third of the input voltage + + + align:start position:0% +down to a third of the input voltage +before your your Lo switching losses + + align:start position:0% +before your your Lo switching losses + + + align:start position:0% +before your your Lo switching losses +become too big won't be quite soft + + align:start position:0% +become too big won't be quite soft + + + align:start position:0% +become too big won't be quite soft +switched but it'll be close so there are + + align:start position:0% +switched but it'll be close so there are + + + align:start position:0% +switched but it'll be close so there are +a lot of constraints around this what's + + align:start position:0% +a lot of constraints around this what's + + + align:start position:0% +a lot of constraints around this what's +your switching frequency range what's + + align:start position:0% +your switching frequency range what's + + + align:start position:0% +your switching frequency range what's +your allowed voltage conversion range + + align:start position:0% +your allowed voltage conversion range + + + align:start position:0% +your allowed voltage conversion range +what's the power range you know you've + + align:start position:0% +what's the power range you know you've + + + align:start position:0% +what's the power range you know you've +put yourself under a lot of constraints + + align:start position:0% +put yourself under a lot of constraints + + + align:start position:0% +put yourself under a lot of constraints +that maybe a normal pwm converter + + align:start position:0% +that maybe a normal pwm converter + + + align:start position:0% +that maybe a normal pwm converter +doesn't have but you get to go to high + + align:start position:0% +doesn't have but you get to go to high + + + align:start position:0% +doesn't have but you get to go to high +frequency and make everything small and + + align:start position:0% +frequency and make everything small and + + + align:start position:0% +frequency and make everything small and +react + + align:start position:0% +react + + + align:start position:0% +react +fast this is another example this is a + + align:start position:0% +fast this is another example this is a + + + align:start position:0% +fast this is another example this is a +different + + align:start position:0% +different + + + align:start position:0% +different +converter um this is a higher voltage + + align:start position:0% +converter um this is a higher voltage + + + align:start position:0% +converter um this is a higher voltage +this is for a wide input voltage range + + align:start position:0% +this is for a wide input voltage range + + + align:start position:0% +this is for a wide input voltage range +higher power this is 1 to 4 mahz you can + + align:start position:0% +higher power this is 1 to 4 mahz you can + + + align:start position:0% +higher power this is 1 to 4 mahz you can +see that we're still getting very high + + align:start position:0% +see that we're still getting very high + + + align:start position:0% +see that we're still getting very high +efficiencies across a wide power range + + align:start position:0% +efficiencies across a wide power range + + + align:start position:0% +efficiencies across a wide power range +like you know so in this example sort of + + align:start position:0% +like you know so in this example sort of + + + align:start position:0% +like you know so in this example sort of +98% this is the converter it went in + + align:start position:0% +98% this is the converter it went in + + + align:start position:0% +98% this is the converter it went in +it's actually a a uh a computer power + + align:start position:0% +it's actually a a uh a computer power + + + align:start position:0% +it's actually a a uh a computer power +supply so it has a + + align:start position:0% +supply so it has a + + + align:start position:0% +supply so it has a +rectifier and then a pair of these Buck + + align:start position:0% +rectifier and then a pair of these Buck + + + align:start position:0% +rectifier and then a pair of these Buck +converters you can see them here and + + align:start position:0% +converters you can see them here and + + + align:start position:0% +converters you can see them here and +then there's another converter to do + + align:start position:0% +then there's another converter to do + + + align:start position:0% +then there's another converter to do +isolation + + align:start position:0% +isolation + + + align:start position:0% +isolation +okay and these are the twice line + + align:start position:0% +okay and these are the twice line + + + align:start position:0% +okay and these are the twice line +frequency Energy caps but the beauty of + + align:start position:0% +frequency Energy caps but the beauty of + + + align:start position:0% +frequency Energy caps but the beauty of +doing this getting to this very high + + align:start position:0% +doing this getting to this very high + + + align:start position:0% +doing this getting to this very high +frequency this is one kind of soft + + align:start position:0% +frequency this is one kind of soft + + + align:start position:0% +frequency this is one kind of soft +switch converter the resident transition + + align:start position:0% +switch converter the resident transition + + + align:start position:0% +switch converter the resident transition +Buck converter there's another kind of + + align:start position:0% +Buck converter there's another kind of + + + align:start position:0% +Buck converter there's another kind of +soft switch converter based on what's + + align:start position:0% +soft switch converter based on what's + + + align:start position:0% +soft switch converter based on what's +known as a dual active Bridge okay but + + align:start position:0% +known as a dual active Bridge okay but + + + align:start position:0% +known as a dual active Bridge okay but +this whole converter end to end AC in to + + align:start position:0% +this whole converter end to end AC in to + + + align:start position:0% +this whole converter end to end AC in to +DC out is sort of like you know almost + + align:start position:0% +DC out is sort of like you know almost + + + align:start position:0% +DC out is sort of like you know almost +96% efficient it's sort of 80 plus + + align:start position:0% +96% efficient it's sort of 80 plus + + + align:start position:0% +96% efficient it's sort of 80 plus +Platinum rated efficiency and you know + + align:start position:0% +Platinum rated efficiency and you know + + + align:start position:0% +Platinum rated efficiency and you know +it's way out there in the combination of + + align:start position:0% +it's way out there in the combination of + + + align:start position:0% +it's way out there in the combination of +what you can get in terms of efficiency + + align:start position:0% +what you can get in terms of efficiency + + + align:start position:0% +what you can get in terms of efficiency +and power density in fact if you look at + + align:start position:0% +and power density in fact if you look at + + + align:start position:0% +and power density in fact if you look at +these designs that are way out here + + align:start position:0% +these designs that are way out here + + + align:start position:0% +these designs that are way out here +giving you high combinations of + + align:start position:0% +giving you high combinations of + + + align:start position:0% +giving you high combinations of +efficiency and power density they tend + + align:start position:0% +efficiency and power density they tend + + + align:start position:0% +efficiency and power density they tend +to all be soft switch + + align:start position:0% +to all be soft switch + + + align:start position:0% +to all be soft switch +designs if you don't care about power + + align:start position:0% +designs if you don't care about power + + + align:start position:0% +designs if you don't care about power +density you can get high efficiency but + + align:start position:0% +density you can get high efficiency but + + + align:start position:0% +density you can get high efficiency but +make it big by using a low switching + + align:start position:0% +make it big by using a low switching + + + align:start position:0% +make it big by using a low switching +frequency right but if you really want + + align:start position:0% +frequency right but if you really want + + + align:start position:0% +frequency right but if you really want +to make something small and efficient + + align:start position:0% +to make something small and efficient + + + align:start position:0% +to make something small and efficient +this is the way to + + align:start position:0% +this is the way to + + + align:start position:0% +this is the way to +go + + align:start position:0% +go + + + align:start position:0% +go +okay that's a zero voltage switching + + align:start position:0% +okay that's a zero voltage switching + + + align:start position:0% +okay that's a zero voltage switching +example and you can see by the way + + align:start position:0% +example and you can see by the way + + + align:start position:0% +example and you can see by the way +there's sort of a duel between zvs turn + + align:start position:0% +there's sort of a duel between zvs turn + + + align:start position:0% +there's sort of a duel between zvs turn +off and zcs turn on and zcs turn + + align:start position:0% +off and zcs turn on and zcs turn + + + align:start position:0% +off and zcs turn on and zcs turn +on and uh zvs I'm sorry zcs turn off and + + align:start position:0% +on and uh zvs I'm sorry zcs turn off and + + + align:start position:0% +on and uh zvs I'm sorry zcs turn off and +zvs turn on Okay so you can do any + + align:start position:0% +zvs turn on Okay so you can do any + + + align:start position:0% +zvs turn on Okay so you can do any +combination of these techniques that you + + align:start position:0% +combination of these techniques that you + + + align:start position:0% +combination of these techniques that you +want they're not all created equal + + align:start position:0% +want they're not all created equal + + + align:start position:0% +want they're not all created equal +however okay + + align:start position:0% +however okay + + + align:start position:0% +however okay +why um all devices have some internal + + align:start position:0% +why um all devices have some internal + + + align:start position:0% +why um all devices have some internal +parasitic capacitance right so even if I + + align:start position:0% +parasitic capacitance right so even if I + + + align:start position:0% +parasitic capacitance right so even if I +turn this switch on with zero current + + align:start position:0% +turn this switch on with zero current + + + align:start position:0% +turn this switch on with zero current +coming from + + align:start position:0% +coming from + + + align:start position:0% +coming from +here if he has voltage across him I + + align:start position:0% +here if he has voltage across him I + + + align:start position:0% +here if he has voltage across him I +still dissipate energy in the + + align:start position:0% +still dissipate energy in the + + + align:start position:0% +still dissipate energy in the +switch right so if I want to think + + align:start position:0% +switch right so if I want to think + + + align:start position:0% +switch right so if I want to think +about the energy associated with the + + align:start position:0% +about the energy associated with the + + + align:start position:0% +about the energy associated with the +switch + + align:start position:0% +switch + + + align:start position:0% +switch +capacitance um I really need zero + + align:start position:0% +capacitance um I really need zero + + + align:start position:0% +capacitance um I really need zero +voltage + + align:start position:0% +voltage + + + align:start position:0% +voltage +switching on the other hand if I had a + + align:start position:0% +switching on the other hand if I had a + + + align:start position:0% +switching on the other hand if I had a +switch that was in a package with a huge + + align:start position:0% +switch that was in a package with a huge + + + align:start position:0% +switch that was in a package with a huge +inductance right zero volt turning on + + align:start position:0% +inductance right zero volt turning on + + + align:start position:0% +inductance right zero volt turning on +this on and off with voltage will not + + align:start position:0% +this on and off with voltage will not + + + align:start position:0% +this on and off with voltage will not +help me if I have energy energ stored in + + align:start position:0% +help me if I have energy energ stored in + + + align:start position:0% +help me if I have energy energ stored in +this parasitic inductance right so + + align:start position:0% +this parasitic inductance right so + + + align:start position:0% +this parasitic inductance right so +depending upon whether I had a lot of + + align:start position:0% +depending upon whether I had a lot of + + + align:start position:0% +depending upon whether I had a lot of +capacitance or I had a lot of inductance + + align:start position:0% +capacitance or I had a lot of inductance + + + align:start position:0% +capacitance or I had a lot of inductance +I might think about doing one or the + + align:start position:0% +I might think about doing one or the + + + align:start position:0% +I might think about doing one or the +other + + align:start position:0% +other + + + align:start position:0% +other +parasitically to go to really high + + align:start position:0% +parasitically to go to really high + + + align:start position:0% +parasitically to go to really high +frequencies where sort of many people in + + align:start position:0% +frequencies where sort of many people in + + + align:start position:0% +frequencies where sort of many people in +my group design converters we tend to + + align:start position:0% +my group design converters we tend to + + + align:start position:0% +my group design converters we tend to +focus on zero voltage switching because + + align:start position:0% +focus on zero voltage switching because + + + align:start position:0% +focus on zero voltage switching because +that lets you push up the switching + + align:start position:0% +that lets you push up the switching + + + align:start position:0% +that lets you push up the switching +frequency in the face of the device + + align:start position:0% +frequency in the face of the device + + + align:start position:0% +frequency in the face of the device +capacitance as being very important but + + align:start position:0% +capacitance as being very important but + + + align:start position:0% +capacitance as being very important but +that's a design decision and in fact + + align:start position:0% +that's a design decision and in fact + + + align:start position:0% +that's a design decision and in fact +that's why there's so many different + + align:start position:0% +that's why there's so many different + + + align:start position:0% +that's why there's so many different +techniques I'm only showing you examples + + align:start position:0% +techniques I'm only showing you examples + + + align:start position:0% +techniques I'm only showing you examples +of these techniques there's a lot of + + align:start position:0% +of these techniques there's a lot of + + + align:start position:0% +of these techniques there's a lot of +different ones because different devices + + align:start position:0% +different ones because different devices + + + align:start position:0% +different ones because different devices +different applications and operating + + align:start position:0% +different applications and operating + + + align:start position:0% +different applications and operating +range all might drive you towards a + + align:start position:0% +range all might drive you towards a + + + align:start position:0% +range all might drive you towards a +different circuit that would have + + align:start position:0% +different circuit that would have + + + align:start position:0% +different circuit that would have +advantage or disadvantage okay and + + align:start position:0% +advantage or disadvantage okay and + + + align:start position:0% +advantage or disadvantage okay and +that's part of the art of Designing a + + align:start position:0% +that's part of the art of Designing a + + + align:start position:0% +that's part of the art of Designing a +high performance converter is knowing + + align:start position:0% +high performance converter is knowing + + + align:start position:0% +high performance converter is knowing +which technique to pick in what + + align:start position:0% +which technique to pick in what + + + align:start position:0% +which technique to pick in what +application and what topology and what + + align:start position:0% +application and what topology and what + + + align:start position:0% +application and what topology and what +control mode to + + align:start position:0% + + + + align:start position:0% + +use let's talk about this one this is a + + align:start position:0% +use let's talk about this one this is a + + + align:start position:0% +use let's talk about this one this is a +zeroc current switch quasi resonant Buck + + align:start position:0% +zeroc current switch quasi resonant Buck + + + align:start position:0% +zeroc current switch quasi resonant Buck +converter um this is part of a + + align:start position:0% +converter um this is part of a + + + align:start position:0% +converter um this is part of a +particular flavor of soft switch + + align:start position:0% +particular flavor of soft switch + + + align:start position:0% +particular flavor of soft switch +converters in this paper reference here + + align:start position:0% +converters in this paper reference here + + + align:start position:0% +converters in this paper reference here +this is actually very famous paper from + + align:start position:0% +this is actually very famous paper from + + + align:start position:0% +this is actually very famous paper from +the late + + align:start position:0% +the late + + + align:start position:0% +the late +1980s um and you will see commercial + + align:start position:0% +1980s um and you will see commercial + + + align:start position:0% +1980s um and you will see commercial +converters using the Quasi resonant + + align:start position:0% +converters using the Quasi resonant + + + align:start position:0% +converters using the Quasi resonant +technique either zvs quasi resonant or + + align:start position:0% +technique either zvs quasi resonant or + + + align:start position:0% +technique either zvs quasi resonant or +zcs quasi resonant it's not as popular + + align:start position:0% +zcs quasi resonant it's not as popular + + + align:start position:0% +zcs quasi resonant it's not as popular +as it used to be but I thought I'd + + align:start position:0% +as it used to be but I thought I'd + + + align:start position:0% +as it used to be but I thought I'd +illustrate a zeroc current switch + + align:start position:0% +illustrate a zeroc current switch + + + align:start position:0% +illustrate a zeroc current switch +converter so if I look at this converter + + align:start position:0% +converter so if I look at this converter + + + align:start position:0% +converter so if I look at this converter +what do I see if I I took away CR and LR + + align:start position:0% +what do I see if I I took away CR and LR + + + align:start position:0% +what do I see if I I took away CR and LR +and I just took them out what kind of + + align:start position:0% +and I just took them out what kind of + + + align:start position:0% +and I just took them out what kind of +converter would this + + align:start position:0% +converter would this + + + align:start position:0% +converter would this +be just be a straight up Buck converter + + align:start position:0% +be just be a straight up Buck converter + + + align:start position:0% +be just be a straight up Buck converter +right what we are doing is we're putting + + align:start position:0% +right what we are doing is we're putting + + + align:start position:0% +right what we are doing is we're putting +a resonant inductor in series with the + + align:start position:0% +a resonant inductor in series with the + + + align:start position:0% +a resonant inductor in series with the +switch so if you told me nothing else + + align:start position:0% +switch so if you told me nothing else + + + align:start position:0% +switch so if you told me nothing else +about this converter and I looked at + + align:start position:0% +about this converter and I looked at + + + align:start position:0% +about this converter and I looked at +that I'd say boy they're probably using + + align:start position:0% +that I'd say boy they're probably using + + + align:start position:0% +that I'd say boy they're probably using +zero current switching because I got + + align:start position:0% +zero current switching because I got + + + align:start position:0% +zero current switching because I got +this inductor in series with the switch + + align:start position:0% +this inductor in series with the switch + + + align:start position:0% +this inductor in series with the switch +and I don't want to you know I I + + align:start position:0% +and I don't want to you know I I + + + align:start position:0% +and I don't want to you know I I +probably that will let me turn on the + + align:start position:0% +probably that will let me turn on the + + + align:start position:0% +probably that will let me turn on the +switch and hold the current low in it + + align:start position:0% +switch and hold the current low in it + + + align:start position:0% +switch and hold the current low in it +right that would be zcs turn on right + + align:start position:0% +right that would be zcs turn on right + + + align:start position:0% +right that would be zcs turn on right +this + + align:start position:0% +this + + + align:start position:0% +this +trick and then that probably means I + + align:start position:0% +trick and then that probably means I + + + align:start position:0% +trick and then that probably means I +need zcs turn off too because if I turn + + align:start position:0% +need zcs turn off too because if I turn + + + align:start position:0% +need zcs turn off too because if I turn +off the switch when current's in that + + align:start position:0% +off the switch when current's in that + + + align:start position:0% +off the switch when current's in that +inductor I'm going to be + + align:start position:0% +inductor I'm going to be + + + align:start position:0% +inductor I'm going to be +unhappy okay so how does this thing + + align:start position:0% +unhappy okay so how does this thing + + + align:start position:0% +unhappy okay so how does this thing +work suppose the diode is conducting + + align:start position:0% +work suppose the diode is conducting + + + align:start position:0% +work suppose the diode is conducting +right so this is acting like a buck + + align:start position:0% +right so this is acting like a buck + + + align:start position:0% +right so this is acting like a buck +converter I'm going to commutate between + + align:start position:0% +converter I'm going to commutate between + + + align:start position:0% +converter I'm going to commutate between +the switch on and the diode on but + + align:start position:0% +the switch on and the diode on but + + + align:start position:0% +the switch on and the diode on but +suppose the diode's conducting this + + align:start position:0% +suppose the diode's conducting this + + + align:start position:0% +suppose the diode's conducting this +inductor here is just a giant inductor + + align:start position:0% +inductor here is just a giant inductor + + + align:start position:0% +inductor here is just a giant inductor +so think of him having as having a + + align:start position:0% +so think of him having as having a + + + align:start position:0% +so think of him having as having a +constant current right when I want + + align:start position:0% +constant current right when I want + + + align:start position:0% +constant current right when I want +to switch I want to turn the switch + + align:start position:0% +to switch I want to turn the switch + + + align:start position:0% +to switch I want to turn the switch +on fine I just turn the switch on he + + align:start position:0% +on fine I just turn the switch on he + + + align:start position:0% +on fine I just turn the switch on he +turns on under zero current because he's + + align:start position:0% +turns on under zero current because he's + + + align:start position:0% +turns on under zero current because he's +in series with this + + align:start position:0% +in series with this + + + align:start position:0% +in series with this +inductor okay so I get this kind of + + align:start position:0% +inductor okay so I get this kind of + + + align:start position:0% +inductor okay so I get this kind of +switching transition he can turn on at + + align:start position:0% +switching transition he can turn on at + + + align:start position:0% +switching transition he can turn on at +low loss at least ignoring his switch + + align:start position:0% + + + + align:start position:0% + +capacitance all right once the switch is + + align:start position:0% +capacitance all right once the switch is + + + align:start position:0% +capacitance all right once the switch is +on now I have VN across the inductor and + + align:start position:0% +on now I have VN across the inductor and + + + align:start position:0% +on now I have VN across the inductor and +the diode's conducting so I basically + + align:start position:0% +the diode's conducting so I basically + + + align:start position:0% +the diode's conducting so I basically +have VN across this resonant inductor + + align:start position:0% +have VN across this resonant inductor + + + align:start position:0% +have VN across this resonant inductor +and the current in the inductor is going + + align:start position:0% +and the current in the inductor is going + + + align:start position:0% +and the current in the inductor is going +to ramp up linearly that's this picture + + align:start position:0% +to ramp up linearly that's this picture + + + align:start position:0% +to ramp up linearly that's this picture +here okay the current in this inductor + + align:start position:0% +here okay the current in this inductor + + + align:start position:0% +here okay the current in this inductor +is going to ramp up linearly eventually + + align:start position:0% +is going to ramp up linearly eventually + + + align:start position:0% +is going to ramp up linearly eventually +the current in the inductor is going to + + align:start position:0% +the current in the inductor is going to + + + align:start position:0% +the current in the inductor is going to +exceed the output current and the + + align:start position:0% +exceed the output current and the + + + align:start position:0% +exceed the output current and the +diode's going to turn + + align:start position:0% +diode's going to turn + + + align:start position:0% +diode's going to turn +off once the diode turns off basically + + align:start position:0% +off once the diode turns off basically + + + align:start position:0% +off once the diode turns off basically +now LR still this no is still at zero + + align:start position:0% +now LR still this no is still at zero + + + align:start position:0% +now LR still this no is still at zero +voltage LR is going to resonate with CR + + align:start position:0% +voltage LR is going to resonate with CR + + + align:start position:0% +voltage LR is going to resonate with CR +here and I'm going to have a current + + align:start position:0% +here and I'm going to have a current + + + align:start position:0% +here and I'm going to have a current +pulse ilr that's going to do this it's + + align:start position:0% +pulse ilr that's going to do this it's + + + align:start position:0% +pulse ilr that's going to do this it's +going to ring up it it was linearly + + align:start position:0% +going to ring up it it was linearly + + + align:start position:0% +going to ring up it it was linearly +charging and then it rings up and then + + align:start position:0% +charging and then it rings up and then + + + align:start position:0% +charging and then it rings up and then +this voltage is going to get bigger than + + align:start position:0% +this voltage is going to get bigger than + + + align:start position:0% +this voltage is going to get bigger than +the input voltage and it's going to ring + + align:start position:0% +the input voltage and it's going to ring + + + align:start position:0% +the input voltage and it's going to ring +down and eventually the current is going + + align:start position:0% +down and eventually the current is going + + + align:start position:0% +down and eventually the current is going +to + + align:start position:0% +to + + + align:start position:0% +to +reverse and charge back this way + + align:start position:0% +reverse and charge back this way + + + align:start position:0% +reverse and charge back this way +once the current's charging back this + + align:start position:0% +once the current's charging back this + + + align:start position:0% +once the current's charging back this +way that means it's going through this + + align:start position:0% +way that means it's going through this + + + align:start position:0% +way that means it's going through this +diode I can turn the FED + + align:start position:0% +diode I can turn the FED + + + align:start position:0% +diode I can turn the FED +off when the fet's off once ilr goes to + + align:start position:0% +off when the fet's off once ilr goes to + + + align:start position:0% +off when the fet's off once ilr goes to +zero again everything just stays + + align:start position:0% +zero again everything just stays + + + align:start position:0% +zero again everything just stays +off and during that time period this + + align:start position:0% +off and during that time period this + + + align:start position:0% +off and during that time period this +diode's going to be conducting again + + align:start position:0% +diode's going to be conducting again + + + align:start position:0% +diode's going to be conducting again +right so we're going to basically take a + + align:start position:0% +right so we're going to basically take a + + + align:start position:0% +right so we're going to basically take a +buck converter and put this LR and CR in + + align:start position:0% +buck converter and put this LR and CR in + + + align:start position:0% +buck converter and put this LR and CR in +it so that basically when I turn on the + + align:start position:0% +it so that basically when I turn on the + + + align:start position:0% +it so that basically when I turn on the +transistor I get a resonant pulse of + + align:start position:0% +transistor I get a resonant pulse of + + + align:start position:0% +transistor I get a resonant pulse of +current current and return to zero and + + align:start position:0% +current current and return to zero and + + + align:start position:0% +current current and return to zero and +then the diode's going to conduct again + + align:start position:0% +then the diode's going to conduct again + + + align:start position:0% +then the diode's going to conduct again +essentially okay because when this I + + align:start position:0% +essentially okay because when this I + + + align:start position:0% +essentially okay because when this I +should have should have been clear this + + align:start position:0% +should have should have been clear this + + + align:start position:0% +should have should have been clear this +Rings up VCR Peaks and then VCR Rings + + align:start position:0% +Rings up VCR Peaks and then VCR Rings + + + align:start position:0% +Rings up VCR Peaks and then VCR Rings +down to zero and the diode picks up the + + align:start position:0% +down to zero and the diode picks up the + + + align:start position:0% +down to zero and the diode picks up the +current so what happens is I have a + + align:start position:0% +current so what happens is I have a + + + align:start position:0% +current so what happens is I have a +situation where this diode's carrying + + align:start position:0% +situation where this diode's carrying + + + align:start position:0% +situation where this diode's carrying +the output current except for pulses + + align:start position:0% +the output current except for pulses + + + align:start position:0% +the output current except for pulses +when I trip this device + + align:start position:0% +when I trip this device + + + align:start position:0% +when I trip this device +on okay and depending upon how often I + + align:start position:0% +on okay and depending upon how often I + + + align:start position:0% +on okay and depending upon how often I +trip this device on I get more and more + + align:start position:0% +trip this device on I get more and more + + + align:start position:0% +trip this device on I get more and more +Pulses from the input okay so this is + + align:start position:0% +Pulses from the input okay so this is + + + align:start position:0% +Pulses from the input okay so this is +another technique we're going to use + + align:start position:0% +another technique we're going to use + + + align:start position:0% +another technique we're going to use +resonant elements introduced into the + + align:start position:0% +resonant elements introduced into the + + + align:start position:0% +resonant elements introduced into the +circuit it doesn't look anything like a + + align:start position:0% +circuit it doesn't look anything like a + + + align:start position:0% +circuit it doesn't look anything like a +pwm converter I'm getting these resonant + + align:start position:0% +pwm converter I'm getting these resonant + + + align:start position:0% +pwm converter I'm getting these resonant +Pulses from the input and it turns out + + align:start position:0% +Pulses from the input and it turns out + + + align:start position:0% +Pulses from the input and it turns out +that the average voltage at this node + + align:start position:0% +that the average voltage at this node + + + align:start position:0% +that the average voltage at this node +which determines the average output + + align:start position:0% +which determines the average output + + + align:start position:0% +which determines the average output +voltage is precisely determined by how + + align:start position:0% +voltage is precisely determined by how + + + align:start position:0% +voltage is precisely determined by how +often I trip this switch on relative to + + align:start position:0% +often I trip this switch on relative to + + + align:start position:0% +often I trip this switch on relative to +the resonant frequency okay so it's + + align:start position:0% +the resonant frequency okay so it's + + + align:start position:0% +the resonant frequency okay so it's +actually really a frequency controlled + + align:start position:0% +actually really a frequency controlled + + + align:start position:0% +actually really a frequency controlled +comp + + align:start position:0% +comp + + + align:start position:0% +comp +inverter okay if I if I trip the switch + + align:start position:0% +inverter okay if I if I trip the switch + + + align:start position:0% +inverter okay if I if I trip the switch +on a lot I get a higher output voltage + + align:start position:0% +on a lot I get a higher output voltage + + + align:start position:0% +on a lot I get a higher output voltage +if I trip the switch on occasionally I + + align:start position:0% +if I trip the switch on occasionally I + + + align:start position:0% +if I trip the switch on occasionally I +get a lower output + + align:start position:0% +get a lower output + + + align:start position:0% +get a lower output +voltage + + align:start position:0% +voltage + + + align:start position:0% +voltage +okay so why might I do this + + align:start position:0% +okay so why might I do this + + + align:start position:0% +okay so why might I do this +technique well notice that the current + + align:start position:0% +technique well notice that the current + + + align:start position:0% +technique well notice that the current +in the switch is very smooth right very + + align:start position:0% +in the switch is very smooth right very + + + align:start position:0% +in the switch is very smooth right very +low Emi that's kind of + + align:start position:0% +low Emi that's kind of + + + align:start position:0% +low Emi that's kind of +nice uh the overlap switching loss is + + align:start position:0% +nice uh the overlap switching loss is + + + align:start position:0% +nice uh the overlap switching loss is +gone because of the zero current + + align:start position:0% +gone because of the zero current + + + align:start position:0% +gone because of the zero current +switching although I still have the + + align:start position:0% +switching although I still have the + + + align:start position:0% +switching although I still have the +capacitive discharge lost in the switch + + align:start position:0% +capacitive discharge lost in the switch + + + align:start position:0% +capacitive discharge lost in the switch +um so it has some + + align:start position:0% +um so it has some + + + align:start position:0% +um so it has some +advantages on the other hand I can still + + align:start position:0% +advantages on the other hand I can still + + + align:start position:0% +advantages on the other hand I can still +get ringing between the device + + align:start position:0% +get ringing between the device + + + align:start position:0% +get ringing between the device +capacitance and the resonant inductance + + align:start position:0% +capacitance and the resonant inductance + + + align:start position:0% +capacitance and the resonant inductance +I can still have problems with ringing + + align:start position:0% +I can still have problems with ringing + + + align:start position:0% +I can still have problems with ringing +so this this kind of technique is good + + align:start position:0% +so this this kind of technique is good + + + align:start position:0% +so this this kind of technique is good +to moderate frequencies but not super + + align:start position:0% +to moderate frequencies but not super + + + align:start position:0% +to moderate frequencies but not super +high frequencies it might be good for a + + align:start position:0% +high frequencies it might be good for a + + + align:start position:0% +high frequencies it might be good for a +device type that likes to turn on and + + align:start position:0% +device type that likes to turn on and + + + align:start position:0% +device type that likes to turn on and +off a low current in + + align:start position:0% +off a low current in + + + align:start position:0% +off a low current in +it + + align:start position:0% +it + + + align:start position:0% +it +okay + + align:start position:0% + + + + align:start position:0% + +um other other limits because I have + + align:start position:0% +um other other limits because I have + + + align:start position:0% +um other other limits because I have +these pulsy kind of waveforms I tend to + + align:start position:0% +these pulsy kind of waveforms I tend to + + + align:start position:0% +these pulsy kind of waveforms I tend to +have a lot of reactive power transfer in + + align:start position:0% +have a lot of reactive power transfer in + + + align:start position:0% +have a lot of reactive power transfer in +this circuit it's not like I've got + + align:start position:0% +this circuit it's not like I've got + + + align:start position:0% +this circuit it's not like I've got +Square wave voltages and currents and + + align:start position:0% +Square wave voltages and currents and + + + align:start position:0% +Square wave voltages and currents and +I'm kind of optimizing how power flows + + align:start position:0% +I'm kind of optimizing how power flows + + + align:start position:0% +I'm kind of optimizing how power flows +through the circuit um and I also tend + + align:start position:0% +through the circuit um and I also tend + + + align:start position:0% +through the circuit um and I also tend +to have increased device stress so this + + align:start position:0% +to have increased device stress so this + + + align:start position:0% +to have increased device stress so this +diode instead of being rated for the + + align:start position:0% +diode instead of being rated for the + + + align:start position:0% +diode instead of being rated for the +input voltage like a normal Buck + + align:start position:0% +input voltage like a normal Buck + + + align:start position:0% +input voltage like a normal Buck +converter might be rated for twice the + + align:start position:0% +converter might be rated for twice the + + + align:start position:0% +converter might be rated for twice the +input voltage all right so I've gotten + + align:start position:0% +input voltage all right so I've gotten + + + align:start position:0% +input voltage all right so I've gotten +some things I've gotten some reduced + + align:start position:0% +some things I've gotten some reduced + + + align:start position:0% +some things I've gotten some reduced +switching loss but I've had to entirely + + align:start position:0% +switching loss but I've had to entirely + + + align:start position:0% +switching loss but I've had to entirely +compromise everything about my converter + + align:start position:0% +compromise everything about my converter + + + align:start position:0% +compromise everything about my converter +to get it + + align:start position:0% +to get it + + + align:start position:0% +to get it +any questions about + + align:start position:0% + + + + align:start position:0% + +that now I would characterize that as + + align:start position:0% +that now I would characterize that as + + + align:start position:0% +that now I would characterize that as +one sort of flavor of soft switch + + align:start position:0% +one sort of flavor of soft switch + + + align:start position:0% +one sort of flavor of soft switch +converters where you design the sort of + + align:start position:0% +converters where you design the sort of + + + align:start position:0% +converters where you design the sort of +the whole converter around the switching + + align:start position:0% +the whole converter around the switching + + + align:start position:0% +the whole converter around the switching +regime to get you the nice soft switched + + align:start position:0% +regime to get you the nice soft switched + + + align:start position:0% +regime to get you the nice soft switched +operation so how you control it how you + + align:start position:0% +operation so how you control it how you + + + align:start position:0% +operation so how you control it how you +pick the components all of that stuff is + + align:start position:0% +pick the components all of that stuff is + + + align:start position:0% +pick the components all of that stuff is +100% determined by getting soft + + align:start position:0% +100% determined by getting soft + + + align:start position:0% +100% determined by getting soft +switching and keeping soft switching + + align:start position:0% +switching and keeping soft switching + + + align:start position:0% +switching and keeping soft switching +where you want it okay so that's sort of + + align:start position:0% +where you want it okay so that's sort of + + + align:start position:0% +where you want it okay so that's sort of +like there's + + align:start position:0% +like there's + + + align:start position:0% +like there's +there's all kinds of classes of soft + + align:start position:0% +there's all kinds of classes of soft + + + align:start position:0% +there's all kinds of classes of soft +switch converter that you can talk about + + align:start position:0% +switch converter that you can talk about + + + align:start position:0% +switch converter that you can talk about +but a big category is circuits that sort + + align:start position:0% +but a big category is circuits that sort + + + align:start position:0% +but a big category is circuits that sort +of you design the circuit around getting + + align:start position:0% +of you design the circuit around getting + + + align:start position:0% +of you design the circuit around getting +the magic operating waveform somehow + + align:start position:0% +the magic operating waveform somehow + + + align:start position:0% +the magic operating waveform somehow +okay another class is how can I augment + + align:start position:0% +okay another class is how can I augment + + + align:start position:0% +okay another class is how can I augment +a standard pwm converter with some extra + + align:start position:0% +a standard pwm converter with some extra + + + align:start position:0% +a standard pwm converter with some extra +circuitry that'll let me run it just + + align:start position:0% +circuitry that'll let me run it just + + + align:start position:0% +circuitry that'll let me run it just +like a normal pwm converter everything + + align:start position:0% +like a normal pwm converter everything + + + align:start position:0% +like a normal pwm converter everything +we've been doing all semester but still + + align:start position:0% +we've been doing all semester but still + + + align:start position:0% +we've been doing all semester but still +soft switch the transistors recover the + + align:start position:0% +soft switch the transistors recover the + + + align:start position:0% +soft switch the transistors recover the +energy in any snubbing and still run it + + align:start position:0% +energy in any snubbing and still run it + + + align:start position:0% +energy in any snubbing and still run it +like a normal converter okay and I'm + + align:start position:0% +like a normal converter okay and I'm + + + align:start position:0% +like a normal converter okay and I'm +sort of almost out of time but I'll + + align:start position:0% +sort of almost out of time but I'll + + + align:start position:0% +sort of almost out of time but I'll +point + + align:start position:0% +point + + + align:start position:0% +point +to one + + align:start position:0% +to one + + + align:start position:0% +to one +example and I'll just give you a notion + + align:start position:0% +example and I'll just give you a notion + + + align:start position:0% +example and I'll just give you a notion +of this and in fact this circuit or a + + align:start position:0% +of this and in fact this circuit or a + + + align:start position:0% +of this and in fact this circuit or a +close version is described in uh + + align:start position:0% +close version is described in uh + + + align:start position:0% +close version is described in uh +kpvs the uh snubbers and soft switching + + align:start position:0% +kpvs the uh snubbers and soft switching + + + align:start position:0% +kpvs the uh snubbers and soft switching +chapter + + align:start position:0% +chapter + + + align:start position:0% +chapter +um here's the idea if I ignore + + align:start position:0% + + + + align:start position:0% + +this LR D1 and S1 what would this + + align:start position:0% +this LR D1 and S1 what would this + + + align:start position:0% +this LR D1 and S1 what would this +circuit and CR if I ignore these + + align:start position:0% +circuit and CR if I ignore these + + + align:start position:0% +circuit and CR if I ignore these +elements what would this circuit be just + + align:start position:0% +elements what would this circuit be just + + + align:start position:0% +elements what would this circuit be just +be a standard boost converter + + align:start position:0% +be a standard boost converter + + + align:start position:0% +be a standard boost converter +right and what we want to do is think + + align:start position:0% +right and what we want to do is think + + + align:start position:0% +right and what we want to do is think +about designing a boost + + align:start position:0% + + + + align:start position:0% + +converter you know so here's my standard + + align:start position:0% +converter you know so here's my standard + + + align:start position:0% +converter you know so here's my standard +boost converter if I if I worked out + + align:start position:0% +boost converter if I if I worked out + + + align:start position:0% +boost converter if I if I worked out +what the switching losses of this thing + + align:start position:0% +what the switching losses of this thing + + + align:start position:0% +what the switching losses of this thing +were right I have + + align:start position:0% + + + + align:start position:0% + +um I have basically the fact that he's + + align:start position:0% +um I have basically the fact that he's + + + align:start position:0% +um I have basically the fact that he's +going to turn on you know turn on and + + align:start position:0% +going to turn on you know turn on and + + + align:start position:0% +going to turn on you know turn on and +turn off loss of this guy and then diode + + align:start position:0% +turn off loss of this guy and then diode + + + align:start position:0% +turn off loss of this guy and then diode +reverse recovery is also often a big + + align:start position:0% +reverse recovery is also often a big + + + align:start position:0% +reverse recovery is also often a big +deal okay well what happens if I came + + align:start position:0% +deal okay well what happens if I came + + + align:start position:0% +deal okay well what happens if I came +along and said look um I want to help so + + align:start position:0% +along and said look um I want to help so + + + align:start position:0% +along and said look um I want to help so +I'm going to go put a snubber capacitor + + align:start position:0% +I'm going to go put a snubber capacitor + + + align:start position:0% +I'm going to go put a snubber capacitor +across my device and give myself Z + + align:start position:0% +across my device and give myself Z + + + align:start position:0% +across my device and give myself Z +voltage turn off right this would still + + align:start position:0% +voltage turn off right this would still + + + align:start position:0% +voltage turn off right this would still +work just like a boost converter right I + + align:start position:0% +work just like a boost converter right I + + + align:start position:0% +work just like a boost converter right I +can turn them off he captures the energy + + align:start position:0% +can turn them off he captures the energy + + + align:start position:0% +can turn them off he captures the energy +and the only problem I have now is that + + align:start position:0% +and the only problem I have now is that + + + align:start position:0% +and the only problem I have now is that +when I turn the switch on I'm going to + + align:start position:0% +when I turn the switch on I'm going to + + + align:start position:0% +when I turn the switch on I'm going to +dump that capacitor energy right so + + align:start position:0% +dump that capacitor energy right so + + + align:start position:0% +dump that capacitor energy right so +maybe I can come up with a circuit that + + align:start position:0% +maybe I can come up with a circuit that + + + align:start position:0% +maybe I can come up with a circuit that +just when I want to go turn the switch + + align:start position:0% +just when I want to go turn the switch + + + align:start position:0% +just when I want to go turn the switch +back on will suck the energy off that + + align:start position:0% +back on will suck the energy off that + + + align:start position:0% +back on will suck the energy off that +capacitor and let me turn on the switch + + align:start position:0% +capacitor and let me turn on the switch + + + align:start position:0% +capacitor and let me turn on the switch +with zero + + align:start position:0% +with zero + + + align:start position:0% +with zero +voltage and the way they do that a very + + align:start position:0% +voltage and the way they do that a very + + + align:start position:0% +voltage and the way they do that a very +clever design is they put in a another + + align:start position:0% +clever design is they put in a another + + + align:start position:0% +clever design is they put in a another +little baby boost circuit like + + align:start position:0% +little baby boost circuit like + + + align:start position:0% +little baby boost circuit like +this and what it'll do is the orange + + align:start position:0% +this and what it'll do is the orange + + + align:start position:0% +this and what it'll do is the orange +circuit doesn't do anything it's you + + align:start position:0% +circuit doesn't do anything it's you + + + align:start position:0% +circuit doesn't do anything it's you +know it's normally off when I turn off + + align:start position:0% +know it's normally off when I turn off + + + align:start position:0% +know it's normally off when I turn off +the switch the capacitor gives me zero + + align:start position:0% +the switch the capacitor gives me zero + + + align:start position:0% +the switch the capacitor gives me zero +voltage switching but other than that it + + align:start position:0% +voltage switching but other than that it + + + align:start position:0% +voltage switching but other than that it +looks just like a normal pwm converter + + align:start position:0% +looks just like a normal pwm converter + + + align:start position:0% +looks just like a normal pwm converter +when I get to the end of the cycle and I + + align:start position:0% +when I get to the end of the cycle and I + + + align:start position:0% +when I get to the end of the cycle and I +want to turn the switch back on what I + + align:start position:0% +want to turn the switch back on what I + + + align:start position:0% +want to turn the switch back on what I +do is I quickly trip on the orang + + align:start position:0% +do is I quickly trip on the orang + + + align:start position:0% +do is I quickly trip on the orang +circuit and basically use this inductor + + align:start position:0% +circuit and basically use this inductor + + + align:start position:0% +circuit and basically use this inductor +to suck all the charge off of this + + align:start position:0% +to suck all the charge off of this + + + align:start position:0% +to suck all the charge off of this +capacitor + + align:start position:0% +capacitor + + + align:start position:0% +capacitor +and recover the energy on this capacitor + + align:start position:0% +and recover the energy on this capacitor + + + align:start position:0% +and recover the energy on this capacitor +at which point I can turn on this + + align:start position:0% +at which point I can turn on this + + + align:start position:0% +at which point I can turn on this +converter with zero voltage switching + + align:start position:0% +converter with zero voltage switching + + + align:start position:0% +converter with zero voltage switching +turn on this transistor with zero + + align:start position:0% +turn on this transistor with zero + + + align:start position:0% +turn on this transistor with zero +voltage switching and then the orange + + align:start position:0% +voltage switching and then the orange + + + align:start position:0% +voltage switching and then the orange +circuit what do I do is I turn this + + align:start position:0% +circuit what do I do is I turn this + + + align:start position:0% +circuit what do I do is I turn this +thing off and this inductor current goes + + align:start position:0% +thing off and this inductor current goes + + + align:start position:0% +thing off and this inductor current goes +to the output and gets delivered okay so + + align:start position:0% +to the output and gets delivered okay so + + + align:start position:0% +to the output and gets delivered okay so +the orange circuit is essentially his + + align:start position:0% +the orange circuit is essentially his + + + align:start position:0% +the orange circuit is essentially his +entire job he only runs once in a little + + align:start position:0% +entire job he only runs once in a little + + + align:start position:0% +entire job he only runs once in a little +for a very short time to basically + + align:start position:0% +for a very short time to basically + + + align:start position:0% +for a very short time to basically +recover the energy that's on the + + align:start position:0% +recover the energy that's on the + + + align:start position:0% +recover the energy that's on the +capacitor so I can get Z volt Vol turn + + align:start position:0% +capacitor so I can get Z volt Vol turn + + + align:start position:0% +capacitor so I can get Z volt Vol turn +off and zero voltage turn on this is + + align:start position:0% +off and zero voltage turn on this is + + + align:start position:0% +off and zero voltage turn on this is +called the zero voltage transition + + align:start position:0% +called the zero voltage transition + + + align:start position:0% +called the zero voltage transition +converter um the main converter in white + + align:start position:0% +converter um the main converter in white + + + align:start position:0% +converter um the main converter in white +is soft + + align:start position:0% +is soft + + + align:start position:0% +is soft +switched this + + align:start position:0% +switched this + + + align:start position:0% +switched this +converter um is got zero current + + align:start position:0% +converter um is got zero current + + + align:start position:0% +converter um is got zero current +switching okay but still this guy's + + align:start position:0% +switching okay but still this guy's + + + align:start position:0% +switching okay but still this guy's +still turning on and off at zero voltage + + align:start position:0% +still turning on and off at zero voltage + + + align:start position:0% +still turning on and off at zero voltage +he's got a very high peak pulse power + + align:start position:0% +he's got a very high peak pulse power + + + align:start position:0% +he's got a very high peak pulse power +but nonetheless as long as I use this + + align:start position:0% +but nonetheless as long as I use this + + + align:start position:0% +but nonetheless as long as I use this +Orange circuit at the opportune time I + + align:start position:0% +Orange circuit at the opportune time I + + + align:start position:0% +Orange circuit at the opportune time I +can run the rest of the converter just + + align:start position:0% +can run the rest of the converter just + + + align:start position:0% +can run the rest of the converter just +like it's a normal pwm converter right + + align:start position:0% +like it's a normal pwm converter right + + + align:start position:0% +like it's a normal pwm converter right +so I'm adding an auxiliary circuit + + align:start position:0% +so I'm adding an auxiliary circuit + + + align:start position:0% +so I'm adding an auxiliary circuit +comprising the green and orange circuit + + align:start position:0% +comprising the green and orange circuit + + + align:start position:0% +comprising the green and orange circuit +to let me operate the regular circuit + + align:start position:0% +to let me operate the regular circuit + + + align:start position:0% +to let me operate the regular circuit +just like a normal pwm converter okay + + align:start position:0% +just like a normal pwm converter okay + + + align:start position:0% +just like a normal pwm converter okay +and that's a whole categories of switch + + align:start position:0% +and that's a whole categories of switch + + + align:start position:0% +and that's a whole categories of switch +capacitor converters how do I augment my + + align:start position:0% +capacitor converters how do I augment my + + + align:start position:0% +capacitor converters how do I augment my +normal pwm design so that it also gives + + align:start position:0% +normal pwm design so that it also gives + + + align:start position:0% +normal pwm design so that it also gives +me soft switching and I can get either a + + align:start position:0% +me soft switching and I can get either a + + + align:start position:0% +me soft switching and I can get either a +higher efficiency or higher + + align:start position:0% + + + + align:start position:0% + +frequency any final questions for today + + align:start position:0% +frequency any final questions for today + + + align:start position:0% +frequency any final questions for today +yeah what would be thees orang + + align:start position:0% +yeah what would be thees orang + + + align:start position:0% +yeah what would be thees orang +is yes it is right I mean he is taking + + align:start position:0% +is yes it is right I mean he is taking + + + align:start position:0% +is yes it is right I mean he is taking +the full Peak current and he's operating + + align:start position:0% +the full Peak current and he's operating + + + align:start position:0% +the full Peak current and he's operating +into the full high output voltage and + + align:start position:0% +into the full high output voltage and + + + align:start position:0% +into the full high output voltage and +you know so it's not negligible but if + + align:start position:0% +you know so it's not negligible but if + + + align:start position:0% +you know so it's not negligible but if +you do it right it's a lot less than + + align:start position:0% +you do it right it's a lot less than + + + align:start position:0% +you do it right it's a lot less than +your original high power circuit was so + + align:start position:0% +your original high power circuit was so + + + align:start position:0% +your original high power circuit was so +he's he's got high peak power you can + + align:start position:0% +he's he's got high peak power you can + + + align:start position:0% +he's he's got high peak power you can +optimize the orange circuit differently + + align:start position:0% +optimize the orange circuit differently + + + align:start position:0% +optimize the orange circuit differently +in the white + + align:start position:0% +in the white + + + align:start position:0% +in the white +circuit and it it will overall be better + + align:start position:0% +circuit and it it will overall be better + + + align:start position:0% +circuit and it it will overall be better +but it's not negligible loss you still + + align:start position:0% +but it's not negligible loss you still + + + align:start position:0% +but it's not negligible loss you still +have to think about + + align:start position:0% +have to think about + + + align:start position:0% +have to think about +it okay we will take this up next class \ No newline at end of file diff --git a/5HfMEUO9vlY.txt b/5HfMEUO9vlY.txt new file mode 100644 index 0000000000000000000000000000000000000000..2423e71495520a4998f2bd0d847d5d1a9a858551 --- /dev/null +++ b/5HfMEUO9vlY.txt @@ -0,0 +1,1531 @@ +align:start position:0% + +yeah so i think that the real difference + + align:start position:0% +yeah so i think that the real difference + + + align:start position:0% +yeah so i think that the real difference +between when you guys + + align:start position:0% +between when you guys + + + align:start position:0% +between when you guys +first ran the course which i think was + + align:start position:0% +first ran the course which i think was + + + align:start position:0% +first ran the course which i think was +in 2015 and + + align:start position:0% +in 2015 and + + + align:start position:0% +in 2015 and +uh now when i run the course is that jen + + align:start position:0% +uh now when i run the course is that jen + + + align:start position:0% +uh now when i run the course is that jen +has helped to develop this online + + align:start position:0% +has helped to develop this online + + + align:start position:0% +has helped to develop this online +mitx platform is that now it's really a + + align:start position:0% +mitx platform is that now it's really a + + + align:start position:0% +mitx platform is that now it's really a +flipped classroom course + + align:start position:0% +flipped classroom course + + + align:start position:0% +flipped classroom course +so it has this blended learning aspect + + align:start position:0% +so it has this blended learning aspect + + + align:start position:0% +so it has this blended learning aspect +to it where the students complete online + + align:start position:0% +to it where the students complete online + + + align:start position:0% +to it where the students complete online +reading + + align:start position:0% +reading + + + align:start position:0% +reading +before they attend the classroom hours + + align:start position:0% +before they attend the classroom hours + + + align:start position:0% +before they attend the classroom hours +and then in the classroom we really go + + align:start position:0% +and then in the classroom we really go + + + align:start position:0% +and then in the classroom we really go +through + + align:start position:0% +through + + + align:start position:0% +through +examples worked examples where the + + align:start position:0% +examples worked examples where the + + + align:start position:0% +examples worked examples where the +students can apply the theory that + + align:start position:0% +students can apply the theory that + + + align:start position:0% +students can apply the theory that +they've learned + + align:start position:0% +they've learned + + + align:start position:0% +they've learned +um while they did the online reading i + + align:start position:0% +um while they did the online reading i + + + align:start position:0% +um while they did the online reading i +think this is the key um + + align:start position:0% +think this is the key um + + + align:start position:0% +think this is the key um +thing that um you guys and jen uh um + + align:start position:0% +thing that um you guys and jen uh um + + + align:start position:0% +thing that um you guys and jen uh um +and and myself really saw the course + + align:start position:0% +and and myself really saw the course + + + align:start position:0% +and and myself really saw the course +being when i started teaching it + + align:start position:0% +being when i started teaching it + + + align:start position:0% +being when i started teaching it +so how do you ensure that they do the + + align:start position:0% +so how do you ensure that they do the + + + align:start position:0% +so how do you ensure that they do the +online reading so um the online reading + + align:start position:0% +online reading so um the online reading + + + align:start position:0% +online reading so um the online reading +uh has many uh examples where the + + align:start position:0% +uh has many uh examples where the + + + align:start position:0% +uh has many uh examples where the +students can + + align:start position:0% +students can + + + align:start position:0% +students can +attempt something attempt a question and + + align:start position:0% +attempt something attempt a question and + + + align:start position:0% +attempt something attempt a question and +uh it's + + align:start position:0% +uh it's + + + align:start position:0% +uh it's +ten percent of the grade for the course + + align:start position:0% +ten percent of the grade for the course + + + align:start position:0% +ten percent of the grade for the course +is given to them for for getting these + + align:start position:0% +is given to them for for getting these + + + align:start position:0% +is given to them for for getting these +questions right + + align:start position:0% +questions right + + + align:start position:0% +questions right +it's a small incentive uh just to make + + align:start position:0% +it's a small incentive uh just to make + + + align:start position:0% +it's a small incentive uh just to make +sure that they complete + + align:start position:0% +sure that they complete + + + align:start position:0% +sure that they complete +the online questions and of course we uh + + align:start position:0% +the online questions and of course we uh + + + align:start position:0% +the online questions and of course we uh +we get feedback of + + align:start position:0% +we get feedback of + + + align:start position:0% +we get feedback of +data to know how many students uh do + + align:start position:0% +data to know how many students uh do + + + align:start position:0% +data to know how many students uh do +those questions and it's + + align:start position:0% +those questions and it's + + + align:start position:0% +those questions and it's +it's it's relatively easy to check to + + align:start position:0% +it's it's relatively easy to check to + + + align:start position:0% +it's it's relatively easy to check to +make sure that there are students doing + + align:start position:0% +make sure that there are students doing + + + align:start position:0% +make sure that there are students doing +them + + align:start position:0% +them + + + align:start position:0% +them +um so that the way that the online notes + + align:start position:0% +um so that the way that the online notes + + + align:start position:0% +um so that the way that the online notes +are structured is that they're hosted + + align:start position:0% +are structured is that they're hosted + + + align:start position:0% +are structured is that they're hosted +on the mitx residential platform and so + + align:start position:0% +on the mitx residential platform and so + + + align:start position:0% +on the mitx residential platform and so +all of the reading there is no text but + + align:start position:0% +all of the reading there is no text but + + + align:start position:0% +all of the reading there is no text but +all of the reading is online and there + + align:start position:0% +all of the reading is online and there + + + align:start position:0% +all of the reading is online and there +are questions + + align:start position:0% +are questions + + + align:start position:0% +are questions +interspersed between the text and so + + align:start position:0% +interspersed between the text and so + + + align:start position:0% +interspersed between the text and so +it's these questions + + align:start position:0% +it's these questions + + + align:start position:0% +it's these questions +that are really depending on the text + + align:start position:0% +that are really depending on the text + + + align:start position:0% +that are really depending on the text +before which tell us if the students + + align:start position:0% +before which tell us if the students + + + align:start position:0% +before which tell us if the students +have been doing the reading + + align:start position:0% +have been doing the reading + + + align:start position:0% +have been doing the reading +because they can't answer these + + align:start position:0% +because they can't answer these + + + align:start position:0% +because they can't answer these +questions without actually attempting + + align:start position:0% +questions without actually attempting + + + align:start position:0% +questions without actually attempting +this work + + align:start position:0% + + + + align:start position:0% + +and i think some of the parts that were + + align:start position:0% +and i think some of the parts that were + + + align:start position:0% +and i think some of the parts that were +really useful about using + + align:start position:0% +really useful about using + + + align:start position:0% +really useful about using +digital tools in having students + + align:start position:0% +digital tools in having students + + + align:start position:0% +digital tools in having students +interact with the content were one is + + align:start position:0% +interact with the content were one is + + + align:start position:0% +interact with the content were one is +that we use the sketch response tool so + + align:start position:0% +that we use the sketch response tool so + + + align:start position:0% +that we use the sketch response tool so +we could actually have + + align:start position:0% +we could actually have + + + align:start position:0% +we could actually have +students draw poll diagrams and pull + + align:start position:0% +students draw poll diagrams and pull + + + align:start position:0% +students draw poll diagrams and pull +zero diagrams + + align:start position:0% +zero diagrams + + + align:start position:0% +zero diagrams +and they could get automatic feedback on + + align:start position:0% +and they could get automatic feedback on + + + align:start position:0% +and they could get automatic feedback on +whether or not that was correct + + align:start position:0% +whether or not that was correct + + + align:start position:0% +whether or not that was correct +um we could also have them sketch + + align:start position:0% +um we could also have them sketch + + + align:start position:0% +um we could also have them sketch +responses + + align:start position:0% +responses + + + align:start position:0% +responses +to a system and get get feedback on that + + align:start position:0% +to a system and get get feedback on that + + + align:start position:0% +to a system and get get feedback on that +the other thing that's nice is that it + + align:start position:0% +the other thing that's nice is that it + + + align:start position:0% +the other thing that's nice is that it +really + + align:start position:0% +really + + + align:start position:0% +really +makes some of those simple examples that + + align:start position:0% +makes some of those simple examples that + + + align:start position:0% +makes some of those simple examples that +you often have to spend a lot of time in + + align:start position:0% +you often have to spend a lot of time in + + + align:start position:0% +you often have to spend a lot of time in +class doing + + align:start position:0% +class doing + + + align:start position:0% +class doing +we can now do those online and have the + + align:start position:0% +we can now do those online and have the + + + align:start position:0% +we can now do those online and have the +student get immediate feedback + + align:start position:0% +student get immediate feedback + + + align:start position:0% +student get immediate feedback +see the answers these are things that + + align:start position:0% +see the answers these are things that + + + align:start position:0% +see the answers these are things that +maybe it's not worth doing in + + align:start position:0% +maybe it's not worth doing in + + + align:start position:0% +maybe it's not worth doing in +in class when you have someone like + + align:start position:0% +in class when you have someone like + + + align:start position:0% +in class when you have someone like +philip who's there and instead now he + + align:start position:0% +philip who's there and instead now he + + + align:start position:0% +philip who's there and instead now he +can spend his time + + align:start position:0% +can spend his time + + + align:start position:0% +can spend his time +working through the really complicated + + align:start position:0% +working through the really complicated + + + align:start position:0% +working through the really complicated +examples and giving the scaffolding and + + align:start position:0% +examples and giving the scaffolding and + + + align:start position:0% +examples and giving the scaffolding and +fading to help them do much more + + align:start position:0% +fading to help them do much more + + + align:start position:0% +fading to help them do much more +interesting problems than on the + + align:start position:0% +interesting problems than on the + + + align:start position:0% +interesting problems than on the +homework + + align:start position:0% +homework + + + align:start position:0% +homework +yeah i agree actually and that's another + + align:start position:0% +yeah i agree actually and that's another + + + align:start position:0% +yeah i agree actually and that's another +way that i really see um + + align:start position:0% +way that i really see um + + + align:start position:0% +way that i really see um +this course is maximizing the kind of + + align:start position:0% +this course is maximizing the kind of + + + align:start position:0% +this course is maximizing the kind of +utility of the time that the students + + align:start position:0% +utility of the time that the students + + + align:start position:0% +utility of the time that the students +spend with me and with with each other + + align:start position:0% +spend with me and with with each other + + + align:start position:0% +spend with me and with with each other +so we go through more involved examples + + align:start position:0% +so we go through more involved examples + + + align:start position:0% +so we go through more involved examples +where they have to really stop and think + + align:start position:0% +where they have to really stop and think + + + align:start position:0% +where they have to really stop and think +about things + + align:start position:0% +about things + + + align:start position:0% +about things +rather than the kind of you know kind of + + align:start position:0% +rather than the kind of you know kind of + + + align:start position:0% +rather than the kind of you know kind of +rote examples where you just really make + + align:start position:0% +rote examples where you just really make + + + align:start position:0% +rote examples where you just really make +sure that you understand the specific + + align:start position:0% +sure that you understand the specific + + + align:start position:0% +sure that you understand the specific +little concept + + align:start position:0% + + + + align:start position:0% + +so do they turn do the students turn in + + align:start position:0% +so do they turn do the students turn in + + + align:start position:0% +so do they turn do the students turn in +homework in this course + + align:start position:0% +homework in this course + + + align:start position:0% +homework in this course +yeah so the way it works is um in terms + + align:start position:0% +yeah so the way it works is um in terms + + + align:start position:0% +yeah so the way it works is um in terms +of them getting a grade + + align:start position:0% +of them getting a grade + + + align:start position:0% +of them getting a grade +is we have the online uh lectures in + + align:start position:0% +is we have the online uh lectures in + + + align:start position:0% +is we have the online uh lectures in +which they have to answer + + align:start position:0% +which they have to answer + + + align:start position:0% +which they have to answer +uh questions and we give that a small uh + + align:start position:0% +uh questions and we give that a small uh + + + align:start position:0% +uh questions and we give that a small uh +a small + + align:start position:0% +a small + + + align:start position:0% +a small +uh ten percent of their grades from the + + align:start position:0% +uh ten percent of their grades from the + + + align:start position:0% +uh ten percent of their grades from the +online examples and then we have problem + + align:start position:0% +online examples and then we have problem + + + align:start position:0% +online examples and then we have problem +sets + + align:start position:0% +sets + + + align:start position:0% +sets +in which they have to answer slightly + + align:start position:0% +in which they have to answer slightly + + + align:start position:0% +in which they have to answer slightly +more involved questions + + align:start position:0% +more involved questions + + + align:start position:0% +more involved questions +and they're handed in once every week + + align:start position:0% +and they're handed in once every week + + + align:start position:0% +and they're handed in once every week +and then we also have a midterm + + align:start position:0% +and then we also have a midterm + + + align:start position:0% +and then we also have a midterm +and a final exam so one of the great + + align:start position:0% +and a final exam so one of the great + + + align:start position:0% +and a final exam so one of the great +virtues of having online questions in my + + align:start position:0% +virtues of having online questions in my + + + align:start position:0% +virtues of having online questions in my +opinion is students get immediate + + align:start position:0% +opinion is students get immediate + + + align:start position:0% +opinion is students get immediate +response to + + align:start position:0% +response to + + + align:start position:0% +response to +to their answers and as opposed to + + align:start position:0% +to their answers and as opposed to + + + align:start position:0% +to their answers and as opposed to +waiting a week or something + + align:start position:0% +waiting a week or something + + + align:start position:0% +waiting a week or something +and getting their homework turned back + + align:start position:0% +and getting their homework turned back + + + align:start position:0% +and getting their homework turned back +to them and of course who needs to be + + align:start position:0% +to them and of course who needs to be + + + align:start position:0% +to them and of course who needs to be +the bad news they don't open the + + align:start position:0% +the bad news they don't open the + + + align:start position:0% +the bad news they don't open the +open the sheet to see where their + + align:start position:0% +open the sheet to see where their + + + align:start position:0% +open the sheet to see where their +mistakes were and with an online setting + + align:start position:0% +mistakes were and with an online setting + + + align:start position:0% +mistakes were and with an online setting +one of the great advantages is students + + align:start position:0% +one of the great advantages is students + + + align:start position:0% +one of the great advantages is students +see right away with + + align:start position:0% +see right away with + + + align:start position:0% +see right away with +whether they understand something or not + + align:start position:0% +whether they understand something or not + + + align:start position:0% +whether they understand something or not +yeah i agree + + align:start position:0% +yeah i agree + + + align:start position:0% +yeah i agree +and then i think also a lot of the + + align:start position:0% +and then i think also a lot of the + + + align:start position:0% +and then i think also a lot of the +literature shows that it's actually when + + align:start position:0% +literature shows that it's actually when + + + align:start position:0% +literature shows that it's actually when +you're first learning something + + align:start position:0% +you're first learning something + + + align:start position:0% +you're first learning something +that that immediate feedback is the most + + align:start position:0% +that that immediate feedback is the most + + + align:start position:0% +that that immediate feedback is the most +useful and actually when you're doing + + align:start position:0% +useful and actually when you're doing + + + align:start position:0% +useful and actually when you're doing +more complicated things + + align:start position:0% +more complicated things + + + align:start position:0% +more complicated things +sometimes then the immediate feedback is + + align:start position:0% +sometimes then the immediate feedback is + + + align:start position:0% +sometimes then the immediate feedback is +less helpful and so that actually really + + align:start position:0% +less helpful and so that actually really + + + align:start position:0% +less helpful and so that actually really +bill is built into the way the course is + + align:start position:0% +bill is built into the way the course is + + + align:start position:0% +bill is built into the way the course is +run um one thing also that we do is that + + align:start position:0% +run um one thing also that we do is that + + + align:start position:0% +run um one thing also that we do is that +we actually + + align:start position:0% +we actually + + + align:start position:0% +we actually +have a problem set checker for the + + align:start position:0% +have a problem set checker for the + + + align:start position:0% +have a problem set checker for the +homework + + align:start position:0% +homework + + + align:start position:0% +homework +so they actually know before they even + + align:start position:0% +so they actually know before they even + + + align:start position:0% +so they actually know before they even +turn it in + + align:start position:0% +turn it in + + + align:start position:0% +turn it in +if their answers are right and that's + + align:start position:0% +if their answers are right and that's + + + align:start position:0% +if their answers are right and that's +something that we decided to + + align:start position:0% +something that we decided to + + + align:start position:0% +something that we decided to +add in this this time that we taught the + + align:start position:0% +add in this this time that we taught the + + + align:start position:0% +add in this this time that we taught the +course this summer i taught the course + + align:start position:0% +course this summer i taught the course + + + align:start position:0% +course this summer i taught the course +so in the previous um the previous time + + align:start position:0% +so in the previous um the previous time + + + align:start position:0% +so in the previous um the previous time +that i taught the course some of the + + align:start position:0% +that i taught the course some of the + + + align:start position:0% +that i taught the course some of the +feedback that we got from the students + + align:start position:0% +feedback that we got from the students + + + align:start position:0% +feedback that we got from the students +was that they would like to have even + + align:start position:0% +was that they would like to have even + + + align:start position:0% +was that they would like to have even +more + + align:start position:0% +more + + + align:start position:0% +more +online examples and one of the things + + align:start position:0% +online examples and one of the things + + + align:start position:0% +online examples and one of the things +that we did to + + align:start position:0% +that we did to + + + align:start position:0% +that we did to +rectify that is that we made this or jen + + align:start position:0% +rectify that is that we made this or jen + + + align:start position:0% +rectify that is that we made this or jen +implemented this problem set checker + + align:start position:0% +implemented this problem set checker + + + align:start position:0% +implemented this problem set checker +so that the students at the end of each + + align:start position:0% +so that the students at the end of each + + + align:start position:0% +so that the students at the end of each +lecture could see the problem set + + align:start position:0% +lecture could see the problem set + + + align:start position:0% +lecture could see the problem set +and uh answer the questions and get some + + align:start position:0% +and uh answer the questions and get some + + + align:start position:0% +and uh answer the questions and get some +immediate feedback on them and by the + + align:start position:0% +immediate feedback on them and by the + + + align:start position:0% +immediate feedback on them and by the +lecture you mean the online unit that + + align:start position:0% +lecture you mean the online unit that + + + align:start position:0% +lecture you mean the online unit that +they were going through + + align:start position:0% +they were going through + + + align:start position:0% +they were going through +yes exactly exactly so after they've + + align:start position:0% +yes exactly exactly so after they've + + + align:start position:0% +yes exactly exactly so after they've +done the online reading they can also + + align:start position:0% +done the online reading they can also + + + align:start position:0% +done the online reading they can also +see the problem set and + + align:start position:0% +see the problem set and + + + align:start position:0% +see the problem set and +answer the questions and get them + + align:start position:0% +answer the questions and get them + + + align:start position:0% +answer the questions and get them +checked + + align:start position:0% + + + + align:start position:0% + +another uh great thing i think about the + + align:start position:0% +another uh great thing i think about the + + + align:start position:0% +another uh great thing i think about the +online version is the way the mathletes + + align:start position:0% +online version is the way the mathletes + + + align:start position:0% +online version is the way the mathletes +get interve + + align:start position:0% +get interve + + + align:start position:0% +get interve +integrated into the course they're + + align:start position:0% +integrated into the course they're + + + align:start position:0% +integrated into the course they're +seamlessly integrated into the text + + align:start position:0% +seamlessly integrated into the text + + + align:start position:0% +seamlessly integrated into the text +i agree because i think that one of the + + align:start position:0% +i agree because i think that one of the + + + align:start position:0% +i agree because i think that one of the +things that is hard for novice students + + align:start position:0% +things that is hard for novice students + + + align:start position:0% +things that is hard for novice students +is to interact with the mathletes + + align:start position:0% +is to interact with the mathletes + + + align:start position:0% +is to interact with the mathletes +because because they were really + + align:start position:0% +because because they were really + + + align:start position:0% +because because they were really +designed both + + align:start position:0% +designed both + + + align:start position:0% +designed both +as a student facing tool but also an + + align:start position:0% +as a student facing tool but also an + + + align:start position:0% +as a student facing tool but also an +instructor-facing tool + + align:start position:0% +instructor-facing tool + + + align:start position:0% +instructor-facing tool +really to demonstrate things in lecture + + align:start position:0% +really to demonstrate things in lecture + + + align:start position:0% +really to demonstrate things in lecture +and so for a student who doesn't know + + align:start position:0% +and so for a student who doesn't know + + + align:start position:0% +and so for a student who doesn't know +what's going on + + align:start position:0% +what's going on + + + align:start position:0% +what's going on +sometimes it can feel like there's just + + align:start position:0% +sometimes it can feel like there's just + + + align:start position:0% +sometimes it can feel like there's just +too much going on too many sliders too + + align:start position:0% +too much going on too many sliders too + + + align:start position:0% +too much going on too many sliders too +many buttons + + align:start position:0% +many buttons + + + align:start position:0% +many buttons +and so instead we can embed it in the + + align:start position:0% +and so instead we can embed it in the + + + align:start position:0% +and so instead we can embed it in the +web page + + align:start position:0% +web page + + + align:start position:0% +web page +and then have really guided problems and + + align:start position:0% +and then have really guided problems and + + + align:start position:0% +and then have really guided problems and +guided activities + + align:start position:0% +guided activities + + + align:start position:0% +guided activities +that help them understand how to + + align:start position:0% +that help them understand how to + + + align:start position:0% +that help them understand how to +interact with it and to help them figure + + align:start position:0% +interact with it and to help them figure + + + align:start position:0% +interact with it and to help them figure +out what they should be looking for and + + align:start position:0% +out what they should be looking for and + + + align:start position:0% +out what they should be looking for and +what are the + + align:start position:0% +what are the + + + align:start position:0% +what are the +real responses of interest \ No newline at end of file diff --git a/6c1jkgSynrI.txt b/6c1jkgSynrI.txt new file mode 100644 index 0000000000000000000000000000000000000000..181e2fb65e83549d25cc4905a4ca18c13de2dcd5 --- /dev/null +++ b/6c1jkgSynrI.txt @@ -0,0 +1,827 @@ +align:start position:0% + +my lab works on the only cool enzyme in + + align:start position:0% +my lab works on the only cool enzyme in + + + align:start position:0% +my lab works on the only cool enzyme in +the world ribonucleotide reductase is + + align:start position:0% +the world ribonucleotide reductase is + + + align:start position:0% +the world ribonucleotide reductase is +the only way in all organisms that you + + align:start position:0% +the only way in all organisms that you + + + align:start position:0% +the only way in all organisms that you +make the building blocks to know bro + + align:start position:0% +make the building blocks to know bro + + + align:start position:0% +make the building blocks to know bro +that are required for DNA biosynthesis + + align:start position:0% +that are required for DNA biosynthesis + + + align:start position:0% +that are required for DNA biosynthesis +and repair so if you inhibit this enzyme + + align:start position:0% +and repair so if you inhibit this enzyme + + + align:start position:0% +and repair so if you inhibit this enzyme +you have no building blocks you you + + align:start position:0% +you have no building blocks you you + + + align:start position:0% +you have no building blocks you you +can't survive so from a practical point + + align:start position:0% +can't survive so from a practical point + + + align:start position:0% +can't survive so from a practical point +of view it's the target of drugs that + + align:start position:0% +of view it's the target of drugs that + + + align:start position:0% +of view it's the target of drugs that +are used therapeutically and the + + align:start position:0% +are used therapeutically and the + + + align:start position:0% +are used therapeutically and the +treatment of cancer and I think it + + align:start position:0% +treatment of cancer and I think it + + + align:start position:0% +treatment of cancer and I think it +probably not so just in future is the + + align:start position:0% +probably not so just in future is the + + + align:start position:0% +probably not so just in future is the +Indy bacterials because I think there + + align:start position:0% +Indy bacterials because I think there + + + align:start position:0% +Indy bacterials because I think there +are sufficient differences between + + align:start position:0% +are sufficient differences between + + + align:start position:0% +are sufficient differences between +humans and bacteria reductases say you + + align:start position:0% +humans and bacteria reductases say you + + + align:start position:0% +humans and bacteria reductases say you +could make specific inhibitors why am i + + align:start position:0% +could make specific inhibitors why am i + + + align:start position:0% +could make specific inhibitors why am i +interested in it because the chemistry + + align:start position:0% +interested in it because the chemistry + + + align:start position:0% +interested in it because the chemistry +is sort of unbelievable + + align:start position:0% +is sort of unbelievable + + + align:start position:0% +is sort of unbelievable +so I mean it was the first example where + + align:start position:0% +so I mean it was the first example where + + + align:start position:0% +so I mean it was the first example where +rat you you learn or you hear about you + + align:start position:0% +rat you you learn or you hear about you + + + align:start position:0% +rat you you learn or you hear about you +heard from John radicals their reactive + + align:start position:0% +heard from John radicals their reactive + + + align:start position:0% +heard from John radicals their reactive +oxygen species and nitrogen species that + + align:start position:0% +oxygen species and nitrogen species that + + + align:start position:0% +oxygen species and nitrogen species that +you can't control they want to pick up + + align:start position:0% +you can't control they want to pick up + + + align:start position:0% +you can't control they want to pick up +an extra electron and form a stable + + align:start position:0% +an extra electron and form a stable + + + align:start position:0% +an extra electron and form a stable +octet and if you let them to their own + + align:start position:0% +octet and if you let them to their own + + + align:start position:0% +octet and if you let them to their own +if they leave them to their own demise + + align:start position:0% +if they leave them to their own demise + + + align:start position:0% +if they leave them to their own demise +they react with anything and destroy it + + align:start position:0% +they react with anything and destroy it + + + align:start position:0% +they react with anything and destroy it +well Nature has figured out how to + + align:start position:0% +well Nature has figured out how to + + + align:start position:0% +well Nature has figured out how to +harness the reactivity of radicals to do + + align:start position:0% +harness the reactivity of radicals to do + + + align:start position:0% +harness the reactivity of radicals to do +really tough chemistry with exquisite + + align:start position:0% +really tough chemistry with exquisite + + + align:start position:0% +really tough chemistry with exquisite +specificity and ribonucleotide reductase + + align:start position:0% +specificity and ribonucleotide reductase + + + align:start position:0% +specificity and ribonucleotide reductase +is have been the paradigm for thinking + + align:start position:0% +is have been the paradigm for thinking + + + align:start position:0% +is have been the paradigm for thinking +about that and from bioinformatics now + + align:start position:0% +about that and from bioinformatics now + + + align:start position:0% +about that and from bioinformatics now +there are there are 50,000 reactions in + + align:start position:0% +there are there are 50,000 reactions in + + + align:start position:0% +there are there are 50,000 reactions in +metabolic systems that are going to be + + align:start position:0% +metabolic systems that are going to be + + + align:start position:0% +metabolic systems that are going to be +radical mediated transformations yet we + + align:start position:0% +radical mediated transformations yet we + + + align:start position:0% +radical mediated transformations yet we +never talk about radicals and + + align:start position:0% +never talk about radicals and + + + align:start position:0% +never talk about radicals and +introductory courses so I think that's + + align:start position:0% +introductory courses so I think that's + + + align:start position:0% +introductory courses so I think that's +all gonna change so why is it unusual + + align:start position:0% +all gonna change so why is it unusual + + + align:start position:0% +all gonna change so why is it unusual +well for the human ribonucleotide + + align:start position:0% +well for the human ribonucleotide + + + align:start position:0% +well for the human ribonucleotide +reductase the key to making this work + + align:start position:0% +reductase the key to making this work + + + align:start position:0% +reductase the key to making this work +catalytically is the amino acid side + + align:start position:0% +catalytically is the amino acid side + + + align:start position:0% +catalytically is the amino acid side +chain tyrosine okay needs to be oxidized + + align:start position:0% +chain tyrosine okay needs to be oxidized + + + align:start position:0% +chain tyrosine okay needs to be oxidized +to at IRA so radical okay so + + align:start position:0% +to at IRA so radical okay so + + + align:start position:0% +to at IRA so radical okay so +automatically nobody believes that at + + align:start position:0% +automatically nobody believes that at + + + align:start position:0% +automatically nobody believes that at +IRA so radical in solution has a + + align:start position:0% +IRA so radical in solution has a + + + align:start position:0% +IRA so radical in solution has a +half-life of a microsecond in the active + + align:start position:0% +half-life of a microsecond in the active + + + align:start position:0% +half-life of a microsecond in the active +site of these enzymes the half-life of + + align:start position:0% +site of these enzymes the half-life of + + + align:start position:0% +site of these enzymes the half-life of +the enzyme can be on the order of four + + align:start position:0% +the enzyme can be on the order of four + + + align:start position:0% +the enzyme can be on the order of four +days and this radical which is again one + + align:start position:0% +days and this radical which is again one + + + align:start position:0% +days and this radical which is again one +electron oxidize amino acid if you + + align:start position:0% +electron oxidize amino acid if you + + + align:start position:0% +electron oxidize amino acid if you +reduce it + + align:start position:0% +reduce it + + + align:start position:0% +reduce it +with an electron and a proton the + + align:start position:0% +with an electron and a proton the + + + align:start position:0% +with an electron and a proton the +enzymes completely dead so this was the + + align:start position:0% +enzymes completely dead so this was the + + + align:start position:0% +enzymes completely dead so this was the +first example of it would be another + + align:start position:0% +first example of it would be another + + + align:start position:0% +first example of it would be another +example of a post translational + + align:start position:0% +example of a post translational + + + align:start position:0% +example of a post translational +modification that we talked about + + align:start position:0% +modification that we talked about + + + align:start position:0% +modification that we talked about +earlier modifying your amino acids and + + align:start position:0% +earlier modifying your amino acids and + + + align:start position:0% +earlier modifying your amino acids and +so Nature has figured out a way how do + + align:start position:0% +so Nature has figured out a way how do + + + align:start position:0% +so Nature has figured out a way how do +you do this oxidation she has a little + + align:start position:0% +you do this oxidation she has a little + + + align:start position:0% +you do this oxidation she has a little +metal cluster right adjacent to where + + align:start position:0% +metal cluster right adjacent to where + + + align:start position:0% +metal cluster right adjacent to where +this tyrosine is and the function of + + align:start position:0% +this tyrosine is and the function of + + + align:start position:0% +this tyrosine is and the function of +this little nano cluster is to put this + + align:start position:0% +this little nano cluster is to put this + + + align:start position:0% +this little nano cluster is to put this +into the oxidize state which is + + align:start position:0% +into the oxidize state which is + + + align:start position:0% +into the oxidize state which is +essential for the way the enzyme works + + align:start position:0% +essential for the way the enzyme works + + + align:start position:0% +essential for the way the enzyme works +so the other thing that's amazing about + + align:start position:0% +so the other thing that's amazing about + + + align:start position:0% +so the other thing that's amazing about +the enzyme is the chemistry there are + + align:start position:0% +the enzyme is the chemistry there are + + + align:start position:0% +the enzyme is the chemistry there are +two subunits the chemistry all happens + + align:start position:0% +two subunits the chemistry all happens + + + align:start position:0% +two subunits the chemistry all happens +in this subunit but the Taira so radical + + align:start position:0% +in this subunit but the Taira so radical + + + align:start position:0% +in this subunit but the Taira so radical +is there in this oxidation normally when + + align:start position:0% +is there in this oxidation normally when + + + align:start position:0% +is there in this oxidation normally when +you do an oxidation the two atoms are + + align:start position:0% +you do an oxidation the two atoms are + + + align:start position:0% +you do an oxidation the two atoms are +sitting within a few angstroms of each + + align:start position:0% +sitting within a few angstroms of each + + + align:start position:0% +sitting within a few angstroms of each +other the oxidation happens over 35 + + align:start position:0% +other the oxidation happens over 35 + + + align:start position:0% +other the oxidation happens over 35 +angstroms okay so that's unprecedented + + align:start position:0% +angstroms okay so that's unprecedented + + + align:start position:0% +angstroms okay so that's unprecedented +it involves hopping radicals which no + + align:start position:0% +it involves hopping radicals which no + + + align:start position:0% +it involves hopping radicals which no +one has ever seen before and so that was + + align:start position:0% +one has ever seen before and so that was + + + align:start position:0% +one has ever seen before and so that was +another thing that was completely + + align:start position:0% +another thing that was completely + + + align:start position:0% +another thing that was completely +fascinating from a chemical perspective + + align:start position:0% +fascinating from a chemical perspective + + + align:start position:0% +fascinating from a chemical perspective +about how this system works the other + + align:start position:0% +about how this system works the other + + + align:start position:0% +about how this system works the other +reason that people in biology are + + align:start position:0% +reason that people in biology are + + + align:start position:0% +reason that people in biology are +interested in this besides the fact that + + align:start position:0% +interested in this besides the fact that + + + align:start position:0% +interested in this besides the fact that +makes a building block for DNA is that + + align:start position:0% +makes a building block for DNA is that + + + align:start position:0% +makes a building block for DNA is that +if you believe in an RNA world okay + + align:start position:0% +if you believe in an RNA world okay + + + align:start position:0% +if you believe in an RNA world okay +we're we have a bride but we have a + + align:start position:0% +we're we have a bride but we have a + + + align:start position:0% +we're we have a bride but we have a +ribosome that we're catalysis a peptide + + align:start position:0% +ribosome that we're catalysis a peptide + + + align:start position:0% +ribosome that we're catalysis a peptide +bond formation is all with the RNA not + + align:start position:0% +bond formation is all with the RNA not + + + align:start position:0% +bond formation is all with the RNA not +with the protein how do you get from an + + align:start position:0% +with the protein how do you get from an + + + align:start position:0% +with the protein how do you get from an +RNA world to a DNA world okay the only + + align:start position:0% +RNA world to a DNA world okay the only + + + align:start position:0% +RNA world to a DNA world okay the only +enzyme that does that transformation + + align:start position:0% +enzyme that does that transformation + + + align:start position:0% +enzyme that does that transformation +making these building blocks are + + align:start position:0% +making these building blocks are + + + align:start position:0% +making these building blocks are +ribonucleotide reductase --is and there + + align:start position:0% +ribonucleotide reductase --is and there + + + align:start position:0% +ribonucleotide reductase --is and there +are many classes of ribonucleotide + + align:start position:0% +are many classes of ribonucleotide + + + align:start position:0% +are many classes of ribonucleotide +reductase and one uses this tyra so + + align:start position:0% +reductase and one uses this tyra so + + + align:start position:0% +reductase and one uses this tyra so +radical but they all use they all have + + align:start position:0% +radical but they all use they all have + + + align:start position:0% +radical but they all use they all have +the same active site and do the same + + align:start position:0% +the same active site and do the same + + + align:start position:0% +the same active site and do the same +chemistry but they have different metal + + align:start position:0% +chemistry but they have different metal + + + align:start position:0% +chemistry but they have different metal +cofactors depending on where they evolve + + align:start position:0% +cofactors depending on where they evolve + + + align:start position:0% +cofactors depending on where they evolve +and the function of the metal cofactors + + align:start position:0% +and the function of the metal cofactors + + + align:start position:0% +and the function of the metal cofactors +in all cases even the ones cobalt ones + + align:start position:0% +in all cases even the ones cobalt ones + + + align:start position:0% +in all cases even the ones cobalt ones +iron sulfur cluster once manganese ones + + align:start position:0% +iron sulfur cluster once manganese ones + + + align:start position:0% +iron sulfur cluster once manganese ones +iron the function in all cases is to + + align:start position:0% +iron the function in all cases is to + + + align:start position:0% +iron the function in all cases is to +generate a radical in the active site + + align:start position:0% +generate a radical in the active site + + + align:start position:0% +generate a radical in the active site +and then the chemistry is the same in + + align:start position:0% +and then the chemistry is the same in + + + align:start position:0% +and then the chemistry is the same in +all these things \ No newline at end of file diff --git a/6nhKL-AuvY4.txt b/6nhKL-AuvY4.txt new file mode 100644 index 0000000000000000000000000000000000000000..5a7f8169cd47e3f919d0dc4a17ee7f831f4b92c8 --- /dev/null +++ b/6nhKL-AuvY4.txt @@ -0,0 +1,13304 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay today we're going to + + align:start position:0% +ocw.mit.edu okay today we're going to + + + align:start position:0% +ocw.mit.edu okay today we're going to +talk about public + + align:start position:0% +talk about public + + + align:start position:0% +talk about public +policy um it'll be a little us Centric + + align:start position:0% +policy um it'll be a little us Centric + + + align:start position:0% +policy um it'll be a little us Centric +we're going to walk through Madison talk + + align:start position:0% +we're going to walk through Madison talk + + + align:start position:0% +we're going to walk through Madison talk +about interest group liberalism other + + align:start position:0% +about interest group liberalism other + + + align:start position:0% +about interest group liberalism other +political processes and then begin the + + align:start position:0% +political processes and then begin the + + + align:start position:0% +political processes and then begin the +discussion of that clean cold dirty air + + align:start position:0% +discussion of that clean cold dirty air + + + align:start position:0% +discussion of that clean cold dirty air +trading filth case with mostly + + align:start position:0% +trading filth case with mostly + + + align:start position:0% +trading filth case with mostly +background and a couple of questions so + + align:start position:0% +background and a couple of questions so + + + align:start position:0% +background and a couple of questions so +I want to review from way back in + + align:start position:0% +I want to review from way back in + + + align:start position:0% +I want to review from way back in +February we talked about this is almost + + align:start position:0% +February we talked about this is almost + + + align:start position:0% +February we talked about this is almost +the same slide not quite we talked about + + align:start position:0% +the same slide not quite we talked about + + + align:start position:0% +the same slide not quite we talked about +differences between Market processes and + + align:start position:0% +differences between Market processes and + + + align:start position:0% +differences between Market processes and +political + + align:start position:0% +political + + + align:start position:0% +political +processes uh I will remind you that + + align:start position:0% +processes uh I will remind you that + + + align:start position:0% +processes uh I will remind you that +governments tend to have need to have a + + align:start position:0% +governments tend to have need to have a + + + align:start position:0% +governments tend to have need to have a +near Monopoly of force and if they're + + align:start position:0% +near Monopoly of force and if they're + + + align:start position:0% +near Monopoly of force and if they're +stable they tend to have legitimacy that + + align:start position:0% +stable they tend to have legitimacy that + + + align:start position:0% +stable they tend to have legitimacy that +is to say there tends to be a general + + align:start position:0% +is to say there tends to be a general + + + align:start position:0% +is to say there tends to be a general +acceptance that it's okay that they make + + align:start position:0% +acceptance that it's okay that they make + + + align:start position:0% +acceptance that it's okay that they make +laws and rules that the processes are + + align:start position:0% +laws and rules that the processes are + + + align:start position:0% +laws and rules that the processes are +okay the people are okay generally + + align:start position:0% +okay the people are okay generally + + + align:start position:0% +okay the people are okay generally +obviously not everybody agrees and there + + align:start position:0% +obviously not everybody agrees and there + + + align:start position:0% +obviously not everybody agrees and there +are people uh in various parts of this + + align:start position:0% +are people uh in various parts of this + + + align:start position:0% +are people uh in various parts of this +country who think the US government + + align:start position:0% +country who think the US government + + + align:start position:0% +country who think the US government +should be overthrown but by and + + align:start position:0% +should be overthrown but by and + + + align:start position:0% +should be overthrown but by and +large uh Syria is an interesting example + + align:start position:0% +large uh Syria is an interesting example + + + align:start position:0% +large uh Syria is an interesting example +the government has a near Monopoly of + + align:start position:0% +the government has a near Monopoly of + + + align:start position:0% +the government has a near Monopoly of +force clearly has very little + + align:start position:0% +force clearly has very little + + + align:start position:0% +force clearly has very little +legitimacy uh and whether it's a near + + align:start position:0% +legitimacy uh and whether it's a near + + + align:start position:0% +legitimacy uh and whether it's a near +Monopoly of force or not quite enough we + + align:start position:0% +Monopoly of force or not quite enough we + + + align:start position:0% +Monopoly of force or not quite enough we +will see we will see um Somalia nobody + + align:start position:0% +will see we will see um Somalia nobody + + + align:start position:0% +will see we will see um Somalia nobody +has + + align:start position:0% +has + + + align:start position:0% +has +either so um the differences + + align:start position:0% +either so um the differences + + + align:start position:0% +either so um the differences +between political processes + + align:start position:0% +between political processes + + + align:start position:0% +between political processes +and uh Market processes in Market + + align:start position:0% +and uh Market processes in Market + + + align:start position:0% +and uh Market processes in Market +processes we think about individuals + + align:start position:0% +processes we think about individuals + + + align:start position:0% +processes we think about individuals +pursuing self interest in the political + + align:start position:0% +pursuing self interest in the political + + + align:start position:0% +pursuing self interest in the political +sphere individuals are actors and so are + + align:start position:0% +sphere individuals are actors and so are + + + align:start position:0% +sphere individuals are actors and so are +groups and self-interest is not the only + + align:start position:0% +groups and self-interest is not the only + + + align:start position:0% +groups and self-interest is not the only +thing that people pursue they pursue + + align:start position:0% +thing that people pursue they pursue + + + align:start position:0% +thing that people pursue they pursue +their view of what's good for everybody + + align:start position:0% +their view of what's good for everybody + + + align:start position:0% +their view of what's good for everybody +else right an awful lot of government + + align:start position:0% +else right an awful lot of government + + + align:start position:0% +else right an awful lot of government +actions are what's good for you not just + + align:start position:0% +actions are what's good for you not just + + + align:start position:0% +actions are what's good for you not just +what's good for the actor um P + + align:start position:0% +what's good for the actor um P + + + align:start position:0% +what's good for the actor um P +Collective choice choice made for all of + + align:start position:0% +Collective choice choice made for all of + + + align:start position:0% +Collective choice choice made for all of +us public goods things that affect all + + align:start position:0% +us public goods things that affect all + + + align:start position:0% +us public goods things that affect all +of + + align:start position:0% +of + + + align:start position:0% +of +us and in Market process es we think + + align:start position:0% +us and in Market process es we think + + + align:start position:0% +us and in Market process es we think +about individuals preferences what do I + + align:start position:0% +about individuals preferences what do I + + + align:start position:0% +about individuals preferences what do I +want in political processes you really + + align:start position:0% +want in political processes you really + + + align:start position:0% +want in political processes you really +have to think about ideologies + + align:start position:0% +have to think about ideologies + + + align:start position:0% +have to think about ideologies +ideologies are views of the proper + + align:start position:0% +ideologies are views of the proper + + + align:start position:0% +ideologies are views of the proper +function of society the proper + + align:start position:0% +function of society the proper + + + align:start position:0% +function of society the proper +organization of society what's good for + + align:start position:0% +organization of society what's good for + + + align:start position:0% +organization of society what's good for +you or what's good for all of us but + + align:start position:0% +you or what's good for all of us but + + + align:start position:0% +you or what's good for all of us but +certainly what's good for you uh that + + align:start position:0% +certainly what's good for you uh that + + + align:start position:0% +certainly what's good for you uh that +doesn't arise in the market it does + + align:start position:0% +doesn't arise in the market it does + + + align:start position:0% +doesn't arise in the market it does +arise in politics inevitably when you're + + align:start position:0% +arise in politics inevitably when you're + + + align:start position:0% +arise in politics inevitably when you're +making decisions that affect the whole + + align:start position:0% +making decisions that affect the whole + + + align:start position:0% +making decisions that affect the whole +community you have to have some notion + + align:start position:0% +community you have to have some notion + + + align:start position:0% +community you have to have some notion +of what those decisions should look like + + align:start position:0% +of what those decisions should look like + + + align:start position:0% +of what those decisions should look like +how they should be made and so forth so + + align:start position:0% +how they should be made and so forth so + + + align:start position:0% +how they should be made and so forth so +ideology always + + align:start position:0% +ideology always + + + align:start position:0% +ideology always +matters Market processes we think mostly + + align:start position:0% +matters Market processes we think mostly + + + align:start position:0% +matters Market processes we think mostly +about + + align:start position:0% +about + + + align:start position:0% +about +competition but competition is not the + + align:start position:0% +competition but competition is not the + + + align:start position:0% +competition but competition is not the +only process in the political sphere + + align:start position:0% +only process in the political sphere + + + align:start position:0% +only process in the political sphere +certainly as we go into elections we + + align:start position:0% +certainly as we go into elections we + + + align:start position:0% +certainly as we go into elections we +will think about + + align:start position:0% +will think about + + + align:start position:0% +will think about +influence as you watch people lining up + + align:start position:0% +influence as you watch people lining up + + + align:start position:0% +influence as you watch people lining up +behind Romney you think about + + align:start position:0% +behind Romney you think about + + + align:start position:0% +behind Romney you think about +cooperation as a key part of the + + align:start position:0% +cooperation as a key part of the + + + align:start position:0% +cooperation as a key part of the +political process and as you see people + + align:start position:0% +political process and as you see people + + + align:start position:0% +political process and as you see people +lining up behind Romney who don't much + + align:start position:0% +lining up behind Romney who don't much + + + align:start position:0% +lining up behind Romney who don't much +like Romney you see the influence of + + align:start position:0% +like Romney you see the influence of + + + align:start position:0% +like Romney you see the influence of +loyalty all those all those processes + + align:start position:0% +loyalty all those all those processes + + + align:start position:0% +loyalty all those all those processes +matter influence cooperation and loyalty + + align:start position:0% +matter influence cooperation and loyalty + + + align:start position:0% +matter influence cooperation and loyalty +matter in the political + + align:start position:0% +matter in the political + + + align:start position:0% +matter in the political +sphere in politics power is a goal for + + align:start position:0% +sphere in politics power is a goal for + + + align:start position:0% +sphere in politics power is a goal for +most of the actors a goal in and of + + align:start position:0% +most of the actors a goal in and of + + + align:start position:0% +most of the actors a goal in and of +itself uh the ability to get other + + align:start position:0% +itself uh the ability to get other + + + align:start position:0% +itself uh the ability to get other +people to act in my interest or in the + + align:start position:0% +people to act in my interest or in the + + + align:start position:0% +people to act in my interest or in the +public interest not in their interest + + align:start position:0% +public interest not in their interest + + + align:start position:0% +public interest not in their interest +uh and finally I remind you that there + + align:start position:0% +uh and finally I remind you that there + + + align:start position:0% +uh and finally I remind you that there +is no there is no perfect + + align:start position:0% +is no there is no perfect + + + align:start position:0% +is no there is no perfect +system we talked briefly about this + + align:start position:0% +system we talked briefly about this + + + align:start position:0% +system we talked briefly about this +voting + + align:start position:0% +voting + + + align:start position:0% +voting +Paradox um back in February that it's + + align:start position:0% +Paradox um back in February that it's + + + align:start position:0% +Paradox um back in February that it's +quite possible uh just to remind you + + align:start position:0% +quite possible uh just to remind you + + + align:start position:0% +quite possible uh just to remind you +what it looks + + align:start position:0% +what it looks + + + align:start position:0% +what it looks +like we have three individuals + + align:start position:0% +like we have three individuals + + + align:start position:0% +like we have three individuals +individual one two and three three + + align:start position:0% +individual one two and three three + + + align:start position:0% +individual one two and three three +Alternatives individual one PR prefers A + + align:start position:0% +Alternatives individual one PR prefers A + + + align:start position:0% +Alternatives individual one PR prefers A +to B to C IND idual + + align:start position:0% +to B to C IND idual + + + align:start position:0% +to B to C IND idual +two let me be sure I get this + + align:start position:0% +two let me be sure I get this + + + align:start position:0% +two let me be sure I get this +right individual two prefers C to A to B + + align:start position:0% +right individual two prefers C to A to B + + + align:start position:0% +right individual two prefers C to A to B +and individual three prefers B to C to + + align:start position:0% + + + + align:start position:0% + +a so if we + + align:start position:0% + + + + align:start position:0% + +vote two people prefer a to B so a a + + align:start position:0% +vote two people prefer a to B so a a + + + align:start position:0% +vote two people prefer a to B so a a +beats + + align:start position:0% +beats + + + align:start position:0% +beats +B two people prefer B to + + align:start position:0% +B two people prefer B to + + + align:start position:0% +B two people prefer B to +C B beats C and two people prefer C to a + + align:start position:0% +C B beats C and two people prefer C to a + + + align:start position:0% +C B beats C and two people prefer C to a +so C beats + + align:start position:0% + + + + align:start position:0% + +a so voting with those preferences + + align:start position:0% +a so voting with those preferences + + + align:start position:0% +a so voting with those preferences +cannot produce consistent decisions + + align:start position:0% +cannot produce consistent decisions + + + align:start position:0% +cannot produce consistent decisions +there's no sense in asking what the + + align:start position:0% +there's no sense in asking what the + + + align:start position:0% +there's no sense in asking what the +optimal decision is + + align:start position:0% +optimal decision is + + + align:start position:0% +optimal decision is +here um if I can control the agenda I + + align:start position:0% +here um if I can control the agenda I + + + align:start position:0% +here um if I can control the agenda I +can determine the outcome right just the + + align:start position:0% +can determine the outcome right just the + + + align:start position:0% +can determine the outcome right just the +order of + + align:start position:0% +order of + + + align:start position:0% +order of +voting if I want if I want + + align:start position:0% +voting if I want if I want + + + align:start position:0% +voting if I want if I want +a uh to win I will uh first first do um + + align:start position:0% +a uh to win I will uh first first do um + + + align:start position:0% +a uh to win I will uh first first do um +what will I do I'll do I'll vote B + + align:start position:0% +what will I do I'll do I'll vote B + + + align:start position:0% +what will I do I'll do I'll vote B +against c b will win I'll then vote a + + align:start position:0% +against c b will win I'll then vote a + + + align:start position:0% +against c b will win I'll then vote a +against B A will win and you can see if + + align:start position:0% +against B A will win and you can see if + + + align:start position:0% +against B A will win and you can see if +you change if you can choose the order + + align:start position:0% +you change if you can choose the order + + + align:start position:0% +you change if you can choose the order +you can choose the outcome so the + + align:start position:0% +you can choose the outcome so the + + + align:start position:0% +you can choose the outcome so the +notion the political system is more + + align:start position:0% +notion the political system is more + + + align:start position:0% +notion the political system is more +complicated in many dimensions than the + + align:start position:0% +complicated in many dimensions than the + + + align:start position:0% +complicated in many dimensions than the +economic system and this last point + + align:start position:0% +economic system and this last point + + + align:start position:0% +economic system and this last point +basically says the notion that there is + + align:start position:0% +basically says the notion that there is + + + align:start position:0% +basically says the notion that there is +an optimal design for + + align:start position:0% +an optimal design for + + + align:start position:0% +an optimal design for +government this is something basically + + align:start position:0% +government this is something basically + + + align:start position:0% +government this is something basically +canero uh got a Nobel Prize for proving + + align:start position:0% +canero uh got a Nobel Prize for proving + + + align:start position:0% +canero uh got a Nobel Prize for proving +in a very very general way in + + align:start position:0% +in a very very general way in + + + align:start position:0% +in a very very general way in +1950 uh in one of the shortest doctoral + + align:start position:0% +1950 uh in one of the shortest doctoral + + + align:start position:0% +1950 uh in one of the shortest doctoral +dissertations in economics um the notion + + align:start position:0% +dissertations in economics um the notion + + + align:start position:0% +dissertations in economics um the notion +that there is an optimal design for + + align:start position:0% +that there is an optimal design for + + + align:start position:0% +that there is an optimal design for +government is a dream there + + align:start position:0% +government is a dream there + + + align:start position:0% +government is a dream there +isn't this says without a dictator you + + align:start position:0% +isn't this says without a dictator you + + + align:start position:0% +isn't this says without a dictator you +can't even get a consistent system and + + align:start position:0% +can't even get a consistent system and + + + align:start position:0% +can't even get a consistent system and +that's a very General result so + + align:start position:0% +that's a very General result so + + + align:start position:0% +that's a very General result so +questions about any of this before we + + align:start position:0% +questions about any of this before we + + + align:start position:0% +questions about any of this before we +go we talked about all of this stuff + + align:start position:0% +go we talked about all of this stuff + + + align:start position:0% +go we talked about all of this stuff +earlier I'm just trying to get you in a + + align:start position:0% +earlier I'm just trying to get you in a + + + align:start position:0% +earlier I'm just trying to get you in a +political frame of mind + + align:start position:0% +political frame of mind + + + align:start position:0% +political frame of mind +here then let's go to + + align:start position:0% + + + + align:start position:0% + +Madison + + align:start position:0% + + + + align:start position:0% + +so Madison is writing in the context of + + align:start position:0% +so Madison is writing in the context of + + + align:start position:0% +so Madison is writing in the context of +Designing a + + align:start position:0% +Designing a + + + align:start position:0% +Designing a +government it's it's easy to forget this + + align:start position:0% +government it's it's easy to forget this + + + align:start position:0% +government it's it's easy to forget this +um having just read this very long long + + align:start position:0% +um having just read this very long long + + + align:start position:0% +um having just read this very long long +biography of Hamilton I will I will do a + + align:start position:0% +biography of Hamilton I will I will do a + + + align:start position:0% +biography of Hamilton I will I will do a +little history lesson + + align:start position:0% + + + + align:start position:0% + +um when the country started if you think + + align:start position:0% +um when the country started if you think + + + align:start position:0% +um when the country started if you think +about it when they sat down to figure + + align:start position:0% +about it when they sat down to figure + + + align:start position:0% +about it when they sat down to figure +out how the government ought to be + + align:start position:0% +out how the government ought to be + + + align:start position:0% +out how the government ought to be +organized there weren't any obvious + + align:start position:0% +organized there weren't any obvious + + + align:start position:0% +organized there weren't any obvious +models there weren't any republics of + + align:start position:0% +models there weren't any republics of + + + align:start position:0% +models there weren't any republics of +any size Venice had sort of had one but + + align:start position:0% +any size Venice had sort of had one but + + + align:start position:0% +any size Venice had sort of had one but +there weren't any republics of any size + + align:start position:0% +there weren't any republics of any size + + + align:start position:0% +there weren't any republics of any size +currently England had a king and they + + align:start position:0% +currently England had a king and they + + + align:start position:0% +currently England had a king and they +didn't want to do a king So how do you + + align:start position:0% +didn't want to do a king So how do you + + + align:start position:0% +didn't want to do a king So how do you +run a government without a king well you + + align:start position:0% +run a government without a king well you + + + align:start position:0% +run a government without a king well you +could look back to Rome you could look + + align:start position:0% +could look back to Rome you could look + + + align:start position:0% +could look back to Rome you could look +to Athens they lasted a while they fell + + align:start position:0% +to Athens they lasted a while they fell + + + align:start position:0% +to Athens they lasted a while they fell +the Roman Republic became a a + + align:start position:0% +the Roman Republic became a a + + + align:start position:0% +the Roman Republic became a a +dictatorship basically and Athens fell + + align:start position:0% +dictatorship basically and Athens fell + + + align:start position:0% +dictatorship basically and Athens fell +uh for a variety of reasons and really + + align:start position:0% +uh for a variety of reasons and really + + + align:start position:0% +uh for a variety of reasons and really +was a + + align:start position:0% +was a + + + align:start position:0% +was a +democracy which they didn't think they + + align:start position:0% +democracy which they didn't think they + + + align:start position:0% +democracy which they didn't think they +wanted they wanted a republic how would + + align:start position:0% +wanted they wanted a republic how would + + + align:start position:0% +wanted they wanted a republic how would +you do a + + align:start position:0% +you do a + + + align:start position:0% +you do a +republic so it is quite extraordinary if + + align:start position:0% +republic so it is quite extraordinary if + + + align:start position:0% +republic so it is quite extraordinary if +you read what they wrote at the time it + + align:start position:0% +you read what they wrote at the time it + + + align:start position:0% +you read what they wrote at the time it +was like well we can we can look at what + + align:start position:0% +was like well we can we can look at what + + + align:start position:0% +was like well we can we can look at what +the Romans did but but if you look at + + align:start position:0% +the Romans did but but if you look at + + + align:start position:0% +the Romans did but but if you look at +the details of the Roman setup it was + + align:start position:0% +the details of the Roman setup it was + + + align:start position:0% +the details of the Roman setup it was +very strange uh and you wouldn't want to + + align:start position:0% +very strange uh and you wouldn't want to + + + align:start position:0% +very strange uh and you wouldn't want to +you know people held office for a year + + align:start position:0% +you know people held office for a year + + + align:start position:0% +you know people held office for a year +and the nobility were the were the + + align:start position:0% +and the nobility were the were the + + + align:start position:0% +and the nobility were the were the +office holders you wouldn't want to do + + align:start position:0% +office holders you wouldn't want to do + + + align:start position:0% +office holders you wouldn't want to do +that um so what would you do the first + + align:start position:0% +that um so what would you do the first + + + align:start position:0% +that um so what would you do the first +thing they did during the revolution + + align:start position:0% +thing they did during the revolution + + + align:start position:0% +thing they did during the revolution +they set up the Articles of + + align:start position:0% +they set up the Articles of + + + align:start position:0% +they set up the Articles of +Confederation and that really was a deal + + align:start position:0% +Confederation and that really was a deal + + + align:start position:0% +Confederation and that really was a deal +between 13 independent + + align:start position:0% +between 13 independent + + + align:start position:0% +between 13 independent +colonies each one a sovereign state in + + align:start position:0% +colonies each one a sovereign state in + + + align:start position:0% +colonies each one a sovereign state in +its own eyes and the Articles of + + align:start position:0% +its own eyes and the Articles of + + + align:start position:0% +its own eyes and the Articles of +Confederation didn't have any executive + + align:start position:0% +Confederation didn't have any executive + + + align:start position:0% +Confederation didn't have any executive +branch they had Congress didn't set up + + align:start position:0% +branch they had Congress didn't set up + + + align:start position:0% +branch they had Congress didn't set up +any courts and the Congress didn't have + + align:start position:0% +any courts and the Congress didn't have + + + align:start position:0% +any courts and the Congress didn't have +the power to raise + + align:start position:0% +the power to raise + + + align:start position:0% +the power to raise +money so Congress had the power to + + align:start position:0% +money so Congress had the power to + + + align:start position:0% +money so Congress had the power to +borrow + + align:start position:0% +borrow + + + align:start position:0% +borrow +money and Congress could ask the states + + align:start position:0% +money and Congress could ask the states + + + align:start position:0% +money and Congress could ask the states +to please send in + + align:start position:0% +to please send in + + + align:start position:0% +to please send in +money and that had mixed results so at + + align:start position:0% +money and that had mixed results so at + + + align:start position:0% +money and that had mixed results so at +the end of the Revolution there was a + + align:start position:0% +the end of the Revolution there was a + + + align:start position:0% +the end of the Revolution there was a +lot of national debt we debt financed + + align:start position:0% +lot of national debt we debt financed + + + align:start position:0% +lot of national debt we debt financed +the revolution because the states by and + + align:start position:0% +the revolution because the states by and + + + align:start position:0% +the revolution because the states by and +large states also borrowed a lot so + + align:start position:0% +large states also borrowed a lot so + + + align:start position:0% +large states also borrowed a lot so +there were a lot it was was a lot of + + align:start position:0% +there were a lot it was was a lot of + + + align:start position:0% +there were a lot it was was a lot of +debt floating around but it it couldn't + + align:start position:0% +debt floating around but it it couldn't + + + align:start position:0% +debt floating around but it it couldn't +tax we tried to run a government that + + align:start position:0% +tax we tried to run a government that + + + align:start position:0% +tax we tried to run a government that +way for a while but that didn't make any + + align:start position:0% +way for a while but that didn't make any + + + align:start position:0% +way for a while but that didn't make any +sense so they sat down and they drafted + + align:start position:0% +sense so they sat down and they drafted + + + align:start position:0% +sense so they sat down and they drafted +the Constitution you will notice that's + + align:start position:0% +the Constitution you will notice that's + + + align:start position:0% +the Constitution you will notice that's +10 years later more or less so they + + align:start position:0% +10 years later more or less so they + + + align:start position:0% +10 years later more or less so they +tried it for a while during and after + + align:start position:0% +tried it for a while during and after + + + align:start position:0% +tried it for a while during and after +the + + align:start position:0% +the + + + align:start position:0% +the +Revolution and then they wrote the + + align:start position:0% +Revolution and then they wrote the + + + align:start position:0% +Revolution and then they wrote the +Constitution that we now have which + + align:start position:0% +Constitution that we now have which + + + align:start position:0% +Constitution that we now have which +everybody sort of treats as yes of + + align:start position:0% +everybody sort of treats as yes of + + + align:start position:0% +everybody sort of treats as yes of +course that's what you would do at the + + align:start position:0% +course that's what you would do at the + + + align:start position:0% +course that's what you would do at the +time it was ridic ridiculously controver + + align:start position:0% +time it was ridic ridiculously controver + + + align:start position:0% +time it was ridic ridiculously controver +I don't mean ridiculously it was + + align:start position:0% +I don't mean ridiculously it was + + + align:start position:0% +I don't mean ridiculously it was +enormously + + align:start position:0% +enormously + + + align:start position:0% +enormously +controversial it was not clear it would + + align:start position:0% +controversial it was not clear it would + + + align:start position:0% +controversial it was not clear it would +be + + align:start position:0% +be + + + align:start position:0% +be +ratified there was intense opposition + + align:start position:0% +ratified there was intense opposition + + + align:start position:0% +ratified there was intense opposition +particularly in New York also in + + align:start position:0% +particularly in New York also in + + + align:start position:0% +particularly in New York also in +Virginia the two leading colonies very + + align:start position:0% +Virginia the two leading colonies very + + + align:start position:0% +Virginia the two leading colonies very +organized opposition the governor of New + + align:start position:0% +organized opposition the governor of New + + + align:start position:0% +organized opposition the governor of New +York opposed it they did not want to + + align:start position:0% +York opposed it they did not want to + + + align:start position:0% +York opposed it they did not want to +centralize power which is what the + + align:start position:0% +centralize power which is what the + + + align:start position:0% +centralize power which is what the +Constitution did it took power to the + + align:start position:0% +Constitution did it took power to the + + + align:start position:0% +Constitution did it took power to the +central government so we think of the + + align:start position:0% +central government so we think of the + + + align:start position:0% +central government so we think of the +Federalist Papers as sort of + + align:start position:0% + + + + align:start position:0% + +Reflections idle + + align:start position:0% +Reflections idle + + + align:start position:0% +Reflections idle +commentary you know people with time on + + align:start position:0% +commentary you know people with time on + + + align:start position:0% +commentary you know people with time on +their hands talking about what we + + align:start position:0% +their hands talking about what we + + + align:start position:0% +their hands talking about what we +intended when we wrote the Constitution + + align:start position:0% +intended when we wrote the Constitution + + + align:start position:0% +intended when we wrote the Constitution +these were political documents Madison + + align:start position:0% +these were political documents Madison + + + align:start position:0% +these were political documents Madison +was all these guys were arguing here are + + align:start position:0% +was all these guys were arguing here are + + + align:start position:0% +was all these guys were arguing here are +reasons to ratify please + + align:start position:0% +reasons to ratify please + + + align:start position:0% +reasons to ratify please +ratify um so this was this was an + + align:start position:0% +ratify um so this was this was an + + + align:start position:0% +ratify um so this was this was an +explicitly political document um at a + + align:start position:0% +explicitly political document um at a + + + align:start position:0% +explicitly political document um at a +somewhat different level than many + + align:start position:0% +somewhat different level than many + + + align:start position:0% +somewhat different level than many +political documents we see today uh but + + align:start position:0% +political documents we see today uh but + + + align:start position:0% +political documents we see today uh but +but it's important to recognize this was + + align:start position:0% +but it's important to recognize this was + + + align:start position:0% +but it's important to recognize this was +In the Heat of combat this was something + + align:start position:0% +In the Heat of combat this was something + + + align:start position:0% +In the Heat of combat this was something +you dash off over a weekend and then get + + align:start position:0% +you dash off over a weekend and then get + + + align:start position:0% +you dash off over a weekend and then get +to the next one this was not written at + + align:start position:0% +to the next one this was not written at + + + align:start position:0% +to the next one this was not written at +leisure uh in the study so that's + + align:start position:0% +leisure uh in the study so that's + + + align:start position:0% +leisure uh in the study so that's +Madison um and and um what's the problem + + align:start position:0% +Madison um and and um what's the problem + + + align:start position:0% +Madison um and and um what's the problem +what's the problem he's addressing in + + align:start position:0% +what's the problem he's addressing in + + + align:start position:0% +what's the problem he's addressing in +Federalist + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +Max faction what's + + align:start position:0% +Max faction what's + + + align:start position:0% +Max faction what's +faction group of people get + + align:start position:0% + + + + align:start position:0% + +together so it's not just the common + + align:start position:0% +together so it's not just the common + + + align:start position:0% +together so it's not just the common +goal it's get what they + + align:start position:0% +goal it's get what they + + + align:start position:0% +goal it's get what they +want which + + align:start position:0% + + + + align:start position:0% + +is not a good thing right he defines + + align:start position:0% +is not a good thing right he defines + + + align:start position:0% +is not a good thing right he defines +faction as you say they get together + + align:start position:0% +faction as you say they get together + + + align:start position:0% +faction as you say they get together +they're United and actuated by a common + + align:start position:0% +they're United and actuated by a common + + + align:start position:0% +they're United and actuated by a common +impulse I think that should be or + + align:start position:0% +impulse I think that should be or + + + align:start position:0% +impulse I think that should be or +passion I think that's my typo uh or + + align:start position:0% +passion I think that's my typo uh or + + + align:start position:0% +passion I think that's my typo uh or +maybe it's passion of in any case it the + + align:start position:0% +maybe it's passion of in any case it the + + + align:start position:0% +maybe it's passion of in any case it the +key is this last part adverse to the + + align:start position:0% +key is this last part adverse to the + + + align:start position:0% +key is this last part adverse to the +rights of other citizens or the + + align:start position:0% +rights of other citizens or the + + + align:start position:0% +rights of other citizens or the +permanent and aggregate interests of the + + align:start position:0% +permanent and aggregate interests of the + + + align:start position:0% +permanent and aggregate interests of the +community uh at the end of the thing in + + align:start position:0% +community uh at the end of the thing in + + + align:start position:0% +community uh at the end of the thing in +his one of his uster of remarks he talks + + align:start position:0% +his one of his uster of remarks he talks + + + align:start position:0% +his one of his uster of remarks he talks +about a rage for proper money a for + + align:start position:0% +about a rage for proper money a for + + + align:start position:0% +about a rage for proper money a for +paper money or for any other improper or + + align:start position:0% +paper money or for any other improper or + + + align:start position:0% +paper money or for any other improper or +Wicked project dot dot dot so that's the + + align:start position:0% +Wicked project dot dot dot so that's the + + + align:start position:0% +Wicked project dot dot dot so that's the +kind of thing he has in mind that a + + align:start position:0% +kind of thing he has in mind that a + + + align:start position:0% +kind of thing he has in mind that a +faction might actually Advocate what we + + align:start position:0% +faction might actually Advocate what we + + + align:start position:0% +faction might actually Advocate what we +carry around in our pockets every day + + align:start position:0% +carry around in our pockets every day + + + align:start position:0% +carry around in our pockets every day +which when he was writing was viewed as + + align:start position:0% +which when he was writing was viewed as + + + align:start position:0% +which when he was writing was viewed as +evil okay let's look at that's the + + align:start position:0% +evil okay let's look at that's the + + + align:start position:0% +evil okay let's look at that's the +problem how in a a representative uh + + align:start position:0% +problem how in a a representative uh + + + align:start position:0% +problem how in a a representative uh +Republic or democracy where you want the + + align:start position:0% +Republic or democracy where you want the + + + align:start position:0% +Republic or democracy where you want the +will of the people to drive + + align:start position:0% +will of the people to drive + + + align:start position:0% +will of the people to drive +decisions how do you guard against a set + + align:start position:0% +decisions how do you guard against a set + + + align:start position:0% +decisions how do you guard against a set +of people who want to do things that + + align:start position:0% +of people who want to do things that + + + align:start position:0% +of people who want to do things that +basically trample on the rights of + + align:start position:0% +basically trample on the rights of + + + align:start position:0% +basically trample on the rights of +others or would harm the + + align:start position:0% +others or would harm the + + + align:start position:0% +others or would harm the +community how do you fix that that's + + align:start position:0% +community how do you fix that that's + + + align:start position:0% +community how do you fix that that's +kind of an interesting design problem so + + align:start position:0% +kind of an interesting design problem so + + + align:start position:0% +kind of an interesting design problem so +let's walk through + + align:start position:0% +let's walk through + + + align:start position:0% +let's walk through +it first could you eliminate factions + + align:start position:0% +it first could you eliminate factions + + + align:start position:0% +it first could you eliminate factions +what's he say about that oh what do you + + align:start position:0% +what's he say about that oh what do you + + + align:start position:0% +what's he say about that oh what do you +think about that could you avoid groups + + align:start position:0% +think about that could you avoid groups + + + align:start position:0% +think about that could you avoid groups +of people who want to do things that + + align:start position:0% +of people who want to do things that + + + align:start position:0% +of people who want to do things that +would trample on the rights of others or + + align:start position:0% +would trample on the rights of others or + + + align:start position:0% +would trample on the rights of others or +be adverse to the long-term interest of + + align:start position:0% +be adverse to the long-term interest of + + + align:start position:0% +be adverse to the long-term interest of +the + + align:start position:0% +the + + + align:start position:0% +the +community could you eliminate + + align:start position:0% + + + + align:start position:0% + +it oh I can't call on you again Max + + align:start position:0% +it oh I can't call on you again Max + + + align:start position:0% +it oh I can't call on you again Max +you've actually read the thing I could + + align:start position:0% +you've actually read the thing I could + + + align:start position:0% +you've actually read the thing I could +tell anybody else Kirsten um you argued + + align:start position:0% +tell anybody else Kirsten um you argued + + + align:start position:0% +tell anybody else Kirsten um you argued +that to eliminate the cause you have to + + align:start position:0% +that to eliminate the cause you have to + + + align:start position:0% +that to eliminate the cause you have to +either eliminate the people's Liberty to + + align:start position:0% +either eliminate the people's Liberty to + + + align:start position:0% +either eliminate the people's Liberty to +choose or eliminate their capability of + + align:start position:0% +choose or eliminate their capability of + + + align:start position:0% +choose or eliminate their capability of +think that would be against + + align:start position:0% +think that would be against + + + align:start position:0% +think that would be against +well uh apart from from Universal free + + align:start position:0% +well uh apart from from Universal free + + + align:start position:0% +well uh apart from from Universal free +beer I'm not sure how you eliminate + + align:start position:0% +beer I'm not sure how you eliminate + + + align:start position:0% +beer I'm not sure how you eliminate +their their ability to think he points + + align:start position:0% +their their ability to think he points + + + align:start position:0% +their their ability to think he points +in another Direction though doesn't he + + align:start position:0% +in another Direction though doesn't he + + + align:start position:0% +in another Direction though doesn't he +suppose he says first you could you can + + align:start position:0% +suppose he says first you could you can + + + align:start position:0% +suppose he says first you could you can +you can eliminate their + + align:start position:0% + + + + align:start position:0% + +Liberty but + + align:start position:0% +Liberty but + + + align:start position:0% +Liberty but +then suppose they were all alike suppose + + align:start position:0% +then suppose they were all alike suppose + + + align:start position:0% +then suppose they were all alike suppose +everybody were the same if you could do + + align:start position:0% +everybody were the same if you could do + + + align:start position:0% +everybody were the same if you could do +that you wouldn't have this problem + + align:start position:0% +that you wouldn't have this problem + + + align:start position:0% +that you wouldn't have this problem +that's not likely given that everybody + + align:start position:0% +that's not likely given that everybody + + + align:start position:0% +that's not likely given that everybody +can think for and just given reason + + align:start position:0% +can think for and just given reason + + + align:start position:0% +can think for and just given reason +people come with different conclusions + + align:start position:0% +people come with different conclusions + + + align:start position:0% +people come with different conclusions +he also points to something else that + + align:start position:0% +he also points to something else that + + + align:start position:0% +he also points to something else that +leads to differences you're right he + + align:start position:0% +leads to differences you're right he + + + align:start position:0% +leads to differences you're right he +says you can't you can't eliminate + + align:start position:0% +says you can't you can't eliminate + + + align:start position:0% +says you can't you can't eliminate +Liberty because that's the whole point + + align:start position:0% +Liberty because that's the whole point + + + align:start position:0% +Liberty because that's the whole point +of the exercise um you can't eliminate + + align:start position:0% +of the exercise um you can't eliminate + + + align:start position:0% +of the exercise um you can't eliminate +differences because people will have + + align:start position:0% +differences because people will have + + + align:start position:0% +differences because people will have +different opinions he points to a + + align:start position:0% +different opinions he points to a + + + align:start position:0% +different opinions he points to a +particular and something we see these + + align:start position:0% +particular and something we see these + + + align:start position:0% +particular and something we see these +days a particularly important source of + + align:start position:0% +days a particularly important source of + + + align:start position:0% +days a particularly important source of +differences of + + align:start position:0% +differences of + + + align:start position:0% +differences of +view Casey um was it property it was + + align:start position:0% +view Casey um was it property it was + + + align:start position:0% +view Casey um was it property it was +property yeah + + align:start position:0% +property yeah + + + align:start position:0% +property yeah +he says you know just the way the way + + align:start position:0% +he says you know just the way the way + + + align:start position:0% +he says you know just the way the way +life goes people get people + + align:start position:0% +life goes people get people + + + align:start position:0% +life goes people get people +accumulate some are rich some are poor + + align:start position:0% +accumulate some are rich some are poor + + + align:start position:0% +accumulate some are rich some are poor +some have a lot some have a little that + + align:start position:0% +some have a lot some have a little that + + + align:start position:0% +some have a lot some have a little that +divides their interests rich people and + + align:start position:0% +divides their interests rich people and + + + align:start position:0% +divides their interests rich people and +poor people have different interests + + align:start position:0% +poor people have different interests + + + align:start position:0% +poor people have different interests +they're going to have different views so + + align:start position:0% +they're going to have different views so + + + align:start position:0% +they're going to have different views so +you can't you can't keep them from + + align:start position:0% +you can't you can't keep them from + + + align:start position:0% +you can't you can't keep them from +expressing their different views that + + align:start position:0% +expressing their different views that + + + align:start position:0% +expressing their different views that +would be to eliminate Liberty that would + + align:start position:0% +would be to eliminate Liberty that would + + + align:start position:0% +would be to eliminate Liberty that would +be unwise and it would be impractical he + + align:start position:0% +be unwise and it would be impractical he + + + align:start position:0% +be unwise and it would be impractical he +says of course the the Communist + + align:start position:0% +says of course the the Communist + + + align:start position:0% +says of course the the Communist +argument was no no no we should + + align:start position:0% +argument was no no no we should + + + align:start position:0% +argument was no no no we should +eliminate differences in property that + + align:start position:0% +eliminate differences in property that + + + align:start position:0% +eliminate differences in property that +will that will take care of it uh he + + align:start position:0% +will that will take care of it uh he + + + align:start position:0% +will that will take care of it uh he +calls that impractical which is pretty + + align:start position:0% +calls that impractical which is pretty + + + align:start position:0% +calls that impractical which is pretty +good diagnosis in advance of Marx um so + + align:start position:0% +good diagnosis in advance of Marx um so + + + align:start position:0% +good diagnosis in advance of Marx um so +if you if you're going to have factions + + align:start position:0% +if you if you're going to have factions + + + align:start position:0% +if you if you're going to have factions +how do you deal with let's say a small + + align:start position:0% +how do you deal with let's say a small + + + align:start position:0% +how do you deal with let's say a small +one is that a problem is that a problem + + align:start position:0% +one is that a problem is that a problem + + + align:start position:0% +one is that a problem is that a problem +you have to worry + + align:start position:0% + + + + align:start position:0% + +about well you don't have to have read + + align:start position:0% +about well you don't have to have read + + + align:start position:0% +about well you don't have to have read +Madison to think about this suppose + + align:start position:0% +Madison to think about this suppose + + + align:start position:0% +Madison to think about this suppose +you're voting is a minority faction of + + align:start position:0% +you're voting is a minority faction of + + + align:start position:0% +you're voting is a minority faction of +problem + + align:start position:0% +problem + + + align:start position:0% +problem +say why I mean as long as they accept + + align:start position:0% +say why I mean as long as they accept + + + align:start position:0% +say why I mean as long as they accept +the decision outcome as long as they as + + align:start position:0% +the decision outcome as long as they as + + + align:start position:0% +the decision outcome as long as they as +long as you're staying within the rules + + align:start position:0% +long as you're staying within the rules + + + align:start position:0% +long as you're staying within the rules +of the game a minority faction loses + + align:start position:0% +of the game a minority faction loses + + + align:start position:0% +of the game a minority faction loses +they lose the vote + + align:start position:0% +they lose the vote + + + align:start position:0% +they lose the vote +okay that ought to take care of + + align:start position:0% +okay that ought to take care of + + + align:start position:0% +okay that ought to take care of +that now suppose he says suppose you + + align:start position:0% +that now suppose he says suppose you + + + align:start position:0% +that now suppose he says suppose you +have a pure democracy you have a small + + align:start position:0% +have a pure democracy you have a small + + + align:start position:0% +have a pure democracy you have a small +number of people gathered in a room uh + + align:start position:0% +number of people gathered in a room uh + + + align:start position:0% +number of people gathered in a room uh +or a small village and it's one person + + align:start position:0% +or a small village and it's one person + + + align:start position:0% +or a small village and it's one person +one + + align:start position:0% +one + + + align:start position:0% +one +vote um + + align:start position:0% +vote um + + + align:start position:0% +vote um +can you ever eliminate the problem of a + + align:start position:0% +can you ever eliminate the problem of a + + + align:start position:0% +can you ever eliminate the problem of a +majority faction which is clearly now + + align:start position:0% +majority faction which is clearly now + + + align:start position:0% +majority faction which is clearly now +the problem to deal with you have a + + align:start position:0% +the problem to deal with you have a + + + align:start position:0% +the problem to deal with you have a +problem of a majority that wants to + + align:start position:0% +problem of a majority that wants to + + + align:start position:0% +problem of a majority that wants to +trample on the rights of others can you + + align:start position:0% +trample on the rights of others can you + + + align:start position:0% +trample on the rights of others can you +can you make that unlikely or rule it + + align:start position:0% +can you make that unlikely or rule it + + + align:start position:0% +can you make that unlikely or rule it +out or rule out its effects when you + + align:start position:0% +out or rule out its effects when you + + + align:start position:0% +out or rule out its effects when you +have a small number when you're small + + align:start position:0% +have a small number when you're small + + + align:start position:0% +have a small number when you're small +enough to have a pure democracy no + + align:start position:0% +enough to have a pure democracy no + + + align:start position:0% +enough to have a pure democracy no +representation just everybody + + align:start position:0% + + + + align:start position:0% + +votes charlot you keep waving your hand + + align:start position:0% +votes charlot you keep waving your hand + + + align:start position:0% +votes charlot you keep waving your hand +I keep thinking you're raising but + + align:start position:0% +I keep thinking you're raising but + + + align:start position:0% +I keep thinking you're raising but +you're not raising it are you no but I + + align:start position:0% +you're not raising it are you no but I + + + align:start position:0% +you're not raising it are you no but I +mean like no you can't eliminate it if + + align:start position:0% +mean like no you can't eliminate it if + + + align:start position:0% +mean like no you can't eliminate it if +democracy exactly how it is unless you + + align:start position:0% +democracy exactly how it is unless you + + + align:start position:0% +democracy exactly how it is unless you +like change the way they're thinking + + align:start position:0% +like change the way they're thinking + + + align:start position:0% +like change the way they're thinking +which like in these rules can't do then + + align:start position:0% +which like in these rules can't do then + + + align:start position:0% +which like in these rules can't do then +if more people want it one way then + + align:start position:0% +if more people want it one way then + + + align:start position:0% +if more people want it one way then +they're going to win then they're going + + align:start position:0% +they're going to win then they're going + + + align:start position:0% +they're going to win then they're going +to win and you majority factions can + + align:start position:0% +to win and you majority factions can + + + align:start position:0% +to win and you majority factions can +happen because you can you can do + + align:start position:0% +happen because you can you can do + + + align:start position:0% +happen because you can you can do +influence you can do various other + + align:start position:0% +influence you can do various other + + + align:start position:0% +influence you can do various other +things so his answer is no you can't so + + align:start position:0% +things so his answer is no you can't so + + + align:start position:0% +things so his answer is no you can't so +he says okay and then he makes an + + align:start position:0% +he says okay and then he makes an + + + align:start position:0% +he says okay and then he makes an +argument that what you really want is a + + align:start position:0% +argument that what you really want is a + + + align:start position:0% +argument that what you really want is a +large Republic + + align:start position:0% +large Republic + + + align:start position:0% +large Republic +that's the way to deal with the problem + + align:start position:0% +that's the way to deal with the problem + + + align:start position:0% +that's the way to deal with the problem +of majority + + align:start position:0% +of majority + + + align:start position:0% +of majority +factions + + align:start position:0% +factions + + + align:start position:0% +factions +why he gives two basic + + align:start position:0% +why he gives two basic + + + align:start position:0% +why he gives two basic +reasons one of which I think is + + align:start position:0% + + + + align:start position:0% + +wrong Jessica one of the Reas is because + + align:start position:0% +wrong Jessica one of the Reas is because + + + align:start position:0% +wrong Jessica one of the Reas is because +it gives some sense of equal power so a + + align:start position:0% +it gives some sense of equal power so a + + + align:start position:0% +it gives some sense of equal power so a +bigger party that can um sort + + align:start position:0% +bigger party that can um sort + + + align:start position:0% +bigger party that can um sort +of decide where that faction + + align:start position:0% +of decide where that faction + + + align:start position:0% +of decide where that faction +well I don't know what you mean by equal + + align:start position:0% +well I don't know what you mean by equal + + + align:start position:0% +well I don't know what you mean by equal +power he says if if it's large there'll + + align:start position:0% +power he says if if it's large there'll + + + align:start position:0% +power he says if if it's large there'll +be diversity but um push that a little + + align:start position:0% +be diversity but um push that a little + + + align:start position:0% +be diversity but um push that a little +more what do you mean by uh a greater + + align:start position:0% +more what do you mean by uh a greater + + + align:start position:0% +more what do you mean by uh a greater +the people ruling in that Republic will + + align:start position:0% +the people ruling in that Republic will + + + align:start position:0% +the people ruling in that Republic will +be able to uh somewhat it's sort of a + + align:start position:0% +be able to uh somewhat it's sort of a + + + align:start position:0% +be able to uh somewhat it's sort of a +check and balance in in a way you'll + + align:start position:0% +check and balance in in a way you'll + + + align:start position:0% +check and balance in in a way you'll +have one of the final States and not and + + align:start position:0% +have one of the final States and not and + + + align:start position:0% +have one of the final States and not and +not if it's not a pure + + align:start position:0% +not if it's not a pure + + + align:start position:0% +not if it's not a pure +democracy + + align:start position:0% +democracy + + + align:start position:0% +democracy +well he has in mind a republic or a + + align:start position:0% +well he has in mind a republic or a + + + align:start position:0% +well he has in mind a republic or a +representative democracy he has in mind + + align:start position:0% +representative democracy he has in mind + + + align:start position:0% +representative democracy he has in mind +a situation where people are elected + + align:start position:0% +a situation where people are elected + + + align:start position:0% +a situation where people are elected +from around the country and those people + + align:start position:0% +from around the country and those people + + + align:start position:0% +from around the country and those people +are the ultimate decision makers + + align:start position:0% +are the ultimate decision makers + + + align:start position:0% +are the ultimate decision makers +so where they're elected you could + + align:start position:0% +so where they're elected you could + + + align:start position:0% +so where they're elected you could +imagine a majority faction maybe but um + + align:start position:0% +imagine a majority faction maybe but um + + + align:start position:0% +imagine a majority faction maybe but um +kir you wanted + + align:start position:0% +kir you wanted + + + align:start position:0% +kir you wanted +to say he's making the assumption that + + align:start position:0% +to say he's making the assumption that + + + align:start position:0% +to say he's making the assumption that +elected officials would represent public + + align:start position:0% +elected officials would represent public + + + align:start position:0% +elected officials would represent public +good + + align:start position:0% +good + + + align:start position:0% +good +necessary said that a he kind of hinted + + align:start position:0% +necessary said that a he kind of hinted + + + align:start position:0% +necessary said that a he kind of hinted +that direction yeah but he points he + + align:start position:0% +that direction yeah but he points he + + + align:start position:0% +that direction yeah but he points he +points someplace else he does sort of + + align:start position:0% +points someplace else he does sort of + + + align:start position:0% +points someplace else he does sort of +say that and then he's he does say at + + align:start position:0% +say that and then he's he does say at + + + align:start position:0% +say that and then he's he does say at +some point that you can't count on it he + + align:start position:0% +some point that you can't count on it he + + + align:start position:0% +some point that you can't count on it he +says + + align:start position:0% +says + + + align:start position:0% +says +um it is vain to say that enlightened + + align:start position:0% +um it is vain to say that enlightened + + + align:start position:0% +um it is vain to say that enlightened +Statesmen will be able to adjust these + + align:start position:0% +Statesmen will be able to adjust these + + + align:start position:0% +Statesmen will be able to adjust these +clashing interests uh enlightened + + align:start position:0% +clashing interests uh enlightened + + + align:start position:0% +clashing interests uh enlightened +statement enlightened Statesmen will not + + align:start position:0% +statement enlightened Statesmen will not + + + align:start position:0% +statement enlightened Statesmen will not +always be at the helm so he's he he + + align:start position:0% +always be at the helm so he's he he + + + align:start position:0% +always be at the helm so he's he he +points in that direction and then and + + align:start position:0% +points in that direction and then and + + + align:start position:0% +points in that direction and then and +then backs + + align:start position:0% +then backs + + + align:start position:0% +then backs +off somebody + + align:start position:0% +off somebody + + + align:start position:0% +off somebody +else Julian what do you + + align:start position:0% +else Julian what do you + + + align:start position:0% +else Julian what do you +think forget Madison what might solve + + align:start position:0% + + + + align:start position:0% + +it yeah but he's not there he's not + + align:start position:0% +it yeah but he's not there he's not + + + align:start position:0% +it yeah but he's not there he's not +there yeah you can induce compromise + + align:start position:0% +there yeah you can induce compromise + + + align:start position:0% +there yeah you can induce compromise +either by having Representatives be + + align:start position:0% +either by having Representatives be + + + align:start position:0% +either by having Representatives be +responsible or be accountable to lots of + + align:start position:0% +responsible or be accountable to lots of + + + align:start position:0% +responsible or be accountable to lots of +people or by having enough people that + + align:start position:0% +people or by having enough people that + + + align:start position:0% +people or by having enough people that +On Any Given issue they might form a + + align:start position:0% +On Any Given issue they might form a + + + align:start position:0% +On Any Given issue they might form a +majority faction but you start + + align:start position:0% +majority faction but you start + + + align:start position:0% +majority faction but you start +compromising because different sets of + + align:start position:0% +compromising because different sets of + + + align:start position:0% +compromising because different sets of +you will be in different majorities and + + align:start position:0% +you will be in different majorities and + + + align:start position:0% +you will be in different majorities and +different ISS that's a process issue and + + align:start position:0% +different ISS that's a process issue and + + + align:start position:0% +different ISS that's a process issue and +maybe you can make sure that kind of + + align:start position:0% +maybe you can make sure that kind of + + + align:start position:0% +maybe you can make sure that kind of +process is followed although if you look + + align:start position:0% +process is followed although if you look + + + align:start position:0% +process is followed although if you look +at how the Constitution works in the US + + align:start position:0% +at how the Constitution works in the US + + + align:start position:0% +at how the Constitution works in the US +you don't necessarily see that happening + + align:start position:0% +you don't necessarily see that happening + + + align:start position:0% +you don't necessarily see that happening +uh but he has in mind a structural + + align:start position:0% +uh but he has in mind a structural + + + align:start position:0% +uh but he has in mind a structural +difference + + align:start position:0% + + + + align:start position:0% + +that think back to what the country + + align:start position:0% +that think back to what the country + + + align:start position:0% +that think back to what the country +looked like when he was + + align:start position:0% +looked like when he was + + + align:start position:0% +looked like when he was +writing + + align:start position:0% +writing + + + align:start position:0% +writing +the No Electronic media weeks months to + + align:start position:0% +the No Electronic media weeks months to + + + align:start position:0% +the No Electronic media weeks months to +communicate north to south east to west + + align:start position:0% +communicate north to south east to west + + + align:start position:0% +communicate north to south east to west +uh lousy + + align:start position:0% +uh lousy + + + align:start position:0% +uh lousy +roads uh most most rapid most efficient + + align:start position:0% +roads uh most most rapid most efficient + + + align:start position:0% +roads uh most most rapid most efficient +communication would be by Sail by o by + + align:start position:0% +communication would be by Sail by o by + + + align:start position:0% +communication would be by Sail by o by +the ocean or on + + align:start position:0% +the ocean or on + + + align:start position:0% +the ocean or on +Riverbats + + align:start position:0% +Riverbats + + + align:start position:0% +Riverbats +um Boston to Philadelphia would be say + + align:start position:0% +um Boston to Philadelphia would be say + + + align:start position:0% +um Boston to Philadelphia would be say +to go to the Constitutional Convention + + align:start position:0% +to go to the Constitutional Convention + + + align:start position:0% +to go to the Constitutional Convention +would be measured not in hours but in + + align:start position:0% +would be measured not in hours but in + + + align:start position:0% +would be measured not in hours but in +days or maybe weeks + + align:start position:0% +days or maybe weeks + + + align:start position:0% +days or maybe weeks +depending um you had very different + + align:start position:0% +depending um you had very different + + + align:start position:0% +depending um you had very different +interests you had people trading on the + + align:start position:0% +interests you had people trading on the + + + align:start position:0% +interests you had people trading on the +coasts you had people farming Inland you + + align:start position:0% +coasts you had people farming Inland you + + + align:start position:0% +coasts you had people farming Inland you +had heavily slave dependent Societies in + + align:start position:0% +had heavily slave dependent Societies in + + + align:start position:0% +had heavily slave dependent Societies in +the South you had some slavery in the + + align:start position:0% +the South you had some slavery in the + + + align:start position:0% +the South you had some slavery in the +north but not as + + align:start position:0% +north but not as + + + align:start position:0% +north but not as +much and he basically argued that that + + align:start position:0% +much and he basically argued that that + + + align:start position:0% +much and he basically argued that that +might be enough to do it how could that + + align:start position:0% +might be enough to do it how could that + + + align:start position:0% +might be enough to do it how could that +work that might be enough to solve the + + align:start position:0% +work that might be enough to solve the + + + align:start position:0% +work that might be enough to solve the +problem I mean he doesn't say that + + align:start position:0% +problem I mean he doesn't say that + + + align:start position:0% +problem I mean he doesn't say that +explicitly but that's the world in which + + align:start position:0% +explicitly but that's the world in which + + + align:start position:0% +explicitly but that's the world in which +he's + + align:start position:0% +he's + + + align:start position:0% +he's +writing + + align:start position:0% + + + + align:start position:0% + +okay Chad you want to take a shot don't + + align:start position:0% +okay Chad you want to take a shot don't + + + align:start position:0% +okay Chad you want to take a shot don't +want to take a shot Pedro you want to + + align:start position:0% +want to take a shot Pedro you want to + + + align:start position:0% +want to take a shot Pedro you want to +take a shot go ahead okay so I just like + + align:start position:0% +take a shot go ahead okay so I just like + + + align:start position:0% +take a shot go ahead okay so I just like +thinking about this why large public are + + align:start position:0% +thinking about this why large public are + + + align:start position:0% +thinking about this why large public are +good and um I think it's like if we have + + align:start position:0% +good and um I think it's like if we have + + + align:start position:0% +good and um I think it's like if we have +bigger majority like it will be a + + align:start position:0% +bigger majority like it will be a + + + align:start position:0% +bigger majority like it will be a +smaller relative to the other one + + align:start position:0% +smaller relative to the other one + + + align:start position:0% +smaller relative to the other one +meaning like if the Republic is bigger + + align:start position:0% +meaning like if the Republic is bigger + + + align:start position:0% +meaning like if the Republic is bigger +the majority will not be as big as be + + align:start position:0% +the majority will not be as big as be + + + align:start position:0% +the majority will not be as big as be +that's close to it he argues if it's + + align:start position:0% +that's close to it he argues if it's + + + align:start position:0% +that's close to it he argues if it's +big you're likely to have local factions + + align:start position:0% +big you're likely to have local factions + + + align:start position:0% +big you're likely to have local factions +that'll happen you could have a majority + + align:start position:0% +that'll happen you could have a majority + + + align:start position:0% +that'll happen you could have a majority +of the people in South + + align:start position:0% +of the people in South + + + align:start position:0% +of the people in South +Carolina want slavery forever in the + + align:start position:0% +Carolina want slavery forever in the + + + align:start position:0% +Carolina want slavery forever in the +Constitution or not in the Constitution + + align:start position:0% +Constitution or not in the Constitution + + + align:start position:0% +Constitution or not in the Constitution +they want some law strongly favoring + + align:start position:0% +they want some law strongly favoring + + + align:start position:0% +they want some law strongly favoring +slavery but that's South Carolina and if + + align:start position:0% +slavery but that's South Carolina and if + + + align:start position:0% +slavery but that's South Carolina and if +there's enough diversity you could have + + align:start position:0% +there's enough diversity you could have + + + align:start position:0% +there's enough diversity you could have +local factions but not National factions + + align:start position:0% +local factions but not National factions + + + align:start position:0% +local factions but not National factions +is is is basic argument he has two two + + align:start position:0% +is is is basic argument he has two two + + + align:start position:0% +is is is basic argument he has two two +arguments one + + align:start position:0% +arguments one + + + align:start position:0% +arguments one +is he says if there are larger districts + + align:start position:0% +is he says if there are larger districts + + + align:start position:0% +is he says if there are larger districts +if you have a large Republic then + + align:start position:0% +if you have a large Republic then + + + align:start position:0% +if you have a large Republic then +everybody's going to be elected by more + + align:start position:0% +everybody's going to be elected by more + + + align:start position:0% +everybody's going to be elected by more +people and uh you'll probably get better + + align:start position:0% +people and uh you'll probably get better + + + align:start position:0% +people and uh you'll probably get better +candidates that way and he says let me + + align:start position:0% +candidates that way and he says let me + + + align:start position:0% +candidates that way and he says let me +get + + align:start position:0% +get + + + align:start position:0% +get +this + + align:start position:0% +this + + + align:start position:0% +this +um the proportion of fit characters be + + align:start position:0% +um the proportion of fit characters be + + + align:start position:0% +um the proportion of fit characters be +not less in the large than in the small + + align:start position:0% +not less in the large than in the small + + + align:start position:0% +not less in the large than in the small +Republic the former will present a + + align:start position:0% +Republic the former will present a + + + align:start position:0% +Republic the former will present a +greater option and consequently a + + align:start position:0% +greater option and consequently a + + + align:start position:0% +greater option and consequently a +greater probability of a fit choice and + + align:start position:0% +greater probability of a fit choice and + + + align:start position:0% +greater probability of a fit choice and +he says also as each representative will + + align:start position:0% +he says also as each representative will + + + align:start position:0% +he says also as each representative will +be chosen by a greater number of + + align:start position:0% +be chosen by a greater number of + + + align:start position:0% +be chosen by a greater number of +citizens in the large than in the small + + align:start position:0% +citizens in the large than in the small + + + align:start position:0% +citizens in the large than in the small +Republic it would be more difficult for + + align:start position:0% +Republic it would be more difficult for + + + align:start position:0% +Republic it would be more difficult for +unworthy candidates to practice with + + align:start position:0% +unworthy candidates to practice with + + + align:start position:0% +unworthy candidates to practice with +success The Vicious Arts by which + + align:start position:0% +success The Vicious Arts by which + + + align:start position:0% +success The Vicious Arts by which +elections are too often + + align:start position:0% +elections are too often + + + align:start position:0% +elections are too often +carried he was not thinking of attack + + align:start position:0% +carried he was not thinking of attack + + + align:start position:0% +carried he was not thinking of attack +ads on television however which are more + + align:start position:0% +ads on television however which are more + + + align:start position:0% +ads on television however which are more +easily done in large than in small + + align:start position:0% +easily done in large than in small + + + align:start position:0% +easily done in large than in small +districts so I'm not persuaded by + + align:start position:0% +districts so I'm not persuaded by + + + align:start position:0% +districts so I'm not persuaded by +that his second argument + + align:start position:0% +that his second argument + + + align:start position:0% +that his second argument +though is is the one we were we were + + align:start position:0% +though is is the one we were we were + + + align:start position:0% +though is is the one we were we were +inching + + align:start position:0% +inching + + + align:start position:0% +inching +toward + + align:start position:0% +toward + + + align:start position:0% +toward +is extend the sphere make it larger make + + align:start position:0% +is extend the sphere make it larger make + + + align:start position:0% +is extend the sphere make it larger make +it more diverse you make it less likely + + align:start position:0% +it more diverse you make it less likely + + + align:start position:0% +it more diverse you make it less likely +that the majority of the whole country + + align:start position:0% +that the majority of the whole country + + + align:start position:0% +that the majority of the whole country +will coales around a particular bad + + align:start position:0% +will coales around a particular bad + + + align:start position:0% +will coales around a particular bad +idea uh right a majority of the + + align:start position:0% +idea uh right a majority of the + + + align:start position:0% +idea uh right a majority of the +whole or if in fact a lot of people + + align:start position:0% +whole or if in fact a lot of people + + + align:start position:0% +whole or if in fact a lot of people +think that just because the place is + + align:start position:0% +think that just because the place is + + + align:start position:0% +think that just because the place is +spread out again no electronic + + align:start position:0% +spread out again no electronic + + + align:start position:0% +spread out again no electronic +communications the place is spread out + + align:start position:0% +communications the place is spread out + + + align:start position:0% +communications the place is spread out +they won't be able to find each other + + align:start position:0% +they won't be able to find each other + + + align:start position:0% +they won't be able to find each other +it'll be harder for them to discover + + align:start position:0% +it'll be harder for them to discover + + + align:start position:0% +it'll be harder for them to discover +their own strength and act in unison so + + align:start position:0% +their own strength and act in unison so + + + align:start position:0% +their own strength and act in unison so +he argues we can deal with + + align:start position:0% +he argues we can deal with + + + align:start position:0% +he argues we can deal with +this basically by you have a large + + align:start position:0% +this basically by you have a large + + + align:start position:0% +this basically by you have a large +Republic you have a lot of parties and + + align:start position:0% +Republic you have a lot of parties and + + + align:start position:0% +Republic you have a lot of parties and +interests and I'm going to spend time on + + align:start position:0% +interests and I'm going to spend time on + + + align:start position:0% +interests and I'm going to spend time on +parties and interests uh you make it + + align:start position:0% +parties and interests uh you make it + + + align:start position:0% +parties and interests uh you make it +less likely that among all that diverse + + align:start position:0% +less likely that among all that diverse + + + align:start position:0% +less likely that among all that diverse +Regional and and industrial and whatever + + align:start position:0% +Regional and and industrial and whatever + + + align:start position:0% +Regional and and industrial and whatever +interest you will get a majority of the + + align:start position:0% +interest you will get a majority of the + + + align:start position:0% +interest you will get a majority of the +whole country pointed in an unpleasant + + align:start position:0% +whole country pointed in an unpleasant + + + align:start position:0% +whole country pointed in an unpleasant +Direction you'll get competing diverse + + align:start position:0% +Direction you'll get competing diverse + + + align:start position:0% +Direction you'll get competing diverse +interests he also is relying on the fact + + align:start position:0% +interests he also is relying on the fact + + + align:start position:0% +interests he also is relying on the fact +that it will be hard to organize if + + align:start position:0% +that it will be hard to organize if + + + align:start position:0% +that it will be hard to organize if +they're all spread + + align:start position:0% +they're all spread + + + align:start position:0% +they're all spread +out I'm going to come back to that too I + + align:start position:0% +out I'm going to come back to that too I + + + align:start position:0% +out I'm going to come back to that too I +don't think it's as true now as it was + + align:start position:0% +don't think it's as true now as it was + + + align:start position:0% +don't think it's as true now as it was +then but there's still truth to it okay + + align:start position:0% +then but there's still truth to it okay + + + align:start position:0% +then but there's still truth to it okay +you see the AR this one I think is a + + align:start position:0% +you see the AR this one I think is a + + + align:start position:0% +you see the AR this one I think is a +little odd um + + align:start position:0% +little odd um + + + align:start position:0% +little odd um +I I once remember + + align:start position:0% +I I once remember + + + align:start position:0% +I I once remember +uh you've never heard of Alan Simpson + + align:start position:0% +uh you've never heard of Alan Simpson + + + align:start position:0% +uh you've never heard of Alan Simpson +unless you really follow politics + + align:start position:0% +unless you really follow politics + + + align:start position:0% +unless you really follow politics +closely and you've heard of the Simpson + + align:start position:0% +closely and you've heard of the Simpson + + + align:start position:0% +closely and you've heard of the Simpson +BS deficit reduction pal uh panel Allan + + align:start position:0% +BS deficit reduction pal uh panel Allan + + + align:start position:0% +BS deficit reduction pal uh panel Allan +Simpson was about 6' five one of the + + align:start position:0% +Simpson was about 6' five one of the + + + align:start position:0% +Simpson was about 6' five one of the +funniest men in Washington and he was a + + align:start position:0% +funniest men in Washington and he was a + + + align:start position:0% +funniest men in Washington and he was a +senator from Wyoming a Republican + + align:start position:0% +senator from Wyoming a Republican + + + align:start position:0% +senator from Wyoming a Republican +senator from + + align:start position:0% +senator from + + + align:start position:0% +senator from +Wyoming who + + align:start position:0% +Wyoming who + + + align:start position:0% +Wyoming who +had a whole set of opinions on a whole + + align:start position:0% +had a whole set of opinions on a whole + + + align:start position:0% +had a whole set of opinions on a whole +set of issues that were not particularly + + align:start position:0% +set of issues that were not particularly + + + align:start position:0% +set of issues that were not particularly +Orthodox Republican positions + + align:start position:0% +Orthodox Republican positions + + + align:start position:0% +Orthodox Republican positions +uh and I remember somebody telling me + + align:start position:0% +uh and I remember somebody telling me + + + align:start position:0% +uh and I remember somebody telling me +that you know Wyoming is a small state + + align:start position:0% +that you know Wyoming is a small state + + + align:start position:0% +that you know Wyoming is a small state +he can actually sit down and explain + + align:start position:0% +he can actually sit down and explain + + + align:start position:0% +he can actually sit down and explain +himself to people in California you have + + align:start position:0% +himself to people in California you have + + + align:start position:0% +himself to people in California you have +to communicate by television in 30 + + align:start position:0% +to communicate by television in 30 + + + align:start position:0% +to communicate by television in 30 +second 30 second spots Simpson can go + + align:start position:0% +second 30 second spots Simpson can go + + + align:start position:0% +second 30 second spots Simpson can go +around and + + align:start position:0% +around and + + + align:start position:0% +around and +talk um so uh it's not clear to me you + + align:start position:0% +talk um so uh it's not clear to me you + + + align:start position:0% +talk um so uh it's not clear to me you +get better better candidates and better + + align:start position:0% +get better better candidates and better + + + align:start position:0% +get better better candidates and better +positions in large districts + + align:start position:0% +positions in large districts + + + align:start position:0% +positions in large districts +um but um that's the solution + + align:start position:0% +um but um that's the solution + + + align:start position:0% +um but um that's the solution +and in this solution you get a model of + + align:start position:0% +and in this solution you get a model of + + + align:start position:0% +and in this solution you get a model of +politics sort of the model of politics + + align:start position:0% +politics sort of the model of politics + + + align:start position:0% +politics sort of the model of politics +is a great variety of parties and + + align:start position:0% +is a great variety of parties and + + + align:start position:0% +is a great variety of parties and +interests + + align:start position:0% +interests + + + align:start position:0% +interests +competing making it + + align:start position:0% +competing making it + + + align:start position:0% +competing making it +impossible or + + align:start position:0% +impossible or + + + align:start position:0% +impossible or +unlikely + + align:start position:0% +unlikely + + + align:start position:0% +unlikely +that a big single group will form and + + align:start position:0% +that a big single group will form and + + + align:start position:0% +that a big single group will form and +trample on the rights of the minority or + + align:start position:0% +trample on the rights of the minority or + + + align:start position:0% +trample on the rights of the minority or +do something or be able to get something + + align:start position:0% +do something or be able to get something + + + align:start position:0% +do something or be able to get something +stupid past something really stupid past + + align:start position:0% +stupid past something really stupid past + + + align:start position:0% +stupid past something really stupid past +okay + + align:start position:0% +okay + + + align:start position:0% +okay +makes some + + align:start position:0% +makes some + + + align:start position:0% +makes some +sense yeah argue the same process kind + + align:start position:0% +sense yeah argue the same process kind + + + align:start position:0% +sense yeah argue the same process kind +of makes it harder to get anything + + align:start position:0% +of makes it harder to get anything + + + align:start position:0% +of makes it harder to get anything +anything well the US Constitution is + + align:start position:0% +anything well the US Constitution is + + + align:start position:0% +anything well the US Constitution is +distinctive + + align:start position:0% +distinctive + + + align:start position:0% +distinctive +internationally in how many obstacles it + + align:start position:0% +internationally in how many obstacles it + + + align:start position:0% +internationally in how many obstacles it +puts in front of getting anything done + + align:start position:0% +puts in front of getting anything done + + + align:start position:0% +puts in front of getting anything done +right there was this great fear of mob + + align:start position:0% +right there was this great fear of mob + + + align:start position:0% +right there was this great fear of mob +rule there was this great fear they'd + + align:start position:0% +rule there was this great fear they'd + + + align:start position:0% +rule there was this great fear they'd +had a king right so you don't want the + + align:start position:0% +had a king right so you don't want the + + + align:start position:0% +had a king right so you don't want the +president to be too powerful so you put + + align:start position:0% +president to be too powerful so you put + + + align:start position:0% +president to be too powerful so you put +a house you put a senate and you you're + + align:start position:0% +a house you put a senate and you you're + + + align:start position:0% +a house you put a senate and you you're +afraid that the house may be governed by + + align:start position:0% +afraid that the house may be governed by + + + align:start position:0% +afraid that the house may be governed by +mob rule because it turns over every two + + align:start position:0% +mob rule because it turns over every two + + + align:start position:0% +mob rule because it turns over every two +years so you have the Senate that's + + align:start position:0% +years so you have the Senate that's + + + align:start position:0% +years so you have the Senate that's +supposed to be deliberative and uh more + + align:start position:0% +supposed to be deliberative and uh more + + + align:start position:0% +supposed to be deliberative and uh more +aristocratic and slower and then + + align:start position:0% +aristocratic and slower and then + + + align:start position:0% +aristocratic and slower and then +although they hadn't really thought of + + align:start position:0% +although they hadn't really thought of + + + align:start position:0% +although they hadn't really thought of +it they got it pretty quickly you have + + align:start position:0% +it they got it pretty quickly you have + + + align:start position:0% +it they got it pretty quickly you have +the Supreme Court that has the ability + + align:start position:0% +the Supreme Court that has the ability + + + align:start position:0% +the Supreme Court that has the ability +to say this violates the + + align:start position:0% +to say this violates the + + + align:start position:0% +to say this violates the +Constitution it isn't in the + + align:start position:0% +Constitution it isn't in the + + + align:start position:0% +Constitution it isn't in the +Constitution that the Supreme Court can + + align:start position:0% +Constitution that the Supreme Court can + + + align:start position:0% +Constitution that the Supreme Court can +do that but the Supreme Court asserted + + align:start position:0% +do that but the Supreme Court asserted + + + align:start position:0% +do that but the Supreme Court asserted +it could and it did and has um so the + + align:start position:0% +it could and it did and has um so the + + + align:start position:0% +it could and it did and has um so the +the US system + + align:start position:0% +the US system + + + align:start position:0% +the US system +it's actually hard to explain to people + + align:start position:0% +it's actually hard to explain to people + + + align:start position:0% +it's actually hard to explain to people +outside the US that we do not have a + + align:start position:0% +outside the US that we do not have a + + + align:start position:0% +outside the US that we do not have a +government in the sense that they have a + + align:start position:0% +government in the sense that they have a + + + align:start position:0% +government in the sense that they have a +government in a parliamentary system the + + align:start position:0% +government in a parliamentary system the + + + align:start position:0% +government in a parliamentary system the +the Coalition that controls Parliament + + align:start position:0% +the Coalition that controls Parliament + + + align:start position:0% +the Coalition that controls Parliament +controls the Prime Minister uh names the + + align:start position:0% +controls the Prime Minister uh names the + + + align:start position:0% +controls the Prime Minister uh names the +Prime Minister if the government of + + align:start position:0% +Prime Minister if the government of + + + align:start position:0% +Prime Minister if the government of +which the prime minister is the head + + align:start position:0% +which the prime minister is the head + + + align:start position:0% +which the prime minister is the head +introduces a major law or introduces a + + align:start position:0% +introduces a major law or introduces a + + + align:start position:0% +introduces a major law or introduces a +budget and it doesn't pass the + + align:start position:0% +budget and it doesn't pass the + + + align:start position:0% +budget and it doesn't pass the +government Falls you have another + + align:start position:0% +government Falls you have another + + + align:start position:0% +government Falls you have another +election so when the Prime Minister says + + align:start position:0% +election so when the Prime Minister says + + + align:start position:0% +election so when the Prime Minister says +we're going to ratify this treaty either + + align:start position:0% +we're going to ratify this treaty either + + + align:start position:0% +we're going to ratify this treaty either +ratifies the treaty or he's + + align:start position:0% +ratifies the treaty or he's + + + align:start position:0% +ratifies the treaty or he's +gone that's we have nothing like that we + + align:start position:0% +gone that's we have nothing like that we + + + align:start position:0% +gone that's we have nothing like that we +we don't have a government that can make + + align:start position:0% +we don't have a government that can make + + + align:start position:0% +we don't have a government that can make +promises most countries do so you're + + align:start position:0% +promises most countries do so you're + + + align:start position:0% +promises most countries do so you're +right we set it up so we were not we + + align:start position:0% +right we set it up so we were not we + + + align:start position:0% +right we set it up so we were not we +don't have a king we don't have the + + align:start position:0% +don't have a king we don't have the + + + align:start position:0% +don't have a king we don't have the +House of Representatives in charge to a + + align:start position:0% +House of Representatives in charge to a + + + align:start position:0% +House of Representatives in charge to a +first approximation we don't have + + align:start position:0% +first approximation we don't have + + + align:start position:0% +first approximation we don't have +anybody in charge now in the 17th + + align:start position:0% +anybody in charge now in the 17th + + + align:start position:0% +anybody in charge now in the 17th +century 18th century rather this was + + align:start position:0% +century 18th century rather this was + + + align:start position:0% +century 18th century rather this was +considered a good + + align:start position:0% +considered a good + + + align:start position:0% +considered a good +thing it it still has its merits it + + align:start position:0% +thing it it still has its merits it + + + align:start position:0% +thing it it still has its merits it +means you know + + align:start position:0% +means you know + + + align:start position:0% +means you know +we we don't it's hard to act in haste + + align:start position:0% +we we don't it's hard to act in haste + + + align:start position:0% +we we don't it's hard to act in haste +one of the critiques of parliamentary + + align:start position:0% +one of the critiques of parliamentary + + + align:start position:0% +one of the critiques of parliamentary +systems is they can go from a set of + + align:start position:0% +systems is they can go from a set of + + + align:start position:0% +systems is they can go from a set of +leftwing policies to a set of right-wing + + align:start position:0% +leftwing policies to a set of right-wing + + + align:start position:0% +leftwing policies to a set of right-wing +policies with one election we move more + + align:start position:0% +policies with one election we move more + + + align:start position:0% +policies with one election we move more +slowly For Better or For Worse but + + align:start position:0% +slowly For Better or For Worse but + + + align:start position:0% +slowly For Better or For Worse but +you're right the whole Constitution is + + align:start position:0% +you're right the whole Constitution is + + + align:start position:0% +you're right the whole Constitution is +designed to prevent + + align:start position:0% +designed to prevent + + + align:start position:0% +designed to prevent +action to a first + + align:start position:0% +action to a first + + + align:start position:0% +action to a first +approximation + + align:start position:0% + + + + align:start position:0% + +okay Madison's model then is is one of + + align:start position:0% +okay Madison's model then is is one of + + + align:start position:0% +okay Madison's model then is is one of +competing interest + + align:start position:0% +competing interest + + + align:start position:0% +competing interest +groups + + align:start position:0% +groups + + + align:start position:0% +groups +um factions are + + align:start position:0% +um factions are + + + align:start position:0% +um factions are +inevitable but if they're weak if + + align:start position:0% +inevitable but if they're weak if + + + align:start position:0% +inevitable but if they're weak if +they're small and weak they don't + + align:start position:0% +they're small and weak they don't + + + align:start position:0% +they're small and weak they don't +Dominate and it's + + align:start position:0% +Dominate and it's + + + align:start position:0% +Dominate and it's +interesting if you go from from Madison + + align:start position:0% +interesting if you go from from Madison + + + align:start position:0% +interesting if you go from from Madison +and I I must say I'm sure you all find + + align:start position:0% +and I I must say I'm sure you all find + + + align:start position:0% +and I I must say I'm sure you all find +Loy easy to read I find him almost + + align:start position:0% +Loy easy to read I find him almost + + + align:start position:0% +Loy easy to read I find him almost +incomprehensible but um this is a + + align:start position:0% +incomprehensible but um this is a + + + align:start position:0% +incomprehensible but um this is a +standard text he argues this is right + + align:start position:0% +standard text he argues this is right + + + align:start position:0% +standard text he argues this is right +written in the 60s but I think it's + + align:start position:0% +written in the 60s but I think it's + + + align:start position:0% +written in the 60s but I think it's +still implicitly + + align:start position:0% +still implicitly + + + align:start position:0% +still implicitly +true that competition among interest + + align:start position:0% +true that competition among interest + + + align:start position:0% +true that competition among interest +groups has been both an accepted + + align:start position:0% +groups has been both an accepted + + + align:start position:0% +groups has been both an accepted +description of + + align:start position:0% +description of + + + align:start position:0% +description of +us politics and politics in some other + + align:start position:0% +us politics and politics in some other + + + align:start position:0% +us politics and politics in some other +settings and implicitly an + + align:start position:0% +settings and implicitly an + + + align:start position:0% +settings and implicitly an +ideal if you go to Washington and look + + align:start position:0% +ideal if you go to Washington and look + + + align:start position:0% +ideal if you go to Washington and look +look in the phone book look in buildings + + align:start position:0% +look in the phone book look in buildings + + + align:start position:0% +look in the phone book look in buildings +on K Street you will + + align:start position:0% +on K Street you will + + + align:start position:0% +on K Street you will +see uh I spoke yesterday to an interest + + align:start position:0% +see uh I spoke yesterday to an interest + + + align:start position:0% +see uh I spoke yesterday to an interest +group composed of large industrial users + + align:start position:0% +group composed of large industrial users + + + align:start position:0% +group composed of large industrial users +of + + align:start position:0% +of + + + align:start position:0% +of +electricity uh I was preceded by uh a + + align:start position:0% +electricity uh I was preceded by uh a + + + align:start position:0% +electricity uh I was preceded by uh a +spokesperson for the American public + + align:start position:0% +spokesperson for the American public + + + align:start position:0% +spokesperson for the American public +Power Association which represents + + align:start position:0% +Power Association which represents + + + align:start position:0% +Power Association which represents +Municipal and + + align:start position:0% +Municipal and + + + align:start position:0% +Municipal and +Cooperative uh Power consumers um if you + + align:start position:0% +Cooperative uh Power consumers um if you + + + align:start position:0% +Cooperative uh Power consumers um if you +just we were sharing quarters with the + + align:start position:0% +just we were sharing quarters with the + + + align:start position:0% +just we were sharing quarters with the +American Forest Products Association + + align:start position:0% +American Forest Products Association + + + align:start position:0% +American Forest Products Association +which represents uh uh Timber Harvesters + + align:start position:0% +which represents uh uh Timber Harvesters + + + align:start position:0% +which represents uh uh Timber Harvesters +um you can go up and down the + + align:start position:0% +um you can go up and down the + + + align:start position:0% +um you can go up and down the +street and there's the Department of + + align:start position:0% +street and there's the Department of + + + align:start position:0% +street and there's the Department of +Agriculture + + align:start position:0% +Agriculture + + + align:start position:0% +Agriculture +set up as an interest group basically to + + align:start position:0% +set up as an interest group basically to + + + align:start position:0% +set up as an interest group basically to +represent the farm community and on and + + align:start position:0% +represent the farm community and on and + + + align:start position:0% +represent the farm community and on and +on so the argument Loy makes is that we + + align:start position:0% +on so the argument Loy makes is that we + + + align:start position:0% +on so the argument Loy makes is that we +we've moved and I think well though he + + align:start position:0% +we've moved and I think well though he + + + align:start position:0% +we've moved and I think well though he +was writing in the 60s it isn't bad that + + align:start position:0% +was writing in the 60s it isn't bad that + + + align:start position:0% +was writing in the 60s it isn't bad that +that that has become both an accepted + + align:start position:0% +that that has become both an accepted + + + align:start position:0% +that that has become both an accepted +description think about how politics are + + align:start position:0% +description think about how politics are + + + align:start position:0% +description think about how politics are +described in the Press not presidential + + align:start position:0% +described in the Press not presidential + + + align:start position:0% +described in the Press not presidential +politics but any kind of legislative + + align:start position:0% +politics but any kind of legislative + + + align:start position:0% +politics but any kind of legislative +decision the environmental Community the + + align:start position:0% +decision the environmental Community the + + + align:start position:0% +decision the environmental Community the +black community women we describe the + + align:start position:0% +black community women we describe the + + + align:start position:0% +black community women we describe the +political process in terms of groups + + align:start position:0% +political process in terms of groups + + + align:start position:0% +political process in terms of groups +often the Cuban community in Atlanta + + align:start position:0% +often the Cuban community in Atlanta + + + align:start position:0% +often the Cuban community in Atlanta +blah blah blah I mean we do a lot of + + align:start position:0% +blah blah blah I mean we do a lot of + + + align:start position:0% +blah blah blah I mean we do a lot of +group description and it's + + align:start position:0% +group description and it's + + + align:start position:0% +group description and it's +almost here's the next + + align:start position:0% +almost here's the next + + + align:start position:0% +almost here's the next +step it's viewed as a good + + align:start position:0% +step it's viewed as a good + + + align:start position:0% +step it's viewed as a good +thing and the question is is it a good + + align:start position:0% +thing and the question is is it a good + + + align:start position:0% +thing and the question is is it a good +thing if that is first of all is it an + + align:start position:0% +thing if that is first of all is it an + + + align:start position:0% +thing if that is first of all is it an +accurate description of of politics and + + align:start position:0% +accurate description of of politics and + + + align:start position:0% +accurate description of of politics and +I'll come back to that sometimes yes + + align:start position:0% +I'll come back to that sometimes yes + + + align:start position:0% +I'll come back to that sometimes yes +sometimes + + align:start position:0% +sometimes + + + align:start position:0% +sometimes +no but first loie has a nice little + + align:start position:0% +no but first loie has a nice little + + + align:start position:0% +no but first loie has a nice little +statement about + + align:start position:0% +statement about + + + align:start position:0% +statement about +well could this be a good if politics + + align:start position:0% +well could this be a good if politics + + + align:start position:0% +well could this be a good if politics +looked like that could it be a good + + align:start position:0% +looked like that could it be a good + + + align:start position:0% +looked like that could it be a good +thing and he argues you you'd sort of + + align:start position:0% +thing and he argues you you'd sort of + + + align:start position:0% +thing and he argues you you'd sort of +need three + + align:start position:0% +need three + + + align:start position:0% +need three +pieces first you + + align:start position:0% +pieces first you + + + align:start position:0% +pieces first you +need you'd need clearly defined + + align:start position:0% +need you'd need clearly defined + + + align:start position:0% +need you'd need clearly defined +groups large consumers of electricity is + + align:start position:0% +groups large consumers of electricity is + + + align:start position:0% +groups large consumers of electricity is +a pretty clearly defined group but you + + align:start position:0% +a pretty clearly defined group but you + + + align:start position:0% +a pretty clearly defined group but you +can see it blurs but certainly uh uh + + align:start position:0% +can see it blurs but certainly uh uh + + + align:start position:0% +can see it blurs but certainly uh uh +cooperative and Municipal Utilities that + + align:start position:0% +cooperative and Municipal Utilities that + + + align:start position:0% +cooperative and Municipal Utilities that +buy electricity that's a well-defined + + align:start position:0% +buy electricity that's a well-defined + + + align:start position:0% +buy electricity that's a well-defined +group The Forest Products Association + + align:start position:0% +group The Forest Products Association + + + align:start position:0% +group The Forest Products Association +probably is + + align:start position:0% +probably is + + + align:start position:0% +probably is +um and then there's this I think of it + + align:start position:0% +um and then there's this I think of it + + + align:start position:0% +um and then there's this I think of it +mathematically as spanning the notion is + + align:start position:0% +mathematically as spanning the notion is + + + align:start position:0% +mathematically as spanning the notion is +that the groups the organized + + align:start position:0% +that the groups the organized + + + align:start position:0% +that the groups the organized +groups pretty much cover the universe + + align:start position:0% +groups pretty much cover the universe + + + align:start position:0% +groups pretty much cover the universe +pretty much every interest that matters + + align:start position:0% +pretty much every interest that matters + + + align:start position:0% +pretty much every interest that matters +is represented well by an organized + + align:start position:0% +is represented well by an organized + + + align:start position:0% +is represented well by an organized +group so that everybody's covered + + align:start position:0% +group so that everybody's covered + + + align:start position:0% +group so that everybody's covered +everybody has a group or not everybody + + align:start position:0% +everybody has a group or not everybody + + + align:start position:0% +everybody has a group or not everybody +every interest so you may be represented + + align:start position:0% +every interest so you may be represented + + + align:start position:0% +every interest so you may be represented +by several groups depending on what + + align:start position:0% +by several groups depending on what + + + align:start position:0% +by several groups depending on what +you're thinking about at the moment and + + align:start position:0% +you're thinking about at the moment and + + + align:start position:0% +you're thinking about at the moment and +then if you believe that as a statement + + align:start position:0% +then if you believe that as a statement + + + align:start position:0% +then if you believe that as a statement +of ideology as a statement about how the + + align:start position:0% +of ideology as a statement about how the + + + align:start position:0% +of ideology as a statement about how the +world should work that the role of + + align:start position:0% +world should work that the role of + + + align:start position:0% +world should work that the role of +government is basically to balance and + + align:start position:0% +government is basically to balance and + + + align:start position:0% +government is basically to balance and +reconcile to to do deals among various + + align:start position:0% +reconcile to to do deals among various + + + align:start position:0% +reconcile to to do deals among various +groups you ensure access so all groups + + align:start position:0% +groups you ensure access so all groups + + + align:start position:0% +groups you ensure access so all groups +can participate + + align:start position:0% +can participate + + + align:start position:0% +can participate +and you this is his language you ratify + + align:start position:0% +and you this is his language you ratify + + + align:start position:0% +and you this is his language you ratify +the agreements and adjustments worked + + align:start position:0% +the agreements and adjustments worked + + + align:start position:0% +the agreements and adjustments worked +out among + + align:start position:0% +out among + + + align:start position:0% +out among +them so again you hear legislative deals + + align:start position:0% +them so again you hear legislative deals + + + align:start position:0% +them so again you hear legislative deals +in Congress and we'll talk about we'll + + align:start position:0% +in Congress and we'll talk about we'll + + + align:start position:0% +in Congress and we'll talk about we'll +talk about some uh at length next time + + align:start position:0% +talk about some uh at length next time + + + align:start position:0% +talk about some uh at length next time +in this not next time the time after + + align:start position:0% +in this not next time the time after + + + align:start position:0% +in this not next time the time after +next in this case that where people + + align:start position:0% +next in this case that where people + + + align:start position:0% +next in this case that where people +explicitly say look these guys won in + + align:start position:0% +explicitly say look these guys won in + + + align:start position:0% +explicitly say look these guys won in +Congress and so our job is to make sure + + align:start position:0% +Congress and so our job is to make sure + + + align:start position:0% +Congress and so our job is to make sure +they get it they get the fruits of their + + align:start position:0% +they get it they get the fruits of their + + + align:start position:0% +they get it they get the fruits of their +Victory so do those make sense as + + align:start position:0% +Victory so do those make sense as + + + align:start position:0% +Victory so do those make sense as +descriptions of the world as you know it + + align:start position:0% +descriptions of the world as you know it + + + align:start position:0% +descriptions of the world as you know it +do those does that make sense as a + + align:start position:0% +do those does that make sense as a + + + align:start position:0% +do those does that make sense as a +description of a good + + align:start position:0% + + + + align:start position:0% + +World + + align:start position:0% + + + + align:start position:0% + +Katherine to comp but the problem is + + align:start position:0% +Katherine to comp but the problem is + + + align:start position:0% +Katherine to comp but the problem is +when you're talking about like business + + align:start position:0% +when you're talking about like business + + + align:start position:0% +when you're talking about like business +interests like generally the interest + + align:start position:0% +interests like generally the interest + + + align:start position:0% +interests like generally the interest +group most money like speaks the loudest + + align:start position:0% +group most money like speaks the loudest + + + align:start position:0% +group most money like speaks the loudest +given that like representatives and + + align:start position:0% +given that like representatives and + + + align:start position:0% +given that like representatives and +Senate and House like they want to get + + align:start position:0% +Senate and House like they want to get + + + align:start position:0% +Senate and House like they want to get +reelected and so like the group that has + + align:start position:0% +reelected and so like the group that has + + + align:start position:0% +reelected and so like the group that has +the most money can have like a larger in + + align:start position:0% +the most money can have like a larger in + + + align:start position:0% +the most money can have like a larger in +so you're pointing and I think I would + + align:start position:0% +so you're pointing and I think I would + + + align:start position:0% +so you're pointing and I think I would +too you're pointing sort of to the + + align:start position:0% +too you're pointing sort of to the + + + align:start position:0% +too you're pointing sort of to the +second of + + align:start position:0% +second of + + + align:start position:0% +second of +those + + align:start position:0% +those + + + align:start position:0% +those +assumptions um particularly the + + align:start position:0% +assumptions um particularly the + + + align:start position:0% +assumptions um particularly the +adequately represent part of it so what + + align:start position:0% +adequately represent part of it so what + + + align:start position:0% +adequately represent part of it so what +your saying is not all organ not all + + align:start position:0% +your saying is not all organ not all + + + align:start position:0% +your saying is not all organ not all +groups are created + + align:start position:0% +groups are created + + + align:start position:0% +groups are created +equal I think that's fair are all + + align:start position:0% +equal I think that's fair are all + + + align:start position:0% +equal I think that's fair are all +possible interests represented by + + align:start position:0% +possible interests represented by + + + align:start position:0% +possible interests represented by +organized + + align:start position:0% +organized + + + align:start position:0% +organized +groups no but I think that if like a + + align:start position:0% +groups no but I think that if like a + + + align:start position:0% +groups no but I think that if like a +group has a view and they're anywhere + + align:start position:0% +group has a view and they're anywhere + + + align:start position:0% +group has a view and they're anywhere +close enough to being like large enough + + align:start position:0% +close enough to being like large enough + + + align:start position:0% +close enough to being like large enough +to influence I + + align:start position:0% + + + + align:start position:0% + +think who represents the interests of + + align:start position:0% +think who represents the interests of + + + align:start position:0% +think who represents the interests of +uh mobile phone + + align:start position:0% +uh mobile phone + + + align:start position:0% +uh mobile phone +users is there an organized + + align:start position:0% +users is there an organized + + + align:start position:0% +users is there an organized +group + + align:start position:0% +group + + + align:start position:0% +group +or buyers of milk we have a federal milk + + align:start position:0% +or buyers of milk we have a federal milk + + + align:start position:0% +or buyers of milk we have a federal milk +price support program that's designed to + + align:start position:0% +price support program that's designed to + + + align:start position:0% +price support program that's designed to +raise the price of whole + + align:start position:0% +raise the price of whole + + + align:start position:0% +raise the price of whole +milk the Dairy Farmers are an + + align:start position:0% +milk the Dairy Farmers are an + + + align:start position:0% +milk the Dairy Farmers are an +effectively organized + + align:start position:0% +effectively organized + + + align:start position:0% +effectively organized +group people who give milk to their kids + + align:start position:0% +group people who give milk to their kids + + + align:start position:0% +group people who give milk to their kids +not so + + align:start position:0% +not so + + + align:start position:0% +not so +much so I would point to both parts I + + align:start position:0% +much so I would point to both parts I + + + align:start position:0% +much so I would point to both parts I +agree with you I agree with you on the + + align:start position:0% +agree with you I agree with you on the + + + align:start position:0% +agree with you I agree with you on the +second not all groups are created equal + + align:start position:0% +second not all groups are created equal + + + align:start position:0% +second not all groups are created equal +so you don't necessarily get the kind of + + align:start position:0% +so you don't necessarily get the kind of + + + align:start position:0% +so you don't necessarily get the kind of +balance you might like but I I'm not + + align:start position:0% +balance you might like but I I'm not + + + align:start position:0% +balance you might like but I I'm not +sure they they fill up most of the + + align:start position:0% +sure they they fill up most of the + + + align:start position:0% +sure they they fill up most of the +sectors of our + + align:start position:0% +sectors of our + + + align:start position:0% +sectors of our +lives + + align:start position:0% +lives + + + align:start position:0% +lives +and what's interesting I will yesterday + + align:start position:0% +and what's interesting I will yesterday + + + align:start position:0% +and what's interesting I will yesterday +was a good day for + + align:start position:0% +was a good day for + + + align:start position:0% +was a good day for +anecdotes + + align:start position:0% +anecdotes + + + align:start position:0% +anecdotes +so the speaker from the public Power + + align:start position:0% +so the speaker from the public Power + + + align:start position:0% +so the speaker from the public Power +Association said she was very happy to + + align:start position:0% +Association said she was very happy to + + + align:start position:0% +Association said she was very happy to +be addressing these large industrial + + align:start position:0% +be addressing these large industrial + + + align:start position:0% +be addressing these large industrial +consumers consumers because she said + + align:start position:0% +consumers consumers because she said + + + align:start position:0% +consumers consumers because she said +your group and my group are the only + + align:start position:0% +your group and my group are the only + + + align:start position:0% +your group and my group are the only +ones that represent consumers of + + align:start position:0% + + + + align:start position:0% + +electricity which probably makes sense + + align:start position:0% +electricity which probably makes sense + + + align:start position:0% +electricity which probably makes sense +right small businesses don't have an + + align:start position:0% +right small businesses don't have an + + + align:start position:0% +right small businesses don't have an +aren't represented in Washington as + + align:start position:0% +aren't represented in Washington as + + + align:start position:0% +aren't represented in Washington as +consumers of electricity the small + + align:start position:0% +consumers of electricity the small + + + align:start position:0% +consumers of electricity the small +business there is a national Federation + + align:start position:0% +business there is a national Federation + + + align:start position:0% +business there is a national Federation +of Independent businesses but it's got a + + align:start position:0% +of Independent businesses but it's got a + + + align:start position:0% +of Independent businesses but it's got a +lot of + + align:start position:0% +lot of + + + align:start position:0% +lot of +issues nobody's representing me as a + + align:start position:0% +issues nobody's representing me as a + + + align:start position:0% +issues nobody's representing me as a +consumer of electricity as far as I can + + align:start position:0% +consumer of electricity as far as I can + + + align:start position:0% +consumer of electricity as far as I can +tell + + align:start position:0% +tell + + + align:start position:0% +tell +um so when we were talking particularly + + align:start position:0% +um so when we were talking particularly + + + align:start position:0% +um so when we were talking particularly +about the firk when there is a proceding + + align:start position:0% +about the firk when there is a proceding + + + align:start position:0% +about the firk when there is a proceding +a regulatory proceeding at the firk a + + align:start position:0% +a regulatory proceeding at the firk a + + + align:start position:0% +a regulatory proceeding at the firk a +notice goes out you don't see it I don't + + align:start position:0% +notice goes out you don't see it I don't + + + align:start position:0% +notice goes out you don't see it I don't +see it they see it that's their job + + align:start position:0% +see it they see it that's their job + + + align:start position:0% +see it they see it that's their job +they're in Washington and they respond + + align:start position:0% +they're in Washington and they respond + + + align:start position:0% +they're in Washington and they respond +to it and with some + + align:start position:0% +to it and with some + + + align:start position:0% +to it and with some +luck they respond as consumers of + + align:start position:0% +luck they respond as consumers of + + + align:start position:0% +luck they respond as consumers of +electricity but they're consumers of + + align:start position:0% +electricity but they're consumers of + + + align:start position:0% +electricity but they're consumers of +electricity with particular issue + + align:start position:0% +electricity with particular issue + + + align:start position:0% +electricity with particular issue +particular + + align:start position:0% +particular + + + align:start position:0% +particular +interests they don't necessarily + + align:start position:0% +interests they don't necessarily + + + align:start position:0% +interests they don't necessarily +represent me + + align:start position:0% + + + + align:start position:0% + +yeah but look at all the residential + + align:start position:0% +yeah but look at all the residential + + + align:start position:0% +yeah but look at all the residential +users of electricity that's a lot of + + align:start position:0% +users of electricity that's a lot of + + + align:start position:0% +users of electricity that's a lot of +that's a lot of volume hard to organize + + align:start position:0% +that's a lot of volume hard to organize + + + align:start position:0% +that's a lot of volume hard to organize +though huh hard to organize so that's + + align:start position:0% +though huh hard to organize so that's + + + align:start position:0% +though huh hard to organize so that's +that's one kicker let me any anybody + + align:start position:0% +that's one kicker let me any anybody + + + align:start position:0% +that's one kicker let me any anybody +else I I I picked on Katherine enough + + align:start position:0% +else I I I picked on Katherine enough + + + align:start position:0% +else I I I picked on Katherine enough +Charlotte I had a question and so like a + + align:start position:0% +Charlotte I had a question and so like a + + + align:start position:0% +Charlotte I had a question and so like a +lot of the things you were listing + + align:start position:0% +lot of the things you were listing + + + align:start position:0% +lot of the things you were listing +earlier about things that Madison was + + align:start position:0% +earlier about things that Madison was + + + align:start position:0% +earlier about things that Madison was +considering factions like slavery or + + align:start position:0% +considering factions like slavery or + + + align:start position:0% +considering factions like slavery or +trade those are all things that I think + + align:start position:0% +trade those are all things that I think + + + align:start position:0% +trade those are all things that I think +of as like having to go with a party + + align:start position:0% +of as like having to go with a party + + + align:start position:0% +of as like having to go with a party +whereas like the things we're talking + + align:start position:0% +whereas like the things we're talking + + + align:start position:0% +whereas like the things we're talking +about now as factions are things that I + + align:start position:0% +about now as factions are things that I + + + align:start position:0% +about now as factions are things that I +wouldn't think about having to go with + + align:start position:0% +wouldn't think about having to go with + + + align:start position:0% +wouldn't think about having to go with +the political party so I guess like how + + align:start position:0% +the political party so I guess like how + + + align:start position:0% +the political party so I guess like how +is Madison relating factions to like + + align:start position:0% +is Madison relating factions to like + + + align:start position:0% +is Madison relating factions to like +political parties or what was the + + align:start position:0% +political parties or what was the + + + align:start position:0% +political parties or what was the +situation they actually hoped a number + + align:start position:0% +situation they actually hoped a number + + + align:start position:0% +situation they actually hoped a number +of them early on that you wouldn't have + + align:start position:0% +of them early on that you wouldn't have + + + align:start position:0% +of them early on that you wouldn't have +parties which was really had been the + + align:start position:0% +parties which was really had been the + + + align:start position:0% +parties which was really had been the +loyalist first hadn't like developed + + align:start position:0% +loyalist first hadn't like developed + + + align:start position:0% +loyalist first hadn't like developed +another one yet no I mean Washington had + + align:start position:0% +another one yet no I mean Washington had + + + align:start position:0% +another one yet no I mean Washington had +sufficient Charisma that until you began + + align:start position:0% +sufficient Charisma that until you began + + + align:start position:0% +sufficient Charisma that until you began +to to coales opposition to Washington in + + align:start position:0% +to to coales opposition to Washington in + + + align:start position:0% +to to coales opposition to Washington in +particular to Hamilton right Hamilton + + align:start position:0% +particular to Hamilton right Hamilton + + + align:start position:0% +particular to Hamilton right Hamilton +had a particular agenda for the central + + align:start position:0% +had a particular agenda for the central + + + align:start position:0% +had a particular agenda for the central +government which is to strengthen it and + + align:start position:0% +government which is to strengthen it and + + + align:start position:0% +government which is to strengthen it and +Jefferson and soon Madison opposed that + + align:start position:0% +Jefferson and soon Madison opposed that + + + align:start position:0% +Jefferson and soon Madison opposed that +strongly + + align:start position:0% + + + + align:start position:0% + +but political parties today also some + + align:start position:0% +but political parties today also some + + + align:start position:0% +but political parties today also some +sort of faction as you find it it's it's + + align:start position:0% +sort of faction as you find it it's it's + + + align:start position:0% +sort of faction as you find it it's it's +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +I and that was that was a fear right + + align:start position:0% +I and that was that was a fear right + + + align:start position:0% +I and that was that was a fear right +that if you manage to if you manage to + + align:start position:0% +that if you manage to if you manage to + + + align:start position:0% +that if you manage to if you manage to +get a large party as faction you you + + align:start position:0% +get a large party as faction you you + + + align:start position:0% +get a large party as faction you you +could have exactly the problem that + + align:start position:0% +could have exactly the problem that + + + align:start position:0% +could have exactly the problem that +Madison Madison thought of which is one + + align:start position:0% +Madison Madison thought of which is one + + + align:start position:0% +Madison Madison thought of which is one +reason why they didn't like parties + + align:start position:0% +reason why they didn't like parties + + + align:start position:0% +reason why they didn't like parties +um + + align:start position:0% +um + + + align:start position:0% +um +traditionally American political + + align:start position:0% +traditionally American political + + + align:start position:0% +traditionally American political +parties have been pretty big tents + + align:start position:0% +parties have been pretty big tents + + + align:start position:0% +parties have been pretty big tents +they've represented a lot of different + + align:start position:0% +they've represented a lot of different + + + align:start position:0% +they've represented a lot of different +interests not always that that didn't + + align:start position:0% +interests not always that that didn't + + + align:start position:0% +interests not always that that didn't +see eye to eye on all issues in the + + align:start position:0% +see eye to eye on all issues in the + + + align:start position:0% +see eye to eye on all issues in the +European tradition parties tended to be + + align:start position:0% +European tradition parties tended to be + + + align:start position:0% +European tradition parties tended to be +narrower so you'll have the labor party + + align:start position:0% +narrower so you'll have the labor party + + + align:start position:0% +narrower so you'll have the labor party +in Britain which is a was a left party + + align:start position:0% +in Britain which is a was a left party + + + align:start position:0% +in Britain which is a was a left party +but traditionally really was aligned + + align:start position:0% +but traditionally really was aligned + + + align:start position:0% +but traditionally really was aligned +with the labor + + align:start position:0% +with the labor + + + align:start position:0% +with the labor +movement as the Democratic party was and + + align:start position:0% +movement as the Democratic party was and + + + align:start position:0% +movement as the Democratic party was and +is but much more tightly than the + + align:start position:0% +is but much more tightly than the + + + align:start position:0% +is but much more tightly than the +Democratic party so I think it depends + + align:start position:0% +Democratic party so I think it depends + + + align:start position:0% +Democratic party so I think it depends +on the nature of the party and in some + + align:start position:0% +on the nature of the party and in some + + + align:start position:0% +on the nature of the party and in some +parliamentary systems you have very + + align:start position:0% +parliamentary systems you have very + + + align:start position:0% +parliamentary systems you have very +little parties are focused on particular + + align:start position:0% +little parties are focused on particular + + + align:start position:0% +little parties are focused on particular +issues think about the the ultra + + align:start position:0% +issues think about the the ultra + + + align:start position:0% +issues think about the the ultra +Orthodox parties in Israel for instance + + align:start position:0% +Orthodox parties in Israel for instance + + + align:start position:0% +Orthodox parties in Israel for instance +or some of the far-left parties uh in in + + align:start position:0% +or some of the far-left parties uh in in + + + align:start position:0% +or some of the far-left parties uh in in +European politics um our parties have + + align:start position:0% +European politics um our parties have + + + align:start position:0% +European politics um our parties have +traditionally not been easily identified + + align:start position:0% +traditionally not been easily identified + + + align:start position:0% +traditionally not been easily identified +with particular factions and you know + + align:start position:0% +with particular factions and you know + + + align:start position:0% +with particular factions and you know +there isn't + + align:start position:0% +there isn't + + + align:start position:0% +there isn't +a well I'm going to talk about this but + + align:start position:0% +a well I'm going to talk about this but + + + align:start position:0% +a well I'm going to talk about this but +most of the interest groups we see in + + align:start position:0% +most of the interest groups we see in + + + align:start position:0% +most of the interest groups we see in +the US try very hard not to be + + align:start position:0% +the US try very hard not to be + + + align:start position:0% +the US try very hard not to be +identified with one party or another + + align:start position:0% +identified with one party or another + + + align:start position:0% +identified with one party or another +because you don't want to if you can + + align:start position:0% +because you don't want to if you can + + + align:start position:0% +because you don't want to if you can +possibly be friends with everybody you + + align:start position:0% +possibly be friends with everybody you + + + align:start position:0% +possibly be friends with everybody you +can + + align:start position:0% +can + + + align:start position:0% +can +survive + + align:start position:0% +survive + + + align:start position:0% +survive +um pro-choice pro-life they have not + + align:start position:0% +um pro-choice pro-life they have not + + + align:start position:0% +um pro-choice pro-life they have not +been able to do that trick um uh there's + + align:start position:0% +been able to do that trick um uh there's + + + align:start position:0% +been able to do that trick um uh there's +a there's a Republican side and a + + align:start position:0% +a there's a Republican side and a + + + align:start position:0% +a there's a Republican side and a +democratic side and and there they are + + align:start position:0% +democratic side and and there they are + + + align:start position:0% +democratic side and and there they are +but uh most the Forest Products + + align:start position:0% +but uh most the Forest Products + + + align:start position:0% +but uh most the Forest Products +Association I am sure contributes to + + align:start position:0% +Association I am sure contributes to + + + align:start position:0% +Association I am sure contributes to +people from both + + align:start position:0% +people from both + + + align:start position:0% +people from both +parties the large consumers of + + align:start position:0% +parties the large consumers of + + + align:start position:0% +parties the large consumers of +electricity I'm sure contribute to + + align:start position:0% +electricity I'm sure contribute to + + + align:start position:0% +electricity I'm sure contribute to +people etc etc so good question though + + align:start position:0% +people etc etc so good question though + + + align:start position:0% +people etc etc so good question though +anything + + align:start position:0% +anything + + + align:start position:0% +anything +else okay + + align:start position:0% +else okay + + + align:start position:0% +else okay +so I guess I'm in I'm + + align:start position:0% +so I guess I'm in I'm + + + align:start position:0% +so I guess I'm in I'm +inclined to agree with uh I think with + + align:start position:0% +inclined to agree with uh I think with + + + align:start position:0% +inclined to agree with uh I think with +Katherine that that uh this + + align:start position:0% +Katherine that that uh this + + + align:start position:0% +Katherine that that uh this +probably doesn't work as well as one + + align:start position:0% +probably doesn't work as well as one + + + align:start position:0% +probably doesn't work as well as one +might like I don't know whether it's an + + align:start position:0% +might like I don't know whether it's an + + + align:start position:0% +might like I don't know whether it's an +ideal whether it would work as an ideal + + align:start position:0% +ideal whether it would work as an ideal + + + align:start position:0% +ideal whether it would work as an ideal +or not it's not a bad story but the + + align:start position:0% +or not it's not a bad story but the + + + align:start position:0% +or not it's not a bad story but the +notion that pretty much everybody's all + + align:start position:0% +notion that pretty much everybody's all + + + align:start position:0% +notion that pretty much everybody's all +interests are represented and they're + + align:start position:0% +interests are represented and they're + + + align:start position:0% +interests are represented and they're +well + + align:start position:0% +well + + + align:start position:0% +well +represented and that government is + + align:start position:0% +represented and that government is + + + align:start position:0% +represented and that government is +about modulo the role of parties is + + align:start position:0% +about modulo the role of parties is + + + align:start position:0% +about modulo the role of parties is +about about refereeing G uh um + + align:start position:0% +about about refereeing G uh um + + + align:start position:0% +about about refereeing G uh um +agreements and adjustments among + + align:start position:0% +agreements and adjustments among + + + align:start position:0% +agreements and adjustments among +interest groups is not a bad description + + align:start position:0% +interest groups is not a bad description + + + align:start position:0% +interest groups is not a bad description +sometimes + + align:start position:0% +sometimes + + + align:start position:0% +sometimes +sometimes once again sometimes uh but + + align:start position:0% +sometimes once again sometimes uh but + + + align:start position:0% +sometimes once again sometimes uh but +I'm not sure it's an + + align:start position:0% +I'm not sure it's an + + + align:start position:0% +I'm not sure it's an +ideal okay let me say let me move + + align:start position:0% +ideal okay let me say let me move + + + align:start position:0% +ideal okay let me say let me move +on uh a little bit about interest group + + align:start position:0% +on uh a little bit about interest group + + + align:start position:0% +on uh a little bit about interest group +competition + + align:start position:0% + + + + align:start position:0% + +first if you think about interest groups + + align:start position:0% +first if you think about interest groups + + + align:start position:0% +first if you think about interest groups +their ability to + + align:start position:0% +their ability to + + + align:start position:0% +their ability to +organize is really + + align:start position:0% +organize is really + + + align:start position:0% +organize is really +key right those large consumers of + + align:start position:0% +key right those large consumers of + + + align:start position:0% +key right those large consumers of +electricity they're about 40 of them + + align:start position:0% +electricity they're about 40 of them + + + align:start position:0% +electricity they're about 40 of them +they're the big industrial buyers they + + align:start position:0% +they're the big industrial buyers they + + + align:start position:0% +they're the big industrial buyers they +sit in a + + align:start position:0% +sit in a + + + align:start position:0% +sit in a +room small consumers of electricity + + align:start position:0% +room small consumers of electricity + + + align:start position:0% +room small consumers of electricity +there are many of us we also have + + align:start position:0% +there are many of us we also have + + + align:start position:0% +there are many of us we also have +different interests we're in different + + align:start position:0% +different interests we're in different + + + align:start position:0% +different interests we're in different +parts of the country hard to + + align:start position:0% +parts of the country hard to + + + align:start position:0% +parts of the country hard to +organize the the more important an issue + + align:start position:0% +organize the the more important an issue + + + align:start position:0% +organize the the more important an issue +is uh that should be higher dollar stake + + align:start position:0% +is uh that should be higher dollar stake + + + align:start position:0% +is uh that should be higher dollar stake +not stage I'm looking at that and saying + + align:start position:0% +not stage I'm looking at that and saying + + + align:start position:0% +not stage I'm looking at that and saying +that makes no sense + + align:start position:0% +that makes no sense + + + align:start position:0% +that makes no sense +stake + + align:start position:0% +stake + + + align:start position:0% +stake +um you know electricity is 2% of I don't + + align:start position:0% +um you know electricity is 2% of I don't + + + align:start position:0% +um you know electricity is 2% of I don't +know 2% of the average family budget + + align:start position:0% +know 2% of the average family budget + + + align:start position:0% +know 2% of the average family budget +you're not not going to get families to + + align:start position:0% +you're not not going to get families to + + + align:start position:0% +you're not not going to get families to +Rally around electricity rate reform + + align:start position:0% +Rally around electricity rate reform + + + align:start position:0% +Rally around electricity rate reform +it's just not important enough it's a + + align:start position:0% +it's just not important enough it's a + + + align:start position:0% +it's just not important enough it's a +big deal to the big guys they'll send + + align:start position:0% +big deal to the big guys they'll send + + + align:start position:0% +big deal to the big guys they'll send +people to Washington uh and there a + + align:start position:0% +people to Washington uh and there a + + + align:start position:0% +people to Washington uh and there a +small number of them so they + + align:start position:0% +small number of them so they + + + align:start position:0% +small number of them so they +organize so in uh a classic example is + + align:start position:0% +organize so in uh a classic example is + + + align:start position:0% +organize so in uh a classic example is +debates about uh Airline deregulation + + align:start position:0% +debates about uh Airline deregulation + + + align:start position:0% +debates about uh Airline deregulation +back in the 70s the airlines were well + + align:start position:0% +back in the 70s the airlines were well + + + align:start position:0% +back in the 70s the airlines were well +organized were very important in + + align:start position:0% +organized were very important in + + + align:start position:0% +organized were very important in +Congress most did not want to be + + align:start position:0% +Congress most did not want to be + + + align:start position:0% +Congress most did not want to be +deregulated thank you very + + align:start position:0% +deregulated thank you very + + + align:start position:0% +deregulated thank you very +much uh Travelers did not have an + + align:start position:0% +much uh Travelers did not have an + + + align:start position:0% +much uh Travelers did not have an +interest group there is an airline + + align:start position:0% +interest group there is an airline + + + align:start position:0% +interest group there is an airline +passengers Association I have no idea + + align:start position:0% +passengers Association I have no idea + + + align:start position:0% +passengers Association I have no idea +who belongs to it but uh but not a + + align:start position:0% +who belongs to it but uh but not a + + + align:start position:0% +who belongs to it but uh but not a +particularly important group nonetheless + + align:start position:0% +particularly important group nonetheless + + + align:start position:0% +particularly important group nonetheless +they were deregulated something we may + + align:start position:0% +they were deregulated something we may + + + align:start position:0% +they were deregulated something we may +come back to but the the the shorthand + + align:start position:0% +come back to but the the the shorthand + + + align:start position:0% +come back to but the the the shorthand +in politics is a concentrated interest + + align:start position:0% +in politics is a concentrated interest + + + align:start position:0% +in politics is a concentrated interest +an interest that affects a small number + + align:start position:0% +an interest that affects a small number + + + align:start position:0% +an interest that affects a small number +of people and has a big stake for each + + align:start position:0% +of people and has a big stake for each + + + align:start position:0% +of people and has a big stake for each +one tends to be a potent interest so + + align:start position:0% +one tends to be a potent interest so + + + align:start position:0% +one tends to be a potent interest so +back to are all interest groups created + + align:start position:0% +back to are all interest groups created + + + align:start position:0% +back to are all interest groups created +equal well no some groups don't + + align:start position:0% +equal well no some groups don't + + + align:start position:0% +equal well no some groups don't +organize back to regulating Electric + + align:start position:0% +organize back to regulating Electric + + + align:start position:0% +organize back to regulating Electric +utilities the utility is cares an + + align:start position:0% +utilities the utility is cares an + + + align:start position:0% +utilities the utility is cares an +enormous amount about the outcome of + + align:start position:0% +enormous amount about the outcome of + + + align:start position:0% +enormous amount about the outcome of +Regulation those of us who buy care a + + align:start position:0% +Regulation those of us who buy care a + + + align:start position:0% +Regulation those of us who buy care a +little bit there are a lot of us we + + align:start position:0% +little bit there are a lot of us we + + + align:start position:0% +little bit there are a lot of us we +don't have that much + + align:start position:0% +don't have that much + + + align:start position:0% +don't have that much +influence except from time to time so a + + align:start position:0% +influence except from time to time so a + + + align:start position:0% +influence except from time to time so a +key factor is how easy is it to organize + + align:start position:0% +key factor is how easy is it to organize + + + align:start position:0% +key factor is how easy is it to organize +in terms of interest group + + align:start position:0% + + + + align:start position:0% + +competition + + align:start position:0% + + + + align:start position:0% + +money money is interesting the simple + + align:start position:0% +money money is interesting the simple + + + align:start position:0% +money money is interesting the simple +assumption is that you buy votes with + + align:start position:0% +assumption is that you buy votes with + + + align:start position:0% +assumption is that you buy votes with +campaign contributions and some of that + + align:start position:0% +campaign contributions and some of that + + + align:start position:0% +campaign contributions and some of that +does happen but if you look at the + + align:start position:0% +does happen but if you look at the + + + align:start position:0% +does happen but if you look at the +pattern of + + align:start position:0% +pattern of + + + align:start position:0% +pattern of +spending you know people contribute to + + align:start position:0% +spending you know people contribute to + + + align:start position:0% +spending you know people contribute to +politicians of both sides uh if you + + align:start position:0% +politicians of both sides uh if you + + + align:start position:0% +politicians of both sides uh if you +become chairman of a congressional + + align:start position:0% +become chairman of a congressional + + + align:start position:0% +become chairman of a congressional +committee you will get campaign + + align:start position:0% +committee you will get campaign + + + align:start position:0% +committee you will get campaign +contributions from anybody your + + align:start position:0% +contributions from anybody your + + + align:start position:0% +contributions from anybody your +committee touches um usually what you + + align:start position:0% +committee touches um usually what you + + + align:start position:0% +committee touches um usually what you +want to do is you want to make sure your + + align:start position:0% +want to do is you want to make sure your + + + align:start position:0% +want to do is you want to make sure your +friends + + align:start position:0% +friends + + + align:start position:0% +friends +win it's it's harder to buy to make + + align:start position:0% +win it's it's harder to buy to make + + + align:start position:0% +win it's it's harder to buy to make +somebody make a 180 degree turn or even + + align:start position:0% +somebody make a 180 degree turn or even + + + align:start position:0% +somebody make a 180 degree turn or even +a 90 degree turn on an issue than it is + + align:start position:0% +a 90 degree turn on an issue than it is + + + align:start position:0% +a 90 degree turn on an issue than it is +to elect somebody who already agrees + + align:start position:0% +to elect somebody who already agrees + + + align:start position:0% +to elect somebody who already agrees +with you so a awful lot of what goes on + + align:start position:0% +with you so a awful lot of what goes on + + + align:start position:0% +with you so a awful lot of what goes on +is electing friends and getting + + align:start position:0% +is electing friends and getting + + + align:start position:0% +is electing friends and getting +access getting access if you've given a + + align:start position:0% +access getting access if you've given a + + + align:start position:0% +access getting access if you've given a +lot of money to somebody they will + + align:start position:0% +lot of money to somebody they will + + + align:start position:0% +lot of money to somebody they will +return your phone call but it's amazing + + align:start position:0% +return your phone call but it's amazing + + + align:start position:0% +return your phone call but it's amazing +people who receive who have no challenge + + align:start position:0% +people who receive who have no challenge + + + align:start position:0% +people who receive who have no challenge +will get no effective opposition we'll + + align:start position:0% +will get no effective opposition we'll + + + align:start position:0% +will get no effective opposition we'll +get campaign contributions from people + + align:start position:0% +get campaign contributions from people + + + align:start position:0% +get campaign contributions from people +who disagree with them on issues just + + align:start position:0% +who disagree with them on issues just + + + align:start position:0% +who disagree with them on issues just +because I want to be able to get in the + + align:start position:0% +because I want to be able to get in the + + + align:start position:0% +because I want to be able to get in the +door um I want you to think well of me + + align:start position:0% +door um I want you to think well of me + + + align:start position:0% +door um I want you to think well of me +if I think you can be beaten by by + + align:start position:0% +if I think you can be beaten by by + + + align:start position:0% +if I think you can be beaten by by +somebody who I like better I will pay a + + align:start position:0% +somebody who I like better I will pay a + + + align:start position:0% +somebody who I like better I will pay a +lot for + + align:start position:0% +lot for + + + align:start position:0% +lot for +them but uh it's it's pretty hard to to + + align:start position:0% +them but uh it's it's pretty hard to to + + + align:start position:0% +them but uh it's it's pretty hard to to +buy votes with campaign contributions + + align:start position:0% +buy votes with campaign contributions + + + align:start position:0% +buy votes with campaign contributions +the other thing and this all merits + + align:start position:0% +the other thing and this all merits + + + align:start position:0% +the other thing and this all merits +discussion the other thing that has to + + align:start position:0% +discussion the other thing that has to + + + align:start position:0% +discussion the other thing that has to +be mentioned is the citizens united + + align:start position:0% +be mentioned is the citizens united + + + align:start position:0% +be mentioned is the citizens united +decision which is this recent Supreme + + align:start position:0% +decision which is this recent Supreme + + + align:start position:0% +decision which is this recent Supreme +Court decision that said corporations + + align:start position:0% +Court decision that said corporations + + + align:start position:0% +Court decision that said corporations +are people and limits on spending are + + align:start position:0% +are people and limits on spending are + + + align:start position:0% +are people and limits on spending are +limits on + + align:start position:0% +limits on + + + align:start position:0% +limits on +speech + + align:start position:0% +speech + + + align:start position:0% +speech +so we you saw it in the primary you + + align:start position:0% +so we you saw it in the primary you + + + align:start position:0% +so we you saw it in the primary you +didn't see it here particular L but + + align:start position:0% +didn't see it here particular L but + + + align:start position:0% +didn't see it here particular L but +other people saw it uh there's really no + + align:start position:0% +other people saw it uh there's really no + + + align:start position:0% +other people saw it uh there's really no +limit on what can be spent to support a + + align:start position:0% +limit on what can be spent to support a + + + align:start position:0% +limit on what can be spent to support a +candidate um by uh by uh uh wealthy + + align:start position:0% +candidate um by uh by uh uh wealthy + + + align:start position:0% +candidate um by uh by uh uh wealthy +individuals mainly more than + + align:start position:0% +individuals mainly more than + + + align:start position:0% +individuals mainly more than +corporations we talked about uh + + align:start position:0% +corporations we talked about uh + + + align:start position:0% +corporations we talked about uh +corporate activ corporate political + + align:start position:0% +corporate activ corporate political + + + align:start position:0% +corporate activ corporate political +action um but that may + + align:start position:0% +action um but that may + + + align:start position:0% +action um but that may +change things dramatically and it goes + + align:start position:0% +change things dramatically and it goes + + + align:start position:0% +change things dramatically and it goes +back to Katherine's point about + + align:start position:0% +back to Katherine's point about + + + align:start position:0% +back to Katherine's point about +money if you're free to speak with your + + align:start position:0% +money if you're free to speak with your + + + align:start position:0% +money if you're free to speak with your +$5 and I'm free to speak speak with my + + align:start position:0% +$5 and I'm free to speak speak with my + + + align:start position:0% +$5 and I'm free to speak speak with my +$50 + + align:start position:0% +$50 + + + align:start position:0% +$50 +million we have different impact so um + + align:start position:0% +million we have different impact so um + + + align:start position:0% +million we have different impact so um +can I get my friends elected well yeah + + align:start position:0% +can I get my friends elected well yeah + + + align:start position:0% +can I get my friends elected well yeah +probably can I buy votes with it that's + + align:start position:0% +probably can I buy votes with it that's + + + align:start position:0% +probably can I buy votes with it that's +buying votes is hard getting friends + + align:start position:0% +buying votes is hard getting friends + + + align:start position:0% +buying votes is hard getting friends +elected getting friends elected is + + align:start position:0% +elected getting friends elected is + + + align:start position:0% +elected getting friends elected is +easier so um we we're going to see more + + align:start position:0% +easier so um we we're going to see more + + + align:start position:0% +easier so um we we're going to see more +of that we're going to see a lot of uh + + align:start position:0% +of that we're going to see a lot of uh + + + align:start position:0% +of that we're going to see a lot of uh +this is this will be a very ugly fall + + align:start position:0% +this is this will be a very ugly fall + + + align:start position:0% +this is this will be a very ugly fall +that's all I have to say comments on any + + align:start position:0% +that's all I have to say comments on any + + + align:start position:0% +that's all I have to say comments on any +of this before I go to the the last one + + align:start position:0% +of this before I go to the the last one + + + align:start position:0% +of this before I go to the the last one +last Point here reactions + + align:start position:0% + + + + align:start position:0% + +thoughts Jacob you look Disturbed David + + align:start position:0% +thoughts Jacob you look Disturbed David + + + align:start position:0% +thoughts Jacob you look Disturbed David +is Disturbed David don't let people like + + align:start position:0% +is Disturbed David don't let people like + + + align:start position:0% +is Disturbed David don't let people like +speak with their money how do you + + align:start position:0% +speak with their money how do you + + + align:start position:0% +speak with their money how do you +determine like what you care about more + + align:start position:0% +determine like what you care about more + + + align:start position:0% +determine like what you care about more +so like I'm I'm buy electricity right + + align:start position:0% +so like I'm I'm buy electricity right + + + align:start position:0% +so like I'm I'm buy electricity right +but it's only 2% of what I have so I + + align:start position:0% +but it's only 2% of what I have so I + + + align:start position:0% +but it's only 2% of what I have so I +don't care about that that much but + + align:start position:0% +don't care about that that much but + + + align:start position:0% +don't care about that that much but +maybe I care more about milk or + + align:start position:0% +maybe I care more about milk or + + + align:start position:0% +maybe I care more about milk or +something so how I choose like do I can + + align:start position:0% +something so how I choose like do I can + + + align:start position:0% +something so how I choose like do I can +I right how do I vote for what + + align:start position:0% +I right how do I vote for what + + + align:start position:0% +I right how do I vote for what +percentage of my care I want to send to + + align:start position:0% +percentage of my care I want to send to + + + align:start position:0% +percentage of my care I want to send to +each group unless you let people do that + + align:start position:0% +each group unless you let people do that + + + align:start position:0% +each group unless you let people do that +with money uh I mean you as an + + align:start position:0% +with money uh I mean you as an + + + align:start position:0% +with money uh I mean you as an +individual you as a really rich + + align:start position:0% + + + + align:start position:0% + +person rich people are individuals too + + align:start position:0% +person rich people are individuals too + + + align:start position:0% +person rich people are individuals too +right yes yes yes yes yes yes yes which + + align:start position:0% +right yes yes yes yes yes yes yes which + + + align:start position:0% +right yes yes yes yes yes yes yes which +are you imagining yourself to be you or + + align:start position:0% +are you imagining yourself to be you or + + + align:start position:0% +are you imagining yourself to be you or +Warren Buffett um because the because + + align:start position:0% +Warren Buffett um because the because + + + align:start position:0% +Warren Buffett um because the because +the answer + + align:start position:0% +the answer + + + align:start position:0% +the answer +differs okay uh yeah for someone who + + align:start position:0% +differs okay uh yeah for someone who + + + align:start position:0% +differs okay uh yeah for someone who +maybe doesn't have a lot of money + + align:start position:0% +maybe doesn't have a lot of money + + + align:start position:0% +maybe doesn't have a lot of money +somebody who doesn't have a lot of money + + align:start position:0% +somebody who doesn't have a lot of money + + + align:start position:0% +somebody who doesn't have a lot of money +uh you basically belong to an + + align:start position:0% +uh you basically belong to an + + + align:start position:0% +uh you basically belong to an +organization you you care about gun + + align:start position:0% +organization you you care about gun + + + align:start position:0% +organization you you care about gun +rights you belong to the National Rifle + + align:start position:0% +rights you belong to the National Rifle + + + align:start position:0% +rights you belong to the National Rifle +Association you care about + + align:start position:0% +Association you care about + + + align:start position:0% +Association you care about +um um abortion you contribute to the + + align:start position:0% +um um abortion you contribute to the + + + align:start position:0% +um um abortion you contribute to the +National Abortion Rights Act whatever + + align:start position:0% +National Abortion Rights Act whatever + + + align:start position:0% +National Abortion Rights Act whatever +the thing is or Planned Parenthood uh + + align:start position:0% +the thing is or Planned Parenthood uh + + + align:start position:0% +the thing is or Planned Parenthood uh +you care about you can contribute to + + align:start position:0% +you care about you can contribute to + + + align:start position:0% +you care about you can contribute to +organizations or you contri can + + align:start position:0% +organizations or you contri can + + + align:start position:0% +organizations or you contri can +contribute to + + align:start position:0% +contribute to + + + align:start position:0% +contribute to +candidates if you're Warren + + align:start position:0% +candidates if you're Warren + + + align:start position:0% +candidates if you're Warren +Buffett you can set up a political + + align:start position:0% +Buffett you can set up a political + + + align:start position:0% +Buffett you can set up a political +political action commit + + align:start position:0% +political action commit + + + align:start position:0% +political action commit +committee put a few he doesn't do this + + align:start position:0% +committee put a few he doesn't do this + + + align:start position:0% +committee put a few he doesn't do this +put a few tens of millions of dollars in + + align:start position:0% +put a few tens of millions of dollars in + + + align:start position:0% +put a few tens of millions of dollars in +it look around the country for + + align:start position:0% +it look around the country for + + + align:start position:0% +it look around the country for +candidates you like and spend for them + + align:start position:0% +candidates you like and spend for them + + + align:start position:0% +candidates you like and spend for them +you can't give it to them you can spend + + align:start position:0% +you can't give it to them you can spend + + + align:start position:0% +you can't give it to them you can spend +for them you can hire people to write + + align:start position:0% +for them you can hire people to write + + + align:start position:0% +for them you can hire people to write +attack ads against their + + align:start position:0% +attack ads against their + + + align:start position:0% +attack ads against their +opponents and put a lot of money in + + align:start position:0% +opponents and put a lot of money in + + + align:start position:0% +opponents and put a lot of money in +television or you can also fund interest + + align:start position:0% +television or you can also fund interest + + + align:start position:0% +television or you can also fund interest +groups so my question is if I care a lot + + align:start position:0% +groups so my question is if I care a lot + + + align:start position:0% +groups so my question is if I care a lot +about you know I have I have a lot of + + align:start position:0% +about you know I have I have a lot of + + + align:start position:0% +about you know I have I have a lot of +different interest right because I buy + + align:start position:0% +different interest right because I buy + + + align:start position:0% +different interest right because I buy +electricity and I buy milk and I but + + align:start position:0% +electricity and I buy milk and I but + + + align:start position:0% +electricity and I buy milk and I but +maybe I really care about you know guns + + align:start position:0% +maybe I really care about you know guns + + + align:start position:0% +maybe I really care about you know guns +or something yeah so how do I what would + + align:start position:0% +or something yeah so how do I what would + + + align:start position:0% +or something yeah so how do I what would +an ideal system be in which I can have + + align:start position:0% +an ideal system be in which I can have + + + align:start position:0% +an ideal system be in which I can have +interest in all these different groups + + align:start position:0% +interest in all these different groups + + + align:start position:0% +interest in all these different groups +but the ones that I care about more get + + align:start position:0% +but the ones that I care about more get + + + align:start position:0% +but the ones that I care about more get +more of my + + align:start position:0% +more of my + + + align:start position:0% +more of my +support well if there are organizations + + align:start position:0% +support well if there are organizations + + + align:start position:0% +support well if there are organizations +I mean the National Rifle Association is + + align:start position:0% +I mean the National Rifle Association is + + + align:start position:0% +I mean the National Rifle Association is +politically active so if you care about + + align:start position:0% +politically active so if you care about + + + align:start position:0% +politically active so if you care about +guns that's a place you can send money + + align:start position:0% +guns that's a place you can send money + + + align:start position:0% +guns that's a place you can send money +they'll spend it for + + align:start position:0% +they'll spend it for + + + align:start position:0% +they'll spend it for +you if you're if you're old you can + + align:start position:0% +you if you're if you're old you can + + + align:start position:0% +you if you're if you're old you can +American Association of retired persons + + align:start position:0% +American Association of retired persons + + + align:start position:0% +American Association of retired persons +I mean there are plenty of pockets so + + align:start position:0% +I mean there are plenty of pockets so + + + align:start position:0% +I mean there are plenty of pockets so +things that I care a lot about I can + + align:start position:0% +things that I care a lot about I can + + + align:start position:0% +things that I care a lot about I can +give more money to than other things + + align:start position:0% +give more money to than other things + + + align:start position:0% +give more money to than other things +right + + align:start position:0% +right + + + align:start position:0% +right +but so that works where money but then + + align:start position:0% +but so that works where money but then + + + align:start position:0% +but so that works where money but then +my voice is smaller because I have less + + align:start position:0% +my voice is smaller because I have less + + + align:start position:0% +my voice is smaller because I have less +money yeah in total so someone who maybe + + align:start position:0% +money yeah in total so someone who maybe + + + align:start position:0% +money yeah in total so someone who maybe +doesn't care as much about this can give + + align:start position:0% +doesn't care as much about this can give + + + align:start position:0% +doesn't care as much about this can give +a little money to it which is still + + align:start position:0% +a little money to it which is still + + + align:start position:0% +a little money to it which is still +larger than yeah my voice so money seems + + align:start position:0% +larger than yeah my voice so money seems + + + align:start position:0% +larger than yeah my voice so money seems +like the most efficient system that I + + align:start position:0% +like the most efficient system that I + + + align:start position:0% +like the most efficient system that I +can think of that allows people to + + align:start position:0% +can think of that allows people to + + + align:start position:0% +can think of that allows people to +contribute to things they care about a + + align:start position:0% +contribute to things they care about a + + + align:start position:0% +contribute to things they care about a +lot I have their voices heard there + + align:start position:0% +lot I have their voices heard there + + + align:start position:0% +lot I have their voices heard there +whereas things they don't care about but + + align:start position:0% +whereas things they don't care about but + + + align:start position:0% +whereas things they don't care about but +they're part of it you know the issue + + align:start position:0% +they're part of it you know the issue + + + align:start position:0% +they're part of it you know the issue +that that disturbs people is sort of + + align:start position:0% +that that disturbs people is sort of + + + align:start position:0% +that that disturbs people is sort of +twofold one of the things that's + + align:start position:0% +twofold one of the things that's + + + align:start position:0% +twofold one of the things that's +happened in this country over the + + align:start position:0% +happened in this country over the + + + align:start position:0% +happened in this country over the +last 30 years maybe it goes back a + + align:start position:0% +last 30 years maybe it goes back a + + + align:start position:0% +last 30 years maybe it goes back a +little farther is increasing inequality + + align:start position:0% +little farther is increasing inequality + + + align:start position:0% +little farther is increasing inequality +of income and wealth um it's I think + + align:start position:0% +of income and wealth um it's I think + + + align:start position:0% +of income and wealth um it's I think +it's it's very hard to point a policy + + align:start position:0% +it's it's very hard to point a policy + + + align:start position:0% +it's it's very hard to point a policy +finger at what's done that and it's very + + align:start position:0% +finger at what's done that and it's very + + + align:start position:0% +finger at what's done that and it's very +complicated to figure out what's done it + + align:start position:0% +complicated to figure out what's done it + + + align:start position:0% +complicated to figure out what's done it +but it has happened one way or another + + align:start position:0% +but it has happened one way or another + + + align:start position:0% +but it has happened one way or another +and so the thing that upsets people + + align:start position:0% +and so the thing that upsets people + + + align:start position:0% +and so the thing that upsets people +is the difference in the size of Warren + + align:start position:0% +is the difference in the size of Warren + + + align:start position:0% +is the difference in the size of Warren +Buffett's voice and your + + align:start position:0% +Buffett's voice and your + + + align:start position:0% +Buffett's voice and your +voice um if it's one person one vote we + + align:start position:0% +voice um if it's one person one vote we + + + align:start position:0% +voice um if it's one person one vote we +don't all have equal impact in on the + + align:start position:0% +don't all have equal impact in on the + + + align:start position:0% +don't all have equal impact in on the +process with contributions in fact they + + align:start position:0% +process with contributions in fact they + + + align:start position:0% +process with contributions in fact they +differ by several dozens of orders of + + align:start position:0% +differ by several dozens of orders of + + + align:start position:0% +differ by several dozens of orders of +not dozens multiple orders of magnitude + + align:start position:0% +not dozens multiple orders of magnitude + + + align:start position:0% +not dozens multiple orders of magnitude +that's the upset I I got no problem with + + align:start position:0% +that's the upset I I got no problem with + + + align:start position:0% +that's the upset I I got no problem with +you know and the the campaign Finance + + align:start position:0% +you know and the the campaign Finance + + + align:start position:0% +you know and the the campaign Finance +laws were supposed to deal with that the + + align:start position:0% +laws were supposed to deal with that the + + + align:start position:0% +laws were supposed to deal with that the +idea was a corporations can't make + + align:start position:0% +idea was a corporations can't make + + + align:start position:0% +idea was a corporations can't make +political Camp uh political + + align:start position:0% +political Camp uh political + + + align:start position:0% +political Camp uh political +contributions and B there's a limit on + + align:start position:0% +contributions and B there's a limit on + + + align:start position:0% +contributions and B there's a limit on +how much an individual can spend that + + align:start position:0% +how much an individual can spend that + + + align:start position:0% +how much an individual can spend that +was intended to equalize voice you can + + align:start position:0% +was intended to equalize voice you can + + + align:start position:0% +was intended to equalize voice you can +still give to various organizations as + + align:start position:0% +still give to various organizations as + + + align:start position:0% +still give to various organizations as +much as you want but in terms of the + + align:start position:0% +much as you want but in terms of the + + + align:start position:0% +much as you want but in terms of the +political the electoral process there + + align:start position:0% +political the electoral process there + + + align:start position:0% +political the electoral process there +were limits those laws are no longer + + align:start position:0% +were limits those laws are no longer + + + align:start position:0% +were limits those laws are no longer +relevant because of citizens united that + + align:start position:0% +relevant because of citizens united that + + + align:start position:0% +relevant because of citizens united that +I that's the issue I mean I got no + + align:start position:0% +I that's the issue I mean I got no + + + align:start position:0% +I that's the issue I mean I got no +problem with with people spending money + + align:start position:0% +problem with with people spending money + + + align:start position:0% +problem with with people spending money +uh I'm not + + align:start position:0% +uh I'm not + + + align:start position:0% +uh I'm not +I'm not profoundly upset at the current + + align:start position:0% +I'm not profoundly upset at the current + + + align:start position:0% +I'm not profoundly upset at the current +system but the huge + + align:start position:0% +system but the huge + + + align:start position:0% +system but the huge +difference in the ability of somebody + + align:start position:0% +difference in the ability of somebody + + + align:start position:0% +difference in the ability of somebody +like this casino owner who gave $15 + + align:start position:0% +like this casino owner who gave $15 + + + align:start position:0% +like this casino owner who gave $15 +million to the N Gingrich + + align:start position:0% +million to the N Gingrich + + + align:start position:0% +million to the N Gingrich +campaign that sort of wom that's one guy + + align:start position:0% +campaign that sort of wom that's one guy + + + align:start position:0% +campaign that sort of wom that's one guy +carrying a presidential campaign + + align:start position:0% +carrying a presidential campaign + + + align:start position:0% +carrying a presidential campaign +wow uh that is that no longer sounds + + align:start position:0% +wow uh that is that no longer sounds + + + align:start position:0% +wow uh that is that no longer sounds +like Athenian + + align:start position:0% +like Athenian + + + align:start position:0% +like Athenian +democracy um yeah 2 points1 a voucher + + align:start position:0% +democracy um yeah 2 points1 a voucher + + + align:start position:0% +democracy um yeah 2 points1 a voucher +system solve this problem like something + + align:start position:0% +system solve this problem like something + + + align:start position:0% +system solve this problem like something +proposed by Lawrence + + align:start position:0% +proposed by Lawrence + + + align:start position:0% +proposed by Lawrence +Le say what you mean by a voucher system + + align:start position:0% +Le say what you mean by a voucher system + + + align:start position:0% +Le say what you mean by a voucher system +I mean so what Lawrence lesic says is + + align:start position:0% +I mean so what Lawrence lesic says is + + + align:start position:0% +I mean so what Lawrence lesic says is +that each individual has say a $50 tax + + align:start position:0% +that each individual has say a $50 tax + + + align:start position:0% +that each individual has say a $50 tax +credit and that money goes towards + + align:start position:0% +credit and that money goes towards + + + align:start position:0% +credit and that money goes towards +funding a candidate and there's no other + + align:start position:0% +funding a candidate and there's no other + + + align:start position:0% +funding a candidate and there's no other +outside money yeah it's the no other + + align:start position:0% +outside money yeah it's the no other + + + align:start position:0% +outside money yeah it's the no other +outside money that violates the + + align:start position:0% +outside money that violates the + + + align:start position:0% +outside money that violates the +Constitution almost certainly so so let + + align:start position:0% +Constitution almost certainly so so let + + + align:start position:0% +Constitution almost certainly so so let +me let me move forward a little bit yeah + + align:start position:0% +me let me move forward a little bit yeah + + + align:start position:0% +me let me move forward a little bit yeah +yeah please capitalism solve this + + align:start position:0% +yeah please capitalism solve this + + + align:start position:0% +yeah please capitalism solve this +problem because the government's not + + align:start position:0% +problem because the government's not + + + align:start position:0% +problem because the government's not +involved then and if you're buying milk + + align:start position:0% +involved then and if you're buying milk + + + align:start position:0% +involved then and if you're buying milk +it's the consumer versus the supplier oh + + align:start position:0% +it's the consumer versus the supplier oh + + + align:start position:0% +it's the consumer versus the supplier oh +you're saying that the that uh you + + align:start position:0% +you're saying that the that uh you + + + align:start position:0% +you're saying that the that uh you +should limit the scope of government so + + align:start position:0% +should limit the scope of government so + + + align:start position:0% +should limit the scope of government so +you can limit the Mischief it can + + align:start position:0% +you can limit the Mischief it can + + + align:start position:0% +you can limit the Mischief it can +do sure why are we supporting the pr why + + align:start position:0% +do sure why are we supporting the pr why + + + align:start position:0% +do sure why are we supporting the pr why +are we trying to raise the price of milk + + align:start position:0% +are we trying to raise the price of milk + + + align:start position:0% +are we trying to raise the price of milk +for heaven's sakes because Dairy Farmers + + align:start position:0% +for heaven's sakes because Dairy Farmers + + + align:start position:0% +for heaven's sakes because Dairy Farmers +are a very effective organized group and + + align:start position:0% +are a very effective organized group and + + + align:start position:0% +are a very effective organized group and +have been why do we raise the price of + + align:start position:0% +have been why do we raise the price of + + + align:start position:0% +have been why do we raise the price of +sugar because uh uh if we didn't have + + align:start position:0% +sugar because uh uh if we didn't have + + + align:start position:0% +sugar because uh uh if we didn't have +barriers to trade in sugar we would + + align:start position:0% +barriers to trade in sugar we would + + + align:start position:0% +barriers to trade in sugar we would +undoubtedly buy Cuban sugar and we don't + + align:start position:0% +undoubtedly buy Cuban sugar and we don't + + + align:start position:0% +undoubtedly buy Cuban sugar and we don't +wish to buy Cuban sugar oh and by the + + align:start position:0% +wish to buy Cuban sugar oh and by the + + + align:start position:0% +wish to buy Cuban sugar oh and by the +way they're sugar producers so um + + align:start position:0% +way they're sugar producers so um + + + align:start position:0% +way they're sugar producers so um +anyway lobbying let me urge you read the + + align:start position:0% +anyway lobbying let me urge you read the + + + align:start position:0% +anyway lobbying let me urge you read the +short piece by kleene and Stellar it's + + align:start position:0% +short piece by kleene and Stellar it's + + + align:start position:0% +short piece by kleene and Stellar it's +not on the syllabus because it came out + + align:start position:0% +not on the syllabus because it came out + + + align:start position:0% +not on the syllabus because it came out +this spring it's a very nice description + + align:start position:0% +this spring it's a very nice description + + + align:start position:0% +this spring it's a very nice description +consistent with all my experience of how + + align:start position:0% +consistent with all my experience of how + + + align:start position:0% +consistent with all my experience of how +lobbying + + align:start position:0% +lobbying + + + align:start position:0% +lobbying +works you don't effective lobbyists + + align:start position:0% +works you don't effective lobbyists + + + align:start position:0% +works you don't effective lobbyists +don't walk in with bags of money to buy + + align:start position:0% +don't walk in with bags of money to buy + + + align:start position:0% +don't walk in with bags of money to buy +votes effective lobbyists make + + align:start position:0% +votes effective lobbyists make + + + align:start position:0% +votes effective lobbyists make +friends they get into talk they provide + + align:start position:0% +friends they get into talk they provide + + + align:start position:0% +friends they get into talk they provide +information the information is of course + + align:start position:0% +information the information is of course + + + align:start position:0% +information the information is of course +slanted but it's your friend it's a very + + align:start position:0% +slanted but it's your friend it's a very + + + align:start position:0% +slanted but it's your friend it's a very +interesting description of what the guy + + align:start position:0% +interesting description of what the guy + + + align:start position:0% +interesting description of what the guy +calls a gift economy or basically you're + + align:start position:0% +calls a gift economy or basically you're + + + align:start position:0% +calls a gift economy or basically you're +doing + + align:start position:0% +doing + + + align:start position:0% +doing +favors you have a complicated piece of + + align:start position:0% +favors you have a complicated piece of + + + align:start position:0% +favors you have a complicated piece of +legislation I'll discuss it with you + + align:start position:0% +legislation I'll discuss it with you + + + align:start position:0% +legislation I'll discuss it with you +when we play golf next + + align:start position:0% +when we play golf next + + + align:start position:0% +when we play golf next +Saturday we're good friends + + align:start position:0% +Saturday we're good friends + + + align:start position:0% +Saturday we're good friends +how did I get hired as a lobbyist + + align:start position:0% +how did I get hired as a lobbyist + + + align:start position:0% +how did I get hired as a lobbyist +because I'm friends with these people + + align:start position:0% +because I'm friends with these people + + + align:start position:0% +because I'm friends with these people +that's how I got hired as a lobbyist so + + align:start position:0% +that's how I got hired as a lobbyist so + + + align:start position:0% +that's how I got hired as a lobbyist so +they'll play golf with me so I can tell + + align:start position:0% +they'll play golf with me so I can tell + + + align:start position:0% +they'll play golf with me so I can tell +them this + + align:start position:0% +them this + + + align:start position:0% +them this +stuff yeah maybe I maybe I give them + + align:start position:0% +stuff yeah maybe I maybe I give them + + + align:start position:0% +stuff yeah maybe I maybe I give them +some tickets but I'm not going to buy + + align:start position:0% +some tickets but I'm not going to buy + + + align:start position:0% +some tickets but I'm not going to buy +their votes with money for a whole set + + align:start position:0% +their votes with money for a whole set + + + align:start position:0% +their votes with money for a whole set +of reasons first of all you go to jail + + align:start position:0% +of reasons first of all you go to jail + + + align:start position:0% +of reasons first of all you go to jail +for that if you're caught and second of + + align:start position:0% +for that if you're caught and second of + + + align:start position:0% +for that if you're caught and second of +all most people in Congress don't think + + align:start position:0% +all most people in Congress don't think + + + align:start position:0% +all most people in Congress don't think +of themselves as + + align:start position:0% +of themselves as + + + align:start position:0% +of themselves as +Crooks they think of themselves as + + align:start position:0% +Crooks they think of themselves as + + + align:start position:0% +Crooks they think of themselves as +trying to do the right thing I + + align:start position:0% +trying to do the right thing I + + + align:start position:0% +trying to do the right thing I +mean so you the process of lobbying is + + align:start position:0% +mean so you the process of lobbying is + + + align:start position:0% +mean so you the process of lobbying is +very very nicely described in that + + align:start position:0% +very very nicely described in that + + + align:start position:0% +very very nicely described in that +article and again it's I've seen it it's + + align:start position:0% +article and again it's I've seen it it's + + + align:start position:0% +article and again it's I've seen it it's +consistent with everything I've seen uh + + align:start position:0% +consistent with everything I've seen uh + + + align:start position:0% +consistent with everything I've seen uh +it's + + align:start position:0% +it's + + + align:start position:0% +it's +it you become an effective Lobby not + + align:start position:0% +it you become an effective Lobby not + + + align:start position:0% +it you become an effective Lobby not +because you have more money to swing + + align:start position:0% +because you have more money to swing + + + align:start position:0% +because you have more money to swing +around but because you can hire people + + align:start position:0% +around but because you can hire people + + + align:start position:0% +around but because you can hire people +who have connections you can H you can + + align:start position:0% +who have connections you can H you can + + + align:start position:0% +who have connections you can H you can +get uh information prepared that's + + align:start position:0% +get uh information prepared that's + + + align:start position:0% +get uh information prepared that's +useful and you have the ability to + + align:start position:0% +useful and you have the ability to + + + align:start position:0% +useful and you have the ability to +affect campaign contributions that does + + align:start position:0% +affect campaign contributions that does + + + align:start position:0% +affect campaign contributions that does +matter but it's it's a very different + + align:start position:0% +matter but it's it's a very different + + + align:start position:0% +matter but it's it's a very different +process it's a process of influence not + + align:start position:0% +process it's a process of influence not + + + align:start position:0% +process it's a process of influence not +a process of bribery so I urge you to + + align:start position:0% +a process of bribery so I urge you to + + + align:start position:0% +a process of bribery so I urge you to +read that it's short so quickly um loie + + align:start position:0% +read that it's short so quickly um loie + + + align:start position:0% +read that it's short so quickly um loie +makes the point this interest group + + align:start position:0% +makes the point this interest group + + + align:start position:0% +makes the point this interest group +competition is one kind of + + align:start position:0% +competition is one kind of + + + align:start position:0% +competition is one kind of +politics it really is inside + + align:start position:0% +politics it really is inside + + + align:start position:0% +politics it really is inside +baseball but if you if you look at + + align:start position:0% +baseball but if you if you look at + + + align:start position:0% +baseball but if you if you look at +various kinds of comp of political + + align:start position:0% +various kinds of comp of political + + + align:start position:0% +various kinds of comp of political +action and various kinds of governmental + + align:start position:0% +action and various kinds of governmental + + + align:start position:0% +action and various kinds of governmental +action uh it doesn't all fit this is a + + align:start position:0% +action uh it doesn't all fit this is a + + + align:start position:0% +action uh it doesn't all fit this is a +set of possibilities this is impacts on + + align:start position:0% +set of possibilities this is impacts on + + + align:start position:0% +set of possibilities this is impacts on +the Federal Reserve well is that + + align:start position:0% +the Federal Reserve well is that + + + align:start position:0% +the Federal Reserve well is that +interest groups uh antitrust policy is + + align:start position:0% +interest groups uh antitrust policy is + + + align:start position:0% +interest groups uh antitrust policy is +that interest groups um uh + + align:start position:0% +that interest groups um uh + + + align:start position:0% +that interest groups um uh +reapportionment well that's more + + align:start position:0% +reapportionment well that's more + + + align:start position:0% +reapportionment well that's more +complicated there a tariffs tariff + + align:start position:0% +complicated there a tariffs tariff + + + align:start position:0% +complicated there a tariffs tariff +policy uh is is winners and losers uh + + align:start position:0% +policy uh is is winners and losers uh + + + align:start position:0% +policy uh is is winners and losers uh +some milk price supports is is uh uh uh + + align:start position:0% +some milk price supports is is uh uh uh + + + align:start position:0% +some milk price supports is is uh uh uh +aiding constituents uh + + align:start position:0% +aiding constituents uh + + + align:start position:0% +aiding constituents uh +regulation can you do make product + + align:start position:0% +regulation can you do make product + + + align:start position:0% +regulation can you do make product +safety regulation interest groups not + + align:start position:0% +safety regulation interest groups not + + + align:start position:0% +safety regulation interest groups not +too easily so the lowy point and you can + + align:start position:0% +too easily so the lowy point and you can + + + align:start position:0% +too easily so the lowy point and you can +read the text around this to interpret + + align:start position:0% +read the text around this to interpret + + + align:start position:0% +read the text around this to interpret +this diagram is that that doesn't always + + align:start position:0% +this diagram is that that doesn't always + + + align:start position:0% +this diagram is that that doesn't always +describe policy well describe politics + + align:start position:0% +describe policy well describe politics + + + align:start position:0% +describe policy well describe politics +well I'm going to come back to that when + + align:start position:0% +well I'm going to come back to that when + + + align:start position:0% +well I'm going to come back to that when +we talk about + + align:start position:0% +we talk about + + + align:start position:0% +we talk about +regulation there's also other models now + + align:start position:0% +regulation there's also other models now + + + align:start position:0% +regulation there's also other models now +this is the this is the piece by Whit + + align:start position:0% +this is the this is the piece by Whit + + + align:start position:0% +this is the this is the piece by Whit +and and Whit is a Marxist so Whit is + + align:start position:0% +and and Whit is a Marxist so Whit is + + + align:start position:0% +and and Whit is a Marxist so Whit is +very big on class + + align:start position:0% +very big on class + + + align:start position:0% +very big on class +dialectic and you know if you can make + + align:start position:0% +dialectic and you know if you can make + + + align:start position:0% +dialectic and you know if you can make +sense out of that you're one up on me + + align:start position:0% +sense out of that you're one up on me + + + align:start position:0% +sense out of that you're one up on me +but I think the middle column the con + + align:start position:0% +but I think the middle column the con + + + align:start position:0% +but I think the middle column the con +the the split between the two columns is + + align:start position:0% +the the split between the two columns is + + + align:start position:0% +the the split between the two columns is +interesting if you think about politics + + align:start position:0% +interesting if you think about politics + + + align:start position:0% +interesting if you think about politics +in China or if you think about + + align:start position:0% +in China or if you think about + + + align:start position:0% +in China or if you think about +traditional politics in Latin American + + align:start position:0% +traditional politics in Latin American + + + align:start position:0% +traditional politics in Latin American +countries where they would talk about + + align:start position:0% +countries where they would talk about + + + align:start position:0% +countries where they would talk about +the oligarchy you you would think + + align:start position:0% +the oligarchy you you would think + + + align:start position:0% +the oligarchy you you would think +about this middle column you would think + + align:start position:0% +about this middle column you would think + + + align:start position:0% +about this middle column you would think +about politics by the + + align:start position:0% +about politics by the + + + align:start position:0% +about politics by the +elite read descriptions of politics in + + align:start position:0% +elite read descriptions of politics in + + + align:start position:0% +elite read descriptions of politics in +Haiti um uh Etc it's if there there are + + align:start position:0% +Haiti um uh Etc it's if there there are + + + align:start position:0% +Haiti um uh Etc it's if there there are +a number of situations in which it makes + + align:start position:0% +a number of situations in which it makes + + + align:start position:0% +a number of situations in which it makes +sense to think about + + align:start position:0% +sense to think about + + + align:start position:0% +sense to think about +and if you read older descriptions in + + align:start position:0% +and if you read older descriptions in + + + align:start position:0% +and if you read older descriptions in +Boston of the vault which is when all + + align:start position:0% +Boston of the vault which is when all + + + align:start position:0% +Boston of the vault which is when all +the business and Civic leaders would get + + align:start position:0% +the business and Civic leaders would get + + + align:start position:0% +the business and Civic leaders would get +together in the Vault of the bank of + + align:start position:0% +together in the Vault of the bank of + + + align:start position:0% +together in the Vault of the bank of +Boston you sort of have a politics that + + align:start position:0% +Boston you sort of have a politics that + + + align:start position:0% +Boston you sort of have a politics that +doesn't look so much like this this is + + align:start position:0% +doesn't look so much like this this is + + + align:start position:0% +doesn't look so much like this this is +really a lowy description over here a + + align:start position:0% +really a lowy description over here a + + + align:start position:0% +really a lowy description over here a +very nice lowy description of how it + + align:start position:0% +very nice lowy description of how it + + + align:start position:0% +very nice lowy description of how it +ought to work but in fact there are + + align:start position:0% +ought to work but in fact there are + + + align:start position:0% +ought to work but in fact there are +situations in which in essence there's a + + align:start position:0% +situations in which in essence there's a + + + align:start position:0% +situations in which in essence there's a +relatively small Elite that controls the + + align:start position:0% +relatively small Elite that controls the + + + align:start position:0% +relatively small Elite that controls the +government they may control the + + align:start position:0% +government they may control the + + + align:start position:0% +government they may control the +government for exploitation they may + + align:start position:0% +government for exploitation they may + + + align:start position:0% +government for exploitation they may +control the government for who knows + + align:start position:0% +control the government for who knows + + + align:start position:0% +control the government for who knows +what but it's a club it's a small + + align:start position:0% +what but it's a club it's a small + + + align:start position:0% +what but it's a club it's a small +club and there are situations that look + + align:start position:0% +club and there are situations that look + + + align:start position:0% +club and there are situations that look +like that us doesn't look like that so + + align:start position:0% +like that us doesn't look like that so + + + align:start position:0% +like that us doesn't look like that so +much because our politics are less well + + align:start position:0% +much because our politics are less well + + + align:start position:0% +much because our politics are less well +organized Latin countries always used to + + align:start position:0% +organized Latin countries always used to + + + align:start position:0% +organized Latin countries always used to +look like that they're less so now but + + align:start position:0% +look like that they're less so now but + + + align:start position:0% +look like that they're less so now but +uh again listen to + + align:start position:0% +uh again listen to + + + align:start position:0% +uh again listen to +uh listen to aita and hear them talk + + align:start position:0% +uh listen to aita and hear them talk + + + align:start position:0% +uh listen to aita and hear them talk +about the oligarchy uh uh so there are a + + align:start position:0% +about the oligarchy uh uh so there are a + + + align:start position:0% +about the oligarchy uh uh so there are a +number of settings in which it makes + + align:start position:0% +number of settings in which it makes + + + align:start position:0% +number of settings in which it makes +sense to think about the Politics as + + align:start position:0% +sense to think about the Politics as + + + align:start position:0% +sense to think about the Politics as +Elite control not interest group + + align:start position:0% +Elite control not interest group + + + align:start position:0% +Elite control not interest group +competition uh you might think about + + align:start position:0% +competition uh you might think about + + + align:start position:0% +competition uh you might think about +that there are also situations that + + align:start position:0% +that there are also situations that + + + align:start position:0% +that there are also situations that +don't fit any of these and I'll talk + + align:start position:0% +don't fit any of these and I'll talk + + + align:start position:0% +don't fit any of these and I'll talk +about some of + + align:start position:0% +about some of + + + align:start position:0% +about some of +those um what I want to do now is begin + + align:start position:0% +those um what I want to do now is begin + + + align:start position:0% +those um what I want to do now is begin +the lead into the discussion of uh clean + + align:start position:0% +the lead into the discussion of uh clean + + + align:start position:0% +the lead into the discussion of uh clean +air um as an example where a number of + + align:start position:0% +air um as an example where a number of + + + align:start position:0% +air um as an example where a number of +these and some other things surface so I + + align:start position:0% +these and some other things surface so I + + + align:start position:0% +these and some other things surface so I +realized that to do that case you have + + align:start position:0% +realized that to do that case you have + + + align:start position:0% +realized that to do that case you have +to have a little background on the + + align:start position:0% +to have a little background on the + + + align:start position:0% +to have a little background on the +structure of Federal Regulation and let + + align:start position:0% +structure of Federal Regulation and let + + + align:start position:0% +structure of Federal Regulation and let +me do that now please try to stay awake + + align:start position:0% +me do that now please try to stay awake + + + align:start position:0% +me do that now please try to stay awake +um the way the US system works + + align:start position:0% +um the way the US system works + + + align:start position:0% +um the way the US system works +typically is laws are + + align:start position:0% +typically is laws are + + + align:start position:0% +typically is laws are +laws say things like EPA must set a + + align:start position:0% +laws say things like EPA must set a + + + align:start position:0% +laws say things like EPA must set a +standard to protect human + + align:start position:0% +standard to protect human + + + align:start position:0% +standard to protect human +health uh or the Public Utility + + align:start position:0% +health uh or the Public Utility + + + align:start position:0% +health uh or the Public Utility +Commission shall ensure that electricity + + align:start position:0% +Commission shall ensure that electricity + + + align:start position:0% +Commission shall ensure that electricity +prices are just reasonable and not + + align:start position:0% +prices are just reasonable and not + + + align:start position:0% +prices are just reasonable and not +unduly + + align:start position:0% +unduly + + + align:start position:0% +unduly +discriminatory very commonly this is a + + align:start position:0% +discriminatory very commonly this is a + + + align:start position:0% +discriminatory very commonly this is a +very standard sometimes that's handed to + + align:start position:0% +very standard sometimes that's handed to + + + align:start position:0% +very standard sometimes that's handed to +a cabinet department the Department of + + align:start position:0% +a cabinet department the Department of + + + align:start position:0% +a cabinet department the Department of +Agriculture the department of interior + + align:start position:0% +Agriculture the department of interior + + + align:start position:0% +Agriculture the department of interior +whatever sometimes it's handed to an + + align:start position:0% +whatever sometimes it's handed to an + + + align:start position:0% +whatever sometimes it's handed to an +agency we're + + align:start position:0% +agency we're + + + align:start position:0% +agency we're +talking here mostly about agen gencies + + align:start position:0% +talking here mostly about agen gencies + + + align:start position:0% +talking here mostly about agen gencies +they come in two + + align:start position:0% +they come in two + + + align:start position:0% +they come in two +forms um they're either independent or + + align:start position:0% +forms um they're either independent or + + + align:start position:0% +forms um they're either independent or +they're part of the executive branch if + + align:start position:0% +they're part of the executive branch if + + + align:start position:0% +they're part of the executive branch if +they're part of the executive branch + + align:start position:0% +they're part of the executive branch + + + align:start position:0% +they're part of the executive branch +like EPA the President appoints the head + + align:start position:0% +like EPA the President appoints the head + + + align:start position:0% +like EPA the President appoints the head +the president can fire the + + align:start position:0% +the president can fire the + + + align:start position:0% +the president can fire the +head if they're independent the + + align:start position:0% +head if they're independent the + + + align:start position:0% +head if they're independent the +president will be able to appoint the + + align:start position:0% +president will be able to appoint the + + + align:start position:0% +president will be able to appoint the +head but not remove them except to show + + align:start position:0% +head but not remove them except to show + + + align:start position:0% +head but not remove them except to show +cause you can fire the head of EPA + + align:start position:0% +cause you can fire the head of EPA + + + align:start position:0% +cause you can fire the head of EPA +because he ticked you he or she ticked + + align:start position:0% +because he ticked you he or she ticked + + + align:start position:0% +because he ticked you he or she ticked +you off to fire the head of FK you have + + align:start position:0% +you off to fire the head of FK you have + + + align:start position:0% +you off to fire the head of FK you have +to show cuse it can be challenged in + + align:start position:0% +to show cuse it can be challenged in + + + align:start position:0% +to show cuse it can be challenged in +court and so forth so they are + + align:start position:0% +court and so forth so they are + + + align:start position:0% +court and so forth so they are +independent they were invented around in + + align:start position:0% +independent they were invented around in + + + align:start position:0% +independent they were invented around in +the teens of the last century the idea + + align:start position:0% +the teens of the last century the idea + + + align:start position:0% +the teens of the last century the idea +was to make them well there was some + + align:start position:0% +was to make them well there was some + + + align:start position:0% +was to make them well there was some +earlier examples but but it was really + + align:start position:0% +earlier examples but but it was really + + + align:start position:0% +earlier examples but but it was really +pushed then um the idea was these will + + align:start position:0% +pushed then um the idea was these will + + + align:start position:0% +pushed then um the idea was these will +be expert bodies immune to politics the + + align:start position:0% +be expert bodies immune to politics the + + + align:start position:0% +be expert bodies immune to politics the +Federal Trade Commission is one such + + align:start position:0% +Federal Trade Commission is one such + + + align:start position:0% +Federal Trade Commission is one such +like that it's it's has its own building + + align:start position:0% +like that it's it's has its own building + + + align:start position:0% +like that it's it's has its own building +it gets its money from Congress it + + align:start position:0% +it gets its money from Congress it + + + align:start position:0% +it gets its money from Congress it +doesn't report to the president uh the + + align:start position:0% +doesn't report to the president uh the + + + align:start position:0% +doesn't report to the president uh the +president Appo Point points people with + + align:start position:0% +president Appo Point points people with + + + align:start position:0% +president Appo Point points people with +the consent of Congress can't fire them + + align:start position:0% +the consent of Congress can't fire them + + + align:start position:0% +the consent of Congress can't fire them +often they they have to be bipartisan + + align:start position:0% +often they they have to be bipartisan + + + align:start position:0% +often they they have to be bipartisan +two Republicans two Democrats something + + align:start position:0% +two Republicans two Democrats something + + + align:start position:0% +two Republicans two Democrats something +like + + align:start position:0% +like + + + align:start position:0% +like +that um they could be + + align:start position:0% +that um they could be + + + align:start position:0% +that um they could be +captured + + align:start position:0% +captured + + + align:start position:0% +captured +uh that the they could be captured by + + align:start position:0% +uh that the they could be captured by + + + align:start position:0% +uh that the they could be captured by +the regulated interests it's argued that + + align:start position:0% +the regulated interests it's argued that + + + align:start position:0% +the regulated interests it's argued that +FK is captured by the utilities I don't + + align:start position:0% +FK is captured by the utilities I don't + + + align:start position:0% +FK is captured by the utilities I don't +think that's true but it's you can make + + align:start position:0% +think that's true but it's you can make + + + align:start position:0% +think that's true but it's you can make +the case and the idea of putting EPA + + align:start position:0% +the case and the idea of putting EPA + + + align:start position:0% +the case and the idea of putting EPA +which is a later Creation in the + + align:start position:0% +which is a later Creation in the + + + align:start position:0% +which is a later Creation in the +executive Branch was to make it + + align:start position:0% +executive Branch was to make it + + + align:start position:0% +executive Branch was to make it +responsive to politics make it + + align:start position:0% + + + + align:start position:0% + +responsible the it affects the kind of + + align:start position:0% +responsible the it affects the kind of + + + align:start position:0% +responsible the it affects the kind of +oversight rules passed by EPA rules + + align:start position:0% +oversight rules passed by EPA rules + + + align:start position:0% +oversight rules passed by EPA rules +proposed by EPA are reviewed by the + + align:start position:0% +proposed by EPA are reviewed by the + + + align:start position:0% +proposed by EPA are reviewed by the +office of information and Regulatory + + align:start position:0% +office of information and Regulatory + + + align:start position:0% +office of information and Regulatory +analysis in the Office of Management and + + align:start position:0% +analysis in the Office of Management and + + + align:start position:0% +analysis in the Office of Management and +budget they can be called in on the + + align:start position:0% +budget they can be called in on the + + + align:start position:0% +budget they can be called in on the +carpet they can be fired all kinds of + + align:start position:0% +carpet they can be fired all kinds of + + + align:start position:0% +carpet they can be fired all kinds of +things can happen the Federal + + align:start position:0% +things can happen the Federal + + + align:start position:0% +things can happen the Federal +Communications Commission or the firk or + + align:start position:0% +Communications Commission or the firk or + + + align:start position:0% +Communications Commission or the firk or +state public utility commissions are not + + align:start position:0% +state public utility commissions are not + + + align:start position:0% +state public utility commissions are not +reviewed in that fashion by the + + align:start position:0% +reviewed in that fashion by the + + + align:start position:0% +reviewed in that fashion by the +president or the president's people or + + align:start position:0% +president or the president's people or + + + align:start position:0% +president or the president's people or +the governor or the governor's people + + align:start position:0% +the governor or the governor's people + + + align:start position:0% +the governor or the governor's people +but all Decisions by Regulatory Agencies + + align:start position:0% +but all Decisions by Regulatory Agencies + + + align:start position:0% +but all Decisions by Regulatory Agencies +can be reviewed in the + + align:start position:0% +can be reviewed in the + + + align:start position:0% +can be reviewed in the +courts so here's the here's the + + align:start position:0% +courts so here's the here's the + + + align:start position:0% +courts so here's the here's the +architecture the law says it's got to be + + align:start position:0% +architecture the law says it's got to be + + + align:start position:0% +architecture the law says it's got to be +just and reasonable it's got to protect + + align:start position:0% +just and reasonable it's got to protect + + + align:start position:0% +just and reasonable it's got to protect +blah blah blah um in some cases the + + align:start position:0% +blah blah blah um in some cases the + + + align:start position:0% +blah blah blah um in some cases the +president or the governor can review it + + align:start position:0% +president or the governor can review it + + + align:start position:0% +president or the governor can review it +more commonly known not it gets reviewed + + align:start position:0% +more commonly known not it gets reviewed + + + align:start position:0% +more commonly known not it gets reviewed +by the courts under the administrative + + align:start position:0% +by the courts under the administrative + + + align:start position:0% +by the courts under the administrative +procedures Act of + + align:start position:0% +procedures Act of + + + align:start position:0% +procedures Act of +1946 or related State acts the court can + + align:start position:0% +1946 or related State acts the court can + + + align:start position:0% +1946 or related State acts the court can +reject an action that's arbitrary and + + align:start position:0% +reject an action that's arbitrary and + + + align:start position:0% +reject an action that's arbitrary and +capricious and abusive discretion or not + + align:start position:0% +capricious and abusive discretion or not + + + align:start position:0% +capricious and abusive discretion or not +otherwise in accordance with the law so + + align:start position:0% +otherwise in accordance with the law so + + + align:start position:0% +otherwise in accordance with the law so +the law says you have to protect human + + align:start position:0% +the law says you have to protect human + + + align:start position:0% +the law says you have to protect human +health the agency has no evidence on + + align:start position:0% +health the agency has no evidence on + + + align:start position:0% +health the agency has no evidence on +health the court will say that's + + align:start position:0% +health the court will say that's + + + align:start position:0% +health the court will say that's +arbitrary and capricious and throw it + + align:start position:0% +arbitrary and capricious and throw it + + + align:start position:0% +arbitrary and capricious and throw it +out or + + align:start position:0% +out or + + + align:start position:0% +out or +or it didn't take into account public + + align:start position:0% +or it didn't take into account public + + + align:start position:0% +or it didn't take into account public +comment so here is where organized + + align:start position:0% +comment so here is where organized + + + align:start position:0% +comment so here is where organized +interest groups + + align:start position:0% +interest groups + + + align:start position:0% +interest groups +matter so the agency is going to make a + + align:start position:0% +matter so the agency is going to make a + + + align:start position:0% +matter so the agency is going to make a +decision it has to take comments + + align:start position:0% +decision it has to take comments + + + align:start position:0% +decision it has to take comments +usually um + + align:start position:0% +usually um + + + align:start position:0% +usually um +and the American public Power + + align:start position:0% +and the American public Power + + + align:start position:0% +and the American public Power +Association will fire file comments on + + align:start position:0% +Association will fire file comments on + + + align:start position:0% +Association will fire file comments on +everything elcon which is this + + align:start position:0% +everything elcon which is this + + + align:start position:0% +everything elcon which is this +electricity consumers organization will + + align:start position:0% +electricity consumers organization will + + + align:start position:0% +electricity consumers organization will +file comments on everything that has to + + align:start position:0% +file comments on everything that has to + + + align:start position:0% +file comments on everything that has to +do with electric + + align:start position:0% +do with electric + + + align:start position:0% +do with electric +you and I + + align:start position:0% +you and I + + + align:start position:0% +you and I +won't as will every utility in the land + + align:start position:0% +won't as will every utility in the land + + + align:start position:0% +won't as will every utility in the land +uh and who knows General Electric + + align:start position:0% +uh and who knows General Electric + + + align:start position:0% +uh and who knows General Electric +organized interest groups will follow + + align:start position:0% +organized interest groups will follow + + + align:start position:0% +organized interest groups will follow +com file comments and the courts will + + align:start position:0% +com file comments and the courts will + + + align:start position:0% +com file comments and the courts will +reject a rule that doesn't take adequate + + align:start position:0% +reject a rule that doesn't take adequate + + + align:start position:0% +reject a rule that doesn't take adequate +account of public comment so if somebody + + align:start position:0% +account of public comment so if somebody + + + align:start position:0% +account of public comment so if somebody +proves that a chemical is uh cancer + + align:start position:0% +proves that a chemical is uh cancer + + + align:start position:0% +proves that a chemical is uh cancer +causing and EPA says no it'll be thrown + + align:start position:0% +causing and EPA says no it'll be thrown + + + align:start position:0% +causing and EPA says no it'll be thrown +out you got to got to take you got to + + align:start position:0% +out you got to got to take you got to + + + align:start position:0% +out you got to got to take you got to +consider the evidence that's submitted + + align:start position:0% +consider the evidence that's submitted + + + align:start position:0% +consider the evidence that's submitted +in the + + align:start position:0% +in the + + + align:start position:0% +in the +process okay that's the regulatory + + align:start position:0% +process okay that's the regulatory + + + align:start position:0% +process okay that's the regulatory +process particularly as it relates to + + align:start position:0% +process particularly as it relates to + + + align:start position:0% +process particularly as it relates to +environmental + + align:start position:0% +environmental + + + align:start position:0% +environmental +regulation fairly vague laws not always + + align:start position:0% +regulation fairly vague laws not always + + + align:start position:0% +regulation fairly vague laws not always +not on all terms but usually fairly + + align:start position:0% +not on all terms but usually fairly + + + align:start position:0% +not on all terms but usually fairly +vague hands it off delegates to the + + align:start position:0% +vague hands it off delegates to the + + + align:start position:0% +vague hands it off delegates to the +agency sometimes in the case of EPA + + align:start position:0% +agency sometimes in the case of EPA + + + align:start position:0% +agency sometimes in the case of EPA +reviewed by the White House sometimes + + align:start position:0% +reviewed by the White House sometimes + + + align:start position:0% +reviewed by the White House sometimes +not always reviewable by the courts + + align:start position:0% +not always reviewable by the courts + + + align:start position:0% +not always reviewable by the courts +always a requirement to take into + + align:start position:0% +always a requirement to take into + + + align:start position:0% +always a requirement to take into +account + + align:start position:0% +account + + + align:start position:0% +account +comments + + align:start position:0% + + + + align:start position:0% + +okay you might ask who would work in a + + align:start position:0% +okay you might ask who would work in a + + + align:start position:0% +okay you might ask who would work in a +regulatory agency and we'll talk about + + align:start position:0% +regulatory agency and we'll talk about + + + align:start position:0% +regulatory agency and we'll talk about +that briefly but is that process + + align:start position:0% +that briefly but is that process + + + align:start position:0% +that briefly but is that process +reasonably + + align:start position:0% + + + + align:start position:0% + +straightforward + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um no you take into account the evidence + + align:start position:0% +um no you take into account the evidence + + + align:start position:0% +um no you take into account the evidence +provided so so if the large electricity + + align:start position:0% +provided so so if the large electricity + + + align:start position:0% +provided so so if the large electricity +consumers say we think that rate's too + + align:start position:0% +consumers say we think that rate's too + + + align:start position:0% +consumers say we think that rate's too +high well there's nothing to take into + + align:start position:0% +high well there's nothing to take into + + + align:start position:0% +high well there's nothing to take into +account if they + + align:start position:0% +account if they + + + align:start position:0% +account if they +say here's some here's a study that + + align:start position:0% +say here's some here's a study that + + + align:start position:0% +say here's some here's a study that +shows that 10% of our members will be + + align:start position:0% +shows that 10% of our members will be + + + align:start position:0% +shows that 10% of our members will be +driven bankrupt by these prices and the + + align:start position:0% +driven bankrupt by these prices and the + + + align:start position:0% +driven bankrupt by these prices and the +study makes and the study is not junk + + align:start position:0% +study makes and the study is not junk + + + align:start position:0% +study makes and the study is not junk +they have to consider + + align:start position:0% +they have to consider + + + align:start position:0% +they have to consider +that so they're not obliged uh in fact + + align:start position:0% +that so they're not obliged uh in fact + + + align:start position:0% +that so they're not obliged uh in fact +they're almost obliged not to take into + + align:start position:0% +they're almost obliged not to take into + + + align:start position:0% +they're almost obliged not to take into +account the source but to focus on the + + align:start position:0% +account the source but to focus on the + + + align:start position:0% +account the source but to focus on the +content which is sort of sensible yeah + + align:start position:0% +content which is sort of sensible yeah + + + align:start position:0% +content which is sort of sensible yeah +anything + + align:start position:0% +anything + + + align:start position:0% +anything +else yeah you have to do you actually + + align:start position:0% +else yeah you have to do you actually + + + align:start position:0% +else yeah you have to do you actually +have to make + + align:start position:0% +have to make + + + align:start position:0% +have to make +arguments + + align:start position:0% +arguments + + + align:start position:0% +arguments +Okay so we've been talking about + + align:start position:0% +Okay so we've been talking about + + + align:start position:0% +Okay so we've been talking about +interest group politics been talking + + align:start position:0% +interest group politics been talking + + + align:start position:0% +interest group politics been talking +about + + align:start position:0% + + + + align:start position:0% + +factions how did that act get + + align:start position:0% +factions how did that act get + + + align:start position:0% +factions how did that act get +passed was that interest group + + align:start position:0% +passed was that interest group + + + align:start position:0% +passed was that interest group +competition did interest group + + align:start position:0% +competition did interest group + + + align:start position:0% +competition did interest group +competition give us the Clean Air Act of + + align:start position:0% + + + + align:start position:0% + +1970 and if so list the + + align:start position:0% + + + + align:start position:0% + +groups Clean Air Act of 1970 was a + + align:start position:0% +groups Clean Air Act of 1970 was a + + + align:start position:0% +groups Clean Air Act of 1970 was a +strong assertion of federal power over + + align:start position:0% +strong assertion of federal power over + + + align:start position:0% +strong assertion of federal power over +the environment it in effect didn't + + align:start position:0% +the environment it in effect didn't + + + align:start position:0% +the environment it in effect didn't +quite but in effect created + + align:start position:0% + + + + align:start position:0% + +EPA put in a whole put in the + + align:start position:0% +EPA put in a whole put in the + + + align:start position:0% +EPA put in a whole put in the +architecture for air pollution control + + align:start position:0% +architecture for air pollution control + + + align:start position:0% +architecture for air pollution control +Water Pollution Control well the air + + align:start position:0% +Water Pollution Control well the air + + + align:start position:0% +Water Pollution Control well the air +pollution control that's still still + + align:start position:0% +pollution control that's still still + + + align:start position:0% +pollution control that's still still +governs took power from the + + align:start position:0% +governs took power from the + + + align:start position:0% +governs took power from the +States interest group + + align:start position:0% + + + + align:start position:0% + +competition + + align:start position:0% +competition + + + align:start position:0% +competition +Brendan competition between + + align:start position:0% +Brendan competition between + + + align:start position:0% +Brendan competition between +environmentalists and those maybe people + + align:start position:0% +environmentalists and those maybe people + + + align:start position:0% +environmentalists and those maybe people +who are using chemicals that the Clean + + align:start position:0% +who are using chemicals that the Clean + + + align:start position:0% +who are using chemicals that the Clean +Air Act was going + + align:start position:0% +Air Act was going + + + align:start position:0% +Air Act was going +against well environmentalists + + align:start position:0% + + + + align:start position:0% + +um let me push you a little farther um + + align:start position:0% +um let me push you a little farther um + + + align:start position:0% +um let me push you a little farther um +if you go back to 1960 could you find + + align:start position:0% +if you go back to 1960 could you find + + + align:start position:0% +if you go back to 1960 could you find +environmentalists no what what happened + + align:start position:0% +environmentalists no what what happened + + + align:start position:0% +environmentalists no what what happened +I think it was 1970 or close to 1970 + + align:start position:0% +I think it was 1970 or close to 1970 + + + align:start position:0% +I think it was 1970 or close to 1970 +there was a big + + align:start position:0% +there was a big + + + align:start position:0% +there was a big +event Earth Day Earth day that was when + + align:start position:0% +event Earth Day Earth day that was when + + + align:start position:0% +event Earth Day Earth day that was when +people started talking not about + + align:start position:0% +people started talking not about + + + align:start position:0% +people started talking not about +environmentalists but about the + + align:start position:0% +environmentalists but about the + + + align:start position:0% +environmentalists but about the +environmental + + align:start position:0% +environmental + + + align:start position:0% +environmental +movement you began to hear the word + + align:start position:0% +movement you began to hear the word + + + align:start position:0% +movement you began to hear the word +movement just as you you start to hear + + align:start position:0% +movement just as you you start to hear + + + align:start position:0% +movement just as you you start to hear +about the Tea Party Movement + + align:start position:0% +about the Tea Party Movement + + + align:start position:0% +about the Tea Party Movement +the Occupy Movement you started to hear + + align:start position:0% +the Occupy Movement you started to hear + + + align:start position:0% +the Occupy Movement you started to hear +about the environmental movement the + + align:start position:0% +about the environmental movement the + + + align:start position:0% +about the environmental movement the +Civil Rights + + align:start position:0% +Civil Rights + + + align:start position:0% +Civil Rights +Movement those aren't really interest + + align:start position:0% +Movement those aren't really interest + + + align:start position:0% +Movement those aren't really interest +groups we'll talk Monday about what they + + align:start position:0% +groups we'll talk Monday about what they + + + align:start position:0% +groups we'll talk Monday about what they +are but social + + align:start position:0% +are but social + + + align:start position:0% +are but social +movements are a bit distinct from + + align:start position:0% +movements are a bit distinct from + + + align:start position:0% +movements are a bit distinct from +organized interest groups they're + + align:start position:0% +organized interest groups they're + + + align:start position:0% +organized interest groups they're +certainly distinct from organized + + align:start position:0% +certainly distinct from organized + + + align:start position:0% +certainly distinct from organized +political parties yet every so often + + align:start position:0% +political parties yet every so often + + + align:start position:0% +political parties yet every so often +they get something like that + + align:start position:0% +they get something like that + + + align:start position:0% +they get something like that +passed Richard Nixon was not a an avid + + align:start position:0% +passed Richard Nixon was not a an avid + + + align:start position:0% +passed Richard Nixon was not a an avid +environmentalist this was not a + + align:start position:0% +environmentalist this was not a + + + align:start position:0% +environmentalist this was not a +republican issue to say the + + align:start position:0% +republican issue to say the + + + align:start position:0% +republican issue to say the +least + + align:start position:0% +least + + + align:start position:0% +least +um there was no industrial support for + + align:start position:0% +um there was no industrial support for + + + align:start position:0% +um there was no industrial support for +the Clean Air maybe a little industrial + + align:start position:0% +the Clean Air maybe a little industrial + + + align:start position:0% +the Clean Air maybe a little industrial +support because the state rules differed + + align:start position:0% +support because the state rules differed + + + align:start position:0% +support because the state rules differed +and that was a little problematic but + + align:start position:0% +and that was a little problematic but + + + align:start position:0% +and that was a little problematic but +not much not noticeable industrial + + align:start position:0% +not much not noticeable industrial + + + align:start position:0% +not much not noticeable industrial +support that was a social + + align:start position:0% +support that was a social + + + align:start position:0% +support that was a social +movement who was it was telling me about + + align:start position:0% +movement who was it was telling me about + + + align:start position:0% +movement who was it was telling me about +all the the no fracking signs in New + + align:start position:0% +all the the no fracking signs in New + + + align:start position:0% +all the the no fracking signs in New +York state somebody who sits over here + + align:start position:0% +York state somebody who sits over here + + + align:start position:0% +York state somebody who sits over here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +huh yeah that's a social movement that's + + align:start position:0% +huh yeah that's a social movement that's + + + align:start position:0% +huh yeah that's a social movement that's +not that's not an organized interest + + align:start position:0% +not that's not an organized interest + + + align:start position:0% +not that's not an organized interest +group in the sense that the American + + align:start position:0% +group in the sense that the American + + + align:start position:0% +group in the sense that the American +Forest Products Association is or the + + align:start position:0% +Forest Products Association is or the + + + align:start position:0% +Forest Products Association is or the +American public Power Association that's + + align:start position:0% +American public Power Association that's + + + align:start position:0% +American public Power Association that's +a bunch of people who get very upset + + align:start position:0% +a bunch of people who get very upset + + + align:start position:0% +a bunch of people who get very upset +about fracking and who by God make noise + + align:start position:0% +about fracking and who by God make noise + + + align:start position:0% +about fracking and who by God make noise +that's that's what got us the Clean Air + + align:start position:0% +that's that's what got us the Clean Air + + + align:start position:0% +that's that's what got us the Clean Air +Act um we may need that to do something + + align:start position:0% +Act um we may need that to do something + + + align:start position:0% +Act um we may need that to do something +about climate change but we don't have a + + align:start position:0% +about climate change but we don't have a + + + align:start position:0% +about climate change but we don't have a +social movement in that direction quite + + align:start position:0% +social movement in that direction quite + + + align:start position:0% +social movement in that direction quite +yet um but we did have interest groups + + align:start position:0% +yet um but we did have interest groups + + + align:start position:0% +yet um but we did have interest groups +after + + align:start position:0% +after + + + align:start position:0% +after +71 so who were + + align:start position:0% +71 so who were + + + align:start position:0% +71 so who were +they who were the interest groups + + align:start position:0% +they who were the interest groups + + + align:start position:0% +they who were the interest groups +affecting so SO2 regulations from power + + align:start position:0% +affecting so SO2 regulations from power + + + align:start position:0% +affecting so SO2 regulations from power +plants and we're going to we're going to + + align:start position:0% +plants and we're going to we're going to + + + align:start position:0% +plants and we're going to we're going to +walk through the case next week so + + align:start position:0% +walk through the case next week so + + + align:start position:0% +walk through the case next week so +please please do get it + + align:start position:0% +please please do get it + + + align:start position:0% +please please do get it +anybody has somebody looked at the case + + align:start position:0% +anybody has somebody looked at the case + + + align:start position:0% +anybody has somebody looked at the case +who were the + + align:start position:0% + + + + align:start position:0% + +groups + + align:start position:0% +groups + + + align:start position:0% +groups +Sarah great coal power plants who how + + align:start position:0% +Sarah great coal power plants who how + + + align:start position:0% +Sarah great coal power plants who how +they might have to retr their facil and + + align:start position:0% +they might have to retr their facil and + + + align:start position:0% +they might have to retr their facil and +where they would get their coal so you + + align:start position:0% +where they would get their coal so you + + + align:start position:0% +where they would get their coal so you +had utilities with coal fired power + + align:start position:0% +had utilities with coal fired power + + + align:start position:0% +had utilities with coal fired power +plants who else you had utilities H well + + align:start position:0% +plants who else you had utilities H well + + + align:start position:0% +plants who else you had utilities H well +utilities oh that utilities yeah with + + align:start position:0% +utilities oh that utilities yeah with + + + align:start position:0% +utilities oh that utilities yeah with +with coal fired power they owned them + + align:start position:0% +with coal fired power they owned them + + + align:start position:0% +with coal fired power they owned them +everybody was vertically integrated in + + align:start position:0% +everybody was vertically integrated in + + + align:start position:0% +everybody was vertically integrated in +those days utilities with coal fired + + align:start position:0% +those days utilities with coal fired + + + align:start position:0% +those days utilities with coal fired +power plants and envir conc + + align:start position:0% +power plants and envir conc + + + align:start position:0% +power plants and envir conc +environmentalists yeah they were pretty + + align:start position:0% +environmentalists yeah they were pretty + + + align:start position:0% +environmentalists yeah they were pretty +well organized by then producers in the + + align:start position:0% +well organized by then producers in the + + + align:start position:0% +well organized by then producers in the +East and West Coal producers in the East + + align:start position:0% +East and West Coal producers in the East + + + align:start position:0% +East and West Coal producers in the East +and in the west two distinct groups + + align:start position:0% +and in the west two distinct groups + + + align:start position:0% +and in the west two distinct groups +two distinct groups eastern and western + + align:start position:0% +two distinct groups eastern and western + + + align:start position:0% +two distinct groups eastern and western +producers Electric utilities uh Western + + align:start position:0% +producers Electric utilities uh Western + + + align:start position:0% +producers Electric utilities uh Western +States uh a little bit on some of the uh + + align:start position:0% +States uh a little bit on some of the uh + + + align:start position:0% +States uh a little bit on some of the uh +uh prevention of significant + + align:start position:0% +uh prevention of significant + + + align:start position:0% +uh prevention of significant +deterioration and the + + align:start position:0% +deterioration and the + + + align:start position:0% +deterioration and the +um um + + align:start position:0% + + + + align:start position:0% + +environmentalists who wasn't represented + + align:start position:0% +environmentalists who wasn't represented + + + align:start position:0% +environmentalists who wasn't represented +anybody to go back to + + align:start position:0% +anybody to go back to + + + align:start position:0% +anybody to go back to +Loy are there any interests not interest + + align:start position:0% +Loy are there any interests not interest + + + align:start position:0% +Loy are there any interests not interest +groups there any interests + + align:start position:0% +groups there any interests + + + align:start position:0% +groups there any interests +David we all buy the electric power so + + align:start position:0% +David we all buy the electric power so + + + align:start position:0% +David we all buy the electric power so +price kind go that affects us so + + align:start position:0% +price kind go that affects us so + + + align:start position:0% +price kind go that affects us so +consumers consumers weren't represented + + align:start position:0% +consumers consumers weren't represented + + + align:start position:0% +consumers consumers weren't represented +except maybe indirectly by Electric + + align:start position:0% +except maybe indirectly by Electric + + + align:start position:0% +except maybe indirectly by Electric +utilities who wanted to keep their cost + + align:start position:0% +utilities who wanted to keep their cost + + + align:start position:0% +utilities who wanted to keep their cost +down so you're not represented as a uh + + align:start position:0% +down so you're not represented as a uh + + + align:start position:0% +down so you're not represented as a uh +as a consumer of electric + + align:start position:0% +as a consumer of electric + + + align:start position:0% +as a consumer of electric +power uh any other interest Charlotte + + align:start position:0% +power uh any other interest Charlotte + + + align:start position:0% +power uh any other interest Charlotte +the people who are like near the + + align:start position:0% +the people who are like near the + + + align:start position:0% +the people who are like near the +power people who breed there right yeah + + align:start position:0% +power people who breed there right yeah + + + align:start position:0% +power people who breed there right yeah +yeah so the environmental groups in a + + align:start position:0% +yeah so the environmental groups in a + + + align:start position:0% +yeah so the environmental groups in a +sansor indirectly + + align:start position:0% +sansor indirectly + + + align:start position:0% +sansor indirectly +representing that interest as we'll see + + align:start position:0% +representing that interest as we'll see + + + align:start position:0% +representing that interest as we'll see +they also had other interests so uh I + + align:start position:0% +they also had other interests so uh I + + + align:start position:0% +they also had other interests so uh I +don't know I think those are the main + + align:start position:0% +don't know I think those are the main + + + align:start position:0% +don't know I think those are the main +ones uh that I think of you had more Oh + + align:start position:0% +ones uh that I think of you had more Oh + + + align:start position:0% +ones uh that I think of you had more Oh +I thought you were just waving + + align:start position:0% +I thought you were just waving + + + align:start position:0% +I thought you were just waving +okay okay um how did the ACT set it up + + align:start position:0% +okay okay um how did the ACT set it up + + + align:start position:0% +okay okay um how did the ACT set it up +what who did what what did EPA have to + + align:start position:0% +what who did what what did EPA have to + + + align:start position:0% +what who did what what did EPA have to +do what did the states do what about new + + align:start position:0% +do what did the states do what about new + + + align:start position:0% +do what did the states do what about new +plants what about old plants what was + + align:start position:0% +plants what about old plants what was + + + align:start position:0% +plants what about old plants what was +the design who did + + align:start position:0% +the design who did + + + align:start position:0% +the design who did +what the 70 act set up Casey the EPA + + align:start position:0% +what the 70 act set up Casey the EPA + + + align:start position:0% +what the 70 act set up Casey the EPA +overarching air pollution limits and + + align:start position:0% +overarching air pollution limits and + + + align:start position:0% +overarching air pollution limits and +then each state kind to figure out how + + align:start position:0% +then each state kind to figure out how + + + align:start position:0% +then each state kind to figure out how +so the EPA would set air quality + + align:start position:0% +so the EPA would set air quality + + + align:start position:0% +so the EPA would set air quality +standard National ambient air quality + + align:start position:0% +standard National ambient air quality + + + align:start position:0% +standard National ambient air quality +standards and then it would as regards + + align:start position:0% +standards and then it would as regards + + + align:start position:0% +standards and then it would as regards +existing plants and existing facilities + + align:start position:0% +existing plants and existing facilities + + + align:start position:0% +existing plants and existing facilities +uh tell the states ask the states for + + align:start position:0% +uh tell the states ask the states for + + + align:start position:0% +uh tell the states ask the states for +State implementation plans to meet those + + align:start position:0% +State implementation plans to meet those + + + align:start position:0% +State implementation plans to meet those +those requirements absolutely right what + + align:start position:0% +those requirements absolutely right what + + + align:start position:0% +those requirements absolutely right what +about new power plants a different set + + align:start position:0% +about new power plants a different set + + + align:start position:0% +about new power plants a different set +of regulations for usually a little B + + align:start position:0% +of regulations for usually a little B + + + align:start position:0% +of regulations for usually a little B +set by um set by the EPA set by the EPA + + align:start position:0% +set by um set by the EPA set by the EPA + + + align:start position:0% +set by um set by the EPA set by the EPA +so the EPA didn't set standards or rules + + align:start position:0% +so the EPA didn't set standards or rules + + + align:start position:0% +so the EPA didn't set standards or rules +for existing plants it set air quality + + align:start position:0% +for existing plants it set air quality + + + align:start position:0% +for existing plants it set air quality +standards let the states figure out how + + align:start position:0% +standards let the states figure out how + + + align:start position:0% +standards let the states figure out how +to do that but for new plants there were + + align:start position:0% +to do that but for new plants there were + + + align:start position:0% +to do that but for new plants there were +National there were national standards + + align:start position:0% +National there were national standards + + + align:start position:0% +National there were national standards +for new + + align:start position:0% +for new + + + align:start position:0% +for new +plants what's the basic rationale why + + align:start position:0% +plants what's the basic rationale why + + + align:start position:0% +plants what's the basic rationale why +would you treat new and old plants so + + align:start position:0% +would you treat new and old plants so + + + align:start position:0% +would you treat new and old plants so +differently + + align:start position:0% +differently + + + align:start position:0% +differently +Matthew because with the existing plants + + align:start position:0% +Matthew because with the existing plants + + + align:start position:0% +Matthew because with the existing plants +order to like retr them you would need + + align:start position:0% +order to like retr them you would need + + + align:start position:0% +order to like retr them you would need +exensive equipment it might not even be + + align:start position:0% +exensive equipment it might not even be + + + align:start position:0% +exensive equipment it might not even be +like worth it but for new ones they can + + align:start position:0% +like worth it but for new ones they can + + + align:start position:0% +like worth it but for new ones they can +already they can design it so that it + + align:start position:0% +already they can design it so that it + + + align:start position:0% +already they can design it so that it +can already fit so that's the basic + + align:start position:0% +can already fit so that's the basic + + + align:start position:0% +can already fit so that's the basic +rationale exactly that that new plants + + align:start position:0% +rationale exactly that that new plants + + + align:start position:0% +rationale exactly that that new plants +in a sense you've got a blank sheet of + + align:start position:0% +in a sense you've got a blank sheet of + + + align:start position:0% +in a sense you've got a blank sheet of +paper and you can design the plant to + + align:start position:0% +paper and you can design the plant to + + + align:start position:0% +paper and you can design the plant to +meet this meet this standard old plants + + align:start position:0% +meet this meet this standard old plants + + + align:start position:0% +meet this meet this standard old plants +differed in so many ways that there's + + align:start position:0% +differed in so many ways that there's + + + align:start position:0% +differed in so many ways that there's +no easy way to to use the same standard + + align:start position:0% +no easy way to to use the same standard + + + align:start position:0% +no easy way to to use the same standard +across all old plants it would be easy + + align:start position:0% +across all old plants it would be easy + + + align:start position:0% +across all old plants it would be easy +for some impossible for others let the + + align:start position:0% +for some impossible for others let the + + + align:start position:0% +for some impossible for others let the +states figure it out okay that is + + align:start position:0% +states figure it out okay that is + + + align:start position:0% +states figure it out okay that is +exactly the basic + + align:start position:0% +exactly the basic + + + align:start position:0% +exactly the basic +rationale um we'll come back to sort of + + align:start position:0% +rationale um we'll come back to sort of + + + align:start position:0% +rationale um we'll come back to sort of +how that how that worked so what we're + + align:start position:0% +how that how that worked so what we're + + + align:start position:0% +how that how that worked so what we're +going to do in the next two sessions + + align:start position:0% +going to do in the next two sessions + + + align:start position:0% +going to do in the next two sessions +we're going to talk about social + + align:start position:0% +we're going to talk about social + + + align:start position:0% +we're going to talk about social +movements on + + align:start position:0% +movements on + + + align:start position:0% +movements on +Monday and one of the reasons we're + + align:start position:0% +Monday and one of the reasons we're + + + align:start position:0% +Monday and one of the reasons we're +talking about social movements is that + + align:start position:0% +talking about social movements is that + + + align:start position:0% +talking about social movements is that +um though is that that what got the 70 P + + align:start position:0% +um though is that that what got the 70 P + + + align:start position:0% +um though is that that what got the 70 P +Act passed the Civil Rights Movement got + + align:start position:0% +Act passed the Civil Rights Movement got + + + align:start position:0% +Act passed the Civil Rights Movement got +civil rights legislation passed not an + + align:start position:0% +civil rights legislation passed not an + + + align:start position:0% +civil rights legislation passed not an +organized party not quite an interest + + align:start position:0% +organized party not quite an interest + + + align:start position:0% +organized party not quite an interest +group not the American Forest Products + + align:start position:0% +group not the American Forest Products + + + align:start position:0% +group not the American Forest Products +Association and then we'll come back to + + align:start position:0% +Association and then we'll come back to + + + align:start position:0% +Association and then we'll come back to +this case and we'll talk about how we + + align:start position:0% +this case and we'll talk about how we + + + align:start position:0% +this case and we'll talk about how we +got the uh the politics of the uh + + align:start position:0% +got the uh the politics of the uh + + + align:start position:0% +got the uh the politics of the uh +standards the two sets of Standards the + + align:start position:0% +standards the two sets of Standards the + + + align:start position:0% +standards the two sets of Standards the +acid rain impass emissions trading other + + align:start position:0% +acid rain impass emissions trading other + + + align:start position:0% +acid rain impass emissions trading other +stuff thank you \ No newline at end of file diff --git a/7_livg-uaVs.txt b/7_livg-uaVs.txt new file mode 100644 index 0000000000000000000000000000000000000000..36e0538cca6ba059527e31bf7b925196a843116f --- /dev/null +++ b/7_livg-uaVs.txt @@ -0,0 +1,1235 @@ +align:start position:0% + +in this segment we will go through the + + align:start position:0% +in this segment we will go through the + + + align:start position:0% +in this segment we will go through the +calculation of the variances of some + + align:start position:0% +calculation of the variances of some + + + align:start position:0% +calculation of the variances of some +familiar random variables starting with + + align:start position:0% +familiar random variables starting with + + + align:start position:0% +familiar random variables starting with +the simplest one that we know which is + + align:start position:0% +the simplest one that we know which is + + + align:start position:0% +the simplest one that we know which is +the Bernoulli random variable so let's X + + align:start position:0% +the Bernoulli random variable so let's X + + + align:start position:0% +the Bernoulli random variable so let's X +take values 0 or 1 and it takes a value + + align:start position:0% +take values 0 or 1 and it takes a value + + + align:start position:0% +take values 0 or 1 and it takes a value +of 1 with probability P we have already + + align:start position:0% +of 1 with probability P we have already + + + align:start position:0% +of 1 with probability P we have already +calculated the expected value of X and + + align:start position:0% +calculated the expected value of X and + + + align:start position:0% +calculated the expected value of X and +we know that it is equal to P let us now + + align:start position:0% +we know that it is equal to P let us now + + + align:start position:0% +we know that it is equal to P let us now +compute its variance one way of + + align:start position:0% +compute its variance one way of + + + align:start position:0% +compute its variance one way of +proceeding is to use the definition and + + align:start position:0% +proceeding is to use the definition and + + + align:start position:0% +proceeding is to use the definition and +then the expected value rule so if we + + align:start position:0% +then the expected value rule so if we + + + align:start position:0% +then the expected value rule so if we +now apply the expected value rule we + + align:start position:0% +now apply the expected value rule we + + + align:start position:0% +now apply the expected value rule we +need a summation over all possible + + align:start position:0% +need a summation over all possible + + + align:start position:0% +need a summation over all possible +values of X there are two values X equal + + align:start position:0% +values of X there are two values X equal + + + align:start position:0% +values of X there are two values X equal +to 1 or X equal to 0 the contribution + + align:start position:0% +to 1 or X equal to 0 the contribution + + + align:start position:0% +to 1 or X equal to 0 the contribution +when X is equal to 1 is 1 minus the + + align:start position:0% +when X is equal to 1 is 1 minus the + + + align:start position:0% +when X is equal to 1 is 1 minus the +expected value which is P squared and + + align:start position:0% +expected value which is P squared and + + + align:start position:0% +expected value which is P squared and +the value of 1 is taken with probability + + align:start position:0% +the value of 1 is taken with probability + + + align:start position:0% +the value of 1 is taken with probability +P there's another contribution to this + + align:start position:0% +P there's another contribution to this + + + align:start position:0% +P there's another contribution to this +sum when little X is equal to 0 and that + + align:start position:0% +sum when little X is equal to 0 and that + + + align:start position:0% +sum when little X is equal to 0 and that +contribution is going to be 0 minus P + + align:start position:0% +contribution is going to be 0 minus P + + + align:start position:0% +contribution is going to be 0 minus P +all of this squared times the + + align:start position:0% +all of this squared times the + + + align:start position:0% +all of this squared times the +probability of a 0 which is 1 minus P + + align:start position:0% +probability of a 0 which is 1 minus P + + + align:start position:0% +probability of a 0 which is 1 minus P +and now we carry out some algebra we + + align:start position:0% +and now we carry out some algebra we + + + align:start position:0% +and now we carry out some algebra we +expand the square here 1 minus 2p plus P + + align:start position:0% +expand the square here 1 minus 2p plus P + + + align:start position:0% +expand the square here 1 minus 2p plus P +squared and after we multiply with this + + align:start position:0% +squared and after we multiply with this + + + align:start position:0% +squared and after we multiply with this +factor of T of P we obtain P minus 2 P + + align:start position:0% +factor of T of P we obtain P minus 2 P + + + align:start position:0% +factor of T of P we obtain P minus 2 P +squared plus P to the third power and + + align:start position:0% +squared plus P to the third power and + + + align:start position:0% +squared plus P to the third power and +then from here we have a factor of P + + align:start position:0% +then from here we have a factor of P + + + align:start position:0% +then from here we have a factor of P +squared times 1p squared minus x minus P + + align:start position:0% +squared times 1p squared minus x minus P + + + align:start position:0% +squared times 1p squared minus x minus P +that gives us a minus P cube then we + + align:start position:0% +that gives us a minus P cube then we + + + align:start position:0% +that gives us a minus P cube then we +notice that this term cancels out with + + align:start position:0% +notice that this term cancels out with + + + align:start position:0% +notice that this term cancels out with +that term P squared minus 2p squared + + align:start position:0% +that term P squared minus 2p squared + + + align:start position:0% +that term P squared minus 2p squared +leaves us with leaves us with P minus P + + align:start position:0% +leaves us with leaves us with P minus P + + + align:start position:0% +leaves us with leaves us with P minus P +squared and we factor this as P times 1 + + align:start position:0% +squared and we factor this as P times 1 + + + align:start position:0% +squared and we factor this as P times 1 +minus P + + align:start position:0% + + + + align:start position:0% + +an alternative calculation uses the + + align:start position:0% +an alternative calculation uses the + + + align:start position:0% +an alternative calculation uses the +formula that we provided a little + + align:start position:0% +formula that we provided a little + + + align:start position:0% +formula that we provided a little +earlier let's see how we how this will + + align:start position:0% +earlier let's see how we how this will + + + align:start position:0% +earlier let's see how we how this will +go we have the following observation the + + align:start position:0% +go we have the following observation the + + + align:start position:0% +go we have the following observation the +random variable x squared and the random + + align:start position:0% +random variable x squared and the random + + + align:start position:0% +random variable x squared and the random +variable X they are one and the same + + align:start position:0% +variable X they are one and the same + + + align:start position:0% +variable X they are one and the same +when X is zero x squared is also zero + + align:start position:0% +when X is zero x squared is also zero + + + align:start position:0% +when X is zero x squared is also zero +when X is 1 x squared is also 1 so as + + align:start position:0% +when X is 1 x squared is also 1 so as + + + align:start position:0% +when X is 1 x squared is also 1 so as +random variables these two random + + align:start position:0% +random variables these two random + + + align:start position:0% +random variables these two random +variables are equal in the case where X + + align:start position:0% +variables are equal in the case where X + + + align:start position:0% +variables are equal in the case where X +is a Bernoulli so what we have here is + + align:start position:0% +is a Bernoulli so what we have here is + + + align:start position:0% +is a Bernoulli so what we have here is +just the expected value of X minus the + + align:start position:0% +just the expected value of X minus the + + + align:start position:0% +just the expected value of X minus the +expected value of x squared to the + + align:start position:0% +expected value of x squared to the + + + align:start position:0% +expected value of x squared to the +second power and this is P minus P + + align:start position:0% +second power and this is P minus P + + + align:start position:0% +second power and this is P minus P +squared which is the same answer as we + + align:start position:0% +squared which is the same answer as we + + + align:start position:0% +squared which is the same answer as we +got before P times 1 minus P and we see + + align:start position:0% +got before P times 1 minus P and we see + + + align:start position:0% +got before P times 1 minus P and we see +that the calculations and the algebra + + align:start position:0% +that the calculations and the algebra + + + align:start position:0% +that the calculations and the algebra +involved using this formula were a + + align:start position:0% +involved using this formula were a + + + align:start position:0% +involved using this formula were a +little simpler than they were before now + + align:start position:0% +little simpler than they were before now + + + align:start position:0% +little simpler than they were before now +the form of the variance of the + + align:start position:0% +the form of the variance of the + + + align:start position:0% +the form of the variance of the +Bernoulli random variable has an + + align:start position:0% +Bernoulli random variable has an + + + align:start position:0% +Bernoulli random variable has an +interesting dependence on P it's + + align:start position:0% +interesting dependence on P it's + + + align:start position:0% +interesting dependence on P it's +instructive to plot it as a function of + + align:start position:0% +instructive to plot it as a function of + + + align:start position:0% +instructive to plot it as a function of +P so this is a plot of the variance of + + align:start position:0% +P so this is a plot of the variance of + + + align:start position:0% +P so this is a plot of the variance of +the Bernoulli as a function of P as P + + align:start position:0% +the Bernoulli as a function of P as P + + + align:start position:0% +the Bernoulli as a function of P as P +ranges between 0 and 1 P times 1 minus P + + align:start position:0% +ranges between 0 and 1 P times 1 minus P + + + align:start position:0% +ranges between 0 and 1 P times 1 minus P +is a parabola and it's a parabola that + + align:start position:0% +is a parabola and it's a parabola that + + + align:start position:0% +is a parabola and it's a parabola that +is 0 when P is either 0 or 1 and it has + + align:start position:0% +is 0 when P is either 0 or 1 and it has + + + align:start position:0% +is 0 when P is either 0 or 1 and it has +this particular shape and the peak of + + align:start position:0% +this particular shape and the peak of + + + align:start position:0% +this particular shape and the peak of +this parabola occurs when P is equal to + + align:start position:0% +this parabola occurs when P is equal to + + + align:start position:0% +this parabola occurs when P is equal to +1/2 in which case the variance is 1/4 in + + align:start position:0% +1/2 in which case the variance is 1/4 in + + + align:start position:0% +1/2 in which case the variance is 1/4 in +some sense the variance is a measure of + + align:start position:0% +some sense the variance is a measure of + + + align:start position:0% +some sense the variance is a measure of +the amount of uncertainty in a random + + align:start position:0% +the amount of uncertainty in a random + + + align:start position:0% +the amount of uncertainty in a random +variable a measure of the amount of + + align:start position:0% +variable a measure of the amount of + + + align:start position:0% +variable a measure of the amount of +randomness a coin is most random if it + + align:start position:0% +randomness a coin is most random if it + + + align:start position:0% +randomness a coin is most random if it +is fair that is when P is equal to 1/2 + + align:start position:0% +is fair that is when P is equal to 1/2 + + + align:start position:0% +is fair that is when P is equal to 1/2 +and in this case the variance confirms + + align:start position:0% +and in this case the variance confirms + + + align:start position:0% +and in this case the variance confirms +this intuition the variance + + align:start position:0% +this intuition the variance + + + align:start position:0% +this intuition the variance +of a coin flip is biggest if that coin + + align:start position:0% +of a coin flip is biggest if that coin + + + align:start position:0% +of a coin flip is biggest if that coin +is fair on the other hand in the extreme + + align:start position:0% +is fair on the other hand in the extreme + + + align:start position:0% +is fair on the other hand in the extreme +cases were P equals 0 so the coin always + + align:start position:0% +cases were P equals 0 so the coin always + + + align:start position:0% +cases were P equals 0 so the coin always +results in tails or if P equals to 1 so + + align:start position:0% +results in tails or if P equals to 1 so + + + align:start position:0% +results in tails or if P equals to 1 so +that the coin always results in heads in + + align:start position:0% +that the coin always results in heads in + + + align:start position:0% +that the coin always results in heads in +those cases we do not have any + + align:start position:0% +those cases we do not have any + + + align:start position:0% +those cases we do not have any +randomness and the variance + + align:start position:0% +randomness and the variance + + + align:start position:0% +randomness and the variance +correspondingly is equal to 0 let us now + + align:start position:0% +correspondingly is equal to 0 let us now + + + align:start position:0% +correspondingly is equal to 0 let us now +calculate the variance of a uniform + + align:start position:0% +calculate the variance of a uniform + + + align:start position:0% +calculate the variance of a uniform +random variable let us start with a + + align:start position:0% +random variable let us start with a + + + align:start position:0% +random variable let us start with a +simple case where the range of the + + align:start position:0% +simple case where the range of the + + + align:start position:0% +simple case where the range of the +uniform random variable starts at 0 and + + align:start position:0% +uniform random variable starts at 0 and + + + align:start position:0% +uniform random variable starts at 0 and +extends up to some n so there is a total + + align:start position:0% +extends up to some n so there is a total + + + align:start position:0% +extends up to some n so there is a total +of n plus 1 possible values each one of + + align:start position:0% +of n plus 1 possible values each one of + + + align:start position:0% +of n plus 1 possible values each one of +them having the same probability 1 over + + align:start position:0% +them having the same probability 1 over + + + align:start position:0% +them having the same probability 1 over +n plus 1 we calculate the variance using + + align:start position:0% +n plus 1 we calculate the variance using + + + align:start position:0% +n plus 1 we calculate the variance using +the alternative formula and let us start + + align:start position:0% +the alternative formula and let us start + + + align:start position:0% +the alternative formula and let us start +with the first term what is it we use + + align:start position:0% +with the first term what is it we use + + + align:start position:0% +with the first term what is it we use +the expected value rule and we argue + + align:start position:0% +the expected value rule and we argue + + + align:start position:0% +the expected value rule and we argue +that with probability 1 over n plus 1 + + align:start position:0% +that with probability 1 over n plus 1 + + + align:start position:0% +that with probability 1 over n plus 1 +the random variable x squared takes the + + align:start position:0% +the random variable x squared takes the + + + align:start position:0% +the random variable x squared takes the +value 0 squared with the same + + align:start position:0% +value 0 squared with the same + + + align:start position:0% +value 0 squared with the same +probability takes the value 1 squared + + align:start position:0% +probability takes the value 1 squared + + + align:start position:0% +probability takes the value 1 squared +with the same probability it takes the + + align:start position:0% +with the same probability it takes the + + + align:start position:0% +with the same probability it takes the +value 2 squared and so on all the way up + + align:start position:0% +value 2 squared and so on all the way up + + + align:start position:0% +value 2 squared and so on all the way up +to N squared and then there's the next + + align:start position:0% +to N squared and then there's the next + + + align:start position:0% +to N squared and then there's the next +term the expected value of the uniform + + align:start position:0% +term the expected value of the uniform + + + align:start position:0% +term the expected value of the uniform +is the midpoint of the distribution by + + align:start position:0% +is the midpoint of the distribution by + + + align:start position:0% +is the midpoint of the distribution by +symmetry so it's n over 2 and we take + + align:start position:0% +symmetry so it's n over 2 and we take + + + align:start position:0% +symmetry so it's n over 2 and we take +the square of that now to make progress + + align:start position:0% +the square of that now to make progress + + + align:start position:0% +the square of that now to make progress +here we need to evaluate this sum + + align:start position:0% +here we need to evaluate this sum + + + align:start position:0% +here we need to evaluate this sum +fortunately this has been done by others + + align:start position:0% +fortunately this has been done by others + + + align:start position:0% +fortunately this has been done by others +and it turns out to be equal to 1 over 6 + + align:start position:0% +and it turns out to be equal to 1 over 6 + + + align:start position:0% +and it turns out to be equal to 1 over 6 +and n times n plus 1 times 2n plus 1 + + align:start position:0% +and n times n plus 1 times 2n plus 1 + + + align:start position:0% +and n times n plus 1 times 2n plus 1 +this formula can be proved by induction + + align:start position:0% +this formula can be proved by induction + + + align:start position:0% +this formula can be proved by induction +but we will just take it for granted + + align:start position:0% +but we will just take it for granted + + + align:start position:0% +but we will just take it for granted +using this formula and after a little + + align:start position:0% +using this formula and after a little + + + align:start position:0% +using this formula and after a little +bit of simple algebra and after we + + align:start position:0% +bit of simple algebra and after we + + + align:start position:0% +bit of simple algebra and after we +simplify we obtain a final answer which + + align:start position:0% +simplify we obtain a final answer which + + + align:start position:0% +simplify we obtain a final answer which +is of the + + align:start position:0% +is of the + + + align:start position:0% +is of the +one over 12 and times n plus 2 how about + + align:start position:0% +one over 12 and times n plus 2 how about + + + align:start position:0% +one over 12 and times n plus 2 how about +the variance of a more general uniform + + align:start position:0% +the variance of a more general uniform + + + align:start position:0% +the variance of a more general uniform +random variable so suppose we have a + + align:start position:0% +random variable so suppose we have a + + + align:start position:0% +random variable so suppose we have a +uniform random variable whose range is + + align:start position:0% +uniform random variable whose range is + + + align:start position:0% +uniform random variable whose range is +from A to B how is this PMF related to + + align:start position:0% +from A to B how is this PMF related to + + + align:start position:0% +from A to B how is this PMF related to +the one that we already studied first + + align:start position:0% +the one that we already studied first + + + align:start position:0% +the one that we already studied first +let us assume that n is chosen so that + + align:start position:0% +let us assume that n is chosen so that + + + align:start position:0% +let us assume that n is chosen so that +it is equal to B minus a so in that case + + align:start position:0% +it is equal to B minus a so in that case + + + align:start position:0% +it is equal to B minus a so in that case +the difference between the last and the + + align:start position:0% +the difference between the last and the + + + align:start position:0% +the difference between the last and the +first value of the random variable is + + align:start position:0% +first value of the random variable is + + + align:start position:0% +first value of the random variable is +the same as the difference between the + + align:start position:0% +the same as the difference between the + + + align:start position:0% +the same as the difference between the +last and the first possible value in + + align:start position:0% +last and the first possible value in + + + align:start position:0% +last and the first possible value in +this PMF so both pmf's have the same + + align:start position:0% +this PMF so both pmf's have the same + + + align:start position:0% +this PMF so both pmf's have the same +number of terms they have exactly the + + align:start position:0% +number of terms they have exactly the + + + align:start position:0% +number of terms they have exactly the +same shape the only difference is that + + align:start position:0% +same shape the only difference is that + + + align:start position:0% +same shape the only difference is that +the second PMF is shifted away from 0 + + align:start position:0% +the second PMF is shifted away from 0 + + + align:start position:0% +the second PMF is shifted away from 0 +and it starts at a instead of starting + + align:start position:0% +and it starts at a instead of starting + + + align:start position:0% +and it starts at a instead of starting +at 0 now what does shifting a PMF + + align:start position:0% +at 0 now what does shifting a PMF + + + align:start position:0% +at 0 now what does shifting a PMF +correspond to it essentially amounts to + + align:start position:0% +correspond to it essentially amounts to + + + align:start position:0% +correspond to it essentially amounts to +taking a random variable let's say with + + align:start position:0% +taking a random variable let's say with + + + align:start position:0% +taking a random variable let's say with +this PMF and adding a constant to that + + align:start position:0% +this PMF and adding a constant to that + + + align:start position:0% +this PMF and adding a constant to that +random variable so if the original + + align:start position:0% +random variable so if the original + + + align:start position:0% +random variable so if the original +random variable takes the value of 0 the + + align:start position:0% +random variable takes the value of 0 the + + + align:start position:0% +random variable takes the value of 0 the +new random variable takes the value of a + + align:start position:0% +new random variable takes the value of a + + + align:start position:0% +new random variable takes the value of a +if the original takes a value of 1 this + + align:start position:0% +if the original takes a value of 1 this + + + align:start position:0% +if the original takes a value of 1 this +new random variable takes the value of a + + align:start position:0% +new random variable takes the value of a + + + align:start position:0% +new random variable takes the value of a +plus 1 and so on + + align:start position:0% +plus 1 and so on + + + align:start position:0% +plus 1 and so on +so this shifting PMF is the PMF + + align:start position:0% +so this shifting PMF is the PMF + + + align:start position:0% +so this shifting PMF is the PMF +associated to a random variable equal to + + align:start position:0% +associated to a random variable equal to + + + align:start position:0% +associated to a random variable equal to +the original random variable plus a + + align:start position:0% +the original random variable plus a + + + align:start position:0% +the original random variable plus a +constant but we know that adding a + + align:start position:0% +constant but we know that adding a + + + align:start position:0% +constant but we know that adding a +constant does not change the variance + + align:start position:0% +constant does not change the variance + + + align:start position:0% +constant does not change the variance +therefore the variance of this PMF is + + align:start position:0% +therefore the variance of this PMF is + + + align:start position:0% +therefore the variance of this PMF is +going to be the same as the variance of + + align:start position:0% +going to be the same as the variance of + + + align:start position:0% +going to be the same as the variance of +the original PMF as long as we make the + + align:start position:0% +the original PMF as long as we make the + + + align:start position:0% +the original PMF as long as we make the +correspondence that n is equal to B + + align:start position:0% +correspondence that n is equal to B + + + align:start position:0% +correspondence that n is equal to B +minus a so doing this substitution in + + align:start position:0% +minus a so doing this substitution in + + + align:start position:0% +minus a so doing this substitution in +the formula that we derived earlier we + + align:start position:0% +the formula that we derived earlier we + + + align:start position:0% +the formula that we derived earlier we +obtain 1 over 12 B minus a times B minus + + align:start position:0% +obtain 1 over 12 B minus a times B minus + + + align:start position:0% +obtain 1 over 12 B minus a times B minus +a plus 2 \ No newline at end of file diff --git a/8XGWocggDjI.txt b/8XGWocggDjI.txt new file mode 100644 index 0000000000000000000000000000000000000000..96b6c380dc43873d8e35fe87a244e5d4aafed1bc --- /dev/null +++ b/8XGWocggDjI.txt @@ -0,0 +1,2747 @@ +align:start position:0% + +in this video let us look at an + + align:start position:0% +in this video let us look at an + + + align:start position:0% +in this video let us look at an +application of the probabilistic method + + align:start position:0% +application of the probabilistic method + + + align:start position:0% +application of the probabilistic method +to graph Theory we'll prove what is + + align:start position:0% +to graph Theory we'll prove what is + + + align:start position:0% +to graph Theory we'll prove what is +known as The Crossing number inequality + + align:start position:0% +known as The Crossing number inequality + + + align:start position:0% +known as The Crossing number inequality +now what is the Crossing number of a + + align:start position:0% +now what is the Crossing number of a + + + align:start position:0% +now what is the Crossing number of a +graph if I give you a graph sometimes + + align:start position:0% +graph if I give you a graph sometimes + + + align:start position:0% +graph if I give you a graph sometimes +it's possible to draw the graph on a + + align:start position:0% +it's possible to draw the graph on a + + + align:start position:0% +it's possible to draw the graph on a +plane without Crossings for example the + + align:start position:0% +plane without Crossings for example the + + + align:start position:0% +plane without Crossings for example the +complete graph on four vertices can be + + align:start position:0% +complete graph on four vertices can be + + + align:start position:0% +complete graph on four vertices can be +drawn on the plane without having any + + align:start position:0% +drawn on the plane without having any + + + align:start position:0% +drawn on the plane without having any +pair of edges cross such graph is called + + align:start position:0% +pair of edges cross such graph is called + + + align:start position:0% +pair of edges cross such graph is called +a planer + + align:start position:0% +a planer + + + align:start position:0% +a planer +graph but sometimes it's not possible to + + align:start position:0% +graph but sometimes it's not possible to + + + align:start position:0% +graph but sometimes it's not possible to +draw such a graph on a plane and the + + align:start position:0% +draw such a graph on a plane and the + + + align:start position:0% +draw such a graph on a plane and the +classic example of such a graph is K5 + + align:start position:0% +classic example of such a graph is K5 + + + align:start position:0% +classic example of such a graph is K5 +the complete graph on five + + align:start position:0% +the complete graph on five + + + align:start position:0% +the complete graph on five +vertices and then in that case maybe you + + align:start position:0% +vertices and then in that case maybe you + + + align:start position:0% +vertices and then in that case maybe you +want to know what's the minimum number + + align:start position:0% +want to know what's the minimum number + + + align:start position:0% +want to know what's the minimum number +of edge Crossings you can have in any + + align:start position:0% +of edge Crossings you can have in any + + + align:start position:0% +of edge Crossings you can have in any +possible drawing of this + + align:start position:0% +possible drawing of this + + + align:start position:0% +possible drawing of this +graph so the Crossing number of a graph + + align:start position:0% +graph so the Crossing number of a graph + + + align:start position:0% +graph so the Crossing number of a graph +is defined to be the minimum number of + + align:start position:0% +is defined to be the minimum number of + + + align:start position:0% +is defined to be the minimum number of +edge Crossings of a drawing of G of this + + align:start position:0% +edge Crossings of a drawing of G of this + + + align:start position:0% +edge Crossings of a drawing of G of this +graph G on a plane using continuous + + align:start position:0% +graph G on a plane using continuous + + + align:start position:0% +graph G on a plane using continuous +curves as + + align:start position:0% +curves as + + + align:start position:0% +curves as +edges it is a classic fact that K5 the + + align:start position:0% +edges it is a classic fact that K5 the + + + align:start position:0% +edges it is a classic fact that K5 the +complete graph on five vertices does not + + align:start position:0% +complete graph on five vertices does not + + + align:start position:0% +complete graph on five vertices does not +have a planer drawing but it is possible + + align:start position:0% +have a planer drawing but it is possible + + + align:start position:0% +have a planer drawing but it is possible +to draw this graph using only one + + align:start position:0% +to draw this graph using only one + + + align:start position:0% +to draw this graph using only one +Crossing and we can do this by adding + + align:start position:0% +Crossing and we can do this by adding + + + align:start position:0% +Crossing and we can do this by adding +one vertex to this K4 drawing and draw + + align:start position:0% +one vertex to this K4 drawing and draw + + + align:start position:0% +one vertex to this K4 drawing and draw +edges like this and the final Edge we + + align:start position:0% +edges like this and the final Edge we + + + align:start position:0% +edges like this and the final Edge we +need to do a crossing over + + align:start position:0% +need to do a crossing over + + + align:start position:0% +need to do a crossing over +here okay so this example illustrates + + align:start position:0% +here okay so this example illustrates + + + align:start position:0% +here okay so this example illustrates +that the Crossing number of K5 is + + align:start position:0% +that the Crossing number of K5 is + + + align:start position:0% +that the Crossing number of K5 is +one if you give me a graph with lots and + + align:start position:0% +one if you give me a graph with lots and + + + align:start position:0% +one if you give me a graph with lots and +lots of edges should I expect that its + + align:start position:0% +lots of edges should I expect that its + + + align:start position:0% +lots of edges should I expect that its +Crossing number is necessarily + + align:start position:0% +Crossing number is necessarily + + + align:start position:0% +Crossing number is necessarily +High turns out that's what the Crossing + + align:start position:0% +High turns out that's what the Crossing + + + align:start position:0% +High turns out that's what the Crossing +number inequality always + + align:start position:0% +number inequality always + + + align:start position:0% +number inequality always +guarantees the theorem says that in a + + align:start position:0% +guarantees the theorem says that in a + + + align:start position:0% +guarantees the theorem says that in a +graph G with vertex set e vertex set V + + align:start position:0% +graph G with vertex set e vertex set V + + + align:start position:0% +graph G with vertex set e vertex set V +and Edge set e + + align:start position:0% +and Edge set e + + + align:start position:0% +and Edge set e +if e this Edge set is at least four + + align:start position:0% +if e this Edge set is at least four + + + align:start position:0% +if e this Edge set is at least four +times the number of + + align:start position:0% +times the number of + + + align:start position:0% +times the number of +vertices then the Crossing number of G + + align:start position:0% +vertices then the Crossing number of G + + + align:start position:0% +vertices then the Crossing number of G +is at least the following quantity so on + + align:start position:0% +is at least the following quantity so on + + + align:start position:0% +is at least the following quantity so on +the order of the number of edges cubed + + align:start position:0% +the order of the number of edges cubed + + + align:start position:0% +the order of the number of edges cubed +divided by number of vertices squared + + align:start position:0% +divided by number of vertices squared + + + align:start position:0% +divided by number of vertices squared +here C is some constant some absolute + + align:start position:0% +here C is some constant some absolute + + + align:start position:0% +here C is some constant some absolute +constant + + align:start position:0% +constant + + + align:start position:0% +constant +okay so this is a theorem that we'll + + align:start position:0% +okay so this is a theorem that we'll + + + align:start position:0% +okay so this is a theorem that we'll +prove in this video before proving it + + align:start position:0% +prove in this video before proving it + + + align:start position:0% +prove in this video before proving it +let me illustrate U one Cory to uh yeah + + align:start position:0% +let me illustrate U one Cory to uh yeah + + + align:start position:0% +let me illustrate U one Cory to uh yeah +let me stay one Cory to illustrate how + + align:start position:0% +let me stay one Cory to illustrate how + + + align:start position:0% +let me stay one Cory to illustrate how +to think about this + + align:start position:0% + + + + align:start position:0% + +result + + align:start position:0% +result + + + align:start position:0% +result +if the number of edges in this graph + + align:start position:0% +if the number of edges in this graph + + + align:start position:0% +if the number of edges in this graph +is on the order of the number of + + align:start position:0% +is on the order of the number of + + + align:start position:0% +is on the order of the number of +vertices squared so + + align:start position:0% +vertices squared so + + + align:start position:0% +vertices squared so +this notation here means that it is + + align:start position:0% +this notation here means that it is + + + align:start position:0% +this notation here means that it is +larger than some + + align:start position:0% +larger than some + + + align:start position:0% +larger than some +constant v^ 2 so here C doesn't have to + + align:start position:0% +constant v^ 2 so here C doesn't have to + + + align:start position:0% +constant v^ 2 so here C doesn't have to +be the same as a c + + align:start position:0% +be the same as a c + + + align:start position:0% +be the same as a c +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +then plugging this hypothesis into the + + align:start position:0% +then plugging this hypothesis into the + + + align:start position:0% +then plugging this hypothesis into the +theorem we obtain that the number of + + align:start position:0% +theorem we obtain that the number of + + + align:start position:0% +theorem we obtain that the number of +Crossings of G + + align:start position:0% +Crossings of G + + + align:start position:0% +Crossings of G +is at + + align:start position:0% +is at + + + align:start position:0% +is at +least on the order of V to the 4th power + + align:start position:0% + + + + align:start position:0% + +so if has a lot of edges then the graph + + align:start position:0% +so if has a lot of edges then the graph + + + align:start position:0% +so if has a lot of edges then the graph +must have a lot of Crossings and in fact + + align:start position:0% +must have a lot of Crossings and in fact + + + align:start position:0% +must have a lot of Crossings and in fact +this is the right order of magnitude + + align:start position:0% +this is the right order of magnitude + + + align:start position:0% +this is the right order of magnitude +because you can only have at most e s + + align:start position:0% +because you can only have at most e s + + + align:start position:0% +because you can only have at most e s +number of Crossings each pair of edges + + align:start position:0% +number of Crossings each pair of edges + + + align:start position:0% +number of Crossings each pair of edges +cross at most + + align:start position:0% +cross at most + + + align:start position:0% +cross at most +once even if you just lay out all the + + align:start position:0% +once even if you just lay out all the + + + align:start position:0% +once even if you just lay out all the +vertices in general position on the + + align:start position:0% +vertices in general position on the + + + align:start position:0% +vertices in general position on the +plane and draw the edges at straight + + align:start position:0% + + + + align:start position:0% + +lines okay so in the rest of the video + + align:start position:0% +lines okay so in the rest of the video + + + align:start position:0% +lines okay so in the rest of the video +let me demonstrate the proof of the + + align:start position:0% +let me demonstrate the proof of the + + + align:start position:0% +let me demonstrate the proof of the +Crossing number + + align:start position:0% + + + + align:start position:0% + +inequality I'll split the proof into + + align:start position:0% +inequality I'll split the proof into + + + align:start position:0% +inequality I'll split the proof into +three + + align:start position:0% +three + + + align:start position:0% +three +steps the first + + align:start position:0% + + + + align:start position:0% + +step is an analysis of planer + + align:start position:0% +step is an analysis of planer + + + align:start position:0% +step is an analysis of planer +graphs namely graphs with no Crossing + + align:start position:0% + + + + align:start position:0% + +the following turns out to be true that + + align:start position:0% +the following turns out to be true that + + + align:start position:0% +the following turns out to be true that +if G is a planer + + align:start position:0% +if G is a planer + + + align:start position:0% +if G is a planer +graph so planer means that it is + + align:start position:0% +graph so planer means that it is + + + align:start position:0% +graph so planer means that it is +possible to draw G in the plane without + + align:start position:0% +possible to draw G in the plane without + + + align:start position:0% +possible to draw G in the plane without +Edge + + align:start position:0% +Edge + + + align:start position:0% +Edge +Crossings then okay so in other + + align:start position:0% +Crossings then okay so in other + + + align:start position:0% +Crossings then okay so in other +words The Crossing number of G is equal + + align:start position:0% +words The Crossing number of G is equal + + + align:start position:0% +words The Crossing number of G is equal +to zero okay so then the conclusion is + + align:start position:0% +to zero okay so then the conclusion is + + + align:start position:0% +to zero okay so then the conclusion is +that the number of edges of G is at most + + align:start position:0% +that the number of edges of G is at most + + + align:start position:0% +that the number of edges of G is at most +three times the number of + + align:start position:0% +three times the number of + + + align:start position:0% +three times the number of +vertices another way to say the + + align:start position:0% +vertices another way to say the + + + align:start position:0% +vertices another way to say the +conclusion is that the average degree of + + align:start position:0% +conclusion is that the average degree of + + + align:start position:0% +conclusion is that the average degree of +this graph is at most + + align:start position:0% + + + + align:start position:0% + +six this conclusion can be + + align:start position:0% + + + + align:start position:0% + +deduced + + align:start position:0% + + + + align:start position:0% + +from a fact from topology known as + + align:start position:0% +from a fact from topology known as + + + align:start position:0% +from a fact from topology known as +Oilers + + align:start position:0% + + + + align:start position:0% + +formula which says that if you draw the + + align:start position:0% +formula which says that if you draw the + + + align:start position:0% +formula which says that if you draw the +graph in the plane in some way so for + + align:start position:0% +graph in the plane in some way so for + + + align:start position:0% +graph in the plane in some way so for +example this is some + + align:start position:0% +example this is some + + + align:start position:0% +example this is some +drawing then the number of vertices + + align:start position:0% +drawing then the number of vertices + + + align:start position:0% +drawing then the number of vertices +minus the number of edges plus the + + align:start position:0% +minus the number of edges plus the + + + align:start position:0% +minus the number of edges plus the +number of faces equals to two here by + + align:start position:0% +number of faces equals to two here by + + + align:start position:0% +number of faces equals to two here by +face we count each individual cell as + + align:start position:0% +face we count each individual cell as + + + align:start position:0% +face we count each individual cell as +well as the outside cell so this drawing + + align:start position:0% +well as the outside cell so this drawing + + + align:start position:0% +well as the outside cell so this drawing +has three + + align:start position:0% +has three + + + align:start position:0% +has three +faces and it has four vertices and five + + align:start position:0% +faces and it has four vertices and five + + + align:start position:0% +faces and it has four vertices and five +five edges and you can verify that this + + align:start position:0% +five edges and you can verify that this + + + align:start position:0% +five edges and you can verify that this +Oiler identity is true in this case but + + align:start position:0% +Oiler identity is true in this case but + + + align:start position:0% +Oiler identity is true in this case but +it is also true in + + align:start position:0% +it is also true in + + + align:start position:0% +it is also true in +general starting with Oilers formula we + + align:start position:0% +general starting with Oilers formula we + + + align:start position:0% +general starting with Oilers formula we +can then put some bounds on the number + + align:start position:0% +can then put some bounds on the number + + + align:start position:0% +can then put some bounds on the number +of edges and faces and vertices relating + + align:start position:0% +of edges and faces and vertices relating + + + align:start position:0% +of edges and faces and vertices relating +them to each other using some + + align:start position:0% +them to each other using some + + + align:start position:0% +them to each other using some +inequalities to derive this conclusion + + align:start position:0% +inequalities to derive this conclusion + + + align:start position:0% +inequalities to derive this conclusion +and so let me not do that step I refer + + align:start position:0% +and so let me not do that step I refer + + + align:start position:0% +and so let me not do that step I refer +you to the lecture notes if you want to + + align:start position:0% +you to the lecture notes if you want to + + + align:start position:0% +you to the lecture notes if you want to +see the + + align:start position:0% + + + + align:start position:0% + +details the second step of the pro + + align:start position:0% + + + + align:start position:0% + +Pro allows us to go from one Crossing to + + align:start position:0% +Pro allows us to go from one Crossing to + + + align:start position:0% +Pro allows us to go from one Crossing to +many Crossings + + align:start position:0% + + + + align:start position:0% + +okay so here's what + + align:start position:0% +okay so here's what + + + align:start position:0% +okay so here's what +happens so + + align:start position:0% + + + + align:start position:0% + +given a graph + + align:start position:0% +given a graph + + + align:start position:0% +given a graph +G it may not be planner so maybe it will + + align:start position:0% +G it may not be planner so maybe it will + + + align:start position:0% +G it may not be planner so maybe it will +require some Crossings to draw G in the + + align:start position:0% +require some Crossings to draw G in the + + + align:start position:0% +require some Crossings to draw G in the +plane but starting with such a Crossing + + align:start position:0% +plane but starting with such a Crossing + + + align:start position:0% +plane but starting with such a Crossing +we can delete some edges to make it + + align:start position:0% +we can delete some edges to make it + + + align:start position:0% +we can delete some edges to make it +planer right so given G + + align:start position:0% +planer right so given G + + + align:start position:0% +planer right so given G +by + + align:start position:0% + + + + align:start position:0% + +deleting The Crossing number of G + + align:start position:0% + + + + align:start position:0% + +edges we + + align:start position:0% +edges we + + + align:start position:0% +edges we +can make + + align:start position:0% +can make + + + align:start position:0% +can make +it pler okay so if you had so an earlier + + align:start position:0% +it pler okay so if you had so an earlier + + + align:start position:0% +it pler okay so if you had so an earlier +example of K5 where this is not planer + + align:start position:0% +example of K5 where this is not planer + + + align:start position:0% +example of K5 where this is not planer +but there's only one Crossing and by + + align:start position:0% +but there's only one Crossing and by + + + align:start position:0% +but there's only one Crossing and by +deleting one of the edges corresponding + + align:start position:0% +deleting one of the edges corresponding + + + align:start position:0% +deleting one of the edges corresponding +to that + + align:start position:0% + + + + align:start position:0% + +Crossing and we remove one Edge and we + + align:start position:0% +Crossing and we remove one Edge and we + + + align:start position:0% +Crossing and we remove one Edge and we +end up with a planer + + align:start position:0% +end up with a planer + + + align:start position:0% +end up with a planer +graph well in this planer graph the + + align:start position:0% +graph well in this planer graph the + + + align:start position:0% +graph well in this planer graph the +inequality in step one must be satisfied + + align:start position:0% +inequality in step one must be satisfied + + + align:start position:0% +inequality in step one must be satisfied +so the number of edges of G minus The + + align:start position:0% +so the number of edges of G minus The + + + align:start position:0% +so the number of edges of G minus The +Crossing number of G so these are the + + align:start position:0% +Crossing number of G so these are the + + + align:start position:0% +Crossing number of G so these are the +deleted + + align:start position:0% +deleted + + + align:start position:0% +deleted +edges must be at most three times the + + align:start position:0% +edges must be at most three times the + + + align:start position:0% +edges must be at most three times the +number of vertices of + + align:start position:0% +number of vertices of + + + align:start position:0% +number of vertices of +G + + align:start position:0% +G + + + align:start position:0% +G +rearranging this + + align:start position:0% +rearranging this + + + align:start position:0% +rearranging this +inequality we obtain the lower + + align:start position:0% +inequality we obtain the lower + + + align:start position:0% +inequality we obtain the lower +bound on the Crossing + + align:start position:0% +bound on the Crossing + + + align:start position:0% +bound on the Crossing +number being the number of edges minus 3 + + align:start position:0% +number being the number of edges minus 3 + + + align:start position:0% +number being the number of edges minus 3 +* the number of vertices + + align:start position:0% + + + + align:start position:0% + +so the idea here is really to go from + + align:start position:0% +so the idea here is really to go from + + + align:start position:0% +so the idea here is really to go from +one Crossing namely that if this + + align:start position:0% +one Crossing namely that if this + + + align:start position:0% +one Crossing namely that if this +inequality e less than equal to 3 V is + + align:start position:0% +inequality e less than equal to 3 V is + + + align:start position:0% +inequality e less than equal to 3 V is +not satisfied then we get at least one + + align:start position:0% +not satisfied then we get at least one + + + align:start position:0% +not satisfied then we get at least one +Crossing but then keep on deleting these + + align:start position:0% +Crossing but then keep on deleting these + + + align:start position:0% +Crossing but then keep on deleting these +Crossings we can go from one Crossing to + + align:start position:0% +Crossings we can go from one Crossing to + + + align:start position:0% +Crossings we can go from one Crossing to +many + + align:start position:0% +many + + + align:start position:0% +many +Crossings let's pause and examine this + + align:start position:0% +Crossings let's pause and examine this + + + align:start position:0% +Crossings let's pause and examine this +bound that we just proved it is a valid + + align:start position:0% +bound that we just proved it is a valid + + + align:start position:0% +bound that we just proved it is a valid +bound but it's not that great for + + align:start position:0% +bound but it's not that great for + + + align:start position:0% +bound but it's not that great for +example in this corollary when e is + + align:start position:0% +example in this corollary when e is + + + align:start position:0% +example in this corollary when e is +under the order of quadratic and number + + align:start position:0% +under the order of quadratic and number + + + align:start position:0% +under the order of quadratic and number +of vertices the conclusion that we will + + align:start position:0% +of vertices the conclusion that we will + + + align:start position:0% +of vertices the conclusion that we will +get at this stage is also quadratic in + + align:start position:0% +get at this stage is also quadratic in + + + align:start position:0% +get at this stage is also quadratic in +the number of vertices which is not as + + align:start position:0% +the number of vertices which is not as + + + align:start position:0% +the number of vertices which is not as +high as we would like which is the + + align:start position:0% +high as we would like which is the + + + align:start position:0% +high as we would like which is the +fourth power in the number of + + align:start position:0% +fourth power in the number of + + + align:start position:0% +fourth power in the number of +vertices so this brings us to the + + align:start position:0% +vertices so this brings us to the + + + align:start position:0% +vertices so this brings us to the +third step and this is a step where + + align:start position:0% +third step and this is a step where + + + align:start position:0% +third step and this is a step where +we'll use the probabilistic method and + + align:start position:0% +we'll use the probabilistic method and + + + align:start position:0% +we'll use the probabilistic method and +this step I'll call the bootstrapping + + align:start position:0% +this step I'll call the bootstrapping + + + align:start position:0% +this step I'll call the bootstrapping +step where we go from a weak bound to a + + align:start position:0% +step where we go from a weak bound to a + + + align:start position:0% +step where we go from a weak bound to a +much stronger Bound by using + + align:start position:0% +much stronger Bound by using + + + align:start position:0% +much stronger Bound by using +sampling in this step + + align:start position:0% +sampling in this step + + + align:start position:0% +sampling in this step +let's consider some P while decide this + + align:start position:0% +let's consider some P while decide this + + + align:start position:0% +let's consider some P while decide this +P later on so to be decided but it's + + align:start position:0% +P later on so to be decided but it's + + + align:start position:0% +P later on so to be decided but it's +some number between zero and + + align:start position:0% +some number between zero and + + + align:start position:0% +some number between zero and +one and let's consider a subgraph of G + + align:start position:0% +one and let's consider a subgraph of G + + + align:start position:0% +one and let's consider a subgraph of G +obtained by keeping + + align:start position:0% +obtained by keeping + + + align:start position:0% +obtained by keeping +every vertex + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +G + + align:start position:0% +G + + + align:start position:0% +G +with + + align:start position:0% + + + + align:start position:0% + +probability P independently at + + align:start position:0% + + + + align:start position:0% + +random and deleting the other vertices + + align:start position:0% + + + + align:start position:0% + +when we delete the other vertices we + + align:start position:0% +when we delete the other vertices we + + + align:start position:0% +when we delete the other vertices we +also throw away all the edges that are + + align:start position:0% +also throw away all the edges that are + + + align:start position:0% +also throw away all the edges that are +adjacent to the deleted + + align:start position:0% + + + + align:start position:0% + +vertices this process then produces a + + align:start position:0% +vertices this process then produces a + + + align:start position:0% +vertices this process then produces a +different graph G + + align:start position:0% +different graph G + + + align:start position:0% +different graph G +Prime which contains a subset V of + + align:start position:0% +Prime which contains a subset V of + + + align:start position:0% +Prime which contains a subset V of +vertices those V Prime so those are the + + align:start position:0% +vertices those V Prime so those are the + + + align:start position:0% +vertices those V Prime so those are the +vertices that are kept by this random + + align:start position:0% +vertices that are kept by this random + + + align:start position:0% +vertices that are kept by this random +process and then V and then e Prime is a + + align:start position:0% +process and then V and then e Prime is a + + + align:start position:0% +process and then V and then e Prime is a +set of edges that were kept namely the + + align:start position:0% +set of edges that were kept namely the + + + align:start position:0% +set of edges that were kept namely the +edges of G that fall between the + + align:start position:0% +edges of G that fall between the + + + align:start position:0% +edges of G that fall between the +remaining vertices in V + + align:start position:0% +remaining vertices in V + + + align:start position:0% +remaining vertices in V +Prime let's think about this graph G + + align:start position:0% +Prime let's think about this graph G + + + align:start position:0% +Prime let's think about this graph G +Prime here well it is a graph so + + align:start position:0% +Prime here well it is a graph so + + + align:start position:0% +Prime here well it is a graph so +whatever we proved in step two still + + align:start position:0% +whatever we proved in step two still + + + align:start position:0% +whatever we proved in step two still +applies to this smaller + + align:start position:0% +applies to this smaller + + + align:start position:0% +applies to this smaller +graph namely The Crossing number of G + + align:start position:0% +graph namely The Crossing number of G + + + align:start position:0% +graph namely The Crossing number of G +Prime is at least the number of edges in + + align:start position:0% +Prime is at least the number of edges in + + + align:start position:0% +Prime is at least the number of edges in +this G Prime minus three times the + + align:start position:0% +this G Prime minus three times the + + + align:start position:0% +this G Prime minus three times the +number of vertices in this G + + align:start position:0% +number of vertices in this G + + + align:start position:0% +number of vertices in this G +Prime okay so this is a true and valid + + align:start position:0% +Prime okay so this is a true and valid + + + align:start position:0% +Prime okay so this is a true and valid +inequality + + align:start position:0% +inequality + + + align:start position:0% +inequality +let's well remember that g is given as a + + align:start position:0% +let's well remember that g is given as a + + + align:start position:0% +let's well remember that g is given as a +graph is deterministic but we introduce + + align:start position:0% +graph is deterministic but we introduce + + + align:start position:0% +graph is deterministic but we introduce +some Randomness to produce G Prime G + + align:start position:0% +some Randomness to produce G Prime G + + + align:start position:0% +some Randomness to produce G Prime G +Prime is a random + + align:start position:0% +Prime is a random + + + align:start position:0% +Prime is a random +graph so this inequality is true for + + align:start position:0% +graph so this inequality is true for + + + align:start position:0% +graph so this inequality is true for +every instance of this random + + align:start position:0% +every instance of this random + + + align:start position:0% +every instance of this random +graph but it's also Al true than in + + align:start position:0% +graph but it's also Al true than in + + + align:start position:0% +graph but it's also Al true than in +expectation so let's take the + + align:start position:0% +expectation so let's take the + + + align:start position:0% +expectation so let's take the +expectation of both + + align:start position:0% +expectation of both + + + align:start position:0% +expectation of both +sides expectation on the left and the + + align:start position:0% +sides expectation on the left and the + + + align:start position:0% +sides expectation on the left and the +expectation on the right which by linear + + align:start position:0% +expectation on the right which by linear + + + align:start position:0% +expectation on the right which by linear +of expectations we + + align:start position:0% +of expectations we + + + align:start position:0% +of expectations we +can distribute the expectation into each + + align:start position:0% + + + + align:start position:0% + +term + + align:start position:0% +term + + + align:start position:0% +term +okay let's think about the various terms + + align:start position:0% +okay let's think about the various terms + + + align:start position:0% +okay let's think about the various terms +the easiest one to think about is the + + align:start position:0% +the easiest one to think about is the + + + align:start position:0% +the easiest one to think about is the +expected number of vertices that remain + + align:start position:0% +expected number of vertices that remain + + + align:start position:0% +expected number of vertices that remain +while each vertex is kept with + + align:start position:0% +while each vertex is kept with + + + align:start position:0% +while each vertex is kept with +probability P so the expected number of + + align:start position:0% +probability P so the expected number of + + + align:start position:0% +probability P so the expected number of +remaining vertices is p * the original + + align:start position:0% +remaining vertices is p * the original + + + align:start position:0% +remaining vertices is p * the original +number of + + align:start position:0% +number of + + + align:start position:0% +number of +vertices next the expected number of + + align:start position:0% +vertices next the expected number of + + + align:start position:0% +vertices next the expected number of +edges well an edge is kept if both its + + align:start position:0% +edges well an edge is kept if both its + + + align:start position:0% +edges well an edge is kept if both its +end points remain and the probability + + align:start position:0% +end points remain and the probability + + + align:start position:0% +end points remain and the probability +that both its end points are chosen is + + align:start position:0% +that both its end points are chosen is + + + align:start position:0% +that both its end points are chosen is +p^ s + + align:start position:0% +p^ s + + + align:start position:0% +p^ s +so this quantity is p^2 + + align:start position:0% +so this quantity is p^2 + + + align:start position:0% +so this quantity is p^2 +time the original number of + + align:start position:0% +time the original number of + + + align:start position:0% +time the original number of +edges and finally and the slightly + + align:start position:0% +edges and finally and the slightly + + + align:start position:0% +edges and finally and the slightly +tricky one is the expected number of + + align:start position:0% +tricky one is the expected number of + + + align:start position:0% +tricky one is the expected number of +Crossings now if I have a Crossing in my + + align:start position:0% +Crossings now if I have a Crossing in my + + + align:start position:0% +Crossings now if I have a Crossing in my +original graph + + align:start position:0% + + + + align:start position:0% + +G one way to go about thinking about G + + align:start position:0% +G one way to go about thinking about G + + + align:start position:0% +G one way to go about thinking about G +Prime is to what take the same planer + + align:start position:0% +Prime is to what take the same planer + + + align:start position:0% +Prime is to what take the same planer +drawing take the same drawing of G on + + align:start position:0% +drawing take the same drawing of G on + + + align:start position:0% +drawing take the same drawing of G on +the + + align:start position:0% +the + + + align:start position:0% +the +plane and use that drawing for G Prime + + align:start position:0% +plane and use that drawing for G Prime + + + align:start position:0% +plane and use that drawing for G Prime +so G Prime is obtained by keeping some + + align:start position:0% +so G Prime is obtained by keeping some + + + align:start position:0% +so G Prime is obtained by keeping some +of the vertices and so if we use the + + align:start position:0% +of the vertices and so if we use the + + + align:start position:0% +of the vertices and so if we use the +same drawings then this Crossing is + + align:start position:0% +same drawings then this Crossing is + + + align:start position:0% +same drawings then this Crossing is +kept with probability P to the 4th + + align:start position:0% + + + + align:start position:0% + +now G Prime is a different graph it's a + + align:start position:0% +now G Prime is a different graph it's a + + + align:start position:0% +now G Prime is a different graph it's a +smaller graph so potentially there's a + + align:start position:0% +smaller graph so potentially there's a + + + align:start position:0% +smaller graph so potentially there's a +different way to draw G Prime that + + align:start position:0% +different way to draw G Prime that + + + align:start position:0% +different way to draw G Prime that +produces even fewer + + align:start position:0% +produces even fewer + + + align:start position:0% +produces even fewer +Crossings but nevertheless we have an + + align:start position:0% +Crossings but nevertheless we have an + + + align:start position:0% +Crossings but nevertheless we have an +inequality because we could have always + + align:start position:0% +inequality because we could have always + + + align:start position:0% +inequality because we could have always +kept the cross the drawing from + + align:start position:0% + + + + align:start position:0% + +G and so we do always have this + + align:start position:0% +G and so we do always have this + + + align:start position:0% +G and so we do always have this +inequality here so so this inequality + + align:start position:0% +inequality here so so this inequality + + + align:start position:0% +inequality here so so this inequality +comes from keeping the same drawing but + + align:start position:0% +comes from keeping the same drawing but + + + align:start position:0% +comes from keeping the same drawing but +keeping in mind that it doesn't have to + + align:start position:0% +keeping in mind that it doesn't have to + + + align:start position:0% +keeping in mind that it doesn't have to +be an equality because we could have + + align:start position:0% +be an equality because we could have + + + align:start position:0% +be an equality because we could have +chosen a different drawing for G + + align:start position:0% +chosen a different drawing for G + + + align:start position:0% +chosen a different drawing for G +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +okay so we derived this inequality here + + align:start position:0% +okay so we derived this inequality here + + + align:start position:0% +okay so we derived this inequality here +and by bringing this P to the 4th power + + align:start position:0% +and by bringing this P to the 4th power + + + align:start position:0% +and by bringing this P to the 4th power +to the other + + align:start position:0% +to the other + + + align:start position:0% +to the other +side and rearranging we obtain the + + align:start position:0% +side and rearranging we obtain the + + + align:start position:0% +side and rearranging we obtain the +inequality that the Crossing number of G + + align:start position:0% +inequality that the Crossing number of G + + + align:start position:0% +inequality that the Crossing number of G +is at least P to Theus + + align:start position:0% +is at least P to Theus + + + align:start position:0% +is at least P to Theus +2times the size of the edge set * 3 to + + align:start position:0% +2times the size of the edge set * 3 to + + + align:start position:0% +2times the size of the edge set * 3 to +the pus 3 * the size of the vertex set + + align:start position:0% +the pus 3 * the size of the vertex set + + + align:start position:0% +the pus 3 * the size of the vertex set +of + + align:start position:0% +of + + + align:start position:0% +of +G + + align:start position:0% +G + + + align:start position:0% +G +okay P was some parameter that we we + + align:start position:0% +okay P was some parameter that we we + + + align:start position:0% +okay P was some parameter that we we +have yet to specify and from this + + align:start position:0% +have yet to specify and from this + + + align:start position:0% +have yet to specify and from this +expression then we can optimize for the + + align:start position:0% +expression then we can optimize for the + + + align:start position:0% +expression then we can optimize for the +value of + + align:start position:0% +value of + + + align:start position:0% +value of +P so and one way to do this and because + + align:start position:0% +P so and one way to do this and because + + + align:start position:0% +P so and one way to do this and because +we only look for a bound that is up to a + + align:start position:0% +we only look for a bound that is up to a + + + align:start position:0% +we only look for a bound that is up to a +constant factor is to set P to be + + align:start position:0% +constant factor is to set P to be + + + align:start position:0% +constant factor is to set P to be +four time the number of vertices divided + + align:start position:0% +four time the number of vertices divided + + + align:start position:0% +four time the number of vertices divided +by the number of edges of the + + align:start position:0% +by the number of edges of the + + + align:start position:0% +by the number of edges of the +graph and it is important here that the + + align:start position:0% +graph and it is important here that the + + + align:start position:0% +graph and it is important here that the +hypothesis of the theorem the number of + + align:start position:0% +hypothesis of the theorem the number of + + + align:start position:0% +hypothesis of the theorem the number of +edges is at least four times the number + + align:start position:0% +edges is at least four times the number + + + align:start position:0% +edges is at least four times the number +of vertices so that this p is indeed + + align:start position:0% +of vertices so that this p is indeed + + + align:start position:0% +of vertices so that this p is indeed +between 0o and one if P ended up being + + align:start position:0% +between 0o and one if P ended up being + + + align:start position:0% +between 0o and one if P ended up being +some number bigger than one then this + + align:start position:0% +some number bigger than one then this + + + align:start position:0% +some number bigger than one then this +proof would not have made sense it would + + align:start position:0% +proof would not have made sense it would + + + align:start position:0% +proof would not have made sense it would +not make sense to choose with + + align:start position:0% +not make sense to choose with + + + align:start position:0% +not make sense to choose with +probability bigger than one but p is + + align:start position:0% +probability bigger than one but p is + + + align:start position:0% +probability bigger than one but p is +between zero and one so this makes sense + + align:start position:0% +between zero and one so this makes sense + + + align:start position:0% +between zero and one so this makes sense +and with this choice of P continuing the + + align:start position:0% +and with this choice of P continuing the + + + align:start position:0% +and with this choice of P continuing the +earlier expression we find that it is + + align:start position:0% +earlier expression we find that it is + + + align:start position:0% +earlier expression we find that it is +equal to + + align:start position:0% + + + + align:start position:0% + +1 over 64 * the number of edges cubed + + align:start position:0% +1 over 64 * the number of edges cubed + + + align:start position:0% +1 over 64 * the number of edges cubed +divided by number of vertices squared + + align:start position:0% +divided by number of vertices squared + + + align:start position:0% +divided by number of vertices squared +and that finishes the proof of the + + align:start position:0% +and that finishes the proof of the + + + align:start position:0% +and that finishes the proof of the +result showing that the Crossing number + + align:start position:0% +result showing that the Crossing number + + + align:start position:0% +result showing that the Crossing number +inequality holds with C being the + + align:start position:0% +inequality holds with C being the + + + align:start position:0% +inequality holds with C being the +constant 1 over 64 although the precise + + align:start position:0% +constant 1 over 64 although the precise + + + align:start position:0% +constant 1 over 64 although the precise +value is not so + + align:start position:0% + + + + align:start position:0% + +important this is a beautiful + + align:start position:0% +important this is a beautiful + + + align:start position:0% +important this is a beautiful +demonstration of the probabilistic + + align:start position:0% +demonstration of the probabilistic + + + align:start position:0% +demonstration of the probabilistic +method and let me Recall review what + + align:start position:0% +method and let me Recall review what + + + align:start position:0% +method and let me Recall review what +happened in this + + align:start position:0% +happened in this + + + align:start position:0% +happened in this +proof first we looked at what happens to + + align:start position:0% +proof first we looked at what happens to + + + align:start position:0% +proof first we looked at what happens to +planer graphs those with no Crossings + + align:start position:0% +planer graphs those with no Crossings + + + align:start position:0% +planer graphs those with no Crossings +and here we derived some bound on the + + align:start position:0% +and here we derived some bound on the + + + align:start position:0% +and here we derived some bound on the +number of edges that such a graph can + + align:start position:0% +number of edges that such a graph can + + + align:start position:0% +number of edges that such a graph can +have and then we said that if you start + + align:start position:0% +have and then we said that if you start + + + align:start position:0% +have and then we said that if you start +with a graph and then remove all its + + align:start position:0% +with a graph and then remove all its + + + align:start position:0% +with a graph and then remove all its +crossings by removing one Edge according + + align:start position:0% +crossings by removing one Edge according + + + align:start position:0% +crossings by removing one Edge according +to its each Crossing we can then deduce + + align:start position:0% +to its each Crossing we can then deduce + + + align:start position:0% +to its each Crossing we can then deduce +some lower bound on the number of + + align:start position:0% +some lower bound on the number of + + + align:start position:0% +some lower bound on the number of +crossings from the first step + + align:start position:0% +crossings from the first step + + + align:start position:0% +crossings from the first step +then it gives us this fairly weak bound + + align:start position:0% +then it gives us this fairly weak bound + + + align:start position:0% +then it gives us this fairly weak bound +lower bound on the number of + + align:start position:0% +lower bound on the number of + + + align:start position:0% +lower bound on the number of +Crossings and the final step I think is + + align:start position:0% +Crossings and the final step I think is + + + align:start position:0% +Crossings and the final step I think is +the most interesting mathematically is + + align:start position:0% +the most interesting mathematically is + + + align:start position:0% +the most interesting mathematically is +this bootstrapping step where starting + + align:start position:0% +this bootstrapping step where starting + + + align:start position:0% +this bootstrapping step where starting +from a fairly weak + + align:start position:0% +from a fairly weak + + + align:start position:0% +from a fairly weak +bound we then take our graph G and + + align:start position:0% +bound we then take our graph G and + + + align:start position:0% +bound we then take our graph G and +Sample it down to a smaller subgraph and + + align:start position:0% +Sample it down to a smaller subgraph and + + + align:start position:0% +Sample it down to a smaller subgraph and +apply the weaker bound to the smaller + + align:start position:0% +apply the weaker bound to the smaller + + + align:start position:0% +apply the weaker bound to the smaller +subgraph this allows us to boost the + + align:start position:0% +subgraph this allows us to boost the + + + align:start position:0% +subgraph this allows us to boost the +weak bound into a much stronger bound + + align:start position:0% +weak bound into a much stronger bound + + + align:start position:0% +weak bound into a much stronger bound +that turns out to be the what is claimed + + align:start position:0% +that turns out to be the what is claimed + + + align:start position:0% +that turns out to be the what is claimed +in the result in the + + align:start position:0% +in the result in the + + + align:start position:0% +in the result in the +theorem so this finishes the proof of + + align:start position:0% +theorem so this finishes the proof of + + + align:start position:0% +theorem so this finishes the proof of +the Crossing number + + align:start position:0% +the Crossing number + + + align:start position:0% +the Crossing number +inequality and it's just one of many + + align:start position:0% +inequality and it's just one of many + + + align:start position:0% +inequality and it's just one of many +beautiful demonstrations of the + + align:start position:0% +beautiful demonstrations of the + + + align:start position:0% +beautiful demonstrations of the +probabilistic method in combinatorics + + align:start position:0% +probabilistic method in combinatorics + + + align:start position:0% +probabilistic method in combinatorics +and graph Theory \ No newline at end of file diff --git a/9lX2FENOe4o.txt b/9lX2FENOe4o.txt new file mode 100644 index 0000000000000000000000000000000000000000..1687c85302bf487982d382a4da17943477c587d7 --- /dev/null +++ b/9lX2FENOe4o.txt @@ -0,0 +1,15320 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right so uh for the next + + align:start position:0% +ocw.mit.edu all right so uh for the next + + + align:start position:0% +ocw.mit.edu all right so uh for the next +for the next six lectures including + + align:start position:0% +for the next six lectures including + + + align:start position:0% +for the next six lectures including +today uh we're going to finish off um + + align:start position:0% +today uh we're going to finish off um + + + align:start position:0% +today uh we're going to finish off um +the course with uh the application of + + align:start position:0% +the course with uh the application of + + + align:start position:0% +the course with uh the application of +everything we've studied so far to a + + align:start position:0% +everything we've studied so far to a + + + align:start position:0% +everything we've studied so far to a +couple of ideas the first being the + + align:start position:0% +couple of ideas the first being the + + + align:start position:0% +couple of ideas the first being the +existence of solids why we have solids + + align:start position:0% +existence of solids why we have solids + + + align:start position:0% +existence of solids why we have solids +and why we have conductivity in solids + + align:start position:0% +and why we have conductivity in solids + + + align:start position:0% +and why we have conductivity in solids +which is you know basic properties of + + align:start position:0% +which is you know basic properties of + + + align:start position:0% +which is you know basic properties of +materials in particular the story I want + + align:start position:0% +materials in particular the story I want + + + align:start position:0% +materials in particular the story I want +you guys to leave the course with is an + + align:start position:0% +you guys to leave the course with is an + + + align:start position:0% +you guys to leave the course with is an +understanding of why diamonds are + + align:start position:0% +understanding of why diamonds are + + + align:start position:0% +understanding of why diamonds are +transparent and why copper isn't um + + align:start position:0% +transparent and why copper isn't um + + + align:start position:0% +transparent and why copper isn't um +which you know is sort of a crude fact + + align:start position:0% +which you know is sort of a crude fact + + + align:start position:0% +which you know is sort of a crude fact +about the world but we can explain it + + align:start position:0% +about the world but we can explain it + + + align:start position:0% +about the world but we can explain it +from first principles which is pretty + + align:start position:0% +from first principles which is pretty + + + align:start position:0% +from first principles which is pretty +awesome um the second is we're going to + + align:start position:0% +awesome um the second is we're going to + + + align:start position:0% +awesome um the second is we're going to +come back to this idea of Spin and of + + align:start position:0% +come back to this idea of Spin and of + + + align:start position:0% +come back to this idea of Spin and of +half integral angular momentum this + + align:start position:0% +half integral angular momentum this + + + align:start position:0% +half integral angular momentum this +intrinsic angular momentum of the + + align:start position:0% +intrinsic angular momentum of the + + + align:start position:0% +intrinsic angular momentum of the +electron and we're going to use that to + + align:start position:0% +electron and we're going to use that to + + + align:start position:0% +electron and we're going to use that to +motivate a couple of ideas first off + + align:start position:0% +motivate a couple of ideas first off + + + align:start position:0% +motivate a couple of ideas first off +we're going to tie back to Bell's + + align:start position:0% +we're going to tie back to Bell's + + + align:start position:0% +we're going to tie back to Bell's +inequality from the very beginning and + + align:start position:0% +inequality from the very beginning and + + + align:start position:0% +inequality from the very beginning and +then we're going to do a little bit on + + align:start position:0% +then we're going to do a little bit on + + + align:start position:0% +then we're going to do a little bit on +Quantum computation that'll be the last + + align:start position:0% +Quantum computation that'll be the last + + + align:start position:0% +Quantum computation that'll be the last +two lectures so um before I get started + + align:start position:0% +two lectures so um before I get started + + + align:start position:0% +two lectures so um before I get started +though with today two things um first + + align:start position:0% +though with today two things um first + + + align:start position:0% +though with today two things um first +I'm going to ask for questions but the + + align:start position:0% +I'm going to ask for questions but the + + + align:start position:0% +I'm going to ask for questions but the +second is uh I got some really good + + align:start position:0% +second is uh I got some really good + + + align:start position:0% +second is uh I got some really good +questions + + align:start position:0% +questions + + + align:start position:0% +questions +about hydrogen so I want to wrap up with + + align:start position:0% +about hydrogen so I want to wrap up with + + + align:start position:0% +about hydrogen so I want to wrap up with +one last comment on hydrogen um because + + align:start position:0% +one last comment on hydrogen um because + + + align:start position:0% +one last comment on hydrogen um because +it's it's entertaining um but before I + + align:start position:0% +it's it's entertaining um but before I + + + align:start position:0% +it's it's entertaining um but before I +get started on that questions uh about + + align:start position:0% +get started on that questions uh about + + + align:start position:0% +get started on that questions uh about +everything up till + + align:start position:0% + + + + align:start position:0% + +now yeah + + align:start position:0% + + + + align:start position:0% + +it absolutely is okay so the question is + + align:start position:0% +it absolutely is okay so the question is + + + align:start position:0% +it absolutely is okay so the question is +this is a very very good question the + + align:start position:0% +this is a very very good question the + + + align:start position:0% +this is a very very good question the +question is look um if you look on + + align:start position:0% +question is look um if you look on + + + align:start position:0% +question is look um if you look on +Wikipedia about uh seriously if you this + + align:start position:0% +Wikipedia about uh seriously if you this + + + align:start position:0% +Wikipedia about uh seriously if you this +is a rational thing to do if you look at + + align:start position:0% +is a rational thing to do if you look at + + + align:start position:0% +is a rational thing to do if you look at +Wikipedia to to learn something about + + align:start position:0% +Wikipedia to to learn something about + + + align:start position:0% +Wikipedia to to learn something about +hydrogen um what you discover is + + align:start position:0% +hydrogen um what you discover is + + + align:start position:0% +hydrogen um what you discover is +everything that we've talked about + + align:start position:0% +everything that we've talked about + + + align:start position:0% +everything that we've talked about +including the fine structure including + + align:start position:0% +including the fine structure including + + + align:start position:0% +including the fine structure including +the zamon effect but you see that there + + align:start position:0% +the zamon effect but you see that there + + + align:start position:0% +the zamon effect but you see that there +are a couple of other effects so one + + align:start position:0% +are a couple of other effects so one + + + align:start position:0% +are a couple of other effects so one +effect for example is uh when you look + + align:start position:0% +effect for example is uh when you look + + + align:start position:0% +effect for example is uh when you look +at the zamon effect a little more + + align:start position:0% +at the zamon effect a little more + + + align:start position:0% +at the zamon effect a little more +carefully than we did there's a second + + align:start position:0% +carefully than we did there's a second + + + align:start position:0% +carefully than we did there's a second +term in the zamon effect which is uh an + + align:start position:0% +term in the zamon effect which is uh an + + + align:start position:0% +term in the zamon effect which is uh an +an sort of induced Magnetic Moment so + + align:start position:0% +an sort of induced Magnetic Moment so + + + align:start position:0% +an sort of induced Magnetic Moment so +even when the angular momentum uh is is + + align:start position:0% +even when the angular momentum uh is is + + + align:start position:0% +even when the angular momentum uh is is +uh is is small or even zero there's + + align:start position:0% +uh is is small or even zero there's + + + align:start position:0% +uh is is small or even zero there's +still a contribution to um to the energy + + align:start position:0% +still a contribution to um to the energy + + + align:start position:0% +still a contribution to um to the energy +from the mag an externally imposed + + align:start position:0% +from the mag an externally imposed + + + align:start position:0% +from the mag an externally imposed +magnetic field um so there are lots of + + align:start position:0% +magnetic field um so there are lots of + + + align:start position:0% +magnetic field um so there are lots of +other Corrections one of them in + + align:start position:0% +other Corrections one of them in + + + align:start position:0% +other Corrections one of them in +particular is something called spin + + align:start position:0% +particular is something called spin + + + align:start position:0% +particular is something called spin +orbit + + align:start position:0% +orbit + + + align:start position:0% +orbit +coupling and um so the form of and so + + align:start position:0% +coupling and um so the form of and so + + + align:start position:0% +coupling and um so the form of and so +the question was look what is that and + + align:start position:0% +the question was look what is that and + + + align:start position:0% +the question was look what is that and +and can do we know enough to explain + + align:start position:0% +and can do we know enough to explain + + + align:start position:0% +and can do we know enough to explain +what spin orbit coupling is so let me + + align:start position:0% +what spin orbit coupling is so let me + + + align:start position:0% +what spin orbit coupling is so let me +give you a very short answer to that + + align:start position:0% +give you a very short answer to that + + + align:start position:0% +give you a very short answer to that +question + + align:start position:0% +question + + + align:start position:0% +question +so we know that if we write down the + + align:start position:0% +so we know that if we write down the + + + align:start position:0% +so we know that if we write down the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +operator for uh for our system we have + + align:start position:0% +operator for uh for our system we have + + + align:start position:0% +operator for uh for our system we have +the energy operator so the full the full + + align:start position:0% +the energy operator so the full the full + + + align:start position:0% +the energy operator so the full the full +energy operator for hydrogen I'll + + align:start position:0% +energy operator for hydrogen I'll + + + align:start position:0% +energy operator for hydrogen I'll +say + + align:start position:0% +say + + + align:start position:0% +say +um is the energy operator for + + align:start position:0% +um is the energy operator for + + + align:start position:0% +um is the energy operator for +kulum plus a bunch of Correction so for + + align:start position:0% +kulum plus a bunch of Correction so for + + + align:start position:0% +kulum plus a bunch of Correction so for +example we had the relativistic + + align:start position:0% +example we had the relativistic + + + align:start position:0% +example we had the relativistic +correction plus a term that was a + + align:start position:0% +correction plus a term that was a + + + align:start position:0% +correction plus a term that was a +coefficient time p and this is on your + + align:start position:0% +coefficient time p and this is on your + + + align:start position:0% +coefficient time p and this is on your +problem set um and this came from + + align:start position:0% +problem set um and this came from + + + align:start position:0% +problem set um and this came from +relativistic corrections I shouldn't + + align:start position:0% +relativistic corrections I shouldn't + + + align:start position:0% +relativistic corrections I shouldn't +call this C I'll call it beta maybe um + + align:start position:0% +call this C I'll call it beta maybe um + + + align:start position:0% +call this C I'll call it beta maybe um +some + + align:start position:0% +some + + + align:start position:0% +some +coefficient um and there are a whole + + align:start position:0% +coefficient um and there are a whole + + + align:start position:0% +coefficient um and there are a whole +bunch of other contributions for example + + align:start position:0% +bunch of other contributions for example + + + align:start position:0% +bunch of other contributions for example +there's the term we studied that + + align:start position:0% +there's the term we studied that + + + align:start position:0% +there's the term we studied that +contributed to the zount effect if + + align:start position:0% +contributed to the zount effect if + + + align:start position:0% +contributed to the zount effect if +there's an external magnetic field + + align:start position:0% +there's an external magnetic field + + + align:start position:0% +there's an external magnetic field +there's a b do uh uh magnetic d a + + align:start position:0% +there's a b do uh uh magnetic d a + + + align:start position:0% +there's a b do uh uh magnetic d a +magnetic um moment of the system and if + + align:start position:0% +magnetic um moment of the system and if + + + align:start position:0% +magnetic um moment of the system and if +the electron is uh in a state with + + align:start position:0% +the electron is uh in a state with + + + align:start position:0% +the electron is uh in a state with +finite angular momentum the Magnetic + + align:start position:0% +finite angular momentum the Magnetic + + + align:start position:0% +finite angular momentum the Magnetic +Moment is some dimensionful coefficient + + align:start position:0% +Moment is some dimensionful coefficient + + + align:start position:0% +Moment is some dimensionful coefficient +which we usually called the Bor Magneton + + align:start position:0% +which we usually called the Bor Magneton + + + align:start position:0% +which we usually called the Bor Magneton +because whatever we like the guy uh + + align:start position:0% +because whatever we like the guy uh + + + align:start position:0% +because whatever we like the guy uh +times the angular + + align:start position:0% +times the angular + + + align:start position:0% +times the angular +momentum okay but there can be + + align:start position:0% +momentum okay but there can be + + + align:start position:0% +momentum okay but there can be +additional + + align:start position:0% +additional + + + align:start position:0% +additional +contributions there there are a whole + + align:start position:0% +contributions there there are a whole + + + align:start position:0% +contributions there there are a whole +bunch of additional terms in this uh in + + align:start position:0% +bunch of additional terms in this uh in + + + align:start position:0% +bunch of additional terms in this uh in +the true potential for hydrogen one of + + align:start position:0% +the true potential for hydrogen one of + + + align:start position:0% +the true potential for hydrogen one of +them takes the following form it's a + + align:start position:0% +them takes the following form it's a + + + align:start position:0% +them takes the following form it's a +it's a + + align:start position:0% +it's a + + + align:start position:0% +it's a +constant plus maybe I'll call it + + align:start position:0% +constant plus maybe I'll call it + + + align:start position:0% +constant plus maybe I'll call it +Kappa + + align:start position:0% +Kappa + + + align:start position:0% +Kappa +times + + align:start position:0% + + + + align:start position:0% + +spin dotted into the angular momentum uh + + align:start position:0% +spin dotted into the angular momentum uh + + + align:start position:0% +spin dotted into the angular momentum uh +of the electron of the the uh electron + + align:start position:0% +of the electron of the the uh electron + + + align:start position:0% +of the electron of the the uh electron +bound to the hydrogen system so where + + align:start position:0% +bound to the hydrogen system so where + + + align:start position:0% +bound to the hydrogen system so where +this comes from is a sort of beautiful + + align:start position:0% +this comes from is a sort of beautiful + + + align:start position:0% +this comes from is a sort of beautiful +story so first off could it be there + + align:start position:0% +story so first off could it be there + + + align:start position:0% +story so first off could it be there +sure this is some this is a term that + + align:start position:0% +sure this is some this is a term that + + + align:start position:0% +sure this is some this is a term that +could exist with some coefficient why + + align:start position:0% +could exist with some coefficient why + + + align:start position:0% +could exist with some coefficient why +not um uh it turns out that you can + + align:start position:0% +not um uh it turns out that you can + + + align:start position:0% +not um uh it turns out that you can +derive its existence from a study of the + + align:start position:0% +derive its existence from a study of the + + + align:start position:0% +derive its existence from a study of the +relativistic uh version of the hydrogen + + align:start position:0% +relativistic uh version of the hydrogen + + + align:start position:0% +relativistic uh version of the hydrogen +equation of the hydrogen system we're + + align:start position:0% +equation of the hydrogen system we're + + + align:start position:0% +equation of the hydrogen system we're +not going to study that in any detail in + + align:start position:0% +not going to study that in any detail in + + + align:start position:0% +not going to study that in any detail in +804 but the basic and what this does uh + + align:start position:0% +804 but the basic and what this does uh + + + align:start position:0% +804 but the basic and what this does uh +is totally amenable to to 804 level + + align:start position:0% +is totally amenable to to 804 level + + + align:start position:0% +is totally amenable to to 804 level +analysis this is just saying that when + + align:start position:0% +analysis this is just saying that when + + + align:start position:0% +analysis this is just saying that when +you have uh some orbital angular + + align:start position:0% +you have uh some orbital angular + + + align:start position:0% +you have uh some orbital angular +momentum and when you have some spin + + align:start position:0% +momentum and when you have some spin + + + align:start position:0% +momentum and when you have some spin +angular momentum both of those + + align:start position:0% +angular momentum both of those + + + align:start position:0% +angular momentum both of those +correspond to angular momentum of an + + align:start position:0% +correspond to angular momentum of an + + + align:start position:0% +correspond to angular momentum of an +object that carries charge and so it's + + align:start position:0% +object that carries charge and so it's + + + align:start position:0% +object that carries charge and so it's +not unreasonable that there's going to + + align:start position:0% +not unreasonable that there's going to + + + align:start position:0% +not unreasonable that there's going to +be some interaction between the two + + align:start position:0% +be some interaction between the two + + + align:start position:0% +be some interaction between the two +where the magnetic moments those two + + align:start position:0% +where the magnetic moments those two + + + align:start position:0% +where the magnetic moments those two +magnetic moments are you know either + + align:start position:0% +magnetic moments are you know either + + + align:start position:0% +magnetic moments are you know either +want to be aligned or anti-aligned + + align:start position:0% +want to be aligned or anti-aligned + + + align:start position:0% +want to be aligned or anti-aligned +depending on the sign of this + + align:start position:0% +depending on the sign of this + + + align:start position:0% +depending on the sign of this +coefficient however we haven't talked + + align:start position:0% +coefficient however we haven't talked + + + align:start position:0% +coefficient however we haven't talked +about spin in any great detail yet we're + + align:start position:0% +about spin in any great detail yet we're + + + align:start position:0% +about spin in any great detail yet we're +going to do that last week of the course + + align:start position:0% +going to do that last week of the course + + + align:start position:0% +going to do that last week of the course +so I'm going to defer talking about this + + align:start position:0% +so I'm going to defer talking about this + + + align:start position:0% +so I'm going to defer talking about this +in any detail we're only going to + + align:start position:0% +in any detail we're only going to + + + align:start position:0% +in any detail we're only going to +discuss it briefly at the end um for a + + align:start position:0% +discuss it briefly at the end um for a + + + align:start position:0% +discuss it briefly at the end um for a +couple of weeks but absolutely this sort + + align:start position:0% +couple of weeks but absolutely this sort + + + align:start position:0% +couple of weeks but absolutely this sort +of these additional couplings are + + align:start position:0% +of these additional couplings are + + + align:start position:0% +of these additional couplings are +important for hydrogen and they're also + + align:start position:0% +important for hydrogen and they're also + + + align:start position:0% +important for hydrogen and they're also +things we can you can study at at this + + align:start position:0% +things we can you can study at at this + + + align:start position:0% +things we can you can study at at this +level at 804 level I should also + + align:start position:0% +level at 804 level I should also + + + align:start position:0% +level at 804 level I should also +emphasize that there are a whole bunch + + align:start position:0% +emphasize that there are a whole bunch + + + align:start position:0% +emphasize that there are a whole bunch +of other Corrections there are lots of + + align:start position:0% +of other Corrections there are lots of + + + align:start position:0% +of other Corrections there are lots of +there are lots of terms I mean one set + + align:start position:0% +there are lots of terms I mean one set + + + align:start position:0% +there are lots of terms I mean one set +of terms an infinite number of terms are + + align:start position:0% +of terms an infinite number of terms are + + + align:start position:0% +of terms an infinite number of terms are +the further subleading relativistic + + align:start position:0% +the further subleading relativistic + + + align:start position:0% +the further subleading relativistic +Corrections of kinetic energy right and + + align:start position:0% +Corrections of kinetic energy right and + + + align:start position:0% +Corrections of kinetic energy right and +there are a whole bunch of other + + align:start position:0% +there are a whole bunch of other + + + align:start position:0% +there are a whole bunch of other +Corrections so I'm I'm going to leave + + align:start position:0% +Corrections so I'm I'm going to leave + + + align:start position:0% +Corrections so I'm I'm going to leave +those out for the moment but + + align:start position:0% +those out for the moment but + + + align:start position:0% +those out for the moment but +um I I want to emphasize to everyone + + align:start position:0% +um I I want to emphasize to everyone + + + align:start position:0% +um I I want to emphasize to everyone +that we're building models of hydrogen + + align:start position:0% +that we're building models of hydrogen + + + align:start position:0% +that we're building models of hydrogen +and they're all approximations + + align:start position:0% + + + + align:start position:0% + +yeah yes there there is so um so on the + + align:start position:0% +yeah yes there there is so um so on the + + + align:start position:0% +yeah yes there there is so um so on the +problem set um you're asked to estimate + + align:start position:0% +problem set um you're asked to estimate + + + align:start position:0% +problem set um you're asked to estimate +the the correction to the energy we + + align:start position:0% +the the correction to the energy we + + + align:start position:0% +the the correction to the energy we +actually I wrote down the answer in + + align:start position:0% +actually I wrote down the answer in + + + align:start position:0% +actually I wrote down the answer in +lecture the other day you're asked asked + + align:start position:0% +lecture the other day you're asked asked + + + align:start position:0% +lecture the other day you're asked asked +to uh compute the uh in particular the + + align:start position:0% +to uh compute the uh in particular the + + + align:start position:0% +to uh compute the uh in particular the +dependence but to estimate the magnitude + + align:start position:0% +dependence but to estimate the magnitude + + + align:start position:0% +dependence but to estimate the magnitude +or to estimate the value of the shift in + + align:start position:0% +or to estimate the value of the shift in + + + align:start position:0% +or to estimate the value of the shift in +the energy I values uh uh to hydrogen + + align:start position:0% +the energy I values uh uh to hydrogen + + + align:start position:0% +the energy I values uh uh to hydrogen +from the first relativistic correction + + align:start position:0% +from the first relativistic correction + + + align:start position:0% +from the first relativistic correction +this P to the fourth + + align:start position:0% +this P to the fourth + + + align:start position:0% +this P to the fourth +correction and for I I expect that this + + align:start position:0% +correction and for I I expect that this + + + align:start position:0% +correction and for I I expect that this +will be covered in your recitation in + + align:start position:0% +will be covered in your recitation in + + + align:start position:0% +will be covered in your recitation in +some detail but um there the question + + align:start position:0% +some detail but um there the question + + + align:start position:0% +some detail but um there the question +was are there is there a trick to make + + align:start position:0% +was are there is there a trick to make + + + align:start position:0% +was are there is there a trick to make +this a little easier I'm not going to + + align:start position:0% +this a little easier I'm not going to + + + align:start position:0% +this a little easier I'm not going to +there there are a couple of good + + align:start position:0% +there there are a couple of good + + + align:start position:0% +there there are a couple of good +physical arguments which I'm not going + + align:start position:0% +physical arguments which I'm not going + + + align:start position:0% +physical arguments which I'm not going +to tell you but there are nice ways to + + align:start position:0% +to tell you but there are nice ways to + + + align:start position:0% +to tell you but there are nice ways to +do this but but at the end of the day + + align:start position:0% +do this but but at the end of the day + + + align:start position:0% +do this but but at the end of the day +you do not want to end up doing the + + align:start position:0% +you do not want to end up doing the + + + align:start position:0% +you do not want to end up doing the +following computation you don't want to + + align:start position:0% +following computation you don't want to + + + align:start position:0% +following computation you don't want to +take the expectation value of P to 4th + + align:start position:0% +take the expectation value of P to 4th + + + align:start position:0% +take the expectation value of P to 4th +and write this as the some integral of s + + align:start position:0% +and write this as the some integral of s + + + align:start position:0% +and write this as the some integral of s +complex conjugate uh derivative to the + + align:start position:0% +complex conjugate uh derivative to the + + + align:start position:0% +complex conjugate uh derivative to the +4th s if you do if you attempt to do + + align:start position:0% +4th s if you do if you attempt to do + + + align:start position:0% +4th s if you do if you attempt to do +this integral you will weep okay this is + + align:start position:0% +this integral you will weep okay this is + + + align:start position:0% +this integral you will weep okay this is +not the way you want to do it and here's + + align:start position:0% +not the way you want to do it and here's + + + align:start position:0% +not the way you want to do it and here's +what you want to do and I'm not going to + + align:start position:0% +what you want to do and I'm not going to + + + align:start position:0% +what you want to do and I'm not going to +tell you how to get here but you want to + + align:start position:0% +tell you how to get here but you want to + + + align:start position:0% +tell you how to get here but you want to +reduce the calculation of this + + align:start position:0% +reduce the calculation of this + + + align:start position:0% +reduce the calculation of this +expectation value to the calculation of + + align:start position:0% +expectation value to the calculation of + + + align:start position:0% +expectation value to the calculation of +the expectation value of one over r and + + align:start position:0% +the expectation value of one over r and + + + align:start position:0% +the expectation value of one over r and +of 1 R + + align:start position:0% +of 1 R + + + align:start position:0% +of 1 R +2 okay and it turns out that if you know + + align:start position:0% +2 okay and it turns out that if you know + + + align:start position:0% +2 okay and it turns out that if you know +these expectation values that entirely + + align:start position:0% +these expectation values that entirely + + + align:start position:0% +these expectation values that entirely +suffices to compute the expectation + + align:start position:0% +suffices to compute the expectation + + + align:start position:0% +suffices to compute the expectation +value of P to 4th if you take into + + align:start position:0% +value of P to 4th if you take into + + + align:start position:0% +value of P to 4th if you take into +account the fact that the energy + + align:start position:0% +account the fact that the energy + + + align:start position:0% +account the fact that the energy +functions uh satisfy the original energy + + align:start position:0% +functions uh satisfy the original energy + + + align:start position:0% +functions uh satisfy the original energy +value equation so P ^2 upon 2 M plus v + + align:start position:0% +value equation so P ^2 upon 2 M plus v + + + align:start position:0% +value equation so P ^2 upon 2 M plus v +of X or V of R is equal to E when acting + + align:start position:0% +of X or V of R is equal to E when acting + + + align:start position:0% +of X or V of R is equal to E when acting +on that on those wave functions so for + + align:start position:0% +on that on those wave functions so for + + + align:start position:0% +on that on those wave functions so for +computing these guys you could try to do + + align:start position:0% +computing these guys you could try to do + + + align:start position:0% +computing these guys you could try to do +this Brute Force not unrelated to the to + + align:start position:0% +this Brute Force not unrelated to the to + + + align:start position:0% +this Brute Force not unrelated to the to +problem I believe two on ridberg atoms + + align:start position:0% +problem I believe two on ridberg atoms + + + align:start position:0% +problem I believe two on ridberg atoms +on the problem set um but there are + + align:start position:0% +on the problem set um but there are + + + align:start position:0% +on the problem set um but there are +actually sneakier ways to do + + align:start position:0% +actually sneakier ways to do + + + align:start position:0% +actually sneakier ways to do +these uh to do these expectation values + + align:start position:0% +these uh to do these expectation values + + + align:start position:0% +these uh to do these expectation values +as well um and um I I will leave that to + + align:start position:0% +as well um and um I I will leave that to + + + align:start position:0% +as well um and um I I will leave that to +you but let me yeah but let me emphasize + + align:start position:0% +you but let me yeah but let me emphasize + + + align:start position:0% +you but let me yeah but let me emphasize +that uh you can do a direct Brute Force + + align:start position:0% +that uh you can do a direct Brute Force + + + align:start position:0% +that uh you can do a direct Brute Force +calculation but you don't need to and I + + align:start position:0% +calculation but you don't need to and I + + + align:start position:0% +calculation but you don't need to and I +would encourage you to try to find an + + align:start position:0% +would encourage you to try to find an + + + align:start position:0% +would encourage you to try to find an +efficient uh indirect way to do these + + align:start position:0% +efficient uh indirect way to do these + + + align:start position:0% +efficient uh indirect way to do these +calculations + + align:start position:0% +calculations + + + align:start position:0% +calculations +that it's your question okay um anything + + align:start position:0% +that it's your question okay um anything + + + align:start position:0% +that it's your question okay um anything +else before we get + + align:start position:0% + + + + align:start position:0% + +yeah uh does adding time um it well it + + align:start position:0% +yeah uh does adding time um it well it + + + align:start position:0% +yeah uh does adding time um it well it +depends on what the how you introduce + + align:start position:0% +depends on what the how you introduce + + + align:start position:0% +depends on what the how you introduce +the time dependence so + + align:start position:0% + + + + align:start position:0% + +the yes yeah absolutely uh what's the + + align:start position:0% +the yes yeah absolutely uh what's the + + + align:start position:0% +the yes yeah absolutely uh what's the +reason for the + + align:start position:0% + + + + align:start position:0% + +question one of the problems on the + + align:start position:0% +question one of the problems on the + + + align:start position:0% +question one of the problems on the +problem + + align:start position:0% + + + + align:start position:0% + +set remind me which problem this is I + + align:start position:0% +set remind me which problem this is I + + + align:start position:0% +set remind me which problem this is I +don't + + align:start position:0% +don't + + + align:start position:0% +don't +remember oh oh + + align:start position:0% + + + + align:start position:0% + +oh sorry I really like that problem + + align:start position:0% + + + + align:start position:0% + +um the let me rephrase your question in + + align:start position:0% +um the let me rephrase your question in + + + align:start position:0% +um the let me rephrase your question in +the following way + + align:start position:0% + + + + align:start position:0% + +is it intrinsically non- herian to have + + align:start position:0% +is it intrinsically non- herian to have + + + align:start position:0% +is it intrinsically non- herian to have +time dependence in a + + align:start position:0% +time dependence in a + + + align:start position:0% +time dependence in a +system so no you can have a so what does + + align:start position:0% +system so no you can have a so what does + + + align:start position:0% +system so no you can have a so what does +heran mean physically what what does it + + align:start position:0% +heran mean physically what what does it + + + align:start position:0% +heran mean physically what what does it +mean for the energy to be herian for + + align:start position:0% +mean for the energy to be herian for + + + align:start position:0% +mean for the energy to be herian for +example what it means for the energy + + align:start position:0% +example what it means for the energy + + + align:start position:0% +example what it means for the energy +operator to be herian is that time + + align:start position:0% +operator to be herian is that time + + + align:start position:0% +operator to be herian is that time +Evolution which is represented by the + + align:start position:0% +Evolution which is represented by the + + + align:start position:0% +Evolution which is represented by the +oper so let me phrase it this way so if + + align:start position:0% +oper so let me phrase it this way so if + + + align:start position:0% +oper so let me phrase it this way so if +we know that the energy operator form + + align:start position:0% +we know that the energy operator form + + + align:start position:0% +we know that the energy operator form +what is that telling us well it tells us + + align:start position:0% +what is that telling us well it tells us + + + align:start position:0% +what is that telling us well it tells us +a lot of things it tells us the energy + + align:start position:0% +a lot of things it tells us the energy + + + align:start position:0% +a lot of things it tells us the energy +values are real that's that's good so e + + align:start position:0% +values are real that's that's good so e + + + align:start position:0% +values are real that's that's good so e +diag is equal to e but it tells us + + align:start position:0% +diag is equal to e but it tells us + + + align:start position:0% +diag is equal to e but it tells us +something else remember that the Shing + + align:start position:0% +something else remember that the Shing + + + align:start position:0% +something else remember that the Shing +equation is that um I DT on S is equal + + align:start position:0% +equation is that um I DT on S is equal + + + align:start position:0% +equation is that um I DT on S is equal +to e on S and we use this to argue that + + align:start position:0% +to e on S and we use this to argue that + + + align:start position:0% +to e on S and we use this to argue that +um the general solution for to the + + align:start position:0% +um the general solution for to the + + + align:start position:0% +um the general solution for to the +straight equation can be written in the + + align:start position:0% +straight equation can be written in the + + + align:start position:0% +straight equation can be written in the +following elegant way s of T is equal to + + align:start position:0% +following elegant way s of T is equal to + + + align:start position:0% +following elegant way s of T is equal to +e to the minus I uh upon H bar + + align:start position:0% +e to the minus I uh upon H bar + + + align:start position:0% +e to the minus I uh upon H bar +uh + + align:start position:0% +uh + + + align:start position:0% +uh +t + + align:start position:0% +t + + + align:start position:0% +t +e uh on side + + align:start position:0% +e uh on side + + + align:start position:0% +e uh on side +zero right where this was the evolution + + align:start position:0% +zero right where this was the evolution + + + align:start position:0% +zero right where this was the evolution +operator U + + align:start position:0% +operator U + + + align:start position:0% +operator U +subt yeah and this is a unitary operator + + align:start position:0% +subt yeah and this is a unitary operator + + + align:start position:0% +subt yeah and this is a unitary operator +and the way to see it's unitary goes + + align:start position:0% +and the way to see it's unitary goes + + + align:start position:0% +and the way to see it's unitary goes +back to the exam the way to see it's + + align:start position:0% +back to the exam the way to see it's + + + align:start position:0% +back to the exam the way to see it's +unitary is this is e to the I herian + + align:start position:0% +unitary is this is e to the I herian + + + align:start position:0% +unitary is this is e to the I herian +operator T is a real number H is a real + + align:start position:0% +operator T is a real number H is a real + + + align:start position:0% +operator T is a real number H is a real +number so so this is e to the I uh + + align:start position:0% +number so so this is e to the I uh + + + align:start position:0% +number so so this is e to the I uh +herian operator and anything of the form + + align:start position:0% +herian operator and anything of the form + + + align:start position:0% +herian operator and anything of the form +e to the I herian operator is UN it's + + align:start position:0% +e to the I herian operator is UN it's + + + align:start position:0% +e to the I herian operator is UN it's +adint is inverse what that tells you is + + align:start position:0% +adint is inverse what that tells you is + + + align:start position:0% +adint is inverse what that tells you is +that since this is unary it preserves + + align:start position:0% +that since this is unary it preserves + + + align:start position:0% +that since this is unary it preserves +the magnitude or the norm of the wave + + align:start position:0% +the magnitude or the norm of the wave + + + align:start position:0% +the magnitude or the norm of the wave +function so probability is conserved + + align:start position:0% +function so probability is conserved + + + align:start position:0% +function so probability is conserved +what would it mean for the energy + + align:start position:0% +what would it mean for the energy + + + align:start position:0% +what would it mean for the energy +operator to be not + + align:start position:0% +operator to be not + + + align:start position:0% +operator to be not +herian what would mean a lot of things + + align:start position:0% +herian what would mean a lot of things + + + align:start position:0% +herian what would mean a lot of things +one thing it would mean is that the + + align:start position:0% +one thing it would mean is that the + + + align:start position:0% +one thing it would mean is that the +energy I values are no longer real + + align:start position:0% +energy I values are no longer real + + + align:start position:0% +energy I values are no longer real +that's a little weird but the much more + + align:start position:0% +that's a little weird but the much more + + + align:start position:0% +that's a little weird but the much more +troubling thing is that the energy would + + align:start position:0% +troubling thing is that the energy would + + + align:start position:0% +troubling thing is that the energy would +no longer be or sorry the probability + + align:start position:0% +no longer be or sorry the probability + + + align:start position:0% +no longer be or sorry the probability +would no longer be conserved the the + + align:start position:0% +would no longer be conserved the the + + + align:start position:0% +would no longer be conserved the the +evolution operator which is the solution + + align:start position:0% +evolution operator which is the solution + + + align:start position:0% +evolution operator which is the solution +to the straing equation would no longer + + align:start position:0% +to the straing equation would no longer + + + align:start position:0% +to the straing equation would no longer +be unary operator and the probability + + align:start position:0% +be unary operator and the probability + + + align:start position:0% +be unary operator and the probability +the norm of the wave function would no + + align:start position:0% +the norm of the wave function would no + + + align:start position:0% +the norm of the wave function would no +longer be + + align:start position:0% +longer be + + + align:start position:0% +longer be +conserved so the question at the end of + + align:start position:0% +conserved so the question at the end of + + + align:start position:0% +conserved so the question at the end of +the the last question in problem four is + + align:start position:0% +the the last question in problem four is + + + align:start position:0% +the the last question in problem four is +really asking in the system you're + + align:start position:0% +really asking in the system you're + + + align:start position:0% +really asking in the system you're +thinking about is probability + + align:start position:0% +thinking about is probability + + + align:start position:0% +thinking about is probability +conserved okay and that's the question + + align:start position:0% +conserved okay and that's the question + + + align:start position:0% +conserved okay and that's the question +that you should be asking + + align:start position:0% +that you should be asking + + + align:start position:0% +that you should be asking +yourself when you finish up problem + + align:start position:0% +yourself when you finish up problem + + + align:start position:0% +yourself when you finish up problem +four + + align:start position:0% +four + + + align:start position:0% +four +good yeah when we solve the dist + + align:start position:0% +good yeah when we solve the dist + + + align:start position:0% +good yeah when we solve the dist +equation in that way um does this + + align:start position:0% +equation in that way um does this + + + align:start position:0% +equation in that way um does this +solution come from the fact that istion + + align:start position:0% +solution come from the fact that istion + + + align:start position:0% +solution come from the fact that istion +or that is time + + align:start position:0% + + + + align:start position:0% + +independent oh absolutely absolutely so + + align:start position:0% +independent oh absolutely absolutely so + + + align:start position:0% +independent oh absolutely absolutely so +um so here I was just focusing on the + + align:start position:0% +um so here I was just focusing on the + + + align:start position:0% +um so here I was just focusing on the +hermeticity and I was assuming in + + align:start position:0% +hermeticity and I was assuming in + + + align:start position:0% +hermeticity and I was assuming in +solving this I'm assuming that the + + align:start position:0% +solving this I'm assuming that the + + + align:start position:0% +solving this I'm assuming that the +energy is time independent if the energy + + align:start position:0% +energy is time independent if the energy + + + align:start position:0% +energy is time independent if the energy +is not time independent then this is not + + align:start position:0% +is not time independent then this is not + + + align:start position:0% +is not time independent then this is not +the right answer as as you're pointing + + align:start position:0% +the right answer as as you're pointing + + + align:start position:0% +the right answer as as you're pointing +out so in fact you have to do an + + align:start position:0% +out so in fact you have to do an + + + align:start position:0% +out so in fact you have to do an +integral and you have to time order + + align:start position:0% +integral and you have to time order + + + align:start position:0% +integral and you have to time order +things and it's a complicated story um + + align:start position:0% +things and it's a complicated story um + + + align:start position:0% +things and it's a complicated story um +but this is not the solution but even if + + align:start position:0% +but this is not the solution but even if + + + align:start position:0% +but this is not the solution but even if +we have a Time independent system if the + + align:start position:0% +we have a Time independent system if the + + + align:start position:0% +we have a Time independent system if the +energy operator is not heran this is not + + align:start position:0% +energy operator is not heran this is not + + + align:start position:0% +energy operator is not heran this is not +unary so indeed you're absolutely right + + align:start position:0% +unary so indeed you're absolutely right + + + align:start position:0% +unary so indeed you're absolutely right +that if the energy operator is time + + align:start position:0% +that if the energy operator is time + + + align:start position:0% +that if the energy operator is time +dependent the story is more complicated + + align:start position:0% +dependent the story is more complicated + + + align:start position:0% +dependent the story is more complicated +than just this but we already see the + + align:start position:0% +than just this but we already see the + + + align:start position:0% +than just this but we already see the +problem that's Salient for problem four + + align:start position:0% +problem that's Salient for problem four + + + align:start position:0% +problem that's Salient for problem four +at this stage with a Time independent + + align:start position:0% +at this stage with a Time independent + + + align:start position:0% +at this stage with a Time independent +operator + + align:start position:0% + + + + align:start position:0% + +yeah my parles + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +comp yeah + + align:start position:0% +comp yeah + + + align:start position:0% +comp yeah +that's well I guess it's sort of a + + align:start position:0% +that's well I guess it's sort of a + + + align:start position:0% +that's well I guess it's sort of a +matter of taste um uh so what these I + + align:start position:0% +matter of taste um uh so what these I + + + align:start position:0% +matter of taste um uh so what these I +would say that they're the same thing in + + align:start position:0% +would say that they're the same thing in + + + align:start position:0% +would say that they're the same thing in +the following sense suppose I have + + align:start position:0% +the following sense suppose I have + + + align:start position:0% +the following sense suppose I have +complex energy values well I know that + + align:start position:0% +complex energy values well I know that + + + align:start position:0% +complex energy values well I know that +if I have a stationary State then that + + align:start position:0% +if I have a stationary State then that + + + align:start position:0% +if I have a stationary State then that +stationary State as a function of time + + align:start position:0% +stationary State as a function of time + + + align:start position:0% +stationary State as a function of time +uh is equal to the stationary State at + + align:start position:0% +uh is equal to the stationary State at + + + align:start position:0% +uh is equal to the stationary State at +time Z times e so this is just an energy + + align:start position:0% +time Z times e so this is just an energy + + + align:start position:0% +time Z times e so this is just an energy +function rather than uh okay is e to + + align:start position:0% +function rather than uh okay is e to + + + align:start position:0% +function rather than uh okay is e to +minus I the energy time T over H bar or + + align:start position:0% +minus I the energy time T over H bar or + + + align:start position:0% +minus I the energy time T over H bar or +this is the energy I can value right now + + align:start position:0% +this is the energy I can value right now + + + align:start position:0% +this is the energy I can value right now +imagine e is complex so if e sorry First + + align:start position:0% +imagine e is complex so if e sorry First + + + align:start position:0% +imagine e is complex so if e sorry First +Imagine e is real that's not hard to + + align:start position:0% +Imagine e is real that's not hard to + + + align:start position:0% +Imagine e is real that's not hard to +imagine because it's usually the case + + align:start position:0% +imagine because it's usually the case + + + align:start position:0% +imagine because it's usually the case +and if if that's true what happens to + + align:start position:0% +and if if that's true what happens to + + + align:start position:0% +and if if that's true what happens to +the norm what happens to the way + + align:start position:0% +the norm what happens to the way + + + align:start position:0% +the norm what happens to the way +function as we evolved through time it + + align:start position:0% +function as we evolved through time it + + + align:start position:0% +function as we evolved through time it +rotates by phase now if e is complex + + align:start position:0% +rotates by phase now if e is complex + + + align:start position:0% +rotates by phase now if e is complex +imagine e is of the form uh e uh exactly + + align:start position:0% +imagine e is of the form uh e uh exactly + + + align:start position:0% +imagine e is of the form uh e uh exactly +let e be complex so e is going to be e + + align:start position:0% +let e be complex so e is going to be e + + + align:start position:0% +let e be complex so e is going to be e +real uh minus I uh uh gamma some + + align:start position:0% +real uh minus I uh uh gamma some + + + align:start position:0% +real uh minus I uh uh gamma some +imaginary piece yeah so what that's + + align:start position:0% +imaginary piece yeah so what that's + + + align:start position:0% +imaginary piece yeah so what that's +going to give me is an e to the minus + + align:start position:0% +going to give me is an e to the minus + + + align:start position:0% +going to give me is an e to the minus +gamma + + align:start position:0% +gamma + + + align:start position:0% +gamma +t Okay so and and that's a decaying + + align:start position:0% +t Okay so and and that's a decaying + + + align:start position:0% +t Okay so and and that's a decaying +thing that when you take its Norm + + align:start position:0% +thing that when you take its Norm + + + align:start position:0% +thing that when you take its Norm +squared gives you a decaying envelope + + align:start position:0% +squared gives you a decaying envelope + + + align:start position:0% +squared gives you a decaying envelope +over time it's going to give you an + + align:start position:0% +over time it's going to give you an + + + align:start position:0% +over time it's going to give you an +exponential decay right this is going to + + align:start position:0% +exponential decay right this is going to + + + align:start position:0% +exponential decay right this is going to +be equal to eus i e real uh T over H bar + + align:start position:0% +be equal to eus i e real uh T over H bar + + + align:start position:0% +be equal to eus i e real uh T over H bar +uh time e to the minus gamma T over H uh + + align:start position:0% +uh time e to the minus gamma T over H uh + + + align:start position:0% +uh time e to the minus gamma T over H uh +5 and when we take the norm Square the + + align:start position:0% +5 and when we take the norm Square the + + + align:start position:0% +5 and when we take the norm Square the +phase goes away but this doesn't so + + align:start position:0% +phase goes away but this doesn't so + + + align:start position:0% +phase goes away but this doesn't so +having loss of + + align:start position:0% +having loss of + + + align:start position:0% +having loss of +probability is having a complex energy I + + align:start position:0% +probability is having a complex energy I + + + align:start position:0% +probability is having a complex energy I +value yeah why are we talking about I + + align:start position:0% +value yeah why are we talking about I + + + align:start position:0% +value yeah why are we talking about I +guess like time independent operator if + + align:start position:0% +guess like time independent operator if + + + align:start position:0% +guess like time independent operator if +there's an electromagnetic field and + + align:start position:0% +there's an electromagnetic field and + + + align:start position:0% +there's an electromagnetic field and +stuff is clearly going on between like + + align:start position:0% +stuff is clearly going on between like + + + align:start position:0% +stuff is clearly going on between like +the atom and the electromagnetic field + + align:start position:0% +the atom and the electromagnetic field + + + align:start position:0% +the atom and the electromagnetic field +this is a very good question and that + + align:start position:0% +this is a very good question and that + + + align:start position:0% +this is a very good question and that +actually leads me into the thing I + + align:start position:0% +actually leads me into the thing I + + + align:start position:0% +actually leads me into the thing I +wanted to talk about first so I got a + + align:start position:0% +wanted to talk about first so I got a + + + align:start position:0% +wanted to talk about first so I got a +bunch of questions thanks for that + + align:start position:0% +bunch of questions thanks for that + + + align:start position:0% +bunch of questions thanks for that +question I got a bunch of questions over + + align:start position:0% +question I got a bunch of questions over + + + align:start position:0% +question I got a bunch of questions over +the past few days about um the the + + align:start position:0% +the past few days about um the the + + + align:start position:0% +the past few days about um the the +Magnetic Moment of the hydrogen system H + + align:start position:0% +Magnetic Moment of the hydrogen system H + + + align:start position:0% +Magnetic Moment of the hydrogen system H +and what a strange idea that is so let + + align:start position:0% +and what a strange idea that is so let + + + align:start position:0% +and what a strange idea that is so let +me talk about that for a second and when + + align:start position:0% +me talk about that for a second and when + + + align:start position:0% +me talk about that for a second and when +I'm done with this little Spiel tell me + + align:start position:0% +I'm done with this little Spiel tell me + + + align:start position:0% +I'm done with this little Spiel tell me +if I've answered your + + align:start position:0% +if I've answered your + + + align:start position:0% +if I've answered your +question okay um let's just leave this + + align:start position:0% +question okay um let's just leave this + + + align:start position:0% +question okay um let's just leave this +up okay + + align:start position:0% +up okay + + + align:start position:0% +up okay +so in particular let's think about this + + align:start position:0% +so in particular let's think about this + + + align:start position:0% +so in particular let's think about this +term for the + + align:start position:0% +term for the + + + align:start position:0% +term for the +moment what this term came from last + + align:start position:0% +moment what this term came from last + + + align:start position:0% +moment what this term came from last +time was we said look we turn on an + + align:start position:0% +time was we said look we turn on an + + + align:start position:0% +time was we said look we turn on an +external magnetic field you know someone + + align:start position:0% +external magnetic field you know someone + + + align:start position:0% +external magnetic field you know someone +turns on a switch and current runs + + align:start position:0% +turns on a switch and current runs + + + align:start position:0% +turns on a switch and current runs +through electromagnet and we get a + + align:start position:0% +through electromagnet and we get a + + + align:start position:0% +through electromagnet and we get a +uniform magnetic field in our fiducial + + align:start position:0% +uniform magnetic field in our fiducial + + + align:start position:0% +uniform magnetic field in our fiducial +volume where we're doing the experiment + + align:start position:0% +volume where we're doing the experiment + + + align:start position:0% +volume where we're doing the experiment +and the electron system has uh if it + + align:start position:0% +and the electron system has uh if it + + + align:start position:0% +and the electron system has uh if it +carries some angular momentum it also + + align:start position:0% +carries some angular momentum it also + + + align:start position:0% +carries some angular momentum it also +has a charge angular momentum charge + + align:start position:0% +has a charge angular momentum charge + + + align:start position:0% +has a charge angular momentum charge +that means it's got a magnetic moment + + align:start position:0% +that means it's got a magnetic moment + + + align:start position:0% +that means it's got a magnetic moment +that's how much Magnetic Moment uh so + + align:start position:0% +that's how much Magnetic Moment uh so + + + align:start position:0% +that's how much Magnetic Moment uh so +this is saying that the Magnetic Moment + + align:start position:0% +this is saying that the Magnetic Moment + + + align:start position:0% +this is saying that the Magnetic Moment +of the electron bound to the with + + align:start position:0% +of the electron bound to the with + + + align:start position:0% +of the electron bound to the with +angular momentum uh wants to uh + + align:start position:0% +angular momentum uh wants to uh + + + align:start position:0% +angular momentum uh wants to uh +anti-align with the magnetic field or + + align:start position:0% +anti-align with the magnetic field or + + + align:start position:0% +anti-align with the magnetic field or +align in this case cuz I put the wrong + + align:start position:0% +align in this case cuz I put the wrong + + + align:start position:0% +align in this case cuz I put the wrong +sign + + align:start position:0% +sign + + + align:start position:0% +sign +um + + align:start position:0% +um + + + align:start position:0% +um +um but here's something really + + align:start position:0% + + + + align:start position:0% + +upsetting about that so what he just + + align:start position:0% +upsetting about that so what he just + + + align:start position:0% +upsetting about that so what he just +said sounds crazy if you think about it + + align:start position:0% +said sounds crazy if you think about it + + + align:start position:0% +said sounds crazy if you think about it +in the following way take an + + align:start position:0% +in the following way take an + + + align:start position:0% +in the following way take an +electron in the Kum system straight up + + align:start position:0% +electron in the Kum system straight up + + + align:start position:0% +electron in the Kum system straight up +Kum take an electron the coolum system + + align:start position:0% +Kum take an electron the coolum system + + + align:start position:0% +Kum take an electron the coolum system +put it in say the ground state lowest + + align:start position:0% +put it in say the ground state lowest + + + align:start position:0% +put it in say the ground state lowest +energy + + align:start position:0% +energy + + + align:start position:0% +energy +State okay uh is is it moving this is + + align:start position:0% +State okay uh is is it moving this is + + + align:start position:0% +State okay uh is is it moving this is +problem four in some right so is it is + + align:start position:0% +problem four in some right so is it is + + + align:start position:0% +problem four in some right so is it is +it moving the expectation value of + + align:start position:0% +it moving the expectation value of + + + align:start position:0% +it moving the expectation value of +position doesn't change in time it's a + + align:start position:0% +position doesn't change in time it's a + + + align:start position:0% +position doesn't change in time it's a +stationary State expectation value of + + align:start position:0% +stationary State expectation value of + + + align:start position:0% +stationary State expectation value of +nothing changes in time right okay fine + + align:start position:0% +nothing changes in time right okay fine + + + align:start position:0% +nothing changes in time right okay fine +but it's the ground state that carries + + align:start position:0% +but it's the ground state that carries + + + align:start position:0% +but it's the ground state that carries +zero angular momentum that's not so + + align:start position:0% +zero angular momentum that's not so + + + align:start position:0% +zero angular momentum that's not so +upsetting go to the first excited state + + align:start position:0% +upsetting go to the first excited state + + + align:start position:0% +upsetting go to the first excited state +with angular momentum the nals 2 lals 1 + + align:start position:0% +with angular momentum the nals 2 lals 1 + + + align:start position:0% +with angular momentum the nals 2 lals 1 +m equals 1 State okay so it's got as + + align:start position:0% +m equals 1 State okay so it's got as + + + align:start position:0% +m equals 1 State okay so it's got as +much angular momentum in LZ as + + align:start position:0% +much angular momentum in LZ as + + + align:start position:0% +much angular momentum in LZ as +possible is that thing + + align:start position:0% +possible is that thing + + + align:start position:0% +possible is that thing +moving yeah it's not moving at all and + + align:start position:0% +moving yeah it's not moving at all and + + + align:start position:0% +moving yeah it's not moving at all and +yet we're saying there's a current + + align:start position:0% +yet we're saying there's a current + + + align:start position:0% +yet we're saying there's a current +associated with it an electric current + + align:start position:0% +associated with it an electric current + + + align:start position:0% +associated with it an electric current +and that electric current is inducing a + + align:start position:0% +and that electric current is inducing a + + + align:start position:0% +and that electric current is inducing a +Magnetic Moment all right hand + + align:start position:0% +Magnetic Moment all right hand + + + align:start position:0% +Magnetic Moment all right hand +rule uh maybe via BOS of art if you want + + align:start position:0% +rule uh maybe via BOS of art if you want + + + align:start position:0% +rule uh maybe via BOS of art if you want +to be fancy and that Magnetic Moment you + + align:start position:0% +to be fancy and that Magnetic Moment you + + + align:start position:0% +to be fancy and that Magnetic Moment you +know little current Loop is uh leading + + align:start position:0% +know little current Loop is uh leading + + + align:start position:0% +know little current Loop is uh leading +to this interaction the zon's + + align:start position:0% +to this interaction the zon's + + + align:start position:0% +to this interaction the zon's +interaction yeah we know that it's true + + align:start position:0% +interaction yeah we know that it's true + + + align:start position:0% +interaction yeah we know that it's true +because the experiments show the zamon + + align:start position:0% +because the experiments show the zamon + + + align:start position:0% +because the experiments show the zamon +spitting so it is definitely true that + + align:start position:0% +spitting so it is definitely true that + + + align:start position:0% +spitting so it is definitely true that +there is a Magnetic Moment of this thing + + align:start position:0% +there is a Magnetic Moment of this thing + + + align:start position:0% +there is a Magnetic Moment of this thing +but it's not moving how can that + + align:start position:0% +but it's not moving how can that + + + align:start position:0% +but it's not moving how can that +be so how can there be a current if + + align:start position:0% +be so how can there be a current if + + + align:start position:0% +be so how can there be a current if +nothing is + + align:start position:0% + + + + align:start position:0% + +moving what's the expectation value of + + align:start position:0% +moving what's the expectation value of + + + align:start position:0% +moving what's the expectation value of +the momentum yeah zero yeah but + + align:start position:0% +the momentum yeah zero yeah but + + + align:start position:0% +the momentum yeah zero yeah but +[Laughter] + + align:start position:0% + + + + align:start position:0% + +first of all the world isn't classical + + align:start position:0% +first of all the world isn't classical + + + align:start position:0% +first of all the world isn't classical +you can't use classical intuition okay + + align:start position:0% +you can't use classical intuition okay + + + align:start position:0% +you can't use classical intuition okay +true second of all even if you have like + + align:start position:0% +true second of all even if you have like + + + align:start position:0% +true second of all even if you have like +let's suppose you have a a uniform ring + + align:start position:0% +let's suppose you have a a uniform ring + + + align:start position:0% +let's suppose you have a a uniform ring +of classical charge yes and set it + + align:start position:0% +of classical charge yes and set it + + + align:start position:0% +of classical charge yes and set it +spinning yes that ring is as a ring not + + align:start position:0% +spinning yes that ring is as a ring not + + + align:start position:0% +spinning yes that ring is as a ring not +moving but there's still a current + + align:start position:0% +moving but there's still a current + + + align:start position:0% +moving but there's still a current +Associated so you're saying that the + + align:start position:0% +Associated so you're saying that the + + + align:start position:0% +Associated so you're saying that the +electron is a + + align:start position:0% +electron is a + + + align:start position:0% +electron is a +ring it might sense to think of it that + + align:start position:0% +ring it might sense to think of it that + + + align:start position:0% +ring it might sense to think of it that +if you I like this no this is good it's + + align:start position:0% +if you I like this no this is good it's + + + align:start position:0% +if you I like this no this is good it's +wrong but it's good and the reason the + + align:start position:0% +wrong but it's good and the reason the + + + align:start position:0% +wrong but it's good and the reason the +reason it's good is that you're really + + align:start position:0% +reason it's good is that you're really + + + align:start position:0% +reason it's good is that you're really +pushing your assumptions to try to + + align:start position:0% +pushing your assumptions to try to + + + align:start position:0% +pushing your assumptions to try to +figure out how the experimental data can + + align:start position:0% +figure out how the experimental data can + + + align:start position:0% +figure out how the experimental data can +possibly match and you're saying look we + + align:start position:0% +possibly match and you're saying look we + + + align:start position:0% +possibly match and you're saying look we +have to just reject our intuition our + + align:start position:0% +have to just reject our intuition our + + + align:start position:0% +have to just reject our intuition our +intuition is clearly leading us astray + + align:start position:0% +intuition is clearly leading us astray + + + align:start position:0% +intuition is clearly leading us astray +and I like that that's correct so what + + align:start position:0% +and I like that that's correct so what + + + align:start position:0% +and I like that that's correct so what +we're going to do in the next few + + align:start position:0% +we're going to do in the next few + + + align:start position:0% +we're going to do in the next few +minutes is work through that and try to + + align:start position:0% +minutes is work through that and try to + + + align:start position:0% +minutes is work through that and try to +find the best way to to to phrase that + + align:start position:0% +find the best way to to to phrase that + + + align:start position:0% +find the best way to to to phrase that +your your your strategy is the correct + + align:start position:0% +your your your strategy is the correct + + + align:start position:0% +your your your strategy is the correct +one so let me let me rephrase that + + align:start position:0% +one so let me let me rephrase that + + + align:start position:0% +one so let me let me rephrase that +slightly look um if you have a classical + + align:start position:0% +slightly look um if you have a classical + + + align:start position:0% +slightly look um if you have a classical +uh distribution of charge that + + align:start position:0% +uh distribution of charge that + + + align:start position:0% +uh distribution of charge that +distribution of charge could be a + + align:start position:0% +distribution of charge could be a + + + align:start position:0% +distribution of charge could be a +stationary + + align:start position:0% +stationary + + + align:start position:0% +stationary +distribution right a distribution which + + align:start position:0% +distribution right a distribution which + + + align:start position:0% +distribution right a distribution which +as a distribution of charge doesn't + + align:start position:0% +as a distribution of charge doesn't + + + align:start position:0% +as a distribution of charge doesn't +change in time but each individual + + align:start position:0% +change in time but each individual + + + align:start position:0% +change in time but each individual +charge in that distribution is itself + + align:start position:0% +charge in that distribution is itself + + + align:start position:0% +charge in that distribution is itself +moving the problem here is that we just + + align:start position:0% +moving the problem here is that we just + + + align:start position:0% +moving the problem here is that we just +have the one electron if you ever look + + align:start position:0% +have the one electron if you ever look + + + align:start position:0% +have the one electron if you ever look +you will find the electron at a + + align:start position:0% +you will find the electron at a + + + align:start position:0% +you will find the electron at a +spot but what you're really saying is + + align:start position:0% +spot but what you're really saying is + + + align:start position:0% +spot but what you're really saying is +look it's it's a mistake to think about + + align:start position:0% +look it's it's a mistake to think about + + + align:start position:0% +look it's it's a mistake to think about +the electron having a definite position + + align:start position:0% +the electron having a definite position + + + align:start position:0% +the electron having a definite position +in the first place you just shouldn't + + align:start position:0% +in the first place you just shouldn't + + + align:start position:0% +in the first place you just shouldn't +think about that the best you can say is + + align:start position:0% +think about that the best you can say is + + + align:start position:0% +think about that the best you can say is +it has some probability of being in any + + align:start position:0% +it has some probability of being in any + + + align:start position:0% +it has some probability of being in any +spot so let's work with that let's take + + align:start position:0% +spot so let's work with that let's take + + + align:start position:0% +spot so let's work with that let's take +that idea and let's push it let's see + + align:start position:0% +that idea and let's push it let's see + + + align:start position:0% +that idea and let's push it let's see +how far we can take this idea that the + + align:start position:0% +how far we can take this idea that the + + + align:start position:0% +how far we can take this idea that the +electron has some probability do so + + align:start position:0% +electron has some probability do so + + + align:start position:0% +electron has some probability do so +suppose we have an electron in a + + align:start position:0% +suppose we have an electron in a + + + align:start position:0% +suppose we have an electron in a +stationary state of the colum potential + + align:start position:0% +stationary state of the colum potential + + + align:start position:0% +stationary state of the colum potential +the stationary states are labeled by + + align:start position:0% +the stationary states are labeled by + + + align:start position:0% +the stationary states are labeled by +three integers n l and m and we've + + align:start position:0% +three integers n l and m and we've + + + align:start position:0% +three integers n l and m and we've +written their wave functions there of + + align:start position:0% +written their wave functions there of + + + align:start position:0% +written their wave functions there of +course an infinite number of ways to + + align:start position:0% +course an infinite number of ways to + + + align:start position:0% +course an infinite number of ways to +write in different + + align:start position:0% +write in different + + + align:start position:0% +write in different +notation there are an infinite number of + + align:start position:0% +notation there are an infinite number of + + + align:start position:0% +notation there are an infinite number of +fonts one could use for the + + align:start position:0% +fonts one could use for the + + + align:start position:0% +fonts one could use for the +normalization constant one/ r r n l of L + + align:start position:0% +normalization constant one/ r r n l of L + + + align:start position:0% +normalization constant one/ r r n l of L +or sorry of of little r y LM of theta + + align:start position:0% +or sorry of of little r y LM of theta + + + align:start position:0% +or sorry of of little r y LM of theta +and + + align:start position:0% + + + + align:start position:0% + +F right and I'm going to rewrite this + + align:start position:0% +F right and I'm going to rewrite this + + + align:start position:0% +F right and I'm going to rewrite this +I'm going to expand this out slightly + + align:start position:0% +I'm going to expand this out slightly + + + align:start position:0% +I'm going to expand this out slightly +this is n 1/ r r of r n + + align:start position:0% +this is n 1/ r r of r n + + + align:start position:0% +this is n 1/ r r of r n +l uh and Y LM remember was of the form + + align:start position:0% +l uh and Y LM remember was of the form + + + align:start position:0% +l uh and Y LM remember was of the form +uh p uh L of cosine + + align:start position:0% +uh p uh L of cosine + + + align:start position:0% +uh p uh L of cosine +Theta time e to the i m + + align:start position:0% +Theta time e to the i m + + + align:start position:0% +Theta time e to the i m +f everyone cool with that so I just + + align:start position:0% +f everyone cool with that so I just + + + align:start position:0% +f everyone cool with that so I just +wrote the spherical harmonic as a + + align:start position:0% +wrote the spherical harmonic as a + + + align:start position:0% +wrote the spherical harmonic as a +polinomial in cosine Theta s an + + align:start position:0% +polinomial in cosine Theta s an + + + align:start position:0% +polinomial in cosine Theta s an +exponential in M5 yeah where the one R + + align:start position:0% +exponential in M5 yeah where the one R + + + align:start position:0% +exponential in M5 yeah where the one R +come from on the one over R was um so + + align:start position:0% +come from on the one over R was um so + + + align:start position:0% +come from on the one over R was um so +most people call capital r the whole + + align:start position:0% +most people call capital r the whole + + + align:start position:0% +most people call capital r the whole +thing but this is the pulling out the + + align:start position:0% +thing but this is the pulling out the + + + align:start position:0% +thing but this is the pulling out the +one over R to simplify the radial wave + + align:start position:0% +one over R to simplify the radial wave + + + align:start position:0% +one over R to simplify the radial wave +equation and the reason I prefer writing + + align:start position:0% +equation and the reason I prefer writing + + + align:start position:0% +equation and the reason I prefer writing +it this way is just that this guy + + align:start position:0% +it this way is just that this guy + + + align:start position:0% +it this way is just that this guy +satisfies a simple One D Shing your + + align:start position:0% +satisfies a simple One D Shing your + + + align:start position:0% +satisfies a simple One D Shing your +equation um that was a thing that we + + align:start position:0% +equation um that was a thing that we + + + align:start position:0% +equation um that was a thing that we +called U of R and then I confused the + + align:start position:0% +called U of R and then I confused the + + + align:start position:0% +called U of R and then I confused the +hell out of everyone by calling three + + align:start position:0% +hell out of everyone by calling three + + + align:start position:0% +hell out of everyone by calling three +different things on the board U which + + align:start position:0% +different things on the board U which + + + align:start position:0% +different things on the board U which +was sort of unnecessary so this is the + + align:start position:0% +was sort of unnecessary so this is the + + + align:start position:0% +was sort of unnecessary so this is the +thing that this is the artist previously + + align:start position:0% +thing that this is the artist previously + + + align:start position:0% +thing that this is the artist previously +known as you + + align:start position:0% + + + + align:start position:0% + +um the dude can sing okay um + + align:start position:0% +um the dude can sing okay um + + + align:start position:0% +um the dude can sing okay um +so so the first question I want to ask + + align:start position:0% +so so the first question I want to ask + + + align:start position:0% +so so the first question I want to ask +is so this is a stationary State uh is + + align:start position:0% +is so this is a stationary State uh is + + + align:start position:0% +is so this is a stationary State uh is +the electron + + align:start position:0% +the electron + + + align:start position:0% +the electron +moving no not in any conventional sense + + align:start position:0% +moving no not in any conventional sense + + + align:start position:0% +moving no not in any conventional sense +if you compute the expectation value of + + align:start position:0% +if you compute the expectation value of + + + align:start position:0% +if you compute the expectation value of +the position and you take its time + + align:start position:0% +the position and you take its time + + + align:start position:0% +the position and you take its time +derivative uh this is zero we could do + + align:start position:0% +derivative uh this is zero we could do + + + align:start position:0% +derivative uh this is zero we could do +this either by calculating it or just by + + align:start position:0% +this either by calculating it or just by + + + align:start position:0% +this either by calculating it or just by +observing that it's a stationary State + + align:start position:0% +observing that it's a stationary State + + + align:start position:0% +observing that it's a stationary State +non principle uh it it can't change in + + align:start position:0% +non principle uh it it can't change in + + + align:start position:0% +non principle uh it it can't change in +time + + align:start position:0% +time + + + align:start position:0% +time +okay so this guy is not + + align:start position:0% +okay so this guy is not + + + align:start position:0% +okay so this guy is not +moving in in any conventional + + align:start position:0% +moving in in any conventional + + + align:start position:0% +moving in in any conventional +sense + + align:start position:0% +sense + + + align:start position:0% +sense +okay um so why is there an electric + + align:start position:0% +okay um so why is there an electric + + + align:start position:0% +okay um so why is there an electric +current why do we get the zamon Magnetic + + align:start position:0% +current why do we get the zamon Magnetic + + + align:start position:0% +current why do we get the zamon Magnetic +Moment the Bor + + align:start position:0% +Moment the Bor + + + align:start position:0% +Moment the Bor +Magneton so as was pointed out look this + + align:start position:0% +Magneton so as was pointed out look this + + + align:start position:0% +Magneton so as was pointed out look this +is quantum mechanics it's not classical + + align:start position:0% +is quantum mechanics it's not classical + + + align:start position:0% +is quantum mechanics it's not classical +mechanics and um in quantum mechanics + + align:start position:0% +mechanics and um in quantum mechanics + + + align:start position:0% +mechanics and um in quantum mechanics +the electron isn't isn't at any + + align:start position:0% + + + + align:start position:0% + +point rather there's some probability + + align:start position:0% +point rather there's some probability + + + align:start position:0% +point rather there's some probability +density and the probability density that + + align:start position:0% +density and the probability density that + + + align:start position:0% +density and the probability density that +we find the electron at some + + align:start position:0% +we find the electron at some + + + align:start position:0% +we find the electron at some +point + + align:start position:0% +point + + + align:start position:0% +point +R is s squ + + align:start position:0% + + + + align:start position:0% + +nlm of r squared okay familiar + + align:start position:0% +nlm of r squared okay familiar + + + align:start position:0% +nlm of r squared okay familiar +beast and meanwhile a wonderful thing + + align:start position:0% +beast and meanwhile a wonderful thing + + + align:start position:0% +beast and meanwhile a wonderful thing +about the probability distribution in + + align:start position:0% +about the probability distribution in + + + align:start position:0% +about the probability distribution in +Quant mechanics that we've already + + align:start position:0% +Quant mechanics that we've already + + + align:start position:0% +Quant mechanics that we've already +discussed here is that it's conserved + + align:start position:0% +discussed here is that it's conserved + + + align:start position:0% +discussed here is that it's conserved +the time derivative of of the + + align:start position:0% +the time derivative of of the + + + align:start position:0% +the time derivative of of the +probability density of R remember this + + align:start position:0% +probability density of R remember this + + + align:start position:0% +probability density of R remember this +is a density not a probability time + + align:start position:0% +is a density not a probability time + + + align:start position:0% +is a density not a probability time +depend the time rate of change of the + + align:start position:0% +depend the time rate of change of the + + + align:start position:0% +depend the time rate of change of the +probability uh distribution is minus the + + align:start position:0% +probability uh distribution is minus the + + + align:start position:0% +probability uh distribution is minus the +gradient or sorry the gradient the + + align:start position:0% +gradient or sorry the gradient the + + + align:start position:0% +gradient or sorry the gradient the +Divergence of the probability current + + align:start position:0% +Divergence of the probability current + + + align:start position:0% +Divergence of the probability current +where the probability current + + align:start position:0% +where the probability current + + + align:start position:0% +where the probability current +J is equal to H + + align:start position:0% +J is equal to H + + + align:start position:0% +J is equal to H +bar over uh the the uh Mass which I'm + + align:start position:0% +bar over uh the the uh Mass which I'm + + + align:start position:0% +bar over uh the the uh Mass which I'm +going to call the mass mu oh gee I don't + + align:start position:0% +going to call the mass mu oh gee I don't + + + align:start position:0% +going to call the mass mu oh gee I don't +want to I'm going to call the mass + + align:start position:0% +want to I'm going to call the mass + + + align:start position:0% +want to I'm going to call the mass +capital M okay that's the mass of the + + align:start position:0% +capital M okay that's the mass of the + + + align:start position:0% +capital M okay that's the mass of the +electron um which a little strange + + align:start position:0% +electron um which a little strange + + + align:start position:0% +electron um which a little strange +because it's a very small quantity but + + align:start position:0% +because it's a very small quantity but + + + align:start position:0% +because it's a very small quantity but +anyway H over capital M uh of the + + align:start position:0% +anyway H over capital M uh of the + + + align:start position:0% +anyway H over capital M uh of the +imaginary part of s complex conjugant + + align:start position:0% +imaginary part of s complex conjugant + + + align:start position:0% +imaginary part of s complex conjugant +gradient + + align:start position:0% +gradient + + + align:start position:0% +gradient +s okay and you showed on a problem set + + align:start position:0% +s okay and you showed on a problem set + + + align:start position:0% +s okay and you showed on a problem set +long ago that this is true if J takes + + align:start position:0% +long ago that this is true if J takes + + + align:start position:0% +long ago that this is true if J takes +this form by virtue of the shinger + + align:start position:0% +this form by virtue of the shinger + + + align:start position:0% +this form by virtue of the shinger +equation okay now we usually write this + + align:start position:0% +equation okay now we usually write this + + + align:start position:0% +equation okay now we usually write this +imaginary 1 over 2 I * s gradient or S + + align:start position:0% +imaginary 1 over 2 I * s gradient or S + + + align:start position:0% +imaginary 1 over 2 I * s gradient or S +star gradient s minus s gradient s star + + align:start position:0% +star gradient s minus s gradient s star + + + align:start position:0% +star gradient s minus s gradient s star +but that's equal to the imaginary part + + align:start position:0% +but that's equal to the imaginary part + + + align:start position:0% +but that's equal to the imaginary part +of the first term okay thing I want to + + align:start position:0% +of the first term okay thing I want to + + + align:start position:0% +of the first term okay thing I want to +emphasize is the imaginary + + align:start position:0% + + + + align:start position:0% + +part so we have this current in our + + align:start position:0% +part so we have this current in our + + + align:start position:0% +part so we have this current in our +system the position expectation value is + + align:start position:0% +system the position expectation value is + + + align:start position:0% +system the position expectation value is +time independent and indeed it's a + + align:start position:0% +time independent and indeed it's a + + + align:start position:0% +time independent and indeed it's a +stationary state so beyond the position + + align:start position:0% +stationary state so beyond the position + + + align:start position:0% +stationary state so beyond the position +expectation to value of being time + + align:start position:0% +expectation to value of being time + + + align:start position:0% +expectation to value of being time +independent the probability dens density + + align:start position:0% +independent the probability dens density + + + align:start position:0% +independent the probability dens density +itself is time independent because the + + align:start position:0% +itself is time independent because the + + + align:start position:0% +itself is time independent because the +wave function evolves by an overall + + align:start position:0% +wave function evolves by an overall + + + align:start position:0% +wave function evolves by an overall +phase and the probability density is the + + align:start position:0% +phase and the probability density is the + + + align:start position:0% +phase and the probability density is the +norm Square so the phase goes away so in + + align:start position:0% +norm Square so the phase goes away so in + + + align:start position:0% +norm Square so the phase goes away so in +our situ in our system in an electron in + + align:start position:0% +our situ in our system in an electron in + + + align:start position:0% +our situ in our system in an electron in +this state in the potential the + + align:start position:0% +this state in the potential the + + + align:start position:0% +this state in the potential the +time rate of change of the potential of + + align:start position:0% +time rate of change of the potential of + + + align:start position:0% +time rate of change of the potential of +the probability density let me actually + + align:start position:0% +the probability density let me actually + + + align:start position:0% +the probability density let me actually +do this over + + align:start position:0% + + + + align:start position:0% + +here so in the stationary + + align:start position:0% + + + + align:start position:0% + +State s LM + + align:start position:0% + + + + align:start position:0% + +the time rate of change of the density + + align:start position:0% +the time rate of change of the density + + + align:start position:0% +the time rate of change of the density +is zero and this tells us by the + + align:start position:0% +is zero and this tells us by the + + + align:start position:0% +is zero and this tells us by the +conservation equation that the + + align:start position:0% +conservation equation that the + + + align:start position:0% +conservation equation that the +Divergence of the current is also zero + + align:start position:0% +Divergence of the current is also zero + + + align:start position:0% +Divergence of the current is also zero +does that tell us that the current is + + align:start position:0% +does that tell us that the current is + + + align:start position:0% +does that tell us that the current is +zero right so what's the + + align:start position:0% + + + + align:start position:0% + +current well we've written everything + + align:start position:0% +current well we've written everything + + + align:start position:0% +current well we've written everything +here in spherical coordinates and the uh + + align:start position:0% +here in spherical coordinates and the uh + + + align:start position:0% +here in spherical coordinates and the uh +gradient the current is given in terms + + align:start position:0% +gradient the current is given in terms + + + align:start position:0% +gradient the current is given in terms +of the gradient operator so let's um let + + align:start position:0% +of the gradient operator so let's um let + + + align:start position:0% +of the gradient operator so let's um let +me remind you quickly of what the + + align:start position:0% +me remind you quickly of what the + + + align:start position:0% +me remind you quickly of what the +gradient operator is in spherical + + align:start position:0% +gradient operator is in spherical + + + align:start position:0% +gradient operator is in spherical +coordinates it has three components a + + align:start position:0% +coordinates it has three components a + + + align:start position:0% +coordinates it has three components a +radial component a a Theta component and + + align:start position:0% +radial component a a Theta component and + + + align:start position:0% +radial component a a Theta component and +then a fi component okay and the radial + + align:start position:0% +then a fi component okay and the radial + + + align:start position:0% +then a fi component okay and the radial +Co the radial part is just Dr + + align:start position:0% +Co the radial part is just Dr + + + align:start position:0% +Co the radial part is just Dr +R the Theta component is 1 / r d + + align:start position:0% +R the Theta component is 1 / r d + + + align:start position:0% +R the Theta component is 1 / r d +Theta and the FI around the equator + + align:start position:0% +Theta and the FI around the equator + + + align:start position:0% +Theta and the FI around the equator +component is equal to 1 / R sin Theta + + align:start position:0% + + + + align:start position:0% + +D5 everyone call + + align:start position:0% +D5 everyone call + + + align:start position:0% +D5 everyone call +that so what's J well J is going to have + + align:start position:0% +that so what's J well J is going to have + + + align:start position:0% +that so what's J well J is going to have +a component J uh in the radial Direction + + align:start position:0% +a component J uh in the radial Direction + + + align:start position:0% +a component J uh in the radial Direction +the current in the radial Direction and + + align:start position:0% +the current in the radial Direction and + + + align:start position:0% +the current in the radial Direction and +intuitively what should that be is there + + align:start position:0% +intuitively what should that be is there + + + align:start position:0% +intuitively what should that be is there +stuff going out or + + align:start position:0% +stuff going out or + + + align:start position:0% +stuff going out or +in shouldn't be it's uh hydrogen right + + align:start position:0% +in shouldn't be it's uh hydrogen right + + + align:start position:0% +in shouldn't be it's uh hydrogen right +it nothing it's not doing this so this + + align:start position:0% +it nothing it's not doing this so this + + + align:start position:0% +it nothing it's not doing this so this +should be zero and we can just quickly + + align:start position:0% +should be zero and we can just quickly + + + align:start position:0% +should be zero and we can just quickly +see that this is H bar upon M imaginary + + align:start position:0% +see that this is H bar upon M imaginary + + + align:start position:0% +see that this is H bar upon M imaginary +part of well this is the r component + + align:start position:0% +part of well this is the r component + + + align:start position:0% +part of well this is the r component +it's going to be the derivative in the + + align:start position:0% +it's going to be the derivative in the + + + align:start position:0% +it's going to be the derivative in the +radial Direction but the derivative in + + align:start position:0% +radial Direction but the derivative in + + + align:start position:0% +radial Direction but the derivative in +the radial + + align:start position:0% +the radial + + + align:start position:0% +the radial +direction is going to be + + align:start position:0% +direction is going to be + + + align:start position:0% +direction is going to be +real right the derivative in the ra + + align:start position:0% +real right the derivative in the ra + + + align:start position:0% +real right the derivative in the ra +radial direction is going to be real so + + align:start position:0% +radial direction is going to be real so + + + align:start position:0% +radial direction is going to be real so +when we take the norm squared we don't + + align:start position:0% +when we take the norm squared we don't + + + align:start position:0% +when we take the norm squared we don't +pick up anything we pick up an overall + + align:start position:0% +pick up anything we pick up an overall + + + align:start position:0% +pick up anything we pick up an overall +coefficient it's going to be strictly + + align:start position:0% +coefficient it's going to be strictly + + + align:start position:0% +coefficient it's going to be strictly +real the phase e to the IM5 cancels out + + align:start position:0% +real the phase e to the IM5 cancels out + + + align:start position:0% +real the phase e to the IM5 cancels out +because this is the complex conjugate so + + align:start position:0% +because this is the complex conjugate so + + + align:start position:0% +because this is the complex conjugate so +the imaginary part of this thing is + + align:start position:0% +the imaginary part of this thing is + + + align:start position:0% +the imaginary part of this thing is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +zero Okay so R is + + align:start position:0% +zero Okay so R is + + + align:start position:0% +zero Okay so R is +zero and + + align:start position:0% +zero and + + + align:start position:0% +zero and +similarly uh J + + align:start position:0% +similarly uh J + + + align:start position:0% +similarly uh J +Theta p is a real function when we take + + align:start position:0% +Theta p is a real function when we take + + + align:start position:0% +Theta p is a real function when we take +a derivative we get a real function and + + align:start position:0% +a derivative we get a real function and + + + align:start position:0% +a derivative we get a real function and +then when we multiply by its complex + + align:start position:0% +then when we multiply by its complex + + + align:start position:0% +then when we multiply by its complex +conjugate again the phase cancels out we + + align:start position:0% +conjugate again the phase cancels out we + + + align:start position:0% +conjugate again the phase cancels out we +just get a whole bunch of real + + align:start position:0% +just get a whole bunch of real + + + align:start position:0% +just get a whole bunch of real +stuff whose imaginary piece is zero so J + + align:start position:0% +stuff whose imaginary piece is zero so J + + + align:start position:0% +stuff whose imaginary piece is zero so J +F J Theta is zero but JF is the cool + + align:start position:0% + + + + align:start position:0% + +one in my head I was just thinking J5 + + align:start position:0% +one in my head I was just thinking J5 + + + align:start position:0% +one in my head I was just thinking J5 +but um + + align:start position:0% +but um + + + align:start position:0% +but um +uh good okay at least someone got that + + align:start position:0% +uh good okay at least someone got that + + + align:start position:0% +uh good okay at least someone got that +um + + align:start position:0% +um + + + align:start position:0% +um +so um so + + align:start position:0% +so um so + + + align:start position:0% +so um so +JF uh however is not going to be zero + + align:start position:0% +JF uh however is not going to be zero + + + align:start position:0% +JF uh however is not going to be zero +for the following reasons so what is it + + align:start position:0% +for the following reasons so what is it + + + align:start position:0% +for the following reasons so what is it +equal to it's equal to H bar upon M the + + align:start position:0% +equal to it's equal to H bar upon M the + + + align:start position:0% +equal to it's equal to H bar upon M the +mass m uh times the imaginary + + align:start position:0% +mass m uh times the imaginary + + + align:start position:0% +mass m uh times the imaginary +part of well s star which is you know s + + align:start position:0% +part of well s star which is you know s + + + align:start position:0% +part of well s star which is you know s +complex conjugate uh and then the + + align:start position:0% +complex conjugate uh and then the + + + align:start position:0% +complex conjugate uh and then the +gradient with respect to + + align:start position:0% +gradient with respect to + + + align:start position:0% +gradient with respect to +F the F component is 1 R sin + + align:start position:0% +F the F component is 1 R sin + + + align:start position:0% +F the F component is 1 R sin +Theta and then deriva with respect to + + align:start position:0% +Theta and then deriva with respect to + + + align:start position:0% +Theta and then deriva with respect to +but the Der respect to five pulls down + + align:start position:0% +but the Der respect to five pulls down + + + align:start position:0% +but the Der respect to five pulls down +a I + + align:start position:0% +a I + + + align:start position:0% +a I +am oh look times + + align:start position:0% +am oh look times + + + align:start position:0% +am oh look times +s which is equal to H upon M times Well + + align:start position:0% +s which is equal to H upon M times Well + + + align:start position:0% +s which is equal to H upon M times Well +s Norm squar that's real s^ squ 1 / R + + align:start position:0% +s Norm squar that's real s^ squ 1 / R + + + align:start position:0% +s Norm squar that's real s^ squ 1 / R +sin Theta that's real so I can pull that + + align:start position:0% +sin Theta that's real so I can pull that + + + align:start position:0% +sin Theta that's real so I can pull that +out and we are left with um imaginary + + align:start position:0% +out and we are left with um imaginary + + + align:start position:0% +out and we are left with um imaginary +part of I which is just m + + align:start position:0% + + + + align:start position:0% + +which is not zero and in particular it's + + align:start position:0% +which is not zero and in particular it's + + + align:start position:0% +which is not zero and in particular it's +proportional to + + align:start position:0% + + + + align:start position:0% + +hm everyone see + + align:start position:0% +hm everyone see + + + align:start position:0% +hm everyone see +that so what this is + + align:start position:0% +that so what this is + + + align:start position:0% +that so what this is +saying is that the + + align:start position:0% +saying is that the + + + align:start position:0% +saying is that the +current the probability current for an + + align:start position:0% +current the probability current for an + + + align:start position:0% +current the probability current for an +electron in the stationary State s nlm + + align:start position:0% +electron in the stationary State s nlm + + + align:start position:0% +electron in the stationary State s nlm +of the coolum potential is equal to uh + + align:start position:0% +of the coolum potential is equal to uh + + + align:start position:0% +of the coolum potential is equal to uh +Norm s^ + + align:start position:0% +Norm s^ + + + align:start position:0% +Norm s^ +squ over m r sin + + align:start position:0% +squ over m r sin + + + align:start position:0% +squ over m r sin +Theta H Bar + + align:start position:0% +Theta H Bar + + + align:start position:0% +Theta H Bar +M in the F Direction + + align:start position:0% +M in the F Direction + + + align:start position:0% +M in the F Direction +e unit + + align:start position:0% +e unit + + + align:start position:0% +e unit +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +cool so nothing is moving but there's a + + align:start position:0% + + + + align:start position:0% + +current what is + + align:start position:0% + + + + align:start position:0% + +moving what is the thing of whose + + align:start position:0% +moving what is the thing of whose + + + align:start position:0% +moving what is the thing of whose +current of whom this is the + + align:start position:0% +current of whom this is the + + + align:start position:0% +current of whom this is the +current the probability density the + + align:start position:0% +current the probability density the + + + align:start position:0% +current the probability density the +probability + + align:start position:0% +probability + + + align:start position:0% +probability +density is + + align:start position:0% +density is + + + align:start position:0% +density is +rotating so what this is telling + + align:start position:0% + + + + align:start position:0% + +us is that it's true the system is + + align:start position:0% +us is that it's true the system is + + + align:start position:0% +us is that it's true the system is +stationary but I want to now I'm looking + + align:start position:0% +stationary but I want to now I'm looking + + + align:start position:0% +stationary but I want to now I'm looking +down at the the equatorial + + align:start position:0% +down at the the equatorial + + + align:start position:0% +down at the the equatorial +plane okay so this plot is going to be + + align:start position:0% +plane okay so this plot is going to be + + + align:start position:0% +plane okay so this plot is going to be +looking down on the equatorial plane uh + + align:start position:0% +looking down on the equatorial plane uh + + + align:start position:0% +looking down on the equatorial plane uh +of hydrogen here's the origin the center + + align:start position:0% +of hydrogen here's the origin the center + + + align:start position:0% +of hydrogen here's the origin the center +of the potential and what the is telling + + align:start position:0% +of the potential and what the is telling + + + align:start position:0% +of the potential and what the is telling +us I'm going to draw these vectors + + align:start position:0% +us I'm going to draw these vectors + + + align:start position:0% +us I'm going to draw these vectors +they're in the EI + + align:start position:0% + + + + align:start position:0% + +Direction okay but their magnitude falls + + align:start position:0% +Direction okay but their magnitude falls + + + align:start position:0% +Direction okay but their magnitude falls +off with 1 / R and the norm square of + + align:start position:0% +off with 1 / R and the norm square of + + + align:start position:0% +off with 1 / R and the norm square of +the wave function which also is falling + + align:start position:0% +the wave function which also is falling + + + align:start position:0% +the wave function which also is falling +off exponentially and it goes to zero at + + align:start position:0% +off exponentially and it goes to zero at + + + align:start position:0% +off exponentially and it goes to zero at +the origin as R the L + 1 and M must be + + align:start position:0% +the origin as R the L + 1 and M must be + + + align:start position:0% +the origin as R the L + 1 and M must be +at least uh must be no bigger than l so + + align:start position:0% +at least uh must be no bigger than l so + + + align:start position:0% +at least uh must be no bigger than l so +in order for M to be non zero L must be + + align:start position:0% +in order for M to be non zero L must be + + + align:start position:0% +in order for M to be non zero L must be +non zero which means this must go like R + + align:start position:0% +non zero which means this must go like R + + + align:start position:0% +non zero which means this must go like R +to the something greater than m + 1 so + + align:start position:0% +to the something greater than m + 1 so + + + align:start position:0% +to the something greater than m + 1 so +the RS cancel out we have it that it + + align:start position:0% +the RS cancel out we have it that it + + + align:start position:0% +the RS cancel out we have it that it +vanishes so the contribution vanishes at + + align:start position:0% +vanishes so the contribution vanishes at + + + align:start position:0% +vanishes so the contribution vanishes at +the origin is small near the + + align:start position:0% + + + + align:start position:0% + +origin is largest at some radius and + + align:start position:0% +origin is largest at some radius and + + + align:start position:0% +origin is largest at some radius and +then falls off again so the magnitude of + + align:start position:0% +then falls off again so the magnitude of + + + align:start position:0% +then falls off again so the magnitude of +the arrow here is meant to indicate the + + align:start position:0% +the arrow here is meant to indicate the + + + align:start position:0% +the arrow here is meant to indicate the +magnitude of the + + align:start position:0% + + + + align:start position:0% + +flux so what we see is that we have a + + align:start position:0% +flux so what we see is that we have a + + + align:start position:0% +flux so what we see is that we have a +dist probability distribution + + align:start position:0% +dist probability distribution + + + align:start position:0% +dist probability distribution +where the + + align:start position:0% +where the + + + align:start position:0% +where the +probability as a distribution is time + + align:start position:0% +probability as a distribution is time + + + align:start position:0% +probability as a distribution is time +independent uh right the probability + + align:start position:0% +independent uh right the probability + + + align:start position:0% +independent uh right the probability +distribution is in fact time independent + + align:start position:0% +distribution is in fact time independent + + + align:start position:0% +distribution is in fact time independent +but there's a current which is a + + align:start position:0% +but there's a current which is a + + + align:start position:0% +but there's a current which is a +persistent stationary + + align:start position:0% + + + + align:start position:0% + +current everyone cool with that so if I + + align:start position:0% +current everyone cool with that so if I + + + align:start position:0% +current everyone cool with that so if I +ask you where is the particle well the + + align:start position:0% +ask you where is the particle well the + + + align:start position:0% +ask you where is the particle well the +probability density tells you that and + + align:start position:0% +probability density tells you that and + + + align:start position:0% +probability density tells you that and +if I ask you what's the current the + + align:start position:0% +if I ask you what's the current the + + + align:start position:0% +if I ask you what's the current the +electric current + + align:start position:0% + + + + align:start position:0% + +minus E * + + align:start position:0% +minus E * + + + align:start position:0% +minus E * +J okay at a point and this is really the + + align:start position:0% +J okay at a point and this is really the + + + align:start position:0% +J okay at a point and this is really the +current density and the probability + + align:start position:0% +current density and the probability + + + align:start position:0% +current density and the probability +current + + align:start position:0% +current + + + align:start position:0% +current +density now what is the consequence of + + align:start position:0% +density now what is the consequence of + + + align:start position:0% +density now what is the consequence of +the of the statement that the + + align:start position:0% +the of the statement that the + + + align:start position:0% +the of the statement that the +probability is not the probability + + align:start position:0% +probability is not the probability + + + align:start position:0% +probability is not the probability +density itself is not changing in time + + align:start position:0% +density itself is not changing in time + + + align:start position:0% +density itself is not changing in time +it's that that there's zero Divergence + + align:start position:0% +it's that that there's zero Divergence + + + align:start position:0% +it's that that there's zero Divergence +of this current and indeed there is zero + + align:start position:0% +of this current and indeed there is zero + + + align:start position:0% +of this current and indeed there is zero +Divergence every little bit going into a + + align:start position:0% +Divergence every little bit going into a + + + align:start position:0% +Divergence every little bit going into a +spot is matched by some equivalent + + align:start position:0% +spot is matched by some equivalent + + + align:start position:0% +spot is matched by some equivalent +amount going out there's zero Divergence + + align:start position:0% +amount going out there's zero Divergence + + + align:start position:0% +amount going out there's zero Divergence +cool and so we + + align:start position:0% +cool and so we + + + align:start position:0% +cool and so we +see and so we see that + + align:start position:0% +see and so we see that + + + align:start position:0% +see and so we see that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um that while it's true that nothing is + + align:start position:0% +um that while it's true that nothing is + + + align:start position:0% +um that while it's true that nothing is +moving it is also true that there is a + + align:start position:0% +moving it is also true that there is a + + + align:start position:0% +moving it is also true that there is a +non-trivial electric current and when + + align:start position:0% +non-trivial electric current and when + + + align:start position:0% +non-trivial electric current and when +you use the bosar law to sum up the + + align:start position:0% +you use the bosar law to sum up the + + + align:start position:0% +you use the bosar law to sum up the +contributions from each little bit of + + align:start position:0% +contributions from each little bit of + + + align:start position:0% +contributions from each little bit of +this current what you get + + align:start position:0% +this current what you get + + + align:start position:0% +this current what you get +is right hand rule a magnetic field a + + align:start position:0% +is right hand rule a magnetic field a + + + align:start position:0% +is right hand rule a magnetic field a +magnetic moment and following nothing + + align:start position:0% +magnetic moment and following nothing + + + align:start position:0% +magnetic moment and following nothing +but the BOS of law and using what you + + align:start position:0% +but the BOS of law and using what you + + + align:start position:0% +but the BOS of law and using what you +know about the wave functions um this + + align:start position:0% +know about the wave functions um this + + + align:start position:0% +know about the wave functions um this +gives us that the Magnetic Moment uh is + + align:start position:0% +gives us that the Magnetic Moment uh is + + + align:start position:0% +gives us that the Magnetic Moment uh is +equal to the bore + + align:start position:0% +equal to the bore + + + align:start position:0% +equal to the bore +Magneton B * + + align:start position:0% + + + + align:start position:0% + +m + + align:start position:0% +m + + + align:start position:0% +m +z okay everyone cool with that yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +um well here's one way to say it there + + align:start position:0% +um well here's one way to say it there + + + align:start position:0% +um well here's one way to say it there +are two let me let me rephrase that + + align:start position:0% +are two let me let me rephrase that + + + align:start position:0% +are two let me let me rephrase that +question let me give you let me tell you + + align:start position:0% +question let me give you let me tell you + + + align:start position:0% +question let me give you let me tell you +a different question to ask and then + + align:start position:0% +a different question to ask and then + + + align:start position:0% +a different question to ask and then +let's think about the answers to that + + align:start position:0% +let's think about the answers to that + + + align:start position:0% +let's think about the answers to that +question and I and I hope that will + + align:start position:0% +question and I and I hope that will + + + align:start position:0% +question and I and I hope that will +answer your question if it doesn't ask + + align:start position:0% +answer your question if it doesn't ask + + + align:start position:0% +answer your question if it doesn't ask +it again so here's the question I would + + align:start position:0% +it again so here's the question I would + + + align:start position:0% +it again so here's the question I would +suggest that you + + align:start position:0% +suggest that you + + + align:start position:0% +suggest that you +ask or that someone ask I'll ask it + + align:start position:0% + + + + align:start position:0% + +um and I just totally lost my train of + + align:start position:0% +um and I just totally lost my train of + + + align:start position:0% +um and I just totally lost my train of +thought that's totally + + align:start position:0% +thought that's totally + + + align:start position:0% +thought that's totally +what was the question I wanted you to + + align:start position:0% +what was the question I wanted you to + + + align:start position:0% +what was the question I wanted you to +ask wow that's amazing I completely just + + align:start position:0% +ask wow that's amazing I completely just + + + align:start position:0% +ask wow that's amazing I completely just +in the blink of an eye totally lost my + + align:start position:0% +in the blink of an eye totally lost my + + + align:start position:0% +in the blink of an eye totally lost my +train of ah yes um so here it was + + align:start position:0% +train of ah yes um so here it was + + + align:start position:0% +train of ah yes um so here it was +crucial in this calculation that the + + align:start position:0% +crucial in this calculation that the + + + align:start position:0% +crucial in this calculation that the +current was given by the imaginary part + + align:start position:0% +current was given by the imaginary part + + + align:start position:0% +current was given by the imaginary part +of the gradient and as you showed in a + + align:start position:0% +of the gradient and as you showed in a + + + align:start position:0% +of the gradient and as you showed in a +problem set a while back um anytime you + + align:start position:0% +problem set a while back um anytime you + + + align:start position:0% +problem set a while back um anytime you +have a wave function which is real + + align:start position:0% +have a wave function which is real + + + align:start position:0% +have a wave function which is real +anytime you have a wave function which + + align:start position:0% +anytime you have a wave function which + + + align:start position:0% +anytime you have a wave function which +is real then the uh current will vanish + + align:start position:0% +is real then the uh current will vanish + + + align:start position:0% +is real then the uh current will vanish +here it was crucial in order to get a + + align:start position:0% +here it was crucial in order to get a + + + align:start position:0% +here it was crucial in order to get a +nonvanishing current it was crucial that + + align:start position:0% +nonvanishing current it was crucial that + + + align:start position:0% +nonvanishing current it was crucial that +the wave function was not real it had a + + align:start position:0% +the wave function was not real it had a + + + align:start position:0% +the wave function was not real it had a +phase right but you also showed on a + + align:start position:0% +phase right but you also showed on a + + + align:start position:0% +phase right but you also showed on a +problem set that you can always take + + align:start position:0% +problem set that you can always take + + + align:start position:0% +problem set that you can always take +your energy functions for bounce States + + align:start position:0% +your energy functions for bounce States + + + align:start position:0% +your energy functions for bounce States +you can always take energy functions and + + align:start position:0% +you can always take energy functions and + + + align:start position:0% +you can always take energy functions and +make them real you can always construct + + align:start position:0% +make them real you can always construct + + + align:start position:0% +make them real you can always construct +a basis of energy functions which are + + align:start position:0% +a basis of energy functions which are + + + align:start position:0% +a basis of energy functions which are +strictly + + align:start position:0% +strictly + + + align:start position:0% +strictly +real sorry in one dimension right yeah + + align:start position:0% +real sorry in one dimension right yeah + + + align:start position:0% +real sorry in one dimension right yeah +well also what what did you use for that + + align:start position:0% +well also what what did you use for that + + + align:start position:0% +well also what what did you use for that +proof just use linear combinations the + + align:start position:0% +proof just use linear combinations the + + + align:start position:0% +proof just use linear combinations the +yeah you just use the energy I value + + align:start position:0% +yeah you just use the energy I value + + + align:start position:0% +yeah you just use the energy I value +equation hermeticity and uh linear the + + align:start position:0% +equation hermeticity and uh linear the + + + align:start position:0% +equation hermeticity and uh linear the +linearity of the energy op and that's + + align:start position:0% +linearity of the energy op and that's + + + align:start position:0% +linearity of the energy op and that's +perfectly true in any number of + + align:start position:0% +perfectly true in any number of + + + align:start position:0% +perfectly true in any number of +Dimensions so that sounds crazy so first + + align:start position:0% +Dimensions so that sounds crazy so first + + + align:start position:0% +Dimensions so that sounds crazy so first +off why do we have a not real energy + + align:start position:0% +off why do we have a not real energy + + + align:start position:0% +off why do we have a not real energy +igen function can we construct purely + + align:start position:0% +igen function can we construct purely + + + align:start position:0% +igen function can we construct purely +real energy IG functions if we can those + + align:start position:0% +real energy IG functions if we can those + + + align:start position:0% +real energy IG functions if we can those +energy igen functions would appear to + + align:start position:0% +energy igen functions would appear to + + + align:start position:0% +energy igen functions would appear to +have no current so they would have no + + align:start position:0% +have no current so they would have no + + + align:start position:0% +have no current so they would have no +Magnetic Moment how do these fit + + align:start position:0% + + + + align:start position:0% + +together can you construct energy igen + + align:start position:0% +together can you construct energy igen + + + align:start position:0% +together can you construct energy igen +functions that are pure real for this + + align:start position:0% +functions that are pure real for this + + + align:start position:0% +functions that are pure real for this +system for the coolant + + align:start position:0% + + + + align:start position:0% + +potential let me give you a hint in 1D + + align:start position:0% +potential let me give you a hint in 1D + + + align:start position:0% +potential let me give you a hint in 1D +for a free particle what are the energy + + align:start position:0% +for a free particle what are the energy + + + align:start position:0% +for a free particle what are the energy +functions + + align:start position:0% +functions + + + align:start position:0% +functions +1D e to the IX right that's not + + align:start position:0% +1D e to the IX right that's not + + + align:start position:0% +1D e to the IX right that's not +real but there's another igen function e + + align:start position:0% +real but there's another igen function e + + + align:start position:0% +real but there's another igen function e +to the minus IX and if you take the sum + + align:start position:0% +to the minus IX and if you take the sum + + + align:start position:0% +to the minus IX and if you take the sum +of those you get e to the IX plus e to + + align:start position:0% +of those you get e to the IX plus e to + + + align:start position:0% +of those you get e to the IX plus e to +the minus IX and let divide by two for + + align:start position:0% +the minus IX and let divide by two for + + + align:start position:0% +the minus IX and let divide by two for +fun and that gives you cosine of KX + + align:start position:0% +fun and that gives you cosine of KX + + + align:start position:0% +fun and that gives you cosine of KX +that's real but there's a second one + + align:start position:0% +that's real but there's a second one + + + align:start position:0% +that's real but there's a second one +which is s of KX which is also real now + + align:start position:0% +which is s of KX which is also real now + + + align:start position:0% +which is s of KX which is also real now +you can take linear combinations of them + + align:start position:0% +you can take linear combinations of them + + + align:start position:0% +you can take linear combinations of them +with I and get the exponentials back but + + align:start position:0% +with I and get the exponentials back but + + + align:start position:0% +with I and get the exponentials back but +let's just take the real part right now + + align:start position:0% +let's just take the real part right now + + + align:start position:0% +let's just take the real part right now +do those carry any momentum what's the + + align:start position:0% +do those carry any momentum what's the + + + align:start position:0% +do those carry any momentum what's the +momentum expectation value for cosine of + + align:start position:0% +momentum expectation value for cosine of + + + align:start position:0% +momentum expectation value for cosine of +KX zero because you get a contribution + + align:start position:0% +KX zero because you get a contribution + + + align:start position:0% +KX zero because you get a contribution +from plus K and one from minus K they + + align:start position:0% +from plus K and one from minus K they + + + align:start position:0% +from plus K and one from minus K they +exactly cancel now look at this + + align:start position:0% +exactly cancel now look at this + + + align:start position:0% +exactly cancel now look at this +solution can you construct a real energy + + align:start position:0% +solution can you construct a real energy + + + align:start position:0% +solution can you construct a real energy +igen function of the coolant potential + + align:start position:0% +igen function of the coolant potential + + + align:start position:0% +igen function of the coolant potential +how + + align:start position:0% + + + + align:start position:0% + +great let's take this and its complex + + align:start position:0% +great let's take this and its complex + + + align:start position:0% +great let's take this and its complex +conjugate so what would that be well if + + align:start position:0% +conjugate so what would that be well if + + + align:start position:0% +conjugate so what would that be well if +we take this s n LM and its complex + + align:start position:0% +we take this s n LM and its complex + + + align:start position:0% +we take this s n LM and its complex +conjugate well what is its complex + + align:start position:0% +conjugate well what is its complex + + + align:start position:0% +conjugate well what is its complex +conjugate these are real that just gives + + align:start position:0% +conjugate these are real that just gives + + + align:start position:0% +conjugate these are real that just gives +me a minus so that's the state plus s n + + align:start position:0% +me a minus so that's the state plus s n + + + align:start position:0% +me a minus so that's the state plus s n +l minus M which is also an allow state + + align:start position:0% +l minus M which is also an allow state + + + align:start position:0% +l minus M which is also an allow state +with the same energy by rotational + + align:start position:0% +with the same energy by rotational + + + align:start position:0% +with the same energy by rotational +invariance and this is thus the state s + + align:start position:0% +invariance and this is thus the state s + + + align:start position:0% +invariance and this is thus the state s +NL and it doesn't have a definite LZ + + align:start position:0% +NL and it doesn't have a definite LZ + + + align:start position:0% +NL and it doesn't have a definite LZ +angular momentum right so I'll just call + + align:start position:0% +angular momentum right so I'll just call + + + align:start position:0% +angular momentum right so I'll just call +it SC sub + + align:start position:0% +it SC sub + + + align:start position:0% +it SC sub +NL you know unhappy face um it is not an + + align:start position:0% +NL you know unhappy face um it is not an + + + align:start position:0% +NL you know unhappy face um it is not an +LZ function but it is an energy function + + align:start position:0% +LZ function but it is an energy function + + + align:start position:0% +LZ function but it is an energy function +and I could also have built a + + align:start position:0% +and I could also have built a + + + align:start position:0% +and I could also have built a +minus with you know divide by 2 I for + + align:start position:0% +minus with you know divide by 2 I for + + + align:start position:0% +minus with you know divide by 2 I for +fun I could have built the sign or the + + align:start position:0% +fun I could have built the sign or the + + + align:start position:0% +fun I could have built the sign or the +cosine of five one of which showed up on + + align:start position:0% +cosine of five one of which showed up on + + + align:start position:0% +cosine of five one of which showed up on +your + + align:start position:0% +your + + + align:start position:0% +your +exam so I can find a basis of these + + align:start position:0% +exam so I can find a basis of these + + + align:start position:0% +exam so I can find a basis of these +states s and cosine instead of e to the + + align:start position:0% +states s and cosine instead of e to the + + + align:start position:0% +states s and cosine instead of e to the +i and e to the minus IM and those would + + align:start position:0% +i and e to the minus IM and those would + + + align:start position:0% +i and e to the minus IM and those would +have been perfectly and in those + + align:start position:0% +have been perfectly and in those + + + align:start position:0% +have been perfectly and in those +situations what would the current have + + align:start position:0% +situations what would the current have + + + align:start position:0% +situations what would the current have +been if I put the system in this + + align:start position:0% +been if I put the system in this + + + align:start position:0% +been if I put the system in this +stationary State what would the current + + align:start position:0% +stationary State what would the current + + + align:start position:0% +stationary State what would the current +have been identically + + align:start position:0% +have been identically + + + align:start position:0% +have been identically +zero + + align:start position:0% +zero + + + align:start position:0% +zero +however that wouldn't be a state with a + + align:start position:0% +however that wouldn't be a state with a + + + align:start position:0% +however that wouldn't be a state with a +definite angular momentum so it wouldn't + + align:start position:0% +definite angular momentum so it wouldn't + + + align:start position:0% +definite angular momentum so it wouldn't +be surprising that it has zero current + + align:start position:0% +be surprising that it has zero current + + + align:start position:0% +be surprising that it has zero current +it's got some contribution it's a + + align:start position:0% +it's got some contribution it's a + + + align:start position:0% +it's got some contribution it's a +superposition of having some angular + + align:start position:0% +superposition of having some angular + + + align:start position:0% +superposition of having some angular +momentum and having the opposite angular + + align:start position:0% +momentum and having the opposite angular + + + align:start position:0% +momentum and having the opposite angular +momentum and the expectation value the + + align:start position:0% +momentum and the expectation value the + + + align:start position:0% +momentum and the expectation value the +expected value is + + align:start position:0% +expected value is + + + align:start position:0% +expected value is +zero I can also study states with a + + align:start position:0% +zero I can also study states with a + + + align:start position:0% +zero I can also study states with a +definite value of the angular mum those + + align:start position:0% +definite value of the angular mum those + + + align:start position:0% +definite value of the angular mum those +are not real there's nothing wrong with + + align:start position:0% +are not real there's nothing wrong with + + + align:start position:0% +are not real there's nothing wrong with +that I could have constructed states + + align:start position:0% +that I could have constructed states + + + align:start position:0% +that I could have constructed states +which don't have a definite angular + + align:start position:0% +which don't have a definite angular + + + align:start position:0% +which don't have a definite angular +momentum but are real but instead I want + + align:start position:0% +momentum but are real but instead I want + + + align:start position:0% +momentum but are real but instead I want +to work with states that have a definite + + align:start position:0% +to work with states that have a definite + + + align:start position:0% +to work with states that have a definite +angular + + align:start position:0% +angular + + + align:start position:0% +angular +momentum that cool so there's no tension + + align:start position:0% +momentum that cool so there's no tension + + + align:start position:0% +momentum that cool so there's no tension +there's no + + align:start position:0% + + + + align:start position:0% + +contradiction it's just that if we're + + align:start position:0% +contradiction it's just that if we're + + + align:start position:0% +contradiction it's just that if we're +interested in finding states that have a + + align:start position:0% +interested in finding states that have a + + + align:start position:0% +interested in finding states that have a +definite energy and a definite LZ + + align:start position:0% +definite energy and a definite LZ + + + align:start position:0% +definite energy and a definite LZ +angular momentum that is not going to be + + align:start position:0% +angular momentum that is not going to be + + + align:start position:0% +angular momentum that is not going to be +a real function and nothing tells us + + align:start position:0% +a real function and nothing tells us + + + align:start position:0% +a real function and nothing tells us +that it has to be and when you have a + + align:start position:0% +that it has to be and when you have a + + + align:start position:0% +that it has to be and when you have a +non-rib LZ when you have a non-trivial + + align:start position:0% +non-rib LZ when you have a non-trivial + + + align:start position:0% +non-rib LZ when you have a non-trivial +angular momentum just like a classical + + align:start position:0% +angular momentum just like a classical + + + align:start position:0% +angular momentum just like a classical +particle with non-trivial angular + + align:start position:0% +particle with non-trivial angular + + + align:start position:0% +particle with non-trivial angular +momentum that has charge we find that + + align:start position:0% +momentum that has charge we find that + + + align:start position:0% +momentum that has charge we find that +there's a current and thus a magnetic + + align:start position:0% +there's a current and thus a magnetic + + + align:start position:0% +there's a current and thus a magnetic +moment so the important thing was having + + align:start position:0% +moment so the important thing was having + + + align:start position:0% +moment so the important thing was having +a definite + + align:start position:0% +a definite + + + align:start position:0% +a definite +nonzero momentum or in this case angular + + align:start position:0% +nonzero momentum or in this case angular + + + align:start position:0% +nonzero momentum or in this case angular +momentum to give us the current + + align:start position:0% +momentum to give us the current + + + align:start position:0% +momentum to give us the current +yeah questions about this yeah using the + + align:start position:0% +yeah questions about this yeah using the + + + align:start position:0% +yeah questions about this yeah using the +same logic it kind of looks like we're + + align:start position:0% +same logic it kind of looks like we're + + + align:start position:0% +same logic it kind of looks like we're +taking a Charged particle and moving it + + align:start position:0% +taking a Charged particle and moving it + + + align:start position:0% +taking a Charged particle and moving it +around in a circle like or we have a + + align:start position:0% +around in a circle like or we have a + + + align:start position:0% +around in a circle like or we have a +distribution we're spinning it yeah we + + align:start position:0% +distribution we're spinning it yeah we + + + align:start position:0% +distribution we're spinning it yeah we +spend the distribtion of charge we're + + align:start position:0% +spend the distribtion of charge we're + + + align:start position:0% +spend the distribtion of charge we're +accelerating the Char particles in it + + align:start position:0% +accelerating the Char particles in it + + + align:start position:0% +accelerating the Char particles in it +yes individually yes accelerate them + + align:start position:0% +yes individually yes accelerate them + + + align:start position:0% +yes individually yes accelerate them +theyit radiation yes hyd ATS don't emit + + align:start position:0% +theyit radiation yes hyd ATS don't emit + + + align:start position:0% +theyit radiation yes hyd ATS don't emit +radiation yes how does that work that + + align:start position:0% +radiation yes how does that work that + + + align:start position:0% +radiation yes how does that work that +sounds a lot like problem four on your + + align:start position:0% +sounds a lot like problem four on your + + + align:start position:0% +sounds a lot like problem four on your +problems + + align:start position:0% +problems + + + align:start position:0% +problems +head problem ah okay well um um that's a + + align:start position:0% +head problem ah okay well um um that's a + + + align:start position:0% +head problem ah okay well um um that's a +great question and you should think + + align:start position:0% +great question and you should think + + + align:start position:0% +great question and you should think +about + + align:start position:0% +about + + + align:start position:0% +about +it how do I how could I say you read my + + align:start position:0% +it how do I how could I say you read my + + + align:start position:0% +it how do I how could I say you read my +mind yes struggling with this is exact + + align:start position:0% +mind yes struggling with this is exact + + + align:start position:0% +mind yes struggling with this is exact +to the point of one of the problems on + + align:start position:0% +to the point of one of the problems on + + + align:start position:0% +to the point of one of the problems on +your problem set and ask me that again + + align:start position:0% +your problem set and ask me that again + + + align:start position:0% +your problem set and ask me that again +after the problem set has been turned in + + align:start position:0% +after the problem set has been turned in + + + align:start position:0% +after the problem set has been turned in +and I'll give you a happy disquisition + + align:start position:0% +and I'll give you a happy disquisition + + + align:start position:0% +and I'll give you a happy disquisition +on it but I want you to struggle with it + + align:start position:0% +on it but I want you to struggle with it + + + align:start position:0% +on it but I want you to struggle with it +because it's it's a hard and interesting + + align:start position:0% +because it's it's a hard and interesting + + + align:start position:0% +because it's it's a hard and interesting +question yeah so um I don't think this + + align:start position:0% +question yeah so um I don't think this + + + align:start position:0% +question yeah so um I don't think this +answers my question necessarily about + + align:start position:0% +answers my question necessarily about + + + align:start position:0% +answers my question necessarily about +the radiation because so um analogously + + align:start position:0% +the radiation because so um analogously + + + align:start position:0% +the radiation because so um analogously +like to classical enm this would be the + + align:start position:0% +like to classical enm this would be the + + + align:start position:0% +like to classical enm this would be the +magnetostatic case where you just have a + + align:start position:0% +magnetostatic case where you just have a + + + align:start position:0% +magnetostatic case where you just have a +radiation you have like quickly + + align:start position:0% +radiation you have like quickly + + + align:start position:0% +radiation you have like quickly +oscillating fields and the transition + + align:start position:0% +oscillating fields and the transition + + + align:start position:0% +oscillating fields and the transition +times are really small and like the + + align:start position:0% +times are really small and like the + + + align:start position:0% +times are really small and like the +frequencies of the really fast so I + + align:start position:0% +frequencies of the really fast so I + + + align:start position:0% +frequencies of the really fast so I +still don't know that's the same so this + + align:start position:0% +still don't know that's the same so this + + + align:start position:0% +still don't know that's the same so this +question is unfortunately a linear + + align:start position:0% +question is unfortunately a linear + + + align:start position:0% +question is unfortunately a linear +combination of a of a really good + + align:start position:0% +combination of a of a really good + + + align:start position:0% +combination of a of a really good +independent question and that question + + align:start position:0% +independent question and that question + + + align:start position:0% +independent question and that question +so ask me after lecture and I'll talk to + + align:start position:0% +so ask me after lecture and I'll talk to + + + align:start position:0% +so ask me after lecture and I'll talk to +you about the part that's linearly + + align:start position:0% +you about the part that's linearly + + + align:start position:0% +you about the part that's linearly +independent thing okay I'm I'm on thin + + align:start position:0% +independent thing okay I'm I'm on thin + + + align:start position:0% +independent thing okay I'm I'm on thin +ice here okay um anything else where we + + align:start position:0% +ice here okay um anything else where we + + + align:start position:0% +ice here okay um anything else where we +dispense with + + align:start position:0% +dispense with + + + align:start position:0% +dispense with +hydrogen okay the the question that um + + align:start position:0% +hydrogen okay the the question that um + + + align:start position:0% +hydrogen okay the the question that um +the the question that you all keep + + align:start position:0% +the the question that you all keep + + + align:start position:0% +the the question that you all keep +coming to about the + + align:start position:0% +coming to about the + + + align:start position:0% +coming to about the +um well problem four on the I think it's + + align:start position:0% +um well problem four on the I think it's + + + align:start position:0% +um well problem four on the I think it's +problem four on the on the problem set + + align:start position:0% +problem four on the on the problem set + + + align:start position:0% +problem four on the on the problem set +maybe it's problem too um uh it involves + + align:start position:0% +maybe it's problem too um uh it involves + + + align:start position:0% +maybe it's problem too um uh it involves +almost no computation but it's the most + + align:start position:0% +almost no computation but it's the most + + + align:start position:0% +almost no computation but it's the most +intellectually challenging problem on + + align:start position:0% +intellectually challenging problem on + + + align:start position:0% +intellectually challenging problem on +the exam on the problem set so take it + + align:start position:0% +the exam on the problem set so take it + + + align:start position:0% +the exam on the problem set so take it +seriously even though it's like + + align:start position:0% +seriously even though it's like + + + align:start position:0% +seriously even though it's like +calculation + + align:start position:0% +calculation + + + align:start position:0% +calculation +free + + align:start position:0% +free + + + align:start position:0% +free +okay + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah it so the the um it's not + + align:start position:0% +yeah yeah yeah it so the the um it's not + + + align:start position:0% +yeah yeah yeah it so the the um it's not +by symmetry because there isn't a + + align:start position:0% +by symmetry because there isn't a + + + align:start position:0% +by symmetry because there isn't a +symmetry the proton is 2,000 times + + align:start position:0% +symmetry the proton is 2,000 times + + + align:start position:0% +symmetry the proton is 2,000 times +heavier than the electron but + + align:start position:0% +heavier than the electron but + + + align:start position:0% +heavier than the electron but +um the so + + align:start position:0% +um the so + + + align:start position:0% +um the so +um so the let me make sure I'm + + align:start position:0% +um so the let me make sure I'm + + + align:start position:0% +um so the let me make sure I'm +understanding your question your + + align:start position:0% +understanding your question your + + + align:start position:0% +understanding your question your +question is um we found that the + + align:start position:0% +question is um we found that the + + + align:start position:0% +question is um we found that the +electron is in uh is in Bound states in + + align:start position:0% +electron is in uh is in Bound states in + + + align:start position:0% +electron is in uh is in Bound states in +the colon potential but in hydrogen you + + align:start position:0% +the colon potential but in hydrogen you + + + align:start position:0% +the colon potential but in hydrogen you +have two particles you have an electron + + align:start position:0% +have two particles you have an electron + + + align:start position:0% +have two particles you have an electron +you have a proton so uh is the electron + + align:start position:0% +you have a proton so uh is the electron + + + align:start position:0% +you have a proton so uh is the electron +in that state and the proton is just + + align:start position:0% +in that state and the proton is just + + + align:start position:0% +in that state and the proton is just +free and cruising on its own thing + + align:start position:0% +free and cruising on its own thing + + + align:start position:0% +free and cruising on its own thing +that's exactly the topic of the next 45 + + align:start position:0% +that's exactly the topic of the next 45 + + + align:start position:0% +that's exactly the topic of the next 45 +minutes okay good question so um with + + align:start position:0% +minutes okay good question so um with + + + align:start position:0% +minutes okay good question so um with +with that Insight um uh let me we turned + + align:start position:0% +with that Insight um uh let me we turned + + + align:start position:0% +with that Insight um uh let me we turned +now to the question of identical + + align:start position:0% +now to the question of identical + + + align:start position:0% +now to the question of identical +particles or multiple + + align:start position:0% +particles or multiple + + + align:start position:0% +particles or multiple +particles okay so we're done with Kum + + align:start position:0% +particles okay so we're done with Kum + + + align:start position:0% +particles okay so we're done with Kum +for the moment pretty much for the rest + + align:start position:0% +for the moment pretty much for the rest + + + align:start position:0% +for the moment pretty much for the rest +of the course so I want to move on to + + align:start position:0% +of the course so I want to move on to + + + align:start position:0% +of the course so I want to move on to +the following question suppose I have a + + align:start position:0% +the following question suppose I have a + + + align:start position:0% +the following question suppose I have a +system we've spent a lot of time + + align:start position:0% +system we've spent a lot of time + + + align:start position:0% +system we've spent a lot of time +thinking about a particle in a potential + + align:start position:0% +thinking about a particle in a potential + + + align:start position:0% +thinking about a particle in a potential +I would like to think about multiple + + align:start position:0% +I would like to think about multiple + + + align:start position:0% +I would like to think about multiple +particles for a + + align:start position:0% + + + + align:start position:0% + +minute okay and neat things happen for + + align:start position:0% +minute okay and neat things happen for + + + align:start position:0% +minute okay and neat things happen for +multiple particles that don't happen for + + align:start position:0% +multiple particles that don't happen for + + + align:start position:0% +multiple particles that don't happen for +indiv ual isolated + + align:start position:0% +indiv ual isolated + + + align:start position:0% +indiv ual isolated +particles so let's think about what + + align:start position:0% +particles so let's think about what + + + align:start position:0% +particles so let's think about what +those let's think about the physics of + + align:start position:0% +those let's think about the physics of + + + align:start position:0% +those let's think about the physics of +multiple particles so in particular + + align:start position:0% +multiple particles so in particular + + + align:start position:0% +multiple particles so in particular +classically In classical mechanics if I + + align:start position:0% +classically In classical mechanics if I + + + align:start position:0% +classically In classical mechanics if I +have two particles what is the + + align:start position:0% +have two particles what is the + + + align:start position:0% +have two particles what is the +information I have to specify to specify + + align:start position:0% +information I have to specify to specify + + + align:start position:0% +information I have to specify to specify +the state I have to specify the position + + align:start position:0% +the state I have to specify the position + + + align:start position:0% +the state I have to specify the position +of the first particle uh X X1 and its + + align:start position:0% +of the first particle uh X X1 and its + + + align:start position:0% +of the first particle uh X X1 and its +momentum P1 and then the position of the + + align:start position:0% +momentum P1 and then the position of the + + + align:start position:0% +momentum P1 and then the position of the +second particle X2 and P2 I'm going to + + align:start position:0% +second particle X2 and P2 I'm going to + + + align:start position:0% +second particle X2 and P2 I'm going to +Omit vectors over everything but + + align:start position:0% +Omit vectors over everything but + + + align:start position:0% +Omit vectors over everything but +everything is in the appropriate number + + align:start position:0% +everything is in the appropriate number + + + align:start position:0% +everything is in the appropriate number +of Dimensions So In classical Mech or in + + align:start position:0% +of Dimensions So In classical Mech or in + + + align:start position:0% +of Dimensions So In classical Mech or in +quantum + + align:start position:0% +quantum + + + align:start position:0% +quantum +mechanics the state of the system is + + align:start position:0% +mechanics the state of the system is + + + align:start position:0% +mechanics the state of the system is +specified by a wave function which is a + + align:start position:0% +specified by a wave function which is a + + + align:start position:0% +specified by a wave function which is a +function of the positions or the the + + align:start position:0% +function of the positions or the the + + + align:start position:0% +function of the positions or the the +degrees of freedom let's say X1 and + + align:start position:0% +degrees of freedom let's say X1 and + + + align:start position:0% +degrees of freedom let's say X1 and +X2 um and x uh one and X2 and P1 and P2 + + align:start position:0% +X2 um and x uh one and X2 and P1 and P2 + + + align:start position:0% +X2 um and x uh one and X2 and P1 and P2 +are promoted to operators representing + + align:start position:0% +are promoted to operators representing + + + align:start position:0% +are promoted to operators representing +these + + align:start position:0% +these + + + align:start position:0% +these +observables right and the wave function + + align:start position:0% +observables right and the wave function + + + align:start position:0% +observables right and the wave function +is a function of now let me just quickly + + align:start position:0% +is a function of now let me just quickly + + + align:start position:0% +is a function of now let me just quickly +tell you what this notation means what + + align:start position:0% +tell you what this notation means what + + + align:start position:0% +tell you what this notation means what +this notation means is X1 is some number + + align:start position:0% +this notation means is X1 is some number + + + align:start position:0% +this notation means is X1 is some number +like seven and the quantity in the first + + align:start position:0% +like seven and the quantity in the first + + + align:start position:0% +like seven and the quantity in the first +spot this means that the first + + align:start position:0% + + + + align:start position:0% + +particle indicated by the first slot is + + align:start position:0% +particle indicated by the first slot is + + + align:start position:0% +particle indicated by the first slot is +at + + align:start position:0% +at + + + align:start position:0% +at +X1 and the second particle is at + + align:start position:0% +X1 and the second particle is at + + + align:start position:0% +X1 and the second particle is at +X2 okay so whenever I write a wave + + align:start position:0% +X2 okay so whenever I write a wave + + + align:start position:0% +X2 okay so whenever I write a wave +function what I mean is this is the + + align:start position:0% +function what I mean is this is the + + + align:start position:0% +function what I mean is this is the +probability amplitude the the thing + + align:start position:0% +probability amplitude the the thing + + + align:start position:0% +probability amplitude the the thing +whose Norm square is a probability to + + align:start position:0% +whose Norm square is a probability to + + + align:start position:0% +whose Norm square is a probability to +find the first particle at this value + + align:start position:0% +find the first particle at this value + + + align:start position:0% +find the first particle at this value +and the second particle that value so + + align:start position:0% +and the second particle that value so + + + align:start position:0% +and the second particle that value so +the one and two label the points not the + + align:start position:0% +the one and two label the points not the + + + align:start position:0% +the one and two label the points not the +particles the particle is labeled by the + + align:start position:0% +particles the particle is labeled by the + + + align:start position:0% +particles the particle is labeled by the +position inside this wave function + + align:start position:0% +position inside this wave function + + + align:start position:0% +position inside this wave function +everyone cool with that okay so that's + + align:start position:0% +everyone cool with that okay so that's + + + align:start position:0% +everyone cool with that okay so that's +just a notation so the quantum + + align:start position:0% +just a notation so the quantum + + + align:start position:0% +just a notation so the quantum +mechanical description of two particles + + align:start position:0% +mechanical description of two particles + + + align:start position:0% +mechanical description of two particles +is a wave function of both positions and + + align:start position:0% +is a wave function of both positions and + + + align:start position:0% +is a wave function of both positions and +operators representing the position and + + align:start position:0% +operators representing the position and + + + align:start position:0% +operators representing the position and +the coordinates um of + + align:start position:0% +the coordinates um of + + + align:start position:0% +the coordinates um of +um guess I can do this um the positions + + align:start position:0% +um guess I can do this um the positions + + + align:start position:0% +um guess I can do this um the positions +and the coordinates of the particles + + align:start position:0% + + + + align:start position:0% + +so and the + + align:start position:0% + + + + align:start position:0% + +probability actually let's go ahead and + + align:start position:0% +probability actually let's go ahead and + + + align:start position:0% +probability actually let's go ahead and +finish up here and the + + align:start position:0% +finish up here and the + + + align:start position:0% +finish up here and the +probability uh density to find uh the + + align:start position:0% +probability uh density to find uh the + + + align:start position:0% +probability uh density to find uh the +first + + align:start position:0% +first + + + align:start position:0% +first +particle oops + + align:start position:0% + + + + align:start position:0% + +first at + + align:start position:0% +first at + + + align:start position:0% +first at +X1 and the + + align:start position:0% +X1 and the + + + align:start position:0% +X1 and the +second at + + align:start position:0% +second at + + + align:start position:0% +second at +X2 is just the norm squared of the + + align:start position:0% +X2 is just the norm squared of the + + + align:start position:0% +X2 is just the norm squared of the +amplitude sx1 X2 + + align:start position:0% +amplitude sx1 X2 + + + align:start position:0% +amplitude sx1 X2 +squ just as usual that's the probability + + align:start position:0% + + + + align:start position:0% + +density all right everyone cool with + + align:start position:0% +density all right everyone cool with + + + align:start position:0% +density all right everyone cool with +that and what are X um one X2 commutator + + align:start position:0% +that and what are X um one X2 commutator + + + align:start position:0% +that and what are X um one X2 commutator +what is this + + align:start position:0% + + + + align:start position:0% + +commutator can you know the position of + + align:start position:0% +commutator can you know the position of + + + align:start position:0% +commutator can you know the position of +the first particle and the position of + + align:start position:0% +the first particle and the position of + + + align:start position:0% +the first particle and the position of +the second + + align:start position:0% +the second + + + align:start position:0% +the second +particle + + align:start position:0% +particle + + + align:start position:0% +particle +simultaneously sure I'm here you're + + align:start position:0% +simultaneously sure I'm here you're + + + align:start position:0% +simultaneously sure I'm here you're +there okay zero and um X1 with P1 just + + align:start position:0% +there okay zero and um X1 with P1 just + + + align:start position:0% +there okay zero and um X1 with P1 just +work in one dimension for the moment is + + align:start position:0% +work in one dimension for the moment is + + + align:start position:0% +work in one dimension for the moment is +equal + + align:start position:0% +equal + + + align:start position:0% +equal +to I bar and the same would have been + + align:start position:0% +to I bar and the same would have been + + + align:start position:0% +to I bar and the same would have been +true of X2 with P2 and what about uh X1 + + align:start position:0% +true of X2 with P2 and what about uh X1 + + + align:start position:0% +true of X2 with P2 and what about uh X1 +with + + align:start position:0% +with + + + align:start position:0% +with +P2 zero these are independent + + align:start position:0% +P2 zero these are independent + + + align:start position:0% +P2 zero these are independent +quantities + + align:start position:0% +quantities + + + align:start position:0% +quantities +okay so it's more or less as you'd + + align:start position:0% +okay so it's more or less as you'd + + + align:start position:0% +okay so it's more or less as you'd +expect so just to be explicit about this + + align:start position:0% +expect so just to be explicit about this + + + align:start position:0% +expect so just to be explicit about this +let's do an example + + align:start position:0% +let's do an example + + + align:start position:0% +let's do an example +two free + + align:start position:0% + + + + align:start position:0% + +particles okay so what's the energy + + align:start position:0% +particles okay so what's the energy + + + align:start position:0% +particles okay so what's the energy +operator well the energy operator is + + align:start position:0% +operator well the energy operator is + + + align:start position:0% +operator well the energy operator is +equal to p^2 upon 2 m for the first + + align:start position:0% +equal to p^2 upon 2 m for the first + + + align:start position:0% +equal to p^2 upon 2 m for the first +particle + + align:start position:0% +particle + + + align:start position:0% +particle +one plus P ^2 2 upon 2 M2 second + + align:start position:0% +one plus P ^2 2 upon 2 M2 second + + + align:start position:0% +one plus P ^2 2 upon 2 M2 second +particle its mass is M2 the first + + align:start position:0% +particle its mass is M2 the first + + + align:start position:0% +particle its mass is M2 the first +particle has mass M1 and the system is + + align:start position:0% +particle has mass M1 and the system is + + + align:start position:0% +particle has mass M1 and the system is +free so uh this is plus zero yeah + + align:start position:0% + + + + align:start position:0% + +yeah okay so the the question is um x1x2 + + align:start position:0% +yeah okay so the the question is um x1x2 + + + align:start position:0% +yeah okay so the the question is um x1x2 +commutator equals zero is that true uh + + align:start position:0% +commutator equals zero is that true uh + + + align:start position:0% +commutator equals zero is that true uh +even if there are forces between the + + align:start position:0% +even if there are forces between the + + + align:start position:0% +even if there are forces between the +particles so what are the forces between + + align:start position:0% +particles so what are the forces between + + + align:start position:0% +particles so what are the forces between +particles what are they going to + + align:start position:0% +particles what are they going to + + + align:start position:0% +particles what are they going to +contribute + + align:start position:0% +contribute + + + align:start position:0% +contribute +to yeah the potential and that's going + + align:start position:0% +to yeah the potential and that's going + + + align:start position:0% +to yeah the potential and that's going +to show up in the energy operator so + + align:start position:0% +to show up in the energy operator so + + + align:start position:0% +to show up in the energy operator so +that will certainly matter and it will + + align:start position:0% +that will certainly matter and it will + + + align:start position:0% +that will certainly matter and it will +change what the energy I values are but + + align:start position:0% +change what the energy I values are but + + + align:start position:0% +change what the energy I values are but +it won't tell you what can or can't be + + align:start position:0% +it won't tell you what can or can't be + + + align:start position:0% +it won't tell you what can or can't be +measured it won't tell you what + + align:start position:0% +measured it won't tell you what + + + align:start position:0% +measured it won't tell you what +properties the system can have or not + + align:start position:0% +properties the system can have or not + + + align:start position:0% +properties the system can have or not +good + + align:start position:0% +good + + + align:start position:0% +good +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +me the we we'll we'll talk about things + + align:start position:0% +me the we we'll we'll talk about things + + + align:start position:0% +me the we we'll we'll talk about things +like that in a minute no that this is + + align:start position:0% +like that in a minute no that this is + + + align:start position:0% +like that in a minute no that this is +this is um does do the computation + + align:start position:0% +this is um does do the computation + + + align:start position:0% +this is um does do the computation +relations care what state you're in they + + align:start position:0% +relations care what state you're in they + + + align:start position:0% +relations care what state you're in they +relations amongst operators so they're + + align:start position:0% +relations amongst operators so they're + + + align:start position:0% +relations amongst operators so they're +independent of the + + align:start position:0% +independent of the + + + align:start position:0% +independent of the +state always okay yeah for the two free + + align:start position:0% +state always okay yeah for the two free + + + align:start position:0% +state always okay yeah for the two free +particles are we assuming that they're + + align:start position:0% +particles are we assuming that they're + + + align:start position:0% +particles are we assuming that they're +not charged particles yeah I'm assuming + + align:start position:0% +not charged particles yeah I'm assuming + + + align:start position:0% +not charged particles yeah I'm assuming +that there are no interactions + + align:start position:0% +that there are no interactions + + + align:start position:0% +that there are no interactions +whatsoever just totally free particles + + align:start position:0% +whatsoever just totally free particles + + + align:start position:0% +whatsoever just totally free particles +potential is zero V of X1 X2 equals + + align:start position:0% +potential is zero V of X1 X2 equals + + + align:start position:0% +potential is zero V of X1 X2 equals +z yeah so they're not charged they're + + align:start position:0% +z yeah so they're not charged they're + + + align:start position:0% +z yeah so they're not charged they're +just totally uninteresting no + + align:start position:0% +just totally uninteresting no + + + align:start position:0% +just totally uninteresting no +interactions no forces no potential okay + + align:start position:0% +interactions no forces no potential okay + + + align:start position:0% +interactions no forces no potential okay +so we know how to solve this problem + + align:start position:0% +so we know how to solve this problem + + + align:start position:0% +so we know how to solve this problem +because we can use separation s of X1 + + align:start position:0% +because we can use separation s of X1 + + + align:start position:0% +because we can use separation s of X1 +comma X2 is can be written as well we + + align:start position:0% +comma X2 is can be written as well we + + + align:start position:0% +comma X2 is can be written as well we +know what the solutions of p1^ 2 upon 2 + + align:start position:0% +know what the solutions of p1^ 2 upon 2 + + + align:start position:0% +know what the solutions of p1^ 2 upon 2 +m uh is equal to e r so we can write + + align:start position:0% +m uh is equal to e r so we can write + + + align:start position:0% +m uh is equal to e r so we can write +this as Kai of + + align:start position:0% +this as Kai of + + + align:start position:0% +this as Kai of +X1 and actually uh I'm going to call the + + align:start position:0% +X1 and actually uh I'm going to call the + + + align:start position:0% +X1 and actually uh I'm going to call the +the positions of these guys A and B + + align:start position:0% +the positions of these guys A and B + + + align:start position:0% +the positions of these guys A and B +because the subscripts are just terribly + + align:start position:0% +because the subscripts are just terribly + + + align:start position:0% +because the subscripts are just terribly +misleading so the first point is called + + align:start position:0% +misleading so the first point is called + + + align:start position:0% +misleading so the first point is called +a the second point is called B so uh uh + + align:start position:0% +a the second point is called B so uh uh + + + align:start position:0% +a the second point is called B so uh uh +A and B and this is p uh p uh P1 and P2 + + align:start position:0% +A and B and this is p uh p uh P1 and P2 + + + align:start position:0% +A and B and this is p uh p uh P1 and P2 +the momento the two guys uh Kai of a and + + align:start position:0% +the momento the two guys uh Kai of a and + + + align:start position:0% +the momento the two guys uh Kai of a and +F of B so all I'm doing here is I'm + + align:start position:0% +F of B so all I'm doing here is I'm + + + align:start position:0% +F of B so all I'm doing here is I'm +using + + align:start position:0% +using + + + align:start position:0% +using +separation okay p a PB so here instead + + align:start position:0% +separation okay p a PB so here instead + + + align:start position:0% +separation okay p a PB so here instead +of calling them the positions X1 and X2 + + align:start position:0% +of calling them the positions X1 and X2 + + + align:start position:0% +of calling them the positions X1 and X2 +I'm going to call them A and B just + + align:start position:0% +I'm going to call them A and B just + + + align:start position:0% +I'm going to call them A and B just +because it's going to be easier to write + + align:start position:0% +because it's going to be easier to write + + + align:start position:0% +because it's going to be easier to write +and make things clear so here I'm using + + align:start position:0% +and make things clear so here I'm using + + + align:start position:0% +and make things clear so here I'm using +separation and um then p1^ s or pa^ S + + align:start position:0% +separation and um then p1^ s or pa^ S + + + align:start position:0% +separation and um then p1^ s or pa^ S +upon 2 m on Kai of a is equal to uh EA + + align:start position:0% +upon 2 m on Kai of a is equal to uh EA + + + align:start position:0% +upon 2 m on Kai of a is equal to uh EA +Kai a and ditto for + + align:start position:0% +Kai a and ditto for + + + align:start position:0% +Kai a and ditto for +B this tells us that Kai of + + align:start position:0% +B this tells us that Kai of + + + align:start position:0% +B this tells us that Kai of +a is equal to e to the some coefficient + + align:start position:0% +a is equal to e to the some coefficient + + + align:start position:0% +a is equal to e to the some coefficient +C uh e to the i k + + align:start position:0% +C uh e to the i k + + + align:start position:0% +C uh e to the i k +a every Rec + + align:start position:0% +a every Rec + + + align:start position:0% +a every Rec +that a is just replacing + + align:start position:0% +that a is just replacing + + + align:start position:0% +that a is just replacing +X1 so it's just the position so this is + + align:start position:0% +X1 so it's just the position so this is + + + align:start position:0% +X1 so it's just the position so this is +just saying that the solution to a free + + align:start position:0% +just saying that the solution to a free + + + align:start position:0% +just saying that the solution to a free +single free particle is a plane wave and + + align:start position:0% +single free particle is a plane wave and + + + align:start position:0% +single free particle is a plane wave and +because this is just the sum of the + + align:start position:0% +because this is just the sum of the + + + align:start position:0% +because this is just the sum of the +momenta squares we can separate the + + align:start position:0% +momenta squares we can separate the + + + align:start position:0% +momenta squares we can separate the +equation and the same thing obtains for + + align:start position:0% +equation and the same thing obtains for + + + align:start position:0% +equation and the same thing obtains for +S so similarly for + + align:start position:0% +S so similarly for + + + align:start position:0% +S so similarly for +fi + + align:start position:0% +fi + + + align:start position:0% +fi +ditto fi of B is equal to the e to the i + + align:start position:0% +ditto fi of B is equal to the e to the i + + + align:start position:0% +ditto fi of B is equal to the e to the i +k sub b b and I'll call this Cas sub a + + align:start position:0% +k sub b b and I'll call this Cas sub a + + + align:start position:0% +k sub b b and I'll call this Cas sub a +to distinguish them so the wave + + align:start position:0% +to distinguish them so the wave + + + align:start position:0% +to distinguish them so the wave +functions a basis for for the uh wave + + align:start position:0% +functions a basis for for the uh wave + + + align:start position:0% +functions a basis for for the uh wave +functions for two particles s of a b + + align:start position:0% +functions for two particles s of a b + + + align:start position:0% +functions for two particles s of a b +with energy e is equal to e to the I Ka + + align:start position:0% +with energy e is equal to e to the I Ka + + + align:start position:0% +with energy e is equal to e to the I Ka +a plus + + align:start position:0% +a plus + + + align:start position:0% +a plus +KB + + align:start position:0% +KB + + + align:start position:0% +KB +B where um e is equal to h bar^ 2 upon 2 + + align:start position:0% +B where um e is equal to h bar^ 2 upon 2 + + + align:start position:0% +B where um e is equal to h bar^ 2 upon 2 +m k sub a 2 plus K sub b^ + + align:start position:0% +m k sub a 2 plus K sub b^ + + + align:start position:0% +m k sub a 2 plus K sub b^ + + align:start position:0% + + + align:start position:0% +yeah for a system of two free particles + + align:start position:0% +yeah for a system of two free particles + + + align:start position:0% +yeah for a system of two free particles +is every wave function of the form uh K + + align:start position:0% +is every wave function of the form uh K + + + align:start position:0% +is every wave function of the form uh K +Kai of a * 5 of B + + align:start position:0% + + + + align:start position:0% + +if you have a system that's separable is + + align:start position:0% +if you have a system that's separable is + + + align:start position:0% +if you have a system that's separable is +every wave function is every solution + + align:start position:0% +every wave function is every solution + + + align:start position:0% +every wave function is every solution +itself separated no because we can have + + align:start position:0% +itself separated no because we can have + + + align:start position:0% +itself separated no because we can have +arbitrary superpositions of forms of of + + align:start position:0% +arbitrary superpositions of forms of of + + + align:start position:0% +arbitrary superpositions of forms of of +this type right so we could have + + align:start position:0% +this type right so we could have + + + align:start position:0% +this type right so we could have +superpositions of plane waves as long as + + align:start position:0% +superpositions of plane waves as long as + + + align:start position:0% +superpositions of plane waves as long as +the energies of each plane wave in the + + align:start position:0% +the energies of each plane wave in the + + + align:start position:0% +the energies of each plane wave in the +superposition are equal to e the total + + align:start position:0% +superposition are equal to e the total + + + align:start position:0% +superposition are equal to e the total +energy equal E I can just superpose them + + align:start position:0% +energy equal E I can just superpose them + + + align:start position:0% +energy equal E I can just superpose them +and I still have an energy I function + + align:start position:0% +and I still have an energy I function + + + align:start position:0% +and I still have an energy I function +everyone cool with + + align:start position:0% +everyone cool with + + + align:start position:0% +everyone cool with +that okay so nothing shocking here but I + + align:start position:0% +that okay so nothing shocking here but I + + + align:start position:0% +that okay so nothing shocking here but I +did this example so that we'd have the + + align:start position:0% +did this example so that we'd have the + + + align:start position:0% +did this example so that we'd have the +notation of Kai uh and fi for the two + + align:start position:0% +notation of Kai uh and fi for the two + + + align:start position:0% +notation of Kai uh and fi for the two +states + + align:start position:0% + + + + align:start position:0% + +okay so now let me come to this question + + align:start position:0% +okay so now let me come to this question + + + align:start position:0% +okay so now let me come to this question +of uh what what about the proton well + + align:start position:0% +of uh what what about the proton well + + + align:start position:0% +of uh what what about the proton well +suppose I have a system now with um + + align:start position:0% +suppose I have a system now with um + + + align:start position:0% +suppose I have a system now with um +which is not a free particle it's two + + align:start position:0% +which is not a free particle it's two + + + align:start position:0% +which is not a free particle it's two +particles A and B and E is equal to PA + + align:start position:0% +particles A and B and E is equal to PA + + + align:start position:0% +particles A and B and E is equal to PA +a^ 2 over 2 ma + + align:start position:0% +a^ 2 over 2 ma + + + align:start position:0% +a^ 2 over 2 ma +a plus pb^ 2 upon 2 + + align:start position:0% +a plus pb^ 2 upon 2 + + + align:start position:0% +a plus pb^ 2 upon 2 +MB plus a potential that depends only on + + align:start position:0% +MB plus a potential that depends only on + + + align:start position:0% +MB plus a potential that depends only on +at a minus + + align:start position:0% + + + + align:start position:0% + +B okay + + align:start position:0% +B okay + + + align:start position:0% +B okay +so this is for example what happens in + + align:start position:0% +so this is for example what happens in + + + align:start position:0% +so this is for example what happens in +the cool potential when you include the + + align:start position:0% +the cool potential when you include the + + + align:start position:0% +the cool potential when you include the +proton having a finite Mass instead of + + align:start position:0% +proton having a finite Mass instead of + + + align:start position:0% +proton having a finite Mass instead of +being infinitely massive and stuck + + align:start position:0% + + + + align:start position:0% + +still so now we can do exactly the same + + align:start position:0% +still so now we can do exactly the same + + + align:start position:0% +still so now we can do exactly the same +thing we did In classical mechanics when + + align:start position:0% +thing we did In classical mechanics when + + + align:start position:0% +thing we did In classical mechanics when +you have a potential that only depends + + align:start position:0% +you have a potential that only depends + + + align:start position:0% +you have a potential that only depends +on the distance between two things I can + + align:start position:0% +on the distance between two things I can + + + align:start position:0% +on the distance between two things I can +reorganize degrees of freedom into the + + align:start position:0% +reorganize degrees of freedom into the + + + align:start position:0% +reorganize degrees of freedom into the +um Center of mass position R is equal to + + align:start position:0% +um Center of mass position R is equal to + + + align:start position:0% +um Center of mass position R is equal to +um 1/ ma+ + + align:start position:0% +um 1/ ma+ + + + align:start position:0% +um 1/ ma+ +MB of ma + + align:start position:0% +MB of ma + + + align:start position:0% +MB of ma +uh a plus uh MB B so that's the center + + align:start position:0% +uh a plus uh MB B so that's the center + + + align:start position:0% +uh a plus uh MB B so that's the center +of mass motion and the + + align:start position:0% +of mass motion and the + + + align:start position:0% +of mass motion and the +relative uh distance is equal to uh uh + + align:start position:0% +relative uh distance is equal to uh uh + + + align:start position:0% +relative uh distance is equal to uh uh +one over + + align:start position:0% +one over + + + align:start position:0% +one over +whoops I don't need that uh a minus + + align:start position:0% + + + + align:start position:0% + +B okay and then if you do this and you + + align:start position:0% +B okay and then if you do this and you + + + align:start position:0% +B okay and then if you do this and you +write out the energy operator e is equal + + align:start position:0% +write out the energy operator e is equal + + + align:start position:0% +write out the energy operator e is equal +to minus h s upon 2 m or to capital M + + align:start position:0% +to minus h s upon 2 m or to capital M + + + align:start position:0% +to minus h s upon 2 m or to capital M +total mass uh Dr r + + align:start position:0% +total mass uh Dr r + + + align:start position:0% +total mass uh Dr r +s plusus h bar^ 2/ 2 + + align:start position:0% +s plusus h bar^ 2/ 2 + + + align:start position:0% +s plusus h bar^ 2/ 2 +mu D little R 2 uh plus v of + + align:start position:0% +mu D little R 2 uh plus v of + + + align:start position:0% +mu D little R 2 uh plus v of +R + + align:start position:0% +R + + + align:start position:0% +R +okay so this is exactly what happens in + + align:start position:0% +okay so this is exactly what happens in + + + align:start position:0% +okay so this is exactly what happens in +classical mechanics you work in terms of + + align:start position:0% +classical mechanics you work in terms of + + + align:start position:0% +classical mechanics you work in terms of +the center of mass coordinate and the + + align:start position:0% +the center of mass coordinate and the + + + align:start position:0% +the center of mass coordinate and the +relative coordinate the relative + + align:start position:0% +relative coordinate the relative + + + align:start position:0% +relative coordinate the relative +coordinate becomes effectively an + + align:start position:0% +coordinate becomes effectively an + + + align:start position:0% +coordinate becomes effectively an +independent degree of Freedom with a + + align:start position:0% +independent degree of Freedom with a + + + align:start position:0% +independent degree of Freedom with a +potential which is the central potential + + align:start position:0% +potential which is the central potential + + + align:start position:0% +potential which is the central potential +and the center of mass coordinate is a + + align:start position:0% +and the center of mass coordinate is a + + + align:start position:0% +and the center of mass coordinate is a +free + + align:start position:0% +free + + + align:start position:0% +free +particle so if we have our proton and + + align:start position:0% +particle so if we have our proton and + + + align:start position:0% +particle so if we have our proton and +our electron and they're attracted to + + align:start position:0% +our electron and they're attracted to + + + align:start position:0% +our electron and they're attracted to +each other by Kum there's a center of + + align:start position:0% +each other by Kum there's a center of + + + align:start position:0% +each other by Kum there's a center of +mass motion and then they do together + + align:start position:0% +mass motion and then they do together + + + align:start position:0% +mass motion and then they do together +whatever they do together all the + + align:start position:0% +whatever they do together all the + + + align:start position:0% +whatever they do together all the +potential every cool that the only + + align:start position:0% +potential every cool that the only + + + align:start position:0% +potential every cool that the only +difference is that the mass in the + + align:start position:0% +difference is that the mass in the + + + align:start position:0% +difference is that the mass in the +potential is not the mass of the + + align:start position:0% +potential is not the mass of the + + + align:start position:0% +potential is not the mass of the +electron but it's the geometric mean mu + + align:start position:0% +electron but it's the geometric mean mu + + + align:start position:0% +electron but it's the geometric mean mu +is equal to M MB over ma plus + + align:start position:0% + + + + align:start position:0% + +MB okay now for a proton and an electron + + align:start position:0% +MB okay now for a proton and an electron + + + align:start position:0% +MB okay now for a proton and an electron +um if ma is the proton and MB is the + + align:start position:0% +um if ma is the proton and MB is the + + + align:start position:0% +um if ma is the proton and MB is the +electron then this is proton electron + + align:start position:0% +electron then this is proton electron + + + align:start position:0% +electron then this is proton electron +over proton plus electron but proton is + + align:start position:0% +over proton plus electron but proton is + + + align:start position:0% +over proton plus electron but proton is +about 2,000 times the mass of the + + align:start position:0% +about 2,000 times the mass of the + + + align:start position:0% +about 2,000 times the mass of the +electron so this is basically the mass + + align:start position:0% +electron so this is basically the mass + + + align:start position:0% +electron so this is basically the mass +of the proton and they factor out so the + + align:start position:0% +of the proton and they factor out so the + + + align:start position:0% +of the proton and they factor out so the +effective uh reduced mass is roughly + + align:start position:0% +effective uh reduced mass is roughly + + + align:start position:0% +effective uh reduced mass is roughly +equal to the electron + + align:start position:0% +equal to the electron + + + align:start position:0% +equal to the electron +Mass Corrections of a part in a + + align:start position:0% + + + + align:start position:0% + +thousand okay so to answer your question + + align:start position:0% +thousand okay so to answer your question + + + align:start position:0% +thousand okay so to answer your question +is the proton also in some complicated + + align:start position:0% +is the proton also in some complicated + + + align:start position:0% +is the proton also in some complicated +state describe it well in fact neither + + align:start position:0% +state describe it well in fact neither + + + align:start position:0% +state describe it well in fact neither +the electron nor the proton are + + align:start position:0% +the electron nor the proton are + + + align:start position:0% +the electron nor the proton are +described by the coolant potential but + + align:start position:0% +described by the coolant potential but + + + align:start position:0% +described by the coolant potential but +the Rel relative + + align:start position:0% +the Rel relative + + + align:start position:0% +the Rel relative +position the relative radial distance + + align:start position:0% +position the relative radial distance + + + align:start position:0% +position the relative radial distance +between them is controlled by the coolum + + align:start position:0% +between them is controlled by the coolum + + + align:start position:0% +between them is controlled by the coolum +potential and the center of mass degree + + align:start position:0% +potential and the center of mass degree + + + align:start position:0% +potential and the center of mass degree +of freedom is a free + + align:start position:0% +of freedom is a free + + + align:start position:0% +of freedom is a free +particle does that make sense okay + + align:start position:0% +particle does that make sense okay + + + align:start position:0% +particle does that make sense okay +good okay so so much for + + align:start position:0% + + + + align:start position:0% + +so much for that example the free + + align:start position:0% +so much for that example the free + + + align:start position:0% +so much for that example the free +particle and the central + + align:start position:0% + + + + align:start position:0% + +potential here's the much more + + align:start position:0% +potential here's the much more + + + align:start position:0% +potential here's the much more +interesting that happens when we have + + align:start position:0% +interesting that happens when we have + + + align:start position:0% +interesting that happens when we have +multiple particles yeah you + + align:start position:0% +multiple particles yeah you + + + align:start position:0% +multiple particles yeah you +exp oh yeah sorry this is the I just + + align:start position:0% +exp oh yeah sorry this is the I just + + + align:start position:0% +exp oh yeah sorry this is the I just +meant the gradient with respect to R so + + align:start position:0% +meant the gradient with respect to R so + + + align:start position:0% +meant the gradient with respect to R so +if R is a vector this is the gradient + + align:start position:0% +if R is a vector this is the gradient + + + align:start position:0% +if R is a vector this is the gradient +with respect to R norm squar and this is + + align:start position:0% +with respect to R norm squar and this is + + + align:start position:0% +with respect to R norm squar and this is +the gradient with respect to the the + + align:start position:0% +the gradient with respect to the the + + + align:start position:0% +the gradient with respect to the the +relative coordinate so for example um uh + + align:start position:0% +relative coordinate so for example um uh + + + align:start position:0% +relative coordinate so for example um uh +this is um if if we're in one dimension + + align:start position:0% +this is um if if we're in one dimension + + + align:start position:0% +this is um if if we're in one dimension +so that this is strictly one dimensional + + align:start position:0% +so that this is strictly one dimensional + + + align:start position:0% +so that this is strictly one dimensional +then this is just derivative with + + align:start position:0% +then this is just derivative with + + + align:start position:0% +then this is just derivative with +respect to + + align:start position:0% +respect to + + + align:start position:0% +respect to +r squared and this is derivative with + + align:start position:0% +r squared and this is derivative with + + + align:start position:0% +r squared and this is derivative with +respect to little + + align:start position:0% +respect to little + + + align:start position:0% +respect to little +r + + align:start position:0% +r + + + align:start position:0% +r +squared just the gradient squared did + + align:start position:0% +squared just the gradient squared did + + + align:start position:0% +squared just the gradient squared did +that answer your question yeah what + + align:start position:0% +that answer your question yeah what + + + align:start position:0% +that answer your question yeah what +about in well then it's the gradient + + align:start position:0% +about in well then it's the gradient + + + align:start position:0% +about in well then it's the gradient +operator the the thing that takes a + + align:start position:0% +operator the the thing that takes a + + + align:start position:0% +operator the the thing that takes a +function gives you a vector which is the + + align:start position:0% +function gives you a vector which is the + + + align:start position:0% +function gives you a vector which is the +the the directional derivative uh of + + align:start position:0% +the the directional derivative uh of + + + align:start position:0% +the the directional derivative uh of +that yeah exactly the r + + align:start position:0% + + + + align:start position:0% + +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +sorry a subtraction + + align:start position:0% + + + + align:start position:0% + +where minus H squ upon 2 m d r 2 minus H + + align:start position:0% +where minus H squ upon 2 m d r 2 minus H + + + align:start position:0% +where minus H squ upon 2 m d r 2 minus H +S 2 mu D this okay so that's those are + + align:start position:0% +S 2 mu D this okay so that's those are + + + align:start position:0% +S 2 mu D this okay so that's those are +SE not multip yeah they're not + + align:start position:0% +SE not multip yeah they're not + + + align:start position:0% +SE not multip yeah they're not +multiplied right this this it's just the + + align:start position:0% +multiplied right this this it's just the + + + align:start position:0% +multiplied right this this it's just the +sum so the energy is kinetic energy of + + align:start position:0% +sum so the energy is kinetic energy of + + + align:start position:0% +sum so the energy is kinetic energy of +the relative of the center of mass + + align:start position:0% +the relative of the center of mass + + + align:start position:0% +the relative of the center of mass +kinetic energy of the relative degree of + + align:start position:0% +kinetic energy of the relative degree of + + + align:start position:0% +kinetic energy of the relative degree of +freedom and then potential + + align:start position:0% +freedom and then potential + + + align:start position:0% +freedom and then potential +energy yeah is exactly what happens in + + align:start position:0% +energy yeah is exactly what happens in + + + align:start position:0% +energy yeah is exactly what happens in +in class mechanics + + align:start position:0% + + + + align:start position:0% + +yeah this one M it's the total mass ma + + align:start position:0% +yeah this one M it's the total mass ma + + + align:start position:0% +yeah this one M it's the total mass ma +plus MB and this one is the reduced + + align:start position:0% +plus MB and this one is the reduced + + + align:start position:0% +plus MB and this one is the reduced +mass m MB upon ma plus + + align:start position:0% +mass m MB upon ma plus + + + align:start position:0% +mass m MB upon ma plus +MB okay so here's a cool thing that + + align:start position:0% +MB okay so here's a cool thing that + + + align:start position:0% +MB okay so here's a cool thing that +happens with multiple particles that + + align:start position:0% +happens with multiple particles that + + + align:start position:0% +happens with multiple particles that +didn't happen previously suppose we have + + align:start position:0% +didn't happen previously suppose we have + + + align:start position:0% +didn't happen previously suppose we have +identical particles + + align:start position:0% + + + + align:start position:0% + +so in particular imagine I have two + + align:start position:0% +so in particular imagine I have two + + + align:start position:0% +so in particular imagine I have two +billiard + + align:start position:0% +billiard + + + align:start position:0% +billiard +balls so I have two billiard balls and I + + align:start position:0% +balls so I have two billiard balls and I + + + align:start position:0% +balls so I have two billiard balls and I +shoot I send one in from one side and I + + align:start position:0% +shoot I send one in from one side and I + + + align:start position:0% +shoot I send one in from one side and I +send the other in from the other side + + align:start position:0% +send the other in from the other side + + + align:start position:0% +send the other in from the other side +and then they Collide and there's some + + align:start position:0% +and then they Collide and there's some + + + align:start position:0% +and then they Collide and there's some +horrible chaos that happens and one goes + + align:start position:0% +horrible chaos that happens and one goes + + + align:start position:0% +horrible chaos that happens and one goes +flying out to this position a and the + + align:start position:0% +flying out to this position a and the + + + align:start position:0% +flying out to this position a and the +other goes flying out to this position + + align:start position:0% +other goes flying out to this position + + + align:start position:0% +other goes flying out to this position +B + + align:start position:0% +B + + + align:start position:0% +B +okay now here's my question which ball + + align:start position:0% +okay now here's my question which ball + + + align:start position:0% +okay now here's my question which ball +went to a and which ball went to + + align:start position:0% +went to a and which ball went to + + + align:start position:0% +went to a and which ball went to +B well if we did this experiment that + + align:start position:0% +B well if we did this experiment that + + + align:start position:0% +B well if we did this experiment that +would be be easy to answer CU we could + + align:start position:0% +would be be easy to answer CU we could + + + align:start position:0% +would be be easy to answer CU we could +paint a little you know one on this one + + align:start position:0% +paint a little you know one on this one + + + align:start position:0% +paint a little you know one on this one +and a little two on this one and they'd + + align:start position:0% +and a little two on this one and they'd + + + align:start position:0% +and a little two on this one and they'd +go flying out uh and then at the end + + align:start position:0% +go flying out uh and then at the end + + + align:start position:0% +go flying out uh and then at the end +when you catch the ball at a and you + + align:start position:0% +when you catch the ball at a and you + + + align:start position:0% +when you catch the ball at a and you +catch the ball at B you can grab them + + align:start position:0% +catch the ball at B you can grab them + + + align:start position:0% +catch the ball at B you can grab them +and look at them and say aha this one in + + align:start position:0% +and look at them and say aha this one in + + + align:start position:0% +and look at them and say aha this one in +my left hand which I got from a has one + + align:start position:0% +my left hand which I got from a has one + + + align:start position:0% +my left hand which I got from a has one +on it this one has two on it and I'm + + align:start position:0% +on it this one has two on it and I'm + + + align:start position:0% +on it this one has two on it and I'm +done right the other way we could have + + align:start position:0% +done right the other way we could have + + + align:start position:0% +done right the other way we could have +uh observed which ball went where is we + + align:start position:0% +uh observed which ball went where is we + + + align:start position:0% +uh observed which ball went where is we +could have taken a high-speed film of + + align:start position:0% +could have taken a high-speed film of + + + align:start position:0% +could have taken a high-speed film of +this and watched frame by frame and said + + align:start position:0% +this and watched frame by frame and said + + + align:start position:0% +this and watched frame by frame and said +aha particle one particle one particle + + align:start position:0% +aha particle one particle one particle + + + align:start position:0% +aha particle one particle one particle +one particle one particle 2 two two two + + align:start position:0% +one particle one particle 2 two two two + + + align:start position:0% +one particle one particle 2 two two two +two right we could have just followed + + align:start position:0% +two right we could have just followed + + + align:start position:0% +two right we could have just followed +the paths and we we haven't done + + align:start position:0% +the paths and we we haven't done + + + align:start position:0% +the paths and we we haven't done +anything to the experiment we just took + + align:start position:0% +anything to the experiment we just took + + + align:start position:0% +anything to the experiment we just took +a film we haven't messed with it we + + align:start position:0% +a film we haven't messed with it we + + + align:start position:0% +a film we haven't messed with it we +don't change the results of the + + align:start position:0% +don't change the results of the + + + align:start position:0% +don't change the results of the +experiment we just watch right perfectly + + align:start position:0% +experiment we just watch right perfectly + + + align:start position:0% +experiment we just watch right perfectly +doable classically Quantum mechanically + + align:start position:0% +doable classically Quantum mechanically + + + align:start position:0% +doable classically Quantum mechanically +is this + + align:start position:0% +is this + + + align:start position:0% +is this +doable no because first off if you watch + + align:start position:0% +doable no because first off if you watch + + + align:start position:0% +doable no because first off if you watch +carefully along and figure out with did + + align:start position:0% +carefully along and figure out with did + + + align:start position:0% +carefully along and figure out with did +it go through this slit did it go + + align:start position:0% +it go through this slit did it go + + + align:start position:0% +it go through this slit did it go +through that slit you know you change + + align:start position:0% +through that slit you know you change + + + align:start position:0% +through that slit you know you change +the results 100% white versus 50/50 + + align:start position:0% +the results 100% white versus 50/50 + + + align:start position:0% +the results 100% white versus 50/50 +right if you go back to the + + align:start position:0% +right if you go back to the + + + align:start position:0% +right if you go back to the +boxes um and meanwhile if they're truly + + align:start position:0% +boxes um and meanwhile if they're truly + + + align:start position:0% +boxes um and meanwhile if they're truly +identical + + align:start position:0% +identical + + + align:start position:0% +identical +particles like electrons there's no way + + align:start position:0% +particles like electrons there's no way + + + align:start position:0% +particles like electrons there's no way +to paint anything on the damn particle + + align:start position:0% +to paint anything on the damn particle + + + align:start position:0% +to paint anything on the damn particle +they're just electrons and they're + + align:start position:0% +they're just electrons and they're + + + align:start position:0% +they're just electrons and they're +completely as far as anyone's ever been + + align:start position:0% +completely as far as anyone's ever been + + + align:start position:0% +completely as far as anyone's ever been +able to tell completely and utterly + + align:start position:0% +able to tell completely and utterly + + + align:start position:0% +able to tell completely and utterly +identical they cannot be distinguished + + align:start position:0% +identical they cannot be distinguished + + + align:start position:0% +identical they cannot be distinguished +in any way whatsoever so you can't do + + align:start position:0% +in any way whatsoever so you can't do + + + align:start position:0% +in any way whatsoever so you can't do +the thing where you grab the one from a + + align:start position:0% +the thing where you grab the one from a + + + align:start position:0% +the thing where you grab the one from a +and grab the one from B and say ah this + + align:start position:0% +and grab the one from B and say ah this + + + align:start position:0% +and grab the one from B and say ah this +one had the one on it they're + + align:start position:0% +one had the one on it they're + + + align:start position:0% +one had the one on it they're +indistinguishable yeah + + align:start position:0% + + + + align:start position:0% + +we're going to come to the poly + + align:start position:0% +we're going to come to the poly + + + align:start position:0% +we're going to come to the poly +Exclusion Principle hold on to that hold + + align:start position:0% +Exclusion Principle hold on to that hold + + + align:start position:0% +Exclusion Principle hold on to that hold +on to that question we're going to come + + align:start position:0% +on to that question we're going to come + + + align:start position:0% +on to that question we're going to come +we're going to get there okay so + + align:start position:0% + + + + align:start position:0% + +um so we we can't in if we have truly + + align:start position:0% +um so we we can't in if we have truly + + + align:start position:0% +um so we we can't in if we have truly +identical particles what we mean by that + + align:start position:0% +identical particles what we mean by that + + + align:start position:0% +identical particles what we mean by that +is there's no way to run this experiment + + align:start position:0% +is there's no way to run this experiment + + + align:start position:0% +is there's no way to run this experiment +and determine which particle ended up + + align:start position:0% +and determine which particle ended up + + + align:start position:0% +and determine which particle ended up +which of these two particles went to a + + align:start position:0% +which of these two particles went to a + + + align:start position:0% +which of these two particles went to a +and which went to B everyone cool with + + align:start position:0% +and which went to B everyone cool with + + + align:start position:0% +and which went to B everyone cool with +that they're identical and what I want + + align:start position:0% +that they're identical and what I want + + + align:start position:0% +that they're identical and what I want +to understand is what are the + + align:start position:0% +to understand is what are the + + + align:start position:0% +to understand is what are the +consequences so the first and basic + + align:start position:0% +consequences so the first and basic + + + align:start position:0% +consequences so the first and basic +consequence of this is that the + + align:start position:0% +consequence of this is that the + + + align:start position:0% +consequence of this is that the +probability that the first particle ends + + align:start position:0% +probability that the first particle ends + + + align:start position:0% +probability that the first particle ends +up at a and the second particle ends up + + align:start position:0% +up at a and the second particle ends up + + + align:start position:0% +up at a and the second particle ends up +at B must be equal to the probability um + + align:start position:0% +at B must be equal to the probability um + + + align:start position:0% +at B must be equal to the probability um +that the first particle ends up at B and + + align:start position:0% +that the first particle ends up at B and + + + align:start position:0% +that the first particle ends up at B and +the second particle ends up at a because + + align:start position:0% +the second particle ends up at a because + + + align:start position:0% +the second particle ends up at a because +you can't tell which is + + align:start position:0% +you can't tell which is + + + align:start position:0% +you can't tell which is +which if you can't tell it must be that + + align:start position:0% +which if you can't tell it must be that + + + align:start position:0% +which if you can't tell it must be that +those probabilities are + + align:start position:0% +those probabilities are + + + align:start position:0% +those probabilities are +equal because if they weren't equal you + + align:start position:0% +equal because if they weren't equal you + + + align:start position:0% +equal because if they weren't equal you +effectively have skewed the result and + + align:start position:0% +effectively have skewed the result and + + + align:start position:0% +effectively have skewed the result and +they're not they're + + align:start position:0% +they're not they're + + + align:start position:0% +they're not they're +distinguishable these are totally IND so + + align:start position:0% +distinguishable these are totally IND so + + + align:start position:0% +distinguishable these are totally IND so +the probability that the first particle + + align:start position:0% +the probability that the first particle + + + align:start position:0% +the probability that the first particle +ends up at a second at B must be equal + + align:start position:0% +ends up at a second at B must be equal + + + align:start position:0% +ends up at a second at B must be equal +to the probability the first particle + + align:start position:0% +to the probability the first particle + + + align:start position:0% +to the probability the first particle +ends up at B and second ends up at a + + align:start position:0% +ends up at B and second ends up at a + + + align:start position:0% +ends up at B and second ends up at a +because you cannot tell the difference + + align:start position:0% +because you cannot tell the difference + + + align:start position:0% +because you cannot tell the difference +this is what it means to be + + align:start position:0% +this is what it means to be + + + align:start position:0% +this is what it means to be +identical that equal sign is what I mean + + align:start position:0% +identical that equal sign is what I mean + + + align:start position:0% +identical that equal sign is what I mean +by saying I have identical + + align:start position:0% +by saying I have identical + + + align:start position:0% +by saying I have identical +particles + + align:start position:0% + + + + align:start position:0% + +cool so let's find out what the + + align:start position:0% +cool so let's find out what the + + + align:start position:0% +cool so let's find out what the +consequences of this are Define the + + align:start position:0% +consequences of this are Define the + + + align:start position:0% +consequences of this are Define the +following operator and Dave Morrison if + + align:start position:0% +following operator and Dave Morrison if + + + align:start position:0% +following operator and Dave Morrison if +you're watching uh this is the viros p + + align:start position:0% +you're watching uh this is the viros p + + + align:start position:0% +you're watching uh this is the viros p +uh so I'm going to call this operator + + align:start position:0% +uh so I'm going to call this operator + + + align:start position:0% +uh so I'm going to call this operator +scripty p sub12 is the operator so it's + + align:start position:0% +scripty p sub12 is the operator so it's + + + align:start position:0% +scripty p sub12 is the operator so it's +got a little hat on it one more fence uh + + align:start position:0% +got a little hat on it one more fence uh + + + align:start position:0% +got a little hat on it one more fence uh +which takes the first particle uh to the + + align:start position:0% +which takes the first particle uh to the + + + align:start position:0% +which takes the first particle uh to the +to and the second particle and swaps + + align:start position:0% +to and the second particle and swaps + + + align:start position:0% +to and the second particle and swaps +them okay so and I guess I don't even + + align:start position:0% +them okay so and I guess I don't even + + + align:start position:0% +them okay so and I guess I don't even +need the one two this P operator swaps + + align:start position:0% +need the one two this P operator swaps + + + align:start position:0% +need the one two this P operator swaps +particle one and particle two so for + + align:start position:0% +particle one and particle two so for + + + align:start position:0% +particle one and particle two so for +example it takes a probability of a to B + + align:start position:0% + + + + align:start position:0% + +uh to probability of B to + + align:start position:0% + + + + align:start position:0% + +a but more + + align:start position:0% +a but more + + + align:start position:0% +a but more +importantly this swapping operation + + align:start position:0% +importantly this swapping operation + + + align:start position:0% +importantly this swapping operation +takes the wave function the amplitude of + + align:start position:0% +takes the wave function the amplitude of + + + align:start position:0% +takes the wave function the amplitude of +a and b and it swaps a and b s of + + align:start position:0% + + + + align:start position:0% + +ba now it's clear that the probability + + align:start position:0% +ba now it's clear that the probability + + + align:start position:0% +ba now it's clear that the probability +or that the swapping operation + + align:start position:0% +or that the swapping operation + + + align:start position:0% +or that the swapping operation +does nothing to the probability because + + align:start position:0% +does nothing to the probability because + + + align:start position:0% +does nothing to the probability because +the fact that they're identical + + align:start position:0% +the fact that they're identical + + + align:start position:0% +the fact that they're identical +particles means that these are equal to + + align:start position:0% +particles means that these are equal to + + + align:start position:0% +particles means that these are equal to +each other so it hasn't changed the + + align:start position:0% +each other so it hasn't changed the + + + align:start position:0% +each other so it hasn't changed the +answer but just because the + + align:start position:0% +answer but just because the + + + align:start position:0% +answer but just because the +probabilities are equal to each other + + align:start position:0% +probabilities are equal to each other + + + align:start position:0% +probabilities are equal to each other +does that tell you that the wave + + align:start position:0% +does that tell you that the wave + + + align:start position:0% +does that tell you that the wave +function is invariant under swapping the + + align:start position:0% +function is invariant under swapping the + + + align:start position:0% +function is invariant under swapping the +particles no it doesn't have to be + + align:start position:0% +particles no it doesn't have to be + + + align:start position:0% +particles no it doesn't have to be +invariant the the important thing is + + align:start position:0% +invariant the the important thing is + + + align:start position:0% +invariant the the important thing is +that the norm squared of s so in + + align:start position:0% +that the norm squared of s so in + + + align:start position:0% +that the norm squared of s so in +principle this could be equal to some + + align:start position:0% +principle this could be equal to some + + + align:start position:0% +principle this could be equal to some +phase e to the i f + + align:start position:0% +phase e to the i f + + + align:start position:0% +phase e to the i f +subab or let me call it Theta subab + + align:start position:0% + + + + align:start position:0% + +uh s of ab and if this was the the case + + align:start position:0% +uh s of ab and if this was the the case + + + align:start position:0% +uh s of ab and if this was the the case +if there was a phase that we got here + + align:start position:0% +if there was a phase that we got here + + + align:start position:0% +if there was a phase that we got here +when we take the norm squared the + + align:start position:0% +when we take the norm squared the + + + align:start position:0% +when we take the norm squared the +probability Remains the + + align:start position:0% +probability Remains the + + + align:start position:0% +probability Remains the +Same + + align:start position:0% + + + + align:start position:0% + +okay on the other hand we know something + + align:start position:0% +okay on the other hand we know something + + + align:start position:0% +okay on the other hand we know something +else we know that if we take the we take + + align:start position:0% +else we know that if we take the we take + + + align:start position:0% +else we know that if we take the we take +the wave function S + + align:start position:0% +the wave function S + + + align:start position:0% +the wave function S +A and we swap it and then we swap it + + align:start position:0% +A and we swap it and then we swap it + + + align:start position:0% +A and we swap it and then we swap it +again what do we + + align:start position:0% +again what do we + + + align:start position:0% +again what do we +get a + + align:start position:0% +get a + + + align:start position:0% +get a +B but that means this is equal to e to + + align:start position:0% +B but that means this is equal to e to + + + align:start position:0% +B but that means this is equal to e to +the 2 I th + + align:start position:0% + + + + align:start position:0% + +AB so swapping twice had better give me + + align:start position:0% +AB so swapping twice had better give me + + + align:start position:0% +AB so swapping twice had better give me +one so this had better be equal to one + + align:start position:0% +one so this had better be equal to one + + + align:start position:0% +one so this had better be equal to one +let me write this slightly differently + + align:start position:0% +let me write this slightly differently + + + align:start position:0% +let me write this slightly differently +this is e to the I + + align:start position:0% +this is e to the I + + + align:start position:0% +this is e to the I +Theta squar is equal to one so what must + + align:start position:0% +Theta squar is equal to one so what must + + + align:start position:0% +Theta squar is equal to one so what must +be true of e to the I Theta of our + + align:start position:0% +be true of e to the I Theta of our + + + align:start position:0% +be true of e to the I Theta of our +phase it's a number that squares to one + + align:start position:0% +phase it's a number that squares to one + + + align:start position:0% +phase it's a number that squares to one +so it could be one of two values it + + align:start position:0% +so it could be one of two values it + + + align:start position:0% +so it could be one of two values it +could be one or could be minus one + + align:start position:0% +could be one or could be minus one + + + align:start position:0% +could be one or could be minus one +that's + + align:start position:0% +that's + + + align:start position:0% +that's +it so what that tells us is + + align:start position:0% +it so what that tells us is + + + align:start position:0% +it so what that tells us is +a uh so that tells us that P whoops + + align:start position:0% +a uh so that tells us that P whoops + + + align:start position:0% +a uh so that tells us that P whoops +script p on S + + align:start position:0% +script p on S + + + align:start position:0% +script p on S +B is equal + + align:start position:0% +B is equal + + + align:start position:0% +B is equal +to plus or minus s + + align:start position:0% +to plus or minus s + + + align:start position:0% +to plus or minus s +ba oh sorry AB + + align:start position:0% + + + + align:start position:0% + +another way to say this is just that so + + align:start position:0% +another way to say this is just that so + + + align:start position:0% +another way to say this is just that so +another way to say this is that + + align:start position:0% +another way to say this is that + + + align:start position:0% +another way to say this is that +p^2 acting on S is just s again so the + + align:start position:0% +p^2 acting on S is just s again so the + + + align:start position:0% +p^2 acting on S is just s again so the +igen values of P have to be plus or + + align:start position:0% +igen values of P have to be plus or + + + align:start position:0% +igen values of P have to be plus or +minus + + align:start position:0% + + + + align:start position:0% + +one here they + + align:start position:0% + + + + align:start position:0% + +are so um in fact this is let me phrase + + align:start position:0% +are so um in fact this is let me phrase + + + align:start position:0% +are so um in fact this is let me phrase +this in a little more correct way um + + align:start position:0% +this in a little more correct way um + + + align:start position:0% +this in a little more correct way um +this tells us that the igen + + align:start position:0% + + + + align:start position:0% + +values of p r plus orus + + align:start position:0% + + + + align:start position:0% + +one yeah + + align:start position:0% + + + + align:start position:0% + +yes good okay so let's let's check this + + align:start position:0% + + + + align:start position:0% + +quickly so the question is how can it be + + align:start position:0% +quickly so the question is how can it be + + + align:start position:0% +quickly so the question is how can it be +minus one how can that that doesn't that + + align:start position:0% +minus one how can that that doesn't that + + + align:start position:0% +minus one how can that that doesn't that +would seem to violate our calculation so + + align:start position:0% +would seem to violate our calculation so + + + align:start position:0% +would seem to violate our calculation so +what this is saying is that um if we + + align:start position:0% +what this is saying is that um if we + + + align:start position:0% +what this is saying is that um if we +know if we take p on uh let's say p on S + + align:start position:0% +know if we take p on uh let's say p on S + + + align:start position:0% +know if we take p on uh let's say p on S +of a let's say let's let s um be uh an + + align:start position:0% +of a let's say let's let s um be uh an + + + align:start position:0% +of a let's say let's let s um be uh an +igen function of P okay so if s is an + + align:start position:0% +igen function of P okay so if s is an + + + align:start position:0% +igen function of P okay so if s is an +igen function of p with igen value minus + + align:start position:0% +igen function of p with igen value minus + + + align:start position:0% +igen function of p with igen value minus +one then this p on S is equal to minus + + align:start position:0% +one then this p on S is equal to minus + + + align:start position:0% +one then this p on S is equal to minus +s + + align:start position:0% +s + + + align:start position:0% +s +yeah now the + + align:start position:0% +yeah now the + + + align:start position:0% +yeah now the +probability is equal to s^ + + align:start position:0% +probability is equal to s^ + + + align:start position:0% +probability is equal to s^ +squ and so p on + + align:start position:0% +squ and so p on + + + align:start position:0% +squ and so p on +S or sorry p on S + + align:start position:0% + + + + align:start position:0% + +squ is equal to + + align:start position:0% +squ is equal to + + + align:start position:0% +squ is equal to +um uh uh minus s squar we take each s it + + align:start position:0% +um uh uh minus s squar we take each s it + + + align:start position:0% +um uh uh minus s squar we take each s it +goes to minus + + align:start position:0% +goes to minus + + + align:start position:0% +goes to minus +s this is just equal to S + + align:start position:0% + + + + align:start position:0% + +squ yeah I who asked the question sorry + + align:start position:0% +squ yeah I who asked the question sorry + + + align:start position:0% +squ yeah I who asked the question sorry +right okay so it leaves the norm squared + + align:start position:0% +right okay so it leaves the norm squared + + + align:start position:0% +right okay so it leaves the norm squared +invariant so even so it's okay to have a + + align:start position:0% +invariant so even so it's okay to have a + + + align:start position:0% +invariant so even so it's okay to have a +minus one I value under P because that + + align:start position:0% +minus one I value under P because that + + + align:start position:0% +minus one I value under P because that +doesn't change the probability + + align:start position:0% +doesn't change the probability + + + align:start position:0% +doesn't change the probability +distribution the probability + + align:start position:0% +distribution the probability + + + align:start position:0% +distribution the probability +distribution is left in + + align:start position:0% +distribution is left in + + + align:start position:0% +distribution is left in +however if we take + + align:start position:0% +however if we take + + + align:start position:0% +however if we take +p^2 on S that's equal to p on p on S + + align:start position:0% +p^2 on S that's equal to p on p on S + + + align:start position:0% +p^2 on S that's equal to p on p on S +it's equal to p on minus s which is + + align:start position:0% +it's equal to p on minus s which is + + + align:start position:0% +it's equal to p on minus s which is +equal to minus minus s which is equal to + + align:start position:0% +equal to minus minus s which is equal to + + + align:start position:0% +equal to minus minus s which is equal to +S okay so and this is the statement that + + align:start position:0% +S okay so and this is the statement that + + + align:start position:0% +S okay so and this is the statement that +the square acts as the + + align:start position:0% + + + + align:start position:0% + +identity did that answer your + + align:start position:0% +identity did that answer your + + + align:start position:0% +identity did that answer your +question okay okay + + align:start position:0% +question okay okay + + + align:start position:0% +question okay okay +um a little why we need on to go back to + + align:start position:0% +um a little why we need on to go back to + + + align:start position:0% +um a little why we need on to go back to +I me it preserve the probability regard + + align:start position:0% +I me it preserve the probability regard + + + align:start position:0% +I me it preserve the probability regard +we had + + align:start position:0% +we had + + + align:start position:0% +we had +two good why did p^ s have to be the + + align:start position:0% +two good why did p^ s have to be the + + + align:start position:0% +two good why did p^ s have to be the +identity because what is p doing P takes + + align:start position:0% +identity because what is p doing P takes + + + align:start position:0% +identity because what is p doing P takes +two particles and it swaps them and if + + align:start position:0% +two particles and it swaps them and if + + + align:start position:0% +two particles and it swaps them and if +it swaps them again what do you get the + + align:start position:0% +it swaps them again what do you get the + + + align:start position:0% +it swaps them again what do you get the +original + + align:start position:0% +original + + + align:start position:0% +original +configuration right if you by swapping + + align:start position:0% +configuration right if you by swapping + + + align:start position:0% +configuration right if you by swapping +if by P you mean the thing that swaps + + align:start position:0% +if by P you mean the thing that swaps + + + align:start position:0% +if by P you mean the thing that swaps +those particles then doing it twice is + + align:start position:0% +those particles then doing it twice is + + + align:start position:0% +those particles then doing it twice is +like not doing anything at all now you + + align:start position:0% +like not doing anything at all now you + + + align:start position:0% +like not doing anything at all now you +can define a different quantity which + + align:start position:0% +can define a different quantity which + + + align:start position:0% +can define a different quantity which +isn't this swapping operation which does + + align:start position:0% +isn't this swapping operation which does + + + align:start position:0% +isn't this swapping operation which does +this twice and gives you something else + + align:start position:0% +this twice and gives you something else + + + align:start position:0% +this twice and gives you something else +that's perfectly reasonable but I'm + + align:start position:0% +that's perfectly reasonable but I'm + + + align:start position:0% +that's perfectly reasonable but I'm +going to be interested in the operator + + align:start position:0% +going to be interested in the operator + + + align:start position:0% +going to be interested in the operator +which is just Swap and if you do it + + align:start position:0% +which is just Swap and if you do it + + + align:start position:0% +which is just Swap and if you do it +twice you get back to the identity okay + + align:start position:0% +twice you get back to the identity okay + + + align:start position:0% +twice you get back to the identity okay +cool okay + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yes uh well what what does it do with + + align:start position:0% +yes uh well what what does it do with + + + align:start position:0% +yes uh well what what does it do with +right so at given any configuration at + + align:start position:0% +right so at given any configuration at + + + align:start position:0% +right so at given any configuration at +any moment in time right pick your wave + + align:start position:0% +any moment in time right pick your wave + + + align:start position:0% +any moment in time right pick your wave +function pick your state for example two + + align:start position:0% +function pick your state for example two + + + align:start position:0% +function pick your state for example two +particles here what the script DP + + align:start position:0% +particles here what the script DP + + + align:start position:0% +particles here what the script DP +operator with the swapping operator does + + align:start position:0% +operator with the swapping operator does + + + align:start position:0% +operator with the swapping operator does +it just swaps them so it swaps the + + align:start position:0% +it just swaps them so it swaps the + + + align:start position:0% +it just swaps them so it swaps the +position of one and the position of the + + align:start position:0% +position of one and the position of the + + + align:start position:0% +position of one and the position of the +other right exactly and that and you do + + align:start position:0% +other right exactly and that and you do + + + align:start position:0% +other right exactly and that and you do +that at some moment in time you do that + + align:start position:0% +that at some moment in time you do that + + + align:start position:0% +that at some moment in time you do that +to a state so in that experiment what I + + align:start position:0% +to a state so in that experiment what I + + + align:start position:0% +to a state so in that experiment what I +mean there's no there's no answer to the + + align:start position:0% +mean there's no there's no answer to the + + + align:start position:0% +mean there's no there's no answer to the +question you know does p swap them + + align:start position:0% +question you know does p swap them + + + align:start position:0% +question you know does p swap them +before or does it swap them after it's + + align:start position:0% +before or does it swap them after it's + + + align:start position:0% +before or does it swap them after it's +up to you you could apply the P operator + + align:start position:0% +up to you you could apply the P operator + + + align:start position:0% +up to you you could apply the P operator +anytime you want cool okay + + align:start position:0% + + + + align:start position:0% + +yeah yeah that sounds reasonable + + align:start position:0% +yeah yeah that sounds reasonable + + + align:start position:0% +yeah yeah that sounds reasonable +sounds yeah this is + + align:start position:0% + + + + align:start position:0% + +disconcerting that's exactly right so + + align:start position:0% +disconcerting that's exactly right so + + + align:start position:0% +disconcerting that's exactly right so +that's an excellent observation let me + + align:start position:0% +that's an excellent observation let me + + + align:start position:0% +that's an excellent observation let me +rephrase that slightly so here's the + + align:start position:0% +rephrase that slightly so here's the + + + align:start position:0% +rephrase that slightly so here's the +observation that she's making it's + + align:start position:0% +observation that she's making it's + + + align:start position:0% +observation that she's making it's +exactly correct and it's where we're + + align:start position:0% +exactly correct and it's where we're + + + align:start position:0% +exactly correct and it's where we're +going to get in a few minutes um so the + + align:start position:0% +going to get in a few minutes um so the + + + align:start position:0% +going to get in a few minutes um so the +observation is this look imagine I take + + align:start position:0% +observation is this look imagine I take + + + align:start position:0% +observation is this look imagine I take +two electrons which for the moment we'll + + align:start position:0% +two electrons which for the moment we'll + + + align:start position:0% +two electrons which for the moment we'll +just call identical particles so we take + + align:start position:0% +just call identical particles so we take + + + align:start position:0% +just call identical particles so we take +two identical particles put one in my + + align:start position:0% +two identical particles put one in my + + + align:start position:0% +two identical particles put one in my +right hand one in my left hand and I + + align:start position:0% +right hand one in my left hand and I + + + align:start position:0% +right hand one in my left hand and I +just hold them there and I wait for a + + align:start position:0% +just hold them there and I wait for a + + + align:start position:0% +just hold them there and I wait for a +while a while later is it the same + + align:start position:0% +while a while later is it the same + + + align:start position:0% +while a while later is it the same +electron in my right + + align:start position:0% + + + + align:start position:0% + +hand I don't know they're identical + + align:start position:0% +hand I don't know they're identical + + + align:start position:0% +hand I don't know they're identical +I can't tell they're completely + + align:start position:0% +I can't tell they're completely + + + align:start position:0% +I can't tell they're completely +identical and so if you think about this + + align:start position:0% +identical and so if you think about this + + + align:start position:0% +identical and so if you think about this +like you do some like weak scattering if + + align:start position:0% +like you do some like weak scattering if + + + align:start position:0% +like you do some like weak scattering if +you did some weak scattering process + + align:start position:0% +you did some weak scattering process + + + align:start position:0% +you did some weak scattering process +between these where you you know you + + align:start position:0% +between these where you you know you + + + align:start position:0% +between these where you you know you +take them very far apart very slowly + + align:start position:0% +take them very far apart very slowly + + + align:start position:0% +take them very far apart very slowly +moving along but they're very far away + + align:start position:0% +moving along but they're very far away + + + align:start position:0% +moving along but they're very far away +so the electrostatic interaction is very + + align:start position:0% +so the electrostatic interaction is very + + + align:start position:0% +so the electrostatic interaction is very +small and so they repel each other just + + align:start position:0% +small and so they repel each other just + + + align:start position:0% +small and so they repel each other just +a little + + align:start position:0% +a little + + + align:start position:0% +a little +bit if this system is in fact identical + + align:start position:0% +bit if this system is in fact identical + + + align:start position:0% +bit if this system is in fact identical +and if the wave function is let's say + + align:start position:0% +and if the wave function is let's say + + + align:start position:0% +and if the wave function is let's say +for the moment we'll talk about whether + + align:start position:0% +for the moment we'll talk about whether + + + align:start position:0% +for the moment we'll talk about whether +this is correct or not if the wave + + align:start position:0% +this is correct or not if the wave + + + align:start position:0% +this is correct or not if the wave +function is invariant under swapping the + + align:start position:0% +function is invariant under swapping the + + + align:start position:0% +function is invariant under swapping the +particles let's just imagine that it's + + align:start position:0% +particles let's just imagine that it's + + + align:start position:0% +particles let's just imagine that it's +invariant under swapping the particles + + align:start position:0% +invariant under swapping the particles + + + align:start position:0% +invariant under swapping the particles +then then there are two things that + + align:start position:0% +then then there are two things that + + + align:start position:0% +then then there are two things that +could have happened the particles could + + align:start position:0% +could have happened the particles could + + + align:start position:0% +could have happened the particles could +have done this or there's also a + + align:start position:0% +have done this or there's also a + + + align:start position:0% +have done this or there's also a +contribution where they do + + align:start position:0% +contribution where they do + + + align:start position:0% +contribution where they do +this which kind of hurts um and uh in + + align:start position:0% +this which kind of hurts um and uh in + + + align:start position:0% +this which kind of hurts um and uh in +order for the system to be symmetric you + + align:start position:0% +order for the system to be symmetric you + + + align:start position:0% +order for the system to be symmetric you +have to have both contributions so let's + + align:start position:0% +have to have both contributions so let's + + + align:start position:0% +have to have both contributions so let's +come to that but indeed it's as if + + align:start position:0% +come to that but indeed it's as if + + + align:start position:0% +come to that but indeed it's as if +there's some + + align:start position:0% +there's some + + + align:start position:0% +there's some +additional interaction some additional + + align:start position:0% +additional interaction some additional + + + align:start position:0% +additional interaction some additional +correlations and that's exactly what we + + align:start position:0% +correlations and that's exactly what we + + + align:start position:0% +correlations and that's exactly what we +want to study so let's get to that very + + align:start position:0% +want to study so let's get to that very + + + align:start position:0% +want to study so let's get to that very +good observation so what I'd like to do + + align:start position:0% +good observation so what I'd like to do + + + align:start position:0% +good observation so what I'd like to do +is make that precise so there are two + + align:start position:0% +is make that precise so there are two + + + align:start position:0% +is make that precise so there are two +kinds of particles + + align:start position:0% +kinds of particles + + + align:start position:0% +kinds of particles +or three kinds of particles I should say + + align:start position:0% +or three kinds of particles I should say + + + align:start position:0% +or three kinds of particles I should say +in the world uh from this point of view + + align:start position:0% +in the world uh from this point of view + + + align:start position:0% +in the world uh from this point of view +the first kind of particle are + + align:start position:0% +the first kind of particle are + + + align:start position:0% +the first kind of particle are +distinguishable particles suppose I have + + align:start position:0% +distinguishable particles suppose I have + + + align:start position:0% +distinguishable particles suppose I have +two particles one with the mass m and + + align:start position:0% +two particles one with the mass m and + + + align:start position:0% +two particles one with the mass m and +one with the mass 2,000 + + align:start position:0% +one with the mass 2,000 + + + align:start position:0% +one with the mass 2,000 +M say just to pick randomly number right + + align:start position:0% +M say just to pick randomly number right + + + align:start position:0% +M say just to pick randomly number right +those are distinguishable because you + + align:start position:0% +those are distinguishable because you + + + align:start position:0% +those are distinguishable because you +can weigh them so you can tell which one + + align:start position:0% +can weigh them so you can tell which one + + + align:start position:0% +can weigh them so you can tell which one +is the heavy one which one is the light + + align:start position:0% +is the heavy one which one is the light + + + align:start position:0% +is the heavy one which one is the light +one and you know you can tell cool so + + align:start position:0% +one and you know you can tell cool so + + + align:start position:0% +one and you know you can tell cool so +there are distinguishable particles and + + align:start position:0% +there are distinguishable particles and + + + align:start position:0% +there are distinguishable particles and +if we have distinguishable particles + + align:start position:0% +if we have distinguishable particles + + + align:start position:0% +if we have distinguishable particles +I'll call s subd for distinguishable + + align:start position:0% +I'll call s subd for distinguishable + + + align:start position:0% +I'll call s subd for distinguishable +then it's okay to have uh the following + + align:start position:0% +then it's okay to have uh the following + + + align:start position:0% +then it's okay to have uh the following +thing s distinguishable first particle + + align:start position:0% +thing s distinguishable first particle + + + align:start position:0% +thing s distinguishable first particle +is the amplitude for the first particle + + align:start position:0% +is the amplitude for the first particle + + + align:start position:0% +is the amplitude for the first particle +to be at a and the amplitude for the + + align:start position:0% +to be at a and the amplitude for the + + + align:start position:0% +to be at a and the amplitude for the +second particle to be a b could be Kai + + align:start position:0% +second particle to be a b could be Kai + + + align:start position:0% +second particle to be a b could be Kai +of a some function of a and fi of B this + + align:start position:0% +of a some function of a and fi of B this + + + align:start position:0% +of a some function of a and fi of B this +is not invariant under a goes to B + + align:start position:0% +is not invariant under a goes to B + + + align:start position:0% +is not invariant under a goes to B +Because under a goes to B it becomes Kai + + align:start position:0% +Because under a goes to B it becomes Kai + + + align:start position:0% +Because under a goes to B it becomes Kai +of B some function of b f of a some + + align:start position:0% +of B some function of b f of a some + + + align:start position:0% +of B some function of b f of a some +different function of a that's distinct + + align:start position:0% +different function of a that's distinct + + + align:start position:0% +different function of a that's distinct +but it doesn't matter they're + + align:start position:0% +but it doesn't matter they're + + + align:start position:0% +but it doesn't matter they're +distinguishable so that's perfectly fine + + align:start position:0% +distinguishable so that's perfectly fine + + + align:start position:0% +distinguishable so that's perfectly fine +it's not + + align:start position:0% +it's not + + + align:start position:0% +it's not +true P of + + align:start position:0% +true P of + + + align:start position:0% +true P of +ab is not equal to P of ba but that's + + align:start position:0% +ab is not equal to P of ba but that's + + + align:start position:0% +ab is not equal to P of ba but that's +okay because they're + + align:start position:0% +okay because they're + + + align:start position:0% +okay because they're +distinguishable everyone cool with + + align:start position:0% + + + + align:start position:0% + +that yeah exactly so P of ab this is by + + align:start position:0% +that yeah exactly so P of ab this is by + + + align:start position:0% +that yeah exactly so P of ab this is by +definition equal to Norm square of S D + + align:start position:0% +definition equal to Norm square of S D + + + align:start position:0% +definition equal to Norm square of S D +um and I should say d d uh Norm square + + align:start position:0% +um and I should say d d uh Norm square + + + align:start position:0% +um and I should say d d uh Norm square +of SD of ab + + align:start position:0% +of SD of ab + + + align:start position:0% +of SD of ab +uh squared which is equal to Norm square + + align:start position:0% +uh squared which is equal to Norm square + + + align:start position:0% +uh squared which is equal to Norm square +of Kai of a 5 + + align:start position:0% +of Kai of a 5 + + + align:start position:0% +of Kai of a 5 +b squared whereas this guy would have + + align:start position:0% +b squared whereas this guy would have + + + align:start position:0% +b squared whereas this guy would have +been Kai of b f of a norm squ and since + + align:start position:0% +been Kai of b f of a norm squ and since + + + align:start position:0% +been Kai of b f of a norm squ and since +those are just some stupid functions I + + align:start position:0% +those are just some stupid functions I + + + align:start position:0% +those are just some stupid functions I +haven't told you what they are just some + + align:start position:0% +haven't told you what they are just some + + + align:start position:0% +haven't told you what they are just some +random functions then they're just + + align:start position:0% +random functions then they're just + + + align:start position:0% +random functions then they're just +different probability + + align:start position:0% + + + + align:start position:0% + +distributions so on the other hand if we + + align:start position:0% +distributions so on the other hand if we + + + align:start position:0% +distributions so on the other hand if we +have indistinguishable wave functions + + align:start position:0% +have indistinguishable wave functions + + + align:start position:0% +have indistinguishable wave functions +then um uh s + + align:start position:0% +then um uh s + + + align:start position:0% +then um uh s +indistinguishable um + + align:start position:0% +indistinguishable um + + + align:start position:0% +indistinguishable um +we need that s squ of + + align:start position:0% +we need that s squ of + + + align:start position:0% +we need that s squ of +ab R squ is equal to S of + + align:start position:0% +ab R squ is equal to S of + + + align:start position:0% +ab R squ is equal to S of +ba + + align:start position:0% + + + + align:start position:0% + +squ and this is not of that + + align:start position:0% +squ and this is not of that + + + align:start position:0% +squ and this is not of that +form okay so we have two possibilities + + align:start position:0% +form okay so we have two possibilities + + + align:start position:0% +form okay so we have two possibilities +I'll write this as s plus minus if I + + align:start position:0% +I'll write this as s plus minus if I + + + align:start position:0% +I'll write this as s plus minus if I +know that one of the particles is in the + + align:start position:0% +know that one of the particles is in the + + + align:start position:0% +know that one of the particles is in the +state described by Kai and the other + + align:start position:0% +state described by Kai and the other + + + align:start position:0% +state described by Kai and the other +particle is in theate state described by + + align:start position:0% +particle is in theate state described by + + + align:start position:0% +particle is in theate state described by +fi this would be an example of a wave + + align:start position:0% +fi this would be an example of a wave + + + align:start position:0% +fi this would be an example of a wave +function with that property however it's + + align:start position:0% +function with that property however it's + + + align:start position:0% +function with that property however it's +not invariant under swapping A and B so + + align:start position:0% +not invariant under swapping A and B so + + + align:start position:0% +not invariant under swapping A and B so +how can I make it invariant under + + align:start position:0% +how can I make it invariant under + + + align:start position:0% +how can I make it invariant under +swapping A and B well I could do the + + align:start position:0% +swapping A and B well I could do the + + + align:start position:0% +swapping A and B well I could do the +following 1un two2 Kai of a 5 of B and + + align:start position:0% +following 1un two2 Kai of a 5 of B and + + + align:start position:0% +following 1un two2 Kai of a 5 of B and +if I want to make it + + align:start position:0% +if I want to make it + + + align:start position:0% +if I want to make it +invariant I could add plus uh Kai of B 5 + + align:start position:0% +invariant I could add plus uh Kai of B 5 + + + align:start position:0% +invariant I could add plus uh Kai of B 5 +a and now if I swap A and B here this + + align:start position:0% +a and now if I swap A and B here this + + + align:start position:0% +a and now if I swap A and B here this +becomes Kai of b f a but that's exactly + + align:start position:0% +becomes Kai of b f a but that's exactly + + + align:start position:0% +becomes Kai of b f a but that's exactly +this term this becomes K of a f b that's + + align:start position:0% +this term this becomes K of a f b that's + + + align:start position:0% +this term this becomes K of a f b that's +this term so we just swapped them yeah + + align:start position:0% +this term so we just swapped them yeah + + + align:start position:0% +this term so we just swapped them yeah +but we don't need the wave function to + + align:start position:0% +but we don't need the wave function to + + + align:start position:0% +but we don't need the wave function to +be invariant under swapping we just need + + align:start position:0% +be invariant under swapping we just need + + + align:start position:0% +be invariant under swapping we just need +it to be invariant under up to a + + align:start position:0% +it to be invariant under up to a + + + align:start position:0% +it to be invariant under up to a +sign so the other option is to have a + + align:start position:0% +sign so the other option is to have a + + + align:start position:0% +sign so the other option is to have a +minus sign + + align:start position:0% + + + + align:start position:0% + +here and this gives us that the swapping + + align:start position:0% +here and this gives us that the swapping + + + align:start position:0% +here and this gives us that the swapping +operation P acting on S plus + + align:start position:0% +operation P acting on S plus + + + align:start position:0% +operation P acting on S plus +minus of + + align:start position:0% +minus of + + + align:start position:0% +minus of +ab is equal to plusus S of a + + align:start position:0% + + + + align:start position:0% + +okay and the plus is generally called + + align:start position:0% +okay and the plus is generally called + + + align:start position:0% +okay and the plus is generally called +the symmetric and the minus the anti- + + align:start position:0% +the symmetric and the minus the anti- + + + align:start position:0% +the symmetric and the minus the anti- +symmetric + + align:start position:0% + + + + align:start position:0% + +combination okay so distinguishable + + align:start position:0% +combination okay so distinguishable + + + align:start position:0% +combination okay so distinguishable +particles can just be in some random + + align:start position:0% +particles can just be in some random + + + align:start position:0% +particles can just be in some random +state but there are constraints on what + + align:start position:0% +state but there are constraints on what + + + align:start position:0% +state but there are constraints on what +states what combinations of states are + + align:start position:0% +states what combinations of states are + + + align:start position:0% +states what combinations of states are +allowed for indistinguishable particles + + align:start position:0% +allowed for indistinguishable particles + + + align:start position:0% +allowed for indistinguishable particles +if you can't tell the difference between + + align:start position:0% +if you can't tell the difference between + + + align:start position:0% +if you can't tell the difference between +two indistinguishable particles and you + + align:start position:0% +two indistinguishable particles and you + + + align:start position:0% +two indistinguishable particles and you +know one is in the state Kai and the + + align:start position:0% +know one is in the state Kai and the + + + align:start position:0% +know one is in the state Kai and the +other is in the state fi this cannot be + + align:start position:0% +other is in the state fi this cannot be + + + align:start position:0% +other is in the state fi this cannot be +the wave function it must be either kaii + + align:start position:0% +the wave function it must be either kaii + + + align:start position:0% +the wave function it must be either kaii +Plus kaii in this fashion or minus + + align:start position:0% +Plus kaii in this fashion or minus + + + align:start position:0% +Plus kaii in this fashion or minus +everyone cool + + align:start position:0% +everyone cool + + + align:start position:0% +everyone cool +that yeah I have a + + align:start position:0% + + + + align:start position:0% + +question + + align:start position:0% +question + + + align:start position:0% +question +meity + + align:start position:0% +meity + + + align:start position:0% +meity +me + + align:start position:0% + + + + align:start position:0% + +yes good so what does probability means + + align:start position:0% +yes good so what does probability means + + + align:start position:0% +yes good so what does probability means +is what's the probability that if that + + align:start position:0% +is what's the probability that if that + + + align:start position:0% +is what's the probability that if that +upon observation the system I find the + + align:start position:0% +upon observation the system I find the + + + align:start position:0% +upon observation the system I find the +first particle to be at a and the second + + align:start position:0% +first particle to be at a and the second + + + align:start position:0% +first particle to be at a and the second +particle to be a b right and I I can + + align:start position:0% +particle to be a b right and I I can + + + align:start position:0% +particle to be a b right and I I can +check that by saying like look I catch + + align:start position:0% +check that by saying like look I catch + + + align:start position:0% +check that by saying like look I catch +the first particle I catch the second + + align:start position:0% +the first particle I catch the second + + + align:start position:0% +the first particle I catch the second +particle uh is this a no okay then that + + align:start position:0% +particle uh is this a no okay then that + + + align:start position:0% +particle uh is this a no okay then that +gives zero to the probability + + align:start position:0% +gives zero to the probability + + + align:start position:0% +gives zero to the probability +distribution I do that a billion times + + align:start position:0% +distribution I do that a billion times + + + align:start position:0% +distribution I do that a billion times +and I build up statistics and I find + + align:start position:0% +and I build up statistics and I find + + + align:start position:0% +and I build up statistics and I find +that you know a fourth of one out of + + align:start position:0% +that you know a fourth of one out of + + + align:start position:0% +that you know a fourth of one out of +four times uh I'll find a particle the + + align:start position:0% +four times uh I'll find a particle the + + + align:start position:0% +four times uh I'll find a particle the +first particle or I'll find a particle + + align:start position:0% +first particle or I'll find a particle + + + align:start position:0% +first particle or I'll find a particle +at a one out of four times I'll find a + + align:start position:0% +at a one out of four times I'll find a + + + align:start position:0% +at a one out of four times I'll find a +particle at + + align:start position:0% +particle at + + + align:start position:0% +particle at +and the probability that I find the + + align:start position:0% +and the probability that I find the + + + align:start position:0% +and the probability that I find the +first particle at a and the second + + align:start position:0% +first particle at a and the second + + + align:start position:0% +first particle at a and the second +particle at B is1 say + + align:start position:0% + + + + align:start position:0% + +okay what you can't do if they're + + align:start position:0% +okay what you can't do if they're + + + align:start position:0% +okay what you can't do if they're +identical is you can't say which + + align:start position:0% +identical is you can't say which + + + align:start position:0% +identical is you can't say which +particle you caught at a this is saying + + align:start position:0% +particle you caught at a this is saying + + + align:start position:0% +particle you caught at a this is saying +a particle at a or a particle at + + align:start position:0% +a particle at a or a particle at + + + align:start position:0% +a particle at a or a particle at +B right but it's but whether this is the + + align:start position:0% +B right but it's but whether this is the + + + align:start position:0% +B right but it's but whether this is the +same or not of probability that I find a + + align:start position:0% +same or not of probability that I find a + + + align:start position:0% +same or not of probability that I find a +particle at B and the the first particle + + align:start position:0% +particle at B and the the first particle + + + align:start position:0% +particle at B and the the first particle +B and second particle at + + align:start position:0% +B and second particle at + + + align:start position:0% +B and second particle at +a if you can't tell the difference then + + align:start position:0% +a if you can't tell the difference then + + + align:start position:0% +a if you can't tell the difference then +they're just a particle at a and a + + align:start position:0% +they're just a particle at a and a + + + align:start position:0% +they're just a particle at a and a +particle at B + + align:start position:0% + + + + align:start position:0% + +okay okay so what does this give us so + + align:start position:0% +okay okay so what does this give us so + + + align:start position:0% +okay okay so what does this give us so +this gives us a couple of nice facts so + + align:start position:0% + + + + align:start position:0% + +imagine that's an exciting + + align:start position:0% +imagine that's an exciting + + + align:start position:0% +imagine that's an exciting +sound so this gives us a couple of nice + + align:start position:0% +sound so this gives us a couple of nice + + + align:start position:0% +sound so this gives us a couple of nice +facts uh with which we + + align:start position:0% +facts uh with which we + + + align:start position:0% +facts uh with which we +can find awesomeness in the world the + + align:start position:0% +can find awesomeness in the world the + + + align:start position:0% +can find awesomeness in the world the +first + + align:start position:0% +first + + + align:start position:0% +first +is the + + align:start position:0% + + + + align:start position:0% + +following if you have identical + + align:start position:0% +following if you have identical + + + align:start position:0% +following if you have identical +particles then the energy can't depend + + align:start position:0% +particles then the energy can't depend + + + align:start position:0% +particles then the energy can't depend +on the order if you have identical + + align:start position:0% +on the order if you have identical + + + align:start position:0% +on the order if you have identical +particles and they're truly identical + + align:start position:0% +particles and they're truly identical + + + align:start position:0% +particles and they're truly identical +you swap them then the energy will be + + align:start position:0% +you swap them then the energy will be + + + align:start position:0% +you swap them then the energy will be +the same if it wasn't the same then + + align:start position:0% +the same if it wasn't the same then + + + align:start position:0% +the same if it wasn't the same then +they're distinguishable by figuring out + + align:start position:0% +they're distinguishable by figuring out + + + align:start position:0% +they're distinguishable by figuring out +what the energy is so in order that + + align:start position:0% +what the energy is so in order that + + + align:start position:0% +what the energy is so in order that +they're identical it must be true that + + align:start position:0% +they're identical it must be true that + + + align:start position:0% +they're identical it must be true that +if you swap the + + align:start position:0% +if you swap the + + + align:start position:0% +if you swap the +particles and then compute the energy + + align:start position:0% +particles and then compute the energy + + + align:start position:0% +particles and then compute the energy +this should be the same as what you get + + align:start position:0% +this should be the same as what you get + + + align:start position:0% +this should be the same as what you get +if you first compute the energy and then + + align:start position:0% +if you first compute the energy and then + + + align:start position:0% +if you first compute the energy and then +swap them + + align:start position:0% + + + + align:start position:0% + +which is to say that the commutator of e + + align:start position:0% +which is to say that the commutator of e + + + align:start position:0% +which is to say that the commutator of e +with the swapping operator p is + + align:start position:0% +with the swapping operator p is + + + align:start position:0% +with the swapping operator p is +zero okay but what that tells + + align:start position:0% +zero okay but what that tells + + + align:start position:0% +zero okay but what that tells +you is that the expectation value of P + + align:start position:0% +you is that the expectation value of P + + + align:start position:0% +you is that the expectation value of P +doesn't change in + + align:start position:0% + + + + align:start position:0% + +time in particular if it's some initial + + align:start position:0% +time in particular if it's some initial + + + align:start position:0% +time in particular if it's some initial +state state if you + + align:start position:0% + + + + align:start position:0% + +initially p on S is equal to plus + + align:start position:0% +initially p on S is equal to plus + + + align:start position:0% +initially p on S is equal to plus +s at Time + + align:start position:0% + + + + align:start position:0% + +Zero then s then P at + + align:start position:0% +Zero then s then P at + + + align:start position:0% +Zero then s then P at +s uh P SI is equal to plus s for all for + + align:start position:0% +s uh P SI is equal to plus s for all for + + + align:start position:0% +s uh P SI is equal to plus s for all for +all future times P of T is equal to plus + + align:start position:0% +all future times P of T is equal to plus + + + align:start position:0% +all future times P of T is equal to plus +s of + + align:start position:0% +s of + + + align:start position:0% +s of +t Okay so if you have two identical + + align:start position:0% +t Okay so if you have two identical + + + align:start position:0% +t Okay so if you have two identical +particles and the wave function is + + align:start position:0% +particles and the wave function is + + + align:start position:0% +particles and the wave function is +invariant under swapping them at some + + align:start position:0% +invariant under swapping them at some + + + align:start position:0% +invariant under swapping them at some +moment in time then it will always be + + align:start position:0% +moment in time then it will always be + + + align:start position:0% +moment in time then it will always be +invariant under swapping them it's a + + align:start position:0% +invariant under swapping them it's a + + + align:start position:0% +invariant under swapping them it's a +persistent property of particles that + + align:start position:0% +persistent property of particles that + + + align:start position:0% +persistent property of particles that +their wave function is invariance under + + align:start position:0% +their wave function is invariance under + + + align:start position:0% +their wave function is invariance under +swapping + + align:start position:0% +swapping + + + align:start position:0% +swapping +them + + align:start position:0% +them + + + align:start position:0% +them +yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +have urani one + + align:start position:0% +have urani one + + + align:start position:0% +have urani one +of heavier isotope and during the time + + align:start position:0% +of heavier isotope and during the time + + + align:start position:0% +of heavier isotope and during the time +that you're like holding them in your + + align:start position:0% +that you're like holding them in your + + + align:start position:0% +that you're like holding them in your +hand of them decay the same yeah that's + + align:start position:0% +hand of them decay the same yeah that's + + + align:start position:0% +hand of them decay the same yeah that's +always this tells you something this is + + align:start position:0% +always this tells you something this is + + + align:start position:0% +always this tells you something this is +a very good question so the question is + + align:start position:0% +a very good question so the question is + + + align:start position:0% +a very good question so the question is +look suppose I have an excited iope + + align:start position:0% +look suppose I have an excited iope + + + align:start position:0% +look suppose I have an excited iope +uranium that's distinguishable from the + + align:start position:0% +uranium that's distinguishable from the + + + align:start position:0% +uranium that's distinguishable from the +from some other isotope of uranium I + + align:start position:0% +from some other isotope of uranium I + + + align:start position:0% +from some other isotope of uranium I +wait for a while and then this thing + + align:start position:0% +wait for a while and then this thing + + + align:start position:0% +wait for a while and then this thing +decays down to the St it won't Decay to + + align:start position:0% +decays down to the St it won't Decay to + + + align:start position:0% +decays down to the St it won't Decay to +the stable isotope of uranium but + + align:start position:0% +the stable isotope of uranium but + + + align:start position:0% +the stable isotope of uranium but +whatever it decays down to we can + + align:start position:0% +whatever it decays down to we can + + + align:start position:0% +whatever it decays down to we can +imagine this a universe in which it did + + align:start position:0% +imagine this a universe in which it did + + + align:start position:0% +imagine this a universe in which it did +it decays down to a a stable State and + + align:start position:0% +it decays down to a a stable State and + + + align:start position:0% +it decays down to a a stable State and +uh well I mean uranium is never stable + + align:start position:0% +uh well I mean uranium is never stable + + + align:start position:0% +uh well I mean uranium is never stable +but anyway you you get the idea um and + + align:start position:0% +but anyway you you get the idea um and + + + align:start position:0% +but anyway you you get the idea um and +so and at which which point they're + + align:start position:0% +so and at which which point they're + + + align:start position:0% +so and at which which point they're +indistinguishable this sounds bad + + align:start position:0% +indistinguishable this sounds bad + + + align:start position:0% +indistinguishable this sounds bad +because now the wave function should be + + align:start position:0% +because now the wave function should be + + + align:start position:0% +because now the wave function should be +invariant uh but it started out not + + align:start position:0% +invariant uh but it started out not + + + align:start position:0% +invariant uh but it started out not +being invariant what's the problem in + + align:start position:0% +being invariant what's the problem in + + + align:start position:0% +being invariant what's the problem in +this + + align:start position:0% +this + + + align:start position:0% +this +argument the system has changed in + + align:start position:0% +argument the system has changed in + + + align:start position:0% +argument the system has changed in +particular something went flying out so + + align:start position:0% +particular something went flying out so + + + align:start position:0% +particular something went flying out so +this is actually kind of a nice way to + + align:start position:0% +this is actually kind of a nice way to + + + align:start position:0% +this is actually kind of a nice way to +argue that oh there must have been + + align:start position:0% +argue that oh there must have been + + + align:start position:0% +argue that oh there must have been +something else the full the wave + + align:start position:0% +something else the full the wave + + + align:start position:0% +something else the full the wave +function describes a full system but if + + align:start position:0% +function describes a full system but if + + + align:start position:0% +function describes a full system but if +something + + align:start position:0% +something + + + align:start position:0% +something +leaves then it's not the same system + + align:start position:0% +leaves then it's not the same system + + + align:start position:0% +leaves then it's not the same system +anymore and the wave function isn't + + align:start position:0% +anymore and the wave function isn't + + + align:start position:0% +anymore and the wave function isn't +describing the same degrees of freedom + + align:start position:0% +describing the same degrees of freedom + + + align:start position:0% +describing the same degrees of freedom +something left but suppose we keep track + + align:start position:0% +something left but suppose we keep track + + + align:start position:0% +something left but suppose we keep track +of that one we still + + align:start position:0% +of that one we still + + + align:start position:0% +of that one we still +can't exactly then well then there's + + align:start position:0% +can't exactly then well then there's + + + align:start position:0% +can't exactly then well then there's +some additional constraint right it must + + align:start position:0% +some additional constraint right it must + + + align:start position:0% +some additional constraint right it must +be invariant under swapping that but it + + align:start position:0% +be invariant under swapping that but it + + + align:start position:0% +be invariant under swapping that but it +must but the wave function also knows + + align:start position:0% +must but the wave function also knows + + + align:start position:0% +must but the wave function also knows +about that extra bit that went flying + + align:start position:0% +about that extra bit that went flying + + + align:start position:0% +about that extra bit that went flying +off and so the whole wave function has + + align:start position:0% +off and so the whole wave function has + + + align:start position:0% +off and so the whole wave function has +to be invariant under swapping The + + align:start position:0% +to be invariant under swapping The + + + align:start position:0% +to be invariant under swapping The +Identical Parts but not invariant under + + align:start position:0% +Identical Parts but not invariant under + + + align:start position:0% +Identical Parts but not invariant under +SWAT under you know the invariance is + + align:start position:0% +SWAT under you know the invariance is + + + align:start position:0% +SWAT under you know the invariance is +not just those two things they they're + + align:start position:0% +not just those two things they they're + + + align:start position:0% +not just those two things they they're +correlated with the thing that went + + align:start position:0% +correlated with the thing that went + + + align:start position:0% +correlated with the thing that went +flying away so another way to think + + align:start position:0% +flying away so another way to think + + + align:start position:0% +flying away so another way to think +about this is Imagine two different uh + + align:start position:0% +about this is Imagine two different uh + + + align:start position:0% +about this is Imagine two different uh +hydrogen atoms here I've got hydrogen + + align:start position:0% +hydrogen atoms here I've got hydrogen + + + align:start position:0% +hydrogen atoms here I've got hydrogen +atom it's an electron and a proton and + + align:start position:0% +atom it's an electron and a proton and + + + align:start position:0% +atom it's an electron and a proton and +here's a deterior derium atom it's a an + + align:start position:0% +here's a deterior derium atom it's a an + + + align:start position:0% +here's a deterior derium atom it's a an +electron bound to a proton and a neutron + + align:start position:0% +electron bound to a proton and a neutron + + + align:start position:0% +electron bound to a proton and a neutron +glued together + + align:start position:0% +glued together + + + align:start position:0% +glued together +deuteron so + + align:start position:0% +deuteron so + + + align:start position:0% +deuteron so +um are the electrons + + align:start position:0% +um are the electrons + + + align:start position:0% +um are the electrons +identical yeah they're totally identical + + align:start position:0% +identical yeah they're totally identical + + + align:start position:0% +identical yeah they're totally identical +so is the wave function invariant does + + align:start position:0% +so is the wave function invariant does + + + align:start position:0% +so is the wave function invariant does +the wave function or the probability + + align:start position:0% +the wave function or the probability + + + align:start position:0% +the wave function or the probability +distribution have to be invariant under + + align:start position:0% +distribution have to be invariant under + + + align:start position:0% +distribution have to be invariant under +swapping the electrons yes they're + + align:start position:0% +swapping the electrons yes they're + + + align:start position:0% +swapping the electrons yes they're +identical so the probability + + align:start position:0% +identical so the probability + + + align:start position:0% +identical so the probability +distribution must be invariant under + + align:start position:0% +distribution must be invariant under + + + align:start position:0% +distribution must be invariant under +swapping the electrons however is it + + align:start position:0% +swapping the electrons however is it + + + align:start position:0% +swapping the electrons however is it +identical under swapping the hydrogen + + align:start position:0% +identical under swapping the hydrogen + + + align:start position:0% +identical under swapping the hydrogen +with the duum + + align:start position:0% +with the duum + + + align:start position:0% +with the duum +no no so it's invariant under swapping + + align:start position:0% +no no so it's invariant under swapping + + + align:start position:0% +no no so it's invariant under swapping +The Identical parts and not the not + + align:start position:0% +The Identical parts and not the not + + + align:start position:0% +The Identical parts and not the not +identical Parts cool + + align:start position:0% +identical Parts cool + + + align:start position:0% +identical Parts cool +okay + + align:start position:0% + + + + align:start position:0% + +so so this tells us that there are two + + align:start position:0% +so so this tells us that there are two + + + align:start position:0% +so so this tells us that there are two +kinds of part particles they're + + align:start position:0% +kinds of part particles they're + + + align:start position:0% +kinds of part particles they're +persistent um or sorry there there are + + align:start position:0% +persistent um or sorry there there are + + + align:start position:0% +persistent um or sorry there there are +three kinds of particles and these + + align:start position:0% +three kinds of particles and these + + + align:start position:0% +three kinds of particles and these +properties are persistent the first kind + + align:start position:0% +properties are persistent the first kind + + + align:start position:0% +properties are persistent the first kind +of particle uh sets of particles are + + align:start position:0% +of particle uh sets of particles are + + + align:start position:0% +of particle uh sets of particles are +distinguishable + + align:start position:0% + + + + align:start position:0% + +particles if you have two particles + + align:start position:0% +particles if you have two particles + + + align:start position:0% +particles if you have two particles +which are distinguishable then you're + + align:start position:0% +which are distinguishable then you're + + + align:start position:0% +which are distinguishable then you're +done they're distinguishable nothing + + align:start position:0% +done they're distinguishable nothing + + + align:start position:0% +done they're distinguishable nothing +else to say two you can have identical + + align:start position:0% + + + + align:start position:0% + +particles with the property that if you + + align:start position:0% +particles with the property that if you + + + align:start position:0% +particles with the property that if you +take p on S + + align:start position:0% +take p on S + + + align:start position:0% +take p on S +AB uh sorry p on S if you swap the + + align:start position:0% +AB uh sorry p on S if you swap the + + + align:start position:0% +AB uh sorry p on S if you swap the +particles this is equal to plus s and + + align:start position:0% +particles this is equal to plus s and + + + align:start position:0% +particles this is equal to plus s and +then you have um so identical uh with + + align:start position:0% +then you have um so identical uh with + + + align:start position:0% +then you have um so identical uh with +plus and you have three identical + + align:start position:0% +plus and you have three identical + + + align:start position:0% +plus and you have three identical +particles where if you swap the + + align:start position:0% +particles where if you swap the + + + align:start position:0% +particles where if you swap the +particles you get a minus sign on + + align:start position:0% + + + + align:start position:0% + +s these particles are called we have a + + align:start position:0% +s these particles are called we have a + + + align:start position:0% +s these particles are called we have a +name for particles of this kind + + align:start position:0% +name for particles of this kind + + + align:start position:0% +name for particles of this kind +bons these are called + + align:start position:0% + + + + align:start position:0% + +Fons my ta did a bad thing to me when I + + align:start position:0% +Fons my ta did a bad thing to me when I + + + align:start position:0% +Fons my ta did a bad thing to me when I +was taking quantum mechanics and said + + align:start position:0% +was taking quantum mechanics and said + + + align:start position:0% +was taking quantum mechanics and said +just imagine them as little tiny fmes so + + align:start position:0% +just imagine them as little tiny fmes so + + + align:start position:0% +just imagine them as little tiny fmes so +just take a picture of fmy in your head + + align:start position:0% +just take a picture of fmy in your head + + + align:start position:0% +just take a picture of fmy in your head +and imagine Little P and and this is + + align:start position:0% +and imagine Little P and and this is + + + align:start position:0% +and imagine Little P and and this is +cruel because I can't help it every time + + align:start position:0% +cruel because I can't help it every time + + + align:start position:0% +cruel because I can't help it every time +someone in a seminar is like blah blah + + align:start position:0% +someone in a seminar is like blah blah + + + align:start position:0% +someone in a seminar is like blah blah +blah F me and I'm like damn damn it + + align:start position:0% +blah F me and I'm like damn damn it + + + align:start position:0% +blah F me and I'm like damn damn it +little fmy + + align:start position:0% +little fmy + + + align:start position:0% +little fmy +um it's really quite annoying um so now + + align:start position:0% +um it's really quite annoying um so now + + + align:start position:0% +um it's really quite annoying um so now +you have it too great um um so what are + + align:start position:0% +you have it too great um um so what are + + + align:start position:0% +you have it too great um um so what are +the consequences what are the + + align:start position:0% +the consequences what are the + + + align:start position:0% +the consequences what are the +consequences of the fact that there are + + align:start position:0% +consequences of the fact that there are + + + align:start position:0% +consequences of the fact that there are +two kinds of particles in the universe + + align:start position:0% +two kinds of particles in the universe + + + align:start position:0% +two kinds of particles in the universe +uh these Fons and um and + + align:start position:0% +uh these Fons and um and + + + align:start position:0% +uh these Fons and um and +bons this has a really lovely + + align:start position:0% +bons this has a really lovely + + + align:start position:0% +bons this has a really lovely +Consequence the first is suppose we have + + align:start position:0% +Consequence the first is suppose we have + + + align:start position:0% +Consequence the first is suppose we have +a uh a suppose we have two Fons okay + + align:start position:0% +a uh a suppose we have two Fons okay + + + align:start position:0% +a uh a suppose we have two Fons okay +examples of Fons are electrons suppose + + align:start position:0% +examples of Fons are electrons suppose + + + align:start position:0% +examples of Fons are electrons suppose +we have a wave function for two Fons + + align:start position:0% +we have a wave function for two Fons + + + align:start position:0% +we have a wave function for two Fons +the first might what's the probability + + align:start position:0% +the first might what's the probability + + + align:start position:0% +the first might what's the probability +amplitude that the first is at a and the + + align:start position:0% +amplitude that the first is at a and the + + + align:start position:0% +amplitude that the first is at a and the +second is at B well it's this s of + + align:start position:0% +second is at B well it's this s of + + + align:start position:0% +second is at B well it's this s of +ab and the statement that it's a firan + + align:start position:0% +ab and the statement that it's a firan + + + align:start position:0% +ab and the statement that it's a firan +is the statement that this is equal to + + align:start position:0% +is the statement that this is equal to + + + align:start position:0% +is the statement that this is equal to +minus s of ba if we swap the positions + + align:start position:0% +minus s of ba if we swap the positions + + + align:start position:0% +minus s of ba if we swap the positions +of the two particles we must pick up a + + align:start position:0% +of the two particles we must pick up a + + + align:start position:0% +of the two particles we must pick up a +minus sign this tells us in particular + + align:start position:0% +minus sign this tells us in particular + + + align:start position:0% +minus sign this tells us in particular +that the probability amplitude for the + + align:start position:0% +that the probability amplitude for the + + + align:start position:0% +that the probability amplitude for the +first particle would be at a and the + + align:start position:0% +first particle would be at a and the + + + align:start position:0% +first particle would be at a and the +second particle to be at a is equal to + + align:start position:0% +second particle to be at a is equal to + + + align:start position:0% +second particle to be at a is equal to +minus itself because upon swapping the + + align:start position:0% +minus itself because upon swapping the + + + align:start position:0% +minus itself because upon swapping the +particles we get minus s of AA so the + + align:start position:0% +particles we get minus s of AA so the + + + align:start position:0% +particles we get minus s of AA so the +probability amplitude to find two Fons + + align:start position:0% +probability amplitude to find two Fons + + + align:start position:0% +probability amplitude to find two Fons +at the same place is equal to zero two + + align:start position:0% +at the same place is equal to zero two + + + align:start position:0% +at the same place is equal to zero two +Fons cannot occupy the same state this + + align:start position:0% +Fons cannot occupy the same state this + + + align:start position:0% +Fons cannot occupy the same state this +was the poly Exclusion Principle which + + align:start position:0% +was the poly Exclusion Principle which + + + align:start position:0% +was the poly Exclusion Principle which +we needed to get the periodic + + align:start position:0% + + + + align:start position:0% + +table + + align:start position:0% +table + + + align:start position:0% +table +po + + align:start position:0% +po + + + align:start position:0% +po +two if we have so this is firion if we + + align:start position:0% +two if we have so this is firion if we + + + align:start position:0% +two if we have so this is firion if we +have bons s bosons s of ab + + align:start position:0% + + + + align:start position:0% + +let me write this out so um s firon or + + align:start position:0% +let me write this out so um s firon or + + + align:start position:0% +let me write this out so um s firon or +boson so firion is going to be with a + + align:start position:0% +boson so firion is going to be with a + + + align:start position:0% +boson so firion is going to be with a +minus and boson is going to be with a + + align:start position:0% +minus and boson is going to be with a + + + align:start position:0% +minus and boson is going to be with a +plus is equal to suppose I have two + + align:start position:0% +plus is equal to suppose I have two + + + align:start position:0% +plus is equal to suppose I have two +particles 1/ < tk2 and one particle is + + align:start position:0% +particles 1/ < tk2 and one particle is + + + align:start position:0% +particles 1/ < tk2 and one particle is +in the state Kai and the other particles + + align:start position:0% +in the state Kai and the other particles + + + align:start position:0% +in the state Kai and the other particles +in the state fi but in order to be + + align:start position:0% +in the state fi but in order to be + + + align:start position:0% +in the state fi but in order to be +fironic or bosonic in order for this to + + align:start position:0% +fironic or bosonic in order for this to + + + align:start position:0% +fironic or bosonic in order for this to +be invariant under swapping A and B we + + align:start position:0% +be invariant under swapping A and B we + + + align:start position:0% +be invariant under swapping A and B we +have to have a plus or a minus uh Kai of + + align:start position:0% +have to have a plus or a minus uh Kai of + + + align:start position:0% +have to have a plus or a minus uh Kai of +B 5 + + align:start position:0% +B 5 + + + align:start position:0% +B 5 +a okay and here immediately see this + + align:start position:0% +a okay and here immediately see this + + + align:start position:0% +a okay and here immediately see this +poly principle at work if I could take + + align:start position:0% +poly principle at work if I could take + + + align:start position:0% +poly principle at work if I could take +the fironic example with a minus sign + + align:start position:0% +the fironic example with a minus sign + + + align:start position:0% +the fironic example with a minus sign +then s evaluated at AA must be K A F at + + align:start position:0% +then s evaluated at AA must be K A F at + + + align:start position:0% +then s evaluated at AA must be K A F at +B minus kayet B fi at a but if a is B + + align:start position:0% +B minus kayet B fi at a but if a is B + + + align:start position:0% +B minus kayet B fi at a but if a is B +this is K A F A minus K A F A that's + + align:start position:0% +this is K A F A minus K A F A that's + + + align:start position:0% +this is K A F A minus K A F A that's +zero but let's think about the bosonic + + align:start position:0% +zero but let's think about the bosonic + + + align:start position:0% +zero but let's think about the bosonic +case if we have a bosonic field or if we + + align:start position:0% +case if we have a bosonic field or if we + + + align:start position:0% +case if we have a bosonic field or if we +have a sorry if we have a bosonic uh + + align:start position:0% +have a sorry if we have a bosonic uh + + + align:start position:0% +have a sorry if we have a bosonic uh +identical particles then s b at a with a + + align:start position:0% +identical particles then s b at a with a + + + align:start position:0% +identical particles then s b at a with a +for a firon it zero but s b of the + + align:start position:0% +for a firon it zero but s b of the + + + align:start position:0% +for a firon it zero but s b of the +amplitude to be at two uh at um at uh + + align:start position:0% +amplitude to be at two uh at um at uh + + + align:start position:0% +amplitude to be at two uh at um at uh +the same place is equal to well if B is + + align:start position:0% +the same place is equal to well if B is + + + align:start position:0% +the same place is equal to well if B is +a then these two terms are identical we + + align:start position:0% +a then these two terms are identical we + + + align:start position:0% +a then these two terms are identical we +have a plus this is + + align:start position:0% +have a plus this is + + + align:start position:0% +have a plus this is +root2 Kai at a f at a which is greater + + align:start position:0% +root2 Kai at a f at a which is greater + + + align:start position:0% +root2 Kai at a f at a which is greater +than what you might have naively guessed + + align:start position:0% +than what you might have naively guessed + + + align:start position:0% +than what you might have naively guessed +which would have been just K fa for bans + + align:start position:0% +which would have been just K fa for bans + + + align:start position:0% +which would have been just K fa for bans +they really like being next to each + + align:start position:0% +they really like being next to each + + + align:start position:0% +they really like being next to each +other they really like being in the same + + align:start position:0% +other they really like being in the same + + + align:start position:0% +other they really like being in the same +place and this will eventually lead to + + align:start position:0% +place and this will eventually lead to + + + align:start position:0% +place and this will eventually lead to +lasers so for from this simple + + align:start position:0% +lasers so for from this simple + + + align:start position:0% +lasers so for from this simple +statistical property under swapping + + align:start position:0% +statistical property under swapping + + + align:start position:0% +statistical property under swapping +picking up a minus sign we get the poly + + align:start position:0% +picking up a minus sign we get the poly + + + align:start position:0% +picking up a minus sign we get the poly +principle which gave us the periodic + + align:start position:0% +principle which gave us the periodic + + + align:start position:0% +principle which gave us the periodic +table and is going to give us in the + + align:start position:0% +table and is going to give us in the + + + align:start position:0% +table and is going to give us in the +next lecture bands in solids and + + align:start position:0% +next lecture bands in solids and + + + align:start position:0% +next lecture bands in solids and +conductivity from the same principle but + + align:start position:0% +conductivity from the same principle but + + + align:start position:0% +conductivity from the same principle but +with a plus and the Persistence of this + + align:start position:0% +with a plus and the Persistence of this + + + align:start position:0% +with a plus and the Persistence of this +sign from the Persistence of the + + align:start position:0% +sign from the Persistence of the + + + align:start position:0% +sign from the Persistence of the +statistics from the fact that we have + + align:start position:0% +statistics from the fact that we have + + + align:start position:0% +statistics from the fact that we have +two identical bons we get that they like + + align:start position:0% +two identical bons we get that they like + + + align:start position:0% +two identical bons we get that they like +to be in the same spot and we'll get + + align:start position:0% +to be in the same spot and we'll get + + + align:start position:0% +to be in the same spot and we'll get +lasers and Bose Einstein condensates and + + align:start position:0% +lasers and Bose Einstein condensates and + + + align:start position:0% +lasers and Bose Einstein condensates and +next time we'll pick up with Fons in a + + align:start position:0% +next time we'll pick up with Fons in a + + + align:start position:0% +next time we'll pick up with Fons in a +periodic potential and we'll study + + align:start position:0% +periodic potential and we'll study + + + align:start position:0% +periodic potential and we'll study +solids and gets a diamond + + align:start position:0% +solids and gets a diamond + + + align:start position:0% +solids and gets a diamond +[Applause] \ No newline at end of file diff --git a/BGE3wb7H2PA.txt b/BGE3wb7H2PA.txt new file mode 100644 index 0000000000000000000000000000000000000000..bdbdc344d479e95cf1c5cac8d89aa9cfc596d3dd --- /dev/null +++ b/BGE3wb7H2PA.txt @@ -0,0 +1,7880 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so again welcome back and + + align:start position:0% +ocw.mit.edu so again welcome back and + + + align:start position:0% +ocw.mit.edu so again welcome back and +today's topic is a continuation of what + + align:start position:0% +today's topic is a continuation of what + + + align:start position:0% +today's topic is a continuation of what +we did last time we still have + + align:start position:0% +we did last time we still have + + + align:start position:0% +we did last time we still have +a little bit of work and thinking to do + + align:start position:0% +a little bit of work and thinking to do + + + align:start position:0% +a little bit of work and thinking to do +concerning Polar Polar + + align:start position:0% + + + + align:start position:0% + +coordinates so we're going to talk about + + align:start position:0% +coordinates so we're going to talk about + + + align:start position:0% +coordinates so we're going to talk about +polar + + align:start position:0% + + + + align:start position:0% + +coordinates and my first job today is to + + align:start position:0% +coordinates and my first job today is to + + + align:start position:0% +coordinates and my first job today is to +talk a little bit about + + align:start position:0% + + + + align:start position:0% + +area that's something we we we didn't + + align:start position:0% +area that's something we we we didn't + + + align:start position:0% +area that's something we we we didn't +mentioned last time and since we're all + + align:start position:0% +mentioned last time and since we're all + + + align:start position:0% +mentioned last time and since we're all +back from + + align:start position:0% +back from + + + align:start position:0% +back from +Thanksgiving we can certainly talk about + + align:start position:0% +Thanksgiving we can certainly talk about + + + align:start position:0% +Thanksgiving we can certainly talk about +it in terms of a + + align:start position:0% +it in terms of a + + + align:start position:0% +it in terms of a +pi which is the basic idea for area and + + align:start position:0% +pi which is the basic idea for area and + + + align:start position:0% +pi which is the basic idea for area and +polar + + align:start position:0% +polar + + + align:start position:0% +polar +coordinates here's our PI and here's a + + align:start position:0% +coordinates here's our PI and here's a + + + align:start position:0% +coordinates here's our PI and here's a +slice of the + + align:start position:0% + + + + align:start position:0% + +pie the + + align:start position:0% +pie the + + + align:start position:0% +pie the +slice has a piece of Arc Length on it + + align:start position:0% +slice has a piece of Arc Length on it + + + align:start position:0% +slice has a piece of Arc Length on it +which I'm going to call Delta Theta and + + align:start position:0% +which I'm going to call Delta Theta and + + + align:start position:0% +which I'm going to call Delta Theta and +the area of that shaded + + align:start position:0% +the area of that shaded + + + align:start position:0% +the area of that shaded +slice I'm going to call Delta + + align:start position:0% +slice I'm going to call Delta + + + align:start position:0% +slice I'm going to call Delta +a and let's suppose that the radius is a + + align:start position:0% +a and let's suppose that the radius is a + + + align:start position:0% +a and let's suppose that the radius is a +little a so this is a a pi of radius + + align:start position:0% + + + + align:start position:0% + +a that's our our our picture now it's + + align:start position:0% +a that's our our our picture now it's + + + align:start position:0% +a that's our our our picture now it's +pretty easy to figure out what the area + + align:start position:0% +pretty easy to figure out what the area + + + align:start position:0% +pretty easy to figure out what the area +of that slice of Pi + + align:start position:0% +of that slice of Pi + + + align:start position:0% +of that slice of Pi +is the total area is of course Pi a 2 we + + align:start position:0% +is the total area is of course Pi a 2 we + + + align:start position:0% +is the total area is of course Pi a 2 we +know that and to get this + + align:start position:0% +know that and to get this + + + align:start position:0% +know that and to get this +fraction Delta a all we have to do is + + align:start position:0% +fraction Delta a all we have to do is + + + align:start position:0% +fraction Delta a all we have to do is +take the percentage of the Arc of the + + align:start position:0% +take the percentage of the Arc of the + + + align:start position:0% +take the percentage of the Arc of the +total circumference that's Delta Theta / + + align:start position:0% +total circumference that's Delta Theta / + + + align:start position:0% +total circumference that's Delta Theta / +2 pi this is the fraction of area uh + + align:start position:0% +2 pi this is the fraction of area uh + + + align:start position:0% +2 pi this is the fraction of area uh +sorry fraction of of the total + + align:start position:0% +sorry fraction of of the total + + + align:start position:0% +sorry fraction of of the total +circumference the total length around + + align:start position:0% +circumference the total length around + + + align:start position:0% +circumference the total length around +the rim and then we multiply that by pi + + align:start position:0% +the rim and then we multiply that by pi + + + align:start position:0% +the rim and then we multiply that by pi +a 2 and that's giving us the total area + + align:start position:0% +a 2 and that's giving us the total area + + + align:start position:0% +a 2 and that's giving us the total area +and if you work that out that's Delta a + + align:start position:0% +and if you work that out that's Delta a + + + align:start position:0% +and if you work that out that's Delta a +is equal to the pies cancel and we have + + align:start position:0% +is equal to the pies cancel and we have + + + align:start position:0% +is equal to the pies cancel and we have +a half a^2 Delta + + align:start position:0% +a half a^2 Delta + + + align:start position:0% +a half a^2 Delta +Theta all right so here's + + align:start position:0% + + + + align:start position:0% + +the the basic + + align:start position:0% + + + + align:start position:0% + +formula and now what we need to do is to + + align:start position:0% +formula and now what we need to do is to + + + align:start position:0% +formula and now what we need to do is to +talk about a a a variable Pi + + align:start position:0% + + + + align:start position:0% + +here that would be a pi with a kind of a + + align:start position:0% +here that would be a pi with a kind of a + + + align:start position:0% +here that would be a pi with a kind of a +wavy + + align:start position:0% +wavy + + + align:start position:0% +wavy +crust right which is coming around like + + align:start position:0% +crust right which is coming around like + + + align:start position:0% +crust right which is coming around like +this so R is equal to R of theta the the + + align:start position:0% +this so R is equal to R of theta the the + + + align:start position:0% +this so R is equal to R of theta the the +distance from the the center is varying + + align:start position:0% +distance from the the center is varying + + + align:start position:0% +distance from the the center is varying +with the uh with the place where we are + + align:start position:0% +with the uh with the place where we are + + + align:start position:0% +with the uh with the place where we are +the angle where we're shooting + + align:start position:0% +the angle where we're shooting + + + align:start position:0% +the angle where we're shooting +out and and I want to subdivide that + + align:start position:0% +out and and I want to subdivide that + + + align:start position:0% +out and and I want to subdivide that +into little chunks + + align:start position:0% + + + + align:start position:0% + +here now the idea for adding up the area + + align:start position:0% +here now the idea for adding up the area + + + align:start position:0% +here now the idea for adding up the area +the total area of this this piece that's + + align:start position:0% +the total area of this this piece that's + + + align:start position:0% +the total area of this this piece that's +swept out is to break it up into little + + align:start position:0% +swept out is to break it up into little + + + align:start position:0% +swept out is to break it up into little +slices whose whose uh areas are almost + + align:start position:0% +slices whose whose uh areas are almost + + + align:start position:0% +slices whose whose uh areas are almost +uh easy to calculate + + align:start position:0% +uh easy to calculate + + + align:start position:0% +uh easy to calculate +namely what we're going to do is to take + + align:start position:0% +namely what we're going to do is to take + + + align:start position:0% +namely what we're going to do is to take +and I'm going to I'm going to label it + + align:start position:0% +and I'm going to I'm going to label it + + + align:start position:0% +and I'm going to I'm going to label it +um this way I'm going to take these + + align:start position:0% +um this way I'm going to take these + + + align:start position:0% +um this way I'm going to take these +little circular arcs which go so I'm + + align:start position:0% +little circular arcs which go so I'm + + + align:start position:0% +little circular arcs which go so I'm +going to extend past where the + + align:start position:0% +going to extend past where the + + + align:start position:0% +going to extend past where the +uh where this goes and then I'm going to + + align:start position:0% +uh where this goes and then I'm going to + + + align:start position:0% +uh where this goes and then I'm going to +take each circular Arc here so here's a + + align:start position:0% +take each circular Arc here so here's a + + + align:start position:0% +take each circular Arc here so here's a +circular AR Arc and then here's another + + align:start position:0% +circular AR Arc and then here's another + + + align:start position:0% +circular AR Arc and then here's another +circular + + align:start position:0% +circular + + + align:start position:0% +circular +Arc and here's another circular Arc it's + + align:start position:0% +Arc and here's another circular Arc it's + + + align:start position:0% +Arc and here's another circular Arc it's +just right on the nose in that case now + + align:start position:0% +just right on the nose in that case now + + + align:start position:0% +just right on the nose in that case now +in these two cases so so basically the + + align:start position:0% +in these two cases so so basically the + + + align:start position:0% +in these two cases so so basically the +picture that I'm trying to draw for you + + align:start position:0% +picture that I'm trying to draw for you + + + align:start position:0% +picture that I'm trying to draw for you +is is this I have + + align:start position:0% +is is this I have + + + align:start position:0% +is is this I have +some some sector and then I have some + + align:start position:0% +some some sector and then I have some + + + align:start position:0% +some some sector and then I have some +circular Arc and it maybe it it it takes + + align:start position:0% +circular Arc and it maybe it it it takes + + + align:start position:0% +circular Arc and it maybe it it it takes +a little + + align:start position:0% +a little + + + align:start position:0% +a little +extra there's a little extra area I'm + + align:start position:0% +extra there's a little extra area I'm + + + align:start position:0% +extra there's a little extra area I'm +making an error in the area this is a + + align:start position:0% +making an error in the area this is a + + + align:start position:0% +making an error in the area this is a +little extra area and maybe to draw but + + align:start position:0% +little extra area and maybe to draw but + + + align:start position:0% +little extra area and maybe to draw but +the other way there's a little I'm a + + align:start position:0% +the other way there's a little I'm a + + + align:start position:0% +the other way there's a little I'm a +little short on this one and let's say + + align:start position:0% +little short on this one and let's say + + + align:start position:0% +little short on this one and let's say +on this one I'm right on the nose I have + + align:start position:0% +on this one I'm right on the nose I have + + + align:start position:0% +on this one I'm right on the nose I have +the same Arc as the curve of the uh of + + align:start position:0% +the same Arc as the curve of the uh of + + + align:start position:0% +the same Arc as the curve of the uh of +the surface all right now this is a + + align:start position:0% +the surface all right now this is a + + + align:start position:0% +the surface all right now this is a +little bit like the step functions that + + align:start position:0% +little bit like the step functions that + + + align:start position:0% +little bit like the step functions that +we used in remon sums it's practically + + align:start position:0% +we used in remon sums it's practically + + + align:start position:0% +we used in remon sums it's practically +the same eventually this little band of + + align:start position:0% +the same eventually this little band of + + + align:start position:0% +the same eventually this little band of +stuff that we're missing by if we take + + align:start position:0% +stuff that we're missing by if we take + + + align:start position:0% +stuff that we're missing by if we take +very very narrow little slices here is + + align:start position:0% +very very narrow little slices here is + + + align:start position:0% +very very narrow little slices here is +going to be um negligible it'll get + + align:start position:0% +going to be um negligible it'll get + + + align:start position:0% +going to be um negligible it'll get +close Clos and closer to the curve + + align:start position:0% +close Clos and closer to the curve + + + align:start position:0% +close Clos and closer to the curve +itself so that area will tend to zero in + + align:start position:0% +itself so that area will tend to zero in + + + align:start position:0% +itself so that area will tend to zero in +the limit so we don't have to worry + + align:start position:0% +the limit so we don't have to worry + + + align:start position:0% +the limit so we don't have to worry +about it and the approximate + + align:start position:0% +about it and the approximate + + + align:start position:0% +about it and the approximate +relationship is sitting here where this + + align:start position:0% +relationship is sitting here where this + + + align:start position:0% +relationship is sitting here where this +distance now is R so this radius is r + + align:start position:0% +distance now is R so this radius is r + + + align:start position:0% +distance now is R so this radius is r +and this is this Delta + + align:start position:0% +and this is this Delta + + + align:start position:0% +and this is this Delta +Theta and so in the approximate case + + align:start position:0% +Theta and so in the approximate case + + + align:start position:0% +Theta and so in the approximate case +what we have is the Delta a is + + align:start position:0% +what we have is the Delta a is + + + align:start position:0% +what we have is the Delta a is +approximately R 2 Delta + + align:start position:0% +approximately R 2 Delta + + + align:start position:0% +approximately R 2 Delta +thet which is practic the same thing we + + align:start position:0% +thet which is practic the same thing we + + + align:start position:0% +thet which is practic the same thing we +had here except that that R is replacing + + align:start position:0% +had here except that that R is replacing + + + align:start position:0% +had here except that that R is replacing +the constant there and it's + + align:start position:0% +the constant there and it's + + + align:start position:0% +the constant there and it's +approximately true because R is + + align:start position:0% +approximately true because R is + + + align:start position:0% +approximately true because R is +varying and then in the limit we have + + align:start position:0% +varying and then in the limit we have + + + align:start position:0% +varying and then in the limit we have +the exact formula for the differential + + align:start position:0% +the exact formula for the differential + + + align:start position:0% +the exact formula for the differential +which is this + + align:start position:0% +which is this + + + align:start position:0% +which is this +one so this is the main formula for area + + align:start position:0% +one so this is the main formula for area + + + align:start position:0% +one so this is the main formula for area +and if you like the total area then is + + align:start position:0% +and if you like the total area then is + + + align:start position:0% +and if you like the total area then is +going to be the integral from some + + align:start position:0% +going to be the integral from some + + + align:start position:0% +going to be the integral from some +starting place to some n place of a half + + align:start position:0% +starting place to some n place of a half + + + align:start position:0% +starting place to some n place of a half +r^ 2 D Theta + + align:start position:0% +r^ 2 D Theta + + + align:start position:0% +r^ 2 D Theta +now this is only useful in the situation + + align:start position:0% +now this is only useful in the situation + + + align:start position:0% +now this is only useful in the situation +that we're in namely so this is the + + align:start position:0% +that we're in namely so this is the + + + align:start position:0% +that we're in namely so this is the +other important formula and this is only + + align:start position:0% +other important formula and this is only + + + align:start position:0% +other important formula and this is only +uh useful when R is a function of theta + + align:start position:0% +uh useful when R is a function of theta + + + align:start position:0% +uh useful when R is a function of theta +when this is the way in which the region + + align:start position:0% +when this is the way in which the region + + + align:start position:0% +when this is the way in which the region +is presented to + + align:start position:0% +is presented to + + + align:start position:0% +is presented to +us all right so that's the that's the + + align:start position:0% +us all right so that's the that's the + + + align:start position:0% +us all right so that's the that's the +setup and that's our formula main + + align:start position:0% +setup and that's our formula main + + + align:start position:0% +setup and that's our formula main +formula Let's do an + + align:start position:0% + + + + align:start position:0% + +example the example that I'm going to + + align:start position:0% +example the example that I'm going to + + + align:start position:0% +example the example that I'm going to +take is the one that we did at the end + + align:start position:0% +take is the one that we did at the end + + + align:start position:0% +take is the one that we did at the end +of last time or near the end of last + + align:start position:0% +of last time or near the end of last + + + align:start position:0% +of last time or near the end of last +time which was this formula here R is + + align:start position:0% +time which was this formula here R is + + + align:start position:0% +time which was this formula here R is +equal to 2 a cosine Theta remember that + + align:start position:0% +equal to 2 a cosine Theta remember that + + + align:start position:0% +equal to 2 a cosine Theta remember that +was the same as uh x - a^ 2 + y^2 = A2 + + align:start position:0% +was the same as uh x - a^ 2 + y^2 = A2 + + + align:start position:0% +was the same as uh x - a^ 2 + y^2 = A2 +so this is what we did last time we + + align:start position:0% +so this is what we did last time we + + + align:start position:0% +so this is what we did last time we +connected this rectangular + + align:start position:0% +connected this rectangular + + + align:start position:0% +connected this rectangular +representation to that polar rep + + align:start position:0% +representation to that polar rep + + + align:start position:0% +representation to that polar rep +representation and the the picture is of + + align:start position:0% +representation and the the picture is of + + + align:start position:0% +representation and the the picture is of +a circle + + align:start position:0% +a circle + + + align:start position:0% +a circle +all right where this is the point 2 a + + align:start position:0% +all right where this is the point 2 a + + + align:start position:0% +all right where this is the point 2 a +comma + + align:start position:0% + + + + align:start position:0% + +0 all right so let's figure out what the + + align:start position:0% +0 all right so let's figure out what the + + + align:start position:0% +0 all right so let's figure out what the +area + + align:start position:0% +area + + + align:start position:0% +area +is well first of all we have to figure + + align:start position:0% +is well first of all we have to figure + + + align:start position:0% +is well first of all we have to figure +out when we sweep out the area we have + + align:start position:0% +out when we sweep out the area we have + + + align:start position:0% +out when we sweep out the area we have +to realize that we only go from minus + + align:start position:0% +to realize that we only go from minus + + + align:start position:0% +to realize that we only go from minus +piun / + + align:start position:0% +piun / + + + align:start position:0% +piun / +2 to Pi / 2 so that's something we can + + align:start position:0% +2 to Pi / 2 so that's something we can + + + align:start position:0% +2 to Pi / 2 so that's something we can +get from the pi picture you can also get + + align:start position:0% +get from the pi picture you can also get + + + align:start position:0% +get from the pi picture you can also get +it directly from this formula if you + + align:start position:0% +it directly from this formula if you + + + align:start position:0% +it directly from this formula if you +realize that cosine is positive in this + + align:start position:0% +realize that cosine is positive in this + + + align:start position:0% +realize that cosine is positive in this +range here and at the ends it's zero so + + align:start position:0% +range here and at the ends it's zero so + + + align:start position:0% +range here and at the ends it's zero so +the thing + + align:start position:0% +the thing + + + align:start position:0% +the thing +uh encloses a region at these ends so at + + align:start position:0% +uh encloses a region at these ends so at + + + align:start position:0% +uh encloses a region at these ends so at +the ends cosine + + align:start position:0% +the ends cosine + + + align:start position:0% +the ends cosine +of cosine of plus orus pi / 2 is equal + + align:start position:0% +of cosine of plus orus pi / 2 is equal + + + align:start position:0% +of cosine of plus orus pi / 2 is equal +to zero that's what what cinches this up + + align:start position:0% +to zero that's what what cinches this up + + + align:start position:0% +to zero that's what what cinches this up +like a little sack if you like + + align:start position:0% +like a little sack if you like + + + align:start position:0% +like a little sack if you like +all right so the area is now going to be + + align:start position:0% +all right so the area is now going to be + + + align:start position:0% +all right so the area is now going to be +the integral from minus piun / 2 to Pi / + + align:start position:0% +the integral from minus piun / 2 to Pi / + + + align:start position:0% +the integral from minus piun / 2 to Pi / +2 of a half * the square of R that's 2 a + + align:start position:0% +2 of a half * the square of R that's 2 a + + + align:start position:0% +2 of a half * the square of R that's 2 a +cosine Theta s d + + align:start position:0% + + + + align:start position:0% + +thet question do you the picture that + + align:start position:0% +thet question do you the picture that + + + align:start position:0% +thet question do you the picture that +you're + + align:start position:0% + + + + align:start position:0% + +going um how do I know from looking at + + align:start position:0% +going um how do I know from looking at + + + align:start position:0% +going um how do I know from looking at +the picture that I'm going from pi/2 to + + align:start position:0% +the picture that I'm going from pi/2 to + + + align:start position:0% +the picture that I'm going from pi/2 to +p/ two is the question um I I do it very + + align:start position:0% +p/ two is the question um I I do it very + + + align:start position:0% +p/ two is the question um I I do it very +uh like with my whole body I say Here I + + align:start position:0% +uh like with my whole body I say Here I + + + align:start position:0% +uh like with my whole body I say Here I +Am pointing down that's negative pi over + + align:start position:0% +Am pointing down that's negative pi over + + + align:start position:0% +Am pointing down that's negative pi over +2 I sweep up that's zero and I get all + + align:start position:0% +2 I sweep up that's zero and I get all + + + align:start position:0% +2 I sweep up that's zero and I get all +the way up to here that's pi over two so + + align:start position:0% +the way up to here that's pi over two so + + + align:start position:0% +the way up to here that's pi over two so +that's the way I do it that's really the + + align:start position:0% +that's the way I do it that's really the + + + align:start position:0% +that's the way I do it that's really the +way I do it I'm being honest now if you + + align:start position:0% +way I do it I'm being honest now if you + + + align:start position:0% +way I do it I'm being honest now if you +if you're a machine you can't actually + + align:start position:0% +if you're a machine you can't actually + + + align:start position:0% +if you're a machine you can't actually +look and you don't have a body so you + + align:start position:0% +look and you don't have a body so you + + + align:start position:0% +look and you don't have a body so you +can't Point your arms then you would + + align:start position:0% +can't Point your arms then you would + + + align:start position:0% +can't Point your arms then you would +have to go by the formula and you'd have + + align:start position:0% +have to go by the formula and you'd have + + + align:start position:0% +have to go by the formula and you'd have +to actually use something like this + + align:start position:0% +to actually use something like this + + + align:start position:0% +to actually use something like this +formula here the fact that that this is + + align:start position:0% +formula here the fact that that this is + + + align:start position:0% +formula here the fact that that this is +where the the the loop cinches up this + + align:start position:0% +where the the the loop cinches up this + + + align:start position:0% +where the the the loop cinches up this +is where the radius comes into zero at + + align:start position:0% +is where the radius comes into zero at + + + align:start position:0% +is where the radius comes into zero at +pi/ 2 so you need to know that in order + + align:start position:0% +pi/ 2 so you need to know that in order + + + align:start position:0% +pi/ 2 so you need to know that in order +to understand the + + align:start position:0% +to understand the + + + align:start position:0% +to understand the +range all + + align:start position:0% +range all + + + align:start position:0% +range all +right another question so + + align:start position:0% + + + + align:start position:0% + +we so when we're doing these should we + + align:start position:0% +we so when we're doing these should we + + + align:start position:0% +we so when we're doing these should we +just guess that it's going to be a loop + + align:start position:0% +just guess that it's going to be a loop + + + align:start position:0% +just guess that it's going to be a loop +uh I'm probably going to give you some + + align:start position:0% +uh I'm probably going to give you some + + + align:start position:0% +uh I'm probably going to give you some +Clues as to what's going on because it's + + align:start position:0% +Clues as to what's going on because it's + + + align:start position:0% +Clues as to what's going on because it's +very hard to figure these things out uh + + align:start position:0% +very hard to figure these things out uh + + + align:start position:0% +very hard to figure these things out uh +sometimes it'll be bounded by one curve + + align:start position:0% +sometimes it'll be bounded by one curve + + + align:start position:0% +sometimes it'll be bounded by one curve +and another curve and I'll say it's the + + align:start position:0% +and another curve and I'll say it's the + + + align:start position:0% +and another curve and I'll say it's the +thing in between those two curves that's + + align:start position:0% +thing in between those two curves that's + + + align:start position:0% +thing in between those two curves that's +the kind of thing that I could do uh + + align:start position:0% +the kind of thing that I could do uh + + + align:start position:0% +the kind of thing that I could do uh +here um uh you really should have know + + align:start position:0% +here um uh you really should have know + + + align:start position:0% +here um uh you really should have know +this one in advance this is by far the + + align:start position:0% +this one in advance this is by far the + + + align:start position:0% +this one in advance this is by far the +the most or this is one of the typical + + align:start position:0% +the most or this is one of the typical + + + align:start position:0% +the most or this is one of the typical +cases anyway I'm going to give you a + + align:start position:0% +cases anyway I'm going to give you a + + + align:start position:0% +cases anyway I'm going to give you a +couple more examples don't don't get too + + align:start position:0% +couple more examples don't don't get too + + + align:start position:0% +couple more examples don't don't get too +worked up over this you will somehow be + + align:start position:0% +worked up over this you will somehow be + + + align:start position:0% +worked up over this you will somehow be +able to visualize it I'll give you some + + align:start position:0% +able to visualize it I'll give you some + + + align:start position:0% +able to visualize it I'll give you some +examples to to help you out with it + + align:start position:0% +examples to to help you out with it + + + align:start position:0% +examples to to help you out with it +later all right so here's the situation + + align:start position:0% +later all right so here's the situation + + + align:start position:0% +later all right so here's the situation +here's my integral and now we're faced + + align:start position:0% +here's my integral and now we're faced + + + align:start position:0% +here's my integral and now we're faced +with a trig integral which we have to + + align:start position:0% +with a trig integral which we have to + + + align:start position:0% +with a trig integral which we have to +remember how to do now the trig integral + + align:start position:0% +remember how to do now the trig integral + + + align:start position:0% +remember how to do now the trig integral +here so first let me factor out the + + align:start position:0% +here so first let me factor out the + + + align:start position:0% +here so first let me factor out the +constants this is 4 a^ 2 / 2 so it's 2 + + align:start position:0% +constants this is 4 a^ 2 / 2 so it's 2 + + + align:start position:0% +constants this is 4 a^ 2 / 2 so it's 2 +a^ 2 integral from- piun / 2 piun / 2 + + align:start position:0% +a^ 2 integral from- piun / 2 piun / 2 + + + align:start position:0% +a^ 2 integral from- piun / 2 piun / 2 +cosine 2 Theta D Theta and now you have + + align:start position:0% +cosine 2 Theta D Theta and now you have + + + align:start position:0% +cosine 2 Theta D Theta and now you have +to remember what you're supposed to do + + align:start position:0% +to remember what you're supposed to do + + + align:start position:0% +to remember what you're supposed to do +at this + + align:start position:0% +at this + + + align:start position:0% +at this +point so think if you haven't done it + + align:start position:0% +point so think if you haven't done it + + + align:start position:0% +point so think if you haven't done it +yet this is practice you need to do uh + + align:start position:0% +yet this is practice you need to do uh + + + align:start position:0% +yet this is practice you need to do uh +this trig integral is handled by a + + align:start position:0% +this trig integral is handled by a + + + align:start position:0% +this trig integral is handled by a +double angle formula as it happens I'm + + align:start position:0% +double angle formula as it happens I'm + + + align:start position:0% +double angle formula as it happens I'm +going to be giving you these formulas on + + align:start position:0% +going to be giving you these formulas on + + + align:start position:0% +going to be giving you these formulas on +the review sheet you'll see they're + + align:start position:0% +the review sheet you'll see they're + + + align:start position:0% +the review sheet you'll see they're +written on the review sheet at least in + + align:start position:0% +written on the review sheet at least in + + + align:start position:0% +written on the review sheet at least in +some + + align:start position:0% +some + + + align:start position:0% +some +form so for example there's a there's a + + align:start position:0% +form so for example there's a there's a + + + align:start position:0% +form so for example there's a there's a +formula right and this will be on the + + align:start position:0% +formula right and this will be on the + + + align:start position:0% +formula right and this will be on the +exam too uh so this is the correct + + align:start position:0% +exam too uh so this is the correct + + + align:start position:0% +exam too uh so this is the correct +formula to use here is that this is 1 + + + align:start position:0% +formula to use here is that this is 1 + + + + align:start position:0% +formula to use here is that this is 1 + +cosine 2 thet / 2 D thet so that's the + + align:start position:0% +cosine 2 thet / 2 D thet so that's the + + + align:start position:0% +cosine 2 thet / 2 D thet so that's the +substitution that you use for the cosine + + align:start position:0% +substitution that you use for the cosine + + + align:start position:0% +substitution that you use for the cosine +squared in order to integrate + + align:start position:0% + + + + align:start position:0% + +it that serves as a little review of + + align:start position:0% +it that serves as a little review of + + + align:start position:0% +it that serves as a little review of +trig integrals and now this is this is + + align:start position:0% +trig integrals and now this is this is + + + align:start position:0% +trig integrals and now this is this is +quite easy all right this + + align:start position:0% +quite easy all right this + + + align:start position:0% +quite easy all right this +is this integral now is + + align:start position:0% + + + + align:start position:0% + +easy why is it easy well because it's + + align:start position:0% +easy why is it easy well because it's + + + align:start position:0% +easy why is it easy well because it's +the anti-derivative of a constant and + + align:start position:0% +the anti-derivative of a constant and + + + align:start position:0% +the anti-derivative of a constant and +cosine 2 Theta it's anti-derivative + + align:start position:0% +cosine 2 Theta it's anti-derivative + + + align:start position:0% +cosine 2 Theta it's anti-derivative +you're supposed to be able to write down + + align:start position:0% +you're supposed to be able to write down + + + align:start position:0% +you're supposed to be able to write down +so the anti-derivative of one is Theta + + align:start position:0% +so the anti-derivative of one is Theta + + + align:start position:0% +so the anti-derivative of one is Theta +and the anti-derivative of the cosine is + + align:start position:0% +and the anti-derivative of the cosine is + + + align:start position:0% +and the anti-derivative of the cosine is +half the S when it's 2 + + align:start position:0% + + + + align:start position:0% + +Theta all + + align:start position:0% + + + + align:start position:0% + +right and that is a^ 2 * piun / 2 - - + + align:start position:0% +right and that is a^ 2 * piun / 2 - - + + + align:start position:0% +right and that is a^ 2 * piun / 2 - - +piun / 2 and the signs go away because + + align:start position:0% +piun / 2 and the signs go away because + + + align:start position:0% +piun / 2 and the signs go away because +they're both zero + + align:start position:0% +they're both zero + + + align:start position:0% +they're both zero +so all told we get uh Pi a s which is + + align:start position:0% +so all told we get uh Pi a s which is + + + align:start position:0% +so all told we get uh Pi a s which is +certainly what we would like it to be + + align:start position:0% +certainly what we would like it to be + + + align:start position:0% +certainly what we would like it to be +it's the area of the + + align:start position:0% +it's the area of the + + + align:start position:0% +it's the area of the +circle another + + align:start position:0% + + + + align:start position:0% + +questionary I + + align:start position:0% +questionary I + + + align:start position:0% +questionary I +see to do it I don't understand why + + align:start position:0% +see to do it I don't understand why + + + align:start position:0% +see to do it I don't understand why +why um the question so I'm not sure + + align:start position:0% +why um the question so I'm not sure + + + align:start position:0% +why um the question so I'm not sure +which question you're asking I pivoted + + align:start position:0% +which question you're asking I pivoted + + + align:start position:0% +which question you're asking I pivoted +my arm around z0 um this point this is + + align:start position:0% +my arm around z0 um this point this is + + + align:start position:0% +my arm around z0 um this point this is +the point we're talking about 0 0 is a + + align:start position:0% +the point we're talking about 0 0 is a + + + align:start position:0% +the point we're talking about 0 0 is a +key point it's where I I guess you could + + align:start position:0% +key point it's where I I guess you could + + + align:start position:0% +key point it's where I I guess you could +say I stuck my elbow there okay now the + + align:start position:0% +say I stuck my elbow there okay now the + + + align:start position:0% +say I stuck my elbow there okay now the +reason is that it's the place where R + + align:start position:0% +reason is that it's the place where R + + + align:start position:0% +reason is that it's the place where R +equals z so it's more or less the center + + align:start position:0% +equals z so it's more or less the center + + + align:start position:0% +equals z so it's more or less the center +of the universe from the point of view + + align:start position:0% +of the universe from the point of view + + + align:start position:0% +of the universe from the point of view +of this this + + align:start position:0% +of this this + + + align:start position:0% +of this this +problem so it's it's the reference point + + align:start position:0% +problem so it's it's the reference point + + + align:start position:0% +problem so it's it's the reference point +and and if you like when you're doing + + align:start position:0% +and and if you like when you're doing + + + align:start position:0% +and and if you like when you're doing +this uh it's a little bit like a radar + + align:start position:0% +this uh it's a little bit like a radar + + + align:start position:0% +this uh it's a little bit like a radar +screen everything is centered at the + + align:start position:0% +screen everything is centered at the + + + align:start position:0% +screen everything is centered at the +origin and you're taking Rays coming out + + align:start position:0% +origin and you're taking Rays coming out + + + align:start position:0% +origin and you're taking Rays coming out +from it and seeing where they're going + + align:start position:0% +from it and seeing where they're going + + + align:start position:0% +from it and seeing where they're going +to + + align:start position:0% +to + + + align:start position:0% +to +go all right so for example this is the + + align:start position:0% +go all right so for example this is the + + + align:start position:0% +go all right so for example this is the +theta equals z Ray this is the Theta + + align:start position:0% +theta equals z Ray this is the Theta + + + align:start position:0% +theta equals z Ray this is the Theta +equal Pi over4 Ray this is the Theta + + align:start position:0% +equal Pi over4 Ray this is the Theta + + + align:start position:0% +equal Pi over4 Ray this is the Theta +equal Pi / 2 Ray and indeed if my elbow + + align:start position:0% +equal Pi / 2 Ray and indeed if my elbow + + + align:start position:0% +equal Pi / 2 Ray and indeed if my elbow +is right at this Center here I'm + + align:start position:0% +is right at this Center here I'm + + + align:start position:0% +is right at this Center here I'm +pointing in those various directions all + + align:start position:0% +pointing in those various directions all + + + align:start position:0% +pointing in those various directions all +right so that's what I had in mind when + + align:start position:0% +right so that's what I had in mind when + + + align:start position:0% +right so that's what I had in mind when +I did that + + align:start position:0% + + + + align:start position:0% + +okay you can always get these formulas + + align:start position:0% +okay you can always get these formulas + + + align:start position:0% +okay you can always get these formulas +by the way from the uh original business + + align:start position:0% +by the way from the uh original business + + + align:start position:0% +by the way from the uh original business +x = r cosine Theta y = r sin Theta but + + align:start position:0% +x = r cosine Theta y = r sin Theta but + + + align:start position:0% +x = r cosine Theta y = r sin Theta but +it's useful to have the geometric + + align:start position:0% +it's useful to have the geometric + + + align:start position:0% +it's useful to have the geometric +picture as well in other words if you + + align:start position:0% +picture as well in other words if you + + + align:start position:0% +picture as well in other words if you +were a machine you'd have to rely on + + align:start position:0% +were a machine you'd have to rely on + + + align:start position:0% +were a machine you'd have to rely on +these formulas and plot things using + + align:start position:0% +these formulas and plot things using + + + align:start position:0% +these formulas and plot things using +these + + align:start position:0% + + + + align:start position:0% + +always okay now in terms of plotting I + + align:start position:0% +always okay now in terms of plotting I + + + align:start position:0% +always okay now in terms of plotting I +want to I want to expand your brain a + + align:start position:0% +want to I want to expand your brain a + + + align:start position:0% +want to I want to expand your brain a +little bit so we need just a little bit + + align:start position:0% +little bit so we need just a little bit + + + align:start position:0% +little bit so we need just a little bit +more practice with plotting uh in polar + + align:start position:0% +more practice with plotting uh in polar + + + align:start position:0% +more practice with plotting uh in polar +coordinates and so the first question + + align:start position:0% +coordinates and so the first question + + + align:start position:0% +coordinates and so the first question +that I want to ask you is what happens + + align:start position:0% +that I want to ask you is what happens + + + align:start position:0% +that I want to ask you is what happens +outside of this range of theta in other + + align:start position:0% +outside of this range of theta in other + + + align:start position:0% +outside of this range of theta in other +words what happens if Theta is beyond Pi + + align:start position:0% +words what happens if Theta is beyond Pi + + + align:start position:0% +words what happens if Theta is beyond Pi +/ + + align:start position:0% +/ + + + align:start position:0% +/ +2 can somebody can somebody see what's + + align:start position:0% +2 can somebody can somebody see what's + + + align:start position:0% +2 can somebody can somebody see what's +happening to the formulas in that case + + align:start position:0% +happening to the formulas in that case + + + align:start position:0% +happening to the formulas in that case +so so what I'm looking at now let's go + + align:start position:0% +so so what I'm looking at now let's go + + + align:start position:0% +so so what I'm looking at now let's go +back to it what I'm looking at is this + + align:start position:0% +back to it what I'm looking at is this + + + align:start position:0% +back to it what I'm looking at is this +formula + + align:start position:0% +formula + + + align:start position:0% +formula +here all + + align:start position:0% + + + + align:start position:0% + +right but uh to use the elbow analy here + + align:start position:0% +right but uh to use the elbow analy here + + + align:start position:0% +right but uh to use the elbow analy here +I'm sweep swept around like this but now + + align:start position:0% +I'm sweep swept around like this but now + + + align:start position:0% +I'm sweep swept around like this but now +I'm going to point this way I'm going to + + align:start position:0% +I'm going to point this way I'm going to + + + align:start position:0% +I'm going to point this way I'm going to +point out out over there my hand is up + + align:start position:0% +point out out over there my hand is up + + + align:start position:0% +point out out over there my hand is up +here in the uh Northwest Direction all + + align:start position:0% +here in the uh Northwest Direction all + + + align:start position:0% +here in the uh Northwest Direction all +right so what's going to happen somebody + + align:start position:0% +right so what's going to happen somebody + + + align:start position:0% +right so what's going to happen somebody +want to tell + + align:start position:0% +want to tell + + + align:start position:0% +want to tell +me it goes It goes around itself that's + + align:start position:0% +me it goes It goes around itself that's + + + align:start position:0% +me it goes It goes around itself that's +right what happens is that when R + + align:start position:0% +right what happens is that when R + + + align:start position:0% +right what happens is that when R +crosses this vertical R is zero when it + + align:start position:0% +crosses this vertical R is zero when it + + + align:start position:0% +crosses this vertical R is zero when it +crosses over here it goes negative so + + align:start position:0% +crosses over here it goes negative so + + + align:start position:0% +crosses over here it goes negative so +although my Theta is pointing me this + + align:start position:0% +although my Theta is pointing me this + + + align:start position:0% +although my Theta is pointing me this +way the thing is going to go backwards + + align:start position:0% +way the thing is going to go backwards + + + align:start position:0% +way the thing is going to go backwards +and there's another clue which is very + + align:start position:0% +and there's another clue which is very + + + align:start position:0% +and there's another clue which is very +important how far backwards is it going + + align:start position:0% +important how far backwards is it going + + + align:start position:0% +important how far backwards is it going +well you don't actually need to know + + align:start position:0% +well you don't actually need to know + + + align:start position:0% +well you don't actually need to know +anything but this equation here to + + align:start position:0% +anything but this equation here to + + + align:start position:0% +anything but this equation here to +understand that it has to be on the same + + align:start position:0% +understand that it has to be on the same + + + align:start position:0% +understand that it has to be on the same +Circle so when I'm pointing this way the + + align:start position:0% +Circle so when I'm pointing this way the + + + align:start position:0% +Circle so when I'm pointing this way the +thing points backwards to this point + + align:start position:0% +thing points backwards to this point + + + align:start position:0% +thing points backwards to this point +over there + + align:start position:0% +over there + + + align:start position:0% +over there +so what happens is it goes around once + + align:start position:0% +so what happens is it goes around once + + + align:start position:0% +so what happens is it goes around once +and then when I point out this way it + + align:start position:0% +and then when I point out this way it + + + align:start position:0% +and then when I point out this way it +sweeps around a second time it just + + align:start position:0% +sweeps around a second time it just + + + align:start position:0% +sweeps around a second time it just +keeps on going around the same Circle so + + align:start position:0% +keeps on going around the same Circle so + + + align:start position:0% +keeps on going around the same Circle so +over here it's empty because it's + + align:start position:0% +over here it's empty because it's + + + align:start position:0% +over here it's empty because it's +pointing the other way and it's sweeping + + align:start position:0% +pointing the other way and it's sweeping + + + align:start position:0% +pointing the other way and it's sweeping +around the same curve a second + + align:start position:0% + + + + align:start position:0% + +time right now if you were foolish + + align:start position:0% +time right now if you were foolish + + + align:start position:0% +time right now if you were foolish +enough to integrate say from 0 to 2 pi + + align:start position:0% +enough to integrate say from 0 to 2 pi + + + align:start position:0% +enough to integrate say from 0 to 2 pi +or some wider range what would happen is + + align:start position:0% +or some wider range what would happen is + + + align:start position:0% +or some wider range what would happen is +you would just double the area because + + align:start position:0% +you would just double the area because + + + align:start position:0% +you would just double the area because +you would have swept it out twice + + align:start position:0% + + + + align:start position:0% + +all right so that's the mistake that + + align:start position:0% +all right so that's the mistake that + + + align:start position:0% +all right so that's the mistake that +you'll make sometimes you'll count + + align:start position:0% +you'll make sometimes you'll count + + + align:start position:0% +you'll make sometimes you'll count +things as negative and positive but + + align:start position:0% +things as negative and positive but + + + align:start position:0% +things as negative and positive but +because there's an AR there's a square + + align:start position:0% +because there's an AR there's a square + + + align:start position:0% +because there's an AR there's a square +here it's always a positive quantity and + + align:start position:0% +here it's always a positive quantity and + + + align:start position:0% +here it's always a positive quantity and +you'll always overcount if you if you go + + align:start position:0% +you'll always overcount if you if you go + + + align:start position:0% +you'll always overcount if you if you go +too + + align:start position:0% +too + + + align:start position:0% +too +far all right so that's that's that's + + align:start position:0% +far all right so that's that's that's + + + align:start position:0% +far all right so that's that's that's +what happens again it sweeps out the + + align:start position:0% +what happens again it sweeps out the + + + align:start position:0% +what happens again it sweeps out the +same region that's because these two + + align:start position:0% +same region that's because these two + + + align:start position:0% +same region that's because these two +equations really are equivalent to each + + align:start position:0% +equations really are equivalent to each + + + align:start position:0% +equations really are equivalent to each +other it's just that this one sweeps it + + align:start position:0% +other it's just that this one sweeps it + + + align:start position:0% +other it's just that this one sweeps it +out twice and this one doesn't say how + + align:start position:0% +out twice and this one doesn't say how + + + align:start position:0% +out twice and this one doesn't say how +it's sweeping it out + + align:start position:0% +it's sweeping it out + + + align:start position:0% +it's sweeping it out +yeah another question doesn't this + + align:start position:0% +yeah another question doesn't this + + + align:start position:0% +yeah another question doesn't this +equation also work if you just go from + + align:start position:0% +equation also work if you just go from + + + align:start position:0% +equation also work if you just go from +zero to Pi does the integration work if + + align:start position:0% +zero to Pi does the integration work if + + + align:start position:0% +zero to Pi does the integration work if +you just go from zero to Pi the answer + + align:start position:0% +you just go from zero to Pi the answer + + + align:start position:0% +you just go from zero to Pi the answer +is yes that's a very weird object though + + align:start position:0% +is yes that's a very weird object though + + + align:start position:0% +is yes that's a very weird object though +let me just show you what that is if you + + align:start position:0% +let me just show you what that is if you + + + align:start position:0% +let me just show you what that is if you +started from 0 to 2 pi um so I I'll + + align:start position:0% +started from 0 to 2 pi um so I I'll + + + align:start position:0% +started from 0 to 2 pi um so I I'll +illustrate it on here um the first thing + + align:start position:0% +illustrate it on here um the first thing + + + align:start position:0% +illustrate it on here um the first thing +that you swept out between 0 and Pi + + align:start position:0% +that you swept out between 0 and Pi + + + align:start position:0% +that you swept out between 0 and Pi +over2 is this part here that was swept + + align:start position:0% +over2 is this part here that was swept + + + align:start position:0% +over2 is this part here that was swept +out and then when you're going around + + align:start position:0% +out and then when you're going around + + + align:start position:0% +out and then when you're going around +this this next quadrant here you're + + align:start position:0% +this this next quadrant here you're + + + align:start position:0% +this this next quadrant here you're +actually sweeping out this Underside + + align:start position:0% +actually sweeping out this Underside + + + align:start position:0% +actually sweeping out this Underside +here so actually you're getting it + + align:start position:0% +here so actually you're getting it + + + align:start position:0% +here so actually you're getting it +because you're getting the half of it on + + align:start position:0% +because you're getting the half of it on + + + align:start position:0% +because you're getting the half of it on +one half and you're getting the other + + align:start position:0% +one half and you're getting the other + + + align:start position:0% +one half and you're getting the other +half on the other quadrant so it's + + align:start position:0% +half on the other quadrant so it's + + + align:start position:0% +half on the other quadrant so it's +actually giving you the right answer + + align:start position:0% +actually giving you the right answer + + + align:start position:0% +actually giving you the right answer +okay so that's that turns out to be okay + + align:start position:0% +okay so that's that turns out to be okay + + + align:start position:0% +okay so that's that turns out to be okay +it's a little weird way to chop up a + + align:start position:0% +it's a little weird way to chop up a + + + align:start position:0% +it's a little weird way to chop up a +circle but it's but it's + + align:start position:0% +circle but it's but it's + + + align:start position:0% +circle but it's but it's +legal + + align:start position:0% + + + + align:start position:0% + +okay but of course that's an accident of + + align:start position:0% +okay but of course that's an accident of + + + align:start position:0% +okay but of course that's an accident of +this particular figure you can't count + + align:start position:0% +this particular figure you can't count + + + align:start position:0% +this particular figure you can't count +on that happening it's much better to + + align:start position:0% +on that happening it's much better to + + + align:start position:0% +on that happening it's much better to +line it up exactly with what the figure + + align:start position:0% +line it up exactly with what the figure + + + align:start position:0% +line it up exactly with what the figure +does all right so don't don't don't do + + align:start position:0% +does all right so don't don't don't do + + + align:start position:0% +does all right so don't don't don't do +that uh too often you might run into + + align:start position:0% +that uh too often you might run into + + + align:start position:0% +that uh too often you might run into +troubles all + + align:start position:0% +troubles all + + + align:start position:0% +troubles all +right so I'm going to give you a couple + + align:start position:0% +right so I'm going to give you a couple + + + align:start position:0% +right so I'm going to give you a couple +more examples uh of practice with + + align:start position:0% +more examples uh of practice with + + + align:start position:0% +more examples uh of practice with +um with these pictures and + + align:start position:0% +um with these pictures and + + + align:start position:0% +um with these pictures and +maybe let's see I'm going to get rid of + + align:start position:0% +maybe let's see I'm going to get rid of + + + align:start position:0% +maybe let's see I'm going to get rid of +this one up + + align:start position:0% + + + + align:start position:0% + +here so here's another favorite + + align:start position:0% + + + + align:start position:0% + +here's another favorite so this if you + + align:start position:0% +here's another favorite so this if you + + + align:start position:0% +here's another favorite so this if you +like is example two I guess we had an + + align:start position:0% +like is example two I guess we had an + + + align:start position:0% +like is example two I guess we had an +example one up there and now we're + + align:start position:0% +example one up there and now we're + + + align:start position:0% +example one up there and now we're +really not going to try to do any more + + align:start position:0% +really not going to try to do any more + + + align:start position:0% +really not going to try to do any more +area examples the area examples are + + align:start position:0% +area examples the area examples are + + + align:start position:0% +area examples the area examples are +actually straightforward it's really + + align:start position:0% +actually straightforward it's really + + + align:start position:0% +actually straightforward it's really +just figuring out what the picture looks + + align:start position:0% +just figuring out what the picture looks + + + align:start position:0% +just figuring out what the picture looks +like so so these are this is examples of + + align:start position:0% +like so so these are this is examples of + + + align:start position:0% +like so so these are this is examples of +drawings + + align:start position:0% + + + + align:start position:0% + +so this one + + align:start position:0% +so this one + + + align:start position:0% +so this one +is is one that's kind of fun to to to do + + align:start position:0% +is is one that's kind of fun to to to do + + + align:start position:0% +is is one that's kind of fun to to to do +this is RS sin 2 Theta something like + + align:start position:0% +this is RS sin 2 Theta something like + + + align:start position:0% +this is RS sin 2 Theta something like +this is on your + + align:start position:0% +this is on your + + + align:start position:0% +this is on your +homework + + align:start position:0% +homework + + + align:start position:0% +homework +and so what happens here is the + + align:start position:0% + + + + align:start position:0% + +following what happens here is that at R + + align:start position:0% +following what happens here is that at R + + + align:start position:0% +following what happens here is that at R +equals sorry at theta equals zero that's + + align:start position:0% +equals sorry at theta equals zero that's + + + align:start position:0% +equals sorry at theta equals zero that's +the first place this is so let's let's + + align:start position:0% +the first place this is so let's let's + + + align:start position:0% +the first place this is so let's let's +just plot a few places here I'm not + + align:start position:0% +just plot a few places here I'm not + + + align:start position:0% +just plot a few places here I'm not +going to plot very many Theta is equal + + align:start position:0% +going to plot very many Theta is equal + + + align:start position:0% +going to plot very many Theta is equal +to I get R is one oh whoops I get R is + + align:start position:0% +to I get R is one oh whoops I get R is + + + align:start position:0% +to I get R is one oh whoops I get R is +zero sorry and then pi over + + align:start position:0% +zero sorry and then pi over + + + align:start position:0% +zero sorry and then pi over +4 that's where I get sin pi over 2 I get + + align:start position:0% +4 that's where I get sin pi over 2 I get + + + align:start position:0% +4 that's where I get sin pi over 2 I get +one here for this and then again at pi/ + + align:start position:0% +one here for this and then again at pi/ + + + align:start position:0% +one here for this and then again at pi/ +2 I get sin Pi which is back at zero + + align:start position:0% +2 I get sin Pi which is back at zero + + + align:start position:0% +2 I get sin Pi which is back at zero +again so it's it's and the other thing + + align:start position:0% +again so it's it's and the other thing + + + align:start position:0% +again so it's it's and the other thing +to say is in between here it's positive + + align:start position:0% +to say is in between here it's positive + + + align:start position:0% +to say is in between here it's positive +in between so what it does is it starts + + align:start position:0% +in between so what it does is it starts + + + align:start position:0% +in between so what it does is it starts +out at zero and it goes out to the + + align:start position:0% +out at zero and it goes out to the + + + align:start position:0% +out at zero and it goes out to the +radius one over here and then it comes + + align:start position:0% +radius one over here and then it comes + + + align:start position:0% +radius one over here and then it comes +back all right so it does something like + + align:start position:0% +back all right so it does something like + + + align:start position:0% +back all right so it does something like +this it goes out and it comes + + align:start position:0% +this it goes out and it comes + + + align:start position:0% +this it goes out and it comes +back now because of the + + align:start position:0% +back now because of the + + + align:start position:0% +back now because of the +symmetries of the sign function this is + + align:start position:0% +symmetries of the sign function this is + + + align:start position:0% +symmetries of the sign function this is +pretty much all you need to know it does + + align:start position:0% +pretty much all you need to know it does + + + align:start position:0% +pretty much all you need to know it does +something similar in all of the + + align:start position:0% +something similar in all of the + + + align:start position:0% +something similar in all of the +quadrants but in order to to to see what + + align:start position:0% +quadrants but in order to to to see what + + + align:start position:0% +quadrants but in order to to to see what +it's doing there's it's useful for you + + align:start position:0% +it's doing there's it's useful for you + + + align:start position:0% +it's doing there's it's useful for you +to watch me draw it because the order is + + align:start position:0% +to watch me draw it because the order is + + + align:start position:0% +to watch me draw it because the order is +very + + align:start position:0% +very + + + align:start position:0% +very +important for understanding what it's + + align:start position:0% +important for understanding what it's + + + align:start position:0% +important for understanding what it's +doing it's similar to this business + + align:start position:0% +doing it's similar to this business + + + align:start position:0% +doing it's similar to this business +weird business with the circle here so + + align:start position:0% +weird business with the circle here so + + + align:start position:0% +weird business with the circle here so +watch me draw this this guy I'll draw it + + align:start position:0% +watch me draw this this guy I'll draw it + + + align:start position:0% +watch me draw this this guy I'll draw it +in red because it usually has a name so + + align:start position:0% +in red because it usually has a name so + + + align:start position:0% +in red because it usually has a name so +here it is it does this + + align:start position:0% +here it is it does this + + + align:start position:0% +here it is it does this +thing and then it does this and then it + + align:start position:0% +thing and then it does this and then it + + + align:start position:0% +thing and then it does this and then it +does this and then it does that all + + align:start position:0% +does this and then it does that all + + + align:start position:0% +does this and then it does that all +right so it's called a + + align:start position:0% +right so it's called a + + + align:start position:0% +right so it's called a +fourleaf rose I drew it in pink because + + align:start position:0% +fourleaf rose I drew it in pink because + + + align:start position:0% +fourleaf rose I drew it in pink because +it's kind of rows here all right so it + + align:start position:0% +it's kind of rows here all right so it + + + align:start position:0% +it's kind of rows here all right so it +started out over here this is step + + align:start position:0% +started out over here this is step + + + align:start position:0% +started out over here this is step +one and this is the range 0 less than + + align:start position:0% +one and this is the range 0 less than + + + align:start position:0% +one and this is the range 0 less than +Theta is less than pi over + + align:start position:0% +Theta is less than pi over + + + align:start position:0% +Theta is less than pi over +4 all right it did this part here and + + align:start position:0% +4 all right it did this part here and + + + align:start position:0% +4 all right it did this part here and +then it went two here so I I should draw + + align:start position:0% +then it went two here so I I should draw + + + align:start position:0% +then it went two here so I I should draw +these in in white because they're harder + + align:start position:0% +these in in white because they're harder + + + align:start position:0% +these in in white because they're harder +to read in in red and but now look at + + align:start position:0% +to read in in red and but now look at + + + align:start position:0% +to read in in red and but now look at +what it did it did not make a right + + align:start position:0% +what it did it did not make a right + + + align:start position:0% +what it did it did not make a right +angle turn it was nice and smooth it + + align:start position:0% +angle turn it was nice and smooth it + + + align:start position:0% +angle turn it was nice and smooth it +went around here and then it went down + + align:start position:0% +went around here and then it went down + + + align:start position:0% +went around here and then it went down +here this is three back here that's four + + align:start position:0% +here this is three back here that's four + + + align:start position:0% +here this is three back here that's four +and then over here that's five back up + + align:start position:0% +and then over here that's five back up + + + align:start position:0% +and then over here that's five back up +here that's six and then around here + + align:start position:0% +here that's six and then around here + + + align:start position:0% +here that's six and then around here +that's seven and down here that's eight + + align:start position:0% +that's seven and down here that's eight + + + align:start position:0% +that's seven and down here that's eight +and then back where it started and goes + + align:start position:0% +and then back where it started and goes + + + align:start position:0% +and then back where it started and goes +around again all right and this is + + align:start position:0% +around again all right and this is + + + align:start position:0% +around again all right and this is +because actually it's switching sign + + align:start position:0% +because actually it's switching sign + + + align:start position:0% +because actually it's switching sign +when it crosses the origin when it was + + align:start position:0% +when it crosses the origin when it was + + + align:start position:0% +when it crosses the origin when it was +over in this quadrant the first time + + align:start position:0% +over in this quadrant the first time + + + align:start position:0% +over in this quadrant the first time +it's actually was tracing what's + + align:start position:0% +it's actually was tracing what's + + + align:start position:0% +it's actually was tracing what's +directly behind + + align:start position:0% + + + + align:start position:0% + +it all right so this is kind of amusing + + align:start position:0% +it all right so this is kind of amusing + + + align:start position:0% +it all right so this is kind of amusing +from this little tiny formula you get + + align:start position:0% +from this little tiny formula you get + + + align:start position:0% +from this little tiny formula you get +this pretty diagram here anyway that's + + align:start position:0% +this pretty diagram here anyway that's + + + align:start position:0% +this pretty diagram here anyway that's +as I say an old favorite and here uh you + + align:start position:0% +as I say an old favorite and here uh you + + + align:start position:0% +as I say an old favorite and here uh you +know if you want to do the area of one + + align:start position:0% +know if you want to do the area of one + + + align:start position:0% +know if you want to do the area of one +leaf you've got to make sure you + + align:start position:0% +leaf you've got to make sure you + + + align:start position:0% +leaf you've got to make sure you +understand that it's a small piece of + + align:start position:0% +understand that it's a small piece of + + + align:start position:0% +understand that it's a small piece of +the + + align:start position:0% + + + + align:start position:0% + +hole okay now I have one last drawing + + align:start position:0% +hole okay now I have one last drawing + + + align:start position:0% +hole okay now I have one last drawing +example that I want to discuss with you + + align:start position:0% +example that I want to discuss with you + + + align:start position:0% +example that I want to discuss with you +and it involves another skill that we + + align:start position:0% +and it involves another skill that we + + + align:start position:0% +and it involves another skill that we +haven't quite gotten enough practice + + align:start position:0% +haven't quite gotten enough practice + + + align:start position:0% +haven't quite gotten enough practice +with + + align:start position:0% +with + + + align:start position:0% +with +so I'm going to do that one and it's + + align:start position:0% +so I'm going to do that one and it's + + + align:start position:0% +so I'm going to do that one and it's +also preparation for an exercise but one + + align:start position:0% +also preparation for an exercise but one + + + align:start position:0% +also preparation for an exercise but one +that we're going to do after the test so + + align:start position:0% +that we're going to do after the test so + + + align:start position:0% +that we're going to do after the test so +so here's my last + + align:start position:0% + + + + align:start position:0% + +example we're going to discuss what + + align:start position:0% +example we're going to discuss what + + + align:start position:0% +example we're going to discuss what +happens with this function + + align:start position:0% +happens with this function + + + align:start position:0% +happens with this function +here sorry that's not legible is it + + align:start position:0% +here sorry that's not legible is it + + + align:start position:0% +here sorry that's not legible is it +that's a + + align:start position:0% + + + + align:start position:0% + +cosine R is equal to 1 1 + 2 cosine + + align:start position:0% + + + + align:start position:0% + +Theta now the first thing I want to do + + align:start position:0% +Theta now the first thing I want to do + + + align:start position:0% +Theta now the first thing I want to do +is just take our time a little bit and + + align:start position:0% +is just take our time a little bit and + + + align:start position:0% +is just take our time a little bit and +plot a few + + align:start position:0% + + + + align:start position:0% + +points so here's the values of theta and + + align:start position:0% +points so here's the values of theta and + + + align:start position:0% +points so here's the values of theta and +here are the values of R and we'll see + + align:start position:0% +here are the values of R and we'll see + + + align:start position:0% +here are the values of R and we'll see +what happens and we'll try to figure out + + align:start position:0% +what happens and we'll try to figure out + + + align:start position:0% +what happens and we'll try to figure out +what it's doing when Theta is equal to + + align:start position:0% +what it's doing when Theta is equal to + + + align:start position:0% +what it's doing when Theta is equal to +zero cosine is 1 so R is a thir + + align:start position:0% + + + + align:start position:0% + +all right that's the denominator is 1 + + + align:start position:0% +all right that's the denominator is 1 + + + + align:start position:0% +all right that's the denominator is 1 + +2 so it's a + + align:start position:0% + + + + align:start position:0% + +third if Theta I'm going to make it easy + + align:start position:0% +third if Theta I'm going to make it easy + + + align:start position:0% +third if Theta I'm going to make it easy +we're not going to do so many I'm going + + align:start position:0% +we're not going to do so many I'm going + + + align:start position:0% +we're not going to do so many I'm going +to do pi/ 2 that's an easy value of the + + align:start position:0% +to do pi/ 2 that's an easy value of the + + + align:start position:0% +to do pi/ 2 that's an easy value of the +cosine uh that's cosine of Pi / 2 is + + align:start position:0% +cosine uh that's cosine of Pi / 2 is + + + align:start position:0% +cosine uh that's cosine of Pi / 2 is +zero so that value of R is + + align:start position:0% + + + + align:start position:0% + +one and now I'm going to back up and do + + align:start position:0% +one and now I'm going to back up and do + + + align:start position:0% +one and now I'm going to back up and do +minus piun / 2 + + align:start position:0% +minus piun / 2 + + + align:start position:0% +minus piun / 2 +minus piun / 2 again cosine is 0er and R + + align:start position:0% +minus piun / 2 again cosine is 0er and R + + + align:start position:0% +minus piun / 2 again cosine is 0er and R +is + + align:start position:0% + + + + align:start position:0% + +1 so now I'd like to just plot those + + align:start position:0% +1 so now I'd like to just plot those + + + align:start position:0% +1 so now I'd like to just plot those +points anyway and see what's going on + + align:start position:0% +points anyway and see what's going on + + + align:start position:0% +points anyway and see what's going on +with this with this uh expression here + + align:start position:0% +with this with this uh expression here + + + align:start position:0% +with this with this uh expression here +the first one is at a rectangular I'm + + align:start position:0% +the first one is at a rectangular I'm + + + align:start position:0% +the first one is at a rectangular I'm +going to write the rectangular + + align:start position:0% +going to write the rectangular + + + align:start position:0% +going to write the rectangular +coordinates here not the uh polar + + align:start position:0% +coordinates here not the uh polar + + + align:start position:0% +coordinates here not the uh polar +coordinates the rectangular coordinates + + align:start position:0% +coordinates the rectangular coordinates + + + align:start position:0% +coordinates the rectangular coordinates +here is um it's a third out at the + + align:start position:0% +here is um it's a third out at the + + + align:start position:0% +here is um it's a third out at the +horizontal so it's a 1/3 zero all right + + align:start position:0% +horizontal so it's a 1/3 zero all right + + + align:start position:0% +horizontal so it's a 1/3 zero all right +the polar coordinates is 0 13 is is 1/30 + + align:start position:0% +the polar coordinates is 0 13 is is 1/30 + + + align:start position:0% +the polar coordinates is 0 13 is is 1/30 +but the rectangular coordinate is also + + align:start position:0% +but the rectangular coordinate is also + + + align:start position:0% +but the rectangular coordinate is also +that and over here at Pi / 2 the + + align:start position:0% +that and over here at Pi / 2 the + + + align:start position:0% +that and over here at Pi / 2 the +distance is 1 so this is the point 0 + + align:start position:0% +distance is 1 so this is the point 0 + + + align:start position:0% +distance is 1 so this is the point 0 +comma 1 in XY + + align:start position:0% +comma 1 in XY + + + align:start position:0% +comma 1 in XY +coordinates and then down here at uhga + + align:start position:0% +coordinates and then down here at uhga + + + align:start position:0% +coordinates and then down here at uhga +Pi / 2 it's 0 comma minus + + align:start position:0% +Pi / 2 it's 0 comma minus + + + align:start position:0% +Pi / 2 it's 0 comma minus +one and let me just emphasize if you you + + align:start position:0% +one and let me just emphasize if you you + + + align:start position:0% +one and let me just emphasize if you you +should be able to think of this visually + + align:start position:0% +should be able to think of this visually + + + align:start position:0% +should be able to think of this visually +if you can crank your arm around and and + + align:start position:0% +if you can crank your arm around and and + + + align:start position:0% +if you can crank your arm around and and +and think it or if you're if you're + + align:start position:0% +and think it or if you're if you're + + + align:start position:0% +and think it or if you're if you're +right-handed you'll have to bend that + + align:start position:0% +right-handed you'll have to bend that + + + align:start position:0% +right-handed you'll have to bend that +way no anyway or you'll have to use but + + align:start position:0% +way no anyway or you'll have to use but + + + align:start position:0% +way no anyway or you'll have to use but +but this also works using this formulas + + align:start position:0% +but this also works using this formulas + + + align:start position:0% +but this also works using this formulas +x = r cosine Theta y = r sin Theta + + align:start position:0% +x = r cosine Theta y = r sin Theta + + + align:start position:0% +x = r cosine Theta y = r sin Theta +notice that in this case r was 1 but the + + align:start position:0% +notice that in this case r was 1 but the + + + align:start position:0% +notice that in this case r was 1 but the +cosine was zero so you plug in Theta = - + + align:start position:0% +cosine was zero so you plug in Theta = - + + + align:start position:0% +cosine was zero so you plug in Theta = - +piun / 2 and R = 1 + + align:start position:0% +piun / 2 and R = 1 + + + align:start position:0% +piun / 2 and R = 1 +and lo and behold you get zero here and + + align:start position:0% +and lo and behold you get zero here and + + + align:start position:0% +and lo and behold you get zero here and +here you get minus one and here you get + + align:start position:0% +here you get minus one and here you get + + + align:start position:0% +here you get minus one and here you get +one so this is minus one all right so + + align:start position:0% +one so this is minus one all right so + + + align:start position:0% +one so this is minus one all right so +this is an example I did it purely + + align:start position:0% +this is an example I did it purely + + + align:start position:0% +this is an example I did it purely +visually or sort of uhu organically but + + align:start position:0% +visually or sort of uhu organically but + + + align:start position:0% +visually or sort of uhu organically but +you can also do it by plugging in the + + align:start position:0% +you can also do it by plugging in the + + + align:start position:0% +you can also do it by plugging in the +numbers all right now in + + align:start position:0% +numbers all right now in + + + align:start position:0% +numbers all right now in +between the denominator is positive and + + align:start position:0% +between the denominator is positive and + + + align:start position:0% +between the denominator is positive and +it's something in between it's going to + + align:start position:0% +it's something in between it's going to + + + align:start position:0% +it's something in between it's going to +it's going to sweep around something + + align:start position:0% +it's going to sweep around something + + + align:start position:0% +it's going to sweep around something +like this all right that's what happens + + align:start position:0% +like this all right that's what happens + + + align:start position:0% +like this all right that's what happens +in between as as Theta increases from + + align:start position:0% +in between as as Theta increases from + + + align:start position:0% +in between as as Theta increases from +minus piun over 2 to Pi / + + align:start position:0% +minus piun over 2 to Pi / + + + align:start position:0% +minus piun over 2 to Pi / +2 and now something interesting happens + + align:start position:0% +2 and now something interesting happens + + + align:start position:0% +2 and now something interesting happens +with this particular function which is + + align:start position:0% +with this particular function which is + + + align:start position:0% +with this particular function which is +that we notice that the denominator is + + align:start position:0% +that we notice that the denominator is + + + align:start position:0% +that we notice that the denominator is +zero at a certain place namely if I + + align:start position:0% +zero at a certain place namely if I + + + align:start position:0% +zero at a certain place namely if I +solve 2 cine Theta is equal to -1 then + + align:start position:0% +solve 2 cine Theta is equal to -1 then + + + align:start position:0% +solve 2 cine Theta is equal to -1 then +the denominator is going to be zero + + align:start position:0% +the denominator is going to be zero + + + align:start position:0% +the denominator is going to be zero +there that's cosine + + align:start position:0% +there that's cosine + + + align:start position:0% +there that's cosine +Theta is equal to minus a half so Theta + + align:start position:0% +Theta is equal to minus a half so Theta + + + align:start position:0% +Theta is equal to minus a half so Theta +is equal to it turns out plus orus 2 + + align:start position:0% +is equal to it turns out plus orus 2 + + + align:start position:0% +is equal to it turns out plus orus 2 +piun over 3 those are the values here so + + align:start position:0% +piun over 3 those are the values here so + + + align:start position:0% +piun over 3 those are the values here so +when we're out here + + align:start position:0% +when we're out here + + + align:start position:0% +when we're out here +somewhere in these directions there's + + align:start position:0% +somewhere in these directions there's + + + align:start position:0% +somewhere in these directions there's +nothing it's going infinitely far + + align:start position:0% +nothing it's going infinitely far + + + align:start position:0% +nothing it's going infinitely far +out those + + align:start position:0% +out those + + + align:start position:0% +out those +ways all + + align:start position:0% + + + + align:start position:0% + +right okay that's about as much as we'll + + align:start position:0% +right okay that's about as much as we'll + + + align:start position:0% +right okay that's about as much as we'll +be able to figure out of this diagram + + align:start position:0% +be able to figure out of this diagram + + + align:start position:0% +be able to figure out of this diagram +without doing some analytic work and + + align:start position:0% +without doing some analytic work and + + + align:start position:0% +without doing some analytic work and +that's the other little piece that I + + align:start position:0% +that's the other little piece that I + + + align:start position:0% +that's the other little piece that I +want to + + align:start position:0% +want to + + + align:start position:0% +want to +explain namely going backwards from + + align:start position:0% +explain namely going backwards from + + + align:start position:0% +explain namely going backwards from +Polar coordinates to rectangular + + align:start position:0% +Polar coordinates to rectangular + + + align:start position:0% +Polar coordinates to rectangular +coordinates which is one thing that we + + align:start position:0% +coordinates which is one thing that we + + + align:start position:0% +coordinates which is one thing that we +haven't done so let's let's do that so + + align:start position:0% +haven't done so let's let's do that so + + + align:start position:0% +haven't done so let's let's do that so +what is the rectangular + + align:start position:0% + + + + align:start position:0% + +equation that means the + + align:start position:0% +equation that means the + + + align:start position:0% +equation that means the +XY + + align:start position:0% + + + + align:start position:0% + +equation for this r = 1 / 1 + 2 cosine + + align:start position:0% +equation for this r = 1 / 1 + 2 cosine + + + align:start position:0% +equation for this r = 1 / 1 + 2 cosine +Theta and let's see what it is well + + align:start position:0% +Theta and let's see what it is well + + + align:start position:0% +Theta and let's see what it is well +first I'm going to clear the denominator + + align:start position:0% +first I'm going to clear the denominator + + + align:start position:0% +first I'm going to clear the denominator +here this is r + 2 R cosine + + align:start position:0% +here this is r + 2 R cosine + + + align:start position:0% +here this is r + 2 R cosine +Theta = + + align:start position:0% +Theta = + + + align:start position:0% +Theta = +1 and now I'm going to rewrite + + align:start position:0% +1 and now I'm going to rewrite + + + align:start position:0% +1 and now I'm going to rewrite +it as r = 1 - 2R cosine Theta and the + + align:start position:0% +it as r = 1 - 2R cosine Theta and the + + + align:start position:0% +it as r = 1 - 2R cosine Theta and the +reason for that is that in a minute I'll + + align:start position:0% +reason for that is that in a minute I'll + + + align:start position:0% +reason for that is that in a minute I'll +I'll explain to you why this is 1 - + + align:start position:0% +I'll explain to you why this is 1 - + + + align:start position:0% +I'll explain to you why this is 1 - +2X and this guy I'm going to square now + + align:start position:0% +2X and this guy I'm going to square now + + + align:start position:0% +2X and this guy I'm going to square now +I'm going to make this um r^2 = 1 - + + align:start position:0% +I'm going to make this um r^2 = 1 - + + + align:start position:0% +I'm going to make this um r^2 = 1 - +2x2 and now with an R 2 I can plug in + + align:start position:0% +2x2 and now with an R 2 I can plug in + + + align:start position:0% +2x2 and now with an R 2 I can plug in +x^2 + + + align:start position:0% + + + + align:start position:0% + +y^2 all right so this is a + + align:start position:0% +y^2 all right so this is a + + + align:start position:0% +y^2 all right so this is a +standard thing to do and it's basically + + align:start position:0% +standard thing to do and it's basically + + + align:start position:0% +standard thing to do and it's basically +what you're going to do anytime you're + + align:start position:0% +what you're going to do anytime you're + + + align:start position:0% +what you're going to do anytime you're +faced with an equation like this is try + + align:start position:0% +faced with an equation like this is try + + + align:start position:0% +faced with an equation like this is try +to work it out and in these + + align:start position:0% +to work it out and in these + + + align:start position:0% +to work it out and in these +situations it will uh where you have 1/ + + align:start position:0% +situations it will uh where you have 1/ + + + align:start position:0% +situations it will uh where you have 1/ +a + b cosine Theta or sin Theta you'll + + align:start position:0% +a + b cosine Theta or sin Theta you'll + + + align:start position:0% +a + b cosine Theta or sin Theta you'll +always come out with some quadratic + + align:start position:0% +always come out with some quadratic + + + align:start position:0% +always come out with some quadratic +expression like + + align:start position:0% +expression like + + + align:start position:0% +expression like +this now I'm going to combine terms so + + align:start position:0% +this now I'm going to combine terms so + + + align:start position:0% +this now I'm going to combine terms so +here I have - 3x^2 + y^2 and put + + align:start position:0% +here I have - 3x^2 + y^2 and put + + + align:start position:0% +here I have - 3x^2 + y^2 and put +everything on the right the left side so + + align:start position:0% +everything on the right the left side so + + + align:start position:0% +everything on the right the left side so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +this all + + align:start position:0% +this all + + + align:start position:0% +this all +right and we recognize well you're + + align:start position:0% +right and we recognize well you're + + + align:start position:0% +right and we recognize well you're +supposed to recognize that this is + + align:start position:0% +supposed to recognize that this is + + + align:start position:0% +supposed to recognize that this is +what's known as a + + align:start position:0% + + + + align:start position:0% + +hyperbola if the signs are the same it's + + align:start position:0% +hyperbola if the signs are the same it's + + + align:start position:0% +hyperbola if the signs are the same it's +an ellipse if the signs are opposite + + align:start position:0% +an ellipse if the signs are opposite + + + align:start position:0% +an ellipse if the signs are opposite +it's a hyperbola and in between if one + + align:start position:0% +it's a hyperbola and in between if one + + + align:start position:0% +it's a hyperbola and in between if one +of the coefficients on the quadratic is + + align:start position:0% +of the coefficients on the quadratic is + + + align:start position:0% +of the coefficients on the quadratic is +zero it's a + + align:start position:0% + + + + align:start position:0% + +parabola so now we see that what we the + + align:start position:0% +parabola so now we see that what we the + + + align:start position:0% +parabola so now we see that what we the +picture that we drew there is + + align:start position:0% +picture that we drew there is + + + align:start position:0% +picture that we drew there is +actually turns out it's going to have + + align:start position:0% +actually turns out it's going to have + + + align:start position:0% +actually turns out it's going to have +ASM tootes it's going to be a hyperbola + + align:start position:0% + + + + align:start position:0% + +all right so now let me ask you the the + + align:start position:0% +all right so now let me ask you the the + + + align:start position:0% +all right so now let me ask you the the +the the the last little mindbending + + align:start position:0% +the the the last little mindbending + + + align:start position:0% +the the the last little mindbending +question that I want to ask which is + + align:start position:0% +question that I want to ask which is + + + align:start position:0% +question that I want to ask which is +what happens so now I'm using my right + + align:start position:0% +what happens so now I'm using my right + + + align:start position:0% +what happens so now I'm using my right +arm I guess but my elbow's at the origin + + align:start position:0% +arm I guess but my elbow's at the origin + + + align:start position:0% +arm I guess but my elbow's at the origin +here what happens if I pass outside to + + align:start position:0% +here what happens if I pass outside to + + + align:start position:0% +here what happens if I pass outside to +the range where uh this denominator is + + align:start position:0% +the range where uh this denominator is + + + align:start position:0% +the range where uh this denominator is +negative it crossed zero and it went to + + align:start position:0% +negative it crossed zero and it went to + + + align:start position:0% +negative it crossed zero and it went to +negative and sweeping out something over + + align:start position:0% +negative and sweeping out something over + + + align:start position:0% +negative and sweeping out something over +here is it is it sweeping out the same + + align:start position:0% +here is it is it sweeping out the same + + + align:start position:0% +here is it is it sweeping out the same +curve anybody have any idea what it's + + align:start position:0% +curve anybody have any idea what it's + + + align:start position:0% +curve anybody have any idea what it's +doing + + align:start position:0% +doing + + + align:start position:0% +doing +yeah part of the hypera yeah exactly + + align:start position:0% +yeah part of the hypera yeah exactly + + + align:start position:0% +yeah part of the hypera yeah exactly +good good answer it's the other branch + + align:start position:0% +good good answer it's the other branch + + + align:start position:0% +good good answer it's the other branch +of the + + align:start position:0% +of the + + + align:start position:0% +of the +hyperbola okay so what's actually + + align:start position:0% +hyperbola okay so what's actually + + + align:start position:0% +hyperbola okay so what's actually +happening is in Disguise there's another + + align:start position:0% +happening is in Disguise there's another + + + align:start position:0% +happening is in Disguise there's another +branch of the hyperbola which is being + + align:start position:0% +branch of the hyperbola which is being + + + align:start position:0% +branch of the hyperbola which is being +swept out by the other piece of this + + align:start position:0% +swept out by the other piece of this + + + align:start position:0% +swept out by the other piece of this +thing now that is consistent with these + + align:start position:0% +thing now that is consistent with these + + + align:start position:0% +thing now that is consistent with these +algebraic equations the algebraic + + align:start position:0% +algebraic equations the algebraic + + + align:start position:0% +algebraic equations the algebraic +equation that I got here doesn't say + + align:start position:0% +equation that I got here doesn't say + + + align:start position:0% +equation that I got here doesn't say +which branch of the hyperbola I've got + + align:start position:0% +which branch of the hyperbola I've got + + + align:start position:0% +which branch of the hyperbola I've got +it's actually got two + + align:start position:0% + + + + align:start position:0% + +branches and the curve really was in + + align:start position:0% +branches and the curve really was in + + + align:start position:0% +branches and the curve really was in +Disguise capturing both of + + align:start position:0% + + + + align:start position:0% + +them I want to make the connection now + + align:start position:0% +them I want to make the connection now + + + align:start position:0% +them I want to make the connection now +with the the the basic formula for uh + + align:start position:0% +with the the the basic formula for uh + + + align:start position:0% +with the the the basic formula for uh +area here because this is this is a a + + align:start position:0% +area here because this is this is a a + + + align:start position:0% +area here because this is this is a a +really beautiful connection and I want + + align:start position:0% +really beautiful connection and I want + + + align:start position:0% +really beautiful connection and I want +to make that connection uh in connection + + align:start position:0% +to make that connection uh in connection + + + align:start position:0% +to make that connection uh in connection +also with this with this example the um + + align:start position:0% +also with this with this example the um + + + align:start position:0% +also with this with this example the um +uh hyperbolas as you probably know are + + align:start position:0% +uh hyperbolas as you probably know are + + + align:start position:0% +uh hyperbolas as you probably know are +the uh trajectories of + + align:start position:0% + + + + align:start position:0% + +comets and uh ellipses which is what you + + align:start position:0% +comets and uh ellipses which is what you + + + align:start position:0% +comets and uh ellipses which is what you +would get if you maybe you put a half + + align:start position:0% +would get if you maybe you put a half + + + align:start position:0% +would get if you maybe you put a half +here instead of a two would be the + + align:start position:0% +here instead of a two would be the + + + align:start position:0% +here instead of a two would be the +trajectories of planets or + + align:start position:0% +trajectories of planets or + + + align:start position:0% +trajectories of planets or +asteroids but there's actually something + + align:start position:0% +asteroids but there's actually something + + + align:start position:0% +asteroids but there's actually something +much uh more important physically that + + align:start position:0% +much uh more important physically that + + + align:start position:0% +much uh more important physically that +goes on that's special about this + + align:start position:0% +goes on that's special about this + + + align:start position:0% +goes on that's special about this +particular + + align:start position:0% +particular + + + align:start position:0% +particular +representation of the uh hyperbola and + + align:start position:0% +representation of the uh hyperbola and + + + align:start position:0% +representation of the uh hyperbola and +what happens when you get the ellipses + + align:start position:0% +what happens when you get the ellipses + + + align:start position:0% +what happens when you get the ellipses +as well which is that in this + + align:start position:0% +as well which is that in this + + + align:start position:0% +as well which is that in this +case r equal Z is the + + align:start position:0% +case r equal Z is the + + + align:start position:0% +case r equal Z is the +focus of the + + align:start position:0% + + + + align:start position:0% + +hyperbola and what that + + align:start position:0% +hyperbola and what that + + + align:start position:0% +hyperbola and what that +means is that it's actually the place + + align:start position:0% +means is that it's actually the place + + + align:start position:0% +means is that it's actually the place +where the sun is + + align:start position:0% + + + + align:start position:0% + +so this is the right representation if + + align:start position:0% +so this is the right representation if + + + align:start position:0% +so this is the right representation if +you want the center of gravity in the + + align:start position:0% +you want the center of gravity in the + + + align:start position:0% +you want the center of gravity in the +center of your + + align:start position:0% + + + + align:start position:0% + +picture and um pretty much any other I + + align:start position:0% +picture and um pretty much any other I + + + align:start position:0% +picture and um pretty much any other I +mean you can't tell that at all from the + + align:start position:0% +mean you can't tell that at all from the + + + align:start position:0% +mean you can't tell that at all from the +algebraic equations here so this + + align:start position:0% +algebraic equations here so this + + + align:start position:0% +algebraic equations here so this +hyperbola is going to be the trajectory + + align:start position:0% +hyperbola is going to be the trajectory + + + align:start position:0% +hyperbola is going to be the trajectory +of some Comet going by + + align:start position:0% + + + + align:start position:0% + +here and this formula here is + + align:start position:0% +here and this formula here is + + + align:start position:0% +here and this formula here is +actually a a rather Central formula in + + align:start position:0% + + + + align:start position:0% + +astronomy + + align:start position:0% + + + + align:start position:0% + +namely there's something called Kepler's + + align:start position:0% + + + + align:start position:0% + +Law which says that the rate of + + align:start position:0% + + + + align:start position:0% + +change of area which is swept out is + + align:start position:0% +change of area which is swept out is + + + align:start position:0% +change of area which is swept out is +constant + + align:start position:0% + + + + align:start position:0% + +the rate of change of area relative to + + align:start position:0% +the rate of change of area relative to + + + align:start position:0% +the rate of change of area relative to +the center of mass relative to the + + align:start position:0% +the center of mass relative to the + + + align:start position:0% +the center of mass relative to the +Sun so in equal areas this is the the + + align:start position:0% +Sun so in equal areas this is the the + + + align:start position:0% +Sun so in equal areas this is the the +amount of area so this tells you now + + align:start position:0% +amount of area so this tells you now + + + align:start position:0% +amount of area so this tells you now +that when a comet + + align:start position:0% +that when a comet + + + align:start position:0% +that when a comet +goes around the Sun like this its speed + + align:start position:0% +goes around the Sun like this its speed + + + align:start position:0% +goes around the Sun like this its speed +varies and its speed varies according to + + align:start position:0% +varies and its speed varies according to + + + align:start position:0% +varies and its speed varies according to +a very specific rule namely this one + + align:start position:0% +a very specific rule namely this one + + + align:start position:0% +a very specific rule namely this one +here and this rule was observed by + + align:start position:0% +here and this rule was observed by + + + align:start position:0% +here and this rule was observed by +Kepler but if you have this connection + + align:start position:0% +Kepler but if you have this connection + + + align:start position:0% +Kepler but if you have this connection +here we also have something else we also + + align:start position:0% +here we also have something else we also + + + align:start position:0% +here we also have something else we also +know that da DT is equal to a half R 2 D + + align:start position:0% +know that da DT is equal to a half R 2 D + + + align:start position:0% +know that da DT is equal to a half R 2 D +Theta + + align:start position:0% +Theta + + + align:start position:0% +Theta +DT all right so that's that's this + + align:start position:0% +DT all right so that's that's this + + + align:start position:0% +DT all right so that's that's this +formula here uh formally dividing by T + + align:start position:0% +formula here uh formally dividing by T + + + align:start position:0% +formula here uh formally dividing by T +that's the rate of change with respect + + align:start position:0% +that's the rate of change with respect + + + align:start position:0% +that's the rate of change with respect +to this time parameter which is the + + align:start position:0% +to this time parameter which is the + + + align:start position:0% +to this time parameter which is the +honest to goodness time real physical + + align:start position:0% +honest to goodness time real physical + + + align:start position:0% +honest to goodness time real physical +time and that + + align:start position:0% + + + + align:start position:0% + +means this quantity here + + align:start position:0% +means this quantity here + + + align:start position:0% +means this quantity here +is + + align:start position:0% + + + + align:start position:0% + +constant and this is one of the key + + align:start position:0% +constant and this is one of the key + + + align:start position:0% +constant and this is one of the key +insights that uh physicists had long + + align:start position:0% +insights that uh physicists had long + + + align:start position:0% +insights that uh physicists had long +after Kepler made his physical + + align:start position:0% +after Kepler made his physical + + + align:start position:0% +after Kepler made his physical +observations they realized that he was + + align:start position:0% +observations they realized that he was + + + align:start position:0% +observations they realized that he was +had managed to get the best physics + + align:start position:0% +had managed to get the best physics + + + align:start position:0% +had managed to get the best physics +experiment at all because it's a + + align:start position:0% +experiment at all because it's a + + + align:start position:0% +experiment at all because it's a +frictionless setup right out Outer Space + + align:start position:0% +frictionless setup right out Outer Space + + + align:start position:0% +frictionless setup right out Outer Space +there's no air nothing is going on this + + align:start position:0% +there's no air nothing is going on this + + + align:start position:0% +there's no air nothing is going on this +is what's known nowadays as + + align:start position:0% + + + + align:start position:0% + +conservation of angular + + align:start position:0% + + + + align:start position:0% + +momentum this is this is the expression + + align:start position:0% +momentum this is this is the expression + + + align:start position:0% +momentum this is this is the expression +for angular momentum and what and what + + align:start position:0% +for angular momentum and what and what + + + align:start position:0% +for angular momentum and what and what +Kepler was observing it turns out is + + align:start position:0% +Kepler was observing it turns out is + + + align:start position:0% +Kepler was observing it turns out is +what we see all the time in real life + + align:start position:0% +what we see all the time in real life + + + align:start position:0% +what we see all the time in real life +which is when you start something + + align:start position:0% +which is when you start something + + + align:start position:0% +which is when you start something +spinning around it continues to spin at + + align:start position:0% +spinning around it continues to spin at + + + align:start position:0% +spinning around it continues to spin at +roughly the same rate or if you're an + + align:start position:0% +roughly the same rate or if you're an + + + align:start position:0% +roughly the same rate or if you're an +ice skater and you get yourself scrunch + + align:start position:0% +ice skater and you get yourself scrunch + + + align:start position:0% +ice skater and you get yourself scrunch +together a little bit more you can spin + + align:start position:0% +together a little bit more you can spin + + + align:start position:0% +together a little bit more you can spin +faster and there's an exact quantitative + + align:start position:0% +faster and there's an exact quantitative + + + align:start position:0% +faster and there's an exact quantitative +rule that does that and it's exactly + + align:start position:0% +rule that does that and it's exactly + + + align:start position:0% +rule that does that and it's exactly +this polar formula + + align:start position:0% +this polar formula + + + align:start position:0% +this polar formula +here all right so that's that's a neat + + align:start position:0% +here all right so that's that's a neat + + + align:start position:0% +here all right so that's that's a neat +thing and we will do a little exercise + + align:start position:0% +thing and we will do a little exercise + + + align:start position:0% +thing and we will do a little exercise +on this rate of change uh after the exam + + align:start position:0% +on this rate of change uh after the exam + + + align:start position:0% +on this rate of change uh after the exam +okay so that's it for uh generalities + + align:start position:0% +okay so that's it for uh generalities + + + align:start position:0% +okay so that's it for uh generalities +and uh a little pep talk on what's + + align:start position:0% +and uh a little pep talk on what's + + + align:start position:0% +and uh a little pep talk on what's +coming up to you uh when you learn a + + align:start position:0% +coming up to you uh when you learn a + + + align:start position:0% +coming up to you uh when you learn a +little more physics + + align:start position:0% +little more physics + + + align:start position:0% +little more physics +uh right now we need to talk about the + + align:start position:0% +uh right now we need to talk about the + + + align:start position:0% +uh right now we need to talk about the +exam + + align:start position:0% + + + + align:start position:0% + +okay so first of + + align:start position:0% +okay so first of + + + align:start position:0% +okay so first of +[Applause] + + align:start position:0% + + + + align:start position:0% + +all let me tell you what the topics are + + align:start position:0% +all let me tell you what the topics are + + + align:start position:0% +all let me tell you what the topics are +they're the same as uh last year's test + + align:start position:0% +they're the same as uh last year's test + + + align:start position:0% +they're the same as uh last year's test +which you can take a look + + align:start position:0% +which you can take a look + + + align:start position:0% +which you can take a look +at + + align:start position:0% +at + + + align:start position:0% +at +and well let's + + align:start position:0% +and well let's + + + align:start position:0% +and well let's +see so what what do we do one of the + + align:start position:0% +see so what what do we do one of the + + + align:start position:0% +see so what what do we do one of the +main topics + + align:start position:0% +main topics + + + align:start position:0% +main topics +of this unit were techniques of + + align:start position:0% + + + + align:start position:0% + +integration and there are three which + + align:start position:0% +integration and there are three which + + + align:start position:0% +integration and there are three which +are which we will test one is um trig + + align:start position:0% + + + + align:start position:0% + +substitution one is integration by + + align:start position:0% + + + + align:start position:0% + +parts and one is partial fractions + + align:start position:0% + + + + align:start position:0% + +so that's more than half of the + + align:start position:0% +so that's more than half of the + + + align:start position:0% +so that's more than half of the +exam right there the other half of the + + align:start position:0% +exam right there the other half of the + + + align:start position:0% +exam right there the other half of the +exam is + + align:start position:0% + + + + align:start position:0% + +parametric + + align:start position:0% +parametric + + + align:start position:0% +parametric +curves Arc + + align:start position:0% +curves Arc + + + align:start position:0% +curves Arc +Length these are all + + align:start position:0% +Length these are all + + + align:start position:0% +Length these are all +interrelated and uh uh + + align:start position:0% +interrelated and uh uh + + + align:start position:0% +interrelated and uh uh +area of surfaces of revolution + + align:start position:0% + + + + align:start position:0% + +those are the only kind that we can + + align:start position:0% +those are the only kind that we can + + + align:start position:0% +those are the only kind that we can +handle just as we did with with with + + align:start position:0% +handle just as we did with with with + + + align:start position:0% +handle just as we did with with with +volume of surfaces of Revolution and + + align:start position:0% +volume of surfaces of Revolution and + + + align:start position:0% +volume of surfaces of Revolution and +then there's a final topic which is + + align:start position:0% +then there's a final topic which is + + + align:start position:0% +then there's a final topic which is +polar + + align:start position:0% + + + + align:start position:0% + +coordinates and uh area in polar + + align:start position:0% +coordinates and uh area in polar + + + align:start position:0% +coordinates and uh area in polar +coordinat including + + align:start position:0% + + + + align:start position:0% + +area all right that's it that's what's + + align:start position:0% +area all right that's it that's what's + + + align:start position:0% +area all right that's it that's what's +on the test there are six problems + + align:start position:0% +on the test there are six problems + + + align:start position:0% +on the test there are six problems +they're very similar well they're not + + align:start position:0% +they're very similar well they're not + + + align:start position:0% +they're very similar well they're not +actually that similar but they're + + align:start position:0% +actually that similar but they're + + + align:start position:0% +actually that similar but they're +somewhat similar to the last years I'd + + align:start position:0% +somewhat similar to the last years I'd + + + align:start position:0% +somewhat similar to the last years I'd +say the test + + align:start position:0% +say the test + + + align:start position:0% +say the test +is a tiny bit well similar similar maybe + + align:start position:0% +is a tiny bit well similar similar maybe + + + align:start position:0% +is a tiny bit well similar similar maybe +a tiny bit more difficult we'll we'll + + align:start position:0% +a tiny bit more difficult we'll we'll + + + align:start position:0% +a tiny bit more difficult we'll we'll +see we'll see + + align:start position:0% + + + + align:start position:0% + +yeah decision the the the question was + + align:start position:0% +yeah decision the the the question was + + + align:start position:0% +yeah decision the the the question was +we didn't do arc length in polar + + align:start position:0% +we didn't do arc length in polar + + + align:start position:0% +we didn't do arc length in polar +coordinates did we and the answer is no + + align:start position:0% +coordinates did we and the answer is no + + + align:start position:0% +coordinates did we and the answer is no +we did not we did not do Arc link and + + align:start position:0% +we did not we did not do Arc link and + + + align:start position:0% +we did not we did not do Arc link and +polar coordinates when I give you an + + align:start position:0% +polar coordinates when I give you an + + + align:start position:0% +polar coordinates when I give you an +exercise I'm going to ask you about if + + align:start position:0% +exercise I'm going to ask you about if + + + align:start position:0% +exercise I'm going to ask you about if +you know the speed of a comet here + + align:start position:0% +you know the speed of a comet here + + + align:start position:0% +you know the speed of a comet here +what's the speed of the Comet there and + + align:start position:0% +what's the speed of the Comet there and + + + align:start position:0% +what's the speed of the Comet there and +we'll have to know about arcl length for + + align:start position:0% +we'll have to know about arcl length for + + + align:start position:0% +we'll have to know about arcl length for +that but we're not doing it on this + + align:start position:0% + + + + align:start position:0% + +exam other + + align:start position:0% +exam other + + + align:start position:0% +exam other +questions yeah uh do you expect us to + + align:start position:0% +questions yeah uh do you expect us to + + + align:start position:0% +questions yeah uh do you expect us to +know for example Ral 3 cosine 3 + + align:start position:0% +know for example Ral 3 cosine 3 + + + align:start position:0% +know for example Ral 3 cosine 3 +or do you have to SK the question is + + align:start position:0% +or do you have to SK the question is + + + align:start position:0% +or do you have to SK the question is +will you will I expect you to know um R + + align:start position:0% +will you will I expect you to know um R + + + align:start position:0% +will you will I expect you to know um R +equals so let let's see if I can + + align:start position:0% +equals so let let's see if I can + + + align:start position:0% +equals so let let's see if I can +formulate this question it's related to + + align:start position:0% +formulate this question it's related to + + + align:start position:0% +formulate this question it's related to +this Four Leaf rows here so the question + + align:start position:0% +this Four Leaf rows here so the question + + + align:start position:0% +this Four Leaf rows here so the question +is suppose I gave you something that + + align:start position:0% +is suppose I gave you something that + + + align:start position:0% +is suppose I gave you something that +looked like + + align:start position:0% + + + + align:start position:0% + +this um would I expect you to be able to + + align:start position:0% +this um would I expect you to be able to + + + align:start position:0% +this um would I expect you to be able to +know what it is uh I think the answer + + align:start position:0% +know what it is uh I think the answer + + + align:start position:0% +know what it is uh I think the answer +the the fair answer to give you is is if + + align:start position:0% +the the fair answer to give you is is if + + + align:start position:0% +the the fair answer to give you is is if +it's this complicated it would there are + + align:start position:0% +it's this complicated it would there are + + + align:start position:0% +it's this complicated it would there are +all I only have two possibilities I can + + align:start position:0% +all I only have two possibilities I can + + + align:start position:0% +all I only have two possibilities I can +give you a long time to sketch this out + + align:start position:0% +give you a long time to sketch this out + + + align:start position:0% +give you a long time to sketch this out +and think about what it does or I can + + align:start position:0% +and think about what it does or I can + + + align:start position:0% +and think about what it does or I can +tell you that it happens to be a three + + align:start position:0% +tell you that it happens to be a three + + + align:start position:0% +tell you that it happens to be a three +leaf Rose and then you then you have + + align:start position:0% +leaf Rose and then you then you have + + + align:start position:0% +leaf Rose and then you then you have +some clue as to what it's doing okay it + + align:start position:0% +some clue as to what it's doing okay it + + + align:start position:0% +some clue as to what it's doing okay it +doesn't have six because of some weird + + align:start position:0% +doesn't have six because of some weird + + + align:start position:0% +doesn't have six because of some weird +thing having to do with repetitions but + + align:start position:0% +thing having to do with repetitions but + + + align:start position:0% +thing having to do with repetitions but +the odds and the evens work differently + + align:start position:0% +the odds and the evens work differently + + + align:start position:0% +the odds and the evens work differently +so so that's so in fact you you so so I + + align:start position:0% +so so that's so in fact you you so so I + + + align:start position:0% +so so that's so in fact you you so so I +would have to tell you what the picture + + align:start position:0% +would have to tell you what the picture + + + align:start position:0% +would have to tell you what the picture +looks like if it's going to be this + + align:start position:0% +looks like if it's going to be this + + + align:start position:0% +looks like if it's going to be this +complicated all right + + align:start position:0% +complicated all right + + + align:start position:0% +complicated all right +similarly so this is an important point + + align:start position:0% +similarly so this is an important point + + + align:start position:0% +similarly so this is an important point +to make when we come to techniques of + + align:start position:0% +to make when we come to techniques of + + + align:start position:0% +to make when we come to techniques of +integration any integral that you + + align:start position:0% +integration any integral that you + + + align:start position:0% +integration any integral that you +have I'm not going to tell you which of + + align:start position:0% +have I'm not going to tell you which of + + + align:start position:0% +have I'm not going to tell you which of +these three techniques to use on the + + align:start position:0% +these three techniques to use on the + + + align:start position:0% +these three techniques to use on the +ones which are straightforward integrals + + align:start position:0% +ones which are straightforward integrals + + + align:start position:0% +ones which are straightforward integrals +but if it's an integral that I think + + align:start position:0% +but if it's an integral that I think + + + align:start position:0% +but if it's an integral that I think +you're going to get stuck on either I'm + + align:start position:0% +you're going to get stuck on either I'm + + + align:start position:0% +you're going to get stuck on either I'm +going to give you a hint I'm going to + + align:start position:0% +going to give you a hint I'm going to + + + align:start position:0% +going to give you a hint I'm going to +tell you how to do it or I'm going to + + align:start position:0% +tell you how to do it or I'm going to + + + align:start position:0% +tell you how to do it or I'm going to +tell you don't do it if I tell you don't + + align:start position:0% +tell you don't do it if I tell you don't + + + align:start position:0% +tell you don't do it if I tell you don't +do it don't try to do it it may be + + align:start position:0% +do it don't try to do it it may be + + + align:start position:0% +do it don't try to do it it may be +impossible and even if it's possible + + align:start position:0% +impossible and even if it's possible + + + align:start position:0% +impossible and even if it's possible +it's going to be very long like you know + + align:start position:0% +it's going to be very long like you know + + + align:start position:0% +it's going to be very long like you know +an hour so don't don't do it unless uh I + + align:start position:0% +an hour so don't don't do it unless uh I + + + align:start position:0% +an hour so don't don't do it unless uh I +tell you to on the other hand all of + + align:start position:0% +tell you to on the other hand all of + + + align:start position:0% +tell you to on the other hand all of +these setups in this second half of this + + align:start position:0% +these setups in this second half of this + + + align:start position:0% +these setups in this second half of this +unit they involve somehow setting + + align:start position:0% +unit they involve somehow setting + + + align:start position:0% +unit they involve somehow setting +something up and the there are there are + + align:start position:0% +something up and the there are there are + + + align:start position:0% +something up and the there are there are +basically three + + align:start position:0% +basically three + + + align:start position:0% +basically three +issues one is what the integrand is one + + align:start position:0% +issues one is what the integrand is one + + + align:start position:0% +issues one is what the integrand is one +is uh one is what the lower limit is and + + align:start position:0% +is uh one is what the lower limit is and + + + align:start position:0% +is uh one is what the lower limit is and +one what is the upper limit right + + align:start position:0% +one what is the upper limit right + + + align:start position:0% +one what is the upper limit right +they're just they're just three things + + align:start position:0% +they're just they're just three things + + + align:start position:0% +they're just they're just three things +three inputs to setting up an integral + + align:start position:0% +three inputs to setting up an integral + + + align:start position:0% +three inputs to setting up an integral +all integrals this is this is going to + + align:start position:0% +all integrals this is this is going to + + + align:start position:0% +all integrals this is this is going to +be the setup for all of them and then + + align:start position:0% +be the setup for all of them and then + + + align:start position:0% +be the setup for all of them and then +the second step is evaluating which + + align:start position:0% +the second step is evaluating which + + + align:start position:0% +the second step is evaluating which +really is what we did in the first half + + align:start position:0% +really is what we did in the first half + + + align:start position:0% +really is what we did in the first half +here and unfortunately we don't have + + align:start position:0% +here and unfortunately we don't have + + + align:start position:0% +here and unfortunately we don't have +infinitely many techniques and indeed + + align:start position:0% +infinitely many techniques and indeed + + + align:start position:0% +infinitely many techniques and indeed +there's some integrals that can't be + + align:start position:0% +there's some integrals that can't be + + + align:start position:0% +there's some integrals that can't be +evaluated and some that are too long so + + align:start position:0% +evaluated and some that are too long so + + + align:start position:0% +evaluated and some that are too long so +we'll just try to avoid those I'm not + + align:start position:0% +we'll just try to avoid those I'm not + + + align:start position:0% +we'll just try to avoid those I'm not +trying to give you ones which are + + align:start position:0% +trying to give you ones which are + + + align:start position:0% +trying to give you ones which are +hopelessly + + align:start position:0% + + + + align:start position:0% + +long all right other questions yes + + align:start position:0% +long all right other questions yes + + + align:start position:0% +long all right other questions yes +Distribution on this exam be the same as + + align:start position:0% +Distribution on this exam be the same as + + + align:start position:0% +Distribution on this exam be the same as +the exam last year because about 70% was + + align:start position:0% +the exam last year because about 70% was + + + align:start position:0% +the exam last year because about 70% was +techniques of integration on the last + + align:start position:0% +techniques of integration on the last + + + align:start position:0% +techniques of integration on the last +exam about 30 on the points two and + + align:start position:0% +exam about 30 on the points two and + + + align:start position:0% +exam about 30 on the points two and +three will it be + + align:start position:0% +three will it be + + + align:start position:0% +three will it be +similar the question is will the + + align:start position:0% +similar the question is will the + + + align:start position:0% +similar the question is will the +percentages be uh the same and the + + align:start position:0% +percentages be uh the same and the + + + align:start position:0% +percentages be uh the same and the +answer is um no uh this I can I'll tell + + align:start position:0% +answer is um no uh this I can I'll tell + + + align:start position:0% +answer is um no uh this I can I'll tell +you exactly this is 55 points unless I + + align:start position:0% +you exactly this is 55 points unless I + + + align:start position:0% +you exactly this is 55 points unless I +change the point values this is 55 and + + align:start position:0% +change the point values this is 55 and + + + align:start position:0% +change the point values this is 55 and +this is + + align:start position:0% + + + + align:start position:0% + +45 all right that's that's what it came + + align:start position:0% +45 all right that's that's what it came + + + align:start position:0% +45 all right that's that's what it came +out to be all right you are going to + + align:start position:0% +out to be all right you are going to + + + align:start position:0% +out to be all right you are going to +want to know about all of the things + + align:start position:0% +want to know about all of the things + + + align:start position:0% +want to know about all of the things +that I've written down here you're + + align:start position:0% +that I've written down here you're + + + align:start position:0% +that I've written down here you're +definitely going to want to know for + + align:start position:0% +definitely going to want to know for + + + align:start position:0% +definitely going to want to know for +example uh surfaces of Revolution how to + + align:start position:0% +example uh surfaces of Revolution how to + + + align:start position:0% +example uh surfaces of Revolution how to +how to set those up yes uh there was + + align:start position:0% +how to set those up yes uh there was + + + align:start position:0% +how to set those up yes uh there was +another question I saw over here yes + + align:start position:0% +another question I saw over here yes + + + align:start position:0% +another question I saw over here yes +just + + align:start position:0% +just + + + align:start position:0% +just +partial rection we have something in the + + align:start position:0% +partial rection we have something in the + + + align:start position:0% +partial rection we have something in the +denominator that's + + align:start position:0% +denominator that's + + + align:start position:0% +denominator that's +s we have + + align:start position:0% +s we have + + + align:start position:0% +s we have +to break it off into every right so like + + align:start position:0% +to break it off into every right so like + + + align:start position:0% +to break it off into every right so like +you + + align:start position:0% +you + + + align:start position:0% +you +had like + + align:start position:0% + + + + align:start position:0% + +X+ one + + align:start position:0% + + + + align:start position:0% + +of so if you have a partial fraction + + align:start position:0% +of so if you have a partial fraction + + + align:start position:0% +of so if you have a partial fraction +with something like x + 2 the quantity + + align:start position:0% +with something like x + 2 the quantity + + + align:start position:0% +with something like x + 2 the quantity +squared in it and maybe an X and maybe + + align:start position:0% +squared in it and maybe an X and maybe + + + align:start position:0% +squared in it and maybe an X and maybe +an x + + + align:start position:0% +an x + + + + align:start position:0% +an x + +one and + + align:start position:0% + + + + align:start position:0% + +a is is this what we're uh is this the + + align:start position:0% +a is is this what we're uh is this the + + + align:start position:0% +a is is this what we're uh is this the +type of so uh and you're you're uh + + align:start position:0% +type of so uh and you're you're uh + + + align:start position:0% +type of so uh and you're you're uh +interested in what happens with this + + align:start position:0% +interested in what happens with this + + + align:start position:0% +interested in what happens with this +denominator here so what what's going to + + align:start position:0% +denominator here so what what's going to + + + align:start position:0% +denominator here so what what's going to +happen + + align:start position:0% + + + + align:start position:0% + +is you're going to need + + align:start position:0% + + + + align:start position:0% + +a coefficient for each degree of this so + + align:start position:0% +a coefficient for each degree of this so + + + align:start position:0% +a coefficient for each degree of this so +Al together the setup is going to be + + align:start position:0% + + + + align:start position:0% + +this plus one for x and one for x + one + + align:start position:0% +this plus one for x and one for x + one + + + align:start position:0% +this plus one for x and one for x + one +this is this is the the uh the setup all + + align:start position:0% +this is this is the the uh the setup all + + + align:start position:0% +this is this is the the uh the setup all +right so you need + + align:start position:0% +right so you need + + + align:start position:0% +right so you need +yeah follow the same idea let's say it + + align:start position:0% +yeah follow the same idea let's say it + + + align:start position:0% +yeah follow the same idea let's say it +was x + 2 3 + + align:start position:0% +was x + 2 3 + + + align:start position:0% +was x + 2 3 +right so if I change this to being a + + align:start position:0% +right so if I change this to being a + + + align:start position:0% +right so if I change this to being a +three here then I need um uh I guess + + align:start position:0% +three here then I need um uh I guess + + + align:start position:0% +three here then I need um uh I guess +I'll have to write call it e x + 2 cubed + + align:start position:0% +I'll have to write call it e x + 2 cubed + + + align:start position:0% +I'll have to write call it e x + 2 cubed +I need that now it gets harder and + + align:start position:0% +I need that now it gets harder and + + + align:start position:0% +I need that now it gets harder and +harder the more repeated Roots there are + + align:start position:0% +harder the more repeated Roots there are + + + align:start position:0% +harder the more repeated Roots there are +the more repeated factors there are the + + align:start position:0% +the more repeated factors there are the + + + align:start position:0% +the more repeated factors there are the +harder it is because the ones you can + + align:start position:0% +harder it is because the ones you can + + + align:start position:0% +harder it is because the ones you can +pick off by the coverup method are is + + align:start position:0% +pick off by the coverup method are is + + + align:start position:0% +pick off by the coverup method are is +the just the top one here and these two + + align:start position:0% +the just the top one here and these two + + + align:start position:0% +the just the top one here and these two +so C D and E you can get but b and a + + align:start position:0% +so C D and E you can get but b and a + + + align:start position:0% +so C D and E you can get but b and a +you're going to have to do by either + + align:start position:0% +you're going to have to do by either + + + align:start position:0% +you're going to have to do by either +plugging in or some other more elaborate + + align:start position:0% +plugging in or some other more elaborate + + + align:start position:0% +plugging in or some other more elaborate +algebra so the more of these lower terms + + align:start position:0% +algebra so the more of these lower terms + + + align:start position:0% +algebra so the more of these lower terms +there are the worse off you + + align:start position:0% + + + + align:start position:0% + +are one does that affect your + + align:start position:0% +are one does that affect your + + + align:start position:0% +are one does that affect your +denominators at all like since you have + + align:start position:0% +denominators at all like since you have + + + align:start position:0% +denominators at all like since you have +an X+ 21 in numat will that affect what + + align:start position:0% +an X+ 21 in numat will that affect what + + + align:start position:0% +an X+ 21 in numat will that affect what +you put in a + + align:start position:0% +you put in a + + + align:start position:0% +you put in a +denominator uh the question is um does + + align:start position:0% +denominator uh the question is um does + + + align:start position:0% +denominator uh the question is um does +this xq + 20 want affect this setup and + + align:start position:0% +this xq + 20 want affect this setup and + + + align:start position:0% +this xq + 20 want affect this setup and +the answer + + align:start position:0% +the answer + + + align:start position:0% +the answer +is almost no that is not at all it's the + + align:start position:0% +is almost no that is not at all it's the + + + align:start position:0% +is almost no that is not at all it's the +same setup exactly but there's one thing + + align:start position:0% +same setup exactly but there's one thing + + + align:start position:0% +same setup exactly but there's one thing +if the degree gets too big then you + + align:start position:0% +if the degree gets too big then you + + + align:start position:0% +if the degree gets too big then you +you've got to use long division first to + + align:start position:0% +you've got to use long division first to + + + align:start position:0% +you've got to use long division first to +knock it down all + + align:start position:0% +knock it down all + + + align:start position:0% +knock it down all +right okay I have I I'll give you an + + align:start position:0% +right okay I have I I'll give you an + + + align:start position:0% +right okay I have I I'll give you an +example of this type of practice unless + + align:start position:0% +example of this type of practice unless + + + align:start position:0% +example of this type of practice unless +there are more questions + + align:start position:0% + + + + align:start position:0% + +yes you're going to have to know how to + + align:start position:0% +yes you're going to have to know how to + + + align:start position:0% +yes you're going to have to know how to +do reduction formulas anything that's a + + align:start position:0% +do reduction formulas anything that's a + + + align:start position:0% +do reduction formulas anything that's a +little out of the ordinary like a + + align:start position:0% +little out of the ordinary like a + + + align:start position:0% +little out of the ordinary like a +reduction formula I will have to coach + + align:start position:0% +reduction formula I will have to coach + + + align:start position:0% +reduction formula I will have to coach +you to do so in other words what you'll + + align:start position:0% +you to do so in other words what you'll + + + align:start position:0% +you to do so in other words what you'll +have to be able to do in that situation + + align:start position:0% +have to be able to do in that situation + + + align:start position:0% +have to be able to do in that situation +is follow directions if I tell you okay + + align:start position:0% +is follow directions if I tell you okay + + + align:start position:0% +is follow directions if I tell you okay +you're faced with this then do an + + align:start position:0% +you're faced with this then do an + + + align:start position:0% +you're faced with this then do an +integration by parts and do that then + + align:start position:0% +integration by parts and do that then + + + align:start position:0% +integration by parts and do that then +you you'll get the reduction formula + + align:start position:0% +you you'll get the reduction formula + + + align:start position:0% +you you'll get the reduction formula +okay yeah okay so the question had to do + + align:start position:0% +okay yeah okay so the question had to do + + + align:start position:0% +okay yeah okay so the question had to do +with uh the partial fractions + + align:start position:0% +with uh the partial fractions + + + align:start position:0% +with uh the partial fractions +method and what happens if you have + + align:start position:0% +method and what happens if you have + + + align:start position:0% +method and what happens if you have +a what happens if you have a + + align:start position:0% +a what happens if you have a + + + align:start position:0% +a what happens if you have a +quadratic so for + + align:start position:0% + + + + align:start position:0% + +instance if it were + + align:start position:0% +instance if it were + + + align:start position:0% +instance if it were +this this one's too disgusting I'm going + + align:start position:0% +this this one's too disgusting I'm going + + + align:start position:0% +this this one's too disgusting I'm going +to just do it with two of + + align:start position:0% +to just do it with two of + + + align:start position:0% +to just do it with two of +them all right so the the parts with X + + align:start position:0% +them all right so the the parts with X + + + align:start position:0% +them all right so the the parts with X +and X plus one are the same but now you + + align:start position:0% +and X plus one are the same but now you + + + align:start position:0% +and X plus one are the same but now you +have linear factors here a x + B / x^2 + + + align:start position:0% +have linear factors here a x + B / x^2 + + + + align:start position:0% +have linear factors here a x + B / x^2 + + + align:start position:0% + + + align:start position:0% +and a maybe I'll call them one and a2x + + + align:start position:0% +and a maybe I'll call them one and a2x + + + + align:start position:0% +and a maybe I'll call them one and a2x + +B2 x^2 + 2 2 plus C /x + d/ x + + + align:start position:0% +B2 x^2 + 2 2 plus C /x + d/ x + + + + align:start position:0% +B2 x^2 + 2 2 plus C /x + d/ x + +1 all right this is this is the way it + + align:start position:0% +1 all right this is this is the way it + + + align:start position:0% +1 all right this is this is the way it +works okay um I'm going to give you one + + align:start position:0% +works okay um I'm going to give you one + + + align:start position:0% +works okay um I'm going to give you one +more quick example of uh an integration + + align:start position:0% +more quick example of uh an integration + + + align:start position:0% +more quick example of uh an integration +technique just to to uh to liven things + + align:start position:0% +technique just to to uh to liven things + + + align:start position:0% +technique just to to uh to liven things +up whatever let's + + align:start position:0% +up whatever let's + + + align:start position:0% +up whatever let's +see so here's a somewhat tricky example + + align:start position:0% +see so here's a somewhat tricky example + + + align:start position:0% +see so here's a somewhat tricky example +this is just a little trickier than I + + align:start position:0% +this is just a little trickier than I + + + align:start position:0% +this is just a little trickier than I +would give you on a test but it's the + + align:start position:0% +would give you on a test but it's the + + + align:start position:0% +would give you on a test but it's the +same principle and I may do this on a on + + align:start position:0% +same principle and I may do this on a on + + + align:start position:0% +same principle and I may do this on a on +a final exam so suppose you're suppose + + align:start position:0% +a final exam so suppose you're suppose + + + align:start position:0% +a final exam so suppose you're suppose +you have this you're face with this + + align:start position:0% +you have this you're face with this + + + align:start position:0% +you have this you're face with this +integral what are you going to + + align:start position:0% + + + + align:start position:0% + +do integration by parts great that's + + align:start position:0% +do integration by parts great that's + + + align:start position:0% +do integration by parts great that's +right that's because this guy is begging + + align:start position:0% +right that's because this guy is begging + + + align:start position:0% +right that's because this guy is begging +to be differentiated to be made simpler + + align:start position:0% +to be differentiated to be made simpler + + + align:start position:0% +to be differentiated to be made simpler +all right so that means that I want this + + align:start position:0% +all right so that means that I want this + + + align:start position:0% +all right so that means that I want this +one to be U and I want this one to be V + + align:start position:0% +one to be U and I want this one to be V + + + align:start position:0% +one to be U and I want this one to be V +Prime and I want to use integration by + + align:start position:0% +Prime and I want to use integration by + + + align:start position:0% +Prime and I want to use integration by +parts and then U Prime is equal to 1 1 + + + align:start position:0% +parts and then U Prime is equal to 1 1 + + + + align:start position:0% +parts and then U Prime is equal to 1 1 + +x^2 and V is equal to x^2 / + + align:start position:0% +x^2 and V is equal to x^2 / + + + align:start position:0% +x^2 and V is equal to x^2 / +2 all right so the answer is now x^2 2 + + align:start position:0% +2 all right so the answer is now x^2 2 + + + align:start position:0% +2 all right so the answer is now x^2 2 +tan inverse xus the integral of this guy + + align:start position:0% +tan inverse xus the integral of this guy + + + align:start position:0% +tan inverse xus the integral of this guy +which is going to be x^2 / 2 and then I + + align:start position:0% +which is going to be x^2 / 2 and then I + + + align:start position:0% +which is going to be x^2 / 2 and then I +have 1 1 + x^2 + + align:start position:0% +have 1 1 + x^2 + + + align:start position:0% +have 1 1 + x^2 +DX all right now you are not done at + + align:start position:0% +DX all right now you are not done at + + + align:start position:0% +DX all right now you are not done at +this point all right you're still in + + align:start position:0% +this point all right you're still in + + + align:start position:0% +this point all right you're still in +slightly hot water all right it's you're + + align:start position:0% +slightly hot water all right it's you're + + + align:start position:0% +slightly hot water all right it's you're +in tepid water anyway so what what is it + + align:start position:0% +in tepid water anyway so what what is it + + + align:start position:0% +in tepid water anyway so what what is it +that you have to do here you're faced + + align:start position:0% +that you have to do here you're faced + + + align:start position:0% +that you have to do here you're faced +with this integral which I'll put on the + + align:start position:0% +with this integral which I'll put on the + + + align:start position:0% +with this integral which I'll put on the +next board + + align:start position:0% + + + + align:start position:0% + +it's a lot simpler than the other one + + align:start position:0% +it's a lot simpler than the other one + + + align:start position:0% +it's a lot simpler than the other one +but it's as I say you're not quite Out + + align:start position:0% +but it's as I say you're not quite Out + + + align:start position:0% +but it's as I say you're not quite Out +of the + + align:start position:0% +of the + + + align:start position:0% +of the +Woods you're faced with the integral of + + align:start position:0% +Woods you're faced with the integral of + + + align:start position:0% +Woods you're faced with the integral of +a half minus a half x^2 over 1 + x^2 + + align:start position:0% + + + + align:start position:0% + +DX Tri substitution actually amazing + + align:start position:0% +DX Tri substitution actually amazing + + + align:start position:0% +DX Tri substitution actually amazing +interestingly will work uh but that + + align:start position:0% +interestingly will work uh but that + + + align:start position:0% +interestingly will work uh but that +wasn't what I wanted you to do I wanted + + align:start position:0% +wasn't what I wanted you to do I wanted + + + align:start position:0% +wasn't what I wanted you to do I wanted +you to yeah go ahead + + align:start position:0% +you to yeah go ahead + + + align:start position:0% +you to yeah go ahead +add and subtract one to the numerator so + + align:start position:0% +add and subtract one to the numerator so + + + align:start position:0% +add and subtract one to the numerator so +now that's the correct answer now this + + align:start position:0% +now that's the correct answer now this + + + align:start position:0% +now that's the correct answer now this +is the case where the numerator and the + + align:start position:0% +is the case where the numerator and the + + + align:start position:0% +is the case where the numerator and the +denominator are tied and so you have to + + align:start position:0% +denominator are tied and so you have to + + + align:start position:0% +denominator are tied and so you have to +use long division but a shortcut is just + + align:start position:0% +use long division but a shortcut is just + + + align:start position:0% +use long division but a shortcut is just +to observe that the the result of long + + align:start position:0% +to observe that the the result of long + + + align:start position:0% +to observe that the the result of long +division is the same thing as doing + + align:start position:0% + + + + align:start position:0% + +this okay and then noticing that that + + align:start position:0% +this okay and then noticing that that + + + align:start position:0% +this okay and then noticing that that +the that this is 1 - 1 1 + x^2 all right + + align:start position:0% +the that this is 1 - 1 1 + x^2 all right + + + align:start position:0% +the that this is 1 - 1 1 + x^2 all right +so this is the same as as long division + + align:start position:0% +so this is the same as as long division + + + align:start position:0% +so this is the same as as long division +in this case because when you divide in + + align:start position:0% +in this case because when you divide in + + + align:start position:0% +in this case because when you divide in +it goes in with a quotient of one all + + align:start position:0% +it goes in with a quotient of one all + + + align:start position:0% +it goes in with a quotient of one all +right and so this guy turns out to be + + align:start position:0% +right and so this guy turns out to be + + + align:start position:0% +right and so this guy turns out to be +minus a half the integral of + + align:start position:0% +minus a half the integral of + + + align:start position:0% +minus a half the integral of +one uh - 1 1 + + + align:start position:0% +one uh - 1 1 + + + + align:start position:0% +one uh - 1 1 + +x^2 DX which is a half x - half tan + + align:start position:0% +x^2 DX which is a half x - half tan + + + align:start position:0% +x^2 DX which is a half x - half tan +inverse + + align:start position:0% +inverse + + + align:start position:0% +inverse +X all right so so so this is + + align:start position:0% +X all right so so so this is + + + align:start position:0% +X all right so so so this is +this is one extra step that you you you + + align:start position:0% +this is one extra step that you you you + + + align:start position:0% +this is one extra step that you you you +may be faced with at some someday in + + align:start position:0% +may be faced with at some someday in + + + align:start position:0% +may be faced with at some someday in +your life and just keep that in mind \ No newline at end of file diff --git a/BhS5s1T1as8.txt b/BhS5s1T1as8.txt new file mode 100644 index 0000000000000000000000000000000000000000..c9a6d8f90d40db19c61f082e624d8a359c754f26 --- /dev/null +++ b/BhS5s1T1as8.txt @@ -0,0 +1,8267 @@ +align:start position:0% + +Julia just mentioned that in a a few of + + align:start position:0% +Julia just mentioned that in a a few of + + + align:start position:0% +Julia just mentioned that in a a few of +you had commented when we were talking + + align:start position:0% +you had commented when we were talking + + + align:start position:0% +you had commented when we were talking +about the uh the genetic code that some + + align:start position:0% +about the uh the genetic code that some + + + align:start position:0% +about the uh the genetic code that some +of you thought the fact that it had some + + align:start position:0% +of you thought the fact that it had some + + + align:start position:0% +of you thought the fact that it had some +it was degenerate and had some + + align:start position:0% +it was degenerate and had some + + + align:start position:0% +it was degenerate and had some +redundancy in it like multiple codons + + align:start position:0% +redundancy in it like multiple codons + + + align:start position:0% +redundancy in it like multiple codons +and for thring that that was kind of + + align:start position:0% +and for thring that that was kind of + + + align:start position:0% +and for thring that that was kind of +cool and some of you thought it was sort + + align:start position:0% +cool and some of you thought it was sort + + + align:start position:0% +cool and some of you thought it was sort +of a + + align:start position:0% +of a + + + align:start position:0% +of a +waste um and uh would have maybe + + align:start position:0% +waste um and uh would have maybe + + + align:start position:0% +waste um and uh would have maybe +designed it uh the thing differently + + align:start position:0% +designed it uh the thing differently + + + align:start position:0% +designed it uh the thing differently +that's you know part of when you study + + align:start position:0% +that's you know part of when you study + + + align:start position:0% +that's you know part of when you study +biology you don't get to design it from + + align:start position:0% +biology you don't get to design it from + + + align:start position:0% +biology you don't get to design it from +first principles you found out what + + align:start position:0% +first principles you found out what + + + align:start position:0% +first principles you found out what +happened during Evolution and what got + + align:start position:0% +happened during Evolution and what got + + + align:start position:0% +happened during Evolution and what got +selected for and once it gets selected + + align:start position:0% +selected for and once it gets selected + + + align:start position:0% +selected for and once it gets selected +for um then that that gets sort of fixed + + align:start position:0% +for um then that that gets sort of fixed + + + align:start position:0% +for um then that that gets sort of fixed +in nature if if there were four um + + align:start position:0% +in nature if if there were four um + + + align:start position:0% +in nature if if there were four um +nucleotides then you could have one two + + align:start position:0% +nucleotides then you could have one two + + + align:start position:0% +nucleotides then you could have one two +and three-letter words and by the it's + + align:start position:0% +and three-letter words and by the it's + + + align:start position:0% +and three-letter words and by the it's +going to be a three-letter word to have + + align:start position:0% +going to be a three-letter word to have + + + align:start position:0% +going to be a three-letter word to have +at least 20 then you've got some um + + align:start position:0% +at least 20 then you've got some um + + + align:start position:0% +at least 20 then you've got some um +degeneracy or redundancy but that's not + + align:start position:0% +degeneracy or redundancy but that's not + + + align:start position:0% +degeneracy or redundancy but that's not +necessarily A Bad Thing and in fact if + + align:start position:0% +necessarily A Bad Thing and in fact if + + + align:start position:0% +necessarily A Bad Thing and in fact if +you go into the evolution of the code + + align:start position:0% +you go into the evolution of the code + + + align:start position:0% +you go into the evolution of the code +more um more deeply people are to + + align:start position:0% +more um more deeply people are to + + + align:start position:0% +more um more deeply people are to +suspect it it evolved from a simpler one + + align:start position:0% +suspect it it evolved from a simpler one + + + align:start position:0% +suspect it it evolved from a simpler one +and there actually some relationships + + align:start position:0% +and there actually some relationships + + + align:start position:0% +and there actually some relationships +between some of the codons that go back + + align:start position:0% +between some of the codons that go back + + + align:start position:0% +between some of the codons that go back +to the similarity the chemical + + align:start position:0% +to the similarity the chemical + + + align:start position:0% +to the similarity the chemical +similarities between the amino acids and + + align:start position:0% +similarities between the amino acids and + + + align:start position:0% +similarities between the amino acids and +it also allows some things for this some + + align:start position:0% +it also allows some things for this some + + + align:start position:0% +it also allows some things for this some +cells for example you make if they want + + align:start position:0% +cells for example you make if they want + + + align:start position:0% +cells for example you make if they want +proteins to be present at very um at + + align:start position:0% +proteins to be present at very um at + + + align:start position:0% +proteins to be present at very um at +very low levels they will use a codon + + align:start position:0% +very low levels they will use a codon + + + align:start position:0% +very low levels they will use a codon +that has just a very little a very low + + align:start position:0% +that has just a very little a very low + + + align:start position:0% +that has just a very little a very low +level of the corresponding TRNA and if + + align:start position:0% +level of the corresponding TRNA and if + + + align:start position:0% +level of the corresponding TRNA and if +they want to make a lot of the protein + + align:start position:0% +they want to make a lot of the protein + + + align:start position:0% +they want to make a lot of the protein +they'll they'll use a TR that it makes + + align:start position:0% +they'll they'll use a TR that it makes + + + align:start position:0% +they'll they'll use a TR that it makes +in abundance and so they could sort of + + align:start position:0% +in abundance and so they could sort of + + + align:start position:0% +in abundance and so they could sort of +another way of controlling levels of + + align:start position:0% +another way of controlling levels of + + + align:start position:0% +another way of controlling levels of +proteins there are a lot of different + + align:start position:0% +proteins there are a lot of different + + + align:start position:0% +proteins there are a lot of different +subtleties in here and also in biology + + align:start position:0% +subtleties in here and also in biology + + + align:start position:0% +subtleties in here and also in biology +redundancy is not necessarily a bad + + align:start position:0% +redundancy is not necessarily a bad + + + align:start position:0% +redundancy is not necessarily a bad +thing it's just like on a space flight + + align:start position:0% +thing it's just like on a space flight + + + align:start position:0% +thing it's just like on a space flight +if something goes wrong if there's some + + align:start position:0% +if something goes wrong if there's some + + + align:start position:0% +if something goes wrong if there's some +kind of redundant function then you've + + align:start position:0% +kind of redundant function then you've + + + align:start position:0% +kind of redundant function then you've +got some some backups too okay well in + + align:start position:0% +got some some backups too okay well in + + + align:start position:0% +got some some backups too okay well in +any case um today's pretty interesting + + align:start position:0% +any case um today's pretty interesting + + + align:start position:0% +any case um today's pretty interesting +uh first part of the lecture uh you know + + align:start position:0% +uh first part of the lecture uh you know + + + align:start position:0% +uh first part of the lecture uh you know +I've heard a few people uh Express The + + align:start position:0% +I've heard a few people uh Express The + + + align:start position:0% +I've heard a few people uh Express The +View that you know why can't I just + + align:start position:0% +View that you know why can't I just + + + align:start position:0% +View that you know why can't I just +teach what's in the textbook and get on + + align:start position:0% +teach what's in the textbook and get on + + + align:start position:0% +teach what's in the textbook and get on +with it and um I think this part for + + align:start position:0% +with it and um I think this part for + + + align:start position:0% +with it and um I think this part for +those of you who are following uh really + + align:start position:0% +those of you who are following uh really + + + align:start position:0% +those of you who are following uh really +think trying to understand I'm trying to + + align:start position:0% +think trying to understand I'm trying to + + + align:start position:0% +think trying to understand I'm trying to +do this course I hope this will will + + align:start position:0% +do this course I hope this will will + + + align:start position:0% +do this course I hope this will will +help you you see this because uh what + + align:start position:0% +help you you see this because uh what + + + align:start position:0% +help you you see this because uh what +I've talked about this thing that that + + align:start position:0% +I've talked about this thing that that + + + align:start position:0% +I've talked about this thing that that +uh Crick called the central dogma which + + align:start position:0% +uh Crick called the central dogma which + + + align:start position:0% +uh Crick called the central dogma which +was the the direction of information + + align:start position:0% +was the the direction of information + + + align:start position:0% +was the the direction of information +flow in DNA in in biology which was from + + align:start position:0% +flow in DNA in in biology which was from + + + align:start position:0% +flow in DNA in in biology which was from +DNA to RNA + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +proteins and I'll just remind you you + + align:start position:0% +proteins and I'll just remind you you + + + align:start position:0% +proteins and I'll just remind you you +know although proteins do many things + + align:start position:0% +know although proteins do many things + + + align:start position:0% +know although proteins do many things +there for example enzymes that are are + + align:start position:0% +there for example enzymes that are are + + + align:start position:0% +there for example enzymes that are are +biological + + align:start position:0% +biological + + + align:start position:0% +biological +catalysts and it was pretty well + + align:start position:0% +catalysts and it was pretty well + + + align:start position:0% +catalysts and it was pretty well +established even by the time I was in + + align:start position:0% +established even by the time I was in + + + align:start position:0% +established even by the time I was in +undergrad that that this was the the way + + align:start position:0% +undergrad that that this was the the way + + + align:start position:0% +undergrad that that this was the the way +information flow went in um biology and + + align:start position:0% +information flow went in um biology and + + + align:start position:0% +information flow went in um biology and +this was how it it worked and there were + + align:start position:0% +this was how it it worked and there were + + + align:start position:0% +this was how it it worked and there were +various statements in the literature + + align:start position:0% +various statements in the literature + + + align:start position:0% +various statements in the literature +that what was true of for e fi was true + + align:start position:0% +that what was true of for e fi was true + + + align:start position:0% +that what was true of for e fi was true +for an elephant and it is still true + + align:start position:0% +for an elephant and it is still true + + + align:start position:0% +for an elephant and it is still true +today in a in a broad in a broad sense + + align:start position:0% +today in a in a broad in a broad sense + + + align:start position:0% +today in a in a broad in a broad sense +that uh as I've tried to emphasize + + align:start position:0% +that uh as I've tried to emphasize + + + align:start position:0% +that uh as I've tried to emphasize +throughout the course you get down to a + + align:start position:0% +throughout the course you get down to a + + + align:start position:0% +throughout the course you get down to a +cellular M molecular level things look + + align:start position:0% +cellular M molecular level things look + + + align:start position:0% +cellular M molecular level things look +there's an awful lot in common and + + align:start position:0% +there's an awful lot in common and + + + align:start position:0% +there's an awful lot in common and +things look much more alike than + + align:start position:0% +things look much more alike than + + + align:start position:0% +things look much more alike than +different compared to what we see at a + + align:start position:0% +different compared to what we see at a + + + align:start position:0% +different compared to what we see at a +more + + align:start position:0% +more + + + align:start position:0% +more +macroscopic scale however that doesn't + + align:start position:0% +macroscopic scale however that doesn't + + + align:start position:0% +macroscopic scale however that doesn't +mean that all the details are the same + + align:start position:0% +mean that all the details are the same + + + align:start position:0% +mean that all the details are the same +and maybe you could begin to get a + + align:start position:0% +and maybe you could begin to get a + + + align:start position:0% +and maybe you could begin to get a +glimmering of that when I told you that + + align:start position:0% +glimmering of that when I told you that + + + align:start position:0% +glimmering of that when I told you that +although the genetic code is virtually + + align:start position:0% +although the genetic code is virtually + + + align:start position:0% +although the genetic code is virtually +Universal that almost every organism + + align:start position:0% +Universal that almost every organism + + + align:start position:0% +Universal that almost every organism +only couple of very tiny exceptions uses + + align:start position:0% +only couple of very tiny exceptions uses + + + align:start position:0% +only couple of very tiny exceptions uses +exactly the same genetic code to have + + align:start position:0% +exactly the same genetic code to have + + + align:start position:0% +exactly the same genetic code to have +nucleotides correspond to three-letter + + align:start position:0% +nucleotides correspond to three-letter + + + align:start position:0% +nucleotides correspond to three-letter +words in the nucleic acid alphabet + + align:start position:0% +words in the nucleic acid alphabet + + + align:start position:0% +words in the nucleic acid alphabet +correspond to particular amino acids in + + align:start position:0% +correspond to particular amino acids in + + + align:start position:0% +correspond to particular amino acids in +a protein but the other languages that + + align:start position:0% +a protein but the other languages that + + + align:start position:0% +a protein but the other languages that +are written in there such as this the + + align:start position:0% +are written in there such as this the + + + align:start position:0% +are written in there such as this the +sequence to start transcribing a gene + + align:start position:0% +sequence to start transcribing a gene + + + align:start position:0% +sequence to start transcribing a gene +making an RNA copy or stop those are are + + align:start position:0% +making an RNA copy or stop those are are + + + align:start position:0% +making an RNA copy or stop those are are +different between different organisms + + align:start position:0% +different between different organisms + + + align:start position:0% +different between different organisms +then + + align:start position:0% + + + + align:start position:0% + +the glycolysis enzymes are amazingly + + align:start position:0% +the glycolysis enzymes are amazingly + + + align:start position:0% +the glycolysis enzymes are amazingly +similar uh they're very clearly very + + align:start position:0% +similar uh they're very clearly very + + + align:start position:0% +similar uh they're very clearly very +clearly they arose once and they've + + align:start position:0% +clearly they arose once and they've + + + align:start position:0% +clearly they arose once and they've +stayed right through Evolution you could + + align:start position:0% +stayed right through Evolution you could + + + align:start position:0% +stayed right through Evolution you could +in principle sometimes you get an + + align:start position:0% +in principle sometimes you get an + + + align:start position:0% +in principle sometimes you get an +evolution you get something that creates + + align:start position:0% +evolution you get something that creates + + + align:start position:0% +evolution you get something that creates +a function and something that starts out + + align:start position:0% +a function and something that starts out + + + align:start position:0% +a function and something that starts out +and then by what they call convergent + + align:start position:0% +and then by what they call convergent + + + align:start position:0% +and then by what they call convergent +evolution you end up with two things + + align:start position:0% +evolution you end up with two things + + + align:start position:0% +evolution you end up with two things +that came from a different evolutionary + + align:start position:0% +that came from a different evolutionary + + + align:start position:0% +that came from a different evolutionary +origin but have learned to do say a + + align:start position:0% +origin but have learned to do say a + + + align:start position:0% +origin but have learned to do say a +catalyze the same biochemical reaction + + align:start position:0% +catalyze the same biochemical reaction + + + align:start position:0% +catalyze the same biochemical reaction +or something something glycolysis came + + align:start position:0% +or something something glycolysis came + + + align:start position:0% +or something something glycolysis came +once but if you were to look inside eoli + + align:start position:0% +once but if you were to look inside eoli + + + align:start position:0% +once but if you were to look inside eoli +or Yeast let's say eoli and look at how + + align:start position:0% +or Yeast let's say eoli and look at how + + + align:start position:0% +or Yeast let's say eoli and look at how +those enzymes are regulated the thing + + align:start position:0% +those enzymes are regulated the thing + + + align:start position:0% +those enzymes are regulated the thing +that says this is a start of a gene + + align:start position:0% +that says this is a start of a gene + + + align:start position:0% +that says this is a start of a gene +start making the RNA it would look + + align:start position:0% +start making the RNA it would look + + + align:start position:0% +start making the RNA it would look +totally different than if you looked in + + align:start position:0% +totally different than if you looked in + + + align:start position:0% +totally different than if you looked in +a mouse because the the the language the + + align:start position:0% +a mouse because the the the language the + + + align:start position:0% +a mouse because the the the language the +promoter does not have the same sequence + + align:start position:0% +promoter does not have the same sequence + + + align:start position:0% +promoter does not have the same sequence +in any coli and in a and in a human or + + align:start position:0% +in any coli and in a and in a human or + + + align:start position:0% +in any coli and in a and in a human or +in a mouse and I'll tell you more about + + align:start position:0% +in a mouse and I'll tell you more about + + + align:start position:0% +in a mouse and I'll tell you more about +that today but um + + align:start position:0% +that today but um + + + align:start position:0% +that today but um +there were I want to just now tell you + + align:start position:0% +there were I want to just now tell you + + + align:start position:0% +there were I want to just now tell you +sort of three things that were sort of + + align:start position:0% +sort of three things that were sort of + + + align:start position:0% +sort of three things that were sort of +exceptions to this General way of + + align:start position:0% +exceptions to this General way of + + + align:start position:0% +exceptions to this General way of +thinking every one of them generated a + + align:start position:0% +thinking every one of them generated a + + + align:start position:0% +thinking every one of them generated a +Nobel Prize and this is a a fun lecture + + align:start position:0% +Nobel Prize and this is a a fun lecture + + + align:start position:0% +Nobel Prize and this is a a fun lecture +for me to give because the individuals + + align:start position:0% +for me to give because the individuals + + + align:start position:0% +for me to give because the individuals +involved in all of these things had a + + align:start position:0% +involved in all of these things had a + + + align:start position:0% +involved in all of these things had a +very very close association with with + + align:start position:0% +very very close association with with + + + align:start position:0% +very very close association with with +MIT and you know when I told you when + + align:start position:0% +MIT and you know when I told you when + + + align:start position:0% +MIT and you know when I told you when +Crick uh called this a central dogma he + + align:start position:0% +Crick uh called this a central dogma he + + + align:start position:0% +Crick uh called this a central dogma he +thought it was he meant a hypothesis for + + align:start position:0% +thought it was he meant a hypothesis for + + + align:start position:0% +thought it was he meant a hypothesis for +or at least an idea for which it was not + + align:start position:0% +or at least an idea for which it was not + + + align:start position:0% +or at least an idea for which it was not +reasonable evidence and he learned later + + align:start position:0% +reasonable evidence and he learned later + + + align:start position:0% +reasonable evidence and he learned later +it was you know something a True + + align:start position:0% +it was you know something a True + + + align:start position:0% +it was you know something a True +Believer cannot doubt and it's once this + + align:start position:0% +Believer cannot doubt and it's once this + + + align:start position:0% +Believer cannot doubt and it's once this +gets established it does get in the + + align:start position:0% +gets established it does get in the + + + align:start position:0% +gets established it does get in the +textbook and it does get in your your + + align:start position:0% +textbook and it does get in your your + + + align:start position:0% +textbook and it does get in your your +thinking and so information goes down + + align:start position:0% +thinking and so information goes down + + + align:start position:0% +thinking and so information goes down +this way but there were a few OD + + align:start position:0% +this way but there were a few OD + + + align:start position:0% +this way but there were a few OD +Oddities I mean there were some + + align:start position:0% + + + + align:start position:0% + +viruses that had um RNA inside them they + + align:start position:0% +viruses that had um RNA inside them they + + + align:start position:0% +viruses that had um RNA inside them they +didn't have DNA so how are the these + + align:start position:0% +didn't have DNA so how are the these + + + align:start position:0% +didn't have DNA so how are the these +handled well there turned out to be two + + align:start position:0% +handled well there turned out to be two + + + align:start position:0% +handled well there turned out to be two +classes of RNA virus one that + + align:start position:0% +classes of RNA virus one that + + + align:start position:0% +classes of RNA virus one that +was studied quite heavily uh called it's + + align:start position:0% +was studied quite heavily uh called it's + + + align:start position:0% +was studied quite heavily uh called it's +a plant virus called The Tobacco mosaic + + align:start position:0% +a plant virus called The Tobacco mosaic + + + align:start position:0% +a plant virus called The Tobacco mosaic +virus and it it had a a + + align:start position:0% +virus and it it had a a + + + align:start position:0% +virus and it it had a a +coat and then it had in + + align:start position:0% + + + + align:start position:0% + +it a piece of RNA now you can see if if + + align:start position:0% +it a piece of RNA now you can see if if + + + align:start position:0% +it a piece of RNA now you can see if if +that virus were to inject RNA the cell + + align:start position:0% +that virus were to inject RNA the cell + + + align:start position:0% +that virus were to inject RNA the cell +it could encode proteins but it that + + align:start position:0% +it could encode proteins but it that + + + align:start position:0% +it could encode proteins but it that +genetic material has to be has to be + + align:start position:0% +genetic material has to be has to be + + + align:start position:0% +genetic material has to be has to be +copied and the RNA was + + align:start position:0% + + + + align:start position:0% + +copied by an + + align:start position:0% + + + + align:start position:0% + +RNA + + align:start position:0% +RNA + + + align:start position:0% +RNA +dependent RNA polymerase + + align:start position:0% + + + + align:start position:0% + +and so it's sort of just like the RNA + + align:start position:0% +and so it's sort of just like the RNA + + + align:start position:0% +and so it's sort of just like the RNA +plase I told you before except instead + + align:start position:0% +plase I told you before except instead + + + align:start position:0% +plase I told you before except instead +of using DNA as as its template it can + + align:start position:0% +of using DNA as as its template it can + + + align:start position:0% +of using DNA as as its template it can +use RNA so that sort of somehow would be + + align:start position:0% +use RNA so that sort of somehow would be + + + align:start position:0% +use RNA so that sort of somehow would be +a little Loop in here about RNA being + + align:start position:0% +a little Loop in here about RNA being + + + align:start position:0% +a little Loop in here about RNA being +able to to copy itself that hadn't been + + align:start position:0% +able to to copy itself that hadn't been + + + align:start position:0% +able to to copy itself that hadn't been +anticipated and + + align:start position:0% +anticipated and + + + align:start position:0% +anticipated and +um although this is an important virus + + align:start position:0% +um although this is an important virus + + + align:start position:0% +um although this is an important virus +in the plan industry it's in the in for + + align:start position:0% +in the plan industry it's in the in for + + + align:start position:0% +in the plan industry it's in the in for +for plants and agriculture it's not so + + align:start position:0% +for plants and agriculture it's not so + + + align:start position:0% +for plants and agriculture it's not so +important for humans but there's another + + align:start position:0% +important for humans but there's another + + + align:start position:0% +important for humans but there's another +RNA vir class of RNA viruses that are + + align:start position:0% +RNA vir class of RNA viruses that are + + + align:start position:0% +RNA vir class of RNA viruses that are +very + + align:start position:0% +very + + + align:start position:0% +very +important and this these are called + + align:start position:0% + + + + align:start position:0% + +retroviruses and the reason these are so + + align:start position:0% +retroviruses and the reason these are so + + + align:start position:0% +retroviruses and the reason these are so +important uh is + + align:start position:0% +important uh is + + + align:start position:0% +important uh is +that the hiv1 virus that's associated + + align:start position:0% +that the hiv1 virus that's associated + + + align:start position:0% +that the hiv1 virus that's associated +with with AIDS is such an uh a + + align:start position:0% +with with AIDS is such an uh a + + + align:start position:0% +with with AIDS is such an uh a +retrovirus it's a virus that has a coat + + align:start position:0% +retrovirus it's a virus that has a coat + + + align:start position:0% +retrovirus it's a virus that has a coat +and it has + + align:start position:0% +and it has + + + align:start position:0% +and it has +um has an + + align:start position:0% + + + + align:start position:0% + +RNA that's uh its genetic material and + + align:start position:0% +RNA that's uh its genetic material and + + + align:start position:0% +RNA that's uh its genetic material and +the person who worked out how this goes + + align:start position:0% +the person who worked out how this goes + + + align:start position:0% +the person who worked out how this goes +was a person at MIT Dave Baltimore he + + align:start position:0% +was a person at MIT Dave Baltimore he + + + align:start position:0% +was a person at MIT Dave Baltimore he +was the colleague of mine here for many + + align:start position:0% +was the colleague of mine here for many + + + align:start position:0% +was the colleague of mine here for many +years he was the person who founded the + + align:start position:0% +years he was the person who founded the + + + align:start position:0% +years he was the person who founded the +Whitehead Institute and got that up and + + align:start position:0% +Whitehead Institute and got that up and + + + align:start position:0% +Whitehead Institute and got that up and +going and he then uh finally to take his + + align:start position:0% +going and he then uh finally to take his + + + align:start position:0% +going and he then uh finally to take his +move up one more administrative + + align:start position:0% +move up one more administrative + + + align:start position:0% +move up one more administrative +challenge he went to c tech to be + + align:start position:0% +challenge he went to c tech to be + + + align:start position:0% +challenge he went to c tech to be +president and that's where he is today + + align:start position:0% +president and that's where he is today + + + align:start position:0% +president and that's where he is today +and uh David was working on this problem + + align:start position:0% +and uh David was working on this problem + + + align:start position:0% +and uh David was working on this problem +trying to figure out how these + + align:start position:0% +trying to figure out how these + + + align:start position:0% +trying to figure out how these +retroviruses work and they're important + + align:start position:0% +retroviruses work and they're important + + + align:start position:0% +retroviruses work and they're important +not only do they is is the aid the HIV 1 + + align:start position:0% +not only do they is is the aid the HIV 1 + + + align:start position:0% +not only do they is is the aid the HIV 1 +virus um but there are certain viruses + + align:start position:0% +virus um but there are certain viruses + + + align:start position:0% +virus um but there are certain viruses +that are associated with cancer in + + align:start position:0% +that are associated with cancer in + + + align:start position:0% +that are associated with cancer in +general what they do is they've they've + + align:start position:0% +general what they do is they've they've + + + align:start position:0% +general what they do is they've they've +picked up what's called an unco Gene + + align:start position:0% +picked up what's called an unco Gene + + + align:start position:0% +picked up what's called an unco Gene +which is sort of often a kind of mutated + + align:start position:0% +which is sort of often a kind of mutated + + + align:start position:0% +which is sort of often a kind of mutated +version of one of your normal genes and + + align:start position:0% +version of one of your normal genes and + + + align:start position:0% +version of one of your normal genes and +if that virus gets inside one of your + + align:start position:0% +if that virus gets inside one of your + + + align:start position:0% +if that virus gets inside one of your +cells and brings in this mutated Gene + + align:start position:0% +cells and brings in this mutated Gene + + + align:start position:0% +cells and brings in this mutated Gene +it's sort of kind of the same way as the + + align:start position:0% +it's sort of kind of the same way as the + + + align:start position:0% +it's sort of kind of the same way as the +same consequences mut mutating one of + + align:start position:0% +same consequences mut mutating one of + + + align:start position:0% +same consequences mut mutating one of +your own genes along that progression to + + align:start position:0% +your own genes along that progression to + + + align:start position:0% +your own genes along that progression to +cancer so can kind of say bring in a + + align:start position:0% +cancer so can kind of say bring in a + + + align:start position:0% +cancer so can kind of say bring in a +cell that screws up the control on when + + align:start position:0% +cell that screws up the control on when + + + align:start position:0% +cell that screws up the control on when +cells are supposed to rep replicate and + + align:start position:0% +cells are supposed to rep replicate and + + + align:start position:0% +cells are supposed to rep replicate and +stop dividing and so on so David started + + align:start position:0% +stop dividing and so on so David started + + + align:start position:0% +stop dividing and so on so David started +to work on these and what he discovered + + align:start position:0% +to work on these and what he discovered + + + align:start position:0% +to work on these and what he discovered +was that these viruses + + align:start position:0% +was that these viruses + + + align:start position:0% +was that these viruses +encoded uh they had information encoding + + align:start position:0% +encoded uh they had information encoding + + + align:start position:0% +encoded uh they had information encoding +proteins and one of the um proteins + + align:start position:0% +proteins and one of the um proteins + + + align:start position:0% +proteins and one of the um proteins +encoded in their RNA is an enzyme he + + align:start position:0% +encoded in their RNA is an enzyme he + + + align:start position:0% +encoded in their RNA is an enzyme he +characterized which is given the name + + align:start position:0% + + + + align:start position:0% + +reverse transcripts and what this can do + + align:start position:0% +reverse transcripts and what this can do + + + align:start position:0% +reverse transcripts and what this can do +is is take an RNA template and make the + + align:start position:0% +is is take an RNA template and make the + + + align:start position:0% +is is take an RNA template and make the +corresponding complimentary DNA strand + + align:start position:0% +corresponding complimentary DNA strand + + + align:start position:0% +corresponding complimentary DNA strand +in this way so that if we took the we'll + + align:start position:0% +in this way so that if we took the we'll + + + align:start position:0% +in this way so that if we took the we'll +just take this this + + align:start position:0% +just take this this + + + align:start position:0% +just take this this +RNA out of the virus what this virus + + align:start position:0% +RNA out of the virus what this virus + + + align:start position:0% +RNA out of the virus what this virus +encodes then is an enzyme that's able to + + align:start position:0% +encodes then is an enzyme that's able to + + + align:start position:0% +encodes then is an enzyme that's able to +take this + + align:start position:0% +take this + + + align:start position:0% +take this +RNA and make the + + align:start position:0% +RNA and make the + + + align:start position:0% +RNA and make the +corresponding + + align:start position:0% +corresponding + + + align:start position:0% +corresponding +DNA copy so there's the original RNA + + align:start position:0% +DNA copy so there's the original RNA + + + align:start position:0% +DNA copy so there's the original RNA +that was in the virus there is the + + align:start position:0% +that was in the virus there is the + + + align:start position:0% +that was in the virus there is the +um uh the RNA that has started out and + + align:start position:0% +um uh the RNA that has started out and + + + align:start position:0% +um uh the RNA that has started out and +so what is happening if you will in that + + align:start position:0% +so what is happening if you will in that + + + align:start position:0% +so what is happening if you will in that +case is the information is + + align:start position:0% +case is the information is + + + align:start position:0% +case is the information is +flowing in the other direction + + align:start position:0% + + + + align:start position:0% + +uh that was a a marvelous uh Discovery + + align:start position:0% +uh that was a a marvelous uh Discovery + + + align:start position:0% +uh that was a a marvelous uh Discovery +and it was discovered by someone who + + align:start position:0% +and it was discovered by someone who + + + align:start position:0% +and it was discovered by someone who +wasn't willing just to take what was in + + align:start position:0% +wasn't willing just to take what was in + + + align:start position:0% +wasn't willing just to take what was in +the the textbooks but was trying to + + align:start position:0% +the the textbooks but was trying to + + + align:start position:0% +the the textbooks but was trying to +figure out what could possibly be going + + align:start position:0% +figure out what could possibly be going + + + align:start position:0% +figure out what could possibly be going +on here now the way the these viruses + + align:start position:0% +on here now the way the these viruses + + + align:start position:0% +on here now the way the these viruses +work then once they've done this it's + + align:start position:0% +work then once they've done this it's + + + align:start position:0% +work then once they've done this it's +not bad because they've got their + + align:start position:0% +not bad because they've got their + + + align:start position:0% +not bad because they've got their +information now in the form of DNA so + + align:start position:0% +information now in the form of DNA so + + + align:start position:0% +information now in the form of DNA so +this strand of + + align:start position:0% +this strand of + + + align:start position:0% +this strand of +DNA can be made into a double + + align:start position:0% + + + + align:start position:0% + +stranded DNA by just using the kinds of + + align:start position:0% +stranded DNA by just using the kinds of + + + align:start position:0% +stranded DNA by just using the kinds of +enzymes that we've already talked about + + align:start position:0% +enzymes that we've already talked about + + + align:start position:0% +enzymes that we've already talked about +a DNA dependent DNA plase will be able + + align:start position:0% +a DNA dependent DNA plase will be able + + + align:start position:0% +a DNA dependent DNA plase will be able +to copy the other thing and now you've + + align:start position:0% +to copy the other thing and now you've + + + align:start position:0% +to copy the other thing and now you've +got a DNA copy of the information that + + align:start position:0% +got a DNA copy of the information that + + + align:start position:0% +got a DNA copy of the information that +used to be in the virus well what + + align:start position:0% +used to be in the virus well what + + + align:start position:0% +used to be in the virus well what +happens to that + + align:start position:0% +happens to that + + + align:start position:0% +happens to that +is that you + + align:start position:0% + + + + align:start position:0% + +have a piece of of the host + + align:start position:0% + + + + align:start position:0% + +DNA and + + align:start position:0% + + + + align:start position:0% + +this viral DNA then inserts into it so + + align:start position:0% +this viral DNA then inserts into it so + + + align:start position:0% +this viral DNA then inserts into it so +you end up with this situation where you + + align:start position:0% +you end up with this situation where you + + + align:start position:0% +you end up with this situation where you +have DNA from the + + align:start position:0% + + + + align:start position:0% + +host and this uh is the virus DNA so + + align:start position:0% +host and this uh is the virus DNA so + + + align:start position:0% +host and this uh is the virus DNA so +this is the + + align:start position:0% + + + + align:start position:0% + +DNA that encodes the information needed + + align:start position:0% +DNA that encodes the information needed + + + align:start position:0% +DNA that encodes the information needed +for the virus and if this was um our DNA + + align:start position:0% +for the virus and if this was um our DNA + + + align:start position:0% +for the virus and if this was um our DNA +then would would be inserted that way + + align:start position:0% +then would would be inserted that way + + + align:start position:0% +then would would be inserted that way +and you know there just a handful of of + + align:start position:0% +and you know there just a handful of of + + + align:start position:0% +and you know there just a handful of of +uh Health messages I've tried to drive + + align:start position:0% +uh Health messages I've tried to drive + + + align:start position:0% +uh Health messages I've tried to drive +home in this thing I mentioned smoking + + align:start position:0% +home in this thing I mentioned smoking + + + align:start position:0% +home in this thing I mentioned smoking +the other day uh if if you smoke if you + + align:start position:0% +the other day uh if if you smoke if you + + + align:start position:0% +the other day uh if if you smoke if you +stop if you stop smoking you've + + align:start position:0% +stop if you stop smoking you've + + + align:start position:0% +stop if you stop smoking you've +basically let me try another the the + + align:start position:0% +basically let me try another the the + + + align:start position:0% +basically let me try another the the +risk of smoking is about equal to the + + align:start position:0% +risk of smoking is about equal to the + + + align:start position:0% +risk of smoking is about equal to the +sum of everything else you can possibly + + align:start position:0% +sum of everything else you can possibly + + + align:start position:0% +sum of everything else you can possibly +do in your life that will affect your + + align:start position:0% +do in your life that will affect your + + + align:start position:0% +do in your life that will affect your +chances of getting cancer leaving aside + + align:start position:0% +chances of getting cancer leaving aside + + + align:start position:0% +chances of getting cancer leaving aside +you know what you inherited from from + + align:start position:0% +you know what you inherited from from + + + align:start position:0% +you know what you inherited from from +Mom and Dad there was one single thing + + align:start position:0% +Mom and Dad there was one single thing + + + align:start position:0% +Mom and Dad there was one single thing +to not do if you want to avoid cancer or + + align:start position:0% +to not do if you want to avoid cancer or + + + align:start position:0% +to not do if you want to avoid cancer or +to help loved ones who smoke avoid + + align:start position:0% +to help loved ones who smoke avoid + + + align:start position:0% +to help loved ones who smoke avoid +cancer is just don't smoke or if you do + + align:start position:0% +cancer is just don't smoke or if you do + + + align:start position:0% +cancer is just don't smoke or if you do +smoke stop you freeze the risk of + + align:start position:0% +smoke stop you freeze the risk of + + + align:start position:0% +smoke stop you freeze the risk of +whatever increased risk you've got and + + align:start position:0% +whatever increased risk you've got and + + + align:start position:0% +whatever increased risk you've got and +then just live with that but it doesn't + + align:start position:0% +then just live with that but it doesn't + + + align:start position:0% +then just live with that but it doesn't +keep getting worse with time the other + + align:start position:0% +keep getting worse with time the other + + + align:start position:0% +keep getting worse with time the other +one is uh practice safe sex and this is + + align:start position:0% +one is uh practice safe sex and this is + + + align:start position:0% +one is uh practice safe sex and this is +why HIV one is a retrovirus if you get + + align:start position:0% +why HIV one is a retrovirus if you get + + + align:start position:0% +why HIV one is a retrovirus if you get +infected with it it makes uh a DNA copy + + align:start position:0% +infected with it it makes uh a DNA copy + + + align:start position:0% +infected with it it makes uh a DNA copy +of the RNA it makes the other strand of + + align:start position:0% +of the RNA it makes the other strand of + + + align:start position:0% +of the RNA it makes the other strand of +the DNA and it sticks itself in so what + + align:start position:0% +the DNA and it sticks itself in so what + + + align:start position:0% +the DNA and it sticks itself in so what +you got is your DNA here your DNA + + align:start position:0% + + + + align:start position:0% + +there and hiv1 is a permanent traveling + + align:start position:0% +there and hiv1 is a permanent traveling + + + align:start position:0% +there and hiv1 is a permanent traveling +companion for the rest of your life + + align:start position:0% +companion for the rest of your life + + + align:start position:0% +companion for the rest of your life +there's no way of getting that out of + + align:start position:0% +there's no way of getting that out of + + + align:start position:0% +there's no way of getting that out of +there right now all the systems for + + align:start position:0% +there right now all the systems for + + + align:start position:0% +there right now all the systems for +dealing with AIDS are just + + align:start position:0% +dealing with AIDS are just + + + align:start position:0% +dealing with AIDS are just +managing the uh the infection so when + + align:start position:0% +managing the uh the infection so when + + + align:start position:0% +managing the uh the infection so when +someone's HIV one um positive they've + + align:start position:0% +someone's HIV one um positive they've + + + align:start position:0% +someone's HIV one um positive they've +got those viral genes now permanently + + align:start position:0% +got those viral genes now permanently + + + align:start position:0% +got those viral genes now permanently +integrated into their into their DNA a + + align:start position:0% +integrated into their into their DNA a + + + align:start position:0% +integrated into their into their DNA a +so it's extremely uh important that you + + align:start position:0% +so it's extremely uh important that you + + + align:start position:0% +so it's extremely uh important that you +you be aware of that or if you know + + align:start position:0% +you be aware of that or if you know + + + align:start position:0% +you be aware of that or if you know +people who don't don't appreciate this + + align:start position:0% +people who don't don't appreciate this + + + align:start position:0% +people who don't don't appreciate this +cuz I haven't got so much so much of a + + align:start position:0% +cuz I haven't got so much so much of a + + + align:start position:0% +cuz I haven't got so much so much of a +biology background uh that you help them + + align:start position:0% +biology background uh that you help them + + + align:start position:0% +biology background uh that you help them +help them understand that okay um so uh + + align:start position:0% +help them understand that okay um so uh + + + align:start position:0% +help them understand that okay um so uh +I just wanted to show you uh I found one + + align:start position:0% +I just wanted to show you uh I found one + + + align:start position:0% +I just wanted to show you uh I found one +other picture last night you this is you + + align:start position:0% +other picture last night you this is you + + + align:start position:0% +other picture last night you this is you +see all these old scientists right of + + align:start position:0% +see all these old scientists right of + + + align:start position:0% +see all these old scientists right of +course David didn't look like this when + + align:start position:0% +course David didn't look like this when + + + align:start position:0% +course David didn't look like this when +he was doing his doing his work in fact + + align:start position:0% +he was doing his doing his work in fact + + + align:start position:0% +he was doing his doing his work in fact +I think he's fairly cleaned up here I + + align:start position:0% +I think he's fairly cleaned up here I + + + align:start position:0% +I think he's fairly cleaned up here I +found this one in the Cold Spring Harbor + + align:start position:0% +found this one in the Cold Spring Harbor + + + align:start position:0% +found this one in the Cold Spring Harbor +archives last night um he I've seen + + align:start position:0% +archives last night um he I've seen + + + align:start position:0% +archives last night um he I've seen +pictures of him looking considerably + + align:start position:0% +pictures of him looking considerably + + + align:start position:0% +pictures of him looking considerably +more more Shaggy and and uh you know + + align:start position:0% +more more Shaggy and and uh you know + + + align:start position:0% +more more Shaggy and and uh you know +perhaps bit disreputable stuff but + + align:start position:0% +perhaps bit disreputable stuff but + + + align:start position:0% +perhaps bit disreputable stuff but +anyway when David was making all these + + align:start position:0% +anyway when David was making all these + + + align:start position:0% +anyway when David was making all these +discoveries he was still quite a young + + align:start position:0% +discoveries he was still quite a young + + + align:start position:0% +discoveries he was still quite a young +man he got his I believe he got his noal + + align:start position:0% +man he got his I believe he got his noal + + + align:start position:0% +man he got his I believe he got his noal +priz well he's still in his 30s and so + + align:start position:0% +priz well he's still in his 30s and so + + + align:start position:0% +priz well he's still in his 30s and so +many of these discoveries are made by + + align:start position:0% +many of these discoveries are made by + + + align:start position:0% +many of these discoveries are made by +people that are not all that much older + + align:start position:0% +people that are not all that much older + + + align:start position:0% +people that are not all that much older +older than you but again you know it's + + align:start position:0% +older than you but again you know it's + + + align:start position:0% +older than you but again you know it's +trying to understand why we know what we + + align:start position:0% +trying to understand why we know what we + + + align:start position:0% +trying to understand why we know what we +know and then trying to fit other things + + align:start position:0% +know and then trying to fit other things + + + align:start position:0% +know and then trying to fit other things +into it now the next thing I want to + + align:start position:0% +into it now the next thing I want to + + + align:start position:0% +into it now the next thing I want to +tell you about that + + align:start position:0% +tell you about that + + + align:start position:0% +tell you about that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um it has some of the same character + + align:start position:0% +um it has some of the same character + + + align:start position:0% +um it has some of the same character +I've sort of told you that you have a + + align:start position:0% +I've sort of told you that you have a + + + align:start position:0% +I've sort of told you that you have a +piece of DNA let's say there's a gene + + align:start position:0% +piece of DNA let's say there's a gene + + + align:start position:0% +piece of DNA let's say there's a gene +here and this is the the coding + + align:start position:0% + + + + align:start position:0% + +region and then we make a messenger + + align:start position:0% +region and then we make a messenger + + + align:start position:0% +region and then we make a messenger +RNA uh copy and then we use the genetic + + align:start position:0% +RNA uh copy and then we use the genetic + + + align:start position:0% +RNA uh copy and then we use the genetic +code + + align:start position:0% + + + + align:start position:0% + +and we make the protein and so if we + + align:start position:0% +and we make the protein and so if we + + + align:start position:0% +and we make the protein and so if we +sequence the DNA and find the beginning + + align:start position:0% +sequence the DNA and find the beginning + + + align:start position:0% +sequence the DNA and find the beginning +of this protein we can read along using + + align:start position:0% +of this protein we can read along using + + + align:start position:0% +of this protein we can read along using +that genetic code and way it should go + + align:start position:0% +that genetic code and way it should go + + + align:start position:0% +that genetic code and way it should go +and that that was uh beautifully uh + + align:start position:0% +and that that was uh beautifully uh + + + align:start position:0% +and that that was uh beautifully uh +worked out understood just like I've + + align:start position:0% +worked out understood just like I've + + + align:start position:0% +worked out understood just like I've +sort of finished up telling you the + + align:start position:0% +sort of finished up telling you the + + + align:start position:0% +sort of finished up telling you the +other day um so + + align:start position:0% +other day um so + + + align:start position:0% +other day um so +Phil Phil Phil + + align:start position:0% +Phil Phil Phil + + + align:start position:0% +Phil Phil Phil +sharp who got a Nobel Prize for this + + align:start position:0% +sharp who got a Nobel Prize for this + + + align:start position:0% +sharp who got a Nobel Prize for this +work and his colleague in the biology + + align:start position:0% +work and his colleague in the biology + + + align:start position:0% +work and his colleague in the biology +Department he's in the in the cancer + + align:start position:0% +Department he's in the in the cancer + + + align:start position:0% +Department he's in the in the cancer +center just across the the street from + + align:start position:0% +center just across the the street from + + + align:start position:0% +center just across the the street from +the building I'm in that was the cancer + + align:start position:0% +the building I'm in that was the cancer + + + align:start position:0% +the building I'm in that was the cancer +center that Salvador Lura um who Jim + + align:start position:0% +center that Salvador Lura um who Jim + + + align:start position:0% +center that Salvador Lura um who Jim +Watson trained with had had founded and + + align:start position:0% +Watson trained with had had founded and + + + align:start position:0% +Watson trained with had had founded and +Phil was studying this process it was + + align:start position:0% +Phil was studying this process it was + + + align:start position:0% +Phil was studying this process it was +before we could sequence DNA it was in + + align:start position:0% +before we could sequence DNA it was in + + + align:start position:0% +before we could sequence DNA it was in +the in the mid '70s and he was working + + align:start position:0% +the in the mid '70s and he was working + + + align:start position:0% +the in the mid '70s and he was working +with the tools we had then trying to map + + align:start position:0% +with the tools we had then trying to map + + + align:start position:0% +with the tools we had then trying to map +the relationship of an of an RNA + + align:start position:0% +the relationship of an of an RNA + + + align:start position:0% +the relationship of an of an RNA +to a gene that was on on a the virus it + + align:start position:0% +to a gene that was on on a the virus it + + + align:start position:0% +to a gene that was on on a the virus it +was a DNA virus not an RNA virus so + + align:start position:0% +was a DNA virus not an RNA virus so + + + align:start position:0% +was a DNA virus not an RNA virus so +don't get yourself mixed up with that + + align:start position:0% +don't get yourself mixed up with that + + + align:start position:0% +don't get yourself mixed up with that +but what he had was basically a fragment + + align:start position:0% +but what he had was basically a fragment + + + align:start position:0% +but what he had was basically a fragment +of of DNA that he knew encoded the gene + + align:start position:0% +of of DNA that he knew encoded the gene + + + align:start position:0% +of of DNA that he knew encoded the gene +so he had he knew somewhere on on this + + align:start position:0% +so he had he knew somewhere on on this + + + align:start position:0% +so he had he knew somewhere on on this +piece of + + align:start position:0% +piece of + + + align:start position:0% +piece of +DNA there was a gene somewhere in + + align:start position:0% + + + + align:start position:0% + +here and he had isolated + + align:start position:0% +here and he had isolated + + + align:start position:0% +here and he had isolated +the messenger RNA and one way you could + + align:start position:0% +the messenger RNA and one way you could + + + align:start position:0% +the messenger RNA and one way you could +map physically see the relationship of + + align:start position:0% +map physically see the relationship of + + + align:start position:0% +map physically see the relationship of +an RNA and a DNA would be to + + align:start position:0% +an RNA and a DNA would be to + + + align:start position:0% +an RNA and a DNA would be to +take let's just take away one of these + + align:start position:0% +take let's just take away one of these + + + align:start position:0% +take let's just take away one of these +strands so we say have the corresponding + + align:start position:0% +strands so we say have the corresponding + + + align:start position:0% +strands so we say have the corresponding +the complimentary strand of the DNA to + + align:start position:0% +the complimentary strand of the DNA to + + + align:start position:0% +the complimentary strand of the DNA to +the RNA and if we mix them together and + + align:start position:0% +the RNA and if we mix them together and + + + align:start position:0% +the RNA and if we mix them together and +let them slowly cool down they will form + + align:start position:0% +let them slowly cool down they will form + + + align:start position:0% +let them slowly cool down they will form +hydrogen bonds they'll form a DNA RNA + + align:start position:0% +hydrogen bonds they'll form a DNA RNA + + + align:start position:0% +hydrogen bonds they'll form a DNA RNA +hybrid just the same way two strands of + + align:start position:0% +hybrid just the same way two strands of + + + align:start position:0% +hybrid just the same way two strands of +DNA come on and so if the gene was a + + align:start position:0% +DNA come on and so if the gene was a + + + align:start position:0% +DNA come on and so if the gene was a +little shorter than the piece of DNA + + align:start position:0% +little shorter than the piece of DNA + + + align:start position:0% +little shorter than the piece of DNA +then you might have expected to see + + align:start position:0% +then you might have expected to see + + + align:start position:0% +then you might have expected to see +something that looked + + align:start position:0% +something that looked + + + align:start position:0% +something that looked +like + + align:start position:0% +like + + + align:start position:0% +like +this and the the way you'd see this if + + align:start position:0% +this and the the way you'd see this if + + + align:start position:0% +this and the the way you'd see this if +you looked in an electron + + align:start position:0% + + + + align:start position:0% + +microscope would perhaps it would look + + align:start position:0% +microscope would perhaps it would look + + + align:start position:0% +microscope would perhaps it would look +sort of like this you can't actually see + + align:start position:0% +sort of like this you can't actually see + + + align:start position:0% +sort of like this you can't actually see +the two strands but you'd see a thick + + align:start position:0% +the two strands but you'd see a thick + + + align:start position:0% +the two strands but you'd see a thick +part that would be the the RNA duplex so + + align:start position:0% +part that would be the the RNA duplex so + + + align:start position:0% +part that would be the the RNA duplex so +this this would be just + + align:start position:0% + + + + align:start position:0% + +DNA and the thick part is + + align:start position:0% +DNA and the thick part is + + + align:start position:0% +DNA and the thick part is +RNA base + + align:start position:0% +RNA base + + + align:start position:0% +RNA base +paired with a single strand of DNA you + + align:start position:0% +paired with a single strand of DNA you + + + align:start position:0% +paired with a single strand of DNA you +got + + align:start position:0% +got + + + align:start position:0% +got +it that's what textbook said should have + + align:start position:0% +it that's what textbook said should have + + + align:start position:0% +it that's what textbook said should have +seen and so this is more this is data + + align:start position:0% +seen and so this is more this is data + + + align:start position:0% +seen and so this is more this is data +from Phil's paper describing this let me + + align:start position:0% +from Phil's paper describing this let me + + + align:start position:0% +from Phil's paper describing this let me +focus on this one in + + align:start position:0% +focus on this one in + + + align:start position:0% +focus on this one in +particular that's + + align:start position:0% +particular that's + + + align:start position:0% +particular that's +what he actually + + align:start position:0% + + + + align:start position:0% + +saw guys got any idea what's going on + + align:start position:0% +saw guys got any idea what's going on + + + align:start position:0% +saw guys got any idea what's going on +why don't you take a minute find + + align:start position:0% +why don't you take a minute find + + + align:start position:0% +why don't you take a minute find +somebody who's near you so you can come + + align:start position:0% +somebody who's near you so you can come + + + align:start position:0% +somebody who's near you so you can come +up with any ideas + + align:start position:0% +up with any ideas + + + align:start position:0% +up with any ideas +here's here's the + + align:start position:0% +here's here's the + + + align:start position:0% +here's here's the +um here's the hybrid forget about this + + align:start position:0% +um here's the hybrid forget about this + + + align:start position:0% +um here's the hybrid forget about this +little bit at the three prime and that's + + align:start position:0% +little bit at the three prime and that's + + + align:start position:0% +little bit at the three prime and that's +not a worry here's the + + align:start position:0% +not a worry here's the + + + align:start position:0% +not a worry here's the +thing and this I think is a piece of + + align:start position:0% +thing and this I think is a piece of + + + align:start position:0% +thing and this I think is a piece of +single stranded DNA sticking out the + + align:start position:0% +single stranded DNA sticking out the + + + align:start position:0% +single stranded DNA sticking out the +end but it looks a bit more + + align:start position:0% + + + + align:start position:0% + +complicated any + + align:start position:0% + + + + align:start position:0% + +ideas most people put this data in their + + align:start position:0% +ideas most people put this data in their + + + align:start position:0% +ideas most people put this data in their +drawers Phil didn't Phil and his + + align:start position:0% +drawers Phil didn't Phil and his + + + align:start position:0% +drawers Phil didn't Phil and his +colleagues didn't what they realized was + + align:start position:0% +colleagues didn't what they realized was + + + align:start position:0% +colleagues didn't what they realized was +I'm going to try and redraw this just + + align:start position:0% +I'm going to try and redraw this just + + + align:start position:0% +I'm going to try and redraw this just +very slightly to help you see what's + + align:start position:0% +very slightly to help you see what's + + + align:start position:0% +very slightly to help you see what's +going on + + align:start position:0% + + + + align:start position:0% + +what they were seeing was something that + + align:start position:0% +what they were seeing was something that + + + align:start position:0% +what they were seeing was something that +looked rather like what they were + + align:start position:0% +looked rather like what they were + + + align:start position:0% +looked rather like what they were +expecting they were seeing a region of + + align:start position:0% +expecting they were seeing a region of + + + align:start position:0% +expecting they were seeing a region of +hybrid DNA and they were seeing a region + + align:start position:0% +hybrid DNA and they were seeing a region + + + align:start position:0% +hybrid DNA and they were seeing a region +of single stranded + + align:start position:0% +of single stranded + + + align:start position:0% +of single stranded +DNA like + + align:start position:0% +DNA like + + + align:start position:0% +DNA like +this but what it looked like was there + + align:start position:0% +this but what it looked like was there + + + align:start position:0% +this but what it looked like was there +were + + align:start position:0% + + + + align:start position:0% + +little + + align:start position:0% +little + + + align:start position:0% +little +Loops of single stranded DNA sticking + + align:start position:0% +Loops of single stranded DNA sticking + + + align:start position:0% +Loops of single stranded DNA sticking +out and what um Phil had discovered was + + align:start position:0% +out and what um Phil had discovered was + + + align:start position:0% +out and what um Phil had discovered was +a pH phenomenon we now know as RNA + + align:start position:0% + + + + align:start position:0% + +splicing and here's here's here's what + + align:start position:0% +splicing and here's here's here's what + + + align:start position:0% +splicing and here's here's here's what +goes on in in + + align:start position:0% +goes on in in + + + align:start position:0% +goes on in in +bacteria with a very few exceptions you + + align:start position:0% +bacteria with a very few exceptions you + + + align:start position:0% +bacteria with a very few exceptions you +can look at the DNA you can find the + + align:start position:0% +can look at the DNA you can find the + + + align:start position:0% +can look at the DNA you can find the +open reading frame and you can just read + + align:start position:0% +open reading frame and you can just read + + + align:start position:0% +open reading frame and you can just read +off the sequence of the protein you find + + align:start position:0% +off the sequence of the protein you find + + + align:start position:0% +off the sequence of the protein you find +the atg AUG methine codon and then keeps + + align:start position:0% +the atg AUG methine codon and then keeps + + + align:start position:0% +the atg AUG methine codon and then keeps +going no stops and finally come a stop + + align:start position:0% +going no stops and finally come a stop + + + align:start position:0% +going no stops and finally come a stop +codone you see there's the protein so + + align:start position:0% +codone you see there's the protein so + + + align:start position:0% +codone you see there's the protein so +the coding information is virtually + + align:start position:0% +the coding information is virtually + + + align:start position:0% +the coding information is virtually +essentially continuous in almost all + + align:start position:0% +essentially continuous in almost all + + + align:start position:0% +essentially continuous in almost all +bacterial genes and there's a few some + + align:start position:0% +bacterial genes and there's a few some + + + align:start position:0% +bacterial genes and there's a few some +genes like that in UK carots but many + + align:start position:0% +genes like that in UK carots but many + + + align:start position:0% +genes like that in UK carots but many +eukariotic genes are constructed it's + + align:start position:0% +eukariotic genes are constructed it's + + + align:start position:0% +eukariotic genes are constructed it's +almost as if you took the the gene you'd + + align:start position:0% +almost as if you took the the gene you'd + + + align:start position:0% +almost as if you took the the gene you'd +find in a bacterium and then you cut it + + align:start position:0% +find in a bacterium and then you cut it + + + align:start position:0% +find in a bacterium and then you cut it +in a bunch of places and stuck extra DNA + + align:start position:0% +in a bunch of places and stuck extra DNA + + + align:start position:0% +in a bunch of places and stuck extra DNA +in between all the pieces so something + + align:start position:0% +in between all the pieces so something + + + align:start position:0% +in between all the pieces so something +you get something like this where + + align:start position:0% +you get something like this where + + + align:start position:0% +you get something like this where +there's in the DNA there'd + + align:start position:0% + + + + align:start position:0% + +be coding information + + align:start position:0% +be coding information + + + align:start position:0% +be coding information +and + + align:start position:0% +and + + + align:start position:0% +and +then non-coding information and another + + align:start position:0% +then non-coding information and another + + + align:start position:0% +then non-coding information and another +block + + align:start position:0% + + + + align:start position:0% + +of coding + + align:start position:0% +of coding + + + align:start position:0% +of coding +information and then a block of non + + align:start position:0% +information and then a block of non + + + align:start position:0% +information and then a block of non +coding say another one + + align:start position:0% + + + + align:start position:0% + +of coding information so this is a + + align:start position:0% +of coding information so this is a + + + align:start position:0% +of coding information so this is a +double + + align:start position:0% +double + + + align:start position:0% +double +stranded uh DNA and what happens then + + align:start position:0% +stranded uh DNA and what happens then + + + align:start position:0% +stranded uh DNA and what happens then +when the cell makes RNA + + align:start position:0% +when the cell makes RNA + + + align:start position:0% +when the cell makes RNA +is the whole thing gets + + align:start position:0% + + + + align:start position:0% + +copied into what's known as a now as a + + align:start position:0% +copied into what's known as a now as a + + + align:start position:0% +copied into what's known as a now as a +pre messenger + + align:start position:0% +pre messenger + + + align:start position:0% +pre messenger +RNA and so there's a a bit of coding + + align:start position:0% +RNA and so there's a a bit of coding + + + align:start position:0% +RNA and so there's a a bit of coding +stuff here there's a bit of coding stuff + + align:start position:0% +stuff here there's a bit of coding stuff + + + align:start position:0% +stuff here there's a bit of coding stuff +here and there's some more coding stuff + + align:start position:0% +here and there's some more coding stuff + + + align:start position:0% +here and there's some more coding stuff +there but what the cell has is sort of + + align:start position:0% +there but what the cell has is sort of + + + align:start position:0% +there but what the cell has is sort of +like your unedited footage from your + + align:start position:0% +like your unedited footage from your + + + align:start position:0% +like your unedited footage from your +family summer vacation when you were + + align:start position:0% +family summer vacation when you were + + + align:start position:0% +family summer vacation when you were +running the the video camera and maybe + + align:start position:0% +running the the video camera and maybe + + + align:start position:0% +running the the video camera and maybe +you don't want to show everybody every + + align:start position:0% +you don't want to show everybody every + + + align:start position:0% +you don't want to show everybody every +second of video that you took during the + + align:start position:0% +second of video that you took during the + + + align:start position:0% +second of video that you took during the +thing so what you do you get in there + + align:start position:0% +thing so what you do you get in there + + + align:start position:0% +thing so what you do you get in there +and you edit it in the old days you used + + align:start position:0% +and you edit it in the old days you used + + + align:start position:0% +and you edit it in the old days you used +to have to take the film and splice it + + align:start position:0% +to have to take the film and splice it + + + align:start position:0% +to have to take the film and splice it +and now you can all do it with iMovie or + + align:start position:0% +and now you can all do it with iMovie or + + + align:start position:0% +and now you can all do it with iMovie or +something like that but what you do is + + align:start position:0% +something like that but what you do is + + + align:start position:0% +something like that but what you do is +what take is the pieces of information + + align:start position:0% +what take is the pieces of information + + + align:start position:0% +what take is the pieces of information +you want and this is what the cell is + + align:start position:0% +you want and this is what the cell is + + + align:start position:0% +you want and this is what the cell is +doing it it takes this part of the RNA + + align:start position:0% + + + + align:start position:0% + +and this part of the + + align:start position:0% + + + + align:start position:0% + +RNA and joins it + + align:start position:0% +RNA and joins it + + + align:start position:0% +RNA and joins it +together and then this + + align:start position:0% + + + + align:start position:0% + +part and when it's + + align:start position:0% + + + + align:start position:0% + +done it has the messenger RNA that now + + align:start position:0% +done it has the messenger RNA that now + + + align:start position:0% +done it has the messenger RNA that now +looks like the me kind of messenger RNA + + align:start position:0% +looks like the me kind of messenger RNA + + + align:start position:0% +looks like the me kind of messenger RNA +that you would find in uh in a bacterium + + align:start position:0% +that you would find in uh in a bacterium + + + align:start position:0% +that you would find in uh in a bacterium +where you can find the start + + align:start position:0% +where you can find the start + + + align:start position:0% +where you can find the start +codon and then you can read in + + align:start position:0% +codon and then you can read in + + + align:start position:0% +codon and then you can read in +three-letter words all the way through + + align:start position:0% +three-letter words all the way through + + + align:start position:0% +three-letter words all the way through +to the end of the end of the protein + + align:start position:0% +to the end of the end of the protein + + + align:start position:0% +to the end of the end of the protein +so in essence what + + align:start position:0% +so in essence what + + + align:start position:0% +so in essence what +Phil found was that in many organisms at + + align:start position:0% +Phil found was that in many organisms at + + + align:start position:0% +Phil found was that in many organisms at +least there's another step in here where + + align:start position:0% +least there's another step in here where + + + align:start position:0% +least there's another step in here where +we get RNA splicing and only after that + + align:start position:0% +we get RNA splicing and only after that + + + align:start position:0% +we get RNA splicing and only after that +you get down to to uh get down to + + align:start position:0% +you get down to to uh get down to + + + align:start position:0% +you get down to to uh get down to +proteins um what was quite remarkable + + align:start position:0% +proteins um what was quite remarkable + + + align:start position:0% +proteins um what was quite remarkable +about this result why I'm kind of + + align:start position:0% +about this result why I'm kind of + + + align:start position:0% +about this result why I'm kind of +hammering on a little bit is this is the + + align:start position:0% +hammering on a little bit is this is the + + + align:start position:0% +hammering on a little bit is this is the +data that that's out of Phil's paper you + + align:start position:0% +data that that's out of Phil's paper you + + + align:start position:0% +data that that's out of Phil's paper you +can look it up on on the internet type + + align:start position:0% +can look it up on on the internet type + + + align:start position:0% +can look it up on on the internet type +in Phil sharp 1977 and you'll you'll + + align:start position:0% +in Phil sharp 1977 and you'll you'll + + + align:start position:0% +in Phil sharp 1977 and you'll you'll +find this original paper with that + + align:start position:0% +find this original paper with that + + + align:start position:0% +find this original paper with that +figure in it uh the moment Phil realized + + align:start position:0% +figure in it uh the moment Phil realized + + + align:start position:0% +figure in it uh the moment Phil realized +what he was and talked about it at a + + align:start position:0% +what he was and talked about it at a + + + align:start position:0% +what he was and talked about it at a +meeting a whole lot of people suddenly + + align:start position:0% +meeting a whole lot of people suddenly + + + align:start position:0% +meeting a whole lot of people suddenly +sort of almost simultaneously discovered + + align:start position:0% +sort of almost simultaneously discovered + + + align:start position:0% +sort of almost simultaneously discovered +RNA spacing because they opened their + + align:start position:0% +RNA spacing because they opened their + + + align:start position:0% +RNA spacing because they opened their +dra drawers and there were all these + + align:start position:0% +dra drawers and there were all these + + + align:start position:0% +dra drawers and there were all these +uninterpretable electron micrographs + + align:start position:0% +uninterpretable electron micrographs + + + align:start position:0% +uninterpretable electron micrographs +they had and they were in very short + + align:start position:0% +they had and they were in very short + + + align:start position:0% +they had and they were in very short +order able to say that in the system + + align:start position:0% +order able to say that in the system + + + align:start position:0% +order able to say that in the system +they worked the same thing was going on + + align:start position:0% +they worked the same thing was going on + + + align:start position:0% +they worked the same thing was going on +but it was just confusing it didn't fit + + align:start position:0% +but it was just confusing it didn't fit + + + align:start position:0% +but it was just confusing it didn't fit +and to some extent most people's minds + + align:start position:0% +and to some extent most people's minds + + + align:start position:0% +and to some extent most people's minds +were set by this Paradigm this central + + align:start position:0% +were set by this Paradigm this central + + + align:start position:0% +were set by this Paradigm this central +dogma something that a True Believer + + align:start position:0% +dogma something that a True Believer + + + align:start position:0% +dogma something that a True Believer +cannot doubt and you had to have a + + align:start position:0% +cannot doubt and you had to have a + + + align:start position:0% +cannot doubt and you had to have a +flexible enough mind to um to be able to + + align:start position:0% +flexible enough mind to um to be able to + + + align:start position:0% +flexible enough mind to um to be able to +see that and and so uh this is um an + + align:start position:0% +see that and and so uh this is um an + + + align:start position:0% +see that and and so uh this is um an +important piece of biology that hadn't + + align:start position:0% +important piece of biology that hadn't + + + align:start position:0% +important piece of biology that hadn't +been anticipated and it can be quite + + align:start position:0% +been anticipated and it can be quite + + + align:start position:0% +been anticipated and it can be quite +remarkable I'm just going to give you um + + align:start position:0% +remarkable I'm just going to give you um + + + align:start position:0% +remarkable I'm just going to give you um +a couple of extreme examp well not even + + align:start position:0% +a couple of extreme examp well not even + + + align:start position:0% +a couple of extreme examp well not even +extreme examples but just show you how + + align:start position:0% +extreme examples but just show you how + + + align:start position:0% +extreme examples but just show you how +much uh non-coding information there can + + align:start position:0% +much uh non-coding information there can + + + align:start position:0% +much uh non-coding information there can +be factor 8 is a protein that plays a + + align:start position:0% +be factor 8 is a protein that plays a + + + align:start position:0% +be factor 8 is a protein that plays a +part in in blood clotting and the + + align:start position:0% +part in in blood clotting and the + + + align:start position:0% +part in in blood clotting and the +gene is + + align:start position:0% +gene is + + + align:start position:0% +gene is +200 kilo base + + align:start position:0% +200 kilo base + + + align:start position:0% +200 kilo base +Pairs and the + + align:start position:0% +Pairs and the + + + align:start position:0% +Pairs and the +pre + + align:start position:0% +pre + + + align:start position:0% +pre +mRNA is then it's just direct a direct + + align:start position:0% +mRNA is then it's just direct a direct + + + align:start position:0% +mRNA is then it's just direct a direct +copy so it's 200 kilobases it's just a + + align:start position:0% +copy so it's 200 kilobases it's just a + + + align:start position:0% +copy so it's 200 kilobases it's just a +single strand so it's not a base pair + + align:start position:0% +single strand so it's not a base pair + + + align:start position:0% +single strand so it's not a base pair +and the um actual spliced messenger RNA + + align:start position:0% +and the um actual spliced messenger RNA + + + align:start position:0% +and the um actual spliced messenger RNA +when it's done is 10 + + align:start position:0% +when it's done is 10 + + + align:start position:0% +when it's done is 10 +kilobases so that means that only 5% of + + align:start position:0% +kilobases so that means that only 5% of + + + align:start position:0% +kilobases so that means that only 5% of +the gene + + align:start position:0% + + + + align:start position:0% + +is coding information and 95% of that + + align:start position:0% +is coding information and 95% of that + + + align:start position:0% +is coding information and 95% of that +information gets thrown away when the AR + + align:start position:0% +information gets thrown away when the AR + + + align:start position:0% +information gets thrown away when the AR +get RNA gets spliced um an even more + + align:start position:0% +get RNA gets spliced um an even more + + + align:start position:0% +get RNA gets spliced um an even more +extreme + + align:start position:0% +extreme + + + align:start position:0% +extreme +example is a protein called disten this + + align:start position:0% +example is a protein called disten this + + + align:start position:0% +example is a protein called disten this +is what's affected in uh a human genetic + + align:start position:0% +is what's affected in uh a human genetic + + + align:start position:0% +is what's affected in uh a human genetic +disease known as the Shan muscular + + align:start position:0% +disease known as the Shan muscular + + + align:start position:0% +disease known as the Shan muscular +distrophy + + align:start position:0% + + + + align:start position:0% + +in this case the gene is two Mega base + + align:start position:0% +in this case the gene is two Mega base + + + align:start position:0% +in this case the gene is two Mega base +pairs so of course then the + + align:start position:0% +pairs so of course then the + + + align:start position:0% +pairs so of course then the +pre + + align:start position:0% +pre + + + align:start position:0% +pre +mRNA is + + align:start position:0% +mRNA is + + + align:start position:0% +mRNA is +also + + align:start position:0% + + + + align:start position:0% + +to Mega bases but the pre RNA is + + align:start position:0% +to Mega bases but the pre RNA is + + + align:start position:0% +to Mega bases but the pre RNA is +16 uh kilobases so in this case + + align:start position:0% +16 uh kilobases so in this case + + + align:start position:0% +16 uh kilobases so in this case +less than 1% of the + + align:start position:0% +less than 1% of the + + + align:start position:0% +less than 1% of the +gene has coding + + align:start position:0% +gene has coding + + + align:start position:0% +gene has coding +information for making a for making a + + align:start position:0% + + + + align:start position:0% + +protein there are a lot of interesting + + align:start position:0% +protein there are a lot of interesting + + + align:start position:0% +protein there are a lot of interesting +reasons as to why why would it be like + + align:start position:0% +reasons as to why why would it be like + + + align:start position:0% +reasons as to why why would it be like +this one thing uh this things can + + align:start position:0% +this one thing uh this things can + + + align:start position:0% +this one thing uh this things can +evolve more rapidly sometimes because + + align:start position:0% +evolve more rapidly sometimes because + + + align:start position:0% +evolve more rapidly sometimes because +you have parts of proteins that are sort + + align:start position:0% +you have parts of proteins that are sort + + + align:start position:0% +you have parts of proteins that are sort +of like modules and you can and + + align:start position:0% +of like modules and you can and + + + align:start position:0% +of like modules and you can and +evolution can probably connect them but + + align:start position:0% +evolution can probably connect them but + + + align:start position:0% +evolution can probably connect them but +uh it also provides uh ways of + + align:start position:0% +uh it also provides uh ways of + + + align:start position:0% +uh it also provides uh ways of +regulating because uh we now know there + + align:start position:0% +regulating because uh we now know there + + + align:start position:0% +regulating because uh we now know there +are alternative ways of splicing rnas + + align:start position:0% +are alternative ways of splicing rnas + + + align:start position:0% +are alternative ways of splicing rnas +you can take one RNA and then splice it + + align:start position:0% +you can take one RNA and then splice it + + + align:start position:0% +you can take one RNA and then splice it +in different ways in different cells and + + align:start position:0% +in different ways in different cells and + + + align:start position:0% +in different ways in different cells and +end up generating different proteins + + align:start position:0% +end up generating different proteins + + + align:start position:0% +end up generating different proteins +that were all encoded by by one by one + + align:start position:0% +that were all encoded by by one by one + + + align:start position:0% +that were all encoded by by one by one +particular Gene and so it it gives cells + + align:start position:0% +particular Gene and so it it gives cells + + + align:start position:0% +particular Gene and so it it gives cells +different kinds of regulatory strategies + + align:start position:0% +different kinds of regulatory strategies + + + align:start position:0% +different kinds of regulatory strategies +they can use now the third one sort of + + align:start position:0% +they can use now the third one sort of + + + align:start position:0% +they can use now the third one sort of +thing that came out that falls in the + + align:start position:0% +thing that came out that falls in the + + + align:start position:0% +thing that came out that falls in the +same kind of thing of of people having + + align:start position:0% +same kind of thing of of people having + + + align:start position:0% +same kind of thing of of people having +their minds open and not fixed by the + + align:start position:0% +their minds open and not fixed by the + + + align:start position:0% +their minds open and not fixed by the +the current understanding or bounded by + + align:start position:0% +the current understanding or bounded by + + + align:start position:0% +the current understanding or bounded by +the current understanding uh is the the + + align:start position:0% +the current understanding uh is the the + + + align:start position:0% +the current understanding uh is the the +discovery that RNA can act as an enzyme + + align:start position:0% +discovery that RNA can act as an enzyme + + + align:start position:0% +discovery that RNA can act as an enzyme +I've already talked to you about that + + align:start position:0% +I've already talked to you about that + + + align:start position:0% +I've already talked to you about that +and I've called told you it was uh + + align:start position:0% +and I've called told you it was uh + + + align:start position:0% +and I've called told you it was uh +ribosy but it was discovered by uh Tom + + align:start position:0% +ribosy but it was discovered by uh Tom + + + align:start position:0% +ribosy but it was discovered by uh Tom +Czech uh Tom's president currently + + align:start position:0% +Czech uh Tom's president currently + + + align:start position:0% +Czech uh Tom's president currently +president of the Howard Hughes Medical + + align:start position:0% +president of the Howard Hughes Medical + + + align:start position:0% +president of the Howard Hughes Medical +Institute but he was he did his post + + align:start position:0% +Institute but he was he did his post + + + align:start position:0% +Institute but he was he did his post +doctoral work at MIT with um Mary L paru + + align:start position:0% +doctoral work at MIT with um Mary L paru + + + align:start position:0% +doctoral work at MIT with um Mary L paru +I've been a postdoc at at Berkeley uh + + align:start position:0% +I've been a postdoc at at Berkeley uh + + + align:start position:0% +I've been a postdoc at at Berkeley uh +when he was just finishing his graduate + + align:start position:0% +when he was just finishing his graduate + + + align:start position:0% +when he was just finishing his graduate +work and I met him out there and he came + + align:start position:0% +work and I met him out there and he came + + + align:start position:0% +work and I met him out there and he came +to MIT to do his postto and a year later + + align:start position:0% +to MIT to do his postto and a year later + + + align:start position:0% +to MIT to do his postto and a year later +I got a job so I become friends there + + align:start position:0% +I got a job so I become friends there + + + align:start position:0% +I got a job so I become friends there +and became uh friends and we started + + align:start position:0% +and became uh friends and we started + + + align:start position:0% +and became uh friends and we started +here so I had a pretty close link to + + align:start position:0% +here so I had a pretty close link to + + + align:start position:0% +here so I had a pretty close link to +this this particular story uh here's a + + align:start position:0% +this this particular story uh here's a + + + align:start position:0% +this this particular story uh here's a +picture of of Tom together with with + + align:start position:0% +picture of of Tom together with with + + + align:start position:0% +picture of of Tom together with with +Phil that's that's actually my wife + + align:start position:0% +Phil that's that's actually my wife + + + align:start position:0% +Phil that's that's actually my wife +right there who was in the this picture + + align:start position:0% +right there who was in the this picture + + + align:start position:0% +right there who was in the this picture +but Tom actually looks much more like + + align:start position:0% +but Tom actually looks much more like + + + align:start position:0% +but Tom actually looks much more like +that he's very uh colorful very fun very + + align:start position:0% +that he's very uh colorful very fun very + + + align:start position:0% +that he's very uh colorful very fun very +uh interesting person but any when Tom + + align:start position:0% +uh interesting person but any when Tom + + + align:start position:0% +uh interesting person but any when Tom +left his uh left MIT to go to um take a + + align:start position:0% +left his uh left MIT to go to um take a + + + align:start position:0% +left his uh left MIT to go to um take a +faculty position at Boulder he was + + align:start position:0% +faculty position at Boulder he was + + + align:start position:0% +faculty position at Boulder he was +interested in trying to understand the + + align:start position:0% +interested in trying to understand the + + + align:start position:0% +interested in trying to understand the +biochemistry of RNA + + align:start position:0% +biochemistry of RNA + + + align:start position:0% +biochemistry of RNA +splicing and so + + align:start position:0% +splicing and so + + + align:start position:0% +splicing and so +um he went + + align:start position:0% + + + + align:start position:0% + +he did + + align:start position:0% +he did + + + align:start position:0% +he did +what a good uh scientist will do they'll + + align:start position:0% +what a good uh scientist will do they'll + + + align:start position:0% +what a good uh scientist will do they'll +try and find an experimental system + + align:start position:0% +try and find an experimental system + + + align:start position:0% +try and find an experimental system +where the question they want to address + + align:start position:0% +where the question they want to address + + + align:start position:0% +where the question they want to address +is simple enough you can actually get an + + align:start position:0% +is simple enough you can actually get an + + + align:start position:0% +is simple enough you can actually get an +answer there's a kind of way of doing + + align:start position:0% +answer there's a kind of way of doing + + + align:start position:0% +answer there's a kind of way of doing +science where you pick a a system that's + + align:start position:0% +science where you pick a a system that's + + + align:start position:0% +science where you pick a a system that's +too complicated you never actually get + + align:start position:0% +too complicated you never actually get + + + align:start position:0% +too complicated you never actually get +an answer it sounds very important + + align:start position:0% +an answer it sounds very important + + + align:start position:0% +an answer it sounds very important +because you're working on something + + align:start position:0% +because you're working on something + + + align:start position:0% +because you're working on something +that's important but it just you can't + + align:start position:0% +that's important but it just you can't + + + align:start position:0% +that's important but it just you can't +you don't have the tools you need to get + + align:start position:0% +you don't have the tools you need to get + + + align:start position:0% +you don't have the tools you need to get +to the answer so Tom wanted to work on + + align:start position:0% +to the answer so Tom wanted to work on + + + align:start position:0% +to the answer so Tom wanted to work on +the biochemistry of RNA SPL ing cuz that + + align:start position:0% +the biochemistry of RNA SPL ing cuz that + + + align:start position:0% +the biochemistry of RNA SPL ing cuz that +had just been discovered and so he went + + align:start position:0% +had just been discovered and so he went + + + align:start position:0% +had just been discovered and so he went +to a little u a small um little tiny + + align:start position:0% +to a little u a small um little tiny + + + align:start position:0% +to a little u a small um little tiny +organism called tetrah Hima and the + + align:start position:0% +organism called tetrah Hima and the + + + align:start position:0% +organism called tetrah Hima and the +reason he looked at that because it it + + align:start position:0% +reason he looked at that because it it + + + align:start position:0% +reason he looked at that because it it +had a ribosomal RNA so it was an RNA + + align:start position:0% +had a ribosomal RNA so it was an RNA + + + align:start position:0% +had a ribosomal RNA so it was an RNA +that was made in great abundance within + + align:start position:0% +that was made in great abundance within + + + align:start position:0% +that was made in great abundance within +the organism and it only had one uh of + + align:start position:0% +the organism and it only had one uh of + + + align:start position:0% +the organism and it only had one uh of +these non-coding regions I should I'll + + align:start position:0% +these non-coding regions I should I'll + + + align:start position:0% +these non-coding regions I should I'll +tell you the the words for these coding + + align:start position:0% +tell you the the words for these coding + + + align:start position:0% +tell you the the words for these coding +and non-coating to me they're they're uh + + align:start position:0% +and non-coating to me they're they're uh + + + align:start position:0% +and non-coating to me they're they're uh +they're nonintuitive but I I guess you + + align:start position:0% +they're nonintuitive but I I guess you + + + align:start position:0% +they're nonintuitive but I I guess you +should know them the coding region is + + align:start position:0% +should know them the coding region is + + + align:start position:0% +should know them the coding region is +called the part that codes is called an + + align:start position:0% +called the part that codes is called an + + + align:start position:0% +called the part that codes is called an +Exxon and the non-coding + + align:start position:0% + + + + align:start position:0% + +part is called an + + align:start position:0% +part is called an + + + align:start position:0% +part is called an +intron so anyway what + + align:start position:0% + + + + align:start position:0% + +Tom was he went to he he worked in this + + align:start position:0% +Tom was he went to he he worked in this + + + align:start position:0% +Tom was he went to he he worked in this +organism because the pre um + + align:start position:0% + + + + align:start position:0% + +RNA was basically + + align:start position:0% + + + + align:start position:0% + +this or the pre RNA before the spacing + + align:start position:0% +this or the pre RNA before the spacing + + + align:start position:0% +this or the pre RNA before the spacing +looked like this this was going to + + align:start position:0% + + + + align:start position:0% + +give + + align:start position:0% + + + + align:start position:0% + +this like that he could get large + + align:start position:0% +this like that he could get large + + + align:start position:0% +this like that he could get large +quantities of this of this RNA so he was + + align:start position:0% +quantities of this of this RNA so he was + + + align:start position:0% +quantities of this of this RNA so he was +uh all set to make extracts of the cells + + align:start position:0% +uh all set to make extracts of the cells + + + align:start position:0% +uh all set to make extracts of the cells +of this organism and then start cooking + + align:start position:0% +of this organism and then start cooking + + + align:start position:0% +of this organism and then start cooking +up the um this RNA substrate with all + + align:start position:0% +up the um this RNA substrate with all + + + align:start position:0% +up the um this RNA substrate with all +sorts of cell extracts and then he was + + align:start position:0% +sorts of cell extracts and then he was + + + align:start position:0% +sorts of cell extracts and then he was +his plan was to purify the enzymes that + + align:start position:0% +his plan was to purify the enzymes that + + + align:start position:0% +his plan was to purify the enzymes that +that did the RNA splicing and so I first + + align:start position:0% +that did the RNA splicing and so I first + + + align:start position:0% +that did the RNA splicing and so I first +heard about this I Tom was working on + + align:start position:0% +heard about this I Tom was working on + + + align:start position:0% +heard about this I Tom was working on +this when he was here and uh um he went + + align:start position:0% +this when he was here and uh um he went + + + align:start position:0% +this when he was here and uh um he went +off to I guess it was Denmark to learn + + align:start position:0% +off to I guess it was Denmark to learn + + + align:start position:0% +off to I guess it was Denmark to learn +how to grow this organism then they were + + align:start position:0% +how to grow this organism then they were + + + align:start position:0% +how to grow this organism then they were +back who was off at Boulder and we used + + align:start position:0% +back who was off at Boulder and we used + + + align:start position:0% +back who was off at Boulder and we used +to play Squash allall the time and + + align:start position:0% +to play Squash allall the time and + + + align:start position:0% +to play Squash allall the time and +whenever I got out to Boulder we'd try + + align:start position:0% +whenever I got out to Boulder we'd try + + + align:start position:0% +whenever I got out to Boulder we'd try +and get in a squash game so I was out + + align:start position:0% +and get in a squash game so I was out + + + align:start position:0% +and get in a squash game so I was out +there at a meeting and we were sitting + + align:start position:0% +there at a meeting and we were sitting + + + align:start position:0% +there at a meeting and we were sitting +around in the locker room and I say so + + align:start position:0% +around in the locker room and I say so + + + align:start position:0% +around in the locker room and I say so +how's how's the how's the splicing + + align:start position:0% +how's how's the how's the splicing + + + align:start position:0% +how's how's the how's the splicing +biochemistry project going and Tom says + + align:start position:0% +biochemistry project going and Tom says + + + align:start position:0% +biochemistry project going and Tom says +well it's going okay I guess it's only + + align:start position:0% +well it's going okay I guess it's only + + + align:start position:0% +well it's going okay I guess it's only +one little problem he says the controls + + align:start position:0% +one little problem he says the controls + + + align:start position:0% +one little problem he says the controls +are + + align:start position:0% +are + + + align:start position:0% +are +splicing now what he meant was the + + align:start position:0% +splicing now what he meant was the + + + align:start position:0% +splicing now what he meant was the +control if you were trying to add cell + + align:start position:0% +control if you were trying to add cell + + + align:start position:0% +control if you were trying to add cell +extract and get this uh this thing to go + + align:start position:0% +extract and get this uh this thing to go + + + align:start position:0% +extract and get this uh this thing to go +what you would start out with is the RNA + + align:start position:0% +what you would start out with is the RNA + + + align:start position:0% +what you would start out with is the RNA +in a tube basically and that would be + + align:start position:0% +in a tube basically and that would be + + + align:start position:0% +in a tube basically and that would be +your control and then You' start adding + + align:start position:0% +your control and then You' start adding + + + align:start position:0% +your control and then You' start adding +stuff to it and start looking for + + align:start position:0% +stuff to it and start looking for + + + align:start position:0% +stuff to it and start looking for +splicing and what Tom was Finding was + + align:start position:0% +splicing and what Tom was Finding was + + + align:start position:0% +splicing and what Tom was Finding was +that if he just took this RNA and let it + + align:start position:0% +that if he just took this RNA and let it + + + align:start position:0% +that if he just took this RNA and let it +sit in a test tube that the splicing + + align:start position:0% +sit in a test tube that the splicing + + + align:start position:0% +sit in a test tube that the splicing +happened without him putting anything in + + align:start position:0% +happened without him putting anything in + + + align:start position:0% +happened without him putting anything in +and here he was already ready to find + + align:start position:0% +and here he was already ready to find + + + align:start position:0% +and here he was already ready to find +all the enzymes the proteins that did it + + align:start position:0% +all the enzymes the proteins that did it + + + align:start position:0% +all the enzymes the proteins that did it +and Tom was did absolutely gorgeous + + align:start position:0% +and Tom was did absolutely gorgeous + + + align:start position:0% +and Tom was did absolutely gorgeous +piece of science to prove that what was + + align:start position:0% +piece of science to prove that what was + + + align:start position:0% +piece of science to prove that what was +happening was the RNA was catalyzing its + + align:start position:0% +happening was the RNA was catalyzing its + + + align:start position:0% +happening was the RNA was catalyzing its +own + + align:start position:0% +own + + + align:start position:0% +own +splicing and he had to work very very + + align:start position:0% +splicing and he had to work very very + + + align:start position:0% +splicing and he had to work very very +hard to prove that it wasn't a + + align:start position:0% +hard to prove that it wasn't a + + + align:start position:0% +hard to prove that it wasn't a +contaminating protein remember we had + + align:start position:0% +contaminating protein remember we had + + + align:start position:0% +contaminating protein remember we had +this sort of discussion we were talking + + align:start position:0% +this sort of discussion we were talking + + + align:start position:0% +this sort of discussion we were talking +about his DNA the genetic material and + + align:start position:0% +about his DNA the genetic material and + + + align:start position:0% +about his DNA the genetic material and +how would we know that it wasn't just a + + align:start position:0% +how would we know that it wasn't just a + + + align:start position:0% +how would we know that it wasn't just a +little tiny bit of something else in our + + align:start position:0% +little tiny bit of something else in our + + + align:start position:0% +little tiny bit of something else in our +DNA prep that was doing it Tom had to go + + align:start position:0% +DNA prep that was doing it Tom had to go + + + align:start position:0% +DNA prep that was doing it Tom had to go +through pretty much a similar exercise + + align:start position:0% +through pretty much a similar exercise + + + align:start position:0% +through pretty much a similar exercise +but this was uh one of these key + + align:start position:0% +but this was uh one of these key + + + align:start position:0% +but this was uh one of these key +insights that led to the the proof that + + align:start position:0% +insights that led to the the proof that + + + align:start position:0% +insights that led to the the proof that +RNA could function as a as a catalyst + + align:start position:0% +RNA could function as a as a catalyst + + + align:start position:0% +RNA could function as a as a catalyst +what we now know is a ribosome and I've + + align:start position:0% +what we now know is a ribosome and I've + + + align:start position:0% +what we now know is a ribosome and I've +shown you now we we now sort of accept + + align:start position:0% +shown you now we we now sort of accept + + + align:start position:0% +shown you now we we now sort of accept +that the actual ribosome itself is a + + align:start position:0% +that the actual ribosome itself is a + + + align:start position:0% +that the actual ribosome itself is a +ribozyme and that the formation of the + + align:start position:0% +ribozyme and that the formation of the + + + align:start position:0% +ribozyme and that the formation of the +peptide bond the thing that's the root + + align:start position:0% +peptide bond the thing that's the root + + + align:start position:0% +peptide bond the thing that's the root +of all pro the heart of all proteins is + + align:start position:0% +of all pro the heart of all proteins is + + + align:start position:0% +of all pro the heart of all proteins is +made by a ribozyme not catalyzed by + + align:start position:0% +made by a ribozyme not catalyzed by + + + align:start position:0% +made by a ribozyme not catalyzed by +ribosome not by not by a + + align:start position:0% +ribosome not by not by a + + + align:start position:0% +ribosome not by not by a +protein okay + + align:start position:0% +protein okay + + + align:start position:0% +protein okay +um so uh the next thing topic that I + + align:start position:0% +um so uh the next thing topic that I + + + align:start position:0% +um so uh the next thing topic that I +want to try and move on which sort of We + + align:start position:0% +want to try and move on which sort of We + + + align:start position:0% +want to try and move on which sort of We +Were already set up from from this is + + align:start position:0% +Were already set up from from this is + + + align:start position:0% +Were already set up from from this is +that if the information is all in in uh + + align:start position:0% +that if the information is all in in uh + + + align:start position:0% +that if the information is all in in uh +in DNA um to begin + + align:start position:0% +in DNA um to begin + + + align:start position:0% +in DNA um to begin +with then if you make an RNA copy you're + + align:start position:0% +with then if you make an RNA copy you're + + + align:start position:0% +with then if you make an RNA copy you're +only taking a segment of that uh that uh + + align:start position:0% +only taking a segment of that uh that uh + + + align:start position:0% +only taking a segment of that uh that uh +information at a time and that op that + + align:start position:0% +information at a time and that op that + + + align:start position:0% +information at a time and that op that +gives the cells um a lot of of + + align:start position:0% +gives the cells um a lot of of + + + align:start position:0% +gives the cells um a lot of of +possibilities for regulating their uh + + align:start position:0% +possibilities for regulating their uh + + + align:start position:0% +possibilities for regulating their uh +how how they respond to the environment + + align:start position:0% +how how they respond to the environment + + + align:start position:0% +how how they respond to the environment +or just controlling what genes are are + + align:start position:0% +or just controlling what genes are are + + + align:start position:0% +or just controlling what genes are are +expressed and they're basically two + + align:start position:0% +expressed and they're basically two + + + align:start position:0% +expressed and they're basically two +kinds of strategies that are involved + + align:start position:0% +kinds of strategies that are involved + + + align:start position:0% +kinds of strategies that are involved +this this + + align:start position:0% +this this + + + align:start position:0% +this this +um these regulatory decisions they can + + align:start position:0% +um these regulatory decisions they can + + + align:start position:0% +um these regulatory decisions they can +either + + align:start position:0% + + + + align:start position:0% + +be can either be reversible changes + + align:start position:0% + + + + align:start position:0% + +for example um a + + align:start position:0% + + + + align:start position:0% + +bacterium and a food + + align:start position:0% +bacterium and a food + + + align:start position:0% +bacterium and a food +source if you're a bacterium and you + + align:start position:0% +source if you're a bacterium and you + + + align:start position:0% +source if you're a bacterium and you +you've got enzymes that let you eat a + + align:start position:0% +you've got enzymes that let you eat a + + + align:start position:0% +you've got enzymes that let you eat a +100 different kinds of food and you're + + align:start position:0% +100 different kinds of food and you're + + + align:start position:0% +100 different kinds of food and you're +in an environment where there's only one + + align:start position:0% +in an environment where there's only one + + + align:start position:0% +in an environment where there's only one +of them there you're really wasting + + align:start position:0% +of them there you're really wasting + + + align:start position:0% +of them there you're really wasting +energy if you make the proteins to to + + align:start position:0% +energy if you make the proteins to to + + + align:start position:0% +energy if you make the proteins to to +make the other 99 so you might guess + + align:start position:0% +make the other 99 so you might guess + + + align:start position:0% +make the other 99 so you might guess +that somehow Evolution has selected for + + align:start position:0% +that somehow Evolution has selected for + + + align:start position:0% +that somehow Evolution has selected for +systems that have learned how to turn on + + align:start position:0% +systems that have learned how to turn on + + + align:start position:0% +systems that have learned how to turn on +and off the things they need to eat + + align:start position:0% +and off the things they need to eat + + + align:start position:0% +and off the things they need to eat +certain food sources depending on + + align:start position:0% +certain food sources depending on + + + align:start position:0% +certain food sources depending on +whether the food source is available you + + align:start position:0% +whether the food source is available you + + + align:start position:0% +whether the food source is available you +know we only carry umbrellas when it + + align:start position:0% +know we only carry umbrellas when it + + + align:start position:0% +know we only carry umbrellas when it +rains you know if you had to carry an + + align:start position:0% +rains you know if you had to carry an + + + align:start position:0% +rains you know if you had to carry an +umbrella and a snowsuit and a surfboard + + align:start position:0% +umbrella and a snowsuit and a surfboard + + + align:start position:0% +umbrella and a snowsuit and a surfboard +everything all the time it would slow + + align:start position:0% +everything all the time it would slow + + + align:start position:0% +everything all the time it would slow +you down in evolution so um the other + + align:start position:0% +you down in evolution so um the other + + + align:start position:0% +you down in evolution so um the other +type which we've talked about as well we + + align:start position:0% +type which we've talked about as well we + + + align:start position:0% +type which we've talked about as well we +talked about starting as a single cell + + align:start position:0% +talked about starting as a single cell + + + align:start position:0% +talked about starting as a single cell +and going up to the very to the 10 14 + + align:start position:0% +and going up to the very to the 10 14 + + + align:start position:0% +and going up to the very to the 10 14 +cells that make us up then many of those + + align:start position:0% +cells that make us up then many of those + + + align:start position:0% +cells that make us up then many of those +changes as those cells go along and + + align:start position:0% +changes as those cells go along and + + + align:start position:0% +changes as those cells go along and +progressively more specialized need to + + align:start position:0% +progressively more specialized need to + + + align:start position:0% +progressively more specialized need to +be + + align:start position:0% + + + + align:start position:0% + +irreversible and this is particularly + + align:start position:0% +irreversible and this is particularly + + + align:start position:0% +irreversible and this is particularly +important in + + align:start position:0% + + + + align:start position:0% + +development we don't want a cell in our + + align:start position:0% +development we don't want a cell in our + + + align:start position:0% +development we don't want a cell in our +retina suddenly deciding it should be + + align:start position:0% +retina suddenly deciding it should be + + + align:start position:0% +retina suddenly deciding it should be +part of a heart and start to make a + + align:start position:0% +part of a heart and start to make a + + + align:start position:0% +part of a heart and start to make a +heart in the middle of your eye or + + align:start position:0% +heart in the middle of your eye or + + + align:start position:0% +heart in the middle of your eye or +something like that so things in + + align:start position:0% +something like that so things in + + + align:start position:0% +something like that so things in +development tend to be once you're off + + align:start position:0% +development tend to be once you're off + + + align:start position:0% +development tend to be once you're off +you're off or once you're on you're on + + align:start position:0% +you're off or once you're on you're on + + + align:start position:0% +you're off or once you're on you're on +or something and I just take give you + + align:start position:0% +or something and I just take give you + + + align:start position:0% +or something and I just take give you +another little look at that picture I've + + align:start position:0% +another little look at that picture I've + + + align:start position:0% +another little look at that picture I've +showed you before of that of the + + align:start position:0% +showed you before of that of the + + + align:start position:0% +showed you before of that of the +nematode and at the time I showed first + + align:start position:0% +nematode and at the time I showed first + + + align:start position:0% +nematode and at the time I showed first +time I showed you this I was just trying + + align:start position:0% +time I showed you this I was just trying + + + align:start position:0% +time I showed you this I was just trying +to emphasize that we could take the gene + + align:start position:0% +to emphasize that we could take the gene + + + align:start position:0% +to emphasize that we could take the gene +encoding green fluoresent protein and + + align:start position:0% +encoding green fluoresent protein and + + + align:start position:0% +encoding green fluoresent protein and +put it in anything and it would go green + + align:start position:0% +put it in anything and it would go green + + + align:start position:0% +put it in anything and it would go green +in this case Barbara Meyer who's at + + align:start position:0% +in this case Barbara Meyer who's at + + + align:start position:0% +in this case Barbara Meyer who's at +Berkeley now but used to be my office M + + align:start position:0% +Berkeley now but used to be my office M + + + align:start position:0% +Berkeley now but used to be my office M +at at MIT for many years what she's done + + align:start position:0% +at at MIT for many years what she's done + + + align:start position:0% +at at MIT for many years what she's done +is she's uh taken that green fluoresent + + align:start position:0% +is she's uh taken that green fluoresent + + + align:start position:0% +is she's uh taken that green fluoresent +protein and she's the gene for that and + + align:start position:0% +protein and she's the gene for that and + + + align:start position:0% +protein and she's the gene for that and +she's put it under the control of a + + align:start position:0% +she's put it under the control of a + + + align:start position:0% +she's put it under the control of a +regulatory system a gene that has is + + align:start position:0% +regulatory system a gene that has is + + + align:start position:0% +regulatory system a gene that has is +made to be EXP exess in the esophagus of + + align:start position:0% +made to be EXP exess in the esophagus of + + + align:start position:0% +made to be EXP exess in the esophagus of +the of the worm and so even though that + + align:start position:0% +the of the worm and so even though that + + + align:start position:0% +the of the worm and so even though that +Gene is present in all the cells of that + + align:start position:0% +Gene is present in all the cells of that + + + align:start position:0% +Gene is present in all the cells of that +organism it's it's under the control of + + align:start position:0% +organism it's it's under the control of + + + align:start position:0% +organism it's it's under the control of +uh A system that usually permits the + + align:start position:0% +uh A system that usually permits the + + + align:start position:0% +uh A system that usually permits the +genes to be made they're needed for + + align:start position:0% +genes to be made they're needed for + + + align:start position:0% +genes to be made they're needed for +making the esophagus but not in other + + align:start position:0% +making the esophagus but not in other + + + align:start position:0% +making the esophagus but not in other +parts of the body so you probably didn't + + align:start position:0% +parts of the body so you probably didn't + + + align:start position:0% +parts of the body so you probably didn't +pick that part up now but sort of there + + align:start position:0% +pick that part up now but sort of there + + + align:start position:0% +pick that part up now but sort of there +take another look at that same thing and + + align:start position:0% +take another look at that same thing and + + + align:start position:0% +take another look at that same thing and +see something different so how did we + + align:start position:0% +see something different so how did we + + + align:start position:0% +see something different so how did we +learn about uh Gene develop uh Gene + + align:start position:0% +learn about uh Gene develop uh Gene + + + align:start position:0% +learn about uh Gene develop uh Gene +regulation + + align:start position:0% +regulation + + + align:start position:0% +regulation +keywork like so many of these things + + align:start position:0% +keywork like so many of these things + + + align:start position:0% +keywork like so many of these things +started uh kind of un + + align:start position:0% + + + + align:start position:0% + +aspicio who was a biochemist franois + + align:start position:0% +aspicio who was a biochemist franois + + + align:start position:0% +aspicio who was a biochemist franois +jaob who were who was uh who was a + + align:start position:0% +jaob who were who was uh who was a + + + align:start position:0% +jaob who were who was uh who was a +geneticist and they were working on the + + align:start position:0% +geneticist and they were working on the + + + align:start position:0% +geneticist and they were working on the +metabolism of + + align:start position:0% + + + + align:start position:0% + +lactose by + + align:start position:0% +lactose by + + + align:start position:0% +lactose by +eoli lactose is + + align:start position:0% + + + + align:start position:0% + +galactose beta 14 + + align:start position:0% + + + + align:start position:0% + +glucose and you don't have to know + + align:start position:0% +glucose and you don't have to know + + + align:start position:0% +glucose and you don't have to know +exactly the structure you can just + + align:start position:0% +exactly the structure you can just + + + align:start position:0% +exactly the structure you can just +remember there were a lot of different + + align:start position:0% +remember there were a lot of different + + + align:start position:0% +remember there were a lot of different +hydroxy and that was one particular + + align:start position:0% +hydroxy and that was one particular + + + align:start position:0% +hydroxy and that was one particular +linkage and there's an enzyme that + + align:start position:0% +linkage and there's an enzyme that + + + align:start position:0% +linkage and there's an enzyme that +Cleaves this + + align:start position:0% +Cleaves this + + + align:start position:0% +Cleaves this +into + + align:start position:0% +into + + + align:start position:0% +into +galactose and glucose + + align:start position:0% +galactose and glucose + + + align:start position:0% +galactose and glucose +and this can go right into + + align:start position:0% + + + + align:start position:0% + +glycolysis and make energy for the + + align:start position:0% +glycolysis and make energy for the + + + align:start position:0% +glycolysis and make energy for the +organism and the galactose under goes a + + align:start position:0% +organism and the galactose under goes a + + + align:start position:0% +organism and the galactose under goes a +couple of different Transformations and + + align:start position:0% +couple of different Transformations and + + + align:start position:0% +couple of different Transformations and +it can get in there as well but in order + + align:start position:0% +it can get in there as well but in order + + + align:start position:0% +it can get in there as well but in order +to get at the energy that's in those + + align:start position:0% +to get at the energy that's in those + + + align:start position:0% +to get at the energy that's in those +carbohydrates this linkage has to be + + align:start position:0% +carbohydrates this linkage has to be + + + align:start position:0% +carbohydrates this linkage has to be +broken and it's broken by an enzyme + + align:start position:0% +broken and it's broken by an enzyme + + + align:start position:0% +broken and it's broken by an enzyme +called beta galactoside + + align:start position:0% +called beta galactoside + + + align:start position:0% +called beta galactoside +a that's a protein that's able to + + align:start position:0% +a that's a protein that's able to + + + align:start position:0% +a that's a protein that's able to +catalyze the cleavage of that those two + + align:start position:0% +catalyze the cleavage of that those two + + + align:start position:0% +catalyze the cleavage of that those two +those two sugars that's what um + + align:start position:0% +those two sugars that's what um + + + align:start position:0% +those two sugars that's what um +um uh Jac Mino and uh + + align:start position:0% +um uh Jac Mino and uh + + + align:start position:0% +um uh Jac Mino and uh +FR and Fran Jacob were studying they + + align:start position:0% +FR and Fran Jacob were studying they + + + align:start position:0% +FR and Fran Jacob were studying they +were helped out in this uh exercise part + + align:start position:0% +were helped out in this uh exercise part + + + align:start position:0% +were helped out in this uh exercise part +I guess part of the reason they got + + align:start position:0% +I guess part of the reason they got + + + align:start position:0% +I guess part of the reason they got +going in this was people had noticed for + + align:start position:0% +going in this was people had noticed for + + + align:start position:0% +going in this was people had noticed for +many years that if you grew + + align:start position:0% + + + + align:start position:0% + +a coli in + + align:start position:0% + + + + align:start position:0% + +glucose there was + + align:start position:0% +glucose there was + + + align:start position:0% +glucose there was +no beta gal I'm going to abbreviate this + + align:start position:0% +no beta gal I'm going to abbreviate this + + + align:start position:0% +no beta gal I'm going to abbreviate this +as beta gal just so I won't have to keep + + align:start position:0% +as beta gal just so I won't have to keep + + + align:start position:0% +as beta gal just so I won't have to keep +writing the the same thing but if they + + align:start position:0% +writing the the same thing but if they + + + align:start position:0% +writing the the same thing but if they +grew eoli in + + align:start position:0% + + + + align:start position:0% + +lactose beta + + align:start position:0% + + + + align:start position:0% + +gal was present and they had to be able + + align:start position:0% +gal was present and they had to be able + + + align:start position:0% +gal was present and they had to be able +to assay for this for this uh enzyme and + + align:start position:0% +to assay for this for this uh enzyme and + + + align:start position:0% +to assay for this for this uh enzyme and +they used + + align:start position:0% + + + + align:start position:0% + +um they were standard types of + + align:start position:0% +um they were standard types of + + + align:start position:0% +um they were standard types of +biochemical assays you can use but some + + align:start position:0% +biochemical assays you can use but some + + + align:start position:0% +biochemical assays you can use but some +chemists that helped design a very + + align:start position:0% +chemists that helped design a very + + + align:start position:0% +chemists that helped design a very +clever kind of substrate that helped + + align:start position:0% +clever kind of substrate that helped + + + align:start position:0% +clever kind of substrate that helped +them that could be used in these kinds + + align:start position:0% +them that could be used in these kinds + + + align:start position:0% +them that could be used in these kinds +of studies and I'll show you one of them + + align:start position:0% +of studies and I'll show you one of them + + + align:start position:0% +of studies and I'll show you one of them +it's what this enzyme really looks at is + + align:start position:0% +it's what this enzyme really looks at is + + + align:start position:0% +it's what this enzyme really looks at is +it looks + + align:start position:0% +it looks + + + align:start position:0% +it looks +at see + + align:start position:0% + + + + align:start position:0% + +galactose what it sees is sort of the + + align:start position:0% +galactose what it sees is sort of the + + + align:start position:0% +galactose what it sees is sort of the +galactose side of this linkage then it + + align:start position:0% +galactose side of this linkage then it + + + align:start position:0% +galactose side of this linkage then it +reaches in and catalyzes the cleavage of + + align:start position:0% +reaches in and catalyzes the cleavage of + + + align:start position:0% +reaches in and catalyzes the cleavage of +what's joined to it and it turns out not + + align:start position:0% +what's joined to it and it turns out not + + + align:start position:0% +what's joined to it and it turns out not +to be specific for whether glucose is on + + align:start position:0% +to be specific for whether glucose is on + + + align:start position:0% +to be specific for whether glucose is on +the other side it can accept substrates + + align:start position:0% +the other side it can accept substrates + + + align:start position:0% +the other side it can accept substrates +that have other things as well so some + + align:start position:0% +that have other things as well so some + + + align:start position:0% +that have other things as well so some +chemists made some uh variants like this + + align:start position:0% +chemists made some uh variants like this + + + align:start position:0% +chemists made some uh variants like this +there's a comp this is a compound that's + + align:start position:0% +there's a comp this is a compound that's + + + align:start position:0% +there's a comp this is a compound that's +Pro commonly known as xgal if you talk + + align:start position:0% +Pro commonly known as xgal if you talk + + + align:start position:0% +Pro commonly known as xgal if you talk +to it in the lab it's got a longer + + align:start position:0% +to it in the lab it's got a longer + + + align:start position:0% +to it in the lab it's got a longer +chemical name but what happens if beta + + align:start position:0% +chemical name but what happens if beta + + + align:start position:0% +chemical name but what happens if beta +glct aidas is there it's able to cleave + + align:start position:0% +glct aidas is there it's able to cleave + + + align:start position:0% +glct aidas is there it's able to cleave +this substrate so you get galactose + + align:start position:0% +this substrate so you get galactose + + + align:start position:0% +this substrate so you get galactose +which is colorless but if you get just X + + align:start position:0% +which is colorless but if you get just X + + + align:start position:0% +which is colorless but if you get just X +this is colored but up here this + + align:start position:0% +this is colored but up here this + + + align:start position:0% +this is colored but up here this +whole this original material is also + + align:start position:0% +whole this original material is also + + + align:start position:0% +whole this original material is also +color less so this is very convenient + + align:start position:0% +color less so this is very convenient + + + align:start position:0% +color less so this is very convenient +because if you use a substrate such as + + align:start position:0% +because if you use a substrate such as + + + align:start position:0% +because if you use a substrate such as +this you could put the um cells on a + + align:start position:0% +this you could put the um cells on a + + + align:start position:0% +this you could put the um cells on a +plate with this indicator and if they uh + + align:start position:0% +plate with this indicator and if they uh + + + align:start position:0% +plate with this indicator and if they uh +if they are colored the color is blue + + align:start position:0% +if they are colored the color is blue + + + align:start position:0% +if they are colored the color is blue +you know they were making beta galac + + align:start position:0% +you know they were making beta galac + + + align:start position:0% +you know they were making beta galac +aides and if you don't see a color you + + align:start position:0% +aides and if you don't see a color you + + + align:start position:0% +aides and if you don't see a color you +know they're not there a variety of ways + + align:start position:0% +know they're not there a variety of ways + + + align:start position:0% +know they're not there a variety of ways +of of uh of um assing for this enzyme + + align:start position:0% +of of uh of um assing for this enzyme + + + align:start position:0% +of of uh of um assing for this enzyme +but that just trying to give you a + + align:start position:0% +but that just trying to give you a + + + align:start position:0% +but that just trying to give you a +little bit of Flavor of the one of the + + align:start position:0% +little bit of Flavor of the one of the + + + align:start position:0% +little bit of Flavor of the one of the +different ways that they could assay for + + align:start position:0% +different ways that they could assay for + + + align:start position:0% +different ways that they could assay for +it now one of the issues was looked as + + align:start position:0% +it now one of the issues was looked as + + + align:start position:0% +it now one of the issues was looked as +though eoli didn't have any beta + + align:start position:0% +though eoli didn't have any beta + + + align:start position:0% +though eoli didn't have any beta +galactosides activity if there was if + + align:start position:0% +galactosides activity if there was if + + + align:start position:0% +galactosides activity if there was if +lactose was absent when growing in + + align:start position:0% +lactose was absent when growing in + + + align:start position:0% +lactose was absent when growing in +glucose and they made it if lactose was + + align:start position:0% +glucose and they made it if lactose was + + + align:start position:0% +glucose and they made it if lactose was +present well that would be kind of what + + align:start position:0% +present well that would be kind of what + + + align:start position:0% +present well that would be kind of what +you would expect Evolution would have + + align:start position:0% +you would expect Evolution would have + + + align:start position:0% +you would expect Evolution would have +figured out how to do only make the + + align:start position:0% +figured out how to do only make the + + + align:start position:0% +figured out how to do only make the +enzyme for for metabolizing lactose if + + align:start position:0% +enzyme for for metabolizing lactose if + + + align:start position:0% +enzyme for for metabolizing lactose if +the lactose is present but they had to + + align:start position:0% +the lactose is present but they had to + + + align:start position:0% +the lactose is present but they had to +figure out what the molecular basis of + + align:start position:0% +figure out what the molecular basis of + + + align:start position:0% +figure out what the molecular basis of +this was and one of the possibilities + + align:start position:0% +this was and one of the possibilities + + + align:start position:0% +this was and one of the possibilities +was that the the the protein was made + + align:start position:0% +was that the the the protein was made + + + align:start position:0% +was that the the the protein was made +but it was all sort of unfolded and when + + align:start position:0% +but it was all sort of unfolded and when + + + align:start position:0% +but it was all sort of unfolded and when +the substrate came in + + align:start position:0% +the substrate came in + + + align:start position:0% +the substrate came in +then it folded all around it and then it + + align:start position:0% +then it folded all around it and then it + + + align:start position:0% +then it folded all around it and then it +could cleave it or another possibility + + align:start position:0% +could cleave it or another possibility + + + align:start position:0% +could cleave it or another possibility +which would be the kind we're talking + + align:start position:0% +which would be the kind we're talking + + + align:start position:0% +which would be the kind we're talking +about now is the protein is not made + + align:start position:0% +about now is the protein is not made + + + align:start position:0% +about now is the protein is not made +until the lactose is present and then it + + align:start position:0% +until the lactose is present and then it + + + align:start position:0% +until the lactose is present and then it +makes it new so they had to figure out + + align:start position:0% +makes it new so they had to figure out + + + align:start position:0% +makes it new so they had to figure out +between these two um which of these two + + align:start position:0% +between these two um which of these two + + + align:start position:0% +between these two um which of these two +was true is when you see the lactose + + align:start position:0% +was true is when you see the lactose + + + align:start position:0% +was true is when you see the lactose +present is it just beta galactosidase is + + align:start position:0% +present is it just beta galactosidase is + + + align:start position:0% +present is it just beta galactosidase is +already made but it's inactive or is it + + align:start position:0% +already made but it's inactive or is it + + + align:start position:0% +already made but it's inactive or is it +being made denovo when you add the + + align:start position:0% +being made denovo when you add the + + + align:start position:0% +being made denovo when you add the +lactose so what they did was they + + align:start position:0% + + + + align:start position:0% + +grew cells in + + align:start position:0% +grew cells in + + + align:start position:0% +grew cells in +glucose plus radioactive + + align:start position:0% +glucose plus radioactive + + + align:start position:0% +glucose plus radioactive +c14 Lucine for a long time so all the + + align:start position:0% + + + + align:start position:0% + +proteins + + align:start position:0% +proteins + + + align:start position:0% +proteins +radioactive once they got that going for + + align:start position:0% +radioactive once they got that going for + + + align:start position:0% +radioactive once they got that going for +a long time so every protein being made + + align:start position:0% +a long time so every protein being made + + + align:start position:0% +a long time so every protein being made +is radioactive then they + + align:start position:0% + + + + align:start position:0% + +add excess + + align:start position:0% + + + + align:start position:0% + +unlabeled + + align:start position:0% + + + + align:start position:0% + +Lucine so this means that from now on + + align:start position:0% +Lucine so this means that from now on + + + align:start position:0% +Lucine so this means that from now on +any new proteins that are made will not + + align:start position:0% +any new proteins that are made will not + + + align:start position:0% +any new proteins that are made will not +be radioactive because you're just going + + align:start position:0% +be radioactive because you're just going + + + align:start position:0% +be radioactive because you're just going +to swamp out any radioactive stuff with + + align:start position:0% +to swamp out any radioactive stuff with + + + align:start position:0% +to swamp out any radioactive stuff with +this they added gluc excuse now they + + align:start position:0% +this they added gluc excuse now they + + + align:start position:0% +this they added gluc excuse now they +added + + align:start position:0% + + + + align:start position:0% + +lactose through the + + align:start position:0% + + + + align:start position:0% + +cells and then they + + align:start position:0% + + + + align:start position:0% + +isolated the beta gal enzyme it was + + align:start position:0% +isolated the beta gal enzyme it was + + + align:start position:0% +isolated the beta gal enzyme it was +actually pretty easy to do it's a it's a + + align:start position:0% +actually pretty easy to do it's a it's a + + + align:start position:0% +actually pretty easy to do it's a it's a +huge en enzyme and I think it's a + + align:start position:0% +huge en enzyme and I think it's a + + + align:start position:0% +huge en enzyme and I think it's a +tetramer it's very large even even in + + align:start position:0% +tetramer it's very large even even in + + + align:start position:0% +tetramer it's very large even even in +those days it was fairly easy to isolate + + align:start position:0% +those days it was fairly easy to isolate + + + align:start position:0% +those days it was fairly easy to isolate +this this enzyme and then they look to + + align:start position:0% +this this enzyme and then they look to + + + align:start position:0% +this this enzyme and then they look to +see is it radioactive if it's + + align:start position:0% +see is it radioactive if it's + + + align:start position:0% +see is it radioactive if it's +radioactive it was there there all along + + align:start position:0% +radioactive it was there there all along + + + align:start position:0% +radioactive it was there there all along +it's refolded to become the active + + align:start position:0% +it's refolded to become the active + + + align:start position:0% +it's refolded to become the active +enzyme or if it had been made only after + + align:start position:0% +enzyme or if it had been made only after + + + align:start position:0% +enzyme or if it had been made only after +lactose then it was would be um made + + align:start position:0% +lactose then it was would be um made + + + align:start position:0% +lactose then it was would be um made +denovo in response to it and what they + + align:start position:0% +denovo in response to it and what they + + + align:start position:0% +denovo in response to it and what they +found was that it was + + align:start position:0% + + + + align:start position:0% + +non-radioactive which implied that it + + align:start position:0% +non-radioactive which implied that it + + + align:start position:0% +non-radioactive which implied that it +was + + align:start position:0% +was + + + align:start position:0% +was +made after + + align:start position:0% + + + + align:start position:0% + +added the lactose so this they knew then + + align:start position:0% +added the lactose so this they knew then + + + align:start position:0% +added the lactose so this they knew then +that they were studying a system in + + align:start position:0% +that they were studying a system in + + + align:start position:0% +that they were studying a system in +which uh a protein was only made after + + align:start position:0% +which uh a protein was only made after + + + align:start position:0% +which uh a protein was only made after +the cells had experienced uh a + + align:start position:0% +the cells had experienced uh a + + + align:start position:0% +the cells had experienced uh a +particular grow grow substrate and so a + + align:start position:0% +particular grow grow substrate and so a + + + align:start position:0% +particular grow grow substrate and so a +lot of work went into to figuring out + + align:start position:0% +lot of work went into to figuring out + + + align:start position:0% +lot of work went into to figuring out +how this this system worked + + align:start position:0% +how this this system worked + + + align:start position:0% +how this this system worked +um see we're a little short on time so + + align:start position:0% +um see we're a little short on time so + + + align:start position:0% +um see we're a little short on time so +tell you what I'll do I'll I'll I'll + + align:start position:0% +tell you what I'll do I'll I'll I'll + + + align:start position:0% +tell you what I'll do I'll I'll I'll +tell you the just put out quickly the + + align:start position:0% +tell you the just put out quickly the + + + align:start position:0% +tell you the just put out quickly the +mechanics of what they saw and we'll + + align:start position:0% +mechanics of what they saw and we'll + + + align:start position:0% +mechanics of what they saw and we'll +start in on the regulation on uh on how + + align:start position:0% +start in on the regulation on uh on how + + + align:start position:0% +start in on the regulation on uh on how +this this works and you may be able some + + align:start position:0% +this this works and you may be able some + + + align:start position:0% +this this works and you may be able some +of you may be able to figure it + + align:start position:0% +of you may be able to figure it + + + align:start position:0% +of you may be able to figure it +out what we now know is that the gene + + align:start position:0% +out what we now know is that the gene + + + align:start position:0% +out what we now know is that the gene +that encodes beta galacti sitas is in a + + align:start position:0% +that encodes beta galacti sitas is in a + + + align:start position:0% +that encodes beta galacti sitas is in a +stretch of DNA that's pretty interesting + + align:start position:0% +stretch of DNA that's pretty interesting + + + align:start position:0% +stretch of DNA that's pretty interesting +it's got three genes it's the gene lack + + align:start position:0% +it's got three genes it's the gene lack + + + align:start position:0% +it's got three genes it's the gene lack +Z this is + + align:start position:0% +Z this is + + + align:start position:0% +Z this is +the gene for beta galacti sitas and + + align:start position:0% +the gene for beta galacti sitas and + + + align:start position:0% +the gene for beta galacti sitas and +another Gene called Lac Y and Lac + + align:start position:0% +another Gene called Lac Y and Lac + + + align:start position:0% +another Gene called Lac Y and Lac +Z these are there there is + + align:start position:0% + + + + align:start position:0% + +a there's a promoter that's a start + + align:start position:0% +a there's a promoter that's a start + + + align:start position:0% +a there's a promoter that's a start +signal for transcription remember that + + align:start position:0% +signal for transcription remember that + + + align:start position:0% +signal for transcription remember that +so there's a sequence + + align:start position:0% + + + + align:start position:0% + +here that says start transcription down + + align:start position:0% +here that says start transcription down + + + align:start position:0% +here that says start transcription down +here here is a + + align:start position:0% +here here is a + + + align:start position:0% +here here is a +Terminator another word written in the E + + align:start position:0% +Terminator another word written in the E + + + align:start position:0% +Terminator another word written in the E +acid alphabet that means stop making + + align:start position:0% +acid alphabet that means stop making + + + align:start position:0% +acid alphabet that means stop making +messenger RNA and there is one long + + align:start position:0% +messenger RNA and there is one long + + + align:start position:0% +messenger RNA and there is one long +messenger RNA as you can see has the + + align:start position:0% +messenger RNA as you can see has the + + + align:start position:0% +messenger RNA as you can see has the +peculiarity of encoding three different + + align:start position:0% +peculiarity of encoding three different + + + align:start position:0% +peculiarity of encoding three different +genes so if you have um more than + + align:start position:0% +genes so if you have um more than + + + align:start position:0% +genes so if you have um more than +one uh more than one gene in a in a + + align:start position:0% +one uh more than one gene in a in a + + + align:start position:0% +one uh more than one gene in a in a +single message then that's called an + + align:start position:0% + + + + align:start position:0% + +operon but one messenger + + align:start position:0% + + + + align:start position:0% + +RNA but in any case so whenever beta + + align:start position:0% +RNA but in any case so whenever beta + + + align:start position:0% +RNA but in any case so whenever beta +galactosidase was being made then RNA + + align:start position:0% +galactosidase was being made then RNA + + + align:start position:0% +galactosidase was being made then RNA +has to start being made here go + + align:start position:0% +has to start being made here go + + + align:start position:0% +has to start being made here go +to there and we won't worry about the + + align:start position:0% +to there and we won't worry about the + + + align:start position:0% +to there and we won't worry about the +functions of these other two genes but + + align:start position:0% +functions of these other two genes but + + + align:start position:0% +functions of these other two genes but +as you might guess from the way + + align:start position:0% +as you might guess from the way + + + align:start position:0% +as you might guess from the way +evolution is selected for it they have + + align:start position:0% +evolution is selected for it they have + + + align:start position:0% +evolution is selected for it they have +related activities to what beta + + align:start position:0% +related activities to what beta + + + align:start position:0% +related activities to what beta +galactosides does and for bacteria it's + + align:start position:0% +galactosides does and for bacteria it's + + + align:start position:0% +galactosides does and for bacteria it's +a very efficient way to control the + + align:start position:0% +a very efficient way to control the + + + align:start position:0% +a very efficient way to control the +expression of a bunch of genes at once + + align:start position:0% +expression of a bunch of genes at once + + + align:start position:0% +expression of a bunch of genes at once +then there was another Gene up here + + align:start position:0% +then there was another Gene up here + + + align:start position:0% +then there was another Gene up here +known as Lac eye that had a promoter and + + align:start position:0% +known as Lac eye that had a promoter and + + + align:start position:0% +known as Lac eye that had a promoter and +a terminator and it made a messenger RNA + + align:start position:0% +a terminator and it made a messenger RNA + + + align:start position:0% +a terminator and it made a messenger RNA +as well and that mess your RNA encoded a + + align:start position:0% +as well and that mess your RNA encoded a + + + align:start position:0% +as well and that mess your RNA encoded a +protein that's known as the + + align:start position:0% + + + + align:start position:0% + +lack repressor and what that lack + + align:start position:0% +lack repressor and what that lack + + + align:start position:0% +lack repressor and what that lack +repressor does it's a a It's A protein + + align:start position:0% +repressor does it's a a It's A protein + + + align:start position:0% +repressor does it's a a It's A protein +that has the ability to uh recognize a + + align:start position:0% +that has the ability to uh recognize a + + + align:start position:0% +that has the ability to uh recognize a +very very specific DNA sequence and bind + + align:start position:0% +very very specific DNA sequence and bind + + + align:start position:0% +very very specific DNA sequence and bind +there and I'm just going to kind of blow + + align:start position:0% +there and I'm just going to kind of blow + + + align:start position:0% +there and I'm just going to kind of blow +up this part of the things what we have + + align:start position:0% +up this part of the things what we have + + + align:start position:0% +up this part of the things what we have +here is + + align:start position:0% + + + + align:start position:0% + +the this is the + + align:start position:0% +the this is the + + + align:start position:0% +the this is the +promoter + + align:start position:0% +promoter + + + align:start position:0% +promoter +here and it happens that + + align:start position:0% +here and it happens that + + + align:start position:0% +here and it happens that +The Binding + + align:start position:0% + + + + align:start position:0% + +sequence for Lac + + align:start position:0% + + + + align:start position:0% + +repressor overlaps with the promoter + + align:start position:0% + + + + align:start position:0% + +weird right maybe not so I'll tell + + align:start position:0% +weird right maybe not so I'll tell + + + align:start position:0% +weird right maybe not so I'll tell +you you can think about this over the + + align:start position:0% +you you can think about this over the + + + align:start position:0% +you you can think about this over the +weekend if you haven't run into this + + align:start position:0% +weekend if you haven't run into this + + + align:start position:0% +weekend if you haven't run into this +system before so this Gene gets made all + + align:start position:0% +system before so this Gene gets made all + + + align:start position:0% +system before so this Gene gets made all +the + + align:start position:0% + + + + align:start position:0% + +time so this protein gets made all the + + align:start position:0% +time so this protein gets made all the + + + align:start position:0% +time so this protein gets made all the +time what does that protein do if it's + + align:start position:0% +time what does that protein do if it's + + + align:start position:0% +time what does that protein do if it's +just like this it knows its job in life + + align:start position:0% +just like this it knows its job in life + + + align:start position:0% +just like this it knows its job in life +is to look for this sequence and bind to + + align:start position:0% +is to look for this sequence and bind to + + + align:start position:0% +is to look for this sequence and bind to +it if it binds to it it covers up the + + align:start position:0% +it if it binds to it it covers up the + + + align:start position:0% +it if it binds to it it covers up the +promoter and + + align:start position:0% +promoter and + + + align:start position:0% +promoter and +the gene the beta galactosides Gene is + + align:start position:0% +the gene the beta galactosides Gene is + + + align:start position:0% +the gene the beta galactosides Gene is +not expressed because the cell can't + + align:start position:0% +not expressed because the cell can't + + + align:start position:0% +not expressed because the cell can't +make messenger + + align:start position:0% +make messenger + + + align:start position:0% +make messenger +RNA so this may seem a little obscure + + align:start position:0% +RNA so this may seem a little obscure + + + align:start position:0% +RNA so this may seem a little obscure +but there's something very important + + align:start position:0% +but there's something very important + + + align:start position:0% +but there's something very important +here is now the conditionality on + + align:start position:0% +here is now the conditionality on + + + align:start position:0% +here is now the conditionality on +whether this this uh Gene is expressed + + align:start position:0% +whether this this uh Gene is expressed + + + align:start position:0% +whether this this uh Gene is expressed +or not is controlled by a protein right + + align:start position:0% +or not is controlled by a protein right + + + align:start position:0% +or not is controlled by a protein right +it's controlled by this Lac repressor if + + align:start position:0% +it's controlled by this Lac repressor if + + + align:start position:0% +it's controlled by this Lac repressor if +if it's on there the gene will be made + + align:start position:0% +if it's on there the gene will be made + + + align:start position:0% +if it's on there the gene will be made +and if it's off the gene now you can + + align:start position:0% +and if it's off the gene now you can + + + align:start position:0% +and if it's off the gene now you can +make it there's the promoter and the + + align:start position:0% +make it there's the promoter and the + + + align:start position:0% +make it there's the promoter and the +Arna pinies will see it and so you've + + align:start position:0% +Arna pinies will see it and so you've + + + align:start position:0% +Arna pinies will see it and so you've +learned something about proteins they + + align:start position:0% +learned something about proteins they + + + align:start position:0% +learned something about proteins they +can bind various things and so what + + align:start position:0% +can bind various things and so what + + + align:start position:0% +can bind various things and so what +lacto uh Lac repressor has it's got a + + align:start position:0% +lacto uh Lac repressor has it's got a + + + align:start position:0% +lacto uh Lac repressor has it's got a +little binding site that + + align:start position:0% +little binding site that + + + align:start position:0% +little binding site that +lactose is able to bind to and change + + align:start position:0% +lactose is able to bind to and change + + + align:start position:0% +lactose is able to bind to and change +the + + align:start position:0% +the + + + align:start position:0% +the +confirmation of the lack repr + + align:start position:0% + + + + align:start position:0% + +so why don't you take those pieces of + + align:start position:0% +so why don't you take those pieces of + + + align:start position:0% +so why don't you take those pieces of +information see if you can figure out + + align:start position:0% +information see if you can figure out + + + align:start position:0% +information see if you can figure out +how the circuitry + + align:start position:0% +how the circuitry + + + align:start position:0% +how the circuitry +goes yeah did I missed something + + align:start position:0% +goes yeah did I missed something + + + align:start position:0% +goes yeah did I missed something +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +sorry oh sorry excuse me yes zya excuse + + align:start position:0% +sorry oh sorry excuse me yes zya excuse + + + align:start position:0% +sorry oh sorry excuse me yes zya excuse +me okay we'll we'll walk over we'll walk + + align:start position:0% +me okay we'll we'll walk over we'll walk + + + align:start position:0% +me okay we'll we'll walk over we'll walk +through that uh on on Monday but focus + + align:start position:0% +through that uh on on Monday but focus + + + align:start position:0% +through that uh on on Monday but focus +on the fact that if the repressor is is + + align:start position:0% +on the fact that if the repressor is is + + + align:start position:0% +on the fact that if the repressor is is +there and lactose isn't it binds to this + + align:start position:0% +there and lactose isn't it binds to this + + + align:start position:0% +there and lactose isn't it binds to this +sequence the repressor is made all the + + align:start position:0% +sequence the repressor is made all the + + + align:start position:0% +sequence the repressor is made all the +time but this repressor is something + + align:start position:0% +time but this repressor is something + + + align:start position:0% +time but this repressor is something +that can tell you whether lactose is + + align:start position:0% +that can tell you whether lactose is + + + align:start position:0% +that can tell you whether lactose is +there or not so you can put the circuit + + align:start position:0% +there or not so you can put the circuit + + + align:start position:0% +there or not so you can put the circuit +together okay \ No newline at end of file diff --git a/CjZjVUWMEz0.txt b/CjZjVUWMEz0.txt new file mode 100644 index 0000000000000000000000000000000000000000..a52828609e9399fbfd5788ff5f480a1ff5cc2107 --- /dev/null +++ b/CjZjVUWMEz0.txt @@ -0,0 +1,9923 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +got much more than one request to do + + align:start position:0% +got much more than one request to do + + + align:start position:0% +got much more than one request to do +some stuff on nuclear materials and I + + align:start position:0% +some stuff on nuclear materials and I + + + align:start position:0% +some stuff on nuclear materials and I +think it's just about the right time you + + align:start position:0% +think it's just about the right time you + + + align:start position:0% +think it's just about the right time you +guys know enough about radiation and + + align:start position:0% +guys know enough about radiation and + + + align:start position:0% +guys know enough about radiation and +driving would matter and everything and + + align:start position:0% +driving would matter and everything and + + + align:start position:0% +driving would matter and everything and +stopping power with prop sections after + + align:start position:0% +stopping power with prop sections after + + + align:start position:0% +stopping power with prop sections after +excess of nuclear materials and + + align:start position:0% +excess of nuclear materials and + + + align:start position:0% +excess of nuclear materials and +radiation damage this is my whole field + + align:start position:0% +radiation damage this is my whole field + + + align:start position:0% +radiation damage this is my whole field +so happy to come talk to you guys about + + align:start position:0% +so happy to come talk to you guys about + + + align:start position:0% +so happy to come talk to you guys about +this and show you why can you finish + + align:start position:0% +this and show you why can you finish + + + align:start position:0% +this and show you why can you finish +because it all of yours it starts out + + align:start position:0% +because it all of yours it starts out + + + align:start position:0% +because it all of yours it starts out +this this slide kind of gets on to it it + + align:start position:0% +this this slide kind of gets on to it it + + + align:start position:0% +this this slide kind of gets on to it it +starts off with the single atom atomic + + align:start position:0% +starts off with the single atom atomic + + + align:start position:0% +starts off with the single atom atomic +defects that make up the basic building + + align:start position:0% +defects that make up the basic building + + + align:start position:0% +defects that make up the basic building +blocks of damage and ends up with things + + align:start position:0% +blocks of damage and ends up with things + + + align:start position:0% +blocks of damage and ends up with things +that break in nuclear reactors under + + align:start position:0% +that break in nuclear reactors under + + + align:start position:0% +that break in nuclear reactors under +radiation and so to understand the whole + + align:start position:0% +radiation and so to understand the whole + + + align:start position:0% +radiation and so to understand the whole +thing you've got to know everything from + + align:start position:0% +thing you've got to know everything from + + + align:start position:0% +thing you've got to know everything from +the single atoms on the sort of + + align:start position:0% +the single atoms on the sort of + + + align:start position:0% +the single atoms on the sort of +femtosecond scale all the way up to the + + align:start position:0% +femtosecond scale all the way up to the + + + align:start position:0% +femtosecond scale all the way up to the +engineering scale where things evolve + + align:start position:0% +engineering scale where things evolve + + + align:start position:0% +engineering scale where things evolve +over years or even decades so I'll be + + align:start position:0% +over years or even decades so I'll be + + + align:start position:0% +over years or even decades so I'll be +talking first probably today we're gonna + + align:start position:0% +talking first probably today we're gonna + + + align:start position:0% +talking first probably today we're gonna +go over a material science primer so who + + align:start position:0% +go over a material science primer so who + + + align:start position:0% +go over a material science primer so who +here's how many courses in material + + align:start position:0% +here's how many courses in material + + + align:start position:0% +here's how many courses in material +science no one that's good because I'm + + align:start position:0% +science no one that's good because I'm + + + align:start position:0% +science no one that's good because I'm +assuming that there's a let's see no one + + align:start position:0% +assuming that there's a let's see no one + + + align:start position:0% +assuming that there's a let's see no one +knows anything here I know there's a + + align:start position:0% +knows anything here I know there's a + + + align:start position:0% +knows anything here I know there's a +couple material scientists in the class + + align:start position:0% +couple material scientists in the class + + + align:start position:0% +couple material scientists in the class +and I apologize ahead of time if it's a + + align:start position:0% +and I apologize ahead of time if it's a + + + align:start position:0% +and I apologize ahead of time if it's a +bit of a review but we'll be going + + align:start position:0% +bit of a review but we'll be going + + + align:start position:0% +bit of a review but we'll be going +mostly through what are materials and + + align:start position:0% +mostly through what are materials and + + + align:start position:0% +mostly through what are materials and +what are the defects that change their + + align:start position:0% +what are the defects that change their + + + align:start position:0% +what are the defects that change their +material properties and how do they + + align:start position:0% +material properties and how do they + + + align:start position:0% +material properties and how do they +behave that'll take us through about + + align:start position:0% +behave that'll take us through about + + + align:start position:0% +behave that'll take us through about +today so then tomorrow we can see how + + align:start position:0% +today so then tomorrow we can see how + + + align:start position:0% +today so then tomorrow we can see how +radiation causes those defects and + + align:start position:0% +radiation causes those defects and + + + align:start position:0% +radiation causes those defects and +actually changes material properties so + + align:start position:0% +actually changes material properties so + + + align:start position:0% +actually changes material properties so +there's a whole laundry list of + + align:start position:0% +there's a whole laundry list of + + + align:start position:0% +there's a whole laundry list of +different ways that materials fail and + + align:start position:0% +different ways that materials fail and + + + align:start position:0% +different ways that materials fail and +most folks are concerned with all of + + align:start position:0% +most folks are concerned with all of + + + align:start position:0% +most folks are concerned with all of +these everyone everything from simple + + align:start position:0% +these everyone everything from simple + + + align:start position:0% +these everyone everything from simple +overload which means you stress + + align:start position:0% +overload which means you stress + + + align:start position:0% +overload which means you stress +something too much and it just breaks to + + align:start position:0% +something too much and it just breaks to + + + align:start position:0% +something too much and it just breaks to +all the different forms of corrosion + + align:start position:0% +all the different forms of corrosion + + + align:start position:0% +all the different forms of corrosion +that's a whole field in itself and then + + align:start position:0% +that's a whole field in itself and then + + + align:start position:0% +that's a whole field in itself and then +there's the things that just we have to + + align:start position:0% +there's the things that just we have to + + + align:start position:0% +there's the things that just we have to +worry about because there are only + + align:start position:0% +worry about because there are only + + + align:start position:0% +worry about because there are only +activated with radiation damage and in + + align:start position:0% +activated with radiation damage and in + + + align:start position:0% +activated with radiation damage and in +this case this isn't quite ionization by + + align:start position:0% +this case this isn't quite ionization by + + + align:start position:0% +this case this isn't quite ionization by +radiation but it's actual radiation + + align:start position:0% +radiation but it's actual radiation + + + align:start position:0% +radiation but it's actual radiation +slamming into nuclei and moving atoms + + align:start position:0% +slamming into nuclei and moving atoms + + + align:start position:0% +slamming into nuclei and moving atoms +out of their place and we've got one + + align:start position:0% +out of their place and we've got one + + + align:start position:0% +out of their place and we've got one +figure that we had recently in a paper + + align:start position:0% +figure that we had recently in a paper + + + align:start position:0% +figure that we had recently in a paper +that sums up the entire multi scale + + align:start position:0% +that sums up the entire multi scale + + + align:start position:0% +that sums up the entire multi scale +picture of radiation damage from the + + align:start position:0% +picture of radiation damage from the + + + align:start position:0% +picture of radiation damage from the +femtosecond + + align:start position:0% +femtosecond + + + align:start position:0% +femtosecond +to let's say the mega second scale or i + + align:start position:0% +to let's say the mega second scale or i + + + align:start position:0% +to let's say the mega second scale or i +think it's more than that maybe Giga + + align:start position:0% +think it's more than that maybe Giga + + + align:start position:0% +think it's more than that maybe Giga +second would be the right word for that + + align:start position:0% +second would be the right word for that + + + align:start position:0% +second would be the right word for that +and all the way down from the angstrom + + align:start position:0% +and all the way down from the angstrom + + + align:start position:0% +and all the way down from the angstrom +to the meters + + align:start position:0% +to the meters + + + align:start position:0% +to the meters +scale and I want to pine WA walk you + + align:start position:0% +scale and I want to pine WA walk you + + + align:start position:0% +scale and I want to pine WA walk you +through sort of a lens scale by lens + + align:start position:0% +through sort of a lens scale by lens + + + align:start position:0% +through sort of a lens scale by lens +scale depiction of radiation damage it + + align:start position:0% +scale depiction of radiation damage it + + + align:start position:0% +scale depiction of radiation damage it +all starts with knocking atoms out of + + align:start position:0% +all starts with knocking atoms out of + + + align:start position:0% +all starts with knocking atoms out of +place we've mentioned this a little bit + + align:start position:0% +place we've mentioned this a little bit + + + align:start position:0% +place we've mentioned this a little bit +when we talked about nuclear stopping + + align:start position:0% +when we talked about nuclear stopping + + + align:start position:0% +when we talked about nuclear stopping +power and this is where it actually + + align:start position:0% +power and this is where it actually + + + align:start position:0% +power and this is where it actually +comes into play sometimes an incoming + + align:start position:0% +comes into play sometimes an incoming + + + align:start position:0% +comes into play sometimes an incoming +Neutron or photon or ion can displace an + + align:start position:0% +Neutron or photon or ion can displace an + + + align:start position:0% +Neutron or photon or ion can displace an +atom from its original site and we call + + align:start position:0% +atom from its original site and we call + + + align:start position:0% +atom from its original site and we call +that a physical that's a displacement + + align:start position:0% +that a physical that's a displacement + + + align:start position:0% +that a physical that's a displacement +and then that atom comes off with quite + + align:start position:0% +and then that atom comes off with quite + + + align:start position:0% +and then that atom comes off with quite +a bit of kinetic energy and can knock + + align:start position:0% +a bit of kinetic energy and can knock + + + align:start position:0% +a bit of kinetic energy and can knock +into a whole bunch of other atoms now + + align:start position:0% +into a whole bunch of other atoms now + + + align:start position:0% +into a whole bunch of other atoms now +this loss of the solid crystalline + + align:start position:0% +this loss of the solid crystalline + + + align:start position:0% +this loss of the solid crystalline +structure you can't really tell what the + + align:start position:0% +structure you can't really tell what the + + + align:start position:0% +structure you can't really tell what the +original structure looked like right it + + align:start position:0% +original structure looked like right it + + + align:start position:0% +original structure looked like right it +actually comprises a very small + + align:start position:0% +actually comprises a very small + + + align:start position:0% +actually comprises a very small +localized zone of melting called the + + align:start position:0% +localized zone of melting called the + + + align:start position:0% +localized zone of melting called the +thermal spike if you think about all + + align:start position:0% +thermal spike if you think about all + + + align:start position:0% +thermal spike if you think about all +these atoms are vibrating at fractions + + align:start position:0% +these atoms are vibrating at fractions + + + align:start position:0% +these atoms are vibrating at fractions +of an AV at thermal energies like the + + align:start position:0% +of an AV at thermal energies like the + + + align:start position:0% +of an AV at thermal energies like the +thermal neutrons we talked about in the + + align:start position:0% +thermal neutrons we talked about in the + + + align:start position:0% +thermal neutrons we talked about in the +reactor then you hit them with an MeV + + align:start position:0% +reactor then you hit them with an MeV + + + align:start position:0% +reactor then you hit them with an MeV +neutron they might transfer a hundred ke + + align:start position:0% +neutron they might transfer a hundred ke + + + align:start position:0% +neutron they might transfer a hundred ke +v of energy and a bunch of these atoms + + align:start position:0% +v of energy and a bunch of these atoms + + + align:start position:0% +v of energy and a bunch of these atoms +will then be moving about at let's say a + + align:start position:0% +will then be moving about at let's say a + + + align:start position:0% +will then be moving about at let's say a +few hundred Evie that's way beyond + + align:start position:0% +few hundred Evie that's way beyond + + + align:start position:0% +few hundred Evie that's way beyond +liquid temperature so actually it's it's + + align:start position:0% +liquid temperature so actually it's it's + + + align:start position:0% +liquid temperature so actually it's it's +been theorized that there's a little + + align:start position:0% +been theorized that there's a little + + + align:start position:0% +been theorized that there's a little +pocket of atoms around three to five + + align:start position:0% +pocket of atoms around three to five + + + align:start position:0% +pocket of atoms around three to five +nanometers wide that reaches like ten + + align:start position:0% +nanometers wide that reaches like ten + + + align:start position:0% +nanometers wide that reaches like ten +thousand Kelvin for a very very short + + align:start position:0% +thousand Kelvin for a very very short + + + align:start position:0% +thousand Kelvin for a very very short +amount of time less than a picosecond + + align:start position:0% +amount of time less than a picosecond + + + align:start position:0% +amount of time less than a picosecond +because almost instantly those atoms + + align:start position:0% +because almost instantly those atoms + + + align:start position:0% +because almost instantly those atoms +knock into the ones around them and this + + align:start position:0% +knock into the ones around them and this + + + align:start position:0% +knock into the ones around them and this +is how the process of heat transfer + + align:start position:0% +is how the process of heat transfer + + + align:start position:0% +is how the process of heat transfer +occurs and so very quickly you get + + align:start position:0% +occurs and so very quickly you get + + + align:start position:0% +occurs and so very quickly you get +what's called the quench where most of + + align:start position:0% +what's called the quench where most of + + + align:start position:0% +what's called the quench where most of +those atoms very quickly knock into + + align:start position:0% +those atoms very quickly knock into + + + align:start position:0% +those atoms very quickly knock into +other ones slowing down finding their + + align:start position:0% +other ones slowing down finding their + + + align:start position:0% +other ones slowing down finding their +equilibrium positions again but not + + align:start position:0% +equilibrium positions again but not + + + align:start position:0% +equilibrium positions again but not +everyone you can see there's a few + + align:start position:0% +everyone you can see there's a few + + + align:start position:0% +everyone you can see there's a few +places where the atoms are still out of + + align:start position:0% +places where the atoms are still out of + + + align:start position:0% +places where the atoms are still out of +their original location and it's those + + align:start position:0% +their original location and it's those + + + align:start position:0% +their original location and it's those +residual defects that actually comprise + + align:start position:0% +residual defects that actually comprise + + + align:start position:0% +residual defects that actually comprise +radiation damage and as those defects + + align:start position:0% +radiation damage and as those defects + + + align:start position:0% +radiation damage and as those defects +build up they start to move they can + + align:start position:0% +build up they start to move they can + + + align:start position:0% +build up they start to move they can +diffuse they can be transported + + align:start position:0% +diffuse they can be transported + + + align:start position:0% +diffuse they can be transported +ballistically by more radiation damage + + align:start position:0% +ballistically by more radiation damage + + + align:start position:0% +ballistically by more radiation damage +they can move by all sorts of different + + align:start position:0% +they can move by all sorts of different + + + align:start position:0% +they can move by all sorts of different +mechanisms and eventually find each + + align:start position:0% +mechanisms and eventually find each + + + align:start position:0% +mechanisms and eventually find each +other forming what's called clusters so + + align:start position:0% +other forming what's called clusters so + + + align:start position:0% +other forming what's called clusters so +a bunch of those missing atoms could + + align:start position:0% +a bunch of those missing atoms could + + + align:start position:0% +a bunch of those missing atoms could +find each other and make a hole which we + + align:start position:0% +find each other and make a hole which we + + + align:start position:0% +find each other and make a hole which we +call a void a bunch of the extra atoms + + align:start position:0% +call a void a bunch of the extra atoms + + + align:start position:0% +call a void a bunch of the extra atoms +shoved in between the other ones can + + align:start position:0% +shoved in between the other ones can + + + align:start position:0% +shoved in between the other ones can +form things called interstitial + + align:start position:0% +form things called interstitial + + + align:start position:0% +form things called interstitial +clusters we say interstitial because + + align:start position:0% +clusters we say interstitial because + + + align:start position:0% +clusters we say interstitial because +it's like in the space in between where + + align:start position:0% +it's like in the space in between where + + + align:start position:0% +it's like in the space in between where +you'd normally find some atoms so let's + + align:start position:0% +you'd normally find some atoms so let's + + + align:start position:0% +you'd normally find some atoms so let's +say you had a whole bunch of those + + align:start position:0% +say you had a whole bunch of those + + + align:start position:0% +say you had a whole bunch of those +missing atoms come together forming a + + align:start position:0% +missing atoms come together forming a + + + align:start position:0% +missing atoms come together forming a +void this is an actual transmission + + align:start position:0% +void this is an actual transmission + + + align:start position:0% +void this is an actual transmission +electron microscope or TEM image of a + + align:start position:0% +electron microscope or TEM image of a + + + align:start position:0% +electron microscope or TEM image of a +void pockets of vacuum in materials no + + align:start position:0% +void pockets of vacuum in materials no + + + align:start position:0% +void pockets of vacuum in materials no +does anything interesting about its + + align:start position:0% +does anything interesting about its + + + align:start position:0% +does anything interesting about its +shape it's rounded but what's the most + + align:start position:0% +shape it's rounded but what's the most + + + align:start position:0% +shape it's rounded but what's the most +striking to me is it isn't actually + + align:start position:0% +striking to me is it isn't actually + + + align:start position:0% +striking to me is it isn't actually +round so you would expect a void or a + + align:start position:0% +round so you would expect a void or a + + + align:start position:0% +round so you would expect a void or a +bubble to be kind of spherical right + + align:start position:0% +bubble to be kind of spherical right + + + align:start position:0% +bubble to be kind of spherical right +that's the minimum energy configuration + + align:start position:0% +that's the minimum energy configuration + + + align:start position:0% +that's the minimum energy configuration +of most things not so when you have a + + align:start position:0% +of most things not so when you have a + + + align:start position:0% +of most things not so when you have a +little pocket of vacuum + + align:start position:0% +little pocket of vacuum + + + align:start position:0% +little pocket of vacuum +it's where crystallinity comes into play + + align:start position:0% +it's where crystallinity comes into play + + + align:start position:0% +it's where crystallinity comes into play +and these voids can end up forming super + + align:start position:0% +and these voids can end up forming super + + + align:start position:0% +and these voids can end up forming super +structures what kind of what curious + + align:start position:0% +structures what kind of what curious + + + align:start position:0% +structures what kind of what curious +thing do you notice here for this whole + + align:start position:0% +thing do you notice here for this whole + + + align:start position:0% +thing do you notice here for this whole +ensemble of voids yeah they are all in + + align:start position:0% +ensemble of voids yeah they are all in + + + align:start position:0% +ensemble of voids yeah they are all in +the same direction kind of funny that's + + align:start position:0% +the same direction kind of funny that's + + + align:start position:0% +the same direction kind of funny that's +that's definitely not an accident right + + align:start position:0% +that's definitely not an accident right + + + align:start position:0% +that's definitely not an accident right +it's not like they're randomly aligned + + align:start position:0% +it's not like they're randomly aligned + + + align:start position:0% +it's not like they're randomly aligned +there's a reason for this that will go + + align:start position:0% +there's a reason for this that will go + + + align:start position:0% +there's a reason for this that will go +into in a couple slides yeah the size + + align:start position:0% +into in a couple slides yeah the size + + + align:start position:0% +into in a couple slides yeah the size +scale I think these are on the order of + + align:start position:0% +scale I think these are on the order of + + + align:start position:0% +scale I think these are on the order of +20 nanometers or so yeah I crop these + + align:start position:0% +20 nanometers or so yeah I crop these + + + align:start position:0% +20 nanometers or so yeah I crop these +images just to get points across let's + + align:start position:0% +images just to get points across let's + + + align:start position:0% +images just to get points across let's +see if it says in the other one not + + align:start position:0% +see if it says in the other one not + + + align:start position:0% +see if it says in the other one not +quite yeah but these voids can get + + align:start position:0% +quite yeah but these voids can get + + + align:start position:0% +quite yeah but these voids can get +upwards of tens of nanometers as + + align:start position:0% +upwards of tens of nanometers as + + + align:start position:0% +upwards of tens of nanometers as +smallest single atoms yeah this is the + + align:start position:0% +smallest single atoms yeah this is the + + + align:start position:0% +smallest single atoms yeah this is the +accumulation of radiation defects into + + align:start position:0% +accumulation of radiation defects into + + + align:start position:0% +accumulation of radiation defects into +what's called voids yeah don't worry + + align:start position:0% +what's called voids yeah don't worry + + + align:start position:0% +what's called voids yeah don't worry +we'll go over in more detail again and + + align:start position:0% +we'll go over in more detail again and + + + align:start position:0% +we'll go over in more detail again and +if you get little pockets of vacuum in + + align:start position:0% +if you get little pockets of vacuum in + + + align:start position:0% +if you get little pockets of vacuum in +your material where you yeah you're not + + align:start position:0% +your material where you yeah you're not + + + align:start position:0% +your material where you yeah you're not +creating or destroying mass you're just + + align:start position:0% +creating or destroying mass you're just + + + align:start position:0% +creating or destroying mass you're just +moving it so those voids where that mass + + align:start position:0% +moving it so those voids where that mass + + + align:start position:0% +moving it so those voids where that mass +was has to go somewhere else and you + + align:start position:0% +was has to go somewhere else and you + + + align:start position:0% +was has to go somewhere else and you +actually get things that swell in the + + align:start position:0% +actually get things that swell in the + + + align:start position:0% +actually get things that swell in the +reactor on their own they don't change + + align:start position:0% +reactor on their own they don't change + + + align:start position:0% +reactor on their own they don't change +mass but they change volume they just + + align:start position:0% +mass but they change volume they just + + + align:start position:0% +mass but they change volume they just +kind of puff up like Swiss cheese + + align:start position:0% +kind of puff up like Swiss cheese + + + align:start position:0% +kind of puff up like Swiss cheese +sometimes upwards of twenty or thirty + + align:start position:0% +sometimes upwards of twenty or thirty + + + align:start position:0% +sometimes upwards of twenty or thirty +percent changes in diameter and length + + align:start position:0% +percent changes in diameter and length + + + align:start position:0% +percent changes in diameter and length +for some tubing now if you're depending + + align:start position:0% +for some tubing now if you're depending + + + align:start position:0% +for some tubing now if you're depending +on these fuel rods being a certain space + + align:start position:0% +on these fuel rods being a certain space + + + align:start position:0% +on these fuel rods being a certain space +apart in a reactor and they start to + + align:start position:0% +apart in a reactor and they start to + + + align:start position:0% +apart in a reactor and they start to +swell squeezing out the coolant you lose + + align:start position:0% +swell squeezing out the coolant you lose + + + align:start position:0% +swell squeezing out the coolant you lose +the ability to cool the reactor + + align:start position:0% +the ability to cool the reactor + + + align:start position:0% +the ability to cool the reactor +because then how can you get water + + align:start position:0% +because then how can you get water + + + align:start position:0% +because then how can you get water +around something where the tubes are + + align:start position:0% +around something where the tubes are + + + align:start position:0% +around something where the tubes are +then swell together there's lots of + + align:start position:0% +then swell together there's lots of + + + align:start position:0% +then swell together there's lots of +other bad things that can happen which + + align:start position:0% +other bad things that can happen which + + + align:start position:0% +other bad things that can happen which +we'll get into and so then that's the + + align:start position:0% +we'll get into and so then that's the + + + align:start position:0% +we'll get into and so then that's the +origin of void swelling from single + + align:start position:0% +origin of void swelling from single + + + align:start position:0% +origin of void swelling from single +missing atoms called vacancies they can + + align:start position:0% +missing atoms called vacancies they can + + + align:start position:0% +missing atoms called vacancies they can +cluster into voids which then caused + + align:start position:0% +cluster into voids which then caused + + + align:start position:0% +cluster into voids which then caused +physical dimensional changes of + + align:start position:0% +physical dimensional changes of + + + align:start position:0% +physical dimensional changes of +materials on the scale of centimeters to + + align:start position:0% +materials on the scale of centimeters to + + + align:start position:0% +materials on the scale of centimeters to +meters and that's why we say it's this + + align:start position:0% +meters and that's why we say it's this + + + align:start position:0% +meters and that's why we say it's this +full multi scale picture of radiation + + align:start position:0% +full multi scale picture of radiation + + + align:start position:0% +full multi scale picture of radiation +damage but to understand what is damage + + align:start position:0% +damage but to understand what is damage + + + align:start position:0% +damage but to understand what is damage +you have to know what is an undamaged + + align:start position:0% +you have to know what is an undamaged + + + align:start position:0% +you have to know what is an undamaged +structure to begin with so it doesn't + + align:start position:0% +structure to begin with so it doesn't + + + align:start position:0% +structure to begin with so it doesn't +make sense to say how does a structure + + align:start position:0% +make sense to say how does a structure + + + align:start position:0% +make sense to say how does a structure +change if you don't know how it behaves + + align:start position:0% +change if you don't know how it behaves + + + align:start position:0% +change if you don't know how it behaves +so I want to give a very quick primer to + + align:start position:0% +so I want to give a very quick primer to + + + align:start position:0% +so I want to give a very quick primer to +material science and apologies to any + + align:start position:0% +material science and apologies to any + + + align:start position:0% +material science and apologies to any +material scientists in the room because + + align:start position:0% +material scientists in the room because + + + align:start position:0% +material scientists in the room because +this is gonna seem really basic but this + + align:start position:0% +this is gonna seem really basic but this + + + align:start position:0% +this is gonna seem really basic but this +is a very quick intro to this whole + + align:start position:0% +is a very quick intro to this whole + + + align:start position:0% +is a very quick intro to this whole +field I want to go over quickly what is + + align:start position:0% +field I want to go over quickly what is + + + align:start position:0% +field I want to go over quickly what is +a crystalline solid and perfectly + + align:start position:0% +a crystalline solid and perfectly + + + align:start position:0% +a crystalline solid and perfectly +undamaged material would be a set of + + align:start position:0% +undamaged material would be a set of + + + align:start position:0% +undamaged material would be a set of +atoms lined up in a very regular lattice + + align:start position:0% +atoms lined up in a very regular lattice + + + align:start position:0% +atoms lined up in a very regular lattice +in a regular array where you move over a + + align:start position:0% +in a regular array where you move over a + + + align:start position:0% +in a regular array where you move over a +certain distance and you find another + + align:start position:0% +certain distance and you find another + + + align:start position:0% +certain distance and you find another +atom and this extends forever and ever + + align:start position:0% +atom and this extends forever and ever + + + align:start position:0% +atom and this extends forever and ever +and ever all the way out to when you + + align:start position:0% +and ever all the way out to when you + + + align:start position:0% +and ever all the way out to when you +reach the free surface and so this what + + align:start position:0% +reach the free surface and so this what + + + align:start position:0% +reach the free surface and so this what +we would call an undamaged material a + + align:start position:0% +we would call an undamaged material a + + + align:start position:0% +we would call an undamaged material a +pristine perfect single crystal by + + align:start position:0% +pristine perfect single crystal by + + + align:start position:0% +pristine perfect single crystal by +crystal I mean an arrangement of atoms + + align:start position:0% +crystal I mean an arrangement of atoms + + + align:start position:0% +crystal I mean an arrangement of atoms +in a certain direction so notice here + + align:start position:0% +in a certain direction so notice here + + + align:start position:0% +in a certain direction so notice here +all the atoms are lined up in let's say + + align:start position:0% +all the atoms are lined up in let's say + + + align:start position:0% +all the atoms are lined up in let's say +some cubic XYZ way that's what we would + + align:start position:0% +some cubic XYZ way that's what we would + + + align:start position:0% +some cubic XYZ way that's what we would +call one crystal or one green you'll + + align:start position:0% +call one crystal or one green you'll + + + align:start position:0% +call one crystal or one green you'll +hear this you'll hear both of those and + + align:start position:0% +hear this you'll hear both of those and + + + align:start position:0% +hear this you'll hear both of those and +you'll notice also that the arrangement + + align:start position:0% +you'll notice also that the arrangement + + + align:start position:0% +you'll notice also that the arrangement +of the atoms tends to determine what the + + align:start position:0% +of the atoms tends to determine what the + + + align:start position:0% +of the atoms tends to determine what the +physical objects look like or we like to + + align:start position:0% +physical objects look like or we like to + + + align:start position:0% +physical objects look like or we like to +say that for that was it formed follows + + align:start position:0% +say that for that was it formed follows + + + align:start position:0% +say that for that was it formed follows +structure in material science so for + + align:start position:0% +structure in material science so for + + + align:start position:0% +structure in material science so for +materials like pyrite which follows a + + align:start position:0% +materials like pyrite which follows a + + + align:start position:0% +materials like pyrite which follows a +simple cubic structure that's the + + align:start position:0% +simple cubic structure that's the + + + align:start position:0% +simple cubic structure that's the +crystals you pull out of the ground they + + align:start position:0% +crystals you pull out of the ground they + + + align:start position:0% +crystals you pull out of the ground they +mimic their atomic configurations in + + align:start position:0% +mimic their atomic configurations in + + + align:start position:0% +mimic their atomic configurations in +physical centimeter sized space for gold + + align:start position:0% +physical centimeter sized space for gold + + + align:start position:0% +physical centimeter sized space for gold +atoms they adopt a slightly different + + align:start position:0% +atoms they adopt a slightly different + + + align:start position:0% +atoms they adopt a slightly different +structure it's still cubic but there's + + align:start position:0% +structure it's still cubic but there's + + + align:start position:0% +structure it's still cubic but there's +atoms shoved into the cube faces so what + + align:start position:0% +atoms shoved into the cube faces so what + + + align:start position:0% +atoms shoved into the cube faces so what +we call a face centered cubic or FCC and + + align:start position:0% +we call a face centered cubic or FCC and + + + align:start position:0% +we call a face centered cubic or FCC and +you start to see Cube looking structures + + align:start position:0% +you start to see Cube looking structures + + + align:start position:0% +you start to see Cube looking structures +all over single crystals of gold another + + align:start position:0% +all over single crystals of gold another + + + align:start position:0% +all over single crystals of gold another +one gypsum it's got a very different + + align:start position:0% +one gypsum it's got a very different + + + align:start position:0% +one gypsum it's got a very different +a structure called monoclinic where none + + align:start position:0% +a structure called monoclinic where none + + + align:start position:0% +a structure called monoclinic where none +of the sides of this parallelogram are + + align:start position:0% +of the sides of this parallelogram are + + + align:start position:0% +of the sides of this parallelogram are +the same and there's some funny angles + + align:start position:0% +the same and there's some funny angles + + + align:start position:0% +the same and there's some funny angles +but if you look at the arrangement of + + align:start position:0% +but if you look at the arrangement of + + + align:start position:0% +but if you look at the arrangement of +the atoms and the actual crystals a bit + + align:start position:0% +the atoms and the actual crystals a bit + + + align:start position:0% +the atoms and the actual crystals a bit +of gypsum that grow you sees a striking + + align:start position:0% +of gypsum that grow you sees a striking + + + align:start position:0% +of gypsum that grow you sees a striking +similarity which I find pretty neat I + + align:start position:0% +similarity which I find pretty neat I + + + align:start position:0% +similarity which I find pretty neat I +also want to mention what is the absence + + align:start position:0% +also want to mention what is the absence + + + align:start position:0% +also want to mention what is the absence +of structure and material science we + + align:start position:0% +of structure and material science we + + + align:start position:0% +of structure and material science we +call that something that's amorphous + + align:start position:0% +call that something that's amorphous + + + align:start position:0% +call that something that's amorphous +amorphous means without form so for + + align:start position:0% +amorphous means without form so for + + + align:start position:0% +amorphous means without form so for +example crystal and indium phosphide + + align:start position:0% +example crystal and indium phosphide + + + align:start position:0% +example crystal and indium phosphide +would have this regular structure like + + align:start position:0% +would have this regular structure like + + + align:start position:0% +would have this regular structure like +this you move over a certain distance + + align:start position:0% +this you move over a certain distance + + + align:start position:0% +this you move over a certain distance +you see another green atom and so on and + + align:start position:0% +you see another green atom and so on and + + + align:start position:0% +you see another green atom and so on and +so on and so on in an amorphous material + + align:start position:0% +so on and so on in an amorphous material + + + align:start position:0% +so on and so on in an amorphous material +it can still be a solid but there's no + + align:start position:0% +it can still be a solid but there's no + + + align:start position:0% +it can still be a solid but there's no +fixed distance between any certain types + + align:start position:0% +fixed distance between any certain types + + + align:start position:0% +fixed distance between any certain types +of atoms and radiation can cause a lot + + align:start position:0% +of atoms and radiation can cause a lot + + + align:start position:0% +of atoms and radiation can cause a lot +of this amorphous a ssin by knocking the + + align:start position:0% +of this amorphous a ssin by knocking the + + + align:start position:0% +of this amorphous a ssin by knocking the +atoms about and having them freeze in + + align:start position:0% +atoms about and having them freeze in + + + align:start position:0% +atoms about and having them freeze in +random configurations this is one of the + + align:start position:0% +random configurations this is one of the + + + align:start position:0% +random configurations this is one of the +ways that radiation damage can in + + align:start position:0% +ways that radiation damage can in + + + align:start position:0% +ways that radiation damage can in +brittle materials because well we'll get + + align:start position:0% +brittle materials because well we'll get + + + align:start position:0% +brittle materials because well we'll get +into that so now let's talk about the + + align:start position:0% +into that so now let's talk about the + + + align:start position:0% +into that so now let's talk about the +defects that can be created in a perfect + + align:start position:0% +defects that can be created in a perfect + + + align:start position:0% +defects that can be created in a perfect +crystal the simplest ones we call point + + align:start position:0% +crystal the simplest ones we call point + + + align:start position:0% +crystal the simplest ones we call point +defects or zero dimensional because + + align:start position:0% +defects or zero dimensional because + + + align:start position:0% +defects or zero dimensional because +they're just single atoms out of place + + align:start position:0% +they're just single atoms out of place + + + align:start position:0% +they're just single atoms out of place +you can have what's called a vacancy + + align:start position:0% +you can have what's called a vacancy + + + align:start position:0% +you can have what's called a vacancy +where if you had let's say a face + + align:start position:0% +where if you had let's say a face + + + align:start position:0% +where if you had let's say a face +centered cubic lattice of atoms or you + + align:start position:0% +centered cubic lattice of atoms or you + + + align:start position:0% +centered cubic lattice of atoms or you +have atoms on every Q corner and every + + align:start position:0% +have atoms on every Q corner and every + + + align:start position:0% +have atoms on every Q corner and every +face if you just pull one out somewhere + + align:start position:0% +face if you just pull one out somewhere + + + align:start position:0% +face if you just pull one out somewhere +we refer to that as a vacancy a missing + + align:start position:0% +we refer to that as a vacancy a missing + + + align:start position:0% +we refer to that as a vacancy a missing +atom it had to go somewhere though and + + align:start position:0% +atom it had to go somewhere though and + + + align:start position:0% +atom it had to go somewhere though and +we'll get to where it is in just a sec + + align:start position:0% +we'll get to where it is in just a sec + + + align:start position:0% +we'll get to where it is in just a sec +so it might be kind of hard to + + align:start position:0% +so it might be kind of hard to + + + align:start position:0% +so it might be kind of hard to +conceptualize how do we know that there + + align:start position:0% +conceptualize how do we know that there + + + align:start position:0% +conceptualize how do we know that there +are missing atoms in all these little + + align:start position:0% +are missing atoms in all these little + + + align:start position:0% +are missing atoms in all these little +cubes or lattices we do have direct + + align:start position:0% +cubes or lattices we do have direct + + + align:start position:0% +cubes or lattices we do have direct +evidence they're what's called quenching + + align:start position:0% +evidence they're what's called quenching + + + align:start position:0% +evidence they're what's called quenching +studies where you can measure the + + align:start position:0% +studies where you can measure the + + + align:start position:0% +studies where you can measure the +resistance or resistivity of a piece of + + align:start position:0% +resistance or resistivity of a piece of + + + align:start position:0% +resistance or resistivity of a piece of +material after heating it to a certain + + align:start position:0% +material after heating it to a certain + + + align:start position:0% +material after heating it to a certain +temperature because it turns out that + + align:start position:0% +temperature because it turns out that + + + align:start position:0% +temperature because it turns out that +the hotter you make something the more + + align:start position:0% +the hotter you make something the more + + + align:start position:0% +the hotter you make something the more +of those vacancies just naturally occur + + align:start position:0% +of those vacancies just naturally occur + + + align:start position:0% +of those vacancies just naturally occur +you won't actually ever find an + + align:start position:0% +you won't actually ever find an + + + align:start position:0% +you won't actually ever find an +absolutely perfect single crystal + + align:start position:0% +absolutely perfect single crystal + + + align:start position:0% +absolutely perfect single crystal +anywhere in nature unless you go to 0 + + align:start position:0% +anywhere in nature unless you go to 0 + + + align:start position:0% +anywhere in nature unless you go to 0 +Kelvin for infinite time and the atoms + + align:start position:0% +Kelvin for infinite time and the atoms + + + align:start position:0% +Kelvin for infinite time and the atoms +arrange themselves thusly there's always + + align:start position:0% +arrange themselves thusly there's always + + + align:start position:0% +arrange themselves thusly there's always +some amount of atomic vibration going on + + align:start position:0% +some amount of atomic vibration going on + + + align:start position:0% +some amount of atomic vibration going on +and there's actually some thermodynamic + + align:start position:0% +and there's actually some thermodynamic + + + align:start position:0% +and there's actually some thermodynamic +energy gain to having a few defects in + + align:start position:0% +energy gain to having a few defects in + + + align:start position:0% +energy gain to having a few defects in +your structure and that game + + align:start position:0% +your structure and that game + + + align:start position:0% +your structure and that game +say that number of defects increases + + align:start position:0% +say that number of defects increases + + + align:start position:0% +say that number of defects increases +with increasing temperature once you get + + align:start position:0% +with increasing temperature once you get + + + align:start position:0% +with increasing temperature once you get +to the melting point of a material like + + align:start position:0% +to the melting point of a material like + + + align:start position:0% +to the melting point of a material like +right before something melts you can + + align:start position:0% +right before something melts you can + + + align:start position:0% +right before something melts you can +have up to one in 10,000 atoms just + + align:start position:0% +have up to one in 10,000 atoms just + + + align:start position:0% +have up to one in 10,000 atoms just +missing moved somewhere else we call + + align:start position:0% +missing moved somewhere else we call + + + align:start position:0% +missing moved somewhere else we call +that the thermal equilibrium vacancy + + align:start position:0% +that the thermal equilibrium vacancy + + + align:start position:0% +that the thermal equilibrium vacancy +concentration and we can measure that + + align:start position:0% +concentration and we can measure that + + + align:start position:0% +concentration and we can measure that +using these resistivity measurements + + align:start position:0% +using these resistivity measurements + + + align:start position:0% +using these resistivity measurements +where you heat materials up to higher + + align:start position:0% +where you heat materials up to higher + + + align:start position:0% +where you heat materials up to higher +and higher temperatures cool them down + + align:start position:0% +and higher temperatures cool them down + + + align:start position:0% +and higher temperatures cool them down +suddenly and like liquid nitrogen or + + align:start position:0% +suddenly and like liquid nitrogen or + + + align:start position:0% +suddenly and like liquid nitrogen or +liquid helium and measure the change in + + align:start position:0% +liquid helium and measure the change in + + + align:start position:0% +liquid helium and measure the change in +resistivity the more defects there are + + align:start position:0% +resistivity the more defects there are + + + align:start position:0% +resistivity the more defects there are +the harder it is for electrons to flow + + align:start position:0% +the harder it is for electrons to flow + + + align:start position:0% +the harder it is for electrons to flow +through and the only thing that can + + align:start position:0% +through and the only thing that can + + + align:start position:0% +through and the only thing that can +really be responsible there in a single + + align:start position:0% +really be responsible there in a single + + + align:start position:0% +really be responsible there in a single +element would be vacancies so we do know + + align:start position:0% +element would be vacancies so we do know + + + align:start position:0% +element would be vacancies so we do know +that these really exist + + align:start position:0% +that these really exist + + + align:start position:0% +that these really exist +they can also cluster up it turns out + + align:start position:0% +they can also cluster up it turns out + + + align:start position:0% +they can also cluster up it turns out +that every time you have a vacancy in a + + align:start position:0% +that every time you have a vacancy in a + + + align:start position:0% +that every time you have a vacancy in a +material the other atoms move in a + + align:start position:0% +material the other atoms move in a + + + align:start position:0% +material the other atoms move in a +little bit towards it relaxing the + + align:start position:0% +little bit towards it relaxing the + + + align:start position:0% +little bit towards it relaxing the +pressure they feel from the atoms nearby + + align:start position:0% +pressure they feel from the atoms nearby + + + align:start position:0% +pressure they feel from the atoms nearby +and one way for a whole bunch of + + align:start position:0% +and one way for a whole bunch of + + + align:start position:0% +and one way for a whole bunch of +vacancies to lower the stress of the + + align:start position:0% +vacancies to lower the stress of the + + + align:start position:0% +vacancies to lower the stress of the +whole atomic configuration is to cluster + + align:start position:0% +whole atomic configuration is to cluster + + + align:start position:0% +whole atomic configuration is to cluster +together so if you have a whole bunch of + + align:start position:0% +together so if you have a whole bunch of + + + align:start position:0% +together so if you have a whole bunch of +vacancies they may not allow as much + + align:start position:0% +vacancies they may not allow as much + + + align:start position:0% +vacancies they may not allow as much +stress accommodation as if they were + + align:start position:0% +stress accommodation as if they were + + + align:start position:0% +stress accommodation as if they were +separate when they're together now you + + align:start position:0% +separate when they're together now you + + + align:start position:0% +separate when they're together now you +might ask what happened to the original + + align:start position:0% +might ask what happened to the original + + + align:start position:0% +might ask what happened to the original +atoms you can't just take atoms away and + + align:start position:0% +atoms you can't just take atoms away and + + + align:start position:0% +atoms you can't just take atoms away and +then go nowhere because you can't just + + align:start position:0% +then go nowhere because you can't just + + + align:start position:0% +then go nowhere because you can't just +destroy matter right unless you turn it + + align:start position:0% +destroy matter right unless you turn it + + + align:start position:0% +destroy matter right unless you turn it +into energy which is what we do in + + align:start position:0% +into energy which is what we do in + + + align:start position:0% +into energy which is what we do in +nuclear engineering so in the material + + align:start position:0% +nuclear engineering so in the material + + + align:start position:0% +nuclear engineering so in the material +science world they end up as what's + + align:start position:0% +science world they end up as what's + + + align:start position:0% +science world they end up as what's +called interstitials where you know you + + align:start position:0% +called interstitials where you know you + + + align:start position:0% +called interstitials where you know you +have a vacancy created from somewhere + + align:start position:0% +have a vacancy created from somewhere + + + align:start position:0% +have a vacancy created from somewhere +that knocks that atom out and it gets + + align:start position:0% +that knocks that atom out and it gets + + + align:start position:0% +that knocks that atom out and it gets +stuck in the next biggest space between + + align:start position:0% +stuck in the next biggest space between + + + align:start position:0% +stuck in the next biggest space between +some other atoms and we refer to those + + align:start position:0% +some other atoms and we refer to those + + + align:start position:0% +some other atoms and we refer to those +as interstitials and those can cluster + + align:start position:0% +as interstitials and those can cluster + + + align:start position:0% +as interstitials and those can cluster +up to to reduce their total stress in + + align:start position:0% +up to to reduce their total stress in + + + align:start position:0% +up to to reduce their total stress in +the lattice they can cluster up into + + align:start position:0% +the lattice they can cluster up into + + + align:start position:0% +the lattice they can cluster up into +what's called split dumbbell + + align:start position:0% +what's called split dumbbell + + + align:start position:0% +what's called split dumbbell +interstitials instead of having one + + align:start position:0% +interstitials instead of having one + + + align:start position:0% +interstitials instead of having one +extra atom shoved in here you might + + align:start position:0% +extra atom shoved in here you might + + + align:start position:0% +extra atom shoved in here you might +rearrange a couple so there's two atoms + + align:start position:0% +rearrange a couple so there's two atoms + + + align:start position:0% +rearrange a couple so there's two atoms +in the center of a cube instead of one + + align:start position:0% +in the center of a cube instead of one + + + align:start position:0% +in the center of a cube instead of one +and that tends to be a lower energy or a + + align:start position:0% +and that tends to be a lower energy or a + + + align:start position:0% +and that tends to be a lower energy or a +more stable configuration so let's look + + align:start position:0% +more stable configuration so let's look + + + align:start position:0% +more stable configuration so let's look +a little bit at the energetics of these + + align:start position:0% +a little bit at the energetics of these + + + align:start position:0% +a little bit at the energetics of these +point defects because understanding how + + align:start position:0% +point defects because understanding how + + + align:start position:0% +point defects because understanding how +they move and why will tell us a lot + + align:start position:0% +they move and why will tell us a lot + + + align:start position:0% +they move and why will tell us a lot +about how radiation damage happens so it + + align:start position:0% +about how radiation damage happens so it + + + align:start position:0% +about how radiation damage happens so it +turns out that interstitials are very + + align:start position:0% +turns out that interstitials are very + + + align:start position:0% +turns out that interstitials are very +hard to make + + align:start position:0% +hard to make + + + align:start position:0% +hard to make +it's really hard to shove an atom where + + align:start position:0% +it's really hard to shove an atom where + + + align:start position:0% +it's really hard to shove an atom where +it doesn't want to be but once you get + + align:start position:0% +it doesn't want to be but once you get + + + align:start position:0% +it doesn't want to be but once you get +it there it moves very easily let's draw + + align:start position:0% +it there it moves very easily let's draw + + + align:start position:0% +it there it moves very easily let's draw +a quick simple cubic lattice to do a + + align:start position:0% +a quick simple cubic lattice to do a + + + align:start position:0% +a quick simple cubic lattice to do a +little thought experiment and explore + + align:start position:0% +little thought experiment and explore + + + align:start position:0% +little thought experiment and explore +why that might be let's say I want to + + align:start position:0% +why that might be let's say I want to + + + align:start position:0% +why that might be let's say I want to +shove an interstitial atom in here + + align:start position:0% +shove an interstitial atom in here + + + align:start position:0% +shove an interstitial atom in here +between these other atoms well their + + align:start position:0% +between these other atoms well their + + + align:start position:0% +between these other atoms well their +electron clouds are going to repel and + + align:start position:0% +electron clouds are going to repel and + + + align:start position:0% +electron clouds are going to repel and +it's going to push all the nearby atoms + + align:start position:0% +it's going to push all the nearby atoms + + + align:start position:0% +it's going to push all the nearby atoms +away by just a little bit and these ones + + align:start position:0% +away by just a little bit and these ones + + + align:start position:0% +away by just a little bit and these ones +might push the other atoms away by just + + align:start position:0% +might push the other atoms away by just + + + align:start position:0% +might push the other atoms away by just +a little bit stretching out the lattice + + align:start position:0% +a little bit stretching out the lattice + + + align:start position:0% +a little bit stretching out the lattice +or adding some compressive stress + + align:start position:0% +or adding some compressive stress + + + align:start position:0% +or adding some compressive stress +wherever that interstitial is but then + + align:start position:0% +wherever that interstitial is but then + + + align:start position:0% +wherever that interstitial is but then +how would it move what's the biggest + + align:start position:0% +how would it move what's the biggest + + + align:start position:0% +how would it move what's the biggest +barrier it has to overcome to get to the + + align:start position:0% +barrier it has to overcome to get to the + + + align:start position:0% +barrier it has to overcome to get to the +next adjacent location well which + + align:start position:0% +next adjacent location well which + + + align:start position:0% +next adjacent location well which +direction would it go would it go this + + align:start position:0% +direction would it go would it go this + + + align:start position:0% +direction would it go would it go this +way probably not there's an atom in the + + align:start position:0% +way probably not there's an atom in the + + + align:start position:0% +way probably not there's an atom in the +way so it's gonna find the path of least + + align:start position:0% +way so it's gonna find the path of least + + + align:start position:0% +way so it's gonna find the path of least +resistance to try to get over here + + align:start position:0% +resistance to try to get over here + + + align:start position:0% +resistance to try to get over here +because like we've talked about before + + align:start position:0% +because like we've talked about before + + + align:start position:0% +because like we've talked about before +all atoms are always in motion vibrating + + align:start position:0% +all atoms are always in motion vibrating + + + align:start position:0% +all atoms are always in motion vibrating +some of them will be energetic enough to + + align:start position:0% +some of them will be energetic enough to + + + align:start position:0% +some of them will be energetic enough to +squeeze through these two atoms and get + + align:start position:0% +squeeze through these two atoms and get + + + align:start position:0% +squeeze through these two atoms and get +over to the next site and that turns out + + align:start position:0% +over to the next site and that turns out + + + align:start position:0% +over to the next site and that turns out +to be a pretty easy process we can look + + align:start position:0% +to be a pretty easy process we can look + + + align:start position:0% +to be a pretty easy process we can look +at the energy required for an + + align:start position:0% +at the energy required for an + + + align:start position:0% +at the energy required for an +interstitial to move we notice it's + + align:start position:0% +interstitial to move we notice it's + + + align:start position:0% +interstitial to move we notice it's +really small fractions of an electron + + align:start position:0% +really small fractions of an electron + + + align:start position:0% +really small fractions of an electron +volt whereas creating them takes 2 or 3 + + align:start position:0% +volt whereas creating them takes 2 or 3 + + + align:start position:0% +volt whereas creating them takes 2 or 3 +electron volts in an atomic land that's + + align:start position:0% +electron volts in an atomic land that's + + + align:start position:0% +electron volts in an atomic land that's +a very high energy penalty now let's + + align:start position:0% +a very high energy penalty now let's + + + align:start position:0% +a very high energy penalty now let's +look at vacancies they're quite the + + align:start position:0% +look at vacancies they're quite the + + + align:start position:0% +look at vacancies they're quite the +opposite + + align:start position:0% +opposite + + + align:start position:0% +opposite +they're rather easy to make but they're + + align:start position:0% +they're rather easy to make but they're + + + align:start position:0% +they're rather easy to make but they're +very hard to move compared to + + align:start position:0% +very hard to move compared to + + + align:start position:0% +very hard to move compared to +interstitials notice that the energy of + + align:start position:0% +interstitials notice that the energy of + + + align:start position:0% +interstitials notice that the energy of +movement is about the same as the energy + + align:start position:0% +movement is about the same as the energy + + + align:start position:0% +movement is about the same as the energy +of formation for vacancies to take an + + align:start position:0% +of formation for vacancies to take an + + + align:start position:0% +of formation for vacancies to take an +atom outer - pluck it out you have to + + align:start position:0% +atom outer - pluck it out you have to + + + align:start position:0% +atom outer - pluck it out you have to +break every bond between nearby atoms so + + align:start position:0% +break every bond between nearby atoms so + + + align:start position:0% +break every bond between nearby atoms so +you actually have to put energy in to + + align:start position:0% +you actually have to put energy in to + + + align:start position:0% +you actually have to put energy in to +break those bonds and then remove the + + align:start position:0% +break those bonds and then remove the + + + align:start position:0% +break those bonds and then remove the +atom somewhere else now these things are + + align:start position:0% +atom somewhere else now these things are + + + align:start position:0% +atom somewhere else now these things are +usually made in pairs so if you think + + align:start position:0% +usually made in pairs so if you think + + + align:start position:0% +usually made in pairs so if you think +about how much energy would it take to + + align:start position:0% +about how much energy would it take to + + + align:start position:0% +about how much energy would it take to +cause a single radiation damage event + + align:start position:0% +cause a single radiation damage event + + + align:start position:0% +cause a single radiation damage event +where you have one vacancy which let's + + align:start position:0% +where you have one vacancy which let's + + + align:start position:0% +where you have one vacancy which let's +say + + align:start position:0% +say + + + align:start position:0% +say +would have been right here and one + + align:start position:0% +would have been right here and one + + + align:start position:0% +would have been right here and one +interstitial it takes the sum of these + + align:start position:0% +interstitial it takes the sum of these + + + align:start position:0% +interstitial it takes the sum of these +two energies usually about four electron + + align:start position:0% +two energies usually about four electron + + + align:start position:0% +two energies usually about four electron +volts that's not something that tends to + + align:start position:0% +volts that's not something that tends to + + + align:start position:0% +volts that's not something that tends to +happen chemically or from stress or from + + align:start position:0% +happen chemically or from stress or from + + + align:start position:0% +happen chemically or from stress or from +something like that but radiation coming + + align:start position:0% +something like that but radiation coming + + + align:start position:0% +something like that but radiation coming +in with hundreds of kV or even MeV + + align:start position:0% +in with hundreds of kV or even MeV + + + align:start position:0% +in with hundreds of kV or even MeV +neutrons anything's on the table because + + align:start position:0% +neutrons anything's on the table because + + + align:start position:0% +neutrons anything's on the table because +it's high enough energy so it would take + + align:start position:0% +it's high enough energy so it would take + + + align:start position:0% +it's high enough energy so it would take +about three or four evey to make a pair + + align:start position:0% +about three or four evey to make a pair + + + align:start position:0% +about three or four evey to make a pair +of a vacancy and an interstitial if you + + align:start position:0% +of a vacancy and an interstitial if you + + + align:start position:0% +of a vacancy and an interstitial if you +just add these two up it comes usually + + align:start position:0% +just add these two up it comes usually + + + align:start position:0% +just add these two up it comes usually +to about three or four evey or electron + + align:start position:0% +to about three or four evey or electron + + + align:start position:0% +to about three or four evey or electron +volts and that's a very difficult thing + + align:start position:0% +volts and that's a very difficult thing + + + align:start position:0% +volts and that's a very difficult thing +to do in sort of chemical world where + + align:start position:0% +to do in sort of chemical world where + + + align:start position:0% +to do in sort of chemical world where +you know reactions might proceed with + + align:start position:0% +you know reactions might proceed with + + + align:start position:0% +you know reactions might proceed with +fractions of an electron volt but when + + align:start position:0% +fractions of an electron volt but when + + + align:start position:0% +fractions of an electron volt but when +you have MeV neutrons coming in they can + + align:start position:0% +you have MeV neutrons coming in they can + + + align:start position:0% +you have MeV neutrons coming in they can +do whatever they want + + align:start position:0% +do whatever they want + + + align:start position:0% +do whatever they want +well they deal what they'll do whatever + + align:start position:0% +well they deal what they'll do whatever + + + align:start position:0% +well they deal what they'll do whatever +they will so someone actually asked me + + align:start position:0% +they will so someone actually asked me + + + align:start position:0% +they will so someone actually asked me +yesterday what sort of materials can you + + align:start position:0% +yesterday what sort of materials can you + + + align:start position:0% +yesterday what sort of materials can you +put in the way of neutrons to stop them + + align:start position:0% +put in the way of neutrons to stop them + + + align:start position:0% +put in the way of neutrons to stop them +from doing damage and the answer is + + align:start position:0% +from doing damage and the answer is + + + align:start position:0% +from doing damage and the answer is +pretty much nothing they test neutrons + + align:start position:0% +pretty much nothing they test neutrons + + + align:start position:0% +pretty much nothing they test neutrons +tend to travel about 10 centimeters even + + align:start position:0% +tend to travel about 10 centimeters even + + + align:start position:0% +tend to travel about 10 centimeters even +in things like steel or water and + + align:start position:0% +in things like steel or water and + + + align:start position:0% +in things like steel or water and +they're gonna hit what they're gonna hit + + align:start position:0% +they're gonna hit what they're gonna hit + + + align:start position:0% +they're gonna hit what they're gonna hit +there's not much you can do but put more + + align:start position:0% +there's not much you can do but put more + + + align:start position:0% +there's not much you can do but put more +things in the way and we can only get to + + align:start position:0% +things in the way and we can only get to + + + align:start position:0% +things in the way and we can only get to +a certain density with regular matter I + + align:start position:0% +a certain density with regular matter I + + + align:start position:0% +a certain density with regular matter I +think osmium has upwards of like 22 + + align:start position:0% +think osmium has upwards of like 22 + + + align:start position:0% +think osmium has upwards of like 22 +grams per cubic centimeter density + + align:start position:0% +grams per cubic centimeter density + + + align:start position:0% +grams per cubic centimeter density +that's not enough to stop neutrons even + + align:start position:0% +that's not enough to stop neutrons even + + + align:start position:0% +that's not enough to stop neutrons even +over a considerable distance unless you + + align:start position:0% +over a considerable distance unless you + + + align:start position:0% +over a considerable distance unless you +had like liquid neutrons star that you + + align:start position:0% +had like liquid neutrons star that you + + + align:start position:0% +had like liquid neutrons star that you +could pack nuclei in and away higher + + align:start position:0% +could pack nuclei in and away higher + + + align:start position:0% +could pack nuclei in and away higher +number density not much you can do so + + align:start position:0% +number density not much you can do so + + + align:start position:0% +number density not much you can do so +I'm moving up in the dimensions there's + + align:start position:0% +I'm moving up in the dimensions there's + + + align:start position:0% +I'm moving up in the dimensions there's +another type of defect called a + + align:start position:0% +another type of defect called a + + + align:start position:0% +another type of defect called a +dislocation where it's actually + + align:start position:0% +dislocation where it's actually + + + align:start position:0% +dislocation where it's actually +energetically favorable to slide an + + align:start position:0% +energetically favorable to slide an + + + align:start position:0% +energetically favorable to slide an +extra half plane of atoms in between two + + align:start position:0% +extra half plane of atoms in between two + + + align:start position:0% +extra half plane of atoms in between two +sets in here in the crystal lattice + + align:start position:0% +sets in here in the crystal lattice + + + align:start position:0% +sets in here in the crystal lattice +creating a sort of bulged out structure + + align:start position:0% +creating a sort of bulged out structure + + + align:start position:0% +creating a sort of bulged out structure +like you see right here and dislocations + + align:start position:0% +like you see right here and dislocations + + + align:start position:0% +like you see right here and dislocations +are one of the most important defects in + + align:start position:0% +are one of the most important defects in + + + align:start position:0% +are one of the most important defects in +material science and radiation damage + + align:start position:0% +material science and radiation damage + + + align:start position:0% +material science and radiation damage +there what I like to call the agents of + + align:start position:0% +there what I like to call the agents of + + + align:start position:0% +there what I like to call the agents of +plasticity + + align:start position:0% +plasticity + + + align:start position:0% +plasticity +if you deform a material enough that it + + align:start position:0% +if you deform a material enough that it + + + align:start position:0% +if you deform a material enough that it +doesn't just spring back then low most + + align:start position:0% +doesn't just spring back then low most + + + align:start position:0% +doesn't just spring back then low most +likely you were creating and moving + + align:start position:0% +likely you were creating and moving + + + align:start position:0% +likely you were creating and moving +dislocations in the material do you + + align:start position:0% +dislocations in the material do you + + + align:start position:0% +dislocations in the material do you +think about a couple of diff + + align:start position:0% +think about a couple of diff + + + align:start position:0% +think about a couple of diff +ways to cause deformation let's bring + + align:start position:0% +ways to cause deformation let's bring + + + align:start position:0% +ways to cause deformation let's bring +our perfect lattice back without all + + align:start position:0% +our perfect lattice back without all + + + align:start position:0% +our perfect lattice back without all +these extra notations if you want to + + align:start position:0% +these extra notations if you want to + + + align:start position:0% +these extra notations if you want to +slide or shear two planes of atoms + + align:start position:0% +slide or shear two planes of atoms + + + align:start position:0% +slide or shear two planes of atoms +across and they're all bonded to each + + align:start position:0% +across and they're all bonded to each + + + align:start position:0% +across and they're all bonded to each +other + + align:start position:0% + + + + align:start position:0% + +what do you physically have to do how + + align:start position:0% +what do you physically have to do how + + + align:start position:0% +what do you physically have to do how +can you get these atoms to slide across + + align:start position:0% +can you get these atoms to slide across + + + align:start position:0% +can you get these atoms to slide across +each other what what sort of energy do + + align:start position:0% +each other what what sort of energy do + + + align:start position:0% +each other what what sort of energy do +you have to put into it yeah yep because + + align:start position:0% +you have to put into it yeah yep because + + + align:start position:0% +you have to put into it yeah yep because +all these atoms are bonded to each other + + align:start position:0% +all these atoms are bonded to each other + + + align:start position:0% +all these atoms are bonded to each other +if you want them to move you have to + + align:start position:0% +if you want them to move you have to + + + align:start position:0% +if you want them to move you have to +break every bond on that plane that's a + + align:start position:0% +break every bond on that plane that's a + + + align:start position:0% +break every bond on that plane that's a +lot of atomic bonds to break and it's + + align:start position:0% +lot of atomic bonds to break and it's + + + align:start position:0% +lot of atomic bonds to break and it's +extremely unlikely that that would + + align:start position:0% +extremely unlikely that that would + + + align:start position:0% +extremely unlikely that that would +happen in fact if you broke an entire + + align:start position:0% +happen in fact if you broke an entire + + + align:start position:0% +happen in fact if you broke an entire +plane of bonds in some material like + + align:start position:0% +plane of bonds in some material like + + + align:start position:0% +plane of bonds in some material like +this what would you physically do to it + + align:start position:0% +this what would you physically do to it + + + align:start position:0% +this what would you physically do to it +it snap it in half + + align:start position:0% +it snap it in half + + + align:start position:0% +it snap it in half +that would be fracture so if you broke + + align:start position:0% +that would be fracture so if you broke + + + align:start position:0% +that would be fracture so if you broke +every bond down this plane you would + + align:start position:0% +every bond down this plane you would + + + align:start position:0% +every bond down this plane you would +then have two pieces of this fuel rod + + align:start position:0% +then have two pieces of this fuel rod + + + align:start position:0% +then have two pieces of this fuel rod +that's usually a pretty high-energy + + align:start position:0% +that's usually a pretty high-energy + + + align:start position:0% +that's usually a pretty high-energy +thing to try to do so instead if you + + align:start position:0% +thing to try to do so instead if you + + + align:start position:0% +thing to try to do so instead if you +shove an extra half plane of atoms in + + align:start position:0% +shove an extra half plane of atoms in + + + align:start position:0% +shove an extra half plane of atoms in +there and the bonds are kind of funny + + align:start position:0% +there and the bonds are kind of funny + + + align:start position:0% +there and the bonds are kind of funny +like so right at that extra half plane + + align:start position:0% +like so right at that extra half plane + + + align:start position:0% +like so right at that extra half plane +location then what you can actually do + + align:start position:0% +location then what you can actually do + + + align:start position:0% +location then what you can actually do +is break one let's say you break this + + align:start position:0% +is break one let's say you break this + + + align:start position:0% +is break one let's say you break this +one form the next one then break this + + align:start position:0% +one form the next one then break this + + + align:start position:0% +one form the next one then break this +one and form the next one and for a few + + align:start position:0% +one and form the next one and for a few + + + align:start position:0% +one and form the next one and for a few +atoms to move over you only have to + + align:start position:0% +atoms to move over you only have to + + + align:start position:0% +atoms to move over you only have to +break a line of bonds not a plane so + + align:start position:0% +break a line of bonds not a plane so + + + align:start position:0% +break a line of bonds not a plane so +it's much less energy-intensive to get a + + align:start position:0% +it's much less energy-intensive to get a + + + align:start position:0% +it's much less energy-intensive to get a +dislocation to move than to just break + + align:start position:0% +dislocation to move than to just break + + + align:start position:0% +dislocation to move than to just break +something in half now you might ask well + + align:start position:0% +something in half now you might ask well + + + align:start position:0% +something in half now you might ask well +then why do things actually break + + align:start position:0% +then why do things actually break + + + align:start position:0% +then why do things actually break +whether or not things deform or break is + + align:start position:0% +whether or not things deform or break is + + + align:start position:0% +whether or not things deform or break is +a balance between this process which we + + align:start position:0% +a balance between this process which we + + + align:start position:0% +a balance between this process which we +call slip and breaking an entire plane + + align:start position:0% +call slip and breaking an entire plane + + + align:start position:0% +call slip and breaking an entire plane +of atoms which we call fracture so this + + align:start position:0% +of atoms which we call fracture so this + + + align:start position:0% +of atoms which we call fracture so this +one's called slip + + align:start position:0% + + + + align:start position:0% + +the other mode is fracture + + align:start position:0% +the other mode is fracture + + + align:start position:0% +the other mode is fracture +we would rather materials to form in + + align:start position:0% +we would rather materials to form in + + + align:start position:0% +we would rather materials to form in +systems like reactors by slip just + + align:start position:0% +systems like reactors by slip just + + + align:start position:0% +systems like reactors by slip just +moving a little bit than just breaking + + align:start position:0% +moving a little bit than just breaking + + + align:start position:0% +moving a little bit than just breaking +all together + + align:start position:0% +all together + + + align:start position:0% +all together +unfortunately when enough radiation hits + + align:start position:0% +unfortunately when enough radiation hits + + + align:start position:0% +unfortunately when enough radiation hits +materials you can fracture things in a + + align:start position:0% +materials you can fracture things in a + + + align:start position:0% +materials you can fracture things in a +brittle manner and we'll see what + + align:start position:0% +brittle manner and we'll see what + + + align:start position:0% +brittle manner and we'll see what +happens then there's a couple kinds of + + align:start position:0% +happens then there's a couple kinds of + + + align:start position:0% +happens then there's a couple kinds of +dislocations one of them is called a + + align:start position:0% +dislocations one of them is called a + + + align:start position:0% +dislocations one of them is called a +screw dislocation so imagine you had a + + align:start position:0% +screw dislocation so imagine you had a + + + align:start position:0% +screw dislocation so imagine you had a +whole bunch of sheets of atoms and you + + align:start position:0% +whole bunch of sheets of atoms and you + + + align:start position:0% +whole bunch of sheets of atoms and you +made a cut halfway through that sheet + + align:start position:0% +made a cut halfway through that sheet + + + align:start position:0% +made a cut halfway through that sheet +and then moved every plane up by one + + align:start position:0% +and then moved every plane up by one + + + align:start position:0% +and then moved every plane up by one +position you then got what's called a + + align:start position:0% +position you then got what's called a + + + align:start position:0% +position you then got what's called a +screw dislocation kind of a spiral + + align:start position:0% +screw dislocation kind of a spiral + + + align:start position:0% +screw dislocation kind of a spiral +parking-garage of atoms surrounding that + + align:start position:0% +parking-garage of atoms surrounding that + + + align:start position:0% +parking-garage of atoms surrounding that +core right there + + align:start position:0% +core right there + + + align:start position:0% +core right there +you can also have what's called an edge + + align:start position:0% +you can also have what's called an edge + + + align:start position:0% +you can also have what's called an edge +dislocation which is like the one I've + + align:start position:0% +dislocation which is like the one I've + + + align:start position:0% +dislocation which is like the one I've +got here on the board right here where + + align:start position:0% +got here on the board right here where + + + align:start position:0% +got here on the board right here where +you just have an extra half plane of + + align:start position:0% +you just have an extra half plane of + + + align:start position:0% +you just have an extra half plane of +atoms shoved in right there so there's + + align:start position:0% +atoms shoved in right there so there's + + + align:start position:0% +atoms shoved in right there so there's +two types and they move in two different + + align:start position:0% +two types and they move in two different + + + align:start position:0% +two types and they move in two different +ways the edge dislocation may behaves + + align:start position:0% +ways the edge dislocation may behaves + + + align:start position:0% +ways the edge dislocation may behaves +like you may physically expect if you + + align:start position:0% +like you may physically expect if you + + + align:start position:0% +like you may physically expect if you +kind of push like this on two planes of + + align:start position:0% +kind of push like this on two planes of + + + align:start position:0% +kind of push like this on two planes of +atoms it moves in the direction you push + + align:start position:0% +atoms it moves in the direction you push + + + align:start position:0% +atoms it moves in the direction you push +it screw dislocations are kind of screwy + + align:start position:0% +it screw dislocations are kind of screwy + + + align:start position:0% +it screw dislocations are kind of screwy +if you push like this it moves + + align:start position:0% +if you push like this it moves + + + align:start position:0% +if you push like this it moves +perpendicular not gonna get into why but + + align:start position:0% +perpendicular not gonna get into why but + + + align:start position:0% +perpendicular not gonna get into why but +just remember screw dislocations are + + align:start position:0% +just remember screw dislocations are + + + align:start position:0% +just remember screw dislocations are +fairly screwy in the way that they + + align:start position:0% +fairly screwy in the way that they + + + align:start position:0% +fairly screwy in the way that they +behave not quite intuitive well that's + + align:start position:0% +behave not quite intuitive well that's + + + align:start position:0% +behave not quite intuitive well that's +okay we don't have to worry about those + + align:start position:0% +okay we don't have to worry about those + + + align:start position:0% +okay we don't have to worry about those +and the way that they actually move like + + align:start position:0% +and the way that they actually move like + + + align:start position:0% +and the way that they actually move like +we showed right here is by what's called + + align:start position:0% +we showed right here is by what's called + + + align:start position:0% +we showed right here is by what's called +glide or slip where dislocations can + + align:start position:0% +glide or slip where dislocations can + + + align:start position:0% +glide or slip where dislocations can +slide just by one plane of atoms or one + + align:start position:0% +slide just by one plane of atoms or one + + + align:start position:0% +slide just by one plane of atoms or one +atomic position in a mechanism that + + align:start position:0% +atomic position in a mechanism that + + + align:start position:0% +atomic position in a mechanism that +looks something like this whereas that + + align:start position:0% +looks something like this whereas that + + + align:start position:0% +looks something like this whereas that +dislocation moves you only have to break + + align:start position:0% +dislocation moves you only have to break + + + align:start position:0% +dislocation moves you only have to break +a line of bonds and then reform a line + + align:start position:0% +a line of bonds and then reform a line + + + align:start position:0% +a line of bonds and then reform a line +of bonds which is a much easier process + + align:start position:0% +of bonds which is a much easier process + + + align:start position:0% +of bonds which is a much easier process +than breaking an entire plane at once + + align:start position:0% +than breaking an entire plane at once + + + align:start position:0% +than breaking an entire plane at once +it's like you have to break the square + + align:start position:0% +it's like you have to break the square + + + align:start position:0% +it's like you have to break the square +root of the same number of bonds when a + + align:start position:0% +root of the same number of bonds when a + + + align:start position:0% +root of the same number of bonds when a +skip head from some of that there's one + + align:start position:0% +skip head from some of that there's one + + + align:start position:0% +skip head from some of that there's one +other mechanism of dislocation movement + + align:start position:0% +other mechanism of dislocation movement + + + align:start position:0% +other mechanism of dislocation movement +that's important to us in radiation + + align:start position:0% +that's important to us in radiation + + + align:start position:0% +that's important to us in radiation +damage and that's called climb this is + + align:start position:0% +damage and that's called climb this is + + + align:start position:0% +damage and that's called climb this is +when you start to think about what + + align:start position:0% +when you start to think about what + + + align:start position:0% +when you start to think about what +happens if you have a dislocation which + + align:start position:0% +happens if you have a dislocation which + + + align:start position:0% +happens if you have a dislocation which +will give this symbol right here + + align:start position:0% +will give this symbol right here + + + align:start position:0% +will give this symbol right here +and you also have a vacancy let's say + + align:start position:0% +and you also have a vacancy let's say + + + align:start position:0% +and you also have a vacancy let's say +created by radiation damage if that + + align:start position:0% +created by radiation damage if that + + + align:start position:0% +created by radiation damage if that +vacancy can move it's going to find the + + align:start position:0% +vacancy can move it's going to find the + + + align:start position:0% +vacancy can move it's going to find the +most stressed-out part of this lattice + + align:start position:0% +most stressed-out part of this lattice + + + align:start position:0% +most stressed-out part of this lattice +most likely the vacancy will move here + + align:start position:0% +most likely the vacancy will move here + + + align:start position:0% +most likely the vacancy will move here +in other words the atom will move over + + align:start position:0% +in other words the atom will move over + + + align:start position:0% +in other words the atom will move over +there leaving this vacancy over there + + align:start position:0% +there leaving this vacancy over there + + + align:start position:0% +there leaving this vacancy over there +it's kind of funny to think like what + + align:start position:0% +it's kind of funny to think like what + + + align:start position:0% +it's kind of funny to think like what +does it mean that a vacancy moves has + + align:start position:0% +does it mean that a vacancy moves has + + + align:start position:0% +does it mean that a vacancy moves has +anyone ever done anything with + + align:start position:0% +anyone ever done anything with + + + align:start position:0% +anyone ever done anything with +semiconductors and talked about electron + + align:start position:0% +semiconductors and talked about electron + + + align:start position:0% +semiconductors and talked about electron +and hole movement okay yeah so what does + + align:start position:0% +and hole movement okay yeah so what does + + + align:start position:0% +and hole movement okay yeah so what does +it really mean for a hole to move right + + align:start position:0% +it really mean for a hole to move right + + + align:start position:0% +it really mean for a hole to move right +it's a holes not a thing a vacancy is + + align:start position:0% +it's a holes not a thing a vacancy is + + + align:start position:0% +it's a holes not a thing a vacancy is +also not a thing it's an absence of an + + align:start position:0% +also not a thing it's an absence of an + + + align:start position:0% +also not a thing it's an absence of an +atom but here we can say that the + + align:start position:0% +atom but here we can say that the + + + align:start position:0% +atom but here we can say that the +vacancy moves in this direction when the + + align:start position:0% +vacancy moves in this direction when the + + + align:start position:0% +vacancy moves in this direction when the +corresponding atom moves in the exact + + align:start position:0% +corresponding atom moves in the exact + + + align:start position:0% +corresponding atom moves in the exact +opposite direction and then what you've + + align:start position:0% +opposite direction and then what you've + + + align:start position:0% +opposite direction and then what you've +actually done is moved your dislocation + + align:start position:0% +actually done is moved your dislocation + + + align:start position:0% +actually done is moved your dislocation +up instead of moving in the slip + + align:start position:0% +up instead of moving in the slip + + + align:start position:0% +up instead of moving in the slip +direction you've now moved it in a + + align:start position:0% +direction you've now moved it in a + + + align:start position:0% +direction you've now moved it in a +perpendicular direction this is usually + + align:start position:0% +perpendicular direction this is usually + + + align:start position:0% +perpendicular direction this is usually +not possible without things like + + align:start position:0% +not possible without things like + + + align:start position:0% +not possible without things like +radiation damage or very high + + align:start position:0% +radiation damage or very high + + + align:start position:0% +radiation damage or very high +temperature and then to make things even + + align:start position:0% +temperature and then to make things even + + + align:start position:0% +temperature and then to make things even +crazier you can also have what's called + + align:start position:0% +crazier you can also have what's called + + + align:start position:0% +crazier you can also have what's called +loops of dislocations some videos of + + align:start position:0% +loops of dislocations some videos of + + + align:start position:0% +loops of dislocations some videos of +which I'll actually get to show you you + + align:start position:0% +which I'll actually get to show you you + + + align:start position:0% +which I'll actually get to show you you +can have a dislocation that has part + + align:start position:0% +can have a dislocation that has part + + + align:start position:0% +can have a dislocation that has part +edge character part screw character if + + align:start position:0% +edge character part screw character if + + + align:start position:0% +edge character part screw character if +you look at how the atoms are arranged + + align:start position:0% +you look at how the atoms are arranged + + + align:start position:0% +you look at how the atoms are arranged +here you're looking from sort of the top + + align:start position:0% +here you're looking from sort of the top + + + align:start position:0% +here you're looking from sort of the top +down you can see that there's an extra + + align:start position:0% +down you can see that there's an extra + + + align:start position:0% +down you can see that there's an extra +half plane of these white atoms shoved + + align:start position:0% +half plane of these white atoms shoved + + + align:start position:0% +half plane of these white atoms shoved +in in the black ones and this right here + + align:start position:0% +in in the black ones and this right here + + + align:start position:0% +in in the black ones and this right here +would be a completely edge dislocation + + align:start position:0% +would be a completely edge dislocation + + + align:start position:0% +would be a completely edge dislocation +you can have a gradual transition or + + align:start position:0% +you can have a gradual transition or + + + align:start position:0% +you can have a gradual transition or +about ninety degrees later it looks like + + align:start position:0% +about ninety degrees later it looks like + + + align:start position:0% +about ninety degrees later it looks like +a spiral and that's a screw dislocation + + align:start position:0% +a spiral and that's a screw dislocation + + + align:start position:0% +a spiral and that's a screw dislocation +and the net effect of that is when you + + align:start position:0% +and the net effect of that is when you + + + align:start position:0% +and the net effect of that is when you +push in this direction on an edge + + align:start position:0% +push in this direction on an edge + + + align:start position:0% +push in this direction on an edge +dislocation it moves that way when you + + align:start position:0% +dislocation it moves that way when you + + + align:start position:0% +dislocation it moves that way when you +push this direction on a screw + + align:start position:0% +push this direction on a screw + + + align:start position:0% +push this direction on a screw +dislocation it moves that way so when + + align:start position:0% +dislocation it moves that way so when + + + align:start position:0% +dislocation it moves that way so when +you stress out a dislocation loop it + + align:start position:0% +you stress out a dislocation loop it + + + align:start position:0% +you stress out a dislocation loop it +just grows you're not actually creating + + align:start position:0% +just grows you're not actually creating + + + align:start position:0% +just grows you're not actually creating +or destroying matter but what you're + + align:start position:0% +or destroying matter but what you're + + + align:start position:0% +or destroying matter but what you're +doing is causing this small loop of + + align:start position:0% +doing is causing this small loop of + + + align:start position:0% +doing is causing this small loop of +extra half plane of atoms to grow + + align:start position:0% +extra half plane of atoms to grow + + + align:start position:0% +extra half plane of atoms to grow +further and further until it actually + + align:start position:0% +further and further until it actually + + + align:start position:0% +further and further until it actually +reaches some obstacle or the outside of + + align:start position:0% +reaches some obstacle or the outside of + + + align:start position:0% +reaches some obstacle or the outside of +a crystal and these dislocations can + + align:start position:0% +a crystal and these dislocations can + + + align:start position:0% +a crystal and these dislocations can +actually feel the force from each other + + align:start position:0% +actually feel the force from each other + + + align:start position:0% +actually feel the force from each other +if I draw a clean one because I think + + align:start position:0% +if I draw a clean one because I think + + + align:start position:0% +if I draw a clean one because I think +it'll be easier to see if I draw a small + + align:start position:0% +it'll be easier to see if I draw a small + + + align:start position:0% +it'll be easier to see if I draw a small +lattice of atoms here and then a + + align:start position:0% +lattice of atoms here and then a + + + align:start position:0% +lattice of atoms here and then a +dislocation core right there let's say + + align:start position:0% +dislocation core right there let's say + + + align:start position:0% +dislocation core right there let's say +that's our dislocation core this region + + align:start position:0% +that's our dislocation core this region + + + align:start position:0% +that's our dislocation core this region +of space right here is compressively + + align:start position:0% +of space right here is compressively + + + align:start position:0% +of space right here is compressively +stressed there's more atoms in that + + align:start position:0% +stressed there's more atoms in that + + + align:start position:0% +stressed there's more atoms in that +space than there want to be and so it's + + align:start position:0% +space than there want to be and so it's + + + align:start position:0% +space than there want to be and so it's +kind of crammed in there + + align:start position:0% +kind of crammed in there + + + align:start position:0% +kind of crammed in there +well this region right here is in what's + + align:start position:0% +well this region right here is in what's + + + align:start position:0% +well this region right here is in what's +called tensile stress there's almost + + align:start position:0% +called tensile stress there's almost + + + align:start position:0% +called tensile stress there's almost +some space like right here where there's + + align:start position:0% +some space like right here where there's + + + align:start position:0% +some space like right here where there's +notice to few atoms and they kind of + + align:start position:0% +notice to few atoms and they kind of + + + align:start position:0% +notice to few atoms and they kind of +want there to be more and these + + align:start position:0% +want there to be more and these + + + align:start position:0% +want there to be more and these +dislocations can feel neighboring stress + + align:start position:0% +dislocations can feel neighboring stress + + + align:start position:0% +dislocations can feel neighboring stress +fields let's say there was another one + + align:start position:0% +fields let's say there was another one + + + align:start position:0% +fields let's say there was another one +right over here that had its own + + align:start position:0% +right over here that had its own + + + align:start position:0% +right over here that had its own +compressive stress field they'll + + align:start position:0% +compressive stress field they'll + + + align:start position:0% +compressive stress field they'll +actually repel each other because you + + align:start position:0% +actually repel each other because you + + + align:start position:0% +actually repel each other because you +don't want to add even more compressive + + align:start position:0% +don't want to add even more compressive + + + align:start position:0% +don't want to add even more compressive +stress to anywhere in this group of + + align:start position:0% +stress to anywhere in this group of + + + align:start position:0% +stress to anywhere in this group of +atoms so they'll actually repel each + + align:start position:0% +atoms so they'll actually repel each + + + align:start position:0% +atoms so they'll actually repel each +other to the point where if you get two + + align:start position:0% +other to the point where if you get two + + + align:start position:0% +other to the point where if you get two +dislocations too close to each other + + align:start position:0% +dislocations too close to each other + + + align:start position:0% +dislocations too close to each other +they'll uh they'll what's called pileup + + align:start position:0% +they'll uh they'll what's called pileup + + + align:start position:0% +they'll uh they'll what's called pileup +or they'll refuse to move a bit so I + + align:start position:0% +or they'll refuse to move a bit so I + + + align:start position:0% +or they'll refuse to move a bit so I +want to show you some videos we can + + align:start position:0% +want to show you some videos we can + + + align:start position:0% +want to show you some videos we can +actually see these dislocations in this + + align:start position:0% +actually see these dislocations in this + + + align:start position:0% +actually see these dislocations in this +one you see that faint line right there + + align:start position:0% +one you see that faint line right there + + + align:start position:0% +one you see that faint line right there +originating from this area that's + + align:start position:0% +originating from this area that's + + + align:start position:0% +originating from this area that's +actually a dislocation loop under stress + + align:start position:0% +actually a dislocation loop under stress + + + align:start position:0% +actually a dislocation loop under stress +and that's actually growing so what + + align:start position:0% +and that's actually growing so what + + + align:start position:0% +and that's actually growing so what +you're seeing here is an image of + + align:start position:0% +you're seeing here is an image of + + + align:start position:0% +you're seeing here is an image of +electrons passing through material and + + align:start position:0% +electrons passing through material and + + + align:start position:0% +electrons passing through material and +looking at regions of differing contrast + + align:start position:0% +looking at regions of differing contrast + + + align:start position:0% +looking at regions of differing contrast +so wherever there's more atoms or fewer + + align:start position:0% +so wherever there's more atoms or fewer + + + align:start position:0% +so wherever there's more atoms or fewer +atoms it looks darker or lighter and + + align:start position:0% +atoms it looks darker or lighter and + + + align:start position:0% +atoms it looks darker or lighter and +that can tell you what sort of defects + + align:start position:0% +that can tell you what sort of defects + + + align:start position:0% +that can tell you what sort of defects +there are you guys all see that faint + + align:start position:0% +there are you guys all see that faint + + + align:start position:0% +there are you guys all see that faint +line right there + + align:start position:0% +line right there + + + align:start position:0% +line right there +notice how the loop just growing it's + + align:start position:0% +notice how the loop just growing it's + + + align:start position:0% +notice how the loop just growing it's +not like you're moving a line but you're + + align:start position:0% +not like you're moving a line but you're + + + align:start position:0% +not like you're moving a line but you're +literally growing the line out of what + + align:start position:0% +literally growing the line out of what + + + align:start position:0% +literally growing the line out of what +looks like nothing there's other one + + align:start position:0% +looks like nothing there's other one + + + align:start position:0% +looks like nothing there's other one +what we call a a Frank Reed source it's + + align:start position:0% +what we call a a Frank Reed source it's + + + align:start position:0% +what we call a a Frank Reed source it's +a source of dislocation loop so what + + align:start position:0% +a source of dislocation loop so what + + + align:start position:0% +a source of dislocation loop so what +you're seeing here each of these lines + + align:start position:0% +you're seeing here each of these lines + + + align:start position:0% +you're seeing here each of these lines +is a single dislocation and then right + + align:start position:0% +is a single dislocation and then right + + + align:start position:0% +is a single dislocation and then right +there you see that loop suddenly form + + align:start position:0% +there you see that loop suddenly form + + + align:start position:0% +there you see that loop suddenly form +let's let's show you that one again I'll + + align:start position:0% +let's let's show you that one again I'll + + + align:start position:0% +let's let's show you that one again I'll +point on where to look by stressing out + + align:start position:0% +point on where to look by stressing out + + + align:start position:0% +point on where to look by stressing out +materials you can actually create + + align:start position:0% +materials you can actually create + + + align:start position:0% +materials you can actually create +additional dislocation loops + + align:start position:0% +additional dislocation loops + + + align:start position:0% +additional dislocation loops +around here and there it is you guys see + + align:start position:0% +around here and there it is you guys see + + + align:start position:0% +around here and there it is you guys see +that one yeah out of what looks like + + align:start position:0% +that one yeah out of what looks like + + + align:start position:0% +that one yeah out of what looks like +nothing but is actually just a couple of + + align:start position:0% +nothing but is actually just a couple of + + + align:start position:0% +nothing but is actually just a couple of +atomic defects you can create a + + align:start position:0% +atomic defects you can create a + + + align:start position:0% +atomic defects you can create a +dislocation loop and allow more plastic + + align:start position:0% +dislocation loop and allow more plastic + + + align:start position:0% +dislocation loop and allow more plastic +deformation to take place which i think + + align:start position:0% +deformation to take place which i think + + + align:start position:0% +deformation to take place which i think +is awesome + + align:start position:0% +is awesome + + + align:start position:0% +is awesome +see this one another dislocation source + + align:start position:0% +see this one another dislocation source + + + align:start position:0% +see this one another dislocation source +in germanium it's a little easier to see + + align:start position:0% +in germanium it's a little easier to see + + + align:start position:0% +in germanium it's a little easier to see +also because it's making this sort of + + align:start position:0% +also because it's making this sort of + + + align:start position:0% +also because it's making this sort of +spiral set of dislocations a little + + align:start position:0% +spiral set of dislocations a little + + + align:start position:0% +spiral set of dislocations a little +slower so you can track its motion a + + align:start position:0% +slower so you can track its motion a + + + align:start position:0% +slower so you can track its motion a +little easier notice how they all kind + + align:start position:0% +little easier notice how they all kind + + + align:start position:0% +little easier notice how they all kind +of line up on certain atomic planes yeah + + align:start position:0% + + + + align:start position:0% + +the topology will change let's say if it + + align:start position:0% +the topology will change let's say if it + + + align:start position:0% +the topology will change let's say if it +hits another optical or another + + align:start position:0% +hits another optical or another + + + align:start position:0% +hits another optical or another +dislocation yeah they can slam into each + + align:start position:0% +dislocation yeah they can slam into each + + + align:start position:0% +dislocation yeah they can slam into each +other and change topology all sorts of + + align:start position:0% +other and change topology all sorts of + + + align:start position:0% +other and change topology all sorts of +things yeah that's a subject for a whole + + align:start position:0% +things yeah that's a subject for a whole + + + align:start position:0% +things yeah that's a subject for a whole +nother class I'd say I want to skip + + align:start position:0% +nother class I'd say I want to skip + + + align:start position:0% +nother class I'd say I want to skip +ahead to the pileup because I think this + + align:start position:0% +ahead to the pileup because I think this + + + align:start position:0% +ahead to the pileup because I think this +kind of gets the point across but + + align:start position:0% +kind of gets the point across but + + + align:start position:0% +kind of gets the point across but +there's actually we can see direct + + align:start position:0% +there's actually we can see direct + + + align:start position:0% +there's actually we can see direct +evidence that dislocations feel each + + align:start position:0% +evidence that dislocations feel each + + + align:start position:0% +evidence that dislocations feel each +other's stress fields when you get + + align:start position:0% +other's stress fields when you get + + + align:start position:0% +other's stress fields when you get +enough of them lined up they won't + + align:start position:0% +enough of them lined up they won't + + + align:start position:0% +enough of them lined up they won't +overlap they actually push each other in + + align:start position:0% +overlap they actually push each other in + + + align:start position:0% +overlap they actually push each other in +a kind of dislocation traffic jam + + align:start position:0% +a kind of dislocation traffic jam + + + align:start position:0% +a kind of dislocation traffic jam +because that what's happening on the + + align:start position:0% +because that what's happening on the + + + align:start position:0% +because that what's happening on the +atomic level is they feel each other + + align:start position:0% +atomic level is they feel each other + + + align:start position:0% +atomic level is they feel each other +stress fields there might be a source of + + align:start position:0% +stress fields there might be a source of + + + align:start position:0% +stress fields there might be a source of +dislocations further away but when they + + align:start position:0% +dislocations further away but when they + + + align:start position:0% +dislocations further away but when they +get too close to each other it literally + + align:start position:0% +get too close to each other it literally + + + align:start position:0% +get too close to each other it literally +is a dislocation traffic jam I mean if + + align:start position:0% +is a dislocation traffic jam I mean if + + + align:start position:0% +is a dislocation traffic jam I mean if +you try and hit the car in front of you + + align:start position:0% +you try and hit the car in front of you + + + align:start position:0% +you try and hit the car in front of you +the repulsion of the electrons between + + align:start position:0% +the repulsion of the electrons between + + + align:start position:0% +the repulsion of the electrons between +your and their bumper will prevent the + + align:start position:0% +your and their bumper will prevent the + + + align:start position:0% +your and their bumper will prevent the +cars from getting a certain distance + + align:start position:0% +cars from getting a certain distance + + + align:start position:0% +cars from getting a certain distance +closer to each other same kind of thing + + align:start position:0% +closer to each other same kind of thing + + + align:start position:0% +closer to each other same kind of thing +here + + align:start position:0% + + + + align:start position:0% + +moving on to grain boundaries a + + align:start position:0% +moving on to grain boundaries a + + + align:start position:0% +moving on to grain boundaries a +two-dimensional defect anytime you have + + align:start position:0% +two-dimensional defect anytime you have + + + align:start position:0% +two-dimensional defect anytime you have +a perfect crystal of atoms that meets + + align:start position:0% +a perfect crystal of atoms that meets + + + align:start position:0% +a perfect crystal of atoms that meets +another perfect crystal at a different + + align:start position:0% +another perfect crystal at a different + + + align:start position:0% +another perfect crystal at a different +orientation where the atoms are arranged + + align:start position:0% +orientation where the atoms are arranged + + + align:start position:0% +orientation where the atoms are arranged +in a different direction you end up with + + align:start position:0% +in a different direction you end up with + + + align:start position:0% +in a different direction you end up with +a boundary between them that we refer to + + align:start position:0% +a boundary between them that we refer to + + + align:start position:0% +a boundary between them that we refer to +as a grain boundary so you can actually + + align:start position:0% +as a grain boundary so you can actually + + + align:start position:0% +as a grain boundary so you can actually +see this is a direct physical image of + + align:start position:0% +see this is a direct physical image of + + + align:start position:0% +see this is a direct physical image of +atoms of two different crystals meaning + + align:start position:0% +atoms of two different crystals meaning + + + align:start position:0% +atoms of two different crystals meaning +at the grain boundary again taken in the + + align:start position:0% +at the grain boundary again taken in the + + + align:start position:0% +at the grain boundary again taken in the +transmission electron microscope so for + + align:start position:0% +transmission electron microscope so for + + + align:start position:0% +transmission electron microscope so for +those who didn't know yes we can see + + align:start position:0% +those who didn't know yes we can see + + + align:start position:0% +those who didn't know yes we can see +individual atoms and the defect + + align:start position:0% +individual atoms and the defect + + + align:start position:0% +individual atoms and the defect +between them I definitely didn't know + + align:start position:0% +between them I definitely didn't know + + + align:start position:0% +between them I definitely didn't know +that in high school they didn't even + + align:start position:0% +that in high school they didn't even + + + align:start position:0% +that in high school they didn't even +mention that whatsoever did you guys + + align:start position:0% +mention that whatsoever did you guys + + + align:start position:0% +mention that whatsoever did you guys +ever seen images like this anyone yes + + align:start position:0% +ever seen images like this anyone yes + + + align:start position:0% +ever seen images like this anyone yes +raise your hand just one okay so yeah + + align:start position:0% +raise your hand just one okay so yeah + + + align:start position:0% +raise your hand just one okay so yeah +it's important for you guys to know that + + align:start position:0% +it's important for you guys to know that + + + align:start position:0% +it's important for you guys to know that +we can have direct evidence for all this + + align:start position:0% +we can have direct evidence for all this + + + align:start position:0% +we can have direct evidence for all this +blackboard stuff because you can see + + align:start position:0% +blackboard stuff because you can see + + + align:start position:0% +blackboard stuff because you can see +atoms in the transmission electron + + align:start position:0% +atoms in the transmission electron + + + align:start position:0% +atoms in the transmission electron +microscope and see what happens when the + + align:start position:0% +microscope and see what happens when the + + + align:start position:0% +microscope and see what happens when the +two of them meet you see this kind of + + align:start position:0% +two of them meet you see this kind of + + + align:start position:0% +two of them meet you see this kind of +regular structure of empty space where + + align:start position:0% +regular structure of empty space where + + + align:start position:0% +regular structure of empty space where +this grain boundary meets right you can + + align:start position:0% +this grain boundary meets right you can + + + align:start position:0% +this grain boundary meets right you can +actually model it as a line of 1d + + align:start position:0% +actually model it as a line of 1d + + + align:start position:0% +actually model it as a line of 1d +dislocations because you take a line of + + align:start position:0% +dislocations because you take a line of + + + align:start position:0% +dislocations because you take a line of +1d lines you end up with a 2d boundary + + align:start position:0% +1d lines you end up with a 2d boundary + + + align:start position:0% +1d lines you end up with a 2d boundary +which you can see very clearly here it's + + align:start position:0% +which you can see very clearly here it's + + + align:start position:0% +which you can see very clearly here it's +almost like there's an extra half plane + + align:start position:0% +almost like there's an extra half plane + + + align:start position:0% +almost like there's an extra half plane +right there another one there another + + align:start position:0% +right there another one there another + + + align:start position:0% +right there another one there another +one there and another one there and we + + align:start position:0% +one there and another one there and we + + + align:start position:0% +one there and another one there and we +call that a tilt grain boundary grain + + align:start position:0% +call that a tilt grain boundary grain + + + align:start position:0% +call that a tilt grain boundary grain +boundaries are nice in that they can + + align:start position:0% +boundaries are nice in that they can + + + align:start position:0% +boundaries are nice in that they can +accommodate lots of these little zero + + align:start position:0% +accommodate lots of these little zero + + + align:start position:0% +accommodate lots of these little zero +dimensional defects moving to them + + align:start position:0% +dimensional defects moving to them + + + align:start position:0% +dimensional defects moving to them +without getting destroyed so grain + + align:start position:0% +without getting destroyed so grain + + + align:start position:0% +without getting destroyed so grain +boundaries are one of those ways that + + align:start position:0% +boundaries are one of those ways that + + + align:start position:0% +boundaries are one of those ways that +radiation damage can be removed and + + align:start position:0% +radiation damage can be removed and + + + align:start position:0% +radiation damage can be removed and +that's one of the reasons why most small + + align:start position:0% +that's one of the reasons why most small + + + align:start position:0% +that's one of the reasons why most small +grain materials are really nano grain + + align:start position:0% +grain materials are really nano grain + + + align:start position:0% +grain materials are really nano grain +materials are more resistant to + + align:start position:0% +materials are more resistant to + + + align:start position:0% +materials are more resistant to +radiation damage than large grain ones + + align:start position:0% +radiation damage than large grain ones + + + align:start position:0% +radiation damage than large grain ones +because they act as what's called sinks + + align:start position:0% +because they act as what's called sinks + + + align:start position:0% +because they act as what's called sinks +or destroyers of radiation damage + + align:start position:0% +or destroyers of radiation damage + + + align:start position:0% +or destroyers of radiation damage +there's another kind of 2d defect called + + align:start position:0% +there's another kind of 2d defect called + + + align:start position:0% +there's another kind of 2d defect called +a twin where you can actually get a + + align:start position:0% +a twin where you can actually get a + + + align:start position:0% +a twin where you can actually get a +little chunk of atoms sort of switch + + align:start position:0% +little chunk of atoms sort of switch + + + align:start position:0% +little chunk of atoms sort of switch +orientation and you can see these very + + align:start position:0% +orientation and you can see these very + + + align:start position:0% +orientation and you can see these very +clearly in again TEM micrographs and the + + align:start position:0% +clearly in again TEM micrographs and the + + + align:start position:0% +clearly in again TEM micrographs and the +evidence actually that the twin actually + + align:start position:0% +evidence actually that the twin actually + + + align:start position:0% +evidence actually that the twin actually +is a different physical arrangement of + + align:start position:0% +is a different physical arrangement of + + + align:start position:0% +is a different physical arrangement of +atoms even though you can't see the + + align:start position:0% +atoms even though you can't see the + + + align:start position:0% +atoms even though you can't see the +atoms in this little bar in this little + + align:start position:0% +atoms in this little bar in this little + + + align:start position:0% +atoms in this little bar in this little +band right there look at the way the + + align:start position:0% +band right there look at the way the + + + align:start position:0% +band right there look at the way the +dislocations line up those dislocations + + align:start position:0% +dislocations line up those dislocations + + + align:start position:0% +dislocations line up those dislocations +tend to line up in energetically + + align:start position:0% +tend to line up in energetically + + + align:start position:0% +tend to line up in energetically +favorable directions and in this screen + + align:start position:0% +favorable directions and in this screen + + + align:start position:0% +favorable directions and in this screen +they're all this way and in the twin + + align:start position:0% +they're all this way and in the twin + + + align:start position:0% +they're all this way and in the twin +they're all lined up like that and then + + align:start position:0% +they're all lined up like that and then + + + align:start position:0% +they're all lined up like that and then +finally there's the most intuitive + + align:start position:0% +finally there's the most intuitive + + + align:start position:0% +finally there's the most intuitive +defect inclusions a 3d piece of some + + align:start position:0% +defect inclusions a 3d piece of some + + + align:start position:0% +defect inclusions a 3d piece of some +other material inside what would + + align:start position:0% +other material inside what would + + + align:start position:0% +other material inside what would +otherwise be a pure material this one I + + align:start position:0% +otherwise be a pure material this one I + + + align:start position:0% +otherwise be a pure material this one I +actually pulled out of the rotor that + + align:start position:0% +actually pulled out of the rotor that + + + align:start position:0% +actually pulled out of the rotor that +powers the Alka Tour fusion reactor I + + align:start position:0% +powers the Alka Tour fusion reactor I + + + align:start position:0% +powers the Alka Tour fusion reactor I +was asked to do some analysis to find + + align:start position:0% +was asked to do some analysis to find + + + align:start position:0% +was asked to do some analysis to find +out is the structure + + align:start position:0% +out is the structure + + + align:start position:0% +out is the structure +of that road are changing because + + align:start position:0% +of that road are changing because + + + align:start position:0% +of that road are changing because +General Electric who was ensuring this + + align:start position:0% +General Electric who was ensuring this + + + align:start position:0% +General Electric who was ensuring this +rotor said we don't want to insure it + + align:start position:0% +rotor said we don't want to insure it + + + align:start position:0% +rotor said we don't want to insure it +anymore thanks for the premiums but + + align:start position:0% +anymore thanks for the premiums but + + + align:start position:0% +anymore thanks for the premiums but +we're not insuring it anymore and we + + align:start position:0% +we're not insuring it anymore and we + + + align:start position:0% +we're not insuring it anymore and we +said why and they said oh it's + + align:start position:0% +said why and they said oh it's + + + align:start position:0% +said why and they said oh it's +structurally unsound so we said oh yeah + + align:start position:0% +structurally unsound so we said oh yeah + + + align:start position:0% +structurally unsound so we said oh yeah +we'll be back in a year and we'll talk + + align:start position:0% +we'll be back in a year and we'll talk + + + align:start position:0% +we'll be back in a year and we'll talk +about it and we did a lot of this work + + align:start position:0% +about it and we did a lot of this work + + + align:start position:0% +about it and we did a lot of this work +to find out that actually the structure + + align:start position:0% +to find out that actually the structure + + + align:start position:0% +to find out that actually the structure +hadn't really changed since 1954 when it + + align:start position:0% +hadn't really changed since 1954 when it + + + align:start position:0% +hadn't really changed since 1954 when it +was made but what we did also see is we + + align:start position:0% +was made but what we did also see is we + + + align:start position:0% +was made but what we did also see is we +could pop out little precipitates of + + align:start position:0% +could pop out little precipitates of + + + align:start position:0% +could pop out little precipitates of +manganese sulfide so there's always + + align:start position:0% +manganese sulfide so there's always + + + align:start position:0% +manganese sulfide so there's always +sulfur and iron and sulfur tends to be a + + align:start position:0% +sulfur and iron and sulfur tends to be a + + + align:start position:0% +sulfur and iron and sulfur tends to be a +bad actor when it comes to material + + align:start position:0% +bad actor when it comes to material + + + align:start position:0% +bad actor when it comes to material +properties you throw manganese into iron + + align:start position:0% +properties you throw manganese into iron + + + align:start position:0% +properties you throw manganese into iron +to scoop up that sulfur in the form of + + align:start position:0% +to scoop up that sulfur in the form of + + + align:start position:0% +to scoop up that sulfur in the form of +these little precipitates or inclusions + + align:start position:0% +these little precipitates or inclusions + + + align:start position:0% +these little precipitates or inclusions +which were able to see perfectly when we + + align:start position:0% +which were able to see perfectly when we + + + align:start position:0% +which were able to see perfectly when we +did an x-ray map just like the one we + + align:start position:0% +did an x-ray map just like the one we + + + align:start position:0% +did an x-ray map just like the one we +did after the first exam it's like we + + align:start position:0% +did after the first exam it's like we + + + align:start position:0% +did after the first exam it's like we +were looking at chris's copper silver + + align:start position:0% +were looking at chris's copper silver + + + align:start position:0% +were looking at chris's copper silver +alloy mapping out where's the copper and + + align:start position:0% +alloy mapping out where's the copper and + + + align:start position:0% +alloy mapping out where's the copper and +silver + + align:start position:0% +silver + + + align:start position:0% +silver +I made this image the same way mapping + + align:start position:0% +I made this image the same way mapping + + + align:start position:0% +I made this image the same way mapping +out where is there iron manganese and + + align:start position:0% +out where is there iron manganese and + + + align:start position:0% +out where is there iron manganese and +sulfur that's how you can tell what it + + align:start position:0% +sulfur that's how you can tell what it + + + align:start position:0% +sulfur that's how you can tell what it +is + + align:start position:0% +is + + + align:start position:0% +is +and so dislocations and defects can + + align:start position:0% +and so dislocations and defects can + + + align:start position:0% +and so dislocations and defects can +actually interact let's say this is the + + align:start position:0% +actually interact let's say this is the + + + align:start position:0% +actually interact let's say this is the +interaction of a 1d defect a dislocation + + align:start position:0% +interaction of a 1d defect a dislocation + + + align:start position:0% +interaction of a 1d defect a dislocation +with a 3d defect avoid if you have a + + align:start position:0% +with a 3d defect avoid if you have a + + + align:start position:0% +with a 3d defect avoid if you have a +material that's deforming plastically + + align:start position:0% +material that's deforming plastically + + + align:start position:0% +material that's deforming plastically +very smoothly and isn't going to undergo + + align:start position:0% +very smoothly and isn't going to undergo + + + align:start position:0% +very smoothly and isn't going to undergo +fracture you want the dislocations to be + + align:start position:0% +fracture you want the dislocations to be + + + align:start position:0% +fracture you want the dislocations to be +able to move if you put anything in + + align:start position:0% +able to move if you put anything in + + + align:start position:0% +able to move if you put anything in +their way they tend to get stuck it's + + align:start position:0% +their way they tend to get stuck it's + + + align:start position:0% +their way they tend to get stuck it's +not easy for that dislocation to shear + + align:start position:0% +not easy for that dislocation to shear + + + align:start position:0% +not easy for that dislocation to shear +through a whole bunch of extra atoms and + + align:start position:0% +through a whole bunch of extra atoms and + + + align:start position:0% +through a whole bunch of extra atoms and +in some cases you can stop the flood + + align:start position:0% +in some cases you can stop the flood + + + align:start position:0% +in some cases you can stop the flood +that motion and favor fracture over slip + + align:start position:0% +that motion and favor fracture over slip + + + align:start position:0% +that motion and favor fracture over slip +so anytime you make slip harder it means + + align:start position:0% +so anytime you make slip harder it means + + + align:start position:0% +so anytime you make slip harder it means +that you're making fracture more likely + + align:start position:0% +that you're making fracture more likely + + + align:start position:0% +that you're making fracture more likely +didn't say you're making it easier but + + align:start position:0% +didn't say you're making it easier but + + + align:start position:0% +didn't say you're making it easier but +you're making it more likely and you + + align:start position:0% +you're making it more likely and you + + + align:start position:0% +you're making it more likely and you +would prefer for materials to deform a + + align:start position:0% +would prefer for materials to deform a + + + align:start position:0% +would prefer for materials to deform a +little bit by a slip then just break by + + align:start position:0% +little bit by a slip then just break by + + + align:start position:0% +little bit by a slip then just break by +fracture so I think now's a good point + + align:start position:0% +fracture so I think now's a good point + + + align:start position:0% +fracture so I think now's a good point +to go over a few key material properties + + align:start position:0% +to go over a few key material properties + + + align:start position:0% +to go over a few key material properties +all of these are sometimes used to + + align:start position:0% +all of these are sometimes used to + + + align:start position:0% +all of these are sometimes used to +describe the same thing in colloquial + + align:start position:0% +describe the same thing in colloquial + + + align:start position:0% +describe the same thing in colloquial +speech that is wrong does anyone hear + + align:start position:0% +speech that is wrong does anyone hear + + + align:start position:0% +speech that is wrong does anyone hear +that anyone here thought that lets say + + align:start position:0% +that anyone here thought that lets say + + + align:start position:0% +that anyone here thought that lets say +stiffness or toughness or strength meant + + align:start position:0% +stiffness or toughness or strength meant + + + align:start position:0% +stiffness or toughness or strength meant +the same thing + + align:start position:0% +the same thing + + + align:start position:0% +the same thing +no okay got a few people it's okay + + align:start position:0% +no okay got a few people it's okay + + + align:start position:0% +no okay got a few people it's okay +because it's used wrong all the time in + + align:start position:0% +because it's used wrong all the time in + + + align:start position:0% +because it's used wrong all the time in +colloquial speech these actually refer + + align:start position:0% +colloquial speech these actually refer + + + align:start position:0% +colloquial speech these actually refer +to different material properties with + + align:start position:0% +to different material properties with + + + align:start position:0% +to different material properties with +different units and we're gonna go into + + align:start position:0% +different units and we're gonna go into + + + align:start position:0% +different units and we're gonna go into +a little bit about what they are and + + align:start position:0% +a little bit about what they are and + + + align:start position:0% +a little bit about what they are and +then show you a few videos to test your + + align:start position:0% +then show you a few videos to test your + + + align:start position:0% +then show you a few videos to test your +intuition about the differences between + + align:start position:0% +intuition about the differences between + + + align:start position:0% +intuition about the differences between +them so first I want to mention what + + align:start position:0% +them so first I want to mention what + + + align:start position:0% +them so first I want to mention what +you're seeing right here is called a + + align:start position:0% +you're seeing right here is called a + + + align:start position:0% +you're seeing right here is called a +stress-strain curve stress is simple + + align:start position:0% +stress-strain curve stress is simple + + + align:start position:0% +stress-strain curve stress is simple +stress is just a force divided by an + + align:start position:0% +stress is just a force divided by an + + + align:start position:0% +stress is just a force divided by an +area and usually the criterion for wheel + + align:start position:0% +area and usually the criterion for wheel + + + align:start position:0% +area and usually the criterion for wheel +and material deform or will it break is + + align:start position:0% +and material deform or will it break is + + + align:start position:0% +and material deform or will it break is +does it reach a certain stress it + + align:start position:0% +does it reach a certain stress it + + + align:start position:0% +does it reach a certain stress it +doesn't matter just how much force you + + align:start position:0% +doesn't matter just how much force you + + + align:start position:0% +doesn't matter just how much force you +put on it but it's like how much force + + align:start position:0% +put on it but it's like how much force + + + align:start position:0% +put on it but it's like how much force +per atom or how much force per area + + align:start position:0% +per atom or how much force per area + + + align:start position:0% +per atom or how much force per area +determines whether bonds are gonna break + + align:start position:0% +determines whether bonds are gonna break + + + align:start position:0% +determines whether bonds are gonna break +and so on the y axis is stress let's say + + align:start position:0% +and so on the y axis is stress let's say + + + align:start position:0% +and so on the y axis is stress let's say +the amount of force per area we're + + align:start position:0% +the amount of force per area we're + + + align:start position:0% +the amount of force per area we're +putting in and strain is the amount of + + align:start position:0% +putting in and strain is the amount of + + + align:start position:0% +putting in and strain is the amount of +deformation so that's stress and strain + + align:start position:0% +deformation so that's stress and strain + + + align:start position:0% +deformation so that's stress and strain +is let's say the change in length over + + align:start position:0% +is let's say the change in length over + + + align:start position:0% +is let's say the change in length over +the original length of some material in + + align:start position:0% +the original length of some material in + + + align:start position:0% +the original length of some material in +what's called the engineering or + + align:start position:0% +what's called the engineering or + + + align:start position:0% +what's called the engineering or +simplified notation and so something + + align:start position:0% +simplified notation and so something + + + align:start position:0% +simplified notation and so something +that is stiff means you can put a lot of + + align:start position:0% +that is stiff means you can put a lot of + + + align:start position:0% +that is stiff means you can put a lot of +force into it but it won't deform very + + align:start position:0% +force into it but it won't deform very + + + align:start position:0% +force into it but it won't deform very +much that's kind of the easiest property + + align:start position:0% +much that's kind of the easiest property + + + align:start position:0% +much that's kind of the easiest property +to understand is something that's very + + align:start position:0% +to understand is something that's very + + + align:start position:0% +to understand is something that's very +stiff will have what's called a high + + align:start position:0% +stiff will have what's called a high + + + align:start position:0% +stiff will have what's called a high +Young's modulus or a high slope right + + align:start position:0% +Young's modulus or a high slope right + + + align:start position:0% +Young's modulus or a high slope right +here something that's super stiff like a + + align:start position:0% +here something that's super stiff like a + + + align:start position:0% +here something that's super stiff like a +ceramic you can really push on it quite + + align:start position:0% +ceramic you can really push on it quite + + + align:start position:0% +ceramic you can really push on it quite +a bit but you won't get it to deform + + align:start position:0% +a bit but you won't get it to deform + + + align:start position:0% +a bit but you won't get it to deform +like you would this metal so the + + align:start position:0% +like you would this metal so the + + + align:start position:0% +like you would this metal so the +opposite of stiff I would call compliant + + align:start position:0% +opposite of stiff I would call compliant + + + align:start position:0% +opposite of stiff I would call compliant +not soft this is one of those tricky + + align:start position:0% +not soft this is one of those tricky + + + align:start position:0% +not soft this is one of those tricky +things right there something that stiff + + align:start position:0% +things right there something that stiff + + + align:start position:0% +things right there something that stiff +you try and flex it and it won't flex + + align:start position:0% +you try and flex it and it won't flex + + + align:start position:0% +you try and flex it and it won't flex +something that's compliant you put a + + align:start position:0% +something that's compliant you put a + + + align:start position:0% +something that's compliant you put a +little bit of force into it and it + + align:start position:0% +little bit of force into it and it + + + align:start position:0% +little bit of force into it and it +undergoes some amount of strain and that + + align:start position:0% +undergoes some amount of strain and that + + + align:start position:0% +undergoes some amount of strain and that +slope right there between the stress and + + align:start position:0% +slope right there between the stress and + + + align:start position:0% +slope right there between the stress and +the strain we call the Youngs modulus we + + align:start position:0% +the strain we call the Youngs modulus we + + + align:start position:0% +the strain we call the Youngs modulus we +also note that this part right here is + + align:start position:0% +also note that this part right here is + + + align:start position:0% +also note that this part right here is +what's called the elastic region of + + align:start position:0% +what's called the elastic region of + + + align:start position:0% +what's called the elastic region of +deformation by elastic we mean + + align:start position:0% +deformation by elastic we mean + + + align:start position:0% +deformation by elastic we mean +reversible or it snaps right back so + + align:start position:0% +reversible or it snaps right back so + + + align:start position:0% +reversible or it snaps right back so +right here when I bend this bar and it + + align:start position:0% +right here when I bend this bar and it + + + align:start position:0% +right here when I bend this bar and it +snaps right back + + align:start position:0% +snaps right back + + + align:start position:0% +snaps right back +that's called elastic + + align:start position:0% +that's called elastic + + + align:start position:0% +that's called elastic +formation and it's reversible because + + align:start position:0% +formation and it's reversible because + + + align:start position:0% +formation and it's reversible because +you can bend one way and it snaps right + + align:start position:0% +you can bend one way and it snaps right + + + align:start position:0% +you can bend one way and it snaps right +back if I bent it more which I don't + + align:start position:0% +back if I bent it more which I don't + + + align:start position:0% +back if I bent it more which I don't +want to do because this is a nice + + align:start position:0% +want to do because this is a nice + + + align:start position:0% +want to do because this is a nice +zirconium fuel cladding rod you would + + align:start position:0% +zirconium fuel cladding rod you would + + + align:start position:0% +zirconium fuel cladding rod you would +deform it irreversibly you to bend it + + align:start position:0% +deform it irreversibly you to bend it + + + align:start position:0% +deform it irreversibly you to bend it +permanently and what the undergo what's + + align:start position:0% +permanently and what the undergo what's + + + align:start position:0% +permanently and what the undergo what's +called plastic deformation when you + + align:start position:0% +called plastic deformation when you + + + align:start position:0% +called plastic deformation when you +deviate from the slope and then a little + + align:start position:0% +deviate from the slope and then a little + + + align:start position:0% +deviate from the slope and then a little +bit more stress can cause a lot more + + align:start position:0% +bit more stress can cause a lot more + + + align:start position:0% +bit more stress can cause a lot more +deformation if any guys ever tried + + align:start position:0% +deformation if any guys ever tried + + + align:start position:0% +deformation if any guys ever tried +pulling copper wire apart before that's + + align:start position:0% +pulling copper wire apart before that's + + + align:start position:0% +pulling copper wire apart before that's +something I'd recommend you try for thin + + align:start position:0% +something I'd recommend you try for thin + + + align:start position:0% +something I'd recommend you try for thin +wire so you don't cut your hands well + + align:start position:0% +wire so you don't cut your hands well + + + align:start position:0% +wire so you don't cut your hands well +you may notice is that it's awfully hard + + align:start position:0% +you may notice is that it's awfully hard + + + align:start position:0% +you may notice is that it's awfully hard +to get the copper deforming in the first + + align:start position:0% +to get the copper deforming in the first + + + align:start position:0% +to get the copper deforming in the first +place but as soon as it starts to + + align:start position:0% +place but as soon as it starts to + + + align:start position:0% +place but as soon as it starts to +stretch it gets really easy so this is + + align:start position:0% +stretch it gets really easy so this is + + + align:start position:0% +stretch it gets really easy so this is +something I recommend go to the + + align:start position:0% +something I recommend go to the + + + align:start position:0% +something I recommend go to the +electronics shop or wherever and try it + + align:start position:0% +electronics shop or wherever and try it + + + align:start position:0% +electronics shop or wherever and try it +out on some really thin copper wire if + + align:start position:0% +out on some really thin copper wire if + + + align:start position:0% +out on some really thin copper wire if +it's thick you'll slice through your + + align:start position:0% +it's thick you'll slice through your + + + align:start position:0% +it's thick you'll slice through your +fingers and you don't want to do that + + align:start position:0% +fingers and you don't want to do that + + + align:start position:0% +fingers and you don't want to do that +strength however that's a different and + + align:start position:0% +strength however that's a different and + + + align:start position:0% +strength however that's a different and +that's a different metric where a + + align:start position:0% +that's a different metric where a + + + align:start position:0% +that's a different metric where a +stiffness describes this slope here + + align:start position:0% +stiffness describes this slope here + + + align:start position:0% +stiffness describes this slope here +strength describes the height or the + + align:start position:0% +strength describes the height or the + + + align:start position:0% +strength describes the height or the +stress at which you start to plastically + + align:start position:0% +stress at which you start to plastically + + + align:start position:0% +stress at which you start to plastically +deform they're in different units + + align:start position:0% +deform they're in different units + + + align:start position:0% +deform they're in different units +stiffness is in stress over strain + + align:start position:0% +stiffness is in stress over strain + + + align:start position:0% +stiffness is in stress over strain +whereas strength is given as a stress so + + align:start position:0% +whereas strength is given as a stress so + + + align:start position:0% +whereas strength is given as a stress so +when you hear things like the yield + + align:start position:0% +when you hear things like the yield + + + align:start position:0% +when you hear things like the yield +stress or the ultimate tensile stress + + align:start position:0% +stress or the ultimate tensile stress + + + align:start position:0% +stress or the ultimate tensile stress +that's referring to how strong something + + align:start position:0% +that's referring to how strong something + + + align:start position:0% +that's referring to how strong something +is which may have nothing to do with how + + align:start position:0% +is which may have nothing to do with how + + + align:start position:0% +is which may have nothing to do with how +stiff it is toughness is another + + align:start position:0% +stiff it is toughness is another + + + align:start position:0% +stiff it is toughness is another +property toughness is actually kind of + + align:start position:0% +property toughness is actually kind of + + + align:start position:0% +property toughness is actually kind of +like the area under this curve because + + align:start position:0% +like the area under this curve because + + + align:start position:0% +like the area under this curve because +if you do a force and apply it over a + + align:start position:0% +if you do a force and apply it over a + + + align:start position:0% +if you do a force and apply it over a +distance that's like putting work into + + align:start position:0% +distance that's like putting work into + + + align:start position:0% +distance that's like putting work into +the material and it ends up being a unit + + align:start position:0% +the material and it ends up being a unit + + + align:start position:0% +the material and it ends up being a unit +of energy so toughness will tell you how + + align:start position:0% +of energy so toughness will tell you how + + + align:start position:0% +of energy so toughness will tell you how +much energy you have to put into + + align:start position:0% +much energy you have to put into + + + align:start position:0% +much energy you have to put into +something before creating a new free + + align:start position:0% +something before creating a new free + + + align:start position:0% +something before creating a new free +surface otherwise known as fracture and + + align:start position:0% +surface otherwise known as fracture and + + + align:start position:0% +surface otherwise known as fracture and +ductility is how much can you deform it + + align:start position:0% +ductility is how much can you deform it + + + align:start position:0% +ductility is how much can you deform it +before it breaks so it would be like + + align:start position:0% +before it breaks so it would be like + + + align:start position:0% +before it breaks so it would be like +this point right here on the strain axis + + align:start position:0% +this point right here on the strain axis + + + align:start position:0% +this point right here on the strain axis +so I'll so give a little bit more + + align:start position:0% +so I'll so give a little bit more + + + align:start position:0% +so I'll so give a little bit more +examples of what this is all about + + align:start position:0% +examples of what this is all about + + + align:start position:0% +examples of what this is all about +toughness again is actually measured as + + align:start position:0% +toughness again is actually measured as + + + align:start position:0% +toughness again is actually measured as +an energy required to form a free + + align:start position:0% +an energy required to form a free + + + align:start position:0% +an energy required to form a free +surface or propagate a crack let's say + + align:start position:0% +surface or propagate a crack let's say + + + align:start position:0% +surface or propagate a crack let's say +where as something that's ductile it + + align:start position:0% +where as something that's ductile it + + + align:start position:0% +where as something that's ductile it +doesn't necessarily mean + + align:start position:0% +doesn't necessarily mean + + + align:start position:0% +doesn't necessarily mean +it's tough like if you have a piece of + + align:start position:0% +it's tough like if you have a piece of + + + align:start position:0% +it's tough like if you have a piece of +chewed chewing gum you can stretch it + + align:start position:0% +chewed chewing gum you can stretch it + + + align:start position:0% +chewed chewing gum you can stretch it +quite a lot with very little energy and + + align:start position:0% +quite a lot with very little energy and + + + align:start position:0% +quite a lot with very little energy and +then it's excu can say it's extremely + + align:start position:0% +then it's excu can say it's extremely + + + align:start position:0% +then it's excu can say it's extremely +ductile but not very strong a piece of + + align:start position:0% +ductile but not very strong a piece of + + + align:start position:0% +ductile but not very strong a piece of +copper wire you can also stretch at an + + align:start position:0% +copper wire you can also stretch at an + + + align:start position:0% +copper wire you can also stretch at an +extremely far distance but it takes more + + align:start position:0% +extremely far distance but it takes more + + + align:start position:0% +extremely far distance but it takes more +energy to do so so that's both ductile + + align:start position:0% +energy to do so so that's both ductile + + + align:start position:0% +energy to do so so that's both ductile +and strong and then if you apply that + + align:start position:0% +and strong and then if you apply that + + + align:start position:0% +and strong and then if you apply that +force over a certain distance stretching + + align:start position:0% +force over a certain distance stretching + + + align:start position:0% +force over a certain distance stretching +out the wire you can also reveal some of + + align:start position:0% +out the wire you can also reveal some of + + + align:start position:0% +out the wire you can also reveal some of +its toughness and how much energy it + + align:start position:0% +its toughness and how much energy it + + + align:start position:0% +its toughness and how much energy it +takes to stretch that wire before it + + align:start position:0% +takes to stretch that wire before it + + + align:start position:0% +takes to stretch that wire before it +breaks hardness is the last material + + align:start position:0% +breaks hardness is the last material + + + align:start position:0% +breaks hardness is the last material +property I want to mention which is not + + align:start position:0% +property I want to mention which is not + + + align:start position:0% +property I want to mention which is not +any of the ones that I showed on the + + align:start position:0% +any of the ones that I showed on the + + + align:start position:0% +any of the ones that I showed on the +stress-strain curve hardness is the + + align:start position:0% +stress-strain curve hardness is the + + + align:start position:0% +stress-strain curve hardness is the +resistance to a little bit of plastic + + align:start position:0% +resistance to a little bit of plastic + + + align:start position:0% +resistance to a little bit of plastic +deformation so assuming that you're + + align:start position:0% +deformation so assuming that you're + + + align:start position:0% +deformation so assuming that you're +already here how much more energy do you + + align:start position:0% +already here how much more energy do you + + + align:start position:0% +already here how much more energy do you +have to put in to get the material to + + align:start position:0% +have to put in to get the material to + + + align:start position:0% +have to put in to get the material to +deform plastically so very different + + align:start position:0% +deform plastically so very different + + + align:start position:0% +deform plastically so very different +material properties all try and mention + + align:start position:0% +material properties all try and mention + + + align:start position:0% +material properties all try and mention +all what they are so if we have a + + align:start position:0% +all what they are so if we have a + + + align:start position:0% +all what they are so if we have a +stress-strain curve like so and it + + align:start position:0% +stress-strain curve like so and it + + + align:start position:0% +stress-strain curve like so and it +follows the elastic region and then + + align:start position:0% +follows the elastic region and then + + + align:start position:0% +follows the elastic region and then +deforms plastically this point what here + + align:start position:0% +deforms plastically this point what here + + + align:start position:0% +deforms plastically this point what here +is what we call the yield strength + + align:start position:0% + + + + align:start position:0% + +whatever that point on the stress axis + + align:start position:0% +whatever that point on the stress axis + + + align:start position:0% +whatever that point on the stress axis +is this point right here our strain to + + align:start position:0% +is this point right here our strain to + + + align:start position:0% +is this point right here our strain to +failure we can use as a measure of + + align:start position:0% +failure we can use as a measure of + + + align:start position:0% +failure we can use as a measure of +ductility this slope right here refers + + align:start position:0% +ductility this slope right here refers + + + align:start position:0% +ductility this slope right here refers +to the stiffness and finally this energy + + align:start position:0% +to the stiffness and finally this energy + + + align:start position:0% +to the stiffness and finally this energy +right here is something like the + + align:start position:0% +right here is something like the + + + align:start position:0% +right here is something like the +toughness and the hardness isn't quite + + align:start position:0% +toughness and the hardness isn't quite + + + align:start position:0% +toughness and the hardness isn't quite +on this plot so I want to see if you + + align:start position:0% +on this plot so I want to see if you + + + align:start position:0% +on this plot so I want to see if you +guys intuitively understand this because + + align:start position:0% +guys intuitively understand this because + + + align:start position:0% +guys intuitively understand this because +the next lecture I'm going to be + + align:start position:0% +the next lecture I'm going to be + + + align:start position:0% +the next lecture I'm going to be +throwing around the words like stiffness + + align:start position:0% +throwing around the words like stiffness + + + align:start position:0% +throwing around the words like stiffness +toughness ductility hardness compliance + + align:start position:0% +toughness ductility hardness compliance + + + align:start position:0% +toughness ductility hardness compliance +hard soft whatever and I want to make + + align:start position:0% +hard soft whatever and I want to make + + + align:start position:0% +hard soft whatever and I want to make +sure that you just at least intuitively + + align:start position:0% +sure that you just at least intuitively + + + align:start position:0% +sure that you just at least intuitively +understand so there's a few videos you + + align:start position:0% +understand so there's a few videos you + + + align:start position:0% +understand so there's a few videos you +may have seen before anyone here watch + + align:start position:0% +may have seen before anyone here watch + + + align:start position:0% +may have seen before anyone here watch +the hydraulic press Channel + + align:start position:0% +the hydraulic press Channel + + + align:start position:0% +the hydraulic press Channel +there we go finally something that half + + align:start position:0% +there we go finally something that half + + + align:start position:0% +there we go finally something that half +the class does we are going to predict + + align:start position:0% +the class does we are going to predict + + + align:start position:0% +the class does we are going to predict +what's going to happen in each of these + + align:start position:0% +what's going to happen in each of these + + + align:start position:0% +what's going to happen in each of these +cases based on these material properties + + align:start position:0% +cases based on these material properties + + + align:start position:0% +cases based on these material properties +so in this case this is a compressor + + align:start position:0% +so in this case this is a compressor + + + align:start position:0% +so in this case this is a compressor +eyes cylinder of co2 it's made of + + align:start position:0% +eyes cylinder of co2 it's made of + + + align:start position:0% +eyes cylinder of co2 it's made of +aluminum + + align:start position:0% +aluminum + + + align:start position:0% +aluminum +which is a very ductile material it's + + align:start position:0% +which is a very ductile material it's + + + align:start position:0% +which is a very ductile material it's +also a very tough material what do you + + align:start position:0% +also a very tough material what do you + + + align:start position:0% +also a very tough material what do you +how do you think it will deform when + + align:start position:0% +how do you think it will deform when + + + align:start position:0% +how do you think it will deform when +smashed anyone ever tried this squishing + + align:start position:0% +smashed anyone ever tried this squishing + + + align:start position:0% +smashed anyone ever tried this squishing +aluminum stuff what happens you compress + + align:start position:0% +aluminum stuff what happens you compress + + + align:start position:0% +aluminum stuff what happens you compress +it and then what happens + + align:start position:0% + + + + align:start position:0% + +will it fracture after a while okay if + + align:start position:0% +will it fracture after a while okay if + + + align:start position:0% +will it fracture after a while okay if +you put a lot of energy into it + + align:start position:0% +you put a lot of energy into it + + + align:start position:0% +you put a lot of energy into it +eventually when you reach this strain to + + align:start position:0% +eventually when you reach this strain to + + + align:start position:0% +eventually when you reach this strain to +failure it should fracture but in your + + align:start position:0% +failure it should fracture but in your + + + align:start position:0% +failure it should fracture but in your +personal hands-on experience does + + align:start position:0% +personal hands-on experience does + + + align:start position:0% +personal hands-on experience does +aluminum tend to fracture when you bend + + align:start position:0% +aluminum tend to fracture when you bend + + + align:start position:0% +aluminum tend to fracture when you bend +it a little bit + + align:start position:0% +it a little bit + + + align:start position:0% +it a little bit +so then what words would you use to + + align:start position:0% +so then what words would you use to + + + align:start position:0% +so then what words would you use to +describe it based on this curve right + + align:start position:0% +describe it based on this curve right + + + align:start position:0% +describe it based on this curve right +here yep ductile I say yep ductile and + + align:start position:0% +here yep ductile I say yep ductile and + + + align:start position:0% +here yep ductile I say yep ductile and +not brittle because you can bend it + + align:start position:0% +not brittle because you can bend it + + + align:start position:0% +not brittle because you can bend it +quite a bit or stretch it quite a bit + + align:start position:0% +quite a bit or stretch it quite a bit + + + align:start position:0% +quite a bit or stretch it quite a bit +before it fractures + + align:start position:0% +before it fractures + + + align:start position:0% +before it fractures +how about stiffness is it really hard or + + align:start position:0% +how about stiffness is it really hard or + + + align:start position:0% +how about stiffness is it really hard or +really easy to get aluminum bending it's + + align:start position:0% +really easy to get aluminum bending it's + + + align:start position:0% +really easy to get aluminum bending it's +fairly easy so would you call that stiff + + align:start position:0% +fairly easy so would you call that stiff + + + align:start position:0% +fairly easy so would you call that stiff +or compliant compliant okay what about + + align:start position:0% +or compliant compliant okay what about + + + align:start position:0% +or compliant compliant okay what about +strength how hard is it to start + + align:start position:0% +strength how hard is it to start + + + align:start position:0% +strength how hard is it to start +deforming aluminum irreversibly compared + + align:start position:0% +deforming aluminum irreversibly compared + + + align:start position:0% +deforming aluminum irreversibly compared +to something like steel not very + + align:start position:0% +to something like steel not very + + + align:start position:0% +to something like steel not very +especially pure aluminum you can almost + + align:start position:0% +especially pure aluminum you can almost + + + align:start position:0% +especially pure aluminum you can almost +you can't you can chew through it if you + + align:start position:0% +you can't you can chew through it if you + + + align:start position:0% +you can't you can chew through it if you +guys ever get a 1 yen coin from Japan + + align:start position:0% +guys ever get a 1 yen coin from Japan + + + align:start position:0% +guys ever get a 1 yen coin from Japan +you can chew through it not very strong + + align:start position:0% +you can chew through it not very strong + + + align:start position:0% +you can chew through it not very strong +and again you know your bite force is + + align:start position:0% +and again you know your bite force is + + + align:start position:0% +and again you know your bite force is +also incredibly strong but anyway let's + + align:start position:0% +also incredibly strong but anyway let's + + + align:start position:0% +also incredibly strong but anyway let's +see what actually happens when you + + align:start position:0% +see what actually happens when you + + + align:start position:0% +see what actually happens when you +compress a rather ductile compliant and + + align:start position:0% +compress a rather ductile compliant and + + + align:start position:0% +compress a rather ductile compliant and +not that strong aluminum canister is it + + align:start position:0% +not that strong aluminum canister is it + + + align:start position:0% +not that strong aluminum canister is it +actually going oh it actually just get + + align:start position:0% +actually going oh it actually just get + + + align:start position:0% +actually going oh it actually just get +the head that's what I wanted was there + + align:start position:0% +the head that's what I wanted was there + + + align:start position:0% +the head that's what I wanted was there +sound + + align:start position:0% + + + + align:start position:0% + +it was also pressurized with co2 but + + align:start position:0% +it was also pressurized with co2 but + + + align:start position:0% +it was also pressurized with co2 but +notice what's left so actually watch in + + align:start position:0% +notice what's left so actually watch in + + + align:start position:0% +notice what's left so actually watch in +slow-mo look how much you can compress + + align:start position:0% +slow-mo look how much you can compress + + + align:start position:0% +slow-mo look how much you can compress +that even after the explosion no + + align:start position:0% +that even after the explosion no + + + align:start position:0% +that even after the explosion no +fracture if you had done that with let's + + align:start position:0% +fracture if you had done that with let's + + + align:start position:0% +fracture if you had done that with let's +say a glass canister what do you guys + + align:start position:0% +say a glass canister what do you guys + + + align:start position:0% +say a glass canister what do you guys +think would have happened would have + + align:start position:0% +think would have happened would have + + + align:start position:0% +think would have happened would have +shattered yeah we'll see that in a bit + + align:start position:0% +shattered yeah we'll see that in a bit + + + align:start position:0% +shattered yeah we'll see that in a bit +with a material that may surprise you it + + align:start position:0% +with a material that may surprise you it + + + align:start position:0% +with a material that may surprise you it +will fracture eventually but the + + align:start position:0% +will fracture eventually but the + + + align:start position:0% +will fracture eventually but the +hydraulic press can't get it that far in + + align:start position:0% +hydraulic press can't get it that far in + + + align:start position:0% +hydraulic press can't get it that far in +compression so that would be something + + align:start position:0% +compression so that would be something + + + align:start position:0% +compression so that would be something +that's extremely ductile not that strong + + align:start position:0% +that's extremely ductile not that strong + + + align:start position:0% +that's extremely ductile not that strong +cuz it wasn't that hard to deform + + align:start position:0% +cuz it wasn't that hard to deform + + + align:start position:0% +cuz it wasn't that hard to deform +certainly we know it wasn't stronger + + align:start position:0% +certainly we know it wasn't stronger + + + align:start position:0% +certainly we know it wasn't stronger +than the steel baseplate that they use + + align:start position:0% +than the steel baseplate that they use + + + align:start position:0% +than the steel baseplate that they use +to do the Smashing because whatever's + + align:start position:0% +to do the Smashing because whatever's + + + align:start position:0% +to do the Smashing because whatever's +the softer material is going to deform + + align:start position:0% +the softer material is going to deform + + + align:start position:0% +the softer material is going to deform +more so here he's gonna have well I'll + + align:start position:0% +more so here he's gonna have well I'll + + + align:start position:0% +more so here he's gonna have well I'll +let him describe it and then I'll let + + align:start position:0% +let him describe it and then I'll let + + + align:start position:0% +let him describe it and then I'll let +you guess what's going to happen + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +what are you guys things gonna happen + + align:start position:0% +what are you guys things gonna happen + + + align:start position:0% +what are you guys things gonna happen +we've got what looks like brass and + + align:start position:0% +we've got what looks like brass and + + + align:start position:0% +we've got what looks like brass and +copper coins on a steel baseplate anyone + + align:start position:0% +copper coins on a steel baseplate anyone + + + align:start position:0% +copper coins on a steel baseplate anyone +have any idea copy yeah everyone's + + align:start position:0% +have any idea copy yeah everyone's + + + align:start position:0% +have any idea copy yeah everyone's +making this motion which means + + align:start position:0% +making this motion which means + + + align:start position:0% +making this motion which means +everything's gonna flatten out right + + align:start position:0% +everything's gonna flatten out right + + + align:start position:0% +everything's gonna flatten out right +let's find out + + align:start position:0% + + + + align:start position:0% + +not nearly as much as you might have + + align:start position:0% +not nearly as much as you might have + + + align:start position:0% +not nearly as much as you might have +expected + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +is anyone surprised by this what + + align:start position:0% +is anyone surprised by this what + + + align:start position:0% +is anyone surprised by this what +happened there what actually happened + + align:start position:0% +happened there what actually happened + + + align:start position:0% +happened there what actually happened +there was already described up here when + + align:start position:0% +there was already described up here when + + + align:start position:0% +there was already described up here when +you get enough dislocations piling up + + align:start position:0% +you get enough dislocations piling up + + + align:start position:0% +you get enough dislocations piling up +against each other during plastic + + align:start position:0% +against each other during plastic + + + align:start position:0% +against each other during plastic +deformation you can undergo a process + + align:start position:0% +deformation you can undergo a process + + + align:start position:0% +deformation you can undergo a process +called work hardening that process can + + align:start position:0% +called work hardening that process can + + + align:start position:0% +called work hardening that process can +be physically described by a lot of + + align:start position:0% +be physically described by a lot of + + + align:start position:0% +be physically described by a lot of +those dislocations piling up and making + + align:start position:0% +those dislocations piling up and making + + + align:start position:0% +those dislocations piling up and making +it more and more difficult to continue + + align:start position:0% +it more and more difficult to continue + + + align:start position:0% +it more and more difficult to continue +that deformation so what happened here + + align:start position:0% +that deformation so what happened here + + + align:start position:0% +that deformation so what happened here +is the brass in the copper which started + + align:start position:0% +is the brass in the copper which started + + + align:start position:0% +is the brass in the copper which started +out quite soft not that hard + + align:start position:0% +out quite soft not that hard + + + align:start position:0% +out quite soft not that hard +quite ductile as you can see and not + + align:start position:0% +quite ductile as you can see and not + + + align:start position:0% +quite ductile as you can see and not +that strong actually got stronger as + + align:start position:0% +that strong actually got stronger as + + + align:start position:0% +that strong actually got stronger as +they were deformed interesting huh did + + align:start position:0% +they were deformed interesting huh did + + + align:start position:0% +they were deformed interesting huh did +anyone expect this to happen okay + + align:start position:0% +anyone expect this to happen okay + + + align:start position:0% +anyone expect this to happen okay +let's go to one that I think everyone + + align:start position:0% +let's go to one that I think everyone + + + align:start position:0% +let's go to one that I think everyone +can guess what's gonna happen a lead + + align:start position:0% +can guess what's gonna happen a lead + + + align:start position:0% +can guess what's gonna happen a lead +ball so has anyone ever tried playing + + align:start position:0% +ball so has anyone ever tried playing + + + align:start position:0% +ball so has anyone ever tried playing +with lead before hopefully not I have + + align:start position:0% +with lead before hopefully not I have + + + align:start position:0% +with lead before hopefully not I have +quite it ok good I'm not alone how would + + align:start position:0% +quite it ok good I'm not alone how would + + + align:start position:0% +quite it ok good I'm not alone how would +you describe lead in terms of the + + align:start position:0% +you describe lead in terms of the + + + align:start position:0% +you describe lead in terms of the +material properties here + + align:start position:0% + + + + align:start position:0% + +yep it's not very stiff it doesn't take + + align:start position:0% +yep it's not very stiff it doesn't take + + + align:start position:0% +yep it's not very stiff it doesn't take +much energy to start deforming it how + + align:start position:0% +much energy to start deforming it how + + + align:start position:0% +much energy to start deforming it how +else + + align:start position:0% + + + + align:start position:0% + +well is it hard or soft okay + + align:start position:0% +well is it hard or soft okay + + + align:start position:0% +well is it hard or soft okay +you think it's ductile or brittle yeah + + align:start position:0% +you think it's ductile or brittle yeah + + + align:start position:0% +you think it's ductile or brittle yeah +you think it's brittle so by that you + + align:start position:0% +you think it's brittle so by that you + + + align:start position:0% +you think it's brittle so by that you +mean it's just gonna break apart right + + align:start position:0% +mean it's just gonna break apart right + + + align:start position:0% +mean it's just gonna break apart right +if you deform it okay cool and would you + + align:start position:0% +if you deform it okay cool and would you + + + align:start position:0% +if you deform it okay cool and would you +say is tough or not tough not a lot of + + align:start position:0% +say is tough or not tough not a lot of + + + align:start position:0% +say is tough or not tough not a lot of +folks have hands-on experience with lead + + align:start position:0% +folks have hands-on experience with lead + + + align:start position:0% +folks have hands-on experience with lead +it's probably good for your brains let's + + align:start position:0% +it's probably good for your brains let's + + + align:start position:0% +it's probably good for your brains let's +find out + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +led pancake so what words would you use + + align:start position:0% +led pancake so what words would you use + + + align:start position:0% +led pancake so what words would you use +to describe what just happened + + align:start position:0% +to describe what just happened + + + align:start position:0% +to describe what just happened +ductile indeed I don't know what sort of + + align:start position:0% +ductile indeed I don't know what sort of + + + align:start position:0% +ductile indeed I don't know what sort of +brittle led was it an alloy that you had + + align:start position:0% +brittle led was it an alloy that you had + + + align:start position:0% +brittle led was it an alloy that you had +been playing with maybe uh-huh okay so + + align:start position:0% +been playing with maybe uh-huh okay so + + + align:start position:0% +been playing with maybe uh-huh okay so +it was a sheet of lead that was easy to + + align:start position:0% +it was a sheet of lead that was easy to + + + align:start position:0% +it was a sheet of lead that was easy to +snap so I would not call lead as a very + + align:start position:0% +snap so I would not call lead as a very + + + align:start position:0% +snap so I would not call lead as a very +tough material because you didn't have + + align:start position:0% +tough material because you didn't have + + + align:start position:0% +tough material because you didn't have +to put a lot of energy into it but did + + align:start position:0% +to put a lot of energy into it but did + + + align:start position:0% +to put a lot of energy into it but did +it deform quite a bit before you snapped + + align:start position:0% +it deform quite a bit before you snapped + + + align:start position:0% +it deform quite a bit before you snapped +it or did it just crumble apart okay so + + align:start position:0% +it or did it just crumble apart okay so + + + align:start position:0% +it or did it just crumble apart okay so +in that case I would call it ductile + + align:start position:0% +in that case I would call it ductile + + + align:start position:0% +in that case I would call it ductile +because it deformed a lot before + + align:start position:0% +because it deformed a lot before + + + align:start position:0% +because it deformed a lot before +breaking but I would not call it tough + + align:start position:0% +breaking but I would not call it tough + + + align:start position:0% +breaking but I would not call it tough +because it took very little energy to + + align:start position:0% +because it took very little energy to + + + align:start position:0% +because it took very little energy to +get it to that breaking point and it + + align:start position:0% +get it to that breaking point and it + + + align:start position:0% +get it to that breaking point and it +wasn't that stiff because it was quite + + align:start position:0% +wasn't that stiff because it was quite + + + align:start position:0% +wasn't that stiff because it was quite +easy to get it let's say it's the amount + + align:start position:0% +easy to get it let's say it's the amount + + + align:start position:0% +easy to get it let's say it's the amount +of energy what it's the amount of stress + + align:start position:0% +of energy what it's the amount of stress + + + align:start position:0% +of energy what it's the amount of stress +you put in versus the strain could be + + align:start position:0% +you put in versus the strain could be + + + align:start position:0% +you put in versus the strain could be +quite low and it would not be very + + align:start position:0% +quite low and it would not be very + + + align:start position:0% +quite low and it would not be very +strong because it didn't take a lot of + + align:start position:0% +strong because it didn't take a lot of + + + align:start position:0% +strong because it didn't take a lot of +energy or stress to get it moving let's + + align:start position:0% +energy or stress to get it moving let's + + + align:start position:0% +energy or stress to get it moving let's +look at another ball in this case a + + align:start position:0% +look at another ball in this case a + + + align:start position:0% +look at another ball in this case a +steel ball bearing what do you guys + + align:start position:0% +steel ball bearing what do you guys + + + align:start position:0% +steel ball bearing what do you guys +think is gonna happen here + + align:start position:0% +think is gonna happen here + + + align:start position:0% +think is gonna happen here +it's gonna shatter so you're guessing + + align:start position:0% +it's gonna shatter so you're guessing + + + align:start position:0% +it's gonna shatter so you're guessing +that the steel is brittle right what + + align:start position:0% +that the steel is brittle right what + + + align:start position:0% +that the steel is brittle right what +else + + align:start position:0% + + + + align:start position:0% + +probably stiff quite stiff and strong + + align:start position:0% +probably stiff quite stiff and strong + + + align:start position:0% +probably stiff quite stiff and strong +yeah I think so too but I don't think + + align:start position:0% +yeah I think so too but I don't think + + + align:start position:0% +yeah I think so too but I don't think +the guy that did this expected that + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +let's surprise anybody + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +yeah quite a surprise right so in this + + align:start position:0% +yeah quite a surprise right so in this + + + align:start position:0% +yeah quite a surprise right so in this +case materials like hardened steel + + align:start position:0% +case materials like hardened steel + + + align:start position:0% +case materials like hardened steel +aren't necessarily that brittle in fact + + align:start position:0% +aren't necessarily that brittle in fact + + + align:start position:0% +aren't necessarily that brittle in fact +you wouldn't want a ball bearing to be + + align:start position:0% +you wouldn't want a ball bearing to be + + + align:start position:0% +you wouldn't want a ball bearing to be +brittle if you get a some small chip in + + align:start position:0% +brittle if you get a some small chip in + + + align:start position:0% +brittle if you get a some small chip in +it or a little bit of grit or sand and + + align:start position:0% +it or a little bit of grit or sand and + + + align:start position:0% +it or a little bit of grit or sand and +the bearings you would shot are the ball + + align:start position:0% +the bearings you would shot are the ball + + + align:start position:0% +the bearings you would shot are the ball +bearing and cause instantaneous failure + + align:start position:0% +bearing and cause instantaneous failure + + + align:start position:0% +bearing and cause instantaneous failure +of the rotating component so what you + + align:start position:0% +of the rotating component so what you + + + align:start position:0% +of the rotating component so what you +actually want out of a high-strength + + align:start position:0% +actually want out of a high-strength + + + align:start position:0% +actually want out of a high-strength +ball bearing is something that's + + align:start position:0% +ball bearing is something that's + + + align:start position:0% +ball bearing is something that's +extremely hard resists deformation so it + + align:start position:0% +extremely hard resists deformation so it + + + align:start position:0% +extremely hard resists deformation so it +doesn't undergo let's say change of + + align:start position:0% +doesn't undergo let's say change of + + + align:start position:0% +doesn't undergo let's say change of +shape that would prevent it from rolling + + align:start position:0% +shape that would prevent it from rolling + + + align:start position:0% +shape that would prevent it from rolling +without friction or with very little + + align:start position:0% +without friction or with very little + + + align:start position:0% +without friction or with very little +friction you want it to be quite stiff + + align:start position:0% +friction you want it to be quite stiff + + + align:start position:0% +friction you want it to be quite stiff +because you don't want the load of + + align:start position:0% +because you don't want the load of + + + align:start position:0% +because you don't want the load of +whatever you're loading onto it to + + align:start position:0% +whatever you're loading onto it to + + + align:start position:0% +whatever you're loading onto it to +deform it but you also don't want it to + + align:start position:0% +deform it but you also don't want it to + + + align:start position:0% +deform it but you also don't want it to +be brittle so it's got to be somewhat + + align:start position:0% +be brittle so it's got to be somewhat + + + align:start position:0% +be brittle so it's got to be somewhat +tough and ductile to prevent sudden + + align:start position:0% +tough and ductile to prevent sudden + + + align:start position:0% +tough and ductile to prevent sudden +failure you'd rather it compress a tiny + + align:start position:0% +failure you'd rather it compress a tiny + + + align:start position:0% +failure you'd rather it compress a tiny +bit than just cracking in half so you + + align:start position:0% +bit than just cracking in half so you + + + align:start position:0% +bit than just cracking in half so you +can make things like ceramic ball + + align:start position:0% +can make things like ceramic ball + + + align:start position:0% +can make things like ceramic ball +bearings which are very brittle very + + align:start position:0% +bearings which are very brittle very + + + align:start position:0% +bearings which are very brittle very +stiff not that tough but also very + + align:start position:0% +stiff not that tough but also very + + + align:start position:0% +stiff not that tough but also very +strong and you just have to make sure + + align:start position:0% +strong and you just have to make sure + + + align:start position:0% +strong and you just have to make sure +that whatever part you make is not going + + align:start position:0% +that whatever part you make is not going + + + align:start position:0% +that whatever part you make is not going +to reach any sort of yield strength + + align:start position:0% +to reach any sort of yield strength + + + align:start position:0% +to reach any sort of yield strength +criterion or crack or anything now the + + align:start position:0% +criterion or crack or anything now the + + + align:start position:0% +criterion or crack or anything now the +last one that's probably the most + + align:start position:0% +last one that's probably the most + + + align:start position:0% +last one that's probably the most +surprising they bought a $4,000 diamond + + align:start position:0% +surprising they bought a $4,000 diamond + + + align:start position:0% +surprising they bought a $4,000 diamond +it's a diamond like that big what do you + + align:start position:0% +it's a diamond like that big what do you + + + align:start position:0% +it's a diamond like that big what do you +know about diamonds as a material in + + align:start position:0% +know about diamonds as a material in + + + align:start position:0% +know about diamonds as a material in +terms of these properties yep both is + + align:start position:0% +terms of these properties yep both is + + + align:start position:0% +terms of these properties yep both is +right they're extremely stiff it's the + + align:start position:0% +right they're extremely stiff it's the + + + align:start position:0% +right they're extremely stiff it's the +hardest material that we know of almost + + align:start position:0% +hardest material that we know of almost + + + align:start position:0% +hardest material that we know of almost +we've made slightly harder ones + + align:start position:0% +we've made slightly harder ones + + + align:start position:0% +we've made slightly harder ones +artificially it's the hardest natural + + align:start position:0% +artificially it's the hardest natural + + + align:start position:0% +artificially it's the hardest natural +material we know of what else do you + + align:start position:0% +material we know of what else do you + + + align:start position:0% +material we know of what else do you +know whether they're strong or tough + + align:start position:0% +know whether they're strong or tough + + + align:start position:0% +know whether they're strong or tough +they're not tough why do you say that + + align:start position:0% +they're not tough why do you say that + + + align:start position:0% +they're not tough why do you say that +and have you seen the video oh wow + + align:start position:0% +and have you seen the video oh wow + + + align:start position:0% +and have you seen the video oh wow +okay what else do we have yeah so you're + + align:start position:0% +okay what else do we have yeah so you're + + + align:start position:0% +okay what else do we have yeah so you're +saying it's not tough you can cut + + align:start position:0% +saying it's not tough you can cut + + + align:start position:0% +saying it's not tough you can cut +diamonds with other diamonds so the + + align:start position:0% +diamonds with other diamonds so the + + + align:start position:0% +diamonds with other diamonds so the +cutting action usually depends on the + + align:start position:0% +cutting action usually depends on the + + + align:start position:0% +cutting action usually depends on the +hardness of the relative hardness of the + + align:start position:0% +hardness of the relative hardness of the + + + align:start position:0% +hardness of the relative hardness of the +material so if you want to polish or cut + + align:start position:0% +material so if you want to polish or cut + + + align:start position:0% +material so if you want to polish or cut +something abrasively you need to use a + + align:start position:0% +something abrasively you need to use a + + + align:start position:0% +something abrasively you need to use a +harder material because then the grit + + align:start position:0% +harder material because then the grit + + + align:start position:0% +harder material because then the grit +itself won't wear away before the + + align:start position:0% +itself won't wear away before the + + + align:start position:0% +itself won't wear away before the +material it's trying to cut but what's + + align:start position:0% +material it's trying to cut but what's + + + align:start position:0% +material it's trying to cut but what's +going to happen here is we're gonna put + + align:start position:0% +going to happen here is we're gonna put + + + align:start position:0% +going to happen here is we're gonna put +a diamond and try compressing it and + + align:start position:0% +a diamond and try compressing it and + + + align:start position:0% +a diamond and try compressing it and +we'll see what its stress-strain curve + + align:start position:0% +we'll see what its stress-strain curve + + + align:start position:0% +we'll see what its stress-strain curve +looks like so votes are what's gonna + + align:start position:0% +looks like so votes are what's gonna + + + align:start position:0% +looks like so votes are what's gonna +happen who says like Monica it's gonna + + align:start position:0% +happen who says like Monica it's gonna + + + align:start position:0% +happen who says like Monica it's gonna +shatter who think it's gonna break the + + align:start position:0% +shatter who think it's gonna break the + + + align:start position:0% +shatter who think it's gonna break the +tools who think it's going to deform + + align:start position:0% +tools who think it's going to deform + + + align:start position:0% +tools who think it's going to deform +plastically yeah I've never seen a + + align:start position:0% +plastically yeah I've never seen a + + + align:start position:0% +plastically yeah I've never seen a +diamond deform plastically + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +oh yeah I could probably still sell + + align:start position:0% +oh yeah I could probably still sell + + + align:start position:0% +oh yeah I could probably still sell +those absolutely no deformation it just + + align:start position:0% +those absolutely no deformation it just + + + align:start position:0% +those absolutely no deformation it just +rotates and explodes yeah this would be + + align:start position:0% +rotates and explodes yeah this would be + + + align:start position:0% +rotates and explodes yeah this would be +a material that we would have say has + + align:start position:0% +a material that we would have say has + + + align:start position:0% +a material that we would have say has +almost zero ductility despite being + + align:start position:0% +almost zero ductility despite being + + + align:start position:0% +almost zero ductility despite being +extremely hard I don't know if there + + align:start position:0% +extremely hard I don't know if there + + + align:start position:0% +extremely hard I don't know if there +would even been enough deformation to + + align:start position:0% +would even been enough deformation to + + + align:start position:0% +would even been enough deformation to +have a slight dent in the tool itself + + align:start position:0% +have a slight dent in the tool itself + + + align:start position:0% +have a slight dent in the tool itself +there's probably a little hole where the + + align:start position:0% +there's probably a little hole where the + + + align:start position:0% +there's probably a little hole where the +point of the diamond poked in but once + + align:start position:0% +point of the diamond poked in but once + + + align:start position:0% +point of the diamond poked in but once +there was enough stress on that diamond + + align:start position:0% +there was enough stress on that diamond + + + align:start position:0% +there was enough stress on that diamond +its stress-strain curve would look + + align:start position:0% +its stress-strain curve would look + + + align:start position:0% +its stress-strain curve would look +something like that maybe like that you + + align:start position:0% +something like that maybe like that you + + + align:start position:0% +something like that maybe like that you +yeah so it's important that you + + align:start position:0% +yeah so it's important that you + + + align:start position:0% +yeah so it's important that you +intuitively understand the differences + + align:start position:0% +intuitively understand the differences + + + align:start position:0% +intuitively understand the differences +between strength ductility hardness + + align:start position:0% +between strength ductility hardness + + + align:start position:0% +between strength ductility hardness +toughness and stiffness because then + + align:start position:0% +toughness and stiffness because then + + + align:start position:0% +toughness and stiffness because then +next class we can explain how radiation + + align:start position:0% +next class we can explain how radiation + + + align:start position:0% +next class we can explain how radiation +changes them so any questions on the + + align:start position:0% +changes them so any questions on the + + + align:start position:0% +changes them so any questions on the +materials and properties from today yeah + + align:start position:0% + + + + align:start position:0% + +mm-hmm so the reason something would be + + align:start position:0% +mm-hmm so the reason something would be + + + align:start position:0% +mm-hmm so the reason something would be +ductile versus brittle is whether or not + + align:start position:0% +ductile versus brittle is whether or not + + + align:start position:0% +ductile versus brittle is whether or not +you can plastically deform it and that + + align:start position:0% +you can plastically deform it and that + + + align:start position:0% +you can plastically deform it and that +means whether or not it's more + + align:start position:0% +means whether or not it's more + + + align:start position:0% +means whether or not it's more +energetically favorable for dislocations + + align:start position:0% +energetically favorable for dislocations + + + align:start position:0% +energetically favorable for dislocations +to keep moving versus just breaking a + + align:start position:0% +to keep moving versus just breaking a + + + align:start position:0% +to keep moving versus just breaking a +plane of atoms in any irregular + + align:start position:0% +plane of atoms in any irregular + + + align:start position:0% +plane of atoms in any irregular +direction and causing fracture so again + + align:start position:0% +direction and causing fracture so again + + + align:start position:0% +direction and causing fracture so again +ductile ductility versus embrittlement + + align:start position:0% +ductile ductility versus embrittlement + + + align:start position:0% +ductile ductility versus embrittlement +is that is the interplay between slip + + align:start position:0% +is that is the interplay between slip + + + align:start position:0% +is that is the interplay between slip +and fracture slip it's normally done by + + align:start position:0% +and fracture slip it's normally done by + + + align:start position:0% +and fracture slip it's normally done by +dislocation movement any defects created + + align:start position:0% +dislocation movement any defects created + + + align:start position:0% +dislocation movement any defects created +by anything especially radiation damage + + align:start position:0% +by anything especially radiation damage + + + align:start position:0% +by anything especially radiation damage +will make slip harder so that any + + align:start position:0% +will make slip harder so that any + + + align:start position:0% +will make slip harder so that any +continued energy you put in will not + + align:start position:0% +continued energy you put in will not + + + align:start position:0% +continued energy you put in will not +move dislocations but move towards + + align:start position:0% +move dislocations but move towards + + + align:start position:0% +move dislocations but move towards +fracture so there's no other questions + + align:start position:0% +fracture so there's no other questions + + + align:start position:0% +fracture so there's no other questions +we'll look at the stress-strain curves + + align:start position:0% +we'll look at the stress-strain curves + + + align:start position:0% +we'll look at the stress-strain curves +of some other familiar materials anyway + + align:start position:0% +of some other familiar materials anyway + + + align:start position:0% +of some other familiar materials anyway +it is ten o'clock in case you guys have + + align:start position:0% +it is ten o'clock in case you guys have + + + align:start position:0% +it is ten o'clock in case you guys have +to go to other classes + + align:start position:0% + + + + align:start position:0% + +yes if you guys have things for nuclear + + align:start position:0% +yes if you guys have things for nuclear + + + align:start position:0% +yes if you guys have things for nuclear +activation analysis handed in do you + + align:start position:0% +activation analysis handed in do you + + + align:start position:0% +activation analysis handed in do you +guys bring stuff in we're running out of + + align:start position:0% +guys bring stuff in we're running out of + + + align:start position:0% +guys bring stuff in we're running out of +opportunities to do this all right in + + align:start position:0% +opportunities to do this all right in + + + align:start position:0% +opportunities to do this all right in +that case entry for the quiz and with + + align:start position:0% +that case entry for the quiz and with + + + align:start position:0% +that case entry for the quiz and with +the entry fee for the quiz will be your + + align:start position:0% +the entry fee for the quiz will be your + + + align:start position:0% +the entry fee for the quiz will be your +nuclear activation analysis sample + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/D8u1LV9CnCk.txt b/D8u1LV9CnCk.txt new file mode 100644 index 0000000000000000000000000000000000000000..47e87991598e2abb5c0f1b5b0bd3381265a28d34 --- /dev/null +++ b/D8u1LV9CnCk.txt @@ -0,0 +1,1227 @@ +align:start position:0% + +hi and welcome back today we're going to + + align:start position:0% +hi and welcome back today we're going to + + + align:start position:0% +hi and welcome back today we're going to +do a problem about the four fundamental + + align:start position:0% +do a problem about the four fundamental + + + align:start position:0% +do a problem about the four fundamental +subspaces so here we have a matrix B B + + align:start position:0% +subspaces so here we have a matrix B B + + + align:start position:0% +subspaces so here we have a matrix B B +is written as the product of a lower + + align:start position:0% +is written as the product of a lower + + + align:start position:0% +is written as the product of a lower +triangular matrix and an upper + + align:start position:0% +triangular matrix and an upper + + + align:start position:0% +triangular matrix and an upper +triangular matrix and we are going to + + align:start position:0% +triangular matrix and we are going to + + + align:start position:0% +triangular matrix and we are going to +find a basis for and compute the + + align:start position:0% +find a basis for and compute the + + + align:start position:0% +find a basis for and compute the +dimension of each of the four + + align:start position:0% +dimension of each of the four + + + align:start position:0% +dimension of each of the four +fundamental subspaces of B now I'll give + + align:start position:0% +fundamental subspaces of B now I'll give + + + align:start position:0% +fundamental subspaces of B now I'll give +you a minute to try that on your own to + + align:start position:0% +you a minute to try that on your own to + + + align:start position:0% +you a minute to try that on your own to +hit pause and then I'll be right back in + + align:start position:0% +hit pause and then I'll be right back in + + + align:start position:0% +hit pause and then I'll be right back in +just a minute and we can do it together + + align:start position:0% + + + + align:start position:0% + +okay we're we're back now the first + + align:start position:0% +okay we're we're back now the first + + + align:start position:0% +okay we're we're back now the first +thing to a notice is that B that is that + + align:start position:0% +thing to a notice is that B that is that + + + align:start position:0% +thing to a notice is that B that is that +this is an Lu decomposition of B so we + + align:start position:0% +this is an Lu decomposition of B so we + + + align:start position:0% +this is an Lu decomposition of B so we +have L here and you here now let's go + + align:start position:0% +have L here and you here now let's go + + + align:start position:0% +have L here and you here now let's go +one space at a time let's start with the + + align:start position:0% +one space at a time let's start with the + + + align:start position:0% +one space at a time let's start with the +column space and first let's just say + + align:start position:0% +column space and first let's just say + + + align:start position:0% +column space and first let's just say +what the dimension of the column space + + align:start position:0% +what the dimension of the column space + + + align:start position:0% +what the dimension of the column space +is okay so let's look at our U matrix + + align:start position:0% +is okay so let's look at our U matrix + + + align:start position:0% +is okay so let's look at our U matrix +how many pivots do we have we have two + + align:start position:0% +how many pivots do we have we have two + + + align:start position:0% +how many pivots do we have we have two +pivots so the column space has dimension + + align:start position:0% +pivots so the column space has dimension + + + align:start position:0% +pivots so the column space has dimension +2 this is the number of pivots good now + + align:start position:0% +2 this is the number of pivots good now + + + align:start position:0% +2 this is the number of pivots good now +how do we find a basis for the column + + align:start position:0% +how do we find a basis for the column + + + align:start position:0% +how do we find a basis for the column +space + + align:start position:0% + + + + align:start position:0% + +how do we find that that a basis well in + + align:start position:0% +how do we find that that a basis well in + + + align:start position:0% +how do we find that that a basis well in +lecture professor Strang had started + + align:start position:0% +lecture professor Strang had started + + + align:start position:0% +lecture professor Strang had started +with a matrix B he did elimination on it + + align:start position:0% +with a matrix B he did elimination on it + + + align:start position:0% +with a matrix B he did elimination on it +and then he took the pivot columns in + + align:start position:0% +and then he took the pivot columns in + + + align:start position:0% +and then he took the pivot columns in +the original matrix and that's great + + align:start position:0% +the original matrix and that's great + + + align:start position:0% +the original matrix and that's great +that works you can also take the pivot + + align:start position:0% +that works you can also take the pivot + + + align:start position:0% +that works you can also take the pivot +columns in the L matrix you can see I + + align:start position:0% +columns in the L matrix you can see I + + + align:start position:0% +columns in the L matrix you can see I +multiplying this this out that it will + + align:start position:0% +multiplying this this out that it will + + + align:start position:0% +multiplying this this out that it will +amount to essentially the same thing so + + align:start position:0% +amount to essentially the same thing so + + + align:start position:0% +amount to essentially the same thing so +a basis for this column space I can just + + align:start position:0% +a basis for this column space I can just + + + align:start position:0% +a basis for this column space I can just +take these these two pivot columns of my + + align:start position:0% +take these these two pivot columns of my + + + align:start position:0% +take these these two pivot columns of my +L matrix 1 2 minus 1 and 0 1 0 good okay + + align:start position:0% +L matrix 1 2 minus 1 and 0 1 0 good okay + + + align:start position:0% +L matrix 1 2 minus 1 and 0 1 0 good okay +so there's the dimension of and a basis + + align:start position:0% +so there's the dimension of and a basis + + + align:start position:0% +so there's the dimension of and a basis +for the column space of B okay next + + align:start position:0% +for the column space of B okay next + + + align:start position:0% +for the column space of B okay next +let's do the null space together ok + + align:start position:0% +let's do the null space together ok + + + align:start position:0% +let's do the null space together ok +what's the dimension of the null space + + align:start position:0% + + + + align:start position:0% + +well the dimension of the null space is + + align:start position:0% +well the dimension of the null space is + + + align:start position:0% +well the dimension of the null space is +always the number of columns minus the + + align:start position:0% +always the number of columns minus the + + + align:start position:0% +always the number of columns minus the +number of pivots right it's the number + + align:start position:0% +number of pivots right it's the number + + + align:start position:0% +number of pivots right it's the number +of free variables so here that's just + + align:start position:0% +of free variables so here that's just + + + align:start position:0% +of free variables so here that's just +one good and how do we find this one + + align:start position:0% +one good and how do we find this one + + + align:start position:0% +one good and how do we find this one +vector in the null space well + + align:start position:0% + + + + align:start position:0% + +well what we do right is we can just + + align:start position:0% +well what we do right is we can just + + + align:start position:0% +well what we do right is we can just +plug in one for our free variable and we + + align:start position:0% +plug in one for our free variable and we + + + align:start position:0% +plug in one for our free variable and we +can back solve to get the other two so + + align:start position:0% +can back solve to get the other two so + + + align:start position:0% +can back solve to get the other two so +this equation tells me that my second + + align:start position:0% +this equation tells me that my second + + + align:start position:0% +this equation tells me that my second +number is negative one and this equation + + align:start position:0% +number is negative one and this equation + + + align:start position:0% +number is negative one and this equation +tells me that that third variable is + + align:start position:0% +tells me that that third variable is + + + align:start position:0% +tells me that that third variable is +negative 3/5 if I can fit it in here + + align:start position:0% + + + + align:start position:0% + +that's a negative 3/5 if you if it's + + align:start position:0% +that's a negative 3/5 if you if it's + + + align:start position:0% +that's a negative 3/5 if you if it's +difficult to see that on the tape okay + + align:start position:0% +difficult to see that on the tape okay + + + align:start position:0% +difficult to see that on the tape okay +now let's move on next to the row space + + align:start position:0% +now let's move on next to the row space + + + align:start position:0% +now let's move on next to the row space +okay so next is the row space so how do + + align:start position:0% +okay so next is the row space so how do + + + align:start position:0% +okay so next is the row space so how do +we find the dimension of the row space + + align:start position:0% +we find the dimension of the row space + + + align:start position:0% +we find the dimension of the row space +I'm going to write row spaces column + + align:start position:0% +I'm going to write row spaces column + + + align:start position:0% +I'm going to write row spaces column +space of B transpose how do we find that + + align:start position:0% +space of B transpose how do we find that + + + align:start position:0% +space of B transpose how do we find that +well well remember that one of our big + + align:start position:0% +well well remember that one of our big + + + align:start position:0% +well well remember that one of our big +facts in this class is that the + + align:start position:0% +facts in this class is that the + + + align:start position:0% +facts in this class is that the +dimension of the row space is the same + + align:start position:0% +dimension of the row space is the same + + + align:start position:0% +dimension of the row space is the same +as the dimension of the column space + + align:start position:0% +as the dimension of the column space + + + align:start position:0% +as the dimension of the column space +it's just the number of pivots so that's + + align:start position:0% +it's just the number of pivots so that's + + + align:start position:0% +it's just the number of pivots so that's +good so it's 2 okay and how do we find a + + align:start position:0% +good so it's 2 okay and how do we find a + + + align:start position:0% +good so it's 2 okay and how do we find a +basis for the row space well there are a + + align:start position:0% +basis for the row space well there are a + + + align:start position:0% +basis for the row space well there are a +couple ways of thinking about this one + + align:start position:0% +couple ways of thinking about this one + + + align:start position:0% +couple ways of thinking about this one +way to thinking about it is we got this + + align:start position:0% +way to thinking about it is we got this + + + align:start position:0% +way to thinking about it is we got this +upper triangular matrix from B by doing + + align:start position:0% +upper triangular matrix from B by doing + + + align:start position:0% +upper triangular matrix from B by doing +elimination and elimination doesn't + + align:start position:0% +elimination and elimination doesn't + + + align:start position:0% +elimination and elimination doesn't +change the row space so I can just use + + align:start position:0% +change the row space so I can just use + + + align:start position:0% +change the row space so I can just use +the two pivot rows of the matrix you + + align:start position:0% +the two pivot rows of the matrix you + + + align:start position:0% +the two pivot rows of the matrix you +good basis for my row space here is I + + align:start position:0% +good basis for my row space here is I + + + align:start position:0% +good basis for my row space here is I +just put these two pivot rows those + + align:start position:0% +just put these two pivot rows those + + + align:start position:0% +just put these two pivot rows those +put I just put those together and I get + + align:start position:0% +put I just put those together and I get + + + align:start position:0% +put I just put those together and I get +a basis for this row space okay the last + + align:start position:0% +a basis for this row space okay the last + + + align:start position:0% +a basis for this row space okay the last +one is always the toughest and the + + align:start position:0% +one is always the toughest and the + + + align:start position:0% +one is always the toughest and the +trickiest we have to do the left null + + align:start position:0% +trickiest we have to do the left null + + + align:start position:0% +trickiest we have to do the left null +space or the null space of B transpose + + align:start position:0% +space or the null space of B transpose + + + align:start position:0% +space or the null space of B transpose +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so first let's compute its dimension + + align:start position:0% +so first let's compute its dimension + + + align:start position:0% +so first let's compute its dimension +what's the dimension of this left null + + align:start position:0% +what's the dimension of this left null + + + align:start position:0% +what's the dimension of this left null +space okay well there's a similar + + align:start position:0% +space okay well there's a similar + + + align:start position:0% +space okay well there's a similar +formula to come to the one we use when + + align:start position:0% +formula to come to the one we use when + + + align:start position:0% +formula to come to the one we use when +we were computing the dimension of the + + align:start position:0% +we were computing the dimension of the + + + align:start position:0% +we were computing the dimension of the +null space it's just the number of rows + + align:start position:0% +null space it's just the number of rows + + + align:start position:0% +null space it's just the number of rows +minus the number of pivots so there are + + align:start position:0% +minus the number of pivots so there are + + + align:start position:0% +minus the number of pivots so there are +three rows our matrix is 3x3 and there + + align:start position:0% +three rows our matrix is 3x3 and there + + + align:start position:0% +three rows our matrix is 3x3 and there +are two pivots so this is just one + + align:start position:0% +are two pivots so this is just one + + + align:start position:0% +are two pivots so this is just one +dimensional again now we need to compute + + align:start position:0% +dimensional again now we need to compute + + + align:start position:0% +dimensional again now we need to compute +now this left null space so let me let + + align:start position:0% +now this left null space so let me let + + + align:start position:0% +now this left null space so let me let +me go go back to our original matrix the + + align:start position:0% +me go go back to our original matrix the + + + align:start position:0% +me go go back to our original matrix the +way to do this is to take B equals Lu + + align:start position:0% +way to do this is to take B equals Lu + + + align:start position:0% +way to do this is to take B equals Lu +and invert L and get EB equals u so we + + align:start position:0% +and invert L and get EB equals u so we + + + align:start position:0% +and invert L and get EB equals u so we +need to move L over to the left hand + + align:start position:0% +need to move L over to the left hand + + + align:start position:0% +need to move L over to the left hand +side okay and if we do that I'm just + + align:start position:0% +side okay and if we do that I'm just + + + align:start position:0% +side okay and if we do that I'm just +gonna write that down here so what's the + + align:start position:0% +gonna write that down here so what's the + + + align:start position:0% +gonna write that down here so what's the +inverse of the L matrix we just get one + + align:start position:0% +inverse of the L matrix we just get one + + + align:start position:0% +inverse of the L matrix we just get one +negative two one zero one one times B is + + align:start position:0% +negative two one zero one one times B is + + + align:start position:0% +negative two one zero one one times B is +our U matrix this upper triangular + + align:start position:0% +our U matrix this upper triangular + + + align:start position:0% +our U matrix this upper triangular +matrix + + align:start position:0% + + + + align:start position:0% + +okay and now now that I've moved L over + + align:start position:0% +okay and now now that I've moved L over + + + align:start position:0% +okay and now now that I've moved L over +to the other side I can read off my the + + align:start position:0% +to the other side I can read off my the + + + align:start position:0% +to the other side I can read off my the +vectors in my left null space now I'm + + align:start position:0% +vectors in my left null space now I'm + + + align:start position:0% +vectors in my left null space now I'm +looking at not my pivot variables but my + + align:start position:0% +looking at not my pivot variables but my + + + align:start position:0% +looking at not my pivot variables but my +free variables because it's some sort of + + align:start position:0% +free variables because it's some sort of + + + align:start position:0% +free variables because it's some sort of +null space but I want to look at this + + align:start position:0% +null space but I want to look at this + + + align:start position:0% +null space but I want to look at this +eeem Atrix so the third row of this + + align:start position:0% +eeem Atrix so the third row of this + + + align:start position:0% +eeem Atrix so the third row of this +email check the third row corresponds to + + align:start position:0% +email check the third row corresponds to + + + align:start position:0% +email check the third row corresponds to +the free row here and when I multiply + + align:start position:0% +the free row here and when I multiply + + + align:start position:0% +the free row here and when I multiply +this by B I just get zeros so this is in + + align:start position:0% +this by B I just get zeros so this is in + + + align:start position:0% +this by B I just get zeros so this is in +the left null space so a basis for this + + align:start position:0% +the left null space so a basis for this + + + align:start position:0% +the left null space so a basis for this +left null space is see if I can fit it + + align:start position:0% +left null space is see if I can fit it + + + align:start position:0% +left null space is see if I can fit it +here just this one zero one good okay + + align:start position:0% +here just this one zero one good okay + + + align:start position:0% +here just this one zero one good okay +so we've found the dimension and of and + + align:start position:0% +so we've found the dimension and of and + + + align:start position:0% +so we've found the dimension and of and +basis for all of the four fundamental + + align:start position:0% +basis for all of the four fundamental + + + align:start position:0% +basis for all of the four fundamental +subspaces before I move on I just want + + align:start position:0% +subspaces before I move on I just want + + + align:start position:0% +subspaces before I move on I just want +to recall which of the L matrix or the U + + align:start position:0% +to recall which of the L matrix or the U + + + align:start position:0% +to recall which of the L matrix or the U +matrix we used for each of these + + align:start position:0% +matrix we used for each of these + + + align:start position:0% +matrix we used for each of these +subspaces so for the column space we + + align:start position:0% +subspaces so for the column space we + + + align:start position:0% +subspaces so for the column space we +used columns the up hibbett columns of + + align:start position:0% +used columns the up hibbett columns of + + + align:start position:0% +used columns the up hibbett columns of +the L matrix for the null space we + + align:start position:0% +the L matrix for the null space we + + + align:start position:0% +the L matrix for the null space we +looked at the U matrix for the row space + + align:start position:0% +looked at the U matrix for the row space + + + align:start position:0% +looked at the U matrix for the row space +we also looked at the U matrix and for + + align:start position:0% +we also looked at the U matrix and for + + + align:start position:0% +we also looked at the U matrix and for +the left null space we needed to invert + + align:start position:0% +the left null space we needed to invert + + + align:start position:0% +the left null space we needed to invert +the L matrix and look at the free row + + align:start position:0% +the L matrix and look at the free row + + + align:start position:0% +the L matrix and look at the free row +okay now the last thing I mean we're + + align:start position:0% +okay now the last thing I mean we're + + + align:start position:0% +okay now the last thing I mean we're +done with the problem but the last thing + + align:start position:0% +done with the problem but the last thing + + + align:start position:0% +done with the problem but the last thing +that's useful is to draw a picture which + + align:start position:0% +that's useful is to draw a picture which + + + align:start position:0% +that's useful is to draw a picture which +I have right here I know in lecture + + align:start position:0% +I have right here I know in lecture + + + align:start position:0% +I have right here I know in lecture +professor Strang is drawing you some + + align:start position:0% +professor Strang is drawing you some + + + align:start position:0% +professor Strang is drawing you some +sort of cartoon pictures of what these + + align:start position:0% +sort of cartoon pictures of what these + + + align:start position:0% +sort of cartoon pictures of what these +subspaces look like but here I want to + + align:start position:0% +subspaces look like but here I want to + + + align:start position:0% +subspaces look like but here I want to +try to actually draw them in a special + + align:start position:0% +try to actually draw them in a special + + + align:start position:0% +try to actually draw them in a special +case so if you can read my drawing here + + align:start position:0% +case so if you can read my drawing here + + + align:start position:0% +case so if you can read my drawing here +what do we have so we have um the the + + align:start position:0% +what do we have so we have um the the + + + align:start position:0% +what do we have so we have um the the +row space here and the null space here + + align:start position:0% + + + + align:start position:0% + +right and so B maps + + align:start position:0% +right and so B maps + + + align:start position:0% +right and so B maps +this this picture into this picture the + + align:start position:0% +this this picture into this picture the + + + align:start position:0% +this this picture into this picture the +null-space here all the scalar multiples + + align:start position:0% +null-space here all the scalar multiples + + + align:start position:0% +null-space here all the scalar multiples +of this vector all go to zero because + + align:start position:0% +of this vector all go to zero because + + + align:start position:0% +of this vector all go to zero because +they're in the null space that's exactly + + align:start position:0% +they're in the null space that's exactly + + + align:start position:0% +they're in the null space that's exactly +what B takes to zero B takes everything + + align:start position:0% +what B takes to zero B takes everything + + + align:start position:0% +what B takes to zero B takes everything +else including the row space into this + + align:start position:0% +else including the row space into this + + + align:start position:0% +else including the row space into this +column space okay and what does B + + align:start position:0% +column space okay and what does B + + + align:start position:0% +column space okay and what does B +transpose do well B transpose kills this + + align:start position:0% +transpose do well B transpose kills this + + + align:start position:0% +transpose do well B transpose kills this +left null space kills this vector and it + + align:start position:0% +left null space kills this vector and it + + + align:start position:0% +left null space kills this vector and it +takes everything else into the row space + + align:start position:0% +takes everything else into the row space + + + align:start position:0% +takes everything else into the row space +into the column space of beat B + + align:start position:0% +into the column space of beat B + + + align:start position:0% +into the column space of beat B +transpose okay thanks for doing this + + align:start position:0% +transpose okay thanks for doing this + + + align:start position:0% +transpose okay thanks for doing this +exercise together + + align:start position:0% +exercise together + + + align:start position:0% +exercise together +I hope this picture is helpful \ No newline at end of file diff --git a/DD0VDr65wmo.txt b/DD0VDr65wmo.txt new file mode 100644 index 0000000000000000000000000000000000000000..0829988af44d377fe8e79e97da2a84dd2b273c31 --- /dev/null +++ b/DD0VDr65wmo.txt @@ -0,0 +1,2332 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation, or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +MARK HARVEY: We have Neil +Leonard with us again. + +You all heard the great +concert we had on Wednesday. + +So we thought we'd +start out just + +by asking if anybody had any +questions or comments based + +or that, that you'd like to ask +the performer while he's here. + +AUDIENCE: Did it go how +you expected it to go? + +NEIL LEONARD: I was +pleased with how it worked. + +I didn't really-- I +wasn't really sure + +how it would all go. + +I kind of had the +basic idea, but there + +was a lot of logistical +stuff to do leading up to it. + +I was finishing a piece of +the final piece we pay played. + +I'd finished that +week, so I just + +had my mind full of +details to take care of. + +But I was really +pleased at how it went. + +And I also was really pleased +because Robin, my collaborator, + +was very enthusiastic and +wanted to do it again. + +And so, that's kind +of like a goal. + +If I do something with +a group of musicians, + +to reach the point where people +would want to do it again. + +Anybody else? + +I think last week I +threatened to make + +everybody ask a question. + +AUDIENCE: Usually I feel +like a lot of the technology + +that people use detracts +from the performance, + +but I felt like, definitely, +in this performance + +it added a lot of value to +what the audience was hearing. + +NEIL LEONARD: How so? + +AUDIENCE: It allows +one person to create + +so much variety of +sound, and the audience + +was able to here all of +the sound at the same time. + +When you're just +playing by yourself, + +there's only so much you can do. + +NEIL LEONARD: I +guess, especially + +if you're playing +a wind instrument. + +I was reading a biography +of this really famous sax + +player, Stan Getz. + +And he did a recording in, +I'm guessing in the '70s, + +with like a echo kind of box. + +Things a tape delay. + +An analog tape delay. + +And he talked about-- +the first recording + +he made was published, +it sounds wonderful--. + +Have you ever heard that, Mark? + +MARK HARVEY: Who's the Guy? + +NEIL LEONARD: Stan Getz. + +Playing through the echo. + +MARK HARVEY: Yes, I have. + +NEIL LEONARD: It's +called "Another World," + +or something like that. + +He plays wonderfully, +but he also + +says that this is a time when, +in the jazz world-- and I think + +that in so-called rock +music, electronics + +were embraced, +and don't really I + +don't remember them +being challenged. + +If Pink Floyd , or Jimi Hendrix, +or somebody had synthesizers, + +that just seemed like it was OK. + +For jazz musicians, it +seemed like it was somehow + +straying from this +tradition that + +shouldn't be tampered with. + +And Stan Getz said that +it felt natural to him. + +And it gave him +something to do, which + +you couldn't do with the sax. + +You play harmony. + +So if he played a delay, +he could play one note, + +and while that note's ringing, +he could play second note, + +and make chords, basically. + +Which he'd never been +able to do before. + +There's also another +instance from around that era + +that caught my attention. + +There was a flute +player named Paul Horn. + +And he did a recording +at the Taj Mahal. + +And I think it was like +this gorilla recording + +where he walked in and +set up his tape deck. + +Now you probably couldn't take +a tape deck into the Taj Mahal. + +I'm guessing. + +Or into the Vatican. + +You'd be screened. + +But he said he pulled the tape +deck out and started to record, + +and it was the same thing. + +It is a very, very +long reverberation, + +so you can build +harmonic structures + +for the flute, which you +can't do in a room like this + +without the use of electronics. + +And so, I don't see a +difference between using the Taj + +Mahal to do that, versus +using, like, analog tape delay. + +If you get to play chords, +and that's a really fun thing + +to play with, then I want to +experiment playing chords. + +If I can get the Taj +Mahal, I'm happy to get it + +but, I'm not going to bring +the Taj Majal to Killian Hall + +downstairs. + +Whatever I bring +is probably going + +to be some kind of +computer software. + +But in principle-- + +AUDIENCE: I wasn't +saying like-- I just + +feel that usually things +don't work as expected. + +People will bring in things, and +mics won't work, or whatever. + +At the end of the +performance, it + +might have been better +if they just played it. + +But in this case, things worked +out the way you wanted them to. + +NEIL LEONARD: Not +everything worked perfectly. + +And I was interested in when +things didn't work perfectly. + +It was still a performance, +and if something doesn't work, + +you go ahead. + +At one point, I put +the wrong page of music + +in the music stand, so +when we got to that point, + +we missed the first Bar. + +But I figured, just go ahead. + +Don't worry about. + +But I also noticed-- and I don't +know if anybody else caught + +this-- but when Robin was +doing the first piece, + +he played one piece of +just kind of like delays, + +and just like a wah +wah on trombone. + +And then he played +a second piece, + +that was-- he started +with a drum pad, + +and started looping that, and +knowing some of those rhythms, + +I knew that if you don't get +the loop right in the drum--. + +You can record it with a kind +of a glitch, which he did. + +And he didn't +remember how to delete + +the last thing he recorded. + +So you just see, do I go +ahead with this thing, + +which is not really perfect? + +And at one point +I could just see, + +like, he's just +going to go with it. + +And put the rest +of the stuff in, + +and start over +dubbing the trombone. + +And start playing on top of it. + +So I could look back and +think of a handful of things + +that, if this is a published +DVD, or published recording, + +you would hope you'd +be able to fix somehow. + +Or have another take +of, or whatever. + +But I think the wonderful +thing about a live performance + +is, it's like how do you get +out of the situation you're in? + +I've seen sax players, +and their neck strap + +breaks during a solo, +and they keep playing. + +Or the snare drum breaks +in the middle of a solo, + +and the drummer keeps playing. + +In a recording, you would stop. + +But in a performance, +it sort of like + +it was like a basketball +game, or something. + +You just can't say, I've +gotta go tie my shoe. + +Everybody wait. + +You just have to +do it, and that's + +a really fascinating kind of +challenge You had a question. + +AUDIENCE: What were you +doing in between solos, + +when you're going +up to your computer. + +Were you changing variables, +or just playing new loops? + +NEIL LEONARD: +Between the pieces? + +AUDIENCE: No. + +NEIL LEONARD: In the piece? + +AUDIENCE: Yes. + +NEIL LEONARD: I'm +trying to remember. + +In the first piece I played--. + +Depends on the piece. + +Sometimes there is +a combination of-- I + +would like to be able to +do everything on the fly, + +and if I had four hands I +could do everything on the fly. + +So I could play the +saxophone, and I + +could be in front +of the computer, + +and make the computer +do its thing. + +So mentally I think +I could do that, too. + +I could set it up so +more hands-on involvement + +with the computer +would be possible, + +but I could still play sax. + +But I only have two hands. + +And the sax is like the banjo. + +Your hands really +have to be there. + +You can't really get them +off, and keep playing. + +You can't get both of +them off and keep playing. + +So some of the music +is created in advance. + +So the stuff, which +I think it played + +in class last week-- +there's a piece I played + +that was like time +stretch voice and bells-- + +we talked about that. + +So that is really +kind of a module + +of a piece that's composed. + +So a lot of time, +it's like working + +in Photoshop or something. + +You sit there and you +work, and you work, + +and you work in sounds. + +And you see if they +need any modifications. + +You see how to combine them. + +You kind of get a sense of the +dramatic flow of the piece. + +You work it out. + +And then you bring that +file to the concert. + +And some of that's playback. + +So some of it's play back, +and some of it's live. + +Anything that sounded like +process saxophone was live. + +But if it sounds like +it was voice, then + +that was a vocalist who was +recorded, and then processed, + +and then kind of montaged. + +So sometimes it was like +triggering the next samples. + +I think in the last +piece I played, + +I made the software for +that just that week, + +if not a couple days before. + +That one I think I managed +to mostly do for the panel. + +But if it was +getting squirrelly, + +I may have gone to +the computer to try + +to get it to behave better. + +So anything from just +triggering files, + +to kind of a small adjustments +to keep it all reined in. + +AUDIENCE: So when you +were playing the pieces, + +I actually thought that some +of the process saxophone + +was recorded. + +As I was watching +your foot and seen + +when you pressed the pedal. + +And it looked like the +pedal did lots of-- I + +initially expected the +pedal would be something + +simple, like the +pedal adds the delay. + +But the pedal caused so +many different effects + +that I assumed some of +the saxophone effects + +has been pre-recorded and the +pedal was playing them back. + +What exactly did you +program the pedal to do? + +NEIL LEONARD: The pedal just +sends a signal to the computer. + +So it's kind of like a mouse. + +It, by itself, is really simple. + +You can read the switches +from the computer. + +But the way the computer +is set up to respond, + +the way I set it up in a concert +to respond to the footwork + +work, was fairly +straightforward. + +The computer does three +things to the sax. + +It will do different +kinds of delays. + +And the delays +will-- maybe when we + +get through, if you're +still interested, + +I could show how the +delay stuff works, + +but-- the delay +business works two ways. + +One is, it makes an echo. + +And the second thing it does, if +you think about the early tape + +delays, they have a tape +loop, that just rotated. + +The tape loop was +played, and then there + +were different playback +heads, to play it back + +at different points. + +So you have one record +head, and then you + +have multiple playback +heads that can be moved. + +And if you move, +they kind of echo. + +The ricochet kind of effect. + +The echo effect changes from +like [MIMING ECHO EFFECT] + +You can change those +echoes where there on time. + +If you move the +playback head, it's + +also a changing the speed +that its reading the tape. + +So if you have a note which +is [MAKES NOTE SOUND]. + +And the tape is going like this. + +And you move the +playback head this way, + +you're going to get +glissando [MAKES NOTE SOUND] + +Because you're increasing the +speed at which the tape is + +passing over the playback head. + +If you move it the +other way, it goes down. + +So in the digital world, +you can get that, too. + +So, the delays are kind of +modeling a tape delay system. + +You can speed up, while you're +sort of moving the playback + +heads, you get +pitch consequences. + +Or kind of result in glassindos, +or glassindi, as well. + +The other, third +thing which makes + +the delay business +complicated, is there's + +a foot pedal which-- +not everything's + +going to delay-- which +changes things radically. + +So if you play a phrase, +and at the end of the phrase + +you feed more of +that into the delay, + +it kind of accentuates +that one thing. + +Sort of like a sustained +pedal on a piano. + +If you put it down for +half of the phrase, + +but not the rest of the +phrase, one part of the phrase + +has this accentuation, or this +effect, that the rest of it + +doesn't have. + +And that can be a +tremendous, dramatic change. + +But to keep it short, +there's a delay. + +There is kind of like +a pitch bend idea. + +There is a flute player +you guys might have heard, + +a gun named Robert Dick, +who made a glissando + +head for the flute. + +And the way it works is, +it slides in and out. + +So you play a note, and +there's a thumb thing. + +And use this thumb thing, +lever, whatever it is, + +to make this head joint slide. + +So I think that the blow +hole's not changing, + +but I think something on +this side of the head joint + +is changing. + +So the glissando flute. + +AUDIENCE: [INAUDIBLE] + +NEIL LEONARD: Is it the +mouth piece that slides? + +I've never actually seen one. + +OK. + +So I wanted to do that +with the saxophone, + +but I resorted to doing +it electronically. + +I wanted, like if +there was a harmonizer, + +there are three voices +playing in harmony. + +I wanted those three +pages all to be variable, + +so they could +slide in real time. + +And I had particular ways in +which I like to slide them. + +But sometimes you +heard a harmony, + +and it sounded like +there was a whammy + +bar, or sort of a glissando. + +I built like a harmonizer with +a glissando mechanism in it. + +And so, the second one. + +And the third one +is really simple. + +I don't use it as much. + +Actually, there's four +things I've been doing. + +The third one was just +a random looping thing. + +It's like so the +random cut and paste. + +So I'd play something +into the computer, + +and it takes snippets of +that, and kind of like + +feeds them back, or +replays them in sort + +of an arbitrary +fashion a real time. + +So it doesn't sound like a +beat-oriented looping effect. + +It's just sending +back fragments of what + +you played in a kind +of unpredictable way. + +So you get a kind of a +stochastic re-compositon, + +or re-improvisiation of +something you played. + +That was the third thing. + +AUDIENCE: The final +one, I just figured out + +a couple days for the concert, +was a kind of freeze effect. + +It's using anybody's intel, +like audio engineering. + +It's using fast Fourier +transforms, which basically + +take a snapshot of +the sound, in terms + +of the pitches that +are in the sound. + +Remember when we looked at that +piece of software last week? + +We took, I think +a trombone sample, + +I think that's what we had. + +And then we were stretching +, and we were cutting it up, + +and playing with it. + +So for software like that, you +can take a so-called frame, + +we'll say it's a +24th of a second, + +and do a spectral analysis +of that 24th of a second. + +And then freeze it. + +Just play those frequencies +in the frequency domain, + +and just hold it. + +And so I have, I think +eight of those going. + +And every time I +hit a peddle, you + +freeze another instance in time. + +So the idea was twofold. + +One was to, again, to +build up harmonies. + +So every time I had a not +that I wanted to freeze, + +I'd hit the peddle, and +that gets sustained. + +But then there was kind +of a poetic idea, which + +is really sort of pun in a way. + +But the song I +playing was playing + +is a song called, +"Round Midnight." + +It's very slow, and +very kind of somber. + +And I thought this idea +also fit with that song, + +because it's like stillness. + +The song is quiet, +slow, still, and this + +would make it extremely still, +because it freezes things. + +So I played around a +little bit with that. + +So those were the things that +you could do with the sax. + +It's actually quite +a bit of stuff. + +And when you think of it, when +you think of what guitarists + +like Jimi Hendrix used, he +didn't have that much stuff. + +He had like fuzz box, +he had wah wah pedal. + +And maybe like one more thing. + +I'm not a guitar +effects connoisseur. + +There isn't a lot of stuff, +but it changes the guitar + +completely. + +So I'm finding +that I, too, don't + +need lots and lots of stuff. + +In fact, the fewer things you +have to use to process the sax, + +the easier it is, because +there's not that many choices. + +So you still think +you're playing + +the sax, with a few, fairly +straight forward things + +you can vary. + +So that's sort of, +I think for Robin + +and myself, soft +of the inspiration. + +We found guitar players +modifying the guitar, + +we think, well, why can't +we do that, as well? + +So, we can. + +We can do it without an +extensive background. + +Robin does not have an extensive +music technology background-- + +or with a different, +more evolved background + +in music technology, +which I have. + +And both of them will work. + +In the case of Robin, he's +such a good trombonist, + +and improviser, that you +give me a couple things, + +and he does great stuff with it. + +Those were some of the +things I was playing around + +with, or using the computer to +do, to extend the performance. + +MARK HARVEY: Let me shift so +we can get our projects in, + +and if people have +questions at the end, + +we will hopefully +have time for that. + +So we have our teams again. + +And so, what I think +we should do is, + +Neil will help with +logistics, if you + +want to set up a computer, +or whatever you have. + +So we should just go. + +And the team should +just say a little bit + +about what it is your idea +is, and then enact it. + +So who would like to go first? + +AUDIENCE: So me and Brian, +we both recorded sounds + +separately. + +I recorded sounds in +my kitchen, and made it + +sort of like a +sound stage thing. + +And then, Brian recorded +some guitar sounds, + +and other sounds he found +[? at the bakery ?], + +and he put on them on this +little mini board, which + +you can play different +sounds and stuff. + +So I'm using Ableton +Live [INAUDIBLE] + +MARK HARVEY: Did you come up +with a design, or a framework, + +or is it just going to +be sort of spontaneous? + +AUDIENCE: The framework +is the kitchen sounds + +kind of form a beat, and we're +going to be going around that. + +[MUSIC SOUNDS] I recorded +most of the sounds here. + +We'll just go into +some of the sounds. + +One was my lamp +switching on and off. + +Another is my +guitar feeding back. + +Another is an +effects pedal that I + +have that does some +really wacky pitch shifts + +and dive bombs, essentially. + +And mine, I was banging +on random things. + +And then I used a +harpoon growler as a jug. + +And some other things. + +I forgot everything. + +Bottle caps. + +[MUSIC PLAYING] + +[MUSIC PLAYING] + +[APPLAUSE] + +NEIL LEONARD: That was cool. + +It sounded like a +voice, that last thing. + +AUDIENCE: Yes, that +actually was my voice. + +NEIL LEONARD: You've +got new careers. + +Very coo. + +AUDIENCE: So we recorded +sounds just on an iPad. + +And then, put them on there. + +And we're just +playing everything. + +About eight different tracks, +[INAUDIBLE], no data tape. + +And we're just going to be +looping those all the time, + +on different tracks, on and off. + +And then, I'm going to briefly +play the piano, at the start. + +And then just come +and control this. + +MARK HARVEY: What +are the sounds? + +AUDIENCE: Right. + +It's sort of more +ambiance, rather than + +snippets of sound bites. + +It's sorta like +longer recordings. + +It's like a shower. + +MARK HARVEY: OK. + +Shower type of-- + +AUDIENCE: Yeah. + +You can figure +out what sort of-- + +MARK HARVEY: So +it's a challenge. + +We've got to figure out +what the sounds are. + +[MUSIC PLAYING] + +[APPLAUSE] + +Did you have that +ending worked out? + +AUDIENCE: Yes. + +That was actually a +recording of a door creaking, + +that had some pitch to it. + +So we decided to use that. + +[INAUDIBLE] + +MARK HARVEY: Very interesting. + +Very interesting. + +Let's give a round of +applause, first of all. + +AUDIENCE: I think a +lot of the other groups + +had some mixed background noise +that they recorded, and then + +improvised with their +instruments on top of that. + +And I was feeling a +little sick, and didn't + +want to play my +trumpet, so I took + +sort of complimentary approach. + +The sounds I recorded +will be the improvisation. + +So I went around my dorm and +recorded 15 different sounds. + +And then wrote a Python +script that sort of generates + +a random way to +play these sounds. + +So at different sections of the +song, like at the beginning, + +it only picks from +a certain number + +of these sounds, all of +which sound like fans. + +At the beginning, it's +like a fan and AC, + +a few other things like that. + +And then as it progresses, it +adds on more of these sounds. + +I have a little solo +section in the middle. + +We'll even hear a couple +of appliances, and noises. + +Big solos, and then it +goes out to some ending. + +So the direction of +the piece is planned, + +but exactly what sound +is played, and when, + +and for how long, +all that is randomly + +generated each time we play it. + +[MUSIC PLAYING] + +[APPLAUSE] + +MARK HARVEY: So +it's your program + +that's doing the improvising? + +AUDIENCE: Yes. + +MARK HARVEY: Very interesting. + +AUDIENCE: So to answer the +other question, what it will do + +is, it will play a sound, +play random sounds, + +wait for a random +amount of time, + +and then play another sound. + +Sometimes it waits until +the sound is finished, + +sometimes it doesn't. + +So that it can be positive, +that can be restive, + +and there can also +be two or three + +sounds playing at the same time. + +The only thing, I put the solos +so there was never two solos + +playing at the same time. + +And I made sure that each +solo was played once. + +But otherwise, all +the other sounds, + +you have multiple [INAUDIBLE]. + +Yes I had the dishwasher sounds +not play until the very end. + +And I closed the +dishwasher a few times + +until I got a nice satisfying +crash and recorded that. + +MARK HARVEY: Did +you break anything? + +OK next contestants. + +AUDIENCE: We +recorded five sounds. + +A door closing, someone typing +on the keyboard, a pencil + +scratching, a zipper, and +a microwave turning on. + +I assigned them to different +keys on the keyboard, here. + +So I'm going to make a +beat with these noises, + +with these sounds, +while they improvise. + +MARK HARVEY: Did you say a beat? + +AUDIENCE: Yeah. + +So I'm using them +mostly as percussion. + +So the sounds were things +that I [INAUDIBLE] homework, + +so I guess that is our theme. + +MARK HARVEY: Homework? + +AUDIENCE: Like you got +the drone or a beat + +or just melody or +some [INAUDIBLE] + +Whatever you want to do. + +[MUSIC PLAYING + +[APPLAUSE] + +MARK HARVEY: So given that's +a sort of existential homework + +moment, what time +of the day or night + +would you project +that to be happening? + +AUDIENCE: After I just ate. + +MARK HARVEY: After you just ate. + +Very cool. + +Very cool. + +OK. + +Another group. + +AUDIENCE: Each of us +had a different idea + +that was discussed +in class last time. + +I think we tried all the +ideas, and none of them + +really worked, because we didn't +have good enough recording + +equipment, and we +weren't good enough + +at using that recording +equipment to effectively do + +anything. + +So we decided on a-- +[INAUDIBLE] So you + +might recognize some +of these Sounds. + +We found a sound +board on the internet. + +Unfortunately it's +mono-phonic, so the amount + +of stuff we could do is +a little bit limited. + +We were planning on +using this sound [PING] + +as a sort of reset button +for between the sections. + +[MUSIC PLAYING] + +[MUSIC PLAYING] + +[APPLAUSE] + +MARK HARVEY: Good. + +Good. + +That the idea. + +AUDIENCE: I don't +feel so guilty saying + +that at times I was +trying to make you + +guys feel uncomfortable. + +[MUSIC PLAYING] + +[APPLAUSE] + +MARK HARVEY: Thanks +for the extra effort. + +That was actually fascinating +to watch you do all that stuff. + +Neil, do you want to +just make a few comments, + +or whatever you want to do. + +NEIL LEONARD: How many people +have done something like this + +before? + +Anybody? + +And suddenly you've +done Ableton Live. + +And how many people +have done Ableton Live? + +One, two. + +So, what have you done +with Ableton Live before? + +AUDIENCE: [INAUDIBLE] Just +learning how to use it. + +I really haven't +been that into it, + +because I feel very limited, +because I haven't actually + +bought the full version. + +NEIL LEONARD: So you're +starting to use it now? + +AUDIENCE: Yeah. + +NEIL LEONARD: OK. + +Just curious. + +AUDIENCE: In the +past, though, I worked + +with Serato Scratch +Live, though. + +Actually, I use that for DJ'ing. + +NEIL LEONARD: OK. + +Yes, but in terms +of-- when I asked + +the question of how many +of you have done something + +like this live, what +I'm wondering about + +is how many people have +recorded sounds on their own, + +and used them in a +musical performance? + +You have? + +For composition. + +OK. + +And performance is a +little bit different, + +but it's a little bit +the same, as well. + +It is really interesting to +hear what you guys came up with, + +not knowing you very well. + +With my Berkeley +students, I always + +feel like, when they bring +in their assignments, + +it sounds so much like them. + +But I have a longer +time to work with them. + +So I can make some +more connections. + +One of the things that came +up in watching you perform, + +is where is the value +in doing something + +you haven't done before, or +something that you may not + +be comfortable with? + +As a sort of +experimental adventure. + +And when I listen to Sarah, +and Ben's and James's piece, + +one of the things which +seems to be interesting, + +is that you guys didn't really +know where it was going to go. + +You didn't know where +it was going to end. + +You said, that's not +quite what we rehearsed. + +And that can be a +really wonderful thing. + +Because the opposite is-- when +I played the concert that you + +saw, if it happened +exactly the way + +it happened a time before, +or happened every time, + +you run the risk +of the spark dying. + +So the excitement of +the performance-- kind + +of like rigor mortis sets in. + +The spontaneity goes +away, and the spark. + +The excitement for +the performer can + +be linked to the spontaneity. + +And you lose the excitement +for the performer, + +and the spontaneity. + +So when you guys +were playing didn't + +know where it was going +to go, I thought, well, + +that's actually a good +thing to just bring up. + +Because that's the +desired effect. + +And it's a struggle +for the improviser, who + +plays for decades, to keep +the thing feeling fresh. + +I know for me, there +are things you can do. + +I guess it's like when +you're performing, + +and you're distracted, or +you're just not really--. + +What I'm getting at is, +for me the performances + +are the least satisfying when +one of two thing happens. + +Either I can't relax, +and get in the play. + +So if it's a concert, +like with Robin, + +for example, if I feel for +any reason uncomfortable, + +if the challenge of it +kinda psych's me out, + +or I don't think I know +the music well enough, + +and I start to play, +and all of a sudden you + +feel that tension, that anxiety +of trying to get to the music. + +It's not like a stage fright, +it's not like a performance + +anxiety, but you feel +like you're forcing it. + +And once you feel like +you're forcing it, + +in a performance of +improvised music, + +you begin to lose a +little bit of control. + +And then the other +thing is if I feel like, + +oh I just played what +I played yesterday. + +I did what I knew +I could do easily. + +Then you don't +discover anything new. + +And I think that what's kind +of fundamental in improvisation + +is this feeling that you're +discovering something new. + +Even if small things +are new, but you + +keeping that little bit +of the activity alive. + +Doing something which is +not necessarily comfortable + +or not something +you've done before + +can sometimes turn +into a big gain. + +The other things I was +thinking about with that piece + +are-- At first I was +thinking I wanted everybody + +to record yourself. + +And then you guys, +Sarah, James, and Ben, + +at first I was a +little bit concerned, + +because you just grabbed some +sounds from the computer, which + +I told you not to do. + +But the thing which I +thought worked really well + +is, we have such a visceral +connection to those sounds. + +They have a tremendous +meaning for us. + +They give us knee +jerk responses, + +Like if my cell phone is +in inadvertently right now. + +And I hear a text message sound, +all of a sudden I kind of jump. + +My body reacts like I +have to do something. + +So those sounds have a +tremendous kind of power. + +And we have very +important associations, + +strong associations, +with those sounds. + +So they're totally loaded, and +the way you played with them, + +I thought was +really, really fun. + +I think that the +Windows operating system + +is more musical than the Mac. + +Side note. + +I'm just putting out +some ideas that I + +was thinking about +listening to everybody play. + +The other thing +I was thinking of + +is-- and this is also very +true in Austin's piece-- + +is that working with computers. + +Computers are not +nearly as responsive + +as a flute, a +violin, as a trumpet. + +You're making music +with your index finger. + +You're not using your whole arm. + +You're not using your mouth. + +You're not using your breathing. + +You're not even +using your hands. + +Are using your index finger. + +You're moving and clicking. + +But I'm also in my +own work, interested + +in the resistance +of the materials. + +So, the computer +is totally limited. + +Or this assignment I gave you. + +Make a performance, it's going +to be three minutes long. + +You only have a week to make it. + +You're going to record +sounds in your own. + +Right there it limits what +you can do quite a bit. + +But when an artist is +presented with limitations, + +it's amazing to see what +artists come up with. + +So the resistance +of the materials + +takes you someplace new. + +So for example, I'm +reviewing a piece of music + +which is very difficult +to improvise on. + +A very complicated +set of chord changes. + +I tried the other day. + +I'm just going to play +with my left hand. + +The metronome was fast, +the harmonic progressions + +really hard. + +I'm playing the same +thing over and over again. + +I'm finding my rut. + +So what if I just play +with my left hand? + +And I tried that for while. + +And all of a sudden, I felt +like I'm getting out of my rut, + +because I had to think +about it differently. + +I had to find new things +that I could do this hand. + +Put them both back +into play again, + +and it feels like it's fresh. + +So the idea of doing this +very short exercise that + +uses this kind of rigid, +somewhat unresponsive tool, + +to make music, has +historically produced + +some really interesting +things that we haven't got out + +of the previous +concert music practice. + +So those are just some of +things I was thinking about. + +I think if we were +to do this again-- + +if this was a four unit +class, of if this was Berkeley + +and you were doing this +as your thesis project-- + +I think the kind of challenges +I found in the last two pieces + +would be very interesting +to continue to explore. + +So what about when you've +overextended yourself. + +And you're playing some +piano, and some violin, + +and some computer. + +Or in my case-- you heard +me in Killian hall-- + +I'm doing delay effects, and +I'm playing back samples, + +and I'm playing saxophone. + +And I'm beginning to +overextend myself. + +It's an interesting +problem, and the solutions + +you found-- it was wonderful +to watch you trying + +to grapple with that +problem, and come up + +with some very +interesting solutions. + +And I am also very +keen on this idea of, + +is there a set of +sounds that you + +can find that have a +really special quality? + +When you hear Glenn Gould +play the Goldberg variations + +on piano-- and the aria +of the Goldberg variations + +is a very, very simple piece-- +and he just sounds phenomenal. + +He's playing quarter notes. + +It's just mind boggling +good, and he has barely + +even started the piece. + +This is amazing. + +It's the way he plays. + +But I guess that's the next +question I have for you guys. + +Are there particular +sounds that you + +hear that would be a +good start to a piece? + +That just have that kind +of mesmerizing effect. + +And they're not +necessarily music. + +I think with the Windows +operating system piece, + +you also had the +advantage of some + +of those micro compositions. + +Like [MAKES NOTE SOUNDS]. + +Whatever that is. + +That's like the shut down +sound, or the boot up sound, + +or something. + +Like there are already kind +of audio jingles, which + +have been very, very +carefully created. + +And we've heard them many times. + +They have tremendous +meaning for us. + +But are there sounds that you +hear in the world around you, + +that would make a really +good beginning of a piece. + +Let's just forget the +whole piece for now. + +Let's just say the +beginning of the piece. + +Something that would +be fantastic to hear + +at the beginning. + +That would be an +interesting thing to pursue. + +I'm trying to remember the +other solo artist in this group. + +Jacob, right? + +Jacob, where I would like +to see that work go is, + +is there a way that you +can share the improvisation + +with the computer? + +So you created a +piece of software + +that basically automates an +idea about improvisation. + +You have an idea of how +the sounds could play. + +Sometimes they play +together, Sometimes + +there's silence between them. + +Sometimes there's 3 over 1. + +Sometimes they're dove +tailing were overlapping. + +Sometimes they're not. + +Is there a way to +extend that so you + +are a physical participant +in the improvisation, + +and the computer is +playing a disembodied you. + +Because basically +what it's doing now + +is like a disembodied you. + +It's your idea implemented +as a program that + +will execute your idea. + +Is there a way to +have two of you? + +The virtual you, which is what +we heard, and the you present. + +So, I'm a teacher, so +I'm always thinking + +for my own students, +what do I do + +to get everybody +to the next step? + +Because we're never done. + +I study all the time. + +I try to learn new stuff. + +I could tell you all about that. + +We don't have the time. + +But I'm always thinking for +you guys, what's the next step? + +And I think that +for Jacob's work, + +that would be a next step. + +I'll just try to +touch on one more. + +Alex, Chelsea, and Chris's, +the homework theme. + +I guess, if you hadn't +told me it was homework. + +I might have been able to +distinguish it from the others. + +But I love the idea of homework. + +And what moment +of homework would + +be really great to zero in on. + +It's so rich. + +Is it like procrastination? + +The feeling that you +learned something new? + +The anxiety of, oh, no +I've got Neil's assignment, + +it's due in and hour +and I haven't started. + +There's all kinds of ways +to think about homework. + +And it's such a central +part of your lives. + +What could you do to +take that another step? + +I think it's a great theme. + +And what could you +do to distinguish it + +from all the other +works we heard? + +So I think that, in short, +all these pieces are really + +wonderful beginnings. + +And I don't think any +of these beginnings + +is more or less +valuable than any other. + +But I guess my bias +is thinking, if we + +were to continue this, +what would be a next step + +to engage in. + +To take the same ideas and +develop them a little bit more? + +MARK HARVEY: Great +thank you so much. + +[APPLAUSE] + +NEIL LEONARD: Thank you. + +It was great to hear your work, +and good to talk to you guys + +about it. + +MARK HARVEY: Great +job everybody. + +Very interesting The +only things I would add + +is that I was interested how +much the percussive element + +came out in a lot +of people's pieces. + +Percussive sounds, the +way you've arranged them, + +and also how the live +instrumentals played with that. + +And actually, very +little silence. + +There were a couple pieces that +had more silence than others, + +but interesting to +think about that. + +So again, more things +to keep in mind. + +NEIL LEONARD: The Windows +piece had great silence. + +MARK HARVEY: Yeah + +NEIL LEONARD: And I +think the performers + +are kept on edge with that. + +MARK HARVEY: It kept +the audience on. + +I didn't know what was going on. + +OK, so please send in +just a little statement + +about what this was, +this project today. + +And your concert reflection +on Neil's concert. + +And we'll see you Wednesday for +something completely different. + +Thank you, thank you. \ No newline at end of file diff --git a/FANl3evX0FQ.txt b/FANl3evX0FQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..ed18207df1f684cdd07a6f8d510caa92302e6636 --- /dev/null +++ b/FANl3evX0FQ.txt @@ -0,0 +1,2852 @@ +MALE SPEAKER: The following +content is provided under a + +Creative Commons License. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So today I +want to finish up + +thinking about circuits. + +And the major topic for +today is just one -- + +thinking about abstractions that +we can use for thinking + +about circuits. + +The attractions are things that +capitalize on linearity. + +And they include things like +[UNINTELLIGIBLE] and + +superposition. + +OK so what I want to +do is finish up + +thinking about circuits. + +And just to get you thinking +about circuits, let's think + +about where we are. + +Last time we saw that one of the +issues in thinking about + +circuit design, is the fact that +every part, in principle, + +interacts with every +other part. + +Which makes the design process +harder than the design process + +was for things like linear +systems, where we thought + +about boxes having inputs +and outputs. + +In linear systems, when we +thought about boxes having + +inputs and outputs, the output +didn't necessarily have any + +affect on the input, +unless there was an + +explicit path feedback. + +In circuits, there's +feedback always. + +There's no way to avoid it. + +And in fact, that coupling can +make thinking about the + +circuits very difficult. + +And we introduce that idea by +just thinking about, even if + +you wanted to close a switch, +you know a circuit, that's + +logically the same as +adding a new part. + +And when you do that, that's +going to change the currents + +and voltages everywhere. + +So that's kind of a big thing-- +that's kind of the + +thing that's different about +circuits from what we've been + +thinking about before. + +Because that complicates design, +we'd like some way of + +dealing with it. + +And the way we introduced, and +the way that you used in the + +lab, so far, has been +to use a buffer. + +We can use an op-amp +to make a buffer. + +And a buffer has this nice +isolation property. + +In this particular circuit, it +has the property that it + +copies this voltage to the +output, regardless of what's + +at the output. + +That means we could put a switch +here, we could change + +the light bulb, we could do +anything we wanted to, and we + +would still know, because of the +properties of the op-amp, + +we would still know that this +voltage is going to be 8 + +Volts, regardless of +what we put there. + +So that's very nice, that gives +us a modularity, that + +gives us a way to +design things. + +It let's us design the left-- + +make a circuit that generates +8 Volts without knowing + +precisely what's going +to be the ultimate + +circuit that that drives. + +So that's nice, it allows +us to do modularity. + +And in many instances, that's +a very good solution. + +In fact in the solution-- in +the problems that you are + +working on in lab, where you're + +trying to drive a motor-- + +that's an excellent solution. + +It's not always an excellent +solution. + +In some sense, it's +very expensive. + +An op-amp is a complicated +part. + +If you were to look inside an +op-amp, there's some two dozen + +transistors in most op-amps. + +So it's not an inexpensive +part, especially when you + +think about this kind of a +circuit that only has three + +parts to the left. + +The op-amp is actually a more +complex device than + +anything else up. + +So op-amps are wonderful, +op-amps allow us to make + +buffers, buffers are wonderful, +but they're not + +always the best solution for +thinking about modularity. + +And, in fact, there's +other ways. + +And so that's what we want to +think about today is -- other + +ways for achieving modularity +in circuit design. + +And the key to thinking about +this, is to think about, well, + +what's the worst thing +that could happen? + +If I changed this part +arbitrarily, just how bad can + +things get? + +So I'll let you answer that. + +Think about that circuit, and +assume that this is a 90 Volt + +power supply, 3 Ohm, 6 Ohm, +but this can change-- + +R0 can change. + +I've tabulated some values of R0 +and putative, corresponding + +values for V0 and I0. + +Are my putative answers right? + +So take a minute, talk to +your neighbor, figure + +out how many of these-- + +let's see-- ten blue numbers +are right or wrong. + +It's very quiet, you are allowed +to talk to people. + +So how many of the numbers +are wrong? + +So raise your hand, indicate +by number fingers how many + +mistakes are in the table. + +More votes, more votes-- + +come on, come on. + +if you had talked more, you +could blame it on your + +neighbor more easily, +so talk quickly. + +OK. + +So does everybody agree +with their neighbor? + +OK, i don't see a single +right answer. + +So take 30 more seconds and +think about it again. + +I don't see any right answers. + +So assume your answer's wrong. + +[CHUCKLES] + +Color blind-- + +OK, so how many of +the voltages and + +currents are incorrect? + +OK, how about a re-vote? + +So how many of the +blue numbers-- + +the currents and voltages, +how many of V0 and I0 -- + +how many of those +are incorrect? + +OK, not very many votes-- + +I'd say about 80% +correct, now. + +That's definitely +an improvement. + +What would have to be true? + +If I wanted to prove that some +of these numbers were wrong, + +what could I do? + +Give me a condition that would +have to be true if the numbers + +were correct. + +AUDIENCE: V0 has to equal I0? + +PROFESSOR: V0 has to equal I0. + +We know that this resistor +better be-- + +better obey Ohm's Law. + +That's what we mean +by that symbol. + +So it had better be the +case that V0 is I0R0. + +So you you'd want this +number to be the + +product of that and that. + +So 0 is the product of 0 and +30, that looks good. + +30 is 2 times 15, 36 is 3 times +12, 48 is 6 times 8. + +60 is-- + +well that's a little marginal. + +how about if I rearrange it +a little bit, and say + +what if R is V/I? + +If I is 0, that would make the +resistor infinity, so there's + +a way of thinking about that +last line as correct. + +That's a little funny. + +Maybe the forward way of +thinking about it is, well + +what if I made the resistor +infinite? + +if I made the resistor infinite, +what would be I? + +0. + +And what would be V? + +What would be the voltage +difference if + +this were right, then? + +The voltage divider-- + +AUDIENCE: Oh, yeah. + +PROFESSOR: So if there's no +current here, then you can use + +the voltage relationship-- +the voltage-divider + +relationship here. + +6 over (3 plus 6) times 90 -- + +which is 60. + +So if you use straightforward +reasoning saying, what if the + +resistor was infinitely large? + +What would happen? + +Then you would conclude that +the bottom line is OK. + +If you choose-- + +if you show that R equals +V over I, are you done? + +What else has to be true +in order for the + +numbers to be true? + +It's not very hard. + +AUDIENCE: The voltages drop out +of the [UNINTELLIGIBLE]. + +The resistor has to be +the same as the-- + +PROFESSOR: So the voltages-- + +that's an instance-- + +what you just said-- is +an instance of KVL. + +Basically, the voltage around +all of the loops better be 0. + +The sum of the voltages around +all of the loops better be 0, + +and the sum of the currents in +all of those closed surfaces + +better be 0, right? + +KVL better be satisfied +everywhere, and KCL better be + +satisfied everywhere. + +So, in particular, we can +ask about this node. + +We could say, do the currents +flowing into + +that node sum to 0? + +So if you take a line here-- +let's take this line-- + +if V0 happened to be-- + +V0 happens to be the voltage +here, right? + +So if V0 were 36, then that puts +some voltage on this leg. + +36 would what, 54? + +So then you'd have to say-- + +you'd have to compute, then, the +current through here and + +the current through there, +and see if those + +currents sum to 0. + +And, in fact, if you do those +calculations, you if you can + +convince yourself of +those are all true. + +So the answer was 0. + +All of those answers +were true. + +The point of doing the exercise +was to just remind + +you about how you solve +circuits, but also to let us + +look at patterns. + +The interesting thing in this +problem is the pattern the + +results between the +V's and the I's. + +So if I were to make a plot, in +fact, those V's and I's all + +fall on a straight line. + +Well that's pretty +interesting. + +So if I plot just this +V versus this I-- + +so V equals 0, 30, 36, +0, 30, 36, 48, 60 -- + +and the corresponding +I's, 30,15,12,6,0 -- + +30,15,12,6,0. + +Those points all fall +on a straight line. + +That suggests that there's +some pattern here. + +And if there's a pattern, then +there might be a way to + +exploit it. + +So that's what I'm trying +to develop-- + +is a way to exploit the pattern +that results when + +parts of circuits interact. + +The interesting thing +that we-- + +so not only is it true that +there's a simple pattern, but + +it turns out that the pattern +is completely independent of + +the thing that I put +on the right. + +The pattern is a property of +the circuit to the left. + +One way to convince yourself +of that is to substitute-- + +take that resistor out, and put +in a voltage source, and + +redo the problem. + +This time, instead of assuming +that there's an Ohm's Law-type + +resistor here, assume there's +a constant voltage, and that + +constant voltage is adjusted +to 0,30,36,48,60. + +If you re-solve that +problem, you get + +exactly these same currents. + +The answer continues to fall +on exactly the same line. + +So that's a very interesting +pattern. + +The idea is that when the +circuit on the left interacts + +with the circuit on the right, +regardless of what the circuit + +on the right is, you get a +simple relationship between + +the voltage and current +that comes out of the + +circuit on the left. + +So that motivates the idea that +we can think about the + +left-hand circuit as some +kind of a generic part. + +We call that generic +part a one-port. + +Think about this circuit on the +left-- the thing that's in + +the red box-- + +it's got at its terminals-- + +the terminals are the things +that poke through the red box. + +First off it has two terminals, +two terminals is + +just like all of our +other parts. + +And it's like a resistor, it's +like a voltage source, it's + +like a current source, it's +a two terminal device. + +And just like a voltage source +or a resistor or a current + +source, there's some voltage +across those terminals, and + +there's some current that flows +in those terminals. + +So there's some current +that goes in the plus. + +And that same current +comes out the minus. + +That'll be true for this +circuit, just the same as it's + +true for a resistor or voltage +source or anything else, the + +only difference is, the thing +that's inside the box-- + +the thing that's inside +the one-port-- + +is more complicated than it was +for a simple resistor or + +voltage source or +current source. + +So what we can think about, is +this whole red box just looks + +like a super part. + +So the interesting thing that +happens is, this red box + +behaves like a one-port, +like a super part. + +And just like a resistor has a +relationship between V and I, + +V equals IR, Or a voltage source +has some kind of a + +constraint, V equals V0. + +Or a current source +has some kind of a + +constraint, I equals I0. + +This funny part has a +relationship between V and I + +that's given by that curve. + +In some sense, it's not +very different. + +So we think that-- + +so what we want to do now is +figure out the rules that + +govern the currents +and voltages that + +flow through one-ports. + +And in particular, how special +was this straight line thing? + +I mean if they were always a +straight line, that would be + +really easy, right? + +So the question-- + +so the next question I'd like to +ask is, just how often are + +we expecting to see straight +lines there? + +I already said, the primitive +elements that we think about-- + +Ohm's Law, resistors, voltage +sources, current sources-- + +they have straight line +constraints between the + +voltages and currents that +they can generate. + +So think about what I'm doing. + +I'm trying to think about a rule +that's going to let me + +describe the currents and +voltages into that red box + +from the previous slide, much +like I would describe the + +voltages and currents in an +Ohm's Law a resistor. + +I can tell you the +voltage-current relationship, + +V equals IR for an Ohm's +resistor, independent of what + +it's connected to. + +That's the reasoning that +I'm using here. + +I'm going to try to figure out, +independent of what it is + +connected to, what will be the +voltage-current relationship + +for the red box? + +So the question is, when are we +expecting straight lines, + +and when are we not expecting +straight lines? + +So here's a simple circuit. + +Here's a super part made out +of one linear resistor, one + +Ohm's Law resistor, and +one voltage source. + +What's the current-voltage +relationship for that part? + +What if I put a red box around +the whole thing, and asked you + +to draw the I-V curve, the +current voltage curve? + +Which would it look +like, A,B,C,D -- + +which should have been +(1), (2), (3), (4) -- + +so you can raise fingers, +or none of the above? + +So take 30 seconds. + +Figure out what would be the +I-V curve for this part. + +So if you map A to D +into (1) to (4) -- + +which of those plots describes +the current-voltage + +relationship for that circuit? + +Map A to D to (1) to (4). + +OK, you're quiet, and the +success rate is smaller than + +usual, about 50% correct. + +Take 30 seconds, reconsider your +answer, try to get this + +up to 85% or so. + +[CHATTER] + +So which is the best plot? + +Which plot best characterizes +the circuit on the top? + +OK, that's much better. + +That's about 75%. + +Certainly not 100%, +but better. + +OK so how do you think +about this? + +One way to think about +it is special cases. + +Can you think about any +special cases that are + +particularly easy to check? + +0 -- + +OK, what equals 0? + +AUDIENCE: V or I -- + +PROFESSOR: V or I -- + +yes. + +So what if you were to make -- + +if you were to make +I equal to 0? + +First off, if you made +I equal to 0, what's + +special in the plots? + +If I equals 0, then you +round up x-axis. + +Sorry, if you make I +0, what will V be? + +If you made I be 0, +how big will be V? + +5 Volts, right? + +If you make I be 0, +then there's no + +voltage across the resistor. + +So the total voltage here will +be the same as the voltage + +across the voltage source, +V equals 5. + +So the intersection on the +x-axis should be at the point + +V equals 5. + +Makes sense? + +Now if you said V equals +0, how big would I be? + +If you set V equal to 0 -- how +do you set V equal to 0? + +AUDIENCE: Negative 2.5. + +PROFESSOR: Negative 2.5, so +what is negative 2.5? + +AUDIENCE: The value of I. + +PROFESSOR: So do you need-- + +how do we set V equal to 0? + +What's the circuit way of +saying, set V equal to 0? + +You set V equals 0 +in a circuit by-- + +AUDIENCE: Grounding. + +PROFESSOR: --grounding, +by setting it-- + +by putting in a wire. + +So you run a wire from +here to here. + +Voltage across a wire +is always 0, right? + +So you set something to 0 by +putting a wire across it. + +We call that a short circuit. + +OK, there's a short path +for the voltage travel. + +So you put a short circuit here, +and then I becomes V + +over R, and the only trick +is that it's up, right? + +Current likes to flow down the +electrochemical gradient. + +So it likes to go down the +electrical gradient. + +So the current is going to +go up, but the reference + +direction for this I is down, +so I is minus 2.5. + +So the intersection on this +axis is minus 2.5. + +So we know that it has to go +through a negative on the + +bottom, and it has to go through +a positive V on the + +x-axis, and the only curve +that does that is (A). + +And if we wanted to be a little +bit more fancy, we + +could figure out the +general rule. + +We could just write an +expression for Vr. + +Well by KVL, Vr is always +the difference + +between V and 5 Volts. + +And we could write an expression +for the current + +through the resistor. + +That's just V over R. Vr +is V minus 5, R is 2. + +So I get some expression which +is, lo and behold, linear in + +V. So just like that more +complicated circuit that I'd + +looked at, I ended up with a +straight line relationship in + +the current voltage-- + +the relationship between the +current and voltage falls on a + +straight line. + +So how special is that? + +Well it actually happens +pretty robustly. + +Think about what would happen +if I had two parts, the + +generically-- + +so I'm thinking about these +being generic boxes, inside + +could be anything. + +There could be a current source, +a voltage source, a + +linear resistor, or some +other one-port. + +So if I had a generic box here, +and a generic box here, + +and I connected them in +parallel, under the condition + +that each of the generic boxes +had a straight line + +current-voltage relationship, +it's easy to argue that the + +resulting relationship between +current and voltage for the + +parallel combination is +also a straight line. + +All you need to do is realize +that if you hook two things in + +parallel, the parallel voltage +is the same as V1 and V2. + +So all the voltages +are the same. + +And the currents add. + +So Ip, the current end of the +parallel combination is the + +sum of the two I's. + +So if you think about the +relationship between V1 and + +I1, and the relationship between +V2 and I2, you could + +derive the relationship +between Ip + +and Vp by just adding. + +V1 equals v2 equals Vp, that's +what we saw here. + +And the current at the +bottom is the sum of + +the other two currents. + +So, in particular, if this was +a straight line, and that was + +a straight line, the sum of +two straight lines is a + +straight line, right? + +If you add two straight lines, +you get a new straight line. + +So what this shows is that if +you started with parts that + +were themselves straight lines, +parallel combinations + +would generate a new part with +another straight line. + +Same sort of thing happens if +the two parts we're in series. + +In series we would +have Iseries -- + +it's the same as +I1 equals I2-- + +so that's the equivalent of the +y-axes, where previously + +we had equivalents +of the x-axes. + +And now if both of these boxes +had linear I-V curves, I would + +now add horizontally rather +than adding vertically. + +But I have the same result. + +If the two, individual one-ports +had linear I-V + +curves, and if I add +horizontally, I'll get a new + +linear I-V curve. + +And in fact, if you start-- + +if you put any combination of +parts that have linear I-V + +curves together to form +a new circuit-- + +a new one-port, the I-V curve +for that new one-port will be + +a linear function. + +And the way to see that, is to +think about linear equations. + +Remember when we solve a +circuit, we have to have one + +law for every element, Like +Ohm's Law-- it's V equals IR, + +or voltage source is V equals +V0 or something like that-- + +we need one law for +every element. + +And then we have KVL and KCL. + +Well all of the-- if we start +with the assumption that each + +component has a straight line +relationship between voltage + +and current, which is true for +linear resistors, voltage + +sources, and current sources. + +Those equations that describe +those parts are what we call + +linear equations. + +Linear equation is an equation +where the function of the + +unknowns is a quote -- + +linear function. + +It has the form-- + +some constant times an unknown, +plus some other + +constant times some other +unknown, plus, in principle, + +any number of those. + +But it has to be a linear +function, so you're not + +allowed to have things like +V-squared in there. + +But if you think about things +like voltage sources and + +current sources and Ohm's Law, +they don't have squares in + +there, they're linear +equations. + +And the idea then, when we're +solving for the I-V + +relationship for this new +one-port thing, all we're + +doing is we're solving a system +of linear equation. + +Sort of in the abstract, the +idea is that we write down all + +of the component equations +inside the box, we write down + +all of the relevant KVL and +KCL, and then we solve. + +So they're all going to have-- + +each one of those equations is +going to be linear, so it's + +going to be something like, say, +a0x0 if x is my unknown. + +'x' could be a current +or a voltage. + +And then I might have sum of x1, +then I might have sum of + +x2, and I might have a whole +bunch of things, and they all + +add together to be some +constant, like that. + +So that might represent +part one-- + +that might represent one of +the components in the box. + +Then I would have another +component, which would be some + +other linear equation. + +Then I'd have a KCL equation, +well KCL is easy, because that + +only has currents in it, +and the multipliers are + +all 1 or minus 1. + +Right, so that's +clearly linear. + +And I have KVL equations. + +Those are linear. + +And the point is, that when you +solve linear equations, + +you get a new linear equation. + +So think about solving this by +the method of substitution. + +I could figure out +what is x0 here. + +If I use this equation +to figure out x0. + +x0 would be a linear function +of all the other x's. + +So then if I plug that linear +function into here, I replace + +this linear equation with a new +linear equation with one + +fewer unknown. + +if I keep doing that, I just +keep replacing linear + +equations with other +linear equations. + +When I'm all done, I'm left with +a new linear equation. + +That's why, if you start with +parts that linear I-V curves, + +you'll end up with a straight +line I-V curve. + +So that idea that the I-V +function is a straight line is + +quite robust. + +It will happen anytime you go +to circuit out of ideal + +parts-- whereby ideal parts, +I mean Ohm's Law resistors, + +voltage sources, and +current sources. + +So that has a very interesting +circuit interpretation. + +If I know that an arbitrary +circuit can be represented by + +a straight line-- + +if the I-V curve can +be represented + +by a straight line-- + +well that generates +an equivalent set. + +There's obviously more than +one circuit that could + +generate the same +straight line. + +Here's a circuit that can +generate that straight line. + +In fact, it will always be true +that I can generate a + +circuit with one voltage source +and one Ohm's Law + +resistor that will mimic the +behavior of any arbitrary + +combination of resistors, +voltage + +sources, and current sources. + +All I need to do is think +about, you take the + +complicated thing, figure out +its straight line plot, now + +you read off some critical +numbers from this plot. + +You say, OK, well what if +the current were 0? + +Well if the current were +0, I'd be on this axis. + +If the current were 0 in the +circuit, V would be V0. + +So that means you look over +here, you figure out the + +x-intercept, and the x-intercept +is the value of + +the voltage source. + +Similarly, if you figure out +the rate of growth of I -- + +so more generally, if you solve +for I, I will be the + +difference between V and V0 +divided by R, that's just + +Ohm's law for the resistor. + +And that then lets you figure +out the law for the slope. + +The slope over here is going +to turn out to be one over + +this resistor-- + +I should have had-- +this should be R0, + +these two should match. + +So the slope of this line is +one over that resistor. + +So in general, regardless of +how complicated the box is, + +figure out the straight line and +I-V curves, read off the + +x-axis, read off the slope, and +that lets you construct a + +simple circuit that has +the same Vi curve. + +We call that circuit the +Thevenin Equivalent. + +What that means is, you can +think about a complicated + +circuit, regardless of how many +parts, by a circuit it + +just has two. + +That's an abstraction that +lets us think more simply + +about complicated circuits even +if there's no buffers. + +This is true always. + +OK, it's not true-- + +it's not it's not the case that +if I change the thing + +that I put here-- + +if I change the thing I put +here, this relationship is + +still true. + +It's the equivalent of Ohm's Law +for complicated circuits. + +Ohm's Law is what I get +if what's in the + +box is a single resistor. + +If what's in the box is +complicated, more generally + +this is what I get, the +Thevenin Equivalent. + +Of course there's lots +of circuits that + +have this I-V curve. + +So a different one is a current + +source with a resistor. + +That's called a Norton +Equivalent. + +You do the same sort of thing. + +What would happen if here, +if I set V to be 0? + +Well how do I make V be 0? + +I make V be 0 -- + +Did I write that on the slide? + +no I didn't write +it on the slide. + +I make V be 0 by putting +a short circuit here. + +I connect a wire. + +If I put a wire here, then +how big is the current I? + +Well if I put a wire here, it's +easier for this current + +to go through the wire +than it is to go + +through that resistor. + +So all of this current goes +through the wire. + +All of this current is I0. + +So if I put a short circuit +across V -- + +if I make V be 0, +how big is i? + +Minus I0 right? + +All the current I0 +goes through, it + +just goes to backwards. + +So that's how I get +this point. + +So if I wanted to replace some +complicated circuit with a + +Norton Equivalent, I would take +the complicated system, + +to figure out the I-V curve, +read off the intercept on this + +axis, change the sign-- + +that's the most confusing +part, by the way. + +This is the error that +you all make. + +There's a minus sign in the +current relationship. + +We like to draw-- it just makes +us feel good to have the + +arrow go up. + +And if you make the arrow +go up, it's in the wrong + +direction to I. So when we did +the Thevenin equivalent, there + +was no sign from it, +this was V0. + +So the voltage on the voltage +source is equal to the + +x-intercept. + +But when we do the Norton, the +current in the current source + +is minus the y-intercept. + +Same idea, though. + +OK? + +So the idea is that Thevenin and +Norton equivalent circuits + +are equivalent, in the +sense that they + +generate the same voltage. + +that the more complicated +circuit did. + +So that means for thinking +about the circuit we can + +ignore the complicated stuff, +and just know two numbers, V0 + +and R0, or I0 and R0. + +So one more step, what this all +means is, that if you can + +represent the current voltage +relationship for an arbitrary + +circuit in terms of a straight +line, that means that when + +we're trying to characterize +an arbitrary circuit, it + +doesn't matter how complicated +it is. + +It could have 100 parts in it. + +Regardless of how complicated it +is, I only need to measure + +two things in order to fully +characterize it. + +If a circuit is made out of +linear resistors, voltage + +sources, and current sources, +three special linear parts-- + +if a circuit is composed +entirely out of linear parts, + +doesn't matter how many parts +are in it, there could 100, + +there could be 1,000-- + +I only need to measure two +things to get a complete + +description. + +And that's because two points +determine a straight line. + +I know, by having proved it by +using linear algebra, I know + +by using linear algebra +that the solution + +is a straight line. + +I know from geometry +that two points + +determine a straight line. + +I only need to find +out two points. + +So by convention, the easiest +two points is usually the + +simplest cases. + +Set the voltage to 0 and set +the current to be 0. + +So that motivates the idea that +if I have an arbitrary + +circuit, if I want to figure +out this reduced complexity + +abstraction-- + +say I want to make a Thevenin +Equivalent-- + +what I would do is first to ask +the question, how big is + +the open circuit voltage? + +Open circuit means there's no + +connection between the terminals. + +That means the current is 0. + +If the current is 0, +I'm on the x-axis. + +So over here I'm on the x-axis, +so I'm thinking about + +the red point. + +Open circuit over here means +there's no connection here, + +which means the current is 0, +and all I need to ask is-- + +regardless of how complicated +it is the circuit-- + +how big is the voltage that +I would measure here? + +So in this circuit, +if I have a-- + +yeah, I confused myself +for a moment. + +if this current is 0, then +this voltage drop is 0. + +This voltage source prescribes +the voltage between these + +nodes to be 1 Volt, +so V0 is 1 Volt. + +So I just fell one point. + +I set I to be 0, I found the +open circuit voltage. + +Then I need to find one +other point, because I + +only to find two. + +So I'll find the short +circuit current. + +Imagine that I put a wire +between the input and the + +output, and I'll compute how +much current that circuit + +generates in that wire. + +Again the only confusing part +is that the reference + +directions are backwards to +the way you might have + +expected them to be. + +If I put a short circuit here, +then the voltage between these + +nodes is still 1 Volt. + +That's what the voltage +source always says. + +So the current that flows +through this wire, the short + +circuit current, is just this V +over that R, except it's in + +the negative direction. + +And the way you can think about +that is that the slope + +of this curve has +to be positive. + +I need-- because of the +way Ohm's Law works-- + +increasing the voltage better +tends to increase the current, + +because that's what Ohm's +Law resistors do. + +So I need to have this slope be +positive if it's going to + +be Ohm's Law. + +So I characterize just those +two points, and then the + +resistance is simply the +ratio of the two. + +So the resistance is related +to the slope. + +It's 1 over the slope, +you don't need + +to worry about that. + +The resistance is always V over +I, so you just take the + +open circuit voltage and divide +by the short circuit + +current, minus sign, and +you get that the + +resistor must be 2 Ohms. + +Is that all clear? + +The idea is that we're trying +to build an abstraction that + +lets us simplify the way we +think about circuits, without + +introducing buffers. + +So that means then that these +two circuits are equivalent to + +that circuit, in the sense +that they all share + +the same I-V curve. + +If you substituted one server +for the other, you couldn't + +tell from outside the red +box which was on the + +inside of the red box. + +OK so I'll do an example now. + +Think about, what if I want +to find the equivalent-- + +the Thevenin equivalent +for this circuit. + +I just do the things I +just told you to do. + +First thing I think about +is, what's the + +open circuit voltage? + +So If I think about open +circuit, there's + +no connection here. + +That means this current is 0. + +That means that the voltage +that develops + +is the voltage divider. + +So I get 7 and a 1/2 volts-- + +3 over (1 plus 3) +times 10, right. + +So that gives me one point-- + +that tells me the voltage +source for the Thevenin + +equivalent. + +Then for the second point, I +want to think about the short + +circuit current. + +So I consider putting a wire +here, and then I compute the + +amount of current that +flows in that wire. + +And in this circuit, this wire +shorts out that resistor, so + +all the current goes through +this wire, and none of the + +current goes through +that resistor. + +So that means that the total +current that flows is 10 Volts + +divided by 1 Ohm, which +is 10 Amps. + +And then I know that the +equivalent resistance is the + +ratio of the open circuit +voltage to the short circuit + +current, except I have to worry +about the minus sign. + +And so I end up with the +equivalent resistance being + +the 7.5 Volts, which is the open +circuit voltage, divided + +by 10 Amps, so I get 7.5 Ohms. + +And so the answer then, is that +here is the circuit I + +started with, here's the +Thevenin equivalent circuit, + +they're identical in the +sense that they have + +the same I-V curve. + +And you can just sort of see +why that has to be true. + +If you think about, here's the +two circuits, and if you think + +about the simple cases, if you +set I to be 0, the voltages + +better be the same. + +Well over here it's 7.5 by the +voltage divider, over here + +it's 7.5 by the fact that +there's no current going + +through that resistor. + +And the short circuit current +better be the same. + +So over here, if you short this +out, you're going to get + +10 Amps, over here if you short +it out, you're going to + +get 10 Amps. + +So you can always go +back and forth. + +The point is, that you can +substitute the simpler circuit + +for the more complex circuit, +because they have + +the same I-V curve. + +OK, just to make sure that +you're following me, here's a + +question that has to do with +taking the same circuit, but + +considering the Thevenin +equivalent-- + +Thevenin or Norton +equivalent-- + +at three different ports. + +Here I'm thinking about what +would happen if I looked in + +terminal A, what if I looked +in terminal B, or looked in + +terminal C? + +Figure out the Thevenin and +Norton parameters, and see if + +there's an error in the table. + +So how many errors +are in the table? + +About 50% correct again. + +So which entry don't you like. + +AUDIENCE: 2D? + +PROFESSOR: That's exactly +right, so 2D is wrong. + +How do I figure out 1A? + +How do I figure out V0 +for the a circuit? + +So the definition of V0 is +the open circuit voltage. + +So I need to figure out, for the +a circuit, how big would + +be the voltage across A if there +was no current flowing + +in the leg of A. Everybody +clear on that? + +So the thing that I would do +is, I would think about, + +there's no connection here. + +What's the voltage here? + +So how would I calculate that? + +Yeah. + +AUDIENCE: You would use the +current-divider relationship + +to figure out that current +flowing through that is going + +to be 4 Amps. + +PROFESSOR: Precisely, so first +I need to take-- here are the + +current sources, so I have two +resistor lengths, so that's a + +perfect set up for the +current divider. + +So the amount of current that +goes in this leg compared to + +that leg is the ratio of this +resistance to the sum of + +resistances, right? + +And if you work that out, you're +going to get 4 Amps + +coming through here. + +So then after you know the +current through this leg, it's + +an easy matter to take the +current and turn it into a + +voltage, so the voltage at the +a port is 4 Amps times 5 Ohms + +is 20 Volts. + +Is that clear? + +And similarly, but with a +different answer, the voltage + +at the B terminal is the same 4 +Amps, but now times 10 Ohms. + +So that's how we got 40. + +And at C, it's the same 4 Amps, +but now it's times the + +sum, 4 times 15 is 60. + +Everybody's happy about that? + +So the point is that when you +generate an equivalent + +circuit, it depends upon which +set of terminals you're using. + +You can't just take a circuit +and say, give me the Thevenin + +Equivalent. + +You have to say, give +me the Thevenin + +equivalent looking somewhere. + +So I could look in the A port, +the B port, or the C port, and + +I get different V0's. + +How would I compute the I0? + +Short circuit current-- + +so what I would do is I +would short this out. + +When I do that, all the current +flows in this leg and + +one of the current +flows that leg. + +So that means I have, +equivalently, 10 Ohms in + +parallel with 10 Ohms. + +Then by the current divider, +how much current + +goes down one leg? + +Half of it. + +I get a different answer over +here, because now I short out + +that node, which shorts out that +resistor, so now I get a + +different ratio of resistors. + +It's not the same as the first, +so I know that this + +answer can't be 5. + +And, in fact, if you work it +out, the answer is 20 over 3. + +And finally, if you short here, +then you know that that + +short circuit shorts out +both this series + +combination and that one. + +So all of the 10 Amps goes +through that, so + +you get that 10 Amps. + +Then how do you get R0, which +is the ratio of V0 over I0. + +So if you take V0 over +I0, you get 4. + +Here if you do right answer, you +get 6, and here if you do + +that you get 6. + +The point is, that the Thevenin + +equivalent you get is different. + +The Norton equivalent that you +get is different, depending on + +which ports you're looking at. + +OK there's two reasons for +thinking about this. + +One-- + +so why am I thinking about all +of these equivalent circuits? + +So I wanted to have an +abstraction that was useful + +for thinking about how +parts interact. + +I wanted a way of thinking about +what would happen if I + +changed the load on the circuit +without having to + +recalculate all the voltages +and currents + +throughout the circuit. + +And so this Thevenin and +Norton idea is a + +way of doing that. + +That's important from a +practical sense, because when + +you buy a part-- + +when you buy an electronic part, +they tell you how it + +works by telling you the +Thevenin equivalent or the + +Norton equivalent, or whatever +is the easy way + +to think about it. + +So there's a practical +reason-- + +when you buy an op-amp, they +tell you how good the op-amp + +is by telling you how big is the +equivalent resistance at + +the output. + +So it has a practical value, +because it lets you-- it's the + +way you specify an +electronic part. + +You can't -- when the +manufacturer makes a part, + +they can't know what you're +going to do with it. + +So they tell you how it works by +telling you something about + +the equivalent circuit. + +There's also a different reason +for thinking about + +this, and that is because it's +conceptually simplifying to + +think about Thevenin and +Norton equivalents. + +So here's an example that's +very much like the first + +problem that I worked out. + +What would be the effect +of closing this switch + +on the current I? + +We solved the problem very much +like this last time, and + +one way you can solve it is you +figure out I in two cases, + +when the switch is open and +when the switch is closed. + +And you figure out whether went +up or down, and you know + +the answer. + +The point is, that if you think +about this in terms of + +equivalent circuits, it's +completely trivial. + +If I think about what +would happen-- + +I'm interested in what happens +at I, what I do is split the + +circuit into two pieces, the +stuff to the left of I, and + +the stuff to the right to +of I. I make a Thevenin + +equivalent for both of them, +and then I jam together the + +two Thevenin equivalents. + +What I get, in detail, +is showed here. + +So if I look left, I see +a 20 Volt source with + +a 4, 4, and a 2. + +That has a Thevenin equivalent +that is showed here, which is + +independent of the state +of the switch. + +So the same Thevenin occurs on +the two sides, switch open, or + +switch closed. + +If i make a Thevenin over here, +there's no sources. + +So it's just going to +be a resistance. + +So when the switch is open, +I have to 2 Ohms, when the + +switch is closed, +I have 1 Ohm. + +I don't even need to figure out +what are these part values + +to see that, if I make this +resistance smaller, which + +happens if I close the switch, +the current goes up. + +I mean it's true that I showed +here that the Thevenin voltage + +is 10 and the Thevenin +resistor is 4. + +I don't even care. + +Regardless of what the +Thevenin voltage was, + +regardless of what the Thevenin +current is, it's + +going to be the same when the +switch is open and closed. + +And that's a powerful +statement. + +I know it's the same, so when +I close this which, all I've + +really done is I've made +that resistor smaller. + +The net series resistance is +down, the current is up. + +So I have two reasons for +thinking about Thevenin and + +Norton equivalence. + +One is practical value, the +other is conceptual + +simplicity. + +It lets you simplify way you +think about a circuit, and + +it's a way of gaining intuition +without ever even + +solving the equations. + +Most circuit designers don't +solve certain equations. + +They know what it's going to do +just by looking at it, and + +this is the kind of reasoning +that they use. + +OK, there's one more topic-- + +the idea of Thevenins and +Nortons really derived from + +linear algebra. + +The basic parts of most +interest are linear. + +And when you put together a +system out of linear parts, + +you get a linear system. + +There's one more consequence of +linearity that is terribly + +useful, and that's the idea +of super position. + +If you have a system of +equations that is linear, and + +if you have multiple sources, +things are very simple. + +You can see that over here. + +If I had multiple sources, the +system of equations that I get + +wouldn't look quite like this. + +These terms, the constant terms, +they're the ones that + +come from the drives, +the voltage + +sources, the current sources. + +So if I had two drives, I would +get something else here. + +I would get plus a at +N+1 for example-- + +source one, source two. + +And I would get source +one, source two. + +So the idea is that, if I have +a system that has multiple + +sources, I know from the +structure of the linear + +equations, there is just +more constant terms. + +OK, well what's that mean? + +That means you can just use +linear algebra to see that the + +answer to this problem is the +sum of the answers to that + +problem plus the answers +to that problem. + +That's just linear algebra. + +What that means in terms of +circuits is, I can figure out + +the response to a circuit +by turning on the + +sources one at a time. + +That's called superposition. + +And generally speaking, it's a +lot easier than solving the + +circuit out the long way. + +So here I've got two sources So +say I wanted to compute I, + +in response to V0 and I0. + +What I would do, is I would turn +off the I0 source, and + +calculate the voltage +that results just + +from the voltage source. + +That's the same as setting +this to 0 and finding the + +response to this. + +So if I want to set I to 0, the +way you set I to be 0 is + +open circuit. + +If you open circuit something, +there's no current going to + +flow through it. + +So I replace the current source +with an open circuit, + +and compute the i that would +be result when the current + +source isn't there. + +OK, well that's easy. + +If their current source +we're not there, this + +would be open circuit. + +The current, i, would just be +the total voltage going + +through R1 and R2. + +So the answer, I1, the first +component of the current I, + +would be V0, the result of the +voltage source divided by the + +sum of R1 and R2. + +Now that's not the +whole answer. + +That would be the whole answer +if I0 weren't there. + +So now I have to worry +about the other case. + +What if only I0 were there? + +Well now I have to +set V to be 0. + +Well setting V to 0 is not +open circuiting it. + +You can't just reach in, grab +the voltage source, and throw + +it away, because that'll +make the current 0. + +If I want the voltage to be 0, +I have to short circuit it. + +So what I do then, is I leave +the current source alone, and + +I replace the voltage source +with a short circuit, + +guaranteeing that V is 0. + +Then I ask, how big is I2, the +component of I that results + +from the current source? + +Well if I've short circuited +this, then I just get a + +current divider. + +This current has to do with +how readily the current + +divides between R1 and R2. + +The amount that goes through the +R1 side is in proportion + +to R2 make R2 bigger, more +of it goes through R1. + +Standard current divider, +except for the + +slippery minus sign. + +So if I only had the current +source, the current I2 would + +have been current divider +operating I0 with the slippery + +minus sign. + +So that means, by superposition, +that the result + +of having both sources on is +just the sum of those answers. + +That's a very big +simplification. + +If you've got multiple sources +in the circuit, you can think + +about them all at once. + +And if you really good at +writing linear equations and + +solving them with pencils, +you'll get the right answer. + +But there's an enormous +simplification if you just + +turn off all but one, and +do them one at a time. + +So here's a problem. + +Here's a very simple +circuit, compute V + +by using super position. + +V is the voltage across +the resistor. + +How big would V be if you used +the idea of super position? + +So what's the answer? + +50% correct, roughly speaking. + +OK I want to use +superposition. + +So how big would the voltage +v be, if all I had was the + +voltage source? + +One. + +How big would the voltage +be if i only + +had the current source? + +Ah, got half of you. + +That explains the 50% correct. + +How big would the voltage +be, if I only + +had the current source? + +It's tempting to say (1). + +I say tempting, because that's +the wrong answer. + +[LAUGHTER] + +What is wrong about +the answer (1)? + +What does the voltage do +to the current source? + +The voltage due to the current +source is the voltage that the + +current source would have +generated if the voltage + +source weren't there. + +If the voltage source weren't +there, then-- + +half of you got it right, +so half of you + +can shout the answer. + +So if the voltage source weren't +there, the voltage + +source would be 0. + +If the voltage source were +0, then V would be 0. + +So if the voltage due to the +voltage source is 1, the + +voltage due to the current +source is 0. + +The sum of the two is 1. + +The answer is 1. + +OK? + +Make sense? + +So, very closely related +problem. + +What's the current I? + +Solve that by superposition. + +So how big is the current I +according to superposition? + +Wonderful, so how big is the +current i generated by the + +voltage source? + +1. + +How big is the I generated +by the current source? + +Negative 1, the sum is 0. + +All right, so those two problems +were trivial by + +superposition. + +They're not too hard by +non-superposition. + +But the point is, that they're +trivial by super position. + +So what we saw today-- + +the goal for today was to +generate some abstractions + +that let you think about the way +parts interact with each + +other, because that's a central +issue when you're + +thinking about circuit design +And we built the idea of + +Thevenins and Nortons +and super positions. + +That was the basic idea. + +And the sub-theme-- + +or maybe I should say the major +theme is really that. + +It's the importance +of linear algebra. + +So the take home message is +probably, take 18.06. + +So this was all about the +application of 18.06 to the + +solving of circuits. + +See you later. \ No newline at end of file diff --git a/G5_u6k9LR3E.txt b/G5_u6k9LR3E.txt new file mode 100644 index 0000000000000000000000000000000000000000..07d53fa3e00580cf81943495a145143e28737d5e --- /dev/null +++ b/G5_u6k9LR3E.txt @@ -0,0 +1,4708 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation, or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK, so let +me just quickly remind + +you of what we've done +what we did last time. + +So unfortunately, today is going +to be a little bit of what I + +wanted to do this time and a +little bit of what I would have + +wanted to have been done +in recitation yesterday, + +because all recitations +were cancelled. + +So today is going to include +a few steps along the way + +that I skipped over last time. + +OK, so to review +from last time, we + +talked about central potentials. + +The energy operator had a radial +derivative term, an angular + +momentum term, and +a potential term. + +So this would be true regardless +of whether we were central + +or not. + +But if we have a central +potential, where this only + +depends on the magnitude +of the radius vector, + +then we can use +separation of variables, + +and write an energy eigenstate +as a radial part-- which + +we will sneakily pull out a +factor of 1 over the radius-- + +as we saw last time, that +was particularly convenient. + +It took care of this r and made +everything nice and simple. + +So a radial part times +a spherical harmonic. + +The reason we use a +spherical harmonic is + +that neither of these two +terms depend on the angular + +coordinates. + +The angular momentum, we know +what its eigenfunctions are, + +so if we use a +spherical harmonic, + +this angular momentum +becomes just a constant. + +And having separated +in this form, + +and pulling out that +sneaky factor of 1 over r, + +the energy eigenvalue equation +reduces to a simple 1-D + +effective energy +eigenvalue equation + +with a simple dr squared, +and an effective potential, + +where the effective potential is +the original central potential + +plus an angular +momentum term, often + +referred to the angular +momentum barrier-- which + +is proportional +to-- as Matt says, + +as Professor Evans +says, in 804, one + +is forced to say h bar +squared upon 2m repeatedly. + +And he pointed out that it would +be much more efficient if I + +would just come up with a +simple variable for saying it + +or sound. + +So I will attempt to +henceforth call it pfft. + +[LAUGHTER] + +So the effective +potential is pfft, + +l, l plus 1 upon r squared +plus the central part + +of the potential-- props +to Professor Evans. + +And this is true in general +for central potential. + +The last thing we notice of +this is that since the energy + +eigenvalue equation has been +reduced to this form, which + +depends on l, but is +independent of m-- m + +appears nowhere here-- +the energy can't possibly + +depend on m, although +it can depend on l. + +It's just e of l. + +And thus, for every +different value of m, + +I will get the same energy-- +fixed l, different m. + +And there are how many +values of m for a fixed l? + +2l plus 1. + +So the degeneracy +of El is 2l plus 1. + +Right? + +That's general for +any central potential. + +It only requires +spherical symmetry. + +So then we say the example of +the cooling potential, where + +the potential is minus +E squared upon r. + +And we solved-- or I quickly +reviewed the solution + +of the energy +eigenvalue equation. + +I'll write it that +way-- where r of what + +I will call-- in place of +E I, will simply write n. + +Rnl is equal to e to +the minus r over 2 + +r naught n times r over r +naught to the l plus 1 times + +some simple function v sub +n of l of r over r naught, + +with the energy nlm +being equal to E naught-- + +or I should say e Rydberg in +our notation of last time-- + +upon n squared +minus bound state. + +So let's talk +about this quickly. + +This term-- the fact that it +goes exponentially-- falls + +exponentially at +large distances-- + +came from the asymptotic +analysis at r goes to infinity. + +And this is just saying +it's a bound state. + +The probability density +falls off exponentially + +as we get to large radius. + +This term came from +the asymptotic analysis + +near r goes to zero. + +And near r goes to +zero, the only term + +that matters is in the +effective-- this is one upon r. + +This is 1 over r squared, so +this gets large more rapidly. + +This term is important, +and that l, l plus 1 + +gave us r to the l plus 1. + +We work in dimensionless +variables, rho. + +And here, I replace rho +with r over r naught, + +where r naught was the +characteristic scale + +we computed last time. + +And finally, this +function V sub nl + +satisfied-- it again satisfied +the energy eigenvalue equation, + +but having pulled +out these factors + +such that asymptotically, +its regular. + +So this function +must be regular, + +smooth-- no +divergences, no poles-- + +as r goes to infinity and to 0. + +OK. + +And then we solved this +by series expansion. + +And from termination of +the series expansion, + +we got that the energy-- +we got a relationship + +between the energy +and l and n, and + +in particular the +relationship-- this + +came from termination +of the series, just + +like it did for the +harmonic oscillator. + +And the termination +series gave us + +that the energy was equal +to minus a constant over n + +squared. + +With one additional +condition, which + +is that n had to +be greater than l. + +n had to be an integer +greater than l. + +And l, of course, has to be +greater than or equal to 0. + +So let me just +quickly tell you how + +this arises, because this is an +important fact about hydrogen + +which I want you to understand. + +So the way that arises is we +got the energy from a series + +expansion for this remaining +function of rv and l of r. + +And that series +expansion started out + +by saying let v be of the +form sum over j of a sub j, r + +over r naught, the dimensionless +variable rho, to the j, + +to the j-th power, so +it's a power series. + +And when we plug this +whole form, together + +with this series expansion, +into that differential equation, + +we get-- just like we did before +for a harmonic oscillator-- + +we get a set of +relations between + +the various coefficients +in that series. + +And we solve that by +saying a sub j plus 1-- + +by deriving a recursion +relation-- is equal to a sub + +j times 2, square +root of epsilon times + +j plus l plus 1 minus 1 upon +j plus 1, j plus 2l plus 2. + +OK, fine. + +We get this recursion relation. + +It looks absolutely +awful, but it tells you + +that if you know a0, say, is +a constant which is not 0-- + +if it's zero, then +they're all 0-- then + +this function is identically +0, because a j plus 1 + +is a j times some constant. + +So this had better +not vanish-- a sub 0. + +So the first term, +the constant term + +doesn't vanish, which is good. + +It tells us V doesn't +vanish, so we've already + +learned something. + +If V doesn't vanish +identically at the origin, + +then we can determine a1 from +a0 by multiplying by this. + +j is 0 in this, and +l is whatever number + +we fix from ylm. + +And so on. + +We can deduce all +the higher a sub l's. + +It's a series expansion. + +This is the recursion +relation for it. + +However, note the following +thing-- as j gets large, + +so we go to higher and +higher orders in the series, + +then j is much larger than +whatever fixed number l is, + +and much larger than +whatever fixed number 2 is. + +So this asymptotes to aj times +roughly 2 epsilon j upon j + +plus 1 j. + +At very large j, this just +goes to 2 epsilon over j. + +Now, let's think +about what that means. + +If I have that aj plus +1 is roughly equal + +to aj times root epsilon +times 2 over j plus 1, + +I guess, then this tells me +that every time I increase j, + +I get a factor of j plus 1 +and another factor of 2 root + +epsilon. + +This tells me that a sub j +is equal to a sub 0 times + +2 root epsilon to the +j over j factorial. + +But those are the +expansion coefficients + +of an exponential-- quantity +to the n over n factorial. + +But that's bad, because +if this series is + +the exponential series with +argument 2 root epsilon, + +then this series becomes E to +the 2 root epsilon r over r0. + +But that's bad, because that +would exactly swamp this term. + +That would defeat the +asymptotic analysis + +we did at the beginning. + +If this term, V, is +growing so large twice + +as rapidly as this +is going to 0, + +then the net is +diverging at infinity. + +That's bad. + +So in order for this-- +for the series expansion-- + +to describe a good function that +really does vanish at infinity, + +we need that this +doesn't happen. + +So it must be true +that j doesn't + +get large enough that +the exponential in V + +overwhelms the +decaying exponential + +from the asymptotic analysis. + +Everyone cool with that? + +So it has to terminate. + +But if it terminates-- let's +look at the coefficient here. + +If it terminates, this says that +2 root epsilon times j plus-- + +and if it terminates, that says +that there's some j maximum. + +Well, let me write it over here. + +If it terminates, +that means there's + +some value j such +that aj plus 1 is 0. + +But if aj plus 1 is zero, +how can that possibly be? + +It must be that for +that maximum value of j, + +the numerator +vanishes-- specifically + +for that maximum value of j. + +Yeah? + +Well, what's the condition +for that numerator + +to vanish for a +specific value of j? + +I'll j sub m, or j +max, the maximum value, + +such that a sub j +max plus 1 vanishes. + +So j plus l plus 1 +must be equal to 1. + +Or said differently, +epsilon-- which + +is the energy in units +of e0, must be equal to 1 + +over 4 g max plus l plus +1, quantity squared. + +Cool? + +So that means that our +solutions, or states psi, + +are now labeled +by three integers. + +they're labeled by l And by +m from spherical harmonics, + +but they're also labeled +by the value j max. + +And j max can be any number +from 0 to infinity, right? + +Strictly, it +shouldn't be infinite, + +but any finite number, any +countable, any integer-- + +because eventually the +series terminates at j max. + +So it's labeled by +these three numbers, + +and the energy of lmj max +is equal to e0 minus over 4. + +And this e0 over 4 we already +saw was e Rydberg, 13.6 dv, + +times what value? + +Well, here's the energy in +units of e0-- jm plus l plus 1, + +quantity squared. + +Where L is greater +than or equal to 0, + +j sub m is greater than +or equal to 0, and 1 is 1. + +But this is sort of cumbersome. + +We can just as well +call this quantity n, + +where n is greater +than l as an integer. + +It can't be equal +to l, but it could + +be 1 greater than l, +or any greater integer. + +Is that cool? + +So instead of labeling +it by jm, the point + +at which the series terminates, +we'll label it by n, + +and you can deduce what jm is +by subtracting I plus 1 from n. + +That tells you where +the series terminates. + +Notice that this tells +you something nice. + +This power series for V, +if n is equal to l plus 1, + +has how many terms in it? + +So say it out loud, just +think about it a second. + +If n is equal to l +plus 1, how many terms + +are there, that are +non-vanishing in the power + +series? + +I won't call on you, +but raise your hand + +when you have an answer. + +What's the value of j max +if n is equal to l plus 1? + +So what term is the first +one to vanish in the series? + +OK, so how many terms +are non-vanishing? + +Yeah, just the one-- +just the first term. + +So when l is as large +as it can possibly + +be-- when l is equal to n minus +1, V is a constant function. + +It's just constant. + +When l is one less, when l is +n minus 1, or n is l plus 2, + +then V has two terms in it-- +a constant, and a linear. + +So the greater the +difference between l and n, + +the more terms there +are in the series. + +OK? + +So anyway, this leads to +this form of the energy. + +But as is usually the case, this +sort of a brute force analysis + +doesn't give us a +whole lot of insight + +into why we get the +qualitative features we do. + +In particular, the +qualitative feature + +that stands out most obviously +to me-- I don't know about you + +guys-- is the fact that +the degeneracy is now much, + +much larger. + +In particular, we know +from basic principles + +of a central potential-- +as we just reviewed-- + +that anytime a potential +is symmetrically invariant, + +is spherically +symmetric-- any time + +the potential is spherically +symmetric, rotationally + +invariant-- then there +must be degeneracy + +of 2l plus 1 for every energy +eigenstate-- there must be. + +The l could be zero, but if +there's any angular momentum, + +then that degeneracy +must be 2l plus 1. + +But this is much +more degenerate. + +And in fact, how +degenerate is it? + +Well, for any given +En, the degeneracy + +is equal to-- well, what are +the possible values of l? + +So we have some state for +every different value of l. + +l could be equal to 0, and it +can go up to n minus 1, right? + +Because, again, +n is some integer + +which could vanish, l plus 1. + +So as small as this can be is 0. + +So n can be l plus 1, +or anything greater. + +I.e.: l can go up to n minus +1, but it can't be any greater. + +Then for every value of +l, there is a state n-- + +there's a value of n which +could be minus l all the way up + +to l in integer steps. + +So how many states are there? + +Well there's one state for +every value of n, l, and m. + +So it's this sum. + +The sum on m for minus +l to l is 2l plus 1. + +So this is the sum n minus +1, l equals 0, of 2l plus 1. + +And this is equal to, +kind of beautifully, n + +squared-- just +arithmetic series. + +So we have this huge +degeneracy, which + +is much larger than 2l plus 1. + +It's the sum over 2l plus +1 from l to 0 to n minus 1. + +Where is this +degeneracy coming from? + +Why? + +So quantum mechanically, +we know the following-- + +we've learned the +following-- and I + +hope it's under your +fingernails at this point-- + +that when you see +a degeneracy, you + +should expect that degeneracy +to follow from some symmetry. + +There's some symmetry +of the system that + +is leading to a degeneracy +by virtue of the fact + +that the generators of that +symmetry-- for example, + +for rotation it's +angular momentum-- + +commute with the energy. + +And when you have an operator +that commutes with the energy + +operator, as we've +seen, you can generally + +construct new states given +a single energy eigenstate + +by acting suitably +with that operator. + +So we should expect there +to be some new symmetry. + +But it's very hard +to see what symmetry. + +I mean, this is hydrogen. + +This is central potential. + +It's just some stupid +central potential. + +What's so special about +the hydrogen system as + +opposed to, for example, +the harmonic oscillator? + +Which hopefully you will see +in recitation at some point. + +The harmonic oscillator +in three dimensions + +has degeneracy 2l plus 1. + +It's a central potential. + +It has to have degeneracy 2l +plus 1-- but not n squared. + +Where did that come from? + +What's so special about +the Kepler problem? + +So there must be some +symmetry, but it's not obvious + +what it is. + +But now let's use a note +from classical mechanics. + +Noether's Theorem tells us +when we have a symmetry, + +we have a conserved quantity. + +We also saw this in the +quantum mechanical version + +for expectation values. + +We have a conserved quantity. + +And in quantum mechanics, +having a conserved quantity + +means that the energy +commutes with some quantity. + +Because that controls +the time evolution + +of the expectation value. + +So there must be +some quantity, which + +I've written by a question mark, +that commutes with the energy + +operator, specifically +in the case + +of the harmonic oscillator. + +So what is that quantity? + +So actually, this quantity +in classical mechanics + +was studied, because +the same thing + +is true in the Kepler case. + +In the Kepler case, +the orbits close, + +and they have simple +ellipses, and they + +have all sorts of +nice properties + +that beg for an explanation +in terms of symmetry. + +And it was pointed out by a +number of people-- Laplace, + +Runge, Lenz, various +people-- and this is often + +called the Runge-Lenz +vector, but I + +think you can blame it +on any number of people-- + +that there's a vector that +in classical mechanics, + +for the Kepler problem-- +or for the Coulomb problem, + +is conserved. + +And that quantity is p cross +l-- momentum cross angular + +momentum-- minus m +e squared-- and let + +me write m sub electrons-- +it's the mass rather + +than the quantum number little +m-- e squared, r vector. + +So it turns out this quantity +is classically conserved, + +and if you make a quantum +operator out of it, + +then e with A is equal to 0. + +Add hat. + +This was enormously non-obvious. + +If it's obvious to +you, you're a freak. + +It's really, really not obvious. + +You can go through and +do the calculation. + +And when I say really not +obvious, I mean-- well, + +I'll show you what I +mean in just a second. + +So you can go through and do +the calculation classically. + +Is this quantity conserved +in the Kepler problem + +using Newton's law? + +And the answer is yes. + +It's amazing. + +Quantum mechanically, you +can do the same thing. + +But I'm going to warn you for +anyone who has the chutzpah + +to try-- because I +encourage you to, + +but it takes a +little bit of brawn-- + +think about this +operator for second. + +Does this classical quantity +have an obvious interpretation + +as a quantum operator? + +No, because l is r cross p. + +But now we have prp. + +There's an ordering ambiguity. + +So you have to decide +which order do you + +put that p and that r, and +the other p-- ppr, rpr, + +prr-- right? + +You can write out which +components you mean here. + +For example, you mean +for the z component of a, + +you're going to get +px ly, and ly px. + +But within that, how do you +order the p's and the r's, + +because ly contains px, and +in particular, it contains x. + +So there's an +ordering ambiguity. + +So just be a little bit +careful about this as a quantum + +mechanical operator if +you do play with this. + +But if you do it, and +you're thoughtful about it, + +it's pretty easy to see that +it can be computed and checked + +that, in fact, the +commutator vanishes. + +So at this point, it's +tempting to say, aha! + +There's an extra +conserved quantity. + +We declare victory. + +The problem is, this didn't +give us the symmetry. + +This just told us there's +a conserved quantity. + +What's the symmetry behind this? + +What's the symmetry +that insures that this + +is a conserved quantity? + +It's obviously not rotations. + +It's something else. + +And so there are many +answers to this question. + +One answer involves an explicit +expression for in phase space, + +the change of +variables dx-- and this + +is a variation that +depends on f of x and p. + +So there's a little +vector parameter, + +and the change of the +physical coordinates + +depends on both the +coordinates and the momenta. + +This is a slightly +strange thing, + +because it's like a +change of variables + +where the position gets mapped +into some non-linear function + +of the positions and momenta. + +That's a little bit weird, +but you can do this. + +But I don't find it a +terribly satisfying answer. + +And here's the answer I find +most satisfying-- it's not + +terribly useful for +our present purposes, + +but you're going to run +into this again in 805, when + +you do what's called the +operator method for the Coulomb + +potential, and it +turns out to be + +an enormously useful machine. + +We're not going +to use it in 804, + +but I want to +advertise it for you. + +I want to give you a +description, though, + +that isn't the description +you're going to get in 805. + +The description is +the following-- 1935, + +guy named Fock, +crazy guy, amazing, + +amazing physicist-- +played a huge role + +in the development of +quantum field theory. + +I'm not exactly sure why he was +thinking about this problem, + +but he was, and this was a +very sort of Soviet thing + +to do at the time, I guess, to +be hard core and mathematical. + +So off he was going, +computing things, + +and he observed the +following fact-- + +how he observed this, +again, crazy long story. + +He observed the following fact-- +if you take a Kepler problem + +and you work in momentum +space-- so you write everything + +in terms of the momentum-- +it turns out that the Kepler + +problem, or he referred +to as the Kepler problem, + +but I'll refer to it as +the Coulomb problem in 3D, + +three spatial dimensions-- +this is really crazy-- + +is exactly equivalent. + +There's a change of variables-- +it's kind of complicated, + +but it's just a +projection, it turns out. + +It's exactly equivalent to +the problem of a free particle + +in four dimensions, +constrained to the surface + +of a sphere-- to a three +sphere in four dimensions. + +So you take a three +sphere in four dimensions. + +You take a marble. + +You kick it, but make sure +that it's stuck to the sphere. + +It will move in +perfect circles, right? + +Obviously-- it's +moving on a sphere, + +it's just going to +move in great circles. + +OK, that's nice and simple. + +What's the symmetry +group of that system? + +Well, the sphere is +invariant under any rotation + +in four dimensions. + +STUDENT: [INAUDIBLE]. + +PROFESSOR: Ah, SO4-- +there's a symmetry SO4-- + +special orthogonal +transformation. + +Special means it +doesn't change length. + +Orthogonal means +that it's a rotation. + +So it's orthogonal rotations +in four dimensions, + +and so now, this +should sound familiar, + +because the angular +momentum group in 3D is SO3. + +It's rotations that don't change +the length in three dimensions. + +OK? + +How many elements does it have? + +How many conserved quantities +go along with this? + +Well, how many conserved +quantities go along + +with rotations in +three dimensions? + +What's conserved by virtue of +rotational invariance in three + +dimensions? + +Angular momentum-- how many +components of angular momentum + +are there? + +Three, right, there are three. + +So it turns out that +if you calculate in SO4 + +how many conserved quantities +are there, there are six. + +And when you do this +mapping back down + +from the free particle in 4D +to the Coulomb problem in 3D, + +three of them are the l's, +and the other three of them + +are this A vector-- +comes out spot on. + +So what it's telling you is +that the spectrum of hydrogen-- + +or at least the I +shouldn't say of hydrogen, + +the spectrum of the +Coulomb system-- + +has an enhanced symmetry. + +It's the symmetry group of +rotations in four dimensions. + +Why? + +I don't know, it's +just kind awesome. + +But I think that's about +the best that can be said. + +It's just true. + +So for certain very +special potentials, + +we find that this +sort of thing happens. + +It happens in +other systems, too. + +You discover that there +are accidental symmetries + +in your system. + +They shouldn't be referred +to as accidental symmetries. + +They are enormously +nontrivial functions + +of the rest of the +system, and we're + +going to break the +symmetry in a minute, + +and you'll see why we shouldn't +refer to it as accidental. + +But in any case, the +answer to the question, + +why do we have this giant +degeneracy in the Coulomb + +problem-- why is it n squared +rather than 2l plus 1-- + +is that there is an +enhanced symmetry group. + +There's more symmetry then +you would have thought. + +And there's a conserved +quantity associated with it. + +And that conserved +quantity corresponds + +quantum mechanically +to an operator + +that commutes with +the energy operator. + +OK? + +Yeah. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Indeed, indeed. + +AUDIENCE: So how do you get +three conserved components + +[INAUDIBLE]. + +PROFESSOR: Excellent. + +What do I mean in classical +mechanics for a quantity + +to be conserved? + +I mean that the time rate +of change of that quantity, + +under the classical dynamics, +under classical evolution, + +is preserved. + +So what's the quantum +mechanical version of that? + +So the mechanical +version of that is, well, + +can we say that d dt +of some operator-- + +or of some observable a is 0. + +Does this makes sense? + +No, because it turns out, +in the language we've + +been using-- in the Schrodinger +evolution description + +that we've been using-- +this doesn't really + +make sense, because this +thing is an operator. + +That's not a quantity. + +Quantity is something +you measure. + +So what do you measure? + +Do you measure the operator? + +In a state, you measure +its expectation values. + +You might measure +its eigenvalues, + +but the more general thing +is expectation values. + +So this is something +that depends on time, + +because the wave function +depends on time-- psi of t. + +OK, so the best to say +something is conserved, + +is to say d dt of A is 0. + +But we've seen +what the condition + +is for the expectation +value to not change in time. + +In general, for any +operator A, the time rate + +of change of its +expectation value + +is given by the +commutator of E with A. + +I can do the symbols-- good. + +OK, so in particular, if +this commutator vanishes, + +if the commutator vanishes-- +equals 0--, this is equal to-- + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Sorry? + +Well, the wave function +can be time variant, + +and I'm going to +assume for the moment + +that the energy operator +and the A operator are not, + +themselves, explicitly +time dependent. + +Yes, that's an +important assumption. + +So let me just +assume for simplicity + +that neither the energy nor the +operator A that I'm looking at + +are explicitly time dependent. + +Like, it shouldn't +be, like, x plus tp. + +That would be annoying. + +So let me assume that +that's not the case. + +You do have to deal +with that sometimes. + +For example, if you are +dealing with a system that + +changes in time, where there's +a background magnetic field, + +or something like that, +that changes in time. + +But module that sort of detail. + +And also, there's an i h bar, +so where do the i h bars go? + +Do the units make sense here? + +A, A, good. + +E and d dt-- whoops. + +So where do the i h bars go? + +Well, it can go on either side. + +You have to tell me +if they go up or down. + +What is the +Schrodinger equation? + +Yeah, exactly, i h bar, +OK so we need an i h bar. + +[LAUGHTER] + +OK, this spring +has got to us all. + +So now, in the case +that e with A as 0, + +imagine we have an operator +a that commutes equal to 0. + +Then d dt of the expectation +value of A in any state + +is equal to 0. + +And that's what +I'll call conserved. + +So classically, to be +a conserved quantity + +means that it's +time independent. + +Quantum mechanically, to +be a conserved quantity + +means that it commutes +with the energy. + +Now, going back to the +question-- the question was, + +look for angular momentum. + +There are only two numbers you +can know at any moment in time. + +You can't know three. + +You can know the total +angular momentum, little l. + +And you can know +the angular momentum + +in a particular direction, +which we conventionally + +call z-- little n, right? + +But you can't know some +other angular momentum, + +like angular momentum in x +direction simultaneously. + +So what does it mean +to say that there + +are three conserved quantities? + +I can't know three conserved +quantities at the same time. + +They're not even well defined +at some moment in time. + +The answer is there are +three operators-- lx, + +and ly, and lz-- +which I will simply + +write as l vector-- all of +which commute with E. So + +while it's true that +systems don't have + +definite values of lx, +ly and lz simultaneously, + +nonetheless lx, ly +and lz all commute + +with the energy operator. + +And as a consequence, their +time expectation values + +are all 0 in a +central potential. + +So the time derivatives +of their expectation + +are all 0s in a +central potential. + +They're all constant +in a central potential. + +Yeah. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: You mean 1 over r? + +STUDENT: Yeah, 1 over r. + +PROFESSOR: So the question is, +if you don't have 1 over r, + +do you get extra-special +things that + +happen for other +potentials that aren't + +1 over r, but something else? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: It's not +quite a unique case. + +So the question is-- this +is a very good question. + +So the question is this-- this +is a great question-- look, + +there's something peculiar +about 1 over r classically. + +The orbit's closed. + +You get ellipses. + +You don't get +progressing ellipses. + +That's what you get if +you have an n harmonic. + +If you have an extra 1 over r +to the sixth term, or something, + +a small correction +to 1 over r, which we + +do in the real solar system. + +It's a many body system +instead of a two-body system, + +so r orbit doesn't close. + +It's close, but-- +so that's special. + +And here we see that there's +an enhanced symmetry. + +Are these things +related to each other? + +So the answer is almost, +in the following sense-- + +for the harmonic oscillator, +we also have it close, + +but there isn't a +Runge-Lenz vector. + +However, the orbits +close, so there's + +something special +about that one, too. + +Is there a conserved +quantity there? + +And it turns out the +answer to that is yes. + +There's an enhanced +symmetry there as well. + +But it's not like this. + +It doesn't lead to this +gigantic degeneracy. + +There is just extra +structure that's + +nice about the +harmonic oscillator. + +But for the harmonic oscillator, +of course, it also closes. + +It's not this orbits this. + +So there's a nice +structure there, + +but it's not quite so simple. + +OK, yeah, one last question. + +AUDIENCE: [INAUDIBLE] +Kepler's problem. + +I was wondering if it's at all +correct thinking [INAUDIBLE] + +symmetry or +degeneracy [INAUDIBLE] + +equal time instead +of equal area? + +PROFESSOR: Yeah, +it's not unrelated. + +I don't know how to make +that connection sharp, + +but the thing I can say sharp-- +so the question is, look, + +is that conserved quantity +somehow related to the fact + +that there's equal time in +equal-- equal areas swept out + +in equal time at all +points in the orbit? + +Which is a true thing +about a Kepler problem. + +That's a good observation. + +I don't know how to +make that connection, + +but it is true in +the following sense-- + +that both of those facts +are guaranteed by the fact + +that you have closed orbits +with a particular ratio. + +And that is, indeed, +can be blamed + +on the conservation of +the Runge-Lenz vector. + +I don't know how to make that +connection direct and explicit, + +but indeed it is. + +So that's fun question. + +I'll have to think about that. + +That's a good one. + +One of the totally awesome +things about teaching 804 + +is that every +single time, someone + +asks a question I've +never even thought + +of before-- forget +never answered. + +Never even thought of. + +I never thought of that. + +It's a great question. + +OK, so everyone cool +with the degeneracy? + +We have this +gigantic degeneracy. + +So knowing what the degeneracy +is, or where it's coming from, + +at least more or +less-- is progress. + +But if you really understand +why something is conserved, + +then you can break +that conservation. + +You can break that degeneracy. + +So here's my question, +is it possible-- can + +we, or indeed must we, can we +break or lift this degeneracy? + +So first, let me tell you +what those words mean. + +So we have this +gigantic degeneracy + +of the n squared of +the Coulomb potential. + +Can we break that +degeneracy or lift it? + +What I mean by lift the +degeneracy, what I mean by lift + +the degeneracy is +the following-- + +suppose I have a system +that's degenerate, + +so it's got two +energy eigenstates + +with the same energy eigenvalue. + +So this is energy. + +Then if I can kick the +system in some way, + +or modify it, or bend it such +that the energy levels are + +no longer to +degenerate, one state + +has been lifted above the other. + +And so we use the word +to lift a degeneracy. + +Now you can see that +they're two different states + +by measuring the energies. + +It's also said to +split a degeneracy, + +or to break a degeneracy. + +So those are just words. + +OK, so can we break or +lift this degeneracy? + +So sure. + +How do we break a degeneracy? + +How do we lift a degeneracy? + +We need to break the symmetry. + +So if we don't +have the symmetry, + +we won't get the degeneracy. + +We've seen this before. + +So first off, let's +think about what + +are the two symmetries +that we want? + +Well, we got this +degeneracy of 2l plus 1 + +from spherical symmetry. + +And we got this extra degeneracy +of n squared from conservation + +of the Runge-Lenz vector. + +And conservation of +the Runge-Lenz vector + +came from the fact that we had +exactly the Coulomb system. + +So anything that isn't +exactly the Coulomb system, + +but is still +rotationally invariant, + +should still have the +2l plus 1 degeneracy, + +but not the n +squared degeneracy-- + +like the harmonic +oscillator, for example. + +So let's change the system. + +Let's find a small correction +to the system that leaves it + +mostly the Coulomb problem, +but with some small correction. + +So what comes to mind? + +So one good way to think +about a physical, natural way + +to break this degeneracy, +to break the symmetry, + +is to think a real system +that's described by the Coulomb + +potential. + +So the system that we usually +talk about is hydrogen. + +Hydrogen is the proton. + +It's got a plus charge, +and it's got electron. + +And it's attractive with +a minus E squared upon r. + +So in hydrogen, is this the +energy operator for hydrogen? + +Is this a good description +of the energy operator + +for hydrogen? + +It's a good start, but +it's not exactly right, + +for a bunch of reasons. + +And in fact, in your +first problem set, + +when you computed the time +it takes for hydrogen, + +classically, to decay from +the classical Bohr radius, + +one of the things you discovered +is that the electron starts out + +being non-relativistic, but very +rapidly becomes relativistic. + +And rapidly is 10 to +the minus 15 seconds. + +This is a non-relativistic, p +squared upon 2m kinetic energy. + +That's probably not a +perfect approximation. + +So the first example is going +to be relativistic corrections. + +Now, will relativistic +corrections + +break rotational symmetry? + +They can't, because +relativity doesn't say, + +this is the z direction. + +In fact, it does +quite the opposite. + +Relativity, among +other things, says, + +don't get too hung up on +what's the z direction. + +But relativistic corrections +will not break the symmetry. + +So if we include +relativistic corrections + +to the kinetic energy, +this will change E, + +change the energy operator. + +But it will preserve +the rotational symmetry. + +E with l is equal to 0. + +So we won't break this +rotational symmetry, + +so we'll preserve the 2l plus 1. + +So let's check to see +that this is true. + +So to check to see +that this is true, + +let's actually estimate out +the correction to the energy + +due to the first nontrivial +relativistic effect + +in the atom. + +The first nontrivial, +relativistic effect + +can be calculated +[INAUDIBLE] kinetic energy + +in special relativity, +of a particle of mass m. + +So that's easy. + +It's the total energy is +the square root of m squared + +c to the 4th plus p squared +c squared minus mc squared. + +That's the rest energy. + +That's the total energy, so +this is the kinetic energy. + +But this is equal to-- +well, if we pull out + +a factor of m squared +c squared, this + +is m c squared times the square +root of 1 plus p squared over n + +squared c squared minus 1. + +And now if we +Taylor expand this-- + +because if the momentum is small +compared to mc squared-- or mc, + +I should say-- the momentum is +small compared to mc which is, + +morally speaking, +at low velocity is, + +the velocity is +small compared to c, + +then this is 1 plus +a small number, + +and we can Taylor expand this to +get 1 plus 1/2 a small number. + +And the 1s will cancel, +giving us only 1/2. + +So this is going to be equal +to 1/2 of that small number, + +p squared over m +squared c squared, + +times mc squared +upstairs, giving us + +the first term, which +is p squared upon 2m. + +That's the familiar +classical kinetic energy. + +Rock on. + +What's next correction? + +The next correction is the next +term for this Taylor series, + +which is going to involve +this quantity squared, + +so it's going to be p to +the 4th over m to the 4th, c + +the 4th times mc to the 4th. + +The coefficient is a minus +1/8, so we get minus p + +to the 4th over 8m +cubed c squared. + +And that's down by a +factor of m squared + +c squared from this +guy, n of p squared + +upstairs-- which is +what you'd get-- p + +squared m squared, +over c squared, OK? + +So the correction to the kinetic +energy for a given momentum p + +is to correct it down +by p to the 4th term. + +Everyone cool with that? + +Yeah. + +AUDIENCE: Why do you make +the assumption [INAUDIBLE]. + +PROFESSOR: Because +you, like Schrodinger, + +did problem Set One. + +And problem Set One said, if +you have an electron at the Bohr + +radius classically, its +velocity is about 1/400 + +of the speed of light. + +200? + +It's small. + +It's a couple of +orders of magnitude + +smaller than the speed of light. + +So that number, that ratio +there, is 1 upon 200, + +or 400-- I don't +remember-- squared. + +That's a very small +number, so it's + +a reasonable approximation. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Because what +is the typical-- that's + +an excellent question. + +So why am I talking about +it as if the electron + +is sitting at that radius? + +And the answer is, well, look-- +what is the average momentum? + +What is the average +value of p squared in, + +let's say, the ground +state of the hydrogen atom? + +What's the average value of p? + +What must be the +average value of p + +in the ground state +of the hydrogen atom? + +Zero on two grounds-- +first off, p is a vector, + +and the ground state of hydrogen +is rotationally invariant. + +It doesn't break anything. + +Secondly, it's not +going anywhere. + +It's a bound state, so +it's just sitting there. + +It's got an average +momentum of 0. + +If it carried momentum, +it would be cruising. + +So it's got average momentum 0. + +OK, fine, but what's the +average momentum squared? + +What's the average of p squared? + +We can actually do +out that calculation. + +You're going to have to do that +calculation on the problem set. + +And it's a small number. + +And it's, in fact, +almost exactly what + +you'd guess classically +from the Bohr radius. + +So you have to know the +h bar to compute the Bohr + +radius in the first place. + +So the answer is, to the +best of anyone's ability + +to define what's the +momentum, or the typical scale + +of momentum, that +typical scale of momentum + +for the electron in the +ground state of hydrogen + +is extraordinarily small +compared to the speed of light + +by a factor of 100, 200, or 400. + +Does that answer your question? + +AUDIENCE: Yes. + +PROFESSOR: It's a +very good question. + +OK, so here's the +kinetic energy. + +And by the way, +another way to say + +that this approximation +must be good + +is that we've already +computed-- ignoring + +the relativistic correction-- +we computed the ground + +state of energy, +and it was 13.6 Ev, + +which is pretty good, since +the binding energy of hydrogen + +is about 13.6 Ev. + +So apparently, that was +a good approximation. + +And you might be disgusted +by answer analysis like that, + +but that's what physics is. + +You write down some +stupid, cockamamie model + +that you know is +wrong, but if it + +does a good job of fitting +the data, you declare triumph, + +and you call Stockholm. + +[LAUGHTER] + +So it depends on the +problem you've just + +solved approximately. + +So here's the first correction. + +And now, what this +tells us is therefore, + +the energy of +hydrogen-- or at least + +a better model of +hydrogen-- I'll + +call it hydrogen tilde-- +is equal to E Coulomb + +minus p to the 4th over +8m cubed c squared. + +OK so this, however, we +know is small compared + +to the kinetic energy, because +13.6 is pretty close to 13.6. + +Notice I didn't include the +rest of the significant digits. + +So this must be in the +insignificant digits. + +So this must be small. + +So here's what I +want to ask-- we + +know that the energy of +the Coulomb problem, nlm, + +is equal to e0 squared +minus e0 squared + +over n squared, +independent of l and m. + +What's the energy in this +toy model of hydrogen + +that includes the first +relativistic correction-- nlm. + +Well, to answer that question +we have to resolve the energy + +eigenvalue equation, right? + +We have to refined the +energy eigenstates, + +and we have to solve that. + +And this is going to be a much +worse problem, because it's + +going to involve a p +to the 4th term, which + +is going to involve +four derivatives. + +That sounds horrible. + +Can anyone think of a better +way to just approximate, + +estimate the magnitude and the +value of the leading correction + +from this quantity? + +Yeah. + +AUDIENCE: Some variation +on take an eigenvalue, + +plug it in, see +what the error is, + +correct for that error-- +something like that. + +PROFESSOR: There's an iterative +method for doing that. + +It's a very good guess, but +there's an even easier way + +to estimate it. + +That's something we will +call perturbation theory when + +we do this in 805. + +And doing that systematically +is exactly the right answer. + +However I want you to do just +the leading part of that. + +Yeah. + +AUDIENCE: Dimensional analysis. + +PROFESSOR: Oh, dimensional +analysis would be awesome. + +That's fantastic, brilliant. + +So how would you compute p? + +OK, so we didn't calculate p. + +You can do a +dimensional analysis + +and get a p, because +you have an e, + +you have an l, you +can probably do it. + +But here's the +problem with that, + +though-- this is the correct +first answer to any question + +of this kind-- +correct first answer + +is plug in dimensional +analysis, and get an estimate + +for the order of magnitude. + +But we want more than the +order of magnitude here. + +We're interested in +splitting the degeneracy + +due to this interaction. + +So what that means is we want +to see that different values + +use of l lead to +different energy. + +What we care about +is the l dependence + +that comes out of +this correction. + +And we're not going to be +able to get the l dependence + +from dimensional analysis, +because l is an integer. + +It is dimensionless. + +Yeah, so that will give +you the correct magnitude, + +and that is the +first thing you do. + +What's the second thing you do? + +AUDIENCE: Stick in +the expectation value + +of p to the 4th. + +PROFESSOR: Excellent. + +Let's just stick in the +expectation value p to the 4th. + +That's not exactly +the right thing to do, + +but if this is small, that's +probably pretty reasonable. + +And what you'll find when you +do it systematically using + +perturbation theory, as +was pointed out earlier, + +we can take the entire system, +the entire energy eigenvalue + +equation-- we can +think of this 1 over m + +cubed c squared +as a small number, + +and we can do perturbation +theory on that small number. + +We can Taylor expand everything +in that small number. + +And when you Taylor expand +the exact equation, what + +you discover is the leading +term in that Taylor expansion + +is the expectation value +p to the 4th over 8m cubed + +c squared. + +OK, so this is a +fantastic guess. + +OK, so let's compute it. + +So E hydrogen is going to be +equal to E nlm, which I'm just + +to write as minus +E0 over m squared. + +OK, so what is the +correct answer here? + +So it's this quantity +minus-- so this + +is making it more tightly bound. + +Notice the sign, +because p to the 4th + +is strictly positive +if p is real. + +So minus E0 over m +squared, and if you go out + +and you do this expectation +value, which I really + +should have put on the +problem set-- oh, I still can. + +It hasn't been posted yet, so +it'll be posted this afternoon. + +But I won't. + +It's not that bad, actually. + +[LAUGHTER] + +Matt, what do you think? + +AUDIENCE: No! + +[LAUGHS] + +PROFESSOR: We'll discuss +this afterwards, OK? + +Which may or may not +appear on your problem set. + +So if you go ahead and you do +this calculation, what you find + +is the correction is En +squared, so E0 squared over n + +to the 4th-- this time it +really is n to the 4th-- + +and now you have to worry +about dimensional analysis. + +This is two energies. + +We want one energy, divided +by-- wait for it-- mc squared, + +because it's a +relativistic correction. + +That shouldn't be +too surprising. + +Times the quantity +4n over-- and here + +where life gets awesome-- +l plus 1/2 minus 3. + +[LAUGHTER] + +PROFESSOR: You laugh, +but I feel delighted + +by this for so many reasons. + +One is, that's beautiful. + +What a crazy +combination of symbols. + +But the second +and more important + +one is, look it has an l in it, +and the l is downstairs, right? + +That's good. + +It has more leverage that way. + +But so we've got +this l appearing, + +so the energy depends on l. + +Good, we've broken +the degeneracy. + +Different values of l +give different energies. + +So let's do that graphically. + +So in particular, +what this tells + +us is that now while the +Coulomb energy commuted + +with the Runge-Lenz +vector, it must be true + +that the energy of +this model of hydrogen, + +which includes the first +relativistic correction, + +does not commute with +the Runge-Lenz vector. + +And indeed, if you +check this-- which + +is effortful, but +not intellectually + +difficult-- indeed, +it doesn't vanish. + +And the failure of this +conservation equation, + +the failure this commutational +relation to vanish, + +tell us that it's +possible for the system + +to not be degenerate. + +And lo and behold, +it is not degenerate. + +OK? + +Yeah. + +AUDIENCE: So I just wanted +to clarify something that-- + +did you say before that the +actual first term when you + +encounter relativity just +includes substituting + +the non-relativistic +p to the 4th? + +PROFESSOR: Yes. + +Sorry, I should have said that. + +There are other things are +important for relativity + +that we'll come to +in a little bit. + +But if you just look +at the kinetic energy, + +this is the first +non-trivial correction. + +Yeah. + +AUDIENCE: So we still have +the 2l plus 1 degeneracy. + +PROFESSOR: We still have the +2l plus 1 degeneracy, exactly. + +Because does this correction +violate rotational invariance? + +No, that's p squared. + +That's a scalar under rotation. + +It's just the +number, not a vector. + +But E still commutes with l. + +And you see that because this +is independent of little m. + +This is the mass +of the electron. + +So this is independent of +the quantum number little m. + +It only depends on the +quantum number little l. + +So indeed, it is +still degenerate. + +So let's go through this and +see the degeneracy explicitly. + +And let me do that by drawing +you the following diagram. + +So what happens if we have +E1, which is the ground state? + +It has some energy which is +negative, which is minus E0. + +And when we include this first +correction, what does it do? + +Well, it decreases +it by some amount. + +Everyone cool with that? + +It doesn't change the number. + +It doesn't split any degeneracy, +because there was only + +one ground state +in the first place, + +because l had to +be 0 when n is 1. + +l has to be one less +than n or smaller. + +And if n is 1, l has to be 0. + +It can't be any smaller +than 0, so it's 0. + +There's just a one state, +with degeneracy 2, 0 + +plus 1, which is 1. + +OK so that's fine. + +It just changes the ground +state by some amount. + +Let's consider the +second excited level. + +So in the second excited +level, we have the states-- + +and let me name this +slightly differently, + +so this has energy minus E0. + +The ground state had l +equals 0, and m equals 0. + +It had to. + +For the second excited +state, n equals 2, + +how many states are there? + +2 squared is 4, so there are +four states, two, three, four. + +And what are their +values of l and m? + +Well, if n is 2, l +can be either 0 or 1. + +If it's 0, then m has to be 0. + +If it's 1, m could be +1, or it could be 0, + +or it could be minus 1. + +So this, again, is lm, lm, lm. + +So those are the four states +with energy E2 in the hydrogen + +atom. + +And now when we ask, what are +the energies of these three + +states, when we include this +so-called fine structure, what + +is this going to do? + +Well, the ground state is +going to get pushed down + +by some amount. + +I should draw this differently +to make it more vivid. + +This gets pushed down by some +amount, with some value of l. + +l here is 0. + +But for these +three states, which + +all have the same +value of little l, 1, + +the denominator is larger. + +So the amount by which it +gets pushed down is less. + +So these three states +get pushed down less, + +but the same amount +as each other. + +That cool? + +So these three states-- +degeneracy is 3, + +and this state degeneracy is 1. + +Now, notice that 1 +plus 3 is equal to 4 + +is equal to n squared. + +So these states split +into multiplets-- groups + +of states-- which have +to have the same energy + +by rotational invariance. + +If they have l +equas 1, there must + +be three states with the +same energy-- there must be. + +And states with l equals 0, +there's just the one state. + +And if we did the +same thing for E3, + +let's just think about +what would happen. + +So I'm just going +to write the l. + +I'm not going to include the m. + +We have the l equals 0 times 1. + +We have the l equals +1 state, times 3. + +And we have l equals 2 state. + +And how many states are there +in the l equals 2 state? + +Times 5, good. + +And again, this gets +pushed down to some value. + +This gets pushed +down to some value. + +This gets pushed +down to some value, + +where this is one, +three, and five. + +And again, these +add up to 9, which + +is 3 squared-- the degeneracy. + +So by turning on the +relativistic corrections, + +we break this degeneracy. + +We lift this degeneracy. + +You break the symmetry, +you lift the degeneracy. + +Now, unfortunately, +this isn't one + +we can control by turning +a dial in the lab. + +No experiment that +I can do in the lab + +will change the value +of the speed of light. + +Well, actually there +are experiments + +that will change the value +of the speed of light. + +If you work in medium, the +effective speed of light + +is different. + +So that's going to change +relativistic effects. + +So that's interesting. + +That tells you that you can +actually vary this continuously + +if you can vary continuously +the index of refraction + +of the ambient system. + +I invite you to think +about how you might do that + +experimentally, because +it's a fun question. + +OK, however, what +I'd really like + +is something where +Professor Evan in his lab + +can actually turn a dial, +and change the spectrum + +in a way that explicitly +breaks the symmetry. + +Meanwhile, I also +want an example + +that breaks the +rotational invariance. + +I want to break the 2l +plus 1 states up into 2l + +plus 1 states with +different energies. + +I want to make them +depend on the angular + +momentum in some direction. + +What must I do in order +to lift that degeneracy? + +AUDIENCE: Add a magnetic field. + +PROFESSOR: Fantastic. + +If you add a magnetic +field, why is that + +going to break the degeneracy? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Give +me an answer that + +depends, not on your +knowledge of chemistry, + +but give me an answer that +depends on symmetries. + +Why doe turning on +a magnetic field + +have the potential to split +the degeneracy of the 2l plus 1 + +states? + +AUDIENCE: You don't have +rotational symmetry. + +PROFESSOR: Thank you, exactly. + +You have no rotational +symmetry, exactly. + +So that's pretty good. + +So let's break the 2l plus 1 by +breaking rotational symmetry. + +There are many ways we could +break rotational symmetry. + +We could turn on +an electric field. + +We could turn on +a magnetic field. + +We could put a +shovel in the room. + +But anything that breaks +rotational symmetry will do it, + +but a very convenient way is +to do it with a magnetic field. + +Magnetic field is +particularly beautiful. + +So this is effect is now +call the Zeeman effect. + +I believe it was +Faraday-- one of + +the classic electromagnetists +of the 19th century attempted + +to look at the spectral +lines coming off glowing gas, + +and see if they +changed by turning + +on an electric or +a magnetic field. + +It turns out to be +a tricky experiment + +to do, because you need to +have a very well-controlled + +magnetic field, +otherwise what you + +get is just a bunch of schmutz. + +So to get a clean +spectrum, you have + +to have a very uniform magnetic +field, which is not trivial. + +It has to be time independent. + +So Zeeman, at the very end of +the 19th century-- in fact, + +this experiment was +done, I believe, in '96. + +So I think the paper +came out in '97 + +but the experiment +was done in '96. + +Zeeman did this experiment. + +He said look, if i turn +on a magnetic field + +next to a hot, glowing gas +and look the spectrum that + +comes off, anything +happen to it? + +Why would you think that +anything might happen? + +And the answer to this +one is really quite nice. + +Look, if we compute +the energy, the energy + +is going to be +equal to the Coulomb + +energy plus a correction, +which is the following-- + +if you think of the atom +as an electron that carries + +some angular momentum in +the presence of a proton, + +if you think of the electron as +a thing carrying some angular + +momentum, and a +thing with a charge-- + +it has a charge and +angular momentum. + +It's going to have +magnetic moment, mu. + +And the magnetic +moment is going to be + +equal to the current of the +charge times the area swept out + +divided by c, because we +work with sensible units. + +And this is equal to minus-- +for the case of the atom-- + +minus mu, the magnetic +moment of the system + +dotted into the magnetic +field that you turn on + +in the background. + +So this is a background +magnetic field. + +I am turning on an +electromagnet, which + +induces a magnetic field +in some known direction, + +with some known magnitude. + +So my dial is the +magnitude of that B field. + +I could make it large, +or I could make it small. + +And it's in a known direction. + +And the point is, our electron +because it's orbiting, + +because it carries +some angular momentum + +and it carries some in charge, +has some magnetic moment. + +So it behaves like +a little bar magnet. + +And that bar magnet wants to +anti-align with the background + +magnetic field that +I've turned on. + +So there's an energy penalty +to not being aligned. + +This is the usual dipole-dipole +potential from electrostatics. + +OK and mu here is equal to minus +E over 2mc-- angular momentum. + +So this can be computed from +a simple model of the atom. + +Whatever, it's easy to compute. + +So this is slightly +annoying, because if E + +is in some arbitrary direction, +let's just simplify our life + +and say that's equal to +E Coulomb minus mu B. + +And I want to turn on a +magnetic field of known + +amplitude in a known direction. + +Let's call it the z direction. + +So this is mu z. + +But this mu z, that's just mu +z is lz times minus E over 2mc. + +So this is going to +be plus E over 2mc, + +Bz-- I'm going to put +this all together, Bz Lz. + +Everyone cool with that? + +So where this is +coming from, again, + +is just the angular momentum +is telling you the velocity. + +The velocity is telling +you the current. + +And then the area is the radius. + +So that's what's giving you +the radius and the angular + +momentum. + +So this is our energy. + +What does this tell you +about the energy eigenvalues? + +They depend on m, right? + +And do we have to solve +the energy eigenvalue + +equation again? + +No, because our energy +eigenfunctions of Ec + +are proportional to +ylm, so they're already + +eigenfunctions of lz. + +So when I take this beast, and +I act on the wave functions + +I erased, but on the 1 upon +little r, capital R, sub nl, y + +sub lm-- when I act +on the ylm's, this + +is just going to give +me h bar m, right? + +So this is just a constant when +acting on the Coulomb energy + +eigenfunction. + +So this is a much +easier problem. + +That way, we don't even have +to make any approximations. + +We can just say exactly energy +Zeeman is equal to minus E0 + +upon n squared, nlm +plus E h bar upon 2mc, + +Bz-- the background +magnetic field, + +and this is the m of electron +mass-- times little m. + +And I'm going to write +little m sub l, just + +to distinguish little +m sub l from m sub E. + +So when we turn +on the prediction + +here, when we turn on the +magnetic field a la Zeeman, + +our energy levels will +get split according + +to the different values of m. + +Now if instead of working +with the pure Coulomb system, + +if we were in fact +a little clever, + +and we'd already noticed that +there's a fine structure-- + +because they already +knew that there + +was a fine structure +at this point-- + +they could see the +different spectra + +in lines coming off of hot gas. + +So it's just an +experimental fact + +you can't turn off +the fine structure. + +This is going to be equal +to e nlm of our correction + +to the hydrogen atom, with +the fine structure corrected. + +So the l equals 1 states and +the l equals 0 states are split. + +Let's focus, for example, on E2. + +So these guys have +a different energy. + +The l equals 1 guys +have a different energy + +than the l equals 0 guys. + +What does this predict +is going to happen + +if I look at my spectral line? + +So what this predicts +is the following-- + +it says that if you +have some spectrum that + +looks like this-- so this is +as a function of wavelength + +and i'm looking literally +at what comes off a prism. + +I'm looking at spectrum lines. + +And I'll have a line here. + +And these are going to +be the l equals 0 states. + +This is n equals 2. + +And then there's the +l equals 1 states. + +This is with zero magnetic +field-- Bz equals 0. + +If we turn on a magnetic +field, Bz not equal to zero, + +what should we see? + +Well, what happens +to this state? + +Nothing-- it's the same thing, +because the m is strictly 0, + +so it's the same value. + +And this guy, what +happens to it? + +The m equals 0 +state is the same. + +But then it breaks +up-- as everyone said, + +it breaks up into three lines +that are equally spaced. + +It breaks up into three +lines, because one of them + +has m which is plus 1, one +of them has m which is 0, + +and one is m is minus 1. + +So energies will +increase or decrease. + +Let's say this is frequency. + +So we get this splitting. + +And another way to draw +this is as a function of B, + +let's draw the energy levels. + +So there's the 1. + +There's the 0. + +And this stays constant. + +And these guys-- one is +constant, one increases, + +and one decreases. + +When you start getting into +strong magnetic fields, + +weird things happen, +like these guys cross, + +and all sorts of subtle +things can happen. + +But let's ignore the +strong magnetic field case, + +and just focus on this. + +So we see that these guys split. + +So this is what the Schrodinger +theory, or the full story + +would predict-- it came +a little bit after this, + +but this experiment +was done in '96, + +so there's actually kind of an +entertaining story about people + +trying to explain this +effect classically. + +Well, look you could +have some angular + +momentum in the z +direction, some angular + +momentum in the x direction, +some angular momentum in the y + +direction. + +The part that has angular +momentum in the x direction + +doesn't do anything, +or in the z direction. + +The part with the x +and part with the y + +can have different polars. + +There's a whole +classical song and dance. + +It's crazy. + +It doesn't make any sense. + +But that's because they were +trying to classical mechanics + +to do quantum mechanics, +which doesn't work. + +So I'm not even going +to bother explaining + +what they were thinking. + +But anyway, so people came up +with a sort of classical crutch + +to say, well that's +not totally insane. + +So this is what Zeeman +got, for example, + +by looking at hydrogen. + +But he did more than +just look at hydrogen. + +I can't remember exactly-- I +think he did it with sodium. + +Matt, do you remember? + +I think he did sodium and iron. + +But anyway, here's +the funny thing + +that he got with +sodium and iron. + +So this is a +different experiment. + +It's exactly the +same set up, but he + +was looking at spectral +lines in sodium. + +And spectral lines in sodium +did a very similar thing. + +There were some +where 1 went to 1. + +And there were +others where 1 went + +to-- why did we have three here? + +Just as quick reminder, why +do we have three states here? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Because we have +three states for l equals 1. + +This one state went to one, +two, three, four states, + +with none of them in the middle. + +And in fact, it's +worse than that, + +because they didn't go +to equally spaced states + +in general. + +In general, they did +something slightly funny. + +And the beautiful plot in +his paper looks like this. + +There are four states, and as +you take the magnetic field + +to 0, these four states +all coalesce exactly + +to this one state. + +So this one line is representing +four different states. + +And this already included +the fine structure, + +so we know that this is +all a single value of l. + +But that apparently +has four states. + +That's should worry you. + +What does that tell you about l? + +What does l have to +be in order to have + +four states in your tower? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Half integer-- +in particular, what value? + +3/2, crap. + +We already know that +these wave functions + +are described by +the ylm's, right? + +We solved that problem. + +We explicitly solved it. + +Here's the exact answer. + +It's the ylm's. + +But we've observed +experimentally + +that l has to be 3/2. + +But if l is 3/2, +ylm is equal to 0, + +because it's equal +to minus itself. + +This is bad. + +This is 0. + +So this effect is called +the Zeeman effect, + +and this effect is called +the anomalous Zeeman effect. + +[LAUGHTER] + +Which is strange +for two reasons. + +The first reason it's +strange is they showed up + +in the same paper. + +And the second thing is, OK, +you call it the Zeeman effect, + +because there's some +guy named Zeeman. + +Is there some guy +named Anomalous Zeeman? + +It's a very strange name. + +Anyway so this was called +the anomalous Zeeman effect, + +despite appearing in the same +paper, because it's weird. + +It was deeply +disconcerting to people. + +We now just call it +the Zeeman effect, + +but we have the bad habit-- +for entertainment value-- + +of referring to it still as +the anamolous Zeeman effect. + +I'm not the only one +responsible for that bad habit. + +I'm going to point out that at +the end of this paper-- it's + +a totally awesome +paper, by the way-- it's + +very readable and short-- +he says-- I was looking + +at it last night-- it +says, quote possibly + +the observed phenomenon +will be regarded + +as nothing of any consequence. + +OK, so a few years later, +Pauli says the following-- + +so Pauli says this, +actually, and this is also + +totally lovely in Science +from 1946 Pauli was in the US + +during the war. + +After the war, he was at the +Institute for Advanced Study. + +At the Institute for Advanced +Studies, while he was there, + +he got the Nobel Prize. + +And he gave-- for the +exclusion principle, which + +we are about to get to-- +and he gave a little spiel, + +and it's written up in +this edition of Science. + +And he says, quote, +a colleague who + +met me strolling +rather aimlessly + +in the beautiful +streets of Copenhagen + +said to me in a friendly +manner, "You look very unhappy." + +Whereupon, I responded fiercely, +"How can one look happy + +when he is thinking about +the anamolous Zeeman effect?" + +[LAUGHTER] + +So this troubled people. + +Yeah. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah he found +all sorts of crazy states. + +So this isn't the only example. + +It's just the only +one I'm going to draw. + +But indeed, you can +find five half states + +you can find states with six. + +AUDIENCE: Why [INAUDIBLE]? + +PROFESSOR: Oh, I didn't +draw all the states. + +The spectrum is complicated +and messy, because it's sodium. + +And so there's +all sorts of crap. + +So I'm just not drawing it. + +I'm just focusing on a +specific set of spectral lines. + +Maybe the best way +to draw that is-- OK. + +So this was really troubling. + +So let's put this on +pause for the moment, + +and we'll come back to +it in just a second. + +So meanwhile, there's +something else + +that's sort of annoying +about this system. + +We've got the Coulomb potential, +and the Coulomb potential + +has the following +beautiful property-- + +the degeneracy of any energy +state is equal to n squared. + +Meanwhile, various +people were fond + +of observing the fact that +the number of states, which + +I will-- in an +abuse of language-- + +call the degeneracy of the +level n in the periodic table, + +is equal to-- well, the +first one there's two. + +And then there's eight, +and then there's 18. + +So two, 8, 8, 18, that's +almost 2n squared. + +Two four 8, 9, 18. + +Cool, maybe there's a +relationship, right? + +And meanwhile, +it's very tempting + +to think there's a +relationship, because imagine + +you have four electrons. + +If you have four electrons, +what you do you do? + +Well, you put an +electron here, and then + +you could put an +electron here, or you + +could put an other +electron here. + +You could also put another +electron here and here. + +Or you could put them +in any combination-- two + +here, put two here, +two here, one, + +one-- you could do all +sorts of stuff, right? + +But if, for the +moment, you imagine + +that electrons have +this funny property. + +Imagine for a moment +that electrons + +have the property that they +can't be in the same state + +at once. + +Then if you have four +electrons-- I don't know why. + +I'm desperate. + +I'm thinking about the +anamolous Zeeman effect, + +among other things. + +I have nothing better to do. + +So just for fun, let's imagine +if I put an elector here, + +I can't put another one. + +So if I have a +two electron atom, + +the second one goes +with one of these. + +A three-electron atom, +a four-electron atom, + +and these guys are all related +to each other, because they + +live in the same +energy level, but they + +have different l +values, so they'll + +have slightly +different properties. + +That suggests that +the one l equals + +0 state should be different +from the 3 l equals 1 states, + +chemically. + +But wait-- there aren't +groupings of one and three. + +They're groupings +of two and six. + +Ah, two-- well, so Pauli +staring at this in 1925 + +said the following-- +he said, look, + +I'm going to +conjecture two things. + +The first is that +no two electrons + +can live in the same state-- +inhabit the same quantum state. + +That doesn't give us the +periodic table, though. + +It gives us half +the periodic table. + +There are twice as many states +in hydrogen as you think. + +And you might think that +I'm being facetious, + +that he said something a +little more sophisticated. + +But he really didn't. + +What he said is, I +posit of the existence + +of an additional quantum number +which the electron can have, + +which takes one of two values. + +Which translated, says, there +are twice as many states + +as you think. + +So that's exactly what he said. + +So this is called the +Pauli exclusion principle. + +And now this does a +totally spectacular thing-- + +and you've probably all seen +this in high school chemistry, + +or even college chemistry. + +Now, first electron goes +here, second electron + +goes here, because there +are twice as many states + +as you think, but then I can't +put another state in there, + +because that's as +many as you can have. + +One can go here, and you +can put up to six in here. + +And that's it. + +So the E2 states, the n squared, +which is 4 times 2 states, + +are somehow related to +each other naturally. + +And this gives you the +structure of the periodic table. + +In fact, an awful +lot of chemistry + +follows directly from this. + +So this is the Pauli +exclusion principle. + +However, it's a little +bit disappointing, + +because while this is +whatever-- some ridiculous rule, + +but we're doing +quantum mechanics + +and they're all +ridiculous rules. + +On the other hand, this +one is just stupid. + +Right? + +This is just, like, look, +it wouldn't it be nice? + +So in '25, a couple guys-- +really interesting characters-- + +named Goudsmit and Uhlenbeck-- +so Uhlenbeck-- wow, + +we're really low on time. + +OK, so I'll just tell +you this, and then I'll + +get to the last of it later. + +So Goudsmit and Uhlenbeck-- +who were young, kind of naive-- + +said, look we've got +two effects here. + +One effect is the +anamolous Zeeman effect, + +and there's this +weird fact that states + +have the wrong total +angular momentum. + +And we have this second +thing, that there are twice + +as many states for +an electron as you + +think in the Coulomb potential. + +How can these two things +fit together naturally? + +Well here's a guess-- +suppose that the angular + +momentum that we +calculated when we + +did the estimate of the braking +due to the Zeeman effect, + +suppose that angular momentum +was not the right angular + +momentum. + +Maybe there's more angular +momentum in the system. + +There's angular momentum in +the system from the electron + +orbiting around, but maybe +like a little, tiny Earth, + +the electron itself can +have some intrinsic angular + +momentum. + +It turns out Pauli had +had this idea before. + +In fact, Kramers +had suggested this + +to him, who was a very +young guy at the time. + +And Pauli said, you're +a blithering idiot, + +because if you calculate +how small an electron has + +to be in order to fit all the +other things we know, and you + +figure out how fast it would +have to rotate to explain + +the anamolous Zeeman +effect, the surface + +would have to be moving +faster the speed of light. + +That's ridiculous. + +Leave my office. + +So then Uhlenbeck and Goudsmit-- +these two guys-- write a paper, + +and say aha! + +Well, we can explain +this, but let's just not + +assume that the stupid +thing is rotating. + +Let's just say an electron +has some intrinsic angular + +momentum. + +I don't know, why not? + +Electrons have intrinsic +angular momentum, + +and if you assume that electrons +have an intrinsic angular + +momentum-- which I'll call +S for the moment-- so then + +the total angular +momentum, j, is + +equal to l, its orbital +angular momentum, + +plus some intrinsic +angular momentum, which-- + +I don't remember what symbol +they used, but we'll call it + +for the moment S-- where +this has the property that S + +squared, for an electron, +sorry, the principle quantum + +number, which I will call +little s is equal to 1/2, + +so m sub s is equal +to plus or minus 1/2. + +So this is like the l equals +1/2 state, but it's not l. + +It's something intrinsic. + +It has nothing to do +with anything rotating. + +It's just a fact +about electrons. + +Suppose electrons have +a little bit of spin. + +Then what you discover is if +you have the l equals 1 state, + +and the electron +has spin 1/2, what's + +the total angular momentum? + +3/2, right? + +So what do you get? + +You get quadruplets, like that. + +So this turns out to +explain-- if you include + +a small relativistic +effect-- this turns out + +to explain the anomalous +Zeeman effect bang on. + +Meanwhile, there +was an experiment + +done in 1922, which is the +Stern-Gerlach experiment, + +in which Stern and Gerlach +discovered that nickel, when + +sent through a magnetic +field gradient, + +bent into one of two +different spots-- never three, + +never zero, always two. + +How can that be? + +Electron spin-- that +wasn't realized until 1929, + +that the connection was there. + +So these guys came up with +this ridiculous postulate. + +This was Uhlenbeck and Goudsmit. + +And let me just quickly-- +U-H-L-E-N-B-E-C-K-- + +so Uhlenbeck-- amazing, +amazing scientist, + +also the father of the +mathematician Uhlenbeck, + +and she was a total badass, +and has inspired an awful lot + +of physics-- Karen +Uhlenbeck, who's at UT. + +So this is a pretty +interesting and prolific guy. + +But he was also prolific +in the following way-- + +he ran a program at the Rad +Lab at MIT during World War II. + +And Goudsmit worked with him. + +And when they were finishing +up, when the war was ending, + +Goudsmit became the scientific +adviser to something + +called Project Alsos. + +Project Alsos was a project +where the military went + +to the conquered +territories in Germany + +to catch the German +atomic scientists, + +and bring them to a +place called Farm Hall + +in England, where they listened +and eavesdropped on them-- + +Heisenberg, all the good guys. + +Well, bad guys-- it depends +on-- all the great physicist + +in the German +territory at the time + +were deeply complicated people. + +And they listened to them. + +Something called the +Farm Hall Transcripts + +are the transcripts +of those recordings. + +They were written up in a book +called "The Epsilon Project," + +which is totally +breathtakingly awesome. + +And Goudsmit wrote a +book called "Alsos" + +about this process of hunting +down the German scientists. + +So Goudsmit, +G-O-U-D-S-M-I-T, I think, + +he wrote a book called "Alsos", +which I heartily recommend + +to you, because it's like a +combination adventure story + +and beautiful bit +of physics history. + +So these guys both were at +MIT during the World War. + +So there's a nice +connection here. + +So these guys-- +fascinating characters, + +and they came up with this +idea of some intrinsic angular + +momentum. + +Pauli then calls it spin. + +He gives it the name. + +And he develops a +mathematical theory of spin. + +And the mathematical +theory of spin + +will lead to quantum field +theory, relativistic quantum + +mechanics, and will +eventually lead + +to quantum computation, +which is going + +to be the topic of the +last week of our course. + +So what we've done +so far is we've + +explained the discreteness +of atomic spectra, + +and we've explained +the structure + +of the periodic table. + +What we haven't +done, is we haven't + +explained why atoms form +molecules or solids. + +And we also haven't explained +what spin is at all. + +Those are the topics in +the next three weeks. + +See you next time. \ No newline at end of file diff --git a/GJ2klfD0Q3g.txt b/GJ2klfD0Q3g.txt new file mode 100644 index 0000000000000000000000000000000000000000..f1766bee2226f7deb479bf2537ac2a226b7d0db6 --- /dev/null +++ b/GJ2klfD0Q3g.txt @@ -0,0 +1,684 @@ +Hi. + +In this video, we're going to +compute some useful quantities + +for the exponential +random variable. + +So we're given that x is +exponential with rate lambda. + +PDF looks like this, and +the formula is here. + +First question, part +a, what's the CDF? + +So let's go right in. + +The CDF of x is the probability +that X is less + +than or equal to little x. + +Let's look at some cases here. + +What if little x +is less than 0? + +Well, x random variable +only takes on these + +non-negative values. + +And so the probability that X is +less than or equal to some + +negative number is +going to be 0. + +On the other hand, if x is +greater than or equal to 0, we + +do actually have to +integrate here. + +So to do that, we take the +integral from minus infinity + +to x of fx of t-- + +the dummy variable +here used is t. + +Notice that again, fx of t is +going to be 0 for negative + +values, so we take the +integral here from 0. + +And now we plug in +for fx of t. + +That's minus lambda t dt. + +And recall that the integral +of u to the a t is 1 over a + +times e to the a t. + +So here in this case, +we'll get lambda, + +which is just a constant. + +And then a here is going +to be negative lambda. + +So we get this, 0 to x. + +Lambdas cancel and we actually +get 1 minus e to the + +minus lambda x. + + + +So do this. + +And we are done with the CDF. + + + +Now for the expectation. + +We use the standard formula, +which is minus infinity to + +infinity t times fx of t dt. + +So again, fx of t is going to +be 0 for a negative value. + +So we do the integral from 0. + +We get 0 to infinity t lambda +e to the minus lambda t dt. + +Now, you can try all you want +to get rid of this t. + +It's not going to go even if +you try all kinds of u + +substitution. + +But at the end the day, you're +going to have to pull out your + +calculus textbook and find +the integration by parts + +formula, which is-- + + + +v du. + + + +So the hope is that this +integral is going to be easier + +than the one on the left. + +Notice that this is the +integral of one + +of the terms here. + +And this is the derivative +of one of the terms. + +So that may help you decide +on how you select u and v. + +In our case actually, I'm +going to use u as-- + +t for u. + +Because when you take +the derivative, it's + +going to become 1. + +And the derivative is what's +going to go in that integral. + + + +So this is going to +be dt for du. + +And then, dv I'm going +to select as + +whatever's left over. + +It's lambda e to minus +lambda t dt. + +So v is going to be-- + +we already did the integral-- + +minus e to the minus lambda t. + + + +And so if we do this, it's going +to be negative t times e + +to the minus lambda t. + +So that's uv. + +Minus v, which is negative +e to the minus + +lambda t times dt. + +That goes from 0 to infinity. + +This is evaluated from +0 to infinity. + +Well, what does it mean +for this to be + +evaluated from 0 to infinity? + +A better and easier way to look +at this is to say, well, + +it's going to go from 0 to x. + +But then you take the limit +as x goes to infinity. + +So that's going to +help us here. + +And this negative-- + +these negatives cancel. + +And we're left with-- + +let's plug in the bounds. + +We're left with negative x +minus lambda x plus the + +integral of this is going to be +1 over negative lambda e to + +the minus lambda t evaluated +from 0 to infinity. + +All right, so now the limit. + +So for the limit, notice +that x increases + +as x goes to infinity. + +And this exponential decays. + +So they're kind of competing +for each other. + +But the exponential is going to +win because it decays way + +faster than x. + +And so this first term +is going to go off-- + +the limit is going to go to 0. + + + +All right. + +For this, if you evaluate +the balance, the + +infinity makes this 0. + +And 0, you're going to +get 1 over lambda. + +So that's 1 over lambda. + +All right. + +And so the expectation +is 1 over lambda. + +OK, so now what's +the variance? + +That's part c, right? + +So we use the standard formula +for variance, which is this. + + + +We already figured out +the expectation. + +We just need to figure out the +expectation of x squared. + +Well, we're just going to follow +the same set of steps + +from before. + +For x squared, it's just going +to be t squared, t squared, t + +squared, x squared. + +The only thing that's going to +change is what we choose for u + +here, for the u substitution. + +So it's going to be t squared. + +So the derivative is going +to change to 2t dt. + +v is going to be exactly +the same. + +And so here in this term, we +get negative 2t e to the + +minus lambda t. + +But there's a negative sign +out here, so the negatives + +cancel and we're left with +a positive sign here. + +This is going to change. + +All right. + +OK. + +So in order to do this integral, +we can use a trick. + +We can move this-- + +so there's a 2t here. + +We move this 2 in here, +leave the t inside. + +And you have to leave +the t inside. + +But multiply by lambda +and divide by lambda. + + + +Now, look at that integral. + +0 to infinity t times lambda +e to the minus lambda t dt. + +Exactly the expectation +that we computed. + +We already did that. + +That is just 1 over lambda, so +it's 2 over lambda times 1 + +over lambda. + +Again, the limit as x +goes to infinity-- + +the exponential will +beat x squared. + +No matter what polynomial +we put in there, the + +exponential's going to win. + +So this is going +to be 0 still. + +This one's going to be 2 +over lambda squared. + +So we're left with 2 over lambda +squared for expectation + +of x squared. + +And so we have 1 over lambda +squared for the variance. + +OK, so we're done with +the variance. + + + +Part d. + +We're given that x1, x2, and +x3 are independent and + +identically distributed. + +They're exponentials +with rate lambda. + +We're asked for the PDF +of z, which is the max + +of x1, x2, and x2. + +How do we generally +find a PDF? + +We take the CDF and then take +the derivative, right? + +We first find the CDF, and +then take the derivative. + +So let's do that. + +So first, let's see. + +Part d, find the CDF of z, +which is going to be the + +probability that Z is less than +or equal to little z, + +which is going to be equal to +the probability that the max + +of x1, x2, x3 is less +than or equal to z. + +And this is going to have +the same sort of + +structure as before. + +If z is less than 0, x1, +x2, x3 are positive-- + +non-negative. + +And so this is the probability +that if you get little z less + +than 0, you're not going to have +any probability there. + +And so if z is greater than or +equal to 0 is where it gets + +interesting. + +We need to do something +special. + + + +So the special thing here +is to recognize that the + +probability of the max being +less than or equal to z is + +actually also the probability +of each of these random + +variables individually being +less than or equal to z. + +Why is that true? + +One way to check whether the +events-- these two events are + +the same is to check +the two directions. + +One direction say, if the max of +x1, x2, x3 is less than or + +equal to z, does that mean x1 is +less than or equal to z, x2 + +is less than or equal +to z, and x3 is less + +than or equal to z? + +Yes. + +OK. + +And then, if x1, x2, and x3 are +individually less than or + +equal to z, then the max is also +less than or equal to z. + +So these two events are +equivalent and this is true. + +By independence we can +break this up. + + + +And we get-- + +these are all CDFs of the +exponential and they + +all have this form. + +So it's just going to +be 1 minus e to the + +minus lambda z cubed. + +Plug this in here. + + + +And then, try to take the +derivative to get the PDF. + + + +Let's see. + +So it's going to be the same, +like this for z less than 0. + +For z greater than or equal +to 0, it's going to be the + +derivative of this thing. + +Derivative of this thing is by +chain rule, 3 times 1 minus e + +to the minus lambda z squared. + +Then the derivative of negative +e to the minus lambda + +z, that's just lambda e +to the minus lambda z. + +There we go. + +This is the PDF we +were looking for. + +So last problem. + +We're looking for the PDF +of w, which is the + +min of x1 and x2. + +So let's try this as +a similar approach. + +Try the same thing, actually. + +See if it works. + + + +So w, w, w, w, min, less +than or equal to w. + + + +OK. + +So let's see if this works. + + + +Is it true that the min-- + +if the min of x1 and x2 is less +than or equal to w, that + +each of them is less +than or equal to w? + +No, right? + +X1 could be less than or +equal to w and x2 could + +be bigger than w. + +And the min could still be +less than or equal to w. + +So that's definitely not true. + +So what do we do here? + +The trick is to flip it and say +we want to compute the min + +of x1 and x2 being +greater than w. + +In that case, let's check +if we can do this trick. + + + +If the min of x1 and x2 is +greater than w, then clearly + +x1 is bigger than w and +x2 is bigger than w. + +And if x1 and x2 are +individually bigger than w, + +then clearly the min's +also bigger than w. + +So this works. + +And now we can use independence +as before. + + + +And for this, this is just +1 minus the CDF here. + +So it's just going to be +e to the minus lambda + +w for each of them. + +But that's the same as e +to the minus lambda 2w. + + + +Or e to the 2 lambda w. + +So it's going to be-- + + + +Notice the similarity between +this and this. + + + +The only difference is this +has a 2 lambda in there. + +That means that w is an +exponential random variable + +with rate 2 lambda. + +So then the PDF is going to be +an exponential, whatever it is + +for an exponential. + +Except with rate 2 lambda. + + + +You can also take the derivative +of this and find + +that you get this. + +OK, so we're done with +the problems. + +We computed some interesting +quantities for the exponential + +random variable in this-- \ No newline at end of file diff --git a/Gbtma_UQpro.txt b/Gbtma_UQpro.txt new file mode 100644 index 0000000000000000000000000000000000000000..fbfce484fb2b174edeb0565f2ad9c972cf88954b --- /dev/null +++ b/Gbtma_UQpro.txt @@ -0,0 +1,2347 @@ +align:start position:0% + +welcome to recitation today in this + + align:start position:0% +welcome to recitation today in this + + + align:start position:0% +welcome to recitation today in this +video what we're going to do is look at + + align:start position:0% +video what we're going to do is look at + + + align:start position:0% +video what we're going to do is look at +how we can determine the graph of a + + align:start position:0% +how we can determine the graph of a + + + align:start position:0% +how we can determine the graph of a +derivative of a function from the graph + + align:start position:0% +derivative of a function from the graph + + + align:start position:0% +derivative of a function from the graph +of the function itself so I've given a + + align:start position:0% +of the function itself so I've given a + + + align:start position:0% +of the function itself so I've given a +function here uh we're calling it just + + align:start position:0% +function here uh we're calling it just + + + align:start position:0% +function here uh we're calling it just +yals F ofx this is or this is the curve + + align:start position:0% +yals F ofx this is or this is the curve + + + align:start position:0% +yals F ofx this is or this is the curve +y equals F ofx so we're thinking about a + + align:start position:0% +y equals F ofx so we're thinking about a + + + align:start position:0% +y equals F ofx so we're thinking about a +function f ofx I'm not giving you the + + align:start position:0% +function f ofx I'm not giving you the + + + align:start position:0% +function f ofx I'm not giving you the +equation for the function I'm just + + align:start position:0% +equation for the function I'm just + + + align:start position:0% +equation for the function I'm just +giving the graph and what I'd like you + + align:start position:0% +giving the graph and what I'd like you + + + align:start position:0% +giving the graph and what I'd like you +to do what I'd like us to do in this + + align:start position:0% +to do what I'd like us to do in this + + + align:start position:0% +to do what I'd like us to do in this +time is to figure out what the the curve + + align:start position:0% +time is to figure out what the the curve + + + align:start position:0% +time is to figure out what the the curve +yal frime of X will look like so that's + + align:start position:0% +yal frime of X will look like so that's + + + align:start position:0% +yal frime of X will look like so that's +our objective um so what we'll do first + + align:start position:0% +our objective um so what we'll do first + + + align:start position:0% +our objective um so what we'll do first +is try and figure out the the things + + align:start position:0% +is try and figure out the the things + + + align:start position:0% +is try and figure out the the things +that we know about fpre of X so what I + + align:start position:0% +that we know about fpre of X so what I + + + align:start position:0% +that we know about fpre of X so what I +want to remind you is that when you + + align:start position:0% +want to remind you is that when you + + + align:start position:0% +want to remind you is that when you +think about a function's derivative + + align:start position:0% +think about a function's derivative + + + align:start position:0% +think about a function's derivative +remember it's derivatives output is + + align:start position:0% +remember it's derivatives output is + + + align:start position:0% +remember it's derivatives output is +measuring the slope of the tangent line + + align:start position:0% +measuring the slope of the tangent line + + + align:start position:0% +measuring the slope of the tangent line +at each point so that's what we're + + align:start position:0% +at each point so that's what we're + + + align:start position:0% +at each point so that's what we're +interested in finding is understanding + + align:start position:0% +interested in finding is understanding + + + align:start position:0% +interested in finding is understanding +the slope of the tangent line of this + + align:start position:0% +the slope of the tangent line of this + + + align:start position:0% +the slope of the tangent line of this +curve uh at each x value so it's always + + align:start position:0% +curve uh at each x value so it's always + + + align:start position:0% +curve uh at each x value so it's always +easiest when you're thinking about a + + align:start position:0% +easiest when you're thinking about a + + + align:start position:0% +easiest when you're thinking about a +derivative to find the places where the + + align:start position:0% +derivative to find the places where the + + + align:start position:0% +derivative to find the places where the +slope of the tangent line is zero + + align:start position:0% +slope of the tangent line is zero + + + align:start position:0% +slope of the tangent line is zero +because those are the only places where + + align:start position:0% +because those are the only places where + + + align:start position:0% +because those are the only places where +you can hope to change the sign on the + + align:start position:0% +you can hope to change the sign on the + + + align:start position:0% +you can hope to change the sign on the +derivative so what we'd like to do is + + align:start position:0% +derivative so what we'd like to do is + + + align:start position:0% +derivative so what we'd like to do is +first identify on this curve where the + + align:start position:0% +first identify on this curve where the + + + align:start position:0% +first identify on this curve where the +tangent line has slope equal to zero and + + align:start position:0% +tangent line has slope equal to zero and + + + align:start position:0% +tangent line has slope equal to zero and +I think there are two places we can find + + align:start position:0% +I think there are two places we can find + + + align:start position:0% +I think there are two places we can find +it fairly easily that would be at + + align:start position:0% +it fairly easily that would be at + + + align:start position:0% +it fairly easily that would be at +whatever this x value is that slope + + align:start position:0% +whatever this x value is that slope + + + align:start position:0% +whatever this x value is that slope +there is zero it's going to be a + + align:start position:0% +there is zero it's going to be a + + + align:start position:0% +there is zero it's going to be a +horizontal tangent line and then + + align:start position:0% +horizontal tangent line and then + + + align:start position:0% +horizontal tangent line and then +whatever this x value is the slope there + + align:start position:0% +whatever this x value is the slope there + + + align:start position:0% +whatever this x value is the slope there +is also zero horizontal tangent line but + + align:start position:0% +is also zero horizontal tangent line but + + + align:start position:0% +is also zero horizontal tangent line but +there's one third place where the slope + + align:start position:0% +there's one third place where the slope + + + align:start position:0% +there's one third place where the slope +of the tangent line is zero and that's + + align:start position:0% +of the tangent line is zero and that's + + + align:start position:0% +of the tangent line is zero and that's +kind of hidden right in here and + + align:start position:0% +kind of hidden right in here and + + + align:start position:0% +kind of hidden right in here and +actually I I've drawn it maybe you think + + align:start position:0% +actually I I've drawn it maybe you think + + + align:start position:0% +actually I I've drawn it maybe you think +there are a few more but we're we're + + align:start position:0% +there are a few more but we're we're + + + align:start position:0% +there are a few more but we're we're +going to assume that this function is + + align:start position:0% +going to assume that this function is + + + align:start position:0% +going to assume that this function is +always continuing down through this + + align:start position:0% +always continuing down through this + + + align:start position:0% +always continuing down through this +region so there are three places where + + align:start position:0% +region so there are three places where + + + align:start position:0% +region so there are three places where +the horiz the tangent line is horizontal + + align:start position:0% +the horiz the tangent line is horizontal + + + align:start position:0% +the horiz the tangent line is horizontal +so I could even sort of draw them light + + align:start position:0% +so I could even sort of draw them light + + + align:start position:0% +so I could even sort of draw them light +lightly through here + + align:start position:0% +lightly through here + + + align:start position:0% +lightly through here +here you have three horizontal tangent + + align:start position:0% +here you have three horizontal tangent + + + align:start position:0% +here you have three horizontal tangent +lines so at those points we know that + + align:start position:0% +lines so at those points we know that + + + align:start position:0% +lines so at those points we know that +the derivatives value is equal to zero + + align:start position:0% +the derivatives value is equal to zero + + + align:start position:0% +the derivatives value is equal to zero +the output is equal to zero and now what + + align:start position:0% +the output is equal to zero and now what + + + align:start position:0% +the output is equal to zero and now what +we can determine is between those + + align:start position:0% +we can determine is between those + + + align:start position:0% +we can determine is between those +regions where are the values of the + + align:start position:0% +regions where are the values of the + + + align:start position:0% +regions where are the values of the +derivative positive and negative so what + + align:start position:0% +derivative positive and negative so what + + + align:start position:0% +derivative positive and negative so what +I'm going to do is is below here I'm + + align:start position:0% +I'm going to do is is below here I'm + + + align:start position:0% +I'm going to do is is below here I'm +just going to make a line and we're + + align:start position:0% +just going to make a line and we're + + + align:start position:0% +just going to make a line and we're +going to sort of keep track of what the + + align:start position:0% +going to sort of keep track of what the + + + align:start position:0% +going to sort of keep track of what the +signs of the derivative are so let me + + align:start position:0% +signs of the derivative are so let me + + + align:start position:0% +signs of the derivative are so let me +just draw this will be sort of our our + + align:start position:0% +just draw this will be sort of our our + + + align:start position:0% +just draw this will be sort of our our +sign + + align:start position:0% + + + + align:start position:0% + +on + + align:start position:0% +on + + + align:start position:0% +on +fime okay so that's going to tell us + + align:start position:0% +fime okay so that's going to tell us + + + align:start position:0% +fime okay so that's going to tell us +what our signs are so right below we'll + + align:start position:0% +what our signs are so right below we'll + + + align:start position:0% +what our signs are so right below we'll +keep track so here this I'll just come + + align:start position:0% +keep track so here this I'll just come + + + align:start position:0% +keep track so here this I'll just come +straight down here we know the sign of + + align:start position:0% +straight down here we know the sign of + + + align:start position:0% +straight down here we know the sign of +frime is equal to zero okay we know it's + + align:start position:0% +frime is equal to zero okay we know it's + + + align:start position:0% +frime is equal to zero okay we know it's +equal to zero there we know it's also + + align:start position:0% +equal to zero there we know it's also + + + align:start position:0% +equal to zero there we know it's also +equal to zero here and we know it's also + + align:start position:0% +equal to zero here and we know it's also + + + align:start position:0% +equal to zero here and we know it's also +equal to zero + + align:start position:0% +equal to zero + + + align:start position:0% +equal to zero +here okay and now the question is what + + align:start position:0% +here okay and now the question is what + + + align:start position:0% +here okay and now the question is what +is the sign of fime in this region so to + + align:start position:0% +is the sign of fime in this region so to + + + align:start position:0% +is the sign of fime in this region so to +the left of whatever that x value is + + align:start position:0% +the left of whatever that x value is + + + align:start position:0% +the left of whatever that x value is +what is the sign of fime in this region + + align:start position:0% +what is the sign of fime in this region + + + align:start position:0% +what is the sign of fime in this region +in this region and then to the right so + + align:start position:0% +in this region and then to the right so + + + align:start position:0% +in this region and then to the right so +there really we can divide up the X + + align:start position:0% +there really we can divide up the X + + + align:start position:0% +there really we can divide up the X +values as left of whatever that x value + + align:start position:0% +values as left of whatever that x value + + + align:start position:0% +values as left of whatever that x value +is in between these two x values in + + align:start position:0% +is in between these two x values in + + + align:start position:0% +is in between these two x values in +between these two x values and to the + + align:start position:0% +between these two x values and to the + + + align:start position:0% +between these two x values and to the +right of this x value that's really + + align:start position:0% +right of this x value that's really + + + align:start position:0% +right of this x value that's really +really what we need to do to determine + + align:start position:0% +really what we need to do to determine + + + align:start position:0% +really what we need to do to determine +what the signs uh of fime are so again + + align:start position:0% +what the signs uh of fime are so again + + + align:start position:0% +what the signs uh of fime are so again +what we want to do to understand fime is + + align:start position:0% +what we want to do to understand fime is + + + align:start position:0% +what we want to do to understand fime is +we look at the slope of the tangent line + + align:start position:0% +we look at the slope of the tangent line + + + align:start position:0% +we look at the slope of the tangent line +of the curve yal FX so let's pick a + + align:start position:0% +of the curve yal FX so let's pick a + + + align:start position:0% +of the curve yal FX so let's pick a +place in this region left of where it's + + align:start position:0% +place in this region left of where it's + + + align:start position:0% +place in this region left of where it's +zero say right here and let's look at + + align:start position:0% +zero say right here and let's look at + + + align:start position:0% +zero say right here and let's look at +the tangent line the tangent + + align:start position:0% + + + + align:start position:0% + +line has what kind of slope well it has + + align:start position:0% +line has what kind of slope well it has + + + align:start position:0% +line has what kind of slope well it has +a positive slope and in fact if you look + + align:start position:0% +a positive slope and in fact if you look + + + align:start position:0% +a positive slope and in fact if you look +along here you see all of the slopes are + + align:start position:0% +along here you see all of the slopes are + + + align:start position:0% +along here you see all of the slopes are +positive so fime is bigger than zero + + align:start position:0% +positive so fime is bigger than zero + + + align:start position:0% +positive so fime is bigger than zero +here and now I'm just going to record + + align:start position:0% +here and now I'm just going to record + + + align:start position:0% +here and now I'm just going to record +that I'm going to keep that in mind as a + + align:start position:0% +that I'm going to keep that in mind as a + + + align:start position:0% +that I'm going to keep that in mind as a +as a plus the sign is positive there now + + align:start position:0% +as a plus the sign is positive there now + + + align:start position:0% +as a plus the sign is positive there now +if I if I look right of where fime + + align:start position:0% +if I if I look right of where fime + + + align:start position:0% +if I if I look right of where fime +equals zero if I look for X values to + + align:start position:0% +equals zero if I look for X values to + + + align:start position:0% +equals zero if I look for X values to +the right I see that as I move to the + + align:start position:0% +the right I see that as I move to the + + + align:start position:0% +the right I see that as I move to the +right the tangent line is curving down + + align:start position:0% +right the tangent line is curving down + + + align:start position:0% +right the tangent line is curving down +so let me do it with the chalk you see + + align:start position:0% +so let me do it with the chalk you see + + + align:start position:0% +so let me do it with the chalk you see +the tangent line Looks has a slope + + align:start position:0% +the tangent line Looks has a slope + + + align:start position:0% +the tangent line Looks has a slope +negative slope if I draw one point in it + + align:start position:0% +negative slope if I draw one point in it + + + align:start position:0% +negative slope if I draw one point in it +looks something like that so the slope + + align:start position:0% +looks something like that so the slope + + + align:start position:0% +looks something like that so the slope +is negative there so here I can record + + align:start position:0% +is negative there so here I can record + + + align:start position:0% +is negative there so here I can record +that the sign of fime is a minus sign + + align:start position:0% +that the sign of fime is a minus sign + + + align:start position:0% +that the sign of fime is a minus sign +there now if I look between these two x + + align:start position:0% +there now if I look between these two x + + + align:start position:0% +there now if I look between these two x +values which I'm saying here it's zero + + align:start position:0% +values which I'm saying here it's zero + + + align:start position:0% +values which I'm saying here it's zero +and here it's zero for the X values and + + align:start position:0% +and here it's zero for the X values and + + + align:start position:0% +and here it's zero for the X values and +I take a take a point which we notice + + align:start position:0% +I take a take a point which we notice + + + align:start position:0% +I take a take a point which we notice +the sign is negative there also so in + + align:start position:0% +the sign is negative there also so in + + + align:start position:0% +the sign is negative there also so in +fact the sign the sign of fime changed + + align:start position:0% +fact the sign the sign of fime changed + + + align:start position:0% +fact the sign the sign of fime changed +at this zero of fime but it stays the + + align:start position:0% +at this zero of fime but it stays the + + + align:start position:0% +at this zero of fime but it stays the +same uh around this zero of fime so it's + + align:start position:0% +same uh around this zero of fime so it's + + + align:start position:0% +same uh around this zero of fime so it's +negative and then it goes to negative + + align:start position:0% +negative and then it goes to negative + + + align:start position:0% +negative and then it goes to negative +again it's negative then zero then + + align:start position:0% +again it's negative then zero then + + + align:start position:0% +again it's negative then zero then +negative and then if I look to the right + + align:start position:0% +negative and then if I look to the right + + + align:start position:0% +negative and then if I look to the right +of this x value and I take a + + align:start position:0% +of this x value and I take a + + + align:start position:0% +of this x value and I take a +point I see that the the slope of the + + align:start position:0% +point I see that the the slope of the + + + align:start position:0% +point I see that the the slope of the +tangent line is positive and so the sign + + align:start position:0% +tangent line is positive and so the sign + + + align:start position:0% +tangent line is positive and so the sign +there is + + align:start position:0% +there is + + + align:start position:0% +there is +positive so we have the Der is positive + + align:start position:0% +positive so we have the Der is positive + + + align:start position:0% +positive so we have the Der is positive +and then zero and then negative and then + + align:start position:0% +and then zero and then negative and then + + + align:start position:0% +and then zero and then negative and then +zero and then negative and then zero and + + align:start position:0% +zero and then negative and then zero and + + + align:start position:0% +zero and then negative and then zero and +then positive so there's a lot going on + + align:start position:0% +then positive so there's a lot going on + + + align:start position:0% +then positive so there's a lot going on +but I if I want to plot now yals fime of + + align:start position:0% +but I if I want to plot now yals fime of + + + align:start position:0% +but I if I want to plot now yals fime of +X I have some sort of launching Point by + + align:start position:0% +X I have some sort of launching Point by + + + align:start position:0% +X I have some sort of launching Point by +which to do that so what I can do is I + + align:start position:0% +which to do that so what I can do is I + + + align:start position:0% +which to do that so what I can do is I +know that the derivative zero I'm going + + align:start position:0% +know that the derivative zero I'm going + + + align:start position:0% +know that the derivative zero I'm going +to draw the derivative in in blue here + + align:start position:0% +to draw the derivative in in blue here + + + align:start position:0% +to draw the derivative in in blue here +the derivative is zero its output is + + align:start position:0% +the derivative is zero its output is + + + align:start position:0% +the derivative is zero its output is +zero at these places so I'm going to put + + align:start position:0% +zero at these places so I'm going to put + + + align:start position:0% +zero at these places so I'm going to put +those points + + align:start position:0% +those points + + + align:start position:0% +those points +on and then if I were just trying to get + + align:start position:0% +on and then if I were just trying to get + + + align:start position:0% +on and then if I were just trying to get +a rough idea of what happen the + + align:start position:0% +a rough idea of what happen the + + + align:start position:0% +a rough idea of what happen the +derivative is positive left of this x + + align:start position:0% +derivative is positive left of this x + + + align:start position:0% +derivative is positive left of this x +value so it's certainly coming + + align:start position:0% +value so it's certainly coming + + + align:start position:0% +value so it's certainly coming +down it's coming down oops let me make + + align:start position:0% +down it's coming down oops let me make + + + align:start position:0% +down it's coming down oops let me make +these a little + + align:start position:0% +these a little + + + align:start position:0% +these a little +darker it's coming down because it's + + align:start position:0% +darker it's coming down because it's + + + align:start position:0% +darker it's coming down because it's +positive it's coming down to zero it has + + align:start position:0% +positive it's coming down to zero it has + + + align:start position:0% +positive it's coming down to zero it has +to stay above the x- axxis but it has to + + align:start position:0% +to stay above the x- axxis but it has to + + + align:start position:0% +to stay above the x- axxis but it has to +head toward zero right what does that + + align:start position:0% +head toward zero right what does that + + + align:start position:0% +head toward zero right what does that +actually correspond to well look at what + + align:start position:0% +actually correspond to well look at what + + + align:start position:0% +actually correspond to well look at what +the slopes are doing the slopes of these + + align:start position:0% +the slopes are doing the slopes of these + + + align:start position:0% +the slopes are doing the slopes of these +tangent lines as I move in the X + + align:start position:0% +tangent lines as I move in the X + + + align:start position:0% +tangent lines as I move in the X +Direction the slope let me just keep my + + align:start position:0% +Direction the slope let me just keep my + + + align:start position:0% +Direction the slope let me just keep my +hand watch what my hand is doing the + + align:start position:0% +hand watch what my hand is doing the + + + align:start position:0% +hand watch what my hand is doing the +slope is is always positive but it's + + align:start position:0% +slope is is always positive but it's + + + align:start position:0% +slope is is always positive but it's +becoming less and less vertical right + + align:start position:0% +becoming less and less vertical right + + + align:start position:0% +becoming less and less vertical right +it's headed towards horizontal so the + + align:start position:0% +it's headed towards horizontal so the + + + align:start position:0% +it's headed towards horizontal so the +slope that was steeper over here is + + align:start position:0% +slope that was steeper over here is + + + align:start position:0% +slope that was steeper over here is +becoming less steep the steepness is + + align:start position:0% +becoming less steep the steepness is + + + align:start position:0% +becoming less steep the steepness is +really the magnitude of the derivative + + align:start position:0% +really the magnitude of the derivative + + + align:start position:0% +really the magnitude of the derivative +that's really measuring how far it is + + align:start position:0% +that's really measuring how far it is + + + align:start position:0% +that's really measuring how far it is +the output is from zero so as the + + align:start position:0% +the output is from zero so as the + + + align:start position:0% +the output is from zero so as the +derivative becomes less steep the + + align:start position:0% +derivative becomes less steep the + + + align:start position:0% +derivative becomes less steep the +derivative values have to be headed + + align:start position:0% +derivative values have to be headed + + + align:start position:0% +derivative values have to be headed +closer to zero now what happens when the + + align:start position:0% +closer to zero now what happens when the + + + align:start position:0% +closer to zero now what happens when the +derivative is equal to zero here well + + align:start position:0% +derivative is equal to zero here well + + + align:start position:0% +derivative is equal to zero here well +all of a sudden the slopes are becoming + + align:start position:0% +all of a sudden the slopes are becoming + + + align:start position:0% +all of a sudden the slopes are becoming +negative so the out puts of the + + align:start position:0% +negative so the out puts of the + + + align:start position:0% +negative so the out puts of the +derivative are negative it's going + + align:start position:0% +derivative are negative it's going + + + align:start position:0% +derivative are negative it's going +down but then once it hits here again + + align:start position:0% +down but then once it hits here again + + + align:start position:0% +down but then once it hits here again +notice what happens the derivative is + + align:start position:0% +notice what happens the derivative is + + + align:start position:0% +notice what happens the derivative is +zero again and notice how I get there + + align:start position:0% +zero again and notice how I get there + + + align:start position:0% +zero again and notice how I get there +the derivative is negative and then it + + align:start position:0% +the derivative is negative and then it + + + align:start position:0% +the derivative is negative and then it +starts to the slope of these tangent + + align:start position:0% +starts to the slope of these tangent + + + align:start position:0% +starts to the slope of these tangent +lines start to get shallower right they + + align:start position:0% +lines start to get shallower right they + + + align:start position:0% +lines start to get shallower right they +start to they were Steep and then + + align:start position:0% +start to they were Steep and then + + + align:start position:0% +start to they were Steep and then +somewhere they start to get shallower so + + align:start position:0% +somewhere they start to get shallower so + + + align:start position:0% +somewhere they start to get shallower so +there's some place sort of in the X + + align:start position:0% +there's some place sort of in the X + + + align:start position:0% +there's some place sort of in the X +values between here and here where the + + align:start position:0% +values between here and here where the + + + align:start position:0% +values between here and here where the +derivative is as steep As It Gets in + + align:start position:0% +derivative is as steep As It Gets in + + + align:start position:0% +derivative is as steep As It Gets in +this region and then gets less steep the + + align:start position:0% +this region and then gets less steep the + + + align:start position:0% +this region and then gets less steep the +steepest point is that point where you + + align:start position:0% +steepest point is that point where you + + + align:start position:0% +steepest point is that point where you +have the biggest magnitude in that + + align:start position:0% +have the biggest magnitude in that + + + align:start position:0% +have the biggest magnitude in that +region for fime so that's where it's + + align:start position:0% +region for fime so that's where it's + + + align:start position:0% +region for fime so that's where it's +going to be furthest from zero so if I'm + + align:start position:0% +going to be furthest from zero so if I'm + + + align:start position:0% +going to be furthest from zero so if I'm +guessing it looks like right around here + + align:start position:0% +guessing it looks like right around here + + + align:start position:0% +guessing it looks like right around here +the tangent line is as steep as it ever + + align:start position:0% +the tangent line is as steep as it ever + + + align:start position:0% +the tangent line is as steep as it ever +gets in that region between these two + + align:start position:0% +gets in that region between these two + + + align:start position:0% +gets in that region between these two +zeros and then it gets less steep so I'd + + align:start position:0% +zeros and then it gets less steep so I'd + + + align:start position:0% +zeros and then it gets less steep so I'd +say right around there we should say + + align:start position:0% +say right around there we should say + + + align:start position:0% +say right around there we should say +okay that's as low as it goes and now + + align:start position:0% +okay that's as low as it goes and now + + + align:start position:0% +okay that's as low as it goes and now +it's going to come back + + align:start position:0% +it's going to come back + + + align:start position:0% +it's going to come back +up okay so hopefully that makes sense + + align:start position:0% +up okay so hopefully that makes sense + + + align:start position:0% +up okay so hopefully that makes sense +we'll get to see it again here between + + align:start position:0% +we'll get to see it again here between + + + align:start position:0% +we'll get to see it again here between +these two zeros the same kind of thing + + align:start position:0% +these two zeros the same kind of thing + + + align:start position:0% +these two zeros the same kind of thing +happens but notice this is we have to be + + align:start position:0% +happens but notice this is we have to be + + + align:start position:0% +happens but notice this is we have to be +careful we shouldn't go through zero + + align:start position:0% +careful we shouldn't go through zero + + + align:start position:0% +careful we shouldn't go through zero +here because the derivatives output the + + align:start position:0% +here because the derivatives output the + + + align:start position:0% +here because the derivatives output the +sign is + + align:start position:0% +sign is + + + align:start position:0% +sign is +negative right notice so the tangent + + align:start position:0% +negative right notice so the tangent + + + align:start position:0% +negative right notice so the tangent +line it was negative negative negative + + align:start position:0% +line it was negative negative negative + + + align:start position:0% +line it was negative negative negative +zero oh it's still negative so the + + align:start position:0% +zero oh it's still negative so the + + + align:start position:0% +zero oh it's still negative so the +outputs are still negative and they're + + align:start position:0% +outputs are still negative and they're + + + align:start position:0% +outputs are still negative and they're +going to be negative all the way to this + + align:start position:0% +going to be negative all the way to this + + + align:start position:0% +going to be negative all the way to this +zero and what we need to see again is + + align:start position:0% +zero and what we need to see again is + + + align:start position:0% +zero and what we need to see again is +the same kind of thing happens as + + align:start position:0% +the same kind of thing happens as + + + align:start position:0% +the same kind of thing happens as +happened happened in this region will + + align:start position:0% +happened happened in this region will + + + align:start position:0% +happened happened in this region will +happen in this region the point being + + align:start position:0% +happen in this region the point being + + + align:start position:0% +happen in this region the point being +that again we're zero here we're zero + + align:start position:0% +that again we're zero here we're zero + + + align:start position:0% +that again we're zero here we're zero +here so somewhere in the midddle we we + + align:start position:0% +here so somewhere in the midddle we we + + + align:start position:0% +here so somewhere in the midddle we we +we start at zero the tangent lines start + + align:start position:0% +we start at zero the tangent lines start + + + align:start position:0% +we start at zero the tangent lines start +to get steeper then at some point they + + align:start position:0% +to get steeper then at some point they + + + align:start position:0% +to get steeper then at some point they +stop getting steeper they start getting + + align:start position:0% +stop getting steeper they start getting + + + align:start position:0% +stop getting steeper they start getting +shallower that place looks maybe right + + align:start position:0% +shallower that place looks maybe right + + + align:start position:0% +shallower that place looks maybe right +around here that's the sort of steepest + + align:start position:0% +around here that's the sort of steepest + + + align:start position:0% +around here that's the sort of steepest +tangent line then it gets less steep so + + align:start position:0% +tangent line then it gets less steep so + + + align:start position:0% +tangent line then it gets less steep so +that's the place where the derivatives + + align:start position:0% +that's the place where the derivatives + + + align:start position:0% +that's the place where the derivatives +magnitude is going to be the biggest in + + align:start position:0% +magnitude is going to be the biggest in + + + align:start position:0% +magnitude is going to be the biggest in +this region and actually I've sort of + + align:start position:0% +this region and actually I've sort of + + + align:start position:0% +this region and actually I've sort of +drawn it they look like they're about + + align:start position:0% +drawn it they look like they're about + + + align:start position:0% +drawn it they look like they're about +the same steepness at those two places + + align:start position:0% +the same steepness at those two places + + + align:start position:0% +the same steepness at those two places +so I should probably put the outputs + + align:start position:0% +so I should probably put the outputs + + + align:start position:0% +so I should probably put the outputs +about the same down here their + + align:start position:0% +about the same down here their + + + align:start position:0% +about the same down here their +magnitudes are about the same so this + + align:start position:0% +magnitudes are about the same so this + + + align:start position:0% +magnitudes are about the same so this +has to bounce + + align:start position:0% +has to bounce + + + align:start position:0% +has to bounce +off come up here I made that a little + + align:start position:0% +off come up here I made that a little + + + align:start position:0% +off come up here I made that a little +sharper than I meant + + align:start position:0% +sharper than I meant + + + align:start position:0% +sharper than I meant +to okay so that's the place that's the + + align:start position:0% +to okay so that's the place that's the + + + align:start position:0% +to okay so that's the place that's the +output the output here or the tangent + + align:start position:0% +output the output here or the tangent + + + align:start position:0% +output the output here or the tangent +line Sorry the tangent line at this x + + align:start position:0% +line Sorry the tangent line at this x + + + align:start position:0% +line Sorry the tangent line at this x +value is the steepest that we get in + + align:start position:0% +value is the steepest that we get in + + + align:start position:0% +value is the steepest that we get in +this region so the output at that x + + align:start position:0% +this region so the output at that x + + + align:start position:0% +this region so the output at that x +value is the lowest we get and then when + + align:start position:0% +value is the lowest we get and then when + + + align:start position:0% +value is the lowest we get and then when +we're to the right of this zero for the + + align:start position:0% +we're to the right of this zero for the + + + align:start position:0% +we're to the right of this zero for the +derivative we start seeing the tangent + + align:start position:0% +derivative we start seeing the tangent + + + align:start position:0% +derivative we start seeing the tangent +lines positive POS we pointed that out + + align:start position:0% +lines positive POS we pointed that out + + + align:start position:0% +lines positive POS we pointed that out +already and it gets more positive so it + + align:start position:0% +already and it gets more positive so it + + + align:start position:0% +already and it gets more positive so it +starts at zero it starts to get positive + + align:start position:0% +starts at zero it starts to get positive + + + align:start position:0% +starts at zero it starts to get positive +and gets more positive so it's going to + + align:start position:0% +and gets more positive so it's going to + + + align:start position:0% +and gets more positive so it's going to +do + + align:start position:0% +do + + + align:start position:0% +do +something like that roughly so let me + + align:start position:0% +something like that roughly so let me + + + align:start position:0% +something like that roughly so let me +fill in the dotted line so we can see it + + align:start position:0% + + + + align:start position:0% + +clearly now this is not exact but this + + align:start position:0% +clearly now this is not exact but this + + + align:start position:0% +clearly now this is not exact but this +is a fairly good drawing I think we can + + align:start position:0% +is a fairly good drawing I think we can + + + align:start position:0% +is a fairly good drawing I think we can +say of frime of X yal frime of + + align:start position:0% +say of frime of X yal frime of + + + align:start position:0% +say of frime of X yal frime of +X and now I'm going to ask you a + + align:start position:0% +X and now I'm going to ask you a + + + align:start position:0% +X and now I'm going to ask you a +question I'm going to write it on the + + align:start position:0% +question I'm going to write it on the + + + align:start position:0% +question I'm going to write it on the +board and then I'm going to give you a + + align:start position:0% +board and then I'm going to give you a + + + align:start position:0% +board and then I'm going to give you a +moment to think about it so let me write + + align:start position:0% +moment to think about it so let me write + + + align:start position:0% +moment to think about it so let me write +the + + align:start position:0% + + + + align:start position:0% + +question it's find a + + align:start position:0% + + + + align:start position:0% + +function uh y equals or sorry find a + + align:start position:0% +function uh y equals or sorry find a + + + align:start position:0% +function uh y equals or sorry find a +function G of + + align:start position:0% + + + + align:start position:0% + +X so that + + align:start position:0% +X so that + + + align:start position:0% +X so that +y = g Prime of + + align:start position:0% + + + + align:start position:0% + +X looks + + align:start position:0% +X looks + + + align:start position:0% +X looks +like yal frime of + + align:start position:0% +like yal frime of + + + align:start position:0% +like yal frime of +X okay let me be clear about that and + + align:start position:0% +X okay let me be clear about that and + + + align:start position:0% +X okay let me be clear about that and +then I'll give you a moment to think + + align:start position:0% +then I'll give you a moment to think + + + align:start position:0% +then I'll give you a moment to think +about it so I want you to find a + + align:start position:0% +about it so I want you to find a + + + align:start position:0% +about it so I want you to find a +function G of X so that its derivative + + align:start position:0% +function G of X so that its derivative + + + align:start position:0% +function G of X so that its derivative +graph yals G Prime of X looks exactly + + align:start position:0% +graph yals G Prime of X looks exactly + + + align:start position:0% +graph yals G Prime of X looks exactly +like the graph we've drawn in blue here + + align:start position:0% +like the graph we've drawn in blue here + + + align:start position:0% +like the graph we've drawn in blue here +yal frime of X now I don't want you to + + align:start position:0% +yal frime of X now I don't want you to + + + align:start position:0% +yal frime of X now I don't want you to +find something in terms of X squar and X + + align:start position:0% +find something in terms of X squar and X + + + align:start position:0% +find something in terms of X squar and X +cub cubes I don't want you to find an + + align:start position:0% +cub cubes I don't want you to find an + + + align:start position:0% +cub cubes I don't want you to find an +actual uh g ofx equals some something in + + align:start position:0% +actual uh g ofx equals some something in + + + align:start position:0% +actual uh g ofx equals some something in +terms of X I want you to just try and + + align:start position:0% +terms of X I want you to just try and + + + align:start position:0% +terms of X I want you to just try and +find a relationship that it must have + + align:start position:0% +find a relationship that it must have + + + align:start position:0% +find a relationship that it must have +with f so I'm going to give you a moment + + align:start position:0% +with f so I'm going to give you a moment + + + align:start position:0% +with f so I'm going to give you a moment +to think about it and and work out your + + align:start position:0% +to think about it and and work out your + + + align:start position:0% +to think about it and and work out your +answer and I'll be back to tell + + align:start position:0% + + + + align:start position:0% + +you okay welcome back so what we're + + align:start position:0% +you okay welcome back so what we're + + + align:start position:0% +you okay welcome back so what we're +looking for is a function G of X so that + + align:start position:0% +looking for is a function G of X so that + + + align:start position:0% +looking for is a function G of X so that +it's derivative when I graph it yal g + + align:start position:0% +it's derivative when I graph it yal g + + + align:start position:0% +it's derivative when I graph it yal g +Prime of X I get exactly the same curve + + align:start position:0% +Prime of X I get exactly the same curve + + + align:start position:0% +Prime of X I get exactly the same curve +as the blue one oh the blue one and the + + align:start position:0% +as the blue one oh the blue one and the + + + align:start position:0% +as the blue one oh the blue one and the +point is that if you thought about it + + align:start position:0% +point is that if you thought about it + + + align:start position:0% +point is that if you thought about it +for a little bit what you really need is + + align:start position:0% +for a little bit what you really need is + + + align:start position:0% +for a little bit what you really need is +a function that looks exactly like this + + align:start position:0% +a function that looks exactly like this + + + align:start position:0% +a function that looks exactly like this +function yal f ofx at all the X values + + align:start position:0% +function yal f ofx at all the X values + + + align:start position:0% +function yal f ofx at all the X values +in terms of its slopes but those slopes + + align:start position:0% +in terms of its slopes but those slopes + + + align:start position:0% +in terms of its slopes but those slopes +can happen shifted up or down anywhere + + align:start position:0% +can happen shifted up or down anywhere + + + align:start position:0% +can happen shifted up or down anywhere +so the point is that if I take the + + align:start position:0% +so the point is that if I take the + + + align:start position:0% +so the point is that if I take the +function yal f ofx and I add a constant + + align:start position:0% +function yal f ofx and I add a constant + + + align:start position:0% +function yal f ofx and I add a constant +to it which shifts the whole graph up or + + align:start position:0% +to it which shifts the whole graph up or + + + align:start position:0% +to it which shifts the whole graph up or +down the tangent lines are unaffected by + + align:start position:0% +down the tangent lines are unaffected by + + + align:start position:0% +down the tangent lines are unaffected by +that shift and so I get exactly the same + + align:start position:0% +that shift and so I get exactly the same + + + align:start position:0% +that shift and so I get exactly the same +picture when I take the derivative of + + align:start position:0% +picture when I take the derivative of + + + align:start position:0% +picture when I take the derivative of +that graph when I look at the the + + align:start position:0% +that graph when I look at the the + + + align:start position:0% +that graph when I look at the the +tangent line slopes of that + + align:start position:0% +tangent line slopes of that + + + align:start position:0% +tangent line slopes of that +graph so you could draw another picture + + align:start position:0% +graph so you could draw another picture + + + align:start position:0% +graph so you could draw another picture +and check it for yourself if you didn't + + align:start position:0% +and check it for yourself if you didn't + + + align:start position:0% +and check it for yourself if you didn't +feel convinced shift this shift this + + align:start position:0% +feel convinced shift this shift this + + + align:start position:0% +feel convinced shift this shift this +curve up and then look at what the + + align:start position:0% +curve up and then look at what the + + + align:start position:0% +curve up and then look at what the +tangent lines do on that curve but then + + align:start position:0% +tangent lines do on that curve but then + + + align:start position:0% +tangent lines do on that curve but then +you'll see its derivative outputs are + + align:start position:0% +you'll see its derivative outputs are + + + align:start position:0% +you'll see its derivative outputs are +exactly the same so we'll stop there \ No newline at end of file diff --git a/GqmQg-cszw4.txt b/GqmQg-cszw4.txt new file mode 100644 index 0000000000000000000000000000000000000000..97918b7327d022fc06c7cd93fe7a6d94ced81029 --- /dev/null +++ b/GqmQg-cszw4.txt @@ -0,0 +1,16307 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu for this class this semester + + align:start position:0% +ocw.mit.edu for this class this semester + + + align:start position:0% +ocw.mit.edu for this class this semester +the other col lecturer uh is going to be + + align:start position:0% +the other col lecturer uh is going to be + + + align:start position:0% +the other col lecturer uh is going to be +James mickens who's a visiting Professor + + align:start position:0% +James mickens who's a visiting Professor + + + align:start position:0% +James mickens who's a visiting Professor +from Microsoft research uh he'll lecture + + align:start position:0% +from Microsoft research uh he'll lecture + + + align:start position:0% +from Microsoft research uh he'll lecture +on some other topics like web security + + align:start position:0% +on some other topics like web security + + + align:start position:0% +on some other topics like web security +later on uh but we'll decide later + + align:start position:0% +later on uh but we'll decide later + + + align:start position:0% +later on uh but we'll decide later +what's going on exactly in terms of + + align:start position:0% +what's going on exactly in terms of + + + align:start position:0% +what's going on exactly in terms of +lecture split up we also have four T + + align:start position:0% +lecture split up we also have four T + + + align:start position:0% +lecture split up we also have four T +this year uh Steven web uh hang and + + align:start position:0% +this year uh Steven web uh hang and + + + align:start position:0% +this year uh Steven web uh hang and +James and hopefully you'll meet them in + + align:start position:0% +James and hopefully you'll meet them in + + + align:start position:0% +James and hopefully you'll meet them in +um office hours uh over the year if you + + align:start position:0% +um office hours uh over the year if you + + + align:start position:0% +um office hours uh over the year if you +need uh help So the plan for this class + + align:start position:0% +need uh help So the plan for this class + + + align:start position:0% +need uh help So the plan for this class +is to understand how to build secure + + align:start position:0% +is to understand how to build secure + + + align:start position:0% +is to understand how to build secure +systems while why computer systems + + align:start position:0% +systems while why computer systems + + + align:start position:0% +systems while why computer systems +sometimes are insecure and how we can + + align:start position:0% +sometimes are insecure and how we can + + + align:start position:0% +sometimes are insecure and how we can +make them better and what goes wrong and + + align:start position:0% +make them better and what goes wrong and + + + align:start position:0% +make them better and what goes wrong and +in order to do this uh there's not + + align:start position:0% +in order to do this uh there's not + + + align:start position:0% +in order to do this uh there's not +really a great textbook about this topic + + align:start position:0% +really a great textbook about this topic + + + align:start position:0% +really a great textbook about this topic +so instead what we're going to do is + + align:start position:0% +so instead what we're going to do is + + + align:start position:0% +so instead what we're going to do is +each lecture other than this one is + + align:start position:0% +each lecture other than this one is + + + align:start position:0% +each lecture other than this one is +going to be focused around some research + + align:start position:0% +going to be focused around some research + + + align:start position:0% +going to be focused around some research +typically paper that we'll assign on the + + align:start position:0% +typically paper that we'll assign on the + + + align:start position:0% +typically paper that we'll assign on the +website and you guys should read ahead + + align:start position:0% +website and you guys should read ahead + + + align:start position:0% +website and you guys should read ahead +of time and there are some question that + + align:start position:0% +of time and there are some question that + + + align:start position:0% +of time and there are some question that +you should answer uh in the submission + + align:start position:0% +you should answer uh in the submission + + + align:start position:0% +you should answer uh in the submission +system about the paper and submit your + + align:start position:0% +system about the paper and submit your + + + align:start position:0% +system about the paper and submit your +own question by 10: p.m. before the + + align:start position:0% +own question by 10: p.m. before the + + + align:start position:0% +own question by 10: p.m. before the +lecture day and then when you come to + + align:start position:0% +lecture day and then when you come to + + + align:start position:0% +lecture day and then when you come to +lecture will actually discuss the paper + + align:start position:0% +lecture will actually discuss the paper + + + align:start position:0% +lecture will actually discuss the paper +figure out what is the system what + + align:start position:0% +figure out what is the system what + + + align:start position:0% +figure out what is the system what +problem does it solve when does it work + + align:start position:0% +problem does it solve when does it work + + + align:start position:0% +problem does it solve when does it work +when does it not work are these ideas + + align:start position:0% +when does it not work are these ideas + + + align:start position:0% +when does it not work are these ideas +any good and other cases Etc and + + align:start position:0% +any good and other cases Etc and + + + align:start position:0% +any good and other cases Etc and +hopefully through these case studies + + align:start position:0% +hopefully through these case studies + + + align:start position:0% +hopefully through these case studies +we'll get some appreciation of how do we + + align:start position:0% +we'll get some appreciation of how do we + + + align:start position:0% +we'll get some appreciation of how do we +actually build systems that are + + align:start position:0% +actually build systems that are + + + align:start position:0% +actually build systems that are +secure and we have some preliminary + + align:start position:0% +secure and we have some preliminary + + + align:start position:0% +secure and we have some preliminary +schedule up on the website if there's + + align:start position:0% +schedule up on the website if there's + + + align:start position:0% +schedule up on the website if there's +other topics you guys are particularly + + align:start position:0% +other topics you guys are particularly + + + align:start position:0% +other topics you guys are particularly +interested in or if there's particular + + align:start position:0% +interested in or if there's particular + + + align:start position:0% +interested in or if there's particular +papers you're excited about just send us + + align:start position:0% +papers you're excited about just send us + + + align:start position:0% +papers you're excited about just send us +email and we'll see if we can fit them + + align:start position:0% +email and we'll see if we can fit them + + + align:start position:0% +email and we'll see if we can fit them +in or do something we're pretty flexible + + align:start position:0% +in or do something we're pretty flexible + + + align:start position:0% +in or do something we're pretty flexible +uh so if there's anything that uh you'd + + align:start position:0% +uh so if there's anything that uh you'd + + + align:start position:0% +uh so if there's anything that uh you'd +like to hear more about just let us + + align:start position:0% +like to hear more about just let us + + + align:start position:0% +like to hear more about just let us +know and in a similar vein if you ever + + align:start position:0% +know and in a similar vein if you ever + + + align:start position:0% +know and in a similar vein if you ever +have a question or if there's some + + align:start position:0% +have a question or if there's some + + + align:start position:0% +have a question or if there's some +mistake just interrupt and ask us what's + + align:start position:0% +mistake just interrupt and ask us what's + + + align:start position:0% +mistake just interrupt and ask us what's +going on and lecture any anytime um + + align:start position:0% +going on and lecture any anytime um + + + align:start position:0% +going on and lecture any anytime um +security is in many ways all about the + + align:start position:0% +security is in many ways all about the + + + align:start position:0% +security is in many ways all about the +details and getting everything right and + + align:start position:0% +details and getting everything right and + + + align:start position:0% +details and getting everything right and +I will inevitably make mistakes so if + + align:start position:0% +I will inevitably make mistakes so if + + + align:start position:0% +I will inevitably make mistakes so if +something doesn't seem right there's a + + align:start position:0% +something doesn't seem right there's a + + + align:start position:0% +something doesn't seem right there's a +good chance it's not and you should just + + align:start position:0% +good chance it's not and you should just + + + align:start position:0% +good chance it's not and you should just +interrupt and ask and we'll figure out + + align:start position:0% +interrupt and ask and we'll figure out + + + align:start position:0% +interrupt and ask and we'll figure out +what's going on and what's the right way + + align:start position:0% +what's going on and what's the right way + + + align:start position:0% +what's going on and what's the right way +to do things + + align:start position:0% +to do things + + + align:start position:0% +to do things +and uh I guess in terms of the class + + align:start position:0% +and uh I guess in terms of the class + + + align:start position:0% +and uh I guess in terms of the class +organization the other large part of the + + align:start position:0% +organization the other large part of the + + + align:start position:0% +organization the other large part of the +class in addition to the lectures is + + align:start position:0% +class in addition to the lectures is + + + align:start position:0% +class in addition to the lectures is +going to be a series of lab assignments + + align:start position:0% +going to be a series of lab assignments + + + align:start position:0% +going to be a series of lab assignments +the first one is already posted on the + + align:start position:0% +the first one is already posted on the + + + align:start position:0% +the first one is already posted on the +website and these lab assignments will + + align:start position:0% +website and these lab assignments will + + + align:start position:0% +website and these lab assignments will +help you go through understanding uh + + align:start position:0% +help you go through understanding uh + + + align:start position:0% +help you go through understanding uh +different range of security problems and + + align:start position:0% +different range of security problems and + + + align:start position:0% +different range of security problems and +how do you prevent them in a simple web + + align:start position:0% +how do you prevent them in a simple web + + + align:start position:0% +how do you prevent them in a simple web +server so in lab one which is out right + + align:start position:0% +server so in lab one which is out right + + + align:start position:0% +server so in lab one which is out right +now you'll actually take a web server + + align:start position:0% +now you'll actually take a web server + + + align:start position:0% +now you'll actually take a web server +that we give you and find ways to + + align:start position:0% +that we give you and find ways to + + + align:start position:0% +that we give you and find ways to +exploit buffer overflow vulnerabilities + + align:start position:0% +exploit buffer overflow vulnerabilities + + + align:start position:0% +exploit buffer overflow vulnerabilities +in it and take control of this website + + align:start position:0% +in it and take control of this website + + + align:start position:0% +in it and take control of this website +by just sending it carefully crafted + + align:start position:0% +by just sending it carefully crafted + + + align:start position:0% +by just sending it carefully crafted +requests and packets uh and in other + + align:start position:0% +requests and packets uh and in other + + + align:start position:0% +requests and packets uh and in other +labs you'll look at ways to defend the + + align:start position:0% +labs you'll look at ways to defend the + + + align:start position:0% +labs you'll look at ways to defend the +web server to find bugs in the code to F + + align:start position:0% +web server to find bugs in the code to F + + + align:start position:0% +web server to find bugs in the code to F +uh write warms that run in the user's + + align:start position:0% +uh write warms that run in the user's + + + align:start position:0% +uh write warms that run in the user's +browser and other kinds of uh + + align:start position:0% +browser and other kinds of uh + + + align:start position:0% +browser and other kinds of uh +interesting security + + align:start position:0% +interesting security + + + align:start position:0% +interesting security +problems one thing that surprises many + + align:start position:0% +problems one thing that surprises many + + + align:start position:0% +problems one thing that surprises many +students is that every lab uses a + + align:start position:0% +students is that every lab uses a + + + align:start position:0% +students is that every lab uses a +different language so lab one is all + + align:start position:0% +different language so lab one is all + + + align:start position:0% +different language so lab one is all +about C and assembly lab two involves a + + align:start position:0% +about C and assembly lab two involves a + + + align:start position:0% +about C and assembly lab two involves a +lot of python coding lab will be + + align:start position:0% +lot of python coding lab will be + + + align:start position:0% +lot of python coding lab will be +something else lab five will be + + align:start position:0% +something else lab five will be + + + align:start position:0% +something else lab five will be +JavaScript and so on this is sort of + + align:start position:0% +JavaScript and so on this is sort of + + + align:start position:0% +JavaScript and so on this is sort of +inevitable and I sort of apologize ahead + + align:start position:0% +inevitable and I sort of apologize ahead + + + align:start position:0% +inevitable and I sort of apologize ahead +of time that you're going to have to + + align:start position:0% +of time that you're going to have to + + + align:start position:0% +of time that you're going to have to +learn all these languages if you haven't + + align:start position:0% +learn all these languages if you haven't + + + align:start position:0% +learn all these languages if you haven't +seen them already um in some ways it's + + align:start position:0% +seen them already um in some ways it's + + + align:start position:0% +seen them already um in some ways it's +useful because the real world is like + + align:start position:0% +useful because the real world is like + + + align:start position:0% +useful because the real world is like +this all the systems are complicated and + + align:start position:0% +this all the systems are complicated and + + + align:start position:0% +this all the systems are complicated and +composed of different parts and in the + + align:start position:0% +composed of different parts and in the + + + align:start position:0% +composed of different parts and in the +long run it'll be useful for you to for + + align:start position:0% +long run it'll be useful for you to for + + + align:start position:0% +long run it'll be useful for you to for +your moral character or something like + + align:start position:0% +your moral character or something like + + + align:start position:0% +your moral character or something like +that uh to learn this stuff but it will + + align:start position:0% +that uh to learn this stuff but it will + + + align:start position:0% +that uh to learn this stuff but it will +take some preparation especially if you + + align:start position:0% +take some preparation especially if you + + + align:start position:0% +take some preparation especially if you +haven't seen these languages before uh + + align:start position:0% +haven't seen these languages before uh + + + align:start position:0% +haven't seen these languages before uh +it might be helpful to start early in a + + align:start position:0% +it might be helpful to start early in a + + + align:start position:0% +it might be helpful to start early in a +particular um lab one is going to rely + + align:start position:0% +particular um lab one is going to rely + + + align:start position:0% +particular um lab one is going to rely +on a lot of subtle details of c and + + align:start position:0% +on a lot of subtle details of c and + + + align:start position:0% +on a lot of subtle details of c and +assembly code that uh we don't really + + align:start position:0% +assembly code that uh we don't really + + + align:start position:0% +assembly code that uh we don't really +teach in other classes here in as much + + align:start position:0% +teach in other classes here in as much + + + align:start position:0% +teach in other classes here in as much +detail so it's probably a good idea to + + align:start position:0% +detail so it's probably a good idea to + + + align:start position:0% +detail so it's probably a good idea to +start early and we'll try to get the Tas + + align:start position:0% +start early and we'll try to get the Tas + + + align:start position:0% +start early and we'll try to get the Tas +to hold office hours next week where + + align:start position:0% +to hold office hours next week where + + + align:start position:0% +to hold office hours next week where +we'll do some sort of a tutorial session + + align:start position:0% +we'll do some sort of a tutorial session + + + align:start position:0% +we'll do some sort of a tutorial session +where we can help you get started with + + align:start position:0% +where we can help you get started with + + + align:start position:0% +where we can help you get started with +understanding what a binary program + + align:start position:0% +understanding what a binary program + + + align:start position:0% +understanding what a binary program +looks like how to disassemble it how to + + align:start position:0% +looks like how to disassemble it how to + + + align:start position:0% +looks like how to disassemble it how to +figure out what's on the stack and so + + align:start position:0% +figure out what's on the stack and so + + + align:start position:0% +figure out what's on the stack and so +on all right and uh I guess the one + + align:start position:0% +on all right and uh I guess the one + + + align:start position:0% +on all right and uh I guess the one +other thing we're actually videotaping + + align:start position:0% +other thing we're actually videotaping + + + align:start position:0% +other thing we're actually videotaping +lectures this year so you might be able + + align:start position:0% +lectures this year so you might be able + + + align:start position:0% +lectures this year so you might be able +to watch these online uh hope we'll post + + align:start position:0% +to watch these online uh hope we'll post + + + align:start position:0% +to watch these online uh hope we'll post +them as soon as we get them ourselves + + align:start position:0% +them as soon as we get them ourselves + + + align:start position:0% +them as soon as we get them ourselves +from the video people um and the last + + align:start position:0% +from the video people um and the last + + + align:start position:0% +from the video people um and the last +bit of administ trivia is uh you should + + align:start position:0% +bit of administ trivia is uh you should + + + align:start position:0% +bit of administ trivia is uh you should +yeah if you have questions online we're + + align:start position:0% +yeah if you have questions online we're + + + align:start position:0% +yeah if you have questions online we're +using Pata so I'm sure you've used this + + align:start position:0% +using Pata so I'm sure you've used this + + + align:start position:0% +using Pata so I'm sure you've used this +in L our + + align:start position:0% +in L our + + + align:start position:0% +in L our +classes all right so before we dive into + + align:start position:0% +classes all right so before we dive into + + + align:start position:0% +classes all right so before we dive into +security I need to tell you one thing uh + + align:start position:0% +security I need to tell you one thing uh + + + align:start position:0% +security I need to tell you one thing uh +there's a set of rules or that M has for + + align:start position:0% +there's a set of rules or that M has for + + + align:start position:0% +there's a set of rules or that M has for +accessing mit's Network and when you're + + align:start position:0% +accessing mit's Network and when you're + + + align:start position:0% +accessing mit's Network and when you're +especially doing security research or + + align:start position:0% +especially doing security research or + + + align:start position:0% +especially doing security research or +playing with security s you should be + + align:start position:0% +playing with security s you should be + + + align:start position:0% +playing with security s you should be +aware that not everything you can + + align:start position:0% +aware that not everything you can + + + align:start position:0% +aware that not everything you can +technically do is legal and there's many + + align:start position:0% +technically do is legal and there's many + + + align:start position:0% +technically do is legal and there's many +things that you'll learn in this class + + align:start position:0% +things that you'll learn in this class + + + align:start position:0% +things that you'll learn in this class +that are technically possible we'll + + align:start position:0% +that are technically possible we'll + + + align:start position:0% +that are technically possible we'll +understand how systems can be uh broken + + align:start position:0% +understand how systems can be uh broken + + + align:start position:0% +understand how systems can be uh broken +or compromised doesn't mean you should + + align:start position:0% +or compromised doesn't mean you should + + + align:start position:0% +or compromised doesn't mean you should +go out and do this everywhere uh and uh + + align:start position:0% +go out and do this everywhere uh and uh + + + align:start position:0% +go out and do this everywhere uh and uh +there's a link in the lecture notes + + align:start position:0% +there's a link in the lecture notes + + + align:start position:0% +there's a link in the lecture notes +we'll post that has some rules that are + + align:start position:0% +we'll post that has some rules that are + + + align:start position:0% +we'll post that has some rules that are +good guidelines but in general if you're + + align:start position:0% +good guidelines but in general if you're + + + align:start position:0% +good guidelines but in general if you're +in doubt ask one of the lecturers or ta + + align:start position:0% +in doubt ask one of the lecturers or ta + + + align:start position:0% +in doubt ask one of the lecturers or ta +as to what you should do uh and + + align:start position:0% +as to what you should do uh and + + + align:start position:0% +as to what you should do uh and +hopefully it's not too puzzling what's + + align:start position:0% +hopefully it's not too puzzling what's + + + align:start position:0% +hopefully it's not too puzzling what's +going on um all right so any questions + + align:start position:0% +going on um all right so any questions + + + align:start position:0% +going on um all right so any questions +about all this administ trivia before we + + align:start position:0% +about all this administ trivia before we + + + align:start position:0% +about all this administ trivia before we +dive in feel free to ask + + align:start position:0% +dive in feel free to ask + + + align:start position:0% +dive in feel free to ask +questions okay so what is security so + + align:start position:0% +questions okay so what is security so + + + align:start position:0% +questions okay so what is security so +we'll start with some basic stuff today + + align:start position:0% +we'll start with some basic stuff today + + + align:start position:0% +we'll start with some basic stuff today +and uh we'll look at just some general + + align:start position:0% +and uh we'll look at just some general + + + align:start position:0% +and uh we'll look at just some general +examples of why security is hard and + + align:start position:0% +examples of why security is hard and + + + align:start position:0% +examples of why security is hard and +what it means to try to build a secure + + align:start position:0% +what it means to try to build a secure + + + align:start position:0% +what it means to try to build a secure +system um because there's not really a + + align:start position:0% +system um because there's not really a + + + align:start position:0% +system um because there's not really a +paper this will not have sort of deep + + align:start position:0% +paper this will not have sort of deep + + + align:start position:0% +paper this will not have sort of deep +intellectual content Maybe uh but it'll + + align:start position:0% +intellectual content Maybe uh but it'll + + + align:start position:0% +intellectual content Maybe uh but it'll +give you some background and context for + + align:start position:0% +give you some background and context for + + + align:start position:0% +give you some background and context for +how to think about secure systems so + + align:start position:0% +how to think about secure systems so + + + align:start position:0% +how to think about secure systems so +Security in general uh is all about + + align:start position:0% +Security in general uh is all about + + + align:start position:0% +Security in general uh is all about +achieving some goal when there's an + + align:start position:0% +achieving some goal when there's an + + + align:start position:0% +achieving some goal when there's an +adversary + + align:start position:0% +adversary + + + align:start position:0% +adversary +present so think of it there's some bad + + align:start position:0% +present so think of it there's some bad + + + align:start position:0% +present so think of it there's some bad +guy out there that wants to make sure + + align:start position:0% +guy out there that wants to make sure + + + align:start position:0% +guy out there that wants to make sure +you don't succeed like they want to + + align:start position:0% +you don't succeed like they want to + + + align:start position:0% +you don't succeed like they want to +steal your files they want to delete + + align:start position:0% +steal your files they want to delete + + + align:start position:0% +steal your files they want to delete +your entire hard drive contents they + + align:start position:0% +your entire hard drive contents they + + + align:start position:0% +your entire hard drive contents they +want to make sure nothing works and your + + align:start position:0% +want to make sure nothing works and your + + + align:start position:0% +want to make sure nothing works and your +phone doesn't connect all these things + + align:start position:0% +phone doesn't connect all these things + + + align:start position:0% +phone doesn't connect all these things +right and a secure system is that can + + align:start position:0% +right and a secure system is that can + + + align:start position:0% +right and a secure system is that can +actually do something regardless of what + + align:start position:0% +actually do something regardless of what + + + align:start position:0% +actually do something regardless of what +the bad guy is trying to do to you so + + align:start position:0% +the bad guy is trying to do to you so + + + align:start position:0% +the bad guy is trying to do to you so +it's kind of cool that we can actually + + align:start position:0% +it's kind of cool that we can actually + + + align:start position:0% +it's kind of cool that we can actually +potentially build systems that are + + align:start position:0% +potentially build systems that are + + + align:start position:0% +potentially build systems that are +resilient to a whole range of bad guys + + align:start position:0% +resilient to a whole range of bad guys + + + align:start position:0% +resilient to a whole range of bad guys +adversaries attackers whatever you want + + align:start position:0% +adversaries attackers whatever you want + + + align:start position:0% +adversaries attackers whatever you want +to call them um and we can still build + + align:start position:0% +to call them um and we can still build + + + align:start position:0% +to call them um and we can still build +computer systems that allow us to get + + align:start position:0% +computer systems that allow us to get + + + align:start position:0% +computer systems that allow us to get +our work + + align:start position:0% +our work + + + align:start position:0% +our work +done and the general way to think about + + align:start position:0% +done and the general way to think about + + + align:start position:0% +done and the general way to think about +security is sort of break it up into + + align:start position:0% +security is sort of break it up into + + + align:start position:0% +security is sort of break it up into +three parts one part is roughly the + + align:start position:0% +three parts one part is roughly the + + + align:start position:0% +three parts one part is roughly the +policy + + align:start position:0% +policy + + + align:start position:0% +policy +that you want your system to enforce + + align:start position:0% +that you want your system to enforce + + + align:start position:0% +that you want your system to enforce +this is roughly the goal that you want + + align:start position:0% +this is roughly the goal that you want + + + align:start position:0% +this is roughly the goal that you want +to achieve like well maybe only I should + + align:start position:0% +to achieve like well maybe only I should + + + align:start position:0% +to achieve like well maybe only I should +be able to read the grades file 4 6858 + + align:start position:0% +be able to read the grades file 4 6858 + + + align:start position:0% +be able to read the grades file 4 6858 +or maybe the Tas as well and all the + + align:start position:0% +or maybe the Tas as well and all the + + + align:start position:0% +or maybe the Tas as well and all the +collectors Etc but there's some + + align:start position:0% +collectors Etc but there's some + + + align:start position:0% +collectors Etc but there's some +statement about what I want my system to + + align:start position:0% +statement about what I want my system to + + + align:start position:0% +statement about what I want my system to +be able to do and then if you want to + + align:start position:0% +be able to do and then if you want to + + + align:start position:0% +be able to do and then if you want to +sort of think about what kinds of + + align:start position:0% +sort of think about what kinds of + + + align:start position:0% +sort of think about what kinds of +policies you might write you know + + align:start position:0% +policies you might write you know + + + align:start position:0% +policies you might write you know +typical ones have to do with either + + align:start position:0% +typical ones have to do with either + + + align:start position:0% +typical ones have to do with either +confidentiality of + + align:start position:0% +confidentiality of + + + align:start position:0% +confidentiality of +data so the grades file is only + + align:start position:0% +data so the grades file is only + + + align:start position:0% +data so the grades file is only +accessible to the 6858 course staff + + align:start position:0% +accessible to the 6858 course staff + + + align:start position:0% +accessible to the 6858 course staff +another example of a security policy has + + align:start position:0% +another example of a security policy has + + + align:start position:0% +another example of a security policy has +something to do with Integrity for + + align:start position:0% +something to do with Integrity for + + + align:start position:0% +something to do with Integrity for +example only the course staff can also + + align:start position:0% +example only the course staff can also + + + align:start position:0% +example only the course staff can also +modify the grades file or only the core + + align:start position:0% +modify the grades file or only the core + + + align:start position:0% +modify the grades file or only the core +staff can upload the final grades to the + + align:start position:0% +staff can upload the final grades to the + + + align:start position:0% +staff can upload the final grades to the +register's office that would be great um + + align:start position:0% +register's office that would be great um + + + align:start position:0% +register's office that would be great um +and you can almost also think about + + align:start position:0% +and you can almost also think about + + + align:start position:0% +and you can almost also think about +things like + + align:start position:0% +things like + + + align:start position:0% +things like +availability so for example a website + + align:start position:0% +availability so for example a website + + + align:start position:0% +availability so for example a website +should be available even if the bad guys + + align:start position:0% +should be available even if the bad guys + + + align:start position:0% +should be available even if the bad guys +try to take it down and mount some sort + + align:start position:0% +try to take it down and mount some sort + + + align:start position:0% +try to take it down and mount some sort +of a Dos denial of service attack on + + align:start position:0% +of a Dos denial of service attack on + + + align:start position:0% +of a Dos denial of service attack on +it so this is all well and good so these + + align:start position:0% +it so this is all well and good so these + + + align:start position:0% +it so this is all well and good so these +are policies that might actually care + + align:start position:0% +are policies that might actually care + + + align:start position:0% +are policies that might actually care +about from a system but because of + + align:start position:0% +about from a system but because of + + + align:start position:0% +about from a system but because of +security there's a bad guy involved you + + align:start position:0% +security there's a bad guy involved you + + + align:start position:0% +security there's a bad guy involved you +need to understand what are we thinking + + align:start position:0% +need to understand what are we thinking + + + align:start position:0% +need to understand what are we thinking +the bad guy is going to do and this is + + align:start position:0% +the bad guy is going to do and this is + + + align:start position:0% +the bad guy is going to do and this is +typically what we call a threat + + align:start position:0% + + + + align:start position:0% + +model and this is basically just a set + + align:start position:0% +model and this is basically just a set + + + align:start position:0% +model and this is basically just a set +of assumptions about the bad + + align:start position:0% + + + + align:start position:0% + +guy about our adversary and it's + + align:start position:0% +guy about our adversary and it's + + + align:start position:0% +guy about our adversary and it's +important to have some sort of + + align:start position:0% +important to have some sort of + + + align:start position:0% +important to have some sort of +assumptions about the bad guy because if + + align:start position:0% +assumptions about the bad guy because if + + + align:start position:0% +assumptions about the bad guy because if +the bad guy is omnipresent and is + + align:start position:0% +the bad guy is omnipresent and is + + + align:start position:0% +the bad guy is omnipresent and is +everywhere at once and can do anything + + align:start position:0% +everywhere at once and can do anything + + + align:start position:0% +everywhere at once and can do anything +they want it's going to be hard to + + align:start position:0% +they want it's going to be hard to + + + align:start position:0% +they want it's going to be hard to +achieve some semblance of security so + + align:start position:0% +achieve some semblance of security so + + + align:start position:0% +achieve some semblance of security so +for example you probably want to assume + + align:start position:0% +for example you probably want to assume + + + align:start position:0% +for example you probably want to assume +the bad guy doesn't exactly know your + + align:start position:0% +the bad guy doesn't exactly know your + + + align:start position:0% +the bad guy doesn't exactly know your +password or they don't actually have + + align:start position:0% +password or they don't actually have + + + align:start position:0% +password or they don't actually have +physical access to your phone and your + + align:start position:0% +physical access to your phone and your + + + align:start position:0% +physical access to your phone and your +keys and your laptop otherwise it's + + align:start position:0% +keys and your laptop otherwise it's + + + align:start position:0% +keys and your laptop otherwise it's +going to be hard to make some sort of a + + align:start position:0% +going to be hard to make some sort of a + + + align:start position:0% +going to be hard to make some sort of a +progress in this + + align:start position:0% +progress in this + + + align:start position:0% +progress in this +game and turns out that well this is + + align:start position:0% +game and turns out that well this is + + + align:start position:0% +game and turns out that well this is +actually quite tricky to come up with + + align:start position:0% +actually quite tricky to come up with + + + align:start position:0% +actually quite tricky to come up with +but um I guess one general rule is it's + + align:start position:0% +but um I guess one general rule is it's + + + align:start position:0% +but um I guess one general rule is it's +much better to ER on the side of sort of + + align:start position:0% +much better to ER on the side of sort of + + + align:start position:0% +much better to ER on the side of sort of +caution and and being conservative in + + align:start position:0% +caution and and being conservative in + + + align:start position:0% +caution and and being conservative in +picking your threat model because bad + + align:start position:0% +picking your threat model because bad + + + align:start position:0% +picking your threat model because bad +guy might Al always surprise you in + + align:start position:0% +guy might Al always surprise you in + + + align:start position:0% +guy might Al always surprise you in +terms of what they might be able to do + + align:start position:0% +terms of what they might be able to do + + + align:start position:0% +terms of what they might be able to do +in + + align:start position:0% +in + + + align:start position:0% +in +practice and finally in order to achieve + + align:start position:0% +practice and finally in order to achieve + + + align:start position:0% +practice and finally in order to achieve +Security in order to achieve our goal + + align:start position:0% +Security in order to achieve our goal + + + align:start position:0% +Security in order to achieve our goal +under these set of assumptions we're + + align:start position:0% +under these set of assumptions we're + + + align:start position:0% +under these set of assumptions we're +going to look at some + + align:start position:0% + + + + align:start position:0% + +mechanism and this is the basically + + align:start position:0% +mechanism and this is the basically + + + align:start position:0% +mechanism and this is the basically +software or Hardware or whatever part of + + align:start position:0% +software or Hardware or whatever part of + + + align:start position:0% +software or Hardware or whatever part of +system design implementation Etc that's + + align:start position:0% +system design implementation Etc that's + + + align:start position:0% +system design implementation Etc that's +going to in try to make sure our icies + + align:start position:0% +going to in try to make sure our icies + + + align:start position:0% +going to in try to make sure our icies +followed as long as the bad guy follows + + align:start position:0% +followed as long as the bad guy follows + + + align:start position:0% +followed as long as the bad guy follows +the threat + + align:start position:0% +the threat + + + align:start position:0% +the threat +model so the end result is that as long + + align:start position:0% +model so the end result is that as long + + + align:start position:0% +model so the end result is that as long +as our threat model was correct + + align:start position:0% +as our threat model was correct + + + align:start position:0% +as our threat model was correct +hopefully will'll satisfy our policy and + + align:start position:0% +hopefully will'll satisfy our policy and + + + align:start position:0% +hopefully will'll satisfy our policy and +it has to be the case that the mechanism + + align:start position:0% +it has to be the case that the mechanism + + + align:start position:0% +it has to be the case that the mechanism +doesn't screw up make sense fairly high + + align:start position:0% +doesn't screw up make sense fairly high + + + align:start position:0% +doesn't screw up make sense fairly high +level story about how to think about + + align:start position:0% +level story about how to think about + + + align:start position:0% +level story about how to think about +this kind of stuff so why is this so + + align:start position:0% +this kind of stuff so why is this so + + + align:start position:0% +this kind of stuff so why is this so +hard right like you know seems like a + + align:start position:0% +hard right like you know seems like a + + + align:start position:0% +hard right like you know seems like a +simple plan like you write down these + + align:start position:0% +simple plan like you write down these + + + align:start position:0% +simple plan like you write down these +three things and you're often running + + align:start position:0% +three things and you're often running + + + align:start position:0% +three things and you're often running +but in practice um as you I'm sure have + + align:start position:0% +but in practice um as you I'm sure have + + + align:start position:0% +but in practice um as you I'm sure have +seen in the world computer systems are + + align:start position:0% +seen in the world computer systems are + + + align:start position:0% +seen in the world computer systems are +almost always compromised in some way or + + align:start position:0% +almost always compromised in some way or + + + align:start position:0% +almost always compromised in some way or +another and break-ins are pretty common + + align:start position:0% +another and break-ins are pretty common + + + align:start position:0% +another and break-ins are pretty common +place and the big reason + + align:start position:0% +place and the big reason + + + align:start position:0% +place and the big reason +why security tends to be a difficult + + align:start position:0% +why security tends to be a difficult + + + align:start position:0% +why security tends to be a difficult +problem is because what we have here is + + align:start position:0% +problem is because what we have here is + + + align:start position:0% +problem is because what we have here is +sort of this will be familiar to those + + align:start position:0% +sort of this will be familiar to those + + + align:start position:0% +sort of this will be familiar to those +of you who do 6033 this is a negative + + align:start position:0% +of you who do 6033 this is a negative + + + align:start position:0% +of you who do 6033 this is a negative +goal meaning that we have to make sure + + align:start position:0% +goal meaning that we have to make sure + + + align:start position:0% +goal meaning that we have to make sure +our security policy is followed + + align:start position:0% +our security policy is followed + + + align:start position:0% +our security policy is followed +regardless of what the attacker can + + align:start position:0% +regardless of what the attacker can + + + align:start position:0% +regardless of what the attacker can +do so just by contrast if you want to + + align:start position:0% +do so just by contrast if you want to + + + align:start position:0% +do so just by contrast if you want to +build a file system and you want to make + + align:start position:0% +build a file system and you want to make + + + align:start position:0% +build a file system and you want to make +sure that you know my Tas can access the + + align:start position:0% +sure that you know my Tas can access the + + + align:start position:0% +sure that you know my Tas can access the +grades file that's pretty easy I just + + align:start position:0% +grades file that's pretty easy I just + + + align:start position:0% +grades file that's pretty easy I just +ask them hey can you guys test and see + + align:start position:0% +ask them hey can you guys test and see + + + align:start position:0% +ask them hey can you guys test and see +can you access the grades file and if + + align:start position:0% +can you access the grades file and if + + + align:start position:0% +can you access the grades file and if +they all can access it done the system + + align:start position:0% +they all can access it done the system + + + align:start position:0% +they all can access it done the system +works but if I want to say that no one + + align:start position:0% +works but if I want to say that no one + + + align:start position:0% +works but if I want to say that no one +other than the Tas can access the grades + + align:start position:0% +other than the Tas can access the grades + + + align:start position:0% +other than the Tas can access the grades +file this is a much harder problem to + + align:start position:0% +file this is a much harder problem to + + + align:start position:0% +file this is a much harder problem to +solve because now I have to figure out + + align:start position:0% +solve because now I have to figure out + + + align:start position:0% +solve because now I have to figure out +what could all these nonta people in the + + align:start position:0% +what could all these nonta people in the + + + align:start position:0% +what could all these nonta people in the +world try to do to get my grades file + + align:start position:0% +world try to do to get my grades file + + + align:start position:0% +world try to do to get my grades file +right they could try to you know just + + align:start position:0% +right they could try to you know just + + + align:start position:0% +right they could try to you know just +open it and read it maybe my file system + + align:start position:0% +open it and read it maybe my file system + + + align:start position:0% +open it and read it maybe my file system +will disallow it but they might try all + + align:start position:0% +will disallow it but they might try all + + + align:start position:0% +will disallow it but they might try all +kinds of other attacks like guessing the + + align:start position:0% +kinds of other attacks like guessing the + + + align:start position:0% +kinds of other attacks like guessing the +password for the Tas or stealing the + + align:start position:0% +password for the Tas or stealing the + + + align:start position:0% +password for the Tas or stealing the +ta's laptops or breaking into their room + + align:start position:0% +ta's laptops or breaking into their room + + + align:start position:0% +ta's laptops or breaking into their room +or who knows right like this is all + + align:start position:0% +or who knows right like this is all + + + align:start position:0% +or who knows right like this is all +stuff that we have to really put into + + align:start position:0% +stuff that we have to really put into + + + align:start position:0% +stuff that we have to really put into +our threat model probably for this class + + align:start position:0% +our threat model probably for this class + + + align:start position:0% +our threat model probably for this class +I'm not that concerned about the grades + + align:start position:0% +I'm not that concerned about the grades + + + align:start position:0% +I'm not that concerned about the grades +file to worry about these guys laptops + + align:start position:0% +file to worry about these guys laptops + + + align:start position:0% +file to worry about these guys laptops +being you know stolen from their dorm + + align:start position:0% +being you know stolen from their dorm + + + align:start position:0% +being you know stolen from their dorm +room although maybe I should be I don't + + align:start position:0% +room although maybe I should be I don't + + + align:start position:0% +room although maybe I should be I don't +know it's it's hard to tell right the + + align:start position:0% +know it's it's hard to tell right the + + + align:start position:0% +know it's it's hard to tell right the +and as a result this uh security game is + + align:start position:0% +and as a result this uh security game is + + + align:start position:0% +and as a result this uh security game is +often not so clear cut as to what the + + align:start position:0% +often not so clear cut as to what the + + + align:start position:0% +often not so clear cut as to what the +right set of assumptions to make is and + + align:start position:0% +right set of assumptions to make is and + + + align:start position:0% +right set of assumptions to make is and +it's only after the fact that you often + + align:start position:0% +it's only after the fact that you often + + + align:start position:0% +it's only after the fact that you often +realize well ah should have thought of + + align:start position:0% +realize well ah should have thought of + + + align:start position:0% +realize well ah should have thought of +that + + align:start position:0% +that + + + align:start position:0% +that +uh all right and sort of as a result + + align:start position:0% +uh all right and sort of as a result + + + align:start position:0% +uh all right and sort of as a result +this is very much an iterative process + + align:start position:0% +this is very much an iterative process + + + align:start position:0% +this is very much an iterative process +and the thing you end up realizing at + + align:start position:0% +and the thing you end up realizing at + + + align:start position:0% +and the thing you end up realizing at +every iteration is well here's the + + align:start position:0% +every iteration is well here's the + + + align:start position:0% +every iteration is well here's the +weakest link in my system maybe I got + + align:start position:0% +weakest link in my system maybe I got + + + align:start position:0% +weakest link in my system maybe I got +the threat model wrong maybe my + + align:start position:0% +the threat model wrong maybe my + + + align:start position:0% +the threat model wrong maybe my +mechanism had some bugs in it because + + align:start position:0% +mechanism had some bugs in it because + + + align:start position:0% +mechanism had some bugs in it because +it's software and it's going to be large + + align:start position:0% +it's software and it's going to be large + + + align:start position:0% +it's software and it's going to be large +systems they'll have lots of bugs uh and + + align:start position:0% +systems they'll have lots of bugs uh and + + + align:start position:0% +systems they'll have lots of bugs uh and +you sort of fix them up you change your + + align:start position:0% +you sort of fix them up you change your + + + align:start position:0% +you sort of fix them up you change your +threat model a little bit and you + + align:start position:0% +threat model a little bit and you + + + align:start position:0% +threat model a little bit and you +iterate and try to design a new system + + align:start position:0% +iterate and try to design a new system + + + align:start position:0% +iterate and try to design a new system +and hopefully uh make things + + align:start position:0% +and hopefully uh make things + + + align:start position:0% +and hopefully uh make things +better so one one possible + + align:start position:0% +better so one one possible + + + align:start position:0% +better so one one possible +interpretation of this class well one + + align:start position:0% +interpretation of this class well one + + + align:start position:0% +interpretation of this class well one +danger uh is that you come away thinking + + align:start position:0% +danger uh is that you come away thinking + + + align:start position:0% +danger uh is that you come away thinking +man everything is just broken nothing + + align:start position:0% +man everything is just broken nothing + + + align:start position:0% +man everything is just broken nothing +works we should just give up and stop + + align:start position:0% +works we should just give up and stop + + + align:start position:0% +works we should just give up and stop +using computers and this is like one + + align:start position:0% +using computers and this is like one + + + align:start position:0% +using computers and this is like one +possible interpretation uh but it's + + align:start position:0% +possible interpretation uh but it's + + + align:start position:0% +possible interpretation uh but it's +probably not quite the right one um the + + align:start position:0% +probably not quite the right one um the + + + align:start position:0% +probably not quite the right one um the +reason this is going to come up or + + align:start position:0% +reason this is going to come up or + + + align:start position:0% +reason this is going to come up or +you're going to think this way is + + align:start position:0% +you're going to think this way is + + + align:start position:0% +you're going to think this way is +because throughout this class we're + + align:start position:0% +because throughout this class we're + + + align:start position:0% +because throughout this class we're +going to look at all these different + + align:start position:0% +going to look at all these different + + + align:start position:0% +going to look at all these different +systems and we're going to sort of push + + align:start position:0% +systems and we're going to sort of push + + + align:start position:0% +systems and we're going to sort of push +them to the edge we're going to see okay + + align:start position:0% +them to the edge we're going to see okay + + + align:start position:0% +them to the edge we're going to see okay +well what if we do this is it going to + + align:start position:0% +well what if we do this is it going to + + + align:start position:0% +well what if we do this is it going to +break what if we do that is it going to + + align:start position:0% +break what if we do that is it going to + + + align:start position:0% +break what if we do that is it going to +break then and inevitably every system + + align:start position:0% +break then and inevitably every system + + + align:start position:0% +break then and inevitably every system +is going to have some sort of a Breaking + + align:start position:0% +is going to have some sort of a Breaking + + + align:start position:0% +is going to have some sort of a Breaking +Point and we'll figure out oh hey you + + align:start position:0% +Point and we'll figure out oh hey you + + + align:start position:0% +Point and we'll figure out oh hey you +know the system you know we can break it + + align:start position:0% +know the system you know we can break it + + + align:start position:0% +know the system you know we can break it +in if we push this way and the system + + align:start position:0% +in if we push this way and the system + + + align:start position:0% +in if we push this way and the system +doesn't work under these set of + + align:start position:0% +doesn't work under these set of + + + align:start position:0% +doesn't work under these set of +assumptions and it's inevitable that + + align:start position:0% +assumptions and it's inevitable that + + + align:start position:0% +assumptions and it's inevitable that +every system will have a breaking point + + align:start position:0% +every system will have a breaking point + + + align:start position:0% +every system will have a breaking point +but that doesn't mean that every system + + align:start position:0% +but that doesn't mean that every system + + + align:start position:0% +but that doesn't mean that every system +is worthless it just means you have to + + align:start position:0% +is worthless it just means you have to + + + align:start position:0% +is worthless it just means you have to +know when to use every system design and + + align:start position:0% +know when to use every system design and + + + align:start position:0% +know when to use every system design and +it's sort of useful to do this pushing + + align:start position:0% +it's sort of useful to do this pushing + + + align:start position:0% +it's sort of useful to do this pushing +exercise to find the weaknesses so that + + align:start position:0% +exercise to find the weaknesses so that + + + align:start position:0% +exercise to find the weaknesses so that +you know when certain ideas work when + + align:start position:0% +you know when certain ideas work when + + + align:start position:0% +you know when certain ideas work when +certain ideas are not uh + + align:start position:0% +certain ideas are not uh + + + align:start position:0% +certain ideas are not uh +applicable and in reality right this is + + align:start position:0% +applicable and in reality right this is + + + align:start position:0% +applicable and in reality right this is +a sort of a fuzzy boundary right the the + + align:start position:0% +a sort of a fuzzy boundary right the the + + + align:start position:0% +a sort of a fuzzy boundary right the the +more secure you make your system the + + align:start position:0% +more secure you make your system the + + + align:start position:0% +more secure you make your system the +less likely you'll have some + + align:start position:0% +less likely you'll have some + + + align:start position:0% +less likely you'll have some +embarrassing you know story on the front + + align:start position:0% +embarrassing you know story on the front + + + align:start position:0% +embarrassing you know story on the front +page of New York Times saying you know + + align:start position:0% +page of New York Times saying you know + + + align:start position:0% +page of New York Times saying you know +your startup company leaked a million + + align:start position:0% +your startup company leaked a million + + + align:start position:0% +your startup company leaked a million +people's you know Social Security + + align:start position:0% +people's you know Social Security + + + align:start position:0% +people's you know Social Security +numbers um and then you pay less money + + align:start position:0% +numbers um and then you pay less money + + + align:start position:0% +numbers um and then you pay less money +to recover from that disaster + + align:start position:0% +to recover from that disaster + + + align:start position:0% +to recover from that disaster +uh and I guess one sort of actually + + align:start position:0% +uh and I guess one sort of actually + + + align:start position:0% +uh and I guess one sort of actually +positive note on security is that in + + align:start position:0% +positive note on security is that in + + + align:start position:0% +positive note on security is that in +many ways security enables cool things + + align:start position:0% +many ways security enables cool things + + + align:start position:0% +many ways security enables cool things +that you couldn't do before um because + + align:start position:0% +that you couldn't do before um because + + + align:start position:0% +that you couldn't do before um because +security especially mechanisms that + + align:start position:0% +security especially mechanisms that + + + align:start position:0% +security especially mechanisms that +allow us + + align:start position:0% +allow us + + + align:start position:0% +allow us +to protect against certain classes of + + align:start position:0% +to protect against certain classes of + + + align:start position:0% +to protect against certain classes of +attacks are pretty powerful as as one + + align:start position:0% +attacks are pretty powerful as as one + + + align:start position:0% +attacks are pretty powerful as as one +example right the browser used to be + + align:start position:0% +example right the browser used to be + + + align:start position:0% +example right the browser used to be +fairly uh boring in terms of what you + + align:start position:0% +fairly uh boring in terms of what you + + + align:start position:0% +fairly uh boring in terms of what you +could do with it you could just view web + + align:start position:0% +could do with it you could just view web + + + align:start position:0% +could do with it you could just view web +pages maybe run some JavaScript code in + + align:start position:0% +pages maybe run some JavaScript code in + + + align:start position:0% +pages maybe run some JavaScript code in +it but now there's all these cool + + align:start position:0% +it but now there's all these cool + + + align:start position:0% +it but now there's all these cool +mechanisms we'll learn about in a couple + + align:start position:0% +mechanisms we'll learn about in a couple + + + align:start position:0% +mechanisms we'll learn about in a couple +of weeks that allow you to run arbitrary + + align:start position:0% +of weeks that allow you to run arbitrary + + + align:start position:0% +of weeks that allow you to run arbitrary +x86 native code in the web browser and + + align:start position:0% +x86 native code in the web browser and + + + align:start position:0% +x86 native code in the web browser and +make sure doesn't do anything funny to + + align:start position:0% +make sure doesn't do anything funny to + + + align:start position:0% +make sure doesn't do anything funny to +your machine and it can send and there's + + align:start position:0% +your machine and it can send and there's + + + align:start position:0% +your machine and it can send and there's +a technique or system called native + + align:start position:0% +a technique or system called native + + + align:start position:0% +a technique or system called native +client from Google that actually allows + + align:start position:0% +client from Google that actually allows + + + align:start position:0% +client from Google that actually allows +us to do this securely and before you + + align:start position:0% +us to do this securely and before you + + + align:start position:0% +us to do this securely and before you +know in order to run some native game on + + align:start position:0% +know in order to run some native game on + + + align:start position:0% +know in order to run some native game on +your machine you have to download and + + align:start position:0% +your machine you have to download and + + + align:start position:0% +your machine you have to download and +install it click on lots of dialogue + + align:start position:0% +install it click on lots of dialogue + + + align:start position:0% +install it click on lots of dialogue +boxes say yes I allow this but now you + + align:start position:0% +boxes say yes I allow this but now you + + + align:start position:0% +boxes say yes I allow this but now you +can just run it in a browser no clicking + + align:start position:0% +can just run it in a browser no clicking + + + align:start position:0% +can just run it in a browser no clicking +required it just runs and the reason + + align:start position:0% +required it just runs and the reason + + + align:start position:0% +required it just runs and the reason +it's so easy and sort of powerful is + + align:start position:0% +it's so easy and sort of powerful is + + + align:start position:0% +it's so easy and sort of powerful is +that our security mechanism can sandbox + + align:start position:0% +that our security mechanism can sandbox + + + align:start position:0% +that our security mechanism can sandbox +this program and not have to assume + + align:start position:0% +this program and not have to assume + + + align:start position:0% +this program and not have to assume +anything about the user choosing the + + align:start position:0% +anything about the user choosing the + + + align:start position:0% +anything about the user choosing the +right game and not some malicious game + + align:start position:0% +right game and not some malicious game + + + align:start position:0% +right game and not some malicious game +to play in their computer or some other + + align:start position:0% +to play in their computer or some other + + + align:start position:0% +to play in their computer or some other +program to run so in many ways sort of + + align:start position:0% +program to run so in many ways sort of + + + align:start position:0% +program to run so in many ways sort of +good security mechanisms are going to + + align:start position:0% +good security mechanisms are going to + + + align:start position:0% +good security mechanisms are going to +enable constructing cool new systems + + align:start position:0% +enable constructing cool new systems + + + align:start position:0% +enable constructing cool new systems +that weren't possible to construct + + align:start position:0% +that weren't possible to construct + + + align:start position:0% +that weren't possible to construct +before all right make sense any + + align:start position:0% +before all right make sense any + + + align:start position:0% +before all right make sense any +questions about this + + align:start position:0% +questions about this + + + align:start position:0% +questions about this +story all right so I guess in the rest + + align:start position:0% +story all right so I guess in the rest + + + align:start position:0% +story all right so I guess in the rest +of the lecture I want to go through a + + align:start position:0% +of the lecture I want to go through a + + + align:start position:0% +of the lecture I want to go through a +bunch of different examples of how + + align:start position:0% +bunch of different examples of how + + + align:start position:0% +bunch of different examples of how +security goes wrong so so far we've seen + + align:start position:0% +security goes wrong so so far we've seen + + + align:start position:0% +security goes wrong so so far we've seen +how you can think of it but inevitably + + align:start position:0% +how you can think of it but inevitably + + + align:start position:0% +how you can think of it but inevitably +it's useful to see examples of what not + + align:start position:0% +it's useful to see examples of what not + + + align:start position:0% +it's useful to see examples of what not +to do so that you can sort of have a + + align:start position:0% +to do so that you can sort of have a + + + align:start position:0% +to do so that you can sort of have a +better mindset when you're approaching + + align:start position:0% +better mindset when you're approaching + + + align:start position:0% +better mindset when you're approaching +security + + align:start position:0% +security + + + align:start position:0% +security +problems and in this sort of breakdown + + align:start position:0% +problems and in this sort of breakdown + + + align:start position:0% +problems and in this sort of breakdown +of a security system pretty much every + + align:start position:0% +of a security system pretty much every + + + align:start position:0% +of a security system pretty much every +one of these three things goes wrong in + + align:start position:0% +one of these three things goes wrong in + + + align:start position:0% +one of these three things goes wrong in +practice people get the policy wrong + + align:start position:0% +practice people get the policy wrong + + + align:start position:0% +practice people get the policy wrong +people get the threat model wrong and + + align:start position:0% +people get the threat model wrong and + + + align:start position:0% +people get the threat model wrong and +people get the mechanism wrong and let's + + align:start position:0% +people get the mechanism wrong and let's + + + align:start position:0% +people get the mechanism wrong and let's +I guess start with policies and examples + + align:start position:0% +I guess start with policies and examples + + + align:start position:0% +I guess start with policies and examples +of how you can um scre a systems + + align:start position:0% +of how you can um scre a systems + + + align:start position:0% +of how you can um scre a systems +policy maybe the cleanest or sort of + + align:start position:0% +policy maybe the cleanest or sort of + + + align:start position:0% +policy maybe the cleanest or sort of +simplest example of this uh are account + + align:start position:0% +simplest example of this uh are account + + + align:start position:0% +simplest example of this uh are account +sort of recovery + + align:start position:0% + + + + align:start position:0% + +questions so typically when you sign + + align:start position:0% +questions so typically when you sign + + + align:start position:0% +questions so typically when you sign +into a website you know you provide a + + align:start position:0% +into a website you know you provide a + + + align:start position:0% +into a website you know you provide a +password but what happens if you lose + + align:start position:0% +password but what happens if you lose + + + align:start position:0% +password but what happens if you lose +your password some sites will send you + + align:start position:0% +your password some sites will send you + + + align:start position:0% +your password some sites will send you +email uh if you lose your password with + + align:start position:0% +email uh if you lose your password with + + + align:start position:0% +email uh if you lose your password with +a link to reset your password so it's + + align:start position:0% +a link to reset your password so it's + + + align:start position:0% +a link to reset your password so it's +easy enough if you have another email + + align:start position:0% +easy enough if you have another email + + + align:start position:0% +easy enough if you have another email +address but what if this is your email + + align:start position:0% +address but what if this is your email + + + align:start position:0% +address but what if this is your email +provider so companies uh well at least + + align:start position:0% +provider so companies uh well at least + + + align:start position:0% +provider so companies uh well at least +several years ago Yahoo you know hosted + + align:start position:0% +several years ago Yahoo you know hosted + + + align:start position:0% +several years ago Yahoo you know hosted +email web mail for anyone on the + + align:start position:0% +email web mail for anyone on the + + + align:start position:0% +email web mail for anyone on the +internet and when you forgot your Yahoo + + align:start position:0% +internet and when you forgot your Yahoo + + + align:start position:0% +internet and when you forgot your Yahoo +password they couldn't really send you + + align:start position:0% +password they couldn't really send you + + + align:start position:0% +password they couldn't really send you +email because you couldn't get it so + + align:start position:0% +email because you couldn't get it so + + + align:start position:0% +email because you couldn't get it so +instead they had you register a couple + + align:start position:0% +instead they had you register a couple + + + align:start position:0% +instead they had you register a couple +of questions with them that hopefully + + align:start position:0% +of questions with them that hopefully + + + align:start position:0% +of questions with them that hopefully +only you know and if you forget your + + align:start position:0% +only you know and if you forget your + + + align:start position:0% +only you know and if you forget your +password you can click on a link and say + + align:start position:0% +password you can click on a link and say + + + align:start position:0% +password you can click on a link and say +well you know what here's the answers to + + align:start position:0% +well you know what here's the answers to + + + align:start position:0% +well you know what here's the answers to +my questions let me have my password + + align:start position:0% +my questions let me have my password + + + align:start position:0% +my questions let me have my password +again and what turns out to be the case + + align:start position:0% +again and what turns out to be the case + + + align:start position:0% +again and what turns out to be the case +is uh well some people fail to realize + + align:start position:0% +is uh well some people fail to realize + + + align:start position:0% +is uh well some people fail to realize +is that this set your this changes your + + align:start position:0% +is that this set your this changes your + + + align:start position:0% +is that this set your this changes your +policy because before your the policy of + + align:start position:0% +policy because before your the policy of + + + align:start position:0% +policy because before your the policy of +the system is people that can log in are + + align:start position:0% +the system is people that can log in are + + + align:start position:0% +the system is people that can log in are +the people that know the password and + + align:start position:0% +the people that know the password and + + + align:start position:0% +the people that know the password and +when you introduce these recovery + + align:start position:0% +when you introduce these recovery + + + align:start position:0% +when you introduce these recovery +questions the policy becomes well you + + align:start position:0% +questions the policy becomes well you + + + align:start position:0% +questions the policy becomes well you +can log in if you know either the + + align:start position:0% +can log in if you know either the + + + align:start position:0% +can log in if you know either the +password or those security questions so + + align:start position:0% +password or those security questions so + + + align:start position:0% +password or those security questions so +it's strictly weakens the security of + + align:start position:0% +it's strictly weakens the security of + + + align:start position:0% +it's strictly weakens the security of +your system and many people have + + align:start position:0% +your system and many people have + + + align:start position:0% +your system and many people have +actually taken advantage of this one + + align:start position:0% +actually taken advantage of this one + + + align:start position:0% +actually taken advantage of this one +sort of well-known example is uh I think + + align:start position:0% +sort of well-known example is uh I think + + + align:start position:0% +sort of well-known example is uh I think +a couple years ago Sarah Palin had an + + align:start position:0% +a couple years ago Sarah Palin had an + + + align:start position:0% +a couple years ago Sarah Palin had an +email account at Yahoo and her recovery + + align:start position:0% +email account at Yahoo and her recovery + + + align:start position:0% +email account at Yahoo and her recovery +questions were things like well where + + align:start position:0% +questions were things like well where + + + align:start position:0% +questions were things like well where +did you go to school what was your you + + align:start position:0% +did you go to school what was your you + + + align:start position:0% +did you go to school what was your you +know friend's you know name what's your + + align:start position:0% +know friend's you know name what's your + + + align:start position:0% +know friend's you know name what's your +birthday Etc these are all things + + align:start position:0% +birthday Etc these are all things + + + align:start position:0% +birthday Etc these are all things +written on her Wikipedia page and as a + + align:start position:0% +written on her Wikipedia page and as a + + + align:start position:0% +written on her Wikipedia page and as a +result someone can quite easily and + + align:start position:0% +result someone can quite easily and + + + align:start position:0% +result someone can quite easily and +someone did actually get into her Yahoo + + align:start position:0% +someone did actually get into her Yahoo + + + align:start position:0% +someone did actually get into her Yahoo +email account just by looking up on + + align:start position:0% +email account just by looking up on + + + align:start position:0% +email account just by looking up on +Wikipedia what her high school was and + + align:start position:0% +Wikipedia what her high school was and + + + align:start position:0% +Wikipedia what her high school was and +what her birthday was so you really have + + align:start position:0% +what her birthday was so you really have + + + align:start position:0% +what her birthday was so you really have +to think carefully about the + + align:start position:0% +to think carefully about the + + + align:start position:0% +to think carefully about the +implications of different security + + align:start position:0% +implications of different security + + + align:start position:0% +implications of different security +policies you're making here perhaps a + + align:start position:0% +policies you're making here perhaps a + + + align:start position:0% +policies you're making here perhaps a +more intricate and maybe interesting + + align:start position:0% +more intricate and maybe interesting + + + align:start position:0% +more intricate and maybe interesting +example + + align:start position:0% +example + + + align:start position:0% +example +is uh how what happens when you have + + align:start position:0% +is uh how what happens when you have + + + align:start position:0% +is uh how what happens when you have +multiple systems that start interacting + + align:start position:0% +multiple systems that start interacting + + + align:start position:0% +multiple systems that start interacting +with one another uh so there's this nice + + align:start position:0% +with one another uh so there's this nice + + + align:start position:0% +with one another uh so there's this nice +story about uh a guy called Matt Hanan + + align:start position:0% +story about uh a guy called Matt Hanan + + + align:start position:0% +story about uh a guy called Matt Hanan +maybe you've read this story a year or + + align:start position:0% +maybe you've read this story a year or + + + align:start position:0% +maybe you've read this story a year or +two ago um he's a editor at this + + align:start position:0% +two ago um he's a editor at this + + + align:start position:0% +two ago um he's a editor at this +wire.com magazine and um had a bit of a + + align:start position:0% +wire.com magazine and um had a bit of a + + + align:start position:0% +wire.com magazine and um had a bit of a +problem someone basically got into his + + align:start position:0% +problem someone basically got into his + + + align:start position:0% +problem someone basically got into his +Gmail account and you know did lots of + + align:start position:0% +Gmail account and you know did lots of + + + align:start position:0% +Gmail account and you know did lots of +bad things but how did they do it right + + align:start position:0% +bad things but how did they do it right + + + align:start position:0% +bad things but how did they do it right +so it's kind of interesting so all + + align:start position:0% +so it's kind of interesting so all + + + align:start position:0% +so it's kind of interesting so all +parties in this story seem to be doing + + align:start position:0% +parties in this story seem to be doing + + + align:start position:0% +parties in this story seem to be doing +reasonable things but we'll see how they + + align:start position:0% +reasonable things but we'll see how they + + + align:start position:0% +reasonable things but we'll see how they +add up to something unfortunate so we + + align:start position:0% +add up to something unfortunate so we + + + align:start position:0% +add up to something unfortunate so we +have Gmail and Gmail um lets you reset + + align:start position:0% +have Gmail and Gmail um lets you reset + + + align:start position:0% +have Gmail and Gmail um lets you reset +your password if you forget as do pretty + + align:start position:0% +your password if you forget as do pretty + + + align:start position:0% +your password if you forget as do pretty +much any every other system and the way + + align:start position:0% +much any every other system and the way + + + align:start position:0% +much any every other system and the way +you sort of do a reset at gmail is you + + align:start position:0% +you sort of do a reset at gmail is you + + + align:start position:0% +you sort of do a reset at gmail is you +send them a reset request and what they + + align:start position:0% +send them a reset request and what they + + + align:start position:0% +send them a reset request and what they +say is well you know you we're not going + + align:start position:0% +say is well you know you we're not going + + + align:start position:0% +say is well you know you we're not going +to do this recovery questions at least + + align:start position:0% +to do this recovery questions at least + + + align:start position:0% +to do this recovery questions at least +not for this guy what they do is they + + align:start position:0% +not for this guy what they do is they + + + align:start position:0% +not for this guy what they do is they +send you a recovery link to a backup + + align:start position:0% +send you a recovery link to a backup + + + align:start position:0% +send you a recovery link to a backup +email address so some other email + + align:start position:0% +email address so some other email + + + align:start position:0% +email address so some other email +address that you have and helpful they + + align:start position:0% +address that you have and helpful they + + + align:start position:0% +address that you have and helpful they +actually print the email address for you + + align:start position:0% +actually print the email address for you + + + align:start position:0% +actually print the email address for you +so for this guy's account someone went + + align:start position:0% +so for this guy's account someone went + + + align:start position:0% +so for this guy's account someone went +and asked Gmail to reset the password + + align:start position:0% +and asked Gmail to reset the password + + + align:start position:0% +and asked Gmail to reset the password +and they said well yeah sure we just + + align:start position:0% +and they said well yeah sure we just + + + align:start position:0% +and they said well yeah sure we just +sent the recovery link to this email Fu + + align:start position:0% +sent the recovery link to this email Fu + + + align:start position:0% +sent the recovery link to this email Fu +me.com which was some apple you know + + align:start position:0% +me.com which was some apple you know + + + align:start position:0% +me.com which was some apple you know +email + + align:start position:0% +email + + + align:start position:0% +email +service okay but the bad guy doesn't + + align:start position:0% +service okay but the bad guy doesn't + + + align:start position:0% +service okay but the bad guy doesn't +have access to me.com either but they + + align:start position:0% +have access to me.com either but they + + + align:start position:0% +have access to me.com either but they +want to get this password reset link to + + align:start position:0% +want to get this password reset link to + + + align:start position:0% +want to get this password reset link to +get access to Gmail well the way things + + align:start position:0% +get access to Gmail well the way things + + + align:start position:0% +get access to Gmail well the way things +worked was that in Apple's case uh this + + align:start position:0% +worked was that in Apple's case uh this + + + align:start position:0% +worked was that in Apple's case uh this +me.com + + align:start position:0% +me.com + + + align:start position:0% +me.com +site allowed you to actually reset your + + align:start position:0% +site allowed you to actually reset your + + + align:start position:0% +site allowed you to actually reset your +password if you know your billing + + align:start position:0% +password if you know your billing + + + align:start position:0% +password if you know your billing +address and the last four digits of your + + align:start position:0% +address and the last four digits of your + + + align:start position:0% +address and the last four digits of your +credit card number so still like not + + align:start position:0% +credit card number so still like not + + + align:start position:0% +credit card number so still like not +clear how you going to get this guy's + + align:start position:0% +clear how you going to get this guy's + + + align:start position:0% +clear how you going to get this guy's +you know well home address maybe you can + + align:start position:0% +you know well home address maybe you can + + + align:start position:0% +you know well home address maybe you can +look it up somewhere this guy's a + + align:start position:0% +look it up somewhere this guy's a + + + align:start position:0% +look it up somewhere this guy's a +well-known person at the time uh but + + align:start position:0% +well-known person at the time uh but + + + align:start position:0% +well-known person at the time uh but +where do you get the last four digits of + + align:start position:0% +where do you get the last four digits of + + + align:start position:0% +where do you get the last four digits of +this credit card number well not clear + + align:start position:0% +this credit card number well not clear + + + align:start position:0% +this credit card number well not clear +but let's keep going further um so you + + align:start position:0% +but let's keep going further um so you + + + align:start position:0% +but let's keep going further um so you +need to send these things to me.com to + + align:start position:0% +need to send these things to me.com to + + + align:start position:0% +need to send these things to me.com to +get access to his email account there + + align:start position:0% +get access to his email account there + + + align:start position:0% +get access to his email account there +well it turns out this guy had an + + align:start position:0% +well it turns out this guy had an + + + align:start position:0% +well it turns out this guy had an +account at Amazon which was another + + align:start position:0% +account at Amazon which was another + + + align:start position:0% +account at Amazon which was another +party in this story um Amazon really + + align:start position:0% +party in this story um Amazon really + + + align:start position:0% +party in this story um Amazon really +wants you to buy things um and as a + + align:start position:0% +wants you to buy things um and as a + + + align:start position:0% +wants you to buy things um and as a +result they actually have a fairly + + align:start position:0% +result they actually have a fairly + + + align:start position:0% +result they actually have a fairly +elaborate account management system and + + align:start position:0% +elaborate account management system and + + + align:start position:0% +elaborate account management system and +in particular because they really want + + align:start position:0% +in particular because they really want + + + align:start position:0% +in particular because they really want +you to buy stuff they don't require you + + align:start position:0% +you to buy stuff they don't require you + + + align:start position:0% +you to buy stuff they don't require you +to sign in in order to purchase some + + align:start position:0% +to sign in in order to purchase some + + + align:start position:0% +to sign in in order to purchase some +item with a credit card so I can + + align:start position:0% +item with a credit card so I can + + + align:start position:0% +item with a credit card so I can +actually go on Amazon or at least at the + + align:start position:0% +actually go on Amazon or at least at the + + + align:start position:0% +actually go on Amazon or at least at the +time I was able to go on Amazon and say + + align:start position:0% +time I was able to go on Amazon and say + + + align:start position:0% +time I was able to go on Amazon and say +well I'm this user and uh I want to buy + + align:start position:0% +well I'm this user and uh I want to buy + + + align:start position:0% +well I'm this user and uh I want to buy +you know this pack of + + align:start position:0% +you know this pack of + + + align:start position:0% +you know this pack of +toothbrushes and if I wanted to use the + + align:start position:0% +toothbrushes and if I wanted to use the + + + align:start position:0% +toothbrushes and if I wanted to use the +saved credit card number in the guy's + + align:start position:0% +saved credit card number in the guy's + + + align:start position:0% +saved credit card number in the guy's +account I shouldn't be able to do this + + align:start position:0% +account I shouldn't be able to do this + + + align:start position:0% +account I shouldn't be able to do this +but if I just provide a new credit card + + align:start position:0% +but if I just provide a new credit card + + + align:start position:0% +but if I just provide a new credit card +what Amazon would do is they can + + align:start position:0% +what Amazon would do is they can + + + align:start position:0% +what Amazon would do is they can +actually add a new credit + + align:start position:0% +actually add a new credit + + + align:start position:0% +actually add a new credit +card to some guy's + + align:start position:0% +card to some guy's + + + align:start position:0% +card to some guy's +account so that seems not too bad right + + align:start position:0% +account so that seems not too bad right + + + align:start position:0% +account so that seems not too bad right +like I'm basically ordering toothbrushes + + align:start position:0% +like I'm basically ordering toothbrushes + + + align:start position:0% +like I'm basically ordering toothbrushes +through one of your Amazon accounts but + + align:start position:0% +through one of your Amazon accounts but + + + align:start position:0% +through one of your Amazon accounts but +it's not your credit card anyway it's + + align:start position:0% +it's not your credit card anyway it's + + + align:start position:0% +it's not your credit card anyway it's +just my credit card number being used so + + align:start position:0% +just my credit card number being used so + + + align:start position:0% +just my credit card number being used so +it's not clear how things go wrong yet + + align:start position:0% +it's not clear how things go wrong yet + + + align:start position:0% +it's not clear how things go wrong yet +but Amazon had another interface like + + align:start position:0% +but Amazon had another interface like + + + align:start position:0% +but Amazon had another interface like +all these are complicated systems and + + align:start position:0% +all these are complicated systems and + + + align:start position:0% +all these are complicated systems and +had an interface for password reset and + + align:start position:0% +had an interface for password reset and + + + align:start position:0% +had an interface for password reset and +in order to reset a password in Amazon + + align:start position:0% +in order to reset a password in Amazon + + + align:start position:0% +in order to reset a password in Amazon +uh what you had to provide is just one + + align:start position:0% +uh what you had to provide is just one + + + align:start position:0% +uh what you had to provide is just one +of the user's credit card numbers so I + + align:start position:0% +of the user's credit card numbers so I + + + align:start position:0% +of the user's credit card numbers so I +can order stuff and add a credit card + + align:start position:0% +can order stuff and add a credit card + + + align:start position:0% +can order stuff and add a credit card +number to your account and then I can + + align:start position:0% +number to your account and then I can + + + align:start position:0% +number to your account and then I can +say hey I want to reset my password this + + align:start position:0% +say hey I want to reset my password this + + + align:start position:0% +say hey I want to reset my password this +is one of my credit card numbers and + + align:start position:0% +is one of my credit card numbers and + + + align:start position:0% +is one of my credit card numbers and +this in fact worked so this is where the + + align:start position:0% +this in fact worked so this is where the + + + align:start position:0% +this in fact worked so this is where the +bad guy uh got a hold of this guy's + + align:start position:0% +bad guy uh got a hold of this guy's + + + align:start position:0% +bad guy uh got a hold of this guy's +mat's Amazon account but okay how do you + + align:start position:0% +mat's Amazon account but okay how do you + + + align:start position:0% +mat's Amazon account but okay how do you +fish out the credit card number for + + align:start position:0% +fish out the credit card number for + + + align:start position:0% +fish out the credit card number for +resetting Apple's site well Amazon is + + align:start position:0% +resetting Apple's site well Amazon is + + + align:start position:0% +resetting Apple's site well Amazon is +actually very careful even if you break + + align:start position:0% +actually very careful even if you break + + + align:start position:0% +actually very careful even if you break +into someone's Amazon account it will + + align:start position:0% +into someone's Amazon account it will + + + align:start position:0% +into someone's Amazon account it will +not print you the saved credit card + + align:start position:0% +not print you the saved credit card + + + align:start position:0% +not print you the saved credit card +numbers from that person but it will + + align:start position:0% +numbers from that person but it will + + + align:start position:0% +numbers from that person but it will +show the last four digits just so you + + align:start position:0% +show the last four digits just so you + + + align:start position:0% +show the last four digits just so you +know which credit card you're talking + + align:start position:0% +know which credit card you're talking + + + align:start position:0% +know which credit card you're talking +about so you can list all the credit + + align:start position:0% +about so you can list all the credit + + + align:start position:0% +about so you can list all the credit +cards other than the one you added you + + align:start position:0% +cards other than the one you added you + + + align:start position:0% +cards other than the one you added you +can then go and break into me.com you + + align:start position:0% +can then go and break into me.com you + + + align:start position:0% +can then go and break into me.com you +can click on this link and get access to + + align:start position:0% +can click on this link and get access to + + + align:start position:0% +can click on this link and get access to +the guy's Gmail account this all very + + align:start position:0% +the guy's Gmail account this all very + + + align:start position:0% +the guy's Gmail account this all very +subtle stuff and in isolation each + + align:start position:0% +subtle stuff and in isolation each + + + align:start position:0% +subtle stuff and in isolation each +system seems to be doing somewhat + + align:start position:0% +system seems to be doing somewhat + + + align:start position:0% +system seems to be doing somewhat +sensible things but it's actually quite + + align:start position:0% +sensible things but it's actually quite + + + align:start position:0% +sensible things but it's actually quite +hard to reason about these uh + + align:start position:0% +hard to reason about these uh + + + align:start position:0% +hard to reason about these uh +vulnerabilities and weaknesses unless + + align:start position:0% +vulnerabilities and weaknesses unless + + + align:start position:0% +vulnerabilities and weaknesses unless +you have sort of this whole picture + + align:start position:0% +you have sort of this whole picture + + + align:start position:0% +you have sort of this whole picture +explained to you and you sort of put all + + align:start position:0% +explained to you and you sort of put all + + + align:start position:0% +explained to you and you sort of put all +the pieces together so this is actually + + align:start position:0% +the pieces together so this is actually + + + align:start position:0% +the pieces together so this is actually +fairly tricky stuff um and + + align:start position:0% +fairly tricky stuff um and + + + align:start position:0% +fairly tricky stuff um and +unfortunately well much like for every + + align:start position:0% +unfortunately well much like for every + + + align:start position:0% +unfortunately well much like for every +one of these three categories the answer + + align:start position:0% +one of these three categories the answer + + + align:start position:0% +one of these three categories the answer +for how to avoid this is often think + + align:start position:0% +for how to avoid this is often think + + + align:start position:0% +for how to avoid this is often think +hard and be careful I guess the one + + align:start position:0% +hard and be careful I guess the one + + + align:start position:0% +hard and be careful I guess the one +General plan is be conservative in terms + + align:start position:0% +General plan is be conservative in terms + + + align:start position:0% +General plan is be conservative in terms +of uh what you set your policy to be to + + align:start position:0% +of uh what you set your policy to be to + + + align:start position:0% +of uh what you set your policy to be to +maybe not depend on things other sites + + align:start position:0% +maybe not depend on things other sites + + + align:start position:0% +maybe not depend on things other sites +might reveal so well I'm not sure if any + + align:start position:0% +might reveal so well I'm not sure if any + + + align:start position:0% +might reveal so well I'm not sure if any +really great advice would have prevented + + align:start position:0% +really great advice would have prevented + + + align:start position:0% +really great advice would have prevented +this problem but now you know and now + + align:start position:0% +this problem but now you know and now + + + align:start position:0% +this problem but now you know and now +you'll make other mistakes um there's + + align:start position:0% +you'll make other mistakes um there's + + + align:start position:0% +you'll make other mistakes um there's +sort of many other examples of policies + + align:start position:0% +sort of many other examples of policies + + + align:start position:0% +sort of many other examples of policies +going wrong and allowing a system to be + + align:start position:0% +going wrong and allowing a system to be + + + align:start position:0% +going wrong and allowing a system to be +compromised that's interesting enough + + align:start position:0% +compromised that's interesting enough + + + align:start position:0% +compromised that's interesting enough +but let's look at how people might uh + + align:start position:0% +but let's look at how people might uh + + + align:start position:0% +but let's look at how people might uh +screw up threat models so let me maybe + + align:start position:0% +screw up threat models so let me maybe + + + align:start position:0% +screw up threat models so let me maybe +turn off this blue square um okay so how + + align:start position:0% +turn off this blue square um okay so how + + + align:start position:0% +turn off this blue square um okay so how +what are examples of threat models + + align:start position:0% +what are examples of threat models + + + align:start position:0% +what are examples of threat models +that go + + align:start position:0% +that go + + + align:start position:0% +that go +wrong well probably a big one in + + align:start position:0% +wrong well probably a big one in + + + align:start position:0% +wrong well probably a big one in +practice is um human factors so we often + + align:start position:0% +practice is um human factors so we often + + + align:start position:0% +practice is um human factors so we often +make M make assumptions about what + + align:start position:0% +make M make assumptions about what + + + align:start position:0% +make M make assumptions about what +people will do in a system like they + + align:start position:0% +people will do in a system like they + + + align:start position:0% +people will do in a system like they +will pick a good strong password or they + + align:start position:0% +will pick a good strong password or they + + + align:start position:0% +will pick a good strong password or they +will not click on random websites that + + align:start position:0% +will not click on random websites that + + + align:start position:0% +will not click on random websites that +they get through email and enter their + + align:start position:0% +they get through email and enter their + + + align:start position:0% +they get through email and enter their +password there so these are well as you + + align:start position:0% +password there so these are well as you + + + align:start position:0% +password there so these are well as you +probably suspect and in practice happens + + align:start position:0% +probably suspect and in practice happens + + + align:start position:0% +probably suspect and in practice happens +to be the case these are not good + + align:start position:0% +to be the case these are not good + + + align:start position:0% +to be the case these are not good +assumptions in all cases and people pick + + align:start position:0% +assumptions in all cases and people pick + + + align:start position:0% +assumptions in all cases and people pick +bad passwords and people will click on + + align:start position:0% +bad passwords and people will click on + + + align:start position:0% +bad passwords and people will click on +random links and people will enter their + + align:start position:0% +random links and people will enter their + + + align:start position:0% +random links and people will enter their +password on sites that are actually not + + align:start position:0% +password on sites that are actually not + + + align:start position:0% +password on sites that are actually not +the right site at all and they will not + + align:start position:0% +the right site at all and they will not + + + align:start position:0% +the right site at all and they will not +be paying a lot of attention um so you + + align:start position:0% +be paying a lot of attention um so you + + + align:start position:0% +be paying a lot of attention um so you +probably don't want to have threat + + align:start position:0% +probably don't want to have threat + + + align:start position:0% +probably don't want to have threat +models that make very strong assumptions + + align:start position:0% +models that make very strong assumptions + + + align:start position:0% +models that make very strong assumptions +about what humans will do because + + align:start position:0% +about what humans will do because + + + align:start position:0% +about what humans will do because +inevitably something will go + + align:start position:0% +inevitably something will go + + + align:start position:0% +inevitably something will go +wrong make sense any questions + + align:start position:0% +wrong make sense any questions + + + align:start position:0% +wrong make sense any questions +all right another sort of good thing to + + align:start position:0% +all right another sort of good thing to + + + align:start position:0% +all right another sort of good thing to +watch out in threat models is that they + + align:start position:0% +watch out in threat models is that they + + + align:start position:0% +watch out in threat models is that they +sometimes change over time or sort of + + align:start position:0% +sometimes change over time or sort of + + + align:start position:0% +sometimes change over time or sort of +whether something is a good assumption + + align:start position:0% +whether something is a good assumption + + + align:start position:0% +whether something is a good assumption +or not changes over time um one example + + align:start position:0% +or not changes over time um one example + + + align:start position:0% +or not changes over time um one example +of this is actually at MIT in the mid99s + + align:start position:0% +of this is actually at MIT in the mid99s + + + align:start position:0% +of this is actually at MIT in the mid99s +mid uh 80s actually uh project Athena + + align:start position:0% +mid uh 80s actually uh project Athena + + + align:start position:0% +mid uh 80s actually uh project Athena +developed this system called Kerberos + + align:start position:0% +developed this system called Kerberos + + + align:start position:0% +developed this system called Kerberos +and we'll read about this in a couple of + + align:start position:0% +and we'll read about this in a couple of + + + align:start position:0% +and we'll read about this in a couple of +weeks in this class and at the time they + + align:start position:0% +weeks in this class and at the time they + + + align:start position:0% +weeks in this class and at the time they +were sort of figuring out well keros is + + align:start position:0% +were sort of figuring out well keros is + + + align:start position:0% +were sort of figuring out well keros is +going to be based on cryptography so we + + align:start position:0% +going to be based on cryptography so we + + + align:start position:0% +going to be based on cryptography so we +need to pick some size keys to make sure + + align:start position:0% +need to pick some size keys to make sure + + + align:start position:0% +need to pick some size keys to make sure +they're not going to be guessed by + + align:start position:0% +they're not going to be guessed by + + + align:start position:0% +they're not going to be guessed by +arbitrary people and they said okay well + + align:start position:0% +arbitrary people and they said okay well + + + align:start position:0% +arbitrary people and they said okay well +you know 56-bit keys at the time for + + align:start position:0% +you know 56-bit keys at the time for + + + align:start position:0% +you know 56-bit keys at the time for +this Cipher called DS seemed like a + + align:start position:0% +this Cipher called DS seemed like a + + + align:start position:0% +this Cipher called DS seemed like a +plausible size maybe not great but + + align:start position:0% +plausible size maybe not great but + + + align:start position:0% +plausible size maybe not great but +certainly not entirely + + align:start position:0% +certainly not entirely + + + align:start position:0% +certainly not entirely +unreasonable and this was in the mid 80s + + align:start position:0% +unreasonable and this was in the mid 80s + + + align:start position:0% +unreasonable and this was in the mid 80s +but then you know the system got popular + + align:start position:0% +but then you know the system got popular + + + align:start position:0% +but then you know the system got popular +got used a lot MIT still uses it and + + align:start position:0% +got used a lot MIT still uses it and + + + align:start position:0% +got used a lot MIT still uses it and +they never really went back to seriously + + align:start position:0% +they never really went back to seriously + + + align:start position:0% +they never really went back to seriously +revisit this assumption and then a + + align:start position:0% +revisit this assumption and then a + + + align:start position:0% +revisit this assumption and then a +couple years ago a group of 6858 + + align:start position:0% +couple years ago a group of 6858 + + + align:start position:0% +couple years ago a group of 6858 +students figured out that actually yeah + + align:start position:0% +students figured out that actually yeah + + + align:start position:0% +students figured out that actually yeah +you can just break this right like it's + + align:start position:0% +you can just break this right like it's + + + align:start position:0% +you can just break this right like it's +easy enough to enumerate all the 256 + + align:start position:0% +easy enough to enumerate all the 256 + + + align:start position:0% +easy enough to enumerate all the 256 +Keys these days computers are so fast + + align:start position:0% +Keys these days computers are so fast + + + align:start position:0% +Keys these days computers are so fast +you can just do it and as a result they + + align:start position:0% +you can just do it and as a result they + + + align:start position:0% +you can just do it and as a result they +were able to with the help of some + + align:start position:0% +were able to with the help of some + + + align:start position:0% +were able to with the help of some +Hardware from uh a particular web + + align:start position:0% +Hardware from uh a particular web + + + align:start position:0% +Hardware from uh a particular web +service we'll have some links in lecture + + align:start position:0% +service we'll have some links in lecture + + + align:start position:0% +service we'll have some links in lecture +notes they were able to get basically + + align:start position:0% +notes they were able to get basically + + + align:start position:0% +notes they were able to get basically +anyone's Kos account key in roughly a + + align:start position:0% +anyone's Kos account key in roughly a + + + align:start position:0% +anyone's Kos account key in roughly a +day so you know this assumption was good + + align:start position:0% +day so you know this assumption was good + + + align:start position:0% +day so you know this assumption was good +in the mid 1980s no longer a good + + align:start position:0% +in the mid 1980s no longer a good + + + align:start position:0% +in the mid 1980s no longer a good +assumption today so you really have to + + align:start position:0% +assumption today so you really have to + + + align:start position:0% +assumption today so you really have to +make make sure your assumptions sort of + + align:start position:0% +make make sure your assumptions sort of + + + align:start position:0% +make make sure your assumptions sort of +keep up with the times maybe a more + + align:start position:0% +keep up with the times maybe a more + + + align:start position:0% +keep up with the times maybe a more +timely example is if your adversary or + + align:start position:0% +timely example is if your adversary or + + + align:start position:0% +timely example is if your adversary or +if you're worried about government + + align:start position:0% +if you're worried about government + + + align:start position:0% +if you're worried about government +attacks you know you might realize that + + align:start position:0% +attacks you know you might realize that + + + align:start position:0% +attacks you know you might realize that +you shouldn't trust Hardware even these + + align:start position:0% +you shouldn't trust Hardware even these + + + align:start position:0% +you shouldn't trust Hardware even these +days right like there was all these + + align:start position:0% +days right like there was all these + + + align:start position:0% +days right like there was all these +Revelations about what the NSA is + + align:start position:0% +Revelations about what the NSA is + + + align:start position:0% +Revelations about what the NSA is +capable of doing and they have Hardware + + align:start position:0% +capable of doing and they have Hardware + + + align:start position:0% +capable of doing and they have Hardware +back doors that they can insert into + + align:start position:0% +back doors that they can insert into + + + align:start position:0% +back doors that they can insert into +computers um maybe up until a couple + + align:start position:0% +computers um maybe up until a couple + + + align:start position:0% +computers um maybe up until a couple +years ago well who knows I guess you + + align:start position:0% +years ago well who knows I guess you + + + align:start position:0% +years ago well who knows I guess you +didn't know about this stuff so uh maybe + + align:start position:0% +didn't know about this stuff so uh maybe + + + align:start position:0% +didn't know about this stuff so uh maybe +there was a reasonable assumption to + + align:start position:0% +there was a reasonable assumption to + + + align:start position:0% +there was a reasonable assumption to +assume your laptop is not going to be + + align:start position:0% +assume your laptop is not going to be + + + align:start position:0% +assume your laptop is not going to be +compromised physically like the hardware + + align:start position:0% +compromised physically like the hardware + + + align:start position:0% +compromised physically like the hardware +itself but now you know like actually if + + align:start position:0% +itself but now you know like actually if + + + align:start position:0% +itself but now you know like actually if +you're worried about the government + + align:start position:0% +you're worried about the government + + + align:start position:0% +you're worried about the government +being after you you probably have a much + + align:start position:0% +being after you you probably have a much + + + align:start position:0% +being after you you probably have a much +harder problem to deal with because your + + align:start position:0% +harder problem to deal with because your + + + align:start position:0% +harder problem to deal with because your +laptop might be compromised physically + + align:start position:0% +laptop might be compromised physically + + + align:start position:0% +laptop might be compromised physically +regardless of what you install in it um + + align:start position:0% +regardless of what you install in it um + + + align:start position:0% +regardless of what you install in it um +so you really have to be careful with + + align:start position:0% +so you really have to be careful with + + + align:start position:0% +so you really have to be careful with +your threat model and really sort of + + align:start position:0% +your threat model and really sort of + + + align:start position:0% +your threat model and really sort of +balance it against who you think is + + align:start position:0% +balance it against who you think is + + + align:start position:0% +balance it against who you think is +trying is out to get you like I think + + align:start position:0% +trying is out to get you like I think + + + align:start position:0% +trying is out to get you like I think +it's going to be a very expensive + + align:start position:0% +it's going to be a very expensive + + + align:start position:0% +it's going to be a very expensive +proposition if you're going to try to + + align:start position:0% +proposition if you're going to try to + + + align:start position:0% +proposition if you're going to try to +protect yourself from the NSA really uh + + align:start position:0% +protect yourself from the NSA really uh + + + align:start position:0% +protect yourself from the NSA really uh +on the other hand if you're just + + align:start position:0% +on the other hand if you're just + + + align:start position:0% +on the other hand if you're just +protecting yourself from random other + + align:start position:0% +protecting yourself from random other + + + align:start position:0% +protecting yourself from random other +students that are I don't know snooping + + align:start position:0% +students that are I don't know snooping + + + align:start position:0% +students that are I don't know snooping +around in your Athena home directory or + + align:start position:0% +around in your Athena home directory or + + + align:start position:0% +around in your Athena home directory or +whatnot maybe you don't have to worry + + align:start position:0% +whatnot maybe you don't have to worry + + + align:start position:0% +whatnot maybe you don't have to worry +about this stuff as much so it's really + + align:start position:0% +about this stuff as much so it's really + + + align:start position:0% +about this stuff as much so it's really +a sort of a balancing game in picking + + align:start position:0% +a sort of a balancing game in picking + + + align:start position:0% +a sort of a balancing game in picking +the right threat + + align:start position:0% +the right threat + + + align:start position:0% +the right threat +model um another sort of example of a + + align:start position:0% +model um another sort of example of a + + + align:start position:0% +model um another sort of example of a +bad threat model um shows up in the way + + align:start position:0% +bad threat model um shows up in the way + + + align:start position:0% +bad threat model um shows up in the way +secure websites these days check + + align:start position:0% +secure websites these days check + + + align:start position:0% +secure websites these days check +certificates of a website that you're + + align:start position:0% +certificates of a website that you're + + + align:start position:0% +certificates of a website that you're +connecting to so in this SSL protocol or + + align:start position:0% +connecting to so in this SSL protocol or + + + align:start position:0% +connecting to so in this SSL protocol or +TLS um when you connect to a website and + + align:start position:0% +TLS um when you connect to a website and + + + align:start position:0% +TLS um when you connect to a website and +it says hgps we'll talk much more about + + align:start position:0% +it says hgps we'll talk much more about + + + align:start position:0% +it says hgps we'll talk much more about +this in later lectures um but uh happens + + align:start position:0% +this in later lectures um but uh happens + + + align:start position:0% +this in later lectures um but uh happens +is that the site you're connecting to + + align:start position:0% +is that the site you're connecting to + + + align:start position:0% +is that the site you're connecting to +presents you a certificate signed by one + + align:start position:0% +presents you a certificate signed by one + + + align:start position:0% +presents you a certificate signed by one +of the certificate authorities out there + + align:start position:0% +of the certificate authorities out there + + + align:start position:0% +of the certificate authorities out there +that Ts that Yep this key belongs to + + align:start position:0% +that Ts that Yep this key belongs to + + + align:start position:0% +that Ts that Yep this key belongs to +amazon.com and architecturally the sort + + align:start position:0% +amazon.com and architecturally the sort + + + align:start position:0% +amazon.com and architecturally the sort +of mistake that or the bad threat model + + align:start position:0% +of mistake that or the bad threat model + + + align:start position:0% +of mistake that or the bad threat model +that these guys uh assumed is that all + + align:start position:0% +that these guys uh assumed is that all + + + align:start position:0% +that these guys uh assumed is that all +these Cas are going to be trustworthy + + align:start position:0% +these Cas are going to be trustworthy + + + align:start position:0% +these Cas are going to be trustworthy +they'll never make a mistake and in fact + + align:start position:0% +they'll never make a mistake and in fact + + + align:start position:0% +they'll never make a mistake and in fact +the way the system works is that there's + + align:start position:0% +the way the system works is that there's + + + align:start position:0% +the way the system works is that there's +hundreds of these Cas out there there's + + align:start position:0% +hundreds of these Cas out there there's + + + align:start position:0% +hundreds of these Cas out there there's +you know the Indian postal Authority I + + align:start position:0% +you know the Indian postal Authority I + + + align:start position:0% +you know the Indian postal Authority I +think has a CA you know you know the + + align:start position:0% +think has a CA you know you know the + + + align:start position:0% +think has a CA you know you know the +Chinese government has a CA lots of + + align:start position:0% +Chinese government has a CA lots of + + + align:start position:0% +Chinese government has a CA lots of +entities are certificate authorities in + + align:start position:0% +entities are certificate authorities in + + + align:start position:0% +entities are certificate authorities in +this design and any of them can make a + + align:start position:0% +this design and any of them can make a + + + align:start position:0% +this design and any of them can make a +certificate for any host name or any + + align:start position:0% +certificate for any host name or any + + + align:start position:0% +certificate for any host name or any +domain name and as a result what happens + + align:start position:0% +domain name and as a result what happens + + + align:start position:0% +domain name and as a result what happens +if you're a bad guy if you want to + + align:start position:0% +if you're a bad guy if you want to + + + align:start position:0% +if you're a bad guy if you want to +compromise Gmail or if you want to + + align:start position:0% +compromise Gmail or if you want to + + + align:start position:0% +compromise Gmail or if you want to +impersonate Gmail's website you just + + align:start position:0% +impersonate Gmail's website you just + + + align:start position:0% +impersonate Gmail's website you just +have to compromise one of these + + align:start position:0% +have to compromise one of these + + + align:start position:0% +have to compromise one of these +certificate authorities and it turns out + + align:start position:0% +certificate authorities and it turns out + + + align:start position:0% +certificate authorities and it turns out +the weakest link is probably you know + + align:start position:0% +the weakest link is probably you know + + + align:start position:0% +the weakest link is probably you know +some poorly run Authority somewhere in + + align:start position:0% +some poorly run Authority somewhere in + + + align:start position:0% +some poorly run Authority somewhere in +some you know not particularly upto-date + + align:start position:0% +some you know not particularly upto-date + + + align:start position:0% +some you know not particularly upto-date +country who knows right uh and as a + + align:start position:0% +country who knows right uh and as a + + + align:start position:0% +country who knows right uh and as a +result it's uh probably a bad assumption + + align:start position:0% +result it's uh probably a bad assumption + + + align:start position:0% +result it's uh probably a bad assumption +to build a system or it's a bad idea to + + align:start position:0% +to build a system or it's a bad idea to + + + align:start position:0% +to build a system or it's a bad idea to +build a system around the assumption + + align:start position:0% +build a system around the assumption + + + align:start position:0% +build a system around the assumption +that you'll manage to keep all 300 + + align:start position:0% +that you'll manage to keep all 300 + + + align:start position:0% +that you'll manage to keep all 300 +certificate authorities spread out + + align:start position:0% +certificate authorities spread out + + + align:start position:0% +certificate authorities spread out +around the globe perfectly secure but + + align:start position:0% +around the globe perfectly secure but + + + align:start position:0% +around the globe perfectly secure but +yet that's the Assumption underpinning + + align:start position:0% +yet that's the Assumption underpinning + + + align:start position:0% +yet that's the Assumption underpinning +the security mechanism of today's sort + + align:start position:0% +the security mechanism of today's sort + + + align:start position:0% +the security mechanism of today's sort +of SSL protocol used by web + + align:start position:0% +of SSL protocol used by web + + + align:start position:0% +of SSL protocol used by web +browsers and there's sort of many other + + align:start position:0% +browsers and there's sort of many other + + + align:start position:0% +browsers and there's sort of many other +I guess examples that are things you + + align:start position:0% +I guess examples that are things you + + + align:start position:0% +I guess examples that are things you +might not have thought of another sort + + align:start position:0% +might not have thought of another sort + + + align:start position:0% +might not have thought of another sort +of amusing example from the 1980s was um + + align:start position:0% +of amusing example from the 1980s was um + + + align:start position:0% +of amusing example from the 1980s was um +you know DARPA this defense uh agency at + + align:start position:0% +you know DARPA this defense uh agency at + + + align:start position:0% +you know DARPA this defense uh agency at +the time really wanted to build secure + + align:start position:0% +the time really wanted to build secure + + + align:start position:0% +the time really wanted to build secure +operating systems and they actually went + + align:start position:0% +operating systems and they actually went + + + align:start position:0% +operating systems and they actually went +so far as to you know get a bunch of + + align:start position:0% +so far as to you know get a bunch of + + + align:start position:0% +so far as to you know get a bunch of +universities and researchers to build + + align:start position:0% +universities and researchers to build + + + align:start position:0% +universities and researchers to build +secure OS prototypes and then they + + align:start position:0% +secure OS prototypes and then they + + + align:start position:0% +secure OS prototypes and then they +actually got a red team like a team of + + align:start position:0% +actually got a red team like a team of + + + align:start position:0% +actually got a red team like a team of +bad or guys pertaining to be the + + align:start position:0% +bad or guys pertaining to be the + + + align:start position:0% +bad or guys pertaining to be the +attackers and told them well go break + + align:start position:0% +attackers and told them well go break + + + align:start position:0% +attackers and told them well go break +into these secure operating systems any + + align:start position:0% +into these secure operating systems any + + + align:start position:0% +into these secure operating systems any +way you can you actually want to know is + + align:start position:0% +way you can you actually want to know is + + + align:start position:0% +way you can you actually want to know is +it secure and it's kind of amusing most + + align:start position:0% +it secure and it's kind of amusing most + + + align:start position:0% +it secure and it's kind of amusing most +of the or some of the surprising ways + + align:start position:0% +of the or some of the surprising ways + + + align:start position:0% +of the or some of the surprising ways +they compromised the systems one was + + align:start position:0% +they compromised the systems one was + + + align:start position:0% +they compromised the systems one was +that um you know there was this OS + + align:start position:0% +that um you know there was this OS + + + align:start position:0% +that um you know there was this OS +research team that seemed to have a + + align:start position:0% +research team that seemed to have a + + + align:start position:0% +research team that seemed to have a +perfectly secure OS but it got + + align:start position:0% +perfectly secure OS but it got + + + align:start position:0% +perfectly secure OS but it got +compromised and the way it happened is + + align:start position:0% +compromised and the way it happened is + + + align:start position:0% +compromised and the way it happened is +that the server in which the source code + + align:start position:0% +that the server in which the source code + + + align:start position:0% +that the server in which the source code +of the operating system was stored was + + align:start position:0% +of the operating system was stored was + + + align:start position:0% +of the operating system was stored was +some development machine in someone's + + align:start position:0% +some development machine in someone's + + + align:start position:0% +some development machine in someone's +office that wasn't secured at all but + + align:start position:0% +office that wasn't secured at all but + + + align:start position:0% +office that wasn't secured at all but +that had all the source code so the bad + + align:start position:0% +that had all the source code so the bad + + + align:start position:0% +that had all the source code so the bad +guys broke into that server it was not + + align:start position:0% +guys broke into that server it was not + + + align:start position:0% +guys broke into that server it was not +protected very well changed the source + + align:start position:0% +protected very well changed the source + + + align:start position:0% +protected very well changed the source +code of the operating system to + + align:start position:0% +code of the operating system to + + + align:start position:0% +code of the operating system to +introduce a back door and then when the + + align:start position:0% +introduce a back door and then when the + + + align:start position:0% +introduce a back door and then when the +researchers built their operating + + align:start position:0% +researchers built their operating + + + align:start position:0% +researchers built their operating +systems well it had this back door and + + align:start position:0% +systems well it had this back door and + + + align:start position:0% +systems well it had this back door and +the bad guys were able to break in so + + align:start position:0% +the bad guys were able to break in so + + + align:start position:0% +the bad guys were able to break in so +you really have to think about all the + + align:start position:0% +you really have to think about all the + + + align:start position:0% +you really have to think about all the +possible sort of assumptions you're + + align:start position:0% +possible sort of assumptions you're + + + align:start position:0% +possible sort of assumptions you're +making about where your software is + + align:start position:0% +making about where your software is + + + align:start position:0% +making about where your software is +coming from about how the bad guy can + + align:start position:0% +coming from about how the bad guy can + + + align:start position:0% +coming from about how the bad guy can +get in in order to make sure your system + + align:start position:0% +get in in order to make sure your system + + + align:start position:0% +get in in order to make sure your system +is really + + align:start position:0% +is really + + + align:start position:0% +is really +secure and oh there's many other + + align:start position:0% +secure and oh there's many other + + + align:start position:0% +secure and oh there's many other +examples in elron notes if you want sort + + align:start position:0% +examples in elron notes if you want sort + + + align:start position:0% +examples in elron notes if you want sort +of some I'm using anecdotes you can uh + + align:start position:0% +of some I'm using anecdotes you can uh + + + align:start position:0% +of some I'm using anecdotes you can uh +page through + + align:start position:0% +page through + + + align:start position:0% +page through +those um probably the most uh pervasive + + align:start position:0% +those um probably the most uh pervasive + + + align:start position:0% +those um probably the most uh pervasive +problem that shows up + + align:start position:0% +problem that shows up + + + align:start position:0% +problem that shows up +of course is in mechanisms though and in + + align:start position:0% +of course is in mechanisms though and in + + + align:start position:0% +of course is in mechanisms though and in +part it's because mechanisms are the + + align:start position:0% +part it's because mechanisms are the + + + align:start position:0% +part it's because mechanisms are the +most complicated part of the story it's + + align:start position:0% +most complicated part of the story it's + + + align:start position:0% +most complicated part of the story it's +of the entirety of all the software and + + align:start position:0% +of the entirety of all the software and + + + align:start position:0% +of the entirety of all the software and +hardware and all the sort of system + + align:start position:0% +hardware and all the sort of system + + + align:start position:0% +hardware and all the sort of system +components that make up what you're what + + align:start position:0% +components that make up what you're what + + + align:start position:0% +components that make up what you're what +is trying to enforce your security + + align:start position:0% +is trying to enforce your security + + + align:start position:0% +is trying to enforce your security +policy and there's of no end of ways in + + align:start position:0% +policy and there's of no end of ways in + + + align:start position:0% +policy and there's of no end of ways in +which mechanisms can fail + + align:start position:0% +which mechanisms can fail + + + align:start position:0% +which mechanisms can fail +and partly as a result much of this + + align:start position:0% +and partly as a result much of this + + + align:start position:0% +and partly as a result much of this +class will talk will focus pretty + + align:start position:0% +class will talk will focus pretty + + + align:start position:0% +class will talk will focus pretty +heavily on mechanisms and how how do you + + align:start position:0% +heavily on mechanisms and how how do you + + + align:start position:0% +heavily on mechanisms and how how do you +make mechanisms that are secure that + + align:start position:0% +make mechanisms that are secure that + + + align:start position:0% +make mechanisms that are secure that +provide correct enforcement of security + + align:start position:0% +provide correct enforcement of security + + + align:start position:0% +provide correct enforcement of security +policies and we'll talk about threat + + align:start position:0% +policies and we'll talk about threat + + + align:start position:0% +policies and we'll talk about threat +models and policies as well but turns + + align:start position:0% +models and policies as well but turns + + + align:start position:0% +models and policies as well but turns +out it's much easier to make clean sort + + align:start position:0% +out it's much easier to make clean sort + + + align:start position:0% +out it's much easier to make clean sort +of crisp statements about mechanisms and + + align:start position:0% +of crisp statements about mechanisms and + + + align:start position:0% +of crisp statements about mechanisms and +ways they work and don't work uh as + + align:start position:0% +ways they work and don't work uh as + + + align:start position:0% +ways they work and don't work uh as +opposed to policies and threat models + + align:start position:0% +opposed to policies and threat models + + + align:start position:0% +opposed to policies and threat models +which really you have to figure out how + + align:start position:0% +which really you have to figure out how + + + align:start position:0% +which really you have to figure out how +to fit them into a particular context + + align:start position:0% +to fit them into a particular context + + + align:start position:0% +to fit them into a particular context +where you're using a + + align:start position:0% +where you're using a + + + align:start position:0% +where you're using a +system so let's look at some examples of + + align:start position:0% +system so let's look at some examples of + + + align:start position:0% +system so let's look at some examples of +I guess mechanism uh bugs um one that + + align:start position:0% +I guess mechanism uh bugs um one that + + + align:start position:0% +I guess mechanism uh bugs um one that +you might have heard in the last couple + + align:start position:0% +you might have heard in the last couple + + + align:start position:0% +you might have heard in the last couple +of days was uh a problem in the security + + align:start position:0% +of days was uh a problem in the security + + + align:start position:0% +of days was uh a problem in the security +mechanism in Apple's Cloud + + align:start position:0% +mechanism in Apple's Cloud + + + align:start position:0% +mechanism in Apple's Cloud +infrastructure called iCloud um they had + + align:start position:0% +infrastructure called iCloud um they had + + + align:start position:0% +infrastructure called iCloud um they had +uh you know well actually any one of you + + align:start position:0% +uh you know well actually any one of you + + + align:start position:0% +uh you know well actually any one of you +that has an iPhone uh might be using + + align:start position:0% +that has an iPhone uh might be using + + + align:start position:0% +that has an iPhone uh might be using +this iCloud service they basically + + align:start position:0% +this iCloud service they basically + + + align:start position:0% +this iCloud service they basically +provide storage for your files and let + + align:start position:0% +provide storage for your files and let + + + align:start position:0% +provide storage for your files and let +you find your iPhone if you lose it and + + align:start position:0% +you find your iPhone if you lose it and + + + align:start position:0% +you find your iPhone if you lose it and +probably lots of other useful features + + align:start position:0% +probably lots of other useful features + + + align:start position:0% +probably lots of other useful features +and I think it's some relative of this + + align:start position:0% +and I think it's some relative of this + + + align:start position:0% +and I think it's some relative of this +med service that was implicated in this + + align:start position:0% +med service that was implicated in this + + + align:start position:0% +med service that was implicated in this +scheme a couple of years back um and the + + align:start position:0% +scheme a couple of years back um and the + + + align:start position:0% +scheme a couple of years back um and the +problem that someone discovered in this + + align:start position:0% +problem that someone discovered in this + + + align:start position:0% +problem that someone discovered in this +iCloud service is that they didn't + + align:start position:0% +iCloud service is that they didn't + + + align:start position:0% +iCloud service is that they didn't +enforce the same sort of mechanism at + + align:start position:0% +enforce the same sort of mechanism at + + + align:start position:0% +enforce the same sort of mechanism at +all interfaces so okay so what does + + align:start position:0% +all interfaces so okay so what does + + + align:start position:0% +all interfaces so okay so what does +iCloud look like well it basically + + align:start position:0% +iCloud look like well it basically + + + align:start position:0% +iCloud look like well it basically +provides lots of + + align:start position:0% +provides lots of + + + align:start position:0% +provides lots of +services you for the same sort of set of + + align:start position:0% +services you for the same sort of set of + + + align:start position:0% +services you for the same sort of set of +accounts so maybe you have your file + + align:start position:0% +accounts so maybe you have your file + + + align:start position:0% +accounts so maybe you have your file +storage on iCloud maybe you have your + + align:start position:0% +storage on iCloud maybe you have your + + + align:start position:0% +storage on iCloud maybe you have your +you know photo sharing maybe you have + + align:start position:0% +you know photo sharing maybe you have + + + align:start position:0% +you know photo sharing maybe you have +other interfaces and one of the inter + + align:start position:0% +other interfaces and one of the inter + + + align:start position:0% +other interfaces and one of the inter +interes into iCloud these are all sort + + align:start position:0% +interes into iCloud these are all sort + + + align:start position:0% +interes into iCloud these are all sort +of different apis that they provide was + + align:start position:0% +of different apis that they provide was + + + align:start position:0% +of different apis that they provide was +this uh feature to find my iPhone I + + align:start position:0% +this uh feature to find my iPhone I + + + align:start position:0% +this uh feature to find my iPhone I +think and all these interfaces want to + + align:start position:0% +think and all these interfaces want to + + + align:start position:0% +think and all these interfaces want to +make sure that you are the right user + + align:start position:0% +make sure that you are the right user + + + align:start position:0% +make sure that you are the right user +you're authenticated correctly and + + align:start position:0% +you're authenticated correctly and + + + align:start position:0% +you're authenticated correctly and +unfortunately the developers of this + + align:start position:0% +unfortunately the developers of this + + + align:start position:0% +unfortunately the developers of this +iCloud system you know it's a giant + + align:start position:0% +iCloud system you know it's a giant + + + align:start position:0% +iCloud system you know it's a giant +piece of software I'm sure it's like + + align:start position:0% +piece of software I'm sure it's like + + + align:start position:0% +piece of software I'm sure it's like +lots of developers working on this but + + align:start position:0% +lots of developers working on this but + + + align:start position:0% +lots of developers working on this but +on this particular interface the find my + + align:start position:0% +on this particular interface the find my + + + align:start position:0% +on this particular interface the find my +iPhone interface when you try to log in + + align:start position:0% +iPhone interface when you try to log in + + + align:start position:0% +iPhone interface when you try to log in +with a username and password + + align:start position:0% +with a username and password + + + align:start position:0% +with a username and password +they didn't keep track of how many times + + align:start position:0% +they didn't keep track of how many times + + + align:start position:0% +they didn't keep track of how many times +you try to log in and the reason this is + + align:start position:0% +you try to log in and the reason this is + + + align:start position:0% +you try to log in and the reason this is +important is that as I mentioned earlier + + align:start position:0% +important is that as I mentioned earlier + + + align:start position:0% +important is that as I mentioned earlier +humans are not that great at picking + + align:start position:0% +humans are not that great at picking + + + align:start position:0% +humans are not that great at picking +good passwords so actually Building A + + align:start position:0% +good passwords so actually Building A + + + align:start position:0% +good passwords so actually Building A +system that authenticates users with + + align:start position:0% +system that authenticates users with + + + align:start position:0% +system that authenticates users with +passwords is pretty tricky we'll + + align:start position:0% +passwords is pretty tricky we'll + + + align:start position:0% +passwords is pretty tricky we'll +actually read a whole paper about this + + align:start position:0% +actually read a whole paper about this + + + align:start position:0% +actually read a whole paper about this +later on but one good strategy is you + + align:start position:0% +later on but one good strategy is you + + + align:start position:0% +later on but one good strategy is you +know there's probably a million + + align:start position:0% +know there's probably a million + + + align:start position:0% +know there's probably a million +passwords out there that will account + + align:start position:0% +passwords out there that will account + + + align:start position:0% +passwords out there that will account +for 50% of the accounts so if you can + + align:start position:0% +for 50% of the accounts so if you can + + + align:start position:0% +for 50% of the accounts so if you can +guess make a million attempts at a + + align:start position:0% +guess make a million attempts at a + + + align:start position:0% +guess make a million attempts at a +someone's account then there's a good + + align:start position:0% +someone's account then there's a good + + + align:start position:0% +someone's account then there's a good +chance you'll get their password because + + align:start position:0% +chance you'll get their password because + + + align:start position:0% +chance you'll get their password because +people actually pick predictable + + align:start position:0% +people actually pick predictable + + + align:start position:0% +people actually pick predictable +passwords and one way to try to defeat + + align:start position:0% +passwords and one way to try to defeat + + + align:start position:0% +passwords and one way to try to defeat +this is to make sure that your system + + align:start position:0% +this is to make sure that your system + + + align:start position:0% +this is to make sure that your system +doesn't allow an arbitrary number of + + align:start position:0% +doesn't allow an arbitrary number of + + + align:start position:0% +doesn't allow an arbitrary number of +attempts to log in an account maybe + + align:start position:0% +attempts to log in an account maybe + + + align:start position:0% +attempts to log in an account maybe +after three or 10 tries you should say + + align:start position:0% +after three or 10 tries you should say + + + align:start position:0% +after three or 10 tries you should say +well you've had enough tries time out + + align:start position:0% +well you've had enough tries time out + + + align:start position:0% +well you've had enough tries time out +you can try again in 10 minutes or in an + + align:start position:0% +you can try again in 10 minutes or in an + + + align:start position:0% +you can try again in 10 minutes or in an +hour and this way you really slow down + + align:start position:0% +hour and this way you really slow down + + + align:start position:0% +hour and this way you really slow down +the attacker so they can only make you + + align:start position:0% +the attacker so they can only make you + + + align:start position:0% +the attacker so they can only make you +know a handful of guesses a day instead + + align:start position:0% +know a handful of guesses a day instead + + + align:start position:0% +know a handful of guesses a day instead +of millions of guesses and as a result + + align:start position:0% +of millions of guesses and as a result + + + align:start position:0% +of millions of guesses and as a result +even if you have not the greatest of + + align:start position:0% +even if you have not the greatest of + + + align:start position:0% +even if you have not the greatest of +passwords it's going to be pretty hard + + align:start position:0% +passwords it's going to be pretty hard + + + align:start position:0% +passwords it's going to be pretty hard +for someone to guess it but what + + align:start position:0% +for someone to guess it but what + + + align:start position:0% +for someone to guess it but what +happened is that you know iCloud had + + align:start position:0% +happened is that you know iCloud had + + + align:start position:0% +happened is that you know iCloud had +this uh you know password guessing + + align:start position:0% +this uh you know password guessing + + + align:start position:0% +this uh you know password guessing +prevention or basically back off on some + + align:start position:0% +prevention or basically back off on some + + + align:start position:0% +prevention or basically back off on some +interfaces like if you tried to log in + + align:start position:0% +interfaces like if you tried to log in + + + align:start position:0% +interfaces like if you tried to log in +through other interfaces and you failed + + align:start position:0% +through other interfaces and you failed + + + align:start position:0% +through other interfaces and you failed +10 times it would say well sorry you + + align:start position:0% +10 times it would say well sorry you + + + align:start position:0% +10 times it would say well sorry you +have to wait until you try again but on + + align:start position:0% +have to wait until you try again but on + + + align:start position:0% +have to wait until you try again but on +this find my iPhone interface they + + align:start position:0% +this find my iPhone interface they + + + align:start position:0% +this find my iPhone interface they +forget this check this probably you know + + align:start position:0% +forget this check this probably you know + + + align:start position:0% +forget this check this probably you know +some guy just forgot to call this + + align:start position:0% +some guy just forgot to call this + + + align:start position:0% +some guy just forgot to call this +function on this API but the result is + + align:start position:0% +function on this API but the result is + + + align:start position:0% +function on this API but the result is +that for the same set of accounts I + + align:start position:0% +that for the same set of accounts I + + + align:start position:0% +that for the same set of accounts I +would a bad guy would be able to now + + align:start position:0% +would a bad guy would be able to now + + + align:start position:0% +would a bad guy would be able to now +guess your password through this + + align:start position:0% +guess your password through this + + + align:start position:0% +guess your password through this +interface at millions of attempts per + + align:start position:0% +interface at millions of attempts per + + + align:start position:0% +interface at millions of attempts per +day easily because this is just limited + + align:start position:0% +day easily because this is just limited + + + align:start position:0% +day easily because this is just limited +at how fast they can send packets to + + align:start position:0% +at how fast they can send packets to + + + align:start position:0% +at how fast they can send packets to +ccloud thing and they can probably guess + + align:start position:0% +ccloud thing and they can probably guess + + + align:start position:0% +ccloud thing and they can probably guess +your password with pretty good accuracy + + align:start position:0% +your password with pretty good accuracy + + + align:start position:0% +your password with pretty good accuracy +or with pretty good success rate uh + + align:start position:0% +or with pretty good success rate uh + + + align:start position:0% +or with pretty good success rate uh +after you know making many many guesses + + align:start position:0% +after you know making many many guesses + + + align:start position:0% +after you know making many many guesses +and this led to some you know + + align:start position:0% +and this led to some you know + + + align:start position:0% +and this led to some you know +unfortunate break-ins and people's you + + align:start position:0% +unfortunate break-ins and people's you + + + align:start position:0% +unfortunate break-ins and people's you +know confidential data got stolen from + + align:start position:0% +know confidential data got stolen from + + + align:start position:0% +know confidential data got stolen from +the ccloud + + align:start position:0% +the ccloud + + + align:start position:0% +the ccloud +service so this is sort of an example of + + align:start position:0% +service so this is sort of an example of + + + align:start position:0% +service so this is sort of an example of +you know you had the right policy only + + align:start position:0% +you know you had the right policy only + + + align:start position:0% +you know you had the right policy only +the user and the right password would + + align:start position:0% +the user and the right password would + + + align:start position:0% +the user and the right password would +get you access to the files you even had + + align:start position:0% +get you access to the files you even had + + + align:start position:0% +get you access to the files you even had +the right threat model that well the bad + + align:start position:0% +the right threat model that well the bad + + + align:start position:0% +the right threat model that well the bad +guy might be able to guess the password + + align:start position:0% +guy might be able to guess the password + + + align:start position:0% +guy might be able to guess the password +so we'll have to rate limit the number + + align:start position:0% +so we'll have to rate limit the number + + + align:start position:0% +so we'll have to rate limit the number +of guess attempts but you just screwed + + align:start position:0% +of guess attempts but you just screwed + + + align:start position:0% +of guess attempts but you just screwed +up like the mechanism had a bug in it we + + align:start position:0% +up like the mechanism had a bug in it we + + + align:start position:0% +up like the mechanism had a bug in it we +just forgot to enforce this right policy + + align:start position:0% +just forgot to enforce this right policy + + + align:start position:0% +just forgot to enforce this right policy +and mechanism at some interface and this + + align:start position:0% +and mechanism at some interface and this + + + align:start position:0% +and mechanism at some interface and this +shows up again and again in systems + + align:start position:0% +shows up again and again in systems + + + align:start position:0% +shows up again and again in systems +where just made a mistake and it has + + align:start position:0% +where just made a mistake and it has + + + align:start position:0% +where just made a mistake and it has +pretty drastic effects on the security + + align:start position:0% +pretty drastic effects on the security + + + align:start position:0% +pretty drastic effects on the security +of the overal + + align:start position:0% +of the overal + + + align:start position:0% +of the overal +system does this make sense + + align:start position:0% +system does this make sense + + + align:start position:0% +system does this make sense +any questions so + + align:start position:0% + + + + align:start position:0% + +far all right okay so another example + + align:start position:0% +far all right okay so another example + + + align:start position:0% +far all right okay so another example +right this is sort of an example of you + + align:start position:0% +right this is sort of an example of you + + + align:start position:0% +right this is sort of an example of you +know you forget to check for password + + align:start position:0% +know you forget to check for password + + + align:start position:0% +know you forget to check for password +guessing attempts there's many other + + align:start position:0% +guessing attempts there's many other + + + align:start position:0% +guessing attempts there's many other +things you can forget you could forget + + align:start position:0% +things you can forget you could forget + + + align:start position:0% +things you can forget you could forget +to check for Access Control Al together + + align:start position:0% +to check for Access Control Al together + + + align:start position:0% +to check for Access Control Al together +um so one example is uh you know City + + align:start position:0% +um so one example is uh you know City + + + align:start position:0% +um so one example is uh you know City +Bank had a website actually still has a + + align:start position:0% +Bank had a website actually still has a + + + align:start position:0% +Bank had a website actually still has a +website that allows you + + align:start position:0% +website that allows you + + + align:start position:0% +website that allows you +to look at your credit card account + + align:start position:0% +to look at your credit card account + + + align:start position:0% +to look at your credit card account +information so if you have a credit card + + align:start position:0% +information so if you have a credit card + + + align:start position:0% +information so if you have a credit card +with City B you go to this website it + + align:start position:0% +with City B you go to this website it + + + align:start position:0% +with City B you go to this website it +tells you yeah you have this credit card + + align:start position:0% +tells you yeah you have this credit card + + + align:start position:0% +tells you yeah you have this credit card +here's all the charges all this great + + align:start position:0% +here's all the charges all this great + + + align:start position:0% +here's all the charges all this great +stuff and the workflow uh a couple of + + align:start position:0% +stuff and the workflow uh a couple of + + + align:start position:0% +stuff and the workflow uh a couple of +years ago was that you know you go to + + align:start position:0% +years ago was that you know you go to + + + align:start position:0% +years ago was that you know you go to +some site you provide a login username + + align:start position:0% +some site you provide a login username + + + align:start position:0% +some site you provide a login username +and password and you get redirected to + + align:start position:0% +and password and you get redirected to + + + align:start position:0% +and password and you get redirected to +another URL which is something like I + + align:start position:0% +another URL which is something like I + + + align:start position:0% +another URL which is something like I +don't know I'm guessing but basically + + align:start position:0% +don't know I'm guessing but basically + + + align:start position:0% +don't know I'm guessing but basically +like city.com account question mark ID + + align:start position:0% +like city.com account question mark ID + + + align:start position:0% +like city.com account question mark ID +equals you know whatever 1 2 3 + + align:start position:0% +equals you know whatever 1 2 3 + + + align:start position:0% +equals you know whatever 1 2 3 +4 and it turns out that some guy figured + + align:start position:0% +4 and it turns out that some guy figured + + + align:start position:0% +4 and it turns out that some guy figured +out well if you change this number you + + align:start position:0% +out well if you change this number you + + + align:start position:0% +out well if you change this number you +just get someone else's + + align:start position:0% +just get someone else's + + + align:start position:0% +just get someone else's +account and it's not clear quite what + + align:start position:0% +account and it's not clear quite what + + + align:start position:0% +account and it's not clear quite what +you know how to think of this like one + + align:start position:0% +you know how to think of this like one + + + align:start position:0% +you know how to think of this like one +possibility is that these guys were just + + align:start position:0% +possibility is that these guys were just + + + align:start position:0% +possibility is that these guys were just +thinking right but they again forgot to + + align:start position:0% +thinking right but they again forgot to + + + align:start position:0% +thinking right but they again forgot to +check a function in this account page + + align:start position:0% +check a function in this account page + + + align:start position:0% +check a function in this account page +that not only do I have a valid ID + + align:start position:0% +that not only do I have a valid ID + + + align:start position:0% +that not only do I have a valid ID +number but it's also the ID number of + + align:start position:0% +number but it's also the ID number of + + + align:start position:0% +number but it's also the ID number of +the guy that's currently logged in + + align:start position:0% +the guy that's currently logged in + + + align:start position:0% +the guy that's currently logged in +that's a important check to make but + + align:start position:0% +that's a important check to make but + + + align:start position:0% +that's a important check to make but +it's easy to forget um you know another + + align:start position:0% +it's easy to forget um you know another + + + align:start position:0% +it's easy to forget um you know another +thing is maybe these guys were thinking + + align:start position:0% +thing is maybe these guys were thinking + + + align:start position:0% +thing is maybe these guys were thinking +no no one can add URLs maybe they had + + align:start position:0% +no no one can add URLs maybe they had + + + align:start position:0% +no no one can add URLs maybe they had +had a bad threat model right maybe + + align:start position:0% +had a bad threat model right maybe + + + align:start position:0% +had a bad threat model right maybe +they're thinking the URL if I don't + + align:start position:0% +they're thinking the URL if I don't + + + align:start position:0% +they're thinking the URL if I don't +print this URL no one can click on it + + align:start position:0% +print this URL no one can click on it + + + align:start position:0% +print this URL no one can click on it +it's like a bad threat model so maybe + + align:start position:0% +it's like a bad threat model so maybe + + + align:start position:0% +it's like a bad threat model so maybe +that's well it's hard to tell exactly + + align:start position:0% +that's well it's hard to tell exactly + + + align:start position:0% +that's well it's hard to tell exactly +what went wrong but anyway these + + align:start position:0% +what went wrong but anyway these + + + align:start position:0% +what went wrong but anyway these +mistakes do happen and they show up a + + align:start position:0% +mistakes do happen and they show up a + + + align:start position:0% +mistakes do happen and they show up a +lot so sort of it's easy to have uh + + align:start position:0% +lot so sort of it's easy to have uh + + + align:start position:0% +lot so sort of it's easy to have uh +small seemingly bugs in your mechanism + + align:start position:0% +small seemingly bugs in your mechanism + + + align:start position:0% +small seemingly bugs in your mechanism +lead to pretty unfortunate um + + align:start position:0% +lead to pretty unfortunate um + + + align:start position:0% +lead to pretty unfortunate um +consequences another example that's not + + align:start position:0% +consequences another example that's not + + + align:start position:0% +consequences another example that's not +so much in you know missing checks uh is + + align:start position:0% +so much in you know missing checks uh is + + + align:start position:0% +so much in you know missing checks uh is +a problem that showed up on Android + + align:start position:0% +a problem that showed up on Android + + + align:start position:0% +a problem that showed up on Android +phones uh a couple of months ago uh + + align:start position:0% +phones uh a couple of months ago uh + + + align:start position:0% +phones uh a couple of months ago uh +maybe I'll use this board over here so + + align:start position:0% +maybe I'll use this board over here so + + + align:start position:0% +maybe I'll use this board over here so +the problem was the related to bitcoin + + align:start position:0% +the problem was the related to bitcoin + + + align:start position:0% +the problem was the related to bitcoin +which is this well I'm sure you've heard + + align:start position:0% +which is this well I'm sure you've heard + + + align:start position:0% +which is this well I'm sure you've heard +this you know electronic currency system + + align:start position:0% +this you know electronic currency system + + + align:start position:0% +this you know electronic currency system +that's pretty popular these days um and + + align:start position:0% +that's pretty popular these days um and + + + align:start position:0% +that's pretty popular these days um and +the way that + + align:start position:0% +the way that + + + align:start position:0% +the way that +uh Bitcoin works at a very high level is + + align:start position:0% +uh Bitcoin works at a very high level is + + + align:start position:0% +uh Bitcoin works at a very high level is +that your sort of balance of Bitcoins is + + align:start position:0% +that your sort of balance of Bitcoins is + + + align:start position:0% +that your sort of balance of Bitcoins is +associated with a private key and if you + + align:start position:0% +associated with a private key and if you + + + align:start position:0% +associated with a private key and if you +have someone's private key you can of + + align:start position:0% +have someone's private key you can of + + + align:start position:0% +have someone's private key you can of +course spend their + + align:start position:0% +course spend their + + + align:start position:0% +course spend their +Bitcoins so the security of Bitcoin + + align:start position:0% +Bitcoins so the security of Bitcoin + + + align:start position:0% +Bitcoins so the security of Bitcoin +relies quite heavily on no one else + + align:start position:0% +relies quite heavily on no one else + + + align:start position:0% +relies quite heavily on no one else +knowing your private key it's kind of + + align:start position:0% +knowing your private key it's kind of + + + align:start position:0% +knowing your private key it's kind of +like a password except it's even more + + align:start position:0% +like a password except it's even more + + + align:start position:0% +like a password except it's even more +important because people can probably + + align:start position:0% +important because people can probably + + + align:start position:0% +important because people can probably +make lots of guesses at your private key + + align:start position:0% +make lots of guesses at your private key + + + align:start position:0% +make lots of guesses at your private key +and there's no real server that's + + align:start position:0% +and there's no real server that's + + + align:start position:0% +and there's no real server that's +checking a key it's just cryptography so + + align:start position:0% +checking a key it's just cryptography so + + + align:start position:0% +checking a key it's just cryptography so +any machine can try to make lots of + + align:start position:0% +any machine can try to make lots of + + + align:start position:0% +any machine can try to make lots of +guesses at your private key and if they + + align:start position:0% +guesses at your private key and if they + + + align:start position:0% +guesses at your private key and if they +guess it then they can transfer your + + align:start position:0% +guess it then they can transfer your + + + align:start position:0% +guess it then they can transfer your +Bitcoins to someone + + align:start position:0% +Bitcoins to someone + + + align:start position:0% +Bitcoins to someone +else and as a result it's critically + + align:start position:0% +else and as a result it's critically + + + align:start position:0% +else and as a result it's critically +important that you generate good random + + align:start position:0% +important that you generate good random + + + align:start position:0% +important that you generate good random +keys that no one else can guess + + align:start position:0% +keys that no one else can guess + + + align:start position:0% +keys that no one else can guess +and there are sort of people using + + align:start position:0% +and there are sort of people using + + + align:start position:0% +and there are sort of people using +Bitcoin on Android and the Android + + align:start position:0% +Bitcoin on Android and the Android + + + align:start position:0% +Bitcoin on Android and the Android +applications for Bitcoin were getting + + align:start position:0% +applications for Bitcoin were getting + + + align:start position:0% +applications for Bitcoin were getting +random values for these Keys uh using + + align:start position:0% +random values for these Keys uh using + + + align:start position:0% +random values for these Keys uh using +this Java API called secure + + align:start position:0% +this Java API called secure + + + align:start position:0% +this Java API called secure +random which sounds great uh but as + + align:start position:0% +random which sounds great uh but as + + + align:start position:0% +random which sounds great uh but as +people figured out well okay so so what + + align:start position:0% +people figured out well okay so so what + + + align:start position:0% +people figured out well okay so so what +it is right it's doesn't really get real + + align:start position:0% +it is right it's doesn't really get real + + + align:start position:0% +it is right it's doesn't really get real +random numbers inside of it there is + + align:start position:0% +random numbers inside of it there is + + + align:start position:0% +random numbers inside of it there is +this construction called a pseudo random + + align:start position:0% +this construction called a pseudo random + + + align:start position:0% +this construction called a pseudo random +number generator or prng that given a + + align:start position:0% +number generator or prng that given a + + + align:start position:0% +number generator or prng that given a +particular seed value like you you get + + align:start position:0% +particular seed value like you you get + + + align:start position:0% +particular seed value like you you get +maybe you know a couple hundred bits of + + align:start position:0% +maybe you know a couple hundred bits of + + + align:start position:0% +maybe you know a couple hundred bits of +Randomness and you shove it into this + + align:start position:0% +Randomness and you shove it into this + + + align:start position:0% +Randomness and you shove it into this +prng and you can keep asking it for more + + align:start position:0% +prng and you can keep asking it for more + + + align:start position:0% +prng and you can keep asking it for more +Randomness can sort of stretch these + + align:start position:0% +Randomness can sort of stretch these + + + align:start position:0% +Randomness can sort of stretch these +random bits into sort of as many random + + align:start position:0% +random bits into sort of as many random + + + align:start position:0% +random bits into sort of as many random +bits as you want so you SE them + + align:start position:0% +bits as you want so you SE them + + + align:start position:0% +bits as you want so you SE them +initially and then you can generate as + + align:start position:0% +initially and then you can generate as + + + align:start position:0% +initially and then you can generate as +many random bits as you want and for + + align:start position:0% +many random bits as you want and for + + + align:start position:0% +many random bits as you want and for +various cryptographic reasons I won't go + + align:start position:0% +various cryptographic reasons I won't go + + + align:start position:0% +various cryptographic reasons I won't go +into here it actually works if you give + + align:start position:0% +into here it actually works if you give + + + align:start position:0% +into here it actually works if you give +it you know a couple of hundred really + + align:start position:0% +it you know a couple of hundred really + + + align:start position:0% +it you know a couple of hundred really +good random bits initially it's going to + + align:start position:0% +good random bits initially it's going to + + + align:start position:0% +good random bits initially it's going to +be very hard for anyone to predict what + + align:start position:0% +be very hard for anyone to predict what + + + align:start position:0% +be very hard for anyone to predict what +the random what the P random values is + + align:start position:0% +the random what the P random values is + + + align:start position:0% +the random what the P random values is +generating are but the problem is that + + align:start position:0% +generating are but the problem is that + + + align:start position:0% +generating are but the problem is that +this Java Library had a small bug in it + + align:start position:0% +this Java Library had a small bug in it + + + align:start position:0% +this Java Library had a small bug in it +in some set of + + align:start position:0% +in some set of + + + align:start position:0% +in some set of +circumstances it forgot to initialize + + align:start position:0% +circumstances it forgot to initialize + + + align:start position:0% +circumstances it forgot to initialize +the prng with a seed so it was just all + + align:start position:0% +the prng with a seed so it was just all + + + align:start position:0% +the prng with a seed so it was just all +zeros which means that everyone could + + align:start position:0% +zeros which means that everyone could + + + align:start position:0% +zeros which means that everyone could +just figure out what your random numbers + + align:start position:0% +just figure out what your random numbers + + + align:start position:0% +just figure out what your random numbers +were if they start with zeros they'll + + align:start position:0% +were if they start with zeros they'll + + + align:start position:0% +were if they start with zeros they'll +produce the same random numbers as you + + align:start position:0% +produce the same random numbers as you + + + align:start position:0% +produce the same random numbers as you +which means they'll produce the same + + align:start position:0% +which means they'll produce the same + + + align:start position:0% +which means they'll produce the same +private key as you so they can just + + align:start position:0% +private key as you so they can just + + + align:start position:0% +private key as you so they can just +generate the same private key and + + align:start position:0% +generate the same private key and + + + align:start position:0% +generate the same private key and +transfer your Bitcoins so this is a you + + align:start position:0% +transfer your Bitcoins so this is a you + + + align:start position:0% +transfer your Bitcoins so this is a you +know again a well small or not small bug + + align:start position:0% +know again a well small or not small bug + + + align:start position:0% +know again a well small or not small bug +depending on I guess who is asking uh + + align:start position:0% +depending on I guess who is asking uh + + + align:start position:0% +depending on I guess who is asking uh +but uh nonetheless right like another + + align:start position:0% +but uh nonetheless right like another + + + align:start position:0% +but uh nonetheless right like another +example of small programming mistakes + + align:start position:0% +example of small programming mistakes + + + align:start position:0% +example of small programming mistakes +leading to pretty catastrophic results + + align:start position:0% +leading to pretty catastrophic results + + + align:start position:0% +leading to pretty catastrophic results +you know lots of people got their + + align:start position:0% +you know lots of people got their + + + align:start position:0% +you know lots of people got their +Bitcoin balances stolen because of this + + align:start position:0% +Bitcoin balances stolen because of this + + + align:start position:0% +Bitcoin balances stolen because of this +weakness of course the fix is pretty + + align:start position:0% +weakness of course the fix is pretty + + + align:start position:0% +weakness of course the fix is pretty +simple at some level you change the Java + + align:start position:0% +simple at some level you change the Java + + + align:start position:0% +simple at some level you change the Java +implementation of secure random to + + align:start position:0% +implementation of secure random to + + + align:start position:0% +implementation of secure random to +always seed this prng with random input + + align:start position:0% +always seed this prng with random input + + + align:start position:0% +always seed this prng with random input +bits and then hopefully you're in good + + align:start position:0% +bits and then hopefully you're in good + + + align:start position:0% +bits and then hopefully you're in good +shape but still it's uh no yet another + + align:start position:0% +shape but still it's uh no yet another + + + align:start position:0% +shape but still it's uh no yet another +example of mechanism failure yeah just C + + align:start position:0% +example of mechanism failure yeah just C + + + align:start position:0% +example of mechanism failure yeah just C +is this a different attack from the DSA + + align:start position:0% +is this a different attack from the DSA + + + align:start position:0% +is this a different attack from the DSA +signature Randomness well yeah so so the + + align:start position:0% +signature Randomness well yeah so so the + + + align:start position:0% +signature Randomness well yeah so so the +actual problem is a little bit more + + align:start position:0% +actual problem is a little bit more + + + align:start position:0% +actual problem is a little bit more +complicated as you're hinting at the + + align:start position:0% +complicated as you're hinting at the + + + align:start position:0% +complicated as you're hinting at the +problem is even if you didn't generate + + align:start position:0% +problem is even if you didn't generate + + + align:start position:0% +problem is even if you didn't generate +your key on the Android device in the + + align:start position:0% +your key on the Android device in the + + + align:start position:0% +your key on the Android device in the +first place the particular signature + + align:start position:0% +first place the particular signature + + + align:start position:0% +first place the particular signature +scheme used by uh Bitcoin assumes that + + align:start position:0% +scheme used by uh Bitcoin assumes that + + + align:start position:0% +scheme used by uh Bitcoin assumes that +every time you generate a new signature + + align:start position:0% +every time you generate a new signature + + + align:start position:0% +every time you generate a new signature +with that key you use a fresh what's + + align:start position:0% +with that key you use a fresh what's + + + align:start position:0% +with that key you use a fresh what's +called a nons for generating that + + align:start position:0% +called a nons for generating that + + + align:start position:0% +called a nons for generating that +signature and if you ever generate two + + align:start position:0% +signature and if you ever generate two + + + align:start position:0% +signature and if you ever generate two +signatures with the same nons then + + align:start position:0% +signatures with the same nons then + + + align:start position:0% +signatures with the same nons then +someone can figure out what your key is + + align:start position:0% +someone can figure out what your key is + + + align:start position:0% +someone can figure out what your key is +the story is pretty similar but the + + align:start position:0% +the story is pretty similar but the + + + align:start position:0% +the story is pretty similar but the +details are a little different so yeah + + align:start position:0% +details are a little different so yeah + + + align:start position:0% +details are a little different so yeah +so even if you actually generated your + + align:start position:0% +so even if you actually generated your + + + align:start position:0% +so even if you actually generated your +key somewhere else and your key was + + align:start position:0% +key somewhere else and your key was + + + align:start position:0% +key somewhere else and your key was +great it's just that every time you + + align:start position:0% +great it's just that every time you + + + align:start position:0% +great it's just that every time you +generate a signature you would uh and + + align:start position:0% +generate a signature you would uh and + + + align:start position:0% +generate a signature you would uh and +you generated two signatures with + + align:start position:0% +you generated two signatures with + + + align:start position:0% +you generated two signatures with +exactly the same nons or random value + + align:start position:0% +exactly the same nons or random value + + + align:start position:0% +exactly the same nons or random value +someone could apply some clever math to + + align:start position:0% +someone could apply some clever math to + + + align:start position:0% +someone could apply some clever math to +your signatures and fig and sort of + + align:start position:0% +your signatures and fig and sort of + + + align:start position:0% +your signatures and fig and sort of +extract your public key out of it or + + align:start position:0% +extract your public key out of it or + + + align:start position:0% +extract your public key out of it or +private key more + + align:start position:0% +private key more + + + align:start position:0% +private key more +importantly all right other questions + + align:start position:0% +importantly all right other questions + + + align:start position:0% +importantly all right other questions +about these + + align:start position:0% +about these + + + align:start position:0% +about these +problems examples + + align:start position:0% +problems examples + + + align:start position:0% +problems examples +Etc all right so I guess uh one thing I + + align:start position:0% +Etc all right so I guess uh one thing I + + + align:start position:0% +Etc all right so I guess uh one thing I +wanted to point out is that actually + + align:start position:0% +wanted to point out is that actually + + + align:start position:0% +wanted to point out is that actually +well as you're starting to appreciate is + + align:start position:0% +well as you're starting to appreciate is + + + align:start position:0% +well as you're starting to appreciate is +that in computer security almost every + + align:start position:0% +that in computer security almost every + + + align:start position:0% +that in computer security almost every +detail has a chance of really mattering + + align:start position:0% +detail has a chance of really mattering + + + align:start position:0% +detail has a chance of really mattering +like if you screw up almost something + + align:start position:0% +like if you screw up almost something + + + align:start position:0% +like if you screw up almost something +seemly inconsequential like forgetting + + align:start position:0% +seemly inconsequential like forgetting + + + align:start position:0% +seemly inconsequential like forgetting +to check something or this or you know + + align:start position:0% +to check something or this or you know + + + align:start position:0% +to check something or this or you know +forgetting to initialize the random SE + + align:start position:0% +forgetting to initialize the random SE + + + align:start position:0% +forgetting to initialize the random SE +it can have pretty dramatic consequences + + align:start position:0% +it can have pretty dramatic consequences + + + align:start position:0% +it can have pretty dramatic consequences +for the overall system and you really + + align:start position:0% +for the overall system and you really + + + align:start position:0% +for the overall system and you really +have to be very clear about what is the + + align:start position:0% +have to be very clear about what is the + + + align:start position:0% +have to be very clear about what is the +specification of your system what is it + + align:start position:0% +specification of your system what is it + + + align:start position:0% +specification of your system what is it +doing exactly what are all the corner + + align:start position:0% +doing exactly what are all the corner + + + align:start position:0% +doing exactly what are all the corner +cases and a good way to sort of think of + + align:start position:0% +cases and a good way to sort of think of + + + align:start position:0% +cases and a good way to sort of think of +breaking a system or conversely figuring + + align:start position:0% +breaking a system or conversely figuring + + + align:start position:0% +breaking a system or conversely figuring +out if your system is secure is to + + align:start position:0% +out if your system is secure is to + + + align:start position:0% +out if your system is secure is to +really push all the edge cases like what + + align:start position:0% +really push all the edge cases like what + + + align:start position:0% +really push all the edge cases like what +happens if my input is just large enough + + align:start position:0% +happens if my input is just large enough + + + align:start position:0% +happens if my input is just large enough +or what is what is the biggest or the + + align:start position:0% +or what is what is the biggest or the + + + align:start position:0% +or what is what is the biggest or the +smallest input what is the strangest uh + + align:start position:0% +smallest input what is the strangest uh + + + align:start position:0% +smallest input what is the strangest uh +set set of inputs I could provide to my + + align:start position:0% +set set of inputs I could provide to my + + + align:start position:0% +set set of inputs I could provide to my +program and push it in all to all these + + align:start position:0% +program and push it in all to all these + + + align:start position:0% +program and push it in all to all these +Corner + + align:start position:0% +Corner + + + align:start position:0% +Corner +cases maybe one example of this + + align:start position:0% +cases maybe one example of this + + + align:start position:0% +cases maybe one example of this +ambiguity um sort of a good example to + + align:start position:0% +ambiguity um sort of a good example to + + + align:start position:0% +ambiguity um sort of a good example to +keep in mind is + + align:start position:0% +keep in mind is + + + align:start position:0% +keep in mind is +uh how SSL certificates again encode + + align:start position:0% +uh how SSL certificates again encode + + + align:start position:0% +uh how SSL certificates again encode +names into the certificate itself so + + align:start position:0% +names into the certificate itself so + + + align:start position:0% +names into the certificate itself so +this is a different problem than the + + align:start position:0% +this is a different problem than the + + + align:start position:0% +this is a different problem than the +problem about the certificate authori is + + align:start position:0% +problem about the certificate authori is + + + align:start position:0% +problem about the certificate authori is +being trusted so these SSL certificates + + align:start position:0% +being trusted so these SSL certificates + + + align:start position:0% +being trusted so these SSL certificates +are just you know sequences of bites + + align:start position:0% +are just you know sequences of bites + + + align:start position:0% +are just you know sequences of bites +that a web server sends to you and + + align:start position:0% +that a web server sends to you and + + + align:start position:0% +that a web server sends to you and +inside of this SSL certificate is the + + align:start position:0% +inside of this SSL certificate is the + + + align:start position:0% +inside of this SSL certificate is the +name of the server you're connecting to + + align:start position:0% +name of the server you're connecting to + + + align:start position:0% +name of the server you're connecting to +so something like + + align:start position:0% +so something like + + + align:start position:0% +so something like +amazon.com you know you can just put + + align:start position:0% +amazon.com you know you can just put + + + align:start position:0% +amazon.com you know you can just put +down those bytes you need to encode it + + align:start position:0% +down those bytes you need to encode it + + + align:start position:0% +down those bytes you need to encode it +somehow and specify well it's amazon.com + + align:start position:0% +somehow and specify well it's amazon.com + + + align:start position:0% +somehow and specify well it's amazon.com +and that's the end of the string so in + + align:start position:0% +and that's the end of the string so in + + + align:start position:0% +and that's the end of the string so in +SSL certificates they use uh a + + align:start position:0% +SSL certificates they use uh a + + + align:start position:0% +SSL certificates they use uh a +particular encoding scheme uh that + + align:start position:0% +particular encoding scheme uh that + + + align:start position:0% +particular encoding scheme uh that +uh writes down amazon.com but by first + + align:start position:0% +uh writes down amazon.com but by first + + + align:start position:0% +uh writes down amazon.com but by first +writing down the number of bytes in the + + align:start position:0% +writing down the number of bytes in the + + + align:start position:0% +writing down the number of bytes in the +string so you first write down okay well + + align:start position:0% +string so you first write down okay well + + + align:start position:0% +string so you first write down okay well +I'm going to have a 10 by string called + + align:start position:0% + + + + align:start position:0% + +amazon.com actually 10 bytes great okay + + align:start position:0% +amazon.com actually 10 bytes great okay + + + align:start position:0% +amazon.com actually 10 bytes great okay +so this is like in the SSL certificate + + align:start position:0% +so this is like in the SSL certificate + + + align:start position:0% +so this is like in the SSL certificate +somewhere in there there is this byte 10 + + align:start position:0% +somewhere in there there is this byte 10 + + + align:start position:0% +somewhere in there there is this byte 10 +followed by 10 bytes saying what the + + align:start position:0% +followed by 10 bytes saying what the + + + align:start position:0% +followed by 10 bytes saying what the +host name is and there's other stuff + + align:start position:0% +host name is and there's other stuff + + + align:start position:0% +host name is and there's other stuff +afterwards right and before and when a + + align:start position:0% +afterwards right and before and when a + + + align:start position:0% +afterwards right and before and when a +browser takes it well you know the + + align:start position:0% +browser takes it well you know the + + + align:start position:0% +browser takes it well you know the +browser is written in C and the way C + + align:start position:0% +browser is written in C and the way C + + + align:start position:0% +browser is written in C and the way C +represents strings is by null + + align:start position:0% +represents strings is by null + + + align:start position:0% +represents strings is by null +terminating them so C A String doesn't + + align:start position:0% +terminating them so C A String doesn't + + + align:start position:0% +terminating them so C A String doesn't +have a length count instead it has all + + align:start position:0% +have a length count instead it has all + + + align:start position:0% +have a length count instead it has all +the bytes and the end of the string is + + align:start position:0% +the bytes and the end of the string is + + + align:start position:0% +the bytes and the end of the string is +just the bite zero and in C you sort of + + align:start position:0% +just the bite zero and in C you sort of + + + align:start position:0% +just the bite zero and in C you sort of +write it with a back slash zero + + align:start position:0% +write it with a back slash zero + + + align:start position:0% +write it with a back slash zero +character so this is in memory in your + + align:start position:0% +character so this is in memory in your + + + align:start position:0% +character so this is in memory in your +browser somewhere in memory there's this + + align:start position:0% +browser somewhere in memory there's this + + + align:start position:0% +browser somewhere in memory there's this +string of 11 bytes Now with an extra + + align:start position:0% +string of 11 bytes Now with an extra + + + align:start position:0% +string of 11 bytes Now with an extra +zero at the end and when a browser + + align:start position:0% +zero at the end and when a browser + + + align:start position:0% +zero at the end and when a browser +interprets the string it just keeps + + align:start position:0% +interprets the string it just keeps + + + align:start position:0% +interprets the string it just keeps +going until it sees an end of string + + align:start position:0% +going until it sees an end of string + + + align:start position:0% +going until it sees an end of string +marker which is the zero + + align:start position:0% +marker which is the zero + + + align:start position:0% +marker which is the zero +byte okay so what can go wrong any + + align:start position:0% +byte okay so what can go wrong any + + + align:start position:0% +byte okay so what can go wrong any +guesses + + align:start position:0% +guesses + + + align:start position:0% +guesses +yeah you can have a zero in the middle + + align:start position:0% +yeah you can have a zero in the middle + + + align:start position:0% +yeah you can have a zero in the middle +of your yeah this is great right so this + + align:start position:0% +of your yeah this is great right so this + + + align:start position:0% +of your yeah this is great right so this +is actually like a bit of a + + align:start position:0% +is actually like a bit of a + + + align:start position:0% +is actually like a bit of a +discontinuity in terms of how this guy + + align:start position:0% +discontinuity in terms of how this guy + + + align:start position:0% +discontinuity in terms of how this guy +represents strings and this guy so + + align:start position:0% +represents strings and this guy so + + + align:start position:0% +represents strings and this guy so +suppose that I own the domain food.com + + align:start position:0% +suppose that I own the domain food.com + + + align:start position:0% +suppose that I own the domain food.com +so I can get certificates for anything. + + align:start position:0% +so I can get certificates for anything. + + + align:start position:0% +so I can get certificates for anything. +food.com so what I could do is ask for a + + align:start position:0% +food.com so what I could do is ask for a + + + align:start position:0% +food.com so what I could do is ask for a +certificate for the name you know + + align:start position:0% +certificate for the name you know + + + align:start position:0% +certificate for the name you know +amazon.com zx. f.com + + align:start position:0% +amazon.com zx. f.com + + + align:start position:0% +amazon.com zx. f.com +that's a perfectly valid string it has + + align:start position:0% +that's a perfectly valid string it has + + + align:start position:0% +that's a perfectly valid string it has +you know a bunch of bytes I guess it's + + align:start position:0% +you know a bunch of bytes I guess it's + + + align:start position:0% +you know a bunch of bytes I guess it's +10 11 12 13 14 15 16 there another four + + align:start position:0% +10 11 12 13 14 15 16 there another four + + + align:start position:0% +10 11 12 13 14 15 16 there another four +20 right so this is a 20 by name of with + + align:start position:0% +20 right so this is a 20 by name of with + + + align:start position:0% +20 right so this is a 20 by name of with +these 20 bytes so it used to be that if + + align:start position:0% +these 20 bytes so it used to be that if + + + align:start position:0% +these 20 bytes so it used to be that if +you go to a certificate Authority in + + align:start position:0% +you go to a certificate Authority in + + + align:start position:0% +you go to a certificate Authority in +many cases you could say Hey you know I + + align:start position:0% +many cases you could say Hey you know I + + + align:start position:0% +many cases you could say Hey you know I +own food.com give me a certificate for + + align:start position:0% +own food.com give me a certificate for + + + align:start position:0% +own food.com give me a certificate for +this thing and they'd be perfectly + + align:start position:0% +this thing and they'd be perfectly + + + align:start position:0% +this thing and they'd be perfectly +willing to do it because it's a + + align:start position:0% +willing to do it because it's a + + + align:start position:0% +willing to do it because it's a +subdomain of food.com it's all yours but + + align:start position:0% +subdomain of food.com it's all yours but + + + align:start position:0% +subdomain of food.com it's all yours but +then when a browser takes this string + + align:start position:0% +then when a browser takes this string + + + align:start position:0% +then when a browser takes this string +and loads it in memory well what it does + + align:start position:0% +and loads it in memory well what it does + + + align:start position:0% +and loads it in memory well what it does +is the same thing it did here it copies + + align:start position:0% +is the same thing it did here it copies + + + align:start position:0% +is the same thing it did here it copies +the + + align:start position:0% +the + + + align:start position:0% +the +string + + align:start position:0% +string + + + align:start position:0% +string +amazon.com back/ + + align:start position:0% +amazon.com back/ + + + align:start position:0% +amazon.com back/ +zx. f.com it'll dutifully add the + + align:start position:0% +zx. f.com it'll dutifully add the + + + align:start position:0% +zx. f.com it'll dutifully add the +terminating zero at the end but then + + align:start position:0% +terminating zero at the end but then + + + align:start position:0% +terminating zero at the end but then +when the rest of the browser software + + align:start position:0% +when the rest of the browser software + + + align:start position:0% +when the rest of the browser software +goes and tries to interpret the string + + align:start position:0% +goes and tries to interpret the string + + + align:start position:0% +goes and tries to interpret the string +at this memory location it'll keep going + + align:start position:0% +at this memory location it'll keep going + + + align:start position:0% +at this memory location it'll keep going +up until it gets to the zero and say + + align:start position:0% +up until it gets to the zero and say + + + align:start position:0% +up until it gets to the zero and say +okay well let end of the string so this + + align:start position:0% +okay well let end of the string so this + + + align:start position:0% +okay well let end of the string so this +is amazon.com that's it so this so sort + + align:start position:0% +is amazon.com that's it so this so sort + + + align:start position:0% +is amazon.com that's it so this so sort +of Disconnect between how C software and + + align:start position:0% +of Disconnect between how C software and + + + align:start position:0% +of Disconnect between how C software and +how SSL certificates represent names led + + align:start position:0% +how SSL certificates represent names led + + + align:start position:0% +how SSL certificates represent names led +to some you know unfortunate security + + align:start position:0% +to some you know unfortunate security + + + align:start position:0% +to some you know unfortunate security +problems this was a you know actually + + align:start position:0% +problems this was a you know actually + + + align:start position:0% +problems this was a you know actually +discovered a number of years ago now by + + align:start position:0% +discovered a number of years ago now by + + + align:start position:0% +discovered a number of years ago now by +this guy Moxy Marlin Spike uh but you + + align:start position:0% +this guy Moxy Marlin Spike uh but you + + + align:start position:0% +this guy Moxy Marlin Spike uh but you +know it's a fairly clever observation + + align:start position:0% +know it's a fairly clever observation + + + align:start position:0% +know it's a fairly clever observation +and uh these kinds of encodings encoding + + align:start position:0% +and uh these kinds of encodings encoding + + + align:start position:0% +and uh these kinds of encodings encoding +bugs are actually also pretty common uh + + align:start position:0% +bugs are actually also pretty common uh + + + align:start position:0% +bugs are actually also pretty common uh +in lots of software Because unless + + align:start position:0% +in lots of software Because unless + + + align:start position:0% +in lots of software Because unless +you're very diligent about exactly how + + align:start position:0% +you're very diligent about exactly how + + + align:start position:0% +you're very diligent about exactly how +you encode things there might be + + align:start position:0% +you encode things there might be + + + align:start position:0% +you encode things there might be +different ways of encoding and whenever + + align:start position:0% +different ways of encoding and whenever + + + align:start position:0% +different ways of encoding and whenever +there's disagreement there's a chance + + align:start position:0% +there's disagreement there's a chance + + + align:start position:0% +there's disagreement there's a chance +the bad guy can take advantage of this + + align:start position:0% +the bad guy can take advantage of this + + + align:start position:0% +the bad guy can take advantage of this +one system thinks that's a fine name and + + align:start position:0% +one system thinks that's a fine name and + + + align:start position:0% +one system thinks that's a fine name and +other thinks that's not something else + + align:start position:0% +other thinks that's not something else + + + align:start position:0% +other thinks that's not something else +so these are good places to sort of push + + align:start position:0% +so these are good places to sort of push + + + align:start position:0% +so these are good places to sort of push +a system to see how it might break that + + align:start position:0% +a system to see how it might break that + + + align:start position:0% +a system to see how it might break that +make + + align:start position:0% +make + + + align:start position:0% +make +sense all right so maybe the last um + + align:start position:0% +sense all right so maybe the last um + + + align:start position:0% +sense all right so maybe the last um +example of um mechanism failure I'm + + align:start position:0% +example of um mechanism failure I'm + + + align:start position:0% +example of um mechanism failure I'm +going to talk about today it's a + + align:start position:0% +going to talk about today it's a + + + align:start position:0% +going to talk about today it's a +reasonably popular one is this problem + + align:start position:0% +reasonably popular one is this problem + + + align:start position:0% +reasonably popular one is this problem +of buffer + + align:start position:0% + + + + align:start position:0% + +overflows so some of you have seen this + + align:start position:0% +overflows so some of you have seen this + + + align:start position:0% +overflows so some of you have seen this +in or at least at some level in 6033 if + + align:start position:0% +in or at least at some level in 6033 if + + + align:start position:0% +in or at least at some level in 6033 if +you did the undergrad course but for + + align:start position:0% +you did the undergrad course but for + + + align:start position:0% +you did the undergrad course but for +those of you that have forgotten or + + align:start position:0% +those of you that have forgotten or + + + align:start position:0% +those of you that have forgotten or +haven't taken o33 we'll sort of go over + + align:start position:0% +haven't taken o33 we'll sort of go over + + + align:start position:0% +haven't taken o33 we'll sort of go over +buffer overflows in more detail and this + + align:start position:0% +buffer overflows in more detail and this + + + align:start position:0% +buffer overflows in more detail and this +will be actually quite critical for you + + align:start position:0% +will be actually quite critical for you + + + align:start position:0% +will be actually quite critical for you +guys because lab one is all about buffer + + align:start position:0% +guys because lab one is all about buffer + + + align:start position:0% +guys because lab one is all about buffer +overflows and you're going to be + + align:start position:0% +overflows and you're going to be + + + align:start position:0% +overflows and you're going to be +exploiting these vulnerabilities in a + + align:start position:0% +exploiting these vulnerabilities in a + + + align:start position:0% +exploiting these vulnerabilities in a +somewhat real web + + align:start position:0% +somewhat real web + + + align:start position:0% +somewhat real web +server so let's figure out what is the + + align:start position:0% +server so let's figure out what is the + + + align:start position:0% +server so let's figure out what is the +setting what are we talking about here + + align:start position:0% +setting what are we talking about here + + + align:start position:0% +setting what are we talking about here +so setting we're going to be considering + + align:start position:0% +so setting we're going to be considering + + + align:start position:0% +so setting we're going to be considering +is uh a system which has let's say a web + + align:start position:0% +is uh a system which has let's say a web + + + align:start position:0% +is uh a system which has let's say a web +server so what we have is you know we + + align:start position:0% +server so what we have is you know we + + + align:start position:0% +server so what we have is you know we +have some computer out there that has a + + align:start position:0% +have some computer out there that has a + + + align:start position:0% +have some computer out there that has a +web server on + + align:start position:0% +web server on + + + align:start position:0% +web server on +it and the web server is a program that + + align:start position:0% +it and the web server is a program that + + + align:start position:0% +it and the web server is a program that +is going to accept connections from the + + align:start position:0% +is going to accept connections from the + + + align:start position:0% +is going to accept connections from the +outside world take + + align:start position:0% +outside world take + + + align:start position:0% +outside world take +requests and which are basically just + + align:start position:0% +requests and which are basically just + + + align:start position:0% +requests and which are basically just +packets and somehow process them and you + + align:start position:0% +packets and somehow process them and you + + + align:start position:0% +packets and somehow process them and you +know do some do some checking probably + + align:start position:0% +know do some do some checking probably + + + align:start position:0% +know do some do some checking probably +if it's an illegal URL or if they're + + align:start position:0% +if it's an illegal URL or if they're + + + align:start position:0% +if it's an illegal URL or if they're +trying to access a file they're not + + align:start position:0% +trying to access a file they're not + + + align:start position:0% +trying to access a file they're not +authorized to access the webs is going + + align:start position:0% +authorized to access the webs is going + + + align:start position:0% +authorized to access the webs is going +to return an error but otherwise it's + + align:start position:0% +to return an error but otherwise it's + + + align:start position:0% +to return an error but otherwise it's +going to you know access some files + + align:start position:0% +going to you know access some files + + + align:start position:0% +going to you know access some files +maybe on disk and send them back out in + + align:start position:0% +maybe on disk and send them back out in + + + align:start position:0% +maybe on disk and send them back out in +some sort of a + + align:start position:0% +some sort of a + + + align:start position:0% +some sort of a +reply so this is a hugely common picture + + align:start position:0% +reply so this is a hugely common picture + + + align:start position:0% +reply so this is a hugely common picture +almost any system you look at what's the + + align:start position:0% +almost any system you look at what's the + + + align:start position:0% +almost any system you look at what's the +policy or what's the threat + + align:start position:0% + + + + align:start position:0% + +model so this is a bit of a problem in + + align:start position:0% +model so this is a bit of a problem in + + + align:start position:0% +model so this is a bit of a problem in +many Real World Systems namely that it's + + align:start position:0% +many Real World Systems namely that it's + + + align:start position:0% +many Real World Systems namely that it's +actually pretty hard to pin down what is + + align:start position:0% +actually pretty hard to pin down what is + + + align:start position:0% +actually pretty hard to pin down what is +the exact policy or threat model that + + align:start position:0% +the exact policy or threat model that + + + align:start position:0% +the exact policy or threat model that +we're talking about and this sort of + + align:start position:0% +we're talking about and this sort of + + + align:start position:0% +we're talking about and this sort of +imprecision or ambiguity about policies + + align:start position:0% +imprecision or ambiguity about policies + + + align:start position:0% +imprecision or ambiguity about policies +threat models Etc is what sometimes + + align:start position:0% +threat models Etc is what sometimes + + + align:start position:0% +threat models Etc is what sometimes +leads to security problems not in this + + align:start position:0% +leads to security problems not in this + + + align:start position:0% +leads to security problems not in this +particular case but we'll see uh but + + align:start position:0% +particular case but we'll see uh but + + + align:start position:0% +particular case but we'll see uh but +maybe just to give you a sense of how to + + align:start position:0% +maybe just to give you a sense of how to + + + align:start position:0% +maybe just to give you a sense of how to +think of a typical web server in the + + align:start position:0% +think of a typical web server in the + + + align:start position:0% +think of a typical web server in the +context of you know this policy threat + + align:start position:0% +context of you know this policy threat + + + align:start position:0% +context of you know this policy threat +model kind of stuff is that well + + align:start position:0% +model kind of stuff is that well + + + align:start position:0% +model kind of stuff is that well +probably the policy is the web server + + align:start position:0% +probably the policy is the web server + + + align:start position:0% +probably the policy is the web server +should do what the programmer intended + + align:start position:0% +should do what the programmer intended + + + align:start position:0% +should do what the programmer intended +it to do it's all vague but that's + + align:start position:0% +it to do it's all vague but that's + + + align:start position:0% +it to do it's all vague but that's +probably what's going on because + + align:start position:0% +probably what's going on because + + + align:start position:0% +probably what's going on because +anything more specific is well the web + + align:start position:0% +anything more specific is well the web + + + align:start position:0% +anything more specific is well the web +server should do exactly what that code + + align:start position:0% +server should do exactly what that code + + + align:start position:0% +server should do exactly what that code +does it's going to be a bit of an op and + + align:start position:0% +does it's going to be a bit of an op and + + + align:start position:0% +does it's going to be a bit of an op and +if a code has a bug well your policy + + align:start position:0% +if a code has a bug well your policy + + + align:start position:0% +if a code has a bug well your policy +says well that's exactly what I should + + align:start position:0% +says well that's exactly what I should + + + align:start position:0% +says well that's exactly what I should +do I should follow the bug um so it's a + + align:start position:0% +do I should follow the bug um so it's a + + + align:start position:0% +do I should follow the bug um so it's a +little hard to State a policy precisely + + align:start position:0% +little hard to State a policy precisely + + + align:start position:0% +little hard to State a policy precisely +but in this case let's go with you know + + align:start position:0% +but in this case let's go with you know + + + align:start position:0% +but in this case let's go with you know +some intuitive version of well the web + + align:start position:0% +some intuitive version of well the web + + + align:start position:0% +some intuitive version of well the web +server should do what the programmer + + align:start position:0% +server should do what the programmer + + + align:start position:0% +server should do what the programmer +wanted it to do um and the threat model + + align:start position:0% +wanted it to do um and the threat model + + + align:start position:0% +wanted it to do um and the threat model +is probably that the attacker you know + + align:start position:0% +is probably that the attacker you know + + + align:start position:0% +is probably that the attacker you know +doesn't have access to this machine + + align:start position:0% +doesn't have access to this machine + + + align:start position:0% +doesn't have access to this machine +can't log into it remotely doesn't have + + align:start position:0% +can't log into it remotely doesn't have + + + align:start position:0% +can't log into it remotely doesn't have +physical access to it but can send any + + align:start position:0% +physical access to it but can send any + + + align:start position:0% +physical access to it but can send any +packet they want so it's they're not + + align:start position:0% +packet they want so it's they're not + + + align:start position:0% +packet they want so it's they're not +restricted to certain kinds of pack it's + + align:start position:0% +restricted to certain kinds of pack it's + + + align:start position:0% +restricted to certain kinds of pack it's +anything it can shape and sort of + + align:start position:0% +anything it can shape and sort of + + + align:start position:0% +anything it can shape and sort of +deliver to this web server that's fair + + align:start position:0% +deliver to this web server that's fair + + + align:start position:0% +deliver to this web server that's fair +game seems like a reasonable threat + + align:start position:0% +game seems like a reasonable threat + + + align:start position:0% +game seems like a reasonable threat +model in practice to have in + + align:start position:0% +model in practice to have in + + + align:start position:0% +model in practice to have in +mind and I guess the goal is that + + align:start position:0% +mind and I guess the goal is that + + + align:start position:0% +mind and I guess the goal is that +uh this web server shouldn't uh allow + + align:start position:0% +uh this web server shouldn't uh allow + + + align:start position:0% +uh this web server shouldn't uh allow +arbitrary stuff to go wrong here uh I + + align:start position:0% +arbitrary stuff to go wrong here uh I + + + align:start position:0% +arbitrary stuff to go wrong here uh I +guess it sort of goes along with what + + align:start position:0% +guess it sort of goes along with what + + + align:start position:0% +guess it sort of goes along with what +the programmer intended the programmer + + align:start position:0% +the programmer intended the programmer + + + align:start position:0% +the programmer intended the programmer +probably didn't intend any request to be + + align:start position:0% +probably didn't intend any request to be + + + align:start position:0% +probably didn't intend any request to be +able to access anything on the server + + align:start position:0% +able to access anything on the server + + + align:start position:0% +able to access anything on the server +and yet it turns out if you make certain + + align:start position:0% +and yet it turns out if you make certain + + + align:start position:0% +and yet it turns out if you make certain +kinds of mistakes in writing the web + + align:start position:0% +kinds of mistakes in writing the web + + + align:start position:0% +kinds of mistakes in writing the web +server software which is basically the + + align:start position:0% +server software which is basically the + + + align:start position:0% +server software which is basically the +mechanism here right the web server + + align:start position:0% +mechanism here right the web server + + + align:start position:0% +mechanism here right the web server +software is the thing that takes a + + align:start position:0% +software is the thing that takes a + + + align:start position:0% +software is the thing that takes a +request and looks at it and makes sure + + align:start position:0% +request and looks at it and makes sure + + + align:start position:0% +request and looks at it and makes sure +that it's not going to do something bad + + align:start position:0% +that it's not going to do something bad + + + align:start position:0% +that it's not going to do something bad +sends a response back if everything is + + align:start position:0% +sends a response back if everything is + + + align:start position:0% +sends a response back if everything is +okay the web server is this mechanism + + align:start position:0% +okay the web server is this mechanism + + + align:start position:0% +okay the web server is this mechanism +it's enforcing your policy and as a + + align:start position:0% +it's enforcing your policy and as a + + + align:start position:0% +it's enforcing your policy and as a +result if the web server software is + + align:start position:0% +result if the web server software is + + + align:start position:0% +result if the web server software is +buggy then you're in trouble and one + + align:start position:0% +buggy then you're in trouble and one + + + align:start position:0% +buggy then you're in trouble and one +sort of common prom if you're writing + + align:start position:0% +sort of common prom if you're writing + + + align:start position:0% +sort of common prom if you're writing +software in C which you know many things + + align:start position:0% +software in C which you know many things + + + align:start position:0% +software in C which you know many things +are still written in C and probably will + + align:start position:0% +are still written in C and probably will + + + align:start position:0% +are still written in C and probably will +continue to be written in C for a while + + align:start position:0% +continue to be written in C for a while + + + align:start position:0% +continue to be written in C for a while +um you can mismanage your memory + + align:start position:0% +um you can mismanage your memory + + + align:start position:0% +um you can mismanage your memory +allocations and as we saw in this uh SSL + + align:start position:0% +allocations and as we saw in this uh SSL + + + align:start position:0% +allocations and as we saw in this uh SSL +certificate naming example even sort of + + align:start position:0% +certificate naming example even sort of + + + align:start position:0% +certificate naming example even sort of +a single bite can really make a huge + + align:start position:0% +a single bite can really make a huge + + + align:start position:0% +a single bite can really make a huge +difference in terms of what goes on um + + align:start position:0% +difference in terms of what goes on um + + + align:start position:0% +difference in terms of what goes on um +and I guess for this example we'll look + + align:start position:0% +and I guess for this example we'll look + + + align:start position:0% +and I guess for this example we'll look +at a small piece of code that's you know + + align:start position:0% +at a small piece of code that's you know + + + align:start position:0% +at a small piece of code that's you know +not quite a real web server in the lab + + align:start position:0% +not quite a real web server in the lab + + + align:start position:0% +not quite a real web server in the lab +you'll have this whole picture to play + + align:start position:0% +you'll have this whole picture to play + + + align:start position:0% +you'll have this whole picture to play +with but for lecture I just want to give + + align:start position:0% +with but for lecture I just want to give + + + align:start position:0% +with but for lecture I just want to give +you a simplified example so we can talk + + align:start position:0% +you a simplified example so we can talk + + + align:start position:0% +you a simplified example so we can talk +about what's sort of at the core of + + align:start position:0% +about what's sort of at the core of + + + align:start position:0% +about what's sort of at the core of +what's going wrong and in particular if + + align:start position:0% +what's going wrong and in particular if + + + align:start position:0% +what's going wrong and in particular if +uh this system wakes up I will show you + + align:start position:0% +uh this system wakes up I will show you + + + align:start position:0% +uh this system wakes up I will show you +um sort of a very small C + + align:start position:0% +um sort of a very small C + + + align:start position:0% +um sort of a very small C +function and we can sort of see what + + align:start position:0% +function and we can sort of see what + + + align:start position:0% +function and we can sort of see what +goes wrong if you provide different + + align:start position:0% +goes wrong if you provide different + + + align:start position:0% +goes wrong if you provide different +inputs um to that piece of code all + + align:start position:0% +inputs um to that piece of code all + + + align:start position:0% +inputs um to that piece of code all +right so the C function that I have in + + align:start position:0% +right so the C function that I have in + + + align:start position:0% +right so the C function that I have in +mind uh is uh this guy um let's + + align:start position:0% +mind uh is uh this guy um let's + + + align:start position:0% +mind uh is uh this guy um let's +see somewhere here I + + align:start position:0% +see somewhere here I + + + align:start position:0% +see somewhere here I +can oh + + align:start position:0% +can oh + + + align:start position:0% +can oh +yeah what's going + + align:start position:0% +yeah what's going + + + align:start position:0% +yeah what's going +on all right + + align:start position:0% +on all right + + + align:start position:0% +on all right +so here's the sort of program I'm + + align:start position:0% +so here's the sort of program I'm + + + align:start position:0% +so here's the sort of program I'm +talking about or I want to use as an + + align:start position:0% +talking about or I want to use as an + + + align:start position:0% +talking about or I want to use as an +example here um so this program is just + + align:start position:0% +example here um so this program is just + + + align:start position:0% +example here um so this program is just +going to read a request and you can sort + + align:start position:0% +going to read a request and you can sort + + + align:start position:0% +going to read a request and you can sort +of imagine it's going to read a request + + align:start position:0% +of imagine it's going to read a request + + + align:start position:0% +of imagine it's going to read a request +from the network but for the purposes of + + align:start position:0% +from the network but for the purposes of + + + align:start position:0% +from the network but for the purposes of +this example it's just going to read a + + align:start position:0% +this example it's just going to read a + + + align:start position:0% +this example it's just going to read a +request from whatever I'm typing in on + + align:start position:0% +request from whatever I'm typing in on + + + align:start position:0% +request from whatever I'm typing in on +the keyboard and it's going to you know + + align:start position:0% +the keyboard and it's going to you know + + + align:start position:0% +the keyboard and it's going to you know +store it in a buffer here then it's + + align:start position:0% +store it in a buffer here then it's + + + align:start position:0% +store it in a buffer here then it's +going to parse it as an integer and + + align:start position:0% +going to parse it as an integer and + + + align:start position:0% +going to parse it as an integer and +return the integer and the program will + + align:start position:0% +return the integer and the program will + + + align:start position:0% +return the integer and the program will +then print whatever integer I get back + + align:start position:0% +then print whatever integer I get back + + + align:start position:0% +then print whatever integer I get back +it's like far from a web server but you + + align:start position:0% +it's like far from a web server but you + + + align:start position:0% +it's like far from a web server but you +know we'll at least see some basics of + + align:start position:0% +know we'll at least see some basics of + + + align:start position:0% +know we'll at least see some basics of +how buffer flows work and what goes + + align:start position:0% +how buffer flows work and what goes + + + align:start position:0% +how buffer flows work and what goes +wrong so let's see actually what happens + + align:start position:0% +wrong so let's see actually what happens + + + align:start position:0% +wrong so let's see actually what happens +if we run this program so I can compile + + align:start position:0% +if we run this program so I can compile + + + align:start position:0% +if we run this program so I can compile +it here and actually you can sort of see + + align:start position:0% +it here and actually you can sort of see + + + align:start position:0% +it here and actually you can sort of see +the it's already telling me what I'm + + align:start position:0% +the it's already telling me what I'm + + + align:start position:0% +the it's already telling me what I'm +screwing up right the get function is + + align:start position:0% +screwing up right the get function is + + + align:start position:0% +screwing up right the get function is +dangerous and should not be used and + + align:start position:0% +dangerous and should not be used and + + + align:start position:0% +dangerous and should not be used and +we'll see in a second why the compiler + + align:start position:0% +we'll see in a second why the compiler + + + align:start position:0% +we'll see in a second why the compiler +is so intent on telling me this and it + + align:start position:0% +is so intent on telling me this and it + + + align:start position:0% +is so intent on telling me this and it +actually is true uh but you know for now + + align:start position:0% +actually is true uh but you know for now + + + align:start position:0% +actually is true uh but you know for now +suppose we are you know a happy go-lucky + + align:start position:0% +suppose we are you know a happy go-lucky + + + align:start position:0% +suppose we are you know a happy go-lucky +developer that is willing to ignore this + + align:start position:0% +developer that is willing to ignore this + + + align:start position:0% +developer that is willing to ignore this +warning so okay you know I read run this + + align:start position:0% +warning so okay you know I read run this + + + align:start position:0% +warning so okay you know I read run this +redir function I provide some input and + + align:start position:0% +redir function I provide some input and + + + align:start position:0% +redir function I provide some input and +it you know Works um let's see if I + + align:start position:0% +it you know Works um let's see if I + + + align:start position:0% +it you know Works um let's see if I +provide large inputs right you know if I + + align:start position:0% +provide large inputs right you know if I + + + align:start position:0% +provide large inputs right you know if I +type in some large number um well at + + align:start position:0% +type in some large number um well at + + + align:start position:0% +type in some large number um well at +least it gives me some large number it + + align:start position:0% +least it gives me some large number it + + + align:start position:0% +least it gives me some large number it +basically maxes out to 2 to the 31 and + + align:start position:0% +basically maxes out to 2 to the 31 and + + + align:start position:0% +basically maxes out to 2 to the 31 and +prints that and doesn't go any higher so + + align:start position:0% +prints that and doesn't go any higher so + + + align:start position:0% +prints that and doesn't go any higher so +that's maybe not disastrous right you + + align:start position:0% +that's maybe not disastrous right you + + + align:start position:0% +that's maybe not disastrous right you +know whatever you provided a you know + + align:start position:0% +know whatever you provided a you know + + + align:start position:0% +know whatever you provided a you know +ridiculously large number you got + + align:start position:0% +ridiculously large number you got + + + align:start position:0% +ridiculously large number you got +something didn't quite work so it's not + + align:start position:0% +something didn't quite work so it's not + + + align:start position:0% +something didn't quite work so it's not +quite a problem yet but if we provide + + align:start position:0% +quite a problem yet but if we provide + + + align:start position:0% +quite a problem yet but if we provide +some really large input we might get + + align:start position:0% +some really large input we might get + + + align:start position:0% +some really large input we might get +some other proms right so suppose I + + align:start position:0% +some other proms right so suppose I + + + align:start position:0% +some other proms right so suppose I +provide in a lot of byes well I just + + align:start position:0% +provide in a lot of byes well I just + + + align:start position:0% +provide in a lot of byes well I just +provide in things that are not numbers + + align:start position:0% +provide in things that are not numbers + + + align:start position:0% +provide in things that are not numbers +you know print zero that's not so bad + + align:start position:0% +you know print zero that's not so bad + + + align:start position:0% +you know print zero that's not so bad +but um suppose I'm going to paste in a + + align:start position:0% +but um suppose I'm going to paste in a + + + align:start position:0% +but um suppose I'm going to paste in a +huge number of A's okay so now the + + align:start position:0% +huge number of A's okay so now the + + + align:start position:0% +huge number of A's okay so now the +program crashes right you know maybe not + + align:start position:0% +program crashes right you know maybe not + + + align:start position:0% +program crashes right you know maybe not +too surprising so if it was the case + + align:start position:0% +too surprising so if it was the case + + + align:start position:0% +too surprising so if it was the case +that if you know I send a bad request to + + align:start position:0% +that if you know I send a bad request to + + + align:start position:0% +that if you know I send a bad request to +a web server it just doesn't get back to + + align:start position:0% +a web server it just doesn't get back to + + + align:start position:0% +a web server it just doesn't get back to +me or doesn't send a reply that would be + + align:start position:0% +me or doesn't send a reply that would be + + + align:start position:0% +me or doesn't send a reply that would be +fine but we'll sort of look inside and + + align:start position:0% +fine but we'll sort of look inside and + + + align:start position:0% +fine but we'll sort of look inside and +see what happens and try to figure out + + align:start position:0% +see what happens and try to figure out + + + align:start position:0% +see what happens and try to figure out +how we can actually take advantage of + + align:start position:0% +how we can actually take advantage of + + + align:start position:0% +how we can actually take advantage of +this crash to maybe do something much + + align:start position:0% +this crash to maybe do something much + + + align:start position:0% +this crash to maybe do something much +more interesting or um well much more + + align:start position:0% +more interesting or um well much more + + + align:start position:0% +more interesting or um well much more +along what an attacker might be + + align:start position:0% +along what an attacker might be + + + align:start position:0% +along what an attacker might be +interesting in doing so to do this we're + + align:start position:0% +interesting in doing so to do this we're + + + align:start position:0% +interesting in doing so to do this we're +going to run this program under a + + align:start position:0% +going to run this program under a + + + align:start position:0% +going to run this program under a +debugger you'll get super familiar with + + align:start position:0% +debugger you'll get super familiar with + + + align:start position:0% +debugger you'll get super familiar with +this in lab one uh but for now what + + align:start position:0% +this in lab one uh but for now what + + + align:start position:0% +this in lab one uh but for now what +we're going to do is uh set a breakpoint + + align:start position:0% +we're going to do is uh set a breakpoint + + + align:start position:0% +we're going to do is uh set a breakpoint +in that redir function and we're going + + align:start position:0% +in that redir function and we're going + + + align:start position:0% +in that redir function and we're going +to sort of run along and see what + + align:start position:0% +to sort of run along and see what + + + align:start position:0% +to sort of run along and see what +happens so when I run the program it's + + align:start position:0% +happens so when I run the program it's + + + align:start position:0% +happens so when I run the program it's +going to start executing in the main + + align:start position:0% +going to start executing in the main + + + align:start position:0% +going to start executing in the main +function and and pretty quickly it calls + + align:start position:0% +function and and pretty quickly it calls + + + align:start position:0% +function and and pretty quickly it calls +rra and the debugger is now stopped at + + align:start position:0% +rra and the debugger is now stopped at + + + align:start position:0% +rra and the debugger is now stopped at +the beginning of rra and we can actually + + align:start position:0% +the beginning of rra and we can actually + + + align:start position:0% +the beginning of rra and we can actually +see what's going on here by uh you know + + align:start position:0% +see what's going on here by uh you know + + + align:start position:0% +see what's going on here by uh you know +for example we can ask it to print the + + align:start position:0% +for example we can ask it to print the + + + align:start position:0% +for example we can ask it to print the +current CPU registers we're going to + + align:start position:0% +current CPU registers we're going to + + + align:start position:0% +current CPU registers we're going to +look at really lowlevel stuff here as + + align:start position:0% +look at really lowlevel stuff here as + + + align:start position:0% +look at really lowlevel stuff here as +opposed to a level of C source code + + align:start position:0% +opposed to a level of C source code + + + align:start position:0% +opposed to a level of C source code +we're going to look at the actual + + align:start position:0% +we're going to look at the actual + + + align:start position:0% +we're going to look at the actual +instructions that my machine is + + align:start position:0% +instructions that my machine is + + + align:start position:0% +instructions that my machine is +executing because that's what really is + + align:start position:0% +executing because that's what really is + + + align:start position:0% +executing because that's what really is +going on the C is actually maybe hiding + + align:start position:0% +going on the C is actually maybe hiding + + + align:start position:0% +going on the C is actually maybe hiding +some things from us so you can actually + + align:start position:0% +some things from us so you can actually + + + align:start position:0% +some things from us so you can actually +print all the registers so on x86 as you + + align:start position:0% +print all the registers so on x86 as you + + + align:start position:0% +print all the registers so on x86 as you +might remember from well on any + + align:start position:0% +might remember from well on any + + + align:start position:0% +might remember from well on any +architecture there's a stack pointer uh + + align:start position:0% +architecture there's a stack pointer uh + + + align:start position:0% +architecture there's a stack pointer uh +so let me start maybe drawing this + + align:start position:0% +so let me start maybe drawing this + + + align:start position:0% +so let me start maybe drawing this +diagram on the board so we can try to + + align:start position:0% +diagram on the board so we can try to + + + align:start position:0% +diagram on the board so we can try to +reconstruct what's happening um so + + align:start position:0% +reconstruct what's happening um so + + + align:start position:0% +reconstruct what's happening um so +what's going on is that my program not + + align:start position:0% +what's going on is that my program not + + + align:start position:0% +what's going on is that my program not +surprisingly has a stack on x86 the + + align:start position:0% +surprisingly has a stack on x86 the + + + align:start position:0% +surprisingly has a stack on x86 the +stack grows down so it sort of is This + + align:start position:0% +stack grows down so it sort of is This + + + align:start position:0% +stack grows down so it sort of is This +stack like this and we can keep pushing + + align:start position:0% +stack like this and we can keep pushing + + + align:start position:0% +stack like this and we can keep pushing +stuff onto it so right now the stack + + align:start position:0% +stuff onto it so right now the stack + + + align:start position:0% +stuff onto it so right now the stack +pointer points at this particular memory + + align:start position:0% +pointer points at this particular memory + + + align:start position:0% +pointer points at this particular memory +location FF d01 1 + + align:start position:0% +location FF d01 1 + + + align:start position:0% +location FF d01 1 +Z so you know some value so we can try + + align:start position:0% +Z so you know some value so we can try + + + align:start position:0% +Z so you know some value so we can try +to figure out how did it get there one + + align:start position:0% +to figure out how did it get there one + + + align:start position:0% +to figure out how did it get there one +way to do it is to disassemble the code + + align:start position:0% +way to do it is to disassemble the code + + + align:start position:0% +way to do it is to disassemble the code +of this redir + + align:start position:0% + + + + align:start position:0% + +functions is that going to work better + + align:start position:0% +functions is that going to work better + + + align:start position:0% +functions is that going to work better +really convenience variable must have + + align:start position:0% +really convenience variable must have + + + align:start position:0% +really convenience variable must have +integer value break break my number man + + align:start position:0% +integer value break break my number man + + + align:start position:0% +integer value break break my number man +what is going on with my debugger + + align:start position:0% + + + + align:start position:0% + +rre all right well we can disassemble + + align:start position:0% +rre all right well we can disassemble + + + align:start position:0% +rre all right well we can disassemble +the function by name so this is what the + + align:start position:0% +the function by name so this is what the + + + align:start position:0% +the function by name so this is what the +function is doing so first off it starts + + align:start position:0% +function is doing so first off it starts + + + align:start position:0% +function is doing so first off it starts +by you know manipulating something with + + align:start position:0% +by you know manipulating something with + + + align:start position:0% +by you know manipulating something with +this EVP register that's not super + + align:start position:0% +this EVP register that's not super + + + align:start position:0% +this EVP register that's not super +interesting but the first thing it does + + align:start position:0% +interesting but the first thing it does + + + align:start position:0% +interesting but the first thing it does +after that is subtract a certain value + + align:start position:0% +after that is subtract a certain value + + + align:start position:0% +after that is subtract a certain value +from the stack pointer and this is + + align:start position:0% +from the stack pointer and this is + + + align:start position:0% +from the stack pointer and this is +basically it's making space for all + + align:start position:0% +basically it's making space for all + + + align:start position:0% +basically it's making space for all +those variables like the buffer and the + + align:start position:0% +those variables like the buffer and the + + + align:start position:0% +those variables like the buffer and the +integer I we saw in the C source code so + + align:start position:0% +integer I we saw in the C source code so + + + align:start position:0% +integer I we saw in the C source code so +we're actually now four instructions + + align:start position:0% +we're actually now four instructions + + + align:start position:0% +we're actually now four instructions +into the function here so that stack + + align:start position:0% +into the function here so that stack + + + align:start position:0% +into the function here so that stack +pointer value that we saw before is + + align:start position:0% +pointer value that we saw before is + + + align:start position:0% +pointer value that we saw before is +actually already in the middle so to say + + align:start position:0% +actually already in the middle so to say + + + align:start position:0% +actually already in the middle so to say +of the stack + + align:start position:0% +of the stack + + + align:start position:0% +of the stack +and currently there's stuff above it + + align:start position:0% +and currently there's stuff above it + + + align:start position:0% +and currently there's stuff above it +that uh is going to be the buffer that + + align:start position:0% +that uh is going to be the buffer that + + + align:start position:0% +that uh is going to be the buffer that +integer value and actually also the + + align:start position:0% +integer value and actually also the + + + align:start position:0% +integer value and actually also the +return address into the main function + + align:start position:0% +return address into the main function + + + align:start position:0% +return address into the main function +Goes On The Stack as well so somewhere + + align:start position:0% +Goes On The Stack as well so somewhere + + + align:start position:0% +Goes On The Stack as well so somewhere +here we'll have the return address and + + align:start position:0% +here we'll have the return address and + + + align:start position:0% +here we'll have the return address and +we can actually try to figure out where + + align:start position:0% +we can actually try to figure out where + + + align:start position:0% +we can actually try to figure out where +are things on the stack so we can print + + align:start position:0% +are things on the stack so we can print + + + align:start position:0% +are things on the stack so we can print +the address of that buffer variable + + align:start position:0% +the address of that buffer variable + + + align:start position:0% +the address of that buffer variable +so the buffer variable is at address d02 + + align:start position:0% +so the buffer variable is at address d02 + + + align:start position:0% +so the buffer variable is at address d02 +C you can also print the V the value of + + align:start position:0% +C you can also print the V the value of + + + align:start position:0% +C you can also print the V the value of +that + + align:start position:0% +that + + + align:start position:0% +that +integer I so that guy is at d0 AC so the + + align:start position:0% +integer I so that guy is at d0 AC so the + + + align:start position:0% +integer I so that guy is at d0 AC so the +I is way up on the stack but the buffer + + align:start position:0% +I is way up on the stack but the buffer + + + align:start position:0% +I is way up on the stack but the buffer +is uh a bit lower so what's going on is + + align:start position:0% +is uh a bit lower so what's going on is + + + align:start position:0% +is uh a bit lower so what's going on is +that we have our buffer here on the + + align:start position:0% +that we have our buffer here on the + + + align:start position:0% +that we have our buffer here on the +stack and Then followed above by I and + + align:start position:0% +stack and Then followed above by I and + + + align:start position:0% +stack and Then followed above by I and +maybe some other stuff and then finally + + align:start position:0% +maybe some other stuff and then finally + + + align:start position:0% +maybe some other stuff and then finally +the return address into the main + + align:start position:0% +the return address into the main + + + align:start position:0% +the return address into the main +function that called GRE R and the + + align:start position:0% +function that called GRE R and the + + + align:start position:0% +function that called GRE R and the +buffer is uh you know this is going the + + align:start position:0% +buffer is uh you know this is going the + + + align:start position:0% +buffer is uh you know this is going the +stack is growing down so these are + + align:start position:0% +stack is growing down so these are + + + align:start position:0% +stack is growing down so these are +higher + + align:start position:0% + + + + align:start position:0% + +addresses so what this means is that uh + + align:start position:0% +addresses so what this means is that uh + + + align:start position:0% +addresses so what this means is that uh +the buffer we actually have to decide + + align:start position:0% +the buffer we actually have to decide + + + align:start position:0% +the buffer we actually have to decide +where is the zeroth element of the + + align:start position:0% +where is the zeroth element of the + + + align:start position:0% +where is the zeroth element of the +buffer and where is the 128th element of + + align:start position:0% +buffer and where is the 128th element of + + + align:start position:0% +buffer and where is the 128th element of +this buffer so where does the zeroth + + align:start position:0% +this buffer so where does the zeroth + + + align:start position:0% +this buffer so where does the zeroth +element of the buffer + + align:start position:0% +element of the buffer + + + align:start position:0% +element of the buffer +go + + align:start position:0% +go + + + align:start position:0% +go +yeah should be at the bottom right + + align:start position:0% +yeah should be at the bottom right + + + align:start position:0% +yeah should be at the bottom right +because yeah higher elements just keep + + align:start position:0% +because yeah higher elements just keep + + + align:start position:0% +because yeah higher elements just keep +going up yeah so buff of zero is down + + align:start position:0% +going up yeah so buff of zero is down + + + align:start position:0% +going up yeah so buff of zero is down +here just keeps going on and buff of 127 + + align:start position:0% +here just keeps going on and buff of 127 + + + align:start position:0% +here just keeps going on and buff of 127 +is going to be up there then we'll have + + align:start position:0% +is going to be up there then we'll have + + + align:start position:0% +is going to be up there then we'll have +I and other + + align:start position:0% +I and other + + + align:start position:0% +I and other +stuff okay well let's see what happens + + align:start position:0% +stuff okay well let's see what happens + + + align:start position:0% +stuff okay well let's see what happens +now if we provide that input that seem + + align:start position:0% +now if we provide that input that seem + + + align:start position:0% +now if we provide that input that seem +to be crashing it before so guess one + + align:start position:0% +to be crashing it before so guess one + + + align:start position:0% +to be crashing it before so guess one +thing we can actually do before this is + + align:start position:0% +thing we can actually do before this is + + + align:start position:0% +thing we can actually do before this is +to see whether we can actually find this + + align:start position:0% +to see whether we can actually find this + + + align:start position:0% +to see whether we can actually find this +return address where it actually happens + + align:start position:0% +return address where it actually happens + + + align:start position:0% +return address where it actually happens +to live is uh at the EBP pointer this is + + align:start position:0% +to live is uh at the EBP pointer this is + + + align:start position:0% +to live is uh at the EBP pointer this is +just a convenient thing in the x86 + + align:start position:0% +just a convenient thing in the x86 + + + align:start position:0% +just a convenient thing in the x86 +calling convention that the EBP pointer + + align:start position:0% +calling convention that the EBP pointer + + + align:start position:0% +calling convention that the EBP pointer +or + + align:start position:0% +or + + + align:start position:0% +or +register actually happens to point to + + align:start position:0% +register actually happens to point to + + + align:start position:0% +register actually happens to point to +something on the stack which is going to + + align:start position:0% +something on the stack which is going to + + + align:start position:0% +something on the stack which is going to +be the called the saved + + align:start position:0% +be the called the saved + + + align:start position:0% +be the called the saved +EBP it's a separate location sort of + + align:start position:0% +EBP it's a separate location sort of + + + align:start position:0% +EBP it's a separate location sort of +after all the variables but before the + + align:start position:0% +after all the variables but before the + + + align:start position:0% +after all the variables but before the +return address and this is the thing + + align:start position:0% +return address and this is the thing + + + align:start position:0% +return address and this is the thing +that's being saved by those first couple + + align:start position:0% +that's being saved by those first couple + + + align:start position:0% +that's being saved by those first couple +of instructions at the top and you can + + align:start position:0% +of instructions at the top and you can + + + align:start position:0% +of instructions at the top and you can +actually sort of examine it in GDB you + + align:start position:0% +actually sort of examine it in GDB you + + + align:start position:0% +actually sort of examine it in GDB you +can say you know examine x uh some value + + align:start position:0% +can say you know examine x uh some value + + + align:start position:0% +can say you know examine x uh some value +so the EBP pointer value so that's the + + align:start position:0% +so the EBP pointer value so that's the + + + align:start position:0% +so the EBP pointer value so that's the +location of the stack d 0 B8 indeed it's + + align:start position:0% +location of the stack d 0 B8 indeed it's + + + align:start position:0% +location of the stack d 0 B8 indeed it's +actually above even the I variable so + + align:start position:0% +actually above even the I variable so + + + align:start position:0% +actually above even the I variable so +it's great and it has some other value + + align:start position:0% +it's great and it has some other value + + + align:start position:0% +it's great and it has some other value +that happens to be the EBP before this + + align:start position:0% +that happens to be the EBP before this + + + align:start position:0% +that happens to be the EBP before this +function was called but then sort of one + + align:start position:0% +function was called but then sort of one + + + align:start position:0% +function was called but then sort of one +more sort of memory location up is going + + align:start position:0% +more sort of memory location up is going + + + align:start position:0% +more sort of memory location up is going +to be the return address so if we print + + align:start position:0% +to be the return address so if we print + + + align:start position:0% +to be the return address so if we print +EBP plus 4 there's something else there + + align:start position:0% +EBP plus 4 there's something else there + + + align:start position:0% +EBP plus 4 there's something else there +this Ox 8 04 8 e5f and let's actually + + align:start position:0% +this Ox 8 04 8 e5f and let's actually + + + align:start position:0% +this Ox 8 04 8 e5f and let's actually +see where that's pointing so this is you + + align:start position:0% +see where that's pointing so this is you + + + align:start position:0% +see where that's pointing so this is you +know something you're going to do a lot + + align:start position:0% +know something you're going to do a lot + + + align:start position:0% +know something you're going to do a lot +in the lab um so you can take this + + align:start position:0% +in the lab um so you can take this + + + align:start position:0% +in the lab um so you can take this +address and you can try to disassemble + + align:start position:0% +address and you can try to disassemble + + + align:start position:0% +address and you can try to disassemble +it so what is this guy where did we end + + align:start position:0% +it so what is this guy where did we end + + + align:start position:0% +it so what is this guy where did we end +up so GDB actually helpfully figures out + + align:start position:0% +up so GDB actually helpfully figures out + + + align:start position:0% +up so GDB actually helpfully figures out +which function contains that address so + + align:start position:0% +which function contains that address so + + + align:start position:0% +which function contains that address so +5f this is the guy that our return + + align:start position:0% +5f this is the guy that our return + + + align:start position:0% +5f this is the guy that our return +address is pointing to and as you can + + align:start position:0% +address is pointing to and as you can + + + align:start position:0% +address is pointing to and as you can +see this is the instruction right after + + align:start position:0% +see this is the instruction right after + + + align:start position:0% +see this is the instruction right after +the call to redre so when we return from + + align:start position:0% +the call to redre so when we return from + + + align:start position:0% +the call to redre so when we return from +redre this is exactly where we're going + + align:start position:0% +redre this is exactly where we're going + + + align:start position:0% +redre this is exactly where we're going +to jump and continue execution this is + + align:start position:0% +to jump and continue execution this is + + + align:start position:0% +to jump and continue execution this is +hopefully fairly straightforward stuff + + align:start position:0% +hopefully fairly straightforward stuff + + + align:start position:0% +hopefully fairly straightforward stuff +from you + + align:start position:0% +from you + + + align:start position:0% +from you +know4 some standard OS class okay so + + align:start position:0% +know4 some standard OS class okay so + + + align:start position:0% +know4 some standard OS class okay so +okay so where are we now just to recap + + align:start position:0% +okay so where are we now just to recap + + + align:start position:0% +okay so where are we now just to recap +we can try to disassemble our + + align:start position:0% +we can try to disassemble our + + + align:start position:0% +we can try to disassemble our +instruction pointer so we're at the + + align:start position:0% +instruction pointer so we're at the + + + align:start position:0% +instruction pointer so we're at the +beginning of rra right now and we can + + align:start position:0% +beginning of rra right now and we can + + + align:start position:0% +beginning of rra right now and we can +run for a bit and maybe run that um gets + + align:start position:0% +run for a bit and maybe run that um gets + + + align:start position:0% +run for a bit and maybe run that um gets +function so okay we run next what this + + align:start position:0% +function so okay we run next what this + + + align:start position:0% +function so okay we run next what this +does is it gets runs gets and it's + + align:start position:0% +does is it gets runs gets and it's + + + align:start position:0% +does is it gets runs gets and it's +waiting for gets to return so we can + + align:start position:0% +waiting for gets to return so we can + + + align:start position:0% +waiting for gets to return so we can +provide our bad input to get us and try + + align:start position:0% +provide our bad input to get us and try + + + align:start position:0% +provide our bad input to get us and try +to get it to crash again and see what's + + align:start position:0% +to get it to crash again and see what's + + + align:start position:0% +to get it to crash again and see what's +going on really there right so we can + + align:start position:0% +going on really there right so we can + + + align:start position:0% +going on really there right so we can +paste of a again okay so we got out of + + align:start position:0% +paste of a again okay so we got out of + + + align:start position:0% +paste of a again okay so we got out of +get us and things are actually still + + align:start position:0% +get us and things are actually still + + + align:start position:0% +get us and things are actually still +okay right the program is still running + + align:start position:0% +okay right the program is still running + + + align:start position:0% +okay right the program is still running +but we can try to figure out like what + + align:start position:0% +but we can try to figure out like what + + + align:start position:0% +but we can try to figure out like what +is in memory right now and why are + + align:start position:0% +is in memory right now and why are + + + align:start position:0% +is in memory right now and why are +things going to go wrong actually what + + align:start position:0% +things going to go wrong actually what + + + align:start position:0% +things going to go wrong actually what +do you guys think what happened right so + + align:start position:0% +do you guys think what happened right so + + + align:start position:0% +do you guys think what happened right so +I printed out a bunch of A's what did + + align:start position:0% +I printed out a bunch of A's what did + + + align:start position:0% +I printed out a bunch of A's what did +get us do to the memory we can yeah yeah + + align:start position:0% +get us do to the memory we can yeah yeah + + + align:start position:0% +get us do to the memory we can yeah yeah +so it just keeps writing A's here right + + align:start position:0% +so it just keeps writing A's here right + + + align:start position:0% +so it just keeps writing A's here right +all we actually passed to get us was a + + align:start position:0% +all we actually passed to get us was a + + + align:start position:0% +all we actually passed to get us was a +single pointer the start of this address + + align:start position:0% +single pointer the start of this address + + + align:start position:0% +single pointer the start of this address +right so this is the argument to get us + + align:start position:0% +right so this is the argument to get us + + + align:start position:0% +right so this is the argument to get us +is a pointer to this memory location on + + align:start position:0% +is a pointer to this memory location on + + + align:start position:0% +is a pointer to this memory location on +the stack so just kept writing A's and + + align:start position:0% +the stack so just kept writing A's and + + + align:start position:0% +the stack so just kept writing A's and +it doesn't actually know what the length + + align:start position:0% +it doesn't actually know what the length + + + align:start position:0% +it doesn't actually know what the length +is so it just keeps going right it's + + align:start position:0% +is so it just keeps going right it's + + + align:start position:0% +is so it just keeps going right it's +going to overwrite A's all the way up + + align:start position:0% +going to overwrite A's all the way up + + + align:start position:0% +going to overwrite A's all the way up +the stack past the return address + + align:start position:0% +the stack past the return address + + + align:start position:0% +the stack past the return address +probably and into whatever was up the + + align:start position:0% +probably and into whatever was up the + + + align:start position:0% +probably and into whatever was up the +stack above us so we can check whether + + align:start position:0% +stack above us so we can check whether + + + align:start position:0% +stack above us so we can check whether +that's the case so we can actually print + + align:start position:0% +that's the case so we can actually print + + + align:start position:0% +that's the case so we can actually print +um the buffer and in fact it tells us + + align:start position:0% +um the buffer and in fact it tells us + + + align:start position:0% +um the buffer and in fact it tells us +yeah we have 180 A's there even though + + align:start position:0% +yeah we have 180 A's there even though + + + align:start position:0% +yeah we have 180 A's there even though +the buffer should be 128 elements large + + align:start position:0% +the buffer should be 128 elements large + + + align:start position:0% +the buffer should be 128 elements large +so this is not so so great uh and we can + + align:start position:0% +so this is not so so great uh and we can + + + align:start position:0% +so this is not so so great uh and we can +actually again examine what's going on + + align:start position:0% +actually again examine what's going on + + + align:start position:0% +actually again examine what's going on +in that EBP pointer uh oops dollar sign + + align:start position:0% +in that EBP pointer uh oops dollar sign + + + align:start position:0% +in that EBP pointer uh oops dollar sign +EBP so in fact yeah it's all Ox 41 which + + align:start position:0% +EBP so in fact yeah it's all Ox 41 which + + + align:start position:0% +EBP so in fact yeah it's all Ox 41 which +is the aski encoding of the letter a and + + align:start position:0% +is the aski encoding of the letter a and + + + align:start position:0% +is the aski encoding of the letter a and +in fact the return address is probably + + align:start position:0% +in fact the return address is probably + + + align:start position:0% +in fact the return address is probably +going to be the same way right if we + + align:start position:0% +going to be the same way right if we + + + align:start position:0% +going to be the same way right if we +print the return address it's also all + + align:start position:0% +print the return address it's also all + + + align:start position:0% +print the return address it's also all +A's so that's not so great in fact + + align:start position:0% +A's so that's not so great in fact + + + align:start position:0% +A's so that's not so great in fact +what's going to happen if we return now + + align:start position:0% +what's going to happen if we return now + + + align:start position:0% +what's going to happen if we return now +is the program will jump to that address + + align:start position:0% +is the program will jump to that address + + + align:start position:0% +is the program will jump to that address +4141 4141 and there's nothing there and + + align:start position:0% +4141 4141 and there's nothing there and + + + align:start position:0% +4141 4141 and there's nothing there and +it'll crash that's the segmentation + + align:start position:0% +it'll crash that's the segmentation + + + align:start position:0% +it'll crash that's the segmentation +fault you're + + align:start position:0% +fault you're + + + align:start position:0% +fault you're +getting so well let's just step up to it + + align:start position:0% +getting so well let's just step up to it + + + align:start position:0% +getting so well let's just step up to it +and see what happens right so let's run + + align:start position:0% +and see what happens right so let's run + + + align:start position:0% +and see what happens right so let's run +next so we keep stepping through the + + align:start position:0% +next so we keep stepping through the + + + align:start position:0% +next so we keep stepping through the +program and uh we can see where we are + + align:start position:0% +program and uh we can see where we are + + + align:start position:0% +program and uh we can see where we are +okay we're getting close to the end of + + align:start position:0% +okay we're getting close to the end of + + + align:start position:0% +okay we're getting close to the end of +the function so we can step over two + + align:start position:0% +the function so we can step over two + + + align:start position:0% +the function so we can step over two +more + + align:start position:0% +more + + + align:start position:0% +more +instructions next ey next ey and now we + + align:start position:0% +instructions next ey next ey and now we + + + align:start position:0% +instructions next ey next ey and now we +can disassemble again okay we're now + + align:start position:0% +can disassemble again okay we're now + + + align:start position:0% +can disassemble again okay we're now +just at the return instruction from this + + align:start position:0% +just at the return instruction from this + + + align:start position:0% +just at the return instruction from this +function and we can actually figure out + + align:start position:0% +function and we can actually figure out + + + align:start position:0% +function and we can actually figure out +so so as you can see at the end of the + + align:start position:0% +so so as you can see at the end of the + + + align:start position:0% +so so as you can see at the end of the +function it runs this leave x86 + + align:start position:0% +function it runs this leave x86 + + + align:start position:0% +function it runs this leave x86 +instruction which basically restores the + + align:start position:0% +instruction which basically restores the + + + align:start position:0% +instruction which basically restores the +stack back to where it was so it sort of + + align:start position:0% +stack back to where it was so it sort of + + + align:start position:0% +stack back to where it was so it sort of +pushes the stack pointer all the way + + align:start position:0% +pushes the stack pointer all the way + + + align:start position:0% +pushes the stack pointer all the way +back to the return address using the + + align:start position:0% +back to the return address using the + + + align:start position:0% +back to the return address using the +saved EBP that's what it's basically for + + align:start position:0% +saved EBP that's what it's basically for + + + align:start position:0% +saved EBP that's what it's basically for +uh and now the stack is pointing at the + + align:start position:0% +uh and now the stack is pointing at the + + + align:start position:0% +uh and now the stack is pointing at the +return address that we're going to use + + align:start position:0% +return address that we're going to use + + + align:start position:0% +return address that we're going to use +and in fact it's all A's and if we run + + align:start position:0% +and in fact it's all A's and if we run + + + align:start position:0% +and in fact it's all A's and if we run +one more instruction the CPU is going to + + align:start position:0% +one more instruction the CPU is going to + + + align:start position:0% +one more instruction the CPU is going to +jump to that exact memory address and + + align:start position:0% +jump to that exact memory address and + + + align:start position:0% +jump to that exact memory address and +start executing code there and crash + + align:start position:0% +start executing code there and crash + + + align:start position:0% +start executing code there and crash +because it's not valid address that's in + + align:start position:0% +because it's not valid address that's in + + + align:start position:0% +because it's not valid address that's in +the page table so let's actually see + + align:start position:0% +the page table so let's actually see + + + align:start position:0% +the page table so let's actually see +what's uh just to double check what's + + align:start position:0% +what's uh just to double check what's + + + align:start position:0% +what's uh just to double check what's +going on uh let's print our buffer again + + align:start position:0% +going on uh let's print our buffer again + + + align:start position:0% +going on uh let's print our buffer again +our buffer well that's actually kind of + + align:start position:0% +our buffer well that's actually kind of + + + align:start position:0% +our buffer well that's actually kind of +interesting right so now buffer for some + + align:start position:0% +interesting right so now buffer for some + + + align:start position:0% +interesting right so now buffer for some +reason it only says a repeats 128 times + + align:start position:0% +reason it only says a repeats 128 times + + + align:start position:0% +reason it only says a repeats 128 times +whereas if you remember before it said a + + align:start position:0% +whereas if you remember before it said a + + + align:start position:0% +whereas if you remember before it said a +repeated 180 times an our + + align:start position:0% +repeated 180 times an our + + + align:start position:0% +repeated 180 times an our +buffer so what happened + + align:start position:0% +buffer so what happened + + + align:start position:0% +buffer so what happened +yeah yeah yeah exactly so there's + + align:start position:0% +yeah yeah yeah exactly so there's + + + align:start position:0% +yeah yeah yeah exactly so there's +actually something going on after the + + align:start position:0% +actually something going on after the + + + align:start position:0% +actually something going on after the +buffer overflow happens that um changes + + align:start position:0% +buffer overflow happens that um changes + + + align:start position:0% +buffer overflow happens that um changes +what's going on so actually if you + + align:start position:0% +what's going on so actually if you + + + align:start position:0% +what's going on so actually if you +remember we do this a toi conversion of + + align:start position:0% +remember we do this a toi conversion of + + + align:start position:0% +remember we do this a toi conversion of +the string to an integer and if we + + align:start position:0% +the string to an integer and if we + + + align:start position:0% +the string to an integer and if we +provide all A's it actually writes zero + + align:start position:0% +provide all A's it actually writes zero + + + align:start position:0% +provide all A's it actually writes zero +to this memory location so so a zero if + + align:start position:0% +to this memory location so so a zero if + + + align:start position:0% +to this memory location so so a zero if +you remember terminates strings in C so + + align:start position:0% +you remember terminates strings in C so + + + align:start position:0% +you remember terminates strings in C so +GDB now thinks yep we have a perfectly + + align:start position:0% +GDB now thinks yep we have a perfectly + + + align:start position:0% +GDB now thinks yep we have a perfectly +well terminated 128 byte string of all + + align:start position:0% +well terminated 128 byte string of all + + + align:start position:0% +well terminated 128 byte string of all +A's but you know it doesn't really + + align:start position:0% +A's but you know it doesn't really + + + align:start position:0% +A's but you know it doesn't really +matter because we still have those A's + + align:start position:0% +matter because we still have those A's + + + align:start position:0% +matter because we still have those A's +up top that already corrupted our + + align:start position:0% +up top that already corrupted our + + + align:start position:0% +up top that already corrupted our +stack okay this is actually kind of an + + align:start position:0% +stack okay this is actually kind of an + + + align:start position:0% +stack okay this is actually kind of an +important lesson that it's actually a + + align:start position:0% +important lesson that it's actually a + + + align:start position:0% +important lesson that it's actually a +little bit tricky sometimes to exploit + + align:start position:0% +little bit tricky sometimes to exploit + + + align:start position:0% +little bit tricky sometimes to exploit +these buffer overflows because even + + align:start position:0% +these buffer overflows because even + + + align:start position:0% +these buffer overflows because even +though you've already changed lots of + + align:start position:0% +though you've already changed lots of + + + align:start position:0% +though you've already changed lots of +stuff on the stack you still have to get + + align:start position:0% +stuff on the stack you still have to get + + + align:start position:0% +stuff on the stack you still have to get +to the point where you use the value + + align:start position:0% +to the point where you use the value + + + align:start position:0% +to the point where you use the value +that you somehow placed on the stack so + + align:start position:0% +that you somehow placed on the stack so + + + align:start position:0% +that you somehow placed on the stack so +there's other code that's going to run + + align:start position:0% +there's other code that's going to run + + + align:start position:0% +there's other code that's going to run +after you've managed to overflow some + + align:start position:0% +after you've managed to overflow some + + + align:start position:0% +after you've managed to overflow some +buffer and corrupt memory you have to + + align:start position:0% +buffer and corrupt memory you have to + + + align:start position:0% +buffer and corrupt memory you have to +make sure that code doesn't do something + + align:start position:0% +make sure that code doesn't do something + + + align:start position:0% +make sure that code doesn't do something +silly like if this a toi just exited + + align:start position:0% +silly like if this a toi just exited + + + align:start position:0% +silly like if this a toi just exited +right away as soon as it saw a non- + + align:start position:0% +right away as soon as it saw a non- + + + align:start position:0% +right away as soon as it saw a non- +integer value we might not get to jump + + align:start position:0% +integer value we might not get to jump + + + align:start position:0% +integer value we might not get to jump +to all this 4141 4141 address so you + + align:start position:0% +to all this 4141 4141 address so you + + + align:start position:0% +to all this 4141 4141 address so you +have to massage your input in some cases + + align:start position:0% +have to massage your input in some cases + + + align:start position:0% +have to massage your input in some cases +Maybe not so much in this case but uh in + + align:start position:0% +Maybe not so much in this case but uh in + + + align:start position:0% +Maybe not so much in this case but uh in +other situations you'll have to be + + align:start position:0% +other situations you'll have to be + + + align:start position:0% +other situations you'll have to be +careful in constructing this input okay + + align:start position:0% +careful in constructing this input okay + + + align:start position:0% +careful in constructing this input okay +so just to see what happens we can jump + + align:start position:0% +so just to see what happens we can jump + + + align:start position:0% +so just to see what happens we can jump +one more time well let's look at our + + align:start position:0% +one more time well let's look at our + + + align:start position:0% +one more time well let's look at our +register so right now our EIP the sort + + align:start position:0% +register so right now our EIP the sort + + + align:start position:0% +register so right now our EIP the sort +of instruction pointer is pointing at + + align:start position:0% +of instruction pointer is pointing at + + + align:start position:0% +of instruction pointer is pointing at +the last thing in red and if we step one + + align:start position:0% +the last thing in red and if we step one + + + align:start position:0% +the last thing in red and if we step one +more time hopefully we'll jump to + + align:start position:0% +more time hopefully we'll jump to + + + align:start position:0% +more time hopefully we'll jump to +finally that unfortunate 4141 address + + align:start position:0% +finally that unfortunate 4141 address + + + align:start position:0% +finally that unfortunate 4141 address +over here and in fact yep the program + + align:start position:0% +over here and in fact yep the program + + + align:start position:0% +over here and in fact yep the program +now seems to be executing there if we + + align:start position:0% +now seems to be executing there if we + + + align:start position:0% +now seems to be executing there if we +ask GDB to print the current set of + + align:start position:0% +ask GDB to print the current set of + + + align:start position:0% +ask GDB to print the current set of +registers yep the current instruction + + align:start position:0% +registers yep the current instruction + + + align:start position:0% +registers yep the current instruction +pointer is this strange value and if we + + align:start position:0% +pointer is this strange value and if we + + + align:start position:0% +pointer is this strange value and if we +execute one more instruction it's going + + align:start position:0% +execute one more instruction it's going + + + align:start position:0% +execute one more instruction it's going +to crash because that's finally trying + + align:start position:0% +to crash because that's finally trying + + + align:start position:0% +to crash because that's finally trying +to execute + + align:start position:0% +to execute + + + align:start position:0% +to execute +a instruction pointer that doesn't + + align:start position:0% +a instruction pointer that doesn't + + + align:start position:0% +a instruction pointer that doesn't +correspond to a valid page in the + + align:start position:0% +correspond to a valid page in the + + + align:start position:0% +correspond to a valid page in the +operating systems page table for this + + align:start position:0% +operating systems page table for this + + + align:start position:0% +operating systems page table for this +process make + + align:start position:0% +process make + + + align:start position:0% +process make +sense any + + align:start position:0% +sense any + + + align:start position:0% +sense any +questions all right + + align:start position:0% +questions all right + + + align:start position:0% +questions all right +well got a question for you guys + + align:start position:0% +well got a question for you guys + + + align:start position:0% +well got a question for you guys +actually so what happens you know this + + align:start position:0% +actually so what happens you know this + + + align:start position:0% +actually so what happens you know this +seems to be exploitable or well okay + + align:start position:0% +seems to be exploitable or well okay + + + align:start position:0% +seems to be exploitable or well okay +maybe let's first figure out why this is + + align:start position:0% +maybe let's first figure out why this is + + + align:start position:0% +maybe let's first figure out why this is +particularly bad right so why why is + + align:start position:0% +particularly bad right so why why is + + + align:start position:0% +particularly bad right so why why is +this a problem so not only does our + + align:start position:0% +this a problem so not only does our + + + align:start position:0% +this a problem so not only does our +program crash but presumably we're going + + align:start position:0% +program crash but presumably we're going + + + align:start position:0% +program crash but presumably we're going +to take it over so I guess first simple + + align:start position:0% +to take it over so I guess first simple + + + align:start position:0% +to take it over so I guess first simple +question is okay so what's what's the + + align:start position:0% +question is okay so what's what's the + + + align:start position:0% +question is okay so what's what's the +problem what can you do + + align:start position:0% +problem what can you do + + + align:start position:0% +problem what can you do +yeah yeah so so I I was actually pretty + + align:start position:0% +yeah yeah so so I I was actually pretty + + + align:start position:0% +yeah yeah so so I I was actually pretty +silly and just put in lots of A's but if + + align:start position:0% +silly and just put in lots of A's but if + + + align:start position:0% +silly and just put in lots of A's but if +you're careful about knowing where to + + align:start position:0% +you're careful about knowing where to + + + align:start position:0% +you're careful about knowing where to +put what values you might be able to put + + align:start position:0% +put what values you might be able to put + + + align:start position:0% +put what values you might be able to put +in a different value and get it to jump + + align:start position:0% +in a different value and get it to jump + + + align:start position:0% +in a different value and get it to jump +somewhere else so let's see if we can + + align:start position:0% +somewhere else so let's see if we can + + + align:start position:0% +somewhere else so let's see if we can +actually do this right we can retra eras + + align:start position:0% +actually do this right we can retra eras + + + align:start position:0% +actually do this right we can retra eras +this whole thing okay rerun the program + + align:start position:0% +this whole thing okay rerun the program + + + align:start position:0% +this whole thing okay rerun the program +again + + align:start position:0% +again + + + align:start position:0% +again +and I guess I have to reset the break + + align:start position:0% +and I guess I have to reset the break + + + align:start position:0% +and I guess I have to reset the break +point so I can break and redirect again + + align:start position:0% +point so I can break and redirect again + + + align:start position:0% +point so I can break and redirect again +and run and this time I'll again um next + + align:start position:0% +and run and this time I'll again um next + + + align:start position:0% +and run and this time I'll again um next +Supply lots of A's and overflow things + + align:start position:0% +Supply lots of A's and overflow things + + + align:start position:0% +Supply lots of A's and overflow things +but I'll sort of you know I'm not going + + align:start position:0% +but I'll sort of you know I'm not going + + + align:start position:0% +but I'll sort of you know I'm not going +to try to carefully construct you know + + align:start position:0% +to try to carefully construct you know + + + align:start position:0% +to try to carefully construct you know +figure out which point in these A's + + align:start position:0% +figure out which point in these A's + + + align:start position:0% +figure out which point in these A's +corresponds to the location in the stack + + align:start position:0% +corresponds to the location in the stack + + + align:start position:0% +corresponds to the location in the stack +that's something you guys going to have + + align:start position:0% +that's something you guys going to have + + + align:start position:0% +that's something you guys going to have +to do for lab one but suppose that you + + align:start position:0% +to do for lab one but suppose that you + + + align:start position:0% +to do for lab one but suppose that you +know I overflow the stack here and then + + align:start position:0% +know I overflow the stack here and then + + + align:start position:0% +know I overflow the stack here and then +I'm going to manually try to change + + align:start position:0% +I'm going to manually try to change + + + align:start position:0% +I'm going to manually try to change +things on the stack to get it to jump to + + align:start position:0% +things on the stack to get it to jump to + + + align:start position:0% +things on the stack to get it to jump to +some point I want to jump to and uh in + + align:start position:0% +some point I want to jump to and uh in + + + align:start position:0% +some point I want to jump to and uh in +this program okay so let's uh + + align:start position:0% +this program okay so let's uh + + + align:start position:0% +this program okay so let's uh +again next ey uh where are we we're + + align:start position:0% +again next ey uh where are we we're + + + align:start position:0% +again next ey uh where are we we're +again at the very end of read W and + + align:start position:0% +again at the very end of read W and + + + align:start position:0% +again at the very end of read W and +let's actually look at the stack right + + align:start position:0% +let's actually look at the stack right + + + align:start position:0% +let's actually look at the stack right +so if we examine ESP here we see our + + align:start position:0% +so if we examine ESP here we see our + + + align:start position:0% +so if we examine ESP here we see our +corrupted pointer okay where could we + + align:start position:0% +corrupted pointer okay where could we + + + align:start position:0% +corrupted pointer okay where could we +jump to what what what interesting + + align:start position:0% +jump to what what what interesting + + + align:start position:0% +jump to what what what interesting +things could we do unfortunately this + + align:start position:0% +things could we do unfortunately this + + + align:start position:0% +things could we do unfortunately this +program is pretty limited there's almost + + align:start position:0% +program is pretty limited there's almost + + + align:start position:0% +program is pretty limited there's almost +nothing in the programs code where you + + align:start position:0% +nothing in the programs code where you + + + align:start position:0% +nothing in the programs code where you +could jump and do anything interesting + + align:start position:0% +could jump and do anything interesting + + + align:start position:0% +could jump and do anything interesting +um but maybe we can do a little bit of + + align:start position:0% +um but maybe we can do a little bit of + + + align:start position:0% +um but maybe we can do a little bit of +something interesting maybe we'll find + + align:start position:0% +something interesting maybe we'll find + + + align:start position:0% +something interesting maybe we'll find +that printf in Main and jump directly + + align:start position:0% +that printf in Main and jump directly + + + align:start position:0% +that printf in Main and jump directly +there and get it to print the X Val or x + + align:start position:0% +there and get it to print the X Val or x + + + align:start position:0% +there and get it to print the X Val or x +equals something so we can do this we + + align:start position:0% +equals something so we can do this we + + + align:start position:0% +equals something so we can do this we +can actually disassemble the main + + align:start position:0% +can actually disassemble the main + + + align:start position:0% +can actually disassemble the main +function and Main you know does a bunch + + align:start position:0% +function and Main you know does a bunch + + + align:start position:0% +function and Main you know does a bunch +of stuff you know initializes calls + + align:start position:0% +of stuff you know initializes calls + + + align:start position:0% +of stuff you know initializes calls +redirect does some more stuff and then + + align:start position:0% +redirect does some more stuff and then + + + align:start position:0% +redirect does some more stuff and then +calls print F so how about we jump to + + align:start position:0% +calls print F so how about we jump to + + + align:start position:0% +calls print F so how about we jump to +this point which is it sets up the + + align:start position:0% +this point which is it sets up the + + + align:start position:0% +this point which is it sets up the +argument to print F which is x equal + + align:start position:0% +argument to print F which is x equal + + + align:start position:0% +argument to print F which is x equal +perc D and then actually calls print F + + align:start position:0% +perc D and then actually calls print F + + + align:start position:0% +perc D and then actually calls print F +so we can actually take this value and + + align:start position:0% +so we can actually take this value and + + + align:start position:0% +so we can actually take this value and +try to stick it in the + + align:start position:0% +try to stick it in the + + + align:start position:0% +try to stick it in the +stack and um should be able to do this + + align:start position:0% +stack and um should be able to do this + + + align:start position:0% +stack and um should be able to do this +with the debugger pretty easily at least + + align:start position:0% +with the debugger pretty easily at least + + + align:start position:0% +with the debugger pretty easily at least +so you can just do this set int ESP + + align:start position:0% +so you can just do this set int ESP + + + align:start position:0% +so you can just do this set int ESP +equals this value so we can examine ESP + + align:start position:0% +equals this value so we can examine ESP + + + align:start position:0% +equals this value so we can examine ESP +again and indeed it actually has this + + align:start position:0% +again and indeed it actually has this + + + align:start position:0% +again and indeed it actually has this +value so if we continue now well it + + align:start position:0% +value so if we continue now well it + + + align:start position:0% +value so if we continue now well it +printed out x equals some garbage which + + align:start position:0% +printed out x equals some garbage which + + + align:start position:0% +printed out x equals some garbage which +I guess was happens to be just whatever + + align:start position:0% +I guess was happens to be just whatever + + + align:start position:0% +I guess was happens to be just whatever +is in on the stack that was passed to + + align:start position:0% +is in on the stack that was passed to + + + align:start position:0% +is in on the stack that was passed to +print F we didn't L set up all the + + align:start position:0% +print F we didn't L set up all the + + + align:start position:0% +print F we didn't L set up all the +arguments because we jumped in the + + align:start position:0% +arguments because we jumped in the + + + align:start position:0% +arguments because we jumped in the +middle of this calling sequence but yeah + + align:start position:0% +middle of this calling sequence but yeah + + + align:start position:0% +middle of this calling sequence but yeah +we printed this value and then it + + align:start position:0% +we printed this value and then it + + + align:start position:0% +we printed this value and then it +crashed why did it crash Why do you + + align:start position:0% +crashed why did it crash Why do you + + + align:start position:0% +crashed why did it crash Why do you +think what actually happens right so so + + align:start position:0% +think what actually happens right so so + + + align:start position:0% +think what actually happens right so so +we jump to print + + align:start position:0% +we jump to print + + + align:start position:0% +we jump to print +F and then something went wrong yeah + + align:start position:0% +F and then something went wrong yeah + + + align:start position:0% +F and then something went wrong yeah +return + + align:start position:0% +return + + + align:start position:0% +return +address well well we changed the return + + align:start position:0% +address well well we changed the return + + + align:start position:0% +address well well we changed the return +address so that when we return from + + align:start position:0% +address so that when we return from + + + align:start position:0% +address so that when we return from +redre we now jump to this new address + + align:start position:0% +redre we now jump to this new address + + + align:start position:0% +redre we now jump to this new address +which is that point up there right after + + align:start position:0% +which is that point up there right after + + + align:start position:0% +which is that point up there right after +printf so what where's this crash coming + + align:start position:0% +printf so what where's this crash coming + + + align:start position:0% +printf so what where's this crash coming +from + + align:start position:0% +from + + + align:start position:0% +from +from yeah it because your ey is supposed + + align:start position:0% +from yeah it because your ey is supposed + + + align:start position:0% +from yeah it because your ey is supposed +to be some of no well the I is like well + + align:start position:0% +to be some of no well the I is like well + + + align:start position:0% +to be some of no well the I is like well +it's a thir ubit register so whatever is + + align:start position:0% +it's a thir ubit register so whatever is + + + align:start position:0% +it's a thir ubit register so whatever is +in the register it'll print in fact + + align:start position:0% +in the register it'll print in fact + + + align:start position:0% +in the register it'll print in fact +that's the thing that's in the register + + align:start position:0% +that's the thing that's in the register + + + align:start position:0% +that's the thing that's in the register +um so that's okay yeah main returns yeah + + align:start position:0% +um so that's okay yeah main returns yeah + + + align:start position:0% +um so that's okay yeah main returns yeah +actually yeah what's going on is you + + align:start position:0% +actually yeah what's going on is you + + + align:start position:0% +actually yeah what's going on is you +have to sort of see here okay so this is + + align:start position:0% +have to sort of see here okay so this is + + + align:start position:0% +have to sort of see here okay so this is +the point where we jumped it set up some + + align:start position:0% +the point where we jumped it set up some + + + align:start position:0% +the point where we jumped it set up some +arguments it actually calls print F + + align:start position:0% +arguments it actually calls print F + + + align:start position:0% +arguments it actually calls print F +printf seems to work print f is going to + + align:start position:0% +printf seems to work print f is going to + + + align:start position:0% +printf seems to work print f is going to +return that actually that's fine because + + align:start position:0% +return that actually that's fine because + + + align:start position:0% +return that actually that's fine because +this call instruction put a return out + + align:start position:0% +this call instruction put a return out + + + align:start position:0% +this call instruction put a return out +on the stack for printf to use that's + + align:start position:0% +on the stack for printf to use that's + + + align:start position:0% +on the stack for printf to use that's +fine then main is going to continue + + align:start position:0% +fine then main is going to continue + + + align:start position:0% +fine then main is going to continue +running it's going to run the sleeve + + align:start position:0% +running it's going to run the sleeve + + + align:start position:0% +running it's going to run the sleeve +instruction which doesn't do anything + + align:start position:0% +instruction which doesn't do anything + + + align:start position:0% +instruction which doesn't do anything +interesting and then it does another + + align:start position:0% +interesting and then it does another + + + align:start position:0% +interesting and then it does another +return but the thing in this up the + + align:start position:0% +return but the thing in this up the + + + align:start position:0% +return but the thing in this up the +stack doesn't actually have a valid + + align:start position:0% +stack doesn't actually have a valid + + + align:start position:0% +stack doesn't actually have a valid +return address so presumably we return + + align:start position:0% +return address so presumably we return + + + align:start position:0% +return address so presumably we return +to some other who knows what memory + + align:start position:0% +to some other who knows what memory + + + align:start position:0% +to some other who knows what memory +location that's up on the stack and + + align:start position:0% +location that's up on the stack and + + + align:start position:0% +location that's up on the stack and +jumped somewhere else so unfortunately + + align:start position:0% +jumped somewhere else so unfortunately + + + align:start position:0% +jumped somewhere else so unfortunately +here our you know pseudo attack didn't + + align:start position:0% +here our you know pseudo attack didn't + + + align:start position:0% +here our you know pseudo attack didn't +really work it you know rans some code + + align:start position:0% +really work it you know rans some code + + + align:start position:0% +really work it you know rans some code +but then it crashed that's probably not + + align:start position:0% +but then it crashed that's probably not + + + align:start position:0% +but then it crashed that's probably not +something you want to do so if you + + align:start position:0% +something you want to do so if you + + + align:start position:0% +something you want to do so if you +really wanted to be careful you would + + align:start position:0% +really wanted to be careful you would + + + align:start position:0% +really wanted to be careful you would +carefully plant not just return address + + align:start position:0% +carefully plant not just return address + + + align:start position:0% +carefully plant not just return address +up on the stack but maybe you'd figure + + align:start position:0% +up on the stack but maybe you'd figure + + + align:start position:0% +up on the stack but maybe you'd figure +out where is this second red going to + + align:start position:0% +out where is this second red going to + + + align:start position:0% +out where is this second red going to +get its return address from and try to + + align:start position:0% +get its return address from and try to + + + align:start position:0% +get its return address from and try to +carefully Place something else on the + + align:start position:0% +carefully Place something else on the + + + align:start position:0% +carefully Place something else on the +stack there that will ensure that your + + align:start position:0% +stack there that will ensure that your + + + align:start position:0% +stack there that will ensure that your +program cleanly exits after it gets + + align:start position:0% +program cleanly exits after it gets + + + align:start position:0% +program cleanly exits after it gets +exploited so that no one notices um so + + align:start position:0% +exploited so that no one notices um so + + + align:start position:0% +exploited so that no one notices um so +this is all stuff you'll sort of try to + + align:start position:0% +this is all stuff you'll sort of try to + + + align:start position:0% +this is all stuff you'll sort of try to +do in lab one in a little bit more + + align:start position:0% +do in lab one in a little bit more + + + align:start position:0% +do in lab one in a little bit more +detail but um I guess one uh thing we + + align:start position:0% +detail but um I guess one uh thing we + + + align:start position:0% +detail but um I guess one uh thing we +can try to think about now is um you + + align:start position:0% +can try to think about now is um you + + + align:start position:0% +can try to think about now is um you +know we sort of understand why it's bad + + align:start position:0% +know we sort of understand why it's bad + + + align:start position:0% +know we sort of understand why it's bad +to jump to the or to have these buffer + + align:start position:0% +to jump to the or to have these buffer + + + align:start position:0% +to jump to the or to have these buffer +close + + align:start position:0% + + + + align:start position:0% + +um one problem or one sort of way to + + align:start position:0% +um one problem or one sort of way to + + + align:start position:0% +um one problem or one sort of way to +think of this is that the problem is + + align:start position:0% +think of this is that the problem is + + + align:start position:0% +think of this is that the problem is +just because the return address is up + + align:start position:0% +just because the return address is up + + + align:start position:0% +just because the return address is up +there right so the buffer keeps growing + + align:start position:0% +there right so the buffer keeps growing + + + align:start position:0% +there right so the buffer keeps growing +and eventually runs over the return + + align:start position:0% +and eventually runs over the return + + + align:start position:0% +and eventually runs over the return +address what if we flip the stack around + + align:start position:0% +address what if we flip the stack around + + + align:start position:0% +address what if we flip the stack around +you know some machines actually have + + align:start position:0% +you know some machines actually have + + + align:start position:0% +you know some machines actually have +stacks that grow + + align:start position:0% +stacks that grow + + + align:start position:0% +stacks that grow +up so an alternative design we could + + align:start position:0% +up so an alternative design we could + + + align:start position:0% +up so an alternative design we could +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +Imagine is one where the stack starts at + + align:start position:0% +Imagine is one where the stack starts at + + + align:start position:0% +Imagine is one where the stack starts at +the bottom and and keeps going up + + align:start position:0% +the bottom and and keeps going up + + + align:start position:0% +the bottom and and keeps going up +instead of growing down so then if you + + align:start position:0% +instead of growing down so then if you + + + align:start position:0% +instead of growing down so then if you +overflow this buffer you'll just keep + + align:start position:0% +overflow this buffer you'll just keep + + + align:start position:0% +overflow this buffer you'll just keep +going up on the stack and maybe there's + + align:start position:0% +going up on the stack and maybe there's + + + align:start position:0% +going up on the stack and maybe there's +nothing bad that'll happen + + align:start position:0% + + + + align:start position:0% + +yeah so you're right right it might be + + align:start position:0% +yeah so you're right right it might be + + + align:start position:0% +yeah so you're right right it might be +that uh if you have well so let me draw + + align:start position:0% +that uh if you have well so let me draw + + + align:start position:0% +that uh if you have well so let me draw +this new stack diagram and we'll sort of + + align:start position:0% +this new stack diagram and we'll sort of + + + align:start position:0% +this new stack diagram and we'll sort of +try to figure out um what it applies to + + align:start position:0% +try to figure out um what it applies to + + + align:start position:0% +try to figure out um what it applies to +a not but okay so we'll basically just + + align:start position:0% +a not but okay so we'll basically just + + + align:start position:0% +a not but okay so we'll basically just +invert the picture so when you call + + align:start position:0% +invert the picture so when you call + + + align:start position:0% +invert the picture so when you call +redirect on this alternative + + align:start position:0% +redirect on this alternative + + + align:start position:0% +redirect on this alternative +architecture what's going to happen is + + align:start position:0% +architecture what's going to happen is + + + align:start position:0% +architecture what's going to happen is +the return address is going to go here + + align:start position:0% +the return address is going to go here + + + align:start position:0% +the return address is going to go here +on the + + align:start position:0% +on the + + + align:start position:0% +on the +stack then we'll have our I variable or + + align:start position:0% +stack then we'll have our I variable or + + + align:start position:0% +stack then we'll have our I variable or +maybe the save + + align:start position:0% + + + + align:start position:0% + +DBP then we'll have our I variable and + + align:start position:0% +DBP then we'll have our I variable and + + + align:start position:0% +DBP then we'll have our I variable and +then we'll have buff so we'll have buff + + align:start position:0% +then we'll have buff so we'll have buff + + + align:start position:0% +then we'll have buff so we'll have buff +of zero of + + align:start position:0% +of zero of + + + align:start position:0% +of zero of +127 and so on right so then when we do + + align:start position:0% +127 and so on right so then when we do + + + align:start position:0% +127 and so on right so then when we do +the Overflow it overflows up there and + + align:start position:0% +the Overflow it overflows up there and + + + align:start position:0% +the Overflow it overflows up there and +maybe doesn't hit anything bad I guess + + align:start position:0% +maybe doesn't hit anything bad I guess + + + align:start position:0% +maybe doesn't hit anything bad I guess +what you're saying is that well maybe we + + align:start position:0% +what you're saying is that well maybe we + + + align:start position:0% +what you're saying is that well maybe we +had a buffer down there and if we had a + + align:start position:0% +had a buffer down there and if we had a + + + align:start position:0% +had a buffer down there and if we had a +buffer down there then yeah that seems + + align:start position:0% +buffer down there then yeah that seems + + + align:start position:0% +buffer down there then yeah that seems +kind of unfortunate it could overrun + + align:start position:0% +kind of unfortunate it could overrun + + + align:start position:0% +kind of unfortunate it could overrun +this return + + align:start position:0% +this return + + + align:start position:0% +this return +address but so so you're right so you + + align:start position:0% +address but so so you're right so you + + + align:start position:0% +address but so so you're right so you +could still run to problems on this + + align:start position:0% +could still run to problems on this + + + align:start position:0% +could still run to problems on this +stack growing up but what about this + + align:start position:0% +stack growing up but what about this + + + align:start position:0% +stack growing up but what about this +exact + + align:start position:0% + + + + align:start position:0% + +program is this particular program safe + + align:start position:0% +program is this particular program safe + + + align:start position:0% +program is this particular program safe +on machines where the stack grows up so + + align:start position:0% +on machines where the stack grows up so + + + align:start position:0% +on machines where the stack grows up so +just to recap what the program is this + + align:start position:0% +just to recap what the program is this + + + align:start position:0% +just to recap what the program is this +guy yeah over return yeah so that's + + align:start position:0% +guy yeah over return yeah so that's + + + align:start position:0% +guy yeah over return yeah so that's +actually clever right so this is the + + align:start position:0% +actually clever right so this is the + + + align:start position:0% +actually clever right so this is the +stack frame for + + align:start position:0% +stack frame for + + + align:start position:0% +stack frame for +redirect I guess it actually spans all + + align:start position:0% +redirect I guess it actually spans all + + + align:start position:0% +redirect I guess it actually spans all +the way up here but what actually + + align:start position:0% +the way up here but what actually + + + align:start position:0% +the way up here but what actually +happens when you call get us is that + + align:start position:0% +happens when you call get us is that + + + align:start position:0% +happens when you call get us is that +redirect makes a function call it + + align:start position:0% +redirect makes a function call it + + + align:start position:0% +redirect makes a function call it +actually saves its return address up + + align:start position:0% +actually saves its return address up + + + align:start position:0% +actually saves its return address up +here on the stack and then gets starts + + align:start position:0% +here on the stack and then gets starts + + + align:start position:0% +here on the stack and then gets starts +running and gets puts its own save DVP + + align:start position:0% +running and gets puts its own save DVP + + + align:start position:0% +running and gets puts its own save DVP +up here and gets is it's going to put + + align:start position:0% +up here and gets is it's going to put + + + align:start position:0% +up here and gets is it's going to put +its own variables higher up and then + + align:start position:0% +its own variables higher up and then + + + align:start position:0% +its own variables higher up and then +getus is going to fill in the + + align:start position:0% +getus is going to fill in the + + + align:start position:0% +getus is going to fill in the +buffer so this is still problematic + + align:start position:0% +buffer so this is still problematic + + + align:start position:0% +buffer so this is still problematic +basically the buffer is surrounded by + + align:start position:0% +basically the buffer is surrounded by + + + align:start position:0% +basically the buffer is surrounded by +your turnes on all sides it's uh either + + align:start position:0% +your turnes on all sides it's uh either + + + align:start position:0% +your turnes on all sides it's uh either +way you're going to be able to overflow + + align:start position:0% +way you're going to be able to overflow + + + align:start position:0% +way you're going to be able to overflow +something so at what point you know + + align:start position:0% +something so at what point you know + + + align:start position:0% +something so at what point you know +suppose we had a stack growing up + + align:start position:0% +suppose we had a stack growing up + + + align:start position:0% +suppose we had a stack growing up +machine at what point would you of be + + align:start position:0% +machine at what point would you of be + + + align:start position:0% +machine at what point would you of be +able to take control of the program's + + align:start position:0% +able to take control of the program's + + + align:start position:0% +able to take control of the program's +execution + + align:start position:0% + + + + align:start position:0% + +then yeah so now it's actually even + + align:start position:0% +then yeah so now it's actually even + + + align:start position:0% +then yeah so now it's actually even +easier in some ways it's you don't have + + align:start position:0% +easier in some ways it's you don't have + + + align:start position:0% +easier in some ways it's you don't have +to wait until redirect returns and maybe + + align:start position:0% +to wait until redirect returns and maybe + + + align:start position:0% +to wait until redirect returns and maybe +there's like stuff that's going to mess + + align:start position:0% +there's like stuff that's going to mess + + + align:start position:0% +there's like stuff that's going to mess +you up like this a2i no it's actually + + align:start position:0% +you up like this a2i no it's actually + + + align:start position:0% +you up like this a2i no it's actually +easier because gets is going to overflow + + align:start position:0% +easier because gets is going to overflow + + + align:start position:0% +easier because gets is going to overflow +the buffer it's going to change the + + align:start position:0% +the buffer it's going to change the + + + align:start position:0% +the buffer it's going to change the +return address and then immediately + + align:start position:0% +return address and then immediately + + + align:start position:0% +return address and then immediately +return and immediately jump to wherever + + align:start position:0% +return and immediately jump to wherever + + + align:start position:0% +return and immediately jump to wherever +you sort of try to uh + + align:start position:0% +you sort of try to uh + + + align:start position:0% +you sort of try to uh +construct makes sense um so what happens + + align:start position:0% +construct makes sense um so what happens + + + align:start position:0% +construct makes sense um so what happens +if we have uh you know a program like + + align:start position:0% +if we have uh you know a program like + + + align:start position:0% +if we have uh you know a program like +this that's pretty boring there's like + + align:start position:0% +this that's pretty boring there's like + + + align:start position:0% +this that's pretty boring there's like +no real interesting code to jump to all + + align:start position:0% +no real interesting code to jump to all + + + align:start position:0% +no real interesting code to jump to all +you can do is get it to print different + + align:start position:0% +you can do is get it to print different + + + align:start position:0% +you can do is get it to print different +X values here what if you wanted to do + + align:start position:0% +X values here what if you wanted to do + + + align:start position:0% +X values here what if you wanted to do +something interesting that uh you didn't + + align:start position:0% +something interesting that uh you didn't + + + align:start position:0% +something interesting that uh you didn't +yeah I mean if you have an executable + + align:start position:0% +yeah I mean if you have an executable + + + align:start position:0% +yeah I mean if you have an executable +stack you you could put put arbitrary + + align:start position:0% +stack you you could put put arbitrary + + + align:start position:0% +stack you you could put put arbitrary +code that for example execute a shell + + align:start position:0% +code that for example execute a shell + + + align:start position:0% +code that for example execute a shell +yeah yeah so that's kind of clever right + + align:start position:0% +yeah yeah so that's kind of clever right + + + align:start position:0% +yeah yeah so that's kind of clever right +because uh you actually can supply other + + align:start position:0% +because uh you actually can supply other + + + align:start position:0% +because uh you actually can supply other +inputs right so at least uh well there + + align:start position:0% +inputs right so at least uh well there + + + align:start position:0% +inputs right so at least uh well there +are some defenses against this and we'll + + align:start position:0% +are some defenses against this and we'll + + + align:start position:0% +are some defenses against this and we'll +go over these in subsequent lectures but + + align:start position:0% +go over these in subsequent lectures but + + + align:start position:0% +go over these in subsequent lectures but +in principle you could have the return + + align:start position:0% +in principle you could have the return + + + align:start position:0% +in principle you could have the return +address here that you overwrite on + + align:start position:0% +address here that you overwrite on + + + align:start position:0% +address here that you overwrite on +either the stack up or Stack Down + + align:start position:0% +either the stack up or Stack Down + + + align:start position:0% +either the stack up or Stack Down +machine and instead of pointing it to + + align:start position:0% +machine and instead of pointing it to + + + align:start position:0% +machine and instead of pointing it to +some existing code like the printf + + align:start position:0% +some existing code like the printf + + + align:start position:0% +some existing code like the printf +inside of mean we can actually have the + + align:start position:0% +inside of mean we can actually have the + + + align:start position:0% +inside of mean we can actually have the +return address Point into the buffer so + + align:start position:0% +return address Point into the buffer so + + + align:start position:0% +return address Point into the buffer so +it's previously just some location on + + align:start position:0% +it's previously just some location on + + + align:start position:0% +it's previously just some location on +the stack but you could jum there and + + align:start position:0% +the stack but you could jum there and + + + align:start position:0% +the stack but you could jum there and +treat it as executable so as part of + + align:start position:0% +treat it as executable so as part of + + + align:start position:0% +treat it as executable so as part of +your request you'll actually send some + + align:start position:0% +your request you'll actually send some + + + align:start position:0% +your request you'll actually send some +btes of data to the server and then have + + align:start position:0% +btes of data to the server and then have + + + align:start position:0% +btes of data to the server and then have +the return address or the thing you + + align:start position:0% +the return address or the thing you + + + align:start position:0% +the return address or the thing you +overwrite here point to the base of the + + align:start position:0% +overwrite here point to the base of the + + + align:start position:0% +overwrite here point to the base of the +buffer you'll just keep going from there + + align:start position:0% +buffer you'll just keep going from there + + + align:start position:0% +buffer you'll just keep going from there +so then you'll be able to sort of + + align:start position:0% +so then you'll be able to sort of + + + align:start position:0% +so then you'll be able to sort of +provide the code you want to run jump to + + align:start position:0% +provide the code you want to run jump to + + + align:start position:0% +provide the code you want to run jump to +it and get the server to run it and in + + align:start position:0% +it and get the server to run it and in + + + align:start position:0% +it and get the server to run it and in +fact traditionally in Unix systems what + + align:start position:0% +fact traditionally in Unix systems what + + + align:start position:0% +fact traditionally in Unix systems what +adversaries would often do is just ask + + align:start position:0% +adversaries would often do is just ask + + + align:start position:0% +adversaries would often do is just ask +the operating system to execute the bin + + align:start position:0% +the operating system to execute the bin + + + align:start position:0% +the operating system to execute the bin +command which lets you sort of type in + + align:start position:0% +command which lets you sort of type in + + + align:start position:0% +command which lets you sort of type in +arbitrary shell commands after that so + + align:start position:0% +arbitrary shell commands after that so + + + align:start position:0% +arbitrary shell commands after that so +as a result this saying this sort of + + align:start position:0% +as a result this saying this sort of + + + align:start position:0% +as a result this saying this sort of +piece of code you inject into this + + align:start position:0% +piece of code you inject into this + + + align:start position:0% +piece of code you inject into this +buffer was often called uh sort of for + + align:start position:0% +buffer was often called uh sort of for + + + align:start position:0% +buffer was often called uh sort of for +historical reasons Shell Code and you'll + + align:start position:0% +historical reasons Shell Code and you'll + + + align:start position:0% +historical reasons Shell Code and you'll +try to construct some in uh in this lab + + align:start position:0% +try to construct some in uh in this lab + + + align:start position:0% +try to construct some in uh in this lab +one uh as + + align:start position:0% +one uh as + + + align:start position:0% +one uh as +well all right make sense what you can + + align:start position:0% +well all right make sense what you can + + + align:start position:0% +well all right make sense what you can +do here any question yeah there + + align:start position:0% +do here any question yeah there + + + align:start position:0% +do here any question yeah there +separation between code and data right + + align:start position:0% +separation between code and data right + + + align:start position:0% +separation between code and data right +so uh is there a separation between code + + align:start position:0% +so uh is there a separation between code + + + align:start position:0% +so uh is there a separation between code +and data here um at least well + + align:start position:0% +and data here um at least well + + + align:start position:0% +and data here um at least well +historically the ma many machines didn't + + align:start position:0% +historically the ma many machines didn't + + + align:start position:0% +historically the ma many machines didn't +enforce any separation of code and data + + align:start position:0% +enforce any separation of code and data + + + align:start position:0% +enforce any separation of code and data +you just have a flat memory address + + align:start position:0% +you just have a flat memory address + + + align:start position:0% +you just have a flat memory address +space the stack pointer points somewhere + + align:start position:0% +space the stack pointer points somewhere + + + align:start position:0% +space the stack pointer points somewhere +the code pointer points some somewhere + + align:start position:0% +the code pointer points some somewhere + + + align:start position:0% +the code pointer points some somewhere +else and you just execute wherever the + + align:start position:0% +else and you just execute wherever the + + + align:start position:0% +else and you just execute wherever the +code pointer instruction pointer is + + align:start position:0% +code pointer instruction pointer is + + + align:start position:0% +code pointer instruction pointer is +pointing uh modern machines try to + + align:start position:0% +pointing uh modern machines try to + + + align:start position:0% +pointing uh modern machines try to +provide some defenses for these kinds of + + align:start position:0% +provide some defenses for these kinds of + + + align:start position:0% +provide some defenses for these kinds of +attacks and what modern machines often + + align:start position:0% +attacks and what modern machines often + + + align:start position:0% +attacks and what modern machines often +do is they actually associate + + align:start position:0% +do is they actually associate + + + align:start position:0% +do is they actually associate +permissions with various memory regions + + align:start position:0% +permissions with various memory regions + + + align:start position:0% +permissions with various memory regions +and the one of the permissions is + + align:start position:0% +and the one of the permissions is + + + align:start position:0% +and the one of the permissions is +execute so the part of your 32-bit or + + align:start position:0% +execute so the part of your 32-bit or + + + align:start position:0% +execute so the part of your 32-bit or +64-bit address space that contains code + + align:start position:0% +64-bit address space that contains code + + + align:start position:0% +64-bit address space that contains code +has the execute permission so if your + + align:start position:0% +has the execute permission so if your + + + align:start position:0% +has the execute permission so if your +instruction pointer points there the CPU + + align:start position:0% +instruction pointer points there the CPU + + + align:start position:0% +instruction pointer points there the CPU +will actually run those things + + align:start position:0% +will actually run those things + + + align:start position:0% +will actually run those things +and the stack and other data portions of + + align:start position:0% +and the stack and other data portions of + + + align:start position:0% +and the stack and other data portions of +your address space typically don't have + + align:start position:0% +your address space typically don't have + + + align:start position:0% +your address space typically don't have +the execute permission so if you happen + + align:start position:0% +the execute permission so if you happen + + + align:start position:0% +the execute permission so if you happen +to somehow set your instruction pointer + + align:start position:0% +to somehow set your instruction pointer + + + align:start position:0% +to somehow set your instruction pointer +to some non-code memory location you can + + align:start position:0% +to some non-code memory location you can + + + align:start position:0% +to some non-code memory location you can +set it but the CPU will refuse to + + align:start position:0% +set it but the CPU will refuse to + + + align:start position:0% +set it but the CPU will refuse to +execute it uh so this is + + align:start position:0% +execute it uh so this is + + + align:start position:0% +execute it uh so this is +a reasonably nice uh way to defend + + align:start position:0% +a reasonably nice uh way to defend + + + align:start position:0% +a reasonably nice uh way to defend +against these kinds of attacks but it + + align:start position:0% +against these kinds of attacks but it + + + align:start position:0% +against these kinds of attacks but it +doesn't prevent anything quite + + align:start position:0% +doesn't prevent anything quite + + + align:start position:0% +doesn't prevent anything quite +everything so just a question okay so + + align:start position:0% +everything so just a question okay so + + + align:start position:0% +everything so just a question okay so +how would you bypass this if you had + + align:start position:0% +how would you bypass this if you had + + + align:start position:0% +how would you bypass this if you had +this non-executable stack + + align:start position:0% +this non-executable stack + + + align:start position:0% +this non-executable stack +I guess we actually saw this example + + align:start position:0% +I guess we actually saw this example + + + align:start position:0% +I guess we actually saw this example +earlier right when I actually jumped to + + align:start position:0% +earlier right when I actually jumped to + + + align:start position:0% +earlier right when I actually jumped to +the middle of Maine so that was a way + + align:start position:0% +the middle of Maine so that was a way + + + align:start position:0% +the middle of Maine so that was a way +sort of of exploiting this buffer + + align:start position:0% +sort of of exploiting this buffer + + + align:start position:0% +sort of of exploiting this buffer +overflow without having to inject new + + align:start position:0% +overflow without having to inject new + + + align:start position:0% +overflow without having to inject new +code of my own so even if the stack was + + align:start position:0% +code of my own so even if the stack was + + + align:start position:0% +code of my own so even if the stack was +nonexecutable I would still be able to + + align:start position:0% +nonexecutable I would still be able to + + + align:start position:0% +nonexecutable I would still be able to +jump in the middle of main this + + align:start position:0% +jump in the middle of main this + + + align:start position:0% +jump in the middle of main this +particular case it's kind of boring it + + align:start position:0% +particular case it's kind of boring it + + + align:start position:0% +particular case it's kind of boring it +just prints X and crashes but in other + + align:start position:0% +just prints X and crashes but in other + + + align:start position:0% +just prints X and crashes but in other +situations you might have other pieces + + align:start position:0% +situations you might have other pieces + + + align:start position:0% +situations you might have other pieces +of code in your program that are doing + + align:start position:0% +of code in your program that are doing + + + align:start position:0% +of code in your program that are doing +interesting stuff that you really do + + align:start position:0% +interesting stuff that you really do + + + align:start position:0% +interesting stuff that you really do +want to execute and that's sort of + + align:start position:0% +want to execute and that's sort of + + + align:start position:0% +want to execute and that's sort of +called return to Lipsy attacks for again + + align:start position:0% +called return to Lipsy attacks for again + + + align:start position:0% +called return to Lipsy attacks for again +somewhat historic reasons but it is a + + align:start position:0% +somewhat historic reasons but it is a + + + align:start position:0% +somewhat historic reasons but it is a +way to bypass these security measures so + + align:start position:0% +way to bypass these security measures so + + + align:start position:0% +way to bypass these security measures so +in the context of buffer overflows um + + align:start position:0% +in the context of buffer overflows um + + + align:start position:0% +in the context of buffer overflows um +there's not really a clearcut solution + + align:start position:0% +there's not really a clearcut solution + + + align:start position:0% +there's not really a clearcut solution +that provides Perfect protection against + + align:start position:0% +that provides Perfect protection against + + + align:start position:0% +that provides Perfect protection against +these mistakes because at the end of the + + align:start position:0% +these mistakes because at the end of the + + + align:start position:0% +these mistakes because at the end of the +day the programmer did make some mistake + + align:start position:0% +day the programmer did make some mistake + + + align:start position:0% +day the programmer did make some mistake +in writing a source code and so the best + + align:start position:0% +in writing a source code and so the best + + + align:start position:0% +in writing a source code and so the best +way to fix it is probably just to change + + align:start position:0% +way to fix it is probably just to change + + + align:start position:0% +way to fix it is probably just to change +the source code and make sure you don't + + align:start position:0% +the source code and make sure you don't + + + align:start position:0% +the source code and make sure you don't +call get ass very much like the compiler + + align:start position:0% +call get ass very much like the compiler + + + align:start position:0% +call get ass very much like the compiler +warned you and there's more subtle + + align:start position:0% +warned you and there's more subtle + + + align:start position:0% +warned you and there's more subtle +things that the compiler doesn't warn + + align:start position:0% +things that the compiler doesn't warn + + + align:start position:0% +things that the compiler doesn't warn +you about and you still have to avoid + + align:start position:0% +you about and you still have to avoid + + + align:start position:0% +you about and you still have to avoid +making those calls but uh because it's + + align:start position:0% +making those calls but uh because it's + + + align:start position:0% +making those calls but uh because it's +hard in practice to change all the + + align:start position:0% +hard in practice to change all the + + + align:start position:0% +hard in practice to change all the +software out there many people try to + + align:start position:0% +software out there many people try to + + + align:start position:0% +software out there many people try to +devise techniques that make it more + + align:start position:0% +devise techniques that make it more + + + align:start position:0% +devise techniques that make it more +difficult to exploit these bugs for + + align:start position:0% +difficult to exploit these bugs for + + + align:start position:0% +difficult to exploit these bugs for +example making the stack non-executable + + align:start position:0% +example making the stack non-executable + + + align:start position:0% +example making the stack non-executable +so you can't inject the Shell Code onto + + align:start position:0% +so you can't inject the Shell Code onto + + + align:start position:0% +so you can't inject the Shell Code onto +the stack and you have to do something + + align:start position:0% +the stack and you have to do something + + + align:start position:0% +the stack and you have to do something +slightly more elaborate and next uh + + align:start position:0% +slightly more elaborate and next uh + + + align:start position:0% +slightly more elaborate and next uh +couple of lectures next two lectures + + align:start position:0% +couple of lectures next two lectures + + + align:start position:0% +couple of lectures next two lectures +actually we'll look at these defense + + align:start position:0% +actually we'll look at these defense + + + align:start position:0% +actually we'll look at these defense +techniques they're not all perfect but + + align:start position:0% +techniques they're not all perfect but + + + align:start position:0% +techniques they're not all perfect but +they do in practice make it much more + + align:start position:0% +they do in practice make it much more + + + align:start position:0% +they do in practice make it much more +difficult for the haacker to exploit + + align:start position:0% +difficult for the haacker to exploit + + + align:start position:0% +difficult for the haacker to exploit +things was it a general administrative + + align:start position:0% +things was it a general administrative + + + align:start position:0% +things was it a general administrative +question yeah I was wondering if there's + + align:start position:0% +question yeah I was wondering if there's + + + align:start position:0% +question yeah I was wondering if there's +a final and also if there are quizzes + + align:start position:0% +a final and also if there are quizzes + + + align:start position:0% +a final and also if there are quizzes +and what date tomor oh yeah um yeah I + + align:start position:0% +and what date tomor oh yeah um yeah I + + + align:start position:0% +and what date tomor oh yeah um yeah I +think if you go to the schedule page + + align:start position:0% +think if you go to the schedule page + + + align:start position:0% +think if you go to the schedule page +there's yeah there's two quizzes and + + align:start position:0% +there's yeah there's two quizzes and + + + align:start position:0% +there's yeah there's two quizzes and +there's no final during the final week + + align:start position:0% +there's no final during the final week + + + align:start position:0% +there's no final during the final week +but there's a quiz right before it uh so + + align:start position:0% +but there's a quiz right before it uh so + + + align:start position:0% +but there's a quiz right before it uh so +you're free for the final week but + + align:start position:0% +you're free for the final week but + + + align:start position:0% +you're free for the final week but +there's still something at the end of + + align:start position:0% +there's still something at the end of + + + align:start position:0% +there's still something at the end of +the class yeah all right okay so I think + + align:start position:0% +the class yeah all right okay so I think + + + align:start position:0% +the class yeah all right okay so I think +that's probably it for buff overflows I + + align:start position:0% +that's probably it for buff overflows I + + + align:start position:0% +that's probably it for buff overflows I +guess the one uh question is okay so + + align:start position:0% +guess the one uh question is okay so + + + align:start position:0% +guess the one uh question is okay so +what do you do about mechanism problems + + align:start position:0% +what do you do about mechanism problems + + + align:start position:0% +what do you do about mechanism problems +and the general answer is to probably + + align:start position:0% +and the general answer is to probably + + + align:start position:0% +and the general answer is to probably +have fewer mechanisms so as we saw here + + align:start position:0% +have fewer mechanisms so as we saw here + + + align:start position:0% +have fewer mechanisms so as we saw here +if you're relying on every piece of + + align:start position:0% +if you're relying on every piece of + + + align:start position:0% +if you're relying on every piece of +software to enforce your security policy + + align:start position:0% +software to enforce your security policy + + + align:start position:0% +software to enforce your security policy +you'll inevitably have mistakes that + + align:start position:0% +you'll inevitably have mistakes that + + + align:start position:0% +you'll inevitably have mistakes that +allow an adversary to bypass your + + align:start position:0% +allow an adversary to bypass your + + + align:start position:0% +allow an adversary to bypass your +mechanism to exploit some bug in the web + + align:start position:0% +mechanism to exploit some bug in the web + + + align:start position:0% +mechanism to exploit some bug in the web +server and a much better design and one + + align:start position:0% +server and a much better design and one + + + align:start position:0% +server and a much better design and one +that you'll explore in lab two is one + + align:start position:0% +that you'll explore in lab two is one + + + align:start position:0% +that you'll explore in lab two is one +where you structure your whole system so + + align:start position:0% +where you structure your whole system so + + + align:start position:0% +where you structure your whole system so +the security of the system doesn't + + align:start position:0% +the security of the system doesn't + + + align:start position:0% +the security of the system doesn't +depend on all the pieces of software + + align:start position:0% +depend on all the pieces of software + + + align:start position:0% +depend on all the pieces of software +enforcing your security policy the + + align:start position:0% +enforcing your security policy the + + + align:start position:0% +enforcing your security policy the +security policy is going to be enforced + + align:start position:0% +security policy is going to be enforced + + + align:start position:0% +security policy is going to be enforced +by a small number of components and the + + align:start position:0% +by a small number of components and the + + + align:start position:0% +by a small number of components and the +rest of the stuff actually doesn't + + align:start position:0% +rest of the stuff actually doesn't + + + align:start position:0% +rest of the stuff actually doesn't +matter for security purposes if it's + + align:start position:0% +matter for security purposes if it's + + + align:start position:0% +matter for security purposes if it's +right or wrong it's not going to violate + + align:start position:0% +right or wrong it's not going to violate + + + align:start position:0% +right or wrong it's not going to violate +your security policy at all so this kind + + align:start position:0% +your security policy at all so this kind + + + align:start position:0% +your security policy at all so this kind +of sort of minimizing your trusted + + align:start position:0% +of sort of minimizing your trusted + + + align:start position:0% +of sort of minimizing your trusted +Computing base is a pretty powerful + + align:start position:0% +Computing base is a pretty powerful + + + align:start position:0% +Computing base is a pretty powerful +technique to get around these mechanism + + align:start position:0% +technique to get around these mechanism + + + align:start position:0% +technique to get around these mechanism +bugs and problems that we've looked at + + align:start position:0% +bugs and problems that we've looked at + + + align:start position:0% +bugs and problems that we've looked at +today at least in a little bit of detail + + align:start position:0% +today at least in a little bit of detail + + + align:start position:0% +today at least in a little bit of detail +all right so read the paper for Monday + + align:start position:0% +all right so read the paper for Monday + + + align:start position:0% +all right so read the paper for Monday +and come to Monday's lecture and submit + + align:start position:0% +and come to Monday's lecture and submit + + + align:start position:0% +and come to Monday's lecture and submit +the questions on the website see you + + align:start position:0% +the questions on the website see you + + + align:start position:0% +the questions on the website see you +guys then \ No newline at end of file diff --git a/HDvYPl8D8Bs.txt b/HDvYPl8D8Bs.txt new file mode 100644 index 0000000000000000000000000000000000000000..da4753937c214888f8a85e922e3b06e763733cc0 --- /dev/null +++ b/HDvYPl8D8Bs.txt @@ -0,0 +1,339 @@ +align:start position:0% + +in this lecture we discussed the + + align:start position:0% +in this lecture we discussed the + + + align:start position:0% +in this lecture we discussed the +simplest non-trivial stochastic process + + align:start position:0% +simplest non-trivial stochastic process + + + align:start position:0% +simplest non-trivial stochastic process +the Bernoulli process time is divided + + align:start position:0% +the Bernoulli process time is divided + + + align:start position:0% +the Bernoulli process time is divided +into slots at each slot we have an + + align:start position:0% +into slots at each slot we have an + + + align:start position:0% +into slots at each slot we have an +independent trial such as a coin flip + + align:start position:0% +independent trial such as a coin flip + + + align:start position:0% +independent trial such as a coin flip +and each trial results in heads or tails + + align:start position:0% +and each trial results in heads or tails + + + align:start position:0% +and each trial results in heads or tails +or in different language each trial may + + align:start position:0% +or in different language each trial may + + + align:start position:0% +or in different language each trial may +or may not result in an arrival or a + + align:start position:0% +or may not result in an arrival or a + + + align:start position:0% +or may not result in an arrival or a +success + + align:start position:0% +success + + + align:start position:0% +success +pretty much everything we will do will + + align:start position:0% +pretty much everything we will do will + + + align:start position:0% +pretty much everything we will do will +be a simple application of skills that + + align:start position:0% +be a simple application of skills that + + + align:start position:0% +be a simple application of skills that +we already have for example we already + + align:start position:0% +we already have for example we already + + + align:start position:0% +we already have for example we already +know that the number of arrivals in n + + align:start position:0% +know that the number of arrivals in n + + + align:start position:0% +know that the number of arrivals in n +time slots is described by the binomial + + align:start position:0% +time slots is described by the binomial + + + align:start position:0% +time slots is described by the binomial +PMF we will then discuss some + + align:start position:0% +PMF we will then discuss some + + + align:start position:0% +PMF we will then discuss some +consequences of the independence of the + + align:start position:0% +consequences of the independence of the + + + align:start position:0% +consequences of the independence of the +different trials basically the process + + align:start position:0% +different trials basically the process + + + align:start position:0% +different trials basically the process +has no memory whatever happens in the + + align:start position:0% +has no memory whatever happens in the + + + align:start position:0% +has no memory whatever happens in the +future is not affected by whatever + + align:start position:0% +future is not affected by whatever + + + align:start position:0% +future is not affected by whatever +happened in the past by exploiting this + + align:start position:0% +happened in the past by exploiting this + + + align:start position:0% +happened in the past by exploiting this +property we will find the distribution + + align:start position:0% +property we will find the distribution + + + align:start position:0% +property we will find the distribution +of the time of the first arrival and + + align:start position:0% +of the time of the first arrival and + + + align:start position:0% +of the time of the first arrival and +more generally of the time of the caithe + + align:start position:0% +more generally of the time of the caithe + + + align:start position:0% +more generally of the time of the caithe +arrival we will also find the + + align:start position:0% +arrival we will also find the + + + align:start position:0% +arrival we will also find the +distribution of the time between + + align:start position:0% +distribution of the time between + + + align:start position:0% +distribution of the time between +consecutive arrivals next we will take + + align:start position:0% +consecutive arrivals next we will take + + + align:start position:0% +consecutive arrivals next we will take +two independent Bernoulli processes + + align:start position:0% +two independent Bernoulli processes + + + align:start position:0% +two independent Bernoulli processes +let's say arrivals of men and arrivals + + align:start position:0% +let's say arrivals of men and arrivals + + + align:start position:0% +let's say arrivals of men and arrivals +of women and merge them to get an + + align:start position:0% +of women and merge them to get an + + + align:start position:0% +of women and merge them to get an +overall arrival process we will see that + + align:start position:0% +overall arrival process we will see that + + + align:start position:0% +overall arrival process we will see that +the merged process is also a Bernoulli + + align:start position:0% +the merged process is also a Bernoulli + + + align:start position:0% +the merged process is also a Bernoulli +process we will also look at the reverse + + align:start position:0% +process we will also look at the reverse + + + align:start position:0% +process we will also look at the reverse +operation namely splitting a Bernoulli + + align:start position:0% +operation namely splitting a Bernoulli + + + align:start position:0% +operation namely splitting a Bernoulli +process into two separate processes + + align:start position:0% +process into two separate processes + + + align:start position:0% +process into two separate processes +finally we will look at a particular + + align:start position:0% +finally we will look at a particular + + + align:start position:0% +finally we will look at a particular +asymptotic regime in which we have a + + align:start position:0% +asymptotic regime in which we have a + + + align:start position:0% +asymptotic regime in which we have a +large number of time slots but a very + + align:start position:0% +large number of time slots but a very + + + align:start position:0% +large number of time slots but a very +small probability of an arrival during + + align:start position:0% +small probability of an arrival during + + + align:start position:0% +small probability of an arrival during +each time slot we will carry out some + + align:start position:0% +each time slot we will carry out some + + + align:start position:0% +each time slot we will carry out some +algebraic manipulations and we will see + + align:start position:0% +algebraic manipulations and we will see + + + align:start position:0% +algebraic manipulations and we will see +that the binomial PMF for the number of + + align:start position:0% +that the binomial PMF for the number of + + + align:start position:0% +that the binomial PMF for the number of +arrivals can be well approximated by the + + align:start position:0% +arrivals can be well approximated by the + + + align:start position:0% +arrivals can be well approximated by the +so-called Poisson PMF \ No newline at end of file diff --git a/J7DzL2_Na80.txt b/J7DzL2_Na80.txt new file mode 100644 index 0000000000000000000000000000000000000000..35f7d75f78a3d808eb3b7a9dc5ad30d609e34811 --- /dev/null +++ b/J7DzL2_Na80.txt @@ -0,0 +1,5283 @@ +align:start position:0% + +hi this is the first lecture in MIT s + + align:start position:0% +hi this is the first lecture in MIT s + + + align:start position:0% +hi this is the first lecture in MIT s +course 1806 linear algebra and I'm + + align:start position:0% +course 1806 linear algebra and I'm + + + align:start position:0% +course 1806 linear algebra and I'm +Gilbert Strang the text for the course + + align:start position:0% +Gilbert Strang the text for the course + + + align:start position:0% +Gilbert Strang the text for the course +is this book introduction to linear + + align:start position:0% +is this book introduction to linear + + + align:start position:0% +is this book introduction to linear +algebra and the course web page which + + align:start position:0% +algebra and the course web page which + + + align:start position:0% +algebra and the course web page which +has got a lot of exercises from the past + + align:start position:0% +has got a lot of exercises from the past + + + align:start position:0% +has got a lot of exercises from the past +MATLAB codes the syllabus for the course + + align:start position:0% +MATLAB codes the syllabus for the course + + + align:start position:0% +MATLAB codes the syllabus for the course +is webbed on mit.edu slash 18 point oh + + align:start position:0% +is webbed on mit.edu slash 18 point oh + + + align:start position:0% +is webbed on mit.edu slash 18 point oh +six and this is the first lecture + + align:start position:0% +six and this is the first lecture + + + align:start position:0% +six and this is the first lecture +lecture one so and later we'll say where + + align:start position:0% +lecture one so and later we'll say where + + + align:start position:0% +lecture one so and later we'll say where +which will give the web address for + + align:start position:0% +which will give the web address for + + + align:start position:0% +which will give the web address for +viewing these videotapes okay so what's + + align:start position:0% +viewing these videotapes okay so what's + + + align:start position:0% +viewing these videotapes okay so what's +in the first lecture this is my plan the + + align:start position:0% +in the first lecture this is my plan the + + + align:start position:0% +in the first lecture this is my plan the +fundamental problem of linear algebra + + align:start position:0% +fundamental problem of linear algebra + + + align:start position:0% +fundamental problem of linear algebra +which is to solve a system of linear + + align:start position:0% +which is to solve a system of linear + + + align:start position:0% +which is to solve a system of linear +equations so let's start with the case + + align:start position:0% +equations so let's start with the case + + + align:start position:0% +equations so let's start with the case +when we have some number of equations + + align:start position:0% +when we have some number of equations + + + align:start position:0% +when we have some number of equations +say n equations and n unknowns so an + + align:start position:0% +say n equations and n unknowns so an + + + align:start position:0% +say n equations and n unknowns so an +equal number of equations and unknowns + + align:start position:0% +equal number of equations and unknowns + + + align:start position:0% +equal number of equations and unknowns +that's the normal nice case and what I + + align:start position:0% +that's the normal nice case and what I + + + align:start position:0% +that's the normal nice case and what I +want to do is with examples of course to + + align:start position:0% +want to do is with examples of course to + + + align:start position:0% +want to do is with examples of course to +describe first what I call the role + + align:start position:0% +describe first what I call the role + + + align:start position:0% +describe first what I call the role +picture that's the picture of one + + align:start position:0% +picture that's the picture of one + + + align:start position:0% +picture that's the picture of one +equation at a time it's the picture + + align:start position:0% +equation at a time it's the picture + + + align:start position:0% +equation at a time it's the picture +you've seen before in two by two + + align:start position:0% +you've seen before in two by two + + + align:start position:0% +you've seen before in two by two +equations where lines meet so in a + + align:start position:0% +equations where lines meet so in a + + + align:start position:0% +equations where lines meet so in a +minute you'll see lines meeting the + + align:start position:0% +minute you'll see lines meeting the + + + align:start position:0% +minute you'll see lines meeting the +second picture well I put a star beside + + align:start position:0% +second picture well I put a star beside + + + align:start position:0% +second picture well I put a star beside +that because that's such an important + + align:start position:0% +that because that's such an important + + + align:start position:0% +that because that's such an important +one and maybe new to you is the picture + + align:start position:0% +one and maybe new to you is the picture + + + align:start position:0% +one and maybe new to you is the picture +a column at a time and those are the + + align:start position:0% +a column at a time and those are the + + + align:start position:0% +a column at a time and those are the +rows and columns of a matrix so the + + align:start position:0% +rows and columns of a matrix so the + + + align:start position:0% +rows and columns of a matrix so the +third the algebra way to look at the + + align:start position:0% +third the algebra way to look at the + + + align:start position:0% +third the algebra way to look at the +problem is the matrix form in using a + + align:start position:0% +problem is the matrix form in using a + + + align:start position:0% +problem is the matrix form in using a +matrix that I'll call a + + align:start position:0% +matrix that I'll call a + + + align:start position:0% +matrix that I'll call a +okay so can I do an example the whole + + align:start position:0% +okay so can I do an example the whole + + + align:start position:0% +okay so can I do an example the whole +semester we'll be examples and then see + + align:start position:0% +semester we'll be examples and then see + + + align:start position:0% +semester we'll be examples and then see +what's going on with it with the example + + align:start position:0% +what's going on with it with the example + + + align:start position:0% +what's going on with it with the example +so take an example two equations two + + align:start position:0% +so take an example two equations two + + + align:start position:0% +so take an example two equations two +unknowns so let me take 2x minus y + + align:start position:0% +unknowns so let me take 2x minus y + + + align:start position:0% +unknowns so let me take 2x minus y +equals zero let's say and minus X plus + + align:start position:0% +equals zero let's say and minus X plus + + + align:start position:0% +equals zero let's say and minus X plus +say two y equals three + + align:start position:0% +say two y equals three + + + align:start position:0% +say two y equals three +okay look I can even say right away + + align:start position:0% +okay look I can even say right away + + + align:start position:0% +okay look I can even say right away +what's the matrix that that is what's + + align:start position:0% +what's the matrix that that is what's + + + align:start position:0% +what's the matrix that that is what's +the coefficient matrix the matrix that + + align:start position:0% +the coefficient matrix the matrix that + + + align:start position:0% +the coefficient matrix the matrix that +involves these numbers a matrix is just + + align:start position:0% +involves these numbers a matrix is just + + + align:start position:0% +involves these numbers a matrix is just +a rectangular array of numbers here the + + align:start position:0% +a rectangular array of numbers here the + + + align:start position:0% +a rectangular array of numbers here the +here it's two rows and two columns so + + align:start position:0% +here it's two rows and two columns so + + + align:start position:0% +here it's two rows and two columns so +two and minus one in the first row minus + + align:start position:0% +two and minus one in the first row minus + + + align:start position:0% +two and minus one in the first row minus +1 and 2 in the second row that's the + + align:start position:0% +1 and 2 in the second row that's the + + + align:start position:0% +1 and 2 in the second row that's the +matrix and the right-hand the unknown + + align:start position:0% +matrix and the right-hand the unknown + + + align:start position:0% +matrix and the right-hand the unknown +well we've got two unknowns so we've got + + align:start position:0% +well we've got two unknowns so we've got + + + align:start position:0% +well we've got two unknowns so we've got +a vector X with two components x and y + + align:start position:0% +a vector X with two components x and y + + + align:start position:0% +a vector X with two components x and y +and we've got two right-hand sides that + + align:start position:0% +and we've got two right-hand sides that + + + align:start position:0% +and we've got two right-hand sides that +go into a vector 0 3 + + align:start position:0% +go into a vector 0 3 + + + align:start position:0% +go into a vector 0 3 +I couldn't resist writing the matrix + + align:start position:0% +I couldn't resist writing the matrix + + + align:start position:0% +I couldn't resist writing the matrix +form right or even before the before the + + align:start position:0% +form right or even before the before the + + + align:start position:0% +form right or even before the before the +pictures so I always will think of this + + align:start position:0% +pictures so I always will think of this + + + align:start position:0% +pictures so I always will think of this +as the matrix a the matrix of + + align:start position:0% +as the matrix a the matrix of + + + align:start position:0% +as the matrix a the matrix of +coefficients then there's a vector of + + align:start position:0% +coefficients then there's a vector of + + + align:start position:0% +coefficients then there's a vector of +unknowns here we've only got two + + align:start position:0% +unknowns here we've only got two + + + align:start position:0% +unknowns here we've only got two +unknowns later we'll have any number of + + align:start position:0% +unknowns later we'll have any number of + + + align:start position:0% +unknowns later we'll have any number of +unknowns and that vector of unknowns + + align:start position:0% +unknowns and that vector of unknowns + + + align:start position:0% +unknowns and that vector of unknowns +well I'll often I'll make that X extra + + align:start position:0% +well I'll often I'll make that X extra + + + align:start position:0% +well I'll often I'll make that X extra +lot extra bold and the right-hand side + + align:start position:0% +lot extra bold and the right-hand side + + + align:start position:0% +lot extra bold and the right-hand side +is also a vector that I'll always call B + + align:start position:0% +is also a vector that I'll always call B + + + align:start position:0% +is also a vector that I'll always call B +so linear equations are ax equal B and + + align:start position:0% +so linear equations are ax equal B and + + + align:start position:0% +so linear equations are ax equal B and +the idea now is to solve this particular + + align:start position:0% +the idea now is to solve this particular + + + align:start position:0% +the idea now is to solve this particular +example and then step back to see the + + align:start position:0% +example and then step back to see the + + + align:start position:0% +example and then step back to see the +bigger picture ok what's the picture for + + align:start position:0% +bigger picture ok what's the picture for + + + align:start position:0% +bigger picture ok what's the picture for +this example the row picture okay so + + align:start position:0% +this example the row picture okay so + + + align:start position:0% +this example the row picture okay so +here comes the rope + + align:start position:0% + + + + align:start position:0% + +so that means I take one row at a time + + align:start position:0% +so that means I take one row at a time + + + align:start position:0% +so that means I take one row at a time +and I'm drawing here the XY plane and + + align:start position:0% +and I'm drawing here the XY plane and + + + align:start position:0% +and I'm drawing here the XY plane and +I'm gonna put plot all the points that + + align:start position:0% +I'm gonna put plot all the points that + + + align:start position:0% +I'm gonna put plot all the points that +satisfy that first equation so I'm + + align:start position:0% +satisfy that first equation so I'm + + + align:start position:0% +satisfy that first equation so I'm +looking at all the points that satisfy + + align:start position:0% +looking at all the points that satisfy + + + align:start position:0% +looking at all the points that satisfy +2x minus y equals zero I'm often it's + + align:start position:0% +2x minus y equals zero I'm often it's + + + align:start position:0% +2x minus y equals zero I'm often it's +often good to start with which point on + + align:start position:0% +often good to start with which point on + + + align:start position:0% +often good to start with which point on +the horizontal line on this horizontal + + align:start position:0% +the horizontal line on this horizontal + + + align:start position:0% +the horizontal line on this horizontal +line y is zero the x axis has y is zero + + align:start position:0% +line y is zero the x axis has y is zero + + + align:start position:0% +line y is zero the x axis has y is zero +and that in this case actually then x is + + align:start position:0% +and that in this case actually then x is + + + align:start position:0% +and that in this case actually then x is +zero so the point the origin the point + + align:start position:0% +zero so the point the origin the point + + + align:start position:0% +zero so the point the origin the point +with coordinates 0 0 is on the line it + + align:start position:0% +with coordinates 0 0 is on the line it + + + align:start position:0% +with coordinates 0 0 is on the line it +solves that equation okay tell me and + + align:start position:0% +solves that equation okay tell me and + + + align:start position:0% +solves that equation okay tell me and +well I guess I have to tell you another + + align:start position:0% +well I guess I have to tell you another + + + align:start position:0% +well I guess I have to tell you another +point that solves this same equation let + + align:start position:0% +point that solves this same equation let + + + align:start position:0% +point that solves this same equation let +me suppose X is 1 so I'll take X to be 1 + + align:start position:0% +me suppose X is 1 so I'll take X to be 1 + + + align:start position:0% +me suppose X is 1 so I'll take X to be 1 +then Y should be 2 right so there's the + + align:start position:0% +then Y should be 2 right so there's the + + + align:start position:0% +then Y should be 2 right so there's the +point 1 2 that also solves this equation + + align:start position:0% +point 1 2 that also solves this equation + + + align:start position:0% +point 1 2 that also solves this equation +then I could put in more points by that + + align:start position:0% +then I could put in more points by that + + + align:start position:0% +then I could put in more points by that +but let me put in all the points at once + + align:start position:0% +but let me put in all the points at once + + + align:start position:0% +but let me put in all the points at once +because they all lie on a straight line + + align:start position:0% +because they all lie on a straight line + + + align:start position:0% +because they all lie on a straight line +this is a linear equation and that word + + align:start position:0% +this is a linear equation and that word + + + align:start position:0% +this is a linear equation and that word +linear we've got the letters for line in + + align:start position:0% +linear we've got the letters for line in + + + align:start position:0% +linear we've got the letters for line in +it that's the equation that's this is + + align:start position:0% +it that's the equation that's this is + + + align:start position:0% +it that's the equation that's this is +the line that of the of solutions to 2x + + align:start position:0% +the line that of the of solutions to 2x + + + align:start position:0% +the line that of the of solutions to 2x +minus y equals 0 my first row first + + align:start position:0% +minus y equals 0 my first row first + + + align:start position:0% +minus y equals 0 my first row first +equation so typically maybe X equal 1/2 + + align:start position:0% +equation so typically maybe X equal 1/2 + + + align:start position:0% +equation so typically maybe X equal 1/2 +y equal 1 will work and it's sure enough + + align:start position:0% +y equal 1 will work and it's sure enough + + + align:start position:0% +y equal 1 will work and it's sure enough +it does ok that's the first one now the + + align:start position:0% +it does ok that's the first one now the + + + align:start position:0% +it does ok that's the first one now the +second one is not going to go through + + align:start position:0% +second one is not going to go through + + + align:start position:0% +second one is not going to go through +the origin + + align:start position:0% +the origin + + + align:start position:0% +the origin +it's always the important do we go + + align:start position:0% +it's always the important do we go + + + align:start position:0% +it's always the important do we go +through the origin or not in this case + + align:start position:0% +through the origin or not in this case + + + align:start position:0% +through the origin or not in this case +yes because there's a 0 over there in + + align:start position:0% +yes because there's a 0 over there in + + + align:start position:0% +yes because there's a 0 over there in +this case we don't go through the origin + + align:start position:0% +this case we don't go through the origin + + + align:start position:0% +this case we don't go through the origin +because if x and y are 0 we don't get 3 + + align:start position:0% +because if x and y are 0 we don't get 3 + + + align:start position:0% +because if x and y are 0 we don't get 3 +so let me again say suppose Y is + + align:start position:0% +so let me again say suppose Y is + + + align:start position:0% +so let me again say suppose Y is +zero what X do we actually get if Y is + + align:start position:0% +zero what X do we actually get if Y is + + + align:start position:0% +zero what X do we actually get if Y is +zero then I get X is minus three so if Y + + align:start position:0% +zero then I get X is minus three so if Y + + + align:start position:0% +zero then I get X is minus three so if Y +is zero I go along minus three so + + align:start position:0% +is zero I go along minus three so + + + align:start position:0% +is zero I go along minus three so +there's one point on this second line + + align:start position:0% +there's one point on this second line + + + align:start position:0% +there's one point on this second line +now let me say well suppose X is minus + + align:start position:0% +now let me say well suppose X is minus + + + align:start position:0% +now let me say well suppose X is minus +one just to take another X if X is minus + + align:start position:0% +one just to take another X if X is minus + + + align:start position:0% +one just to take another X if X is minus +one then this is a 1 and I think Y + + align:start position:0% +one then this is a 1 and I think Y + + + align:start position:0% +one then this is a 1 and I think Y +should be a 1 because if X is minus 1 + + align:start position:0% +should be a 1 because if X is minus 1 + + + align:start position:0% +should be a 1 because if X is minus 1 +then I think why should be a 1 and we'll + + align:start position:0% +then I think why should be a 1 and we'll + + + align:start position:0% +then I think why should be a 1 and we'll +get that point is that right if X is + + align:start position:0% +get that point is that right if X is + + + align:start position:0% +get that point is that right if X is +minus 1 that's a 1 if Y is a 1 that's a + + align:start position:0% +minus 1 that's a 1 if Y is a 1 that's a + + + align:start position:0% +minus 1 that's a 1 if Y is a 1 that's a +2 and the 1 and the 2 make 3 and that + + align:start position:0% +2 and the 1 and the 2 make 3 and that + + + align:start position:0% +2 and the 1 and the 2 make 3 and that +points on the equation ok now I should + + align:start position:0% +points on the equation ok now I should + + + align:start position:0% +points on the equation ok now I should +just draw the line right connecting + + align:start position:0% +just draw the line right connecting + + + align:start position:0% +just draw the line right connecting +those two points that depth will give me + + align:start position:0% +those two points that depth will give me + + + align:start position:0% +those two points that depth will give me +the whole line and if I've done this + + align:start position:0% +the whole line and if I've done this + + + align:start position:0% +the whole line and if I've done this +reasonably well I think it's going to + + align:start position:0% +reasonably well I think it's going to + + + align:start position:0% +reasonably well I think it's going to +happen to go through + + align:start position:0% +happen to go through + + + align:start position:0% +happen to go through +well not happen it was arranged to go + + align:start position:0% +well not happen it was arranged to go + + + align:start position:0% +well not happen it was arranged to go +through that point so I think that the + + align:start position:0% +through that point so I think that the + + + align:start position:0% +through that point so I think that the +second line is this one and this is the + + align:start position:0% +second line is this one and this is the + + + align:start position:0% +second line is this one and this is the +all-important point that lies on both + + align:start position:0% +all-important point that lies on both + + + align:start position:0% +all-important point that lies on both +lines shall we just checked at that + + align:start position:0% +lines shall we just checked at that + + + align:start position:0% +lines shall we just checked at that +point which which is the point X equal 1 + + align:start position:0% +point which which is the point X equal 1 + + + align:start position:0% +point which which is the point X equal 1 +and Y was two right that's the point + + align:start position:0% +and Y was two right that's the point + + + align:start position:0% +and Y was two right that's the point +there and that I believe solves both + + align:start position:0% +there and that I believe solves both + + + align:start position:0% +there and that I believe solves both +equations let's just check this if X is + + align:start position:0% +equations let's just check this if X is + + + align:start position:0% +equations let's just check this if X is +1 I have a minus 1 plus 4 equals 3 okay + + align:start position:0% +1 I have a minus 1 plus 4 equals 3 okay + + + align:start position:0% +1 I have a minus 1 plus 4 equals 3 okay +apologies for drawing this picture that + + align:start position:0% +apologies for drawing this picture that + + + align:start position:0% +apologies for drawing this picture that +you've seen before but this seeing the + + align:start position:0% +you've seen before but this seeing the + + + align:start position:0% +you've seen before but this seeing the +row picture first of all for n equal to + + align:start position:0% +row picture first of all for n equal to + + + align:start position:0% +row picture first of all for n equal to +2 equations in two unknowns it's the + + align:start position:0% +2 equations in two unknowns it's the + + + align:start position:0% +2 equations in two unknowns it's the +right place to start + + align:start position:0% +right place to start + + + align:start position:0% +right place to start +ok so we've got the solution the point + + align:start position:0% +ok so we've got the solution the point + + + align:start position:0% +ok so we've got the solution the point +that lies on both lines now can I come + + align:start position:0% +that lies on both lines now can I come + + + align:start position:0% +that lies on both lines now can I come +to the column picture pay attention this + + align:start position:0% +to the column picture pay attention this + + + align:start position:0% +to the column picture pay attention this +is the P point so the column picture I'm + + align:start position:0% +is the P point so the column picture I'm + + + align:start position:0% +is the P point so the column picture I'm +now going to look at the columns of the + + align:start position:0% +now going to look at the columns of the + + + align:start position:0% +now going to look at the columns of the +matrix I'm going to look at this part + + align:start position:0% +matrix I'm going to look at this part + + + align:start position:0% +matrix I'm going to look at this part +and this part I'm gonna say that that + + align:start position:0% +and this part I'm gonna say that that + + + align:start position:0% +and this part I'm gonna say that that +the X part is really so so is really x + + align:start position:0% +the X part is really so so is really x + + + align:start position:0% +the X part is really so so is really x +times you see I'm putting the two I'm + + align:start position:0% +times you see I'm putting the two I'm + + + align:start position:0% +times you see I'm putting the two I'm +kind of getting the two equations at + + align:start position:0% +kind of getting the two equations at + + + align:start position:0% +kind of getting the two equations at +once that part and then I have a y and + + align:start position:0% +once that part and then I have a y and + + + align:start position:0% +once that part and then I have a y and +and in the first equation it's + + align:start position:0% +and in the first equation it's + + + align:start position:0% +and in the first equation it's +multiplying a minus 1 and in second + + align:start position:0% +multiplying a minus 1 and in second + + + align:start position:0% +multiplying a minus 1 and in second +equation a 2 and on the right hand side + + align:start position:0% +equation a 2 and on the right hand side + + + align:start position:0% +equation a 2 and on the right hand side +0 and 3 you see the columns of the + + align:start position:0% +0 and 3 you see the columns of the + + + align:start position:0% +0 and 3 you see the columns of the +matrix the columns of a are here and the + + align:start position:0% +matrix the columns of a are here and the + + + align:start position:0% +matrix the columns of a are here and the +right-hand side B is there and now what + + align:start position:0% +right-hand side B is there and now what + + + align:start position:0% +right-hand side B is there and now what +is the equation asking for it's asking + + align:start position:0% +is the equation asking for it's asking + + + align:start position:0% +is the equation asking for it's asking +us to find some how to combine that + + align:start position:0% +us to find some how to combine that + + + align:start position:0% +us to find some how to combine that +vector and this one in the right amounts + + align:start position:0% +vector and this one in the right amounts + + + align:start position:0% +vector and this one in the right amounts +to get that one it's asking us to find + + align:start position:0% +to get that one it's asking us to find + + + align:start position:0% +to get that one it's asking us to find +the right linear combination this is + + align:start position:0% +the right linear combination this is + + + align:start position:0% +the right linear combination this is +called a linear combination and it's the + + align:start position:0% +called a linear combination and it's the + + + align:start position:0% +called a linear combination and it's the +most fundamental operation in the whole + + align:start position:0% +most fundamental operation in the whole + + + align:start position:0% +most fundamental operation in the whole +course it's a linear combination of the + + align:start position:0% +course it's a linear combination of the + + + align:start position:0% +course it's a linear combination of the +columns that's what we're seeing on the + + align:start position:0% +columns that's what we're seeing on the + + + align:start position:0% +columns that's what we're seeing on the +left side again I don't want to write + + align:start position:0% +left side again I don't want to write + + + align:start position:0% +left side again I don't want to write +down a big definition you can see what + + align:start position:0% +down a big definition you can see what + + + align:start position:0% +down a big definition you can see what +it is + + align:start position:0% +it is + + + align:start position:0% +it is +there's column one there's column two I + + align:start position:0% +there's column one there's column two I + + + align:start position:0% +there's column one there's column two I +multiply by some numbers and I add + + align:start position:0% +multiply by some numbers and I add + + + align:start position:0% +multiply by some numbers and I add +that's a combination a linear + + align:start position:0% +that's a combination a linear + + + align:start position:0% +that's a combination a linear +combination and I want to make those + + align:start position:0% +combination and I want to make those + + + align:start position:0% +combination and I want to make those +numbers the right numbers to produce 0 3 + + align:start position:0% +numbers the right numbers to produce 0 3 + + + align:start position:0% +numbers the right numbers to produce 0 3 +ok now I want to draw a picture that + + align:start position:0% +ok now I want to draw a picture that + + + align:start position:0% +ok now I want to draw a picture that +represents what this this is algebra + + align:start position:0% +represents what this this is algebra + + + align:start position:0% +represents what this this is algebra +what's the geometry what's the picture + + align:start position:0% +what's the geometry what's the picture + + + align:start position:0% +what's the geometry what's the picture +that goes with it ok so again these + + align:start position:0% +that goes with it ok so again these + + + align:start position:0% +that goes with it ok so again these +vectors have two components so I better + + align:start position:0% +vectors have two components so I better + + + align:start position:0% +vectors have two components so I better +draw a picture like that so can I put + + align:start position:0% +draw a picture like that so can I put + + + align:start position:0% +draw a picture like that so can I put +down these columns I'll draw these + + align:start position:0% +down these columns I'll draw these + + + align:start position:0% +down these columns I'll draw these +columns as they are and then I'll do do + + align:start position:0% +columns as they are and then I'll do do + + + align:start position:0% +columns as they are and then I'll do do +a combination of them so the first + + align:start position:0% +a combination of them so the first + + + align:start position:0% +a combination of them so the first +column is over 2 and down 1 right so + + align:start position:0% +column is over 2 and down 1 right so + + + align:start position:0% +column is over 2 and down 1 right so +there's the first column + + align:start position:0% +there's the first column + + + align:start position:0% +there's the first column +the first column column one it's the + + align:start position:0% +the first column column one it's the + + + align:start position:0% +the first column column one it's the +vector 2 minus 1 the second column is C + + align:start position:0% +vector 2 minus 1 the second column is C + + + align:start position:0% +vector 2 minus 1 the second column is C +I go over minus 1 is the first component + + align:start position:0% +I go over minus 1 is the first component + + + align:start position:0% +I go over minus 1 is the first component +and up to its here + + align:start position:0% +and up to its here + + + align:start position:0% +and up to its here +there's column 2 so this again you see + + align:start position:0% +there's column 2 so this again you see + + + align:start position:0% +there's column 2 so this again you see +what its components are its components + + align:start position:0% +what its components are its components + + + align:start position:0% +what its components are its components +are minus 1/2 good + + align:start position:0% +are minus 1/2 good + + + align:start position:0% +are minus 1/2 good +that's this guy now what is what now I + + align:start position:0% +that's this guy now what is what now I + + + align:start position:0% +that's this guy now what is what now I +have to take a combination what + + align:start position:0% +have to take a combination what + + + align:start position:0% +have to take a combination what +combination shall I take + + align:start position:0% +combination shall I take + + + align:start position:0% +combination shall I take +why not the right combination what the + + align:start position:0% +why not the right combination what the + + + align:start position:0% +why not the right combination what the +hell okay so what the combination I'm + + align:start position:0% +hell okay so what the combination I'm + + + align:start position:0% +hell okay so what the combination I'm +going to take is the right one to + + align:start position:0% +going to take is the right one to + + + align:start position:0% +going to take is the right one to +produce 0 3 and that and then we'll see + + align:start position:0% +produce 0 3 and that and then we'll see + + + align:start position:0% +produce 0 3 and that and then we'll see +it happen in the picture so the right + + align:start position:0% +it happen in the picture so the right + + + align:start position:0% +it happen in the picture so the right +combination is to take X is one of those + + align:start position:0% +combination is to take X is one of those + + + align:start position:0% +combination is to take X is one of those +and two of these it's because we already + + align:start position:0% +and two of these it's because we already + + + align:start position:0% +and two of these it's because we already +know that that's the right x and y so + + align:start position:0% +know that that's the right x and y so + + + align:start position:0% +know that that's the right x and y so +why not take the correct combination + + align:start position:0% +why not take the correct combination + + + align:start position:0% +why not take the correct combination +here and see it happen ok so how do I + + align:start position:0% +here and see it happen ok so how do I + + + align:start position:0% +here and see it happen ok so how do I +picture this this linear combination so + + align:start position:0% +picture this this linear combination so + + + align:start position:0% +picture this this linear combination so +I start with this vector that's already + + align:start position:0% +I start with this vector that's already + + + align:start position:0% +I start with this vector that's already +here so that's one of column 1 that's 1 + + align:start position:0% +here so that's one of column 1 that's 1 + + + align:start position:0% +here so that's one of column 1 that's 1 +times column 1 right there and now I + + align:start position:0% +times column 1 right there and now I + + + align:start position:0% +times column 1 right there and now I +want to add on so I'm going to hook the + + align:start position:0% +want to add on so I'm going to hook the + + + align:start position:0% +want to add on so I'm going to hook the +next vector on to the front of the arrow + + align:start position:0% +next vector on to the front of the arrow + + + align:start position:0% +next vector on to the front of the arrow +we'll start the next vector and it'll go + + align:start position:0% +we'll start the next vector and it'll go + + + align:start position:0% +we'll start the next vector and it'll go +this way so let's see if can I do it + + align:start position:0% +this way so let's see if can I do it + + + align:start position:0% +this way so let's see if can I do it +right if I add it on one of these + + align:start position:0% +right if I add it on one of these + + + align:start position:0% +right if I add it on one of these +vectors it would go left one and up two + + align:start position:0% +vectors it would go left one and up two + + + align:start position:0% +vectors it would go left one and up two +so it would go left 1 and up 2 so it + + align:start position:0% +so it would go left 1 and up 2 so it + + + align:start position:0% +so it would go left 1 and up 2 so it +would probably get us to there maybe + + align:start position:0% +would probably get us to there maybe + + + align:start position:0% +would probably get us to there maybe +I'll do dotted line for that okay that's + + align:start position:0% +I'll do dotted line for that okay that's + + + align:start position:0% +I'll do dotted line for that okay that's +one of column to tuck down to the end + + align:start position:0% +one of column to tuck down to the end + + + align:start position:0% +one of column to tuck down to the end +but I wanted to talk on two of column 2 + + align:start position:0% +but I wanted to talk on two of column 2 + + + align:start position:0% +but I wanted to talk on two of column 2 +so that the second one will go up but + + align:start position:0% +so that the second one will go up but + + + align:start position:0% +so that the second one will go up but +left one and up two also it'll probably + + align:start position:0% +left one and up two also it'll probably + + + align:start position:0% +left one and up two also it'll probably +end there and there's another one so so + + align:start position:0% +end there and there's another one so so + + + align:start position:0% +end there and there's another one so so +what I've put in here is two of column + + align:start position:0% +what I've put in here is two of column + + + align:start position:0% +what I've put in here is two of column +two + + align:start position:0% + + + + align:start position:0% + +added on and where did I end up what are + + align:start position:0% +added on and where did I end up what are + + + align:start position:0% +added on and where did I end up what are +the coordinates of this result what do I + + align:start position:0% +the coordinates of this result what do I + + + align:start position:0% +the coordinates of this result what do I +get when I take one of this plus two of + + align:start position:0% +get when I take one of this plus two of + + + align:start position:0% +get when I take one of this plus two of +that I do get that of course there it is + + align:start position:0% +that I do get that of course there it is + + + align:start position:0% +that I do get that of course there it is +there it is X is zero Y is three that's + + align:start position:0% +there it is X is zero Y is three that's + + + align:start position:0% +there it is X is zero Y is three that's +B that's the that's the answer we wanted + + align:start position:0% +B that's the that's the answer we wanted + + + align:start position:0% +B that's the that's the answer we wanted +and how do I do it + + align:start position:0% +and how do I do it + + + align:start position:0% +and how do I do it +you see I do it just like the first + + align:start position:0% +you see I do it just like the first + + + align:start position:0% +you see I do it just like the first +component I have a 2 and a minus 2 that + + align:start position:0% +component I have a 2 and a minus 2 that + + + align:start position:0% +component I have a 2 and a minus 2 that +produces a zero and in the second + + align:start position:0% +produces a zero and in the second + + + align:start position:0% +produces a zero and in the second +component I have a minus 1 and a 4 they + + align:start position:0% +component I have a minus 1 and a 4 they + + + align:start position:0% +component I have a minus 1 and a 4 they +combine to give the 3 but look at this + + align:start position:0% +combine to give the 3 but look at this + + + align:start position:0% +combine to give the 3 but look at this +picture so that here's our key picture I + + align:start position:0% +picture so that here's our key picture I + + + align:start position:0% +picture so that here's our key picture I +combine this column and this column to + + align:start position:0% +combine this column and this column to + + + align:start position:0% +combine this column and this column to +get maybe I better to get this guy that + + align:start position:0% +get maybe I better to get this guy that + + + align:start position:0% +get maybe I better to get this guy that +was the B that's the zero 3 okay so that + + align:start position:0% +was the B that's the zero 3 okay so that + + + align:start position:0% +was the B that's the zero 3 okay so that +idea of linear combinations is crucial + + align:start position:0% +idea of linear combinations is crucial + + + align:start position:0% +idea of linear combinations is crucial +and and also do we want to think about + + align:start position:0% +and and also do we want to think about + + + align:start position:0% +and and also do we want to think about +this question sure why not what are all + + align:start position:0% +this question sure why not what are all + + + align:start position:0% +this question sure why not what are all +the combinations if I took can I go back + + align:start position:0% +the combinations if I took can I go back + + + align:start position:0% +the combinations if I took can I go back +to X's and Y's this is a this is a + + align:start position:0% +to X's and Y's this is a this is a + + + align:start position:0% +to X's and Y's this is a this is a +question for really it's it's going to + + align:start position:0% +question for really it's it's going to + + + align:start position:0% +question for really it's it's going to +come up over and over but why don't we + + align:start position:0% +come up over and over but why don't we + + + align:start position:0% +come up over and over but why don't we +see it once now if I took all the X's + + align:start position:0% +see it once now if I took all the X's + + + align:start position:0% +see it once now if I took all the X's +and all the Y's all the combinations + + align:start position:0% +and all the Y's all the combinations + + + align:start position:0% +and all the Y's all the combinations +what would be all the results and + + align:start position:0% +what would be all the results and + + + align:start position:0% +what would be all the results and +actually the result would be that I + + align:start position:0% +actually the result would be that I + + + align:start position:0% +actually the result would be that I +could get any right-hand side at all the + + align:start position:0% +could get any right-hand side at all the + + + align:start position:0% +could get any right-hand side at all the +combinations of this and this would fill + + align:start position:0% +combinations of this and this would fill + + + align:start position:0% +combinations of this and this would fill +the whole plane you can tuck that away + + align:start position:0% +the whole plane you can tuck that away + + + align:start position:0% +the whole plane you can tuck that away +we'll just explore it further but this + + align:start position:0% +we'll just explore it further but this + + + align:start position:0% +we'll just explore it further but this +idea of what linear combination gives B + + align:start position:0% +idea of what linear combination gives B + + + align:start position:0% +idea of what linear combination gives B +and what do all the linear combinations + + align:start position:0% +and what do all the linear combinations + + + align:start position:0% +and what do all the linear combinations +give what are all the possible + + align:start position:0% +give what are all the possible + + + align:start position:0% +give what are all the possible +achievable right-hand sides B that's + + align:start position:0% +achievable right-hand sides B that's + + + align:start position:0% +achievable right-hand sides B that's +going to be basic ok can I move to three + + align:start position:0% +going to be basic ok can I move to three + + + align:start position:0% +going to be basic ok can I move to three +equations in three on + + align:start position:0% +equations in three on + + + align:start position:0% +equations in three on +because it's easy to picture the 2 by 2 + + align:start position:0% +because it's easy to picture the 2 by 2 + + + align:start position:0% +because it's easy to picture the 2 by 2 +case let me do a 3 by 3 example okay + + align:start position:0% +case let me do a 3 by 3 example okay + + + align:start position:0% +case let me do a 3 by 3 example okay +I'll sort of start it the same way say + + align:start position:0% +I'll sort of start it the same way say + + + align:start position:0% +I'll sort of start it the same way say +maybe 2x minus y and maybe I'll take no + + align:start position:0% +maybe 2x minus y and maybe I'll take no + + + align:start position:0% +maybe 2x minus y and maybe I'll take no +no Z's is a zero and maybe a minus X and + + align:start position:0% +no Z's is a zero and maybe a minus X and + + + align:start position:0% +no Z's is a zero and maybe a minus X and +a 2y and maybe a minus Z is a oh let me + + align:start position:0% +a 2y and maybe a minus Z is a oh let me + + + align:start position:0% +a 2y and maybe a minus Z is a oh let me +make that a minus one and just for + + align:start position:0% +make that a minus one and just for + + + align:start position:0% +make that a minus one and just for +variety let me take minus 3 Z minus 3 + + align:start position:0% +variety let me take minus 3 Z minus 3 + + + align:start position:0% +variety let me take minus 3 Z minus 3 +wise I should keep the Y's in that line + + align:start position:0% +wise I should keep the Y's in that line + + + align:start position:0% +wise I should keep the Y's in that line +and for Z's is say 4 okay that's three + + align:start position:0% +and for Z's is say 4 okay that's three + + + align:start position:0% +and for Z's is say 4 okay that's three +equations I'm in three dimensions X Y Z + + align:start position:0% +equations I'm in three dimensions X Y Z + + + align:start position:0% +equations I'm in three dimensions X Y Z +and I don't have a solution yet so I + + align:start position:0% +and I don't have a solution yet so I + + + align:start position:0% +and I don't have a solution yet so I +want to understand the equations and + + align:start position:0% +want to understand the equations and + + + align:start position:0% +want to understand the equations and +then solve them ok so how do i how do + + align:start position:0% +then solve them ok so how do i how do + + + align:start position:0% +then solve them ok so how do i how do +you understand them the row picture is + + align:start position:0% +you understand them the row picture is + + + align:start position:0% +you understand them the row picture is +one way the column picture is another + + align:start position:0% +one way the column picture is another + + + align:start position:0% +one way the column picture is another +very important way just let's remember + + align:start position:0% +very important way just let's remember + + + align:start position:0% +very important way just let's remember +the matrix form here because that's easy + + align:start position:0% +the matrix form here because that's easy + + + align:start position:0% +the matrix form here because that's easy +the matrix form + + align:start position:0% +the matrix form + + + align:start position:0% +the matrix form +what's our matrix a our matrix a is this + + align:start position:0% +what's our matrix a our matrix a is this + + + align:start position:0% +what's our matrix a our matrix a is this +right hand side the 2 and the minus 1 + + align:start position:0% +right hand side the 2 and the minus 1 + + + align:start position:0% +right hand side the 2 and the minus 1 +and the 0 from the first row the minus 1 + + align:start position:0% +and the 0 from the first row the minus 1 + + + align:start position:0% +and the 0 from the first row the minus 1 +and the 2 and the minus 1 from the + + align:start position:0% +and the 2 and the minus 1 from the + + + align:start position:0% +and the 2 and the minus 1 from the +second row the 0 the minus 3 and the 4 + + align:start position:0% +second row the 0 the minus 3 and the 4 + + + align:start position:0% +second row the 0 the minus 3 and the 4 +from the third row so it's a three by + + align:start position:0% +from the third row so it's a three by + + + align:start position:0% +from the third row so it's a three by +three matrix three equations three + + align:start position:0% +three matrix three equations three + + + align:start position:0% +three matrix three equations three +unknowns and what's our right-hand side + + align:start position:0% +unknowns and what's our right-hand side + + + align:start position:0% +unknowns and what's our right-hand side +of course it's the vector 0 minus 1/4 + + align:start position:0% +of course it's the vector 0 minus 1/4 + + + align:start position:0% +of course it's the vector 0 minus 1/4 +okay so that's the way we'll that's the + + align:start position:0% +okay so that's the way we'll that's the + + + align:start position:0% +okay so that's the way we'll that's the +shorthand to write out the three + + align:start position:0% +shorthand to write out the three + + + align:start position:0% +shorthand to write out the three +equations but it's the picture that I'm + + align:start position:0% +equations but it's the picture that I'm + + + align:start position:0% +equations but it's the picture that I'm +looking for today okay so the row + + align:start position:0% +looking for today okay so the row + + + align:start position:0% +looking for today okay so the row +picture + + align:start position:0% + + + + align:start position:0% + +all right so I'm in three dimensions X Y + + align:start position:0% +all right so I'm in three dimensions X Y + + + align:start position:0% +all right so I'm in three dimensions X Y +& Z and I want to take those equations + + align:start position:0% +& Z and I want to take those equations + + + align:start position:0% +& Z and I want to take those equations +one at a time and s and make a picture + + align:start position:0% +one at a time and s and make a picture + + + align:start position:0% +one at a time and s and make a picture +of all the points that satisfy let's + + align:start position:0% +of all the points that satisfy let's + + + align:start position:0% +of all the points that satisfy let's +take equation number two if I make a + + align:start position:0% +take equation number two if I make a + + + align:start position:0% +take equation number two if I make a +picture of all the points that satisfy + + align:start position:0% +picture of all the points that satisfy + + + align:start position:0% +picture of all the points that satisfy +all the XYZ points that solve this + + align:start position:0% +all the XYZ points that solve this + + + align:start position:0% +all the XYZ points that solve this +equation well first of all the origin is + + align:start position:0% +equation well first of all the origin is + + + align:start position:0% +equation well first of all the origin is +not one of them X Y Z being zero zero + + align:start position:0% +not one of them X Y Z being zero zero + + + align:start position:0% +not one of them X Y Z being zero zero +zero would not solve that equation so + + align:start position:0% +zero would not solve that equation so + + + align:start position:0% +zero would not solve that equation so +what what are some points that do solve + + align:start position:0% +what what are some points that do solve + + + align:start position:0% +what what are some points that do solve +the equation let's see maybe if X is one + + align:start position:0% +the equation let's see maybe if X is one + + + align:start position:0% +the equation let's see maybe if X is one +y + Z could be zero that would work + + align:start position:0% +y + Z could be zero that would work + + + align:start position:0% +y + Z could be zero that would work +right so there's one point I'm looking + + align:start position:0% +right so there's one point I'm looking + + + align:start position:0% +right so there's one point I'm looking +at this second equation here just to + + align:start position:0% +at this second equation here just to + + + align:start position:0% +at this second equation here just to +start with let's see also I guess if Z Z + + align:start position:0% +start with let's see also I guess if Z Z + + + align:start position:0% +start with let's see also I guess if Z Z +could be 1x and Y could be zero so that + + align:start position:0% +could be 1x and Y could be zero so that + + + align:start position:0% +could be 1x and Y could be zero so that +would just go straight up that axis and + + align:start position:0% +would just go straight up that axis and + + + align:start position:0% +would just go straight up that axis and +probably I want a third point here let + + align:start position:0% +probably I want a third point here let + + + align:start position:0% +probably I want a third point here let +me take X to be 0 let's say X to be 0 Z + + align:start position:0% +me take X to be 0 let's say X to be 0 Z + + + align:start position:0% +me take X to be 0 let's say X to be 0 Z +to be 0 then Y would be minus 1/2 right + + align:start position:0% +to be 0 then Y would be minus 1/2 right + + + align:start position:0% +to be 0 then Y would be minus 1/2 right +so there's a third point somewhere oh ok + + align:start position:0% +so there's a third point somewhere oh ok + + + align:start position:0% +so there's a third point somewhere oh ok +let's see I want to put in all the + + align:start position:0% +let's see I want to put in all the + + + align:start position:0% +let's see I want to put in all the +points that satisfy that equation do you + + align:start position:0% +points that satisfy that equation do you + + + align:start position:0% +points that satisfy that equation do you +know what that bunch of points will be + + align:start position:0% +know what that bunch of points will be + + + align:start position:0% +know what that bunch of points will be +it's a plane if we have a linear + + align:start position:0% +it's a plane if we have a linear + + + align:start position:0% +it's a plane if we have a linear +equation then fortunately the graph of + + align:start position:0% +equation then fortunately the graph of + + + align:start position:0% +equation then fortunately the graph of +the thing the plot of all the points + + align:start position:0% +the thing the plot of all the points + + + align:start position:0% +the thing the plot of all the points +that solve it or a plane so I and three + + align:start position:0% +that solve it or a plane so I and three + + + align:start position:0% +that solve it or a plane so I and three +these three points determine a plane but + + align:start position:0% + + + + align:start position:0% + +your lecture is not Rembrandt and this + + align:start position:0% +your lecture is not Rembrandt and this + + + align:start position:0% +your lecture is not Rembrandt and this +the art is going to be the weak point + + align:start position:0% +the art is going to be the weak point + + + align:start position:0% +the art is going to be the weak point +here so I'm just going to draw a plane + + align:start position:0% +here so I'm just going to draw a plane + + + align:start position:0% +here so I'm just going to draw a plane +right there's a plane somewhere that's + + align:start position:0% +right there's a plane somewhere that's + + + align:start position:0% +right there's a plane somewhere that's +my plane they draw that + + align:start position:0% +my plane they draw that + + + align:start position:0% +my plane they draw that +that plane is all the points it solves + + align:start position:0% +that plane is all the points it solves + + + align:start position:0% +that plane is all the points it solves +this guy then what about this one + + align:start position:0% +this guy then what about this one + + + align:start position:0% +this guy then what about this one +2x minus y plus zero Z so Z actually can + + align:start position:0% +2x minus y plus zero Z so Z actually can + + + align:start position:0% +2x minus y plus zero Z so Z actually can +be anything again it's going to be + + align:start position:0% +be anything again it's going to be + + + align:start position:0% +be anything again it's going to be +another plane each row in a 3x3 problem + + align:start position:0% +another plane each row in a 3x3 problem + + + align:start position:0% +another plane each row in a 3x3 problem +gives us a plane in three dimensions so + + align:start position:0% +gives us a plane in three dimensions so + + + align:start position:0% +gives us a plane in three dimensions so +this one is going to be some other plane + + align:start position:0% +this one is going to be some other plane + + + align:start position:0% +this one is going to be some other plane +maybe it maybe I'll try to draw it like + + align:start position:0% +maybe it maybe I'll try to draw it like + + + align:start position:0% +maybe it maybe I'll try to draw it like +this and those two planes meet in a line + + align:start position:0% +this and those two planes meet in a line + + + align:start position:0% +this and those two planes meet in a line +so if I have two equations just the + + align:start position:0% +so if I have two equations just the + + + align:start position:0% +so if I have two equations just the +first two equations in in three + + align:start position:0% +first two equations in in three + + + align:start position:0% +first two equations in in three +dimensions those give me a line the line + + align:start position:0% +dimensions those give me a line the line + + + align:start position:0% +dimensions those give me a line the line +where those two planes meet and now the + + align:start position:0% +where those two planes meet and now the + + + align:start position:0% +where those two planes meet and now the +third guy is a third plane and it goes + + align:start position:0% +third guy is a third plane and it goes + + + align:start position:0% +third guy is a third plane and it goes +some somewhere okay those three things + + align:start position:0% +some somewhere okay those three things + + + align:start position:0% +some somewhere okay those three things +meet at a point now I don't know where + + align:start position:0% +meet at a point now I don't know where + + + align:start position:0% +meet at a point now I don't know where +that point is frankly but linear algebra + + align:start position:0% +that point is frankly but linear algebra + + + align:start position:0% +that point is frankly but linear algebra +will find it the main point is that + + align:start position:0% +will find it the main point is that + + + align:start position:0% +will find it the main point is that +there is that the three planes because + + align:start position:0% +there is that the three planes because + + + align:start position:0% +there is that the three planes because +they're you know they're not parallel + + align:start position:0% +they're you know they're not parallel + + + align:start position:0% +they're you know they're not parallel +they don't they're not special there + + align:start position:0% +they don't they're not special there + + + align:start position:0% +they don't they're not special there +they do meet in one point and that's a + + align:start position:0% +they do meet in one point and that's a + + + align:start position:0% +they do meet in one point and that's a +solution but maybe you can see that this + + align:start position:0% +solution but maybe you can see that this + + + align:start position:0% +solution but maybe you can see that this +row picture is getting a little hard to + + align:start position:0% +row picture is getting a little hard to + + + align:start position:0% +row picture is getting a little hard to +see the road picture was a cinch when we + + align:start position:0% +see the road picture was a cinch when we + + + align:start position:0% +see the road picture was a cinch when we +looked at to me two lines meeting when + + align:start position:0% +looked at to me two lines meeting when + + + align:start position:0% +looked at to me two lines meeting when +we look at three planes meeting it's not + + align:start position:0% +we look at three planes meeting it's not + + + align:start position:0% +we look at three planes meeting it's not +so clear and in four dimensions probably + + align:start position:0% +so clear and in four dimensions probably + + + align:start position:0% +so clear and in four dimensions probably +a little less clear so can I quit on the + + align:start position:0% +a little less clear so can I quit on the + + + align:start position:0% +a little less clear so can I quit on the +row picture I'll quit on the row picture + + align:start position:0% +row picture I'll quit on the row picture + + + align:start position:0% +row picture I'll quit on the row picture +before I've successfully found the point + + align:start position:0% +before I've successfully found the point + + + align:start position:0% +before I've successfully found the point +where the three planes meet all I really + + align:start position:0% +where the three planes meet all I really + + + align:start position:0% +where the three planes meet all I really +want to see is that there that the row + + align:start position:0% +want to see is that there that the row + + + align:start position:0% +want to see is that there that the row +picture consists of three planes and if + + align:start position:0% +picture consists of three planes and if + + + align:start position:0% +picture consists of three planes and if +everything works right three planes meet + + align:start position:0% +everything works right three planes meet + + + align:start position:0% +everything works right three planes meet +in one point and that's a solution now + + align:start position:0% +in one point and that's a solution now + + + align:start position:0% +in one point and that's a solution now +you can tell I prefer the column picture + + align:start position:0% +you can tell I prefer the column picture + + + align:start position:0% +you can tell I prefer the column picture +okay so let me take the column picture + + align:start position:0% +okay so let me take the column picture + + + align:start position:0% +okay so let me take the column picture +that's x times so there were two x's in + + align:start position:0% +that's x times so there were two x's in + + + align:start position:0% +that's x times so there were two x's in +the first equation minus 1 X's I'm just + + align:start position:0% +the first equation minus 1 X's I'm just + + + align:start position:0% +the first equation minus 1 X's I'm just +take and no X's in the third it's just + + align:start position:0% +take and no X's in the third it's just + + + align:start position:0% +take and no X's in the third it's just +the first column of that and how many + + align:start position:0% +the first column of that and how many + + + align:start position:0% +the first column of that and how many +Y's are there there's minus 1 in the + + align:start position:0% +Y's are there there's minus 1 in the + + + align:start position:0% +Y's are there there's minus 1 in the +first equation 2 in the second and maybe + + align:start position:0% +first equation 2 in the second and maybe + + + align:start position:0% +first equation 2 in the second and maybe +minus three in the third just the second + + align:start position:0% +minus three in the third just the second + + + align:start position:0% +minus three in the third just the second +column of my matrix and Z times no Z's - + + align:start position:0% +column of my matrix and Z times no Z's - + + + align:start position:0% +column of my matrix and Z times no Z's - +onesies and four Z's and it's those + + align:start position:0% +onesies and four Z's and it's those + + + align:start position:0% +onesies and four Z's and it's those +three columns right that I have to + + align:start position:0% +three columns right that I have to + + + align:start position:0% +three columns right that I have to +combine to produce the right-hand side + + align:start position:0% +combine to produce the right-hand side + + + align:start position:0% +combine to produce the right-hand side +which is 0-1 4 okay + + align:start position:0% +which is 0-1 4 okay + + + align:start position:0% +which is 0-1 4 okay +so what have we got on this left-hand + + align:start position:0% +so what have we got on this left-hand + + + align:start position:0% +so what have we got on this left-hand +side a linear combination it's a linear + + align:start position:0% +side a linear combination it's a linear + + + align:start position:0% +side a linear combination it's a linear +combination now of three vectors and + + align:start position:0% +combination now of three vectors and + + + align:start position:0% +combination now of three vectors and +they happen to be each one is a + + align:start position:0% +they happen to be each one is a + + + align:start position:0% +they happen to be each one is a +3-dimensional vector so we want to we + + align:start position:0% +3-dimensional vector so we want to we + + + align:start position:0% +3-dimensional vector so we want to we +want to know what combination of those + + align:start position:0% +want to know what combination of those + + + align:start position:0% +want to know what combination of those +three vectors produces that one shall I + + align:start position:0% +three vectors produces that one shall I + + + align:start position:0% +three vectors produces that one shall I +try to draw the column picture then so + + align:start position:0% +try to draw the column picture then so + + + align:start position:0% +try to draw the column picture then so +since these vectors have three + + align:start position:0% +since these vectors have three + + + align:start position:0% +since these vectors have three +components so it's some multiple let me + + align:start position:0% +components so it's some multiple let me + + + align:start position:0% +components so it's some multiple let me +draw in the first column as before so I + + align:start position:0% +draw in the first column as before so I + + + align:start position:0% +draw in the first column as before so I +X is 2 and Y is minus 1 maybe maybe + + align:start position:0% +X is 2 and Y is minus 1 maybe maybe + + + align:start position:0% +X is 2 and Y is minus 1 maybe maybe +there's the first column Y the second + + align:start position:0% +there's the first column Y the second + + + align:start position:0% +there's the first column Y the second +column has maybe a minus 1 and a 2 and + + align:start position:0% +column has maybe a minus 1 and a 2 and + + + align:start position:0% +column has maybe a minus 1 and a 2 and +the Y's and minus 3 some somewhere there + + align:start position:0% +the Y's and minus 3 some somewhere there + + + align:start position:0% +the Y's and minus 3 some somewhere there +possibly column 2 and the third column + + align:start position:0% +possibly column 2 and the third column + + + align:start position:0% +possibly column 2 and the third column +has no no 0 minus 1/4 so how shall I + + align:start position:0% +has no no 0 minus 1/4 so how shall I + + + align:start position:0% +has no no 0 minus 1/4 so how shall I +draw that so nothing in this is this was + + align:start position:0% +draw that so nothing in this is this was + + + align:start position:0% +draw that so nothing in this is this was +that this was the first component the + + align:start position:0% +that this was the first component the + + + align:start position:0% +that this was the first component the +second component was a minus 1 maybe up + + align:start position:0% +second component was a minus 1 maybe up + + + align:start position:0% +second component was a minus 1 maybe up +here that's column 3 that's that's the + + align:start position:0% +here that's column 3 that's that's the + + + align:start position:0% +here that's column 3 that's that's the +column 0 minus 1 and for this guy so + + align:start position:0% + + + + align:start position:0% + +again what's my problem + + align:start position:0% +again what's my problem + + + align:start position:0% +again what's my problem +my what this equation is asking me to do + + align:start position:0% +my what this equation is asking me to do + + + align:start position:0% +my what this equation is asking me to do +is to combine these three vectors with + + align:start position:0% +is to combine these three vectors with + + + align:start position:0% +is to combine these three vectors with +the right combination to produce this + + align:start position:0% +the right combination to produce this + + + align:start position:0% +the right combination to produce this +one well you can see what the right + + align:start position:0% +one well you can see what the right + + + align:start position:0% +one well you can see what the right +combination is because in this special + + align:start position:0% +combination is because in this special + + + align:start position:0% +combination is because in this special +problem especially chosen by the + + align:start position:0% +problem especially chosen by the + + + align:start position:0% +problem especially chosen by the +lecturer that right hand side that I'm + + align:start position:0% +lecturer that right hand side that I'm + + + align:start position:0% +lecturer that right hand side that I'm +trying to get is actually one of these + + align:start position:0% +trying to get is actually one of these + + + align:start position:0% +trying to get is actually one of these +columns so I know how to get that one so + + align:start position:0% +columns so I know how to get that one so + + + align:start position:0% +columns so I know how to get that one so +what's the solution what combination + + align:start position:0% +what's the solution what combination + + + align:start position:0% +what's the solution what combination +will work I just want one of these and + + align:start position:0% +will work I just want one of these and + + + align:start position:0% +will work I just want one of these and +none of these so X should be 0 y should + + align:start position:0% +none of these so X should be 0 y should + + + align:start position:0% +none of these so X should be 0 y should +be 0 and Z should be 1 to come that's + + align:start position:0% +be 0 and Z should be 1 to come that's + + + align:start position:0% +be 0 and Z should be 1 to come that's +the combination none of that none of + + align:start position:0% +the combination none of that none of + + + align:start position:0% +the combination none of that none of +that one of those is obviously the right + + align:start position:0% +that one of those is obviously the right + + + align:start position:0% +that one of those is obviously the right +one so this column 3 is actually the + + align:start position:0% +one so this column 3 is actually the + + + align:start position:0% +one so this column 3 is actually the +same as B in this particular problem I + + align:start position:0% + + + + align:start position:0% + +made it work that way just so we would + + align:start position:0% +made it work that way just so we would + + + align:start position:0% +made it work that way just so we would +get an answer 0 0 1 so somehow that's + + align:start position:0% +get an answer 0 0 1 so somehow that's + + + align:start position:0% +get an answer 0 0 1 so somehow that's +the point that where those three planes + + align:start position:0% +the point that where those three planes + + + align:start position:0% +the point that where those three planes +met and I couldn't see it before of + + align:start position:0% +met and I couldn't see it before of + + + align:start position:0% +met and I couldn't see it before of +course I won't always be able to see it + + align:start position:0% +course I won't always be able to see it + + + align:start position:0% +course I won't always be able to see it +from the column picture either it's the + + align:start position:0% +from the column picture either it's the + + + align:start position:0% +from the column picture either it's the +next lecture actually which is about + + align:start position:0% +next lecture actually which is about + + + align:start position:0% +next lecture actually which is about +elimination which is the systematic way + + align:start position:0% +elimination which is the systematic way + + + align:start position:0% +elimination which is the systematic way +that everybody every every bit of + + align:start position:0% +that everybody every every bit of + + + align:start position:0% +that everybody every every bit of +software to a production large scale + + align:start position:0% +software to a production large scale + + + align:start position:0% +software to a production large scale +software would solve the equations so + + align:start position:0% +software would solve the equations so + + + align:start position:0% +software would solve the equations so +the lecture that's coming up if I was to + + align:start position:0% +the lecture that's coming up if I was to + + + align:start position:0% +the lecture that's coming up if I was to +add that to the syllabus will be about + + align:start position:0% +add that to the syllabus will be about + + + align:start position:0% +add that to the syllabus will be about +how to find X Y Z in in all cases can I + + align:start position:0% +how to find X Y Z in in all cases can I + + + align:start position:0% +how to find X Y Z in in all cases can I +just think again though about the big + + align:start position:0% +just think again though about the big + + + align:start position:0% +just think again though about the big +picture the big buy the big picture I + + align:start position:0% +picture the big buy the big picture I + + + align:start position:0% +picture the big buy the big picture I +mean let's keep this same matrix on the + + align:start position:0% +mean let's keep this same matrix on the + + + align:start position:0% +mean let's keep this same matrix on the +left but imagine that we have a + + align:start position:0% +left but imagine that we have a + + + align:start position:0% +left but imagine that we have a +different right-hand side oh let me take + + align:start position:0% +different right-hand side oh let me take + + + align:start position:0% +different right-hand side oh let me take +a different right-hand side so I'll + + align:start position:0% +a different right-hand side so I'll + + + align:start position:0% +a different right-hand side so I'll +change + + align:start position:0% +change + + + align:start position:0% +change +right hand side to something that + + align:start position:0% +right hand side to something that + + + align:start position:0% +right hand side to something that +actually is also pretty special let me + + align:start position:0% +actually is also pretty special let me + + + align:start position:0% +actually is also pretty special let me +change it to suppose I if I add those + + align:start position:0% +change it to suppose I if I add those + + + align:start position:0% +change it to suppose I if I add those +first two columns that would give me a 1 + + align:start position:0% +first two columns that would give me a 1 + + + align:start position:0% +first two columns that would give me a 1 +and a 1 and a minus 3 there's a very + + align:start position:0% +and a 1 and a minus 3 there's a very + + + align:start position:0% +and a 1 and a minus 3 there's a very +special right hand side I just cooked it + + align:start position:0% +special right hand side I just cooked it + + + align:start position:0% +special right hand side I just cooked it +up by adding this one to this one now + + align:start position:0% +up by adding this one to this one now + + + align:start position:0% +up by adding this one to this one now +what's the solution with this new right + + align:start position:0% +what's the solution with this new right + + + align:start position:0% +what's the solution with this new right +hand side the solution with this new + + align:start position:0% +hand side the solution with this new + + + align:start position:0% +hand side the solution with this new +right hand side is clear it took now I + + align:start position:0% +right hand side is clear it took now I + + + align:start position:0% +right hand side is clear it took now I +took one of these one of these and none + + align:start position:0% +took one of these one of these and none + + + align:start position:0% +took one of these one of these and none +of those so so actually it just changed + + align:start position:0% +of those so so actually it just changed + + + align:start position:0% +of those so so actually it just changed +around on this when I took this new + + align:start position:0% +around on this when I took this new + + + align:start position:0% +around on this when I took this new +right hand side okay so the in there in + + align:start position:0% +right hand side okay so the in there in + + + align:start position:0% +right hand side okay so the in there in +the role picture I have three different + + align:start position:0% +the role picture I have three different + + + align:start position:0% +the role picture I have three different +planes three three three new planes + + align:start position:0% +planes three three three new planes + + + align:start position:0% +planes three three three new planes +meeting now at this point in the column + + align:start position:0% +meeting now at this point in the column + + + align:start position:0% +meeting now at this point in the column +picture I have the same three columns + + align:start position:0% +picture I have the same three columns + + + align:start position:0% +picture I have the same three columns +but now I'm combining them to produce + + align:start position:0% +but now I'm combining them to produce + + + align:start position:0% +but now I'm combining them to produce +this guy and it turned out that column + + align:start position:0% +this guy and it turned out that column + + + align:start position:0% +this guy and it turned out that column +one plus column two which would be + + align:start position:0% +one plus column two which would be + + + align:start position:0% +one plus column two which would be +somewhere there there is the right + + align:start position:0% +somewhere there there is the right + + + align:start position:0% +somewhere there there is the right +column one of this and one of this would + + align:start position:0% +column one of this and one of this would + + + align:start position:0% +column one of this and one of this would +give me the the new B okay so that's + + align:start position:0% +give me the the new B okay so that's + + + align:start position:0% +give me the the new B okay so that's +like we squeezed in an extra example but + + align:start position:0% +like we squeezed in an extra example but + + + align:start position:0% +like we squeezed in an extra example but +now think about all B's all right hand + + align:start position:0% +now think about all B's all right hand + + + align:start position:0% +now think about all B's all right hand +sides could I get can I solve these + + align:start position:0% +sides could I get can I solve these + + + align:start position:0% +sides could I get can I solve these +equations for every right hand side can + + align:start position:0% +equations for every right hand side can + + + align:start position:0% +equations for every right hand side can +I say that ask that question so that's + + align:start position:0% +I say that ask that question so that's + + + align:start position:0% +I say that ask that question so that's +the algebra question can I solve ax + + align:start position:0% +the algebra question can I solve ax + + + align:start position:0% +the algebra question can I solve ax +equal B for every B let me write that + + align:start position:0% +equal B for every B let me write that + + + align:start position:0% +equal B for every B let me write that +down + + align:start position:0% +down + + + align:start position:0% +down +can I solve ax equal B for every right + + align:start position:0% +can I solve ax equal B for every right + + + align:start position:0% +can I solve ax equal B for every right +hand side B I mean is there a solution + + align:start position:0% +hand side B I mean is there a solution + + + align:start position:0% +hand side B I mean is there a solution +and then if there is elimination will + + align:start position:0% +and then if there is elimination will + + + align:start position:0% +and then if there is elimination will +give me a way to find it I'm just I + + align:start position:0% +give me a way to find it I'm just I + + + align:start position:0% +give me a way to find it I'm just I +really wanted to ask is there a solution + + align:start position:0% +really wanted to ask is there a solution + + + align:start position:0% +really wanted to ask is there a solution +for every right-hand side so now can I + + align:start position:0% +for every right-hand side so now can I + + + align:start position:0% +for every right-hand side so now can I +put that in different words in this + + align:start position:0% +put that in different words in this + + + align:start position:0% +put that in different words in this +linear combination + + align:start position:0% +linear combination + + + align:start position:0% +linear combination +words so in linear combination words do + + align:start position:0% +words so in linear combination words do + + + align:start position:0% +words so in linear combination words do +the linear combinations of the columns + + align:start position:0% + + + + align:start position:0% + +fill three-dimensional space every B + + align:start position:0% +fill three-dimensional space every B + + + align:start position:0% +fill three-dimensional space every B +means all the B's in three-dimensional + + align:start position:0% +means all the B's in three-dimensional + + + align:start position:0% +means all the B's in three-dimensional +space so do you see that I'm just asking + + align:start position:0% +space so do you see that I'm just asking + + + align:start position:0% +space so do you see that I'm just asking +the same question in in different words + + align:start position:0% +the same question in in different words + + + align:start position:0% +the same question in in different words +solving a ax + + align:start position:0% +solving a ax + + + align:start position:0% +solving a ax +oh that's very important a times X when + + align:start position:0% +oh that's very important a times X when + + + align:start position:0% +oh that's very important a times X when +I multiply a matrix by a vector I get a + + align:start position:0% +I multiply a matrix by a vector I get a + + + align:start position:0% +I multiply a matrix by a vector I get a +combination of the columns let me I'll + + align:start position:0% +combination of the columns let me I'll + + + align:start position:0% +combination of the columns let me I'll +write that down in a moment + + align:start position:0% +write that down in a moment + + + align:start position:0% +write that down in a moment +so that you see but in my column picture + + align:start position:0% +so that you see but in my column picture + + + align:start position:0% +so that you see but in my column picture +that's really what I'm doing I'm taking + + align:start position:0% +that's really what I'm doing I'm taking + + + align:start position:0% +that's really what I'm doing I'm taking +linear combinations of these three + + align:start position:0% +linear combinations of these three + + + align:start position:0% +linear combinations of these three +columns and I'm trying to find B and + + align:start position:0% +columns and I'm trying to find B and + + + align:start position:0% +columns and I'm trying to find B and +actually the answer for this matrix will + + align:start position:0% +actually the answer for this matrix will + + + align:start position:0% +actually the answer for this matrix will +be yes for this matrix for this for this + + align:start position:0% +be yes for this matrix for this for this + + + align:start position:0% +be yes for this matrix for this for this +matrix a for these columns the answer is + + align:start position:0% + + + + align:start position:0% + +yes this matrix is this this this matrix + + align:start position:0% +yes this matrix is this this this matrix + + + align:start position:0% +yes this matrix is this this this matrix +that that I chose for an example is a + + align:start position:0% +that that I chose for an example is a + + + align:start position:0% +that that I chose for an example is a +good matrix a non singular matrix an + + align:start position:0% +good matrix a non singular matrix an + + + align:start position:0% +good matrix a non singular matrix an +invertible matrix so those will be the + + align:start position:0% +invertible matrix so those will be the + + + align:start position:0% +invertible matrix so those will be the +matrices that we like best there could + + align:start position:0% +matrices that we like best there could + + + align:start position:0% +matrices that we like best there could +be other and we will see other matrices + + align:start position:0% +be other and we will see other matrices + + + align:start position:0% +be other and we will see other matrices +where the answer becomes no oh actually + + align:start position:0% +where the answer becomes no oh actually + + + align:start position:0% +where the answer becomes no oh actually +you can see when it would become no when + + align:start position:0% +you can see when it would become no when + + + align:start position:0% +you can see when it would become no when +could what what could go wrong how could + + align:start position:0% +could what what could go wrong how could + + + align:start position:0% +could what what could go wrong how could +it go wrong that out of these out of + + align:start position:0% +it go wrong that out of these out of + + + align:start position:0% +it go wrong that out of these out of +three columns and all their combinations + + align:start position:0% +three columns and all their combinations + + + align:start position:0% +three columns and all their combinations +when would I not be able to produce some + + align:start position:0% +when would I not be able to produce some + + + align:start position:0% +when would I not be able to produce some +be off here when when could it go wrong + + align:start position:0% +be off here when when could it go wrong + + + align:start position:0% +be off here when when could it go wrong +do you see that the combinations + + align:start position:0% +do you see that the combinations + + + align:start position:0% +do you see that the combinations +supposed let me say when it goes wrong + + align:start position:0% +supposed let me say when it goes wrong + + + align:start position:0% +supposed let me say when it goes wrong +if these three columns all lie in the + + align:start position:0% +if these three columns all lie in the + + + align:start position:0% +if these three columns all lie in the +same plane then their combinations will + + align:start position:0% +same plane then their combinations will + + + align:start position:0% +same plane then their combinations will +lie in that same plane so then we're in + + align:start position:0% +lie in that same plane so then we're in + + + align:start position:0% +lie in that same plane so then we're in +trouble if the three columns of my + + align:start position:0% +trouble if the three columns of my + + + align:start position:0% +trouble if the three columns of my +matrix if those three vectors happen to + + align:start position:0% +matrix if those three vectors happen to + + + align:start position:0% +matrix if those three vectors happen to +lie in the same plane + + align:start position:0% +lie in the same plane + + + align:start position:0% +lie in the same plane +for example if column 3 is just the sum + + align:start position:0% +for example if column 3 is just the sum + + + align:start position:0% +for example if column 3 is just the sum +of column 1 and column 2 I would be in + + align:start position:0% +of column 1 and column 2 I would be in + + + align:start position:0% +of column 1 and column 2 I would be in +trouble that would be a matrix a where + + align:start position:0% +trouble that would be a matrix a where + + + align:start position:0% +trouble that would be a matrix a where +the answer would be no because the + + align:start position:0% +the answer would be no because the + + + align:start position:0% +the answer would be no because the +combinations if column 3 is in the same + + align:start position:0% +combinations if column 3 is in the same + + + align:start position:0% +combinations if column 3 is in the same +plane as column 1 and 2 I don't get + + align:start position:0% +plane as column 1 and 2 I don't get + + + align:start position:0% +plane as column 1 and 2 I don't get +anything new from that all the + + align:start position:0% +anything new from that all the + + + align:start position:0% +anything new from that all the +combinations are in the plane and the + + align:start position:0% +combinations are in the plane and the + + + align:start position:0% +combinations are in the plane and the +only right-hand sides B that I could get + + align:start position:0% +only right-hand sides B that I could get + + + align:start position:0% +only right-hand sides B that I could get +would be the ones in that plane so I + + align:start position:0% +would be the ones in that plane so I + + + align:start position:0% +would be the ones in that plane so I +could solve it for some right-hand sides + + align:start position:0% +could solve it for some right-hand sides + + + align:start position:0% +could solve it for some right-hand sides +when B is in the in the plane but most + + align:start position:0% +when B is in the in the plane but most + + + align:start position:0% +when B is in the in the plane but most +right-hand sides would be out of the + + align:start position:0% +right-hand sides would be out of the + + + align:start position:0% +right-hand sides would be out of the +plane and unreachable so that would be a + + align:start position:0% +plane and unreachable so that would be a + + + align:start position:0% +plane and unreachable so that would be a +singular case the matrix would be not + + align:start position:0% +singular case the matrix would be not + + + align:start position:0% +singular case the matrix would be not +invertible there would not be a solution + + align:start position:0% +invertible there would not be a solution + + + align:start position:0% +invertible there would not be a solution +for every B the answer would become no + + align:start position:0% +for every B the answer would become no + + + align:start position:0% +for every B the answer would become no +for that okay I don't know so we take + + align:start position:0% +for that okay I don't know so we take + + + align:start position:0% +for that okay I don't know so we take +just a little shot at thinking about + + align:start position:0% +just a little shot at thinking about + + + align:start position:0% +just a little shot at thinking about +nine dimensions imagine that we have + + align:start position:0% +nine dimensions imagine that we have + + + align:start position:0% +nine dimensions imagine that we have +vectors with nine components well it's + + align:start position:0% +vectors with nine components well it's + + + align:start position:0% +vectors with nine components well it's +gonna be hard to visualize those I don't + + align:start position:0% +gonna be hard to visualize those I don't + + + align:start position:0% +gonna be hard to visualize those I don't +pretend to do it but somehow pretend you + + align:start position:0% +pretend to do it but somehow pretend you + + + align:start position:0% +pretend to do it but somehow pretend you +do pretend we have if if this was nine + + align:start position:0% +do pretend we have if if this was nine + + + align:start position:0% +do pretend we have if if this was nine +equations in nine unknowns then we would + + align:start position:0% +equations in nine unknowns then we would + + + align:start position:0% +equations in nine unknowns then we would +have nine columns and each one would be + + align:start position:0% +have nine columns and each one would be + + + align:start position:0% +have nine columns and each one would be +a vector in nine dimensional space and + + align:start position:0% +a vector in nine dimensional space and + + + align:start position:0% +a vector in nine dimensional space and +we would be looking at their linear + + align:start position:0% +we would be looking at their linear + + + align:start position:0% +we would be looking at their linear +combinations so we'd be having the + + align:start position:0% +combinations so we'd be having the + + + align:start position:0% +combinations so we'd be having the +linear combination + + align:start position:0% +linear combination + + + align:start position:0% +linear combination +of nine vectors in nine dimensional + + align:start position:0% +of nine vectors in nine dimensional + + + align:start position:0% +of nine vectors in nine dimensional +space and we would be trying to find the + + align:start position:0% +space and we would be trying to find the + + + align:start position:0% +space and we would be trying to find the +combination that hit the correct right + + align:start position:0% +combination that hit the correct right + + + align:start position:0% +combination that hit the correct right +hand side B and we might also ask the + + align:start position:0% +hand side B and we might also ask the + + + align:start position:0% +hand side B and we might also ask the +question can we always do it + + align:start position:0% +question can we always do it + + + align:start position:0% +question can we always do it +can we get every right hand side B and + + align:start position:0% +can we get every right hand side B and + + + align:start position:0% +can we get every right hand side B and +certainly it will depend on those nine + + align:start position:0% +certainly it will depend on those nine + + + align:start position:0% +certainly it will depend on those nine +columns some sometimes the answer will + + align:start position:0% +columns some sometimes the answer will + + + align:start position:0% +columns some sometimes the answer will +be yes if I picked a random matrix it + + align:start position:0% +be yes if I picked a random matrix it + + + align:start position:0% +be yes if I picked a random matrix it +would be yes actually if I use MATLAB + + align:start position:0% +would be yes actually if I use MATLAB + + + align:start position:0% +would be yes actually if I use MATLAB +and just use the random command picked + + align:start position:0% +and just use the random command picked + + + align:start position:0% +and just use the random command picked +out a 9 by 9 matrix I guarantee it would + + align:start position:0% +out a 9 by 9 matrix I guarantee it would + + + align:start position:0% +out a 9 by 9 matrix I guarantee it would +be good it would be non-singular it + + align:start position:0% +be good it would be non-singular it + + + align:start position:0% +be good it would be non-singular it +would be invertible all beautiful but if + + align:start position:0% +would be invertible all beautiful but if + + + align:start position:0% +would be invertible all beautiful but if +I choose those columns so that they're + + align:start position:0% +I choose those columns so that they're + + + align:start position:0% +I choose those columns so that they're +not independent so that they're there so + + align:start position:0% +not independent so that they're there so + + + align:start position:0% +not independent so that they're there so +that the the ninth column is the same as + + align:start position:0% +that the the ninth column is the same as + + + align:start position:0% +that the the ninth column is the same as +the 8th column then it contributes + + align:start position:0% +the 8th column then it contributes + + + align:start position:0% +the 8th column then it contributes +nothing new and there would be + + align:start position:0% +nothing new and there would be + + + align:start position:0% +nothing new and there would be +right-hand sides B that I couldn't get + + align:start position:0% +right-hand sides B that I couldn't get + + + align:start position:0% +right-hand sides B that I couldn't get +can you sort of think about nine vectors + + align:start position:0% +can you sort of think about nine vectors + + + align:start position:0% +can you sort of think about nine vectors +in nine dimensional space and take their + + align:start position:0% +in nine dimensional space and take their + + + align:start position:0% +in nine dimensional space and take their +combinations that's really the central + + align:start position:0% +combinations that's really the central + + + align:start position:0% +combinations that's really the central +thought that that you get kind of used + + align:start position:0% +thought that that you get kind of used + + + align:start position:0% +thought that that you get kind of used +to in linear algebra even so you can't + + align:start position:0% +to in linear algebra even so you can't + + + align:start position:0% +to in linear algebra even so you can't +really visualize it you sort of think + + align:start position:0% +really visualize it you sort of think + + + align:start position:0% +really visualize it you sort of think +you can after a while those nine columns + + align:start position:0% +you can after a while those nine columns + + + align:start position:0% +you can after a while those nine columns +and all their combinations may very well + + align:start position:0% +and all their combinations may very well + + + align:start position:0% +and all their combinations may very well +fill out the whole nine dimensional + + align:start position:0% +fill out the whole nine dimensional + + + align:start position:0% +fill out the whole nine dimensional +space but if the ninth column happened + + align:start position:0% +space but if the ninth column happened + + + align:start position:0% +space but if the ninth column happened +to be the same as the eighth column and + + align:start position:0% +to be the same as the eighth column and + + + align:start position:0% +to be the same as the eighth column and +gave nothing new then probably what it + + align:start position:0% +gave nothing new then probably what it + + + align:start position:0% +gave nothing new then probably what it +would fill out would be I hesitate even + + align:start position:0% +would fill out would be I hesitate even + + + align:start position:0% +would fill out would be I hesitate even +to say this it would be a a sort of + + align:start position:0% +to say this it would be a a sort of + + + align:start position:0% +to say this it would be a a sort of +plain an eight dimensional plane inside + + align:start position:0% +plain an eight dimensional plane inside + + + align:start position:0% +plain an eight dimensional plane inside +nine dimensional space and it's those + + align:start position:0% +nine dimensional space and it's those + + + align:start position:0% +nine dimensional space and it's those +eight dimensional planes inside nine + + align:start position:0% +eight dimensional planes inside nine + + + align:start position:0% +eight dimensional planes inside nine +dimensional space that we have to work + + align:start position:0% +dimensional space that we have to work + + + align:start position:0% +dimensional space that we have to work +with eventually + + align:start position:0% +with eventually + + + align:start position:0% +with eventually +for now let's stay with a nice case + + align:start position:0% +for now let's stay with a nice case + + + align:start position:0% +for now let's stay with a nice case +where + + align:start position:0% +where + + + align:start position:0% +where +the matrices work we can get every + + align:start position:0% +the matrices work we can get every + + + align:start position:0% +the matrices work we can get every +right-hand side B and here we see how to + + align:start position:0% +right-hand side B and here we see how to + + + align:start position:0% +right-hand side B and here we see how to +do it with columns okay there was one + + align:start position:0% +do it with columns okay there was one + + + align:start position:0% +do it with columns okay there was one +step that I realize which I realized I + + align:start position:0% +step that I realize which I realized I + + + align:start position:0% +step that I realize which I realized I +was saying in words that I now want to + + align:start position:0% +was saying in words that I now want to + + + align:start position:0% +was saying in words that I now want to +write in letters because I'm coming back + + align:start position:0% +write in letters because I'm coming back + + + align:start position:0% +write in letters because I'm coming back +to the matrix form of the equation so + + align:start position:0% +to the matrix form of the equation so + + + align:start position:0% +to the matrix form of the equation so +let me write it here the matrix form of + + align:start position:0% +let me write it here the matrix form of + + + align:start position:0% +let me write it here the matrix form of +my equation of my of my system is some + + align:start position:0% +my equation of my of my system is some + + + align:start position:0% +my equation of my of my system is some +matrix a times some vector X equals some + + align:start position:0% +matrix a times some vector X equals some + + + align:start position:0% +matrix a times some vector X equals some +right-hand side B okay so this is a + + align:start position:0% +right-hand side B okay so this is a + + + align:start position:0% +right-hand side B okay so this is a +multiplication a times X matrix times + + align:start position:0% +multiplication a times X matrix times + + + align:start position:0% +multiplication a times X matrix times +vector and I just want to say how do you + + align:start position:0% +vector and I just want to say how do you + + + align:start position:0% +vector and I just want to say how do you +multiply a matrix by a vector okay so + + align:start position:0% +multiply a matrix by a vector okay so + + + align:start position:0% +multiply a matrix by a vector okay so +I'm just going to create a a matrix let + + align:start position:0% +I'm just going to create a a matrix let + + + align:start position:0% +I'm just going to create a a matrix let +me take 2 5 1 3 and let me take a vector + + align:start position:0% +me take 2 5 1 3 and let me take a vector + + + align:start position:0% +me take 2 5 1 3 and let me take a vector +X to be say 1 and 2 how do I multiply a + + align:start position:0% +X to be say 1 and 2 how do I multiply a + + + align:start position:0% +X to be say 1 and 2 how do I multiply a +matrix by a vector and we'll just think + + align:start position:0% +matrix by a vector and we'll just think + + + align:start position:0% +matrix by a vector and we'll just think +a little bit about matrix notation and + + align:start position:0% +a little bit about matrix notation and + + + align:start position:0% +a little bit about matrix notation and +how to do that multiplication so let me + + align:start position:0% +how to do that multiplication so let me + + + align:start position:0% +how to do that multiplication so let me +say how I multiply a matrix by a vector + + align:start position:0% +say how I multiply a matrix by a vector + + + align:start position:0% +say how I multiply a matrix by a vector +actually there are two ways to do it let + + align:start position:0% +actually there are two ways to do it let + + + align:start position:0% +actually there are two ways to do it let +me tell you my favorite way it's a it's + + align:start position:0% +me tell you my favorite way it's a it's + + + align:start position:0% +me tell you my favorite way it's a it's +its columns again it's a column at a + + align:start position:0% +its columns again it's a column at a + + + align:start position:0% +its columns again it's a column at a +time for me that matrix mode this matrix + + align:start position:0% +time for me that matrix mode this matrix + + + align:start position:0% +time for me that matrix mode this matrix +multiplication says I take one of that + + align:start position:0% +multiplication says I take one of that + + + align:start position:0% +multiplication says I take one of that +column and two of that column and add so + + align:start position:0% +column and two of that column and add so + + + align:start position:0% +column and two of that column and add so +this is in my the way I would think of + + align:start position:0% +this is in my the way I would think of + + + align:start position:0% +this is in my the way I would think of +it is one of the first column and two of + + align:start position:0% +it is one of the first column and two of + + + align:start position:0% +it is one of the first column and two of +the second column and and let's just see + + align:start position:0% +the second column and and let's just see + + + align:start position:0% +the second column and and let's just see +what we get so in the first component + + align:start position:0% +what we get so in the first component + + + align:start position:0% +what we get so in the first component +I'm getting a two and a 10 I'm getting a + + align:start position:0% +I'm getting a two and a 10 I'm getting a + + + align:start position:0% +I'm getting a two and a 10 I'm getting a +12 there and the second component I'm + + align:start position:0% +12 there and the second component I'm + + + align:start position:0% +12 there and the second component I'm +giving a 1 and a 6 I'm getting a 7 so + + align:start position:0% +giving a 1 and a 6 I'm getting a 7 so + + + align:start position:0% +giving a 1 and a 6 I'm getting a 7 so +that that matrix times that vector is 12 + + align:start position:0% +that that matrix times that vector is 12 + + + align:start position:0% +that that matrix times that vector is 12 +7 now + + align:start position:0% +7 now + + + align:start position:0% +7 now +you could do that another way you could + + align:start position:0% +you could do that another way you could + + + align:start position:0% +you could do that another way you could +do it a row at a time you could do and + + align:start position:0% +do it a row at a time you could do and + + + align:start position:0% +do it a row at a time you could do and +you would get this 12 and actually I + + align:start position:0% +you would get this 12 and actually I + + + align:start position:0% +you would get this 12 and actually I +pretty much did it here this way + + align:start position:0% +pretty much did it here this way + + + align:start position:0% +pretty much did it here this way +- I could take that row times my vector + + align:start position:0% +- I could take that row times my vector + + + align:start position:0% +- I could take that row times my vector +this is this is all the time this is the + + align:start position:0% +this is this is all the time this is the + + + align:start position:0% +this is this is all the time this is the +idea of a dot product this vector times + + align:start position:0% +idea of a dot product this vector times + + + align:start position:0% +idea of a dot product this vector times +this vector 2 times 1 plus 5 times 2 is + + align:start position:0% +this vector 2 times 1 plus 5 times 2 is + + + align:start position:0% +this vector 2 times 1 plus 5 times 2 is +the 12 this vector times this vector 1 + + align:start position:0% +the 12 this vector times this vector 1 + + + align:start position:0% +the 12 this vector times this vector 1 +times 1 plus 3 times 2 is the 7 so I can + + align:start position:0% +times 1 plus 3 times 2 is the 7 so I can + + + align:start position:0% +times 1 plus 3 times 2 is the 7 so I can +do it by rows and in each row each row + + align:start position:0% +do it by rows and in each row each row + + + align:start position:0% +do it by rows and in each row each row +times my X is what I'll later call a dot + + align:start position:0% +times my X is what I'll later call a dot + + + align:start position:0% +times my X is what I'll later call a dot +product but I also like to see it by + + align:start position:0% +product but I also like to see it by + + + align:start position:0% +product but I also like to see it by +columns I see this as a linear + + align:start position:0% +columns I see this as a linear + + + align:start position:0% +columns I see this as a linear +combination of the columns so here's my + + align:start position:0% +combination of the columns so here's my + + + align:start position:0% +combination of the columns so here's my +point a times X is a combination of the + + align:start position:0% +point a times X is a combination of the + + + align:start position:0% +point a times X is a combination of the +columns of a that's that's how I hope + + align:start position:0% +columns of a that's that's how I hope + + + align:start position:0% +columns of a that's that's how I hope +you will think of a times X when we need + + align:start position:0% +you will think of a times X when we need + + + align:start position:0% +you will think of a times X when we need +it right now we've got with small ones + + align:start position:0% +it right now we've got with small ones + + + align:start position:0% +it right now we've got with small ones +we can always do it in different ways + + align:start position:0% +we can always do it in different ways + + + align:start position:0% +we can always do it in different ways +but later think of it that way ok so + + align:start position:0% +but later think of it that way ok so + + + align:start position:0% +but later think of it that way ok so +that's the picture for a 2 by 2 system + + align:start position:0% +that's the picture for a 2 by 2 system + + + align:start position:0% +that's the picture for a 2 by 2 system +and if the right-hand side B happened to + + align:start position:0% +and if the right-hand side B happened to + + + align:start position:0% +and if the right-hand side B happened to +be 12 7 then of course the correct + + align:start position:0% +be 12 7 then of course the correct + + + align:start position:0% +be 12 7 then of course the correct +solution would be 1 2 okay so let me + + align:start position:0% +solution would be 1 2 okay so let me + + + align:start position:0% +solution would be 1 2 okay so let me +come back next time to a systematic way + + align:start position:0% +come back next time to a systematic way + + + align:start position:0% +come back next time to a systematic way +using elimination to find the solution + + align:start position:0% +using elimination to find the solution + + + align:start position:0% +using elimination to find the solution +if there is one to any a system of any + + align:start position:0% +if there is one to any a system of any + + + align:start position:0% +if there is one to any a system of any +size and find out because the system + + align:start position:0% +size and find out because the system + + + align:start position:0% +size and find out because the system +because eliminate if elimination fails + + align:start position:0% +because eliminate if elimination fails + + + align:start position:0% +because eliminate if elimination fails +find out when there isn't a solution ok + + align:start position:0% +find out when there isn't a solution ok + + + align:start position:0% +find out when there isn't a solution ok +thanks \ No newline at end of file diff --git a/JTePtoM_MeM.txt b/JTePtoM_MeM.txt new file mode 100644 index 0000000000000000000000000000000000000000..6cc05a6368b687b0f154f9617e1cccf1459754b3 --- /dev/null +++ b/JTePtoM_MeM.txt @@ -0,0 +1,1355 @@ +align:start position:0% + +we'd like to consider velocity dependent + + align:start position:0% +we'd like to consider velocity dependent + + + align:start position:0% +we'd like to consider velocity dependent +resistive forces so let's imagine a + + align:start position:0% +resistive forces so let's imagine a + + + align:start position:0% +resistive forces so let's imagine a +situation where we have an object and + + align:start position:0% +situation where we have an object and + + + align:start position:0% +situation where we have an object and +it's falling in a gravitational field so + + align:start position:0% +it's falling in a gravitational field so + + + align:start position:0% +it's falling in a gravitational field so +we have a gravitational force and this + + align:start position:0% +we have a gravitational force and this + + + align:start position:0% +we have a gravitational force and this +object is like a marble falling in a vat + + align:start position:0% +object is like a marble falling in a vat + + + align:start position:0% +object is like a marble falling in a vat +of oil um and there is a velocity + + align:start position:0% +of oil um and there is a velocity + + + align:start position:0% +of oil um and there is a velocity +dependent resistive force that is acting + + align:start position:0% +dependent resistive force that is acting + + + align:start position:0% +dependent resistive force that is acting +on this object and let's again choose it + + align:start position:0% +on this object and let's again choose it + + + align:start position:0% +on this object and let's again choose it +positive Direction down and now for + + align:start position:0% +positive Direction down and now for + + + align:start position:0% +positive Direction down and now for +objects that are moving very slowly in a + + align:start position:0% +objects that are moving very slowly in a + + + align:start position:0% +objects that are moving very slowly in a +fluid let's make a model for our + + align:start position:0% +fluid let's make a model for our + + + align:start position:0% +fluid let's make a model for our +velocity dependent resistive Force we'll + + align:start position:0% +velocity dependent resistive Force we'll + + + align:start position:0% +velocity dependent resistive Force we'll +assume that the resistive force is + + align:start position:0% +assume that the resistive force is + + + align:start position:0% +assume that the resistive force is +proportional to the velocity it's + + align:start position:0% +proportional to the velocity it's + + + align:start position:0% +proportional to the velocity it's +opposing the direction of motion and + + align:start position:0% +opposing the direction of motion and + + + align:start position:0% +opposing the direction of motion and +we'll put a coefficient Alpha in front + + align:start position:0% +we'll put a coefficient Alpha in front + + + align:start position:0% +we'll put a coefficient Alpha in front +and this is our model for velocity + + align:start position:0% +and this is our model for velocity + + + align:start position:0% +and this is our model for velocity +dependent resistive forces for objects + + align:start position:0% +dependent resistive forces for objects + + + align:start position:0% +dependent resistive forces for objects +that are moving very slowly for our case + + align:start position:0% +that are moving very slowly for our case + + + align:start position:0% +that are moving very slowly for our case +let's consider the units of the + + align:start position:0% +let's consider the units of the + + + align:start position:0% +let's consider the units of the +coefficient Alpha + + align:start position:0% +coefficient Alpha + + + align:start position:0% +coefficient Alpha +so the units of alpha have the units of + + align:start position:0% +so the units of alpha have the units of + + + align:start position:0% +so the units of alpha have the units of +force ID velocity so the units of force + + align:start position:0% +force ID velocity so the units of force + + + align:start position:0% +force ID velocity so the units of force +are we have the units of force divided + + align:start position:0% +are we have the units of force divided + + + align:start position:0% +are we have the units of force divided +by the units of velocity and that gives + + align:start position:0% +by the units of velocity and that gives + + + align:start position:0% +by the units of velocity and that gives +us kilogram m/s squar divided by the + + align:start position:0% +us kilogram m/s squar divided by the + + + align:start position:0% +us kilogram m/s squar divided by the +units of velocity which are Velocity per + + align:start position:0% +units of velocity which are Velocity per + + + align:start position:0% +units of velocity which are Velocity per +second and so we see that the + + align:start position:0% +second and so we see that the + + + align:start position:0% +second and so we see that the +coefficient of alpha has the units of + + align:start position:0% +coefficient of alpha has the units of + + + align:start position:0% +coefficient of alpha has the units of +kilogram per inverse second now now what + + align:start position:0% +kilogram per inverse second now now what + + + align:start position:0% +kilogram per inverse second now now what +we'd like to do is apply Newton's Second + + align:start position:0% +we'd like to do is apply Newton's Second + + + align:start position:0% +we'd like to do is apply Newton's Second +Law so let's + + align:start position:0% +Law so let's + + + align:start position:0% +Law so let's +analyze the + + align:start position:0% +analyze the + + + align:start position:0% +analyze the +forces and get the equation of motion + + align:start position:0% +forces and get the equation of motion + + + align:start position:0% +forces and get the equation of motion +for this object falling in a viscous + + align:start position:0% +for this object falling in a viscous + + + align:start position:0% +for this object falling in a viscous +medium with a resistive force in the + + align:start position:0% +medium with a resistive force in the + + + align:start position:0% +medium with a resistive force in the +jhot direction we have the gravitational + + align:start position:0% +jhot direction we have the gravitational + + + align:start position:0% +jhot direction we have the gravitational +force and we have our resistive friction + + align:start position:0% +force and we have our resistive friction + + + align:start position:0% +force and we have our resistive friction +Force which we're writing VY as the Y + + align:start position:0% +Force which we're writing VY as the Y + + + align:start position:0% +Force which we're writing VY as the Y +component of the velocity and that's + + align:start position:0% +component of the velocity and that's + + + align:start position:0% +component of the velocity and that's +equal to M * dvy DT now notice that the + + align:start position:0% +equal to M * dvy DT now notice that the + + + align:start position:0% +equal to M * dvy DT now notice that the +acceleration we're not treating as a + + align:start position:0% +acceleration we're not treating as a + + + align:start position:0% +acceleration we're not treating as a +constant it's a the derivative of the + + align:start position:0% +constant it's a the derivative of the + + + align:start position:0% +constant it's a the derivative of the +Velocity this leads us to our + + align:start position:0% +Velocity this leads us to our + + + align:start position:0% +Velocity this leads us to our +differential equation which is written + + align:start position:0% +differential equation which is written + + + align:start position:0% +differential equation which is written +as + + align:start position:0% +as + + + align:start position:0% +as +dydt I'll divide through by m g minus + + align:start position:0% +dydt I'll divide through by m g minus + + + align:start position:0% +dydt I'll divide through by m g minus +Alpha m b y now this is a linear linear + + align:start position:0% +Alpha m b y now this is a linear linear + + + align:start position:0% +Alpha m b y now this is a linear linear +in velocity first order differential + + align:start position:0% +in velocity first order differential + + + align:start position:0% +in velocity first order differential +equation with a constant term in here + + align:start position:0% +equation with a constant term in here + + + align:start position:0% +equation with a constant term in here +which is called mogeneous linear first + + align:start position:0% +which is called mogeneous linear first + + + align:start position:0% +which is called mogeneous linear first +order differential equation we shall + + align:start position:0% +order differential equation we shall + + + align:start position:0% +order differential equation we shall +solve this like we did with our other + + align:start position:0% +solve this like we did with our other + + + align:start position:0% +solve this like we did with our other +equations by separation of variables so + + align:start position:0% +equations by separation of variables so + + + align:start position:0% +equations by separation of variables so +what we do is we bring + + align:start position:0% +what we do is we bring + + + align:start position:0% +what we do is we bring +the velocity terms to one side and the + + align:start position:0% +the velocity terms to one side and the + + + align:start position:0% +the velocity terms to one side and the +time terms to the other side and now we + + align:start position:0% +time terms to the other side and now we + + + align:start position:0% +time terms to the other side and now we +can integrate both sides directly but + + align:start position:0% +can integrate both sides directly but + + + align:start position:0% +can integrate both sides directly but +before I integrate this side I'd like to + + align:start position:0% +before I integrate this side I'd like to + + + align:start position:0% +before I integrate this side I'd like to +rewrite it by writing it as dvy and I'd + + align:start position:0% +rewrite it by writing it as dvy and I'd + + + align:start position:0% +rewrite it by writing it as dvy and I'd +like to pull out a minus Alpha M and + + align:start position:0% +like to pull out a minus Alpha M and + + + align:start position:0% +like to pull out a minus Alpha M and +this term here becomes minus mg over + + align:start position:0% +this term here becomes minus mg over + + + align:start position:0% +this term here becomes minus mg over +Alpha why did I do this for the + + align:start position:0% +Alpha why did I do this for the + + + align:start position:0% +Alpha why did I do this for the +integration it just makes my natural + + align:start position:0% +integration it just makes my natural + + + align:start position:0% +integration it just makes my natural +logarithm integral look a little bit + + align:start position:0% +logarithm integral look a little bit + + + align:start position:0% +logarithm integral look a little bit +easier and over here I have DT now what + + align:start position:0% +easier and over here I have DT now what + + + align:start position:0% +easier and over here I have DT now what +I want to do is integrate and we're + + align:start position:0% +I want to do is integrate and we're + + + align:start position:0% +I want to do is integrate and we're +going to integrate from some initial + + align:start position:0% +going to integrate from some initial + + + align:start position:0% +going to integrate from some initial +velocity which we're going to take to be + + align:start position:0% +velocity which we're going to take to be + + + align:start position:0% +velocity which we're going to take to be +zero we're going to drop this let this + + align:start position:0% +zero we're going to drop this let this + + + align:start position:0% +zero we're going to drop this let this +object be released from rest and we're + + align:start position:0% +object be released from rest and we're + + + align:start position:0% +object be released from rest and we're +going to integrate to some final speed + + align:start position:0% +going to integrate to some final speed + + + align:start position:0% +going to integrate to some final speed +VY of T over here let's just call our + + align:start position:0% +VY of T over here let's just call our + + + align:start position:0% +VY of T over here let's just call our +integration variable T Prime and we + + align:start position:0% +integration variable T Prime and we + + + align:start position:0% +integration variable T Prime and we +integrate T Prime from zero to sometime + + align:start position:0% +integrate T Prime from zero to sometime + + + align:start position:0% +integrate T Prime from zero to sometime +T so this is our variable and the + + align:start position:0% +T so this is our variable and the + + + align:start position:0% +T so this is our variable and the +velocity is a function of time now doing + + align:start position:0% +velocity is a function of time now doing + + + align:start position:0% +velocity is a function of time now doing +this integral um first off this constant + + align:start position:0% +this integral um first off this constant + + + align:start position:0% +this integral um first off this constant +term comes out so we have 1 /us Alpha M + + align:start position:0% +term comes out so we have 1 /us Alpha M + + + align:start position:0% +term comes out so we have 1 /us Alpha M +and the integral is just a natural log + + align:start position:0% +and the integral is just a natural log + + + align:start position:0% +and the integral is just a natural log +integral of V Yus mg over Alpha and we + + align:start position:0% +integral of V Yus mg over Alpha and we + + + align:start position:0% +integral of V Yus mg over Alpha and we +have to divide that in the lower limit v + + align:start position:0% +have to divide that in the lower limit v + + + align:start position:0% +have to divide that in the lower limit v +y is zero and we have just minus mg over + + align:start position:0% +y is zero and we have just minus mg over + + + align:start position:0% +y is zero and we have just minus mg over +Alpha and this side is very simply T now + + align:start position:0% +Alpha and this side is very simply T now + + + align:start position:0% +Alpha and this side is very simply T now +we can rewrite this equation by bringing + + align:start position:0% +we can rewrite this equation by bringing + + + align:start position:0% +we can rewrite this equation by bringing +the M over Alpha to the other side and + + align:start position:0% +the M over Alpha to the other side and + + + align:start position:0% +the M over Alpha to the other side and +we have log of Vy minus mg Alpha over + + align:start position:0% +we have log of Vy minus mg Alpha over + + + align:start position:0% +we have log of Vy minus mg Alpha over +minus mg + + align:start position:0% +minus mg + + + align:start position:0% +minus mg +Alpha equals minus Alpha m t now recall + + align:start position:0% +Alpha equals minus Alpha m t now recall + + + align:start position:0% +Alpha equals minus Alpha m t now recall +that e to the log of any quantity X is + + align:start position:0% +that e to the log of any quantity X is + + + align:start position:0% +that e to the log of any quantity X is +equal to X so if I exponentiate both + + align:start position:0% +equal to X so if I exponentiate both + + + align:start position:0% +equal to X so if I exponentiate both +sides I get v y + + align:start position:0% +sides I get v y + + + align:start position:0% +sides I get v y +- mg/ Alpha / - mg Alpha is equal to the + + align:start position:0% +- mg/ Alpha / - mg Alpha is equal to the + + + align:start position:0% +- mg/ Alpha / - mg Alpha is equal to the +exponential e to the minus Alpha Mt now + + align:start position:0% +exponential e to the minus Alpha Mt now + + + align:start position:0% +exponential e to the minus Alpha Mt now +the last step is simply to bring this + + align:start position:0% +the last step is simply to bring this + + + align:start position:0% +the last step is simply to bring this +over there multiply and do a little bit + + align:start position:0% +over there multiply and do a little bit + + + align:start position:0% +over there multiply and do a little bit +of algebra and so I get that the + + align:start position:0% +of algebra and so I get that the + + + align:start position:0% +of algebra and so I get that the +velocity as a function of Y is equal to + + align:start position:0% +velocity as a function of Y is equal to + + + align:start position:0% +velocity as a function of Y is equal to +mg Alpha * 1 - e to minus Alpha m t + + align:start position:0% +mg Alpha * 1 - e to minus Alpha m t + + + align:start position:0% +mg Alpha * 1 - e to minus Alpha m t +now there's a few interesting things + + align:start position:0% +now there's a few interesting things + + + align:start position:0% +now there's a few interesting things +here that we want to look at suppose we + + align:start position:0% +here that we want to look at suppose we + + + align:start position:0% +here that we want to look at suppose we +Define this exponential e to the minus + + align:start position:0% +Define this exponential e to the minus + + + align:start position:0% +Define this exponential e to the minus +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +Mt as equal to eus T over + + align:start position:0% +Mt as equal to eus T over + + + align:start position:0% +Mt as equal to eus T over +to where + + align:start position:0% +to where + + + align:start position:0% +to where +to is M over Alpha the units of to when + + align:start position:0% +to is M over Alpha the units of to when + + + align:start position:0% +to is M over Alpha the units of to when +we look at the units it has the units of + + align:start position:0% +we look at the units it has the units of + + + align:start position:0% +we look at the units it has the units of +mass which is kilograms over the units + + align:start position:0% +mass which is kilograms over the units + + + align:start position:0% +mass which is kilograms over the units +of alpha which we worked out before so + + align:start position:0% +of alpha which we worked out before so + + + align:start position:0% +of alpha which we worked out before so +we have kilograms over kilogram inverse + + align:start position:0% +we have kilograms over kilogram inverse + + + align:start position:0% +we have kilograms over kilogram inverse +second that gives us units of seconds + + align:start position:0% +second that gives us units of seconds + + + align:start position:0% +second that gives us units of seconds +and that's what we expect because T + + align:start position:0% +and that's what we expect because T + + + align:start position:0% +and that's what we expect because T +seconds over seconds gives us + + align:start position:0% +seconds over seconds gives us + + + align:start position:0% +seconds over seconds gives us +dimensionist quantity for the + + align:start position:0% +dimensionist quantity for the + + + align:start position:0% +dimensionist quantity for the +exponential now the last thing we'd like + + align:start position:0% +exponential now the last thing we'd like + + + align:start position:0% +exponential now the last thing we'd like +to look at is let's just see what + + align:start position:0% +to look at is let's just see what + + + align:start position:0% +to look at is let's just see what +happens when we plot this well if we're + + align:start position:0% +happens when we plot this well if we're + + + align:start position:0% +happens when we plot this well if we're +plotting + + align:start position:0% +plotting + + + align:start position:0% +plotting +by as a function of T we start off at + + align:start position:0% +by as a function of T we start off at + + + align:start position:0% +by as a function of T we start off at +zero and we're going to reach some + + align:start position:0% +zero and we're going to reach some + + + align:start position:0% +zero and we're going to reach some +terminal quantity VY + + align:start position:0% +terminal quantity VY + + + align:start position:0% +terminal quantity VY +terminal which is when + + align:start position:0% +terminal which is when + + + align:start position:0% +terminal which is when +we have a graph like that and we can see + + align:start position:0% +we have a graph like that and we can see + + + align:start position:0% +we have a graph like that and we can see +what that terminal speed is when we set + + align:start position:0% +what that terminal speed is when we set + + + align:start position:0% +what that terminal speed is when we set +t equal to Infinity e to the minus + + align:start position:0% +t equal to Infinity e to the minus + + + align:start position:0% +t equal to Infinity e to the minus +infinity is zero and so this terminal + + align:start position:0% +infinity is zero and so this terminal + + + align:start position:0% +infinity is zero and so this terminal +speed is equal to just this coefficient + + align:start position:0% +speed is equal to just this coefficient + + + align:start position:0% +speed is equal to just this coefficient +mg over Alpha and that's the terminal + + align:start position:0% +mg over Alpha and that's the terminal + + + align:start position:0% +mg over Alpha and that's the terminal +speed now notice that as a check for + + align:start position:0% +speed now notice that as a check for + + + align:start position:0% +speed now notice that as a check for +what we did we can come back to our + + align:start position:0% +what we did we can come back to our + + + align:start position:0% +what we did we can come back to our +differential equation and what does + + align:start position:0% +differential equation and what does + + + align:start position:0% +differential equation and what does +terminal speed mean notice that when you + + align:start position:0% +terminal speed mean notice that when you + + + align:start position:0% +terminal speed mean notice that when you +get to this limit as T approaches + + align:start position:0% +get to this limit as T approaches + + + align:start position:0% +get to this limit as T approaches +Infinity the slope of the Velocity curve + + align:start position:0% +Infinity the slope of the Velocity curve + + + align:start position:0% +Infinity the slope of the Velocity curve +is zero and that's really the statement + + align:start position:0% +is zero and that's really the statement + + + align:start position:0% +is zero and that's really the statement +over here that + + align:start position:0% +over here that + + + align:start position:0% +over here that +VY + + align:start position:0% + + + + align:start position:0% + +terminal is + + align:start position:0% +terminal is + + + align:start position:0% +terminal is +when the veloc + + align:start position:0% +when the veloc + + + align:start position:0% +when the veloc +is no longer changing in time you can + + align:start position:0% +is no longer changing in time you can + + + align:start position:0% +is no longer changing in time you can +see it graphically and this is the + + align:start position:0% +see it graphically and this is the + + + align:start position:0% +see it graphically and this is the +statement when we go back to Newton's + + align:start position:0% +statement when we go back to Newton's + + + align:start position:0% +statement when we go back to Newton's +second law that there's acceleration is + + align:start position:0% +second law that there's acceleration is + + + align:start position:0% +second law that there's acceleration is +zero so the sum of the forces at + + align:start position:0% +zero so the sum of the forces at + + + align:start position:0% +zero so the sum of the forces at +Terminal speed are zero the resistive + + align:start position:0% +Terminal speed are zero the resistive + + + align:start position:0% +Terminal speed are zero the resistive +force is equal to the gravitational + + align:start position:0% +force is equal to the gravitational + + + align:start position:0% +force is equal to the gravitational +force and so from this equation here as + + align:start position:0% +force and so from this equation here as + + + align:start position:0% +force and so from this equation here as +a check we can see that VY + + align:start position:0% +a check we can see that VY + + + align:start position:0% +a check we can see that VY +terminal equals mg + + align:start position:0% +terminal equals mg + + + align:start position:0% +terminal equals mg +over Alpha which checks with our + + align:start position:0% +over Alpha which checks with our + + + align:start position:0% +over Alpha which checks with our +calculation and so we have confidence + + align:start position:0% +calculation and so we have confidence + + + align:start position:0% +calculation and so we have confidence +that we Analyze This + + align:start position:0% +that we Analyze This + + + align:start position:0% +that we Analyze This +correctly and that gives us our motion + + align:start position:0% +correctly and that gives us our motion + + + align:start position:0% +correctly and that gives us our motion +one last thing that's quite interesting + + align:start position:0% +one last thing that's quite interesting + + + align:start position:0% +one last thing that's quite interesting +um notice that the terminal speed + + align:start position:0% +um notice that the terminal speed + + + align:start position:0% +um notice that the terminal speed +depends on mass this coefficient Alpha + + align:start position:0% +depends on mass this coefficient Alpha + + + align:start position:0% +depends on mass this coefficient Alpha +is only a function of the properties of + + align:start position:0% +is only a function of the properties of + + + align:start position:0% +is only a function of the properties of +the object the size the shape the + + align:start position:0% +the object the size the shape the + + + align:start position:0% +the object the size the shape the +geometric properties of the object not + + align:start position:0% +geometric properties of the object not + + + align:start position:0% +geometric properties of the object not +how dense it is so if you had two + + align:start position:0% +how dense it is so if you had two + + + align:start position:0% +how dense it is so if you had two +objects like two balls same radius but + + align:start position:0% +objects like two balls same radius but + + + align:start position:0% +objects like two balls same radius but +one was denser than the other then the + + align:start position:0% +one was denser than the other then the + + + align:start position:0% +one was denser than the other then the +other one Mass would be heavier and the + + align:start position:0% +other one Mass would be heavier and the + + + align:start position:0% +other one Mass would be heavier and the +terminal speed would be greater so what + + align:start position:0% +terminal speed would be greater so what + + + align:start position:0% +terminal speed would be greater so what +we see is that two identical objects one + + align:start position:0% +we see is that two identical objects one + + + align:start position:0% +we see is that two identical objects one +heavier than the other the heavier + + align:start position:0% +heavier than the other the heavier + + + align:start position:0% +heavier than the other the heavier +object reaches a faster terminal speed + + align:start position:0% +object reaches a faster terminal speed + + + align:start position:0% +object reaches a faster terminal speed +than the lighter object which explains a + + align:start position:0% +than the lighter object which explains a + + + align:start position:0% +than the lighter object which explains a +well observed phenomena \ No newline at end of file diff --git a/K3QfVXBqbYM.txt b/K3QfVXBqbYM.txt new file mode 100644 index 0000000000000000000000000000000000000000..e2bd9fea3749d35d335fce51ee8d40bec7a0dd10 --- /dev/null +++ b/K3QfVXBqbYM.txt @@ -0,0 +1,7219 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +we go into the reading today so this is + + align:start position:0% +we go into the reading today so this is + + + align:start position:0% +we go into the reading today so this is +a interesting book that came out from + + align:start position:0% +a interesting book that came out from + + + align:start position:0% +a interesting book that came out from +something called a new games movement + + align:start position:0% +something called a new games movement + + + align:start position:0% +something called a new games movement +which I had mentioned a few times in + + align:start position:0% +which I had mentioned a few times in + + + align:start position:0% +which I had mentioned a few times in +class but just as a reminder I think I + + align:start position:0% +class but just as a reminder I think I + + + align:start position:0% +class but just as a reminder I think I +read mostly in the 60s but how many of + + align:start position:0% +read mostly in the 60s but how many of + + + align:start position:0% +read mostly in the 60s but how many of +you kind of got that vibe while you were + + align:start position:0% +you kind of got that vibe while you were + + + align:start position:0% +you kind of got that vibe while you were +reading this but that's interesting + + align:start position:0% +reading this but that's interesting + + + align:start position:0% +reading this but that's interesting +because you know it's it's a it's + + align:start position:0% +because you know it's it's a it's + + + align:start position:0% +because you know it's it's a it's +written in this sort of like almost + + align:start position:0% +written in this sort of like almost + + + align:start position:0% +written in this sort of like almost +Hemingway ish I know you know a short + + align:start position:0% +Hemingway ish I know you know a short + + + align:start position:0% +Hemingway ish I know you know a short +little sentences short short little + + align:start position:0% +little sentences short short little + + + align:start position:0% +little sentences short short little +declarative sentences about wellness and + + align:start position:0% +declarative sentences about wellness and + + + align:start position:0% +declarative sentences about wellness and +happiness and getting along with the + + align:start position:0% +happiness and getting along with the + + + align:start position:0% +happiness and getting along with the +community is that right that but all + + align:start position:0% +community is that right that but all + + + align:start position:0% +community is that right that but all +principals in at least in the in the + + align:start position:0% +principals in at least in the in the + + + align:start position:0% +principals in at least in the in the +chapter in today's reading aren't + + align:start position:0% +chapter in today's reading aren't + + + align:start position:0% +chapter in today's reading aren't +actually all that different from what + + align:start position:0% +actually all that different from what + + + align:start position:0% +actually all that different from what +I've been teaching all semester long + + align:start position:0% +I've been teaching all semester long + + + align:start position:0% +I've been teaching all semester long +regarding game design and play testing + + align:start position:0% +regarding game design and play testing + + + align:start position:0% +regarding game design and play testing +if you worry if it's your job to + + align:start position:0% +if you worry if it's your job to + + + align:start position:0% +if you worry if it's your job to +actually make a game + + align:start position:0% +actually make a game + + + align:start position:0% +actually make a game +what Bernie de Colvin and some of his + + align:start position:0% +what Bernie de Colvin and some of his + + + align:start position:0% +what Bernie de Colvin and some of his +other colleagues at once read of the + + align:start position:0% +other colleagues at once read of the + + + align:start position:0% +other colleagues at once read of the +Whole Earth Catalog Stewart Brand was it + + align:start position:0% +Whole Earth Catalog Stewart Brand was it + + + align:start position:0% +Whole Earth Catalog Stewart Brand was it +yeah student the Whole Earth Catalog + + align:start position:0% +yeah student the Whole Earth Catalog + + + align:start position:0% +yeah student the Whole Earth Catalog +well actually that's the new game + + align:start position:0% +well actually that's the new game + + + align:start position:0% +well actually that's the new game +movement in particular yeah but it's + + align:start position:0% +movement in particular yeah but it's + + + align:start position:0% +movement in particular yeah but it's +kind of the same community of people who + + align:start position:0% +kind of the same community of people who + + + align:start position:0% +kind of the same community of people who +are just trying to find ways to not only + + align:start position:0% +are just trying to find ways to not only + + + align:start position:0% +are just trying to find ways to not only +to find ways for people to get along + + align:start position:0% +to find ways for people to get along + + + align:start position:0% +to find ways for people to get along +with each other but also things like + + align:start position:0% +with each other but also things like + + + align:start position:0% +with each other but also things like +where the party is like taking military + + align:start position:0% +where the party is like taking military + + + align:start position:0% +where the party is like taking military +equipment and then turning them into + + align:start position:0% +equipment and then turning them into + + + align:start position:0% +equipment and then turning them into +things that you play away um so this was + + align:start position:0% +things that you play away um so this was + + + align:start position:0% +things that you play away um so this was +today's chapter it has a lot of stuff + + align:start position:0% +today's chapter it has a lot of stuff + + + align:start position:0% +today's chapter it has a lot of stuff +about how people who are you know who + + align:start position:0% +about how people who are you know who + + + align:start position:0% +about how people who are you know who +don't necessarily see themselves as game + + align:start position:0% +don't necessarily see themselves as game + + + align:start position:0% +don't necessarily see themselves as game +makers can use some of the practices + + align:start position:0% +makers can use some of the practices + + + align:start position:0% +makers can use some of the practices +that we've been talking about in this + + align:start position:0% +that we've been talking about in this + + + align:start position:0% +that we've been talking about in this +class to basically change the way how + + align:start position:0% +class to basically change the way how + + + align:start position:0% +class to basically change the way how +they play games that they already that + + align:start position:0% +they play games that they already that + + + align:start position:0% +they play games that they already that +they already play + + align:start position:0% +they already play + + + align:start position:0% +they already play +oh you know and in the process of that + + align:start position:0% +oh you know and in the process of that + + + align:start position:0% +oh you know and in the process of that +create you new games the new games we + + align:start position:0% +create you new games the new games we + + + align:start position:0% +create you new games the new games we +play there's actually a whole new a new + + align:start position:0% +play there's actually a whole new a new + + + align:start position:0% +play there's actually a whole new a new +games book that is more about the kinds + + align:start position:0% +games book that is more about the kinds + + + align:start position:0% +games book that is more about the kinds +of games that you can play it includes + + align:start position:0% +of games that you can play it includes + + + align:start position:0% +of games that you can play it includes +things like parachute if you've ever + + align:start position:0% +things like parachute if you've ever + + + align:start position:0% +things like parachute if you've ever +done that game where that's life to + + align:start position:0% +done that game where that's life to + + + align:start position:0% +done that game where that's life to +people back to back you're sitting back + + align:start position:0% +people back to back you're sitting back + + + align:start position:0% +people back to back you're sitting back +to back and then your job is to stand up + + align:start position:0% +to back and then your job is to stand up + + + align:start position:0% +to back and then your job is to stand up +you know I think without using your + + align:start position:0% +you know I think without using your + + + align:start position:0% +you know I think without using your +hands + + align:start position:0% +hands + + + align:start position:0% +hands +like you lock your eyes you're not + + align:start position:0% +like you lock your eyes you're not + + + align:start position:0% +like you lock your eyes you're not +you're yeah + + align:start position:0% +you're yeah + + + align:start position:0% +you're yeah +also that game player that you read + + align:start position:0% +also that game player that you read + + + align:start position:0% +also that game player that you read +everyone we reach us in in everyone be + + align:start position:0% +everyone we reach us in in everyone be + + + align:start position:0% +everyone we reach us in in everyone be +sort of gets into a tight circle reaches + + align:start position:0% +sort of gets into a tight circle reaches + + + align:start position:0% +sort of gets into a tight circle reaches +and grab somebody else's hand and the + + align:start position:0% +and grab somebody else's hand and the + + + align:start position:0% +and grab somebody else's hand and the +hotel is right it's what title it okay + + align:start position:0% +hotel is right it's what title it okay + + + align:start position:0% +hotel is right it's what title it okay +that you see how the schools a lot + + align:start position:0% +that you see how the schools a lot + + + align:start position:0% +that you see how the schools a lot +nowadays I as far as sleeps by parachute + + align:start position:0% +nowadays I as far as sleeps by parachute + + + align:start position:0% +nowadays I as far as sleeps by parachute +and all that came from this new games + + align:start position:0% +and all that came from this new games + + + align:start position:0% +and all that came from this new games +movement again it's a reaction to to was + + align:start position:0% +movement again it's a reaction to to was + + + align:start position:0% +movement again it's a reaction to to was +in Vietnam and and I guess career am I + + align:start position:0% +in Vietnam and and I guess career am I + + + align:start position:0% +in Vietnam and and I guess career am I +am I getting my micro not like yeah yeah + + align:start position:0% +am I getting my micro not like yeah yeah + + + align:start position:0% +am I getting my micro not like yeah yeah +and you know just trying to say how do + + align:start position:0% +and you know just trying to say how do + + + align:start position:0% +and you know just trying to say how do +we play learn how to play with other + + align:start position:0% +we play learn how to play with other + + + align:start position:0% +we play learn how to play with other +people instead of fighting other people + + align:start position:0% +people instead of fighting other people + + + align:start position:0% +people instead of fighting other people +but there's a couple of interesting + + align:start position:0% +but there's a couple of interesting + + + align:start position:0% +but there's a couple of interesting +ideas and here that I thought that were + + align:start position:0% +ideas and here that I thought that were + + + align:start position:0% +ideas and here that I thought that were +kind of unique to today's reading that + + align:start position:0% +kind of unique to today's reading that + + + align:start position:0% +kind of unique to today's reading that +we haven't necessarily we haven't + + align:start position:0% +we haven't necessarily we haven't + + + align:start position:0% +we haven't necessarily we haven't +necessarily a drastic class there + + align:start position:0% +necessarily a drastic class there + + + align:start position:0% +necessarily a drastic class there +anything deep up in the game and it's + + align:start position:0% +anything deep up in the game and it's + + + align:start position:0% +anything deep up in the game and it's +kind of funny cause the example that he + + align:start position:0% +kind of funny cause the example that he + + + align:start position:0% +kind of funny cause the example that he +talks about is kind of like switching + + align:start position:0% +talks about is kind of like switching + + + align:start position:0% +talks about is kind of like switching +like borrowing the rule on the fly right + + align:start position:0% +like borrowing the rule on the fly right + + + align:start position:0% +like borrowing the rule on the fly right +it's like you know like from a different + + align:start position:0% +it's like you know like from a different + + + align:start position:0% +it's like you know like from a different +variant of the same game but I think the + + align:start position:0% +variant of the same game but I think the + + + align:start position:0% +variant of the same game but I think the +same principle can actually be applied + + align:start position:0% +same principle can actually be applied + + + align:start position:0% +same principle can actually be applied +to a much wider range of things like + + align:start position:0% +to a much wider range of things like + + + align:start position:0% +to a much wider range of things like +like safety rules you know is if say + + align:start position:0% +like safety rules you know is if say + + + align:start position:0% +like safety rules you know is if say +you're playing a game like tag or + + align:start position:0% +you're playing a game like tag or + + + align:start position:0% +you're playing a game like tag or +something like that you don't + + align:start position:0% +something like that you don't + + + align:start position:0% +something like that you don't +necessarily you haven't necessarily + + align:start position:0% +necessarily you haven't necessarily + + + align:start position:0% +necessarily you haven't necessarily +mapped out the boundaries of your game + + align:start position:0% +mapped out the boundaries of your game + + + align:start position:0% +mapped out the boundaries of your game +but the game that you've played with + + align:start position:0% +but the game that you've played with + + + align:start position:0% +but the game that you've played with +your friends + + align:start position:0% +your friends + + + align:start position:0% +your friends +or decided that about 1:1 the boundaries + + align:start position:0% +or decided that about 1:1 the boundaries + + + align:start position:0% +or decided that about 1:1 the boundaries +was going to be the edge of that road + + align:start position:0% +was going to be the edge of that road + + + align:start position:0% +was going to be the edge of that road +right no one can run past that road this + + align:start position:0% +right no one can run past that road this + + + align:start position:0% +right no one can run past that road this +is that's a fairly sensible safety rule + + align:start position:0% +is that's a fairly sensible safety rule + + + align:start position:0% +is that's a fairly sensible safety rule +it'd be easy enough to just borrow a + + align:start position:0% +it'd be easy enough to just borrow a + + + align:start position:0% +it'd be easy enough to just borrow a +rule from that and just say you know + + align:start position:0% +rule from that and just say you know + + + align:start position:0% +rule from that and just say you know +just let that last game that we play no + + align:start position:0% +just let that last game that we play no + + + align:start position:0% +just let that last game that we play no +one crosses that road you know for + + align:start position:0% +one crosses that road you know for + + + align:start position:0% +one crosses that road you know for +safety reasons just not having to worry + + align:start position:0% +safety reasons just not having to worry + + + align:start position:0% +safety reasons just not having to worry +about like how the combat actually works + + align:start position:0% +about like how the combat actually works + + + align:start position:0% +about like how the combat actually works +and just like we we've borrowed a few + + align:start position:0% +and just like we we've borrowed a few + + + align:start position:0% +and just like we we've borrowed a few +different ones we tried we tried + + align:start position:0% +different ones we tried we tried + + + align:start position:0% +different ones we tried we tried +actually want to say finally developing + + align:start position:0% +actually want to say finally developing + + + align:start position:0% +actually want to say finally developing +a fair combat system sure I mean as game + + align:start position:0% +a fair combat system sure I mean as game + + + align:start position:0% +a fair combat system sure I mean as game +designers you can certainly sort of be + + align:start position:0% +designers you can certainly sort of be + + + align:start position:0% +designers you can certainly sort of be +inspired by what other people have have + + align:start position:0% +inspired by what other people have have + + + align:start position:0% +inspired by what other people have have +done and then of course again yeah yeah + + align:start position:0% +done and then of course again yeah yeah + + + align:start position:0% +done and then of course again yeah yeah +you're designing a game meant for + + align:start position:0% +you're designing a game meant for + + + align:start position:0% +you're designing a game meant for +somebody else to play whereas what + + align:start position:0% +somebody else to play whereas what + + + align:start position:0% +somebody else to play whereas what +birdies decoder is writing about is + + align:start position:0% +birdies decoder is writing about is + + + align:start position:0% +birdies decoder is writing about is +about making about changing a rule that + + align:start position:0% +about making about changing a rule that + + + align:start position:0% +about making about changing a rule that +you are about to play or maybe even a + + align:start position:0% +you are about to play or maybe even a + + + align:start position:0% +you are about to play or maybe even a +possible plane + + align:start position:0% + + + + align:start position:0% + +actually change mm-hmm right so the + + align:start position:0% +actually change mm-hmm right so the + + + align:start position:0% +actually change mm-hmm right so the +reels that sort of clarify what it is + + align:start position:0% +reels that sort of clarify what it is + + + align:start position:0% +reels that sort of clarify what it is +that you can or you cannot do right you + + align:start position:0% +that you can or you cannot do right you + + + align:start position:0% +that you can or you cannot do right you +know and then there are rules where that + + align:start position:0% +know and then there are rules where that + + + align:start position:0% +know and then there are rules where that +which which which he he explicitly + + align:start position:0% +which which which he he explicitly + + + align:start position:0% +which which which he he explicitly +states as as one of as the definition of + + align:start position:0% +states as as one of as the definition of + + + align:start position:0% +states as as one of as the definition of +a change game right there's one that + + align:start position:0% +a change game right there's one that + + + align:start position:0% +a change game right there's one that +requires you to come up with a new + + align:start position:0% +requires you to come up with a new + + + align:start position:0% +requires you to come up with a new +strategy so things like that that safety + + align:start position:0% +strategy so things like that that safety + + + align:start position:0% +strategy so things like that that safety +rule that I described earlier isn't + + align:start position:0% +rule that I described earlier isn't + + + align:start position:0% +rule that I described earlier isn't +necessarily doesn't necessarily fit that + + align:start position:0% +necessarily doesn't necessarily fit that + + + align:start position:0% +necessarily doesn't necessarily fit that +but it fulfills other purposes like you + + align:start position:0% +but it fulfills other purposes like you + + + align:start position:0% +but it fulfills other purposes like you +know being able to play well they giving + + align:start position:0% +know being able to play well they giving + + + align:start position:0% +know being able to play well they giving +you this feeling oh well this I cut the + + align:start position:0% +you this feeling oh well this I cut the + + + align:start position:0% +you this feeling oh well this I cut the +leave that light but it's great and then + + align:start position:0% +leave that light but it's great and then + + + align:start position:0% +leave that light but it's great and then +but that's also rules like we're going + + align:start position:0% +but that's also rules like we're going + + + align:start position:0% +but that's also rules like we're going +to change the game because it's not + + align:start position:0% +to change the game because it's not + + + align:start position:0% +to change the game because it's not +challenging given the way how it's + + align:start position:0% +challenging given the way how it's + + + align:start position:0% +challenging given the way how it's +currently played maybe this hard set of + + align:start position:0% +currently played maybe this hard set of + + + align:start position:0% +currently played maybe this hard set of +rules has a simple exploit you know that + + align:start position:0% +rules has a simple exploit you know that + + + align:start position:0% +rules has a simple exploit you know that +just leads to one person winning all the + + align:start position:0% +just leads to one person winning all the + + + align:start position:0% +just leads to one person winning all the +time maybe someone's just way more + + align:start position:0% +time maybe someone's just way more + + + align:start position:0% +time maybe someone's just way more +skilled at this game and somebody else + + align:start position:0% +skilled at this game and somebody else + + + align:start position:0% +skilled at this game and somebody else +oh you know you played with a five-year + + align:start position:0% +oh you know you played with a five-year + + + align:start position:0% +oh you know you played with a five-year +or something like that and you know you + + align:start position:0% +or something like that and you know you + + + align:start position:0% +or something like that and you know you +wanna you wanna you wanna have some + + align:start position:0% +wanna you wanna you wanna have some + + + align:start position:0% +wanna you wanna you wanna have some +challenge you want to keep some + + align:start position:0% +challenge you want to keep some + + + align:start position:0% +challenge you want to keep some +challenge for the kid whether you just + + align:start position:0% +challenge for the kid whether you just + + + align:start position:0% +challenge for the kid whether you just +stick with the rules right now you know + + align:start position:0% +stick with the rules right now you know + + + align:start position:0% +stick with the rules right now you know +the kids will be emphasized and they + + align:start position:0% +the kids will be emphasized and they + + + align:start position:0% +the kids will be emphasized and they +will not ever be able to win and then + + align:start position:0% +will not ever be able to win and then + + + align:start position:0% +will not ever be able to win and then +you're young you're not being challenged + + align:start position:0% +you're young you're not being challenged + + + align:start position:0% +you're young you're not being challenged +at all that that's where you give + + align:start position:0% +at all that that's where you give + + + align:start position:0% +at all that that's where you give +yourself and he breaks this up how do + + align:start position:0% +yourself and he breaks this up how do + + + align:start position:0% +yourself and he breaks this up how do +you what's the what what what's the + + align:start position:0% +you what's the what what what's the + + + align:start position:0% +you what's the what what what's the +thing you introduce into the game to be + + align:start position:0% +thing you introduce into the game to be + + + align:start position:0% +thing you introduce into the game to be +able to back to me balance that you + + align:start position:0% +able to back to me balance that you + + + align:start position:0% +able to back to me balance that you +should know it even even if you didn't + + align:start position:0% +should know it even even if you didn't + + + align:start position:0% +should know it even even if you didn't +read it did you're playing with somebody + + align:start position:0% +read it did you're playing with somebody + + + align:start position:0% +read it did you're playing with somebody +who is way less skilled than you you get + + align:start position:0% +who is way less skilled than you you get + + + align:start position:0% +who is way less skilled than you you get +handicapped yeah yeah so so so and and + + align:start position:0% +handicapped yeah yeah so so so and and + + + align:start position:0% +handicapped yeah yeah so so so and and +handicapping is a really interesting + + align:start position:0% +handicapping is a really interesting + + + align:start position:0% +handicapping is a really interesting +concept regarding game balance because + + align:start position:0% +concept regarding game balance because + + + align:start position:0% +concept regarding game balance because +probably when we think about game + + align:start position:0% +probably when we think about game + + + align:start position:0% +probably when we think about game +balance it's all about you know how do + + align:start position:0% +balance it's all about you know how do + + + align:start position:0% +balance it's all about you know how do +we how do we think of the rules so that + + align:start position:0% +we how do we think of the rules so that + + + align:start position:0% +we how do we think of the rules so that +if everybody's kind of equally skilled + + align:start position:0% +if everybody's kind of equally skilled + + + align:start position:0% +if everybody's kind of equally skilled +everyone kind of has a fair chance of + + align:start position:0% +everyone kind of has a fair chance of + + + align:start position:0% +everyone kind of has a fair chance of +winning a decent chance maybe not + + align:start position:0% +winning a decent chance maybe not + + + align:start position:0% +winning a decent chance maybe not +50-plus exactly even chance of winning + + align:start position:0% +50-plus exactly even chance of winning + + + align:start position:0% +50-plus exactly even chance of winning +but at least a fair chance of winning + + align:start position:0% +but at least a fair chance of winning + + + align:start position:0% +but at least a fair chance of winning +but he's introducing the concept of a + + align:start position:0% +but he's introducing the concept of a + + + align:start position:0% +but he's introducing the concept of a +handicap capping is a way to be able to + + align:start position:0% +handicap capping is a way to be able to + + + align:start position:0% +handicap capping is a way to be able to +reintroduce challenge the situation + + align:start position:0% +reintroduce challenge the situation + + + align:start position:0% +reintroduce challenge the situation +where players are not equally skilled + + align:start position:0% +where players are not equally skilled + + + align:start position:0% +where players are not equally skilled +they because of physical reason is + + align:start position:0% +they because of physical reason is + + + align:start position:0% +they because of physical reason is +because of expert help expertise or + + align:start position:0% +because of expert help expertise or + + + align:start position:0% +because of expert help expertise or +familiarity with the game that sort of + + align:start position:0% +familiarity with the game that sort of + + + align:start position:0% +familiarity with the game that sort of +thing so let me see that anything else + + align:start position:0% +thing so let me see that anything else + + + align:start position:0% +thing so let me see that anything else +that people remember from the reading I + + align:start position:0% + + + + align:start position:0% + +again a lot of the stuff there is an + + align:start position:0% +again a lot of the stuff there is an + + + align:start position:0% +again a lot of the stuff there is an +interesting little bit that he talks + + align:start position:0% +interesting little bit that he talks + + + align:start position:0% +interesting little bit that he talks +about cheating as a thing that players + + align:start position:0% +about cheating as a thing that players + + + align:start position:0% +about cheating as a thing that players +should be trying to do if you are + + align:start position:0% +should be trying to do if you are + + + align:start position:0% +should be trying to do if you are +already in the mood to be able to do + + align:start position:0% +already in the mood to be able to do + + + align:start position:0% +already in the mood to be able to do +then suggest rule changes to the rest of + + align:start position:0% +then suggest rule changes to the rest of + + + align:start position:0% +then suggest rule changes to the rest of +your community and you should be finding + + align:start position:0% +your community and you should be finding + + + align:start position:0% +your community and you should be finding +the loopholes right you should be trying + + align:start position:0% +the loopholes right you should be trying + + + align:start position:0% +the loopholes right you should be trying +to figure out where given the current + + align:start position:0% +to figure out where given the current + + + align:start position:0% +to figure out where given the current +set of rules that you are playing right + + align:start position:0% +set of rules that you are playing right + + + align:start position:0% +set of rules that you are playing right +now what are the problems with that set + + align:start position:0% +now what are the problems with that set + + + align:start position:0% +now what are the problems with that set +of rules and how do you improve on them + + align:start position:0% +of rules and how do you improve on them + + + align:start position:0% +of rules and how do you improve on them +and the way how you you figure out + + align:start position:0% +and the way how you you figure out + + + align:start position:0% +and the way how you you figure out +whether these rules are important or + + align:start position:0% +whether these rules are important or + + + align:start position:0% +whether these rules are important or +well-written or problematic is you try + + align:start position:0% +well-written or problematic is you try + + + align:start position:0% +well-written or problematic is you try +to break them and then if you break them + + align:start position:0% +to break them and then if you break them + + + align:start position:0% +to break them and then if you break them +and then you realize that all okay that + + align:start position:0% +and then you realize that all okay that + + + align:start position:0% +and then you realize that all okay that +rule was really necessary in order for + + align:start position:0% +rule was really necessary in order for + + + align:start position:0% +rule was really necessary in order for +the game to play but your attitude is + + align:start position:0% +the game to play but your attitude is + + + align:start position:0% +the game to play but your attitude is +where I want to continue playing with + + align:start position:0% +where I want to continue playing with + + + align:start position:0% +where I want to continue playing with +all of you then then you say all right + + align:start position:0% +all of you then then you say all right + + + align:start position:0% +all of you then then you say all right +you know we're not going to do that + + align:start position:0% +you know we're not going to do that + + + align:start position:0% +you know we're not going to do that +anymore I know I think it takes a + + align:start position:0% +anymore I know I think it takes a + + + align:start position:0% +anymore I know I think it takes a +tremendous amount of trust among players + + align:start position:0% +tremendous amount of trust among players + + + align:start position:0% +tremendous amount of trust among players +to be able to accommodate that I don't + + align:start position:0% +to be able to accommodate that I don't + + + align:start position:0% +to be able to accommodate that I don't +know how many people actually play + + align:start position:0% +know how many people actually play + + + align:start position:0% +know how many people actually play +regularly and environments like that + + align:start position:0% + + + + align:start position:0% + +that you should be trying to find find + + align:start position:0% +that you should be trying to find find + + + align:start position:0% +that you should be trying to find find +the exploits but you should be trying to + + align:start position:0% +the exploits but you should be trying to + + + align:start position:0% +the exploits but you should be trying to +fight to figure out whether exactly how + + align:start position:0% +fight to figure out whether exactly how + + + align:start position:0% +fight to figure out whether exactly how +I am glad this rule actually is right or + + align:start position:0% +I am glad this rule actually is right or + + + align:start position:0% +I am glad this rule actually is right or +what did this rule is a good idea in the + + align:start position:0% +what did this rule is a good idea in the + + + align:start position:0% +what did this rule is a good idea in the +first place by but by breaking them it's + + align:start position:0% +first place by but by breaking them it's + + + align:start position:0% +first place by but by breaking them it's +very very straight it's a very very + + align:start position:0% +very very straight it's a very very + + + align:start position:0% +very very straight it's a very very +interesting suggestion I am don't I + + align:start position:0% +interesting suggestion I am don't I + + + align:start position:0% +interesting suggestion I am don't I +can't recall awful situation where I've + + align:start position:0% +can't recall awful situation where I've + + + align:start position:0% +can't recall awful situation where I've +been in a play community as he describes + + align:start position:0% +been in a play community as he describes + + + align:start position:0% +been in a play community as he describes +it where it has enough trust to be able + + align:start position:0% +it where it has enough trust to be able + + + align:start position:0% +it where it has enough trust to be able +to let people get away with that I think + + align:start position:0% +to let people get away with that I think + + + align:start position:0% +to let people get away with that I think +it's a lot more interesting to actually + + align:start position:0% +it's a lot more interesting to actually + + + align:start position:0% +it's a lot more interesting to actually +try to find the broken strategies in a + + align:start position:0% + + + + align:start position:0% + +okay to find these sort of degenerate + + align:start position:0% +okay to find these sort of degenerate + + + align:start position:0% +okay to find these sort of degenerate +strategies within the rules as opposed + + align:start position:0% +strategies within the rules as opposed + + + align:start position:0% +strategies within the rules as opposed +to figure out whether rules are broken + + align:start position:0% + + + + align:start position:0% + +playing like playing games or like how + + align:start position:0% +playing like playing games or like how + + + align:start position:0% +playing like playing games or like how +do we do this but I feel like right and + + align:start position:0% +do we do this but I feel like right and + + + align:start position:0% +do we do this but I feel like right and +this one thing that he's very very cute + + align:start position:0% +this one thing that he's very very cute + + + align:start position:0% +this one thing that he's very very cute +clearly speaks it's like it's like you + + align:start position:0% +clearly speaks it's like it's like you + + + align:start position:0% +clearly speaks it's like it's like you +you are cheating publicly you are + + align:start position:0% +you are cheating publicly you are + + + align:start position:0% +you are cheating publicly you are +broadcasting the fact that you're + + align:start position:0% +broadcasting the fact that you're + + + align:start position:0% +broadcasting the fact that you're +cheating which brings up the question + + align:start position:0% +cheating which brings up the question + + + align:start position:0% +cheating which brings up the question +are you ready cheering are you just + + align:start position:0% +are you ready cheering are you just + + + align:start position:0% +are you ready cheering are you just +proposing a rule change right but but + + align:start position:0% +proposing a rule change right but but + + + align:start position:0% +proposing a rule change right but but +the idea of treating the rules as + + align:start position:0% +the idea of treating the rules as + + + align:start position:0% +the idea of treating the rules as +something that could be valuable I think + + align:start position:0% +something that could be valuable I think + + + align:start position:0% +something that could be valuable I think +is what you really he's really getting + + align:start position:0% +is what you really he's really getting + + + align:start position:0% +is what you really he's really getting +at he just decides to use the word + + align:start position:0% +at he just decides to use the word + + + align:start position:0% +at he just decides to use the word +cheating which I'm not entirely sure it + + align:start position:0% +cheating which I'm not entirely sure it + + + align:start position:0% +cheating which I'm not entirely sure it +is that's right what + + align:start position:0% + + + + align:start position:0% + +sorry like what's underneath the game so + + align:start position:0% +sorry like what's underneath the game so + + + align:start position:0% +sorry like what's underneath the game so +if you like to start breaking a rule and + + align:start position:0% +if you like to start breaking a rule and + + + align:start position:0% +if you like to start breaking a rule and +you're doing it publicly with the + + align:start position:0% +you're doing it publicly with the + + + align:start position:0% +you're doing it publicly with the +knowledge of other people just to see + + align:start position:0% +knowledge of other people just to see + + + align:start position:0% +knowledge of other people just to see +what happens if we start to break this + + align:start position:0% +what happens if we start to break this + + + align:start position:0% +what happens if we start to break this +from I'm making them to some interesting + + align:start position:0% +from I'm making them to some interesting + + + align:start position:0% +from I'm making them to some interesting +issues it like well what makes the game + + align:start position:0% +issues it like well what makes the game + + + align:start position:0% +issues it like well what makes the game +tick and like I don't know I feel like a + + align:start position:0% +tick and like I don't know I feel like a + + + align:start position:0% +tick and like I don't know I feel like a +lot of games they used to play as a kid + + align:start position:0% +lot of games they used to play as a kid + + + align:start position:0% +lot of games they used to play as a kid +we would like explicitly break the rules + + align:start position:0% +we would like explicitly break the rules + + + align:start position:0% +we would like explicitly break the rules +and we would know as a rule of the game + + align:start position:0% +and we would know as a rule of the game + + + align:start position:0% +and we would know as a rule of the game +but we would choose to either not play + + align:start position:0% +but we would choose to either not play + + + align:start position:0% +but we would choose to either not play +with it or - oh you know this limited + + align:start position:0% +with it or - oh you know this limited + + + align:start position:0% +with it or - oh you know this limited +this resource is one of it it's like + + align:start position:0% +this resource is one of it it's like + + + align:start position:0% +this resource is one of it it's like +well you know at this time we play it's + + align:start position:0% +well you know at this time we play it's + + + align:start position:0% +well you know at this time we play it's +not going to be let's just see what + + align:start position:0% +not going to be let's just see what + + + align:start position:0% +not going to be let's just see what +happens right right right yeah that's a + + align:start position:0% +happens right right right yeah that's a + + + align:start position:0% +happens right right right yeah that's a +better attitude that he's trying to + + align:start position:0% +better attitude that he's trying to + + + align:start position:0% +better attitude that he's trying to +encourage + + align:start position:0% + + + + align:start position:0% + +I took this art too frequently yeah okay + + align:start position:0% +I took this art too frequently yeah okay + + + align:start position:0% +I took this art too frequently yeah okay +I um that's let's dig into that what why + + align:start position:0% +I um that's let's dig into that what why + + + align:start position:0% +I um that's let's dig into that what why +too frequently what do why do you feel + + align:start position:0% +too frequently what do why do you feel + + + align:start position:0% +too frequently what do why do you feel +that happens - okay but what but what if + + align:start position:0% +that happens - okay but what but what if + + + align:start position:0% +that happens - okay but what but what if +you were trying to change the rules for + + align:start position:0% +you were trying to change the rules for + + + align:start position:0% +you were trying to change the rules for +other people so say say say I'm in a you + + align:start position:0% +other people so say say say I'm in a you + + + align:start position:0% +other people so say say say I'm in a you +know I don't fighting gave her 20 + + align:start position:0% +know I don't fighting gave her 20 + + + align:start position:0% +know I don't fighting gave her 20 +minutes or something like that + + align:start position:0% +minutes or something like that + + + align:start position:0% +minutes or something like that +and we're you know usually the rules are + + align:start position:0% +and we're you know usually the rules are + + + align:start position:0% +and we're you know usually the rules are +you know pretty rigidly enforced right + + align:start position:0% +you know pretty rigidly enforced right + + + align:start position:0% +you know pretty rigidly enforced right +yeah but I'm not like a top-level player + + align:start position:0% +yeah but I'm not like a top-level player + + + align:start position:0% +yeah but I'm not like a top-level player +I just happen to be winning be like on a + + align:start position:0% +I just happen to be winning be like on a + + + align:start position:0% +I just happen to be winning be like on a +real winning streak among people that I + + align:start position:0% +real winning streak among people that I + + + align:start position:0% +real winning streak among people that I +know and I don't seem to be able to lose + + align:start position:0% +know and I don't seem to be able to lose + + + align:start position:0% +know and I don't seem to be able to lose +right now so I think what birdie is + + align:start position:0% +right now so I think what birdie is + + + align:start position:0% +right now so I think what birdie is +talking about is describing a situation + + align:start position:0% +talking about is describing a situation + + + align:start position:0% +talking about is describing a situation +where especially if you are that person + + align:start position:0% +where especially if you are that person + + + align:start position:0% +where especially if you are that person +this needs to be on a winning streak you + + align:start position:0% +this needs to be on a winning streak you + + + align:start position:0% +this needs to be on a winning streak you +might want to suggest a rule change to + + align:start position:0% +might want to suggest a rule change to + + + align:start position:0% +might want to suggest a rule change to +be able to bring the challenge back to + + align:start position:0% +be able to bring the challenge back to + + + align:start position:0% +be able to bring the challenge back to +you to you right I've seen players do + + align:start position:0% +you to you right I've seen players do + + + align:start position:0% +you to you right I've seen players do +this specifically in our case where it's + + align:start position:0% +this specifically in our case where it's + + + align:start position:0% +this specifically in our case where it's +like I'm going to pick the gate that + + align:start position:0% +like I'm going to pick the gate that + + + align:start position:0% +like I'm going to pick the gate that +character - I'm crappy is that because I + + align:start position:0% +character - I'm crappy is that because I + + + align:start position:0% +character - I'm crappy is that because I +can't seem to be able to lose by playing + + align:start position:0% +can't seem to be able to lose by playing + + + align:start position:0% +can't seem to be able to lose by playing +the characters I hid good at and that + + align:start position:0% +the characters I hid good at and that + + + align:start position:0% +the characters I hid good at and that +that's no longer interesting for me yeah + + align:start position:0% + + + + align:start position:0% + +like those changes the light oh let's + + align:start position:0% +like those changes the light oh let's + + + align:start position:0% +like those changes the light oh let's +give that bundling it there to play I'm + + align:start position:0% +give that bundling it there to play I'm + + + align:start position:0% +give that bundling it there to play I'm +calling it you yeah I guess me cheating + + align:start position:0% +calling it you yeah I guess me cheating + + + align:start position:0% +calling it you yeah I guess me cheating +implies that you are not me changing the + + align:start position:0% +implies that you are not me changing the + + + align:start position:0% +implies that you are not me changing the +rules and everyone agrees on the rules + + align:start position:0% +rules and everyone agrees on the rules + + + align:start position:0% +rules and everyone agrees on the rules +will changer that's not then you have + + align:start position:0% +will changer that's not then you have + + + align:start position:0% +will changer that's not then you have +you have changeable you are now plagued + + align:start position:0% +you have changeable you are now plagued + + + align:start position:0% +you have changeable you are now plagued +by a different set of rules if you play + + align:start position:0% +by a different set of rules if you play + + + align:start position:0% +by a different set of rules if you play +by those you're not cheating because + + align:start position:0% +by those you're not cheating because + + + align:start position:0% +by those you're not cheating because +you're not playing well and cheating + + align:start position:0% +you're not playing well and cheating + + + align:start position:0% +you're not playing well and cheating +also I think has a certain assumption + + align:start position:0% +also I think has a certain assumption + + + align:start position:0% +also I think has a certain assumption +that everybody else is trying it's not + + align:start position:0% +that everybody else is trying it's not + + + align:start position:0% +that everybody else is trying it's not +breaking the rules right no one's + + align:start position:0% +breaking the rules right no one's + + + align:start position:0% +breaking the rules right no one's +playing with a different set of rules + + align:start position:0% +playing with a different set of rules + + + align:start position:0% +playing with a different set of rules +but you all but the cheat + + align:start position:0% +but you all but the cheat + + + align:start position:0% +but you all but the cheat +in fact a lot of cheats only work if + + align:start position:0% +in fact a lot of cheats only work if + + + align:start position:0% +in fact a lot of cheats only work if +everyone else sticks to the rules that's + + align:start position:0% +everyone else sticks to the rules that's + + + align:start position:0% +everyone else sticks to the rules that's +where telling them the other one only + + align:start position:0% +where telling them the other one only + + + align:start position:0% +where telling them the other one only +one Chile so again I I think he's trying + + align:start position:0% +one Chile so again I I think he's trying + + + align:start position:0% +one Chile so again I I think he's trying +to get across the attitude but he used + + align:start position:0% +to get across the attitude but he used + + + align:start position:0% +to get across the attitude but he used +the wrong word for it + + align:start position:0% + + + + align:start position:0% + +that's truth yeah well yeah I guess I + + align:start position:0% +that's truth yeah well yeah I guess I + + + align:start position:0% +that's truth yeah well yeah I guess I +tried to sort of think of like the + + align:start position:0% +tried to sort of think of like the + + + align:start position:0% +tried to sort of think of like the +implicit maybe not a rules change but + + align:start position:0% +implicit maybe not a rules change but + + + align:start position:0% +implicit maybe not a rules change but +it's more her like values change that + + align:start position:0% +it's more her like values change that + + + align:start position:0% +it's more her like values change that +you should be playing to it oh yeah + + align:start position:0% +you should be playing to it oh yeah + + + align:start position:0% +you should be playing to it oh yeah +you'll get to choose my character or + + align:start position:0% +you'll get to choose my character or + + + align:start position:0% +you'll get to choose my character or +something like that like that you know + + align:start position:0% +something like that like that you know + + + align:start position:0% +something like that like that you know +that you tell me who you want to play + + align:start position:0% +that you tell me who you want to play + + + align:start position:0% +that you tell me who you want to play +against and I'll try to my best to play + + align:start position:0% +against and I'll try to my best to play + + + align:start position:0% +against and I'll try to my best to play +that group that's starting with Miguel + + align:start position:0% +that group that's starting with Miguel + + + align:start position:0% +that group that's starting with Miguel +and then all the more + + align:start position:0% + + + + align:start position:0% + +it's like one person isn't being + + align:start position:0% +it's like one person isn't being + + + align:start position:0% +it's like one person isn't being +challenged in baking like start + + align:start position:0% +challenged in baking like start + + + align:start position:0% +challenged in baking like start +experimenting but in my experiences or + + align:start position:0% +experimenting but in my experiences or + + + align:start position:0% +experimenting but in my experiences or +often happens when the entire group is + + align:start position:0% +often happens when the entire group is + + + align:start position:0% +often happens when the entire group is +not me + + align:start position:0% +not me + + + align:start position:0% +not me +mm-hmm displayed the concrete clients + + align:start position:0% +mm-hmm displayed the concrete clients + + + align:start position:0% +mm-hmm displayed the concrete clients +over the last few days kind of like + + align:start position:0% +over the last few days kind of like + + + align:start position:0% +over the last few days kind of like +tired at the time but you don't really + + align:start position:0% +tired at the time but you don't really + + + align:start position:0% +tired at the time but you don't really +look like you're kind of ready to do + + align:start position:0% +look like you're kind of ready to do + + + align:start position:0% +look like you're kind of ready to do +something else look like you don't have + + align:start position:0% +something else look like you don't have + + + align:start position:0% +something else look like you don't have +a different working with us or something + + align:start position:0% +a different working with us or something + + + align:start position:0% +a different working with us or something +so let's see so let's make a barrier of + + align:start position:0% +so let's see so let's make a barrier of + + + align:start position:0% +so let's see so let's make a barrier of +different variants up and then it's like + + align:start position:0% +different variants up and then it's like + + + align:start position:0% +different variants up and then it's like +kind of everyone is trying to appease + + align:start position:0% +kind of everyone is trying to appease + + + align:start position:0% +kind of everyone is trying to appease +the challenge not because it's not + + align:start position:0% +the challenge not because it's not + + + align:start position:0% +the challenge not because it's not +challenging like this but like it's not + + align:start position:0% +challenging like this but like it's not + + + align:start position:0% +challenging like this but like it's not +challenging in the sense + + align:start position:0% +challenging in the sense + + + align:start position:0% +challenging in the sense +I think I think the reason why it's + + align:start position:0% +I think I think the reason why it's + + + align:start position:0% +I think I think the reason why it's +easier to do it when there's a lot of + + align:start position:0% +easier to do it when there's a lot of + + + align:start position:0% +easier to do it when there's a lot of +people kind of like find a sign to find + + align:start position:0% +people kind of like find a sign to find + + + align:start position:0% +people kind of like find a sign to find +a game uninteresting is because it's + + align:start position:0% +a game uninteresting is because it's + + + align:start position:0% +a game uninteresting is because it's +easier to get consensus to be able to + + align:start position:0% +easier to get consensus to be able to + + + align:start position:0% +easier to get consensus to be able to +enforce a change of the rules right it's + + align:start position:0% +enforce a change of the rules right it's + + + align:start position:0% +enforce a change of the rules right it's +a lot harder to say you know say I'm 12 + + align:start position:0% +a lot harder to say you know say I'm 12 + + + align:start position:0% +a lot harder to say you know say I'm 12 +and I'm playing with a whole bunch of + + align:start position:0% +and I'm playing with a whole bunch of + + + align:start position:0% +and I'm playing with a whole bunch of +other 12 year olds and it happens to be + + align:start position:0% +other 12 year olds and it happens to be + + + align:start position:0% +other 12 year olds and it happens to be +a nine year old in the group they were + + align:start position:0% +a nine year old in the group they were + + + align:start position:0% +a nine year old in the group they were +playing soccer or something like that + + align:start position:0% +playing soccer or something like that + + + align:start position:0% +playing soccer or something like that +it's it's harder for anyone to convince + + align:start position:0% +it's it's harder for anyone to convince + + + align:start position:0% +it's it's harder for anyone to convince +the rest of the 12 year old to take it + + align:start position:0% +the rest of the 12 year old to take it + + + align:start position:0% +the rest of the 12 year old to take it +easy on an annual oh alright what if we + + align:start position:0% +easy on an annual oh alright what if we + + + align:start position:0% +easy on an annual oh alright what if we +you know give give an extra player or + + align:start position:0% +you know give give an extra player or + + + align:start position:0% +you know give give an extra player or +the nine year old team something at that + + align:start position:0% +the nine year old team something at that + + + align:start position:0% +the nine year old team something at that +so wishes must say can't be done but and + + align:start position:0% +so wishes must say can't be done but and + + + align:start position:0% +so wishes must say can't be done but and +I think that's what Bernie the + + align:start position:0% +I think that's what Bernie the + + + align:start position:0% +I think that's what Bernie the +convincing no you should be able to do + + align:start position:0% +convincing no you should be able to do + + + align:start position:0% +convincing no you should be able to do +that sort of thing even you know and + + align:start position:0% +that sort of thing even you know and + + + align:start position:0% +that sort of thing even you know and +it's kind of like makes the game more + + align:start position:0% +it's kind of like makes the game more + + + align:start position:0% +it's kind of like makes the game more +interesting for everybody not just for + + align:start position:0% +interesting for everybody not just for + + + align:start position:0% +interesting for everybody not just for +the person who's having a hard time + + align:start position:0% +the person who's having a hard time + + + align:start position:0% +the person who's having a hard time +makes the game more interesting even for + + align:start position:0% +makes the game more interesting even for + + + align:start position:0% +makes the game more interesting even for +the people who have an advantage because + + align:start position:0% +the people who have an advantage because + + + align:start position:0% +the people who have an advantage because +now it makes it a big more of a fight I + + align:start position:0% +now it makes it a big more of a fight I + + + align:start position:0% +now it makes it a big more of a fight I +guess to for them to be able to win + + align:start position:0% + + + + align:start position:0% + +and like less I guess for individual + + align:start position:0% +and like less I guess for individual + + + align:start position:0% +and like less I guess for individual +players but like I never accept their + + align:start position:0% +players but like I never accept their + + + align:start position:0% +players but like I never accept their +games and I played sometimes a little + + align:start position:0% +games and I played sometimes a little + + + align:start position:0% +games and I played sometimes a little +work it wasn't really intentional but + + align:start position:0% +work it wasn't really intentional but + + + align:start position:0% +work it wasn't really intentional but +we're not + + align:start position:0% +we're not + + + align:start position:0% +we're not +like nicely seven and I learned how to + + align:start position:0% +like nicely seven and I learned how to + + + align:start position:0% +like nicely seven and I learned how to +play you know when I believe you're glue + + align:start position:0% +play you know when I believe you're glue + + + align:start position:0% +play you know when I believe you're glue +or some + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +more importantly everybody in the rooms + + align:start position:0% +more importantly everybody in the rooms + + + align:start position:0% +more importantly everybody in the rooms +agreed to that set of this new set of + + align:start position:0% +agreed to that set of this new set of + + + align:start position:0% +agreed to that set of this new set of +rules right so so cheating + + align:start position:0% + + + + align:start position:0% + +the friends that we nerf the aquadolls + + align:start position:0% +the friends that we nerf the aquadolls + + + align:start position:0% +the friends that we nerf the aquadolls +because it's fine hmm + + align:start position:0% +because it's fine hmm + + + align:start position:0% +because it's fine hmm +it's and because it's it's really + + align:start position:0% +it's and because it's it's really + + + align:start position:0% +it's and because it's it's really +overpowered if you just like it's really + + align:start position:0% +overpowered if you just like it's really + + + align:start position:0% +overpowered if you just like it's really +overpower strategy to go forth and like + + align:start position:0% +overpower strategy to go forth and like + + + align:start position:0% +overpower strategy to go forth and like +sometimes if you send them to do it some + + align:start position:0% +sometimes if you send them to do it some + + + align:start position:0% +sometimes if you send them to do it some +groups are like a lot more or less + + align:start position:0% +groups are like a lot more or less + + + align:start position:0% +groups are like a lot more or less +willing to it would serve another + + align:start position:0% +willing to it would serve another + + + align:start position:0% +willing to it would serve another +difference like what they were plagued + + align:start position:0% +difference like what they were plagued + + + align:start position:0% +difference like what they were plagued +accomplished they took a lot of crimes + + align:start position:0% +accomplished they took a lot of crimes + + + align:start position:0% +accomplished they took a lot of crimes +before they're probably going to like + + align:start position:0% +before they're probably going to like + + + align:start position:0% +before they're probably going to like +never make sure you have a powered + + align:start position:0% +never make sure you have a powered + + + align:start position:0% +never make sure you have a powered +strategy mm-hmm and like different + + align:start position:0% +strategy mm-hmm and like different + + + align:start position:0% +strategy mm-hmm and like different +gameplay nations after playing it like + + align:start position:0% +gameplay nations after playing it like + + + align:start position:0% +gameplay nations after playing it like +twice we've like we've like nerves one + + align:start position:0% +twice we've like we've like nerves one + + + align:start position:0% +twice we've like we've like nerves one +leader in there they've seen us because + + align:start position:0% +leader in there they've seen us because + + + align:start position:0% +leader in there they've seen us because +he's ridiculously overpowered right and + + align:start position:0% +he's ridiculously overpowered right and + + + align:start position:0% +he's ridiculously overpowered right and +so because it's also sort of differing + + align:start position:0% +so because it's also sort of differing + + + align:start position:0% +so because it's also sort of differing +you're sort of in different levels of + + align:start position:0% +you're sort of in different levels of + + + align:start position:0% +you're sort of in different levels of +that slide like there's like making + + align:start position:0% +that slide like there's like making + + + align:start position:0% +that slide like there's like making +things and there's like + + align:start position:0% +things and there's like + + + align:start position:0% +things and there's like +mm-hmm yeah I think in the end birdy de + + align:start position:0% +mm-hmm yeah I think in the end birdy de + + + align:start position:0% +mm-hmm yeah I think in the end birdy de +cousins kind of go coming from a sort of + + align:start position:0% +cousins kind of go coming from a sort of + + + align:start position:0% +cousins kind of go coming from a sort of +you should be free to challenge + + align:start position:0% +you should be free to challenge + + + align:start position:0% +you should be free to challenge +authority you know I mean that's that's + + align:start position:0% +authority you know I mean that's that's + + + align:start position:0% +authority you know I mean that's that's +kind of like the implicit thing that you + + align:start position:0% +kind of like the implicit thing that you + + + align:start position:0% +kind of like the implicit thing that you +get from the whole for example like + + align:start position:0% +get from the whole for example like + + + align:start position:0% +get from the whole for example like +something might seem initially + + align:start position:0% +something might seem initially + + + align:start position:0% +something might seem initially +overpowered and then you play it like + + align:start position:0% +overpowered and then you play it like + + + align:start position:0% +overpowered and then you play it like +you might be like after the first game + + align:start position:0% +you might be like after the first game + + + align:start position:0% +you might be like after the first game +like everybody just like oh yes broken + + align:start position:0% +like everybody just like oh yes broken + + + align:start position:0% +like everybody just like oh yes broken +my pledge changer right whereas if you + + align:start position:0% +my pledge changer right whereas if you + + + align:start position:0% +my pledge changer right whereas if you +like played another game you might have + + align:start position:0% +like played another game you might have + + + align:start position:0% +like played another game you might have +realized oh wait even actually founded + + align:start position:0% +realized oh wait even actually founded + + + align:start position:0% +realized oh wait even actually founded +this like by just doing acts so actually + + align:start position:0% +this like by just doing acts so actually + + + align:start position:0% +this like by just doing acts so actually +a really interesting counterpoint which + + align:start position:0% +a really interesting counterpoint which + + + align:start position:0% +a really interesting counterpoint which +is not part of our reading as Dave + + align:start position:0% +is not part of our reading as Dave + + + align:start position:0% +is not part of our reading as Dave +Eiland who is a MIT alum actually who + + align:start position:0% +Eiland who is a MIT alum actually who + + + align:start position:0% +Eiland who is a MIT alum actually who +wrote a book called playing to win this + + align:start position:0% +wrote a book called playing to win this + + + align:start position:0% +wrote a book called playing to win this +is not part of our class reading but he + + align:start position:0% +is not part of our class reading but he + + + align:start position:0% +is not part of our class reading but he +will he will definitely back that up + + align:start position:0% +will he will definitely back that up + + + align:start position:0% +will he will definitely back that up +right this is like no it's everyone's + + align:start position:0% +right this is like no it's everyone's + + + align:start position:0% +right this is like no it's everyone's +responsibility to play as hard as they + + align:start position:0% +responsibility to play as hard as they + + + align:start position:0% +responsibility to play as hard as they +can because you have an especially for + + align:start position:0% +can because you have an especially for + + + align:start position:0% +can because you have an especially for +certain kinds of games you haven't + + align:start position:0% +certain kinds of games you haven't + + + align:start position:0% +certain kinds of games you haven't +discovered everything that is getting + + align:start position:0% +discovered everything that is getting + + + align:start position:0% +discovered everything that is getting +that your game systems are capable off + + align:start position:0% +that your game systems are capable off + + + align:start position:0% +that your game systems are capable off +and if somebody can beat you playing + + align:start position:0% +and if somebody can beat you playing + + + align:start position:0% +and if somebody can beat you playing +that same game with the same set of + + align:start position:0% +that same game with the same set of + + + align:start position:0% +that same game with the same set of +rules that clearly is possible to beat + + align:start position:0% +rules that clearly is possible to beat + + + align:start position:0% +rules that clearly is possible to beat +that player or at least get up to the + + align:start position:0% +that player or at least get up to the + + + align:start position:0% +that player or at least get up to the +point where you're equally for your + + align:start position:0% +point where you're equally for your + + + align:start position:0% +point where you're equally for your +equally skilled so now there's a whole + + align:start position:0% +equally skilled so now there's a whole + + + align:start position:0% +equally skilled so now there's a whole +bunch of game design philosophies that + + align:start position:0% +bunch of game design philosophies that + + + align:start position:0% +bunch of game design philosophies that +come out of that as well and I believe + + align:start position:0% +come out of that as well and I believe + + + align:start position:0% +come out of that as well and I believe +play do we play Yami in his class before + + align:start position:0% +play do we play Yami in his class before + + + align:start position:0% +play do we play Yami in his class before +we used to yeah okay that's actually + + align:start position:0% +we used to yeah okay that's actually + + + align:start position:0% +we used to yeah okay that's actually +there's an iPad version of it now it's + + align:start position:0% +there's an iPad version of it now it's + + + align:start position:0% +there's an iPad version of it now it's +definitely not an iPhone version because + + align:start position:0% +definitely not an iPhone version because + + + align:start position:0% +definitely not an iPhone version because +it's way too much text to iPhone screen + + align:start position:0% +it's way too much text to iPhone screen + + + align:start position:0% +it's way too much text to iPhone screen +but yomi is a game that it's a card game + + align:start position:0% +but yomi is a game that it's a card game + + + align:start position:0% +but yomi is a game that it's a card game +version of basically a street fighter + + align:start position:0% +version of basically a street fighter + + + align:start position:0% +version of basically a street fighter +type fighting game and it's all about + + align:start position:0% +type fighting game and it's all about + + + align:start position:0% +type fighting game and it's all about +you know anticipating what your players + + align:start position:0% +you know anticipating what your players + + + align:start position:0% +you know anticipating what your players +I got what the other player is going to + + align:start position:0% +I got what the other player is going to + + + align:start position:0% +I got what the other player is going to +do and if you manage to get it right you + + align:start position:0% +do and if you manage to get it right you + + + align:start position:0% +do and if you manage to get it right you +can build up the combos and everything + + align:start position:0% +can build up the combos and everything + + + align:start position:0% +can build up the combos and everything +but the whole idea of that everything + + align:start position:0% +but the whole idea of that everything + + + align:start position:0% +but the whole idea of that everything +that Dave silence worked on Mikey the + + align:start position:0% +that Dave silence worked on Mikey the + + + align:start position:0% +that Dave silence worked on Mikey the +remix version of Street Fighter which + + align:start position:0% +remix version of Street Fighter which + + + align:start position:0% +remix version of Street Fighter which +was keep on universe yeah the HD remix + + align:start position:0% +was keep on universe yeah the HD remix + + + align:start position:0% +was keep on universe yeah the HD remix +versions the whole idea of everything + + align:start position:0% +versions the whole idea of everything + + + align:start position:0% +versions the whole idea of everything +that you wrote about and know and + + align:start position:0% +that you wrote about and know and + + + align:start position:0% +that you wrote about and know and +everything that he made is that these + + align:start position:0% +everything that he made is that these + + + align:start position:0% +everything that he made is that these +kinds of competitive games really should + + align:start position:0% +kinds of competitive games really should + + + align:start position:0% +kinds of competitive games really should +be more about how do you challenge + + align:start position:0% +be more about how do you challenge + + + align:start position:0% +be more about how do you challenge +yourself to improve that + + align:start position:0% +yourself to improve that + + + align:start position:0% +yourself to improve that +and it's going to be it's a lot less + + align:start position:0% +and it's going to be it's a lot less + + + align:start position:0% +and it's going to be it's a lot less +about the community around you it's a + + align:start position:0% +about the community around you it's a + + + align:start position:0% +about the community around you it's a +lot more about you and the game system + + align:start position:0% +lot more about you and the game system + + + align:start position:0% +lot more about you and the game system +so you are submitting yourself willingly + + align:start position:0% +so you are submitting yourself willingly + + + align:start position:0% +so you are submitting yourself willingly +to the authority of the game system + + align:start position:0% +to the authority of the game system + + + align:start position:0% +to the authority of the game system +which of course game designers create + + align:start position:0% +which of course game designers create + + + align:start position:0% +which of course game designers create +and then you you know you and and and if + + align:start position:0% +and then you you know you and and and if + + + align:start position:0% +and then you you know you and and and if +there's anything that you should be + + align:start position:0% +there's anything that you should be + + + align:start position:0% +there's anything that you should be +challenging you should be telling your + + align:start position:0% +challenging you should be telling your + + + align:start position:0% +challenging you should be telling your +ability to be able to rise to the + + align:start position:0% +ability to be able to rise to the + + + align:start position:0% +ability to be able to rise to the +occasion + + align:start position:0% +occasion + + + align:start position:0% +occasion +right right if they're not fighting as + + align:start position:0% +right right if they're not fighting as + + + align:start position:0% +right right if they're not fighting as +hard as you can if you know and and even + + align:start position:0% +hard as you can if you know and and even + + + align:start position:0% +hard as you can if you know and and even +birdie describes this right the whole + + align:start position:0% +birdie describes this right the whole + + + align:start position:0% +birdie describes this right the whole +idea is that it what what happens if + + align:start position:0% +idea is that it what what happens if + + + align:start position:0% +idea is that it what what happens if +you're if you give somebody a chance to + + align:start position:0% +you're if you give somebody a chance to + + + align:start position:0% +you're if you give somebody a chance to +you know it's like I could have played + + align:start position:0% +you know it's like I could have played + + + align:start position:0% +you know it's like I could have played +this game optimally because I know this + + align:start position:0% +this game optimally because I know this + + + align:start position:0% +this game optimally because I know this +game so well I'd have beaten you two + + align:start position:0% +game so well I'd have beaten you two + + + align:start position:0% +game so well I'd have beaten you two +into the ground but I'm just going to + + align:start position:0% +into the ground but I'm just going to + + + align:start position:0% +into the ground but I'm just going to +like instead of of handicapping myself + + align:start position:0% +like instead of of handicapping myself + + + align:start position:0% +like instead of of handicapping myself +which is a sort of public declaration + + align:start position:0% +which is a sort of public declaration + + + align:start position:0% +which is a sort of public declaration +that this is how I'm going to be doing + + align:start position:0% +that this is how I'm going to be doing + + + align:start position:0% +that this is how I'm going to be doing +it I'm just not going to play optimally + + align:start position:0% +it I'm just not going to play optimally + + + align:start position:0% +it I'm just not going to play optimally +then then I think both Dave Stirling and + + align:start position:0% +then then I think both Dave Stirling and + + + align:start position:0% +then then I think both Dave Stirling and +buddy to come and hide you in agreement + + align:start position:0% +buddy to come and hide you in agreement + + + align:start position:0% +buddy to come and hide you in agreement +this is not a good way to play this is + + align:start position:0% +this is not a good way to play this is + + + align:start position:0% +this is not a good way to play this is +this is this is the because the person + + align:start position:0% +this is this is the because the person + + + align:start position:0% +this is this is the because the person +who's getting the who is getting the + + align:start position:0% +who's getting the who is getting the + + + align:start position:0% +who's getting the who is getting the +benefit of that feels cheated out of the + + align:start position:0% +benefit of that feels cheated out of the + + + align:start position:0% +benefit of that feels cheated out of the +experience as well + + align:start position:0% + + + + align:start position:0% + +playing for sub-optimally with something + + align:start position:0% +playing for sub-optimally with something + + + align:start position:0% +playing for sub-optimally with something +platypus and it's like in a game with + + align:start position:0% +platypus and it's like in a game with + + + align:start position:0% +platypus and it's like in a game with +something fairly defined strategy you + + align:start position:0% +something fairly defined strategy you + + + align:start position:0% +something fairly defined strategy you +could sort of you could sort of be going + + align:start position:0% +could sort of you could sort of be going + + + align:start position:0% +could sort of you could sort of be going +for some like strategy that you believe + + align:start position:0% +for some like strategy that you believe + + + align:start position:0% +for some like strategy that you believe +to be suboptimal because you want to + + align:start position:0% +to be suboptimal because you want to + + + align:start position:0% +to be suboptimal because you want to +experiment this and it could be okay so + + align:start position:0% +experiment this and it could be okay so + + + align:start position:0% +experiment this and it could be okay so +the players that you are like and it + + align:start position:0% +the players that you are like and it + + + align:start position:0% +the players that you are like and it +couldn't be like and you sort of are + + align:start position:0% +couldn't be like and you sort of are + + + align:start position:0% +couldn't be like and you sort of are +just an internal underlines about you + + align:start position:0% +just an internal underlines about you + + + align:start position:0% +just an internal underlines about you +might not explore all the possibilities + + align:start position:0% +might not explore all the possibilities + + + align:start position:0% +might not explore all the possibilities +of the game there I'm so like to try + + align:start position:0% +of the game there I'm so like to try + + + align:start position:0% +of the game there I'm so like to try +hearts you can do that who think like + + align:start position:0% +hearts you can do that who think like + + + align:start position:0% +hearts you can do that who think like +you're actually you're actually like + + align:start position:0% +you're actually you're actually like + + + align:start position:0% +you're actually you're actually like +working towards that purpose if you do + + align:start position:0% +working towards that purpose if you do + + + align:start position:0% +working towards that purpose if you do +something like you know I'm gonna like + + align:start position:0% +something like you know I'm gonna like + + + align:start position:0% +something like you know I'm gonna like +try this strategy that's probably bad + + align:start position:0% +try this strategy that's probably bad + + + align:start position:0% +try this strategy that's probably bad +but like who knows maybe you know I I do + + align:start position:0% +but like who knows maybe you know I I do + + + align:start position:0% +but like who knows maybe you know I I do +that a lot and I always feel compelled + + align:start position:0% +that a lot and I always feel compelled + + + align:start position:0% +that a lot and I always feel compelled +to publicly declare that this is what + + align:start position:0% +to publicly declare that this is what + + + align:start position:0% +to publicly declare that this is what +I'm doing like I think because I don't + + align:start position:0% +I'm doing like I think because I don't + + + align:start position:0% +I'm doing like I think because I don't +want anyone to think that I'm stupid I + + align:start position:0% +want anyone to think that I'm stupid I + + + align:start position:0% +want anyone to think that I'm stupid I +play with people who are like really + + align:start position:0% +play with people who are like really + + + align:start position:0% +play with people who are like really +really good + + align:start position:0% +really good + + + align:start position:0% +really good +just like understanding and like making + + align:start position:0% +just like understanding and like making + + + align:start position:0% +just like understanding and like making +board games do so if I think that + + align:start position:0% +board games do so if I think that + + + align:start position:0% +board games do so if I think that +something might be an interesting way to + + align:start position:0% +something might be an interesting way to + + + align:start position:0% +something might be an interesting way to +play that + + align:start position:0% +play that + + + align:start position:0% +play that +like say it out and then it becomes + + align:start position:0% +like say it out and then it becomes + + + align:start position:0% +like say it out and then it becomes +actually more of like a cooperative like + + align:start position:0% +actually more of like a cooperative like + + + align:start position:0% +actually more of like a cooperative like +how could this strategy be let's play + + align:start position:0% +how could this strategy be let's play + + + align:start position:0% +how could this strategy be let's play +this all this year what happens right + + align:start position:0% +this all this year what happens right + + + align:start position:0% +this all this year what happens right +place of their own experience very well + + align:start position:0% +place of their own experience very well + + + align:start position:0% +place of their own experience very well +what would you have done + + align:start position:0% +what would you have done + + + align:start position:0% +what would you have done +from my shoot like it this one we're not + + align:start position:0% +from my shoot like it this one we're not + + + align:start position:0% +from my shoot like it this one we're not +even playing we're playing to develop + + align:start position:0% +even playing we're playing to develop + + + align:start position:0% +even playing we're playing to develop +yeah + + align:start position:0% + + + + align:start position:0% + +and I think that that's in keeping with + + align:start position:0% +and I think that that's in keeping with + + + align:start position:0% +and I think that that's in keeping with +what Bernie's trying to write about is + + align:start position:0% +what Bernie's trying to write about is + + + align:start position:0% +what Bernie's trying to write about is +it's like you are he ends up the chapter + + align:start position:0% +it's like you are he ends up the chapter + + + align:start position:0% +it's like you are he ends up the chapter +by talking about how you're scoring + + align:start position:0% +by talking about how you're scoring + + + align:start position:0% +by talking about how you're scoring +right how are you deciding what witness + + align:start position:0% +right how are you deciding what witness + + + align:start position:0% +right how are you deciding what witness +a a witness and and in this particular + + align:start position:0% +a a witness and and in this particular + + + align:start position:0% +a a witness and and in this particular +case it's a situation that we're + + align:start position:0% +case it's a situation that we're + + + align:start position:0% +case it's a situation that we're +describing a win is learning how a new + + align:start position:0% +describing a win is learning how a new + + + align:start position:0% +describing a win is learning how a new +untested strategy is gonna play out it's + + align:start position:0% +untested strategy is gonna play out it's + + + align:start position:0% +untested strategy is gonna play out it's +like it becomes less about that our who + + align:start position:0% +like it becomes less about that our who + + + align:start position:0% +like it becomes less about that our who +is the individual who is actually + + align:start position:0% +is the individual who is actually + + + align:start position:0% +is the individual who is actually +winning and more about are we getting + + align:start position:0% +winning and more about are we getting + + + align:start position:0% +winning and more about are we getting +something new from our understanding of + + align:start position:0% +something new from our understanding of + + + align:start position:0% +something new from our understanding of +this game which which can be you know + + align:start position:0% +this game which which can be you know + + + align:start position:0% +this game which which can be you know +really entertaining so whereas I think + + align:start position:0% +really entertaining so whereas I think + + + align:start position:0% +really entertaining so whereas I think +this one's not quite so willing to let + + align:start position:0% +this one's not quite so willing to let + + + align:start position:0% +this one's not quite so willing to let +that go he's a little bit more adamant + + align:start position:0% +that go he's a little bit more adamant + + + align:start position:0% +that go he's a little bit more adamant +that no you should just be winning based + + align:start position:0% +that no you should just be winning based + + + align:start position:0% +that no you should just be winning based +on that the definition of the rule set + + align:start position:0% +on that the definition of the rule set + + + align:start position:0% +on that the definition of the rule set +not based on some sort of like extra + + align:start position:0% +not based on some sort of like extra + + + align:start position:0% +not based on some sort of like extra +community arrive decision and but in the + + align:start position:0% +community arrive decision and but in the + + + align:start position:0% +community arrive decision and but in the +Commons trying to fight for no community + + align:start position:0% +Commons trying to fight for no community + + + align:start position:0% +Commons trying to fight for no community +determine conditions are right in fact + + align:start position:0% +determine conditions are right in fact + + + align:start position:0% +determine conditions are right in fact +you know are very good reasons for you + + align:start position:0% +you know are very good reasons for you + + + align:start position:0% +you know are very good reasons for you +to go for that different parts of you + + align:start position:0% +to go for that different parts of you + + + align:start position:0% +to go for that different parts of you +this I'm not saying that anyone is there + + align:start position:0% +this I'm not saying that anyone is there + + + align:start position:0% +this I'm not saying that anyone is there +are just think that about their + + align:start position:0% + + + + align:start position:0% + +absolutely yeah I I will agree with if + + align:start position:0% +absolutely yeah I I will agree with if + + + align:start position:0% +absolutely yeah I I will agree with if +you're a professional player who is in a + + align:start position:0% +you're a professional player who is in a + + + align:start position:0% +you're a professional player who is in a +team you are probably going to be + + align:start position:0% +team you are probably going to be + + + align:start position:0% +team you are probably going to be +working with your teammates a lot of + + align:start position:0% +working with your teammates a lot of + + + align:start position:0% +working with your teammates a lot of +time not to determine who is better at + + align:start position:0% +time not to determine who is better at + + + align:start position:0% +time not to determine who is better at +the game but they try to make everybody + + align:start position:0% +the game but they try to make everybody + + + align:start position:0% +the game but they try to make everybody +else play better right and there's just + + align:start position:0% +else play better right and there's just + + + align:start position:0% +else play better right and there's just +two different perspectives on how you + + align:start position:0% +two different perspectives on how you + + + align:start position:0% +two different perspectives on how you +arrive at that one is to play as hard as + + align:start position:0% +arrive at that one is to play as hard as + + + align:start position:0% +arrive at that one is to play as hard as +you always can and I always play as hard + + align:start position:0% +you always can and I always play as hard + + + align:start position:0% +you always can and I always play as hard +as you can so that everyone has to sort + + align:start position:0% +as you can so that everyone has to sort + + + align:start position:0% +as you can so that everyone has to sort +of rise to the occasion and the other + + align:start position:0% +of rise to the occasion and the other + + + align:start position:0% +of rise to the occasion and the other +way is just know it's okay to do things + + align:start position:0% +way is just know it's okay to do things + + + align:start position:0% +way is just know it's okay to do things +like experiments it's okay to do things + + align:start position:0% +like experiments it's okay to do things + + + align:start position:0% +like experiments it's okay to do things +like handicaps it's okay to do things + + align:start position:0% +like handicaps it's okay to do things + + + align:start position:0% +like handicaps it's okay to do things +like I'm just going to play I'm just + + align:start position:0% +like I'm just going to play I'm just + + + align:start position:0% +like I'm just going to play I'm just +playing a game just recently where like + + align:start position:0% +playing a game just recently where like + + + align:start position:0% +playing a game just recently where like +I'm going to do a suboptimal strategy on + + align:start position:0% +I'm going to do a suboptimal strategy on + + + align:start position:0% +I'm going to do a suboptimal strategy on +purpose just to see whether my opponent + + align:start position:0% +purpose just to see whether my opponent + + + align:start position:0% +purpose just to see whether my opponent +is capable fighting enough because it's + + align:start position:0% +is capable fighting enough because it's + + + align:start position:0% +is capable fighting enough because it's +just ridiculous so yeah I have fun even + + align:start position:0% +just ridiculous so yeah I have fun even + + + align:start position:0% +just ridiculous so yeah I have fun even +though I didn't win + + align:start position:0% + + + + align:start position:0% + +so today let's test I was thinking of + + align:start position:0% +so today let's test I was thinking of + + + align:start position:0% +so today let's test I was thinking of +going to three games for what time is it + + align:start position:0% +going to three games for what time is it + + + align:start position:0% +going to three games for what time is it +now this one's three okay so I think + + align:start position:0% +now this one's three okay so I think + + + align:start position:0% +now this one's three okay so I think +we're gonna do two games but I'm gonna + + align:start position:0% +we're gonna do two games but I'm gonna + + + align:start position:0% +we're gonna do two games but I'm gonna +very quickly have a discussion about + + align:start position:0% +very quickly have a discussion about + + + align:start position:0% +very quickly have a discussion about +what are all the different versions of + + align:start position:0% +what are all the different versions of + + + align:start position:0% +what are all the different versions of +mafia that people have played how many + + align:start position:0% +mafia that people have played how many + + + align:start position:0% +mafia that people have played how many +of you play a version of mafia all where + + align:start position:0% +of you play a version of mafia all where + + + align:start position:0% +of you play a version of mafia all where +we'll put something again no ok alright + + align:start position:0% +we'll put something again no ok alright + + + align:start position:0% +we'll put something again no ok alright +so let me quickly give a description the + + align:start position:0% +so let me quickly give a description the + + + align:start position:0% +so let me quickly give a description the +general framework up these games is + + align:start position:0% +general framework up these games is + + + align:start position:0% +general framework up these games is +everybody gets a card and the card gives + + align:start position:0% +everybody gets a card and the card gives + + + align:start position:0% +everybody gets a card and the card gives +you a roll + + align:start position:0% +you a roll + + + align:start position:0% +you a roll +these are usually just regular playing + + align:start position:0% +these are usually just regular playing + + + align:start position:0% +these are usually just regular playing +cards where you know one version that + + align:start position:0% +cards where you know one version that + + + align:start position:0% +cards where you know one version that +I've played is that if you have a king + + align:start position:0% +I've played is that if you have a king + + + align:start position:0% +I've played is that if you have a king +or a queen or a Jack of Clubs you are + + align:start position:0% +or a queen or a Jack of Clubs you are + + + align:start position:0% +or a queen or a Jack of Clubs you are +mafia and it's your job is to kill + + align:start position:0% +mafia and it's your job is to kill + + + align:start position:0% +mafia and it's your job is to kill +everybody else who didn't receive a king + + align:start position:0% +everybody else who didn't receive a king + + + align:start position:0% +everybody else who didn't receive a king +and queen and Jack of Clubs and then + + align:start position:0% +and queen and Jack of Clubs and then + + + align:start position:0% +and queen and Jack of Clubs and then +everybody else is a villager who job is + + align:start position:0% +everybody else is a villager who job is + + + align:start position:0% +everybody else is a villager who job is +to figure out who are the mafia players + + align:start position:0% +to figure out who are the mafia players + + + align:start position:0% +to figure out who are the mafia players +so everyone closes their eyes and opens + + align:start position:0% +so everyone closes their eyes and opens + + + align:start position:0% +so everyone closes their eyes and opens +the eyes based on the cues of a person + + align:start position:0% +the eyes based on the cues of a person + + + align:start position:0% +the eyes based on the cues of a person +who is like a moderator you know I if I + + align:start position:0% +who is like a moderator you know I if I + + + align:start position:0% +who is like a moderator you know I if I +read the game here in class I'd be the + + align:start position:0% +read the game here in class I'd be the + + + align:start position:0% +read the game here in class I'd be the +moderator I and I say like like + + align:start position:0% +moderator I and I say like like + + + align:start position:0% +moderator I and I say like like +nighttime everyone kills us the eyes + + align:start position:0% +nighttime everyone kills us the eyes + + + align:start position:0% +nighttime everyone kills us the eyes +Mafia awakes and then you and then the + + align:start position:0% +Mafia awakes and then you and then the + + + align:start position:0% +Mafia awakes and then you and then the +Mafia do not say anything but I can + + align:start position:0% +Mafia do not say anything but I can + + + align:start position:0% +Mafia do not say anything but I can +communicate with things like gestures + + align:start position:0% +communicate with things like gestures + + + align:start position:0% +communicate with things like gestures +are moving their head and they're + + align:start position:0% +are moving their head and they're + + + align:start position:0% +are moving their head and they're +basically sort of using body language to + + align:start position:0% +basically sort of using body language to + + + align:start position:0% +basically sort of using body language to +vote on who dies that might and if you + + align:start position:0% +vote on who dies that might and if you + + + align:start position:0% +vote on who dies that might and if you +know usually by nodding or by pointing + + align:start position:0% +know usually by nodding or by pointing + + + align:start position:0% +know usually by nodding or by pointing +or something of that and then everyone + + align:start position:0% +or something of that and then everyone + + + align:start position:0% +or something of that and then everyone +closes the eyelids the moderator + + align:start position:0% +closes the eyelids the moderator + + + align:start position:0% +closes the eyelids the moderator +declares who dies everyone opens their + + align:start position:0% +declares who dies everyone opens their + + + align:start position:0% +declares who dies everyone opens their +eyes again and that person reveals their + + align:start position:0% +eyes again and that person reveals their + + + align:start position:0% +eyes again and that person reveals their +card well whether and that shows whether + + align:start position:0% +card well whether and that shows whether + + + align:start position:0% +card well whether and that shows whether +they were mafia or not and the whole + + align:start position:0% +they were mafia or not and the whole + + + align:start position:0% +they were mafia or not and the whole +idea is that in between rounds + + align:start position:0% +idea is that in between rounds + + + align:start position:0% +idea is that in between rounds +everyone which speaks freely and so the + + align:start position:0% +everyone which speaks freely and so the + + + align:start position:0% +everyone which speaks freely and so the +accusations that are flying around and + + align:start position:0% +accusations that are flying around and + + + align:start position:0% +accusations that are flying around and +suspicions and exchanging off off off + + align:start position:0% +suspicions and exchanging off off off + + + align:start position:0% +suspicions and exchanging off off off +very very tangential evidence like I + + align:start position:0% +very very tangential evidence like I + + + align:start position:0% +very very tangential evidence like I +thought I heard rustling over there you + + align:start position:0% +thought I heard rustling over there you + + + align:start position:0% +thought I heard rustling over there you +know it's like no that could be the + + align:start position:0% +know it's like no that could be the + + + align:start position:0% +know it's like no that could be the +Mafia person just trying to throw you + + align:start position:0% +Mafia person just trying to throw you + + + align:start position:0% +Mafia person just trying to throw you +off the track that could be somebody who + + align:start position:0% +off the track that could be somebody who + + + align:start position:0% +off the track that could be somebody who +is actually the villager + + align:start position:0% + + + + align:start position:0% + +so I already won and will say like okay + + align:start position:0% +so I already won and will say like okay + + + align:start position:0% +so I already won and will say like okay +under journey will result in a kill but + + align:start position:0% +under journey will result in a kill but + + + align:start position:0% +under journey will result in a kill but +where where they failed to kill that + + align:start position:0% +where where they failed to kill that + + + align:start position:0% +where where they failed to kill that +person and then people can feel free to + + align:start position:0% +person and then people can feel free to + + + align:start position:0% +person and then people can feel free to +like put up more people link to just + + align:start position:0% +like put up more people link to just + + + align:start position:0% +like put up more people link to just +point out another person clearly no I + + align:start position:0% +point out another person clearly no I + + + align:start position:0% +point out another person clearly no I +you had your head up are you most basic + + align:start position:0% +you had your head up are you most basic + + + align:start position:0% +you had your head up are you most basic +roles in addition villagers that she's + + align:start position:0% +roles in addition villagers that she's + + + align:start position:0% +roles in addition villagers that she's +pretty much every game is the metal + + align:start position:0% +pretty much every game is the metal + + + align:start position:0% +pretty much every game is the metal +detector where the medics every night + + align:start position:0% +detector where the medics every night + + + align:start position:0% +detector where the medics every night +gets the point at someone and if the + + align:start position:0% +gets the point at someone and if the + + + align:start position:0% +gets the point at someone and if the +Mafia we're trying to hit that person + + align:start position:0% +Mafia we're trying to hit that person + + + align:start position:0% +Mafia we're trying to hit that person +that person stays alive the detective + + align:start position:0% +that person stays alive the detective + + + align:start position:0% +that person stays alive the detective +every night gets it like officially + + align:start position:0% +every night gets it like officially + + + align:start position:0% +every night gets it like officially +appointed someone while they're not + + align:start position:0% +appointed someone while they're not + + + align:start position:0% +appointed someone while they're not +sleeping the moderator will like either + + align:start position:0% +sleeping the moderator will like either + + + align:start position:0% +sleeping the moderator will like either +novice head saying yes he's mafia or no + + align:start position:0% +novice head saying yes he's mafia or no + + + align:start position:0% +novice head saying yes he's mafia or no +he's not so in a variant of mafia that's + + align:start position:0% +he's not so in a variant of mafia that's + + + align:start position:0% +he's not so in a variant of mafia that's +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +actually mafia and the way this works is + + align:start position:0% +actually mafia and the way this works is + + + align:start position:0% +actually mafia and the way this works is +one day is one day so I gotta know + + align:start position:0% +one day is one day so I gotta know + + + align:start position:0% +one day is one day so I gotta know +performing for like mafia box one that + + align:start position:0% +performing for like mafia box one that + + + align:start position:0% +performing for like mafia box one that +assignment so this version two mafia you + + align:start position:0% +assignment so this version two mafia you + + + align:start position:0% +assignment so this version two mafia you +kill someone once per day by tapping + + align:start position:0% +kill someone once per day by tapping + + + align:start position:0% +kill someone once per day by tapping +them on the shoulder and same thing and + + align:start position:0% +them on the shoulder and same thing and + + + align:start position:0% +them on the shoulder and same thing and +it's interesting with you you obviously + + align:start position:0% +it's interesting with you you obviously + + + align:start position:0% +it's interesting with you you obviously +like in the same you treat do this if + + align:start position:0% +like in the same you treat do this if + + + align:start position:0% +like in the same you treat do this if +your mom yet you treat me tell someone + + align:start position:0% +your mom yet you treat me tell someone + + + align:start position:0% +your mom yet you treat me tell someone +that in front of all the Mafia plumbers + + align:start position:0% +that in front of all the Mafia plumbers + + + align:start position:0% +that in front of all the Mafia plumbers +because they will see you kill that + + align:start position:0% +because they will see you kill that + + + align:start position:0% +because they will see you kill that +person and will tell everyone that you + + align:start position:0% +person and will tell everyone that you + + + align:start position:0% +person and will tell everyone that you +killed that person and then to be + + align:start position:0% +killed that person and then to be + + + align:start position:0% +killed that person and then to be +lynched or it's an amazing game of often + + align:start position:0% +lynched or it's an amazing game of often + + + align:start position:0% +lynched or it's an amazing game of often +senses we try to be good like me people + + align:start position:0% +senses we try to be good like me people + + + align:start position:0% +senses we try to be good like me people +like established travel by step so they + + align:start position:0% +like established travel by step so they + + + align:start position:0% +like established travel by step so they +get friends alive for them about where + + align:start position:0% +get friends alive for them about where + + + align:start position:0% +get friends alive for them about where +they were in that location they're in + + align:start position:0% +they were in that location they're in + + + align:start position:0% +they were in that location they're in +one of the games recently there someone + + align:start position:0% +one of the games recently there someone + + + align:start position:0% +one of the games recently there someone +said I was working on my life + + align:start position:0% +said I was working on my life + + + align:start position:0% +said I was working on my life +working in a lab until like 4:30 or + + align:start position:0% +working in a lab until like 4:30 or + + + align:start position:0% +working in a lab until like 4:30 or +something and then some Dino that part + + align:start position:0% +something and then some Dino that part + + + align:start position:0% +something and then some Dino that part +found over the partner was in that lab + + align:start position:0% +found over the partner was in that lab + + + align:start position:0% +found over the partner was in that lab +you know the partner and the partner + + align:start position:0% +you know the partner and the partner + + + align:start position:0% +you know the partner and the partner +said they got up at 4:00 and so it's + + align:start position:0% +said they got up at 4:00 and so it's + + + align:start position:0% +said they got up at 4:00 and so it's +closed at 4:15 that person was less + + align:start position:0% +closed at 4:15 that person was less + + + align:start position:0% +closed at 4:15 that person was less +successful yeah and so there are like a + + align:start position:0% +successful yeah and so there are like a + + + align:start position:0% +successful yeah and so there are like a +number of special roles of powers but + + align:start position:0% +number of special roles of powers but + + + align:start position:0% +number of special roles of powers but +like it's been a navigating we're like + + align:start position:0% +like it's been a navigating we're like + + + align:start position:0% +like it's been a navigating we're like +the focus is on actually like figuring + + align:start position:0% +the focus is on actually like figuring + + + align:start position:0% +the focus is on actually like figuring +out where what one thing that I think + + align:start position:0% +out where what one thing that I think + + + align:start position:0% +out where what one thing that I think +one reason why that works well on the + + align:start position:0% +one reason why that works well on the + + + align:start position:0% +one reason why that works well on the +MIT campus is because it's a fairly + + align:start position:0% +MIT campus is because it's a fairly + + + align:start position:0% +MIT campus is because it's a fairly +small campus compared to other + + align:start position:0% +small campus compared to other + + + align:start position:0% +small campus compared to other +university campuses even in + + align:start position:0% +university campuses even in + + + align:start position:0% +university campuses even in +Massachusetts and even when you're off + + align:start position:0% +Massachusetts and even when you're off + + + align:start position:0% +Massachusetts and even when you're off +campus you are often in close proximity + + align:start position:0% +campus you are often in close proximity + + + align:start position:0% +campus you are often in close proximity +to a lot of other MIT people do people + + align:start position:0% +to a lot of other MIT people do people + + + align:start position:0% +to a lot of other MIT people do people +know who else is playing in this game it + + align:start position:0% +know who else is playing in this game it + + + align:start position:0% +know who else is playing in this game it +like in a round of live action market um + + align:start position:0% +like in a round of live action market um + + + align:start position:0% +like in a round of live action market um +you're no closer it gets there an + + align:start position:0% +you're no closer it gets there an + + + align:start position:0% +you're no closer it gets there an +occasionally there's some there are + + align:start position:0% + + + + align:start position:0% + +okay Mike listen to random there's + + align:start position:0% +okay Mike listen to random there's + + + align:start position:0% +okay Mike listen to random there's +always people playing at this + + align:start position:0% +always people playing at this + + + align:start position:0% +always people playing at this +opportunity across the river in Brooklyn + + align:start position:0% +opportunity across the river in Brooklyn + + + align:start position:0% +opportunity across the river in Brooklyn +that are bt service and so it's all one + + align:start position:0% +that are bt service and so it's all one + + + align:start position:0% +that are bt service and so it's all one +like it'd kill happens there and so + + align:start position:0% +like it'd kill happens there and so + + + align:start position:0% +like it'd kill happens there and so +media never was trying to figure out who + + align:start position:0% +media never was trying to figure out who + + + align:start position:0% +media never was trying to figure out who +resolving MIT campus how many people + + align:start position:0% +resolving MIT campus how many people + + + align:start position:0% +resolving MIT campus how many people +were trying to figure out who could like + + align:start position:0% +were trying to figure out who could like + + + align:start position:0% +were trying to figure out who could like +have gone back there + + align:start position:0% +have gone back there + + + align:start position:0% +have gone back there +right there's nice because it helps you + + align:start position:0% +right there's nice because it helps you + + + align:start position:0% +right there's nice because it helps you +do the detective work nicely played but + + align:start position:0% +do the detective work nicely played but + + + align:start position:0% +do the detective work nicely played but +I'm not friends with like a lot of I + + align:start position:0% +I'm not friends with like a lot of I + + + align:start position:0% +I'm not friends with like a lot of I +guess the people who are in the game I + + align:start position:0% +guess the people who are in the game I + + + align:start position:0% +guess the people who are in the game I +just had a couple friends who always + + align:start position:0% +just had a couple friends who always + + + align:start position:0% +just had a couple friends who always +invited me to play and so I usually go + + align:start position:0% +invited me to play and so I usually go + + + align:start position:0% +invited me to play and so I usually go +this pretty quickly because if you like + + align:start position:0% +this pretty quickly because if you like + + + align:start position:0% +this pretty quickly because if you like +I don't we don't know this big just like + + align:start position:0% +I don't we don't know this big just like + + + align:start position:0% +I don't we don't know this big just like +you know I said the the table I realize + + align:start position:0% +you know I said the the table I realize + + + align:start position:0% +you know I said the the table I realize +it's like there's like no yeah and so + + align:start position:0% +it's like there's like no yeah and so + + + align:start position:0% +it's like there's like no yeah and so +like what will end up happening at least + + align:start position:0% +like what will end up happening at least + + + align:start position:0% +like what will end up happening at least +on the first round is like your job you + + align:start position:0% +on the first round is like your job you + + + align:start position:0% +on the first round is like your job you +look suspicious + + align:start position:0% +look suspicious + + + align:start position:0% +look suspicious +I think John's mafia everyone but yes + + align:start position:0% +I think John's mafia everyone but yes + + + align:start position:0% +I think John's mafia everyone but yes +when everyone let's just need I'd be + + align:start position:0% +when everyone let's just need I'd be + + + align:start position:0% +when everyone let's just need I'd be +sitting there like I was gonna say that + + align:start position:0% +sitting there like I was gonna say that + + + align:start position:0% +sitting there like I was gonna say that +a couple of interesting very insightful + + align:start position:0% +a couple of interesting very insightful + + + align:start position:0% +a couple of interesting very insightful +favorites are like where you have things + + align:start position:0% +favorites are like where you have things + + + align:start position:0% +favorites are like where you have things +like the for his job is to try and get + + align:start position:0% +like the for his job is to try and get + + + align:start position:0% +like the for his job is to try and get +killed as mafia like an innocent where + + align:start position:0% +killed as mafia like an innocent where + + + align:start position:0% +killed as mafia like an innocent where +like if the town accidentally kills them + + align:start position:0% +like if the town accidentally kills them + + + align:start position:0% +like if the town accidentally kills them +then they just like on that we lose + + align:start position:0% + + + + align:start position:0% + +very mafia made the detective then they + + align:start position:0% +very mafia made the detective then they + + + align:start position:0% +very mafia made the detective then they +also had I think the serial killer it + + align:start position:0% +also had I think the serial killer it + + + align:start position:0% +also had I think the serial killer it +was supposed to be philosophers insanity + + align:start position:0% +was supposed to be philosophers insanity + + + align:start position:0% +was supposed to be philosophers insanity +was an arsonist I have member in school + + align:start position:0% +was an arsonist I have member in school + + + align:start position:0% +was an arsonist I have member in school +then there was the transporter who could + + align:start position:0% +then there was the transporter who could + + + align:start position:0% +then there was the transporter who could +if they switch targets like mommy take + + align:start position:0% +if they switch targets like mommy take + + + align:start position:0% +if they switch targets like mommy take +one person + + align:start position:0% +one person + + + align:start position:0% +one person +the transport of having to take that + + align:start position:0% +the transport of having to take that + + + align:start position:0% +the transport of having to take that +other person maybe switch the mafia's + + align:start position:0% +other person maybe switch the mafia's + + + align:start position:0% +other person maybe switch the mafia's +turn and then there was me and the seer + + align:start position:0% +turn and then there was me and the seer + + + align:start position:0% +turn and then there was me and the seer +who did talk to that who specifies like + + align:start position:0% +who did talk to that who specifies like + + + align:start position:0% +who did talk to that who specifies like +who specified the rules is it just like + + align:start position:0% +who specified the rules is it just like + + + align:start position:0% +who specified the rules is it just like +was a stable set of rules on online + + align:start position:0% +was a stable set of rules on online + + + align:start position:0% +was a stable set of rules on online +server or is it like every round has a + + align:start position:0% +server or is it like every round has a + + + align:start position:0% +server or is it like every round has a +different set of technologies oh so + + align:start position:0% +different set of technologies oh so + + + align:start position:0% +different set of technologies oh so +you're setting up of the lobby for this + + align:start position:0% + + + + align:start position:0% + +it's actually like in balance but it's + + align:start position:0% +it's actually like in balance but it's + + + align:start position:0% +it's actually like in balance but it's +still on its own a crazy cop who's + + align:start position:0% +still on its own a crazy cop who's + + + align:start position:0% +still on its own a crazy cop who's +always so ever they're basically three + + align:start position:0% +always so ever they're basically three + + + align:start position:0% +always so ever they're basically three +cops in a mafia and the cops don't know + + align:start position:0% +cops in a mafia and the cops don't know + + + align:start position:0% +cops in a mafia and the cops don't know +which cop they are there's a crazy cop + + align:start position:0% +which cop they are there's a crazy cop + + + align:start position:0% +which cop they are there's a crazy cop +who always gets everything inverted + + align:start position:0% +who always gets everything inverted + + + align:start position:0% +who always gets everything inverted +today is a regular cop and then there's + + align:start position:0% +today is a regular cop and then there's + + + align:start position:0% +today is a regular cop and then there's +a cop who like always sees everything is + + align:start position:0% +a cop who like always sees everything is + + + align:start position:0% +a cop who like always sees everything is +truthful or always sees everything is + + align:start position:0% +truthful or always sees everything is + + + align:start position:0% +truthful or always sees everything is +like I'm really sorry everything is + + align:start position:0% +like I'm really sorry everything is + + + align:start position:0% +like I'm really sorry everything is +gonna Center everything is founded on + + align:start position:0% +gonna Center everything is founded on + + + align:start position:0% +gonna Center everything is founded on +religious it's it's actually really + + align:start position:0% +religious it's it's actually really + + + align:start position:0% +religious it's it's actually really +unfair for the Mafia members there's a + + align:start position:0% +unfair for the Mafia members there's a + + + align:start position:0% +unfair for the Mafia members there's a +meadow where you just like say this is + + align:start position:0% +meadow where you just like say this is + + + align:start position:0% +meadow where you just like say this is +what I got and then someone dies and you + + align:start position:0% +what I got and then someone dies and you + + + align:start position:0% +what I got and then someone dies and you +say this is what I got and then + + align:start position:0% +say this is what I got and then + + + align:start position:0% +say this is what I got and then +basically just be together who's lying + + align:start position:0% +basically just be together who's lying + + + align:start position:0% +basically just be together who's lying +but this is interesting + + align:start position:0% + + + + align:start position:0% + +kiddie games for that paternity where + + align:start position:0% +kiddie games for that paternity where + + + align:start position:0% +kiddie games for that paternity where +someone will swap the players okay so + + align:start position:0% +someone will swap the players okay so + + + align:start position:0% +someone will swap the players okay so +this person role swaps God is one of the + + align:start position:0% +this person role swaps God is one of the + + + align:start position:0% +this person role swaps God is one of the +players oh okay well yeah and so the + + align:start position:0% +players oh okay well yeah and so the + + + align:start position:0% +players oh okay well yeah and so the +gospel role became a villager okay + + align:start position:0% +gospel role became a villager okay + + + align:start position:0% +gospel role became a villager okay +moderator V Manila was like the + + align:start position:0% +moderator V Manila was like the + + + align:start position:0% +moderator V Manila was like the +moderators role is now a villager and + + align:start position:0% +moderators role is now a villager and + + + align:start position:0% +moderators role is now a villager and +like one of the random builders like + + align:start position:0% +like one of the random builders like + + + align:start position:0% +like one of the random builders like +they're all is now not like this person + + align:start position:0% +they're all is now not like this person + + + align:start position:0% +they're all is now not like this person +that the person who is now the new + + align:start position:0% +that the person who is now the new + + + align:start position:0% +that the person who is now the new +cognitive that the player who is the + + align:start position:0% +cognitive that the player who is the + + + align:start position:0% +cognitive that the player who is the +head of the mopping that they complete + + align:start position:0% +head of the mopping that they complete + + + align:start position:0% +head of the mopping that they complete +till the end of game and like after + + align:start position:0% +till the end of game and like after + + + align:start position:0% +till the end of game and like after +smiting like ten different people of + + align:start position:0% +smiting like ten different people of + + + align:start position:0% +smiting like ten different people of +this + + align:start position:0% + + + + align:start position:0% + +not by accident but it's not like + + align:start position:0% +not by accident but it's not like + + + align:start position:0% +not by accident but it's not like +someone it's not like their standards + + align:start position:0% +someone it's not like their standards + + + align:start position:0% +someone it's not like their standards +are they you get together with your + + align:start position:0% +are they you get together with your + + + align:start position:0% +are they you get together with your +group that that's playing + + align:start position:0% +group that that's playing + + + align:start position:0% +group that that's playing +what goals there are or someone's like + + align:start position:0% +what goals there are or someone's like + + + align:start position:0% +what goals there are or someone's like +oh I thought about this beforehand then + + align:start position:0% +oh I thought about this beforehand then + + + align:start position:0% +oh I thought about this beforehand then +I have some like a set up I think would + + align:start position:0% +I have some like a set up I think would + + + align:start position:0% +I have some like a set up I think would +be really cool so my brother was put + + align:start position:0% +be really cool so my brother was put + + + align:start position:0% +be really cool so my brother was put +together a setup like that which had I + + align:start position:0% +together a setup like that which had I + + + align:start position:0% +together a setup like that which had I +believe 17 + + align:start position:0% +believe 17 + + + align:start position:0% +believe 17 +people three of which were vanilla + + align:start position:0% +people three of which were vanilla + + + align:start position:0% +people three of which were vanilla +villagers with I know there was four or + + align:start position:0% +villagers with I know there was four or + + + align:start position:0% +villagers with I know there was four or +five different science practices so that + + align:start position:0% +five different science practices so that + + + align:start position:0% +five different science practices so that +they're five like four or five different + + align:start position:0% +they're five like four or five different + + + align:start position:0% +they're five like four or five different +factions so they were just playing like + + align:start position:0% +factions so they were just playing like + + + align:start position:0% +factions so they were just playing like +there's like mafia and then there's like + + align:start position:0% +there's like mafia and then there's like + + + align:start position:0% +there's like mafia and then there's like +werewolves which are identical to Mafia + + align:start position:0% +werewolves which are identical to Mafia + + + align:start position:0% +werewolves which are identical to Mafia +and I'll also get a kill him I think and + + align:start position:0% +and I'll also get a kill him I think and + + + align:start position:0% +and I'll also get a kill him I think and +then there's the serial killer who's + + align:start position:0% +then there's the serial killer who's + + + align:start position:0% +then there's the serial killer who's +bulletproof so you can't get killed that + + align:start position:0% +bulletproof so you can't get killed that + + + align:start position:0% +bulletproof so you can't get killed that +night and he was also a separate + + align:start position:0% +night and he was also a separate + + + align:start position:0% +night and he was also a separate +connection trying to kill everyone else + + align:start position:0% +connection trying to kill everyone else + + + align:start position:0% +connection trying to kill everyone else +and then there's the vigilante who's + + align:start position:0% +and then there's the vigilante who's + + + align:start position:0% +and then there's the vigilante who's +like a good guy who also gets a kill at + + align:start position:0% +like a good guy who also gets a kill at + + + align:start position:0% +like a good guy who also gets a kill at +night and so like that this game like is + + align:start position:0% +night and so like that this game like is + + + align:start position:0% +night and so like that this game like is +actually it was actually surprisingly + + align:start position:0% +actually it was actually surprisingly + + + align:start position:0% +actually it was actually surprisingly +very good because the everyone basically + + align:start position:0% +very good because the everyone basically + + + align:start position:0% +very good because the everyone basically +had it rolls but no one was like unhappy + + align:start position:0% +had it rolls but no one was like unhappy + + + align:start position:0% +had it rolls but no one was like unhappy +about that + + align:start position:0% +about that + + + align:start position:0% +about that +and everyone was more or less try to + + align:start position:0% +and everyone was more or less try to + + + align:start position:0% +and everyone was more or less try to +like heaven it games quick because even + + align:start position:0% +like heaven it games quick because even + + + align:start position:0% +like heaven it games quick because even +though it's 17 people you've got like + + align:start position:0% +though it's 17 people you've got like + + + align:start position:0% +though it's 17 people you've got like +four or five people dying every every + + align:start position:0% +four or five people dying every every + + + align:start position:0% +four or five people dying every every +run for the first couple rounds so I I'm + + align:start position:0% +run for the first couple rounds so I I'm + + + align:start position:0% +run for the first couple rounds so I I'm +trying to find to figure out why there + + align:start position:0% +trying to find to figure out why there + + + align:start position:0% +trying to find to figure out why there +are so many variants I'm not here like + + align:start position:0% +are so many variants I'm not here like + + + align:start position:0% +are so many variants I'm not here like +like like it's that there's something + + align:start position:0% +like like it's that there's something + + + align:start position:0% +like like it's that there's something +about Mafia or werewolf or any of the + + align:start position:0% +about Mafia or werewolf or any of the + + + align:start position:0% +about Mafia or werewolf or any of the +names that people it seems to lend + + align:start position:0% +names that people it seems to lend + + + align:start position:0% +names that people it seems to lend +itself to people coming up with new + + align:start position:0% +itself to people coming up with new + + + align:start position:0% +itself to people coming up with new +variants and then adopting it oh yeah + + align:start position:0% +variants and then adopting it oh yeah + + + align:start position:0% +variants and then adopting it oh yeah +clearly it makes sense for you need to + + align:start position:0% +clearly it makes sense for you need to + + + align:start position:0% +clearly it makes sense for you need to +be able to have a large group of people + + align:start position:0% +be able to have a large group of people + + + align:start position:0% +be able to have a large group of people +agree on the rules before it's at so you + + align:start position:0% +agree on the rules before it's at so you + + + align:start position:0% +agree on the rules before it's at so you +know I I'm not so confused about that I + + align:start position:0% +know I I'm not so confused about that I + + + align:start position:0% +know I I'm not so confused about that I +wondering why my feelings the one it's + + align:start position:0% +wondering why my feelings the one it's + + + align:start position:0% +wondering why my feelings the one it's +really fast playthrough it makes it very + + align:start position:0% +really fast playthrough it makes it very + + + align:start position:0% +really fast playthrough it makes it very +tough right and then to it + + align:start position:0% +tough right and then to it + + + align:start position:0% +tough right and then to it +easy to extend like there's you can + + align:start position:0% +easy to extend like there's you can + + + align:start position:0% +easy to extend like there's you can +always make your own roll but Steve + + align:start position:0% +always make your own roll but Steve + + + align:start position:0% +always make your own roll but Steve +honestly don't need to like there's a + + align:start position:0% +honestly don't need to like there's a + + + align:start position:0% +honestly don't need to like there's a +welt like at least 100 different roles + + align:start position:0% +welt like at least 100 different roles + + + align:start position:0% +welt like at least 100 different roles +you could just like you meenie miney moe + + align:start position:0% +you could just like you meenie miney moe + + + align:start position:0% +you could just like you meenie miney moe +and like aggregate into a game right + + align:start position:0% + + + + align:start position:0% + +sort of boring for the villagers + + align:start position:0% + + + + align:start position:0% + +so there's a clear flaw in the game + + align:start position:0% +so there's a clear flaw in the game + + + align:start position:0% +so there's a clear flaw in the game +pinyin every one of these variants is + + align:start position:0% +pinyin every one of these variants is + + + align:start position:0% +pinyin every one of these variants is +trying to address which is same things a + + align:start position:0% +trying to address which is same things a + + + align:start position:0% +trying to address which is same things a +little bit more interesting but a + + align:start position:0% +little bit more interesting but a + + + align:start position:0% +little bit more interesting but a +possibility and I that's I think the the + + align:start position:0% +possibility and I that's I think the the + + + align:start position:0% +possibility and I that's I think the the +the fact that is very clear that all the + + align:start position:0% +the fact that is very clear that all the + + + align:start position:0% +the fact that is very clear that all the +rules are just like enforced by the + + align:start position:0% +rules are just like enforced by the + + + align:start position:0% +rules are just like enforced by the +people in the room then you know that + + align:start position:0% +people in the room then you know that + + + align:start position:0% +people in the room then you know that +there isn't a mafia woman at the + + align:start position:0% +there isn't a mafia woman at the + + + align:start position:0% +there isn't a mafia woman at the +sparring right now I guess we could have + + align:start position:0% +sparring right now I guess we could have + + + align:start position:0% +sparring right now I guess we could have +mafia 21 spring up in the middle of + + align:start position:0% +mafia 21 spring up in the middle of + + + align:start position:0% +mafia 21 spring up in the middle of +conflict of conventions of everybody but + + align:start position:0% +conflict of conventions of everybody but + + + align:start position:0% +conflict of conventions of everybody but +it won't be in last very long it's hard + + align:start position:0% +it won't be in last very long it's hard + + + align:start position:0% +it won't be in last very long it's hard +to imagine a version of mafia where you + + align:start position:0% +to imagine a version of mafia where you + + + align:start position:0% +to imagine a version of mafia where you +aren't in direct contact with the person + + align:start position:0% +aren't in direct contact with the person + + + align:start position:0% +aren't in direct contact with the person +to establish the rules for the round + + align:start position:0% +to establish the rules for the round + + + align:start position:0% +to establish the rules for the round +that you're playing right now so it's + + align:start position:0% +that you're playing right now so it's + + + align:start position:0% +that you're playing right now so it's +very easy to just think that there's no + + align:start position:0% +very easy to just think that there's no + + + align:start position:0% +very easy to just think that there's no +canonical set of rules + + align:start position:0% + + + + align:start position:0% + +we're failed to get out in Oh + + align:start position:0% +we're failed to get out in Oh + + + align:start position:0% +we're failed to get out in Oh +so he cheated spare seconds and answer + + align:start position:0% +so he cheated spare seconds and answer + + + align:start position:0% +so he cheated spare seconds and answer +so God chose someone to kill every night + + align:start position:0% +so God chose someone to kill every night + + + align:start position:0% +so God chose someone to kill every night +and pretended that they're not mafia + + align:start position:0% +and pretended that they're not mafia + + + align:start position:0% +and pretended that they're not mafia +doing + + align:start position:0% +doing + + + align:start position:0% +doing +the group started at like probably + + align:start position:0% +the group started at like probably + + + align:start position:0% +the group started at like probably +around 12 people and like that and + + align:start position:0% +around 12 people and like that and + + + align:start position:0% +around 12 people and like that and +around five people they were like okay + + align:start position:0% +around five people they were like okay + + + align:start position:0% +around five people they were like okay +this is impossible as in like it is like + + align:start position:0% +this is impossible as in like it is like + + + align:start position:0% +this is impossible as in like it is like +like the previous boat they were like + + align:start position:0% +like the previous boat they were like + + + align:start position:0% +like the previous boat they were like +okay if this happens then why this + + align:start position:0% +okay if this happens then why this + + + align:start position:0% +okay if this happens then why this +happens to the block and then like they + + align:start position:0% +happens to the block and then like they + + + align:start position:0% +happens to the block and then like they +kill someone and that person was like + + align:start position:0% +kill someone and that person was like + + + align:start position:0% +kill someone and that person was like +innocent even though they had to be + + align:start position:0% +innocent even though they had to be + + + align:start position:0% +innocent even though they had to be +guilty of them right so they were like + + align:start position:0% +guilty of them right so they were like + + + align:start position:0% +guilty of them right so they were like +what's going on I thought I think that's + + align:start position:0% +what's going on I thought I think that's + + + align:start position:0% +what's going on I thought I think that's +the sort of cheating they're burning + + align:start position:0% +the sort of cheating they're burning + + + align:start position:0% +the sort of cheating they're burning +decoders back to the discarding yes + + align:start position:0% +decoders back to the discarding yes + + + align:start position:0% +decoders back to the discarding yes +maybe we should try that once in a while + + align:start position:0% +maybe we should try that once in a while + + + align:start position:0% +maybe we should try that once in a while +right + + align:start position:0% + + + + align:start position:0% + +maybe that's because our God so actually + + align:start position:0% +maybe that's because our God so actually + + + align:start position:0% +maybe that's because our God so actually +what it's called but we called spy it's + + align:start position:0% +what it's called but we called spy it's + + + align:start position:0% +what it's called but we called spy it's +basically there's a certain of our spies + + align:start position:0% +basically there's a certain of our spies + + + align:start position:0% +basically there's a certain of our spies +a certain number of resistance players + + align:start position:0% + + + + align:start position:0% + +it's very expensive minimal Fiat except + + align:start position:0% +it's very expensive minimal Fiat except + + + align:start position:0% +it's very expensive minimal Fiat except +that you have to have certain number of + + align:start position:0% +that you have to have certain number of + + + align:start position:0% +that you have to have certain number of +missions by putting people on their + + align:start position:0% +missions by putting people on their + + + align:start position:0% +missions by putting people on their +student spies trying to tell them what + + align:start position:0% +student spies trying to tell them what + + + align:start position:0% +student spies trying to tell them what +it is trying to pass them the resistance + + align:start position:0% +it is trying to pass them the resistance + + + align:start position:0% +it is trying to pass them the resistance +up and we did something very similar to + + align:start position:0% +up and we did something very similar to + + + align:start position:0% +up and we did something very similar to +that where we had one of our friends + + align:start position:0% +that where we had one of our friends + + + align:start position:0% +that where we had one of our friends +left the room for a minute + + align:start position:0% +left the room for a minute + + + align:start position:0% +left the room for a minute +then we go okay guys next round will all + + align:start position:0% +then we go okay guys next round will all + + + align:start position:0% +then we go okay guys next round will all +spies and we can be like a pecking order + + align:start position:0% +spies and we can be like a pecking order + + + align:start position:0% +spies and we can be like a pecking order +for who does what at one time we all + + align:start position:0% +for who does what at one time we all + + + align:start position:0% +for who does what at one time we all +types like blade one kid for being spy + + align:start position:0% +types like blade one kid for being spy + + + align:start position:0% +types like blade one kid for being spy +higher time at the end we finally got we + + align:start position:0% +higher time at the end we finally got we + + + align:start position:0% +higher time at the end we finally got we +managed to at the point where everyone + + align:start position:0% +managed to at the point where everyone + + + align:start position:0% +managed to at the point where everyone +just voted for this only curse comes not + + align:start position:0% +just voted for this only curse comes not + + + align:start position:0% +just voted for this only curse comes not +spy to be despised so you guys we messed + + align:start position:0% +spy to be despised so you guys we messed + + + align:start position:0% +spy to be despised so you guys we messed +the game up to try and like excuse him + + align:start position:0% + + + + align:start position:0% + +yes and resistant this a little bit + + align:start position:0% +yes and resistant this a little bit + + + align:start position:0% +yes and resistant this a little bit +easier to identify that there is + + align:start position:0% +easier to identify that there is + + + align:start position:0% +easier to identify that there is +actually a set of rules because + + align:start position:0% +actually a set of rules because + + + align:start position:0% +actually a set of rules because +resistance is a box product with a rule + + align:start position:0% +resistance is a box product with a rule + + + align:start position:0% +resistance is a box product with a rule +equipment you know so I like a lot of + + align:start position:0% +equipment you know so I like a lot of + + + align:start position:0% +equipment you know so I like a lot of +other games of raffia where you kind of + + align:start position:0% +other games of raffia where you kind of + + + align:start position:0% +other games of raffia where you kind of +think things that things are pretty + + align:start position:0% +think things that things are pretty + + + align:start position:0% +think things that things are pretty +malleable I don't want it to move on to + + align:start position:0% +malleable I don't want it to move on to + + + align:start position:0% +malleable I don't want it to move on to +something else but while I get the last + + align:start position:0% +something else but while I get the last + + + align:start position:0% +something else but while I get the last +cup couple of questions if you have a + + align:start position:0% +cup couple of questions if you have a + + + align:start position:0% +cup couple of questions if you have a +smartphone try downloading this I think + + align:start position:0% +smartphone try downloading this I think + + + align:start position:0% +smartphone try downloading this I think +both Android and it's free on both the + + align:start position:0% +both Android and it's free on both the + + + align:start position:0% +both Android and it's free on both the +Android and the app store because we're + + align:start position:0% +Android and the app store because we're + + + align:start position:0% +Android and the app store because we're +gonna play a couple of rounds of this if + + align:start position:0% +gonna play a couple of rounds of this if + + + align:start position:0% +gonna play a couple of rounds of this if +the Wi-Fi push Mary Jamie not I really + + align:start position:0% +the Wi-Fi push Mary Jamie not I really + + + align:start position:0% +the Wi-Fi push Mary Jamie not I really +like this because there's actually only + + align:start position:0% +like this because there's actually only + + + align:start position:0% +like this because there's actually only +information Jobs guilty he's ready yeah + + align:start position:0% +information Jobs guilty he's ready yeah + + + align:start position:0% +information Jobs guilty he's ready yeah +you don't just start the game by picking + + align:start position:0% +you don't just start the game by picking + + + align:start position:0% +you don't just start the game by picking +stuff up yeah now anybody who doesn't + + align:start position:0% +stuff up yeah now anybody who doesn't + + + align:start position:0% +stuff up yeah now anybody who doesn't +have a smartphone you're welcome to use + + align:start position:0% +have a smartphone you're welcome to use + + + align:start position:0% +have a smartphone you're welcome to use +mine + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +steam is the game + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/Krb1fF2Ycgo.txt b/Krb1fF2Ycgo.txt new file mode 100644 index 0000000000000000000000000000000000000000..f3efdfc4ae67c3ec3ca3c44dc5b1ba346007b9e3 --- /dev/null +++ b/Krb1fF2Ycgo.txt @@ -0,0 +1,2296 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to lecture + +number seven. + +In this lecture, I would like +to present to you the + +formulation of structural +elements. + +We will be discussing beam, +plate, and shell elements, and + +I would like to introduce to you +the isoparametric approach + +for interpolations. + +There are two approaches in the + +formulation that we can follow. + +The first one is a strength of +materials approach, in which + +case we look at a straight beam +element, we use a beam + +theory including +shear effects. + +If you look at a plate element, +we use a plate theory + +including shear effects, also. + +The names associated with these +theories that we're + +using are the names of +Reissner and Mindlin. + +In the second approach, we have +the continuum mechanics + +approach, in which we use the +general principle of virtual + +displacement, but we exclude +the stress components not + +applicable. + +For example, in a plate, we +set the stress through the + +thickness of the plate +equal to zero. + +In addition, also, we have to +impose in the use of the + +principle of virtual +displacement the kinematic + +constraints for particles on +sections or originally normal + +to the mid-surface. + +Namely, we have to put the +constraint into the structure + +that the particles remain on +a straight line during + +deformation. + +Well, as examples, I've plotted +here, I've shown here + +two structures, a beam +and a shell. + +Let's look first at a beam. + +In this case, we have that the +original particles normal to + +the mid-surface, or the neutral +axis of the beam, are + +on this orange line. + +I've shown here a large +number of particles. + +The kinematic constraint that +we're talking about is that + +during deformations, these +particles remain + +on a straight line. + +They move over to the +yellow line here. + +In other words, point A +goes to point a prime. + +Another particle here goes over +to this particle here. + +This particles goes over to that +particle, and so on, and + +these particles remain +on a straight line. + +That is the basic kinematic +assumption. + +However, + +We should also notice that +there's a right angle between + +the mid-surface, or neutral axis +off the beam, and this + +line of particles initially. + +This right angle is not +preserved during deformation. + +In other words, this angle +here is not a right angle + +after deformations anymore. + +In the case of the shell, +the kinematic + +constraint is quite similar. + +Here, we have now the +mid-surface of the shell shown + +as a dashed line. + +The particles on a line normal +to that mid-surface are shown + +here again in orange. + +This is the initial line. + +And during deformation, +these particles remain + +on a straight line. + +Now they have come to be the +yellow line here, and we + +notice that, again, there's a +right angle initially here, + +but that right angle is not +preserved during deformations + +because, in each case, we are +including shear effects. + +Here, we include shear effects, +and similarly here, + +we also include shear effects. + +Well, I've prepared some view +graphs to show these facts a + +little bit more distinct. + +Here, we have a first view +graph on which I show the + +assumptions of the basic +Bernoulli-Euler beam theory + +that is used in the development +of conventional + +beam elements. + +We have here the original beam +element with its neutral axis + +in a dashed line. + +And that beam element, during +deformation, becomes this. + +It goes into this shape here. + +We notice-- and this +is important-- + +that this section here, which I +now mark in blue, goes over + +into that section, and that the +displacement is w at the + +mid-surface, and that the slope +here at right angles to + +that section is nothing +else than dw dx. + +In other words, this angle here +is really nothing else + +than that angle, dw dx. + +This is the Bernoulli-Euler beam +theory excluding shear + +deformations. + +The important point is that when +we use this beam theory, + +we have to match between two +elements, w, in other words, + +the displacement at the +mid-surface has to be the same + +for element one and +element two. + +And in addition, this slope has +to be the same for both + +elements, dw dx for element one +on the left-hand side must + +be equal to dw dx on the +right-hand side. + +This is the conventional beam +theory that is used to develop + +the Hermitian beam elements. + +And what I'd like to introduce +to you now is the beam theory + +that we're using in the +isoparametric formulation, + +namely in the development of +modern beam elements, pipe + +elements, shell elements, +and plate elements. + +I should say at this point +that the conventional + +Hermitian beam element that +you're probably familiar with + +is more effective in engineering +analysis than the + +beam element that I'm talking +about here when we just look + +at a straight beam. + +However, I want to look at the +straight beam here as an + +example to introduce to you +the formulation of the + +structural elements that +I'm talking about. + +The formulation is very well +displayed, very well + +demonstrated. + +The basic features are very well +demonstrated looking at + +the beam element, although +the application of this + +formulation to a straight beam +element is not as effective as + +just the usage of a Hermitian +beam element. + +However, if we talk about curved +beam elements, pipe + +elements, then this formulation + +is indeed very effective. + +And, of course, for plates +and shells, it + +is really very effective. + +Let me show to you, then, +the basic points-- + +the basic important points-- + +that are being used in +the formulation. + +Here we have, again, our +original beam element. + +The neutral access is shown +here, and this beam element + +now moves over into this piece, +into that shape, during + +deformations. + +We have a section here, and as +I pointed out earlier, that + +section has to remain straight +during deformations. + +In fact, it moves right +to that section here. + +Now notice that what we're +talking about is a slope, dw + +dx here, which is this angle +here, plus a shear deformation + +angle, gamma, and dw dx minus +gamma is this angle. + +And that is the angle beta. + +In fact, this is the rotation +of this line of particles. + +In other words, we are not +talking just about one state + +variable, w, as we do in the +Hermitian formulation, but we + +talk about two state variables +now, beta and w. + +Beta and w both are independent, +and we will see + +that, later on, we will +interpolate them as + +independent quantities. + +The important point, then, +that if you look at two + +elements, if you do interpolate +w and beta + +independently, then we need, +between two elements, + +continuity in w and continuity +in beta. + +We do not talk about continuity +in dw dx. + +We do not talk about that, and +that is the important point, + +particularly when we talk about +the formulation of plate + +elements and shell elements. + +The fact that we'll talk about +independent interpolations of + +w and beta, including shear +effects, of course, in an + +approximate way, but including +shear affects, that fact + +alleviates us of many +difficulties that + +we encounter otherwise. + +In other words, that we +encounter if we use a + +classical plate theory excluding +shear deformations. + +A good starting point for the +development of the elements is + +the use of the total potential, +pi, of an element. + +That total potential I've +written down here, and we have + +set pi is equal to a +contribution from the bending + +part plus a contribution from +the shearing part, or the + +shearing deformations, and, of +course, there is the external + +work due to distributed +pressure, p, on a beam + +element, and moments, externally +applied moments, m, + +onto the beam element. + +Now, notice the quantities +that I'm using here. + +The bending part is given by dw +dx squared, of course with + +the flex or rigidity in front, +and this part here is given + +only in terms of the section +rotation beta, which is + +independent of the translation +of the neutral axes, w. + +Here, we have the shearing part, +dw dx, minus beta As, + +the shear strength. + +And they have been written +down here once more. + +If we look at this equation, +here we get dw dx minus beta + +is equal to gamma. + +The other quantities, of course, +that I used in the + +derivation of this-- + +pi, the stress being equal to +v over as, v being the shear + +force on the section, As +is the shear area. + +Notice that we are assuming the +shear strength through the + +thickness of the beam element +to be constant. + +They are constant because of +this equation here, basically. + +w, of course, varies along +the length of the beam. + +Beta varies along the length +of the beam, but that means + +gamma is constant through to +the thickness of the beam. + +Now, since gamma is constant +through the thickness of the + +beam, we have to say, of course, +that also our shear + +stress is constant through the +thickness of the beam, and we + +have to introduce a shear +correction factor, k, which is + +equal to As over A, where As is +an equivalent shear area. + +Using these quantities we obtain +this pi functional, + +where, once again, we simply add +the bending contribution, + +bending strain energy to the +shear strain energy, and we + +subtract the total potential +of the external loads. + +If we invoke the stationarity +of this functional, in other + +words, we invoke that delta pi +is equal to zero, we obtain + +the principle of virtual work, +or principle of virtual + +displacement, which I have +discussed with you in an + +earlier lecture. + +The result of invoking that del +pi is equal to zero, or + +invoking the stationarity of +pi is this equation here. + +Now notice that in this equation +we have, if we want + +to interpret it once physically +here, basically the + +real stress part, here, the +virtual strain part. + +Similarly here, the real stress +part and the virtual + +strain part, and, of course, +the virtual work of the + +external loads. + +The important point is that we +only integrate along the + +length of the beam, and not +through the thickness anymore, + +because we talk about quantities +stress resultants + +over the thickness. + +Well, once we have arrived at +this equation, we can proceed + +in much the same way as we have +been proceeding in the + +development of continuum +isoparametric elements. + +Here, we look at a +particular case. + +Let us say we have a beam +elements such as shown here. + +Of course, this is the loading +applied, P. The bending moment + +that they're talking about +here is shown here. + +It is a distributed bending +moment over + +any part of the beam. + +Similarly, P is only +applied over a + +certain part of the beam. + +The depth of the beam is b, the +width of the beam is a. + +As a shear factor for a +rectangular beam, the sheer + +fact k that I introduced +to you briefly is 5/6. + +Of course, I, the moment +of inertia, is ab + +cubed divided by 12. + +The interpolations that we +would use for such a beam + +element are one dimensional +interpolations. + +We only integrate along +the length, x. + +And the one dimension +interpolations we discussed + +already earlier. + +We simply use the same that we +have been using already in the + +formulation of truss elements. + +Two point interpolation would +be this element here. + +Here, we use a three point +interpolation. + +Notice-- + +and this is important-- + +that we're talking about w and +beta, the section rotations, + +as independent quantities. + +So for a three point, or three +nodal point beam, we would + +have, in just a plane analysis, +we would have six + +degrees of freedom. + +For a cubic element, we have +eight degrees of freedom. + +Of course, for a Hermitian beam +element, we would have + +only these degrees of freedom +and those degrees of freedom, + +w and dw dx here, and +w, dw dx here. + +So, that is the reason why +the Hermitian beam + +element is more effective. + +However, we can use these +interpolations directly to + +develop curved beam elements, +pipe elements, and then, of + +course, this approach is-- +even for beam elements-- + +more effective, as I +mentioned earlier. + +Well, let us then write down the +basic interpolations that + +we are using. + +Here, we have w being +the sum of hi wi. + +hi, we discussed earlier +already. + +And these, of course, are +nodal point transverse + +displacement. + +These are the nodal +point rotations of + +the sections, beta. + +In other words, I could have +used here, as a notation, beta + +i, but I chose to use theta i. + +If you write these equations +in matrix form, we directly + +obtain this relation here, where +hw simply list hi, u + +lists the displacements and +section rotations, and similar + +here, beta is given in terms +of an h beta matrix. + +We take the differentiations of +hw and h beta, and we get + +dw dx equal to Bw times u d beta +dx equal beta times u. + +Once we have the principle +virtual work established for + +the element that we're +considering and have chosen + +our interpolations, the approach +of developing the + +stiffness matrices, the load +vectors, is exactly the same + +as in the development of +continuum elements. + +Well here, I have written down +the various quantities. + +U transposed lists, as I said +earlier, the displacement + +vector nodal points and the +rotation vector nodal points. + +Hw simply gives the +interpolation functions, q, of + +course, being equal to +the number of nodal + +points we are using. + +And here, we have H beta. + +The Bw is given right here. + +Notice our J inverse comes in +there because we have to + +transform from r to x, x being +the actual physical coordinate + +along the length. + +Similarly, B beta being +given here. + +Again, the J inverse here +to transform from r to x + +coordinates. + +Once we have written down +these, we can directly + +substitute into the principal +of virtual work, and we come + +up with the stiffness matrix, +given here, and the load + +vector given here. + +Let me point out a few important +things here. + +Of course, this B beta matrix +here-- just to remind you-- + +comes from d beta dx. + +It's in fact, really, d beta +dr, but because we're + +integrating from -1 to plus +1, however, we have our + +determinant J there to take +into account the volume + +transformation. + +Here, of course, we have +d beta dx transposed. + +This comes from the virtual +strains, and that comes from + +the real strains. + +Of course, we have +the stresses. + +Here, so these strains times +the stress strain law, E, + +being the Young's modulus, +gives us the stresses. + +Here, we talk about shearing +deformations. + +Notice that we have here +dw dx, that is, the + +Bw minus the beta. + +So we have the derivative in +here of w, but no derivative + +in H beta because we are simply +interpolating here the + +beta values. + +Again, of course, a +transformation to x, and + +therefore we have a determine +J in there. + +The load vector looks just the +same way as in the development + +of continuum elements. + +This is the transverse loading +applied P. This is, of course, + +interpolating-- + +this [UNINTELLIGIBLE] + +interpolates the virtual +transverse displacements. + +Here, we have the moment loads, +the real moment loads, + +and this interpolates here the +section rotations, beta, along + +the lengths of the beam. + +Of course, again, the volume +transformation from r to x. + +This is really a straightforward +application of + +what we discussed earlier. + +There is one important point, +however, now, that I have to + +point out to you. + +If we consider the functional +pi, as I mentioned earlier, + +there's a bending part +here and there's a + +shearing part here. + +Notice that in this development +I have divided + +through by EI over 2, so that +I introduce a value alpha + +there, and that alpha is really +GAK divided by EI. + +Now, if we look at that alpha +value, and let's look at the + +value for a rectangular section, +we would see that the + +a value, of course, is a times +b, and the I value gives us + +really an ab cubed, if this is, +here, b, and that is a. + +An ab cubed over +12, of course. + +And we have, also, the GK that +gives us these, and of course + +an E in front here. + +But the important point that I +want to now concentrate on is + +really this b over b cubed. + +We can see that as the element +gets thinner and thinner, as + +the element gets thinner and +thinner, that alpha gets + +larger and larger. + +If alpha gets larger and larger, +this term here will be + +predominant. + +This term will be predominant. + +Now this means, however, that if +we want to finally converge + +to a beam in which the shear +strengths are negligible, in + +other words, in which the shear +strengths are extremely + +small, what we would have to +be able to represent in the + +formulation is that this value +here goes to zero. + +And what happens in the +formulation, really, is that + +as this value gets larger and +larger, any error introduced + +in the formulation, due to the +fact that this is not exactly + +zero in the finite element +interpolation, that error is + +largely magnified. + +Is magnified and, in fact, can +introduce a very large error + +if this value is not zero due to +the fact that alpha becomes + +larger and larger +if the element + +becomes thinner and thinner. + +In other words, in summary once +more, if we are talking + +about a beam element that gets +thinner and thinner for which + +we know the shear strengths +should becomes smaller and + +smaller, our finite element +interpolation must be able to + +represent this fact. + +Now, if we look at the shear +strengths, and this is, of + +course here, nothing else then +basically the shear strength + +squared, we now identify that +dw dx minus beta, when + +interpolated using our +interpolation functions, must + +be able to be very, +very, very small. + +And that is a restriction +on the formulation. + +So what we have to do, really, +is use high enough order + +interpolations so that dw dx +minus beta can be smaller for + +thin elements. + +Of course for thick beam +elements, that is not really a + +constraint because we know +that there are shearing + +deformations, and the shear +deformations can be quite + +significant. + +However, for thin elements, we +must be able to represent the + +fact that gamma is small, and +therefore, we have to use high + +order interpolations. + +In fact, the parabolic +interpolation is really the + +lowest interpolation that +one can recommend. + +It would be better to use +cubic interpolation. + +In fact, we use the cubic +interpolation in practice. + +In that case, this gamma value +can be small, and we run into + +no difficulties and +the element can be + +very, very, very thin. + +Another approach would be to +use a discrete Kirchhoff + +theory or reduced numerical +integration. + +These approaches have +been developed + +for low order elements. + +The discrete Kirchhoff theory +approach is very effective. + +The reduced numerical +integration can also be + +effective, but has to +be used with care. + +In particular, as I will point +out in the next lecture, we + +have to be careful that we do +not introduce spurious rigid + +body modes into the system. + +The development that I just +talked about really is + +applicable to an element that +has a rectangular section and + +the element was also +lying in a plane. + +We looked at a straight +element. + +Let us now see how we can +generalize these concepts + +directly to the formulation of +general curved beam elements. + +And for that purpose +I've shown here-- + +I'm showing here-- + +a more general beam element +that lies in a + +three-dimensional space. + +It's still rectangular, however, +we could also have a + +circular section instead. + +In fact, when we look at a +pipe element, we do talk + +about-- we have, of course, +a circular section. + +Well, in this particular beam +element, notice I'm looking at + +node one here, node two there, +and generally node three here + +and node four here, because we +want to pick up the curvature + +of the element. + +I have this element lying +in a three dimensional + +space, x, y, z. + +Notice that that element has +local coordinates r, s, t. + +These are the isoparametric +coordinates. + +And psi, eta, zeta, these are +the actual continuous physical + +coordinates in the +beam element. + +We define normals at +each nodal point. + +The normal in the t direction +here is 0 Vt 1. + +The normal into the s +direction is 0 Vs 1. + +And similarly, we have two +normals at each nodal point. + +Notice that for this particular +rectangular beam + +element, I have the thickness, +a1, here and b1, there, and a2 + +here, b2 there. + +These thicknesses can +be different. + +Now what I want to use are the +same basic assumptions that we + +have familiarize ourselves +already with when we looked at + +the special case of a straight +beam element in planar + +deformations. + +I want to use those basic +assumption now in the + +development of this more +general beam element. + +And I want to use a continuum +approach. + +Well, what we are doing, +then, is the following. + +We interpolate the coordinates, +x, y, and z, + +along the beam element in +terms the nodal point + +coordinates of the nodes that +lie on the neutral axes of the + +beam plus an effect that +comes in due to the + +thickness of the beam. + +Now let us go and look +in detail at the x + +interpolations. + +The L denotes 0 or 1, 0 being +the initial configuration, 1 + +being the final configuration. + +So let's put simply a 0 in +there, think in terms of a 0 + +there, and let's look at the +initial configuration first. + +Well, here we have the initial +x-coordinates of the nodal + +points, and there +are q of them. + +These are the one dimensional +interpolation functions, just + +the same that we use for a truss +element, for example. + +Here, we have the t-axis. + +This is the t-axis into the +direction of the normal into + +the t direction. + +In other words, this +is a t-axis here. + +Notice that that t-axis +here corresponds + +to this normal here. + +That s axis here corresponds +to this normal here. + +So here, we have t/2, and ak +being the total thickness of + +the beam corresponding to that +t direction, hk being the one + +dimensional interpolation +functions again, and these are + +the direction cosines of the +normal in the t direction. + +Here, I should really say, this +is a direction cosine + +corresponding to the x-axis, +corresponding to the x-axis. + +When we talk later about the y +and z-axis, then we use the y + +direction cosine and the +z direction cosine. + +This part comes in because the +beam basically has a thickness + +into the t direction. + +Now, we have also to introduce +the s direction part, and here + +we s/2, the thickness into s +direction, the one dimensional + +interpolation functions, and the +direction cosine in the x + +direction of the normal +in the s direction. + +Well, if we want to find, in +other words, the coordinates + +of any point in the beam +element, and let us look, once + +more, back at the +beam element. + +If I want to find the coordinate +of a point, p, + +lying in that beam element +here-- there's, say, point p-- + +what I have to do is I have to +identify the r, s, and t + +coordinates of that point, p, +and then substitute these r, + +s, and t-coordinates into +this part here. + +And I would get the +corresponding x-coordinate. + +I proceed similarly with the +y and z-coordinates. + +Notice, as I pointed out +earlier, we are talking still + +about the thickness ak hk here, +here, and here, but + +we're using the x direction +cosines, the y direction + +cosines, and the z direction +cosines here. + +And similarly for the s +direction, we are using + +similar quantities. + +So this is the interpolation of +the beam element, and using + +these three formerly, we +can directly obtain-- + +we can directly obtain-- + +the x, y, and z-coordinates in +this system of axes of any + +point in the beam element. + +This is the most +important fact. + +The interpolations that I've +listed here are the starting + +point of the development of +the strain displacement + +matrices and displacement +interpolation matrices. + +Now, let us identify that if +these are the original + +coordinates for L being 0, then +we can also apply, of + +course, after the deformation, +the same interpolation, and we + +put L equal to 1. + +If we subtract the x1 minus +zero x, we should get the + +displacements, u. + +Notice that the displacements, +u, are in the directions of + +the x-axis. + +Well, this is exactly +how we proceed. + +We use these interpolations +for before deformation and + +after deformation. + +And we subtract these +interpolations as shown here + +and directly obtain the u, v, +and w displacements, of + +course, as a functional +of r, s, and t. + +Notice that if I proceed +this way-- + +notice that if I proceed this +way, I have used the basic + +assumption that plane sections +remain plane during + +deformation. + +This was the assumption that I +pointed out to your earlier. + +And we are using it in this +general information just in + +the same way as in the special +application that + +I showed you earlier. + +Well, having then-- + +just to refresh your memory, the +u, v, and w, in terms of + +r, s, and t, of course, via +these subtractions, we obtain + +directly these equations here. + +Notice that here we have, now, +the nodal point displacements, + +uk, vk, wk, and we have +the change in + +the direction cosines. + +These are the changes in +the direction cosines. + +Well, these changes in the +direction cosines we want to + +express in terms nodal +points rotations. + +And that is achieved as shown +on this view graph. + +We can express these changes +in the direction cosines + +directly by taking the cross +product of a vector of nodal + +points rotations, and I've +listed here this vector, this + +is a nodal point rotation about +the x, y, and z-axis at + +nodal point, k. + +You're taking the cross product +of this vector times + +the original normal. + +Time the original normal. + +And we get, then, the change in +the normal, of course, for + +the t direction and for +the s direction. + +If we substitute this relation +here, of course, remember that + +these quantities are known. + +They are given. + +So the unknowns now +are theta k. + +If you substitute from here into +our relation here that I + +developed earlier, we directly +obtain the displacements of + +any point, p, in the beam +in terms of nodal point + +displacements and nodal +points rotations. + +Because these quantities here +now have been eliminated and + +have been expressed in terms +of nodal point rotations. + +Well, now we have all the +quantities that we need to + +develop our strain displacement +matrix for the + +beam element. + +Remember, all we need are the +coordinate interpolations, + +which I have developed already, +and the displacement + +interpolations. + +With those two quantities, we +can immediately calculate, via + +the procedures that I discussed +with you earlier, + +the strain displacement +transformation matrix. + +And here it is given. + +Notice that we are now talking +about strain into the eta + +directions. + +In other words, the eta, psy, +and zeta directions. + +These are the directions that I +pointed out to you earlier, + +which are the physical +coordinate + +directions along the beam. + +Let me show it to you once +more, the picture. + +The r, s, and t-coordinates +are the isoparametric + +coordinates. + +The eta, psy, and zeta +coordinates are the physical + +coordinates along the beam. + +In other words, for the one +dimensional beam that we + +looked at, this eta axis was, +in fact, the x-axis. + +Of course, our x, y, and +z-axes are now global + +Cartesian axes. + +Well then, with that +information, we can directly + +calculate the strain +displacement matrix here. + +This is done effectively using +numerical integration, as I + +will be discussing in +the next lecture. + +The transformations that are +necessary are also done on the + +integration point level. + +Notice that the uk here lists +the nodal point displacements + +and the nodal point rotations, +and, of course, we have to + +also remember one important +fact, that for the beam we are + +talking about stresses into +the eta, psy, and zeta + +directions, normal stresses, +shear stresses here, that are + +related via this stress strain +law to the normal strains and + +shear strains. + +Notice that there's again the +shear correction factor, k, + +which we want to also include in +the formulation because we + +have assumed constant shearing +strains through the thickness + +of the beam, whereas we know +that for a rectangular beam, + +for example, we have parabolic +shear strain distributions if + +the beam is straight. + +I'd like to now go on with the +development of plate elements. + +Here, we are talking basically +about the same approach. + +As I mentioned already once, +the beam element that I'm + +talking about here-- + +that I have been talking about-- +is really only an + +effective formulation when we +talk about, and we want to + +develop, a curved +beam element. + +For pipe elements also, in the +case of pipe elements, I + +should briefly mention that, +of course, we have to + +introduce, also, an ovalization +degree of freedom. + +That ovalization degree of +freedom interpolates basically + +the ovalization along +the curved pipe. + +That is an additional degree +of freedom that has to be + +introduced in the curved beam +element formulation. + +So, the beam element formulation +is effective for + +curved beams, pipes. + +However, it does show the basic +procedure that we are + +following also in the +development of + +plate and shell elements. + +And here, we have a typical +plate element. + +In other words, a flat shell. + +The u, v, and w displacements +are now + +interpolated in this way. + +Notice u be the displacement +into the x direction, v the + +displacement into the y +direction, w being the + +transverse displacement, and +again, we're talking about + +section rotations. + +Beta x being the section +rotation about the y-axis. + +That is, the beta x +section rotation. + +Beta y is a section rotation +about the x-axis. + +So that our v, measuring +z positive upwards. + +Notice, our [? v4 ?] point here +is negative, and that's + +why we have a negative +sign there. + +Well, with that then given, we +can immediately develop our + +strains by using the strength +of material equations that + +tell us epsilon xx is del u del +x, epsilon yy is del v del + +y, et cetera. + +And, of course, we're getting +also our shear strengths. + +Having developed the strains, +we also recognize that our + +stresses are given in terms of +these formulae, where we have + +now the stress strain law for +planed stress analysis, + +because we are looking at the +plate as an assemblage of thin + +elements, plane stress +elements, lying + +on top of each other. + +The stress through the plate, of +course, is 0, and this is, + +therefore, the plane stress +[? material ?] + +that we have been +putting in here. + +And the z times this vector +here gives us the strains. + +The shearing stresses are given +here, and our functional + +pi that I used also for +the beam element + +already is given here. + +Notice that we now have to +integrate through this + +thickness of the +plate element. + +Here's our shear correction +factor again, which is + +introduced just the same way +as in the beam element. + +Notice here we have the work, or +the total potential of the + +external loads, I should say. + +It is convenient now to +integrate through the + +thickness because we can +integrate prior to + +interpolating the quantities, +and that then yields this + +value for pi, where our Cb parts +and Cs part here, these + +two matrices, embody the fact +that we have integrated + +through the thickness, +so we have the + +following definitions here. + +Kappa simply lists basically +the bending strains, or I + +should say the rotations +of the sections. + +Of course here, we have +the shearing strains. + +Gamma lists the shearing +strains. + +Cb now is a function of h cubed, +just like in classic + +plate theory. + +Of course, we also have an +h cubed entering into the + +formulation. + +And this Cb matrix embodies +the fact that we have + +integrated through +the thickness. + +Here is our Cs. + +Of course, in the Cs, we +also have the k part. + +Notice that, again, we have an +h cubed here and an h there. + +Therefore, to use our +interpolation for plate and + +shell elements, we will have +to use high enough shell + +interpolations to be able to +represent the fact that the + +shear strains go to 0 for thin +plates if we want to use this + +formulation for thin +plates and shells. + +Well, invoking now the fact that +pi shall be stationary, + +we directly obtain this +equation here. + +And this, of course, is +nothing else than the + +principal of virtual +displacement + +for the plate element. + +Notice that from this point +onwards, we simply need to + +substitute only our +interpolations. + +The interpolations that we are +using are now interpolations + +for w, beta x, and beta y. + +And, of course, we also +interpolate x and y. + +These interpolations, beta x +and beta y, are independent + +from the interpolations of w, +and that is the important + +points, as I mentioned in the + +development of the beam element. + +The fact that we are dealing, +here, with three + +interpolations of course means +that an each nodal point, we + +have three unknowns, w's, +and section rotations. + +Let us now look very briefly +at shell elements. + +The same concept that we used +to develop the general beam + +element after having discussed +the special beam element is + +also employed now in the +development of what you might + +call a general shell element, +versus the special plate + +element that I just discussed, +or the special shell element + +that I just discussed, because +a flat shell is of course + +nothing else than a plate, +if we also don't + +have membrane forces. + +Well here, I'm showing +a shell element, a + +nine-noded shell element. + +And notice that in this case, +now, we are talking about this + +normal only. + +In the beam, we had two normals, +vt and vs. Now we + +only have one normal. + +At a nodal point, we are +defining the membrane + +displacements, uk, vk, wk, +being a transverse + +displacement, and the rotations, +alpha k and beta k. + +These rotations are defined +about the axis v1 k and v2 k. + +Now notice that these two +rotations, alpha k and beta k, + +will give us the change in +vn during deformations. + +And this is really how we +use alpha k and beta k. + +We express a change in vn in +terms of alpha k and beta k. + +The procedure is the +same as in the + +case of the beam element. + +First, we express our x, +y, and z-coordinates. + +And we're using here the +original normal, vn, the x, y + +and z direction cosines. + +These are, here, the x, y +and z-coordinates of the + +nodal point, k. + +We have our two dimensional +interpolation functions, hk, + +now here, because we talk +about a two dimensional + +surface, the mid-surface +of the shell. + +Of course, at each nodal point, +the shell can have a + +different thickness, and that +is denoted by using a + +different ak value at +each nodal point. + +Applying this interpolation +here to the initial + +configuration and the final +configuration and subtracting + +0x from 1x, and similar for y +and z, we directly obtain the + +displacements u, v, and w. + +Notice that the displacements +now are involving the nodal + +point displacements and the +change in the direction + +cosines of the normal, +denoted here. + +These changes in the direction +cosines of the normal can + +directly be expressed in +terms of the rotations, + +alpha k and beta k. + +Now, notice here that once we +have done this, of course here + +we involve now, as I mentioned +earlier, the v1 and v2 + +directions. + +And these v1 and v2 directions +are arbitrarily selected. + +In fact, they are-- + +for our shell element here-- +selected as shown here. + +But once we have selected v1 +and v2 at each nodal point, + +and they can vary from nodal +point to nodal point, then we + +can use this relation to attain +directly the change in + +the direction cosines of the +normal during deformations, + +when the deformations are +alpha k and beta k. + +So with this equation, then, and +the earlier equation that + +I've given to you, we can +directly obtain the + +displacement interpolation +matrix and the strain + +interpolation matrix. + +One important point that I +should briefly mention is + +that, of course, for the shell, +we have 0 stresses + +through the thickness. + +So, we have to use this stress +strain law here. + +Notice there are 0's in +this row and column. + +And this is, here, the plane +stress part for the bending, + +and that is the shear +part here. + +This is the stress strain law +defined in a local convected + +coordinate system where we are +talking about the stresses + +through the thickness being +this direction here. + +And these other stresses +are aligned with + +the coordinate system. + +We have to transform this one +here to the global coordinate + +system in order to be able +to use it directly in our + +formulation. + +And that transformation +is achieved via these + +transformation matrices. + +Now, this element has been +effectively implemented in the + +ADINA computer program, and we +want to use it using high + +order interpolation, as I +mentioned earlier, as the + +basic element that therefore is +very useful, which can be + +used as a flat element, a curved +element, all curved + +element, or it can have +curvature in both directions. + +Also, this is the basic element +that is being used. + +We can also collapse nodes and +derive other elements. + +As I pointed out earlier, the +low order elements should only + +be used in very special cases. + +I would not recommend +these elements. + +Although they can be used in +principle, the element that is + +really useful is this +one and that one. + +Both, of course, can be used +as curved elements as I + +pointed out. + +Another feature, and this is +the final view graph that I + +wanted to show in this lecture, +is that we can use + +these elements also in +transition regions. + +Namely, here we have the shell +element, now being flat-- + +that I discussed-- + +and we can directly couple +this element into another + +element, which we call a +transition element, which has + +the shell degrees of freedom +at these nodes, but + +translational degrees of +freedom only here. + +In other words, a continuum +element degrees of freedom + +right here. + +Notice, three degrees of freedom +at this node, only + +translations, whereas here, we +would have five degrees of + +freedom-- three translations, +two rotations. + +Similarly, here we have a curved +shell going into a + +solid, and again here, we have +a transition element. + +Here, we show the five degrees +of freedom at a shell node and + +the three degrees of freedom at +a continuum element node. + +This is an effective approach to +be able to couple director + +shell elements into +solid elements. + +I have not talked, of course, +about the actual derivation of + +the matrices used in +the formulation of + +the transition element. + +That is a little bit beyond what +I wanted to present in + +this lecture. + +But the basic concepts are +those that we discussed + +already in the earlier lecture +for continuum element and in + +this lecture for structural +elements. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/M0Sa8fLOajA.txt b/M0Sa8fLOajA.txt new file mode 100644 index 0000000000000000000000000000000000000000..462f8f62b7f55442a1ddc0620fcfa6da0dbbad44 --- /dev/null +++ b/M0Sa8fLOajA.txt @@ -0,0 +1,6853 @@ +align:start position:0% + +okay this is a lecture where complex + + align:start position:0% +okay this is a lecture where complex + + + align:start position:0% +okay this is a lecture where complex +numbers come in it's uh complex numbers + + align:start position:0% +numbers come in it's uh complex numbers + + + align:start position:0% +numbers come in it's uh complex numbers +have slipped into this course because + + align:start position:0% +have slipped into this course because + + + align:start position:0% +have slipped into this course because +even a real Matrix can have complex igen + + align:start position:0% +even a real Matrix can have complex igen + + + align:start position:0% +even a real Matrix can have complex igen +values so we met complex numbers there + + align:start position:0% +values so we met complex numbers there + + + align:start position:0% +values so we met complex numbers there +as the igen values and complex igen + + align:start position:0% +as the igen values and complex igen + + + align:start position:0% +as the igen values and complex igen +vectors and we + + align:start position:0% +vectors and we + + + align:start position:0% +vectors and we +are this is probably the last we have a + + align:start position:0% +are this is probably the last we have a + + + align:start position:0% +are this is probably the last we have a +lot of other things to do about igen + + align:start position:0% +lot of other things to do about igen + + + align:start position:0% +lot of other things to do about igen +values and igen vectors and that will be + + align:start position:0% +values and igen vectors and that will be + + + align:start position:0% +values and igen vectors and that will be +mostly real but at one point somewhere + + align:start position:0% +mostly real but at one point somewhere + + + align:start position:0% +mostly real but at one point somewhere +we have to see what do you do when the + + align:start position:0% +we have to see what do you do when the + + + align:start position:0% +we have to see what do you do when the +numbers become complex numbers what + + align:start position:0% +numbers become complex numbers what + + + align:start position:0% +numbers become complex numbers what +happens when the vectors are complex + + align:start position:0% +happens when the vectors are complex + + + align:start position:0% +happens when the vectors are complex +when the matrices are complex when the + + align:start position:0% +when the matrices are complex when the + + + align:start position:0% +when the matrices are complex when the +what's the inner product of two the + + align:start position:0% +what's the inner product of two the + + + align:start position:0% +what's the inner product of two the +product of two complex + + align:start position:0% +product of two complex + + + align:start position:0% +product of two complex +vectors we just have to make the change + + align:start position:0% +vectors we just have to make the change + + + align:start position:0% +vectors we just have to make the change +just see what is the change when numbers + + align:start position:0% +just see what is the change when numbers + + + align:start position:0% +just see what is the change when numbers +become complex + + align:start position:0% +become complex + + + align:start position:0% +become complex +then can I tell you about the most + + align:start position:0% +then can I tell you about the most + + + align:start position:0% +then can I tell you about the most +important example of complex matrices it + + align:start position:0% +important example of complex matrices it + + + align:start position:0% +important example of complex matrices it +comes in The forier Matrix so the forier + + align:start position:0% +comes in The forier Matrix so the forier + + + align:start position:0% +comes in The forier Matrix so the forier +Matrix which I'll describe is a complex + + align:start position:0% +Matrix which I'll describe is a complex + + + align:start position:0% +Matrix which I'll describe is a complex +matrix it's certainly the most important + + align:start position:0% +matrix it's certainly the most important + + + align:start position:0% +matrix it's certainly the most important +complex matrix it's the Matrix that we + + align:start position:0% +complex matrix it's the Matrix that we + + + align:start position:0% +complex matrix it's the Matrix that we +need in the 48 + + align:start position:0% +need in the 48 + + + align:start position:0% +need in the 48 +transform and the Really the special + + align:start position:0% +transform and the Really the special + + + align:start position:0% +transform and the Really the special +thing that I want to tell you about is + + align:start position:0% +thing that I want to tell you about is + + + align:start position:0% +thing that I want to tell you about is +What's called the fast 4A + + align:start position:0% +What's called the fast 4A + + + align:start position:0% +What's called the fast 4A +transform and everybody refers to it as + + align:start position:0% +transform and everybody refers to it as + + + align:start position:0% +transform and everybody refers to it as +the + + align:start position:0% +the + + + align:start position:0% +the +fft and it's in all computers and it's + + align:start position:0% +fft and it's in all computers and it's + + + align:start position:0% +fft and it's in all computers and it's +used it's being used as we speak in a + + align:start position:0% +used it's being used as we speak in a + + + align:start position:0% +used it's being used as we speak in a +thousand places because it has like + + align:start position:0% +thousand places because it has like + + + align:start position:0% +thousand places because it has like +transformed + + align:start position:0% +transformed + + + align:start position:0% +transformed +whole Industries to be a able to do the + + align:start position:0% +whole Industries to be a able to do the + + + align:start position:0% +whole Industries to be a able to do the +forier transform fast which means + + align:start position:0% +forier transform fast which means + + + align:start position:0% +forier transform fast which means +multiplying how do I multiply fast by + + align:start position:0% +multiplying how do I multiply fast by + + + align:start position:0% +multiplying how do I multiply fast by +that matrix by that by that n byn Matrix + + align:start position:0% +that matrix by that by that n byn Matrix + + + align:start position:0% +that matrix by that by that n byn Matrix +normally + + align:start position:0% +normally + + + align:start position:0% +normally +multiplications by an N byn Matrix would + + align:start position:0% +multiplications by an N byn Matrix would + + + align:start position:0% +multiplications by an N byn Matrix would +normally be n sared + + align:start position:0% +normally be n sared + + + align:start position:0% +normally be n sared +multiplications because I've got n squ + + align:start position:0% +multiplications because I've got n squ + + + align:start position:0% +multiplications because I've got n squ +entries and none of them is zero this is + + align:start position:0% +entries and none of them is zero this is + + + align:start position:0% +entries and none of them is zero this is +a full + + align:start position:0% +a full + + + align:start position:0% +a full +Matrix and it's a matrix with orthogonal + + align:start position:0% +Matrix and it's a matrix with orthogonal + + + align:start position:0% +Matrix and it's a matrix with orthogonal +columns I mean it's just like the best + + align:start position:0% +columns I mean it's just like the best + + + align:start position:0% +columns I mean it's just like the best +Matrix and this fast 48 transform idea + + align:start position:0% +Matrix and this fast 48 transform idea + + + align:start position:0% +Matrix and this fast 48 transform idea +reduces this n SAR which was slowing + + align:start position:0% +reduces this n SAR which was slowing + + + align:start position:0% +reduces this n SAR which was slowing +up the calculation of 48 transforms down + + align:start position:0% +up the calculation of 48 transforms down + + + align:start position:0% +up the calculation of 48 transforms down +to n log + + align:start position:0% +to n log + + + align:start position:0% +to n log +n n log n log to the base 2 actually and + + align:start position:0% +n n log n log to the base 2 actually and + + + align:start position:0% +n n log n log to the base 2 actually and +it's this when that hit when that + + align:start position:0% +it's this when that hit when that + + + align:start position:0% +it's this when that hit when that +possibility hit it made a big difference + + align:start position:0% +possibility hit it made a big difference + + + align:start position:0% +possibility hit it made a big difference +everybody realized gradually what uh + + align:start position:0% +everybody realized gradually what uh + + + align:start position:0% +everybody realized gradually what uh +that this simple idea you'll see it's + + align:start position:0% +that this simple idea you'll see it's + + + align:start position:0% +that this simple idea you'll see it's +just a simple Matrix + + align:start position:0% +just a simple Matrix + + + align:start position:0% +just a simple Matrix +factorization but it changed everything + + align:start position:0% +factorization but it changed everything + + + align:start position:0% +factorization but it changed everything +okay so I want to talk about complex + + align:start position:0% +okay so I want to talk about complex + + + align:start position:0% +okay so I want to talk about complex +vectors and matrices in general recap a + + align:start position:0% +vectors and matrices in general recap a + + + align:start position:0% +vectors and matrices in general recap a +little bit from last time + + align:start position:0% +little bit from last time + + + align:start position:0% +little bit from last time +and the forier Matrix in particular okay + + align:start position:0% +and the forier Matrix in particular okay + + + align:start position:0% +and the forier Matrix in particular okay +so what's the deal + + align:start position:0% +so what's the deal + + + align:start position:0% +so what's the deal +all right the main point is what about + + align:start position:0% +all right the main point is what about + + + align:start position:0% +all right the main point is what about +length I I'm given a vector I I have a + + align:start position:0% +length I I'm given a vector I I have a + + + align:start position:0% +length I I'm given a vector I I have a +vector X or let me call it Z as a + + align:start position:0% +vector X or let me call it Z as a + + + align:start position:0% +vector X or let me call it Z as a +reminder that it's complex for the + + align:start position:0% +reminder that it's complex for the + + + align:start position:0% +reminder that it's complex for the +moment but I can later I'll call the + + align:start position:0% +moment but I can later I'll call the + + + align:start position:0% +moment but I can later I'll call the +components X they'll be complex numbers + + align:start position:0% +components X they'll be complex numbers + + + align:start position:0% +components X they'll be complex numbers +but it's a vector Z1 Z2 down to + + align:start position:0% +but it's a vector Z1 Z2 down to + + + align:start position:0% +but it's a vector Z1 Z2 down to +ZN so the only novelty is it's not in RN + + align:start position:0% +ZN so the only novelty is it's not in RN + + + align:start position:0% +ZN so the only novelty is it's not in RN +any + + align:start position:0% +any + + + align:start position:0% +any +anymore it's in complex n dimensional + + align:start position:0% +anymore it's in complex n dimensional + + + align:start position:0% +anymore it's in complex n dimensional +space each of those numbers is a complex + + align:start position:0% +space each of those numbers is a complex + + + align:start position:0% +space each of those numbers is a complex +number so this Z Z1 is + + align:start position:0% +number so this Z Z1 is + + + align:start position:0% +number so this Z Z1 is +in CN n dimensional complex space + + align:start position:0% +in CN n dimensional complex space + + + align:start position:0% +in CN n dimensional complex space +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +RN it's just a different letter there + + align:start position:0% +RN it's just a different letter there + + + align:start position:0% +RN it's just a different letter there +but now the point about its length is + + align:start position:0% +but now the point about its length is + + + align:start position:0% +but now the point about its length is +what the point about its length is that + + align:start position:0% +what the point about its length is that + + + align:start position:0% +what the point about its length is that +Z transpose + + align:start position:0% +Z transpose + + + align:start position:0% +Z transpose +Z is no good + + align:start position:0% + + + + align:start position:0% + +Z transpose Z if I just put down Z + + align:start position:0% +Z transpose Z if I just put down Z + + + align:start position:0% +Z transpose Z if I just put down Z +transpose here it would be Z1 Z2 to + + align:start position:0% + + + + align:start position:0% + +ZN doing that multiplication doesn't + + align:start position:0% +ZN doing that multiplication doesn't + + + align:start position:0% +ZN doing that multiplication doesn't +give me the right thing what why not + + align:start position:0% +give me the right thing what why not + + + align:start position:0% +give me the right thing what why not +because the length squared should be + + align:start position:0% +because the length squared should be + + + align:start position:0% +because the length squared should be +positive and If I multiply suppose this + + align:start position:0% +positive and If I multiply suppose this + + + align:start position:0% +positive and If I multiply suppose this +is is like one and I what's the length + + align:start position:0% +is is like one and I what's the length + + + align:start position:0% +is is like one and I what's the length +of the vector with components one and I + + align:start position:0% +of the vector with components one and I + + + align:start position:0% +of the vector with components one and I +what if I do this so n is just two I'm + + align:start position:0% +what if I do this so n is just two I'm + + + align:start position:0% +what if I do this so n is just two I'm +inan C2 two-dimensional space complex + + align:start position:0% +inan C2 two-dimensional space complex + + + align:start position:0% +inan C2 two-dimensional space complex +space with the vector whose components + + align:start position:0% +space with the vector whose components + + + align:start position:0% +space with the vector whose components +are one and I all right so if I took 1 + + align:start position:0% +are one and I all right so if I took 1 + + + align:start position:0% +are one and I all right so if I took 1 +Time 1 and I * + + align:start position:0% +Time 1 and I * + + + align:start position:0% +Time 1 and I * +I and added z z transpose Z would be + + align:start position:0% +I and added z z transpose Z would be + + + align:start position:0% +I and added z z transpose Z would be +zero but I don't that Vector is not + + align:start position:0% +zero but I don't that Vector is not + + + align:start position:0% +zero but I don't that Vector is not +doesn't have length zero the vector with + + align:start position:0% +doesn't have length zero the vector with + + + align:start position:0% +doesn't have length zero the vector with +components one and + + align:start position:0% +components one and + + + align:start position:0% +components one and +I this + + align:start position:0% +I this + + + align:start position:0% +I this +multiplication what I really want is Z1 + + align:start position:0% +multiplication what I really want is Z1 + + + align:start position:0% +multiplication what I really want is Z1 +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +Z1 you remember that Z1 conjugate Z1 is + + align:start position:0% +Z1 you remember that Z1 conjugate Z1 is + + + align:start position:0% +Z1 you remember that Z1 conjugate Z1 is +so you see that first step will be Z1 + + align:start position:0% +so you see that first step will be Z1 + + + align:start position:0% +so you see that first step will be Z1 +conjugate Z1 which is the magnitude of + + align:start position:0% +conjugate Z1 which is the magnitude of + + + align:start position:0% +conjugate Z1 which is the magnitude of +Z1 squared which is what I + + align:start position:0% +Z1 squared which is what I + + + align:start position:0% +Z1 squared which is what I +want that's like 3 squar or 5 squar + + align:start position:0% +want that's like 3 squar or 5 squar + + + align:start position:0% +want that's like 3 squar or 5 squar +now if it's if if Z1 is + + align:start position:0% + + + + align:start position:0% + +I then I multiplied by minus I gives + + align:start position:0% +I then I multiplied by minus I gives + + + align:start position:0% +I then I multiplied by minus I gives +1+ one so the component of length the + + align:start position:0% +1+ one so the component of length the + + + align:start position:0% +1+ one so the component of length the +component I its modulus squared is + one + + align:start position:0% +component I its modulus squared is + one + + + align:start position:0% +component I its modulus squared is + one +that's great so what I want to do then + + align:start position:0% +that's great so what I want to do then + + + align:start position:0% +that's great so what I want to do then +is do that I want Z1 bar Z1 Z2 bar Z2 Z + + align:start position:0% +is do that I want Z1 bar Z1 Z2 bar Z2 Z + + + align:start position:0% +is do that I want Z1 bar Z1 Z2 bar Z2 Z +n bar is the n and remember that you + + align:start position:0% +n bar is the n and remember that you + + + align:start position:0% +n bar is the n and remember that you +remember this complex conjugate so + + align:start position:0% +remember this complex conjugate so + + + align:start position:0% +remember this complex conjugate so +so there's the point now I can erase the + + align:start position:0% +so there's the point now I can erase the + + + align:start position:0% +so there's the point now I can erase the +no good and put is + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +because that now gives the answer zero + + align:start position:0% +because that now gives the answer zero + + + align:start position:0% +because that now gives the answer zero +for the zero Vector of course but it + + align:start position:0% +for the zero Vector of course but it + + + align:start position:0% +for the zero Vector of course but it +gives a positive length squared for any + + align:start position:0% +gives a positive length squared for any + + + align:start position:0% +gives a positive length squared for any +other + + align:start position:0% +other + + + align:start position:0% +other +Vector so it's a it's the right + + align:start position:0% +Vector so it's a it's the right + + + align:start position:0% +Vector so it's a it's the right +definition of length and + + align:start position:0% +definition of length and + + + align:start position:0% +definition of length and +essentially the message is that we're + + align:start position:0% +essentially the message is that we're + + + align:start position:0% +essentially the message is that we're +always going to be + + align:start position:0% +always going to be + + + align:start position:0% +always going to be +taking when we transpose we also take + + align:start position:0% +taking when we transpose we also take + + + align:start position:0% +taking when we transpose we also take +complex conjugate so let's let's find + + align:start position:0% +complex conjugate so let's let's find + + + align:start position:0% +complex conjugate so let's let's find +the length of one so the vector 1 + + align:start position:0% +the length of one so the vector 1 + + + align:start position:0% +the length of one so the vector 1 +I that's Z that's that Vector z now I + + align:start position:0% +I that's Z that's that Vector z now I + + + align:start position:0% +I that's Z that's that Vector z now I +take the conjugate of one is one the + + align:start position:0% +take the conjugate of one is one the + + + align:start position:0% +take the conjugate of one is one the +conjugate of I is minus I I take this + + align:start position:0% +conjugate of I is minus I I take this + + + align:start position:0% +conjugate of I is minus I I take this +Vector I get one + one I get + + align:start position:0% + + + + align:start position:0% + +two so that's a vector and that's a + + align:start position:0% +two so that's a vector and that's a + + + align:start position:0% +two so that's a vector and that's a +vector of length square root of two + + align:start position:0% +vector of length square root of two + + + align:start position:0% +vector of length square root of two +square root of two is the length and not + + align:start position:0% +square root of two is the length and not + + + align:start position:0% +square root of two is the length and not +the zero that we would have got from 1 + + align:start position:0% +the zero that we would have got from 1 + + + align:start position:0% +the zero that we would have got from 1 +minus i^ 2 + + align:start position:0% +minus i^ 2 + + + align:start position:0% +minus i^ 2 +okay so the message really is whenever + + align:start position:0% +okay so the message really is whenever + + + align:start position:0% +okay so the message really is whenever +we transpose we also take conjugates so + + align:start position:0% +we transpose we also take conjugates so + + + align:start position:0% +we transpose we also take conjugates so +here's a symbol one symbol to do + + align:start position:0% +here's a symbol one symbol to do + + + align:start position:0% +here's a symbol one symbol to do +both so that symbol h + + align:start position:0% +both so that symbol h + + + align:start position:0% +both so that symbol h +it stands + + align:start position:0% +it stands + + + align:start position:0% +it stands +for a guy named herit who didn't + + align:start position:0% +for a guy named herit who didn't + + + align:start position:0% +for a guy named herit who didn't +actually pronounce the h but let's + + align:start position:0% +actually pronounce the h but let's + + + align:start position:0% +actually pronounce the h but let's +pronounce it so I would call that z + + align:start position:0% +pronounce it so I would call that z + + + align:start position:0% +pronounce it so I would call that z +heran + + align:start position:0% +heran + + + align:start position:0% +heran +z now let me write that word her so his + + align:start position:0% +z now let me write that word her so his + + + align:start position:0% +z now let me write that word her so his +name was air + + align:start position:0% + + + + align:start position:0% + +meat and then we make it + + align:start position:0% +meat and then we make it + + + align:start position:0% +meat and then we make it +into an adjective + + align:start position:0% +into an adjective + + + align:start position:0% +into an adjective +Hermes + + align:start position:0% +Hermes + + + align:start position:0% +Hermes +so Z Z + + align:start position:0% +so Z Z + + + align:start position:0% +so Z Z +zhz + + align:start position:0% +zhz + + + align:start position:0% +zhz +okay so uh that's the that's the uh + + align:start position:0% +okay so uh that's the that's the uh + + + align:start position:0% +okay so uh that's the that's the uh +length squared now what's the inner + + align:start position:0% +length squared now what's the inner + + + align:start position:0% +length squared now what's the inner +product well it should match the inner + + align:start position:0% +product well it should match the inner + + + align:start position:0% +product well it should match the inner +product of two + + align:start position:0% +product of two + + + align:start position:0% +product of two +vectors so inner + + align:start position:0% + + + + align:start position:0% + +product is no + + align:start position:0% +product is no + + + align:start position:0% +product is no +longer used to be y transpose X that's + + align:start position:0% +longer used to be y transpose X that's + + + align:start position:0% +longer used to be y transpose X that's +for real vectors for complex vectors + + align:start position:0% +for real vectors for complex vectors + + + align:start position:0% +for real vectors for complex vectors +whenever we transpose we also take the + + align:start position:0% +whenever we transpose we also take the + + + align:start position:0% +whenever we transpose we also take the +conjugate so it's y Permian + + align:start position:0% +conjugate so it's y Permian + + + align:start position:0% +conjugate so it's y Permian +X of course it's not real anymore + + align:start position:0% +X of course it's not real anymore + + + align:start position:0% +X of course it's not real anymore +usually that the inner product will + + align:start position:0% +usually that the inner product will + + + align:start position:0% +usually that the inner product will +usually be complex + + align:start position:0% +usually be complex + + + align:start position:0% +usually be complex +number but if Y and X are the same if + + align:start position:0% +number but if Y and X are the same if + + + align:start position:0% +number but if Y and X are the same if +they're the same Z then we have Z zhz we + + align:start position:0% +they're the same Z then we have Z zhz we + + + align:start position:0% +they're the same Z then we have Z zhz we +have the length squared and that's + + align:start position:0% +have the length squared and that's + + + align:start position:0% +have the length squared and that's +that's what we want the inner product of + + align:start position:0% +that's what we want the inner product of + + + align:start position:0% +that's what we want the inner product of +a vector with itself should be its + + align:start position:0% +a vector with itself should be its + + + align:start position:0% +a vector with itself should be its +length squared so this is like forced on + + align:start position:0% +length squared so this is like forced on + + + align:start position:0% +length squared so this is like forced on +us because this is forced on us so so + + align:start position:0% +us because this is forced on us so so + + + align:start position:0% +us because this is forced on us so so +this Z this everybody's picking up what + + align:start position:0% +this Z this everybody's picking up what + + + align:start position:0% +this Z this everybody's picking up what +this equals this is Z1 SAR plus ZN 2 + + align:start position:0% +this equals this is Z1 SAR plus ZN 2 + + + align:start position:0% +this equals this is Z1 SAR plus ZN 2 +that's the length squared and that's the + + align:start position:0% +that's the length squared and that's the + + + align:start position:0% +that's the length squared and that's the +inner product that we have to go with so + + align:start position:0% +inner product that we have to go with so + + + align:start position:0% +inner product that we have to go with so +it could be a complex number now + + align:start position:0% +it could be a complex number now + + + align:start position:0% +it could be a complex number now +one more + + align:start position:0% +one more + + + align:start position:0% +one more +change well two more changes we've got + + align:start position:0% +change well two more changes we've got + + + align:start position:0% +change well two more changes we've got +to change the idea of a symmetric + + align:start position:0% +to change the idea of a symmetric + + + align:start position:0% +to change the idea of a symmetric +matric so I I'll just recap on symmetric + + align:start position:0% +matric so I I'll just recap on symmetric + + + align:start position:0% +matric so I I'll just recap on symmetric +matrices + + align:start position:0% + + + + align:start position:0% + +symmetric means a transpose equals + + align:start position:0% +symmetric means a transpose equals + + + align:start position:0% +symmetric means a transpose equals +a but not no + + align:start position:0% + + + + align:start position:0% + +good if a is complex + + align:start position:0% +good if a is complex + + + align:start position:0% +good if a is complex +so what do we CH what do we + + align:start position:0% +so what do we CH what do we + + + align:start position:0% +so what do we CH what do we +instead if + + align:start position:0% +instead if + + + align:start position:0% +instead if +I that applies perfectly to real + + align:start position:0% +I that applies perfectly to real + + + align:start position:0% +I that applies perfectly to real +matrices but now if my matrices are + + align:start position:0% +matrices but now if my matrices are + + + align:start position:0% +matrices but now if my matrices are +complex I want to + + align:start position:0% +complex I want to + + + align:start position:0% +complex I want to +take the transpose and the conjugate to + + align:start position:0% +take the transpose and the conjugate to + + + align:start position:0% +take the transpose and the conjugate to +equal + + align:start position:0% +equal + + + align:start position:0% +equal +a so there is that's the the right + + align:start position:0% +a so there is that's the the right + + + align:start position:0% +a so there is that's the the right +complex version of symmetry the the + + align:start position:0% +complex version of symmetry the the + + + align:start position:0% +complex version of symmetry the the +Symmetry now means when I transpose it + + align:start position:0% +Symmetry now means when I transpose it + + + align:start position:0% +Symmetry now means when I transpose it +flip across the diagonal and take + + align:start position:0% +flip across the diagonal and take + + + align:start position:0% +flip across the diagonal and take +conjugate so for example here would be + + align:start position:0% +conjugate so for example here would be + + + align:start position:0% +conjugate so for example here would be +an + + align:start position:0% +an + + + align:start position:0% +an +example on the diagonal it better be + + align:start position:0% +example on the diagonal it better be + + + align:start position:0% +example on the diagonal it better be +real because when I flip it the diagonal + + align:start position:0% +real because when I flip it the diagonal + + + align:start position:0% +real because when I flip it the diagonal +is still + + align:start position:0% +is still + + + align:start position:0% +is still +there and it has to and then when I take + + align:start position:0% +there and it has to and then when I take + + + align:start position:0% +there and it has to and then when I take +the complex conjugate it has to be still + + align:start position:0% +the complex conjugate it has to be still + + + align:start position:0% +the complex conjugate it has to be still +there so it better be a real number let + + align:start position:0% +there so it better be a real number let + + + align:start position:0% +there so it better be a real number let +me say two and + + align:start position:0% +me say two and + + + align:start position:0% +me say two and +five what about entries off the + + align:start position:0% +five what about entries off the + + + align:start position:0% +five what about entries off the +diagonal if this entry is say 3 + + + align:start position:0% +diagonal if this entry is say 3 + + + + align:start position:0% +diagonal if this entry is say 3 + +I then this entry had better + + align:start position:0% +I then this entry had better + + + align:start position:0% +I then this entry had better +be because I want whatever this when I + + align:start position:0% +be because I want whatever this when I + + + align:start position:0% +be because I want whatever this when I +transpose it'll show up here and I + + align:start position:0% +transpose it'll show up here and I + + + align:start position:0% +transpose it'll show up here and I +conjugate so I need 3 minus I there so + + align:start position:0% +conjugate so I need 3 minus I there so + + + align:start position:0% +conjugate so I need 3 minus I there so +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +matrix with that's that's that cor that + + align:start position:0% +matrix with that's that's that cor that + + + align:start position:0% +matrix with that's that's that cor that +corresponds the Symmetry but it's + + align:start position:0% +corresponds the Symmetry but it's + + + align:start position:0% +corresponds the Symmetry but it's +complex and those matrices are called + + align:start position:0% +complex and those matrices are called + + + align:start position:0% +complex and those matrices are called +herian matri + + align:start position:0% +herian matri + + + align:start position:0% +herian matri +mat herian matrices + + align:start position:0% +mat herian matrices + + + align:start position:0% +mat herian matrices +AAL a + + align:start position:0% +AAL a + + + align:start position:0% +AAL a +fine okay that's and those matrices have + + align:start position:0% +fine okay that's and those matrices have + + + align:start position:0% +fine okay that's and those matrices have +real igen + + align:start position:0% +real igen + + + align:start position:0% +real igen +values and they have perpendicular igen + + align:start position:0% +values and they have perpendicular igen + + + align:start position:0% +values and they have perpendicular igen +vectors what does perpendicular + + align:start position:0% +vectors what does perpendicular + + + align:start position:0% +vectors what does perpendicular +mean perpendicular means the inner + + align:start position:0% +mean perpendicular means the inner + + + align:start position:0% +mean perpendicular means the inner +product so let's go on to + + align:start position:0% + + + + align:start position:0% + +perpendicular well when I had + + align:start position:0% +perpendicular well when I had + + + align:start position:0% +perpendicular well when I had +perpendicular vectors for example they + + align:start position:0% +perpendicular vectors for example they + + + align:start position:0% +perpendicular vectors for example they +were like q1 + + align:start position:0% +were like q1 + + + align:start position:0% +were like q1 +Q2 up to + + align:start position:0% +Q2 up to + + + align:start position:0% +Q2 up to +qn that's my Q is my letter that I use + + align:start position:0% +qn that's my Q is my letter that I use + + + align:start position:0% +qn that's my Q is my letter that I use +for perpendicular actually I usually I I + + align:start position:0% +for perpendicular actually I usually I I + + + align:start position:0% +for perpendicular actually I usually I I +I also mean unit length so those are + + align:start position:0% +I also mean unit length so those are + + + align:start position:0% +I also mean unit length so those are +perpendicular unit vectors but now what + + align:start position:0% +perpendicular unit vectors but now what + + + align:start position:0% +perpendicular unit vectors but now what +is so it's a orthonormal basis I'll + + align:start position:0% +is so it's a orthonormal basis I'll + + + align:start position:0% +is so it's a orthonormal basis I'll +still use those words but how do I + + align:start position:0% +still use those words but how do I + + + align:start position:0% +still use those words but how do I +compute perpendicular how do I check + + align:start position:0% +compute perpendicular how do I check + + + align:start position:0% +compute perpendicular how do I check +perpendicular this means that the inner + + align:start position:0% +perpendicular this means that the inner + + + align:start position:0% +perpendicular this means that the inner +product of + + align:start position:0% +product of + + + align:start position:0% +product of +Qi with + + align:start position:0% +Qi with + + + align:start position:0% +Qi with +QJ but now I not only transpose I must + + align:start position:0% +QJ but now I not only transpose I must + + + align:start position:0% +QJ but now I not only transpose I must +conjugate right to + + align:start position:0% +conjugate right to + + + align:start position:0% +conjugate right to +get zero if I is not J and one if I is J + + align:start position:0% +get zero if I is not J and one if I is J + + + align:start position:0% +get zero if I is not J and one if I is J +so it's a unit Vector meaning unit + + align:start position:0% +so it's a unit Vector meaning unit + + + align:start position:0% +so it's a unit Vector meaning unit +length + + align:start position:0% +length + + + align:start position:0% +length +orthogonal all the angles are right + + align:start position:0% +orthogonal all the angles are right + + + align:start position:0% +orthogonal all the angles are right +angles but these are angles in in + + align:start position:0% +angles but these are angles in in + + + align:start position:0% +angles but these are angles in in +complex n dimensional space so it's q1 + + align:start position:0% +complex n dimensional space so it's q1 + + + align:start position:0% +complex n dimensional space so it's q1 +q1 Qi bar + + align:start position:0% + + + + align:start position:0% + +transpose or for short + + align:start position:0% +transpose or for short + + + align:start position:0% +transpose or for short +qih + + align:start position:0% +qih + + + align:start position:0% +qih +QJ so it will still be true so let me + + align:start position:0% +QJ so it will still be true so let me + + + align:start position:0% +QJ so it will still be true so let me +again I'll create a matrix out of those + + align:start position:0% +again I'll create a matrix out of those + + + align:start position:0% +again I'll create a matrix out of those +guys The Matrix will have these qes in + + align:start position:0% +guys The Matrix will have these qes in + + + align:start position:0% +guys The Matrix will have these qes in +its columns Q2 to qn + + align:start position:0% + + + + align:start position:0% + +and I want to turn that into Matrix + + align:start position:0% +and I want to turn that into Matrix + + + align:start position:0% +and I want to turn that into Matrix +language just like before what does that + + align:start position:0% +language just like before what does that + + + align:start position:0% +language just like before what does that +mean that means I want all these inner + + align:start position:0% +mean that means I want all these inner + + + align:start position:0% +mean that means I want all these inner +products so I take these Columns of Q + + align:start position:0% +products so I take these Columns of Q + + + align:start position:0% +products so I take these Columns of Q +multiply by their rows so it was it used + + align:start position:0% +multiply by their rows so it was it used + + + align:start position:0% +multiply by their rows so it was it used +to be Q it used to be Q transpose qals I + + align:start position:0% +to be Q it used to be Q transpose qals I + + + align:start position:0% +to be Q it used to be Q transpose qals I +right this was an orthogonal + + align:start position:0% + + + + align:start position:0% + +Matrix but what's changed + + align:start position:0% +Matrix but what's changed + + + align:start position:0% +Matrix but what's changed +these are now complex vectors their + + align:start position:0% +these are now complex vectors their + + + align:start position:0% +these are now complex vectors their +inner products are involve conjugating + + align:start position:0% +inner products are involve conjugating + + + align:start position:0% +inner products are involve conjugating +the first + + align:start position:0% +the first + + + align:start position:0% +the first +Factor so it's not it's the conjugate of + + align:start position:0% +Factor so it's not it's the conjugate of + + + align:start position:0% +Factor so it's not it's the conjugate of +Q transpose it's Q Bar transpose Q + + align:start position:0% +Q transpose it's Q Bar transpose Q + + + align:start position:0% +Q transpose it's Q Bar transpose Q +qh so can I call this let me call it qh + + align:start position:0% +qh so can I call this let me call it qh + + + align:start position:0% +qh so can I call this let me call it qh +Q which is I so that's our new you you + + align:start position:0% +Q which is I so that's our new you you + + + align:start position:0% +Q which is I so that's our new you you +see I'm just translating and the the + + align:start position:0% +see I'm just translating and the the + + + align:start position:0% +see I'm just translating and the the +book on one page gives a little like + + align:start position:0% +book on one page gives a little like + + + align:start position:0% +book on one page gives a little like +dictionary + + align:start position:0% +dictionary + + + align:start position:0% +dictionary +of the WR words in the real case RN and + + align:start position:0% +of the WR words in the real case RN and + + + align:start position:0% +of the WR words in the real case RN and +the corresponding words in the complex + + align:start position:0% +the corresponding words in the complex + + + align:start position:0% +the corresponding words in the complex +case for the vector space CN of course + + align:start position:0% +case for the vector space CN of course + + + align:start position:0% +case for the vector space CN of course +CN is a vector space the numbers we + + align:start position:0% +CN is a vector space the numbers we + + + align:start position:0% +CN is a vector space the numbers we +multiply are now complex numbers we just + + align:start position:0% +multiply are now complex numbers we just + + + align:start position:0% +multiply are now complex numbers we just +moving in the + + align:start position:0% +moving in the + + + align:start position:0% +moving in the +complex n dimensional space okay + + align:start position:0% +complex n dimensional space okay + + + align:start position:0% +complex n dimensional space okay +now actually I have to say we changed + + align:start position:0% +now actually I have to say we changed + + + align:start position:0% +now actually I have to say we changed +the word SYM symmetric to Hermes for + + align:start position:0% +the word SYM symmetric to Hermes for + + + align:start position:0% +the word SYM symmetric to Hermes for +those + + align:start position:0% +those + + + align:start position:0% +those +matrices people also change this word + + align:start position:0% +matrices people also change this word + + + align:start position:0% +matrices people also change this word +orthogonal into another word that + + align:start position:0% +orthogonal into another word that + + + align:start position:0% +orthogonal into another word that +happens to be + + align:start position:0% + + + + align:start position:0% + +unitary as + + align:start position:0% +unitary as + + + align:start position:0% +unitary as +a word that + + align:start position:0% +a word that + + + align:start position:0% +a word that +applies the signals that we might be + + align:start position:0% +applies the signals that we might be + + + align:start position:0% +applies the signals that we might be +dealing with a complex Matrix here so + + align:start position:0% +dealing with a complex Matrix here so + + + align:start position:0% +dealing with a complex Matrix here so +what's a unitary Matrix + + align:start position:0% +what's a unitary Matrix + + + align:start position:0% +what's a unitary Matrix +it's just like an orthogonal matrix it's + + align:start position:0% +it's just like an orthogonal matrix it's + + + align:start position:0% +it's just like an orthogonal matrix it's +a + + align:start position:0% + + + + align:start position:0% + +square n byn Matrix with orthonormal + + align:start position:0% +square n byn Matrix with orthonormal + + + align:start position:0% +square n byn Matrix with orthonormal +columns perpendicular columns unit + + align:start position:0% +columns perpendicular columns unit + + + align:start position:0% +columns perpendicular columns unit +vectors unit vectors + + align:start position:0% +vectors unit vectors + + + align:start position:0% +vectors unit vectors +computed by and and and perpendicularity + + align:start position:0% +computed by and and and perpendicularity + + + align:start position:0% +computed by and and and perpendicularity +computed by remembering that there's a + + align:start position:0% +computed by remembering that there's a + + + align:start position:0% +computed by remembering that there's a +conjugate as well as a transpose okay so + + align:start position:0% +conjugate as well as a transpose okay so + + + align:start position:0% +conjugate as well as a transpose okay so +those are the + + align:start position:0% +those are the + + + align:start position:0% +those are the +words now I'm ready ready to get into + + align:start position:0% +words now I'm ready ready to get into + + + align:start position:0% +words now I'm ready ready to get into +the substance of the lecture which is + + align:start position:0% +the substance of the lecture which is + + + align:start position:0% +the substance of the lecture which is +the most famous complex Matrix which + + align:start position:0% +the most famous complex Matrix which + + + align:start position:0% +the most famous complex Matrix which +happens to be uh one of these guys it it + + align:start position:0% +happens to be uh one of these guys it it + + + align:start position:0% +happens to be uh one of these guys it it +has + + align:start position:0% +has + + + align:start position:0% +has +orthogonal + + align:start position:0% +orthogonal + + + align:start position:0% +orthogonal +columns and it's named after forier + + align:start position:0% +columns and it's named after forier + + + align:start position:0% +columns and it's named after forier +because it comes into the forier + + align:start position:0% +because it comes into the forier + + + align:start position:0% +because it comes into the forier +transform so it's the Matrix that's all + + align:start position:0% +transform so it's the Matrix that's all + + + align:start position:0% +transform so it's the Matrix that's all +around us + + align:start position:0% +around us + + + align:start position:0% +around us +okay let me tell tell you what it is + + align:start position:0% +okay let me tell tell you what it is + + + align:start position:0% +okay let me tell tell you what it is +first of all in the N byn + + align:start position:0% +first of all in the N byn + + + align:start position:0% +first of all in the N byn +case then often I'll let N be four + + align:start position:0% +case then often I'll let N be four + + + align:start position:0% +case then often I'll let N be four +because four is a good size to work with + + align:start position:0% +because four is a good size to work with + + + align:start position:0% +because four is a good size to work with +but here's the N byn 4A + + align:start position:0% + + + + align:start position:0% + +Matrix its first column is the vector of + + align:start position:0% + + + + align:start position:0% + +ones it's n byn of course its second + + align:start position:0% +ones it's n byn of course its second + + + align:start position:0% +ones it's n byn of course its second +column is the Powers the + + align:start position:0% +column is the Powers the + + + align:start position:0% +column is the Powers the +actually better if I move from the math + + align:start position:0% +actually better if I move from the math + + + align:start position:0% +actually better if I move from the math +department to e for this one half hour + + align:start position:0% +department to e for this one half hour + + + align:start position:0% +department to e for this one half hour +and then please let me move back again + + align:start position:0% +and then please let me move back again + + + align:start position:0% +and then please let me move back again +okay what's the difference between those + + align:start position:0% +okay what's the difference between those + + + align:start position:0% +okay what's the difference between those +two departments it's + + align:start position:0% +two departments it's + + + align:start position:0% +two departments it's +just uh math starts counting with one + + align:start position:0% +just uh math starts counting with one + + + align:start position:0% +just uh math starts counting with one +and uh electrical engineers start + + align:start position:0% +and uh electrical engineers start + + + align:start position:0% +and uh electrical engineers start +counting at + + align:start position:0% +counting at + + + align:start position:0% +counting at +zero actually they're probably right so + + align:start position:0% +zero actually they're probably right so + + + align:start position:0% +zero actually they're probably right so +anyway well give them humor them so this + + align:start position:0% +anyway well give them humor them so this + + + align:start position:0% +anyway well give them humor them so this +is really the zeroth + + align:start position:0% +is really the zeroth + + + align:start position:0% +is really the zeroth +column and the First Column up to the N + + align:start position:0% +column and the First Column up to the N + + + align:start position:0% +column and the First Column up to the N +minus one that's the one inconvenience + + align:start position:0% +minus one that's the one inconvenience + + + align:start position:0% +minus one that's the one inconvenience +spot in electrical engineering all these + + align:start position:0% +spot in electrical engineering all these + + + align:start position:0% +spot in electrical engineering all these +Expressions start at zero no problem but + + align:start position:0% +Expressions start at zero no problem but + + + align:start position:0% +Expressions start at zero no problem but +they end at n minus one well that's uh + + align:start position:0% +they end at n minus one well that's uh + + + align:start position:0% +they end at n minus one well that's uh +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +difficulty that course six has so what's + + align:start position:0% +difficulty that course six has so what's + + + align:start position:0% +difficulty that course six has so what's +they're the powers of a number that I'm + + align:start position:0% +they're the powers of a number that I'm + + + align:start position:0% +they're the powers of a number that I'm +going to call W W 2 W Cub W to the now + + align:start position:0% +going to call W W 2 W Cub W to the now + + + align:start position:0% +going to call W W 2 W Cub W to the now +what is the W here what's the power this + + align:start position:0% +what is the W here what's the power this + + + align:start position:0% +what is the W here what's the power this +was the 0th power first Power second + + align:start position:0% +was the 0th power first Power second + + + align:start position:0% +was the 0th power first Power second +power this will be n minus first + + align:start position:0% +power this will be n minus first + + + align:start position:0% +power this will be n minus first +Power that's the column what's the next + + align:start position:0% +Power that's the column what's the next + + + align:start position:0% +Power that's the column what's the next +column it's the powers of w 2ar w 4th W + + align:start position:0% +column it's the powers of w 2ar w 4th W + + + align:start position:0% +column it's the powers of w 2ar w 4th W +to the 6th W to the 2 N + + align:start position:0% +to the 6th W to the 2 N + + + align:start position:0% +to the 6th W to the 2 N +minus1 and then more columns and more + + align:start position:0% +minus1 and then more columns and more + + + align:start position:0% +minus1 and then more columns and more +columns more columns and what's the last + + align:start position:0% +columns more columns and what's the last + + + align:start position:0% +columns more columns and what's the last +column it's the + + align:start position:0% +column it's the + + + align:start position:0% +column it's the +powers of let's see actually if we look + + align:start position:0% +powers of let's see actually if we look + + + align:start position:0% +powers of let's see actually if we look +along rows this Matrix is symmetric it's + + align:start position:0% +along rows this Matrix is symmetric it's + + + align:start position:0% +along rows this Matrix is symmetric it's +symmetric in the old not quite perfect + + align:start position:0% +symmetric in the old not quite perfect + + + align:start position:0% +symmetric in the old not quite perfect +way not perfect because these numbers + + align:start position:0% +way not perfect because these numbers + + + align:start position:0% +way not perfect because these numbers +are + + align:start position:0% +are + + + align:start position:0% +are +complex and so it's that first row is + + align:start position:0% +complex and so it's that first row is + + + align:start position:0% +complex and so it's that first row is +all ones one w w s up to W the N minus + + align:start position:0% +all ones one w w s up to W the N minus + + + align:start position:0% +all ones one w w s up to W the N minus +one that's the the the last column is + + align:start position:0% +one that's the the the last column is + + + align:start position:0% +one that's the the the last column is +the powers of w the N minus1 so this guy + + align:start position:0% +the powers of w the N minus1 so this guy + + + align:start position:0% +the powers of w the N minus1 so this guy +matches that and finally we get W to + + align:start position:0% +matches that and finally we get W to + + + align:start position:0% +matches that and finally we get W to +something + + align:start position:0% + + + + align:start position:0% + +here I guess we could actually figure + + align:start position:0% +here I guess we could actually figure + + + align:start position:0% +here I guess we could actually figure +out what that something is what are the + + align:start position:0% +out what that something is what are the + + + align:start position:0% +out what that something is what are the +entries of this Matrix the IJ + + align:start position:0% +entries of this Matrix the IJ + + + align:start position:0% +entries of this Matrix the IJ +entry + + align:start position:0% +entry + + + align:start position:0% +entry +of this + + align:start position:0% + + + + align:start position:0% + +Matrix am I going to you going to allow + + align:start position:0% +Matrix am I going to you going to allow + + + align:start position:0% +Matrix am I going to you going to allow +me to let I go from 0 to n minus one so + + align:start position:0% +me to let I go from 0 to n minus one so + + + align:start position:0% +me to let I go from 0 to n minus one so +I and J go from Z to n minus1 so the one + + align:start position:0% +I and J go from Z to n minus1 so the one + + + align:start position:0% +I and J go from Z to n minus1 so the one +the Z 0 entry is a one it's just the + + align:start position:0% +the Z 0 entry is a one it's just the + + + align:start position:0% +the Z 0 entry is a one it's just the +same W guy to the power I times + + align:start position:0% + + + + align:start position:0% + +J let's see I'm jumping into formulas + + align:start position:0% +J let's see I'm jumping into formulas + + + align:start position:0% +J let's see I'm jumping into formulas +here and I have to tell you what w is + + align:start position:0% +here and I have to tell you what w is + + + align:start position:0% +here and I have to tell you what w is +and then you know everything about this + + align:start position:0% +and then you know everything about this + + + align:start position:0% +and then you know everything about this +Matrix + + align:start position:0% + + + + align:start position:0% + +so w is well should we finish here what + + align:start position:0% +so w is well should we finish here what + + + align:start position:0% +so w is well should we finish here what +was this this is the n minus one n + + align:start position:0% +was this this is the n minus one n + + + align:start position:0% +was this this is the n minus one n +minus1 entry this is W to the + + align:start position:0% +minus1 entry this is W to the + + + align:start position:0% +minus1 entry this is W to the +nus1 squared everything's looking like a + + align:start position:0% +nus1 squared everything's looking like a + + + align:start position:0% +nus1 squared everything's looking like a +mess here because we have not too bad + + align:start position:0% +mess here because we have not too bad + + + align:start position:0% +mess here because we have not too bad +because all the entries are powers of + + align:start position:0% +because all the entries are powers of + + + align:start position:0% +because all the entries are powers of +w there none of them are zero this is a + + align:start position:0% +w there none of them are zero this is a + + + align:start position:0% +w there none of them are zero this is a +full + + align:start position:0% +full + + + align:start position:0% +full +Matrix but W is a very special number + + align:start position:0% +Matrix but W is a very special number + + + align:start position:0% +Matrix but W is a very special number +W is the special number whose n power is + + align:start position:0% +W is the special number whose n power is + + + align:start position:0% +W is the special number whose n power is +one in fact well actually there are n + + align:start position:0% +one in fact well actually there are n + + + align:start position:0% +one in fact well actually there are n +numbers like that one of them is one of + + align:start position:0% +numbers like that one of them is one of + + + align:start position:0% +numbers like that one of them is one of +course but the one we the w we want + + align:start position:0% +course but the one we the w we want + + + align:start position:0% +course but the one we the w we want +is the angle + + align:start position:0% +is the angle + + + align:start position:0% +is the angle +is 2 pi over + + align:start position:0% + + + + align:start position:0% + +n is that what I mean + + align:start position:0% +n is that what I mean + + + align:start position:0% +n is that what I mean +n over 2 + + align:start position:0% +n over 2 + + + align:start position:0% +n over 2 +pi No 2 pi over n w is e to the I and + + align:start position:0% +pi No 2 pi over n w is e to the I and + + + align:start position:0% +pi No 2 pi over n w is e to the I and +the angle is 2 pi over + + align:start position:0% +the angle is 2 pi over + + + align:start position:0% +the angle is 2 pi over +M right where is this W in the complex + + align:start position:0% +M right where is this W in the complex + + + align:start position:0% +M right where is this W in the complex +plane it's it's on the unit circle right + + align:start position:0% +plane it's it's on the unit circle right + + + align:start position:0% +plane it's it's on the unit circle right +this is It's the + + align:start position:0% +this is It's the + + + align:start position:0% +this is It's the +cosine of 2 piun / n + I * the S of 2 + + align:start position:0% +cosine of 2 piun / n + I * the S of 2 + + + align:start position:0% +cosine of 2 piun / n + I * the S of 2 +piun / n + + align:start position:0% +piun / n + + + align:start position:0% +piun / n +but actually forget this it's never good + + align:start position:0% +but actually forget this it's never good + + + align:start position:0% +but actually forget this it's never good +to work with the real and imaginary + + align:start position:0% +to work with the real and imaginary + + + align:start position:0% +to work with the real and imaginary +Parts the rectangular + + align:start position:0% +Parts the rectangular + + + align:start position:0% +Parts the rectangular +coordinates when we're taking powers to + + align:start position:0% +coordinates when we're taking powers to + + + align:start position:0% +coordinates when we're taking powers to +to take that to the tenth power we can't + + align:start position:0% +to take that to the tenth power we can't + + + align:start position:0% +to take that to the tenth power we can't +see what we're doing to take this form + + align:start position:0% +see what we're doing to take this form + + + align:start position:0% +see what we're doing to take this form +to the tenth power we see immediately + + align:start position:0% +to the tenth power we see immediately + + + align:start position:0% +to the tenth power we see immediately +what we're go doing it would be e to the + + align:start position:0% +what we're go doing it would be e to the + + + align:start position:0% +what we're go doing it would be e to the +I 20 pi/ + + align:start position:0% +I 20 pi/ + + + align:start position:0% +I 20 pi/ +n so when our Matrix is full of powers + + align:start position:0% +n so when our Matrix is full of powers + + + align:start position:0% +n so when our Matrix is full of powers +so it's it's this formula and where is + + align:start position:0% +so it's it's this formula and where is + + + align:start position:0% +so it's it's this formula and where is +this on the complex plane here are the + + align:start position:0% +this on the complex plane here are the + + + align:start position:0% +this on the complex plane here are the +real numbers here's the imaginary axis + + align:start position:0% +real numbers here's the imaginary axis + + + align:start position:0% +real numbers here's the imaginary axis +here's the unit circle of radius + + align:start position:0% +here's the unit circle of radius + + + align:start position:0% +here's the unit circle of radius +one and this number is on the unit + + align:start position:0% +one and this number is on the unit + + + align:start position:0% +one and this number is on the unit +circle at this angle which is 1 nth of + + align:start position:0% +circle at this angle which is 1 nth of + + + align:start position:0% +circle at this angle which is 1 nth of +the full way round so if I drew for + + align:start position:0% +the full way round so if I drew for + + + align:start position:0% +the full way round so if I drew for +example Nal + + align:start position:0% +example Nal + + + align:start position:0% +example Nal +6 this would be e 2 I 2 pi over 6 it + + align:start position:0% +6 this would be e 2 I 2 pi over 6 it + + + align:start position:0% +6 this would be e 2 I 2 pi over 6 it +would be 1 16 of the way round it' be + + align:start position:0% + + + + align:start position:0% + +60° and where is + + align:start position:0% +60° and where is + + + align:start position:0% +60° and where is +W2 so I I I my w is e to the 2 pi I over + + align:start position:0% +W2 so I I I my w is e to the 2 pi I over + + + align:start position:0% +W2 so I I I my w is e to the 2 pi I over +6 in this case in the 6 by for the 6x6 + + align:start position:0% +6 in this case in the 6 by for the 6x6 + + + align:start position:0% +6 in this case in the 6 by for the 6x6 + + align:start position:0% + + + align:start position:0% +transform it's totally constructed out + + align:start position:0% +transform it's totally constructed out + + + align:start position:0% +transform it's totally constructed out +of this number and its + + align:start position:0% +of this number and its + + + align:start position:0% +of this number and its +powers so what are its powers well its + + align:start position:0% +powers so what are its powers well its + + + align:start position:0% +powers so what are its powers well its +powers are on the unit circle right + + align:start position:0% +powers are on the unit circle right + + + align:start position:0% +powers are on the unit circle right +because when I Square + + align:start position:0% +because when I Square + + + align:start position:0% +because when I Square +square a number a complex number I + + align:start position:0% +square a number a complex number I + + + align:start position:0% +square a number a complex number I +Square its absolute + + align:start position:0% +Square its absolute + + + align:start position:0% +Square its absolute +value which gives me one again all the + + align:start position:0% +value which gives me one again all the + + + align:start position:0% +value which gives me one again all the +powers have are on the unit circle and + + align:start position:0% +powers have are on the unit circle and + + + align:start position:0% +powers have are on the unit circle and +they the angle gets doubled to 120 so + + align:start position:0% +they the angle gets doubled to 120 so + + + align:start position:0% +they the angle gets doubled to 120 so +there's W2 there's W Cub there's W 4th + + align:start position:0% +there's W2 there's W Cub there's W 4th + + + align:start position:0% +there's W2 there's W Cub there's W 4th +there's W 5th and there is W 6th as we + + align:start position:0% +there's W 5th and there is W 6th as we + + + align:start position:0% +there's W 5th and there is W 6th as we +hoped W the Six coming back to + + align:start position:0% +hoped W the Six coming back to + + + align:start position:0% +hoped W the Six coming back to +one so those are the the + + align:start position:0% +one so those are the the + + + align:start position:0% +one so those are the the +six can I say this on TV the six six + + align:start position:0% +six can I say this on TV the six six + + + align:start position:0% +six can I say this on TV the six six +roots of one and it's this + + align:start position:0% +roots of one and it's this + + + align:start position:0% +roots of one and it's this +one that primitive one we say the first + + align:start position:0% +one that primitive one we say the first + + + align:start position:0% +one that primitive one we say the first +one which is + + align:start position:0% +one which is + + + align:start position:0% +one which is +W okay so what let me change let me I + + align:start position:0% +W okay so what let me change let me I + + + align:start position:0% +W okay so what let me change let me I +said I would probably switch to n equal + + align:start position:0% +said I would probably switch to n equal + + + align:start position:0% +said I would probably switch to n equal +4 what's W for + + align:start position:0% +4 what's W for + + + align:start position:0% +4 what's W for +that it's the fourth root of one W to + + align:start position:0% +that it's the fourth root of one W to + + + align:start position:0% +that it's the fourth root of one W to +the 4th will be one W will be e to the 2 + + align:start position:0% +the 4th will be one W will be e to the 2 + + + align:start position:0% +the 4th will be one W will be e to the 2 +pi I over 4 + + align:start position:0% + + + + align:start position:0% + +now what's + + align:start position:0% +now what's + + + align:start position:0% +now what's +that this is e to the I pi over 2 this + + align:start position:0% +that this is e to the I pi over 2 this + + + align:start position:0% +that this is e to the I pi over 2 this +is a quarter of the way round the unit + + align:start position:0% +is a quarter of the way round the unit + + + align:start position:0% +is a quarter of the way round the unit +circle and that's + + align:start position:0% +circle and that's + + + align:start position:0% +circle and that's +exactly I a quarter of the way + + align:start position:0% +exactly I a quarter of the way + + + align:start position:0% +exactly I a quarter of the way +round and sure enough the powers are i i + + align:start position:0% +round and sure enough the powers are i i + + + align:start position:0% +round and sure enough the powers are i i +s which is -1 I cubed which is - I and + + align:start position:0% +s which is -1 I cubed which is - I and + + + align:start position:0% +s which is -1 I cubed which is - I and +finally I 4th which is one + + align:start position:0% +finally I 4th which is one + + + align:start position:0% +finally I 4th which is one +right so there is w w^2 w Cub W 4th I'm + + align:start position:0% +right so there is w w^2 w Cub W 4th I'm + + + align:start position:0% +right so there is w w^2 w Cub W 4th I'm +really ready to write down this Fier + + align:start position:0% +really ready to write down this Fier + + + align:start position:0% +really ready to write down this Fier +Matrix for the 4x4 + + align:start position:0% +Matrix for the 4x4 + + + align:start position:0% +Matrix for the 4x4 +case just so we see that clearly let me + + align:start position:0% +case just so we see that clearly let me + + + align:start position:0% +case just so we see that clearly let me +do it here + + align:start position:0% +do it here + + + align:start position:0% +do it here +F4 is all right one one one one one one + + align:start position:0% +F4 is all right one one one one one one + + + align:start position:0% +F4 is all right one one one one one one +one W it's + + align:start position:0% +one W it's + + + align:start position:0% +one W it's +i i 2 that's minus one I cubed is minus + + align:start position:0% + + + + align:start position:0% + +I I I could write i^ s and I Cub why + + align:start position:0% +I I I could write i^ s and I Cub why + + + align:start position:0% +I I I could write i^ s and I Cub why +don't I just so we see the pattern for + + align:start position:0% +don't I just so we see the pattern for + + + align:start position:0% +don't I just so we see the pattern for +sure I 2 I cubed I 2 I cubed I4 I6 i4th + + align:start position:0% +sure I 2 I cubed I 2 I cubed I4 I6 i4th + + + align:start position:0% +sure I 2 I cubed I 2 I cubed I4 I6 i4th +I6 and I 9th + + align:start position:0% +I6 and I 9th + + + align:start position:0% +I6 and I 9th +you see the exponents fall in this nice + + align:start position:0% +you see the exponents fall in this nice + + + align:start position:0% +you see the exponents fall in this nice +the exponent is the row number times the + + align:start position:0% +the exponent is the row number times the + + + align:start position:0% +the exponent is the row number times the +column number always starting at + + align:start position:0% +column number always starting at + + + align:start position:0% +column number always starting at +zero okay and now I can put in those + + align:start position:0% +zero okay and now I can put in those + + + align:start position:0% +zero okay and now I can put in those +numbers if you like one one one one 1 i + + align:start position:0% +numbers if you like one one one one 1 i + + + align:start position:0% +numbers if you like one one one one 1 i +- one - I 1 - one 1 - one and 1 - + + align:start position:0% +- one - I 1 - one 1 - one and 1 - + + + align:start position:0% +- one - I 1 - one 1 - one and 1 - +i - 1 I + + align:start position:0% +i - 1 I + + + align:start position:0% +i - 1 I +no + + align:start position:0% +no + + + align:start position:0% +no +yes + + align:start position:0% + + + + align:start position:0% + +right what's why do I think that Matrix + + align:start position:0% +right what's why do I think that Matrix + + + align:start position:0% +right what's why do I think that Matrix +is so + + align:start position:0% + + + + align:start position:0% + +remarkable it's the 4x4 Matrix that + + align:start position:0% +remarkable it's the 4x4 Matrix that + + + align:start position:0% +remarkable it's the 4x4 Matrix that +comes into the + + align:start position:0% +comes into the + + + align:start position:0% +comes into the +4o 4A + + align:start position:0% +4o 4A + + + align:start position:0% +4o 4A +transform when we want to find the for + + align:start position:0% +transform when we want to find the for + + + align:start position:0% +transform when we want to find the for +transform the 44A transform + + align:start position:0% +transform the 44A transform + + + align:start position:0% +transform the 44A transform +of a vector with four + + align:start position:0% +of a vector with four + + + align:start position:0% +of a vector with four +components we want to multiply by this + + align:start position:0% +components we want to multiply by this + + + align:start position:0% +components we want to multiply by this +F4 or we want to multiply by F4 + + align:start position:0% +F4 or we want to multiply by F4 + + + align:start position:0% +F4 or we want to multiply by F4 +inverse one way we're taking the + + align:start position:0% +inverse one way we're taking the + + + align:start position:0% +inverse one way we're taking the +transform one way we're taking the + + align:start position:0% +transform one way we're taking the + + + align:start position:0% +transform one way we're taking the +inverse transform actually they're so + + align:start position:0% +inverse transform actually they're so + + + align:start position:0% +inverse transform actually they're so +close that it's easy to confuse the two + + align:start position:0% +close that it's easy to confuse the two + + + align:start position:0% +close that it's easy to confuse the two +the inverse of this Matrix will be a + + align:start position:0% +the inverse of this Matrix will be a + + + align:start position:0% +the inverse of this Matrix will be a +nice Matrix + + align:start position:0% + + + + align:start position:0% + +also so and that's of course what makes + + align:start position:0% +also so and that's of course what makes + + + align:start position:0% +also so and that's of course what makes +it + + align:start position:0% +it + + + align:start position:0% +it +that that I guess Fier knew that he knew + + align:start position:0% +that that I guess Fier knew that he knew + + + align:start position:0% +that that I guess Fier knew that he knew +the inverse of this + + align:start position:0% + + + + align:start position:0% + +Matrix as you'll see it just comes from + + align:start position:0% +Matrix as you'll see it just comes from + + + align:start position:0% +Matrix as you'll see it just comes from +the fact that the columns are + + align:start position:0% +the fact that the columns are + + + align:start position:0% +the fact that the columns are +orthogonal from the fact that the + + align:start position:0% +orthogonal from the fact that the + + + align:start position:0% +orthogonal from the fact that the +columns are orthogonal we will quickly + + align:start position:0% +columns are orthogonal we will quickly + + + align:start position:0% +columns are orthogonal we will quickly +figure out what + + align:start position:0% +figure out what + + + align:start position:0% +figure out what +is the + + align:start position:0% +is the + + + align:start position:0% +is the +inverse but for8 didn't know didn't + + align:start position:0% +inverse but for8 didn't know didn't + + + align:start position:0% +inverse but for8 didn't know didn't +notice I think gaus noticed it but + + align:start position:0% +notice I think gaus noticed it but + + + align:start position:0% +notice I think gaus noticed it but +didn't make a point of it and then it + + align:start position:0% +didn't make a point of it and then it + + + align:start position:0% +didn't make a point of it and then it +turned out to be really important was + + align:start position:0% +turned out to be really important was + + + align:start position:0% +turned out to be really important was +the fact that this Matrix is so special + + align:start position:0% +the fact that this Matrix is so special + + + align:start position:0% +the fact that this Matrix is so special +that you can break it up into nice + + align:start position:0% +that you can break it up into nice + + + align:start position:0% +that you can break it up into nice +pieces with lots of + + align:start position:0% +pieces with lots of + + + align:start position:0% +pieces with lots of +zeros factors that have lots of zeros + + align:start position:0% +zeros factors that have lots of zeros + + + align:start position:0% +zeros factors that have lots of zeros +and multiply by it or by its inverse + + align:start position:0% +and multiply by it or by its inverse + + + align:start position:0% +and multiply by it or by its inverse +very very fast + + align:start position:0% +very very fast + + + align:start position:0% +very very fast +okay but how did it get into this + + align:start position:0% +okay but how did it get into this + + + align:start position:0% +okay but how did it get into this +lecture first because the columns are + + align:start position:0% +lecture first because the columns are + + + align:start position:0% +lecture first because the columns are +orthogonal can I just check that the + + align:start position:0% +orthogonal can I just check that the + + + align:start position:0% +orthogonal can I just check that the +columns of this Matrix are + + align:start position:0% + + + + align:start position:0% + +orthogonal so the inner product of that + + align:start position:0% +orthogonal so the inner product of that + + + align:start position:0% +orthogonal so the inner product of that +column with that + + align:start position:0% +column with that + + + align:start position:0% +column with that +column is + + align:start position:0% +column is + + + align:start position:0% +column is +zero the inner product of column one + + align:start position:0% +zero the inner product of column one + + + align:start position:0% +zero the inner product of column one +with column + + align:start position:0% +with column + + + align:start position:0% +with column +3 is + + align:start position:0% +3 is + + + align:start position:0% +3 is +zero how about the inner product + + align:start position:0% +zero how about the inner product + + + align:start position:0% +zero how about the inner product +of two and + + align:start position:0% +of two and + + + align:start position:0% +of two and +four can I take the inner product of + + align:start position:0% +four can I take the inner product of + + + align:start position:0% +four can I take the inner product of +column two + + align:start position:0% +column two + + + align:start position:0% +column two +with column four or even the inner + + align:start position:0% +with column four or even the inner + + + align:start position:0% +with column four or even the inner +product of two with three let's let's + + align:start position:0% +product of two with three let's let's + + + align:start position:0% +product of two with three let's let's +see does + + align:start position:0% +see does + + + align:start position:0% +see does +that let me do two and + + align:start position:0% + + + + align:start position:0% + +four + + align:start position:0% +four + + + align:start position:0% +four +okay what oh I see + + align:start position:0% + + + + align:start position:0% + +yes see I believe that those two column + + align:start position:0% +yes see I believe that those two column + + + align:start position:0% +yes see I believe that those two column +s are orthogonal so let me take their + + align:start position:0% +s are orthogonal so let me take their + + + align:start position:0% +s are orthogonal so let me take their +end product and hope to get zero okay + + align:start position:0% +end product and hope to get zero okay + + + align:start position:0% +end product and hope to get zero okay +now if you hadn't listened to the first + + align:start position:0% +now if you hadn't listened to the first + + + align:start position:0% +now if you hadn't listened to the first +half of this + + align:start position:0% +half of this + + + align:start position:0% +half of this +lecture when you took the inner product + + align:start position:0% +lecture when you took the inner product + + + align:start position:0% +lecture when you took the inner product +of that with that you would have + + align:start position:0% +of that with that you would have + + + align:start position:0% +of that with that you would have +multiplied one by one I by minus I and + + align:start position:0% +multiplied one by one I by minus I and + + + align:start position:0% +multiplied one by one I by minus I and +that would have given you + + align:start position:0% +that would have given you + + + align:start position:0% +that would have given you +one Min -1 by minus1 would have given + + align:start position:0% +one Min -1 by minus1 would have given + + + align:start position:0% +one Min -1 by minus1 would have given +you another one - I by I would have been + + align:start position:0% +you another one - I by I would have been + + + align:start position:0% +you another one - I by I would have been +minus i^ 2 that's another one + + align:start position:0% + + + + align:start position:0% + +so do I conclude that the inner product + + align:start position:0% +so do I conclude that the inner product + + + align:start position:0% +so do I conclude that the inner product +of columns I said columns two and four + + align:start position:0% +of columns I said columns two and four + + + align:start position:0% +of columns I said columns two and four +that's because I forgot those are + + align:start position:0% +that's because I forgot those are + + + align:start position:0% +that's because I forgot those are +columns one and + + align:start position:0% + + + + align:start position:0% + +three I'm interested in their inner + + align:start position:0% +three I'm interested in their inner + + + align:start position:0% +three I'm interested in their inner +product and I'm hoping it's zero but it + + align:start position:0% +product and I'm hoping it's zero but it + + + align:start position:0% +product and I'm hoping it's zero but it +doesn't look like + + align:start position:0% +doesn't look like + + + align:start position:0% +doesn't look like +zero nevertheless it is zero those + + align:start position:0% +zero nevertheless it is zero those + + + align:start position:0% +zero nevertheless it is zero those +columns are perpendicular why because + + align:start position:0% +columns are perpendicular why because + + + align:start position:0% +columns are perpendicular why because +the inner + + align:start position:0% +the inner + + + align:start position:0% +the inner +product we conjugate you remember that + + align:start position:0% +product we conjugate you remember that + + + align:start position:0% +product we conjugate you remember that +one the vectors in the inner product has + + align:start position:0% +one the vectors in the inner product has + + + align:start position:0% +one the vectors in the inner product has +to get conjugated so when I conjugate it + + align:start position:0% +to get conjugated so when I conjugate it + + + align:start position:0% +to get conjugated so when I conjugate it +it changes that I to a minus I changes + + align:start position:0% +it changes that I to a minus I changes + + + align:start position:0% +it changes that I to a minus I changes +this to a plus I changes those that + + align:start position:0% +this to a plus I changes those that + + + align:start position:0% +this to a plus I changes those that +second sign and that fourth sign and I + + align:start position:0% +second sign and that fourth sign and I + + + align:start position:0% +second sign and that fourth sign and I +do get + + align:start position:0% +do get + + + align:start position:0% +do get +zero so those columns are orthogonal so + + align:start position:0% +zero so those columns are orthogonal so + + + align:start position:0% +zero so those columns are orthogonal so +columns are + + align:start position:0% +columns are + + + align:start position:0% +columns are +orthogonal they're not quite + + align:start position:0% +orthogonal they're not quite + + + align:start position:0% +orthogonal they're not quite +orthonormal but I could fix that easily + + align:start position:0% +orthonormal but I could fix that easily + + + align:start position:0% +orthonormal but I could fix that easily +they all those columns have length + + align:start position:0% +they all those columns have length + + + align:start position:0% +they all those columns have length +two length squared is + + align:start position:0% +two length squared is + + + align:start position:0% +two length squared is +four like this the four I had there this + + align:start position:0% +four like this the four I had there this + + + align:start position:0% +four like this the four I had there this +length squar 1+ 1 squ 1 squ 1 squ 1 squ + + align:start position:0% +length squar 1+ 1 squ 1 squ 1 squ 1 squ + + + align:start position:0% +length squar 1+ 1 squ 1 squ 1 squ 1 squ +is four square root is two so if I + + align:start position:0% +is four square root is two so if I + + + align:start position:0% +is four square root is two so if I +really wanted them suppose I really + + align:start position:0% +really wanted them suppose I really + + + align:start position:0% +really wanted them suppose I really +wanted to fix life up perfectly I could + + align:start position:0% +wanted to fix life up perfectly I could + + + align:start position:0% +wanted to fix life up perfectly I could +divide by two and now I + + align:start position:0% +divide by two and now I + + + align:start position:0% +divide by two and now I +have columns that are actually + + align:start position:0% +have columns that are actually + + + align:start position:0% +have columns that are actually +orthonormal + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +what so I can invert right away right + + align:start position:0% +what so I can invert right away right + + + align:start position:0% +what so I can invert right away right +orthonormal columns means now I'm + + align:start position:0% +orthonormal columns means now I'm + + + align:start position:0% +orthonormal columns means now I'm +keeping this one/ half in here for the + + align:start position:0% +keeping this one/ half in here for the + + + align:start position:0% +keeping this one/ half in here for the +moment means F4 herian can I use that + + align:start position:0% +moment means F4 herian can I use that + + + align:start position:0% +moment means F4 herian can I use that +conjugate transpose time + + align:start position:0% +conjugate transpose time + + + align:start position:0% +conjugate transpose time +F4 is + + align:start position:0% + + + + align:start position:0% + +I so I see what the inverse is + + align:start position:0% +I so I see what the inverse is + + + align:start position:0% +I so I see what the inverse is +the inverse of f4 is it's just like a or + + align:start position:0% +the inverse of f4 is it's just like a or + + + align:start position:0% +the inverse of f4 is it's just like a or +orthogonal Matrix the inverse is the + + align:start position:0% +orthogonal Matrix the inverse is the + + + align:start position:0% +orthogonal Matrix the inverse is the +transpose here the inverse is the + + align:start position:0% +transpose here the inverse is the + + + align:start position:0% +transpose here the inverse is the +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +transpose so fine that that tells me + + align:start position:0% +transpose so fine that that tells me + + + align:start position:0% +transpose so fine that that tells me +that + + align:start position:0% +that + + + align:start position:0% +that +anything good that I learn about + + align:start position:0% + + + + align:start position:0% + +F4 I'll know the same I'll know a + + align:start position:0% +F4 I'll know the same I'll know a + + + align:start position:0% +F4 I'll know the same I'll know a +similar fact about its inverse because + + align:start position:0% +similar fact about its inverse because + + + align:start position:0% +similar fact about its inverse because +its inverse is just its conjugate + + align:start position:0% +its inverse is just its conjugate + + + align:start position:0% +its inverse is just its conjugate +transpose okay now so what's good well + + align:start position:0% +transpose okay now so what's good well + + + align:start position:0% +transpose okay now so what's good well +first The Columns are orthogonal + + align:start position:0% +first The Columns are orthogonal + + + align:start position:0% +first The Columns are orthogonal +that's a key fact that's the thing that + + align:start position:0% +that's a key fact that's the thing that + + + align:start position:0% +that's a key fact that's the thing that +makes the inverse easy but what property + + align:start position:0% +makes the inverse easy but what property + + + align:start position:0% +makes the inverse easy but what property +is it that leads to the fast 4A + + align:start position:0% +is it that leads to the fast 4A + + + align:start position:0% +is it that leads to the fast 4A +transform so now I'm going to talk in + + align:start position:0% +transform so now I'm going to talk in + + + align:start position:0% +transform so now I'm going to talk in +these last minutes about the fast 4A + + align:start position:0% +these last minutes about the fast 4A + + + align:start position:0% +these last minutes about the fast 4A +transform what here's the + + align:start position:0% +transform what here's the + + + align:start position:0% +transform what here's the +idea F six our 6x6 Matrix will there's a + + align:start position:0% +idea F six our 6x6 Matrix will there's a + + + align:start position:0% +idea F six our 6x6 Matrix will there's a +neat connection to + + align:start position:0% +neat connection to + + + align:start position:0% +neat connection to +F3 half as + + align:start position:0% +F3 half as + + + align:start position:0% +F3 half as +big there's a connection of f8 to + + align:start position:0% +big there's a connection of f8 to + + + align:start position:0% +big there's a connection of f8 to +F4 there's a connection of f64 to + + align:start position:0% +F4 there's a connection of f64 to + + + align:start position:0% +F4 there's a connection of f64 to +F32 shall I write down what that + + align:start position:0% +F32 shall I write down what that + + + align:start position:0% +F32 shall I write down what that +connection is what's the connection of + + align:start position:0% +connection is what's the connection of + + + align:start position:0% +connection is what's the connection of +f64 to F32 so + + align:start position:0% +f64 to F32 so + + + align:start position:0% +f64 to F32 so +f64 is a 64x 64 + + align:start position:0% +f64 is a 64x 64 + + + align:start position:0% +f64 is a 64x 64 +Matrix whose W is the 64th root of 1 so + + align:start position:0% +Matrix whose W is the 64th root of 1 so + + + align:start position:0% +Matrix whose W is the 64th root of 1 so +it's 16 4 of the way around in + + align:start position:0% +it's 16 4 of the way around in + + + align:start position:0% +it's 16 4 of the way around in +f64 and and F32 is a 32x 32 Matrix + + align:start position:0% +f64 and and F32 is a 32x 32 Matrix + + + align:start position:0% +f64 and and F32 is a 32x 32 Matrix +remember they're different + + align:start position:0% + + + + align:start position:0% + +sizes and the W in that 32x 32 Matrix is + + align:start position:0% +sizes and the W in that 32x 32 Matrix is + + + align:start position:0% +sizes and the W in that 32x 32 Matrix is +the 32nd root of one which is twice as + + align:start position:0% +the 32nd root of one which is twice as + + + align:start position:0% +the 32nd root of one which is twice as +far that see that key Point that's the + + align:start position:0% +far that see that key Point that's the + + + align:start position:0% +far that see that key Point that's the +that's how 32 and 64 are connected in + + align:start position:0% +that's how 32 and 64 are connected in + + + align:start position:0% +that's how 32 and 64 are connected in +the W's the W for 64 is is 164 of the + + align:start position:0% +the W's the W for 64 is is 164 of the + + + align:start position:0% +the W's the W for 64 is is 164 of the +way so all I'm saying is that if I + + align:start position:0% +way so all I'm saying is that if I + + + align:start position:0% +way so all I'm saying is that if I +Square the W w64 that's what I'm using + + align:start position:0% +Square the W w64 that's what I'm using + + + align:start position:0% +Square the W w64 that's what I'm using +for the one over + + align:start position:0% +for the one over + + + align:start position:0% +for the one over +W6 this is w n is e to the i 2 pi/ N so + + align:start position:0% +W6 this is w n is e to the i 2 pi/ N so + + + align:start position:0% +W6 this is w n is e to the i 2 pi/ N so +w 64 is 164 of the way round it when I + + align:start position:0% +w 64 is 164 of the way round it when I + + + align:start position:0% +w 64 is 164 of the way round it when I +square that what do I get but + + align:start position:0% + + + + align:start position:0% + +w32 right if I Square this Matrix + + align:start position:0% +w32 right if I Square this Matrix + + + align:start position:0% +w32 right if I Square this Matrix +I double the angle if I Square this + + align:start position:0% +I double the angle if I Square this + + + align:start position:0% +I double the angle if I Square this +number I double the angle I get uh the + + align:start position:0% +number I double the angle I get uh the + + + align:start position:0% +number I double the angle I get uh the +the + + align:start position:0% +the + + + align:start position:0% +the +w32 so somehow there's a little hope + + align:start position:0% +w32 so somehow there's a little hope + + + align:start position:0% +w32 so somehow there's a little hope +here to connect f64 with F32 and here's + + align:start position:0% +here to connect f64 with F32 and here's + + + align:start position:0% +here to connect f64 with F32 and here's +the + + align:start position:0% +the + + + align:start position:0% +the +connection okay let me let me go back uh + + align:start position:0% +connection okay let me let me go back uh + + + align:start position:0% +connection okay let me let me go back uh +yeah let me I'll do it here + + align:start position:0% + + + + align:start position:0% + +here's the connection + + align:start position:0% +here's the connection + + + align:start position:0% +here's the connection +f64 the 64x 64 fora + + align:start position:0% +f64 the 64x 64 fora + + + align:start position:0% +f64 the 64x 64 fora +matrix it's connected to two copies of + + align:start position:0% +matrix it's connected to two copies of + + + align:start position:0% +matrix it's connected to two copies of +F32 let me leave a little space for the + + align:start position:0% +F32 let me leave a little space for the + + + align:start position:0% +F32 let me leave a little space for the +connection so this is 64x + + align:start position:0% +connection so this is 64x + + + align:start position:0% +connection so this is 64x +64 here's a matrix of that same size + + align:start position:0% +64 here's a matrix of that same size + + + align:start position:0% +64 here's a matrix of that same size +because it's got two copies of F32 and + + align:start position:0% +because it's got two copies of F32 and + + + align:start position:0% +because it's got two copies of F32 and +two zero + + align:start position:0% +two zero + + + align:start position:0% +two zero +matrices those zero matrices are the key + + align:start position:0% +matrices those zero matrices are the key + + + align:start position:0% +matrices those zero matrices are the key +because when I multiply by this Matrix + + align:start position:0% +because when I multiply by this Matrix + + + align:start position:0% +because when I multiply by this Matrix +just as it is regular multiplication I + + align:start position:0% +just as it is regular multiplication I + + + align:start position:0% +just as it is regular multiplication I +would take need 64 I I would have 64 + + align:start position:0% +would take need 64 I I would have 64 + + + align:start position:0% +would take need 64 I I would have 64 +squared little multiplications to do but + + align:start position:0% +squared little multiplications to do but + + + align:start position:0% +squared little multiplications to do but +this Matrix is half + + align:start position:0% +this Matrix is half + + + align:start position:0% +this Matrix is half +zero well of course the two aren't equal + + align:start position:0% +zero well of course the two aren't equal + + + align:start position:0% +zero well of course the two aren't equal +I'm going to put an equal sign but there + + align:start position:0% +I'm going to put an equal sign but there + + + align:start position:0% +I'm going to put an equal sign but there +has to be some fix up factors one there + + align:start position:0% +has to be some fix up factors one there + + + align:start position:0% +has to be some fix up factors one there +and one + + align:start position:0% +and one + + + align:start position:0% +and one +there to make it + + align:start position:0% +there to make it + + + align:start position:0% +there to make it +true the beauty is that these fix up + + align:start position:0% +true the beauty is that these fix up + + + align:start position:0% +true the beauty is that these fix up +factors will be really almost all + + align:start position:0% +factors will be really almost all + + + align:start position:0% +factors will be really almost all +zeros so that as soon as we get this + + align:start position:0% +zeros so that as soon as we get this + + + align:start position:0% +zeros so that as soon as we get this +formula + + align:start position:0% +formula + + + align:start position:0% +formula +right we've got a great idea for how to + + align:start position:0% +right we've got a great idea for how to + + + align:start position:0% +right we've got a great idea for how to +get from the 6 from the 64 squared + + align:start position:0% +get from the 6 from the 64 squared + + + align:start position:0% +get from the 6 from the 64 squared +calculations so this original originally + + align:start position:0% +calculations so this original originally + + + align:start position:0% +calculations so this original originally +we have 64 squared calculations from + + align:start position:0% +we have 64 squared calculations from + + + align:start position:0% +we have 64 squared calculations from +there but this one with will give us + + align:start position:0% +there but this one with will give us + + + align:start position:0% +there but this one with will give us +this is this will we don't need that + + align:start position:0% +this is this will we don't need that + + + align:start position:0% +this is this will we don't need that +many we only need 2 * 32 sared because + + align:start position:0% +many we only need 2 * 32 sared because + + + align:start position:0% +many we only need 2 * 32 sared because +we've got that + + align:start position:0% +we've got that + + + align:start position:0% +we've got that +twice and plus the fix + + align:start position:0% +twice and plus the fix + + + align:start position:0% +twice and plus the fix +up so I have to tell you what's in this + + align:start position:0% +up so I have to tell you what's in this + + + align:start position:0% +up so I have to tell you what's in this +fix up + + align:start position:0% +fix up + + + align:start position:0% +fix up +Matrix the one on the right is actually + + align:start position:0% +Matrix the one on the right is actually + + + align:start position:0% +Matrix the one on the right is actually +a permutation Matrix a very simple odds + + align:start position:0% +a permutation Matrix a very simple odds + + + align:start position:0% +a permutation Matrix a very simple odds +and evens permutation Matrix the the the + + align:start position:0% +and evens permutation Matrix the the the + + + align:start position:0% +and evens permutation Matrix the the the +ones show up + + align:start position:0% +ones show up + + + align:start position:0% +ones show up +I haven't put enough ones I really need + + align:start position:0% +I haven't put enough ones I really need + + + align:start position:0% +I haven't put enough ones I really need +a 32 of these guys a double space and + + align:start position:0% +a 32 of these guys a double space and + + + align:start position:0% +a 32 of these guys a double space and +[Music] + + align:start position:0% + + + + align:start position:0% + +then you see it's a it's a permutation + + align:start position:0% +then you see it's a it's a permutation + + + align:start position:0% +then you see it's a it's a permutation +Matrix what it does shall I call it + + align:start position:0% +Matrix what it does shall I call it + + + align:start position:0% +Matrix what it does shall I call it +P for permutation Matrix so what that P + + align:start position:0% +P for permutation Matrix so what that P + + + align:start position:0% +P for permutation Matrix so what that P +does when it multiplies a vector it + + align:start position:0% +does when it multiplies a vector it + + + align:start position:0% +does when it multiplies a vector it +takes the odd the even numbered + + align:start position:0% +takes the odd the even numbered + + + align:start position:0% +takes the odd the even numbered +component onon first and then the odds + + align:start position:0% +component onon first and then the odds + + + align:start position:0% +component onon first and then the odds +you see this this one skipping every + + align:start position:0% +you see this this one skipping every + + + align:start position:0% +you see this this one skipping every +time is going to pick out x0 X2 X4 X6 + + align:start position:0% +time is going to pick out x0 X2 X4 X6 + + + align:start position:0% +time is going to pick out x0 X2 X4 X6 +and then below that will come we will + + align:start position:0% +and then below that will come we will + + + align:start position:0% +and then below that will come we will +pick out X1 X3 + + align:start position:0% + + + + align:start position:0% + +X5 and of course uh that can be + + align:start position:0% +X5 and of course uh that can be + + + align:start position:0% +X5 and of course uh that can be +hardwired in the computer to be + + align:start position:0% +hardwired in the computer to be + + + align:start position:0% +hardwired in the computer to be +instantaneous so + + align:start position:0% +instantaneous so + + + align:start position:0% +instantaneous so +that says so far what have we said we're + + align:start position:0% +that says so far what have we said we're + + + align:start position:0% +that says so far what have we said we're +saying that the 64x 64 forier Matrix is + + align:start position:0% +saying that the 64x 64 forier Matrix is + + + align:start position:0% +saying that the 64x 64 forier Matrix is +really separated it into separate your + + align:start position:0% +really separated it into separate your + + + align:start position:0% +really separated it into separate your +vector into the odd into the even + + align:start position:0% +vector into the odd into the even + + + align:start position:0% +vector into the odd into the even +components and the odd + + align:start position:0% +components and the odd + + + align:start position:0% +components and the odd +components then do a 32 size 48 + + align:start position:0% +components then do a 32 size 48 + + + align:start position:0% +components then do a 32 size 48 +transform on those + + align:start position:0% +transform on those + + + align:start position:0% +transform on those +separately and then put the pieces + + align:start position:0% +separately and then put the pieces + + + align:start position:0% +separately and then put the pieces +together again so the pieces putting + + align:start position:0% +together again so the pieces putting + + + align:start position:0% +together again so the pieces putting +them together turns out to be I and a + + align:start position:0% +them together turns out to be I and a + + + align:start position:0% +them together turns out to be I and a +diagonal matrix and I and a minus that + + align:start position:0% +diagonal matrix and I and a minus that + + + align:start position:0% +diagonal matrix and I and a minus that +same diagonal matrix + + align:start position:0% +same diagonal matrix + + + align:start position:0% +same diagonal matrix +so the fix up cost is really the cost of + + align:start position:0% +so the fix up cost is really the cost of + + + align:start position:0% +so the fix up cost is really the cost of +multiplying by D this diagonal matrix + + align:start position:0% +multiplying by D this diagonal matrix + + + align:start position:0% +multiplying by D this diagonal matrix +because there's essentially no cost in + + align:start position:0% +because there's essentially no cost in + + + align:start position:0% +because there's essentially no cost in +in the I part or in the permutation part + + align:start position:0% +in the I part or in the permutation part + + + align:start position:0% +in the I part or in the permutation part +so really it's the fix up + + align:start position:0% +so really it's the fix up + + + align:start position:0% +so really it's the fix up +cost is + + align:start position:0% +cost is + + + align:start position:0% +cost is +essentially because D is + + align:start position:0% +essentially because D is + + + align:start position:0% +essentially because D is +diagonal is 32 multiplications + + align:start position:0% + + + + align:start position:0% + +that's the there you seeing of course we + + align:start position:0% +that's the there you seeing of course we + + + align:start position:0% +that's the there you seeing of course we +didn't check the formula or we didn't + + align:start position:0% +didn't check the formula or we didn't + + + align:start position:0% +didn't check the formula or we didn't +even say what D is yet but I will this + + align:start position:0% +even say what D is yet but I will this + + + align:start position:0% +even say what D is yet but I will this +diagonal matrix D is powers of w 1 W w^2 + + align:start position:0% +diagonal matrix D is powers of w 1 W w^2 + + + align:start position:0% +diagonal matrix D is powers of w 1 W w^2 +down to W to the + + align:start position:0% + + + + align:start position:0% + +31st so you see that when I to do a + + align:start position:0% +31st so you see that when I to do a + + + align:start position:0% +31st so you see that when I to do a +multiplication by D I need to do 32 + + align:start position:0% +multiplication by D I need to do 32 + + + align:start position:0% +multiplication by D I need to do 32 +multiplications there they are + + align:start position:0% +multiplications there they are + + + align:start position:0% +multiplications there they are +then but the the other the more serious + + align:start position:0% +then but the the other the more serious + + + align:start position:0% +then but the the other the more serious +work is to do the F32 twice on the + + align:start position:0% +work is to do the F32 twice on the + + + align:start position:0% +work is to do the F32 twice on the +separately on the even numbered and odd + + align:start position:0% +separately on the even numbered and odd + + + align:start position:0% +separately on the even numbered and odd +numbered components so twice 32 squar so + + align:start position:0% +numbered components so twice 32 squar so + + + align:start position:0% +numbered components so twice 32 squar so +64 squar is gone + + align:start position:0% +64 squar is gone + + + align:start position:0% +64 squar is gone +now and that's the new + + align:start position:0% +now and that's the new + + + align:start position:0% +now and that's the new +count okay great but what + + align:start position:0% +count okay great but what + + + align:start position:0% +count okay great but what +next so that's we now have the key idea + + align:start position:0% +next so that's we now have the key idea + + + align:start position:0% +next so that's we now have the key idea +we would have to check the + + align:start position:0% +we would have to check the + + + align:start position:0% +we would have to check the +algebra but it's just uh checking a lot + + align:start position:0% +algebra but it's just uh checking a lot + + + align:start position:0% +algebra but it's just uh checking a lot +of sums that come out correctly this is + + align:start position:0% +of sums that come out correctly this is + + + align:start position:0% +of sums that come out correctly this is +right the right way to see the fast for + + align:start position:0% +right the right way to see the fast for + + + align:start position:0% +right the right way to see the fast for +transform or one right way to see + + align:start position:0% +transform or one right way to see + + + align:start position:0% +transform or one right way to see +it then you got to see what's the next + + align:start position:0% +it then you got to see what's the next + + + align:start position:0% +it then you got to see what's the next +idea the next idea is to break the 32s + + align:start position:0% +idea the next idea is to break the 32s + + + align:start position:0% +idea the next idea is to break the 32s +down break those 32s down so we have + + align:start position:0% +down break those 32s down so we have + + + align:start position:0% +down break those 32s down so we have +this factor and now we have the F32 but + + align:start position:0% +this factor and now we have the F32 but + + + align:start position:0% +this factor and now we have the F32 but +that breaks + + align:start position:0% +that breaks + + + align:start position:0% +that breaks +into some guy here f30 F6 F 16 F-16 each + + align:start position:0% +into some guy here f30 F6 F 16 F-16 each + + + align:start position:0% +into some guy here f30 F6 F 16 F-16 each +each F32 is breaking into two copies of + + align:start position:0% +each F32 is breaking into two copies of + + + align:start position:0% +each F32 is breaking into two copies of +F-16 and then we have a permutation and + + align:start position:0% +F-16 and then we have a permutation and + + + align:start position:0% +F-16 and then we have a permutation and +then + + align:start position:0% +then + + + align:start position:0% +then +the so this is a like this was a 64 size + + align:start position:0% +the so this is a like this was a 64 size + + + align:start position:0% +the so this is a like this was a 64 size +permutation this is a 32 size + + align:start position:0% +permutation this is a 32 size + + + align:start position:0% +permutation this is a 32 size +permutation ah I guess I've got it twice + + align:start position:0% +permutation ah I guess I've got it twice + + + align:start position:0% +permutation ah I guess I've got it twice +is I'm I'm just using the same idea + + align:start position:0% +is I'm I'm just using the same idea + + + align:start position:0% +is I'm I'm just using the same idea +recursively recursion is the key word + + align:start position:0% +recursively recursion is the key word + + + align:start position:0% +recursively recursion is the key word +that on each of those F32 so here's 0 0 + + align:start position:0% +that on each of those F32 so here's 0 0 + + + align:start position:0% +that on each of those F32 so here's 0 0 +it's just to get + + align:start position:0% + + + + align:start position:0% + +F32 this is the odd even + + align:start position:0% +F32 this is the odd even + + + align:start position:0% +F32 this is the odd even +permutations so you see we're we're the + + align:start position:0% +permutations so you see we're we're the + + + align:start position:0% +permutations so you see we're we're the +combination of those + + align:start position:0% +combination of those + + + align:start position:0% +combination of those +permutations what's it + + align:start position:0% +permutations what's it + + + align:start position:0% +permutations what's it +doing this guy separates into odds and + + align:start position:0% +doing this guy separates into odds and + + + align:start position:0% +doing this guy separates into odds and +into evens and odds + + align:start position:0% +into evens and odds + + + align:start position:0% +into evens and odds +and then this guy separates the evens + + align:start position:0% +and then this guy separates the evens + + + align:start position:0% +and then this guy separates the evens +into the + + align:start position:0% +into the + + + align:start position:0% +into the +ones the numbers of mult the even + + align:start position:0% +ones the numbers of mult the even + + + align:start position:0% +ones the numbers of mult the even +evens which means + + align:start position:0% +evens which means + + + align:start position:0% +evens which means +0486 and even odds which + + align:start position:0% +0486 and even odds which + + + align:start position:0% +0486 and even odds which +means 2 + + align:start position:0% +means 2 + + + align:start position:0% +means 2 +6 10 14 and then OD evens and OD odds + + align:start position:0% +6 10 14 and then OD evens and OD odds + + + align:start position:0% +6 10 14 and then OD evens and OD odds +you see together these permutations then + + align:start position:0% +you see together these permutations then + + + align:start position:0% +you see together these permutations then +break it break our Vector down down into + + align:start position:0% +break it break our Vector down down into + + + align:start position:0% +break it break our Vector down down into +X even even and three other pieces those + + align:start position:0% +X even even and three other pieces those + + + align:start position:0% +X even even and three other pieces those +are the four pieces that separately get + + align:start position:0% +are the four pieces that separately get + + + align:start position:0% +are the four pieces that separately get +multiplied by + + align:start position:0% +multiplied by + + + align:start position:0% +multiplied by +F16 separately fixed up by these I's and + + align:start position:0% +F16 separately fixed up by these I's and + + + align:start position:0% +F16 separately fixed up by these I's and +D's and I's and minus + + align:start position:0% + + + + align:start position:0% + +D's so this count is now + + align:start position:0% +D's so this count is now + + + align:start position:0% +D's so this count is now +reduced this count is now what's it + + align:start position:0% +reduced this count is now what's it + + + align:start position:0% +reduced this count is now what's it +reduced to so that's going to be + + align:start position:0% +reduced to so that's going to be + + + align:start position:0% +reduced to so that's going to be +gone cuz 32 squ that's that's the change + + align:start position:0% +gone cuz 32 squ that's that's the change + + + align:start position:0% +gone cuz 32 squ that's that's the change +I'm making right the 32 + + align:start position:0% +I'm making right the 32 + + + align:start position:0% +I'm making right the 32 +squar so it's this that's now reduced so + + align:start position:0% +squar so it's this that's now reduced so + + + align:start position:0% +squar so it's this that's now reduced so +I still have two times it but now what's + + align:start position:0% +I still have two times it but now what's + + + align:start position:0% +I still have two times it but now what's + + align:start position:0% + + + align:start position:0% +squar it's gone in favor of two 16 + + align:start position:0% +squar it's gone in favor of two 16 + + + align:start position:0% +squar it's gone in favor of two 16 +squar + + + align:start position:0% +squar + + + + align:start position:0% +squar + +16 that's and that that was and and then + + align:start position:0% +16 that's and that that was and and then + + + align:start position:0% +16 that's and that that was and and then +the original 32 to fix + + align:start position:0% + + + + align:start position:0% + +maybe you see what's happening even + + align:start position:0% +maybe you see what's happening even + + + align:start position:0% +maybe you see what's happening even +easier than this formula is what's when + + align:start position:0% +easier than this formula is what's when + + + align:start position:0% +easier than this formula is what's when +I do the recursion more and more + + align:start position:0% +I do the recursion more and more + + + align:start position:0% +I do the recursion more and more +times I get simpler and simpler factors + + align:start position:0% +times I get simpler and simpler factors + + + align:start position:0% +times I get simpler and simpler factors +in the middle eventually I'll be down to + + align:start position:0% +in the middle eventually I'll be down to + + + align:start position:0% +in the middle eventually I'll be down to +two point or one point for a + + align:start position:0% +two point or one point for a + + + align:start position:0% +two point or one point for a +transforms but I get more and more + + align:start position:0% +transforms but I get more and more + + + align:start position:0% +transforms but I get more and more +factors piling up on the right and left + + align:start position:0% +factors piling up on the right and left + + + align:start position:0% +factors piling up on the right and left +on the right I'm just getting + + align:start position:0% +on the right I'm just getting + + + align:start position:0% +on the right I'm just getting +permutation matrices on the left I'm + + align:start position:0% +permutation matrices on the left I'm + + + align:start position:0% +permutation matrices on the left I'm +getting these guys these I's and + + align:start position:0% +getting these guys these I's and + + + align:start position:0% +getting these guys these I's and +D's so that there was a 32 there and a + + align:start position:0% +D's so that there was a 32 there and a + + + align:start position:0% +D's so that there was a 32 there and a +each one of these is costing + + align:start position:0% +each one of these is costing + + + align:start position:0% +each one of these is costing +32 each one of those is costing 32 and + + align:start position:0% +32 each one of those is costing 32 and + + + align:start position:0% +32 each one of those is costing 32 and +how many will there + + align:start position:0% + + + + align:start position:0% + +be see you see the 32 for this original + + align:start position:0% +be see you see the 32 for this original + + + align:start position:0% +be see you see the 32 for this original +fix up because D had 32 numbers 32 for + + align:start position:0% +fix up because D had 32 numbers 32 for + + + align:start position:0% +fix up because D had 32 numbers 32 for +this next fix up because D is 16 and 16 + + align:start position:0% +this next fix up because D is 16 and 16 + + + align:start position:0% +this next fix up because D is 16 and 16 +more I keep + + align:start position:0% +more I keep + + + align:start position:0% +more I keep +going so the count in the middle goes + + align:start position:0% +going so the count in the middle goes + + + align:start position:0% +going so the count in the middle goes +down to zip but these fix up counts are + + align:start position:0% +down to zip but these fix up counts are + + + align:start position:0% +down to zip but these fix up counts are +all that I'm left with and how many + + align:start position:0% +all that I'm left with and how many + + + align:start position:0% +all that I'm left with and how many +factors how many fix UPS have I got log + + align:start position:0% +factors how many fix UPS have I got log + + + align:start position:0% +factors how many fix UPS have I got log +in from 64 one step to 32 one step to 16 + + align:start position:0% +in from 64 one step to 32 one step to 16 + + + align:start position:0% +in from 64 one step to 32 one step to 16 +one step to eight four 2 and one six + + align:start position:0% +one step to eight four 2 and one six + + + align:start position:0% +one step to eight four 2 and one six +steps so I have six fed up six fix up + + align:start position:0% +steps so I have six fed up six fix up + + + align:start position:0% +steps so I have six fed up six fix up +factors finally I get to six time + + align:start position:0% +factors finally I get to six time + + + align:start position:0% +factors finally I get to six time +the + + align:start position:0% + + + + align:start position:0% + +32 that's my final count instead of + + align:start position:0% +32 that's my final count instead of + + + align:start position:0% +32 that's my final count instead of +642 this is log to the base 2 of 64 * + + align:start position:0% +642 this is log to the base 2 of 64 * + + + align:start position:0% +642 this is log to the base 2 of 64 * +64 actually half of 64 so actually the + + align:start position:0% +64 actually half of 64 so actually the + + + align:start position:0% +64 actually half of 64 so actually the +final count is n log to the base 2 of n + + align:start position:0% +final count is n log to the base 2 of n + + + align:start position:0% +final count is n log to the base 2 of n +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +32 ah a half so can I put a box around + + align:start position:0% +32 ah a half so can I put a box around + + + align:start position:0% +32 ah a half so can I put a box around +that + + align:start position:0% +that + + + align:start position:0% +that +wonderful extremely important and + + align:start position:0% +wonderful extremely important and + + + align:start position:0% +wonderful extremely important and +satisfying + + align:start position:0% +satisfying + + + align:start position:0% +satisfying +conclusion that the fast 4A + + align:start position:0% +conclusion that the fast 4A + + + align:start position:0% +conclusion that the fast 4A +transform multiplies by an N byn Matrix + + align:start position:0% +transform multiplies by an N byn Matrix + + + align:start position:0% +transform multiplies by an N byn Matrix +but it does it not in N squ steps but in + + align:start position:0% +but it does it not in N squ steps but in + + + align:start position:0% +but it does it not in N squ steps but in +1 12 n log n steps and if we just com + + align:start position:0% +1 12 n log n steps and if we just com + + + align:start position:0% +1 12 n log n steps and if we just com +complete by doing a count let's + + align:start position:0% +complete by doing a count let's + + + align:start position:0% +complete by doing a count let's +suppose suppose uh a + + align:start position:0% + + + + align:start position:0% + +typical case would be 2 to the + + align:start position:0% + + + + align:start position:0% + +10th now + + align:start position:0% +10th now + + + align:start position:0% +10th now +n^2 is bigger than a + + align:start position:0% + + + + align:start position:0% + +million so it's 1,24 * + + align:start position:0% +million so it's 1,24 * + + + align:start position:0% +million so it's 1,24 * +1,24 but what is n what is 1 12 what is + + align:start position:0% +1,24 but what is n what is 1 12 what is + + + align:start position:0% +1,24 but what is n what is 1 12 what is +the the new count done the right + + align:start position:0% +the the new count done the right + + + align:start position:0% +the the new count done the right +way it's + + align:start position:0% +way it's + + + align:start position:0% +way it's +n the + + align:start position:0% +n the + + + align:start position:0% +n the +1024 time 12 and what's the + + align:start position:0% +1024 time 12 and what's the + + + align:start position:0% +1024 time 12 and what's the +logarithm it's 10 so times 10/ 2 so it's + + align:start position:0% +logarithm it's 10 so times 10/ 2 so it's + + + align:start position:0% +logarithm it's 10 so times 10/ 2 so it's +five * it's 5 * + + align:start position:0% +five * it's 5 * + + + align:start position:0% +five * it's 5 * +1,24 where this one was + + align:start position:0% +1,24 where this one was + + + align:start position:0% +1,24 where this one was +1,24 * + + align:start position:0% + + + + align:start position:0% + +1,24 we've reduced the calculation by a + + align:start position:0% +1,24 we've reduced the calculation by a + + + align:start position:0% +1,24 we've reduced the calculation by a +factor of 200 just by factoring The + + align:start position:0% +factor of 200 just by factoring The + + + align:start position:0% +factor of 200 just by factoring The +Matrix tricks + + align:start position:0% +Matrix tricks + + + align:start position:0% +Matrix tricks +properly this was a th000 * n we're now + + align:start position:0% +properly this was a th000 * n we're now + + + align:start position:0% +properly this was a th000 * n we're now +down to 5 * + + align:start position:0% +down to 5 * + + + align:start position:0% +down to 5 * +n so we can do 200 48 + + align:start position:0% +n so we can do 200 48 + + + align:start position:0% +n so we can do 200 48 +transforms where before we could do one + + align:start position:0% +transforms where before we could do one + + + align:start position:0% +transforms where before we could do one +and in real scientific calculations + + align:start position:0% +and in real scientific calculations + + + align:start position:0% +and in real scientific calculations +where 4 transforms are happening all the + + align:start position:0% +where 4 transforms are happening all the + + + align:start position:0% +where 4 transforms are happening all the +time we're saving a factor of 200 in one + + align:start position:0% +time we're saving a factor of 200 in one + + + align:start position:0% +time we're saving a factor of 200 in one +of the major steps of modern scientific + + align:start position:0% +of the major steps of modern scientific + + + align:start position:0% +of the major steps of modern scientific +Computing so that's the idea of the fast + + align:start position:0% +Computing so that's the idea of the fast + + + align:start position:0% +Computing so that's the idea of the fast +for a transform and you see the whole + + align:start position:0% +for a transform and you see the whole + + + align:start position:0% +for a transform and you see the whole +thing hinged on being a + + align:start position:0% +thing hinged on being a + + + align:start position:0% +thing hinged on being a +special Matrix with orthonormal columns + + align:start position:0% +special Matrix with orthonormal columns + + + align:start position:0% +special Matrix with orthonormal columns +okay that's + + align:start position:0% +okay that's + + + align:start position:0% +okay that's +actually it for complex numbers I'm back + + align:start position:0% +actually it for complex numbers I'm back + + + align:start position:0% +actually it for complex numbers I'm back +next time really to to real + + align:start position:0% +next time really to to real + + + align:start position:0% +next time really to to real +numbers uh igen values and I vectors and + + align:start position:0% +numbers uh igen values and I vectors and + + + align:start position:0% +numbers uh igen values and I vectors and +the key idea of positive definite Matrix + + align:start position:0% +the key idea of positive definite Matrix + + + align:start position:0% +the key idea of positive definite Matrix +is going to show up what's a positive + + align:start position:0% +is going to show up what's a positive + + + align:start position:0% +is going to show up what's a positive +definite Matrix and it's terrific that + + align:start position:0% +definite Matrix and it's terrific that + + + align:start position:0% +definite Matrix and it's terrific that +this course is going to reach positive + + align:start position:0% +this course is going to reach positive + + + align:start position:0% +this course is going to reach positive +definiteness because those are the + + align:start position:0% +definiteness because those are the + + + align:start position:0% +definiteness because those are the +matrixes that you see the most in + + align:start position:0% +matrixes that you see the most in + + + align:start position:0% +matrixes that you see the most in +applications okay see you next time + + align:start position:0% +applications okay see you next time + + + align:start position:0% +applications okay see you next time +thanks \ No newline at end of file diff --git a/M3F_hAHJzNQ.txt b/M3F_hAHJzNQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..4e66b9ba049eecaa0a5d13d83d49be7f0e9deee8 --- /dev/null +++ b/M3F_hAHJzNQ.txt @@ -0,0 +1,8963 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so here's what I'm going to do I'm + + align:start position:0% +okay so here's what I'm going to do I'm + + + align:start position:0% +okay so here's what I'm going to do I'm +going to + + align:start position:0% +going to + + + align:start position:0% +going to +um uh just briefly + + align:start position:0% +um uh just briefly + + + align:start position:0% +um uh just briefly +mention the three theories of + + align:start position:0% +mention the three theories of + + + align:start position:0% +mention the three theories of +Consciousness that I think are taken + + align:start position:0% +Consciousness that I think are taken + + + align:start position:0% +Consciousness that I think are taken +seriously in + + align:start position:0% +seriously in + + + align:start position:0% +seriously in +Neuroscience um I'll say something about + + align:start position:0% +Neuroscience um I'll say something about + + + align:start position:0% +Neuroscience um I'll say something about +the explanatory Gap and why that's + + align:start position:0% +the explanatory Gap and why that's + + + align:start position:0% +the explanatory Gap and why that's +relevant to the these three theories + + align:start position:0% +relevant to the these three theories + + + align:start position:0% +relevant to the these three theories +then I'll say something general about + + align:start position:0% +then I'll say something general about + + + align:start position:0% +then I'll say something general about +first order versus high order theories + + align:start position:0% +first order versus high order theories + + + align:start position:0% +first order versus high order theories +and U then I'll go on from there and + + align:start position:0% +and U then I'll go on from there and + + + align:start position:0% +and U then I'll go on from there and +we'll look at this again later so first + + align:start position:0% +we'll look at this again later so first + + + align:start position:0% +we'll look at this again later so first +the three theories so the first theory + + align:start position:0% +the three theories so the first theory + + + align:start position:0% +the three theories so the first theory +is the higher order Theory Of + + align:start position:0% +is the higher order Theory Of + + + align:start position:0% +is the higher order Theory Of +Consciousness that is what it is to have + + align:start position:0% +Consciousness that is what it is to have + + + align:start position:0% +Consciousness that is what it is to have +a conscious pain is to have a pain + + align:start position:0% +a conscious pain is to have a pain + + + align:start position:0% +a conscious pain is to have a pain +accompanied by another state that is + + align:start position:0% +accompanied by another state that is + + + align:start position:0% +accompanied by another state that is +about that + + align:start position:0% +about that + + + align:start position:0% +about that +pain um and that's what makes the pain a + + align:start position:0% +pain um and that's what makes the pain a + + + align:start position:0% +pain um and that's what makes the pain a +conscious pain so the intuition here is + + align:start position:0% +conscious pain so the intuition here is + + + align:start position:0% +conscious pain so the intuition here is +if you had two animals say say both of + + align:start position:0% +if you had two animals say say both of + + + align:start position:0% +if you had two animals say say both of +whom have a pain but only one of them + + align:start position:0% +whom have a pain but only one of them + + + align:start position:0% +whom have a pain but only one of them +has a say a thought about that pain + + align:start position:0% +has a say a thought about that pain + + + align:start position:0% +has a say a thought about that pain +that's that one would be having a + + align:start position:0% +that's that one would be having a + + + align:start position:0% +that's that one would be having a +conscious pain and the other one would + + align:start position:0% +conscious pain and the other one would + + + align:start position:0% +conscious pain and the other one would +not that's the sort of pick the idea of + + align:start position:0% +not that's the sort of pick the idea of + + + align:start position:0% +not that's the sort of pick the idea of +it um now this view comes in both higher + + align:start position:0% +it um now this view comes in both higher + + + align:start position:0% +it um now this view comes in both higher +order thought and higher order + + align:start position:0% +order thought and higher order + + + align:start position:0% +order thought and higher order +perception versions here's a bunch of + + align:start position:0% +perception versions here's a bunch of + + + align:start position:0% +perception versions here's a bunch of +historical figures well some of them + + align:start position:0% +historical figures well some of them + + + align:start position:0% +historical figures well some of them +historical um um John Lock historical + + align:start position:0% +historical um um John Lock historical + + + align:start position:0% +historical um um John Lock historical +the rest uh contemporary who have held + + align:start position:0% +the rest uh contemporary who have held + + + align:start position:0% +the rest uh contemporary who have held +this view + + align:start position:0% +this view + + + align:start position:0% +this view +um and uh I'll get I'll say more about + + align:start position:0% +um and uh I'll get I'll say more about + + + align:start position:0% +um and uh I'll get I'll say more about +this View later the second view which I + + align:start position:0% +this View later the second view which I + + + align:start position:0% +this View later the second view which I +think is I don't know my estimation of + + align:start position:0% +think is I don't know my estimation of + + + align:start position:0% +think is I don't know my estimation of +is that of people + + align:start position:0% +is that of people + + + align:start position:0% +is that of people +who neuroscience and psychology who work + + align:start position:0% +who neuroscience and psychology who work + + + align:start position:0% +who neuroscience and psychology who work +on Consciousness I think most of them + + align:start position:0% +on Consciousness I think most of them + + + align:start position:0% +on Consciousness I think most of them +are likely to have this view so uh the + + align:start position:0% +are likely to have this view so uh the + + + align:start position:0% +are likely to have this view so uh the +view was first put it's Global workspace + + align:start position:0% +view was first put it's Global workspace + + + align:start position:0% +view was first put it's Global workspace +Theory Christ was controlled by Bernard + + align:start position:0% +Theory Christ was controlled by Bernard + + + align:start position:0% +Theory Christ was controlled by Bernard +bars and then some simulation nice + + align:start position:0% +bars and then some simulation nice + + + align:start position:0% +bars and then some simulation nice +simulation work was done by + + align:start position:0% +simulation work was done by + + + align:start position:0% +simulation work was done by +Dan and at some point D Den jumped on + + align:start position:0% +Dan and at some point D Den jumped on + + + align:start position:0% +Dan and at some point D Den jumped on +the bandwagon with his idea of + + align:start position:0% +the bandwagon with his idea of + + + align:start position:0% +the bandwagon with his idea of +Consciousness as Fame in the brain that + + align:start position:0% +Consciousness as Fame in the brain that + + + align:start position:0% +Consciousness as Fame in the brain that +is what it is for a representation in + + align:start position:0% +is what it is for a representation in + + + align:start position:0% +is what it is for a representation in +the brain to be Consciousness to be + + align:start position:0% +the brain to be Consciousness to be + + + align:start position:0% +the brain to be Consciousness to be +famous with respect to other + + align:start position:0% +famous with respect to other + + + align:start position:0% +famous with respect to other +representations so this is a picture + + align:start position:0% +representations so this is a picture + + + align:start position:0% +representations so this is a picture +from some paper by the hung and the idea + + align:start position:0% +from some paper by the hung and the idea + + + align:start position:0% +from some paper by the hung and the idea +is this the the so the outer ring here + + align:start position:0% +is this the the so the outer ring here + + + align:start position:0% +is this the the so the outer ring here +here is the sensory + + align:start position:0% +here is the sensory + + + align:start position:0% +here is the sensory +periphery the inner part is frontal + + align:start position:0% +periphery the inner part is frontal + + + align:start position:0% +periphery the inner part is frontal +based thought + + align:start position:0% +based thought + + + align:start position:0% +based thought +networks and Rings going in are get more + + align:start position:0% +networks and Rings going in are get more + + + align:start position:0% +networks and Rings going in are get more +and more + + align:start position:0% +and more + + + align:start position:0% +and more +Central each circle each one of these + + align:start position:0% +Central each circle each one of these + + + align:start position:0% +Central each circle each one of these +little circles is a neural processor + + align:start position:0% +little circles is a neural processor + + + align:start position:0% +little circles is a neural processor +which doesn't mean a neuron but it means + + align:start position:0% +which doesn't mean a neuron but it means + + + align:start position:0% +which doesn't mean a neuron but it means +some um collection of neurons some some + + align:start position:0% +some um collection of neurons some some + + + align:start position:0% +some um collection of neurons some some +something that does a processing job the + + align:start position:0% +something that does a processing job the + + + align:start position:0% +something that does a processing job the +uh gray ones are inactive the black ones + + align:start position:0% +uh gray ones are inactive the black ones + + + align:start position:0% +uh gray ones are inactive the black ones +are active and the lines show the the + + align:start position:0% +are active and the lines show the the + + + align:start position:0% +are active and the lines show the the +connection so the idea is of this model + + align:start position:0% +connection so the idea is of this model + + + align:start position:0% +connection so the idea is of this model +is that you have sensory stimulations + + align:start position:0% +is that you have sensory stimulations + + + align:start position:0% +is that you have sensory stimulations +that are that are um that pinge on the + + align:start position:0% +that are that are um that pinge on the + + + align:start position:0% +that are that are um that pinge on the +outer um + + align:start position:0% +outer um + + + align:start position:0% +outer um +Circle um sometimes they form little + + align:start position:0% +Circle um sometimes they form little + + + align:start position:0% +Circle um sometimes they form little +coalitions little neural networks and + + align:start position:0% +coalitions little neural networks and + + + align:start position:0% +coalitions little neural networks and +that is one of these circles with the + + align:start position:0% +that is one of these circles with the + + + align:start position:0% +that is one of these circles with the +but some kind of reverberating signal in + + align:start position:0% +but some kind of reverberating signal in + + + align:start position:0% +but some kind of reverberating signal in +them and sometimes those those little + + align:start position:0% +them and sometimes those those little + + + align:start position:0% +them and sometimes those those little +networks actually trigger an internal + + align:start position:0% +networks actually trigger an internal + + + align:start position:0% +networks actually trigger an internal +Network which then um um feeds back to + + align:start position:0% +Network which then um um feeds back to + + + align:start position:0% +Network which then um um feeds back to +the peripheral Network and the idea is + + align:start position:0% +the peripheral Network and the idea is + + + align:start position:0% +the peripheral Network and the idea is +that these uh the these um um uh when + + align:start position:0% +that these uh the these um um uh when + + + align:start position:0% +that these uh the these um um uh when +that when that happens then you have a + + align:start position:0% +that when that happens then you have a + + + align:start position:0% +that when that happens then you have a +workspace activation in which the + + align:start position:0% +workspace activation in which the + + + align:start position:0% +workspace activation in which the +sensory activation is made available to + + align:start position:0% +sensory activation is made available to + + + align:start position:0% +sensory activation is made available to +all consuming systems in the brain at + + align:start position:0% +all consuming systems in the brain at + + + align:start position:0% +all consuming systems in the brain at +once and that underlies the idea we have + + align:start position:0% +once and that underlies the idea we have + + + align:start position:0% +once and that underlies the idea we have +that when we have a conscious + + align:start position:0% +that when we have a conscious + + + align:start position:0% +that when we have a conscious +experience um uh it can be used by our + + align:start position:0% +experience um uh it can be used by our + + + align:start position:0% +experience um uh it can be used by our +planning our reporting um our memory um + + align:start position:0% +planning our reporting um our memory um + + + align:start position:0% +planning our reporting um our memory um +um our decision making um a whole lot of + + align:start position:0% +um our decision making um a whole lot of + + + align:start position:0% +um our decision making um a whole lot of +you know what sometimes called consuming + + align:start position:0% +you know what sometimes called consuming + + + align:start position:0% +you know what sometimes called consuming +systems in the brain and the idea is + + align:start position:0% +systems in the brain and the idea is + + + align:start position:0% +systems in the brain and the idea is +that what it is for a representation to + + align:start position:0% +that what it is for a representation to + + + align:start position:0% +that what it is for a representation to +be a conscious representation is simply + + align:start position:0% +be a conscious representation is simply + + + align:start position:0% +be a conscious representation is simply +to be globally broadcast in that way so + + align:start position:0% +to be globally broadcast in that way so + + + align:start position:0% +to be globally broadcast in that way so +that's the global broadcasting account + + align:start position:0% +that's the global broadcasting account + + + align:start position:0% +that's the global broadcasting account +um the third of the three is what one + + align:start position:0% +um the third of the three is what one + + + align:start position:0% +um the third of the three is what one +might think of the as the biological + + align:start position:0% +might think of the as the biological + + + align:start position:0% +might think of the as the biological +theory that is the Consciousness is some + + align:start position:0% +theory that is the Consciousness is some + + + align:start position:0% +theory that is the Consciousness is some +kind of neural State these are some um + + align:start position:0% +kind of neural State these are some um + + + align:start position:0% +kind of neural State these are some um +historical figures and philosophy but + + align:start position:0% +historical figures and philosophy but + + + align:start position:0% +historical figures and philosophy but +the the view is I think first really + + align:start position:0% +the the view is I think first really + + + align:start position:0% +the the view is I think first really +made um um um um uh into a viable + + align:start position:0% +made um um um um uh into a viable + + + align:start position:0% +made um um um um uh into a viable +program + + align:start position:0% +program + + + align:start position:0% +program +by Francis Crick and Kristoff and + + align:start position:0% +by Francis Crick and Kristoff and + + + align:start position:0% +by Francis Crick and Kristoff and +um it's a little hard to I think at + + align:start position:0% +um it's a little hard to I think at + + + align:start position:0% +um it's a little hard to I think at +first to quite see the difference + + align:start position:0% +first to quite see the difference + + + align:start position:0% +first to quite see the difference +between this and the global broadcasting + + align:start position:0% +between this and the global broadcasting + + + align:start position:0% +between this and the global broadcasting +view but I'll say a bit more about what + + align:start position:0% +view but I'll say a bit more about what + + + align:start position:0% +view but I'll say a bit more about what +the difference is so this is a monkey + + align:start position:0% +the difference is so this is a monkey + + + align:start position:0% +the difference is so this is a monkey +brain this is just a sort of fix + + align:start position:0% +brain this is just a sort of fix + + + align:start position:0% +brain this is just a sort of fix +ideas um this is a little slice out of + + align:start position:0% +ideas um this is a little slice out of + + + align:start position:0% +ideas um this is a little slice out of +the visual cortex so the idea is we can + + align:start position:0% +the visual cortex so the idea is we can + + + align:start position:0% +the visual cortex so the idea is we can +think of the content of the visual + + align:start position:0% +think of the content of the visual + + + align:start position:0% +think of the content of the visual +experience of motion as maybe this is + + align:start position:0% +experience of motion as maybe this is + + + align:start position:0% +experience of motion as maybe this is +just like a guess illustration has some + + align:start position:0% +just like a guess illustration has some + + + align:start position:0% +just like a guess illustration has some +kind of a recurrent Loop between this + + align:start position:0% +kind of a recurrent Loop between this + + + align:start position:0% +kind of a recurrent Loop between this +area V5 and V1 the idea is you got + + align:start position:0% +area V5 and V1 the idea is you got + + + align:start position:0% +area V5 and V1 the idea is you got +signals going back and forth between V5 + + align:start position:0% +signals going back and forth between V5 + + + align:start position:0% +signals going back and forth between V5 +and V1 and that's what creates the + + align:start position:0% +and V1 and that's what creates the + + + align:start position:0% +and V1 and that's what creates the +content of an experience of + + align:start position:0% +content of an experience of + + + align:start position:0% +content of an experience of +motion but I'm this VI there's a + + align:start position:0% +motion but I'm this VI there's a + + + align:start position:0% +motion but I'm this VI there's a +difference between that content and what + + align:start position:0% +difference between that content and what + + + align:start position:0% +difference between that content and what +makes that content + + align:start position:0% +makes that content + + + align:start position:0% +makes that content +conscious um so here are some things + + align:start position:0% +conscious um so here are some things + + + align:start position:0% +conscious um so here are some things +that have been proposed as to what makes + + align:start position:0% +that have been proposed as to what makes + + + align:start position:0% +that have been proposed as to what makes +that content + + align:start position:0% +that content + + + align:start position:0% +that content +um High activation the loop the + + align:start position:0% +um High activation the loop the + + + align:start position:0% +um High activation the loop the +corticothalamic loop from the CeX down + + align:start position:0% +corticothalamic loop from the CeX down + + + align:start position:0% +corticothalamic loop from the CeX down +to the thalamus in the middle of the + + align:start position:0% +to the thalamus in the middle of the + + + align:start position:0% +to the thalamus in the middle of the +brain maybe a special kind of + + align:start position:0% +brain maybe a special kind of + + + align:start position:0% +brain maybe a special kind of +computation as for example suggested by + + align:start position:0% +computation as for example suggested by + + + align:start position:0% +computation as for example suggested by +Julio tanon although he thinks it's a + + align:start position:0% +Julio tanon although he thinks it's a + + + align:start position:0% +Julio tanon although he thinks it's a +standalone account another possibility + + align:start position:0% +standalone account another possibility + + + align:start position:0% +standalone account another possibility +suggested by a number of people is that + + align:start position:0% +suggested by a number of people is that + + + align:start position:0% +suggested by a number of people is that +there are certain self oriented circuits + + align:start position:0% +there are certain self oriented circuits + + + align:start position:0% +there are certain self oriented circuits +that have to be activated + + align:start position:0% +that have to be activated + + + align:start position:0% +that have to be activated +so the critical question which I'm not + + align:start position:0% +so the critical question which I'm not + + + align:start position:0% +so the critical question which I'm not +going to be able to go into uh today is + + align:start position:0% +going to be able to go into uh today is + + + align:start position:0% +going to be able to go into uh today is +um what really what the difference is + + align:start position:0% +um what really what the difference is + + + align:start position:0% +um what really what the difference is +between this and the global workspace + + align:start position:0% +between this and the global workspace + + + align:start position:0% +between this and the global workspace +kind what I'm really going to be mainly + + align:start position:0% +kind what I'm really going to be mainly + + + align:start position:0% +kind what I'm really going to be mainly +talking about is the first order versus + + align:start position:0% +talking about is the first order versus + + + align:start position:0% +talking about is the first order versus +higher order where both the biological + + align:start position:0% +higher order where both the biological + + + align:start position:0% +higher order where both the biological +and the global workspace account Origins + + align:start position:0% +and the global workspace account Origins + + + align:start position:0% +and the global workspace account Origins +are first order and the higher order + + align:start position:0% +are first order and the higher order + + + align:start position:0% +are first order and the higher order +account different kind of theory but + + align:start position:0% +account different kind of theory but + + + align:start position:0% +account different kind of theory but +I'll say just very briefly that if you + + align:start position:0% +I'll say just very briefly that if you + + + align:start position:0% +I'll say just very briefly that if you +hold this kind of a theory you have room + + align:start position:0% +hold this kind of a theory you have room + + + align:start position:0% +hold this kind of a theory you have room +for um a conscious experience that + + align:start position:0% +for um a conscious experience that + + + align:start position:0% +for um a conscious experience that +involves activation in the back of the + + align:start position:0% +involves activation in the back of the + + + align:start position:0% +involves activation in the back of the +bra + + align:start position:0% +bra + + + align:start position:0% +bra +that that where where those contents are + + align:start position:0% +that that where where those contents are + + + align:start position:0% +that that where where those contents are +conscious because of one of these things + + align:start position:0% +conscious because of one of these things + + + align:start position:0% +conscious because of one of these things +even though you don't have Global + + align:start position:0% +even though you don't have Global + + + align:start position:0% +even though you don't have Global +broadcasting in the front of the head so + + align:start position:0% +broadcasting in the front of the head so + + + align:start position:0% +broadcasting in the front of the head so +that's probably the clearest way to see + + align:start position:0% +that's probably the clearest way to see + + + align:start position:0% +that's probably the clearest way to see +how there might be a difference between + + align:start position:0% +how there might be a difference between + + + align:start position:0% +how there might be a difference between +these + + align:start position:0% +these + + + align:start position:0% +these +VI um more abstractly the idea is that + + align:start position:0% +VI um more abstractly the idea is that + + + align:start position:0% +VI um more abstractly the idea is that +this view allows that um um uh conscious + + align:start position:0% +this view allows that um um uh conscious + + + align:start position:0% +this view allows that um um uh conscious +experiences a certain kind of brain + + align:start position:0% +experiences a certain kind of brain + + + align:start position:0% +experiences a certain kind of brain +activation that um um uh has to be + + align:start position:0% +activation that um um uh has to be + + + align:start position:0% +activation that um um uh has to be +described at a lower level the global + + align:start position:0% +described at a lower level the global + + + align:start position:0% +described at a lower level the global +workspace account is something that in + + align:start position:0% +workspace account is something that in + + + align:start position:0% +workspace account is something that in +its usual forms Works equally well on a + + align:start position:0% +its usual forms Works equally well on a + + + align:start position:0% +its usual forms Works equally well on a +computer as is in a brain so the global + + align:start position:0% +computer as is in a brain so the global + + + align:start position:0% +computer as is in a brain so the global +workspace account is making a bet as to + + align:start position:0% +workspace account is making a bet as to + + + align:start position:0% +workspace account is making a bet as to +the level of abstractness required to + + align:start position:0% +the level of abstractness required to + + + align:start position:0% +the level of abstractness required to +specify Consciousness the idea is that + + align:start position:0% +specify Consciousness the idea is that + + + align:start position:0% +specify Consciousness the idea is that +the matter doesn't matter um it's what + + align:start position:0% +the matter doesn't matter um it's what + + + align:start position:0% +the matter doesn't matter um it's what +that M it's what those signals do that + + align:start position:0% +that M it's what those signals do that + + + align:start position:0% +that M it's what those signals do that +count in those signals and what those + + align:start position:0% +count in those signals and what those + + + align:start position:0% +count in those signals and what those +signals do can be described and it's + + align:start position:0% +signals do can be described and it's + + + align:start position:0% +signals do can be described and it's +very abst way in terms of a global + + align:start position:0% +very abst way in terms of a global + + + align:start position:0% +very abst way in terms of a global +workspace that could equally well be + + align:start position:0% +workspace that could equally well be + + + align:start position:0% +workspace that could equally well be +implemented in many different things if + + align:start position:0% +implemented in many different things if + + + align:start position:0% +implemented in many different things if +you think that there is a possibility + + align:start position:0% +you think that there is a possibility + + + align:start position:0% +you think that there is a possibility +that something might function um a lot + + align:start position:0% +that something might function um a lot + + + align:start position:0% +that something might function um a lot +like a um um Consciousness functions in + + align:start position:0% +like a um um Consciousness functions in + + + align:start position:0% +like a um um Consciousness functions in +people but that they but but that it + + align:start position:0% +people but that they but but that it + + + align:start position:0% +people but that they but but that it +might be a zombie you know many of you + + align:start position:0% +might be a zombie you know many of you + + + align:start position:0% +might be a zombie you know many of you +may have seen the um old Star Trek movie + + align:start position:0% +may have seen the um old Star Trek movie + + + align:start position:0% +may have seen the um old Star Trek movie +on Commander Data where he's a a robot + + align:start position:0% +on Commander Data where he's a a robot + + + align:start position:0% +on Commander Data where he's a a robot +made who you know just like the person + + align:start position:0% +made who you know just like the person + + + align:start position:0% +made who you know just like the person +and then the issue comes up as to + + align:start position:0% +and then the issue comes up as to + + + align:start position:0% +and then the issue comes up as to +whether he's really conscious or not and + + align:start position:0% +whether he's really conscious or not and + + + align:start position:0% +whether he's really conscious or not and +there's a trial about it so if you find + + align:start position:0% +there's a trial about it so if you find + + + align:start position:0% +there's a trial about it so if you find +that intelligible that it's possible + + align:start position:0% +that intelligible that it's possible + + + align:start position:0% +that intelligible that it's possible +that Commander Data might not actually + + align:start position:0% +that Commander Data might not actually + + + align:start position:0% +that Commander Data might not actually +be having conscious experiences but he + + align:start position:0% +be having conscious experiences but he + + + align:start position:0% +be having conscious experiences but he +might nonetheless have a global + + align:start position:0% +might nonetheless have a global + + + align:start position:0% +might nonetheless have a global +workspace then you are you're seeing a + + align:start position:0% +workspace then you are you're seeing a + + + align:start position:0% +workspace then you are you're seeing a +wedge between the global workspace View + + align:start position:0% +wedge between the global workspace View + + + align:start position:0% +wedge between the global workspace View +and this more grainy view the idea being + + align:start position:0% +and this more grainy view the idea being + + + align:start position:0% +and this more grainy view the idea being +that maybe say for example something + + align:start position:0% +that maybe say for example something + + + align:start position:0% +that maybe say for example something +about the electrochemical nature of the + + align:start position:0% +about the electrochemical nature of the + + + align:start position:0% +about the electrochemical nature of the +way the brain works really is crucial um + + align:start position:0% +way the brain works really is crucial um + + + align:start position:0% +way the brain works really is crucial um +to Consciousness so neurons signal each + + align:start position:0% +to Consciousness so neurons signal each + + + align:start position:0% +to Consciousness so neurons signal each +other via chemicals well what if you + + align:start position:0% +other via chemicals well what if you + + + align:start position:0% +other via chemicals well what if you +just simulate that in the brain is that + + align:start position:0% +just simulate that in the brain is that + + + align:start position:0% +just simulate that in the brain is that +going to be something that is enough for + + align:start position:0% +going to be something that is enough for + + + align:start position:0% +going to be something that is enough for +Consciousness so there is this + + align:start position:0% +Consciousness so there is this + + + align:start position:0% +Consciousness so there is this +difference between the biological + + align:start position:0% +difference between the biological + + + align:start position:0% +difference between the biological +account and the global + + align:start position:0% +account and the global + + + align:start position:0% +account and the global +workspace um but I'm not going to go + + align:start position:0% +workspace um but I'm not going to go + + + align:start position:0% +workspace um but I'm not going to go +into that much um what I'm going to do + + align:start position:0% +into that much um what I'm going to do + + + align:start position:0% +into that much um what I'm going to do +is say a little bit about the the + + align:start position:0% +is say a little bit about the the + + + align:start position:0% +is say a little bit about the the +advantages of these three views and then + + align:start position:0% +advantages of these three views and then + + + align:start position:0% +advantages of these three views and then +um so here are I think the key intuitive + + align:start position:0% +um so here are I think the key intuitive + + + align:start position:0% +um so here are I think the key intuitive +advantages um the global workspace VI I + + align:start position:0% +advantages um the global workspace VI I + + + align:start position:0% +advantages um the global workspace VI I +think this is a little thermometer of + + align:start position:0% +think this is a little thermometer of + + + align:start position:0% +think this is a little thermometer of +intuitiveness um the global workspace + + align:start position:0% +intuitiveness um the global workspace + + + align:start position:0% +intuitiveness um the global workspace +view captures this Common Sense idea + + align:start position:0% +view captures this Common Sense idea + + + align:start position:0% +view captures this Common Sense idea +that a conscious State as I said is one + + align:start position:0% +that a conscious State as I said is one + + + align:start position:0% +that a conscious State as I said is one +that is available to all these consuming + + align:start position:0% +that is available to all these consuming + + + align:start position:0% +that is available to all these consuming +system once that's kind of a intuitive + + align:start position:0% +system once that's kind of a intuitive + + + align:start position:0% +system once that's kind of a intuitive +Advantage the high order view captures + + align:start position:0% +Advantage the high order view captures + + + align:start position:0% +Advantage the high order view captures +this transitivity principle that a + + align:start position:0% +this transitivity principle that a + + + align:start position:0% +this transitivity principle that a +conscious state is a state that one is + + align:start position:0% +conscious state is a state that one is + + + align:start position:0% +conscious state is a state that one is +conscious of being in and that's a very + + align:start position:0% +conscious of being in and that's a very + + + align:start position:0% +conscious of being in and that's a very +intuitive principle and so I think + + align:start position:0% +intuitive principle and so I think + + + align:start position:0% +intuitive principle and so I think +that's a plus for the higher order view + + align:start position:0% +that's a plus for the higher order view + + + align:start position:0% +that's a plus for the higher order view +the biological view I think is the least + + align:start position:0% +the biological view I think is the least + + + align:start position:0% +the biological view I think is the least +immediately plausible of and that + + align:start position:0% +immediately plausible of and that + + + align:start position:0% +immediately plausible of and that +assuming allows you to see a difference + + align:start position:0% +assuming allows you to see a difference + + + align:start position:0% +assuming allows you to see a difference +between it and the global work space you + + align:start position:0% +between it and the global work space you + + + align:start position:0% +between it and the global work space you +but I think its intuitive plausibility + + align:start position:0% +but I think its intuitive plausibility + + + align:start position:0% +but I think its intuitive plausibility +is a little more subtle + + align:start position:0% +is a little more subtle + + + align:start position:0% +is a little more subtle +um often people have the + + align:start position:0% +um often people have the + + + align:start position:0% +um often people have the +sense that there's more in their + + align:start position:0% +sense that there's more in their + + + align:start position:0% +sense that there's more in their +conscious experience than they can + + align:start position:0% +conscious experience than they can + + + align:start position:0% +conscious experience than they can +cognize so you look around the room you + + align:start position:0% +cognize so you look around the room you + + + align:start position:0% +cognize so you look around the room you +see this Rich array of colors and + + align:start position:0% +see this Rich array of colors and + + + align:start position:0% +see this Rich array of colors and +textures and shapes and you know before + + align:start position:0% +textures and shapes and you know before + + + align:start position:0% +textures and shapes and you know before +you know it most of it is gone and it + + align:start position:0% +you know it most of it is gone and it + + + align:start position:0% +you know it most of it is gone and it +doesn't seem possible to capture that in + + align:start position:0% +doesn't seem possible to capture that in + + + align:start position:0% +doesn't seem possible to capture that in +any kind of cognition so that sense that + + align:start position:0% +any kind of cognition so that sense that + + + align:start position:0% +any kind of cognition so that sense that +not everybody has but a lot of people + + align:start position:0% +not everybody has but a lot of people + + + align:start position:0% +not everybody has but a lot of people +have um is that there's something + + align:start position:0% +have um is that there's something + + + align:start position:0% +have um is that there's something +elusive about the character of conscious + + align:start position:0% +elusive about the character of conscious + + + align:start position:0% +elusive about the character of conscious +experience um that can all be captured + + align:start position:0% +experience um that can all be captured + + + align:start position:0% +experience um that can all be captured +in thought that elusiveness is a plus + + align:start position:0% +in thought that elusiveness is a plus + + + align:start position:0% +in thought that elusiveness is a plus +for the biological Theory because the + + align:start position:0% +for the biological Theory because the + + + align:start position:0% +for the biological Theory because the +idea is that um the um uh there's more + + align:start position:0% +idea is that um the um uh there's more + + + align:start position:0% +idea is that um the um uh there's more +both more both finer grain and more um + + align:start position:0% +both more both finer grain and more um + + + align:start position:0% +both more both finer grain and more um +uh capactive in the in the phenomenology + + align:start position:0% +uh capactive in the in the phenomenology + + + align:start position:0% +uh capactive in the in the phenomenology +of perception is that gets into that is + + align:start position:0% +of perception is that gets into that is + + + align:start position:0% +of perception is that gets into that is +categorizable in this Global workspace + + align:start position:0% +categorizable in this Global workspace + + + align:start position:0% +categorizable in this Global workspace +or that can be thought about in terms of + + align:start position:0% +or that can be thought about in terms of + + + align:start position:0% +or that can be thought about in terms of +high thought so those are just now it's + + align:start position:0% +high thought so those are just now it's + + + align:start position:0% +high thought so those are just now it's +important of course that these intuitive + + align:start position:0% +important of course that these intuitive + + + align:start position:0% +important of course that these intuitive +advantages aren't just the beginning + + align:start position:0% +advantages aren't just the beginning + + + align:start position:0% +advantages aren't just the beginning +right it might motivate you to to push + + align:start position:0% +right it might motivate you to to push + + + align:start position:0% +right it might motivate you to to push +for one rather than another but that + + align:start position:0% +for one rather than another but that + + + align:start position:0% +for one rather than another but that +shouldn't be what decides it after all + + align:start position:0% +shouldn't be what decides it after all + + + align:start position:0% +shouldn't be what decides it after all +it should you should think it's an + + align:start position:0% +it should you should think it's an + + + align:start position:0% +it should you should think it's an +empirical issue what the Right theory of + + align:start position:0% +empirical issue what the Right theory of + + + align:start position:0% +empirical issue what the Right theory of +Consciousness is so I'm an advocate of + + align:start position:0% +Consciousness is so I'm an advocate of + + + align:start position:0% +Consciousness is so I'm an advocate of +this bottom Theory despite it's I think + + align:start position:0% +this bottom Theory despite it's I think + + + align:start position:0% +this bottom Theory despite it's I think +uh scoring a bit lower on the immediate + + align:start position:0% +uh scoring a bit lower on the immediate + + + align:start position:0% +uh scoring a bit lower on the immediate +um uh uh intuitive Advantage scale so + + align:start position:0% +um uh uh intuitive Advantage scale so + + + align:start position:0% +um uh uh intuitive Advantage scale so +according to to + + align:start position:0% +according to to + + + align:start position:0% +according to to +me um the the global broadcasting and + + align:start position:0% +me um the the global broadcasting and + + + align:start position:0% +me um the the global broadcasting and +the formation of a higher order state is + + align:start position:0% +the formation of a higher order state is + + + align:start position:0% +the formation of a higher order state is +something that Consciousness does rather + + align:start position:0% +something that Consciousness does rather + + + align:start position:0% +something that Consciousness does rather +than what Consciousness is so I think + + align:start position:0% +than what Consciousness is so I think + + + align:start position:0% +than what Consciousness is so I think +that higher order views are too + + align:start position:0% +that higher order views are too + + + align:start position:0% +that higher order views are too +intellectual they require too much in + + align:start position:0% +intellectual they require too much in + + + align:start position:0% +intellectual they require too much in +the way of of uh intellectual activity + + align:start position:0% +the way of of uh intellectual activity + + + align:start position:0% +the way of of uh intellectual activity +that Consciousness is something + + align:start position:0% +that Consciousness is something + + + align:start position:0% +that Consciousness is something +simpler important thing to remember in + + align:start position:0% +simpler important thing to remember in + + + align:start position:0% +simpler important thing to remember in +this debate is that the uh biological + + align:start position:0% +this debate is that the uh biological + + + align:start position:0% +this debate is that the uh biological +and Global broadcasting views can + + align:start position:0% +and Global broadcasting views can + + + align:start position:0% +and Global broadcasting views can +recognize a kind of Consciousness a + + align:start position:0% +recognize a kind of Consciousness a + + + align:start position:0% +recognize a kind of Consciousness a +higher order thought Consciousness that + + align:start position:0% +higher order thought Consciousness that + + + align:start position:0% +higher order thought Consciousness that +is distinct from the primary phenomenal + + align:start position:0% +is distinct from the primary phenomenal + + + align:start position:0% +is distinct from the primary phenomenal +Consciousness that they're about and + + align:start position:0% +Consciousness that they're about and + + + align:start position:0% +Consciousness that they're about and +then the idea is that they can they can + + align:start position:0% +then the idea is that they can they can + + + align:start position:0% +then the idea is that they can they can +allow for top down effects of that high + + align:start position:0% +allow for top down effects of that high + + + align:start position:0% +allow for top down effects of that high +order state and those things and that + + align:start position:0% +order state and those things and that + + + align:start position:0% +order state and those things and that +can satisfy some of the advantages that + + align:start position:0% +can satisfy some of the advantages that + + + align:start position:0% +can satisfy some of the advantages that +the higher order people like to talk + + align:start position:0% +the higher order people like to talk + + + align:start position:0% +the higher order people like to talk +about like the idea that knowing about + + align:start position:0% +about like the idea that knowing about + + + align:start position:0% +about like the idea that knowing about +your your wine can make it taste + + align:start position:0% +your your wine can make it taste + + + align:start position:0% +your your wine can make it taste +different if you can have these top- + + align:start position:0% +different if you can have these top- + + + align:start position:0% +different if you can have these top- +down + + align:start position:0% +down + + + align:start position:0% +down +effects um then on any of the three + + align:start position:0% +effects um then on any of the three + + + align:start position:0% +effects um then on any of the three +views you can explain how learning what + + align:start position:0% +views you can explain how learning what + + + align:start position:0% +views you can explain how learning what +Tenon is in one can change the actual + + align:start position:0% +Tenon is in one can change the actual + + + align:start position:0% +Tenon is in one can change the actual +taste experience so um + + align:start position:0% +taste experience so um + + + align:start position:0% +taste experience so um +um the um uh so the the uh the high + + align:start position:0% +um the um uh so the the uh the high + + + align:start position:0% +um the um uh so the the uh the high +order thought view doesn't have a a um a + + align:start position:0% +order thought view doesn't have a a um a + + + align:start position:0% +order thought view doesn't have a a um a +lock on that on that point because the + + align:start position:0% +lock on that on that point because the + + + align:start position:0% +lock on that on that point because the +other views can reog ASE a special + + align:start position:0% +other views can reog ASE a special + + + align:start position:0% +other views can reog ASE a special +additional kind of + + align:start position:0% +additional kind of + + + align:start position:0% +additional kind of +Consciousness + + align:start position:0% +Consciousness + + + align:start position:0% +Consciousness +um so um The Challenge to the higher + + align:start position:0% +um so um The Challenge to the higher + + + align:start position:0% +um so um The Challenge to the higher +order view would be to find additional + + align:start position:0% +order view would be to find additional + + + align:start position:0% +order view would be to find additional +um empirical points in favor of the view + + align:start position:0% +um empirical points in favor of the view + + + align:start position:0% +um empirical points in favor of the view +so for now what I'll do is move to the + + align:start position:0% +so for now what I'll do is move to the + + + align:start position:0% +so for now what I'll do is move to the +explanatory Gap um so what is the + + align:start position:0% +explanatory Gap um so what is the + + + align:start position:0% +explanatory Gap um so what is the +explanatory Gap so there is this + + align:start position:0% +explanatory Gap so there is this + + + align:start position:0% +explanatory Gap so there is this +question that we can ask which is what + + align:start position:0% +question that we can ask which is what + + + align:start position:0% +question that we can ask which is what +suppose here I'm looking at a blue thing + + align:start position:0% +suppose here I'm looking at a blue thing + + + align:start position:0% +suppose here I'm looking at a blue thing +and I have a you know experience of + + align:start position:0% +and I have a you know experience of + + + align:start position:0% +and I have a you know experience of +something that's blue so the question + + align:start position:0% +something that's blue so the question + + + align:start position:0% +something that's blue so the question +arises why is that um the neural basis + + align:start position:0% +arises why is that um the neural basis + + + align:start position:0% +arises why is that um the neural basis +of that experience the neural basis of + + align:start position:0% +of that experience the neural basis of + + + align:start position:0% +of that experience the neural basis of +that experience rather than some other + + align:start position:0% +that experience rather than some other + + + align:start position:0% +that experience rather than some other +experience or none at + + align:start position:0% +experience or none at + + + align:start position:0% +experience or none at +all okay so it's a puzzling question how + + align:start position:0% +all okay so it's a puzzling question how + + + align:start position:0% +all okay so it's a puzzling question how +do we going explain that that what's the + + align:start position:0% +do we going explain that that what's the + + + align:start position:0% +do we going explain that that what's the +explanatory I answer that and uh many + + align:start position:0% +explanatory I answer that and uh many + + + align:start position:0% +explanatory I answer that and uh many +people feel that that is a genuine + + align:start position:0% +people feel that that is a genuine + + + align:start position:0% +people feel that that is a genuine +question um and that it's a deep problem + + align:start position:0% +question um and that it's a deep problem + + + align:start position:0% +question um and that it's a deep problem +because not only can no one think of an + + align:start position:0% +because not only can no one think of an + + + align:start position:0% +because not only can no one think of an +actual solution but no one can think of + + align:start position:0% +actual solution but no one can think of + + + align:start position:0% +actual solution but no one can think of +even a hypothetical solution and uh my + + align:start position:0% +even a hypothetical solution and uh my + + + align:start position:0% +even a hypothetical solution and uh my +colleague um Tom Nagel has uh put this + + align:start position:0% +colleague um Tom Nagel has uh put this + + + align:start position:0% +colleague um Tom Nagel has uh put this +in the following way um which is the + + align:start position:0% +in the following way um which is the + + + align:start position:0% +in the following way um which is the +experience is subjective the brain is + + align:start position:0% +experience is subjective the brain is + + + align:start position:0% +experience is subjective the brain is +state is objective and it seems puzzling + + align:start position:0% +state is objective and it seems puzzling + + + align:start position:0% +state is objective and it seems puzzling +that something subjective could be + + align:start position:0% +that something subjective could be + + + align:start position:0% +that something subjective could be +something object and that there seems + + align:start position:0% +something object and that there seems + + + align:start position:0% +something object and that there seems +some need for some kind of account of + + align:start position:0% +some need for some kind of account of + + + align:start position:0% +some need for some kind of account of +how that could be + + align:start position:0% +how that could be + + + align:start position:0% +how that could be +true um so there's there a big issue + + align:start position:0% +true um so there's there a big issue + + + align:start position:0% +true um so there's there a big issue +there that philosophers have written a + + align:start position:0% +there that philosophers have written a + + + align:start position:0% +there that philosophers have written a +lot about but there does seem something + + align:start position:0% +lot about but there does seem something + + + align:start position:0% +lot about but there does seem something +genuinely puzzling there um now if you + + align:start position:0% +genuinely puzzling there um now if you + + + align:start position:0% +genuinely puzzling there um now if you +think that there is there well first of + + align:start position:0% +think that there is there well first of + + + align:start position:0% +think that there is there well first of +all let me say that I think it just + + align:start position:0% +all let me say that I think it just + + + align:start position:0% +all let me say that I think it just +should be undeniable that there seems to + + align:start position:0% +should be undeniable that there seems to + + + align:start position:0% +should be undeniable that there seems to +be a deep Prof here maybe that deep + + align:start position:0% +be a deep Prof here maybe that deep + + + align:start position:0% +be a deep Prof here maybe that deep +problem is some kind of a confusion but + + align:start position:0% +problem is some kind of a confusion but + + + align:start position:0% +problem is some kind of a confusion but +at least there seems to be a deep + + align:start position:0% +at least there seems to be a deep + + + align:start position:0% +at least there seems to be a deep +problem so there has to be some response + + align:start position:0% +problem so there has to be some response + + + align:start position:0% +problem so there has to be some response +to another part + + align:start position:0% +to another part + + + align:start position:0% +to another part +theories so I think there really is a + + align:start position:0% +theories so I think there really is a + + + align:start position:0% +theories so I think there really is a +deep problem here um and I think a + + align:start position:0% +deep problem here um and I think a + + + align:start position:0% +deep problem here um and I think a +problem with the global workspace and + + align:start position:0% +problem with the global workspace and + + + align:start position:0% +problem with the global workspace and +higher order accounts is it's a little + + align:start position:0% +higher order accounts is it's a little + + + align:start position:0% +higher order accounts is it's a little +hard to see on those accounts how they + + align:start position:0% +hard to see on those accounts how they + + + align:start position:0% +hard to see on those accounts how they +can acknowledge the problem so the + + align:start position:0% +can acknowledge the problem so the + + + align:start position:0% +can acknowledge the problem so the +global workspace has an has an answer + + align:start position:0% +global workspace has an has an answer + + + align:start position:0% +global workspace has an has an answer +the experience of blue is phenomenally + + align:start position:0% +the experience of blue is phenomenally + + + align:start position:0% +the experience of blue is phenomenally +conscious if and only if it is globally + + align:start position:0% +conscious if and only if it is globally + + + align:start position:0% +conscious if and only if it is globally +broadcast that's all that Neuroscience + + align:start position:0% +broadcast that's all that Neuroscience + + + align:start position:0% +broadcast that's all that Neuroscience +can explain how it's globally broadcast + + align:start position:0% +can explain how it's globally broadcast + + + align:start position:0% +can explain how it's globally broadcast +but that doesn't seem to acknowledge the + + align:start position:0% +but that doesn't seem to acknowledge the + + + align:start position:0% +but that doesn't seem to acknowledge the +Deep problem um and the higher order + + align:start position:0% +Deep problem um and the higher order + + + align:start position:0% +Deep problem um and the higher order +account is there's a I'll get to the + + align:start position:0% +account is there's a I'll get to the + + + align:start position:0% +account is there's a I'll get to the +special kind of causation of a higher + + align:start position:0% +special kind of causation of a higher + + + align:start position:0% +special kind of causation of a higher +order thought about the experience and + + align:start position:0% +order thought about the experience and + + + align:start position:0% +order thought about the experience and +again there's nothing more for + + align:start position:0% +again there's nothing more for + + + align:start position:0% +again there's nothing more for +Neuroscience to explain um so there's a + + align:start position:0% +Neuroscience to explain um so there's a + + + align:start position:0% +Neuroscience to explain um so there's a +short argument + + align:start position:0% +short argument + + + align:start position:0% +short argument +against those two views which is only + + align:start position:0% +against those two views which is only + + + align:start position:0% +against those two views which is only +the biological view can recognize the + + align:start position:0% +the biological view can recognize the + + + align:start position:0% +the biological view can recognize the +depth of the explanatory Gap so it's + + align:start position:0% +depth of the explanatory Gap so it's + + + align:start position:0% +depth of the explanatory Gap so it's +it's better + + align:start position:0% +it's better + + + align:start position:0% +it's better +view + + align:start position:0% +view + + + align:start position:0% +view +um the another way to put it is David + + align:start position:0% +um the another way to put it is David + + + align:start position:0% +um the another way to put it is David +chers has made the distinction between + + align:start position:0% +chers has made the distinction between + + + align:start position:0% +chers has made the distinction between +the hard problem of Consciousness which + + align:start position:0% +the hard problem of Consciousness which + + + align:start position:0% +the hard problem of Consciousness which +is the explanatory Gap solving closing + + align:start position:0% +is the explanatory Gap solving closing + + + align:start position:0% +is the explanatory Gap solving closing +the problem of closing it he's + + align:start position:0% +the problem of closing it he's + + + align:start position:0% +the problem of closing it he's +distinguish between that and easy + + align:start position:0% +distinguish between that and easy + + + align:start position:0% +distinguish between that and easy +problems having to do with the function + + align:start position:0% +problems having to do with the function + + + align:start position:0% +problems having to do with the function +of + + align:start position:0% +of + + + align:start position:0% +of +and the problem for the global workspace + + align:start position:0% +and the problem for the global workspace + + + align:start position:0% +and the problem for the global workspace +and the higher order account is that + + align:start position:0% +and the higher order account is that + + + align:start position:0% +and the higher order account is that +both try to reduce the hard problem to + + align:start position:0% +both try to reduce the hard problem to + + + align:start position:0% +both try to reduce the hard problem to +the easy problems so the idea is that um + + align:start position:0% +the easy problems so the idea is that um + + + align:start position:0% +the easy problems so the idea is that um +explaining Global broadcasting is an + + align:start position:0% +explaining Global broadcasting is an + + + align:start position:0% +explaining Global broadcasting is an +easy problem not that it's really easy + + align:start position:0% +easy problem not that it's really easy + + + align:start position:0% +easy problem not that it's really easy +but it's not as hard as the hard problem + + align:start position:0% +but it's not as hard as the hard problem + + + align:start position:0% +but it's not as hard as the hard problem +um and causation the way an experience + + align:start position:0% +um and causation the way an experience + + + align:start position:0% +um and causation the way an experience +causes a higher order thought about it + + align:start position:0% +causes a higher order thought about it + + + align:start position:0% +causes a higher order thought about it +that um again is a problem about the + + align:start position:0% +that um again is a problem about the + + + align:start position:0% +that um again is a problem about the +function of Consciousness how it has + + align:start position:0% +function of Consciousness how it has + + + align:start position:0% +function of Consciousness how it has +effects + + align:start position:0% +effects + + + align:start position:0% +effects +um and that's another easy problem so + + align:start position:0% +um and that's another easy problem so + + + align:start position:0% +um and that's another easy problem so +both the global workspace and the higher + + align:start position:0% +both the global workspace and the higher + + + align:start position:0% +both the global workspace and the higher +order reduce the hard + + align:start position:0% + + + + align:start position:0% + +problem um let me say by the way that um + + align:start position:0% +problem um let me say by the way that um + + + align:start position:0% +problem um let me say by the way that um +if you have questions you know or + + align:start position:0% +if you have questions you know or + + + align:start position:0% +if you have questions you know or +comments you should feel free to ask + + align:start position:0% +comments you should feel free to ask + + + align:start position:0% +comments you should feel free to ask +that how do you usually do + + align:start position:0% + + + + align:start position:0% + +this terminology + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +what thank you + + align:start position:0% +what thank you + + + align:start position:0% +what thank you +for um okay so um here so I will so look + + align:start position:0% +for um okay so um here so I will so look + + + align:start position:0% +for um okay so um here so I will so look +there's always a decision is to that of + + align:start position:0% +there's always a decision is to that of + + + align:start position:0% +there's always a decision is to that of +course isn't like what in the world + + align:start position:0% +course isn't like what in the world + + + align:start position:0% +course isn't like what in the world +that's supposed to mean it's not like a + + align:start position:0% +that's supposed to mean it's not like a + + + align:start position:0% +that's supposed to mean it's not like a +minor issue um but there's the question + + align:start position:0% +minor issue um but there's the question + + + align:start position:0% +minor issue um but there's the question +of when when SCH so I will'll get to it + + align:start position:0% +of when when SCH so I will'll get to it + + + align:start position:0% +of when when SCH so I will'll get to it +in a minute + + align:start position:0% +in a minute + + + align:start position:0% +in a minute +um okay so um suppose you um so + + align:start position:0% +um okay so um suppose you um so + + + align:start position:0% +um okay so um suppose you um so +according to the high order + + align:start position:0% +according to the high order + + + align:start position:0% +according to the high order +view um what it is for um a + + align:start position:0% +view um what it is for um a + + + align:start position:0% +view um what it is for um a +um uh state of seeing an apple to be + + align:start position:0% +um uh state of seeing an apple to be + + + align:start position:0% +um uh state of seeing an apple to be +conscious is for a representation of the + + align:start position:0% +conscious is for a representation of the + + + align:start position:0% +conscious is for a representation of the +say redness of the + + align:start position:0% +say redness of the + + + align:start position:0% +say redness of the +Apple um to be accompanied by a thought + + align:start position:0% +Apple um to be accompanied by a thought + + + align:start position:0% +Apple um to be accompanied by a thought +to the effect that you're seeing in + + align:start position:0% +to the effect that you're seeing in + + + align:start position:0% +to the effect that you're seeing in +example and that this has the aboutness + + align:start position:0% +example and that this has the aboutness + + + align:start position:0% +example and that this has the aboutness +relation to + + align:start position:0% +relation to + + + align:start position:0% +relation to +that + + align:start position:0% +that + + + align:start position:0% +that +um so on the higher order + + align:start position:0% +um so on the higher order + + + align:start position:0% +um so on the higher order +account um all those ingredients can + + align:start position:0% +account um all those ingredients can + + + align:start position:0% +account um all those ingredients can +exist + + align:start position:0% +exist + + + align:start position:0% +exist +unconsciously um and this is a + + align:start position:0% +unconsciously um and this is a + + + align:start position:0% +unconsciously um and this is a +consequence of the higher order view + + align:start position:0% +consequence of the higher order view + + + align:start position:0% +consequence of the higher order view +itself something that high order + + align:start position:0% +itself something that high order + + + align:start position:0% +itself something that high order +theorists often comment on we can have + + align:start position:0% +theorists often comment on we can have + + + align:start position:0% +theorists often comment on we can have +unconscious perceptions representations + + align:start position:0% +unconscious perceptions representations + + + align:start position:0% +unconscious perceptions representations +of a red apple we can have unconscious + + align:start position:0% +of a red apple we can have unconscious + + + align:start position:0% +of a red apple we can have unconscious +thoughts and those unconscious repres + + align:start position:0% +thoughts and those unconscious repres + + + align:start position:0% +thoughts and those unconscious repres +presentations can be about things um so + + align:start position:0% +presentations can be about things um so + + + align:start position:0% +presentations can be about things um so +all those ingredients can exist + + align:start position:0% +all those ingredients can exist + + + align:start position:0% +all those ingredients can exist +unconsciously + + align:start position:0% +unconsciously + + + align:start position:0% +unconsciously +and if you have a neural account that + + align:start position:0% +and if you have a neural account that + + + align:start position:0% +and if you have a neural account that +explains what thought is what aboutness + + align:start position:0% +explains what thought is what aboutness + + + align:start position:0% +explains what thought is what aboutness +is and what what something what it is + + align:start position:0% +is and what what something what it is + + + align:start position:0% +is and what what something what it is +for something to represent red you can + + align:start position:0% +for something to represent red you can + + + align:start position:0% +for something to represent red you can +put those together and you'll get an + + align:start position:0% +put those together and you'll get an + + + align:start position:0% +put those together and you'll get an +account of Consciousness according to + + align:start position:0% +account of Consciousness according to + + + align:start position:0% +account of Consciousness according to +them but nobody thinks that a + + align:start position:0% +them but nobody thinks that a + + + align:start position:0% +them but nobody thinks that a +neuroscience view will predict anything + + align:start position:0% +neuroscience view will predict anything + + + align:start position:0% +neuroscience view will predict anything +you know wowe happening when these three + + align:start position:0% +you know wowe happening when these three + + + align:start position:0% +you know wowe happening when these three +things happen together those are just + + align:start position:0% +things happen together those are just + + + align:start position:0% +things happen together those are just +the ingredients of what Consciousness is + + align:start position:0% +the ingredients of what Consciousness is + + + align:start position:0% +the ingredients of what Consciousness is +and so it's another way of seeing that + + align:start position:0% +and so it's another way of seeing that + + + align:start position:0% +and so it's another way of seeing that +the higher order of you doesn't seem to + + align:start position:0% +the higher order of you doesn't seem to + + + align:start position:0% +the higher order of you doesn't seem to +have anything to say about the + + align:start position:0% +have anything to say about the + + + align:start position:0% +have anything to say about the +explanatory + + align:start position:0% +explanatory + + + align:start position:0% +explanatory +Gap um okay so now I'm going to + + align:start position:0% +Gap um okay so now I'm going to + + + align:start position:0% +Gap um okay so now I'm going to +um things are um turned around here um + + align:start position:0% +um things are um turned around here um + + + align:start position:0% +um things are um turned around here um +but anyway so now I'm going to get to + + align:start position:0% +but anyway so now I'm going to get to + + + align:start position:0% +but anyway so now I'm going to get to +the problem that Alex raised which is + + align:start position:0% +the problem that Alex raised which is + + + align:start position:0% +the problem that Alex raised which is +what this phenomenal Consciousness is + + align:start position:0% +what this phenomenal Consciousness is + + + align:start position:0% +what this phenomenal Consciousness is +and one way to put it is you have these + + align:start position:0% +and one way to put it is you have these + + + align:start position:0% +and one way to put it is you have these +first order and hired reviews but what + + align:start position:0% +first order and hired reviews but what + + + align:start position:0% +first order and hired reviews but what +what exactly is the difference and you + + align:start position:0% +what exactly is the difference and you + + + align:start position:0% +what exactly is the difference and you +see the problem this way which is that + + align:start position:0% +see the problem this way which is that + + + align:start position:0% +see the problem this way which is that +so you have first order so here's me bi + + align:start position:0% +so you have first order so here's me bi + + + align:start position:0% +so you have first order so here's me bi +an exponent of the biological View and + + align:start position:0% +an exponent of the biological View and + + + align:start position:0% +an exponent of the biological View and +stand exponent of + + align:start position:0% +stand exponent of + + + align:start position:0% +stand exponent of +theal workspace View and then there's + + align:start position:0% +theal workspace View and then there's + + + align:start position:0% +theal workspace View and then there's +David Rosen an exponent of the high + + align:start position:0% +David Rosen an exponent of the high + + + align:start position:0% +David Rosen an exponent of the high +order so we say there are two kinds of + + align:start position:0% +order so we say there are two kinds of + + + align:start position:0% +order so we say there are two kinds of +Consciousness phenomenal Consciousness + + align:start position:0% +Consciousness phenomenal Consciousness + + + align:start position:0% +Consciousness phenomenal Consciousness +and reflective consciousness + + align:start position:0% +and reflective consciousness + + + align:start position:0% +and reflective consciousness +he says there's one kind of + + align:start position:0% +he says there's one kind of + + + align:start position:0% +he says there's one kind of +Consciousness that phenomenal + + align:start position:0% +Consciousness that phenomenal + + + align:start position:0% +Consciousness that phenomenal +Consciousness just is refle conscious + + align:start position:0% +Consciousness just is refle conscious + + + align:start position:0% +Consciousness just is refle conscious +but this is a useless way of + + align:start position:0% +but this is a useless way of + + + align:start position:0% +but this is a useless way of +distinguishing between them + + align:start position:0% +distinguishing between them + + + align:start position:0% +distinguishing between them +because + + align:start position:0% +because + + + align:start position:0% +because +what what we the first order theorists + + align:start position:0% +what what we the first order theorists + + + align:start position:0% +what what we the first order theorists +say is phenomenal Consciousness without + + align:start position:0% +say is phenomenal Consciousness without + + + align:start position:0% +say is phenomenal Consciousness without +reflective Consciousness he the higher + + align:start position:0% +reflective Consciousness he the higher + + + align:start position:0% +reflective Consciousness he the higher +order theorist just calls an case of an + + align:start position:0% +order theorist just calls an case of an + + + align:start position:0% +order theorist just calls an case of an +unconscious quality so he allow do two + + align:start position:0% +unconscious quality so he allow do two + + + align:start position:0% +unconscious quality so he allow do two +things too so we say there are two + + align:start position:0% +things too so we say there are two + + + align:start position:0% +things too so we say there are two +things there's phenomenal Consciousness + + align:start position:0% +things there's phenomenal Consciousness + + + align:start position:0% +things there's phenomenal Consciousness +there's reflective Consciousness and in + + align:start position:0% +there's reflective Consciousness and in + + + align:start position:0% +there's reflective Consciousness and in +principle you could have perhaps + + align:start position:0% +principle you could have perhaps + + + align:start position:0% +principle you could have perhaps +phenomenal Consciousness without + + align:start position:0% +phenomenal Consciousness without + + + align:start position:0% +phenomenal Consciousness without +reflective Consciousness he says well + + align:start position:0% +reflective Consciousness he says well + + + align:start position:0% +reflective Consciousness he says well +yeah I believe in those two things it's + + align:start position:0% +yeah I believe in those two things it's + + + align:start position:0% +yeah I believe in those two things it's +just the first that you call phenomenal + + align:start position:0% +just the first that you call phenomenal + + + align:start position:0% +just the first that you call phenomenal +Consciousness I call unconsciousness + + align:start position:0% +Consciousness I call unconsciousness + + + align:start position:0% +Consciousness I call unconsciousness +unconscious representation of a of a + + align:start position:0% +unconscious representation of a of a + + + align:start position:0% +unconscious representation of a of a +quality like you redness so it seems + + align:start position:0% +quality like you redness so it seems + + + align:start position:0% +quality like you redness so it seems +like the views are on a par just + + align:start position:0% +like the views are on a par just + + + align:start position:0% +like the views are on a par just +different how they apply the word + + align:start position:0% +different how they apply the word + + + align:start position:0% +different how they apply the word +conscious so so um how are we going to + + align:start position:0% +conscious so so um how are we going to + + + align:start position:0% +conscious so so um how are we going to +distinguish between those things well + + align:start position:0% +distinguish between those things well + + + align:start position:0% +distinguish between those things well +here's something one might say from the + + align:start position:0% +here's something one might say from the + + + align:start position:0% +here's something one might say from the +first order point of view phenomenal + + align:start position:0% +first order point of view phenomenal + + + align:start position:0% +first order point of view phenomenal +Consciousness is first order reflective + + align:start position:0% +Consciousness is first order reflective + + + align:start position:0% +Consciousness is first order reflective +Consciousness is higher + + align:start position:0% +Consciousness is higher + + + align:start position:0% +Consciousness is higher +order um and of course we're asking what + + align:start position:0% +order um and of course we're asking what + + + align:start position:0% +order um and of course we're asking what +phenomenal Consciousness is but one + + align:start position:0% +phenomenal Consciousness is but one + + + align:start position:0% +phenomenal Consciousness is but one +thing we can say with um my colleague + + align:start position:0% +thing we can say with um my colleague + + + align:start position:0% +thing we can say with um my colleague +Tom Nel is that it's what it's like to + + align:start position:0% +Tom Nel is that it's what it's like to + + + align:start position:0% +Tom Nel is that it's what it's like to +see a sunset or what it's like to taste + + align:start position:0% +see a sunset or what it's like to taste + + + align:start position:0% +see a sunset or what it's like to taste +to see a red apple or what it's like + + align:start position:0% +to see a red apple or what it's like + + + align:start position:0% +to see a red apple or what it's like +generally but that's useless too because + + align:start position:0% +generally but that's useless too because + + + align:start position:0% +generally but that's useless too because +we want to know what is this what it's + + align:start position:0% +we want to know what is this what it's + + + align:start position:0% +we want to know what is this what it's +like so this is really a problem that + + align:start position:0% +like so this is really a problem that + + + align:start position:0% +like so this is really a problem that +dogs all discussions of Consciousness is + + align:start position:0% +dogs all discussions of Consciousness is + + + align:start position:0% +dogs all discussions of Consciousness is +the main thing to be explained that can + + align:start position:0% +the main thing to be explained that can + + + align:start position:0% +the main thing to be explained that can +become a little elusive exactly what it + + align:start position:0% +become a little elusive exactly what it + + + align:start position:0% +become a little elusive exactly what it +is um so here is an attempt by uh John + + align:start position:0% +is um so here is an attempt by uh John + + + align:start position:0% +is um so here is an attempt by uh John +serlo famous philosopher Berkeley to get + + align:start position:0% +serlo famous philosopher Berkeley to get + + + align:start position:0% +serlo famous philosopher Berkeley to get +around this problem he says + + align:start position:0% +around this problem he says + + + align:start position:0% +around this problem he says +Consciousness does not admit of a + + align:start position:0% +Consciousness does not admit of a + + + align:start position:0% +Consciousness does not admit of a +definition nonetheless it is important + + align:start position:0% +definition nonetheless it is important + + + align:start position:0% +definition nonetheless it is important +to say exactly what we're talking about + + align:start position:0% +to say exactly what we're talking about + + + align:start position:0% +to say exactly what we're talking about +because the phenomenon of Consciousness + + align:start position:0% +because the phenomenon of Consciousness + + + align:start position:0% +because the phenomenon of Consciousness +that we are interested in needs to be + + align:start position:0% +that we are interested in needs to be + + + align:start position:0% +that we are interested in needs to be +distinguished from certain other + + align:start position:0% +distinguished from certain other + + + align:start position:0% +distinguished from certain other +phenomena such as attention knowledge + + align:start position:0% +phenomena such as attention knowledge + + + align:start position:0% +phenomena such as attention knowledge +and self-consciousness you might have + + align:start position:0% +and self-consciousness you might have + + + align:start position:0% +and self-consciousness you might have +added higher thought Consciousness by + + align:start position:0% +added higher thought Consciousness by + + + align:start position:0% +added higher thought Consciousness by +Consciousness he says I simply mean + + align:start position:0% +Consciousness he says I simply mean + + + align:start position:0% +Consciousness he says I simply mean +those subjective states of sentience or + + align:start position:0% +those subjective states of sentience or + + + align:start position:0% +those subjective states of sentience or +awareness that begin when one awakes in + + align:start position:0% +awareness that begin when one awakes in + + + align:start position:0% +awareness that begin when one awakes in +the morning from a dreamless sleep and + + align:start position:0% +the morning from a dreamless sleep and + + + align:start position:0% +the morning from a dreamless sleep and +continue throughout the day until one + + align:start position:0% +continue throughout the day until one + + + align:start position:0% +continue throughout the day until one +goes to sleep at night or Falls into a + + align:start position:0% +goes to sleep at night or Falls into a + + + align:start position:0% +goes to sleep at night or Falls into a +coma or dies or otherwise becomes as one + + align:start position:0% +coma or dies or otherwise becomes as one + + + align:start position:0% +coma or dies or otherwise becomes as one +would say + + align:start position:0% +would say + + + align:start position:0% +would say +unconscious now of course this is just a + + align:start position:0% +unconscious now of course this is just a + + + align:start position:0% +unconscious now of course this is just a +way of pointing Consciousness if you're + + align:start position:0% +way of pointing Consciousness if you're + + + align:start position:0% +way of pointing Consciousness if you're +not sure which of a number of things is + + align:start position:0% +not sure which of a number of things is + + + align:start position:0% +not sure which of a number of things is +is being pointed at the the presence of + + align:start position:0% +is being pointed at the the presence of + + + align:start position:0% +is being pointed at the the presence of +this word here is going to make the + + align:start position:0% +this word here is going to make the + + + align:start position:0% +this word here is going to make the +thing useless um so it's not clear that + + align:start position:0% +thing useless um so it's not clear that + + + align:start position:0% +thing useless um so it's not clear that +that helps um so the thing is it's one + + align:start position:0% +that helps um so the thing is it's one + + + align:start position:0% +that helps um so the thing is it's one +of these cases where + + align:start position:0% +of these cases where + + + align:start position:0% +of these cases where +some people seem to feel like okay I see + + align:start position:0% +some people seem to feel like okay I see + + + align:start position:0% +some people seem to feel like okay I see +at least conceptually the distinction + + align:start position:0% +at least conceptually the distinction + + + align:start position:0% +at least conceptually the distinction +between phenomenal Consciousness that's + + align:start position:0% +between phenomenal Consciousness that's + + + align:start position:0% +between phenomenal Consciousness that's +that what that what its likeness of + + align:start position:0% +that what that what its likeness of + + + align:start position:0% +that what that what its likeness of +perception and a higher order thought + + align:start position:0% +perception and a higher order thought + + + align:start position:0% +perception and a higher order thought +about some people say and I say I can + + align:start position:0% +about some people say and I say I can + + + align:start position:0% +about some people say and I say I can +certainly conceive that maybe what it is + + align:start position:0% +certainly conceive that maybe what it is + + + align:start position:0% +certainly conceive that maybe what it is +for a state to be phenomenally conscious + + align:start position:0% +for a state to be phenomenally conscious + + + align:start position:0% +for a state to be phenomenally conscious +is for there to be a higher order of + + align:start position:0% +is for there to be a higher order of + + + align:start position:0% +is for there to be a higher order of +thought about it but I see the + + align:start position:0% +thought about it but I see the + + + align:start position:0% +thought about it but I see the +conceptual distinction other people say + + align:start position:0% +conceptual distinction other people say + + + align:start position:0% +conceptual distinction other people say +I'm not sure what that phenomenal + + align:start position:0% +I'm not sure what that phenomenal + + + align:start position:0% +I'm not sure what that phenomenal +Consciousness is if it's something + + align:start position:0% +Consciousness is if it's something + + + align:start position:0% +Consciousness is if it's something +distinct from what you get if you plug + + align:start position:0% +distinct from what you get if you plug + + + align:start position:0% +distinct from what you get if you plug +in the higher order thought about and so + + align:start position:0% +in the higher order thought about and so + + + align:start position:0% +in the higher order thought about and so +there is a kind of divide where people + + align:start position:0% +there is a kind of divide where people + + + align:start position:0% +there is a kind of divide where people +argue with each other but it's not + + align:start position:0% +argue with each other but it's not + + + align:start position:0% +argue with each other but it's not +entirely clear that they're arguing + + align:start position:0% +entirely clear that they're arguing + + + align:start position:0% +entirely clear that they're arguing +about a nonverbal issue is the issue + + align:start position:0% +about a nonverbal issue is the issue + + + align:start position:0% +about a nonverbal issue is the issue +just some people like to use the word + + align:start position:0% +just some people like to use the word + + + align:start position:0% +just some people like to use the word +Consciousness in a different way from + + align:start position:0% +Consciousness in a different way from + + + align:start position:0% +Consciousness in a different way from +others so look at this is a difficult + + align:start position:0% +others so look at this is a difficult + + + align:start position:0% +others so look at this is a difficult +issue and I'm not sure that I'm going to + + align:start position:0% +issue and I'm not sure that I'm going to + + + align:start position:0% +issue and I'm not sure that I'm going to +say something that will satisfy you and + + align:start position:0% +say something that will satisfy you and + + + align:start position:0% +say something that will satisfy you and +the problem really is what what s is + + align:start position:0% +the problem really is what what s is + + + align:start position:0% +the problem really is what what s is +that the term does not admit of the + + align:start position:0% +that the term does not admit of the + + + align:start position:0% +that the term does not admit of the +definition it has to be pointed to if + + align:start position:0% +definition it has to be pointed to if + + + align:start position:0% +definition it has to be pointed to if +you are unsure whether what that arrow + + align:start position:0% +you are unsure whether what that arrow + + + align:start position:0% +you are unsure whether what that arrow +is pointing to then you are going to be + + align:start position:0% +is pointing to then you are going to be + + + align:start position:0% +is pointing to then you are going to be +unsure what the debate is about but + + align:start position:0% +unsure what the debate is about but + + + align:start position:0% +unsure what the debate is about but +there are a couple things one can say so + + align:start position:0% +there are a couple things one can say so + + + align:start position:0% +there are a couple things one can say so +one thing one can say is just appeal to + + align:start position:0% +one thing one can say is just appeal to + + + align:start position:0% +one thing one can say is just appeal to +the explanatory Gap + + align:start position:0% +the explanatory Gap + + + align:start position:0% +the explanatory Gap +itself so it's what is puzzling + + align:start position:0% +itself so it's what is puzzling + + + align:start position:0% +itself so it's what is puzzling +if so here's a little exercise if you + + align:start position:0% +if so here's a little exercise if you + + + align:start position:0% +if so here's a little exercise if you +think the explanatory Gap really is + + align:start position:0% +think the explanatory Gap really is + + + align:start position:0% +think the explanatory Gap really is +positive um then you'll think that um + + align:start position:0% +positive um then you'll think that um + + + align:start position:0% +positive um then you'll think that um +the um uh uh the higher order and the um + + align:start position:0% +the um uh uh the higher order and the um + + + align:start position:0% +the um uh uh the higher order and the um +um the global workspace accounts really + + align:start position:0% +um the global workspace accounts really + + + align:start position:0% +um the global workspace accounts really +need something out they don't have seem + + align:start position:0% +need something out they don't have seem + + + align:start position:0% +need something out they don't have seem +to have room for explaining it of course + + align:start position:0% +to have room for explaining it of course + + + align:start position:0% +to have room for explaining it of course +the biological view has room for a but + + align:start position:0% +the biological view has room for a but + + + align:start position:0% +the biological view has room for a but +it's not clear that it can explain it + + align:start position:0% +it's not clear that it can explain it + + + align:start position:0% +it's not clear that it can explain it +but at least it gets the if you believe + + align:start position:0% +but at least it gets the if you believe + + + align:start position:0% +but at least it gets the if you believe +in the Gap at least it gets the + + align:start position:0% +in the Gap at least it gets the + + + align:start position:0% +in the Gap at least it gets the +existence of the Gap there so there are + + align:start position:0% +existence of the Gap there so there are + + + align:start position:0% +existence of the Gap there so there are +two other well-known U um issues that + + align:start position:0% +two other well-known U um issues that + + + align:start position:0% +two other well-known U um issues that +can be brought up to um um Each of which + + align:start position:0% +can be brought up to um um Each of which + + + align:start position:0% +can be brought up to um um Each of which +is itself um uh controversial uh so the + + align:start position:0% +is itself um uh controversial uh so the + + + align:start position:0% +is itself um uh controversial uh so the +basis of what Marion learns that's + + align:start position:0% +basis of what Marion learns that's + + + align:start position:0% +basis of what Marion learns that's +another way you can uh get at it so this + + align:start position:0% +another way you can uh get at it so this + + + align:start position:0% +another way you can uh get at it so this +is a um famous example of produced by + + align:start position:0% +is a um famous example of produced by + + + align:start position:0% +is a um famous example of produced by +Frank + + align:start position:0% +Frank + + + align:start position:0% +Frank +Jackson so the idea is you're supposed + + align:start position:0% +Jackson so the idea is you're supposed + + + align:start position:0% +Jackson so the idea is you're supposed +to imagine imagine a um um uh + + align:start position:0% +to imagine imagine a um um uh + + + align:start position:0% +to imagine imagine a um um uh +neuroscientist named Mary who is raised + + align:start position:0% +neuroscientist named Mary who is raised + + + align:start position:0% +neuroscientist named Mary who is raised +in a black and white room and never sees + + align:start position:0% +in a black and white room and never sees + + + align:start position:0% +in a black and white room and never sees +anything red let's say or is it blue do + + align:start position:0% +anything red let's say or is it blue do + + + align:start position:0% +anything red let's say or is it blue do +I have blue here blue never sees + + align:start position:0% +I have blue here blue never sees + + + align:start position:0% +I have blue here blue never sees +anything blue um then so she learns what + + align:start position:0% +anything blue um then so she learns what + + + align:start position:0% +anything blue um then so she learns what +the experience of blue is from a a + + align:start position:0% +the experience of blue is from a a + + + align:start position:0% +the experience of blue is from a a +neuroscience point of view from a + + align:start position:0% +neuroscience point of view from a + + + align:start position:0% +neuroscience point of view from a +computation point from every point of + + align:start position:0% +computation point from every point of + + + align:start position:0% +computation point from every point of +view that science can um uh can give her + + align:start position:0% +view that science can um uh can give her + + + align:start position:0% +view that science can um uh can give her +um and then she leaves the room and + + align:start position:0% +um and then she leaves the room and + + + align:start position:0% +um and then she leaves the room and +learns a new fact what it's like to see + + align:start position:0% +learns a new fact what it's like to see + + + align:start position:0% +learns a new fact what it's like to see +something blue so Jackson argues there + + align:start position:0% +something blue so Jackson argues there + + + align:start position:0% +something blue so Jackson argues there +must be facts about color vision that + + align:start position:0% +must be facts about color vision that + + + align:start position:0% +must be facts about color vision that +are not physical functional effects he + + align:start position:0% +are not physical functional effects he + + + align:start position:0% +are not physical functional effects he +argues for a kind of dualism but whether + + align:start position:0% +argues for a kind of dualism but whether + + + align:start position:0% +argues for a kind of dualism but whether +you believe the AR argument as an + + align:start position:0% +you believe the AR argument as an + + + align:start position:0% +you believe the AR argument as an +argument for dualism or not um at least + + align:start position:0% +argument for dualism or not um at least + + + align:start position:0% +argument for dualism or not um at least +you can identify so there she is I'm so + + align:start position:0% +you can identify so there she is I'm so + + + align:start position:0% +you can identify so there she is I'm so +glad to see something blue finally but + + align:start position:0% +glad to see something blue finally but + + + align:start position:0% +glad to see something blue finally but +at least you can say phenomenal + + align:start position:0% +at least you can say phenomenal + + + align:start position:0% +at least you can say phenomenal +Consciousness is the basis of what she + + align:start position:0% +Consciousness is the basis of what she + + + align:start position:0% +Consciousness is the basis of what she +learns so even if you don't think it's + + align:start position:0% +learns so even if you don't think it's + + + align:start position:0% +learns so even if you don't think it's +an argument for dualism you can think ah + + align:start position:0% +an argument for dualism you can think ah + + + align:start position:0% +an argument for dualism you can think ah +yes when she sees something blue finally + + align:start position:0% +yes when she sees something blue finally + + + align:start position:0% +yes when she sees something blue finally +what it is for her to learn what it's + + align:start position:0% +what it is for her to learn what it's + + + align:start position:0% +what it is for her to learn what it's +like to see blue is for her to have a + + align:start position:0% +like to see blue is for her to have a + + + align:start position:0% +like to see blue is for her to have a +certain kind of phenomenal experience so + + align:start position:0% +certain kind of phenomenal experience so + + + align:start position:0% +certain kind of phenomenal experience so +that is a way of kind of pointing to + + align:start position:0% +that is a way of kind of pointing to + + + align:start position:0% +that is a way of kind of pointing to +what's meant by phenomenal + + align:start position:0% +what's meant by phenomenal + + + align:start position:0% +what's meant by phenomenal +Consciousness so the Third Way is what's + + align:start position:0% +Consciousness so the Third Way is what's + + + align:start position:0% +Consciousness so the Third Way is what's +important in suffering and this is + + align:start position:0% +important in suffering and this is + + + align:start position:0% +important in suffering and this is +something I'll get unto I think there is + + align:start position:0% +something I'll get unto I think there is + + + align:start position:0% +something I'll get unto I think there is +a case that be made that a dog a + + align:start position:0% +a case that be made that a dog a + + + align:start position:0% +a case that be made that a dog a +one-year-old baby um an autistic kid and + + align:start position:0% +one-year-old baby um an autistic kid and + + + align:start position:0% +one-year-old baby um an autistic kid and +deaf children who seem to acquire higher + + align:start position:0% +deaf children who seem to acquire higher + + + align:start position:0% +deaf children who seem to acquire higher +order + + align:start position:0% +order + + + align:start position:0% +order +States uh well after other CH the case + + align:start position:0% +States uh well after other CH the case + + + align:start position:0% +States uh well after other CH the case +of dogs and and case of dogs maybe they + + align:start position:0% +of dogs and and case of dogs maybe they + + + align:start position:0% +of dogs and and case of dogs maybe they +never do one-year-olds seem to not have + + align:start position:0% +never do one-year-olds seem to not have + + + align:start position:0% +never do one-year-olds seem to not have +anything you could call a higher order + + align:start position:0% +anything you could call a higher order + + + align:start position:0% +anything you could call a higher order +State death children are a little + + align:start position:0% +State death children are a little + + + align:start position:0% +State death children are a little +delayed in in showing signs of higher + + align:start position:0% +delayed in in showing signs of higher + + + align:start position:0% +delayed in in showing signs of higher +ordered States + + align:start position:0% +ordered States + + + align:start position:0% +ordered States +um so the question is can these + + align:start position:0% +um so the question is can these + + + align:start position:0% +um so the question is can these +creatures have have + + align:start position:0% +creatures have have + + + align:start position:0% +creatures have have +suffering um and if they can um um that + + align:start position:0% +suffering um and if they can um um that + + + align:start position:0% +suffering um and if they can um um that +suggests that um there's a fault with + + align:start position:0% +suggests that um there's a fault with + + + align:start position:0% +suggests that um there's a fault with +the higher order of account because it + + align:start position:0% +the higher order of account because it + + + align:start position:0% +the higher order of account because it +looks like suffering is bad in itself + + align:start position:0% +looks like suffering is bad in itself + + + align:start position:0% +looks like suffering is bad in itself +whereas High theorists have to say that + + align:start position:0% +whereas High theorists have to say that + + + align:start position:0% +whereas High theorists have to say that +in these people and creatures it's + + align:start position:0% +in these people and creatures it's + + + align:start position:0% +in these people and creatures it's +unconscious and so only bad in its + + align:start position:0% +unconscious and so only bad in its + + + align:start position:0% +unconscious and so only bad in its +effects um so this a point of view has + + align:start position:0% +effects um so this a point of view has + + + align:start position:0% +effects um so this a point of view has +actually been embraced by one high order + + align:start position:0% +actually been embraced by one high order + + + align:start position:0% +actually been embraced by one high order +theorist who says pains in cattle sheep + + align:start position:0% +theorist who says pains in cattle sheep + + + align:start position:0% +theorist who says pains in cattle sheep +pigs and chickens are not felt that is + + align:start position:0% +pigs and chickens are not felt that is + + + align:start position:0% +pigs and chickens are not felt that is +they're not conscious pains and hence + + align:start position:0% +they're not conscious pains and hence + + + align:start position:0% +they're not conscious pains and hence +are of no moral significance I should + + align:start position:0% +are of no moral significance I should + + + align:start position:0% +are of no moral significance I should +say he later takes it back but only that + + align:start position:0% +say he later takes it back but only that + + + align:start position:0% +say he later takes it back but only that +is takes back the idea that we don't + + align:start position:0% +is takes back the idea that we don't + + + align:start position:0% +is takes back the idea that we don't +have to pay attention to how the + + align:start position:0% +have to pay attention to how the + + + align:start position:0% +have to pay attention to how the +conditions that we keep these animals in + + align:start position:0% +conditions that we keep these animals in + + + align:start position:0% +conditions that we keep these animals in +but he he does it not because he thinks + + align:start position:0% +but he he does it not because he thinks + + + align:start position:0% +but he he does it not because he thinks +their pains are felt that is conscious + + align:start position:0% +their pains are felt that is conscious + + + align:start position:0% +their pains are felt that is conscious +but because he thinks their desires are + + align:start position:0% +but because he thinks their desires are + + + align:start position:0% +but because he thinks their desires are +of moral + + align:start position:0% +of moral + + + align:start position:0% +of moral +significance um + + align:start position:0% +significance um + + + align:start position:0% +significance um +so you could one way to point at + + align:start position:0% +so you could one way to point at + + + align:start position:0% +so you could one way to point at +phenomenal Consciousness is to say it's + + align:start position:0% +phenomenal Consciousness is to say it's + + + align:start position:0% +phenomenal Consciousness is to say it's +the basis of what's bad about suffering + + align:start position:0% +the basis of what's bad about suffering + + + align:start position:0% +the basis of what's bad about suffering +it's that feeling of suffering that's + + align:start position:0% +it's that feeling of suffering that's + + + align:start position:0% +it's that feeling of suffering that's +bad + + align:start position:0% +bad + + + align:start position:0% +bad +um okay so just to summarize these these + + align:start position:0% +um okay so just to summarize these these + + + align:start position:0% +um okay so just to summarize these these +three points uh Mary learns what it's + + align:start position:0% +three points uh Mary learns what it's + + + align:start position:0% +three points uh Mary learns what it's +like to see red not what it's like to + + align:start position:0% +like to see red not what it's like to + + + align:start position:0% +like to see red not what it's like to +think about seeing red so that's a way + + align:start position:0% +think about seeing red so that's a way + + + align:start position:0% +think about seeing red so that's a way +of pointing um U the subject of the + + align:start position:0% +of pointing um U the subject of the + + + align:start position:0% +of pointing um U the subject of the +explanatory Gap representation and + + align:start position:0% +explanatory Gap representation and + + + align:start position:0% +explanatory Gap representation and +thought not completely mysterious from a + + align:start position:0% +thought not completely mysterious from a + + + align:start position:0% +thought not completely mysterious from a +scientific point of view so it's a + + align:start position:0% +scientific point of view so it's a + + + align:start position:0% +scientific point of view so it's a +little hard to see how cashing out the + + align:start position:0% +little hard to see how cashing out the + + + align:start position:0% +little hard to see how cashing out the +explanatory Gap in those terms is going + + align:start position:0% +explanatory Gap in those terms is going + + + align:start position:0% +explanatory Gap in those terms is going +to do anything and the suffering point + + align:start position:0% +to do anything and the suffering point + + + align:start position:0% +to do anything and the suffering point +that I that I just made anyway the the + + align:start position:0% +that I that I just made anyway the the + + + align:start position:0% +that I that I just made anyway the the +general issue is um oh sorry so maybe + + align:start position:0% +general issue is um oh sorry so maybe + + + align:start position:0% +general issue is um oh sorry so maybe +maybe I should pause for a + + align:start position:0% + + + + align:start position:0% + +moment + + align:start position:0% + + + + align:start position:0% + +questions biolog + + align:start position:0% + + + + align:start position:0% + +biology yeah okay so + + align:start position:0% +biology yeah okay so + + + align:start position:0% +biology yeah okay so +um so the point of view view of the + + align:start position:0% +um so the point of view view of the + + + align:start position:0% +um so the point of view view of the +biological theory + + align:start position:0% +biological theory + + + align:start position:0% +biological theory +is um that there is an + + align:start position:0% +is um that there is an + + + align:start position:0% +is um that there is an +explanatory and that we lack the + + align:start position:0% +explanatory and that we lack the + + + align:start position:0% +explanatory and that we lack the +concepts needed to Clos it so the + + align:start position:0% +concepts needed to Clos it so the + + + align:start position:0% +concepts needed to Clos it so the +analogy that we people who hold the + + align:start position:0% +analogy that we people who hold the + + + align:start position:0% +analogy that we people who hold the +biological Theory like is the analogy + + align:start position:0% +biological Theory like is the analogy + + + align:start position:0% +biological Theory like is the analogy +with life + + align:start position:0% +with life + + + align:start position:0% +with life +um so at one point people could not + + align:start position:0% +um so at one point people could not + + + align:start position:0% +um so at one point people could not +conceive of how it is that + + align:start position:0% +conceive of how it is that + + + align:start position:0% +conceive of how it is that +um um some kind of mechanical you know + + align:start position:0% +um um some kind of mechanical you know + + + align:start position:0% +um um some kind of mechanical you know +motions of molecules could be life and + + align:start position:0% +motions of molecules could be life and + + + align:start position:0% +motions of molecules could be life and +that was because people didn't have the + + align:start position:0% +that was because people didn't have the + + + align:start position:0% +that was because people didn't have the +the needed Concepts so one of the needed + + align:start position:0% +the needed Concepts so one of the needed + + + align:start position:0% +the needed Concepts so one of the needed +Concepts was a concept of a mechanism of + + align:start position:0% +Concepts was a concept of a mechanism of + + + align:start position:0% +Concepts was a concept of a mechanism of +reproduction that could go thousands of + + align:start position:0% +reproduction that could go thousands of + + + align:start position:0% +reproduction that could go thousands of +generations without any serious change + + align:start position:0% +generations without any serious change + + + align:start position:0% +generations without any serious change +in fact there was an argument in the + + align:start position:0% +in fact there was an argument in the + + + align:start position:0% +in fact there was an argument in the +19th century given that reproduction + + align:start position:0% +19th century given that reproduction + + + align:start position:0% +19th century given that reproduction +required an act of God because people + + align:start position:0% +required an act of God because people + + + align:start position:0% +required an act of God because people +had the fossil evidence for some + + align:start position:0% +had the fossil evidence for some + + + align:start position:0% +had the fossil evidence for some +creatures of many many many generations + + align:start position:0% +creatures of many many many generations + + + align:start position:0% +creatures of many many many generations +but the only mechanisms for copying that + + align:start position:0% +but the only mechanisms for copying that + + + align:start position:0% +but the only mechanisms for copying that +they knew about were ones that + + align:start position:0% +they knew about were ones that + + + align:start position:0% +they knew about were ones that +introduced fuzziness like you know the + + align:start position:0% +introduced fuzziness like you know the + + + align:start position:0% +introduced fuzziness like you know the +Xerox of the Xerox the Xerox of the + + align:start position:0% +Xerox of the Xerox the Xerox of the + + + align:start position:0% +Xerox of the Xerox the Xerox of the +Xerox so the idea is that the biological + + align:start position:0% +Xerox so the idea is that the biological + + + align:start position:0% +Xerox so the idea is that the biological +account it's not that anybody knows what + + align:start position:0% +account it's not that anybody knows what + + + align:start position:0% +account it's not that anybody knows what +the solution is on the biological + + align:start position:0% +the solution is on the biological + + + align:start position:0% +the solution is on the biological +account but at least it acknowledges the + + align:start position:0% +account but at least it acknowledges the + + + align:start position:0% +account but at least it acknowledges the +problem you know as Tom Nel puts it this + + align:start position:0% +problem you know as Tom Nel puts it this + + + align:start position:0% +problem you know as Tom Nel puts it this +discussion of this we are like the + + align:start position:0% +discussion of this we are like the + + + align:start position:0% +discussion of this we are like the +pratic philosopher who is told that + + align:start position:0% +pratic philosopher who is told that + + + align:start position:0% +pratic philosopher who is told that +matter is energy but doesn't have the + + align:start position:0% +matter is energy but doesn't have the + + + align:start position:0% +matter is energy but doesn't have the +concept of matter and the concept of + + align:start position:0% +concept of matter and the concept of + + + align:start position:0% +concept of matter and the concept of +energy that allows us to see how those + + align:start position:0% +energy that allows us to see how those + + + align:start position:0% +energy that allows us to see how those +could be concepts of the same thing so + + align:start position:0% +could be concepts of the same thing so + + + align:start position:0% +could be concepts of the same thing so +the biological account doesn't say that + + align:start position:0% +the biological account doesn't say that + + + align:start position:0% +the biological account doesn't say that +we have a solution to it or even that we + + align:start position:0% +we have a solution to it or even that we + + + align:start position:0% +we have a solution to it or even that we +know how to get it but the idea would be + + align:start position:0% +know how to get it but the idea would be + + + align:start position:0% +know how to get it but the idea would be +it's better to + + align:start position:0% +it's better to + + + align:start position:0% +it's better to +recognize problems that are real than to + + align:start position:0% +recognize problems that are real than to + + + align:start position:0% +recognize problems that are real than to +adopt views that close the door to their + + align:start position:0% +adopt views that close the door to their + + + align:start position:0% +adopt views that close the door to their +solution which is what the biological + + align:start position:0% +solution which is what the biological + + + align:start position:0% +solution which is what the biological +theorist thinks about the global + + align:start position:0% +theorist thinks about the global + + + align:start position:0% +theorist thinks about the global +workspace and the higher order view so + + align:start position:0% +workspace and the higher order view so + + + align:start position:0% +workspace and the higher order view so +we biological theorists think there is + + align:start position:0% +we biological theorists think there is + + + align:start position:0% +we biological theorists think there is +an + + align:start position:0% +an + + + align:start position:0% +an +explanatory maybe it can be closed or + + align:start position:0% +explanatory maybe it can be closed or + + + align:start position:0% +explanatory maybe it can be closed or +partially closed maybe it can't but + + align:start position:0% +partially closed maybe it can't but + + + align:start position:0% +partially closed maybe it can't but +we're in a lot better position to close + + align:start position:0% +we're in a lot better position to close + + + align:start position:0% +we're in a lot better position to close +it if we recognize that it exists and + + align:start position:0% +it if we recognize that it exists and + + + align:start position:0% +it if we recognize that it exists and +the global workspace view says it + + align:start position:0% +the global workspace view says it + + + align:start position:0% +the global workspace view says it +doesn't any room for closing it it just + + align:start position:0% +doesn't any room for closing it it just + + + align:start position:0% +doesn't any room for closing it it just +says oh well there'll be a causal + + align:start position:0% +says oh well there'll be a causal + + + align:start position:0% +says oh well there'll be a causal +process by which um which we already + + align:start position:0% +process by which um which we already + + + align:start position:0% +process by which um which we already +know a lot about by which a + + align:start position:0% +know a lot about by which a + + + align:start position:0% +know a lot about by which a +representation perceptual representation + + align:start position:0% +representation perceptual representation + + + align:start position:0% +representation perceptual representation +is you know globally broadcast and the + + align:start position:0% +is you know globally broadcast and the + + + align:start position:0% +is you know globally broadcast and the +high order view says there will be a + + align:start position:0% +high order view says there will be a + + + align:start position:0% +high order view says there will be a +causal process by which a high order + + align:start position:0% +causal process by which a high order + + + align:start position:0% +causal process by which a high order +thought can be formed first order state + + align:start position:0% +thought can be formed first order state + + + align:start position:0% +thought can be formed first order state +so they don't leave room for it so + + align:start position:0% +so they don't leave room for it so + + + align:start position:0% +so they don't leave room for it so +that's the picture y + + align:start position:0% +that's the picture y + + + align:start position:0% +that's the picture y +sur's uh idea of emergence I know it + + align:start position:0% +sur's uh idea of emergence I know it + + + align:start position:0% +sur's uh idea of emergence I know it +doesn't solve the + + align:start position:0% +doesn't solve the + + + align:start position:0% +doesn't solve the +problem this explanatory Gap doesn't + + align:start position:0% +problem this explanatory Gap doesn't + + + align:start position:0% +problem this explanatory Gap doesn't +sort of like posit a space where that + + align:start position:0% +sort of like posit a space where that + + + align:start position:0% +sort of like posit a space where that +can be likey + + align:start position:0% +can be likey + + + align:start position:0% +can be likey +explored well okay so s what's view is + + align:start position:0% +explored well okay so s what's view is + + + align:start position:0% +explored well okay so s what's view is +is a little hard to uh ascertain so what + + align:start position:0% +is a little hard to uh ascertain so what + + + align:start position:0% +is a little hard to uh ascertain so what +he says is that Consciousness is a + + align:start position:0% +he says is that Consciousness is a + + + align:start position:0% +he says is that Consciousness is a +higher order property of the brain but + + align:start position:0% +higher order property of the brain but + + + align:start position:0% +higher order property of the brain but +when he says what that comes to it looks + + align:start position:0% +when he says what that comes to it looks + + + align:start position:0% +when he says what that comes to it looks +like he's a + + align:start position:0% +like he's a + + + align:start position:0% +like he's a +duelist + + align:start position:0% +duelist + + + align:start position:0% +duelist +so he's a little vague on this he + + align:start position:0% +so he's a little vague on this he + + + align:start position:0% +so he's a little vague on this he +doesn't like the standard + + align:start position:0% +doesn't like the standard + + + align:start position:0% +doesn't like the standard +categories + + align:start position:0% +categories + + + align:start position:0% +categories +so now he doesn't really say much about + + align:start position:0% +so now he doesn't really say much about + + + align:start position:0% +so now he doesn't really say much about +what kind of duelist he is um and so + + align:start position:0% +what kind of duelist he is um and so + + + align:start position:0% +what kind of duelist he is um and so +it's a little hard to know exactly what + + align:start position:0% +it's a little hard to know exactly what + + + align:start position:0% +it's a little hard to know exactly what +room he leaves for closing + + align:start position:0% + + + + align:start position:0% + +explanatory so what line of reasoning + + align:start position:0% +explanatory so what line of reasoning + + + align:start position:0% +explanatory so what line of reasoning +characters that they is that phenomenal + + align:start position:0% +characters that they is that phenomenal + + + align:start position:0% +characters that they is that phenomenal +P + + align:start position:0% +P + + + align:start position:0% +P +inan what what kind of evidence would he + + align:start position:0% +inan what what kind of evidence would he + + + align:start position:0% +inan what what kind of evidence would he +Marsh in order + + align:start position:0% +Marsh in order + + + align:start position:0% +Marsh in order +to others would he Marshall to argue + + align:start position:0% +to others would he Marshall to argue + + + align:start position:0% +to others would he Marshall to argue +that there is that animals do not + + align:start position:0% +that there is that animals do not + + + align:start position:0% +that there is that animals do not +experience uh pain + + align:start position:0% +experience uh pain + + + align:start position:0% +experience uh pain +okay what he would do and what he has + + align:start position:0% +okay what he would do and what he has + + + align:start position:0% +okay what he would do and what he has +done is um look at the literature on + + align:start position:0% +done is um look at the literature on + + + align:start position:0% +done is um look at the literature on +metacognition in animals argue that the + + align:start position:0% +metacognition in animals argue that the + + + align:start position:0% +metacognition in animals argue that the +inherent evidence for metacognition is + + align:start position:0% +inherent evidence for metacognition is + + + align:start position:0% +inherent evidence for metacognition is +is poor and that first order so what he + + align:start position:0% +is poor and that first order so what he + + + align:start position:0% +is poor and that first order so what he +he argues I think with some persuasion + + align:start position:0% +he argues I think with some persuasion + + + align:start position:0% +he argues I think with some persuasion +some persuasive Force it's in a recent + + align:start position:0% +some persuasive Force it's in a recent + + + align:start position:0% +some persuasive Force it's in a recent +issue actually of M Journal mind and + + align:start position:0% +issue actually of M Journal mind and + + + align:start position:0% +issue actually of M Journal mind and +language is that certainly outside of + + align:start position:0% +language is that certainly outside of + + + align:start position:0% +language is that certainly outside of +primates the the evidence for + + align:start position:0% +primates the the evidence for + + + align:start position:0% +primates the the evidence for +metacognition is extremely weak um there + + align:start position:0% +metacognition is extremely weak um there + + + align:start position:0% +metacognition is extremely weak um there +is some evidence and then he goes + + align:start position:0% +is some evidence and then he goes + + + align:start position:0% +is some evidence and then he goes +through it and tries to show how a first + + align:start position:0% +through it and tries to show how a first + + + align:start position:0% +through it and tries to show how a first +order account really does do a better + + align:start position:0% +order account really does do a better + + + align:start position:0% +order account really does do a better +job of dealing with the evidence so he + + align:start position:0% +job of dealing with the evidence so he + + + align:start position:0% +job of dealing with the evidence so he +thinks that you know cats and dogs Etc + + align:start position:0% +thinks that you know cats and dogs Etc + + + align:start position:0% +thinks that you know cats and dogs Etc +just don't have thoughts about their + + align:start position:0% +just don't have thoughts about their + + + align:start position:0% +just don't have thoughts about their +perceptual to other states now I think + + align:start position:0% +perceptual to other states now I think + + + align:start position:0% +perceptual to other states now I think +it isn't necessary to have such an + + align:start position:0% +it isn't necessary to have such an + + + align:start position:0% +it isn't necessary to have such an +extreme view to see the problem if those + + align:start position:0% +extreme view to see the problem if those + + + align:start position:0% +extreme view to see the problem if those +thoughts can are possible but + + align:start position:0% +thoughts can are possible but + + + align:start position:0% +thoughts can are possible but +rare um still we think you know you ever + + align:start position:0% +rare um still we think you know you ever + + + align:start position:0% +rare um still we think you know you ever +step on your dog's tail you know you + + align:start position:0% +step on your dog's tail you know you + + + align:start position:0% +step on your dog's tail you know you +really think that the dog is suffering + + align:start position:0% +really think that the dog is suffering + + + align:start position:0% +really think that the dog is suffering +and the question of whether the dog is + + align:start position:0% +and the question of whether the dog is + + + align:start position:0% +and the question of whether the dog is +suffering does not at least intuitively + + align:start position:0% +suffering does not at least intuitively + + + align:start position:0% +suffering does not at least intuitively +seem to depend on whether the dog has + + align:start position:0% +seem to depend on whether the dog has + + + align:start position:0% +seem to depend on whether the dog has +managed to have a higher order thought + + align:start position:0% +managed to have a higher order thought + + + align:start position:0% +managed to have a higher order thought +about his his State um so I think you + + align:start position:0% +about his his State um so I think you + + + align:start position:0% +about his his State um so I think you +know there is an open empirical question + + align:start position:0% +know there is an open empirical question + + + align:start position:0% +know there is an open empirical question +here it's the extent of higher order + + align:start position:0% +here it's the extent of higher order + + + align:start position:0% +here it's the extent of higher order +thoughts or higher order States in in + + align:start position:0% +thoughts or higher order States in in + + + align:start position:0% +thoughts or higher order States in in +animals and you know there is a + + align:start position:0% +animals and you know there is a + + + align:start position:0% +animals and you know there is a +literature and he he just gone through + + align:start position:0% +literature and he he just gone through + + + align:start position:0% +literature and he he just gone through +quite a bit of it and it is surprising + + align:start position:0% +quite a bit of it and it is surprising + + + align:start position:0% +quite a bit of it and it is surprising +just how weak it is although maybe not + + align:start position:0% +just how weak it is although maybe not + + + align:start position:0% +just how weak it is although maybe not +so surprising when you look at the + + align:start position:0% +so surprising when you look at the + + + align:start position:0% +so surprising when you look at the +literature on human children where it + + align:start position:0% +literature on human children where it + + + align:start position:0% +literature on human children where it +again there is and I if I get to this + + align:start position:0% +again there is and I if I get to this + + + align:start position:0% +again there is and I if I get to this +I'll mention some of um evidence that to + + align:start position:0% +I'll mention some of um evidence that to + + + align:start position:0% +I'll mention some of um evidence that to +a surprising extent human children up to + + align:start position:0% +a surprising extent human children up to + + + align:start position:0% +a surprising extent human children up to +even the age of four have a lot of + + align:start position:0% +even the age of four have a lot of + + + align:start position:0% +even the age of four have a lot of +difficulty with higher order States + + align:start position:0% +difficulty with higher order States + + + align:start position:0% +difficulty with higher order States +about their first order States but I + + align:start position:0% +about their first order States but I + + + align:start position:0% +about their first order States but I +don't think we have any problem in + + align:start position:0% +don't think we have any problem in + + + align:start position:0% +don't think we have any problem in +realizing that they have conscious + + align:start position:0% +realizing that they have conscious + + + align:start position:0% +realizing that they have conscious +States conscious visual States conscious + + align:start position:0% +States conscious visual States conscious + + + align:start position:0% +States conscious visual States conscious +pains Etc um so it leads you to think + + align:start position:0% +pains Etc um so it leads you to think + + + align:start position:0% +pains Etc um so it leads you to think +that there really is a kind of pun here + + align:start position:0% +that there really is a kind of pun here + + + align:start position:0% +that there really is a kind of pun here +that okay maybe maybe without the H + + align:start position:0% +that okay maybe maybe without the H + + + align:start position:0% +that okay maybe maybe without the H +thought they're not conscious in this + + align:start position:0% +thought they're not conscious in this + + + align:start position:0% +thought they're not conscious in this +reflective sense but Surly they're + + align:start position:0% +reflective sense but Surly they're + + + align:start position:0% +reflective sense but Surly they're +phenomenal in conscious um so that's my + + align:start position:0% +phenomenal in conscious um so that's my + + + align:start position:0% +phenomenal in conscious um so that's my +view my view is that um for children if + + align:start position:0% +view my view is that um for children if + + + align:start position:0% +view my view is that um for children if +you I I'll get to some of this this work + + align:start position:0% +you I I'll get to some of this this work + + + align:start position:0% +you I I'll get to some of this this work +um and there's some other strange cases + + align:start position:0% +um and there's some other strange cases + + + align:start position:0% +um and there's some other strange cases +that mention how + + align:start position:0% +that mention how + + + align:start position:0% +that mention how +much um + + align:start position:0% + + + + align:start position:0% + +12 12 minutes oh + + align:start position:0% +12 12 minutes oh + + + align:start position:0% +12 12 minutes oh +God so I think I + + align:start position:0% +God so I think I + + + align:start position:0% +God so I think I +better G okay so let me just um um um so + + align:start position:0% +better G okay so let me just um um um so + + + align:start position:0% +better G okay so let me just um um um so +I'll mention just a brief um so I really + + align:start position:0% +I'll mention just a brief um so I really + + + align:start position:0% +I'll mention just a brief um so I really +have to skip around I've see + + align:start position:0% +have to skip around I've see + + + align:start position:0% +have to skip around I've see +overestimate how much time I have so + + align:start position:0% +overestimate how much time I have so + + + align:start position:0% +overestimate how much time I have so +this is some work by um Israeli + + align:start position:0% +this is some work by um Israeli + + + align:start position:0% +this is some work by um Israeli +neuroscientist R mik where he showed + + align:start position:0% +neuroscientist R mik where he showed + + + align:start position:0% +neuroscientist R mik where he showed +people a movie the good the bad the ugly + + align:start position:0% +people a movie the good the bad the ugly + + + align:start position:0% +people a movie the good the bad the ugly +and found surprisingly small these are + + align:start position:0% +and found surprisingly small these are + + + align:start position:0% +and found surprisingly small these are +these are the front side this is the + + align:start position:0% +these are the front side this is the + + + align:start position:0% +these are the front side this is the +front and this is the front of the left + + align:start position:0% +front and this is the front of the left + + + align:start position:0% +front and this is the front of the left +hemisphere front of the right hemisphere + + align:start position:0% +hemisphere front of the right hemisphere + + + align:start position:0% +hemisphere front of the right hemisphere +big activations in the back very little + + align:start position:0% +big activations in the back very little + + + align:start position:0% +big activations in the back very little +activation in the front and then he did + + align:start position:0% +activation in the front and then he did + + + align:start position:0% +activation in the front and then he did +another experiment even more impressive + + align:start position:0% +another experiment even more impressive + + + align:start position:0% +another experiment even more impressive +where he showed a subject rapid series + + align:start position:0% +where he showed a subject rapid series + + + align:start position:0% +where he showed a subject rapid series +of of pictures that they had to very + + align:start position:0% +of of pictures that they had to very + + + align:start position:0% +of of pictures that they had to very +quickly identify in a kind of rope way + + align:start position:0% +quickly identify in a kind of rope way + + + align:start position:0% +quickly identify in a kind of rope way +he found not only did he find little + + align:start position:0% +he found not only did he find little + + + align:start position:0% +he found not only did he find little +activation in the fle areas in both + + align:start position:0% +activation in the fle areas in both + + + align:start position:0% +activation in the fle areas in both +cortices but he found + + align:start position:0% +cortices but he found + + + align:start position:0% +cortices but he found +suppression suppression um um um uh + + align:start position:0% +suppression suppression um um um uh + + + align:start position:0% +suppression suppression um um um uh +frontal activity and he um so sorry I'm + + align:start position:0% +frontal activity and he um so sorry I'm + + + align:start position:0% +frontal activity and he um so sorry I'm +I'm going so fast I'm not describing he + + align:start position:0% +I'm going so fast I'm not describing he + + + align:start position:0% +I'm going so fast I'm not describing he +did two experiments quick pictures U + + align:start position:0% +did two experiments quick pictures U + + + align:start position:0% +did two experiments quick pictures U +quick identification of pictures uh one + + align:start position:0% +quick identification of pictures uh one + + + align:start position:0% +quick identification of pictures uh one +experiment the using the same pictures + + align:start position:0% +experiment the using the same pictures + + + align:start position:0% +experiment the using the same pictures +slower um questions of how you react + + align:start position:0% +slower um questions of how you react + + + align:start position:0% +slower um questions of how you react +what your what your evaluation the + + align:start position:0% +what your what your evaluation the + + + align:start position:0% +what your what your evaluation the +pictures were there he found big + + align:start position:0% +pictures were there he found big + + + align:start position:0% +pictures were there he found big +activations in frontal areas um in the + + align:start position:0% +activations in frontal areas um in the + + + align:start position:0% +activations in frontal areas um in the +quick categorization he found + + align:start position:0% +quick categorization he found + + + align:start position:0% +quick categorization he found +suppression front Earth um which he he + + align:start position:0% +suppression front Earth um which he he + + + align:start position:0% +suppression front Earth um which he he +says um here um uh is compatible with + + align:start position:0% +says um here um uh is compatible with + + + align:start position:0% +says um here um uh is compatible with +the strong intuitive sense we have a + + align:start position:0% +the strong intuitive sense we have a + + + align:start position:0% +the strong intuitive sense we have a +losing ourselves in a highly engaging + + align:start position:0% +losing ourselves in a highly engaging + + + align:start position:0% +losing ourselves in a highly engaging +sensory motor act um so some empirical + + align:start position:0% +sensory motor act um so some empirical + + + align:start position:0% +sensory motor act um so some empirical +evidence that um um um + + align:start position:0% +evidence that um um um + + + align:start position:0% +evidence that um um um +in conscious experience we might not + + align:start position:0% +in conscious experience we might not + + + align:start position:0% +in conscious experience we might not +have high order States so since I don't + + align:start position:0% +have high order States so since I don't + + + align:start position:0% +have high order States so since I don't +have much time so let me um just very + + align:start position:0% +have much time so let me um just very + + + align:start position:0% +have much time so let me um just very +quickly talk about a kind of a weirdness + + align:start position:0% +quickly talk about a kind of a weirdness + + + align:start position:0% +quickly talk about a kind of a weirdness +in the high order of view so according + + align:start position:0% +in the high order of view so according + + + align:start position:0% +in the high order of view so according +to the high order of view what it is for + + align:start position:0% +to the high order of view what it is for + + + align:start position:0% +to the high order of view what it is for +a pain to be conscious is forther to be + + align:start position:0% +a pain to be conscious is forther to be + + + align:start position:0% +a pain to be conscious is forther to be +another state that is about + + align:start position:0% +another state that is about + + + align:start position:0% +another state that is about +it um that makes the pain conscious what + + align:start position:0% +it um that makes the pain conscious what + + + align:start position:0% +it um that makes the pain conscious what +it would be for this state to be + + align:start position:0% +it would be for this state to be + + + align:start position:0% +it would be for this state to be +conscious would be there be another + + align:start position:0% +conscious would be there be another + + + align:start position:0% +conscious would be there be another +state about it what it would be for that + + align:start position:0% +state about it what it would be for that + + + align:start position:0% +state about it what it would be for that +state to be conscious would be for there + + align:start position:0% +state to be conscious would be for there + + + align:start position:0% +state to be conscious would be for there +to be another thought about it um but + + align:start position:0% +to be another thought about it um but + + + align:start position:0% +to be another thought about it um but +the last one in the series would be + + align:start position:0% +the last one in the series would be + + + align:start position:0% +the last one in the series would be +unconscious if there was no further + + align:start position:0% +unconscious if there was no further + + + align:start position:0% +unconscious if there was no further +thought about it and so in general + + align:start position:0% +thought about it and so in general + + + align:start position:0% +thought about it and so in general +higher order thoughts cannot be + + align:start position:0% +higher order thoughts cannot be + + + align:start position:0% +higher order thoughts cannot be +conscious because we can't have just an + + align:start position:0% +conscious because we can't have just an + + + align:start position:0% +conscious because we can't have just an +infinite array of them so this leads to + + align:start position:0% +infinite array of them so this leads to + + + align:start position:0% +infinite array of them so this leads to +the question why should being the object + + align:start position:0% +the question why should being the object + + + align:start position:0% +the question why should being the object +of an unconscious thought make a stake + + align:start position:0% +of an unconscious thought make a stake + + + align:start position:0% +of an unconscious thought make a stake +another thought or a desire or pain + + align:start position:0% +another thought or a desire or pain + + + align:start position:0% +another thought or a desire or pain +conscious why should the source of all + + align:start position:0% +conscious why should the source of all + + + align:start position:0% +conscious why should the source of all +Consciousness be something unconscious + + align:start position:0% +Consciousness be something unconscious + + + align:start position:0% +Consciousness be something unconscious +that's a puzzle for + + align:start position:0% + + + + align:start position:0% + +the um so let's see a + + align:start position:0% +the um so let's see a + + + align:start position:0% +the um so let's see a +[Music] + + align:start position:0% + + + + align:start position:0% + +um here is a second puzzle suppose you + + align:start position:0% +um here is a second puzzle suppose you + + + align:start position:0% +um here is a second puzzle suppose you +have a sensation of green that causes a + + align:start position:0% +have a sensation of green that causes a + + + align:start position:0% +have a sensation of green that causes a +higher order thought to the effect that + + align:start position:0% +higher order thought to the effect that + + + align:start position:0% +higher order thought to the effect that +you have a sensation of red what's the + + align:start position:0% +you have a sensation of red what's the + + + align:start position:0% +you have a sensation of red what's the +phenomenology does the pH ology go with + + align:start position:0% +phenomenology does the pH ology go with + + + align:start position:0% +phenomenology does the pH ology go with +the first order State the sensation of + + align:start position:0% +the first order State the sensation of + + + align:start position:0% +the first order State the sensation of +green but then you might wonder why you + + align:start position:0% +green but then you might wonder why you + + + align:start position:0% +green but then you might wonder why you +need the higher order State at all for + + align:start position:0% +need the higher order State at all for + + + align:start position:0% +need the higher order State at all for +Consciousness does the phenomenology go + + align:start position:0% +Consciousness does the phenomenology go + + + align:start position:0% +Consciousness does the phenomenology go +with the higher order state if so what's + + align:start position:0% +with the higher order state if so what's + + + align:start position:0% +with the higher order state if so what's +the difference between having a + + align:start position:0% +the difference between having a + + + align:start position:0% +the difference between having a +conscious pain and thinking you + + align:start position:0% +conscious pain and thinking you + + + align:start position:0% +conscious pain and thinking you +have maybe with both but there are two + + align:start position:0% +have maybe with both but there are two + + + align:start position:0% +have maybe with both but there are two +different colors so I I take this to be + + align:start position:0% +different colors so I I take this to be + + + align:start position:0% +different colors so I I take this to be +a serious kind of incoherence in the + + align:start position:0% +a serious kind of incoherence in the + + + align:start position:0% +a serious kind of incoherence in the +higher order view it's not clear whether + + align:start position:0% +higher order view it's not clear whether + + + align:start position:0% +higher order view it's not clear whether +the oh and by the way Alex burn is the + + align:start position:0% +the oh and by the way Alex burn is the + + + align:start position:0% +the oh and by the way Alex burn is the +person who first thought of this problem + + align:start position:0% +person who first thought of this problem + + + align:start position:0% +person who first thought of this problem +for the high order view um does the + + align:start position:0% +for the high order view um does the + + + align:start position:0% +for the high order view um does the +phenomenology go with the first order + + align:start position:0% +phenomenology go with the first order + + + align:start position:0% +phenomenology go with the first order +State the second order State both none + + align:start position:0% +State the second order State both none + + + align:start position:0% +State the second order State both none +of them seems to be um adequate + + align:start position:0% +of them seems to be um adequate + + + align:start position:0% +of them seems to be um adequate +um + + align:start position:0% +um + + + align:start position:0% +um +so now this may seem to be a kind of + + align:start position:0% +so now this may seem to be a kind of + + + align:start position:0% +so now this may seem to be a kind of +abstract + + align:start position:0% +abstract + + + align:start position:0% +abstract +problem um but actually it's a real + + align:start position:0% +problem um but actually it's a real + + + align:start position:0% +problem um but actually it's a real +problem and I um there it's a real + + align:start position:0% +problem and I um there it's a real + + + align:start position:0% +problem and I um there it's a real +problem because there are these + + align:start position:0% +problem because there are these + + + align:start position:0% +problem because there are these +bizarre um um U neurological syndromes + + align:start position:0% +bizarre um um U neurological syndromes + + + align:start position:0% +bizarre um um U neurological syndromes +in which + + align:start position:0% +in which + + + align:start position:0% +in which +um subjects have high order states that + + align:start position:0% +um subjects have high order states that + + + align:start position:0% +um subjects have high order states that +are quite at odds with their first order + + align:start position:0% +are quite at odds with their first order + + + align:start position:0% +are quite at odds with their first order +States at least a parent one of them is + + align:start position:0% +States at least a parent one of them is + + + align:start position:0% +States at least a parent one of them is +Anton syndrome where people are blind + + align:start position:0% +Anton syndrome where people are blind + + + align:start position:0% +Anton syndrome where people are blind +but they vociferously deny being blind + + align:start position:0% +but they vociferously deny being blind + + + align:start position:0% +but they vociferously deny being blind +this is a picture of Mr Anon so I won't + + align:start position:0% +this is a picture of Mr Anon so I won't + + + align:start position:0% +this is a picture of Mr Anon so I won't +read this whole thing + + align:start position:0% +read this whole thing + + + align:start position:0% +read this whole thing +um so this is a case of peripheral + + align:start position:0% +um so this is a case of peripheral + + + align:start position:0% +um so this is a case of peripheral +blinds the patient had no visual Acy or + + align:start position:0% +blinds the patient had no visual Acy or + + + align:start position:0% +blinds the patient had no visual Acy or +light perception in the right eye um but + + align:start position:0% +light perception in the right eye um but + + + align:start position:0% +light perception in the right eye um but +she in she insisted that she wasn't + + align:start position:0% +she in she insisted that she wasn't + + + align:start position:0% +she in she insisted that she wasn't +blind in the right side of fabul + + align:start position:0% +blind in the right side of fabul + + + align:start position:0% +blind in the right side of fabul +response most of the patients who have + + align:start position:0% +response most of the patients who have + + + align:start position:0% +response most of the patients who have +Anin syndrome are completely blind but + + align:start position:0% +Anin syndrome are completely blind but + + + align:start position:0% +Anin syndrome are completely blind but +insist that they're + + align:start position:0% +insist that they're + + + align:start position:0% +insist that they're +same now one issue in this + + align:start position:0% +same now one issue in this + + + align:start position:0% +same now one issue in this +literature um is + + align:start position:0% +literature um is + + + align:start position:0% +literature um is +um are are these p patients having some + + align:start position:0% +um are are these p patients having some + + + align:start position:0% +um are are these p patients having some +kind of a hallucination so I'll just + + align:start position:0% +kind of a hallucination so I'll just + + + align:start position:0% +kind of a hallucination so I'll just +very quickly show you a little movie of + + align:start position:0% +very quickly show you a little movie of + + + align:start position:0% +very quickly show you a little movie of +one of these + + align:start position:0% +one of these + + + align:start position:0% +one of these +patients so this is an Italian I don't + + align:start position:0% +patients so this is an Italian I don't + + + align:start position:0% +patients so this is an Italian I don't +know the sounds hooked up so his left + + align:start position:0% +know the sounds hooked up so his left + + + align:start position:0% +know the sounds hooked up so his left +arm is + + align:start position:0% + + + + align:start position:0% + +paralyzed he's depressed very bored all + + align:start position:0% +paralyzed he's depressed very bored all + + + align:start position:0% +paralyzed he's depressed very bored all +these patients seem to be depressed + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so he's trying to move his left arm + + align:start position:0% + + + + align:start position:0% + +see he says he's moved + + align:start position:0% + + + + align:start position:0% + +it okay so what you see with these + + align:start position:0% +it okay so what you see with these + + + align:start position:0% +it okay so what you see with these +patients is for a variety of + + align:start position:0% +patients is for a variety of + + + align:start position:0% +patients is for a variety of +syndromes they have some problem like + + align:start position:0% +syndromes they have some problem like + + + align:start position:0% +syndromes they have some problem like +they can't move their left arm but they + + align:start position:0% +they can't move their left arm but they + + + align:start position:0% +they can't move their left arm but they +think they've moved it now in some cases + + align:start position:0% +think they've moved it now in some cases + + + align:start position:0% +think they've moved it now in some cases +there is evidence for hallucinatory + + align:start position:0% +there is evidence for hallucinatory + + + align:start position:0% +there is evidence for hallucinatory +movement but there's good reason to + + align:start position:0% +movement but there's good reason to + + + align:start position:0% +movement but there's good reason to +think in a number of the cases that + + align:start position:0% +think in a number of the cases that + + + align:start position:0% +think in a number of the cases that +what's going on as a mechanism called + + align:start position:0% +what's going on as a mechanism called + + + align:start position:0% +what's going on as a mechanism called +confabulation it's a disorder of thought + + align:start position:0% +confabulation it's a disorder of thought + + + align:start position:0% +confabulation it's a disorder of thought +um they something to do with having a + + align:start position:0% +um they something to do with having a + + + align:start position:0% +um they something to do with having a +certain image of themselves makes them + + align:start position:0% +certain image of themselves makes them + + + align:start position:0% +certain image of themselves makes them +um think that they can do something when + + align:start position:0% +um think that they can do something when + + + align:start position:0% +um think that they can do something when +they can't and uh so a lot of the um um + + align:start position:0% +they can't and uh so a lot of the um um + + + align:start position:0% +they can't and uh so a lot of the um um +um the work in this area is in matter of + + align:start position:0% +um the work in this area is in matter of + + + align:start position:0% +um the work in this area is in matter of +trying to um um uh show what the causes + + align:start position:0% +trying to um um uh show what the causes + + + align:start position:0% +trying to um um uh show what the causes +particular causes are now unfortunately + + align:start position:0% +particular causes are now unfortunately + + + align:start position:0% +particular causes are now unfortunately +I have some other films which I don't + + align:start position:0% +I have some other films which I don't + + + align:start position:0% +I have some other films which I don't +really have time to show but um so the + + align:start position:0% +really have time to show but um so the + + + align:start position:0% +really have time to show but um so the +cases that illustrate that it's not + + align:start position:0% +cases that illustrate that it's not + + + align:start position:0% +cases that illustrate that it's not +always + + align:start position:0% +always + + + align:start position:0% +always +hallucination are um cases where you can + + align:start position:0% +hallucination are um cases where you can + + + align:start position:0% +hallucination are um cases where you can +see in one way or another the workings + + align:start position:0% +see in one way or another the workings + + + align:start position:0% +see in one way or another the workings +of the confabulation mechanism um for + + align:start position:0% +of the confabulation mechanism um for + + + align:start position:0% +of the confabulation mechanism um for +example let's see + + align:start position:0% + + + + align:start position:0% + +so there are patients who with brain + + align:start position:0% +so there are patients who with brain + + + align:start position:0% +so there are patients who with brain +damage who um um seem to be um lead + + align:start position:0% +damage who um um seem to be um lead + + + align:start position:0% +damage who um um seem to be um lead +lead this kind of cognitive distance in + + align:start position:0% +lead this kind of cognitive distance in + + + align:start position:0% +lead this kind of cognitive distance in +the case of anosia for + + align:start position:0% +the case of anosia for + + + align:start position:0% +the case of anosia for +prosia um this is a case where prosia is + + align:start position:0% +prosia um this is a case where prosia is + + + align:start position:0% +prosia um this is a case where prosia is +the U brain damage cause inability to + + align:start position:0% +the U brain damage cause inability to + + + align:start position:0% +the U brain damage cause inability to +recognize + + align:start position:0% +recognize + + + align:start position:0% +recognize +faces um the um or can be congenital as + + align:start position:0% +faces um the um or can be congenital as + + + align:start position:0% +faces um the um or can be congenital as +well and actually it turns out that + + align:start position:0% +well and actually it turns out that + + + align:start position:0% +well and actually it turns out that +something like 2% of people are + + align:start position:0% +something like 2% of people are + + + align:start position:0% +something like 2% of people are +congenitally prognostic probably some + + align:start position:0% +congenitally prognostic probably some + + + align:start position:0% +congenitally prognostic probably some +you know I'm a little bit proos myself + + align:start position:0% +you know I'm a little bit proos myself + + + align:start position:0% +you know I'm a little bit proos myself +um so but people can be Pro agnosic and + + align:start position:0% +um so but people can be Pro agnosic and + + + align:start position:0% +um so but people can be Pro agnosic and +insist that they recognized face I have + + align:start position:0% +insist that they recognized face I have + + + align:start position:0% +insist that they recognized face I have +a little um um um protocol which I don't + + align:start position:0% +a little um um um protocol which I don't + + + align:start position:0% +a little um um um protocol which I don't +have time to sh show you of a patient + + align:start position:0% +have time to sh show you of a patient + + + align:start position:0% +have time to sh show you of a patient +who was a painter and she's shown her + + align:start position:0% +who was a painter and she's shown her + + + align:start position:0% +who was a painter and she's shown her +own paintings of people and cannot + + align:start position:0% +own paintings of people and cannot + + + align:start position:0% +own paintings of people and cannot +recognize them but she can sometimes + + align:start position:0% +recognize them but she can sometimes + + + align:start position:0% +recognize them but she can sometimes +figure them out and there the protocol + + align:start position:0% +figure them out and there the protocol + + + align:start position:0% +figure them out and there the protocol +shows how she confabulates in order to + + align:start position:0% +shows how she confabulates in order to + + + align:start position:0% +shows how she confabulates in order to +convince herself that she really can + + align:start position:0% +convince herself that she really can + + + align:start position:0% +convince herself that she really can +recognize the people um another uh fact + + align:start position:0% +recognize the people um another uh fact + + + align:start position:0% +recognize the people um another uh fact +is that sometimes you can ask these + + align:start position:0% +is that sometimes you can ask these + + + align:start position:0% +is that sometimes you can ask these +people um um once they've recovered what + + align:start position:0% +people um um once they've recovered what + + + align:start position:0% +people um um once they've recovered what +was going on when um uh when they were + + align:start position:0% +was going on when um uh when they were + + + align:start position:0% +was going on when um uh when they were +um + + align:start position:0% +um + + + align:start position:0% +um +um having the the problem and they can + + align:start position:0% +um having the the problem and they can + + + align:start position:0% +um having the the problem and they can +um say look actually I wasn't seeing + + align:start position:0% +um say look actually I wasn't seeing + + + align:start position:0% +um say look actually I wasn't seeing +anything or I was I know I wasn't + + align:start position:0% +anything or I was I know I wasn't + + + align:start position:0% +anything or I was I know I wasn't +raising my arm but I was hoping that it + + align:start position:0% +raising my arm but I was hoping that it + + + align:start position:0% +raising my arm but I was hoping that it +would go up and that's why I said it was + + align:start position:0% +would go up and that's why I said it was + + + align:start position:0% +would go up and that's why I said it was +going up something like that so they + + align:start position:0% +going up something like that so they + + + align:start position:0% +going up something like that so they +they will say in they'll explain what + + align:start position:0% +they will say in they'll explain what + + + align:start position:0% +they will say in they'll explain what +was going on in a way that suggests that + + align:start position:0% +was going on in a way that suggests that + + + align:start position:0% +was going on in a way that suggests that +it was kind + + align:start position:0% +it was kind + + + align:start position:0% +it was kind +of so here's the deal there they are + + align:start position:0% +of so here's the deal there they are + + + align:start position:0% +of so here's the deal there they are +having the higher appar certainly having + + align:start position:0% +having the higher appar certainly having + + + align:start position:0% +having the higher appar certainly having +the higher order thoughts to the effect + + align:start position:0% +the higher order thoughts to the effect + + + align:start position:0% +the higher order thoughts to the effect +that they're having a certain experience + + align:start position:0% +that they're having a certain experience + + + align:start position:0% +that they're having a certain experience +but they're not having the experience so + + align:start position:0% +but they're not having the experience so + + + align:start position:0% +but they're not having the experience so +this is + + align:start position:0% +this is + + + align:start position:0% +this is +empirical empirical filling in of Alex's + + align:start position:0% +empirical empirical filling in of Alex's + + + align:start position:0% +empirical empirical filling in of Alex's +point that there could be this conflict + + align:start position:0% +point that there could be this conflict + + + align:start position:0% +point that there could be this conflict +between the um high order and the first + + align:start position:0% +between the um high order and the first + + + align:start position:0% +between the um high order and the first +order + + align:start position:0% +order + + + align:start position:0% +order +um so let's see + + align:start position:0% + + + + align:start position:0% + +well I guess I only have a few minutes + + align:start position:0% +well I guess I only have a few minutes + + + align:start position:0% +well I guess I only have a few minutes +left so um what like two minutes + + align:start position:0% +left so um what like two minutes + + + align:start position:0% +left so um what like two minutes +left yeah let me just switch to + + align:start position:0% +left yeah let me just switch to + + + align:start position:0% +left yeah let me just switch to +something completely different um so on + + align:start position:0% +something completely different um so on + + + align:start position:0% +something completely different um so on +the case of little children sometimes + + align:start position:0% +the case of little children sometimes + + + align:start position:0% +the case of little children sometimes +people don't realize just to the extent + + align:start position:0% +people don't realize just to the extent + + + align:start position:0% +people don't realize just to the extent +to which the amazing extent to which + + align:start position:0% +to which the amazing extent to which + + + align:start position:0% +to which the amazing extent to which +small children have trouble thinking + + align:start position:0% +small children have trouble thinking + + + align:start position:0% +small children have trouble thinking +about representational States and + + align:start position:0% +about representational States and + + + align:start position:0% +about representational States and +representation more generally here is a + + align:start position:0% +representation more generally here is a + + + align:start position:0% +representation more generally here is a +um a little movie of a one-year-old + + align:start position:0% +um a little movie of a one-year-old + + + align:start position:0% +um a little movie of a one-year-old +trying to + + align:start position:0% + + + + align:start position:0% + +pick trying to pick up the pictures off + + align:start position:0% +pick trying to pick up the pictures off + + + align:start position:0% +pick trying to pick up the pictures off +of a book this is very widely observed + + align:start position:0% +of a book this is very widely observed + + + align:start position:0% +of a book this is very widely observed +in in + + align:start position:0% +in in + + + align:start position:0% +in in +one-year-olds so the kids just don't + + align:start position:0% +one-year-olds so the kids just don't + + + align:start position:0% +one-year-olds so the kids just don't +understand that it is a + + align:start position:0% + + + + align:start position:0% + +representation and these problems are + + align:start position:0% +representation and these problems are + + + align:start position:0% +representation and these problems are +not just about representations but about + + align:start position:0% +not just about representations but about + + + align:start position:0% +not just about representations but about +representational States + + align:start position:0% +representational States + + + align:start position:0% +representational States +generally um + + align:start position:0% + + + + align:start position:0% + +so I'll show you a slightly different + + align:start position:0% +so I'll show you a slightly different + + + align:start position:0% +so I'll show you a slightly different +kind of thing here so these are a little + + align:start position:0% +kind of thing here so these are a little + + + align:start position:0% +kind of thing here so these are a little +these are kids older kids these are like + + align:start position:0% +these are kids older kids these are like + + + align:start position:0% +these are kids older kids these are like +two or three kids this age routinely + + align:start position:0% +two or three kids this age routinely + + + align:start position:0% +two or three kids this age routinely +think that they can get into cars or + + align:start position:0% +think that they can get into cars or + + + align:start position:0% +think that they can get into cars or +slide down + + align:start position:0% + + + + align:start position:0% + +slides I mean you know really it's an + + align:start position:0% +slides I mean you know really it's an + + + align:start position:0% +slides I mean you know really it's an +astonishing thing when you see a large + + align:start position:0% +astonishing thing when you see a large + + + align:start position:0% +astonishing thing when you see a large +child trying to do this they don't + + align:start position:0% +child trying to do this they don't + + + align:start position:0% +child trying to do this they don't +understand the difference between + + align:start position:0% +understand the difference between + + + align:start position:0% +understand the difference between +something that's a representation and a + + align:start position:0% +something that's a representation and a + + + align:start position:0% +something that's a representation and a +real + + align:start position:0% +real + + + align:start position:0% +real +thing um so here I'll give you one more + + align:start position:0% +thing um so here I'll give you one more + + + align:start position:0% +thing um so here I'll give you one more +of + + align:start position:0% + + + + align:start position:0% + +these so this is a kid going to there's + + align:start position:0% +these so this is a kid going to there's + + + align:start position:0% +these so this is a kid going to there's +a slide he's going to try to slide down + + align:start position:0% +a slide he's going to try to slide down + + + align:start position:0% +a slide he's going to try to slide down +the + + align:start position:0% + + + + align:start position:0% + +slide um okay so the general issue here + + align:start position:0% +slide um okay so the general issue here + + + align:start position:0% +slide um okay so the general issue here +here is that um + + align:start position:0% +here is that um + + + align:start position:0% +here is that um +um + + align:start position:0% +um + + + align:start position:0% +um +uh a wide variety of experiments show + + align:start position:0% +uh a wide variety of experiments show + + + align:start position:0% +uh a wide variety of experiments show +that kids have trouble forming um mental + + align:start position:0% +that kids have trouble forming um mental + + + align:start position:0% +that kids have trouble forming um mental +States about representations in these + + align:start position:0% +States about representations in these + + + align:start position:0% +States about representations in these +cases and um more generally about + + align:start position:0% +cases and um more generally about + + + align:start position:0% +cases and um more generally about +representational states there is + + align:start position:0% +representational states there is + + + align:start position:0% +representational states there is +evidence that kids have a harder time + + align:start position:0% +evidence that kids have a harder time + + + align:start position:0% +evidence that kids have a harder time +knowing about their own representational + + align:start position:0% +knowing about their own representational + + + align:start position:0% +knowing about their own representational +States and they do knowing about closely + + align:start position:0% +States and they do knowing about closely + + + align:start position:0% +States and they do knowing about closely +related skills for example so just in + + align:start position:0% +related skills for example so just in + + + align:start position:0% +related skills for example so just in +one experiment um um kids uh this done + + align:start position:0% +one experiment um um kids uh this done + + + align:start position:0% +one experiment um um kids uh this done +by marjerie Taylor um kids were um uh + + align:start position:0% +by marjerie Taylor um kids were um uh + + + align:start position:0% +by marjerie Taylor um kids were um uh +taught to count in Japanese and when + + align:start position:0% +taught to count in Japanese and when + + + align:start position:0% +taught to count in Japanese and when +they were asked um the American Kids + + align:start position:0% +they were asked um the American Kids + + + align:start position:0% +they were asked um the American Kids +taught to count in Japanese when they + + align:start position:0% +taught to count in Japanese when they + + + align:start position:0% +taught to count in Japanese when they +were asked how they knew the Japanese + + align:start position:0% +were asked how they knew the Japanese + + + align:start position:0% +were asked how they knew the Japanese +word for how they where they learned to + + align:start position:0% +word for how they where they learned to + + + align:start position:0% +word for how they where they learned to +count they would say that the + + align:start position:0% +count they would say that the + + + align:start position:0% +count they would say that the +experimentor just taught them but kids + + align:start position:0% +experimentor just taught them but kids + + + align:start position:0% +experimentor just taught them but kids +who were first asked first um how they + + align:start position:0% +who were first asked first um how they + + + align:start position:0% +who were first asked first um how they +knew the Japanese word for two say + + align:start position:0% +knew the Japanese word for two say + + + align:start position:0% +knew the Japanese word for two say +thought that they all always knew it or + + align:start position:0% +thought that they all always knew it or + + + align:start position:0% +thought that they all always knew it or +gave random answers so they seem much + + align:start position:0% +gave random answers so they seem much + + + align:start position:0% +gave random answers so they seem much +less good much more what sometimes is + + align:start position:0% +less good much more what sometimes is + + + align:start position:0% +less good much more what sometimes is +called source amesia for their mental + + align:start position:0% +called source amesia for their mental + + + align:start position:0% +called source amesia for their mental +States than their + + align:start position:0% +States than their + + + align:start position:0% +States than their +skills um so look the general Point here + + align:start position:0% +skills um so look the general Point here + + + align:start position:0% +skills um so look the general Point here +is that + + align:start position:0% +is that + + + align:start position:0% +is that +um um uh there's very good reason to + + align:start position:0% +um um uh there's very good reason to + + + align:start position:0% +um um uh there's very good reason to +think that these children have um + + align:start position:0% +think that these children have um + + + align:start position:0% +think that these children have um +conscious perceptual States um conscious + + align:start position:0% +conscious perceptual States um conscious + + + align:start position:0% +conscious perceptual States um conscious +pain + + align:start position:0% +pain + + + align:start position:0% +pain +all kinds of C States but their capacity + + align:start position:0% +all kinds of C States but their capacity + + + align:start position:0% +all kinds of C States but their capacity +to have higher order States about those + + align:start position:0% +to have higher order States about those + + + align:start position:0% +to have higher order States about those +States seems + + align:start position:0% +States seems + + + align:start position:0% +States seems +limited um and we have other evidence um + + align:start position:0% +limited um and we have other evidence um + + + align:start position:0% +limited um and we have other evidence um +uh so just to try to sum up the + + align:start position:0% +uh so just to try to sum up the + + + align:start position:0% +uh so just to try to sum up the +evidential + + align:start position:0% +evidential + + + align:start position:0% +evidential +situation um we have evidence for a um + + align:start position:0% +situation um we have evidence for a um + + + align:start position:0% +situation um we have evidence for a um +um for high order for discrepancy + + align:start position:0% +um for high order for discrepancy + + + align:start position:0% +um for high order for discrepancy +between um those um brain damage cases + + align:start position:0% +between um those um brain damage cases + + + align:start position:0% +between um those um brain damage cases +between high order the contents of high + + align:start position:0% +between high order the contents of high + + + align:start position:0% +between high order the contents of high +order States and the contents of lower + + align:start position:0% +order States and the contents of lower + + + align:start position:0% +order States and the contents of lower +order States + + align:start position:0% +order States + + + align:start position:0% +order States +and then there were these kind of + + align:start position:0% + + + + align:start position:0% + +um coherence problems in the higher + + align:start position:0% +um coherence problems in the higher + + + align:start position:0% +um coherence problems in the higher +order point of view so my general + + align:start position:0% +order point of view so my general + + + align:start position:0% +order point of view so my general +thought is that of these three the uh of + + align:start position:0% +thought is that of these three the uh of + + + align:start position:0% +thought is that of these three the uh of +ways of looking at scientific theories + + align:start position:0% +ways of looking at scientific theories + + + align:start position:0% +ways of looking at scientific theories +of + + align:start position:0% +of + + + align:start position:0% +of +of Consciousness the the biological the + + align:start position:0% +of Consciousness the the biological the + + + align:start position:0% +of Consciousness the the biological the +global workspace and the higher order + + align:start position:0% +global workspace and the higher order + + + align:start position:0% +global workspace and the higher order +one I don't think I think the higher + + align:start position:0% +one I don't think I think the higher + + + align:start position:0% +one I don't think I think the higher +order one is the one that works most + + align:start position:0% +order one is the one that works most + + + align:start position:0% +order one is the one that works most +well um as between the global workspace + + align:start position:0% +well um as between the global workspace + + + align:start position:0% +well um as between the global workspace +and the biological account um uh that uh + + align:start position:0% +and the biological account um uh that uh + + + align:start position:0% +and the biological account um uh that uh +is a topic for further investigation + + align:start position:0% + + + + align:start position:0% + +[Applause] \ No newline at end of file diff --git a/MTxjpJSp43A.txt b/MTxjpJSp43A.txt new file mode 100644 index 0000000000000000000000000000000000000000..d51226a063df3d9a0d01bb6c81192ceb65dafd2b --- /dev/null +++ b/MTxjpJSp43A.txt @@ -0,0 +1,915 @@ +align:start position:0% + +one thing I thought was effective was + + align:start position:0% +one thing I thought was effective was + + + align:start position:0% +one thing I thought was effective was +the way that Chris I think on the first + + align:start position:0% +the way that Chris I think on the first + + + align:start position:0% +the way that Chris I think on the first +the first day I attended and watched you + + align:start position:0% +the first day I attended and watched you + + + align:start position:0% +the first day I attended and watched you +kind of laid out a sort of more + + align:start position:0% +kind of laid out a sort of more + + + align:start position:0% +kind of laid out a sort of more +theoretical framework you know about + + align:start position:0% +theoretical framework you know about + + + align:start position:0% +theoretical framework you know about +storytelling and that sort of thing and + + align:start position:0% +storytelling and that sort of thing and + + + align:start position:0% +storytelling and that sort of thing and +I think that was nice because it for me + + align:start position:0% +I think that was nice because it for me + + + align:start position:0% +I think that was nice because it for me +it's you know I think it's effective and + + align:start position:0% +it's you know I think it's effective and + + + align:start position:0% +it's you know I think it's effective and +I'm just one kind of learner but to sort + + align:start position:0% +I'm just one kind of learner but to sort + + + align:start position:0% +I'm just one kind of learner but to sort +of have a sort of theory laid out first + + align:start position:0% +of have a sort of theory laid out first + + + align:start position:0% +of have a sort of theory laid out first +and then practice later you know sorry I + + align:start position:0% +and then practice later you know sorry I + + + align:start position:0% +and then practice later you know sorry I +got the big idea of the Y and then it + + align:start position:0% +got the big idea of the Y and then it + + + align:start position:0% +got the big idea of the Y and then it +felt to me like the course dove into + + align:start position:0% +felt to me like the course dove into + + + align:start position:0% +felt to me like the course dove into +some of the details of how you know this + + align:start position:0% +some of the details of how you know this + + + align:start position:0% +some of the details of how you know this +was like a theory practice kind of + + align:start position:0% +was like a theory practice kind of + + + align:start position:0% +was like a theory practice kind of +structure which I which work you know + + align:start position:0% +structure which I which work you know + + + align:start position:0% +structure which I which work you know +would have been quite useful to me how + + align:start position:0% +would have been quite useful to me how + + + align:start position:0% +would have been quite useful to me how +to take in the whole course you know + + align:start position:0% +to take in the whole course you know + + + align:start position:0% +to take in the whole course you know +yeah one of the big one of the big + + align:start position:0% +yeah one of the big one of the big + + + align:start position:0% +yeah one of the big one of the big +challenges I think with any kind of + + align:start position:0% +challenges I think with any kind of + + + align:start position:0% +challenges I think with any kind of +media course or you know film video is + + align:start position:0% +media course or you know film video is + + + align:start position:0% +media course or you know film video is +that that the technical stuff is so + + align:start position:0% +that that the technical stuff is so + + + align:start position:0% +that that the technical stuff is so +overwhelming potentially people who are + + align:start position:0% +overwhelming potentially people who are + + + align:start position:0% +overwhelming potentially people who are +new you know that there's such a big + + align:start position:0% +new you know that there's such a big + + + align:start position:0% +new you know that there's such a big +learning curve that you know you can get + + align:start position:0% +learning curve that you know you can get + + + align:start position:0% +learning curve that you know you can get +lost in those details really fast and + + align:start position:0% +lost in those details really fast and + + + align:start position:0% +lost in those details really fast and +you go oh my god you know as you say + + align:start position:0% +you go oh my god you know as you say + + + align:start position:0% +you go oh my god you know as you say +I'll never learn final cut why does + + align:start position:0% +I'll never learn final cut why does + + + align:start position:0% +I'll never learn final cut why does +everything I shoot suck oh this is + + align:start position:0% +everything I shoot suck oh this is + + + align:start position:0% +everything I shoot suck oh this is +terrible i'm a failure and if you kind + + align:start position:0% +terrible i'm a failure and if you kind + + + align:start position:0% +terrible i'm a failure and if you kind +of go well those aren't really the + + align:start position:0% +of go well those aren't really the + + + align:start position:0% +of go well those aren't really the +learning objectives which are you very + + align:start position:0% +learning objectives which are you very + + + align:start position:0% +learning objectives which are you very +clearly articulated then it's like kind + + align:start position:0% +clearly articulated then it's like kind + + + align:start position:0% +clearly articulated then it's like kind +of a big unclench it's like okay what + + align:start position:0% +of a big unclench it's like okay what + + + align:start position:0% +of a big unclench it's like okay what +I'm really learning here is to be a + + align:start position:0% +I'm really learning here is to be a + + + align:start position:0% +I'm really learning here is to be a +communicator be a storyteller carry + + align:start position:0% +communicator be a storyteller carry + + + align:start position:0% +communicator be a storyteller carry +myself understand this medium and maybe + + align:start position:0% +myself understand this medium and maybe + + + align:start position:0% +myself understand this medium and maybe +maybe someday I'll be a terrific editor + + align:start position:0% +maybe someday I'll be a terrific editor + + + align:start position:0% +maybe someday I'll be a terrific editor +or maybe I won't but either way maybe + + align:start position:0% +or maybe I won't but either way maybe + + + align:start position:0% +or maybe I won't but either way maybe +you'll plug into the process and some + + align:start position:0% +you'll plug into the process and some + + + align:start position:0% +you'll plug into the process and some +other it some other way exactly yeah but + + align:start position:0% +other it some other way exactly yeah but + + + align:start position:0% +other it some other way exactly yeah but +you have to understand the whole process + + align:start position:0% +you have to understand the whole process + + + align:start position:0% +you have to understand the whole process +right I remember when I first proposed + + align:start position:0% +right I remember when I first proposed + + + align:start position:0% +right I remember when I first proposed +like because you were like what do you + + align:start position:0% +like because you were like what do you + + + align:start position:0% +like because you were like what do you +want me to do because i was just like + + align:start position:0% +want me to do because i was just like + + + align:start position:0% +want me to do because i was just like +can you be involved in this and how and + + align:start position:0% +can you be involved in this and how and + + + align:start position:0% +can you be involved in this and how and +it was sort of like well maybe you could + + align:start position:0% +it was sort of like well maybe you could + + + align:start position:0% +it was sort of like well maybe you could +cover the actual basics of shooting and + + align:start position:0% +cover the actual basics of shooting and + + + align:start position:0% +cover the actual basics of shooting and +everything being said something like + + align:start position:0% +everything being said something like + + + align:start position:0% +everything being said something like +they seem like very technical things and + + align:start position:0% +they seem like very technical things and + + + align:start position:0% +they seem like very technical things and +i was like oh shoot like this is + + align:start position:0% +i was like oh shoot like this is + + + align:start position:0% +i was like oh shoot like this is +terrible i'm doing the thing that i tell + + align:start position:0% +terrible i'm doing the thing that i tell + + + align:start position:0% +terrible i'm doing the thing that i tell +people not to do so we made a very + + align:start position:0% +people not to do so we made a very + + + align:start position:0% +people not to do so we made a very +conscious decision to take all those + + align:start position:0% +conscious decision to take all those + + + align:start position:0% +conscious decision to take all those +technical elements like we did not teach + + align:start position:0% +technical elements like we did not teach + + + align:start position:0% +technical elements like we did not teach +how to edit on soft on final cut or + + align:start position:0% +how to edit on soft on final cut or + + + align:start position:0% +how to edit on soft on final cut or +anything + + align:start position:0% +anything + + + align:start position:0% +anything +instead mit has free window licensing + + align:start position:0% +instead mit has free window licensing + + + align:start position:0% +instead mit has free window licensing +and honestly like their videos teach it + + align:start position:0% +and honestly like their videos teach it + + + align:start position:0% +and honestly like their videos teach it +better than I do like I I don't know + + align:start position:0% +better than I do like I I don't know + + + align:start position:0% +better than I do like I I don't know +final cut well enough to teach it but + + align:start position:0% +final cut well enough to teach it but + + + align:start position:0% +final cut well enough to teach it but +not all the students used it so we said + + align:start position:0% +not all the students used it so we said + + + align:start position:0% +not all the students used it so we said +for all like the technical learning + + align:start position:0% +for all like the technical learning + + + align:start position:0% +for all like the technical learning +stuff it was all on like digital blended + + align:start position:0% +stuff it was all on like digital blended + + + align:start position:0% +stuff it was all on like digital blended +learning mm-hmm flipped classroom yeah + + align:start position:0% +learning mm-hmm flipped classroom yeah + + + align:start position:0% +learning mm-hmm flipped classroom yeah +thank you and class time was really + + align:start position:0% +thank you and class time was really + + + align:start position:0% +thank you and class time was really +about teaching big picture stuff and + + align:start position:0% +about teaching big picture stuff and + + + align:start position:0% +about teaching big picture stuff and +then workshopping specific examples and + + align:start position:0% +then workshopping specific examples and + + + align:start position:0% +then workshopping specific examples and +specific things they came up with yeah + + align:start position:0% +specific things they came up with yeah + + + align:start position:0% +specific things they came up with yeah +cuz time is limited and it's so daunting + + align:start position:0% +cuz time is limited and it's so daunting + + + align:start position:0% +cuz time is limited and it's so daunting +I mean to become a director on-camera + + align:start position:0% +I mean to become a director on-camera + + + align:start position:0% +I mean to become a director on-camera +host writer-editor camera person all in + + align:start position:0% +host writer-editor camera person all in + + + align:start position:0% +host writer-editor camera person all in +a few weeks I mean it's just not going + + align:start position:0% +a few weeks I mean it's just not going + + + align:start position:0% +a few weeks I mean it's just not going +to happen this is the expectation that + + align:start position:0% +to happen this is the expectation that + + + align:start position:0% +to happen this is the expectation that +they come out with a notion of + + align:start position:0% +they come out with a notion of + + + align:start position:0% +they come out with a notion of +storytelling I think would be sufficient + + align:start position:0% +storytelling I think would be sufficient + + + align:start position:0% +storytelling I think would be sufficient +yeah yeah it really ended up being a + + align:start position:0% +yeah yeah it really ended up being a + + + align:start position:0% +yeah yeah it really ended up being a +class on pre-production it was like two + + align:start position:0% +class on pre-production it was like two + + + align:start position:0% +class on pre-production it was like two +weeks of intense scripting and planning + + align:start position:0% +weeks of intense scripting and planning + + + align:start position:0% +weeks of intense scripting and planning +yeah um and the rest just sort of + + align:start position:0% +yeah um and the rest just sort of + + + align:start position:0% +yeah um and the rest just sort of +happened to him the last couple days + + align:start position:0% +happened to him the last couple days + + + align:start position:0% +happened to him the last couple days +they just have to figure out yeah that's + + align:start position:0% +they just have to figure out yeah that's + + + align:start position:0% +they just have to figure out yeah that's +that's great I mean your technical + + align:start position:0% +that's great I mean your technical + + + align:start position:0% +that's great I mean your technical +execution gets pushed to the margin and + + align:start position:0% +execution gets pushed to the margin and + + + align:start position:0% +execution gets pushed to the margin and +the more creative you know stuff takes + + align:start position:0% +the more creative you know stuff takes + + + align:start position:0% +the more creative you know stuff takes +precedence yeah I mean it's a different + + align:start position:0% +precedence yeah I mean it's a different + + + align:start position:0% +precedence yeah I mean it's a different +class like I there were a couple people + + align:start position:0% +class like I there were a couple people + + + align:start position:0% +class like I there were a couple people +who dropped because they came in + + align:start position:0% +who dropped because they came in + + + align:start position:0% +who dropped because they came in +thinking like this is going to be a + + align:start position:0% +thinking like this is going to be a + + + align:start position:0% +thinking like this is going to be a +class on how to make a video and it's + + align:start position:0% +class on how to make a video and it's + + + align:start position:0% +class on how to make a video and it's +not exactly about that mm-hmm and + + align:start position:0% +not exactly about that mm-hmm and + + + align:start position:0% +not exactly about that mm-hmm and +because there are other classes like + + align:start position:0% +because there are other classes like + + + align:start position:0% +because there are other classes like +that that already exist on campus so + + align:start position:0% +that that already exist on campus so + + + align:start position:0% +that that already exist on campus so +there's no reason for us to redo that + + align:start position:0% +there's no reason for us to redo that + + + align:start position:0% +there's no reason for us to redo that +and you learn that stuff by like + + align:start position:0% +and you learn that stuff by like + + + align:start position:0% +and you learn that stuff by like +shooting your own stuff yeah yeah yeah + + align:start position:0% +shooting your own stuff yeah yeah yeah + + + align:start position:0% +shooting your own stuff yeah yeah yeah +but like if someone's going to watch + + align:start position:0% +but like if someone's going to watch + + + align:start position:0% +but like if someone's going to watch +this class on it open courseware for + + align:start position:0% +this class on it open courseware for + + + align:start position:0% +this class on it open courseware for +instance they're not necessarily going + + align:start position:0% +instance they're not necessarily going + + + align:start position:0% +instance they're not necessarily going +to pick up the practical skills that + + align:start position:0% +to pick up the practical skills that + + + align:start position:0% +to pick up the practical skills that +they might be expecting to like yeah + + align:start position:0% +they might be expecting to like yeah + + + align:start position:0% +they might be expecting to like yeah +yeah but like a teacher who might be + + align:start position:0% +yeah but like a teacher who might be + + + align:start position:0% +yeah but like a teacher who might be +watching this might be like how do I + + align:start position:0% +watching this might be like how do I + + + align:start position:0% +watching this might be like how do I +teach a video production class and I'm + + align:start position:0% +teach a video production class and I'm + + + align:start position:0% +teach a video production class and I'm +not sure this is necessarily exactly + + align:start position:0% +not sure this is necessarily exactly + + + align:start position:0% +not sure this is necessarily exactly +that sorry + + align:start position:0% + + + + align:start position:0% + +oops yeah but it is hopefully maybe a + + align:start position:0% +oops yeah but it is hopefully maybe a + + + align:start position:0% +oops yeah but it is hopefully maybe a +conceptual framework that you could then + + align:start position:0% +conceptual framework that you could then + + + align:start position:0% +conceptual framework that you could then +plug in production modules into I mean + + align:start position:0% +plug in production modules into I mean + + + align:start position:0% +plug in production modules into I mean +yeah for a larger course yeah it was so + + align:start position:0% +yeah for a larger course yeah it was so + + + align:start position:0% +yeah for a larger course yeah it was so +short yeah I guess friend yeah what can + + align:start position:0% +short yeah I guess friend yeah what can + + + align:start position:0% +short yeah I guess friend yeah what can +you do Claire can you accomplish in that + + align:start position:0% +you do Claire can you accomplish in that + + + align:start position:0% +you do Claire can you accomplish in that +time really yeah I was impressed by how + + align:start position:0% +time really yeah I was impressed by how + + + align:start position:0% +time really yeah I was impressed by how +ambitious it was he was very ambitious i + + align:start position:0% +ambitious it was he was very ambitious i + + + align:start position:0% +ambitious it was he was very ambitious i +thought yeah yeah yeah \ No newline at end of file diff --git a/N0CVIoVQkmc.txt b/N0CVIoVQkmc.txt new file mode 100644 index 0000000000000000000000000000000000000000..5af010eba41a9e10920cf47f6dff4be10762f066 --- /dev/null +++ b/N0CVIoVQkmc.txt @@ -0,0 +1,7747 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu welcome one quick + + align:start position:0% +ocw.mit.edu welcome one quick + + + align:start position:0% +ocw.mit.edu welcome one quick +announcement if you have not yet picked + + align:start position:0% +announcement if you have not yet picked + + + align:start position:0% +announcement if you have not yet picked +up your graded + + align:start position:0% +up your graded + + + align:start position:0% +up your graded +exams you can do so by seeing the Tas + + align:start position:0% +exams you can do so by seeing the Tas + + + align:start position:0% +exams you can do so by seeing the Tas +after the + + align:start position:0% +after the + + + align:start position:0% +after the +hour + + align:start position:0% +hour + + + align:start position:0% +hour +okay so uh today I want to continue to + + align:start position:0% +okay so uh today I want to continue to + + + align:start position:0% +okay so uh today I want to continue to +think about what we started last week + + align:start position:0% +think about what we started last week + + + align:start position:0% +think about what we started last week +thinking about 4A + + align:start position:0% +thinking about 4A + + + align:start position:0% +thinking about 4A +series the idea is to develop a + + align:start position:0% +series the idea is to develop a + + + align:start position:0% +series the idea is to develop a +theory + + align:start position:0% +theory + + + align:start position:0% +theory +that lets us look at + + align:start position:0% +that lets us look at + + + align:start position:0% +that lets us look at +signals on the basis of frequency + + align:start position:0% +signals on the basis of frequency + + + align:start position:0% +signals on the basis of frequency +content much as we looked at frequency + + align:start position:0% +content much as we looked at frequency + + + align:start position:0% +content much as we looked at frequency +responses as a characterization of + + align:start position:0% +responses as a characterization of + + + align:start position:0% +responses as a characterization of +systems according to the way they + + align:start position:0% +systems according to the way they + + + align:start position:0% +systems according to the way they +processed uh frequencies and we saw last + + align:start position:0% +processed uh frequencies and we saw last + + + align:start position:0% +processed uh frequencies and we saw last +time that there were a number of kinds + + align:start position:0% +time that there were a number of kinds + + + align:start position:0% +time that there were a number of kinds +of signals for example musical signals + + align:start position:0% +of signals for example musical signals + + + align:start position:0% +of signals for example musical signals +where that kind of an of an approach + + align:start position:0% +where that kind of an of an approach + + + align:start position:0% +where that kind of an of an approach +thinking about what's thinking about the + + align:start position:0% +thinking about what's thinking about the + + + align:start position:0% +thinking about what's thinking about the +signal according to the frequencies that + + align:start position:0% +signal according to the frequencies that + + + align:start position:0% +signal according to the frequencies that +are in it makes a lot of sense and can + + align:start position:0% +are in it makes a lot of sense and can + + + align:start position:0% +are in it makes a lot of sense and can +lead to + + align:start position:0% +lead to + + + align:start position:0% +lead to +Insight we also developed some formalism + + align:start position:0% +Insight we also developed some formalism + + + align:start position:0% +Insight we also developed some formalism +we figured out how you can break a + + align:start position:0% +we figured out how you can break a + + + align:start position:0% +we figured out how you can break a +signal into components and then assemble + + align:start position:0% +signal into components and then assemble + + + align:start position:0% +signal into components and then assemble +the the components to um generate the + + align:start position:0% +the the components to um generate the + + + align:start position:0% +the the components to um generate the +signal and what I want to mention at the + + align:start position:0% +signal and what I want to mention at the + + + align:start position:0% +signal and what I want to mention at the +beginning of the hour today is just how + + align:start position:0% +beginning of the hour today is just how + + + align:start position:0% +beginning of the hour today is just how +to think about this operation in uh in a + + align:start position:0% +to think about this operation in uh in a + + + align:start position:0% +to think about this operation in uh in a +more familiar way we do this kind of a + + align:start position:0% +more familiar way we do this kind of a + + + align:start position:0% +more familiar way we do this kind of a +thing breaking a breaking something into + + align:start position:0% +thing breaking a breaking something into + + + align:start position:0% +thing breaking a breaking something into +components all the + + align:start position:0% +components all the + + + align:start position:0% +components all the +time one of the more familiar examples + + align:start position:0% +time one of the more familiar examples + + + align:start position:0% +time one of the more familiar examples +might be thinking about three space + + align:start position:0% +might be thinking about three space + + + align:start position:0% +might be thinking about three space +right uh the cartisian analysis of three + + align:start position:0% +right uh the cartisian analysis of three + + + align:start position:0% +right uh the cartisian analysis of three +spaces based on the idea that you can + + align:start position:0% +spaces based on the idea that you can + + + align:start position:0% +spaces based on the idea that you can +think about a vector location in three + + align:start position:0% +think about a vector location in three + + + align:start position:0% +think about a vector location in three +space as having components there's a + + align:start position:0% +space as having components there's a + + + align:start position:0% +space as having components there's a +component in the X Direction the y + + align:start position:0% +component in the X Direction the y + + + align:start position:0% +component in the X Direction the y +direction Z Direction that's completely + + align:start position:0% +direction Z Direction that's completely + + + align:start position:0% +direction Z Direction that's completely +analogous to the way we're thinking + + align:start position:0% +analogous to the way we're thinking + + + align:start position:0% +analogous to the way we're thinking +about 4A representations for signals so + + align:start position:0% +about 4A representations for signals so + + + align:start position:0% +about 4A representations for signals so +just like we would think about uh + + align:start position:0% +just like we would think about uh + + + align:start position:0% +just like we would think about uh +synthesizing the location of a point by + + align:start position:0% +synthesizing the location of a point by + + + align:start position:0% +synthesizing the location of a point by +adding together three + + align:start position:0% +adding together three + + + align:start position:0% +adding together three +pieces and we would think about + + align:start position:0% +pieces and we would think about + + + align:start position:0% +pieces and we would think about +analyzing a point to figure out how big + + align:start position:0% +analyzing a point to figure out how big + + + align:start position:0% +analyzing a point to figure out how big +the components are in each of those + + align:start position:0% +the components are in each of those + + + align:start position:0% +the components are in each of those +directions it's exactly the same when we + + align:start position:0% +directions it's exactly the same when we + + + align:start position:0% +directions it's exactly the same when we +think about 4A series we think about + + align:start position:0% +think about 4A series we think about + + + align:start position:0% +think about 4A series we think about +representing a signal as a sum of things + + align:start position:0% +representing a signal as a sum of things + + + align:start position:0% +representing a signal as a sum of things +so the sum is precisely the same this + + align:start position:0% +so the sum is precisely the same this + + + align:start position:0% +so the sum is precisely the same this +one happens to have an infinite number + + align:start position:0% +one happens to have an infinite number + + + align:start position:0% +one happens to have an infinite number +of + + align:start position:0% +of + + + align:start position:0% +of +terms the top one has three + + align:start position:0% +terms the top one has three + + + align:start position:0% +terms the top one has three +terms the principles are very similar so + + align:start position:0% +terms the principles are very similar so + + + align:start position:0% +terms the principles are very similar so +we think about representing a signal as + + align:start position:0% +we think about representing a signal as + + + align:start position:0% +we think about representing a signal as +a sum of components we think about + + align:start position:0% +a sum of components we think about + + + align:start position:0% +a sum of components we think about +representing a point in three space as a + + align:start position:0% +representing a point in three space as a + + + align:start position:0% +representing a point in three space as a +sum of components and we think about + + align:start position:0% +sum of components and we think about + + + align:start position:0% +sum of components and we think about +analyzing the signal or the vector in + + align:start position:0% +analyzing the signal or the vector in + + + align:start position:0% +analyzing the signal or the vector in +three space so that we figure out what + + align:start position:0% +three space so that we figure out what + + + align:start position:0% +three space so that we figure out what +each of those components + + align:start position:0% +each of those components + + + align:start position:0% +each of those components +are and we do it in an operation where + + align:start position:0% +are and we do it in an operation where + + + align:start position:0% +are and we do it in an operation where +it's actually very convenient to think + + align:start position:0% +it's actually very convenient to think + + + align:start position:0% +it's actually very convenient to think +about the decomposition of the 48 + + align:start position:0% +about the decomposition of the 48 + + + align:start position:0% +about the decomposition of the 48 +components using precisely the same + + align:start position:0% +components using precisely the same + + + align:start position:0% +components using precisely the same +language that we would use for thinking + + align:start position:0% +language that we would use for thinking + + + align:start position:0% +language that we would use for thinking +about Vector spaces so we would think + + align:start position:0% +about Vector spaces so we would think + + + align:start position:0% +about Vector spaces so we would think +about uh in the case of the forier we + + align:start position:0% +about uh in the case of the forier we + + + align:start position:0% +about uh in the case of the forier we +think about integrating over the period + + align:start position:0% +think about integrating over the period + + + align:start position:0% +think about integrating over the period +Zs out a + + align:start position:0% +Zs out a + + + align:start position:0% +Zs out a +component the analogous operation for + + align:start position:0% +component the analogous operation for + + + align:start position:0% +component the analogous operation for +three space is to think about a DOT + + align:start position:0% +three space is to think about a DOT + + + align:start position:0% +three space is to think about a DOT +product the way you take a vector and + + align:start position:0% +product the way you take a vector and + + + align:start position:0% +product the way you take a vector and +figure out the component in the X + + align:start position:0% +figure out the component in the X + + + align:start position:0% +figure out the component in the X +direction is to dot it with + + align:start position:0% +direction is to dot it with + + + align:start position:0% +direction is to dot it with +it the dot product in the Fier case we + + align:start position:0% +it the dot product in the Fier case we + + + align:start position:0% +it the dot product in the Fier case we +think about it as being an inner + + align:start position:0% +think about it as being an inner + + + align:start position:0% +think about it as being an inner +product the idea is completely analogous + + align:start position:0% +product the idea is completely analogous + + + align:start position:0% +product the idea is completely analogous +so we think about having the inner + + align:start position:0% +so we think about having the inner + + + align:start position:0% +so we think about having the inner +product of two things the reference + + align:start position:0% +product of two things the reference + + + align:start position:0% +product of two things the reference +Direction and the vector + + align:start position:0% +Direction and the vector + + + align:start position:0% +Direction and the vector +so reference Direction and Vector we + + align:start position:0% +so reference Direction and Vector we + + + align:start position:0% +so reference Direction and Vector we +think about it exactly the same way + + align:start position:0% +think about it exactly the same way + + + align:start position:0% +think about it exactly the same way +except now it's an inner product which + + align:start position:0% +except now it's an inner product which + + + align:start position:0% +except now it's an inner product which +means that after we've multiplied we + + align:start position:0% +means that after we've multiplied we + + + align:start position:0% +means that after we've multiplied we +have to integrate that's the only + + align:start position:0% +have to integrate that's the only + + + align:start position:0% +have to integrate that's the only +difference between uh inner product in + + align:start position:0% +difference between uh inner product in + + + align:start position:0% +difference between uh inner product in +inner product implies Sumer integrate + + align:start position:0% +inner product implies Sumer integrate + + + align:start position:0% +inner product implies Sumer integrate +after you've done the + + align:start position:0% +after you've done the + + + align:start position:0% +after you've done the +multiplication so we do exactly the same + + align:start position:0% +multiplication so we do exactly the same + + + align:start position:0% +multiplication so we do exactly the same +thing except that now we think about the + + align:start position:0% +thing except that now we think about the + + + align:start position:0% +thing except that now we think about the +inner product of A and + + align:start position:0% +inner product of A and + + + align:start position:0% +inner product of A and +B that's just the + + align:start position:0% +B that's just the + + + align:start position:0% +B that's just the +integral where we take the complex conj + + align:start position:0% +integral where we take the complex conj + + + align:start position:0% +integral where we take the complex conj +of of one of the signals only because by + + align:start position:0% +of of one of the signals only because by + + + align:start position:0% +of of one of the signals only because by +defining it with the complex conjugate + + align:start position:0% +defining it with the complex conjugate + + + align:start position:0% +defining it with the complex conjugate +there we set up the inner product so + + align:start position:0% +there we set up the inner product so + + + align:start position:0% +there we set up the inner product so +that the answer is zero unless we uh + + align:start position:0% +that the answer is zero unless we uh + + + align:start position:0% +that the answer is zero unless we uh +take the inner product of the of two + + align:start position:0% +take the inner product of the of two + + + align:start position:0% +take the inner product of the of two +things in the same + + align:start position:0% +things in the same + + + align:start position:0% +things in the same +direction okay so by putting the minus + + align:start position:0% +direction okay so by putting the minus + + + align:start position:0% +direction okay so by putting the minus +sign there if the two reference + + align:start position:0% +sign there if the two reference + + + align:start position:0% +sign there if the two reference +directions that is to say the one + + align:start position:0% +directions that is to say the one + + + align:start position:0% +directions that is to say the one +characterized by K and M the ones + + align:start position:0% +characterized by K and M the ones + + + align:start position:0% +characterized by K and M the ones +characterized by K and M the in product + + align:start position:0% +characterized by K and M the in product + + + align:start position:0% +characterized by K and M the in product +will be zero if we take the complex + + align:start position:0% +will be zero if we take the complex + + + align:start position:0% +will be zero if we take the complex +conjugate as long as K is not equal to m + + align:start position:0% +conjugate as long as K is not equal to m + + + align:start position:0% +conjugate as long as K is not equal to m +k equals m is the only non zero + + align:start position:0% +k equals m is the only non zero + + + align:start position:0% +k equals m is the only non zero +component okay is that all + + align:start position:0% +component okay is that all + + + align:start position:0% +component okay is that all +clear so to make clear to make sure that + + align:start position:0% +clear so to make clear to make sure that + + + align:start position:0% +clear so to make clear to make sure that +it's clear here's a + + align:start position:0% + + + + align:start position:0% + +question how many of the following pairs + + align:start position:0% +question how many of the following pairs + + + align:start position:0% +question how many of the following pairs +of functions are + + align:start position:0% +of functions are + + + align:start position:0% +of functions are +orthogonal in tal + + align:start position:0% +orthogonal in tal + + + align:start position:0% +orthogonal in tal +3 part of the goal of the exercise is to + + align:start position:0% +3 part of the goal of the exercise is to + + + align:start position:0% +3 part of the goal of the exercise is to +figure out what the little caveat in t + + align:start position:0% +figure out what the little caveat in t + + + align:start position:0% +figure out what the little caveat in t +equals 3 means so look at your neighbor + + align:start position:0% +equals 3 means so look at your neighbor + + + align:start position:0% +equals 3 means so look at your neighbor +say hello figure out a number between Z + + align:start position:0% +say hello figure out a number between Z + + + align:start position:0% +say hello figure out a number between Z +and + + align:start position:0% + + + + align:start position:0% + +four + + align:start position:0% + + + + align:start position:0% + +for e + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +should + + align:start position:0% + + + + align:start position:0% + +beix thank + + align:start position:0% +beix thank + + + align:start position:0% +beix thank +you okay so how many signals how many of + + align:start position:0% +you okay so how many signals how many of + + + align:start position:0% +you okay so how many signals how many of +the pairs are orthogonal to each + + align:start position:0% +the pairs are orthogonal to each + + + align:start position:0% +the pairs are orthogonal to each +other raise your hand with some number + + align:start position:0% +other raise your hand with some number + + + align:start position:0% +other raise your hand with some number +between zero and four unless you're + + align:start position:0% +between zero and four unless you're + + + align:start position:0% +between zero and four unless you're +completely bizarre and raise five I mean + + align:start position:0% +completely bizarre and raise five I mean + + + align:start position:0% +completely bizarre and raise five I mean +okay come on come on high so I can see + + align:start position:0% +okay come on come on high so I can see + + + align:start position:0% +okay come on come on high so I can see +them remember if you're wrong it's your + + align:start position:0% +them remember if you're wrong it's your + + + align:start position:0% +them remember if you're wrong it's your +partner's fault it's not your fault uh + + align:start position:0% +partner's fault it's not your fault uh + + + align:start position:0% +partner's fault it's not your fault uh +okay not + + align:start position:0% +okay not + + + align:start position:0% +okay not +quite a lot of bad Partners uh no no um + + align:start position:0% +quite a lot of bad Partners uh no no um + + + align:start position:0% +quite a lot of bad Partners uh no no um +let's do the first one is the COS of 2 + + align:start position:0% +let's do the first one is the COS of 2 + + + align:start position:0% +let's do the first one is the COS of 2 +pi t orthogonal to the S of 2 pi T over + + align:start position:0% +pi t orthogonal to the S of 2 pi T over + + + align:start position:0% +pi t orthogonal to the S of 2 pi T over +the interval capital T equals + + align:start position:0% + + + + align:start position:0% + +3 yes + + align:start position:0% + + + + align:start position:0% + +no I haven't a + + align:start position:0% +no I haven't a + + + align:start position:0% +no I haven't a +clue I don't care no no no no no you all + + align:start position:0% +clue I don't care no no no no no you all + + + align:start position:0% +clue I don't care no no no no no you all +care + + align:start position:0% +care + + + align:start position:0% +care +no are they orthogonal so what how how + + align:start position:0% +no are they orthogonal so what how how + + + align:start position:0% +no are they orthogonal so what how how +do I formally ask the question are they + + align:start position:0% + + + + align:start position:0% + +orthogonal okay so it's either the last + + align:start position:0% +orthogonal okay so it's either the last + + + align:start position:0% +orthogonal okay so it's either the last +slide or the next slide so go back to + + align:start position:0% +slide or the next slide so go back to + + + align:start position:0% +slide or the next slide so go back to +the last slide what's it mean if they're + + align:start position:0% +the last slide what's it mean if they're + + + align:start position:0% +the last slide what's it mean if they're +orthogonal + + align:start position:0% + + + + align:start position:0% + +yeah so how do you so how do I take the + + align:start position:0% +yeah so how do you so how do I take the + + + align:start position:0% +yeah so how do you so how do I take the +dot product what do I + + align:start position:0% + + + + align:start position:0% + +do conjugate one so I want to I'm + + align:start position:0% +do conjugate one so I want to I'm + + + align:start position:0% +do conjugate one so I want to I'm +thinking about one over T the integral + + align:start position:0% +thinking about one over T the integral + + + align:start position:0% +thinking about one over T the integral +over t a star of t b of T DT + + align:start position:0% +over t a star of t b of T DT + + + align:start position:0% +over t a star of t b of T DT +right so the t comes in here right I'm + + align:start position:0% +right so the t comes in here right I'm + + + align:start position:0% +right so the t comes in here right I'm +integrating over a period T so I take + + align:start position:0% +integrating over a period T so I take + + + align:start position:0% +integrating over a period T so I take +the two functions and I multiply them + + align:start position:0% +the two functions and I multiply them + + + align:start position:0% +the two functions and I multiply them +together + + align:start position:0% +together + + + align:start position:0% +together +so I have this function I have that + + align:start position:0% +so I have this function I have that + + + align:start position:0% +so I have this function I have that +function I multiply them + + align:start position:0% +function I multiply them + + + align:start position:0% +function I multiply them +together if you multiply two fun two + + align:start position:0% +together if you multiply two fun two + + + align:start position:0% +together if you multiply two fun two +sinusoids of the same frequency but + + align:start position:0% +sinusoids of the same frequency but + + + align:start position:0% +sinusoids of the same frequency but +different phase what do you + + align:start position:0% +different phase what do you + + + align:start position:0% +different phase what do you +get another sinusoid right so you all + + align:start position:0% +get another sinusoid right so you all + + + align:start position:0% +get another sinusoid right so you all +know all these complicated trig + + align:start position:0% +know all these complicated trig + + + align:start position:0% +know all these complicated trig +relationships right here's one of them + + align:start position:0% +relationships right here's one of them + + + align:start position:0% +relationships right here's one of them +if you multiply COS of 2 pi T * the S of + + align:start position:0% +if you multiply COS of 2 pi T * the S of + + + align:start position:0% +if you multiply COS of 2 pi T * the S of +Pi T you get half the sign of double the + + align:start position:0% +Pi T you get half the sign of double the + + + align:start position:0% +Pi T you get half the sign of double the +frequency okay you don't need to + + align:start position:0% +frequency okay you don't need to + + + align:start position:0% +frequency okay you don't need to +memorize that you just look at this + + align:start position:0% +memorize that you just look at this + + + align:start position:0% +memorize that you just look at this +picture you look at that + + align:start position:0% +picture you look at that + + + align:start position:0% +picture you look at that +picture this one over the interval three + + align:start position:0% +picture this one over the interval three + + + align:start position:0% +picture this one over the interval three +has three periods right there are three + + align:start position:0% +has three periods right there are three + + + align:start position:0% +has three periods right there are three +periods of that + + align:start position:0% +periods of that + + + align:start position:0% +periods of that +waveform over the period capital T + + align:start position:0% +waveform over the period capital T + + + align:start position:0% +waveform over the period capital T +there's an integer number three same + + align:start position:0% +there's an integer number three same + + + align:start position:0% +there's an integer number three same +here here how many periods twice that + + align:start position:0% +here here how many periods twice that + + + align:start position:0% +here here how many periods twice that +but it's exactly six so you get a pure + + align:start position:0% +but it's exactly six so you get a pure + + + align:start position:0% +but it's exactly six so you get a pure +sign you get a pure sinusoid you get an + + align:start position:0% +sign you get a pure sinusoid you get an + + + align:start position:0% +sign you get a pure sinusoid you get an +integer number of periods you integrate + + align:start position:0% +integer number of periods you integrate + + + align:start position:0% +integer number of periods you integrate +over an integer number of periods you + + align:start position:0% +over an integer number of periods you + + + align:start position:0% +over an integer number of periods you +get zero they're + + align:start position:0% +get zero they're + + + align:start position:0% +get zero they're +orthogonal had I chosen the period + + align:start position:0% +orthogonal had I chosen the period + + + align:start position:0% +orthogonal had I chosen the period +differently they may not have been + + align:start position:0% +differently they may not have been + + + align:start position:0% +differently they may not have been +orthogonal it depends on the + + align:start position:0% +orthogonal it depends on the + + + align:start position:0% +orthogonal it depends on the +period okay so the inner product depends + + align:start position:0% +period okay so the inner product depends + + + align:start position:0% +period okay so the inner product depends +on the period because the inner product + + align:start position:0% +on the period because the inner product + + + align:start position:0% +on the period because the inner product +has something to do with integrate or + + align:start position:0% +has something to do with integrate or + + + align:start position:0% +has something to do with integrate or +sum and so the range over which you sum + + align:start position:0% +sum and so the range over which you sum + + + align:start position:0% +sum and so the range over which you sum +or integrate + + align:start position:0% +or integrate + + + align:start position:0% +or integrate +matters how about uh cos 2i T cos 4 Pi T + + align:start position:0% + + + + align:start position:0% + +orthogonal yeah + + align:start position:0% +orthogonal yeah + + + align:start position:0% +orthogonal yeah +yes and the reason + + align:start position:0% + + + + align:start position:0% + +is so now we've got two different + + align:start position:0% +is so now we've got two different + + + align:start position:0% +is so now we've got two different +frequencies but we still get these funny + + align:start position:0% +frequencies but we still get these funny + + + align:start position:0% +frequencies but we still get these funny +cosine relationships that have to do + + align:start position:0% +cosine relationships that have to do + + + align:start position:0% +cosine relationships that have to do +with sums and differences and sums and + + align:start position:0% +with sums and differences and sums and + + + align:start position:0% +with sums and differences and sums and +differences both happen to be periodic + + align:start position:0% +differences both happen to be periodic + + + align:start position:0% +differences both happen to be periodic +over three over the interval capital + + align:start position:0% +over three over the interval capital + + + align:start position:0% +over three over the interval capital +capital T equals 3 right so we still get + + align:start position:0% +capital T equals 3 right so we still get + + + align:start position:0% +capital T equals 3 right so we still get +the property that the average value here + + align:start position:0% +the property that the average value here + + + align:start position:0% +the property that the average value here +which is what the integral is pulling + + align:start position:0% +which is what the integral is pulling + + + align:start position:0% +which is what the integral is pulling +out the average value is zero so they're + + align:start position:0% +out the average value is zero so they're + + + align:start position:0% +out the average value is zero so they're +also + + align:start position:0% +also + + + align:start position:0% +also +orthogonal how about COs 2 pi T sin Pi + + align:start position:0% + + + + align:start position:0% + +T okay I've asked two questions and they + + align:start position:0% +T okay I've asked two questions and they + + + align:start position:0% +T okay I've asked two questions and they +were both yes so I'm getting bored at + + align:start position:0% +were both yes so I'm getting bored at + + + align:start position:0% +were both yes so I'm getting bored at +this point so by the theory of questions + + align:start position:0% +this point so by the theory of questions + + + align:start position:0% +this point so by the theory of questions +in lecture the answer + + align:start position:0% + + + + align:start position:0% + +is now wait a minute I'm not that boring + + align:start position:0% +is now wait a minute I'm not that boring + + + align:start position:0% +is now wait a minute I'm not that boring +um well maybe uh + + align:start position:0% +um well maybe uh + + + align:start position:0% +um well maybe uh +so uh is this periodic over capital t + + align:start position:0% +so uh is this periodic over capital t + + + align:start position:0% +so uh is this periodic over capital t +equal + + align:start position:0% + + + + align:start position:0% + +3 excuse me does it I didn't say the + + align:start position:0% +3 excuse me does it I didn't say the + + + align:start position:0% +3 excuse me does it I didn't say the +right question sorry is this function + + align:start position:0% +right question sorry is this function + + + align:start position:0% +right question sorry is this function +have an even number have an integer + + align:start position:0% +have an even number have an integer + + + align:start position:0% +have an even number have an integer +number of + + align:start position:0% +number of + + + align:start position:0% +number of +periods in the time interval capital T + + align:start position:0% +periods in the time interval capital T + + + align:start position:0% +periods in the time interval capital T +equals + + align:start position:0% +equals + + + align:start position:0% +equals +3 what's the period what's the + + align:start position:0% +3 what's the period what's the + + + align:start position:0% +3 what's the period what's the +fundamental period of this + + align:start position:0% +fundamental period of this + + + align:start position:0% +fundamental period of this +waveform one so it has three periods + + align:start position:0% +waveform one so it has three periods + + + align:start position:0% +waveform one so it has three periods +over the interval Capt equals 3 what + + align:start position:0% +over the interval Capt equals 3 what + + + align:start position:0% +over the interval Capt equals 3 what +about this + + align:start position:0% + + + + align:start position:0% + +one period is two how many periods are + + align:start position:0% +one period is two how many periods are + + + align:start position:0% +one period is two how many periods are +there in the time interval capital T + + align:start position:0% +there in the time interval capital T + + + align:start position:0% +there in the time interval capital T +equals + + align:start position:0% + + + + align:start position:0% + +3 the period is two how many periods are + + align:start position:0% +3 the period is two how many periods are + + + align:start position:0% +3 the period is two how many periods are +there one and a half not an integer bad + + align:start position:0% +there one and a half not an integer bad + + + align:start position:0% +there one and a half not an integer bad +news right so integer number three not + + align:start position:0% +news right so integer number three not + + + align:start position:0% +news right so integer number three not +integer + + align:start position:0% +integer + + + align:start position:0% +integer +number if you were to integrate this + + align:start position:0% +number if you were to integrate this + + + align:start position:0% +number if you were to integrate this +over the period T = + + align:start position:0% +over the period T = + + + align:start position:0% +over the period T = +3 if if I didn't multiply them if I just + + align:start position:0% +3 if if I didn't multiply them if I just + + + align:start position:0% +3 if if I didn't multiply them if I just +did that if I just thought about that + + align:start position:0% +did that if I just thought about that + + + align:start position:0% +did that if I just thought about that +integral I wouldn't get zero right + + align:start position:0% +integral I wouldn't get zero right + + + align:start position:0% +integral I wouldn't get zero right +there's more positives than there are + + align:start position:0% +there's more positives than there are + + + align:start position:0% +there's more positives than there are +negatives and when I multiply them the + + align:start position:0% +negatives and when I multiply them the + + + align:start position:0% +negatives and when I multiply them the +same sort of thing happens I get two big + + align:start position:0% +same sort of thing happens I get two big + + + align:start position:0% +same sort of thing happens I get two big +Peaks down and only one big peak up it's + + align:start position:0% +Peaks down and only one big peak up it's + + + align:start position:0% +Peaks down and only one big peak up it's +because the resulting waveform is no + + align:start position:0% +because the resulting waveform is no + + + align:start position:0% +because the resulting waveform is no +longer no longer has an integer number + + align:start position:0% +longer no longer has an integer number + + + align:start position:0% +longer no longer has an integer number +of periods in the interval capital T + + align:start position:0% +of periods in the interval capital T + + + align:start position:0% +of periods in the interval capital T +equals 3 + + align:start position:0% + + + + align:start position:0% + +okay last one cos 2i t e to the uh + + align:start position:0% + + + + align:start position:0% + +whoops is that what I actually + + align:start position:0% +whoops is that what I actually + + + align:start position:0% +whoops is that what I actually +said good I forgot the J because uh + + align:start position:0% +said good I forgot the J because uh + + + align:start position:0% +said good I forgot the J because uh +without the J they would obviously not + + align:start position:0% +without the J they would obviously not + + + align:start position:0% +without the J they would obviously not +be orthogonal obviously right okay I + + align:start position:0% +be orthogonal obviously right okay I + + + align:start position:0% +be orthogonal obviously right okay I +didn't mean to ask something quite that + + align:start position:0% +didn't mean to ask something quite that + + + align:start position:0% +didn't mean to ask something quite that +obvious so what about um uh Co 2 pi T + + align:start position:0% +obvious so what about um uh Co 2 pi T + + + align:start position:0% +obvious so what about um uh Co 2 pi T +and e to the J 2 pi + + align:start position:0% +and e to the J 2 pi + + + align:start position:0% +and e to the J 2 pi +t orthogonal + + align:start position:0% + + + + align:start position:0% + +not I'm as clueless as I was on part + + align:start position:0% + + + + align:start position:0% + +A no no no no you're not no you're not + + align:start position:0% +A no no no no you're not no you're not + + + align:start position:0% +A no no no no you're not no you're not +no you're + + align:start position:0% +no you're + + + align:start position:0% +no you're +not so uh so how do you think about that + + align:start position:0% +not so uh so how do you think about that + + + align:start position:0% +not so uh so how do you think about that +you can use oil's expression and if + + align:start position:0% +you can use oil's expression and if + + + align:start position:0% +you can use oil's expression and if +there had been a j there this would have + + align:start position:0% +there had been a j there this would have + + + align:start position:0% +there had been a j there this would have +been a correct + + align:start position:0% +been a correct + + + align:start position:0% +been a correct +expression okay it's not quite a correct + + align:start position:0% +expression okay it's not quite a correct + + + align:start position:0% +expression okay it's not quite a correct +expression because I forgot to put the J + + align:start position:0% +expression because I forgot to put the J + + + align:start position:0% +expression because I forgot to put the J +there but had there been a j there it + + align:start position:0% +there but had there been a j there it + + + align:start position:0% +there but had there been a j there it +would have been cos 2i t plus J sin Pi T + + align:start position:0% +would have been cos 2i t plus J sin Pi T + + + align:start position:0% +would have been cos 2i t plus J sin Pi T +and the awkward thing is that the co and + + align:start position:0% +and the awkward thing is that the co and + + + align:start position:0% +and the awkward thing is that the co and +the coast are obviously not orthogonal + + align:start position:0% +the coast are obviously not orthogonal + + + align:start position:0% +the coast are obviously not orthogonal +with each other a signal is not + + align:start position:0% +with each other a signal is not + + + align:start position:0% +with each other a signal is not +orthogonal with + + align:start position:0% +orthogonal with + + + align:start position:0% +orthogonal with +itself okay so because part of this + + align:start position:0% +itself okay so because part of this + + + align:start position:0% +itself okay so because part of this +signal is that signal those two signals + + align:start position:0% +signal is that signal those two signals + + + align:start position:0% +signal is that signal those two signals +are not + + align:start position:0% +are not + + + align:start position:0% +are not +orthogonal okay + + align:start position:0% +orthogonal okay + + + align:start position:0% +orthogonal okay +yes okay so that's kind of so that's the + + align:start position:0% +yes okay so that's kind of so that's the + + + align:start position:0% +yes okay so that's kind of so that's the +idea of orthogonality it's a very good + + align:start position:0% +idea of orthogonality it's a very good + + + align:start position:0% +idea of orthogonality it's a very good +way to think about decompos + + align:start position:0% + + + + align:start position:0% + +positions and even though we only spent + + align:start position:0% +positions and even though we only spent + + + align:start position:0% +positions and even though we only spent +about half an hour last time and only + + align:start position:0% +about half an hour last time and only + + + align:start position:0% +about half an hour last time and only +about 15 minutes this time that is the + + align:start position:0% +about 15 minutes this time that is the + + + align:start position:0% +about 15 minutes this time that is the +whole theory of 48 series that doesn't + + align:start position:0% +whole theory of 48 series that doesn't + + + align:start position:0% +whole theory of 48 series that doesn't +mean we can't ask hard questions there + + align:start position:0% +mean we can't ask hard questions there + + + align:start position:0% +mean we can't ask hard questions there +were a couple of questions yes you you + + align:start position:0% +were a couple of questions yes you you + + + align:start position:0% +were a couple of questions yes you you +were + + align:start position:0% + + + + align:start position:0% + +first well the 48 coefficients are the + + align:start position:0% +first well the 48 coefficients are the + + + align:start position:0% +first well the 48 coefficients are the +are the result of orthogonality I don't + + align:start position:0% +are the result of orthogonality I don't + + + align:start position:0% +are the result of orthogonality I don't +think you can tell if I just told you a + + align:start position:0% +think you can tell if I just told you a + + + align:start position:0% +think you can tell if I just told you a +bunch of 48 coefficients I don't know if + + align:start position:0% +bunch of 48 coefficients I don't know if + + + align:start position:0% +bunch of 48 coefficients I don't know if +you can tell me something about the + + align:start position:0% +you can tell me something about the + + + align:start position:0% +you can tell me something about the +orthogonality of the underlying signals + + align:start position:0% +orthogonality of the underlying signals + + + align:start position:0% +orthogonality of the underlying signals +or + + align:start position:0% + + + + align:start position:0% + +not excuse me you tell me the period + + align:start position:0% + + + + align:start position:0% + +and uh let's see so it um I'm not + + align:start position:0% +and uh let's see so it um I'm not + + + align:start position:0% +and uh let's see so it um I'm not +completely sure I know what you're + + align:start position:0% +completely sure I know what you're + + + align:start position:0% +completely sure I know what you're +asking certainly if you tell me that the + + align:start position:0% +asking certainly if you tell me that the + + + align:start position:0% +asking certainly if you tell me that the +48 coefficients are blah blah blah 3 + + align:start position:0% +48 coefficients are blah blah blah 3 + + + align:start position:0% +48 coefficients are blah blah blah 3 +276 and if you tell me that you're + + align:start position:0% +276 and if you tell me that you're + + + align:start position:0% +276 and if you tell me that you're +working with a simple frea series + + align:start position:0% +working with a simple frea series + + + align:start position:0% +working with a simple frea series +periodic three then you've told me + + align:start position:0% +periodic three then you've told me + + + align:start position:0% +periodic three then you've told me +everything and so there's a way for me + + align:start position:0% +everything and so there's a way for me + + + align:start position:0% +everything and so there's a way for me +to backtrack that it was orthogonal I I + + align:start position:0% +to backtrack that it was orthogonal I I + + + align:start position:0% +to backtrack that it was orthogonal I I +I'm not sure if I'm connecting with you + + align:start position:0% +I'm not sure if I'm connecting with you + + + align:start position:0% +I'm not sure if I'm connecting with you +so if I'm not let ask me after lecture + + align:start position:0% +so if I'm not let ask me after lecture + + + align:start position:0% +so if I'm not let ask me after lecture +to make sure that + + align:start position:0% + + + + align:start position:0% + +sure and for two signals can I tell + + align:start position:0% +sure and for two signals can I tell + + + align:start position:0% +sure and for two signals can I tell +those two signals + + align:start position:0% +those two signals + + + align:start position:0% +those two signals +areal + + align:start position:0% + + + + align:start position:0% + +the uh if they have component in + + align:start position:0% +the uh if they have component in + + + align:start position:0% +the uh if they have component in +common they couldn't possibly be + + align:start position:0% +common they couldn't possibly be + + + align:start position:0% +common they couldn't possibly be +orthogonal so uh I would answer yes to + + align:start position:0% +orthogonal so uh I would answer yes to + + + align:start position:0% +orthogonal so uh I would answer yes to +that + + align:start position:0% +that + + + align:start position:0% +that +question uh so if that's what you were + + align:start position:0% +question uh so if that's what you were + + + align:start position:0% +question uh so if that's what you were +so I think that's probably right does it + + align:start position:0% +so I think that's probably right does it + + + align:start position:0% +so I think that's probably right does it +sound does that sound right yeah okay + + align:start position:0% +sound does that sound right yeah okay + + + align:start position:0% +sound does that sound right yeah okay +and + + align:start position:0% + + + + align:start position:0% + +yes yes yes + + align:start position:0% +yes yes yes + + + align:start position:0% +yes yes yes +yes complex conjugate of + + align:start position:0% +yes complex conjugate of + + + align:start position:0% +yes complex conjugate of +a we're taking the complex conjugate of + + align:start position:0% +a we're taking the complex conjugate of + + + align:start position:0% +a we're taking the complex conjugate of +the entire function + + align:start position:0% +the entire function + + + align:start position:0% +the entire function +at every point in time we take the + + align:start position:0% +at every point in time we take the + + + align:start position:0% +at every point in time we take the +complex conjugate of it and it's + + align:start position:0% +complex conjugate of it and it's + + + align:start position:0% +complex conjugate of it and it's +especially uh useful to think about if + + align:start position:0% +especially uh useful to think about if + + + align:start position:0% +especially uh useful to think about if +you're doing something of the form if if + + align:start position:0% +you're doing something of the form if if + + + align:start position:0% +you're doing something of the form if if +a of + + align:start position:0% +a of + + + align:start position:0% +a of +T were e to the J uh 2 pi Mt and if B of + + align:start position:0% +T were e to the J uh 2 pi Mt and if B of + + + align:start position:0% +T were e to the J uh 2 pi Mt and if B of +T were e to the J 2i + + align:start position:0% +T were e to the J 2i + + + align:start position:0% +T were e to the J 2i +LT the only thing we're trying to do but + + align:start position:0% +LT the only thing we're trying to do but + + + align:start position:0% +LT the only thing we're trying to do but +this comes up quite frequently the only + + align:start position:0% +this comes up quite frequently the only + + + align:start position:0% +this comes up quite frequently the only +thing we're trying to do is when you + + align:start position:0% +thing we're trying to do is when you + + + align:start position:0% +thing we're trying to do is when you +conjugate one of + + align:start position:0% +conjugate one of + + + align:start position:0% +conjugate one of +these you rig it so that when you add + + align:start position:0% +these you rig it so that when you add + + + align:start position:0% +these you rig it so that when you add +the exponents the result Goes To Zero by + + align:start position:0% +the exponents the result Goes To Zero by + + + align:start position:0% +the exponents the result Goes To Zero by +putting the minus up there that's + + align:start position:0% + + + + align:start position:0% + +all oh + + align:start position:0% +all oh + + + align:start position:0% +all oh +interesting uh that's uh be that's a + + align:start position:0% +interesting uh that's uh be that's a + + + align:start position:0% +interesting uh that's uh be that's a +very good point that's a that's + + align:start position:0% +very good point that's a that's + + + align:start position:0% +very good point that's a that's +interesting so I didn't intend to to + + align:start position:0% +interesting so I didn't intend to to + + + align:start position:0% +interesting so I didn't intend to to +throw you a ringer these were signals + + align:start position:0% +throw you a ringer these were signals + + + align:start position:0% +throw you a ringer these were signals +all all of these except that one are + + align:start position:0% +all all of these except that one are + + + align:start position:0% +all all of these except that one are +real functions of + + align:start position:0% +real functions of + + + align:start position:0% +real functions of +time that's why the complex conjugate + + align:start position:0% +time that's why the complex conjugate + + + align:start position:0% +time that's why the complex conjugate +bit didn't come up so I apologize I + + align:start position:0% +bit didn't come up so I apologize I + + + align:start position:0% +bit didn't come up so I apologize I +wasn't trying to make it seem tricky + + align:start position:0% +wasn't trying to make it seem tricky + + + align:start position:0% +wasn't trying to make it seem tricky +okay so it's because this function of + + align:start position:0% +okay so it's because this function of + + + align:start position:0% +okay so it's because this function of +time is everywhere real that we didn't + + align:start position:0% +time is everywhere real that we didn't + + + align:start position:0% +time is everywhere real that we didn't +need to to rehearse this we did have to + + align:start position:0% +need to to rehearse this we did have to + + + align:start position:0% +need to to rehearse this we did have to +do it in that + + align:start position:0% +do it in that + + + align:start position:0% +do it in that +one + + align:start position:0% + + + + align:start position:0% + +okay okay so the point is that we've + + align:start position:0% +okay okay so the point is that we've + + + align:start position:0% +okay okay so the point is that we've +already covered even though we've only + + align:start position:0% +already covered even though we've only + + + align:start position:0% +already covered even though we've only +done a little bit of work in lecture + + align:start position:0% +done a little bit of work in lecture + + + align:start position:0% +done a little bit of work in lecture +we've already covered all of the + + align:start position:0% +we've already covered all of the + + + align:start position:0% +we've already covered all of the +theory what remains though is to do some + + align:start position:0% +theory what remains though is to do some + + + align:start position:0% +theory what remains though is to do some +practice and also what remains is to + + align:start position:0% +practice and also what remains is to + + + align:start position:0% +practice and also what remains is to +understand how this is useful so it's + + align:start position:0% +understand how this is useful so it's + + + align:start position:0% +understand how this is useful so it's +not just music the example that I want + + align:start position:0% +not just music the example that I want + + + align:start position:0% +not just music the example that I want +to talk about today is + + align:start position:0% +to talk about today is + + + align:start position:0% +to talk about today is +speech the same sort of thing that we + + align:start position:0% +speech the same sort of thing that we + + + align:start position:0% +speech the same sort of thing that we +could do with music last time we can do + + align:start position:0% +could do with music last time we can do + + + align:start position:0% +could do with music last time we can do +with speech and here are some + + align:start position:0% + + + + align:start position:0% + +utterances beat fight boot but boot okay + + align:start position:0% +utterances beat fight boot but boot okay + + + align:start position:0% +utterances beat fight boot but boot okay +it was just intended to be a bunch of + + align:start position:0% +it was just intended to be a bunch of + + + align:start position:0% +it was just intended to be a bunch of +sounds that we can analyze with fora + + align:start position:0% +sounds that we can analyze with fora + + + align:start position:0% +sounds that we can analyze with fora +analysis to get some insight into how to + + align:start position:0% +analysis to get some insight into how to + + + align:start position:0% +analysis to get some insight into how to +think about in particular speech + + align:start position:0% +think about in particular speech + + + align:start position:0% +think about in particular speech +recognition and speech um uh + + align:start position:0% +recognition and speech um uh + + + align:start position:0% +recognition and speech um uh +synthesis so we can take those + + align:start position:0% +synthesis so we can take those + + + align:start position:0% +synthesis so we can take those +utterances and all I did was write a + + align:start position:0% +utterances and all I did was write a + + + align:start position:0% +utterances and all I did was write a +little Python program to do the + + align:start position:0% +little Python program to do the + + + align:start position:0% +little Python program to do the +decomposition that I showed on the in + + align:start position:0% +decomposition that I showed on the in + + + align:start position:0% +decomposition that I showed on the in +the previous + + align:start position:0% +the previous + + + align:start position:0% +the previous +slides so that I could break these time + + align:start position:0% +slides so that I could break these time + + + align:start position:0% +slides so that I could break these time +wave forms here I'm illustrating one two + + align:start position:0% +wave forms here I'm illustrating one two + + + align:start position:0% +wave forms here I'm illustrating one two +3 four five six periods so I took uh one + + align:start position:0% +3 four five six periods so I took uh one + + + align:start position:0% +3 four five six periods so I took uh one +period of that + + align:start position:0% +period of that + + + align:start position:0% +period of that +sound and ran it through uh that kind of + + align:start position:0% +sound and ran it through uh that kind of + + + align:start position:0% +sound and ran it through uh that kind of +an integral to break it into 48 + + align:start position:0% +an integral to break it into 48 + + + align:start position:0% +an integral to break it into 48 +components which are showed here and + + align:start position:0% +components which are showed here and + + + align:start position:0% +components which are showed here and +what I want you to see is just like you + + align:start position:0% +what I want you to see is just like you + + + align:start position:0% +what I want you to see is just like you +could have recognized a pattern here and + + align:start position:0% +could have recognized a pattern here and + + + align:start position:0% +could have recognized a pattern here and +you might try to recognize which valow + + align:start position:0% +you might try to recognize which valow + + + align:start position:0% +you might try to recognize which valow +is + + align:start position:0% +is + + + align:start position:0% +is +which by the time by the signature in + + align:start position:0% +which by the time by the signature in + + + align:start position:0% +which by the time by the signature in +time an alternative and far more useful + + align:start position:0% +time an alternative and far more useful + + + align:start position:0% +time an alternative and far more useful +way of thinking about it is to try to + + align:start position:0% +way of thinking about it is to try to + + + align:start position:0% +way of thinking about it is to try to +recognize the pattern in + + align:start position:0% +recognize the pattern in + + + align:start position:0% +recognize the pattern in +frequency so there are characteristic + + align:start position:0% +frequency so there are characteristic + + + align:start position:0% +frequency so there are characteristic +differences in the sounds and we'll look + + align:start position:0% +differences in the sounds and we'll look + + + align:start position:0% +differences in the sounds and we'll look +at the basis for why there are there are + + align:start position:0% +at the basis for why there are there are + + + align:start position:0% +at the basis for why there are there are +characteristic differences in the sound + + align:start position:0% +characteristic differences in the sound + + + align:start position:0% +characteristic differences in the sound +that can help us to + + align:start position:0% +that can help us to + + + align:start position:0% +that can help us to +identify automatically by a machine what + + align:start position:0% +identify automatically by a machine what + + + align:start position:0% +identify automatically by a machine what +was being + + align:start position:0% +was being + + + align:start position:0% +was being +said and so what we want to do is learn + + align:start position:0% +said and so what we want to do is learn + + + align:start position:0% +said and so what we want to do is learn +to think about a pattern that + + align:start position:0% +to think about a pattern that + + + align:start position:0% +to think about a pattern that +characterizes + + align:start position:0% +characterizes + + + align:start position:0% +characterizes +e in the frequency domain as opposed to + + align:start position:0% +e in the frequency domain as opposed to + + + align:start position:0% +e in the frequency domain as opposed to +the time + + align:start position:0% +the time + + + align:start position:0% +the time +domain so there's something different + + align:start position:0% +domain so there's something different + + + align:start position:0% +domain so there's something different +about those sounds that manifests a + + align:start position:0% +about those sounds that manifests a + + + align:start position:0% +about those sounds that manifests a +difference in this forier + + align:start position:0% +difference in this forier + + + align:start position:0% +difference in this forier +signature so that's the one of the + + align:start position:0% +signature so that's the one of the + + + align:start position:0% +signature so that's the one of the +useful applications of this and we' like + + align:start position:0% +useful applications of this and we' like + + + align:start position:0% +useful applications of this and we' like +to understand that better there's a + + align:start position:0% +to understand that better there's a + + + align:start position:0% +to understand that better there's a +really good physical reason why that + + align:start position:0% +really good physical reason why that + + + align:start position:0% +really good physical reason why that +happens and it has to do with the way we + + align:start position:0% +happens and it has to do with the way we + + + align:start position:0% +happens and it has to do with the way we +produce speech so you can think about + + align:start position:0% +produce speech so you can think about + + + align:start position:0% +produce speech so you can think about +speech as being generated by some Source + + align:start position:0% +speech as being generated by some Source + + + align:start position:0% +speech as being generated by some Source +ultimately the source of my speech is + + align:start position:0% +ultimately the source of my speech is + + + align:start position:0% +ultimately the source of my speech is +somewhere down + + align:start position:0% +somewhere down + + + align:start position:0% +somewhere down +here okay which always amuses me when I + + align:start position:0% +here okay which always amuses me when I + + + align:start position:0% +here okay which always amuses me when I +see the cut off heads talking like at + + align:start position:0% +see the cut off heads talking like at + + + align:start position:0% +see the cut off heads talking like at +Halloween and like on some cartoon shows + + align:start position:0% +Halloween and like on some cartoon shows + + + align:start position:0% +Halloween and like on some cartoon shows +because you can't do that right because + + align:start position:0% +because you can't do that right because + + + align:start position:0% +because you can't do that right because +the source has to do with down here + + align:start position:0% +the source has to do with down here + + + align:start position:0% +the source has to do with down here +someplace right so my lungs are push in + + align:start position:0% +someplace right so my lungs are push in + + + align:start position:0% +someplace right so my lungs are push in +that pushes air through something and + + align:start position:0% +that pushes air through something and + + + align:start position:0% +that pushes air through something and +starts making noise somehow uh I'm going + + align:start position:0% +starts making noise somehow uh I'm going + + + align:start position:0% +starts making noise somehow uh I'm going +to focus today on things that we call + + align:start position:0% +to focus today on things that we call + + + align:start position:0% +to focus today on things that we call +voiced in a voiced sound ah in a voiced + + align:start position:0% +voiced in a voiced sound ah in a voiced + + + align:start position:0% +voiced in a voiced sound ah in a voiced +sound it's caused by vibrations of the + + align:start position:0% +sound it's caused by vibrations of the + + + align:start position:0% +sound it's caused by vibrations of the +vocal cords so if you were to stick a + + align:start position:0% +vocal cords so if you were to stick a + + + align:start position:0% +vocal cords so if you were to stick a +camera down someone's throat this is the + + align:start position:0% +camera down someone's throat this is the + + + align:start position:0% +camera down someone's throat this is the +sort of thing that you would see it's an + + align:start position:0% +sort of thing that you would see it's an + + + align:start position:0% +sort of thing that you would see it's an +enormously complex + + align:start position:0% +enormously complex + + + align:start position:0% +enormously complex +structure whose mechanics are extremely + + align:start position:0% +structure whose mechanics are extremely + + + align:start position:0% +structure whose mechanics are extremely +difficult to understand because what + + align:start position:0% +difficult to understand because what + + + align:start position:0% +difficult to understand because what +happens is when you um when you want to + + align:start position:0% +happens is when you um when you want to + + + align:start position:0% +happens is when you um when you want to +make a high sound you tense the + + align:start position:0% +make a high sound you tense the + + + align:start position:0% +make a high sound you tense the +structure you pull on some muscles that + + align:start position:0% +structure you pull on some muscles that + + + align:start position:0% +structure you pull on some muscles that +pull the cord the cords are normally + + align:start position:0% +pull the cord the cords are normally + + + align:start position:0% +pull the cord the cords are normally +rattling pretty + + align:start position:0% +rattling pretty + + + align:start position:0% +rattling pretty +fast and what you do is you pull on a + + align:start position:0% +fast and what you do is you pull on a + + + align:start position:0% +fast and what you do is you pull on a +muscle that tenses them to make it go + + align:start position:0% +muscle that tenses them to make it go + + + align:start position:0% +muscle that tenses them to make it go +higher but your intuition should say now + + align:start position:0% +higher but your intuition should say now + + + align:start position:0% +higher but your intuition should say now +wait a minute you're making it longer to + + align:start position:0% +wait a minute you're making it longer to + + + align:start position:0% +wait a minute you're making it longer to +make it higher and your intuition would + + align:start position:0% +make it higher and your intuition would + + + align:start position:0% +make it higher and your intuition would +be + + align:start position:0% +be + + + align:start position:0% +be +right normally + + align:start position:0% +right normally + + + align:start position:0% +right normally +long organ pipes are higher or lower in + + align:start position:0% +long organ pipes are higher or lower in + + + align:start position:0% +long organ pipes are higher or lower in +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +lower so you have to do a lot of mental + + align:start position:0% +lower so you have to do a lot of mental + + + align:start position:0% +lower so you have to do a lot of mental +calculations in order to to move these + + align:start position:0% +calculations in order to to move these + + + align:start position:0% +calculations in order to to move these +muscles correctly so that the resulting + + align:start position:0% +muscles correctly so that the resulting + + + align:start position:0% +muscles correctly so that the resulting +frequency of the vibration comes out + + align:start position:0% +frequency of the vibration comes out + + + align:start position:0% +frequency of the vibration comes out +right it's not obvious because two + + align:start position:0% +right it's not obvious because two + + + align:start position:0% +right it's not obvious because two +things happen as you tense the muscle + + align:start position:0% +things happen as you tense the muscle + + + align:start position:0% +things happen as you tense the muscle +the folds the vocal cords get longer + + align:start position:0% +the folds the vocal cords get longer + + + align:start position:0% +the folds the vocal cords get longer +which you would think would make the + + align:start position:0% +which you would think would make the + + + align:start position:0% +which you would think would make the +frequency lower but they get + + align:start position:0% +frequency lower but they get + + + align:start position:0% +frequency lower but they get +tighter which of course goes the other + + align:start position:0% +tighter which of course goes the other + + + align:start position:0% +tighter which of course goes the other +direction right so it's a very + + align:start position:0% +direction right so it's a very + + + align:start position:0% +direction right so it's a very +complicated thing and in fact it's + + align:start position:0% +complicated thing and in fact it's + + + align:start position:0% +complicated thing and in fact it's +something that goes bad with + + align:start position:0% +something that goes bad with + + + align:start position:0% +something that goes bad with +professional speakers but even more + + align:start position:0% +professional speakers but even more + + + align:start position:0% +professional speakers but even more +professional + + align:start position:0% +professional + + + align:start position:0% +professional +singers uh often have a lot of trouble + + align:start position:0% +singers uh often have a lot of trouble + + + align:start position:0% +singers uh often have a lot of trouble +with the enormous stress that happens on + + align:start position:0% +with the enormous stress that happens on + + + align:start position:0% +with the enormous stress that happens on +this structure with repeated use and + + align:start position:0% +this structure with repeated use and + + + align:start position:0% +this structure with repeated use and +repeated + + align:start position:0% +repeated + + + align:start position:0% +repeated +overuse anyway this takes a real + + align:start position:0% +overuse anyway this takes a real + + + align:start position:0% +overuse anyway this takes a real +beating but that's ultimately the source + + align:start position:0% +beating but that's ultimately the source + + + align:start position:0% +beating but that's ultimately the source +of speech but if that where all you had + + align:start position:0% +of speech but if that where all you had + + + align:start position:0% +of speech but if that where all you had +it wouldn't sound much like + + align:start position:0% +it wouldn't sound much like + + + align:start position:0% +it wouldn't sound much like +speech a lot of the interesting stuff + + align:start position:0% +speech a lot of the interesting stuff + + + align:start position:0% +speech a lot of the interesting stuff +comes from these + + align:start position:0% +comes from these + + + align:start position:0% +comes from these +cavities that you intentionally + + align:start position:0% +cavities that you intentionally + + + align:start position:0% +cavities that you intentionally +manipulate as you're speaking to make + + align:start position:0% +manipulate as you're speaking to make + + + align:start position:0% +manipulate as you're speaking to make +the different characteristics + + align:start position:0% +the different characteristics + + + align:start position:0% +the different characteristics +sounds uh so the idea then is that you + + align:start position:0% +sounds uh so the idea then is that you + + + align:start position:0% +sounds uh so the idea then is that you +have a + + align:start position:0% +have a + + + align:start position:0% +have a +source that contains information like + + align:start position:0% +source that contains information like + + + align:start position:0% +source that contains information like +frequency what's the + + align:start position:0% +frequency what's the + + + align:start position:0% +frequency what's the +pitch of the utterance but you have this + + align:start position:0% +pitch of the utterance but you have this + + + align:start position:0% +pitch of the utterance but you have this +other thing which is acting like a + + align:start position:0% +other thing which is acting like a + + + align:start position:0% +other thing which is acting like a +filter if you think about the whole + + align:start position:0% +filter if you think about the whole + + + align:start position:0% +filter if you think about the whole +thing as a system we have a block which + + align:start position:0% +thing as a system we have a block which + + + align:start position:0% +thing as a system we have a block which +represents a + + align:start position:0% +represents a + + + align:start position:0% +represents a +filter which is the thing that has has a + + align:start position:0% +filter which is the thing that has has a + + + align:start position:0% +filter which is the thing that has has a +frequency response the frequency + + align:start position:0% +frequency response the frequency + + + align:start position:0% +frequency response the frequency +response depends on how I've put my + + align:start position:0% +response depends on how I've put my + + + align:start position:0% +response depends on how I've put my +tongue in my mouth and how I've opened + + align:start position:0% +tongue in my mouth and how I've opened + + + align:start position:0% +tongue in my mouth and how I've opened +my lips and stuff like that we'll see + + align:start position:0% +my lips and stuff like that we'll see + + + align:start position:0% +my lips and stuff like that we'll see +that in a minute but it also depends on + + align:start position:0% +that in a minute but it also depends on + + + align:start position:0% +that in a minute but it also depends on +how the the vocal folds it has an input + + align:start position:0% +how the the vocal folds it has an input + + + align:start position:0% +how the the vocal folds it has an input +which is the vocal + + align:start position:0% +which is the vocal + + + align:start position:0% +which is the vocal +folds so the idea then is the same kind + + align:start position:0% +folds so the idea then is the same kind + + + align:start position:0% +folds so the idea then is the same kind +of a source filter idea that we + + align:start position:0% +of a source filter idea that we + + + align:start position:0% +of a source filter idea that we +motivated Last Time by way of the RC + + align:start position:0% +motivated Last Time by way of the RC + + + align:start position:0% +motivated Last Time by way of the RC +filter example if you put uh an a + + align:start position:0% +filter example if you put uh an a + + + align:start position:0% +filter example if you put uh an a +resistor in a capacitor together with a + + align:start position:0% +resistor in a capacitor together with a + + + align:start position:0% +resistor in a capacitor together with a +a source a convenient way to think about + + align:start position:0% +a source a convenient way to think about + + + align:start position:0% +a source a convenient way to think about +that is as a low pass filter we think + + align:start position:0% +that is as a low pass filter we think + + + align:start position:0% +that is as a low pass filter we think +about it having a frequency response so + + align:start position:0% +about it having a frequency response so + + + align:start position:0% +about it having a frequency response so +the system just the RC part uh has a + + align:start position:0% +the system just the RC part uh has a + + + align:start position:0% +the system just the RC part uh has a +frequency response which we can + + align:start position:0% +frequency response which we can + + + align:start position:0% +frequency response which we can +characterize by a Bodi + + align:start position:0% +characterize by a Bodi + + + align:start position:0% +characterize by a Bodi +diagram so we can think about we did + + align:start position:0% +diagram so we can think about we did + + + align:start position:0% +diagram so we can think about we did +this last time we so we can think about + + align:start position:0% +this last time we so we can think about + + + align:start position:0% +this last time we so we can think about +the low frequencies go through without + + align:start position:0% +the low frequencies go through without + + + align:start position:0% +the low frequencies go through without +attenuation the gain is + + align:start position:0% +attenuation the gain is + + + align:start position:0% +attenuation the gain is +one and the phase is zero so basically + + align:start position:0% +one and the phase is zero so basically + + + align:start position:0% +one and the phase is zero so basically +low frequencies go through the filter + + align:start position:0% +low frequencies go through the filter + + + align:start position:0% +low frequencies go through the filter +without any + + align:start position:0% +without any + + + align:start position:0% +without any +change high frequencies are attenuated + + align:start position:0% +change high frequencies are attenuated + + + align:start position:0% +change high frequencies are attenuated +the higher the frequency the more the + + align:start position:0% +the higher the frequency the more the + + + align:start position:0% +the higher the frequency the more the +attenuation and phase shifted by be by + + align:start position:0% +attenuation and phase shifted by be by + + + align:start position:0% +attenuation and phase shifted by be by +lagging Pi + + align:start position:0% +lagging Pi + + + align:start position:0% +lagging Pi +over2 so that's a way of thinking about + + align:start position:0% +over2 so that's a way of thinking about + + + align:start position:0% +over2 so that's a way of thinking about +the RC circuit as a low pass filter and + + align:start position:0% +the RC circuit as a low pass filter and + + + align:start position:0% +the RC circuit as a low pass filter and +it gives us Insight in the kinds of + + align:start position:0% +it gives us Insight in the kinds of + + + align:start position:0% +it gives us Insight in the kinds of +signals that go through and don't go + + align:start position:0% +signals that go through and don't go + + + align:start position:0% +signals that go through and don't go +through so that if we think about a + + align:start position:0% +through so that if we think about a + + + align:start position:0% +through so that if we think about a +signal like a square wave having a 4A + + align:start position:0% +signal like a square wave having a 4A + + + align:start position:0% +signal like a square wave having a 4A +series + + align:start position:0% +series + + + align:start position:0% +series +decomposition the compon it only has odd + + align:start position:0% +decomposition the compon it only has odd + + + align:start position:0% +decomposition the compon it only has odd +components and the odd components fall + + align:start position:0% +components and the odd components fall + + + align:start position:0% +components and the odd components fall +with K the the magnitude of the + + align:start position:0% +with K the the magnitude of the + + + align:start position:0% +with K the the magnitude of the +component is inverse with K so we get + + align:start position:0% +component is inverse with K so we get + + + align:start position:0% +component is inverse with K so we get +components that if I plot on a log + + align:start position:0% +components that if I plot on a log + + + align:start position:0% +components that if I plot on a log +scale the reciprocal relationship of the + + align:start position:0% +scale the reciprocal relationship of the + + + align:start position:0% +scale the reciprocal relationship of the +weight of the components the magnitude + + align:start position:0% +weight of the components the magnitude + + + align:start position:0% +weight of the components the magnitude +of the components makes it a straight + + align:start position:0% +of the components makes it a straight + + + align:start position:0% +of the components makes it a straight +line with a slope of minus one + + align:start position:0% +line with a slope of minus one + + + align:start position:0% +line with a slope of minus one +and now we can think about putting this + + align:start position:0% +and now we can think about putting this + + + align:start position:0% +and now we can think about putting this +signal into the RC filter and thinking + + align:start position:0% +signal into the RC filter and thinking + + + align:start position:0% +signal into the RC filter and thinking +about what the output should look like + + align:start position:0% +about what the output should look like + + + align:start position:0% +about what the output should look like +if the frequency of the square wave if + + align:start position:0% +if the frequency of the square wave if + + + align:start position:0% +if the frequency of the square wave if +the fundamental + + align:start position:0% +the fundamental + + + align:start position:0% +the fundamental +frequency 2 pi over the + + align:start position:0% +frequency 2 pi over the + + + align:start position:0% +frequency 2 pi over the +period if 2 pi over capital + + align:start position:0% +period if 2 pi over capital + + + align:start position:0% +period if 2 pi over capital +T if 2 pi over capital t is some + + align:start position:0% +T if 2 pi over capital t is some + + + align:start position:0% +T if 2 pi over capital t is some +frequency that's low compared to the + + align:start position:0% +frequency that's low compared to the + + + align:start position:0% +frequency that's low compared to the +corner frequency of the low pass + + align:start position:0% +corner frequency of the low pass + + + align:start position:0% +corner frequency of the low pass +filter basically the output of the + + align:start position:0% +filter basically the output of the + + + align:start position:0% +filter basically the output of the +filter which is showed in green overlaps + + align:start position:0% +filter which is showed in green overlaps + + + align:start position:0% +filter which is showed in green overlaps +the input which is showed in red you + + align:start position:0% +the input which is showed in red you + + + align:start position:0% +the input which is showed in red you +can't tell the difference because all + + align:start position:0% +can't tell the difference because all + + + align:start position:0% +can't tell the difference because all +the components have the same magnitude + + align:start position:0% +the components have the same magnitude + + + align:start position:0% +the components have the same magnitude +and phase as the + + align:start position:0% +and phase as the + + + align:start position:0% +and phase as the +input but if you change the frequency of + + align:start position:0% +input but if you change the frequency of + + + align:start position:0% +input but if you change the frequency of +the square wave so that the fundamental + + align:start position:0% +the square wave so that the fundamental + + + align:start position:0% +the square wave so that the fundamental +is higher some of the higher frequencies + + align:start position:0% +is higher some of the higher frequencies + + + align:start position:0% +is higher some of the higher frequencies +are attenuated and phase + + align:start position:0% +are attenuated and phase + + + align:start position:0% +are attenuated and phase +shifted the shape of the waveform showed + + align:start position:0% +shifted the shape of the waveform showed + + + align:start position:0% +shifted the shape of the waveform showed +in green starts to deviate if you go to + + align:start position:0% +in green starts to deviate if you go to + + + align:start position:0% +in green starts to deviate if you go to +still higher frequencies the deviation + + align:start position:0% +still higher frequencies the deviation + + + align:start position:0% +still higher frequencies the deviation +is even greater and if you go to high + + align:start position:0% +is even greater and if you go to high + + + align:start position:0% +is even greater and if you go to high +enough + + align:start position:0% +enough + + + align:start position:0% +enough +frequencies they're all in the region + + align:start position:0% +frequencies they're all in the region + + + align:start position:0% +frequencies they're all in the region +where the magnitude is being attenuated + + align:start position:0% +where the magnitude is being attenuated + + + align:start position:0% +where the magnitude is being attenuated +by uh one over frequency so my + + align:start position:0% +by uh one over frequency so my + + + align:start position:0% +by uh one over frequency so my +dependence of 1 over K becomes 1 over K + + align:start position:0% +dependence of 1 over K becomes 1 over K + + + align:start position:0% +dependence of 1 over K becomes 1 over K +squ and it's goes from being a square + + align:start position:0% +squ and it's goes from being a square + + + align:start position:0% +squ and it's goes from being a square +wave to a triangle + + align:start position:0% +wave to a triangle + + + align:start position:0% +wave to a triangle +wave so that's a way of thinking about + + align:start position:0% +wave so that's a way of thinking about + + + align:start position:0% +wave so that's a way of thinking about +the the signal transformation in terms + + align:start position:0% +the the signal transformation in terms + + + align:start position:0% +the the signal transformation in terms +of a filter we did that last time what's + + align:start position:0% +of a filter we did that last time what's + + + align:start position:0% +of a filter we did that last time what's +going on with speech is exactly the same + + align:start position:0% +going on with speech is exactly the same + + + align:start position:0% +going on with speech is exactly the same +thing what we want to do is think about + + align:start position:0% +thing what we want to do is think about + + + align:start position:0% +thing what we want to do is think about +the glotus some kind of a sound that + + align:start position:0% +the glotus some kind of a sound that + + + align:start position:0% +the glotus some kind of a sound that +goes into a filter the filter is this + + align:start position:0% +goes into a filter the filter is this + + + align:start position:0% +goes into a filter the filter is this +thing that is controlled by my tongue's + + align:start position:0% +thing that is controlled by my tongue's + + + align:start position:0% +thing that is controlled by my tongue's +position and my jaw position and my lip + + align:start position:0% +position and my jaw position and my lip + + + align:start position:0% +position and my jaw position and my lip +position and stuff like that and what + + align:start position:0% +position and stuff like that and what + + + align:start position:0% +position and stuff like that and what +comes out of + + align:start position:0% +comes out of + + + align:start position:0% +comes out of +speech to demonstrate that here's a film + + align:start position:0% +speech to demonstrate that here's a film + + + align:start position:0% +speech to demonstrate that here's a film +that was made by Ken Stevens Ken Stevens + + align:start position:0% +that was made by Ken Stevens Ken Stevens + + + align:start position:0% +that was made by Ken Stevens Ken Stevens +was a professor in this department he + + align:start position:0% +was a professor in this department he + + + align:start position:0% +was a professor in this department he +just recently + + align:start position:0% +just recently + + + align:start position:0% +just recently +retired this was done when he was a + + align:start position:0% +retired this was done when he was a + + + align:start position:0% +retired this was done when he was a +graduate student it's very hard to see + + align:start position:0% +graduate student it's very hard to see + + + align:start position:0% +graduate student it's very hard to see +because the the uh contrast is not great + + align:start position:0% +because the the uh contrast is not great + + + align:start position:0% +because the the uh contrast is not great +but you have to take into a + + align:start position:0% +but you have to take into a + + + align:start position:0% +but you have to take into a +consideration this was made with x-rays + + align:start position:0% +consideration this was made with x-rays + + + align:start position:0% +consideration this was made with x-rays +okay we probably wouldn't do this today + + align:start position:0% +okay we probably wouldn't do this today + + + align:start position:0% +okay we probably wouldn't do this today +okay uh there was rather relatively + + align:start position:0% +okay uh there was rather relatively + + + align:start position:0% +okay uh there was rather relatively +large exposure to x-rays which we sort + + align:start position:0% +large exposure to x-rays which we sort + + + align:start position:0% +large exposure to x-rays which we sort +of frown on these days just so you're + + align:start position:0% +of frown on these days just so you're + + + align:start position:0% +of frown on these days just so you're +not too worried Ken Stevens when he + + align:start position:0% +not too worried Ken Stevens when he + + + align:start position:0% +not too worried Ken Stevens when he +retired had the longest teaching career + + align:start position:0% +retired had the longest teaching career + + + align:start position:0% +retired had the longest teaching career +in our history he was a lecturer who + + align:start position:0% +in our history he was a lecturer who + + + align:start position:0% +in our history he was a lecturer who +actively lectured for 50 years so he + + align:start position:0% +actively lectured for 50 years so he + + + align:start position:0% +actively lectured for 50 years so he +seemed to have done okay he survived so + + align:start position:0% +seemed to have done okay he survived so + + + align:start position:0% +seemed to have done okay he survived so +you don't need to worry about what + + align:start position:0% +you don't need to worry about what + + + align:start position:0% +you don't need to worry about what +happened to him but we probably wouldn't + + align:start position:0% +happened to him but we probably wouldn't + + + align:start position:0% +happened to him but we probably wouldn't +repeat this + + align:start position:0% +repeat this + + + align:start position:0% +repeat this +it's a little hard to see uh the bone is + + align:start position:0% +it's a little hard to see uh the bone is + + + align:start position:0% +it's a little hard to see uh the bone is +easy right because x-rays don't go + + align:start position:0% +easy right because x-rays don't go + + + align:start position:0% +easy right because x-rays don't go +through bones very well what you can + + align:start position:0% +through bones very well what you can + + + align:start position:0% +through bones very well what you can +just barely see is his lips and it's + + align:start position:0% +just barely see is his lips and it's + + + align:start position:0% +just barely see is his lips and it's +important to keep uh to watch the lips + + align:start position:0% +important to keep uh to watch the lips + + + align:start position:0% +important to keep uh to watch the lips +too his it's also important that his + + align:start position:0% +too his it's also important that his + + + align:start position:0% +too his it's also important that his +chin is on a chin + + align:start position:0% +chin is on a chin + + + align:start position:0% +chin is on a chin +rest to simplify analysis the idea of + + align:start position:0% +rest to simplify analysis the idea of + + + align:start position:0% +rest to simplify analysis the idea of +this was to get quantitative anal uh get + + align:start position:0% +this was to get quantitative anal uh get + + + align:start position:0% +this was to get quantitative anal uh get +quantitative measurements to fit the + + align:start position:0% +quantitative measurements to fit the + + + align:start position:0% +quantitative measurements to fit the +source filter IDE + + align:start position:0% +source filter IDE + + + align:start position:0% +source filter IDE +yeah okay so now I'm going to play a + + align:start position:0% +yeah okay so now I'm going to play a + + + align:start position:0% +yeah okay so now I'm going to play a +film a a recording of him + + align:start position:0% + + + + align:start position:0% + +h h h the T the t + + align:start position:0% +h h h the T the t + + + align:start position:0% +h h h the T the t +t + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +two why did Ken set the net on top of + + align:start position:0% +two why did Ken set the net on top of + + + align:start position:0% +two why did Ken set the net on top of +his + + align:start position:0% +his + + + align:start position:0% +his +I have put blood under twole yellow + + align:start position:0% + + + + align:start position:0% + +shoes okay so what you were supposed to + + align:start position:0% + + + + align:start position:0% + +see is that the thing that we associate + + align:start position:0% +see is that the thing that we associate + + + align:start position:0% +see is that the thing that we associate +with speech is only a small part of it + + align:start position:0% +with speech is only a small part of it + + + align:start position:0% +with speech is only a small part of it +his lips were obviously moving that's + + align:start position:0% +his lips were obviously moving that's + + + align:start position:0% +his lips were obviously moving that's +what we + + align:start position:0% +what we + + + align:start position:0% +what we +see but if you were paying attention his + + align:start position:0% +see but if you were paying attention his + + + align:start position:0% +see but if you were paying attention his +tongue was going up and down not a + + align:start position:0% +tongue was going up and down not a + + + align:start position:0% +tongue was going up and down not a +little bit but a + + align:start position:0% +little bit but a + + + align:start position:0% +little bit but a +lot so the gap between his tongue and + + align:start position:0% +lot so the gap between his tongue and + + + align:start position:0% +lot so the gap between his tongue and +the roof of his mouth was going from + + align:start position:0% +the roof of his mouth was going from + + + align:start position:0% +the roof of his mouth was going from +zero to about that + + align:start position:0% +zero to about that + + + align:start position:0% +zero to about that +far uh the the vum back here was opening + + align:start position:0% +far uh the the vum back here was opening + + + align:start position:0% +far uh the the vum back here was opening +very broadly on occasion so there was a + + align:start position:0% +very broadly on occasion so there was a + + + align:start position:0% +very broadly on occasion so there was a +significant variation in the + + align:start position:0% +significant variation in the + + + align:start position:0% +significant variation in the +shape of the the structure through which + + align:start position:0% +shape of the the structure through which + + + align:start position:0% +shape of the the structure through which +the glotus waveform was passing and + + align:start position:0% +the glotus waveform was passing and + + + align:start position:0% +the glotus waveform was passing and +that's the basis of of the + + align:start position:0% +that's the basis of of the + + + align:start position:0% +that's the basis of of the +filtering that gives rise to the + + align:start position:0% +filtering that gives rise to the + + + align:start position:0% +filtering that gives rise to the +different speech + + align:start position:0% +different speech + + + align:start position:0% +different speech +sounds so + + align:start position:0% +sounds so + + + align:start position:0% +sounds so +uh to convince you of that here I have a + + align:start position:0% +uh to convince you of that here I have a + + + align:start position:0% +uh to convince you of that here I have a +carefully machined item um let's see I + + align:start position:0% +carefully machined item um let's see I + + + align:start position:0% +carefully machined item um let's see I +don't want this one I want this one so + + align:start position:0% +don't want this one I want this one so + + + align:start position:0% +don't want this one I want this one so +this is a Japanese oo okay now I don't + + align:start position:0% +this is a Japanese oo okay now I don't + + + align:start position:0% +this is a Japanese oo okay now I don't +know Japanese so I have to just sort of + + align:start position:0% +know Japanese so I have to just sort of + + + align:start position:0% +know Japanese so I have to just sort of +trust the guy who made this that it + + align:start position:0% +trust the guy who made this that it + + + align:start position:0% +trust the guy who made this that it +actually sounds like a Japanese o the + + align:start position:0% +actually sounds like a Japanese o the + + + align:start position:0% +actually sounds like a Japanese o the +second one I'll show is a Japanese e + + align:start position:0% +second one I'll show is a Japanese e + + + align:start position:0% +second one I'll show is a Japanese e +which actually sounds more like an e to + + align:start position:0% +which actually sounds more like an e to + + + align:start position:0% +which actually sounds more like an e to +me but anyway this model was made from + + align:start position:0% +me but anyway this model was made from + + + align:start position:0% +me but anyway this model was made from +measurements of the type that I just + + align:start position:0% +measurements of the type that I just + + + align:start position:0% +measurements of the type that I just +showed with Kent so the idea was to + + align:start position:0% +showed with Kent so the idea was to + + + align:start position:0% +showed with Kent so the idea was to +estimate the size of those cavities + + align:start position:0% +estimate the size of those cavities + + + align:start position:0% +estimate the size of those cavities +through which the air was passing and + + align:start position:0% +through which the air was passing and + + + align:start position:0% +through which the air was passing and +then make by Machining imp plexiglass a + + align:start position:0% +then make by Machining imp plexiglass a + + + align:start position:0% +then make by Machining imp plexiglass a +structure that has that + + align:start position:0% +structure that has that + + + align:start position:0% +structure that has that +shape so this was an early test of + + align:start position:0% +shape so this was an early test of + + + align:start position:0% +shape so this was an early test of +whether the source filter idea works so + + align:start position:0% +whether the source filter idea works so + + + align:start position:0% +whether the source filter idea works so +if that is the explanation for how + + align:start position:0% +if that is the explanation for how + + + align:start position:0% +if that is the explanation for how +speech is generated then I ought to be + + align:start position:0% +speech is generated then I ought to be + + + align:start position:0% +speech is generated then I ought to be +able to take a boring sound of the type + + align:start position:0% +able to take a boring sound of the type + + + align:start position:0% +able to take a boring sound of the type +that's generated by the + + align:start position:0% + + + + align:start position:0% + +glotus and put it to this and it should + + align:start position:0% +glotus and put it to this and it should + + + align:start position:0% +glotus and put it to this and it should +sound more like a vowel okay got it know + + align:start position:0% +sound more like a vowel okay got it know + + + align:start position:0% +sound more like a vowel okay got it know +what I'm talking about so this is a + + align:start position:0% +what I'm talking about so this is a + + + align:start position:0% +what I'm talking about so this is a +Japanese uh + + align:start position:0% + + + + align:start position:0% + +o I don't know if anybody knows Japanese + + align:start position:0% +o I don't know if anybody knows Japanese + + + align:start position:0% +o I don't know if anybody knows Japanese +I don't know if that sounds like an O + + align:start position:0% +I don't know if that sounds like an O + + + align:start position:0% +I don't know if that sounds like an O +anybody know Japanese and does that + + align:start position:0% +anybody know Japanese and does that + + + align:start position:0% +anybody know Japanese and does that +sound like an U or + + align:start position:0% + + + + align:start position:0% + +not okay I'll pass + + align:start position:0% + + + + align:start position:0% + +this is an e okay now notice that the E + + align:start position:0% +this is an e okay now notice that the E + + + align:start position:0% +this is an e okay now notice that the E +looks very different right the question + + align:start position:0% +looks very different right the question + + + align:start position:0% +looks very different right the question +is whether that's a big enough + + align:start position:0% +is whether that's a big enough + + + align:start position:0% +is whether that's a big enough +difference to to make the difference + + align:start position:0% +difference to to make the difference + + + align:start position:0% +difference to to make the difference +between an an U and an + + align:start position:0% +between an an U and an + + + align:start position:0% +between an an U and an +e I'm pressing the same button not + + align:start position:0% +e I'm pressing the same button not + + + align:start position:0% +e I'm pressing the same button not +nothing up my sleeves nothing okay so + + align:start position:0% +nothing up my sleeves nothing okay so + + + align:start position:0% +nothing up my sleeves nothing okay so +same button um + + align:start position:0% + + + + align:start position:0% + +okay so what you're supposed to be + + align:start position:0% +okay so what you're supposed to be + + + align:start position:0% +okay so what you're supposed to be +convinced of + + align:start position:0% +convinced of + + + align:start position:0% +convinced of +is there's enough + + align:start position:0% +is there's enough + + + align:start position:0% +is there's enough +information in the shape of the vocal um + + align:start position:0% +information in the shape of the vocal um + + + align:start position:0% +information in the shape of the vocal um +structures to account for the difference + + align:start position:0% +structures to account for the difference + + + align:start position:0% +structures to account for the difference +in the + + align:start position:0% +in the + + + align:start position:0% +in the +sounds now of course we don't really + + align:start position:0% +sounds now of course we don't really + + + align:start position:0% +sounds now of course we don't really +care about the Acoustics if we're trying + + align:start position:0% +care about the Acoustics if we're trying + + + align:start position:0% +care about the Acoustics if we're trying +to for example + + align:start position:0% +to for example + + + align:start position:0% +to for example +synthesize or analyze speech we don't + + align:start position:0% +synthesize or analyze speech we don't + + + align:start position:0% +synthesize or analyze speech we don't +particularly care about that we do like + + align:start position:0% +particularly care about that we do like + + + align:start position:0% +particularly care about that we do like +to know that there's a theory that + + align:start position:0% +to know that there's a theory that + + + align:start position:0% +to know that there's a theory that +underlines it right and there's a very + + align:start position:0% +underlines it right and there's a very + + + align:start position:0% +underlines it right and there's a very +sound physical basis for why we should + + align:start position:0% +sound physical basis for why we should + + + align:start position:0% +sound physical basis for why we should +think about this Source filter idea when + + align:start position:0% +think about this Source filter idea when + + + align:start position:0% +think about this Source filter idea when +I say Source + + align:start position:0% +I say Source + + + align:start position:0% +I say Source +filter Source filter so everybody calls + + align:start position:0% +filter Source filter so everybody calls + + + align:start position:0% +filter Source filter so everybody calls +it the source filter model of + + align:start position:0% +it the source filter model of + + + align:start position:0% +it the source filter model of +speech so there's a very good physical + + align:start position:0% +speech so there's a very good physical + + + align:start position:0% +speech so there's a very good physical +reason for why that should be true of + + align:start position:0% +reason for why that should be true of + + + align:start position:0% +reason for why that should be true of +course what we care + + align:start position:0% +course what we care + + + align:start position:0% +course what we care +about is the frequency + + align:start position:0% +about is the frequency + + + align:start position:0% +about is the frequency +response so here what's showed is + + align:start position:0% +response so here what's showed is + + + align:start position:0% +response so here what's showed is +measured measurements of frequency + + align:start position:0% +measured measurements of frequency + + + align:start position:0% +measured measurements of frequency +responses taken from speakers so now we + + align:start position:0% +responses taken from speakers so now we + + + align:start position:0% +responses taken from speakers so now we +don't do the X-ray thing all we do is + + align:start position:0% +don't do the X-ray thing all we do is + + + align:start position:0% +don't do the X-ray thing all we do is +record somebody saying heed head had + + align:start position:0% +record somebody saying heed head had + + + align:start position:0% +record somebody saying heed head had +Hood had + + align:start position:0% +Hood had + + + align:start position:0% +Hood had +hood and we look at men women and + + align:start position:0% +hood and we look at men women and + + + align:start position:0% +hood and we look at men women and +children and we characterize how their + + align:start position:0% +children and we characterize how their + + + align:start position:0% +children and we characterize how their +frequency responses + + align:start position:0% +frequency responses + + + align:start position:0% +frequency responses +change when they make those different + + align:start position:0% +change when they make those different + + + align:start position:0% +change when they make those different +sounds so what's showed here is uh that + + align:start position:0% +sounds so what's showed here is uh that + + + align:start position:0% +sounds so what's showed here is uh that +you get get a relatively good + + align:start position:0% +you get get a relatively good + + + align:start position:0% +you get get a relatively good +fit by thinking about the frequency + + align:start position:0% +fit by thinking about the frequency + + + align:start position:0% +fit by thinking about the frequency +response having three + + align:start position:0% +response having three + + + align:start position:0% +response having three +formats the formats are the peak + + align:start position:0% +formats the formats are the peak + + + align:start position:0% +formats the formats are the peak +frequencies there's a theory for which I + + align:start position:0% +frequencies there's a theory for which I + + + align:start position:0% +frequencies there's a theory for which I +won't go into for how you take this + + align:start position:0% +won't go into for how you take this + + + align:start position:0% +won't go into for how you take this +shape and turn it into a format + + align:start position:0% +shape and turn it into a format + + + align:start position:0% +shape and turn it into a format +frequency and given just the format + + align:start position:0% +frequency and given just the format + + + align:start position:0% +frequency and given just the format +frequencies or given the frequency + + align:start position:0% +frequencies or given the frequency + + + align:start position:0% +frequencies or given the frequency +response measured at uniform spacing + + align:start position:0% +response measured at uniform spacing + + + align:start position:0% +response measured at uniform spacing +across frequencies there's a theory for + + align:start position:0% +across frequencies there's a theory for + + + align:start position:0% +across frequencies there's a theory for +how you can generate the smooth + + align:start position:0% +how you can generate the smooth + + + align:start position:0% +how you can generate the smooth +line which is really this is an 11th + + align:start position:0% +line which is really this is an 11th + + + align:start position:0% +line which is really this is an 11th +order fit which means that there are 11 + + align:start position:0% +order fit which means that there are 11 + + + align:start position:0% +order fit which means that there are 11 +poles and no + + align:start position:0% +poles and no + + + align:start position:0% +poles and no +zeros so what you do to get this shape + + align:start position:0% +zeros so what you do to get this shape + + + align:start position:0% +zeros so what you do to get this shape +then is take the locations and + + align:start position:0% +then is take the locations and + + + align:start position:0% +then is take the locations and +amplitudes of the format frequencies and + + align:start position:0% +amplitudes of the format frequencies and + + + align:start position:0% +amplitudes of the format frequencies and +do a fit using + + align:start position:0% +do a fit using + + + align:start position:0% +do a fit using +poles and you so here's a table showing + + align:start position:0% +poles and you so here's a table showing + + + align:start position:0% +poles and you so here's a table showing +measured format frequencies F1 F2 and F3 + + align:start position:0% +measured format frequencies F1 F2 and F3 + + + align:start position:0% +measured format frequencies F1 F2 and F3 +for uh uh whatever eight six different + + align:start position:0% +for uh uh whatever eight six different + + + align:start position:0% +for uh uh whatever eight six different +sounds for nine different categories for + + align:start position:0% +sounds for nine different categories for + + + align:start position:0% +sounds for nine different categories for +three different categories of speakers + + align:start position:0% +three different categories of speakers + + + align:start position:0% +three different categories of speakers +okay and that's kind of a complete + + align:start position:0% +okay and that's kind of a complete + + + align:start position:0% +okay and that's kind of a complete +analysis then in terms of the source + + align:start position:0% +analysis then in terms of the source + + + align:start position:0% +analysis then in terms of the source +filter idea so this figure uh summarizes + + align:start position:0% +filter idea so this figure uh summarizes + + + align:start position:0% +filter idea so this figure uh summarizes +the idea we think about Source filter so + + align:start position:0% +the idea we think about Source filter so + + + align:start position:0% +the idea we think about Source filter so +the source is the glotus the filter is + + align:start position:0% +the source is the glotus the filter is + + + align:start position:0% +the source is the glotus the filter is +the formance created by the + + align:start position:0% +the formance created by the + + + align:start position:0% +the formance created by the +throat and speech is the thing that + + align:start position:0% +throat and speech is the thing that + + + align:start position:0% +throat and speech is the thing that +comes out of the source filter the + + align:start position:0% +comes out of the source filter the + + + align:start position:0% +comes out of the source filter the +source is some periodic waveform caused + + align:start position:0% +source is some periodic waveform caused + + + align:start position:0% +source is some periodic waveform caused +by the banging together of the vocal + + align:start position:0% +by the banging together of the vocal + + + align:start position:0% +by the banging together of the vocal +folds the filter is the uh frequency + + align:start position:0% +folds the filter is the uh frequency + + + align:start position:0% +folds the filter is the uh frequency +response of the + + align:start position:0% +response of the + + + align:start position:0% +response of the +throat and the result then is just + + align:start position:0% +throat and the result then is just + + + align:start position:0% +throat and the result then is just +passing this glotus waveform so This Is + + align:start position:0% +passing this glotus waveform so This Is + + + align:start position:0% +passing this glotus waveform so This Is +The glotus Wave this is a measured by + + align:start position:0% +The glotus Wave this is a measured by + + + align:start position:0% +The glotus Wave this is a measured by +sticking a microphone in somebody's + + align:start position:0% +sticking a microphone in somebody's + + + align:start position:0% +sticking a microphone in somebody's +throat this is a measurement of what the + + align:start position:0% +throat this is a measurement of what the + + + align:start position:0% +throat this is a measurement of what the +glotus Acoustics looks like + + align:start position:0% +glotus Acoustics looks like + + + align:start position:0% +glotus Acoustics looks like +this is a fora + + align:start position:0% +this is a fora + + + align:start position:0% +this is a fora +decomposition of that periodic + + align:start position:0% +decomposition of that periodic + + + align:start position:0% +decomposition of that periodic +waveform then this is the frequency + + align:start position:0% +waveform then this is the frequency + + + align:start position:0% +waveform then this is the frequency +response of that thing and this is the + + align:start position:0% +response of that thing and this is the + + + align:start position:0% +response of that thing and this is the +fora uh the fora coefficients of the + + align:start position:0% +fora uh the fora coefficients of the + + + align:start position:0% +fora uh the fora coefficients of the +output for different uh uh sound so + + align:start position:0% +output for different uh uh sound so + + + align:start position:0% +output for different uh uh sound so +here's the frequency so the same glotus + + align:start position:0% +here's the frequency so the same glotus + + + align:start position:0% +here's the frequency so the same glotus +signal underlies an e sound and an a + + align:start position:0% +signal underlies an e sound and an a + + + align:start position:0% +signal underlies an e sound and an a +sound and generates two different + + align:start position:0% +sound and generates two different + + + align:start position:0% +sound and generates two different +Spectrum we call that combination of + + align:start position:0% +Spectrum we call that combination of + + + align:start position:0% +Spectrum we call that combination of +magnitudes and angles we call that the + + align:start position:0% +magnitudes and angles we call that the + + + align:start position:0% +magnitudes and angles we call that the +fora Spectra so you get two different + + align:start position:0% +fora Spectra so you get two different + + + align:start position:0% +fora Spectra so you get two different +Spectra depending on the uh filter shape + + align:start position:0% +Spectra depending on the uh filter shape + + + align:start position:0% +Spectra depending on the uh filter shape +okay and that's the basis this Theory + + align:start position:0% +okay and that's the basis this Theory + + + align:start position:0% +okay and that's the basis this Theory +this Source filter idea is the basis of + + align:start position:0% +this Source filter idea is the basis of + + + align:start position:0% +this Source filter idea is the basis of +the current technology for speech + + align:start position:0% +the current technology for speech + + + align:start position:0% +the current technology for speech +recognition and speech and speech + + align:start position:0% +recognition and speech and speech + + + align:start position:0% +recognition and speech and speech +production so I actually cheated those + + align:start position:0% +production so I actually cheated those + + + align:start position:0% +production so I actually cheated those +sounds that I played earlier bit bat bot + + align:start position:0% +sounds that I played earlier bit bat bot + + + align:start position:0% +sounds that I played earlier bit bat bot +beat all those things those were + + align:start position:0% +beat all those things those were + + + align:start position:0% +beat all those things those were +actually synthetic + + align:start position:0% +actually synthetic + + + align:start position:0% +actually synthetic +speech okay all I did is I ran a speech + + align:start position:0% +speech okay all I did is I ran a speech + + + align:start position:0% +speech okay all I did is I ran a speech +synthesizer and and I said synthesize + + align:start position:0% +synthesizer and and I said synthesize + + + align:start position:0% +synthesizer and and I said synthesize +bit so that was really a synthesized + + align:start position:0% +bit so that was really a synthesized + + + align:start position:0% +bit so that was really a synthesized +thing that was not a real + + align:start position:0% +thing that was not a real + + + align:start position:0% +thing that was not a real +person and so uh the synthesizer used + + align:start position:0% +person and so uh the synthesizer used + + + align:start position:0% +person and so uh the synthesizer used +this + + align:start position:0% +this + + + align:start position:0% +this +theory in order to to generate the + + align:start position:0% +theory in order to to generate the + + + align:start position:0% +theory in order to to generate the +synthetic speech we also use this theory + + align:start position:0% +synthetic speech we also use this theory + + + align:start position:0% +synthetic speech we also use this theory +in order to recognize speech and you'll + + align:start position:0% +in order to recognize speech and you'll + + + align:start position:0% +in order to recognize speech and you'll +do a homework problem in homework 10 I + + align:start position:0% +do a homework problem in homework 10 I + + + align:start position:0% +do a homework problem in homework 10 I +think it + + align:start position:0% +think it + + + align:start position:0% +think it +is in which you'll build the Primitive + + align:start position:0% +is in which you'll build the Primitive + + + align:start position:0% +is in which you'll build the Primitive +front end of a speech of a spe speech + + align:start position:0% +front end of a speech of a spe speech + + + align:start position:0% +front end of a speech of a spe speech +recognizer using the + + align:start position:0% +recognizer using the + + + align:start position:0% +recognizer using the +Theory and I'll give you a couple of + + align:start position:0% +Theory and I'll give you a couple of + + + align:start position:0% +Theory and I'll give you a couple of +utterances of different vowels and + + align:start position:0% +utterances of different vowels and + + + align:start position:0% +utterances of different vowels and +you'll have to classify which vow is + + align:start position:0% +you'll have to classify which vow is + + + align:start position:0% +you'll have to classify which vow is +being said according to some automatic + + align:start position:0% +being said according to some automatic + + + align:start position:0% +being said according to some automatic +um speech recognizer based on this + + align:start position:0% +um speech recognizer based on this + + + align:start position:0% +um speech recognizer based on this +Theory the theory is also just fun + + align:start position:0% +Theory the theory is also just fun + + + align:start position:0% +Theory the theory is also just fun +because the theory lets us figure out + + align:start position:0% +because the theory lets us figure out + + + align:start position:0% +because the theory lets us figure out +anomalies so when somebody has a speech + + align:start position:0% +anomalies so when somebody has a speech + + + align:start position:0% +anomalies so when somebody has a speech +impediment for example when I did when I + + align:start position:0% +impediment for example when I did when I + + + align:start position:0% +impediment for example when I did when I +was a little kid I did and I was spent + + align:start position:0% +was a little kid I did and I was spent + + + align:start position:0% +was a little kid I did and I was spent +to to speech school now they do a much + + align:start position:0% +to to speech school now they do a much + + + align:start position:0% +to to speech school now they do a much +better job because they do analysis to + + align:start position:0% +better job because they do analysis to + + + align:start position:0% +better job because they do analysis to +figure out what I'm doing + + align:start position:0% +figure out what I'm doing + + + align:start position:0% +figure out what I'm doing +wrong you the sort of source filter idea + + align:start position:0% +wrong you the sort of source filter idea + + + align:start position:0% +wrong you the sort of source filter idea +we can also use the source filter idea + + align:start position:0% +we can also use the source filter idea + + + align:start position:0% +we can also use the source filter idea +to understand um uh paradoxes so for + + align:start position:0% +to understand um uh paradoxes so for + + + align:start position:0% +to understand um uh paradoxes so for +example uh I've told you before I work + + align:start position:0% +example uh I've told you before I work + + + align:start position:0% +example uh I've told you before I work +on hearing aids I try to make hearing + + align:start position:0% +on hearing aids I try to make hearing + + + align:start position:0% +on hearing aids I try to make hearing +aids he so uh people with hearing + + align:start position:0% +aids he so uh people with hearing + + + align:start position:0% +aids he so uh people with hearing +deficiencies like mine where I have sort + + align:start position:0% +deficiencies like mine where I have sort + + + align:start position:0% +deficiencies like mine where I have sort +of progressive age related because I'm + + align:start position:0% +of progressive age related because I'm + + + align:start position:0% +of progressive age related because I'm +old right that's what happens uh I have + + align:start position:0% +old right that's what happens uh I have + + + align:start position:0% +old right that's what happens uh I have +age related hearing loss which H which + + align:start position:0% +age related hearing loss which H which + + + align:start position:0% +age related hearing loss which H which +means that I'm losing high frequencies + + align:start position:0% +means that I'm losing high frequencies + + + align:start position:0% +means that I'm losing high frequencies +I'm less sensitive high frequencies + + align:start position:0% +I'm less sensitive high frequencies + + + align:start position:0% +I'm less sensitive high frequencies +people like me which is the vast + + align:start position:0% +people like me which is the vast + + + align:start position:0% +people like me which is the vast +majority of people my + + align:start position:0% +majority of people my + + + align:start position:0% +majority of people my +age uh have it's easier to understand + + align:start position:0% +age uh have it's easier to understand + + + align:start position:0% +age uh have it's easier to understand +male speech than female speech + + align:start position:0% + + + + align:start position:0% + +why higher frequencies so those higher + + align:start position:0% +why higher frequencies so those higher + + + align:start position:0% +why higher frequencies so those higher +frequencies uh are shift some of the + + align:start position:0% +frequencies uh are shift some of the + + + align:start position:0% +frequencies uh are shift some of the +important stuff that I should be + + align:start position:0% +important stuff that I should be + + + align:start position:0% +important stuff that I should be +listening to into frequencies I don't + + align:start position:0% +listening to into frequencies I don't + + + align:start position:0% +listening to into frequencies I don't +hear + + align:start position:0% +hear + + + align:start position:0% +hear +anymore right so that's a way of using + + align:start position:0% +anymore right so that's a way of using + + + align:start position:0% +anymore right so that's a way of using +this Theory to try to understand what's + + align:start position:0% +this Theory to try to understand what's + + + align:start position:0% +this Theory to try to understand what's +wrong with me but there's also things + + align:start position:0% +wrong with me but there's also things + + + align:start position:0% +wrong with me but there's also things +it's not just me normal people have + + align:start position:0% +it's not just me normal people have + + + align:start position:0% +it's not just me normal people have +trouble distinguishing female speech + + align:start position:0% +trouble distinguishing female speech + + + align:start position:0% +trouble distinguishing female speech +especially in taxing environments and + + align:start position:0% +especially in taxing environments and + + + align:start position:0% +especially in taxing environments and +one of those is + + align:start position:0% + + + + align:start position:0% + +singing so if you consider uh alos and + + align:start position:0% +singing so if you consider uh alos and + + + align:start position:0% +singing so if you consider uh alos and +Sopranos Sopranos are like the worst + + align:start position:0% +Sopranos Sopranos are like the worst + + + align:start position:0% +Sopranos Sopranos are like the worst +right because they are not only female + + align:start position:0% +right because they are not only female + + + align:start position:0% +right because they are not only female +but they're at the high end of + + align:start position:0% +but they're at the high end of + + + align:start position:0% +but they're at the high end of +females and there are those who complain + + align:start position:0% +females and there are those who complain + + + align:start position:0% +females and there are those who complain +about not being able to understand + + align:start position:0% +about not being able to understand + + + align:start position:0% +about not being able to understand +female singers okay so here's a demo + + align:start position:0% +female singers okay so here's a demo + + + align:start position:0% +female singers okay so here's a demo +that will help us to understand whether + + align:start position:0% +that will help us to understand whether + + + align:start position:0% +that will help us to understand whether +that's a uh a valid uh kind of a + + align:start position:0% +that's a uh a valid uh kind of a + + + align:start position:0% +that's a uh a valid uh kind of a +criticism or not so what I've got got is + + align:start position:0% +criticism or not so what I've got got is + + + align:start position:0% +criticism or not so what I've got got is +um a professional singer singing la la + + align:start position:0% +um a professional singer singing la la + + + align:start position:0% +um a professional singer singing la la +on a scale so from low frequency to high + + align:start position:0% +on a scale so from low frequency to high + + + align:start position:0% +on a scale so from low frequency to high +frequency then a different sound a + + align:start position:0% +frequency then a different sound a + + + align:start position:0% +frequency then a different sound a +different sound a different sound a + + align:start position:0% +different sound a different sound a + + + align:start position:0% +different sound a different sound a +different + + align:start position:0% +different + + + align:start position:0% +different +sound so the first thing what I want to + + align:start position:0% +sound so the first thing what I want to + + + align:start position:0% +sound so the first thing what I want to +do I want you to listen to those + + align:start position:0% +do I want you to listen to those + + + align:start position:0% +do I want you to listen to those +different sounds as as she goes across + + align:start position:0% +different sounds as as she goes across + + + align:start position:0% +different sounds as as she goes across +the scale then I'm going to play just + + align:start position:0% +the scale then I'm going to play just + + + align:start position:0% +the scale then I'm going to play just +the low ones and just the high ones just + + align:start position:0% +the low ones and just the high ones just + + + align:start position:0% +the low ones and just the high ones just +the low frequency ones and just the high + + align:start position:0% +the low frequency ones and just the high + + + align:start position:0% +the low frequency ones and just the high +frequency ones so first uh the different + + align:start position:0% +frequency ones so first uh the different + + + align:start position:0% +frequency ones so first uh the different +scales la + + align:start position:0% +scales la + + + align:start position:0% +scales la +la okay + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +la + + align:start position:0% +la + + + align:start position:0% +la +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay so now what I've done is I've + + align:start position:0% +okay so now what I've done is I've + + + align:start position:0% +okay so now what I've done is I've +sliced out the + + align:start position:0% +sliced out the + + + align:start position:0% +sliced out the +lowest frequency the very first of the + + align:start position:0% +lowest frequency the very first of the + + + align:start position:0% +lowest frequency the very first of the +scale from each of the sounds and pasted + + align:start position:0% +scale from each of the sounds and pasted + + + align:start position:0% +scale from each of the sounds and pasted +them together to get the low frequency + + align:start position:0% +them together to get the low frequency + + + align:start position:0% +them together to get the low frequency +run and then I took out the high ones + + align:start position:0% +run and then I took out the high ones + + + align:start position:0% +run and then I took out the high ones +and pasted them + + align:start position:0% +and pasted them + + + align:start position:0% +and pasted them +together okay this exactly the same + + align:start position:0% +together okay this exactly the same + + + align:start position:0% +together okay this exactly the same +sounds just played in a different + + align:start position:0% +sounds just played in a different + + + align:start position:0% +sounds just played in a different +order so first the low frequency + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +ones and the high frequency + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +once it's not her fault + + align:start position:0% +once it's not her fault + + + align:start position:0% +once it's not her fault +she's doing everything + + align:start position:0% +she's doing everything + + + align:start position:0% +she's doing everything +right and you can see that here's uh + + align:start position:0% +right and you can see that here's uh + + + align:start position:0% +right and you can see that here's uh +again a Python program analyzing those + + align:start position:0% +again a Python program analyzing those + + + align:start position:0% +again a Python program analyzing those +same + + align:start position:0% +same + + + align:start position:0% +same +segments so what's showed here is the E + + align:start position:0% +segments so what's showed here is the E + + + align:start position:0% +segments so what's showed here is the E +the filter derived from the e by + + align:start position:0% +the filter derived from the e by + + + align:start position:0% +the filter derived from the e by +thinking about the uh + + align:start position:0% +thinking about the uh + + + align:start position:0% +thinking about the uh +Le by looking at that + + align:start position:0% +Le by looking at that + + + align:start position:0% +Le by looking at that +sequence and averaging across the um uh + + align:start position:0% +sequence and averaging across the um uh + + + align:start position:0% +sequence and averaging across the um uh +frequencies + + align:start position:0% +frequencies + + + align:start position:0% +frequencies +so here's the + + align:start position:0% +so here's the + + + align:start position:0% +so here's the +filter here's the uh filtered glotus + + align:start position:0% +filter here's the uh filtered glotus + + + align:start position:0% +filter here's the uh filtered glotus +Spectrum for a low frequency an + + align:start position:0% +Spectrum for a low frequency an + + + align:start position:0% +Spectrum for a low frequency an +intermediate frequency and a high + + align:start position:0% +intermediate frequency and a high + + + align:start position:0% +intermediate frequency and a high +frequency what's what's the difference + + align:start position:0% +frequency what's what's the difference + + + align:start position:0% +frequency what's what's the difference +between the low middle and + + align:start position:0% + + + + align:start position:0% + +high what's characteristically different + + align:start position:0% +high what's characteristically different + + + align:start position:0% +high what's characteristically different +at low and high + + align:start position:0% + + + + align:start position:0% + +so if you look at the low frequency the + + align:start position:0% +so if you look at the low frequency the + + + align:start position:0% +so if you look at the low frequency the +low + + align:start position:0% +low + + + align:start position:0% +low +pitch there are more frequency + + align:start position:0% +pitch there are more frequency + + + align:start position:0% +pitch there are more frequency +components in a given + + align:start position:0% +components in a given + + + align:start position:0% +components in a given +range so if I say analyze the + + align:start position:0% +range so if I say analyze the + + + align:start position:0% +range so if I say analyze the +frequencies between 0 and 1,000 + + align:start position:0% +frequencies between 0 and 1,000 + + + align:start position:0% +frequencies between 0 and 1,000 +Hertz 1,000 cycles per second there are + + align:start position:0% +Hertz 1,000 cycles per second there are + + + align:start position:0% +Hertz 1,000 cycles per second there are +more lines when you have a low + + align:start position:0% +more lines when you have a low + + + align:start position:0% +more lines when you have a low +frequency and so you get the density of + + align:start position:0% +frequency and so you get the density of + + + align:start position:0% +frequency and so you get the density of +the lines is greater for the low + + align:start position:0% +the lines is greater for the low + + + align:start position:0% +the lines is greater for the low +frequency utterance than it is for the + + align:start position:0% +frequency utterance than it is for the + + + align:start position:0% +frequency utterance than it is for the +high frequency + + align:start position:0% +high frequency + + + align:start position:0% +high frequency +utterance the low frequency utterance is + + align:start position:0% +utterance the low frequency utterance is + + + align:start position:0% +utterance the low frequency utterance is +spaced close enough that you can clearly + + align:start position:0% +spaced close enough that you can clearly + + + align:start position:0% +spaced close enough that you can clearly +figure out this + + align:start position:0% +figure out this + + + align:start position:0% +figure out this +pattern from that + + align:start position:0% +pattern from that + + + align:start position:0% +pattern from that +spacing because there are multiple lines + + align:start position:0% +spacing because there are multiple lines + + + align:start position:0% +spacing because there are multiple lines +per + + align:start position:0% +per + + + align:start position:0% +per +Peak the problem is that the speech + + align:start position:0% +Peak the problem is that the speech + + + align:start position:0% +Peak the problem is that the speech +waveforms have very sharp + + align:start position:0% +waveforms have very sharp + + + align:start position:0% +waveforms have very sharp +resonances the the Peaks are narrow so + + align:start position:0% +resonances the the Peaks are narrow so + + + align:start position:0% +resonances the the Peaks are narrow so +that as you go to a higher + + align:start position:0% +that as you go to a higher + + + align:start position:0% +that as you go to a higher +frequency now it's very hard to see so + + align:start position:0% +frequency now it's very hard to see so + + + align:start position:0% +frequency now it's very hard to see so +there where there was two lines + + align:start position:0% +there where there was two lines + + + align:start position:0% +there where there was two lines +characterizing this guy now there's + + align:start position:0% +characterizing this guy now there's + + + align:start position:0% +characterizing this guy now there's +one and at the highest frequency there's + + align:start position:0% +one and at the highest frequency there's + + + align:start position:0% +one and at the highest frequency there's +nothing + + align:start position:0% + + + + align:start position:0% + +there similarly with these Peaks again + + align:start position:0% +there similarly with these Peaks again + + + align:start position:0% +there similarly with these Peaks again +several lines representing each peak one + + align:start position:0% +several lines representing each peak one + + + align:start position:0% +several lines representing each peak one +line representing nothing representing + + align:start position:0% +line representing nothing representing + + + align:start position:0% +line representing nothing representing +this peak nothing representing that Peak + + align:start position:0% +this peak nothing representing that Peak + + + align:start position:0% +this peak nothing representing that Peak +there is nothing about + + align:start position:0% +there is nothing about + + + align:start position:0% +there is nothing about +e in that + + align:start position:0% +e in that + + + align:start position:0% +e in that +signal and if you do the same analysis + + align:start position:0% +signal and if you do the same analysis + + + align:start position:0% +signal and if you do the same analysis +for + + align:start position:0% +for + + + align:start position:0% +for +ah you get the same result there's + + align:start position:0% +ah you get the same result there's + + + align:start position:0% +ah you get the same result there's +nothing about e and there's nothing + + align:start position:0% +nothing about e and there's nothing + + + align:start position:0% +nothing about e and there's nothing +about ah there's just nothing there + + align:start position:0% +about ah there's just nothing there + + + align:start position:0% +about ah there's just nothing there +there's no way anybody is going to tell + + align:start position:0% +there's no way anybody is going to tell + + + align:start position:0% +there's no way anybody is going to tell +those two sounds apart so if the singer + + align:start position:0% +those two sounds apart so if the singer + + + align:start position:0% +those two sounds apart so if the singer +put her voice her U vocal uh uh track in + + align:start position:0% +put her voice her U vocal uh uh track in + + + align:start position:0% +put her voice her U vocal uh uh track in +precisely the right location + + align:start position:0% + + + + align:start position:0% + +there would be no difference between + + align:start position:0% +there would be no difference between + + + align:start position:0% +there would be no difference between +those sounds okay regardless of what the + + align:start position:0% +those sounds okay regardless of what the + + + align:start position:0% +those sounds okay regardless of what the +director said okay so that's the problem + + align:start position:0% +director said okay so that's the problem + + + align:start position:0% +director said okay so that's the problem +so that's a way of using the 4A analysis + + align:start position:0% +so that's a way of using the 4A analysis + + + align:start position:0% +so that's a way of using the 4A analysis +to gain some insight into some anomalous + + align:start position:0% +to gain some insight into some anomalous + + + align:start position:0% +to gain some insight into some anomalous +uh uh uh situations + + align:start position:0% + + + + align:start position:0% + +yeah it no it has to do only with the + + align:start position:0% +yeah it no it has to do only with the + + + align:start position:0% +yeah it no it has to do only with the +frequency content of the glotus + + align:start position:0% +frequency content of the glotus + + + align:start position:0% +frequency content of the glotus +waveform the glotus W you can think + + align:start position:0% +waveform the glotus W you can think + + + align:start position:0% +waveform the glotus W you can think +about it as sampling and that's a good + + align:start position:0% +about it as sampling and that's a good + + + align:start position:0% +about it as sampling and that's a good +Insight because the the the the 4A + + align:start position:0% +Insight because the the the the 4A + + + align:start position:0% +Insight because the the the the 4A +series only has components at integer + + align:start position:0% +series only has components at integer + + + align:start position:0% +series only has components at integer +multiples of a base + + align:start position:0% +multiples of a base + + + align:start position:0% +multiples of a base +frequency so that means we're sampling + + align:start position:0% +frequency so that means we're sampling + + + align:start position:0% +frequency so that means we're sampling +in frequency not in + + align:start position:0% +in frequency not in + + + align:start position:0% +in frequency not in +time so we have this continuous we have + + align:start position:0% +time so we have this continuous we have + + + align:start position:0% +time so we have this continuous we have +this potentially continuous frequency + + align:start position:0% +this potentially continuous frequency + + + align:start position:0% +this potentially continuous frequency +response which is characterizing this + + align:start position:0% +response which is characterizing this + + + align:start position:0% +response which is characterizing this +that is continuous I could excite this + + align:start position:0% +that is continuous I could excite this + + + align:start position:0% +that is continuous I could excite this +at any frequency that I want to but the + + align:start position:0% +at any frequency that I want to but the + + + align:start position:0% +at any frequency that I want to but the +glotus waveform of the + + align:start position:0% +glotus waveform of the + + + align:start position:0% +glotus waveform of the +singer is only sampling that at + + align:start position:0% +singer is only sampling that at + + + align:start position:0% +singer is only sampling that at +particular + + align:start position:0% +particular + + + align:start position:0% +particular +frequencies c c prime cble prime b b + + align:start position:0% +frequencies c c prime cble prime b b + + + align:start position:0% +frequencies c c prime cble prime b b +prime bouble prime right so there's only + + align:start position:0% +prime bouble prime right so there's only + + + align:start position:0% +prime bouble prime right so there's only +certain frequencies at which the singer + + align:start position:0% +certain frequencies at which the singer + + + align:start position:0% +certain frequencies at which the singer +is sampling this so there is a way of + + align:start position:0% +is sampling this so there is a way of + + + align:start position:0% +is sampling this so there is a way of +thinking about it as sampling but it's + + align:start position:0% +thinking about it as sampling but it's + + + align:start position:0% +thinking about it as sampling but it's +not sampling due to my addd converter or + + align:start position:0% +not sampling due to my addd converter or + + + align:start position:0% +not sampling due to my addd converter or +anything like that it's sampling in + + align:start position:0% +anything like that it's sampling in + + + align:start position:0% +anything like that it's sampling in +frequency so the point is that uh this + + align:start position:0% +frequency so the point is that uh this + + + align:start position:0% +frequency so the point is that uh this +kind of a source filter idea this and + + align:start position:0% +kind of a source filter idea this and + + + align:start position:0% +kind of a source filter idea this and +more generally the filter idea is such a + + align:start position:0% +more generally the filter idea is such a + + + align:start position:0% +more generally the filter idea is such a +powerful uh representation that next + + align:start position:0% +powerful uh representation that next + + + align:start position:0% +powerful uh representation that next +time we'll think about how to do the + + align:start position:0% +time we'll think about how to do the + + + align:start position:0% +time we'll think about how to do the +same sort of thing for non-periodic + + align:start position:0% +same sort of thing for non-periodic + + + align:start position:0% +same sort of thing for non-periodic +stimul see you then \ No newline at end of file diff --git a/NAQhRc3OQAw.txt b/NAQhRc3OQAw.txt new file mode 100644 index 0000000000000000000000000000000000000000..06f64dbe2e157c6a7a65a2a4097e02809e30768a --- /dev/null +++ b/NAQhRc3OQAw.txt @@ -0,0 +1,148 @@ +Let us see what we learn about +the patterns that emerge. + +We will show that the +clusters are interpretable + +and reveal unique patterns +of diagnostic history + +among the population. + +We selected six patterns to +present in this lecture-- + +Cluster 1, 6, and +7, in Cost Bucket 2, + +and Clusters 4, 5, and +10, in Cost Bucket 3. + +The first pattern shows the +occurrence of chest pain + +three months before +the heart attack. + +Note that the red dots depict +the visits per diagnosis + +for patients in Cluster +1-- this is, we think, + +Bucket 2-- and the blue +dots depict the visits + +per diagnosis for patients +in Bucket 2 throughout. + +Note the very +significant increase + +for visits related +to chest pains + +three months before the event. + +About 17, three months +before for the red patients, + +and about 1 and 1/2 visits +for the blue patients. + +The next pattern reveals +an increasing occurrence + +of chronic obstructive pulmonary +disease, COPD, for short. + +Patients from +Cluster 7 in Bucket 2 + +have regular doctor +visits for COPD. + +Note that nine months +before, we have + +4 and 1/2 visits +versus 0.5 visits. + +Six months before, we have +almost 7 visits versus 1/2 + +a visit, and three +months before, we + +have 9 visits versus +1/2 a visit for COPD, + +so a clear increasing pattern. + +The next pattern shows +gradually increasing occurrence + +of anemia. + +The red line shows the +patient's in Cluster 4 + +increasingly visit the doctor +for anemia from nine months + +on before the event. + +Nine months before, members +have an average of 9 visits + +to the doctor for anemia. + +This increases to an average +of 11 visits six months + +before the event, and +then an average of 15 + +visits three months before +the event, a clear increasing + +pattern. + +The final pattern shows +the occurrence of diabetes + +as a pattern for heart attacks. + +It is well known that +both types 1 and 2 + +diabetes are associated with +accelerated atherosclerosis, + +one of the main causes of +myocardial infarction-- heart + +attacks, that is. + +Well known diagnoses +associated with heart attacks, + +such as diabetes, hypertension, +and hyperlipidemia, + +characterize many of the +patterns of the consistency + +of care throughout all of the +cost buckets and clustering + +models. + +You observe a difference, +here, of the number + +of visits for diabetes +for the population + +that had the event versus +the other population. \ No newline at end of file diff --git a/NRnAuKxx6XA.txt b/NRnAuKxx6XA.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4ff7051c3e36f711c92516c65a4eec4f6ea7339 --- /dev/null +++ b/NRnAuKxx6XA.txt @@ -0,0 +1,923 @@ +align:start position:0% + +as a warm-up towards finding the + + align:start position:0% +as a warm-up towards finding the + + + align:start position:0% +as a warm-up towards finding the +distribution of a function of random + + align:start position:0% +distribution of a function of random + + + align:start position:0% +distribution of a function of random +variables let us start by considering + + align:start position:0% +variables let us start by considering + + + align:start position:0% +variables let us start by considering +the discrete case so let X be a discrete + + align:start position:0% +the discrete case so let X be a discrete + + + align:start position:0% +the discrete case so let X be a discrete +random variable and let Y be defined as + + align:start position:0% +random variable and let Y be defined as + + + align:start position:0% +random variable and let Y be defined as +a given function of X we know the PMF of + + align:start position:0% +a given function of X we know the PMF of + + + align:start position:0% +a given function of X we know the PMF of +X and wish to find the PMF of Y here is + + align:start position:0% +X and wish to find the PMF of Y here is + + + align:start position:0% +X and wish to find the PMF of Y here is +a simple example the random variable X + + align:start position:0% +a simple example the random variable X + + + align:start position:0% +a simple example the random variable X +takes the values 2 3 4 and 5 with the + + align:start position:0% +takes the values 2 3 4 and 5 with the + + + align:start position:0% +takes the values 2 3 4 and 5 with the +probabilities given in the failure and Y + + align:start position:0% +probabilities given in the failure and Y + + + align:start position:0% +probabilities given in the failure and Y +is the function indicated here then for + + align:start position:0% +is the function indicated here then for + + + align:start position:0% +is the function indicated here then for +example the probability that Y takes a + + align:start position:0% +example the probability that Y takes a + + + align:start position:0% +example the probability that Y takes a +value of 4 this is also the value of the + + align:start position:0% +value of 4 this is also the value of the + + + align:start position:0% +value of 4 this is also the value of the +PMF of Y evaluated at 4 this is simply + + align:start position:0% +PMF of Y evaluated at 4 this is simply + + + align:start position:0% +PMF of Y evaluated at 4 this is simply +the sum of the probabilities of the + + align:start position:0% +the sum of the probabilities of the + + + align:start position:0% +the sum of the probabilities of the +possible values of X that give rise to a + + align:start position:0% +possible values of X that give rise to a + + + align:start position:0% +possible values of X that give rise to a +value of y that is equal to 4 therefore + + align:start position:0% +value of y that is equal to 4 therefore + + + align:start position:0% +value of y that is equal to 4 therefore +this expression is equal to the + + align:start position:0% +this expression is equal to the + + + align:start position:0% +this expression is equal to the +probability that x equals to 4 plus the + + align:start position:0% +probability that x equals to 4 plus the + + + align:start position:0% +probability that x equals to 4 plus the +probability that X is equal to 5 or in + + align:start position:0% +probability that X is equal to 5 or in + + + align:start position:0% +probability that X is equal to 5 or in +PMF notation we can write it in this + + align:start position:0% +PMF notation we can write it in this + + + align:start position:0% +PMF notation we can write it in this +manner and in this numerical example it + + align:start position:0% +manner and in this numerical example it + + + align:start position:0% +manner and in this numerical example it +would be 0.3 plus 0.4 more generally for + + align:start position:0% +would be 0.3 plus 0.4 more generally for + + + align:start position:0% +would be 0.3 plus 0.4 more generally for +any given value of little Y the + + align:start position:0% +any given value of little Y the + + + align:start position:0% +any given value of little Y the +probability that the random variable + + align:start position:0% +probability that the random variable + + + align:start position:0% +probability that the random variable +capital y takes this particular value is + + align:start position:0% +capital y takes this particular value is + + + align:start position:0% +capital y takes this particular value is +the sum of the probabilities of the + + align:start position:0% +the sum of the probabilities of the + + + align:start position:0% +the sum of the probabilities of the +little X that result in that particular + + align:start position:0% +little X that result in that particular + + + align:start position:0% +little X that result in that particular +value so the probability that the random + + align:start position:0% +value so the probability that the random + + + align:start position:0% +value so the probability that the random +variable capital y which is the same as + + align:start position:0% +variable capital y which is the same as + + + align:start position:0% +variable capital y which is the same as +G of X takes on a specific value is the + + align:start position:0% +G of X takes on a specific value is the + + + align:start position:0% +G of X takes on a specific value is the +sum of the probabilities of all possible + + align:start position:0% +sum of the probabilities of all possible + + + align:start position:0% +sum of the probabilities of all possible +values of little X where we only + + align:start position:0% +values of little X where we only + + + align:start position:0% +values of little X where we only +consider those values of little X that + + align:start position:0% +consider those values of little X that + + + align:start position:0% +consider those values of little X that +give rise to the specific value little Y + + align:start position:0% +give rise to the specific value little Y + + + align:start position:0% +give rise to the specific value little Y +that were interested in let us now look + + align:start position:0% +that were interested in let us now look + + + align:start position:0% +that were interested in let us now look +into the special case where we have a + + align:start position:0% +into the special case where we have a + + + align:start position:0% +into the special case where we have a +linear function of a discrete random + + align:start position:0% +linear function of a discrete random + + + align:start position:0% +linear function of a discrete random +variable + + align:start position:0% +variable + + + align:start position:0% +variable +suppose that X is described by the PMF + + align:start position:0% +suppose that X is described by the PMF + + + align:start position:0% +suppose that X is described by the PMF +shown in this diagram and let us + + align:start position:0% +shown in this diagram and let us + + + align:start position:0% +shown in this diagram and let us +consider the random variable Z which is + + align:start position:0% +consider the random variable Z which is + + + align:start position:0% +consider the random variable Z which is +defined as two times X we would like to + + align:start position:0% +defined as two times X we would like to + + + align:start position:0% +defined as two times X we would like to +plot the PMF of Z first let us note the + + align:start position:0% +plot the PMF of Z first let us note the + + + align:start position:0% +plot the PMF of Z first let us note the +values that Z can take when X is equal + + align:start position:0% +values that Z can take when X is equal + + + align:start position:0% +values that Z can take when X is equal +to minus 1 Z is going to be equal to + + align:start position:0% +to minus 1 Z is going to be equal to + + + align:start position:0% +to minus 1 Z is going to be equal to +minus 2 when X is equal to 1 Z is going + + align:start position:0% +minus 2 when X is equal to 1 Z is going + + + align:start position:0% +minus 2 when X is equal to 1 Z is going +to be equal to 2 and when X is equal to + + align:start position:0% +to be equal to 2 and when X is equal to + + + align:start position:0% +to be equal to 2 and when X is equal to +2 Z is going to be equal to 4 this event + + align:start position:0% +2 Z is going to be equal to 4 this event + + + align:start position:0% +2 Z is going to be equal to 4 this event +that X is equal to minus 1 happens with + + align:start position:0% +that X is equal to minus 1 happens with + + + align:start position:0% +that X is equal to minus 1 happens with +probability 2 over 6 and when that event + + align:start position:0% +probability 2 over 6 and when that event + + + align:start position:0% +probability 2 over 6 and when that event +happens Z will take a value of minus 2 + + align:start position:0% +happens Z will take a value of minus 2 + + + align:start position:0% +happens Z will take a value of minus 2 +so this event happens with probability 2 + + align:start position:0% +so this event happens with probability 2 + + + align:start position:0% +so this event happens with probability 2 +over 6 with probability 1 6 X takes a + + align:start position:0% +over 6 with probability 1 6 X takes a + + + align:start position:0% +over 6 with probability 1 6 X takes a +value of 1 so that Z takes a value of 2 + + align:start position:0% +value of 1 so that Z takes a value of 2 + + + align:start position:0% +value of 1 so that Z takes a value of 2 +and this happens with probability 1 over + + align:start position:0% +and this happens with probability 1 over + + + align:start position:0% +and this happens with probability 1 over +6 and finally this last event here + + align:start position:0% +6 and finally this last event here + + + align:start position:0% +6 and finally this last event here +happens with probability 3 over 6 we + + align:start position:0% +happens with probability 3 over 6 we + + + align:start position:0% +happens with probability 3 over 6 we +have thus found the PMF of Z notice that + + align:start position:0% +have thus found the PMF of Z notice that + + + align:start position:0% +have thus found the PMF of Z notice that +it has the same shape as the PMF of X + + align:start position:0% +it has the same shape as the PMF of X + + + align:start position:0% +it has the same shape as the PMF of X +except that it is stretched or scaled + + align:start position:0% +except that it is stretched or scaled + + + align:start position:0% +except that it is stretched or scaled +horizontally by a factor of 2 let us now + + align:start position:0% +horizontally by a factor of 2 let us now + + + align:start position:0% +horizontally by a factor of 2 let us now +consider the random variable Y defined + + align:start position:0% +consider the random variable Y defined + + + align:start position:0% +consider the random variable Y defined +as 2 X plus 3 or what is the same as Z + + align:start position:0% +as 2 X plus 3 or what is the same as Z + + + align:start position:0% +as 2 X plus 3 or what is the same as Z +plus 3 + + align:start position:0% + + + + align:start position:0% + +with probability 2/6 Z is equal to minus + + align:start position:0% +with probability 2/6 Z is equal to minus + + + align:start position:0% +with probability 2/6 Z is equal to minus +2 and in that case Y is going to be + + align:start position:0% +2 and in that case Y is going to be + + + align:start position:0% +2 and in that case Y is going to be +equal to plus 1 and this event happens + + align:start position:0% +equal to plus 1 and this event happens + + + align:start position:0% +equal to plus 1 and this event happens +with probability 2 over 6 with + + align:start position:0% +with probability 2 over 6 with + + + align:start position:0% +with probability 2 over 6 with +probability 1 over 6 Z takes a value of + + align:start position:0% +probability 1 over 6 Z takes a value of + + + align:start position:0% +probability 1 over 6 Z takes a value of +2 so that Y takes a value of 5 and + + align:start position:0% +2 so that Y takes a value of 5 and + + + align:start position:0% +2 so that Y takes a value of 5 and +finally with probability 3 over 6 Z + + align:start position:0% +finally with probability 3 over 6 Z + + + align:start position:0% +finally with probability 3 over 6 Z +takes a value of 4 so that Y takes a + + align:start position:0% +takes a value of 4 so that Y takes a + + + align:start position:0% +takes a value of 4 so that Y takes a +value of 7 + + align:start position:0% + + + + align:start position:0% + +what we see here is that the PMF of Y + + align:start position:0% +what we see here is that the PMF of Y + + + align:start position:0% +what we see here is that the PMF of Y +has exactly the same shape as the PMF of + + align:start position:0% +has exactly the same shape as the PMF of + + + align:start position:0% +has exactly the same shape as the PMF of +Z except that it is shifted to the right + + align:start position:0% +Z except that it is shifted to the right + + + align:start position:0% +Z except that it is shifted to the right +by 3 to summarize in order to find the + + align:start position:0% +by 3 to summarize in order to find the + + + align:start position:0% +by 3 to summarize in order to find the +PMF of a linear function such as 2x plus + + align:start position:0% +PMF of a linear function such as 2x plus + + + align:start position:0% +PMF of a linear function such as 2x plus +3 what we do is that we first stretch + + align:start position:0% +3 what we do is that we first stretch + + + align:start position:0% +3 what we do is that we first stretch +the PMF of x by a factor of 2 and then + + align:start position:0% +the PMF of x by a factor of 2 and then + + + align:start position:0% +the PMF of x by a factor of 2 and then +shifted horizontally by 3 we can also + + align:start position:0% +shifted horizontally by 3 we can also + + + align:start position:0% +shifted horizontally by 3 we can also +describe the PMF of Y through a formula + + align:start position:0% +describe the PMF of Y through a formula + + + align:start position:0% +describe the PMF of Y through a formula +for any given value of little Y the PMF + + align:start position:0% +for any given value of little Y the PMF + + + align:start position:0% +for any given value of little Y the PMF +is going to be equal to the probability + + align:start position:0% +is going to be equal to the probability + + + align:start position:0% +is going to be equal to the probability +that our random variable Y takes on this + + align:start position:0% +that our random variable Y takes on this + + + align:start position:0% +that our random variable Y takes on this +specific value little Y then we recall + + align:start position:0% +specific value little Y then we recall + + + align:start position:0% +specific value little Y then we recall +that Y has been defined in our example + + align:start position:0% +that Y has been defined in our example + + + align:start position:0% +that Y has been defined in our example +to be equal to 2x plus 3 so we're + + align:start position:0% +to be equal to 2x plus 3 so we're + + + align:start position:0% +to be equal to 2x plus 3 so we're +looking at the probability of this event + + align:start position:0% +looking at the probability of this event + + + align:start position:0% +looking at the probability of this event +but this is the same as the event that X + + align:start position:0% +but this is the same as the event that X + + + align:start position:0% +but this is the same as the event that X +takes a value equal to Y minus 3 divided + + align:start position:0% +takes a value equal to Y minus 3 divided + + + align:start position:0% +takes a value equal to Y minus 3 divided +by 2 and in PMF notation we can write it + + align:start position:0% +by 2 and in PMF notation we can write it + + + align:start position:0% +by 2 and in PMF notation we can write it +in this form so what this is saying is + + align:start position:0% +in this form so what this is saying is + + + align:start position:0% +in this form so what this is saying is +that the probability that Y takes on a + + align:start position:0% +that the probability that Y takes on a + + + align:start position:0% +that the probability that Y takes on a +specific value is the same as the + + align:start position:0% +specific value is the same as the + + + align:start position:0% +specific value is the same as the +probability that X takes on some other + + align:start position:0% +probability that X takes on some other + + + align:start position:0% +probability that X takes on some other +specific value and that value here is + + align:start position:0% +specific value and that value here is + + + align:start position:0% +specific value and that value here is +that value of x that would give rise to + + align:start position:0% +that value of x that would give rise to + + + align:start position:0% +that value of x that would give rise to +this particular value little Y now we + + align:start position:0% +this particular value little Y now we + + + align:start position:0% +this particular value little Y now we +can generalize the calculation that we + + align:start position:0% +can generalize the calculation that we + + + align:start position:0% +can generalize the calculation that we +just did and more generally if we have a + + align:start position:0% +just did and more generally if we have a + + + align:start position:0% +just did and more generally if we have a +linear function over discrete random + + align:start position:0% +linear function over discrete random + + + align:start position:0% +linear function over discrete random +variable X the PMF of the random + + align:start position:0% +variable X the PMF of the random + + + align:start position:0% +variable X the PMF of the random +variable Y is given by this formula in + + align:start position:0% +variable Y is given by this formula in + + + align:start position:0% +variable Y is given by this formula in +terms of the PMF of the random variable + + align:start position:0% +terms of the PMF of the random variable + + + align:start position:0% +terms of the PMF of the random variable +X the derivation is the same we use B + + align:start position:0% +X the derivation is the same we use B + + + align:start position:0% +X the derivation is the same we use B +instead of the specific number 3 and we + + align:start position:0% +instead of the specific number 3 and we + + + align:start position:0% +instead of the specific number 3 and we +have a general constant a instead of the + + align:start position:0% +have a general constant a instead of the + + + align:start position:0% +have a general constant a instead of the +two that we had in this example and this + + align:start position:0% +two that we had in this example and this + + + align:start position:0% +two that we had in this example and this +formula describes exactly what we did + + align:start position:0% +formula describes exactly what we did + + + align:start position:0% +formula describes exactly what we did +graphically + + align:start position:0% +graphically + + + align:start position:0% +graphically +in our previous example this factor of a + + align:start position:0% +in our previous example this factor of a + + + align:start position:0% +in our previous example this factor of a +here serves to stretch the PMF by a + + align:start position:0% +here serves to stretch the PMF by a + + + align:start position:0% +here serves to stretch the PMF by a +factor of a and this term B here serves + + align:start position:0% +factor of a and this term B here serves + + + align:start position:0% +factor of a and this term B here serves +to shift the PMF by B \ No newline at end of file diff --git a/OMdGWyruixk.txt b/OMdGWyruixk.txt new file mode 100644 index 0000000000000000000000000000000000000000..0f38f0ccddfba7cb0d39654da4b4ea896debcb84 --- /dev/null +++ b/OMdGWyruixk.txt @@ -0,0 +1,2889 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All right. + +Then let's go back to +our discussion of what + +happens to classical and quantum +mechanical magnetic moments + +when they are exposed +to magnetic fields. + +I just want to remind you +of what we did last class + +and what we want +to wrap up today. + +This is rapid adiabatic passage. + +I mentioned to you and +explained it to you + +that rapid adiabatic +passage is a powerful way + +to manipulate a classical +and quantum system, + +and what we discussed is that +when a spin points in the up + +direction and you +sweep the resonance + +of an oscillating magnetic +field-- the frequency + +of an oscillating magnetic +field, through the resonance, + +you create an effective magnetic +field in the moving frame which + +will rotate. + +And the atom, when the +change is done adiabatically, + +will follow the rotation and +therefore invert the spin. + +So it's a perfect, +very robust method + +to invert population +in spin systems. + +What I want to pick up +today is the question, + +how slow is adiabatic. + +We have to fulfill an +adiabatic condition + +and we have already +an idea already + +of what the adiabatic +condition is + +but now we want to derive it. + +That we had this +picture of a spin + +which is rapidly precessing. + +It always precesses +around the direction + +of the effective magnetic field, +and the condition adiabadicity + +is that the rotation of the +effective magnetic field + +has to be much slower +than the precession. + +Let me just make it clear +by a counter example. + +If the atom precesses +around the magnetic field + +and the magnetic field +would suddenly jump, + +then the atom would +now start precessing + +about the new direction +of the magnetic field + +and it would have +completely changed its angle + +relative to the magnetic field. + +It would have lost its alignment +with the magnetic field. + +So you clearly see +that the condition is + +the direction of the +magnetic field must not jump, + +and the only other time scheme +is the frequency of the Larmor + +precession, so our +condition for adiabadicity + +is the rotation of the +effective magnetic field + +has to be slow compared to +the precession frequency. + +And so we want to now +derive from that condition + +the conditions for adiabadicity. + +And just as an outlook +to make it interesting, + +what I will derive for you +in the classical picture + +is now something +which you will later + +encounter as the +Landau-Zener parameter. + +But Landau-Zener sweeps, we +talk about it later today + +is a quantum mechanical version +of rapid adiabatic passage, + +but we now get +classically a result, + +which will feature the +Landau-Zener parameter. + +So with that, let us write +down what we want to look at. + +It is adiabatic condition, +and to write it down in words + +is that the Larmor +frequency, omega L, which + +is given by the +effective magnetic field, + +has to be much larger +than theta dot. + +Now things in general +are rather complicated. + +If we are far away +from resonance, + +you change the frequency, +but the effective field + +is not changing a lot. + +The critical moment is really +when we have the real field, we + +add the fictitious field +and that cause a rotation. + +The critical moment is +when we are near resonance. + +So in other words, we have +to fulfill an inequality. + +The left side has to be +larger than the right side, + +but the left side +is actually smallest + +in the vicinity +of the resonance, + +and the angle theta +dot is actually + +largest near resonance. + +That's when it sort of +quickly goes to 90 degrees. + +So therefore, if we want to find +the condition of adiabadicity, + +we can derive it by +looking at the region + +around the resonance. + +So the effective magnetic +field is the real field + +minus the fictitious +field caused + +by the rotation by +the transformation + +into the rotating frame. + +So we have the magnetic field +at an angle theta with respect + +to the z-axis. + +I've just written down +the z component for you, + +and the transverse component +is-- so this is this component + +and the transverse component +is the amplitude of our drive + +field B1. + +So we can just read +it form the diagram. + +The resonance data +is 90 degrees, + +and the correction +angle is whatever + +we have of the effective +z field over B1, + +and that means that the +derivative, the angle theta + +dot, the angular velocity +at which the magnetic field + +rotates, there's a time +derivative because we + +sweep the frequency. + +So therefore, theta +dot is nothing else + +than omega dot, the sweep +rate of the frequency divided + +by gamma B1. + +But gamma B1 is nothing else +than the Rabi frequency. + +And on resonance, the Larmor +frequency is just a Rabi + +frequency, because on +resonance-- sorry for repeating + +myself-- the fictitious field +has canceled the bias field, + +and the only field left +is the rotating field, + +but the rotating field +is the Rabi frequency + +with a gamma factor. + +So therefore, we have +the adiabatic condition + +that omega dot +over omega Rabi has + +to be smaller than omega Rabi +or to say it inverts the change + +delta omega of your +drive frequency, + +the change delta omega +in one Ravi period + +has to be smaller than +the Rabi frequency. + +So omega has units of frequency. + +Omega dot is a derivative that's +in units of frequency squared, + +and this is to be smaller than +the Rabi frequency squared. + +You find that actually +quite often if you + +do an adiabatic change +of your trap frequency, + +things are adiabatic as long +as the change of the trap + +frequency in one period +of the trap frequency + +is smaller than +the trap frequency, + +and you find something else +that the derivative of your trap + +frequency has to be smaller +than the trap frequency squared. + +So these are +adiabatic conditions, + +when you tighten up magnetic or +optical confinement for atoms. + +So this is very, very genetic. + +The small rate of the +frequency you change + +has to be smaller than the +relevant frequency squared. + +As I said, we come +back to that when + +we do the quantized treatment +of rapid adiabatic passage + +and we encounter +that combination + +in the Landau-Zener +parameter, which + +takes us to our next topic. + +We want to now talk +about quantized spin + +in a magnetic field. + +And one of the first things +I will be telling you + +is that everything +we have learned + +about the classical magnetic +moment you don't have + +to unlearn or +re-learn, it exactly + +applies to the quantum spin. + +Before we look at +the Hamiltonian + +and the standard Hamiltonian +for two-level system, + +let us first look at +something more general, which + +is Heisenberg +equations of motion. + +So we want to write down +the differential equation, + +the equation of motion +for expectation values. + +So for an atom in +a magnetic field, + +our Hamiltonian is simply +the same Hamiltonian, + +which involves the gyromagnetic +ratio, the angular momentum + +operator, and the +magnetic field. + +And you know from +quantum mechanics + +that Heisenberg's equation +of motion for any operator + +are simply that the time +derivative of the operator + +equals the commutator +with the Hamiltonian. + +In some cases, if you have +an explicit time derivative + +of the operator, +you have to edit, + +but we are talking here +about the angular momentum + +operator which has no +explicit time dependents. + +So we are interested +in the operator which + +describes the magnetic moment, +but the magnetic moment + +is nothing else than +the gyromagnetic ratio + +times the angular momentum. + +So therefore, the +relevant commutator + +is the commutator of the +Hamiltonian with the angular + +momentum operator. + +Just to remind you, +the Hamiltonian + +was proportional to z. + +So what we are talking about is +commutators, not surprisingly, + +between the angular +momentum operators + +and those commutators are +just this cyclic commutation + +involving the epsilon tensor. + +So if you just put that +in component by component, + +you realize immediately that the +operator equation for the time + +derivative of the +magnetic moment + +is nothing else than the cross +product, the vector product, + +of the operator of +the magnetic moment + +times the magnetic field. + +To commence, this is +exact, but also it + +looks exactly like +the classical result. + +Well, you would say it's +an operator equation. + +Usually operator +equation some of them + +are pretty useless because you +can't calculate the operators, + +but in this case, +we can immediately + +take the expectation +value, so we + +can get some immediately +meaningfully equation + +namely that the +expectation value follows + +the same equation, +and this tells us + +that whenever we have +a quantum system, + +it has a magnetic moment. + +In an applied external +magnetic field, + +the result is simply rotation, +precession, and this is exact. + +It's not a classical +approximation. + +It's an exact result +for quantum mechanics. + +So the way how we derived +it makes it obvious that + +it's an exact result, which is +valid not only for spin-1/2, + +but it is valid for any spin. + +If you have a magnetic moment +corresponding to a spin of 10 H + +bar, this spin follows the same +equation of motion as spin-1/2. + +Of course, a special case +is valid for spin-1/2, + +but spin-1/2 is isomorphous +to a two-level system. + +Any two-level system can be +regarded as spin-1/2 system, + +therefore, this geometric +interpretation that + +the dynamics of the quantum +system is just a precession + +rigorously, exactly applies +to any two-level system. + +It's also valid, and this +will be relevant for atoms, + +if we have composite +angular momentum. + +For instance, we will encounter +the total angular momentum + +F of an atom which +has components + +from the orbital +motion of the electron, + +the spin of the electron, +and the spin of the nucleus. + +But if we have such +an angular momentum, + +F, the creation of motion +is it will precess around + +a magnetic field. + +Well the small print here is, +unless the B field is so strong + +that it de-couples +the components + +or that it breaks up the +coupling of the different parts + +of the angular momentum. + +In other words, we have +simply assumed here + +that magnetic moment is +gamma times angular momentum, + +and that requires that +the angular momentum are + +coupled in a certain way. + +If we don't fully +understand what + +coupling of angular +momentum is, we really + +talk about that when we +talk about atomic structure. + +So as long as the spin state +coupled to one total spin, + +this total spin +will just precess. + +This picture of +precession will also + +be valid for a system +of N two-level systems + +coupled to an external +field, and this + +will be the example of +Dicke superrradiance, which + +we will discussed towards +the end of the course. + +So very simple result, +but very powerful, + +and this is your +permission whenever + +you encounter any of +the systems to see + +a vector precessing +in your head. + +This is exact. + +So we've talked about +Heisenberg equation of motion + +for general spin, but-- +you have a question, Nancy? + +AUDIENCE: What did you mean +by N two-level systems here? + +Are we talking about +coherent systems + +or non-coherent systems? + +PROFESSOR: We talk about +in two-level systems + +and to be more specific the +coupling comes because they all + +talk to the same magnetic field. + +So we have in two-level +systems connected + +to the modes of the +electromagnetic field. + +We start with the +symmetric state. + +The coupling is +symmetric and that + +preserves the symmetry +of the atomic state. + +In other words, we will have +a situation where the angular + +momentum is the maximum +angular momentum we + +can get in two-level +system, and the dynamics + +of this two-level system, +the description of Dicke + +superradiance has the +geometric visualization + +of this precessing motion. + +I know I'm not +explaining it exactly. + +I want to sort of whet your +appetite for what comes later + +and also sort of prep you that +some of the simple pictures + +will really carry +through the course. + +OK, so this is for +very general spin. + +Let's now talk about +features of, yes, + +the most important spin for us, +namely the two-level system, + +which is spin-1/2. + +Well, the most generic +system is an electron + +in a magnetic field B times ez. + +And well, why don't we start +with a clicker question. + +So the question is, what +is the level structure + +of the electron in +the magnetic field? + +It's a two-level system, +and you have two options + +A and B. One option is the +upper state is spin up. + +The ground state is spin +down or the opposite. + +So in other words, and +tell me whether an electron + +is in the lower state +when the speed is up + +or when the spin is down. + +You would say it's +a stupid definition, + +but we talk all the +time about an electron + +is in the spin down +state or the spin + +up state, which is the lower +energy state of the electron. + +So I think by exchanging +the better recent number + +of responses has +considerably gone up. + +OK. + +The answer is the electron +is in the ground state. + +Spin down is the lowest +state for the electron. + +To say it in words, of +course, a compass needle + +wants to be aligned +with the magnetic field. + +So you want the magnetic +moment to be aligned + +with the magnetic +field, and that + +means the magnetic +moment has to point + +in the plus e direction, +which up but the electron has + +negative charge, the +gamma factor is negative, + +and that's why for the +electron, the vector of the spin + +and the vector of the +magnetic moment are opposite. + +So just try to find some +main-mode technical thing. + +The electron lives +in the basement. + +It wants to be down, spin down. + +This is the lowest +state for the electron. + +However, if you +have a system which + +has a positive gyromagnetic +ratio, which would correspond + +to, well, positive charge, +nucleus if it has somewhat + +normal magnetic moment, then +in that case, the spin up state + +is less energetic than +the spin down state. + +So let me just write that down. + +So the correct +answer is this one, + +and it involves that +gamma is negative. + +The gamma is a +gyromagnetic ratio, + +the ratio between magnetic +moment and angular momentum, + +and for negative +charges, it's negative. + +For positive gamma, the +situation is inverted. + +So let's just use for +a moment the result + +we got from Heisenberg's +equation of motion. + +We know the classical result. + +We have already derived +for the classic spin, + +the classical result +for the expectation + +value of the magnetic moment. + +But now I want to sort of +relate it to something quantum + +mechanical because we know that +the classical solution equals + +the quantum mechanical solution. + +So if you have a +two-level system, + +the z component of +the magnetic moment + +is the difference between +spin down and spin up. + +And because of conservation +probability, p up and p down + +is unity, we can also +write that as 2 times-- + +let me now introduce +e for excited state, + +just I know it's hard to keep +track of spin up, spin down. + +I want to make sure that I +mean now the excited state, + +so the excited state for +the electron is spin up. + +So we have this condition, so +therefore, the excited state + +fraction of a two-level system +is related to the expectation + +value of the magnetic +moment in that wave, + +and now we want to use the +classical result we derived. + +We derived the +classical result when + +for t equals 0 all the spins +were in the ground state, + +and by using the result +we derived previously, + +we have the 1/2 from +the previous line + +and then the magnetic +moment, mu z. + +We found an expression which +involved the Rabi frequency, + +and the off resonant +Rabi frequency + +are sine square generalized Rabi +frequency times time over 2. + +So the two factors +of 1/2 and 1/2 + +cancel, and what we find now for +the quantum mechanical system + +using Heisenberg's +equation of motion + +is that if you prepare +a system initially + +in the ground state, +the excited state + +probability, the fraction, +the excited state oscillates + +with a Rabi frequency, +and this is, + +I think, the second time in this +course and not the last time + +that we see the +Rabi, that we obtain, + +the Rabi transition probability. + +But let's go further. + +We have now discussed +the classical spin. + +We have sort of done classical +quantum correspondence + +with Heisenberg's +equation of motion. + +We know that this in general, +it implies Rabi oscillations, + +but now we want to go deeper +into the quantum domain + +by talking about the +spin-1/2 Hamiltonian. + +So in other words, we want to +go beyond expectation values. + +We want to talk about +the wave function itself. + +So the Hamiltonian, +which we will + +use for major parts +in this course, + +it's one of the fundamental +Hamiltonians in physics. + +Of course, there's the +harmonic oscillator. + +There is a hydrogen +atom, but then there's + +this Hamiltonian, which is a +two-level system with splitting + +omega naught. + +And then we make, which +is often a simplification, + +where we use a pure exponential, +so a single frequency + +in complex notation where +the complex exponential e + +to the i omega t +is the drive term. + +So this is one of the +simplest Hamiltonian + +for this kind of system. + +It's a two-level system with a +splitting, and now it is driven + +and the simplest drive term +is not cosine omega t or sine + +omega t as we will see. + +The simplest drive term +is e to the i omega t. + +So this is now our Hamiltonian. + +and since it is +so important, let + +me ask you a clicker question +whether this Hamiltonian can + +be exactly realized in nature +or it is an approximation. + +For instance, that you always +have cosine omega t as a drive, + +and cosine omega t is +e to the plus i omega t + +and e to the minus i omega t. + +And then maybe with the +rotating wave approximation, + +you throw away a term. + +So I sort of wanted +to ask you, is this + +an idealization that we +have a coupling which + +is a simple, complex +exponential, this nature always + +more complicated or +is there a simple way + +to realize this +Hamiltonian in nature? + +So what do you think? + +Stop display. + +What's funny about that? + +AUDIENCE: Equal to. + +AUDIENCE: There are +two [INAUDIBLE]. + +PROFESSOR: Oh, they +couldn't make up their mind. + +The system should +reject those votes. + +Anyway, it means most of +you anticipate what I want + +to derive to you that we can +actually exactly get this + +Hamiltonian and indeed, this is +the Hamiltonian I will derive + +for you in the next few minutes, +which is the Hamiltonian + +of spin-1/2 in a magnetic field +coupled to a rotating magnetic + +field. + +So we start out +with fields which + +are real, real field, +no imaginary numbers, + +no complex numbers. + +These are real fields, but +when we write down how the real + +fields couple to spin-1/2, we +get e to the i omega t and e + +to the minus omega t +without any approximation. + +So since at least 80% +of you know the result, + +just regard it as an exercise to +introduce how we spin matrices + +in a nice way, also +this will help you + +how to do pre-set number 1. + +So the Hamiltonian is the spin +coupled to a magnetic field, + +and if we express that by +angular momentum operators, + +the gyromagnetic ratio +it involves the operator + +for the spin in the z direction. + +So the two-level system has +a splitting of H bar omega, + +so it's plus 1/2 +minus 1/2 H bar omega, + +and that means +the diagonal part, + +the non-driven part is simply +given by the Pauli spin matrix + +sigma z and omega naught +is the energy splitting, + +which is proportional to +the applied magnetic field. + +And up-down, and +excited and ground + +are the eigenstates of this +Hamiltonian with energies + +plus minus H bar +omega naught over 2. + +So this is the same Hamiltonian, +but now add a real rotating B + +field B1. + +So the drive Hamiltonian H1 +is the same magnetic moment + +but now coupled to a +time-dependent rotating field. + +The amplitude of +the rotating field + +is the Rabi frequency +divided by gamma, + +and we assume that the field +is rotating in the xy plane. + +So it's ex ey cosine +omega t sine omega t. + +And now I put in two minus +signs here for convenience. + +If you want, I've just shifted-- +it's just a definition. + +I've changed the definition of +the amplitude by a minus sign. + +So this is the Rabi frequency, +and the magnetic moment + +divided by gamma is +nothing than the spin. + +Magnetic moment is +gamma times the spin, + +so therefore, we are back +to the spin operators + +and the spin operators, +if I factor out 1/2 H bar, + +are now the Pauli spin +matrices sigma x and sigma y. + +And if you look at +those spin matrices, + +then you'll realize that we +go complex in our Hamiltonian, + +not because we have approximated +a real field cosine omega + +t by some e to the i +omega t, but because when + +we have a rotating field and +we write down it in Pauli spin + +matrices, we get imaginary units +form the sigma y spin matrix. + +So that means we have +now for this system + +rewritten the coupling term took +you to the rotating field H1 + +as 0 0 e to the plus i omega +t e to the minus i omega t. + +And therefore, +the Hamiltonian is + +the famous two-level +Hamiltonian with omega naught + +and the Rabi frequency, +which I wrote down + +at the beginning +of this chapter. + +So we'll leave that here, but we +will use it even more in 8.421. + +This is the famous +dressed atom Hamiltonian. + +It is the starting point +to calculate eigenstates + +and eigenvalues, not just +in perturbation theory. + +You can go to oscillating +fields at arbitrary strengths, + +so you can solve exactly in +the dressed atom picture using + +this Hamiltonian, the +problem of a two-level system + +plus one mode of the +electromagnetic field + +no matter what the +drive term, what + +the strengths of the +electromagnetic field + +in the spin mode is. + +So this describes +the two-level system + +plus one mode of the +electromagnetic field + +with arbitrary strengths. + +And as I said, we talk +about some things here + +but others I explored in 8.422. + +Questions? + +Yes, Will. + +AUDIENCE: We refer to the +eigenstates and eigenenergies + +of this Hamiltonian as dressed +in states in the same way + +as we refer to address states +in a fully quantized fiction? + +Do we refer to both +cases as dressed states? + +PROFESSOR: Yes. + +That's a good question. + +The question is now, what are +the dressed states, and Will, + +I think you are +referring that there + +are two ways to talk about the +coupling of a two-level system + +to one mode of the +electromagnetic field. + +It is this same +classical picture + +where we introduce and let +me say an analog amplitude + +of the electromagnetic +field which drives it. + +And then there is a +fully quantized picture + +where you first quantize +electromagnetic field + +and you couple to +photon number states. + +Actually the beauty of +it that the two solutions + +are exactly the same. + +So in other words, how to +say, if you couple an atom + +to one mode of the +electromagnetic field. + +We have two ways +how we can solve it. + +One is, we introduce a +coherent electromagnetic field, + +and there is an exact unitary +transformation which tells us + +if we have the quantized +field in a coherent state, + +we can do unitary +transformation, + +and what we get is +exactly this Hamiltonian. + +So therefore, this is also-- +you may not recognize it-- + +this is actually the +quantum description + +of the electromagnetic field +when it is in a coherent state. + +The other option is, we use +the dressed atom picture maybe + +following some work of +[INAUDIBLE] and others + +where we assume this single +mode of electromagnetic field + +has in photons, and +then we solve it + +for this photon number state. + +So in other words, +these are the two ways + +how we can relatively, +easily treat the problem. + +Either we assume the quantum +field is in a coherence state + +or it's in a flux state. + +But since the dressed atom +picture in the standard way + +assumes that the photon +number, N, is large, + +there is a correspondence +that in the limit of N of N + +being large, the flux +state description + +and the coherent state +description fully agree. + +And you pick what you want. + +If you introduce the +electromagnetic field + +explicitly with +it's quantum state, + +you get the dressed atom +picture as a solution of a time + +independent problem, whereas +here with a coherent state + +description, the coherent state +oscillates, cosine omega t, + +with a time-dependent problem. + +And actually I +should say whenever + +I get confused in one picture, +I look in the other picture + +and it becomes clear. + +I generally prefer +where we have N photons, + +it's because we can +discuss everything + +in a time-independent way, but +for certain intuitive aspects, + +this is also variable, so in +the end, you have to learn both. + +And in your homework, +you will actually + +write down the general +solution for this Hamiltonian + +as an exercise. + +Nancy. + +AUDIENCE: I think I'm +confused a little bit. + +So in the flux state +picture, the dressed states + +can be exactly part of an +independent matter of coupling + +between a lesser photon +on any excited state. + +So like we can write eN as 1 +and g or something like that. + +PROFESSOR: Yeah. + +You couple a photon field +with N photons and energy + +in H bar omega to N +minus 1 H bar omega. + +AUDIENCE: But in this one, +is there like a direct photon + +number thing, because we +haven't quantized the field yet? + +So what do the dressed +states mean at this point? + +PROFESSOR: Well, the fact +is that if you start out + +with a coherent state, your +photon field is not in photons, + +it's a laser beam. + +The laser beam or +the coherent state + +is in a quantized description, +a superposition of many flux + +states. + +So therefore, the number of +photons in a coherent state + +fluctuates or has a large +Plutonian statistics, + +and if you take one +photon out or not, + +it doesn't make +a big difference. + +For instance, for +those of you who + +know how the coherent +state is state defined, + +the coherent state +is defined as when + +you act on the coherent state +with an annihilation operator, + +you get the eigenvalue +times the coherent state. + +So that tells you you have a +fully-quantized description + +of your laser in terms +of a coherent state. + +You take one photon +out and what you get? + +the same state back. + +And this may immediately justify +that what we write down here + +is simply the coherent +state with its amplitude + +and the amplitude of +the coherent state + +would be B1, the amplitude +of the drive field. + +And we don't really +need other states + +because a coherent +state has the property. + +You to take a photon out and +you still have the same state. + +So therefore, we +don't have to keep + +track of the coherent state. + +It's there all the time. + +But what I'm saying +can be formulated + +more exactly when we use +the appropriate formulas. + +But this is sort of the bridge. + +That's why we do not have to +keep track of the photon state. + +It's because the coherent state +has those wonderful properties. + +Other questions? + +OK. + +So this is the +famous Hamiltonian. + +And of course, if it's +the famous Hamiltonian, + +we want to solve it. + +As I said, the general solution +is left to the homework, + +but I want to sort +of show you parts + +of the solution to tell a story. + +And the question is, well, how +do we solve this Hamiltonian? + +The answer is, we +do exactly what we + +did in the classical problem. + +We transform to +the rotating frame. + +In other words, this +Hamiltonian is best + +solved by doing-- you can +actually solve it directly. + +You can just put in a tri +wave function and solve it. + +But I want to sort of +bring out the big idea here + +which is analogous +to what we have done + +in the last few +classes, namely we + +have involved rotating frames. + +So what solves this Hamiltonian +is a unitary transformation, + +and the unitary +transformation is this one. + +And so this unitary +transformation, + +let me first write it down, +it transforms the Hamiltonian + +to the time independent one. + +We have now time independent +of diagonal matrix elements. + +Our diagonal matrix +element have changed. + +Delta is now the detuning of the +tri frequency from the energy + +splitting of the +two-level system. + +In particular, when +we are on resonance, + +the diagonal matrix +elements have disappeared. + +This is the result of the +unitary transformation, + +and let me just show you this +transformation over here. + +Can be actually written +as an operator involving + +the z component of +the magnetic field. + +And what I just wrote +down for you is actually + +the quantum mechanical +operator, the rotation + +operator for performing at +rotation around the z-axis. + +So by selecting the rotation +angle to be omega t, + +that's how I can generate +the unitary transformation, + +and this unitary transformation +makes the Hamiltonian time + +independent. + +So in other words, everything +is in the classical system. + +We just go to a frame which +rotates with a [INAUDIBLE], + +and we find the +time-independent problem. + +So now this Hamiltonian +can be easily solved. + +And you will find +as a special case + +when you start +with an amplitude, + +initially you start +in the ground state, + +then the excited +state amplitude square + +is the Rabi +oscillation, something + +we discussed 40 minutes +ago, but before, we + +got it from the +classical quantum + +mechanical correspondence +using the Heisenberg equation + +of motion and here it comes +out by explicitly solving + +for the wave function for +the dressed Hamiltonian. + +Questions? + +I want to say a few words now +about rapid adiabatic passage, + +but this time by emphasizing +the quantum mechanical aspects. + +In other words, we have +a clear understanding + +what happens classically. + +We have a clear +understanding what + +happens in the adiabatic +limit, but I just + +want to sort of in +the next 10 minutes + +use what we have +already learned, + +combine it with the quantum +mechanical Hamiltonian + +and tell you that, well, when +you are not fully adiabatic, + +you actually have transition +probabilities between the two + +states. + +So I want to sort of bring +in the concept of transition + +probabilities to +the case of-- what + +I want to say is rapid +adiabatic passage when it's + +no longer adiabatic, but what +this just means when we sweep + +the frequency and we're +not in the adiabatic limit. + +So how do we describe +it quantum mechanically? + +We start out with a Hamiltonian, +which has-- we use our rotating + +framework for convenience +that allows to write down + +exactly the same Hamiltonian +in time-independent picture. + +So the Hamiltonian has +two parts, a diagonal part + +and an off-diagonal part. + +So if I show the energy as a +function of detuning delta-- + +well, maybe I should +times 2 over H bar, + +just normalize it so then it +becomes just the straight line + +at 45 degree y equals x. + +So the unperturbed-- the +Hamiltonian without drive + +has a level crossing +at detuning 0. + +Then we add to it +the drive term. + +Well, let me just +write down, not + +the drive term but +the full Hamiltonian. + +So the full Hamiltonian with +the addition of the drive term + +has delta minus +delta and now it has + +the coupling with +the Rabi frequency. + +That means that on resonance, +the degeneracy between the two + +levels is split by +the Rabi frequency, + +and if I now show +you the energy eigen + +levels of this +two-by-two Hamiltonian, + +it will asymptotically +coincide with a dashed line + +through this and through that. + +So in other words, +I'm just reminding you + +that a non-diagonal matrix +element turns a crossing + +into an avoided crossing. + +So when we take +the frequency omega + +and we sweep the detuning, +so we change delta + +and do a sweep of the frequency +omega at a rate omega dot, + +then we sweep through the +resonance and in one limit, + +we have rapid adiabatic +passage or in general, we + +realize the Landau-Zener +problem of a sweep + +through an avoided crossing. + +So what I'm formulating +here is it's + +the so-called +Landau-Zener crossing + +or the Landau-Zener +problem, which + +is the quantum mechanical +description of you take + +a system by changing +an external parameter. + +Here, we sweep the frequency +of the rotating field, + +but by changing the +external parameter, + +we sweep the system through +the avoided crossing. + +And it has the +two limiting cases + +that when we go through this +crossing very, very slowly, + +the adiabatic field +then tells us we + +stay on one of these +adiabatic solid curves, + +and this is the case of rapid +adiabatic passage, which + +we discuss in the +classical limit. + +But it is also +the other solution + +if you would sweep through +it very, very fast, + +you're in the diabatic limit, +you follow the dashed line + +and you start up here +and you wind up there. + +The Landau-Zener +problem is actually + +a problem which you find +it in all it text books, + +but to the best of +my knowledge, there + +is no simple, +elementary derivation + +which I could give +you in a few minutes. + +And if the +mathematical problem is + +a nice, mathematical +demonstration + +of an exact, solvable model, +but to my knowledge explicitly + +deriving it is not providing +additional insight. + +It's one of the cases +where the result is + +more insightful and much +simpler than the derivation. + +So what I want to give +you is, therefore, + +simply the textbook result. + +So in the adiabatic limit, +you stay on the solid line. + +If you do not cross the avoided +crossing very, very slowly, + +you'll have a +non-adiabatic probability + +to jump from one level +to the other one. + +And this non-adiabatic +probability + +is expressed as an +exponential function which + +involves the +Landau-Zener parameter. + +And the Landau-Zener parameter +in this exact solution + +is omega Rabi squared times +this new rate, d omega + +dt or d delta dt minus 1. + +This square should go +outside the brackets, + +so therefore, what we find +is from the exact solution + +that the Landau-Zener +parameter is a quarter times-- + +and this should +now look familiar, + +the omega Ravi frequencies +squared over omega dot. + +And when we discussed the limit +of adiabaticity classically, + +I hope you remember I gave +you the argument by looking + +at the adiabatic condition that +the adiabatic case requires + +omega dot to be much smaller +than omega Rabi squared. + +So here very naturally +what appears in the quantum + +mechanical problem is just the +ratio of the two quantities + +we compared when we looked +for the limit of adiabaticity. + +So therefore, the probability +for a non-adiabatic transition + +is simply involving this +ratio omega Rabi squared + +over omega dot. + +So in other words, +we know already + +from the classical +argument, but here we + +confirm it, adiabaticity require +that this inequality is met. + +OK, I could stop +here, but since we + +are using sort of diabatic +sweeps in the laboratory, + +as long as I've been involved +in doing quote "atom science," + +I want to sort of go one +step further and teach you + +a little bit more +about this formula + +and try to provide +insight, and often + +insight is also provided when +you apply perturbation theory. + +So I know the adiabatic +case is very simple, + +but I want to look +at the diabatic case + +and then look at +transition probabilities + +in a perturbative way. + +This is actually the way how +we often transfer population + +in the laboratory. + +So I want to understand +better the way how we transfer + +population from one +curve to the other one. + +So if we do a fast sweep, +we call it diabatic. + +So in other words, if +we have this crossing + +and we go really fast, +well, what happens + +is this is the crossing +between spin up and spin down. + +If you go much, much faster +than the Rabi frequency, + +the spin has no opportunity +to change its orientation. + +So therefore, the wave function, +the spin has to stay up or down + +and that means the +system just goes straight + +through the crossing. + +Because spin up has +positive slopes, + +spin down has negative slope. + +Being adiabatic, staying on +this lower adiabatic curve + +would actually +require the system + +to go from spin up in this +part of the adiabatic curve + +to spin down in the other part. + +And to flip a spin cannot +be done faster than the Rabi + +frequency, so if you sweep +fast, that's what's happening. + +So we have two trivial limits, +one is the adiabatic limit + +or just the adiabatic +curve and nothing happens. + +The other limit is the +infinitely-fast limit + +and nothing happens +again when we + +look at the diabatic basis, +which is spin up and spin down. + +But now let's be +almost adiabatic, + +and this is a problem +which we really + +want to understand physically +and intuitively because that + +means the system spins the +small timelier resonance, + +and there is a small probability +to make a transition. + +So if you had one of +your hyperfine states, + +pick your favorite +hyperfine state, + +you'll rapidly +sweep the frequency. + +You will find, unless you +sweep it infinitely fast + +that there's a small probability +in the other hyperfine state. + +And that's what you +want to calculate now, + +and I want you to +understand how would you + +estimate and calculate +the small probability. + +So let's now estimate +the result, namely + +for the small probability +in perturbation theory. + +And actually what I'm +calculating for you here is, + +if you've used evaporation-- +I know half of the class + +is doing that-- if you +apply an i F field, + +you don't have to +make it so strong + +that you and the +adiabatic limit. + +You are exactly in this limit. + +The atom will +slosh several times + +through the resonance in +an almost diabatic way, + +but there is a finite +spin flip probability + +and that's how you +evaporate atoms. + +And I want you now +to fully understand + +the derivation, what is the +probability of ejecting atoms + +in the almost diabatic +limit with i F spin flips. + +That's a limit where 90% of +the BEC experiments operate. + +So I hope everyone realize +it's an important question + +and also I hope +everybody understands + +the question because now I +have bigger questions for you. + +The first question +which I will ask you, + +should we calculate that +transition probability + +by using perturbation theory +for an incoherent transition + +or for coherent transition? + +Let me just explain you +what I mean and then I + +ask you for your opinion. + +Coherently, we simply say +in perturbation theory, + +we start with our +population in state 1. + +We have to do the +coupling Hamiltonian time + +dependence of the +population in state 2 + +and that means if we integrate +this equation for a short time, + +we find an amplitude a2. + +And the probability +to be in the state + +2, which is the +amplitude squared, + +is proportional to the +Rabi frequency squared + +times the effective +time squared, + +the effective time of +tribing the system. + +Coherent processes are +always quadratic in time. + +If we do it incoherently, +well, the way + +how we describe +incoherent processes + +are Fermi's golden rule, +which we've all seen. + +And the probability in Fermi's +golden rule is very different. + +Well, it is proportional to +the Rabi frequency squared, + +to the matrix element squared, +but Fermi's golden rule + +gives us a constant rate, +and for constant rate, + +the probability is +rate times time. + +So now it is linear +in time and then + +because of the delta function +in Fermi's golden rule-- + +I'm missing a symbol +so I use gamma here. + +It has nothing to do with +the Landau-Zener probability. + +This is just the +density of states. + +So I hope you know now +what is the difference + +between coherent or incoherent. + +The most important +part is that things + +are linear in time for an +incoherent pulses rate equation + +and at least for small +times quadratic in time + +for coherent pulses. + +So now we come to +this process where + +we take atoms from +spin up to spin down. + +We evaporate with a weak, +course, almost adiabatic + +with weaker f drive, so we are +closer to the diabatic limit. + +And so if you think +about this problem, + +I want you to tell +me if this process, + +the perturbative transition +close to the diabatic case + +is that should we use +when we apply perturbation + +theory, the coherent picture +or the incoherent picture. + +In other words, is the dynamics +of the quantum system, when + +we go relatively quickly for +the Landau-Zener crossing, + +is that a coherent or +an incoherent process? + +I could see where it doesn't +matter, but it does matter. + +So I think it's +an open question. + +Let me give you the answer. + +It is coherent, and you can +see it in the following way. + +What is the source +of incoherent here? + +We have a Hamiltonian. + +The Hilbert space +is by two-by-two. + +There is no coherence +which can be lost. + +There is no spontaneous +emission to other states. + +There is no reservoir. + +We don't have a small system +which couples to a bigger + +system, and then +the small system-- + +we do that on Wednesday-- +has to-- tomorrow, + +Wednesday-- has to be +described by density matrix. + +We have the none of +the physics which + +would give arise to +incoherent physics. + +It is coherent. + +But maybe I'm oversimplifying. + +Is somebody who +said it's incoherent + +who wants to maybe press +me harder and tell me + +why you think it is incoherent. + +Well, one possibility +is-- and this + +is why we often use +Landau-Zener sweeps in the lab. + +We have fluctuations of +the resonance frequency. + +And when we go and +sweep through it, + +we don't know exactly +when we hit the resonance. + +And if you would take +an ensemble of systems + +and you go through the +resonance at different times, + +you will get an ensemble +of wave functions, which + +has different phase factors +in it, and in the end, + +you will actually need a +density matrix to describe it. + +But this is now an +experimental imperfection + +which I haven't assumed here. + +So in other words, what you +should do is the following. + +Whenever you sweep through +Landau-Zener crossing, + +you start with the ground +state and what you get out + +is a superposition of +ground and excited state. + +And the Hamiltonian determines +absolutely every aspect + +of the amplitude in the ground +and the excited state including + +all phase factors. + +In other words, if you do a +Landau-Zener crossing in a way + +that you prepare +50-50% of the atoms, + +they are always face coherent +and you can use this process + +as a beam splitter in +an atomic thermometer. + +Fully coherent. + +We have five minutes, +so if we assume now, + +I hope we all agree that +the amplitude is obtained + +in this coherent wave, then, +of course, the question is, + +but what is the effective time? + +When we sweep the +resonance, we are far away. + +Nothing happens. + +Nothing happens. + +Nothing happens. + +We go through the resonance, +everything happens. + +Nothing happens. + +Nothing happens. + +Nothing happens. + +So this is the effective time +when the wave function really + +changes and we create +the coherent and mixture + +in the second state. + +And it is this +effective times squared + +which determines what +happens, what our transmission + +amplitude is. + +So therefore, the +question is, what + +is the effective time in +the Landau-Zener crossing? + +I can give you three choices. + +One is, the effective time +is, well, we change omega + +and the effective time +is, how long, what + +is the time until we +have a detuning, which + +is equal to the Rabi frequency. + +Another possibility is that +the effective time where + +we coherently +drive the system is + +1 over the Rabi frequency, +just the Rabi period. + +Or another choice, how +I can construct time out + +of the two frequencies where +it's omega Rabi and omega dot. + +These are our two elements. + +So another possibility +how I can get time + +is, omega dot is +frequency squared, + +and the square root of 1 +over omega dot at least + +fulfills the dimensional +criterion that this is time. + +So my question for you +is, what do you think + +is the effective +time during which + +we drive the system coherently? + +I have to tell you before +I made up the problem, + +I do not know the answer. + +But I can also +tell you that there + +is only one answer +which is correct. + +All right. + +I have to say I expected A +to be the correct answer, + +but I convinced +myself it's only B. + +And the answer is the following, +and I know I have to stop, + +but I only need +three more lines. + +The effective time is not the +time until you are detuned, + +the effective time is which +I can call the dephasing + +time, the time during which +everything is coherent. + +What happens is, we change +the frequency delta omega, + +and the delta omega +is, of course, + +omega dot times delta t. + +So if we change the frequency +by sweeping it in such a way + +that we are detuning and +now with that detuning, + +if we let the system evolve, we +would get a phase shift of pi. + +That's sort of the maximum where +everything adds up coherently. + +If we would go longer +in time, the frequency + +has changed to the +point that what + +we add to the amplitude +of the other state + +is no longer in phase to +what we have added before. + +You can sort of look +at it like this. + +You have a little bit of +phase a2, You build up. + +You build up. + +You build up by adding +amplitude with the same phase. + +But now you are +sweeping, and this + +is the criterion where +you start to pile up + +things with the +wrong phase and then + +the phase eventually +becomes randomized + +and you're not +effectively contributing. + +This equation defines +the window delta + +t during which we effectively +add substantial amplitude + +in the second state, and it +involves delta t squared, + +so neglecting factors of +unity, the result of this + +is that, indeed, delta t +is 1 over omega dot plus. + +And indeed, if we say the +probability for coherent drive + +is Rabi frequency squared times +delta t squared, what we now + +obtain is the Rabi frequency +squared over omega dot, + +and this is our +Landau-Zener parameter. + +So in other words, if we +check with the exact result, + +the Landau-Zener probability, +1 minus p non-adiabatic-- + +the Landau-Zener problem +is e to the minus 2 pi + +over gamma or gamma pi over +2 over the Landau-Zener + +parameter, if I do an expansion +of the Landau-Zener parameter + +for a small value +of the exponent, + +the exact result is +2 pi times gamma, + +and this is indeed proportional +to omega Rabi squared + +over omega dot. + +So in other words, +what I've shown + +you is that coherent +time evolution + +with this weird effective time, +what I motivated physically, + +exactly that produce +the limit of small gamma + +from the exact result for +the Landau-Zener crossing. + +OK. + +I know time is over. + +Any questions? + +OK. + +So today was officially +our Monday class, + +so we meet again tomorrow, +the same place, the same time. \ No newline at end of file diff --git a/OOrT17RsVxE.txt b/OOrT17RsVxE.txt new file mode 100644 index 0000000000000000000000000000000000000000..b5885809227d74d26f710abda205c0d3fb3455b1 --- /dev/null +++ b/OOrT17RsVxE.txt @@ -0,0 +1,16699 @@ +align:start position:0% + +talk some about noise gain + + align:start position:0% +talk some about noise gain + + + align:start position:0% +talk some about noise gain +and + + align:start position:0% + + + + align:start position:0% + +in the 1d case + + align:start position:0% + + + + align:start position:0% + +where we have one unknown and one + + align:start position:0% +where we have one unknown and one + + + align:start position:0% +where we have one unknown and one +measurement it was pretty simple because + + align:start position:0% +measurement it was pretty simple because + + + align:start position:0% +measurement it was pretty simple because +we just looked at + + align:start position:0% + + + + align:start position:0% + +the inverse of the slope so we looked at + + align:start position:0% + + + + align:start position:0% + +so we had some small increment here and + + align:start position:0% +so we had some small increment here and + + + align:start position:0% +so we had some small increment here and +the relationship with the small + + align:start position:0% +the relationship with the small + + + align:start position:0% +the relationship with the small +increment over here so x + + align:start position:0% +increment over here so x + + + align:start position:0% +increment over here so x +in this case is the unknown quantity and + + align:start position:0% +in this case is the unknown quantity and + + + align:start position:0% +in this case is the unknown quantity and +y is the measurement we're making and + + align:start position:0% +y is the measurement we're making and + + + align:start position:0% +y is the measurement we're making and +we're trying to estimate x and obviously + + align:start position:0% +we're trying to estimate x and obviously + + + align:start position:0% +we're trying to estimate x and obviously +if this curve is very uh low slope + + align:start position:0% +if this curve is very uh low slope + + + align:start position:0% +if this curve is very uh low slope +then a small error here can + + align:start position:0% +then a small error here can + + + align:start position:0% +then a small error here can +be amplified into a large area there so + + align:start position:0% +be amplified into a large area there so + + + align:start position:0% +be amplified into a large area there so +that's very + + align:start position:0% +that's very + + + align:start position:0% +that's very +simple in the 1d case but of course + + align:start position:0% +simple in the 1d case but of course + + + align:start position:0% +simple in the 1d case but of course +we'll be looking + + align:start position:0% +we'll be looking + + + align:start position:0% +we'll be looking +at more complicated cases where we're + + align:start position:0% +at more complicated cases where we're + + + align:start position:0% +at more complicated cases where we're +trying to estimate uh three-dimensional + + align:start position:0% +trying to estimate uh three-dimensional + + + align:start position:0% +trying to estimate uh three-dimensional +quantities and so + + align:start position:0% +quantities and so + + + align:start position:0% +quantities and so +i want to take a little detour now and + + align:start position:0% +i want to take a little detour now and + + + align:start position:0% +i want to take a little detour now and +talk about at least the the 2d case + + align:start position:0% +talk about at least the the 2d case + + + align:start position:0% +talk about at least the the 2d case +which comes up + + align:start position:0% +which comes up + + + align:start position:0% +which comes up +in the optical mouse and + + align:start position:0% +in the optical mouse and + + + align:start position:0% +in the optical mouse and +some other things that we'll be talking + + align:start position:0% +some other things that we'll be talking + + + align:start position:0% +some other things that we'll be talking +about pretty soon + + align:start position:0% +about pretty soon + + + align:start position:0% +about pretty soon +so we're going to talk a little bit + + align:start position:0% +so we're going to talk a little bit + + + align:start position:0% +so we're going to talk a little bit +about + + align:start position:0% + + + + align:start position:0% + +um eigenvectors and eigenvalues and if + + align:start position:0% +um eigenvectors and eigenvalues and if + + + align:start position:0% +um eigenvectors and eigenvalues and if +you are familiar with them then + + align:start position:0% +you are familiar with them then + + + align:start position:0% +you are familiar with them then +just go to sleep for the next 10 minutes + + align:start position:0% +just go to sleep for the next 10 minutes + + + align:start position:0% +just go to sleep for the next 10 minutes +but i think it's important to get + + align:start position:0% +but i think it's important to get + + + align:start position:0% +but i think it's important to get +everyone up to speed on this so so what + + align:start position:0% +everyone up to speed on this so so what + + + align:start position:0% +everyone up to speed on this so so what +are these well if we take a matrix m + + align:start position:0% +are these well if we take a matrix m + + + align:start position:0% +are these well if we take a matrix m +and we multiply + + align:start position:0% +and we multiply + + + align:start position:0% +and we multiply +some vector + + align:start position:0% +some vector + + + align:start position:0% +some vector +we're going to get a new vector which is + + align:start position:0% +we're going to get a new vector which is + + + align:start position:0% +we're going to get a new vector which is +a different size typically and pointing + + align:start position:0% +a different size typically and pointing + + + align:start position:0% +a different size typically and pointing +in a different direction + + align:start position:0% +in a different direction + + + align:start position:0% +in a different direction +and so + + align:start position:0% +and so + + + align:start position:0% +and so +the interesting question is + + align:start position:0% +the interesting question is + + + align:start position:0% +the interesting question is +do we ever have a situation where + + align:start position:0% +do we ever have a situation where + + + align:start position:0% +do we ever have a situation where +the vector we get is pointing in the + + align:start position:0% +the vector we get is pointing in the + + + align:start position:0% +the vector we get is pointing in the +same direction as the vector that we + + align:start position:0% +same direction as the vector that we + + + align:start position:0% +same direction as the vector that we +multiply the matrix with + + align:start position:0% +multiply the matrix with + + + align:start position:0% +multiply the matrix with +and so + + align:start position:0% +and so + + + align:start position:0% +and so +those are considered special and in some + + align:start position:0% +those are considered special and in some + + + align:start position:0% +those are considered special and in some +sense they're characteristic of that + + align:start position:0% +sense they're characteristic of that + + + align:start position:0% +sense they're characteristic of that +matrix and so sometimes they're called + + align:start position:0% +matrix and so sometimes they're called + + + align:start position:0% +matrix and so sometimes they're called +characteristic vectors with + + align:start position:0% +characteristic vectors with + + + align:start position:0% +characteristic vectors with +characteristic values + + align:start position:0% +characteristic values + + + align:start position:0% +characteristic values +and i guess eigen is the german word for + + align:start position:0% +and i guess eigen is the german word for + + + align:start position:0% +and i guess eigen is the german word for +for own + + align:start position:0% +for own + + + align:start position:0% +for own +it's the vectors and values that the + + align:start position:0% +it's the vectors and values that the + + + align:start position:0% +it's the vectors and values that the +matrix owns and so we're looking at a + + align:start position:0% +matrix owns and so we're looking at a + + + align:start position:0% +matrix owns and so we're looking at a +situation where + + align:start position:0% + + + + align:start position:0% + +the vector we get is parallel to the + + align:start position:0% +the vector we get is parallel to the + + + align:start position:0% +the vector we get is parallel to the +vector that we pump into the matrix + + align:start position:0% +vector that we pump into the matrix + + + align:start position:0% +vector that we pump into the matrix +and it may be a different size + + align:start position:0% +and it may be a different size + + + align:start position:0% +and it may be a different size +so + + align:start position:0% +so + + + align:start position:0% +so +that's the definition and we're mostly + + align:start position:0% +that's the definition and we're mostly + + + align:start position:0% +that's the definition and we're mostly +going to focus on real symmetric + + align:start position:0% +going to focus on real symmetric + + + align:start position:0% +going to focus on real symmetric +matrices we can generalize this but for + + align:start position:0% +matrices we can generalize this but for + + + align:start position:0% +matrices we can generalize this but for +the moment that's all we need + + align:start position:0% +the moment that's all we need + + + align:start position:0% +the moment that's all we need +and so obviously this isn't going to be + + align:start position:0% +and so obviously this isn't going to be + + + align:start position:0% +and so obviously this isn't going to be +true for typical vectors also notice + + align:start position:0% +true for typical vectors also notice + + + align:start position:0% +true for typical vectors also notice +that the the scale doesn't matter + + align:start position:0% +that the the scale doesn't matter + + + align:start position:0% +that the the scale doesn't matter +because + + align:start position:0% +because + + + align:start position:0% +because +if e is an eigenvector and i multiply it + + align:start position:0% +if e is an eigenvector and i multiply it + + + align:start position:0% +if e is an eigenvector and i multiply it +by k + + align:start position:0% +by k + + + align:start position:0% +by k +this equation still holds it's still an + + align:start position:0% +this equation still holds it's still an + + + align:start position:0% +this equation still holds it's still an +eigenvector so for many purposes we'll + + align:start position:0% +eigenvector so for many purposes we'll + + + align:start position:0% +eigenvector so for many purposes we'll +either + + align:start position:0% +either + + + align:start position:0% +either +just ignore the magnitude or make it a + + align:start position:0% +just ignore the magnitude or make it a + + + align:start position:0% +just ignore the magnitude or make it a +unit vector for simplicity + + align:start position:0% +unit vector for simplicity + + + align:start position:0% +unit vector for simplicity +so the size doesn't matter and by the + + align:start position:0% +so the size doesn't matter and by the + + + align:start position:0% +so the size doesn't matter and by the +way that includes multiplication by + + align:start position:0% +way that includes multiplication by + + + align:start position:0% +way that includes multiplication by +minus 1. + + align:start position:0% +minus 1. + + + align:start position:0% +minus 1. +so if b is an eigenvector then minus v + + align:start position:0% +so if b is an eigenvector then minus v + + + align:start position:0% +so if b is an eigenvector then minus v +is also an eigenvector + + align:start position:0% +is also an eigenvector + + + align:start position:0% +is also an eigenvector +okay so then the question is how do we + + align:start position:0% +okay so then the question is how do we + + + align:start position:0% +okay so then the question is how do we +find these things and how many are there + + align:start position:0% +find these things and how many are there + + + align:start position:0% +find these things and how many are there +and + + align:start position:0% +and + + + align:start position:0% +and +things of that nature well one thing we + + align:start position:0% +things of that nature well one thing we + + + align:start position:0% +things of that nature well one thing we +can do is + + align:start position:0% +can do is + + + align:start position:0% +can do is +we can try and solve this equation + + align:start position:0% + + + + align:start position:0% + +by + + align:start position:0% +by + + + align:start position:0% +by +bringing this over to the other side so + + align:start position:0% +bringing this over to the other side so + + + align:start position:0% +bringing this over to the other side so +i is just the identity matrix of the + + align:start position:0% +i is just the identity matrix of the + + + align:start position:0% +i is just the identity matrix of the +appropriate size + + align:start position:0% +appropriate size + + + align:start position:0% +appropriate size +um you know m is n by n then i will be n + + align:start position:0% +um you know m is n by n then i will be n + + + align:start position:0% +um you know m is n by n then i will be n +by n + + align:start position:0% +by n + + + align:start position:0% +by n +and so + + align:start position:0% +and so + + + align:start position:0% +and so +this is exactly the same equation m + + align:start position:0% +this is exactly the same equation m + + + align:start position:0% +this is exactly the same equation m +times e minus lambda times e is 0. + + align:start position:0% +times e minus lambda times e is 0. + + + align:start position:0% +times e minus lambda times e is 0. +okay so there's a + + align:start position:0% +okay so there's a + + + align:start position:0% +okay so there's a +set of linear equations + + align:start position:0% +set of linear equations + + + align:start position:0% +set of linear equations +and + + align:start position:0% +and + + + align:start position:0% +and +you know we've been bragging about how + + align:start position:0% +you know we've been bragging about how + + + align:start position:0% +you know we've been bragging about how +linear equations are so easy + + align:start position:0% +linear equations are so easy + + + align:start position:0% +linear equations are so easy +and obviously what we can say is + + align:start position:0% + + + + align:start position:0% + +is that you know we just invert that + + align:start position:0% +is that you know we just invert that + + + align:start position:0% +is that you know we just invert that +matrix + + align:start position:0% +matrix + + + align:start position:0% +matrix +and we multiply by + + align:start position:0% +and we multiply by + + + align:start position:0% +and we multiply by +and and what do we get uh zero right so + + align:start position:0% +and and what do we get uh zero right so + + + align:start position:0% +and and what do we get uh zero right so +so that's called the trivial solution + + align:start position:0% +so that's called the trivial solution + + + align:start position:0% +so that's called the trivial solution +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +if if we can do this then + + align:start position:0% +if if we can do this then + + + align:start position:0% +if if we can do this then +that's not going to be helpful so what + + align:start position:0% +that's not going to be helpful so what + + + align:start position:0% +that's not going to be helpful so what +what is it we're looking for well we're + + align:start position:0% +what is it we're looking for well we're + + + align:start position:0% +what is it we're looking for well we're +looking for the case where actually this + + align:start position:0% +looking for the case where actually this + + + align:start position:0% +looking for the case where actually this +inverse doesn't exist + + align:start position:0% +inverse doesn't exist + + + align:start position:0% +inverse doesn't exist +so usually we're very keen to make sure + + align:start position:0% +so usually we're very keen to make sure + + + align:start position:0% +so usually we're very keen to make sure +that inverses exist in this case uh + + align:start position:0% +that inverses exist in this case uh + + + align:start position:0% +that inverses exist in this case uh +we're not so first of all + + align:start position:0% + + + + align:start position:0% + +terminology + + align:start position:0% + + + + align:start position:0% + +here we have a set of equations that are + + align:start position:0% +here we have a set of equations that are + + + align:start position:0% +here we have a set of equations that are +homogeneous that means that + + align:start position:0% +homogeneous that means that + + + align:start position:0% +homogeneous that means that +the right-hand side is zero + + align:start position:0% +the right-hand side is zero + + + align:start position:0% +the right-hand side is zero +and amongst other things that means that + + align:start position:0% +and amongst other things that means that + + + align:start position:0% +and amongst other things that means that +if you have a solution then any multiple + + align:start position:0% +if you have a solution then any multiple + + + align:start position:0% +if you have a solution then any multiple +of that solution is also a solution + + align:start position:0% +of that solution is also a solution + + + align:start position:0% +of that solution is also a solution +which is not the case normally when + + align:start position:0% +which is not the case normally when + + + align:start position:0% +which is not the case normally when +we're solving uh linear equations you + + align:start position:0% +we're solving uh linear equations you + + + align:start position:0% +we're solving uh linear equations you +know there's a + + align:start position:0% +know there's a + + + align:start position:0% +know there's a +unique solution and any multiple of it + + align:start position:0% +unique solution and any multiple of it + + + align:start position:0% +unique solution and any multiple of it +is not a solution so + + align:start position:0% +is not a solution so + + + align:start position:0% +is not a solution so +any + + align:start position:0% +any + + + align:start position:0% +any +non + + align:start position:0% +non + + + align:start position:0% +non +non one multiple + + align:start position:0% +non one multiple + + + align:start position:0% +non one multiple +okay so uh what we're looking for then + + align:start position:0% +okay so uh what we're looking for then + + + align:start position:0% +okay so uh what we're looking for then +is + + align:start position:0% +is + + + align:start position:0% +is +that + + align:start position:0% +that + + + align:start position:0% +that +we have a singular + + align:start position:0% + + + + align:start position:0% + +matrix that means that the determinant + + align:start position:0% +matrix that means that the determinant + + + align:start position:0% +matrix that means that the determinant +of that matrix is uh zero + + align:start position:0% +of that matrix is uh zero + + + align:start position:0% +of that matrix is uh zero +and so um + + align:start position:0% +and so um + + + align:start position:0% +and so um +what what does that mean well + + align:start position:0% +what what does that mean well + + + align:start position:0% +what what does that mean well +unfortunately the determinant + + align:start position:0% +unfortunately the determinant + + + align:start position:0% +unfortunately the determinant +is this complicated messy thing + + align:start position:0% +is this complicated messy thing + + + align:start position:0% +is this complicated messy thing +but if you think about it + + align:start position:0% +but if you think about it + + + align:start position:0% +but if you think about it +we can say + + align:start position:0% +we can say + + + align:start position:0% +we can say +something about the determinant + + align:start position:0% + + + + align:start position:0% + +but if we write this thing out + + align:start position:0% +but if we write this thing out + + + align:start position:0% +but if we write this thing out +i don't know 3 + + align:start position:0% +i don't know 3 + + + align:start position:0% +i don't know 3 +minus lambda + + align:start position:0% +minus lambda + + + align:start position:0% +minus lambda +what we've done is we've taken the + + align:start position:0% +what we've done is we've taken the + + + align:start position:0% +what we've done is we've taken the +matrix m which is some + + align:start position:0% +matrix m which is some + + + align:start position:0% +matrix m which is some +n by n real symmetric matrix and we + + align:start position:0% +n by n real symmetric matrix and we + + + align:start position:0% +n by n real symmetric matrix and we +subtracted lambda off the diagonal + + align:start position:0% +subtracted lambda off the diagonal + + + align:start position:0% +subtracted lambda off the diagonal +and now we're + + align:start position:0% +and now we're + + + align:start position:0% +and now we're +talking about the properties of this + + align:start position:0% +talking about the properties of this + + + align:start position:0% +talking about the properties of this +matrix and we we actually want this one + + align:start position:0% +matrix and we we actually want this one + + + align:start position:0% +matrix and we we actually want this one +to be singular because otherwise that + + align:start position:0% +to be singular because otherwise that + + + align:start position:0% +to be singular because otherwise that +equation has nothing but the uh + + align:start position:0% +equation has nothing but the uh + + + align:start position:0% +equation has nothing but the uh +obvious + + align:start position:0% +obvious + + + align:start position:0% +obvious +uh solution + + align:start position:0% +uh solution + + + align:start position:0% +uh solution +so what's the determinant of this well i + + align:start position:0% +so what's the determinant of this well i + + + align:start position:0% +so what's the determinant of this well i +don't know you might remember that the + + align:start position:0% +don't know you might remember that the + + + align:start position:0% +don't know you might remember that the +determinant + + align:start position:0% +determinant + + + align:start position:0% +determinant +involves taking this and multiplying it + + align:start position:0% +involves taking this and multiplying it + + + align:start position:0% +involves taking this and multiplying it +by the determinant of that matrix + + align:start position:0% +by the determinant of that matrix + + + align:start position:0% +by the determinant of that matrix +plus + + align:start position:0% +plus + + + align:start position:0% +plus +this times the determinant of some other + + align:start position:0% +this times the determinant of some other + + + align:start position:0% +this times the determinant of some other +sub matrix + + align:start position:0% +sub matrix + + + align:start position:0% +sub matrix +or you may may remember it as you know + + align:start position:0% +or you may may remember it as you know + + + align:start position:0% +or you may may remember it as you know +take one from column a one from column b + + align:start position:0% +take one from column a one from column b + + + align:start position:0% +take one from column a one from column b +and one from column c and depending on + + align:start position:0% +and one from column c and depending on + + + align:start position:0% +and one from column c and depending on +whether the number of switches in + + align:start position:0% +whether the number of switches in + + + align:start position:0% +whether the number of switches in +direction is even or odd you add a minus + + align:start position:0% +direction is even or odd you add a minus + + + align:start position:0% +direction is even or odd you add a minus +sign + + align:start position:0% +sign + + + align:start position:0% +sign +uh don't need to remember the exact + + align:start position:0% +uh don't need to remember the exact + + + align:start position:0% +uh don't need to remember the exact +formula the key thing is that we're + + align:start position:0% +formula the key thing is that we're + + + align:start position:0% +formula the key thing is that we're +taking something from here and something + + align:start position:0% +taking something from here and something + + + align:start position:0% +taking something from here and something +from there and so on + + align:start position:0% +from there and so on + + + align:start position:0% +from there and so on +never repeating columns or rows + + align:start position:0% +never repeating columns or rows + + + align:start position:0% +never repeating columns or rows +and there you know large numbers of ways + + align:start position:0% +and there you know large numbers of ways + + + align:start position:0% +and there you know large numbers of ways +of doing that which is why it's actually + + align:start position:0% +of doing that which is why it's actually + + + align:start position:0% +of doing that which is why it's actually +computationally expensive + + align:start position:0% +computationally expensive + + + align:start position:0% +computationally expensive +but the key thing is that we can get a + + align:start position:0% +but the key thing is that we can get a + + + align:start position:0% +but the key thing is that we can get a +term as large as + + align:start position:0% +term as large as + + + align:start position:0% +term as large as +this one along the diagonal in terms of + + align:start position:0% +this one along the diagonal in terms of + + + align:start position:0% +this one along the diagonal in terms of +lambda so if we look at the product of + + align:start position:0% +lambda so if we look at the product of + + + align:start position:0% +lambda so if we look at the product of +all of the terms on the diagonal that'll + + align:start position:0% +all of the terms on the diagonal that'll + + + align:start position:0% +all of the terms on the diagonal that'll +be part of the determinant one of many + + align:start position:0% +be part of the determinant one of many + + + align:start position:0% +be part of the determinant one of many +parts + + align:start position:0% +parts + + + align:start position:0% +parts +and it's got + + align:start position:0% +and it's got + + + align:start position:0% +and it's got +lambda to the n in it right we're taking + + align:start position:0% +lambda to the n in it right we're taking + + + align:start position:0% +lambda to the n in it right we're taking +m one one minus lambda m two two minus + + align:start position:0% +m one one minus lambda m two two minus + + + align:start position:0% +m one one minus lambda m two two minus +lambda and so on so so what's the + + align:start position:0% +lambda and so on so so what's the + + + align:start position:0% +lambda and so on so so what's the +determinant well it's a polynomial + + align:start position:0% +determinant well it's a polynomial + + + align:start position:0% +determinant well it's a polynomial +in + + align:start position:0% +in + + + align:start position:0% +in +in lambda + + align:start position:0% +in lambda + + + align:start position:0% +in lambda +and it's an nth order polynomial in + + align:start position:0% +and it's an nth order polynomial in + + + align:start position:0% +and it's an nth order polynomial in +lambda and polynomials of nth order have + + align:start position:0% +lambda and polynomials of nth order have + + + align:start position:0% +lambda and polynomials of nth order have +how many roots + + align:start position:0% +how many roots + + + align:start position:0% +how many roots +n + + align:start position:0% +n + + + align:start position:0% +n +good so so we're going to have n roots + + align:start position:0% +good so so we're going to have n roots + + + align:start position:0% +good so so we're going to have n roots +and so that means that + + align:start position:0% +and so that means that + + + align:start position:0% +and so that means that +not only is there a solution to this but + + align:start position:0% +not only is there a solution to this but + + + align:start position:0% +not only is there a solution to this but +they're going to be uh n solutions + + align:start position:0% +they're going to be uh n solutions + + + align:start position:0% +they're going to be uh n solutions +and um + + align:start position:0% +and um + + + align:start position:0% +and um +those are the things that that we'll be + + align:start position:0% +those are the things that that we'll be + + + align:start position:0% +those are the things that that we'll be +uh we'll be looking for + + align:start position:0% +uh we'll be looking for + + + align:start position:0% +uh we'll be looking for +so uh just to make this concrete let's + + align:start position:0% +so uh just to make this concrete let's + + + align:start position:0% +so uh just to make this concrete let's +look at a + + align:start position:0% +look at a + + + align:start position:0% +look at a +very simple example + + align:start position:0% +very simple example + + + align:start position:0% +very simple example +also because uh that's the one that + + align:start position:0% +also because uh that's the one that + + + align:start position:0% +also because uh that's the one that +we're + + align:start position:0% +we're + + + align:start position:0% +we're +dealing with right now + + align:start position:0% +dealing with right now + + + align:start position:0% +dealing with right now +with say the optical mouse + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +we already mentioned that just saying + + align:start position:0% +we already mentioned that just saying + + + align:start position:0% +we already mentioned that just saying +that the solution is unstable that the + + align:start position:0% +that the solution is unstable that the + + + align:start position:0% +that the solution is unstable that the +noise gain is high + + align:start position:0% +noise gain is high + + + align:start position:0% +noise gain is high +isn't enough when we're dealing with + + align:start position:0% +isn't enough when we're dealing with + + + align:start position:0% +isn't enough when we're dealing with +multi-dimensional problems it's fine for + + align:start position:0% +multi-dimensional problems it's fine for + + + align:start position:0% +multi-dimensional problems it's fine for +this this is it it's the the noise gain + + align:start position:0% +this this is it it's the the noise gain + + + align:start position:0% +this this is it it's the the noise gain +is a scalar + + align:start position:0% +is a scalar + + + align:start position:0% +is a scalar +we're done with but + + align:start position:0% +we're done with but + + + align:start position:0% +we're done with but +in the case of the optical mass we're + + align:start position:0% +in the case of the optical mass we're + + + align:start position:0% +in the case of the optical mass we're +recovering u and v + + align:start position:0% +recovering u and v + + + align:start position:0% +recovering u and v +so it's a two dimensional problem and it + + align:start position:0% +so it's a two dimensional problem and it + + + align:start position:0% +so it's a two dimensional problem and it +may very well be that the error in + + align:start position:0% +may very well be that the error in + + + align:start position:0% +may very well be that the error in +certain directions is very different + + align:start position:0% +certain directions is very different + + + align:start position:0% +certain directions is very different +from the error in other directions so we + + align:start position:0% +from the error in other directions so we + + + align:start position:0% +from the error in other directions so we +want to have a more nuanced picture i + + align:start position:0% +want to have a more nuanced picture i + + + align:start position:0% +want to have a more nuanced picture i +mean we can have a kind of a gross + + align:start position:0% +mean we can have a kind of a gross + + + align:start position:0% +mean we can have a kind of a gross +statement that says okay it's bad if the + + align:start position:0% +statement that says okay it's bad if the + + + align:start position:0% +statement that says okay it's bad if the +determinant is small that's a good start + + align:start position:0% +determinant is small that's a good start + + + align:start position:0% +determinant is small that's a good start +but it's that's a scalar constraint and + + align:start position:0% +but it's that's a scalar constraint and + + + align:start position:0% +but it's that's a scalar constraint and +it doesn't tell you that oh actually if + + align:start position:0% +it doesn't tell you that oh actually if + + + align:start position:0% +it doesn't tell you that oh actually if +you move in this direction you have very + + align:start position:0% +you move in this direction you have very + + + align:start position:0% +you move in this direction you have very +good knowledge of the motion but if you + + align:start position:0% +good knowledge of the motion but if you + + + align:start position:0% +good knowledge of the motion but if you +move in some other direction you don't + + align:start position:0% +move in some other direction you don't + + + align:start position:0% +move in some other direction you don't +okay so let's look at this well + + align:start position:0% +okay so let's look at this well + + + align:start position:0% +okay so let's look at this well +following what we did over there + + align:start position:0% + + + + align:start position:0% + +that's the condition for that set of + + align:start position:0% +that's the condition for that set of + + + align:start position:0% +that's the condition for that set of +homogeneous equations to have a + + align:start position:0% +homogeneous equations to have a + + + align:start position:0% +homogeneous equations to have a +non-trivial solution + + align:start position:0% +non-trivial solution + + + align:start position:0% +non-trivial solution +so you know homogeneous equations we + + align:start position:0% +so you know homogeneous equations we + + + align:start position:0% +so you know homogeneous equations we +don't run across a whole lot we almost + + align:start position:0% +don't run across a whole lot we almost + + + align:start position:0% +don't run across a whole lot we almost +always have inhomogeneous equations then + + align:start position:0% +always have inhomogeneous equations then + + + align:start position:0% +always have inhomogeneous equations then +they have a + + align:start position:0% +they have a + + + align:start position:0% +they have a +solution unless the determinant is zero + + align:start position:0% +solution unless the determinant is zero + + + align:start position:0% +solution unless the determinant is zero +and homogeneous equations have some very + + align:start position:0% +and homogeneous equations have some very + + + align:start position:0% +and homogeneous equations have some very +interesting properties + + align:start position:0% +interesting properties + + + align:start position:0% +interesting properties +and we'll just look at them a little bit + + align:start position:0% +and we'll just look at them a little bit + + + align:start position:0% +and we'll just look at them a little bit +okay so what is the determinant of that + + align:start position:0% +okay so what is the determinant of that + + + align:start position:0% +okay so what is the determinant of that +well it's just + + align:start position:0% + + + + align:start position:0% + +right it's just that times that minus + + align:start position:0% +right it's just that times that minus + + + align:start position:0% +right it's just that times that minus +that times that + + align:start position:0% +that times that + + + align:start position:0% +that times that +and if i multiply that out + + align:start position:0% + + + + align:start position:0% + +i get a second-order polynomial in + + align:start position:0% +i get a second-order polynomial in + + + align:start position:0% +i get a second-order polynomial in +lambda that i can solve + + align:start position:0% +lambda that i can solve + + + align:start position:0% +lambda that i can solve +and uh using the usual formula for + + align:start position:0% +and uh using the usual formula for + + + align:start position:0% +and uh using the usual formula for +quadratic + + align:start position:0% + + + + align:start position:0% + +so well actually i + + align:start position:0% +so well actually i + + + align:start position:0% +so well actually i +simplified something here so this was + + align:start position:0% +simplified something here so this was + + + align:start position:0% +simplified something here so this was +before i simplified it this was + + align:start position:0% +before i simplified it this was + + + align:start position:0% +before i simplified it this was +a plus c squared minus 4 ac minus + + align:start position:0% +a plus c squared minus 4 ac minus + + + align:start position:0% +a plus c squared minus 4 ac minus +b squared + + align:start position:0% +b squared + + + align:start position:0% +b squared +right so + + align:start position:0% +right so + + + align:start position:0% +right so +it's um + + align:start position:0% +it's um + + + align:start position:0% +it's um +b squared which is now this term minus + + align:start position:0% +b squared which is now this term minus + + + align:start position:0% +b squared which is now this term minus +four times uh that term + + align:start position:0% +four times uh that term + + + align:start position:0% +four times uh that term +and then when i multiply that out and + + align:start position:0% +and then when i multiply that out and + + + align:start position:0% +and then when i multiply that out and +rearrange terms i i get this + + align:start position:0% +rearrange terms i i get this + + + align:start position:0% +rearrange terms i i get this +uh so uh those are the eigenvalues so um + + align:start position:0% +uh so uh those are the eigenvalues so um + + + align:start position:0% +uh so uh those are the eigenvalues so um +they'll will be + + align:start position:0% +they'll will be + + + align:start position:0% +they'll will be +two vectors + + align:start position:0% +two vectors + + + align:start position:0% +two vectors +that have this property that when you + + align:start position:0% +that have this property that when you + + + align:start position:0% +that have this property that when you +multiply that matrix by the vector you + + align:start position:0% +multiply that matrix by the vector you + + + align:start position:0% +multiply that matrix by the vector you +get a vector in the same direction + + align:start position:0% +get a vector in the same direction + + + align:start position:0% +get a vector in the same direction +and their length will be changed by this + + align:start position:0% +and their length will be changed by this + + + align:start position:0% +and their length will be changed by this +quantity + + align:start position:0% +quantity + + + align:start position:0% +quantity +that's how much they'll be + + align:start position:0% +that's how much they'll be + + + align:start position:0% +that's how much they'll be +magnified or demagnified and we're very + + align:start position:0% +magnified or demagnified and we're very + + + align:start position:0% +magnified or demagnified and we're very +interested in that because + + align:start position:0% +interested in that because + + + align:start position:0% +interested in that because +typically what's on the right hand side + + align:start position:0% +typically what's on the right hand side + + + align:start position:0% +typically what's on the right hand side +is the error the measurement including + + align:start position:0% +is the error the measurement including + + + align:start position:0% +is the error the measurement including +the error and so + + align:start position:0% +the error and so + + + align:start position:0% +the error and so +these eigenvalues will determine how + + align:start position:0% +these eigenvalues will determine how + + + align:start position:0% +these eigenvalues will determine how +much the error will be will be magnified + + align:start position:0% +much the error will be will be magnified + + + align:start position:0% +much the error will be will be magnified +so just for + + align:start position:0% +so just for + + + align:start position:0% +so just for +cutting down on the writing let me give + + align:start position:0% +cutting down on the writing let me give + + + align:start position:0% +cutting down on the writing let me give +this a name so that i can + + align:start position:0% + + + + align:start position:0% + +abbreviate things + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so uh those are the eigen values and + + align:start position:0% +so uh those are the eigen values and + + + align:start position:0% +so uh those are the eigen values and +i'll be interested in how big they are + + align:start position:0% +i'll be interested in how big they are + + + align:start position:0% +i'll be interested in how big they are +now in our case you know with optical + + align:start position:0% +now in our case you know with optical + + + align:start position:0% +now in our case you know with optical +mouse these were integrals of e x + + align:start position:0% +mouse these were integrals of e x + + + align:start position:0% +mouse these were integrals of e x +squared and integrals of e x e y and + + align:start position:0% +squared and integrals of e x e y and + + + align:start position:0% +squared and integrals of e x e y and +stuff like that and then we can plug + + align:start position:0% +stuff like that and then we can plug + + + align:start position:0% +stuff like that and then we can plug +that into this formula to find out what + + align:start position:0% +that into this formula to find out what + + + align:start position:0% +that into this formula to find out what +those eigenvalues actually are + + align:start position:0% + + + + align:start position:0% + +now in practice you know if someone's + + align:start position:0% +now in practice you know if someone's + + + align:start position:0% +now in practice you know if someone's +finding eigenvalues and eigenvectors + + align:start position:0% +finding eigenvalues and eigenvectors + + + align:start position:0% +finding eigenvalues and eigenvectors +they just go to matlab or whatever so + + align:start position:0% +they just go to matlab or whatever so + + + align:start position:0% +they just go to matlab or whatever so +but + + align:start position:0% +but + + + align:start position:0% +but +i i want you to get a feel for this at + + align:start position:0% +i i want you to get a feel for this at + + + align:start position:0% +i i want you to get a feel for this at +this trivial level of two by two and + + align:start position:0% +this trivial level of two by two and + + + align:start position:0% +this trivial level of two by two and +then yeah you know if you're going to do + + align:start position:0% +then yeah you know if you're going to do + + + align:start position:0% +then yeah you know if you're going to do +a 13 by 13 matrix of course you're not + + align:start position:0% +a 13 by 13 matrix of course you're not + + + align:start position:0% +a 13 by 13 matrix of course you're not +going to do it by hand but it's useful + + align:start position:0% +going to do it by hand but it's useful + + + align:start position:0% +going to do it by hand but it's useful +to + + align:start position:0% +to + + + align:start position:0% +to +do this and get a clear idea of what + + align:start position:0% +do this and get a clear idea of what + + + align:start position:0% +do this and get a clear idea of what +it's all about + + align:start position:0% +it's all about + + + align:start position:0% +it's all about +okay so those are the eigenvalues what + + align:start position:0% +okay so those are the eigenvalues what + + + align:start position:0% +okay so those are the eigenvalues what +about the eigenvectors so they're going + + align:start position:0% +about the eigenvectors so they're going + + + align:start position:0% +about the eigenvectors so they're going +to be + + align:start position:0% +to be + + + align:start position:0% +to be +special directions in which + + align:start position:0% +special directions in which + + + align:start position:0% +special directions in which +this property holds + + align:start position:0% +this property holds + + + align:start position:0% +this property holds +and so how do we solve for those well + + align:start position:0% +and so how do we solve for those well + + + align:start position:0% +and so how do we solve for those well +now we have to solve the homogeneous + + align:start position:0% +now we have to solve the homogeneous + + + align:start position:0% +now we have to solve the homogeneous +equations so we got this matrix a minus + + align:start position:0% +equations so we got this matrix a minus + + + align:start position:0% +equations so we got this matrix a minus +lambda b + + align:start position:0% + + + + align:start position:0% + +um so this is going to be our + + align:start position:0% +um so this is going to be our + + + align:start position:0% +um so this is going to be our +eigenvector + + align:start position:0% + + + + align:start position:0% + +the one that corresponds to the lambda + + align:start position:0% +the one that corresponds to the lambda + + + align:start position:0% +the one that corresponds to the lambda +well we have two choices uh that we pick + + align:start position:0% +well we have two choices uh that we pick + + + align:start position:0% +well we have two choices uh that we pick +and so we're now assuming that we'll be + + align:start position:0% +and so we're now assuming that we'll be + + + align:start position:0% +and so we're now assuming that we'll be +plugging in a specific value of lambda + + align:start position:0% +plugging in a specific value of lambda + + + align:start position:0% +plugging in a specific value of lambda +namely one of one of these two + + align:start position:0% +namely one of one of these two + + + align:start position:0% +namely one of one of these two +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +what does this mean well it means that + + align:start position:0% +what does this mean well it means that + + + align:start position:0% +what does this mean well it means that +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +relationship between + + align:start position:0% +relationship between + + + align:start position:0% +relationship between +this vector and that vector and between + + align:start position:0% +this vector and that vector and between + + + align:start position:0% +this vector and that vector and between +this vector and that vector namely their + + align:start position:0% +this vector and that vector namely their + + + align:start position:0% +this vector and that vector namely their +orthogonal so so why is that well + + align:start position:0% +orthogonal so so why is that well + + + align:start position:0% +orthogonal so so why is that well +this value this zero up here comes from + + align:start position:0% +this value this zero up here comes from + + + align:start position:0% +this value this zero up here comes from +multiplying this row vector by this + + align:start position:0% +multiplying this row vector by this + + + align:start position:0% +multiplying this row vector by this +column vector so it's + + align:start position:0% +column vector so it's + + + align:start position:0% +column vector so it's +a minus lambda times x plus b y is 0. + + align:start position:0% +a minus lambda times x plus b y is 0. + + + align:start position:0% +a minus lambda times x plus b y is 0. +that that's the first equation and then + + align:start position:0% +that that's the first equation and then + + + align:start position:0% +that that's the first equation and then +the other zero comes from multiplying + + align:start position:0% +the other zero comes from multiplying + + + align:start position:0% +the other zero comes from multiplying +this row vector by that vector so i get + + align:start position:0% +this row vector by that vector so i get + + + align:start position:0% +this row vector by that vector so i get +b x + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +i can + + align:start position:0% +i can + + + align:start position:0% +i can +think of this as a dot product + + align:start position:0% + + + + align:start position:0% + +and i can think of this then as + + align:start position:0% + + + + align:start position:0% + +vectors being orthogonal to one another + + align:start position:0% +vectors being orthogonal to one another + + + align:start position:0% +vectors being orthogonal to one another +right so this means that + + align:start position:0% +right so this means that + + + align:start position:0% +right so this means that +a minus lambda b is perpendicular to x y + + align:start position:0% +a minus lambda b is perpendicular to x y + + + align:start position:0% +a minus lambda b is perpendicular to x y +and by the way + + align:start position:0% +and by the way + + + align:start position:0% +and by the way +b minus c lambda + + align:start position:0% +b minus c lambda + + + align:start position:0% +b minus c lambda +c minus lambda is also perpendicular to + + align:start position:0% +c minus lambda is also perpendicular to + + + align:start position:0% +c minus lambda is also perpendicular to +x and + + align:start position:0% +x and + + + align:start position:0% +x and +y so in solving these homogeneous + + align:start position:0% +y so in solving these homogeneous + + + align:start position:0% +y so in solving these homogeneous +equations + + align:start position:0% +equations + + + align:start position:0% +equations +uh i can note that basically i'm saying + + align:start position:0% +uh i can note that basically i'm saying + + + align:start position:0% +uh i can note that basically i'm saying +that + + align:start position:0% +that + + + align:start position:0% +that +the solution is perpendicular + + align:start position:0% +the solution is perpendicular + + + align:start position:0% +the solution is perpendicular +to the rows and so i can + + align:start position:0% + + + + align:start position:0% + +i can write down the answer very easily + + align:start position:0% +i can write down the answer very easily + + + align:start position:0% +i can write down the answer very easily +particularly in the 2x2 case + + align:start position:0% +particularly in the 2x2 case + + + align:start position:0% +particularly in the 2x2 case +all i need to do is find something + + align:start position:0% +all i need to do is find something + + + align:start position:0% +all i need to do is find something +that's perpendicular to a minus lambda b + + align:start position:0% +that's perpendicular to a minus lambda b + + + align:start position:0% +that's perpendicular to a minus lambda b +and so how about this + + align:start position:0% + + + + align:start position:0% + +right that + + align:start position:0% +right that + + + align:start position:0% +right that +if i multiply that by a minus lambda b + + align:start position:0% +if i multiply that by a minus lambda b + + + align:start position:0% +if i multiply that by a minus lambda b +i just get two terms with opposite signs + + align:start position:0% +i just get two terms with opposite signs + + + align:start position:0% +i just get two terms with opposite signs +and they cancel out so uh there's a + + align:start position:0% +and they cancel out so uh there's a + + + align:start position:0% +and they cancel out so uh there's a +there's an eigenvector + + align:start position:0% +there's an eigenvector + + + align:start position:0% +there's an eigenvector +uh how big is it well as we said in a + + align:start position:0% +uh how big is it well as we said in a + + + align:start position:0% +uh how big is it well as we said in a +sense it doesn't matter because + + align:start position:0% +sense it doesn't matter because + + + align:start position:0% +sense it doesn't matter because +uh any pr any multiple of an eigenvector + + align:start position:0% +uh any pr any multiple of an eigenvector + + + align:start position:0% +uh any pr any multiple of an eigenvector +is also an eigenvector + + align:start position:0% +is also an eigenvector + + + align:start position:0% +is also an eigenvector +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +that's one of them + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +actually + + align:start position:0% +actually + + + align:start position:0% +actually +that's two of them because + + align:start position:0% +that's two of them because + + + align:start position:0% +that's two of them because +we can plug in the two different values + + align:start position:0% +we can plug in the two different values + + + align:start position:0% +we can plug in the two different values +of lambda we get two different vectors + + align:start position:0% +of lambda we get two different vectors + + + align:start position:0% +of lambda we get two different vectors +but why focus on the first row you know + + align:start position:0% +but why focus on the first row you know + + + align:start position:0% +but why focus on the first row you know +this should be true of the other row as + + align:start position:0% +this should be true of the other row as + + + align:start position:0% +this should be true of the other row as +well so let's try it on the other row + + align:start position:0% +well so let's try it on the other row + + + align:start position:0% +well so let's try it on the other row +well on the other row + + align:start position:0% + + + + align:start position:0% + +here's a perpendicular to the other row + + align:start position:0% +here's a perpendicular to the other row + + + align:start position:0% +here's a perpendicular to the other row +if i take the dot product of that with + + align:start position:0% +if i take the dot product of that with + + + align:start position:0% +if i take the dot product of that with +the second row i get two terms that are + + align:start position:0% +the second row i get two terms that are + + + align:start position:0% +the second row i get two terms that are +equal in magnitude and opposite and sine + + align:start position:0% +equal in magnitude and opposite and sine + + + align:start position:0% +equal in magnitude and opposite and sine +so they cancel out so that that's also + + align:start position:0% +so they cancel out so that that's also + + + align:start position:0% +so they cancel out so that that's also +an eigenvector + + align:start position:0% +an eigenvector + + + align:start position:0% +an eigenvector +and now that's getting a little + + align:start position:0% +and now that's getting a little + + + align:start position:0% +and now that's getting a little +confusing because + + align:start position:0% +confusing because + + + align:start position:0% +confusing because +now i can plug in the two different + + align:start position:0% +now i can plug in the two different + + + align:start position:0% +now i can plug in the two different +values of lambda so i get four + + align:start position:0% +values of lambda so i get four + + + align:start position:0% +values of lambda so i get four +eigenvectors so + + align:start position:0% +eigenvectors so + + + align:start position:0% +eigenvectors so +well it turns out + + align:start position:0% +well it turns out + + + align:start position:0% +well it turns out +those actually point in the same + + align:start position:0% +those actually point in the same + + + align:start position:0% +those actually point in the same +direction + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +they're the same + + align:start position:0% +they're the same + + + align:start position:0% +they're the same +if lambda is + + align:start position:0% +if lambda is + + + align:start position:0% +if lambda is +given by that expression up there + + align:start position:0% + + + + align:start position:0% + +and you know i'm not going to + + align:start position:0% +and you know i'm not going to + + + align:start position:0% +and you know i'm not going to +bore you with algebra it's pretty + + align:start position:0% +bore you with algebra it's pretty + + + align:start position:0% +bore you with algebra it's pretty +straightforward to show that + + align:start position:0% +straightforward to show that + + + align:start position:0% +straightforward to show that +so + + align:start position:0% +so + + + align:start position:0% +so +so all together we can actually write + + align:start position:0% +so all together we can actually write + + + align:start position:0% +so all together we can actually write +the result + + align:start position:0% +the result + + + align:start position:0% +the result +if we want a unit eigenvector we can + + align:start position:0% +if we want a unit eigenvector we can + + + align:start position:0% +if we want a unit eigenvector we can +normalize these so we just divide by the + + align:start position:0% +normalize these so we just divide by the + + + align:start position:0% +normalize these so we just divide by the +sum of squares the square root of the + + align:start position:0% +sum of squares the square root of the + + + align:start position:0% +sum of squares the square root of the +sum of squares of of these two terms + + align:start position:0% +sum of squares of of these two terms + + + align:start position:0% +sum of squares of of these two terms +and we get something like this + + align:start position:0% + + + + align:start position:0% + +and the plus minus applies to the two + + align:start position:0% +and the plus minus applies to the two + + + align:start position:0% +and the plus minus applies to the two +different solutions + + align:start position:0% +different solutions + + + align:start position:0% +different solutions +the top sign always corresponding to + + align:start position:0% + + + + align:start position:0% + +one case + + align:start position:0% +one case + + + align:start position:0% +one case +minus a minus c + + align:start position:0% +minus a minus c + + + align:start position:0% +minus a minus c +so um oh i should mention that + + align:start position:0% +so um oh i should mention that + + + align:start position:0% +so um oh i should mention that +this is + + align:start position:0% +this is + + + align:start position:0% +this is +this is all written up + + align:start position:0% +this is all written up + + + align:start position:0% +this is all written up +in in this little four page pamphlet + + align:start position:0% +in in this little four page pamphlet + + + align:start position:0% +in in this little four page pamphlet +that's on under materials + + align:start position:0% +that's on under materials + + + align:start position:0% +that's on under materials +so + + align:start position:0% +so + + + align:start position:0% +so +you can + + align:start position:0% +you can + + + align:start position:0% +you can +check on it there i'm leaving out some + + align:start position:0% +check on it there i'm leaving out some + + + align:start position:0% +check on it there i'm leaving out some +details but + + align:start position:0% +details but + + + align:start position:0% +details but +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +i mean you might you might think well + + align:start position:0% +i mean you might you might think well + + + align:start position:0% +i mean you might you might think well +gee this is what it is for two by two + + align:start position:0% +gee this is what it is for two by two + + + align:start position:0% +gee this is what it is for two by two +this must be pretty complicated you know + + align:start position:0% +this must be pretty complicated you know + + + align:start position:0% +this must be pretty complicated you know +if i get to + + align:start position:0% +if i get to + + + align:start position:0% +if i get to +ten by ten and it is + + align:start position:0% +ten by ten and it is + + + align:start position:0% +ten by ten and it is +and that's why + + align:start position:0% +and that's why + + + align:start position:0% +and that's why +you know typically you use uh some + + align:start position:0% +you know typically you use uh some + + + align:start position:0% +you know typically you use uh some +pre-packaged tools + + align:start position:0% +pre-packaged tools + + + align:start position:0% +pre-packaged tools +but it's good to see how this works so + + align:start position:0% +but it's good to see how this works so + + + align:start position:0% +but it's good to see how this works so +for an n by n matrix + + align:start position:0% +for an n by n matrix + + + align:start position:0% +for an n by n matrix +real symmetric matrix we're going to + + align:start position:0% +real symmetric matrix we're going to + + + align:start position:0% +real symmetric matrix we're going to +have n of these typically and um + + align:start position:0% +have n of these typically and um + + + align:start position:0% +have n of these typically and um +there'll be + + align:start position:0% +there'll be + + + align:start position:0% +there'll be +corresponding eigenvalues and + + align:start position:0% +corresponding eigenvalues and + + + align:start position:0% +corresponding eigenvalues and +eigenvectors and + + align:start position:0% +eigenvectors and + + + align:start position:0% +eigenvectors and +they allow us to talk about + + align:start position:0% +they allow us to talk about + + + align:start position:0% +they allow us to talk about +error amplification and let's see how + + align:start position:0% +error amplification and let's see how + + + align:start position:0% +error amplification and let's see how +that works why + + align:start position:0% +that works why + + + align:start position:0% +that works why +what's the relationship to error + + align:start position:0% +what's the relationship to error + + + align:start position:0% +what's the relationship to error +amplification + + align:start position:0% +amplification + + + align:start position:0% +amplification +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so let me just + + align:start position:0% +so let me just + + + align:start position:0% +so let me just +i think i mentioned this before + + align:start position:0% +i think i mentioned this before + + + align:start position:0% +i think i mentioned this before +but we're thinking of our vectors as + + align:start position:0% +but we're thinking of our vectors as + + + align:start position:0% +but we're thinking of our vectors as +column vectors + + align:start position:0% + + + + align:start position:0% + +and we can alternatively + + align:start position:0% +and we can alternatively + + + align:start position:0% +and we can alternatively +or equivalently think of them as you + + align:start position:0% +or equivalently think of them as you + + + align:start position:0% +or equivalently think of them as you +know skinny matrices + + align:start position:0% +know skinny matrices + + + align:start position:0% +know skinny matrices +and so + + align:start position:0% +and so + + + align:start position:0% +and so +i can on the one hand write a dot + + align:start position:0% +i can on the one hand write a dot + + + align:start position:0% +i can on the one hand write a dot +product this way + + align:start position:0% +product this way + + + align:start position:0% +product this way +or i can write it like this and so what + + align:start position:0% +or i can write it like this and so what + + + align:start position:0% +or i can write it like this and so what +what is that well you know a1 a2 + + align:start position:0% + + + + align:start position:0% + +and you know obviously if i multiply + + align:start position:0% +and you know obviously if i multiply + + + align:start position:0% +and you know obviously if i multiply +these two skinny matrices i get a scalar + + align:start position:0% +these two skinny matrices i get a scalar + + + align:start position:0% +these two skinny matrices i get a scalar +which is just the product of a1 and b1 + + align:start position:0% +which is just the product of a1 and b1 + + + align:start position:0% +which is just the product of a1 and b1 +plus the product of a2 and b2 and so on + + align:start position:0% +plus the product of a2 and b2 and so on + + + align:start position:0% +plus the product of a2 and b2 and so on +so that's just the dot product + + align:start position:0% +so that's just the dot product + + + align:start position:0% +so that's just the dot product +and that's a + + align:start position:0% +and that's a + + + align:start position:0% +and that's a +convenient notation and we extend that + + align:start position:0% +convenient notation and we extend that + + + align:start position:0% +convenient notation and we extend that +to matrices as well + + align:start position:0% +to matrices as well + + + align:start position:0% +to matrices as well +so + + align:start position:0% +so + + + align:start position:0% +so +in in our context over here + + align:start position:0% +in in our context over here + + + align:start position:0% +in in our context over here +what we can show is + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +you know there there's a line of algebra + + align:start position:0% +you know there there's a line of algebra + + + align:start position:0% +you know there there's a line of algebra +which i'm leaving out uh which is in + + align:start position:0% +which i'm leaving out uh which is in + + + align:start position:0% +which i'm leaving out uh which is in +this pamphlet so you can you can verify + + align:start position:0% +this pamphlet so you can you can verify + + + align:start position:0% +this pamphlet so you can you can verify +it + + align:start position:0% +it + + + align:start position:0% +it +so that's sort of surprising what this + + align:start position:0% +so that's sort of surprising what this + + + align:start position:0% +so that's sort of surprising what this +is saying is okay i'm going to take + + align:start position:0% +is saying is okay i'm going to take + + + align:start position:0% +is saying is okay i'm going to take +eigenvector 1 + + align:start position:0% +eigenvector 1 + + + align:start position:0% +eigenvector 1 +multiply the matrix by that + + align:start position:0% +multiply the matrix by that + + + align:start position:0% +multiply the matrix by that +and then i get something new + + align:start position:0% +and then i get something new + + + align:start position:0% +and then i get something new +and i take the dot product with the + + align:start position:0% +and i take the dot product with the + + + align:start position:0% +and i take the dot product with the +other eigenvector + + align:start position:0% +other eigenvector + + + align:start position:0% +other eigenvector +and it's the same as flipping it + + align:start position:0% +and it's the same as flipping it + + + align:start position:0% +and it's the same as flipping it +you know like i don't know it's + + align:start position:0% +you know like i don't know it's + + + align:start position:0% +you know like i don't know it's +m could be a rotation so it's like i'm + + align:start position:0% +m could be a rotation so it's like i'm + + + align:start position:0% +m could be a rotation so it's like i'm +rotating e1 and then taking the dot + + align:start position:0% +rotating e1 and then taking the dot + + + align:start position:0% +rotating e1 and then taking the dot +product with e2 and that's the same as + + align:start position:0% +product with e2 and that's the same as + + + align:start position:0% +product with e2 and that's the same as +rotating e2 and taking the dot product + + align:start position:0% +rotating e2 and taking the dot product + + + align:start position:0% +rotating e2 and taking the dot product +with e1 + + align:start position:0% + + + + align:start position:0% + +well if that's the case + + align:start position:0% +well if that's the case + + + align:start position:0% +well if that's the case +um then + + align:start position:0% +um then + + + align:start position:0% +um then +we can uh + + align:start position:0% +we can uh + + + align:start position:0% +we can uh +show that these have to actually be + + align:start position:0% +show that these have to actually be + + + align:start position:0% +show that these have to actually be +orthogonal + + align:start position:0% +orthogonal + + + align:start position:0% +orthogonal +so that's where we're going we want to + + align:start position:0% +so that's where we're going we want to + + + align:start position:0% +so that's where we're going we want to +show that these + + align:start position:0% +show that these + + + align:start position:0% +show that these +eigenvectors are actually orthogonal so + + align:start position:0% +eigenvectors are actually orthogonal so + + + align:start position:0% +eigenvectors are actually orthogonal so +let's first look at this so this is + + align:start position:0% + + + + align:start position:0% + +how do i know that well because the + + align:start position:0% +how do i know that well because the + + + align:start position:0% +how do i know that well because the +whole point of these eigenvector + + align:start position:0% +whole point of these eigenvector + + + align:start position:0% +whole point of these eigenvector +eigenvalues was that m e1 is going to be + + align:start position:0% +eigenvalues was that m e1 is going to be + + + align:start position:0% +eigenvalues was that m e1 is going to be +in the direction e1 but a different + + align:start position:0% +in the direction e1 but a different + + + align:start position:0% +in the direction e1 but a different +length + + align:start position:0% +length + + + align:start position:0% +length +multiplied by + + align:start position:0% +multiplied by + + + align:start position:0% +multiplied by +by the eigen eigenvalue + + align:start position:0% +by the eigen eigenvalue + + + align:start position:0% +by the eigen eigenvalue +and this one here + + align:start position:0% +and this one here + + + align:start position:0% +and this one here +is going to be + + align:start position:0% + + + + align:start position:0% + +me2 is the vector e2 just multiplied by + + align:start position:0% +me2 is the vector e2 just multiplied by + + + align:start position:0% +me2 is the vector e2 just multiplied by +the eigenvector + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the part that takes a few steps is + + align:start position:0% +so the part that takes a few steps is + + + align:start position:0% +so the part that takes a few steps is +proving that these are actually equal + + align:start position:0% +proving that these are actually equal + + + align:start position:0% +proving that these are actually equal +but it's in the paper okay now what does + + align:start position:0% +but it's in the paper okay now what does + + + align:start position:0% +but it's in the paper okay now what does +this say + + align:start position:0% +this say + + + align:start position:0% +this say +well + + align:start position:0% + + + + align:start position:0% + +i can gather this up + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +that tells me that + + align:start position:0% + + + + align:start position:0% + +you know e1 dot e2 is zero + + align:start position:0% +you know e1 dot e2 is zero + + + align:start position:0% +you know e1 dot e2 is zero +so that means they're perpendicular + + align:start position:0% +so that means they're perpendicular + + + align:start position:0% +so that means they're perpendicular +well there's a + + align:start position:0% +well there's a + + + align:start position:0% +well there's a +another thing that can happen + + align:start position:0% + + + + align:start position:0% + +right if lambda 2 is the same as lambda + + align:start position:0% +right if lambda 2 is the same as lambda + + + align:start position:0% +right if lambda 2 is the same as lambda +1 then that doesn't uh follow + + align:start position:0% + + + + align:start position:0% + +so um when i take the roots of this + + align:start position:0% +so um when i take the roots of this + + + align:start position:0% +so um when i take the roots of this +polynomial and the roots are all + + align:start position:0% +polynomial and the roots are all + + + align:start position:0% +polynomial and the roots are all +different + + align:start position:0% +different + + + align:start position:0% +different +that means that all of the eigenvectors + + align:start position:0% +that means that all of the eigenvectors + + + align:start position:0% +that means that all of the eigenvectors +are orthogonal + + align:start position:0% +are orthogonal + + + align:start position:0% +are orthogonal +so that's what that says and if they're + + align:start position:0% +so that's what that says and if they're + + + align:start position:0% +so that's what that says and if they're +not + + align:start position:0% +not + + + align:start position:0% +not +all different if there's a multiplicity + + align:start position:0% +all different if there's a multiplicity + + + align:start position:0% +all different if there's a multiplicity +it turns out i can pick the eigenvectors + + align:start position:0% +it turns out i can pick the eigenvectors + + + align:start position:0% +it turns out i can pick the eigenvectors +to be orthogonal so the the answer the + + align:start position:0% +to be orthogonal so the the answer the + + + align:start position:0% +to be orthogonal so the the answer the +example would be + + align:start position:0% +example would be + + + align:start position:0% +example would be +the eigenvectors are in a plane + + align:start position:0% +the eigenvectors are in a plane + + + align:start position:0% +the eigenvectors are in a plane +and i can pick any two vectors in that + + align:start position:0% +and i can pick any two vectors in that + + + align:start position:0% +and i can pick any two vectors in that +plane + + align:start position:0% +plane + + + align:start position:0% +plane +they'll all work all of the vectors in + + align:start position:0% +they'll all work all of the vectors in + + + align:start position:0% +they'll all work all of the vectors in +that plane are eigenvectors + + align:start position:0% +that plane are eigenvectors + + + align:start position:0% +that plane are eigenvectors +but i i can + + align:start position:0% +but i i can + + + align:start position:0% +but i i can +pick two of them that are orthogonal + + align:start position:0% +pick two of them that are orthogonal + + + align:start position:0% +pick two of them that are orthogonal +so yes if um + + align:start position:0% +so yes if um + + + align:start position:0% +so yes if um +if two of the roots happen to be the + + align:start position:0% +if two of the roots happen to be the + + + align:start position:0% +if two of the roots happen to be the +same then + + align:start position:0% +same then + + + align:start position:0% +same then +um this doesn't force the eigenvectors + + align:start position:0% +um this doesn't force the eigenvectors + + + align:start position:0% +um this doesn't force the eigenvectors +to be orthogonal but i can just pick out + + align:start position:0% +to be orthogonal but i can just pick out + + + align:start position:0% +to be orthogonal but i can just pick out +of all the possible ones two that r + + align:start position:0% +of all the possible ones two that r + + + align:start position:0% +of all the possible ones two that r +and the idea is to construct a whole + + align:start position:0% +and the idea is to construct a whole + + + align:start position:0% +and the idea is to construct a whole +coordinate system so i've got all of + + align:start position:0% +coordinate system so i've got all of + + + align:start position:0% +coordinate system so i've got all of +these orthogonal vectors and they of + + align:start position:0% +these orthogonal vectors and they of + + + align:start position:0% +these orthogonal vectors and they of +course define a basis for for the vector + + align:start position:0% +course define a basis for for the vector + + + align:start position:0% +course define a basis for for the vector +space + + align:start position:0% +space + + + align:start position:0% +space +so um + + align:start position:0% + + + + align:start position:0% + +so in the two by two case you know what + + align:start position:0% +so in the two by two case you know what + + + align:start position:0% +so in the two by two case you know what +happens well i get a eigenvector here + + align:start position:0% + + + + align:start position:0% + +and the other one + + align:start position:0% +and the other one + + + align:start position:0% +and the other one +better be + + align:start position:0% +better be + + + align:start position:0% +better be +perpendicular to it + + align:start position:0% +perpendicular to it + + + align:start position:0% +perpendicular to it +and of course i can use those to talk + + align:start position:0% +and of course i can use those to talk + + + align:start position:0% +and of course i can use those to talk +about points in the plane just as i can + + align:start position:0% +about points in the plane just as i can + + + align:start position:0% +about points in the plane just as i can +use my original x and y axes + + align:start position:0% + + + + align:start position:0% + +they form a basis and so that means that + + align:start position:0% +they form a basis and so that means that + + + align:start position:0% +they form a basis and so that means that +i can write any vector + + align:start position:0% + + + + align:start position:0% + +can write any vector as a weighted sum + + align:start position:0% +can write any vector as a weighted sum + + + align:start position:0% +can write any vector as a weighted sum +of these eigenvectors + + align:start position:0% +of these eigenvectors + + + align:start position:0% +of these eigenvectors +so because they they form a basis + + align:start position:0% +so because they they form a basis + + + align:start position:0% +so because they they form a basis +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so what are these what are these alpha + + align:start position:0% +so what are these what are these alpha + + + align:start position:0% +so what are these what are these alpha +i's how do i find them + + align:start position:0% +i's how do i find them + + + align:start position:0% +i's how do i find them +well that's pretty easy because i just + + align:start position:0% +well that's pretty easy because i just + + + align:start position:0% +well that's pretty easy because i just +do + + align:start position:0% +do + + + align:start position:0% +do +v dot e i don't know let's call it j + + align:start position:0% +v dot e i don't know let's call it j + + + align:start position:0% +v dot e i don't know let's call it j +we don't want to get in conflict with + + align:start position:0% +we don't want to get in conflict with + + + align:start position:0% +we don't want to get in conflict with +the i which is a dummy variable in the + + align:start position:0% +the i which is a dummy variable in the + + + align:start position:0% +the i which is a dummy variable in the +sum + + align:start position:0% + + + + align:start position:0% + +and we said that the eigenvectors are + + align:start position:0% +and we said that the eigenvectors are + + + align:start position:0% +and we said that the eigenvectors are +orthogonal to each other so that means + + align:start position:0% +orthogonal to each other so that means + + + align:start position:0% +orthogonal to each other so that means +that all of these dot products are zero + + align:start position:0% +that all of these dot products are zero + + + align:start position:0% +that all of these dot products are zero +well except one which is e i dot e i + + align:start position:0% +well except one which is e i dot e i + + + align:start position:0% +well except one which is e i dot e i +right and so this is going to give me + + align:start position:0% +right and so this is going to give me + + + align:start position:0% +right and so this is going to give me +alpha i right because uh if i pick the + + align:start position:0% +alpha i right because uh if i pick the + + + align:start position:0% +alpha i right because uh if i pick the +unit vector version so so okay so this + + align:start position:0% +unit vector version so so okay so this + + + align:start position:0% +unit vector version so so okay so this +is a sum but i don't care about most of + + align:start position:0% +is a sum but i don't care about most of + + + align:start position:0% +is a sum but i don't care about most of +the terms because + + align:start position:0% +the terms because + + + align:start position:0% +the terms because +they're + + align:start position:0% +they're + + + align:start position:0% +they're +multiplied by zero this dot product the + + align:start position:0% +multiplied by zero this dot product the + + + align:start position:0% +multiplied by zero this dot product the +only one i care about is where these two + + align:start position:0% +only one i care about is where these two + + + align:start position:0% +only one i care about is where these two +are the same vectors + + align:start position:0% +are the same vectors + + + align:start position:0% +are the same vectors +and in that case i can if i pick unit + + align:start position:0% +and in that case i can if i pick unit + + + align:start position:0% +and in that case i can if i pick unit +vectors that's just one so i just get + + align:start position:0% +vectors that's just one so i just get + + + align:start position:0% +vectors that's just one so i just get +alpha i so + + align:start position:0% +alpha i so + + + align:start position:0% +alpha i so +um so it's very easy to + + align:start position:0% +um so it's very easy to + + + align:start position:0% +um so it's very easy to +re-express any vector in terms of the + + align:start position:0% +re-express any vector in terms of the + + + align:start position:0% +re-express any vector in terms of the +eigenvectors + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so then let's look at mv + + align:start position:0% +so then let's look at mv + + + align:start position:0% +so then let's look at mv +is + + align:start position:0% +is + + + align:start position:0% +is +sigma alpha r m + + align:start position:0% + + + + align:start position:0% + +so now we get to the juicy part the + + align:start position:0% +so now we get to the juicy part the + + + align:start position:0% +so now we get to the juicy part the +conclusion here + + align:start position:0% +conclusion here + + + align:start position:0% +conclusion here +which is that if we take an arbitrary + + align:start position:0% +which is that if we take an arbitrary + + + align:start position:0% +which is that if we take an arbitrary +vector measurement and we multiply the + + align:start position:0% +vector measurement and we multiply the + + + align:start position:0% +vector measurement and we multiply the +matrix by that measurement to obtain + + align:start position:0% +matrix by that measurement to obtain + + + align:start position:0% +matrix by that measurement to obtain +our unknown variables + + align:start position:0% +our unknown variables + + + align:start position:0% +our unknown variables +what happens is that + + align:start position:0% + + + + align:start position:0% + +different components are magnified by + + align:start position:0% +different components are magnified by + + + align:start position:0% +different components are magnified by +different amounts + + align:start position:0% + + + + align:start position:0% + +right so those directions are special in + + align:start position:0% +right so those directions are special in + + + align:start position:0% +right so those directions are special in +that along those directions we know how + + align:start position:0% +that along those directions we know how + + + align:start position:0% +that along those directions we know how +much the error is magnified and so + + align:start position:0% +much the error is magnified and so + + + align:start position:0% +much the error is magnified and so +you know in this case obviously + + align:start position:0% +you know in this case obviously + + + align:start position:0% +you know in this case obviously +if we + + align:start position:0% +if we + + + align:start position:0% +if we +have a large eigen value + + align:start position:0% +have a large eigen value + + + align:start position:0% +have a large eigen value +the component in that direction will be + + align:start position:0% +the component in that direction will be + + + align:start position:0% +the component in that direction will be +magnified a lot + + align:start position:0% +magnified a lot + + + align:start position:0% +magnified a lot +if we have a small eigenvalue it'll be + + align:start position:0% +if we have a small eigenvalue it'll be + + + align:start position:0% +if we have a small eigenvalue it'll be +minified it'll it'll be uh diminished + + align:start position:0% +minified it'll it'll be uh diminished + + + align:start position:0% +minified it'll it'll be uh diminished +and and we'll be happy so + + align:start position:0% +and and we'll be happy so + + + align:start position:0% +and and we'll be happy so +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's the connection to to the error + + align:start position:0% +so that's the connection to to the error + + + align:start position:0% +so that's the connection to to the error +gain but we mostly are dealing with + + align:start position:0% +gain but we mostly are dealing with + + + align:start position:0% +gain but we mostly are dealing with +inverses so this is what happens if we + + align:start position:0% +inverses so this is what happens if we + + + align:start position:0% +inverses so this is what happens if we +multiply by a matrix m but we're + + align:start position:0% +multiply by a matrix m but we're + + + align:start position:0% +multiply by a matrix m but we're +typically solving inverse problems where + + align:start position:0% +typically solving inverse problems where + + + align:start position:0% +typically solving inverse problems where +we're dealing with the inverse matrix + + align:start position:0% +we're dealing with the inverse matrix + + + align:start position:0% +we're dealing with the inverse matrix +and so what are the eigenvalues and + + align:start position:0% +and so what are the eigenvalues and + + + align:start position:0% +and so what are the eigenvalues and +eigenvectors of the inverse matrix + + align:start position:0% +eigenvectors of the inverse matrix + + + align:start position:0% +eigenvectors of the inverse matrix +so + + align:start position:0% +so + + + align:start position:0% +so +to see that + + align:start position:0% +to see that + + + align:start position:0% +to see that +i want to first introduce something else + + align:start position:0% +i want to first introduce something else + + + align:start position:0% +i want to first introduce something else +we're going to need + + align:start position:0% + + + + align:start position:0% + +so that looks like what we did for dot + + align:start position:0% +so that looks like what we did for dot + + + align:start position:0% +so that looks like what we did for dot +product + + align:start position:0% +product + + + align:start position:0% +product +uh but not quite + + align:start position:0% +uh but not quite + + + align:start position:0% +uh but not quite +now it's the other one that's the has + + align:start position:0% +now it's the other one that's the has + + + align:start position:0% +now it's the other one that's the has +the transpose on it and we'll use this + + align:start position:0% +the transpose on it and we'll use this + + + align:start position:0% +the transpose on it and we'll use this +notation quite a bit + + align:start position:0% +notation quite a bit + + + align:start position:0% +notation quite a bit +and so let's write this out a1 a2 a n + + align:start position:0% + + + + align:start position:0% + +and that's not a scalar it's not a dot + + align:start position:0% +and that's not a scalar it's not a dot + + + align:start position:0% +and that's not a scalar it's not a dot +product + + align:start position:0% +product + + + align:start position:0% +product +because what we're going to do is + + align:start position:0% +because what we're going to do is + + + align:start position:0% +because what we're going to do is +multiply the first term here by the + + align:start position:0% +multiply the first term here by the + + + align:start position:0% +multiply the first term here by the +first term here a1 b1 and then the first + + align:start position:0% +first term here a1 b1 and then the first + + + align:start position:0% +first term here a1 b1 and then the first +term here by the first term there a1 b2 + + align:start position:0% +term here by the first term there a1 b2 + + + align:start position:0% +term here by the first term there a1 b2 +data that a1 bn + + align:start position:0% +data that a1 bn + + + align:start position:0% +data that a1 bn +and then we go down to the next row here + + align:start position:0% +and then we go down to the next row here + + + align:start position:0% +and then we go down to the next row here +we get a2 + + align:start position:0% +we get a2 + + + align:start position:0% +we get a2 +so + + align:start position:0% +so + + + align:start position:0% +so +again if we treat these vectors as + + align:start position:0% +again if we treat these vectors as + + + align:start position:0% +again if we treat these vectors as +skinny matrices + + align:start position:0% +skinny matrices + + + align:start position:0% +skinny matrices +this is what we get + + align:start position:0% + + + + align:start position:0% + +so all together + + align:start position:0% + + + + align:start position:0% + +the dyadic product of n vectors is + + align:start position:0% +the dyadic product of n vectors is + + + align:start position:0% +the dyadic product of n vectors is +n by an n by n matrix + + align:start position:0% +n by an n by n matrix + + + align:start position:0% +n by an n by n matrix +and + + align:start position:0% +and + + + align:start position:0% +and +and that'll be handy for us so + + align:start position:0% +and that'll be handy for us so + + + align:start position:0% +and that'll be handy for us so +let's apply that idea so we got v + + align:start position:0% + + + + align:start position:0% + +we expanded + + align:start position:0% + + + + align:start position:0% + +it right over there we said that + + align:start position:0% +it right over there we said that + + + align:start position:0% +it right over there we said that +because these eigenvectors form a bases + + align:start position:0% +because these eigenvectors form a bases + + + align:start position:0% +because these eigenvectors form a bases +we can express an arbitrary vector in + + align:start position:0% +we can express an arbitrary vector in + + + align:start position:0% +we can express an arbitrary vector in +terms of it + + align:start position:0% +terms of it + + + align:start position:0% +terms of it +and then we found the actual weights and + + align:start position:0% +and then we found the actual weights and + + + align:start position:0% +and then we found the actual weights and +when we plug that in we we get this + + align:start position:0% +when we plug that in we we get this + + + align:start position:0% +when we plug that in we we get this +formula + + align:start position:0% +formula + + + align:start position:0% +formula +and so + + align:start position:0% +and so + + + align:start position:0% +and so +we can now rewrite that in various ways + + align:start position:0% +we can now rewrite that in various ways + + + align:start position:0% +we can now rewrite that in various ways +so + + align:start position:0% +so + + + align:start position:0% +so +one way to rewrite this is v + + align:start position:0% +one way to rewrite this is v + + + align:start position:0% +one way to rewrite this is v +times + + align:start position:0% +times + + + align:start position:0% +times +v transpose times e i + + align:start position:0% + + + + align:start position:0% + +uh or another way of writing it is let's + + align:start position:0% +uh or another way of writing it is let's + + + align:start position:0% +uh or another way of writing it is let's +see we want to do this + + align:start position:0% +see we want to do this + + + align:start position:0% +see we want to do this +e i + + align:start position:0% +e i + + + align:start position:0% +e i +e i transpose + + align:start position:0% +e i transpose + + + align:start position:0% +e i transpose +v + + align:start position:0% +v + + + align:start position:0% +v +so this is just taking the dot product + + align:start position:0% +so this is just taking the dot product + + + align:start position:0% +so this is just taking the dot product +and rewriting it + + align:start position:0% +and rewriting it + + + align:start position:0% +and rewriting it +and how do we get here well in a dot + + align:start position:0% +and how do we get here well in a dot + + + align:start position:0% +and how do we get here well in a dot +product that it's commutative we can we + + align:start position:0% +product that it's commutative we can we + + + align:start position:0% +product that it's commutative we can we +can flip the v and the e i + + align:start position:0% +can flip the v and the e i + + + align:start position:0% +can flip the v and the e i +and therefore we can get this expression + + align:start position:0% +and therefore we can get this expression + + + align:start position:0% +and therefore we can get this expression +for the dot product just as easily as + + align:start position:0% +for the dot product just as easily as + + + align:start position:0% +for the dot product just as easily as +that one + + align:start position:0% +that one + + + align:start position:0% +that one +and then taking a scalar times a vector + + align:start position:0% +and then taking a scalar times a vector + + + align:start position:0% +and then taking a scalar times a vector +is the same as + + align:start position:0% +is the same as + + + align:start position:0% +is the same as +multiplying the vector by a scalar so so + + align:start position:0% +multiplying the vector by a scalar so so + + + align:start position:0% +multiplying the vector by a scalar so so +we get this and why is this interesting + + align:start position:0% +we get this and why is this interesting + + + align:start position:0% +we get this and why is this interesting +well because when we do these matrix + + align:start position:0% +well because when we do these matrix + + + align:start position:0% +well because when we do these matrix +products + + align:start position:0% +products + + + align:start position:0% +products +uh they're associative so we can rewrite + + align:start position:0% +uh they're associative so we can rewrite + + + align:start position:0% +uh they're associative so we can rewrite +this as + + align:start position:0% +this as + + + align:start position:0% +this as +e i e i transpose v + + align:start position:0% +e i e i transpose v + + + align:start position:0% +e i e i transpose v +and up there we have a sum + + align:start position:0% +and up there we have a sum + + + align:start position:0% +and up there we have a sum +over i + + align:start position:0% +over i + + + align:start position:0% +over i +and + + align:start position:0% +and + + + align:start position:0% +and +v is not dependent on i so + + align:start position:0% +v is not dependent on i so + + + align:start position:0% +v is not dependent on i so +we can actually factor this out like + + align:start position:0% +we can actually factor this out like + + + align:start position:0% +we can actually factor this out like +this + + align:start position:0% +this + + + align:start position:0% +this +so so + + align:start position:0% +so so + + + align:start position:0% +so so +you see that + + align:start position:0% +you see that + + + align:start position:0% +you see that +these terms all depend on i so in the + + align:start position:0% +these terms all depend on i so in the + + + align:start position:0% +these terms all depend on i so in the +sum every term has a different one but + + align:start position:0% +sum every term has a different one but + + + align:start position:0% +sum every term has a different one but +the v is the same so i can separate that + + align:start position:0% +the v is the same so i can separate that + + + align:start position:0% +the v is the same so i can separate that +out + + align:start position:0% +out + + + align:start position:0% +out +and wait a minute i'm saying v equals + + align:start position:0% +and wait a minute i'm saying v equals + + + align:start position:0% +and wait a minute i'm saying v equals +something times v + + align:start position:0% +something times v + + + align:start position:0% +something times v +so so what is this + + align:start position:0% + + + + align:start position:0% + +that's the identity matrix + + align:start position:0% +that's the identity matrix + + + align:start position:0% +that's the identity matrix +so this is a very long way around to + + align:start position:0% +so this is a very long way around to + + + align:start position:0% +so this is a very long way around to +write the identity matrix + + align:start position:0% +write the identity matrix + + + align:start position:0% +write the identity matrix +and the reason we're doing it is because + + align:start position:0% +and the reason we're doing it is because + + + align:start position:0% +and the reason we're doing it is because +with a slight change we can now write + + align:start position:0% +with a slight change we can now write + + + align:start position:0% +with a slight change we can now write +the matrix m + + align:start position:0% +the matrix m + + + align:start position:0% +the matrix m +using the same + + align:start position:0% +using the same + + + align:start position:0% +using the same +idea + + align:start position:0% + + + + align:start position:0% + +and so um + + align:start position:0% + + + + align:start position:0% + +we can actually + + align:start position:0% + + + + align:start position:0% + +get to this version of m + + align:start position:0% +get to this version of m + + + align:start position:0% +get to this version of m +and why is this interesting well because + + align:start position:0% +and why is this interesting well because + + + align:start position:0% +and why is this interesting well because +now we can see + + align:start position:0% +now we can see + + + align:start position:0% +now we can see +the properties of the eigenvalues that + + align:start position:0% +the properties of the eigenvalues that + + + align:start position:0% +the properties of the eigenvalues that +we're interested in + + align:start position:0% +we're interested in + + + align:start position:0% +we're interested in +and then how do we check this + + align:start position:0% +and then how do we check this + + + align:start position:0% +and then how do we check this +well we can perform operations of m on + + align:start position:0% +well we can perform operations of m on + + + align:start position:0% +well we can perform operations of m on +some vector and see whether it produces + + align:start position:0% +some vector and see whether it produces + + + align:start position:0% +some vector and see whether it produces +the same result so we can we can check + + align:start position:0% +the same result so we can we can check + + + align:start position:0% +the same result so we can we can check +this + + align:start position:0% +this + + + align:start position:0% +this +by doing for example m times e i + + align:start position:0% +by doing for example m times e i + + + align:start position:0% +by doing for example m times e i +checking that this is true well let's + + align:start position:0% +checking that this is true well let's + + + align:start position:0% +checking that this is true well let's +make it + + align:start position:0% +make it + + + align:start position:0% +make it +i guess we've got e i here so make this + + align:start position:0% +i guess we've got e i here so make this + + + align:start position:0% +i guess we've got e i here so make this +j + + align:start position:0% +j + + + align:start position:0% +j +that's very easy to check and if that's + + align:start position:0% +that's very easy to check and if that's + + + align:start position:0% +that's very easy to check and if that's +true then then this is true + + align:start position:0% +true then then this is true + + + align:start position:0% +true then then this is true +um + + align:start position:0% +um + + + align:start position:0% +um +more interestingly is this one so this + + align:start position:0% +more interestingly is this one so this + + + align:start position:0% +more interestingly is this one so this +is the one we finally get to that's the + + align:start position:0% +is the one we finally get to that's the + + + align:start position:0% +is the one we finally get to that's the +most interesting + + align:start position:0% + + + + align:start position:0% + +and how do we check this + + align:start position:0% +and how do we check this + + + align:start position:0% +and how do we check this +well an easy way is + + align:start position:0% +well an easy way is + + + align:start position:0% +well an easy way is +to take this expression for m multiplied + + align:start position:0% +to take this expression for m multiplied + + + align:start position:0% +to take this expression for m multiplied +by this expression for m inverse and + + align:start position:0% +by this expression for m inverse and + + + align:start position:0% +by this expression for m inverse and +show that you get the id you get this + + align:start position:0% +show that you get the id you get this + + + align:start position:0% +show that you get the id you get this +expression the identity matrix + + align:start position:0% +expression the identity matrix + + + align:start position:0% +expression the identity matrix +okay so um you know this may be going a + + align:start position:0% +okay so um you know this may be going a + + + align:start position:0% +okay so um you know this may be going a +little bit fast but remember it's it's + + align:start position:0% +little bit fast but remember it's it's + + + align:start position:0% +little bit fast but remember it's it's +all there and it all fits on four pages + + align:start position:0% +all there and it all fits on four pages + + + align:start position:0% +all there and it all fits on four pages +it's you know like those uh + + align:start position:0% +it's you know like those uh + + + align:start position:0% +it's you know like those uh +facebook come ons that say oh and it all + + align:start position:0% +facebook come ons that say oh and it all + + + align:start position:0% +facebook come ons that say oh and it all +is only three pages long + + align:start position:0% +is only three pages long + + + align:start position:0% +is only three pages long +okay so uh why are we interested in this + + align:start position:0% +okay so uh why are we interested in this + + + align:start position:0% +okay so uh why are we interested in this +here's the key + + align:start position:0% +here's the key + + + align:start position:0% +here's the key +um + + align:start position:0% +um + + + align:start position:0% +um +this + + align:start position:0% +this + + + align:start position:0% +this +matrix we're using to solve our vision + + align:start position:0% +matrix we're using to solve our vision + + + align:start position:0% +matrix we're using to solve our vision +problem + + align:start position:0% +problem + + + align:start position:0% +problem +which takes a measurement and turns it + + align:start position:0% +which takes a measurement and turns it + + + align:start position:0% +which takes a measurement and turns it +into some + + align:start position:0% +into some + + + align:start position:0% +into some +quantity of interest to us displacement + + align:start position:0% +quantity of interest to us displacement + + + align:start position:0% +quantity of interest to us displacement +velocity whatever + + align:start position:0% +velocity whatever + + + align:start position:0% +velocity whatever +it multiplies + + align:start position:0% +it multiplies + + + align:start position:0% +it multiplies +components of the signal by 1 over + + align:start position:0% +components of the signal by 1 over + + + align:start position:0% +components of the signal by 1 over +lambda i + + align:start position:0% +lambda i + + + align:start position:0% +lambda i +so + + align:start position:0% +so + + + align:start position:0% +so +it's bad + + align:start position:0% +it's bad + + + align:start position:0% +it's bad +if lambda i + + align:start position:0% +if lambda i + + + align:start position:0% +if lambda i +is small + + align:start position:0% +is small + + + align:start position:0% +is small +so so that's where we're going with this + + align:start position:0% +so so that's where we're going with this + + + align:start position:0% +so so that's where we're going with this +so that + + align:start position:0% +so that + + + align:start position:0% +so that +often the way we can understand the + + align:start position:0% +often the way we can understand the + + + align:start position:0% +often the way we can understand the +performance of one of these methods is + + align:start position:0% +performance of one of these methods is + + + align:start position:0% +performance of one of these methods is +to look at how + + align:start position:0% +to look at how + + + align:start position:0% +to look at how +what the noise gain is and when we get + + align:start position:0% +what the noise gain is and when we get + + + align:start position:0% +what the noise gain is and when we get +pat you know up from one dimension this + + align:start position:0% +pat you know up from one dimension this + + + align:start position:0% +pat you know up from one dimension this +is the way to do it + + align:start position:0% +is the way to do it + + + align:start position:0% +is the way to do it +we take that matrix we find its + + align:start position:0% +we take that matrix we find its + + + align:start position:0% +we take that matrix we find its +eigenvalues + + align:start position:0% +eigenvalues + + + align:start position:0% +eigenvalues +and if some of them are small we know + + align:start position:0% +and if some of them are small we know + + + align:start position:0% +and if some of them are small we know +that it's ill an ill pose problem + + align:start position:0% +that it's ill an ill pose problem + + + align:start position:0% +that it's ill an ill pose problem +it's not going to have a stable solution + + align:start position:0% +it's not going to have a stable solution + + + align:start position:0% +it's not going to have a stable solution +if you make a small change in the + + align:start position:0% +if you make a small change in the + + + align:start position:0% +if you make a small change in the +measurement you'll get a big change in + + align:start position:0% +measurement you'll get a big change in + + + align:start position:0% +measurement you'll get a big change in +the result so + + align:start position:0% +the result so + + + align:start position:0% +the result so +i know i'm saying this again and again + + align:start position:0% +i know i'm saying this again and again + + + align:start position:0% +i know i'm saying this again and again +and again and it's because it's you know + + align:start position:0% +and again and it's because it's you know + + + align:start position:0% +and again and it's because it's you know +key it's important + + align:start position:0% +key it's important + + + align:start position:0% +key it's important +so for example in our optical mouse + + align:start position:0% +so for example in our optical mouse + + + align:start position:0% +so for example in our optical mouse +situation where we just have the two by + + align:start position:0% +situation where we just have the two by + + + align:start position:0% +situation where we just have the two by +two case + + align:start position:0% + + + + align:start position:0% + +we end up with a diagram like this + + align:start position:0% +we end up with a diagram like this + + + align:start position:0% +we end up with a diagram like this +where we have two directions + + align:start position:0% +where we have two directions + + + align:start position:0% +where we have two directions +that are eigenvectors and + + align:start position:0% + + + + align:start position:0% + +if one of them has a small eigenvalue + + align:start position:0% +if one of them has a small eigenvalue + + + align:start position:0% +if one of them has a small eigenvalue +then it's going to be hard for us to + + align:start position:0% +then it's going to be hard for us to + + + align:start position:0% +then it's going to be hard for us to +accurately compute the motion of the + + align:start position:0% +accurately compute the motion of the + + + align:start position:0% +accurately compute the motion of the +mouse and it turns out that in that case + + align:start position:0% +mouse and it turns out that in that case + + + align:start position:0% +mouse and it turns out that in that case +one of them + + align:start position:0% +one of them + + + align:start position:0% +one of them +is the direction of the isofold + + align:start position:0% +is the direction of the isofold + + + align:start position:0% +is the direction of the isofold +and the other one is the direction of + + align:start position:0% +and the other one is the direction of + + + align:start position:0% +and the other one is the direction of +the gradient + + align:start position:0% + + + + align:start position:0% + +so so remember that + + align:start position:0% +so so remember that + + + align:start position:0% +so so remember that +you know isophotes are just lines of + + align:start position:0% +you know isophotes are just lines of + + + align:start position:0% +you know isophotes are just lines of +brightness is constant + + align:start position:0% +brightness is constant + + + align:start position:0% +brightness is constant +and they're very handy for drawing + + align:start position:0% +and they're very handy for drawing + + + align:start position:0% +and they're very handy for drawing +things on the blackboard because i can't + + align:start position:0% +things on the blackboard because i can't + + + align:start position:0% +things on the blackboard because i can't +draw gray levels + + align:start position:0% +draw gray levels + + + align:start position:0% +draw gray levels +and they have the property that they're + + align:start position:0% +and they have the property that they're + + + align:start position:0% +and they have the property that they're +perpendicular to the gradient + + align:start position:0% + + + + align:start position:0% + +where the gradient is just the + + align:start position:0% +where the gradient is just the + + + align:start position:0% +where the gradient is just the +two vector + + align:start position:0% +two vector + + + align:start position:0% +two vector +of + + align:start position:0% +of + + + align:start position:0% +of +derivatives with respect to x and y + + align:start position:0% +derivatives with respect to x and y + + + align:start position:0% +derivatives with respect to x and y +okay and it turns out that the + + align:start position:0% + + + + align:start position:0% + +eigenvalue that corresponds to + + align:start position:0% +eigenvalue that corresponds to + + + align:start position:0% +eigenvalue that corresponds to +the uh isofoat direction + + align:start position:0% +the uh isofoat direction + + + align:start position:0% +the uh isofoat direction +is very small + + align:start position:0% +is very small + + + align:start position:0% +is very small +in the ideal case zero + + align:start position:0% +in the ideal case zero + + + align:start position:0% +in the ideal case zero +and the one in the gradient direction is + + align:start position:0% +and the one in the gradient direction is + + + align:start position:0% +and the one in the gradient direction is +not + + align:start position:0% +not + + + align:start position:0% +not +so that invert that that means that + + align:start position:0% +so that invert that that means that + + + align:start position:0% +so that invert that that means that +the in the in the isoford direction any + + align:start position:0% +the in the in the isoford direction any + + + align:start position:0% +the in the in the isoford direction any +sort of small error will be magnified + + align:start position:0% +sort of small error will be magnified + + + align:start position:0% +sort of small error will be magnified +hugely + + align:start position:0% +hugely + + + align:start position:0% +hugely +whereas in the other direction the + + align:start position:0% +whereas in the other direction the + + + align:start position:0% +whereas in the other direction the +gradient direction + + align:start position:0% +gradient direction + + + align:start position:0% +gradient direction +it's okay + + align:start position:0% +it's okay + + + align:start position:0% +it's okay +and so that corresponds with our + + align:start position:0% +and so that corresponds with our + + + align:start position:0% +and so that corresponds with our +understanding that + + align:start position:0% +understanding that + + + align:start position:0% +understanding that +if you move this image in the gradient + + align:start position:0% +if you move this image in the gradient + + + align:start position:0% +if you move this image in the gradient +direction you know things change this + + align:start position:0% +direction you know things change this + + + align:start position:0% +direction you know things change this +isophote is now down here and the + + align:start position:0% +isophote is now down here and the + + + align:start position:0% +isophote is now down here and the +brightness here has changed + + align:start position:0% +brightness here has changed + + + align:start position:0% +brightness here has changed +whereas if you move it in the direction + + align:start position:0% +whereas if you move it in the direction + + + align:start position:0% +whereas if you move it in the direction +of the isophote + + align:start position:0% +of the isophote + + + align:start position:0% +of the isophote +you know by definition isofoat meaning + + align:start position:0% +you know by definition isofoat meaning + + + align:start position:0% +you know by definition isofoat meaning +constant brightness the brightness tends + + align:start position:0% +constant brightness the brightness tends + + + align:start position:0% +constant brightness the brightness tends +not to change + + align:start position:0% +not to change + + + align:start position:0% +not to change +or not change by much and so that's then + + align:start position:0% +or not change by much and so that's then + + + align:start position:0% +or not change by much and so that's then +a motion that is not easy to detect + + align:start position:0% +a motion that is not easy to detect + + + align:start position:0% +a motion that is not easy to detect +accurately so + + align:start position:0% +accurately so + + + align:start position:0% +accurately so +so this is kind of a little a story + + align:start position:0% +so this is kind of a little a story + + + align:start position:0% +so this is kind of a little a story +about eigenvectors and eigenvalues and + + align:start position:0% +about eigenvectors and eigenvalues and + + + align:start position:0% +about eigenvectors and eigenvalues and +we will see that + + align:start position:0% +we will see that + + + align:start position:0% +we will see that +they don't they play a role in this not + + align:start position:0% +they don't they play a role in this not + + + align:start position:0% +they don't they play a role in this not +just in error analysis but + + align:start position:0% +just in error analysis but + + + align:start position:0% +just in error analysis but +this is one of their + + align:start position:0% +this is one of their + + + align:start position:0% +this is one of their +main + + align:start position:0% +main + + + align:start position:0% +main +uses + + align:start position:0% +uses + + + align:start position:0% +uses +okay back back to + + align:start position:0% +okay back back to + + + align:start position:0% +okay back back to +slightly less abstract stuff + + align:start position:0% +slightly less abstract stuff + + + align:start position:0% +slightly less abstract stuff +photometric stereo + + align:start position:0% +photometric stereo + + + align:start position:0% +photometric stereo +and we we discussed that uh somewhat + + align:start position:0% +and we we discussed that uh somewhat + + + align:start position:0% +and we we discussed that uh somewhat +last time + + align:start position:0% +last time + + + align:start position:0% +last time +so the idea is that + + align:start position:0% + + + + align:start position:0% + +a single brightness measurement + + align:start position:0% +a single brightness measurement + + + align:start position:0% +a single brightness measurement +doesn't give us enough information + + align:start position:0% +doesn't give us enough information + + + align:start position:0% +doesn't give us enough information +to recover + + align:start position:0% +to recover + + + align:start position:0% +to recover +surface orientation because surface + + align:start position:0% +surface orientation because surface + + + align:start position:0% +surface orientation because surface +orientation has two degrees of freedom + + align:start position:0% +orientation has two degrees of freedom + + + align:start position:0% +orientation has two degrees of freedom +and so we need more constraints and and + + align:start position:0% +and so we need more constraints and and + + + align:start position:0% +and so we need more constraints and and +one way to get more constraint is to + + align:start position:0% +one way to get more constraint is to + + + align:start position:0% +one way to get more constraint is to +take more pictures but of course if + + align:start position:0% +take more pictures but of course if + + + align:start position:0% +take more pictures but of course if +they're under the same conditions + + align:start position:0% +they're under the same conditions + + + align:start position:0% +they're under the same conditions +they'll be just the same picture with a + + align:start position:0% +they'll be just the same picture with a + + + align:start position:0% +they'll be just the same picture with a +little bit of different noise + + align:start position:0% +little bit of different noise + + + align:start position:0% +little bit of different noise +but you know the difference in noise + + align:start position:0% +but you know the difference in noise + + + align:start position:0% +but you know the difference in noise +isn't going to buy you much other than + + align:start position:0% +isn't going to buy you much other than + + + align:start position:0% +isn't going to buy you much other than +maybe you can average them to reduce the + + align:start position:0% +maybe you can average them to reduce the + + + align:start position:0% +maybe you can average them to reduce the +noise but + + align:start position:0% +noise but + + + align:start position:0% +noise but +so we ended up with a system where we + + align:start position:0% +so we ended up with a system where we + + + align:start position:0% +so we ended up with a system where we +took three pictures + + align:start position:0% +took three pictures + + + align:start position:0% +took three pictures +um to make things simple + + align:start position:0% +um to make things simple + + + align:start position:0% +um to make things simple +under three different lighting + + align:start position:0% +under three different lighting + + + align:start position:0% +under three different lighting +conditions + + align:start position:0% + + + + align:start position:0% + +okay so and we started off with real + + align:start position:0% +okay so and we started off with real + + + align:start position:0% +okay so and we started off with real +simple case + + align:start position:0% +simple case + + + align:start position:0% +simple case +where we said that the brightness was + + align:start position:0% +where we said that the brightness was + + + align:start position:0% +where we said that the brightness was +proportional + + align:start position:0% +proportional + + + align:start position:0% +proportional +the cosine of the incident angle + + align:start position:0% +the cosine of the incident angle + + + align:start position:0% +the cosine of the incident angle +and that of course is the dot product of + + align:start position:0% + + + + align:start position:0% + +the surface normal and the direction to + + align:start position:0% +the surface normal and the direction to + + + align:start position:0% +the surface normal and the direction to +the light source + + align:start position:0% +the light source + + + align:start position:0% +the light source +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and we'll in a minute we'll talk about + + align:start position:0% +and we'll in a minute we'll talk about + + + align:start position:0% +and we'll in a minute we'll talk about +well what if the surface doesn't satisfy + + align:start position:0% +well what if the surface doesn't satisfy + + + align:start position:0% +well what if the surface doesn't satisfy +that constraint because obviously real + + align:start position:0% +that constraint because obviously real + + + align:start position:0% +that constraint because obviously real +surfaces don't they may approximate this + + align:start position:0% +surfaces don't they may approximate this + + + align:start position:0% +surfaces don't they may approximate this +some surfaces approximate this rather + + align:start position:0% +some surfaces approximate this rather + + + align:start position:0% +some surfaces approximate this rather +well but we want to deal with arbitrary + + align:start position:0% +well but we want to deal with arbitrary + + + align:start position:0% +well but we want to deal with arbitrary +surfaces + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we might have for example + + align:start position:0% + + + + align:start position:0% + +uh one brightness measurement so we're + + align:start position:0% +uh one brightness measurement so we're + + + align:start position:0% +uh one brightness measurement so we're +not talking about a particular pixel + + align:start position:0% +not talking about a particular pixel + + + align:start position:0% +not talking about a particular pixel +right so we're gonna focus on + + align:start position:0% +right so we're gonna focus on + + + align:start position:0% +right so we're gonna focus on +doing this at every pixel and so + + align:start position:0% +doing this at every pixel and so + + + align:start position:0% +doing this at every pixel and so +looking at a particular pixel and this + + align:start position:0% +looking at a particular pixel and this + + + align:start position:0% +looking at a particular pixel and this +is the brightness the gray level we + + align:start position:0% +is the brightness the gray level we + + + align:start position:0% +is the brightness the gray level we +measure there + + align:start position:0% +measure there + + + align:start position:0% +measure there +and i've put in this row + + align:start position:0% +and i've put in this row + + + align:start position:0% +and i've put in this row +which i call the albedo + + align:start position:0% + + + + align:start position:0% + +as a way of describing how much light + + align:start position:0% +as a way of describing how much light + + + align:start position:0% +as a way of describing how much light +the surface reflects so a white surface + + align:start position:0% +the surface reflects so a white surface + + + align:start position:0% +the surface reflects so a white surface +the row would be one and a black surface + + align:start position:0% +the row would be one and a black surface + + + align:start position:0% +the row would be one and a black surface +row would be zero and you know real + + align:start position:0% +row would be zero and you know real + + + align:start position:0% +row would be zero and you know real +surface would be somewhere in between + + align:start position:0% +surface would be somewhere in between + + + align:start position:0% +surface would be somewhere in between +and one reason i do that is + + align:start position:0% +and one reason i do that is + + + align:start position:0% +and one reason i do that is +because i can + + align:start position:0% +because i can + + + align:start position:0% +because i can +and because it makes the problem + + align:start position:0% +and because it makes the problem + + + align:start position:0% +and because it makes the problem +actually easier because now i've got + + align:start position:0% +actually easier because now i've got + + + align:start position:0% +actually easier because now i've got +three unknowns and + + align:start position:0% +three unknowns and + + + align:start position:0% +three unknowns and +if i have three constraints that are + + align:start position:0% +if i have three constraints that are + + + align:start position:0% +if i have three constraints that are +linear i can use my great linear + + align:start position:0% +linear i can use my great linear + + + align:start position:0% +linear i can use my great linear +equation solving methods to solve them + + align:start position:0% +equation solving methods to solve them + + + align:start position:0% +equation solving methods to solve them +in a way + + align:start position:0% +in a way + + + align:start position:0% +in a way +two two images would be enough + + align:start position:0% +two two images would be enough + + + align:start position:0% +two two images would be enough +because by + + align:start position:0% +because by + + + align:start position:0% +because by +you know if we have two + + align:start position:0% +you know if we have two + + + align:start position:0% +you know if we have two +equations in two unknowns there's + + align:start position:0% +equations in two unknowns there's + + + align:start position:0% +equations in two unknowns there's +usually a finite number of solutions + + align:start position:0% +usually a finite number of solutions + + + align:start position:0% +usually a finite number of solutions +the trouble is the finite number may not + + align:start position:0% +the trouble is the finite number may not + + + align:start position:0% +the trouble is the finite number may not +be one + + align:start position:0% +be one + + + align:start position:0% +be one +and in this case the finite number is + + align:start position:0% +and in this case the finite number is + + + align:start position:0% +and in this case the finite number is +two and so you know i've disambiguated + + align:start position:0% +two and so you know i've disambiguated + + + align:start position:0% +two and so you know i've disambiguated +hugely before i didn't know what the + + align:start position:0% +hugely before i didn't know what the + + + align:start position:0% +hugely before i didn't know what the +orientation was at all now i know it's + + align:start position:0% +orientation was at all now i know it's + + + align:start position:0% +orientation was at all now i know it's +one of these two possibilities but it's + + align:start position:0% +one of these two possibilities but it's + + + align:start position:0% +one of these two possibilities but it's +not + + align:start position:0% +not + + + align:start position:0% +not +it's easier to deal first with a case + + align:start position:0% +it's easier to deal first with a case + + + align:start position:0% +it's easier to deal first with a case +where we can completely disambiguate it + + align:start position:0% +where we can completely disambiguate it + + + align:start position:0% +where we can completely disambiguate it +by introducing + + align:start position:0% +by introducing + + + align:start position:0% +by introducing +a problem with three unknowns and three + + align:start position:0% +a problem with three unknowns and three + + + align:start position:0% +a problem with three unknowns and three +measurements + + align:start position:0% +measurements + + + align:start position:0% +measurements +okay so then + + align:start position:0% + + + + align:start position:0% + +i use a different light source + + align:start position:0% +i use a different light source + + + align:start position:0% +i use a different light source +and i get a second measurement + + align:start position:0% +and i get a second measurement + + + align:start position:0% +and i get a second measurement +and then i use a third light source and + + align:start position:0% +and then i use a third light source and + + + align:start position:0% +and then i use a third light source and +i get a third measurement + + align:start position:0% +i get a third measurement + + + align:start position:0% +i get a third measurement +and you know we did this last time + + align:start position:0% +and you know we did this last time + + + align:start position:0% +and you know we did this last time +and this is where we use that notation + + align:start position:0% +and this is where we use that notation + + + align:start position:0% +and this is where we use that notation +for dot product + + align:start position:0% +for dot product + + + align:start position:0% +for dot product +and we use it to talk about uh + + align:start position:0% +and we use it to talk about uh + + + align:start position:0% +and we use it to talk about uh +let's do that + + align:start position:0% + + + + align:start position:0% + +right so what what's this this is a + + align:start position:0% +right so what what's this this is a + + + align:start position:0% +right so what what's this this is a +three by three matrix + + align:start position:0% +three by three matrix + + + align:start position:0% +three by three matrix +uh s1 transpose is the vector to the + + align:start position:0% +uh s1 transpose is the vector to the + + + align:start position:0% +uh s1 transpose is the vector to the +light source one just flipped from being + + align:start position:0% +light source one just flipped from being + + + align:start position:0% +light source one just flipped from being +a column vector into a row vector so the + + align:start position:0% +a column vector into a row vector so the + + + align:start position:0% +a column vector into a row vector so the +first row of this matrix is s1 just + + align:start position:0% +first row of this matrix is s1 just + + + align:start position:0% +first row of this matrix is s1 just +turned on its side and this is students + + align:start position:0% +turned on its side and this is students + + + align:start position:0% +turned on its side and this is students +on and so when you multiply this matrix + + align:start position:0% +on and so when you multiply this matrix + + + align:start position:0% +on and so when you multiply this matrix +by that vector the first thing you get + + align:start position:0% +by that vector the first thing you get + + + align:start position:0% +by that vector the first thing you get +is the dot product of s1 and n + + align:start position:0% +is the dot product of s1 and n + + + align:start position:0% +is the dot product of s1 and n +and that of course is e1 + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and here i'm using the shorthand + + align:start position:0% +and here i'm using the shorthand + + + align:start position:0% +and here i'm using the shorthand +notation + + align:start position:0% + + + + align:start position:0% + +so i'm absorbing that lambda into the n + + align:start position:0% +so i'm absorbing that lambda into the n + + + align:start position:0% +so i'm absorbing that lambda into the n +and that's convenient because now + + align:start position:0% +and that's convenient because now + + + align:start position:0% +and that's convenient because now +instead of having to deal with a unit + + align:start position:0% +instead of having to deal with a unit + + + align:start position:0% +instead of having to deal with a unit +vector i have a arbitrary 3 vector and + + align:start position:0% +vector i have a arbitrary 3 vector and + + + align:start position:0% +vector i have a arbitrary 3 vector and +that means i don't need to deal with the + + align:start position:0% +that means i don't need to deal with the + + + align:start position:0% +that means i don't need to deal with the +nasty uh + + align:start position:0% +nasty uh + + + align:start position:0% +nasty uh +non-linear constraint + + align:start position:0% +non-linear constraint + + + align:start position:0% +non-linear constraint +see the the thing that leads to + + align:start position:0% +see the the thing that leads to + + + align:start position:0% +see the the thing that leads to +two solutions is a quadratic and why is + + align:start position:0% +two solutions is a quadratic and why is + + + align:start position:0% +two solutions is a quadratic and why is +it why do we get a quadratic well + + align:start position:0% +it why do we get a quadratic well + + + align:start position:0% +it why do we get a quadratic well +because we have this second order + + align:start position:0% +because we have this second order + + + align:start position:0% +because we have this second order +constraint on n but + + align:start position:0% +constraint on n but + + + align:start position:0% +constraint on n but +by doing this we + + align:start position:0% +by doing this we + + + align:start position:0% +by doing this we +avoid + + align:start position:0% +avoid + + + align:start position:0% +avoid +having to do that + + align:start position:0% +having to do that + + + align:start position:0% +having to do that +okay so that i can just write as a + + align:start position:0% +okay so that i can just write as a + + + align:start position:0% +okay so that i can just write as a +matrix s times vector n + + align:start position:0% +matrix s times vector n + + + align:start position:0% +matrix s times vector n +is + + align:start position:0% +is + + + align:start position:0% +is +vector e so the vector e is just i'm + + align:start position:0% +vector e so the vector e is just i'm + + + align:start position:0% +vector e so the vector e is just i'm +stacking up my three measurements + + align:start position:0% +stacking up my three measurements + + + align:start position:0% +stacking up my three measurements +so again to to be clear so i take one + + align:start position:0% +so again to to be clear so i take one + + + align:start position:0% +so again to to be clear so i take one +picture i look at this pixel i get e1 + + align:start position:0% +picture i look at this pixel i get e1 + + + align:start position:0% +picture i look at this pixel i get e1 +then i turn on a different light source + + align:start position:0% +then i turn on a different light source + + + align:start position:0% +then i turn on a different light source +i take a picture at that same pixel i + + align:start position:0% +i take a picture at that same pixel i + + + align:start position:0% +i take a picture at that same pixel i +get e2 + + align:start position:0% +get e2 + + + align:start position:0% +get e2 +and then i turn on the third light + + align:start position:0% +and then i turn on the third light + + + align:start position:0% +and then i turn on the third light +source i look at that particular pixel + + align:start position:0% +source i look at that particular pixel + + + align:start position:0% +source i look at that particular pixel +and i get e3 and i stack them together + + align:start position:0% +and i get e3 and i stack them together + + + align:start position:0% +and i get e3 and i stack them together +to make this vector e1 + + align:start position:0% + + + + align:start position:0% + +and so you know the solution is very + + align:start position:0% +and so you know the solution is very + + + align:start position:0% +and so you know the solution is very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +and extremely cheap to compute + + align:start position:0% +and extremely cheap to compute + + + align:start position:0% +and extremely cheap to compute +in particular + + align:start position:0% +in particular + + + align:start position:0% +in particular +i can pre-compute this matrix assuming + + align:start position:0% +i can pre-compute this matrix assuming + + + align:start position:0% +i can pre-compute this matrix assuming +that the light sources are in fixed + + align:start position:0% +that the light sources are in fixed + + + align:start position:0% +that the light sources are in fixed +positions so if i know where the light + + align:start position:0% +positions so if i know where the light + + + align:start position:0% +positions so if i know where the light +sources are i know s1 s2 and s3 i can + + align:start position:0% +sources are i know s1 s2 and s3 i can + + + align:start position:0% +sources are i know s1 s2 and s3 i can +just construct this matrix and + + align:start position:0% +just construct this matrix and + + + align:start position:0% +just construct this matrix and +invert it ahead of time and then this is + + align:start position:0% +invert it ahead of time and then this is + + + align:start position:0% +invert it ahead of time and then this is +just a multiplication of a three by + + align:start position:0% +just a multiplication of a three by + + + align:start position:0% +just a multiplication of a three by +three matrix by a 3 vector and you know + + align:start position:0% +three matrix by a 3 vector and you know + + + align:start position:0% +three matrix by a 3 vector and you know +we talked about this last time + + align:start position:0% +we talked about this last time + + + align:start position:0% +we talked about this last time +and we also said that well + + align:start position:0% +and we also said that well + + + align:start position:0% +and we also said that well +that's assuming that this matrix doesn't + + align:start position:0% +that's assuming that this matrix doesn't + + + align:start position:0% +that's assuming that this matrix doesn't +give us problems + + align:start position:0% +give us problems + + + align:start position:0% +give us problems +so the problem would be where the matrix + + align:start position:0% +so the problem would be where the matrix + + + align:start position:0% +so the problem would be where the matrix +is singular + + align:start position:0% +is singular + + + align:start position:0% +is singular +then we can't invert it + + align:start position:0% +then we can't invert it + + + align:start position:0% +then we can't invert it +or if it's nearly singular we can't + + align:start position:0% +or if it's nearly singular we can't + + + align:start position:0% +or if it's nearly singular we can't +invert it so when does that happen well + + align:start position:0% +invert it so when does that happen well + + + align:start position:0% +invert it so when does that happen well +it happens when the rows are not + + align:start position:0% +it happens when the rows are not + + + align:start position:0% +it happens when the rows are not +linearly independent + + align:start position:0% +linearly independent + + + align:start position:0% +linearly independent +so that's when this blows up and for + + align:start position:0% +so that's when this blows up and for + + + align:start position:0% +so that's when this blows up and for +example if let's try this s3 + + align:start position:0% +example if let's try this s3 + + + align:start position:0% +example if let's try this s3 +is some combination + + align:start position:0% +is some combination + + + align:start position:0% +is some combination +of s1 some linear combination of s2 + + align:start position:0% +of s1 some linear combination of s2 + + + align:start position:0% +of s1 some linear combination of s2 +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +that's how we create problems right if + + align:start position:0% +that's how we create problems right if + + + align:start position:0% +that's how we create problems right if +the third row is just a combination of + + align:start position:0% +the third row is just a combination of + + + align:start position:0% +the third row is just a combination of +the first two rows for or + + align:start position:0% +the first two rows for or + + + align:start position:0% +the first two rows for or +in general if there's a linear + + align:start position:0% +in general if there's a linear + + + align:start position:0% +in general if there's a linear +combination of the three rows that gives + + align:start position:0% +combination of the three rows that gives + + + align:start position:0% +combination of the three rows that gives +us zero + + align:start position:0% +us zero + + + align:start position:0% +us zero +so okay um so + + align:start position:0% +so okay um so + + + align:start position:0% +so okay um so +why is this bad well because this means + + align:start position:0% +why is this bad well because this means + + + align:start position:0% +why is this bad well because this means +that e3 is alpha e1 plus + + align:start position:0% +that e3 is alpha e1 plus + + + align:start position:0% +that e3 is alpha e1 plus +beta e2 + + align:start position:0% +beta e2 + + + align:start position:0% +beta e2 +right i just need to take the dot + + align:start position:0% +right i just need to take the dot + + + align:start position:0% +right i just need to take the dot +product of this equation with n + + align:start position:0% +product of this equation with n + + + align:start position:0% +product of this equation with n +and i get this result and that tells me + + align:start position:0% +and i get this result and that tells me + + + align:start position:0% +and i get this result and that tells me +that the third measurement is redundant + + align:start position:0% +that the third measurement is redundant + + + align:start position:0% +that the third measurement is redundant +it's not telling me anything new so no + + align:start position:0% +it's not telling me anything new so no + + + align:start position:0% +it's not telling me anything new so no +wonder it blows up right it's like + + align:start position:0% +wonder it blows up right it's like + + + align:start position:0% +wonder it blows up right it's like +you're cheating + + align:start position:0% +you're cheating + + + align:start position:0% +you're cheating +you know if you made for example if you + + align:start position:0% +you know if you made for example if you + + + align:start position:0% +you know if you made for example if you +made the third row the same as the first + + align:start position:0% +made the third row the same as the first + + + align:start position:0% +made the third row the same as the first +row + + align:start position:0% +row + + + align:start position:0% +row +it's pretty clear the matrix is singular + + align:start position:0% +it's pretty clear the matrix is singular + + + align:start position:0% +it's pretty clear the matrix is singular +and it's also pretty clear that you're + + align:start position:0% +and it's also pretty clear that you're + + + align:start position:0% +and it's also pretty clear that you're +not getting any new information so so it + + align:start position:0% +not getting any new information so so it + + + align:start position:0% +not getting any new information so so it +all makes intuitive sense + + align:start position:0% +all makes intuitive sense + + + align:start position:0% +all makes intuitive sense +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +i can + + align:start position:0% + + + + align:start position:0% + +think about this as a sort of picture + + align:start position:0% + + + + align:start position:0% + +this is a case where s1 plus s2 plus s3 + + align:start position:0% +this is a case where s1 plus s2 plus s3 + + + align:start position:0% +this is a case where s1 plus s2 plus s3 +is 0 and that's you know clearly a bad + + align:start position:0% +is 0 and that's you know clearly a bad + + + align:start position:0% +is 0 and that's you know clearly a bad +case + + align:start position:0% +case + + + align:start position:0% +case +and i can be fancier and i can you know + + align:start position:0% +and i can be fancier and i can you know + + + align:start position:0% +and i can be fancier and i can you know +put multipliers on these i can put alpha + + align:start position:0% +put multipliers on these i can put alpha + + + align:start position:0% +put multipliers on these i can put alpha +on this and + + align:start position:0% +on this and + + + align:start position:0% +on this and +beta on that + + align:start position:0% +beta on that + + + align:start position:0% +beta on that +and if you like gamma on that so if some + + align:start position:0% +and if you like gamma on that so if some + + + align:start position:0% +and if you like gamma on that so if some +multiple of those + + align:start position:0% +multiple of those + + + align:start position:0% +multiple of those +three vectors + + align:start position:0% +three vectors + + + align:start position:0% +three vectors +adds up to zero + + align:start position:0% +adds up to zero + + + align:start position:0% +adds up to zero +uh this won't work and what is that + + align:start position:0% +uh this won't work and what is that + + + align:start position:0% +uh this won't work and what is that +condition + + align:start position:0% +condition + + + align:start position:0% +condition +how can i geometrically + + align:start position:0% +how can i geometrically + + + align:start position:0% +how can i geometrically +say + + align:start position:0% +say + + + align:start position:0% +say +uh what the condition is for this to go + + align:start position:0% +uh what the condition is for this to go + + + align:start position:0% +uh what the condition is for this to go +wrong so the vectors s1 s2 and s3 + + align:start position:0% +wrong so the vectors s1 s2 and s3 + + + align:start position:0% +wrong so the vectors s1 s2 and s3 +are + + align:start position:0% + + + + align:start position:0% + +for this loop to close remember this is + + align:start position:0% +for this loop to close remember this is + + + align:start position:0% +for this loop to close remember this is +now in 3d so we've got a vector going a + + align:start position:0% +now in 3d so we've got a vector going a + + + align:start position:0% +now in 3d so we've got a vector going a +certain way + + align:start position:0% +certain way + + + align:start position:0% +certain way +then of a certain length then another + + align:start position:0% +then of a certain length then another + + + align:start position:0% +then of a certain length then another +vector + + align:start position:0% +vector + + + align:start position:0% +vector +you start at the tip of that first + + align:start position:0% +you start at the tip of that first + + + align:start position:0% +you start at the tip of that first +vector and you put the tail of the + + align:start position:0% +vector and you put the tail of the + + + align:start position:0% +vector and you put the tail of the +second vector there + + align:start position:0% +second vector there + + + align:start position:0% +second vector there +and then when you get to the third + + align:start position:0% +and then when you get to the third + + + align:start position:0% +and then when you get to the third +vector it closes + + align:start position:0% +vector it closes + + + align:start position:0% +vector it closes +so what is the condition on those three + + align:start position:0% +so what is the condition on those three + + + align:start position:0% +so what is the condition on those three +vectors geometrically that makes that + + align:start position:0% +vectors geometrically that makes that + + + align:start position:0% +vectors geometrically that makes that +possible + + align:start position:0% + + + + align:start position:0% + +they're in the same plane right if i had + + align:start position:0% +they're in the same plane right if i had + + + align:start position:0% +they're in the same plane right if i had +you know x y and z axes obviously you + + align:start position:0% +you know x y and z axes obviously you + + + align:start position:0% +you know x y and z axes obviously you +can't do that you you know the one goes + + align:start position:0% +can't do that you you know the one goes + + + align:start position:0% +can't do that you you know the one goes +off in the x direction one goes off in + + align:start position:0% +off in the x direction one goes off in + + + align:start position:0% +off in the x direction one goes off in +the y direction one goes off in the z + + align:start position:0% +the y direction one goes off in the z + + + align:start position:0% +the y direction one goes off in the z +direction it's never going to close so + + align:start position:0% +direction it's never going to close so + + + align:start position:0% +direction it's never going to close so +the problem is if they're coplanar + + align:start position:0% +the problem is if they're coplanar + + + align:start position:0% +the problem is if they're coplanar +so so that's uh bad that's when this + + align:start position:0% +so so that's uh bad that's when this + + + align:start position:0% +so so that's uh bad that's when this +method fails and so obviously um + + align:start position:0% +method fails and so obviously um + + + align:start position:0% +method fails and so obviously um +you should when you do this you should + + align:start position:0% +you should when you do this you should + + + align:start position:0% +you should when you do this you should +place them so that they're + + align:start position:0% + + + + align:start position:0% + +kind of as far as possible from being + + align:start position:0% +kind of as far as possible from being + + + align:start position:0% +kind of as far as possible from being +co-planar + + align:start position:0% +co-planar + + + align:start position:0% +co-planar +for example + + align:start position:0% +for example + + + align:start position:0% +for example +you could put them + + align:start position:0% +you could put them + + + align:start position:0% +you could put them +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +at you know x y z axes so you could have + + align:start position:0% +at you know x y z axes so you could have + + + align:start position:0% +at you know x y z axes so you could have +an arrangement where the object is down + + align:start position:0% +an arrangement where the object is down + + + align:start position:0% +an arrangement where the object is down +here + + align:start position:0% +here + + + align:start position:0% +here +and + + align:start position:0% +and + + + align:start position:0% +and +then you can erect some + + align:start position:0% +then you can erect some + + + align:start position:0% +then you can erect some +rectangular coordinate system and s1 + + align:start position:0% +rectangular coordinate system and s1 + + + align:start position:0% +rectangular coordinate system and s1 +goes there and s2 goes there and s3 goes + + align:start position:0% +goes there and s2 goes there and s3 goes + + + align:start position:0% +goes there and s2 goes there and s3 goes +there and now they're not coplanar so + + align:start position:0% +there and now they're not coplanar so + + + align:start position:0% +there and now they're not coplanar so +this won't happen they won't fall apart + + align:start position:0% +this won't happen they won't fall apart + + + align:start position:0% +this won't happen they won't fall apart +and then they're questions of well you + + align:start position:0% +and then they're questions of well you + + + align:start position:0% +and then they're questions of well you +know which is best + + align:start position:0% +know which is best + + + align:start position:0% +know which is best +obviously if i make them almost + + align:start position:0% +obviously if i make them almost + + + align:start position:0% +obviously if i make them almost +coplanar i'm going to get uh unstable + + align:start position:0% +coplanar i'm going to get uh unstable + + + align:start position:0% +coplanar i'm going to get uh unstable +results + + align:start position:0% +results + + + align:start position:0% +results +the some eigenvalue will be small and if + + align:start position:0% +the some eigenvalue will be small and if + + + align:start position:0% +the some eigenvalue will be small and if +i take the inverse + + align:start position:0% +i take the inverse + + + align:start position:0% +i take the inverse +the inverse of the eigenvalue will be + + align:start position:0% +the inverse of the eigenvalue will be + + + align:start position:0% +the inverse of the eigenvalue will be +large and so the noise amplification + + align:start position:0% +large and so the noise amplification + + + align:start position:0% +large and so the noise amplification +will be large + + align:start position:0% +will be large + + + align:start position:0% +will be large +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +you know if you're doing this in an + + align:start position:0% +you know if you're doing this in an + + + align:start position:0% +you know if you're doing this in an +industrial setting + + align:start position:0% +industrial setting + + + align:start position:0% +industrial setting +you're in control of where the light + + align:start position:0% +you're in control of where the light + + + align:start position:0% +you're in control of where the light +sources go so that that's all you need + + align:start position:0% +sources go so that that's all you need + + + align:start position:0% +sources go so that that's all you need +to know that + + align:start position:0% +to know that + + + align:start position:0% +to know that +you know don't don't make them co-planar + + align:start position:0% +you know don't don't make them co-planar + + + align:start position:0% +you know don't don't make them co-planar +um and uh + + align:start position:0% +um and uh + + + align:start position:0% +um and uh +probably if the closer you can get to + + align:start position:0% +probably if the closer you can get to + + + align:start position:0% +probably if the closer you can get to +this arrangement the better where + + align:start position:0% +this arrangement the better where + + + align:start position:0% +this arrangement the better where +they're actually at right angles to each + + align:start position:0% +they're actually at right angles to each + + + align:start position:0% +they're actually at right angles to each +other + + align:start position:0% +other + + + align:start position:0% +other +so this is where + + align:start position:0% +so this is where + + + align:start position:0% +so this is where +i want to talk briefly about + + align:start position:0% + + + + align:start position:0% + +the earth moon and the sun so + + align:start position:0% + + + + align:start position:0% + +so let's suppose that the moon is made + + align:start position:0% +so let's suppose that the moon is made + + + align:start position:0% +so let's suppose that the moon is made +of green cheese and green cheese has a + + align:start position:0% +of green cheese and green cheese has a + + + align:start position:0% +of green cheese and green cheese has a +lamborghini reflecting property + + align:start position:0% +lamborghini reflecting property + + + align:start position:0% +lamborghini reflecting property +and so we're on earth and we're trying + + align:start position:0% +and so we're on earth and we're trying + + + align:start position:0% +and so we're on earth and we're trying +to + + align:start position:0% +to + + + align:start position:0% +to +get a topographic map of the moon + + align:start position:0% +get a topographic map of the moon + + + align:start position:0% +get a topographic map of the moon +which would be useful thing to do before + + align:start position:0% +which would be useful thing to do before + + + align:start position:0% +which would be useful thing to do before +people land there and of course now we + + align:start position:0% +people land there and of course now we + + + align:start position:0% +people land there and of course now we +we did a long time ago but before people + + align:start position:0% +we did a long time ago but before people + + + align:start position:0% +we did a long time ago but before people +landed there there's a lot of + + align:start position:0% +landed there there's a lot of + + + align:start position:0% +landed there there's a lot of +uncertainty you know people didn't know + + align:start position:0% +uncertainty you know people didn't know + + + align:start position:0% +uncertainty you know people didn't know +for example whether + + align:start position:0% +for example whether + + + align:start position:0% +for example whether +the solar wind had pummeled the surface + + align:start position:0% +the solar wind had pummeled the surface + + + align:start position:0% +the solar wind had pummeled the surface +to such an extent that there was you + + align:start position:0% +to such an extent that there was you + + + align:start position:0% +to such an extent that there was you +know 10 meters of dust and if you're + + align:start position:0% +know 10 meters of dust and if you're + + + align:start position:0% +know 10 meters of dust and if you're +landing on it you'll just disappear into + + align:start position:0% +landing on it you'll just disappear into + + + align:start position:0% +landing on it you'll just disappear into +that dust so anyway so there was a lot + + align:start position:0% +that dust so anyway so there was a lot + + + align:start position:0% +that dust so anyway so there was a lot +of interest in trying to figure out you + + align:start position:0% +of interest in trying to figure out you + + + align:start position:0% +of interest in trying to figure out you +know how how tall are these craters i + + align:start position:0% +know how how tall are these craters i + + + align:start position:0% +know how how tall are these craters i +mean we can see these nice craters but + + align:start position:0% +mean we can see these nice craters but + + + align:start position:0% +mean we can see these nice craters but +what's the slope we don't want to land + + align:start position:0% +what's the slope we don't want to land + + + align:start position:0% +what's the slope we don't want to land +on something that has a very large slope + + align:start position:0% +on something that has a very large slope + + + align:start position:0% +on something that has a very large slope +so it would be really great if we could + + align:start position:0% +so it would be really great if we could + + + align:start position:0% +so it would be really great if we could +use photometric stereo + + align:start position:0% +use photometric stereo + + + align:start position:0% +use photometric stereo +and uh because the sun does illuminate + + align:start position:0% +and uh because the sun does illuminate + + + align:start position:0% +and uh because the sun does illuminate +the moon in different ways different + + align:start position:0% +the moon in different ways different + + + align:start position:0% +the moon in different ways different +parts of the cycle so you know here + + align:start position:0% +parts of the cycle so you know here + + + align:start position:0% +parts of the cycle so you know here +as you + + align:start position:0% +as you + + + align:start position:0% +as you +uh know + + align:start position:0% +uh know + + + align:start position:0% +uh know +the moon is always + + align:start position:0% +the moon is always + + + align:start position:0% +the moon is always +showing the same face uh to the earth + + align:start position:0% +showing the same face uh to the earth + + + align:start position:0% +showing the same face uh to the earth +and the other side which is stupidly + + align:start position:0% +and the other side which is stupidly + + + align:start position:0% +and the other side which is stupidly +called the dark side of the moon + + align:start position:0% +called the dark side of the moon + + + align:start position:0% +called the dark side of the moon +is not visible from the earth + + align:start position:0% +is not visible from the earth + + + align:start position:0% +is not visible from the earth +and so if you think about let's take a + + align:start position:0% +and so if you think about let's take a + + + align:start position:0% +and so if you think about let's take a +particular point here uh + + align:start position:0% +particular point here uh + + + align:start position:0% +particular point here uh +while it's in the cycle here the the sun + + align:start position:0% +while it's in the cycle here the the sun + + + align:start position:0% +while it's in the cycle here the the sun +is uh over there uh but here uh the sun + + align:start position:0% +is uh over there uh but here uh the sun + + + align:start position:0% +is uh over there uh but here uh the sun +is in that direction and here the sun is + + align:start position:0% +is in that direction and here the sun is + + + align:start position:0% +is in that direction and here the sun is +in that direction + + align:start position:0% +in that direction + + + align:start position:0% +in that direction +so we could easily arrange + + align:start position:0% +so we could easily arrange + + + align:start position:0% +so we could easily arrange +you know 3 10 + + align:start position:0% +you know 3 10 + + + align:start position:0% +you know 3 10 +however many measurements at different + + align:start position:0% +however many measurements at different + + + align:start position:0% +however many measurements at different +positions in the orbit + + align:start position:0% +positions in the orbit + + + align:start position:0% +positions in the orbit +and we can use this method + + align:start position:0% +and we can use this method + + + align:start position:0% +and we can use this method +well there's some assumptions one of + + align:start position:0% +well there's some assumptions one of + + + align:start position:0% +well there's some assumptions one of +them is that it's + + align:start position:0% +them is that it's + + + align:start position:0% +them is that it's +has lambertian reflectance which which + + align:start position:0% +has lambertian reflectance which which + + + align:start position:0% +has lambertian reflectance which which +it doesn't but we'll + + align:start position:0% +it doesn't but we'll + + + align:start position:0% +it doesn't but we'll +we'll try and fix that later + + align:start position:0% +we'll try and fix that later + + + align:start position:0% +we'll try and fix that later +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +annoyingly + + align:start position:0% +annoyingly + + + align:start position:0% +annoyingly +it doesn't work + + align:start position:0% +it doesn't work + + + align:start position:0% +it doesn't work +and the reason is that + + align:start position:0% +and the reason is that + + + align:start position:0% +and the reason is that +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +this plane here + + align:start position:0% +this plane here + + + align:start position:0% +this plane here +that + + align:start position:0% +that + + + align:start position:0% +that +contains the moon's orbit is the same is + + align:start position:0% +contains the moon's orbit is the same is + + + align:start position:0% +contains the moon's orbit is the same is +pretty much the same plane as the plane + + align:start position:0% +pretty much the same plane as the plane + + + align:start position:0% +pretty much the same plane as the plane +that contains the orbit of the earth + + align:start position:0% +that contains the orbit of the earth + + + align:start position:0% +that contains the orbit of the earth +around the sun + + align:start position:0% +around the sun + + + align:start position:0% +around the sun +so + + align:start position:0% +so + + + align:start position:0% +so +you can see what's going to happen that + + align:start position:0% +you can see what's going to happen that + + + align:start position:0% +you can see what's going to happen that +these three vectors or more + + align:start position:0% +these three vectors or more + + + align:start position:0% +these three vectors or more +uh are coplanar or almost coplanar i + + align:start position:0% +uh are coplanar or almost coplanar i + + + align:start position:0% +uh are coplanar or almost coplanar i +mean the the moon's orbit is a couple of + + align:start position:0% +mean the the moon's orbit is a couple of + + + align:start position:0% +mean the the moon's orbit is a couple of +degrees off the + + align:start position:0% +degrees off the + + + align:start position:0% +degrees off the +earth orbit around the sun so you get a + + align:start position:0% +earth orbit around the sun so you get a + + + align:start position:0% +earth orbit around the sun so you get a +tiny change but it's not enough to make + + align:start position:0% +tiny change but it's not enough to make + + + align:start position:0% +tiny change but it's not enough to make +a useful measurement + + align:start position:0% +a useful measurement + + + align:start position:0% +a useful measurement +and so um + + align:start position:0% +and so um + + + align:start position:0% +and so um +you know it's amazing we've just done + + align:start position:0% +you know it's amazing we've just done + + + align:start position:0% +you know it's amazing we've just done +something very simple here and we've + + align:start position:0% +something very simple here and we've + + + align:start position:0% +something very simple here and we've +already reached a very profound + + align:start position:0% +already reached a very profound + + + align:start position:0% +already reached a very profound +conclusion which is that + + align:start position:0% +conclusion which is that + + + align:start position:0% +conclusion which is that +you can't get the moon's topography + + align:start position:0% +you can't get the moon's topography + + + align:start position:0% +you can't get the moon's topography +from earth measurements + + align:start position:0% +from earth measurements + + + align:start position:0% +from earth measurements +as it goes through its orbit and + + align:start position:0% +as it goes through its orbit and + + + align:start position:0% +as it goes through its orbit and +different parts are illuminated + + align:start position:0% +different parts are illuminated + + + align:start position:0% +different parts are illuminated +differently as it does so + + align:start position:0% +differently as it does so + + + align:start position:0% +differently as it does so +which is you know a + + align:start position:0% +which is you know a + + + align:start position:0% +which is you know a +pretty amazing thing um + + align:start position:0% +pretty amazing thing um + + + align:start position:0% +pretty amazing thing um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +let's talk a little bit about the + + align:start position:0% +let's talk a little bit about the + + + align:start position:0% +let's talk a little bit about the +lamborghini assumption + + align:start position:0% +lamborghini assumption + + + align:start position:0% +lamborghini assumption +so lambert was his monk + + align:start position:0% +so lambert was his monk + + + align:start position:0% +so lambert was his monk +and uh he did these experiments + + align:start position:0% +and uh he did these experiments + + + align:start position:0% +and uh he did these experiments +now why was he a monk well because there + + align:start position:0% +now why was he a monk well because there + + + align:start position:0% +now why was he a monk well because there +was a time in our history + + align:start position:0% +was a time in our history + + + align:start position:0% +was a time in our history +in the western world where the only + + align:start position:0% +in the western world where the only + + + align:start position:0% +in the western world where the only +people who could learn anything were in + + align:start position:0% +people who could learn anything were in + + + align:start position:0% +people who could learn anything were in +in the religious domain + + align:start position:0% +in the religious domain + + + align:start position:0% +in the religious domain +you know + + align:start position:0% +you know + + + align:start position:0% +you know +ordinary people + + align:start position:0% +ordinary people + + + align:start position:0% +ordinary people +uh couldn't read or write and they + + align:start position:0% +uh couldn't read or write and they + + + align:start position:0% +uh couldn't read or write and they +weren't allowed to read or write and and + + align:start position:0% +weren't allowed to read or write and and + + + align:start position:0% +weren't allowed to read or write and and +monks did all these interesting things + + align:start position:0% +monks did all these interesting things + + + align:start position:0% +monks did all these interesting things +like you know figure out how to brew rum + + align:start position:0% +like you know figure out how to brew rum + + + align:start position:0% +like you know figure out how to brew rum +and whatnot and + + align:start position:0% +and whatnot and + + + align:start position:0% +and whatnot and +and this particular guy + + align:start position:0% +and this particular guy + + + align:start position:0% +and this particular guy +he + + align:start position:0% +he + + + align:start position:0% +he +you know had wrapped up his + + align:start position:0% +you know had wrapped up his + + + align:start position:0% +you know had wrapped up his +lunch in paper + + align:start position:0% +lunch in paper + + + align:start position:0% +lunch in paper +and it contained some oily fish and so a + + align:start position:0% +and it contained some oily fish and so a + + + align:start position:0% +and it contained some oily fish and so a +piece of the paper + + align:start position:0% +piece of the paper + + + align:start position:0% +piece of the paper +was infused with oil and i think you've + + align:start position:0% +was infused with oil and i think you've + + + align:start position:0% +was infused with oil and i think you've +seen this wise piece of paper with some + + align:start position:0% +seen this wise piece of paper with some + + + align:start position:0% +seen this wise piece of paper with some +oil on it the oil looks kind of oily + + align:start position:0% +oil on it the oil looks kind of oily + + + align:start position:0% +oil on it the oil looks kind of oily +area looks kind of darker + + align:start position:0% +area looks kind of darker + + + align:start position:0% +area looks kind of darker +and then if you hold it up and move it + + align:start position:0% +and then if you hold it up and move it + + + align:start position:0% +and then if you hold it up and move it +around you see that it has different + + align:start position:0% +around you see that it has different + + + align:start position:0% +around you see that it has different +reflecting and transmitting properties + + align:start position:0% +reflecting and transmitting properties + + + align:start position:0% +reflecting and transmitting properties +and so what he discovered was that he + + align:start position:0% +and so what he discovered was that he + + + align:start position:0% +and so what he discovered was that he +could make measurements of light + + align:start position:0% +could make measurements of light + + + align:start position:0% +could make measurements of light +using this tool this you know + + align:start position:0% +using this tool this you know + + + align:start position:0% +using this tool this you know +today of course we'd use a you know 100 + + align:start position:0% +today of course we'd use a you know 100 + + + align:start position:0% +today of course we'd use a you know 100 +000 computer and + + align:start position:0% +000 computer and + + + align:start position:0% +000 computer and +pin photodiodes and + + align:start position:0% +pin photodiodes and + + + align:start position:0% +pin photodiodes and +he used the piece of paper + + align:start position:0% +he used the piece of paper + + + align:start position:0% +he used the piece of paper +and so the idea the idea is this so + + align:start position:0% +and so the idea the idea is this so + + + align:start position:0% +and so the idea the idea is this so +here's our piece of paper and here's the + + align:start position:0% +here's our piece of paper and here's the + + + align:start position:0% +here's our piece of paper and here's the +fatty spot + + align:start position:0% +fatty spot + + + align:start position:0% +fatty spot +and what happens is that the paper is + + align:start position:0% +and what happens is that the paper is + + + align:start position:0% +and what happens is that the paper is +not absorbing any light it's it's a + + align:start position:0% +not absorbing any light it's it's a + + + align:start position:0% +not absorbing any light it's it's a +white paper i mean ideally it could + + align:start position:0% +white paper i mean ideally it could + + + align:start position:0% +white paper i mean ideally it could +absorb a little bit but let's assume it + + align:start position:0% +absorb a little bit but let's assume it + + + align:start position:0% +absorb a little bit but let's assume it +absorbs none so it only has sort of two + + align:start position:0% +absorbs none so it only has sort of two + + + align:start position:0% +absorbs none so it only has sort of two +choices the one is sunlight + + align:start position:0% +choices the one is sunlight + + + align:start position:0% +choices the one is sunlight +arrives and is reflected back + + align:start position:0% +arrives and is reflected back + + + align:start position:0% +arrives and is reflected back +and a little bit of it goes through to + + align:start position:0% +and a little bit of it goes through to + + + align:start position:0% +and a little bit of it goes through to +the other side + + align:start position:0% + + + + align:start position:0% + +now in the fatty part + + align:start position:0% +now in the fatty part + + + align:start position:0% +now in the fatty part +some light arrives + + align:start position:0% +some light arrives + + + align:start position:0% +some light arrives +and a little bit of it is reflected back + + align:start position:0% +and a little bit of it is reflected back + + + align:start position:0% +and a little bit of it is reflected back +but a lot goes through + + align:start position:0% + + + + align:start position:0% + +okay so that's the difference about the + + align:start position:0% +okay so that's the difference about the + + + align:start position:0% +okay so that's the difference about the +two parts the fat the fatty + + align:start position:0% +two parts the fat the fatty + + + align:start position:0% +two parts the fat the fatty +substance basically fills in the air + + align:start position:0% +substance basically fills in the air + + + align:start position:0% +substance basically fills in the air +voids and so the surface is no longer as + + align:start position:0% +voids and so the surface is no longer as + + + align:start position:0% +voids and so the surface is no longer as +reflective as before but it's not an + + align:start position:0% +reflective as before but it's not an + + + align:start position:0% +reflective as before but it's not an +absorbing material so what happens is + + align:start position:0% +absorbing material so what happens is + + + align:start position:0% +absorbing material so what happens is +the light just goes through okay so why + + align:start position:0% +the light just goes through okay so why + + + align:start position:0% +the light just goes through okay so why +would this be of interest well it allows + + align:start position:0% +would this be of interest well it allows + + + align:start position:0% +would this be of interest well it allows +you to compare + + align:start position:0% +you to compare + + + align:start position:0% +you to compare +two + + align:start position:0% +two + + + align:start position:0% +two +illumination + + align:start position:0% +illumination + + + align:start position:0% +illumination +intensities + + align:start position:0% +intensities + + + align:start position:0% +intensities +and you do it basically by illuminating + + align:start position:0% +and you do it basically by illuminating + + + align:start position:0% +and you do it basically by illuminating +this side + + align:start position:0% + + + + align:start position:0% + +with one sauce + + align:start position:0% +with one sauce + + + align:start position:0% +with one sauce +and this side with the other sauce + + align:start position:0% +and this side with the other sauce + + + align:start position:0% +and this side with the other sauce +and then you balance it so that you + + align:start position:0% +and then you balance it so that you + + + align:start position:0% +and then you balance it so that you +can't see the fatty spot + + align:start position:0% +can't see the fatty spot + + + align:start position:0% +can't see the fatty spot +right because + + align:start position:0% +right because + + + align:start position:0% +right because +when can that happen well we could write + + align:start position:0% +when can that happen well we could write + + + align:start position:0% +when can that happen well we could write +out equations but i think you can see + + align:start position:0% +out equations but i think you can see + + + align:start position:0% +out equations but i think you can see +what's going to happen is if the same + + align:start position:0% +what's going to happen is if the same + + + align:start position:0% +what's going to happen is if the same +amount of lights coming in from this + + align:start position:0% +amount of lights coming in from this + + + align:start position:0% +amount of lights coming in from this +side as from that side + + align:start position:0% +side as from that side + + + align:start position:0% +side as from that side +then um these will balance that this + + align:start position:0% +then um these will balance that this + + + align:start position:0% +then um these will balance that this +this will appear equally bright when + + align:start position:0% +this will appear equally bright when + + + align:start position:0% +this will appear equally bright when +looked at from here as that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's a very powerful idea and he + + align:start position:0% +so that's a very powerful idea and he + + + align:start position:0% +so that's a very powerful idea and he +didn't really do this with his lunch + + align:start position:0% +didn't really do this with his lunch + + + align:start position:0% +didn't really do this with his lunch +paper but you know + + align:start position:0% +paper but you know + + + align:start position:0% +paper but you know +that was + + align:start position:0% +that was + + + align:start position:0% +that was +where he went he had white paper which + + align:start position:0% +where he went he had white paper which + + + align:start position:0% +where he went he had white paper which +was pretty precious at the time you may + + align:start position:0% +was pretty precious at the time you may + + + align:start position:0% +was pretty precious at the time you may +remember that people would sometimes + + align:start position:0% +remember that people would sometimes + + + align:start position:0% +remember that people would sometimes +you know write something and then + + align:start position:0% +you know write something and then + + + align:start position:0% +you know write something and then +because paper was expensive they would + + align:start position:0% +because paper was expensive they would + + + align:start position:0% +because paper was expensive they would +write something at 45 degrees on top of + + align:start position:0% +write something at 45 degrees on top of + + + align:start position:0% +write something at 45 degrees on top of +it and maybe more so anyway he had this + + align:start position:0% +it and maybe more so anyway he had this + + + align:start position:0% +it and maybe more so anyway he had this +nice piece of paper and this way he + + align:start position:0% +nice piece of paper and this way he + + + align:start position:0% +nice piece of paper and this way he +could + + align:start position:0% +could + + + align:start position:0% +could +compare brightness and one of the things + + align:start position:0% +compare brightness and one of the things + + + align:start position:0% +compare brightness and one of the things +you can do then is get the inverse + + align:start position:0% +you can do then is get the inverse + + + align:start position:0% +you can do then is get the inverse +square law + + align:start position:0% +square law + + + align:start position:0% +square law +so he might put four candles on this + + align:start position:0% +so he might put four candles on this + + + align:start position:0% +so he might put four candles on this +side + + align:start position:0% +side + + + align:start position:0% +side +and one + + align:start position:0% +and one + + + align:start position:0% +and one +at + + align:start position:0% +at + + + align:start position:0% +at +two at twice the distance as one candle + + align:start position:0% +two at twice the distance as one candle + + + align:start position:0% +two at twice the distance as one candle +on this side right + + align:start position:0% +on this side right + + + align:start position:0% +on this side right +and so it should match right so so he + + align:start position:0% +and so it should match right so so he + + + align:start position:0% +and so it should match right so so he +was able to do all of these amazing + + align:start position:0% +was able to do all of these amazing + + + align:start position:0% +was able to do all of these amazing +experiments um with this very simple + + align:start position:0% +experiments um with this very simple + + + align:start position:0% +experiments um with this very simple +apparatus + + align:start position:0% +apparatus + + + align:start position:0% +apparatus +um and um get the inverse square law + + align:start position:0% +um and um get the inverse square law + + + align:start position:0% +um and um get the inverse square law +and of course you know people like + + align:start position:0% +and of course you know people like + + + align:start position:0% +and of course you know people like +newton would say well it's obvious you + + align:start position:0% +newton would say well it's obvious you + + + align:start position:0% +newton would say well it's obvious you +don't need to do an experiment it's + + align:start position:0% +don't need to do an experiment it's + + + align:start position:0% +don't need to do an experiment it's +just the energy is going over the + + align:start position:0% +just the energy is going over the + + + align:start position:0% +just the energy is going over the +surface of a sphere and the surface of + + align:start position:0% +surface of a sphere and the surface of + + + align:start position:0% +surface of a sphere and the surface of +the sphere is 4 pi r squared ah r + + align:start position:0% +the sphere is 4 pi r squared ah r + + + align:start position:0% +the sphere is 4 pi r squared ah r +squared so anyway + + align:start position:0% +squared so anyway + + + align:start position:0% +squared so anyway +so then the next thing he did was he + + align:start position:0% +so then the next thing he did was he + + + align:start position:0% +so then the next thing he did was he +wondered how surfaces reflect light when + + align:start position:0% +wondered how surfaces reflect light when + + + align:start position:0% +wondered how surfaces reflect light when +they illuminated from different + + align:start position:0% +they illuminated from different + + + align:start position:0% +they illuminated from different +directions + + align:start position:0% +directions + + + align:start position:0% +directions +and using methods like this he came up + + align:start position:0% +and using methods like this he came up + + + align:start position:0% +and using methods like this he came up +with uh + + align:start position:0% +with uh + + + align:start position:0% +with uh +what's now called lambert's law + + align:start position:0% + + + + align:start position:0% + +which is that it's a cosine of incident + + align:start position:0% +which is that it's a cosine of incident + + + align:start position:0% +which is that it's a cosine of incident +angle + + align:start position:0% + + + + align:start position:0% + +the brightness is proportional cosine of + + align:start position:0% +the brightness is proportional cosine of + + + align:start position:0% +the brightness is proportional cosine of +incident angle now of course + + align:start position:0% +incident angle now of course + + + align:start position:0% +incident angle now of course +part of that is again not something that + + align:start position:0% +part of that is again not something that + + + align:start position:0% +part of that is again not something that +you need to do an experiment about we + + align:start position:0% +you need to do an experiment about we + + + align:start position:0% +you need to do an experiment about we +already talked about foreshortening and + + align:start position:0% +already talked about foreshortening and + + + align:start position:0% +already talked about foreshortening and +we know that the amount of light falling + + align:start position:0% +we know that the amount of light falling + + + align:start position:0% +we know that the amount of light falling +on the surface varies as the cosine of + + align:start position:0% +on the surface varies as the cosine of + + + align:start position:0% +on the surface varies as the cosine of +the incident angle + + align:start position:0% +the incident angle + + + align:start position:0% +the incident angle +but what's what he uh talked about was + + align:start position:0% +but what's what he uh talked about was + + + align:start position:0% +but what's what he uh talked about was +how bright does it look in other words + + align:start position:0% +how bright does it look in other words + + + align:start position:0% +how bright does it look in other words +how much light does it reflect and in + + align:start position:0% +how much light does it reflect and in + + + align:start position:0% +how much light does it reflect and in +what direction + + align:start position:0% +what direction + + + align:start position:0% +what direction +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now to um + + align:start position:0% +now to um + + + align:start position:0% +now to um +to talk about this in more detail we + + align:start position:0% +to talk about this in more detail we + + + align:start position:0% +to talk about this in more detail we +need to have a way of talking about + + align:start position:0% +need to have a way of talking about + + + align:start position:0% +need to have a way of talking about +surface orientation + + align:start position:0% +surface orientation + + + align:start position:0% +surface orientation +because the brightness is going to + + align:start position:0% +because the brightness is going to + + + align:start position:0% +because the brightness is going to +depend on surface orientation + + align:start position:0% +depend on surface orientation + + + align:start position:0% +depend on surface orientation +and + + align:start position:0% +and + + + align:start position:0% +and +and it may do so in a more complicated + + align:start position:0% +and it may do so in a more complicated + + + align:start position:0% +and it may do so in a more complicated +way than lambert + + align:start position:0% +way than lambert + + + align:start position:0% +way than lambert +i mean i put law in quotation marks + + align:start position:0% +i mean i put law in quotation marks + + + align:start position:0% +i mean i put law in quotation marks +because it's not a law it's + + align:start position:0% +because it's not a law it's + + + align:start position:0% +because it's not a law it's +a phenomenological model + + align:start position:0% +a phenomenological model + + + align:start position:0% +a phenomenological model +what does that mean that means that you + + align:start position:0% +what does that mean that means that you + + + align:start position:0% +what does that mean that means that you +kind of postulate a particular way + + align:start position:0% +kind of postulate a particular way + + + align:start position:0% +kind of postulate a particular way +something behaves + + align:start position:0% +something behaves + + + align:start position:0% +something behaves +and then give it a name and it's not + + align:start position:0% +and then give it a name and it's not + + + align:start position:0% +and then give it a name and it's not +like + + align:start position:0% +like + + + align:start position:0% +like +you know there's a real surface that + + align:start position:0% +you know there's a real surface that + + + align:start position:0% +you know there's a real surface that +does exactly this many real surfaces + + align:start position:0% +does exactly this many real surfaces + + + align:start position:0% +does exactly this many real surfaces +like paper are good approximations but + + align:start position:0% +like paper are good approximations but + + + align:start position:0% +like paper are good approximations but +they don't do exactly that + + align:start position:0% +they don't do exactly that + + + align:start position:0% +they don't do exactly that +okay we already talked a little bit + + align:start position:0% +okay we already talked a little bit + + + align:start position:0% +okay we already talked a little bit +about talking about surface orientation + + align:start position:0% + + + + align:start position:0% + +we said that + + align:start position:0% +we said that + + + align:start position:0% +we said that +we can erect a unit normal + + align:start position:0% +we can erect a unit normal + + + align:start position:0% +we can erect a unit normal +so + + align:start position:0% + + + + align:start position:0% + +so here's a little patch of the surface + + align:start position:0% +so here's a little patch of the surface + + + align:start position:0% +so here's a little patch of the surface +and we've erected something that's + + align:start position:0% +and we've erected something that's + + + align:start position:0% +and we've erected something that's +perpendicular to the surface and that's + + align:start position:0% +perpendicular to the surface and that's + + + align:start position:0% +perpendicular to the surface and that's +a way of talking about orientation and + + align:start position:0% +a way of talking about orientation and + + + align:start position:0% +a way of talking about orientation and +we mentioned that it has two degrees of + + align:start position:0% +we mentioned that it has two degrees of + + + align:start position:0% +we mentioned that it has two degrees of +freedom because it's a three vector but + + align:start position:0% +freedom because it's a three vector but + + + align:start position:0% +freedom because it's a three vector but +there's a constraint that is a unit + + align:start position:0% +there's a constraint that is a unit + + + align:start position:0% +there's a constraint that is a unit +vector so two minus one three minus one + + align:start position:0% +vector so two minus one three minus one + + + align:start position:0% +vector so two minus one three minus one +is two + + align:start position:0% +is two + + + align:start position:0% +is two +so that's one way of talking about it + + align:start position:0% +so that's one way of talking about it + + + align:start position:0% +so that's one way of talking about it +and for an extended surface you can + + align:start position:0% +and for an extended surface you can + + + align:start position:0% +and for an extended surface you can +imagine that + + align:start position:0% +imagine that + + + align:start position:0% +imagine that +you know we do this for little facets + + align:start position:0% +you know we do this for little facets + + + align:start position:0% +you know we do this for little facets +all over the surface and they'll all be + + align:start position:0% +all over the surface and they'll all be + + + align:start position:0% +all over the surface and they'll all be +pointing different ways + + align:start position:0% +pointing different ways + + + align:start position:0% +pointing different ways +but if you pick a small enough area + + align:start position:0% +but if you pick a small enough area + + + align:start position:0% +but if you pick a small enough area +as long as the surface is reasonably + + align:start position:0% +as long as the surface is reasonably + + + align:start position:0% +as long as the surface is reasonably +smooth + + align:start position:0% +smooth + + + align:start position:0% +smooth +then + + align:start position:0% +then + + + align:start position:0% +then +we we can + + align:start position:0% +we we can + + + align:start position:0% +we we can +reduce it to this case + + align:start position:0% +reduce it to this case + + + align:start position:0% +reduce it to this case +and you know we have to exclude things + + align:start position:0% +and you know we have to exclude things + + + align:start position:0% +and you know we have to exclude things +that + + align:start position:0% +that + + + align:start position:0% +that +mathematicians will construct like a + + align:start position:0% +mathematicians will construct like a + + + align:start position:0% +mathematicians will construct like a +surface that + + align:start position:0% +surface that + + + align:start position:0% +surface that +you know one + + align:start position:0% +you know one + + + align:start position:0% +you know one +where x is a rational number and 0 where + + align:start position:0% +where x is a rational number and 0 where + + + align:start position:0% +where x is a rational number and 0 where +x is an irrational number we can't do + + align:start position:0% +x is an irrational number we can't do + + + align:start position:0% +x is an irrational number we can't do +that there but but for real surfaces we + + align:start position:0% +that there but but for real surfaces we + + + align:start position:0% +that there but but for real surfaces we +can facet it and for different facets we + + align:start position:0% +can facet it and for different facets we + + + align:start position:0% +can facet it and for different facets we +can do that + + align:start position:0% +can do that + + + align:start position:0% +can do that +then we also mentioned since it's a unit + + align:start position:0% +then we also mentioned since it's a unit + + + align:start position:0% +then we also mentioned since it's a unit +vector + + align:start position:0% +vector + + + align:start position:0% +vector +we can talk about orientation in terms + + align:start position:0% +we can talk about orientation in terms + + + align:start position:0% +we can talk about orientation in terms +of point on the unit sphere and we'll + + align:start position:0% +of point on the unit sphere and we'll + + + align:start position:0% +of point on the unit sphere and we'll +find that pretty handy later on you know + + align:start position:0% +find that pretty handy later on you know + + + align:start position:0% +find that pretty handy later on you know +for example if you want to talk about + + align:start position:0% +for example if you want to talk about + + + align:start position:0% +for example if you want to talk about +all possible orientations + + align:start position:0% +all possible orientations + + + align:start position:0% +all possible orientations +well that's the whole surface of the + + align:start position:0% +well that's the whole surface of the + + + align:start position:0% +well that's the whole surface of the +sphere + + align:start position:0% +sphere + + + align:start position:0% +sphere +or you know there's certain operations + + align:start position:0% +or you know there's certain operations + + + align:start position:0% +or you know there's certain operations +that we'll be doing on the surface of + + align:start position:0% +that we'll be doing on the surface of + + + align:start position:0% +that we'll be doing on the surface of +the sphere so those are representations + + align:start position:0% +the sphere so those are representations + + + align:start position:0% +the sphere so those are representations +but we we need something else so + + align:start position:0% + + + + align:start position:0% + +let's look at this so here's a taylor + + align:start position:0% +let's look at this so here's a taylor + + + align:start position:0% +let's look at this so here's a taylor +series expansion + + align:start position:0% + + + + align:start position:0% + +right where + + align:start position:0% +right where + + + align:start position:0% +right where +the dots indicate higher order terms + + align:start position:0% +the dots indicate higher order terms + + + align:start position:0% +the dots indicate higher order terms +which we can ignore as long as we make + + align:start position:0% +which we can ignore as long as we make + + + align:start position:0% +which we can ignore as long as we make +the + + align:start position:0% +the + + + align:start position:0% +the +infinitesimals small enough + + align:start position:0% +infinitesimals small enough + + + align:start position:0% +infinitesimals small enough +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now to + + align:start position:0% + + + + align:start position:0% + +so the difference of these two + + align:start position:0% +so the difference of these two + + + align:start position:0% +so the difference of these two +we can write as delta z so + + align:start position:0% + + + + align:start position:0% + +so that's the same equation + + align:start position:0% +so that's the same equation + + + align:start position:0% +so that's the same equation +and then + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +just as + + align:start position:0% +just as + + + align:start position:0% +just as +so i'm introducing p and q as shorthands + + align:start position:0% +so i'm introducing p and q as shorthands + + + align:start position:0% +so i'm introducing p and q as shorthands +for + + align:start position:0% +for + + + align:start position:0% +for +these + + align:start position:0% +these + + + align:start position:0% +these +derivatives + + align:start position:0% + + + + align:start position:0% + +and this is just analogous to what we've + + align:start position:0% +and this is just analogous to what we've + + + align:start position:0% +and this is just analogous to what we've +done before where + + align:start position:0% +done before where + + + align:start position:0% +done before where +you know we introduced u and b as + + align:start position:0% +you know we introduced u and b as + + + align:start position:0% +you know we introduced u and b as +shorthand for dx dt and dydt + + align:start position:0% +shorthand for dx dt and dydt + + + align:start position:0% +shorthand for dx dt and dydt +partly because it's too much bother + + align:start position:0% +partly because it's too much bother + + + align:start position:0% +partly because it's too much bother +writing all that stuff and partly + + align:start position:0% +writing all that stuff and partly + + + align:start position:0% +writing all that stuff and partly +because it makes it look too + + align:start position:0% +because it makes it look too + + + align:start position:0% +because it makes it look too +intimidating when it's actually very + + align:start position:0% +intimidating when it's actually very + + + align:start position:0% +intimidating when it's actually very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +so p and q are slopes + + align:start position:0% +so p and q are slopes + + + align:start position:0% +so p and q are slopes +and in fact p and q + + align:start position:0% +and in fact p and q + + + align:start position:0% +and in fact p and q +is the gradient on the surface + + align:start position:0% +is the gradient on the surface + + + align:start position:0% +is the gradient on the surface +so remember how i said that one way to + + align:start position:0% +so remember how i said that one way to + + + align:start position:0% +so remember how i said that one way to +think about an image is that it + + align:start position:0% +think about an image is that it + + + align:start position:0% +think about an image is that it +height above some + + align:start position:0% +height above some + + + align:start position:0% +height above some +ground level so we have x and y uh in + + align:start position:0% +ground level so we have x and y uh in + + + align:start position:0% +ground level so we have x and y uh in +the image plane and then we can plot the + + align:start position:0% +the image plane and then we can plot the + + + align:start position:0% +the image plane and then we can plot the +brightness as height above that and then + + align:start position:0% +brightness as height above that and then + + + align:start position:0% +brightness as height above that and then +when we talked about the brightness + + align:start position:0% +when we talked about the brightness + + + align:start position:0% +when we talked about the brightness +gradient e x e y i was saying that it's + + align:start position:0% +gradient e x e y i was saying that it's + + + align:start position:0% +gradient e x e y i was saying that it's +like the great gradient of that surface + + align:start position:0% +like the great gradient of that surface + + + align:start position:0% +like the great gradient of that surface +well here's a case where we actually are + + align:start position:0% +well here's a case where we actually are + + + align:start position:0% +well here's a case where we actually are +talking about a surface in 3d + + align:start position:0% +talking about a surface in 3d + + + align:start position:0% +talking about a surface in 3d +and this is its gradient it's you know z + + align:start position:0% +and this is its gradient it's you know z + + + align:start position:0% +and this is its gradient it's you know z +d x d z d y + + align:start position:0% +d x d z d y + + + align:start position:0% +d x d z d y +okay uh one way to + + align:start position:0% +okay uh one way to + + + align:start position:0% +okay uh one way to +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +make a picture of that is this + + align:start position:0% + + + + align:start position:0% + +okay so this is our surface with uni + + align:start position:0% +okay so this is our surface with uni + + + align:start position:0% +okay so this is our surface with uni +with normal vector + + align:start position:0% +with normal vector + + + align:start position:0% +with normal vector +and this edge is delta x and this edge + + align:start position:0% +and this edge is delta x and this edge + + + align:start position:0% +and this edge is delta x and this edge +is delta y + + align:start position:0% +is delta y + + + align:start position:0% +is delta y +and this part here is q + + align:start position:0% +and this part here is q + + + align:start position:0% +and this part here is q +delta y + + align:start position:0% +delta y + + + align:start position:0% +delta y +and this part is p delta x + + align:start position:0% +and this part is p delta x + + + align:start position:0% +and this part is p delta x +so this is a diagram that basically + + align:start position:0% +so this is a diagram that basically + + + align:start position:0% +so this is a diagram that basically +illustrates this idea + + align:start position:0% +illustrates this idea + + + align:start position:0% +illustrates this idea +i take a small step in the x direction + + align:start position:0% +i take a small step in the x direction + + + align:start position:0% +i take a small step in the x direction +delta x + + align:start position:0% +delta x + + + align:start position:0% +delta x +and the surface goes up + + align:start position:0% +and the surface goes up + + + align:start position:0% +and the surface goes up +by you know dz dx times the delta x + + align:start position:0% +by you know dz dx times the delta x + + + align:start position:0% +by you know dz dx times the delta x +then i take a small step in the y + + align:start position:0% +then i take a small step in the y + + + align:start position:0% +then i take a small step in the y +direction and the surface goes up by d z + + align:start position:0% +direction and the surface goes up by d z + + + align:start position:0% +direction and the surface goes up by d z +d y times delta y because it might go + + align:start position:0% +d y times delta y because it might go + + + align:start position:0% +d y times delta y because it might go +down just + + align:start position:0% +down just + + + align:start position:0% +down just +in this particular picture it goes up so + + align:start position:0% +in this particular picture it goes up so + + + align:start position:0% +in this particular picture it goes up so +this is another way of understanding + + align:start position:0% +this is another way of understanding + + + align:start position:0% +this is another way of understanding +what this equation is saying + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +we'll find that + + align:start position:0% +we'll find that + + + align:start position:0% +we'll find that +they're places where + + align:start position:0% +they're places where + + + align:start position:0% +they're places where +the unit normal notation works for us + + align:start position:0% +the unit normal notation works for us + + + align:start position:0% +the unit normal notation works for us +and they're places where the gradient + + align:start position:0% +and they're places where the gradient + + + align:start position:0% +and they're places where the gradient +notation works for us and so we need to + + align:start position:0% +notation works for us and so we need to + + + align:start position:0% +notation works for us and so we need to +have ways of switching back and forth + + align:start position:0% +have ways of switching back and forth + + + align:start position:0% +have ways of switching back and forth +and this is very common + + align:start position:0% +and this is very common + + + align:start position:0% +and this is very common +uh in you know computational problems + + align:start position:0% +uh in you know computational problems + + + align:start position:0% +uh in you know computational problems +where you know some problems are easily + + align:start position:0% +where you know some problems are easily + + + align:start position:0% +where you know some problems are easily +done in one domain and some are easily + + align:start position:0% +done in one domain and some are easily + + + align:start position:0% +done in one domain and some are easily +done in another domain so it ends up + + align:start position:0% +done in another domain so it ends up + + + align:start position:0% +done in another domain so it ends up +being a problem of conversion + + align:start position:0% +being a problem of conversion + + + align:start position:0% +being a problem of conversion +you know like + + align:start position:0% +you know like + + + align:start position:0% +you know like +cartesian coordinates to polar + + align:start position:0% +cartesian coordinates to polar + + + align:start position:0% +cartesian coordinates to polar +coordinates some things are easy to do + + align:start position:0% +coordinates some things are easy to do + + + align:start position:0% +coordinates some things are easy to do +in polar coordinates uh some are easy to + + align:start position:0% +in polar coordinates uh some are easy to + + + align:start position:0% +in polar coordinates uh some are easy to +do in cartesian coordinates so you just + + align:start position:0% +do in cartesian coordinates so you just + + + align:start position:0% +do in cartesian coordinates so you just +want to be able to convert back and + + align:start position:0% +want to be able to convert back and + + + align:start position:0% +want to be able to convert back and +forth + + align:start position:0% +forth + + + align:start position:0% +forth +and so same here so how are these + + align:start position:0% +and so same here so how are these + + + align:start position:0% +and so same here so how are these +related how is + + align:start position:0% +related how is + + + align:start position:0% +related how is +n + + align:start position:0% +n + + + align:start position:0% +n +related to p and q + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +one thing we can do is + + align:start position:0% +one thing we can do is + + + align:start position:0% +one thing we can do is +look at this surface which has a normal + + align:start position:0% +look at this surface which has a normal + + + align:start position:0% +look at this surface which has a normal +n + + align:start position:0% +n + + + align:start position:0% +n +any line in the surface has to be + + align:start position:0% +any line in the surface has to be + + + align:start position:0% +any line in the surface has to be +perpendicular to n right that's the + + align:start position:0% +perpendicular to n right that's the + + + align:start position:0% +perpendicular to n right that's the +whole idea of + + align:start position:0% +whole idea of + + + align:start position:0% +whole idea of +n is perpendicular to the surface + + align:start position:0% +n is perpendicular to the surface + + + align:start position:0% +n is perpendicular to the surface +meaning it's perpendicular to any line + + align:start position:0% +meaning it's perpendicular to any line + + + align:start position:0% +meaning it's perpendicular to any line +in that surface + + align:start position:0% +in that surface + + + align:start position:0% +in that surface +and + + align:start position:0% +and + + + align:start position:0% +and +if i have any two lines in the surface + + align:start position:0% +if i have any two lines in the surface + + + align:start position:0% +if i have any two lines in the surface +that are not the same + + align:start position:0% +that are not the same + + + align:start position:0% +that are not the same +then i'm done because right i got if n + + align:start position:0% +then i'm done because right i got if n + + + align:start position:0% +then i'm done because right i got if n +is perpendicular to two lines i can just + + align:start position:0% +is perpendicular to two lines i can just + + + align:start position:0% +is perpendicular to two lines i can just +take the cross product so + + align:start position:0% +take the cross product so + + + align:start position:0% +take the cross product so +right because the cross product of two + + align:start position:0% +right because the cross product of two + + + align:start position:0% +right because the cross product of two +vectors is perpendicular to both of + + align:start position:0% +vectors is perpendicular to both of + + + align:start position:0% +vectors is perpendicular to both of +those vectors so + + align:start position:0% +those vectors so + + + align:start position:0% +those vectors so +okay so i need to find some tangents in + + align:start position:0% +okay so i need to find some tangents in + + + align:start position:0% +okay so i need to find some tangents in +this surface + + align:start position:0% +this surface + + + align:start position:0% +this surface +well here's one this is an edge which + + align:start position:0% +well here's one this is an edge which + + + align:start position:0% +well here's one this is an edge which +lies in that surface + + align:start position:0% +lies in that surface + + + align:start position:0% +lies in that surface +and + + align:start position:0% +and + + + align:start position:0% +and +what is its uh direction + + align:start position:0% +what is its uh direction + + + align:start position:0% +what is its uh direction +well in in the x the x component of that + + align:start position:0% +well in in the x the x component of that + + + align:start position:0% +well in in the x the x component of that +vector + + align:start position:0% +vector + + + align:start position:0% +vector +is delta x it has no y component so + + align:start position:0% +is delta x it has no y component so + + + align:start position:0% +is delta x it has no y component so +that's zero + + align:start position:0% +that's zero + + + align:start position:0% +that's zero +and the + + align:start position:0% +and the + + + align:start position:0% +and the +z component is p delta x + + align:start position:0% +z component is p delta x + + + align:start position:0% +z component is p delta x +so that's that's a vector in the red + + align:start position:0% +so that's that's a vector in the red + + + align:start position:0% +so that's that's a vector in the red +direction and i can take the delta x + + align:start position:0% +direction and i can take the delta x + + + align:start position:0% +direction and i can take the delta x +outside + + align:start position:0% +outside + + + align:start position:0% +outside +because it's you know arbitrary length + + align:start position:0% +because it's you know arbitrary length + + + align:start position:0% +because it's you know arbitrary length +and i get + + align:start position:0% +and i get + + + align:start position:0% +and i get +that that vector so that's a tangent + + align:start position:0% +that that vector so that's a tangent + + + align:start position:0% +that that vector so that's a tangent +well i can get another one i can get + + align:start position:0% +well i can get another one i can get + + + align:start position:0% +well i can get another one i can get +this one here + + align:start position:0% +this one here + + + align:start position:0% +this one here +and + + align:start position:0% +and + + + align:start position:0% +and +that one + + align:start position:0% +that one + + + align:start position:0% +that one +if i move along that edge there's no + + align:start position:0% +if i move along that edge there's no + + + align:start position:0% +if i move along that edge there's no +change in x so this is zero + + align:start position:0% +change in x so this is zero + + + align:start position:0% +change in x so this is zero +there's a change in y right i'm moving + + align:start position:0% +there's a change in y right i'm moving + + + align:start position:0% +there's a change in y right i'm moving +along here so delta y + + align:start position:0% +along here so delta y + + + align:start position:0% +along here so delta y +and there's a change in height which is + + align:start position:0% +and there's a change in height which is + + + align:start position:0% +and there's a change in height which is +q + + align:start position:0% +q + + + align:start position:0% +q +delta y + + align:start position:0% +delta y + + + align:start position:0% +delta y +and so i can take the delta y of + + align:start position:0% + + + + align:start position:0% + +okay so what have i got + + align:start position:0% +okay so what have i got + + + align:start position:0% +okay so what have i got +i have two directions that lie in the + + align:start position:0% +i have two directions that lie in the + + + align:start position:0% +i have two directions that lie in the +surface + + align:start position:0% +surface + + + align:start position:0% +surface +and you know i could have picked some + + align:start position:0% +and you know i could have picked some + + + align:start position:0% +and you know i could have picked some +other directions those just happen to be + + align:start position:0% +other directions those just happen to be + + + align:start position:0% +other directions those just happen to be +very uh convenient to calculate + + align:start position:0% +very uh convenient to calculate + + + align:start position:0% +very uh convenient to calculate +and so what i need to do is take the + + align:start position:0% +and so what i need to do is take the + + + align:start position:0% +and so what i need to do is take the +cross product + + align:start position:0% + + + + align:start position:0% + +and that should be + + align:start position:0% +and that should be + + + align:start position:0% +and that should be +parallel to n + + align:start position:0% +parallel to n + + + align:start position:0% +parallel to n +i mean it'll have some size + + align:start position:0% +i mean it'll have some size + + + align:start position:0% +i mean it'll have some size +which we don't care about we're only + + align:start position:0% +which we don't care about we're only + + + align:start position:0% +which we don't care about we're only +worried about direction of that unit + + align:start position:0% +worried about direction of that unit + + + align:start position:0% +worried about direction of that unit +vector + + align:start position:0% +vector + + + align:start position:0% +vector +okay so what's that cross product + + align:start position:0% +okay so what's that cross product + + + align:start position:0% +okay so what's that cross product +i think it's uh minus p + + align:start position:0% +i think it's uh minus p + + + align:start position:0% +i think it's uh minus p +minus q1 + + align:start position:0% + + + + align:start position:0% + +so that's the connection between the two + + align:start position:0% +so that's the connection between the two + + + align:start position:0% +so that's the connection between the two +representations + + align:start position:0% +representations + + + align:start position:0% +representations +and now i can you know go a little bit + + align:start position:0% +and now i can you know go a little bit + + + align:start position:0% +and now i can you know go a little bit +further i can say the unit vector is + + align:start position:0% + + + + align:start position:0% + +just normalize it + + align:start position:0% + + + + align:start position:0% + +so if you give me p and q i can compute + + align:start position:0% +so if you give me p and q i can compute + + + align:start position:0% +so if you give me p and q i can compute +the unit normal n + + align:start position:0% +the unit normal n + + + align:start position:0% +the unit normal n +and i guess we also want to be able to + + align:start position:0% +and i guess we also want to be able to + + + align:start position:0% +and i guess we also want to be able to +go the other direction + + align:start position:0% +go the other direction + + + align:start position:0% +go the other direction +so p is minus n dot x + + align:start position:0% + + + + align:start position:0% + +so if i have to ever go the other + + align:start position:0% +so if i have to ever go the other + + + align:start position:0% +so if i have to ever go the other +direction i can do this + + align:start position:0% +direction i can do this + + + align:start position:0% +direction i can do this +and you know this looks sort of + + align:start position:0% +and you know this looks sort of + + + align:start position:0% +and you know this looks sort of +intimidating but it's just saying take + + align:start position:0% +intimidating but it's just saying take + + + align:start position:0% +intimidating but it's just saying take +the take the first component of n + + align:start position:0% +the take the first component of n + + + align:start position:0% +the take the first component of n +namely this minus p + + align:start position:0% +namely this minus p + + + align:start position:0% +namely this minus p +and divided by the last component of n + + align:start position:0% +and divided by the last component of n + + + align:start position:0% +and divided by the last component of n +which is one + + align:start position:0% +which is one + + + align:start position:0% +which is one +so why did i do that well because what + + align:start position:0% +so why did i do that well because what + + + align:start position:0% +so why did i do that well because what +if n isn't the unit vector + + align:start position:0% +if n isn't the unit vector + + + align:start position:0% +if n isn't the unit vector +then this will take care of it + + align:start position:0% +then this will take care of it + + + align:start position:0% +then this will take care of it +if it is a unit vector i don't need to + + align:start position:0% +if it is a unit vector i don't need to + + + align:start position:0% +if it is a unit vector i don't need to +be this fancy but + + align:start position:0% +be this fancy but + + + align:start position:0% +be this fancy but +okay so i can go back and forth between + + align:start position:0% +okay so i can go back and forth between + + + align:start position:0% +okay so i can go back and forth between +the two notations representing surface + + align:start position:0% +the two notations representing surface + + + align:start position:0% +the two notations representing surface +and what do i do with this well the + + align:start position:0% +and what do i do with this well the + + + align:start position:0% +and what do i do with this well the +great thing now is i have a way of + + align:start position:0% +great thing now is i have a way of + + + align:start position:0% +great thing now is i have a way of +mapping in the plane + + align:start position:0% +mapping in the plane + + + align:start position:0% +mapping in the plane +all possible surface orientations + + align:start position:0% +all possible surface orientations + + + align:start position:0% +all possible surface orientations +i already kind of had that because i had + + align:start position:0% +i already kind of had that because i had + + + align:start position:0% +i already kind of had that because i had +the sphere i said that you know all + + align:start position:0% +the sphere i said that you know all + + + align:start position:0% +the sphere i said that you know all +possible surface orientation correspond + + align:start position:0% +possible surface orientation correspond + + + align:start position:0% +possible surface orientation correspond +to points on the sphere trouble is you + + align:start position:0% +to points on the sphere trouble is you + + + align:start position:0% +to points on the sphere trouble is you +know i don't have spherical paper and i + + align:start position:0% +know i don't have spherical paper and i + + + align:start position:0% +know i don't have spherical paper and i +don't have a spherical blackboard so + + align:start position:0% +don't have a spherical blackboard so + + + align:start position:0% +don't have a spherical blackboard so +this is a projection + + align:start position:0% +this is a projection + + + align:start position:0% +this is a projection +of the surface of that sphere into the + + align:start position:0% +of the surface of that sphere into the + + + align:start position:0% +of the surface of that sphere into the +plane that's particularly easy to + + align:start position:0% +plane that's particularly easy to + + + align:start position:0% +plane that's particularly easy to +understand because you know this is just + + align:start position:0% +understand because you know this is just + + + align:start position:0% +understand because you know this is just +the zdx + + align:start position:0% +the zdx + + + align:start position:0% +the zdx +and this is just d z d y + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +as with + + align:start position:0% +as with + + + align:start position:0% +as with +velocity space this is a very useful + + align:start position:0% +velocity space this is a very useful + + + align:start position:0% +velocity space this is a very useful +construct but you know takes some + + align:start position:0% +construct but you know takes some + + + align:start position:0% +construct but you know takes some +getting used to + + align:start position:0% +getting used to + + + align:start position:0% +getting used to +so points in this plane + + align:start position:0% +so points in this plane + + + align:start position:0% +so points in this plane +are not points in the image + + align:start position:0% +are not points in the image + + + align:start position:0% +are not points in the image +points in this plane correspond to + + align:start position:0% +points in this plane correspond to + + + align:start position:0% +points in this plane correspond to +different p and q + + align:start position:0% +different p and q + + + align:start position:0% +different p and q +i.e different surface orientations so + + align:start position:0% +i.e different surface orientations so + + + align:start position:0% +i.e different surface orientations so +for example let's consider that point + + align:start position:0% +for example let's consider that point + + + align:start position:0% +for example let's consider that point +so that's the point where p is zero and + + align:start position:0% +so that's the point where p is zero and + + + align:start position:0% +so that's the point where p is zero and +q is zero and that's + + align:start position:0% +q is zero and that's + + + align:start position:0% +q is zero and that's +a plane + + align:start position:0% +a plane + + + align:start position:0% +a plane +now if suppose that the floor here has + + align:start position:0% +now if suppose that the floor here has + + + align:start position:0% +now if suppose that the floor here has +an x-y coordinate system and z comes up + + align:start position:0% +an x-y coordinate system and z comes up + + + align:start position:0% +an x-y coordinate system and z comes up +out of the floor + + align:start position:0% +out of the floor + + + align:start position:0% +out of the floor +uh what type of a surface + + align:start position:0% +uh what type of a surface + + + align:start position:0% +uh what type of a surface +would have this point in this + + align:start position:0% +would have this point in this + + + align:start position:0% +would have this point in this +representation + + align:start position:0% +representation + + + align:start position:0% +representation +yes + + align:start position:0% +yes + + + align:start position:0% +yes +right the floor for example anything + + align:start position:0% +right the floor for example anything + + + align:start position:0% +right the floor for example anything +that's level + + align:start position:0% +that's level + + + align:start position:0% +that's level +so right why well because dz dx is zero + + align:start position:0% +so right why well because dz dx is zero + + + align:start position:0% +so right why well because dz dx is zero +and the zdy is zero so if it had any + + align:start position:0% +and the zdy is zero so if it had any + + + align:start position:0% +and the zdy is zero so if it had any +tilt at all then dz dx or dz dy would be + + align:start position:0% +tilt at all then dz dx or dz dy would be + + + align:start position:0% +tilt at all then dz dx or dz dy would be +non-zero so it's the floor has this + + align:start position:0% +non-zero so it's the floor has this + + + align:start position:0% +non-zero so it's the floor has this +property + + align:start position:0% +property + + + align:start position:0% +property +uh but also actually any surface above + + align:start position:0% +uh but also actually any surface above + + + align:start position:0% +uh but also actually any surface above +the floor that has the same orientation + + align:start position:0% +the floor that has the same orientation + + + align:start position:0% +the floor that has the same orientation +so there's the there's an ambiguity here + + align:start position:0% +so there's the there's an ambiguity here + + + align:start position:0% +so there's the there's an ambiguity here +it's not telling us where this thing is + + align:start position:0% +it's not telling us where this thing is + + + align:start position:0% +it's not telling us where this thing is +it's only telling us how it's you know + + align:start position:0% +it's only telling us how it's you know + + + align:start position:0% +it's only telling us how it's you know +oriented in space + + align:start position:0% +oriented in space + + + align:start position:0% +oriented in space +and so that's going to be a secondary + + align:start position:0% +and so that's going to be a secondary + + + align:start position:0% +and so that's going to be a secondary +problem suppose that we come up with a + + align:start position:0% +problem suppose that we come up with a + + + align:start position:0% +problem suppose that we come up with a +machine vision method which for every + + align:start position:0% +machine vision method which for every + + + align:start position:0% +machine vision method which for every +pixel allows us to recover + + align:start position:0% +pixel allows us to recover + + + align:start position:0% +pixel allows us to recover +surface orientation + + align:start position:0% +surface orientation + + + align:start position:0% +surface orientation +either this way or in p and q + + align:start position:0% +either this way or in p and q + + + align:start position:0% +either this way or in p and q +we still have to patch it together to + + align:start position:0% +we still have to patch it together to + + + align:start position:0% +we still have to patch it together to +make a complete surface but that turns + + align:start position:0% +make a complete surface but that turns + + + align:start position:0% +make a complete surface but that turns +out to be easy because it's over + + align:start position:0% +out to be easy because it's over + + + align:start position:0% +out to be easy because it's over +determined unlike most of the problems + + align:start position:0% +determined unlike most of the problems + + + align:start position:0% +determined unlike most of the problems +we deal with which are underdetermined + + align:start position:0% +we deal with which are underdetermined + + + align:start position:0% +we deal with which are underdetermined +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +that's that surface now if i go over + + align:start position:0% +that's that surface now if i go over + + + align:start position:0% +that's that surface now if i go over +here + + align:start position:0% +here + + + align:start position:0% +here +to p equals one let's suppose that x + + align:start position:0% +to p equals one let's suppose that x + + + align:start position:0% +to p equals one let's suppose that x +goes to the right and y goes forward + + align:start position:0% +goes to the right and y goes forward + + + align:start position:0% +goes to the right and y goes forward +that corresponds to a surface where the + + align:start position:0% +that corresponds to a surface where the + + + align:start position:0% +that corresponds to a surface where the +slope going to the right is one you know + + align:start position:0% +slope going to the right is one you know + + + align:start position:0% +slope going to the right is one you know +45 degree up + + align:start position:0% +45 degree up + + + align:start position:0% +45 degree up +that that would be pretty steep i would + + align:start position:0% +that that would be pretty steep i would + + + align:start position:0% +that that would be pretty steep i would +slide off it with these shoes so that + + align:start position:0% +slide off it with these shoes so that + + + align:start position:0% +slide off it with these shoes so that +then if i go over here uh what's that + + align:start position:0% +then if i go over here uh what's that + + + align:start position:0% +then if i go over here uh what's that +well that's the surface where the slope + + align:start position:0% +well that's the surface where the slope + + + align:start position:0% +well that's the surface where the slope +in the y direction is one so it's you + + align:start position:0% +in the y direction is one so it's you + + + align:start position:0% +in the y direction is one so it's you +know the kind of thing you + + align:start position:0% +know the kind of thing you + + + align:start position:0% +know the kind of thing you +find at ems to check out your rock + + align:start position:0% +find at ems to check out your rock + + + align:start position:0% +find at ems to check out your rock +climbing boots uh make sure that they + + align:start position:0% +climbing boots uh make sure that they + + + align:start position:0% +climbing boots uh make sure that they +are fitting well and you stand with your + + align:start position:0% +are fitting well and you stand with your + + + align:start position:0% +are fitting well and you stand with your +toes up like this and then this one of + + align:start position:0% +toes up like this and then this one of + + + align:start position:0% +toes up like this and then this one of +course is a combination where we have + + align:start position:0% +course is a combination where we have + + + align:start position:0% +course is a combination where we have +the slope to the right and the slope to + + align:start position:0% +the slope to the right and the slope to + + + align:start position:0% +the slope to the right and the slope to +to the forward and so on and the further + + align:start position:0% +to the forward and so on and the further + + + align:start position:0% +to the forward and so on and the further +out i go uh the steeper it gets + + align:start position:0% +out i go uh the steeper it gets + + + align:start position:0% +out i go uh the steeper it gets +so that's what this plane is every point + + align:start position:0% +so that's what this plane is every point + + + align:start position:0% +so that's what this plane is every point +in this plane + + align:start position:0% +in this plane + + + align:start position:0% +in this plane +corresponds to a particular surface + + align:start position:0% +corresponds to a particular surface + + + align:start position:0% +corresponds to a particular surface +orientation + + align:start position:0% +orientation + + + align:start position:0% +orientation +now in + + align:start position:0% +now in + + + align:start position:0% +now in +application to machine vision + + align:start position:0% +application to machine vision + + + align:start position:0% +application to machine vision +we find that the brightness depends on + + align:start position:0% +we find that the brightness depends on + + + align:start position:0% +we find that the brightness depends on +surface orientation + + align:start position:0% +surface orientation + + + align:start position:0% +surface orientation +so this is a wonderful tool to plot + + align:start position:0% +so this is a wonderful tool to plot + + + align:start position:0% +so this is a wonderful tool to plot +brightness + + align:start position:0% +brightness + + + align:start position:0% +brightness +right so i could you know just + + align:start position:0% +right so i could you know just + + + align:start position:0% +right so i could you know just +experimentally i could take a patch of + + align:start position:0% +experimentally i could take a patch of + + + align:start position:0% +experimentally i could take a patch of +this material + + align:start position:0% +this material + + + align:start position:0% +this material +i could orient it flat + + align:start position:0% +i could orient it flat + + + align:start position:0% +i could orient it flat +parallel to the ground i measure how + + align:start position:0% +parallel to the ground i measure how + + + align:start position:0% +parallel to the ground i measure how +bright it appears and i put that number + + align:start position:0% +bright it appears and i put that number + + + align:start position:0% +bright it appears and i put that number +here you know e1 + + align:start position:0% +here you know e1 + + + align:start position:0% +here you know e1 +then i tilt it up 45 degrees and i put + + align:start position:0% +then i tilt it up 45 degrees and i put + + + align:start position:0% +then i tilt it up 45 degrees and i put +that number over here and i tilt it up + + align:start position:0% +that number over here and i tilt it up + + + align:start position:0% +that number over here and i tilt it up +uh what's the slope of 2 + + align:start position:0% +uh what's the slope of 2 + + + align:start position:0% +uh what's the slope of 2 +the inverse tangent of 2 + + align:start position:0% +the inverse tangent of 2 + + + align:start position:0% +the inverse tangent of 2 +and i plot it there so i can plot + + align:start position:0% +and i plot it there so i can plot + + + align:start position:0% +and i plot it there so i can plot +my brightness values + + align:start position:0% +my brightness values + + + align:start position:0% +my brightness values +as a function of surface orientation + + align:start position:0% +as a function of surface orientation + + + align:start position:0% +as a function of surface orientation +so this becomes kind of an image because + + align:start position:0% +so this becomes kind of an image because + + + align:start position:0% +so this becomes kind of an image because +at every point there's a brightness but + + align:start position:0% +at every point there's a brightness but + + + align:start position:0% +at every point there's a brightness but +it's not it's not a transformation of an + + align:start position:0% +it's not it's not a transformation of an + + + align:start position:0% +it's not it's not a transformation of an +image that you take with an optical + + align:start position:0% +image that you take with an optical + + + align:start position:0% +image that you take with an optical +system at all it's + + align:start position:0% +system at all it's + + + align:start position:0% +system at all it's +that's perhaps confusing but it's not + + align:start position:0% +that's perhaps confusing but it's not + + + align:start position:0% +that's perhaps confusing but it's not +so everything in here + + align:start position:0% +so everything in here + + + align:start position:0% +so everything in here +corresponds to orientation and then we + + align:start position:0% +corresponds to orientation and then we + + + align:start position:0% +corresponds to orientation and then we +can plot whatever we want + + align:start position:0% +can plot whatever we want + + + align:start position:0% +can plot whatever we want +such as brightness + + align:start position:0% +such as brightness + + + align:start position:0% +such as brightness +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so where is this going well one idea is + + align:start position:0% +so where is this going well one idea is + + + align:start position:0% +so where is this going well one idea is +we can then invert this suppose that + + align:start position:0% +we can then invert this suppose that + + + align:start position:0% +we can then invert this suppose that +we've made this map + + align:start position:0% +we've made this map + + + align:start position:0% +we've made this map +then you measure the certain brightness + + align:start position:0% +then you measure the certain brightness + + + align:start position:0% +then you measure the certain brightness +and then you go back to it and say oh + + align:start position:0% +and then you go back to it and say oh + + + align:start position:0% +and then you go back to it and say oh +that means the surface orientation is + + align:start position:0% +that means the surface orientation is + + + align:start position:0% +that means the surface orientation is +such and such + + align:start position:0% +such and such + + + align:start position:0% +such and such +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +that's the idea + + align:start position:0% +that's the idea + + + align:start position:0% +that's the idea +and you're probably saying well + + align:start position:0% +and you're probably saying well + + + align:start position:0% +and you're probably saying well +really + + align:start position:0% +really + + + align:start position:0% +really +um because you know maybe brightness + + align:start position:0% +um because you know maybe brightness + + + align:start position:0% +um because you know maybe brightness +down here is the same as there + + align:start position:0% +down here is the same as there + + + align:start position:0% +down here is the same as there +and maybe the brightness down here is + + align:start position:0% +and maybe the brightness down here is + + + align:start position:0% +and maybe the brightness down here is +the same as there + + align:start position:0% +the same as there + + + align:start position:0% +the same as there +and in fact maybe there's a whole line + + align:start position:0% +and in fact maybe there's a whole line + + + align:start position:0% +and in fact maybe there's a whole line +of + + align:start position:0% +of + + + align:start position:0% +of +points that have the same brightness and + + align:start position:0% +points that have the same brightness and + + + align:start position:0% +points that have the same brightness and +the whole line of points that have the + + align:start position:0% +the whole line of points that have the + + + align:start position:0% +the whole line of points that have the +same brightness + + align:start position:0% +same brightness + + + align:start position:0% +same brightness +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +you know just counting equations and + + align:start position:0% +you know just counting equations and + + + align:start position:0% +you know just counting equations and +constraints tells you what the problem + + align:start position:0% +constraints tells you what the problem + + + align:start position:0% +constraints tells you what the problem +is + + align:start position:0% +is + + + align:start position:0% +is +if we make one brightness measurement we + + align:start position:0% +if we make one brightness measurement we + + + align:start position:0% +if we make one brightness measurement we +can't recover two unknowns + + align:start position:0% +can't recover two unknowns + + + align:start position:0% +can't recover two unknowns +so + + align:start position:0% +so + + + align:start position:0% +so +uh just as with + + align:start position:0% +uh just as with + + + align:start position:0% +uh just as with +our velocity determination + + align:start position:0% +our velocity determination + + + align:start position:0% +our velocity determination +a single measurement uh won't be enough + + align:start position:0% +a single measurement uh won't be enough + + + align:start position:0% +a single measurement uh won't be enough +it will be a dramatic improvement over + + align:start position:0% +it will be a dramatic improvement over + + + align:start position:0% +it will be a dramatic improvement over +no measurement so if we don't take a + + align:start position:0% +no measurement so if we don't take a + + + align:start position:0% +no measurement so if we don't take a +measurement we don't know where we are + + align:start position:0% +measurement we don't know where we are + + + align:start position:0% +measurement we don't know where we are +in this plane at all we could have any + + align:start position:0% +in this plane at all we could have any + + + align:start position:0% +in this plane at all we could have any +orientation for a surface element if we + + align:start position:0% +orientation for a surface element if we + + + align:start position:0% +orientation for a surface element if we +take one measurement we'll be + + align:start position:0% +take one measurement we'll be + + + align:start position:0% +take one measurement we'll be +constrained to some curve + + align:start position:0% +constrained to some curve + + + align:start position:0% +constrained to some curve +and then we need more constraint to + + align:start position:0% +and then we need more constraint to + + + align:start position:0% +and then we need more constraint to +actually pin it down to a particular + + align:start position:0% +actually pin it down to a particular + + + align:start position:0% +actually pin it down to a particular +orientation + + align:start position:0% +orientation + + + align:start position:0% +orientation +so just + + align:start position:0% +so just + + + align:start position:0% +so just +let's relate that to what we + + align:start position:0% +let's relate that to what we + + + align:start position:0% +let's relate that to what we +did in our example of photometric stereo + + align:start position:0% +did in our example of photometric stereo + + + align:start position:0% +did in our example of photometric stereo +and also our discussion of lambert + + align:start position:0% +and also our discussion of lambert + + + align:start position:0% +and also our discussion of lambert +let's suppose that + + align:start position:0% +let's suppose that + + + align:start position:0% +let's suppose that +we have a lamborghini surface + + align:start position:0% + + + + align:start position:0% + +so there's a common confusion + + align:start position:0% +so there's a common confusion + + + align:start position:0% +so there's a common confusion +which is that oh this stuff only applies + + align:start position:0% +which is that oh this stuff only applies + + + align:start position:0% +which is that oh this stuff only applies +to lamborghini surfaces why are we doing + + align:start position:0% +to lamborghini surfaces why are we doing + + + align:start position:0% +to lamborghini surfaces why are we doing +lamborghini surfaces because for + + align:start position:0% +lamborghini surfaces because for + + + align:start position:0% +lamborghini surfaces because for +lamborghini surfaces i can show you nice + + align:start position:0% +lamborghini surfaces i can show you nice + + + align:start position:0% +lamborghini surfaces i can show you nice +diagrams i can solve equations in the + + align:start position:0% +diagrams i can solve equations in the + + + align:start position:0% +diagrams i can solve equations in the +real world + + align:start position:0% +real world + + + align:start position:0% +real world +nothing is exactly lamborghini so if you + + align:start position:0% +nothing is exactly lamborghini so if you + + + align:start position:0% +nothing is exactly lamborghini so if you +want accurate result you will have to + + align:start position:0% +want accurate result you will have to + + + align:start position:0% +want accurate result you will have to +measure calibrate and we'll see how to + + align:start position:0% +measure calibrate and we'll see how to + + + align:start position:0% +measure calibrate and we'll see how to +do that but for the moment let's just + + align:start position:0% +do that but for the moment let's just + + + align:start position:0% +do that but for the moment let's just +assume that magically we're dealing with + + align:start position:0% +assume that magically we're dealing with + + + align:start position:0% +assume that magically we're dealing with +a a lamborgh + + align:start position:0% +a a lamborgh + + + align:start position:0% +a a lamborgh +so then we have that surface normal + + align:start position:0% + + + + align:start position:0% + +proportional to brightness so brightness + + align:start position:0% +proportional to brightness so brightness + + + align:start position:0% +proportional to brightness so brightness +is proportional to the cosine of the + + align:start position:0% +is proportional to the cosine of the + + + align:start position:0% +is proportional to the cosine of the +incident angle and that's the dot + + align:start position:0% +incident angle and that's the dot + + + align:start position:0% +incident angle and that's the dot +product of the surface normal and + + align:start position:0% +product of the surface normal and + + + align:start position:0% +product of the surface normal and +and the incident direction and now + + align:start position:0% +and the incident direction and now + + + align:start position:0% +and the incident direction and now +uh we want to translate that + + align:start position:0% +uh we want to translate that + + + align:start position:0% +uh we want to translate that +into this notation p and q + + align:start position:0% +into this notation p and q + + + align:start position:0% +into this notation p and q +but + + align:start position:0% +but + + + align:start position:0% +but +one thing that's important is we're + + align:start position:0% +one thing that's important is we're + + + align:start position:0% +one thing that's important is we're +looking for isophotes in here we're + + align:start position:0% +looking for isophotes in here we're + + + align:start position:0% +looking for isophotes in here we're +looking for these curves + + align:start position:0% + + + + align:start position:0% + +and so we'll be looking at places where + + align:start position:0% +and so we'll be looking at places where + + + align:start position:0% +and so we'll be looking at places where +this is a constant but let's first + + align:start position:0% +this is a constant but let's first + + + align:start position:0% +this is a constant but let's first +replace so the unit vector n is minus p + + align:start position:0% +replace so the unit vector n is minus p + + + align:start position:0% +replace so the unit vector n is minus p +minus q one + + align:start position:0% + + + + align:start position:0% + +and we can take the dot product of that + + align:start position:0% + + + + align:start position:0% + +with some + + align:start position:0% +with some + + + align:start position:0% +with some +light source direction + + align:start position:0% + + + + align:start position:0% + +and then we can you know plot that + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +there + + align:start position:0% +there + + + align:start position:0% +there +it'll be handy to introduce another + + align:start position:0% +it'll be handy to introduce another + + + align:start position:0% +it'll be handy to introduce another +little shortcut + + align:start position:0% +little shortcut + + + align:start position:0% +little shortcut +which is + + align:start position:0% +which is + + + align:start position:0% +which is +a different way of writing the direction + + align:start position:0% +a different way of writing the direction + + + align:start position:0% +a different way of writing the direction +to the light source + + align:start position:0% + + + + align:start position:0% + +so we sort of that equation there's kind + + align:start position:0% +so we sort of that equation there's kind + + + align:start position:0% +so we sort of that equation there's kind +of a mixture we've sort of halfway gone + + align:start position:0% +of a mixture we've sort of halfway gone + + + align:start position:0% +of a mixture we've sort of halfway gone +from unit vectors to pq space + + align:start position:0% +from unit vectors to pq space + + + align:start position:0% +from unit vectors to pq space +let's go fully and so the full way is to + + align:start position:0% +let's go fully and so the full way is to + + + align:start position:0% +let's go fully and so the full way is to +say well + + align:start position:0% + + + + align:start position:0% + +to perform the same transformation on + + align:start position:0% +to perform the same transformation on + + + align:start position:0% +to perform the same transformation on +that unit vector that we did on n it's + + align:start position:0% +that unit vector that we did on n it's + + + align:start position:0% +that unit vector that we did on n it's +just the same equation just this time + + align:start position:0% +just the same equation just this time + + + align:start position:0% +just the same equation just this time +we're talking about the vector to the + + align:start position:0% +we're talking about the vector to the + + + align:start position:0% +we're talking about the vector to the +light source rather than the unit normal + + align:start position:0% +light source rather than the unit normal + + + align:start position:0% +light source rather than the unit normal +and so to to make that uh clearer + + align:start position:0% +and so to to make that uh clearer + + + align:start position:0% +and so to to make that uh clearer +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that point p s q s + + align:start position:0% +that point p s q s + + + align:start position:0% +that point p s q s +it's it's in the in that plane + + align:start position:0% +it's it's in the in that plane + + + align:start position:0% +it's it's in the in that plane +and and what is it + + align:start position:0% +and and what is it + + + align:start position:0% +and and what is it +well it's the orientation + + align:start position:0% +well it's the orientation + + + align:start position:0% +well it's the orientation +where the incident light rays are + + align:start position:0% +where the incident light rays are + + + align:start position:0% +where the incident light rays are +parallel to the surface normal + + align:start position:0% +parallel to the surface normal + + + align:start position:0% +parallel to the surface normal +right so this is the point where + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +and so for the lamborghini surface um + + align:start position:0% +and so for the lamborghini surface um + + + align:start position:0% +and so for the lamborghini surface um +that's going to be the brightest spot + + align:start position:0% +that's going to be the brightest spot + + + align:start position:0% +that's going to be the brightest spot +right because + + align:start position:0% +right because + + + align:start position:0% +right because +the there's no the angle between those + + align:start position:0% +the there's no the angle between those + + + align:start position:0% +the there's no the angle between those +two vectors is zero so the cosine of the + + align:start position:0% +two vectors is zero so the cosine of the + + + align:start position:0% +two vectors is zero so the cosine of the +incident angle is one and that's as big + + align:start position:0% +incident angle is one and that's as big + + + align:start position:0% +incident angle is one and that's as big +as cosine can get so um we picked this + + align:start position:0% +as cosine can get so um we picked this + + + align:start position:0% +as cosine can get so um we picked this +particular point psqs because it's uh in + + align:start position:0% +particular point psqs because it's uh in + + + align:start position:0% +particular point psqs because it's uh in +that plane because it's the one that + + align:start position:0% +that plane because it's the one that + + + align:start position:0% +that plane because it's the one that +gives us the brightest surface so it has + + align:start position:0% +gives us the brightest surface so it has + + + align:start position:0% +gives us the brightest surface so it has +some real meaning + + align:start position:0% +some real meaning + + + align:start position:0% +some real meaning +other than geometrically it just means + + align:start position:0% +other than geometrically it just means + + + align:start position:0% +other than geometrically it just means +that we're + + align:start position:0% +that we're + + + align:start position:0% +that we're +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +we're illuminating the surface right + + align:start position:0% +we're illuminating the surface right + + + align:start position:0% +we're illuminating the surface right +down + + align:start position:0% +down + + + align:start position:0% +down +the + + align:start position:0% +the + + + align:start position:0% +the +normal + + align:start position:0% +normal + + + align:start position:0% +normal +another way think about it is the + + align:start position:0% +another way think about it is the + + + align:start position:0% +another way think about it is the +foreshortening there's no foreshortening + + align:start position:0% +foreshortening there's no foreshortening + + + align:start position:0% +foreshortening there's no foreshortening +we haven't tilted the surface relative + + align:start position:0% +we haven't tilted the surface relative + + + align:start position:0% +we haven't tilted the surface relative +to the light source so we don't have the + + align:start position:0% +to the light source so we don't have the + + + align:start position:0% +to the light source so we don't have the +same power + + align:start position:0% +same power + + + align:start position:0% +same power +spread over a larger area here here it's + + align:start position:0% +spread over a larger area here here it's + + + align:start position:0% +spread over a larger area here here it's +concentrated in the smallest possible + + align:start position:0% +concentrated in the smallest possible + + + align:start position:0% +concentrated in the smallest possible +area it's the most efficient it's what + + align:start position:0% +area it's the most efficient it's what + + + align:start position:0% +area it's the most efficient it's what +you do with your solar collectors + + align:start position:0% +you do with your solar collectors + + + align:start position:0% +you do with your solar collectors +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so that means we can rewrite the n + + align:start position:0% +uh so that means we can rewrite the n + + + align:start position:0% +uh so that means we can rewrite the n +dot s in this form + + align:start position:0% + + + + align:start position:0% + +so this is starting to look a little bit + + align:start position:0% +so this is starting to look a little bit + + + align:start position:0% +so this is starting to look a little bit +messy + + align:start position:0% + + + + align:start position:0% + +and what are we doing well we want we + + align:start position:0% +and what are we doing well we want we + + + align:start position:0% +and what are we doing well we want we +want isophodes so we want to know where + + align:start position:0% +want isophodes so we want to know where + + + align:start position:0% +want isophodes so we want to know where +is this quantity constant what are the + + align:start position:0% +is this quantity constant what are the + + + align:start position:0% +is this quantity constant what are the +curves in that + + align:start position:0% +curves in that + + + align:start position:0% +curves in that +pq space in gradient space + + align:start position:0% +pq space in gradient space + + + align:start position:0% +pq space in gradient space +where + + align:start position:0% +where + + + align:start position:0% +where +that quantity is constant well + + align:start position:0% +that quantity is constant well + + + align:start position:0% +that quantity is constant well +i can square this and move things around + + align:start position:0% +i can square this and move things around + + + align:start position:0% +i can square this and move things around +a bit + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +this quantity here + + align:start position:0% +this quantity here + + + align:start position:0% +this quantity here +this is just some constant + + align:start position:0% +this is just some constant + + + align:start position:0% +this is just some constant +right because i'm not + + align:start position:0% +right because i'm not + + + align:start position:0% +right because i'm not +i'm keeping the light source in the + + align:start position:0% +i'm keeping the light source in the + + + align:start position:0% +i'm keeping the light source in the +fixed position + + align:start position:0% +fixed position + + + align:start position:0% +fixed position +and + + align:start position:0% +and + + + align:start position:0% +and +then + + align:start position:0% +then + + + align:start position:0% +then +the question is you know what kind of + + align:start position:0% +the question is you know what kind of + + + align:start position:0% +the question is you know what kind of +curve does this define + + align:start position:0% +curve does this define + + + align:start position:0% +curve does this define +in pq space + + align:start position:0% +in pq space + + + align:start position:0% +in pq space +well if you multiply it out you're going + + align:start position:0% +well if you multiply it out you're going + + + align:start position:0% +well if you multiply it out you're going +to get some constant terms some terms + + align:start position:0% +to get some constant terms some terms + + + align:start position:0% +to get some constant terms some terms +proportional to p some proportional to q + + align:start position:0% +proportional to p some proportional to q + + + align:start position:0% +proportional to p some proportional to q +the highest order terms you're going to + + align:start position:0% +the highest order terms you're going to + + + align:start position:0% +the highest order terms you're going to +get are second order + + align:start position:0% + + + + align:start position:0% + +so when you multiply it all out which is + + align:start position:0% +so when you multiply it all out which is + + + align:start position:0% +so when you multiply it all out which is +sort of messy + + align:start position:0% +sort of messy + + + align:start position:0% +sort of messy +uh you'll have something that's second + + align:start position:0% +uh you'll have something that's second + + + align:start position:0% +uh you'll have something that's second +order in p and q + + align:start position:0% +order in p and q + + + align:start position:0% +order in p and q +and so the question is what kind of a + + align:start position:0% +and so the question is what kind of a + + + align:start position:0% +and so the question is what kind of a +curve does does that define + + align:start position:0% + + + + align:start position:0% + +and it may be hard to think about it in + + align:start position:0% +and it may be hard to think about it in + + + align:start position:0% +and it may be hard to think about it in +terms of p and q i mean we're not just + + align:start position:0% +terms of p and q i mean we're not just + + + align:start position:0% +terms of p and q i mean we're not just +talking about geometry in the plane + + align:start position:0% +talking about geometry in the plane + + + align:start position:0% +talking about geometry in the plane +so imagine you have uh in x and y you + + align:start position:0% +so imagine you have uh in x and y you + + + align:start position:0% +so imagine you have uh in x and y you +have an equation that's got x squared y + + align:start position:0% +have an equation that's got x squared y + + + align:start position:0% +have an equation that's got x squared y +squared x times y x y and a constant in + + align:start position:0% +squared x times y x y and a constant in + + + align:start position:0% +squared x times y x y and a constant in +it + + align:start position:0% +it + + + align:start position:0% +it +and all added up uh what sort of uh + + align:start position:0% +and all added up uh what sort of uh + + + align:start position:0% +and all added up uh what sort of uh +curve would that correspond yes + + align:start position:0% + + + + align:start position:0% + +it could be a parabola yeah + + align:start position:0% +it could be a parabola yeah + + + align:start position:0% +it could be a parabola yeah +anything else + + align:start position:0% + + + + align:start position:0% + +ellipse yes okay + + align:start position:0% +ellipse yes okay + + + align:start position:0% +ellipse yes okay +great uh generalize it a little bit more + + align:start position:0% +great uh generalize it a little bit more + + + align:start position:0% +great uh generalize it a little bit more +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +it's a conic section okay so yes those + + align:start position:0% +it's a conic section okay so yes those + + + align:start position:0% +it's a conic section okay so yes those +are uh great examples overall uh they're + + align:start position:0% +are uh great examples overall uh they're + + + align:start position:0% +are uh great examples overall uh they're +comic sections and so yes uh we can have + + align:start position:0% +comic sections and so yes uh we can have + + + align:start position:0% +comic sections and so yes uh we can have +a parabola + + align:start position:0% +a parabola + + + align:start position:0% +a parabola +we can have an ellipse + + align:start position:0% +we can have an ellipse + + + align:start position:0% +we can have an ellipse +we can even have a circle + + align:start position:0% +we can even have a circle + + + align:start position:0% +we can even have a circle +we can have a line a special + + align:start position:0% +we can have a line a special + + + align:start position:0% +we can have a line a special +degenerative case + + align:start position:0% +degenerative case + + + align:start position:0% +degenerative case +we can have a point even more special + + align:start position:0% +we can have a point even more special + + + align:start position:0% +we can have a point even more special +general + + align:start position:0% +general + + + align:start position:0% +general +degenerate case + + align:start position:0% +degenerate case + + + align:start position:0% +degenerate case +and we can even have a hyperbola + + align:start position:0% +and we can even have a hyperbola + + + align:start position:0% +and we can even have a hyperbola +okay so so that's uh + + align:start position:0% +okay so so that's uh + + + align:start position:0% +okay so so that's uh +i want to plot this thing and + + align:start position:0% + + + + align:start position:0% + +this is like a preview + + align:start position:0% +this is like a preview + + + align:start position:0% +this is like a preview +you know what + + align:start position:0% +you know what + + + align:start position:0% +you know what +what it's going to look like + + align:start position:0% +what it's going to look like + + + align:start position:0% +what it's going to look like +so uh + + align:start position:0% + + + + align:start position:0% + +if c is zero + + align:start position:0% +if c is zero + + + align:start position:0% +if c is zero +let's let's look at that special case + + align:start position:0% +let's let's look at that special case + + + align:start position:0% +let's let's look at that special case +if z is zero then this is zero and that + + align:start position:0% +if z is zero then this is zero and that + + + align:start position:0% +if z is zero then this is zero and that +means that uh one plus psp + + align:start position:0% +means that uh one plus psp + + + align:start position:0% +means that uh one plus psp +plus q as q is zero + + align:start position:0% +plus q as q is zero + + + align:start position:0% +plus q as q is zero +now what kind of an equation in p and q + + align:start position:0% +now what kind of an equation in p and q + + + align:start position:0% +now what kind of an equation in p and q +is that + + align:start position:0% +is that + + + align:start position:0% +is that +it's a line it's a linear equation so + + align:start position:0% +it's a line it's a linear equation so + + + align:start position:0% +it's a line it's a linear equation so +it's just a straight line so that's that + + align:start position:0% +it's just a straight line so that's that + + + align:start position:0% +it's just a straight line so that's that +one special case + + align:start position:0% +one special case + + + align:start position:0% +one special case +so there's going to be some sort of line + + align:start position:0% +so there's going to be some sort of line + + + align:start position:0% +so there's going to be some sort of line +in here and and it's where the + + align:start position:0% +in here and and it's where the + + + align:start position:0% +in here and and it's where the +brightness is zero + + align:start position:0% +brightness is zero + + + align:start position:0% +brightness is zero +and um okay and then another special + + align:start position:0% +and um okay and then another special + + + align:start position:0% +and um okay and then another special +case is where p equals ps and q equals + + align:start position:0% +case is where p equals ps and q equals + + + align:start position:0% +case is where p equals ps and q equals +qs + + align:start position:0% +qs + + + align:start position:0% +qs +and that's a special case where we there + + align:start position:0% +and that's a special case where we there + + + align:start position:0% +and that's a special case where we there +we talked about here + + align:start position:0% +we talked about here + + + align:start position:0% +we talked about here +where the normal is pointing straight at + + align:start position:0% +where the normal is pointing straight at + + + align:start position:0% +where the normal is pointing straight at +the light source + + align:start position:0% +the light source + + + align:start position:0% +the light source +and + + align:start position:0% +and + + + align:start position:0% +and +we're getting the maximum brightness so + + align:start position:0% +we're getting the maximum brightness so + + + align:start position:0% +we're getting the maximum brightness so +there's some point over here + + align:start position:0% +there's some point over here + + + align:start position:0% +there's some point over here +where + + align:start position:0% +where + + + align:start position:0% +where +e is one + + align:start position:0% +e is one + + + align:start position:0% +e is one +if we normalize it + + align:start position:0% +if we normalize it + + + align:start position:0% +if we normalize it +appropriately + + align:start position:0% +appropriately + + + align:start position:0% +appropriately +okay and then the rest you know you can + + align:start position:0% +okay and then the rest you know you can + + + align:start position:0% +okay and then the rest you know you can +plot from using some sort of program if + + align:start position:0% +plot from using some sort of program if + + + align:start position:0% +plot from using some sort of program if +you like + + align:start position:0% + + + + align:start position:0% + +okay so that's a very handy diagram + + align:start position:0% +okay so that's a very handy diagram + + + align:start position:0% +okay so that's a very handy diagram +a very handy diagram for graphics + + align:start position:0% +a very handy diagram for graphics + + + align:start position:0% +a very handy diagram for graphics +because + + align:start position:0% +because + + + align:start position:0% +because +if i have a surface that i'm plotting i + + align:start position:0% +if i have a surface that i'm plotting i + + + align:start position:0% +if i have a surface that i'm plotting i +can easily determine the + + align:start position:0% +can easily determine the + + + align:start position:0% +can easily determine the +unit normal from it i can get p and q or + + align:start position:0% +unit normal from it i can get p and q or + + + align:start position:0% +unit normal from it i can get p and q or +i can get p and q directly and then i + + align:start position:0% +i can get p and q directly and then i + + + align:start position:0% +i can get p and q directly and then i +just go to this diagram and i read off + + align:start position:0% +just go to this diagram and i read off + + + align:start position:0% +just go to this diagram and i read off +you know whatever the brightness is here + + align:start position:0% +you know whatever the brightness is here + + + align:start position:0% +you know whatever the brightness is here +and i use that as a gray level or color + + align:start position:0% +and i use that as a gray level or color + + + align:start position:0% +and i use that as a gray level or color +uh in the image that i'm plotting + + align:start position:0% +uh in the image that i'm plotting + + + align:start position:0% +uh in the image that i'm plotting +what we're doing is kind of the other + + align:start position:0% +what we're doing is kind of the other + + + align:start position:0% +what we're doing is kind of the other +way around what we want to do is um + + align:start position:0% +way around what we want to do is um + + + align:start position:0% +way around what we want to do is um +say okay i've measured + + align:start position:0% +say okay i've measured + + + align:start position:0% +say okay i've measured +you know e is 0.2 + + align:start position:0% +you know e is 0.2 + + + align:start position:0% +you know e is 0.2 +what's the orientation + + align:start position:0% +what's the orientation + + + align:start position:0% +what's the orientation +well + + align:start position:0% +well + + + align:start position:0% +well +in this case that's + + align:start position:0% +in this case that's + + + align:start position:0% +in this case that's +that curve so + + align:start position:0% +that curve so + + + align:start position:0% +that curve so +i don't get a unique answer + + align:start position:0% +i don't get a unique answer + + + align:start position:0% +i don't get a unique answer +but it's heavily constrained it's it has + + align:start position:0% +but it's heavily constrained it's it has + + + align:start position:0% +but it's heavily constrained it's it has +to be uh on that curve + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now if i have more constraint i can + + align:start position:0% +now if i have more constraint i can + + + align:start position:0% +now if i have more constraint i can +improve on this for example suppose now + + align:start position:0% +improve on this for example suppose now + + + align:start position:0% +improve on this for example suppose now +i move the light source then this whole + + align:start position:0% +i move the light source then this whole + + + align:start position:0% +i move the light source then this whole +diagram changes right + + align:start position:0% +diagram changes right + + + align:start position:0% +diagram changes right +because this remember this point here + + align:start position:0% +because this remember this point here + + + align:start position:0% +because this remember this point here +is + + align:start position:0% + + + + align:start position:0% + +one that basically depends on the + + align:start position:0% +one that basically depends on the + + + align:start position:0% +one that basically depends on the +position of the light source + + align:start position:0% +position of the light source + + + align:start position:0% +position of the light source +right it's psqs + + align:start position:0% +right it's psqs + + + align:start position:0% +right it's psqs +is the + + align:start position:0% +is the + + + align:start position:0% +is the +from this equation it's related to the + + align:start position:0% +from this equation it's related to the + + + align:start position:0% +from this equation it's related to the +direction to the light source + + align:start position:0% +direction to the light source + + + align:start position:0% +direction to the light source +okay so imagine + + align:start position:0% +okay so imagine + + + align:start position:0% +okay so imagine +i don't want to mess up this diagram but + + align:start position:0% +i don't want to mess up this diagram but + + + align:start position:0% +i don't want to mess up this diagram but +imagine that i've mirror-imaged this by + + align:start position:0% +imagine that i've mirror-imaged this by + + + align:start position:0% +imagine that i've mirror-imaged this by +moving the light source over here so + + align:start position:0% +moving the light source over here so + + + align:start position:0% +moving the light source over here so +i'll have a + + align:start position:0% +i'll have a + + + align:start position:0% +i'll have a +a second set of isofoads that now + + align:start position:0% +a second set of isofoads that now + + + align:start position:0% +a second set of isofoads that now +intersect with these + + align:start position:0% +intersect with these + + + align:start position:0% +intersect with these +and if i make a measurement under those + + align:start position:0% +and if i make a measurement under those + + + align:start position:0% +and if i make a measurement under those +other light conditions + + align:start position:0% +other light conditions + + + align:start position:0% +other light conditions +then the answer has to be on both curves + + align:start position:0% +then the answer has to be on both curves + + + align:start position:0% +then the answer has to be on both curves +and + + align:start position:0% +and + + + align:start position:0% +and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +then i get the solution + + align:start position:0% +then i get the solution + + + align:start position:0% +then i get the solution +from that so + + align:start position:0% +from that so + + + align:start position:0% +from that so +just for fun let's suppose that the + + align:start position:0% +just for fun let's suppose that the + + + align:start position:0% +just for fun let's suppose that the +other curve was i don't know like this + + align:start position:0% +other curve was i don't know like this + + + align:start position:0% +other curve was i don't know like this +i mean they're they're curves they're + + align:start position:0% +i mean they're they're curves they're + + + align:start position:0% +i mean they're they're curves they're +not lines so it is quite possible for + + align:start position:0% +not lines so it is quite possible for + + + align:start position:0% +not lines so it is quite possible for +them to uh + + align:start position:0% +them to uh + + + align:start position:0% +them to uh +intersect in uh in two places + + align:start position:0% + + + + align:start position:0% + +so i have a finite number of solutions + + align:start position:0% +so i have a finite number of solutions + + + align:start position:0% +so i have a finite number of solutions +in general um + + align:start position:0% +in general um + + + align:start position:0% +in general um +not one + + align:start position:0% +not one + + + align:start position:0% +not one +so and that's why + + align:start position:0% +so and that's why + + + align:start position:0% +so and that's why +we focus more on the case where we use + + align:start position:0% +we focus more on the case where we use + + + align:start position:0% +we focus more on the case where we use +three light sources instead of two + + align:start position:0% +three light sources instead of two + + + align:start position:0% +three light sources instead of two +so just a note on why are they conic + + align:start position:0% +so just a note on why are they conic + + + align:start position:0% +so just a note on why are they conic +sections + + align:start position:0% +sections + + + align:start position:0% +sections +well that actually also has a easy + + align:start position:0% +well that actually also has a easy + + + align:start position:0% +well that actually also has a easy +answer which is you know suppose i take + + align:start position:0% +answer which is you know suppose i take + + + align:start position:0% +answer which is you know suppose i take +a brightness measurement of a + + align:start position:0% +a brightness measurement of a + + + align:start position:0% +a brightness measurement of a +lamborghini surface so here's my light + + align:start position:0% +lamborghini surface so here's my light + + + align:start position:0% +lamborghini surface so here's my light +source + + align:start position:0% +source + + + align:start position:0% +source +here's the surface + + align:start position:0% +here's the surface + + + align:start position:0% +here's the surface +and from the brightness + + align:start position:0% +and from the brightness + + + align:start position:0% +and from the brightness +i can calculate this angle + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +of course i can spin this vector around + + align:start position:0% +of course i can spin this vector around + + + align:start position:0% +of course i can spin this vector around +this line to the light source i can spin + + align:start position:0% +this line to the light source i can spin + + + align:start position:0% +this line to the light source i can spin +that around + + align:start position:0% + + + + align:start position:0% + +and what do i get i get a cone + + align:start position:0% +and what do i get i get a cone + + + align:start position:0% +and what do i get i get a cone +if i measure a different brightness + + align:start position:0% +if i measure a different brightness + + + align:start position:0% +if i measure a different brightness +it'll be different angle + + align:start position:0% +it'll be different angle + + + align:start position:0% +it'll be different angle +i'll get a different cone + + align:start position:0% + + + + align:start position:0% + +and so on so i can you know imagine + + align:start position:0% +and so on so i can you know imagine + + + align:start position:0% +and so on so i can you know imagine +some third surface element i measure yet + + align:start position:0% +some third surface element i measure yet + + + align:start position:0% +some third surface element i measure yet +another angle and i get say this this + + align:start position:0% +another angle and i get say this this + + + align:start position:0% +another angle and i get say this this +chord + + align:start position:0% +chord + + + align:start position:0% +chord +so they're these uh nested cones + + align:start position:0% +so they're these uh nested cones + + + align:start position:0% +so they're these uh nested cones +and now imagine that you cut this with a + + align:start position:0% +and now imagine that you cut this with a + + + align:start position:0% +and now imagine that you cut this with a +plane so + + align:start position:0% +plane so + + + align:start position:0% +plane so +this is our pq plane + + align:start position:0% +this is our pq plane + + + align:start position:0% +this is our pq plane +and + + align:start position:0% +and + + + align:start position:0% +and +tada conic sections + + align:start position:0% + + + + align:start position:0% + +and yes + + align:start position:0% +and yes + + + align:start position:0% +and yes +you won't just get ellipsis + + align:start position:0% +you won't just get ellipsis + + + align:start position:0% +you won't just get ellipsis +you may get a hyperbola you know as long + + align:start position:0% +you may get a hyperbola you know as long + + + align:start position:0% +you may get a hyperbola you know as long +as this bottom edge of the cone is + + align:start position:0% +as this bottom edge of the cone is + + + align:start position:0% +as this bottom edge of the cone is +actually below this plane + + align:start position:0% +actually below this plane + + + align:start position:0% +actually below this plane +you will not get a closed curve so + + align:start position:0% +you will not get a closed curve so + + + align:start position:0% +you will not get a closed curve so +parabolas are possible yeah + + align:start position:0% +parabolas are possible yeah + + + align:start position:0% +parabolas are possible yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +let me let me first address that one + + align:start position:0% +let me let me first address that one + + + align:start position:0% +let me let me first address that one +other side of the line so we + + align:start position:0% +other side of the line so we + + + align:start position:0% +other side of the line so we +said that it's cosine theta except when + + align:start position:0% +said that it's cosine theta except when + + + align:start position:0% +said that it's cosine theta except when +it's negative + + align:start position:0% +it's negative + + + align:start position:0% +it's negative +this is where uh cosine theta i goes + + align:start position:0% +this is where uh cosine theta i goes + + + align:start position:0% +this is where uh cosine theta i goes +negative + + align:start position:0% +negative + + + align:start position:0% +negative +and i haven't purposefully drawn this + + align:start position:0% +and i haven't purposefully drawn this + + + align:start position:0% +and i haven't purposefully drawn this +part of the diagram because in practice + + align:start position:0% +part of the diagram because in practice + + + align:start position:0% +part of the diagram because in practice +brightness doesn't go negative it's a + + align:start position:0% +brightness doesn't go negative it's a + + + align:start position:0% +brightness doesn't go negative it's a +measure of power so it can't be negative + + align:start position:0% +measure of power so it can't be negative + + + align:start position:0% +measure of power so it can't be negative +so + + align:start position:0% +so + + + align:start position:0% +so +if i were to just plot cosine theta it + + align:start position:0% +if i were to just plot cosine theta it + + + align:start position:0% +if i were to just plot cosine theta it +would continue but we're having max of 0 + + align:start position:0% +would continue but we're having max of 0 + + + align:start position:0% +would continue but we're having max of 0 +and cosine theta so so we have this part + + align:start position:0% +and cosine theta so so we have this part + + + align:start position:0% +and cosine theta so so we have this part +and so where does it turn + + align:start position:0% +and so where does it turn + + + align:start position:0% +and so where does it turn +uh the other part of the question is you + + align:start position:0% +uh the other part of the question is you + + + align:start position:0% +uh the other part of the question is you +know where does it turn from being a + + align:start position:0% +know where does it turn from being a + + + align:start position:0% +know where does it turn from being a +closed curve to being uh open + + align:start position:0% +closed curve to being uh open + + + align:start position:0% +closed curve to being uh open +um i'll leave that as a puzzle for + + align:start position:0% +um i'll leave that as a puzzle for + + + align:start position:0% +um i'll leave that as a puzzle for +future homework problems so + + align:start position:0% +future homework problems so + + + align:start position:0% +future homework problems so +why because i don't know the answer so + + align:start position:0% +why because i don't know the answer so + + + align:start position:0% +why because i don't know the answer so +let you figure it out okay uh that + + align:start position:0% +let you figure it out okay uh that + + + align:start position:0% +let you figure it out okay uh that +that's it for today so um + + align:start position:0% +that's it for today so um + + + align:start position:0% +that's it for today so um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +i guess you all know there's a homework + + align:start position:0% +i guess you all know there's a homework + + + align:start position:0% +i guess you all know there's a homework +problem out that will be due + + align:start position:0% +problem out that will be due + + + align:start position:0% +problem out that will be due +and please make sure you + + align:start position:0% +and please make sure you + + + align:start position:0% +and please make sure you +are signed up on piazza because a lot of + + align:start position:0% +are signed up on piazza because a lot of + + + align:start position:0% +are signed up on piazza because a lot of +announcements are on there about office + + align:start position:0% +announcements are on there about office + + + align:start position:0% +announcements are on there about office +hours + + align:start position:0% +hours + + + align:start position:0% +hours +homework problems and stuff like that \ No newline at end of file diff --git a/QXhQO_cOpjQ.txt b/QXhQO_cOpjQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..767b179cd8acc8683cce7ba8410cda97da4a2006 --- /dev/null +++ b/QXhQO_cOpjQ.txt @@ -0,0 +1,16155 @@ +align:start position:0% + +so we're very fortunate today to have Dr + + align:start position:0% +so we're very fortunate today to have Dr + + + align:start position:0% +so we're very fortunate today to have Dr +Maria gathu Johnson uh join us to give a + + align:start position:0% +Maria gathu Johnson uh join us to give a + + + align:start position:0% +Maria gathu Johnson uh join us to give a +guest lecture on Neutron Diagnostics + + align:start position:0% +guest lecture on Neutron Diagnostics + + + align:start position:0% +guest lecture on Neutron Diagnostics +Maria is a principal research scientist + + align:start position:0% +Maria is a principal research scientist + + + align:start position:0% +Maria is a principal research scientist +at the psfc uh she did her PhD working + + align:start position:0% +at the psfc uh she did her PhD working + + + align:start position:0% +at the psfc uh she did her PhD working +on Neutron spectroscopy on jet uh on + + align:start position:0% +on Neutron spectroscopy on jet uh on + + + align:start position:0% +on Neutron spectroscopy on jet uh on +magnetic confinement but now she works + + align:start position:0% +magnetic confinement but now she works + + + align:start position:0% +magnetic confinement but now she works +on inertial confinement fusion and in + + align:start position:0% +on inertial confinement fusion and in + + + align:start position:0% +on inertial confinement fusion and in +particular her work on the magnetic + + align:start position:0% +particular her work on the magnetic + + + align:start position:0% +particular her work on the magnetic +recoil spectrometer on nith was a key to + + align:start position:0% +recoil spectrometer on nith was a key to + + + align:start position:0% +recoil spectrometer on nith was a key to +understanding the record Neutron yield + + align:start position:0% +understanding the record Neutron yield + + + align:start position:0% +understanding the record Neutron yield +that we got last year in the ignition + + align:start position:0% +that we got last year in the ignition + + + align:start position:0% +that we got last year in the ignition +shots so we're very fortunate to have + + align:start position:0% +shots so we're very fortunate to have + + + align:start position:0% +shots so we're very fortunate to have +Maria here and looking forward to + + align:start position:0% +Maria here and looking forward to + + + align:start position:0% +Maria here and looking forward to +hearing her talk okay thanks jck so um + + align:start position:0% +hearing her talk okay thanks jck so um + + + align:start position:0% +hearing her talk okay thanks jck so um +an hour and a half on nuclear diagnostic + + align:start position:0% +an hour and a half on nuclear diagnostic + + + align:start position:0% +an hour and a half on nuclear diagnostic +for ICF that's a kind of a lot to + + align:start position:0% +for ICF that's a kind of a lot to + + + align:start position:0% +for ICF that's a kind of a lot to +squeeze in so I I did a bit of a + + align:start position:0% +squeeze in so I I did a bit of a + + + align:start position:0% +squeeze in so I I did a bit of a +sampling I want you guys to ask + + align:start position:0% +sampling I want you guys to ask + + + align:start position:0% +sampling I want you guys to ask +questions as we go through uh if there's + + align:start position:0% +questions as we go through uh if there's + + + align:start position:0% +questions as we go through uh if there's +anything you're particularly interested + + align:start position:0% +anything you're particularly interested + + + align:start position:0% +anything you're particularly interested +in Sp me when we'll talk a little bit + + align:start position:0% +in Sp me when we'll talk a little bit + + + align:start position:0% +in Sp me when we'll talk a little bit +more about it um try try to touch on the + + align:start position:0% +more about it um try try to touch on the + + + align:start position:0% +more about it um try try to touch on the +key things also there's a lot of + + align:start position:0% +key things also there's a lot of + + + align:start position:0% +key things also there's a lot of +familiar faes today so a lot of you know + + align:start position:0% +familiar faes today so a lot of you know + + + align:start position:0% +familiar faes today so a lot of you know +details of what we'll be talking about + + align:start position:0% +details of what we'll be talking about + + + align:start position:0% +details of what we'll be talking about +today in some cases better than I do so + + align:start position:0% +today in some cases better than I do so + + + align:start position:0% +today in some cases better than I do so +then feel free to chime in as well so + + align:start position:0% +then feel free to chime in as well so + + + align:start position:0% +then feel free to chime in as well so +with that we'll we'll get + + align:start position:0% +with that we'll we'll get + + + align:start position:0% +with that we'll we'll get +started so yeah as Jack said we're going + + align:start position:0% +started so yeah as Jack said we're going + + + align:start position:0% +started so yeah as Jack said we're going +to be talking about nuclear diagnostics + + align:start position:0% +to be talking about nuclear diagnostics + + + align:start position:0% +to be talking about nuclear diagnostics +for uh ICF plasmas + + align:start position:0% +for uh ICF plasmas + + + align:start position:0% +for uh ICF plasmas +uh this in particular illustrates Street + + align:start position:0% +uh this in particular illustrates Street + + + align:start position:0% +uh this in particular illustrates Street +facilities where we do ICF for the + + align:start position:0% +facilities where we do ICF for the + + + align:start position:0% +facilities where we do ICF for the +national facility in limore in + + align:start position:0% +national facility in limore in + + + align:start position:0% +national facility in limore in +California the Z facility at s National + + align:start position:0% +California the Z facility at s National + + + align:start position:0% +California the Z facility at s National +Labs in Albuquerque New Mexico in the + + align:start position:0% +Labs in Albuquerque New Mexico in the + + + align:start position:0% +Labs in Albuquerque New Mexico in the +Omega laser in Lester state New York and + + align:start position:0% +Omega laser in Lester state New York and + + + align:start position:0% +Omega laser in Lester state New York and +this is actually a picture of the + + align:start position:0% +this is actually a picture of the + + + align:start position:0% +this is actually a picture of the +instrument that Jack just talked about + + align:start position:0% +instrument that Jack just talked about + + + align:start position:0% +instrument that Jack just talked about +in his introduction the magnetic me + + align:start position:0% +in his introduction the magnetic me + + + align:start position:0% +in his introduction the magnetic me +spectometer installed on the N part of + + align:start position:0% +spectometer installed on the N part of + + + align:start position:0% +spectometer installed on the N part of +the chamber which is the blue kind + + align:start position:0% +the chamber which is the blue kind + + + align:start position:0% +the chamber which is the blue kind +of cical part you can see there the + + align:start position:0% +of cical part you can see there the + + + align:start position:0% +of cical part you can see there the +background so but I thought uh as part + + align:start position:0% +background so but I thought uh as part + + + align:start position:0% +background so but I thought uh as part +of this we'll touch a little bit on if I + + align:start position:0% +of this we'll touch a little bit on if I + + + align:start position:0% +of this we'll touch a little bit on if I +can get this to move forward some + + align:start position:0% +can get this to move forward some + + + align:start position:0% +can get this to move forward some +comparisons to diagnostics for magnetic + + align:start position:0% +comparisons to diagnostics for magnetic + + + align:start position:0% +comparisons to diagnostics for magnetic +confinement Fusion as well U so these + + align:start position:0% +confinement Fusion as well U so these + + + align:start position:0% +confinement Fusion as well U so these +pictures here that's the inside of the + + align:start position:0% +pictures here that's the inside of the + + + align:start position:0% +pictures here that's the inside of the +jet to and this is a time of FL nomer at + + align:start position:0% +jet to and this is a time of FL nomer at + + + align:start position:0% +jet to and this is a time of FL nomer at +the jet to which I did build for for my + + align:start position:0% +the jet to which I did build for for my + + + align:start position:0% +the jet to which I did build for for my +R work so we'll talk about that one a + + align:start position:0% +R work so we'll talk about that one a + + + align:start position:0% +R work so we'll talk about that one a +little bit as well we get to that + + align:start position:0% +little bit as well we get to that + + + align:start position:0% +little bit as well we get to that +point um brief + + align:start position:0% +point um brief + + + align:start position:0% +point um brief +outline finds a little weird between + + align:start position:0% +outline finds a little weird between + + + align:start position:0% +outline finds a little weird between +switching the computer the camera + + align:start position:0% +switching the computer the camera + + + align:start position:0% +switching the computer the camera +um we'll start by talking about + + align:start position:0% +um we'll start by talking about + + + align:start position:0% +um we'll start by talking about +implosion parameters in nuclear + + align:start position:0% +implosion parameters in nuclear + + + align:start position:0% +implosion parameters in nuclear +signatures what are we actually looking + + align:start position:0% +signatures what are we actually looking + + + align:start position:0% +signatures what are we actually looking +for in the ICF implosions what do we get + + align:start position:0% +for in the ICF implosions what do we get + + + align:start position:0% +for in the ICF implosions what do we get +from the nuclear Diagnostics uh so + + align:start position:0% +from the nuclear Diagnostics uh so + + + align:start position:0% +from the nuclear Diagnostics uh so +that's kind of the broad overview + + align:start position:0% +that's kind of the broad overview + + + align:start position:0% +that's kind of the broad overview +background and then we'll go into a + + align:start position:0% +background and then we'll go into a + + + align:start position:0% +background and then we'll go into a +little bit more technical stuff the + + align:start position:0% +little bit more technical stuff the + + + align:start position:0% +little bit more technical stuff the +nuclear Diagnostics that we use and we + + align:start position:0% +nuclear Diagnostics that we use and we + + + align:start position:0% +nuclear Diagnostics that we use and we +I've divided it into Neutron activation + + align:start position:0% +I've divided it into Neutron activation + + + align:start position:0% +I've divided it into Neutron activation +Neutron spectrometry Neutron Imaging + + align:start position:0% +Neutron spectrometry Neutron Imaging + + + align:start position:0% +Neutron spectrometry Neutron Imaging +charged particle spectrometry touching a + + align:start position:0% +charged particle spectrometry touching a + + + align:start position:0% +charged particle spectrometry touching a +little bit on other charged particle + + align:start position:0% +little bit on other charged particle + + + align:start position:0% +little bit on other charged particle +diagnoses as well and then finally + + align:start position:0% +diagnoses as well and then finally + + + align:start position:0% +diagnoses as well and then finally +reaction rate history and finally if we + + align:start position:0% +reaction rate history and finally if we + + + align:start position:0% +reaction rate history and finally if we +time will just uh spend a few slides + + align:start position:0% +time will just uh spend a few slides + + + align:start position:0% +time will just uh spend a few slides +discussing the impact of nuclear + + align:start position:0% +discussing the impact of nuclear + + + align:start position:0% +discussing the impact of nuclear +measurements on the ICF program at the e + + align:start position:0% +measurements on the ICF program at the e + + + align:start position:0% +measurements on the ICF program at the e +in + + align:start position:0% + + + + align:start position:0% + +particular uh so let's start with the uh + + align:start position:0% +particular uh so let's start with the uh + + + align:start position:0% +particular uh so let's start with the uh +implosion parameters and nuclear + + align:start position:0% +implosion parameters and nuclear + + + align:start position:0% +implosion parameters and nuclear +signatures so the nuclear emission from + + align:start position:0% +signatures so the nuclear emission from + + + align:start position:0% +signatures so the nuclear emission from +an ICF experiment carries information + + align:start position:0% +an ICF experiment carries information + + + align:start position:0% +an ICF experiment carries information +about the state of the Fusion fuel and I + + align:start position:0% +about the state of the Fusion fuel and I + + + align:start position:0% +about the state of the Fusion fuel and I +this is actually what really excites me + + align:start position:0% +this is actually what really excites me + + + align:start position:0% +this is actually what really excites me +about nuclear Diagnostics is that they + + align:start position:0% +about nuclear Diagnostics is that they + + + align:start position:0% +about nuclear Diagnostics is that they +carry information directly uh about + + align:start position:0% +carry information directly uh about + + + align:start position:0% +carry information directly uh about +what's happening + + align:start position:0% +what's happening + + + align:start position:0% +what's happening +in the reactions they're the products of + + align:start position:0% +in the reactions they're the products of + + + align:start position:0% +in the reactions they're the products of +the reactions so they know exactly + + align:start position:0% +the reactions so they know exactly + + + align:start position:0% +the reactions so they know exactly +what's going on in the fuel uh we can + + align:start position:0% +what's going on in the fuel uh we can + + + align:start position:0% +what's going on in the fuel uh we can +count the number of nuclear products and + + align:start position:0% +count the number of nuclear products and + + + align:start position:0% +count the number of nuclear products and +that gives us a measure of the number of + + align:start position:0% +that gives us a measure of the number of + + + align:start position:0% +that gives us a measure of the number of +fusion reactions that happen we can look + + align:start position:0% +fusion reactions that happen we can look + + + align:start position:0% +fusion reactions that happen we can look +at the energy spread of the fusion + + align:start position:0% +at the energy spread of the fusion + + + align:start position:0% +at the energy spread of the fusion +products and give that gives us a + + align:start position:0% +products and give that gives us a + + + align:start position:0% +products and give that gives us a +measure of the plasma iron temperature + + align:start position:0% +measure of the plasma iron temperature + + + align:start position:0% +measure of the plasma iron temperature +we can look at the energy upshift of the + + align:start position:0% +we can look at the energy upshift of the + + + align:start position:0% +we can look at the energy upshift of the +fusion products velocity was there a + + align:start position:0% +fusion products velocity was there a + + + align:start position:0% +fusion products velocity was there a +commment downline can you guys hear me + + align:start position:0% +commment downline can you guys hear me + + + align:start position:0% +commment downline can you guys hear me +okay we can hear you great thanks great + + align:start position:0% +okay we can hear you great thanks great + + + align:start position:0% +okay we can hear you great thanks great +uh and we can look at a scatter or + + align:start position:0% +uh and we can look at a scatter or + + + align:start position:0% +uh and we can look at a scatter or +downshift of the uh nuclear products uh + + align:start position:0% +downshift of the uh nuclear products uh + + + align:start position:0% +downshift of the uh nuclear products uh +to study area of density which I'll + + align:start position:0% +to study area of density which I'll + + + align:start position:0% +to study area of density which I'll +discuss what that is of the compressed + + align:start position:0% +discuss what that is of the compressed + + + align:start position:0% +discuss what that is of the compressed +Fuel and shell we can also take an image + + align:start position:0% +Fuel and shell we can also take an image + + + align:start position:0% +Fuel and shell we can also take an image +of nuclear emission to study the spatial + + align:start position:0% +of nuclear emission to study the spatial + + + align:start position:0% +of nuclear emission to study the spatial +burn profile and we can look at the + + align:start position:0% +burn profile and we can look at the + + + align:start position:0% +burn profile and we can look at the +temporal Evolution to determine how + + align:start position:0% +temporal Evolution to determine how + + + align:start position:0% +temporal Evolution to determine how +nuclear burn evolves in time and + + align:start position:0% +nuclear burn evolves in time and + + + align:start position:0% +nuclear burn evolves in time and +actually if you look at this quite a few + + align:start position:0% +actually if you look at this quite a few + + + align:start position:0% +actually if you look at this quite a few +of these are also relevant for magnetic + + align:start position:0% +of these are also relevant for magnetic + + + align:start position:0% +of these are also relevant for magnetic +confin Fusion uh we can obtain similar + + align:start position:0% +confin Fusion uh we can obtain similar + + + align:start position:0% +confin Fusion uh we can obtain similar +information by looking at the + + align:start position:0% +information by looking at the + + + align:start position:0% +information by looking at the +information from uh the Tok M for + + align:start position:0% +information from uh the Tok M for + + + align:start position:0% +information from uh the Tok M for +example the exception is the aerial + + align:start position:0% +example the exception is the aerial + + + align:start position:0% +example the exception is the aerial +density uh which is the specific + + align:start position:0% +density uh which is the specific + + + align:start position:0% +density uh which is the specific +quantity to ICF so let's I want to spend + + align:start position:0% +quantity to ICF so let's I want to spend + + + align:start position:0% +quantity to ICF so let's I want to spend +a few slides talking about why that's + + align:start position:0% +a few slides talking about why that's + + + align:start position:0% +a few slides talking about why that's +important uh as I think all of you know + + align:start position:0% +important uh as I think all of you know + + + align:start position:0% +important uh as I think all of you know +already ICF uses the inertia of a dense + + align:start position:0% +already ICF uses the inertia of a dense + + + align:start position:0% +already ICF uses the inertia of a dense +shell to confine the plasma before it + + align:start position:0% +shell to confine the plasma before it + + + align:start position:0% +shell to confine the plasma before it +blows apart apart under its own pressure + + align:start position:0% +blows apart apart under its own pressure + + + align:start position:0% +blows apart apart under its own pressure +um we can express the confinement time + + align:start position:0% +um we can express the confinement time + + + align:start position:0% +um we can express the confinement time +uh in terms of the be CS here this is + + align:start position:0% +uh in terms of the be CS here this is + + + align:start position:0% +uh in terms of the be CS here this is +kind of illustration of all hard works + + align:start position:0% +kind of illustration of all hard works + + + align:start position:0% +kind of illustration of all hard works +and if we take + + align:start position:0% + + + + align:start position:0% + +ausing turn this one around and then you + + align:start position:0% +ausing turn this one around and then you + + + align:start position:0% +ausing turn this one around and then you +got one pure computer to look at trying + + align:start position:0% +got one pure computer to look at trying + + + align:start position:0% +got one pure computer to look at trying +to switch slides + + align:start position:0% +to switch slides + + + align:start position:0% +to switch slides +your that's there we go uh we can take a + + align:start position:0% +your that's there we go uh we can take a + + + align:start position:0% +your that's there we go uh we can take a +mass average of the local confinement + + align:start position:0% +mass average of the local confinement + + + align:start position:0% +mass average of the local confinement +time and that gives us uh the + + align:start position:0% +time and that gives us uh the + + + align:start position:0% +time and that gives us uh the +confinement time um as the radius over + + align:start position:0% +confinement time um as the radius over + + + align:start position:0% +confinement time um as the radius over +the Sound Speed uh with a um one quar + + align:start position:0% +the Sound Speed uh with a um one quar + + + align:start position:0% +the Sound Speed uh with a um one quar +comp inut so I'm I'm not going to go + + align:start position:0% +comp inut so I'm I'm not going to go + + + align:start position:0% +comp inut so I'm I'm not going to go +through that integral in detail but it's + + align:start position:0% +through that integral in detail but it's + + + align:start position:0% +through that integral in detail but it's +a very very simple + + align:start position:0% +a very very simple + + + align:start position:0% +a very very simple +one uh yeah so this is the confinement + + align:start position:0% +one uh yeah so this is the confinement + + + align:start position:0% +one uh yeah so this is the confinement +time okay so then if we look at the + + align:start position:0% +time okay so then if we look at the + + + align:start position:0% +time okay so then if we look at the +standard number density times + + align:start position:0% +standard number density times + + + align:start position:0% +standard number density times +confinement and plug this expression + + align:start position:0% +confinement and plug this expression + + + align:start position:0% +confinement and plug this expression +from the previous slide in for the + + align:start position:0% +from the previous slide in for the + + + align:start position:0% +from the previous slide in for the +confinement + + align:start position:0% +confinement + + + align:start position:0% +confinement +time it gives us this + + align:start position:0% +time it gives us this + + + align:start position:0% +time it gives us this +expression so we see that number density + + align:start position:0% +expression so we see that number density + + + align:start position:0% +expression so we see that number density +times defining time direct function of + + align:start position:0% +times defining time direct function of + + + align:start position:0% +times defining time direct function of +row R which is this area of density that + + align:start position:0% +row R which is this area of density that + + + align:start position:0% +row R which is this area of density that +keep talking about which is essentially + + align:start position:0% +keep talking about which is essentially + + + align:start position:0% +keep talking about which is essentially +a confinement parameter in inertial + + align:start position:0% +a confinement parameter in inertial + + + align:start position:0% +a confinement parameter in inertial +confinement fusion and that's why we + + align:start position:0% +confinement fusion and that's why we + + + align:start position:0% +confinement fusion and that's why we +care about it so + + align:start position:0% +care about it so + + + align:start position:0% +care about it so +much um oh yeah been highlighting it + + align:start position:0% +much um oh yeah been highlighting it + + + align:start position:0% +much um oh yeah been highlighting it +there um High aerial density or rowar + + align:start position:0% +there um High aerial density or rowar + + + align:start position:0% +there um High aerial density or rowar +which I us refer to it as is required + + align:start position:0% +which I us refer to it as is required + + + align:start position:0% +which I us refer to it as is required +for a significant uh fraction of the + + align:start position:0% +for a significant uh fraction of the + + + align:start position:0% +for a significant uh fraction of the +fuel to burn before disassembles under + + align:start position:0% +fuel to burn before disassembles under + + + align:start position:0% +fuel to burn before disassembles under +its own pressure + + align:start position:0% +its own pressure + + + align:start position:0% +its own pressure +um we can express the the burn fraction + + align:start position:0% +um we can express the the burn fraction + + + align:start position:0% +um we can express the the burn fraction +FB as row R row R * 6 G per cm squared + + align:start position:0% +FB as row R row R * 6 G per cm squared + + + align:start position:0% +FB as row R row R * 6 G per cm squared +that's said an ion temperature 30k you + + align:start position:0% +that's said an ion temperature 30k you + + + align:start position:0% +that's said an ion temperature 30k you +can derive it at different I temperature + + align:start position:0% +can derive it at different I temperature + + + align:start position:0% +can derive it at different I temperature +as well that's kind of high compared + + align:start position:0% +as well that's kind of high compared + + + align:start position:0% +as well that's kind of high compared +where we usually operate at uh and this + + align:start position:0% +where we usually operate at uh and this + + + align:start position:0% +where we usually operate at uh and this +expression actually is um derived from + + align:start position:0% +expression actually is um derived from + + + align:start position:0% +expression actually is um derived from +the fusion burn rate integrated over the + + align:start position:0% +the fusion burn rate integrated over the + + + align:start position:0% +the fusion burn rate integrated over the +confin the time um if we throw in some + + align:start position:0% +confin the time um if we throw in some + + + align:start position:0% +confin the time um if we throw in some +numbers on this we can throw in that we + + align:start position:0% +numbers on this we can throw in that we + + + align:start position:0% +numbers on this we can throw in that we +want to a burn a fraction to 25% which + + align:start position:0% +want to a burn a fraction to 25% which + + + align:start position:0% +want to a burn a fraction to 25% which +really would be required for High Gain + + align:start position:0% +really would be required for High Gain + + + align:start position:0% +really would be required for High Gain +that means we need a rowar of two gram + + align:start position:0% +that means we need a rowar of two gram + + + align:start position:0% +that means we need a rowar of two gram +per centimet squar okay to just to put + + align:start position:0% +per centimet squar okay to just to put + + + align:start position:0% +per centimet squar okay to just to put +this in perspective the best performing + + align:start position:0% +this in perspective the best performing + + + align:start position:0% +this in perspective the best performing +n implosions today they had a burnup + + align:start position:0% +n implosions today they had a burnup + + + align:start position:0% +n implosions today they had a burnup +fraction of about 5% so so this is + + align:start position:0% +fraction of about 5% so so this is + + + align:start position:0% +fraction of about 5% so so this is +really high performance um and then if + + align:start position:0% +really high performance um and then if + + + align:start position:0% +really high performance um and then if +we assume solid DT DTI ice has a density + + align:start position:0% +we assume solid DT DTI ice has a density + + + align:start position:0% +we assume solid DT DTI ice has a density +of 25 gram per cubic cm um then we find + + align:start position:0% +of 25 gram per cubic cm um then we find + + + align:start position:0% +of 25 gram per cubic cm um then we find +that for ignition we need a fuel Mass + + align:start position:0% +that for ignition we need a fuel Mass + + + align:start position:0% +that for ignition we need a fuel Mass +about a half a kilogram again is this + + align:start position:0% +about a half a kilogram again is this + + + align:start position:0% +about a half a kilogram again is this +with this exception solid + + align:start position:0% +with this exception solid + + + align:start position:0% +with this exception solid +DTI so then the question is this I'm + + align:start position:0% +DTI so then the question is this I'm + + + align:start position:0% +DTI so then the question is this I'm +sure you've seen this thousand times + + align:start position:0% +sure you've seen this thousand times + + + align:start position:0% +sure you've seen this thousand times +before in ICF presentations can we + + align:start position:0% +before in ICF presentations can we + + + align:start position:0% +before in ICF presentations can we +really work with .5 kilograms of D2 fuel + + align:start position:0% +really work with .5 kilograms of D2 fuel + + + align:start position:0% +really work with .5 kilograms of D2 fuel +in a + + align:start position:0% +in a + + + align:start position:0% +in a +laboratory of course the answer is no uh + + align:start position:0% +laboratory of course the answer is no uh + + + align:start position:0% +laboratory of course the answer is no uh +that gives us a little too much yield + + align:start position:0% +that gives us a little too much yield + + + align:start position:0% +that gives us a little too much yield +which is not quite what we + + align:start position:0% +which is not quite what we + + + align:start position:0% +which is not quite what we +want and that motivates uh that in order + + align:start position:0% +want and that motivates uh that in order + + + align:start position:0% +want and that motivates uh that in order +to achieve the required aerial density + + align:start position:0% +to achieve the required aerial density + + + align:start position:0% +to achieve the required aerial density +or confinement parameter iron + + align:start position:0% +or confinement parameter iron + + + align:start position:0% +or confinement parameter iron +temperature and confine and time without + + align:start position:0% +temperature and confine and time without + + + align:start position:0% +temperature and confine and time without +destroying the Lavin compressed + + align:start position:0% +destroying the Lavin compressed + + + align:start position:0% +destroying the Lavin compressed +capsule um we actually have to compress + + align:start position:0% +capsule um we actually have to compress + + + align:start position:0% +capsule um we actually have to compress +it quite a lot we get these rough + + align:start position:0% +it quite a lot we get these rough + + + align:start position:0% +it quite a lot we get these rough +parameters um starting from about a 2 mm + + align:start position:0% +parameters um starting from about a 2 mm + + + align:start position:0% +parameters um starting from about a 2 mm +size capsule get down the radius of 30 + + align:start position:0% +size capsule get down the radius of 30 + + + align:start position:0% +size capsule get down the radius of 30 +to 50 microns um density like 700 gram + + align:start position:0% +to 50 microns um density like 700 gram + + + align:start position:0% +to 50 microns um density like 700 gram +per cubic centimeters from the 25 that + + align:start position:0% +per cubic centimeters from the 25 that + + + align:start position:0% +per cubic centimeters from the 25 that +we started like um an aerial density of + + align:start position:0% +we started like um an aerial density of + + + align:start position:0% +we started like um an aerial density of +2 G per cenm squ temperatures from 5 to + + align:start position:0% +2 G per cenm squ temperatures from 5 to + + + align:start position:0% +2 G per cenm squ temperatures from 5 to +40 and confin times from about 12 P + + align:start position:0% +40 and confin times from about 12 P + + + align:start position:0% +40 and confin times from about 12 P +seconds so looking at these + + align:start position:0% +seconds so looking at these + + + align:start position:0% +seconds so looking at these +numbers these enclos parameters really + + align:start position:0% +numbers these enclos parameters really + + + align:start position:0% +numbers these enclos parameters really +set the requirements on the different + + align:start position:0% +set the requirements on the different + + + align:start position:0% +set the requirements on the different +measurements typically we want to + + align:start position:0% +measurements typically we want to + + + align:start position:0% +measurements typically we want to +achieve with five to 10% accuracy on + + align:start position:0% +achieve with five to 10% accuracy on + + + align:start position:0% +achieve with five to 10% accuracy on +these kinds of numbers so that really + + align:start position:0% +these kinds of numbers so that really + + + align:start position:0% +these kinds of numbers so that really +tells you how how well we need to be + + align:start position:0% +tells you how how well we need to be + + + align:start position:0% +tells you how how well we need to be +able to make these + + align:start position:0% + + + + align:start position:0% + +measurements okay so then we have a lot + + align:start position:0% +measurements okay so then we have a lot + + + align:start position:0% +measurements okay so then we have a lot +of Nu fa products that we can work with + + align:start position:0% +of Nu fa products that we can work with + + + align:start position:0% +of Nu fa products that we can work with +and they they really carry a wealth of + + align:start position:0% +and they they really carry a wealth of + + + align:start position:0% +and they they really carry a wealth of +information about ICF implosions um + + align:start position:0% +information about ICF implosions um + + + align:start position:0% +information about ICF implosions um +first of all we have our primary product + + align:start position:0% +first of all we have our primary product + + + align:start position:0% +first of all we have our primary product +um and all of you know that it primarily + + align:start position:0% +um and all of you know that it primarily + + + align:start position:0% +um and all of you know that it primarily +work the DT reaction which gives alra + + align:start position:0% +work the DT reaction which gives alra + + + align:start position:0% +work the DT reaction which gives alra +particle in neutron + + align:start position:0% + + + + align:start position:0% + +as I don't think so unfortunately okay + + align:start position:0% +as I don't think so unfortunately okay + + + align:start position:0% +as I don't think so unfortunately okay +keep jumping yeah sorry you could use a + + align:start position:0% +keep jumping yeah sorry you could use a + + + align:start position:0% +keep jumping yeah sorry you could use a +border razor but that's only going to + + align:start position:0% +border razor but that's only going to + + + align:start position:0% +border razor but that's only going to +give you an extra + + align:start position:0% + + + + align:start position:0% + +bot okay so that's the the primary one + + align:start position:0% +bot okay so that's the the primary one + + + align:start position:0% +bot okay so that's the the primary one +we with um if you look over here that + + align:start position:0% +we with um if you look over here that + + + align:start position:0% +we with um if you look over here that +gives us the yield the ion temperature + + align:start position:0% +gives us the yield the ion temperature + + + align:start position:0% +gives us the yield the ion temperature +the aerial density we can also use it + + align:start position:0% +the aerial density we can also use it + + + align:start position:0% +the aerial density we can also use it +for yield versus time uh and use it to + + align:start position:0% +for yield versus time uh and use it to + + + align:start position:0% +for yield versus time uh and use it to +infer the confinement time and the + + align:start position:0% +infer the confinement time and the + + + align:start position:0% +infer the confinement time and the +radius of the capsule um there's also + + align:start position:0% +radius of the capsule um there's also + + + align:start position:0% +radius of the capsule um there's also +another branch that which gives us a + + align:start position:0% +another branch that which gives us a + + + align:start position:0% +another branch that which gives us a +gamma particle which is actually quite + + align:start position:0% +gamma particle which is actually quite + + + align:start position:0% +gamma particle which is actually quite +useful and looking little bit at that as + + align:start position:0% +useful and looking little bit at that as + + + align:start position:0% +useful and looking little bit at that as +well later in the p in addition to DD we + + align:start position:0% +well later in the p in addition to DD we + + + align:start position:0% +well later in the p in addition to DD we +can also look at primary products from + + align:start position:0% +can also look at primary products from + + + align:start position:0% +can also look at primary products from +the DD reactions we have two one that + + align:start position:0% +the DD reactions we have two one that + + + align:start position:0% +the DD reactions we have two one that +gives the Tron and the prot done once + + align:start position:0% +gives the Tron and the prot done once + + + align:start position:0% +gives the Tron and the prot done once +give helium 3 and a neutron and actually + + align:start position:0% +give helium 3 and a neutron and actually + + + align:start position:0% +give helium 3 and a neutron and actually +a lot of magnetic confinement + + align:start position:0% +a lot of magnetic confinement + + + align:start position:0% +a lot of magnetic confinement +experiments have been working primarily + + align:start position:0% +experiments have been working primarily + + + align:start position:0% +experiments have been working primarily +with DD today so you can use that nutr + + align:start position:0% +with DD today so you can use that nutr + + + align:start position:0% +with DD today so you can use that nutr +for a lot of measurements as well uh and + + align:start position:0% +for a lot of measurements as well uh and + + + align:start position:0% +for a lot of measurements as well uh and +then dhum 3 we also work within a lot of + + align:start position:0% +then dhum 3 we also work within a lot of + + + align:start position:0% +then dhum 3 we also work within a lot of +surrogate experiments where where we + + align:start position:0% +surrogate experiments where where we + + + align:start position:0% +surrogate experiments where where we +don't want to put DT in and St of things + + align:start position:0% +don't want to put DT in and St of things + + + align:start position:0% +don't want to put DT in and St of things +and then actually it's quite similar to + + align:start position:0% +and then actually it's quite similar to + + + align:start position:0% +and then actually it's quite similar to +DT we also get an alpha particle get a + + align:start position:0% +DT we also get an alpha particle get a + + + align:start position:0% +DT we also get an alpha particle get a +proton instead of a neutron with pretty + + align:start position:0% +proton instead of a neutron with pretty + + + align:start position:0% +proton instead of a neutron with pretty +high + + align:start position:0% +high + + + align:start position:0% +high +energy okay so those are the primaries + + align:start position:0% +energy okay so those are the primaries + + + align:start position:0% +energy okay so those are the primaries +count the number of primaries we + + align:start position:0% +count the number of primaries we + + + align:start position:0% +count the number of primaries we +generate gives us a direct measurement + + align:start position:0% +generate gives us a direct measurement + + + align:start position:0% +generate gives us a direct measurement +of how many F reactions we add obviously + + align:start position:0% +of how many F reactions we add obviously + + + align:start position:0% +of how many F reactions we add obviously +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +um quick way of getting the yield for + + align:start position:0% +um quick way of getting the yield for + + + align:start position:0% +um quick way of getting the yield for +new potion not necessarily always easy + + align:start position:0% +new potion not necessarily always easy + + + align:start position:0% +new potion not necessarily always easy +but basically that's how works we can + + align:start position:0% +but basically that's how works we can + + + align:start position:0% +but basically that's how works we can +also have secondary products which I + + align:start position:0% +also have secondary products which I + + + align:start position:0% +also have secondary products which I +actually won't be spending much time on + + align:start position:0% +actually won't be spending much time on + + + align:start position:0% +actually won't be spending much time on +today but if you're interested in that + + align:start position:0% +today but if you're interested in that + + + align:start position:0% +today but if you're interested in that +um I'm happy to answer questions + + align:start position:0% +um I'm happy to answer questions + + + align:start position:0% +um I'm happy to answer questions +afterwards so that's when one of the + + align:start position:0% +afterwards so that's when one of the + + + align:start position:0% +afterwards so that's when one of the +fast products produced in a primary + + align:start position:0% +fast products produced in a primary + + + align:start position:0% +fast products produced in a primary +reaction goes on to react with a a + + align:start position:0% +reaction goes on to react with a a + + + align:start position:0% +reaction goes on to react with a a +thermal fuel Lon to give a broad ener + + align:start position:0% +thermal fuel Lon to give a broad ener + + + align:start position:0% +thermal fuel Lon to give a broad ener +spectrum of of the reaction + + align:start position:0% +spectrum of of the reaction + + + align:start position:0% +spectrum of of the reaction +products and then we have knock + + align:start position:0% +products and then we have knock + + + align:start position:0% +products and then we have knock +reactions we'll spend a little bit of + + align:start position:0% +reactions we'll spend a little bit of + + + align:start position:0% +reactions we'll spend a little bit of +time looking at how this works so that's + + align:start position:0% +time looking at how this works so that's + + + align:start position:0% +time looking at how this works so that's +when the fast neutrons are born in the + + align:start position:0% +when the fast neutrons are born in the + + + align:start position:0% +when the fast neutrons are born in the +D2 + + align:start position:0% +D2 + + + align:start position:0% +D2 +reaction hit one of the fuel ions to + + align:start position:0% +reaction hit one of the fuel ions to + + + align:start position:0% +reaction hit one of the fuel ions to +give a faster Fuel iion and a scattered + + align:start position:0% +give a faster Fuel iion and a scattered + + + align:start position:0% +give a faster Fuel iion and a scattered +Neutron we actually use this quite a + + align:start position:0% +Neutron we actually use this quite a + + + align:start position:0% +Neutron we actually use this quite a +lot uh and we can also have similar + + align:start position:0% +lot uh and we can also have similar + + + align:start position:0% +lot uh and we can also have similar +Reactions where the alpha particles + + align:start position:0% +Reactions where the alpha particles + + + align:start position:0% +Reactions where the alpha particles +scatter on the fuel iion + + align:start position:0% +scatter on the fuel iion + + + align:start position:0% +scatter on the fuel iion +upshift and fewu Alliance won't spend + + align:start position:0% +upshift and fewu Alliance won't spend + + + align:start position:0% +upshift and fewu Alliance won't spend +much time on this today but this is the + + align:start position:0% +much time on this today but this is the + + + align:start position:0% +much time on this today but this is the +signature that we can + + align:start position:0% +signature that we can + + + align:start position:0% +signature that we can +use uh to look at what the alpha + + align:start position:0% +use uh to look at what the alpha + + + align:start position:0% +use uh to look at what the alpha +particles are doing in the plasma in + + align:start position:0% +particles are doing in the plasma in + + + align:start position:0% +particles are doing in the plasma in +particular when these fast D and trions + + align:start position:0% +particular when these fast D and trions + + + align:start position:0% +particular when these fast D and trions +react again in a tertiary reaction which + + align:start position:0% +react again in a tertiary reaction which + + + align:start position:0% +react again in a tertiary reaction which +I think that example is in here yeah to + + align:start position:0% +I think that example is in here yeah to + + + align:start position:0% +I think that example is in here yeah to +give these fast neutrons which are + + align:start position:0% +give these fast neutrons which are + + + align:start position:0% +give these fast neutrons which are +called alpha n + + align:start position:0% +called alpha n + + + align:start position:0% +called alpha n +neutrons I think some of you have heard + + align:start position:0% +neutrons I think some of you have heard + + + align:start position:0% +neutrons I think some of you have heard +about that + + align:start position:0% +about that + + + align:start position:0% +about that +before um okay okay yeah + + align:start position:0% + + + + align:start position:0% + +so this is actually pretty cool the + + align:start position:0% +so this is actually pretty cool the + + + align:start position:0% +so this is actually pretty cool the +these KnockOn reactions are the easiest + + align:start position:0% +these KnockOn reactions are the easiest + + + align:start position:0% +these KnockOn reactions are the easiest +way of measuring gr so we look at some + + align:start position:0% +way of measuring gr so we look at some + + + align:start position:0% +way of measuring gr so we look at some +examples of that as we go + + align:start position:0% + + + + align:start position:0% + +through okay we already talked about + + align:start position:0% +through okay we already talked about + + + align:start position:0% +through okay we already talked about +this counting the number of emitted + + align:start position:0% +this counting the number of emitted + + + align:start position:0% +this counting the number of emitted +primary Fusion products in a set + + align:start position:0% +primary Fusion products in a set + + + align:start position:0% +primary Fusion products in a set +um solid angle and scaling it up to four + + align:start position:0% +um solid angle and scaling it up to four + + + align:start position:0% +um solid angle and scaling it up to four +Pi gives us a measure of the total yield + + align:start position:0% +Pi gives us a measure of the total yield + + + align:start position:0% +Pi gives us a measure of the total yield +so this this is basically the Y + + align:start position:0% +so this this is basically the Y + + + align:start position:0% +so this this is basically the Y +reaction um I forgot to put the Y in + + align:start position:0% +reaction um I forgot to put the Y in + + + align:start position:0% +reaction um I forgot to put the Y in +front of it but if you do the the + + align:start position:0% +front of it but if you do the the + + + align:start position:0% +front of it but if you do the the +integral over volume and time of the + + align:start position:0% +integral over volume and time of the + + + align:start position:0% +integral over volume and time of the +densities of the uh reactants typically + + align:start position:0% +densities of the uh reactants typically + + + align:start position:0% +densities of the uh reactants typically +it could be Deary mums or plasma and the + + align:start position:0% +it could be Deary mums or plasma and the + + + align:start position:0% +it could be Deary mums or plasma and the +reactivity uh and this is just a chronic + + align:start position:0% +reactivity uh and this is just a chronic + + + align:start position:0% +reactivity uh and this is just a chronic +result that so if it's 2D you get a + + align:start position:0% +result that so if it's 2D you get a + + + align:start position:0% +result that so if it's 2D you get a +factor + + align:start position:0% +factor + + + align:start position:0% +factor +one2 um that gives you right and the + + align:start position:0% +one2 um that gives you right and the + + + align:start position:0% +one2 um that gives you right and the +reactivity is integral over the reactant + + align:start position:0% +reactivity is integral over the reactant + + + align:start position:0% +reactivity is integral over the reactant +of the fuel l distributions the + + align:start position:0% +of the fuel l distributions the + + + align:start position:0% +of the fuel l distributions the +cross-section um and then you can get + + align:start position:0% +cross-section um and then you can get + + + align:start position:0% +cross-section um and then you can get +the reactivity this actually example + + align:start position:0% +the reactivity this actually example + + + align:start position:0% +the reactivity this actually example +reactivity is calculated foring that + + align:start position:0% +reactivity is calculated foring that + + + align:start position:0% +reactivity is calculated foring that +formula um as written up in this paper + + align:start position:0% +formula um as written up in this paper + + + align:start position:0% +formula um as written up in this paper +which if you haven't seen this paper + + align:start position:0% +which if you haven't seen this paper + + + align:start position:0% +which if you haven't seen this paper +before this is really a key key + + align:start position:0% +before this is really a key key + + + align:start position:0% +before this is really a key key +reference to go to if you want to look + + align:start position:0% +reference to go to if you want to look + + + align:start position:0% +reference to go to if you want to look +at How likely a reaction is that um + + align:start position:0% +at How likely a reaction is that um + + + align:start position:0% +at How likely a reaction is that um +obviously DT is the most probable then + + align:start position:0% +obviously DT is the most probable then + + + align:start position:0% +obviously DT is the most probable then +we have the two D reactions lower + + align:start position:0% +we have the two D reactions lower + + + align:start position:0% +we have the two D reactions lower +probability and you can go to lower + + align:start position:0% +probability and you can go to lower + + + align:start position:0% +probability and you can go to lower +probability on for D and three or t as + + align:start position:0% +probability on for D and three or t as + + + align:start position:0% +probability on for D and three or t as +much okay yes go ahead John um how do + + align:start position:0% +much okay yes go ahead John um how do + + + align:start position:0% +much okay yes go ahead John um how do +you deal with the fact that you're + + align:start position:0% +you deal with the fact that you're + + + align:start position:0% +you deal with the fact that you're +technically not so when you do this + + align:start position:0% +technically not so when you do this + + + align:start position:0% +technically not so when you do this +calculation of integrating over four Pi + + align:start position:0% +calculation of integrating over four Pi + + + align:start position:0% +calculation of integrating over four Pi +you're assuming some spherical symmetry + + align:start position:0% +you're assuming some spherical symmetry + + + align:start position:0% +you're assuming some spherical symmetry +but we know for fact great + + align:start position:0% +but we know for fact great + + + align:start position:0% +but we know for fact great +question um so in ICF actually you can + + align:start position:0% +question um so in ICF actually you can + + + align:start position:0% +question um so in ICF actually you can +typically assume four Pi there are some + + align:start position:0% +typically assume four Pi there are some + + + align:start position:0% +typically assume four Pi there are some +variations which we can look at will + + align:start position:0% +variations which we can look at will + + + align:start position:0% +variations which we can look at will +look at later in the the talk but in + + align:start position:0% +look at later in the the talk but in + + + align:start position:0% +look at later in the the talk but in +magnetic confir Fusion you don't have + + align:start position:0% +magnetic confir Fusion you don't have + + + align:start position:0% +magnetic confir Fusion you don't have +for p symmetry so then you have to + + align:start position:0% +for p symmetry so then you have to + + + align:start position:0% +for p symmetry so then you have to +correct for it and actually this leads + + align:start position:0% +correct for it and actually this leads + + + align:start position:0% +correct for it and actually this leads +to the work that you doing this is an + + align:start position:0% +to the work that you doing this is an + + + align:start position:0% +to the work that you doing this is an +example from a paper in 2010 by Henry + + align:start position:0% +example from a paper in 2010 by Henry + + + align:start position:0% +example from a paper in 2010 by Henry +Pan um where he's using a neutron + + align:start position:0% +Pan um where he's using a neutron + + + align:start position:0% +Pan um where he's using a neutron +spectrometer to infer the total yield of + + align:start position:0% +spectrometer to infer the total yield of + + + align:start position:0% +spectrometer to infer the total yield of +neutrons from of the ma but he needs to + + align:start position:0% +neutrons from of the ma but he needs to + + + align:start position:0% +neutrons from of the ma but he needs to +correct the emission profile of using + + align:start position:0% +correct the emission profile of using + + + align:start position:0% +correct the emission profile of using +the profile monitor head so he can scale + + align:start position:0% +the profile monitor head so he can scale + + + align:start position:0% +the profile monitor head so he can scale +that single line site counting neutr + + align:start position:0% +that single line site counting neutr + + + align:start position:0% +that single line site counting neutr +into one4 Pi emission of the + + align:start position:0% +into one4 Pi emission of the + + + align:start position:0% +into one4 Pi emission of the +great + + align:start position:0% +great + + + align:start position:0% +great +question + + align:start position:0% +question + + + align:start position:0% +question +okay uh okay + + align:start position:0% +okay uh okay + + + align:start position:0% +okay uh okay +so thinking about what happens to the + + align:start position:0% +so thinking about what happens to the + + + align:start position:0% +so thinking about what happens to the +particles after they Bor most neutrons + + align:start position:0% +particles after they Bor most neutrons + + + align:start position:0% +particles after they Bor most neutrons +Escape an implosion and can be + + align:start position:0% +Escape an implosion and can be + + + align:start position:0% +Escape an implosion and can be +counted but um some of them scatter we + + align:start position:0% +counted but um some of them scatter we + + + align:start position:0% +counted but um some of them scatter we +talking more about but for charge Fusion + + align:start position:0% +talking more about but for charge Fusion + + + align:start position:0% +talking more about but for charge Fusion +products like from the D3 reaction um + + align:start position:0% +products like from the D3 reaction um + + + align:start position:0% +products like from the D3 reaction um +stopping in the assembled fuel has to be + + align:start position:0% +stopping in the assembled fuel has to be + + + align:start position:0% +stopping in the assembled fuel has to be +comped so the neutrons they might + + align:start position:0% +comped so the neutrons they might + + + align:start position:0% +comped so the neutrons they might +scatter on their way out lose other + + align:start position:0% +scatter on their way out lose other + + + align:start position:0% +scatter on their way out lose other +energy but most of them Escape directly + + align:start position:0% +energy but most of them Escape directly + + + align:start position:0% +energy but most of them Escape directly +scaning probability is relatively low um + + align:start position:0% +scaning probability is relatively low um + + + align:start position:0% +scaning probability is relatively low um +any charged particles are in lose energy + + align:start position:0% +any charged particles are in lose energy + + + align:start position:0% +any charged particles are in lose energy +as they Traverse the assembled fields + + align:start position:0% +as they Traverse the assembled fields + + + align:start position:0% +as they Traverse the assembled fields +and in fact so an example what that can + + align:start position:0% +and in fact so an example what that can + + + align:start position:0% +and in fact so an example what that can +look like we have the hel 3 Pro Spectrum + + align:start position:0% +look like we have the hel 3 Pro Spectrum + + + align:start position:0% +look like we have the hel 3 Pro Spectrum +be born at 14.7 energy this is the lower + + align:start position:0% +be born at 14.7 energy this is the lower + + + align:start position:0% +be born at 14.7 energy this is the lower +water osion lose just a little bit of + + align:start position:0% +water osion lose just a little bit of + + + align:start position:0% +water osion lose just a little bit of +energy on its way out of the capsule for + + align:start position:0% +energy on its way out of the capsule for + + + align:start position:0% +energy on its way out of the capsule for +high convergence potions with high R + + align:start position:0% +high convergence potions with high R + + + align:start position:0% +high convergence potions with high R +water the ions will be fully stopped in + + align:start position:0% +water the ions will be fully stopped in + + + align:start position:0% +water the ions will be fully stopped in +C be counted so then we really can't + + align:start position:0% +C be counted so then we really can't + + + align:start position:0% +C be counted so then we really can't +rely on measuring primary Fusion + + align:start position:0% +rely on measuring primary Fusion + + + align:start position:0% +rely on measuring primary Fusion +products charged Fusion products uh for + + align:start position:0% +products charged Fusion products uh for + + + align:start position:0% +products charged Fusion products uh for +those experiments and actually it turns + + align:start position:0% +those experiments and actually it turns + + + align:start position:0% +those experiments and actually it turns +out that ion stopping plasmas is a rich + + align:start position:0% +out that ion stopping plasmas is a rich + + + align:start position:0% +out that ion stopping plasmas is a rich +research topic um that our group has + + align:start position:0% +research topic um that our group has + + + align:start position:0% +research topic um that our group has +been working on and few example + + align:start position:0% +been working on and few example + + + align:start position:0% +been working on and few example +references there and there are a lot of + + align:start position:0% +references there and there are a lot of + + + align:start position:0% +references there and there are a lot of +other + + align:start position:0% +other + + + align:start position:0% +other +references um okay let's see yes so + + align:start position:0% +references um okay let's see yes so + + + align:start position:0% +references um okay let's see yes so +coming back a little bit to the KnockOn + + align:start position:0% +coming back a little bit to the KnockOn + + + align:start position:0% +coming back a little bit to the KnockOn +reactions so the neutrons um when they + + align:start position:0% +reactions so the neutrons um when they + + + align:start position:0% +reactions so the neutrons um when they +scatter off the fuel + + align:start position:0% +scatter off the fuel + + + align:start position:0% +scatter off the fuel +allance they will also UPS scatter the + + align:start position:0% +allance they will also UPS scatter the + + + align:start position:0% +allance they will also UPS scatter the +fuel Alles in energy so Fu lons that are + + align:start position:0% +fuel Alles in energy so Fu lons that are + + + align:start position:0% +fuel Alles in energy so Fu lons that are +um you know start in the thermal + + align:start position:0% +um you know start in the thermal + + + align:start position:0% +um you know start in the thermal +distribution basically cold can be UPS + + align:start position:0% +distribution basically cold can be UPS + + + align:start position:0% +distribution basically cold can be UPS +scattered with much higher energy by the + + align:start position:0% +scattered with much higher energy by the + + + align:start position:0% +scattered with much higher energy by the +14 M neutrons the energy of the ion we + + align:start position:0% +14 M neutrons the energy of the ion we + + + align:start position:0% +14 M neutrons the energy of the ion we +calculate according that react or that + + align:start position:0% +calculate according that react or that + + + align:start position:0% +calculate according that react or that +equation where a is the mass number of + + align:start position:0% +equation where a is the mass number of + + + align:start position:0% +equation where a is the mass number of +the scattering + + align:start position:0% +the scattering + + + align:start position:0% +the scattering +nucleus and um th is the scattering + + align:start position:0% +nucleus and um th is the scattering + + + align:start position:0% +nucleus and um th is the scattering +angle + + align:start position:0% +angle + + + align:start position:0% +angle +is a neutr energy um and this is + + align:start position:0% +is a neutr energy um and this is + + + align:start position:0% +is a neutr energy um and this is +examples of what it can look like so + + align:start position:0% +examples of what it can look like so + + + align:start position:0% +examples of what it can look like so +this is the scattered Spectrum uh for + + align:start position:0% +this is the scattered Spectrum uh for + + + align:start position:0% +this is the scattered Spectrum uh for +trions deuterons and protons and + + align:start position:0% +trions deuterons and protons and + + + align:start position:0% +trions deuterons and protons and +basically um the energy of it de Tron + + align:start position:0% +basically um the energy of it de Tron + + + align:start position:0% +basically um the energy of it de Tron +proton that's scattered in this way is + + align:start position:0% +proton that's scattered in this way is + + + align:start position:0% +proton that's scattered in this way is +going to depend on the scattering angle + + align:start position:0% +going to depend on the scattering angle + + + align:start position:0% +going to depend on the scattering angle +so this is what you get if integr with + + align:start position:0% +so this is what you get if integr with + + + align:start position:0% +so this is what you get if integr with +all + + align:start position:0% +all + + + align:start position:0% +all +scatter + + align:start position:0% +scatter + + + align:start position:0% +scatter +um okay and we can use this + + align:start position:0% +um okay and we can use this + + + align:start position:0% +um okay and we can use this +fact we can we often measure these + + align:start position:0% +fact we can we often measure these + + + align:start position:0% +fact we can we often measure these +products um and we use a number of those + + align:start position:0% +products um and we use a number of those + + + align:start position:0% +products um and we use a number of those +products to infer aerial density because + + align:start position:0% +products to infer aerial density because + + + align:start position:0% +products to infer aerial density because +the aerial density depends on the ratio + + align:start position:0% +the aerial density depends on the ratio + + + align:start position:0% +the aerial density depends on the ratio +part of scale basically the opposite the + + align:start position:0% +part of scale basically the opposite the + + + align:start position:0% +part of scale basically the opposite the +ratio of the number of knon ions to the + + align:start position:0% +ratio of the number of knon ions to the + + + align:start position:0% +ratio of the number of knon ions to the +neutron yield will be a functional VAR + + align:start position:0% +neutron yield will be a functional VAR + + + align:start position:0% +neutron yield will be a functional VAR +of + + align:start position:0% +of + + + align:start position:0% +of +that so that makes sense the more fuel + + align:start position:0% +that so that makes sense the more fuel + + + align:start position:0% +that so that makes sense the more fuel +that's assembled the more of the nutr + + align:start position:0% +that's assembled the more of the nutr + + + align:start position:0% +that's assembled the more of the nutr +are going to scatter + + align:start position:0% +are going to scatter + + + align:start position:0% +are going to scatter +um so we can use that relationship to + + align:start position:0% +um so we can use that relationship to + + + align:start position:0% +um so we can use that relationship to +infer what the aial density of an + + align:start position:0% +infer what the aial density of an + + + align:start position:0% +infer what the aial density of an +implosion is but this only works up to a + + align:start position:0% +implosion is but this only works up to a + + + align:start position:0% +implosion is but this only works up to a +certain aerial density like the the knus + + align:start position:0% +certain aerial density like the the knus + + + align:start position:0% +certain aerial density like the the knus +for example would be fully ranged out of + + align:start position:0% +for example would be fully ranged out of + + + align:start position:0% +for example would be fully ranged out of +the aerial grip the density is 200 + + align:start position:0% +the aerial grip the density is 200 + + + align:start position:0% +the aerial grip the density is 200 +milligrams and we talked about before + + align:start position:0% +milligrams and we talked about before + + + align:start position:0% +milligrams and we talked about before +the might need order two grams per C + + align:start position:0% +the might need order two grams per C + + + align:start position:0% +the might need order two grams per C +Square so this is really relatively well + + align:start position:0% +Square so this is really relatively well + + + align:start position:0% +Square so this is really relatively well +performing potions that we looking + + align:start position:0% +performing potions that we looking + + + align:start position:0% +performing potions that we looking +at + + align:start position:0% +at + + + align:start position:0% +at +um so we often look at the nutrients + + align:start position:0% +um so we often look at the nutrients + + + align:start position:0% +um so we often look at the nutrients +instead and we can can derive the energy + + align:start position:0% +instead and we can can derive the energy + + + align:start position:0% +instead and we can can derive the energy +of the scattered neutrons to see that + + align:start position:0% +of the scattered neutrons to see that + + + align:start position:0% +of the scattered neutrons to see that +the neutrons carry information about the + + align:start position:0% +the neutrons carry information about the + + + align:start position:0% +the neutrons carry information about the +symmetry of the assembled plasma because + + align:start position:0% +symmetry of the assembled plasma because + + + align:start position:0% +symmetry of the assembled plasma because +again the scattered Neutron energy will + + align:start position:0% +again the scattered Neutron energy will + + + align:start position:0% +again the scattered Neutron energy will +depend on the mass number of the + + align:start position:0% +depend on the mass number of the + + + align:start position:0% +depend on the mass number of the +scattering nucleus and the scattering + + align:start position:0% +scattering nucleus and the scattering + + + align:start position:0% +scattering nucleus and the scattering +angle so we find if we do that math that + + align:start position:0% +angle so we find if we do that math that + + + align:start position:0% +angle so we find if we do that math that +for a detector at a set angle T + + align:start position:0% +for a detector at a set angle T + + + align:start position:0% +for a detector at a set angle T +potion neutrons are end up at the + + align:start position:0% +potion neutrons are end up at the + + + align:start position:0% +potion neutrons are end up at the +detector in a certain energy range I'm + + align:start position:0% +detector in a certain energy range I'm + + + align:start position:0% +detector in a certain energy range I'm +going to be sampling a certain part of + + align:start position:0% +going to be sampling a certain part of + + + align:start position:0% +going to be sampling a certain part of +the sh + + align:start position:0% +the sh + + + align:start position:0% +the sh +theion um so at the ni in particular we + + align:start position:0% +theion um so at the ni in particular we + + + align:start position:0% +theion um so at the ni in particular we +often infer the compression by looking + + align:start position:0% +often infer the compression by looking + + + align:start position:0% +often infer the compression by looking +energy range 10 to 12 M which is a + + align:start position:0% +energy range 10 to 12 M which is a + + + align:start position:0% +energy range 10 to 12 M which is a +really clean energy range of the neutron + + align:start position:0% +really clean energy range of the neutron + + + align:start position:0% +really clean energy range of the neutron +Spectrum I think I might have an example + + align:start position:0% +Spectrum I think I might have an example + + + align:start position:0% +Spectrum I think I might have an example +later you can see there are no other + + align:start position:0% +later you can see there are no other + + + align:start position:0% +later you can see there are no other +sources of nutrients that might + + align:start position:0% +sources of nutrients that might + + + align:start position:0% +sources of nutrients that might +contribute in that range so by looking + + align:start position:0% +contribute in that range so by looking + + + align:start position:0% +contribute in that range so by looking +at the number of nutrients in that range + + align:start position:0% +at the number of nutrients in that range + + + align:start position:0% +at the number of nutrients in that range +you really get a measurement of uh only + + align:start position:0% +you really get a measurement of uh only + + + align:start position:0% +you really get a measurement of uh only +the nutr that are sced um okay so if you + + align:start position:0% +the nutr that are sced um okay so if you + + + align:start position:0% +the nutr that are sced um okay so if you +do that if you look at the range for 10 + + align:start position:0% +do that if you look at the range for 10 + + + align:start position:0% +do that if you look at the range for 10 +to 12v the neutr scatter Tron Pro this + + align:start position:0% +to 12v the neutr scatter Tron Pro this + + + align:start position:0% +to 12v the neutr scatter Tron Pro this +part of the Shelf neut scatter Pro this + + align:start position:0% +part of the Shelf neut scatter Pro this + + + align:start position:0% +part of the Shelf neut scatter Pro this +part of the shelf and it's a little bit + + align:start position:0% +part of the shelf and it's a little bit + + + align:start position:0% +part of the shelf and it's a little bit +different because d and a different + + align:start position:0% +different because d and a different + + + align:start position:0% +different because d and a different +not and you can also broaden the range + + align:start position:0% +not and you can also broaden the range + + + align:start position:0% +not and you can also broaden the range +and actually we'll look a little bit at + + align:start position:0% +and actually we'll look a little bit at + + + align:start position:0% +and actually we'll look a little bit at +Neutron Imaging Neutron Imaging + + align:start position:0% +Neutron Imaging Neutron Imaging + + + align:start position:0% +Neutron Imaging Neutron Imaging +typically typically looks over a broader + + align:start position:0% +typically typically looks over a broader + + + align:start position:0% +typically typically looks over a broader +neutr energy range in order to get + + align:start position:0% +neutr energy range in order to get + + + align:start position:0% +neutr energy range in order to get +enough + + align:start position:0% +enough + + + align:start position:0% +enough +statistic the broader part of the shelf + + align:start position:0% +statistic the broader part of the shelf + + + align:start position:0% +statistic the broader part of the shelf +so okay this looks nice and simple in + + align:start position:0% +so okay this looks nice and simple in + + + align:start position:0% +so okay this looks nice and simple in +reality + + align:start position:0% +reality + + + align:start position:0% +reality +typically the source of neutrons is + + align:start position:0% +typically the source of neutrons is + + + align:start position:0% +typically the source of neutrons is +significantly broader so this smears out + + align:start position:0% +significantly broader so this smears out + + + align:start position:0% +significantly broader so this smears out +you're not going to have all the + + align:start position:0% +you're not going to have all the + + + align:start position:0% +you're not going to have all the +neutrons coming exactly from the center + + align:start position:0% +neutrons coming exactly from the center + + + align:start position:0% +neutrons coming exactly from the center +but this is kind of the basic + + align:start position:0% +but this is kind of the basic + + + align:start position:0% +but this is kind of the basic +idea um the unscattered energy Spectrum + + align:start position:0% +idea um the unscattered energy Spectrum + + + align:start position:0% +idea um the unscattered energy Spectrum +the neutrons that go straight out like + + align:start position:0% +the neutrons that go straight out like + + + align:start position:0% +the neutrons that go straight out like +the Green Arrow here and don't lose + + align:start position:0% +the Green Arrow here and don't lose + + + align:start position:0% +the Green Arrow here and don't lose +energy on the way out um will carry + + align:start position:0% +energy on the way out um will carry + + + align:start position:0% +energy on the way out um will carry +information about iron temperature and + + align:start position:0% +information about iron temperature and + + + align:start position:0% +information about iron temperature and +velocity of the assembled Fuel and + + align:start position:0% +velocity of the assembled Fuel and + + + align:start position:0% +velocity of the assembled Fuel and +actually in principle this would be true + + align:start position:0% +actually in principle this would be true + + + align:start position:0% +actually in principle this would be true +at any Fusion products right when + + align:start position:0% +at any Fusion products right when + + + align:start position:0% +at any Fusion products right when +they're born it will be born with this + + align:start position:0% +they're born it will be born with this + + + align:start position:0% +they're born it will be born with this +information the problem is if it's a + + align:start position:0% +information the problem is if it's a + + + align:start position:0% +information the problem is if it's a +charge Fusion product it's going to lose + + align:start position:0% +charge Fusion product it's going to lose + + + align:start position:0% +charge Fusion product it's going to lose +a lot of that information as it's losing + + align:start position:0% +a lot of that information as it's losing + + + align:start position:0% +a lot of that information as it's losing +energy on the way out of the Tex we a + + align:start position:0% +energy on the way out of the Tex we a + + + align:start position:0% +energy on the way out of the Tex we a +lot harder to infer that + + align:start position:0% +lot harder to infer that + + + align:start position:0% +lot harder to infer that +information um this is the expression + + align:start position:0% +information um this is the expression + + + align:start position:0% +information um this is the expression +for the energy of the single Fusion + + align:start position:0% +for the energy of the single Fusion + + + align:start position:0% +for the energy of the single Fusion +product then um we can take the moments + + align:start position:0% +product then um we can take the moments + + + align:start position:0% +product then um we can take the moments +of this energy over the distribution of + + align:start position:0% +of this energy over the distribution of + + + align:start position:0% +of this energy over the distribution of +reacting ions to find that the the width + + align:start position:0% +reacting ions to find that the the width + + + align:start position:0% +reacting ions to find that the the width +of the neutron spectrum is proportional + + align:start position:0% +of the neutron spectrum is proportional + + + align:start position:0% +of the neutron spectrum is proportional +to the ion temperature the small iron + + align:start position:0% +to the ion temperature the small iron + + + align:start position:0% +to the ion temperature the small iron +temperature related peak upshift of the + + align:start position:0% +temperature related peak upshift of the + + + align:start position:0% +temperature related peak upshift of the +spectrum and the peak will be shifted to + + align:start position:0% +spectrum and the peak will be shifted to + + + align:start position:0% +spectrum and the peak will be shifted to +the directional flow of the emitting + + align:start position:0% +the directional flow of the emitting + + + align:start position:0% +the directional flow of the emitting +plasma this is actually one piece of key + + align:start position:0% +plasma this is actually one piece of key + + + align:start position:0% +plasma this is actually one piece of key +information that we gotten from Neutron + + align:start position:0% +information that we gotten from Neutron + + + align:start position:0% +information that we gotten from Neutron +data on the N we found early on that the + + align:start position:0% +data on the N we found early on that the + + + align:start position:0% +data on the N we found early on that the +capsule when it was pushed for the + + align:start position:0% +capsule when it was pushed for the + + + align:start position:0% +capsule when it was pushed for the +lasers ran off in One Direction + + align:start position:0% +lasers ran off in One Direction + + + align:start position:0% +lasers ran off in One Direction +basically based on the neutral Spector + + align:start position:0% +basically based on the neutral Spector + + + align:start position:0% +basically based on the neutral Spector +being shifted uh which we had to correct + + align:start position:0% +being shifted uh which we had to correct + + + align:start position:0% +being shifted uh which we had to correct +for because that prevented efficient + + align:start position:0% +for because that prevented efficient + + + align:start position:0% +for because that prevented efficient +conversion of the compression energy + + align:start position:0% +conversion of the compression energy + + + align:start position:0% +conversion of the compression energy +into to thermal energy of the + + align:start position:0% +into to thermal energy of the + + + align:start position:0% +into to thermal energy of the +capsule um to so this is a + + align:start position:0% +capsule um to so this is a + + + align:start position:0% +capsule um to so this is a +non-relativistic expression really + + align:start position:0% +non-relativistic expression really + + + align:start position:0% +non-relativistic expression really +recommend you read this paper to get the + + align:start position:0% +recommend you read this paper to get the + + + align:start position:0% +recommend you read this paper to get the +relativistic MTH for how this works I'm + + align:start position:0% +relativistic MTH for how this works I'm + + + align:start position:0% +relativistic MTH for how this works I'm +going to go through it today but this is + + align:start position:0% +going to go through it today but this is + + + align:start position:0% +going to go through it today but this is +a excellent reference which everyone + + align:start position:0% +a excellent reference which everyone + + + align:start position:0% +a excellent reference which everyone +that does neutron diagnostics for uses + + align:start position:0% +that does neutron diagnostics for uses + + + align:start position:0% +that does neutron diagnostics for uses +all the + + align:start position:0% +all the + + + align:start position:0% +all the +time and it's actually originally comes + + align:start position:0% +time and it's actually originally comes + + + align:start position:0% +time and it's actually originally comes +from the magnetic environment communic + + align:start position:0% +from the magnetic environment communic + + + align:start position:0% +from the magnetic environment communic +so it's another example of the + + align:start position:0% +so it's another example of the + + + align:start position:0% +so it's another example of the +connections okay so I think by now + + align:start position:0% +connections okay so I think by now + + + align:start position:0% +connections okay so I think by now +you've understood that the neutron + + align:start position:0% +you've understood that the neutron + + + align:start position:0% +you've understood that the neutron +Spectrum provides information on aerial + + align:start position:0% +Spectrum provides information on aerial + + + align:start position:0% +Spectrum provides information on aerial +density ion temperature and yield and + + align:start position:0% +density ion temperature and yield and + + + align:start position:0% +density ion temperature and yield and +this is an example of what a neutron + + align:start position:0% +this is an example of what a neutron + + + align:start position:0% +this is an example of what a neutron +Spectrum can look like so you'll have + + align:start position:0% +Spectrum can look like so you'll have + + + align:start position:0% +Spectrum can look like so you'll have +the primary D2 Neutron that are + + align:start position:0% +the primary D2 Neutron that are + + + align:start position:0% +the primary D2 Neutron that are +unscattered for M the width of that + + align:start position:0% +unscattered for M the width of that + + + align:start position:0% +unscattered for M the width of that +primary + + align:start position:0% +primary + + + align:start position:0% +primary +spectrum is um related to the ion + + align:start position:0% +spectrum is um related to the ion + + + align:start position:0% +spectrum is um related to the ion +temperature of the plasma and we can + + align:start position:0% +temperature of the plasma and we can + + + align:start position:0% +temperature of the plasma and we can +also not Illustrated here but we can + + align:start position:0% +also not Illustrated here but we can + + + align:start position:0% +also not Illustrated here but we can +have up shift that's related to the + + align:start position:0% +have up shift that's related to the + + + align:start position:0% +have up shift that's related to the +velocity uh and then by counting them we + + align:start position:0% +velocity uh and then by counting them we + + + align:start position:0% +velocity uh and then by counting them we +get the yield scaling up to 4 high and + + align:start position:0% +get the yield scaling up to 4 high and + + + align:start position:0% +get the yield scaling up to 4 high and +then by taking the ratio of the neutrons + + align:start position:0% +then by taking the ratio of the neutrons + + + align:start position:0% +then by taking the ratio of the neutrons +in the down scattered range the neutrons + + align:start position:0% +in the down scattered range the neutrons + + + align:start position:0% +in the down scattered range the neutrons +in the primary range we get a measure of + + align:start position:0% +in the primary range we get a measure of + + + align:start position:0% +in the primary range we get a measure of +the aerial density and actually we often + + align:start position:0% +the aerial density and actually we often + + + align:start position:0% +the aerial density and actually we often +talk about a down scatter ratio rather + + align:start position:0% +talk about a down scatter ratio rather + + + align:start position:0% +talk about a down scatter ratio rather +than an aerial density because we can + + align:start position:0% +than an aerial density because we can + + + align:start position:0% +than an aerial density because we can +measure the number of neutrons in this + + align:start position:0% +measure the number of neutrons in this + + + align:start position:0% +measure the number of neutrons in this +range compared to the number of neutrons + + align:start position:0% +range compared to the number of neutrons + + + align:start position:0% +range compared to the number of neutrons +in this range and yeah how do you + + align:start position:0% +in this range and yeah how do you + + + align:start position:0% +in this range and yeah how do you +distinguished between neutrons that have + + align:start position:0% +distinguished between neutrons that have + + + align:start position:0% +distinguished between neutrons that have +down scattered within the fuel versus + + align:start position:0% +down scattered within the fuel versus + + + align:start position:0% +down scattered within the fuel versus +neutrons that are down scattered in the + + align:start position:0% +neutrons that are down scattered in the + + + align:start position:0% +neutrons that are down scattered in the +lab um Okay so that's come becomes the + + align:start position:0% +lab um Okay so that's come becomes the + + + align:start position:0% +lab um Okay so that's come becomes the +technicality of the instruments you have + + align:start position:0% +technicality of the instruments you have + + + align:start position:0% +technicality of the instruments you have +to cumate them really well uh in order + + align:start position:0% +to cumate them really well uh in order + + + align:start position:0% +to cumate them really well uh in order +to look at the right so and it turns out + + align:start position:0% +to look at the right so and it turns out + + + align:start position:0% +to look at the right so and it turns out +the way that ICF is set up the capsule + + align:start position:0% +the way that ICF is set up the capsule + + + align:start position:0% +the way that ICF is set up the capsule +is at the center of the large chamber so + + align:start position:0% +is at the center of the large chamber so + + + align:start position:0% +is at the center of the large chamber so +the room return from the back wall of + + align:start position:0% +the room return from the back wall of + + + align:start position:0% +the room return from the back wall of +the chamber becomes a much much smaller + + align:start position:0% +the chamber becomes a much much smaller + + + align:start position:0% +the chamber becomes a much much smaller +fraction of the neutrons that go down + + align:start position:0% +fraction of the neutrons that go down + + + align:start position:0% +fraction of the neutrons that go down +Airline sight + + align:start position:0% +Airline sight + + + align:start position:0% +Airline sight +so basically the way it set up um for + + align:start position:0% +so basically the way it set up um for + + + align:start position:0% +so basically the way it set up um for +Chris is actually looking at exactly + + align:start position:0% +Chris is actually looking at exactly + + + align:start position:0% +Chris is actually looking at exactly +this problem for the magnetic recoil + + align:start position:0% +this problem for the magnetic recoil + + + align:start position:0% +this problem for the magnetic recoil +Spectrum which we'll be talking about + + align:start position:0% +Spectrum which we'll be talking about + + + align:start position:0% +Spectrum which we'll be talking about +later the foil is 26 centimeters from + + align:start position:0% +later the foil is 26 centimeters from + + + align:start position:0% +later the foil is 26 centimeters from +Target chamber Center back wall is five + + align:start position:0% +Target chamber Center back wall is five + + + align:start position:0% +Target chamber Center back wall is five +meters away so the solid angle for + + align:start position:0% +meters away so the solid angle for + + + align:start position:0% +meters away so the solid angle for +scatter neutrons coming down the same L + + align:start position:0% +scatter neutrons coming down the same L + + + align:start position:0% +scatter neutrons coming down the same L +side is just so much smaller it becomes + + align:start position:0% +side is just so much smaller it becomes + + + align:start position:0% +side is just so much smaller it becomes +negligible um for the end Toops I don't + + align:start position:0% +negligible um for the end Toops I don't + + + align:start position:0% +negligible um for the end Toops I don't +think it's been okay we get that I don't + + align:start position:0% +think it's been okay we get that I don't + + + align:start position:0% +think it's been okay we get that I don't +think it's been looked at in detail but + + align:start position:0% +think it's been looked at in detail but + + + align:start position:0% +think it's been looked at in detail but +what they do is they take reference in + + align:start position:0% +what they do is they take reference in + + + align:start position:0% +what they do is they take reference in +Clos so that they know if there's no + + align:start position:0% +Clos so that they know if there's no + + + align:start position:0% +Clos so that they know if there's no +assembled row R they know what in the + + align:start position:0% +assembled row R they know what in the + + + align:start position:0% +assembled row R they know what in the +background in that range is where yeah + + align:start position:0% +background in that range is where yeah + + + align:start position:0% +background in that range is where yeah +and then Chris is looking at the concept + + align:start position:0% +and then Chris is looking at the concept + + + align:start position:0% +and then Chris is looking at the concept +of putting the MS for really far away + + align:start position:0% +of putting the MS for really far away + + + align:start position:0% +of putting the MS for really far away +and I'm making him those simulations to + + align:start position:0% +and I'm making him those simulations to + + + align:start position:0% +and I'm making him those simulations to +see if that's going to work or if we're + + align:start position:0% +see if that's going to work or if we're + + + align:start position:0% +see if that's going to work or if we're +going to have a problem with + + align:start position:0% + + + + align:start position:0% + +the um why do you cut why do you cut off + + align:start position:0% +the um why do you cut why do you cut off + + + align:start position:0% +the um why do you cut why do you cut off +the down scattered region at four and a + + align:start position:0% +the down scattered region at four and a + + + align:start position:0% +the down scattered region at four and a +half + + align:start position:0% +half + + + align:start position:0% +half +M okay so that's actually just kind of + + align:start position:0% +M okay so that's actually just kind of + + + align:start position:0% +M okay so that's actually just kind of +random uh what we typically do when we + + align:start position:0% +random uh what we typically do when we + + + align:start position:0% +random uh what we typically do when we +do this is + + align:start position:0% +do this is + + + align:start position:0% +do this is +we um + + align:start position:0% +we um + + + align:start position:0% +we um +this is not the best Spectrum to look at + + align:start position:0% +this is not the best Spectrum to look at + + + align:start position:0% +this is not the best Spectrum to look at +let's see if you can see this on the + + align:start position:0% +let's see if you can see this on the + + + align:start position:0% +let's see if you can see this on the +camera you look at DSR down scatter + + align:start position:0% +camera you look at DSR down scatter + + + align:start position:0% +camera you look at DSR down scatter +ratios we call it and that's the + + align:start position:0% +ratios we call it and that's the + + + align:start position:0% +ratios we call it and that's the +integral in the + + align:start position:0% +integral in the + + + align:start position:0% +integral in the +kind sorty integral in the 10 to 12 en + + align:start position:0% +kind sorty integral in the 10 to 12 en + + + align:start position:0% +kind sorty integral in the 10 to 12 en +range divided by the 13 15 en range to + + align:start position:0% +range divided by the 13 15 en range to + + + align:start position:0% +range divided by the 13 15 en range to +just get a quantitative + + align:start position:0% +just get a quantitative + + + align:start position:0% +just get a quantitative +number so that's this range here divided + + align:start position:0% +number so that's this range here divided + + + align:start position:0% +number so that's this range here divided +by that range here and the reason we + + align:start position:0% +by that range here and the reason we + + + align:start position:0% +by that range here and the reason we +look at that range is because we have + + align:start position:0% +look at that range is because we have + + + align:start position:0% +look at that range is because we have +contributions from neutrons from the TT + + align:start position:0% +contributions from neutrons from the TT + + + align:start position:0% +contributions from neutrons from the TT +reaction contributing up to 9 and a half + + align:start position:0% +reaction contributing up to 9 and a half + + + align:start position:0% +reaction contributing up to 9 and a half +and maybe we have the DD neutr + + align:start position:0% +and maybe we have the DD neutr + + + align:start position:0% +and maybe we have the DD neutr +contributing here kind of see that Peak + + align:start position:0% +contributing here kind of see that Peak + + + align:start position:0% +contributing here kind of see that Peak +here uh and there's also multiple + + align:start position:0% +here uh and there's also multiple + + + align:start position:0% +here uh and there's also multiple +scatters that kind of break the + + align:start position:0% +scatters that kind of break the + + + align:start position:0% +scatters that kind of break the +correlation between row R and the number + + align:start position:0% +correlation between row R and the number + + + align:start position:0% +correlation between row R and the number +of neutrons that you get so it's the + + align:start position:0% +of neutrons that you get so it's the + + + align:start position:0% +of neutrons that you get so it's the +cleanest region to look at in the + + align:start position:0% +cleanest region to look at in the + + + align:start position:0% +cleanest region to look at in the +Spectrum so let's + + align:start position:0% +Spectrum so let's + + + align:start position:0% +Spectrum so let's +that um any other questions + + align:start position:0% + + + + align:start position:0% + +okay um so I mentioned that we can also + + align:start position:0% +okay um so I mentioned that we can also + + + align:start position:0% +okay um so I mentioned that we can also +use uh the uh Fusion products to look at + + align:start position:0% +use uh the uh Fusion products to look at + + + align:start position:0% +use uh the uh Fusion products to look at +the spatial emission so then we can take + + align:start position:0% +the spatial emission so then we can take + + + align:start position:0% +the spatial emission so then we can take +images of primary and Scattered neutrons + + align:start position:0% +images of primary and Scattered neutrons + + + align:start position:0% +images of primary and Scattered neutrons +for example to provide information on + + align:start position:0% +for example to provide information on + + + align:start position:0% +for example to provide information on +the burn region size are and also the + + align:start position:0% +the burn region size are and also the + + + align:start position:0% +the burn region size are and also the +the thickness of the high density + + align:start position:0% +the thickness of the high density + + + align:start position:0% +the thickness of the high density +shell uh so in this case uh this is + + align:start position:0% +shell uh so in this case uh this is + + + align:start position:0% +shell uh so in this case uh this is +actually reconstruction taking primary + + align:start position:0% +actually reconstruction taking primary + + + align:start position:0% +actually reconstruction taking primary +images in the 10 to 12 M range down + + align:start position:0% +images in the 10 to 12 M range down + + + align:start position:0% +images in the 10 to 12 M range down +scatter images in the 6 to 12 view range + + align:start position:0% +scatter images in the 6 to 12 view range + + + align:start position:0% +scatter images in the 6 to 12 view range +and then doing a fluance compensated + + align:start position:0% +and then doing a fluance compensated + + + align:start position:0% +and then doing a fluance compensated +image which gives us this artifact here + + align:start position:0% +image which gives us this artifact here + + + align:start position:0% +image which gives us this artifact here +which kind of gives us the picture of + + align:start position:0% +which kind of gives us the picture of + + + align:start position:0% +which kind of gives us the picture of +the neutr source which is the primary + + align:start position:0% +the neutr source which is the primary + + + align:start position:0% +the neutr source which is the primary +neutrons and the high density shell + + align:start position:0% +neutrons and the high density shell + + + align:start position:0% +neutrons and the high density shell +which is the scattered + + align:start position:0% + + + + align:start position:0% + +neutr and we can measure the nuclear + + align:start position:0% +neutr and we can measure the nuclear + + + align:start position:0% +neutr and we can measure the nuclear +reaction rate to get information about + + align:start position:0% +reaction rate to get information about + + + align:start position:0% +reaction rate to get information about +the confinement time and the the Bane + + align:start position:0% +the confinement time and the the Bane + + + align:start position:0% +the confinement time and the the Bane +time of the implosion so what this is + + align:start position:0% +time of the implosion so what this is + + + align:start position:0% +time of the implosion so what this is +here is um we call it the the grand plot + + align:start position:0% +here is um we call it the the grand plot + + + align:start position:0% +here is um we call it the the grand plot +where you follow this is imulation you + + align:start position:0% +where you follow this is imulation you + + + align:start position:0% +where you follow this is imulation you +follow the same fluid element as a + + align:start position:0% +follow the same fluid element as a + + + align:start position:0% +follow the same fluid element as a +function of time and then you see that + + align:start position:0% +function of time and then you see that + + + align:start position:0% +function of time and then you see that +the red is the interface between the + + align:start position:0% +the red is the interface between the + + + align:start position:0% +the red is the interface between the +capsule shell and the gas on the inside + + align:start position:0% +capsule shell and the gas on the inside + + + align:start position:0% +capsule shell and the gas on the inside +this is gas F implosion example rather + + align:start position:0% +this is gas F implosion example rather + + + align:start position:0% +this is gas F implosion example rather +the layer DTI you drive it with the + + align:start position:0% +the layer DTI you drive it with the + + + align:start position:0% +the layer DTI you drive it with the +lasers you get ablation of the surface + + align:start position:0% +lasers you get ablation of the surface + + + align:start position:0% +lasers you get ablation of the surface +material which this why some curves are + + align:start position:0% +material which this why some curves are + + + align:start position:0% +material which this why some curves are +going off and the other curves are + + align:start position:0% +going off and the other curves are + + + align:start position:0% +going off and the other curves are +compressing inwards until you get + + align:start position:0% +compressing inwards until you get + + + align:start position:0% +compressing inwards until you get +convergence the fu shell moves inwards + + align:start position:0% +convergence the fu shell moves inwards + + + align:start position:0% +convergence the fu shell moves inwards +the rest of is converging get a little a + + align:start position:0% +the rest of is converging get a little a + + + align:start position:0% +the rest of is converging get a little a +little bit of burn here when the shocks + + align:start position:0% +little bit of burn here when the shocks + + + align:start position:0% +little bit of burn here when the shocks +hit the center and you get more burn + + align:start position:0% +hit the center and you get more burn + + + align:start position:0% +hit the center and you get more burn +here uh where the capsule is a peak + + align:start position:0% +here uh where the capsule is a peak + + + align:start position:0% +here uh where the capsule is a peak +convergence when it's maximally um + + align:start position:0% +convergence when it's maximally um + + + align:start position:0% +convergence when it's maximally um +heated and then you can measure the + + align:start position:0% +heated and then you can measure the + + + align:start position:0% +heated and then you can measure the +emission history as a function of time + + align:start position:0% +emission history as a function of time + + + align:start position:0% +emission history as a function of time +and you can see this shock burn and this + + align:start position:0% +and you can see this shock burn and this + + + align:start position:0% +and you can see this shock burn and this +compression burn and this particular + + align:start position:0% +compression burn and this particular + + + align:start position:0% +compression burn and this particular +example the de3 implosion SO gas F so + + align:start position:0% +example the de3 implosion SO gas F so + + + align:start position:0% +example the de3 implosion SO gas F so +then you're obiously get both of these + + align:start position:0% +then you're obiously get both of these + + + align:start position:0% +then you're obiously get both of these +components in then L CL you're going to + + align:start position:0% +components in then L CL you're going to + + + align:start position:0% +components in then L CL you're going to +have very little sh bur you're going + + align:start position:0% +have very little sh bur you're going + + + align:start position:0% +have very little sh bur you're going +have a lot more compression but would be + + align:start position:0% +have a lot more compression but would be + + + align:start position:0% +have a lot more compression but would be +completely dominated by + + align:start position:0% +completely dominated by + + + align:start position:0% +completely dominated by +the okay those so those are some + + align:start position:0% +the okay those so those are some + + + align:start position:0% +the okay those so those are some +examples of the parameters for looking + + align:start position:0% +examples of the parameters for looking + + + align:start position:0% +examples of the parameters for looking +for so with that I plan to go into more + + align:start position:0% +for so with that I plan to go into more + + + align:start position:0% +for so with that I plan to go into more +about the technical detector details so + + align:start position:0% +about the technical detector details so + + + align:start position:0% +about the technical detector details so +any questions before we move + + align:start position:0% +any questions before we move + + + align:start position:0% +any questions before we move +on actually have no idea how I'm doing + + align:start position:0% +on actually have no idea how I'm doing + + + align:start position:0% +on actually have no idea how I'm doing +you half an hourish should be + + align:start position:0% + + + + align:start position:0% + +good okay then let's jump into it so the + + align:start position:0% +good okay then let's jump into it so the + + + align:start position:0% +good okay then let's jump into it so the +first one I thought we talk about is + + align:start position:0% +first one I thought we talk about is + + + align:start position:0% +first one I thought we talk about is +nuclear activation Diagnostics so + + align:start position:0% +nuclear activation Diagnostics so + + + align:start position:0% +nuclear activation Diagnostics so +they're typically based on uh indium 115 + + align:start position:0% +they're typically based on uh indium 115 + + + align:start position:0% +they're typically based on uh indium 115 +copper 63 or cium 90 Isotopes for + + align:start position:0% +copper 63 or cium 90 Isotopes for + + + align:start position:0% +copper 63 or cium 90 Isotopes for +measurement of primary DD or DT Neutron + + align:start position:0% +measurement of primary DD or DT Neutron + + + align:start position:0% +measurement of primary DD or DT Neutron +yelds um if we look at DD first let's + + align:start position:0% +yelds um if we look at DD first let's + + + align:start position:0% +yelds um if we look at DD first let's +really use Indian when D Neutron hits + + align:start position:0% +really use Indian when D Neutron hits + + + align:start position:0% +really use Indian when D Neutron hits +Indian we get + + align:start position:0% +Indian we get + + + align:start position:0% +Indian we get +a isomer and the scattered Neutron the + + align:start position:0% +a isomer and the scattered Neutron the + + + align:start position:0% +a isomer and the scattered Neutron the +threshold for that reaction is about one + + align:start position:0% +threshold for that reaction is about one + + + align:start position:0% +threshold for that reaction is about one +and a half m uh and this isomer St will + + align:start position:0% +and a half m uh and this isomer St will + + + align:start position:0% +and a half m uh and this isomer St will +Decay emitting gamma that half 4.5 hours + + align:start position:0% +Decay emitting gamma that half 4.5 hours + + + align:start position:0% +Decay emitting gamma that half 4.5 hours +and this is the gamma that we count for + + align:start position:0% +and this is the gamma that we count for + + + align:start position:0% +and this is the gamma that we count for +many reactions + + align:start position:0% +many reactions + + + align:start position:0% +many reactions +happen um on Omega we use copper to um + + align:start position:0% +happen um on Omega we use copper to um + + + align:start position:0% +happen um on Omega we use copper to um +measure the DT yield uh and again copper + + align:start position:0% +measure the DT yield uh and again copper + + + align:start position:0% +measure the DT yield uh and again copper +63 and then Neutron fortun Neutron need + + align:start position:0% +63 and then Neutron fortun Neutron need + + + align:start position:0% +63 and then Neutron fortun Neutron need +copper will be an m2n reactions we help + + align:start position:0% +copper will be an m2n reactions we help + + + align:start position:0% +copper will be an m2n reactions we help +two two neutrons theal is about 11 en + + align:start position:0% +two two neutrons theal is about 11 en + + + align:start position:0% +two two neutrons theal is about 11 en +look at the shape of the cross-section + + align:start position:0% +look at the shape of the cross-section + + + align:start position:0% +look at the shape of the cross-section +if you go on the next slide um and then + + align:start position:0% +if you go on the next slide um and then + + + align:start position:0% +if you go on the next slide um and then +what happens is that copper 62 is + + align:start position:0% +what happens is that copper 62 is + + + align:start position:0% +what happens is that copper 62 is +radioactive will Decay to Nickel 62 and + + align:start position:0% +radioactive will Decay to Nickel 62 and + + + align:start position:0% +radioactive will Decay to Nickel 62 and +the half life for this is 9.8 minutes uh + + align:start position:0% +the half life for this is 9.8 minutes uh + + + align:start position:0% +the half life for this is 9.8 minutes uh +and what be actually count for the gamma + + align:start position:0% +and what be actually count for the gamma + + + align:start position:0% +and what be actually count for the gamma +here as well uh cirium Neutron hits + + align:start position:0% +here as well uh cirium Neutron hits + + + align:start position:0% +here as well uh cirium Neutron hits +cirium 90 we again get M2 reaction + + align:start position:0% +cirium 90 we again get M2 reaction + + + align:start position:0% +cirium 90 we again get M2 reaction +threshold about 12 m in this case which + + align:start position:0% +threshold about 12 m in this case which + + + align:start position:0% +threshold about 12 m in this case which +means we're really narrowing in on the + + align:start position:0% +means we're really narrowing in on the + + + align:start position:0% +means we're really narrowing in on the +primary neutrons um at + + align:start position:0% +primary neutrons um at + + + align:start position:0% +primary neutrons um at +14 this is what we use as an if uh and + + align:start position:0% +14 this is what we use as an if uh and + + + align:start position:0% +14 this is what we use as an if uh and +again circum 89 is not stable the end + + align:start position:0% +again circum 89 is not stable the end + + + align:start position:0% +again circum 89 is not stable the end +product that we get is gam 99 K which is + + align:start position:0% +product that we get is gam 99 K which is + + + align:start position:0% +product that we get is gam 99 K which is +what we're + + align:start position:0% +what we're + + + align:start position:0% +what we're +counting and if we look at uh okay so + + align:start position:0% +counting and if we look at uh okay so + + + align:start position:0% +counting and if we look at uh okay so +this first PL has the indium and + + align:start position:0% +this first PL has the indium and + + + align:start position:0% +this first PL has the indium and +syconium reaction cross-sections so you + + align:start position:0% +syconium reaction cross-sections so you + + + align:start position:0% +syconium reaction cross-sections so you +can clearly see what used cirium for DT + + align:start position:0% +can clearly see what used cirium for DT + + + align:start position:0% +can clearly see what used cirium for DT +the threshold is at about 12 3D covers + + align:start position:0% +the threshold is at about 12 3D covers + + + align:start position:0% +the threshold is at about 12 3D covers +are primary DP it's also really sharp bu + + align:start position:0% +are primary DP it's also really sharp bu + + + align:start position:0% +are primary DP it's also really sharp bu +which is actually a useful tool because + + align:start position:0% +which is actually a useful tool because + + + align:start position:0% +which is actually a useful tool because +if the peak is shifted up or down it's + + align:start position:0% +if the peak is shifted up or down it's + + + align:start position:0% +if the peak is shifted up or down it's +going to impact what you're count which + + align:start position:0% +going to impact what you're count which + + + align:start position:0% +going to impact what you're count which +means you you get an impact of velocity + + align:start position:0% +means you you get an impact of velocity + + + align:start position:0% +means you you get an impact of velocity +uh on + + align:start position:0% +uh on + + + align:start position:0% +uh on +the OB Ser so you can see differences + + align:start position:0% +the OB Ser so you can see differences + + + align:start position:0% +the OB Ser so you can see differences +around the + + align:start position:0% +around the + + + align:start position:0% +around the +otion uh and then in them on the other + + align:start position:0% +otion uh and then in them on the other + + + align:start position:0% +otion uh and then in them on the other +hand is a really broad crosssection + + align:start position:0% +hand is a really broad crosssection + + + align:start position:0% +hand is a really broad crosssection +which is actually makes it a really + + align:start position:0% +which is actually makes it a really + + + align:start position:0% +which is actually makes it a really +blunt + + align:start position:0% +blunt + + + align:start position:0% +blunt +tool um if you want to use it to measure + + align:start position:0% +tool um if you want to use it to measure + + + align:start position:0% +tool um if you want to use it to measure +DD uh it's by far the easiest in a pure + + align:start position:0% +DD uh it's by far the easiest in a pure + + + align:start position:0% +DD uh it's by far the easiest in a pure +D2 implosion we don't have downstair + + align:start position:0% + + + + align:start position:0% + +D2 um in principle you can use a + + align:start position:0% +D2 um in principle you can use a + + + align:start position:0% +D2 um in principle you can use a +cocktail of different nuclear activation + + align:start position:0% +cocktail of different nuclear activation + + + align:start position:0% +cocktail of different nuclear activation +detectors to piece together information + + align:start position:0% +detectors to piece together information + + + align:start position:0% +detectors to piece together information +about the full Neutron spectrum and here + + align:start position:0% +about the full Neutron spectrum and here + + + align:start position:0% +about the full Neutron spectrum and here +we have some examples of parts of the + + align:start position:0% +we have some examples of parts of the + + + align:start position:0% +we have some examples of parts of the +spectrum that can be of interest so in a + + align:start position:0% +spectrum that can be of interest so in a + + + align:start position:0% +spectrum that can be of interest so in a +DT implosion this is what the + + align:start position:0% +DT implosion this is what the + + + align:start position:0% +DT implosion this is what the +DD spectrum look like you actually have + + align:start position:0% +DD spectrum look like you actually have + + + align:start position:0% +DD spectrum look like you actually have +some of those secondary nutr that we + + align:start position:0% +some of those secondary nutr that we + + + align:start position:0% +some of those secondary nutr that we +talked about about before uh that are at + + align:start position:0% +talked about about before uh that are at + + + align:start position:0% +talked about about before uh that are at +14 M you have the primary DTS at 2 and a + + align:start position:0% +14 M you have the primary DTS at 2 and a + + + align:start position:0% +14 M you have the primary DTS at 2 and a +half M down scattered DTS and then just + + align:start position:0% +half M down scattered DTS and then just + + + align:start position:0% +half M down scattered DTS and then just +a little bit of scatter in between uh + + align:start position:0% +a little bit of scatter in between uh + + + align:start position:0% +a little bit of scatter in between uh +and that we can get add with indium in + + align:start position:0% +and that we can get add with indium in + + + align:start position:0% +and that we can get add with indium in +principle we have the TT entrance which + + align:start position:0% +principle we have the TT entrance which + + + align:start position:0% +principle we have the TT entrance which +um have a Peak at about N9 maybe and go + + align:start position:0% +um have a Peak at about N9 maybe and go + + + align:start position:0% +um have a Peak at about N9 maybe and go +from N9 and a half all the way down zero + + align:start position:0% +from N9 and a half all the way down zero + + + align:start position:0% +from N9 and a half all the way down zero +those you can also attack a little bit + + align:start position:0% +those you can also attack a little bit + + + align:start position:0% +those you can also attack a little bit +uh and then really the primary thing + + align:start position:0% +uh and then really the primary thing + + + align:start position:0% +uh and then really the primary thing +we're looking at is the DTs which some + + align:start position:0% +we're looking at is the DTs which some + + + align:start position:0% +we're looking at is the DTs which some +of the UPS + + align:start position:0% +of the UPS + + + align:start position:0% +of the UPS +scattered + + align:start position:0% +scattered + + + align:start position:0% +scattered +the we we looked at this before uh where + + align:start position:0% +the we we looked at this before uh where + + + align:start position:0% +the we we looked at this before uh where +the neutron has hit a fuel ion giving it + + align:start position:0% +the neutron has hit a fuel ion giving it + + + align:start position:0% +the neutron has hit a fuel ion giving it +a lot of energy that energy in turn + + align:start position:0% +a lot of energy that energy in turn + + + align:start position:0% +a lot of energy that energy in turn +reacts to produce another Neutron that's + + align:start position:0% +reacts to produce another Neutron that's + + + align:start position:0% +reacts to produce another Neutron that's +going to be at these really high energy + + align:start position:0% +going to be at these really high energy + + + align:start position:0% +going to be at these really high energy +tertiary neutrons 15 to 30 and that's + + align:start position:0% +tertiary neutrons 15 to 30 and that's + + + align:start position:0% +tertiary neutrons 15 to 30 and that's +actually in many cases also really + + align:start position:0% +actually in many cases also really + + + align:start position:0% +actually in many cases also really +interesting oh that fell + + align:start position:0% +interesting oh that fell + + + align:start position:0% +interesting oh that fell +off oh yeah that completely fell off + + align:start position:0% +off oh yeah that completely fell off + + + align:start position:0% +off oh yeah that completely fell off +there's another reaction here that has + + align:start position:0% +there's another reaction here that has + + + align:start position:0% +there's another reaction here that has +this cross option here here it's an + + align:start position:0% +this cross option here here it's an + + + align:start position:0% +this cross option here here it's an +isotope of carbon but I honestly don't + + align:start position:0% +isotope of carbon but I honestly don't + + + align:start position:0% +isotope of carbon but I honestly don't +remember which one so but then you can + + align:start position:0% +remember which one so but then you can + + + align:start position:0% +remember which one so but then you can +really focus in just those highest + + align:start position:0% +really focus in just those highest + + + align:start position:0% +really focus in just those highest +energy + + align:start position:0% + + + + align:start position:0% + +nutr and this actually also shows you um + + align:start position:0% +nutr and this actually also shows you um + + + align:start position:0% +nutr and this actually also shows you um +we have cop oh yeah car carbon + + align:start position:0% +we have cop oh yeah car carbon + + + align:start position:0% +we have cop oh yeah car carbon +12 um copper you kind of see is this + + align:start position:0% +12 um copper you kind of see is this + + + align:start position:0% +12 um copper you kind of see is this +orange line here and we have cine as the + + align:start position:0% +orange line here and we have cine as the + + + align:start position:0% +orange line here and we have cine as the +red line so Chum is a much sharper + + align:start position:0% +red line so Chum is a much sharper + + + align:start position:0% +red line so Chum is a much sharper +Threshold at 12 and copper starts + + align:start position:0% +Threshold at 12 and copper starts + + + align:start position:0% +Threshold at 12 and copper starts +already at 11 so they have a little bit + + align:start position:0% +already at 11 so they have a little bit + + + align:start position:0% +already at 11 so they have a little bit +different sensitivity than 18 + + align:start position:0% +different sensitivity than 18 + + + align:start position:0% +different sensitivity than 18 +Neons um at Omega uh copper activation + + align:start position:0% +Neons um at Omega uh copper activation + + + align:start position:0% +Neons um at Omega uh copper activation +is used for measurements of the primary + + align:start position:0% +is used for measurements of the primary + + + align:start position:0% +is used for measurements of the primary +DT Neutron yield we have um basically a + + align:start position:0% +DT Neutron yield we have um basically a + + + align:start position:0% +DT Neutron yield we have um basically a +little retractor tube that allows a a + + align:start position:0% +little retractor tube that allows a a + + + align:start position:0% +little retractor tube that allows a a +puck to be inserted and then dropped + + align:start position:0% +puck to be inserted and then dropped + + + align:start position:0% +puck to be inserted and then dropped +after shop by pushing a button but it's + + align:start position:0% +after shop by pushing a button but it's + + + align:start position:0% +after shop by pushing a button but it's +still very manual so many times I've + + align:start position:0% +still very manual so many times I've + + + align:start position:0% +still very manual so many times I've +been up there for a shot day and um this + + align:start position:0% +been up there for a shot day and um this + + + align:start position:0% +been up there for a shot day and um this +old Russian guy Vladimir Glo pushes the + + align:start position:0% +old Russian guy Vladimir Glo pushes the + + + align:start position:0% +old Russian guy Vladimir Glo pushes the +button gets the black disc and then runs + + align:start position:0% +button gets the black disc and then runs + + + align:start position:0% +button gets the black disc and then runs +it over to the counting detector in a + + align:start position:0% +it over to the counting detector in a + + + align:start position:0% +it over to the counting detector in a +different + + align:start position:0% +different + + + align:start position:0% +different +lab so and it's using sodium iodide + + align:start position:0% +lab so and it's using sodium iodide + + + align:start position:0% +lab so and it's using sodium iodide +detectors to detect the gamas and + + align:start position:0% +detectors to detect the gamas and + + + align:start position:0% +detectors to detect the gamas and +coincidence and and it's actually quite + + align:start position:0% +coincidence and and it's actually quite + + + align:start position:0% +coincidence and and it's actually quite +useful because you can go down to really + + align:start position:0% +useful because you can go down to really + + + align:start position:0% +useful because you can go down to really +low neutrient thresholds the cogenic + + align:start position:0% +low neutrient thresholds the cogenic + + + align:start position:0% +low neutrient thresholds the cogenic +implosions that Omega produce upwards of + + align:start position:0% +implosions that Omega produce upwards of + + + align:start position:0% +implosions that Omega produce upwards of +10 to 14 nutrients but you can measure + + align:start position:0% +10 to 14 nutrients but you can measure + + + align:start position:0% +10 to 14 nutrients but you can measure +nutrients down to 10 the seven which + + align:start position:0% +nutrients down to 10 the seven which + + + align:start position:0% +nutrients down to 10 the seven which +mean you can look at uh experiments for + + align:start position:0% +mean you can look at uh experiments for + + + align:start position:0% +mean you can look at uh experiments for +you're not producing many nutrients at + + align:start position:0% +you're not producing many nutrients at + + + align:start position:0% +you're not producing many nutrients at +all and still still know what you + + align:start position:0% +all and still still know what you + + + align:start position:0% +all and still still know what you +produce uh on the N syconium is the + + align:start position:0% +produce uh on the N syconium is the + + + align:start position:0% +produce uh on the N syconium is the +primary activation uh element used uh + + align:start position:0% +primary activation uh element used uh + + + align:start position:0% +primary activation uh element used uh +and it's used routinely for measurements + + align:start position:0% +and it's used routinely for measurements + + + align:start position:0% +and it's used routinely for measurements +of primary DT Neutron yield in fact from + + align:start position:0% +of primary DT Neutron yield in fact from + + + align:start position:0% +of primary DT Neutron yield in fact from +like from the high performing implosions + + align:start position:0% +like from the high performing implosions + + + align:start position:0% +like from the high performing implosions +there are two measurements that provide + + align:start position:0% +there are two measurements that provide + + + align:start position:0% +there are two measurements that provide +the yield that's then reported out uh + + align:start position:0% +the yield that's then reported out uh + + + align:start position:0% +the yield that's then reported out uh +one is the cium uh nuclear activation + + align:start position:0% +one is the cium uh nuclear activation + + + align:start position:0% +one is the cium uh nuclear activation +the other one is + + align:start position:0% +the other one is + + + align:start position:0% +the other one is +mrss so uh it's implemented in a number + + align:start position:0% +mrss so uh it's implemented in a number + + + align:start position:0% +mrss so uh it's implemented in a number +of different um + + align:start position:0% +of different um + + + align:start position:0% +of different um +versions We have the well nads which is + + align:start position:0% +versions We have the well nads which is + + + align:start position:0% +versions We have the well nads which is +kind of go to reference it's h inserted + + align:start position:0% +kind of go to reference it's h inserted + + + align:start position:0% +kind of go to reference it's h inserted +to four meters from Target chinger + + align:start position:0% +to four meters from Target chinger + + + align:start position:0% +to four meters from Target chinger +Center there three different pups that + + align:start position:0% +Center there three different pups that + + + align:start position:0% +Center there three different pups that +sit very close to each other so you can + + align:start position:0% +sit very close to each other so you can + + + align:start position:0% +sit very close to each other so you can +compare the numbers from the three and + + align:start position:0% +compare the numbers from the three and + + + align:start position:0% +compare the numbers from the three and +make sure you're not making any mistakes + + align:start position:0% +make sure you're not making any mistakes + + + align:start position:0% +make sure you're not making any mistakes +um and then you have the snout P which + + align:start position:0% +um and then you have the snout P which + + + align:start position:0% +um and then you have the snout P which +you can insert much closer and actually + + align:start position:0% +you can insert much closer and actually + + + align:start position:0% +you can insert much closer and actually +it's more common with VAR the elements + + align:start position:0% +it's more common with VAR the elements + + + align:start position:0% +it's more common with VAR the elements +in in these packets I have sort of the + + align:start position:0% +in in these packets I have sort of the + + + align:start position:0% +in in these packets I have sort of the +cocktails to look at different neutri + + align:start position:0% +cocktails to look at different neutri + + + align:start position:0% +cocktails to look at different neutri +interactions and finally have the the + + align:start position:0% +interactions and finally have the the + + + align:start position:0% +interactions and finally have the the +flanch nads which sit on the outside of + + align:start position:0% +flanch nads which sit on the outside of + + + align:start position:0% +flanch nads which sit on the outside of +the chamber and there's a large number + + align:start position:0% +the chamber and there's a large number + + + align:start position:0% +the chamber and there's a large number +of those attached in different positions + + align:start position:0% +of those attached in different positions + + + align:start position:0% +of those attached in different positions +around the chamber to look at + + align:start position:0% +around the chamber to look at + + + align:start position:0% +around the chamber to look at +symmetries um their cirone detectors are + + align:start position:0% +symmetries um their cirone detectors are + + + align:start position:0% +symmetries um their cirone detectors are +transported well actually this is um + + align:start position:0% +transported well actually this is um + + + align:start position:0% +transported well actually this is um +kind of modified truth the flange nads + + align:start position:0% +kind of modified truth the flange nads + + + align:start position:0% +kind of modified truth the flange nads +we'll talk more about later are now + + align:start position:0% +we'll talk more about later are now + + + align:start position:0% +we'll talk more about later are now +counted in situ at the niif but they + + align:start position:0% +counted in situ at the niif but they + + + align:start position:0% +counted in situ at the niif but they +used to be transported C con detectors + + align:start position:0% +used to be transported C con detectors + + + align:start position:0% +used to be transported C con detectors +are transported to um the Lawrence + + align:start position:0% +are transported to um the Lawrence + + + align:start position:0% +are transported to um the Lawrence +limore National Lab NAD data analysis + + align:start position:0% +limore National Lab NAD data analysis + + + align:start position:0% +limore National Lab NAD data analysis +facility which looks like this it's some + + align:start position:0% +facility which looks like this it's some + + + align:start position:0% +facility which looks like this it's some +really old Hardware but still does its + + align:start position:0% + + + + align:start position:0% + +job uh and then yeah so the flange sads + + align:start position:0% +job uh and then yeah so the flange sads + + + align:start position:0% +job uh and then yeah so the flange sads +has actually been converted fairly + + align:start position:0% +has actually been converted fairly + + + align:start position:0% +has actually been converted fairly +recently to 48 real time uh cium um + + align:start position:0% +recently to 48 real time uh cium um + + + align:start position:0% +recently to 48 real time uh cium um +nuclear activation Diagnostics or RT + + align:start position:0% +nuclear activation Diagnostics or RT + + + align:start position:0% +nuclear activation Diagnostics or RT +nads that uh are permanently installed + + align:start position:0% +nads that uh are permanently installed + + + align:start position:0% +nads that uh are permanently installed +semi-permanently installed on the + + align:start position:0% +semi-permanently installed on the + + + align:start position:0% +semi-permanently installed on the +chamber with a l and then tell you bro + + align:start position:0% +chamber with a l and then tell you bro + + + align:start position:0% +chamber with a l and then tell you bro +my detector counting the activation from + + align:start position:0% +my detector counting the activation from + + + align:start position:0% +my detector counting the activation from +those like continuously and you can see + + align:start position:0% +those like continuously and you can see + + + align:start position:0% +those like continuously and you can see +the piece when there is an implosion so + + align:start position:0% +the piece when there is an implosion so + + + align:start position:0% +the piece when there is an implosion so +but recently used to be 48 which is + + align:start position:0% +but recently used to be 48 which is + + + align:start position:0% +but recently used to be 48 which is +great you can really look at the + + align:start position:0% +great you can really look at the + + + align:start position:0% +great you can really look at the +symmetry of the emission which I think + + align:start position:0% +symmetry of the emission which I think + + + align:start position:0% +symmetry of the emission which I think +I'll get to this on the next slide but + + align:start position:0% +I'll get to this on the next slide but + + + align:start position:0% +I'll get to this on the next slide but +the Symmetry emission tells us about the + + align:start position:0% +the Symmetry emission tells us about the + + + align:start position:0% +the Symmetry emission tells us about the +aial density + + align:start position:0% +aial density + + + align:start position:0% +aial density +symmetry so we could really look at the + + align:start position:0% +symmetry so we could really look at the + + + align:start position:0% +symmetry so we could really look at the +Symmetry emission the reason High Yi + + align:start position:0% +Symmetry emission the reason High Yi + + + align:start position:0% +Symmetry emission the reason High Yi +implosions have started killing these + + align:start position:0% +implosions have started killing these + + + align:start position:0% +implosions have started killing these +detectors so we're now down to 21 where + + align:start position:0% +detectors so we're now down to 21 where + + + align:start position:0% +detectors so we're now down to 21 where +and we actually have to remove them + + align:start position:0% +and we actually have to remove them + + + align:start position:0% +and we actually have to remove them +before every High shot so they're no + + align:start position:0% +before every High shot so they're no + + + align:start position:0% +before every High shot so they're no +longer permanently installed on the + + align:start position:0% + + + + align:start position:0% + +chamber yeah so this is what I was uh + + align:start position:0% +chamber yeah so this is what I was uh + + + align:start position:0% +chamber yeah so this is what I was uh +trying to get to the nuclear activation + + align:start position:0% +trying to get to the nuclear activation + + + align:start position:0% +trying to get to the nuclear activation +Diagnostics often show large low mode + + align:start position:0% +Diagnostics often show large low mode + + + align:start position:0% +Diagnostics often show large low mode +aerial density symmetries in different + + align:start position:0% +aerial density symmetries in different + + + align:start position:0% +aerial density symmetries in different +FL so this is when you have this network + + align:start position:0% +FL so this is when you have this network + + + align:start position:0% +FL so this is when you have this network +of 48 detectors that all provide a + + align:start position:0% +of 48 detectors that all provide a + + + align:start position:0% +of 48 detectors that all provide a +measurement of the yield above the + + align:start position:0% +measurement of the yield above the + + + align:start position:0% +measurement of the yield above the +threshold of 12 MV if you're starting to + + align:start position:0% +threshold of 12 MV if you're starting to + + + align:start position:0% +threshold of 12 MV if you're starting to +see variations and that's above 12 MV + + align:start position:0% +see variations and that's above 12 MV + + + align:start position:0% +see variations and that's above 12 MV +threshold that means you know that the + + align:start position:0% +threshold that means you know that the + + + align:start position:0% +threshold that means you know that the +the birth distribution is uniform in for + + align:start position:0% +the birth distribution is uniform in for + + + align:start position:0% +the birth distribution is uniform in for +pi so that means something must have + + align:start position:0% +pi so that means something must have + + + align:start position:0% +pi so that means something must have +happened on the way out for some of them + + align:start position:0% +happened on the way out for some of them + + + align:start position:0% +happened on the way out for some of them +more than others with um scattered on + + align:start position:0% +more than others with um scattered on + + + align:start position:0% +more than others with um scattered on +the way up which means that the AAL + + align:start position:0% +the way up which means that the AAL + + + align:start position:0% +the way up which means that the AAL +density is not symmetric around the + + align:start position:0% +density is not symmetric around the + + + align:start position:0% +density is not symmetric around the +implosion um and actually turns out the + + align:start position:0% +implosion um and actually turns out the + + + align:start position:0% +implosion um and actually turns out the +typical scatter neutr fraction is about + + align:start position:0% +typical scatter neutr fraction is about + + + align:start position:0% +typical scatter neutr fraction is about +20% you look at the the number density + + align:start position:0% +20% you look at the the number density + + + align:start position:0% +20% you look at the the number density +times CR sometimes the sh to get just a + + align:start position:0% +times CR sometimes the sh to get just a + + + align:start position:0% +times CR sometimes the sh to get just a +rough measurement of how many Nutri + + align:start position:0% +rough measurement of how many Nutri + + + align:start position:0% +rough measurement of how many Nutri +scatter on the way out it's about 20% + + align:start position:0% +scatter on the way out it's about 20% + + + align:start position:0% +scatter on the way out it's about 20% +um if then we frequently see variations + + align:start position:0% +um if then we frequently see variations + + + align:start position:0% +um if then we frequently see variations +of plus minus 8% in the unscattered + + align:start position:0% +of plus minus 8% in the unscattered + + + align:start position:0% +of plus minus 8% in the unscattered +Nutri yeld which means it's it's a large + + align:start position:0% +Nutri yeld which means it's it's a large + + + align:start position:0% +Nutri yeld which means it's it's a large +aerial density variation from one side + + align:start position:0% +aerial density variation from one side + + + align:start position:0% +aerial density variation from one side +of the capsule to the other and this has + + align:start position:0% +of the capsule to the other and this has + + + align:start position:0% +of the capsule to the other and this has +also been a really useful diagnostic + + align:start position:0% +also been a really useful diagnostic + + + align:start position:0% +also been a really useful diagnostic +though we figuring out what's going on + + align:start position:0% +though we figuring out what's going on + + + align:start position:0% +though we figuring out what's going on +to these implosions as we're trying to + + align:start position:0% +to these implosions as we're trying to + + + align:start position:0% +to these implosions as we're trying to +improve them further make them perform + + align:start position:0% +improve them further make them perform + + + align:start position:0% +improve them further make them perform +better and yeah so I mentioned + + align:start position:0% +better and yeah so I mentioned + + + align:start position:0% +better and yeah so I mentioned +before uh that you also have an impact + + align:start position:0% +before uh that you also have an impact + + + align:start position:0% +before uh that you also have an impact +of peak shift here uh because the + + align:start position:0% +of peak shift here uh because the + + + align:start position:0% +of peak shift here uh because the +cross-sections higher at higher energy + + align:start position:0% +cross-sections higher at higher energy + + + align:start position:0% +cross-sections higher at higher energy +so if you have a flow where the capital + + align:start position:0% +so if you have a flow where the capital + + + align:start position:0% +so if you have a flow where the capital +runs off in One Direction and have + + align:start position:0% +runs off in One Direction and have + + + align:start position:0% +runs off in One Direction and have +upshift of the peak in that direction + + align:start position:0% +upshift of the peak in that direction + + + align:start position:0% +upshift of the peak in that direction +downshift of peak in the other direction + + align:start position:0% +downshift of peak in the other direction + + + align:start position:0% +downshift of peak in the other direction +it turns out it's a smaller effect than + + align:start position:0% +it turns out it's a smaller effect than + + + align:start position:0% +it turns out it's a smaller effect than +the rowar symmetries but it's + + align:start position:0% +the rowar symmetries but it's + + + align:start position:0% +the rowar symmetries but it's +significant enough for it has to be + + align:start position:0% +significant enough for it has to be + + + align:start position:0% +significant enough for it has to be +corrected for so you have to measure + + align:start position:0% +corrected for so you have to measure + + + align:start position:0% +corrected for so you have to measure +that directional flow and correct um the + + align:start position:0% +that directional flow and correct um the + + + align:start position:0% +that directional flow and correct um the +distribution for that effect as well and + + align:start position:0% +distribution for that effect as well and + + + align:start position:0% +distribution for that effect as well and +we use low aial density gas field DT + + align:start position:0% +we use low aial density gas field DT + + + align:start position:0% +we use low aial density gas field DT +exploding pushers to set the Baseline + + align:start position:0% +exploding pushers to set the Baseline + + + align:start position:0% +exploding pushers to set the Baseline +variations basically as + + align:start position:0% +variations basically as + + + align:start position:0% +variations basically as +a ah losing the + + align:start position:0% +a ah losing the + + + align:start position:0% +a ah losing the +word uh baselining H there's another + + align:start position:0% +word uh baselining H there's another + + + align:start position:0% +word uh baselining H there's another +word come to me + + align:start position:0% +word come to me + + + align:start position:0% +word come to me +later um okay did that all make sense + + align:start position:0% +later um okay did that all make sense + + + align:start position:0% +later um okay did that all make sense +nuclear activation + + align:start position:0% +nuclear activation + + + align:start position:0% +nuclear activation +detectors so why is it that you use + + align:start position:0% +detectors so why is it that you use + + + align:start position:0% +detectors so why is it that you use +copper on Omega and zonum on historical + + align:start position:0% +copper on Omega and zonum on historical + + + align:start position:0% +copper on Omega and zonum on historical +okay + + align:start position:0% +okay + + + align:start position:0% +okay +is one better than the other or that + + align:start position:0% +is one better than the other or that + + + align:start position:0% +is one better than the other or that +could be I I actually um the guy who + + align:start position:0% +could be I I actually um the guy who + + + align:start position:0% +could be I I actually um the guy who +runs the neutron Diagnostics on Omega + + align:start position:0% +runs the neutron Diagnostics on Omega + + + align:start position:0% +runs the neutron Diagnostics on Omega +now would like to start using cirium + + align:start position:0% +now would like to start using cirium + + + align:start position:0% +now would like to start using cirium +instead uh and if I remember + + align:start position:0% + + + + align:start position:0% + +correctly yeah the reason for that is + + align:start position:0% +correctly yeah the reason for that is + + + align:start position:0% +correctly yeah the reason for that is +the longer halflife it's really hard to + + align:start position:0% +the longer halflife it's really hard to + + + align:start position:0% +the longer halflife it's really hard to +work with a 10-minute half lifee you + + align:start position:0% +work with a 10-minute half lifee you + + + align:start position:0% +work with a 10-minute half lifee you +have to really run um to get that + + align:start position:0% +have to really run um to get that + + + align:start position:0% +have to really run um to get that +detector fast enough H whereas C the + + align:start position:0% +detector fast enough H whereas C the + + + align:start position:0% +detector fast enough H whereas C the +three days uh is a little bit easier and + + align:start position:0% +three days uh is a little bit easier and + + + align:start position:0% +three days uh is a little bit easier and +also the threshold is actually better 12 + + align:start position:0% +also the threshold is actually better 12 + + + align:start position:0% +also the threshold is actually better 12 +compared to + + align:start position:0% +compared to + + + align:start position:0% +compared to +11 yeah looking at the upshift from + + align:start position:0% +11 yeah looking at the upshift from + + + align:start position:0% +11 yeah looking at the upshift from +zirconium do you just compare that to + + align:start position:0% +zirconium do you just compare that to + + + align:start position:0% +zirconium do you just compare that to +like a baseline where you have a more + + align:start position:0% +like a baseline where you have a more + + + align:start position:0% +like a baseline where you have a more +uniform emission profile versus a + + align:start position:0% +uniform emission profile versus a + + + align:start position:0% +uniform emission profile versus a +nonuniform one where that steepness of + + align:start position:0% +nonuniform one where that steepness of + + + align:start position:0% +nonuniform one where that steepness of +the cross-section actually is matters or + + align:start position:0% +the cross-section actually is matters or + + + align:start position:0% +the cross-section actually is matters or +do you compare it to like a baseline + + align:start position:0% +do you compare it to like a baseline + + + align:start position:0% +do you compare it to like a baseline +cross-section that's + + align:start position:0% +cross-section that's + + + align:start position:0% +cross-section that's +FL I I'm not sure if I fully understand + + align:start position:0% +FL I I'm not sure if I fully understand + + + align:start position:0% +FL I I'm not sure if I fully understand +the question but was so what you're + + align:start position:0% +the question but was so what you're + + + align:start position:0% +the question but was so what you're +doing is you're you're looking in many + + align:start position:0% +doing is you're you're looking in many + + + align:start position:0% +doing is you're you're looking in many +different directions and you compare the + + align:start position:0% +different directions and you compare the + + + align:start position:0% +different directions and you compare the +result in different directions but but + + align:start position:0% +result in different directions but but + + + align:start position:0% +result in different directions but but +you know do you so but you just you know + + align:start position:0% +you know do you so but you just you know + + + align:start position:0% +you know do you so but you just you know +your Baseline just by like assuming a + + align:start position:0% +your Baseline just by like assuming a + + + align:start position:0% +your Baseline just by like assuming a +14.1 that like un + + align:start position:0% +14.1 that like un + + + align:start position:0% +14.1 that like un +profile okay so there there's a couple + + align:start position:0% +profile okay so there there's a couple + + + align:start position:0% +profile okay so there there's a couple +steps to this if you get a map kind of + + align:start position:0% +steps to this if you get a map kind of + + + align:start position:0% +steps to this if you get a map kind of +like this one I I mention you have to + + align:start position:0% +like this one I I mention you have to + + + align:start position:0% +like this one I I mention you have to +correct for the velocity which is the + + align:start position:0% +correct for the velocity which is the + + + align:start position:0% +correct for the velocity which is the +the peak shift we actually don't get the + + align:start position:0% +the peak shift we actually don't get the + + + align:start position:0% +the peak shift we actually don't get the +velocity from this diagnostic we get it + + align:start position:0% +velocity from this diagnostic we get it + + + align:start position:0% +velocity from this diagnostic we get it +from the neutral spectr + + align:start position:0% +from the neutral spectr + + + align:start position:0% +from the neutral spectr +so if you have neutr spectrometers in + + align:start position:0% +so if you have neutr spectrometers in + + + align:start position:0% +so if you have neutr spectrometers in +six lines site you can measure there you + + align:start position:0% +six lines site you can measure there you + + + align:start position:0% +six lines site you can measure there you +don't just measure a number above + + align:start position:0% +don't just measure a number above + + + align:start position:0% +don't just measure a number above +threshold you actually measure the + + align:start position:0% +threshold you actually measure the + + + align:start position:0% +threshold you actually measure the +neutrons vors you know what the option + + align:start position:0% +neutrons vors you know what the option + + + align:start position:0% +neutrons vors you know what the option +is which means you can infer the actual + + align:start position:0% +is which means you can infer the actual + + + align:start position:0% +is which means you can infer the actual +4 Pi velocity vector and then you can + + align:start position:0% +4 Pi velocity vector and then you can + + + align:start position:0% +4 Pi velocity vector and then you can +correct this for + + align:start position:0% + + + + align:start position:0% + +that neutr + + align:start position:0% +that neutr + + + align:start position:0% +that neutr +speters um any other activation + + align:start position:0% +speters um any other activation + + + align:start position:0% +speters um any other activation +question okay with that let's go into + + align:start position:0% +question okay with that let's go into + + + align:start position:0% +question okay with that let's go into +Neutron + + align:start position:0% +Neutron + + + align:start position:0% +Neutron +spectrometry this is kind of touching on + + align:start position:0% +spectrometry this is kind of touching on + + + align:start position:0% +spectrometry this is kind of touching on +exactly that point we do have a large + + align:start position:0% +exactly that point we do have a large + + + align:start position:0% +exactly that point we do have a large +suite of neutron spectrometers on the N + + align:start position:0% +suite of neutron spectrometers on the N + + + align:start position:0% +suite of neutron spectrometers on the N +um these five with the kind of blue + + align:start position:0% +um these five with the kind of blue + + + align:start position:0% +um these five with the kind of blue +lines here are all based on the same + + align:start position:0% +lines here are all based on the same + + + align:start position:0% +lines here are all based on the same +techology they're Neutron time flight + + align:start position:0% +techology they're Neutron time flight + + + align:start position:0% +techology they're Neutron time flight +spectrometers which we'll discuss in + + align:start position:0% +spectrometers which we'll discuss in + + + align:start position:0% +spectrometers which we'll discuss in +detail and then this one in red is the + + align:start position:0% +detail and then this one in red is the + + + align:start position:0% +detail and then this one in red is the +magnetic Rec spectrometer which I + + align:start position:0% +magnetic Rec spectrometer which I + + + align:start position:0% +magnetic Rec spectrometer which I +already mentioned a couple times there's + + align:start position:0% +already mentioned a couple times there's + + + align:start position:0% +already mentioned a couple times there's +actually one more that's not included on + + align:start position:0% +actually one more that's not included on + + + align:start position:0% +actually one more that's not included on +um this cartoon which is um also a + + align:start position:0% +um this cartoon which is um also a + + + align:start position:0% +um this cartoon which is um also a +neutron thite spectrometer based on + + align:start position:0% +neutron thite spectrometer based on + + + align:start position:0% +neutron thite spectrometer based on +different detector technology that's + + align:start position:0% +different detector technology that's + + + align:start position:0% +different detector technology that's +fied together with a um nutr imature on + + align:start position:0% +fied together with a um nutr imature on + + + align:start position:0% +fied together with a um nutr imature on +roughly this time ofite it's been a few + + align:start position:0% +roughly this time ofite it's been a few + + + align:start position:0% +roughly this time ofite it's been a few +years since it was working but we're + + align:start position:0% +years since it was working but we're + + + align:start position:0% +years since it was working but we're +trying to bring it back to result some + + align:start position:0% +trying to bring it back to result some + + + align:start position:0% +trying to bring it back to result some +everything so total of seven neutr + + align:start position:0% +everything so total of seven neutr + + + align:start position:0% +everything so total of seven neutr +spectrometers on the N that provide good + + align:start position:0% +spectrometers on the N that provide good + + + align:start position:0% +spectrometers on the N that provide good +implosion coverage together and this + + align:start position:0% +implosion coverage together and this + + + align:start position:0% +implosion coverage together and this +similar setup exists on other ICF + + align:start position:0% +similar setup exists on other ICF + + + align:start position:0% +similar setup exists on other ICF +facilities like on Omega for example I + + align:start position:0% +facilities like on Omega for example I + + + align:start position:0% +facilities like on Omega for example I +think there + + align:start position:0% +think there + + + align:start position:0% +think there +are six now that run on DT in different + + align:start position:0% +are six now that run on DT in different + + + align:start position:0% +are six now that run on DT in different +L of sites so you can compare the + + align:start position:0% +L of sites so you can compare the + + + align:start position:0% +L of sites so you can compare the +results in those six lineside to again + + align:start position:0% +results in those six lineside to again + + + align:start position:0% +results in those six lineside to again +infer the flow Vector in addition to + + align:start position:0% +infer the flow Vector in addition to + + + align:start position:0% +infer the flow Vector in addition to +measuring the ion + + align:start position:0% +measuring the ion + + + align:start position:0% +measuring the ion +temperature and ion temperature + + align:start position:0% +temperature and ion temperature + + + align:start position:0% +temperature and ion temperature +variations um and fewer that work on DD + + align:start position:0% +variations um and fewer that work on DD + + + align:start position:0% +variations um and fewer that work on DD +but still enough to to get a good good + + align:start position:0% + + + + align:start position:0% + +coverage um okay so let's start with the + + align:start position:0% +coverage um okay so let's start with the + + + align:start position:0% +coverage um okay so let's start with the +magnetic recall spectrometer so again + + align:start position:0% +magnetic recall spectrometer so again + + + align:start position:0% +magnetic recall spectrometer so again +this this is what I've been working with + + align:start position:0% +this this is what I've been working with + + + align:start position:0% +this this is what I've been working with +since since 2010 so it's um happy to + + align:start position:0% +since since 2010 so it's um happy to + + + align:start position:0% +since since 2010 so it's um happy to +take any questions on this one and Chris + + align:start position:0% +take any questions on this one and Chris + + + align:start position:0% +take any questions on this one and Chris +is working on a very similar concept uh + + align:start position:0% +is working on a very similar concept uh + + + align:start position:0% +is working on a very similar concept uh +Sean's kind of working on a similar + + align:start position:0% +Sean's kind of working on a similar + + + align:start position:0% +Sean's kind of working on a similar +concept too for spark so you guys are + + align:start position:0% +concept too for spark so you guys are + + + align:start position:0% +concept too for spark so you guys are +very familiar with this already uh but + + align:start position:0% +very familiar with this already uh but + + + align:start position:0% +very familiar with this already uh but +for those who have not heard about it + + align:start position:0% +for those who have not heard about it + + + align:start position:0% +for those who have not heard about it +before the way it works you will have + + align:start position:0% +before the way it works you will have + + + align:start position:0% +before the way it works you will have +the neutrons emitted from Target chamber + + align:start position:0% +the neutrons emitted from Target chamber + + + align:start position:0% +the neutrons emitted from Target chamber +Center that will gled out a fraction of + + align:start position:0% +Center that will gled out a fraction of + + + align:start position:0% +Center that will gled out a fraction of +those neutrons will reach a a conversion + + align:start position:0% +those neutrons will reach a a conversion + + + align:start position:0% +those neutrons will reach a a conversion +file a plastic conversion fil 26 cm in + + align:start position:0% +file a plastic conversion fil 26 cm in + + + align:start position:0% +file a plastic conversion fil 26 cm in +the case of nith from Target chamber + + align:start position:0% +the case of nith from Target chamber + + + align:start position:0% +the case of nith from Target chamber +Center and this is actually deuterated + + align:start position:0% +Center and this is actually deuterated + + + align:start position:0% +Center and this is actually deuterated +foil so the nutrients that interact with + + align:start position:0% +foil so the nutrients that interact with + + + align:start position:0% +foil so the nutrients that interact with +the foil some of them will not get dter + + align:start position:0% +the foil some of them will not get dter + + + align:start position:0% +the foil some of them will not get dter +forward scattered Vons will reach this + + align:start position:0% +forward scattered Vons will reach this + + + align:start position:0% +forward scattered Vons will reach this +magnet which is outside of the target + + align:start position:0% +magnet which is outside of the target + + + align:start position:0% +magnet which is outside of the target +chain the wall it's just a vacuum in + + align:start position:0% +chain the wall it's just a vacuum in + + + align:start position:0% +chain the wall it's just a vacuum in +between so they all reach the magnet and + + align:start position:0% +between so they all reach the magnet and + + + align:start position:0% +between so they all reach the magnet and +then there was momentum separated in the + + align:start position:0% +then there was momentum separated in the + + + align:start position:0% +then there was momentum separated in the +magnet in different physical location of + + align:start position:0% +magnet in different physical location of + + + align:start position:0% +magnet in different physical location of +the detector R depending on the and you + + align:start position:0% +the detector R depending on the and you + + + align:start position:0% +the detector R depending on the and you +use that to reconstruct a Rec D energy + + align:start position:0% +use that to reconstruct a Rec D energy + + + align:start position:0% +use that to reconstruct a Rec D energy +spectrum and then from that Spectrum you + + align:start position:0% +spectrum and then from that Spectrum you + + + align:start position:0% +spectrum and then from that Spectrum you +can infer what the inul + + align:start position:0% +can infer what the inul + + + align:start position:0% +can infer what the inul +spect must like we use uh doated plastic + + align:start position:0% +spect must like we use uh doated plastic + + + align:start position:0% +spect must like we use uh doated plastic +in particular because the detector we + + align:start position:0% +in particular because the detector we + + + align:start position:0% +in particular because the detector we +use in this instrument is Si 39 and it + + align:start position:0% +use in this instrument is Si 39 and it + + + align:start position:0% +use in this instrument is Si 39 and it +turns out the good tracks are much much + + align:start position:0% +turns out the good tracks are much much + + + align:start position:0% +turns out the good tracks are much much +easier to distinguish the background + + align:start position:0% +easier to distinguish the background + + + align:start position:0% +easier to distinguish the background +compared to using protons um yeah and we + + align:start position:0% +compared to using protons um yeah and we + + + align:start position:0% +compared to using protons um yeah and we +also there's a number of detectors with + + align:start position:0% +also there's a number of detectors with + + + align:start position:0% +also there's a number of detectors with +exol sodium hydroxides scan them in + + align:start position:0% +exol sodium hydroxides scan them in + + + align:start position:0% +exol sodium hydroxides scan them in +microscopes after shot in this Digital + + align:start position:0% +microscopes after shot in this Digital + + + align:start position:0% +microscopes after shot in this Digital +Data + + align:start position:0% +Data + + + align:start position:0% +Data +together um look look at zooming in on + + align:start position:0% +together um look look at zooming in on + + + align:start position:0% +together um look look at zooming in on +the foil here so the neutron will hit a + + align:start position:0% +the foil here so the neutron will hit a + + + align:start position:0% +the foil here so the neutron will hit a +Deon in the foil and then the vehicle + + align:start position:0% +Deon in the foil and then the vehicle + + + align:start position:0% +Deon in the foil and then the vehicle +Deon energy U will depend on the instant + + align:start position:0% +Deon energy U will depend on the instant + + + align:start position:0% +Deon energy U will depend on the instant +Neutron energy and then also the energy + + align:start position:0% +Neutron energy and then also the energy + + + align:start position:0% +Neutron energy and then also the energy +loss that the D has from its place of + + align:start position:0% +loss that the D has from its place of + + + align:start position:0% +loss that the D has from its place of +birth until it hits the back of the foil + + align:start position:0% +birth until it hits the back of the foil + + + align:start position:0% +birth until it hits the back of the foil +so Neutron born at the start of the fo + + align:start position:0% +so Neutron born at the start of the fo + + + align:start position:0% +so Neutron born at the start of the fo +would come out with lower energy than a + + align:start position:0% +would come out with lower energy than a + + + align:start position:0% +would come out with lower energy than a +neutron born at the end of the + + align:start position:0% +neutron born at the end of the + + + align:start position:0% +neutron born at the end of the +fo that has to be considered in the + + align:start position:0% +fo that has to be considered in the + + + align:start position:0% +fo that has to be considered in the +analysis of Thea + + align:start position:0% + + + + align:start position:0% + +uh we can look at also a couple of other + + align:start position:0% +uh we can look at also a couple of other + + + align:start position:0% +uh we can look at also a couple of other +um aspects of this so when I have we + + align:start position:0% +um aspects of this so when I have we + + + align:start position:0% +um aspects of this so when I have we +used to want a high efficiency to be + + align:start position:0% +used to want a high efficiency to be + + + align:start position:0% +used to want a high efficiency to be +able to count all the nutrients that + + align:start position:0% +able to count all the nutrients that + + + align:start position:0% +able to count all the nutrients that +came out today we're actually running + + align:start position:0% +came out today we're actually running + + + align:start position:0% +came out today we're actually running +into saturation problems instead we + + align:start position:0% +into saturation problems instead we + + + align:start position:0% +into saturation problems instead we +don't really want this to be so high + + align:start position:0% +don't really want this to be so high + + + align:start position:0% +don't really want this to be so high +anymore but the efficiency of the + + align:start position:0% +anymore but the efficiency of the + + + align:start position:0% +anymore but the efficiency of the +mrss uh can be uh you know back of the + + align:start position:0% +mrss uh can be uh you know back of the + + + align:start position:0% +mrss uh can be uh you know back of the +envelope calculated as the foil solid + + align:start position:0% +envelope calculated as the foil solid + + + align:start position:0% +envelope calculated as the foil solid +angle times the number of number density + + align:start position:0% +angle times the number of number density + + + align:start position:0% +angle times the number of number density +pruter in the foil times the 12 + + align:start position:0% +pruter in the foil times the 12 + + + align:start position:0% +pruter in the foil times the 12 +thickness um the ND differential + + align:start position:0% +thickness um the ND differential + + + align:start position:0% +thickness um the ND differential +cross-section for forward scatter and + + align:start position:0% +cross-section for forward scatter and + + + align:start position:0% +cross-section for forward scatter and +the uh aperture solid where the aperture + + align:start position:0% +the uh aperture solid where the aperture + + + align:start position:0% +the uh aperture solid where the aperture +is opening in front of the + + align:start position:0% +is opening in front of the + + + align:start position:0% +is opening in front of the +magnet you can throw some numbers on + + align:start position:0% +magnet you can throw some numbers on + + + align:start position:0% +magnet you can throw some numbers on +that U this is an example from the ni + + align:start position:0% +that U this is an example from the ni + + + align:start position:0% +that U this is an example from the ni +the foil solid angle will be the area of + + align:start position:0% +the foil solid angle will be the area of + + + align:start position:0% +the foil solid angle will be the area of +the foil divided by um the total sphere + + align:start position:0% +the foil divided by um the total sphere + + + align:start position:0% +the foil divided by um the total sphere +at that distance where the foil is + + align:start position:0% +at that distance where the foil is + + + align:start position:0% +at that distance where the foil is +sitting uh and then number density you + + align:start position:0% +sitting uh and then number density you + + + align:start position:0% +sitting uh and then number density you +can calculate based on manufacturer + + align:start position:0% +can calculate based on manufacturer + + + align:start position:0% +can calculate based on manufacturer +specification for the thickness is + + align:start position:0% +specification for the thickness is + + + align:start position:0% +specification for the thickness is +measured um this differential + + align:start position:0% +measured um this differential + + + align:start position:0% +measured um this differential +crosssection for get direction is + + align:start position:0% +crosssection for get direction is + + + align:start position:0% +crosssection for get direction is +roughly this number aperture solid you + + align:start position:0% +roughly this number aperture solid you + + + align:start position:0% +roughly this number aperture solid you +take the area of the aperture um and + + align:start position:0% +take the area of the aperture um and + + + align:start position:0% +take the area of the aperture um and +just divided by the aperture distance + + align:start position:0% +just divided by the aperture distance + + + align:start position:0% +just divided by the aperture distance +squar and this is a correction for the + + align:start position:0% +squar and this is a correction for the + + + align:start position:0% +squar and this is a correction for the +fact that the isn't sitting straight + + align:start position:0% +fact that the isn't sitting straight + + + align:start position:0% +fact that the isn't sitting straight +it's to in front of + + align:start position:0% +it's to in front of + + + align:start position:0% +it's to in front of +the and then this is the purity of the + + align:start position:0% +the and then this is the purity of the + + + align:start position:0% +the and then this is the purity of the +imploy which show also as the + + align:start position:0% +imploy which show also as the + + + align:start position:0% +imploy which show also as the +correction um this gives us a rough + + align:start position:0% +correction um this gives us a rough + + + align:start position:0% +correction um this gives us a rough +number in reality this is not we use to + + align:start position:0% +number in reality this is not we use to + + + align:start position:0% +number in reality this is not we use to +get the yield number out we use mcmp + + align:start position:0% +get the yield number out we use mcmp + + + align:start position:0% +get the yield number out we use mcmp +simulation um actually I thought on the + + align:start position:0% +simulation um actually I thought on the + + + align:start position:0% +simulation um actually I thought on the +way over here I should have included a + + align:start position:0% +way over here I should have included a + + + align:start position:0% +way over here I should have included a +slide on mcmp because we use mcmp a lot + + align:start position:0% +slide on mcmp because we use mcmp a lot + + + align:start position:0% +slide on mcmp because we use mcmp a lot +as a tool in understanding the response + + align:start position:0% +as a tool in understanding the response + + + align:start position:0% +as a tool in understanding the response +of the detectives that we're looking at + + align:start position:0% +of the detectives that we're looking at + + + align:start position:0% +of the detectives that we're looking at +even for the nuclear activation + + align:start position:0% +even for the nuclear activation + + + align:start position:0% +even for the nuclear activation +detectors that we looked at before to + + align:start position:0% +detectors that we looked at before to + + + align:start position:0% +detectors that we looked at before to +know how many neutrons that they see uh + + align:start position:0% +know how many neutrons that they see uh + + + align:start position:0% +know how many neutrons that they see uh +how many might be scattered before they + + align:start position:0% +how many might be scattered before they + + + align:start position:0% +how many might be scattered before they +hit the nuer activation detective also + + align:start position:0% +hit the nuer activation detective also + + + align:start position:0% +hit the nuer activation detective also +have to use um mon Neutron transport + + align:start position:0% +have to use um mon Neutron transport + + + align:start position:0% +have to use um mon Neutron transport +tools such as mcmp so that's um it's + + align:start position:0% +tools such as mcmp so that's um it's + + + align:start position:0% +tools such as mcmp so that's um it's +it's not just building detectors there's + + align:start position:0% +it's not just building detectors there's + + + align:start position:0% +it's not just building detectors there's +a lot of modeling that goes into this as + + align:start position:0% + + + + align:start position:0% + +well okay we can also look at what we + + align:start position:0% +well okay we can also look at what we + + + align:start position:0% +well okay we can also look at what we +expect for the resolution so for what + + align:start position:0% +expect for the resolution so for what + + + align:start position:0% +expect for the resolution so for what +that is basically is if you have montic + + align:start position:0% +that is basically is if you have montic + + + align:start position:0% +that is basically is if you have montic +nutrients uh emitted from Target chamber + + align:start position:0% +nutrients uh emitted from Target chamber + + + align:start position:0% +nutrients uh emitted from Target chamber +Center going through that whole system + + align:start position:0% +Center going through that whole system + + + align:start position:0% +Center going through that whole system +then we're going to end up with a wider + + align:start position:0% +then we're going to end up with a wider + + + align:start position:0% +then we're going to end up with a wider +Spectrum than just montic on the mrss so + + align:start position:0% +Spectrum than just montic on the mrss so + + + align:start position:0% +Spectrum than just montic on the mrss so +we look at how why would that Spectrum + + align:start position:0% +we look at how why would that Spectrum + + + align:start position:0% +we look at how why would that Spectrum +be a had montic to understand the + + align:start position:0% +be a had montic to understand the + + + align:start position:0% +be a had montic to understand the +broadening the instrumental broadening + + align:start position:0% +broadening the instrumental broadening + + + align:start position:0% +broadening the instrumental broadening +um so and we can look at that as three + + align:start position:0% +um so and we can look at that as three + + + align:start position:0% +um so and we can look at that as three +components we have a broadening effect + + align:start position:0% +components we have a broadening effect + + + align:start position:0% +components we have a broadening effect +due to the foil thickness and this is + + align:start position:0% +due to the foil thickness and this is + + + align:start position:0% +due to the foil thickness and this is +again where DS are born in one end or + + align:start position:0% +again where DS are born in one end or + + + align:start position:0% +again where DS are born in one end or +the other and they're going to lose + + align:start position:0% +the other and they're going to lose + + + align:start position:0% +the other and they're going to lose +energy as they go through which gives + + align:start position:0% +energy as they go through which gives + + + align:start position:0% +energy as they go through which gives +you a broadening uh we're going to have + + align:start position:0% +you a broadening uh we're going to have + + + align:start position:0% +you a broadening uh we're going to have +broadening based on the scattering + + align:start position:0% +broadening based on the scattering + + + align:start position:0% +broadening based on the scattering +geometry we have neutrons that hit the + + align:start position:0% +geometry we have neutrons that hit the + + + align:start position:0% +geometry we have neutrons that hit the +FR head on Neons that go straight out + + align:start position:0% +FR head on Neons that go straight out + + + align:start position:0% +FR head on Neons that go straight out +but then we also have neutrons that hit + + align:start position:0% +but then we also have neutrons that hit + + + align:start position:0% +but then we also have neutrons that hit +one Edge so the foil and gohe and angle + + align:start position:0% +one Edge so the foil and gohe and angle + + + align:start position:0% +one Edge so the foil and gohe and angle +and that gives us a effect and then + + align:start position:0% +and that gives us a effect and then + + + align:start position:0% +and that gives us a effect and then +finally we have some broadening + + align:start position:0% +finally we have some broadening + + + align:start position:0% +finally we have some broadening +depending on the ion Optical properties + + align:start position:0% +depending on the ion Optical properties + + + align:start position:0% +depending on the ion Optical properties +of the magnet and that leads us to a + + align:start position:0% +of the magnet and that leads us to a + + + align:start position:0% +of the magnet and that leads us to a +total broadening and it actually turns + + align:start position:0% +total broadening and it actually turns + + + align:start position:0% +total broadening and it actually turns +out that these are counter related so if + + align:start position:0% +out that these are counter related so if + + + align:start position:0% +out that these are counter related so if +you want higher efficiency you had have + + align:start position:0% +you want higher efficiency you had have + + + align:start position:0% +you want higher efficiency you had have +to add more foil material which also + + align:start position:0% +to add more foil material which also + + + align:start position:0% +to add more foil material which also +enhances the broadening you you want a + + align:start position:0% +enhances the broadening you you want a + + + align:start position:0% +enhances the broadening you you want a +narrow broadening you want high + + align:start position:0% +narrow broadening you want high + + + align:start position:0% +narrow broadening you want high +efficiency it becomes optimization + + align:start position:0% +efficiency it becomes optimization + + + align:start position:0% +efficiency it becomes optimization +problem um in the design of a magnetic + + align:start position:0% +problem um in the design of a magnetic + + + align:start position:0% +problem um in the design of a magnetic +recoil spectrometer you have to balance + + align:start position:0% +recoil spectrometer you have to balance + + + align:start position:0% +recoil spectrometer you have to balance +efficiency and resolution against each + + align:start position:0% +efficiency and resolution against each + + + align:start position:0% +efficiency and resolution against each +other this is an example for that thin + + align:start position:0% +other this is an example for that thin + + + align:start position:0% +other this is an example for that thin +fil magnetic prot veter at jet which is + + align:start position:0% +fil magnetic prot veter at jet which is + + + align:start position:0% +fil magnetic prot veter at jet which is +very similar to Ms and maybe even more + + align:start position:0% +very similar to Ms and maybe even more + + + align:start position:0% +very similar to Ms and maybe even more +similar to what Sean is working on first + + align:start position:0% +similar to what Sean is working on first + + + align:start position:0% +similar to what Sean is working on first +part so this is looking at proten colus + + align:start position:0% +part so this is looking at proten colus + + + align:start position:0% +part so this is looking at proten colus +and P thickness and seeing how varying + + align:start position:0% +and P thickness and seeing how varying + + + align:start position:0% +and P thickness and seeing how varying +those two will impact efficienc and + + align:start position:0% +those two will impact efficienc and + + + align:start position:0% +those two will impact efficienc and +resolution trying to find some set + + align:start position:0% +resolution trying to find some set + + + align:start position:0% +resolution trying to find some set +points that would be ideal operation for + + align:start position:0% +points that would be ideal operation for + + + align:start position:0% +points that would be ideal operation for +getting the signal you need and still + + align:start position:0% +getting the signal you need and still + + + align:start position:0% +getting the signal you need and still +having a good enough resolution to make + + align:start position:0% +having a good enough resolution to make + + + align:start position:0% +having a good enough resolution to make +the measurements you want + + align:start position:0% +the measurements you want + + + align:start position:0% +the measurements you want +uh and that actually we can take a look + + align:start position:0% +uh and that actually we can take a look + + + align:start position:0% +uh and that actually we can take a look +at what that looks like at De this is + + align:start position:0% +at what that looks like at De this is + + + align:start position:0% +at what that looks like at De this is +the + + align:start position:0% +the + + + align:start position:0% +the +NPR proton spectometer in this case we + + align:start position:0% +NPR proton spectometer in this case we + + + align:start position:0% +NPR proton spectometer in this case we +do use protons not D because this + + align:start position:0% +do use protons not D because this + + + align:start position:0% +do use protons not D because this +simulator detector a king count protons + + align:start position:0% +simulator detector a king count protons + + + align:start position:0% +simulator detector a king count protons +without any problems um this is what it + + align:start position:0% +without any problems um this is what it + + + align:start position:0% +without any problems um this is what it +looked like before the shielding was + + align:start position:0% +looked like before the shielding was + + + align:start position:0% +looked like before the shielding was +added this is the magnet housing and you + + align:start position:0% +added this is the magnet housing and you + + + align:start position:0% +added this is the magnet housing and you +add a lot of shielding to prevent + + align:start position:0% +add a lot of shielding to prevent + + + align:start position:0% +add a lot of shielding to prevent +contributions from scatterings that you + + align:start position:0% +contributions from scatterings that you + + + align:start position:0% +contributions from scatterings that you +don't want to look at uh and it's you + + align:start position:0% +don't want to look at uh and it's you + + + align:start position:0% +don't want to look at uh and it's you +know the same concept as for you have + + align:start position:0% +know the same concept as for you have + + + align:start position:0% +know the same concept as for you have +the neutrons emitted from the basma over + + align:start position:0% +the neutrons emitted from the basma over + + + align:start position:0% +the neutrons emitted from the basma over +here you have cators so they only look + + align:start position:0% +here you have cators so they only look + + + align:start position:0% +here you have cators so they only look +at a certain fraction of them the foil + + align:start position:0% +at a certain fraction of them the foil + + + align:start position:0% +at a certain fraction of them the foil +is + + align:start position:0% +is + + + align:start position:0% +is +inside the magnet house in here you have + + align:start position:0% +inside the magnet house in here you have + + + align:start position:0% +inside the magnet house in here you have +the second proile or second cator for + + align:start position:0% +the second proile or second cator for + + + align:start position:0% +the second proile or second cator for +the protons are born in foil here and + + align:start position:0% +the protons are born in foil here and + + + align:start position:0% +the protons are born in foil here and +then the protons are momentum analyz in + + align:start position:0% +then the protons are momentum analyz in + + + align:start position:0% +then the protons are momentum analyz in +the magnet and up in a different + + align:start position:0% +the magnet and up in a different + + + align:start position:0% +the magnet and up in a different +physical location of the array this case + + align:start position:0% +physical location of the array this case + + + align:start position:0% +physical location of the array this case +it's an electromag per maybe I probably + + align:start position:0% +it's an electromag per maybe I probably + + + align:start position:0% +it's an electromag per maybe I probably +forgot some at F but f is a Perman + + align:start position:0% +forgot some at F but f is a Perman + + + align:start position:0% +forgot some at F but f is a Perman +magnet um an advantage with an + + align:start position:0% +magnet um an advantage with an + + + align:start position:0% +magnet um an advantage with an +electromagnet is you can tune it so you + + align:start position:0% +electromagnet is you can tune it so you + + + align:start position:0% +electromagnet is you can tune it so you +can operate at different + + align:start position:0% +can operate at different + + + align:start position:0% +can operate at different +energies the NPR in particular can be + + align:start position:0% +energies the NPR in particular can be + + + align:start position:0% +energies the NPR in particular can be +tuned to operate either for 14 D + + align:start position:0% +tuned to operate either for 14 D + + + align:start position:0% +tuned to operate either for 14 D +neutrons or to half neutrons and you + + align:start position:0% +neutrons or to half neutrons and you + + + align:start position:0% +neutrons or to half neutrons and you +used the the + + align:start position:0% +used the the + + + align:start position:0% +used the the +jet with oblique + + align:start position:0% +jet with oblique + + + align:start position:0% +jet with oblique +angle that if you went from the top + + align:start position:0% +angle that if you went from the top + + + align:start position:0% +angle that if you went from the top +traverses all through why B angle + + align:start position:0% +traverses all through why B angle + + + align:start position:0% +traverses all through why B angle +use I'm not sure okay there's + + align:start position:0% +use I'm not sure okay there's + + + align:start position:0% +use I'm not sure okay there's +interesting choice yeah I think it might + + align:start position:0% +interesting choice yeah I think it might + + + align:start position:0% +interesting choice yeah I think it might +have actually been to maximize + + align:start position:0% +have actually been to maximize + + + align:start position:0% +have actually been to maximize +efficiency because you you see more of + + align:start position:0% +efficiency because you you see more of + + + align:start position:0% +efficiency because you you see more of +the plasma level + + align:start position:0% +the plasma level + + + align:start position:0% +the plasma level +okay it's a question for Yan though he + + align:start position:0% +okay it's a question for Yan though he + + + align:start position:0% +okay it's a question for Yan though he +was involved in the actual building of + + align:start position:0% +was involved in the actual building of + + + align:start position:0% +was involved in the actual building of +this this + + align:start position:0% +this this + + + align:start position:0% +this this +system okay and then so just look at + + align:start position:0% +system okay and then so just look at + + + align:start position:0% +system okay and then so just look at +what a recall Dy Spectrum can look like + + align:start position:0% +what a recall Dy Spectrum can look like + + + align:start position:0% +what a recall Dy Spectrum can look like +this an example from n it's a really old + + align:start position:0% +this an example from n it's a really old + + + align:start position:0% +this an example from n it's a really old +example H but you have the primary GP + + align:start position:0% +example H but you have the primary GP + + + align:start position:0% +example H but you have the primary GP +and then you have the down SC neutrons + + align:start position:0% +and then you have the down SC neutrons + + + align:start position:0% +and then you have the down SC neutrons +and then from this youer the neutr by + + align:start position:0% +and then from this youer the neutr by + + + align:start position:0% +and then from this youer the neutr by +scaling for p the aial density by + + align:start position:0% +scaling for p the aial density by + + + align:start position:0% +scaling for p the aial density by +comparing the number of nutr here dter + + align:start position:0% +comparing the number of nutr here dter + + + align:start position:0% +comparing the number of nutr here dter +here the deance here and the ion + + align:start position:0% +here the deance here and the ion + + + align:start position:0% +here the deance here and the ion +temperature from it and what you do when + + align:start position:0% +temperature from it and what you do when + + + align:start position:0% +temperature from it and what you do when +you analyze this kind of data is you + + align:start position:0% +you analyze this kind of data is you + + + align:start position:0% +you analyze this kind of data is you +take a model Neutron spectrum and fold + + align:start position:0% +take a model Neutron spectrum and fold + + + align:start position:0% +take a model Neutron spectrum and fold +it with the instrument response function + + align:start position:0% +it with the instrument response function + + + align:start position:0% +it with the instrument response function +simulated using gon4 or mcmp or a + + align:start position:0% +simulated using gon4 or mcmp or a + + + align:start position:0% +simulated using gon4 or mcmp or a +combination thereof and get it on the + + align:start position:0% +combination thereof and get it on the + + + align:start position:0% +combination thereof and get it on the +different energy scale and then adjust + + align:start position:0% +different energy scale and then adjust + + + align:start position:0% +different energy scale and then adjust +the iron temperature the peak position + + align:start position:0% +the iron temperature the peak position + + + align:start position:0% +the iron temperature the peak position +which is related to Velocity the + + align:start position:0% +which is related to Velocity the + + + align:start position:0% +which is related to Velocity the +amplitude which is related to yield and + + align:start position:0% +amplitude which is related to yield and + + + align:start position:0% +amplitude which is related to yield and +the rowar which is related to the down + + align:start position:0% +the rowar which is related to the down + + + align:start position:0% +the rowar which is related to the down +SC relative to primary exraction so you + + align:start position:0% +SC relative to primary exraction so you + + + align:start position:0% +SC relative to primary exraction so you +get those numbers out of the + + align:start position:0% +get those numbers out of the + + + align:start position:0% +get those numbers out of the +analysis yeah you're going past just + + align:start position:0% +analysis yeah you're going past just + + + align:start position:0% +analysis yeah you're going past just +fitting a g this PE you're using a more + + align:start position:0% +fitting a g this PE you're using a more + + + align:start position:0% +fitting a g this PE you're using a more +sophisticated analytic model um so + + align:start position:0% +sophisticated analytic model um so + + + align:start position:0% +sophisticated analytic model um so +actually in most cases I fit a go into + + align:start position:0% +actually in most cases I fit a go into + + + align:start position:0% +actually in most cases I fit a go into +the peak and then just have second + + align:start position:0% +the peak and then just have second + + + align:start position:0% +the peak and then just have second +component that accounts for the + + align:start position:0% +component that accounts for the + + + align:start position:0% +component that accounts for the +scatter um but yeah there there are some + + align:start position:0% +scatter um but yeah there there are some + + + align:start position:0% +scatter um but yeah there there are some +slightly more advanced models as well + + align:start position:0% +slightly more advanced models as well + + + align:start position:0% +slightly more advanced models as well +and for magnetic confin Fusion you + + align:start position:0% +and for magnetic confin Fusion you + + + align:start position:0% +and for magnetic confin Fusion you +typically have to have more advanced + + align:start position:0% +typically have to have more advanced + + + align:start position:0% +typically have to have more advanced +models because you have um fast ions due + + align:start position:0% +models because you have um fast ions due + + + align:start position:0% +models because you have um fast ions due +to heating that contribute to the + + align:start position:0% +to heating that contribute to the + + + align:start position:0% +to heating that contribute to the +broadening of the peak and to resolve + + align:start position:0% +broadening of the peak and to resolve + + + align:start position:0% +broadening of the peak and to resolve +those you have to have like a model for + + align:start position:0% +those you have to have like a model for + + + align:start position:0% +those you have to have like a model for +the beam thermal reactions or the beam + + align:start position:0% +the beam thermal reactions or the beam + + + align:start position:0% +the beam thermal reactions or the beam +beam reactions that have slightly + + align:start position:0% +beam reactions that have slightly + + + align:start position:0% +beam reactions that have slightly +different shapes and you can um you can + + align:start position:0% +different shapes and you can um you can + + + align:start position:0% +different shapes and you can um you can +find the relative contributions of those + + align:start position:0% +find the relative contributions of those + + + align:start position:0% +find the relative contributions of those +by by fitting those different shapes of + + align:start position:0% +by by fitting those different shapes of + + + align:start position:0% +by by fitting those different shapes of +the + + align:start position:0% +the + + + align:start position:0% +the +P other question + + align:start position:0% + + + + align:start position:0% + +okay so with that let's look at the + + align:start position:0% +okay so with that let's look at the + + + align:start position:0% +okay so with that let's look at the +neutron time of flight technique so for + + align:start position:0% +neutron time of flight technique so for + + + align:start position:0% +neutron time of flight technique so for +ICF this is actually + + align:start position:0% +ICF this is actually + + + align:start position:0% +ICF this is actually +simple because all the particles are + + align:start position:0% +simple because all the particles are + + + align:start position:0% +simple because all the particles are +assumed to be emitted at the same time + + align:start position:0% +assumed to be emitted at the same time + + + align:start position:0% +assumed to be emitted at the same time +the burn time is so short or 100 p a + + align:start position:0% +the burn time is so short or 100 p a + + + align:start position:0% +the burn time is so short or 100 p a +seconds you can make that assumption so + + align:start position:0% +seconds you can make that assumption so + + + align:start position:0% +seconds you can make that assumption so +then you really only have to measure the + + align:start position:0% +then you really only have to measure the + + + align:start position:0% +then you really only have to measure the +neutrons as they arrive on a simulator + + align:start position:0% +neutrons as they arrive on a simulator + + + align:start position:0% +neutrons as they arrive on a simulator +at a set distance D from the implosion + + align:start position:0% +at a set distance D from the implosion + + + align:start position:0% +at a set distance D from the implosion +uh and you use + + align:start position:0% + + + + align:start position:0% + +that to infer the neutr + + align:start position:0% +that to infer the neutr + + + align:start position:0% +that to infer the neutr +Spectrum um yeah and I mean this in + + align:start position:0% +Spectrum um yeah and I mean this in + + + align:start position:0% +Spectrum um yeah and I mean this in +particular it's already been converted + + align:start position:0% +particular it's already been converted + + + align:start position:0% +particular it's already been converted +to temperature expression but really + + align:start position:0% +to temperature expression but really + + + align:start position:0% +to temperature expression but really +what what you're looking at is the the + + align:start position:0% +what what you're looking at is the the + + + align:start position:0% +what what you're looking at is the the +neutrient energy um just on the time + + align:start position:0% +neutrient energy um just on the time + + + align:start position:0% +neutrient energy um just on the time +scale uh yeah so and same same as for + + align:start position:0% +scale uh yeah so and same same as for + + + align:start position:0% +scale uh yeah so and same same as for +temper deter on the the width and + + align:start position:0% +temper deter on the the width and + + + align:start position:0% +temper deter on the the width and +actually + + align:start position:0% +actually + + + align:start position:0% +actually +so on Omega the MS are still used as a + + align:start position:0% +so on Omega the MS are still used as a + + + align:start position:0% +so on Omega the MS are still used as a +as a yield measurement too on the ni we + + align:start position:0% +as a yield measurement too on the ni we + + + align:start position:0% +as a yield measurement too on the ni we +gave on that a while ago because it's so + + align:start position:0% +gave on that a while ago because it's so + + + align:start position:0% +gave on that a while ago because it's so +hard to know um how the the gain of the + + align:start position:0% +hard to know um how the the gain of the + + + align:start position:0% +hard to know um how the the gain of the +electronics FR drifts in time so what we + + align:start position:0% +electronics FR drifts in time so what we + + + align:start position:0% +electronics FR drifts in time so what we +do is + + align:start position:0% +do is + + + align:start position:0% +do is +we um we calibrate it relatively + + align:start position:0% +we um we calibrate it relatively + + + align:start position:0% +we um we calibrate it relatively +routinely to the nuclear activation + + align:start position:0% +routinely to the nuclear activation + + + align:start position:0% +routinely to the nuclear activation +detectors and mrss and since it's cross + + align:start position:0% +detectors and mrss and since it's cross + + + align:start position:0% +detectors and mrss and since it's cross +calibrated we don't no longer use it as + + align:start position:0% +calibrated we don't no longer use it as + + + align:start position:0% +calibrated we don't no longer use it as +as the absolute + + align:start position:0% + + + + align:start position:0% + +number um and tough detectors are also + + align:start position:0% +number um and tough detectors are also + + + align:start position:0% +number um and tough detectors are also +used to diagnose aial density and I I + + align:start position:0% +used to diagnose aial density and I I + + + align:start position:0% +used to diagnose aial density and I I +think I already mentioned at some point + + align:start position:0% +think I already mentioned at some point + + + align:start position:0% +think I already mentioned at some point +that we use that by comparing to what we + + align:start position:0% +that we use that by comparing to what we + + + align:start position:0% +that we use that by comparing to what we +call zero potion really just DT gas with + + align:start position:0% +call zero potion really just DT gas with + + + align:start position:0% +call zero potion really just DT gas with +a really thin shell drive it really hard + + align:start position:0% +a really thin shell drive it really hard + + + align:start position:0% +a really thin shell drive it really hard +wrecking the laser so we know there's no + + align:start position:0% +wrecking the laser so we know there's no + + + align:start position:0% +wrecking the laser so we know there's no +um a density or negl errity and then we + + align:start position:0% +um a density or negl errity and then we + + + align:start position:0% +um a density or negl errity and then we +can look at the difference between + + align:start position:0% +can look at the difference between + + + align:start position:0% +can look at the difference between +inflation and one signific lar ter + + align:start position:0% + + + + align:start position:0% + +from uh and yeah this is identifying on + + align:start position:0% +from uh and yeah this is identifying on + + + align:start position:0% +from uh and yeah this is identifying on +the time scale what the 10 to 12 + + align:start position:0% + + + + align:start position:0% + +um the detectors at the niche I think + + align:start position:0% +um the detectors at the niche I think + + + align:start position:0% +um the detectors at the niche I think +the closest one is at 18 meters from the + + align:start position:0% +the closest one is at 18 meters from the + + + align:start position:0% +the closest one is at 18 meters from the +implosion and the furthest one is at 27 + + align:start position:0% +implosion and the furthest one is at 27 + + + align:start position:0% +implosion and the furthest one is at 27 +meters from the + + align:start position:0% +meters from the + + + align:start position:0% +meters from the +implosion uh this is what the original + + align:start position:0% +implosion uh this is what the original + + + align:start position:0% +implosion uh this is what the original +um equatorial and look like it says + + align:start position:0% +um equatorial and look like it says + + + align:start position:0% +um equatorial and look like it says +since It upgraded to look more like that + + align:start position:0% +since It upgraded to look more like that + + + align:start position:0% +since It upgraded to look more like that +this that actually looks like this but + + align:start position:0% +this that actually looks like this but + + + align:start position:0% +this that actually looks like this but +it's kind of hard to tell um the way it + + align:start position:0% +it's kind of hard to tell um the way it + + + align:start position:0% +it's kind of hard to tell um the way it +works now is instead of having + + align:start position:0% +works now is instead of having + + + align:start position:0% +works now is instead of having +PM tubes directly attached to the + + align:start position:0% +PM tubes directly attached to the + + + align:start position:0% +PM tubes directly attached to the +culator which is in this volume here you + + align:start position:0% +culator which is in this volume here you + + + align:start position:0% +culator which is in this volume here you +have light guides and you have the photo + + align:start position:0% +have light guides and you have the photo + + + align:start position:0% +have light guides and you have the photo +multiplier tubes facing so implosion I'm + + align:start position:0% +multiplier tubes facing so implosion I'm + + + align:start position:0% +multiplier tubes facing so implosion I'm +the implosion detector is over here the + + align:start position:0% +the implosion detector is over here the + + + align:start position:0% +the implosion detector is over here the +photo multipliers is facing this way so + + align:start position:0% +photo multipliers is facing this way so + + + align:start position:0% +photo multipliers is facing this way so +that neutrons hit the simulator and the + + align:start position:0% +that neutrons hit the simulator and the + + + align:start position:0% +that neutrons hit the simulator and the +light is collect in this direction so + + align:start position:0% +light is collect in this direction so + + + align:start position:0% +light is collect in this direction so +they have mess contributions from + + align:start position:0% +they have mess contributions from + + + align:start position:0% +they have mess contributions from +scattering in the detectors themselves + + align:start position:0% +scattering in the detectors themselves + + + align:start position:0% +scattering in the detectors themselves +and there's four po multiplier tubes on + + align:start position:0% +and there's four po multiplier tubes on + + + align:start position:0% +and there's four po multiplier tubes on +each simulator um so you can have + + align:start position:0% +each simulator um so you can have + + + align:start position:0% +each simulator um so you can have +different settings on different for + + align:start position:0% +different settings on different for + + + align:start position:0% +different settings on different for +multiplier tubes to to um optimize into + + align:start position:0% +multiplier tubes to to um optimize into + + + align:start position:0% +multiplier tubes to to um optimize into +looking at different parts of the neutr + + align:start position:0% +looking at different parts of the neutr + + + align:start position:0% +looking at different parts of the neutr +spectrum um there's caters on the way + + align:start position:0% +spectrum um there's caters on the way + + + align:start position:0% +spectrum um there's caters on the way +this is an example of how neutrons come + + align:start position:0% +this is an example of how neutrons come + + + align:start position:0% +this is an example of how neutrons come +through a wall cator hit this detector + + align:start position:0% +through a wall cator hit this detector + + + align:start position:0% +through a wall cator hit this detector +um in this case you can also see get + + align:start position:0% +um in this case you can also see get + + + align:start position:0% +um in this case you can also see get +both neutrons and gamas from coming + + align:start position:0% +both neutrons and gamas from coming + + + align:start position:0% +both neutrons and gamas from coming +through the the cator um hit + + align:start position:0% +through the the cator um hit + + + align:start position:0% +through the the cator um hit +this High sensitivity and F detectors + + align:start position:0% +this High sensitivity and F detectors + + + align:start position:0% +this High sensitivity and F detectors +which we call a spec detector um which + + align:start position:0% +which we call a spec detector um which + + + align:start position:0% +which we call a spec detector um which +we used to measure also recently + + align:start position:0% +we used to measure also recently + + + align:start position:0% +we used to measure also recently +installed the + + align:start position:0% +installed the + + + align:start position:0% +installed the +um quartz strink of detectors to just a + + align:start position:0% +um quartz strink of detectors to just a + + + align:start position:0% +um quartz strink of detectors to just a +really thin rod in the same line sight + + align:start position:0% +really thin rod in the same line sight + + + align:start position:0% +really thin rod in the same line sight +which you can use to look at both the + + align:start position:0% +which you can use to look at both the + + + align:start position:0% +which you can use to look at both the +nutrients and gamas and these are + + align:start position:0% +nutrients and gamas and these are + + + align:start position:0% +nutrients and gamas and these are +actually more optimal for the velocity + + align:start position:0% +actually more optimal for the velocity + + + align:start position:0% +actually more optimal for the velocity +measurement because you get a really + + align:start position:0% +measurement because you get a really + + + align:start position:0% +measurement because you get a really +precise measurements of the paramet + + align:start position:0% +precise measurements of the paramet + + + align:start position:0% +precise measurements of the paramet +those yeah and it's similar at Omega so + + align:start position:0% +those yeah and it's similar at Omega so + + + align:start position:0% +those yeah and it's similar at Omega so +this is at Omega it's below the target + + align:start position:0% +this is at Omega it's below the target + + + align:start position:0% +this is at Omega it's below the target +chamber centering kind of a basement + + align:start position:0% +chamber centering kind of a basement + + + align:start position:0% +chamber centering kind of a basement +which we call a cob um it's this large + + align:start position:0% +which we call a cob um it's this large + + + align:start position:0% +which we call a cob um it's this large +detector which is it's a liquid + + align:start position:0% +detector which is it's a liquid + + + align:start position:0% +detector which is it's a liquid +simulated mat material it's quenched + + align:start position:0% +simulated mat material it's quenched + + + align:start position:0% +simulated mat material it's quenched +siling which allows you to have a really + + align:start position:0% +siling which allows you to have a really + + + align:start position:0% +siling which allows you to have a really +fast time response so it falls off as + + align:start position:0% +fast time response so it falls off as + + + align:start position:0% +fast time response so it falls off as +quickly as possible after a primary Peak + + align:start position:0% +quickly as possible after a primary Peak + + + align:start position:0% +quickly as possible after a primary Peak +which makes it easier to measure uh the + + align:start position:0% +which makes it easier to measure uh the + + + align:start position:0% +which makes it easier to measure uh the +down scar neutrons actually another + + align:start position:0% +down scar neutrons actually another + + + align:start position:0% +down scar neutrons actually another +detail on Omega the enops Do Not measure + + align:start position:0% +detail on Omega the enops Do Not measure + + + align:start position:0% +detail on Omega the enops Do Not measure +down scan neutrons in this energy range + + align:start position:0% +down scan neutrons in this energy range + + + align:start position:0% +down scan neutrons in this energy range +because the row R is much lower on Omega + + align:start position:0% +because the row R is much lower on Omega + + + align:start position:0% +because the row R is much lower on Omega +than on the ni it's a much lower power + + align:start position:0% +than on the ni it's a much lower power + + + align:start position:0% +than on the ni it's a much lower power +laser so instead we using the back + + align:start position:0% +laser so instead we using the back + + + align:start position:0% +laser so instead we using the back +scatter edge of ND back scattering so + + align:start position:0% +scatter edge of ND back scattering so + + + align:start position:0% +scatter edge of ND back scattering so +neutrons that hit the back of the + + align:start position:0% +neutrons that hit the back of the + + + align:start position:0% +neutrons that hit the back of the +implosion scatter up from Crum and reach + + align:start position:0% +implosion scatter up from Crum and reach + + + align:start position:0% +implosion scatter up from Crum and reach +the electron this side which gives us an + + align:start position:0% +the electron this side which gives us an + + + align:start position:0% +the electron this side which gives us an +edge at 3.4 M which is much easier to + + align:start position:0% +edge at 3.4 M which is much easier to + + + align:start position:0% +edge at 3.4 M which is much easier to +distinguish on + + align:start position:0% +distinguish on + + + align:start position:0% +distinguish on +Omega and that's so that's done to this + + align:start position:0% +Omega and that's so that's done to this + + + align:start position:0% +Omega and that's so that's done to this +detector again for f multiplier tubes uh + + align:start position:0% +detector again for f multiplier tubes uh + + + align:start position:0% +detector again for f multiplier tubes uh +they're optimized for different ranges + + align:start position:0% +they're optimized for different ranges + + + align:start position:0% +they're optimized for different ranges +of the spectrum and there's look Clos + + align:start position:0% +of the spectrum and there's look Clos + + + align:start position:0% +of the spectrum and there's look Clos +you can see there's two detectors in + + align:start position:0% +you can see there's two detectors in + + + align:start position:0% +you can see there's two detectors in +front here one shrink of detector as + + align:start position:0% +front here one shrink of detector as + + + align:start position:0% +front here one shrink of detector as +well that's in r and this padd detector + + align:start position:0% +well that's in r and this padd detector + + + align:start position:0% +well that's in r and this padd detector +which is one of the primary temperature + + align:start position:0% +which is one of the primary temperature + + + align:start position:0% +which is one of the primary temperature +detectors has much better resolution + + align:start position:0% +detectors has much better resolution + + + align:start position:0% +detectors has much better resolution +than this large siling + + align:start position:0% + + + + align:start position:0% + +detector any questions about that is the + + align:start position:0% +detector any questions about that is the + + + align:start position:0% +detector any questions about that is the +thickness of the detector a significant + + align:start position:0% +thickness of the detector a significant + + + align:start position:0% +thickness of the detector a significant +source of uncertainty I guess I'm + + align:start position:0% +source of uncertainty I guess I'm + + + align:start position:0% +source of uncertainty I guess I'm +guessing that the thickness of these + + align:start position:0% +guessing that the thickness of these + + + align:start position:0% +guessing that the thickness of these +detectors versus the length of these be + + align:start position:0% +detectors versus the length of these be + + + align:start position:0% +detectors versus the length of these be +lines really small to be negligible but + + align:start position:0% +lines really small to be negligible but + + + align:start position:0% +lines really small to be negligible but +is that a source of + + align:start position:0% +is that a source of + + + align:start position:0% +is that a source of +uncertainty so depends on what you mean + + align:start position:0% +uncertainty so depends on what you mean + + + align:start position:0% +uncertainty so depends on what you mean +with uncertainty I mean it so definitely + + align:start position:0% +with uncertainty I mean it so definitely + + + align:start position:0% +with uncertainty I mean it so definitely +you get a broader Spectrum from this lar + + align:start position:0% +you get a broader Spectrum from this lar + + + align:start position:0% +you get a broader Spectrum from this lar +than from those thinner ones in front + + align:start position:0% +than from those thinner ones in front + + + align:start position:0% +than from those thinner ones in front +which uh reduces your resolutions it's + + align:start position:0% +which uh reduces your resolutions it's + + + align:start position:0% +which uh reduces your resolutions it's +harder in Fr temperature so that's why + + align:start position:0% +harder in Fr temperature so that's why + + + align:start position:0% +harder in Fr temperature so that's why +like in this case this detector is + + align:start position:0% +like in this case this detector is + + + align:start position:0% +like in this case this detector is +optimized for the rowar measurement and + + align:start position:0% +optimized for the rowar measurement and + + + align:start position:0% +optimized for the rowar measurement and +this one's optimized for the ey + + align:start position:0% +this one's optimized for the ey + + + align:start position:0% +this one's optimized for the ey +temperature measurement this one needs + + align:start position:0% +temperature measurement this one needs + + + align:start position:0% +temperature measurement this one needs +high efficiency to get the that weak + + align:start position:0% +high efficiency to get the that weak + + + align:start position:0% +high efficiency to get the that weak +component of those get neutrons this one + + align:start position:0% +component of those get neutrons this one + + + align:start position:0% +component of those get neutrons this one +needs high resolution to measure the + + align:start position:0% +needs high resolution to measure the + + + align:start position:0% +needs high resolution to measure the +peak accur so similar to mrss is a trade + + align:start position:0% +peak accur so similar to mrss is a trade + + + align:start position:0% +peak accur so similar to mrss is a trade +offun efficiency and resolution yeah + + align:start position:0% + + + + align:start position:0% + +uh someone asked at APS and I didn't + + align:start position:0% +uh someone asked at APS and I didn't + + + align:start position:0% +uh someone asked at APS and I didn't +know why what are the benefits of the + + align:start position:0% +know why what are the benefits of the + + + align:start position:0% +know why what are the benefits of the +they all + + align:start position:0% + + + + align:start position:0% + +temper so okay I my perspective the + + align:start position:0% +temper so okay I my perspective the + + + align:start position:0% +temper so okay I my perspective the +primary benefit is having more than one + + align:start position:0% +primary benefit is having more than one + + + align:start position:0% +primary benefit is having more than one +technique uh because you really need to + + align:start position:0% +technique uh because you really need to + + + align:start position:0% +technique uh because you really need to +know independently what you're measuring + + align:start position:0% +know independently what you're measuring + + + align:start position:0% +know independently what you're measuring +you can compare the results from both + + align:start position:0% +you can compare the results from both + + + align:start position:0% +you can compare the results from both +and many times over the years has one + + align:start position:0% +and many times over the years has one + + + align:start position:0% +and many times over the years has one +technique started drifting and then we + + align:start position:0% +technique started drifting and then we + + + align:start position:0% +technique started drifting and then we +we figure out what's going wrong by + + align:start position:0% +we figure out what's going wrong by + + + align:start position:0% +we figure out what's going wrong by +comparing with the other technique so I + + align:start position:0% +comparing with the other technique so I + + + align:start position:0% +comparing with the other technique so I +think that's the primary advantage you + + align:start position:0% +think that's the primary advantage you + + + align:start position:0% +think that's the primary advantage you +can also say that one is that the mrss + + align:start position:0% +can also say that one is that the mrss + + + align:start position:0% +can also say that one is that the mrss +gives you the absolute yield it's + + align:start position:0% +gives you the absolute yield it's + + + align:start position:0% +gives you the absolute yield it's +calibrated from first principles + + align:start position:0% +calibrated from first principles + + + align:start position:0% +calibrated from first principles +compared to cross calibrated to other + + align:start position:0% +compared to cross calibrated to other + + + align:start position:0% +compared to cross calibrated to other +detectors but I think it's really + + align:start position:0% +detectors but I think it's really + + + align:start position:0% +detectors but I think it's really +important + + align:start position:0% +important + + + align:start position:0% +important +to but this data is available like + + align:start position:0% +to but this data is available like + + + align:start position:0% +to but this data is available like +directly after the shop the mrss is is + + align:start position:0% +directly after the shop the mrss is is + + + align:start position:0% +directly after the shop the mrss is is +what that's true that's true which which + + align:start position:0% +what that's true that's true which which + + + align:start position:0% +what that's true that's true which which +is a hugee huge advantage and yeah and + + align:start position:0% +is a hugee huge advantage and yeah and + + + align:start position:0% +is a hugee huge advantage and yeah and +this could be scaled up to rep rat as + + align:start position:0% +this could be scaled up to rep rat as + + + align:start position:0% +this could be scaled up to rep rat as +well because you can make sure you can + + align:start position:0% +well because you can make sure you can + + + align:start position:0% +well because you can make sure you can +can analyze it quickly after shot versus + + align:start position:0% +can analyze it quickly after shot versus + + + align:start position:0% +can analyze it quickly after shot versus +mrss with z39 + + align:start position:0% +mrss with z39 + + + align:start position:0% +mrss with z39 +definely well Chris is working on + + align:start position:0% +definely well Chris is working on + + + align:start position:0% +definely well Chris is working on +electronic + + align:start position:0% + + + + align:start position:0% + +detection other + + align:start position:0% + + + + align:start position:0% + +questions um okay so then um the + + align:start position:0% +questions um okay so then um the + + + align:start position:0% +questions um okay so then um the +magnetic confinement Fusion equivalent + + align:start position:0% +magnetic confinement Fusion equivalent + + + align:start position:0% +magnetic confinement Fusion equivalent +we do have a neutron time of flight + + align:start position:0% +we do have a neutron time of flight + + + align:start position:0% +we do have a neutron time of flight +system here too but here it becomes more + + align:start position:0% +system here too but here it becomes more + + + align:start position:0% +system here too but here it becomes more +complicated because we can no longer + + align:start position:0% +complicated because we can no longer + + + align:start position:0% +complicated because we can no longer +assume that all the neutrons are emitted + + align:start position:0% +assume that all the neutrons are emitted + + + align:start position:0% +assume that all the neutrons are emitted +at the same time so here we have to have + + align:start position:0% +at the same time so here we have to have + + + align:start position:0% +at the same time so here we have to have +two sets of simulators we have a start + + align:start position:0% +two sets of simulators we have a start + + + align:start position:0% +two sets of simulators we have a start +simulator which should call S1 here and + + align:start position:0% +simulator which should call S1 here and + + + align:start position:0% +simulator which should call S1 here and +the stop simulator which is S2 um this + + align:start position:0% +the stop simulator which is S2 um this + + + align:start position:0% +the stop simulator which is S2 um this +is what it actually looks like in real + + align:start position:0% +is what it actually looks like in real + + + align:start position:0% +is what it actually looks like in real +life there's a cator through the floor + + align:start position:0% +life there's a cator through the floor + + + align:start position:0% +life there's a cator through the floor +here thisor is sitting in the roof lab + + align:start position:0% +here thisor is sitting in the roof lab + + + align:start position:0% +here thisor is sitting in the roof lab +above the jet Tok so the neut come + + align:start position:0% +above the jet Tok so the neut come + + + align:start position:0% +above the jet Tok so the neut come +through the colum in the floor hit the + + align:start position:0% +through the colum in the floor hit the + + + align:start position:0% +through the colum in the floor hit the +start detector first and then the stock + + align:start position:0% +start detector first and then the stock + + + align:start position:0% +start detector first and then the stock +detector we have the stock detector is + + align:start position:0% +detector we have the stock detector is + + + align:start position:0% +detector we have the stock detector is +nered to allow us to count at a higher + + align:start position:0% +nered to allow us to count at a higher + + + align:start position:0% +nered to allow us to count at a higher +rate there's five layers in there um and + + align:start position:0% +rate there's five layers in there um and + + + align:start position:0% +rate there's five layers in there um and +then the stop detector is divided into + + align:start position:0% +then the stop detector is divided into + + + align:start position:0% +then the stop detector is divided into +32 segments um to actually that's more + + align:start position:0% +32 segments um to actually that's more + + + align:start position:0% +32 segments um to actually that's more +resolution thaning because you you want + + align:start position:0% +resolution thaning because you you want + + + align:start position:0% +resolution thaning because you you want +to know where the light is coming from + + align:start position:0% +to know where the light is coming from + + + align:start position:0% +to know where the light is coming from +uh in + + align:start position:0% +uh in + + + align:start position:0% +uh in +order measure the + + align:start position:0% +order measure the + + + align:start position:0% +order measure the +time uh and we're placing them on the + + align:start position:0% +time uh and we're placing them on the + + + align:start position:0% +time uh and we're placing them on the +constant time of flight sphere so you + + align:start position:0% +constant time of flight sphere so you + + + align:start position:0% +constant time of flight sphere so you +can compare the data from all the + + align:start position:0% +can compare the data from all the + + + align:start position:0% +can compare the data from all the +different protectors in SK Spectrum yes + + align:start position:0% +different protectors in SK Spectrum yes + + + align:start position:0% +different protectors in SK Spectrum yes +got um how do you know like if a neutron + + align:start position:0% +got um how do you know like if a neutron + + + align:start position:0% +got um how do you know like if a neutron +that hits the S2 is the same one that + + align:start position:0% +that hits the S2 is the same one that + + + align:start position:0% +that hits the S2 is the same one that +you just measured as S one great + + align:start position:0% +you just measured as S one great + + + align:start position:0% +you just measured as S one great +question so you don't and that's where + + align:start position:0% +question so you don't and that's where + + + align:start position:0% +question so you don't and that's where +this comes in so we H look at data from + + align:start position:0% +this comes in so we H look at data from + + + align:start position:0% +this comes in so we H look at data from +the different simulators in coincidence + + align:start position:0% +the different simulators in coincidence + + + align:start position:0% +the different simulators in coincidence +so you take this but this example this + + align:start position:0% +so you take this but this example this + + + align:start position:0% +so you take this but this example this +is it all it's um events that you can + + align:start position:0% +is it all it's um events that you can + + + align:start position:0% +is it all it's um events that you can +get in the S1 detector on the top you + + align:start position:0% +get in the S1 detector on the top you + + + align:start position:0% +get in the S1 detector on the top you +get a lot more events in S1 because it's + + align:start position:0% +get a lot more events in S1 because it's + + + align:start position:0% +get a lot more events in S1 because it's +closer and like it's directly in beam of + + align:start position:0% +closer and like it's directly in beam of + + + align:start position:0% +closer and like it's directly in beam of +nut from + + align:start position:0% +nut from + + + align:start position:0% +nut from +the S2 the beam actually goes through in + + align:start position:0% +the S2 the beam actually goes through in + + + align:start position:0% +the S2 the beam actually goes through in +the hole in the center so it doesn't hit + + align:start position:0% +the hole in the center so it doesn't hit + + + align:start position:0% +the hole in the center so it doesn't hit +the S2s directly the S2 is Al only see + + align:start position:0% +the S2s directly the S2 is Al only see + + + align:start position:0% +the S2s directly the S2 is Al only see +scattered + + align:start position:0% +scattered + + + align:start position:0% +scattered +the but that means you get a lot fewer + + align:start position:0% +the but that means you get a lot fewer + + + align:start position:0% +the but that means you get a lot fewer +events in S2s and what you do is you go + + align:start position:0% +events in S2s and what you do is you go + + + align:start position:0% +events in S2s and what you do is you go +through and look at coincidences between + + align:start position:0% +through and look at coincidences between + + + align:start position:0% +through and look at coincidences between +the two detectors and actually what you + + align:start position:0% +the two detectors and actually what you + + + align:start position:0% +the two detectors and actually what you +get is you get all the coincidence you + + align:start position:0% +get is you get all the coincidence you + + + align:start position:0% +get is you get all the coincidence you +get the true coincidences and you get + + align:start position:0% +get the true coincidences and you get + + + align:start position:0% +get the true coincidences and you get +back on random coincidences and you have + + align:start position:0% +back on random coincidences and you have + + + align:start position:0% +back on random coincidences and you have +to subtract that back up but when you do + + align:start position:0% +to subtract that back up but when you do + + + align:start position:0% +to subtract that back up but when you do +that the PE will appear because that's + + align:start position:0% +that the PE will appear because that's + + + align:start position:0% +that the PE will appear because that's +the the true correlation that it will be + + align:start position:0% +the the true correlation that it will be + + + align:start position:0% +the the true correlation that it will be +the same between + + align:start position:0% + + + + align:start position:0% + +all so in this case that the flight for + + align:start position:0% +all so in this case that the flight for + + + align:start position:0% +all so in this case that the flight for +two and a half going to be neutr between + + align:start position:0% +two and a half going to be neutr between + + + align:start position:0% +two and a half going to be neutr between +S1 and S2 is about 65 n second + + align:start position:0% +S1 and S2 is about 65 n second + + + align:start position:0% +S1 and S2 is about 65 n second +gu but the I guess the the beam drift + + align:start position:0% +gu but the I guess the the beam drift + + + align:start position:0% +gu but the I guess the the beam drift +time here the amount of time Neutron + + align:start position:0% +time here the amount of time Neutron + + + align:start position:0% +time here the amount of time Neutron +spends moving between S1 and S2 is very + + align:start position:0% +spends moving between S1 and S2 is very + + + align:start position:0% +spends moving between S1 and S2 is very +short looking these + + align:start position:0% +short looking these + + + align:start position:0% +short looking these +detectors and this is so does this + + align:start position:0% +detectors and this is so does this + + + align:start position:0% +detectors and this is so does this +function for DT neutrons or is this is D + + align:start position:0% +function for DT neutrons or is this is D + + + align:start position:0% +function for DT neutrons or is this is D +so it's best for d + + align:start position:0% +so it's best for d + + + align:start position:0% +so it's best for d +we can so this it will see the + + align:start position:0% +we can so this it will see the + + + align:start position:0% +we can so this it will see the +difference as well they show up at 27 + + align:start position:0% +difference as well they show up at 27 + + + align:start position:0% +difference as well they show up at 27 +and a seconds the time resolution is + + align:start position:0% +and a seconds the time resolution is + + + align:start position:0% +and a seconds the time resolution is +good if you wanted read good resolution + + align:start position:0% + + + + align:start position:0% + +make but of course another difference + + align:start position:0% +make but of course another difference + + + align:start position:0% +make but of course another difference +here here I didn't really make that + + align:start position:0% +here here I didn't really make that + + + align:start position:0% +here here I didn't really make that +point with the um inertial confir and + + align:start position:0% +point with the um inertial confir and + + + align:start position:0% +point with the um inertial confir and +fusion enops but we're looking at here + + align:start position:0% +fusion enops but we're looking at here + + + align:start position:0% +fusion enops but we're looking at here +is running the simulators in current + + align:start position:0% +is running the simulators in current + + + align:start position:0% +is running the simulators in current +mode we're just opening them up looking + + align:start position:0% +mode we're just opening them up looking + + + align:start position:0% +mode we're just opening them up looking +at uh the signal current as a function + + align:start position:0% +at uh the signal current as a function + + + align:start position:0% +at uh the signal current as a function +of time in this case we're looking at + + align:start position:0% +of time in this case we're looking at + + + align:start position:0% +of time in this case we're looking at +individual pules from single neutrons + + align:start position:0% +individual pules from single neutrons + + + align:start position:0% +individual pules from single neutrons +interacting with the simulator so we can + + align:start position:0% +interacting with the simulator so we can + + + align:start position:0% +interacting with the simulator so we can +divide it into be recorded over the + + align:start position:0% +divide it into be recorded over the + + + align:start position:0% +divide it into be recorded over the +entire duration of the pulse and we can + + align:start position:0% +entire duration of the pulse and we can + + + align:start position:0% +entire duration of the pulse and we can +reconstruct neutral Spectra for any time + + align:start position:0% +reconstruct neutral Spectra for any time + + + align:start position:0% +reconstruct neutral Spectra for any time +interval we want where we get enough + + align:start position:0% +interval we want where we get enough + + + align:start position:0% +interval we want where we get enough +statistics so we can actually look at + + align:start position:0% +statistics so we can actually look at + + + align:start position:0% +statistics so we can actually look at +the the time evolution of the neutron + + align:start position:0% +the the time evolution of the neutron + + + align:start position:0% +the the time evolution of the neutron +Spectre this way in ICF we simple we get + + align:start position:0% +Spectre this way in ICF we simple we get + + + align:start position:0% +Spectre this way in ICF we simple we get +too many neutrons at the same time soon + + align:start position:0% +too many neutrons at the same time soon + + + align:start position:0% +too many neutrons at the same time soon +becomes complicated but Chris has spent + + align:start position:0% +becomes complicated but Chris has spent + + + align:start position:0% +becomes complicated but Chris has spent +quite a bit of time trying to figure out + + align:start position:0% +quite a bit of time trying to figure out + + + align:start position:0% +quite a bit of time trying to figure out +how to do + + align:start position:0% +how to do + + + align:start position:0% +how to do +that um okay so that's all I plan to say + + align:start position:0% +that um okay so that's all I plan to say + + + align:start position:0% +that um okay so that's all I plan to say +about neutr spectometry any more + + align:start position:0% +about neutr spectometry any more + + + align:start position:0% +about neutr spectometry any more +questions before we move + + align:start position:0% + + + + align:start position:0% + +on + + align:start position:0% +on + + + align:start position:0% +on +okay okay I think I have just a very + + align:start position:0% +okay okay I think I have just a very + + + align:start position:0% +okay okay I think I have just a very +short section on Neutron Imaging so what + + align:start position:0% +short section on Neutron Imaging so what + + + align:start position:0% +short section on Neutron Imaging so what +what we do in Neutron Imaging is we use + + align:start position:0% +what we do in Neutron Imaging is we use + + + align:start position:0% +what we do in Neutron Imaging is we use +um a pinhole or aperture close to the + + align:start position:0% +um a pinhole or aperture close to the + + + align:start position:0% +um a pinhole or aperture close to the +implosion and the detector really far + + align:start position:0% +implosion and the detector really far + + + align:start position:0% +implosion and the detector really far +away to obtain good magnification this + + align:start position:0% +away to obtain good magnification this + + + align:start position:0% +away to obtain good magnification this +is actually very um you have the source + + align:start position:0% +is actually very um you have the source + + + align:start position:0% +is actually very um you have the source +again here which is the turg chamber + + align:start position:0% +again here which is the turg chamber + + + align:start position:0% +again here which is the turg chamber +Center which is where the nut are + + align:start position:0% +Center which is where the nut are + + + align:start position:0% +Center which is where the nut are +emitted you have um a lined aperture + + align:start position:0% +emitted you have um a lined aperture + + + align:start position:0% +emitted you have um a lined aperture +which can even have either have pin + + align:start position:0% +which can even have either have pin + + + align:start position:0% +which can even have either have pin +numra which um will encode the signal or + + align:start position:0% +numra which um will encode the signal or + + + align:start position:0% +numra which um will encode the signal or +a simple pinol where you have a direct + + align:start position:0% +a simple pinol where you have a direct + + + align:start position:0% +a simple pinol where you have a direct +correlation basically between the + + align:start position:0% +correlation basically between the + + + align:start position:0% +correlation basically between the +neutral emission and opposite they kind + + align:start position:0% +neutral emission and opposite they kind + + + align:start position:0% +neutral emission and opposite they kind +of inverted to the detector um the + + align:start position:0% +of inverted to the detector um the + + + align:start position:0% +of inverted to the detector um the +magnification will depend on the Pinal + + align:start position:0% +magnification will depend on the Pinal + + + align:start position:0% +magnification will depend on the Pinal +stand UPF distance and the detector + + align:start position:0% +stand UPF distance and the detector + + + align:start position:0% +stand UPF distance and the detector +distance um and + + align:start position:0% + + + + align:start position:0% + +so okay so I took the slide from + + align:start position:0% +so okay so I took the slide from + + + align:start position:0% +so okay so I took the slide from +somewhere else and I don't know what + + align:start position:0% +somewhere else and I don't know what + + + align:start position:0% +somewhere else and I don't know what +numbers they actually threw in there oh + + align:start position:0% +numbers they actually threw in there oh + + + align:start position:0% +numbers they actually threw in there oh +assuming a magnification of 200 which + + align:start position:0% +assuming a magnification of 200 which + + + align:start position:0% +assuming a magnification of 200 which +you would get depending on what L1 and + + align:start position:0% +you would get depending on what L1 and + + + align:start position:0% +you would get depending on what L1 and +L2 values you have if you have five M at + + align:start position:0% +L2 values you have if you have five M at + + + align:start position:0% +L2 values you have if you have five M at +the source it's going to be one at the + + align:start position:0% +the source it's going to be one at the + + + align:start position:0% +the source it's going to be one at the +detector which um magnifies your or I I + + align:start position:0% +detector which um magnifies your or I I + + + align:start position:0% +detector which um magnifies your or I I +talked about before that implosion would + + align:start position:0% +talked about before that implosion would + + + align:start position:0% +talked about before that implosion would +be like 30 to 50 Micron radius you + + align:start position:0% +be like 30 to 50 Micron radius you + + + align:start position:0% +be like 30 to 50 Micron radius you +magnify them so you can separate + + align:start position:0% +magnify them so you can separate + + + align:start position:0% +magnify them so you can separate +features much easier on their detector + + align:start position:0% +features much easier on their detector + + + align:start position:0% +features much easier on their detector +on the outside of the chamber and + + align:start position:0% +on the outside of the chamber and + + + align:start position:0% +on the outside of the chamber and +actually for the ni in particular I + + align:start position:0% +actually for the ni in particular I + + + align:start position:0% +actually for the ni in particular I +think typically the apperture is about + + align:start position:0% +think typically the apperture is about + + + align:start position:0% +think typically the apperture is about +20 cm from Target chamber Center the + + align:start position:0% +20 cm from Target chamber Center the + + + align:start position:0% +20 cm from Target chamber Center the +detector is 28 meters + + align:start position:0% + + + + align:start position:0% + +away uh yeah and this is what actually + + align:start position:0% +away uh yeah and this is what actually + + + align:start position:0% +away uh yeah and this is what actually +those are the exact + + align:start position:0% +those are the exact + + + align:start position:0% +those are the exact +numbers um so this is what it looks like + + align:start position:0% +numbers um so this is what it looks like + + + align:start position:0% +numbers um so this is what it looks like +you have the N Target chamber over here + + align:start position:0% +you have the N Target chamber over here + + + align:start position:0% +you have the N Target chamber over here +that's Target chamber Center the + + align:start position:0% +that's Target chamber Center the + + + align:start position:0% +that's Target chamber Center the +aperture is fed right here 20 C from 30 + + align:start position:0% +aperture is fed right here 20 C from 30 + + + align:start position:0% +aperture is fed right here 20 C from 30 +chamber Center um and then the nutrients + + align:start position:0% +chamber Center um and then the nutrients + + + align:start position:0% +chamber Center um and then the nutrients +that are selected by the aperture will + + align:start position:0% +that are selected by the aperture will + + + align:start position:0% +that are selected by the aperture will +travel through this color structure all + + align:start position:0% +travel through this color structure all + + + align:start position:0% +travel through this color structure all +the way to the detector back here 28 M + + align:start position:0% +the way to the detector back here 28 M + + + align:start position:0% +the way to the detector back here 28 M +away and the way so the nutrients this + + align:start position:0% +away and the way so the nutrients this + + + align:start position:0% +away and the way so the nutrients this +is just look looks like the neutr come + + align:start position:0% +is just look looks like the neutr come + + + align:start position:0% +is just look looks like the neutr come +out here through the line of side cator + + align:start position:0% +out here through the line of side cator + + + align:start position:0% +out here through the line of side cator +um this is that other end detector I + + align:start position:0% +um this is that other end detector I + + + align:start position:0% +um this is that other end detector I +talked about you can kind of see this + + align:start position:0% +talked about you can kind of see this + + + align:start position:0% +talked about you can kind of see this +different Technologies flat plastic + + align:start position:0% +different Technologies flat plastic + + + align:start position:0% +different Technologies flat plastic +simulators um with phot multi tubes and + + align:start position:0% +simulators um with phot multi tubes and + + + align:start position:0% +simulators um with phot multi tubes and +but then the primary so that that's just + + align:start position:0% +but then the primary so that that's just + + + align:start position:0% +but then the primary so that that's just +another nut the primary for the Imaging + + align:start position:0% +another nut the primary for the Imaging + + + align:start position:0% +another nut the primary for the Imaging +system culating fiber way which is fiber + + align:start position:0% +system culating fiber way which is fiber + + + align:start position:0% +system culating fiber way which is fiber +coupled to a + + align:start position:0% +coupled to a + + + align:start position:0% +coupled to a +camera and it's done this way in order + + align:start position:0% +camera and it's done this way in order + + + align:start position:0% +camera and it's done this way in order +for you to be able to gate the camera + + align:start position:0% +for you to be able to gate the camera + + + align:start position:0% +for you to be able to gate the camera +and get two snapshots so you can get the + + align:start position:0% +and get two snapshots so you can get the + + + align:start position:0% +and get two snapshots so you can get the +primary nutrients and then the scattered + + align:start position:0% +primary nutrients and then the scattered + + + align:start position:0% +primary nutrients and then the scattered +nutrients at a later + + align:start position:0% +nutrients at a later + + + align:start position:0% +nutrients at a later +time U there's actually also n this is + + align:start position:0% +time U there's actually also n this is + + + align:start position:0% +time U there's actually also n this is +the original n Neutron Imaging system + + align:start position:0% +the original n Neutron Imaging system + + + align:start position:0% +the original n Neutron Imaging system +there's two more now so we can look at + + align:start position:0% +there's two more now so we can look at + + + align:start position:0% +there's two more now so we can look at +symmetries around the chamber one of + + align:start position:0% +symmetries around the chamber one of + + + align:start position:0% +symmetries around the chamber one of +them only has image plate detectors + + align:start position:0% +them only has image plate detectors + + + align:start position:0% +them only has image plate detectors +which I plan to bring image plate but I + + align:start position:0% +which I plan to bring image plate but I + + + align:start position:0% +which I plan to bring image plate but I +forgot but it's + + align:start position:0% +forgot but it's + + + align:start position:0% +forgot but it's +um + + align:start position:0% + + + + align:start position:0% + +uh we discussed it actually we talked + + align:start position:0% +uh we discussed it actually we talked + + + align:start position:0% +uh we discussed it actually we talked +about XR diagnostic so we talked about a + + align:start position:0% +about XR diagnostic so we talked about a + + + align:start position:0% +about XR diagnostic so we talked about a +little bit yeah so you know it's you + + align:start position:0% +little bit yeah so you know it's you + + + align:start position:0% +little bit yeah so you know it's you +can't do time gting an image place so + + align:start position:0% +can't do time gting an image place so + + + align:start position:0% +can't do time gting an image place so +then you just get one image um okay and + + align:start position:0% +then you just get one image um okay and + + + align:start position:0% +then you just get one image um okay and +wish a better picture but these pinhole + + align:start position:0% +wish a better picture but these pinhole + + + align:start position:0% +wish a better picture but these pinhole +apertures are actually extremely + + align:start position:0% +apertures are actually extremely + + + align:start position:0% +apertures are actually extremely +complicated so they're made of gold + + align:start position:0% +complicated so they're made of gold + + + align:start position:0% +complicated so they're made of gold +they're about that long and you have to + + align:start position:0% +they're about that long and you have to + + + align:start position:0% +they're about that long and you have to +make pin holes that are precise all the + + align:start position:0% +make pin holes that are precise all the + + + align:start position:0% +make pin holes that are precise all the +way through uh it's too hard to drill + + align:start position:0% +way through uh it's too hard to drill + + + align:start position:0% +way through uh it's too hard to drill +them circular so they make them + + align:start position:0% +them circular so they make them + + + align:start position:0% +them circular so they make them +triangular instead um and then they're + + align:start position:0% +triangular instead um and then they're + + + align:start position:0% +triangular instead um and then they're +tapered so to minimize scatter so + + align:start position:0% +tapered so to minimize scatter so + + + align:start position:0% +tapered so to minimize scatter so +basically you have an opening and then + + align:start position:0% +basically you have an opening and then + + + align:start position:0% +basically you have an opening and then +the neutrons that go through that + + align:start position:0% +the neutrons that go through that + + + align:start position:0% +the neutrons that go through that +opening are all going to + + align:start position:0% +opening are all going to + + + align:start position:0% +opening are all going to +be captured at the back end none of them + + align:start position:0% +be captured at the back end none of them + + + align:start position:0% +be captured at the back end none of them +are going to stop um because of the + + align:start position:0% +are going to stop um because of the + + + align:start position:0% +are going to stop um because of the +taper inside um it's still a really hard + + align:start position:0% +taper inside um it's still a really hard + + + align:start position:0% +taper inside um it's still a really hard +Machining problem to get those even + + align:start position:0% +Machining problem to get those even + + + align:start position:0% +Machining problem to get those even +triangular pinoles precise all the way + + align:start position:0% +triangular pinoles precise all the way + + + align:start position:0% +triangular pinoles precise all the way +through we need gold because as we + + align:start position:0% +through we need gold because as we + + + align:start position:0% +through we need gold because as we +talked about nutrients have pretty low + + align:start position:0% +talked about nutrients have pretty low + + + align:start position:0% +talked about nutrients have pretty low +like you for interacting in matter and + + align:start position:0% +like you for interacting in matter and + + + align:start position:0% +like you for interacting in matter and +you want to only select the ones that go + + align:start position:0% +you want to only select the ones that go + + + align:start position:0% +you want to only select the ones that go +through the Pinel you don't want all the + + align:start position:0% +through the Pinel you don't want all the + + + align:start position:0% +through the Pinel you don't want all the +ones around to also make their way all + + align:start position:0% +ones around to also make their way all + + + align:start position:0% +ones around to also make their way all +the way back to the detector um yeah so + + align:start position:0% +the way back to the detector um yeah so + + + align:start position:0% +the way back to the detector um yeah so +so that's fun these are examples of the + + align:start position:0% +so that's fun these are examples of the + + + align:start position:0% +so that's fun these are examples of the +penumbral aperatures where the + + align:start position:0% +penumbral aperatures where the + + + align:start position:0% +penumbral aperatures where the +information will be decoded uh in the + + align:start position:0% +information will be decoded uh in the + + + align:start position:0% +information will be decoded uh in the +pin uh you also get straight through + + align:start position:0% +pin uh you also get straight through + + + align:start position:0% +pin uh you also get straight through +neutrons inra um that you can't used to + + align:start position:0% +neutrons inra um that you can't used to + + + align:start position:0% +neutrons inra um that you can't used to +infer anything about the shape of + + align:start position:0% +infer anything about the shape of + + + align:start position:0% +infer anything about the shape of +the um so this this kind of aperture R + + align:start position:0% +the um so this this kind of aperture R + + + align:start position:0% +the um so this this kind of aperture R +is used on all three lines toite now but + + align:start position:0% +is used on all three lines toite now but + + + align:start position:0% +is used on all three lines toite now but +there's development going on to make a + + align:start position:0% +there's development going on to make a + + + align:start position:0% +there's development going on to make a +coated aperture which is supposedly + + align:start position:0% +coated aperture which is supposedly + + + align:start position:0% +coated aperture which is supposedly +going to be simpler and thinner and + + align:start position:0% +going to be simpler and thinner and + + + align:start position:0% +going to be simpler and thinner and +easier to manufacture we can see see if + + align:start position:0% +easier to manufacture we can see see if + + + align:start position:0% +easier to manufacture we can see see if +that actually works + + align:start position:0% +that actually works + + + align:start position:0% +that actually works +out um see oh yeah so these are examples + + align:start position:0% +out um see oh yeah so these are examples + + + align:start position:0% +out um see oh yeah so these are examples +of primary and Scattered neutr images + + align:start position:0% +of primary and Scattered neutr images + + + align:start position:0% +of primary and Scattered neutr images +and again they're routinely obtain and + + align:start position:0% +and again they're routinely obtain and + + + align:start position:0% +and again they're routinely obtain and +all DT implosions these days it's even + + align:start position:0% +all DT implosions these days it's even + + + align:start position:0% +all DT implosions these days it's even +in three lines of site and there's a lot + + align:start position:0% +in three lines of site and there's a lot + + + align:start position:0% +in three lines of site and there's a lot +of work going into tomographic + + align:start position:0% +of work going into tomographic + + + align:start position:0% +of work going into tomographic +reconstructions so make sure you + + align:start position:0% +reconstructions so make sure you + + + align:start position:0% +reconstructions so make sure you +understand the full emission region and + + align:start position:0% +understand the full emission region and + + + align:start position:0% +understand the full emission region and +we have our equivalent in magnetic + + align:start position:0% +we have our equivalent in magnetic + + + align:start position:0% +we have our equivalent in magnetic +confirming Fusion which you know John is + + align:start position:0% +confirming Fusion which you know John is + + + align:start position:0% +confirming Fusion which you know John is +working on um and we call them Neutron + + align:start position:0% +working on um and we call them Neutron + + + align:start position:0% +working on um and we call them Neutron +profile cameras so it's again the idea + + align:start position:0% +profile cameras so it's again the idea + + + align:start position:0% +profile cameras so it's again the idea +again is to prove the the shape of the + + align:start position:0% +again is to prove the the shape of the + + + align:start position:0% +again is to prove the the shape of the +neutron Source distribution but it's + + align:start position:0% +neutron Source distribution but it's + + + align:start position:0% +neutron Source distribution but it's +much bigger here and more complicated so + + align:start position:0% +much bigger here and more complicated so + + + align:start position:0% +much bigger here and more complicated so +instead of um that pinhole array that's + + align:start position:0% +instead of um that pinhole array that's + + + align:start position:0% +instead of um that pinhole array that's +trying to reconstruct the 50 micr spot + + align:start position:0% +trying to reconstruct the 50 micr spot + + + align:start position:0% +trying to reconstruct the 50 micr spot +we're looking at the much larger in + + align:start position:0% +we're looking at the much larger in + + + align:start position:0% +we're looking at the much larger in +Mission and we do it by using a number + + align:start position:0% +Mission and we do it by using a number + + + align:start position:0% +Mission and we do it by using a number +of different lines of s and Counting + + align:start position:0% +of different lines of s and Counting + + + align:start position:0% +of different lines of s and Counting +particles along this + + align:start position:0% +particles along this + + + align:start position:0% +particles along this +um line sight and then try to + + align:start position:0% +um line sight and then try to + + + align:start position:0% +um line sight and then try to +reconstruct the full like and John can + + align:start position:0% +reconstruct the full like and John can + + + align:start position:0% +reconstruct the full like and John can +answer a lot more questions + + align:start position:0% + + + + align:start position:0% + +here okay so with that I'm gonna jump + + align:start position:0% +here okay so with that I'm gonna jump + + + align:start position:0% +here okay so with that I'm gonna jump +right into charged particle + + align:start position:0% + + + + align:start position:0% + +spectrometry uh and I think it touched + + align:start position:0% +spectrometry uh and I think it touched + + + align:start position:0% +spectrometry uh and I think it touched +on the in the beginning but it's + + align:start position:0% +on the in the beginning but it's + + + align:start position:0% +on the in the beginning but it's +routinely used to diagnose low to medium + + align:start position:0% +routinely used to diagnose low to medium + + + align:start position:0% +routinely used to diagnose low to medium +rowar implosions um and they can be + + align:start position:0% +rowar implosions um and they can be + + + align:start position:0% +rowar implosions um and they can be +filled with duum DT or deum 3 Fuel and + + align:start position:0% +filled with duum DT or deum 3 Fuel and + + + align:start position:0% +filled with duum DT or deum 3 Fuel and +the reason we don't typically use it for + + align:start position:0% +the reason we don't typically use it for + + + align:start position:0% +the reason we don't typically use it for +H implosions is again because the charge + + align:start position:0% +H implosions is again because the charge + + + align:start position:0% +H implosions is again because the charge +particles stop in the assembled fuel so + + align:start position:0% +particles stop in the assembled fuel so + + + align:start position:0% +particles stop in the assembled fuel so +they they don't become indicators on the + + align:start position:0% +they they don't become indicators on the + + + align:start position:0% +they they don't become indicators on the +outside + + align:start position:0% +outside + + + align:start position:0% +outside +um okay this example is um showing the + + align:start position:0% +um okay this example is um showing the + + + align:start position:0% +um okay this example is um showing the +proton from Le reaction 44.7 M downshift + + align:start position:0% +proton from Le reaction 44.7 M downshift + + + align:start position:0% +proton from Le reaction 44.7 M downshift +about 11 M we can look at this downshift + + align:start position:0% +about 11 M we can look at this downshift + + + align:start position:0% +about 11 M we can look at this downshift +to infer the are of density which in + + align:start position:0% +to infer the are of density which in + + + align:start position:0% +to infer the are of density which in +this case was about 85 + + align:start position:0% +this case was about 85 + + + align:start position:0% +this case was about 85 +milligrams and you can actually see yeah + + align:start position:0% +milligrams and you can actually see yeah + + + align:start position:0% +milligrams and you can actually see yeah +um example one this nice little protons + + align:start position:0% +um example one this nice little protons + + + align:start position:0% +um example one this nice little protons +the cool thing is you can do this thing + + align:start position:0% +the cool thing is you can do this thing + + + align:start position:0% +the cool thing is you can do this thing +in a number of different locations + + align:start position:0% +in a number of different locations + + + align:start position:0% +in a number of different locations +around the target chamber to look at + + align:start position:0% +around the target chamber to look at + + + align:start position:0% +around the target chamber to look at +symmetry again to see what if things are + + align:start position:0% +symmetry again to see what if things are + + + align:start position:0% +symmetry again to see what if things are +compressed uniformly or if there's + + align:start position:0% +compressed uniformly or if there's + + + align:start position:0% +compressed uniformly or if there's +non-uniform + + align:start position:0% +non-uniform + + + align:start position:0% +non-uniform +issues so this a super simple + + align:start position:0% +issues so this a super simple + + + align:start position:0% +issues so this a super simple +spectrometer we call it wedge range + + align:start position:0% +spectrometer we call it wedge range + + + align:start position:0% +spectrometer we call it wedge range +filter + + align:start position:0% +filter + + + align:start position:0% +filter +spectrometer it's just an aluminum + + align:start position:0% +spectrometer it's just an aluminum + + + align:start position:0% +spectrometer it's just an aluminum +filter that's shaped like a + + align:start position:0% +filter that's shaped like a + + + align:start position:0% +filter that's shaped like a +wedge passes around you can see it so + + align:start position:0% +wedge passes around you can see it so + + + align:start position:0% +wedge passes around you can see it so +the way this is fied it's it's got a + + align:start position:0% +the way this is fied it's it's got a + + + align:start position:0% +the way this is fied it's it's got a +bunch of holes in front uh and you know + + align:start position:0% +bunch of holes in front uh and you know + + + align:start position:0% +bunch of holes in front uh and you know +the so the holes are used to register + + align:start position:0% +the so the holes are used to register + + + align:start position:0% +the so the holes are used to register +where the detector was filled behind + + align:start position:0% +where the detector was filled behind + + + align:start position:0% +where the detector was filled behind +that wedge you know the thickness of the + + align:start position:0% +that wedge you know the thickness of the + + + align:start position:0% +that wedge you know the thickness of the +functional position in this + + align:start position:0% +functional position in this + + + align:start position:0% +functional position in this +and based on actually the whole size in + + align:start position:0% +and based on actually the whole size in + + + align:start position:0% +and based on actually the whole size in +the cr39 detector as the function of + + align:start position:0% +the cr39 detector as the function of + + + align:start position:0% +the cr39 detector as the function of +position relative to those holes you + + align:start position:0% +position relative to those holes you + + + align:start position:0% +position relative to those holes you +infer the propin energy Spector and it's + + align:start position:0% +infer the propin energy Spector and it's + + + align:start position:0% +infer the propin energy Spector and it's +a little bit more complicated than it + + align:start position:0% +a little bit more complicated than it + + + align:start position:0% +a little bit more complicated than it +sounds because you need to know the + + align:start position:0% +sounds because you need to know the + + + align:start position:0% +sounds because you need to know the +diameter versus energy respones Ser 39 + + align:start position:0% +diameter versus energy respones Ser 39 + + + align:start position:0% +diameter versus energy respones Ser 39 +and that varies from P of the9 to P of + + align:start position:0% +and that varies from P of the9 to P of + + + align:start position:0% +and that varies from P of the9 to P of +the 39 so you have to come up with a + + align:start position:0% +the 39 so you have to come up with a + + + align:start position:0% +the 39 so you have to come up with a +pretty intricate method for inferring + + align:start position:0% +pretty intricate method for inferring + + + align:start position:0% +pretty intricate method for inferring +that from the data but uh that's done + + align:start position:0% +that from the data but uh that's done + + + align:start position:0% +that from the data but uh that's done +and these are routinely used to measure + + align:start position:0% +and these are routinely used to measure + + + align:start position:0% +and these are routinely used to measure +row are from the helium 3 gas fi + + align:start position:0% +row are from the helium 3 gas fi + + + align:start position:0% +row are from the helium 3 gas fi +implosions in many different locations + + align:start position:0% +implosions in many different locations + + + align:start position:0% +implosions in many different locations +around the target chamber um pass that + + align:start position:0% +around the target chamber um pass that + + + align:start position:0% +around the target chamber um pass that +around it's a small 5 cimeter round + + align:start position:0% +around it's a small 5 cimeter round + + + align:start position:0% +around it's a small 5 cimeter round +packet so you really can get it in many + + align:start position:0% +packet so you really can get it in many + + + align:start position:0% +packet so you really can get it in many +locations and this is also the detector + + align:start position:0% +locations and this is also the detector + + + align:start position:0% +locations and this is also the detector +material material that's used for mrss + + align:start position:0% +material material that's used for mrss + + + align:start position:0% +material material that's used for mrss +as we talked about before Ser 39 + + align:start position:0% +as we talked about before Ser 39 + + + align:start position:0% +as we talked about before Ser 39 +plastic um so the wed shange filter + + align:start position:0% +plastic um so the wed shange filter + + + align:start position:0% +plastic um so the wed shange filter +spectrometer is one example that can see + + align:start position:0% +spectrometer is one example that can see + + + align:start position:0% +spectrometer is one example that can see +here too um we also have charg particle + + align:start position:0% +here too um we also have charg particle + + + align:start position:0% +here too um we also have charg particle +spectrometers which are very similar to + + align:start position:0% +spectrometers which are very similar to + + + align:start position:0% +spectrometers which are very similar to +mrss it's a magnet outside of the target + + align:start position:0% +mrss it's a magnet outside of the target + + + align:start position:0% +mrss it's a magnet outside of the target +chamber Target chamber wall the + + align:start position:0% +chamber Target chamber wall the + + + align:start position:0% +chamber Target chamber wall the +difference is we don't have conversion + + align:start position:0% +difference is we don't have conversion + + + align:start position:0% +difference is we don't have conversion +fil so we're just looking at charge + + align:start position:0% +fil so we're just looking at charge + + + align:start position:0% +fil so we're just looking at charge +particles directly from the implosion + + align:start position:0% +particles directly from the implosion + + + align:start position:0% +particles directly from the implosion +and you can actually this is another + + align:start position:0% +and you can actually this is another + + + align:start position:0% +and you can actually this is another +advantage of mrss you can also run Mr in + + align:start position:0% +advantage of mrss you can also run Mr in + + + align:start position:0% +advantage of mrss you can also run Mr in +charge particle mode for experiments we + + align:start position:0% +charge particle mode for experiments we + + + align:start position:0% +charge particle mode for experiments we +not interested in the neutr Spectrum and + + align:start position:0% +not interested in the neutr Spectrum and + + + align:start position:0% +not interested in the neutr Spectrum and +then you can look at the charge + + align:start position:0% +then you can look at the charge + + + align:start position:0% +then you can look at the charge +particles that come directly from the + + align:start position:0% +particles that come directly from the + + + align:start position:0% +particles that come directly from the +implosion uh yeah and this is an example + + align:start position:0% +implosion uh yeah and this is an example + + + align:start position:0% +implosion uh yeah and this is an example +of looking at that Symmetry and how it + + align:start position:0% +of looking at that Symmetry and how it + + + align:start position:0% +of looking at that Symmetry and how it +can vary around the Imp + + align:start position:0% +can vary around the Imp + + + align:start position:0% +can vary around the Imp +um this this is an insertion module on + + align:start position:0% +um this this is an insertion module on + + + align:start position:0% +um this this is an insertion module on +the N where we can feel actually up to + + align:start position:0% +the N where we can feel actually up to + + + align:start position:0% +the N where we can feel actually up to +six of these wed filter spectrometers on + + align:start position:0% +six of these wed filter spectrometers on + + + align:start position:0% +six of these wed filter spectrometers on +a single insertion module there's four + + align:start position:0% +a single insertion module there's four + + + align:start position:0% +a single insertion module there's four +insertion modules that have capability + + align:start position:0% +insertion modules that have capability + + + align:start position:0% +insertion modules that have capability +of feeling these uh so we can as you + + align:start position:0% +of feeling these uh so we can as you + + + align:start position:0% +of feeling these uh so we can as you +understand we can feel a lot on one + + align:start position:0% +understand we can feel a lot on one + + + align:start position:0% +understand we can feel a lot on one +implosion on Omega we can feel up to + + align:start position:0% +implosion on Omega we can feel up to + + + align:start position:0% +implosion on Omega we can feel up to +seven on one implosion in different + + align:start position:0% +seven on one implosion in different + + + align:start position:0% +seven on one implosion in different +directions and in each Direction you can + + align:start position:0% +directions and in each Direction you can + + + align:start position:0% +directions and in each Direction you can +add a few more if you want to a lot um + + align:start position:0% +add a few more if you want to a lot um + + + align:start position:0% +add a few more if you want to a lot um +yeah so in this case these are filled at + + align:start position:0% +yeah so in this case these are filled at + + + align:start position:0% +yeah so in this case these are filled at +50 cm fromion these are fed at 10 cm + + align:start position:0% +50 cm fromion these are fed at 10 cm + + + align:start position:0% +50 cm fromion these are fed at 10 cm +fromion at and we can look in different + + align:start position:0% +fromion at and we can look in different + + + align:start position:0% +fromion at and we can look in different +directions this is actually really old + + align:start position:0% +directions this is actually really old + + + align:start position:0% +directions this is actually really old +example from the pap in 2004 where is + + align:start position:0% +example from the pap in 2004 where is + + + align:start position:0% +example from the pap in 2004 where is +Fielding protons spect in different + + align:start position:0% +Fielding protons spect in different + + + align:start position:0% +Fielding protons spect in different +locations around the omega3 chamber can + + align:start position:0% +locations around the omega3 chamber can + + + align:start position:0% +locations around the omega3 chamber can +look at differ than the Spectrum and + + align:start position:0% +look at differ than the Spectrum and + + + align:start position:0% +look at differ than the Spectrum and +this if you + + align:start position:0% +this if you + + + align:start position:0% +this if you +um think back to + + align:start position:0% +um think back to + + + align:start position:0% +um think back to +this for d three uh you often get these + + align:start position:0% +this for d three uh you often get these + + + align:start position:0% +this for d three uh you often get these +two peaks in time a shock Peak and a + + align:start position:0% +two peaks in time a shock Peak and a + + + align:start position:0% +two peaks in time a shock Peak and a +compression Peak so you can also say + + align:start position:0% +compression Peak so you can also say + + + align:start position:0% +compression Peak so you can also say +something about the evolution of the + + align:start position:0% +something about the evolution of the + + + align:start position:0% +something about the evolution of the +experiment here you have the time + + align:start position:0% +experiment here you have the time + + + align:start position:0% +experiment here you have the time +Evolution you see the small shock Peak + + align:start position:0% +Evolution you see the small shock Peak + + + align:start position:0% +Evolution you see the small shock Peak +um larger compression Peak and then you + + align:start position:0% +um larger compression Peak and then you + + + align:start position:0% +um larger compression Peak and then you +can also see that in the energy Spectre + + align:start position:0% +can also see that in the energy Spectre + + + align:start position:0% +can also see that in the energy Spectre +have less range down Shar more range + + align:start position:0% +have less range down Shar more range + + + align:start position:0% +have less range down Shar more range +down compression protons so you can tell + + align:start position:0% +down compression protons so you can tell + + + align:start position:0% +down compression protons so you can tell +the difference in areal Den between + + align:start position:0% +the difference in areal Den between + + + align:start position:0% +the difference in areal Den between +those two types + + align:start position:0% +those two types + + + align:start position:0% +those two types +ofion it's kind of + + align:start position:0% + + + + align:start position:0% + +NE okay feel like I'm running out of + + align:start position:0% +NE okay feel like I'm running out of + + + align:start position:0% +NE okay feel like I'm running out of +time so I get speed up already talked + + align:start position:0% +time so I get speed up already talked + + + align:start position:0% +time so I get speed up already talked +about image plates don't need to talk + + align:start position:0% +about image plates don't need to talk + + + align:start position:0% +about image plates don't need to talk +about that uh ser39 I kind of touched on + + align:start position:0% +about that uh ser39 I kind of touched on + + + align:start position:0% +about that uh ser39 I kind of touched on +um this is an example of what it can + + align:start position:0% +um this is an example of what it can + + + align:start position:0% +um this is an example of what it can +look like after we edting sodium + + align:start position:0% +look like after we edting sodium + + + align:start position:0% +look like after we edting sodium +hydroxide at 80 degrees Celsius for of + + align:start position:0% +hydroxide at 80 degrees Celsius for of + + + align:start position:0% +hydroxide at 80 degrees Celsius for of +order hours we put it on one of these + + align:start position:0% +order hours we put it on one of these + + + align:start position:0% +order hours we put it on one of these +microscopes step over and make pictures + + align:start position:0% +microscopes step over and make pictures + + + align:start position:0% +microscopes step over and make pictures +for um roughly 400 micr by 400 micr + + align:start position:0% +for um roughly 400 micr by 400 micr + + + align:start position:0% +for um roughly 400 micr by 400 micr +frames the um microscope automatically + + align:start position:0% +frames the um microscope automatically + + + align:start position:0% +frames the um microscope automatically +picks up tracks which are due to + + align:start position:0% +picks up tracks which are due to + + + align:start position:0% +picks up tracks which are due to +particles interacting in the SI 39 and + + align:start position:0% +particles interacting in the SI 39 and + + + align:start position:0% +particles interacting in the SI 39 and +Records their roundness their + + align:start position:0% +Records their roundness their + + + align:start position:0% +Records their roundness their +eccentricity and the track size and we + + align:start position:0% +eccentricity and the track size and we + + + align:start position:0% +eccentricity and the track size and we +use that um to reconstruct whatever + + align:start position:0% +use that um to reconstruct whatever + + + align:start position:0% +use that um to reconstruct whatever +information they wanted from that + + align:start position:0% + + + + align:start position:0% + +diagnostic okay so then spend a few + + align:start position:0% +diagnostic okay so then spend a few + + + align:start position:0% +diagnostic okay so then spend a few +minutes on reaction rate + + align:start position:0% +minutes on reaction rate + + + align:start position:0% +minutes on reaction rate +history so there's a number of ways to + + align:start position:0% +history so there's a number of ways to + + + align:start position:0% +history so there's a number of ways to +do this and again so we're looking a + + align:start position:0% +do this and again so we're looking a + + + align:start position:0% +do this and again so we're looking a +really short burn order 100 PCS uh we + + align:start position:0% +really short burn order 100 PCS uh we + + + align:start position:0% +really short burn order 100 PCS uh we +can feel a plastic culator really close + + align:start position:0% +can feel a plastic culator really close + + + align:start position:0% +can feel a plastic culator really close +to the implosion and combine it with the + + align:start position:0% +to the implosion and combine it with the + + + align:start position:0% +to the implosion and combine it with the +street camera to measure the reaction + + align:start position:0% +street camera to measure the reaction + + + align:start position:0% +street camera to measure the reaction +radi hisory this is done at Omega so + + align:start position:0% +radi hisory this is done at Omega so + + + align:start position:0% +radi hisory this is done at Omega so +this picture is of the Omega Target + + align:start position:0% +this picture is of the Omega Target + + + align:start position:0% +this picture is of the Omega Target +chamber this is the laser so this is not + + align:start position:0% +chamber this is the laser so this is not + + + align:start position:0% +chamber this is the laser so this is not +part of the diagnostic this is how we + + align:start position:0% +part of the diagnostic this is how we + + + align:start position:0% +part of the diagnostic this is how we +drive the actual + + align:start position:0% +drive the actual + + + align:start position:0% +drive the actual +osion this is what the detector will + + align:start position:0% +osion this is what the detector will + + + align:start position:0% +osion this is what the detector will +look like so it will be feeling close to + + align:start position:0% +look like so it will be feeling close to + + + align:start position:0% +look like so it will be feeling close to +the Target chamber there's a plastic + + align:start position:0% +the Target chamber there's a plastic + + + align:start position:0% +the Target chamber there's a plastic +culator the light from the simulator + + align:start position:0% +culator the light from the simulator + + + align:start position:0% +culator the light from the simulator +will be coupled through an optical light + + align:start position:0% +will be coupled through an optical light + + + align:start position:0% +will be coupled through an optical light +path through spe camera to record a + + align:start position:0% +path through spe camera to record a + + + align:start position:0% +path through spe camera to record a +streak image and this is where the burn + + align:start position:0% +streak image and this is where the burn + + + align:start position:0% +streak image and this is where the burn +his DRS en coed and that cator would + + align:start position:0% +his DRS en coed and that cator would + + + align:start position:0% +his DRS en coed and that cator would +have a rise time about 20 PCS but a fall + + align:start position:0% +have a rise time about 20 PCS but a fall + + + align:start position:0% +have a rise time about 20 PCS but a fall +time of like one and a half NCS so the + + align:start position:0% +time of like one and a half NCS so the + + + align:start position:0% +time of like one and a half NCS so the +information really is encoded in Rising + + align:start position:0% +information really is encoded in Rising + + + align:start position:0% +information really is encoded in Rising +edge of the you have to unfold it but + + align:start position:0% +edge of the you have to unfold it but + + + align:start position:0% +edge of the you have to unfold it but +when you do that you can get the the + + align:start position:0% +when you do that you can get the the + + + align:start position:0% +when you do that you can get the the +burn history of functional time for shot + + align:start position:0% +burn history of functional time for shot + + + align:start position:0% +burn history of functional time for shot +in compression and this is used a lot + + align:start position:0% +in compression and this is used a lot + + + align:start position:0% +in compression and this is used a lot +for neutrons and Omega in the neutron + + align:start position:0% +for neutrons and Omega in the neutron + + + align:start position:0% +for neutrons and Omega in the neutron +temporal diagnostic um and there's also + + align:start position:0% +temporal diagnostic um and there's also + + + align:start position:0% +temporal diagnostic um and there's also +the particle temporal diagnostic or the + + align:start position:0% +the particle temporal diagnostic or the + + + align:start position:0% +the particle temporal diagnostic or the +particle and x-ray temporal diagnostic + + align:start position:0% +particle and x-ray temporal diagnostic + + + align:start position:0% +particle and x-ray temporal diagnostic +similar concept where you can tweak that + + align:start position:0% +similar concept where you can tweak that + + + align:start position:0% +similar concept where you can tweak that +simulator up in the center have number + + align:start position:0% +simulator up in the center have number + + + align:start position:0% +simulator up in the center have number +of different channels um some of them + + align:start position:0% +of different channels um some of them + + + align:start position:0% +of different channels um some of them +optimized for x-rays some optimized for + + align:start position:0% +optimized for x-rays some optimized for + + + align:start position:0% +optimized for x-rays some optimized for +protons some optimized for neutrons + + align:start position:0% +protons some optimized for neutrons + + + align:start position:0% +protons some optimized for neutrons +depending on how you filter them and + + align:start position:0% +depending on how you filter them and + + + align:start position:0% +depending on how you filter them and +what neutral density for will be on all + + align:start position:0% +what neutral density for will be on all + + + align:start position:0% +what neutral density for will be on all +can record on the street camp and + + align:start position:0% +can record on the street camp and + + + align:start position:0% +can record on the street camp and +reconstructed after so that's actually + + align:start position:0% +reconstructed after so that's actually + + + align:start position:0% +reconstructed after so that's actually +really neat diagnostic that's useful for + + align:start position:0% +really neat diagnostic that's useful for + + + align:start position:0% +really neat diagnostic that's useful for +a lot of things I told you promised you + + align:start position:0% +a lot of things I told you promised you + + + align:start position:0% +a lot of things I told you promised you +early on that we get back to what we + + align:start position:0% +early on that we get back to what we + + + align:start position:0% +early on that we get back to what we +used the gamas for so one cool thing + + align:start position:0% +used the gamas for so one cool thing + + + align:start position:0% +used the gamas for so one cool thing +about the gamas uh is they don't have + + align:start position:0% +about the gamas uh is they don't have + + + align:start position:0% +about the gamas uh is they don't have +the same time dispersion that Nutri do + + align:start position:0% +the same time dispersion that Nutri do + + + align:start position:0% +the same time dispersion that Nutri do +so the the neutrons when they're emitted + + align:start position:0% +so the the neutrons when they're emitted + + + align:start position:0% +so the the neutrons when they're emitted +from Target chamber Center they're going + + align:start position:0% +from Target chamber Center they're going + + + align:start position:0% +from Target chamber Center they're going +to disperse in time which is really why + + align:start position:0% +to disperse in time which is really why + + + align:start position:0% +to disperse in time which is really why +we can use just the neutron time + + align:start position:0% +we can use just the neutron time + + + align:start position:0% +we can use just the neutron time +dispersion for a neutron time flight + + align:start position:0% +dispersion for a neutron time flight + + + align:start position:0% +dispersion for a neutron time flight +right so if we put the en detector 20 + + align:start position:0% +right so if we put the en detector 20 + + + align:start position:0% +right so if we put the en detector 20 +meters away look at the neutrons we + + align:start position:0% +meters away look at the neutrons we + + + align:start position:0% +meters away look at the neutrons we +measure the energy Spectrum not the + + align:start position:0% +measure the energy Spectrum not the + + + align:start position:0% +measure the energy Spectrum not the +emission history um for the gamas they + + align:start position:0% +emission history um for the gamas they + + + align:start position:0% +emission history um for the gamas they +don't disperse in time so we can have a + + align:start position:0% +don't disperse in time so we can have a + + + align:start position:0% +don't disperse in time so we can have a +gamma detector relatively far away you + + align:start position:0% +gamma detector relatively far away you + + + align:start position:0% +gamma detector relatively far away you +still retain that time history so that's + + align:start position:0% +still retain that time history so that's + + + align:start position:0% +still retain that time history so that's +the cool part we have a lot lower + + align:start position:0% +the cool part we have a lot lower + + + align:start position:0% +the cool part we have a lot lower +probability for getting gamas I think we + + align:start position:0% +probability for getting gamas I think we + + + align:start position:0% +probability for getting gamas I think we +saw the branch ratio is about 10 the + + align:start position:0% +saw the branch ratio is about 10 the + + + align:start position:0% +saw the branch ratio is about 10 the +minus five of the neutrons but there is + + align:start position:0% +minus five of the neutrons but there is + + + align:start position:0% +minus five of the neutrons but there is +enough of them count and by counting the + + align:start position:0% +enough of them count and by counting the + + + align:start position:0% +enough of them count and by counting the +gamas in this example we're using the um + + align:start position:0% +gamas in this example we're using the um + + + align:start position:0% +gamas in this example we're using the um +gamma reaction history detector which is + + align:start position:0% +gamma reaction history detector which is + + + align:start position:0% +gamma reaction history detector which is +based on + + align:start position:0% +based on + + + align:start position:0% +based on +um uh converter regates they converted + + align:start position:0% +um uh converter regates they converted + + + align:start position:0% +um uh converter regates they converted +to electrons electrons generate strength + + align:start position:0% +to electrons electrons generate strength + + + align:start position:0% +to electrons electrons generate strength +of light in this gaso and then it's + + align:start position:0% +of light in this gaso and then it's + + + align:start position:0% +of light in this gaso and then it's +detected as the function of time and + + align:start position:0% +detected as the function of time and + + + align:start position:0% +detected as the function of time and +that's how you infer the bank time or + + align:start position:0% +that's how you infer the bank time or + + + align:start position:0% +that's how you infer the bank time or +burn history get both from this + + align:start position:0% +burn history get both from this + + + align:start position:0% +burn history get both from this +measurement this is what this detector + + align:start position:0% +measurement this is what this detector + + + align:start position:0% +measurement this is what this detector +looks like on Omega and this is what it + + align:start position:0% +looks like on Omega and this is what it + + + align:start position:0% +looks like on Omega and this is what it +looks like on the n and on the N um + + align:start position:0% +looks like on the n and on the N um + + + align:start position:0% +looks like on the n and on the N um +there are four different channels which + + align:start position:0% +there are four different channels which + + + align:start position:0% +there are four different channels which +you can vary the gas pressure to set a + + align:start position:0% +you can vary the gas pressure to set a + + + align:start position:0% +you can vary the gas pressure to set a +different gamma detection threshold um + + align:start position:0% +different gamma detection threshold um + + + align:start position:0% +different gamma detection threshold um +it you don't get Spectral information + + align:start position:0% +it you don't get Spectral information + + + align:start position:0% +it you don't get Spectral information +but you can set a threshold and compare + + align:start position:0% +but you can set a threshold and compare + + + align:start position:0% +but you can set a threshold and compare +the results from + + align:start position:0% +the results from + + + align:start position:0% +the results from +before and actually it even made it into + + align:start position:0% +before and actually it even made it into + + + align:start position:0% +before and actually it even made it into +a movie this + + align:start position:0% +a movie this + + + align:start position:0% +a movie this +detector this is the gam reaction + + align:start position:0% +detector this is the gam reaction + + + align:start position:0% +detector this is the gam reaction +history + + align:start position:0% +history + + + align:start position:0% +history +detective Hans Herman who built this Det + + align:start position:0% +detective Hans Herman who built this Det + + + align:start position:0% +detective Hans Herman who built this Det +actor was really proud to be able to + + align:start position:0% +actor was really proud to be able to + + + align:start position:0% +actor was really proud to be able to +take his kids to this movie at the + + align:start position:0% + + + + align:start position:0% + +mov um okay so coming back to Magnetic + + align:start position:0% +mov um okay so coming back to Magnetic + + + align:start position:0% +mov um okay so coming back to Magnetic +confirming Fusion again here we + + align:start position:0% +confirming Fusion again here we + + + align:start position:0% +confirming Fusion again here we +typically use fish and Chambers to + + align:start position:0% +typically use fish and Chambers to + + + align:start position:0% +typically use fish and Chambers to +measure the nuclear reaction + + align:start position:0% +measure the nuclear reaction + + + align:start position:0% +measure the nuclear reaction +rate uh and the way this works is you + + align:start position:0% +rate uh and the way this works is you + + + align:start position:0% +rate uh and the way this works is you +have the file material um you get the + + align:start position:0% +have the file material um you get the + + + align:start position:0% +have the file material um you get the +fishing prodct going into the Fill gas + + align:start position:0% +fishing prodct going into the Fill gas + + + align:start position:0% +fishing prodct going into the Fill gas +they ion or sorry yeah they ionize the F + + align:start position:0% +they ion or sorry yeah they ionize the F + + + align:start position:0% +they ion or sorry yeah they ionize the F +gas and then you get an electric P that + + align:start position:0% +gas and then you get an electric P that + + + align:start position:0% +gas and then you get an electric P that +goes out and you measure that as a + + align:start position:0% +goes out and you measure that as a + + + align:start position:0% +goes out and you measure that as a +function of time and here again you need + + align:start position:0% +function of time and here again you need + + + align:start position:0% +function of time and here again you need +mCP + + align:start position:0% +mCP + + + align:start position:0% +mCP +model in order to determine what your + + align:start position:0% +model in order to determine what your + + + align:start position:0% +model in order to determine what your +measured signal actually means in terms + + align:start position:0% +measured signal actually means in terms + + + align:start position:0% +measured signal actually means in terms +of neutron yeld these are often also + + align:start position:0% +of neutron yeld these are often also + + + align:start position:0% +of neutron yeld these are often also +ined calibrated where you move a source + + align:start position:0% +ined calibrated where you move a source + + + align:start position:0% +ined calibrated where you move a source +around inside the chamber and see what + + align:start position:0% +around inside the chamber and see what + + + align:start position:0% +around inside the chamber and see what +the signal looks like on the ficient + + align:start position:0% +the signal looks like on the ficient + + + align:start position:0% +the signal looks like on the ficient +chambers on the + + align:start position:0% +chambers on the + + + align:start position:0% +chambers on the +outside H okay and I think I have like + + align:start position:0% +outside H okay and I think I have like + + + align:start position:0% +outside H okay and I think I have like +five more minutes Jack right so we'll + + align:start position:0% +five more minutes Jack right so we'll + + + align:start position:0% +five more minutes Jack right so we'll +take a few minutes on the impact of + + align:start position:0% +take a few minutes on the impact of + + + align:start position:0% +take a few minutes on the impact of +nuclear measurements on the ICF program + + align:start position:0% +nuclear measurements on the ICF program + + + align:start position:0% +nuclear measurements on the ICF program +at the + + align:start position:0% +at the + + + align:start position:0% +at the +N uh and I think we really touched on + + align:start position:0% +N uh and I think we really touched on + + + align:start position:0% +N uh and I think we really touched on +this throughout the talk today right + + align:start position:0% +this throughout the talk today right + + + align:start position:0% +this throughout the talk today right +that nuclear data have been essential + + align:start position:0% +that nuclear data have been essential + + + align:start position:0% +that nuclear data have been essential +for guiding the N experiment recognition + + align:start position:0% +for guiding the N experiment recognition + + + align:start position:0% +for guiding the N experiment recognition +this is the time axis of the yield from + + align:start position:0% +this is the time axis of the yield from + + + align:start position:0% +this is the time axis of the yield from +the experiments from 2010 through now to + + align:start position:0% +the experiments from 2010 through now to + + + align:start position:0% +the experiments from 2010 through now to +2024 you can see that the Y this + + align:start position:0% +2024 you can see that the Y this + + + align:start position:0% +2024 you can see that the Y this +logorithm scale is obviously increased a + + align:start position:0% +logorithm scale is obviously increased a + + + align:start position:0% +logorithm scale is obviously increased a +lot over that time frame and like mrss + + align:start position:0% +lot over that time frame and like mrss + + + align:start position:0% +lot over that time frame and like mrss +has been part of it from the beginning I + + align:start position:0% +has been part of it from the beginning I + + + align:start position:0% +has been part of it from the beginning I +started here at MIT in August + + align:start position:0% +started here at MIT in August + + + align:start position:0% +started here at MIT in August +2010 I think the First Data from the N + + align:start position:0% +2010 I think the First Data from the N + + + align:start position:0% +2010 I think the First Data from the N +came back from + + align:start position:0% +came back from + + + align:start position:0% +came back from +Mr like a we two two weeks after I + + align:start position:0% +Mr like a we two two weeks after I + + + align:start position:0% +Mr like a we two two weeks after I +started it came it shipped it back in + + align:start position:0% +started it came it shipped it back in + + + align:start position:0% +started it came it shipped it back in +this huge moonlander looking container + + align:start position:0% +this huge moonlander looking container + + + align:start position:0% +this huge moonlander looking container +was like octagonal box with lots of cool + + align:start position:0% +was like octagonal box with lots of cool + + + align:start position:0% +was like octagonal box with lots of cool +packs to keep the C cold and then we had + + align:start position:0% +packs to keep the C cold and then we had + + + align:start position:0% +packs to keep the C cold and then we had +to you know work day and night to action + + align:start position:0% +to you know work day and night to action + + + align:start position:0% +to you know work day and night to action +scan it and turn it around and that's + + align:start position:0% +scan it and turn it around and that's + + + align:start position:0% +scan it and turn it around and that's +when we're at this yield level right not + + align:start position:0% +when we're at this yield level right not + + + align:start position:0% +when we're at this yield level right not +this r on this scale um and then we + + align:start position:0% +this r on this scale um and then we + + + align:start position:0% +this r on this scale um and then we +working our way through um up to to the + + align:start position:0% +working our way through um up to to the + + + align:start position:0% +working our way through um up to to the +reason we actually have Target + + align:start position:0% +reason we actually have Target + + + align:start position:0% +reason we actually have Target +gain and we've looked at many of these + + align:start position:0% +gain and we've looked at many of these + + + align:start position:0% +gain and we've looked at many of these +Diagnostics today that have been + + align:start position:0% +Diagnostics today that have been + + + align:start position:0% +Diagnostics today that have been +essential for C if experiments to + + align:start position:0% +essential for C if experiments to + + + align:start position:0% +essential for C if experiments to +ignition we looked at how we get iron + + align:start position:0% +ignition we looked at how we get iron + + + align:start position:0% +ignition we looked at how we get iron +temperature Hotpot velocity fuel density + + align:start position:0% +temperature Hotpot velocity fuel density + + + align:start position:0% +temperature Hotpot velocity fuel density +or aerial density and yield from the + + align:start position:0% +or aerial density and yield from the + + + align:start position:0% +or aerial density and yield from the +neutron spectrometers we looked at how + + align:start position:0% +neutron spectrometers we looked at how + + + align:start position:0% +neutron spectrometers we looked at how +we get the burn M and bang time from the + + align:start position:0% +we get the burn M and bang time from the + + + align:start position:0% +we get the burn M and bang time from the +gam reaction instute detector which is + + align:start position:0% +gam reaction instute detector which is + + + align:start position:0% +gam reaction instute detector which is +related to The Shining time um we also + + align:start position:0% +related to The Shining time um we also + + + align:start position:0% +related to The Shining time um we also +get neutral from the activation + + align:start position:0% +get neutral from the activation + + + align:start position:0% +get neutral from the activation +detectors as well as a math of the fuel + + align:start position:0% +detectors as well as a math of the fuel + + + align:start position:0% +detectors as well as a math of the fuel +uniformity from the Real Time activation + + align:start position:0% +uniformity from the Real Time activation + + + align:start position:0% +uniformity from the Real Time activation +detectors uh and we use Nutri just with + + align:start position:0% +detectors uh and we use Nutri just with + + + align:start position:0% +detectors uh and we use Nutri just with +the hot spot F shape and really in + + align:start position:0% +the hot spot F shape and really in + + + align:start position:0% +the hot spot F shape and really in +particular these two have been essential + + align:start position:0% +particular these two have been essential + + + align:start position:0% +particular these two have been essential +for identifying those asymmetries and + + align:start position:0% +for identifying those asymmetries and + + + align:start position:0% +for identifying those asymmetries and +seeds to asymmetries have been really + + align:start position:0% +seeds to asymmetries have been really + + + align:start position:0% +seeds to asymmetries have been really +had to eliminate along the way to get + + align:start position:0% + + + + align:start position:0% + +there okay + + align:start position:0% +there okay + + + align:start position:0% +there okay +um this is an example that um Yan put + + align:start position:0% +um this is an example that um Yan put + + + align:start position:0% +um this is an example that um Yan put +together two years ago on August 8 2021 + + align:start position:0% +together two years ago on August 8 2021 + + + align:start position:0% +together two years ago on August 8 2021 +and implosion experiment then if ignited + + align:start position:0% +and implosion experiment then if ignited + + + align:start position:0% +and implosion experiment then if ignited +and generated a then record Neutron + + align:start position:0% +and generated a then record Neutron + + + align:start position:0% +and generated a then record Neutron +yield of 4.5 17 or 1.35 me this is the + + align:start position:0% +yield of 4.5 17 or 1.35 me this is the + + + align:start position:0% +yield of 4.5 17 or 1.35 me this is the +mrss Spectrum from that particular + + align:start position:0% +mrss Spectrum from that particular + + + align:start position:0% +mrss Spectrum from that particular +experiment we were so excited about that + + align:start position:0% +experiment we were so excited about that + + + align:start position:0% +experiment we were so excited about that +experiment uh which really internally in + + align:start position:0% +experiment uh which really internally in + + + align:start position:0% +experiment uh which really internally in +the community that was ignition I'll + + align:start position:0% +the community that was ignition I'll + + + align:start position:0% +the community that was ignition I'll +explain why in the next slide um but so + + align:start position:0% +explain why in the next slide um but so + + + align:start position:0% +explain why in the next slide um but so +this explains what I was talking about + + align:start position:0% +this explains what I was talking about + + + align:start position:0% +this explains what I was talking about +before we have a model neutr Spectrum + + align:start position:0% +before we have a model neutr Spectrum + + + align:start position:0% +before we have a model neutr Spectrum +which is a gan with the with termined by + + align:start position:0% +which is a gan with the with termined by + + + align:start position:0% +which is a gan with the with termined by +the temperature the mean energy uh + + align:start position:0% +the temperature the mean energy uh + + + align:start position:0% +the temperature the mean energy uh +determined by the birth energy plus the + + align:start position:0% +determined by the birth energy plus the + + + align:start position:0% +determined by the birth energy plus the +peak shift which is related to the + + align:start position:0% +peak shift which is related to the + + + align:start position:0% +peak shift which is related to the +velocity and then they have this + + align:start position:0% +velocity and then they have this + + + align:start position:0% +velocity and then they have this +component which is related to the aerial + + align:start position:0% +component which is related to the aerial + + + align:start position:0% +component which is related to the aerial +density we vary those parameters to fit + + align:start position:0% +density we vary those parameters to fit + + + align:start position:0% +density we vary those parameters to fit +it to our measured Rec eny spectrum and + + align:start position:0% +it to our measured Rec eny spectrum and + + + align:start position:0% +it to our measured Rec eny spectrum and +we get a Best F NR Spectrum which + + align:start position:0% +we get a Best F NR Spectrum which + + + align:start position:0% +we get a Best F NR Spectrum which +explains what what we actually + + align:start position:0% +explains what what we actually + + + align:start position:0% +explains what what we actually +had um and so if you look in particular + + align:start position:0% +had um and so if you look in particular + + + align:start position:0% +had um and so if you look in particular +at this implosion from + + align:start position:0% +at this implosion from + + + align:start position:0% +at this implosion from +21808 many of the key nuclear observes + + align:start position:0% +21808 many of the key nuclear observes + + + align:start position:0% +21808 many of the key nuclear observes +point to this implosion being + + align:start position:0% +point to this implosion being + + + align:start position:0% +point to this implosion being +fundamentally new regime we saw how the + + align:start position:0% +fundamentally new regime we saw how the + + + align:start position:0% +fundamentally new regime we saw how the +iron temperature took off earlier + + align:start position:0% +iron temperature took off earlier + + + align:start position:0% +iron temperature took off earlier +implosions in the same pay K now we + + align:start position:0% +implosions in the same pay K now we + + + align:start position:0% +implosions in the same pay K now we +measuring Neutron average I in + + align:start position:0% +measuring Neutron average I in + + + align:start position:0% +measuring Neutron average I in +temperature 10 KV a dramatic step up we + + align:start position:0% +temperature 10 KV a dramatic step up we + + + align:start position:0% +temperature 10 KV a dramatic step up we +saw how um the burn history is a little + + align:start position:0% +saw how um the burn history is a little + + + align:start position:0% +saw how um the burn history is a little +bit hard to see but what happened + + align:start position:0% +bit hard to see but what happened + + + align:start position:0% +bit hard to see but what happened +actually the burn history um Peak + + align:start position:0% +actually the burn history um Peak + + + align:start position:0% +actually the burn history um Peak +later and got narrower and what this is + + align:start position:0% +later and got narrower and what this is + + + align:start position:0% +later and got narrower and what this is +saying is + + align:start position:0% +saying is + + + align:start position:0% +saying is +that the yield took off during + + align:start position:0% +that the yield took off during + + + align:start position:0% +that the yield took off during +compression so where the yield would + + align:start position:0% +compression so where the yield would + + + align:start position:0% +compression so where the yield would +have previously tanked you start having + + align:start position:0% +have previously tanked you start having + + + align:start position:0% +have previously tanked you start having +to Cline more and more + + align:start position:0% +to Cline more and more + + + align:start position:0% +to Cline more and more +instead um and then becomes a really + + align:start position:0% +instead um and then becomes a really + + + align:start position:0% +instead um and then becomes a really +narrow burn because it's burning on AA + + align:start position:0% +narrow burn because it's burning on AA + + + align:start position:0% +narrow burn because it's burning on AA +implosion is exploding rather than a and + + align:start position:0% +implosion is exploding rather than a and + + + align:start position:0% +implosion is exploding rather than a and +you can kind of see in the neutron + + align:start position:0% +you can kind of see in the neutron + + + align:start position:0% +you can kind of see in the neutron +images as well these are Neutron images + + align:start position:0% +images as well these are Neutron images + + + align:start position:0% +images as well these are Neutron images +and as well as one extra on the top from + + align:start position:0% +and as well as one extra on the top from + + + align:start position:0% +and as well as one extra on the top from +two predecessor inions this one you can + + align:start position:0% +two predecessor inions this one you can + + + align:start position:0% +two predecessor inions this one you can +see how it gets a lot bigger and this is + + align:start position:0% +see how it gets a lot bigger and this is + + + align:start position:0% +see how it gets a lot bigger and this is +again because going on the + + align:start position:0% +again because going on the + + + align:start position:0% +again because going on the +expansion um yeah and then the other one + + align:start position:0% +expansion um yeah and then the other one + + + align:start position:0% +expansion um yeah and then the other one +what we're actually measuring uh it's + + align:start position:0% +what we're actually measuring uh it's + + + align:start position:0% +what we're actually measuring uh it's +not the best part to show it but what + + align:start position:0% +not the best part to show it but what + + + align:start position:0% +not the best part to show it but what +we're finding is that we're actually + + align:start position:0% +we're finding is that we're actually + + + align:start position:0% +we're finding is that we're actually +measuring a lower down scale ratio and + + align:start position:0% +measuring a lower down scale ratio and + + + align:start position:0% +measuring a lower down scale ratio and +the reason for that as we're now probing + + align:start position:0% +the reason for that as we're now probing + + + align:start position:0% +the reason for that as we're now probing +because the neut the down ratio that + + align:start position:0% +because the neut the down ratio that + + + align:start position:0% +because the neut the down ratio that +we're measuring is probing later timeing + + align:start position:0% +we're measuring is probing later timeing + + + align:start position:0% +we're measuring is probing later timeing +thetion after Peak compression so even + + align:start position:0% +thetion after Peak compression so even + + + align:start position:0% +thetion after Peak compression so even +though the actual downscale ratio the + + align:start position:0% +though the actual downscale ratio the + + + align:start position:0% +though the actual downscale ratio the +actual compression is the same we're + + align:start position:0% +actual compression is the same we're + + + align:start position:0% +actual compression is the same we're +seeing fous neutr because the peak + + align:start position:0% +seeing fous neutr because the peak + + + align:start position:0% +seeing fous neutr because the peak +compression is before the prot does that + + align:start position:0% +compression is before the prot does that + + + align:start position:0% +compression is before the prot does that +make + + align:start position:0% +make + + + align:start position:0% +make +sense + + align:start position:0% +sense + + + align:start position:0% +sense +um + + align:start position:0% +um + + + align:start position:0% +um +okay uh and yeah this is just another + + align:start position:0% +okay uh and yeah this is just another + + + align:start position:0% +okay uh and yeah this is just another +ill illustration of the same points + + align:start position:0% +ill illustration of the same points + + + align:start position:0% +ill illustration of the same points +where you really see + + align:start position:0% +where you really see + + + align:start position:0% +where you really see +um the temperature fli of junk this is + + align:start position:0% +um the temperature fli of junk this is + + + align:start position:0% +um the temperature fli of junk this is +not the fusion vied on the y axis the + + align:start position:0% +not the fusion vied on the y axis the + + + align:start position:0% +not the fusion vied on the y axis the +this is inferred Hotpot mass and Hotpot + + align:start position:0% +this is inferred Hotpot mass and Hotpot + + + align:start position:0% +this is inferred Hotpot mass and Hotpot +energy also jump through this one equ + + align:start position:0% +energy also jump through this one equ + + + align:start position:0% +energy also jump through this one equ +otion um Neutron radius increased and + + align:start position:0% +otion um Neutron radius increased and + + + align:start position:0% +otion um Neutron radius increased and +burn decreased really showing in a in a + + align:start position:0% +burn decreased really showing in a in a + + + align:start position:0% +burn decreased really showing in a in a +new + + align:start position:0% +new + + + align:start position:0% +new +regime + + align:start position:0% +regime + + + align:start position:0% +regime +and that was this + + align:start position:0% +and that was this + + + align:start position:0% +and that was this +one couple years ago so definitely done + + align:start position:0% +one couple years ago so definitely done + + + align:start position:0% +one couple years ago so definitely done +some better ones since then and uh + + align:start position:0% +some better ones since then and uh + + + align:start position:0% +some better ones since then and uh +there's another one from October 29th + + align:start position:0% +there's another one from October 29th + + + align:start position:0% +there's another one from October 29th +it's not yet on this chart too which is + + align:start position:0% +it's not yet on this chart too which is + + + align:start position:0% +it's not yet on this chart too which is +the second best performing ever so Falls + + align:start position:0% +the second best performing ever so Falls + + + align:start position:0% +the second best performing ever so Falls +right between these two and I we're at + + align:start position:0% +right between these two and I we're at + + + align:start position:0% +right between these two and I we're at +um four with gain over one at this + + align:start position:0% +um four with gain over one at this + + + align:start position:0% +um four with gain over one at this +point okay I think that's that's all I + + align:start position:0% +point okay I think that's that's all I + + + align:start position:0% +point okay I think that's that's all I +had for + + align:start position:0% +had for + + + align:start position:0% +had for +today + + align:start position:0% + + + + align:start position:0% + +than have a l + + align:start position:0% +than have a l + + + align:start position:0% +than have a l +questions yep what's next to try to go + + align:start position:0% +questions yep what's next to try to go + + + align:start position:0% +questions yep what's next to try to go +even higher on the game like because you + + align:start position:0% +even higher on the game like because you + + + align:start position:0% +even higher on the game like because you +know I think a lot of the changes were + + align:start position:0% +know I think a lot of the changes were + + + align:start position:0% +know I think a lot of the changes were +capsule quality Etc and is is there + + align:start position:0% +capsule quality Etc and is is there + + + align:start position:0% +capsule quality Etc and is is there +anything that you're seeing in your new + + align:start position:0% +anything that you're seeing in your new + + + align:start position:0% +anything that you're seeing in your new +Neutron data from this new regime that's + + align:start position:0% +Neutron data from this new regime that's + + + align:start position:0% +Neutron data from this new regime that's +guiding for the + + align:start position:0% +guiding for the + + + align:start position:0% +guiding for the +changes um good + + align:start position:0% +changes um good + + + align:start position:0% +changes um good +question I I don't think there's + + align:start position:0% +question I I don't think there's + + + align:start position:0% +question I I don't think there's +anything super obvious right now + + align:start position:0% + + + + align:start position:0% + +um part of it is um pushing to bigger + + align:start position:0% +um part of it is um pushing to bigger + + + align:start position:0% +um part of it is um pushing to bigger +implosions uh which is not directly + + align:start position:0% +implosions uh which is not directly + + + align:start position:0% +implosions uh which is not directly +related the the neutron data yeah yeah + + align:start position:0% +related the the neutron data yeah yeah + + + align:start position:0% +related the the neutron data yeah yeah +no I don't think there's any like defect + + align:start position:0% +no I don't think there's any like defect + + + align:start position:0% +no I don't think there's any like defect +signatures right now we + + align:start position:0% +signatures right now we + + + align:start position:0% +signatures right now we +go are there any open questions that you + + align:start position:0% +go are there any open questions that you + + + align:start position:0% +go are there any open questions that you +see in the neutron data com out yes + + align:start position:0% +see in the neutron data com out yes + + + align:start position:0% +see in the neutron data com out yes +there's a big one great question so + + align:start position:0% +there's a big one great question so + + + align:start position:0% +there's a big one great question so +actually I talked a lot about Peak up + + align:start position:0% +actually I talked a lot about Peak up + + + align:start position:0% +actually I talked a lot about Peak up +shifts and having even F velocity from + + align:start position:0% +shifts and having even F velocity from + + + align:start position:0% +shifts and having even F velocity from +that so there's two aspects to that + + align:start position:0% +that so there's two aspects to that + + + align:start position:0% +that so there's two aspects to that +there is the Pak shift that's different + + align:start position:0% +there is the Pak shift that's different + + + align:start position:0% +there is the Pak shift that's different +in each of the different lines of site + + align:start position:0% +in each of the different lines of site + + + align:start position:0% +in each of the different lines of site +that's showing us in which Direction the + + align:start position:0% +that's showing us in which Direction the + + + align:start position:0% +that's showing us in which Direction the +implosion is you know taken off in but + + align:start position:0% +implosion is you know taken off in but + + + align:start position:0% +implosion is you know taken off in but +there's also turns out that there is a + + align:start position:0% +there's also turns out that there is a + + + align:start position:0% +there's also turns out that there is a +uniform object that's the same in all + + align:start position:0% +uniform object that's the same in all + + + align:start position:0% +uniform object that's the same in all +isite that's anomalus that's not + + align:start position:0% +isite that's anomalus that's not + + + align:start position:0% +isite that's anomalus that's not +explained by the ion temperature um and + + align:start position:0% +explained by the ion temperature um and + + + align:start position:0% +explained by the ion temperature um and +not explained by the directional + + align:start position:0% +not explained by the directional + + + align:start position:0% +not explained by the directional +velocity and right now it looks like the + + align:start position:0% +velocity and right now it looks like the + + + align:start position:0% +velocity and right now it looks like the +only way to explain that upshift is by + + align:start position:0% +only way to explain that upshift is by + + + align:start position:0% +only way to explain that upshift is by +non-an effects in the fu loss + + align:start position:0% +non-an effects in the fu loss + + + align:start position:0% +non-an effects in the fu loss +distributions uh it's not clear why + + align:start position:0% +distributions uh it's not clear why + + + align:start position:0% +distributions uh it's not clear why +those would arise so so that's + + align:start position:0% +those would arise so so that's + + + align:start position:0% +those would arise so so that's +definitely a big outstanding question of + + align:start position:0% +definitely a big outstanding question of + + + align:start position:0% +definitely a big outstanding question of +that were + + align:start position:0% +that were + + + align:start position:0% +that were +yeah which excites me a lot I like + + align:start position:0% +yeah which excites me a lot I like + + + align:start position:0% +yeah which excites me a lot I like +puzzles \ No newline at end of file diff --git a/QfuVAKCO61M.txt b/QfuVAKCO61M.txt new file mode 100644 index 0000000000000000000000000000000000000000..eb50c51a60db972c153d9c4526f54742848cae77 --- /dev/null +++ b/QfuVAKCO61M.txt @@ -0,0 +1,22483 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu + + align:start position:0% +ocw.mit.edu + + + align:start position:0% +ocw.mit.edu +yeah I will talk in behalf of siss M do + + align:start position:0% +yeah I will talk in behalf of siss M do + + + align:start position:0% +yeah I will talk in behalf of siss M do +he should be here this moment but he had + + align:start position:0% +he should be here this moment but he had + + + align:start position:0% +he should be here this moment but he had +problems in his flight in Chicago he + + align:start position:0% +problems in his flight in Chicago he + + + align:start position:0% +problems in his flight in Chicago he +will be arriving a bit later today + + align:start position:0% +will be arriving a bit later today + + + align:start position:0% +will be arriving a bit later today +so er he's not with us this + + align:start position:0% +so er he's not with us this + + + align:start position:0% +so er he's not with us this +moment no problem this day was planed + + align:start position:0% +moment no problem this day was planed + + + align:start position:0% +moment no problem this day was planed +for my + + align:start position:0% +for my + + + align:start position:0% +for my +responsibility I with Claudia + + align:start position:0% +responsibility I with Claudia + + + align:start position:0% +responsibility I with Claudia +canipa + + align:start position:0% +canipa + + + align:start position:0% +canipa +and the next day will + + align:start position:0% + + + + align:start position:0% + +be but under the responsibility + + align:start position:0% +be but under the responsibility + + + align:start position:0% +be but under the responsibility +responsibility of + + align:start position:0% +responsibility of + + + align:start position:0% +responsibility of +ciss okay and he will be + + align:start position:0% +ciss okay and he will be + + + align:start position:0% +ciss okay and he will be +here and the course is about refective + + align:start position:0% + + + + align:start position:0% + +practice I will not introduce a this + + align:start position:0% +practice I will not introduce a this + + + align:start position:0% +practice I will not introduce a this +moment of reflective practice but only + + align:start position:0% +moment of reflective practice but only + + + align:start position:0% +moment of reflective practice but only +the course in + + align:start position:0% +the course in + + + align:start position:0% +the course in +itself we will + + align:start position:0% + + + + align:start position:0% + +be we we have 10 + + align:start position:0% +be we we have 10 + + + align:start position:0% +be we we have 10 +days we have a format each day we have a + + align:start position:0% +days we have a format each day we have a + + + align:start position:0% +days we have a format each day we have a +brief introduction to each theme and + + align:start position:0% +brief introduction to each theme and + + + align:start position:0% +brief introduction to each theme and +exercise and after that an analysis of + + align:start position:0% +exercise and after that an analysis of + + + align:start position:0% +exercise and after that an analysis of +the exercise the analysis of the + + align:start position:0% +the exercise the analysis of the + + + align:start position:0% +the exercise the analysis of the +exercise will be the most + + align:start position:0% +exercise will be the most + + + align:start position:0% +exercise will be the most +important part of the + + align:start position:0% +important part of the + + + align:start position:0% +important part of the +course so we can go to the + + align:start position:0% +course so we can go to the + + + align:start position:0% +course so we can go to the +conceptual elements at the end of each + + align:start position:0% +conceptual elements at the end of each + + + align:start position:0% +conceptual elements at the end of each +day uh the course itself will have three + + align:start position:0% +day uh the course itself will have three + + + align:start position:0% +day uh the course itself will have three +three main + + align:start position:0% +three main + + + align:start position:0% +three main +parts this week is an introduction to + + align:start position:0% +parts this week is an introduction to + + + align:start position:0% +parts this week is an introduction to +the refle practice + + align:start position:0% +the refle practice + + + align:start position:0% +the refle practice +how sean conceived this approach and the + + align:start position:0% +how sean conceived this approach and the + + + align:start position:0% +how sean conceived this approach and the +main characteristic of + + align:start position:0% +main characteristic of + + + align:start position:0% +main characteristic of +it in the next week second week we will + + align:start position:0% +it in the next week second week we will + + + align:start position:0% +it in the next week second week we will +have two parts one + + align:start position:0% +have two parts one + + + align:start position:0% +have two parts one +is about how to apply this method in + + align:start position:0% +is about how to apply this method in + + + align:start position:0% +is about how to apply this method in +some + + align:start position:0% +some + + + align:start position:0% +some +situations basically + + align:start position:0% +situations basically + + + align:start position:0% +situations basically +in policies and in + + align:start position:0% +in policies and in + + + align:start position:0% +in policies and in +strategies we will try to + + align:start position:0% +strategies we will try to + + + align:start position:0% +strategies we will try to +use the method + + align:start position:0% +use the method + + + align:start position:0% +use the method +for to solve controversies and to + + align:start position:0% +for to solve controversies and to + + + align:start position:0% +for to solve controversies and to +improve creativity in the + + align:start position:0% +improve creativity in the + + + align:start position:0% +improve creativity in the +strategies and the second part of the + + align:start position:0% +strategies and the second part of the + + + align:start position:0% +strategies and the second part of the +second week will be about the + + align:start position:0% +second week will be about the + + + align:start position:0% +second week will be about the +future the work of show is 20 years + + align:start position:0% +future the work of show is 20 years + + + align:start position:0% +future the work of show is 20 years +old and after him a lot of people have + + align:start position:0% +old and after him a lot of people have + + + align:start position:0% +old and after him a lot of people have +made + + align:start position:0% +made + + + align:start position:0% +made +some developments that can enhance his + + align:start position:0% +some developments that can enhance his + + + align:start position:0% +some developments that can enhance his +approach + + align:start position:0% +approach + + + align:start position:0% +approach +and the effort is to to give you a + + align:start position:0% +and the effort is to to give you a + + + align:start position:0% +and the effort is to to give you a +perspective about the new methods that + + align:start position:0% +perspective about the new methods that + + + align:start position:0% +perspective about the new methods that +are emerging now and how they are + + align:start position:0% +are emerging now and how they are + + + align:start position:0% +are emerging now and how they are +connected with reflective + + align:start position:0% +connected with reflective + + + align:start position:0% +connected with reflective +practice indeed + + align:start position:0% +practice indeed + + + align:start position:0% +practice indeed +it's very impressive that he was able to + + align:start position:0% +it's very impressive that he was able to + + + align:start position:0% +it's very impressive that he was able to +to conceive this method + + align:start position:0% +to conceive this method + + + align:start position:0% +to conceive this method +so so timely so adequate adequated for + + align:start position:0% +so so timely so adequate adequated for + + + align:start position:0% +so so timely so adequate adequated for +the 20 first + + align:start position:0% +the 20 first + + + align:start position:0% +the 20 first +Century I think that I hope that at the + + align:start position:0% +Century I think that I hope that at the + + + align:start position:0% +Century I think that I hope that at the +end this will be clear for for all the + + align:start position:0% +end this will be clear for for all the + + + align:start position:0% +end this will be clear for for all the +participants + + align:start position:0% +participants + + + align:start position:0% +participants +and I think that I we should present + + align:start position:0% +and I think that I we should present + + + align:start position:0% +and I think that I we should present +ourselves + + align:start position:0% +ourselves + + + align:start position:0% +ourselves +no my name is Sebastian + + align:start position:0% +no my name is Sebastian + + + align:start position:0% +no my name is Sebastian +fera I am + + align:start position:0% +fera I am + + + align:start position:0% +fera I am +Brazilian I + + align:start position:0% +Brazilian I + + + align:start position:0% +Brazilian I +am I have been working for 36 years in + + align:start position:0% +am I have been working for 36 years in + + + align:start position:0% +am I have been working for 36 years in +development + + align:start position:0% +development + + + align:start position:0% +development +in South America at the beginning after + + align:start position:0% +in South America at the beginning after + + + align:start position:0% +in South America at the beginning after +that in Latin America in + + align:start position:0% +that in Latin America in + + + align:start position:0% +that in Latin America in +general + + align:start position:0% +general + + + align:start position:0% +general +and I + + align:start position:0% +and I + + + align:start position:0% +and I +my I preparation was in physics + + align:start position:0% +my I preparation was in physics + + + align:start position:0% +my I preparation was in physics +physics but I was not working in that + + align:start position:0% +physics but I was not working in that + + + align:start position:0% +physics but I was not working in that +for a long very long + + align:start position:0% +for a long very long + + + align:start position:0% +for a long very long +time + + align:start position:0% + + + + align:start position:0% + +uh I think that is all you + + align:start position:0% +uh I think that is all you + + + align:start position:0% +uh I think that is all you +and all the work you've done in + + align:start position:0% +and all the work you've done in + + + align:start position:0% +and all the work you've done in +Knowledge Management for 20 years you + + align:start position:0% +Knowledge Management for 20 years you + + + align:start position:0% +Knowledge Management for 20 years you +forgot about that uh yes I have been my + + align:start position:0% +forgot about that uh yes I have been my + + + align:start position:0% +forgot about that uh yes I have been my +work was help people to organize their + + align:start position:0% +work was help people to organize their + + + align:start position:0% +work was help people to organize their +knowledge to make + + align:start position:0% +knowledge to make + + + align:start position:0% +knowledge to make +decisions I have been make doing plans + + align:start position:0% +decisions I have been make doing plans + + + align:start position:0% +decisions I have been make doing plans +of cities plans of companies plans of + + align:start position:0% +of cities plans of companies plans of + + + align:start position:0% +of cities plans of companies plans of +Institutions and I was not using my + + align:start position:0% +Institutions and I was not using my + + + align:start position:0% +Institutions and I was not using my +knowledge but most of all the knowledge + + align:start position:0% +knowledge but most of all the knowledge + + + align:start position:0% +knowledge but most of all the knowledge +people have so my effort have been to + + align:start position:0% +people have so my effort have been to + + + align:start position:0% +people have so my effort have been to +help people to be aware of the knowledge + + align:start position:0% +help people to be aware of the knowledge + + + align:start position:0% +help people to be aware of the knowledge +they have about the issue they are + + align:start position:0% +they have about the issue they are + + + align:start position:0% +they have about the issue they are +working with and to organize this + + align:start position:0% +working with and to organize this + + + align:start position:0% +working with and to organize this +knowledge for making + + align:start position:0% +knowledge for making + + + align:start position:0% +knowledge for making +decisions thank + + align:start position:0% +decisions thank + + + align:start position:0% +decisions thank +you and seasal is a visiting scholar at + + align:start position:0% +you and seasal is a visiting scholar at + + + align:start position:0% +you and seasal is a visiting scholar at +the center for reflective Community + + align:start position:0% +the center for reflective Community + + + align:start position:0% +the center for reflective Community +Practice um and I think it would it's + + align:start position:0% +Practice um and I think it would it's + + + align:start position:0% +Practice um and I think it would it's +you have a there's this interesting + + align:start position:0% +you have a there's this interesting + + + align:start position:0% +you have a there's this interesting +story about how he became connected to + + align:start position:0% +story about how he became connected to + + + align:start position:0% +story about how he became connected to +CR CP and how he came across uh Caesar + + align:start position:0% +CR CP and how he came across uh Caesar + + + align:start position:0% +CR CP and how he came across uh Caesar +mdow um I don't know if you want to tell + + align:start position:0% +mdow um I don't know if you want to tell + + + align:start position:0% +mdow um I don't know if you want to tell +the story before I go into why who I am + + align:start position:0% +the story before I go into why who I am + + + align:start position:0% +the story before I go into why who I am +all that do you want to okay I can after + + align:start position:0% +all that do you want to okay I can after + + + align:start position:0% +all that do you want to okay I can after +that you can okay I was designed the + + align:start position:0% +that you can okay I was designed the + + + align:start position:0% +that you can okay I was designed the +knowledge management system for care in + + align:start position:0% +knowledge management system for care in + + + align:start position:0% +knowledge management system for care in +Latino America some years ago and I was + + align:start position:0% +Latino America some years ago and I was + + + align:start position:0% +Latino America some years ago and I was +looking for who in the world was used + + align:start position:0% +looking for who in the world was used + + + align:start position:0% +looking for who in the world was used +with with reflective practice because I + + align:start position:0% +with with reflective practice because I + + + align:start position:0% +with with reflective practice because I +was very convinced + + align:start position:0% +was very convinced + + + align:start position:0% +was very convinced +that reflective practice is a cognitive + + align:start position:0% +that reflective practice is a cognitive + + + align:start position:0% +that reflective practice is a cognitive +to that's very important for people who + + align:start position:0% +to that's very important for people who + + + align:start position:0% +to that's very important for people who +are in the ground who cannot base their + + align:start position:0% +are in the ground who cannot base their + + + align:start position:0% +are in the ground who cannot base their +decision on what they have studied in + + align:start position:0% +decision on what they have studied in + + + align:start position:0% +decision on what they have studied in +the + + align:start position:0% +the + + + align:start position:0% +the +University so it's it required to be + + align:start position:0% +University so it's it required to be + + + align:start position:0% +University so it's it required to be +much + + align:start position:0% +much + + + align:start position:0% +much +more in control of their analytic + + align:start position:0% +more in control of their analytic + + + align:start position:0% +more in control of their analytic +methods so for care I was looking for + + align:start position:0% +methods so for care I was looking for + + + align:start position:0% +methods so for care I was looking for +people who knows about reflective + + align:start position:0% +people who knows about reflective + + + align:start position:0% +people who knows about reflective +practice I went to to the internet I + + align:start position:0% +practice I went to to the internet I + + + align:start position:0% +practice I went to to the internet I +found a center + + align:start position:0% +found a center + + + align:start position:0% +found a center +no here in MIT directed + + align:start position:0% +no here in MIT directed + + + align:start position:0% +no here in MIT directed +by Don Mr C mdo and I tried to connect + + align:start position:0% +by Don Mr C mdo and I tried to connect + + + align:start position:0% +by Don Mr C mdo and I tried to connect +him with care we organized a knowledge + + align:start position:0% +him with care we organized a knowledge + + + align:start position:0% +him with care we organized a knowledge +fair in care in + + align:start position:0% +fair in care in + + + align:start position:0% +fair in care in +194 in in + + align:start position:0% +194 in in + + + align:start position:0% +194 in in +2004 and that time my effort was to + + align:start position:0% +2004 and that time my effort was to + + + align:start position:0% +2004 and that time my effort was to +bring Cesar as a speaker for the fa + + align:start position:0% +bring Cesar as a speaker for the fa + + + align:start position:0% +bring Cesar as a speaker for the fa +however it was not possible and after + + align:start position:0% +however it was not possible and after + + + align:start position:0% +however it was not possible and after +that care her s MD for doing evaluation + + align:start position:0% +that care her s MD for doing evaluation + + + align:start position:0% +that care her s MD for doing evaluation +of the work we have done in Latin + + align:start position:0% +of the work we have done in Latin + + + align:start position:0% +of the work we have done in Latin +America about the fair for preparing the + + align:start position:0% +America about the fair for preparing the + + + align:start position:0% +America about the fair for preparing the +fair and the impact of the fair in the + + align:start position:0% +fair and the impact of the fair in the + + + align:start position:0% +fair and the impact of the fair in the +communities we were was Pro trying to + + align:start position:0% +communities we were was Pro trying to + + + align:start position:0% +communities we were was Pro trying to +help communities to organize their + + align:start position:0% +help communities to organize their + + + align:start position:0% +help communities to organize their +knowledge and to be more + + align:start position:0% +knowledge and to be more + + + align:start position:0% +knowledge and to be more +Innovative to be more resourceful be to + + align:start position:0% +Innovative to be more resourceful be to + + + align:start position:0% +Innovative to be more resourceful be to +be more capable of organize their own + + align:start position:0% +be more capable of organize their own + + + align:start position:0% +be more capable of organize their own +development + + align:start position:0% +development + + + align:start position:0% +development +and San made the evaluation no and after + + align:start position:0% +and San made the evaluation no and after + + + align:start position:0% +and San made the evaluation no and after +the evaluation he invited me to come + + align:start position:0% +the evaluation he invited me to come + + + align:start position:0% +the evaluation he invited me to come +here in the evaluation was Claudia + + align:start position:0% +here in the evaluation was Claudia + + + align:start position:0% +here in the evaluation was Claudia +canipa working with him + + align:start position:0% +canipa working with him + + + align:start position:0% +canipa working with him +and I met her this + + align:start position:0% +and I met her this + + + align:start position:0% +and I met her this +opportunity okay so um this is just to + + align:start position:0% +opportunity okay so um this is just to + + + align:start position:0% +opportunity okay so um this is just to +let you know that you know this course + + align:start position:0% +let you know that you know this course + + + align:start position:0% +let you know that you know this course +is about reflective practice for for you + + align:start position:0% +is about reflective practice for for you + + + align:start position:0% +is about reflective practice for for you +so that you can begin to to practice + + align:start position:0% +so that you can begin to to practice + + + align:start position:0% +so that you can begin to to practice +some of these methods but it's a skill + + align:start position:0% +some of these methods but it's a skill + + + align:start position:0% +some of these methods but it's a skill +that you can teach others and that is + + align:start position:0% +that you can teach others and that is + + + align:start position:0% +that you can teach others and that is +what what seasal and Caesar have + + align:start position:0% +what what seasal and Caesar have + + + align:start position:0% +what what seasal and Caesar have +dedicated their their work to you know + + align:start position:0% +dedicated their their work to you know + + + align:start position:0% +dedicated their their work to you know +that's that's what their expertise is in + + align:start position:0% +that's that's what their expertise is in + + + align:start position:0% +that's that's what their expertise is in +so + + align:start position:0% +so + + + align:start position:0% +so +my my name is Claudia kipa and I um + + align:start position:0% +my my name is Claudia kipa and I um + + + align:start position:0% +my my name is Claudia kipa and I um +graduated from MIT in + + align:start position:0% +graduated from MIT in + + + align:start position:0% +graduated from MIT in +2005 um I was an mCP and + + align:start position:0% +2005 um I was an mCP and + + + align:start position:0% +2005 um I was an mCP and +idrp uh for those folks who are not from + + align:start position:0% +idrp uh for those folks who are not from + + + align:start position:0% +idrp uh for those folks who are not from +MIT we've got two people who are + + align:start position:0% +MIT we've got two people who are + + + align:start position:0% +MIT we've got two people who are +visiting here from care um sitting in + + align:start position:0% +visiting here from care um sitting in + + + align:start position:0% +visiting here from care um sitting in +the back and we'll all introduce + + align:start position:0% +the back and we'll all introduce + + + align:start position:0% +the back and we'll all introduce +ourselves later but um mCP is Masters in + + align:start position:0% +ourselves later but um mCP is Masters in + + + align:start position:0% +ourselves later but um mCP is Masters in +City Planning and idrp is International + + align:start position:0% +City Planning and idrp is International + + + align:start position:0% +City Planning and idrp is International +Development + + align:start position:0% +Development + + + align:start position:0% +Development +um and Regional planning which is a + + align:start position:0% +um and Regional planning which is a + + + align:start position:0% +um and Regional planning which is a +specialization within the master's + + align:start position:0% +specialization within the master's + + + align:start position:0% +specialization within the master's +program um I had the opportunity to to + + align:start position:0% +program um I had the opportunity to to + + + align:start position:0% +program um I had the opportunity to to +work with Bish SEL while I was here who + + align:start position:0% +work with Bish SEL while I was here who + + + align:start position:0% +work with Bish SEL while I was here who +was a a very good friend of Donald Shum + + align:start position:0% +was a a very good friend of Donald Shum + + + align:start position:0% +was a a very good friend of Donald Shum +and so through my work with him I was + + align:start position:0% +and so through my work with him I was + + + align:start position:0% +and so through my work with him I was +able to I didn't even know that this was + + align:start position:0% +able to I didn't even know that this was + + + align:start position:0% +able to I didn't even know that this was +happening but in my thesis work um the + + align:start position:0% +happening but in my thesis work um the + + + align:start position:0% +happening but in my thesis work um the +types of questions that that be would + + align:start position:0% +types of questions that that be would + + + align:start position:0% +types of questions that that be would +make to me the of like I mean the + + align:start position:0% +make to me the of like I mean the + + + align:start position:0% +make to me the of like I mean the +criticisms the the type of Paradigm + + align:start position:0% +criticisms the the type of Paradigm + + + align:start position:0% +criticisms the the type of Paradigm +shifting that he would do with me during + + align:start position:0% +shifting that he would do with me during + + + align:start position:0% +shifting that he would do with me during +the two years that I worked with him um + + align:start position:0% +the two years that I worked with him um + + + align:start position:0% +the two years that I worked with him um +I so I I didn't know that I was going + + align:start position:0% +I so I I didn't know that I was going + + + align:start position:0% +I so I I didn't know that I was going +through that process but um a lot of + + align:start position:0% +through that process but um a lot of + + + align:start position:0% +through that process but um a lot of +what will be talking this course is kind + + align:start position:0% +what will be talking this course is kind + + + align:start position:0% +what will be talking this course is kind +of what what I went through with be and + + align:start position:0% +of what what I went through with be and + + + align:start position:0% +of what what I went through with be and +then later with Caesar when I started + + align:start position:0% +then later with Caesar when I started + + + align:start position:0% +then later with Caesar when I started +working with him on this evaluation of + + align:start position:0% +working with him on this evaluation of + + + align:start position:0% +working with him on this evaluation of +the knowledge fair and uh for care care + + align:start position:0% +the knowledge fair and uh for care care + + + align:start position:0% +the knowledge fair and uh for care care +is a nonprofit organization + + align:start position:0% +is a nonprofit organization + + + align:start position:0% +is a nonprofit organization +uh that does development work um in many + + align:start position:0% +uh that does development work um in many + + + align:start position:0% +uh that does development work um in many +different countries so okay that's + + align:start position:0% +different countries so okay that's + + + align:start position:0% +different countries so okay that's +me we would like you to present + + align:start position:0% +me we would like you to present + + + align:start position:0% +me we would like you to present +yourselves and to explain us the + + align:start position:0% +yourselves and to explain us the + + + align:start position:0% +yourselves and to explain us the +motivation you have to come in into this + + align:start position:0% +motivation you have to come in into this + + + align:start position:0% +motivation you have to come in into this +course it's + + align:start position:0% + + + + align:start position:0% + +possible okay so who are you where do + + align:start position:0% +possible okay so who are you where do + + + align:start position:0% +possible okay so who are you where do +you come from why why are you interested + + align:start position:0% +you come from why why are you interested + + + align:start position:0% +you come from why why are you interested +in this question what do ECT from this + + align:start position:0% +in this question what do ECT from this + + + align:start position:0% +in this question what do ECT from this +course oh and we have one more person + + align:start position:0% +course oh and we have one more person + + + align:start position:0% +course oh and we have one more person +here who we need to present this is + + align:start position:0% +here who we need to present this is + + + align:start position:0% +here who we need to present this is +Janet she's from open + + align:start position:0% +Janet she's from open + + + align:start position:0% +Janet she's from open +courseware uh she's going to be helping + + align:start position:0% +courseware uh she's going to be helping + + + align:start position:0% +courseware uh she's going to be helping +us uh take notes for this course so that + + align:start position:0% +us uh take notes for this course so that + + + align:start position:0% +us uh take notes for this course so that +we can put it up on open course where + + align:start position:0% +we can put it up on open course where + + + align:start position:0% +we can put it up on open course where +and we have someone taking + + align:start position:0% +and we have someone taking + + + align:start position:0% +and we have someone taking +videos I thought before people introduce + + align:start position:0% +videos I thought before people introduce + + + align:start position:0% +videos I thought before people introduce +themselves this might be a good time to + + align:start position:0% +themselves this might be a good time to + + + align:start position:0% +themselves this might be a good time to +you might have seen the sign on the door + + align:start position:0% +you might have seen the sign on the door + + + align:start position:0% +you might have seen the sign on the door +as he came in but as you can see we're + + align:start position:0% +as he came in but as you can see we're + + + align:start position:0% +as he came in but as you can see we're +videotaping the course um of a standard + + align:start position:0% +videotaping the course um of a standard + + + align:start position:0% +videotaping the course um of a standard +thing we say for any videotaping project + + align:start position:0% +thing we say for any videotaping project + + + align:start position:0% +thing we say for any videotaping project +is if you don't want to be in the + + align:start position:0% +is if you don't want to be in the + + + align:start position:0% +is if you don't want to be in the +videotape for whatever reason um you can + + align:start position:0% +videotape for whatever reason um you can + + + align:start position:0% +videotape for whatever reason um you can +sit in the in the back two rows because + + align:start position:0% +sit in the in the back two rows because + + + align:start position:0% +sit in the in the back two rows because +that won't be covered by the camera um + + align:start position:0% +that won't be covered by the camera um + + + align:start position:0% +that won't be covered by the camera um +and I guess cludia you mentioned + + align:start position:0% +and I guess cludia you mentioned + + + align:start position:0% +and I guess cludia you mentioned +something about how if you say something + + align:start position:0% +something about how if you say something + + + align:start position:0% +something about how if you say something +in class that you're not comfortable + + align:start position:0% +in class that you're not comfortable + + + align:start position:0% +in class that you're not comfortable +with we can probably take that out later + + align:start position:0% +with we can probably take that out later + + + align:start position:0% +with we can probably take that out later +a lot of this is excessive but mostly to + + align:start position:0% +a lot of this is excessive but mostly to + + + align:start position:0% +a lot of this is excessive but mostly to +say this class is being videotaped um if + + align:start position:0% +say this class is being videotaped um if + + + align:start position:0% +say this class is being videotaped um if +and to be aware of that yeah so if + + align:start position:0% +and to be aware of that yeah so if + + + align:start position:0% +and to be aware of that yeah so if +there's anything you don't want + + align:start position:0% +there's anything you don't want + + + align:start position:0% +there's anything you don't want +videotape let us know and we'll take it + + align:start position:0% +videotape let us know and we'll take it + + + align:start position:0% +videotape let us know and we'll take it +out it's + + align:start position:0% +out it's + + + align:start position:0% +out it's +okay so who wants to + + align:start position:0% + + + + align:start position:0% + +start I can start since I'm in the front + + align:start position:0% +start I can start since I'm in the front + + + align:start position:0% +start I can start since I'm in the front +row here um my name is e Goldman I'm a + + align:start position:0% +row here um my name is e Goldman I'm a + + + align:start position:0% +row here um my name is e Goldman I'm a +second year Master's student in City + + align:start position:0% +second year Master's student in City + + + align:start position:0% +second year Master's student in City +Planning um my thesis work is on uh + + align:start position:0% +Planning um my thesis work is on uh + + + align:start position:0% +Planning um my thesis work is on uh +laptop usage and how that affects + + align:start position:0% +laptop usage and how that affects + + + align:start position:0% +laptop usage and how that affects +people's spatial uh Choice decisions and + + align:start position:0% +people's spatial uh Choice decisions and + + + align:start position:0% +people's spatial uh Choice decisions and +um interaction patterns and my thes + + align:start position:0% +um interaction patterns and my thes + + + align:start position:0% +um interaction patterns and my thes +adviser is Bill Porter who also worked + + align:start position:0% +adviser is Bill Porter who also worked + + + align:start position:0% +adviser is Bill Porter who also worked +with Donald sh on uh some projects and + + align:start position:0% +with Donald sh on uh some projects and + + + align:start position:0% +with Donald sh on uh some projects and +so he recommended that I read his book + + align:start position:0% +so he recommended that I read his book + + + align:start position:0% +so he recommended that I read his book +and taking a a quick look at it and U + + align:start position:0% +and taking a a quick look at it and U + + + align:start position:0% +and taking a a quick look at it and U +found it very interesting and thought it + + align:start position:0% +found it very interesting and thought it + + + align:start position:0% +found it very interesting and thought it +might be useful to take the sports and + + align:start position:0% +might be useful to take the sports and + + + align:start position:0% +might be useful to take the sports and +learn a little more about it interested + + align:start position:0% +learn a little more about it interested + + + align:start position:0% +learn a little more about it interested +in the second half and I realized that + + align:start position:0% +in the second half and I realized that + + + align:start position:0% +in the second half and I realized that +it was going to go into detail on the + + align:start position:0% +it was going to go into detail on the + + + align:start position:0% +it was going to go into detail on the +Future Okay than you uh I'm Chris I'm + + align:start position:0% +Future Okay than you uh I'm Chris I'm + + + align:start position:0% +Future Okay than you uh I'm Chris I'm +also a second year mCP uh I have a lot + + align:start position:0% +also a second year mCP uh I have a lot + + + align:start position:0% +also a second year mCP uh I have a lot +of interest in this class um one I just + + align:start position:0% +of interest in this class um one I just + + + align:start position:0% +of interest in this class um one I just +think it's a really interesting + + align:start position:0% +think it's a really interesting + + + align:start position:0% +think it's a really interesting +educational model personally um I don't + + align:start position:0% +educational model personally um I don't + + + align:start position:0% +educational model personally um I don't +think there's enough learning how to + + align:start position:0% +think there's enough learning how to + + + align:start position:0% +think there's enough learning how to +learn that goes on in school um I'm + + align:start position:0% +learn that goes on in school um I'm + + + align:start position:0% +learn that goes on in school um I'm +really interested in how people organize + + align:start position:0% +really interested in how people organize + + + align:start position:0% +really interested in how people organize +their behavior um I'm working my thesis + + align:start position:0% +their behavior um I'm working my thesis + + + align:start position:0% +their behavior um I'm working my thesis +is on environmental leadership um and + + align:start position:0% +is on environmental leadership um and + + + align:start position:0% +is on environmental leadership um and +trying to understand how people can ship + + align:start position:0% +trying to understand how people can ship + + + align:start position:0% +trying to understand how people can ship +the way others sort of engage with + + align:start position:0% +the way others sort of engage with + + + align:start position:0% +the way others sort of engage with +various situations particularly relating + + align:start position:0% +various situations particularly relating + + + align:start position:0% +various situations particularly relating +to the + + align:start position:0% +to the + + + align:start position:0% +to the +environment um and I'm also really + + align:start position:0% +environment um and I'm also really + + + align:start position:0% +environment um and I'm also really +interested in the whole Fifth Discipline + + align:start position:0% +interested in the whole Fifth Discipline + + + align:start position:0% +interested in the whole Fifth Discipline +Peter S movement over at Sloan in the + + align:start position:0% +Peter S movement over at Sloan in the + + + align:start position:0% +Peter S movement over at Sloan in the +organization studies group um and I + + align:start position:0% +organization studies group um and I + + + align:start position:0% +organization studies group um and I +think he draws a lot on reflective + + align:start position:0% +think he draws a lot on reflective + + + align:start position:0% +think he draws a lot on reflective +practice so I thought it' be good he + + align:start position:0% +practice so I thought it' be good he + + + align:start position:0% +practice so I thought it' be good he +coaching okay my name is nikisha Smith + + align:start position:0% +coaching okay my name is nikisha Smith + + + align:start position:0% +coaching okay my name is nikisha Smith +um I'm also mCP student second year um + + align:start position:0% +um I'm also mCP student second year um + + + align:start position:0% +um I'm also mCP student second year um +and last year I went to uh New Orleans + + align:start position:0% +and last year I went to uh New Orleans + + + align:start position:0% +and last year I went to uh New Orleans +and um at during towards the end of the + + align:start position:0% +and um at during towards the end of the + + + align:start position:0% +and um at during towards the end of the +semester um we kind of had a few + + align:start position:0% +semester um we kind of had a few + + + align:start position:0% +semester um we kind of had a few +sessions with Caesar kind of doing some + + align:start position:0% +sessions with Caesar kind of doing some + + + align:start position:0% +sessions with Caesar kind of doing some +trying to do some reflective practice on + + align:start position:0% +trying to do some reflective practice on + + + align:start position:0% +trying to do some reflective practice on +the work that um several of us had done + + align:start position:0% +the work that um several of us had done + + + align:start position:0% +the work that um several of us had done +in New Orleans that were on the ground + + align:start position:0% +in New Orleans that were on the ground + + + align:start position:0% +in New Orleans that were on the ground +there so just um taking this class to um + + align:start position:0% +there so just um taking this class to um + + + align:start position:0% +there so just um taking this class to um +kind of continue that process and um + + align:start position:0% +kind of continue that process and um + + + align:start position:0% +kind of continue that process and um +just to learn how I can apply it you + + align:start position:0% +just to learn how I can apply it you + + + align:start position:0% +just to learn how I can apply it you +know to my practice as a planner um in + + align:start position:0% +know to my practice as a planner um in + + + align:start position:0% +know to my practice as a planner um in +the future okay thank + + align:start position:0% + + + + align:start position:0% + +you I'm Jody oldum and by profession as + + align:start position:0% +you I'm Jody oldum and by profession as + + + align:start position:0% +you I'm Jody oldum and by profession as +a Spanish teacher but I've been working + + align:start position:0% +a Spanish teacher but I've been working + + + align:start position:0% +a Spanish teacher but I've been working +for kater in Latin America for the last + + align:start position:0% +for kater in Latin America for the last + + + align:start position:0% +for kater in Latin America for the last +seven years and was a part of planning + + align:start position:0% +seven years and was a part of planning + + + align:start position:0% +seven years and was a part of planning +for the knowledge bear that we had for + + align:start position:0% +for the knowledge bear that we had for + + + align:start position:0% +for the knowledge bear that we had for +the region and the followup inv + + align:start position:0% +the region and the followup inv + + + align:start position:0% +the region and the followup inv +valuation and given our uh care in Latin + + align:start position:0% +valuation and given our uh care in Latin + + + align:start position:0% +valuation and given our uh care in Latin +America has been working with knowledge + + align:start position:0% +America has been working with knowledge + + + align:start position:0% +America has been working with knowledge +sharing and Knowledge Management and + + align:start position:0% +sharing and Knowledge Management and + + + align:start position:0% +sharing and Knowledge Management and +care as an organization has a new focus + + align:start position:0% +care as an organization has a new focus + + + align:start position:0% +care as an organization has a new focus +on social learning and knowledge sharing + + align:start position:0% +on social learning and knowledge sharing + + + align:start position:0% +on social learning and knowledge sharing +so this class fits on a number of levels + + align:start position:0% +so this class fits on a number of levels + + + align:start position:0% +so this class fits on a number of levels +and we hope to perhaps replicate or use + + align:start position:0% +and we hope to perhaps replicate or use + + + align:start position:0% +and we hope to perhaps replicate or use +part of it uh at + + align:start position:0% +part of it uh at + + + align:start position:0% +part of it uh at +[Music] + + align:start position:0% + + + + align:start position:0% + +Care thank you + + align:start position:0% +Care thank you + + + align:start position:0% +Care thank you +have you finished I have okay uh reaa I + + align:start position:0% +have you finished I have okay uh reaa I + + + align:start position:0% +have you finished I have okay uh reaa I +am also part of care and working Latin + + align:start position:0% +am also part of care and working Latin + + + align:start position:0% +am also part of care and working Latin +americ Caribbean um and again as Jody + + align:start position:0% +americ Caribbean um and again as Jody + + + align:start position:0% +americ Caribbean um and again as Jody +mentioned our purpose here and is to uh + + align:start position:0% +mentioned our purpose here and is to uh + + + align:start position:0% +mentioned our purpose here and is to uh +consider this kind of uh practice for + + align:start position:0% +consider this kind of uh practice for + + + align:start position:0% +consider this kind of uh practice for +our staff that work on various Community + + align:start position:0% +our staff that work on various Community + + + align:start position:0% +our staff that work on various Community +Development projects across the region + + align:start position:0% +Development projects across the region + + + align:start position:0% +Development projects across the region +and how we can work with communities to + + align:start position:0% +and how we can work with communities to + + + align:start position:0% +and how we can work with communities to +um reflect on their knowledge as + + align:start position:0% +um reflect on their knowledge as + + + align:start position:0% +um reflect on their knowledge as +Sebastian mentioned as as well as how + + align:start position:0% +Sebastian mentioned as as well as how + + + align:start position:0% +Sebastian mentioned as as well as how +care itself can improve its own + + align:start position:0% +care itself can improve its own + + + align:start position:0% +care itself can improve its own +practices its own programs uh to have a + + align:start position:0% +practices its own programs uh to have a + + + align:start position:0% +practices its own programs uh to have a +better impact on the lives of of the + + align:start position:0% + + + + align:start position:0% + +poor I'm Kate Thomas I'm a first year + + align:start position:0% +poor I'm Kate Thomas I'm a first year + + + align:start position:0% +poor I'm Kate Thomas I'm a first year +mCP student um originally from + + align:start position:0% +mCP student um originally from + + + align:start position:0% +mCP student um originally from +Chicago so + + align:start position:0% +Chicago so + + + align:start position:0% +Chicago so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um and I think I'm here + + align:start position:0% +um and I think I'm here + + + align:start position:0% +um and I think I'm here +because I missed the consideration of + + align:start position:0% +because I missed the consideration of + + + align:start position:0% +because I missed the consideration of +practice in my study + + align:start position:0% + + + + align:start position:0% + +my name is Austin I'm also in the idrp + + align:start position:0% +my name is Austin I'm also in the idrp + + + align:start position:0% +my name is Austin I'm also in the idrp +bit of D um my research is um + + align:start position:0% +bit of D um my research is um + + + align:start position:0% +bit of D um my research is um +about cities in the developing world + + align:start position:0% +about cities in the developing world + + + align:start position:0% +about cities in the developing world +that are growing particularly fast and + + align:start position:0% +that are growing particularly fast and + + + align:start position:0% +that are growing particularly fast and +how the type of growth that they're + + align:start position:0% +how the type of growth that they're + + + align:start position:0% +how the type of growth that they're +experiencing will may or may not + + align:start position:0% +experiencing will may or may not + + + align:start position:0% +experiencing will may or may not +translate into social + + align:start position:0% +translate into social + + + align:start position:0% +translate into social +instability um I became aware of + + align:start position:0% +instability um I became aware of + + + align:start position:0% +instability um I became aware of +reflective practice I was working in + + align:start position:0% +reflective practice I was working in + + + align:start position:0% +reflective practice I was working in +politics in London for a couple of years + + align:start position:0% +politics in London for a couple of years + + + align:start position:0% +politics in London for a couple of years +and I like I found myself thinking a lot + + align:start position:0% +and I like I found myself thinking a lot + + + align:start position:0% +and I like I found myself thinking a lot +about what I was doing what I saw other + + align:start position:0% +about what I was doing what I saw other + + + align:start position:0% +about what I was doing what I saw other +people doing and then I came into + + align:start position:0% +people doing and then I came into + + + align:start position:0% +people doing and then I came into +contact with an organization called + + align:start position:0% +contact with an organization called + + + align:start position:0% +contact with an organization called +conciliation resources in London that + + align:start position:0% +conciliation resources in London that + + + align:start position:0% +conciliation resources in London that +does conflict resolution and their + + align:start position:0% +does conflict resolution and their + + + align:start position:0% +does conflict resolution and their +director was talking about being a + + align:start position:0% +director was talking about being a + + + align:start position:0% +director was talking about being a +reflective practitioner so I kind of + + align:start position:0% +reflective practitioner so I kind of + + + align:start position:0% +reflective practitioner so I kind of +Googled it and and came across these + + align:start position:0% +Googled it and and came across these + + + align:start position:0% +Googled it and and came across these +books and had a quick look at them and + + align:start position:0% +books and had a quick look at them and + + + align:start position:0% +books and had a quick look at them and +found them interesting but didn't really + + align:start position:0% +found them interesting but didn't really + + + align:start position:0% +found them interesting but didn't really +follow it up + + align:start position:0% +follow it up + + + align:start position:0% +follow it up +and then I saw this course and yeah so + + align:start position:0% +and then I saw this course and yeah so + + + align:start position:0% +and then I saw this course and yeah so +then I thought it would be a nice time + + align:start position:0% +then I thought it would be a nice time + + + align:start position:0% +then I thought it would be a nice time +to follow it + + align:start position:0% +to follow it + + + align:start position:0% +to follow it +up thank you we are presenting ourselves + + align:start position:0% +up thank you we are presenting ourselves + + + align:start position:0% +up thank you we are presenting ourselves +you both arri a bit late can you present + + align:start position:0% +you both arri a bit late can you present + + + align:start position:0% +you both arri a bit late can you present +yourself I'm rilda um I come from the + + align:start position:0% +yourself I'm rilda um I come from the + + + align:start position:0% +yourself I'm rilda um I come from the +Philippines and I basically work with a + + align:start position:0% +Philippines and I basically work with a + + + align:start position:0% +Philippines and I basically work with a +civil society for um around 10 years and + + align:start position:0% +civil society for um around 10 years and + + + align:start position:0% +civil society for um around 10 years and +around 5 years with students teaching + + align:start position:0% +around 5 years with students teaching + + + align:start position:0% +around 5 years with students teaching +um my interest in this course is um when + + align:start position:0% +um my interest in this course is um when + + + align:start position:0% +um my interest in this course is um when +I came here I realized that in my + + align:start position:0% +I came here I realized that in my + + + align:start position:0% +I came here I realized that in my +courses um several of the things that + + align:start position:0% +courses um several of the things that + + + align:start position:0% +courses um several of the things that +professors asked I've actually asked + + align:start position:0% +professors asked I've actually asked + + + align:start position:0% +professors asked I've actually asked +them in the course of my work but the + + align:start position:0% +them in the course of my work but the + + + align:start position:0% +them in the course of my work but the +difference is that um I realize um what + + align:start position:0% +difference is that um I realize um what + + + align:start position:0% +difference is that um I realize um what +colleagues um used to say and this is + + align:start position:0% +colleagues um used to say and this is + + + align:start position:0% +colleagues um used to say and this is +not without offense to um America or + + align:start position:0% +not without offense to um America or + + + align:start position:0% +not without offense to um America or +Europe or to the thinkers + + align:start position:0% +Europe or to the thinkers + + + align:start position:0% +Europe or to the thinkers +um because one of the things they used + + align:start position:0% +um because one of the things they used + + + align:start position:0% +um because one of the things they used +to to say is like um you know um the + + align:start position:0% +to to say is like um you know um the + + + align:start position:0% +to to say is like um you know um the +West uh loves + + align:start position:0% +West uh loves + + + align:start position:0% +West uh loves +to get um buil theories upon our + + align:start position:0% +to get um buil theories upon our + + + align:start position:0% +to get um buil theories upon our +practice from the developing countries + + align:start position:0% +practice from the developing countries + + + align:start position:0% +practice from the developing countries +and there's a realization that um I us I + + align:start position:0% +and there's a realization that um I us I + + + align:start position:0% +and there's a realization that um I us I +used not to really just um think that um + + align:start position:0% +used not to really just um think that um + + + align:start position:0% +used not to really just um think that um +take that Hook Line and Sinker you know + + align:start position:0% +take that Hook Line and Sinker you know + + + align:start position:0% +take that Hook Line and Sinker you know +um because then I thought like um the + + align:start position:0% +um because then I thought like um the + + + align:start position:0% +um because then I thought like um the +westerners are great thinkers but when I + + align:start position:0% +westerners are great thinkers but when I + + + align:start position:0% +westerners are great thinkers but when I +came um there's a bit of questioning + + align:start position:0% +came um there's a bit of questioning + + + align:start position:0% +came um there's a bit of questioning +that I realize that there + + align:start position:0% +that I realize that there + + + align:start position:0% +that I realize that there +must probably is a grain of Truth in + + align:start position:0% +must probably is a grain of Truth in + + + align:start position:0% +must probably is a grain of Truth in +that but the whole difference is the + + align:start position:0% +that but the whole difference is the + + + align:start position:0% +that but the whole difference is the +westerners are good um systematizer of + + align:start position:0% +westerners are good um systematizer of + + + align:start position:0% +westerners are good um systematizer of +knowledge you know of what happens in a + + align:start position:0% +knowledge you know of what happens in a + + + align:start position:0% +knowledge you know of what happens in a +lot of developing countries because then + + align:start position:0% +lot of developing countries because then + + + align:start position:0% +lot of developing countries because then +they ask it in a very the questions I + + align:start position:0% +they ask it in a very the questions I + + + align:start position:0% +they ask it in a very the questions I +realize that the questions I asked + + align:start position:0% +realize that the questions I asked + + + align:start position:0% +realize that the questions I asked +sporadically they are asked here + + align:start position:0% +sporadically they are asked here + + + align:start position:0% +sporadically they are asked here +systematically and they are part of a + + align:start position:0% +systematically and they are part of a + + + align:start position:0% +systematically and they are part of a +body of knowledge + + align:start position:0% +body of knowledge + + + align:start position:0% +body of knowledge +already and and yet + + align:start position:0% +already and and yet + + + align:start position:0% +already and and yet +um also I guess without offense to MIT + + align:start position:0% +um also I guess without offense to MIT + + + align:start position:0% +um also I guess without offense to MIT +and yet I guess when you um have classes + + align:start position:0% +and yet I guess when you um have classes + + + align:start position:0% +and yet I guess when you um have classes +it seems that professors think that you + + align:start position:0% +it seems that professors think that you + + + align:start position:0% +it seems that professors think that you +have never really come from anywhere or + + align:start position:0% +have never really come from anywhere or + + + align:start position:0% +have never really come from anywhere or +any sort of a base experience when you + + align:start position:0% +any sort of a base experience when you + + + align:start position:0% +any sort of a base experience when you +know um I mean so I was thinking like I + + align:start position:0% +know um I mean so I was thinking like I + + + align:start position:0% +know um I mean so I was thinking like I +needed more course actually that is + + align:start position:0% +needed more course actually that is + + + align:start position:0% +needed more course actually that is +sensitive um to the experiences of + + align:start position:0% +sensitive um to the experiences of + + + align:start position:0% +sensitive um to the experiences of +developing countries and helping their + + align:start position:0% +developing countries and helping their + + + align:start position:0% +developing countries and helping their +students actually um what's that develop + + align:start position:0% +students actually um what's that develop + + + align:start position:0% +students actually um what's that develop +from that practice you know a sort of a + + align:start position:0% +from that practice you know a sort of a + + + align:start position:0% +from that practice you know a sort of a +reflection from that practice so that we + + align:start position:0% +reflection from that practice so that we + + + align:start position:0% +reflection from that practice so that we +can actually uh that so that um you can + + align:start position:0% +can actually uh that so that um you can + + + align:start position:0% +can actually uh that so that um you can +actually help us how to put it in some + + align:start position:0% +actually help us how to put it in some + + + align:start position:0% +actually help us how to put it in some +sort of if not as systematized as the + + align:start position:0% +sort of if not as systematized as the + + + align:start position:0% +sort of if not as systematized as the +way you people do it then maybe + + align:start position:0% +way you people do it then maybe + + + align:start position:0% +way you people do it then maybe +something that can help us do that I I + + align:start position:0% +something that can help us do that I I + + + align:start position:0% +something that can help us do that I I +was thinking this is a + + align:start position:0% +was thinking this is a + + + align:start position:0% +was thinking this is a +good um start okay thank you very + + align:start position:0% + + + + align:start position:0% + +much Patricia my name is Patricia aosta + + align:start position:0% +much Patricia my name is Patricia aosta + + + align:start position:0% +much Patricia my name is Patricia aosta +I'm a hum fellow of the SP program this + + align:start position:0% +I'm a hum fellow of the SP program this + + + align:start position:0% +I'm a hum fellow of the SP program this +year um I thought this would be very + + align:start position:0% +year um I thought this would be very + + + align:start position:0% +year um I thought this would be very +useful because my year is about uh P + + align:start position:0% +useful because my year is about uh P + + + align:start position:0% +useful because my year is about uh P +purp purposeful learning that's um what + + align:start position:0% +purp purposeful learning that's um what + + + align:start position:0% +purp purposeful learning that's um what +I've come to do I've come to reflect + + align:start position:0% +I've come to do I've come to reflect + + + align:start position:0% +I've come to do I've come to reflect +upon my practice I'm a architect urban + + align:start position:0% +upon my practice I'm a architect urban + + + align:start position:0% +upon my practice I'm a architect urban +planner I worked 10 years in the B SCH + + align:start position:0% +planner I worked 10 years in the B SCH + + + align:start position:0% +planner I worked 10 years in the B SCH +planning department and um I've been + + align:start position:0% +planning department and um I've been + + + align:start position:0% +planning department and um I've been +manager of the M master plan and uh so + + align:start position:0% +manager of the M master plan and uh so + + + align:start position:0% +manager of the M master plan and uh so +this is my reflective year and so I + + align:start position:0% +this is my reflective year and so I + + + align:start position:0% +this is my reflective year and so I +thought this was + + align:start position:0% +thought this was + + + align:start position:0% +thought this was +very okay thank you very + + align:start position:0% +very okay thank you very + + + align:start position:0% +very okay thank you very +much okay we have a great group really + + align:start position:0% +much okay we have a great group really + + + align:start position:0% +much okay we have a great group really +great group I hope we will be able + + align:start position:0% +great group I hope we will be able + + + align:start position:0% +great group I hope we will be able +to to use our expectation and our + + align:start position:0% +to to use our expectation and our + + + align:start position:0% +to to use our expectation and our +experience + + align:start position:0% +experience + + + align:start position:0% +experience +to + + align:start position:0% +to + + + align:start position:0% +to +to synthesize what we can learn from + + align:start position:0% +to synthesize what we can learn from + + + align:start position:0% +to synthesize what we can learn from +each other this + + align:start position:0% +each other this + + + align:start position:0% +each other this +period okay I I will try to to organize + + align:start position:0% +period okay I I will try to to organize + + + align:start position:0% +period okay I I will try to to organize +some process of + + align:start position:0% +some process of + + + align:start position:0% +some process of +thinking but I will depend a lot of your + + align:start position:0% +thinking but I will depend a lot of your + + + align:start position:0% +thinking but I will depend a lot of your +own effort for going deeper in the + + align:start position:0% +own effort for going deeper in the + + + align:start position:0% +own effort for going deeper in the +analysis and I hope that the this + + align:start position:0% +analysis and I hope that the this + + + align:start position:0% +analysis and I hope that the this +process should be very interactive + + align:start position:0% +process should be very interactive + + + align:start position:0% +process should be very interactive +between us everything you should want to + + align:start position:0% +between us everything you should want to + + + align:start position:0% +between us everything you should want to +discuss we are open to it + + align:start position:0% + + + + align:start position:0% + +and the idea is that we can go as far as + + align:start position:0% +and the idea is that we can go as far as + + + align:start position:0% +and the idea is that we can go as far as +we dare in our analysis + + align:start position:0% +we dare in our analysis + + + align:start position:0% +we dare in our analysis +okay and + + align:start position:0% + + + + align:start position:0% + +now let me see + + align:start position:0% +now let me see + + + align:start position:0% +now let me see +it's the first time I am using a program + + align:start position:0% +it's the first time I am using a program + + + align:start position:0% +it's the first time I am using a program +in my life I never use a program I + + align:start position:0% +in my life I never use a program I + + + align:start position:0% +in my life I never use a program I +always improvise in my activities but I + + align:start position:0% +always improvise in my activities but I + + + align:start position:0% +always improvise in my activities but I +am doing for the first time + + align:start position:0% +am doing for the first time + + + align:start position:0% +am doing for the first time +I'm fing up people who knows me before + + align:start position:0% +I'm fing up people who knows me before + + + align:start position:0% +I'm fing up people who knows me before +knows + + align:start position:0% +knows + + + align:start position:0% +knows +that okay now the syllabus for you the + + align:start position:0% +that okay now the syllabus for you the + + + align:start position:0% +that okay now the syllabus for you the +presentation of the + + align:start position:0% +presentation of the + + + align:start position:0% +presentation of the +syllabus everyone has the sius no I have + + align:start position:0% +syllabus everyone has the sius no I have + + + align:start position:0% +syllabus everyone has the sius no I have +some people who have not + + align:start position:0% + + + + align:start position:0% + +and the materials for you + + align:start position:0% +and the materials for you + + + align:start position:0% +and the materials for you +to + + align:start position:0% + + + + align:start position:0% + +this the the materials the reading + + align:start position:0% +this the the materials the reading + + + align:start position:0% +this the the materials the reading +materials are + + align:start position:0% +materials are + + + align:start position:0% +materials are +organized not exactly day by day but + + align:start position:0% +organized not exactly day by day but + + + align:start position:0% +organized not exactly day by day but +almost foring day by day because the + + align:start position:0% +almost foring day by day because the + + + align:start position:0% +almost foring day by day because the +difference is that if an author is used + + align:start position:0% +difference is that if an author is used + + + align:start position:0% +difference is that if an author is used +in the first day I put all the articles + + align:start position:0% +in the first day I put all the articles + + + align:start position:0% +in the first day I put all the articles +of this author together auor the author + + align:start position:0% +of this author together auor the author + + + align:start position:0% +of this author together auor the author +together okay + + align:start position:0% +together okay + + + align:start position:0% +together okay +but in spite of that it's basically in + + align:start position:0% +but in spite of that it's basically in + + + align:start position:0% +but in spite of that it's basically in +this + + align:start position:0% +this + + + align:start position:0% +this +order we have some articles that we will + + align:start position:0% +order we have some articles that we will + + + align:start position:0% +order we have some articles that we will +give you later it's not complete yet + + align:start position:0% +give you later it's not complete yet + + + align:start position:0% +give you later it's not complete yet +but uh I there is one article there is + + align:start position:0% +but uh I there is one article there is + + + align:start position:0% +but uh I there is one article there is +in + + align:start position:0% +in + + + align:start position:0% +in +Spanish but it's optional for people who + + align:start position:0% +Spanish but it's optional for people who + + + align:start position:0% +Spanish but it's optional for people who +knows Spanish no problem but not + + align:start position:0% +knows Spanish no problem but not + + + align:start position:0% +knows Spanish no problem but not +everyone knows + + align:start position:0% + + + + align:start position:0% + +that let's take a look to + + align:start position:0% +that let's take a look to + + + align:start position:0% +that let's take a look to +the syus + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% + + + + align:start position:0% + +yeah today we will present the course + + align:start position:0% +yeah today we will present the course + + + align:start position:0% +yeah today we will present the course +the + + align:start position:0% +the + + + align:start position:0% +the +methodology I will do a brief + + align:start position:0% +methodology I will do a brief + + + align:start position:0% +methodology I will do a brief +presentation of reflective practice the + + align:start position:0% +presentation of reflective practice the + + + align:start position:0% +presentation of reflective practice the +work of + + align:start position:0% +work of + + + align:start position:0% +work of +Sean we will do an + + align:start position:0% +Sean we will do an + + + align:start position:0% +Sean we will do an +exercise about learning very simple + + align:start position:0% +exercise about learning very simple + + + align:start position:0% +exercise about learning very simple +introd story but after that we will + + align:start position:0% +introd story but after that we will + + + align:start position:0% +introd story but after that we will +discuss about the different kind of + + align:start position:0% +discuss about the different kind of + + + align:start position:0% +discuss about the different kind of +learning strategies of learning each one + + align:start position:0% +learning strategies of learning each one + + + align:start position:0% +learning strategies of learning each one +of us + + align:start position:0% +of us + + + align:start position:0% +of us +have the next + + align:start position:0% +have the next + + + align:start position:0% +have the next +day so the first day is an introduction + + align:start position:0% +day so the first day is an introduction + + + align:start position:0% +day so the first day is an introduction +to learning the second day is in + + align:start position:0% +to learning the second day is in + + + align:start position:0% +to learning the second day is in +introduction to a + + align:start position:0% +introduction to a + + + align:start position:0% +introduction to a +to a reflective + + align:start position:0% +to a reflective + + + align:start position:0% +to a reflective +methodology it will be Cesar mdo who + + align:start position:0% +methodology it will be Cesar mdo who + + + align:start position:0% +methodology it will be Cesar mdo who +will lead the section the second + + align:start position:0% +will lead the section the second + + + align:start position:0% +will lead the section the second +day the reflective meth methodology is a + + align:start position:0% +day the reflective meth methodology is a + + + align:start position:0% +day the reflective meth methodology is a +way for learning to be a reflective + + align:start position:0% +way for learning to be a reflective + + + align:start position:0% +way for learning to be a reflective +practitioner it's a + + align:start position:0% +practitioner it's a + + + align:start position:0% +practitioner it's a +uh one way to to get experience in + + align:start position:0% +uh one way to to get experience in + + + align:start position:0% +uh one way to to get experience in +reflecting and Cesar mdo developed this + + align:start position:0% +reflecting and Cesar mdo developed this + + + align:start position:0% +reflecting and Cesar mdo developed this +methodology he's + + align:start position:0% + + + + align:start position:0% + +very it's very + + align:start position:0% +very it's very + + + align:start position:0% +very it's very +useful he applied imens situations he us + + align:start position:0% +useful he applied imens situations he us + + + align:start position:0% +useful he applied imens situations he us +it in Latin America with us for + + align:start position:0% +it in Latin America with us for + + + align:start position:0% +it in Latin America with us for +evaluating our experience he have been + + align:start position:0% +evaluating our experience he have been + + + align:start position:0% +evaluating our experience he have been +applying here in the United + + align:start position:0% +applying here in the United + + + align:start position:0% +applying here in the United +States and he will make an exercise with + + align:start position:0% +States and he will make an exercise with + + + align:start position:0% +States and he will make an exercise with +the methodology with + + align:start position:0% +the methodology with + + + align:start position:0% +the methodology with +you the object of the exercise will be + + align:start position:0% +you the object of the exercise will be + + + align:start position:0% +you the object of the exercise will be +the experience of you + + align:start position:0% +the experience of you + + + align:start position:0% +the experience of you +today okay tomorrow you will tell + + align:start position:0% +today okay tomorrow you will tell + + + align:start position:0% +today okay tomorrow you will tell +about how you live it this first day of + + align:start position:0% +about how you live it this first day of + + + align:start position:0% +about how you live it this first day of +the course + + align:start position:0% +the course + + + align:start position:0% +the course +and we will use it + + align:start position:0% +and we will use it + + + align:start position:0% +and we will use it +to go through this + + align:start position:0% +to go through this + + + align:start position:0% +to go through this +methodology the third day is about + + align:start position:0% +methodology the third day is about + + + align:start position:0% +methodology the third day is about +knowledge + + align:start position:0% + + + + align:start position:0% + +generation it's interesting + + align:start position:0% +generation it's interesting + + + align:start position:0% +generation it's interesting +because there is a lot of ways for + + align:start position:0% +because there is a lot of ways for + + + align:start position:0% +because there is a lot of ways for +generating knowledge but we are not use + + align:start position:0% +generating knowledge but we are not use + + + align:start position:0% +generating knowledge but we are not use +it with most of them + + align:start position:0% +it with most of them + + + align:start position:0% +it with most of them +officially we use them in our experience + + align:start position:0% +officially we use them in our experience + + + align:start position:0% +officially we use them in our experience +but we have not studied the other + + align:start position:0% +but we have not studied the other + + + align:start position:0% +but we have not studied the other +methods + + align:start position:0% +methods + + + align:start position:0% +methods +this third day we we introduce different + + align:start position:0% +this third day we we introduce different + + + align:start position:0% +this third day we we introduce different +methods for knowledge + + align:start position:0% +methods for knowledge + + + align:start position:0% +methods for knowledge +creation and why the reflective practice + + align:start position:0% +creation and why the reflective practice + + + align:start position:0% +creation and why the reflective practice +is so important for improving our + + align:start position:0% +is so important for improving our + + + align:start position:0% +is so important for improving our +capacity for generating + + align:start position:0% + + + + align:start position:0% + +knowledge + + align:start position:0% + + + + align:start position:0% + +and the first day will be on some + + align:start position:0% +and the first day will be on some + + + align:start position:0% +and the first day will be on some +Concepts that are basics for reflective + + align:start position:0% +Concepts that are basics for reflective + + + align:start position:0% +Concepts that are basics for reflective +practice about theories about knowledge + + align:start position:0% +practice about theories about knowledge + + + align:start position:0% +practice about theories about knowledge +about + + align:start position:0% +about + + + align:start position:0% +about +practice + + align:start position:0% +practice + + + align:start position:0% +practice +and uh we will try + + align:start position:0% +and uh we will try + + + align:start position:0% +and uh we will try +to to get a basic domain + + align:start position:0% +to to get a basic domain + + + align:start position:0% +to to get a basic domain +about the this + + align:start position:0% + + + + align:start position:0% + +approach the last day in the week will + + align:start position:0% +approach the last day in the week will + + + align:start position:0% +approach the last day in the week will +be on Virtual + + align:start position:0% +be on Virtual + + + align:start position:0% +be on Virtual +words we will not talk about + + align:start position:0% + + + + align:start position:0% + +virtual words in the sense that we are + + align:start position:0% +virtual words in the sense that we are + + + align:start position:0% +virtual words in the sense that we are +more used to with it but about virtual + + align:start position:0% +more used to with it but about virtual + + + align:start position:0% +more used to with it but about virtual +words as construct that we do in our + + align:start position:0% +words as construct that we do in our + + + align:start position:0% +words as construct that we do in our +mind for working we always that we are + + align:start position:0% +mind for working we always that we are + + + align:start position:0% +mind for working we always that we are +working we have images in our mind and + + align:start position:0% +working we have images in our mind and + + + align:start position:0% +working we have images in our mind and +we work in a dialogue with these images + + align:start position:0% +we work in a dialogue with these images + + + align:start position:0% +we work in a dialogue with these images +we + + align:start position:0% +we + + + align:start position:0% +we +have and I will explain later about this + + align:start position:0% +have and I will explain later about this + + + align:start position:0% +have and I will explain later about this +but we always are working with this kind + + align:start position:0% +but we always are working with this kind + + + align:start position:0% +but we always are working with this kind +of + + align:start position:0% +of + + + align:start position:0% +of +images + + align:start position:0% +images + + + align:start position:0% +images +and what Sean discovered is that + + align:start position:0% +and what Sean discovered is that + + + align:start position:0% +and what Sean discovered is that +this image is very important for the + + align:start position:0% +this image is very important for the + + + align:start position:0% +this image is very important for the +performance of what we are + + align:start position:0% +performance of what we are + + + align:start position:0% +performance of what we are +doing in his book he analyzed the kind + + align:start position:0% +doing in his book he analyzed the kind + + + align:start position:0% +doing in his book he analyzed the kind +of virtual words that the architect use + + align:start position:0% +of virtual words that the architect use + + + align:start position:0% +of virtual words that the architect use +when they are + + align:start position:0% +when they are + + + align:start position:0% +when they are +dry and + + align:start position:0% +dry and + + + align:start position:0% +dry and +the p analystic p + + align:start position:0% +the p analystic p + + + align:start position:0% +the p analystic p +analyst how it's it's much more abstract + + align:start position:0% +analyst how it's it's much more abstract + + + align:start position:0% +analyst how it's it's much more abstract +the virtual word they use for interpret + + align:start position:0% +the virtual word they use for interpret + + + align:start position:0% +the virtual word they use for interpret +what people + + align:start position:0% +what people + + + align:start position:0% +what people +is is telling to + + align:start position:0% +is is telling to + + + align:start position:0% +is is telling to +them okay no it's okay it's + + align:start position:0% + + + + align:start position:0% + +free okay + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so we are presenting the syllabus + + align:start position:0% +so we are presenting the syllabus + + + align:start position:0% +so we are presenting the syllabus +okay the first day of the second week + + align:start position:0% +okay the first day of the second week + + + align:start position:0% +okay the first day of the second week +will be + + align:start position:0% +will be + + + align:start position:0% +will be +about + + align:start position:0% +about + + + align:start position:0% +about +reframing one of the most important + + align:start position:0% +reframing one of the most important + + + align:start position:0% +reframing one of the most important +operations in reflective practice is the + + align:start position:0% +operations in reflective practice is the + + + align:start position:0% +operations in reflective practice is the +activity of reframing reinking + + align:start position:0% +activity of reframing reinking + + + align:start position:0% +activity of reframing reinking +the the way we are + + align:start position:0% +the the way we are + + + align:start position:0% +the the way we are +understanding it's when we disorganize + + align:start position:0% +understanding it's when we disorganize + + + align:start position:0% +understanding it's when we disorganize +all our IDE our our ideas and to + + align:start position:0% +all our IDE our our ideas and to + + + align:start position:0% +all our IDE our our ideas and to +construct it + + align:start position:0% +construct it + + + align:start position:0% +construct it +again it's very important for to + + align:start position:0% +again it's very important for to + + + align:start position:0% +again it's very important for to +renew our our mind for renewing our + + align:start position:0% +renew our our mind for renewing our + + + align:start position:0% +renew our our mind for renewing our +approach for be able to understand + + align:start position:0% +approach for be able to understand + + + align:start position:0% +approach for be able to understand +the same problem in new + + align:start position:0% + + + + align:start position:0% + +ways it's one of the most important + + align:start position:0% +ways it's one of the most important + + + align:start position:0% +ways it's one of the most important +operation that one professional can do + + align:start position:0% +operation that one professional can do + + + align:start position:0% +operation that one professional can do +for improving his capacity to to solve + + align:start position:0% +for improving his capacity to to solve + + + align:start position:0% +for improving his capacity to to solve +problems most of + + align:start position:0% +problems most of + + + align:start position:0% +problems most of +the difficult problems are not possible + + align:start position:0% +the difficult problems are not possible + + + align:start position:0% +the difficult problems are not possible +to be solved with the approach we are + + align:start position:0% +to be solved with the approach we are + + + align:start position:0% +to be solved with the approach we are +using when we was stud the + + align:start position:0% +using when we was stud the + + + align:start position:0% +using when we was stud the +problem most of the in most of the + + align:start position:0% +problem most of the in most of the + + + align:start position:0% +problem most of the in most of the +situations we have in concrete words for + + align:start position:0% +situations we have in concrete words for + + + align:start position:0% +situations we have in concrete words for +example for poor people in poor + + align:start position:0% +example for poor people in poor + + + align:start position:0% +example for poor people in poor +countries it's impossible for them to to + + align:start position:0% +countries it's impossible for them to to + + + align:start position:0% +countries it's impossible for them to to +develop with with their current frames + + align:start position:0% +develop with with their current frames + + + align:start position:0% +develop with with their current frames +framing the problems the way they are + + align:start position:0% +framing the problems the way they are + + + align:start position:0% +framing the problems the way they are +framing currently is impossible for them + + align:start position:0% +framing currently is impossible for them + + + align:start position:0% +framing currently is impossible for them +to + + align:start position:0% +to + + + align:start position:0% +to +develop if it should be possible they + + align:start position:0% +develop if it should be possible they + + + align:start position:0% +develop if it should be possible they +was + + align:start position:0% +was + + + align:start position:0% +was +developing so it's very important to + + align:start position:0% +developing so it's very important to + + + align:start position:0% +developing so it's very important to +help to help people to + + align:start position:0% +help to help people to + + + align:start position:0% +help to help people to +reframe the way they are analyzing the + + align:start position:0% +reframe the way they are analyzing the + + + align:start position:0% +reframe the way they are analyzing the +problems and the way they are designed + + align:start position:0% +problems and the way they are designed + + + align:start position:0% +problems and the way they are designed +Solutions we will dedicate three days in + + align:start position:0% +Solutions we will dedicate three days in + + + align:start position:0% +Solutions we will dedicate three days in +the next week to this issue the issue of + + align:start position:0% +the next week to this issue the issue of + + + align:start position:0% +the next week to this issue the issue of +reframing the first day will be an + + align:start position:0% +reframing the first day will be an + + + align:start position:0% +reframing the first day will be an +introduction the second day will + + align:start position:0% + + + + align:start position:0% + +be about intractable controversies + + align:start position:0% +be about intractable controversies + + + align:start position:0% +be about intractable controversies +it's we will base in the + + align:start position:0% +it's we will base in the + + + align:start position:0% +it's we will base in the +book written + + align:start position:0% +book written + + + align:start position:0% +book written +by Sean and Martin + + align:start position:0% + + + + align:start position:0% + +rain the third day will be about + + align:start position:0% +rain the third day will be about + + + align:start position:0% +rain the third day will be about +strategic + + align:start position:0% +strategic + + + align:start position:0% +strategic +creativity how we can + + align:start position:0% +creativity how we can + + + align:start position:0% +creativity how we can +innovate for creating new strategy for + + align:start position:0% +innovate for creating new strategy for + + + align:start position:0% +innovate for creating new strategy for +people + + align:start position:0% +people + + + align:start position:0% +people +and + + align:start position:0% +and + + + align:start position:0% +and +the two days at the end of the course + + align:start position:0% +the two days at the end of the course + + + align:start position:0% +the two days at the end of the course +will be one about conceptual + + align:start position:0% +will be one about conceptual + + + align:start position:0% +will be one about conceptual +learning yeah the the effort here will + + align:start position:0% +learning yeah the the effort here will + + + align:start position:0% +learning yeah the the effort here will +be to introduce we you to a new way of + + align:start position:0% +be to introduce we you to a new way of + + + align:start position:0% +be to introduce we you to a new way of +of + + align:start position:0% +of + + + align:start position:0% +of +learning is the learning not only on + + align:start position:0% +learning is the learning not only on + + + align:start position:0% +learning is the learning not only on +techniques or on structor theories but + + align:start position:0% +techniques or on structor theories but + + + align:start position:0% +techniques or on structor theories but +how we can + + align:start position:0% + + + + align:start position:0% + +learn in + + align:start position:0% + + + + align:start position:0% + +about the understanding we have some + + align:start position:0% +about the understanding we have some + + + align:start position:0% +about the understanding we have some +different components of our analytical + + align:start position:0% +different components of our analytical + + + align:start position:0% +different components of our analytical +framework and we can have a more + + align:start position:0% +framework and we can have a more + + + align:start position:0% +framework and we can have a more +flexible mind if we have this kind of + + align:start position:0% +flexible mind if we have this kind of + + + align:start position:0% +flexible mind if we have this kind of +learning and it's the only possibility I + + align:start position:0% +learning and it's the only possibility I + + + align:start position:0% +learning and it's the only possibility I +think for one to to modernize to update + + align:start position:0% +think for one to to modernize to update + + + align:start position:0% +think for one to to modernize to update +our mind at the pace of the world is + + align:start position:0% +our mind at the pace of the world is + + + align:start position:0% +our mind at the pace of the world is +changing we will talk about why some + + align:start position:0% +changing we will talk about why some + + + align:start position:0% +changing we will talk about why some +professionals get + + align:start position:0% +professionals get + + + align:start position:0% +professionals get +old and are not able to to get the pace + + align:start position:0% +old and are not able to to get the pace + + + align:start position:0% +old and are not able to to get the pace +of the times and they feel tired they + + align:start position:0% +of the times and they feel tired they + + + align:start position:0% +of the times and they feel tired they +feel that they are not enough + + align:start position:0% +feel that they are not enough + + + align:start position:0% +feel that they are not enough +intelligent they make a lot of effort + + align:start position:0% +intelligent they make a lot of effort + + + align:start position:0% +intelligent they make a lot of effort +and when they are just to understand + + align:start position:0% +and when they are just to understand + + + align:start position:0% +and when they are just to understand +something come something new that + + align:start position:0% +something come something new that + + + align:start position:0% +something come something new that +disorganized everything they have just + + align:start position:0% +disorganized everything they have just + + + align:start position:0% +disorganized everything they have just +learned + + align:start position:0% +learned + + + align:start position:0% +learned +and in Latin America I have a lot of + + align:start position:0% +and in Latin America I have a lot of + + + align:start position:0% +and in Latin America I have a lot of +this problem with professionals people + + align:start position:0% +this problem with professionals people + + + align:start position:0% +this problem with professionals people +always crying that they was just + + align:start position:0% +always crying that they was just + + + align:start position:0% +always crying that they was just +beginning to understand something and + + align:start position:0% +beginning to understand something and + + + align:start position:0% +beginning to understand something and +now it's it's out of + + align:start position:0% +now it's it's out of + + + align:start position:0% +now it's it's out of +date and they will need to learn + + align:start position:0% +date and they will need to learn + + + align:start position:0% +date and they will need to learn +everything + + align:start position:0% +everything + + + align:start position:0% +everything +again this problem is very + + align:start position:0% +again this problem is very + + + align:start position:0% +again this problem is very +interesting it's more important when + + align:start position:0% +interesting it's more important when + + + align:start position:0% +interesting it's more important when +people get a bit older not 20 in the 20s + + align:start position:0% +people get a bit older not 20 in the 20s + + + align:start position:0% +people get a bit older not 20 in the 20s +but in the 30s and the for this people + + align:start position:0% +but in the 30s and the for this people + + + align:start position:0% +but in the 30s and the for this people +began to feel tired and they give up + + align:start position:0% +began to feel tired and they give up + + + align:start position:0% +began to feel tired and they give up +okay and they began to to read something + + align:start position:0% +okay and they began to to read something + + + align:start position:0% +okay and they began to to read something +interesting in the weekends but they + + align:start position:0% +interesting in the weekends but they + + + align:start position:0% +interesting in the weekends but they +begin to feel that they are not living + + align:start position:0% +begin to feel that they are not living + + + align:start position:0% +begin to feel that they are not living +the current times we will talk about + + align:start position:0% +the current times we will talk about + + + align:start position:0% +the current times we will talk about +this conceptual learning the way to to + + align:start position:0% +this conceptual learning the way to to + + + align:start position:0% +this conceptual learning the way to to +to get to renew our mind in the pace of + + align:start position:0% +to get to renew our mind in the pace of + + + align:start position:0% +to get to renew our mind in the pace of +the change + + align:start position:0% +the change + + + align:start position:0% +the change +and the the last thing the last day will + + align:start position:0% +and the the last thing the last day will + + + align:start position:0% +and the the last thing the last day will +be + + align:start position:0% +be + + + align:start position:0% +be +on what are the future of this effort of + + align:start position:0% +on what are the future of this effort of + + + align:start position:0% +on what are the future of this effort of +knowledge Creation in the + + align:start position:0% +knowledge Creation in the + + + align:start position:0% +knowledge Creation in the +world + + align:start position:0% +world + + + align:start position:0% +world +this + + align:start position:0% +this + + + align:start position:0% +this +open + + align:start position:0% +open + + + align:start position:0% +open +ER processes of knowledge generation and + + align:start position:0% + + + + align:start position:0% + +er how refective practice can be useful + + align:start position:0% +er how refective practice can be useful + + + align:start position:0% +er how refective practice can be useful +in this new + + align:start position:0% +in this new + + + align:start position:0% +in this new +environment okay + + align:start position:0% +environment okay + + + align:start position:0% +environment okay +yeah + + align:start position:0% + + + + align:start position:0% + +uh I don't know if you if you have some + + align:start position:0% +uh I don't know if you if you have some + + + align:start position:0% +uh I don't know if you if you have some +questions comments now that you have a + + align:start position:0% +questions comments now that you have a + + + align:start position:0% +questions comments now that you have a +more not so much clear but a more a bit + + align:start position:0% +more not so much clear but a more a bit + + + align:start position:0% +more not so much clear but a more a bit +Clear Vision of the + + align:start position:0% + + + + align:start position:0% + +course ah I didn't talk about some issue + + align:start position:0% +course ah I didn't talk about some issue + + + align:start position:0% +course ah I didn't talk about some issue +that are relevant no one + + align:start position:0% +that are relevant no one + + + align:start position:0% +that are relevant no one +is + + align:start position:0% +is + + + align:start position:0% +is +how this course will be + + align:start position:0% +how this course will be + + + align:start position:0% +how this course will be +evaluated we will have three elements + + align:start position:0% +evaluated we will have three elements + + + align:start position:0% +evaluated we will have three elements +for + + align:start position:0% +for + + + align:start position:0% +for +evaluating the + + align:start position:0% +evaluating the + + + align:start position:0% +evaluating the +attendance the participation and a brief + + align:start position:0% +attendance the participation and a brief + + + align:start position:0% +attendance the participation and a brief +paper at the end of the + + align:start position:0% +paper at the end of the + + + align:start position:0% +paper at the end of the +course uh and the idea is that + + align:start position:0% + + + + align:start position:0% + +ER I will not put notes I will + + align:start position:0% +ER I will not put notes I will + + + align:start position:0% +ER I will not put notes I will +only put that you have approv it or not + + align:start position:0% +only put that you have approv it or not + + + align:start position:0% +only put that you have approv it or not +path fail uh path fail that's + + align:start position:0% +path fail uh path fail that's + + + align:start position:0% +path fail uh path fail that's +okay okay thank you are each of the + + align:start position:0% +okay okay thank you are each of the + + + align:start position:0% +okay okay thank you are each of the +proportions for the attendance + + align:start position:0% +proportions for the attendance + + + align:start position:0% +proportions for the attendance +participation in the paper equally + + align:start position:0% +participation in the paper equally + + + align:start position:0% +participation in the paper equally +distributed the each are worth one3 or + + align:start position:0% +distributed the each are worth one3 or + + + align:start position:0% +distributed the each are worth one3 or +they wait + + align:start position:0% +they wait + + + align:start position:0% +they wait +to the proportions + + align:start position:0% + + + + align:start position:0% + +it's they have different + + align:start position:0% +it's they have different + + + align:start position:0% +it's they have different +character the attendance is a + + align:start position:0% +character the attendance is a + + + align:start position:0% +character the attendance is a +condition the other two will + + align:start position:0% +condition the other two will + + + align:start position:0% +condition the other two will +be some + + align:start position:0% +be some + + + align:start position:0% +be some +points this moment I have not yet + + align:start position:0% +points this moment I have not yet + + + align:start position:0% +points this moment I have not yet +the decided about the importance but I + + align:start position:0% +the decided about the importance but I + + + align:start position:0% +the decided about the importance but I +think that the participation will be + + align:start position:0% +think that the participation will be + + + align:start position:0% +think that the participation will be +much more important than the paper the + + align:start position:0% +much more important than the paper the + + + align:start position:0% +much more important than the paper the +paper in + + align:start position:0% +paper in + + + align:start position:0% +paper in +is for helping you to organize what you + + align:start position:0% +is for helping you to organize what you + + + align:start position:0% +is for helping you to organize what you +have learned in this process and it will + + align:start position:0% +have learned in this process and it will + + + align:start position:0% +have learned in this process and it will +be very important for me as a feedback + + align:start position:0% +be very important for me as a feedback + + + align:start position:0% +be very important for me as a feedback +but the most important is your + + align:start position:0% +but the most important is your + + + align:start position:0% +but the most important is your +participation in the course it's okay + + align:start position:0% +participation in the course it's okay + + + align:start position:0% +participation in the course it's okay +okay any other + + align:start position:0% + + + + align:start position:0% + +question + + align:start position:0% + + + + align:start position:0% + +no comments feelings + + align:start position:0% + + + + align:start position:0% + +we have three more people huh we have + + align:start position:0% +we have three more people huh we have + + + align:start position:0% +we have three more people huh we have +three more people who have arrived maybe + + align:start position:0% +three more people who have arrived maybe + + + align:start position:0% +three more people who have arrived maybe +they cance them ah + + align:start position:0% +they cance them ah + + + align:start position:0% +they cance them ah +yes yes please okay my name is also a + + align:start position:0% +yes yes please okay my name is also a + + + align:start position:0% +yes yes please okay my name is also a +fellow at the center very pleased to be + + align:start position:0% +fellow at the center very pleased to be + + + align:start position:0% +fellow at the center very pleased to be +here I'm developing a project in nor of + + align:start position:0% +here I'm developing a project in nor of + + + align:start position:0% +here I'm developing a project in nor of +Brazil with the indigenous TR and also + + align:start position:0% + + + + align:start position:0% + +the okay thank you my name is Lee Arrow + + align:start position:0% +the okay thank you my name is Lee Arrow + + + align:start position:0% +the okay thank you my name is Lee Arrow +I'm also a fellow + + align:start position:0% +I'm also a fellow + + + align:start position:0% +I'm also a fellow +commun practice I'm the uh 2006 2007 now + + align:start position:0% +commun practice I'm the uh 2006 2007 now + + + align:start position:0% +commun practice I'm the uh 2006 2007 now +King fellow just coming off of a uh 2 + + align:start position:0% +King fellow just coming off of a uh 2 + + + align:start position:0% +King fellow just coming off of a uh 2 +and A2 year uh employment uh with the + + align:start position:0% +and A2 year uh employment uh with the + + + align:start position:0% +and A2 year uh employment uh with the +center to lead the Boston Community + + align:start position:0% +center to lead the Boston Community + + + align:start position:0% +center to lead the Boston Community +learning project which is a reflective + + align:start position:0% +learning project which is a reflective + + + align:start position:0% +learning project which is a reflective +learning process with uh several Boston + + align:start position:0% +learning process with uh several Boston + + + align:start position:0% +learning process with uh several Boston +neighborhoods Matan um Dorchester uh + + align:start position:0% +neighborhoods Matan um Dorchester uh + + + align:start position:0% +neighborhoods Matan um Dorchester uh +South B and dougle area um I'm also um + + align:start position:0% +South B and dougle area um I'm also um + + + align:start position:0% +South B and dougle area um I'm also um +formerly from New York and actually run + + align:start position:0% +formerly from New York and actually run + + + align:start position:0% +formerly from New York and actually run +including practice in New York for over + + align:start position:0% +including practice in New York for over + + + align:start position:0% +including practice in New York for over +30 years before coming + + align:start position:0% +30 years before coming + + + align:start position:0% +30 years before coming +toate thank you my name + + align:start position:0% +toate thank you my name + + + align:start position:0% +toate thank you my name +is I'm a h fellow in sports uh + + align:start position:0% +is I'm a h fellow in sports uh + + + align:start position:0% +is I'm a h fellow in sports uh +Department um normally I'm in + + align:start position:0% +Department um normally I'm in + + + align:start position:0% +Department um normally I'm in +international business field I'm working + + align:start position:0% +international business field I'm working + + + align:start position:0% +international business field I'm working +on making the trade easy in + + align:start position:0% +on making the trade easy in + + + align:start position:0% +on making the trade easy in +international trade what we call Trade + + align:start position:0% +international trade what we call Trade + + + align:start position:0% +international trade what we call Trade +facilitation so everything comes new so + + align:start position:0% +facilitation so everything comes new so + + + align:start position:0% +facilitation so everything comes new so +we need some new forms of learning so + + align:start position:0% +we need some new forms of learning so + + + align:start position:0% +we need some new forms of learning so +this a kind of rctic practice is a kind + + align:start position:0% +this a kind of rctic practice is a kind + + + align:start position:0% +this a kind of rctic practice is a kind +of learning technique so it will be fun + + align:start position:0% +of learning technique so it will be fun + + + align:start position:0% +of learning technique so it will be fun +for me to follow the + + align:start position:0% +for me to follow the + + + align:start position:0% +for me to follow the +H thank you very + + align:start position:0% + + + + align:start position:0% + +much + + align:start position:0% +much + + + align:start position:0% +much +okay so we can + + align:start position:0% +okay so we can + + + align:start position:0% +okay so we can +begin + + align:start position:0% +begin + + + align:start position:0% +begin +and I would make now a a brief + + align:start position:0% +and I would make now a a brief + + + align:start position:0% +and I would make now a a brief +introduction to reflective + + align:start position:0% +introduction to reflective + + + align:start position:0% +introduction to reflective +practice and after that we will do an + + align:start position:0% +practice and after that we will do an + + + align:start position:0% +practice and after that we will do an +exercise + + align:start position:0% +exercise + + + align:start position:0% +exercise +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is the idea Theory and Art In + + align:start position:0% +so this is the idea Theory and Art In + + + align:start position:0% +so this is the idea Theory and Art In +Action many people thinks that when we + + align:start position:0% +Action many people thinks that when we + + + align:start position:0% +Action many people thinks that when we +are acting we don't think that's not so + + align:start position:0% +are acting we don't think that's not so + + + align:start position:0% +are acting we don't think that's not so +true when we are in the spot of the + + align:start position:0% +true when we are in the spot of the + + + align:start position:0% +true when we are in the spot of the +action we are at the same time we are + + align:start position:0% +action we are at the same time we are + + + align:start position:0% +action we are at the same time we are +thinking we have a lot of images in our + + align:start position:0% +thinking we have a lot of images in our + + + align:start position:0% +thinking we have a lot of images in our +mind we we + + align:start position:0% +mind we we + + + align:start position:0% +mind we we +foresee what will happen we + + align:start position:0% +foresee what will happen we + + + align:start position:0% +foresee what will happen we +act based in this idea we have and we + + align:start position:0% +act based in this idea we have and we + + + align:start position:0% +act based in this idea we have and we +go we not + + align:start position:0% +go we not + + + align:start position:0% +go we not +we we don't put too much attention how + + align:start position:0% +we we don't put too much attention how + + + align:start position:0% +we we don't put too much attention how +we are thinking but we think very + + align:start position:0% +we are thinking but we think very + + + align:start position:0% +we are thinking but we think very +hard the most complex is the problem the + + align:start position:0% +hard the most complex is the problem the + + + align:start position:0% +hard the most complex is the problem the +most hard we think but most of the + + align:start position:0% +most hard we think but most of the + + + align:start position:0% +most hard we think but most of the +thinking is tcid we are + + align:start position:0% +thinking is tcid we are + + + align:start position:0% +thinking is tcid we are +we we don't put attention in it because + + align:start position:0% +we we don't put attention in it because + + + align:start position:0% +we we don't put attention in it because +we are focus in the problem and we don't + + align:start position:0% +we are focus in the problem and we don't + + + align:start position:0% +we are focus in the problem and we don't +remember what we have + + align:start position:0% +remember what we have + + + align:start position:0% +remember what we have +thought + + align:start position:0% +thought + + + align:start position:0% +thought +but the kind of thought we have our mind + + align:start position:0% +but the kind of thought we have our mind + + + align:start position:0% +but the kind of thought we have our mind +at the time we are acting it's very + + align:start position:0% +at the time we are acting it's very + + + align:start position:0% +at the time we are acting it's very +important for the performance what we + + align:start position:0% +important for the performance what we + + + align:start position:0% +important for the performance what we +are + + align:start position:0% +are + + + align:start position:0% +are +doing we will talk about the + + align:start position:0% +doing we will talk about the + + + align:start position:0% +doing we will talk about the +firefighters there's a book about this + + align:start position:0% +firefighters there's a book about this + + + align:start position:0% +firefighters there's a book about this +how they think + + align:start position:0% +how they think + + + align:start position:0% +how they think +when they are + + align:start position:0% +when they are + + + align:start position:0% +when they are +fighting + + align:start position:0% +fighting + + + align:start position:0% +fighting +for to protect lives for to stop the + + align:start position:0% +for to protect lives for to stop the + + + align:start position:0% +for to protect lives for to stop the +fires it's very interesting one author + + align:start position:0% +fires it's very interesting one author + + + align:start position:0% +fires it's very interesting one author +made research with them asking them how + + align:start position:0% +made research with them asking them how + + + align:start position:0% +made research with them asking them how +they think we will talk about this + + align:start position:0% +they think we will talk about this + + + align:start position:0% +they think we will talk about this +later + + align:start position:0% +later + + + align:start position:0% +later +okay reflective + + align:start position:0% +okay reflective + + + align:start position:0% +okay reflective +practice now is + + align:start position:0% + + + + align:start position:0% + +what's the relation between our actions + + align:start position:0% +what's the relation between our actions + + + align:start position:0% +what's the relation between our actions +and our + + align:start position:0% + + + + align:start position:0% + +thinking how we can get back to our + + align:start position:0% +thinking how we can get back to our + + + align:start position:0% +thinking how we can get back to our +experience through + + align:start position:0% +experience through + + + align:start position:0% +experience through +reflection what kind of strategy we + + align:start position:0% +reflection what kind of strategy we + + + align:start position:0% +reflection what kind of strategy we +learning strategy we + + align:start position:0% + + + + align:start position:0% + +use + + align:start position:0% +use + + + align:start position:0% +use +H + + align:start position:0% +H + + + align:start position:0% +H +and why some + + align:start position:0% +and why some + + + align:start position:0% +and why some +some professionals can design much + + align:start position:0% +some professionals can design much + + + align:start position:0% +some professionals can design much +better than + + align:start position:0% + + + + align:start position:0% + +others it's + + align:start position:0% +others it's + + + align:start position:0% +others it's +very it's usual to think about that if + + align:start position:0% +very it's usual to think about that if + + + align:start position:0% +very it's usual to think about that if +one profession One + + align:start position:0% +one profession One + + + align:start position:0% +one profession One +Professional perform better than other + + align:start position:0% +Professional perform better than other + + + align:start position:0% +Professional perform better than other +it's for two + + align:start position:0% +it's for two + + + align:start position:0% +it's for two +reasons we normally think one is because + + align:start position:0% +reasons we normally think one is because + + + align:start position:0% +reasons we normally think one is because +he's well prepared best prepared and he + + align:start position:0% +he's well prepared best prepared and he + + + align:start position:0% +he's well prepared best prepared and he +is smarter more + + align:start position:0% +is smarter more + + + align:start position:0% +is smarter more +intelligent however the these two + + align:start position:0% +intelligent however the these two + + + align:start position:0% +intelligent however the these two +explanation are from the + + align:start position:0% +explanation are from the + + + align:start position:0% +explanation are from the +outside the the real reason + + align:start position:0% +outside the the real reason + + + align:start position:0% +outside the the real reason +is in + + align:start position:0% +is in + + + align:start position:0% +is in +the cognitive tools that he deploys in + + align:start position:0% +the cognitive tools that he deploys in + + + align:start position:0% +the cognitive tools that he deploys in +his mind as he is doing his + + align:start position:0% +his mind as he is doing his + + + align:start position:0% +his mind as he is doing his +work and reflective practice is a way to + + align:start position:0% +work and reflective practice is a way to + + + align:start position:0% +work and reflective practice is a way to +be aware about these cognitive tools + + align:start position:0% +be aware about these cognitive tools + + + align:start position:0% +be aware about these cognitive tools +that we are using in at the same time + + align:start position:0% +that we are using in at the same time + + + align:start position:0% +that we are using in at the same time +that we are + + align:start position:0% +that we are + + + align:start position:0% +that we are +working + + align:start position:0% + + + + align:start position:0% + +okay who created this approach basically + + align:start position:0% +okay who created this approach basically + + + align:start position:0% +okay who created this approach basically +two two + + align:start position:0% +two two + + + align:start position:0% +two two +people Sean and Chris + + align:start position:0% +people Sean and Chris + + + align:start position:0% +people Sean and Chris +arer they was working with + + align:start position:0% +arer they was working with + + + align:start position:0% +arer they was working with +Consultants they was trying to + + align:start position:0% +Consultants they was trying to + + + align:start position:0% +Consultants they was trying to +understand why some + + align:start position:0% +understand why some + + + align:start position:0% +understand why some +Consultants are better than + + align:start position:0% + + + + align:start position:0% + +others and they began to work organized + + align:start position:0% +others and they began to work organized + + + align:start position:0% +others and they began to work organized +this knowledge in in in an approach in + + align:start position:0% +this knowledge in in in an approach in + + + align:start position:0% +this knowledge in in in an approach in +this approach Sean developed this + + align:start position:0% +this approach Sean developed this + + + align:start position:0% +this approach Sean developed this +approach more and made a great effort + + align:start position:0% +approach more and made a great effort + + + align:start position:0% +approach more and made a great effort +for applying this approach here in MIT + + align:start position:0% +for applying this approach here in MIT + + + align:start position:0% +for applying this approach here in MIT +in the in the dasp no the department of + + align:start position:0% +in the in the dasp no the department of + + + align:start position:0% +in the in the dasp no the department of +urban studies and planning + + align:start position:0% +urban studies and planning + + + align:start position:0% +urban studies and planning +for to redesign the + + align:start position:0% +for to redesign the + + + align:start position:0% +for to redesign the +methodology of the Department of for + + align:start position:0% +methodology of the Department of for + + + align:start position:0% +methodology of the Department of for +teaching ecture and for planning + + align:start position:0% +teaching ecture and for planning + + + align:start position:0% +teaching ecture and for planning +and he used a lot of this experience for + + align:start position:0% +and he used a lot of this experience for + + + align:start position:0% +and he used a lot of this experience for +explaining the + + align:start position:0% +explaining the + + + align:start position:0% +explaining the +method in the in his book we we read the + + align:start position:0% +method in the in his book we we read the + + + align:start position:0% +method in the in his book we we read the +first example that he gives is about an + + align:start position:0% +first example that he gives is about an + + + align:start position:0% +first example that he gives is about an +architect designing their + + align:start position:0% +architect designing their + + + align:start position:0% +architect designing their +buildings + + align:start position:0% + + + + align:start position:0% + +and after + + align:start position:0% +and after + + + align:start position:0% +and after +sh many people + + align:start position:0% +sh many people + + + align:start position:0% +sh many people +began to use the + + align:start position:0% +began to use the + + + align:start position:0% +began to use the +approach but until now most of this + + align:start position:0% +approach but until now most of this + + + align:start position:0% +approach but until now most of this +application of the method of of Shan is + + align:start position:0% +application of the method of of Shan is + + + align:start position:0% +application of the method of of Shan is +on + + align:start position:0% +on + + + align:start position:0% +on +reflection the effort of most people who + + align:start position:0% +reflection the effort of most people who + + + align:start position:0% +reflection the effort of most people who +work after Shan was to help them to + + align:start position:0% +work after Shan was to help them to + + + align:start position:0% +work after Shan was to help them to +reflect on their + + align:start position:0% +reflect on their + + + align:start position:0% +reflect on their +work most of the cases after their work + + align:start position:0% + + + + align:start position:0% + +and this is just a small piece of the + + align:start position:0% +and this is just a small piece of the + + + align:start position:0% +and this is just a small piece of the +contribution of Donal + + align:start position:0% + + + + align:start position:0% + +Chan he was + + align:start position:0% +Chan he was + + + align:start position:0% +Chan he was +trying to help people to be aware how we + + align:start position:0% +trying to help people to be aware how we + + + align:start position:0% +trying to help people to be aware how we +think not + + align:start position:0% +think not + + + align:start position:0% +think not +necessarily training people in to get + + align:start position:0% +necessarily training people in to get + + + align:start position:0% +necessarily training people in to get +back to their + + align:start position:0% +back to their + + + align:start position:0% +back to their +experience + + align:start position:0% +experience + + + align:start position:0% +experience +ER for understanding this + + align:start position:0% + + + + align:start position:0% + +experience he was trying to to help me + + align:start position:0% +experience he was trying to to help me + + + align:start position:0% +experience he was trying to to help me +to understand in a different way how + + align:start position:0% +to understand in a different way how + + + align:start position:0% +to understand in a different way how +we use our theories and I will talk a + + align:start position:0% +we use our theories and I will talk a + + + align:start position:0% +we use our theories and I will talk a +bit later about that and + + align:start position:0% +bit later about that and + + + align:start position:0% +bit later about that and +how er we + + align:start position:0% +how er we + + + align:start position:0% +how er we +can learn during the process in + + align:start position:0% + + + + align:start position:0% + +itself the reflection that we can do + + align:start position:0% +itself the reflection that we can do + + + align:start position:0% +itself the reflection that we can do +after the the work is done it's useful + + align:start position:0% +after the the work is done it's useful + + + align:start position:0% +after the the work is done it's useful +for training ourself but not the core of + + align:start position:0% +for training ourself but not the core of + + + align:start position:0% +for training ourself but not the core of +the idea of reflective + + align:start position:0% +the idea of reflective + + + align:start position:0% +the idea of reflective +practice my effort will be + + align:start position:0% +practice my effort will be + + + align:start position:0% +practice my effort will be +to to to try to explain this these + + align:start position:0% +to to to try to explain this these + + + align:start position:0% +to to to try to explain this these +elements would it be safe to say that + + align:start position:0% +elements would it be safe to say that + + + align:start position:0% +elements would it be safe to say that +his work was basically just looking at + + align:start position:0% +his work was basically just looking at + + + align:start position:0% +his work was basically just looking at +self-consciousness just trying trying to + + align:start position:0% +self-consciousness just trying trying to + + + align:start position:0% +self-consciousness just trying trying to +understand our mind basically or bring + + align:start position:0% +understand our mind basically or bring + + + align:start position:0% +understand our mind basically or bring +the subconscious to the conscious yes + + align:start position:0% +the subconscious to the conscious yes + + + align:start position:0% +the subconscious to the conscious yes +yes it's correct it's it's to be able to + + align:start position:0% +yes it's correct it's it's to be able to + + + align:start position:0% +yes it's correct it's it's to be able to +to to see oneself and one's mind at the + + align:start position:0% +to to see oneself and one's mind at the + + + align:start position:0% +to to see oneself and one's mind at the +same time that we are working for + + align:start position:0% +same time that we are working for + + + align:start position:0% +same time that we are working for +understanding how we work we indeed work + + align:start position:0% +understanding how we work we indeed work + + + align:start position:0% +understanding how we work we indeed work +okay the the the the practice of + + align:start position:0% +okay the the the the practice of + + + align:start position:0% +okay the the the the practice of +reflection that we will make tomorrow is + + align:start position:0% +reflection that we will make tomorrow is + + + align:start position:0% +reflection that we will make tomorrow is +useful for training our mind but the + + align:start position:0% +useful for training our mind but the + + + align:start position:0% +useful for training our mind but the +main issue is to be able to observe + + align:start position:0% +main issue is to be able to observe + + + align:start position:0% +main issue is to be able to observe +oneself as we are working and to observe + + align:start position:0% +oneself as we are working and to observe + + + align:start position:0% +oneself as we are working and to observe +other people to to see how they how they + + align:start position:0% +other people to to see how they how they + + + align:start position:0% +other people to to see how they how they +think as they are working it's very + + align:start position:0% +think as they are working it's very + + + align:start position:0% +think as they are working it's very +interesting because we can see two + + align:start position:0% +interesting because we can see two + + + align:start position:0% +interesting because we can see two +things happen at the same time we can + + align:start position:0% +things happen at the same time we can + + + align:start position:0% +things happen at the same time we can +see the people working and we can see + + align:start position:0% +see the people working and we can see + + + align:start position:0% +see the people working and we can see +the people thinking about their work and + + align:start position:0% +the people thinking about their work and + + + align:start position:0% +the people thinking about their work and +we can exract their theories the real + + align:start position:0% +we can exract their theories the real + + + align:start position:0% +we can exract their theories the real +theories they are + + align:start position:0% +theories they are + + + align:start position:0% +theories they are +using it's very instructive for oneself + + align:start position:0% +using it's very instructive for oneself + + + align:start position:0% +using it's very instructive for oneself +because we can establish a dialogue with + + align:start position:0% +because we can establish a dialogue with + + + align:start position:0% +because we can establish a dialogue with +them much more real because it's not + + align:start position:0% +them much more real because it's not + + + align:start position:0% +them much more real because it's not +about their formal ideas it's about the + + align:start position:0% +about their formal ideas it's about the + + + align:start position:0% +about their formal ideas it's about the +the idea they use in their work okay we + + align:start position:0% +the idea they use in their work okay we + + + align:start position:0% +the idea they use in their work okay we +get a much + + align:start position:0% +get a much + + + align:start position:0% +get a much +more real touch with the the persons and + + align:start position:0% +more real touch with the the persons and + + + align:start position:0% +more real touch with the the persons and +and what he's saying what is saying is + + align:start position:0% +and what he's saying what is saying is + + + align:start position:0% +and what he's saying what is saying is +key like the distinction a lot of people + + align:start position:0% +key like the distinction a lot of people + + + align:start position:0% +key like the distinction a lot of people +think that reflective practice is + + align:start position:0% +think that reflective practice is + + + align:start position:0% +think that reflective practice is +reflecting on the actions that you've + + align:start position:0% +reflecting on the actions that you've + + + align:start position:0% +reflecting on the actions that you've +already done and that's just one small + + align:start position:0% +already done and that's just one small + + + align:start position:0% +already done and that's just one small +part of what this really is um and then + + align:start position:0% +part of what this really is um and then + + + align:start position:0% +part of what this really is um and then +one quick thing about professional + + align:start position:0% +one quick thing about professional + + + align:start position:0% +one quick thing about professional +schools Donald shown um talked he + + align:start position:0% +schools Donald shown um talked he + + + align:start position:0% +schools Donald shown um talked he +criticized a lot of the the methods used + + align:start position:0% +criticized a lot of the the methods used + + + align:start position:0% +criticized a lot of the the methods used +in teaching in professional schools was + + align:start position:0% +in teaching in professional schools was + + + align:start position:0% +in teaching in professional schools was +was like he called it the battery model + + align:start position:0% +was like he called it the battery model + + + align:start position:0% +was like he called it the battery model +it's like we're batteries we go to + + align:start position:0% +it's like we're batteries we go to + + + align:start position:0% +it's like we're batteries we go to +school and they fill us up with + + align:start position:0% +school and they fill us up with + + + align:start position:0% +school and they fill us up with +knowledge and then we go out of school + + align:start position:0% +knowledge and then we go out of school + + + align:start position:0% +knowledge and then we go out of school +and was use it up right and he was like + + align:start position:0% +and was use it up right and he was like + + + align:start position:0% +and was use it up right and he was like +no what we need to do is help people + + align:start position:0% +no what we need to do is help people + + + align:start position:0% +no what we need to do is help people +like teach them how to think critically + + align:start position:0% +like teach them how to think critically + + + align:start position:0% +like teach them how to think critically +about how they do work how they do their + + align:start position:0% +about how they do work how they do their + + + align:start position:0% +about how they do work how they do their +own work and how they generate knowledge + + align:start position:0% +own work and how they generate knowledge + + + align:start position:0% +own work and how they generate knowledge +through their work because that's really + + align:start position:0% +through their work because that's really + + + align:start position:0% +through their work because that's really +how they're going to be more effective + + align:start position:0% +how they're going to be more effective + + + align:start position:0% +how they're going to be more effective +once they leave + + align:start position:0% +once they leave + + + align:start position:0% +once they leave +um okay thank + + align:start position:0% +um okay thank + + + align:start position:0% +um okay thank +you we all were trained with this method + + align:start position:0% +you we all were trained with this method + + + align:start position:0% +you we all were trained with this method +okay the technique of rationality we + + align:start position:0% +okay the technique of rationality we + + + align:start position:0% +okay the technique of rationality we +learn a theory we acquire some tools we + + align:start position:0% +learn a theory we acquire some tools we + + + align:start position:0% +learn a theory we acquire some tools we +apply the + + align:start position:0% +apply the + + + align:start position:0% +apply the +Tools in some concrete situation and we + + align:start position:0% +Tools in some concrete situation and we + + + align:start position:0% +Tools in some concrete situation and we +solve the + + align:start position:0% + + + + align:start position:0% + +problem okay this is the reason why we + + align:start position:0% +problem okay this is the reason why we + + + align:start position:0% +problem okay this is the reason why we +go to the university for acquiring these + + align:start position:0% +go to the university for acquiring these + + + align:start position:0% +go to the university for acquiring these +theories and this tools + + align:start position:0% + + + + align:start position:0% + +okay the problem is that in some cases + + align:start position:0% +okay the problem is that in some cases + + + align:start position:0% +okay the problem is that in some cases +the problem is not + + align:start position:0% +the problem is not + + + align:start position:0% +the problem is not +identified or we have the problem but we + + align:start position:0% +identified or we have the problem but we + + + align:start position:0% +identified or we have the problem but we +have not the story for this problem or + + align:start position:0% +have not the story for this problem or + + + align:start position:0% +have not the story for this problem or +as we will see later we may have this + + align:start position:0% +as we will see later we may have this + + + align:start position:0% +as we will see later we may have this +Theory but we may not be able to use + + align:start position:0% +Theory but we may not be able to use + + + align:start position:0% +Theory but we may not be able to use +this Theory + + align:start position:0% +this Theory + + + align:start position:0% +this Theory +adequated + + align:start position:0% +adequated + + + align:start position:0% +adequated +okay let's + + align:start position:0% + + + + align:start position:0% + +go the reflective practice is built on + + align:start position:0% +go the reflective practice is built on + + + align:start position:0% +go the reflective practice is built on +the critic to this + + align:start position:0% +the critic to this + + + align:start position:0% +the critic to this +method + + align:start position:0% + + + + align:start position:0% + +okay should make the CR made the CRS + + align:start position:0% +okay should make the CR made the CRS + + + align:start position:0% +okay should make the CR made the CRS +critics in two + + align:start position:0% +critics in two + + + align:start position:0% +critics in two +components in two + + align:start position:0% +components in two + + + align:start position:0% +components in two +areas one on the applicability of the + + align:start position:0% +areas one on the applicability of the + + + align:start position:0% +areas one on the applicability of the +theory you may have the problem you + + align:start position:0% +theory you may have the problem you + + + align:start position:0% +theory you may have the problem you +may have the theory + + align:start position:0% +may have the theory + + + align:start position:0% +may have the theory +but you may not be able to apply the + + align:start position:0% + + + + align:start position:0% + +theory the is the Dilemma between rigor + + align:start position:0% +theory the is the Dilemma between rigor + + + align:start position:0% +theory the is the Dilemma between rigor +and relevance I will explain a bit later + + align:start position:0% +and relevance I will explain a bit later + + + align:start position:0% +and relevance I will explain a bit later +the other question is the difference + + align:start position:0% +the other question is the difference + + + align:start position:0% +the other question is the difference +between theory in use and spoused Theory + + align:start position:0% +between theory in use and spoused Theory + + + align:start position:0% +between theory in use and spoused Theory +I will explain later what are these two + + align:start position:0% + + + + align:start position:0% + +concepts yes can + + align:start position:0% +concepts yes can + + + align:start position:0% +concepts yes can +yeah + + align:start position:0% + + + + align:start position:0% + +uh if we go to a real + + align:start position:0% + + + + align:start position:0% + +situation I always remember + + align:start position:0% +situation I always remember + + + align:start position:0% +situation I always remember +uh a small town in the highlands in Peru + + align:start position:0% +uh a small town in the highlands in Peru + + + align:start position:0% +uh a small town in the highlands in Peru +it's a very good reference for + + align:start position:0% +it's a very good reference for + + + align:start position:0% +it's a very good reference for +me + + align:start position:0% +me + + + align:start position:0% +me +12,000 fets over the sea level very poor + + align:start position:0% +12,000 fets over the sea level very poor + + + align:start position:0% +12,000 fets over the sea level very poor +people we come in the + + align:start position:0% +people we come in the + + + align:start position:0% +people we come in the +city in a small town not a city just a + + align:start position:0% +city in a small town not a city just a + + + align:start position:0% +city in a small town not a city just a +small town and people are waiting for a + + align:start position:0% +small town and people are waiting for a + + + align:start position:0% +small town and people are waiting for a +solution for their problems they think + + align:start position:0% +solution for their problems they think + + + align:start position:0% +solution for their problems they think +that after three or four days workshop + + align:start position:0% +that after three or four days workshop + + + align:start position:0% +that after three or four days workshop +with them they will find + + align:start position:0% +with them they will find + + + align:start position:0% +with them they will find +the way to get out of poverty and that + + align:start position:0% +the way to get out of poverty and that + + + align:start position:0% +the way to get out of poverty and that +the consultant will be able to to do + + align:start position:0% +the consultant will be able to to do + + + align:start position:0% +the consultant will be able to to do +them this for them no + + align:start position:0% + + + + align:start position:0% + +and the problem is that it's very + + align:start position:0% +and the problem is that it's very + + + align:start position:0% +and the problem is that it's very +difficult to understand the real + + align:start position:0% +difficult to understand the real + + + align:start position:0% +difficult to understand the real +condition they are + + align:start position:0% +condition they are + + + align:start position:0% +condition they are +living it's very hard to indeed no one + + align:start position:0% +living it's very hard to indeed no one + + + align:start position:0% +living it's very hard to indeed no one +knows how they will develop this is the + + align:start position:0% +knows how they will develop this is the + + + align:start position:0% +knows how they will develop this is the +real + + align:start position:0% +real + + + align:start position:0% +real +situation + + align:start position:0% +situation + + + align:start position:0% +situation +and we can use all + + align:start position:0% +and we can use all + + + align:start position:0% +and we can use all +the the material we have learned about + + align:start position:0% +the the material we have learned about + + + align:start position:0% +the the material we have learned about +competitivity about City Planning + + align:start position:0% +competitivity about City Planning + + + align:start position:0% +competitivity about City Planning +about + + align:start position:0% +about + + + align:start position:0% +about +ER how + + align:start position:0% +ER how + + + align:start position:0% +ER how +to to help people to go out from poverty + + align:start position:0% +to to help people to go out from poverty + + + align:start position:0% +to to help people to go out from poverty +but when we have a concrete + + align:start position:0% +but when we have a concrete + + + align:start position:0% +but when we have a concrete +situation all this theories are + + align:start position:0% +situation all this theories are + + + align:start position:0% +situation all this theories are +just + + align:start position:0% +just + + + align:start position:0% +just +ER it's impossible to apply + + align:start position:0% +ER it's impossible to apply + + + align:start position:0% +ER it's impossible to apply +them + + align:start position:0% +them + + + align:start position:0% +them +in this we need to in some way to + + align:start position:0% +in this we need to in some way to + + + align:start position:0% +in this we need to in some way to +combine everything we have in in our + + align:start position:0% +combine everything we have in in our + + + align:start position:0% +combine everything we have in in our +mind and to see what part of each one of + + align:start position:0% +mind and to see what part of each one of + + + align:start position:0% +mind and to see what part of each one of +this this pieces of knowledge + + align:start position:0% +this this pieces of knowledge + + + align:start position:0% +this this pieces of knowledge +theoretical knowledge we have that can + + align:start position:0% +theoretical knowledge we have that can + + + align:start position:0% +theoretical knowledge we have that can +be useful for this group of people + + align:start position:0% +be useful for this group of people + + + align:start position:0% +be useful for this group of people +and we need to construct In This Moment + + align:start position:0% +and we need to construct In This Moment + + + align:start position:0% +and we need to construct In This Moment +an approach for the problem they + + align:start position:0% +an approach for the problem they + + + align:start position:0% +an approach for the problem they +have + + align:start position:0% +have + + + align:start position:0% +have +and + + align:start position:0% +and + + + align:start position:0% +and +if this way to to use the theoretical + + align:start position:0% +if this way to to use the theoretical + + + align:start position:0% +if this way to to use the theoretical +knowledge we have is one of the main + + align:start position:0% +knowledge we have is one of the main + + + align:start position:0% +knowledge we have is one of the main +efforts of Sean + + align:start position:0% +efforts of Sean + + + align:start position:0% +efforts of Sean +to to help us to be more free to use + + align:start position:0% +to to help us to be more free to use + + + align:start position:0% +to to help us to be more free to use +just one approach and to combine + + align:start position:0% +just one approach and to combine + + + align:start position:0% +just one approach and to combine +everything we think that we can + + align:start position:0% +everything we think that we can + + + align:start position:0% +everything we think that we can +use okay + + align:start position:0% +use okay + + + align:start position:0% +use okay +and in at this + + align:start position:0% +and in at this + + + align:start position:0% +and in at this +moment we + + align:start position:0% +moment we + + + align:start position:0% +moment we +we need not only the our professional + + align:start position:0% +we need not only the our professional + + + align:start position:0% +we need not only the our professional +training + + align:start position:0% +training + + + align:start position:0% +training +but our experience our intuition our + + align:start position:0% +but our experience our intuition our + + + align:start position:0% +but our experience our intuition our +feeling about what could work okay + + align:start position:0% +feeling about what could work okay + + + align:start position:0% +feeling about what could work okay +and to for tackling relevant problems we + + align:start position:0% +and to for tackling relevant problems we + + + align:start position:0% +and to for tackling relevant problems we +always need to be much more in artist + + align:start position:0% +always need to be much more in artist + + + align:start position:0% +always need to be much more in artist +than in + + align:start position:0% +than in + + + align:start position:0% +than in +technique + + align:start position:0% +technique + + + align:start position:0% +technique +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay theory in use in the spous + + align:start position:0% +okay theory in use in the spous + + + align:start position:0% +okay theory in use in the spous +theories + + align:start position:0% + + + + align:start position:0% + +and 3 weeks ago I was trying + + align:start position:0% +and 3 weeks ago I was trying + + + align:start position:0% +and 3 weeks ago I was trying +to to design an strategic planning for + + align:start position:0% +to to design an strategic planning for + + + align:start position:0% +to to design an strategic planning for +scientific and Tech and technological + + align:start position:0% +scientific and Tech and technological + + + align:start position:0% +scientific and Tech and technological +development in Peru for the National + + align:start position:0% +development in Peru for the National + + + align:start position:0% +development in Peru for the National +Council of Science and + + align:start position:0% +Council of Science and + + + align:start position:0% +Council of Science and +Technology I met with the scientist for + + align:start position:0% +Technology I met with the scientist for + + + align:start position:0% +Technology I met with the scientist for +talking about this issue how a a small + + align:start position:0% +talking about this issue how a a small + + + align:start position:0% +talking about this issue how a a small +country like Peru + + align:start position:0% +country like Peru + + + align:start position:0% +country like Peru +could ER + + align:start position:0% +could ER + + + align:start position:0% +could ER +evolved ER in this world + + align:start position:0% +evolved ER in this world + + + align:start position:0% +evolved ER in this world +most of the + + align:start position:0% +most of the + + + align:start position:0% +most of the +scientists had an assumption + + align:start position:0% +scientists had an assumption + + + align:start position:0% +scientists had an assumption +that the science should be us it for + + align:start position:0% +that the science should be us it for + + + align:start position:0% +that the science should be us it for +helping the poor people to get out from + + align:start position:0% +helping the poor people to get out from + + + align:start position:0% +helping the poor people to get out from +poverty this was the main idea they have + + align:start position:0% +poverty this was the main idea they have + + + align:start position:0% +poverty this was the main idea they have +in their mind but they was not aware + + align:start position:0% +in their mind but they was not aware + + + align:start position:0% +in their mind but they was not aware +about that they was talking + + align:start position:0% +about that they was talking + + + align:start position:0% +about that they was talking +about + + align:start position:0% + + + + align:start position:0% + +how how to improve the universities how + + align:start position:0% +how how to improve the universities how + + + align:start position:0% +how how to improve the universities how +to improve research how to connect + + align:start position:0% +to improve research how to connect + + + align:start position:0% +to improve research how to connect +research with the companies how to + + align:start position:0% +research with the companies how to + + + align:start position:0% +research with the companies how to +contribute to the + + align:start position:0% +contribute to the + + + align:start position:0% +contribute to the +competition to the competitivity of the + + align:start position:0% +competition to the competitivity of the + + + align:start position:0% +competition to the competitivity of the +companies this was the formal discuss + + align:start position:0% +companies this was the formal discuss + + + align:start position:0% +companies this was the formal discuss +discuss but when we go to when we went + + align:start position:0% +discuss but when we go to when we went + + + align:start position:0% +discuss but when we go to when we went +to + + align:start position:0% +to + + + align:start position:0% +to +the priorities they designed for the + + align:start position:0% +the priorities they designed for the + + + align:start position:0% +the priorities they designed for the +country all the priorities were in + + align:start position:0% +country all the priorities were in + + + align:start position:0% +country all the priorities were in +function to the + + align:start position:0% +function to the + + + align:start position:0% +function to the +most poor people in the country they was + + align:start position:0% +most poor people in the country they was + + + align:start position:0% +most poor people in the country they was +concerned with + + align:start position:0% +concerned with + + + align:start position:0% +concerned with +camit + + align:start position:0% +camit + + + align:start position:0% +camit +cits + + align:start position:0% +cits + + + align:start position:0% +cits +alaka Y Lama alaka + + align:start position:0% + + + + align:start position:0% + +velam llamas + + align:start position:0% + + + + align:start position:0% + +AAS it's a they are camels they live at + + align:start position:0% +AAS it's a they are camels they live at + + + align:start position:0% +AAS it's a they are camels they live at +very high length very very high length + + align:start position:0% +very high length very very high length + + + align:start position:0% +very high length very very high length +Okay 12,000 ft very high and their + + align:start position:0% +Okay 12,000 ft very high and their + + + align:start position:0% +Okay 12,000 ft very high and their +priorities were chalits + + align:start position:0% +priorities were chalits + + + align:start position:0% +priorities were chalits +biodiversity chits + + align:start position:0% +biodiversity chits + + + align:start position:0% +biodiversity chits +biodiversity + + align:start position:0% +biodiversity + + + align:start position:0% +biodiversity +and + + align:start position:0% + + + + align:start position:0% + +Fisheries and these priorities have + + align:start position:0% +Fisheries and these priorities have + + + align:start position:0% +Fisheries and these priorities have +nothing to do with the trends in science + + align:start position:0% +nothing to do with the trends in science + + + align:start position:0% +nothing to do with the trends in science +and technology in the world and they + + align:start position:0% +and technology in the world and they + + + align:start position:0% +and technology in the world and they +were + + align:start position:0% +were + + + align:start position:0% +were +scientists it's very interesting because + + align:start position:0% +scientists it's very interesting because + + + align:start position:0% +scientists it's very interesting because +forly they were able to tell about + + align:start position:0% +forly they were able to tell about + + + align:start position:0% +forly they were able to tell about +science today the trends but in the + + align:start position:0% +science today the trends but in the + + + align:start position:0% +science today the trends but in the +moment they decide their priorities they + + align:start position:0% +moment they decide their priorities they + + + align:start position:0% +moment they decide their priorities they +go to another + + align:start position:0% +go to another + + + align:start position:0% +go to another +framework so they have in their minds + + align:start position:0% +framework so they have in their minds + + + align:start position:0% +framework so they have in their minds +two different scheme for thinking one is + + align:start position:0% +two different scheme for thinking one is + + + align:start position:0% +two different scheme for thinking one is +the formal and the other is the real + + align:start position:0% + + + + align:start position:0% + +okay it's not clear about this um + + align:start position:0% +okay it's not clear about this um + + + align:start position:0% +okay it's not clear about this um +another example another example me give + + align:start position:0% +another example another example me give + + + align:start position:0% +another example another example me give +you another example in in City Planning + + align:start position:0% +you another example in in City Planning + + + align:start position:0% +you another example in in City Planning +um you have a lot of people who will uh + + align:start position:0% +um you have a lot of people who will uh + + + align:start position:0% +um you have a lot of people who will uh +work in developing information systems + + align:start position:0% +work in developing information systems + + + align:start position:0% +work in developing information systems +for city planners so that they can + + align:start position:0% +for city planners so that they can + + + align:start position:0% +for city planners so that they can +better plan Service delivery in in the + + align:start position:0% +better plan Service delivery in in the + + + align:start position:0% +better plan Service delivery in in the +city um and uh if you can have people + + align:start position:0% +city um and uh if you can have people + + + align:start position:0% +city um and uh if you can have people +work really hard at trying to collect + + align:start position:0% +work really hard at trying to collect + + + align:start position:0% +work really hard at trying to collect +the data you know make it as accurate as + + align:start position:0% +the data you know make it as accurate as + + + align:start position:0% +the data you know make it as accurate as +possible as user friendly the the system + + align:start position:0% +possible as user friendly the the system + + + align:start position:0% +possible as user friendly the the system +so people can use it and so people will + + align:start position:0% +so people can use it and so people will + + + align:start position:0% +so people can use it and so people will +talk a lot about about the empowerment + + align:start position:0% +talk a lot about about the empowerment + + + align:start position:0% +talk a lot about about the empowerment +effects of data + + align:start position:0% +effects of data + + + align:start position:0% +effects of data +like um so those are the the spouse + + align:start position:0% +like um so those are the the spouse + + + align:start position:0% +like um so those are the the spouse +theories right + + align:start position:0% +theories right + + + align:start position:0% +theories right +the + + align:start position:0% +the + + + align:start position:0% +the +um but if you if what they don't a more + + align:start position:0% +um but if you if what they don't a more + + + align:start position:0% +um but if you if what they don't a more +subtle assumption or Theory inter use is + + align:start position:0% +subtle assumption or Theory inter use is + + + align:start position:0% +subtle assumption or Theory inter use is +that they they're thinking that if that + + align:start position:0% +that they they're thinking that if that + + + align:start position:0% +that they they're thinking that if that +the problem for Service delivery in a + + align:start position:0% +the problem for Service delivery in a + + + align:start position:0% +the problem for Service delivery in a +city is lack of + + align:start position:0% +city is lack of + + + align:start position:0% +city is lack of +data and they focused they'll focused a + + align:start position:0% +data and they focused they'll focused a + + + align:start position:0% +data and they focused they'll focused a +lot on I mean it's the idea that it's + + align:start position:0% +lot on I mean it's the idea that it's + + + align:start position:0% +lot on I mean it's the idea that it's +like the black box you put + + align:start position:0% +like the black box you put + + + align:start position:0% +like the black box you put +in if you give if you provide the right + + align:start position:0% +in if you give if you provide the right + + + align:start position:0% +in if you give if you provide the right +data then Service delivery will improve + + align:start position:0% +data then Service delivery will improve + + + align:start position:0% +data then Service delivery will improve +and this is I'm thinking more in like + + align:start position:0% +and this is I'm thinking more in like + + + align:start position:0% +and this is I'm thinking more in like +developing world where where you've got + + align:start position:0% +developing world where where you've got + + + align:start position:0% +developing world where where you've got +like cities are growing by 5% per year + + align:start position:0% +like cities are growing by 5% per year + + + align:start position:0% +like cities are growing by 5% per year +and you know so it's it's very volatile + + align:start position:0% +and you know so it's it's very volatile + + + align:start position:0% +and you know so it's it's very volatile +so it's it's interesting that when you + + align:start position:0% +so it's it's interesting that when you + + + align:start position:0% +so it's it's interesting that when you +get some of these technocrats that are + + align:start position:0% +get some of these technocrats that are + + + align:start position:0% +get some of these technocrats that are +really focused on building Information + + align:start position:0% +really focused on building Information + + + align:start position:0% +really focused on building Information +Systems to to make that assumption + + align:start position:0% +Systems to to make that assumption + + + align:start position:0% +Systems to to make that assumption +explicit suddenly they start approaching + + align:start position:0% +explicit suddenly they start approaching + + + align:start position:0% +explicit suddenly they start approaching +their work differently and they realize + + align:start position:0% +their work differently and they realize + + + align:start position:0% +their work differently and they realize +it's not just about collecting data + + align:start position:0% +it's not just about collecting data + + + align:start position:0% +it's not just about collecting data +they're other they other factors that + + align:start position:0% +they're other they other factors that + + + align:start position:0% +they're other they other factors that +are preventing these governments to to + + align:start position:0% +are preventing these governments to to + + + align:start position:0% +are preventing these governments to to +provide the services that are trying to + + align:start position:0% +provide the services that are trying to + + + align:start position:0% +provide the services that are trying to +you know that have I don't know if + + align:start position:0% +you know that have I don't know if + + + align:start position:0% +you know that have I don't know if +that's clear maybe that's not clear and + + align:start position:0% +that's clear maybe that's not clear and + + + align:start position:0% +that's clear maybe that's not clear and +it's about assumptions theory in use is + + align:start position:0% +it's about assumptions theory in use is + + + align:start position:0% +it's about assumptions theory in use is +about assumptions that we use in our + + align:start position:0% +about assumptions that we use in our + + + align:start position:0% +about assumptions that we use in our +work for example in MIT a lot of people + + align:start position:0% +work for example in MIT a lot of people + + + align:start position:0% +work for example in MIT a lot of people +think + + align:start position:0% +think + + + align:start position:0% +think +that if I go to a poor country and I + + align:start position:0% +that if I go to a poor country and I + + + align:start position:0% +that if I go to a poor country and I +help them to innovate their + + align:start position:0% +help them to innovate their + + + align:start position:0% +help them to innovate their +technology they will be + + align:start position:0% +technology they will be + + + align:start position:0% +technology they will be +better okay there's a lot of programs of + + align:start position:0% +better okay there's a lot of programs of + + + align:start position:0% +better okay there's a lot of programs of +of this in MIT okay we can work in the + + align:start position:0% +of this in MIT okay we can work in the + + + align:start position:0% +of this in MIT okay we can work in the +no this is the Assumption the the real + + align:start position:0% +no this is the Assumption the the real + + + align:start position:0% +no this is the Assumption the the real +assumption is + + align:start position:0% +assumption is + + + align:start position:0% +assumption is +that it's a lack of + + align:start position:0% +that it's a lack of + + + align:start position:0% +that it's a lack of +Technology the main reason for + + align:start position:0% +Technology the main reason for + + + align:start position:0% +Technology the main reason for +poverty if I operate on this variable + + align:start position:0% +poverty if I operate on this variable + + + align:start position:0% +poverty if I operate on this variable +everything will work + + align:start position:0% +everything will work + + + align:start position:0% +everything will work +better okay this + + align:start position:0% +better okay this + + + align:start position:0% +better okay this +ISS I think that with this example no we + + align:start position:0% +ISS I think that with this example no we + + + align:start position:0% +ISS I think that with this example no we +get the exposed Theory is the + + align:start position:0% +get the exposed Theory is the + + + align:start position:0% +get the exposed Theory is the +explanation about why we + + align:start position:0% +explanation about why we + + + align:start position:0% +explanation about why we +work this is f of theory is the when + + align:start position:0% +work this is f of theory is the when + + + align:start position:0% +work this is f of theory is the when +someone try ask us how we are working we + + align:start position:0% +someone try ask us how we are working we + + + align:start position:0% +someone try ask us how we are working we +explain how we are working but most of + + align:start position:0% +explain how we are working but most of + + + align:start position:0% +explain how we are working but most of +the cases the way we work and the + + align:start position:0% +the cases the way we work and the + + + align:start position:0% +the cases the way we work and the +explanation that we use are + + align:start position:0% +explanation that we use are + + + align:start position:0% +explanation that we use are +different okay + + align:start position:0% + + + + align:start position:0% + +yeah the question is how to combine this + + align:start position:0% +yeah the question is how to combine this + + + align:start position:0% +yeah the question is how to combine this +part theories and the experience for + + align:start position:0% +part theories and the experience for + + + align:start position:0% +part theories and the experience for +creating Solutions + + align:start position:0% +creating Solutions + + + align:start position:0% +creating Solutions +okay the + + align:start position:0% +okay the + + + align:start position:0% +okay the +awareness okay and how we can be more + + align:start position:0% +awareness okay and how we can be more + + + align:start position:0% +awareness okay and how we can be more +professional in situations that require + + align:start position:0% +professional in situations that require + + + align:start position:0% +professional in situations that require +a lot of after + + align:start position:0% +a lot of after + + + align:start position:0% +a lot of after +three this is a big contribution of + + align:start position:0% +three this is a big contribution of + + + align:start position:0% +three this is a big contribution of +reflective + + align:start position:0% +reflective + + + align:start position:0% +reflective +practice we can improve + + align:start position:0% +practice we can improve + + + align:start position:0% +practice we can improve +our + + align:start position:0% +our + + + align:start position:0% +our +professionalism in concrete situ + + align:start position:0% +professionalism in concrete situ + + + align:start position:0% +professionalism in concrete situ +situations that requires a lot of + + align:start position:0% +situations that requires a lot of + + + align:start position:0% +situations that requires a lot of +creativity a lot of improvisation a lot + + align:start position:0% +creativity a lot of improvisation a lot + + + align:start position:0% +creativity a lot of improvisation a lot +of doing things that we have never we + + align:start position:0% +of doing things that we have never we + + + align:start position:0% +of doing things that we have never we +have never done before how we can be + + align:start position:0% +have never done before how we can be + + + align:start position:0% +have never done before how we can be +more professional in this kind of + + align:start position:0% +more professional in this kind of + + + align:start position:0% +more professional in this kind of +situations and this kind of situation we + + align:start position:0% +situations and this kind of situation we + + + align:start position:0% +situations and this kind of situation we +face every day when we are working in + + align:start position:0% +face every day when we are working in + + + align:start position:0% +face every day when we are working in +the + + align:start position:0% +the + + + align:start position:0% +the +ground okay + + align:start position:0% + + + + align:start position:0% + +this Sean explaining he he made this + + align:start position:0% +this Sean explaining he he made this + + + align:start position:0% +this Sean explaining he he made this +questions no what procedures I'm + + align:start position:0% +questions no what procedures I'm + + + align:start position:0% +questions no what procedures I'm +enacting when I perform this + + align:start position:0% +enacting when I perform this + + + align:start position:0% +enacting when I perform this +skill how I am framing the problem that + + align:start position:0% +skill how I am framing the problem that + + + align:start position:0% +skill how I am framing the problem that +I'm trying to solve + + align:start position:0% +I'm trying to solve + + + align:start position:0% +I'm trying to solve +no + + align:start position:0% + + + + align:start position:0% + +ER this kind of + + align:start position:0% +ER this kind of + + + align:start position:0% +ER this kind of +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +okay + + align:start position:0% +okay + + + align:start position:0% +okay +finally it's about on ship of our + + align:start position:0% +finally it's about on ship of our + + + align:start position:0% +finally it's about on ship of our +knowledge it's very important for us + + align:start position:0% +knowledge it's very important for us + + + align:start position:0% +knowledge it's very important for us +it's much more important for people we + + align:start position:0% +it's much more important for people we + + + align:start position:0% +it's much more important for people we +are working + + align:start position:0% +are working + + + align:start position:0% +are working +with in less developed countries people + + align:start position:0% +with in less developed countries people + + + align:start position:0% +with in less developed countries people +have a lot of + + align:start position:0% +have a lot of + + + align:start position:0% +have a lot of +knowledge that we don't we are not aware + + align:start position:0% +knowledge that we don't we are not aware + + + align:start position:0% +knowledge that we don't we are not aware +about this knowledge we don't recognize + + align:start position:0% +about this knowledge we don't recognize + + + align:start position:0% +about this knowledge we don't recognize +the knowledge they have and if we don't + + align:start position:0% +the knowledge they have and if we don't + + + align:start position:0% +the knowledge they have and if we don't +recognize their knowledge they don't + + align:start position:0% +recognize their knowledge they don't + + + align:start position:0% +recognize their knowledge they don't +recognize their + + align:start position:0% +recognize their + + + align:start position:0% +recognize their +knowledge okay people need + + align:start position:0% +knowledge okay people need + + + align:start position:0% +knowledge okay people need +recognition social recognition formal + + align:start position:0% +recognition social recognition formal + + + align:start position:0% +recognition social recognition formal +recognition one of the most important + + align:start position:0% +recognition one of the most important + + + align:start position:0% +recognition one of the most important +thing we have learned with the knowledge + + align:start position:0% +thing we have learned with the knowledge + + + align:start position:0% +thing we have learned with the knowledge +F we have organized is that to recognize + + align:start position:0% +F we have organized is that to recognize + + + align:start position:0% +F we have organized is that to recognize +the knowledge that people have is very + + align:start position:0% +the knowledge that people have is very + + + align:start position:0% +the knowledge that people have is very +important for them they feel much more + + align:start position:0% +important for them they feel much more + + + align:start position:0% +important for them they feel much more +empowered if they + + align:start position:0% + + + + align:start position:0% + +if some other people external to them + + align:start position:0% +if some other people external to them + + + align:start position:0% +if some other people external to them +help them to recognize their knowledge + + align:start position:0% +help them to recognize their knowledge + + + align:start position:0% +help them to recognize their knowledge +they feel much more strong they can + + align:start position:0% +they feel much more strong they can + + + align:start position:0% +they feel much more strong they can +decide much + + align:start position:0% + + + + align:start position:0% + +better + + align:start position:0% +better + + + align:start position:0% +better +and the one of the main effort of + + align:start position:0% +and the one of the main effort of + + + align:start position:0% +and the one of the main effort of +reflective practice is to help people to + + align:start position:0% +reflective practice is to help people to + + + align:start position:0% +reflective practice is to help people to +get ownership about their + + align:start position:0% +get ownership about their + + + align:start position:0% +get ownership about their +knowledge and for ourself too and F this + + align:start position:0% +knowledge and for ourself too and F this + + + align:start position:0% +knowledge and for ourself too and F this +is finally + + align:start position:0% +is finally + + + align:start position:0% +is finally +it's how to have an evolving + + align:start position:0% +it's how to have an evolving + + + align:start position:0% +it's how to have an evolving +brain so I wasn't + + align:start position:0% +brain so I wasn't + + + align:start position:0% +brain so I wasn't +imagining okay it's the best to have + + align:start position:0% +imagining okay it's the best to have + + + align:start position:0% +imagining okay it's the best to have +known how to get involving + + align:start position:0% +known how to get involving + + + align:start position:0% +known how to get involving +brain if you work always with the same + + align:start position:0% +brain if you work always with the same + + + align:start position:0% +brain if you work always with the same +theories the synapsis and the connection + + align:start position:0% +theories the synapsis and the connection + + + align:start position:0% +theories the synapsis and the connection +is our brain are always the same + + align:start position:0% +is our brain are always the same + + + align:start position:0% +is our brain are always the same +one if we are evolving in our series and + + align:start position:0% +one if we are evolving in our series and + + + align:start position:0% +one if we are evolving in our series and +most of all if we are evolving in the + + align:start position:0% +most of all if we are evolving in the + + + align:start position:0% +most of all if we are evolving in the +concepts we are + + align:start position:0% +concepts we are + + + align:start position:0% +concepts we are +using the concepts are like we will talk + + align:start position:0% +using the concepts are like we will talk + + + align:start position:0% +using the concepts are like we will talk +about this + + align:start position:0% +about this + + + align:start position:0% +about this +later are like neurons the concepts the + + align:start position:0% +later are like neurons the concepts the + + + align:start position:0% +later are like neurons the concepts the +concept is something that have a lot of + + align:start position:0% +concept is something that have a lot of + + + align:start position:0% +concept is something that have a lot of +connection with a lot of things at the + + align:start position:0% +connection with a lot of things at the + + + align:start position:0% +connection with a lot of things at the +time I begin to use a New Concept my + + align:start position:0% +time I begin to use a New Concept my + + + align:start position:0% +time I begin to use a New Concept my +brain begins to use new + + align:start position:0% +brain begins to use new + + + align:start position:0% +brain begins to use new +connections so to evolve conceptually is + + align:start position:0% +connections so to evolve conceptually is + + + align:start position:0% +connections so to evolve conceptually is +a way to evolve our brains okay it's not + + align:start position:0% +a way to evolve our brains okay it's not + + + align:start position:0% +a way to evolve our brains okay it's not +the + + align:start position:0% +the + + + align:start position:0% +the +use ER Source but it's very effective to + + align:start position:0% +use ER Source but it's very effective to + + + align:start position:0% +use ER Source but it's very effective to +for maintaining our brain + + align:start position:0% +for maintaining our brain + + + align:start position:0% +for maintaining our brain +active that's all I think no this is the + + align:start position:0% +active that's all I think no this is the + + + align:start position:0% +active that's all I think no this is the +presentation okay is it's a very brief + + align:start position:0% +presentation okay is it's a very brief + + + align:start position:0% +presentation okay is it's a very brief +introduction I am not trying to be much + + align:start position:0% +introduction I am not trying to be much + + + align:start position:0% +introduction I am not trying to be much +Clear just to give an uh a brief glance + + align:start position:0% +Clear just to give an uh a brief glance + + + align:start position:0% +Clear just to give an uh a brief glance +about what is this reflective practice + + align:start position:0% +about what is this reflective practice + + + align:start position:0% +about what is this reflective practice +yes um as I'm watching this I'm thinking + + align:start position:0% +yes um as I'm watching this I'm thinking + + + align:start position:0% +yes um as I'm watching this I'm thinking +about the the not that my brain is + + align:start position:0% +about the the not that my brain is + + + align:start position:0% +about the the not that my brain is +working that well but I'm trying to put + + align:start position:0% +working that well but I'm trying to put + + + align:start position:0% +working that well but I'm trying to put +it together and reflect and reflect and + + align:start position:0% +it together and reflect and reflect and + + + align:start position:0% +it together and reflect and reflect and +the practice and one of the temp that I + + align:start position:0% +the practice and one of the temp that I + + + align:start position:0% +the practice and one of the temp that I +was thinking it's been thinking a lot + + align:start position:0% +was thinking it's been thinking a lot + + + align:start position:0% +was thinking it's been thinking a lot +about the process the OA did in Africa + + align:start position:0% +about the process the OA did in Africa + + + align:start position:0% +about the process the OA did in Africa +where uh you trying to find a solution + + align:start position:0% +where uh you trying to find a solution + + + align:start position:0% +where uh you trying to find a solution +for a problem outside of the country we + + align:start position:0% +for a problem outside of the country we + + + align:start position:0% +for a problem outside of the country we +40 million $40,000 million dollar + + align:start position:0% +40 million $40,000 million dollar + + + align:start position:0% +40 million $40,000 million dollar +whatever much did invest for + + align:start position:0% +whatever much did invest for + + + align:start position:0% +whatever much did invest for +150 students when we have millions of + + align:start position:0% +150 students when we have millions of + + + align:start position:0% +150 students when we have millions of +students they need to be educated in + + align:start position:0% +students they need to be educated in + + + align:start position:0% +students they need to be educated in +that part of the country and after and I + + align:start position:0% +that part of the country and after and I + + + align:start position:0% +that part of the country and after and I +was thinking to myself as I was reading + + align:start position:0% +was thinking to myself as I was reading + + + align:start position:0% +was thinking to myself as I was reading +uh was I was reading your material uh + + align:start position:0% +uh was I was reading your material uh + + + align:start position:0% +uh was I was reading your material uh +this weekend and it was nice spending + + align:start position:0% +this weekend and it was nice spending + + + align:start position:0% +this weekend and it was nice spending +the weekend with it and also reading + + align:start position:0% +the weekend with it and also reading + + + align:start position:0% +the weekend with it and also reading +about those article people who who take + + align:start position:0% +about those article people who who take + + + align:start position:0% +about those article people who who take +action immediately they you sign this + + align:start position:0% +action immediately they you sign this + + + align:start position:0% +action immediately they you sign this +immediate reaction but it they have the + + align:start position:0% +immediate reaction but it they have the + + + align:start position:0% +immediate reaction but it they have the +power to do that because they either + + align:start position:0% +power to do that because they either + + + align:start position:0% +power to do that because they either +have the money or they have the + + align:start position:0% +have the money or they have the + + + align:start position:0% +have the money or they have the +knowledge but they don't have the + + align:start position:0% +knowledge but they don't have the + + + align:start position:0% +knowledge but they don't have the +reflection of the outcome of what that + + align:start position:0% +reflection of the outcome of what that + + + align:start position:0% +reflection of the outcome of what that +action is so I wonder if you know about + + align:start position:0% +action is so I wonder if you know about + + + align:start position:0% +action is so I wonder if you know about +this and what do you think + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% + + + + align:start position:0% + +and my understanding is that + + align:start position:0% + + + + align:start position:0% + +for for for people the if they + + align:start position:0% +for for for people the if they + + + align:start position:0% +for for for people the if they +can understand better the the the the + + align:start position:0% +can understand better the the the the + + + align:start position:0% +can understand better the the the the +kind of problem they they are + + align:start position:0% + + + + align:start position:0% + +facing it's much more feasible to to get + + align:start position:0% +facing it's much more feasible to to get + + + align:start position:0% +facing it's much more feasible to to get +resources for + + align:start position:0% +resources for + + + align:start position:0% +resources for +them + + align:start position:0% +them + + + align:start position:0% +them +and my assumption is that there is much + + align:start position:0% +and my assumption is that there is much + + + align:start position:0% +and my assumption is that there is much +more resources in the world than that we + + align:start position:0% +more resources in the world than that we + + + align:start position:0% +more resources in the world than that we +can channel to the poor people and much + + align:start position:0% +can channel to the poor people and much + + + align:start position:0% +can channel to the poor people and much +more resources than people + + align:start position:0% +more resources than people + + + align:start position:0% +more resources than people +can get for them for their development + + align:start position:0% +can get for them for their development + + + align:start position:0% +can get for them for their development +and the main problem is + + align:start position:0% +and the main problem is + + + align:start position:0% +and the main problem is +not + + align:start position:0% + + + + align:start position:0% + +ER it's not something that we can do + + align:start position:0% +ER it's not something that we can do + + + align:start position:0% +ER it's not something that we can do +here in the developed country but how we + + align:start position:0% +here in the developed country but how we + + + align:start position:0% +here in the developed country but how we +can help them to to take control of + + align:start position:0% +can help them to to take control of + + + align:start position:0% +can help them to to take control of +their their + + align:start position:0% +their their + + + align:start position:0% +their their +situation + + align:start position:0% +situation + + + align:start position:0% +situation +uh I think that there + + align:start position:0% +uh I think that there + + + align:start position:0% +uh I think that there +is the problem is not to put much money + + align:start position:0% +is the problem is not to put much money + + + align:start position:0% +is the problem is not to put much money +in a small group of people but how this + + align:start position:0% +in a small group of people but how this + + + align:start position:0% +in a small group of people but how this +will irradiate in the country how the + + align:start position:0% +will irradiate in the country how the + + + align:start position:0% +will irradiate in the country how the +other people will be able to to use what + + align:start position:0% +other people will be able to to use what + + + align:start position:0% +other people will be able to to use what +I small group can learn I think that + + align:start position:0% +I small group can learn I think that + + + align:start position:0% +I small group can learn I think that +most more important is is to + + align:start position:0% +most more important is is to + + + align:start position:0% +most more important is is to +to help people to take charge of their + + align:start position:0% +to help people to take charge of their + + + align:start position:0% +to help people to take charge of their +situation and if they do that they will + + align:start position:0% +situation and if they do that they will + + + align:start position:0% +situation and if they do that they will +get this kind of money and will not be + + align:start position:0% +get this kind of money and will not be + + + align:start position:0% +get this kind of money and will not be +necessary that we design the + + align:start position:0% +necessary that we design the + + + align:start position:0% +necessary that we design the +intervention from the north most of the + + align:start position:0% +intervention from the north most of the + + + align:start position:0% +intervention from the north most of the +problem we have now is the most the + + align:start position:0% +problem we have now is the most the + + + align:start position:0% +problem we have now is the most the +programs the development programs are + + align:start position:0% +programs the development programs are + + + align:start position:0% +programs the development programs are +designed from here they are not designed + + align:start position:0% +designed from here they are not designed + + + align:start position:0% +designed from here they are not designed +from the people who are facing the + + align:start position:0% +from the people who are facing the + + + align:start position:0% +from the people who are facing the +problem s and we have I have been + + align:start position:0% +problem s and we have I have been + + + align:start position:0% +problem s and we have I have been +working 36 years with these + + align:start position:0% +working 36 years with these + + + align:start position:0% +working 36 years with these +people when we try to talk with them + + align:start position:0% +people when we try to talk with them + + + align:start position:0% +people when we try to talk with them +about their + + align:start position:0% +about their + + + align:start position:0% +about their +development they don't feel enough + + align:start position:0% +development they don't feel enough + + + align:start position:0% +development they don't feel enough +confidence to + + align:start position:0% +confidence to + + + align:start position:0% +confidence to +decide what they will do how they will + + align:start position:0% +decide what they will do how they will + + + align:start position:0% +decide what they will do how they will +invert the resource of the corporation + + align:start position:0% +invert the resource of the corporation + + + align:start position:0% +invert the resource of the corporation +they are very dependent + + align:start position:0% +they are very dependent + + + align:start position:0% +they are very dependent +of of the + + align:start position:0% +of of the + + + align:start position:0% +of of the +professionals because we are the only + + align:start position:0% +professionals because we are the only + + + align:start position:0% +professionals because we are the only +people who have + + align:start position:0% +people who have + + + align:start position:0% +people who have +formal ER + + align:start position:0% +formal ER + + + align:start position:0% +formal ER +recogniz we are the engineers we are the + + align:start position:0% +recogniz we are the engineers we are the + + + align:start position:0% +recogniz we are the engineers we are the +doctors and we always make very clear + + align:start position:0% +doctors and we always make very clear + + + align:start position:0% +doctors and we always make very clear +for them that we are and they are + + align:start position:0% +for them that we are and they are + + + align:start position:0% +for them that we are and they are +not so for me this kind of approach is + + align:start position:0% +not so for me this kind of approach is + + + align:start position:0% +not so for me this kind of approach is +very useful because they can control + + align:start position:0% +very useful because they can control + + + align:start position:0% +very useful because they can control +their knowledge once they began to learn + + align:start position:0% +their knowledge once they began to learn + + + align:start position:0% +their knowledge once they began to learn +to to think this way I don't know if I + + align:start position:0% +to to think this way I don't know if I + + + align:start position:0% +to to think this way I don't know if I +answer your question okay + + align:start position:0% +answer your question okay + + + align:start position:0% +answer your question okay +yes um I was wondering if um you would + + align:start position:0% +yes um I was wondering if um you would + + + align:start position:0% +yes um I was wondering if um you would +consider + + align:start position:0% +consider + + + align:start position:0% +consider +um in the practice of indigenous peoples + + align:start position:0% +um in the practice of indigenous peoples + + + align:start position:0% +um in the practice of indigenous peoples +as something that engages into + + align:start position:0% +as something that engages into + + + align:start position:0% +as something that engages into +reflective practice I am asking this + + align:start position:0% +reflective practice I am asking this + + + align:start position:0% +reflective practice I am asking this +question because + + align:start position:0% +question because + + + align:start position:0% +question because +um with the the indigenous peoples in my + + align:start position:0% +um with the the indigenous peoples in my + + + align:start position:0% +um with the the indigenous peoples in my +experience especially those who are at + + align:start position:0% +experience especially those who are at + + + align:start position:0% +experience especially those who are at +the + + align:start position:0% +the + + + align:start position:0% +the +Hinterlands um mainstream Society those + + align:start position:0% +Hinterlands um mainstream Society those + + + align:start position:0% +Hinterlands um mainstream Society those +who are as you say so Define themselves + + align:start position:0% +who are as you say so Define themselves + + + align:start position:0% +who are as you say so Define themselves +who are uh + + align:start position:0% +who are uh + + + align:start position:0% +who are uh +professionals usually + + align:start position:0% +professionals usually + + + align:start position:0% +professionals usually +um what's + + align:start position:0% +um what's + + + align:start position:0% +um what's +this + + align:start position:0% +this + + + align:start position:0% +this +um create and impose + + align:start position:0% +um create and impose + + + align:start position:0% +um create and impose +Solutions um of how like for example how + + align:start position:0% +Solutions um of how like for example how + + + align:start position:0% +Solutions um of how like for example how +this tribal communities should manage + + align:start position:0% +this tribal communities should manage + + + align:start position:0% +this tribal communities should manage +sources you know and yet we + + align:start position:0% +sources you know and yet we + + + align:start position:0% +sources you know and yet we +know um that communities have survived + + align:start position:0% +know um that communities have survived + + + align:start position:0% +know um that communities have survived +you know + + align:start position:0% +you know + + + align:start position:0% +you know +centuries you know that means thousands + + align:start position:0% +centuries you know that means thousands + + + align:start position:0% +centuries you know that means thousands +of years and that says something about + + align:start position:0% +of years and that says something about + + + align:start position:0% +of years and that says something about +their ability to adopt you know about to + + align:start position:0% +their ability to adopt you know about to + + + align:start position:0% +their ability to adopt you know about to +their knowledge of the environment you + + align:start position:0% +their knowledge of the environment you + + + align:start position:0% +their knowledge of the environment you +know um so that I do you need is that a + + align:start position:0% +know um so that I do you need is that a + + + align:start position:0% +know um so that I do you need is that a +reflective practice they're doing you + + align:start position:0% +reflective practice they're doing you + + + align:start position:0% +reflective practice they're doing you +know or do you need to be explicit be + + align:start position:0% +know or do you need to be explicit be + + + align:start position:0% +know or do you need to be explicit be +able to + + align:start position:0% +able to + + + align:start position:0% +able to +explicit yeah that you know what you + + align:start position:0% +explicit yeah that you know what you + + + align:start position:0% +explicit yeah that you know what you +know when you're doing it so that it + + align:start position:0% +know when you're doing it so that it + + + align:start position:0% +know when you're doing it so that it +becomes qualified as reflective + + align:start position:0% +becomes qualified as reflective + + + align:start position:0% +becomes qualified as reflective +practice okay I'm not so + + align:start position:0% +practice okay I'm not so + + + align:start position:0% +practice okay I'm not so +sure reflective practice this approach + + align:start position:0% +sure reflective practice this approach + + + align:start position:0% +sure reflective practice this approach +is an effort to make our tet thinking + + align:start position:0% +is an effort to make our tet thinking + + + align:start position:0% +is an effort to make our tet thinking +and our or t it knowledge + + align:start position:0% +and our or t it knowledge + + + align:start position:0% +and our or t it knowledge +explicit with with people + + align:start position:0% +explicit with with people + + + align:start position:0% +explicit with with people +in with indigenous people my experience + + align:start position:0% +in with indigenous people my experience + + + align:start position:0% +in with indigenous people my experience +is that they are very smart they are + + align:start position:0% +is that they are very smart they are + + + align:start position:0% +is that they are very smart they are +very intelligent they are very + + align:start position:0% +very intelligent they are very + + + align:start position:0% +very intelligent they are very +knowledgeable okay but it's very + + align:start position:0% +knowledgeable okay but it's very + + + align:start position:0% +knowledgeable okay but it's very +difficult for us to + + align:start position:0% +difficult for us to + + + align:start position:0% +difficult for us to +be enough flexible to to enable them to + + align:start position:0% +be enough flexible to to enable them to + + + align:start position:0% +be enough flexible to to enable them to +express their ideas in the way way they + + align:start position:0% +express their ideas in the way way they + + + align:start position:0% +express their ideas in the way way they +they + + align:start position:0% +they + + + align:start position:0% +they +prefer okay + + align:start position:0% +prefer okay + + + align:start position:0% +prefer okay +and + + align:start position:0% +and + + + align:start position:0% +and +I 10 years ago I made a workshop with + + align:start position:0% +I 10 years ago I made a workshop with + + + align:start position:0% +I 10 years ago I made a workshop with +Chiefs only Chiefs all them are Chiefs + + align:start position:0% +Chiefs only Chiefs all them are Chiefs + + + align:start position:0% +Chiefs only Chiefs all them are Chiefs +of their tribes okay very interesting + + align:start position:0% +of their tribes okay very interesting + + + align:start position:0% +of their tribes okay very interesting +and I made no + + align:start position:0% +and I made no + + + align:start position:0% +and I made no +concession intellectual concession to + + align:start position:0% +concession intellectual concession to + + + align:start position:0% +concession intellectual concession to +them I was absolutely rigorous in their + + align:start position:0% +them I was absolutely rigorous in their + + + align:start position:0% +them I was absolutely rigorous in their +analysis and I have I had no problem + + align:start position:0% +analysis and I have I had no problem + + + align:start position:0% +analysis and I have I had no problem +with them but we have different + + align:start position:0% +with them but we have different + + + align:start position:0% +with them but we have different +languages in the workshop I explain + + align:start position:0% +languages in the workshop I explain + + + align:start position:0% +languages in the workshop I explain +explained the Strategic thinking in a + + align:start position:0% +explained the Strategic thinking in a + + + align:start position:0% +explained the Strategic thinking in a +concrete way not theoretical but in + + align:start position:0% +concrete way not theoretical but in + + + align:start position:0% +concrete way not theoretical but in +concrete way how we think when we try to + + align:start position:0% +concrete way how we think when we try to + + + align:start position:0% +concrete way how we think when we try to +design in + + align:start position:0% +design in + + + align:start position:0% +design in +strategy and after that + + align:start position:0% +strategy and after that + + + align:start position:0% +strategy and after that +they our dialogue was after the + + align:start position:0% +they our dialogue was after the + + + align:start position:0% +they our dialogue was after the +explanation + + align:start position:0% +explanation + + + align:start position:0% +explanation +they told me an an + + align:start position:0% +they told me an an + + + align:start position:0% +they told me an an +story and through the story + + align:start position:0% +story and through the story + + + align:start position:0% +story and through the story +they are trying to verify if they have + + align:start position:0% +they are trying to verify if they have + + + align:start position:0% +they are trying to verify if they have +it understood what I was explaining all + + align:start position:0% +it understood what I was explaining all + + + align:start position:0% +it understood what I was explaining all +the stories they told me were absolutely + + align:start position:0% +the stories they told me were absolutely + + + align:start position:0% +the stories they told me were absolutely +correct okay they are very capable of of + + align:start position:0% +correct okay they are very capable of of + + + align:start position:0% +correct okay they are very capable of of +understanding strategic thinking I have + + align:start position:0% +understanding strategic thinking I have + + + align:start position:0% +understanding strategic thinking I have +had no problem with them we designed + + align:start position:0% +had no problem with them we designed + + + align:start position:0% +had no problem with them we designed +very good + + align:start position:0% +very good + + + align:start position:0% +very good +plan + + align:start position:0% +plan + + + align:start position:0% +plan +and er the question is that one man the + + align:start position:0% +and er the question is that one man the + + + align:start position:0% +and er the question is that one man the +facilitator need to adapt himself + + align:start position:0% +facilitator need to adapt himself + + + align:start position:0% +facilitator need to adapt himself +to the way of thinking that they have + + align:start position:0% +to the way of thinking that they have + + + align:start position:0% +to the way of thinking that they have +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +problem reflective practice help us to + + align:start position:0% +problem reflective practice help us to + + + align:start position:0% +problem reflective practice help us to +be aware + + align:start position:0% +be aware + + + align:start position:0% +be aware +how + + align:start position:0% + + + + align:start position:0% + +T award thank you very much how awkward + + align:start position:0% +T award thank you very much how awkward + + + align:start position:0% +T award thank you very much how awkward +we can be with when we are talking with + + align:start position:0% +we can be with when we are talking with + + + align:start position:0% +we can be with when we are talking with +people okay but if we are not perfect + + align:start position:0% +people okay but if we are not perfect + + + align:start position:0% +people okay but if we are not perfect +but not so much ER + + align:start position:0% +but not so much ER + + + align:start position:0% +but not so much ER +award they + + align:start position:0% +award they + + + align:start position:0% +award they +take the lead and they begin to express + + align:start position:0% +take the lead and they begin to express + + + align:start position:0% +take the lead and they begin to express +their knowledge and I think it's very + + align:start position:0% +their knowledge and I think it's very + + + align:start position:0% +their knowledge and I think it's very +important for them to to be the author + + align:start position:0% +important for them to to be the author + + + align:start position:0% +important for them to to be the author +of their + + align:start position:0% +of their + + + align:start position:0% +of their +plans because if they are the author of + + align:start position:0% +plans because if they are the author of + + + align:start position:0% +plans because if they are the author of +their plants they will learn from their + + align:start position:0% +their plants they will learn from their + + + align:start position:0% +their plants they will learn from their +mistakes if we are the auor of the + + align:start position:0% +mistakes if we are the auor of the + + + align:start position:0% +mistakes if we are the auor of the +plants they will not learn from our + + align:start position:0% +plants they will not learn from our + + + align:start position:0% +plants they will not learn from our +mistakes they will just dis discard us + + align:start position:0% +mistakes they will just dis discard us + + + align:start position:0% +mistakes they will just dis discard us +but they will not + + align:start position:0% +but they will not + + + align:start position:0% +but they will not +learn but they will waste waste time and + + align:start position:0% +learn but they will waste waste time and + + + align:start position:0% +learn but they will waste waste time and +waste money and waste opportunities so + + align:start position:0% +waste money and waste opportunities so + + + align:start position:0% +waste money and waste opportunities so +it's very important when we are working + + align:start position:0% +it's very important when we are working + + + align:start position:0% +it's very important when we are working +with people to help to enable them to + + align:start position:0% +with people to help to enable them to + + + align:start position:0% +with people to help to enable them to +express the ideas in the way they are us + + align:start position:0% +express the ideas in the way they are us + + + align:start position:0% +express the ideas in the way they are us +it to do and be very aware that the + + align:start position:0% +it to do and be very aware that the + + + align:start position:0% +it to do and be very aware that the +responsibility of the conclusions and + + align:start position:0% +responsibility of the conclusions and + + + align:start position:0% +responsibility of the conclusions and +the decisions are of + + align:start position:0% +the decisions are of + + + align:start position:0% +the decisions are of +them okay just for organizing their + + align:start position:0% +them okay just for organizing their + + + align:start position:0% +them okay just for organizing their +learning see there you're adding + + align:start position:0% +learning see there you're adding + + + align:start position:0% +learning see there you're adding +something + + align:start position:0% +something + + + align:start position:0% +something +different just one quick question which + + align:start position:0% +different just one quick question which + + + align:start position:0% +different just one quick question which +has to do with you're you're talking + + align:start position:0% +has to do with you're you're talking + + + align:start position:0% +has to do with you're you're talking +about seeing how trying to identify + + align:start position:0% +about seeing how trying to identify + + + align:start position:0% +about seeing how trying to identify +other people's logic not just your own + + align:start position:0% +other people's logic not just your own + + + align:start position:0% +other people's logic not just your own +logic but other people's logic so that + + align:start position:0% +logic but other people's logic so that + + + align:start position:0% +logic but other people's logic so that +you can + + align:start position:0% +you can + + + align:start position:0% +you can +understand what they have to they their + + align:start position:0% +understand what they have to they their + + + align:start position:0% +understand what they have to they their +knowledge and that's that's something + + align:start position:0% +knowledge and that's that's something + + + align:start position:0% +knowledge and that's that's something +new that you haven't talked about this + + align:start position:0% +new that you haven't talked about this + + + align:start position:0% +new that you haven't talked about this +is a new element okay yes so I don't + + align:start position:0% +is a new element okay yes so I don't + + + align:start position:0% +is a new element okay yes so I don't +know where that will fall in in the + + align:start position:0% +know where that will fall in in the + + + align:start position:0% +know where that will fall in in the +course oh I I will talk about I I + + align:start position:0% +course oh I I will talk about I I + + + align:start position:0% +course oh I I will talk about I I +suggested + + align:start position:0% +suggested + + + align:start position:0% +suggested +one one reading about the Anthropologist + + align:start position:0% +one one reading about the Anthropologist + + + align:start position:0% +one one reading about the Anthropologist +it's I would treat it more at the less + + align:start position:0% +it's I would treat it more at the less + + + align:start position:0% +it's I would treat it more at the less +day of the the day before the last day + + align:start position:0% +day of the the day before the last day + + + align:start position:0% +day of the the day before the last day +of the course okay how we can adapt our + + align:start position:0% +of the course okay how we can adapt our + + + align:start position:0% +of the course okay how we can adapt our +mind to the logic of other people okay + + align:start position:0% +mind to the logic of other people okay + + + align:start position:0% +mind to the logic of other people okay +thank you very much in order to really + + align:start position:0% +thank you very much in order to really + + + align:start position:0% +thank you very much in order to really +understand them because often you're + + align:start position:0% +understand them because often you're + + + align:start position:0% +understand them because often you're +just you're interpreting what people are + + align:start position:0% +just you're interpreting what people are + + + align:start position:0% +just you're interpreting what people are +saying um and + + align:start position:0% +saying um and + + + align:start position:0% +saying um and +trans then you don't in that process of + + align:start position:0% +trans then you don't in that process of + + + align:start position:0% +trans then you don't in that process of +interpretation you're no longer you're + + align:start position:0% +interpretation you're no longer you're + + + align:start position:0% +interpretation you're no longer you're +you're modifying what they know in order + + align:start position:0% +you're modifying what they know in order + + + align:start position:0% +you're modifying what they know in order +to understand it through your logic yeah + + align:start position:0% +to understand it through your logic yeah + + + align:start position:0% +to understand it through your logic yeah +just one minute two two persons are + + align:start position:0% +just one minute two two persons are + + + align:start position:0% +just one minute two two persons are +asking to tell to talk the question is + + align:start position:0% +asking to tell to talk the question is + + + align:start position:0% +asking to tell to talk the question is +we need to learn to take our logic our + + align:start position:0% +we need to learn to take our logic our + + + align:start position:0% +we need to learn to take our logic our +thinking and to + + align:start position:0% +thinking and to + + + align:start position:0% +thinking and to +put at the table to forget it for a + + align:start position:0% +put at the table to forget it for a + + + align:start position:0% +put at the table to forget it for a +moment okay and to follow to follow the + + align:start position:0% +moment okay and to follow to follow the + + + align:start position:0% +moment okay and to follow to follow the +logic of the other + + align:start position:0% +logic of the other + + + align:start position:0% +logic of the other +people forgetting how is my way to + + align:start position:0% +people forgetting how is my way to + + + align:start position:0% +people forgetting how is my way to +understand the problem I put my personal + + align:start position:0% +understand the problem I put my personal + + + align:start position:0% +understand the problem I put my personal +understanding aside and I just + + align:start position:0% +understanding aside and I just + + + align:start position:0% +understanding aside and I just +concentrate in listen + + align:start position:0% +concentrate in listen + + + align:start position:0% +concentrate in listen +how they are reasoning yeah him and + + align:start position:0% +how they are reasoning yeah him and + + + align:start position:0% +how they are reasoning yeah him and +after you you're saying that the will + + align:start position:0% +after you you're saying that the will + + + align:start position:0% +after you you're saying that the will +not learn our from our mistakes but they + + align:start position:0% +not learn our from our mistakes but they + + + align:start position:0% +not learn our from our mistakes but they +will learn from their mistakes so isn't + + align:start position:0% +will learn from their mistakes so isn't + + + align:start position:0% +will learn from their mistakes so isn't +there any communication this is one + + align:start position:0% +there any communication this is one + + + align:start position:0% +there any communication this is one +thing uh the other thing is that are you + + align:start position:0% +thing uh the other thing is that are you + + + align:start position:0% +thing uh the other thing is that are you +talking about feeling the responsibility + + align:start position:0% +talking about feeling the responsibility + + + align:start position:0% +talking about feeling the responsibility +of the mistakes and that's what makes + + align:start position:0% +of the mistakes and that's what makes + + + align:start position:0% +of the mistakes and that's what makes +the people + + align:start position:0% +the people + + + align:start position:0% +the people +learn oh it's very different the + + align:start position:0% +learn oh it's very different the + + + align:start position:0% +learn oh it's very different the +actitude the learning actitude for we + + align:start position:0% +actitude the learning actitude for we + + + align:start position:0% +actitude the learning actitude for we +have when + + align:start position:0% +have when + + + align:start position:0% +have when +we feel + + align:start position:0% +we feel + + + align:start position:0% +we feel +that the mistake is + + align:start position:0% +that the mistake is + + + align:start position:0% +that the mistake is +our and when we feel that the mistake is + + align:start position:0% +our and when we feel that the mistake is + + + align:start position:0% +our and when we feel that the mistake is +of other person if the other person + + align:start position:0% +of other person if the other person + + + align:start position:0% +of other person if the other person +committed the mistake we we + + align:start position:0% +committed the mistake we we + + + align:start position:0% +committed the mistake we we +don't do the same effort for + + align:start position:0% +don't do the same effort for + + + align:start position:0% +don't do the same effort for +understanding the reasons of this + + align:start position:0% +understanding the reasons of this + + + align:start position:0% +understanding the reasons of this +mistake we can discard the person we + + align:start position:0% +mistake we can discard the person we + + + align:start position:0% +mistake we can discard the person we +will not work with him again we have + + align:start position:0% +will not work with him again we have + + + align:start position:0% +will not work with him again we have +different options we are not so + + align:start position:0% +different options we are not so + + + align:start position:0% +different options we are not so +analytical if I committed the mistake I + + align:start position:0% +analytical if I committed the mistake I + + + align:start position:0% +analytical if I committed the mistake I +will feel much + + align:start position:0% +will feel much + + + align:start position:0% +will feel much +worse okay I will feel ashamed of + + align:start position:0% +worse okay I will feel ashamed of + + + align:start position:0% +worse okay I will feel ashamed of +my ER my mistake my lack of + + align:start position:0% +my ER my mistake my lack of + + + align:start position:0% +my ER my mistake my lack of +intelligence okay but this is not + + align:start position:0% +intelligence okay but this is not + + + align:start position:0% +intelligence okay but this is not +problem we can recuperate from this oh + + align:start position:0% +problem we can recuperate from this oh + + + align:start position:0% +problem we can recuperate from this oh +this this sh will help us to to get back + + align:start position:0% +this this sh will help us to to get back + + + align:start position:0% +this this sh will help us to to get back +what we this is the kind of reflection + + align:start position:0% +what we this is the kind of reflection + + + align:start position:0% +what we this is the kind of reflection +we do in a very accelerated way when we + + align:start position:0% +we do in a very accelerated way when we + + + align:start position:0% +we do in a very accelerated way when we +feel + + align:start position:0% +feel + + + align:start position:0% +feel +ashamed okay we get back to experience + + align:start position:0% +ashamed okay we get back to experience + + + align:start position:0% +ashamed okay we get back to experience +we remember what we should do and we + + align:start position:0% +we remember what we should do and we + + + align:start position:0% +we remember what we should do and we +didn't okay this process very important + + align:start position:0% +didn't okay this process very important + + + align:start position:0% +didn't okay this process very important +for + + align:start position:0% +for + + + align:start position:0% +for +Learning + + align:start position:0% +Learning + + + align:start position:0% +Learning +and if I am aware that I am the + + align:start position:0% +and if I am aware that I am the + + + align:start position:0% +and if I am aware that I am the +responsible for the decisions I will be + + align:start position:0% +responsible for the decisions I will be + + + align:start position:0% +responsible for the decisions I will be +much more analytical before the + + align:start position:0% +much more analytical before the + + + align:start position:0% +much more analytical before the +decision a great problem of the project + + align:start position:0% +decision a great problem of the project + + + align:start position:0% +decision a great problem of the project +of development we not discuss this now + + align:start position:0% +of development we not discuss this now + + + align:start position:0% +of development we not discuss this now +but is that the projects or the programs + + align:start position:0% +but is that the projects or the programs + + + align:start position:0% +but is that the projects or the programs +development programs are idea with + + align:start position:0% +development programs are idea with + + + align:start position:0% +development programs are idea with +money idea with money is a very bad + + align:start position:0% + + + + align:start position:0% + +combination okay the money block the + + align:start position:0% +combination okay the money block the + + + align:start position:0% +combination okay the money block the +analysis + + align:start position:0% + + + + align:start position:0% + +yeah so this is the reason why it's so + + align:start position:0% +yeah so this is the reason why it's so + + + align:start position:0% +yeah so this is the reason why it's so +important to get people aware that they + + align:start position:0% +important to get people aware that they + + + align:start position:0% +important to get people aware that they +are deciding about their + + align:start position:0% +are deciding about their + + + align:start position:0% +are deciding about their +future yeah okay I don't know if I + + align:start position:0% +future yeah okay I don't know if I + + + align:start position:0% +future yeah okay I don't know if I +answer + + align:start position:0% +answer + + + align:start position:0% +answer +it + + align:start position:0% +it + + + align:start position:0% +it +um I think one I the question for me was + + align:start position:0% +um I think one I the question for me was + + + align:start position:0% +um I think one I the question for me was +about the tacit to tacit uh uh handing + + align:start position:0% +about the tacit to tacit uh uh handing + + + align:start position:0% +about the tacit to tacit uh uh handing +down of knowledge and whether it's a + + align:start position:0% +down of knowledge and whether it's a + + + align:start position:0% +down of knowledge and whether it's a +indigenous Community or whether it's an + + align:start position:0% +indigenous Community or whether it's an + + + align:start position:0% +indigenous Community or whether it's an +urban community I think there are + + align:start position:0% +urban community I think there are + + + align:start position:0% +urban community I think there are +practices that that communities have or + + align:start position:0% +practices that that communities have or + + + align:start position:0% +practices that that communities have or +that people have that they demonstrate + + align:start position:0% +that people have that they demonstrate + + + align:start position:0% +that people have that they demonstrate +that they model for their children or + + align:start position:0% +that they model for their children or + + + align:start position:0% +that they model for their children or +their community and they keep practicing + + align:start position:0% +their community and they keep practicing + + + align:start position:0% +their community and they keep practicing +those um the the issue I think and that + + align:start position:0% +those um the the issue I think and that + + + align:start position:0% +those um the the issue I think and that +goes to when the problem is known when + + align:start position:0% +goes to when the problem is known when + + + align:start position:0% +goes to when the problem is known when +the experience is is Con is repetitive + + align:start position:0% +the experience is is Con is repetitive + + + align:start position:0% +the experience is is Con is repetitive +and I think what we're trying to do here + + align:start position:0% +and I think what we're trying to do here + + + align:start position:0% +and I think what we're trying to do here +is recognize that there are moments when + + align:start position:0% +is recognize that there are moments when + + + align:start position:0% +is recognize that there are moments when +there are where the problem is not known + + align:start position:0% +there are where the problem is not known + + + align:start position:0% +there are where the problem is not known +when there is a new challenge when the + + align:start position:0% +when there is a new challenge when the + + + align:start position:0% +when there is a new challenge when the +challenge is known and uh traditional or + + align:start position:0% +challenge is known and uh traditional or + + + align:start position:0% +challenge is known and uh traditional or +regular Behavior or assumptions whether + + align:start position:0% +regular Behavior or assumptions whether + + + align:start position:0% +regular Behavior or assumptions whether +they're they are uh professional or + + align:start position:0% +they're they are uh professional or + + + align:start position:0% +they're they are uh professional or +technological or or intellectual um and + + align:start position:0% +technological or or intellectual um and + + + align:start position:0% +technological or or intellectual um and +you apply them to a known challenge they + + align:start position:0% +you apply them to a known challenge they + + + align:start position:0% +you apply them to a known challenge they +work you don't have to do a lot of uh + + align:start position:0% +work you don't have to do a lot of uh + + + align:start position:0% +work you don't have to do a lot of uh +exp uh making your tasset knowledge + + align:start position:0% +exp uh making your tasset knowledge + + + align:start position:0% +exp uh making your tasset knowledge +explicit and so one of the couple of + + align:start position:0% +explicit and so one of the couple of + + + align:start position:0% +explicit and so one of the couple of +words that I heard here were about + + align:start position:0% +words that I heard here were about + + + align:start position:0% +words that I heard here were about +interpretation in different languages + + align:start position:0% +interpretation in different languages + + + align:start position:0% +interpretation in different languages +you were speaking different languages as + + align:start position:0% +you were speaking different languages as + + + align:start position:0% +you were speaking different languages as +an you know as a professional versus a + + align:start position:0% +an you know as a professional versus a + + + align:start position:0% +an you know as a professional versus a +Chieftain or whatever and you know + + align:start position:0% +Chieftain or whatever and you know + + + align:start position:0% +Chieftain or whatever and you know +communicating AC acoss uh across + + align:start position:0% +communicating AC acoss uh across + + + align:start position:0% +communicating AC acoss uh across +languages and that that happens when we + + align:start position:0% +languages and that that happens when we + + + align:start position:0% +languages and that that happens when we +try to go be to when we try to resolve a + + align:start position:0% +try to go be to when we try to resolve a + + + align:start position:0% +try to go be to when we try to resolve a +new problem or something that we haven't + + align:start position:0% +new problem or something that we haven't + + + align:start position:0% +new problem or something that we haven't +faced before and um and that's when I + + align:start position:0% +faced before and um and that's when I + + + align:start position:0% +faced before and um and that's when I +think we're trying to figure out how to + + align:start position:0% +think we're trying to figure out how to + + + align:start position:0% +think we're trying to figure out how to +make our tacit knowledge explicit for + + align:start position:0% +make our tacit knowledge explicit for + + + align:start position:0% +make our tacit knowledge explicit for +ourselves as as gladia was focusing you + + align:start position:0% +ourselves as as gladia was focusing you + + + align:start position:0% +ourselves as as gladia was focusing you +know the course the the purpose of this + + align:start position:0% +know the course the the purpose of this + + + align:start position:0% +know the course the the purpose of this +course is again reflective practice of + + align:start position:0% +course is again reflective practice of + + + align:start position:0% +course is again reflective practice of +oneself and then trying to share that + + align:start position:0% +oneself and then trying to share that + + + align:start position:0% +oneself and then trying to share that +with others is which is where you + + align:start position:0% +with others is which is where you + + + align:start position:0% +with others is which is where you +started going um and trying to learn + + align:start position:0% +started going um and trying to learn + + + align:start position:0% +started going um and trying to learn +that from others is when you put your + + align:start position:0% +that from others is when you put your + + + align:start position:0% +that from others is when you put your +own trying to make your own knowledge + + align:start position:0% +own trying to make your own knowledge + + + align:start position:0% +own trying to make your own knowledge +explicit and trying to understand the + + align:start position:0% +explicit and trying to understand the + + + align:start position:0% +explicit and trying to understand the +tacit knowledge of others and helping + + align:start position:0% +tacit knowledge of others and helping + + + align:start position:0% +tacit knowledge of others and helping +them make it explicit and so I think + + align:start position:0% +them make it explicit and so I think + + + align:start position:0% +them make it explicit and so I think +that is when when we want to do that is + + align:start position:0% +that is when when we want to do that is + + + align:start position:0% +that is when when we want to do that is +when we're faced with a new challenge if + + align:start position:0% +when we're faced with a new challenge if + + + align:start position:0% +when we're faced with a new challenge if +we're faced with continuous repetitive + + align:start position:0% +we're faced with continuous repetitive + + + align:start position:0% +we're faced with continuous repetitive +challenges tacit to tacet knowledge + + align:start position:0% +challenges tacit to tacet knowledge + + + align:start position:0% +challenges tacit to tacet knowledge +seems to be seems to have worked for + + align:start position:0% +seems to be seems to have worked for + + + align:start position:0% +seems to be seems to have worked for +Millennia MH okay can I say something + + align:start position:0% +Millennia MH okay can I say something + + + align:start position:0% +Millennia MH okay can I say something +about that yeah um if you say like + + align:start position:0% +about that yeah um if you say like + + + align:start position:0% +about that yeah um if you say like +people are using different language and + + align:start position:0% +people are using different language and + + + align:start position:0% +people are using different language and +all that um yeah that's one that's true + + align:start position:0% +all that um yeah that's one that's true + + + align:start position:0% +all that um yeah that's one that's true +um I think at the + + align:start position:0% +um I think at the + + + align:start position:0% +um I think at the +surface but for me the language itself + + align:start position:0% +surface but for me the language itself + + + align:start position:0% +surface but for me the language itself +tells you that the assumptions are very + + align:start position:0% +tells you that the assumptions are very + + + align:start position:0% +tells you that the assumptions are very +different you know when people frame + + align:start position:0% +different you know when people frame + + + align:start position:0% +different you know when people frame +when they talk and there they seem to be + + align:start position:0% +when they talk and there they seem to be + + + align:start position:0% +when they talk and there they seem to be +like we're talking both English and but + + align:start position:0% +like we're talking both English and but + + + align:start position:0% +like we're talking both English and but +it seems like the language is not coming + + align:start position:0% +it seems like the language is not coming + + + align:start position:0% +it seems like the language is not coming +all together sensible for both of us um + + align:start position:0% +all together sensible for both of us um + + + align:start position:0% +all together sensible for both of us um +it is because in my sense um we are + + align:start position:0% +it is because in my sense um we are + + + align:start position:0% +it is because in my sense um we are +basically basically coming from very + + align:start position:0% +basically basically coming from very + + + align:start position:0% +basically basically coming from very +different assumptions and I think that's + + align:start position:0% +different assumptions and I think that's + + + align:start position:0% +different assumptions and I think that's +what what happens with um you know + + align:start position:0% +what what happens with um you know + + + align:start position:0% +what what happens with um you know +professionals going into developing + + align:start position:0% +professionals going into developing + + + align:start position:0% +professionals going into developing +countries or going into development work + + align:start position:0% +countries or going into development work + + + align:start position:0% +countries or going into development work +you know or going into communities + + align:start position:0% +you know or going into communities + + + align:start position:0% +you know or going into communities +because you know um as as you say so you + + align:start position:0% +because you know um as as you say so you + + + align:start position:0% +because you know um as as you say so you +you try to take out your eyeglasses you + + align:start position:0% +you try to take out your eyeglasses you + + + align:start position:0% +you try to take out your eyeglasses you +know the lenses that you use M but the + + align:start position:0% +know the lenses that you use M but the + + + align:start position:0% +know the lenses that you use M but the +lenses that you use is basically even it + + align:start position:0% +lenses that you use is basically even it + + + align:start position:0% +lenses that you use is basically even it +also contains even taking away the very + + align:start position:0% +also contains even taking away the very + + + align:start position:0% +also contains even taking away the very +Pride that we have that we are + + align:start position:0% +Pride that we have that we are + + + align:start position:0% +Pride that we have that we are +profession + + align:start position:0% +profession + + + align:start position:0% +profession +because the moment you bring that + + align:start position:0% +because the moment you bring that + + + align:start position:0% +because the moment you bring that +thought that you are a professional and + + align:start position:0% +thought that you are a professional and + + + align:start position:0% +thought that you are a professional and +you go to a + + align:start position:0% +you go to a + + + align:start position:0% +you go to a +community you start I don't know um + + align:start position:0% +community you start I don't know um + + + align:start position:0% +community you start I don't know um +that's what my experience is you know + + align:start position:0% +that's what my experience is you know + + + align:start position:0% +that's what my experience is you know +for for for the many blunders + + align:start position:0% +for for for the many blunders + + + align:start position:0% +for for for the many blunders +too I think that's what + + align:start position:0% +too I think that's what + + + align:start position:0% +too I think that's what +happens then you go there and you bring + + align:start position:0% +happens then you go there and you bring + + + align:start position:0% +happens then you go there and you bring +that lens even of being a professional + + align:start position:0% +that lens even of being a professional + + + align:start position:0% +that lens even of being a professional +of being an MIT student or being you + + align:start position:0% +of being an MIT student or being you + + + align:start position:0% +of being an MIT student or being you +know a graduate of here and there or + + align:start position:0% +know a graduate of here and there or + + + align:start position:0% +know a graduate of here and there or +what um that factors in into the whole + + align:start position:0% +what um that factors in into the whole + + + align:start position:0% +what um that factors in into the whole +into the whole language into the whole + + align:start position:0% +into the whole language into the whole + + + align:start position:0% +into the whole language into the whole +assumptions you know um and then about + + align:start position:0% +assumptions you know um and then about + + + align:start position:0% +assumptions you know um and then about +something about + + align:start position:0% +something about + + + align:start position:0% +something about +new new problems and old problems I + + align:start position:0% + + + + align:start position:0% + +think there are things that you may say + + align:start position:0% +think there are things that you may say + + + align:start position:0% +think there are things that you may say +can be + + align:start position:0% +can be + + + align:start position:0% +can be +constantly they stay the way they are + + align:start position:0% +constantly they stay the way they are + + + align:start position:0% +constantly they stay the way they are +but I think like because things are + + align:start position:0% +but I think like because things are + + + align:start position:0% +but I think like because things are +changing + + align:start position:0% +changing + + + align:start position:0% +changing +context is actually + + align:start position:0% +context is actually + + + align:start position:0% +context is actually +ly changing you know because when you + + align:start position:0% +ly changing you know because when you + + + align:start position:0% +ly changing you know because when you +say things are not changing the problems + + align:start position:0% +say things are not changing the problems + + + align:start position:0% +say things are not changing the problems +are not the problems are still the same + + align:start position:0% +are not the problems are still the same + + + align:start position:0% +are not the problems are still the same +you have the assumption that context is + + align:start position:0% +you have the assumption that context is + + + align:start position:0% +you have the assumption that context is +not changing or that several factors + + align:start position:0% +not changing or that several factors + + + align:start position:0% +not changing or that several factors +that Define a certain problem is are not + + align:start position:0% +that Define a certain problem is are not + + + align:start position:0% +that Define a certain problem is are not +changing and to + + align:start position:0% +changing and to + + + align:start position:0% +changing and to +my and to me that rarely + + align:start position:0% +my and to me that rarely + + + align:start position:0% +my and to me that rarely +happens because every day a lot of + + align:start position:0% +happens because every day a lot of + + + align:start position:0% +happens because every day a lot of +different kns and vaults out there that + + align:start position:0% +different kns and vaults out there that + + + align:start position:0% +different kns and vaults out there that +actually make up a problem are actually + + align:start position:0% +actually make up a problem are actually + + + align:start position:0% +actually make up a problem are actually +moving including people people because + + align:start position:0% +moving including people people because + + + align:start position:0% +moving including people people because +the pro what defines of people also the + + align:start position:0% +the pro what defines of people also the + + + align:start position:0% +the pro what defines of people also the +interaction of people in a certain + + align:start position:0% +interaction of people in a certain + + + align:start position:0% +interaction of people in a certain +context also is part of the + + align:start position:0% +context also is part of the + + + align:start position:0% +context also is part of the +problem right and I think that's why I + + align:start position:0% +problem right and I think that's why I + + + align:start position:0% +problem right and I think that's why I +always say like there's nothing actually + + align:start position:0% +always say like there's nothing actually + + + align:start position:0% +always say like there's nothing actually +that's actually like constant constant + + align:start position:0% +that's actually like constant constant + + + align:start position:0% +that's actually like constant constant +I'm I'm not so sure if I okay thank you + + align:start position:0% +I'm I'm not so sure if I okay thank you + + + align:start position:0% +I'm I'm not so sure if I okay thank you +indeed we + + align:start position:0% +indeed we + + + align:start position:0% +indeed we +have talk about different aspects no one + + align:start position:0% +have talk about different aspects no one + + + align:start position:0% +have talk about different aspects no one +is if the problem is new or is not new + + align:start position:0% +is if the problem is new or is not new + + + align:start position:0% +is if the problem is new or is not new +the order is we have different + + align:start position:0% +the order is we have different + + + align:start position:0% +the order is we have different +assumptions and one of the assumptions + + align:start position:0% +assumptions and one of the assumptions + + + align:start position:0% +assumptions and one of the assumptions +we have is that the problem is the same + + align:start position:0% +we have is that the problem is the same + + + align:start position:0% +we have is that the problem is the same +problem before + + align:start position:0% +problem before + + + align:start position:0% +problem before +no + + align:start position:0% +no + + + align:start position:0% +no +ER and we talk about the relation + + align:start position:0% +ER and we talk about the relation + + + align:start position:0% +ER and we talk about the relation +between professional and common + + align:start position:0% +between professional and common + + + align:start position:0% +between professional and common +people know that make much more + + align:start position:0% +people know that make much more + + + align:start position:0% +people know that make much more +difficult the + + align:start position:0% +difficult the + + + align:start position:0% +difficult the +knowledge change + + align:start position:0% +knowledge change + + + align:start position:0% +knowledge change +no okay do you have something do you you + + align:start position:0% +no okay do you have something do you you + + + align:start position:0% +no okay do you have something do you you +need want to talk before we do the + + align:start position:0% +need want to talk before we do the + + + align:start position:0% +need want to talk before we do the +exercise yes just briefly I don't I + + align:start position:0% +exercise yes just briefly I don't I + + + align:start position:0% +exercise yes just briefly I don't I +think also it's not just common + + align:start position:0% +think also it's not just common + + + align:start position:0% +think also it's not just common +professional it's uh different uh + + align:start position:0% +professional it's uh different uh + + + align:start position:0% +professional it's uh different uh +perspectives on a situation whether they + + align:start position:0% +perspectives on a situation whether they + + + align:start position:0% +perspectives on a situation whether they +be professional or different professions + + align:start position:0% +be professional or different professions + + + align:start position:0% +be professional or different professions +you know as as we see a health + + align:start position:0% +you know as as we see a health + + + align:start position:0% +you know as as we see a health +professional will look at an HIV crisis + + align:start position:0% +professional will look at an HIV crisis + + + align:start position:0% +professional will look at an HIV crisis +very differently than a um you know than + + align:start position:0% +very differently than a um you know than + + + align:start position:0% +very differently than a um you know than +a than a a social scientist or an + + align:start position:0% +a than a a social scientist or an + + + align:start position:0% +a than a a social scientist or an +economist or eom no yes and from South + + align:start position:0% +economist or eom no yes and from South + + + align:start position:0% +economist or eom no yes and from South +and North + + align:start position:0% +and North + + + align:start position:0% +and North +Soo for me that I am from the south it's + + align:start position:0% +Soo for me that I am from the south it's + + + align:start position:0% +Soo for me that I am from the south it's +very complex this society and even again + + align:start position:0% +very complex this society and even again + + + align:start position:0% +very complex this society and even again +taking it's very difficult for me + + align:start position:0% +taking it's very difficult for me + + + align:start position:0% +taking it's very difficult for me +understanding how this Society work the + + align:start position:0% +understanding how this Society work the + + + align:start position:0% +understanding how this Society work the +United States because I live all my life + + align:start position:0% +United States because I live all my life + + + align:start position:0% +United States because I live all my life +in the South I think that it's the same + + align:start position:0% +in the South I think that it's the same + + + align:start position:0% +in the South I think that it's the same +when we go to the South how to + + align:start position:0% +when we go to the South how to + + + align:start position:0% +when we go to the South how to +understand the logic that the society + + align:start position:0% +understand the logic that the society + + + align:start position:0% +understand the logic that the society +have there and again not just the + + align:start position:0% +have there and again not just the + + + align:start position:0% +have there and again not just the +professionals I mean I think that from + + align:start position:0% +professionals I mean I think that from + + + align:start position:0% +professionals I mean I think that from +within a community we tend to sometimes + + align:start position:0% +within a community we tend to sometimes + + + align:start position:0% +within a community we tend to sometimes +say you know Community X but within the + + align:start position:0% +say you know Community X but within the + + + align:start position:0% +say you know Community X but within the +community there are very different + + align:start position:0% +community there are very different + + + align:start position:0% +community there are very different +perspectives that we need to uh consider + + align:start position:0% +perspectives that we need to uh consider + + + align:start position:0% +perspectives that we need to uh consider +when we're when we're looking at + + align:start position:0% +when we're when we're looking at + + + align:start position:0% +when we're when we're looking at +Solutions or problems or whatever we + + align:start position:0% +Solutions or problems or whatever we + + + align:start position:0% +Solutions or problems or whatever we +might want to call them M + + align:start position:0% +might want to call them M + + + align:start position:0% +might want to call them M +okay + + align:start position:0% + + + + align:start position:0% + +yeah we need a break my idea is to make + + align:start position:0% +yeah we need a break my idea is to make + + + align:start position:0% +yeah we need a break my idea is to make +a small break and to do the exercise + + align:start position:0% +a small break and to do the exercise + + + align:start position:0% +a small break and to do the exercise +later + + align:start position:0% + + + + align:start position:0% + +okay 10 minutes okay for + + align:start position:0% + + + + align:start position:0% + +you okay + + align:start position:0% +you okay + + + align:start position:0% +you okay +let's start let's start the game it's we + + align:start position:0% +let's start let's start the game it's we + + + align:start position:0% +let's start let's start the game it's we +will do a very simple exercise + + align:start position:0% +will do a very simple exercise + + + align:start position:0% +will do a very simple exercise +the the exercise try + + align:start position:0% +the the exercise try + + + align:start position:0% +the the exercise try +to to visualize a learning + + align:start position:0% + + + + align:start position:0% + +process with s MD we was talking about + + align:start position:0% +process with s MD we was talking about + + + align:start position:0% +process with s MD we was talking about +which kind of exercise should be useful + + align:start position:0% +which kind of exercise should be useful + + + align:start position:0% +which kind of exercise should be useful +for you and our idea is some experience + + align:start position:0% +for you and our idea is some experience + + + align:start position:0% +for you and our idea is some experience +from + + align:start position:0% +from + + + align:start position:0% +from +childhood the first time you how you + + align:start position:0% +childhood the first time you how you + + + align:start position:0% +childhood the first time you how you +learn to write a bike or how you learn + + align:start position:0% +learn to write a bike or how you learn + + + align:start position:0% +learn to write a bike or how you learn +to drive a car is not childhood but it's + + align:start position:0% +to drive a car is not childhood but it's + + + align:start position:0% +to drive a car is not childhood but it's +very similar or how you learn to ride + + align:start position:0% +very similar or how you learn to ride + + + align:start position:0% +very similar or how you learn to ride +your name for the first time in this + + align:start position:0% +your name for the first time in this + + + align:start position:0% +your name for the first time in this +school or something + + align:start position:0% +school or something + + + align:start position:0% +school or something +else if if you have another learning + + align:start position:0% +else if if you have another learning + + + align:start position:0% +else if if you have another learning +experience you can use it you are free + + align:start position:0% +experience you can use it you are free + + + align:start position:0% +experience you can use it you are free +for using the experience you prefer but + + align:start position:0% +for using the experience you prefer but + + + align:start position:0% +for using the experience you prefer but +we are giving this + + align:start position:0% +we are giving this + + + align:start position:0% +we are giving this +these examples just for + + align:start position:0% + + + + align:start position:0% + +for you use if you have not another one + + align:start position:0% +for you use if you have not another one + + + align:start position:0% +for you use if you have not another one +ride a bike drive a car ride our Name an + + align:start position:0% +ride a bike drive a car ride our Name an + + + align:start position:0% +ride a bike drive a car ride our Name an +experience the idea is that you will + + align:start position:0% +experience the idea is that you will + + + align:start position:0% +experience the idea is that you will +describe this + + align:start position:0% + + + + align:start position:0% + +experience in as steps in a + + align:start position:0% + + + + align:start position:0% + +process + + align:start position:0% +process + + + align:start position:0% +process +okay not to if you want you can describe + + align:start position:0% +okay not to if you want you can describe + + + align:start position:0% +okay not to if you want you can describe +it to + + align:start position:0% +it to + + + align:start position:0% +it to +uh through phrases but the idea is to + + align:start position:0% +uh through phrases but the idea is to + + + align:start position:0% +uh through phrases but the idea is to +describe it + + align:start position:0% +describe it + + + align:start position:0% +describe it +graphically yes so it has to be if not + + align:start position:0% +graphically yes so it has to be if not + + + align:start position:0% +graphically yes so it has to be if not +any of those if I don't remember any of + + align:start position:0% +any of those if I don't remember any of + + + align:start position:0% +any of those if I don't remember any of +those uh a + + align:start position:0% +those uh a + + + align:start position:0% +those uh a +skill like when I learned a skill is + + align:start position:0% +skill like when I learned a skill is + + + align:start position:0% +skill like when I learned a skill is +that the purpose that the idea is to + + align:start position:0% +that the purpose that the idea is to + + + align:start position:0% +that the purpose that the idea is to +learn and scale because it's simpler + + align:start position:0% +learn and scale because it's simpler + + + align:start position:0% +learn and scale because it's simpler +than to acquire a concept or + + align:start position:0% +than to acquire a concept or + + + align:start position:0% +than to acquire a concept or +to understand a new + + align:start position:0% +to understand a new + + + align:start position:0% +to understand a new +technique okay and skill is simpler to + + align:start position:0% +technique okay and skill is simpler to + + + align:start position:0% +technique okay and skill is simpler to +to + + align:start position:0% +to + + + align:start position:0% +to +describe + + align:start position:0% +describe + + + align:start position:0% +describe +okay it will not + + align:start position:0% +okay it will not + + + align:start position:0% +okay it will not +be useful for more complex analysis it's + + align:start position:0% +be useful for more complex analysis it's + + + align:start position:0% +be useful for more complex analysis it's +for introducing to learning process okay + + align:start position:0% +for introducing to learning process okay + + + align:start position:0% +for introducing to learning process okay +we cannot talk about second + + align:start position:0% +we cannot talk about second + + + align:start position:0% +we cannot talk about second +Loop + + align:start position:0% +Loop + + + align:start position:0% +Loop +okay ER learning we will be just the + + align:start position:0% +okay ER learning we will be just the + + + align:start position:0% +okay ER learning we will be just the +simple process okay the idea is each one + + align:start position:0% +simple process okay the idea is each one + + + align:start position:0% +simple process okay the idea is each one +of you to remember one experience and to + + align:start position:0% +of you to remember one experience and to + + + align:start position:0% +of you to remember one experience and to +to to describe the process how it was + + align:start position:0% +to to describe the process how it was + + + align:start position:0% +to to describe the process how it was +and you will do in your in in your + + align:start position:0% +and you will do in your in in your + + + align:start position:0% +and you will do in your in in your +notebook after that each one will put we + + align:start position:0% +notebook after that each one will put we + + + align:start position:0% +notebook after that each one will put we +design it here we we + + align:start position:0% +design it here we we + + + align:start position:0% +design it here we we +put all the war the wall and we we walk + + align:start position:0% +put all the war the wall and we we walk + + + align:start position:0% +put all the war the wall and we we walk +and talk to the each Alor and he will + + align:start position:0% +and talk to the each Alor and he will + + + align:start position:0% +and talk to the each Alor and he will +explain us + + align:start position:0% +explain us + + + align:start position:0% +explain us +his experience after that we will try to + + align:start position:0% +his experience after that we will try to + + + align:start position:0% +his experience after that we will try to +discover + + align:start position:0% +discover + + + align:start position:0% +discover +patterns what are common in this process + + align:start position:0% +patterns what are common in this process + + + align:start position:0% +patterns what are common in this process +and what are the + + align:start position:0% +and what are the + + + align:start position:0% +and what are the +differences okay it's a small + + align:start position:0% +differences okay it's a small + + + align:start position:0% +differences okay it's a small +introduction to the learning processes + + align:start position:0% +introduction to the learning processes + + + align:start position:0% +introduction to the learning processes +we have to describe the experience + + align:start position:0% +we have to describe the experience + + + align:start position:0% +we have to describe the experience +graphically graphically only graphically + + align:start position:0% +graphically graphically only graphically + + + align:start position:0% +graphically graphically only graphically +only graphically and then we need after + + align:start position:0% +only graphically and then we need after + + + align:start position:0% +only graphically and then we need after +when we talk about we need to talk more + + align:start position:0% +when we talk about we need to talk more + + + align:start position:0% +when we talk about we need to talk more +detailed about yes when we visit your + + align:start position:0% +detailed about yes when we visit your + + + align:start position:0% +detailed about yes when we visit your +boo you you have a booth okay when we + + align:start position:0% +boo you you have a booth okay when we + + + align:start position:0% +boo you you have a booth okay when we +visit your booth you will explain Us in + + align:start position:0% +visit your booth you will explain Us in + + + align:start position:0% +visit your booth you will explain Us in +very briefly 1 + + align:start position:0% +very briefly 1 + + + align:start position:0% +very briefly 1 +minute how the process + + align:start position:0% +minute how the process + + + align:start position:0% +minute how the process +was okay yes graic mean that a flow + + align:start position:0% +was okay yes graic mean that a flow + + + align:start position:0% +was okay yes graic mean that a flow +chart it yes a flow chart okay you can + + align:start position:0% +chart it yes a flow chart okay you can + + + align:start position:0% +chart it yes a flow chart okay you can +decide you can use the way you prefer + + align:start position:0% +decide you can use the way you prefer + + + align:start position:0% +decide you can use the way you prefer +you can put it as a mind map okay or a + + align:start position:0% +you can put it as a mind map okay or a + + + align:start position:0% +you can put it as a mind map okay or a +FL or + + align:start position:0% +FL or + + + align:start position:0% +FL or +anyway but I was not I was not thinking + + align:start position:0% +anyway but I was not I was not thinking + + + align:start position:0% +anyway but I was not I was not thinking +about + + align:start position:0% +about + + + align:start position:0% +about +um landscape not a + + align:start position:0% +um landscape not a + + + align:start position:0% +um landscape not a +landscape okay not drawing okay but a + + align:start position:0% +landscape okay not drawing okay but a + + + align:start position:0% +landscape okay not drawing okay but a +flowchart or a a concept map okay so you + + align:start position:0% +flowchart or a a concept map okay so you + + + align:start position:0% +flowchart or a a concept map okay so you +have 5 minutes to to think about your + + align:start position:0% +have 5 minutes to to think about your + + + align:start position:0% +have 5 minutes to to think about your +learning + + align:start position:0% +learning + + + align:start position:0% +learning +experience we made an exercise with + + align:start position:0% +experience we made an exercise with + + + align:start position:0% +experience we made an exercise with +childhood it it + + align:start position:0% + + + + align:start position:0% + +worked I think that mine childhood is + + align:start position:0% +worked I think that mine childhood is + + + align:start position:0% +worked I think that mine childhood is +longer than + + align:start position:0% + + + + align:start position:0% + +yours and I remember to to ride a + + align:start position:0% +yours and I remember to to ride a + + + align:start position:0% +yours and I remember to to ride a +bike the first fall what I did later do + + align:start position:0% +bike the first fall what I did later do + + + align:start position:0% +bike the first fall what I did later do +that be childhood or can it just be + + align:start position:0% +that be childhood or can it just be + + + align:start position:0% +that be childhood or can it just be +learning anything anything you can you + + align:start position:0% +learning anything anything you can you + + + align:start position:0% +learning anything anything you can you +can but should be something very + + align:start position:0% +can but should be something very + + + align:start position:0% +can but should be something very +concrete for be easier huh and and + + align:start position:0% +concrete for be easier huh and and + + + align:start position:0% +concrete for be easier huh and and +simple simple simple not not too much + + align:start position:0% +simple simple simple not not too much + + + align:start position:0% +simple simple simple not not too much +complex if you want to go to + + align:start position:0% +complex if you want to go to + + + align:start position:0% +complex if you want to go to +complexities you have not much + + align:start position:0% +complexities you have not much + + + align:start position:0% +complexities you have not much +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +time + + align:start position:0% + + + + align:start position:0% + +learning I + + align:start position:0% + + + + align:start position:0% + +abstract did you want pleas like very + + align:start position:0% +abstract did you want pleas like very + + + align:start position:0% +abstract did you want pleas like very +concrete or did you want more more + + align:start position:0% +concrete or did you want more more + + + align:start position:0% +concrete or did you want more more +abstract the example or the description + + align:start position:0% +abstract the example or the description + + + align:start position:0% +abstract the example or the description +the description the description can be + + align:start position:0% +the description the description can be + + + align:start position:0% +the description the description can be +abstract you can use Concepts if you + + align:start position:0% +abstract you can use Concepts if you + + + align:start position:0% +abstract you can use Concepts if you +want of or of or if it's difficult for + + align:start position:0% +want of or of or if it's difficult for + + + align:start position:0% +want of or of or if it's difficult for +you to describe as concept you can + + align:start position:0% +you to describe as concept you can + + + align:start position:0% +you to describe as concept you can +describe as actions okay okay you can + + align:start position:0% +describe as actions okay okay you can + + + align:start position:0% +describe as actions okay okay you can +decide the level of abstraction you feel + + align:start position:0% +decide the level of abstraction you feel + + + align:start position:0% +decide the level of abstraction you feel +comfortable with it learning + + align:start position:0% +comfortable with it learning + + + align:start position:0% +comfortable with it learning +language can be learning a + + align:start position:0% +language can be learning a + + + align:start position:0% +language can be learning a +language you will it it will be a bit + + align:start position:0% +language you will it it will be a bit + + + align:start position:0% +language you will it it will be a bit +more difficult but you can use to + + align:start position:0% +more difficult but you can use to + + + align:start position:0% +more difficult but you can use to +language I just can't + + align:start position:0% +language I just can't + + + align:start position:0% +language I just can't +remember okay no problem no problem + + align:start position:0% + + + + align:start position:0% + +the experience of man to ride a bike + + align:start position:0% + + + + align:start position:0% + +istic + + align:start position:0% + + + + align:start position:0% + +foree speech + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +I + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +good because I + + align:start position:0% + + + + align:start position:0% + +no I have + + align:start position:0% + + + + align:start position:0% + +to for + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +t + + align:start position:0% +t + + + align:start position:0% +t +[Music] + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +[Music] + + align:start position:0% + + + + align:start position:0% + +May that's his + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +spe for + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +pleas + + align:start position:0% + + + + align:start position:0% + +okay you have made if each one of you + + align:start position:0% +okay you have made if each one of you + + + align:start position:0% +okay you have made if each one of you +please put your experience in this in + + align:start position:0% +please put your experience in this in + + + align:start position:0% +please put your experience in this in +one sheet for show to + + align:start position:0% +one sheet for show to + + + align:start position:0% +one sheet for show to +everyone and it's it has sticky it's + + align:start position:0% +everyone and it's it has sticky it's + + + align:start position:0% +everyone and it's it has sticky it's +sticky in the back so you can put it up + + align:start position:0% +sticky in the back so you can put it up + + + align:start position:0% +sticky in the back so you can put it up +to right + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Time s it up to + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +right thank + + align:start position:0% +right thank + + + align:start position:0% +right thank +you okay so each one + + align:start position:0% +you okay so each one + + + align:start position:0% +you okay so each one +will yes we'll draw here is came from + + align:start position:0% +will yes we'll draw here is came from + + + align:start position:0% +will yes we'll draw here is came from +the process you know things like + + align:start position:0% +the process you know things like + + + align:start position:0% +the process you know things like +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +no I think + + align:start position:0% + + + + align:start position:0% + +uh we should be careful because perhaps + + align:start position:0% +uh we should be careful because perhaps + + + align:start position:0% +uh we should be careful because perhaps +the + + align:start position:0% + + + + align:start position:0% + +the it's possible + + align:start position:0% +the it's possible + + + align:start position:0% +the it's possible +perhaps should be better to design to to + + align:start position:0% +perhaps should be better to design to to + + + align:start position:0% +perhaps should be better to design to to +draw + + align:start position:0% +draw + + + align:start position:0% +draw +here excuse me I am + + align:start position:0% +here excuse me I am + + + align:start position:0% +here excuse me I am +afraid yes no no problem no but this one + + align:start position:0% +afraid yes no no problem no but this one + + + align:start position:0% +afraid yes no no problem no but this one +may be possible + + align:start position:0% + + + + align:start position:0% + +it's okay so far but I could use a + + align:start position:0% +it's okay so far but I could use a + + + align:start position:0% +it's okay so far but I could use a +different marker + + align:start position:0% +different marker + + + align:start position:0% +different marker +or yeah this is not + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so ah to Sky okay + + align:start position:0% +so ah to Sky okay + + + align:start position:0% +so ah to Sky okay +and you to tight yeah + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% + + + + align:start position:0% + +markering bike GRE I'm up okay + + align:start position:0% + + + + align:start position:0% + +ride a bike drive a car anything + + align:start position:0% +ride a bike drive a car anything + + + align:start position:0% +ride a bike drive a car anything +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +yeah okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Very Yes Yes + + align:start position:0% + + + + align:start position:0% + +markers + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Fore they just + + align:start position:0% + + + + align:start position:0% + +been + + align:start position:0% + + + + align:start position:0% + +yeah yeah okay you make some scheme like + + align:start position:0% +yeah yeah okay you make some scheme like + + + align:start position:0% +yeah yeah okay you make some scheme like +this after okay + + align:start position:0% + + + + align:start position:0% + +yeah want okay + + align:start position:0% + + + + align:start position:0% + +yes okay + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah can I gener and DET the + + align:start position:0% + + + + align:start position:0% + +yes yes because it's too much text for + + align:start position:0% +yes yes because it's too much text for + + + align:start position:0% +yes yes because it's too much text for +put in here no it's okay but after that + + align:start position:0% +put in here no it's okay but after that + + + align:start position:0% +put in here no it's okay but after that +you can add this with this for the the + + align:start position:0% +you can add this with this for the the + + + align:start position:0% +you can add this with this for the the +course for for the record of the course + + align:start position:0% +course for for the record of the course + + + align:start position:0% +course for for the record of the course +okay but you can explain + + align:start position:0% + + + + align:start position:0% + +never seen + + align:start position:0% + + + + align:start position:0% + +TR + + align:start position:0% + + + + align:start position:0% + +yeah you're right + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +what's going on there + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +do for + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +stop + + align:start position:0% + + + + align:start position:0% + +it that's exactly right but apparently + + align:start position:0% +it that's exactly right but apparently + + + align:start position:0% +it that's exactly right but apparently +we stop using + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% + + + + align:start position:0% + +okay let's + + align:start position:0% + + + + align:start position:0% + +begin yeah okay we we follow the + + align:start position:0% +begin yeah okay we we follow the + + + align:start position:0% +begin yeah okay we we follow the +spatial order okay we can begin for this + + align:start position:0% +spatial order okay we can begin for this + + + align:start position:0% +spatial order okay we can begin for this +huh + + align:start position:0% +huh + + + align:start position:0% +huh +yes don't get covered by video right + + align:start position:0% +yes don't get covered by video right + + + align:start position:0% +yes don't get covered by video right +this this I think I can okay great yes + + align:start position:0% +this this I think I can okay great yes + + + align:start position:0% +this this I think I can okay great yes +okay yeah let's begin + + align:start position:0% +okay yeah let's begin + + + align:start position:0% +okay yeah let's begin +here this one is riding a bite + + align:start position:0% +here this one is riding a bite + + + align:start position:0% +here this one is riding a bite +sorry + + align:start position:0% + + + + align:start position:0% + +please I remember when I was a kid um + + align:start position:0% +please I remember when I was a kid um + + + align:start position:0% +please I remember when I was a kid um +the first thing I'd do was really um to + + align:start position:0% +the first thing I'd do was really um to + + + align:start position:0% +the first thing I'd do was really um to +get prepared I'd really see if I have I + + align:start position:0% +get prepared I'd really see if I have I + + + align:start position:0% +get prepared I'd really see if I have I +in pants because I know I'll fall I know + + align:start position:0% +in pants because I know I'll fall I know + + + align:start position:0% +in pants because I know I'll fall I know +I'll get hurt and so I'm inan pants I'm + + align:start position:0% +I'll get hurt and so I'm inan pants I'm + + + align:start position:0% +I'll get hurt and so I'm inan pants I'm +in long sleeve okay and well I'm in the + + align:start position:0% +in long sleeve okay and well I'm in the + + + align:start position:0% +in long sleeve okay and well I'm in the +ne I'm I'm not in any sleeper but at + + align:start position:0% +ne I'm I'm not in any sleeper but at + + + align:start position:0% +ne I'm I'm not in any sleeper but at +least in a rubber shoes and I'll see to + + align:start position:0% +least in a rubber shoes and I'll see to + + + align:start position:0% +least in a rubber shoes and I'll see to +it that um I'll get on the bike to try + + align:start position:0% +it that um I'll get on the bike to try + + + align:start position:0% +it that um I'll get on the bike to try +if the chair is like low or you know if + + align:start position:0% +if the chair is like low or you know if + + + align:start position:0% +if the chair is like low or you know if +it actually fits me and it can be + + align:start position:0% +it actually fits me and it can be + + + align:start position:0% +it actually fits me and it can be +comfortable and I'll make sure when + + align:start position:0% +comfortable and I'll make sure when + + + align:start position:0% +comfortable and I'll make sure when +preparing that my brother is around you + + align:start position:0% +preparing that my brother is around you + + + align:start position:0% +preparing that my brother is around you +know he has to be there so and then I'll + + align:start position:0% +know he has to be there so and then I'll + + + align:start position:0% +know he has to be there so and then I'll +get on the trial which means my trial + + align:start position:0% +get on the trial which means my trial + + + align:start position:0% +get on the trial which means my trial +would be like my brother has to hold on + + align:start position:0% +would be like my brother has to hold on + + + align:start position:0% +would be like my brother has to hold on +the end of the bike so um I move on and + + align:start position:0% +the end of the bike so um I move on and + + + align:start position:0% +the end of the bike so um I move on and +it sways but I keep like are you there + + align:start position:0% +it sways but I keep like are you there + + + align:start position:0% +it sways but I keep like are you there +are you it's doing like that so I'm + + align:start position:0% +are you it's doing like that so I'm + + + align:start position:0% +are you it's doing like that so I'm +ensuring so I move I way I stop I move I + + align:start position:0% +ensuring so I move I way I stop I move I + + + align:start position:0% +ensuring so I move I way I stop I move I +way I stop and it's called him like uh + + align:start position:0% +way I stop and it's called him like uh + + + align:start position:0% +way I stop and it's called him like uh +you know you're not holding it too tight + + align:start position:0% +you know you're not holding it too tight + + + align:start position:0% +you know you're not holding it too tight +so that's it and then I would and then + + align:start position:0% +so that's it and then I would and then + + + align:start position:0% +so that's it and then I would and then +unconsciously I would not be aware that + + align:start position:0% +unconsciously I would not be aware that + + + align:start position:0% +unconsciously I would not be aware that +he would like um let go and so like I + + align:start position:0% +he would like um let go and so like I + + + align:start position:0% +he would like um let go and so like I +would fall so I moved move I fall I stop + + align:start position:0% +would fall so I moved move I fall I stop + + + align:start position:0% +would fall so I moved move I fall I stop +then I go back again to this one and + + align:start position:0% +then I go back again to this one and + + + align:start position:0% +then I go back again to this one and +tell him no come on you've got a hold + + align:start position:0% +tell him no come on you've got a hold + + + align:start position:0% +tell him no come on you've got a hold +you don't let let go first and all that + + align:start position:0% +you don't let let go first and all that + + + align:start position:0% +you don't let let go first and all that +but then um there'll be times that I'll + + align:start position:0% +but then um there'll be times that I'll + + + align:start position:0% +but then um there'll be times that I'll +succeed like um um I he he's he's going + + align:start position:0% +succeed like um um I he he's he's going + + + align:start position:0% +succeed like um um I he he's he's going +to let go and he succeeds and so I'll be + + align:start position:0% +to let go and he succeeds and so I'll be + + + align:start position:0% +to let go and he succeeds and so I'll be +like um moving moving and then I'll + + align:start position:0% +like um moving moving and then I'll + + + align:start position:0% +like um moving moving and then I'll +realize it's not there I stop but then + + align:start position:0% +realize it's not there I stop but then + + + align:start position:0% +realize it's not there I stop but then +it makes gives me confidence that yeah + + align:start position:0% +it makes gives me confidence that yeah + + + align:start position:0% +it makes gives me confidence that yeah +so we made I he was not around but then + + align:start position:0% +so we made I he was not around but then + + + align:start position:0% +so we made I he was not around but then +if I fall I'd go back to to the process + + align:start position:0% +if I fall I'd go back to to the process + + + align:start position:0% +if I fall I'd go back to to the process +of this one you know all this and then + + align:start position:0% +of this one you know all this and then + + + align:start position:0% +of this one you know all this and then +goes back to there so this one moving + + align:start position:0% +goes back to there so this one moving + + + align:start position:0% +goes back to there so this one moving +forth and trying to configure among all + + align:start position:0% +forth and trying to configure among all + + + align:start position:0% +forth and trying to configure among all +this it's trying to configure what I did + + align:start position:0% +this it's trying to configure what I did + + + align:start position:0% +this it's trying to configure what I did +well why why why I was I moving you know + + align:start position:0% +well why why why I was I moving you know + + + align:start position:0% +well why why why I was I moving you know +while he he let go and all that and um + + align:start position:0% +while he he let go and all that and um + + + align:start position:0% +while he he let go and all that and um +um so this will be like trying to see + + align:start position:0% +um so this will be like trying to see + + + align:start position:0% +um so this will be like trying to see +okay how was I how did I do it um but at + + align:start position:0% +okay how was I how did I do it um but at + + + align:start position:0% +okay how was I how did I do it um but at +the same time while I'm doing it like I + + align:start position:0% +the same time while I'm doing it like I + + + align:start position:0% +the same time while I'm doing it like I +get nervous and like okay this one I + + align:start position:0% +get nervous and like okay this one I + + + align:start position:0% +get nervous and like okay this one I +should hold this one I should hold no + + align:start position:0% +should hold this one I should hold no + + + align:start position:0% +should hold this one I should hold no +this one and they go together and hold + + align:start position:0% +this one and they go together and hold + + + align:start position:0% +this one and they go together and hold +so while doing all this and then it goes + + align:start position:0% +so while doing all this and then it goes + + + align:start position:0% +so while doing all this and then it goes +this stu okay thank you very much no I + + align:start position:0% +this stu okay thank you very much no I + + + align:start position:0% +this stu okay thank you very much no I +think that was very clear my my my + + align:start position:0% +think that was very clear my my my + + + align:start position:0% +think that was very clear my my my +feeling is that + + align:start position:0% +feeling is that + + + align:start position:0% +feeling is that +you from here you + + align:start position:0% +you from here you + + + align:start position:0% +you from here you +always not necessarily go through this + + align:start position:0% +always not necessarily go through this + + + align:start position:0% +always not necessarily go through this +getting prepared you went directly to + + align:start position:0% +getting prepared you went directly to + + + align:start position:0% +getting prepared you went directly to +this one or not no um this one is just + + align:start position:0% +this one or not no um this one is just + + + align:start position:0% +this one or not no um this one is just +like when I go and start all over again + + align:start position:0% +like when I go and start all over again + + + align:start position:0% +like when I go and start all over again +so I go all over when there's another + + align:start position:0% +so I go all over when there's another + + + align:start position:0% +so I go all over when there's another +practice round of practice again how old + + align:start position:0% +practice round of practice again how old + + + align:start position:0% +practice round of practice again how old +were you I was um I + + align:start position:0% +were you I was um I + + + align:start position:0% +were you I was um I +think + + align:start position:0% +think + + + align:start position:0% +think +seven + + align:start position:0% +seven + + + align:start position:0% +seven +yes okay thank you very much the idea is + + align:start position:0% +yes okay thank you very much the idea is + + + align:start position:0% +yes okay thank you very much the idea is +to identify P patterns okay but it was + + align:start position:0% +to identify P patterns okay but it was + + + align:start position:0% +to identify P patterns okay but it was +the big bike already I did not start + + align:start position:0% +the big bike already I did not start + + + align:start position:0% +the big bike already I did not start +with small children's bikes so it was + + align:start position:0% +with small children's bikes so it was + + + align:start position:0% +with small children's bikes so it was +like when I went into it + + align:start position:0% + + + + align:start position:0% + +who is the + + align:start position:0% + + + + align:start position:0% + +next p + + align:start position:0% + + + + align:start position:0% + +down can can you put the the title and + + align:start position:0% +down can can you put the the title and + + + align:start position:0% +down can can you put the the title and +your name + + align:start position:0% +your name + + + align:start position:0% +your name +please can you put your name + + align:start position:0% +please can you put your name + + + align:start position:0% +please can you put your name +[Music] + + align:start position:0% + + + + align:start position:0% + +CH put your name + + align:start position:0% + + + + align:start position:0% + +snowboarder so it's another it's another + + align:start position:0% +snowboarder so it's another it's another + + + align:start position:0% +snowboarder so it's another it's another +physical one just began to wonder + + align:start position:0% +physical one just began to wonder + + + align:start position:0% +physical one just began to wonder +whether there'll be differences between + + align:start position:0% +whether there'll be differences between + + + align:start position:0% +whether there'll be differences between +the the physical ones and the kind of + + align:start position:0% +the the physical ones and the kind of + + + align:start position:0% +the the physical ones and the kind of +non physical ones that we've got here + + align:start position:0% +non physical ones that we've got here + + + align:start position:0% +non physical ones that we've got here +but + + align:start position:0% +but + + + align:start position:0% +but +um yeah I mean I I've tried to put on + + align:start position:0% +um yeah I mean I I've tried to put on + + + align:start position:0% +um yeah I mean I I've tried to put on +I've tried to + + align:start position:0% +I've tried to + + + align:start position:0% +I've tried to +describe processes that I went through + + align:start position:0% +describe processes that I went through + + + align:start position:0% +describe processes that I went through +as I was learning and I kind of + + align:start position:0% +as I was learning and I kind of + + + align:start position:0% +as I was learning and I kind of +compressed it + + align:start position:0% +compressed it + + + align:start position:0% +compressed it +into thematic or kind of conceptual way + + align:start position:0% +into thematic or kind of conceptual way + + + align:start position:0% +into thematic or kind of conceptual way +of looking at it but basically from what + + align:start position:0% +of looking at it but basically from what + + + align:start position:0% +of looking at it but basically from what +I remember this is um when I was about + + align:start position:0% +I remember this is um when I was about + + + align:start position:0% +I remember this is um when I was about +14 um I had I started off not having + + align:start position:0% +14 um I had I started off not having + + + align:start position:0% +14 um I had I started off not having +done this thing before I went into a + + align:start position:0% +done this thing before I went into a + + + align:start position:0% +done this thing before I went into a +rental shop and I had uh some + + align:start position:0% +rental shop and I had uh some + + + align:start position:0% +rental shop and I had uh some +instructions given to me by the man who + + align:start position:0% +instructions given to me by the man who + + + align:start position:0% +instructions given to me by the man who +was renting a snowboard which was along + + align:start position:0% +was renting a snowboard which was along + + + align:start position:0% +was renting a snowboard which was along +the lines of you know you have your feet + + align:start position:0% +the lines of you know you have your feet + + + align:start position:0% +the lines of you know you have your feet +strapped in you put one in front of the + + align:start position:0% +strapped in you put one in front of the + + + align:start position:0% +strapped in you put one in front of the +other you have to test out whether + + align:start position:0% +other you have to test out whether + + + align:start position:0% +other you have to test out whether +you're going to slide this way or or + + align:start position:0% +you're going to slide this way or or + + + align:start position:0% +you're going to slide this way or or +this way that that's kind of um + + align:start position:0% +this way that that's kind of um + + + align:start position:0% +this way that that's kind of um +determined from one person to another + + align:start position:0% +determined from one person to another + + + align:start position:0% +determined from one person to another +but apart from that there are some um uh + + align:start position:0% +but apart from that there are some um uh + + + align:start position:0% +but apart from that there are some um uh +Universal things which you should be + + align:start position:0% +Universal things which you should be + + + align:start position:0% +Universal things which you should be +mindful of is how to balance yourself + + align:start position:0% +mindful of is how to balance yourself + + + align:start position:0% +mindful of is how to balance yourself +and what you should be aiming for and + + align:start position:0% +and what you should be aiming for and + + + align:start position:0% +and what you should be aiming for and +always stay on one Edge and be careful + + align:start position:0% +always stay on one Edge and be careful + + + align:start position:0% +always stay on one Edge and be careful +not to catch another Edge cuz you Em Up + + align:start position:0% +not to catch another Edge cuz you Em Up + + + align:start position:0% +not to catch another Edge cuz you Em Up +flat on your face and I also have a + + align:start position:0% +flat on your face and I also have a + + + align:start position:0% +flat on your face and I also have a +background knowledge of a of a different + + align:start position:0% +background knowledge of a of a different + + + align:start position:0% +background knowledge of a of a different +but somewhat related skill which is ski + + align:start position:0% +but somewhat related skill which is ski + + + align:start position:0% +but somewhat related skill which is ski +then so I took the the snowboard and + + align:start position:0% +then so I took the the snowboard and + + + align:start position:0% +then so I took the the snowboard and +went out on the slopes and um initially + + align:start position:0% +went out on the slopes and um initially + + + align:start position:0% +went out on the slopes and um initially +experienced some painful failors which + + align:start position:0% +experienced some painful failors which + + + align:start position:0% +experienced some painful failors which +involve you catching an edge and falling + + align:start position:0% +involve you catching an edge and falling + + + align:start position:0% +involve you catching an edge and falling +on the face and almost breaking your + + align:start position:0% +on the face and almost breaking your + + + align:start position:0% +on the face and almost breaking your +nose or hurting your wrist or something + + align:start position:0% +nose or hurting your wrist or something + + + align:start position:0% +nose or hurting your wrist or something +like that so um if we have this on a + + align:start position:0% +like that so um if we have this on a + + + align:start position:0% +like that so um if we have this on a +different plane like go from you know + + align:start position:0% +different plane like go from you know + + + align:start position:0% +different plane like go from you know +initial confidence of seeing other + + align:start position:0% +initial confidence of seeing other + + + align:start position:0% +initial confidence of seeing other +people doing it successfully bound to + + align:start position:0% +people doing it successfully bound to + + + align:start position:0% +people doing it successfully bound to +the de of pain and and general + + align:start position:0% +the de of pain and and general + + + align:start position:0% +the de of pain and and general +depression um getting to the next stage + + align:start position:0% +depression um getting to the next stage + + + align:start position:0% +depression um getting to the next stage +I thought that there was a kind of + + align:start position:0% +I thought that there was a kind of + + + align:start position:0% +I thought that there was a kind of +combination of lots of things going on + + align:start position:0% +combination of lots of things going on + + + align:start position:0% +combination of lots of things going on +in my mind at once which is watching + + align:start position:0% +in my mind at once which is watching + + + align:start position:0% +in my mind at once which is watching +other people doing it successfully + + align:start position:0% +other people doing it successfully + + + align:start position:0% +other people doing it successfully +learning how to forget the skill that I + + align:start position:0% +learning how to forget the skill that I + + + align:start position:0% +learning how to forget the skill that I +thought was similar but in fact turned + + align:start position:0% +thought was similar but in fact turned + + + align:start position:0% +thought was similar but in fact turned +out not to be similar um concentrating + + align:start position:0% +out not to be similar um concentrating + + + align:start position:0% +out not to be similar um concentrating +on the instructions which the person who + + align:start position:0% +on the instructions which the person who + + + align:start position:0% +on the instructions which the person who +could do it successfully he given me + + align:start position:0% +could do it successfully he given me + + + align:start position:0% +could do it successfully he given me +already um and um also sort of in anzing + + align:start position:0% +already um and um also sort of in anzing + + + align:start position:0% +already um and um also sort of in anzing +those instructions and learning how I + + align:start position:0% +those instructions and learning how I + + + align:start position:0% +those instructions and learning how I +was feeling related to the instructions + + align:start position:0% +was feeling related to the instructions + + + align:start position:0% +was feeling related to the instructions +that I've been given and I thought that + + align:start position:0% +that I've been given and I thought that + + + align:start position:0% +that I've been given and I thought that +those four areas eventually came + + align:start position:0% +those four areas eventually came + + + align:start position:0% +those four areas eventually came +together um and gave me my first + + align:start position:0% +together um and gave me my first + + + align:start position:0% +together um and gave me my first +successes which is this feeling of + + align:start position:0% +successes which is this feeling of + + + align:start position:0% +successes which is this feeling of +relation where when you are able to do a + + align:start position:0% +relation where when you are able to do a + + + align:start position:0% +relation where when you are able to do a +new skill for the first time and that + + align:start position:0% +new skill for the first time and that + + + align:start position:0% +new skill for the first time and that +was really nice + + align:start position:0% +was really nice + + + align:start position:0% +was really nice +um from there s I'm I am I doing + + align:start position:0% +um from there s I'm I am I doing + + + align:start position:0% +um from there s I'm I am I doing +something wrong is that why you're + + align:start position:0% +something wrong is that why you're + + + align:start position:0% +something wrong is that why you're +talking it's okay okay um + + align:start position:0% +talking it's okay okay um + + + align:start position:0% +talking it's okay okay um +I need to explain you I I have + + align:start position:0% +I need to explain you I I have + + + align:start position:0% +I need to explain you I I have +limitation for understanding some kind + + align:start position:0% +limitation for understanding some kind + + + align:start position:0% +limitation for understanding some kind +of your AC is different okay + + align:start position:0% +of your AC is different okay + + + align:start position:0% +of your AC is different okay +okay he he's helping me + + align:start position:0% +okay he he's helping me + + + align:start position:0% +okay he he's helping me +okay and we haven't brought to + + align:start position:0% +okay and we haven't brought to + + + align:start position:0% +okay and we haven't brought to +snowboarding yet but we will okay + + align:start position:0% +snowboarding yet but we will okay + + + align:start position:0% +snowboarding yet but we will okay +um from we I'll speed up a little + + align:start position:0% +um from we I'll speed up a little + + + align:start position:0% +um from we I'll speed up a little +bit no + + align:start position:0% + + + + align:start position:0% + +so I found that um that this was kind of + + align:start position:0% +so I found that um that this was kind of + + + align:start position:0% +so I found that um that this was kind of +an important bit for me cuz I found that + + align:start position:0% +an important bit for me cuz I found that + + + align:start position:0% +an important bit for me cuz I found that +the first time that I felt I was really + + align:start position:0% +the first time that I felt I was really + + + align:start position:0% +the first time that I felt I was really +in control of what I was doing and I I + + align:start position:0% +in control of what I was doing and I I + + + align:start position:0% +in control of what I was doing and I I +was able to to kind of be conscious off + + align:start position:0% +was able to to kind of be conscious off + + + align:start position:0% +was able to to kind of be conscious off +and measure in my mind what I was doing + + align:start position:0% +and measure in my mind what I was doing + + + align:start position:0% +and measure in my mind what I was doing +right and when it worked so this this is + + align:start position:0% +right and when it worked so this this is + + + align:start position:0% +right and when it worked so this this is +kind of important stage um after that I + + align:start position:0% +kind of important stage um after that I + + + align:start position:0% +kind of important stage um after that I +found that I was refining my technique + + align:start position:0% +found that I was refining my technique + + + align:start position:0% +found that I was refining my technique +by experimenting with what I was doing + + align:start position:0% +by experimenting with what I was doing + + + align:start position:0% +by experimenting with what I was doing +and watching other people more and sort + + align:start position:0% +and watching other people more and sort + + + align:start position:0% +and watching other people more and sort +of um this I guess there's a sort of + + align:start position:0% +of um this I guess there's a sort of + + + align:start position:0% +of um this I guess there's a sort of +circle going on here with some failures + + align:start position:0% +circle going on here with some failures + + + align:start position:0% +circle going on here with some failures +and some successes and some more painful + + align:start position:0% +and some successes and some more painful + + + align:start position:0% +and some successes and some more painful +Falls and then eventually um I would + + align:start position:0% +Falls and then eventually um I would + + + align:start position:0% +Falls and then eventually um I would +find I'm progressing to what um you + + align:start position:0% +find I'm progressing to what um you + + + align:start position:0% +find I'm progressing to what um you +would call a more advanced level and I + + align:start position:0% +would call a more advanced level and I + + + align:start position:0% +would call a more advanced level and I +just wonder um maybe there's an + + align:start position:0% +just wonder um maybe there's an + + + align:start position:0% +just wonder um maybe there's an +interesting discussion to be had about + + align:start position:0% +interesting discussion to be had about + + + align:start position:0% +interesting discussion to be had about +how we deem + + align:start position:0% +how we deem + + + align:start position:0% +how we deem +um how we how we judge Advanced levels + + align:start position:0% +um how we how we judge Advanced levels + + + align:start position:0% +um how we how we judge Advanced levels +like whether it's what we consider to be + + align:start position:0% +like whether it's what we consider to be + + + align:start position:0% +like whether it's what we consider to be +advanced so what you know other people + + align:start position:0% +advanced so what you know other people + + + align:start position:0% +advanced so what you know other people +um set the the criteria for being + + align:start position:0% +um set the the criteria for being + + + align:start position:0% +um set the the criteria for being +Advanced or whatever that that was just + + align:start position:0% +Advanced or whatever that that was just + + + align:start position:0% +Advanced or whatever that that was just +like turn + + align:start position:0% +like turn + + + align:start position:0% +like turn +forward okay thank you very much great + + align:start position:0% +forward okay thank you very much great + + + align:start position:0% +forward okay thank you very much great +explanation who will be the next one + + align:start position:0% +explanation who will be the next one + + + align:start position:0% +explanation who will be the next one +learning to read a map that okay can you + + align:start position:0% +learning to read a map that okay can you + + + align:start position:0% +learning to read a map that okay can you +come + + align:start position:0% +come + + + align:start position:0% +come +here but I think there's one before no + + align:start position:0% +here but I think there's one before no + + + align:start position:0% +here but I think there's one before no +no this is mine I I just put it out + + align:start position:0% + + + + align:start position:0% + +it's okay + + align:start position:0% + + + + align:start position:0% + +for learning to read a map which will be + + align:start position:0% +for learning to read a map which will be + + + align:start position:0% +for learning to read a map which will be +much easier for you and to read my + + align:start position:0% +much easier for you and to read my + + + align:start position:0% +much easier for you and to read my +handwriting + + align:start position:0% +handwriting + + + align:start position:0% +handwriting +um so I think I + + align:start position:0% +um so I think I + + + align:start position:0% +um so I think I +was or fifth grade sixth grade and we + + align:start position:0% +was or fifth grade sixth grade and we + + + align:start position:0% +was or fifth grade sixth grade and we +did a unit in my social studies class on + + align:start position:0% +did a unit in my social studies class on + + + align:start position:0% +did a unit in my social studies class on +how to read map and we got the basic + + align:start position:0% +how to read map and we got the basic + + + align:start position:0% +how to read map and we got the basic +explanation from our teacher of the + + align:start position:0% +explanation from our teacher of the + + + align:start position:0% +explanation from our teacher of the +rules of mapping your compass your scale + + align:start position:0% +rules of mapping your compass your scale + + + align:start position:0% +rules of mapping your compass your scale +notations grids how to make your roads + + align:start position:0% +notations grids how to make your roads + + + align:start position:0% +notations grids how to make your roads +and boundaries with the different size + + align:start position:0% +and boundaries with the different size + + + align:start position:0% +and boundaries with the different size +little lines and um Geographic and + + align:start position:0% +little lines and um Geographic and + + + align:start position:0% +little lines and um Geographic and +topological features and the assignment + + align:start position:0% +topological features and the assignment + + + align:start position:0% +topological features and the assignment +was + + align:start position:0% +was + + + align:start position:0% +was +to apply what I knew and draw a map of + + align:start position:0% +to apply what I knew and draw a map of + + + align:start position:0% +to apply what I knew and draw a map of +the United States making the notations + + align:start position:0% +the United States making the notations + + + align:start position:0% +the United States making the notations +as required and it was an enormous piece + + align:start position:0% +as required and it was an enormous piece + + + align:start position:0% +as required and it was an enormous piece +of paper it was not as small + + align:start position:0% +of paper it was not as small + + + align:start position:0% +of paper it was not as small +um then I can remember + + align:start position:0% +um then I can remember + + + align:start position:0% +um then I can remember +specifically transferring the idea and + + align:start position:0% +specifically transferring the idea and + + + align:start position:0% +specifically transferring the idea and +letting it evolve um and three basic + + align:start position:0% +letting it evolve um and three basic + + + align:start position:0% +letting it evolve um and three basic +points the guidelines apply to any MTH + + align:start position:0% +points the guidelines apply to any MTH + + + align:start position:0% +points the guidelines apply to any MTH +basic or complex and now I can get + + align:start position:0% +basic or complex and now I can get + + + align:start position:0% +basic or complex and now I can get +anywhere in the world that I want to go + + align:start position:0% +anywhere in the world that I want to go + + + align:start position:0% +anywhere in the world that I want to go +um Maps show more than geography they + + align:start position:0% +um Maps show more than geography they + + + align:start position:0% +um Maps show more than geography they +express a lot of ideas Transit maps + + align:start position:0% +express a lot of ideas Transit maps + + + align:start position:0% +express a lot of ideas Transit maps +being one of the immediate examples um + + align:start position:0% +being one of the immediate examples um + + + align:start position:0% +being one of the immediate examples um +and that I can make a map following + + align:start position:0% +and that I can make a map following + + + align:start position:0% +and that I can make a map following +basic standards which which can be read + + align:start position:0% +basic standards which which can be read + + + align:start position:0% +basic standards which which can be read +by others and reasonably understood so + + align:start position:0% +by others and reasonably understood so + + + align:start position:0% +by others and reasonably understood so +that I had the potential to + + align:start position:0% +that I had the potential to + + + align:start position:0% +that I had the potential to +actually uh pass that along this is my + + align:start position:0% +actually uh pass that along this is my + + + align:start position:0% +actually uh pass that along this is my +addendum these skills ceased to apply + + align:start position:0% +addendum these skills ceased to apply + + + align:start position:0% +addendum these skills ceased to apply +when navigating am's canvas and I have + + align:start position:0% +when navigating am's canvas and I have + + + align:start position:0% +when navigating am's canvas and I have +learned to wander aimlessly for + + align:start position:0% +learned to wander aimlessly for + + + align:start position:0% +learned to wander aimlessly for +prolonged periods of time and enjoy it + + align:start position:0% +prolonged periods of time and enjoy it + + + align:start position:0% +prolonged periods of time and enjoy it +relying greatly on local knowledge + + align:start position:0% +relying greatly on local knowledge + + + align:start position:0% +relying greatly on local knowledge +pointing me in the right direction so um + + align:start position:0% +pointing me in the right direction so um + + + align:start position:0% +pointing me in the right direction so um +but I can I can remember this very + + align:start position:0% +but I can I can remember this very + + + align:start position:0% +but I can I can remember this very +explicitly that you take these basic + + align:start position:0% +explicitly that you take these basic + + + align:start position:0% +explicitly that you take these basic +ideas which are numbers different colors + + align:start position:0% +ideas which are numbers different colors + + + align:start position:0% +ideas which are numbers different colors +of lines one is dotted one is solid you + + align:start position:0% +of lines one is dotted one is solid you + + + align:start position:0% +of lines one is dotted one is solid you +know you take these basic tiny things + + align:start position:0% +know you take these basic tiny things + + + align:start position:0% +know you take these basic tiny things +you know this is an inch but it's really + + align:start position:0% +you know this is an inch but it's really + + + align:start position:0% +you know this is an inch but it's really +10 miles and all of a sudden all these + + align:start position:0% +10 miles and all of a sudden all these + + + align:start position:0% +10 miles and all of a sudden all these +things click into place and it works on + + align:start position:0% +things click into place and it works on + + + align:start position:0% +things click into place and it works on +a an incredibly intricate + + align:start position:0% +a an incredibly intricate + + + align:start position:0% +a an incredibly intricate +level um although I remember + + align:start position:0% +level um although I remember + + + align:start position:0% +level um although I remember +specifically figuring out that Maps + + align:start position:0% +specifically figuring out that Maps + + + align:start position:0% +specifically figuring out that Maps +could not be too detailed like if you + + align:start position:0% +could not be too detailed like if you + + + align:start position:0% +could not be too detailed like if you +map the table and then somebody moves + + align:start position:0% +map the table and then somebody moves + + + align:start position:0% +map the table and then somebody moves +the scissors your map is irrelevant so + + align:start position:0% +the scissors your map is irrelevant so + + + align:start position:0% +the scissors your map is irrelevant so +but that you can have incredibly + + align:start position:0% +but that you can have incredibly + + + align:start position:0% +but that you can have incredibly +intricate things and then you can have + + align:start position:0% +intricate things and then you can have + + + align:start position:0% +intricate things and then you can have +incredibly broad things and um sort of + + align:start position:0% +incredibly broad things and um sort of + + + align:start position:0% +incredibly broad things and um sort of +like in the language of mathematics that + + align:start position:0% +like in the language of mathematics that + + + align:start position:0% +like in the language of mathematics that +it can be universally understood um and + + align:start position:0% +it can be universally understood um and + + + align:start position:0% +it can be universally understood um and +the security the feeling of security + + align:start position:0% +the security the feeling of security + + + align:start position:0% +the security the feeling of security +particularly I think as I was a child + + align:start position:0% +particularly I think as I was a child + + + align:start position:0% +particularly I think as I was a child +that came along with knowing that I had + + align:start position:0% +that came along with knowing that I had + + + align:start position:0% +that came along with knowing that I had +the potential not to get lost and had + + align:start position:0% +the potential not to get lost and had + + + align:start position:0% +the potential not to get lost and had +some control over the physical + + align:start position:0% +some control over the physical + + + align:start position:0% +some control over the physical +environment in which I existed um and I + + align:start position:0% +environment in which I existed um and I + + + align:start position:0% +environment in which I existed um and I +grew up in an enormous City so that was + + align:start position:0% +grew up in an enormous City so that was + + + align:start position:0% +grew up in an enormous City so that was +really quite a was really quite an event + + align:start position:0% +really quite a was really quite an event + + + align:start position:0% +really quite a was really quite an event +okay so Kate L to read a minut thank you + + align:start position:0% +okay so Kate L to read a minut thank you + + + align:start position:0% +okay so Kate L to read a minut thank you +very + + align:start position:0% + + + + align:start position:0% + +much who is this one I'm should I move + + align:start position:0% + + + + align:start position:0% + +it no you don't need to move + + align:start position:0% + + + + align:start position:0% + +it I love this + + align:start position:0% + + + + align:start position:0% + +I okay mine is about riding a + + align:start position:0% +I okay mine is about riding a + + + align:start position:0% +I okay mine is about riding a +bike um the context is that uh when I + + align:start position:0% +bike um the context is that uh when I + + + align:start position:0% +bike um the context is that uh when I +was little I was I fell and I just gave + + align:start position:0% +was little I was I fell and I just gave + + + align:start position:0% +was little I was I fell and I just gave +up on riding a bike so uh I missed out + + align:start position:0% +up on riding a bike so uh I missed out + + + align:start position:0% +up on riding a bike so uh I missed out +like on so many fun things that when I + + align:start position:0% +like on so many fun things that when I + + + align:start position:0% +like on so many fun things that when I +was older actually when I was already + + align:start position:0% +was older actually when I was already + + + align:start position:0% +was older actually when I was already +married and had a kid I went to another + + align:start position:0% +married and had a kid I went to another + + + align:start position:0% +married and had a kid I went to another +trip and I was about to miss out on one + + align:start position:0% +trip and I was about to miss out on one + + + align:start position:0% +trip and I was about to miss out on one +of the greatest bike rides that you know + + align:start position:0% +of the greatest bike rides that you know + + + align:start position:0% +of the greatest bike rides that you know +ever and I decided I was going to do + + align:start position:0% +ever and I decided I was going to do + + + align:start position:0% +ever and I decided I was going to do +that so the day before the trip I + + align:start position:0% +that so the day before the trip I + + + align:start position:0% +that so the day before the trip I +decided I was going to just go for it + + align:start position:0% +decided I was going to just go for it + + + align:start position:0% +decided I was going to just go for it +and do it and so I tried to uh sort of + + align:start position:0% +and do it and so I tried to uh sort of + + + align:start position:0% +and do it and so I tried to uh sort of +um I don't know make that those ideas + + align:start position:0% +um I don't know make that those ideas + + + align:start position:0% +um I don't know make that those ideas +that went through my head like put them + + align:start position:0% +that went through my head like put them + + + align:start position:0% +that went through my head like put them +into concer or so whatever so I I just + + align:start position:0% +into concer or so whatever so I I just + + + align:start position:0% +into concer or so whatever so I I just +decided that the point. one was deciding + + align:start position:0% +decided that the point. one was deciding + + + align:start position:0% +decided that the point. one was deciding +the outcome I really wanted it so much + + align:start position:0% +the outcome I really wanted it so much + + + align:start position:0% +the outcome I really wanted it so much +to go to that trip that uh it made the + + align:start position:0% +to go to that trip that uh it made the + + + align:start position:0% +to go to that trip that uh it made the +fear go away it was like secondary and I + + align:start position:0% +fear go away it was like secondary and I + + + align:start position:0% +fear go away it was like secondary and I +just wanted to go so I had my mindset on + + align:start position:0% +just wanted to go so I had my mindset on + + + align:start position:0% +just wanted to go so I had my mindset on +that which was was what kept me from + + align:start position:0% +that which was was what kept me from + + + align:start position:0% +that which was was what kept me from +doing it before then I just thought of + + align:start position:0% +doing it before then I just thought of + + + align:start position:0% +doing it before then I just thought of +the idea of visualizing myself riding + + align:start position:0% +the idea of visualizing myself riding + + + align:start position:0% +the idea of visualizing myself riding +the bike because what I wanted to do was + + align:start position:0% +the bike because what I wanted to do was + + + align:start position:0% +the bike because what I wanted to do was +not really just ride it I just wanted to + + align:start position:0% +not really just ride it I just wanted to + + + align:start position:0% +not really just ride it I just wanted to +feel um you know I wanted to feel the + + align:start position:0% +feel um you know I wanted to feel the + + + align:start position:0% +feel um you know I wanted to feel the +air in my face and I wanted to be able + + align:start position:0% +air in my face and I wanted to be able + + + align:start position:0% +air in my face and I wanted to be able +to look at all the all the the + + align:start position:0% +to look at all the all the the + + + align:start position:0% +to look at all the all the the +Landscapes that that we were going to go + + align:start position:0% +Landscapes that that we were going to go + + + align:start position:0% +Landscapes that that we were going to go +and and see and I just saw myself + + align:start position:0% +and and see and I just saw myself + + + align:start position:0% +and and see and I just saw myself +writing it and I thought okay I I can do + + align:start position:0% +writing it and I thought okay I I can do + + + align:start position:0% +writing it and I thought okay I I can do +this then I was of course I've been + + align:start position:0% +this then I was of course I've been + + + align:start position:0% +this then I was of course I've been +watching others do it all the time so I + + align:start position:0% +watching others do it all the time so I + + + align:start position:0% +watching others do it all the time so I +figured yeah could probably just go + + align:start position:0% +figured yeah could probably just go + + + align:start position:0% +figured yeah could probably just go +ahead and do that and I started so I got + + align:start position:0% +ahead and do that and I started so I got + + + align:start position:0% +ahead and do that and I started so I got +on uh and I started sort of calibrating + + align:start position:0% +on uh and I started sort of calibrating + + + align:start position:0% +on uh and I started sort of calibrating +the movements cuz I I just did it by + + align:start position:0% +the movements cuz I I just did it by + + + align:start position:0% +the movements cuz I I just did it by +myself but I knew I had I had a deadline + + align:start position:0% +myself but I knew I had I had a deadline + + + align:start position:0% +myself but I knew I had I had a deadline +I had to by the end of the day I had to + + align:start position:0% +I had to by the end of the day I had to + + + align:start position:0% +I had to by the end of the day I had to +you know get it done so I just started + + align:start position:0% +you know get it done so I just started + + + align:start position:0% +you know get it done so I just started +just quickly checking on my different + + align:start position:0% +just quickly checking on my different + + + align:start position:0% +just quickly checking on my different +body parts but at the beginning it was + + align:start position:0% +body parts but at the beginning it was + + + align:start position:0% +body parts but at the beginning it was +it was painfully um very conscious I was + + align:start position:0% +it was painfully um very conscious I was + + + align:start position:0% +it was painfully um very conscious I was +very conscious of every part of my body + + align:start position:0% +very conscious of every part of my body + + + align:start position:0% +very conscious of every part of my body +and everything sort of hurt because I + + align:start position:0% +and everything sort of hurt because I + + + align:start position:0% +and everything sort of hurt because I +was very very tense but as I started to + + align:start position:0% +was very very tense but as I started to + + + align:start position:0% +was very very tense but as I started to +sort of getting it along I would start + + align:start position:0% +sort of getting it along I would start + + + align:start position:0% +sort of getting it along I would start +losing in up a little bit of my + + align:start position:0% +losing in up a little bit of my + + + align:start position:0% +losing in up a little bit of my +different body parts until and of course + + align:start position:0% +different body parts until and of course + + + align:start position:0% +different body parts until and of course +I fell and I bumped into things and but + + align:start position:0% +I fell and I bumped into things and but + + + align:start position:0% +I fell and I bumped into things and but +I started sort of checking what went on + + align:start position:0% +I started sort of checking what went on + + + align:start position:0% +I started sort of checking what went on +and as soon as I that part of the body + + align:start position:0% +and as soon as I that part of the body + + + align:start position:0% +and as soon as I that part of the body +was sort of get go Loose as I figured + + align:start position:0% +was sort of get go Loose as I figured + + + align:start position:0% +was sort of get go Loose as I figured +you know how that part work and uh well + + align:start position:0% +you know how that part work and uh well + + + align:start position:0% +you know how that part work and uh well +that's reaching trying to reach balance + + align:start position:0% +that's reaching trying to reach balance + + + align:start position:0% +that's reaching trying to reach balance +uh and the small results of course would + + align:start position:0% +uh and the small results of course would + + + align:start position:0% +uh and the small results of course would +be like the best thing because as soon + + align:start position:0% +be like the best thing because as soon + + + align:start position:0% +be like the best thing because as soon +as I was able to just go through a small + + align:start position:0% +as I was able to just go through a small + + + align:start position:0% +as I was able to just go through a small +uh length successfully I I would just + + align:start position:0% +uh length successfully I I would just + + + align:start position:0% +uh length successfully I I would just +get a feeling of the air on my on my + + align:start position:0% +get a feeling of the air on my on my + + + align:start position:0% +get a feeling of the air on my on my +face and then I would just decide I + + align:start position:0% +face and then I would just decide I + + + align:start position:0% +face and then I would just decide I +wanted to keep on going and keep on + + align:start position:0% +wanted to keep on going and keep on + + + align:start position:0% +wanted to keep on going and keep on +doing that and of course so I started to + + align:start position:0% +doing that and of course so I started to + + + align:start position:0% +doing that and of course so I started to +practice and I was there you know all + + align:start position:0% +practice and I was there you know all + + + align:start position:0% +practice and I was there you know all +afternoon making sure that I would be + + align:start position:0% +afternoon making sure that I would be + + + align:start position:0% +afternoon making sure that I would be +ready for the next day okay thank you + + align:start position:0% +ready for the next day okay thank you + + + align:start position:0% +ready for the next day okay thank you +very much yeah next one + + align:start position:0% +very much yeah next one + + + align:start position:0% +very much yeah next one +[Applause] + + align:start position:0% + + + + align:start position:0% + +um so when I was 17 or 16 or something I + + align:start position:0% +um so when I was 17 or 16 or something I + + + align:start position:0% +um so when I was 17 or 16 or something I +went to Sweden uh as an exchange student + + align:start position:0% +went to Sweden uh as an exchange student + + + align:start position:0% +went to Sweden uh as an exchange student +in high school and so in order to do + + align:start position:0% +in high school and so in order to do + + + align:start position:0% +in high school and so in order to do +that I was just thrown into a normal + + align:start position:0% +that I was just thrown into a normal + + + align:start position:0% +that I was just thrown into a normal +family and a normal high school so I had + + align:start position:0% +family and a normal high school so I had + + + align:start position:0% +family and a normal high school so I had +to learn the language I didn't know the + + align:start position:0% +to learn the language I didn't know the + + + align:start position:0% +to learn the language I didn't know the +language at all so I wrote about that + + align:start position:0% +language at all so I wrote about that + + + align:start position:0% +language at all so I wrote about that +and I think a little bit differently + + align:start position:0% +and I think a little bit differently + + + align:start position:0% +and I think a little bit differently +from some of these other ones I I I + + align:start position:0% +from some of these other ones I I I + + + align:start position:0% +from some of these other ones I I I +noticed that I focused a lot on Less on + + align:start position:0% +noticed that I focused a lot on Less on + + + align:start position:0% +noticed that I focused a lot on Less on +How I Learned and more on how I felt + + align:start position:0% +How I Learned and more on how I felt + + + align:start position:0% +How I Learned and more on how I felt +while I was going through the process so + + align:start position:0% +while I was going through the process so + + + align:start position:0% +while I was going through the process so +it's a little bit more of a cognitive + + align:start position:0% +it's a little bit more of a cognitive + + + align:start position:0% +it's a little bit more of a cognitive +psychology math um so at the very + + align:start position:0% +psychology math um so at the very + + + align:start position:0% +psychology math um so at the very +beginning uh the first couple months + + align:start position:0% +beginning uh the first couple months + + + align:start position:0% +beginning uh the first couple months +over the summer before I went I took a + + align:start position:0% +over the summer before I went I took a + + + align:start position:0% +over the summer before I went I took a +couple of classes so there was sort of a + + align:start position:0% +couple of classes so there was sort of a + + + align:start position:0% +couple of classes so there was sort of a +professional help and I had a book and I + + align:start position:0% +professional help and I had a book and I + + + align:start position:0% +professional help and I had a book and I +initially was I think I I sort of felt + + align:start position:0% +initially was I think I I sort of felt + + + align:start position:0% +initially was I think I I sort of felt +oh this is no problem I can do this this + + align:start position:0% +oh this is no problem I can do this this + + + align:start position:0% +oh this is no problem I can do this this +is you know it's hard but I can do it + + align:start position:0% +is you know it's hard but I can do it + + + align:start position:0% +is you know it's hard but I can do it +and then I got there and the first the + + align:start position:0% +and then I got there and the first the + + + align:start position:0% +and then I got there and the first the +maybe the first month or so I still + + align:start position:0% +maybe the first month or so I still + + + align:start position:0% +maybe the first month or so I still +still kind of felt that way but then it + + align:start position:0% +still kind of felt that way but then it + + + align:start position:0% +still kind of felt that way but then it +started getting more and more difficult + + align:start position:0% +started getting more and more difficult + + + align:start position:0% +started getting more and more difficult +especially as school started happening + + align:start position:0% +especially as school started happening + + + align:start position:0% +especially as school started happening +and everything was in foreign language + + align:start position:0% +and everything was in foreign language + + + align:start position:0% +and everything was in foreign language +and sure number of people here can + + align:start position:0% +and sure number of people here can + + + align:start position:0% +and sure number of people here can +probably relate to this experience um so + + align:start position:0% +probably relate to this experience um so + + + align:start position:0% +probably relate to this experience um so +I didn't know what was going on a lot of + + align:start position:0% +I didn't know what was going on a lot of + + + align:start position:0% +I didn't know what was going on a lot of +confusion very feeling overwhelmed + + align:start position:0% +confusion very feeling overwhelmed + + + align:start position:0% +confusion very feeling overwhelmed +feeling very Alone um and feeling kind + + align:start position:0% +feeling very Alone um and feeling kind + + + align:start position:0% +feeling very Alone um and feeling kind +of childlike and unable to really + + align:start position:0% +of childlike and unable to really + + + align:start position:0% +of childlike and unable to really +participate um and so there was a lot of + + align:start position:0% +participate um and so there was a lot of + + + align:start position:0% +participate um and so there was a lot of +incentive and motivation it comes back + + align:start position:0% +incentive and motivation it comes back + + + align:start position:0% +incentive and motivation it comes back +to some of the other comments that + + align:start position:0% +to some of the other comments that + + + align:start position:0% +to some of the other comments that +people been talking about the + + align:start position:0% +people been talking about the + + + align:start position:0% +people been talking about the +requirement + + align:start position:0% +requirement + + + align:start position:0% +requirement +or the and the uh extreme motivation + + align:start position:0% +or the and the uh extreme motivation + + + align:start position:0% +or the and the uh extreme motivation +just by you know whatever it you know + + align:start position:0% +just by you know whatever it you know + + + align:start position:0% +just by you know whatever it you know +you really wanted to learn it for for + + align:start position:0% +you really wanted to learn it for for + + + align:start position:0% +you really wanted to learn it for for +whatever reason um here it was it was + + align:start position:0% +whatever reason um here it was it was + + + align:start position:0% +whatever reason um here it was it was +sort of a necessity so there was a lot + + align:start position:0% +sort of a necessity so there was a lot + + + align:start position:0% +sort of a necessity so there was a lot +of in to learn um throughout this time + + align:start position:0% +of in to learn um throughout this time + + + align:start position:0% +of in to learn um throughout this time +there were a lot of moments of of + + align:start position:0% +there were a lot of moments of of + + + align:start position:0% +there were a lot of moments of of +failure and struggle and Challenge and + + align:start position:0% +failure and struggle and Challenge and + + + align:start position:0% +failure and struggle and Challenge and +this made me feel like I uh I had a lack + + align:start position:0% +this made me feel like I uh I had a lack + + + align:start position:0% +this made me feel like I uh I had a lack +of self-worth during this period um but + + align:start position:0% +of self-worth during this period um but + + + align:start position:0% +of self-worth during this period um but +then there were also uh breakthrough + + align:start position:0% +then there were also uh breakthrough + + + align:start position:0% +then there were also uh breakthrough +moments um where you know you felt very + + align:start position:0% +moments um where you know you felt very + + + align:start position:0% +moments um where you know you felt very +satisfied very elated be S Like This + + align:start position:0% +satisfied very elated be S Like This + + + align:start position:0% +satisfied very elated be S Like This +Magic Moment here um feeling you know + + align:start position:0% +Magic Moment here um feeling you know + + + align:start position:0% +Magic Moment here um feeling you know +successful times uh and there was sort + + align:start position:0% +successful times uh and there was sort + + + align:start position:0% +successful times uh and there was sort +of a sense overall here of of growing + + align:start position:0% +of a sense overall here of of growing + + + align:start position:0% +of a sense overall here of of growing +movement and transition sort of like + + align:start position:0% +movement and transition sort of like + + + align:start position:0% +movement and transition sort of like +going from childhood to adulthood all + + align:start position:0% +going from childhood to adulthood all + + + align:start position:0% +going from childhood to adulthood all +very short order and sort of like going + + align:start position:0% +very short order and sort of like going + + + align:start position:0% +very short order and sort of like going +from being unable to speak to being able + + align:start position:0% +from being unable to speak to being able + + + align:start position:0% +from being unable to speak to being able +to speak is a very much like growing + + align:start position:0% +to speak is a very much like growing + + + align:start position:0% +to speak is a very much like growing +process um and then there was sort of a + + align:start position:0% +process um and then there was sort of a + + + align:start position:0% +process um and then there was sort of a +point where I I started to be able to + + align:start position:0% +point where I I started to be able to + + + align:start position:0% +point where I I started to be able to +communicate on a sort of more more uh + + align:start position:0% +communicate on a sort of more more uh + + + align:start position:0% +communicate on a sort of more more uh +day-to-day level I mean it wasn't + + align:start position:0% +day-to-day level I mean it wasn't + + + align:start position:0% +day-to-day level I mean it wasn't +fluency necessarily but I could sort of + + align:start position:0% +fluency necessarily but I could sort of + + + align:start position:0% +fluency necessarily but I could sort of +get my basic needs across and and do + + align:start position:0% +get my basic needs across and and do + + + align:start position:0% +get my basic needs across and and do +things um there's actually a chart down + + align:start position:0% +things um there's actually a chart down + + + align:start position:0% +things um there's actually a chart down +here so these are the first two months + + align:start position:0% +here so these are the first two months + + + align:start position:0% +here so these are the first two months +this is my fluency and this is time so + + align:start position:0% +this is my fluency and this is time so + + + align:start position:0% +this is my fluency and this is time so +these are s the first two months are + + align:start position:0% +these are s the first two months are + + + align:start position:0% +these are s the first two months are +sort of a slow curve then I get there + + align:start position:0% +sort of a slow curve then I get there + + + align:start position:0% +sort of a slow curve then I get there +I'm actually in the country and bang I + + align:start position:0% +I'm actually in the country and bang I + + + align:start position:0% +I'm actually in the country and bang I +start really working very hard and being + + align:start position:0% +start really working very hard and being + + + align:start position:0% +start really working very hard and being +immersed and you know there's very steep + + align:start position:0% +immersed and you know there's very steep + + + align:start position:0% +immersed and you know there's very steep +learning curve and then um kind kind of + + align:start position:0% +learning curve and then um kind kind of + + + align:start position:0% +learning curve and then um kind kind of +starts to to Plateau out once you get + + align:start position:0% +starts to to Plateau out once you get + + + align:start position:0% +starts to to Plateau out once you get +kind of a basic rudimentary + + align:start position:0% +kind of a basic rudimentary + + + align:start position:0% +kind of a basic rudimentary +understanding of the language um and so + + align:start position:0% +understanding of the language um and so + + + align:start position:0% +understanding of the language um and so +then the the last section here which I'm + + align:start position:0% +then the the last section here which I'm + + + align:start position:0% +then the the last section here which I'm +going to talk about there's more of a + + align:start position:0% +going to talk about there's more of a + + + align:start position:0% +going to talk about there's more of a +plateau where there's still there's + + align:start position:0% +plateau where there's still there's + + + align:start position:0% +plateau where there's still there's +still uh transformation and change but + + align:start position:0% +still uh transformation and change but + + + align:start position:0% +still uh transformation and change but +you've kind of got the basics down and + + align:start position:0% +you've kind of got the basics down and + + + align:start position:0% +you've kind of got the basics down and +so what you're learning is more like + + align:start position:0% +so what you're learning is more like + + + align:start position:0% +so what you're learning is more like +nuances and more complicated ideas + + align:start position:0% +nuances and more complicated ideas + + + align:start position:0% +nuances and more complicated ideas +rather than your sort of basic grammar + + align:start position:0% +rather than your sort of basic grammar + + + align:start position:0% +rather than your sort of basic grammar +and vocabulary um and also along with + + align:start position:0% +and vocabulary um and also along with + + + align:start position:0% +and vocabulary um and also along with +that there was sort of a gradual + + align:start position:0% +that there was sort of a gradual + + + align:start position:0% +that there was sort of a gradual +incorporation into society where I + + align:start position:0% +incorporation into society where I + + + align:start position:0% +incorporation into society where I +started feeling like a real person that + + align:start position:0% +started feeling like a real person that + + + align:start position:0% +started feeling like a real person that +could really communicate and interact on + + align:start position:0% +could really communicate and interact on + + + align:start position:0% +could really communicate and interact on +on a regular way with other people and a + + align:start position:0% +on a regular way with other people and a + + + align:start position:0% +on a regular way with other people and a +strong sense of satisfaction + + align:start position:0% +strong sense of satisfaction + + + align:start position:0% +strong sense of satisfaction +accomplishment and self worth that comes + + align:start position:0% +accomplishment and self worth that comes + + + align:start position:0% +accomplishment and self worth that comes +along with acquiring a skill like Austin + + align:start position:0% +along with acquiring a skill like Austin + + + align:start position:0% +along with acquiring a skill like Austin +was talking about uh and a feeling like + + align:start position:0% +was talking about uh and a feeling like + + + align:start position:0% +was talking about uh and a feeling like +I sort of come come to some sort of well + + align:start position:0% +I sort of come come to some sort of well + + + align:start position:0% +I sort of come come to some sort of well +I said adulthood here maybe it's more + + align:start position:0% +I said adulthood here maybe it's more + + + align:start position:0% +I said adulthood here maybe it's more +like adolescent like + + align:start position:0% +like adolescent like + + + align:start position:0% +like adolescent like +teenager you know at least I wasn't you + + align:start position:0% +teenager you know at least I wasn't you + + + align:start position:0% +teenager you know at least I wasn't you +know I remember sitting on the bus at at + + align:start position:0% +know I remember sitting on the bus at at + + + align:start position:0% +know I remember sitting on the bus at at +at various points and hearing all these + + align:start position:0% +at various points and hearing all these + + + align:start position:0% +at various points and hearing all these +little kids talking to each other being + + align:start position:0% +little kids talking to each other being + + + align:start position:0% +little kids talking to each other being +like I give so much to just be able to + + align:start position:0% +like I give so much to just be able to + + + align:start position:0% +like I give so much to just be able to +talk like a fourth grade level second + + align:start position:0% +talk like a fourth grade level second + + + align:start position:0% +talk like a fourth grade level second +grade like being able to like + + align:start position:0% +grade like being able to like + + + align:start position:0% +grade like being able to like +communicate effectively even at like a + + align:start position:0% +communicate effectively even at like a + + + align:start position:0% +communicate effectively even at like a +12year old level you know whatever it + + align:start position:0% +12year old level you know whatever it + + + align:start position:0% +12year old level you know whatever it +was it was it was pretty + + align:start position:0% +was it was it was pretty + + + align:start position:0% +was it was it was pretty +exciting okay thank you very much the + + align:start position:0% +exciting okay thank you very much the + + + align:start position:0% +exciting okay thank you very much the +next + + align:start position:0% + + + + align:start position:0% + +one I did drive a car and sitting back + + align:start position:0% +one I did drive a car and sitting back + + + align:start position:0% +one I did drive a car and sitting back +there think this is definitely not the + + align:start position:0% +there think this is definitely not the + + + align:start position:0% +there think this is definitely not the +way that you should learn to drive a car + + align:start position:0% +way that you should learn to drive a car + + + align:start position:0% +way that you should learn to drive a car +but um it was the way I had to do it so + + align:start position:0% +but um it was the way I had to do it so + + + align:start position:0% +but um it was the way I had to do it so +um not given the opportunity until I was + + align:start position:0% +um not given the opportunity until I was + + + align:start position:0% +um not given the opportunity until I was +in college I was determined that I was + + align:start position:0% +in college I was determined that I was + + + align:start position:0% +in college I was determined that I was +going to get my mobility and I so I I + + align:start position:0% +going to get my mobility and I so I I + + + align:start position:0% +going to get my mobility and I so I I +didn't have a car so I contracted with + + align:start position:0% +didn't have a car so I contracted with + + + align:start position:0% +didn't have a car so I contracted with +the driving school of course it was + + align:start position:0% +the driving school of course it was + + + align:start position:0% +the driving school of course it was +seven lessons that it was paid for so + + align:start position:0% +seven lessons that it was paid for so + + + align:start position:0% +seven lessons that it was paid for so +each lesson concentrated on specific + + align:start position:0% +each lesson concentrated on specific + + + align:start position:0% +each lesson concentrated on specific +skills with some + + align:start position:0% +skills with some + + + align:start position:0% +skills with some +practice and with those skills I and I + + align:start position:0% +practice and with those skills I and I + + + align:start position:0% +practice and with those skills I and I +should have added here licensed driver + + align:start position:0% +should have added here licensed driver + + + align:start position:0% +should have added here licensed driver +then as a result of the seven one hour + + align:start position:0% +then as a result of the seven one hour + + + align:start position:0% +then as a result of the seven one hour +lessons and um what was lacking of + + align:start position:0% +lessons and um what was lacking of + + + align:start position:0% +lessons and um what was lacking of +course in that learning process was + + align:start position:0% +course in that learning process was + + + align:start position:0% +course in that learning process was +practice which is really frightening + + align:start position:0% +practice which is really frightening + + + align:start position:0% +practice which is really frightening +when I think back on it but with that + + align:start position:0% +when I think back on it but with that + + + align:start position:0% +when I think back on it but with that +license I was able then to buy my car + + align:start position:0% +license I was able then to buy my car + + + align:start position:0% +license I was able then to buy my car +and then I had + + align:start position:0% +and then I had + + + align:start position:0% +and then I had +practice so I not ADV this as the way to + + align:start position:0% +practice so I not ADV this as the way to + + + align:start position:0% +practice so I not ADV this as the way to +do it but um it was the way it + + align:start position:0% +do it but um it was the way it + + + align:start position:0% +do it but um it was the way it +happened and the expression you you + + align:start position:0% +happened and the expression you you + + + align:start position:0% +happened and the expression you you +these are things my feelings at the time + + align:start position:0% +these are things my feelings at the time + + + align:start position:0% +these are things my feelings at the time +can't think it changed much + + align:start position:0% + + + + align:start position:0% + +okay thank you very + + align:start position:0% +okay thank you very + + + align:start position:0% +okay thank you very +much can you + + align:start position:0% +much can you + + + align:start position:0% +much can you +be um Renee hi and uh this is about rock + + align:start position:0% +be um Renee hi and uh this is about rock + + + align:start position:0% +be um Renee hi and uh this is about rock +climbing and first the first uh level + + align:start position:0% +climbing and first the first uh level + + + align:start position:0% +climbing and first the first uh level +was actually kind of understanding The + + align:start position:0% +was actually kind of understanding The + + + align:start position:0% +was actually kind of understanding The +Challenge looking at the mountain and + + align:start position:0% +Challenge looking at the mountain and + + + align:start position:0% +Challenge looking at the mountain and +kind of saying oh + + align:start position:0% +kind of saying oh + + + align:start position:0% +kind of saying oh +crap thought that was you falling + + align:start position:0% + + + + align:start position:0% + +then I would I would look at other + + align:start position:0% +then I would I would look at other + + + align:start position:0% +then I would I would look at other +people doing it you just kind of climb + + align:start position:0% +people doing it you just kind of climb + + + align:start position:0% +people doing it you just kind of climb +you know that's no problem and then on + + align:start position:0% +you know that's no problem and then on + + + align:start position:0% +you know that's no problem and then on +my way to the mountain someone stopped + + align:start position:0% +my way to the mountain someone stopped + + + align:start position:0% +my way to the mountain someone stopped +me and said no there are + + align:start position:0% +me and said no there are + + + align:start position:0% +me and said no there are +rules and there's equipment that you + + align:start position:0% +rules and there's equipment that you + + + align:start position:0% +rules and there's equipment that you +need to learn how to + + align:start position:0% +need to learn how to + + + align:start position:0% +need to learn how to +use and so then okay fine I put it on + + align:start position:0% +use and so then okay fine I put it on + + + align:start position:0% +use and so then okay fine I put it on +and I started climbing and someone was + + align:start position:0% +and I started climbing and someone was + + + align:start position:0% +and I started climbing and someone was +holding me someone was taking care of me + + align:start position:0% +holding me someone was taking care of me + + + align:start position:0% +holding me someone was taking care of me +and then someone's giving me guidance do + + align:start position:0% +and then someone's giving me guidance do + + + align:start position:0% +and then someone's giving me guidance do +this do that um and then of course this + + align:start position:0% +this do that um and then of course this + + + align:start position:0% +this do that um and then of course this +is where I fall went ah yeah you had the + + align:start position:0% +is where I fall went ah yeah you had the + + + align:start position:0% +is where I fall went ah yeah you had the +safety Roes on exactly and my instructor + + align:start position:0% +safety Roes on exactly and my instructor + + + align:start position:0% +safety Roes on exactly and my instructor +went ah and the guy holding me went + + align:start position:0% +went ah and the guy holding me went + + + align:start position:0% +went ah and the guy holding me went +ah and then my friend + + align:start position:0% + + + + align:start position:0% + +went so there lots of things going at + + align:start position:0% +went so there lots of things going at + + + align:start position:0% +went so there lots of things going at +the same + + align:start position:0% +the same + + + align:start position:0% +the same +time and um so after falling a number of + + align:start position:0% +time and um so after falling a number of + + + align:start position:0% +time and um so after falling a number of +times not really reaching my my goal um + + align:start position:0% +times not really reaching my my goal um + + + align:start position:0% +times not really reaching my my goal um +one of the thing what I realized was + + align:start position:0% +one of the thing what I realized was + + + align:start position:0% +one of the thing what I realized was +that I actually needed to I guess what I + + align:start position:0% +that I actually needed to I guess what I + + + align:start position:0% +that I actually needed to I guess what I +did here actually was change my + + align:start position:0% +did here actually was change my + + + align:start position:0% +did here actually was change my +perspective it wasn't about going up it + + align:start position:0% +perspective it wasn't about going up it + + + align:start position:0% +perspective it wasn't about going up it +was about looking at it from as a wall + + align:start position:0% +was about looking at it from as a wall + + + align:start position:0% +was about looking at it from as a wall +and not as a as a goal and so it was + + align:start position:0% +and not as a as a goal and so it was + + + align:start position:0% +and not as a as a goal and so it was +about looking for the little places + + align:start position:0% +about looking for the little places + + + align:start position:0% +about looking for the little places +where to put my feet and hold and put my + + align:start position:0% +where to put my feet and hold and put my + + + align:start position:0% +where to put my feet and hold and put my +hands and that is what I was learning + + align:start position:0% +hands and that is what I was learning + + + align:start position:0% +hands and that is what I was learning +really not how to get to the top and + + align:start position:0% +really not how to get to the top and + + + align:start position:0% +really not how to get to the top and +that is what I used to get to the top + + align:start position:0% +that is what I used to get to the top + + + align:start position:0% +that is what I used to get to the top +but it was this was the skill that I was + + align:start position:0% +but it was this was the skill that I was + + + align:start position:0% +but it was this was the skill that I was +really learning okay thank you very + + align:start position:0% +really learning okay thank you very + + + align:start position:0% +really learning okay thank you very +much this + + align:start position:0% +much this + + + align:start position:0% +much this +who is the next + + align:start position:0% + + + + align:start position:0% + +one should I move it or is it okay here + + align:start position:0% +one should I move it or is it okay here + + + align:start position:0% +one should I move it or is it okay here +I can see it there okay okay so uh this + + align:start position:0% +I can see it there okay okay so uh this + + + align:start position:0% +I can see it there okay okay so uh this +is my representation about an experience + + align:start position:0% +is my representation about an experience + + + align:start position:0% +is my representation about an experience +that didn't happen in the past but it's + + align:start position:0% +that didn't happen in the past but it's + + + align:start position:0% +that didn't happen in the past but it's +still happening so it's something it's a + + align:start position:0% +still happening so it's something it's a + + + align:start position:0% +still happening so it's something it's a +combination between what goes throughout + + align:start position:0% +combination between what goes throughout + + + align:start position:0% +combination between what goes throughout +my mind and how do I feel towards the + + align:start position:0% +my mind and how do I feel towards the + + + align:start position:0% +my mind and how do I feel towards the +experience I'm going to I'm going + + align:start position:0% +experience I'm going to I'm going + + + align:start position:0% +experience I'm going to I'm going +through so it's an experience about a + + align:start position:0% +through so it's an experience about a + + + align:start position:0% +through so it's an experience about a +specific integration in a group uh in a + + align:start position:0% +specific integration in a group uh in a + + + align:start position:0% +specific integration in a group uh in a +focus group that has a different vision + + align:start position:0% +focus group that has a different vision + + + align:start position:0% +focus group that has a different vision +of the world that than compared to the + + align:start position:0% +of the world that than compared to the + + + align:start position:0% +of the world that than compared to the +one I had before I I came into this + + align:start position:0% +one I had before I I came into this + + + align:start position:0% +one I had before I I came into this +focus group so here the first thing that + + align:start position:0% +focus group so here the first thing that + + + align:start position:0% +focus group so here the first thing that +I did was why did I go there and for + + align:start position:0% +I did was why did I go there and for + + + align:start position:0% +I did was why did I go there and for +what reasons I was I was searching for + + align:start position:0% +what reasons I was I was searching for + + + align:start position:0% +what reasons I was I was searching for +something that I didn't know exactly + + align:start position:0% +something that I didn't know exactly + + + align:start position:0% +something that I didn't know exactly +what it was and and that it was an + + align:start position:0% +what it was and and that it was an + + + align:start position:0% +what it was and and that it was an +understanding of the world which I said + + align:start position:0% +understanding of the world which I said + + + align:start position:0% +understanding of the world which I said +I say here it's understanding of the + + align:start position:0% +I say here it's understanding of the + + + align:start position:0% +I say here it's understanding of the +world number one which is specific one + + align:start position:0% +world number one which is specific one + + + align:start position:0% +world number one which is specific one +and when I came into there there was a + + align:start position:0% +and when I came into there there was a + + + align:start position:0% +and when I came into there there was a +period perod of adaptation of simulation + + align:start position:0% +period perod of adaptation of simulation + + + align:start position:0% +period perod of adaptation of simulation +of different ideas of different views of + + align:start position:0% +of different ideas of different views of + + + align:start position:0% +of different ideas of different views of +the world of why we are here what what + + align:start position:0% +the world of why we are here what what + + + align:start position:0% +the world of why we are here what what +is your understanding about our + + align:start position:0% +is your understanding about our + + + align:start position:0% +is your understanding about our +relationship with others and how do we + + align:start position:0% +relationship with others and how do we + + + align:start position:0% +relationship with others and how do we +deal with that um so what is the role + + align:start position:0% +deal with that um so what is the role + + + align:start position:0% +deal with that um so what is the role +and the first question that came into my + + align:start position:0% +and the first question that came into my + + + align:start position:0% +and the first question that came into my +mind was what is the role of the + + align:start position:0% +mind was what is the role of the + + + align:start position:0% +mind was what is the role of the +individual in in the world in the cosm + + align:start position:0% +individual in in the world in the cosm + + + align:start position:0% +individual in in the world in the cosm +as a whole uh so there's this uh bubble + + align:start position:0% +as a whole uh so there's this uh bubble + + + align:start position:0% +as a whole uh so there's this uh bubble +here where you go through this process + + align:start position:0% +here where you go through this process + + + align:start position:0% +here where you go through this process +of ass simulation of new ideas and new + + align:start position:0% +of ass simulation of new ideas and new + + + align:start position:0% +of ass simulation of new ideas and new +conceptions of the world and then you go + + align:start position:0% +conceptions of the world and then you go + + + align:start position:0% +conceptions of the world and then you go +through a + + align:start position:0% +through a + + + align:start position:0% +through a +confused process of reconfiguration of + + align:start position:0% +confused process of reconfiguration of + + + align:start position:0% +confused process of reconfiguration of +your own ideas compared to the ones that + + align:start position:0% +your own ideas compared to the ones that + + + align:start position:0% +your own ideas compared to the ones that +you are receiving from the others uh and + + align:start position:0% +you are receiving from the others uh and + + + align:start position:0% +you are receiving from the others uh and +then you go through a new readaptation + + align:start position:0% +then you go through a new readaptation + + + align:start position:0% +then you go through a new readaptation +to a new language after you have + + align:start position:0% +to a new language after you have + + + align:start position:0% +to a new language after you have +simulated this all these new ideas and + + align:start position:0% +simulated this all these new ideas and + + + align:start position:0% +simulated this all these new ideas and +then I mean this is a process that it + + align:start position:0% +then I mean this is a process that it + + + align:start position:0% +then I mean this is a process that it +doesn't exactly goes like this it can go + + align:start position:0% +doesn't exactly goes like this it can go + + + align:start position:0% +doesn't exactly goes like this it can go +this way back and it can go from here to + + align:start position:0% +this way back and it can go from here to + + + align:start position:0% +this way back and it can go from here to +here I mean it's not a linear thing + + align:start position:0% +here I mean it's not a linear thing + + + align:start position:0% +here I mean it's not a linear thing +probably it should be more like around + + align:start position:0% +probably it should be more like around + + + align:start position:0% +probably it should be more like around +thing and then the thing is that you go + + align:start position:0% +thing and then the thing is that you go + + + align:start position:0% +thing and then the thing is that you go +back to the beginning again there's no + + align:start position:0% +back to the beginning again there's no + + + align:start position:0% +back to the beginning again there's no +there's not it's not a a particular + + align:start position:0% +there's not it's not a a particular + + + align:start position:0% +there's not it's not a a particular +objective way you go through this this + + align:start position:0% +objective way you go through this this + + + align:start position:0% +objective way you go through this this +and this and the result is that you + + align:start position:0% +and this and the result is that you + + + align:start position:0% +and this and the result is that you +don't know exactly what the result is + + align:start position:0% +don't know exactly what the result is + + + align:start position:0% +don't know exactly what the result is +and you keep searching for something I + + align:start position:0% +and you keep searching for something I + + + align:start position:0% +and you keep searching for something I +mean there's no answers for a specific + + align:start position:0% +mean there's no answers for a specific + + + align:start position:0% +mean there's no answers for a specific +question or specific fear or specific + + align:start position:0% +question or specific fear or specific + + + align:start position:0% +question or specific fear or specific +whatever uh and then you you actually + + align:start position:0% +whatever uh and then you you actually + + + align:start position:0% +whatever uh and then you you actually +have and you you actually need to have a + + align:start position:0% +have and you you actually need to have a + + + align:start position:0% +have and you you actually need to have a +new understanding of the world which is + + align:start position:0% +new understanding of the world which is + + + align:start position:0% +new understanding of the world which is +understanding of the world too which + + align:start position:0% +understanding of the world too which + + + align:start position:0% +understanding of the world too which +doesn't does doesn't mean it's a + + align:start position:0% +doesn't does doesn't mean it's a + + + align:start position:0% +doesn't does doesn't mean it's a +different one it's a different one from + + align:start position:0% +different one it's a different one from + + + align:start position:0% +different one it's a different one from +this one but it's not opposed to that + + align:start position:0% +this one but it's not opposed to that + + + align:start position:0% +this one but it's not opposed to that +one + + align:start position:0% +one + + + align:start position:0% +one +so yeah + + align:start position:0% +so yeah + + + align:start position:0% +so yeah +okay thank you very much stop + + align:start position:0% +okay thank you very much stop + + + align:start position:0% +okay thank you very much stop +here who will be the + + align:start position:0% +here who will be the + + + align:start position:0% +here who will be the +next uh so this is how I learned to type + + align:start position:0% +next uh so this is how I learned to type + + + align:start position:0% +next uh so this is how I learned to type +um so first I had to construct a + + align:start position:0% +um so first I had to construct a + + + align:start position:0% +um so first I had to construct a +supportive environment for learning + + align:start position:0% +supportive environment for learning + + + align:start position:0% +supportive environment for learning +which you know get a computer get a + + align:start position:0% +which you know get a computer get a + + + align:start position:0% +which you know get a computer get a +comfortable chair uh get a a program + + align:start position:0% +comfortable chair uh get a a program + + + align:start position:0% +comfortable chair uh get a a program +that would help you practice um then you + + align:start position:0% +that would help you practice um then you + + + align:start position:0% +that would help you practice um then you +have to select the first skill to learn + + align:start position:0% +have to select the first skill to learn + + + align:start position:0% +have to select the first skill to learn +a very concrete skill practice and so + + align:start position:0% +a very concrete skill practice and so + + + align:start position:0% +a very concrete skill practice and so +obviously the first and slow but then + + align:start position:0% +obviously the first and slow but then + + + align:start position:0% +obviously the first and slow but then +after a while you start to get fast and + + align:start position:0% +after a while you start to get fast and + + + align:start position:0% +after a while you start to get fast and +sort of semiconscious you don't really + + align:start position:0% +sort of semiconscious you don't really + + + align:start position:0% +sort of semiconscious you don't really +have to think about what you're doing + + align:start position:0% +have to think about what you're doing + + + align:start position:0% +have to think about what you're doing +too much then you sort of you sort once + + align:start position:0% +too much then you sort of you sort once + + + align:start position:0% +too much then you sort of you sort once +you feel comfortable with that you start + + align:start position:0% +you feel comfortable with that you start + + + align:start position:0% +you feel comfortable with that you start +thinking well what's the next skill I + + align:start position:0% +thinking well what's the next skill I + + + align:start position:0% +thinking well what's the next skill I +learned to learn um you determine that + + align:start position:0% +learned to learn um you determine that + + + align:start position:0% +learned to learn um you determine that +and then just keep looping around um so + + align:start position:0% +and then just keep looping around um so + + + align:start position:0% +and then just keep looping around um so +the skills that I went through were just + + align:start position:0% +the skills that I went through were just + + + align:start position:0% +the skills that I went through were just +the physical position of my body and + + align:start position:0% +the physical position of my body and + + + align:start position:0% +the physical position of my body and +hands typing a single character typing a + + align:start position:0% +hands typing a single character typing a + + + align:start position:0% +hands typing a single character typing a +short string of characters + + align:start position:0% +short string of characters + + + align:start position:0% +short string of characters +typing more complex strings and then + + align:start position:0% +typing more complex strings and then + + + align:start position:0% +typing more complex strings and then +progressively getting um using less of + + align:start position:0% +progressively getting um using less of + + + align:start position:0% +progressively getting um using less of +my brain less cognitive resources uh and + + align:start position:0% +my brain less cognitive resources uh and + + + align:start position:0% +my brain less cognitive resources uh and +attention to devoted uh devoted to the + + align:start position:0% +attention to devoted uh devoted to the + + + align:start position:0% +attention to devoted uh devoted to the +physical side of it and I could start + + align:start position:0% +physical side of it and I could start + + + align:start position:0% +physical side of it and I could start +bringing more uh mental aspects of + + align:start position:0% +bringing more uh mental aspects of + + + align:start position:0% +bringing more uh mental aspects of +thinking about what I was typing uh + + align:start position:0% +thinking about what I was typing uh + + + align:start position:0% +thinking about what I was typing uh +while I was tapping away okay thank + + align:start position:0% +while I was tapping away okay thank + + + align:start position:0% +while I was tapping away okay thank +you this the process in the right + + align:start position:0% +you this the process in the right + + + align:start position:0% +you this the process in the right +is the cycle + + align:start position:0% +is the cycle + + + align:start position:0% +is the cycle +yeah loopes of the cycle different Loops + + align:start position:0% +yeah loopes of the cycle different Loops + + + align:start position:0% +yeah loopes of the cycle different Loops +of the cycle yeah so like basically + + align:start position:0% +of the cycle yeah so like basically + + + align:start position:0% +of the cycle yeah so like basically +skill one go around there yeah okay okay + + align:start position:0% +skill one go around there yeah okay okay + + + align:start position:0% +skill one go around there yeah okay okay +thank you very + + align:start position:0% +thank you very + + + align:start position:0% +thank you very +much how I learn it from Skye yeah so + + align:start position:0% +much how I learn it from Skye yeah so + + + align:start position:0% +much how I learn it from Skye yeah so +learning how to ski was very memorable + + align:start position:0% +learning how to ski was very memorable + + + align:start position:0% +learning how to ski was very memorable +for me because I was born and raised in + + align:start position:0% +for me because I was born and raised in + + + align:start position:0% +for me because I was born and raised in +the Caribbean so the only white thing I + + align:start position:0% +the Caribbean so the only white thing I + + + align:start position:0% +the Caribbean so the only white thing I +was used to seeing on the ground was + + align:start position:0% +was used to seeing on the ground was + + + align:start position:0% +was used to seeing on the ground was +sand you know I'd never seen snow before + + align:start position:0% +sand you know I'd never seen snow before + + + align:start position:0% +sand you know I'd never seen snow before +um so that was the first thing and then + + align:start position:0% +um so that was the first thing and then + + + align:start position:0% +um so that was the first thing and then +and secondly I had a onelegged ski + + align:start position:0% +and secondly I had a onelegged ski + + + align:start position:0% +and secondly I had a onelegged ski +instructor so that was also really + + align:start position:0% +instructor so that was also really + + + align:start position:0% +instructor so that was also really +interesting so I really remember it um + + align:start position:0% +interesting so I really remember it um + + + align:start position:0% +interesting so I really remember it um +so anyway you start off you know you're + + align:start position:0% +so anyway you start off you know you're + + + align:start position:0% +so anyway you start off you know you're +piled into the ski school with all these + + align:start position:0% +piled into the ski school with all these + + + align:start position:0% +piled into the ski school with all these +people that you don't know and they kind + + align:start position:0% +people that you don't know and they kind + + + align:start position:0% +people that you don't know and they kind +of give you verbal instructions and tell + + align:start position:0% +of give you verbal instructions and tell + + + align:start position:0% +of give you verbal instructions and tell +you you know how to lean and put your + + align:start position:0% +you you know how to lean and put your + + + align:start position:0% +you you know how to lean and put your +feet like this if you want to stop and + + align:start position:0% +feet like this if you want to stop and + + + align:start position:0% +feet like this if you want to stop and +so I was like okay you know I can do + + align:start position:0% +so I was like okay you know I can do + + + align:start position:0% +so I was like okay you know I can do +that that's no problem so then they put + + align:start position:0% +that that's no problem so then they put + + + align:start position:0% +that that's no problem so then they put +you on this bunny slope you know which + + align:start position:0% +you on this bunny slope you know which + + + align:start position:0% +you on this bunny slope you know which +is this small hill but it seems really + + align:start position:0% +is this small hill but it seems really + + + align:start position:0% +is this small hill but it seems really +big to me + + align:start position:0% +big to me + + + align:start position:0% +big to me +um and then you have to put into + + align:start position:0% +um and then you have to put into + + + align:start position:0% +um and then you have to put into +practice you know these directives that + + align:start position:0% +practice you know these directives that + + + align:start position:0% +practice you know these directives that +that they've given to you um and so + + align:start position:0% +that they've given to you um and so + + + align:start position:0% +that they've given to you um and so +through the process you know I made a + + align:start position:0% +through the process you know I made a + + + align:start position:0% +through the process you know I made a +lot of mistakes um I fell down a lot and + + align:start position:0% +lot of mistakes um I fell down a lot and + + + align:start position:0% +lot of mistakes um I fell down a lot and +actually my favorite way of stopping was + + align:start position:0% +actually my favorite way of stopping was + + + align:start position:0% +actually my favorite way of stopping was +just crashing into somebody that's how I + + align:start position:0% +just crashing into somebody that's how I + + + align:start position:0% +just crashing into somebody that's how I +would stop myself that's my + + align:start position:0% +would stop myself that's my + + + align:start position:0% +would stop myself that's my +um yeah so you know you embarrass + + align:start position:0% +um yeah so you know you embarrass + + + align:start position:0% +um yeah so you know you embarrass +yourself and you know but then you know + + align:start position:0% +yourself and you know but then you know + + + align:start position:0% +yourself and you know but then you know +you just get up and you try again again + + align:start position:0% +you just get up and you try again again + + + align:start position:0% +you just get up and you try again again +and so then I learned how to correct my + + align:start position:0% +and so then I learned how to correct my + + + align:start position:0% +and so then I learned how to correct my +mistakes and my instructor you know + + align:start position:0% +mistakes and my instructor you know + + + align:start position:0% +mistakes and my instructor you know +didn't abandon me um you know so their + + align:start position:0% +didn't abandon me um you know so their + + + align:start position:0% +didn't abandon me um you know so their +encouragement then you get the hang of + + align:start position:0% +encouragement then you get the hang of + + + align:start position:0% +encouragement then you get the hang of +it and you kind of build confidence and + + align:start position:0% +it and you kind of build confidence and + + + align:start position:0% +it and you kind of build confidence and +then I was like a Speed Demon and I + + align:start position:0% +then I was like a Speed Demon and I + + + align:start position:0% +then I was like a Speed Demon and I +would like Zoom everywhere so bu that + + align:start position:0% +would like Zoom everywhere so bu that + + + align:start position:0% +would like Zoom everywhere so bu that +was fun once yeah no off the bunny soap + + align:start position:0% +was fun once yeah no off the bunny soap + + + align:start position:0% +was fun once yeah no off the bunny soap +I actually graduated um off the bunny + + align:start position:0% +I actually graduated um off the bunny + + + align:start position:0% +I actually graduated um off the bunny +soap you know and it was good cuz I + + align:start position:0% +soap you know and it was good cuz I + + + align:start position:0% +soap you know and it was good cuz I +realized that I had a lot you know a + + align:start position:0% +realized that I had a lot you know a + + + align:start position:0% +realized that I had a lot you know a +less way to fall than the adults did + + align:start position:0% +less way to fall than the adults did + + + align:start position:0% +less way to fall than the adults did +because I was just a little kid so that + + align:start position:0% +because I was just a little kid so that + + + align:start position:0% +because I was just a little kid so that +gave me confidence too but I just + + align:start position:0% +gave me confidence too but I just + + + align:start position:0% +gave me confidence too but I just +summarized the cycle as you know + + align:start position:0% +summarized the cycle as you know + + + align:start position:0% +summarized the cycle as you know +listening and receiving verbal + + align:start position:0% +listening and receiving verbal + + + align:start position:0% +listening and receiving verbal +instructions and then um practice and + + align:start position:0% +instructions and then um practice and + + + align:start position:0% +instructions and then um practice and +implementation of the knowledge that I + + align:start position:0% +implementation of the knowledge that I + + + align:start position:0% +implementation of the knowledge that I +received and then taking that knowledge + + align:start position:0% +received and then taking that knowledge + + + align:start position:0% +received and then taking that knowledge +and trying it but you know having to + + align:start position:0% +and trying it but you know having to + + + align:start position:0% +and trying it but you know having to +make mistakes because it's not you know + + align:start position:0% +make mistakes because it's not you know + + + align:start position:0% +make mistakes because it's not you know +perfect perfectly translated from Theory + + align:start position:0% +perfect perfectly translated from Theory + + + align:start position:0% +perfect perfectly translated from Theory +to practice um but through making those + + align:start position:0% +to practice um but through making those + + + align:start position:0% +to practice um but through making those +mistakes improving um and correcting um + + align:start position:0% +mistakes improving um and correcting um + + + align:start position:0% +mistakes improving um and correcting um +myself so that I achieve the goal of + + align:start position:0% +myself so that I achieve the goal of + + + align:start position:0% +myself so that I achieve the goal of +Cy okay thank you very much + + align:start position:0% + + + + align:start position:0% + +is that okay here yeah so mine is a very + + align:start position:0% +is that okay here yeah so mine is a very + + + align:start position:0% +is that okay here yeah so mine is a very +recent experience actually which I have + + align:start position:0% +recent experience actually which I have + + + align:start position:0% +recent experience actually which I have +still uh something to learn because I'm + + align:start position:0% +still uh something to learn because I'm + + + align:start position:0% +still uh something to learn because I'm +a long learning process because it's so + + align:start position:0% +a long learning process because it's so + + + align:start position:0% +a long learning process because it's so +Dynamic it is the how I learn key line + + align:start position:0% +Dynamic it is the how I learn key line + + + align:start position:0% +Dynamic it is the how I learn key line +system + + align:start position:0% + + + + align:start position:0% + +ambass that is a good one I like to love + + align:start position:0% +ambass that is a good one I like to love + + + align:start position:0% +ambass that is a good one I like to love +that one + + align:start position:0% +that one + + + align:start position:0% +that one +coming here you know I had some + + align:start position:0% +coming here you know I had some + + + align:start position:0% +coming here you know I had some +experience with different ke lines in + + align:start position:0% +experience with different ke lines in + + + align:start position:0% +experience with different ke lines in +different STS including some in Europe + + align:start position:0% +different STS including some in Europe + + + align:start position:0% +different STS including some in Europe +and I had some impression uh about the + + align:start position:0% +and I had some impression uh about the + + + align:start position:0% +and I had some impression uh about the +one in the United States and before + + align:start position:0% +one in the United States and before + + + align:start position:0% +one in the United States and before +coming uh to Boston we were given some + + align:start position:0% +coming uh to Boston we were given some + + + align:start position:0% +coming uh to Boston we were given some +information about it so I had some pain + + align:start position:0% +information about it so I had some pain + + + align:start position:0% +information about it so I had some pain +assumptions and I was expecting really + + align:start position:0% +assumptions and I was expecting really + + + align:start position:0% +assumptions and I was expecting really +it is good I was expecting after the to + + align:start position:0% +it is good I was expecting after the to + + + align:start position:0% +it is good I was expecting after the to +information something else different + + align:start position:0% +information something else different + + + align:start position:0% +information something else different +then I come here so those were the + + align:start position:0% +then I come here so those were the + + + align:start position:0% +then I come here so those were the +assumptions that I had uh with my uh + + align:start position:0% +assumptions that I had uh with my uh + + + align:start position:0% +assumptions that I had uh with my uh +previous practically uh the experience + + align:start position:0% +previous practically uh the experience + + + align:start position:0% +previous practically uh the experience +and also the knowledge about FAS then we + + align:start position:0% +and also the knowledge about FAS then we + + + align:start position:0% +and also the knowledge about FAS then we +came here and we tried with Once how to + + align:start position:0% +came here and we tried with Once how to + + + align:start position:0% +came here and we tried with Once how to +ride uh within a uh T line uh in that + + align:start position:0% +ride uh within a uh T line uh in that + + + align:start position:0% +ride uh within a uh T line uh in that +was + + align:start position:0% +was + + + align:start position:0% +was +okay and I started to use my + + align:start position:0% +okay and I started to use my + + + align:start position:0% +okay and I started to use my +mouse and there were some that I learned + + align:start position:0% +mouse and there were some that I learned + + + align:start position:0% +mouse and there were some that I learned +which were explicit that all that can be + + align:start position:0% +which were explicit that all that can be + + + align:start position:0% +which were explicit that all that can be +learned by observation so how the people + + align:start position:0% +learned by observation so how the people + + + align:start position:0% +learned by observation so how the people +stay there how the people go in how do + + align:start position:0% +stay there how the people go in how do + + + align:start position:0% +stay there how the people go in how do +people go out something like that and + + align:start position:0% +people go out something like that and + + + align:start position:0% +people go out something like that and +there are some things that uh you know + + align:start position:0% +there are some things that uh you know + + + align:start position:0% +there are some things that uh you know +the rules how to buy ticket how to uh I + + align:start position:0% +the rules how to buy ticket how to uh I + + + align:start position:0% +the rules how to buy ticket how to uh I +mean observe the changes something like + + align:start position:0% +mean observe the changes something like + + + align:start position:0% +mean observe the changes something like +that and I didn't know about some of the + + align:start position:0% +that and I didn't know about some of the + + + align:start position:0% +that and I didn't know about some of the +things that are Happ happen but you know + + align:start position:0% +things that are Happ happen but you know + + + align:start position:0% +things that are Happ happen but you know +it requires some experience observation + + align:start position:0% +it requires some experience observation + + + align:start position:0% +it requires some experience observation +for instance arrival + + align:start position:0% +for instance arrival + + + align:start position:0% +for instance arrival +time I was trying to find out at what + + align:start position:0% +time I was trying to find out at what + + + align:start position:0% +time I was trying to find out at what +time I should be in the uh in the stops + + align:start position:0% +time I should be in the uh in the stops + + + align:start position:0% +time I should be in the uh in the stops +and I couldn't find anywhere in the + + align:start position:0% +and I couldn't find anywhere in the + + + align:start position:0% +and I couldn't find anywhere in the +schedule and I and I found out sometime + + align:start position:0% +schedule and I and I found out sometime + + + align:start position:0% +schedule and I and I found out sometime +I think it was in such a strange place + + align:start position:0% +I think it was in such a strange place + + + align:start position:0% +I think it was in such a strange place +that nobody was looking at there because + + align:start position:0% +that nobody was looking at there because + + + align:start position:0% +that nobody was looking at there because +nobody was King but it was very strange + + align:start position:0% +nobody was King but it was very strange + + + align:start position:0% +nobody was King but it was very strange +to me yeah then afterwards I understood + + align:start position:0% +to me yeah then afterwards I understood + + + align:start position:0% +to me yeah then afterwards I understood +that it the train does not for the + + align:start position:0% +that it the train does not for the + + + align:start position:0% +that it the train does not for the +schedule that's why + + align:start position:0% +schedule that's why + + + align:start position:0% +schedule that's why +I I was scaring and looking at that and + + align:start position:0% +I I was scaring and looking at that and + + + align:start position:0% +I I was scaring and looking at that and +um yeah there are sometimes uh it is a + + align:start position:0% +um yeah there are sometimes uh it is a + + + align:start position:0% +um yeah there are sometimes uh it is a +green line and I was waiting for in the + + align:start position:0% +green line and I was waiting for in the + + + align:start position:0% +green line and I was waiting for in the +green line + + align:start position:0% +green line + + + align:start position:0% +green line +there and I think there was something BL + + align:start position:0% +there and I think there was something BL + + + align:start position:0% +there and I think there was something BL +in that line and the D line didn't come + + align:start position:0% +in that line and the D line didn't come + + + align:start position:0% +in that line and the D line didn't come +now too long time after a while I didn't + + align:start position:0% +now too long time after a while I didn't + + + align:start position:0% +now too long time after a while I didn't +realize and then there was you know + + align:start position:0% +realize and then there was you know + + + align:start position:0% +realize and then there was you know +B I said was at the other + + align:start position:0% +B I said was at the other + + + align:start position:0% +B I said was at the other +side I should go to the other so this is + + align:start position:0% +side I should go to the other so this is + + + align:start position:0% +side I should go to the other so this is +the experience that there have there are + + align:start position:0% +the experience that there have there are + + + align:start position:0% +the experience that there have there are +happening some uh immediate changes that + + align:start position:0% +happening some uh immediate changes that + + + align:start position:0% +happening some uh immediate changes that +you cannot I mean uh be told that you + + align:start position:0% +you cannot I mean uh be told that you + + + align:start position:0% +you cannot I mean uh be told that you +should be there and you shouldn't + + align:start position:0% +should be there and you shouldn't + + + align:start position:0% +should be there and you shouldn't +observe it and I L sometimes some uh + + align:start position:0% +observe it and I L sometimes some uh + + + align:start position:0% +observe it and I L sometimes some uh +Goods in the te line and I understood + + align:start position:0% +Goods in the te line and I understood + + + align:start position:0% +Goods in the te line and I understood +that no one nobody should lose anything + + align:start position:0% +that no one nobody should lose anything + + + align:start position:0% +that no one nobody should lose anything +in the T line otherwise they cannot find + + align:start position:0% +in the T line otherwise they cannot find + + + align:start position:0% +in the T line otherwise they cannot find +it anyway so these kind of things that + + align:start position:0% +it anyway so these kind of things that + + + align:start position:0% +it anyway so these kind of things that +uh are + + align:start position:0% +uh are + + + align:start position:0% +uh are +um learn and when I come here after + + align:start position:0% +um learn and when I come here after + + + align:start position:0% +um learn and when I come here after +these uh stages and then when I compare + + align:start position:0% +these uh stages and then when I compare + + + align:start position:0% +these uh stages and then when I compare +it with my assumptions there were lots + + align:start position:0% +it with my assumptions there were lots + + + align:start position:0% +it with my assumptions there were lots +of things that didn't match beforehand + + align:start position:0% +of things that didn't match beforehand + + + align:start position:0% +of things that didn't match beforehand +with my Lage so I understand that + + align:start position:0% +with my Lage so I understand that + + + align:start position:0% +with my Lage so I understand that +learning is Not Enough by reading or by + + align:start position:0% +learning is Not Enough by reading or by + + + align:start position:0% +learning is Not Enough by reading or by +being told or with the experiences of + + align:start position:0% +being told or with the experiences of + + + align:start position:0% +being told or with the experiences of +others and you go I mean knowing what is + + align:start position:0% +others and you go I mean knowing what is + + + align:start position:0% +others and you go I mean knowing what is +going on beforehand on on the on the + + align:start position:0% +going on beforehand on on the on the + + + align:start position:0% +going on beforehand on on the on the +what information given to you even your + + align:start position:0% +what information given to you even your + + + align:start position:0% +what information given to you even your +observation may not mean uh everything + + align:start position:0% +observation may not mean uh everything + + + align:start position:0% +observation may not mean uh everything +unless you don't try the thing by + + align:start position:0% +unless you don't try the thing by + + + align:start position:0% +unless you don't try the thing by +yourself by application then you + + align:start position:0% +yourself by application then you + + + align:start position:0% +yourself by application then you +understand and of course there are some + + align:start position:0% +understand and of course there are some + + + align:start position:0% +understand and of course there are some +things that from one point to the other + + align:start position:0% +things that from one point to the other + + + align:start position:0% +things that from one point to the other +one which would be the best connection + + align:start position:0% +one which would be the best connection + + + align:start position:0% +one which would be the best connection +is that it Line bus another teal line or + + align:start position:0% +is that it Line bus another teal line or + + + align:start position:0% +is that it Line bus another teal line or +teal line teal line another teal line + + align:start position:0% +teal line teal line another teal line + + + align:start position:0% +teal line teal line another teal line +some kind of things are um learned by + + align:start position:0% +some kind of things are um learned by + + + align:start position:0% +some kind of things are um learned by +experience by okay thank you very much + + align:start position:0% +experience by okay thank you very much + + + align:start position:0% +experience by okay thank you very much +okay + + align:start position:0% +okay + + + align:start position:0% +okay +everybody I want to show my even though + + align:start position:0% +everybody I want to show my even though + + + align:start position:0% +everybody I want to show my even though +I see the graphic but I think it's it's + + align:start position:0% +I see the graphic but I think it's it's + + + align:start position:0% +I see the graphic but I think it's it's +an important one to + + align:start position:0% + + + + align:start position:0% + +show and I'm going to show you why I + + align:start position:0% +show and I'm going to show you why I + + + align:start position:0% +show and I'm going to show you why I +think this is a I learned to ski when I + + align:start position:0% +think this is a I learned to ski when I + + + align:start position:0% +think this is a I learned to ski when I +was 26 where should + + align:start position:0% + + + + align:start position:0% + +I okay I learned this ski when I was 26 + + align:start position:0% +I okay I learned this ski when I was 26 + + + align:start position:0% +I okay I learned this ski when I was 26 +28 my daughter was four years old the + + align:start position:0% +28 my daughter was four years old the + + + align:start position:0% +28 my daughter was four years old the +only reason I went to learn to ski was + + align:start position:0% +only reason I went to learn to ski was + + + align:start position:0% +only reason I went to learn to ski was +because she wants to learn to ski I want + + align:start position:0% +because she wants to learn to ski I want + + + align:start position:0% +because she wants to learn to ski I want +I didn't want her to be afraid of ski so + + align:start position:0% +I didn't want her to be afraid of ski so + + + align:start position:0% +I didn't want her to be afraid of ski so +I never left the roope I mean this is + + align:start position:0% +I never left the roope I mean this is + + + align:start position:0% +I never left the roope I mean this is +day small the bunny I was not sure the + + align:start position:0% +day small the bunny I was not sure the + + + align:start position:0% +day small the bunny I was not sure the +bunny so that was the spot we got the + + align:start position:0% +bunny so that was the spot we got the + + + align:start position:0% +bunny so that was the spot we got the +biggest the main reason I couldn't get + + align:start position:0% +biggest the main reason I couldn't get + + + align:start position:0% +biggest the main reason I couldn't get +to the biggest ones because my only + + align:start position:0% +to the biggest ones because my only + + + align:start position:0% +to the biggest ones because my only +concern was the Rope I hate the rope and + + align:start position:0% +concern was the Rope I hate the rope and + + + align:start position:0% +concern was the Rope I hate the rope and +because I couldn't pass the world I + + align:start position:0% +because I couldn't pass the world I + + + align:start position:0% +because I couldn't pass the world I +couldn't get to the ler one and of + + align:start position:0% +couldn't get to the ler one and of + + + align:start position:0% +couldn't get to the ler one and of +course I was afraid so my daughter + + align:start position:0% +course I was afraid so my daughter + + + align:start position:0% +course I was afraid so my daughter +finally she was able to teach me how to + + align:start position:0% +finally she was able to teach me how to + + + align:start position:0% +finally she was able to teach me how to +get to the RO and once that we got to + + align:start position:0% +get to the RO and once that we got to + + + align:start position:0% +get to the RO and once that we got to +the RO of course I would be more afraid + + align:start position:0% +the RO of course I would be more afraid + + + align:start position:0% +the RO of course I would be more afraid +when I was holding her I was able to go + + align:start position:0% +when I was holding her I was able to go + + + align:start position:0% +when I was holding her I was able to go +all the way down because my concern was + + align:start position:0% +all the way down because my concern was + + + align:start position:0% +all the way down because my concern was +I was Focus that I needed to do because + + align:start position:0% +I was Focus that I needed to do because + + + align:start position:0% +I was Focus that I needed to do because +she was doing but anyways so the first + + align:start position:0% +she was doing but anyways so the first + + + align:start position:0% +she was doing but anyways so the first +when I started to figure out in my see + + align:start position:0% +when I started to figure out in my see + + + align:start position:0% +when I started to figure out in my see +was the + + align:start position:0% +was the + + + align:start position:0% +was the +RO I started then to understand the + + align:start position:0% +RO I started then to understand the + + + align:start position:0% +RO I started then to understand the +prospects of what I needed to do and I + + align:start position:0% +prospects of what I needed to do and I + + + align:start position:0% +prospects of what I needed to do and I +was able to go to the small hill then + + align:start position:0% +was able to go to the small hill then + + + align:start position:0% +was able to go to the small hill then +once that we did this we're able to get + + align:start position:0% +once that we did this we're able to get + + + align:start position:0% +once that we did this we're able to get +to the larger one but even though in the + + align:start position:0% +to the larger one but even though in the + + + align:start position:0% +to the larger one but even though in the +larger one I still had my same concern + + align:start position:0% +larger one I still had my same concern + + + align:start position:0% +larger one I still had my same concern +was how she was going to get down and we + + align:start position:0% +was how she was going to get down and we + + + align:start position:0% +was how she was going to get down and we +did together for the first time but once + + align:start position:0% +did together for the first time but once + + + align:start position:0% +did together for the first time but once +she realized that she knew better than I + + align:start position:0% +she realized that she knew better than I + + + align:start position:0% +she realized that she knew better than I +did and I went down with her she I was + + align:start position:0% +did and I went down with her she I was + + + align:start position:0% +did and I went down with her she I was +able to go all the way down but once + + align:start position:0% +able to go all the way down but once + + + align:start position:0% +able to go all the way down but once +they she learned how to do and I knew + + align:start position:0% +they she learned how to do and I knew + + + align:start position:0% +they she learned how to do and I knew +she was going by myself I never made it + + align:start position:0% +she was going by myself I never made it + + + align:start position:0% +she was going by myself I never made it +until the made somebody always had to + + align:start position:0% +until the made somebody always had to + + + align:start position:0% +until the made somebody always had to +come to recruit me to the end so anyways + + align:start position:0% +come to recruit me to the end so anyways + + + align:start position:0% +come to recruit me to the end so anyways +my idea was that the only way I went + + align:start position:0% +my idea was that the only way I went + + + align:start position:0% +my idea was that the only way I went +because I hate the cold the only way I + + align:start position:0% +because I hate the cold the only way I + + + align:start position:0% +because I hate the cold the only way I +could see myself doing was to CH her not + + align:start position:0% +could see myself doing was to CH her not + + + align:start position:0% +could see myself doing was to CH her not +to do it myself so after that I went + + align:start position:0% +to do it myself so after that I went + + + align:start position:0% +to do it myself so after that I went +couple other times but I rather do the + + align:start position:0% +couple other times but I rather do the + + + align:start position:0% +couple other times but I rather do the +lunch than I did do the ski myself and + + align:start position:0% +lunch than I did do the ski myself and + + + align:start position:0% +lunch than I did do the ski myself and +then of course two years later I went + + align:start position:0% +then of course two years later I went + + + align:start position:0% +then of course two years later I went +again to do my sons which then chose to + + align:start position:0% +again to do my sons which then chose to + + + align:start position:0% +again to do my sons which then chose to +do the snowboarding and that was the end + + align:start position:0% +do the snowboarding and that was the end + + + align:start position:0% +do the snowboarding and that was the end +of my skin career so but anyways I think + + align:start position:0% +of my skin career so but anyways I think + + + align:start position:0% +of my skin career so but anyways I think +the fear it was my main fact but the + + align:start position:0% +the fear it was my main fact but the + + + align:start position:0% +the fear it was my main fact but the +confidence of helping them to ski it was + + align:start position:0% +confidence of helping them to ski it was + + + align:start position:0% +confidence of helping them to ski it was +the best thing of all but now one thing + + align:start position:0% +the best thing of all but now one thing + + + align:start position:0% +the best thing of all but now one thing +that found my kids today when my + + align:start position:0% +that found my kids today when my + + + align:start position:0% +that found my kids today when my +daughter's in college she had to ride it + + align:start position:0% +daughter's in college she had to ride it + + + align:start position:0% +daughter's in college she had to ride it +my mother taught me how to ski nobody + + align:start position:0% +my mother taught me how to ski nobody + + + align:start position:0% +my mother taught me how to ski nobody +believes but I did + + align:start position:0% + + + + align:start position:0% + +thank you very much we have 10 minutes + + align:start position:0% +thank you very much we have 10 minutes + + + align:start position:0% +thank you very much we have 10 minutes +or + + align:start position:0% +or + + + align:start position:0% +or +no no I have a class at 1 and I have + + align:start position:0% +no no I have a class at 1 and I have + + + align:start position:0% +no no I have a class at 1 and I have +okay doesn't mean I don't love you it + + align:start position:0% +okay doesn't mean I don't love you it + + + align:start position:0% +okay doesn't mean I don't love you it +just means I'm + + align:start position:0% + + + + align:start position:0% + +hungry 5 minutes okay Claudia was trying + + align:start position:0% +hungry 5 minutes okay Claudia was trying + + + align:start position:0% +hungry 5 minutes okay Claudia was trying +to identify some problems in your + + align:start position:0% +to identify some problems in your + + + align:start position:0% +to identify some problems in your +morning again what we meeting tomorrow + + align:start position:0% +morning again what we meeting tomorrow + + + align:start position:0% +morning again what we meeting tomorrow +morning again days is yes + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +okay it was interesting + + align:start position:0% + + + + align:start position:0% + +because things + + align:start position:0% +because things + + + align:start position:0% +because things +that brought in my mind was + + align:start position:0% +that brought in my mind was + + + align:start position:0% +that brought in my mind was +that most of the cases we began with + + align:start position:0% +that most of the cases we began with + + + align:start position:0% +that most of the cases we began with +instructions okay but with the + + align:start position:0% +instructions okay but with the + + + align:start position:0% +instructions okay but with the +instruction we had some assumptions too + + align:start position:0% +instruction we had some assumptions too + + + align:start position:0% +instruction we had some assumptions too +so we in assimilate the instructions + + align:start position:0% +so we in assimilate the instructions + + + align:start position:0% +so we in assimilate the instructions +using the Assumption we have about ski + + align:start position:0% +using the Assumption we have about ski + + + align:start position:0% +using the Assumption we have about ski +for + + align:start position:0% +for + + + align:start position:0% +for +snowboarding about the use of the T but + + align:start position:0% +snowboarding about the use of the T but + + + align:start position:0% +snowboarding about the use of the T but +in another country + + align:start position:0% +in another country + + + align:start position:0% +in another country +so we we don't receive the + + align:start position:0% +so we we don't receive the + + + align:start position:0% +so we we don't receive the +instructions in a pure way no we + + align:start position:0% +instructions in a pure way no we + + + align:start position:0% +instructions in a pure way no we +understand the instruction in some way + + align:start position:0% +understand the instruction in some way + + + align:start position:0% +understand the instruction in some way +different basing on our preview + + align:start position:0% +different basing on our preview + + + align:start position:0% +different basing on our preview +experience the the other thing important + + align:start position:0% +experience the the other thing important + + + align:start position:0% +experience the the other thing important +is + + align:start position:0% +is + + + align:start position:0% +is +the ER the role of the mistakes no I + + align:start position:0% +the ER the role of the mistakes no I + + + align:start position:0% +the ER the role of the mistakes no I +think was very important + + align:start position:0% +think was very important + + + align:start position:0% +think was very important +for everyone the the other thing was the + + align:start position:0% +for everyone the the other thing was the + + + align:start position:0% +for everyone the the other thing was the +the rule of the + + align:start position:0% +the rule of the + + + align:start position:0% +the rule of the +success the Magic Moment no it's very we + + align:start position:0% +success the Magic Moment no it's very we + + + align:start position:0% +success the Magic Moment no it's very we +can improve our learning when we have + + align:start position:0% +can improve our learning when we have + + + align:start position:0% +can improve our learning when we have +some kind of success that works as as a + + align:start position:0% +some kind of success that works as as a + + + align:start position:0% +some kind of success that works as as a +a ground for the new a level of learning + + align:start position:0% +a ground for the new a level of learning + + + align:start position:0% +a ground for the new a level of learning +no I think that + + align:start position:0% +no I think that + + + align:start position:0% +no I think that +is many people talk talk about this this + + align:start position:0% +is many people talk talk about this this + + + align:start position:0% +is many people talk talk about this this +component + + align:start position:0% + + + + align:start position:0% + +and in in some cases I thought much more + + align:start position:0% +and in in some cases I thought much more + + + align:start position:0% +and in in some cases I thought much more +complex because you told about different + + align:start position:0% +complex because you told about different + + + align:start position:0% +complex because you told about different +levels of + + align:start position:0% +levels of + + + align:start position:0% +levels of +acquiring ER the domain of the skill no + + align:start position:0% +acquiring ER the domain of the skill no + + + align:start position:0% +acquiring ER the domain of the skill no +and + + align:start position:0% +and + + + align:start position:0% +and +in in in other cases + + align:start position:0% +in in in other cases + + + align:start position:0% +in in in other cases +I it was described just like a a single + + align:start position:0% +I it was described just like a a single + + + align:start position:0% +I it was described just like a a single +process from learning the instruction + + align:start position:0% +process from learning the instruction + + + align:start position:0% +process from learning the instruction +until to be able to do something and not + + align:start position:0% +until to be able to do something and not + + + align:start position:0% +until to be able to do something and not +as a cycle no some + + align:start position:0% +as a cycle no some + + + align:start position:0% +as a cycle no some +explanations + + align:start position:0% + + + + align:start position:0% + +but the the other thing that I would + + align:start position:0% +but the the other thing that I would + + + align:start position:0% +but the the other thing that I would +like you to put attention is for your + + align:start position:0% +like you to put attention is for your + + + align:start position:0% +like you to put attention is for your +experience in describing a learning + + align:start position:0% +experience in describing a learning + + + align:start position:0% +experience in describing a learning +experience okay the experience of the + + align:start position:0% +experience okay the experience of the + + + align:start position:0% +experience okay the experience of the +last half hour or 1 hour perhaps okay + + align:start position:0% +last half hour or 1 hour perhaps okay + + + align:start position:0% +last half hour or 1 hour perhaps okay +it's an effort for ER making explicit + + align:start position:0% +it's an effort for ER making explicit + + + align:start position:0% +it's an effort for ER making explicit +some tcid knowledge you + + align:start position:0% +some tcid knowledge you + + + align:start position:0% +some tcid knowledge you +have okay so the the effort for + + align:start position:0% +have okay so the the effort for + + + align:start position:0% +have okay so the the effort for +explaining us one way to to to make tcid + + align:start position:0% +explaining us one way to to to make tcid + + + align:start position:0% +explaining us one way to to to make tcid +knowledge explicit + + align:start position:0% +knowledge explicit + + + align:start position:0% +knowledge explicit +is when when we try to to explain to + + align:start position:0% +is when when we try to to explain to + + + align:start position:0% +is when when we try to to explain to +other people we have never sought + + align:start position:0% +other people we have never sought + + + align:start position:0% +other people we have never sought +consciously about that before we try to + + align:start position:0% +consciously about that before we try to + + + align:start position:0% +consciously about that before we try to +explain in the effort for explain other + + align:start position:0% +explain in the effort for explain other + + + align:start position:0% +explain in the effort for explain other +people we get aware of of how we have + + align:start position:0% +people we get aware of of how we have + + + align:start position:0% +people we get aware of of how we have +our + + align:start position:0% +our + + + align:start position:0% +our +experience + + align:start position:0% +experience + + + align:start position:0% +experience +okay tomorrow we will begin 9:00 we will + + align:start position:0% +okay tomorrow we will begin 9:00 we will + + + align:start position:0% +okay tomorrow we will begin 9:00 we will +be dedicated + + align:start position:0% +be dedicated + + + align:start position:0% +be dedicated +to the practice of reflection the way + + align:start position:0% +to the practice of reflection the way + + + align:start position:0% +to the practice of reflection the way +how to step back to an experience in a + + align:start position:0% +how to step back to an experience in a + + + align:start position:0% +how to step back to an experience in a +more structured way like more than we + + align:start position:0% +more structured way like more than we + + + align:start position:0% +more structured way like more than we +made + + align:start position:0% +made + + + align:start position:0% +made +today we made today we will do this with + + align:start position:0% +today we made today we will do this with + + + align:start position:0% +today we made today we will do this with +Cesar mdo he will be what us with us + + align:start position:0% +Cesar mdo he will be what us with us + + + align:start position:0% +Cesar mdo he will be what us with us +tomorrow I just wanted to make one + + align:start position:0% +tomorrow I just wanted to make one + + + align:start position:0% +tomorrow I just wanted to make one +comment that I thought was s interesting + + align:start position:0% +comment that I thought was s interesting + + + align:start position:0% +comment that I thought was s interesting +was the way in which people describe + + align:start position:0% +was the way in which people describe + + + align:start position:0% +was the way in which people describe +their learning processes and how they + + align:start position:0% +their learning processes and how they + + + align:start position:0% +their learning processes and how they +related to the surrounding context and + + align:start position:0% +related to the surrounding context and + + + align:start position:0% +related to the surrounding context and +how some people were more focused on the + + align:start position:0% +how some people were more focused on the + + + align:start position:0% +how some people were more focused on the +cont and other people kind of edited out + + align:start position:0% +cont and other people kind of edited out + + + align:start position:0% +cont and other people kind of edited out +the context either the the physical + + align:start position:0% +the context either the the physical + + + align:start position:0% +the context either the the physical +context or the the psychological context + + align:start position:0% +context or the the psychological context + + + align:start position:0% +context or the the psychological context +or the social context of you know other + + align:start position:0% +or the social context of you know other + + + align:start position:0% +or the social context of you know other +people who help them or the the actual + + align:start position:0% +people who help them or the the actual + + + align:start position:0% +people who help them or the the actual +physicality of it or you it was just + + align:start position:0% +physicality of it or you it was just + + + align:start position:0% +physicality of it or you it was just +interesting to me how that factored into + + align:start position:0% +interesting to me how that factored into + + + align:start position:0% +interesting to me how that factored into +the way that people described it and and + + align:start position:0% +the way that people described it and and + + + align:start position:0% +the way that people described it and and +how that might tell us something about + + align:start position:0% +how that might tell us something about + + + align:start position:0% +how that might tell us something about +it like it's not all just a mental thing + + align:start position:0% +it like it's not all just a mental thing + + + align:start position:0% +it like it's not all just a mental thing +but there's something happening around + + align:start position:0% +but there's something happening around + + + align:start position:0% +but there's something happening around +us there different levels of abstraction + + align:start position:0% +us there different levels of abstraction + + + align:start position:0% +us there different levels of abstraction +too every person and different I + + align:start position:0% +too every person and different I + + + align:start position:0% +too every person and different I +different levels of ability to + + align:start position:0% +different levels of ability to + + + align:start position:0% +different levels of ability to +abstract and many people begins but + + align:start position:0% +abstract and many people begins but + + + align:start position:0% +abstract and many people begins but +getting + + align:start position:0% +getting + + + align:start position:0% +getting +prepared okay some others don't get + + align:start position:0% +prepared okay some others don't get + + + align:start position:0% +prepared okay some others don't get +prepared they just go to the action the + + align:start position:0% +prepared they just go to the action the + + + align:start position:0% +prepared they just go to the action the +other thing is that the the moment this + + align:start position:0% +other thing is that the the moment this + + + align:start position:0% +other thing is that the the moment this +moment that you told here to feel + + align:start position:0% +moment that you told here to feel + + + align:start position:0% +moment that you told here to feel +confused no that we will may we can fail + + align:start position:0% +confused no that we will may we can fail + + + align:start position:0% +confused no that we will may we can fail +and this triggers a lot of effort for to + + align:start position:0% +and this triggers a lot of effort for to + + + align:start position:0% +and this triggers a lot of effort for to +to learn in a new way no it's two two + + align:start position:0% +to learn in a new way no it's two two + + + align:start position:0% +to learn in a new way no it's two two +critical moments I I feel one is this + + align:start position:0% +critical moments I I feel one is this + + + align:start position:0% +critical moments I I feel one is this +one of the feeling of failure and the + + align:start position:0% +one of the feeling of failure and the + + + align:start position:0% +one of the feeling of failure and the +other one is the magic moment when + + align:start position:0% +other one is the magic moment when + + + align:start position:0% +other one is the magic moment when +we achieving to to get things done okay + + align:start position:0% +we achieving to to get things done okay + + + align:start position:0% +we achieving to to get things done okay +we have no time to analyze the + + align:start position:0% +we have no time to analyze the + + + align:start position:0% +we have no time to analyze the +experience today a bit more I'd like you + + align:start position:0% +experience today a bit more I'd like you + + + align:start position:0% +experience today a bit more I'd like you +before leave leaving please each one put + + align:start position:0% +before leave leaving please each one put + + + align:start position:0% +before leave leaving please each one put +put your name in The Experience okay \ No newline at end of file diff --git a/Qh3ZoZAzFT8.txt b/Qh3ZoZAzFT8.txt new file mode 100644 index 0000000000000000000000000000000000000000..7b46e5d11d81983dd6b35dae23bdfa0f7c22586d --- /dev/null +++ b/Qh3ZoZAzFT8.txt @@ -0,0 +1,2083 @@ +align:start position:0% + +okay good + + align:start position:0% + + + + align:start position:0% + +a lot of visual control here yeah so + + align:start position:0% +a lot of visual control here yeah so + + + align:start position:0% +a lot of visual control here yeah so +this so I wanted to talk to you about + + align:start position:0% +this so I wanted to talk to you about + + + align:start position:0% +this so I wanted to talk to you about +that before we talk about the um the + + align:start position:0% +that before we talk about the um the + + + align:start position:0% +that before we talk about the um the +stitching cell okay T time flow flow + + align:start position:0% +stitching cell okay T time flow flow + + + align:start position:0% +stitching cell okay T time flow flow +coordinators are required to + + align:start position:0% +coordinators are required to + + + align:start position:0% +coordinators are required to +keep detail of you have detail here of + + align:start position:0% +keep detail of you have detail here of + + + align:start position:0% +keep detail of you have detail here of +the pl versus actual if there are any + + align:start position:0% +the pl versus actual if there are any + + + align:start position:0% +the pl versus actual if there are any +deviation okay this is the production + + align:start position:0% +deviation okay this is the production + + + align:start position:0% +deviation okay this is the production +board for the last team that we haven't + + align:start position:0% +board for the last team that we haven't + + + align:start position:0% +board for the last team that we haven't +Lo yet but if there is a + + align:start position:0% +Lo yet but if there is a + + + align:start position:0% +Lo yet but if there is a +negative they have to put a reason in + + align:start position:0% +negative they have to put a reason in + + + align:start position:0% +negative they have to put a reason in +this case was waiting for the closing + + align:start position:0% +this case was waiting for the closing + + + align:start position:0% +this case was waiting for the closing +closing happen to be this is this is + + align:start position:0% +closing happen to be this is this is + + + align:start position:0% +closing happen to be this is this is +today's this is today so I have 5 after + + align:start position:0% +today's this is today so I have 5 after + + + align:start position:0% +today's this is today so I have 5 after +8 this ISS 7 8:00 so immediately this is + + align:start position:0% +8 this ISS 7 8:00 so immediately this is + + + align:start position:0% +8 this ISS 7 8:00 so immediately this is +filled in yes cuz we're now in this Shi + + align:start position:0% +filled in yes cuz we're now in this Shi + + + align:start position:0% +filled in yes cuz we're now in this Shi +here right so we'll see and we'll see + + align:start position:0% +here right so we'll see and we'll see + + + align:start position:0% +here right so we'll see and we'll see +what happen Okay um yeah that's a good + + align:start position:0% +what happen Okay um yeah that's a good + + + align:start position:0% +what happen Okay um yeah that's a good +observation so from a + + align:start position:0% +observation so from a + + + align:start position:0% +observation so from a +management for supervisors managers you + + align:start position:0% +management for supervisors managers you + + + align:start position:0% +management for supervisors managers you +can here and you know what waiting for + + align:start position:0% +can here and you know what waiting for + + + align:start position:0% +can here and you know what waiting for +closing so the first question I would + + align:start position:0% +closing so the first question I would + + + align:start position:0% +closing so the first question I would +have okay why what happened in the + + align:start position:0% +have okay why what happened in the + + + align:start position:0% +have okay why what happened in the +closing the + + align:start position:0% +closing the + + + align:start position:0% +closing the +teaching you have a board here that then + + align:start position:0% +teaching you have a board here that then + + + align:start position:0% +teaching you have a board here that then +the Flor says machine number seven was + + align:start position:0% +the Flor says machine number seven was + + + align:start position:0% +the Flor says machine number seven was +done for 10 minutes just big picture + + align:start position:0% +done for 10 minutes just big picture + + + align:start position:0% +done for 10 minutes just big picture +detail they have in their on their desk + + align:start position:0% +detail they have in their on their desk + + + align:start position:0% +detail they have in their on their desk +they have a more detail look that will + + align:start position:0% +they have a more detail look that will + + + align:start position:0% +they have a more detail look that will +tell them what happened with that + + align:start position:0% +tell them what happened with that + + + align:start position:0% +tell them what happened with that +particular machine but you see how + + align:start position:0% +particular machine but you see how + + + align:start position:0% +particular machine but you see how +they're connected very very good and + + align:start position:0% +they're connected very very good and + + + align:start position:0% +they're connected very very good and +it's part of the supervisor and + + align:start position:0% +it's part of the supervisor and + + + align:start position:0% +it's part of the supervisor and +management to make sure that they make + + align:start position:0% +management to make sure that they make + + + align:start position:0% +management to make sure that they make +sense they make sense morning here they + + align:start position:0% +sense they make sense morning here they + + + align:start position:0% +sense they make sense morning here they +broken the thread good morning how are + + align:start position:0% +broken the thread good morning how are + + + align:start position:0% +broken the thread good morning how are +you good you see they broke the thread + + align:start position:0% +you good you see they broke the thread + + + align:start position:0% +you good you see they broke the thread +that's why thre broke the thre broke + + align:start position:0% +that's why thre broke the thre broke + + + align:start position:0% +that's why thre broke the thre broke +that's what we talking about she knows + + align:start position:0% +that's what we talking about she knows + + + align:start position:0% +that's what we talking about she knows +about it I okay she the flow coordinator + + align:start position:0% +about it I okay she the flow coordinator + + + align:start position:0% +about it I okay she the flow coordinator +she a supervisor 25 years in the company + + align:start position:0% +she a supervisor 25 years in the company + + + align:start position:0% +she a supervisor 25 years in the company +what an asset that's my team yeah so + + align:start position:0% +what an asset that's my team yeah so + + + align:start position:0% +what an asset that's my team yeah so +this is her team I saw you're way up + + align:start position:0% +this is her team I saw you're way up + + + align:start position:0% +this is her team I saw you're way up +there so like we were talking before um + + align:start position:0% +there so like we were talking before um + + + align:start position:0% +there so like we were talking before um +we talk about the a generation problem + + align:start position:0% +we talk about the a generation problem + + + align:start position:0% +we talk about the a generation problem +solving involvement and we have a very + + align:start position:0% +solving involvement and we have a very + + + align:start position:0% +solving involvement and we have a very +simple way to um appreciate the ideas of + + align:start position:0% +simple way to um appreciate the ideas of + + + align:start position:0% +simple way to um appreciate the ideas of +our Associates um to talk about + + align:start position:0% +our Associates um to talk about + + + align:start position:0% +our Associates um to talk about +interaction supervisor Associates I will + + align:start position:0% +interaction supervisor Associates I will + + + align:start position:0% +interaction supervisor Associates I will +introduce to Rosary Munoz she's our + + align:start position:0% +introduce to Rosary Munoz she's our + + + align:start position:0% +introduce to Rosary Munoz she's our +supervisor + + align:start position:0% +supervisor + + + align:start position:0% +supervisor +W in the wi value stream she's been with + + align:start position:0% +W in the wi value stream she's been with + + + align:start position:0% +W in the wi value stream she's been with +the company 25 years so she's seen a lot + + align:start position:0% +the company 25 years so she's seen a lot + + + align:start position:0% +the company 25 years so she's seen a lot +from the the bat and Q world to the + + align:start position:0% +from the the bat and Q world to the + + + align:start position:0% +from the the bat and Q world to the +um it's okay B and Q world to to the + + align:start position:0% +um it's okay B and Q world to to the + + + align:start position:0% +um it's okay B and Q world to to the +lean world so any questions you want to + + align:start position:0% +lean world so any questions you want to + + + align:start position:0% +lean world so any questions you want to +ask her it's um yeah that Rosemary that + + align:start position:0% +ask her it's um yeah that Rosemary that + + + align:start position:0% +ask her it's um yeah that Rosemary that +is U really critic in lean + + align:start position:0% +is U really critic in lean + + + align:start position:0% +is U really critic in lean +transformation lean the people are + + align:start position:0% +transformation lean the people are + + + align:start position:0% +transformation lean the people are +really to me the key part critical part + + align:start position:0% +really to me the key part critical part + + + align:start position:0% +really to me the key part critical part +and you're a Frontline supervisor and + + align:start position:0% +and you're a Frontline supervisor and + + + align:start position:0% +and you're a Frontline supervisor and +you have a value stream I guess this is + + align:start position:0% +you have a value stream I guess this is + + + align:start position:0% +you have a value stream I guess this is +a kind of a picture of your value stream + + align:start position:0% +a kind of a picture of your value stream + + + align:start position:0% +a kind of a picture of your value stream +here yours is the gold value stream + + align:start position:0% +here yours is the gold value stream + + + align:start position:0% +here yours is the gold value stream +uhhuh so supervisor what are some of the + + align:start position:0% +uhhuh so supervisor what are some of the + + + align:start position:0% +uhhuh so supervisor what are some of the +things that you do when you work with + + align:start position:0% +things that you do when you work with + + + align:start position:0% +things that you do when you work with +your value stream team the most + + align:start position:0% +your value stream team the most + + + align:start position:0% +your value stream team the most +important is to work you know with asso + + align:start position:0% +important is to work you know with asso + + + align:start position:0% +important is to work you know with asso +and because like you know L is9 like 90% + + align:start position:0% +and because like you know L is9 like 90% + + + align:start position:0% +and because like you know L is9 like 90% +aoci and0 10% you know the rest material + + align:start position:0% +aoci and0 10% you know the rest material + + + align:start position:0% +aoci and0 10% you know the rest material +maybe supervisor the most important was + + align:start position:0% +maybe supervisor the most important was + + + align:start position:0% +maybe supervisor the most important was +you know to introduce lean uh system and + + align:start position:0% +you know to introduce lean uh system and + + + align:start position:0% +you know to introduce lean uh system and +they understand work with them you know + + align:start position:0% +they understand work with them you know + + + align:start position:0% +they understand work with them you know +that's the most important thing you know + + align:start position:0% +that's the most important thing you know + + + align:start position:0% +that's the most important thing you know +that we can do to + + align:start position:0% +that we can do to + + + align:start position:0% +that we can do to +get now CIO was told me that that one of + + align:start position:0% +get now CIO was told me that that one of + + + align:start position:0% +get now CIO was told me that that one of +the ways you do this is you get + + align:start position:0% +the ways you do this is you get + + + align:start position:0% +the ways you do this is you get +suggestions from them you engage them + + align:start position:0% +suggestions from them you engage them + + + align:start position:0% +suggestions from them you engage them +with suggestions so like Maria here + + align:start position:0% +with suggestions so like Maria here + + + align:start position:0% +with suggestions so like Maria here +she's contributed some kinds of + + align:start position:0% +she's contributed some kinds of + + + align:start position:0% +she's contributed some kinds of +suggestions and what happens to those + + align:start position:0% +suggestions and what happens to those + + + align:start position:0% +suggestions and what happens to those +suggestions when she contributes the + + align:start position:0% +suggestions when she contributes the + + + align:start position:0% +suggestions when she contributes the +suggestion they're giv you know that we + + align:start position:0% +suggestion they're giv you know that we + + + align:start position:0% +suggestion they're giv you know that we +we check if we try to implement most the + + align:start position:0% +we check if we try to implement most the + + + align:start position:0% +we check if we try to implement most the +all the idea that they have to you know + + align:start position:0% +all the idea that they have to you know + + + align:start position:0% +all the idea that they have to you know +when they give some idea we try to + + align:start position:0% +when they give some idea we try to + + + align:start position:0% +when they give some idea we try to +implement we work with them that way + + align:start position:0% +implement we work with them that way + + + align:start position:0% +implement we work with them that way +they feel more you know more um + + align:start position:0% +they feel more you know more um + + + align:start position:0% +they feel more you know more um +how I can say more involved you in in + + align:start position:0% +how I can say more involved you in in + + + align:start position:0% +how I can say more involved you in in +help you know the thing yeah how how do + + align:start position:0% +help you know the thing yeah how how do + + + align:start position:0% +help you know the thing yeah how how do +you help them with the idea how do you + + align:start position:0% +you help them with the idea how do you + + + align:start position:0% +you help them with the idea how do you +do you help them think to it do they + + align:start position:0% +do you help them think to it do they + + + align:start position:0% +do you help them think to it do they +come out with the idea by themselves + + align:start position:0% +come out with the idea by themselves + + + align:start position:0% +come out with the idea by themselves +they they come out with idea by + + align:start position:0% +they they come out with idea by + + + align:start position:0% +they they come out with idea by +themselves when they don't have no idea + + align:start position:0% +themselves when they don't have no idea + + + align:start position:0% +themselves when they don't have no idea +I go with them you know I say you know + + align:start position:0% +I go with them you know I say you know + + + align:start position:0% +I go with them you know I say you know +for example uh what you think you don't + + align:start position:0% +for example uh what you think you don't + + + align:start position:0% +for example uh what you think you don't +have no idea how you can get any idea + + align:start position:0% +have no idea how you can get any idea + + + align:start position:0% +have no idea how you can get any idea +sometime they say oh maybe I don't have + + align:start position:0% +sometime they say oh maybe I don't have + + + align:start position:0% +sometime they say oh maybe I don't have +too many time to think and something I + + align:start position:0% +too many time to think and something I + + + align:start position:0% +too many time to think and something I +what do you think if I put you know for + + align:start position:0% +what do you think if I put you know for + + + align:start position:0% +what do you think if I put you know for +example the B here close to you you can + + align:start position:0% +example the B here close to you you can + + + align:start position:0% +example the B here close to you you can +save you know one second I said that + + align:start position:0% +save you know one second I said that + + + align:start position:0% +save you know one second I said that +come in that's fine we can try you know + + align:start position:0% +come in that's fine we can try you know + + + align:start position:0% +come in that's fine we can try you know +they all try anything you know that I + + align:start position:0% +they all try anything you know that I + + + align:start position:0% +they all try anything you know that I +can them to yeah so what a as a + + align:start position:0% +can them to yeah so what a as a + + + align:start position:0% +can them to yeah so what a as a +supervisor what is a what what's the + + align:start position:0% +supervisor what is a what what's the + + + align:start position:0% +supervisor what is a what what's the +biggest challenge you have in this job + + align:start position:0% +biggest challenge you have in this job + + + align:start position:0% +biggest challenge you have in this job +you got 25 people that's a that's a lot + + align:start position:0% +you got 25 people that's a that's a lot + + + align:start position:0% +you got 25 people that's a that's a lot +right there work work together work + + align:start position:0% +right there work work together work + + + align:start position:0% +right there work work together work +together team work that's the most + + align:start position:0% +together team work that's the most + + + align:start position:0% +together team work that's the most +important you know when we work like te + + align:start position:0% +important you know when we work like te + + + align:start position:0% +important you know when we work like te +you can get anything you want you know + + align:start position:0% +you can get anything you want you know + + + align:start position:0% +you can get anything you want you know +if you work well super well let's go + + align:start position:0% +if you work well super well let's go + + + align:start position:0% +if you work well super well let's go +back in the factory you got you got a + + align:start position:0% +back in the factory you got you got a + + + align:start position:0% +back in the factory you got you got a +lot of work to do okay thank you thank + + align:start position:0% +lot of work to do okay thank you thank + + + align:start position:0% +lot of work to do okay thank you thank +you so this was + + align:start position:0% +you so this was + + + align:start position:0% +you so this was +called stitching before the computer + + align:start position:0% +called stitching before the computer + + + align:start position:0% +called stitching before the computer +stitching the upper was in the flat form + + align:start position:0% +stitching the upper was in the flat form + + + align:start position:0% +stitching the upper was in the flat form +yeah here is the first time the upper + + align:start position:0% +yeah here is the first time the upper + + + align:start position:0% +yeah here is the first time the upper +takes a 3D phone okay so it's a cell and + + align:start position:0% +takes a 3D phone okay so it's a cell and + + + align:start position:0% +takes a 3D phone okay so it's a cell and +basically it will + + align:start position:0% +basically it will + + + align:start position:0% +basically it will +follow DP stop here to understand you + + align:start position:0% +follow DP stop here to understand you + + + align:start position:0% +follow DP stop here to understand you +will follow this view y + + align:start position:0% + + + + align:start position:0% + +to Fed to what we call the assembly + + align:start position:0% +to Fed to what we call the assembly + + + align:start position:0% +to Fed to what we call the assembly +Department okay what is this the soul + + align:start position:0% +Department okay what is this the soul + + + align:start position:0% +Department okay what is this the soul +okay still in the stitching Department + + align:start position:0% +okay still in the stitching Department + + + align:start position:0% +okay still in the stitching Department +you still have flow Continuous Flow if + + align:start position:0% +you still have flow Continuous Flow if + + + align:start position:0% +you still have flow Continuous Flow if +you looked between the stations to Upper + + align:start position:0% +you looked between the stations to Upper + + + align:start position:0% +you looked between the stations to Upper +to Upper to Upper that associate just + + align:start position:0% +to Upper to Upper that associate just + + + align:start position:0% +to Upper to Upper that associate just +noted he did not put another shoe on + + align:start position:0% +noted he did not put another shoe on + + + align:start position:0% +noted he did not put another shoe on +that tray until one was removed conb + + align:start position:0% +that tray until one was removed conb + + + align:start position:0% +that tray until one was removed conb +okay so they pulling pulling yeah very + + align:start position:0% +okay so they pulling pulling yeah very + + + align:start position:0% +okay so they pulling pulling yeah very +critical that discipline is very very + + align:start position:0% +critical that discipline is very very + + + align:start position:0% +critical that discipline is very very +important you don't want that over + + align:start position:0% +important you don't want that over + + + align:start position:0% +important you don't want that over +production you're right two they're two + + align:start position:0% +production you're right two they're two + + + align:start position:0% +production you're right two they're two +there two there and you saw how they + + align:start position:0% +there two there and you saw how they + + + align:start position:0% +there two there and you saw how they +were stop I saw the switch yeah and they + + align:start position:0% +were stop I saw the switch yeah and they + + + align:start position:0% +were stop I saw the switch yeah and they +were stopped as soon as she pulled one + + align:start position:0% +were stopped as soon as she pulled one + + + align:start position:0% +were stopped as soon as she pulled one +off he put one there yeah it takes + + align:start position:0% +off he put one there yeah it takes + + + align:start position:0% +off he put one there yeah it takes +months and years to get that but they + + align:start position:0% +months and years to get that but they + + + align:start position:0% +months and years to get that but they +understand they understand uh that they + + align:start position:0% +understand they understand uh that they + + + align:start position:0% +understand they understand uh that they +over the shoes are not going anywhere if + + align:start position:0% +over the shoes are not going anywhere if + + + align:start position:0% +over the shoes are not going anywhere if +they over produce you know it looks like + + align:start position:0% +they over produce you know it looks like + + + align:start position:0% +they over produce you know it looks like +a symphony everybody's playing together + + align:start position:0% +a symphony everybody's playing together + + + align:start position:0% +a symphony everybody's playing together +yeah yes exactly it's a tack it's like a + + align:start position:0% +yeah yes exactly it's a tack it's like a + + + align:start position:0% +yeah yes exactly it's a tack it's like a +rhythm + + align:start position:0% +rhythm + + + align:start position:0% +rhythm +the R so Sho + + align:start position:0% +the R so Sho + + + align:start position:0% +the R so Sho +circulates to the department they stop + + align:start position:0% +circulates to the department they stop + + + align:start position:0% +circulates to the department they stop +that's why they don't have a shoot here + + align:start position:0% +that's why they don't have a shoot here + + + align:start position:0% +that's why they don't have a shoot here +will the associ uh and basically the + + align:start position:0% +will the associ uh and basically the + + + align:start position:0% +will the associ uh and basically the +department is there are two basic + + align:start position:0% +department is there are two basic + + + align:start position:0% +department is there are two basic +operation it's called the last thing + + align:start position:0% +operation it's called the last thing + + + align:start position:0% +operation it's called the last thing +where you this is called the last last + + align:start position:0% +where you this is called the last last + + + align:start position:0% +where you this is called the last last +you have a last this is a style and you + + align:start position:0% +you have a last this is a style and you + + + align:start position:0% +you have a last this is a style and you +have a last for a foot foots are very + + align:start position:0% +have a last for a foot foots are very + + + align:start position:0% +have a last for a foot foots are very +different uh it happens to be 10 and + + align:start position:0% +different uh it happens to be 10 and + + + align:start position:0% +different uh it happens to be 10 and +half + + align:start position:0% +half + + + align:start position:0% +half +the width is Da D call it David um no + + align:start position:0% +the width is Da D call it David um no + + + align:start position:0% +the width is Da D call it David um no +balance you know specializes in width so + + align:start position:0% +balance you know specializes in width so + + + align:start position:0% +balance you know specializes in width so +this particular shoe goes from B very + + align:start position:0% +this particular shoe goes from B very + + + align:start position:0% +this particular shoe goes from B very +narrow to 6 e very wide and each one + + align:start position:0% +narrow to 6 e very wide and each one + + + align:start position:0% +narrow to 6 e very wide and each one +each foot requires a different last so + + align:start position:0% +each foot requires a different last so + + + align:start position:0% +each foot requires a different last so +does a so how do we know when the shoes + + align:start position:0% +does a so how do we know when the shoes + + + align:start position:0% +does a so how do we know when the shoes +are going through this cell that are + + align:start position:0% +are going through this cell that are + + + align:start position:0% +are going through this cell that are +they making it for a particular size L + + align:start position:0% +they making it for a particular size L + + + align:start position:0% +they making it for a particular size L +there is um a document that is printed + + align:start position:0% +there is um a document that is printed + + + align:start position:0% +there is um a document that is printed +every day and distributed to all the + + align:start position:0% +every day and distributed to all the + + + align:start position:0% +every day and distributed to all the +supervisors per value stream that they + + align:start position:0% +supervisors per value stream that they + + + align:start position:0% +supervisors per value stream that they +know exactly the sequence so he knows + + align:start position:0% +know exactly the sequence so he knows + + + align:start position:0% +know exactly the sequence so he knows +very well the CL coordinators in this + + align:start position:0% +very well the CL coordinators in this + + + align:start position:0% +very well the CL coordinators in this +team knows very well what's coming but + + align:start position:0% +team knows very well what's coming but + + + align:start position:0% +team knows very well what's coming but +that's done on a daily basis so you're + + align:start position:0% +that's done on a daily basis so you're + + + align:start position:0% +that's done on a daily basis so you're +really responding almost a daily basis + + align:start position:0% +really responding almost a daily basis + + + align:start position:0% +really responding almost a daily basis +to the PO in customer right yeah it's a + + align:start position:0% +to the PO in customer right yeah it's a + + + align:start position:0% +to the PO in customer right yeah it's a +daily yeah daily they we know sometimes + + align:start position:0% +daily yeah daily they we know sometimes + + + align:start position:0% +daily yeah daily they we know sometimes +are weekly sometime are daily but we + + align:start position:0% +are weekly sometime are daily but we + + + align:start position:0% +are weekly sometime are daily but we +know exactly it gets um at the beginning + + align:start position:0% +know exactly it gets um at the beginning + + + align:start position:0% +know exactly it gets um at the beginning +of the day or the the afternoon before + + align:start position:0% +of the day or the the afternoon before + + + align:start position:0% +of the day or the the afternoon before +it gets put in this um you know document + + align:start position:0% +it gets put in this um you know document + + + align:start position:0% +it gets put in this um you know document +is that based on the orders that are + + align:start position:0% +is that based on the orders that are + + + align:start position:0% +is that based on the orders that are +coming in for shoes yeah depends on the + + align:start position:0% +coming in for shoes yeah depends on the + + + align:start position:0% +coming in for shoes yeah depends on the +work order some shoes are directly go + + align:start position:0% +work order some shoes are directly go + + + align:start position:0% +work order some shoes are directly go +direct to customers some orders go to + + align:start position:0% +direct to customers some orders go to + + + align:start position:0% +direct to customers some orders go to +the + + align:start position:0% +the + + + align:start position:0% +the +warehouse inde depends of where they are + + align:start position:0% +warehouse inde depends of where they are + + + align:start position:0% +warehouse inde depends of where they are +who they are for can be a weekly work + + align:start position:0% +who they are for can be a weekly work + + + align:start position:0% +who they are for can be a weekly work +order or a daily work order regardless + + align:start position:0% +order or a daily work order regardless + + + align:start position:0% +order or a daily work order regardless +of that this document is daily and it + + align:start position:0% +of that this document is daily and it + + + align:start position:0% +of that this document is daily and it +gets distributed again to the supervisor + + align:start position:0% +gets distributed again to the supervisor + + + align:start position:0% +gets distributed again to the supervisor +flos and set up people set up people the + + align:start position:0% +flos and set up people set up people the + + + align:start position:0% +flos and set up people set up people the +ones that bring the work so it's like no + + align:start position:0% +ones that bring the work so it's like no + + + align:start position:0% +ones that bring the work so it's like no +it's no question so in the face of the + + align:start position:0% +it's no question so in the face of the + + + align:start position:0% +it's no question so in the face of the +last the set up person will have this + + align:start position:0% +last the set up person will have this + + + align:start position:0% +last the set up person will have this +document so no need to talk no need to + + align:start position:0% +document so no need to talk no need to + + + align:start position:0% +document so no need to talk no need to +talk every every single transaction is + + align:start position:0% +talk every every single transaction is + + + align:start position:0% +talk every every single transaction is +very clear who's responsible for need to + + align:start position:0% +very clear who's responsible for need to + + + align:start position:0% +very clear who's responsible for need to +be done so this must give you a + + align:start position:0% +be done so this must give you a + + + align:start position:0% +be done so this must give you a +Competitive Edge over your competitors + + align:start position:0% +Competitive Edge over your competitors + + + align:start position:0% +Competitive Edge over your competitors +who's shoes are being made in another + + align:start position:0% +who's shoes are being made in another + + + align:start position:0% +who's shoes are being made in another +country and the market is here and + + align:start position:0% +country and the market is here and + + + align:start position:0% +country and the market is here and +there's a timel between those two this + + align:start position:0% +there's a timel between those two this + + + align:start position:0% +there's a timel between those two this +is one um yes it is like you know we can + + align:start position:0% +is one um yes it is like you know we can + + + align:start position:0% +is one um yes it is like you know we can +we're working right now we our lead time + + align:start position:0% +we're working right now we our lead time + + + align:start position:0% +we're working right now we our lead time +of three days is to try to help the + + align:start position:0% +of three days is to try to help the + + + align:start position:0% +of three days is to try to help the +retailers to minimize the inventory so + + align:start position:0% +retailers to minimize the inventory so + + + align:start position:0% +retailers to minimize the inventory so +if Saturday Fridays Saturday and satday + + align:start position:0% +if Saturday Fridays Saturday and satday + + + align:start position:0% +if Saturday Fridays Saturday and satday +the big day on Monday they place an + + align:start position:0% +the big day on Monday they place an + + + align:start position:0% +the big day on Monday they place an +order 3 days later we can deliver back + + align:start position:0% +order 3 days later we can deliver back + + + align:start position:0% +order 3 days later we can deliver back +to them so and this lady is doing it + + align:start position:0% +to them so and this lady is doing it + + + align:start position:0% +to them so and this lady is doing it +right now under absolutely okay this + + align:start position:0% +right now under absolutely okay this + + + align:start position:0% +right now under absolutely okay this +used to be in a customer in three or + + align:start position:0% +used to be in a customer in three or + + + align:start position:0% +used to be in a customer in three or +four days and that makes a big + + align:start position:0% + + + + align:start position:0% + +difference basically in this + + align:start position:0% +difference basically in this + + + align:start position:0% +difference basically in this +department this Associates + + align:start position:0% +department this Associates + + + align:start position:0% +department this Associates +the shoe is put into what's called a + + align:start position:0% +the shoe is put into what's called a + + + align:start position:0% +the shoe is put into what's called a +conditioner just get some steam to + + align:start position:0% +conditioner just get some steam to + + + align:start position:0% +conditioner just get some steam to +soften up a little bit so when he + + align:start position:0% +soften up a little bit so when he + + + align:start position:0% +soften up a little bit so when he +removes + + align:start position:0% + + + + align:start position:0% + +elas put on the paint and put the shoe + + align:start position:0% +elas put on the paint and put the shoe + + + align:start position:0% +elas put on the paint and put the shoe +on it's flexible enough to F you to fit + + align:start position:0% +on it's flexible enough to F you to fit + + + align:start position:0% +on it's flexible enough to F you to fit +uh the shoe gets cemented the bottom + + align:start position:0% +uh the shoe gets cemented the bottom + + + align:start position:0% +uh the shoe gets cemented the bottom +okay um the so is deliver from + + align:start position:0% +okay um the so is deliver from + + + align:start position:0% +okay um the so is deliver from +behind that Associates with that um + + align:start position:0% +behind that Associates with that um + + + align:start position:0% +behind that Associates with that um +yellow machiner there that basically + + align:start position:0% +yellow machiner there that basically + + + align:start position:0% +yellow machiner there that basically +does it activates maybe I'll show you a + + align:start position:0% +does it activates maybe I'll show you a + + + align:start position:0% +does it activates maybe I'll show you a +little more closely here so the shoe is + + align:start position:0% +little more closely here so the shoe is + + + align:start position:0% +little more closely here so the shoe is +cemented okay is put in this big dryer + + align:start position:0% +cemented okay is put in this big dryer + + + align:start position:0% +cemented okay is put in this big dryer +okay to dry the salt underneath to come + + align:start position:0% +okay to dry the salt underneath to come + + + align:start position:0% +okay to dry the salt underneath to come +from behind Okay the right salt for the + + align:start position:0% +from behind Okay the right salt for the + + + align:start position:0% +from behind Okay the right salt for the +right upper um the cement gets a little + + align:start position:0% +right upper um the cement gets a little + + + align:start position:0% +right upper um the cement gets a little +heat heat in that uh B activator oven + + align:start position:0% +heat heat in that uh B activator oven + + + align:start position:0% +heat heat in that uh B activator oven +then the associate will get the upper + + align:start position:0% +then the associate will get the upper + + + align:start position:0% +then the associate will get the upper +and the salt you know activated just + + align:start position:0% +and the salt you know activated just + + + align:start position:0% +and the salt you know activated just +stick it together put in this big press + + align:start position:0% +stick it together put in this big press + + + align:start position:0% +stick it together put in this big press +where they should stay for 2 minutes to + + align:start position:0% +where they should stay for 2 minutes to + + + align:start position:0% +where they should stay for 2 minutes to +ensure bonding okay and then go to our + + align:start position:0% +ensure bonding okay and then go to our + + + align:start position:0% +ensure bonding okay and then go to our +table where they backing associat will + + align:start position:0% +table where they backing associat will + + + align:start position:0% +table where they backing associat will +do some basic inspection we'll remove + + align:start position:0% +do some basic inspection we'll remove + + + align:start position:0% +do some basic inspection we'll remove +any cement we'll apply the laces any + + align:start position:0% +any cement we'll apply the laces any + + + align:start position:0% +any cement we'll apply the laces any +tags + + align:start position:0% +tags + + + align:start position:0% +tags +advertisement uh some tissue inside the + + align:start position:0% +advertisement uh some tissue inside the + + + align:start position:0% +advertisement uh some tissue inside the +shoe to keep the shape Inside the + + align:start position:0% +shoe to keep the shape Inside the + + + align:start position:0% +shoe to keep the shape Inside the +Box y get pack and that's it and that's + + align:start position:0% +Box y get pack and that's it and that's + + + align:start position:0% +Box y get pack and that's it and that's +it okay so quality of this now goes to + + align:start position:0% +it okay so quality of this now goes to + + + align:start position:0% +it okay so quality of this now goes to +your customer and iFly yeah if I go to a + + align:start position:0% +your customer and iFly yeah if I go to a + + + align:start position:0% +your customer and iFly yeah if I go to a +New Balance Outlet or a shoe store I can + + align:start position:0% +New Balance Outlet or a shoe store I can + + + align:start position:0% +New Balance Outlet or a shoe store I can +buy this you see those shoes absolutely + + align:start position:0% +buy this you see those shoes absolutely + + + align:start position:0% +buy this you see those shoes absolutely +AIO thanks so much for showing this it's + + align:start position:0% +AIO thanks so much for showing this it's + + + align:start position:0% +AIO thanks so much for showing this it's +been a pleasure really a pleasure and + + align:start position:0% +been a pleasure really a pleasure and + + + align:start position:0% +been a pleasure really a pleasure and +you know as we're leaving I kind of want + + align:start position:0% +you know as we're leaving I kind of want + + + align:start position:0% +you know as we're leaving I kind of want +to know what's the next step of your + + align:start position:0% +to know what's the next step of your + + + align:start position:0% +to know what's the next step of your +lean Journey it's interesting the answer + + align:start position:0% +lean Journey it's interesting the answer + + + align:start position:0% +lean Journey it's interesting the answer +is more of the same but what I mean by + + align:start position:0% +is more of the same but what I mean by + + + align:start position:0% +is more of the same but what I mean by +that everything is about the thinking so + + align:start position:0% +that everything is about the thinking so + + + align:start position:0% +that everything is about the thinking so +what we'll do we will work in more + + align:start position:0% +what we'll do we will work in more + + + align:start position:0% +what we'll do we will work in more +sophisticated problems we continue + + align:start position:0% +sophisticated problems we continue + + + align:start position:0% +sophisticated problems we continue +sharpening our problem solving skills so + + align:start position:0% +sharpening our problem solving skills so + + + align:start position:0% +sharpening our problem solving skills so +we will be to resolve more complicated + + align:start position:0% +we will be to resolve more complicated + + + align:start position:0% +we will be to resolve more complicated +waste problems \ No newline at end of file diff --git a/RFTa52F8YZ0.txt b/RFTa52F8YZ0.txt new file mode 100644 index 0000000000000000000000000000000000000000..d1a487f566bc8e6ac58f22b50b3635be34d387a7 --- /dev/null +++ b/RFTa52F8YZ0.txt @@ -0,0 +1,3038 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: We began our +discussion by talking about + +how society would choose +across different income + +distributions, which involve +the trade-off between + +preferences for more equal +distribution of income and the + +efficiency cost of transferring +income through + +both taxation and welfare +programs. We then moved on to + +talk about what the government +does in practice in terms of + +taxation and income +redistribution. + +What we're going to do today is +actually recognize that, in + +fact, most of government +spending, most of what we + +raise taxes for is not pure +income redistribution. + +We talked about things like the +TANF program, which gives + +money to single mothers, or the +SSI program, which gives + +money to disabled people. + +That's not most of what the +government raises money for. + +In fact, 95% of the transfers +that the government makes are + +not income based transfers. + +They're transfers of what we +call social insurance. + +So most of what the government +does today is not take from + +the rich and give to the poor. + +Most of what the government +does today is take from + +everyone to provide insurance +for everyone. + +Now basically, we talked in the +uncertainty lecture about + +why people would value +insurance. + +So essentially we think about +people choosing across states + +of nature like they're choosing +across goods. + +Then they will want to optimize +across those states, + +hit by a car versus not hit by +a car, the way they optimize + +across goods like +CDs and movies. + +And we said the way they +optimize across states is by + +buying insurance. + +That's the way you essentially +transfer resources from the + +state where something goes +bad to the state + +where something goes-- + +I'm sorry, from the state where +something goes good to + +the state where it goes bad. + +The way you effect that +transfer, effectively, is by + +paying insurers when things go +good and getting from insurers + +when things go bad. + +That's insurance, and insurance +is an enormous share + +of the US economy. + +Currently, US as a whole spends +about $2 trillion a + +year on insuring ourselves +against adverse risks of + +various types. + +There's health insurance, which +is money we pay up front + +to insurers, and they cover our +medical costs should we + +get sick or become injured. + +There's disability insurance, +which is money that you pay in + +the form of taxation, and the +government uses that money to + +give you a benefit should +you become disabled. + +There's unemployment +insurance. + +We know about that. + +Unemployment insurance is money +that your employer pays + +in taxes, and in return, should +you lose your job due + +to a layoff you receive income +when you're laid off. + +That's certainly a topic +of much conversation + +these days, et cetera. + +So there are a number of social +insurance programs that + +are out there to help +individuals with the adverse + +risks they face. + +The big question we have to ask +in starting this lecture + +is, well, why does social +insurance exist? + +After all, there's actually +an enormous robust private + +insurance market. + +There's health insurance, +there's life insurance, + +there's casualty insurance. + +The private market insures +us for lots of risks. + +The question is why does the +government come in and also + +provide us this social +insurance? + +So we individuals will demand +insurance for risk. + +We know private insurance exists +for things like health + +insurance, life insurance, fire + +insurance, auto insurance. + +We know it exists, and that adds +up to about $2 trillion + +of private spending. + +Yet at the same time the +government also provides on + +the order of another trillion +dollars of social insurance + +spending every year for things +like health insurance, and + +disability, and other things. + +So the issue is why does the +government need to do that? + +Why does the government +need to roll + +in and provide insurance? + +We know individuals want it. + +We know a private market exists +that provides it. + +What's the market failure +that justifies a + +government role here? + +Think about the role of the +government in the economy-- + +and this is a very small +part of this course-- + +but the focus of the other +course I teach, 14.41. + +The basic question is in this +course we've largely learned + +the governments serves to screw +up the market if the + +market's working well. + +The only time the government +can help is if there's a + +market failure, if +there's something + +wrong with the market. + +Well in this case, what could +the market failure be? + +And the market failure, in the +context of insurance, is the + +problem of asymmetric +information. + +Asymmetric information, +information that is held + +differentially between parties +on either side of a + +transaction. + +And that when there's asymmetric +information, when + +different parties know different +amounts about a + +transaction, that can lead +to market failures. + +So the classic example of this +comes from the Nobel Prize + +winning economist +George Akerlof. + +It's called the lemons +problem. + +The lemons problem is, +basically, he did the example + +of the used car market. + +Imagine you've got a used car +market, which is a set of + +individuals who want to sell +their cars and a set of + +individuals who want +to buy those cars. + +And let's start with the full +information benchmark. + +Let's imagine there was perfect +information about the + +exact quality of every car. + +Imagine there was some test +you could do which would + +perfectly tell you exactly how +long the car is going to last, + +how well it's going +to run, et cetera. + +In that world there will be +a set of transactions. + +Some individuals will want to +sell their cars because they + +want to buy up, other individual +will be happy to + +pay that price, there will +be a set of transactions. + +Now imagine we go to the real +world, especially a real world + +when Akerlof wrote his article +in the '70s when, basically, + +if you went to buy a used car +you had to look at it and + +decide does it look OK. + +There's clearly asymmetric +information. + +Clearly the seller of the car +knows much more about its + +underlying qualities than +the buyer of the car. + +And in particular, the buyer +should be suspicious saying, + +wait a second, why are +you selling this car? + +If it's such a good car why +are you selling it? + +And the very fact that I see +you selling it makes me + +suspicious that something's +wrong with it. + +Given that I'm suspicious +something's wrong with it I'm + +going to be willing to pay less +for it than I would if I + +knew for sure it was OK. + +The fact that I don't have full +information as a buyer + +means that I'm going to pay less +for it than I would if I + +had full information. + +Well if I'm going to pay less +for it but the seller has a + +certain amount he's willing to +sell it at, the seller will + +say, well, I'm not going to +sell it to you for less. + +I have a certain supply curve +at which I want to sell. + +If I can get x for the car I'll +sell it, but if you're + +not going to pay me x I'm +not going to sell it. + +So the sale doesn't happen. + +So what you have is a car where +in a full information + +world a sale would happen, both +parties would be happy + +with that sale. + +But in an asymmetric information +world, since the + +first party, since the buyer's +suspicious of the quality and + +is therefore willing to pay +less, and the seller won't + +accept less the sale +doesn't happen. + +And that's a market failure. + +Relative to the 14.01 world we +started with, where everybody + +knows everything, where there's +full information, the + +market has failed because sales +which would make both + +parties better off do not +occur due to asymmetric + +information. + +So that is an example of the +market failure caused by + +asymmetric information. + +Now let's flip this around +and talk about insurance. + +In insurance it's the +opposite case. + +In insurance, I, the person +demanding the insurance, know + +more about me than the insurers + +who's selling me insurance. + +I know whether I'm someone who +gets sick a lot, whether I + +like skydiving, whether I +engage in other risky + +behaviors that may have health +problems for me, whether I am + +someone who smokes in bed so I'm +likely to catch my house + +on fire so that I really want +house insurance because I'm + +going to catch my house +on fire, et cetera. + +I know all that stuff about +me, the insurer doesn't. + +So the insurer, as a result, +might be unwilling to sell me + +insurance at a fair price. + +So to put this in numbers, let's +consider an example. + +Imagine that you are starting up +a health insurance program + +for MIT graduates. + +You want to say look, MIT +graduates are a pretty healthy + +lot, and so I'm going to start +up a health insurance program + +for MIT graduates. + +I'm going to make money since +they're basically pretty + +healthy, but they're +risk averse so they + +will buy the insurance. + +So imagine the facts +are the following. + +Imagine that for every for every +100 MIT graduates, over + +the next year, 90 of them will +spend nothing on medical care, + +and 10 of them will +spend $1,000. + +But we don't know which ones, +there's uncertainty. + +So I'm left with this +90% chance of zero, + +10% chance of $1,000. + +So everybody graduating, since +we're a pretty healthy crop, + +90% of you will spend nothing +but 10% of you will spend + +$1,000, and you don't +know which. + +And you're going to start +an insurance. + +You could say look, I'm going +to start an insurance. + +What I'm going to do is I'm +going to say is what's the + +expected payout that I'm going +to have as an insurer + +over the next year? + +Well, the expected payout over +the next year is $10,000 + +total, right? + +And let's say there's +100 students you are + +going to sell to. + +The expected payout the next +year is $10,000 total. + +10 students will cost you $1,000 +nine students will cost + +you nothing. + +Expected payout next year is +$10,000, or per student you're + +selling to the expected +payout is $100. + +Right? + +Have I got that right? + +Yeah. + +$100 per student you're +selling to. + +So if you sell to 100 students +at $100 you will break even. + +You will collect $10,000 +at an expectation + +you'll pay out $10,000. + +So if you roll in and offer +insurance for $100 and you + +sell to all these students +then you'll break even. + +Let's say you then said +fine, I'm going to + +offer it for $110. + +Well, as long as people are +somewhat risk averse, in our + +standard model they'd still +like insurance for $110. + +They'd still be willing to pay +a little risk premium-- + +remember about risk premiums +to get health insurance. + +So you still sell it, let's +say, and you make $1,000. + +Then you're going to sell to +100 students at 10 extra + +dollars to make $1,000 profit. + +So this is a pretty +good product. + +I'll make a $1,000 +profit on this. + +Now, what's in fact the problem +with this analysis? + +The problem is that what +if some of the + +healthy guys say, look-- + +what if people know whether +they're healthy or sick? + +What if it's not uncertain? + +Or what if people have +a good inkling? + +What if, in fact, half of the 90 +people who will spend zero, + +what if 50 of them actually +know they're + +going to spend zero? + +What if, in fact, the +story is different? + +It's not totally uncertain, +but 50 people know they're + +going to spend zero. + +They're really healthy and they +don't like the doctor, + +they know they're going +to spend zero. + +Whereas the other 50, well, 40 +of them might spend zero and + +10 might spend $1,000. + +Well in that case, the 50 that +knows they're going to spend + +zero won't buy the +health insurance. + +They'll be like why +should I buy it? + +I know I'm going to spend zero, +why should I pay $100 or + +$110 dollars for health +insurance? + +So then, how much +will you sell? + +And let's say you charge +$110 to make a profit. + +You'll sell to 40 +guys, 40 healthy + +guys, and 10 sick guys. + +So 50 guys times $110, so +you'll make $5,500. + +What will you pay out? + +You'll pay out $10,000 because +the 10 sick guys are + +definitely buying, right? + +The 10 guys who'll end up +getting sick are definitely + +buying along with +40 healthy guys. + +So you will collect $5,500 but +you'll pay out $10,000. + +You'll lose money. + +Why will you lose money? + +You'll lose money because you'll +be collecting as if + +you're dealing with a full +probability distribution but + +you're only going to see +a truncated probability + +distribution. + +You're only going to see the +distribution for the people + +who have some chance +of getting sick. + +The very healthy people +drop out. + +As a result you lose money. + +This is the insurer problem. + +If the healthiest people don't +buy insurance then they can't + +price it fairly. + +How would you overcome this? + +Well, you would have to raise +your price a lot, right? + +So let's say you say fine, I'm +going to overcome this. + +If I raise my price to +$200 or to $210 then + +I'd make money again. + +If I raise my price +$210 that's 50 + +people buying at $210. + +Then I get $11,000 in premiums +and I don't have to spend + +$10,000, and I make +money again. + +What's the problem with +that solution? + +Yeah? + +AUDIENCE: People will +probably be dropping + +out because you just-- + +PROFESSOR: Some of these 40 will +say, well, I was happy to + +pay $100 but I'm not +happy to pay $200. + +The chances are really low +I'm going to get sick. + +So this goes down. + +So you collect less money +but you still pay + +out to the sick people. + +And you never win. + +You can never win. + +As you raise the price the +healthier and healthier people + +drop out until you just simply +can't make money. + +Yeah? + +AUDIENCE: Is there any situation +where if you have a + +large enough number of people +that you're supplying to you + +can set the price at a certain +level such that you're + +guaranteed that there are at +least going to be a large + +number of people left after +dropping out so that you won't + +lose money? + +PROFESSOR: Yes, and what's +that going to depend on? + +So one extreme example is what +I've described here, where as + +you raise the price more healthy +drop out and so you + +can never make money. + +Under what conditions will that +be a particular problem + +or not be a problem? + +Well there's two key factors. + +First of all, it's going +to be how imperfect + +the information is. + +For example, if people know for +sure whether they're going + +to be in the zero bucket or +the $1,000 bucket then by + +definition you can't +make money. + +If you know for sure, with 100% +certainty, then why would + +you ever buy insurance unless +you're going to be in the + +$1,000 bucket? + +And why would you ever pay +more than $1,000 for it? + +So there's no way to make money +if people know for sure. + +So the first thing is where +nobody has any idea at all. + +Then this is going to be less +of a problem because healthy + +people won't drop out because +nobody knows who's healthy. + +So the first issue is going to +be the asymmetry of your + +information. + +The second factors is +going to be what? + +The level of risk aversion, +because if people are very + +risk averse then they may be +willing to pay a lot for + +insurance even if the odds are +low it's going to hurt them. + +So in this case, once again if +people know for sure, risk + +aversion doesn't matter. + +But if people don't know for +sure, if there's some + +uncertainty, then you may get +healthy people buying health + +insurance because they're +risk averse. + +They may buy it anyway, and +so then you may not + +have a market failure. + +So basically, the more asymmetry +of information there + +is the more likely you're +going to lose money? + +What happens if you're +going to lose money? + +You're not going to start your +insurance company and MIT + +students will end +up uninsured. + +That's a market failure. + +The market for insurance will +fail, the market for insurance + +will fail because you will +end up not being + +able to make money. + +You're not going to be able to +make money because only the + +sickest people will buy, and +you lose by definition. + +That's the problem that we have +with private insurance. + +If the healthiest people stay +out, then the insurer can't + +make money. + +The insurers need a distribution +of healthy and + +sick to make money, they +can't make money if the + +healthy stay out. + +So what can we do about this? + +What can we do about this? + +Well there's two classes of +solutions we can have. The + +first is we can subsidize. + +Imagine if we said, we MIT, will +roll in and provide the + +insurance for free +to everyone. + +And then we'll pay the insurer +what they want. + +So MIT will come in, they'll +absorb the cost of the insurer + +and give it to MIT students +for free. + +Well, in that case all the MIT +students would take it, it + +would be free, and the insurer +could charge $100 or $110 + +based on the negotiation +with MIT. + +And the insurer will provide the +insurance because everyone + +would take it. + +And MIT would just +pay the cost. + +So the market failure would be +solved, but of course at a + +cost of MIT having to pay +$10,000 or $11,000, or + +whatever it's going to be. + +So the market failure would be +solved by subsidizing the + +healthy people to come in. + +So essentially, if you pay off +the best risks to come in the + +market you solve the market +failure because then the + +insurer knows they're getting a +good distribution of risks. + +What's the other thing +you can do? + +Well the other thing you can do +is the centerpiece of the + +current health care reform bill, +which I'll talk about + +next time, which is you can +mandate that everyone buy + +health insurance. + +If there was a law that every +MIT student had to have health + +insurance when they graduate +then, once again, the insurer + +would know what the distribution +of risks are and + +they could sell insurance +at a fair price. + +They wouldn't have to worry if +the healthy drop out because + +the healthy couldn't, +it would be illegal. + +Now, these two solutions-- + +so you can subsidize +or you can mandate. + +Now these solutions-- + +Yeah? + +AUDIENCE: Weren't a lot of +health insurance companies + +also looking at medical +records of + +people before deciding-- + +were they unequally pricing +health care based + +on someone's history? + +And I know that caused a lot +of controversy say over + +pre-existing conditions. + +PROFESSOR: Yeah. + +Let me talk about +that next time. + +What you're asking is isn't it +in fact possible asymmetric + +information could flip? + +Isn't it possible insurers could +now know so much about + +us from public records that they +could start to have more + +information about us than we +even have about ourselves? + +And then they could decide to +get rid of us because they + +know we're a bad risk even +if we don't know. + +So could we be soon living in a +world of reverse asymmetric + +information? + +And that's possible, and I'll +talk about that next time. + +But for now let's assume we live +in a world where you know + +more than the insurer. + +So you can subsidize the guys, +you can mandate it. + +Now each of these have +pros and cons. + +If you subsidize them then the +MIT students are happy. + +They get insurance for free, +but MIT is out $10,000. + +Or if it's the government, +the government's + +out a lot of money. + +How does the government +raise that money? + +It taxes people, and that +has efficiency costs. + +So one thing we could +do is make health + +insurance free for everyone. + +That's what Canada does. + +Health insurance is +free for everyone. + +And the problem is to do that in +the US would cost something + +like a couple of trillion +dollars. + +That's a lot of money +to raise in taxes. + +And that would cause +inefficiency from raising that + +money in taxes. + +On the other hand the +mandate doesn't cost + +the government anything. + +But it makes healthy people very +upset because suddenly + +you're an MIT student, you know +for sure you're not going + +to spend zero but the government +mandates you have + +to pay that $100 premium. + +Well now you're upset. + +So basically there's no good +answer here to solve this + +asymmetric information +problem. + +Either we have to spend a lot +of money and then people + +aren't upset but +taxpayers are. + +Insurers aren't but +taxpayers are. + +Or we have to mandate people +to buy, in which case the + +healthy will be upset they're +being forced to buy something + +they don't want. + +And that's the difficult +position we face ourselves in + +with social insurance +programs. + +But the bottom line is what +we have is this failure of + +private insurance markets due to +asymmetric information and + +the need for the government to +come in and take one or both + +of these routes to +fix the problem. + +If the government doesn't then +you don't get people getting + +insurance that they'd +like to have. You + +get a market failure. + +You get a market failure in +people not having insurance + +that they would value. + +And that's why we have +governments come in and + +provide social insurance. + +Now, as I said, the government +comes in and provide many + +types of social insurance +of many types. + +There's medical social +insurance, and here the + +government does that through the +form of what we call two + +programs, Medicare +and Medicaid. + +Medicare is universal, heavily +subsidized health insurance + +for the elderly. + +Medicaid is like a +welfare program. + +It's means tested, categorical, +free health + +insurance for the poor. + +So Medicare's for the elderly, +Medicaid's for the poor. + +In neither case is there a +mandate, in both cases the + +government, essentially, +is making it free. + +Essentially it's gone the +subsidy route, as a result at + +an enormous cost to +the US taxpayer. + +Medicare is now about a $500 +billion a year program. + +Medicaid is approaching a $400 +billion a year program. + +It's almost a trillion dollars +US taxpayers are paying to get + +people to buy health +insurance. + +So by solving it with this route +these are incredibly, + +especially Medicare is an +incredibly politically popular + +program because why not? + +People are getting +it for free. + +But the cost is an enormous +budgetary pressure on the US + +government. + +That's for health. + +We also have disability +insurance, DI. + +That's for people who have +a career-ending injury. + +If you fall off your motorcycle +and get paralyzed + +and can't work anymore you can +get disability insurance, + +which is money which compensates +you for being + +unable to work having a +career-ending injury. + +So this is another form +of social insurance. + +We have workers' compensation, +which is insurance that you + +have to insure yourself against +injuries on the job. + +So if you slip and fall on the +job and have to miss a couple + +weeks of work this covers +your medical costs + +and your lost wages. + +And we have unemployment +insurance, which as I + +mentioned, is insurance for +people who lose their jobs due + +to economic circumstances. + +Unemployment insurance is not +for people who get fired + +because they're crappy +workers. + +It's for people who lose their +job because they're laid off + +for economic circumstances. + +They get some replacement of +wages under that unemployment + +insurance programs. + +These are the kind of social +insurance programs that we + +have in the US. + +And the arguments for them is +basically more complicated + +version of the arguments +I just made over there. + +The argument for all these +programs is that private + +insurance markets for things +like unemployment or injury + +will not function well due to +asymmetric information so the + +government needs to come in and +provide that insurance. + +But at the same time all of +these insurance programs have + +a cost. Not just the cost of +raising the money but the cost + +of what we call moral hazard, +which is that when you insure + +people against adverse risk you + +encourage adverse behavior. + +When you insure people against +adverse risk you encourage + +adverse behavior. + +And the problem here is another +form of asymmetric + +information. + +So one problem of asymmetric +information is since insurers + +don't know enough about you +they'll under insure you. + +So it's a market failure. + +This is a flip side market +failure, which is since + +insurers can't perfectly be sure +about what's wrong with + +you, you will be encouraged to +misrepresent your state in + +order to collect money. + +So a classic example +here is workers' + +compensation insurance. + +Workers' compensation insurance +is about a $50 + +billion a year program that +provides money to people who + +are injured on the job. + +The problem is injured on the +job is very hard to verify. + +Most of the injuries are +not losing an arm. + +Most of the injuries are +straining your back. + +As anyone with back problems +knows it's pretty darn hard to + +verify if your back's +hurt or not. + +My first job in my first summer +after MIT was I was a + +filing clerk at a +doctor's office. + +The doctor did workers' comp-- +this is a real story. + +Doctors do workers' comp claims. +It was one doctor with + +a staff of five secretaries and +an enormous filing staff. + +And the reason was the doctor +saw a patient every three + +minutes all day. + +They'd come in, he'd say, yeah, +you're hurt, here's your + +chit for workers' comp, +off you go. + +All day. + +So basically, because it's +incredibly hard to verify, + +this doctor was just-- basically +his role was saying + +yes to people so they could +get out of work. + +This is the problem we +have with a system-- + +this is another information +asymmetry, which is now you, + +the insured, know more about +what's wrong with you than the + +insurer does. + +But it's a different form of +information asymmetry. + +Now it's that you may actually +not be as injured as you claim + +or need insurance +as you claim. + +As a result you over claim +insurance, and that costs the + +insurance industry money. + +Now, moral hazard, +theoretically, is unambiguous. + +But obviously it's going to +vary across situations. + +There's not going to be a whole +lot of moral hazard in + +programs that insure you +against blindness. + +And in that case that's because +it's pretty easy to + +observe if someone's +really blind. + +There's not a whole lot of +information asymmetry. + +There's going to be a lot of +moral hazard in programs that + +insure you against having a bad +back because that's harder + +to observe. + +And in fact we have lots of +evidence that moral hazard's a + +big problem with social +insurance programs. So one + +type of evidence is sort +of fun stories. + +So there's stories about, for +example, the Massachusetts + +prison guard who got about +$25,000 in workers' comp + +claims because he claimed he +hurt his back at work until + +people went online in order to +see that the same guy was + +running a karate school. + +And there was videos of him +doing karate moves and stuff + +online running his +karate school. + +Or the other guy, who +unfortunately had good + +instincts, he was on workers' +comp because he was injured. + +But then there was footage of +him at 9/11 flying down and + +carrying buckets back and forth +and helping put out the + +fire, which was a nice thing +for him to do, but clearly + +illustrated that he was not +too injured to be able to + +carry out his job. + +So basically, there's lots of +observational evidence. + +But there's also very clear +statistical evidence, which is + +if moral hazard doesn't exist +then when the program gets + +more generous I shouldn't +be more injured, right? + +My injury should be +something that + +happens or doesn't happen. + +But if more generous programs +lead to more injuries, or + +people staying out of work +longer, or people using more + +health care then that suggests +moral hazard. + +The generosity, whether you're +sick or not, shouldn't be + +affected by the generosity +of health insurance. + +But if you suddenly see more +generous health insurance + +leads to more people +being sick that + +suggests moral hazard. + +And there's hundreds of studies +of this type showing, + +in all these realms, enormous +moral hazard. + +Showing, for example, for +workers' comp, that when you + +make workers' comp more generous +people report more + +injuries on the job. + +Here's my favorite +fact about that. + +Someone did a study of type of +injury reported to workers' + +comp by day of the week. + +And what they found was on +Mondays compared to other days + +of the week there was a very +high share of sprains and + +strains and a low share of +lacerations, of cuts. + +So every other day of the week, +say it was 50% cuts and + +50% strains. + +On Monday it was 75% strains +and 25% cuts. + +Why is that? + +Well, that's because guys got +hurt over the weekend playing + +softball and they came in on +Monday and they said they got + +hurt on the job. + +Now you can't do that if you cut +yourself on the weekend in + +your shop because it's scabbed +over by Monday. + +But if you hurt your back on +the weekend you can drag + +yourself over and say, ooh, +I hurt my back at work. + +So that's exactly the kind of +evidence that's consistent + +with moral hazard. + +And we see that everywhere. + +There's huge amounts +of moral hazard. + +Moral hazard, for example, in +health insurance the best + +estimates are that the amount +of extra money that we spend + +on society on health care +because of moral hazard on the + +order of $500 billion a year in +terms of extra care that's + +used because people +are insured. + +That does nothing to improve +their health, they just use it + +because they're insured. + +It's on the order of $500 +billion a year. + +This is an enormous problem. + +So here we have what we call +the classic social + +insurance trade off. + +On the one hand, people +value insurance. + +Insurance is very valuable to +help you in the state when you + +get in an accident or are +injured in some way. + +On the other hand, giving people +insurance against those + +bad outcomes will encourage +bad behavior. + +And that bad behavior has +two forms of costs. + +There's two costs to +that bad behavior. + +The first cost is the tax costs +and the deadweight loss + +of taxation, which is if there's +$500 billion extra in + +medical care used because people +are insured then that + +means that's $500 billion of +taxes we have to raise, or + +$500 billion in resource +costs to society. + +Well, not all that's +government. + +But a couple hundred billion +in taxes we have to raise, + +that causes deadweight loss. + +The more important cost is +really the overall efficiency + +loss from people using resources +inefficiently, from + +people not behaving optimally +because of the incentives of + +social insurance. + +So let's go back and think about +the case of workers' + +comp, and let's think about +our standard leisure + +consumption trade off. + +We have our standard leisure +consumption trade off where + +you have leisure on this axis, +consumption on this axis, some + +budget constraint, and people +choose how much leisure to + +take and how much consumption +to take. + +Now the slope of this budget +constraint is minus your wage. + +That's the price of leisure. + +So the price of sitting at home +is the wage you could + +have earned out in the market. + +What this means is you will sit +at home until the value + +you get from sitting at home +falls below the value you get + +out in the market. + +So in other words, you wouldn't +work 24 hours a day + +because that 24th hour, the +sleep would be so valuable + +that it would clearly exceed +the wage you could earn. + +So when you decide how hard to +work, when an individual + +decides how-- + +presuming we can freely +choose our hours-- + +we decide how hard to work, we +basically trade off how much + +we value not working versus +how much we'd + +earn if we do work. + +If you're in a high wage you +might work more hours, if + +you're in a low wage you'll earn +less because if you're in + +a low wage you might as well sit +at home and watch Oprah. + +If you earn a high wage you're +not going to watch Oprah + +you're going to go +earn the money. + +And that's how we make our +labor supply decisions. + +We set the wage equal to the +marginal value of leisure. + +That's how we make our labor +decisions, is we say if the + +marginal value of the next hour +of leisure exceeds my + +wage I'll stay home. + +If the marginal value of the +next hour of leisure is below + +my wage I'll going to work. + +And that's how we make our +labor supply decisions. + +What does workers' comp do +to this, or UI or other + +programs like that? + +What that says is wait a second, +now if I sit at home I + +don't just get the marginal +value of my leisure, I also + +get a check from +the government. + +So now if I sit at home I get +the marginal value of my + +leisure plus a workers' +comp check. + +Whereas if I work I still +just get my wage. + +So what's that going to do to +the amount of hours I'm going + +to want to work? + +It's going to reduce them +because now it's makes sitting + +at home more attractive because +now I'm going to work + +only until my wage exceeds my +marginal value of leisure plus + +workers' comp. + +So if workers' comp is big +enough and my wage isn't that + +high, in the limit, if workers +comp replaced all my wages I + +would never work. + +If workers' comp had what we +call a 100% replacement rate, + +replacement rate, if it replaced +100% of my wages I + +would never work. + +Why? + +Because by definition this side +would always be less than + +this side, so I'd never work. + +And that's the efficiency loss +of these social insurance + +programs. That people are not +engaging in productive trades. + +Society just cares +about this part. + +Society just cares about your +wage versus your marginal + +value of leisure. + +So if you work less than that +because of this part then + +that's a distortion, that's an +efficiency cost to society. + +You are sitting at home when +you should be making a + +productive trade of your +labor for output goods. + +And that's the efficiency cost +of social insurance. + +So what do we do? + +We want social insurance, on the +one hand, because private + +insurance markets fail. + +We don't want social insurance, +on the other hand, + +because people are going +to sit at home. + +What do we do? + +Well the answer is +we compromise. + +We have social insurance but +don't make it that generous. + +So for example, the unemployment +insurance + +program, that's insurance that +is valuable because there's no + +way to get private insurance +against losing your job. + +I'd never want to sell +that product. + +We know who'd take +that, right? + +On the other hand, we know +there's moral hazard. + +We know that people sit at home +longer rather looking for + +a job because they +get UI checks. + +There's great evidence +of that. + +For example, if you look at how +long people sit at home, + +everyone sits at home and then +suddenly gets a job the week + +UI runs out. + +That's an exaggeration, but +roughly speaking, there's a + +huge amount of people +sitting at home + +collecting the UI checks. + +What do we do? + +Well the UI replacement +rate is around 50%. + +We say, look, we know you're +going to want to sit home so + +we're going to make your +life uncomfortable. + +We'll only give you half of what +you'd earn at work, but + +we don't want you to starve so +we'll give you half of what + +you earn at work. + +And so the replacement rate +is chosen to trade off the + +benefits of insuring people +against these bad events + +against the costs of distorting +their behavior + +through moral hazard. + +And that's the social +insurance trade off. + +That's how we set up these +social insurance programs. + +They sort of embody +that trade off. + +Questions about that? + +Now, so what I want to do in the +remaining time is I want + +to talk about the nation's +largest single social + +insurance program, one you've +heard about a lot, which is + +Social Security. + +We're going to talk about +Social Security. + +I'm going to come back next +lecture and we'll go over a + +bit what's going to be on +the final in the last 15 + +minutes next time. + +But the first part of the +lecture I want to talk about + +health insurance, which is our +single largest government + +expenditure. + +But the single biggest +government program right now, + +social insurance program, it +remains Social Security. + +Medicare is going to pass it +in about two years, but for + +now it's still Social +Security. + +What is Social Security? + +Social Security is insurance +against the income loss from + +retirement. + +We know that when you have to +retire you're going to suffer + +a big income loss. + +What the government does is +insures you against that + +income loss by providing +you Social Security. + +And here's how it works. + +How many of you have seen a pay +stub and you've seen the + +word FICA on it, and then +there's a charge that's coming + +out of your pay? + +FICA is the Federal Insurance +Contribution Amount. + +That's the money you're paying +in to support the social + +insurance program. + +You pay that in, and that's +currently 12.4% of wages, well + +6.2% on you and 6.2% +on your employer. + +You each pay 6.2% +of your wages. + +That goes into a trust fund and +that money then gets paid + +out to retirees, and hopefully +paid out to + +you when you retire. + +So the way Social Security works +is you pay in money when + +you're young, that money +gets paid out to + +you when you retire. + +Not that same money because +your money going in now is + +going to today's retirees. + +Future workers will pay in and +that money will go to you. + +And the Social Security +replacement + +rate is around 50%. + +So to try to deal with this +problem the Social Security + +replacement rate's around 50%. + +So what's the benefit +of Social Security? + +Well, clearly the benefit is +people don't want to starve + +when they retire. + +We'd like insurance +against the income + +loss of when we retire. + +Now, our own savings can do that +to some extent but it's + +not perfect because you don't +know exactly how much to save, + +you don't know when you retire, +you don't know how + +long you'll live. + +So the government +social insurance + +program helps with that. + +But there's also a moral hazard +cost, which is if you + +insure people against retirement +you encourage + +retirement, because now we're +saying is if you work you get + +your wage but if you retire you +get your Social Security. + +So now, you're eligible for +Social Security at age 62. + +So at age 62 you're suddenly +eligible for about half your + +wage in Social Security. + +So now your decision +is, gee, do I work? + +Well that's contrasted against +my marginal value of leisure + +plus half my wage. + +So unless the marginal value of +leisure is less than half + +my wage I'm going to quit. + +So what Social Security is +doing is distorting your + +decision and causing you +to retire early. + +That's the moral hazard part. + +Now in the US we recognize +this, and we do + +sort of a neat trick. + +What we do in US is we have +something called an actuarial + +adjustment to your Social +Security benefits. + +What that means is the +following, you're 62 and you + +say, wait a second, I can retire +now, and if I retire + +now I'm going to get +half my wage. + +So why not retire now? + +We say, wait a second, we've +got a deal for you. + +If you work one more year and +retire next year then we'll + +give you 7% more every year +for the rest of your life. + +Your check will be 7% higher +for the rest your life. + +If you work two more years it +will be 14% higher, 3 more + +years 21% higher, et cetera. + +We recognize the moral hazard, +and we raise the check the + +longer you work to +make up for it. + +So the US recognizes that, and +as a result there's not a huge + +moral hazard from Social +Security in the US. + +It's pretty modest. In Europe +this is not the case. + +Let's take the country-- + +let me back up. + +So what the actuarial adjustment +does is says we + +recognize that Social +Security is + +essentially taxing your work. + +To offset that we're going to +subsidize you to work more by + +raising your Social Security +check the more you work. + +In Europe they're not +as smart as us. + +They don't recognize this, or +if they do they're not smart + +enough to reflect it. + +They don't have an actuarial +adjustment. + +So here's how the Social +Security system works in the + +Netherlands, for example. + +When you reach 55 in the +Netherlands your choice is you + +can work or you can stop working +and get a Social + +Security check which is +90% of your wage. + +So literally, your choice is +work or sit at home and get + +90% of your wage with no +actuarial adjustment. + +So unless the value of your +leisure is less than 10% of + +your wage you can just +sit at home. + +But wait, that's not all. + +This is a very generous +program, right? + +How do they pay for that? + +They pay for it by +taxing workers. + +So if you work you get your wage +but then you pay a 40% + +payroll tax. + +So actually, you can work and +get 60% of your wage or sit at + +home and get 90% of your wage. + +Guess what? + +No one works after age 55 +in the Netherlands. + +Literally. + +Now people will do +some underground + +work that's not taxed. + +They'll paint houses or things +which they can do on the + +underground economy. + +But literally, nobody works +after 55 in the Netherlands. + +Economics works. + +When you make the incentives +that blatant economics works. + +And that's the moral hazard. + +That's an example of not +respecting the social + +insurance trade off, erring on +the side of insuring people + +over respecting the problems +of moral hazard. + +And the answer is part of the +major problem that they have + +in these countries, part of the +major deficit, prolonged + +deficit problem they face is +that older people don't work. + +Now these countries have started +to recognize this, and + +they're starting to try +to deal with this. + +In fact, the country of France, +you may have noticed, + +recently tried to +deal with this. + +They have proposed raising their +retirement age, which is + +age 60, beyond which, +essentially, no one works in + +France, to age 62. + +What happened? + +You may have heard, massive +strikes, enormous political + +strife because people don't +understand economics. + +People don't understand that, +gee, yes that'll be a bummer + +if you work a couple years +longer, but that's what's + +going to make our +economy fiscally + +sound and more efficient. + +And in the long run we all +benefit from that. + +So the government's, by the +way, not proposing that + +today's retirees are hurt, +saying starting in 20 years + +you have to work two +years longer. + +So overall everyone's going to +benefit, but the bottom line + +is people are too short-sighted +to understand + +the economics, and that leads +to the rioting and things we + +saw in France. + +This stuff is hard to +a normal person. + +You guys are smart and you spent +a semester learning it. + +If you take a regular person in +the street they just don't + +understand this trade off, +and that's the problem. + +That's the problem in trying +to deal with these moral + +hazard issues by making social +insurance less generous. + +Now, let me talk about one +other issue with Social + +Security because it's been in +the news and will be in the + +news, which is the fact that +Social Security is + +running out of money. + +Now, Social Security is running +out of money because + +here's a dirty secret +about Social + +Security you may not know. + +How many of you have ever +heard of a Ponzi scheme? + +Anyone watch Boardwalk Empire? + +They're doing that now, +Boardwalk Empire. + +A Ponzi scheme was named after +Charles Ponzi, a Boston + +investor, and here's how the +Ponzi scheme worked. + +I teach two classes. + +I teach now and I teach +again at 2:30. + +I teach 14.01 now, +14.41 at 2:30. + +Let's say I walked in here this +morning and I said, tell + +you what guys, you each give +me $1 and on Wednesday I'll + +give you $2. + +Now you're thinking, well, +that's bullshit, but you know + +what, I want a good grade so +I'll give him the dollar. + +So you give me the dollar. + +I then go to my 2:30 1441 class +and say, hey guys, you + +each give me $3 and on Wednesday +I'll give you $5. + +They are like same thing, +whatever, but they're higher + +classmen than you, they +have more money, + +they give me the money. + +I take their $3, I pocket $1. + +I come back on Wednesday +and give you each $2. + +You're like, holy shit, +that worked. + +I'm like, I've got a better +deal for you. + +You guys give me $6 and next +time I see you in class-- + +semester's ending, but +you get the point-- + +I'll give you $10. + +You're like, great, this guy's +trustworthy, we'll do that. + +You give me the $6. + +I pocket $1, + +I go back to my 14.41 and say +here's the $5 I owe you. + +They say, wow, that's great. + +I say, so I've got a better +deal for you. + +You give me $11, and +so on and so on. + +And as long as you're both +willing to play I can continue + +to pocket the money +and make money. + +This is also called the +pyramid scheme. + +You might have heard a guy +named Bernie Madoff. + +Never invest your money with a +guy who's last name is Madoff. + +Bernie Madoff, for 20 years ran +this kind of Ponzi scheme. + +What he'd do is he'd find +investors, he'd take money + +from them and promise them a +return, he'd then find more + +investors, take the money from +the new investors and pay off + +the old investors, +and keep going. + +There was nothing real behind +what he was doing. + +He made it work for 20 years +until someone didn't want to + +play anymore. + +What if we did this, and it +was the last class and you + +guys said, well, see you +Professor Gruber. + +I'm like, wait a second, if you +give me $20, and you're + +out the door. + +Now I got to go to my next class +and I don't have any + +money for them. + +Then the whole thing collapses +And it collapses because a + +Ponzi scheme is not +a real investment. + +The asset behind a Ponzi scheme +is not a bank account. + +The asset behind a Ponzi +scheme is trust. And + +basically, as long as someone's +no longer trusting + +or can no longer pay +in, it goes away. + +Now, here's a little secret. + +Our Social Security system +is a Ponzi scheme. + +The nation's largest +social insurance + +program is a Ponzi scheme. + +How is that so? + +Well because you guys are +paying in now, and those + +checks are going to +today's elders. + +There's no guarantee that 40 +years from now kids will pay + +in to support you. + +No guarantee at all. + +You can pay in your whole life, +and then people could + +vote out Social Security +when you're + +retired and you're screwed. + +It's a Ponzi scheme. + +There's nothing behind this +except trust in the + +government's programs. + +The only asset behind this is +the trust the government would + +never screw the voter, +the elderly voters, + +by ending the program. + +As long as the government is +willing to force young people + +to pay checks to support +older people the + +program can never end. + +But if the government ever is +unwilling to do that then a + +whole generation is going to +suffer from the Ponzi scheme. + +Now that's pretty unlikely +because elderly voters are + +pretty powerful. + +It seems unlikely that Ponzi +scheme will ever collapse. + +That's why we don't think of +it in those terms. But it + +really is just that. + +It's just a Ponzi scheme, in +this case supported by trust + +in the government. + +The problem is this Ponzi scheme +works well so long as + +more people are paying in than +are collecting money. + +So right now we have, in the US, +we have about 10 workers + +for every elderly person, or +about eight workers for every + +elderly person. + +So we can collect a lot of money +to pay off the elderly. + +The problem is that number's +diminishing rapidly because of + +the aging of the baby boomers. + +There's a huge bulge of +individuals who are about to + +become elderly and collect +their Social Security. + +By the year 2025 that 8:1 will +ratio be more like 4:1, and + +we're suddenly going to +be short on money. + +Here's the way I think about +it most scarily. + +How many of you guys have +grandparents in Florida? + +OK, you've got a few +grandparents in Florida. + +The US in 2025, the US as a +whole, will be older than + +Florida is today. + +Because if you think of Florida +as full of old people, + +that's the US in 20 years, +in 15 years. + +We're moving to a very aging +society, and that's going to + +put enormous pressure on +this Ponzi scheme. + +And that's why, in about 30 +years or in about 25 years, + +Social Security goes bankrupt. + +We actually run out of money +unless we fix the program. + +So currently we have a situation +where we are + +projected for that program to go +bankrupt-- it's actually in + +about 30 years-- + +the program to go bankrupt +because we have to pay out so + +much to this large +group of elderly. + +And that's a problem the +government needs to deal with. + +And it's going to have to deal +with it in one of two ways. + +It's going to either have +to raise taxes. + +We currently pay about +12.4% in payroll. + +To solve this problem forever +that tax rate would have to go + +up by about three and +a half to 4%. + +So we'd have to pay the three +and a half to 4% more of our + +wages to solve this problem. + +Or we're going to have to cut +benefits, do things like + +saying to people they can't get +their benefits at 62, that + +goes up to 64. + +And you can see US style rioting +rather than French + +style rioting. + +That's the difficult problem +the government faces going + +forward is that something +has to give. + +We either have to raise taxes to +support this program or we + +have to cut the benefits that +elderly people get. + +Yeah? + +AUDIENCE: This might just +postpone the problem, but + +would it be possible for +the government to + +taper off the benefits? + +So for instance, at 62, when +you're eligible, you could get + +let's say 50% of what you'd +normally would be getting, and + +that amount would slowly +increase as you get older. + +So when you're making your +labor decisions you would + +work, but maybe only half or +quarter time what you normally + +would work and that might-- + +PROFESSOR: Certainly there are +compromises along the way but + +that still goes in the category +of benefit cuts. + +You're just talking about +a different way to + +do a benefits cut. + +There's lots of very subtle +and interesting ways-- + +and believe me, when the time +comes I'm not just going to + +say we're cutting everybody's +benefit 10%. + +It will be something much more +subtle along the lines you're + +describing, sufficiently +complicated that people don't + +understand it so that they can +try and slip it by people. + +If they're going to cut benefits +it's going to be that + +complicated, and that's the +trade off we're going to face. + +All right. + +OK. + +So next class we'll talk about +health insurance and we'll do + +a final session. \ No newline at end of file diff --git a/SC-K2GC2LQk.txt b/SC-K2GC2LQk.txt new file mode 100644 index 0000000000000000000000000000000000000000..2a56358a69c02771d164e011c4fc15b3a174a59a --- /dev/null +++ b/SC-K2GC2LQk.txt @@ -0,0 +1,9139 @@ +align:start position:0% + +My name is Kik. I'm visiting scholar + + align:start position:0% +My name is Kik. I'm visiting scholar + + + align:start position:0% +My name is Kik. I'm visiting scholar +here at MIT. I'm actually assistant + + align:start position:0% +here at MIT. I'm actually assistant + + + align:start position:0% +here at MIT. I'm actually assistant +professor at poly techchnical university + + align:start position:0% +professor at poly techchnical university + + + align:start position:0% +professor at poly techchnical university +of Madrid. And my background is actually + + align:start position:0% +of Madrid. And my background is actually + + + align:start position:0% +of Madrid. And my background is actually +on engineering. I am aerospace engineer. + + align:start position:0% +on engineering. I am aerospace engineer. + + + align:start position:0% +on engineering. I am aerospace engineer. +Uh I did my PhD on numerical methods. + + align:start position:0% +Uh I did my PhD on numerical methods. + + + align:start position:0% +Uh I did my PhD on numerical methods. +But uh after my post dog I decided to + + align:start position:0% +But uh after my post dog I decided to + + + align:start position:0% +But uh after my post dog I decided to +start doing things that really + + align:start position:0% +start doing things that really + + + align:start position:0% +start doing things that really +passionates me and that's how I end up + + align:start position:0% +passionates me and that's how I end up + + + align:start position:0% +passionates me and that's how I end up +doing something related with music. No. + + align:start position:0% +doing something related with music. No. + + + align:start position:0% +doing something related with music. No. +So I'm relatively new in this field and + + align:start position:0% +So I'm relatively new in this field and + + + align:start position:0% +So I'm relatively new in this field and +today I'm going to show you an algorithm + + align:start position:0% +today I'm going to show you an algorithm + + + align:start position:0% +today I'm going to show you an algorithm +that I came up for pattern detection in + + align:start position:0% +that I came up for pattern detection in + + + align:start position:0% +that I came up for pattern detection in +music which is what I've been working on + + align:start position:0% +music which is what I've been working on + + + align:start position:0% +music which is what I've been working on +for the last year and a half more or + + align:start position:0% +for the last year and a half more or + + + align:start position:0% +for the last year and a half more or +less. So as running example uh I'm going + + align:start position:0% +less. So as running example uh I'm going + + + align:start position:0% +less. So as running example uh I'm going +to use the most listened song of the + + align:start position:0% +to use the most listened song of the + + + align:start position:0% +to use the most listened song of the +history which is uh Baby Sark. + + align:start position:0% +history which is uh Baby Sark. + + + align:start position:0% +history which is uh Baby Sark. +>> So I don't know if I can play it. Yeah. + + align:start position:0% +>> So I don't know if I can play it. Yeah. + + + align:start position:0% +>> So I don't know if I can play it. Yeah. +At least it's the most listened song of + + align:start position:0% +At least it's the most listened song of + + + align:start position:0% +At least it's the most listened song of +the history of YouTube. + + align:start position:0% + + + + align:start position:0% + +>> Baby Shark doo doo doo doo doo doo. Baby + + align:start position:0% +>> Baby Shark doo doo doo doo doo doo. Baby + + + align:start position:0% +>> Baby Shark doo doo doo doo doo doo. Baby +Shark doo doo doo doo doo doo. Baby + + align:start position:0% +Shark doo doo doo doo doo doo. Baby + + + align:start position:0% +Shark doo doo doo doo doo doo. Baby +Shark doo doo doo doo doo doo. Baby + + align:start position:0% +Shark doo doo doo doo doo doo. Baby + + + align:start position:0% +Shark doo doo doo doo doo doo. Baby +Shark, + + align:start position:0% +Shark, + + + align:start position:0% +Shark, +>> Mommy Shark, doo doo doo doo doo doo. + + align:start position:0% +>> Mommy Shark, doo doo doo doo doo doo. + + + align:start position:0% +>> Mommy Shark, doo doo doo doo doo doo. +Mommy shark, doo doo doo doo doo doo. + + align:start position:0% +Mommy shark, doo doo doo doo doo doo. + + + align:start position:0% +Mommy shark, doo doo doo doo doo doo. +Mommy shark, doo doo doo doo doo doo. + + align:start position:0% +Mommy shark, doo doo doo doo doo doo. + + + align:start position:0% +Mommy shark, doo doo doo doo doo doo. +Mommy shark, + + align:start position:0% +Mommy shark, + + + align:start position:0% +Mommy shark, +>> pretty much like that all the song. This + + align:start position:0% +>> pretty much like that all the song. This + + + align:start position:0% +>> pretty much like that all the song. This +is the melody. So what's the problem of + + align:start position:0% +is the melody. So what's the problem of + + + align:start position:0% +is the melody. So what's the problem of +pattern detection in music? Okay, we + + align:start position:0% +pattern detection in music? Okay, we + + + align:start position:0% +pattern detection in music? Okay, we +would like to have a tool, an automatic + + align:start position:0% +would like to have a tool, an automatic + + + align:start position:0% +would like to have a tool, an automatic +to tool that help us to identify over + + align:start position:0% +to tool that help us to identify over + + + align:start position:0% +to tool that help us to identify over +the score or over a corpus like the + + align:start position:0% +the score or over a corpus like the + + + align:start position:0% +the score or over a corpus like the +important musical ideas there. No. So + + align:start position:0% +important musical ideas there. No. So + + + align:start position:0% +important musical ideas there. No. So +I'm highlighting here some fragments. + + align:start position:0% +I'm highlighting here some fragments. + + + align:start position:0% +I'm highlighting here some fragments. +Have a look first at the blue fragment + + align:start position:0% +Have a look first at the blue fragment + + + align:start position:0% +Have a look first at the blue fragment +over there. There are three fragments, + + align:start position:0% +over there. There are three fragments, + + + align:start position:0% +over there. There are three fragments, +three occurrences of them. All of them + + align:start position:0% +three occurrences of them. All of them + + + align:start position:0% +three occurrences of them. All of them +are exactly the same. They have the same + + align:start position:0% +are exactly the same. They have the same + + + align:start position:0% +are exactly the same. They have the same +notes with the same pitches and same + + align:start position:0% +notes with the same pitches and same + + + align:start position:0% +notes with the same pitches and same +durations. The only difference is that + + align:start position:0% +durations. The only difference is that + + + align:start position:0% +durations. The only difference is that +they occur at different moment of the + + align:start position:0% +they occur at different moment of the + + + align:start position:0% +they occur at different moment of the +score. But it seems logical. It seems + + align:start position:0% +score. But it seems logical. It seems + + + align:start position:0% +score. But it seems logical. It seems +reasonable to group them as the same + + align:start position:0% +reasonable to group them as the same + + + align:start position:0% +reasonable to group them as the same +musical idea and say that they represent + + align:start position:0% +musical idea and say that they represent + + + align:start position:0% +musical idea and say that they represent +the same the same pattern. No, we can + + align:start position:0% +the same the same pattern. No, we can + + + align:start position:0% +the same the same pattern. No, we can +call them uh we can put them a label + + align:start position:0% +call them uh we can put them a label + + + align:start position:0% +call them uh we can put them a label +blue pattern. Okay, for the green one is + + align:start position:0% +blue pattern. Okay, for the green one is + + + align:start position:0% +blue pattern. Okay, for the green one is +a little trickier because the occurrence + + align:start position:0% +a little trickier because the occurrence + + + align:start position:0% +a little trickier because the occurrence +number two and the occurrence number + + align:start position:0% +number two and the occurrence number + + + align:start position:0% +number two and the occurrence number +three are exactly the same. Okay, + + align:start position:0% +three are exactly the same. Okay, + + + align:start position:0% +three are exactly the same. Okay, +probably makes sense to group them + + align:start position:0% +probably makes sense to group them + + + align:start position:0% +probably makes sense to group them +together. Occurrence number one has a + + align:start position:0% +together. Occurrence number one has a + + + align:start position:0% +together. Occurrence number one has a +different durations for the notes and + + align:start position:0% +different durations for the notes and + + + align:start position:0% +different durations for the notes and +the occurrence number four is even + + align:start position:0% +the occurrence number four is even + + + align:start position:0% +the occurrence number four is even +trickier because + + align:start position:0% +trickier because + + + align:start position:0% +trickier because +they just serve with the rest that it's + + align:start position:0% +they just serve with the rest that it's + + + align:start position:0% +they just serve with the rest that it's +three notes also and the lyrics. No, but + + align:start position:0% +three notes also and the lyrics. No, but + + + align:start position:0% +three notes also and the lyrics. No, but +it's pretty different. No. So that's one + + align:start position:0% +it's pretty different. No. So that's one + + + align:start position:0% +it's pretty different. No. So that's one +of the main difficulties of the problem + + align:start position:0% +of the main difficulties of the problem + + + align:start position:0% +of the main difficulties of the problem +of pattern mining in music that even + + align:start position:0% +of pattern mining in music that even + + + align:start position:0% +of pattern mining in music that even +though uh objects that we want to group + + align:start position:0% +though uh objects that we want to group + + + align:start position:0% +though uh objects that we want to group +together because in our mind represent + + align:start position:0% +together because in our mind represent + + + align:start position:0% +together because in our mind represent +the same musical idea over the table + + align:start position:0% +the same musical idea over the table + + + align:start position:0% +the same musical idea over the table +they might look pretty different and + + align:start position:0% +they might look pretty different and + + + align:start position:0% +they might look pretty different and +there are two mechanisms involved here. + + align:start position:0% +there are two mechanisms involved here. + + + align:start position:0% +there are two mechanisms involved here. +The first one is something that we have + + align:start position:0% +The first one is something that we have + + + align:start position:0% +The first one is something that we have +already studied the transformations. So + + align:start position:0% +already studied the transformations. So + + + align:start position:0% +already studied the transformations. So +if we have a a music fragment, if we + + align:start position:0% +if we have a a music fragment, if we + + + align:start position:0% +if we have a a music fragment, if we +apply the mathematical transformation + + align:start position:0% +apply the mathematical transformation + + + align:start position:0% +apply the mathematical transformation +over the notes there, we obtain other + + align:start position:0% +over the notes there, we obtain other + + + align:start position:0% +over the notes there, we obtain other +fragments that under some circumstances + + align:start position:0% +fragments that under some circumstances + + + align:start position:0% +fragments that under some circumstances +our mind will process them as + + align:start position:0% +our mind will process them as + + + align:start position:0% +our mind will process them as +equivalent. + + align:start position:0% +equivalent. + + + align:start position:0% +equivalent. +And how to deal with this + + align:start position:0% +And how to deal with this + + + align:start position:0% +And how to deal with this +computationally from the point of view + + align:start position:0% +computationally from the point of view + + + align:start position:0% +computationally from the point of view +of a pattern mining algorithm? My + + align:start position:0% +of a pattern mining algorithm? My + + + align:start position:0% +of a pattern mining algorithm? My +approach was to use the concept of + + align:start position:0% +approach was to use the concept of + + + align:start position:0% +approach was to use the concept of +viewpoint. I'm going to show you an + + align:start position:0% +viewpoint. I'm going to show you an + + + align:start position:0% +viewpoint. I'm going to show you an +example of what is this about but for + + align:start position:0% +example of what is this about but for + + + align:start position:0% +example of what is this about but for +the moment it's enough to know that it + + align:start position:0% +the moment it's enough to know that it + + + align:start position:0% +the moment it's enough to know that it +it's it have a double task know on the + + align:start position:0% +it's it have a double task know on the + + + align:start position:0% +it's it have a double task know on the +first hand um it directly takes into + + align:start position:0% +first hand um it directly takes into + + + align:start position:0% +first hand um it directly takes into +account this transformations you will + + align:start position:0% +account this transformations you will + + + align:start position:0% +account this transformations you will +see it in a minute and probably more + + align:start position:0% +see it in a minute and probably more + + + align:start position:0% +see it in a minute and probably more +important it simplifies the + + align:start position:0% +important it simplifies the + + + align:start position:0% +important it simplifies the +representation because one of the + + align:start position:0% +representation because one of the + + + align:start position:0% +representation because one of the +constants in this course in this classes + + align:start position:0% +constants in this course in this classes + + + align:start position:0% +constants in this course in this classes +is that music is something complex no it + + align:start position:0% +is that music is something complex no it + + + align:start position:0% +is that music is something complex no it +has like complex logical structures + + align:start position:0% +has like complex logical structures + + + align:start position:0% +has like complex logical structures +among among the elements of the score + + align:start position:0% +among among the elements of the score + + + align:start position:0% +among among the elements of the score +and if we find a way to simplify that + + align:start position:0% +and if we find a way to simplify that + + + align:start position:0% +and if we find a way to simplify that +representation would be helpful for from + + align:start position:0% +representation would be helpful for from + + + align:start position:0% +representation would be helpful for from +the computational point of view. So the + + align:start position:0% +the computational point of view. So the + + + align:start position:0% +the computational point of view. So the +viewpoint representation is pretty + + align:start position:0% +viewpoint representation is pretty + + + align:start position:0% +viewpoint representation is pretty +simple. It's just I'm going to + + align:start position:0% +simple. It's just I'm going to + + + align:start position:0% +simple. It's just I'm going to +substitute a complex tune like this one + + align:start position:0% +substitute a complex tune like this one + + + align:start position:0% +substitute a complex tune like this one +by a single sequence of symbols. So + + align:start position:0% +by a single sequence of symbols. So + + + align:start position:0% +by a single sequence of symbols. So +actually here I'm showing three + + align:start position:0% +actually here I'm showing three + + + align:start position:0% +actually here I'm showing three +viewpoints representation. The pitch + + align:start position:0% +viewpoints representation. The pitch + + + align:start position:0% +viewpoints representation. The pitch +viewpoint it's the sequence of these + + align:start position:0% +viewpoint it's the sequence of these + + + align:start position:0% +viewpoint it's the sequence of these +symbols 83 83 83 85 it's the MIDI note + + align:start position:0% +symbols 83 83 83 85 it's the MIDI note + + + align:start position:0% +symbols 83 83 83 85 it's the MIDI note +then we have the duration and the onset + + align:start position:0% +then we have the duration and the onset + + + align:start position:0% +then we have the duration and the onset +time I'm going to highlight there a a + + align:start position:0% +time I'm going to highlight there a a + + + align:start position:0% +time I'm going to highlight there a a +fragment so you can see the different + + align:start position:0% +fragment so you can see the different + + + align:start position:0% +fragment so you can see the different +viewpoints representation for that + + align:start position:0% +viewpoints representation for that + + + align:start position:0% +viewpoints representation for that +fragment and it's nice that idea of + + align:start position:0% +fragment and it's nice that idea of + + + align:start position:0% +fragment and it's nice that idea of +constructing the score by overlapping + + align:start position:0% +constructing the score by overlapping + + + align:start position:0% +constructing the score by overlapping +layers of information no that's the idea + + align:start position:0% +layers of information no that's the idea + + + align:start position:0% +layers of information no that's the idea +formally a viewpoint is a mapping + + align:start position:0% +formally a viewpoint is a mapping + + + align:start position:0% +formally a viewpoint is a mapping +between the current event, the current + + align:start position:0% +between the current event, the current + + + align:start position:0% +between the current event, the current +time slice and all the former ones into + + align:start position:0% +time slice and all the former ones into + + + align:start position:0% +time slice and all the former ones into +a symbol. Usually an integral or float, + + align:start position:0% +a symbol. Usually an integral or float, + + + align:start position:0% +a symbol. Usually an integral or float, +but could be others. Those there are + + align:start position:0% +but could be others. Those there are + + + align:start position:0% +but could be others. Those there are +derived viewpoints + + align:start position:0% +derived viewpoints + + + align:start position:0% +derived viewpoints +and perhaps for your own particular + + align:start position:0% +and perhaps for your own particular + + + align:start position:0% +and perhaps for your own particular +music application, you need to develop + + align:start position:0% +music application, you need to develop + + + align:start position:0% +music application, you need to develop +your own viewpoint representation. + + align:start position:0% +your own viewpoint representation. + + + align:start position:0% +your own viewpoint representation. +Uh and here is clearly highlighted how + + align:start position:0% +Uh and here is clearly highlighted how + + + align:start position:0% +Uh and here is clearly highlighted how +the transformations could be directly + + align:start position:0% +the transformations could be directly + + + align:start position:0% +the transformations could be directly +taken into account by using this + + align:start position:0% +taken into account by using this + + + align:start position:0% +taken into account by using this +technique. You know for instance if you + + align:start position:0% +technique. You know for instance if you + + + align:start position:0% +technique. You know for instance if you +apply uh the octave transformation to + + align:start position:0% +apply uh the octave transformation to + + + align:start position:0% +apply uh the octave transformation to +that pattern there that fragment you + + align:start position:0% +that pattern there that fragment you + + + align:start position:0% +that pattern there that fragment you +obtain that one over there which one + + align:start position:0% +obtain that one over there which one + + + align:start position:0% +obtain that one over there which one +which by the interval uh viewpoint + + align:start position:0% +which by the interval uh viewpoint + + + align:start position:0% +which by the interval uh viewpoint +representation + + align:start position:0% +representation + + + align:start position:0% +representation +uh will have the same symbol. So for + + align:start position:0% +uh will have the same symbol. So for + + + align:start position:0% +uh will have the same symbol. So for +sure any pattern mining algorithm that + + align:start position:0% +sure any pattern mining algorithm that + + + align:start position:0% +sure any pattern mining algorithm that +is trying to uh find this sequence uh + + align:start position:0% +is trying to uh find this sequence uh + + + align:start position:0% +is trying to uh find this sequence uh +will see that that one is the same. No. + + align:start position:0% +will see that that one is the same. No. + + + align:start position:0% +will see that that one is the same. No. +Is that enough to deal with the concept + + align:start position:0% +Is that enough to deal with the concept + + + align:start position:0% +Is that enough to deal with the concept +of dissimilarity in music? + + align:start position:0% +of dissimilarity in music? + + + align:start position:0% +of dissimilarity in music? +Unfortunately, not. So have a look at + + align:start position:0% +Unfortunately, not. So have a look at + + + align:start position:0% +Unfortunately, not. So have a look at +these two occurrences of the green + + align:start position:0% +these two occurrences of the green + + + align:start position:0% +these two occurrences of the green +pattern of baby sark. There is no + + align:start position:0% +pattern of baby sark. There is no + + + align:start position:0% +pattern of baby sark. There is no +viewpoint representation that can take + + align:start position:0% +viewpoint representation that can take + + + align:start position:0% +viewpoint representation that can take +us from one to the other. So someone + + align:start position:0% +us from one to the other. So someone + + + align:start position:0% +us from one to the other. So someone +said at some point okay it would be nice + + align:start position:0% +said at some point okay it would be nice + + + align:start position:0% +said at some point okay it would be nice +to have a kind of measure uh a + + align:start position:0% +to have a kind of measure uh a + + + align:start position:0% +to have a kind of measure uh a +mathematical tool that help us to + + align:start position:0% +mathematical tool that help us to + + + align:start position:0% +mathematical tool that help us to +evaluate how different two fragments + + align:start position:0% +evaluate how different two fragments + + + align:start position:0% +evaluate how different two fragments +are. + + align:start position:0% +are. + + + align:start position:0% +are. +like uh the aim here is that okay if I + + align:start position:0% +like uh the aim here is that okay if I + + + align:start position:0% +like uh the aim here is that okay if I +use that matrix with this guy and this + + align:start position:0% +use that matrix with this guy and this + + + align:start position:0% +use that matrix with this guy and this +guy I would expect a lower value than + + align:start position:0% +guy I would expect a lower value than + + + align:start position:0% +guy I would expect a lower value than +the one that I would obtain when taking + + align:start position:0% +the one that I would obtain when taking + + + align:start position:0% +the one that I would obtain when taking +this guy and this guy no because they + + align:start position:0% +this guy and this guy no because they + + + align:start position:0% +this guy and this guy no because they +are uh more far no they represent uh + + align:start position:0% +are uh more far no they represent uh + + + align:start position:0% +are uh more far no they represent uh +farther ideas. So in computer science + + align:start position:0% +farther ideas. So in computer science + + + align:start position:0% +farther ideas. So in computer science +they use what is called the distance + + align:start position:0% +they use what is called the distance + + + align:start position:0% +they use what is called the distance +functions. is in a general scenario is + + align:start position:0% +functions. is in a general scenario is + + + align:start position:0% +functions. is in a general scenario is +that you can give to a function two + + align:start position:0% +that you can give to a function two + + + align:start position:0% +that you can give to a function two +objects two random objects for instance + + align:start position:0% +objects two random objects for instance + + + align:start position:0% +objects two random objects for instance +me myself and this computer and it + + align:start position:0% +me myself and this computer and it + + + align:start position:0% +me myself and this computer and it +returns a non- negative real number + + align:start position:0% +returns a non- negative real number + + + align:start position:0% +returns a non- negative real number +evaluating the degree of dissimilarity + + align:start position:0% +evaluating the degree of dissimilarity + + + align:start position:0% +evaluating the degree of dissimilarity +between the two objects in the context + + align:start position:0% +between the two objects in the context + + + align:start position:0% +between the two objects in the context +of sequences because we are using + + align:start position:0% +of sequences because we are using + + + align:start position:0% +of sequences because we are using +viewpoint representation so now this + + align:start position:0% +viewpoint representation so now this + + + align:start position:0% +viewpoint representation so now this +fragment will be a sequence for instance + + align:start position:0% +fragment will be a sequence for instance + + + align:start position:0% +fragment will be a sequence for instance +let's see let's think that I'm using the + + align:start position:0% +let's see let's think that I'm using the + + + align:start position:0% +let's see let's think that I'm using the +duration viewpoint point. So in the + + align:start position:0% +duration viewpoint point. So in the + + + align:start position:0% +duration viewpoint point. So in the +literature we have like plenty of + + align:start position:0% +literature we have like plenty of + + + align:start position:0% +literature we have like plenty of +distance functions. This was very a very + + align:start position:0% +distance functions. This was very a very + + + align:start position:0% +distance functions. This was very a very +trending topic in music information + + align:start position:0% +trending topic in music information + + + align:start position:0% +trending topic in music information +retrieval like 15 years ago more or + + align:start position:0% +retrieval like 15 years ago more or + + + align:start position:0% +retrieval like 15 years ago more or +less. There were many studies and papers + + align:start position:0% +less. There were many studies and papers + + + align:start position:0% +less. There were many studies and papers +trying to figure out which was the best + + align:start position:0% +trying to figure out which was the best + + + align:start position:0% +trying to figure out which was the best +distance function depending on the + + align:start position:0% +distance function depending on the + + + align:start position:0% +distance function depending on the +style. + + align:start position:0% +style. + + + align:start position:0% +style. +The lestain distance function perhaps is + + align:start position:0% +The lestain distance function perhaps is + + + align:start position:0% +The lestain distance function perhaps is +not the most advanced one but is one of + + align:start position:0% +not the most advanced one but is one of + + + align:start position:0% +not the most advanced one but is one of +the simplest one and probably the most + + align:start position:0% +the simplest one and probably the most + + + align:start position:0% +the simplest one and probably the most +used one and it accounts for the number + + align:start position:0% +used one and it accounts for the number + + + align:start position:0% +used one and it accounts for the number +of substitutions + + align:start position:0% +of substitutions + + + align:start position:0% +of substitutions +or insertions to go from one sequence to + + align:start position:0% +or insertions to go from one sequence to + + + align:start position:0% +or insertions to go from one sequence to +the other. So uh to go from the sequence + + align:start position:0% +the other. So uh to go from the sequence + + + align:start position:0% +the other. So uh to go from the sequence +0.5 + + align:start position:0% +0.5 + + + align:start position:0% +0.5 +to the sequence 0.52 + + align:start position:0% +to the sequence 0.52 + + + align:start position:0% +to the sequence 0.52 +we just need a single substitution. So + + align:start position:0% +we just need a single substitution. So + + + align:start position:0% +we just need a single substitution. So +the leven distance function between the + + align:start position:0% +the leven distance function between the + + + align:start position:0% +the leven distance function between the +fragment two and fragment four is one. + + align:start position:0% +fragment two and fragment four is one. + + + align:start position:0% +fragment two and fragment four is one. +Okay. Probably the leven distance + + align:start position:0% +Okay. Probably the leven distance + + + align:start position:0% +Okay. Probably the leven distance +function between this guy and this guy + + align:start position:0% +function between this guy and this guy + + + align:start position:0% +function between this guy and this guy +it's I don't know two or three at least. + + align:start position:0% +it's I don't know two or three at least. + + + align:start position:0% +it's I don't know two or three at least. +No. So cool. Now we have like all the + + align:start position:0% +No. So cool. Now we have like all the + + + align:start position:0% +No. So cool. Now we have like all the +ingredients needed to understand the + + align:start position:0% +ingredients needed to understand the + + + align:start position:0% +ingredients needed to understand the +inputs and outputs of my algorithm. We + + align:start position:0% +inputs and outputs of my algorithm. We + + + align:start position:0% +inputs and outputs of my algorithm. We +have a corpus or a piece of music. We + + align:start position:0% +have a corpus or a piece of music. We + + + align:start position:0% +have a corpus or a piece of music. We +have also the viewpoint representation + + align:start position:0% +have also the viewpoint representation + + + align:start position:0% +have also the viewpoint representation +that the user want to choose and some + + align:start position:0% +that the user want to choose and some + + + align:start position:0% +that the user want to choose and some +parameters at the input. The minimum + + align:start position:0% +parameters at the input. The minimum + + + align:start position:0% +parameters at the input. The minimum +support is the minimum number of + + align:start position:0% +support is the minimum number of + + + align:start position:0% +support is the minimum number of +repetitions that we uh require to a + + align:start position:0% +repetitions that we uh require to a + + + align:start position:0% +repetitions that we uh require to a +pattern to be considered frequent and to + + align:start position:0% +pattern to be considered frequent and to + + + align:start position:0% +pattern to be considered frequent and to +be included in the result list. These + + align:start position:0% +be included in the result list. These + + + align:start position:0% +be included in the result list. These +two guys the minimum length and maximum + + align:start position:0% +two guys the minimum length and maximum + + + align:start position:0% +two guys the minimum length and maximum +length are the parameters to control the + + align:start position:0% +length are the parameters to control the + + + align:start position:0% +length are the parameters to control the +lengths of the patterns that we want to + + align:start position:0% +lengths of the patterns that we want to + + + align:start position:0% +lengths of the patterns that we want to +mine and some parameters to control the + + align:start position:0% +mine and some parameters to control the + + + align:start position:0% +mine and some parameters to control the +degree of dissimilarity + + align:start position:0% +degree of dissimilarity + + + align:start position:0% +degree of dissimilarity +from the former slide. And the result is + + align:start position:0% +from the former slide. And the result is + + + align:start position:0% +from the former slide. And the result is +yes like the list of frequent patterns + + align:start position:0% +yes like the list of frequent patterns + + + align:start position:0% +yes like the list of frequent patterns +together with the position. This is an + + align:start position:0% +together with the position. This is an + + + align:start position:0% +together with the position. This is an +example with the piece of the former + + align:start position:0% +example with the piece of the former + + + align:start position:0% +example with the piece of the former +slide. Now I'm selecting the interval + + align:start position:0% +slide. Now I'm selecting the interval + + + align:start position:0% +slide. Now I'm selecting the interval +viewpoint + + align:start position:0% +viewpoint + + + align:start position:0% +viewpoint +uh and those parameters over there. And + + align:start position:0% +uh and those parameters over there. And + + + align:start position:0% +uh and those parameters over there. And +this is an example of the output that we + + align:start position:0% +this is an example of the output that we + + + align:start position:0% +this is an example of the output that we +might obtain. So we have a yellow + + align:start position:0% +might obtain. So we have a yellow + + + align:start position:0% +might obtain. So we have a yellow +pattern that has four occurrences. and + + align:start position:0% +pattern that has four occurrences. and + + + align:start position:0% +pattern that has four occurrences. and +have a look that each of these fragments + + align:start position:0% +have a look that each of these fragments + + + align:start position:0% +have a look that each of these fragments +are at most distance one from any of the + + align:start position:0% +are at most distance one from any of the + + + align:start position:0% +are at most distance one from any of the +rest. No, taking the Levenstein distance + + align:start position:0% +rest. No, taking the Levenstein distance + + + align:start position:0% +rest. No, taking the Levenstein distance +function and we might have for instance + + align:start position:0% +function and we might have for instance + + + align:start position:0% +function and we might have for instance +also this guy the purple pattern and + + align:start position:0% +also this guy the purple pattern and + + + align:start position:0% +also this guy the purple pattern and +this green one which is of length four. + + align:start position:0% +this green one which is of length four. + + + align:start position:0% +this green one which is of length four. +So yeah in a real case the pattern + + align:start position:0% +So yeah in a real case the pattern + + + align:start position:0% +So yeah in a real case the pattern +structure might be complex as you see + + align:start position:0% +structure might be complex as you see + + + align:start position:0% +structure might be complex as you see +because you have nested patterns you + + align:start position:0% +because you have nested patterns you + + + align:start position:0% +because you have nested patterns you +have many overlapping I won't go into + + align:start position:0% +have many overlapping I won't go into + + + align:start position:0% +have many overlapping I won't go into +the details on how I implemented the + + align:start position:0% +the details on how I implemented the + + + align:start position:0% +the details on how I implemented the +algorithm just a brief overview uh I + + align:start position:0% +algorithm just a brief overview uh I + + + align:start position:0% +algorithm just a brief overview uh I +divided in four steps the one is the + + align:start position:0% +divided in four steps the one is the + + + align:start position:0% +divided in four steps the one is the +creation of a an initial database a a + + align:start position:0% +creation of a an initial database a a + + + align:start position:0% +creation of a an initial database a a +vertical database it's called sometimes + + align:start position:0% +vertical database it's called sometimes + + + align:start position:0% +vertical database it's called sometimes +where I just take a sliding window of + + align:start position:0% +where I just take a sliding window of + + + align:start position:0% +where I just take a sliding window of +length minimum length the minimum length + + align:start position:0% +length minimum length the minimum length + + + align:start position:0% +length minimum length the minimum length +selected by the user and I just create a + + align:start position:0% +selected by the user and I just create a + + + align:start position:0% +selected by the user and I just create a +database of do all the patterns together + + align:start position:0% +database of do all the patterns together + + + align:start position:0% +database of do all the patterns together +with their positions within the score. + + align:start position:0% +with their positions within the score. + + + align:start position:0% +with their positions within the score. +Then in the next step I compare every + + align:start position:0% +Then in the next step I compare every + + + align:start position:0% +Then in the next step I compare every +pattern against all the rest trying to + + align:start position:0% +pattern against all the rest trying to + + + align:start position:0% +pattern against all the rest trying to +uh see if they satisfies the distance + + align:start position:0% +uh see if they satisfies the distance + + + align:start position:0% +uh see if they satisfies the distance +constraint. No. And in that case I group + + align:start position:0% +constraint. No. And in that case I group + + + align:start position:0% +constraint. No. And in that case I group +them together into uh what I call metric + + align:start position:0% +them together into uh what I call metric + + + align:start position:0% +them together into uh what I call metric +patterns which are like groups of + + align:start position:0% +patterns which are like groups of + + + align:start position:0% +patterns which are like groups of +fragments of music. you know at this + + align:start position:0% +fragments of music. you know at this + + + align:start position:0% +fragments of music. you know at this +stage it's safe to deate the entries + + align:start position:0% +stage it's safe to deate the entries + + + align:start position:0% +stage it's safe to deate the entries +that doesn't reach the minimum support + + align:start position:0% +that doesn't reach the minimum support + + + align:start position:0% +that doesn't reach the minimum support +constraint like they don't have enough + + align:start position:0% +constraint like they don't have enough + + + align:start position:0% +constraint like they don't have enough +occurrences to be considered frequent + + align:start position:0% +occurrences to be considered frequent + + + align:start position:0% +occurrences to be considered frequent +and finally as here I still have + + align:start position:0% +and finally as here I still have + + + align:start position:0% +and finally as here I still have +patterns of length equal to the minimum + + align:start position:0% +patterns of length equal to the minimum + + + align:start position:0% +patterns of length equal to the minimum +length and we actually want longer + + align:start position:0% +length and we actually want longer + + + align:start position:0% +length and we actually want longer +patterns so the last stage is + + align:start position:0% +patterns so the last stage is + + + align:start position:0% +patterns so the last stage is +overlapping different patterns to form + + align:start position:0% +overlapping different patterns to form + + + align:start position:0% +overlapping different patterns to form +longer ones + + align:start position:0% +longer ones + + + align:start position:0% +longer ones +okay and to finish this I'm going to + + align:start position:0% +okay and to finish this I'm going to + + + align:start position:0% +okay and to finish this I'm going to +show you some results this is the last + + align:start position:0% +show you some results this is the last + + + align:start position:0% +show you some results this is the last +slide + + align:start position:0% +slide + + + align:start position:0% +slide +Uh I'm actually already using this I + + align:start position:0% +Uh I'm actually already using this I + + + align:start position:0% +Uh I'm actually already using this I +started using collaborating with these + + align:start position:0% +started using collaborating with these + + + align:start position:0% +started using collaborating with these +research groups like seven months ago. + + align:start position:0% +research groups like seven months ago. + + + align:start position:0% +research groups like seven months ago. +This has a a research group from + + align:start position:0% +This has a a research group from + + + align:start position:0% +This has a a research group from +another university of Madrid. They got a + + align:start position:0% +another university of Madrid. They got a + + + align:start position:0% +another university of Madrid. They got a +good amount of money of the European + + align:start position:0% +good amount of money of the European + + + align:start position:0% +good amount of money of the European +Union to study the Italian operas. They + + align:start position:0% +Union to study the Italian operas. They + + + align:start position:0% +Union to study the Italian operas. They +have a huge database with many features + + align:start position:0% +have a huge database with many features + + + align:start position:0% +have a huge database with many features +for each piece and in particular they + + align:start position:0% +for each piece and in particular they + + + align:start position:0% +for each piece and in particular they +are interested in the emotion that the + + align:start position:0% +are interested in the emotion that the + + + align:start position:0% +are interested in the emotion that the +piece evoke. So here we are trying to + + align:start position:0% +piece evoke. So here we are trying to + + + align:start position:0% +piece evoke. So here we are trying to +find some correlations between the + + align:start position:0% +find some correlations between the + + + align:start position:0% +find some correlations between the +emotions and the pattern structure of + + align:start position:0% +emotions and the pattern structure of + + + align:start position:0% +emotions and the pattern structure of +the different pieces. These two other + + align:start position:0% +the different pieces. These two other + + + align:start position:0% +the different pieces. These two other +projects are pretty similar. The number + + align:start position:0% +projects are pretty similar. The number + + + align:start position:0% +projects are pretty similar. The number +two it's on a corpus of folk music from + + align:start position:0% +two it's on a corpus of folk music from + + + align:start position:0% +two it's on a corpus of folk music from +a very concrete region of Europe in + + align:start position:0% +a very concrete region of Europe in + + + align:start position:0% +a very concrete region of Europe in +around the Pyrenees. And the second one + + align:start position:0% +around the Pyrenees. And the second one + + + align:start position:0% +around the Pyrenees. And the second one +is the + + align:start position:0% +is the + + + align:start position:0% +is the +a database of just solos. So here we are + + align:start position:0% +a database of just solos. So here we are + + + align:start position:0% +a database of just solos. So here we are +building classifiers like similar to + + align:start position:0% +building classifiers like similar to + + + align:start position:0% +building classifiers like similar to +what we did in the last uh class. Here + + align:start position:0% +what we did in the last uh class. Here + + + align:start position:0% +what we did in the last uh class. Here +I'm showing like uh the number of + + align:start position:0% +I'm showing like uh the number of + + + align:start position:0% +I'm showing like uh the number of +patterns per style for the different + + align:start position:0% +patterns per style for the different + + + align:start position:0% +patterns per style for the different +styles in this uh corpus. uh but perhaps + + align:start position:0% +styles in this uh corpus. uh but perhaps + + + align:start position:0% +styles in this uh corpus. uh but perhaps +here uh we can see a cool thing of the + + align:start position:0% +here uh we can see a cool thing of the + + + align:start position:0% +here uh we can see a cool thing of the +algorithm that it returns also the + + align:start position:0% +algorithm that it returns also the + + + align:start position:0% +algorithm that it returns also the +position of the patterns not only the + + align:start position:0% +position of the patterns not only the + + + align:start position:0% +position of the patterns not only the +fact that a piece contain the pattern no + + align:start position:0% +fact that a piece contain the pattern no + + + align:start position:0% +fact that a piece contain the pattern no +so here I'm plotting it's called + + align:start position:0% +so here I'm plotting it's called + + + align:start position:0% +so here I'm plotting it's called +coverage this variable but it's actually + + align:start position:0% +coverage this variable but it's actually + + + align:start position:0% +coverage this variable but it's actually +like the + + align:start position:0% +like the + + + align:start position:0% +like the +probability function of encountering a + + align:start position:0% +probability function of encountering a + + + align:start position:0% +probability function of encountering a +pattern within a solo no so I normalize + + align:start position:0% +pattern within a solo no so I normalize + + + align:start position:0% +pattern within a solo no so I normalize +the length of the all the solos by style + + align:start position:0% +the length of the all the solos by style + + + align:start position:0% +the length of the all the solos by style +and the thin line is the average for the + + align:start position:0% +and the thin line is the average for the + + + align:start position:0% +and the thin line is the average for the +solos we You can see for instance that + + align:start position:0% +solos we You can see for instance that + + + align:start position:0% +solos we You can see for instance that +the concentrations of of patterns tends + + align:start position:0% +the concentrations of of patterns tends + + + align:start position:0% +the concentrations of of patterns tends +to be at the beginning and not in the + + align:start position:0% +to be at the beginning and not in the + + + align:start position:0% +to be at the beginning and not in the +end. This is intuitive because like the + + align:start position:0% +end. This is intuitive because like the + + + align:start position:0% +end. This is intuitive because like the +impro improvisors usually start their + + align:start position:0% +impro improvisors usually start their + + + align:start position:0% +impro improvisors usually start their +solos like in a more organized way + + align:start position:0% +solos like in a more organized way + + + align:start position:0% +solos like in a more organized way +taking thematic material from the + + align:start position:0% +taking thematic material from the + + + align:start position:0% +taking thematic material from the +original melody and then they start to + + align:start position:0% +original melody and then they start to + + + align:start position:0% +original melody and then they start to +do more crazy stuff. No. Then I'm also + + align:start position:0% +do more crazy stuff. No. Then I'm also + + + align:start position:0% +do more crazy stuff. No. Then I'm also +trying to build up a pattern dictionary + + align:start position:0% +trying to build up a pattern dictionary + + + align:start position:0% +trying to build up a pattern dictionary +of uh in an Iris corpus. These are the + + align:start position:0% +of uh in an Iris corpus. These are the + + + align:start position:0% +of uh in an Iris corpus. These are the +five most frequent patterns in the + + align:start position:0% +five most frequent patterns in the + + + align:start position:0% +five most frequent patterns in the +subset of minor rs in the corpus that + + align:start position:0% +subset of minor rs in the corpus that + + + align:start position:0% +subset of minor rs in the corpus that +I'm working on. So I don't know for a + + align:start position:0% +I'm working on. So I don't know for a + + + align:start position:0% +I'm working on. So I don't know for a +performance that is interested in + + align:start position:0% +performance that is interested in + + + align:start position:0% +performance that is interested in +playing this music perhaps the takeaway + + align:start position:0% +playing this music perhaps the takeaway + + + align:start position:0% +playing this music perhaps the takeaway +of this is okay you might want to start + + align:start position:0% +of this is okay you might want to start + + + align:start position:0% +of this is okay you might want to start +studying these patterns no because they + + align:start position:0% +studying these patterns no because they + + + align:start position:0% +studying these patterns no because they +appear quite often in the in the corpus. + + align:start position:0% +appear quite often in the in the corpus. + + + align:start position:0% +appear quite often in the in the corpus. +So better to first master them and for + + align:start position:0% +So better to first master them and for + + + align:start position:0% +So better to first master them and for +the future with Michael + + align:start position:0% +the future with Michael + + + align:start position:0% +the future with Michael +we want to study uh how the algorithm + + align:start position:0% +we want to study uh how the algorithm + + + align:start position:0% +we want to study uh how the algorithm +performs in a nice corpus of early music + + align:start position:0% +performs in a nice corpus of early music + + + align:start position:0% +performs in a nice corpus of early music +that he has and also we want to analyze + + align:start position:0% +that he has and also we want to analyze + + + align:start position:0% +that he has and also we want to analyze +some solos of Charlie Parker who was one + + align:start position:0% +some solos of Charlie Parker who was one + + + align:start position:0% +some solos of Charlie Parker who was one +of the most mathematical improvisers of + + align:start position:0% +of the most mathematical improvisers of + + + align:start position:0% +of the most mathematical improvisers of +the history and also for the close + + align:start position:0% +the history and also for the close + + + align:start position:0% +the history and also for the close +future I would like to see if this tool + + align:start position:0% +future I would like to see if this tool + + + align:start position:0% +future I would like to see if this tool +can be helpful for plagiaris detection. + + align:start position:0% +can be helpful for plagiaris detection. + + + align:start position:0% +can be helpful for plagiaris detection. +No, I suspect that two pieces that uh + + align:start position:0% +No, I suspect that two pieces that uh + + + align:start position:0% +No, I suspect that two pieces that uh +are very similar share also some + + align:start position:0% +are very similar share also some + + + align:start position:0% +are very similar share also some +similarities in their pattern structure. + + align:start position:0% +similarities in their pattern structure. + + + align:start position:0% +similarities in their pattern structure. +And that's all. Thank you very much, + + align:start position:0% +And that's all. Thank you very much, + + + align:start position:0% +And that's all. Thank you very much, +guys. Any questions? + + align:start position:0% +guys. Any questions? + + + align:start position:0% +guys. Any questions? +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +>> By the way, just so you get a sense for + + align:start position:0% +>> By the way, just so you get a sense for + + + align:start position:0% +>> By the way, just so you get a sense for +your final things, that was 12 minutes. + + align:start position:0% +your final things, that was 12 minutes. + + + align:start position:0% +your final things, that was 12 minutes. +So, a tiny bit longer than what you have + + align:start position:0% +So, a tiny bit longer than what you have + + + align:start position:0% +So, a tiny bit longer than what you have +as a maximum. + + align:start position:0% + + + + align:start position:0% + +Cool. + + align:start position:0% +Cool. + + + align:start position:0% +Cool. +>> If any of you are interested in a + + align:start position:0% +>> If any of you are interested in a + + + align:start position:0% +>> If any of you are interested in a +particular thing of the algorithm, just + + align:start position:0% +particular thing of the algorithm, just + + + align:start position:0% +particular thing of the algorithm, just +drop me an email and we can talk about + + align:start position:0% +drop me an email and we can talk about + + + align:start position:0% +drop me an email and we can talk about +it. Okay. + + align:start position:0% +it. Okay. + + + align:start position:0% +it. Okay. +Thank you. + + align:start position:0% +Thank you. + + + align:start position:0% +Thank you. +>> So, what I want to do is I want to + + align:start position:0% +>> So, what I want to do is I want to + + + align:start position:0% +>> So, what I want to do is I want to +immediately start by putting some of uh + + align:start position:0% +immediately start by putting some of uh + + + align:start position:0% +immediately start by putting some of uh +thoughts to work. So, uh get with a + + align:start position:0% +thoughts to work. So, uh get with a + + + align:start position:0% +thoughts to work. So, uh get with a +partner next to you. You can um you can + + align:start position:0% +partner next to you. You can um you can + + + align:start position:0% +partner next to you. You can um you can +do that if over here we need a group of + + align:start position:0% +do that if over here we need a group of + + + align:start position:0% +do that if over here we need a group of +three or unless you want to participate + + align:start position:0% +three or unless you want to participate + + + align:start position:0% +three or unless you want to participate +with a friend or or jump over there. + + align:start position:0% +with a friend or or jump over there. + + + align:start position:0% +with a friend or or jump over there. +Well, jump over with uh with yeah with + + align:start position:0% +Well, jump over with uh with yeah with + + + align:start position:0% +Well, jump over with uh with yeah with +uh with Jordan if you do. Um and here + + align:start position:0% +uh with Jordan if you do. Um and here + + + align:start position:0% +uh with Jordan if you do. Um and here +are um six melodies. I'm going to play + + align:start position:0% +are um six melodies. I'm going to play + + + align:start position:0% +are um six melodies. I'm going to play +um each one of them. I'm going to play a + + align:start position:0% +um each one of them. I'm going to play a + + + align:start position:0% +um each one of them. I'm going to play a +a bunch of times also. So I'll tell you + + align:start position:0% +a bunch of times also. So I'll tell you + + + align:start position:0% +a bunch of times also. So I'll tell you +which one I'm playing and you're going + + align:start position:0% +which one I'm playing and you're going + + + align:start position:0% +which one I'm playing and you're going +to So and you can talk during this or + + align:start position:0% +to So and you can talk during this or + + + align:start position:0% +to So and you can talk during this or +wait till just after playing. You're + + align:start position:0% +wait till just after playing. You're + + + align:start position:0% +wait till just after playing. You're +going to tell me which melody is the um + + align:start position:0% +going to tell me which melody is the um + + + align:start position:0% +going to tell me which melody is the um +is most or least similar to A. + + align:start position:0% +is most or least similar to A. + + + align:start position:0% +is most or least similar to A. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Okay. And this is and and + + align:start position:0% +Okay. And this is and and + + + align:start position:0% +Okay. And this is and and +this is B. And I want you to know say + + align:start position:0% +this is B. And I want you to know say + + + align:start position:0% +this is B. And I want you to know say +why + + align:start position:0% +why + + + align:start position:0% +why +[Music] + + align:start position:0% + + + + align:start position:0% + +This is C. + + align:start position:0% +This is C. + + + align:start position:0% +This is C. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +And I'm going to play A one more time to + + align:start position:0% +And I'm going to play A one more time to + + + align:start position:0% +And I'm going to play A one more time to +get it back into our heads. + + align:start position:0% +get it back into our heads. + + + align:start position:0% +get it back into our heads. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +And now D. + + align:start position:0% +And now D. + + + align:start position:0% +And now D. +Oh, and by the way, this isn't a right + + align:start position:0% +Oh, and by the way, this isn't a right + + + align:start position:0% +Oh, and by the way, this isn't a right +there isn't a right answer one. + + align:start position:0% + + + + align:start position:0% + +Great. + + align:start position:0% +Great. + + + align:start position:0% +Great. +Now E. + + align:start position:0% + + + + align:start position:0% + +And now A one more time before doing F. + + align:start position:0% +And now A one more time before doing F. + + + align:start position:0% +And now A one more time before doing F. +So this is A again. + + align:start position:0% +So this is A again. + + + align:start position:0% +So this is A again. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +And now F. + + align:start position:0% + + + + align:start position:0% + +Oops, that's F and E simultaneously, + + align:start position:0% +Oops, that's F and E simultaneously, + + + align:start position:0% +Oops, that's F and E simultaneously, +which is very different. Now F. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Great. Talk amongst yourself. I want a + + align:start position:0% +Great. Talk amongst yourself. I want a + + + align:start position:0% +Great. Talk amongst yourself. I want a +ranking from your group. So, somebody + + align:start position:0% +ranking from your group. So, somebody + + + align:start position:0% +ranking from your group. So, somebody +write it down. + + align:start position:0% + + + + align:start position:0% + +>> And I want to know why. + + align:start position:0% + + + + align:start position:0% + +>> Okay, let's bring it all back together. + + align:start position:0% + + + + align:start position:0% + +Let's bring it all all back together. + + align:start position:0% +Let's bring it all all back together. + + + align:start position:0% +Let's bring it all all back together. +So, look at look at your look at your + + align:start position:0% +So, look at look at your look at your + + + align:start position:0% +So, look at look at your look at your +list and we'll we'll count like normal + + align:start position:0% +list and we'll we'll count like normal + + + align:start position:0% +list and we'll we'll count like normal +human beings. whichever one is the top + + align:start position:0% +human beings. whichever one is the top + + + align:start position:0% +human beings. whichever one is the top +in your list is one, whichever one's + + align:start position:0% +in your list is one, whichever one's + + + align:start position:0% +in your list is one, whichever one's +second to stuff. And we'll we'll vote by + + align:start position:0% +second to stuff. And we'll we'll vote by + + + align:start position:0% +second to stuff. And we'll we'll vote by +fingers first off for the general + + align:start position:0% +fingers first off for the general + + + align:start position:0% +fingers first off for the general +ranking. So when if you hold up the + + align:start position:0% +ranking. So when if you hold up the + + + align:start position:0% +ranking. So when if you hold up the +number of fingers that um you know, if + + align:start position:0% +number of fingers that um you know, if + + + align:start position:0% +number of fingers that um you know, if +it's closest, it's pulled up one finger. + + align:start position:0% +it's closest, it's pulled up one finger. + + + align:start position:0% +it's closest, it's pulled up one finger. +If not to, you know, whatever. And pull + + align:start position:0% +If not to, you know, whatever. And pull + + + align:start position:0% +If not to, you know, whatever. And pull +palm means I have no idea what that is. + + align:start position:0% +palm means I have no idea what that is. + + + align:start position:0% +palm means I have no idea what that is. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +B. + + align:start position:0% + + + + align:start position:0% + +Oh, B's doing pretty pretty well. Okay. + + align:start position:0% +Oh, B's doing pretty pretty well. Okay. + + + align:start position:0% +Oh, B's doing pretty pretty well. Okay. +Not a lot of twos. A couple ones. C. + + align:start position:0% + + + + align:start position:0% + +Okay. A little bit more variety. Hold + + align:start position:0% +Okay. A little bit more variety. Hold + + + align:start position:0% +Okay. A little bit more variety. Hold +them up so other people can see also. + + align:start position:0% +them up so other people can see also. + + + align:start position:0% +them up so other people can see also. +Yeah. Look around the room. It's not + + align:start position:0% +Yeah. Look around the room. It's not + + + align:start position:0% +Yeah. Look around the room. It's not +just for me. Great. Great. Uh D. + + align:start position:0% + + + + align:start position:0% + +Oh, okay. We got a variety. No. No. + + align:start position:0% +Oh, okay. We got a variety. No. No. + + + align:start position:0% +Oh, okay. We got a variety. No. No. +Whatever. Great. Uh E. + + align:start position:0% + + + + align:start position:0% + +Oh, that's still see some palms or + + align:start position:0% +Oh, that's still see some palms or + + + align:start position:0% +Oh, that's still see some palms or +things. Great. And F. + + align:start position:0% +things. Great. And F. + + + align:start position:0% +things. Great. And F. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Oh, we have one one four. Good. Good. + + align:start position:0% +Oh, we have one one four. Good. Good. + + + align:start position:0% +Oh, we have one one four. Good. Good. +Uh, what did you what you what you you + + align:start position:0% +Uh, what did you what you what you you + + + align:start position:0% +Uh, what did you what you what you you +put it down? What do you guys Those who + + align:start position:0% +put it down? What do you guys Those who + + + align:start position:0% +put it down? What do you guys Those who +put uh F as four, what' you put as five? + + align:start position:0% +put uh F as four, what' you put as five? + + + align:start position:0% +put uh F as four, what' you put as five? +>> D. + + align:start position:0% +>> D. + + + align:start position:0% +>> D. +>> B. + + align:start position:0% +>> B. + + + align:start position:0% +>> B. +>> D. + + align:start position:0% +>> D. + + + align:start position:0% +>> D. +>> D. Okay. D. Good. Good. Great. Um, + + align:start position:0% +>> D. Okay. D. Good. Good. Great. Um, + + + align:start position:0% +>> D. Okay. D. Good. Good. Great. Um, +somebody who had who had uh C above B, + + align:start position:0% +somebody who had who had uh C above B, + + + align:start position:0% +somebody who had who had uh C above B, +justify your answer. Who who had C above + + align:start position:0% +justify your answer. Who who had C above + + + align:start position:0% +justify your answer. Who who had C above +B? There were a couple people. Yeah. Uh, + + align:start position:0% +B? There were a couple people. Yeah. Uh, + + + align:start position:0% +B? There were a couple people. Yeah. Uh, +go ahead, Jake. First. + + align:start position:0% +go ahead, Jake. First. + + + align:start position:0% +go ahead, Jake. First. +Yeah. Groups. Yeah. + + align:start position:0% +Yeah. Groups. Yeah. + + + align:start position:0% +Yeah. Groups. Yeah. +>> C was basically just a transposition + + align:start position:0% +>> C was basically just a transposition + + + align:start position:0% +>> C was basically just a transposition +whereas B like B changed a lot of the + + align:start position:0% +whereas B like B changed a lot of the + + + align:start position:0% +whereas B like B changed a lot of the +rhythms a bit. Like B H B I think fits + + align:start position:0% +rhythms a bit. Like B H B I think fits + + + align:start position:0% +rhythms a bit. Like B H B I think fits +the exact pitches a little better, but + + align:start position:0% +the exact pitches a little better, but + + + align:start position:0% +the exact pitches a little better, but +or aside from a couple places where it + + align:start position:0% +or aside from a couple places where it + + + align:start position:0% +or aside from a couple places where it +has some accidentals, but it changes the + + align:start position:0% +has some accidentals, but it changes the + + + align:start position:0% +has some accidentals, but it changes the +rhythm quite a bit. Whereas C is just a + + align:start position:0% +rhythm quite a bit. Whereas C is just a + + + align:start position:0% +rhythm quite a bit. Whereas C is just a +transposition. So for relative pitch + + align:start position:0% +transposition. So for relative pitch + + + align:start position:0% +transposition. So for relative pitch +especially, + + align:start position:0% +especially, + + + align:start position:0% +especially, +>> yeah, we waited transposition on. Okay, + + align:start position:0% +>> yeah, we waited transposition on. Okay, + + + align:start position:0% +>> yeah, we waited transposition on. Okay, +good. Good. I'm already hearing words + + align:start position:0% +good. Good. I'm already hearing words + + + align:start position:0% +good. Good. I'm already hearing words +that I that I'm liking and stuff. Great. + + align:start position:0% +that I that I'm liking and stuff. Great. + + + align:start position:0% +that I that I'm liking and stuff. Great. +Um, somebody who had it the other way + + align:start position:0% +Um, somebody who had it the other way + + + align:start position:0% +Um, somebody who had it the other way +around to justify your answer. Who who + + align:start position:0% +around to justify your answer. Who who + + + align:start position:0% +around to justify your answer. Who who +had it the other way around? + + align:start position:0% +had it the other way around? + + + align:start position:0% +had it the other way around? +Who had a bunch of people had B above C? + + align:start position:0% +Who had a bunch of people had B above C? + + + align:start position:0% +Who had a bunch of people had B above C? +Yeah, John. + + align:start position:0% +Yeah, John. + + + align:start position:0% +Yeah, John. +>> For like the kind like styling feel that + + align:start position:0% +>> For like the kind like styling feel that + + + align:start position:0% +>> For like the kind like styling feel that +A had. Um, because are similar between A + + align:start position:0% +A had. Um, because are similar between A + + + align:start position:0% +A had. Um, because are similar between A +and B is why we put a bit higher + + align:start position:0% +and B is why we put a bit higher + + + align:start position:0% +and B is why we put a bit higher +relative C. And when you take + + align:start position:0% +relative C. And when you take + + + align:start position:0% +relative C. And when you take +transposition into account, only part of + + align:start position:0% +transposition into account, only part of + + + align:start position:0% +transposition into account, only part of +C's coming transposed. So it doesn't + + align:start position:0% +C's coming transposed. So it doesn't + + + align:start position:0% +C's coming transposed. So it doesn't +even feel like it's like a full + + align:start position:0% +even feel like it's like a full + + + align:start position:0% +even feel like it's like a full +transposition. + + align:start position:0% +transposition. + + + align:start position:0% +transposition. +>> Great. Only part of it transpose. Yeah. + + align:start position:0% +>> Great. Only part of it transpose. Yeah. + + + align:start position:0% +>> Great. Only part of it transpose. Yeah. +Yeah. It kind of gets back on for a bit + + align:start position:0% +Yeah. It kind of gets back on for a bit + + + align:start position:0% +Yeah. It kind of gets back on for a bit +and then comes back off. Great. Uh okay. + + align:start position:0% +and then comes back off. Great. Uh okay. + + + align:start position:0% +and then comes back off. Great. Uh okay. +Who had who had D um who had D1 or two? + + align:start position:0% +Who had who had D um who had D1 or two? + + + align:start position:0% +Who had who had D um who had D1 or two? +Anybody? I can't remember. + + align:start position:0% +Anybody? I can't remember. + + + align:start position:0% +Anybody? I can't remember. +Yeah. Why' you have a one or two? + + align:start position:0% +Yeah. Why' you have a one or two? + + + align:start position:0% +Yeah. Why' you have a one or two? +>> Um because it basically has this. Sorry. + + align:start position:0% +>> Um because it basically has this. Sorry. + + + align:start position:0% +>> Um because it basically has this. Sorry. +It has all of the same notes in the + + align:start position:0% +It has all of the same notes in the + + + align:start position:0% +It has all of the same notes in the +right position or or basically. Yeah. + + align:start position:0% +right position or or basically. Yeah. + + + align:start position:0% +right position or or basically. Yeah. +Yeah. All you have to do is remove notes + + align:start position:0% +Yeah. All you have to do is remove notes + + + align:start position:0% +Yeah. All you have to do is remove notes +and then you get the same thing and I + + align:start position:0% +and then you get the same thing and I + + + align:start position:0% +and then you get the same thing and I +think with a few exceptions but that + + align:start position:0% +think with a few exceptions but that + + + align:start position:0% +think with a few exceptions but that +never happened in + + align:start position:0% +never happened in + + + align:start position:0% +never happened in +>> Okay, great. Who had uh D very low? + + align:start position:0% +>> Okay, great. Who had uh D very low? + + + align:start position:0% +>> Okay, great. Who had uh D very low? +>> Yeah. Go ahead. + + align:start position:0% +>> Yeah. Go ahead. + + + align:start position:0% +>> Yeah. Go ahead. +>> Sorry. Sorry. Can you speak a lot? + + align:start position:0% + + + + align:start position:0% + +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Great. Um, and who had um did anybody + + align:start position:0% +>> Great. Um, and who had um did anybody + + + align:start position:0% +>> Great. Um, and who had um did anybody +have E above um above four? + + align:start position:0% +have E above um above four? + + + align:start position:0% +have E above um above four? +>> Okay, + + align:start position:0% +>> Okay, + + + align:start position:0% +>> Okay, +we have EX3 + + align:start position:0% +we have EX3 + + + align:start position:0% +we have EX3 +and we put it there because the pattern + + align:start position:0% +and we put it there because the pattern + + + align:start position:0% +and we put it there because the pattern +was very similar. I even though the + + align:start position:0% +was very similar. I even though the + + + align:start position:0% +was very similar. I even though the +melody wasn't all that close, we figured + + align:start position:0% +melody wasn't all that close, we figured + + + align:start position:0% +melody wasn't all that close, we figured +that count. + + align:start position:0% +that count. + + + align:start position:0% +that count. +>> So, so when you say pattern, what the + + align:start position:0% +>> So, so when you say pattern, what the + + + align:start position:0% +>> So, so when you say pattern, what the +rhythm the rhythmic pattern is about the + + align:start position:0% +rhythm the rhythmic pattern is about the + + + align:start position:0% +rhythm the rhythmic pattern is about the +same? Good. + + align:start position:0% +same? Good. + + + align:start position:0% +same? Good. +That's an inversion, right? + + align:start position:0% +That's an inversion, right? + + + align:start position:0% +That's an inversion, right? +>> Is it an inversion? No. No. That would I + + align:start position:0% +>> Is it an inversion? No. No. That would I + + + align:start position:0% +>> Is it an inversion? No. No. That would I +would I do that? + + align:start position:0% +would I do that? + + + align:start position:0% +would I do that? +>> I can't, by the way, I can't remember + + align:start position:0% +>> I can't, by the way, I can't remember + + + align:start position:0% +>> I can't, by the way, I can't remember +where melody I I think melody a comes + + align:start position:0% +where melody I I think melody a comes + + + align:start position:0% +where melody I I think melody a comes +from uh here on uh book and then gives + + align:start position:0% +from uh here on uh book and then gives + + + align:start position:0% +from uh here on uh book and then gives +there's uh some some search book and I + + align:start position:0% +there's uh some some search book and I + + + align:start position:0% +there's uh some some search book and I +should I should have my notes better and + + align:start position:0% +should I should have my notes better and + + + align:start position:0% +should I should have my notes better and +I'll try to make sure it gets annotated + + align:start position:0% +I'll try to make sure it gets annotated + + + align:start position:0% +I'll try to make sure it gets annotated +later. Um that had three other melodies. + + align:start position:0% +later. Um that had three other melodies. + + + align:start position:0% +later. Um that had three other melodies. +I tried this in the past and it was so + + align:start position:0% +I tried this in the past and it was so + + + align:start position:0% +I tried this in the past and it was so +obvious everybody had the exact same + + align:start position:0% +obvious everybody had the exact same + + + align:start position:0% +obvious everybody had the exact same +ranking. I had to agree with them, but I + + align:start position:0% +ranking. I had to agree with them, but I + + + align:start position:0% +ranking. I had to agree with them, but I +think this is better for making some + + align:start position:0% +think this is better for making some + + + align:start position:0% +think this is better for making some +arguments. Good. Who um who had F + + align:start position:0% +arguments. Good. Who um who had F + + + align:start position:0% +arguments. Good. Who um who had F +anything but F? Actually, somebody who + + align:start position:0% +anything but F? Actually, somebody who + + + align:start position:0% +anything but F? Actually, somebody who +gave F5. Jonathan, why would you did you + + align:start position:0% +gave F5. Jonathan, why would you did you + + + align:start position:0% +gave F5. Jonathan, why would you did you +give F5? + + align:start position:0% +give F5? + + + align:start position:0% +give F5? +>> Yeah. Why'd you give it five? + + align:start position:0% +>> Yeah. Why'd you give it five? + + + align:start position:0% +>> Yeah. Why'd you give it five? +>> I mean, it didn't have any noticeable + + align:start position:0% +>> I mean, it didn't have any noticeable + + + align:start position:0% +>> I mean, it didn't have any noticeable +similarity. Like at first it seemed + + align:start position:0% +similarity. Like at first it seemed + + + align:start position:0% +similarity. Like at first it seemed +closer to like E in like it might have + + align:start position:0% +closer to like E in like it might have + + + align:start position:0% +closer to like E in like it might have +been inversion, but then not really. + + align:start position:0% +been inversion, but then not really. + + + align:start position:0% +been inversion, but then not really. +is also completely different or not + + align:start position:0% +is also completely different or not + + + align:start position:0% +is also completely different or not +completely but like it's fairly + + align:start position:0% +completely but like it's fairly + + + align:start position:0% +completely but like it's fairly +different. + + align:start position:0% +different. + + + align:start position:0% +different. +>> Great. So, um I'm just going to point + + align:start position:0% +>> Great. So, um I'm just going to point + + + align:start position:0% +>> Great. So, um I'm just going to point +and we'll get some um some uh just what + + align:start position:0% +and we'll get some um some uh just what + + + align:start position:0% +and we'll get some um some uh just what +your ranking is. So, so say them from + + align:start position:0% +your ranking is. So, so say them from + + + align:start position:0% +your ranking is. So, so say them from +thing. Matthew, what was your your + + align:start position:0% +thing. Matthew, what was your your + + + align:start position:0% +thing. Matthew, what was your your +>> alphabetical order? + + align:start position:0% +>> alphabetical order? + + + align:start position:0% +>> alphabetical order? +>> BCDE F. Okay, good. + + align:start position:0% + + + + align:start position:0% + +BCDEF + + align:start position:0% + + + + align:start position:0% + +>> BCE DF. Great. Great. Um, what's it? + + align:start position:0% +>> BCE DF. Great. Great. Um, what's it? + + + align:start position:0% +>> BCE DF. Great. Great. Um, what's it? +>> Yeah, CBDF. + + align:start position:0% +>> Yeah, CBDF. + + + align:start position:0% +>> Yeah, CBDF. +>> CBD EF. Good. Any anything that feels + + align:start position:0% +>> CBD EF. Good. Any anything that feels + + + align:start position:0% +>> CBD EF. Good. Any anything that feels +like you're not being represented on the + + align:start position:0% +like you're not being represented on the + + + align:start position:0% +like you're not being represented on the +Hannah, what's your group? + + align:start position:0% +Hannah, what's your group? + + + align:start position:0% +Hannah, what's your group? +>> Um, I think I put CBD. + + align:start position:0% +>> Um, I think I put CBD. + + + align:start position:0% +>> Um, I think I put CBD. +>> CBDF. CBDF. Great. Super. Now, what I + + align:start position:0% +>> CBDF. CBDF. Great. Super. Now, what I + + + align:start position:0% +>> CBDF. CBDF. Great. Super. Now, what I +want you to do, we're not going to get + + align:start position:0% +want you to do, we're not going to get + + + align:start position:0% +want you to do, we're not going to get +through all of the exercises today, uh, + + align:start position:0% +through all of the exercises today, uh, + + + align:start position:0% +through all of the exercises today, uh, +but I think this is the most important + + align:start position:0% +but I think this is the most important + + + align:start position:0% +but I think this is the most important +part. What I want you to do is think + + align:start position:0% +part. What I want you to do is think + + + align:start position:0% +part. What I want you to do is think +about what ways, + + align:start position:0% +about what ways, + + + align:start position:0% +about what ways, +um, start thinking. I'll give you a + + align:start position:0% +um, start thinking. I'll give you a + + + align:start position:0% +um, start thinking. I'll give you a +little bit of things. What are some ways + + align:start position:0% +little bit of things. What are some ways + + + align:start position:0% +little bit of things. What are some ways +you can make sure that your computer + + align:start position:0% +you can make sure that your computer + + + align:start position:0% +you can make sure that your computer +system that is going to classify things + + align:start position:0% +system that is going to classify things + + + align:start position:0% +system that is going to classify things +by similarity follows your intuition of + + align:start position:0% +by similarity follows your intuition of + + + align:start position:0% +by similarity follows your intuition of +what is similar and not somebody else's + + align:start position:0% +what is similar and not somebody else's + + + align:start position:0% +what is similar and not somebody else's +intuition for what is similar. So that's + + align:start position:0% +intuition for what is similar. So that's + + + align:start position:0% +intuition for what is similar. So that's +going to be the main theme for the rest + + align:start position:0% +going to be the main theme for the rest + + + align:start position:0% +going to be the main theme for the rest +of this that we are intelligent people. + + align:start position:0% +of this that we are intelligent people. + + + align:start position:0% +of this that we are intelligent people. +We are intelligent musicians. We are uh + + align:start position:0% +We are intelligent musicians. We are uh + + + align:start position:0% +We are intelligent musicians. We are uh +make these choices and yet we are making + + align:start position:0% +make these choices and yet we are making + + + align:start position:0% +make these choices and yet we are making +differences on how far and how similar + + align:start position:0% +differences on how far and how similar + + + align:start position:0% +differences on how far and how similar +they are. So in fact I'm going to blake + + align:start position:0% +they are. So in fact I'm going to blake + + + align:start position:0% +they are. So in fact I'm going to blake +the screen and say the one the one uh + + align:start position:0% +the screen and say the one the one uh + + + align:start position:0% +the screen and say the one the one uh +takeaway from today's lecture I hope and + + align:start position:0% +takeaway from today's lecture I hope and + + + align:start position:0% +takeaway from today's lecture I hope and +from Kiki from all these things is that + + align:start position:0% +from Kiki from all these things is that + + + align:start position:0% +from Kiki from all these things is that +there is no right answer for the + + align:start position:0% +there is no right answer for the + + + align:start position:0% +there is no right answer for the +similarity between two melodies between + + align:start position:0% +similarity between two melodies between + + + align:start position:0% +similarity between two melodies between +the si similarity between two pieces. + + align:start position:0% +the si similarity between two pieces. + + + align:start position:0% +the si similarity between two pieces. +There may be wrong answers. I will not + + align:start position:0% +There may be wrong answers. I will not + + + align:start position:0% +There may be wrong answers. I will not +deny that that if if somebody said that + + align:start position:0% +deny that that if if somebody said that + + + align:start position:0% +deny that that if if somebody said that +uh that f was uh closer to I don't know + + align:start position:0% +uh that f was uh closer to I don't know + + + align:start position:0% +uh that f was uh closer to I don't know +than the same thing with one note + + align:start position:0% +than the same thing with one note + + + align:start position:0% +than the same thing with one note +changed or something I would you know + + align:start position:0% +changed or something I would you know + + + align:start position:0% +changed or something I would you know +think that that might be wrong then your + + align:start position:0% +think that that might be wrong then your + + + align:start position:0% +think that that might be wrong then your +problem program might be malfunctioning + + align:start position:0% +problem program might be malfunctioning + + + align:start position:0% +problem program might be malfunctioning +but there isn't a right answer and a lot + + align:start position:0% +but there isn't a right answer and a lot + + + align:start position:0% +but there isn't a right answer and a lot +of it the what different between good + + align:start position:0% +of it the what different between good + + + align:start position:0% +of it the what different between good +answers are what we think of u as + + align:start position:0% +answers are what we think of u as + + + align:start position:0% +answers are what we think of u as +important when thinking similarity there + + align:start position:0% +important when thinking similarity there + + + align:start position:0% +important when thinking similarity there +is a yearly competition I think it's + + align:start position:0% +is a yearly competition I think it's + + + align:start position:0% +is a yearly competition I think it's +been suspended since since co so I don't + + align:start position:0% +been suspended since since co so I don't + + + align:start position:0% +been suspended since since co so I don't +if it's restarted but um for the + + align:start position:0% +if it's restarted but um for the + + + align:start position:0% +if it's restarted but um for the +algorithm that can that can classify + + align:start position:0% +algorithm that can that can classify + + + align:start position:0% +algorithm that can that can classify +songs as the most similar and here is a + + align:start position:0% +songs as the most similar and here is a + + + align:start position:0% +songs as the most similar and here is a +place where I would say what are your + + align:start position:0% +place where I would say what are your + + + align:start position:0% +place where I would say what are your +ground truths how do we trust that you + + align:start position:0% +ground truths how do we trust that you + + + align:start position:0% +ground truths how do we trust that you +have gotten it right and are we just + + align:start position:0% +have gotten it right and are we just + + + align:start position:0% +have gotten it right and are we just +trying having to recreate the views I + + align:start position:0% +trying having to recreate the views I + + + align:start position:0% +trying having to recreate the views I +won't say biases but the views of the + + align:start position:0% +won't say biases but the views of the + + + align:start position:0% +won't say biases but the views of the +people who organize the um the + + align:start position:0% +people who organize the um the + + + align:start position:0% +people who organize the um the +conference and you know what's that + + align:start position:0% +conference and you know what's that + + + align:start position:0% +conference and you know what's that +going to do for us okay so I want you + + align:start position:0% +going to do for us okay so I want you + + + align:start position:0% +going to do for us okay so I want you +start thinking that um and I will tell + + align:start position:0% +start thinking that um and I will tell + + + align:start position:0% +start thinking that um and I will tell +you what f is beforehand. + + align:start position:0% +you what f is beforehand. + + + align:start position:0% +you what f is beforehand. +F is one that a lot of computers + + align:start position:0% +F is one that a lot of computers + + + align:start position:0% +F is one that a lot of computers +programs in fact what I like went aha + + align:start position:0% +programs in fact what I like went aha + + + align:start position:0% +programs in fact what I like went aha +during one of uh Kiki's uh al algorithms + + align:start position:0% +during one of uh Kiki's uh al algorithms + + + align:start position:0% +during one of uh Kiki's uh al algorithms +that could F is one that a number of + + align:start position:0% +that could F is one that a number of + + + align:start position:0% +that could F is one that a number of +algorithms especially older ones will + + align:start position:0% +algorithms especially older ones will + + + align:start position:0% +algorithms especially older ones will +classify as the most similar + + align:start position:0% +classify as the most similar + + + align:start position:0% +classify as the most similar +because what is F unlike any of the + + align:start position:0% +because what is F unlike any of the + + + align:start position:0% +because what is F unlike any of the +other lines F has every single note and + + align:start position:0% +other lines F has every single note and + + + align:start position:0% +other lines F has every single note and +every single rhythm if I did it right I + + align:start position:0% +every single rhythm if I did it right I + + + align:start position:0% +every single rhythm if I did it right I +was doing it in my head. Every single + + align:start position:0% +was doing it in my head. Every single + + + align:start position:0% +was doing it in my head. Every single +note and every single rhythm from A just + + align:start position:0% +note and every single rhythm from A just + + + align:start position:0% +note and every single rhythm from A just +order didn't matter. + + align:start position:0% +order didn't matter. + + + align:start position:0% +order didn't matter. +A is the counter set function, the + + align:start position:0% +A is the counter set function, the + + + align:start position:0% +A is the counter set function, the +unordered version, the the P. Well, + + align:start position:0% +unordered version, the the P. Well, + + + align:start position:0% +unordered version, the the P. Well, +yeah, the permutation does not matter + + align:start position:0% +yeah, the permutation does not matter + + + align:start position:0% +yeah, the permutation does not matter +version of F + + align:start position:0% +version of F + + + align:start position:0% +version of F +or F is the permutation does not matter + + align:start position:0% +or F is the permutation does not matter + + + align:start position:0% +or F is the permutation does not matter +version of A. Did I get it right? + + align:start position:0% +version of A. Did I get it right? + + + align:start position:0% +version of A. Did I get it right? +>> Right. + + align:start position:0% +>> Right. + + + align:start position:0% +>> Right. +>> That looks right. + + align:start position:0% +>> That looks right. + + + align:start position:0% +>> That looks right. +>> Looks right. Okay. + + align:start position:0% + + + + align:start position:0% + +So, I'm going to go quickly through some + + align:start position:0% +So, I'm going to go quickly through some + + + align:start position:0% +So, I'm going to go quickly through some +things I think you've probably seen + + align:start position:0% +things I think you've probably seen + + + align:start position:0% +things I think you've probably seen +before. Some some ways of measuring + + align:start position:0% +before. Some some ways of measuring + + + align:start position:0% +before. Some some ways of measuring +distance. You all learned this in some + + align:start position:0% +distance. You all learned this in some + + + align:start position:0% +distance. You all learned this in some +point. The um uklidian distance between + + align:start position:0% +point. The um uklidian distance between + + + align:start position:0% +point. The um uklidian distance between +two points. Take the square root of the + + align:start position:0% +two points. Take the square root of the + + + align:start position:0% +two points. Take the square root of the +x terms. Take square root of the y term + + align:start position:0% +x terms. Take square root of the y term + + + align:start position:0% +x terms. Take square root of the y term +add what difference squared plus + + align:start position:0% +add what difference squared plus + + + align:start position:0% +add what difference squared plus +difference squared square root. Right. + + align:start position:0% +difference squared square root. Right. + + + align:start position:0% +difference squared square root. Right. +Yeah. Square root of x^2 plus difference + + align:start position:0% +Yeah. Square root of x^2 plus difference + + + align:start position:0% +Yeah. Square root of x^2 plus difference +between x and difference between y. + + align:start position:0% + + + + align:start position:0% + +So anyone seen this u thing where the + + align:start position:0% +So anyone seen this u thing where the + + + align:start position:0% +So anyone seen this u thing where the +distance between these two points 3 + + align:start position:0% +distance between these two points 3 + + + align:start position:0% +distance between these two points 3 +comma 2 and 7 comma 8 is 10 who's soon + + align:start position:0% +comma 2 and 7 comma 8 is 10 who's soon + + + align:start position:0% +comma 2 and 7 comma 8 is 10 who's soon +taxi cab distance Manhattan distance uh + + align:start position:0% +taxi cab distance Manhattan distance uh + + + align:start position:0% +taxi cab distance Manhattan distance uh +we'll go with we'll go with taxi cab + + align:start position:0% +we'll go with we'll go with taxi cab + + + align:start position:0% +we'll go with we'll go with taxi cab +since not all of us have been to a + + align:start position:0% +since not all of us have been to a + + + align:start position:0% +since not all of us have been to a +Manhattan and had the joys of taking a + + align:start position:0% +Manhattan and had the joys of taking a + + + align:start position:0% +Manhattan and had the joys of taking a +taxi there and stuff what why this here + + align:start position:0% +taxi there and stuff what why this here + + + align:start position:0% +taxi there and stuff what why this here +the distance was 10 here it's approx + + align:start position:0% +the distance was 10 here it's approx + + + align:start position:0% +the distance was 10 here it's approx +that's not a negative sign this + + align:start position:0% +that's not a negative sign this + + + align:start position:0% +that's not a negative sign this +approximate sign approximately 7.2. + + align:start position:0% +approximate sign approximately 7.2. + + + align:start position:0% +approximate sign approximately 7.2. +Why is the distance greater here? + + align:start position:0% +Why is the distance greater here? + + + align:start position:0% +Why is the distance greater here? +Somebody who's + + align:start position:0% +Somebody who's + + + align:start position:0% +Somebody who's +>> triangle inequality. What's talk talk + + align:start position:0% +>> triangle inequality. What's talk talk + + + align:start position:0% +>> triangle inequality. What's talk talk +English to me for a second? Talk talk + + align:start position:0% +English to me for a second? Talk talk + + + align:start position:0% +English to me for a second? Talk talk +like you're talking to the uh your cab + + align:start position:0% +like you're talking to the uh your cab + + + align:start position:0% +like you're talking to the uh your cab +driver and who's who you're explaining + + align:start position:0% +driver and who's who you're explaining + + + align:start position:0% +driver and who's who you're explaining +to this. No, cab drivers are really + + align:start position:0% +to this. No, cab drivers are really + + + align:start position:0% +to this. No, cab drivers are really +smart. Talk but who may not have heard + + align:start position:0% +smart. Talk but who may not have heard + + + align:start position:0% +smart. Talk but who may not have heard +the time inequality. What what is + + align:start position:0% +the time inequality. What what is + + + align:start position:0% +the time inequality. What what is +represented by the term Manhattan + + align:start position:0% +represented by the term Manhattan + + + align:start position:0% +represented by the term Manhattan +distance or triang or um taxi cab + + align:start position:0% +distance or triang or um taxi cab + + + align:start position:0% +distance or triang or um taxi cab +distance? What's the notion + + align:start position:0% +distance? What's the notion + + + align:start position:0% +distance? What's the notion +intuition? + + align:start position:0% + + + + align:start position:0% + +>> Go along the axis. + + align:start position:0% +>> Go along the axis. + + + align:start position:0% +>> Go along the axis. +>> Go along the axis or that go along let's + + align:start position:0% +>> Go along the axis or that go along let's + + + align:start position:0% +>> Go along the axis or that go along let's +let's get get more literal. Let's one of + + align:start position:0% +let's get get more literal. Let's one of + + + align:start position:0% +let's get get more literal. Let's one of +the things that we science don't do so + + align:start position:0% +the things that we science don't do so + + + align:start position:0% +the things that we science don't do so +well is step back into the real world. + + align:start position:0% +well is step back into the real world. + + + align:start position:0% +well is step back into the real world. +What is the distance traveled? What + + align:start position:0% +What is the distance traveled? What + + + align:start position:0% +What is the distance traveled? What +constrains the taxi cab from not hitting + + align:start position:0% +constrains the taxi cab from not hitting + + + align:start position:0% +constrains the taxi cab from not hitting +distance of 7.2 but instead 10? Yeah, + + align:start position:0% +distance of 7.2 but instead 10? Yeah, + + + align:start position:0% +distance of 7.2 but instead 10? Yeah, +>> you go straight up and down to the side. + + align:start position:0% +>> you go straight up and down to the side. + + + align:start position:0% +>> you go straight up and down to the side. +>> You can only go straight up and down the + + align:start position:0% +>> You can only go straight up and down the + + + align:start position:0% +>> You can only go straight up and down the +side. You can only go on Let's go even + + align:start position:0% +side. You can only go on Let's go even + + + align:start position:0% +side. You can only go on Let's go even +further back. What can What in + + align:start position:0% +further back. What can What in + + + align:start position:0% +further back. What can What in +Manhattan? If you don't want to get + + align:start position:0% +Manhattan? If you don't want to get + + + align:start position:0% +Manhattan? If you don't want to get +arrested, you can only drive on + + align:start position:0% +arrested, you can only drive on + + + align:start position:0% +arrested, you can only drive on +>> streets. And the streets in Manhattan + + align:start position:0% +>> streets. And the streets in Manhattan + + + align:start position:0% +>> streets. And the streets in Manhattan +goal + + align:start position:0% +goal + + + align:start position:0% +goal +>> Yeah. They're orthogonal. There are + + align:start position:0% +>> Yeah. They're orthogonal. There are + + + align:start position:0% +>> Yeah. They're orthogonal. There are +these little lines. So, you are + + align:start position:0% +these little lines. So, you are + + + align:start position:0% +these little lines. So, you are +constrained in where you can go. So if + + align:start position:0% +constrained in where you can go. So if + + + align:start position:0% +constrained in where you can go. So if +there are constraints on your distance + + align:start position:0% +there are constraints on your distance + + + align:start position:0% +there are constraints on your distance +and the most common one is you can go up + + align:start position:0% +and the most common one is you can go up + + + align:start position:0% +and the most common one is you can go up +down left or right um can't always do + + align:start position:0% +down left or right um can't always do + + + align:start position:0% +down left or right um can't always do +that in Manhattan but um because of one + + align:start position:0% +that in Manhattan but um because of one + + + align:start position:0% +that in Manhattan but um because of one +ways but you know let's assume that we + + align:start position:0% +ways but you know let's assume that we + + + align:start position:0% +ways but you know let's assume that we +have certain constraints you can be + + align:start position:0% +have certain constraints you can be + + + align:start position:0% +have certain constraints you can be +brought down good I wanted to make sure + + align:start position:0% +brought down good I wanted to make sure + + + align:start position:0% +brought down good I wanted to make sure +that we all have that and so that we can + + align:start position:0% +that we all have that and so that we can + + + align:start position:0% +that we all have that and so that we can +start thinking about um + + align:start position:0% +start thinking about um + + + align:start position:0% +start thinking about um +that first off that what operations are + + align:start position:0% +that first off that what operations are + + + align:start position:0% +that first off that what operations are +allowed determines the distance metric + + align:start position:0% +allowed determines the distance metric + + + align:start position:0% +allowed determines the distance metric +What operations are around determines + + align:start position:0% +What operations are around determines + + + align:start position:0% +What operations are around determines +how far the distance are? What are some + + align:start position:0% +how far the distance are? What are some + + + align:start position:0% +how far the distance are? What are some +operations we do in music? + + align:start position:0% + + + + align:start position:0% + +That's the question. What what + + align:start position:0% +That's the question. What what + + + align:start position:0% +That's the question. What what +operations do we allow and not allow? + + align:start position:0% +operations do we allow and not allow? + + + align:start position:0% +operations do we allow and not allow? +Adam, + + align:start position:0% +Adam, + + + align:start position:0% +Adam, +>> we can look at MIDI. + + align:start position:0% +>> we can look at MIDI. + + + align:start position:0% +>> we can look at MIDI. +>> We can look at MIDI difference between + + align:start position:0% +>> We can look at MIDI difference between + + + align:start position:0% +>> We can look at MIDI difference between +notes. So therefore, we can take notes + + align:start position:0% +notes. So therefore, we can take notes + + + align:start position:0% +notes. So therefore, we can take notes +and bring them + + align:start position:0% +and bring them + + + align:start position:0% +and bring them +higher and lower, right? We can we can + + align:start position:0% +higher and lower, right? We can we can + + + align:start position:0% +higher and lower, right? We can we can +raise and lower notes. What are other + + align:start position:0% +raise and lower notes. What are other + + + align:start position:0% +raise and lower notes. What are other +things we can do? + + align:start position:0% + + + + align:start position:0% + +What are some some things you've ever + + align:start position:0% +What are some some things you've ever + + + align:start position:0% +What are some some things you've ever +done with a piece to make it a little + + align:start position:0% +done with a piece to make it a little + + + align:start position:0% +done with a piece to make it a little +bit different or interesting? + + align:start position:0% +bit different or interesting? + + + align:start position:0% +bit different or interesting? +>> Yeah, + + align:start position:0% +>> Yeah, + + + align:start position:0% +>> Yeah, +>> you can subdivide or combine. + + align:start position:0% +>> you can subdivide or combine. + + + align:start position:0% +>> you can subdivide or combine. +>> You can subdivide or combine notes. + + align:start position:0% +>> You can subdivide or combine notes. + + + align:start position:0% +>> You can subdivide or combine notes. +Maybe you can, maybe you can't, but + + align:start position:0% +Maybe you can, maybe you can't, but + + + align:start position:0% +Maybe you can, maybe you can't, but +yeah, quite often you can. This context + + align:start position:0% +yeah, quite often you can. This context + + + align:start position:0% +yeah, quite often you can. This context +where you can um other Yeah, other + + align:start position:0% +where you can um other Yeah, other + + + align:start position:0% +where you can um other Yeah, other +>> you can change durations. Great. Super. + + align:start position:0% +>> you can change durations. Great. Super. + + + align:start position:0% +>> you can change durations. Great. Super. +Super super. Um, how about this? What is + + align:start position:0% +Super super. Um, how about this? What is + + + align:start position:0% +Super super. Um, how about this? What is +which of these two chords are closer to + + align:start position:0% +which of these two chords are closer to + + + align:start position:0% +which of these two chords are closer to +the first one? The first one's going to + + align:start position:0% +the first one? The first one's going to + + + align:start position:0% +the first one? The first one's going to +be C major + + align:start position:0% + + + + align:start position:0% + +versus + + align:start position:0% +versus + + + align:start position:0% +versus +[Music] + + align:start position:0% + + + + align:start position:0% + +another little similarity problem. + + align:start position:0% +another little similarity problem. + + + align:start position:0% +another little similarity problem. +Second one was G + + align:start position:0% +Second one was G + + + align:start position:0% +Second one was G +major. The sorry the the first chord the + + align:start position:0% +major. The sorry the the first chord the + + + align:start position:0% +major. The sorry the the first chord the +first one it was G major second one I + + align:start position:0% +first one it was G major second one I + + + align:start position:0% +first one it was G major second one I +went from C major to + + align:start position:0% +went from C major to + + + align:start position:0% +went from C major to +>> C augmented great C augmented triad so + + align:start position:0% +>> C augmented great C augmented triad so + + + align:start position:0% +>> C augmented great C augmented triad so +those are two things which one who votes + + align:start position:0% +those are two things which one who votes + + + align:start position:0% +those are two things which one who votes +that from going from C major to G major + + align:start position:0% +that from going from C major to G major + + + align:start position:0% +that from going from C major to G major +is closer + + align:start position:0% +is closer + + + align:start position:0% +is closer +who votes that C major and C augmented + + align:start position:0% +who votes that C major and C augmented + + + align:start position:0% +who votes that C major and C augmented +are closer + + align:start position:0% +are closer + + + align:start position:0% +are closer +people. Okay, great. So, a lot of it has + + align:start position:0% +people. Okay, great. So, a lot of it has + + + align:start position:0% +people. Okay, great. So, a lot of it has +to do with your thought um about, you + + align:start position:0% +to do with your thought um about, you + + + align:start position:0% +to do with your thought um about, you +know, well, one one you're the + + align:start position:0% +know, well, one one you're the + + + align:start position:0% +know, well, one one you're the +augmented, you're only changing one note + + align:start position:0% +augmented, you're only changing one note + + + align:start position:0% +augmented, you're only changing one note +and you're only changing by a half step. + + align:start position:0% +and you're only changing by a half step. + + + align:start position:0% +and you're only changing by a half step. +The minimum distance in our + + align:start position:0% +The minimum distance in our + + + align:start position:0% +The minimum distance in our +Manhattanized musical world of MIDI and + + align:start position:0% +Manhattanized musical world of MIDI and + + + align:start position:0% +Manhattanized musical world of MIDI and +piano keyboards, right? That is their + + align:start position:0% +piano keyboards, right? That is their + + + align:start position:0% +piano keyboards, right? That is their +minimum distance is one half step there. + + align:start position:0% +minimum distance is one half step there. + + + align:start position:0% +minimum distance is one half step there. +Not for all music in the world. Great. C + + align:start position:0% +Not for all music in the world. Great. C + + + align:start position:0% +Not for all music in the world. Great. C +major to G major, you're also just + + align:start position:0% +major to G major, you're also just + + + align:start position:0% +major to G major, you're also just +moving one. If you think of something + + align:start position:0% +moving one. If you think of something + + + align:start position:0% +moving one. If you think of something +this way, you were moving one distance + + align:start position:0% +this way, you were moving one distance + + + align:start position:0% +this way, you were moving one distance +in what space? + + align:start position:0% + + + + align:start position:0% + +>> Oh, what's that word? + + align:start position:0% +>> Oh, what's that word? + + + align:start position:0% +>> Oh, what's that word? +>> Circle. + + align:start position:0% +>> Circle. + + + align:start position:0% +>> Circle. +>> In circle of fifth space, C and G are + + align:start position:0% +>> In circle of fifth space, C and G are + + + align:start position:0% +>> In circle of fifth space, C and G are +about as close as you can get without + + align:start position:0% +about as close as you can get without + + + align:start position:0% +about as close as you can get without +being the identity. C and F probably the + + align:start position:0% +being the identity. C and F probably the + + + align:start position:0% +being the identity. C and F probably the +other way. Although, I don't know, maybe + + align:start position:0% +other way. Although, I don't know, maybe + + + align:start position:0% +other way. Although, I don't know, maybe +it's a one-way circle of fifths. You + + align:start position:0% +it's a one-way circle of fifths. You + + + align:start position:0% +it's a one-way circle of fifths. You +only go around uh one direction or + + align:start position:0% +only go around uh one direction or + + + align:start position:0% +only go around uh one direction or +another. Great. + + align:start position:0% +another. Great. + + + align:start position:0% +another. Great. +based on the time. I don't not going to + + align:start position:0% +based on the time. I don't not going to + + + align:start position:0% +based on the time. I don't not going to +go through all these other measurements + + align:start position:0% +go through all these other measurements + + + align:start position:0% +go through all these other measurements +of distance that people can do. Who has + + align:start position:0% +of distance that people can do. Who has + + + align:start position:0% +of distance that people can do. Who has +heard of Earth Mus distance? That is the + + align:start position:0% +heard of Earth Mus distance? That is the + + + align:start position:0% +heard of Earth Mus distance? That is the +amount of work that it takes to move one + + align:start position:0% +amount of work that it takes to move one + + + align:start position:0% +amount of work that it takes to move one +mound of things over to another place + + align:start position:0% +mound of things over to another place + + + align:start position:0% +mound of things over to another place +and um sometimes you optimizing + + align:start position:0% +and um sometimes you optimizing + + + align:start position:0% +and um sometimes you optimizing +depending on how um how much it costs to + + align:start position:0% +depending on how um how much it costs to + + + align:start position:0% +depending on how um how much it costs to +move distance and how much it costs to + + align:start position:0% +move distance and how much it costs to + + + align:start position:0% +move distance and how much it costs to +move material. Um you can end up with + + align:start position:0% +move material. Um you can end up with + + + align:start position:0% +move material. Um you can end up with +different results. + + align:start position:0% +different results. + + + align:start position:0% +different results. +Um, I always, this was one of the charts + + align:start position:0% +Um, I always, this was one of the charts + + + align:start position:0% +Um, I always, this was one of the charts +I think I showed early in the semester, + + align:start position:0% +I think I showed early in the semester, + + + align:start position:0% +I think I showed early in the semester, +uh, is here's one place where Earth + + align:start position:0% +uh, is here's one place where Earth + + + align:start position:0% +uh, is here's one place where Earth +mover distance might be a good use of + + align:start position:0% +mover distance might be a good use of + + + align:start position:0% +mover distance might be a good use of +things, uh, of distances. And then, uh, + + align:start position:0% +things, uh, of distances. And then, uh, + + + align:start position:0% +things, uh, of distances. And then, uh, +Levvenstein or edit distance is one that + + align:start position:0% +Levvenstein or edit distance is one that + + + align:start position:0% +Levvenstein or edit distance is one that +was mentioned in, um, do you use it in + + align:start position:0% +was mentioned in, um, do you use it in + + + align:start position:0% +was mentioned in, um, do you use it in +your work? + + align:start position:0% +your work? + + + align:start position:0% +your work? +>> Yep. So, that's that's what you're + + align:start position:0% +>> Yep. So, that's that's what you're + + + align:start position:0% +>> Yep. So, that's that's what you're +talking about. Um so the idea of how to + + align:start position:0% +talking about. Um so the idea of how to + + + align:start position:0% +talking about. Um so the idea of how to +change the word Hondaai into Honda um + + align:start position:0% +change the word Hondaai into Honda um + + + align:start position:0% +change the word Hondaai into Honda um +and uh no no international East Asian uh + + align:start position:0% +and uh no no international East Asian uh + + + align:start position:0% +and uh no no international East Asian uh +politics uh please for a second and um + + align:start position:0% +politics uh please for a second and um + + + align:start position:0% +politics uh please for a second and um +we'll you can think of every time okay H + + align:start position:0% +we'll you can think of every time okay H + + + align:start position:0% +we'll you can think of every time okay H +and H are the same so it has a cost of + + align:start position:0% +and H are the same so it has a cost of + + + align:start position:0% +and H are the same so it has a cost of +zero or we can delete the H and start on + + align:start position:0% +zero or we can delete the H and start on + + + align:start position:0% +zero or we can delete the H and start on +O and we have a cost of one but we can + + align:start position:0% +O and we have a cost of one but we can + + + align:start position:0% +O and we have a cost of one but we can +kind of find the pattern of as we change + + align:start position:0% +kind of find the pattern of as we change + + + align:start position:0% +kind of find the pattern of as we change +we're going to insert a Y after the H + + align:start position:0% +we're going to insert a Y after the H + + + align:start position:0% +we're going to insert a Y after the H +we're going to substitute a U for an O. + + align:start position:0% +we're going to substitute a U for an O. + + + align:start position:0% +we're going to substitute a U for an O. +This should be symmetrical the other way + + align:start position:0% +This should be symmetrical the other way + + + align:start position:0% +This should be symmetrical the other way +around different operations. N is the + + align:start position:0% +around different operations. N is the + + + align:start position:0% +around different operations. N is the +same. So that's good. D is the same. So + + align:start position:0% +same. So that's good. D is the same. So + + + align:start position:0% +same. So that's good. D is the same. So +it doesn't cost anything. So our cost + + align:start position:0% +it doesn't cost anything. So our cost + + + align:start position:0% +it doesn't cost anything. So our cost +function goes here. And so we're trying + + align:start position:0% +function goes here. And so we're trying + + + align:start position:0% +function goes here. And so we're trying +to find the minimum cost from going from + + align:start position:0% +to find the minimum cost from going from + + + align:start position:0% +to find the minimum cost from going from +one end to another. Uh we don't have + + align:start position:0% +one end to another. Uh we don't have + + + align:start position:0% +one end to another. Uh we don't have +time to go through all of the algorithms + + align:start position:0% +time to go through all of the algorithms + + + align:start position:0% +time to go through all of the algorithms +for this but uh Levvenstein distance + + align:start position:0% +for this but uh Levvenstein distance + + + align:start position:0% +for this but uh Levvenstein distance +edit distance has a lot of good um + + align:start position:0% +edit distance has a lot of good um + + + align:start position:0% +edit distance has a lot of good um +qualities that makes it useful for a lot + + align:start position:0% +qualities that makes it useful for a lot + + + align:start position:0% +qualities that makes it useful for a lot +of musical similarity tasks uh just so + + align:start position:0% +of musical similarity tasks uh just so + + + align:start position:0% +of musical similarity tasks uh just so +that you know you can say your professor + + align:start position:0% +that you know you can say your professor + + + align:start position:0% +that you know you can say your professor +at least uh put the algorithm up on the + + align:start position:0% +at least uh put the algorithm up on the + + + align:start position:0% +at least uh put the algorithm up on the +head for a second. But more importantly, + + align:start position:0% +head for a second. But more importantly, + + + align:start position:0% +head for a second. But more importantly, +I think a lot of times is thinking about + + align:start position:0% +I think a lot of times is thinking about + + + align:start position:0% +I think a lot of times is thinking about +um the particular costs of things in a + + align:start position:0% +um the particular costs of things in a + + + align:start position:0% +um the particular costs of things in a +musical spa in a musical world. So for + + align:start position:0% +musical spa in a musical world. So for + + + align:start position:0% +musical spa in a musical world. So for +instance, + + align:start position:0% +instance, + + + align:start position:0% +instance, +is deleting what we're trying to think + + align:start position:0% +is deleting what we're trying to think + + + align:start position:0% +is deleting what we're trying to think +about two pieces, two uh melodies. Um + + align:start position:0% +about two pieces, two uh melodies. Um + + + align:start position:0% +about two pieces, two uh melodies. Um +one of them deletes the first note. + + align:start position:0% +one of them deletes the first note. + + + align:start position:0% +one of them deletes the first note. +What would you call the cost on that? + + align:start position:0% +What would you call the cost on that? + + + align:start position:0% +What would you call the cost on that? +Maybe maybe one. But then if it doesn't + + align:start position:0% +Maybe maybe one. But then if it doesn't + + + align:start position:0% +Maybe maybe one. But then if it doesn't +make up the rhythm, the total rhythm + + align:start position:0% +make up the rhythm, the total rhythm + + + align:start position:0% +make up the rhythm, the total rhythm +later and everything from here on is + + align:start position:0% +later and everything from here on is + + + align:start position:0% +later and everything from here on is +going to be off and it's one line within + + align:start position:0% +going to be off and it's one line within + + + align:start position:0% +going to be off and it's one line within +a orchestral piece, that might be a + + align:start position:0% +a orchestral piece, that might be a + + + align:start position:0% +a orchestral piece, that might be a +higher um cost. Maybe um some and the + + align:start position:0% +higher um cost. Maybe um some and the + + + align:start position:0% +higher um cost. Maybe um some and the +classic debate is whether changing a + + align:start position:0% +classic debate is whether changing a + + + align:start position:0% +classic debate is whether changing a +note is that the same or changing a + + align:start position:0% +note is that the same or changing a + + + align:start position:0% +note is that the same or changing a +letter uh um in something like this. Is + + align:start position:0% +letter uh um in something like this. Is + + + align:start position:0% +letter uh um in something like this. Is +this the same? Does this cost one or + + align:start position:0% +this the same? Does this cost one or + + + align:start position:0% +this the same? Does this cost one or +does this cost? Well, one way you can + + align:start position:0% +does this cost? Well, one way you can + + + align:start position:0% +does this cost? Well, one way you can +change a letter is you delete it and + + align:start position:0% +change a letter is you delete it and + + + align:start position:0% +change a letter is you delete it and +then you add a new letter back with a + + align:start position:0% +then you add a new letter back with a + + + align:start position:0% +then you add a new letter back with a +cost of two. And these are these are + + align:start position:0% +cost of two. And these are these are + + + align:start position:0% +cost of two. And these are these are +things that come up quite a bit in + + align:start position:0% +things that come up quite a bit in + + + align:start position:0% +things that come up quite a bit in +similarity search. Um, and just really + + align:start position:0% +similarity search. Um, and just really + + + align:start position:0% +similarity search. Um, and just really +want to say that it comes up a lot in + + align:start position:0% +want to say that it comes up a lot in + + + align:start position:0% +want to say that it comes up a lot in +music. Don't borrow your distance metric + + align:start position:0% +music. Don't borrow your distance metric + + + align:start position:0% +music. Don't borrow your distance metric +from somebody else. Different ones might + + align:start position:0% +from somebody else. Different ones might + + + align:start position:0% +from somebody else. Different ones might +be used for different situations. So, + + align:start position:0% +be used for different situations. So, + + + align:start position:0% +be used for different situations. So, +the distance between dog and gate. Um, + + align:start position:0% +the distance between dog and gate. Um, + + + align:start position:0% +the distance between dog and gate. Um, +well, we can substitute d for g. Um, I + + align:start position:0% +well, we can substitute d for g. Um, I + + + align:start position:0% +well, we can substitute d for g. Um, I +don't know, maybe or maybe we add other + + align:start position:0% +don't know, maybe or maybe we add other + + + align:start position:0% +don't know, maybe or maybe we add other +things, but I'm going to assert that in + + align:start position:0% +things, but I'm going to assert that in + + + align:start position:0% +things, but I'm going to assert that in +different some situations the distance + + align:start position:0% +different some situations the distance + + + align:start position:0% +different some situations the distance +might be two between dog and gut. What + + align:start position:0% +might be two between dog and gut. What + + + align:start position:0% +might be two between dog and gut. What +we do is we use the substitute uh + + align:start position:0% +we do is we use the substitute uh + + + align:start position:0% +we do is we use the substitute uh +closely related pet function for cost of + + align:start position:0% +closely related pet function for cost of + + + align:start position:0% +closely related pet function for cost of +one. So dog becomes cat and then + + align:start position:0% +one. So dog becomes cat and then + + + align:start position:0% +one. So dog becomes cat and then +translate English to Spanish might cost + + align:start position:0% +translate English to Spanish might cost + + + align:start position:0% +translate English to Spanish might cost +one. And if you think about large + + align:start position:0% +one. And if you think about large + + + align:start position:0% +one. And if you think about large +language learning models and things, you + + align:start position:0% +language learning models and things, you + + + align:start position:0% +language learning models and things, you +might want to have functions like this. + + align:start position:0% +might want to have functions like this. + + + align:start position:0% +might want to have functions like this. +And in fact, um this is not a digital + + align:start position:0% +And in fact, um this is not a digital + + + align:start position:0% +And in fact, um this is not a digital +humanities text class, but if it were + + align:start position:0% +humanities text class, but if it were + + + align:start position:0% +humanities text class, but if it were +and we were doing computation, we'd + + align:start position:0% +and we were doing computation, we'd + + + align:start position:0% +and we were doing computation, we'd +definitely be talking about an algorithm + + align:start position:0% +definitely be talking about an algorithm + + + align:start position:0% +definitely be talking about an algorithm +called wordtovect, which uh was one of + + align:start position:0% +called wordtovect, which uh was one of + + + align:start position:0% +called wordtovect, which uh was one of +the uh earlier successful algorithms for + + align:start position:0% +the uh earlier successful algorithms for + + + align:start position:0% +the uh earlier successful algorithms for +trying to predict what words are similar + + align:start position:0% +trying to predict what words are similar + + + align:start position:0% +trying to predict what words are similar +to other words, what words are synonyms. + + align:start position:0% +to other words, what words are synonyms. + + + align:start position:0% +to other words, what words are synonyms. +So you can create a kind of cost + + align:start position:0% +So you can create a kind of cost + + + align:start position:0% +So you can create a kind of cost +function for uh that is for this word is + + align:start position:0% +function for uh that is for this word is + + + align:start position:0% +function for uh that is for this word is +a synonym for this one that has been + + align:start position:0% +a synonym for this one that has been + + + align:start position:0% +a synonym for this one that has been +substituted that is lower than this then + + align:start position:0% +substituted that is lower than this then + + + align:start position:0% +substituted that is lower than this then +this sentence is different from this one + + align:start position:0% +this sentence is different from this one + + + align:start position:0% +this sentence is different from this one +because um it's using a completely + + align:start position:0% +because um it's using a completely + + + align:start position:0% +because um it's using a completely +different concept. + + align:start position:0% +different concept. + + + align:start position:0% +different concept. +Um I'll skip that. + + align:start position:0% +Um I'll skip that. + + + align:start position:0% +Um I'll skip that. +So when we're thinking about um these + + align:start position:0% +So when we're thinking about um these + + + align:start position:0% +So when we're thinking about um these +distances and these weird things like + + align:start position:0% +distances and these weird things like + + + align:start position:0% +distances and these weird things like +substitute dog for cat on low cost, + + align:start position:0% +substitute dog for cat on low cost, + + + align:start position:0% +substitute dog for cat on low cost, +substitute cat for gateto at low cost. + + align:start position:0% +substitute cat for gateto at low cost. + + + align:start position:0% +substitute cat for gateto at low cost. +What's the term that we spent a lot of + + align:start position:0% +What's the term that we spent a lot of + + + align:start position:0% +What's the term that we spent a lot of +time, maybe even too much time if it + + align:start position:0% +time, maybe even too much time if it + + + align:start position:0% +time, maybe even too much time if it +felt like at the time talking about + + align:start position:0% +felt like at the time talking about + + + align:start position:0% +felt like at the time talking about +earlier in the semester that helps to + + align:start position:0% +earlier in the semester that helps to + + + align:start position:0% +earlier in the semester that helps to +think about things that are not the same + + align:start position:0% +think about things that are not the same + + + align:start position:0% +think about things that are not the same +but might be closely related to each + + align:start position:0% +but might be closely related to each + + + align:start position:0% +but might be closely related to each +other + + align:start position:0% + + + + align:start position:0% + +>> equivalence. + + align:start position:0% +>> equivalence. + + + align:start position:0% +>> equivalence. +>> Equivalence or equivalence classes. Yes. + + align:start position:0% +>> Equivalence or equivalence classes. Yes. + + + align:start position:0% +>> Equivalence or equivalence classes. Yes. +So, one of the things you might want to + + align:start position:0% +So, one of the things you might want to + + + align:start position:0% +So, one of the things you might want to +do is define what equivalence classes it + + align:start position:0% +do is define what equivalence classes it + + + align:start position:0% +do is define what equivalence classes it +could be. I mean I I think last other + + align:start position:0% +could be. I mean I I think last other + + + align:start position:0% +could be. I mean I I think last other +times I've given the exact same melody + + align:start position:0% +times I've given the exact same melody + + + align:start position:0% +times I've given the exact same melody +up an octave and everybody immediately + + align:start position:0% +up an octave and everybody immediately + + + align:start position:0% +up an octave and everybody immediately +said oh that is basically the same + + align:start position:0% +said oh that is basically the same + + + align:start position:0% +said oh that is basically the same +thing. So everybody was very quickly + + align:start position:0% +thing. So everybody was very quickly + + + align:start position:0% +thing. So everybody was very quickly +putting in an O equivalence class + + align:start position:0% +putting in an O equivalence class + + + align:start position:0% +putting in an O equivalence class +things. So I wanted to make sure that we + + align:start position:0% +things. So I wanted to make sure that we + + + align:start position:0% +things. So I wanted to make sure that we +had that and um yeah and so once you + + align:start position:0% +had that and um yeah and so once you + + + align:start position:0% +had that and um yeah and so once you +have these um these distances we tend to + + align:start position:0% +have these um these distances we tend to + + + align:start position:0% +have these um these distances we tend to +go through and this is if you're in a + + align:start position:0% +go through and this is if you're in a + + + align:start position:0% +go through and this is if you're in a +biology class you'll spend a lot of + + align:start position:0% +biology class you'll spend a lot of + + + align:start position:0% +biology class you'll spend a lot of +computational biology a lot of time on + + align:start position:0% +computational biology a lot of time on + + + align:start position:0% +computational biology a lot of time on +this sequence alignment uh a kind of + + align:start position:0% +this sequence alignment uh a kind of + + + align:start position:0% +this sequence alignment uh a kind of +distance metric where you're trying to + + align:start position:0% +distance metric where you're trying to + + + align:start position:0% +distance metric where you're trying to +find the minimum distance between two + + align:start position:0% +find the minimum distance between two + + + align:start position:0% +find the minimum distance between two +things that you believe might represent + + align:start position:0% +things that you believe might represent + + + align:start position:0% +things that you believe might represent +the same type of thing or you might say + + align:start position:0% +the same type of thing or you might say + + + align:start position:0% +the same type of thing or you might say +it's innocent until proven guilty. we'll + + align:start position:0% +it's innocent until proven guilty. we'll + + + align:start position:0% +it's innocent until proven guilty. we'll +first try to see if they can be changed + + align:start position:0% +first try to see if they can be changed + + + align:start position:0% +first try to see if they can be changed +into another thing at a low cost and + + align:start position:0% +into another thing at a low cost and + + + align:start position:0% +into another thing at a low cost and +then discard once we realize the cost + + align:start position:0% +then discard once we realize the cost + + + align:start position:0% +then discard once we realize the cost +cannot be u minimized. Um I will say + + align:start position:0% +cannot be u minimized. Um I will say + + + align:start position:0% +cannot be u minimized. Um I will say +that algorithms that can be + + align:start position:0% +that algorithms that can be + + + align:start position:0% +that algorithms that can be +shortcircuited that you can prove at a + + align:start position:0% +shortcircuited that you can prove at a + + + align:start position:0% +shortcircuited that you can prove at a +certain point you can't do better than + + align:start position:0% +certain point you can't do better than + + + align:start position:0% +certain point you can't do better than +this cost will save speed up a lot of + + align:start position:0% +this cost will save speed up a lot of + + + align:start position:0% +this cost will save speed up a lot of +your um run times because once you know + + align:start position:0% +your um run times because once you know + + + align:start position:0% +your um run times because once you know +you might say um you know that there's + + align:start position:0% +you might say um you know that there's + + + align:start position:0% +you might say um you know that there's +no way that this could be more could be + + align:start position:0% +no way that this could be more could be + + + align:start position:0% +no way that this could be more could be +better than um 20% or could be yeah + + align:start position:0% +better than um 20% or could be yeah + + + align:start position:0% +better than um 20% or could be yeah +there's no way that this could possibly + + align:start position:0% +there's no way that this could possibly + + + align:start position:0% +there's no way that this could possibly +be better than 90%. % similar to this. + + align:start position:0% +be better than 90%. % similar to this. + + + align:start position:0% +be better than 90%. % similar to this. +So, I'm going to stop looking at the + + align:start position:0% +So, I'm going to stop looking at the + + + align:start position:0% +So, I'm going to stop looking at the +rest of the piece or whatever your cut + + align:start position:0% +rest of the piece or whatever your cut + + + align:start position:0% +rest of the piece or whatever your cut +off. Um, one of the classic uh things + + align:start position:0% +off. Um, one of the classic uh things + + + align:start position:0% +off. Um, one of the classic uh things +for sequence alignment is trying to find + + align:start position:0% +for sequence alignment is trying to find + + + align:start position:0% +for sequence alignment is trying to find +uh this is Google's uh data set they + + align:start position:0% +uh this is Google's uh data set they + + + align:start position:0% +uh this is Google's uh data set they +released at the height of Britney Spears + + align:start position:0% +released at the height of Britney Spears + + + align:start position:0% +released at the height of Britney Spears +um popularity of all the number of + + align:start position:0% +um popularity of all the number of + + + align:start position:0% +um popularity of all the number of +searches that they believed were uh + + align:start position:0% +searches that they believed were uh + + + align:start position:0% +searches that they believed were uh +trying to find the top left one, Britney + + align:start position:0% +trying to find the top left one, Britney + + + align:start position:0% +trying to find the top left one, Britney +Spears. Um, actually really really + + align:start position:0% +Spears. Um, actually really really + + + align:start position:0% +Spears. Um, actually really really +impressed that that the number of + + align:start position:0% +impressed that that the number of + + + align:start position:0% +impressed that that the number of +correct spellings um of a hard name to + + align:start position:0% +correct spellings um of a hard name to + + + align:start position:0% +correct spellings um of a hard name to +spell uh outweighs the rest. Anyhow, + + align:start position:0% +spell uh outweighs the rest. Anyhow, + + + align:start position:0% +spell uh outweighs the rest. Anyhow, +that's not what I'm talking and um the + + align:start position:0% +that's not what I'm talking and um the + + + align:start position:0% +that's not what I'm talking and um the +people who are who are really really + + align:start position:0% +people who are who are really really + + + align:start position:0% +people who are who are really really +good at this and like anytime I'm trying + + align:start position:0% +good at this and like anytime I'm trying + + + align:start position:0% +good at this and like anytime I'm trying +to figure out a similarity sequence + + align:start position:0% +to figure out a similarity sequence + + + align:start position:0% +to figure out a similarity sequence +alignment or similarity task that I + + align:start position:0% +alignment or similarity task that I + + + align:start position:0% +alignment or similarity task that I +don't know is to look at the people who + + align:start position:0% +don't know is to look at the people who + + + align:start position:0% +don't know is to look at the people who +are trying to align um base pairs in + + align:start position:0% +are trying to align um base pairs in + + + align:start position:0% +are trying to align um base pairs in +biology or trying to align genes um so + + align:start position:0% +biology or trying to align genes um so + + + align:start position:0% +biology or trying to align genes um so +that um because they have many many uh + + align:start position:0% +that um because they have many many uh + + + align:start position:0% +that um because they have many many uh +many many options + + align:start position:0% +many many options + + + align:start position:0% +many many options +Okay. So, I'm just going to keep + + align:start position:0% +Okay. So, I'm just going to keep + + + align:start position:0% +Okay. So, I'm just going to keep +pounding this term in and as many + + align:start position:0% +pounding this term in and as many + + + align:start position:0% +pounding this term in and as many +different ways I can do uh all the + + align:start position:0% +different ways I can do uh all the + + + align:start position:0% +different ways I can do uh all the +things that we're just working like + + align:start position:0% +things that we're just working like + + + align:start position:0% +things that we're just working like +Honda Britney Spears uh jeans those are + + align:start position:0% +Honda Britney Spears uh jeans those are + + + align:start position:0% +Honda Britney Spears uh jeans those are +all strings but we work on notes and and + + align:start position:0% +all strings but we work on notes and and + + + align:start position:0% +all strings but we work on notes and and +clefts and things like notes and stuff + + align:start position:0% +clefts and things like notes and stuff + + + align:start position:0% +clefts and things like notes and stuff +but things like that. So, how do we get + + align:start position:0% +but things like that. So, how do we get + + + align:start position:0% +but things like that. So, how do we get +them in? Uh so, this is great to get + + align:start position:0% +them in? Uh so, this is great to get + + + align:start position:0% +them in? Uh so, this is great to get +this from two different people. Same + + align:start position:0% +this from two different people. Same + + + align:start position:0% +this from two different people. Same +thing. We use things called hashes which + + align:start position:0% +thing. We use things called hashes which + + + align:start position:0% +thing. We use things called hashes which +are very similar to uh the concept of + + align:start position:0% +are very similar to uh the concept of + + + align:start position:0% +are very similar to uh the concept of +viewpoints um to the rescue. So that try + + align:start position:0% +viewpoints um to the rescue. So that try + + + align:start position:0% +viewpoints um to the rescue. So that try +to convert things note hash and note we + + align:start position:0% +to convert things note hash and note we + + + align:start position:0% +to convert things note hash and note we +might say that here our equivalence + + align:start position:0% +might say that here our equivalence + + + align:start position:0% +might say that here our equivalence +class is all notes that are names with + + align:start position:0% +class is all notes that are names with + + + align:start position:0% +class is all notes that are names with +octave and so we might hash a stream by + + align:start position:0% +octave and so we might hash a stream by + + + align:start position:0% +octave and so we might hash a stream by +just joining all the hash notes for all + + align:start position:0% +just joining all the hash notes for all + + + align:start position:0% +just joining all the hash notes for all +the notes in there. Um, you will find in + + align:start position:0% +the notes in there. Um, you will find in + + + align:start position:0% +the notes in there. Um, you will find in +music 21 if you're working on it, + + align:start position:0% +music 21 if you're working on it, + + + align:start position:0% +music 21 if you're working on it, +there's a bunch of tools for this + + align:start position:0% +there's a bunch of tools for this + + + align:start position:0% +there's a bunch of tools for this +already there in music21.sarch, a module + + align:start position:0% +already there in music21.sarch, a module + + + align:start position:0% +already there in music21.sarch, a module +that we have not talked about now and we + + align:start position:0% +that we have not talked about now and we + + + align:start position:0% +that we have not talked about now and we +will not talk about again, but if you're + + align:start position:0% +will not talk about again, but if you're + + + align:start position:0% +will not talk about again, but if you're +doing a lot of searching, it's probably + + align:start position:0% +doing a lot of searching, it's probably + + + align:start position:0% +doing a lot of searching, it's probably +worth reading the um reading the uh + + align:start position:0% +worth reading the um reading the uh + + + align:start position:0% +worth reading the um reading the uh +module reference for it. I think that + + align:start position:0% +module reference for it. I think that + + + align:start position:0% +module reference for it. I think that +there might be a user's guide, but I + + align:start position:0% +there might be a user's guide, but I + + + align:start position:0% +there might be a user's guide, but I +can't remember if I finished it or if it + + align:start position:0% +can't remember if I finished it or if it + + + align:start position:0% +can't remember if I finished it or if it +just trails off after a few words. So we + + align:start position:0% +just trails off after a few words. So we + + + align:start position:0% +just trails off after a few words. So we +might take a a string a string convert + + align:start position:0% +might take a a string a string convert + + + align:start position:0% +might take a a string a string convert +it to a stream that's hard to say very + + align:start position:0% +it to a stream that's hard to say very + + + align:start position:0% +it to a stream that's hard to say very +fast and um translate it and we might + + align:start position:0% +fast and um translate it and we might + + + align:start position:0% +fast and um translate it and we might +have some sort of hash function that + + align:start position:0% +have some sort of hash function that + + + align:start position:0% +have some sort of hash function that +tries to make everything into um into an + + align:start position:0% +tries to make everything into um into an + + + align:start position:0% +tries to make everything into um into an +asky character. + + align:start position:0% +asky character. + + + align:start position:0% +asky character. +Um though there's no reason that + + align:start position:0% +Um though there's no reason that + + + align:start position:0% +Um though there's no reason that +everything needs to be turned into a + + align:start position:0% +everything needs to be turned into a + + + align:start position:0% +everything needs to be turned into a +string like name with octave. um in a + + align:start position:0% +string like name with octave. um in a + + + align:start position:0% +string like name with octave. um in a +lot of ways uh and um strings are just + + align:start position:0% +lot of ways uh and um strings are just + + + align:start position:0% +lot of ways uh and um strings are just +arrays of ints + + align:start position:0% + + + + align:start position:0% + +if you know we're talking about that the + + align:start position:0% +if you know we're talking about that the + + + align:start position:0% +if you know we're talking about that the +um + + align:start position:0% + + + + align:start position:0% + +that the you know that a is it lower no + + align:start position:0% +that the you know that a is it lower no + + + align:start position:0% +that the you know that a is it lower no +lowercase a is generally represented + + align:start position:0% +lowercase a is generally represented + + + align:start position:0% +lowercase a is generally represented +internally as anyone remember number + + align:start position:0% + + + + align:start position:0% +remember number remember number remember +number remember number remember number + + align:start position:0% +number remember number remember number + + + align:start position:0% +number remember number remember number +>> what's that + + align:start position:0% +>> what's that + + + align:start position:0% +>> what's that +>> 96 97 or 96. I can't remember. 96. Yep. + + align:start position:0% +>> 96 97 or 96. I can't remember. 96. Yep. + + + align:start position:0% +>> 96 97 or 96. I can't remember. 96. Yep. +In capital A. Is that one 60? + + align:start position:0% +In capital A. Is that one 60? + + + align:start position:0% +In capital A. Is that one 60? +>> 65. Okay. So, some people some people + + align:start position:0% +>> 65. Okay. So, some people some people + + + align:start position:0% +>> 65. Okay. So, some people some people +know these. I used to have them all top + + align:start position:0% +know these. I used to have them all top + + + align:start position:0% +know these. I used to have them all top +of the head. So, all the letters you're + + align:start position:0% +of the head. So, all the letters you're + + + align:start position:0% +of the head. So, all the letters you're +doing have a particular representation. + + align:start position:0% +doing have a particular representation. + + + align:start position:0% +doing have a particular representation. +And mo back in the bad bad days of the + + align:start position:0% +And mo back in the bad bad days of the + + + align:start position:0% +And mo back in the bad bad days of the +60s and 70s, different computers would + + align:start position:0% +60s and 70s, different computers would + + + align:start position:0% +60s and 70s, different computers would +have different representations for this. + + align:start position:0% +have different representations for this. + + + align:start position:0% +have different representations for this. +And then we all agreed on the same + + align:start position:0% +And then we all agreed on the same + + + align:start position:0% +And then we all agreed on the same +representation for uh letters. And then + + align:start position:0% +representation for uh letters. And then + + + align:start position:0% +representation for uh letters. And then +we remembered that there are other + + align:start position:0% +we remembered that there are other + + + align:start position:0% +we remembered that there are other +things in the uh um other characters in + + align:start position:0% +things in the uh um other characters in + + + align:start position:0% +things in the uh um other characters in +the world. That looks too much like an a + + align:start position:0% +the world. That looks too much like an a + + + align:start position:0% +the world. That looks too much like an a +how do I do a jin or something or an + + align:start position:0% +how do I do a jin or something or an + + + align:start position:0% +how do I do a jin or something or an +alpha beta things like that. And and + + align:start position:0% +alpha beta things like that. And and + + + align:start position:0% +alpha beta things like that. And and +then for a while we had a big problem + + align:start position:0% +then for a while we had a big problem + + + align:start position:0% +then for a while we had a big problem +that they weren't all converting the + + align:start position:0% +that they weren't all converting the + + + align:start position:0% +that they weren't all converting the +same thing. Anyhow, degression aside, + + align:start position:0% +same thing. Anyhow, degression aside, + + + align:start position:0% +same thing. Anyhow, degression aside, +maybe we'll get to the point where we + + align:start position:0% +maybe we'll get to the point where we + + + align:start position:0% +maybe we'll get to the point where we +can start converting things besides MIDI + + align:start position:0% +can start converting things besides MIDI + + + align:start position:0% +can start converting things besides MIDI +numbers and notes into something um more + + align:start position:0% +numbers and notes into something um more + + + align:start position:0% +numbers and notes into something um more +standardized because right now the MIDI + + align:start position:0% +standardized because right now the MIDI + + + align:start position:0% +standardized because right now the MIDI +numbers is basically the only + + align:start position:0% +numbers is basically the only + + + align:start position:0% +numbers is basically the only +standardized notes, which is probably + + align:start position:0% +standardized notes, which is probably + + + align:start position:0% +standardized notes, which is probably +why MIDI keeps um uh being used for a + + align:start position:0% +why MIDI keeps um uh being used for a + + + align:start position:0% +why MIDI keeps um uh being used for a +lot of computational projects. + + align:start position:0% +lot of computational projects. + + + align:start position:0% +lot of computational projects. +So the hard part is always finding out + + align:start position:0% +So the hard part is always finding out + + + align:start position:0% +So the hard part is always finding out +what numbers we should use to represent + + align:start position:0% +what numbers we should use to represent + + + align:start position:0% +what numbers we should use to represent +a note. + + align:start position:0% + + + + align:start position:0% + +So if we're going to convert name with + + align:start position:0% +So if we're going to convert name with + + + align:start position:0% +So if we're going to convert name with +octave and we want to make a string and + + align:start position:0% +octave and we want to make a string and + + + align:start position:0% +octave and we want to make a string and +then we want to make it a number and + + align:start position:0% +then we want to make it a number and + + + align:start position:0% +then we want to make it a number and +then we want to have a whole bunch of + + align:start position:0% +then we want to have a whole bunch of + + + align:start position:0% +then we want to have a whole bunch of +numbers. What have we just recently seen + + align:start position:0% +numbers. What have we just recently seen + + + align:start position:0% +numbers. What have we just recently seen +that looks like a tool to take a score + + align:start position:0% +that looks like a tool to take a score + + + align:start position:0% +that looks like a tool to take a score +or a part or something and works like a + + align:start position:0% +or a part or something and works like a + + + align:start position:0% +or a part or something and works like a +hash or a viewpoint that tries to + + align:start position:0% +hash or a viewpoint that tries to + + + align:start position:0% +hash or a viewpoint that tries to +convert it to a bunch of numbers. + + align:start position:0% + + + + align:start position:0% + +Not asking you to think too far back + + align:start position:0% +Not asking you to think too far back + + + align:start position:0% +Not asking you to think too far back +but farther back than today. + + align:start position:0% + + + + align:start position:0% + +Yeah, I'm + + align:start position:0% +Yeah, I'm + + + align:start position:0% +Yeah, I'm +>> getting a feature representation. + + align:start position:0% +>> getting a feature representation. + + + align:start position:0% +>> getting a feature representation. +>> Get extracting features. Getting a + + align:start position:0% +>> Get extracting features. Getting a + + + align:start position:0% +>> Get extracting features. Getting a +feature representation. Yeah. So feature + + align:start position:0% +feature representation. Yeah. So feature + + + align:start position:0% +feature representation. Yeah. So feature +extraction and this kind of viewpoint + + align:start position:0% +extraction and this kind of viewpoint + + + align:start position:0% +extraction and this kind of viewpoint +searching are very go hand inand with + + align:start position:0% +searching are very go hand inand with + + + align:start position:0% +searching are very go hand inand with +each other. So if you're it's partially + + align:start position:0% +each other. So if you're it's partially + + + align:start position:0% +each other. So if you're it's partially +why on you know once you finish up a + + align:start position:0% +why on you know once you finish up a + + + align:start position:0% +why on you know once you finish up a +search function you're just going to + + align:start position:0% +search function you're just going to + + + align:start position:0% +search function you're just going to +want to probably try to see if um AI or + + align:start position:0% +want to probably try to see if um AI or + + + align:start position:0% +want to probably try to see if um AI or +machine learning can do it better + + align:start position:0% +machine learning can do it better + + + align:start position:0% +machine learning can do it better +because you have everything ready to go + + align:start position:0% +because you have everything ready to go + + + align:start position:0% +because you have everything ready to go +for it. But sometimes what we extract is + + align:start position:0% +for it. But sometimes what we extract is + + + align:start position:0% +for it. But sometimes what we extract is +different from others. Um I want to give + + align:start position:0% +different from others. Um I want to give + + + align:start position:0% +different from others. Um I want to give +a little bit of a caution that um uh + + align:start position:0% +a little bit of a caution that um uh + + + align:start position:0% +a little bit of a caution that um uh +great uh back then course six you had to + + align:start position:0% +great uh back then course six you had to + + + align:start position:0% +great uh back then course six you had to +do a little final a final project called + + align:start position:0% +do a little final a final project called + + + align:start position:0% +do a little final a final project called +the UAP and we thought that making these + + align:start position:0% +the UAP and we thought that making these + + + align:start position:0% +the UAP and we thought that making these +viewpoints making a hashing system for + + align:start position:0% +viewpoints making a hashing system for + + + align:start position:0% +viewpoints making a hashing system for +music 21 for comparisons would be a nice + + align:start position:0% +music 21 for comparisons would be a nice + + + align:start position:0% +music 21 for comparisons would be a nice +um would would be a nice senior project + + align:start position:0% +um would would be a nice senior project + + + align:start position:0% +um would would be a nice senior project +and then we both realized that no it's + + align:start position:0% +and then we both realized that no it's + + + align:start position:0% +and then we both realized that no it's +uh it's a lot bigger than we thought and + + align:start position:0% +uh it's a lot bigger than we thought and + + + align:start position:0% +uh it's a lot bigger than we thought and +a lot more complex than we thought and + + align:start position:0% +a lot more complex than we thought and + + + align:start position:0% +a lot more complex than we thought and +so it needed to be an MN And Emily Zang + + align:start position:0% +so it needed to be an MN And Emily Zang + + + align:start position:0% +so it needed to be an MN And Emily Zang +was great at creating this and great we + + align:start position:0% +was great at creating this and great we + + + align:start position:0% +was great at creating this and great we +did a really great Menge project and + + align:start position:0% +did a really great Menge project and + + + align:start position:0% +did a really great Menge project and +then we realized no this this really + + align:start position:0% +then we realized no this this really + + + align:start position:0% +then we realized no this this really +needs to be a PhD project. We did not + + align:start position:0% +needs to be a PhD project. We did not + + + align:start position:0% +needs to be a PhD project. We did not +continue on. You can work there are so + + align:start position:0% +continue on. You can work there are so + + + align:start position:0% +continue on. You can work there are so +many difficult parts of um hash + + align:start position:0% +many difficult parts of um hash + + + align:start position:0% +many difficult parts of um hash +algorithms because you want to think + + align:start position:0% +algorithms because you want to think + + + align:start position:0% +algorithms because you want to think +about things like um yeah we'll not get + + align:start position:0% +about things like um yeah we'll not get + + + align:start position:0% +about things like um yeah we'll not get +to it. um going all the way back to the + + align:start position:0% +to it. um going all the way back to the + + + align:start position:0% +to it. um going all the way back to the +beginning. Um + + align:start position:0% + + + + align:start position:0% + +how can we create a viewpoint or + + align:start position:0% +how can we create a viewpoint or + + + align:start position:0% +how can we create a viewpoint or +something that allows D not to be + + align:start position:0% +something that allows D not to be + + + align:start position:0% +something that allows D not to be +totally totally different for anybody + + align:start position:0% +totally totally different for anybody + + + align:start position:0% +totally totally different for anybody +who didn't put D as the last of all + + align:start position:0% +who didn't put D as the last of all + + + align:start position:0% +who didn't put D as the last of all +possible results? + + align:start position:0% +possible results? + + + align:start position:0% +possible results? +What kinds of hash what kinds of numbers + + align:start position:0% +What kinds of hash what kinds of numbers + + + align:start position:0% +What kinds of hash what kinds of numbers +would we need to represent a piece on to + + align:start position:0% +would we need to represent a piece on to + + + align:start position:0% +would we need to represent a piece on to +make D not the worst + + align:start position:0% +make D not the worst + + + align:start position:0% +make D not the worst +and to really make sure that F isn't the + + align:start position:0% +and to really make sure that F isn't the + + + align:start position:0% +and to really make sure that F isn't the +best. So that's going to be our last + + align:start position:0% +best. So that's going to be our last + + + align:start position:0% +best. So that's going to be our last +five six minutes of class. I want you to + + align:start position:0% +five six minutes of class. I want you to + + + align:start position:0% +five six minutes of class. I want you to +talk five minutes of y'all talking with + + align:start position:0% +talk five minutes of y'all talking with + + + align:start position:0% +talk five minutes of y'all talking with +each other and five minutes of y'all + + align:start position:0% +each other and five minutes of y'all + + + align:start position:0% +each other and five minutes of y'all +talk and talking to me. So what kinds of + + align:start position:0% +talk and talking to me. So what kinds of + + + align:start position:0% +talk and talking to me. So what kinds of +what kinds of feature extractions? What + + align:start position:0% +what kinds of feature extractions? What + + + align:start position:0% +what kinds of feature extractions? What +kind of hash function? What kind of + + align:start position:0% +kind of hash function? What kind of + + + align:start position:0% +kind of hash function? What kind of +viewpoints? These are all slightly + + align:start position:0% +viewpoints? These are all slightly + + + align:start position:0% +viewpoints? These are all slightly +different concepts, but they're all in + + align:start position:0% +different concepts, but they're all in + + + align:start position:0% +different concepts, but they're all in +the same area. What kinds of equivalence + + align:start position:0% +the same area. What kinds of equivalence + + + align:start position:0% +the same area. What kinds of equivalence +classes will you need in order to make + + align:start position:0% +classes will you need in order to make + + + align:start position:0% +classes will you need in order to make +this happen? + + align:start position:0% +this happen? + + + align:start position:0% +this happen? +Go ahead. + + align:start position:0% +Go ahead. + + + align:start position:0% +Go ahead. +Okay. I hear I hear words um continuing + + align:start position:0% +Okay. I hear I hear words um continuing + + + align:start position:0% +Okay. I hear I hear words um continuing +but but less frequently. Let's talk + + align:start position:0% +but but less frequently. Let's talk + + + align:start position:0% +but but less frequently. Let's talk +about what are some of the ways that um + + align:start position:0% +about what are some of the ways that um + + + align:start position:0% +about what are some of the ways that um +that people thought to create a strategy + + align:start position:0% +that people thought to create a strategy + + + align:start position:0% +that people thought to create a strategy +that doesn't make D and F about the + + align:start position:0% +that doesn't make D and F about the + + + align:start position:0% +that doesn't make D and F about the +same. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. Go ahead. + + align:start position:0% +>> Yeah. Go ahead. + + + align:start position:0% +>> Yeah. Go ahead. +>> Look at the sequence of like local + + align:start position:0% +>> Look at the sequence of like local + + + align:start position:0% +>> Look at the sequence of like local +maxima and minima. + + align:start position:0% +maxima and minima. + + + align:start position:0% +maxima and minima. +>> Local maxima and minima. Okay. I think I + + align:start position:0% +>> Local maxima and minima. Okay. I think I + + + align:start position:0% +>> Local maxima and minima. Okay. I think I +know what you talk about, but let's give + + align:start position:0% +know what you talk about, but let's give + + + align:start position:0% +know what you talk about, but let's give +me a little example. What um let's talk + + align:start position:0% +me a little example. What um let's talk + + + align:start position:0% +me a little example. What um let's talk +about A. What do you what do you + + align:start position:0% +about A. What do you what do you + + + align:start position:0% +about A. What do you what do you +>> So you could maybe argue that the C is + + align:start position:0% +>> So you could maybe argue that the C is + + + align:start position:0% +>> So you could maybe argue that the C is +the local minimum and then the F is + + align:start position:0% +the local minimum and then the F is + + + align:start position:0% +the local minimum and then the F is +higher than both of its neighbors. So + + align:start position:0% +higher than both of its neighbors. So + + + align:start position:0% +higher than both of its neighbors. So +it's a maximum and then the D is a + + align:start position:0% +it's a maximum and then the D is a + + + align:start position:0% +it's a maximum and then the D is a +minimum. The E is a maximum and then the + + align:start position:0% +minimum. The E is a maximum and then the + + + align:start position:0% +minimum. The E is a maximum and then the +D and C after that are not really + + align:start position:0% +D and C after that are not really + + + align:start position:0% +D and C after that are not really +anything until you hit the A on the 16th + + align:start position:0% +anything until you hit the A on the 16th + + + align:start position:0% +anything until you hit the A on the 16th +note. + + align:start position:0% +note. + + + align:start position:0% +note. +>> Cool. So yeah, we're just looking at + + align:start position:0% +>> Cool. So yeah, we're just looking at + + + align:start position:0% +>> Cool. So yeah, we're just looking at +every time the direction changes of the + + align:start position:0% +every time the direction changes of the + + + align:start position:0% +every time the direction changes of the +pitches. Great. And compare that. So + + align:start position:0% +pitches. Great. And compare that. So + + + align:start position:0% +pitches. Great. And compare that. So +beginning A has D F D E here we have D F + + align:start position:0% +beginning A has D F D E here we have D F + + + align:start position:0% +beginning A has D F D E here we have D F +D tiny bit different D F but then going + + align:start position:0% +D tiny bit different D F but then going + + + align:start position:0% +D tiny bit different D F but then going +down to a little bit different but it's + + align:start position:0% +down to a little bit different but it's + + + align:start position:0% +down to a little bit different but it's +at least giving some numbers we have um + + align:start position:0% +at least giving some numbers we have um + + + align:start position:0% +at least giving some numbers we have um +yeah does always the question is does + + align:start position:0% +yeah does always the question is does + + + align:start position:0% +yeah does always the question is does +your current streak end when you hit a + + align:start position:0% +your current streak end when you hit a + + + align:start position:0% +your current streak end when you hit a +rest or not and maybe it depends on how + + align:start position:0% +rest or not and maybe it depends on how + + + align:start position:0% +rest or not and maybe it depends on how +long the rest is. So good. Other other + + align:start position:0% +long the rest is. So good. Other other + + + align:start position:0% +long the rest is. So good. Other other +strategies? + + align:start position:0% +strategies? + + + align:start position:0% +strategies? +>> Adam, + + align:start position:0% +>> Adam, + + + align:start position:0% +>> Adam, +>> I would look at where offsets are the + + align:start position:0% +>> I would look at where offsets are the + + + align:start position:0% +>> I would look at where offsets are the +same and then check if their notes are + + align:start position:0% +same and then check if their notes are + + + align:start position:0% +same and then check if their notes are +the same or not. + + align:start position:0% +the same or not. + + + align:start position:0% +the same or not. +>> Great. So, we're gonna look at offsets + + align:start position:0% +>> Great. So, we're gonna look at offsets + + + align:start position:0% +>> Great. So, we're gonna look at offsets +that are the same and see if notes are + + align:start position:0% +that are the same and see if notes are + + + align:start position:0% +that are the same and see if notes are +the same or not. That works really well. + + align:start position:0% +the same or not. That works really well. + + + align:start position:0% +the same or not. That works really well. +And what I'd love to do if if this were + + align:start position:0% +And what I'd love to do if if this were + + + align:start position:0% +And what I'd love to do if if this were +um what do you call the the generalized + + align:start position:0% +um what do you call the the generalized + + + align:start position:0% +um what do you call the the generalized +adversarial problem set, the GAN problem + + align:start position:0% +adversarial problem set, the GAN problem + + + align:start position:0% +adversarial problem set, the GAN problem +set, where one one team has to solve the + + align:start position:0% +set, where one one team has to solve the + + + align:start position:0% +set, where one one team has to solve the +problem, the other team has to keep + + align:start position:0% +problem, the other team has to keep + + + align:start position:0% +problem, the other team has to keep +giving them things that break that. Uh, + + align:start position:0% +giving them things that break that. Uh, + + + align:start position:0% +giving them things that break that. Uh, +and I think it was a great idea and I + + align:start position:0% +and I think it was a great idea and I + + + align:start position:0% +and I think it was a great idea and I +think it would work in general, but I + + align:start position:0% +think it would work in general, but I + + + align:start position:0% +think it would work in general, but I +could generate something like um where + + align:start position:0% +could generate something like um where + + + align:start position:0% +could generate something like um where +all I insert is let's insert a 64th rest + + align:start position:0% +all I insert is let's insert a 64th rest + + + align:start position:0% +all I insert is let's insert a 64th rest +at the beginning and then put all random + + align:start position:0% +at the beginning and then put all random + + + align:start position:0% +at the beginning and then put all random +notes and you're going to end up with + + align:start position:0% +notes and you're going to end up with + + + align:start position:0% +notes and you're going to end up with +and then maybe we'll put one note that's + + align:start position:0% +and then maybe we'll put one note that's + + + align:start position:0% +and then maybe we'll put one note that's +the same at the end and you could end up + + align:start position:0% +the same at the end and you could end up + + + align:start position:0% +the same at the end and you could end up +with 100% of the notes on the same + + align:start position:0% +with 100% of the notes on the same + + + align:start position:0% +with 100% of the notes on the same +offset are the same. Uh I think you I + + align:start position:0% +offset are the same. Uh I think you I + + + align:start position:0% +offset are the same. Uh I think you I +think we we would really work in the + + align:start position:0% +think we we would really work in the + + + align:start position:0% +think we we would really work in the +real world but but we might want to + + align:start position:0% +real world but but we might want to + + + align:start position:0% +real world but but we might want to +always think about something like that + + align:start position:0% +always think about something like that + + + align:start position:0% +always think about something like that +too. Great great idea John then + + align:start position:0% +too. Great great idea John then + + + align:start position:0% +too. Great great idea John then +>> ours kind of builds up on Adam. So + + align:start position:0% +>> ours kind of builds up on Adam. So + + + align:start position:0% +>> ours kind of builds up on Adam. So +>> you kind of start kind of builds up on + + align:start position:0% +>> you kind of start kind of builds up on + + + align:start position:0% +>> you kind of start kind of builds up on +what Adam was saying. + + align:start position:0% +what Adam was saying. + + + align:start position:0% +what Adam was saying. +>> Um but first you like take a look at the + + align:start position:0% +>> Um but first you like take a look at the + + + align:start position:0% +>> Um but first you like take a look at the +notes and kind like kind of do like a + + align:start position:0% +notes and kind like kind of do like a + + + align:start position:0% +notes and kind like kind of do like a +set kind of like crossover between like + + align:start position:0% +set kind of like crossover between like + + + align:start position:0% +set kind of like crossover between like +a set of D's and A notes and then like A + + align:start position:0% +a set of D's and A notes and then like A + + + align:start position:0% +a set of D's and A notes and then like A +and S notes. So both those would still + + align:start position:0% +and S notes. So both those would still + + + align:start position:0% +and S notes. So both those would still +like show up like relatively high and + + align:start position:0% +like show up like relatively high and + + + align:start position:0% +like show up like relatively high and +then like compare the offsets which we + + align:start position:0% +then like compare the offsets which we + + + align:start position:0% +then like compare the offsets which we +want to like take half of it but still + + align:start position:0% +want to like take half of it but still + + + align:start position:0% +want to like take half of it but still +keep D relatively high. + + align:start position:0% +keep D relatively high. + + + align:start position:0% +keep D relatively high. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Super. When we're talking about offsets, + + align:start position:0% +>> Super. When we're talking about offsets, + + + align:start position:0% +>> Super. When we're talking about offsets, +are we talking about um what kind of + + align:start position:0% +are we talking about um what kind of + + + align:start position:0% +are we talking about um what kind of +offsets + + align:start position:0% +offsets + + + align:start position:0% +offsets +>> like um where in the guess like within + + align:start position:0% +>> like um where in the guess like within + + + align:start position:0% +>> like um where in the guess like within +the two measures? + + align:start position:0% +the two measures? + + + align:start position:0% +the two measures? +>> Great. Yeah. Where in the two measures + + align:start position:0% +>> Great. Yeah. Where in the two measures + + + align:start position:0% +>> Great. Yeah. Where in the two measures +where in the measure um we sometimes + + align:start position:0% +where in the measure um we sometimes + + + align:start position:0% +where in the measure um we sometimes +want to do global offset from the + + align:start position:0% +want to do global offset from the + + + align:start position:0% +want to do global offset from the +beginning of the measure, but then you + + align:start position:0% +beginning of the measure, but then you + + + align:start position:0% +beginning of the measure, but then you +can't identify similar phrases or all it + + align:start position:0% +can't identify similar phrases or all it + + + align:start position:0% +can't identify similar phrases or all it +takes is put a repeat, put the first + + align:start position:0% +takes is put a repeat, put the first + + + align:start position:0% +takes is put a repeat, put the first +four measures, repeat it once and + + align:start position:0% +four measures, repeat it once and + + + align:start position:0% +four measures, repeat it once and +suddenly the whole rest of the piece is + + align:start position:0% +suddenly the whole rest of the piece is + + + align:start position:0% +suddenly the whole rest of the piece is +different. So yeah, that's great. + + align:start position:0% +different. So yeah, that's great. + + + align:start position:0% +different. So yeah, that's great. +also similar but a little duration based + + align:start position:0% +also similar but a little duration based + + + align:start position:0% +also similar but a little duration based +I guess like if you just start at time= + + align:start position:0% +I guess like if you just start at time= + + + align:start position:0% +I guess like if you just start at time= +0 and go all the way through the piece + + align:start position:0% +0 and go all the way through the piece + + + align:start position:0% +0 and go all the way through the piece +like anytime the two pieces have the + + align:start position:0% +like anytime the two pieces have the + + + align:start position:0% +like anytime the two pieces have the +same pitch if you score so like the F + + align:start position:0% +same pitch if you score so like the F + + + align:start position:0% +same pitch if you score so like the F +that they both have on beat two would be + + align:start position:0% +that they both have on beat two would be + + + align:start position:0% +that they both have on beat two would be +like a quarter point because + + align:start position:0% +like a quarter point because + + + align:start position:0% +like a quarter point because +>> the F the F that they both have on beat + + align:start position:0% +>> the F the F that they both have on beat + + + align:start position:0% +>> the F the F that they both have on beat +two would be a quarter point because + + align:start position:0% +two would be a quarter point because + + + align:start position:0% +two would be a quarter point because +>> shared duration is only for that 16th + + align:start position:0% +>> shared duration is only for that 16th + + + align:start position:0% +>> shared duration is only for that 16th +note. + + align:start position:0% +note. + + + align:start position:0% +note. +>> Gotcha. So we look at shared. + + align:start position:0% +>> Gotcha. So we look at shared. + + + align:start position:0% +>> Gotcha. So we look at shared. +Great. I like that a lot. Did anybody + + align:start position:0% +Great. I like that a lot. Did anybody + + + align:start position:0% +Great. I like that a lot. Did anybody +try to come up with equivalence? Yeah. + + align:start position:0% +try to come up with equivalence? Yeah. + + + align:start position:0% +try to come up with equivalence? Yeah. +Yeah. The contour ends up being a kind + + align:start position:0% +Yeah. The contour ends up being a kind + + + align:start position:0% +Yeah. The contour ends up being a kind +of a new equivalence class that we + + align:start position:0% +of a new equivalence class that we + + + align:start position:0% +of a new equivalence class that we +hadn't talked about which kind of works + + align:start position:0% +hadn't talked about which kind of works + + + align:start position:0% +hadn't talked about which kind of works +out in thinking that everything that + + align:start position:0% +out in thinking that everything that + + + align:start position:0% +out in thinking that everything that +doesn't change directions is a kind of + + align:start position:0% +doesn't change directions is a kind of + + + align:start position:0% +doesn't change directions is a kind of +passing tone even though not in the + + align:start position:0% +passing tone even though not in the + + + align:start position:0% +passing tone even though not in the +proper music theory term and so can kind + + align:start position:0% +proper music theory term and so can kind + + + align:start position:0% +proper music theory term and so can kind +of be ignored. + + align:start position:0% +of be ignored. + + + align:start position:0% +of be ignored. +By the way, I the one I use quite often + + align:start position:0% +By the way, I the one I use quite often + + + align:start position:0% +By the way, I the one I use quite often +is I'm just going to look on down beats + + align:start position:0% +is I'm just going to look on down beats + + + align:start position:0% +is I'm just going to look on down beats +or strong or on beats and ignore + + align:start position:0% +or strong or on beats and ignore + + + align:start position:0% +or strong or on beats and ignore +everything else. Um, and that would + + align:start position:0% +everything else. Um, and that would + + + align:start position:0% +everything else. Um, and that would +works pretty well for a lot of a lot of + + align:start position:0% +works pretty well for a lot of a lot of + + + align:start position:0% +works pretty well for a lot of a lot of +things. \ No newline at end of file diff --git a/Sqhb-TGC4aQ.txt b/Sqhb-TGC4aQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..3635820453ee57af9d6916782f66c9eaa749396d --- /dev/null +++ b/Sqhb-TGC4aQ.txt @@ -0,0 +1,296 @@ +A compiler is a program that translates a +high-level language program into a functionally + +equivalent sequence of machine instructions, +i.e., an assembly language program. + +A compiler first checks that the high-level +program is correct, i.e., that the statements + +are well formed, the programmer isn't asking +for nonsensical computations, + +e.g., adding a string value and an integer, +or attempting to use the value of a variable + +before it has been properly initialized. +The compiler may also provide warnings when + +operations may not produce the expected results, +e.g., when converting from a floating-point + +number to an integer, where the floating-point +value may be too large to fit in the number + +of bits provided by the integer. +If the program passes scrutiny, the compiler + +then proceeds to generate efficient sequences +of instructions, often finding ways to rearrange + +the computation so that the resulting sequences +are shorter and faster. + +It's hard to beat a modern optimizing compiler +at producing assembly language, since the + +compiler will patiently explore alternatives +and deduce properties of the program that + +may not be apparent to even diligent assembly +language programmers. + +In this section, we'll look at a simple technique +for compiling C programs into assembly. + +Then, in the next section, we'll dive more +deeply into how a modern compiler works. + +There are two main routines in our simple +compiler: compile_statement and compile_expr. + +The job of compile_statement is to compile +a single statement from the source program. + +Since the source program is a sequence of +statements, we'll be calling compile_statement + +repeatedly. +We'll focus on the compilation technique for + +four types of statements. +An unconditional statement is simply an expression + +that's evaluated once. +A compound statement is simply a sequence + +of statements to be executed in turn. +Conditional statements, sometimes called "if + +statements", compute the value of an test +expression, e.g., a comparison such as "A + +< B". +If the test is true then statement_1 is executed, + +otherwise statement_2 is executed. +Iteration statements also contain a test expression. + +In each iteration, if the test true, then +the statement is executed, and the process + +repeats. +If the test is false, the iteration is terminated. + +The other main routine is compile_expr whose +job it is to generate code to compute the + +value of an expression, leaving the result +in some register. + +Expressions take many forms: +simple constant values + +values from scalar or array variables, +assignment expressions that compute a value + +and then store the result in some variable, +unary or binary operations that combine the + +values of their operands with the specified +operator. + +Complex arithmetic expressions can be decomposed +into sequences of unary and binary operations. + +And, finally, procedure calls, where a named +sequence of statements will be executed with + +the values of the supplied arguments assigned +as the values for the formal parameters of + +the procedure. +Compiling procedures and procedure calls is + +a topic that we'll tackle next lecture since +there are some complications to understand + +and deal with. +Happily, compiling the other types of expressions + +and statements is straightforward, so let's +get started. + +What code do we need to put the value of a +constant into a register? + +If the constant will fit into the 16-bit constant +field of an instruction, we can use CMOVE + +to load the sign-extended constant into a +register. + +This approach works for constants between +-32768 and +32767. + +If the constant is too large, it's stored +in a main memory location and we use a LD + +instruction to get the value into a register. +Loading the value of a variable is much the + +same as loading the value of a large constant. +We use a LD instruction to access the memory + +location that holds the value of the variable. +Performing an array access is slightly more + +complicated: arrays are stored as consecutive +locations in main memory, starting with index + +0. +Each element of the array occupies some fixed + +number bytes. +So we need code to convert the array index + +into the actual main memory address for the +specified array element. + +We first invoke compile_expr to generate code +that evaluates the index expression and leaves + +the result in Rx. +That will be a value between 0 and the size + +of the array minus 1. +We'll use a LD instruction to access the appropriate + +array entry, but that means we need to convert +the index into a byte offset, which we do + +by multiplying the index by bsize, the number +of bytes in one element. + +If b was an array of integers, bsize would +be 4. + +Now that we have the byte offset in a register, +we can use LD to add the offset to the base + +address of the array computing the address +of the desired array element, then load the + +memory value at that address into a register. +Assignment expressions are easy + +Invoke compile_expr to generate code that +loads the value of the expression into a register, + +then generate a ST instruction to store the +value into the specified variable. + +Arithmetic operations are pretty easy too. +Use compile_expr to generate code for each + +of the operand expressions, leaving the results +in registers. + +Then generate the appropriate ALU instruction +to combine the operands and leave the answer + +in a register. +Let's look at example to see how all this + +works. +Here have an assignment expression that requires + +a subtract, a multiply, and an addition to +compute the required value. + +Let's follow the compilation process from +start to finish as we invoke compile_expr + +to generate the necessary code. +Following the template for assignment expressions + +from the previous page, we recursively call +compile_expr to compute value of the right-hand-side + +of the assignment. +That's a multiply operation, so, following + +the Operations template, we need to compile +the left-hand operand of the multiply. + +That's a subtract operation, so, we call compile_expr +again to compile the left-hand operand of + +the subtract. +Aha, we know how to get the value of a variable + +into a register. So we generate a LD instruction +to load the value of x into r1. + +The process we're following is called "recursive +descent". + +We've used recursive calls to compile_expr +to process each level of the expression tree. + +At each recursive call the expressions get +simpler, until we reach a variable or constant, + +where we can generate the appropriate instruction +without descending further. + +At this point we've reach a leaf of the expression +tree and we're done with this branch of the + +recursion. +Now we need to get the value of the right-hand + +operand of the subtract into a register. +In case it's a small constant, so we generate + +a CMOVE instruction. +Now that both operand values are in registers, + +we return to the subtract template and generate +a SUB instruction to do the subtraction. + +We now have the value for the left-hand operand +of the multiply in r1. + +We follow the same process for the right-hand +operand of the multiply, recursively calling + +compile_expr to process each level of the +expression until we reach a variable or constant. + +Then we return up the expression tree, generating +the appropriate instructions as we go, following + +the dictates of the appropriate template from +the previous slide. + +The generated code is shown on the left of +the slide. + +The recursive-descent technique makes short +work of generating code for even the most + +complicated of expressions. +There's even opportunity to find some simple + +optimizations by looking at adjacent instructions. +For example, a CMOVE followed by an arithmetic + +operation can often be shorted to a single +arithmetic instruction with the constant as + +its second operand. +These local transformations are called "peephole + +optimizations" since we're only considering +just one or two instructions at a time. \ No newline at end of file diff --git a/T0GdXZusbKI.txt b/T0GdXZusbKI.txt new file mode 100644 index 0000000000000000000000000000000000000000..300dd8888a2103e5abc21893f36c0f6bc7c62da9 --- /dev/null +++ b/T0GdXZusbKI.txt @@ -0,0 +1,275 @@ +align:start position:0% + +so one thought that I have for uh + + align:start position:0% +so one thought that I have for uh + + + align:start position:0% +so one thought that I have for uh +Educators who running this classes be + + align:start position:0% +Educators who running this classes be + + + align:start position:0% +Educators who running this classes be +very clear to yourself and then to the + + align:start position:0% +very clear to yourself and then to the + + + align:start position:0% +very clear to yourself and then to the +students about whether you are running a + + align:start position:0% +students about whether you are running a + + + align:start position:0% +students about whether you are running a +class about game + + align:start position:0% +class about game + + + align:start position:0% +class about game +design or game programming or project + + align:start position:0% +design or game programming or project + + + align:start position:0% +design or game programming or project +management when we started this class we + + align:start position:0% +management when we started this class we + + + align:start position:0% +management when we started this class we +were very very we were trying to be as + + align:start position:0% +were very very we were trying to be as + + + align:start position:0% +were very very we were trying to be as +clear as possible to the students this + + align:start position:0% +clear as possible to the students this + + + align:start position:0% +clear as possible to the students this +is a class about project management you + + align:start position:0% +is a class about project management you + + + align:start position:0% +is a class about project management you +will do all those other things in the + + align:start position:0% +will do all those other things in the + + + align:start position:0% +will do all those other things in the +process of this class and many of you + + align:start position:0% +process of this class and many of you + + + align:start position:0% +process of this class and many of you +are here for that reason uh but that's + + align:start position:0% +are here for that reason uh but that's + + + align:start position:0% +are here for that reason uh but that's +the that's the important thing that we + + align:start position:0% +the that's the important thing that we + + + align:start position:0% +the that's the important thing that we +want uh you to understand and it's + + align:start position:0% +want uh you to understand and it's + + + align:start position:0% +want uh you to understand and it's +important because it gives you clarity + + align:start position:0% +important because it gives you clarity + + + align:start position:0% +important because it gives you clarity +as an educator on how you're going to be + + align:start position:0% +as an educator on how you're going to be + + + align:start position:0% +as an educator on how you're going to be +assessing your students what how you're + + align:start position:0% +assessing your students what how you're + + + align:start position:0% +assessing your students what how you're +going to be teaching your students what + + align:start position:0% +going to be teaching your students what + + + align:start position:0% +going to be teaching your students what +you're going to be valuing over the + + align:start position:0% +you're going to be valuing over the + + + align:start position:0% +you're going to be valuing over the +other you know the game can be poorly + + align:start position:0% +other you know the game can be poorly + + + align:start position:0% +other you know the game can be poorly +designed and maybe have bugs but the + + align:start position:0% +designed and maybe have bugs but the + + + align:start position:0% +designed and maybe have bugs but the +team clearly understands how to + + align:start position:0% +team clearly understands how to + + + align:start position:0% +team clearly understands how to +communicate with the each other well + + align:start position:0% +communicate with the each other well + + + align:start position:0% +communicate with the each other well +that is a team that should be awarded + + align:start position:0% +that is a team that should be awarded + + + align:start position:0% +that is a team that should be awarded +for their work right um at least in in + + align:start position:0% +for their work right um at least in in + + + align:start position:0% +for their work right um at least in in +the version that we teach other schools + + align:start position:0% +the version that we teach other schools + + + align:start position:0% +the version that we teach other schools +may can are definitely free to have a + + align:start position:0% +may can are definitely free to have a + + + align:start position:0% +may can are definitely free to have a +different perspective on this it could + + align:start position:0% +different perspective on this it could + + + align:start position:0% +different perspective on this it could +be about the quality of code it could be + + align:start position:0% +be about the quality of code it could be + + + align:start position:0% +be about the quality of code it could be +about the you know how Brave the + + align:start position:0% +about the you know how Brave the + + + align:start position:0% +about the you know how Brave the +students were when it came to design and + + align:start position:0% +students were when it came to design and + + + align:start position:0% +students were when it came to design and +you can award it accordingly but you got + + align:start position:0% +you can award it accordingly but you got + + + align:start position:0% +you can award it accordingly but you got +to be very very clear both to yourself + + align:start position:0% +to be very very clear both to yourself + + + align:start position:0% +to be very very clear both to yourself +and to the students \ No newline at end of file diff --git a/TJh7KPABk6I.txt b/TJh7KPABk6I.txt new file mode 100644 index 0000000000000000000000000000000000000000..f70179d305b8e135f8b43bc084d3cf77156b4cc4 --- /dev/null +++ b/TJh7KPABk6I.txt @@ -0,0 +1,2374 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to this + +course on nonlinear finite +element analysis of solids and + +structures. + +A few years ago, we produced at +MIT a course on the linear + +analysis of solids +and structures. + +That course was quite +well-received. + +And we obtained a number of +requests to also produce a + +course on the nonlinear +analysis of solids and + +structures. + +The present course is the answer +to those requests. + +In this course, we will be using +my book as a textbook. + +You might be already a bit +familiar with this book. + +We will be referring to +some of the sections + +in quite some detail. + +In addition, of course, you +also have the study guide. + +Let me now share with you, +briefly, some thoughts that I + +had while designing +this course. + +The field of nonlinear, finite +element analysis is a very + +large field. + +And, in fact, four large fields +come to mind as feeding + +into nonlinear, finite element +methods, continuum mechanics, + +finite element discretizations, +numerical + +algorithms, software +considerations. + +Because the field of nonlinear, +finite element + +analysis is such a large field, +I had to select certain + +topics as the topics of this +finite series of lectures. + +I believe that the lectures +provide a good introduction + +and foundation to a nonlinear, +finite element analysis. + +Of course, the lectures cannot +answer all the questions that + +you might have regarding +nonlinear, + +finite element analysis. + +I believe, though, that they +will be answering some of the + +questions and, hopefully, +stimulate discussions that you + +might have while watching +these lectures with your + +colleagues. + +We, at MIT, continue to +work in nonlinear, + +finite element analysis. + +And we also offer, from time +to time, short courses. + +It would be very nice to meet +you at one of these short + +courses and to discuss any +questions that you might have + +regarding these lectures, once +you have seen them, and + +regarding your work on +nonlinear, finite element + +analysis in general. + +Let me now return to +what I like to talk + +about in this course. + +In this course, we want to +concentrate on methods that + +are generally applicable, +modern techniques and + +practical procedures. + +I believe it is important that +we discuss in this course + +practical and effective +procedures. + +In particular, methods that +are or are now becoming an + +integral part of computer-aided +design, + +computer-aided engineering +software. + +In this course, I would like to +discuss with you geometric + +and material nonlinear analysis, +static and dynamic + +solutions, basic principles and +their use, and share with + +you example solutions. + +I believe that the course will +be of interest in many + +branches of engineering +throughout the world. + +And in this spirit, +we have designed a + +logo for this course. + +The logo is shown here. + +It shows the whole world as an + +assemblage off finite elements. + +If you're watching me from +Chicago, you're watching me + +from about here. + +If you're watching from +Munich, you're + +watching about there. + +And if you are in Tokyo, +you're watching + +me from about there. + +Welcome to this course. + +I'd like to now start with the +first lecture, which has the + +title Introduction to +Nonlinear Analysis. + +And let me take off my jacket, +because we have a lot of work + +ahead, and summarize to you what +I would like to present + +to you in this first lecture. + +We discuss, first, some +introductory view graphs and + +show some short movies. + +We then classify nonlinear +analyses. + +We then discuss the +basic approach of + +an incremental solution. + +And we share some example +solutions. + +Let me walk over to my view +graphs which I've prepared for + +this lecture so that we can +start with a discussion of + +this material. + +Finite element nonlinear +analysis in engineering + +mechanics can be an art, but it +can also be a frustration. + +For those of you who have been +doing some nonlinear analysis + +already, I think you will value +that it can be an art + +and it can be a frustration +because it can be a very + +difficult matter. + +But it's always provides +a great challenge. + +And that, of course, is the +exciting part of working in + +nonlinear, finite element +analysis. + +Some important engineering +phenomena can only be assessed + +using nonlinear analysis +techniques. + +For example, the collapse or +buckling of structures due to + +sudden overloads-- + +I'm thinking here, typically +of shell structures, say-- + +the progressive damage behavior +due to long-lasting + +severe loads such as, for +example, high-temperature + +loads in nuclear reactor +components and, for certain + +structures such as cables and +transmission towers, nonlinear + +phenomena need be included in +the analysis, even for service + +load calculations. + +The need for nonlinear analysis +has certainly + +increased in recent years due +to the need for the use of + +optimized structures, the use +of new materials that are + +being introduced or have been +introduced over the recent + +years, the addressing of +safety-related issues of + +structures. + +There's more rigorous attention +being given to such + +safety-related issues now and +certain the corresponding + +benefits can be most +important. + +Problems that are addressed by +nonlinear, finite element + +analysis can be found in many +branches of engineering. + +And I've listed here some such +branches, nuclear engineering, + +earthquake engineering, the +automobile industries, defense + +industries, in aeronautical +engineering, mining + +industries, offshore engineering +and so on. + +I'd like to now show you some +movies that we have assembled + +regarding some finite element +analysis in certain fields. + +And let us start with a movie +related to the defense + +industries, then go on to a +movie related to some work in + +the automobile industries, and +then look at a movie related + +to some work in earthquake +engineering. + +And finally, I'd like to also +show you an interesting movie + +regarding a structural +engineering problem. + +So let me now introduce you to +the first movie, which is a + +movie in which a tank is modeled +using a geometric + +model first and then setting +up a finite element mesh. + +Here we see a tank +in a maneuver. + +You surely have seen such +structure before. + +And here you see, in the top +part of the picture, the + +geometric model of a tank and, +in the bottom part of the + +picture, a finite element +discretization. + +The top model was generated +using a geometric modeler. + +And the bottom model was +obtained using a finite + +element mesh generator. + +These models were constructed +by Structural Dynamics + +Research Corporation. + +The second movie relates to a +problem that has obtained much + +attention in the automobile +industry, namely the problem + +of what happens when a motor +car crashes against + +another motor car. + +And tests have been performed of +motor cars crashing against + +rigid walls. + +Test results have +been assembled. + +And finite element methods may +well be used in the analysis + +of such types of problems. + +Here we see a test performed by +the Ford Motor Company of a + +car crashing against +a rigid wall. + +And here, a close-up of what +happens to the passengers not + +wearing seat belts, and +another such test. + +Here now, in more detail, +what happens to the + +front part of the car. + +There is since some time much +interest in modeling these + +phenomena on the computer. + +And finite element methods can +be applied and are very + +valuable here. + +This certain movie relates to +the use of finite element + +methods in earthquake +engineering. + +Here we look at the finite +element model of a tank and + +the dynamic motions +of that model. + +We are surely all aware that +earthquake motions can cause + +severe structural vibrations +and possibly collapse of + +structures. + +Here we see a transformer and +the tank to be modeled on it. + +Here a close-up view +of the tank. + +The finite element model of the +tank was constructed by + +Asea, a Swedish company. + +And here we see some vibratory +motions of the model. + +The fourth movie shows the +dynamic response and collapse + +of the Tacoma Narrows +bridge in 1940. + +The Tacoma Narrows bridge +collapsed on November 7, 1940, + +about four months after its +opening in winds of 40 to 45 + +miles per hour. + +Here you see the dynamic motions +of the bridge prior to + +its collapse, a side view, +and now a view + +along its center line. + +Notice the high torsion of +vibrations of the bridge. + +The bridge went through large +dynamic motions for hours + +until its collapse. + +We only show a very small +segment of that time. + +And here you see how the +bridge collapsed. + +Of course, these movies only +indicate, to some extent, + +where finite element methods +might be applied in + +engineering practice, but I +thought you might like, you + +might enjoy, seeing +the movies. + +Let me now continue with the +material that I have + +documented on the view graphs. + +For an effective nonlinear +analysis, a good physical and + +theoretical understanding +is most important. + +You want to have some good +physical insight in the + +problem, setup, and mathematical +formulation of + +finite element model. + +Solve that model, and +that will enrich + +your physical insight. + +It is this interaction and +mutual enrichment between the + +physical insight and +mathematical formulation that + +can be most valuable. + +The best approach for a +nonlinear finite element + +analysis is to use reliable +and generally applicable + +finite elements. + +With such methods, we can +establish models that we can + +understand, that we have +confidence in. + +We start with simple +models of nature. + +And we find these +as need arises. + +In fact, I like to think of an +engineer as developing a first + +model on the back of an envelope +using, of course, + +simple equations. + +And these equations will give +some insight into the + +structural response. + +If necessary, then the finite +element model is set up. + +The first finite element +model is set up. + +And this finite element +model is then + +refined as need arises. + +To perform a nonlinear +analysis, we want to, + +altogether, stay then with +simple, relatively small and + +reliable models. + +We always want to perform +a linear analysis first. + +I will show examples in this +course particular related to + +this item here. + +It is very important, in my +view, to first do a linear + +analysis and then only go on +to a nonlinear analysis. + +As I mentioned already, we want +to refine the model by + +introducing nonlinearities as +desired and, once again, use + +reliable and well-understood +models, obtain accurate + +solutions of the models. + +This is very important for +possible proper interpretation + +of the results. + +Here we show schematically +the finite + +element modeling process. + +We have a problem in nature. + +We model that problem, the +kinematic conditions, the + +constitutive relations, the +boundary conditions, the + +loads, and so on, using +finite elements. + +We solve the model and interpret +the results. + +Now this model surely can +only approximate the + +actual problem in nature. + +And on interpretation of the +results, we may find that we + +really should refine +our model. + +And we do so, set up a new +model, solve again. + +And like this, we may cycle +a number of times + +through this process. + +Of course, traditionally, test +results have been sought for + +very complex problems, +laboratory test results have + +been sought. + +And this may still +be necessary now. + +However, the finite element +modeling process will + +certainly compliment these +laboratory test results. + +Let's look at a typical +nonlinear problem. + +Here we have a bracket +of mild steel + +subjected to the load shown. + +And the possible questions that +we might ask are, what is + +the yield load of +this bracket? + +In other words, at what load +do we see first plastic + +deformations? + +What is the limit load? + +What is the maximum load that +this bracket can take? + +What are the plastic zones? + +What are the residual stresses +when the load is removed? + +Is there adhering where +the loads are applied + +right around here? + +What is the creep response of +the bracket when the bracket + +is subjected to high temperature +conditions and + +these loads? + +And what are the permanent +deflections of + +the bracket, et cetera. + +There are many more questions +that could be asked. + +And certainly, these questions +here can only be answered by a + +nonlinear analysis. + +Possible analyses that we might + +consider are the following. + +First we, of course, would +always perform, as I mentioned + +earlier, a linear elastic +analysis. + +The linear elastic analysis +would determine the total + +stiffness and the yield +load of the bracket. + +Notice here we show the +displacements in red. + +Actually, these displacements +would be very small. + +And they are magnified +in this view graph. + +Another analysis now would be to +perform a plastic analysis, + +but assuming still small +deformations. + +This analysis would determine +sizes and shapes of the + +plastic zones. + +The displacements here +are still small. + +We have not shown them +at all actually here. + +They are very small, however. + +Then we might want to +go on to a large + +deformation plastic analysis. + +This analysis would determine +the ultimate load capacity of + +the bracket. + +And notice the displacements +are now large, they are + +actually large. + +Here, we have had small +displacement assumptions. + +Here, we have included the large +deformation effects as + +also shown on the view graph. + +For analysis, it is very good +to actually classify all the + +types of analysis that one +might want to perform. + +And the first category of +nonlinear analysis is the one + +that we call +Materially-nonlinear-only + +analysis, MNO analysis. + +In this analysis, we assume +that the displacements are + +infinitesimal, the strains +are infinitesimal. + +In other words, both +of these quantities + +are very, very small. + +And the stress-strain +relationship is nonlinear. + +So all nonlinearities lie, +really, in here, in the + +stress-strain relationship. + +Here, I'm showing a +schematic example. + +You're looking at a four-node +element that is subjected to + +the loads shown, and delta +is the displacement. + +Notice that delta/l +is very small. + +In fact, even this four is +already relatively large. + +We should really have here, +possibly, a two. + +So nonlinearity lies in the +material description. + +The material is an +elasto-plastic material, + +Young's modulus, E, yield +stress, sigma y and + +strain-hardening modulus, Et. + +As long as the stresses do not +exceed sigma y, we really have + +a linear analysis. + +So if you use a computer +program with an MNO + +formulation and you subject your +model to forces such that + +the stresses are below sigma +yield everywhere in the model, + +then you should really obtain +the linear analysis results. + +The next category of problems +is the one of large + +displacements, large rotations, +but small strains. + +Here, in other words, we still +keep the assumption of small + +strain, but we allow large + +displacements and large rotations. + +The stress-strain relations can +be linear or nonlinear. + +Schematically here, once again, +our four-node element. + +This four-node element now would +move, as shown, going + +through large displacements +and large rotations. + +But the strains in the element, +expressed by delta + +prime over l are still small. + +Once again, you may actually +want to make this 0.02. + +As long as the displacements are +very small, we have now, + +really, an MNO analysis. + +The third category of problems +is the one of large + +displacements, large rotations +and large strains. + +Here we have included all +kinematic nonlinearities. + +And the stress-strain relation +is probably also nonlinear + +because we are dealing +with large strains. + +As an example, we have, again, +our four-node element here + +moving as shown. + +Notice material fibers here, +displaced by a large amount, + +rotate and are also stretched +by a large amount. + +This, of course, is +the most general + +formulation of a problem. + +However, still not considering +any nonlinearities in the + +boundary conditions, +nonlinearities in the boundary + +conditions provide +contact problems. + +And here, we look schematically +at a simple + +contact problem. + +The four-node element, once +again, subjected to loads, + +there's a gap here between this +element and the spring. + +And as soon as this gap is +closed, the spring, of course, + +provides stiffness into the +system, the system being now + +the four-node element. + +And, well, that difference has +to be taken into account in + +the analysis. + +And there are procedures to +solve contact problems. + +This is, of course, a very +simple contact problem. + +But there are procedures to +solve contact problems. + +Contact problems are very +difficult problems to handle, + +particularly if you're dealing +with frictional effects. + +We will, in this course, in this +set of lectures, really + +not address contact problems, +except that, in the last + +lecture, we actually +look at one + +particular contact problem. + +We use a computer program for +the analysis of a contact + +problem there. + +Let's turn to an example +analysis. + +And I'd like to consider +with you, briefly, the + +analysis of a bracket. + +Here is a bracket of +the kind that we + +looked earlier at already. + +Notice the dimensions +are as shown. + +The thickness of the bracket +is one inch. + +And this bracket is going to +be loaded to large loads. + +We make a material assumption, +namely the one of an + +elasto-plastic material +with isotopic + +hardening as shown here. + +The yield stress +is 26,000 psi. + +Here you have the +Young's modulus. + +And here you have the +strain-hardening modulus. + +We use symmetry conditions to +analyze the bracket the same + +way as we would do it, of +course, in a linear analysis. + +And with the symmetry +conditions, we consider on + +this view graph just the lower +part of the bracket. + +You see a pin here, +rollers there. + +And we're using eight-node, +isopolymetric elements to + +model this part of +the bracket. + +We apply the load +as shown here. + +Notice no special considerations +to the hole + +which the load is applied. + +Our interest really lies in +predicting the stresses and + +strains in this region and to +also predict the overall + +collapse of the bracket. + +We will use three kinematic +formulations for the analysis. + +First of all, we use the +Material-nonlinear-only + +analysis assumption. + +In other words, small +displacements, small rotations + +and small strains are +assumed in the + +analysis of this bracket. + +Then we will perform an analysis +using the total + +Lagrangian formulation. + +We will discuss this formulation +quite extensively + +in later lectures +of the course. + +This formulation assumes large +displacements, large rotations + +and large strains +kinematically. + +Kinematically, these are +the assumptions. + +However, we will point out that +the material law that we + +are using, or the material law +description that we are using, + +is only applicable with this +formulation to small strains. + +So the overall analysis, using +this total Lagrangian + +formulation, is then only +applicable to model large + +displacements, large rotations, + +but only small strains. + +I get back to that just now. + +We will also use an updated +Lagrangian formulation which + +kinetically includes large +displacements, large rotations + +and large strains. + +And on the material model level, +we also include there + +large strain effects. + +So once again here, as +summarized on this view graph, + +the material used in conjunction +with the total + +Lagrangian formulation is +actually not applicable to + +large-strain situations, but +only to large displacements, + +rotation in small-strain +conditions. + +So once again, our total +analysis is only applicable to + +this kind of situation. + +Whereas, the updated Lagrangian +formulation does + +model, kinematically and on the +stress-strain level, large + +displacements, large rotations +and large strains. + +The analysis results obtained +are shown here. + +Notice we are plotting here +the force applied and the + +total deflection between points +of load application. + +The three analyses give us three +distinct curves at large + +displacements. + +But for small displacements, +of course, these curves are + +indistinguishable. + +Notice here we have about 10% +strain at point A. I will show + +you just now where point A is. + +The important point to notice +is that these are three + +distinct curves. + +They are distinct because +we have made different + +assumptions, kinematically +and on the + +stress-strain load level. + +We will talk about such +assumptions in the later + +lectures of this course. + +On this view graph, now you +see this point A, which I + +mentioned earlier. + +And you see also the original +mesh shown in dashed, black + +lines, and the deformed mesh, +shown in red, corresponding to + +a level of load of +12,000 pounds. + +I'd like to now look with you +at two animations regarding + +problems that show +nonlinearities typical of the + +nonlinearities that we are +talking about in this course. + +The first animation shows a +plate with a hole that is + +subjected to high +tensile forces. + +The plate undergoes plastic +deformations. + +And, in fact, the load becomes +so large that the plate + +basically ruptures. + +Let's look at this +animation now. + +Here we see one quarter +of the plate. + +The plate is subjected to a +uniformly distributed tensile + +load along its upper edge. + +For the quarter model of the +plate, symmetry boundary + +conditions are imposed along +the left vertical and lower + +horizontal edges. + +The time code given above +the plate gives the + +time of the load step. + +Also given is the load +applied at that time. + +However, note that we perform +a static analysis. + +Therefore, the time code merely +denotes a load level, + +as we will discuss +later in detail. + +Each time increment of one milli +corresponds to a load + +increment of 12.5 megapascal. + +We will increase the +load monotonically. + +The plate will become +plastic at the hole. + +And this plasticity will then +spread until, in essence, the + +plate ruptures. + +We used 288 eight-node plane +stress finite elements for the + +quarter of the plate. + +And we show to spread of +plasticity in the plate by + +darkening the areas +that are plastic. + +Here now you see the time +and load increasing. + +In the first load steps, the +plate remains elastic and the + +deformations are small. + +Now you see the first +plasticity + +developing near the hole. + +The plastic zone increases +rapidly as the higher load + +levels are reached until a large +portion of the plate is + +plastic and, in essence, the +maximum load-carrying capacity + +has been reached. + +We will consider the analysis +of this plate in more detail + +later in the course. + +The second animation shows a +frame that is subjected to + +forces such that the frame +undergoes very large + +displacements. + +Here we see the frame model, +using beam elements that we + +discuss later in the course. + +The frame is loaded, as shown, +by the force arrows. + +There are pin connections +at the points of load + +application. + +The frame is assumed to be of an +elastic material, hence, no + +plasticity is assumed to develop +or that the frame will + +be subjected to very large +displacements. + +The indicated loads will push +the top of the frame down and + +the bottom up to such an extent +that the points of load + +application cross over. + +You see above the frame +a time and a + +corresponding load level. + +This is, again, a +static analysis. + +And each time increment of one +corresponds merely to a load + +increment of 250 pounds. + +Here now, you see the +deformations of the frame + +develop as the load +is increased. + +The displacements are +very large at + +the higher load levels. + +Of course, this is only a +numerical experiment at the + +high load levels, but an +interesting one that indicates + +in a simple manner what +can all be done in + +finite element analysis. + +We will consider this problem +solution also in more detail + +later in the course. + +Let us now look at the +basic approach of + +an incremental solution. + +We consider a body, a structure +or solid subjected + +to force and displacement +boundary conditions that are + +changing, and we describe the +externally applied forces and + +the displacement boundary +conditions as + +a function of time. + +Schematically, here we show a +body, of course, supported as + +shown and subjected to a force +varying as a function of time + +and a prescribed displacement +varying as a function of time. + +The time variation of the force +is shown down here. + +And the time variation of the +prescribed displacement is + +shown here. + +Notice that here we have a +particular time point, T. And + +here we have a time point +T plus delta t. + +Here we have, similarly, the +time point T and here, also, + +the time point T plus delta t. + +Since we anticipate +nonlinearities, we use an + +incremental approach measured +in load steps or time steps. + +And this means that the loads, +the prescribed loads, the + +imposed loads and the prescribed +displacements, are + +discretized as a function +of time, as shown + +on this view graph. + +Notice here we have, at time +T, the impulse load TRI. + +This upper, superscript T means +at time T then delta t, + +in advance, time +T plus delta t. + +We would have, in other words, +T plus delta t ri. + +In other words this T would +now be replaced by T plus + +delta t and so on. + +This is how we are inputting +or prescribing the impulse + +loads and also the prescribed +displacements. + +When they apply forces and +displacements very slowly, + +meaning that the frequencies of +the loads are much smaller + +than the natural frequencies +of the structure, we have a + +static analysis. + +This, of course, means that the +periods of the loads are + +very long when measured +on the natural + +periods of the structure. + +In other words, you have a +spring and you apply a load + +that varies very slowly. + +And this means we have +a static analysis. + +If the load's very fast, and +by that we mean that the + +frequencies of the loads are +in the range of the natural + +frequency of the structure, +then we + +have a dynamic analysis. + +Let us look a bit closer at the + +meaning of the time variable. + +Time is a pseudo-variable, only +denoting the load level + +in nonlinear static analysis +with time-independent material + +properties. + +As an example. + +here we have a cantilever +subjected to a load, R, a tip + +load, R. And if we were to +perform a run, 1, in which we + +prescribe the loads +as shown here-- + +and notice, at time 1, a +load of 100, at time + +2, a load of 200-- + +delta t is equal to 1. + +If we were to perform this +analysis and, in addition, + +this analysis where delta t is +equal to 2 and the load at + +time 2 is equal to 100, the +load at time 4 is equal to + +200, then we would obtain +identically the same results + +in run 1 and run 2 because it's +a static analysis and the + +material properties are +time-independent. + +So in this particular case, +certainly, time is a + +pseudo-variable. + +And we can design +a time-stepping. + +We can design many different +time-stepping schemes using + +different time steps and +always obtain the same + +results, provided, at the end +of the first time step, we + +have the load 100 and at the end +of the second time step we + +have the load 200. + +However, time is an actual +variable in dynamic analysis + +and in nonlinear static analysis +with time-dependent + +material properties, for +example, when the material + +contains grid conditions. + +Now delta t must be chosen very +carefully with respect to + +the physics of the problem, with +respect to the numerical + +techniques used and the +costs involved. + +If delta t is not chosen +appropriately, you may have a + +very high cost for +the analysis. + +And on the other hand, you may, +with improper choice of + +delta t, also obtain +very bad results. + +So it is very important to +choose delta t judiciously for + +an accurate and cost-effective +analysis. + +At the end of each load or time +step, we need to satisfy + +the three basic requirements +of mechanics, equilibrium, + +compatibility and the +stress-strain law. + +These are the three fundamental +requirements to be + +satisfied in mechanics. + +This is achieved in finite +element analysis in an + +approximate manner using +finite elements by the + +application of the principle +of virtual work. + +Now there is a lot +of information + +on this view graph. + +And we don't have time in this +lecture to go into any depth. + +There is, of course, quite a bit +of mathematics that has to + +be introduced for the discussion +of all of what we + +see here on the view graph. + +And that's what we do in +the later lectures. + +I do not have time now to go +into these mathematics, but + +let us just very briefly +look at the basic + +procedure that we using. + +We are saying that, at any time +step, T plus delta t, the + +externally applied loads, the +vector of externally applied + +loads and this vector, includes +pressure loads. + +Concentrated loads and, in the +dynamic analysis also inertial + +forces, this vector must at any +time T plus delta t equal + +to the vector F at time T plus +delta t where this vector F + +corresponds to the internal +element stresses at time T + +plus delta t. + +We will talk in the later +lectures about how we + +calculate this vector +T plus delta tF. + +Of course, there are some very +important considerations in + +the proper calculation +of this vector F. + +Let us now assume that the +solution at time T is known. + +Hence, the stresses, at +time T, are known. + +The volume surface area and so +on, all of the information + +corresponding to the body +at time T is known. + +And we now want to obtain the +solution corresponding to time + +T plus delta t, that is for the +loads applied at time T + +plus delta t. + +Of course, this is +a typical step of + +the incremental solution. + +Once we have the solution for +time T plus delta t, we can + +use the same scheme to calculate +the solution for + +time T plus 2 delta +t and so on. + +For this purpose, we +solve, in static + +analysis, this set of equations. + +TK is a tangent stiffness +matrix of the system. + +Delta u is a vector of +increments in the nodal point + +displacements. + +On the right-hand side, we have +the externally applied + +loads corresponding to time T +plus delta t in this R vector. + +And here, TF corresponds to or +is the vector of nodal point + +forces that correspond to the +internal element stresses at + +time T. + +Notice this is an out-of-balance +load vector. + +And this out-of-balance load +vector gives us an increment + +in displacements. + +This increment in displacements +is added to the + +displacements at time T. And +that gives us a displacement + +vector corresponding to +time T plus delta t. + +Notice I have an approximation +sign there. + +This approximation sign is a +result of the fact that we + +obtained this set of equations +by linearization. + +We will talk about how these +equations are obtained in the + +later lectures. + +We will start from the basic +principle of virtual work and + +use continuum mechanics +considerations to derive, in a + +very consistent manner, +this set of equations. + +Of course, there are many +details involved. + +We will talk about the total +Lagrangian formulations, the + +updated Lagrangian +formulation, the + +Material-nonlinear-only +analysis, the details that go + +into these formulations +in terms of kinematic + +approximations, kinematic +approximations related to + +large displacements, large +rotations, large strains. + +We also will talk about the +constitutive relations that + +enter in this tangent stiffness +matrix and in this + +force vector and so on. + +Anyway, this set of equations +gives us an approximation to + +the displacements at time T plus +delta t because of the + +linearization process used to +arrive at these equations. + +And, more generally, we want +to solve this set of + +equations, tangent stiffness +matrix, still on the left-hand + +side, times a displacement +increment corresponding to the + +iteration, I. And on the +right-hand side, we have the + +load vector corresponding to the +loads at time T plus delta + +t and the nodal point force +vector corresponding to the + +internal element stresses at +time T plus delta t and at the + +end of iteration I minus 1. + +This is here the out-of-balance +load vector + +corresponding to the start +of iteration I. This + +out-of-balance load vector, +and with that tangent + +stiffness matrix, gives us an +increment in the nodal point + +displacement vector +corresponding to iteration I. + +We take this one, add it to +the previous displacements + +that we had already, namely +those corresponding to time T + +plus delta t at the end of +iteration I minus 1, and we + +obtain a better approximation to +the displacements at time T + +plus delta t. + +Notice, in this iteration, we +have initial conditions that + +I've given down here in +iteration I equal to 1. + +On the right-hand side we need, +of this equation here, + +we need this vector. + +And that vector is given by the +vector TF, the nodal point + +force vector corresponding to +the internal element stresses + +at time T. We also need initial +conditions on the + +displacement vector, and those +are given right here. + +Notice that, when I is equal +to 1, this set of equations + +reduces to the equations +that we had on the + +previous view graph. + +Once again, we will derive these +equations from basic + +continuum mechanics principles +in the later lectures. + +And we will also talk about +iterative schemes to + +accelerate the convergence +in the + +solution of these equations. + +This then brings me to the end +of what I wanted to discuss + +this you on the view graphs. + +I'd like to now turn to an +example solution, an + +interesting example solution. + +But, moreover, it displays the +kinds of nonlinearalities that + +we will be talking about in +this set of lectures. + +This example solution is +documented on slides. + +So let me walk over here and +put on the first slide. + +Here we show the structure +that we want to consider. + +It's a spherical shell subjected +to pressure loading. + +The material data for the +shell are given here. + +Notice we also include the mass +density because we will + +be talking about dynamic +analysis of + +this shell as well. + +We will also introduce an +imperfection of the shell. + +And that imperfection +is given down here. + +Notice it is given as a function +of the angle phi, + +which you see up here, as well +as a thickness, H, of the + +shell, the Legendre polynomial +given here and parameter data + +that we will be varying. + +First, we will consider a static +analysis of the shell + +and then the dynamic analysis +of the shell. + +On the next slide, now you see +the model that was used for + +the analysis of the shell, +twenty 8-node elements, + +axisymmetric elements subjected +to the pressure + +loading, and, we are modeling, +the pressure loading in + +deformation-dependent loading. + +That means that, as the shell +deforms, the pressure will + +remain perpendicular to +the shell surface + +to which it is applied. + +On the next slide now, we show +the first analysis results. + +On this axis, we plot P/PCR +where PCR is the buckling + +pressure of the shell, assuming +elastic conditions, + +and calculated using analytical +solution. + +On this axis, we plot the rate +of displacement of the shell + +at phi equal to zero. + +The dotted line here shows the +linear elastic solution to the + +shell problem. + +Notice that these dots, +of course, could + +be continued here. + +The total Lagrangian +formulation, which includes + +large displacement and large +rotation effects, gives us a + +buckling pressure of 0.98 PRC. + +A Material-nonlinear-only +analysis, including the + +elasto-plastic material +conditions, but not including, + +in other words, large +displacement, large rotation + +effects, gives us this +solution here. + +Notice that, of course, this MNO +analysis does not give us + +a proper bucking prediction +for the shell. + +To obtain the elastic-plastic +buckling load of the shell, we + +have to perform a total + +Lagrangian formulation solution. + +And we obtain this load level +here as the bucking pressure. + +This analysis was performed +with no + +imperfections on the shell. + +The next slide now shows +the results of the + +same kind of analyses. + +But at an imperfection of delta +0.1, notice here the + +linear analysis, denoted as E, +the Material-nonlinear-only + +analysis results, denoted as +EP, the large displacement, + +large rotation analysis +results. + +But assuming an elastic +condition for the shell, + +denoted as E, TL, TL standing +for total Lagrangian + +formulation and the +elasto-plastic large + +displacement solution given +here, the results given here + +and denoted as EP, TL. + +Notice that, because of the +imperfection, the load, the + +maximum load-carrying capacity +of the shell, is decreased. + +On the next slide now we show +the maximum load-carrying + +capacities for delta equal to +zero, delta equal to 0.1, + +delta equal to 0.2, delta +equal to 0.4. + +In each case, we have used the +total Lagrangian formulation + +including elasto-plastic +conditions. + +In other words, of course, we +had to include the large + +displacement effects in order to +pick up the proper buckling + +load or load-carrying capacity +of the shell, so these are the + +load-carrying capacities of +the shell for different + +imperfection levels. + +The next slide now shows the +results obtained using a + +dynamic analysis. + +At this time, we apply the +pressure instantaneously as a + +step load, constant in time. + +Notice we are plotting here now +mean displacement data of + +the shell and time +along this axis. + +The Etl solution results +are very close to + +the E solution results. + +I think you know now what +I mean by E and Etl. + +The E Ptl solution results +are quite close to + +the EP solution results. + +This means that the shell is +stable under this load + +application. + +In other words, there is no +buckling, no increase in + +deformations as time +progresses. + +The next slide now shows, as we +increase the imperfection + +level from delta equal to zero +to delta equal to 0.1, the + +displacements of the shell using +the E Ptl solution or + +formulation increase +with time. + +Therefore, the shell is unstable +under this pressure + +application. + +Of course, dynamic pressure +application, no. + +Notice the other solution +results are given here. + +Therefore, we now can play with +the imperfection level + +and with the load level in +order to estimate the + +load-carrying capacity of the +shell for each of these cases. + +And on this slide, you're +seeing for a constant + +imperfection level, we +increase the load + +applied to the shell. + +And you can see that, +at 0.4 PCR, the + +shell is still stable. + +At 0.5 PCR, the shell +is unstable. + +On the final slide now, we show +all the information that + +we have obtained in +the analysis. + +On this axis, we are plotting +the buckling load, on this + +axis, the amplitude +of imperfection. + +This curve here corresponds +to the static + +backing of the shell. + +And this curve corresponds +to the dynamic + +buckling of the shell. + +Of course, we could not discuss +all the details + +regarding these analyses +in this short time. + +Please refer to the study guide +in which you'll find a + +reference to the paper in which +we have discussed the + +details of these analyses. + +This then brings me to the +end of this lecture. + +And I hope you enjoy +the course. \ No newline at end of file diff --git a/WUTak0K4F-Q.txt b/WUTak0K4F-Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..0ecbd6abc507b2de48e502fc8052263430e209e0 --- /dev/null +++ b/WUTak0K4F-Q.txt @@ -0,0 +1,179 @@ +align:start position:0% + +you know for me experimental physics is + + align:start position:0% +you know for me experimental physics is + + + align:start position:0% +you know for me experimental physics is +a true joy I really love what I do I do + + align:start position:0% +a true joy I really love what I do I do + + + align:start position:0% +a true joy I really love what I do I do +neutrino physics + + align:start position:0% +neutrino physics + + + align:start position:0% +neutrino physics +I'm experimentalist I think it is + + align:start position:0% +I'm experimentalist I think it is + + + align:start position:0% +I'm experimentalist I think it is +absolutely fantastic and so I believe + + align:start position:0% +absolutely fantastic and so I believe + + + align:start position:0% +absolutely fantastic and so I believe +that lamps should be really happy places + + align:start position:0% +that lamps should be really happy places + + + align:start position:0% +that lamps should be really happy places +and I want the students to really find + + align:start position:0% +and I want the students to really find + + + align:start position:0% +and I want the students to really find +what they're doing to be really + + align:start position:0% +what they're doing to be really + + + align:start position:0% +what they're doing to be really +interesting to really be something that + + align:start position:0% +interesting to really be something that + + + align:start position:0% +interesting to really be something that +they care about and and so that's the + + align:start position:0% +they care about and and so that's the + + + align:start position:0% +they care about and and so that's the +approach that I like to take when + + align:start position:0% +approach that I like to take when + + + align:start position:0% +approach that I like to take when +teaching junior lab I don't believe in + + align:start position:0% +teaching junior lab I don't believe in + + + align:start position:0% +teaching junior lab I don't believe in +this you break them down to build them + + align:start position:0% +this you break them down to build them + + + align:start position:0% +this you break them down to build them +back up again I think that that that + + align:start position:0% +back up again I think that that that + + + align:start position:0% +back up again I think that that that +doesn't really work you know I really + + align:start position:0% +doesn't really work you know I really + + + align:start position:0% +doesn't really work you know I really +think that what you do is you very + + align:start position:0% +think that what you do is you very + + + align:start position:0% +think that what you do is you very +gently lead people and shape people you + + align:start position:0% +gently lead people and shape people you + + + align:start position:0% +gently lead people and shape people you +have them trust you so that the comments + + align:start position:0% +have them trust you so that the comments + + + align:start position:0% +have them trust you so that the comments +that you're making are not taken wrong + + align:start position:0% +that you're making are not taken wrong + + + align:start position:0% +that you're making are not taken wrong +you know that they understand that + + align:start position:0% +you know that they understand that + + + align:start position:0% +you know that they understand that +that's to make them a better physicist + + align:start position:0% +that's to make them a better physicist + + + align:start position:0% +that's to make them a better physicist +and and I think that's very important so + + align:start position:0% +and and I think that's very important so + + + align:start position:0% +and and I think that's very important so +that's sort of my approach \ No newline at end of file diff --git a/WWZ_CeiRnIo.txt b/WWZ_CeiRnIo.txt new file mode 100644 index 0000000000000000000000000000000000000000..781254b66e395188ef1a4be8d8133d343c9af6d4 --- /dev/null +++ b/WWZ_CeiRnIo.txt @@ -0,0 +1,12171 @@ +align:start position:0% + +we'll continue our discussion of the + + align:start position:0% +we'll continue our discussion of the + + + align:start position:0% +we'll continue our discussion of the +riemann integral so let me just recall a + + align:start position:0% +riemann integral so let me just recall a + + + align:start position:0% +riemann integral so let me just recall a +few uh + + align:start position:0% + + + + align:start position:0% + +bits of notation from last time and then + + align:start position:0% +bits of notation from last time and then + + + align:start position:0% +bits of notation from last time and then +also the main result that we proved at + + align:start position:0% +also the main result that we proved at + + + align:start position:0% +also the main result that we proved at +the end of last class + + align:start position:0% +the end of last class + + + align:start position:0% +the end of last class +so + + align:start position:0% + + + + align:start position:0% + +we had partitions + + align:start position:0% +we had partitions + + + align:start position:0% +we had partitions +which are just finite sets + + align:start position:0% + + + + align:start position:0% + +so here + + align:start position:0% +so here + + + align:start position:0% +so here +a is less than b and we're looking at an + + align:start position:0% +a is less than b and we're looking at an + + + align:start position:0% +a is less than b and we're looking at an +interval a b + + align:start position:0% +interval a b + + + align:start position:0% +interval a b +partitions they're just finite sets + + align:start position:0% +partitions they're just finite sets + + + align:start position:0% +partitions they're just finite sets +of a b + + align:start position:0% +of a b + + + align:start position:0% +of a b +and then we also had tags which were um + + align:start position:0% +and then we also had tags which were um + + + align:start position:0% +and then we also had tags which were um +finite sets as well + + align:start position:0% +finite sets as well + + + align:start position:0% +finite sets as well +with + + align:start position:0% + + + + align:start position:0% + +c1 between + + align:start position:0% +c1 between + + + align:start position:0% +c1 between +x naught and x1 + + align:start position:0% +x naught and x1 + + + align:start position:0% +x naught and x1 +which is less than or equal to xc2 which + + align:start position:0% +which is less than or equal to xc2 which + + + align:start position:0% +which is less than or equal to xc2 which +is + + align:start position:0% +is + + + align:start position:0% +is +less than or equal to x2 + + align:start position:0% +less than or equal to x2 + + + align:start position:0% +less than or equal to x2 +and so on + + align:start position:0% + + + + align:start position:0% + +and we call these + + align:start position:0% + + + + align:start position:0% + +tag partitions + + align:start position:0% + + + + align:start position:0% + +and we also had + + align:start position:0% +and we also had + + + align:start position:0% +and we also had +the norm + + align:start position:0% +the norm + + + align:start position:0% +the norm +of a partition + + align:start position:0% +of a partition + + + align:start position:0% +of a partition +this is the max + + align:start position:0% +this is the max + + + align:start position:0% +this is the max +of + + align:start position:0% +of + + + align:start position:0% +of +so we think of partitions as being + + align:start position:0% +so we think of partitions as being + + + align:start position:0% +so we think of partitions as being +as breaking up the interval a b up into + + align:start position:0% +as breaking up the interval a b up into + + + align:start position:0% +as breaking up the interval a b up into +smaller + + align:start position:0% +smaller + + + align:start position:0% +smaller +sub intervals + + align:start position:0% +sub intervals + + + align:start position:0% +sub intervals +x x0 to x1 + + align:start position:0% +x x0 to x1 + + + align:start position:0% +x x0 to x1 +um + + align:start position:0% + + + + align:start position:0% + +i got to get a different piece of chalk + + align:start position:0% +i got to get a different piece of chalk + + + align:start position:0% +i got to get a different piece of chalk +this one is going psychedelic on me + + align:start position:0% + + + + align:start position:0% + +and then the exceed ones are just + + align:start position:0% +and then the exceed ones are just + + + align:start position:0% +and then the exceed ones are just +points + + align:start position:0% +points + + + align:start position:0% +points +chosen uh in these smaller sub-intervals + + align:start position:0% +chosen uh in these smaller sub-intervals + + + align:start position:0% +chosen uh in these smaller sub-intervals +the norm of a partition is the length of + + align:start position:0% +the norm of a partition is the length of + + + align:start position:0% +the norm of a partition is the length of +the largest sub-interval + + align:start position:0% + + + + align:start position:0% + +and then we have the riemann sum + + align:start position:0% +and then we have the riemann sum + + + align:start position:0% +and then we have the riemann sum +associated to + + align:start position:0% +associated to + + + align:start position:0% +associated to +partition + + align:start position:0% +partition + + + align:start position:0% +partition +tag partition + + align:start position:0% +tag partition + + + align:start position:0% +tag partition +xc + + align:start position:0% +xc + + + align:start position:0% +xc +which is the sum from + + align:start position:0% +which is the sum from + + + align:start position:0% +which is the sum from +j equals 1 to n + + align:start position:0% +j equals 1 to n + + + align:start position:0% +j equals 1 to n +f of x c + + align:start position:0% +f of x c + + + align:start position:0% +f of x c +j + + align:start position:0% + + + + align:start position:0% + +x j minus xj minus 1. + + align:start position:0% +x j minus xj minus 1. + + + align:start position:0% +x j minus xj minus 1. +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this uh just + + align:start position:0% + + + + align:start position:0% + +some notation from last time and then + + align:start position:0% +some notation from last time and then + + + align:start position:0% +some notation from last time and then +what did we prove + + align:start position:0% + + + + align:start position:0% + +prove the following theorem + + align:start position:0% +prove the following theorem + + + align:start position:0% +prove the following theorem +which is the existence for the riemann + + align:start position:0% +which is the existence for the riemann + + + align:start position:0% +which is the existence for the riemann +integral + + align:start position:0% +integral + + + align:start position:0% +integral +which is + + align:start position:0% +which is + + + align:start position:0% +which is +the following that + + align:start position:0% + + + + align:start position:0% + +for all continuous functions on a b + + align:start position:0% +for all continuous functions on a b + + + align:start position:0% +for all continuous functions on a b +there exists + + align:start position:0% + + + + align:start position:0% + +a unique number + + align:start position:0% +a unique number + + + align:start position:0% +a unique number +which we denote integral a b f + + align:start position:0% + + + + align:start position:0% + +with the property that + + align:start position:0% + + + + align:start position:0% + +with the following property that if i + + align:start position:0% +with the following property that if i + + + align:start position:0% +with the following property that if i +take any sequence of tag partitions with + + align:start position:0% +take any sequence of tag partitions with + + + align:start position:0% +take any sequence of tag partitions with +norm going to zero so this is the + + align:start position:0% +norm going to zero so this is the + + + align:start position:0% +norm going to zero so this is the +partitions are getting + + align:start position:0% +partitions are getting + + + align:start position:0% +partitions are getting +finer and finer + + align:start position:0% + + + + align:start position:0% + +we're all sequence of tagged partitions + + align:start position:0% + + + + align:start position:0% + +with norms going to zero + + align:start position:0% + + + + align:start position:0% + +we have that + + align:start position:0% + + + + align:start position:0% + +the associated riemann sums + + align:start position:0% +the associated riemann sums + + + align:start position:0% +the associated riemann sums +this sequence converges so this is now a + + align:start position:0% +this sequence converges so this is now a + + + align:start position:0% +this sequence converges so this is now a +sequence of real numbers + + align:start position:0% + + + + align:start position:0% + +and equals this + + align:start position:0% + + + + align:start position:0% + +number uh integral abf okay no matter + + align:start position:0% +number uh integral abf okay no matter + + + align:start position:0% +number uh integral abf okay no matter +what sequence of tag partitions i take + + align:start position:0% +what sequence of tag partitions i take + + + align:start position:0% +what sequence of tag partitions i take +with norms converging to zero + + align:start position:0% +with norms converging to zero + + + align:start position:0% +with norms converging to zero +um + + align:start position:0% +um + + + align:start position:0% +um +the riemann sums converge + + align:start position:0% +the riemann sums converge + + + align:start position:0% +the riemann sums converge +to this number which we call the riemann + + align:start position:0% +to this number which we call the riemann + + + align:start position:0% +to this number which we call the riemann +integral of f + + align:start position:0% +integral of f + + + align:start position:0% +integral of f +that + + align:start position:0% +that + + + align:start position:0% +that +i think the very last thing we proved + + align:start position:0% +i think the very last thing we proved + + + align:start position:0% +i think the very last thing we proved +was that + + align:start position:0% +was that + + + align:start position:0% +was that +the riemann integral is linear + + align:start position:0% +the riemann integral is linear + + + align:start position:0% +the riemann integral is linear +the integral of the sum is the sum of + + align:start position:0% +the integral of the sum is the sum of + + + align:start position:0% +the integral of the sum is the sum of +the integrals + + align:start position:0% +the integrals + + + align:start position:0% +the integrals +and if i multiply a continuous function + + align:start position:0% +and if i multiply a continuous function + + + align:start position:0% +and if i multiply a continuous function +by + + align:start position:0% +by + + + align:start position:0% +by +a scalar then the scalar pulls out + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +so now we're going to discuss some + + align:start position:0% +so now we're going to discuss some + + + align:start position:0% +so now we're going to discuss some +properties of the riemann integral + + align:start position:0% +properties of the riemann integral + + + align:start position:0% +properties of the riemann integral +so + + align:start position:0% +so + + + align:start position:0% +so +the next is that + + align:start position:0% + + + + align:start position:0% + +in some sense + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +area of the union if you like is the sum + + align:start position:0% +area of the union if you like is the sum + + + align:start position:0% +area of the union if you like is the sum +of the areas if we think of the integral + + align:start position:0% +of the areas if we think of the integral + + + align:start position:0% +of the areas if we think of the integral +as being + + align:start position:0% + + + + align:start position:0% + +the area underneath the curve + + align:start position:0% +the area underneath the curve + + + align:start position:0% +the area underneath the curve +so + + align:start position:0% + + + + align:start position:0% + +this next property is the additivity of + + align:start position:0% +this next property is the additivity of + + + align:start position:0% +this next property is the additivity of +the riemann integral which states the + + align:start position:0% +the riemann integral which states the + + + align:start position:0% +the riemann integral which states the +following + + align:start position:0% +following + + + align:start position:0% +following +if f is in c + + align:start position:0% + + + + align:start position:0% + +a b + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +i take a point between c and b + + align:start position:0% +i take a point between c and b + + + align:start position:0% +i take a point between c and b +then + + align:start position:0% +then + + + align:start position:0% +then +the integral from a to b of f is equal + + align:start position:0% +the integral from a to b of f is equal + + + align:start position:0% +the integral from a to b of f is equal +to the integral from a to c + + align:start position:0% +to the integral from a to c + + + align:start position:0% +to the integral from a to c +of f plus the integral from c + + align:start position:0% + + + + align:start position:0% + +to b + + align:start position:0% +to b + + + align:start position:0% +to b +of f + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +prove it again + + align:start position:0% +prove it again + + + align:start position:0% +prove it again +all we know about + + align:start position:0% +all we know about + + + align:start position:0% +all we know about +these numbers is that they satisfy this + + align:start position:0% +these numbers is that they satisfy this + + + align:start position:0% +these numbers is that they satisfy this +property so what we'll do is + + align:start position:0% +property so what we'll do is + + + align:start position:0% +property so what we'll do is +we'll take a sequence of tagged + + align:start position:0% +we'll take a sequence of tagged + + + align:start position:0% +we'll take a sequence of tagged +partitions + + align:start position:0% +partitions + + + align:start position:0% +partitions +of ac converging to this integral + + align:start position:0% +of ac converging to this integral + + + align:start position:0% +of ac converging to this integral +in a sequence of tag partitions + + align:start position:0% +in a sequence of tag partitions + + + align:start position:0% +in a sequence of tag partitions +uh from c to b + + align:start position:0% +uh from c to b + + + align:start position:0% +uh from c to b +converging to this integral uh when i + + align:start position:0% +converging to this integral uh when i + + + align:start position:0% +converging to this integral uh when i +stick them into the riemann sums + + align:start position:0% +stick them into the riemann sums + + + align:start position:0% +stick them into the riemann sums +but then when i take the union of those + + align:start position:0% +but then when i take the union of those + + + align:start position:0% +but then when i take the union of those +tag partitions i get a partition of a b + + align:start position:0% +tag partitions i get a partition of a b + + + align:start position:0% +tag partitions i get a partition of a b +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and uh which will approach the integral + + align:start position:0% +and uh which will approach the integral + + + align:start position:0% +and uh which will approach the integral +of a b that's the + + align:start position:0% +of a b that's the + + + align:start position:0% +of a b that's the +basic + + align:start position:0% +basic + + + align:start position:0% +basic +the basic + + align:start position:0% +the basic + + + align:start position:0% +the basic +intuition and of course + + align:start position:0% + + + + align:start position:0% + +what was i saying a minute ago about + + align:start position:0% + + + + align:start position:0% + +the area of the union being + + align:start position:0% +the area of the union being + + + align:start position:0% +the area of the union being +some of the areas well again like i said + + align:start position:0% +some of the areas well again like i said + + + align:start position:0% +some of the areas well again like i said +if we think of + + align:start position:0% +if we think of + + + align:start position:0% +if we think of +the riemann integral as being the area + + align:start position:0% +the riemann integral as being the area + + + align:start position:0% +the riemann integral as being the area +underneath the curve then this says that + + align:start position:0% +underneath the curve then this says that + + + align:start position:0% +underneath the curve then this says that +the area + + align:start position:0% +the area + + + align:start position:0% +the area +from a to b underneath the curve is + + align:start position:0% +from a to b underneath the curve is + + + align:start position:0% +from a to b underneath the curve is +equal to the area underneath the curve + + align:start position:0% +equal to the area underneath the curve + + + align:start position:0% +equal to the area underneath the curve +from a to c plus the area underneath the + + align:start position:0% +from a to c plus the area underneath the + + + align:start position:0% +from a to c plus the area underneath the +curve from c to b + + align:start position:0% +curve from c to b + + + align:start position:0% +curve from c to b +okay + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +let's take + + align:start position:0% + + + + align:start position:0% + +when we use the right notation here + + align:start position:0% +when we use the right notation here + + + align:start position:0% +when we use the right notation here +let's uh + + align:start position:0% + + + + align:start position:0% + +take two partitions let + + align:start position:0% + + + + align:start position:0% + +be a sequence of partitions + + align:start position:0% + + + + align:start position:0% + +so a sequence of tag partitions i should + + align:start position:0% +so a sequence of tag partitions i should + + + align:start position:0% +so a sequence of tag partitions i should +say + + align:start position:0% +say + + + align:start position:0% +say +of + + align:start position:0% +of + + + align:start position:0% +of +ac + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% + + + + align:start position:0% + +norm of this partition + + align:start position:0% +norm of this partition + + + align:start position:0% +norm of this partition +goes to zero so this is a a now a + + align:start position:0% +goes to zero so this is a a now a + + + align:start position:0% +goes to zero so this is a a now a +partition + + align:start position:0% + + + + align:start position:0% + +of ac + + align:start position:0% +of ac + + + align:start position:0% +of ac +and then we'll take another sequence of + + align:start position:0% +and then we'll take another sequence of + + + align:start position:0% +and then we'll take another sequence of +tag partitions of cb + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +for those + + align:start position:0% +for those + + + align:start position:0% +for those +watching at home wondering what these + + align:start position:0% +watching at home wondering what these + + + align:start position:0% +watching at home wondering what these +letters are it's the greek ada that's + + align:start position:0% +letters are it's the greek ada that's + + + align:start position:0% +letters are it's the greek ada that's +the greek zeta + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +we have + + align:start position:0% +we have + + + align:start position:0% +we have +sequence of partitions + + align:start position:0% +sequence of partitions + + + align:start position:0% +sequence of partitions +of ac these are the y and eta and then + + align:start position:0% +of ac these are the y and eta and then + + + align:start position:0% +of ac these are the y and eta and then +we also have a sequence of partitions of + + align:start position:0% +we also have a sequence of partitions of + + + align:start position:0% +we also have a sequence of partitions of +c b + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% +such that + + + align:start position:0% +such that +the + + align:start position:0% + + + + align:start position:0% + +norm of these guys + + align:start position:0% +norm of these guys + + + align:start position:0% +norm of these guys +goes to 0 as well as r goes to infinity + + align:start position:0% +goes to 0 as well as r goes to infinity + + + align:start position:0% +goes to 0 as well as r goes to infinity +okay so now if i have a partition of a c + + align:start position:0% +okay so now if i have a partition of a c + + + align:start position:0% +okay so now if i have a partition of a c +in a partition of c b + + align:start position:0% +in a partition of c b + + + align:start position:0% +in a partition of c b +if i take their union + + align:start position:0% +if i take their union + + + align:start position:0% +if i take their union +then i will get a partition of a b + + align:start position:0% + + + + align:start position:0% + +this will be the union of these guys + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +it's easy to see that this is now a + + align:start position:0% + + + + align:start position:0% + +a sequence of tagged partitions of a b + + align:start position:0% +a sequence of tagged partitions of a b + + + align:start position:0% +a sequence of tagged partitions of a b +so + + align:start position:0% + + + + align:start position:0% + +and moreover so + + align:start position:0% +and moreover so + + + align:start position:0% +and moreover so +what is the norm of uh this new tag + + align:start position:0% +what is the norm of uh this new tag + + + align:start position:0% +what is the norm of uh this new tag +partition what is the maximum length of + + align:start position:0% +partition what is the maximum length of + + + align:start position:0% +partition what is the maximum length of +the sub intervals well it's just going + + align:start position:0% +the sub intervals well it's just going + + + align:start position:0% +the sub intervals well it's just going +to be the maximum of the + + align:start position:0% +to be the maximum of the + + + align:start position:0% +to be the maximum of the +norms of y and z right so + + align:start position:0% + + + + align:start position:0% + +and note + + align:start position:0% +and note + + + align:start position:0% +and note +that + + align:start position:0% + + + + align:start position:0% + +the norm of x so bar this is equal to + + align:start position:0% +the norm of x so bar this is equal to + + + align:start position:0% +the norm of x so bar this is equal to +the maximum + + align:start position:0% +the maximum + + + align:start position:0% +the maximum +of the norm of y + + align:start position:0% + + + + align:start position:0% + +r + + align:start position:0% + + + + align:start position:0% + +and the norm of z are and since both of + + align:start position:0% +and the norm of z are and since both of + + + align:start position:0% +and the norm of z are and since both of +these converges to zero the maximum of + + align:start position:0% +these converges to zero the maximum of + + + align:start position:0% +these converges to zero the maximum of +them also converges to zero + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so now we just put this all together + + align:start position:0% + + + + align:start position:0% + +so by this theorem + + align:start position:0% + + + + align:start position:0% + +what do we know we know that + + align:start position:0% +what do we know we know that + + + align:start position:0% +what do we know we know that +the riemann sum associated to + + align:start position:0% + + + + align:start position:0% + +this converges to the integral a b + + align:start position:0% +this converges to the integral a b + + + align:start position:0% +this converges to the integral a b +of f + + align:start position:0% +of f + + + align:start position:0% +of f +the riemann sum associated to + + align:start position:0% + + + + align:start position:0% + +this sequence of tag partitions + + align:start position:0% +this sequence of tag partitions + + + align:start position:0% +this sequence of tag partitions +converges to + + align:start position:0% + + + + align:start position:0% + +now ac f + + align:start position:0% +now ac f + + + align:start position:0% +now ac f +and then + + align:start position:0% + + + + align:start position:0% + +this sequence of + + align:start position:0% +this sequence of + + + align:start position:0% +this sequence of +riemann sums associated to these tag + + align:start position:0% +riemann sums associated to these tag + + + align:start position:0% +riemann sums associated to these tag +partitions + + align:start position:0% +partitions + + + align:start position:0% +partitions +converge to + + align:start position:0% +converge to + + + align:start position:0% +converge to +cbf + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and now we just use the fact that taking + + align:start position:0% +and now we just use the fact that taking + + + align:start position:0% +and now we just use the fact that taking +a riemann sum is uh + + align:start position:0% + + + + align:start position:0% + +island is uh additive right + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +the riemann sum + + align:start position:0% + + + + align:start position:0% + +associated to this partition which is + + align:start position:0% +associated to this partition which is + + + align:start position:0% +associated to this partition which is +just a union of these partitions + + align:start position:0% + + + + align:start position:0% + +is equal to + + align:start position:0% + + + + align:start position:0% + +this implies taking the limit as r goes + + align:start position:0% +this implies taking the limit as r goes + + + align:start position:0% +this implies taking the limit as r goes +to infinity the left hand side as i + + align:start position:0% +to infinity the left hand side as i + + + align:start position:0% +to infinity the left hand side as i +wrote down here converges to + + align:start position:0% +wrote down here converges to + + + align:start position:0% +wrote down here converges to +a b f + + align:start position:0% +a b f + + + align:start position:0% +a b f +and then the right hand side the sum the + + align:start position:0% +and then the right hand side the sum the + + + align:start position:0% +and then the right hand side the sum the +limit of the sum is the sum of the + + align:start position:0% +limit of the sum is the sum of the + + + align:start position:0% +limit of the sum is the sum of the +limits so this converges to + + align:start position:0% +limits so this converges to + + + align:start position:0% +limits so this converges to +ac f + + align:start position:0% +ac f + + + align:start position:0% +ac f +and then the right + + align:start position:0% +and then the right + + + align:start position:0% +and then the right +thing here converges to + + align:start position:0% +thing here converges to + + + align:start position:0% +thing here converges to +the second thing here converges to the + + align:start position:0% +the second thing here converges to the + + + align:start position:0% +the second thing here converges to the +integral from c to b at f + + align:start position:0% +integral from c to b at f + + + align:start position:0% +integral from c to b at f +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's it so really um + + align:start position:0% +and that's it so really um + + + align:start position:0% +and that's it so really um +the fact that the integral is additive + + align:start position:0% +the fact that the integral is additive + + + align:start position:0% +the fact that the integral is additive +uh follows from + + align:start position:0% + + + + align:start position:0% + +the simple fact that kind of uh riemann + + align:start position:0% +the simple fact that kind of uh riemann + + + align:start position:0% +the simple fact that kind of uh riemann +sums are additive okay + + align:start position:0% + + + + align:start position:0% + +and the fact that limits respect + + align:start position:0% +and the fact that limits respect + + + align:start position:0% +and the fact that limits respect +algebraic operations the the + + align:start position:0% +algebraic operations the the + + + align:start position:0% +algebraic operations the the +limit of the sum is the sum of the + + align:start position:0% +limit of the sum is the sum of the + + + align:start position:0% +limit of the sum is the sum of the +limits + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right so um + + align:start position:0% +all right so um + + + align:start position:0% +all right so um +the riemann integral is additive this is + + align:start position:0% +the riemann integral is additive this is + + + align:start position:0% +the riemann integral is additive this is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and also linear so we see that + + align:start position:0% +and also linear so we see that + + + align:start position:0% +and also linear so we see that +the riemann integral is something that + + align:start position:0% +the riemann integral is something that + + + align:start position:0% +the riemann integral is something that +respects + + align:start position:0% +respects + + + align:start position:0% +respects +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +um algebraic operations + + align:start position:0% +um algebraic operations + + + align:start position:0% +um algebraic operations +with respect to the + + align:start position:0% +with respect to the + + + align:start position:0% +with respect to the +real numbers namely adding and + + align:start position:0% + + + + align:start position:0% + +scalar multiplication + + align:start position:0% + + + + align:start position:0% + +and it sort of respects + + align:start position:0% + + + + align:start position:0% + +i guess what you could say um + + align:start position:0% +i guess what you could say um + + + align:start position:0% +i guess what you could say um +topological uh considerations or not + + align:start position:0% +topological uh considerations or not + + + align:start position:0% +topological uh considerations or not +really topological but + + align:start position:0% +really topological but + + + align:start position:0% +really topological but +um + + align:start position:0% + + + + align:start position:0% + +this additive property is is a very + + align:start position:0% +this additive property is is a very + + + align:start position:0% +this additive property is is a very +natural property um what am i getting at + + align:start position:0% +natural property um what am i getting at + + + align:start position:0% +natural property um what am i getting at +here so now one could ask how does um + + align:start position:0% +here so now one could ask how does um + + + align:start position:0% +here so now one could ask how does um +the integral + + align:start position:0% +the integral + + + align:start position:0% +the integral +interact with inequalities so this is + + align:start position:0% +interact with inequalities so this is + + + align:start position:0% +interact with inequalities so this is +something we ask about uh all limits + + align:start position:0% +something we ask about uh all limits + + + align:start position:0% +something we ask about uh all limits +right + + align:start position:0% +right + + + align:start position:0% +right +at least limits of sequences that we saw + + align:start position:0% +at least limits of sequences that we saw + + + align:start position:0% +at least limits of sequences that we saw +you know if one sequence lies below + + align:start position:0% +you know if one sequence lies below + + + align:start position:0% +you know if one sequence lies below +another one + + align:start position:0% +another one + + + align:start position:0% +another one +taking limits respects that okay + + align:start position:0% + + + + align:start position:0% + +of course that's not true for the + + align:start position:0% +of course that's not true for the + + + align:start position:0% +of course that's not true for the +derivative i can have two functions one + + align:start position:0% +derivative i can have two functions one + + + align:start position:0% +derivative i can have two functions one +bigger than the other and + + align:start position:0% +bigger than the other and + + + align:start position:0% +bigger than the other and +the second derivative and the derivative + + align:start position:0% +the second derivative and the derivative + + + align:start position:0% +the second derivative and the derivative +of the smaller one be bigger than the + + align:start position:0% +of the smaller one be bigger than the + + + align:start position:0% +of the smaller one be bigger than the +derivative of the first one + + align:start position:0% +derivative of the first one + + + align:start position:0% +derivative of the first one +um + + align:start position:0% +um + + + align:start position:0% +um +but so one can ask the question let's + + align:start position:0% +but so one can ask the question let's + + + align:start position:0% +but so one can ask the question let's +suppose i have two functions one smaller + + align:start position:0% +suppose i have two functions one smaller + + + align:start position:0% +suppose i have two functions one smaller +than the other + + align:start position:0% + + + + align:start position:0% + +what is the uh + + align:start position:0% +what is the uh + + + align:start position:0% +what is the uh +what is the um + + align:start position:0% + + + + align:start position:0% + +what's the relationship between the + + align:start position:0% +what's the relationship between the + + + align:start position:0% +what's the relationship between the +integrals + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +f and g + + align:start position:0% +f and g + + + align:start position:0% +f and g +are now two continuous functions + + align:start position:0% +are now two continuous functions + + + align:start position:0% +are now two continuous functions +on a b + + align:start position:0% +on a b + + + align:start position:0% +on a b +so then the first + + align:start position:0% + + + + align:start position:0% + +part of this theorem is that + + align:start position:0% +part of this theorem is that + + + align:start position:0% +part of this theorem is that +if for all x + + align:start position:0% +if for all x + + + align:start position:0% +if for all x +and a b + + align:start position:0% + + + + align:start position:0% + +f of x is less than or equal to g of x + + align:start position:0% +f of x is less than or equal to g of x + + + align:start position:0% +f of x is less than or equal to g of x +then + + align:start position:0% + + + + align:start position:0% + +the integral from a b of f is less than + + align:start position:0% +the integral from a b of f is less than + + + align:start position:0% +the integral from a b of f is less than +or equal to the integral from a b of g + + align:start position:0% +or equal to the integral from a b of g + + + align:start position:0% +or equal to the integral from a b of g +all right and this is kind of + + align:start position:0% +all right and this is kind of + + + align:start position:0% +all right and this is kind of +understandable i mean again if we think + + align:start position:0% +understandable i mean again if we think + + + align:start position:0% +understandable i mean again if we think +of the integral as being a theory of the + + align:start position:0% +of the integral as being a theory of the + + + align:start position:0% +of the integral as being a theory of the +area underneath the curve right if i + + align:start position:0% +area underneath the curve right if i + + + align:start position:0% +area underneath the curve right if i +have one function sitting above another + + align:start position:0% +have one function sitting above another + + + align:start position:0% +have one function sitting above another +function then the area should be + + align:start position:0% +function then the area should be + + + align:start position:0% +function then the area should be +uh bigger than the area of the smaller + + align:start position:0% +uh bigger than the area of the smaller + + + align:start position:0% +uh bigger than the area of the smaller +one + + align:start position:0% +one + + + align:start position:0% +one +the the curve which sits below + + align:start position:0% +the the curve which sits below + + + align:start position:0% +the the curve which sits below +the first one + + align:start position:0% +the first one + + + align:start position:0% +the first one +and + + align:start position:0% + + + + align:start position:0% + +now um + + align:start position:0% +now um + + + align:start position:0% +now um +the riemann integral is a limit of + + align:start position:0% +the riemann integral is a limit of + + + align:start position:0% +the riemann integral is a limit of +sums + + align:start position:0% +sums + + + align:start position:0% +sums +in in some sense and a limit of certain + + align:start position:0% +in in some sense and a limit of certain + + + align:start position:0% +in in some sense and a limit of certain +uh sums involving f + + align:start position:0% +uh sums involving f + + + align:start position:0% +uh sums involving f +and + + align:start position:0% +and + + + align:start position:0% +and +what + + align:start position:0% +what + + + align:start position:0% +what +so + + align:start position:0% +so + + + align:start position:0% +so +we do have this relationship uh + + align:start position:0% +we do have this relationship uh + + + align:start position:0% +we do have this relationship uh +involving + + align:start position:0% +involving + + + align:start position:0% +involving +um + + align:start position:0% +um + + + align:start position:0% +um +sums and absolute values with the + + align:start position:0% +sums and absolute values with the + + + align:start position:0% +sums and absolute values with the +triangle inequality which says the + + align:start position:0% +triangle inequality which says the + + + align:start position:0% +triangle inequality which says the +absolute value of the sum is less than + + align:start position:0% +absolute value of the sum is less than + + + align:start position:0% +absolute value of the sum is less than +or equal to the sum of the absolute + + align:start position:0% +or equal to the sum of the absolute + + + align:start position:0% +or equal to the sum of the absolute +values + + align:start position:0% +values + + + align:start position:0% +values +and if you think of the integral as + + align:start position:0% +and if you think of the integral as + + + align:start position:0% +and if you think of the integral as +being essentially in + + align:start position:0% +being essentially in + + + align:start position:0% +being essentially in +a limit of sums or if you like a + + align:start position:0% +a limit of sums or if you like a + + + align:start position:0% +a limit of sums or if you like a +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +sum + + align:start position:0% + + + + align:start position:0% + +then you should expect that the integral + + align:start position:0% +then you should expect that the integral + + + align:start position:0% +then you should expect that the integral +the absolute value of the integral is + + align:start position:0% +the absolute value of the integral is + + + align:start position:0% +the absolute value of the integral is +less than or equal to the integral of + + align:start position:0% +less than or equal to the integral of + + + align:start position:0% +less than or equal to the integral of +the absolute value and that's indeed + + align:start position:0% +the absolute value and that's indeed + + + align:start position:0% +the absolute value and that's indeed +what we have + + align:start position:0% +what we have + + + align:start position:0% +what we have +so + + align:start position:0% +so + + + align:start position:0% +so +second is + + align:start position:0% + + + + align:start position:0% + +the absolute value of the integral from + + align:start position:0% +the absolute value of the integral from + + + align:start position:0% +the absolute value of the integral from +a b of f is less than or equal to the + + align:start position:0% +a b of f is less than or equal to the + + + align:start position:0% +a b of f is less than or equal to the +integral from a b + + align:start position:0% +integral from a b + + + align:start position:0% +integral from a b +of the absolute value of f so + + align:start position:0% +of the absolute value of f so + + + align:start position:0% +of the absolute value of f so +like this is + + align:start position:0% +like this is + + + align:start position:0% +like this is +the triangle in + + align:start position:0% +the triangle in + + + align:start position:0% +the triangle in +quality for integrals + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right so we'll prove + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +using again the the main property we + + align:start position:0% +using again the the main property we + + + align:start position:0% +using again the the main property we +have about uh riemann integrals + + align:start position:0% +have about uh riemann integrals + + + align:start position:0% +have about uh riemann integrals +that they satisfy this um + + align:start position:0% +that they satisfy this um + + + align:start position:0% +that they satisfy this um +property and then we'll deduce two + + align:start position:0% +property and then we'll deduce two + + + align:start position:0% +property and then we'll deduce two +directly from number one okay + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +let + + align:start position:0% + + + + align:start position:0% + +let's take a sequence of + + align:start position:0% +let's take a sequence of + + + align:start position:0% +let's take a sequence of +tagged partitions + + align:start position:0% +tagged partitions + + + align:start position:0% +tagged partitions +with norms converging to zero + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +for all r + + align:start position:0% +for all r + + + align:start position:0% +for all r +if we take + + align:start position:0% +if we take + + + align:start position:0% +if we take +the riemann sum approaching + + align:start position:0% +the riemann sum approaching + + + align:start position:0% +the riemann sum approaching +with respect to f of + + align:start position:0% + + + + align:start position:0% + +this tag partition this is equal to + + align:start position:0% +this tag partition this is equal to + + + align:start position:0% +this tag partition this is equal to +j equals 1 to n this is just the + + align:start position:0% +j equals 1 to n this is just the + + + align:start position:0% +j equals 1 to n this is just the +definition + + align:start position:0% + + + + align:start position:0% + +r here is just + + align:start position:0% +r here is just + + + align:start position:0% +r here is just +indexing the the sequence of tag + + align:start position:0% +indexing the the sequence of tag + + + align:start position:0% +indexing the the sequence of tag +partitions i should say this is + + align:start position:0% +partitions i should say this is + + + align:start position:0% +partitions i should say this is +doesn't have to end at some single + + align:start position:0% +doesn't have to end at some single + + + align:start position:0% +doesn't have to end at some single +number um + + align:start position:0% +number um + + + align:start position:0% +number um +in fact it can't + + align:start position:0% +in fact it can't + + + align:start position:0% +in fact it can't +in common with all of these tag + + align:start position:0% +in common with all of these tag + + + align:start position:0% +in common with all of these tag +partitions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so here n of r is just the number of + + align:start position:0% +so here n of r is just the number of + + + align:start position:0% +so here n of r is just the number of +partition points + + align:start position:0% +partition points + + + align:start position:0% +partition points +um + + align:start position:0% +um + + + align:start position:0% +um +that we have in our partition x + + align:start position:0% +that we have in our partition x + + + align:start position:0% +that we have in our partition x +superscript r + + align:start position:0% +superscript r + + + align:start position:0% +superscript r +and since we're assuming f of x is less + + align:start position:0% +and since we're assuming f of x is less + + + align:start position:0% +and since we're assuming f of x is less +than or equal to g of x for all x and a + + align:start position:0% +than or equal to g of x for all x and a + + + align:start position:0% +than or equal to g of x for all x and a +b this is less than or equal to + + align:start position:0% +b this is less than or equal to + + + align:start position:0% +b this is less than or equal to +sum from j equals 1 to n of r + + align:start position:0% +sum from j equals 1 to n of r + + + align:start position:0% +sum from j equals 1 to n of r +g of c j of r + + align:start position:0% + + + + align:start position:0% + +r + + align:start position:0% +r + + + align:start position:0% +r +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and what is this last thing this last + + align:start position:0% +and what is this last thing this last + + + align:start position:0% +and what is this last thing this last +thing is just equal to the riemann sum + + align:start position:0% +thing is just equal to the riemann sum + + + align:start position:0% +thing is just equal to the riemann sum +of g with respect to this tag partition + + align:start position:0% + + + + align:start position:0% + +x and xc + + align:start position:0% +x and xc + + + align:start position:0% +x and xc +so + + align:start position:0% +so + + + align:start position:0% +so +[Applause] + + align:start position:0% + + + + align:start position:0% + +we started off with the riemann sum + + align:start position:0% +we started off with the riemann sum + + + align:start position:0% +we started off with the riemann sum +associated to f + + align:start position:0% +associated to f + + + align:start position:0% +associated to f +and we showed that's less than or equal + + align:start position:0% +and we showed that's less than or equal + + + align:start position:0% +and we showed that's less than or equal +to + + align:start position:0% +to + + + align:start position:0% +to +um + + align:start position:0% + + + + align:start position:0% + +just kind of summarizing here + + align:start position:0% + + + + align:start position:0% + +that this riemann sum + + align:start position:0% +that this riemann sum + + + align:start position:0% +that this riemann sum +is less than or equal to this riemann + + align:start position:0% +is less than or equal to this riemann + + + align:start position:0% +is less than or equal to this riemann +sum + + align:start position:0% + + + + align:start position:0% + +so now if i take the limit as r goes to + + align:start position:0% +so now if i take the limit as r goes to + + + align:start position:0% +so now if i take the limit as r goes to +infinity + + align:start position:0% + + + + align:start position:0% + +this on the left hand side approaches + + align:start position:0% +this on the left hand side approaches + + + align:start position:0% +this on the left hand side approaches +the integral from a b + + align:start position:0% +the integral from a b + + + align:start position:0% +the integral from a b +and since + + align:start position:0% +and since + + + align:start position:0% +and since +limits respect inequalities + + align:start position:0% + + + + align:start position:0% + +i get this + + align:start position:0% +i get this + + + align:start position:0% +i get this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +which is what we wanted to prove + + align:start position:0% + + + + align:start position:0% + +all right and from number two i mean + + align:start position:0% +all right and from number two i mean + + + align:start position:0% +all right and from number two i mean +from for number two we get from number + + align:start position:0% +from for number two we get from number + + + align:start position:0% +from for number two we get from number +one uh + + align:start position:0% +one uh + + + align:start position:0% +one uh +i mean we get number two from number one + + align:start position:0% +i mean we get number two from number one + + + align:start position:0% +i mean we get number two from number one +essentially quite quickly so + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +plus or minus f is less than or equal to + + align:start position:0% +plus or minus f is less than or equal to + + + align:start position:0% +plus or minus f is less than or equal to +the absolute value of f + + align:start position:0% +the absolute value of f + + + align:start position:0% +the absolute value of f +we get that plus or minus + + align:start position:0% +we get that plus or minus + + + align:start position:0% +we get that plus or minus +so integral of plus or minus f + + align:start position:0% +so integral of plus or minus f + + + align:start position:0% +so integral of plus or minus f +is less than or equal to + + align:start position:0% + + + + align:start position:0% + +the integral from a b + + align:start position:0% +the integral from a b + + + align:start position:0% +the integral from a b +of the absolute value now + + align:start position:0% +of the absolute value now + + + align:start position:0% +of the absolute value now +scalar multiplication we proved last we + + align:start position:0% +scalar multiplication we proved last we + + + align:start position:0% +scalar multiplication we proved last we +proved last time pulls out + + align:start position:0% +proved last time pulls out + + + align:start position:0% +proved last time pulls out +so that means + + align:start position:0% +so that means + + + align:start position:0% +so that means +plus or minus the integral of + + align:start position:0% +plus or minus the integral of + + + align:start position:0% +plus or minus the integral of +f is less than or equal to + + align:start position:0% +f is less than or equal to + + + align:start position:0% +f is less than or equal to +the integral of the absolute value of f + + align:start position:0% +the integral of the absolute value of f + + + align:start position:0% +the integral of the absolute value of f +which is the same as + + align:start position:0% +which is the same as + + + align:start position:0% +which is the same as +so for the minus sign this tells me + + align:start position:0% + + + + align:start position:0% + +this inequality and for the plus sign + + align:start position:0% + + + + align:start position:0% + +i get that inequality but that's + + align:start position:0% +i get that inequality but that's + + + align:start position:0% +i get that inequality but that's +equivalent to saying that the absolute + + align:start position:0% +equivalent to saying that the absolute + + + align:start position:0% +equivalent to saying that the absolute +value of the integral of f + + align:start position:0% + + + + align:start position:0% + +is less than or equal to + + align:start position:0% + + + + align:start position:0% + +the integral of the absolute value + + align:start position:0% +the integral of the absolute value + + + align:start position:0% +the integral of the absolute value +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's the proof of the theorem let + + align:start position:0% +and that's the proof of the theorem let + + + align:start position:0% +and that's the proof of the theorem let +me make a + + align:start position:0% +me make a + + + align:start position:0% +me make a +small remark here so + + align:start position:0% +small remark here so + + + align:start position:0% +small remark here so +and this will be a + + align:start position:0% +and this will be a + + + align:start position:0% +and this will be a +an exercise on the homework + + align:start position:0% +an exercise on the homework + + + align:start position:0% +an exercise on the homework +to prove this + + align:start position:0% +to prove this + + + align:start position:0% +to prove this +is the following well + + align:start position:0% + + + + align:start position:0% + +we know that taking limits respects + + align:start position:0% +we know that taking limits respects + + + align:start position:0% +we know that taking limits respects +inequalities but not necessarily strict + + align:start position:0% +inequalities but not necessarily strict + + + align:start position:0% +inequalities but not necessarily strict +inequalities right so + + align:start position:0% +inequalities right so + + + align:start position:0% +inequalities right so +i can have two sequences + + align:start position:0% +i can have two sequences + + + align:start position:0% +i can have two sequences +one strictly less than the other for all + + align:start position:0% +one strictly less than the other for all + + + align:start position:0% +one strictly less than the other for all +n + + align:start position:0% +n + + + align:start position:0% +n +and then as n goes to infinity their + + align:start position:0% +and then as n goes to infinity their + + + align:start position:0% +and then as n goes to infinity their +limits could in fact equal each other + + align:start position:0% +limits could in fact equal each other + + + align:start position:0% +limits could in fact equal each other +right so for example if i take + + align:start position:0% +right so for example if i take + + + align:start position:0% +right so for example if i take +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the first sequence to be zero the second + + align:start position:0% +the first sequence to be zero the second + + + align:start position:0% +the first sequence to be zero the second +sequence would be one over n one over n + + align:start position:0% +sequence would be one over n one over n + + + align:start position:0% +sequence would be one over n one over n +is always bigger than zero yet they both + + align:start position:0% +is always bigger than zero yet they both + + + align:start position:0% +is always bigger than zero yet they both +converge to zero so + + align:start position:0% +converge to zero so + + + align:start position:0% +converge to zero so +um + + align:start position:0% +um + + + align:start position:0% +um +you know taking limits does not respect + + align:start position:0% +you know taking limits does not respect + + + align:start position:0% +you know taking limits does not respect +strict + + align:start position:0% + + + + align:start position:0% + +inequality however in this setting + + align:start position:0% +inequality however in this setting + + + align:start position:0% +inequality however in this setting +um + + align:start position:0% +um + + + align:start position:0% +um +which is a + + align:start position:0% +which is a + + + align:start position:0% +which is a +you know very nice i mean it's actually + + align:start position:0% +you know very nice i mean it's actually + + + align:start position:0% +you know very nice i mean it's actually +an extremely important + + align:start position:0% +an extremely important + + + align:start position:0% +an extremely important +um + + align:start position:0% + + + + align:start position:0% + +property of the integral is that uh this + + align:start position:0% +property of the integral is that uh this + + + align:start position:0% +property of the integral is that uh this +limiting process that we do to take + + align:start position:0% +limiting process that we do to take + + + align:start position:0% +limiting process that we do to take +integrals in fact does + + align:start position:0% +integrals in fact does + + + align:start position:0% +integrals in fact does +um it's not just any old limiting + + align:start position:0% +um it's not just any old limiting + + + align:start position:0% +um it's not just any old limiting +process it actually does + + align:start position:0% +process it actually does + + + align:start position:0% +process it actually does +uh + + align:start position:0% +uh + + + align:start position:0% +uh +respect strict inequality so what am i + + align:start position:0% +respect strict inequality so what am i + + + align:start position:0% +respect strict inequality so what am i +saying + + align:start position:0% +saying + + + align:start position:0% +saying +is that we can prove uh + + align:start position:0% + + + + align:start position:0% + +something a little bit stronger and + + align:start position:0% +something a little bit stronger and + + + align:start position:0% +something a little bit stronger and +that's which i'll state in its kind of + + align:start position:0% +that's which i'll state in its kind of + + + align:start position:0% +that's which i'll state in its kind of +reduced form here if i take a continuous + + align:start position:0% +reduced form here if i take a continuous + + + align:start position:0% +reduced form here if i take a continuous +function + + align:start position:0% + + + + align:start position:0% + +and it's positive + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +we already know that the integral of f + + align:start position:0% +we already know that the integral of f + + + align:start position:0% +we already know that the integral of f +is going to be non-negative by what we + + align:start position:0% +is going to be non-negative by what we + + + align:start position:0% +is going to be non-negative by what we +just proved + + align:start position:0% +just proved + + + align:start position:0% +just proved +but in fact the integral of f is + + align:start position:0% +but in fact the integral of f is + + + align:start position:0% +but in fact the integral of f is +positive okay + + align:start position:0% + + + + align:start position:0% + +and again so this is also kind of + + align:start position:0% +and again so this is also kind of + + + align:start position:0% +and again so this is also kind of +important from + + align:start position:0% +important from + + + align:start position:0% +important from +you know psychological standpoint if + + align:start position:0% +you know psychological standpoint if + + + align:start position:0% +you know psychological standpoint if +we're thinking of the integral as being + + align:start position:0% +we're thinking of the integral as being + + + align:start position:0% +we're thinking of the integral as being +a theory of the area underneath the + + align:start position:0% +a theory of the area underneath the + + + align:start position:0% +a theory of the area underneath the +curve + + align:start position:0% +curve + + + align:start position:0% +curve +so what this states is that um + + align:start position:0% +so what this states is that um + + + align:start position:0% +so what this states is that um +and again i'm not i'm not going to prove + + align:start position:0% +and again i'm not i'm not going to prove + + + align:start position:0% +and again i'm not i'm not going to prove +this this will be on the assignment + + align:start position:0% + + + + align:start position:0% + +again so so this you know + + align:start position:0% + + + + align:start position:0% + +coincides with our intuition of what a + + align:start position:0% +coincides with our intuition of what a + + + align:start position:0% +coincides with our intuition of what a +theory of the area underneath the curve + + align:start position:0% +theory of the area underneath the curve + + + align:start position:0% +theory of the area underneath the curve +should be so this says if a continuous + + align:start position:0% +should be so this says if a continuous + + + align:start position:0% +should be so this says if a continuous +function is positive so like the picture + + align:start position:0% +function is positive so like the picture + + + align:start position:0% +function is positive so like the picture +i drew you then + + align:start position:0% +i drew you then + + + align:start position:0% +i drew you then +the integral which we interpret again as + + align:start position:0% +the integral which we interpret again as + + + align:start position:0% +the integral which we interpret again as +the area underneath the curve is + + align:start position:0% +the area underneath the curve is + + + align:start position:0% +the area underneath the curve is +positive so that matches what our + + align:start position:0% +positive so that matches what our + + + align:start position:0% +positive so that matches what our +our uh + + align:start position:0% +our uh + + + align:start position:0% +our uh +you know desire for this to be a theory + + align:start position:0% +you know desire for this to be a theory + + + align:start position:0% +you know desire for this to be a theory +of the area underneath the curve should + + align:start position:0% +of the area underneath the curve should + + + align:start position:0% +of the area underneath the curve should +be + + align:start position:0% +be + + + align:start position:0% +be +all right + + align:start position:0% +all right + + + align:start position:0% +all right +but um + + align:start position:0% +but um + + + align:start position:0% +but um +okay + + align:start position:0% + + + + align:start position:0% + +and so um + + align:start position:0% +and so um + + + align:start position:0% +and so um +you know we have + + align:start position:0% +you know we have + + + align:start position:0% +you know we have +if you + + align:start position:0% +if you + + + align:start position:0% +if you +like i mean we could have proved this + + align:start position:0% +like i mean we could have proved this + + + align:start position:0% +like i mean we could have proved this +from + + align:start position:0% +from + + + align:start position:0% +from +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +um + + align:start position:0% +um + + + align:start position:0% +um +you know basic considerations in what + + align:start position:0% +you know basic considerations in what + + + align:start position:0% +you know basic considerations in what +the definition of the integral is + + align:start position:0% +the definition of the integral is + + + align:start position:0% +the definition of the integral is +but + + align:start position:0% +but + + + align:start position:0% +but +we have the following + + align:start position:0% + + + + align:start position:0% + +theorem that + + align:start position:0% + + + + align:start position:0% + +for all alpha and r + + align:start position:0% + + + + align:start position:0% + +i could just say the following + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +let me not uh + + align:start position:0% +let me not uh + + + align:start position:0% +let me not uh +not state it this way + + align:start position:0% +not state it this way + + + align:start position:0% +not state it this way +so um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +going a little off script here but it's + + align:start position:0% +going a little off script here but it's + + + align:start position:0% +going a little off script here but it's +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +we actually haven't computed a single + + align:start position:0% +we actually haven't computed a single + + + align:start position:0% +we actually haven't computed a single +integral yet okay + + align:start position:0% +integral yet okay + + + align:start position:0% +integral yet okay +really it's it's tough to with this + + align:start position:0% +really it's it's tough to with this + + + align:start position:0% +really it's it's tough to with this +definition in a minute you know we'll + + align:start position:0% +definition in a minute you know we'll + + + align:start position:0% +definition in a minute you know we'll +prove the fundamental theorem of + + align:start position:0% +prove the fundamental theorem of + + + align:start position:0% +prove the fundamental theorem of +calculus and be able to do it uh very + + align:start position:0% +calculus and be able to do it uh very + + + align:start position:0% +calculus and be able to do it uh very +easily but + + align:start position:0% +easily but + + + align:start position:0% +easily but +let me first prove at least you know the + + align:start position:0% +let me first prove at least you know the + + + align:start position:0% +let me first prove at least you know the +most basic + + align:start position:0% +most basic + + + align:start position:0% +most basic +uh integral so + + align:start position:0% +uh integral so + + + align:start position:0% +uh integral so +integral from a b of the function one + + align:start position:0% +integral from a b of the function one + + + align:start position:0% +integral from a b of the function one +equals + + align:start position:0% +equals + + + align:start position:0% +equals +b minus a + + align:start position:0% +b minus a + + + align:start position:0% +b minus a +okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +what's the proof + + align:start position:0% +what's the proof + + + align:start position:0% +what's the proof +take a sequence of partitions converge + + align:start position:0% +take a sequence of partitions converge + + + align:start position:0% +take a sequence of partitions converge +with the norms converging to zero and we + + align:start position:0% +with the norms converging to zero and we + + + align:start position:0% +with the norms converging to zero and we +just look at the riemann sum + + align:start position:0% + + + + align:start position:0% + +and for + + align:start position:0% +and for + + + align:start position:0% +and for +1 this will be quite easy to compute + + align:start position:0% +1 this will be quite easy to compute + + + align:start position:0% +1 this will be quite easy to compute +what + + align:start position:0% +what + + + align:start position:0% +what +the riemann sums are + + align:start position:0% + + + + align:start position:0% + +so this is a sequence of partitions with + + align:start position:0% +so this is a sequence of partitions with + + + align:start position:0% +so this is a sequence of partitions with +norm + + align:start position:0% + + + + align:start position:0% + +converging to zero + + align:start position:0% +converging to zero + + + align:start position:0% +converging to zero +then + + align:start position:0% +then + + + align:start position:0% +then +if i look at + + align:start position:0% + + + + align:start position:0% + +associated riemann sums + + align:start position:0% +associated riemann sums + + + align:start position:0% +associated riemann sums +this is equal to j equals 1 to n of r + + align:start position:0% +this is equal to j equals 1 to n of r + + + align:start position:0% +this is equal to j equals 1 to n of r +no matter what i no matter what x c is i + + align:start position:0% +no matter what i no matter what x c is i + + + align:start position:0% +no matter what i no matter what x c is i +just get 1 and then times the length of + + align:start position:0% +just get 1 and then times the length of + + + align:start position:0% +just get 1 and then times the length of +the interval + + align:start position:0% +the interval + + + align:start position:0% +the interval +the sub interval + + align:start position:0% + + + + align:start position:0% + +now this is a telescoping sum + + align:start position:0% +now this is a telescoping sum + + + align:start position:0% +now this is a telescoping sum +right + + align:start position:0% +right + + + align:start position:0% +right +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know meaning this is equal to + + align:start position:0% +you know meaning this is equal to + + + align:start position:0% +you know meaning this is equal to +x1 minus x0 plus x2 minus x1 plus + + align:start position:0% +x1 minus x0 plus x2 minus x1 plus + + + align:start position:0% +x1 minus x0 plus x2 minus x1 plus +up until xn minus xn minus 1. so all i + + align:start position:0% +up until xn minus xn minus 1. so all i + + + align:start position:0% +up until xn minus xn minus 1. so all i +pick up is + + align:start position:0% + + + + align:start position:0% + +not x1 but + + align:start position:0% +not x1 but + + + align:start position:0% +not x1 but +x0 and xn so this is equal to + + align:start position:0% +x0 and xn so this is equal to + + + align:start position:0% +x0 and xn so this is equal to +x j of r x n + + align:start position:0% +x j of r x n + + + align:start position:0% +x j of r x n +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +of r + + align:start position:0% +of r + + + align:start position:0% +of r +minus + + align:start position:0% +minus + + + align:start position:0% +minus +x 0 + + align:start position:0% +x 0 + + + align:start position:0% +x 0 +of r + + align:start position:0% +of r + + + align:start position:0% +of r +and this is the last point in the + + align:start position:0% +and this is the last point in the + + + align:start position:0% +and this is the last point in the +partition this is the first point in the + + align:start position:0% +partition this is the first point in the + + + align:start position:0% +partition this is the first point in the +partition + + align:start position:0% +partition + + + align:start position:0% +partition +and as always for partitions the last + + align:start position:0% +and as always for partitions the last + + + align:start position:0% +and as always for partitions the last +point is b the first point is a + + align:start position:0% +point is b the first point is a + + + align:start position:0% +point is b the first point is a +so this is equal to + + align:start position:0% +so this is equal to + + + align:start position:0% +so this is equal to +b minus a + + align:start position:0% +b minus a + + + align:start position:0% +b minus a +and + + align:start position:0% +and + + + align:start position:0% +and +now + + align:start position:0% +now + + + align:start position:0% +now +this thing on the left hand side is + + align:start position:0% +this thing on the left hand side is + + + align:start position:0% +this thing on the left hand side is +equal to b minus a + + align:start position:0% + + + + align:start position:0% + +so this tells me + + align:start position:0% + + + + align:start position:0% + +that the integral + + align:start position:0% +that the integral + + + align:start position:0% +that the integral +which is equal to this limit of riemann + + align:start position:0% +which is equal to this limit of riemann + + + align:start position:0% +which is equal to this limit of riemann +sums is equal to b minus a + + align:start position:0% +sums is equal to b minus a + + + align:start position:0% +sums is equal to b minus a +right and then the assignment for this + + align:start position:0% +right and then the assignment for this + + + align:start position:0% +right and then the assignment for this +i guess uh when you see this last week + + align:start position:0% +i guess uh when you see this last week + + + align:start position:0% +i guess uh when you see this last week +was to essentially compute the integral + + align:start position:0% +was to essentially compute the integral + + + align:start position:0% +was to essentially compute the integral +for the integral from a b of x dx + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and so we get from + + align:start position:0% +and so we get from + + + align:start position:0% +and so we get from +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this theorem and this theorem um + + align:start position:0% +this theorem and this theorem um + + + align:start position:0% +this theorem and this theorem um +following bound + + align:start position:0% + + + + align:start position:0% + +kind of for + + align:start position:0% +kind of for + + + align:start position:0% +kind of for +the area so let me draw a picture + + align:start position:0% +the area so let me draw a picture + + + align:start position:0% +the area so let me draw a picture +and so that this is not so surprising + + align:start position:0% +and so that this is not so surprising + + + align:start position:0% +and so that this is not so surprising +let's say i have a function from a + + align:start position:0% +let's say i have a function from a + + + align:start position:0% +let's say i have a function from a +b + + align:start position:0% + + + + align:start position:0% + +there's uh the function f + + align:start position:0% +there's uh the function f + + + align:start position:0% +there's uh the function f +and + + align:start position:0% + + + + align:start position:0% + +so that was supposed to go through this + + align:start position:0% +so that was supposed to go through this + + + align:start position:0% +so that was supposed to go through this +point so let's make that a little bit + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i suppose i don't need these parts but + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +let's say i have so for a continuous + + align:start position:0% +let's say i have so for a continuous + + + align:start position:0% +let's say i have so for a continuous +function it always achieves a minimum + + align:start position:0% +function it always achieves a minimum + + + align:start position:0% +function it always achieves a minimum +and maximum and at least for this + + align:start position:0% +and maximum and at least for this + + + align:start position:0% +and maximum and at least for this +picture the minimum occurs here the + + align:start position:0% +picture the minimum occurs here the + + + align:start position:0% +picture the minimum occurs here the +maximum occurs here + + align:start position:0% +maximum occurs here + + + align:start position:0% +maximum occurs here +um + + align:start position:0% +um + + + align:start position:0% +um +now what's the comparison about uh areas + + align:start position:0% +now what's the comparison about uh areas + + + align:start position:0% +now what's the comparison about uh areas +from this picture well the area + + align:start position:0% +from this picture well the area + + + align:start position:0% +from this picture well the area +underneath the curve of f + + align:start position:0% +underneath the curve of f + + + align:start position:0% +underneath the curve of f +will be bigger than or equal to the area + + align:start position:0% +will be bigger than or equal to the area + + + align:start position:0% +will be bigger than or equal to the area +underneath the curve of the constant + + align:start position:0% +underneath the curve of the constant + + + align:start position:0% +underneath the curve of the constant +function + + align:start position:0% +function + + + align:start position:0% +function +equal to little m sub f and that's just + + align:start position:0% +equal to little m sub f and that's just + + + align:start position:0% +equal to little m sub f and that's just +b times a times m sub f again by + + align:start position:0% +b times a times m sub f again by + + + align:start position:0% +b times a times m sub f again by +you know intuition but this is also seen + + align:start position:0% +you know intuition but this is also seen + + + align:start position:0% +you know intuition but this is also seen +from the theorem we just proved along + + align:start position:0% +from the theorem we just proved along + + + align:start position:0% +from the theorem we just proved along +with the linearity of the riemann + + align:start position:0% +with the linearity of the riemann + + + align:start position:0% +with the linearity of the riemann +integral which we've already proved + + align:start position:0% +integral which we've already proved + + + align:start position:0% +integral which we've already proved +and the integral of f + + align:start position:0% +and the integral of f + + + align:start position:0% +and the integral of f +the area underneath this curve is also + + align:start position:0% +the area underneath this curve is also + + + align:start position:0% +the area underneath this curve is also +less than or equal to the area + + align:start position:0% +less than or equal to the area + + + align:start position:0% +less than or equal to the area +underneath the curve where f achieves a + + align:start position:0% +underneath the curve where f achieves a + + + align:start position:0% +underneath the curve where f achieves a +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +i + + align:start position:0% +i + + + align:start position:0% +i +it's the 12th week of uh class and i + + align:start position:0% +it's the 12th week of uh class and i + + + align:start position:0% +it's the 12th week of uh class and i +still haven't brought colored chalk so + + align:start position:0% +still haven't brought colored chalk so + + + align:start position:0% +still haven't brought colored chalk so +hopefully that was clear enough without + + align:start position:0% +hopefully that was clear enough without + + + align:start position:0% +hopefully that was clear enough without +me having to color stuff in + + align:start position:0% +me having to color stuff in + + + align:start position:0% +me having to color stuff in +so + + align:start position:0% +so + + + align:start position:0% +so +the theorem is the following + + align:start position:0% +the theorem is the following + + + align:start position:0% +the theorem is the following +if f + + align:start position:0% +if f + + + align:start position:0% +if f +again we're working with continuous + + align:start position:0% +again we're working with continuous + + + align:start position:0% +again we're working with continuous +functions because that's all we + + align:start position:0% +functions because that's all we + + + align:start position:0% +functions because that's all we +can integrate or are going to integrate + + align:start position:0% +can integrate or are going to integrate + + + align:start position:0% +can integrate or are going to integrate +in this section + + align:start position:0% + + + + align:start position:0% + +and i have these two numbers the + + align:start position:0% + + + + align:start position:0% + +m of f x + + align:start position:0% + + + + align:start position:0% + +which we know is in fact a min meaning + + align:start position:0% +which we know is in fact a min meaning + + + align:start position:0% +which we know is in fact a min meaning +there exists a point in here + + align:start position:0% +there exists a point in here + + + align:start position:0% +there exists a point in here +so in fact i'm going to write min we + + align:start position:0% +so in fact i'm going to write min we + + + align:start position:0% +so in fact i'm going to write min we +know that by the min max theorem that + + align:start position:0% +know that by the min max theorem that + + + align:start position:0% +know that by the min max theorem that +for every continuous function it + + align:start position:0% +for every continuous function it + + + align:start position:0% +for every continuous function it +achieves its minimum + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +max + + align:start position:0% + + + + align:start position:0% + +then as i was saying a minute ago + + align:start position:0% +then as i was saying a minute ago + + + align:start position:0% +then as i was saying a minute ago +the area underneath the curve m little m + + align:start position:0% +the area underneath the curve m little m + + + align:start position:0% +the area underneath the curve m little m +sub f which is this smaller square is + + align:start position:0% +sub f which is this smaller square is + + + align:start position:0% +sub f which is this smaller square is +less than or equal to the area + + align:start position:0% +less than or equal to the area + + + align:start position:0% +less than or equal to the area +underneath the curve + + align:start position:0% +underneath the curve + + + align:start position:0% +underneath the curve +of + + align:start position:0% +of + + + align:start position:0% +of +f so + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +little m sub f times b minus a the area + + align:start position:0% +little m sub f times b minus a the area + + + align:start position:0% +little m sub f times b minus a the area +underneath the minimum is less than or + + align:start position:0% +underneath the minimum is less than or + + + align:start position:0% +underneath the minimum is less than or +equal to the area underneath the curve + + align:start position:0% +equal to the area underneath the curve + + + align:start position:0% +equal to the area underneath the curve +of + + align:start position:0% +of + + + align:start position:0% +of +f + + align:start position:0% +f + + + align:start position:0% +f +which is less than or equal to + + align:start position:0% +which is less than or equal to + + + align:start position:0% +which is less than or equal to +the area underneath the curve + + align:start position:0% +the area underneath the curve + + + align:start position:0% +the area underneath the curve +of + + align:start position:0% +of + + + align:start position:0% +of +the + + align:start position:0% +the + + + align:start position:0% +the +taller line capital m sub f + + align:start position:0% +taller line capital m sub f + + + align:start position:0% +taller line capital m sub f +okay + + align:start position:0% + + + + align:start position:0% + +so how do we prove this well we just + + align:start position:0% +so how do we prove this well we just + + + align:start position:0% +so how do we prove this well we just +used these previous two theorems right + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% + + + + align:start position:0% + +little imps of f is less than or equal + + align:start position:0% +little imps of f is less than or equal + + + align:start position:0% +little imps of f is less than or equal +to capital m sub f + + align:start position:0% +to capital m sub f + + + align:start position:0% +to capital m sub f +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so since little m sub f is less than or + + align:start position:0% +so since little m sub f is less than or + + + align:start position:0% +so since little m sub f is less than or +equal to f of x which is less than or + + align:start position:0% +equal to f of x which is less than or + + + align:start position:0% +equal to f of x which is less than or +equal to capital m sub f + + align:start position:0% +equal to capital m sub f + + + align:start position:0% +equal to capital m sub f +for all x + + align:start position:0% +for all x + + + align:start position:0% +for all x +and a b + + align:start position:0% +and a b + + + align:start position:0% +and a b +we can apply + + align:start position:0% +we can apply + + + align:start position:0% +we can apply +that theorem up there to get that the + + align:start position:0% +that theorem up there to get that the + + + align:start position:0% +that theorem up there to get that the +integral + + align:start position:0% + + + + align:start position:0% + +of little m sub f again this is just a + + align:start position:0% +of little m sub f again this is just a + + + align:start position:0% +of little m sub f again this is just a +fixed number + + align:start position:0% +fixed number + + + align:start position:0% +fixed number +is less than or equal to the integral of + + align:start position:0% +is less than or equal to the integral of + + + align:start position:0% +is less than or equal to the integral of +from a b of f + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and now again these are just fixed + + align:start position:0% +and now again these are just fixed + + + align:start position:0% +and now again these are just fixed +numbers so by what we proved here that + + align:start position:0% +numbers so by what we proved here that + + + align:start position:0% +numbers so by what we proved here that +the integral from a to b of 1 is b minus + + align:start position:0% +the integral from a to b of 1 is b minus + + + align:start position:0% +the integral from a to b of 1 is b minus +a + + align:start position:0% +a + + + align:start position:0% +a +and the fact that scalars pull out so + + align:start position:0% +and the fact that scalars pull out so + + + align:start position:0% +and the fact that scalars pull out so +this + + align:start position:0% +this + + + align:start position:0% +this +number here can come out and this is + + align:start position:0% +number here can come out and this is + + + align:start position:0% +number here can come out and this is +just m sub f times the integral from a b + + align:start position:0% +just m sub f times the integral from a b + + + align:start position:0% +just m sub f times the integral from a b +of 1. + + align:start position:0% +of 1. + + + align:start position:0% +of 1. +so this is little m sub f times b minus + + align:start position:0% +so this is little m sub f times b minus + + + align:start position:0% +so this is little m sub f times b minus +a + + align:start position:0% +a + + + align:start position:0% +a +and over here this is capital m sub f + + align:start position:0% +and over here this is capital m sub f + + + align:start position:0% +and over here this is capital m sub f +times + + align:start position:0% +times + + + align:start position:0% +times +b minus a + + align:start position:0% +b minus a + + + align:start position:0% +b minus a +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's the proof + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so now let me uh make a few comments + + align:start position:0% +so now let me uh make a few comments + + + align:start position:0% +so now let me uh make a few comments +about uh + + align:start position:0% +about uh + + + align:start position:0% +about uh +um + + align:start position:0% +um + + + align:start position:0% +um +some conventions or really + + align:start position:0% + + + + align:start position:0% + +so we've been talking about + + align:start position:0% +so we've been talking about + + + align:start position:0% +so we've been talking about +at least i've been talking about you're + + align:start position:0% +at least i've been talking about you're + + + align:start position:0% +at least i've been talking about you're +not here so we haven't been talking at + + align:start position:0% +not here so we haven't been talking at + + + align:start position:0% +not here so we haven't been talking at +all + + align:start position:0% +all + + + align:start position:0% +all +so + + align:start position:0% + + + + align:start position:0% + +we've been talking about the + + align:start position:0% +we've been talking about the + + + align:start position:0% +we've been talking about the +integral from a b to f when a is less + + align:start position:0% +integral from a b to f when a is less + + + align:start position:0% +integral from a b to f when a is less +than b + + align:start position:0% +than b + + + align:start position:0% +than b +um + + align:start position:0% +um + + + align:start position:0% +um +but uh + + align:start position:0% +but uh + + + align:start position:0% +but uh +i'm gonna use i'm just gonna set down + + align:start position:0% +i'm gonna use i'm just gonna set down + + + align:start position:0% +i'm gonna use i'm just gonna set down +some + + align:start position:0% +some + + + align:start position:0% +some +uh + + align:start position:0% +uh + + + align:start position:0% +uh +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +convention or you could you could say + + align:start position:0% +convention or you could you could say + + + align:start position:0% +convention or you could you could say +this is really notation + + align:start position:0% +this is really notation + + + align:start position:0% +this is really notation +that + + align:start position:0% + + + + align:start position:0% + +when i have this + + align:start position:0% + + + + align:start position:0% + +when i write down this symbol integral a + + align:start position:0% +when i write down this symbol integral a + + + align:start position:0% +when i write down this symbol integral a +to a of f + + align:start position:0% + + + + align:start position:0% + +this is really just another way of + + align:start position:0% +this is really just another way of + + + align:start position:0% +this is really just another way of +writing 0 and + + align:start position:0% +writing 0 and + + + align:start position:0% +writing 0 and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +another is that if in fact b is less + + align:start position:0% +another is that if in fact b is less + + + align:start position:0% +another is that if in fact b is less +than a then the integral from + + align:start position:0% +than a then the integral from + + + align:start position:0% +than a then the integral from +a b + + align:start position:0% +a b + + + align:start position:0% +a b +to f + + align:start position:0% +to f + + + align:start position:0% +to f +so remember we've been talking about the + + align:start position:0% +so remember we've been talking about the + + + align:start position:0% +so remember we've been talking about the +integrals from over intervals uh + + align:start position:0% +integrals from over intervals uh + + + align:start position:0% +integrals from over intervals uh +um + + align:start position:0% +um + + + align:start position:0% +um +or + + align:start position:0% +or + + + align:start position:0% +or +where the number on the bottom is less + + align:start position:0% +where the number on the bottom is less + + + align:start position:0% +where the number on the bottom is less +than the number on the top + + align:start position:0% +than the number on the top + + + align:start position:0% +than the number on the top +so + + align:start position:0% +so + + + align:start position:0% +so +whenever i write this symbol with + + align:start position:0% +whenever i write this symbol with + + + align:start position:0% +whenever i write this symbol with +the bigger number on the bottom + + align:start position:0% +the bigger number on the bottom + + + align:start position:0% +the bigger number on the bottom +and the smaller number on the top you + + align:start position:0% +and the smaller number on the top you + + + align:start position:0% +and the smaller number on the top you +should read this as + + align:start position:0% +should read this as + + + align:start position:0% +should read this as +minus the integral of + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +with + + align:start position:0% +with + + + align:start position:0% +with +this being you know the right in the + + align:start position:0% +this being you know the right in the + + + align:start position:0% +this being you know the right in the +right place meaning this number here is + + align:start position:0% +right place meaning this number here is + + + align:start position:0% +right place meaning this number here is +less than this number here okay + + align:start position:0% +less than this number here okay + + + align:start position:0% +less than this number here okay +and so + + align:start position:0% +and so + + + align:start position:0% +and so +um one + + align:start position:0% +um one + + + align:start position:0% +um one +again these are these are really just + + align:start position:0% +again these are these are really just + + + align:start position:0% +again these are these are really just +notations that if i write this this is a + + align:start position:0% +notations that if i write this this is a + + + align:start position:0% +notations that if i write this this is a +fancy way of writing 0. when i write + + align:start position:0% +fancy way of writing 0. when i write + + + align:start position:0% +fancy way of writing 0. when i write +this you should + + align:start position:0% +this you should + + + align:start position:0% +this you should +this means + + align:start position:0% +this means + + + align:start position:0% +this means +minus the integral with um the right + + align:start position:0% +minus the integral with um the right + + + align:start position:0% +minus the integral with um the right +numbers on top and bottom meaning + + align:start position:0% +numbers on top and bottom meaning + + + align:start position:0% +numbers on top and bottom meaning +uh the smaller numbers on the bottom the + + align:start position:0% +uh the smaller numbers on the bottom the + + + align:start position:0% +uh the smaller numbers on the bottom the +bigger numbers on the top + + align:start position:0% +bigger numbers on the top + + + align:start position:0% +bigger numbers on the top +okay + + align:start position:0% + + + + align:start position:0% + +all right and so maybe you ask so this + + align:start position:0% +all right and so maybe you ask so this + + + align:start position:0% +all right and so maybe you ask so this +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +so why + + align:start position:0% +so why + + + align:start position:0% +so why +why do i define that to be zero well if + + align:start position:0% +why do i define that to be zero well if + + + align:start position:0% +why do i define that to be zero well if +you if you like um + + align:start position:0% +you if you like um + + + align:start position:0% +you if you like um +one is + + align:start position:0% + + + + align:start position:0% + +consistent + + align:start position:0% +consistent + + + align:start position:0% +consistent +with the fact that + + align:start position:0% + + + + align:start position:0% + +for all + + align:start position:0% +for all + + + align:start position:0% +for all +continuous functions if i take the + + align:start position:0% +continuous functions if i take the + + + align:start position:0% +continuous functions if i take the +integral + + align:start position:0% +integral + + + align:start position:0% +integral +from a to b with b bigger than a + + align:start position:0% +from a to b with b bigger than a + + + align:start position:0% +from a to b with b bigger than a +and i take the limit as b goes to a + + align:start position:0% +and i take the limit as b goes to a + + + align:start position:0% +and i take the limit as b goes to a +this equals zero + + align:start position:0% +this equals zero + + + align:start position:0% +this equals zero +okay + + align:start position:0% + + + + align:start position:0% + +and two is then consistent with number + + align:start position:0% +and two is then consistent with number + + + align:start position:0% +and two is then consistent with number +one and then additivity + + align:start position:0% +one and then additivity + + + align:start position:0% +one and then additivity +okay + + align:start position:0% + + + + align:start position:0% + +with additivity and number one because + + align:start position:0% +with additivity and number one because + + + align:start position:0% +with additivity and number one because +then by number one i get that the + + align:start position:0% +then by number one i get that the + + + align:start position:0% +then by number one i get that the +so additivity will tell me that the + + align:start position:0% +so additivity will tell me that the + + + align:start position:0% +so additivity will tell me that the +integral from a to a of f is equal to + + align:start position:0% +integral from a to a of f is equal to + + + align:start position:0% +integral from a to a of f is equal to +the integral from a b to f + + align:start position:0% +the integral from a b to f + + + align:start position:0% +the integral from a b to f +plus the integral from b a + + align:start position:0% +plus the integral from b a + + + align:start position:0% +plus the integral from b a +f here assuming b is less than a + + align:start position:0% +f here assuming b is less than a + + + align:start position:0% +f here assuming b is less than a +and so + + align:start position:0% +and so + + + align:start position:0% +and so +if by one + + align:start position:0% +if by one + + + align:start position:0% +if by one +this is zero + + align:start position:0% +this is zero + + + align:start position:0% +this is zero +then + + align:start position:0% +then + + + align:start position:0% +then +to be consistent with additivity this + + align:start position:0% +to be consistent with additivity this + + + align:start position:0% +to be consistent with additivity this +would force the integral from + + align:start position:0% +would force the integral from + + + align:start position:0% +would force the integral from +a b to f to b minus the integral from b + + align:start position:0% +a b to f to b minus the integral from b + + + align:start position:0% +a b to f to b minus the integral from b +a + + align:start position:0% +a + + + align:start position:0% +a +of f okay so + + align:start position:0% +of f okay so + + + align:start position:0% +of f okay so +both of these um + + align:start position:0% +both of these um + + + align:start position:0% +both of these um +conventions if you like + + align:start position:0% + + + + align:start position:0% + +are um + + align:start position:0% +are um + + + align:start position:0% +are um +consistent with + + align:start position:0% +consistent with + + + align:start position:0% +consistent with +um + + align:start position:0% +um + + + align:start position:0% +um +you know the properties of the riemann + + align:start position:0% +you know the properties of the riemann + + + align:start position:0% +you know the properties of the riemann +integral namely that + + align:start position:0% +integral namely that + + + align:start position:0% +integral namely that +the limit as b goes to a of + + align:start position:0% +the limit as b goes to a of + + + align:start position:0% +the limit as b goes to a of +you know the area underneath this curve + + align:start position:0% +you know the area underneath this curve + + + align:start position:0% +you know the area underneath this curve +as the base gets smaller and smaller is + + align:start position:0% +as the base gets smaller and smaller is + + + align:start position:0% +as the base gets smaller and smaller is +zero and then from + + align:start position:0% +zero and then from + + + align:start position:0% +zero and then from +if i assume this then + + align:start position:0% +if i assume this then + + + align:start position:0% +if i assume this then +additivity tells me that the integral + + align:start position:0% +additivity tells me that the integral + + + align:start position:0% +additivity tells me that the integral +from a b has to be minus the integral + + align:start position:0% +from a b has to be minus the integral + + + align:start position:0% +from a b has to be minus the integral +from b to a of f okay + + align:start position:0% + + + + align:start position:0% + +all right so now + + align:start position:0% +all right so now + + + align:start position:0% +all right so now +we computed successfully one integral + + align:start position:0% + + + + align:start position:0% + +and of course when you took calculus + + align:start position:0% +and of course when you took calculus + + + align:start position:0% +and of course when you took calculus +that was not all you could do + + align:start position:0% + + + + align:start position:0% + +calculus is what it is because + + align:start position:0% +calculus is what it is because + + + align:start position:0% +calculus is what it is because +of + + align:start position:0% +of + + + align:start position:0% +of +the hero of the story + + align:start position:0% +the hero of the story + + + align:start position:0% +the hero of the story +which is + + align:start position:0% +which is + + + align:start position:0% +which is +a fundamental theorem of calculus which + + align:start position:0% +a fundamental theorem of calculus which + + + align:start position:0% +a fundamental theorem of calculus which +is what we'll prove now + + align:start position:0% +is what we'll prove now + + + align:start position:0% +is what we'll prove now +theorem + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +fundamental theorem of + + align:start position:0% +fundamental theorem of + + + align:start position:0% +fundamental theorem of +calculus which states the following + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% + + + + align:start position:0% + +i have a function + + align:start position:0% +i have a function + + + align:start position:0% +i have a function +big f + + align:start position:0% +big f + + + align:start position:0% +big f +so + + align:start position:0% +so + + + align:start position:0% +so +first off + + align:start position:0% +first off + + + align:start position:0% +first off +let little f be a continuous function + + align:start position:0% + + + + align:start position:0% + +so the first statement is + + align:start position:0% +so the first statement is + + + align:start position:0% +so the first statement is +um if how to basically how to compute + + align:start position:0% +um if how to basically how to compute + + + align:start position:0% +um if how to basically how to compute +integrals if capital f integral from a b + + align:start position:0% +integrals if capital f integral from a b + + + align:start position:0% +integrals if capital f integral from a b +to r + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +differentiable everywhere on a b + + align:start position:0% +differentiable everywhere on a b + + + align:start position:0% +differentiable everywhere on a b +and + + align:start position:0% + + + + align:start position:0% + +f prime equals little f + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the integral from a b of little f equals + + align:start position:0% +the integral from a b of little f equals + + + align:start position:0% +the integral from a b of little f equals +f of b minus + + align:start position:0% +f of b minus + + + align:start position:0% +f of b minus +f of a + + align:start position:0% + + + + align:start position:0% + +right another way of stating this is + + align:start position:0% +right another way of stating this is + + + align:start position:0% +right another way of stating this is +that the integral from a b of + + align:start position:0% +that the integral from a b of + + + align:start position:0% +that the integral from a b of +capital f prime is equal to + + align:start position:0% +capital f prime is equal to + + + align:start position:0% +capital f prime is equal to +f of b minus f of a + + align:start position:0% + + + + align:start position:0% + +and then the second part so + + align:start position:0% +and then the second part so + + + align:start position:0% +and then the second part so +the first part is about computing + + align:start position:0% +the first part is about computing + + + align:start position:0% +the first part is about computing +integrals the second part is about + + align:start position:0% +integrals the second part is about + + + align:start position:0% +integrals the second part is about +solving + + align:start position:0% +solving + + + align:start position:0% +solving +uh differential equations basically + + align:start position:0% +uh differential equations basically + + + align:start position:0% +uh differential equations basically +so + + align:start position:0% + + + + align:start position:0% + +the function + + align:start position:0% + + + + align:start position:0% + +g of x + + align:start position:0% +g of x + + + align:start position:0% +g of x +equals + + align:start position:0% +equals + + + align:start position:0% +equals +the integral from a to x + + align:start position:0% +the integral from a to x + + + align:start position:0% +the integral from a to x +of + + align:start position:0% + + + + align:start position:0% + +f + + align:start position:0% +f + + + align:start position:0% +f +so for each x and a b + + align:start position:0% +so for each x and a b + + + align:start position:0% +so for each x and a b +so + + align:start position:0% + + + + align:start position:0% + +i stick it in + + align:start position:0% +i stick it in + + + align:start position:0% +i stick it in +as + + align:start position:0% +as + + + align:start position:0% +as +the upper limit on this integral + + align:start position:0% + + + + align:start position:0% + +this function is + + align:start position:0% + + + + align:start position:0% + +differentiable on a b + + align:start position:0% + + + + align:start position:0% + +and it satisfies the simplest + + align:start position:0% +and it satisfies the simplest + + + align:start position:0% +and it satisfies the simplest +differential equation + + align:start position:0% +differential equation + + + align:start position:0% +differential equation +which is + + align:start position:0% +which is + + + align:start position:0% +which is +g prime equals f + + align:start position:0% +g prime equals f + + + align:start position:0% +g prime equals f +and + + align:start position:0% +and + + + align:start position:0% +and +g of a equals 0. + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so this is a fundamental theorem of + + align:start position:0% +so this is a fundamental theorem of + + + align:start position:0% +so this is a fundamental theorem of +calculus the first part being about how + + align:start position:0% +calculus the first part being about how + + + align:start position:0% +calculus the first part being about how +do you compute integrals the second how + + align:start position:0% +do you compute integrals the second how + + + align:start position:0% +do you compute integrals the second how +do you compute solutions to a + + align:start position:0% +do you compute solutions to a + + + align:start position:0% +do you compute solutions to a +differential equation namely + + align:start position:0% +differential equation namely + + + align:start position:0% +differential equation namely +how do i find the solution to the + + align:start position:0% +how do i find the solution to the + + + align:start position:0% +how do i find the solution to the +problem g prime equals little f so + + align:start position:0% +problem g prime equals little f so + + + align:start position:0% +problem g prime equals little f so +little f is the given i want to find a + + align:start position:0% +little f is the given i want to find a + + + align:start position:0% +little f is the given i want to find a +function g that satisfies g prime equals + + align:start position:0% +function g that satisfies g prime equals + + + align:start position:0% +function g that satisfies g prime equals +little f with initial condition capital + + align:start position:0% +little f with initial condition capital + + + align:start position:0% +little f with initial condition capital +g of a equals 0 that's given by this + + align:start position:0% +g of a equals 0 that's given by this + + + align:start position:0% +g of a equals 0 that's given by this +function here where i take little f and + + align:start position:0% +function here where i take little f and + + + align:start position:0% +function here where i take little f and +i integrate it from a to x + + align:start position:0% +i integrate it from a to x + + + align:start position:0% +i integrate it from a to x +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's how i interpret the + + align:start position:0% +so that's how i interpret the + + + align:start position:0% +so that's how i interpret the +fundamental theorem of calculus the + + align:start position:0% +fundamental theorem of calculus the + + + align:start position:0% +fundamental theorem of calculus the +first about + + align:start position:0% +first about + + + align:start position:0% +first about +solving integrals a second about + + align:start position:0% +solving integrals a second about + + + align:start position:0% +solving integrals a second about +solving differential equations + + align:start position:0% + + + + align:start position:0% + +all right so this is the hero of uh + + align:start position:0% +all right so this is the hero of uh + + + align:start position:0% +all right so this is the hero of uh +calculus + + align:start position:0% +calculus + + + align:start position:0% +calculus +the batman of the story + + align:start position:0% +the batman of the story + + + align:start position:0% +the batman of the story +and i said at one point that the mean + + align:start position:0% +and i said at one point that the mean + + + align:start position:0% +and i said at one point that the mean +value theorem is + + align:start position:0% +value theorem is + + + align:start position:0% +value theorem is +the alfred of this story + + align:start position:0% +the alfred of this story + + + align:start position:0% +the alfred of this story +and therefore it should play a decisive + + align:start position:0% +and therefore it should play a decisive + + + align:start position:0% +and therefore it should play a decisive +role in proving + + align:start position:0% + + + + align:start position:0% + +this theorem + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so we're uh + + align:start position:0% + + + + align:start position:0% + +going to connect these two things so in + + align:start position:0% +going to connect these two things so in + + + align:start position:0% +going to connect these two things so in +order to even get at this guy let's we + + align:start position:0% +order to even get at this guy let's we + + + align:start position:0% +order to even get at this guy let's we +have to take a partition a sequence of + + align:start position:0% +have to take a partition a sequence of + + + align:start position:0% +have to take a partition a sequence of +partitions converging with norm + + align:start position:0% +partitions converging with norm + + + align:start position:0% +partitions converging with norm +converging to zero so + + align:start position:0% +converging to zero so + + + align:start position:0% +converging to zero so +um + + align:start position:0% +um + + + align:start position:0% +um +and then see what we get so + + align:start position:0% +and then see what we get so + + + align:start position:0% +and then see what we get so +this is the proof of part one + + align:start position:0% + + + + align:start position:0% + +so let's take + + align:start position:0% + + + + align:start position:0% + +a sequence of tag partitions i keep + + align:start position:0% +a sequence of tag partitions i keep + + + align:start position:0% +a sequence of tag partitions i keep +forgetting to write tag and say the word + + align:start position:0% +forgetting to write tag and say the word + + + align:start position:0% +forgetting to write tag and say the word +tag but + + align:start position:0% +tag but + + + align:start position:0% +tag but +uh you should hear that even though i + + align:start position:0% +uh you should hear that even though i + + + align:start position:0% +uh you should hear that even though i +don't say it + + align:start position:0% +don't say it + + + align:start position:0% +don't say it +with norm + + align:start position:0% + + + + align:start position:0% + +actually we're not even going to + + align:start position:0% + + + + align:start position:0% + +this is correct so + + align:start position:0% + + + + align:start position:0% + +i'm actually going to come up with the + + align:start position:0% +i'm actually going to come up with the + + + align:start position:0% +i'm actually going to come up with the +tags in a minute so let's first take + + align:start position:0% +tags in a minute so let's first take + + + align:start position:0% +tags in a minute so let's first take +a sequence of partitions so this is + + align:start position:0% +a sequence of partitions so this is + + + align:start position:0% +a sequence of partitions so this is +actually completely correct + + align:start position:0% +actually completely correct + + + align:start position:0% +actually completely correct +so + + align:start position:0% +so + + + align:start position:0% +so +no tags yet no points chosen in between + + align:start position:0% +no tags yet no points chosen in between + + + align:start position:0% +no tags yet no points chosen in between +with norm converging to 0. + + align:start position:0% +with norm converging to 0. + + + align:start position:0% +with norm converging to 0. +and then i'm going to choose a special + + align:start position:0% +and then i'm going to choose a special + + + align:start position:0% +and then i'm going to choose a special +tag for each r + + align:start position:0% +tag for each r + + + align:start position:0% +tag for each r +so that + + align:start position:0% +so that + + + align:start position:0% +so that +in the limit i get this equality between + + align:start position:0% +in the limit i get this equality between + + + align:start position:0% +in the limit i get this equality between +the integral of f and capital f of b + + align:start position:0% +the integral of f and capital f of b + + + align:start position:0% +the integral of f and capital f of b +minus f capital f of a + + align:start position:0% +minus f capital f of a + + + align:start position:0% +minus f capital f of a +all right + + align:start position:0% + + + + align:start position:0% + +so here comes alfred by + + align:start position:0% + + + + align:start position:0% + +the mean value theorem so on + + align:start position:0% +the mean value theorem so on + + + align:start position:0% +the mean value theorem so on +so we have this + + align:start position:0% + + + + align:start position:0% + +sub interval + + align:start position:0% + + + + align:start position:0% + +x sub j minus 1 and x sub + + align:start position:0% +x sub j minus 1 and x sub + + + align:start position:0% +x sub j minus 1 and x sub +j so by the mean value theorem there + + align:start position:0% +j so by the mean value theorem there + + + align:start position:0% +j so by the mean value theorem there +exists + + align:start position:0% + + + + align:start position:0% + +for each j + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% +there exists + + + align:start position:0% +there exists +a point in between these two guys + + align:start position:0% + + + + align:start position:0% + +such + + align:start position:0% +such + + + align:start position:0% +such +that um + + align:start position:0% +that um + + + align:start position:0% +that um +if i take f of x of j + + align:start position:0% +if i take f of x of j + + + align:start position:0% +if i take f of x of j +of r + + align:start position:0% +of r + + + align:start position:0% +of r +minus f so capital f remember is this + + align:start position:0% +minus f so capital f remember is this + + + align:start position:0% +minus f so capital f remember is this +function that's differentiable and whose + + align:start position:0% +function that's differentiable and whose + + + align:start position:0% +function that's differentiable and whose +derivative gives me little f + + align:start position:0% + + + + align:start position:0% + +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +capital f prime of x c j of r + + align:start position:0% +capital f prime of x c j of r + + + align:start position:0% +capital f prime of x c j of r +times + + align:start position:0% +times + + + align:start position:0% +times +x j + + align:start position:0% +x j + + + align:start position:0% +x j +minus x j minus 1. + + align:start position:0% + + + + align:start position:0% + +and by assumption the derivative of + + align:start position:0% +and by assumption the derivative of + + + align:start position:0% +and by assumption the derivative of +capital f is equal to little f right so + + align:start position:0% +capital f is equal to little f right so + + + align:start position:0% +capital f is equal to little f right so +i'm going to replace this + + align:start position:0% +i'm going to replace this + + + align:start position:0% +i'm going to replace this +f prime with + + align:start position:0% +f prime with + + + align:start position:0% +f prime with +little f + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now these exc's i will take as my tag + + align:start position:0% +so now these exc's i will take as my tag + + + align:start position:0% +so now these exc's i will take as my tag +my sequence of tags + + align:start position:0% + + + + align:start position:0% + +put a star by this relation here + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +what do we + + align:start position:0% +what do we + + + align:start position:0% +what do we +conclude + + align:start position:0% +conclude + + + align:start position:0% +conclude +if i look at + + align:start position:0% + + + + align:start position:0% + +the riemann sum for f associated to now + + align:start position:0% + + + + align:start position:0% + +this sequence of + + align:start position:0% +this sequence of + + + align:start position:0% +this sequence of +tags where now the xc's + + align:start position:0% +tags where now the xc's + + + align:start position:0% +tags where now the xc's +are exactly these exceeds that satisfy + + align:start position:0% +are exactly these exceeds that satisfy + + + align:start position:0% +are exactly these exceeds that satisfy +this relation + + align:start position:0% + + + + align:start position:0% + +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +as before sum from j equals 1 to + + align:start position:0% +as before sum from j equals 1 to + + + align:start position:0% +as before sum from j equals 1 to +n of r + + align:start position:0% +n of r + + + align:start position:0% +n of r +f of x g + + align:start position:0% +f of x g + + + align:start position:0% +f of x g +c sub j + + align:start position:0% + + + + align:start position:0% + +now by + + align:start position:0% +now by + + + align:start position:0% +now by +how these exceeds were chosen remember + + align:start position:0% +how these exceeds were chosen remember + + + align:start position:0% +how these exceeds were chosen remember +they were chosen to satisfy + + align:start position:0% +they were chosen to satisfy + + + align:start position:0% +they were chosen to satisfy +this + + align:start position:0% +this + + + align:start position:0% +this +relation here star by the mean value + + align:start position:0% +relation here star by the mean value + + + align:start position:0% +relation here star by the mean value +theorem so this is + + align:start position:0% +theorem so this is + + + align:start position:0% +theorem so this is +equal to the sum from j equals 1 to n + + align:start position:0% +equal to the sum from j equals 1 to n + + + align:start position:0% +equal to the sum from j equals 1 to n +sub r + + align:start position:0% +sub r + + + align:start position:0% +sub r +f of x sub j + + align:start position:0% +f of x sub j + + + align:start position:0% +f of x sub j +minus f of x sub j minus 1 + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +and again this is a telescoping sum + + align:start position:0% +and again this is a telescoping sum + + + align:start position:0% +and again this is a telescoping sum +and so all i pick up is when j equals n + + align:start position:0% +and so all i pick up is when j equals n + + + align:start position:0% +and so all i pick up is when j equals n +sub n of r the last point and when + + align:start position:0% +sub n of r the last point and when + + + align:start position:0% +sub n of r the last point and when +j equals 0 so this is equal to f of + + align:start position:0% + + + + align:start position:0% + +f of the last point + + align:start position:0% +f of the last point + + + align:start position:0% +f of the last point +minus f of the first point + + align:start position:0% + + + + align:start position:0% + +now for partition this is always + + align:start position:0% +now for partition this is always + + + align:start position:0% +now for partition this is always +b + + align:start position:0% +b + + + align:start position:0% +b +and this is always a so this is f of b + + align:start position:0% +and this is always a so this is f of b + + + align:start position:0% +and this is always a so this is f of b +minus f of a + + align:start position:0% +minus f of a + + + align:start position:0% +minus f of a +so every one of these riemann sums + + align:start position:0% +so every one of these riemann sums + + + align:start position:0% +so every one of these riemann sums +this + + align:start position:0% +this + + + align:start position:0% +this +uh sequence of tag partitions gives me f + + align:start position:0% +uh sequence of tag partitions gives me f + + + align:start position:0% +uh sequence of tag partitions gives me f +of b minus f of a so then i get take the + + align:start position:0% +of b minus f of a so then i get take the + + + align:start position:0% +of b minus f of a so then i get take the +limit and i get the integral + + align:start position:0% +limit and i get the integral + + + align:start position:0% +limit and i get the integral +and therefore + + align:start position:0% + + + + align:start position:0% + +the integral from a b to f which is + + align:start position:0% +the integral from a b to f which is + + + align:start position:0% +the integral from a b to f which is +limited as r goes to infinity of s of f + + align:start position:0% + + + + align:start position:0% + +equals + + align:start position:0% +equals + + + align:start position:0% +equals +and we just computed this is always + + align:start position:0% +and we just computed this is always + + + align:start position:0% +and we just computed this is always +equal to f of b minus f of a so + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +we took a sequence of just a + + align:start position:0% +we took a sequence of just a + + + align:start position:0% +we took a sequence of just a +recap we took a sequence of partitions + + align:start position:0% +recap we took a sequence of partitions + + + align:start position:0% +recap we took a sequence of partitions +with norms converging to zero + + align:start position:0% +with norms converging to zero + + + align:start position:0% +with norms converging to zero +and we chose special tags okay + + align:start position:0% +and we chose special tags okay + + + align:start position:0% +and we chose special tags okay +using the mean value theorem so by the + + align:start position:0% +using the mean value theorem so by the + + + align:start position:0% +using the mean value theorem so by the +mean value theorem on each one of these + + align:start position:0% +mean value theorem on each one of these + + + align:start position:0% +mean value theorem on each one of these +sub intervals + + align:start position:0% +sub intervals + + + align:start position:0% +sub intervals +capital f evaluated at the right + + align:start position:0% +capital f evaluated at the right + + + align:start position:0% +capital f evaluated at the right +endpoint minus f evaluated at the left + + align:start position:0% +endpoint minus f evaluated at the left + + + align:start position:0% +endpoint minus f evaluated at the left +endpoint + + align:start position:0% +endpoint + + + align:start position:0% +endpoint +is equal to f so which is the derivative + + align:start position:0% +is equal to f so which is the derivative + + + align:start position:0% +is equal to f so which is the derivative +of capital f evaluated at some point in + + align:start position:0% +of capital f evaluated at some point in + + + align:start position:0% +of capital f evaluated at some point in +between times the length of the interval + + align:start position:0% +between times the length of the interval + + + align:start position:0% +between times the length of the interval +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now if we take the riemann sum + + align:start position:0% +so now if we take the riemann sum + + + align:start position:0% +so now if we take the riemann sum +associated to this + + align:start position:0% +associated to this + + + align:start position:0% +associated to this +sequence of tag partitions where these + + align:start position:0% +sequence of tag partitions where these + + + align:start position:0% +sequence of tag partitions where these +xc's are defined by this condition + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +we can actually compute this riemann sum + + align:start position:0% +we can actually compute this riemann sum + + + align:start position:0% +we can actually compute this riemann sum +and it just gives me f of b minus f of a + + align:start position:0% +and it just gives me f of b minus f of a + + + align:start position:0% +and it just gives me f of b minus f of a +no matter what + + align:start position:0% +no matter what + + + align:start position:0% +no matter what +r is so then when i take the limit as r + + align:start position:0% +r is so then when i take the limit as r + + + align:start position:0% +r is so then when i take the limit as r +goes to infinity + + align:start position:0% +goes to infinity + + + align:start position:0% +goes to infinity +uh the left side goes to the integral + + align:start position:0% +uh the left side goes to the integral + + + align:start position:0% +uh the left side goes to the integral +but it's always equal to capital f of b + + align:start position:0% +but it's always equal to capital f of b + + + align:start position:0% +but it's always equal to capital f of b +minus f of a + + align:start position:0% +minus f of a + + + align:start position:0% +minus f of a +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so that proves number one + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so for number two + + align:start position:0% +so for number two + + + align:start position:0% +so for number two +um + + align:start position:0% + + + + align:start position:0% + +what do we want to show we want to show + + align:start position:0% +what do we want to show we want to show + + + align:start position:0% +what do we want to show we want to show +this function so first off it's by um + + align:start position:0% +this function so first off it's by um + + + align:start position:0% +this function so first off it's by um +convention + + align:start position:0% +convention + + + align:start position:0% +convention +g of a which is the integral from a to a + + align:start position:0% +g of a which is the integral from a to a + + + align:start position:0% +g of a which is the integral from a to a +of f this is zero so i don't have to + + align:start position:0% +of f this is zero so i don't have to + + + align:start position:0% +of f this is zero so i don't have to +check the second condition i just need + + align:start position:0% +check the second condition i just need + + + align:start position:0% +check the second condition i just need +to check that this function is + + align:start position:0% +to check that this function is + + + align:start position:0% +to check that this function is +differentiable and uh the derivative of + + align:start position:0% +differentiable and uh the derivative of + + + align:start position:0% +differentiable and uh the derivative of +that function is little f + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let's see b in + + align:start position:0% +let's see b in + + + align:start position:0% +let's see b in +a b + + align:start position:0% +a b + + + align:start position:0% +a b +so what do we want to show + + align:start position:0% +so what do we want to show + + + align:start position:0% +so what do we want to show +we want to show + + align:start position:0% +we want to show + + + align:start position:0% +we want to show +the derivative of capital g + + align:start position:0% +the derivative of capital g + + + align:start position:0% +the derivative of capital g +is equal to little f so + + align:start position:0% +is equal to little f so + + + align:start position:0% +is equal to little f so +we would like to show that the limit as + + align:start position:0% +we would like to show that the limit as + + + align:start position:0% +we would like to show that the limit as +x goes to c of the integral + + align:start position:0% +x goes to c of the integral + + + align:start position:0% +x goes to c of the integral +from + + align:start position:0% + + + + align:start position:0% + +a to x of f + + align:start position:0% +a to x of f + + + align:start position:0% +a to x of f +minus the integral from a to c of f + + align:start position:0% +minus the integral from a to c of f + + + align:start position:0% +minus the integral from a to c of f +over x minus c which is this is just g + + align:start position:0% +over x minus c which is this is just g + + + align:start position:0% +over x minus c which is this is just g +of x minus g of c equals + + align:start position:0% +of x minus g of c equals + + + align:start position:0% +of x minus g of c equals +f c + + align:start position:0% +f c + + + align:start position:0% +f c +okay + + align:start position:0% + + + + align:start position:0% + +so we're going to do this by + + align:start position:0% +so we're going to do this by + + + align:start position:0% +so we're going to do this by +uh + + align:start position:0% +uh + + + align:start position:0% +uh +by the books by the book i guess + + align:start position:0% +by the books by the book i guess + + + align:start position:0% +by the books by the book i guess +um + + align:start position:0% +um + + + align:start position:0% +um +when i say so that's + + align:start position:0% +when i say so that's + + + align:start position:0% +when i say so that's +that's kind of a bad pun i guess i don't + + align:start position:0% +that's kind of a bad pun i guess i don't + + + align:start position:0% +that's kind of a bad pun i guess i don't +know but + + align:start position:0% +know but + + + align:start position:0% +know but +meaning an epsilon delta + + align:start position:0% +meaning an epsilon delta + + + align:start position:0% +meaning an epsilon delta +proof for this limit so + + align:start position:0% +proof for this limit so + + + align:start position:0% +proof for this limit so +let epsilon be positive + + align:start position:0% +let epsilon be positive + + + align:start position:0% +let epsilon be positive +the delta that we pick in the end + + align:start position:0% +the delta that we pick in the end + + + align:start position:0% +the delta that we pick in the end +depends on + + align:start position:0% +depends on + + + align:start position:0% +depends on +and we'll use crucially the fact that f + + align:start position:0% +and we'll use crucially the fact that f + + + align:start position:0% +and we'll use crucially the fact that f +is continuous + + align:start position:0% +is continuous + + + align:start position:0% +is continuous +at c + + align:start position:0% +at c + + + align:start position:0% +at c +okay + + align:start position:0% + + + + align:start position:0% + +so since + + align:start position:0% + + + + align:start position:0% + +f is + + align:start position:0% +f is + + + align:start position:0% +f is +continuous at c + + align:start position:0% +continuous at c + + + align:start position:0% +continuous at c +there exists a delta 0 positive + + align:start position:0% +there exists a delta 0 positive + + + align:start position:0% +there exists a delta 0 positive +such that + + align:start position:0% +such that + + + align:start position:0% +such that +what + + align:start position:0% +what + + + align:start position:0% +what +t minus c less than delta 0 + + align:start position:0% +t minus c less than delta 0 + + + align:start position:0% +t minus c less than delta 0 +implies that + + align:start position:0% +implies that + + + align:start position:0% +implies that +f of t minus + + align:start position:0% +f of t minus + + + align:start position:0% +f of t minus +f c is less than epsilon let's give + + align:start position:0% +f c is less than epsilon let's give + + + align:start position:0% +f c is less than epsilon let's give +ourselves a little room over 2. + + align:start position:0% +ourselves a little room over 2. + + + align:start position:0% +ourselves a little room over 2. +okay + + align:start position:0% +okay + + + align:start position:0% +okay +choose delta to be + + align:start position:0% + + + + align:start position:0% + +this delta zero remember we have to show + + align:start position:0% +this delta zero remember we have to show + + + align:start position:0% +this delta zero remember we have to show +for every epsilon there exists a delta + + align:start position:0% +for every epsilon there exists a delta + + + align:start position:0% +for every epsilon there exists a delta +so that if x minus c is less than delta + + align:start position:0% +so that if x minus c is less than delta + + + align:start position:0% +so that if x minus c is less than delta +then this minus this an absolute value + + align:start position:0% +then this minus this an absolute value + + + align:start position:0% +then this minus this an absolute value +is less than epsilon i'm now saying + + align:start position:0% +is less than epsilon i'm now saying + + + align:start position:0% +is less than epsilon i'm now saying +choose delta to be this delta 0 where + + align:start position:0% +choose delta to be this delta 0 where + + + align:start position:0% +choose delta to be this delta 0 where +this delta 0 is ensuring + + align:start position:0% + + + + align:start position:0% + +this right here + + align:start position:0% + + + + align:start position:0% + +okay as long as t minus e is less than + + align:start position:0% +okay as long as t minus e is less than + + + align:start position:0% +okay as long as t minus e is less than +delta zero + + align:start position:0% + + + + align:start position:0% + +now because of uh sign conventions um + + align:start position:0% +now because of uh sign conventions um + + + align:start position:0% +now because of uh sign conventions um +we'll do two cases so + + align:start position:0% +we'll do two cases so + + + align:start position:0% +we'll do two cases so +not really i'm just going to do + + align:start position:0% +not really i'm just going to do + + + align:start position:0% +not really i'm just going to do +1k so + + align:start position:0% +1k so + + + align:start position:0% +1k so +suppose that + + align:start position:0% + + + + align:start position:0% + +x is between c and c plus delta so we + + align:start position:0% +x is between c and c plus delta so we + + + align:start position:0% +x is between c and c plus delta so we +want to also show uh + + align:start position:0% +want to also show uh + + + align:start position:0% +want to also show uh +we'll also need to be able to do the + + align:start position:0% +we'll also need to be able to do the + + + align:start position:0% +we'll also need to be able to do the +case that x is between c minus delta and + + align:start position:0% +case that x is between c minus delta and + + + align:start position:0% +case that x is between c minus delta and +c that would cover the whole range of + + align:start position:0% +c that would cover the whole range of + + + align:start position:0% +c that would cover the whole range of +uh the absolute value of x minus c is + + align:start position:0% +uh the absolute value of x minus c is + + + align:start position:0% +uh the absolute value of x minus c is +less than delta but bigger than zero 0 + + align:start position:0% +less than delta but bigger than zero 0 + + + align:start position:0% +less than delta but bigger than zero 0 +i'm just going to do this case + + align:start position:0% + + + + align:start position:0% + +so now we want to show that if x is in + + align:start position:0% +so now we want to show that if x is in + + + align:start position:0% +so now we want to show that if x is in +here then this thing minus this thing in + + align:start position:0% +here then this thing minus this thing in + + + align:start position:0% +here then this thing minus this thing in +absolute value is less than epsilon + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +first off i would like to note that + + align:start position:0% +first off i would like to note that + + + align:start position:0% +first off i would like to note that +if + + align:start position:0% + + + + align:start position:0% + +t is in + + align:start position:0% + + + + align:start position:0% + +this integral this interval c to x + + align:start position:0% +this integral this interval c to x + + + align:start position:0% +this integral this interval c to x +then that tells me that + + align:start position:0% +then that tells me that + + + align:start position:0% +then that tells me that +so the absolute value of t minus c which + + align:start position:0% +so the absolute value of t minus c which + + + align:start position:0% +so the absolute value of t minus c which +is equal just + + align:start position:0% +is equal just + + + align:start position:0% +is equal just +t minus c this is less than or equal to + + align:start position:0% +t minus c this is less than or equal to + + + align:start position:0% +t minus c this is less than or equal to +x minus c + + align:start position:0% +x minus c + + + align:start position:0% +x minus c +which is less than delta + + align:start position:0% +which is less than delta + + + align:start position:0% +which is less than delta +and remember this equals delta zero all + + align:start position:0% +and remember this equals delta zero all + + + align:start position:0% +and remember this equals delta zero all +right + + align:start position:0% +right + + + align:start position:0% +right +so + + align:start position:0% + + + + align:start position:0% + +as long as i'm in this interval here + + align:start position:0% +as long as i'm in this interval here + + + align:start position:0% +as long as i'm in this interval here +the absolute value of t minus e is less + + align:start position:0% +the absolute value of t minus e is less + + + align:start position:0% +the absolute value of t minus e is less +than delta zero so let me just draw a + + align:start position:0% +than delta zero so let me just draw a + + + align:start position:0% +than delta zero so let me just draw a +picture so that this is pretty clear + + align:start position:0% +picture so that this is pretty clear + + + align:start position:0% +picture so that this is pretty clear +this length is delta if i take any + + align:start position:0% +this length is delta if i take any + + + align:start position:0% +this length is delta if i take any +t in between then this distance from t + + align:start position:0% +t in between then this distance from t + + + align:start position:0% +t in between then this distance from t +to c is also going to be less than delta + + align:start position:0% +to c is also going to be less than delta + + + align:start position:0% +to c is also going to be less than delta +so that's all i've written down + + align:start position:0% +so that's all i've written down + + + align:start position:0% +so that's all i've written down +okay + + align:start position:0% + + + + align:start position:0% + +thus + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +right now compute + + align:start position:0% +right now compute + + + align:start position:0% +right now compute +the difference quotient minus the + + align:start position:0% +the difference quotient minus the + + + align:start position:0% +the difference quotient minus the +proposed limit + + align:start position:0% +proposed limit + + + align:start position:0% +proposed limit +so + + align:start position:0% +so + + + align:start position:0% +so +looking at 1 over x minus c + + align:start position:0% +looking at 1 over x minus c + + + align:start position:0% +looking at 1 over x minus c +times the integral + + align:start position:0% + + + + align:start position:0% + +minus the integral from a + + align:start position:0% +minus the integral from a + + + align:start position:0% +minus the integral from a +c of f + + align:start position:0% + + + + align:start position:0% + +minus + + align:start position:0% +minus + + + align:start position:0% +minus +f c this is the thing i want to show is + + align:start position:0% +f c this is the thing i want to show is + + + align:start position:0% +f c this is the thing i want to show is +less than epsilon now by additivity the + + align:start position:0% +less than epsilon now by additivity the + + + align:start position:0% +less than epsilon now by additivity the +integral from a to x since x is uh + + align:start position:0% +integral from a to x since x is uh + + + align:start position:0% +integral from a to x since x is uh +well the integral from a to x of f is + + align:start position:0% +well the integral from a to x of f is + + + align:start position:0% +well the integral from a to x of f is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +the integral from a to c plus the + + align:start position:0% +the integral from a to c plus the + + + align:start position:0% +the integral from a to c plus the +integral from c to x + + align:start position:0% +integral from c to x + + + align:start position:0% +integral from c to x +right so this is equal to + + align:start position:0% +right so this is equal to + + + align:start position:0% +right so this is equal to +1 over x minus c + + align:start position:0% +1 over x minus c + + + align:start position:0% +1 over x minus c +integral from + + align:start position:0% +integral from + + + align:start position:0% +integral from +c to x of f + + align:start position:0% +c to x of f + + + align:start position:0% +c to x of f +minus f of c + + align:start position:0% + + + + align:start position:0% + +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +this is just a fixed number okay + + align:start position:0% +this is just a fixed number okay + + + align:start position:0% +this is just a fixed number okay +and therefore + + align:start position:0% + + + + align:start position:0% + +i'm going to do a little trick + + align:start position:0% + + + + align:start position:0% + +minus the integral from so + + align:start position:0% +minus the integral from so + + + align:start position:0% +minus the integral from so +in fact let me do this let me throw in + + align:start position:0% +in fact let me do this let me throw in + + + align:start position:0% +in fact let me do this let me throw in +some integration + + align:start position:0% +some integration + + + align:start position:0% +some integration +variables so that this becomes clear + + align:start position:0% + + + + align:start position:0% + +so this is um + + align:start position:0% +so this is um + + + align:start position:0% +so this is um +f of t dt minus integral of f of t + + align:start position:0% +f of t dt minus integral of f of t + + + align:start position:0% +f of t dt minus integral of f of t +dt i've been using the notation where i + + align:start position:0% +dt i've been using the notation where i + + + align:start position:0% +dt i've been using the notation where i +just don't write down the integration + + align:start position:0% +just don't write down the integration + + + align:start position:0% +just don't write down the integration +variable but let me do that here + + align:start position:0% +variable but let me do that here + + + align:start position:0% +variable but let me do that here +f of t dt minus f of c + + align:start position:0% +f of t dt minus f of c + + + align:start position:0% +f of t dt minus f of c +okay + + align:start position:0% + + + + align:start position:0% + +now this is equal to minus + + align:start position:0% +now this is equal to minus + + + align:start position:0% +now this is equal to minus +f of c over x minus c + + align:start position:0% +f of c over x minus c + + + align:start position:0% +f of c over x minus c +integral from + + align:start position:0% +integral from + + + align:start position:0% +integral from +c to x of 1 + + align:start position:0% +c to x of 1 + + + align:start position:0% +c to x of 1 +dt + + align:start position:0% +dt + + + align:start position:0% +dt +right + + align:start position:0% +right + + + align:start position:0% +right +because the integral from c to x of the + + align:start position:0% +because the integral from c to x of the + + + align:start position:0% +because the integral from c to x of the +constant 1 gives me x minus c that + + align:start position:0% +constant 1 gives me x minus c that + + + align:start position:0% +constant 1 gives me x minus c that +cancels with this guy now f of c is just + + align:start position:0% +cancels with this guy now f of c is just + + + align:start position:0% +cancels with this guy now f of c is just +a number it's just a fixed number so i + + align:start position:0% +a number it's just a fixed number so i + + + align:start position:0% +a number it's just a fixed number so i +can bring this inside the integral + + align:start position:0% +can bring this inside the integral + + + align:start position:0% +can bring this inside the integral +and then use + + align:start position:0% + + + + align:start position:0% + +the linearity of the integral to in fact + + align:start position:0% +the linearity of the integral to in fact + + + align:start position:0% +the linearity of the integral to in fact +rewrite all of this as + + align:start position:0% +rewrite all of this as + + + align:start position:0% +rewrite all of this as +1 over the absolute value of x minus c + + align:start position:0% +1 over the absolute value of x minus c + + + align:start position:0% +1 over the absolute value of x minus c +integral from c to x of f of t + + align:start position:0% + + + + align:start position:0% + +minus + + align:start position:0% +minus + + + align:start position:0% +minus +f of c + + align:start position:0% +f of c + + + align:start position:0% +f of c +dt an absolute value + + align:start position:0% + + + + align:start position:0% + +now 1 over x minus c this is positive + + align:start position:0% +now 1 over x minus c this is positive + + + align:start position:0% +now 1 over x minus c this is positive +because x is bigger than c so + + align:start position:0% +because x is bigger than c so + + + align:start position:0% +because x is bigger than c so +i can pull this out just like that + + align:start position:0% + + + + align:start position:0% + +and now what do i know for t + + align:start position:0% +and now what do i know for t + + + align:start position:0% +and now what do i know for t +in between this uh between c and x + + align:start position:0% +in between this uh between c and x + + + align:start position:0% +in between this uh between c and x +the absolute value of t minus c + + align:start position:0% +the absolute value of t minus c + + + align:start position:0% +the absolute value of t minus c +is less than delta + + align:start position:0% +is less than delta + + + align:start position:0% +is less than delta +zero right so by + + align:start position:0% +zero right so by + + + align:start position:0% +zero right so by +um + + align:start position:0% +um + + + align:start position:0% +um +what i have here + + align:start position:0% +what i have here + + + align:start position:0% +what i have here +as long as i'm in this interval cx + + align:start position:0% +as long as i'm in this interval cx + + + align:start position:0% +as long as i'm in this interval cx +i'm going to have this inequality + + align:start position:0% +i'm going to have this inequality + + + align:start position:0% +i'm going to have this inequality +hold + + align:start position:0% +hold + + + align:start position:0% +hold +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +so before i do that let me first apply + + align:start position:0% +so before i do that let me first apply + + + align:start position:0% +so before i do that let me first apply +the triangle inequality for integrals + + align:start position:0% +the triangle inequality for integrals + + + align:start position:0% +the triangle inequality for integrals +this is less than or equal to the + + align:start position:0% +this is less than or equal to the + + + align:start position:0% +this is less than or equal to the +integral from c to x of + + align:start position:0% +integral from c to x of + + + align:start position:0% +integral from c to x of +f of t minus f of c + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so by the second thing that i've + + align:start position:0% +so by the second thing that i've + + + align:start position:0% +so by the second thing that i've +underlined + + align:start position:0% +underlined + + + align:start position:0% +underlined +uh for t in this interval c to x this + + align:start position:0% +uh for t in this interval c to x this + + + align:start position:0% +uh for t in this interval c to x this +thing here + + align:start position:0% +thing here + + + align:start position:0% +thing here +is always less than epsilon over two + + align:start position:0% +is always less than epsilon over two + + + align:start position:0% +is always less than epsilon over two +so by what we know about integrals um + + align:start position:0% +so by what we know about integrals um + + + align:start position:0% +so by what we know about integrals um +respecting inequalities + + align:start position:0% +respecting inequalities + + + align:start position:0% +respecting inequalities +this is going to be less than or equal + + align:start position:0% +this is going to be less than or equal + + + align:start position:0% +this is going to be less than or equal +to 1 over integral x minus c integral c + + align:start position:0% +to 1 over integral x minus c integral c + + + align:start position:0% +to 1 over integral x minus c integral c +to x + + align:start position:0% +to x + + + align:start position:0% +to x +epsilon over 2 + + align:start position:0% +epsilon over 2 + + + align:start position:0% +epsilon over 2 +dt + + align:start position:0% +dt + + + align:start position:0% +dt +and now this is just equal to so this is + + align:start position:0% +and now this is just equal to so this is + + + align:start position:0% +and now this is just equal to so this is +a number it comes out so i get one c + + align:start position:0% +a number it comes out so i get one c + + + align:start position:0% +a number it comes out so i get one c +integral from c to x of one so i get x + + align:start position:0% +integral from c to x of one so i get x + + + align:start position:0% +integral from c to x of one so i get x +minus c + + align:start position:0% +minus c + + + align:start position:0% +minus c +so + + align:start position:0% + + + + align:start position:0% + +times the integral of one so x minus c + + align:start position:0% +times the integral of one so x minus c + + + align:start position:0% +times the integral of one so x minus c +and that cancels + + align:start position:0% + + + + align:start position:0% + +less than epsilon + + align:start position:0% +less than epsilon + + + align:start position:0% +less than epsilon +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and you know so this was for x between c + + align:start position:0% +and you know so this was for x between c + + + align:start position:0% +and you know so this was for x between c +and c plus delta the argument for c + + align:start position:0% +and c plus delta the argument for c + + + align:start position:0% +and c plus delta the argument for c +between c and c minus delta is + + align:start position:0% +between c and c minus delta is + + + align:start position:0% +between c and c minus delta is +essentially the same okay just with + + align:start position:0% +essentially the same okay just with + + + align:start position:0% +essentially the same okay just with +you know minor sign changes + + align:start position:0% + + + + align:start position:0% + +so similarly + + align:start position:0% +so similarly + + + align:start position:0% +so similarly +c minus delta + + align:start position:0% +c minus delta + + + align:start position:0% +c minus delta +less than c implies that the integral + + align:start position:0% +less than c implies that the integral + + + align:start position:0% +less than c implies that the integral +from + + align:start position:0% +from + + + align:start position:0% +from +a to x of f minus integral a to c of f + + align:start position:0% +a to x of f minus integral a to c of f + + + align:start position:0% +a to x of f minus integral a to c of f +over x minus c + + align:start position:0% +over x minus c + + + align:start position:0% +over x minus c +minus f of c + + align:start position:0% +minus f of c + + + align:start position:0% +minus f of c +is + + align:start position:0% + + + + align:start position:0% + +less than epsilon + + align:start position:0% +less than epsilon + + + align:start position:0% +less than epsilon +so we've done + + align:start position:0% +so we've done + + + align:start position:0% +so we've done +x between c minus delta and c x between + + align:start position:0% +x between c minus delta and c x between + + + align:start position:0% +x between c minus delta and c x between +c and c plus delta so + + align:start position:0% +c and c plus delta so + + + align:start position:0% +c and c plus delta so +which implies that + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +which is what we wanted to prove + + align:start position:0% +which is what we wanted to prove + + + align:start position:0% +which is what we wanted to prove +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +we've + + align:start position:0% +we've + + + align:start position:0% +we've +concluded the proof of the batman of the + + align:start position:0% +concluded the proof of the batman of the + + + align:start position:0% +concluded the proof of the batman of the +story + + align:start position:0% +story + + + align:start position:0% +story +um + + align:start position:0% +um + + + align:start position:0% +um +and this gives us not only a way of + + align:start position:0% +and this gives us not only a way of + + + align:start position:0% +and this gives us not only a way of +computing integrals but + + align:start position:0% +computing integrals but + + + align:start position:0% +computing integrals but +useful way of um + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +if you like shifting the the burden or + + align:start position:0% +if you like shifting the the burden or + + + align:start position:0% +if you like shifting the the burden or +shifting the blame whenever we do + + align:start position:0% +shifting the blame whenever we do + + + align:start position:0% +shifting the blame whenever we do +compute the integrals of certain + + align:start position:0% +compute the integrals of certain + + + align:start position:0% +compute the integrals of certain +products so what i'm talking about is + + align:start position:0% +products so what i'm talking about is + + + align:start position:0% +products so what i'm talking about is +the integration by parts + + align:start position:0% +the integration by parts + + + align:start position:0% +the integration by parts +which i can't remember if i said it was + + align:start position:0% +which i can't remember if i said it was + + + align:start position:0% +which i can't remember if i said it was +first or second i think it was second + + align:start position:0% +first or second i think it was second + + + align:start position:0% +first or second i think it was second +okay first most useful thing from + + align:start position:0% +okay first most useful thing from + + + align:start position:0% +okay first most useful thing from +analysis is um the triangle inequality + + align:start position:0% +analysis is um the triangle inequality + + + align:start position:0% +analysis is um the triangle inequality +the second being integration by parts + + align:start position:0% + + + + align:start position:0% + +and a close third being the koshi + + align:start position:0% +and a close third being the koshi + + + align:start position:0% +and a close third being the koshi +koshi schwartz inequality + + align:start position:0% +koshi schwartz inequality + + + align:start position:0% +koshi schwartz inequality +which in conjunction with integration by + + align:start position:0% +which in conjunction with integration by + + + align:start position:0% +which in conjunction with integration by +parts is quite a + + align:start position:0% + + + + align:start position:0% + +most research current research papers + + align:start position:0% +most research current research papers + + + align:start position:0% +most research current research papers +are based on these two things right and + + align:start position:0% +are based on these two things right and + + + align:start position:0% +are based on these two things right and +using them in a very clever way + + align:start position:0% +using them in a very clever way + + + align:start position:0% +using them in a very clever way +so integration by parts is + + align:start position:0% + + + + align:start position:0% + +suppose f and g + + align:start position:0% +suppose f and g + + + align:start position:0% +suppose f and g +are + + align:start position:0% + + + + align:start position:0% + +continuously differentiable + + align:start position:0% + + + + align:start position:0% + +what that means is that + + align:start position:0% + + + + align:start position:0% + +the derivatives exist on a b and they're + + align:start position:0% +the derivatives exist on a b and they're + + + align:start position:0% +the derivatives exist on a b and they're +also continuous + + align:start position:0% + + + + align:start position:0% + +so if i you hear me say continuously + + align:start position:0% +so if i you hear me say continuously + + + align:start position:0% +so if i you hear me say continuously +differentiable in the future that means + + align:start position:0% +differentiable in the future that means + + + align:start position:0% +differentiable in the future that means +that the function has a derivative + + align:start position:0% +that the function has a derivative + + + align:start position:0% +that the function has a derivative +that's continuous + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the integral from a b + + align:start position:0% +the integral from a b + + + align:start position:0% +the integral from a b +of f prime times g so the one with the + + align:start position:0% +of f prime times g so the one with the + + + align:start position:0% +of f prime times g so the one with the +burden because remember + + align:start position:0% +burden because remember + + + align:start position:0% +burden because remember +differentiability is kind of a miracle + + align:start position:0% +differentiability is kind of a miracle + + + align:start position:0% +differentiability is kind of a miracle +so + + align:start position:0% +so + + + align:start position:0% +so +miracles always + + align:start position:0% +miracles always + + + align:start position:0% +miracles always +come with some sort of burden this is + + align:start position:0% +come with some sort of burden this is + + + align:start position:0% +come with some sort of burden this is +equal to f of + + align:start position:0% +equal to f of + + + align:start position:0% +equal to f of +b times g of b + + align:start position:0% +b times g of b + + + align:start position:0% +b times g of b +minus f of a times g of a + + align:start position:0% +minus f of a times g of a + + + align:start position:0% +minus f of a times g of a +minus the integral from a to b + + align:start position:0% +minus the integral from a to b + + + align:start position:0% +minus the integral from a to b +and now we shift that burden to g times + + align:start position:0% +and now we shift that burden to g times + + + align:start position:0% +and now we shift that burden to g times +g prime + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so let me put a parenthesis around that + + align:start position:0% +so let me put a parenthesis around that + + + align:start position:0% +so let me put a parenthesis around that +so you can no i don't + + align:start position:0% +so you can no i don't + + + align:start position:0% +so you can no i don't +let's do it this way g prime f + + align:start position:0% +let's do it this way g prime f + + + align:start position:0% +let's do it this way g prime f +all right so i can take that derivative + + align:start position:0% +all right so i can take that derivative + + + align:start position:0% +all right so i can take that derivative +and put it on g + + align:start position:0% +and put it on g + + + align:start position:0% +and put it on g +and what's the proof the proof is just + + align:start position:0% +and what's the proof the proof is just + + + align:start position:0% +and what's the proof the proof is just +the fundamental theorem of calculus and + + align:start position:0% +the fundamental theorem of calculus and + + + align:start position:0% +the fundamental theorem of calculus and +the product rule + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +the derivative of f times g is equal to + + align:start position:0% +the derivative of f times g is equal to + + + align:start position:0% +the derivative of f times g is equal to +f prime times g plus + + align:start position:0% +f prime times g plus + + + align:start position:0% +f prime times g plus +g prime times f + + align:start position:0% +g prime times f + + + align:start position:0% +g prime times f +we get by the fundamental theorem of + + align:start position:0% +we get by the fundamental theorem of + + + align:start position:0% +we get by the fundamental theorem of +calculus the integral + + align:start position:0% + + + + align:start position:0% + +from a b of let's say the right hand + + align:start position:0% +from a b of let's say the right hand + + + align:start position:0% +from a b of let's say the right hand +side so this is f prime g + + align:start position:0% +side so this is f prime g + + + align:start position:0% +side so this is f prime g +plus g prime f + + align:start position:0% +plus g prime f + + + align:start position:0% +plus g prime f +is equal to the integral from a to b of + + align:start position:0% +is equal to the integral from a to b of + + + align:start position:0% +is equal to the integral from a to b of +f + + align:start position:0% +f + + + align:start position:0% +f +times g prime + + align:start position:0% +times g prime + + + align:start position:0% +times g prime +so + + align:start position:0% +so + + + align:start position:0% +so +by fundamental theorem + + align:start position:0% +by fundamental theorem + + + align:start position:0% +by fundamental theorem +of calculus + + align:start position:0% +of calculus + + + align:start position:0% +of calculus +and now the integral of the derivative + + align:start position:0% +and now the integral of the derivative + + + align:start position:0% +and now the integral of the derivative +is + + align:start position:0% +is + + + align:start position:0% +is +the function evaluated at the endpoints + + align:start position:0% +the function evaluated at the endpoints + + + align:start position:0% +the function evaluated at the endpoints +so that's f of + + align:start position:0% +so that's f of + + + align:start position:0% +so that's f of +b times g of b + + align:start position:0% +b times g of b + + + align:start position:0% +b times g of b +minus f of a + + align:start position:0% +minus f of a + + + align:start position:0% +minus f of a +times g of a + + align:start position:0% +times g of a + + + align:start position:0% +times g of a +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +that's integration by parts which is a + + align:start position:0% +that's integration by parts which is a + + + align:start position:0% +that's integration by parts which is a +consequence of + + align:start position:0% +consequence of + + + align:start position:0% +consequence of +you know + + align:start position:0% +you know + + + align:start position:0% +you know +the product rule + + align:start position:0% + + + + align:start position:0% + +the quotient rule is something it's just + + align:start position:0% +the quotient rule is something it's just + + + align:start position:0% +the quotient rule is something it's just +really the product rule in disguise kind + + align:start position:0% +really the product rule in disguise kind + + + align:start position:0% +really the product rule in disguise kind +of so we don't get really anything new + + align:start position:0% +of so we don't get really anything new + + + align:start position:0% +of so we don't get really anything new +from there + + align:start position:0% + + + + align:start position:0% + +but we also remember have the chain rule + + align:start position:0% +but we also remember have the chain rule + + + align:start position:0% +but we also remember have the chain rule +which then results in + + align:start position:0% +which then results in + + + align:start position:0% +which then results in +the change of variables formula + + align:start position:0% +the change of variables formula + + + align:start position:0% +the change of variables formula +theorem + + align:start position:0% + + + + align:start position:0% + +let v from a b + + align:start position:0% +let v from a b + + + align:start position:0% +let v from a b +to c d + + align:start position:0% + + + + align:start position:0% + +be + + align:start position:0% + + + + align:start position:0% + +continuously differentiable + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +this means the function is continuous + + align:start position:0% +this means the function is continuous + + + align:start position:0% +this means the function is continuous +and its derivative is also continuous + + align:start position:0% + + + + align:start position:0% + +with the property + + align:start position:0% + + + + align:start position:0% + +that the derivative is positive + + align:start position:0% + + + + align:start position:0% + +on a b + + align:start position:0% +on a b + + + align:start position:0% +on a b +b of a equals c + + align:start position:0% +b of a equals c + + + align:start position:0% +b of a equals c +b of b equals d + + align:start position:0% + + + + align:start position:0% + +it's hard to see that a + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you can think of phi as being a + + align:start position:0% +so you can think of phi as being a + + + align:start position:0% +so you can think of phi as being a +change of variables from c d to a b + + align:start position:0% + + + + align:start position:0% + +then the integral from c to d + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +f + + align:start position:0% +f + + + align:start position:0% +f +of u d u is equal to + + align:start position:0% +of u d u is equal to + + + align:start position:0% +of u d u is equal to +the integral from a to b + + align:start position:0% + + + + align:start position:0% + +f of p of x + + align:start position:0% +f of p of x + + + align:start position:0% +f of p of x +a prime of x + + align:start position:0% +a prime of x + + + align:start position:0% +a prime of x +dx so + + align:start position:0% +dx so + + + align:start position:0% +dx so +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +instead of change of variables + + align:start position:0% + + + + align:start position:0% + +so this is + + align:start position:0% + + + + align:start position:0% + +change of variables aka + + align:start position:0% + + + + align:start position:0% + +u-substitution + + align:start position:0% +u-substitution + + + align:start position:0% +u-substitution +where you set u equal to phi of x then d + + align:start position:0% +where you set u equal to phi of x then d + + + align:start position:0% +where you set u equal to phi of x then d +u is equal to v prime of x dx + + align:start position:0% +u is equal to v prime of x dx + + + align:start position:0% +u is equal to v prime of x dx +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and again the proof of this + + align:start position:0% +and again the proof of this + + + align:start position:0% +and again the proof of this +just follows from the fundamental + + align:start position:0% +just follows from the fundamental + + + align:start position:0% +just follows from the fundamental +theorem of calculus and the chain rule + + align:start position:0% +theorem of calculus and the chain rule + + + align:start position:0% +theorem of calculus and the chain rule +um + + align:start position:0% + + + + align:start position:0% + +that we know so + + align:start position:0% + + + + align:start position:0% + +let f be a function from a b to r + + align:start position:0% +let f be a function from a b to r + + + align:start position:0% +let f be a function from a b to r +such that + + align:start position:0% +such that + + + align:start position:0% +such that +f prime equals little f + + align:start position:0% +f prime equals little f + + + align:start position:0% +f prime equals little f +uh we can always find one by the second + + align:start position:0% +uh we can always find one by the second + + + align:start position:0% +uh we can always find one by the second +part of the fundamental theorem of + + align:start position:0% +part of the fundamental theorem of + + + align:start position:0% +part of the fundamental theorem of +calculus right we can always solve that + + align:start position:0% +calculus right we can always solve that + + + align:start position:0% +calculus right we can always solve that +differenti this differential equation + + align:start position:0% +differenti this differential equation + + + align:start position:0% +differenti this differential equation +up to a constant + + align:start position:0% + + + + align:start position:0% + +then if i look at the function + + align:start position:0% + + + + align:start position:0% + +f of p of x and i take its derivative + + align:start position:0% +f of p of x and i take its derivative + + + align:start position:0% +f of p of x and i take its derivative +with respect to x by the chain rule this + + align:start position:0% +with respect to x by the chain rule this + + + align:start position:0% +with respect to x by the chain rule this +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +f + + align:start position:0% +f + + + align:start position:0% +f +prime of + + align:start position:0% +prime of + + + align:start position:0% +prime of +p of x times phi + + align:start position:0% +p of x times phi + + + align:start position:0% +p of x times phi +prime of x + + align:start position:0% +prime of x + + + align:start position:0% +prime of x +which equals f of + + align:start position:0% +which equals f of + + + align:start position:0% +which equals f of +v of x + + align:start position:0% +v of x + + + align:start position:0% +v of x +p prime of x + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so then when i integrate that + + align:start position:0% + + + + align:start position:0% + +integral from a b + + align:start position:0% +integral from a b + + + align:start position:0% +integral from a b +or b of x + + align:start position:0% + + + + align:start position:0% + +f of b of x + + align:start position:0% + + + + align:start position:0% + +the prime of x + + align:start position:0% +the prime of x + + + align:start position:0% +the prime of x +dx this is equal to + + align:start position:0% +dx this is equal to + + + align:start position:0% +dx this is equal to +the integral from a b + + align:start position:0% +the integral from a b + + + align:start position:0% +the integral from a b +of f of phi of + + align:start position:0% +of f of phi of + + + align:start position:0% +of f of phi of +x + + align:start position:0% +x + + + align:start position:0% +x +prime dx + + align:start position:0% +prime dx + + + align:start position:0% +prime dx +now by part one of the fundamental + + align:start position:0% +now by part one of the fundamental + + + align:start position:0% +now by part one of the fundamental +theorem of calculus this is equal to + + align:start position:0% +theorem of calculus this is equal to + + + align:start position:0% +theorem of calculus this is equal to +um + + align:start position:0% +um + + + align:start position:0% +um +the integral of the derivative is this + + align:start position:0% +the integral of the derivative is this + + + align:start position:0% +the integral of the derivative is this +thing evaluated at the end point so f of + + align:start position:0% +thing evaluated at the end point so f of + + + align:start position:0% +thing evaluated at the end point so f of +v of b + + align:start position:0% +v of b + + + align:start position:0% +v of b +minus f of v of a + + align:start position:0% +minus f of v of a + + + align:start position:0% +minus f of v of a +this is equal to f of + + align:start position:0% +this is equal to f of + + + align:start position:0% +this is equal to f of +d minus f of + + align:start position:0% +d minus f of + + + align:start position:0% +d minus f of +c because phi of b equals d + + align:start position:0% +c because phi of b equals d + + + align:start position:0% +c because phi of b equals d +b of c + + align:start position:0% +b of c + + + align:start position:0% +b of c +phi of a equals c + + align:start position:0% +phi of a equals c + + + align:start position:0% +phi of a equals c +and phi of b equals d + + align:start position:0% +and phi of b equals d + + + align:start position:0% +and phi of b equals d +but again by the fundamental theorem of + + align:start position:0% +but again by the fundamental theorem of + + + align:start position:0% +but again by the fundamental theorem of +calculus since capital f is when you + + align:start position:0% +calculus since capital f is when you + + + align:start position:0% +calculus since capital f is when you +differentiate it gives me little f + + align:start position:0% +differentiate it gives me little f + + + align:start position:0% +differentiate it gives me little f +this is equal to the integral from c to + + align:start position:0% +this is equal to the integral from c to + + + align:start position:0% +this is equal to the integral from c to +d of + + align:start position:0% +d of + + + align:start position:0% +d of +f prime + + align:start position:0% +f prime + + + align:start position:0% +f prime +of u d u which is equal to + + align:start position:0% + + + + align:start position:0% + +f of u + + align:start position:0% +f of u + + + align:start position:0% +f of u +d u + + align:start position:0% +d u + + + align:start position:0% +d u +again so we just applied the fundamental + + align:start position:0% +again so we just applied the fundamental + + + align:start position:0% +again so we just applied the fundamental +theorem of calculus really three times + + align:start position:0% +theorem of calculus really three times + + + align:start position:0% +theorem of calculus really three times +okay first to find a function whose + + align:start position:0% +okay first to find a function whose + + + align:start position:0% +okay first to find a function whose +derivative is little f + + align:start position:0% +derivative is little f + + + align:start position:0% +derivative is little f +then we use the chain rule to to + + align:start position:0% +then we use the chain rule to to + + + align:start position:0% +then we use the chain rule to to +conclude that the derivative of capital + + align:start position:0% +conclude that the derivative of capital + + + align:start position:0% +conclude that the derivative of capital +f of phi equals this thing which is the + + align:start position:0% +f of phi equals this thing which is the + + + align:start position:0% +f of phi equals this thing which is the +thing we're integrating on the right + + align:start position:0% +thing we're integrating on the right + + + align:start position:0% +thing we're integrating on the right +hand side + + align:start position:0% +hand side + + + align:start position:0% +hand side +so that when we integrate that that's + + align:start position:0% +so that when we integrate that that's + + + align:start position:0% +so that when we integrate that that's +equal to the integral of a derivative + + align:start position:0% +equal to the integral of a derivative + + + align:start position:0% +equal to the integral of a derivative +and therefore we just pick up the + + align:start position:0% +and therefore we just pick up the + + + align:start position:0% +and therefore we just pick up the +endpoints + + align:start position:0% +endpoints + + + align:start position:0% +endpoints +f of d minus f of c but because capital + + align:start position:0% +f of d minus f of c but because capital + + + align:start position:0% +f of d minus f of c but because capital +f is equal to + + align:start position:0% +f is equal to + + + align:start position:0% +f is equal to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is an anti-derivative of little f + + align:start position:0% +is an anti-derivative of little f + + + align:start position:0% +is an anti-derivative of little f +meaning its derivative is little f it's + + align:start position:0% +meaning its derivative is little f it's + + + align:start position:0% +meaning its derivative is little f it's +also + + align:start position:0% +also + + + align:start position:0% +also +this number here is also equal to this + + align:start position:0% +this number here is also equal to this + + + align:start position:0% +this number here is also equal to this +integral here which is this guy + + align:start position:0% +integral here which is this guy + + + align:start position:0% +integral here which is this guy +and + + align:start position:0% +and + + + align:start position:0% +and +so then we get the the + + align:start position:0% +so then we get the the + + + align:start position:0% +so then we get the the +change of variables formula so i think + + align:start position:0% +change of variables formula so i think + + + align:start position:0% +change of variables formula so i think +we'll stop there and next time we'll do + + align:start position:0% +we'll stop there and next time we'll do + + + align:start position:0% +we'll stop there and next time we'll do +a quick application of + + align:start position:0% +a quick application of + + + align:start position:0% +a quick application of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the most second most useful thing on + + align:start position:0% +the most second most useful thing on + + + align:start position:0% +the most second most useful thing on +earth which is integration by parts + + align:start position:0% +earth which is integration by parts + + + align:start position:0% +earth which is integration by parts +and then we'll move on to sequences of + + align:start position:0% +and then we'll move on to sequences of + + + align:start position:0% +and then we'll move on to sequences of +functions + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/X5ivIqH5rB4.txt b/X5ivIqH5rB4.txt new file mode 100644 index 0000000000000000000000000000000000000000..5918006a68f7ba5e3e0e9128ceff76a8c37f221d --- /dev/null +++ b/X5ivIqH5rB4.txt @@ -0,0 +1,1395 @@ +align:start position:0% + +so 271 2710 is an introductory Optics + + align:start position:0% +so 271 2710 is an introductory Optics + + + align:start position:0% +so 271 2710 is an introductory Optics +course uh the idea is that the students + + align:start position:0% +course uh the idea is that the students + + + align:start position:0% +course uh the idea is that the students +do not know anything or very little + + align:start position:0% +do not know anything or very little + + + align:start position:0% +do not know anything or very little +about Optics to begin with and so the + + align:start position:0% +about Optics to begin with and so the + + + align:start position:0% +about Optics to begin with and so the +goal is that by the end of the course + + align:start position:0% +goal is that by the end of the course + + + align:start position:0% +goal is that by the end of the course +they will be able to not only understand + + align:start position:0% +they will be able to not only understand + + + align:start position:0% +they will be able to not only understand +very basics of light propagation but + + align:start position:0% +very basics of light propagation but + + + align:start position:0% +very basics of light propagation but +also they will be able to understand + + align:start position:0% +also they will be able to understand + + + align:start position:0% +also they will be able to understand +systems that utilize light for things + + align:start position:0% +systems that utilize light for things + + + align:start position:0% +systems that utilize light for things +like Imaging or telecommunications or or + + align:start position:0% +like Imaging or telecommunications or or + + + align:start position:0% +like Imaging or telecommunications or or +a number of different engineering + + align:start position:0% +a number of different engineering + + + align:start position:0% +a number of different engineering +applications and they will also be able + + align:start position:0% +applications and they will also be able + + + align:start position:0% +applications and they will also be able +to Design Systems of their own perhaps + + align:start position:0% +to Design Systems of their own perhaps + + + align:start position:0% +to Design Systems of their own perhaps +not very complicated systems but uh + + align:start position:0% +not very complicated systems but uh + + + align:start position:0% +not very complicated systems but uh +definitely systems that can do something + + align:start position:0% +definitely systems that can do something + + + align:start position:0% +definitely systems that can do something +useful so it is H so by definition then + + align:start position:0% +useful so it is H so by definition then + + + align:start position:0% +useful so it is H so by definition then +it means that it is oriented for + + align:start position:0% +it means that it is oriented for + + + align:start position:0% +it means that it is oriented for +students who are not necessarily into + + align:start position:0% +students who are not necessarily into + + + align:start position:0% +students who are not necessarily into +the physics or electrical engineering + + align:start position:0% +the physics or electrical engineering + + + align:start position:0% +the physics or electrical engineering +this disciplines where normally you get + + align:start position:0% +this disciplines where normally you get + + + align:start position:0% +this disciplines where normally you get +a lot of background in Optics even early + + align:start position:0% +a lot of background in Optics even early + + + align:start position:0% +a lot of background in Optics even early +on and the course has a lot of this + + align:start position:0% +on and the course has a lot of this + + + align:start position:0% +on and the course has a lot of this +orientation of starting with a very + + align:start position:0% +orientation of starting with a very + + + align:start position:0% +orientation of starting with a very +Basics and then building upon them so + + align:start position:0% +Basics and then building upon them so + + + align:start position:0% +Basics and then building upon them so +the general uh pedagogy is Guided by + + align:start position:0% +the general uh pedagogy is Guided by + + + align:start position:0% +the general uh pedagogy is Guided by +that a lot of the basic tools have to be + + align:start position:0% +that a lot of the basic tools have to be + + + align:start position:0% +that a lot of the basic tools have to be +taught from scratch but also I think + + align:start position:0% +taught from scratch but also I think + + + align:start position:0% +taught from scratch but also I think +that helps because the students actually + + align:start position:0% +that helps because the students actually + + + align:start position:0% +that helps because the students actually +pick up a lot of the material for + + align:start position:0% +pick up a lot of the material for + + + align:start position:0% +pick up a lot of the material for +example for transforms which is a + + align:start position:0% +example for transforms which is a + + + align:start position:0% +example for transforms which is a +mathematical technique they actually + + align:start position:0% +mathematical technique they actually + + + align:start position:0% +mathematical technique they actually +pick it up in the context of Optics and + + align:start position:0% +pick it up in the context of Optics and + + + align:start position:0% +pick it up in the context of Optics and +that really I + + align:start position:0% +that really I + + + align:start position:0% +that really I +from students and their advisor + + align:start position:0% +from students and their advisor + + + align:start position:0% +from students and their advisor +reactions I think this is something that + + align:start position:0% +reactions I think this is something that + + + align:start position:0% +reactions I think this is something that +they actually + + align:start position:0% +they actually + + + align:start position:0% +they actually +appreciate and um in terms of of judging + + align:start position:0% +appreciate and um in terms of of judging + + + align:start position:0% +appreciate and um in terms of of judging +performance obviously you have to take + + align:start position:0% +performance obviously you have to take + + + align:start position:0% +performance obviously you have to take +that into account that they are actually + + align:start position:0% +that into account that they are actually + + + align:start position:0% +that into account that they are actually +building the background there but by the + + align:start position:0% +building the background there but by the + + + align:start position:0% +building the background there but by the +end of the class they actually complete + + align:start position:0% +end of the class they actually complete + + + align:start position:0% +end of the class they actually complete +a project at least The Graduate students + + align:start position:0% +a project at least The Graduate students + + + align:start position:0% +a project at least The Graduate students +do and they typically do very very well + + align:start position:0% +do and they typically do very very well + + + align:start position:0% +do and they typically do very very well +so so my impression is that that from + + align:start position:0% +so so my impression is that that from + + + align:start position:0% +so so my impression is that that from +that point of view the course succeeds + + align:start position:0% +that point of view the course succeeds + + + align:start position:0% +that point of view the course succeeds +in this in its goals so I came to MIT + + align:start position:0% +in this in its goals so I came to MIT + + + align:start position:0% +in this in its goals so I came to MIT +about 5 years ago and before that a + + align:start position:0% +about 5 years ago and before that a + + + align:start position:0% +about 5 years ago and before that a +colleague who is a senior lecturer his + + align:start position:0% +colleague who is a senior lecturer his + + + align:start position:0% +colleague who is a senior lecturer his +name is Steve fanton he taught a version + + align:start position:0% +name is Steve fanton he taught a version + + + align:start position:0% +name is Steve fanton he taught a version +of this course three times and uh so + + align:start position:0% +of this course three times and uh so + + + align:start position:0% +of this course three times and uh so +this was really the first time that our + + align:start position:0% +this was really the first time that our + + + align:start position:0% +this was really the first time that our +department offered an Optics course and + + align:start position:0% +department offered an Optics course and + + + align:start position:0% +department offered an Optics course and +it was wildly successful he got very + + align:start position:0% +it was wildly successful he got very + + + align:start position:0% +it was wildly successful he got very +good attendance and very good reviews + + align:start position:0% +good attendance and very good reviews + + + align:start position:0% +good attendance and very good reviews +but Steve actually runs a company + + align:start position:0% +but Steve actually runs a company + + + align:start position:0% +but Steve actually runs a company +outside MIT he's not a full-time U + + align:start position:0% +outside MIT he's not a full-time U + + + align:start position:0% +outside MIT he's not a full-time U +employee so MIT decided this was a good + + align:start position:0% +employee so MIT decided this was a good + + + align:start position:0% +employee so MIT decided this was a good +direction for the Department to go so + + align:start position:0% +direction for the Department to go so + + + align:start position:0% +direction for the Department to go so +when I came here one of my missions was + + align:start position:0% +when I came here one of my missions was + + + align:start position:0% +when I came here one of my missions was +was actually to create that sequence and + + align:start position:0% +was actually to create that sequence and + + + align:start position:0% +was actually to create that sequence and +uh substantially why mechanical + + align:start position:0% +uh substantially why mechanical + + + align:start position:0% +uh substantially why mechanical +engineering needs that course is because + + align:start position:0% +engineering needs that course is because + + + align:start position:0% +engineering needs that course is because +Optics is fundamental in many of the + + align:start position:0% +Optics is fundamental in many of the + + + align:start position:0% +Optics is fundamental in many of the +core mechanical engineering disciplines + + align:start position:0% +core mechanical engineering disciplines + + + align:start position:0% +core mechanical engineering disciplines +for example uh measurement + + align:start position:0% +for example uh measurement + + + align:start position:0% +for example uh measurement +instrumentation uh controls uh Imaging + + align:start position:0% +instrumentation uh controls uh Imaging + + + align:start position:0% +instrumentation uh controls uh Imaging +is a very important part very often of + + align:start position:0% +is a very important part very often of + + + align:start position:0% +is a very important part very often of +mechanical engineering for things such + + align:start position:0% +mechanical engineering for things such + + + align:start position:0% +mechanical engineering for things such +as Robotics and of course these are all + + align:start position:0% +as Robotics and of course these are all + + + align:start position:0% +as Robotics and of course these are all +interdisciplinary subjects but to a very + + align:start position:0% +interdisciplinary subjects but to a very + + + align:start position:0% +interdisciplinary subjects but to a very +large degree they belong to Makey now in + + align:start position:0% +large degree they belong to Makey now in + + + align:start position:0% +large degree they belong to Makey now in +addition to that the course of course is + + align:start position:0% +addition to that the course of course is + + + align:start position:0% +addition to that the course of course is +open to all MIT students in fact I do + + align:start position:0% +open to all MIT students in fact I do + + + align:start position:0% +open to all MIT students in fact I do +get students from electrical engineering + + align:start position:0% +get students from electrical engineering + + + align:start position:0% +get students from electrical engineering +and physics occasionally but also from + + align:start position:0% +and physics occasionally but also from + + + align:start position:0% +and physics occasionally but also from +other disciplines I've had students from + + align:start position:0% +other disciplines I've had students from + + + align:start position:0% +other disciplines I've had students from +Ocean engineering from AO asro even + + align:start position:0% +Ocean engineering from AO asro even + + + align:start position:0% +Ocean engineering from AO asro even +architecture actually in my course and + + align:start position:0% +architecture actually in my course and + + + align:start position:0% +architecture actually in my course and +of course typically these are graduate + + align:start position:0% +of course typically these are graduate + + + align:start position:0% +of course typically these are graduate +students for whom some aspect of Optics + + align:start position:0% +students for whom some aspect of Optics + + + align:start position:0% +students for whom some aspect of Optics +typical Imaging becomes important in + + align:start position:0% +typical Imaging becomes important in + + + align:start position:0% +typical Imaging becomes important in +their research and then the course + + align:start position:0% +their research and then the course + + + align:start position:0% +their research and then the course +serves them very well because it gives + + align:start position:0% +serves them very well because it gives + + + align:start position:0% +serves them very well because it gives +them the tools and the fundamentals to + + align:start position:0% +them the tools and the fundamentals to + + + align:start position:0% +them the tools and the fundamentals to +use it but the it does not require the + + align:start position:0% +use it but the it does not require the + + + align:start position:0% +use it but the it does not require the +heavy physics background that is + + align:start position:0% +heavy physics background that is + + + align:start position:0% +heavy physics background that is +typically to be expected in an Optics + + align:start position:0% +typically to be expected in an Optics + + + align:start position:0% +typically to be expected in an Optics +course so I have a slightly unusual + + align:start position:0% +course so I have a slightly unusual + + + align:start position:0% +course so I have a slightly unusual +schedule in the class uh one of the + + align:start position:0% +schedule in the class uh one of the + + + align:start position:0% +schedule in the class uh one of the +there's two lectures per week one of + + align:start position:0% +there's two lectures per week one of + + + align:start position:0% +there's two lectures per week one of +them lasts for two hours and the other + + align:start position:0% +them lasts for two hours and the other + + + align:start position:0% +them lasts for two hours and the other +last for 1 hour so I try to to design + + align:start position:0% +last for 1 hour so I try to to design + + + align:start position:0% +last for 1 hour so I try to to design +the the sequence of topics so that in + + align:start position:0% +the the sequence of topics so that in + + + align:start position:0% +the the sequence of topics so that in +the 2hour session we cover a lot of the + + align:start position:0% +the 2hour session we cover a lot of the + + + align:start position:0% +the 2hour session we cover a lot of the +fundamental material and uh a lot of so + + align:start position:0% +fundamental material and uh a lot of so + + + align:start position:0% +fundamental material and uh a lot of so +to speak the heavy stuff if I can use + + align:start position:0% +to speak the heavy stuff if I can use + + + align:start position:0% +to speak the heavy stuff if I can use +the term and then in the one hour + + align:start position:0% +the term and then in the one hour + + + align:start position:0% +the term and then in the one hour +session we actually solve problems or we + + align:start position:0% +session we actually solve problems or we + + + align:start position:0% +session we actually solve problems or we +look into some more detail into + + align:start position:0% +look into some more detail into + + + align:start position:0% +look into some more detail into +applications and so on so the 2our + + align:start position:0% +applications and so on so the 2our + + + align:start position:0% +applications and so on so the 2our +session sometimes ends up being a little + + align:start position:0% +session sometimes ends up being a little + + + align:start position:0% +session sometimes ends up being a little +bit difficult to carry out both for me + + align:start position:0% +bit difficult to carry out both for me + + + align:start position:0% +bit difficult to carry out both for me +and the students because it requires you + + align:start position:0% +and the students because it requires you + + + align:start position:0% +and the students because it requires you +know it requires concentrated attention + + align:start position:0% +know it requires concentrated attention + + + align:start position:0% +know it requires concentrated attention +for a long time but I think it pays off + + align:start position:0% +for a long time but I think it pays off + + + align:start position:0% +for a long time but I think it pays off +because uh with a proper structure + + align:start position:0% +because uh with a proper structure + + + align:start position:0% +because uh with a proper structure +typically we break once or twice for a + + align:start position:0% +typically we break once or twice for a + + + align:start position:0% +typically we break once or twice for a +few minutes and then I try to interject + + align:start position:0% +few minutes and then I try to interject + + + align:start position:0% +few minutes and then I try to interject +jokes and so on during the lecture so + + align:start position:0% +jokes and so on during the lecture so + + + align:start position:0% +jokes and so on during the lecture so +the students sort of they recover their + + align:start position:0% +the students sort of they recover their + + + align:start position:0% +the students sort of they recover their +attention as opposed to falling asleep + + align:start position:0% +attention as opposed to falling asleep + + + align:start position:0% +attention as opposed to falling asleep +and um and by the end of the two-hour + + align:start position:0% +and um and by the end of the two-hour + + + align:start position:0% +and um and by the end of the two-hour +lecture they have received the material + + align:start position:0% +lecture they have received the material + + + align:start position:0% +lecture they have received the material +which then they see again in a more + + align:start position:0% +which then they see again in a more + + + align:start position:0% +which then they see again in a more +practical form in the one hour so I + + align:start position:0% +practical form in the one hour so I + + + align:start position:0% +practical form in the one hour so I +think it reinforces quite a bit so the + + align:start position:0% +think it reinforces quite a bit so the + + + align:start position:0% +think it reinforces quite a bit so the +class has the typical requirements the + + align:start position:0% +class has the typical requirements the + + + align:start position:0% +class has the typical requirements the +students have to do homeworks they have + + align:start position:0% +students have to do homeworks they have + + + align:start position:0% +students have to do homeworks they have +to take exams and in addition The + + align:start position:0% +to take exams and in addition The + + + align:start position:0% +to take exams and in addition The +Graduate students they have to carry out + + align:start position:0% +Graduate students they have to carry out + + + align:start position:0% +Graduate students they have to carry out +a project so let me start by saying why + + align:start position:0% +a project so let me start by saying why + + + align:start position:0% +a project so let me start by saying why +the under I do not require a project + + align:start position:0% +the under I do not require a project + + + align:start position:0% +the under I do not require a project +from the undergraduates the reasons are + + align:start position:0% +from the undergraduates the reasons are + + + align:start position:0% +from the undergraduates the reasons are +purely logistical uh I tend to get a lot + + align:start position:0% +purely logistical uh I tend to get a lot + + + align:start position:0% +purely logistical uh I tend to get a lot +of seniors and juniors from our + + align:start position:0% +of seniors and juniors from our + + + align:start position:0% +of seniors and juniors from our +department and both of them near the end + + align:start position:0% +department and both of them near the end + + + align:start position:0% +department and both of them near the end +of the semester when the project would + + align:start position:0% +of the semester when the project would + + + align:start position:0% +of the semester when the project would +have to be carried out they're busy by + + align:start position:0% +have to be carried out they're busy by + + + align:start position:0% +have to be carried out they're busy by +other projects in other classes so it + + align:start position:0% +other projects in other classes so it + + + align:start position:0% +other projects in other classes so it +would really become a huge burden on + + align:start position:0% +would really become a huge burden on + + + align:start position:0% +would really become a huge burden on +them um for the grad graduate students + + align:start position:0% +them um for the grad graduate students + + + align:start position:0% +them um for the grad graduate students +typically do not have that limitation so + + align:start position:0% +typically do not have that limitation so + + + align:start position:0% +typically do not have that limitation so +so so it is okay what I find is that at + + align:start position:0% +so so it is okay what I find is that at + + + align:start position:0% +so so it is okay what I find is that at +the end when The Graduate students + + align:start position:0% +the end when The Graduate students + + + align:start position:0% +the end when The Graduate students +present their projects then the + + align:start position:0% +present their projects then the + + + align:start position:0% +present their projects then the +graduates they typically typically come + + align:start position:0% +graduates they typically typically come + + + align:start position:0% +graduates they typically typically come +into that session and attend so they're + + align:start position:0% +into that session and attend so they're + + + align:start position:0% +into that session and attend so they're +definitely interested and occasionally + + align:start position:0% +definitely interested and occasionally + + + align:start position:0% +definitely interested and occasionally +had one or two undergraduates who got + + align:start position:0% +had one or two undergraduates who got + + + align:start position:0% +had one or two undergraduates who got +involved in projects but it doesn't + + align:start position:0% +involved in projects but it doesn't + + + align:start position:0% +involved in projects but it doesn't +happen so often so what the project is + + align:start position:0% +happen so often so what the project is + + + align:start position:0% +happen so often so what the project is +about is actually very simple uh + + align:start position:0% +about is actually very simple uh + + + align:start position:0% +about is actually very simple uh +typically I give the students a few + + align:start position:0% +typically I give the students a few + + + align:start position:0% +typically I give the students a few +papers from the literature typically + + align:start position:0% +papers from the literature typically + + + align:start position:0% +papers from the literature typically +three or four papers what they have to + + align:start position:0% +three or four papers what they have to + + + align:start position:0% +three or four papers what they have to +do is H prepare a presentation almost a + + align:start position:0% +do is H prepare a presentation almost a + + + align:start position:0% +do is H prepare a presentation almost a +conference Style presentation it is + + align:start position:0% +conference Style presentation it is + + + align:start position:0% +conference Style presentation it is +about a 15 20 minute talk as if they + + align:start position:0% +about a 15 20 minute talk as if they + + + align:start position:0% +about a 15 20 minute talk as if they +were presenting their own work at the + + align:start position:0% +were presenting their own work at the + + + align:start position:0% +were presenting their own work at the +conference but of course it is not their + + align:start position:0% +conference but of course it is not their + + + align:start position:0% +conference but of course it is not their +own work it is what they read in the + + align:start position:0% +own work it is what they read in the + + + align:start position:0% +own work it is what they read in the +papers they gave them and typically I + + align:start position:0% +papers they gave them and typically I + + + align:start position:0% +papers they gave them and typically I +assigned them a mentor it could be me it + + align:start position:0% +assigned them a mentor it could be me it + + + align:start position:0% +assigned them a mentor it could be me it +could be the teaching assistant or some + + align:start position:0% +could be the teaching assistant or some + + + align:start position:0% +could be the teaching assistant or some +of my research students from my research + + align:start position:0% +of my research students from my research + + + align:start position:0% +of my research students from my research +group and then uh the mentors uh I + + align:start position:0% +group and then uh the mentors uh I + + + align:start position:0% +group and then uh the mentors uh I +instruct them to try to go a little bit + + align:start position:0% +instruct them to try to go a little bit + + + align:start position:0% +instruct them to try to go a little bit +beyond the papers not too far of course + + align:start position:0% +beyond the papers not too far of course + + + align:start position:0% +beyond the papers not too far of course +because it's is a class project not a + + align:start position:0% +because it's is a class project not a + + + align:start position:0% +because it's is a class project not a +project but typically before the + + align:start position:0% +project but typically before the + + + align:start position:0% +project but typically before the +students present they have to do some + + align:start position:0% +students present they have to do some + + + align:start position:0% +students present they have to do some +calculation or some additional design + + align:start position:0% +calculation or some additional design + + + align:start position:0% +calculation or some additional design +based on what they saw in the papers and + + align:start position:0% +based on what they saw in the papers and + + + align:start position:0% +based on what they saw in the papers and +I think that works very well because it + + align:start position:0% +I think that works very well because it + + + align:start position:0% +I think that works very well because it +really forces them to understand a + + align:start position:0% +really forces them to understand a + + + align:start position:0% +really forces them to understand a +little bit deeper than a traditional + + align:start position:0% +little bit deeper than a traditional + + + align:start position:0% +little bit deeper than a traditional +lecture presentation and that lasts for + + align:start position:0% +lecture presentation and that lasts for + + + align:start position:0% +lecture presentation and that lasts for +about a month actually and at the end + + align:start position:0% +about a month actually and at the end + + + align:start position:0% +about a month actually and at the end +they give a presentation of course this + + align:start position:0% +they give a presentation of course this + + + align:start position:0% +they give a presentation of course this +is a university so we buy free piz for + + align:start position:0% +is a university so we buy free piz for + + + align:start position:0% +is a university so we buy free piz for +them and all that stuff and uh it's a + + align:start position:0% +them and all that stuff and uh it's a + + + align:start position:0% +them and all that stuff and uh it's a +lot of fun usually the projects are the + + align:start position:0% +lot of fun usually the projects are the + + + align:start position:0% +lot of fun usually the projects are the +comments I get said that the projects + + align:start position:0% +comments I get said that the projects + + + align:start position:0% +comments I get said that the projects +are the one thing that I enjoy a lot + + align:start position:0% +are the one thing that I enjoy a lot + + + align:start position:0% +are the one thing that I enjoy a lot +about the class \ No newline at end of file diff --git a/Yw8vBDhVs8o.txt b/Yw8vBDhVs8o.txt new file mode 100644 index 0000000000000000000000000000000000000000..1195421094b8aa6798f8fc29dc06d4d4b7340e35 --- /dev/null +++ b/Yw8vBDhVs8o.txt @@ -0,0 +1,5611 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi today we finish up the last of the + + align:start position:0% +hi today we finish up the last of the + + + align:start position:0% +hi today we finish up the last of the +basic Vector operations today what we're + + align:start position:0% +basic Vector operations today what we're + + + align:start position:0% +basic Vector operations today what we're +going to discuss is something called the + + align:start position:0% +going to discuss is something called the + + + align:start position:0% +going to discuss is something called the +vector product or the cross product and + + align:start position:0% +vector product or the cross product and + + + align:start position:0% +vector product or the cross product and +it's a new type of multiplication + + align:start position:0% +it's a new type of multiplication + + + align:start position:0% +it's a new type of multiplication +whereby we now multiply two vectors to + + align:start position:0% +whereby we now multiply two vectors to + + + align:start position:0% +whereby we now multiply two vectors to +obtain a vector you see the dot product + + align:start position:0% +obtain a vector you see the dot product + + + align:start position:0% +obtain a vector you see the dot product +multiplied two vectors but it gave a + + align:start position:0% +multiplied two vectors but it gave a + + + align:start position:0% +multiplied two vectors but it gave a +Scala this is why the dot product was + + align:start position:0% +Scala this is why the dot product was + + + align:start position:0% +Scala this is why the dot product was +called a Scala product product now the + + align:start position:0% +called a Scala product product now the + + + align:start position:0% +called a Scala product product now the +idea is again we can go to the physical + + align:start position:0% +idea is again we can go to the physical + + + align:start position:0% +idea is again we can go to the physical +world to seek motivation and uh my only + + align:start position:0% +world to seek motivation and uh my only + + + align:start position:0% +world to seek motivation and uh my only +problem with that is that some of the + + align:start position:0% +problem with that is that some of the + + + align:start position:0% +problem with that is that some of the +examples that motivated this are not + + align:start position:0% +examples that motivated this are not + + + align:start position:0% +examples that motivated this are not +quite as Elementary as the work equals + + align:start position:0% +quite as Elementary as the work equals + + + align:start position:0% +quite as Elementary as the work equals +force time distance formula of last time + + align:start position:0% +force time distance formula of last time + + + align:start position:0% +force time distance formula of last time +uh the cross product does come up in + + align:start position:0% +uh the cross product does come up in + + + align:start position:0% +uh the cross product does come up in +sort of trivial applications in terms of + + align:start position:0% +sort of trivial applications in terms of + + + align:start position:0% +sort of trivial applications in terms of +moments angular momentum in terms of + + align:start position:0% +moments angular momentum in terms of + + + align:start position:0% +moments angular momentum in terms of +mechanics and in more Advanced + + align:start position:0% +mechanics and in more Advanced + + + align:start position:0% +mechanics and in more Advanced +situations in terms of the Maxwell + + align:start position:0% +situations in terms of the Maxwell + + + align:start position:0% +situations in terms of the Maxwell +equations where you may remember in + + align:start position:0% +equations where you may remember in + + + align:start position:0% +equations where you may remember in +physics courses going through this + + align:start position:0% +physics courses going through this + + + align:start position:0% +physics courses going through this +routine of the uh force and the flux and + + align:start position:0% +routine of the uh force and the flux and + + + align:start position:0% +routine of the uh force and the flux and +the intensity and what have you and at + + align:start position:0% +the intensity and what have you and at + + + align:start position:0% +the intensity and what have you and at +any rate rather than waste time and I + + align:start position:0% +any rate rather than waste time and I + + + align:start position:0% +any rate rather than waste time and I +mean I use the word waste here + + align:start position:0% +mean I use the word waste here + + + align:start position:0% +mean I use the word waste here +judiciously because for the purpose of + + align:start position:0% +judiciously because for the purpose of + + + align:start position:0% +judiciously because for the purpose of +our course it is not nearly as crucial + + align:start position:0% +our course it is not nearly as crucial + + + align:start position:0% +our course it is not nearly as crucial +to motivate why we invented the cross + + align:start position:0% +to motivate why we invented the cross + + + align:start position:0% +to motivate why we invented the cross +product physically as it is to define it + + align:start position:0% +product physically as it is to define it + + + align:start position:0% +product physically as it is to define it +mathematically and to use it + + align:start position:0% +mathematically and to use it + + + align:start position:0% +mathematically and to use it +structurally you see what I want to do + + align:start position:0% +structurally you see what I want to do + + + align:start position:0% +structurally you see what I want to do +is simply get to the Crux of the + + align:start position:0% +is simply get to the Crux of the + + + align:start position:0% +is simply get to the Crux of the +situation discuss the concept of a pro + + align:start position:0% +situation discuss the concept of a pro + + + align:start position:0% +situation discuss the concept of a pro +cross product and simply point out that + + align:start position:0% +cross product and simply point out that + + + align:start position:0% +cross product and simply point out that +if a and b are vectors by A cross B + + align:start position:0% +if a and b are vectors by A cross B + + + align:start position:0% +if a and b are vectors by A cross B +written this way A cross B we mean a + + align:start position:0% +written this way A cross B we mean a + + + align:start position:0% +written this way A cross B we mean a +vector now here's the kicker again as + + align:start position:0% +vector now here's the kicker again as + + + align:start position:0% +vector now here's the kicker again as +soon as I say Vector that means to + + align:start position:0% +soon as I say Vector that means to + + + align:start position:0% +soon as I say Vector that means to +Define it I have to tell you three + + align:start position:0% +Define it I have to tell you three + + + align:start position:0% +Define it I have to tell you three +ingredients namely magnitude Direction + + align:start position:0% +ingredients namely magnitude Direction + + + align:start position:0% +ingredients namely magnitude Direction +and sense right now for the magnitude of + + align:start position:0% +and sense right now for the magnitude of + + + align:start position:0% +and sense right now for the magnitude of +A cross + + align:start position:0% +A cross + + + align:start position:0% +A cross +B it's simply the magnitude of a Time + + align:start position:0% +B it's simply the magnitude of a Time + + + align:start position:0% +B it's simply the magnitude of a Time +the magnitude of B times the magnitude + + align:start position:0% +the magnitude of B times the magnitude + + + align:start position:0% +the magnitude of B times the magnitude +of the sign of the angle between a and b + + align:start position:0% +of the sign of the angle between a and b + + + align:start position:0% +of the sign of the angle between a and b +and I'm going to come back and comment + + align:start position:0% +and I'm going to come back and comment + + + align:start position:0% +and I'm going to come back and comment +on that in a few moments about the + + align:start position:0% +on that in a few moments about the + + + align:start position:0% +on that in a few moments about the +difference between the sign here versus + + align:start position:0% +difference between the sign here versus + + + align:start position:0% +difference between the sign here versus +the cosine of the previous lecture again + + align:start position:0% +the cosine of the previous lecture again + + + align:start position:0% +the cosine of the previous lecture again +physically there's a motivation for this + + align:start position:0% +physically there's a motivation for this + + + align:start position:0% +physically there's a motivation for this +as far as far as we're concerned all we + + align:start position:0% +as far as far as we're concerned all we + + + align:start position:0% +as far as far as we're concerned all we +have to do is say this is what the + + align:start position:0% +have to do is say this is what the + + + align:start position:0% +have to do is say this is what the +magnitude is defined to be this is the + + align:start position:0% +magnitude is defined to be this is the + + + align:start position:0% +magnitude is defined to be this is the +game we Define it this way next thing I + + align:start position:0% +game we Define it this way next thing I + + + align:start position:0% +game we Define it this way next thing I +have to do is tell you its + + align:start position:0% +have to do is tell you its + + + align:start position:0% +have to do is tell you its +direction and the direction of A cross B + + align:start position:0% +direction and the direction of A cross B + + + align:start position:0% +direction and the direction of A cross B +is by definition perpendicular to both A + + align:start position:0% +is by definition perpendicular to both A + + + align:start position:0% +is by definition perpendicular to both A +and B all + + align:start position:0% +and B all + + + align:start position:0% +and B all +right another way of saying that is in + + align:start position:0% +right another way of saying that is in + + + align:start position:0% +right another way of saying that is in +the event that A and B are not parallel + + align:start position:0% +the event that A and B are not parallel + + + align:start position:0% +the event that A and B are not parallel +then the vectors A and B determine a + + align:start position:0% +then the vectors A and B determine a + + + align:start position:0% +then the vectors A and B determine a +plane and what we're saying is that a + + align:start position:0% +plane and what we're saying is that a + + + align:start position:0% +plane and what we're saying is that a +cross B is then a vector perpendicular + + align:start position:0% +cross B is then a vector perpendicular + + + align:start position:0% +cross B is then a vector perpendicular +to the plane determined by A and B right + + align:start position:0% +to the plane determined by A and B right + + + align:start position:0% +to the plane determined by A and B right +by the way if a and b are parallel they + + align:start position:0% +by the way if a and b are parallel they + + + align:start position:0% +by the way if a and b are parallel they +don't determine a plane right because + + align:start position:0% +don't determine a plane right because + + + align:start position:0% +don't determine a plane right because +they coincide they have only one + + align:start position:0% +they coincide they have only one + + + align:start position:0% +they coincide they have only one +direction but if a and b are parallel + + align:start position:0% +direction but if a and b are parallel + + + align:start position:0% +direction but if a and b are parallel +the angle between them is 0 or 180 + + align:start position:0% +the angle between them is 0 or 180 + + + align:start position:0% +the angle between them is 0 or 180 +depending on whether their senses the + + align:start position:0% +depending on whether their senses the + + + align:start position:0% +depending on whether their senses the +same or not once the angle is either 0 + + align:start position:0% +same or not once the angle is either 0 + + + align:start position:0% +same or not once the angle is either 0 +or 180 the sign of that angle is zero + + align:start position:0% +or 180 the sign of that angle is zero + + + align:start position:0% +or 180 the sign of that angle is zero +once one of the factors here is zero the + + align:start position:0% +once one of the factors here is zero the + + + align:start position:0% +once one of the factors here is zero the +whole product is zero so in the event + + align:start position:0% +whole product is zero so in the event + + + align:start position:0% +whole product is zero so in the event +that A and B do not determine a plane + + align:start position:0% +that A and B do not determine a plane + + + align:start position:0% +that A and B do not determine a plane +the magnitude of A cross B is zero which + + align:start position:0% +the magnitude of A cross B is zero which + + + align:start position:0% +the magnitude of A cross B is zero which +means that A cross B is the zero vector + + align:start position:0% +means that A cross B is the zero vector + + + align:start position:0% +means that A cross B is the zero vector +and that's a pretty trivial situation so + + align:start position:0% +and that's a pretty trivial situation so + + + align:start position:0% +and that's a pretty trivial situation so +we just won't even worry about that and + + align:start position:0% +we just won't even worry about that and + + + align:start position:0% +we just won't even worry about that and +thirdly I must now give you the sense of + + align:start position:0% +thirdly I must now give you the sense of + + + align:start position:0% +thirdly I must now give you the sense of +A cross B and the sense is the usual + + align:start position:0% +A cross B and the sense is the usual + + + align:start position:0% +A cross B and the sense is the usual +right hand rule other words the + + align:start position:0% +right hand rule other words the + + + align:start position:0% +right hand rule other words the +direction in which a right-handed thread + + align:start position:0% +direction in which a right-handed thread + + + align:start position:0% +direction in which a right-handed thread +screw would turn as a is rotated into B + + align:start position:0% +screw would turn as a is rotated into B + + + align:start position:0% +screw would turn as a is rotated into B +and now I have to be careful because of + + align:start position:0% +and now I have to be careful because of + + + align:start position:0% +and now I have to be careful because of +this sign situation through the smaller + + align:start position:0% +this sign situation through the smaller + + + align:start position:0% +this sign situation through the smaller +angle you see look at notice that this + + align:start position:0% +angle you see look at notice that this + + + align:start position:0% +angle you see look at notice that this +sense is going to depend on what if you + + align:start position:0% +sense is going to depend on what if you + + + align:start position:0% +sense is going to depend on what if you +rotate a into B you get the opposite + + align:start position:0% +rotate a into B you get the opposite + + + align:start position:0% +rotate a into B you get the opposite +sense than if you rotated B into a and + + align:start position:0% +sense than if you rotated B into a and + + + align:start position:0% +sense than if you rotated B into a and +not only that but if you rotate a into B + + align:start position:0% +not only that but if you rotate a into B + + + align:start position:0% +not only that but if you rotate a into B +through the larger of the two angles + + align:start position:0% +through the larger of the two angles + + + align:start position:0% +through the larger of the two angles +notice that rotating a into B through + + align:start position:0% +notice that rotating a into B through + + + align:start position:0% +notice that rotating a into B through +one angle say the smaller one gives you + + align:start position:0% +one angle say the smaller one gives you + + + align:start position:0% +one angle say the smaller one gives you +a different sense than rotating a into B + + align:start position:0% +a different sense than rotating a into B + + + align:start position:0% +a different sense than rotating a into B +through the loger of the two angles so + + align:start position:0% +through the loger of the two angles so + + + align:start position:0% +through the loger of the two angles so +there's a certain ambiguity that comes + + align:start position:0% +there's a certain ambiguity that comes + + + align:start position:0% +there's a certain ambiguity that comes +up here and the ambiguity occurs because + + align:start position:0% +up here and the ambiguity occurs because + + + align:start position:0% +up here and the ambiguity occurs because +of the fact that we're using the sign + + align:start position:0% +of the fact that we're using the sign + + + align:start position:0% +of the fact that we're using the sign +rather than the cosine in other words if + + align:start position:0% +rather than the cosine in other words if + + + align:start position:0% +rather than the cosine in other words if +you reverse the sense of an angle if you + + align:start position:0% +you reverse the sense of an angle if you + + + align:start position:0% +you reverse the sense of an angle if you +change its sign the algebraic sign the + + align:start position:0% +change its sign the algebraic sign the + + + align:start position:0% +change its sign the algebraic sign the +trigonometric sign s n + + align:start position:0% +trigonometric sign s n + + + align:start position:0% +trigonometric sign s n +changes okay and similarly uh the sign + + align:start position:0% +changes okay and similarly uh the sign + + + align:start position:0% +changes okay and similarly uh the sign +of an angle is the negative of the sign + + align:start position:0% +of an angle is the negative of the sign + + + align:start position:0% +of an angle is the negative of the sign +of + + align:start position:0% +of + + + align:start position:0% +of +360° minus that angle okay but that at + + align:start position:0% +360° minus that angle okay but that at + + + align:start position:0% +360° minus that angle okay but that at +any rate is the definition of the cross + + align:start position:0% +any rate is the definition of the cross + + + align:start position:0% +any rate is the definition of the cross +product given two vectors their cross + + align:start position:0% +product given two vectors their cross + + + align:start position:0% +product given two vectors their cross +product is what a vector whose magnitude + + align:start position:0% +product is what a vector whose magnitude + + + align:start position:0% +product is what a vector whose magnitude +is the product of the two magnitudes + + align:start position:0% +is the product of the two magnitudes + + + align:start position:0% +is the product of the two magnitudes +times the magnitude of the of the sign + + align:start position:0% +times the magnitude of the of the sign + + + align:start position:0% +times the magnitude of the of the sign +of the angle between the two vectors the + + align:start position:0% +of the angle between the two vectors the + + + align:start position:0% +of the angle between the two vectors the +cross product is perpendicular to each + + align:start position:0% +cross product is perpendicular to each + + + align:start position:0% +cross product is perpendicular to each +of the two vectors and its senses the + + align:start position:0% +of the two vectors and its senses the + + + align:start position:0% +of the two vectors and its senses the +right hand rule as the first is rotated + + align:start position:0% +right hand rule as the first is rotated + + + align:start position:0% +right hand rule as the first is rotated +into the second through the smaller of + + align:start position:0% +into the second through the smaller of + + + align:start position:0% +into the second through the smaller of +the two angles + + align:start position:0% +the two angles + + + align:start position:0% +the two angles +okay this is important because you see + + align:start position:0% +okay this is important because you see + + + align:start position:0% +okay this is important because you see +what happens is that is important as the + + align:start position:0% +what happens is that is important as the + + + align:start position:0% +what happens is that is important as the +cross product is from a physical point + + align:start position:0% +cross product is from a physical point + + + align:start position:0% +cross product is from a physical point +of view arithmetically it's a nuisance + + align:start position:0% +of view arithmetically it's a nuisance + + + align:start position:0% +of view arithmetically it's a nuisance +we can take very few liberties with the + + align:start position:0% +we can take very few liberties with the + + + align:start position:0% +we can take very few liberties with the +cross product it turns out that almost + + align:start position:0% +cross product it turns out that almost + + + align:start position:0% +cross product it turns out that almost +every rule that we would like to be true + + align:start position:0% +every rule that we would like to be true + + + align:start position:0% +every rule that we would like to be true +about numerical multiplication is false + + align:start position:0% +about numerical multiplication is false + + + align:start position:0% +about numerical multiplication is false +for Vector cross products for example + + align:start position:0% +for Vector cross products for example + + + align:start position:0% +for Vector cross products for example +among other things A cross B is not + + align:start position:0% +among other things A cross B is not + + + align:start position:0% +among other things A cross B is not +equal to B cross a in fact A cross B is + + align:start position:0% +equal to B cross a in fact A cross B is + + + align:start position:0% +equal to B cross a in fact A cross B is +the negative of B cross a and the reason + + align:start position:0% +the negative of B cross a and the reason + + + align:start position:0% +the negative of B cross a and the reason +for this is simply as you check this + + align:start position:0% +for this is simply as you check this + + + align:start position:0% +for this is simply as you check this +thing through a cross B and B cross a + + align:start position:0% +thing through a cross B and B cross a + + + align:start position:0% +thing through a cross B and B cross a +certainly have the same magnitude they + + align:start position:0% +certainly have the same magnitude they + + + align:start position:0% +certainly have the same magnitude they +have the same direction because each is + + align:start position:0% +have the same direction because each is + + + align:start position:0% +have the same direction because each is +perpendicular to both A and B but notice + + align:start position:0% +perpendicular to both A and B but notice + + + align:start position:0% +perpendicular to both A and B but notice +that the sense is different namely A + + align:start position:0% +that the sense is different namely A + + + align:start position:0% +that the sense is different namely A +cross B tells us to rotate a into B + + align:start position:0% +cross B tells us to rotate a into B + + + align:start position:0% +cross B tells us to rotate a into B +through the smaller of the two angles + + align:start position:0% +through the smaller of the two angles + + + align:start position:0% +through the smaller of the two angles +and in that particular diagram that is + + align:start position:0% +and in that particular diagram that is + + + align:start position:0% +and in that particular diagram that is +what the counterclockwise Direction on + + align:start position:0% +what the counterclockwise Direction on + + + align:start position:0% +what the counterclockwise Direction on +the other hand B cross a says rotate B + + align:start position:0% +the other hand B cross a says rotate B + + + align:start position:0% +the other hand B cross a says rotate B +into a through the smaller of the two + + align:start position:0% +into a through the smaller of the two + + + align:start position:0% +into a through the smaller of the two +angles and if we do that notice that we + + align:start position:0% +angles and if we do that notice that we + + + align:start position:0% +angles and if we do that notice that we +get the clockwise Direction so that b + + align:start position:0% +get the clockwise Direction so that b + + + align:start position:0% +get the clockwise Direction so that b +cross A and A cross B have the same + + align:start position:0% +cross A and A cross B have the same + + + align:start position:0% +cross A and A cross B have the same +magnitude they have the same direction + + align:start position:0% +magnitude they have the same direction + + + align:start position:0% +magnitude they have the same direction +but they have the opposite sense that is + + align:start position:0% +but they have the opposite sense that is + + + align:start position:0% +but they have the opposite sense that is +a cross B is the negative of B cross a + + align:start position:0% +a cross B is the negative of B cross a + + + align:start position:0% +a cross B is the negative of B cross a +and what that means you see in + + align:start position:0% +and what that means you see in + + + align:start position:0% +and what that means you see in +computations is that every time you + + align:start position:0% +computations is that every time you + + + align:start position:0% +computations is that every time you +change the order of A and B in a cross + + align:start position:0% +change the order of A and B in a cross + + + align:start position:0% +change the order of A and B in a cross +product you must remember to change the + + align:start position:0% +product you must remember to change the + + + align:start position:0% +product you must remember to change the +sign in fact what's particularly + + align:start position:0% +sign in fact what's particularly + + + align:start position:0% +sign in fact what's particularly +embarrassing is if you forget to do this + + align:start position:0% +embarrassing is if you forget to do this + + + align:start position:0% +embarrassing is if you forget to do this +if this particular term is going to be + + align:start position:0% +if this particular term is going to be + + + align:start position:0% +if this particular term is going to be +added on to something and you forget to + + align:start position:0% +added on to something and you forget to + + + align:start position:0% +added on to something and you forget to +change its sign you're going to be off + + align:start position:0% +change its sign you're going to be off + + + align:start position:0% +change its sign you're going to be off +by more than just the error of a sign in + + align:start position:0% +by more than just the error of a sign in + + + align:start position:0% +by more than just the error of a sign in +other words if something was supposed to + + align:start position:0% +other words if something was supposed to + + + align:start position:0% +other words if something was supposed to +be + + align:start position:0% +be + + + align:start position:0% +be +plus4 and you have it as minus 4 or vice + + align:start position:0% +plus4 and you have it as minus 4 or vice + + + align:start position:0% +plus4 and you have it as minus 4 or vice +versa the error is going to be eight if + + align:start position:0% +versa the error is going to be eight if + + + align:start position:0% +versa the error is going to be eight if +you add it rather than subtract it you + + align:start position:0% +you add it rather than subtract it you + + + align:start position:0% +you add it rather than subtract it you +see so the error gets hidden in other + + align:start position:0% +see so the error gets hidden in other + + + align:start position:0% +see so the error gets hidden in other +computations but you in other words you + + align:start position:0% +computations but you in other words you + + + align:start position:0% +computations but you in other words you +can change the order of the factors but + + align:start position:0% +can change the order of the factors but + + + align:start position:0% +can change the order of the factors but +you must remember to change the sign + + align:start position:0% +you must remember to change the sign + + + align:start position:0% +you must remember to change the sign +another interesting thing is that unlike + + align:start position:0% +another interesting thing is that unlike + + + align:start position:0% +another interesting thing is that unlike +in the dot product where a dot b do c + + align:start position:0% +in the dot product where a dot b do c + + + align:start position:0% +in the dot product where a dot b do c +didn't even make sense it is true that a + + align:start position:0% +didn't even make sense it is true that a + + + align:start position:0% +didn't even make sense it is true that a +cross B Cross C and A cross B Cross C do + + align:start position:0% +cross B Cross C and A cross B Cross C do + + + align:start position:0% +cross B Cross C and A cross B Cross C do +make sense and by the way what are these + + align:start position:0% +make sense and by the way what are these + + + align:start position:0% +make sense and by the way what are these +things they're vectors B Cross C is a + + align:start position:0% +things they're vectors B Cross C is a + + + align:start position:0% +things they're vectors B Cross C is a +vector which is perpendicular to both B + + align:start position:0% +vector which is perpendicular to both B + + + align:start position:0% +vector which is perpendicular to both B +and C I mean it's it's per you see and a + + align:start position:0% +and C I mean it's it's per you see and a + + + align:start position:0% +and C I mean it's it's per you see and a +is a vector and the cross product of two + + align:start position:0% +is a vector and the cross product of two + + + align:start position:0% +is a vector and the cross product of two +vectors is again a vector Etc these are + + align:start position:0% +vectors is again a vector Etc these are + + + align:start position:0% +vectors is again a vector Etc these are +two vectors but in general these two + + align:start position:0% +two vectors but in general these two + + + align:start position:0% +two vectors but in general these two +vectors do not have to be equal in fact + + align:start position:0% +vectors do not have to be equal in fact + + + align:start position:0% +vectors do not have to be equal in fact +as I shall show you in a moment these + + align:start position:0% +as I shall show you in a moment these + + + align:start position:0% +as I shall show you in a moment these +two vectors don't even have to be in the + + align:start position:0% +two vectors don't even have to be in the + + + align:start position:0% +two vectors don't even have to be in the +same plane let alone being equal they + + align:start position:0% +same plane let alone being equal they + + + align:start position:0% +same plane let alone being equal they +don't even have to be in parallel planes + + align:start position:0% +don't even have to be in parallel planes + + + align:start position:0% +don't even have to be in parallel planes +and again without making too much of a + + align:start position:0% +and again without making too much of a + + + align:start position:0% +and again without making too much of a +fuss over this let's take a look and see + + align:start position:0% +fuss over this let's take a look and see + + + align:start position:0% +fuss over this let's take a look and see +if we can see why let's look at a cross + + align:start position:0% +if we can see why let's look at a cross + + + align:start position:0% +if we can see why let's look at a cross +B Cross C by definition let's just even + + align:start position:0% +B Cross C by definition let's just even + + + align:start position:0% +B Cross C by definition let's just even +look at the direction let's not even + + align:start position:0% +look at the direction let's not even + + + align:start position:0% +look at the direction let's not even +worry about magnitudes what is the + + align:start position:0% +worry about magnitudes what is the + + + align:start position:0% +worry about magnitudes what is the +direction of A cross B Cross C it must + + align:start position:0% +direction of A cross B Cross C it must + + + align:start position:0% +direction of A cross B Cross C it must +be what it must be on the one hand + + align:start position:0% +be what it must be on the one hand + + + align:start position:0% +be what it must be on the one hand +perpendicular to a and on the other hand + + align:start position:0% +perpendicular to a and on the other hand + + + align:start position:0% +perpendicular to a and on the other hand +perpendicular to B Cross + + align:start position:0% +perpendicular to B Cross + + + align:start position:0% +perpendicular to B Cross +C okay that's the + + align:start position:0% +C okay that's the + + + align:start position:0% +C okay that's the +definition of being a cross product on + + align:start position:0% +definition of being a cross product on + + + align:start position:0% +definition of being a cross product on +the other hand what about B Cross C as a + + align:start position:0% +the other hand what about B Cross C as a + + + align:start position:0% +the other hand what about B Cross C as a +vector itself B Cross C is perpendicular + + align:start position:0% +vector itself B Cross C is perpendicular + + + align:start position:0% +vector itself B Cross C is perpendicular +to both B and C so what do you have here + + align:start position:0% +to both B and C so what do you have here + + + align:start position:0% +to both B and C so what do you have here +you have that whatever A cross B Cross C + + align:start position:0% +you have that whatever A cross B Cross C + + + align:start position:0% +you have that whatever A cross B Cross C +is it's perpendicular to B Cross C which + + align:start position:0% +is it's perpendicular to B Cross C which + + + align:start position:0% +is it's perpendicular to B Cross C which +in turn is perpendicular to both B and C + + align:start position:0% +in turn is perpendicular to both B and C + + + align:start position:0% +in turn is perpendicular to both B and C +that sounds like a tongue twister but if + + align:start position:0% +that sounds like a tongue twister but if + + + align:start position:0% +that sounds like a tongue twister but if +you decipher it all it says is that a + + align:start position:0% +you decipher it all it says is that a + + + align:start position:0% +you decipher it all it says is that a +cross B Cross C is perpendicular to the + + align:start position:0% +cross B Cross C is perpendicular to the + + + align:start position:0% +cross B Cross C is perpendicular to the +perpendicular to B and C and I call that + + align:start position:0% +perpendicular to B and C and I call that + + + align:start position:0% +perpendicular to B and C and I call that +deciphering it what is the perpendicular + + align:start position:0% +deciphering it what is the perpendicular + + + align:start position:0% +deciphering it what is the perpendicular +to the + + align:start position:0% +to the + + + align:start position:0% +to the +perpendicular you see let's just look at + + align:start position:0% +perpendicular you see let's just look at + + + align:start position:0% +perpendicular you see let's just look at +it this way here are two vectors in the + + align:start position:0% +it this way here are two vectors in the + + + align:start position:0% +it this way here are two vectors in the +plane here's a perpendicular I now take + + align:start position:0% +plane here's a perpendicular I now take + + + align:start position:0% +plane here's a perpendicular I now take +a perpendicular to that and that's going + + align:start position:0% +a perpendicular to that and that's going + + + align:start position:0% +a perpendicular to that and that's going +to be parallel to the original plane + + align:start position:0% +to be parallel to the original plane + + + align:start position:0% +to be parallel to the original plane +this is written up in the text it's + + align:start position:0% +this is written up in the text it's + + + align:start position:0% +this is written up in the text it's +written up as one of our learning + + align:start position:0% +written up as one of our learning + + + align:start position:0% +written up as one of our learning +exercises but just for a quick run + + align:start position:0% +exercises but just for a quick run + + + align:start position:0% +exercises but just for a quick run +through now all I want you to see is + + align:start position:0% +through now all I want you to see is + + + align:start position:0% +through now all I want you to see is +that a cross B Cross C is parallel to + + align:start position:0% +that a cross B Cross C is parallel to + + + align:start position:0% +that a cross B Cross C is parallel to +the plane determined by B and C in fact + + align:start position:0% +the plane determined by B and C in fact + + + align:start position:0% +the plane determined by B and C in fact +the easy way to memorize this is look at + + align:start position:0% +the easy way to memorize this is look at + + + align:start position:0% +the easy way to memorize this is look at +the vector that's in parentheses and the + + align:start position:0% +the vector that's in parentheses and the + + + align:start position:0% +the vector that's in parentheses and the +cross product is what it's parallel to + + align:start position:0% +cross product is what it's parallel to + + + align:start position:0% +cross product is what it's parallel to +the plane determined by the two vectors + + align:start position:0% +the plane determined by the two vectors + + + align:start position:0% +the plane determined by the two vectors +in parentheses the only time these two + + align:start position:0% +in parentheses the only time these two + + + align:start position:0% +in parentheses the only time these two +vectors by the way won't determine a + + align:start position:0% +vectors by the way won't determine a + + + align:start position:0% +vectors by the way won't determine a +plane is if they're parallel but in that + + align:start position:0% +plane is if they're parallel but in that + + + align:start position:0% +plane is if they're parallel but in that +case the cross product would have been + + align:start position:0% +case the cross product would have been + + + align:start position:0% +case the cross product would have been +zero anyway in other words to summarize + + align:start position:0% +zero anyway in other words to summarize + + + align:start position:0% +zero anyway in other words to summarize +what I've written on the blackboards + + align:start position:0% +what I've written on the blackboards + + + align:start position:0% +what I've written on the blackboards +here A cross B Cross C is a vector which + + align:start position:0% +here A cross B Cross C is a vector which + + + align:start position:0% +here A cross B Cross C is a vector which +lies in the plane determined by by B and + + align:start position:0% +lies in the plane determined by by B and + + + align:start position:0% +lies in the plane determined by by B and +C after all if a vector is parallel to + + align:start position:0% +C after all if a vector is parallel to + + + align:start position:0% +C after all if a vector is parallel to +the plane you can assume it lies in the + + align:start position:0% +the plane you can assume it lies in the + + + align:start position:0% +the plane you can assume it lies in the +plane because you can shift it parallel + + align:start position:0% +plane because you can shift it parallel + + + align:start position:0% +plane because you can shift it parallel +to + + align:start position:0% +to + + + align:start position:0% +to +itself and correspondingly A cross B + + align:start position:0% +itself and correspondingly A cross B + + + align:start position:0% +itself and correspondingly A cross B +Cross C is a vector in the plane + + align:start position:0% +Cross C is a vector in the plane + + + align:start position:0% +Cross C is a vector in the plane +determined by A and B in particular + + align:start position:0% +determined by A and B in particular + + + align:start position:0% +determined by A and B in particular +there's no reason why the ab plane and + + align:start position:0% +there's no reason why the ab plane and + + + align:start position:0% +there's no reason why the ab plane and +the BC plane have to be the same plane + + align:start position:0% +the BC plane have to be the same plane + + + align:start position:0% +the BC plane have to be the same plane +no law says that our three vectors A B + + align:start position:0% +no law says that our three vectors A B + + + align:start position:0% +no law says that our three vectors A B +and C all lie on the same plane so in + + align:start position:0% +and C all lie on the same plane so in + + + align:start position:0% +and C all lie on the same plane so in +particular this is why the associative + + align:start position:0% +particular this is why the associative + + + align:start position:0% +particular this is why the associative +property doesn't hold for a cross + + align:start position:0% +property doesn't hold for a cross + + + align:start position:0% +property doesn't hold for a cross +product that as soon as you shift the + + align:start position:0% +product that as soon as you shift the + + + align:start position:0% +product that as soon as you shift the +parentheses you actually shift the plane + + align:start position:0% +parentheses you actually shift the plane + + + align:start position:0% +parentheses you actually shift the plane +in which the vector exists okay but + + align:start position:0% +in which the vector exists okay but + + + align:start position:0% +in which the vector exists okay but +again I just want to go through these + + align:start position:0% +again I just want to go through these + + + align:start position:0% +again I just want to go through these +highlights to make sure that you don't + + align:start position:0% +highlights to make sure that you don't + + + align:start position:0% +highlights to make sure that you don't +miss them but these are done in more + + align:start position:0% +miss them but these are done in more + + + align:start position:0% +miss them but these are done in more +detail in the + + align:start position:0% +detail in the + + + align:start position:0% +detail in the +notes before I start blasting the cross + + align:start position:0% +notes before I start blasting the cross + + + align:start position:0% +notes before I start blasting the cross +product too much let me point out that + + align:start position:0% +product too much let me point out that + + + align:start position:0% +product too much let me point out that +certain properties that we like in + + align:start position:0% +certain properties that we like in + + + align:start position:0% +certain properties that we like in +numerical arithmetic are present in the + + align:start position:0% +numerical arithmetic are present in the + + + align:start position:0% +numerical arithmetic are present in the +cross product + + align:start position:0% + + + + align:start position:0% + +for example there is a I say this there + + align:start position:0% +for example there is a I say this there + + + align:start position:0% +for example there is a I say this there +there's a little structure the associate + + align:start position:0% +there's a little structure the associate + + + align:start position:0% +there's a little structure the associate +the distributive property holds for the + + align:start position:0% +the distributive property holds for the + + + align:start position:0% +the distributive property holds for the +cross product in other words if the + + align:start position:0% +cross product in other words if the + + + align:start position:0% +cross product in other words if the +vector a is crossed with the sum of the + + align:start position:0% +vector a is crossed with the sum of the + + + align:start position:0% +vector a is crossed with the sum of the +two vectors B and C and by the way again + + align:start position:0% +two vectors B and C and by the way again + + + align:start position:0% +two vectors B and C and by the way again +notice if B and C are vectors B plus C + + align:start position:0% +notice if B and C are vectors B plus C + + + align:start position:0% +notice if B and C are vectors B plus C +is a vector I'll put a v down here to + + align:start position:0% +is a vector I'll put a v down here to + + + align:start position:0% +is a vector I'll put a v down here to +indicate Vector a is a vector and the + + align:start position:0% +indicate Vector a is a vector and the + + + align:start position:0% +indicate Vector a is a vector and the +cross product of two vectors is a vector + + align:start position:0% +cross product of two vectors is a vector + + + align:start position:0% +cross product of two vectors is a vector +notice that again with cross product all + + align:start position:0% +notice that again with cross product all + + + align:start position:0% +notice that again with cross product all +of the things that you're working with + + align:start position:0% +of the things that you're working with + + + align:start position:0% +of the things that you're working with +happen to be vectors but my claim is + + align:start position:0% +happen to be vectors but my claim is + + + align:start position:0% +happen to be vectors but my claim is +that a crossed with B plus C is equal to + + align:start position:0% +that a crossed with B plus C is equal to + + + align:start position:0% +that a crossed with B plus C is equal to +a crossed with B plus the product of a + + align:start position:0% +a crossed with B plus the product of a + + + align:start position:0% +a crossed with B plus the product of a +crossed with C all right that's a very + + align:start position:0% +crossed with C all right that's a very + + + align:start position:0% +crossed with C all right that's a very +nice structural property again as usual + + align:start position:0% +nice structural property again as usual + + + align:start position:0% +nice structural property again as usual +cartisian coordinates have a lot to + + align:start position:0% +cartisian coordinates have a lot to + + + align:start position:0% +cartisian coordinates have a lot to +offer us if we switch to cartisan + + align:start position:0% +offer us if we switch to cartisan + + + align:start position:0% +offer us if we switch to cartisan +coordinates again as usual writing a as + + align:start position:0% +coordinates again as usual writing a as + + + align:start position:0% +coordinates again as usual writing a as +A1 I + A2 J plus A3 k + + align:start position:0% +A1 I + A2 J plus A3 k + + + align:start position:0% +A1 I + A2 J plus A3 k +and B is B1 I + B2 J plus B3 K and + + align:start position:0% +and B is B1 I + B2 J plus B3 K and + + + align:start position:0% +and B is B1 I + B2 J plus B3 K and +multiplying term by term we observe a + + align:start position:0% +multiplying term by term we observe a + + + align:start position:0% +multiplying term by term we observe a +rather interesting situation you see + + align:start position:0% +rather interesting situation you see + + + align:start position:0% +rather interesting situation you see +notice things like this when you cross I + + align:start position:0% +notice things like this when you cross I + + + align:start position:0% +notice things like this when you cross I +with i j with j and k with K you're + + align:start position:0% +with i j with j and k with K you're + + + align:start position:0% +with i j with j and k with K you're +always going to get the zero vector and + + align:start position:0% +always going to get the zero vector and + + + align:start position:0% +always going to get the zero vector and +the reason for that is we already saw + + align:start position:0% +the reason for that is we already saw + + + align:start position:0% +the reason for that is we already saw +that since the sign of the angle between + + align:start position:0% +that since the sign of the angle between + + + align:start position:0% +that since the sign of the angle between +two parallel vectors is zero the + + align:start position:0% +two parallel vectors is zero the + + + align:start position:0% +two parallel vectors is zero the +magnitude of the cross product is zero + + align:start position:0% +magnitude of the cross product is zero + + + align:start position:0% +magnitude of the cross product is zero +that means that the cross product is the + + align:start position:0% +that means that the cross product is the + + + align:start position:0% +that means that the cross product is the +zero Vector the question comes up what + + align:start position:0% +zero Vector the question comes up what + + + align:start position:0% +zero Vector the question comes up what +happens when you cross I with j or J + + align:start position:0% +happens when you cross I with j or J + + + align:start position:0% +happens when you cross I with j or J +with i i with k k with J Etc I think + + align:start position:0% +with i i with k k with J Etc I think + + + align:start position:0% +with i i with k k with J Etc I think +it's easy to see that when you cross I + + align:start position:0% +it's easy to see that when you cross I + + + align:start position:0% +it's easy to see that when you cross I +and J and J and I you're going to get + + align:start position:0% +and J and J and I you're going to get + + + align:start position:0% +and J and J and I you're going to get +either K or minus K the right-handed + + align:start position:0% +either K or minus K the right-handed + + + align:start position:0% +either K or minus K the right-handed +rule is set up very very conveniently + + align:start position:0% +rule is set up very very conveniently + + + align:start position:0% +rule is set up very very conveniently +again to help us with a memory device + + align:start position:0% +again to help us with a memory device + + + align:start position:0% +again to help us with a memory device +the easiest way to remember how these + + align:start position:0% +the easiest way to remember how these + + + align:start position:0% +the easiest way to remember how these +things go is i j and k were set up to + + align:start position:0% +things go is i j and k were set up to + + + align:start position:0% +things go is i j and k were set up to +form a right-handed rule a right-handed + + align:start position:0% +form a right-handed rule a right-handed + + + align:start position:0% +form a right-handed rule a right-handed +system write i j and k sequentially see + + align:start position:0% +system write i j and k sequentially see + + + align:start position:0% +system write i j and k sequentially see +i j k i j k Etc call the normal order + + align:start position:0% +i j k i j k Etc call the normal order + + + align:start position:0% +i j k i j k Etc call the normal order +the positive direction and the opposite + + align:start position:0% +the positive direction and the opposite + + + align:start position:0% +the positive direction and the opposite +order the negative direction for example + + align:start position:0% +order the negative direction for example + + + align:start position:0% +order the negative direction for example +when you want I cross J just read this + + align:start position:0% +when you want I cross J just read this + + + align:start position:0% +when you want I cross J just read this +list as you go along I followed by J + + align:start position:0% +list as you go along I followed by J + + + align:start position:0% +list as you go along I followed by J +gives K which is in the right order see + + align:start position:0% +gives K which is in the right order see + + + align:start position:0% +gives K which is in the right order see +I J K so I cross J is K on the other + + align:start position:0% +I J K so I cross J is K on the other + + + align:start position:0% +I J K so I cross J is K on the other +hand J cross I means what J followed by + + align:start position:0% +hand J cross I means what J followed by + + + align:start position:0% +hand J cross I means what J followed by +i j followed by I is this way that also + + align:start position:0% +i j followed by I is this way that also + + + align:start position:0% +i j followed by I is this way that also +yields K but you're now going in the + + align:start position:0% +yields K but you're now going in the + + + align:start position:0% +yields K but you're now going in the +negative direction to summarize these + + align:start position:0% +negative direction to summarize these + + + align:start position:0% +negative direction to summarize these +results I cross J is the same as minus J + + align:start position:0% +results I cross J is the same as minus J + + + align:start position:0% +results I cross J is the same as minus J +cross I which is k k cross I is the + + align:start position:0% +cross I which is k k cross I is the + + + align:start position:0% +cross I which is k k cross I is the +negative of I cross K which is J I cross + + align:start position:0% +negative of I cross K which is J I cross + + + align:start position:0% +negative of I cross K which is J I cross +i j cross J and K cross K are all zero + + align:start position:0% +i j cross J and K cross K are all zero + + + align:start position:0% +i j cross J and K cross K are all zero +and notice the use here of zero Vector + + align:start position:0% +and notice the use here of zero Vector + + + align:start position:0% +and notice the use here of zero Vector +because we're dealing with vectors and + + align:start position:0% +because we're dealing with vectors and + + + align:start position:0% +because we're dealing with vectors and +again leaving the details to you they're + + align:start position:0% +again leaving the details to you they're + + + align:start position:0% +again leaving the details to you they're +very simple to come up with just carry + + align:start position:0% +very simple to come up with just carry + + + align:start position:0% +very simple to come up with just carry +out the multiplication and what you find + + align:start position:0% +out the multiplication and what you find + + + align:start position:0% +out the multiplication and what you find +is that a cross B is given by the + + align:start position:0% +is that a cross B is given by the + + + align:start position:0% +is that a cross B is given by the +following the I component of the vector + + align:start position:0% +following the I component of the vector + + + align:start position:0% +following the I component of the vector +is A2 B3 minus A3 + + align:start position:0% +is A2 B3 minus A3 + + + align:start position:0% +is A2 B3 minus A3 +B2 the J component is A3 B1 minus A1 B3 + + align:start position:0% +B2 the J component is A3 B1 minus A1 B3 + + + align:start position:0% +B2 the J component is A3 B1 minus A1 B3 +and the K component is A1 B2 minus A2 B1 + + align:start position:0% +and the K component is A1 B2 minus A2 B1 + + + align:start position:0% +and the K component is A1 B2 minus A2 B1 +and if you want a convenient way of + + align:start position:0% +and if you want a convenient way of + + + align:start position:0% +and if you want a convenient way of +memorizing this again write 1 two 3 in + + align:start position:0% +memorizing this again write 1 two 3 in + + + align:start position:0% +memorizing this again write 1 two 3 in +their correct sequential order and what + + align:start position:0% +their correct sequential order and what + + + align:start position:0% +their correct sequential order and what +you're saying is each term in a cross B + + align:start position:0% +you're saying is each term in a cross B + + + align:start position:0% +you're saying is each term in a cross B +involves what an a factor followed by a + + align:start position:0% +involves what an a factor followed by a + + + align:start position:0% +involves what an a factor followed by a +b Factor the subscripts involve the + + align:start position:0% +b Factor the subscripts involve the + + + align:start position:0% +b Factor the subscripts involve the +component which isn't present see for + + align:start position:0% +component which isn't present see for + + + align:start position:0% +component which isn't present see for +the first component I the subscripts are + + align:start position:0% +the first component I the subscripts are + + + align:start position:0% +the first component I the subscripts are +two and three for the second component J + + align:start position:0% +two and three for the second component J + + + align:start position:0% +two and three for the second component J +the second component the subscripts are + + align:start position:0% +the second component the subscripts are + + + align:start position:0% +the second component the subscripts are +three and one and for the third + + align:start position:0% +three and one and for the third + + + align:start position:0% +three and one and for the third +component K the subscripts are one and + + align:start position:0% +component K the subscripts are one and + + + align:start position:0% +component K the subscripts are one and +two and notice that the way the signs + + align:start position:0% +two and notice that the way the signs + + + align:start position:0% +two and notice that the way the signs +are determined is that if the subscripts + + align:start position:0% +are determined is that if the subscripts + + + align:start position:0% +are determined is that if the subscripts +occur in the correct sequential order + + align:start position:0% +occur in the correct sequential order + + + align:start position:0% +occur in the correct sequential order +it's positive otherwise negative for + + align:start position:0% +it's positive otherwise negative for + + + align:start position:0% +it's positive otherwise negative for +example two followed by three is the + + align:start position:0% +example two followed by three is the + + + align:start position:0% +example two followed by three is the +correct order but 3 followed by two is + + align:start position:0% +correct order but 3 followed by two is + + + align:start position:0% +correct order but 3 followed by two is +the negative order notice in this + + align:start position:0% +the negative order notice in this + + + align:start position:0% +the negative order notice in this +sequence one follows three whereas 1 to + + align:start position:0% +sequence one follows three whereas 1 to + + + align:start position:0% +sequence one follows three whereas 1 to +3 is in the negative order see just the + + align:start position:0% +3 is in the negative order see just the + + + align:start position:0% +3 is in the negative order see just the +same this works out very very nicely and + + align:start position:0% +same this works out very very nicely and + + + align:start position:0% +same this works out very very nicely and +the reason I went through this it may + + align:start position:0% +the reason I went through this it may + + + align:start position:0% +the reason I went through this it may +seem like an awful lot of work to go + + align:start position:0% +seem like an awful lot of work to go + + + align:start position:0% +seem like an awful lot of work to go +through that to show you how logical + + align:start position:0% +through that to show you how logical + + + align:start position:0% +through that to show you how logical +this thing is is that something comes up + + align:start position:0% +this thing is is that something comes up + + + align:start position:0% +this thing is is that something comes up +in the textbook which is not bad but + + align:start position:0% +in the textbook which is not bad but + + + align:start position:0% +in the textbook which is not bad but +which I find is frightening if you have + + align:start position:0% +which I find is frightening if you have + + + align:start position:0% +which I find is frightening if you have +not had experience with something called + + align:start position:0% +not had experience with something called + + + align:start position:0% +not had experience with something called +determinance you see the author + + align:start position:0% +determinance you see the author + + + align:start position:0% +determinance you see the author +Professor Thomas elects to introduce a + + align:start position:0% +Professor Thomas elects to introduce a + + + align:start position:0% +Professor Thomas elects to introduce a +convenient device for memorizing this + + align:start position:0% +convenient device for memorizing this + + + align:start position:0% +convenient device for memorizing this +result and he writes it as a 3x3 + + align:start position:0% +result and he writes it as a 3x3 + + + align:start position:0% +result and he writes it as a 3x3 +determinant and let me just write down + + align:start position:0% +determinant and let me just write down + + + align:start position:0% +determinant and let me just write down +the 3X3 determinant and then we'll talk + + align:start position:0% +the 3X3 determinant and then we'll talk + + + align:start position:0% +the 3X3 determinant and then we'll talk +about it later I put convenient in + + align:start position:0% +about it later I put convenient in + + + align:start position:0% +about it later I put convenient in +quotation marks to emphasize to you that + + align:start position:0% +quotation marks to emphasize to you that + + + align:start position:0% +quotation marks to emphasize to you that +this is convenient only if you already + + align:start position:0% +this is convenient only if you already + + + align:start position:0% +this is convenient only if you already +know determinants if you don't know + + align:start position:0% +know determinants if you don't know + + + align:start position:0% +know determinants if you don't know +determinants this is not only not + + align:start position:0% +determinants this is not only not + + + align:start position:0% +determinants this is not only not +convenient but it's frightening we're + + align:start position:0% +convenient but it's frightening we're + + + align:start position:0% +convenient but it's frightening we're +always frightened of things that we + + align:start position:0% +always frightened of things that we + + + align:start position:0% +always frightened of things that we +don't understand too well and I call it + + align:start position:0% +don't understand too well and I call it + + + align:start position:0% +don't understand too well and I call it +a memory device because you do not have + + align:start position:0% +a memory device because you do not have + + + align:start position:0% +a memory device because you do not have +to have determinants to remember this + + align:start position:0% +to have determinants to remember this + + + align:start position:0% +to have determinants to remember this +particular result in fact if one we're + + align:start position:0% +particular result in fact if one we're + + + align:start position:0% +particular result in fact if one we're +going to list in order the reasons for + + align:start position:0% +going to list in order the reasons for + + + align:start position:0% +going to list in order the reasons for +inventing + + align:start position:0% +inventing + + + align:start position:0% +inventing +determinants and the man was reading off + + align:start position:0% +determinants and the man was reading off + + + align:start position:0% +determinants and the man was reading off +a very very long list and you were + + align:start position:0% +a very very long list and you were + + + align:start position:0% +a very very long list and you were +getting + + align:start position:0% +getting + + + align:start position:0% +getting +bored as soon as he came to the reason + + align:start position:0% +bored as soon as he came to the reason + + + align:start position:0% +bored as soon as he came to the reason +that it was convenient to list AC cross + + align:start position:0% +that it was convenient to list AC cross + + + align:start position:0% +that it was convenient to list AC cross +product you could heave a sigh of relief + + align:start position:0% +product you could heave a sigh of relief + + + align:start position:0% +product you could heave a sigh of relief +because you would know that he's near + + align:start position:0% +because you would know that he's near + + + align:start position:0% +because you would know that he's near +the end of the list in other words to + + align:start position:0% +the end of the list in other words to + + + align:start position:0% +the end of the list in other words to +make a long story short of all the + + align:start position:0% +make a long story short of all the + + + align:start position:0% +make a long story short of all the +reasons for inventing the + + align:start position:0% +reasons for inventing the + + + align:start position:0% +reasons for inventing the +terminants using them for a cross + + align:start position:0% +terminants using them for a cross + + + align:start position:0% +terminants using them for a cross +product rep representation is perhaps + + align:start position:0% +product rep representation is perhaps + + + align:start position:0% +product rep representation is perhaps +the least significant but you see in + + align:start position:0% +the least significant but you see in + + + align:start position:0% +the least significant but you see in +Professor Thomas's approach uh + + align:start position:0% +Professor Thomas's approach uh + + + align:start position:0% +Professor Thomas's approach uh +determinants are assumed to be known and + + align:start position:0% +determinants are assumed to be known and + + + align:start position:0% +determinants are assumed to be known and +uh if you do know them it's a good it's + + align:start position:0% +uh if you do know them it's a good it's + + + align:start position:0% +uh if you do know them it's a good it's +a good notation if you don't forget it + + align:start position:0% +a good notation if you don't forget it + + + align:start position:0% +a good notation if you don't forget it +the trouble is I tell you to forget it + + align:start position:0% +the trouble is I tell you to forget it + + + align:start position:0% +the trouble is I tell you to forget it +and you won't forget it it always works + + align:start position:0% +and you won't forget it it always works + + + align:start position:0% +and you won't forget it it always works +that way when you tell the student not + + align:start position:0% +that way when you tell the student not + + + align:start position:0% +that way when you tell the student not +to forget something he forgets when you + + align:start position:0% +to forget something he forgets when you + + + align:start position:0% +to forget something he forgets when you +say please ignore it and forget it he + + align:start position:0% +say please ignore it and forget it he + + + align:start position:0% +say please ignore it and forget it he +doesn't forget so since you you may be a + + align:start position:0% +doesn't forget so since you you may be a + + + align:start position:0% +doesn't forget so since you you may be a +little bit Rusty on determinance let me + + align:start position:0% +little bit Rusty on determinance let me + + + align:start position:0% +little bit Rusty on determinance let me +give you a very very brief review of + + align:start position:0% +give you a very very brief review of + + + align:start position:0% +give you a very very brief review of +determin + + align:start position:0% +determin + + + align:start position:0% +determin +in fact it's not only very brief it's a + + align:start position:0% +in fact it's not only very brief it's a + + + align:start position:0% +in fact it's not only very brief it's a +pseudo review because I will give you no + + align:start position:0% +pseudo review because I will give you no + + + align:start position:0% +pseudo review because I will give you no +logic behind this at all I'm just going + + align:start position:0% +logic behind this at all I'm just going + + + align:start position:0% +logic behind this at all I'm just going +to tell you the recipe first of all by a + + align:start position:0% +to tell you the recipe first of all by a + + + align:start position:0% +to tell you the recipe first of all by a +2X two determinant you mean a square + + align:start position:0% +2X two determinant you mean a square + + + align:start position:0% +2X two determinant you mean a square +array of numbers consisting of two rows + + align:start position:0% +array of numbers consisting of two rows + + + align:start position:0% +array of numbers consisting of two rows +and two columns you use absolute value + + align:start position:0% +and two columns you use absolute value + + + align:start position:0% +and two columns you use absolute value +signs to indicate the + + align:start position:0% +signs to indicate the + + + align:start position:0% +signs to indicate the +determinant and by definition the 2x two + + align:start position:0% +determinant and by definition the 2x two + + + align:start position:0% +determinant and by definition the 2x two +determinant a b c d is the product of + + align:start position:0% +determinant a b c d is the product of + + + align:start position:0% +determinant a b c d is the product of +the two term terms A and + + align:start position:0% +the two term terms A and + + + align:start position:0% +the two term terms A and +D minus the product of the two terms B + + align:start position:0% +D minus the product of the two terms B + + + align:start position:0% +D minus the product of the two terms B +and C in other words if you multiply the + + align:start position:0% +and C in other words if you multiply the + + + align:start position:0% +and C in other words if you multiply the +upper left by the lower right and + + align:start position:0% +upper left by the lower right and + + + align:start position:0% +upper left by the lower right and +subtract from that the upper right times + + align:start position:0% +subtract from that the upper right times + + + align:start position:0% +subtract from that the upper right times +the lower left that is by definition the + + align:start position:0% +the lower left that is by definition the + + + align:start position:0% +the lower left that is by definition the +value of the 2x two determinant okay + + align:start position:0% +value of the 2x two determinant okay + + + align:start position:0% +value of the 2x two determinant okay +just by definition I by the way in Block + + align:start position:0% +just by definition I by the way in Block + + + align:start position:0% +just by definition I by the way in Block +seven of our course we're going to do + + align:start position:0% +seven of our course we're going to do + + + align:start position:0% +seven of our course we're going to do +this in much more detail for now I just + + align:start position:0% +this in much more detail for now I just + + + align:start position:0% +this in much more detail for now I just +want to give you enough of a hint so if + + align:start position:0% +want to give you enough of a hint so if + + + align:start position:0% +want to give you enough of a hint so if +you are frightened by determinants you + + align:start position:0% +you are frightened by determinants you + + + align:start position:0% +you are frightened by determinants you +can see what Professor Thomas is talking + + align:start position:0% +can see what Professor Thomas is talking + + + align:start position:0% +can see what Professor Thomas is talking +about in the text here now to expand a + + align:start position:0% +about in the text here now to expand a + + + align:start position:0% +about in the text here now to expand a +3X3 determinant one uses a little sign + + align:start position:0% +3X3 determinant one uses a little sign + + + align:start position:0% +3X3 determinant one uses a little sign +code starting at the upper left hand + + align:start position:0% +code starting at the upper left hand + + + align:start position:0% +code starting at the upper left hand +corner you put a little plus sign then + + align:start position:0% +corner you put a little plus sign then + + + align:start position:0% +corner you put a little plus sign then +you alternate plus minus plus + + align:start position:0% +you alternate plus minus plus + + + align:start position:0% +you alternate plus minus plus +Etc the plus simply is a code to tell + + align:start position:0% +Etc the plus simply is a code to tell + + + align:start position:0% +Etc the plus simply is a code to tell +you leave the sign of the term alone and + + align:start position:0% +you leave the sign of the term alone and + + + align:start position:0% +you leave the sign of the term alone and +the minus tells you change the sign of + + align:start position:0% +the minus tells you change the sign of + + + align:start position:0% +the minus tells you change the sign of +the term what that means is this by + + align:start position:0% +the term what that means is this by + + + align:start position:0% +the term what that means is this by +definition this 3x3 determinant is is + + align:start position:0% +definition this 3x3 determinant is is + + + align:start position:0% +definition this 3x3 determinant is is +obtained as follows take X1 as it + + align:start position:0% +obtained as follows take X1 as it + + + align:start position:0% +obtained as follows take X1 as it +appears and strike out the row and + + align:start position:0% +appears and strike out the row and + + + align:start position:0% +appears and strike out the row and +column in which X1 appears and multiply + + align:start position:0% +column in which X1 appears and multiply + + + align:start position:0% +column in which X1 appears and multiply +X1 by the remaining 2x two determinant + + align:start position:0% +X1 by the remaining 2x two determinant + + + align:start position:0% +X1 by the remaining 2x two determinant +then what you do is you factor out X2 + + align:start position:0% +then what you do is you factor out X2 + + + align:start position:0% +then what you do is you factor out X2 +with a minus sign strike out the row and + + align:start position:0% +with a minus sign strike out the row and + + + align:start position:0% +with a minus sign strike out the row and +column in which X2 appears and multiply + + align:start position:0% +column in which X2 appears and multiply + + + align:start position:0% +column in which X2 appears and multiply +X2 by the remaining 2x2 determinant + + align:start position:0% +X2 by the remaining 2x2 determinant + + + align:start position:0% +X2 by the remaining 2x2 determinant +that's left similarly take out X3 with + + align:start position:0% +that's left similarly take out X3 with + + + align:start position:0% +that's left similarly take out X3 with +the sign the appears with strike out the + + align:start position:0% +the sign the appears with strike out the + + + align:start position:0% +the sign the appears with strike out the +row and column in which it appears and + + align:start position:0% +row and column in which it appears and + + + align:start position:0% +row and column in which it appears and +multiply by the remaining 2x two + + align:start position:0% +multiply by the remaining 2x two + + + align:start position:0% +multiply by the remaining 2x two +determinant summarized to expand this + + align:start position:0% +determinant summarized to expand this + + + align:start position:0% +determinant summarized to expand this +3x3 determinant it's X1 times the + + align:start position:0% +3x3 determinant it's X1 times the + + + align:start position:0% +3x3 determinant it's X1 times the +determinant Y2 Y3 Z2 Z3 Min - X2 * the + + align:start position:0% +determinant Y2 Y3 Z2 Z3 Min - X2 * the + + + align:start position:0% +determinant Y2 Y3 Z2 Z3 Min - X2 * the +determinant y1 Y3 Z1 Z3 plus X3 * the + + align:start position:0% +determinant y1 Y3 Z1 Z3 plus X3 * the + + + align:start position:0% +determinant y1 Y3 Z1 Z3 plus X3 * the +determinant y1 Y2 Z1 Z2 now that happens + + align:start position:0% +determinant y1 Y2 Z1 Z2 now that happens + + + align:start position:0% +determinant y1 Y2 Z1 Z2 now that happens +to have very practical application as I + + align:start position:0% +to have very practical application as I + + + align:start position:0% +to have very practical application as I +say for this particular situation I just + + align:start position:0% +say for this particular situation I just + + + align:start position:0% +say for this particular situation I just +want to do it with you to have you see + + align:start position:0% +want to do it with you to have you see + + + align:start position:0% +want to do it with you to have you see +how it works let me come back to what we + + align:start position:0% +how it works let me come back to what we + + + align:start position:0% +how it works let me come back to what we +were doing before and show you how if we + + align:start position:0% +were doing before and show you how if we + + + align:start position:0% +were doing before and show you how if we +use this definition we can mechanically + + align:start position:0% +use this definition we can mechanically + + + align:start position:0% +use this definition we can mechanically +write down A cross B in a hurry what did + + align:start position:0% +write down A cross B in a hurry what did + + + align:start position:0% +write down A cross B in a hurry what did +the rule say it says to expand the 3X3 + + align:start position:0% +the rule say it says to expand the 3X3 + + + align:start position:0% +the rule say it says to expand the 3X3 +determinant take + + align:start position:0% +determinant take + + + align:start position:0% +determinant take +out I as it appears and multiply by the + + align:start position:0% +out I as it appears and multiply by the + + + align:start position:0% +out I as it appears and multiply by the +2x two determinant that's left when you + + align:start position:0% +2x two determinant that's left when you + + + align:start position:0% +2x two determinant that's left when you +strike out the row and column that I + + align:start position:0% +strike out the row and column that I + + + align:start position:0% +strike out the row and column that I +appears in + + align:start position:0% + + + + align:start position:0% + +okay then it says what take out J with a + + align:start position:0% +okay then it says what take out J with a + + + align:start position:0% +okay then it says what take out J with a +minus sign strike out the row and column + + align:start position:0% +minus sign strike out the row and column + + + align:start position:0% +minus sign strike out the row and column +multiply by the remaining 2x two + + align:start position:0% + + + + align:start position:0% + +determinant then it says factor out + + align:start position:0% +determinant then it says factor out + + + align:start position:0% +determinant then it says factor out +K and mult strike out the row and column + + align:start position:0% +K and mult strike out the row and column + + + align:start position:0% +K and mult strike out the row and column +that K appears in multiply by the + + align:start position:0% +that K appears in multiply by the + + + align:start position:0% +that K appears in multiply by the +remaining 2x two + + align:start position:0% +remaining 2x two + + + align:start position:0% +remaining 2x two +determinant well look at + + align:start position:0% +determinant well look at + + + align:start position:0% +determinant well look at +by our rule of multiplying a 2X two + + align:start position:0% +by our rule of multiplying a 2X two + + + align:start position:0% +by our rule of multiplying a 2X two +determinant what is this thing here this + + align:start position:0% +determinant what is this thing here this + + + align:start position:0% +determinant what is this thing here this +is nothing more than A2 B3 minus A3 + + align:start position:0% + + + + align:start position:0% + +B2 I'm not going to go through this + + align:start position:0% +B2 I'm not going to go through this + + + align:start position:0% +B2 I'm not going to go through this +because time is short and you can carry + + align:start position:0% +because time is short and you can carry + + + align:start position:0% +because time is short and you can carry +this operation out by yourself what I + + align:start position:0% +this operation out by yourself what I + + + align:start position:0% +this operation out by yourself what I +would like you to see however is that + + align:start position:0% +would like you to see however is that + + + align:start position:0% +would like you to see however is that +this term here is + + align:start position:0% +this term here is + + + align:start position:0% +this term here is +precisely the same as the term we had + + align:start position:0% +precisely the same as the term we had + + + align:start position:0% +precisely the same as the term we had +here in other words if I carry out this + + align:start position:0% +here in other words if I carry out this + + + align:start position:0% +here in other words if I carry out this +mechanical recipe + + align:start position:0% +mechanical recipe + + + align:start position:0% +mechanical recipe +I am going to be able to get the same + + align:start position:0% +I am going to be able to get the same + + + align:start position:0% +I am going to be able to get the same +answer that I got logically only without + + align:start position:0% +answer that I got logically only without + + + align:start position:0% +answer that I got logically only without +having to worry about keeping track of + + align:start position:0% +having to worry about keeping track of + + + align:start position:0% +having to worry about keeping track of +things in my head in other words if I do + + align:start position:0% +things in my head in other words if I do + + + align:start position:0% +things in my head in other words if I do +know determinants it is very convenient + + align:start position:0% +know determinants it is very convenient + + + align:start position:0% +know determinants it is very convenient +to write down the cut the cross product + + align:start position:0% +to write down the cut the cross product + + + align:start position:0% +to write down the cut the cross product +of two vectors using cartisian + + align:start position:0% +of two vectors using cartisian + + + align:start position:0% +of two vectors using cartisian +coordinates and just to illustrate that + + align:start position:0% +coordinates and just to illustrate that + + + align:start position:0% +coordinates and just to illustrate that +let me give you a few + + align:start position:0% +let me give you a few + + + align:start position:0% +let me give you a few +examples I call this example one find a + + align:start position:0% +examples I call this example one find a + + + align:start position:0% +examples I call this example one find a +vector perpendicular to the plane + + align:start position:0% +vector perpendicular to the plane + + + align:start position:0% +vector perpendicular to the plane +determined by the three points 1 12 3 + + align:start position:0% +determined by the three points 1 12 3 + + + align:start position:0% +determined by the three points 1 12 3 +594 and + + align:start position:0% +594 and + + + align:start position:0% +594 and +768 now you + + align:start position:0% +768 now you + + + align:start position:0% +768 now you +know try to visualize this problem if + + align:start position:0% +know try to visualize this problem if + + + align:start position:0% +know try to visualize this problem if +you didn't know vectors try to visualize + + align:start position:0% +you didn't know vectors try to visualize + + + align:start position:0% +you didn't know vectors try to visualize +drawing this thing to scale trying to + + align:start position:0% +drawing this thing to scale trying to + + + align:start position:0% +drawing this thing to scale trying to +imagine what slope the plane has and how + + align:start position:0% +imagine what slope the plane has and how + + + align:start position:0% +imagine what slope the plane has and how +you find a vector or or a line + + align:start position:0% +you find a vector or or a line + + + align:start position:0% +you find a vector or or a line +perpendicular to the plane and by the + + align:start position:0% +perpendicular to the plane and by the + + + align:start position:0% +perpendicular to the plane and by the +way I don't even need the word Vector in + + align:start position:0% +way I don't even need the word Vector in + + + align:start position:0% +way I don't even need the word Vector in +here later I could say find a Direction + + align:start position:0% +here later I could say find a Direction + + + align:start position:0% +here later I could say find a Direction +but we'll worry about that more next + + align:start position:0% +but we'll worry about that more next + + + align:start position:0% +but we'll worry about that more next +time the thing that I want to emphasize + + align:start position:0% +time the thing that I want to emphasize + + + align:start position:0% +time the thing that I want to emphasize +here is I just very quickly draw myself + + align:start position:0% +here is I just very quickly draw myself + + + align:start position:0% +here is I just very quickly draw myself +a little convenient device I don't draw + + align:start position:0% +a little convenient device I don't draw + + + align:start position:0% +a little convenient device I don't draw +it to scale I assume that the points a B + + align:start position:0% +it to scale I assume that the points a B + + + align:start position:0% +it to scale I assume that the points a B +and C are not in the same straight line + + align:start position:0% +and C are not in the same straight line + + + align:start position:0% +and C are not in the same straight line +and if they are it'll become very + + align:start position:0% +and if they are it'll become very + + + align:start position:0% +and if they are it'll become very +interesting that I simply won't get I'll + + align:start position:0% +interesting that I simply won't get I'll + + + align:start position:0% +interesting that I simply won't get I'll +get zero for a cross product to tell me + + align:start position:0% +get zero for a cross product to tell me + + + align:start position:0% +get zero for a cross product to tell me +that they don't form two non-parallel + + align:start position:0% +that they don't form two non-parallel + + + align:start position:0% +that they don't form two non-parallel +vectors but I mark off a b and c and the + + align:start position:0% +vectors but I mark off a b and c and the + + + align:start position:0% +vectors but I mark off a b and c and the +first thing I do as always is I + + align:start position:0% +first thing I do as always is I + + + align:start position:0% +first thing I do as always is I +vectorize I draw the lines ab and AC and + + align:start position:0% +vectorize I draw the lines ab and AC and + + + align:start position:0% +vectorize I draw the lines ab and AC and +I vectorize them that forms for me as + + align:start position:0% +I vectorize them that forms for me as + + + align:start position:0% +I vectorize them that forms for me as +usual the vector ab and the vector AC + + align:start position:0% +usual the vector ab and the vector AC + + + align:start position:0% +usual the vector ab and the vector AC +remembering how I form a vector from two + + align:start position:0% +remembering how I form a vector from two + + + align:start position:0% +remembering how I form a vector from two +points in cartisian coordinates again + + align:start position:0% +points in cartisian coordinates again + + + align:start position:0% +points in cartisian coordinates again +subtracting the coordinates of the point + + align:start position:0% +subtracting the coordinates of the point + + + align:start position:0% +subtracting the coordinates of the point +that I'm going from the point that I'm + + align:start position:0% +that I'm going from the point that I'm + + + align:start position:0% +that I'm going from the point that I'm +going to I subtract away the coordinates + + align:start position:0% +going to I subtract away the coordinates + + + align:start position:0% +going to I subtract away the coordinates +of the point that I'm leaving in other + + align:start position:0% +of the point that I'm leaving in other + + + align:start position:0% +of the point that I'm leaving in other +words 5 -1 9 - 2 4 - 3 the vector AB + + align:start position:0% +words 5 -1 9 - 2 4 - 3 the vector AB + + + align:start position:0% +words 5 -1 9 - 2 4 - 3 the vector AB +very simply is 4 I + 7 J + K and + + align:start position:0% +very simply is 4 I + 7 J + K and + + + align:start position:0% +very simply is 4 I + 7 J + K and +similarly the vector AC very + + align:start position:0% +similarly the vector AC very + + + align:start position:0% +similarly the vector AC very +conveniently is 6 I + 4 J + 5 K you see + + align:start position:0% +conveniently is 6 I + 4 J + 5 K you see + + + align:start position:0% +conveniently is 6 I + 4 J + 5 K you see +7 -1 6 - 2 8 - 3 I better stop checking + + align:start position:0% +7 -1 6 - 2 8 - 3 I better stop checking + + + align:start position:0% +7 -1 6 - 2 8 - 3 I better stop checking +these things because with my luck I've + + align:start position:0% +these things because with my luck I've + + + align:start position:0% +these things because with my luck I've +probably subtracted wrong and you might + + align:start position:0% +probably subtracted wrong and you might + + + align:start position:0% +probably subtracted wrong and you might +not notice it if we just go through it + + align:start position:0% +not notice it if we just go through it + + + align:start position:0% +not notice it if we just go through it +rapidly but look at how quickly I've got + + align:start position:0% +rapidly but look at how quickly I've got + + + align:start position:0% +rapidly but look at how quickly I've got +a and AC now now here's the beauty what + + align:start position:0% +a and AC now now here's the beauty what + + + align:start position:0% +a and AC now now here's the beauty what +do I want I want a vector perpendicular + + align:start position:0% +do I want I want a vector perpendicular + + + align:start position:0% +do I want I want a vector perpendicular +to the plane determined by a b and c in + + align:start position:0% +to the plane determined by a b and c in + + + align:start position:0% +to the plane determined by a b and c in +particular if I can find a vector + + align:start position:0% +particular if I can find a vector + + + align:start position:0% +particular if I can find a vector +perpendicular to both ab and AC namely + + align:start position:0% +perpendicular to both ab and AC namely + + + align:start position:0% +perpendicular to both ab and AC namely +if a vector is perpendicular to two + + align:start position:0% +if a vector is perpendicular to two + + + align:start position:0% +if a vector is perpendicular to two +lines in a plane it's perpendicular to + + align:start position:0% +lines in a plane it's perpendicular to + + + align:start position:0% +lines in a plane it's perpendicular to +the plane itself if I can find a vector + + align:start position:0% +the plane itself if I can find a vector + + + align:start position:0% +the plane itself if I can find a vector +perpendicular to both ab and AC I'm home + + align:start position:0% +perpendicular to both ab and AC I'm home + + + align:start position:0% +perpendicular to both ab and AC I'm home +free that's the vector I'm looking for + + align:start position:0% +free that's the vector I'm looking for + + + align:start position:0% +free that's the vector I'm looking for +or at least a vector that I'm looking + + align:start position:0% +or at least a vector that I'm looking + + + align:start position:0% +or at least a vector that I'm looking +for do I know conveniently a vector + + align:start position:0% +for do I know conveniently a vector + + + align:start position:0% +for do I know conveniently a vector +perpendicular to two given vectors and + + align:start position:0% +perpendicular to two given vectors and + + + align:start position:0% +perpendicular to two given vectors and +the answer had Dan well better hinge + + align:start position:0% +the answer had Dan well better hinge + + + align:start position:0% +the answer had Dan well better hinge +somehow on the title of today's lecture + + align:start position:0% +somehow on the title of today's lecture + + + align:start position:0% +somehow on the title of today's lecture +being the cross product yes by + + align:start position:0% +being the cross product yes by + + + align:start position:0% +being the cross product yes by +definition if I cross ab and AC whatever + + align:start position:0% +definition if I cross ab and AC whatever + + + align:start position:0% +definition if I cross ab and AC whatever +Vector I get is going to be + + align:start position:0% +Vector I get is going to be + + + align:start position:0% +Vector I get is going to be +perpendicular to the plane determined by + + align:start position:0% +perpendicular to the plane determined by + + + align:start position:0% +perpendicular to the plane determined by +a b and c and now what I'm saying is + + align:start position:0% +a b and c and now what I'm saying is + + + align:start position:0% +a b and c and now what I'm saying is +that the beauty of cartisian coordinates + + align:start position:0% +that the beauty of cartisian coordinates + + + align:start position:0% +that the beauty of cartisian coordinates +is that I can now very quickly write + + align:start position:0% +is that I can now very quickly write + + + align:start position:0% +is that I can now very quickly write +down what AB cross a is as a determinant + + align:start position:0% +down what AB cross a is as a determinant + + + align:start position:0% +down what AB cross a is as a determinant +namely I write down i j k then I write + + align:start position:0% +namely I write down i j k then I write + + + align:start position:0% +namely I write down i j k then I write +down the components of ab then I write + + align:start position:0% +down the components of ab then I write + + + align:start position:0% +down the components of ab then I write +down the components of AC see 471 645 + + align:start position:0% +down the components of AC see 471 645 + + + align:start position:0% +down the components of AC see 471 645 +and now now I do what I strike out the + + align:start position:0% +and now now I do what I strike out the + + + align:start position:0% +and now now I do what I strike out the +row and column in which I appears and + + align:start position:0% +row and column in which I appears and + + + align:start position:0% +row and column in which I appears and +the remaining 2x two determinant is what + + align:start position:0% +the remaining 2x two determinant is what + + + align:start position:0% +the remaining 2x two determinant is what +7 * 5 - 1 * 4 in other words 35 - 4 I + + align:start position:0% +7 * 5 - 1 * 4 in other words 35 - 4 I + + + align:start position:0% +7 * 5 - 1 * 4 in other words 35 - 4 I +take out minus J strike out the row and + + align:start position:0% +take out minus J strike out the row and + + + align:start position:0% +take out minus J strike out the row and +column in which J appears the remaining + + align:start position:0% +column in which J appears the remaining + + + align:start position:0% +column in which J appears the remaining +2x two determinant is 4 * 5 - 1 * 6 in + + align:start position:0% +2x two determinant is 4 * 5 - 1 * 6 in + + + align:start position:0% +2x two determinant is 4 * 5 - 1 * 6 in +other words 20 - 6 I strike out the row + + align:start position:0% +other words 20 - 6 I strike out the row + + + align:start position:0% +other words 20 - 6 I strike out the row +and column in which K appears the + + align:start position:0% +and column in which K appears the + + + align:start position:0% +and column in which K appears the +remaining 2x2 determinant is 4 * 4 - 7 * + + align:start position:0% +remaining 2x2 determinant is 4 * 4 - 7 * + + + align:start position:0% +remaining 2x2 determinant is 4 * 4 - 7 * +6 that's 16 - 42 and now simplifying + + align:start position:0% +6 that's 16 - 42 and now simplifying + + + align:start position:0% +6 that's 16 - 42 and now simplifying +what do I have I have 31 I minus 14 + + align:start position:0% +what do I have I have 31 I minus 14 + + + align:start position:0% +what do I have I have 31 I minus 14 +Jus 26 K in other words the vector 31 i + + align:start position:0% +Jus 26 K in other words the vector 31 i + + + align:start position:0% +Jus 26 K in other words the vector 31 i +- 14 J - 26 K is the vector that I'm + + align:start position:0% +- 14 J - 26 K is the vector that I'm + + + align:start position:0% +- 14 J - 26 K is the vector that I'm +looking for it's a vector perpendicular + + align:start position:0% +looking for it's a vector perpendicular + + + align:start position:0% +looking for it's a vector perpendicular +to to the PL and what I would like you + + align:start position:0% +to to the PL and what I would like you + + + align:start position:0% +to to the PL and what I would like you +to see is how + + align:start position:0% +to see is how + + + align:start position:0% +to see is how +convenient this Vector arithmetic is to + + align:start position:0% +convenient this Vector arithmetic is to + + + align:start position:0% +convenient this Vector arithmetic is to +studying space geometry and in the next + + align:start position:0% +studying space geometry and in the next + + + align:start position:0% +studying space geometry and in the next +lesson you know I'm going to say some + + align:start position:0% +lesson you know I'm going to say some + + + align:start position:0% +lesson you know I'm going to say some +more about space geometry but for now I + + align:start position:0% +more about space geometry but for now I + + + align:start position:0% +more about space geometry but for now I +thought maybe another nice example + + align:start position:0% +thought maybe another nice example + + + align:start position:0% +thought maybe another nice example +before we finish up and uh let it go + + align:start position:0% +before we finish up and uh let it go + + + align:start position:0% +before we finish up and uh let it go +with that let me just do one more + + align:start position:0% +with that let me just do one more + + + align:start position:0% +with that let me just do one more +example for + + align:start position:0% +example for + + + align:start position:0% +example for +you and to simplify the computation I + + align:start position:0% +you and to simplify the computation I + + + align:start position:0% +you and to simplify the computation I +might as well use the vectors I've + + align:start position:0% +might as well use the vectors I've + + + align:start position:0% +might as well use the vectors I've +already used let's take the same three + + align:start position:0% +already used let's take the same three + + + align:start position:0% +already used let's take the same three +points we had before 1 2 3 594 768 and + + align:start position:0% +points we had before 1 2 3 594 768 and + + + align:start position:0% +points we had before 1 2 3 594 768 and +we're going to ask what is the area of + + align:start position:0% +we're going to ask what is the area of + + + align:start position:0% +we're going to ask what is the area of +the triangle determined by these three + + align:start position:0% +the triangle determined by these three + + + align:start position:0% +the triangle determined by these three +points and the subtlety that I wanted to + + align:start position:0% +points and the subtlety that I wanted to + + + align:start position:0% +points and the subtlety that I wanted to +bring out here was an excuse to show you + + align:start position:0% +bring out here was an excuse to show you + + + align:start position:0% +bring out here was an excuse to show you +how the magnitude of the cross product + + align:start position:0% +how the magnitude of the cross product + + + align:start position:0% +how the magnitude of the cross product +of two vectors can be interpreted namely + + align:start position:0% +of two vectors can be interpreted namely + + + align:start position:0% +of two vectors can be interpreted namely +look at two + + align:start position:0% +look at two + + + align:start position:0% +look at two +vectors all right call them X and Y draw + + align:start position:0% +vectors all right call them X and Y draw + + + align:start position:0% +vectors all right call them X and Y draw +them into scale from a common point and + + align:start position:0% +them into scale from a common point and + + + align:start position:0% +them into scale from a common point and +let Theta be the angle form between + + align:start position:0% +let Theta be the angle form between + + + align:start position:0% +let Theta be the angle form between +these two vectors all right consider the + + align:start position:0% +these two vectors all right consider the + + + align:start position:0% +these two vectors all right consider the +parallelogram formed by these two + + align:start position:0% +parallelogram formed by these two + + + align:start position:0% +parallelogram formed by these two +vectors the area of a parallelogram is + + align:start position:0% +vectors the area of a parallelogram is + + + align:start position:0% +vectors the area of a parallelogram is +what it's the base times the height now + + align:start position:0% +what it's the base times the height now + + + align:start position:0% +what it's the base times the height now +look at the base of this parallelogram + + align:start position:0% +look at the base of this parallelogram + + + align:start position:0% +look at the base of this parallelogram +is the magnitude of + + align:start position:0% +is the magnitude of + + + align:start position:0% +is the magnitude of +Y and the height of this parallelogram + + align:start position:0% +Y and the height of this parallelogram + + + align:start position:0% +Y and the height of this parallelogram +remember this magnitude is X so this + + align:start position:0% +remember this magnitude is X so this + + + align:start position:0% +remember this magnitude is X so this +height is X sin + + align:start position:0% + + + + align:start position:0% + +Theta this is the area of the + + align:start position:0% +Theta this is the area of the + + + align:start position:0% +Theta this is the area of the +parallelogram but notice that this is + + align:start position:0% +parallelogram but notice that this is + + + align:start position:0% +parallelogram but notice that this is +also by definition the magnitude of X + + align:start position:0% +also by definition the magnitude of X + + + align:start position:0% +also by definition the magnitude of X +cross Y in other words + + align:start position:0% + + + + align:start position:0% + +notice that this is by definition the + + align:start position:0% +notice that this is by definition the + + + align:start position:0% +notice that this is by definition the +magnitude of X cross y x cross Y is a + + align:start position:0% +magnitude of X cross y x cross Y is a + + + align:start position:0% +magnitude of X cross y x cross Y is a +vector whose magnitude is this in other + + align:start position:0% +vector whose magnitude is this in other + + + align:start position:0% +vector whose magnitude is this in other +words the magnitude of X cross Y is the + + align:start position:0% +words the magnitude of X cross Y is the + + + align:start position:0% +words the magnitude of X cross Y is the +area of the parallelogram determined by + + align:start position:0% +area of the parallelogram determined by + + + align:start position:0% +area of the parallelogram determined by +X and Y which gives you a rather nice + + align:start position:0% +X and Y which gives you a rather nice + + + align:start position:0% +X and Y which gives you a rather nice +interesting interpretation imagine for + + align:start position:0% +interesting interpretation imagine for + + + align:start position:0% +interesting interpretation imagine for +example that X and Y don't change in + + align:start position:0% +example that X and Y don't change in + + + align:start position:0% +example that X and Y don't change in +length is it clear to you that as I + + align:start position:0% +length is it clear to you that as I + + + align:start position:0% +length is it clear to you that as I +change the angle between X and Y the + + align:start position:0% +change the angle between X and Y the + + + align:start position:0% +change the angle between X and Y the +area of the parallelogram formed by X + + align:start position:0% +area of the parallelogram formed by X + + + align:start position:0% +area of the parallelogram formed by X +and Y changes in other words one extreme + + align:start position:0% +and Y changes in other words one extreme + + + align:start position:0% +and Y changes in other words one extreme +case is when the angle between X and Y + + align:start position:0% +case is when the angle between X and Y + + + align:start position:0% +case is when the angle between X and Y +is zero in which case the parallelogram + + align:start position:0% +is zero in which case the parallelogram + + + align:start position:0% +is zero in which case the parallelogram +has no area another extreme case is when + + align:start position:0% +has no area another extreme case is when + + + align:start position:0% +has no area another extreme case is when +the angle between X and Y is 90° in + + align:start position:0% +the angle between X and Y is 90° in + + + align:start position:0% +the angle between X and Y is 90° in +other words X and Y are perpendicular to + + align:start position:0% +other words X and Y are perpendicular to + + + align:start position:0% +other words X and Y are perpendicular to +each other but if the lengths of X and Y + + align:start position:0% +each other but if the lengths of X and Y + + + align:start position:0% +each other but if the lengths of X and Y +remain fixed as I alter the angle + + align:start position:0% +remain fixed as I alter the angle + + + align:start position:0% +remain fixed as I alter the angle +between them I alter the area of the + + align:start position:0% +between them I alter the area of the + + + align:start position:0% +between them I alter the area of the +parallelogram determined by them all + + align:start position:0% +parallelogram determined by them all + + + align:start position:0% +parallelogram determined by them all +right I just thought that's a cute + + align:start position:0% +right I just thought that's a cute + + + align:start position:0% +right I just thought that's a cute +little device whereby you can visualize + + align:start position:0% +little device whereby you can visualize + + + align:start position:0% +little device whereby you can visualize +how the magnitude of the cross product + + align:start position:0% +how the magnitude of the cross product + + + align:start position:0% +how the magnitude of the cross product +of two vectors varies think of the two + + align:start position:0% +of two vectors varies think of the two + + + align:start position:0% +of two vectors varies think of the two +vectors as a at a common origin and the + + align:start position:0% +vectors as a at a common origin and the + + + align:start position:0% +vectors as a at a common origin and the +magnitude is affected by the area of + + align:start position:0% +magnitude is affected by the area of + + + align:start position:0% +magnitude is affected by the area of +that par + + align:start position:0% +that par + + + align:start position:0% +that par +parallelogram as the angle change ches + + align:start position:0% +parallelogram as the angle change ches + + + align:start position:0% +parallelogram as the angle change ches +okay in other words if you change the + + align:start position:0% +okay in other words if you change the + + + align:start position:0% +okay in other words if you change the +angle the area of the parallelogram + + align:start position:0% +angle the area of the parallelogram + + + align:start position:0% +angle the area of the parallelogram +changes but at any rate getting back to + + align:start position:0% +changes but at any rate getting back to + + + align:start position:0% +changes but at any rate getting back to +our original problem the corollary to + + align:start position:0% +our original problem the corollary to + + + align:start position:0% +our original problem the corollary to +that is the following we already know + + align:start position:0% +that is the following we already know + + + align:start position:0% +that is the following we already know +what the magnitude of ab cross a is from + + align:start position:0% +what the magnitude of ab cross a is from + + + align:start position:0% +what the magnitude of ab cross a is from +example one but what does that mean now + + align:start position:0% +example one but what does that mean now + + + align:start position:0% +example one but what does that mean now +geometrically from what we've just seen + + align:start position:0% +geometrically from what we've just seen + + + align:start position:0% +geometrically from what we've just seen +the magnitude of ab cross a is the area + + align:start position:0% +the magnitude of ab cross a is the area + + + align:start position:0% +the magnitude of ab cross a is the area +of the parallelogram which has AB and AC + + align:start position:0% +of the parallelogram which has AB and AC + + + align:start position:0% +of the parallelogram which has AB and AC +as + + align:start position:0% +as + + + align:start position:0% +as +edges notice that that parall + + align:start position:0% +edges notice that that parall + + + align:start position:0% +edges notice that that parall +is precisely 1 + + align:start position:0% +is precisely 1 + + + align:start position:0% +is precisely 1 +12 I should say that I shouldn't say + + align:start position:0% +12 I should say that I shouldn't say + + + align:start position:0% +12 I should say that I shouldn't say +that the triangle that we're looking for + + align:start position:0% +that the triangle that we're looking for + + + align:start position:0% +that the triangle that we're looking for +is precisely 1 half the parallelogram in + + align:start position:0% +is precisely 1 half the parallelogram in + + + align:start position:0% +is precisely 1 half the parallelogram in +other words notice that the area of the + + align:start position:0% +other words notice that the area of the + + + align:start position:0% +other words notice that the area of the +triangle is simply 1/2 the magnitude of + + align:start position:0% +triangle is simply 1/2 the magnitude of + + + align:start position:0% +triangle is simply 1/2 the magnitude of +ab cross a how do we find the magnitude + + align:start position:0% +ab cross a how do we find the magnitude + + + align:start position:0% +ab cross a how do we find the magnitude +of a cross C we Square each of its + + align:start position:0% +of a cross C we Square each of its + + + align:start position:0% +of a cross C we Square each of its +components add them and extract the + + align:start position:0% +components add them and extract the + + + align:start position:0% +components add them and extract the +positive square root as usual without + + align:start position:0% +positive square root as usual without + + + align:start position:0% +positive square root as usual without +going through the details it's simply + + align:start position:0% +going through the details it's simply + + + align:start position:0% +going through the details it's simply +going to be what + + align:start position:0% +going to be what + + + align:start position:0% +going to be what +this + + align:start position:0% +this + + + align:start position:0% +this +particular amount and the rest is + + align:start position:0% +particular amount and the rest is + + + align:start position:0% +particular amount and the rest is +arithmetics baby so to speak right now + + align:start position:0% +arithmetics baby so to speak right now + + + align:start position:0% +arithmetics baby so to speak right now +what I'm hoping is is that by this stage + + align:start position:0% +what I'm hoping is is that by this stage + + + align:start position:0% +what I'm hoping is is that by this stage +of the game you now have a better + + align:start position:0% +of the game you now have a better + + + align:start position:0% +of the game you now have a better +feeling as to what the cross product + + align:start position:0% +feeling as to what the cross product + + + align:start position:0% +feeling as to what the cross product +means uh going back to the beginning of + + align:start position:0% +means uh going back to the beginning of + + + align:start position:0% +means uh going back to the beginning of +my lecture notice that I played down the + + align:start position:0% +my lecture notice that I played down the + + + align:start position:0% +my lecture notice that I played down the +physical applications because one of the + + align:start position:0% +physical applications because one of the + + + align:start position:0% +physical applications because one of the +things that I want you to see is that + + align:start position:0% +things that I want you to see is that + + + align:start position:0% +things that I want you to see is that +the cross product has tremendous + + align:start position:0% +the cross product has tremendous + + + align:start position:0% +the cross product has tremendous +application just to space geometry alone + + align:start position:0% +application just to space geometry alone + + + align:start position:0% +application just to space geometry alone +quite apart from anything else well at + + align:start position:0% +quite apart from anything else well at + + + align:start position:0% +quite apart from anything else well at +any rate what I'm going to do next time + + align:start position:0% +any rate what I'm going to do next time + + + align:start position:0% +any rate what I'm going to do next time +is now that we've talked about lines and + + align:start position:0% +is now that we've talked about lines and + + + align:start position:0% +is now that we've talked about lines and +planes and what have you is to get down + + align:start position:0% +planes and what have you is to get down + + + align:start position:0% +planes and what have you is to get down +to the cartisian representation of what + + align:start position:0% +to the cartisian representation of what + + + align:start position:0% +to the cartisian representation of what +lines and planes would look like they + + align:start position:0% +lines and planes would look like they + + + align:start position:0% +lines and planes would look like they +play a very vital role in the study of + + align:start position:0% +play a very vital role in the study of + + + align:start position:0% +play a very vital role in the study of +functions of several variables we'll see + + align:start position:0% +functions of several variables we'll see + + + align:start position:0% +functions of several variables we'll see +more about that as the course continues + + align:start position:0% +more about that as the course continues + + + align:start position:0% +more about that as the course continues +to unfold so until next time + + align:start position:0% +to unfold so until next time + + + align:start position:0% +to unfold so until next time +goodbye funding for the publication of + + align:start position:0% +goodbye funding for the publication of + + + align:start position:0% +goodbye funding for the publication of +this video was provided by the Gabriella + + align:start position:0% +this video was provided by the Gabriella + + + align:start position:0% +this video was provided by the Gabriella +and Paul rosenbom + + align:start position:0% +and Paul rosenbom + + + align:start position:0% +and Paul rosenbom +foundation help ocw continue to provide + + align:start position:0% +foundation help ocw continue to provide + + + align:start position:0% +foundation help ocw continue to provide +free and open access to MIT courses by + + align:start position:0% +free and open access to MIT courses by + + + align:start position:0% +free and open access to MIT courses by +making a donation at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu/donate \ No newline at end of file diff --git a/ZWzCHjN3_3s.txt b/ZWzCHjN3_3s.txt new file mode 100644 index 0000000000000000000000000000000000000000..ccbb7a7bbc40d273180538084bcd424f554cd205 --- /dev/null +++ b/ZWzCHjN3_3s.txt @@ -0,0 +1,13315 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +for simple functions + + align:start position:0% + + + + align:start position:0% + +which you know have this canonical uh + + align:start position:0% +which you know have this canonical uh + + + align:start position:0% +which you know have this canonical uh +representation + + align:start position:0% +representation + + + align:start position:0% +representation +as + + align:start position:0% +as + + + align:start position:0% +as +a finite linear combination of + + align:start position:0% +a finite linear combination of + + + align:start position:0% +a finite linear combination of +indicator functions on sets which are + + align:start position:0% +indicator functions on sets which are + + + align:start position:0% +indicator functions on sets which are +pairwise disjoint and whose Union gives + + align:start position:0% +pairwise disjoint and whose Union gives + + + align:start position:0% +pairwise disjoint and whose Union gives +me e + + align:start position:0% + + + + align:start position:0% + +um we defined their integral + + align:start position:0% + + + + align:start position:0% + +the integral of V + + align:start position:0% +the integral of V + + + align:start position:0% +the integral of V +was defined to be the sum from J equals + + align:start position:0% +was defined to be the sum from J equals + + + align:start position:0% +was defined to be the sum from J equals +1 to n + + align:start position:0% +1 to n + + + align:start position:0% +1 to n +A J times the measure + + align:start position:0% +A J times the measure + + + align:start position:0% +A J times the measure +of capital AJ uh + + align:start position:0% +of capital AJ uh + + + align:start position:0% +of capital AJ uh +some as J goes from 1 to n and we proved + + align:start position:0% +some as J goes from 1 to n and we proved + + + align:start position:0% +some as J goes from 1 to n and we proved +a couple of properties of this namely + + align:start position:0% +a couple of properties of this namely + + + align:start position:0% +a couple of properties of this namely +um + + align:start position:0% +um + + + align:start position:0% +um +we proved that if I multiply a simple + + align:start position:0% +we proved that if I multiply a simple + + + align:start position:0% +we proved that if I multiply a simple +function by a non-negative scalar then + + align:start position:0% +function by a non-negative scalar then + + + align:start position:0% +function by a non-negative scalar then +the scalar pulls out of the integral the + + align:start position:0% +the scalar pulls out of the integral the + + + align:start position:0% +the scalar pulls out of the integral the +integral of the scalar multiple of Phi + + align:start position:0% +integral of the scalar multiple of Phi + + + align:start position:0% +integral of the scalar multiple of Phi +is equal to scalar multiple of the + + align:start position:0% +is equal to scalar multiple of the + + + align:start position:0% +is equal to scalar multiple of the +integral if I have two non-negative + + align:start position:0% +integral if I have two non-negative + + + align:start position:0% +integral if I have two non-negative +simple functions and I add them I get + + align:start position:0% +simple functions and I add them I get + + + align:start position:0% +simple functions and I add them I get +another non-negative simple function and + + align:start position:0% +another non-negative simple function and + + + align:start position:0% +another non-negative simple function and +the integral of the sum is the sum of + + align:start position:0% +the integral of the sum is the sum of + + + align:start position:0% +the integral of the sum is the sum of +the integrals and we also proved that if + + align:start position:0% +the integrals and we also proved that if + + + align:start position:0% +the integrals and we also proved that if +I have two simple functions one less + + align:start position:0% +I have two simple functions one less + + + align:start position:0% +I have two simple functions one less +than or equal to the other then the + + align:start position:0% +than or equal to the other then the + + + align:start position:0% +than or equal to the other then the +integrals respect this inequality the + + align:start position:0% +integrals respect this inequality the + + + align:start position:0% +integrals respect this inequality the +integral of the smaller one is less than + + align:start position:0% +integral of the smaller one is less than + + + align:start position:0% +integral of the smaller one is less than +or equal to the integral of the bigger + + align:start position:0% +or equal to the integral of the bigger + + + align:start position:0% +or equal to the integral of the bigger +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +um + + align:start position:0% +um + + + align:start position:0% +um +so now we're going to Define + + align:start position:0% + + + + align:start position:0% + +the lebeg integral + + align:start position:0% +the lebeg integral + + + align:start position:0% +the lebeg integral +for non-net for a general non-negative + + align:start position:0% +for non-net for a general non-negative + + + align:start position:0% +for non-net for a general non-negative +measurable function + + align:start position:0% +measurable function + + + align:start position:0% +measurable function +in some sense you know + + align:start position:0% + + + + align:start position:0% + +how one should view the lebeg integral + + align:start position:0% +how one should view the lebeg integral + + + align:start position:0% +how one should view the lebeg integral +is kind of how you know one should view + + align:start position:0% +is kind of how you know one should view + + + align:start position:0% +is kind of how you know one should view +the Riemann integral I guess if you or + + align:start position:0% +the Riemann integral I guess if you or + + + align:start position:0% +the Riemann integral I guess if you or +at least when you think about the + + align:start position:0% +at least when you think about the + + + align:start position:0% +at least when you think about the +Riemann integral as you know you build + + align:start position:0% +Riemann integral as you know you build + + + align:start position:0% +Riemann integral as you know you build +up these uh approximations to the + + align:start position:0% +up these uh approximations to the + + + align:start position:0% +up these uh approximations to the +integral by cutting up the domain for + + align:start position:0% +integral by cutting up the domain for + + + align:start position:0% +integral by cutting up the domain for +the Riemann integral and you know you + + align:start position:0% +the Riemann integral and you know you + + + align:start position:0% +the Riemann integral and you know you +choose points in between and you form + + align:start position:0% +choose points in between and you form + + + align:start position:0% +choose points in between and you form +these boxes now you know you have some + + align:start position:0% +these boxes now you know you have some + + + align:start position:0% +these boxes now you know you have some +freedom in how you choose these boxes + + align:start position:0% +freedom in how you choose these boxes + + + align:start position:0% +freedom in how you choose these boxes +that approximate the + + align:start position:0% +that approximate the + + + align:start position:0% +that approximate the +integral of f but one way to choose the + + align:start position:0% +integral of f but one way to choose the + + + align:start position:0% +integral of f but one way to choose the +boxes or at least when I picture it I + + align:start position:0% +boxes or at least when I picture it I + + + align:start position:0% +boxes or at least when I picture it I +always picture the boxes sitting below + + align:start position:0% +always picture the boxes sitting below + + + align:start position:0% +always picture the boxes sitting below +the graph of F and as the you know as + + align:start position:0% +the graph of F and as the you know as + + + align:start position:0% +the graph of F and as the you know as +you Dice up the domain smaller and + + align:start position:0% +you Dice up the domain smaller and + + + align:start position:0% +you Dice up the domain smaller and +smaller then these things are kind of + + align:start position:0% +smaller then these things are kind of + + + align:start position:0% +smaller then these things are kind of +um + + align:start position:0% +um + + + align:start position:0% +um +these boxes are getting narrower and + + align:start position:0% +these boxes are getting narrower and + + + align:start position:0% +these boxes are getting narrower and +kind of your approximation is filling in + + align:start position:0% +kind of your approximation is filling in + + + align:start position:0% +kind of your approximation is filling in +uh the integral or the area underneath + + align:start position:0% +uh the integral or the area underneath + + + align:start position:0% +uh the integral or the area underneath +the curve From Below okay and + + align:start position:0% +the curve From Below okay and + + + align:start position:0% +the curve From Below okay and +we've already seen that for non-negative + + align:start position:0% +we've already seen that for non-negative + + + align:start position:0% +we've already seen that for non-negative +measurable functions there always exist + + align:start position:0% +measurable functions there always exist + + + align:start position:0% +measurable functions there always exist +a sequence of simple functions that + + align:start position:0% +a sequence of simple functions that + + + align:start position:0% +a sequence of simple functions that +increase to F right so that for every X + + align:start position:0% +increase to F right so that for every X + + + align:start position:0% +increase to F right so that for every X +I stick into the sequence of functions + + align:start position:0% +I stick into the sequence of functions + + + align:start position:0% +I stick into the sequence of functions +V1 is less than or equal to V2 is less + + align:start position:0% +V1 is less than or equal to V2 is less + + + align:start position:0% +V1 is less than or equal to V2 is less +than or equal to V3 and so on and these + + align:start position:0% +than or equal to V3 and so on and these + + + align:start position:0% +than or equal to V3 and so on and these +fees are increasing Point wise to F + + align:start position:0% +fees are increasing Point wise to F + + + align:start position:0% +fees are increasing Point wise to F +right so one would you know if you're + + align:start position:0% +right so one would you know if you're + + + align:start position:0% +right so one would you know if you're +trying to build this on your own you + + align:start position:0% +trying to build this on your own you + + + align:start position:0% +trying to build this on your own you +would think okay let me Define the + + align:start position:0% +would think okay let me Define the + + + align:start position:0% +would think okay let me Define the +integral as of a function of a + + align:start position:0% +integral as of a function of a + + + align:start position:0% +integral as of a function of a +non-negative measurable function as you + + align:start position:0% +non-negative measurable function as you + + + align:start position:0% +non-negative measurable function as you +know the limit of the integrals of you + + align:start position:0% +know the limit of the integrals of you + + + align:start position:0% +know the limit of the integrals of you +know a sequence of + + align:start position:0% +know a sequence of + + + align:start position:0% +know a sequence of +simple functions increasing to F which I + + align:start position:0% +simple functions increasing to F which I + + + align:start position:0% +simple functions increasing to F which I +know exists because we constructed one + + align:start position:0% +know exists because we constructed one + + + align:start position:0% +know exists because we constructed one +of course + + align:start position:0% +of course + + + align:start position:0% +of course +um and that's one way to do it and some + + align:start position:0% +um and that's one way to do it and some + + + align:start position:0% +um and that's one way to do it and some +textbooks do that but you come across + + align:start position:0% +textbooks do that but you come across + + + align:start position:0% +textbooks do that but you come across +this problem that you know this number + + align:start position:0% +this problem that you know this number + + + align:start position:0% +this problem that you know this number +that you've defined to be the limit of + + align:start position:0% +that you've defined to be the limit of + + + align:start position:0% +that you've defined to be the limit of +these integrals maybe it depends on the + + align:start position:0% +these integrals maybe it depends on the + + + align:start position:0% +these integrals maybe it depends on the +the sequence of + + align:start position:0% +the sequence of + + + align:start position:0% +the sequence of +um + + align:start position:0% +um + + + align:start position:0% +um +you know measurable functions that you + + align:start position:0% +you know measurable functions that you + + + align:start position:0% +you know measurable functions that you +took + + align:start position:0% +took + + + align:start position:0% +took +uh in the beginning so we're not going + + align:start position:0% +uh in the beginning so we're not going + + + align:start position:0% +uh in the beginning so we're not going +to quite do that in the end we'll see + + align:start position:0% +to quite do that in the end we'll see + + + align:start position:0% +to quite do that in the end we'll see +that this number we Define can be given + + align:start position:0% +that this number we Define can be given + + + align:start position:0% +that this number we Define can be given +as the limit of uh simple as of the + + align:start position:0% +as the limit of uh simple as of the + + + align:start position:0% +as the limit of uh simple as of the +limit of + + align:start position:0% +limit of + + + align:start position:0% +limit of +the integrals of simple functions so for + + align:start position:0% +the integrals of simple functions so for + + + align:start position:0% +the integrals of simple functions so for +a general non-negative measurable + + align:start position:0% +a general non-negative measurable + + + align:start position:0% +a general non-negative measurable +function + + align:start position:0% + + + + align:start position:0% + +we Define + + align:start position:0% +we Define + + + align:start position:0% +we Define +the integral of f over e + + align:start position:0% +the integral of f over e + + + align:start position:0% +the integral of f over e +to be the soup + + align:start position:0% +to be the soup + + + align:start position:0% +to be the soup +of the integral over e of Phi + + align:start position:0% +of the integral over e of Phi + + + align:start position:0% +of the integral over e of Phi +where now Phi + + align:start position:0% + + + + align:start position:0% + +is a non-negative simple function + + align:start position:0% + + + + align:start position:0% + +and V sits below f + + align:start position:0% +and V sits below f + + + align:start position:0% +and V sits below f +okay + + align:start position:0% + + + + align:start position:0% + +all right so in some sense this is kind + + align:start position:0% +all right so in some sense this is kind + + + align:start position:0% +all right so in some sense this is kind +of like you know taking the integral of + + align:start position:0% +of like you know taking the integral of + + + align:start position:0% +of like you know taking the integral of +f to be defined as + + align:start position:0% +f to be defined as + + + align:start position:0% +f to be defined as +you know as kind of uh I don't want to + + align:start position:0% +you know as kind of uh I don't want to + + + align:start position:0% +you know as kind of uh I don't want to +say limit because it's not exactly a + + align:start position:0% +say limit because it's not exactly a + + + align:start position:0% +say limit because it's not exactly a +limit but in some sense the thing that's + + align:start position:0% +limit but in some sense the thing that's + + + align:start position:0% +limit but in some sense the thing that's +getting filled up by all the the the + + align:start position:0% +getting filled up by all the the the + + + align:start position:0% +getting filled up by all the the the +integrals of the simple functions below + + align:start position:0% +integrals of the simple functions below + + + align:start position:0% +integrals of the simple functions below +the the graph that sit below the graph + + align:start position:0% +the the graph that sit below the graph + + + align:start position:0% +the the graph that sit below the graph +of f + + align:start position:0% +of f + + + align:start position:0% +of f +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% + + + + align:start position:0% + +okay so let me uh just prove uh + + align:start position:0% +okay so let me uh just prove uh + + + align:start position:0% +okay so let me uh just prove uh +very simple theorem which is useful + + align:start position:0% +very simple theorem which is useful + + + align:start position:0% +very simple theorem which is useful +so + + align:start position:0% + + + + align:start position:0% + +if e is a subset of R is measurable in + + align:start position:0% +if e is a subset of R is measurable in + + + align:start position:0% +if e is a subset of R is measurable in +fact + + align:start position:0% + + + + align:start position:0% + +it's a set of measure zero so remember + + align:start position:0% +it's a set of measure zero so remember + + + align:start position:0% +it's a set of measure zero so remember +all sets of outer measure zero are + + align:start position:0% +all sets of outer measure zero are + + + align:start position:0% +all sets of outer measure zero are +measurable so when I I don't have to say + + align:start position:0% +measurable so when I I don't have to say + + + align:start position:0% +measurable so when I I don't have to say +really if e is a subset of r with e + + align:start position:0% +really if e is a subset of r with e + + + align:start position:0% +really if e is a subset of r with e +measurable when I say this I'm kind of + + align:start position:0% +measurable when I say this I'm kind of + + + align:start position:0% +measurable when I say this I'm kind of +saying two things at once it's out Outer + + align:start position:0% +saying two things at once it's out Outer + + + align:start position:0% +saying two things at once it's out Outer +measure V is zero or one and therefore + + align:start position:0% +measure V is zero or one and therefore + + + align:start position:0% +measure V is zero or one and therefore +it's measurable + + align:start position:0% +it's measurable + + + align:start position:0% +it's measurable +uh + + align:start position:0% + + + + align:start position:0% + +so then for all f + + align:start position:0% +so then for all f + + + align:start position:0% +so then for all f +that are non-negative + + align:start position:0% +that are non-negative + + + align:start position:0% +that are non-negative +and measurable on E + + align:start position:0% +and measurable on E + + + align:start position:0% +and measurable on E +the integral over e of f is zero okay so + + align:start position:0% +the integral over e of f is zero okay so + + + align:start position:0% +the integral over e of f is zero okay so +it's only kind of interesting to take + + align:start position:0% +it's only kind of interesting to take + + + align:start position:0% +it's only kind of interesting to take +the integral over uh sets that have + + align:start position:0% +the integral over uh sets that have + + + align:start position:0% +the integral over uh sets that have +positive measure + + align:start position:0% +positive measure + + + align:start position:0% +positive measure +okay so no matter what function I take + + align:start position:0% +okay so no matter what function I take + + + align:start position:0% +okay so no matter what function I take +the integral over a set of measures zero + + align:start position:0% +the integral over a set of measures zero + + + align:start position:0% +the integral over a set of measures zero +is zero okay this is kind of a you know + + align:start position:0% +is zero okay this is kind of a you know + + + align:start position:0% +is zero okay this is kind of a you know +akin to in Riemann integration the + + align:start position:0% +akin to in Riemann integration the + + + align:start position:0% +akin to in Riemann integration the +integral over a point being zero but now + + align:start position:0% +integral over a point being zero but now + + + align:start position:0% +integral over a point being zero but now +we have you know more interesting sets + + align:start position:0% +we have you know more interesting sets + + + align:start position:0% +we have you know more interesting sets +of measure zero other than just a point + + align:start position:0% +of measure zero other than just a point + + + align:start position:0% +of measure zero other than just a point +so what's the proof of this well we + + align:start position:0% +so what's the proof of this well we + + + align:start position:0% +so what's the proof of this well we +don't have much to go off of we just + + align:start position:0% +don't have much to go off of we just + + + align:start position:0% +don't have much to go off of we just +have the definition so let's use the + + align:start position:0% +have the definition so let's use the + + + align:start position:0% +have the definition so let's use the +definition let + + align:start position:0% +definition let + + + align:start position:0% +definition let +fee + + align:start position:0% + + + + align:start position:0% + +be simple + + align:start position:0% +be simple + + + align:start position:0% +be simple +with this sort of canonical + + align:start position:0% + + + + align:start position:0% + +representation + + align:start position:0% + + + + align:start position:0% + +with the less than or equal to F so what + + align:start position:0% +with the less than or equal to F so what + + + align:start position:0% +with the less than or equal to F so what +I'd like to show is that the integral of + + align:start position:0% +I'd like to show is that the integral of + + + align:start position:0% +I'd like to show is that the integral of +Phi is zero but this is and therefore + + align:start position:0% +Phi is zero but this is and therefore + + + align:start position:0% +Phi is zero but this is and therefore +the integral of f which is the soup over + + align:start position:0% +the integral of f which is the soup over + + + align:start position:0% +the integral of f which is the soup over +all of these integrals is therefore zero + + align:start position:0% +all of these integrals is therefore zero + + + align:start position:0% +all of these integrals is therefore zero +but this is clear + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +since all of these ajs are subsets of e + + align:start position:0% +since all of these ajs are subsets of e + + + align:start position:0% +since all of these ajs are subsets of e +which is a sub which is a set of measure + + align:start position:0% +which is a sub which is a set of measure + + + align:start position:0% +which is a sub which is a set of measure +zero + + align:start position:0% + + + + align:start position:0% + +this implies the measure of AJ + + align:start position:0% +this implies the measure of AJ + + + align:start position:0% +this implies the measure of AJ +equals zero for all J and therefore + + align:start position:0% +equals zero for all J and therefore + + + align:start position:0% +equals zero for all J and therefore +um + + align:start position:0% + + + + align:start position:0% + +the integral of Phi over e + + align:start position:0% +the integral of Phi over e + + + align:start position:0% +the integral of Phi over e +which is equal to + + align:start position:0% +which is equal to + + + align:start position:0% +which is equal to +ah measure of AJ + + align:start position:0% +ah measure of AJ + + + align:start position:0% +ah measure of AJ +equals zero and thus + + align:start position:0% +equals zero and thus + + + align:start position:0% +equals zero and thus +the interval of f which is the soup over + + align:start position:0% +the interval of f which is the soup over + + + align:start position:0% +the interval of f which is the soup over +all of these is just a soup of zero then + + align:start position:0% + + + + align:start position:0% + +okay so I guess I should have started + + align:start position:0% +okay so I guess I should have started + + + align:start position:0% +okay so I guess I should have started +this proof off with let F be in uh L + + align:start position:0% +this proof off with let F be in uh L + + + align:start position:0% +this proof off with let F be in uh L +plus of E + + align:start position:0% +plus of E + + + align:start position:0% +plus of E +so I left that off but uh + + align:start position:0% +so I left that off but uh + + + align:start position:0% +so I left that off but uh +you know what I was doing hopefully + + align:start position:0% + + + + align:start position:0% + +um Okay so + + align:start position:0% + + + + align:start position:0% + +it's only interesting to take the + + align:start position:0% +it's only interesting to take the + + + align:start position:0% +it's only interesting to take the +integral over sets of positive measure + + align:start position:0% + + + + align:start position:0% + +um now we have a few facts which + + align:start position:0% +um now we have a few facts which + + + align:start position:0% +um now we have a few facts which +carry over + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +well not really karaoke well one of them + + align:start position:0% +well not really karaoke well one of them + + + align:start position:0% +well not really karaoke well one of them +carries over from what we did for simple + + align:start position:0% +carries over from what we did for simple + + + align:start position:0% +carries over from what we did for simple +functions and the others just kind of + + align:start position:0% +functions and the others just kind of + + + align:start position:0% +functions and the others just kind of +follow from the definition + + align:start position:0% +follow from the definition + + + align:start position:0% +follow from the definition +and it'll be exercising the assignment + + align:start position:0% +and it'll be exercising the assignment + + + align:start position:0% +and it'll be exercising the assignment +so it's uh the following if + + align:start position:0% + + + + align:start position:0% + +B is + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +the two definitions of the integral of V + + align:start position:0% + + + + align:start position:0% + +agree + + align:start position:0% +agree + + + align:start position:0% +agree +okay and so I'll say exactly what I mean + + align:start position:0% +okay and so I'll say exactly what I mean + + + align:start position:0% +okay and so I'll say exactly what I mean +in just a second + + align:start position:0% +in just a second + + + align:start position:0% +in just a second +two + + align:start position:0% + + + + align:start position:0% + +f and g are in L plus of E + + align:start position:0% + + + + align:start position:0% + +and C is + + align:start position:0% + + + + align:start position:0% + +non-negative a real number + + align:start position:0% +non-negative a real number + + + align:start position:0% +non-negative a real number +and + + align:start position:0% + + + + align:start position:0% + +f is less than or equal to G + + align:start position:0% +f is less than or equal to G + + + align:start position:0% +f is less than or equal to G +on E + + align:start position:0% +on E + + + align:start position:0% +on E +then + + align:start position:0% +then + + + align:start position:0% +then +a couple of things + + align:start position:0% +a couple of things + + + align:start position:0% +a couple of things +the integral of c times f is equal to c + + align:start position:0% +the integral of c times f is equal to c + + + align:start position:0% +the integral of c times f is equal to c +times the integral of f + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +the integral over e of f is less than or + + align:start position:0% +the integral over e of f is less than or + + + align:start position:0% +the integral over e of f is less than or +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +uh the integral of G over e + + align:start position:0% + + + + align:start position:0% + +and one final property is the following + + align:start position:0% + + + + align:start position:0% + +if f is + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a measurable function on E + + align:start position:0% + + + + align:start position:0% + +and F is a + + align:start position:0% +and F is a + + + align:start position:0% +and F is a +measurable subset + + align:start position:0% +measurable subset + + + align:start position:0% +measurable subset +of E + + align:start position:0% + + + + align:start position:0% + +then I can integrate F also on capital F + + align:start position:0% +then I can integrate F also on capital F + + + align:start position:0% +then I can integrate F also on capital F +so this is in the I think maybe X or + + align:start position:0% +so this is in the I think maybe X or + + + align:start position:0% +so this is in the I think maybe X or +sine of five that you know if I have a + + align:start position:0% +sine of five that you know if I have a + + + align:start position:0% +sine of five that you know if I have a +function which is measurable on a set + + align:start position:0% +function which is measurable on a set + + + align:start position:0% +function which is measurable on a set +and I take any subset of that measurable + + align:start position:0% +and I take any subset of that measurable + + + align:start position:0% +and I take any subset of that measurable +set which is measurable then F + + align:start position:0% +set which is measurable then F + + + align:start position:0% +set which is measurable then F +restricted to this set is also + + align:start position:0% +restricted to this set is also + + + align:start position:0% +restricted to this set is also +measurable so what I'm about to say + + align:start position:0% +measurable so what I'm about to say + + + align:start position:0% +measurable so what I'm about to say +makes sense then the integral of f + + align:start position:0% +makes sense then the integral of f + + + align:start position:0% +makes sense then the integral of f +over so of little F over capital F is + + align:start position:0% +over so of little F over capital F is + + + align:start position:0% +over so of little F over capital F is +equal to the integral of e + + align:start position:0% +equal to the integral of e + + + align:start position:0% +equal to the integral of e +of little F times the indicator function + + align:start position:0% +of little F times the indicator function + + + align:start position:0% +of little F times the indicator function +of F + + align:start position:0% +of F + + + align:start position:0% +of F +and + + align:start position:0% +and + + + align:start position:0% +and +um which is less than or equal to + + align:start position:0% + + + + align:start position:0% + +the integral over e of cap of little f + + align:start position:0% +the integral over e of cap of little f + + + align:start position:0% +the integral over e of cap of little f +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +I think all the rest of the statements + + align:start position:0% +I think all the rest of the statements + + + align:start position:0% +I think all the rest of the statements +statements two and three are completely + + align:start position:0% +statements two and three are completely + + + align:start position:0% +statements two and three are completely +unambiguous maybe you're wondering what + + align:start position:0% +unambiguous maybe you're wondering what + + + align:start position:0% +unambiguous maybe you're wondering what +exactly did I mean by one + + align:start position:0% +exactly did I mean by one + + + align:start position:0% +exactly did I mean by one +so we had kind of two definitions of a + + align:start position:0% +so we had kind of two definitions of a + + + align:start position:0% +so we had kind of two definitions of a +of the integral of a simple function + + align:start position:0% +of the integral of a simple function + + + align:start position:0% +of the integral of a simple function +right we defined it first as you know + + align:start position:0% +right we defined it first as you know + + + align:start position:0% +right we defined it first as you know +uh the sum of the coefficients times the + + align:start position:0% +uh the sum of the coefficients times the + + + align:start position:0% +uh the sum of the coefficients times the +measure of these sets + + align:start position:0% +measure of these sets + + + align:start position:0% +measure of these sets +and then we also have a second + + align:start position:0% +and then we also have a second + + + align:start position:0% +and then we also have a second +definition + + align:start position:0% +definition + + + align:start position:0% +definition +right because a simple function which is + + align:start position:0% +right because a simple function which is + + + align:start position:0% +right because a simple function which is +a measurable non-negative simple + + align:start position:0% +a measurable non-negative simple + + + align:start position:0% +a measurable non-negative simple +function is also in this set so I should + + align:start position:0% +function is also in this set so I should + + + align:start position:0% +function is also in this set so I should +have that what's + + align:start position:0% +have that what's + + + align:start position:0% +have that what's +here should be equal to + + align:start position:0% +here should be equal to + + + align:start position:0% +here should be equal to +what's on the right + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +statement one is a statement that what's + + align:start position:0% +statement one is a statement that what's + + + align:start position:0% +statement one is a statement that what's +underlined three times is equal to + + align:start position:0% +underlined three times is equal to + + + align:start position:0% +underlined three times is equal to +what was underlined four times + + align:start position:0% + + + + align:start position:0% + +that's a lot of lines + + align:start position:0% +that's a lot of lines + + + align:start position:0% +that's a lot of lines +okay + + align:start position:0% + + + + align:start position:0% + +all right so this will be a + + align:start position:0% +all right so this will be a + + + align:start position:0% +all right so this will be a +fairly straightforward exercise + + align:start position:0% +fairly straightforward exercise + + + align:start position:0% +fairly straightforward exercise +just using the definitions and also what + + align:start position:0% +just using the definitions and also what + + + align:start position:0% +just using the definitions and also what +we did for for simple functions + + align:start position:0% + + + + align:start position:0% + +um one consequence of + + align:start position:0% + + + + align:start position:0% + +this theorem and the one before it is + + align:start position:0% +this theorem and the one before it is + + + align:start position:0% +this theorem and the one before it is +the following is that I can relax + + align:start position:0% +the following is that I can relax + + + align:start position:0% +the following is that I can relax +this condition here in two to an almost + + align:start position:0% +this condition here in two to an almost + + + align:start position:0% +this condition here in two to an almost +everywhere statement + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +if f and g + + align:start position:0% + + + + align:start position:0% + +are non-negative measurable functions + + align:start position:0% + + + + align:start position:0% + +and F is less than or equal to G + + align:start position:0% +and F is less than or equal to G + + + align:start position:0% +and F is less than or equal to G +almost everywhere on E + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the integral of e of f is equal to + + align:start position:0% +the integral of e of f is equal to + + + align:start position:0% +the integral of e of f is equal to +is less than or equal to the integral of + + align:start position:0% +is less than or equal to the integral of + + + align:start position:0% +is less than or equal to the integral of +uh G + + align:start position:0% +uh G + + + align:start position:0% +uh G +okay + + align:start position:0% + + + + align:start position:0% + +so let's write the the proof of this so + + align:start position:0% +so let's write the the proof of this so + + + align:start position:0% +so let's write the the proof of this so +if + + align:start position:0% +if + + + align:start position:0% +if +so let + + align:start position:0% + + + + align:start position:0% + +F be the set of all x's in e + + align:start position:0% +F be the set of all x's in e + + + align:start position:0% +F be the set of all x's in e +such that uh + + align:start position:0% +such that uh + + + align:start position:0% +such that uh +f of x is less than or equal to G of x + + align:start position:0% +f of x is less than or equal to G of x + + + align:start position:0% +f of x is less than or equal to G of x +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +so it's not difficult to to realize that + + align:start position:0% +so it's not difficult to to realize that + + + align:start position:0% +so it's not difficult to to realize that +this is a you know a measurable set this + + align:start position:0% +this is a you know a measurable set this + + + align:start position:0% +this is a you know a measurable set this +is if you'd like + + align:start position:0% +is if you'd like + + + align:start position:0% +is if you'd like +um + + align:start position:0% +um + + + align:start position:0% +um +F minus G + + align:start position:0% +F minus G + + + align:start position:0% +F minus G +the inverse image of + + align:start position:0% +the inverse image of + + + align:start position:0% +the inverse image of +or let's do it this way + + align:start position:0% + + + + align:start position:0% + +write this as + + align:start position:0% +write this as + + + align:start position:0% +write this as +G minus F inverse image of + + align:start position:0% +G minus F inverse image of + + + align:start position:0% +G minus F inverse image of +zero + + align:start position:0% +zero + + + align:start position:0% +zero +Infinity + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and since G and F are measurable + + align:start position:0% +and since G and F are measurable + + + align:start position:0% +and since G and F are measurable +functions their difference uh + + align:start position:0% +functions their difference uh + + + align:start position:0% +functions their difference uh +is measurable + + align:start position:0% +is measurable + + + align:start position:0% +is measurable +um + + align:start position:0% + + + + align:start position:0% + +not negative so this is always + + align:start position:0% +not negative so this is always + + + align:start position:0% +not negative so this is always +non-negative + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +okay maybe there's a small issue with + + align:start position:0% +okay maybe there's a small issue with + + + align:start position:0% +okay maybe there's a small issue with +what happens in Infinity but you're + + align:start position:0% +what happens in Infinity but you're + + + align:start position:0% +what happens in Infinity but you're +dealing with that in the assignment so + + align:start position:0% +dealing with that in the assignment so + + + align:start position:0% +dealing with that in the assignment so +I'm just going to erase this from the + + align:start position:0% +I'm just going to erase this from the + + + align:start position:0% +I'm just going to erase this from the +board and you'll just have to accept + + align:start position:0% +board and you'll just have to accept + + + align:start position:0% +board and you'll just have to accept +that this is measurable + + align:start position:0% +that this is measurable + + + align:start position:0% +that this is measurable +under the wisdom that I gave you that if + + align:start position:0% +under the wisdom that I gave you that if + + + align:start position:0% +under the wisdom that I gave you that if +you can write it down typically it's + + align:start position:0% +you can write it down typically it's + + + align:start position:0% +you can write it down typically it's +measurable + + align:start position:0% + + + + align:start position:0% + +and what is the measure of the + + align:start position:0% +and what is the measure of the + + + align:start position:0% +and what is the measure of the +complement + + align:start position:0% + + + + align:start position:0% + +zero because this is supposed to hold + + align:start position:0% +zero because this is supposed to hold + + + align:start position:0% +zero because this is supposed to hold +almost everywhere + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% + + + + align:start position:0% + +okay so I left off a fact which + + align:start position:0% +okay so I left off a fact which + + + align:start position:0% +okay so I left off a fact which +strictly speaking we might need + + align:start position:0% +strictly speaking we might need + + + align:start position:0% +strictly speaking we might need +for this but + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is also an exercise Let's uh + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +then the integral over + + align:start position:0% +then the integral over + + + align:start position:0% +then the integral over +of little F over + + align:start position:0% +of little F over + + + align:start position:0% +of little F over +e which is equal to the integral of over + + align:start position:0% +e which is equal to the integral of over + + + align:start position:0% +e which is equal to the integral of over +e of f Union F complement here + + align:start position:0% + + + + align:start position:0% + +this is equal to the integral over f + + align:start position:0% +this is equal to the integral over f + + + align:start position:0% +this is equal to the integral over f +little f + + align:start position:0% +little f + + + align:start position:0% +little f +plus the integral of over F complement + + align:start position:0% +plus the integral of over F complement + + + align:start position:0% +plus the integral of over F complement +of little F okay so + + align:start position:0% +of little F okay so + + + align:start position:0% +of little F okay so +um I didn't strictly speaking I mean + + align:start position:0% +um I didn't strictly speaking I mean + + + align:start position:0% +um I didn't strictly speaking I mean +strictly speaking I didn't write why + + align:start position:0% +strictly speaking I didn't write why + + + align:start position:0% +strictly speaking I didn't write why +this is true down but uh let's uh think + + align:start position:0% +this is true down but uh let's uh think + + + align:start position:0% +this is true down but uh let's uh think +about it just for a moment so these are + + align:start position:0% +about it just for a moment so these are + + + align:start position:0% +about it just for a moment so these are +two disjoint subsets that make up e okay + + align:start position:0% +two disjoint subsets that make up e okay + + + align:start position:0% +two disjoint subsets that make up e okay +why is this going to be equal to this + + align:start position:0% +why is this going to be equal to this + + + align:start position:0% +why is this going to be equal to this +well it's true for simple functions okay + + align:start position:0% +well it's true for simple functions okay + + + align:start position:0% +well it's true for simple functions okay +so I mean if I make the statement in the + + align:start position:0% +so I mean if I make the statement in the + + + align:start position:0% +so I mean if I make the statement in the +zoom fee I mean f is simple then + + align:start position:0% +zoom fee I mean f is simple then + + + align:start position:0% +zoom fee I mean f is simple then +um + + align:start position:0% +um + + + align:start position:0% +um +you know it's not hard to convince + + align:start position:0% +you know it's not hard to convince + + + align:start position:0% +you know it's not hard to convince +yourself that this is true and if it's + + align:start position:0% +yourself that this is true and if it's + + + align:start position:0% +yourself that this is true and if it's +true for simple functions then from how + + align:start position:0% +true for simple functions then from how + + + align:start position:0% +true for simple functions then from how +we've defined the integral as to be the + + align:start position:0% +we've defined the integral as to be the + + + align:start position:0% +we've defined the integral as to be the +soup it should it will carry over to to + + align:start position:0% +soup it should it will carry over to to + + + align:start position:0% +soup it should it will carry over to to +uh General non-negative measurable + + align:start position:0% +uh General non-negative measurable + + + align:start position:0% +uh General non-negative measurable +functions so + + align:start position:0% +functions so + + + align:start position:0% +functions so +um let's just accept this and you can + + align:start position:0% +um let's just accept this and you can + + + align:start position:0% +um let's just accept this and you can +prove it on your own it's it's not + + align:start position:0% +prove it on your own it's it's not + + + align:start position:0% +prove it on your own it's it's not +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +but since we have this + + align:start position:0% + + + + align:start position:0% + +uh and F complement is a set of measure + + align:start position:0% +uh and F complement is a set of measure + + + align:start position:0% +uh and F complement is a set of measure +zero this is + + align:start position:0% +zero this is + + + align:start position:0% +zero this is +the integral of + + align:start position:0% +the integral of + + + align:start position:0% +the integral of +a little f okay + + align:start position:0% + + + + align:start position:0% + +all right since this is zero now on + + align:start position:0% +all right since this is zero now on + + + align:start position:0% +all right since this is zero now on +capital F little f is less than or equal + + align:start position:0% +capital F little f is less than or equal + + + align:start position:0% +capital F little f is less than or equal +to G so this is less than or equal to + + align:start position:0% +to G so this is less than or equal to + + + align:start position:0% +to G so this is less than or equal to +the integral of G + + align:start position:0% +the integral of G + + + align:start position:0% +the integral of G +over capital F and just going backwards + + align:start position:0% +over capital F and just going backwards + + + align:start position:0% +over capital F and just going backwards +this is equal to the integral + + align:start position:0% +this is equal to the integral + + + align:start position:0% +this is equal to the integral +of F G Plus + + align:start position:0% +of F G Plus + + + align:start position:0% +of F G Plus +F complement which is equal to the + + align:start position:0% +F complement which is equal to the + + + align:start position:0% +F complement which is equal to the +integral of G + + align:start position:0% + + + + align:start position:0% + +G okay + + align:start position:0% +G okay + + + align:start position:0% +G okay +so modulo uh you know this + + align:start position:0% +so modulo uh you know this + + + align:start position:0% +so modulo uh you know this +equality which I leave to you to fill in + + align:start position:0% +equality which I leave to you to fill in + + + align:start position:0% +equality which I leave to you to fill in +um + + align:start position:0% +um + + + align:start position:0% +um +proves the theorem + + align:start position:0% +proves the theorem + + + align:start position:0% +proves the theorem +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so now we have the definition of + + align:start position:0% +um so now we have the definition of + + + align:start position:0% +um so now we have the definition of +um + + align:start position:0% +um + + + align:start position:0% +um +the label integral for non-negative + + align:start position:0% +the label integral for non-negative + + + align:start position:0% +the label integral for non-negative +measurable functions we have some + + align:start position:0% +measurable functions we have some + + + align:start position:0% +measurable functions we have some +properties of it what's kind of missing + + align:start position:0% +properties of it what's kind of missing + + + align:start position:0% +properties of it what's kind of missing +from this list that I've given so far is + + align:start position:0% +from this list that I've given so far is + + + align:start position:0% +from this list that I've given so far is +that uh linearity I guess right the + + align:start position:0% +that uh linearity I guess right the + + + align:start position:0% +that uh linearity I guess right the +integral of the sum of two non-negative + + align:start position:0% +integral of the sum of two non-negative + + + align:start position:0% +integral of the sum of two non-negative +measurable functions is equal to the sum + + align:start position:0% +measurable functions is equal to the sum + + + align:start position:0% +measurable functions is equal to the sum +of the integrals we had that for simple + + align:start position:0% +of the integrals we had that for simple + + + align:start position:0% +of the integrals we had that for simple +functions uh how do we get that for + + align:start position:0% +functions uh how do we get that for + + + align:start position:0% +functions uh how do we get that for +um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +General non-negative measurable + + align:start position:0% +General non-negative measurable + + + align:start position:0% +General non-negative measurable +functions so + + align:start position:0% + + + + align:start position:0% + +okay so this you know what I'm about to + + align:start position:0% +okay so this you know what I'm about to + + + align:start position:0% +okay so this you know what I'm about to +prove is not just a tool for proving + + align:start position:0% +prove is not just a tool for proving + + + align:start position:0% +prove is not just a tool for proving +that but uh it's one of the you know big + + align:start position:0% +that but uh it's one of the you know big + + + align:start position:0% +that but uh it's one of the you know big +three convergence theorems that you find + + align:start position:0% +three convergence theorems that you find + + + align:start position:0% +three convergence theorems that you find +in a big measure and integration or the + + align:start position:0% +in a big measure and integration or the + + + align:start position:0% +in a big measure and integration or the +big integration so which is the + + align:start position:0% +big integration so which is the + + + align:start position:0% +big integration so which is the +following + + align:start position:0% + + + + align:start position:0% + +monotone + + align:start position:0% + + + + align:start position:0% + +convergence theorem + + align:start position:0% + + + + align:start position:0% + +which is the following that if + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +is + + align:start position:0% + + + + align:start position:0% + +a sequence of non-negative measurable + + align:start position:0% +a sequence of non-negative measurable + + + align:start position:0% +a sequence of non-negative measurable +functions + + align:start position:0% +functions + + + align:start position:0% +functions +such that + + align:start position:0% +such that + + + align:start position:0% +such that +F1 is less than or equal to F2 is less + + align:start position:0% +F1 is less than or equal to F2 is less + + + align:start position:0% +F1 is less than or equal to F2 is less +than riff equal to F3 + + align:start position:0% + + + + align:start position:0% + +on E + + align:start position:0% +on E + + + align:start position:0% +on E +so Point wise they are increasing + + align:start position:0% +so Point wise they are increasing + + + align:start position:0% +so Point wise they are increasing +sequence is increasing + + align:start position:0% +sequence is increasing + + + align:start position:0% +sequence is increasing +and + + align:start position:0% + + + + align:start position:0% + +there's just a function f so that FN + + align:start position:0% +there's just a function f so that FN + + + align:start position:0% +there's just a function f so that FN +goes to f + + align:start position:0% + + + + align:start position:0% + +Point wise on E so let me just recall + + align:start position:0% +Point wise on E so let me just recall + + + align:start position:0% +Point wise on E so let me just recall +this means we're all + + align:start position:0% +this means we're all + + + align:start position:0% +this means we're all +X and E + + align:start position:0% +X and E + + + align:start position:0% +X and E +limit as n goes to Infinity + + align:start position:0% +limit as n goes to Infinity + + + align:start position:0% +limit as n goes to Infinity +of f n of x + + align:start position:0% +of f n of x + + + align:start position:0% +of f n of x +equals f of x + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so in particular f is going to be a + + align:start position:0% +so in particular f is going to be a + + + align:start position:0% +so in particular f is going to be a +non-negative measurable functions + + align:start position:0% +non-negative measurable functions + + + align:start position:0% +non-negative measurable functions +because remember the pointwise limit of + + align:start position:0% +because remember the pointwise limit of + + + align:start position:0% +because remember the pointwise limit of +measurable functions is measurable + + align:start position:0% +measurable functions is measurable + + + align:start position:0% +measurable functions is measurable +so what I'm about to say makes sense + + align:start position:0% +so what I'm about to say makes sense + + + align:start position:0% +so what I'm about to say makes sense +then + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +integrals converge + + align:start position:0% +integrals converge + + + align:start position:0% +integrals converge +to the integrals of the + + align:start position:0% +to the integrals of the + + + align:start position:0% +to the integrals of the +limit so the limit of the integrals is + + align:start position:0% +limit so the limit of the integrals is + + + align:start position:0% +limit so the limit of the integrals is +the integral of the limits okay + + align:start position:0% +the integral of the limits okay + + + align:start position:0% +the integral of the limits okay +so this is a much stronger statement + + align:start position:0% +so this is a much stronger statement + + + align:start position:0% +so this is a much stronger statement +than you know anything you come across + + align:start position:0% +than you know anything you come across + + + align:start position:0% +than you know anything you come across +in Riemann integration right Riemann + + align:start position:0% +in Riemann integration right Riemann + + + align:start position:0% +in Riemann integration right Riemann +integration you know usually requires + + align:start position:0% +integration you know usually requires + + + align:start position:0% +integration you know usually requires +uniform convergence while here at least + + align:start position:0% +uniform convergence while here at least + + + align:start position:0% +uniform convergence while here at least +for monotone uh you know sequences uh we + + align:start position:0% +for monotone uh you know sequences uh we + + + align:start position:0% +for monotone uh you know sequences uh we +have we just need Point wise convergence + + align:start position:0% +have we just need Point wise convergence + + + align:start position:0% +have we just need Point wise convergence +I think there is a you know a version of + + align:start position:0% +I think there is a you know a version of + + + align:start position:0% +I think there is a you know a version of +this theorem that one could state for uh + + align:start position:0% +this theorem that one could state for uh + + + align:start position:0% +this theorem that one could state for uh +Riemann integration + + align:start position:0% +Riemann integration + + + align:start position:0% +Riemann integration +um but still just on the face of it you + + align:start position:0% +um but still just on the face of it you + + + align:start position:0% +um but still just on the face of it you +have a point-wise statement implying uh + + align:start position:0% +have a point-wise statement implying uh + + + align:start position:0% +have a point-wise statement implying uh +you know convergence of integrals so + + align:start position:0% +you know convergence of integrals so + + + align:start position:0% +you know convergence of integrals so +that's it should immediately kind of + + align:start position:0% +that's it should immediately kind of + + + align:start position:0% +that's it should immediately kind of +um + + align:start position:0% +um + + + align:start position:0% +um +you know suggest to you that what we've + + align:start position:0% +you know suggest to you that what we've + + + align:start position:0% +you know suggest to you that what we've +built up this lebag integration is much + + align:start position:0% +built up this lebag integration is much + + + align:start position:0% +built up this lebag integration is much +more powerful than Riemann integration + + align:start position:0% +more powerful than Riemann integration + + + align:start position:0% +more powerful than Riemann integration +so uh let's prove + + align:start position:0% +so uh let's prove + + + align:start position:0% +so uh let's prove +the theorem + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um since F1 + + align:start position:0% + + + + align:start position:0% + +is less than or equal to F2 is less than + + align:start position:0% +is less than or equal to F2 is less than + + + align:start position:0% +is less than or equal to F2 is less than +or equal to F3 and so on + + align:start position:0% +or equal to F3 and so on + + + align:start position:0% +or equal to F3 and so on +this implies the integral of e of F1 is + + align:start position:0% +this implies the integral of e of F1 is + + + align:start position:0% +this implies the integral of e of F1 is +less than or equal to the integral of F2 + + align:start position:0% +less than or equal to the integral of F2 + + + align:start position:0% +less than or equal to the integral of F2 +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +and + + align:start position:0% +and + + + align:start position:0% +and +what else so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +which implies that + + align:start position:0% +which implies that + + + align:start position:0% +which implies that +the limit as n goes to Infinity + + align:start position:0% +the limit as n goes to Infinity + + + align:start position:0% +the limit as n goes to Infinity +of + + align:start position:0% +of + + + align:start position:0% +of +the integrals of f in + + align:start position:0% + + + + align:start position:0% + +exists in + + align:start position:0% + + + + align:start position:0% + +zero Infinity so this is a non-negative + + align:start position:0% +zero Infinity so this is a non-negative + + + align:start position:0% +zero Infinity so this is a non-negative +increasing sequence of real numbers now + + align:start position:0% +increasing sequence of real numbers now + + + align:start position:0% +increasing sequence of real numbers now +right the integral over e of F1 that's a + + align:start position:0% +right the integral over e of F1 that's a + + + align:start position:0% +right the integral over e of F1 that's a +real number this is a real number all of + + align:start position:0% +real number this is a real number all of + + + align:start position:0% +real number this is a real number all of +these are non-negative numbers because + + align:start position:0% +these are non-negative numbers because + + + align:start position:0% +these are non-negative numbers because +this is a soup over non-negative numbers + + align:start position:0% +this is a soup over non-negative numbers + + + align:start position:0% +this is a soup over non-negative numbers +so I have an increasing sequence of + + align:start position:0% +so I have an increasing sequence of + + + align:start position:0% +so I have an increasing sequence of +non-negative numbers + + align:start position:0% +non-negative numbers + + + align:start position:0% +non-negative numbers +so that either has the limit a finite + + align:start position:0% +so that either has the limit a finite + + + align:start position:0% +so that either has the limit a finite +limit or it must go to Infinity okay + + align:start position:0% +limit or it must go to Infinity okay + + + align:start position:0% +limit or it must go to Infinity okay +that's not uh difficult to prove knowing + + align:start position:0% +that's not uh difficult to prove knowing + + + align:start position:0% +that's not uh difficult to prove knowing +what you know from basic analysis + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +moreover since there are pointwise + + align:start position:0% +moreover since there are pointwise + + + align:start position:0% +moreover since there are pointwise +increasing + + align:start position:0% + + + + align:start position:0% + +and converging to + + align:start position:0% + + + + align:start position:0% + +for all X this implies uh + + align:start position:0% +for all X this implies uh + + + align:start position:0% +for all X this implies uh +that + + align:start position:0% + + + + align:start position:0% + +we still have F1 is less than or equal + + align:start position:0% +we still have F1 is less than or equal + + + align:start position:0% +we still have F1 is less than or equal +to F3 and so on but they all sit below + + align:start position:0% +to F3 and so on but they all sit below + + + align:start position:0% +to F3 and so on but they all sit below +uh F okay so for each X this is a F1 of + + align:start position:0% +uh F okay so for each X this is a F1 of + + + align:start position:0% +uh F okay so for each X this is a F1 of +x f 2 of x f 3 of X and so on this is an + + align:start position:0% +x f 2 of x f 3 of X and so on this is an + + + align:start position:0% +x f 2 of x f 3 of X and so on this is an +increasing sequence of real numbers + + align:start position:0% +increasing sequence of real numbers + + + align:start position:0% +increasing sequence of real numbers +converging to f of x which is either a + + align:start position:0% +converging to f of x which is either a + + + align:start position:0% +converging to f of x which is either a +finite number or Infinity + + align:start position:0% +finite number or Infinity + + + align:start position:0% +finite number or Infinity +so these numbers are increasing to this + + align:start position:0% +so these numbers are increasing to this + + + align:start position:0% +so these numbers are increasing to this +limit + + align:start position:0% +limit + + + align:start position:0% +limit +and therefore they must always sit below + + align:start position:0% +and therefore they must always sit below + + + align:start position:0% +and therefore they must always sit below +the limit okay + + align:start position:0% + + + + align:start position:0% + +and since + + align:start position:0% +and since + + + align:start position:0% +and since +all of these functions sit below f + + align:start position:0% +all of these functions sit below f + + + align:start position:0% +all of these functions sit below f +this implies it for all in + + align:start position:0% + + + + align:start position:0% + +the integral of FN over e is less than + + align:start position:0% +the integral of FN over e is less than + + + align:start position:0% +the integral of FN over e is less than +or equal to the integral of F and + + align:start position:0% +or equal to the integral of F and + + + align:start position:0% +or equal to the integral of F and +therefore the limit + + align:start position:0% +therefore the limit + + + align:start position:0% +therefore the limit +which we know exists + + align:start position:0% + + + + align:start position:0% + +as either a finite number or Infinity is + + align:start position:0% +as either a finite number or Infinity is + + + align:start position:0% +as either a finite number or Infinity is +less than or equal to + + align:start position:0% +less than or equal to + + + align:start position:0% +less than or equal to +the integral of f + + align:start position:0% +the integral of f + + + align:start position:0% +the integral of f +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +just based on the assumptions we + + align:start position:0% +just based on the assumptions we + + + align:start position:0% +just based on the assumptions we +immediately get that + + align:start position:0% +immediately get that + + + align:start position:0% +immediately get that +one of these quantities that we want to + + align:start position:0% +one of these quantities that we want to + + + align:start position:0% +one of these quantities that we want to +show is equal to the other is less than + + align:start position:0% +show is equal to the other is less than + + + align:start position:0% +show is equal to the other is less than +or equal to + + align:start position:0% +or equal to + + + align:start position:0% +or equal to +the other quantity okay so + + align:start position:0% +the other quantity okay so + + + align:start position:0% +the other quantity okay so +um you know standard trick of analysis + + align:start position:0% +um you know standard trick of analysis + + + align:start position:0% +um you know standard trick of analysis +if you get kind of for free one quantity + + align:start position:0% +if you get kind of for free one quantity + + + align:start position:0% +if you get kind of for free one quantity +is less than or equal to the other + + align:start position:0% +is less than or equal to the other + + + align:start position:0% +is less than or equal to the other +quantity that you want to show or equal + + align:start position:0% +quantity that you want to show or equal + + + align:start position:0% +quantity that you want to show or equal +let's try and go the reverse Direction + + align:start position:0% +let's try and go the reverse Direction + + + align:start position:0% +let's try and go the reverse Direction +so now we show + + align:start position:0% + + + + align:start position:0% + +that um + + align:start position:0% +that um + + + align:start position:0% +that um +the integral of f over e is less than or + + align:start position:0% +the integral of f over e is less than or + + + align:start position:0% +the integral of f over e is less than or +equal to the integral + + align:start position:0% +equal to the integral + + + align:start position:0% +equal to the integral +limit as n goes to Infinity of the + + align:start position:0% +limit as n goes to Infinity of the + + + align:start position:0% +limit as n goes to Infinity of the +integral over e + + align:start position:0% +integral over e + + + align:start position:0% +integral over e +of FN + + align:start position:0% +of FN + + + align:start position:0% +of FN +okay and therefore the two are equal + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um now to show this we're going to show + + align:start position:0% +um now to show this we're going to show + + + align:start position:0% +um now to show this we're going to show +that for every simple function less than + + align:start position:0% +that for every simple function less than + + + align:start position:0% +that for every simple function less than +or equal to F the integral of that + + align:start position:0% +or equal to F the integral of that + + + align:start position:0% +or equal to F the integral of that +simple function sits below this okay + + align:start position:0% +simple function sits below this okay + + + align:start position:0% +simple function sits below this okay +now we know these F ins so here's the + + align:start position:0% +now we know these F ins so here's the + + + align:start position:0% +now we know these F ins so here's the +game plan we know the FNS are increasing + + align:start position:0% +game plan we know the FNS are increasing + + + align:start position:0% +game plan we know the FNS are increasing +to f right so if I take a simple + + align:start position:0% +to f right so if I take a simple + + + align:start position:0% +to f right so if I take a simple +function less than or equal to F if the + + align:start position:0% +function less than or equal to F if the + + + align:start position:0% +function less than or equal to F if the +simple function is less than F then + + align:start position:0% +simple function is less than F then + + + align:start position:0% +simple function is less than F then +eventually F in is going to pass it up + + align:start position:0% +eventually F in is going to pass it up + + + align:start position:0% +eventually F in is going to pass it up +right because the F ins are increasing + + align:start position:0% +right because the F ins are increasing + + + align:start position:0% +right because the F ins are increasing +to F and the simple function sits below + + align:start position:0% +to F and the simple function sits below + + + align:start position:0% +to F and the simple function sits below +f + + align:start position:0% +f + + + align:start position:0% +f +right + + align:start position:0% +right + + + align:start position:0% +right +and therefore eventually we should have + + align:start position:0% +and therefore eventually we should have + + + align:start position:0% +and therefore eventually we should have +this is bigger than or equal to the + + align:start position:0% +this is bigger than or equal to the + + + align:start position:0% +this is bigger than or equal to the +integral of that simple function now you + + align:start position:0% +integral of that simple function now you + + + align:start position:0% +integral of that simple function now you +know we're only requiring the simple + + align:start position:0% +know we're only requiring the simple + + + align:start position:0% +know we're only requiring the simple +function to be less than or equal to F + + align:start position:0% +function to be less than or equal to F + + + align:start position:0% +function to be less than or equal to F +so we'll give ourselves a little bit of + + align:start position:0% +so we'll give ourselves a little bit of + + + align:start position:0% +so we'll give ourselves a little bit of +room and then send that bit of room to + + align:start position:0% +room and then send that bit of room to + + + align:start position:0% +room and then send that bit of room to +to zero so + + align:start position:0% +to zero so + + + align:start position:0% +to zero so +um + + align:start position:0% + + + + align:start position:0% + +let fee + + align:start position:0% + + + + align:start position:0% + +the non-negative simple function + + align:start position:0% + + + + align:start position:0% + +b equals sum + + align:start position:0% +b equals sum + + + align:start position:0% +b equals sum +J equals 1 to n + + align:start position:0% +J equals 1 to n + + + align:start position:0% +J equals 1 to n +A J Chi + + align:start position:0% +A J Chi + + + align:start position:0% +A J Chi +AJ + + align:start position:0% +AJ + + + align:start position:0% +AJ +um + + align:start position:0% + + + + align:start position:0% + +with Phi + + align:start position:0% +with Phi + + + align:start position:0% +with Phi +less than or equal to F and our goal is + + align:start position:0% +less than or equal to F and our goal is + + + align:start position:0% +less than or equal to F and our goal is +to show that the integral of Phi is less + + align:start position:0% +to show that the integral of Phi is less + + + align:start position:0% +to show that the integral of Phi is less +than or equal to the Limit as n goes to + + align:start position:0% +than or equal to the Limit as n goes to + + + align:start position:0% +than or equal to the Limit as n goes to +Infinity of f in + + align:start position:0% +Infinity of f in + + + align:start position:0% +Infinity of f in +okay + + align:start position:0% + + + + align:start position:0% + +so here's that little bit of room I was + + align:start position:0% +so here's that little bit of room I was + + + align:start position:0% +so here's that little bit of room I was +uh referring to let Epsilon be a small + + align:start position:0% +uh referring to let Epsilon be a small + + + align:start position:0% +uh referring to let Epsilon be a small +number between 0 and 1. + + align:start position:0% +number between 0 and 1. + + + align:start position:0% +number between 0 and 1. +and uh + + align:start position:0% + + + + align:start position:0% + +let e in be the set of all x's in e + + align:start position:0% +let e in be the set of all x's in e + + + align:start position:0% +let e in be the set of all x's in e +such that + + align:start position:0% +such that + + + align:start position:0% +such that +um + + align:start position:0% +um + + + align:start position:0% +um +f n of x + + align:start position:0% +f n of x + + + align:start position:0% +f n of x +is greater than or equal to 1 minus + + align:start position:0% +is greater than or equal to 1 minus + + + align:start position:0% +is greater than or equal to 1 minus +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +f of x I mean Phi of x + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so note + + align:start position:0% + + + + align:start position:0% + +for all X and E + + align:start position:0% +for all X and E + + + align:start position:0% +for all X and E +1 minus + + align:start position:0% +1 minus + + + align:start position:0% +1 minus +Epsilon times + + align:start position:0% +Epsilon times + + + align:start position:0% +Epsilon times +V of X this is strictly less than now f + + align:start position:0% +V of X this is strictly less than now f + + + align:start position:0% +V of X this is strictly less than now f +of x so we had Phi of X is less than or + + align:start position:0% +of x so we had Phi of X is less than or + + + align:start position:0% +of x so we had Phi of X is less than or +equal to f of x but now if I multiply + + align:start position:0% +equal to f of x but now if I multiply + + + align:start position:0% +equal to f of x but now if I multiply +this by you know a small number that's + + align:start position:0% +this by you know a small number that's + + + align:start position:0% +this by you know a small number that's +close to or a number that's + + align:start position:0% +close to or a number that's + + + align:start position:0% +close to or a number that's +slightly less than one then I will have + + align:start position:0% +slightly less than one then I will have + + + align:start position:0% +slightly less than one then I will have +strict inequality okay + + align:start position:0% + + + + align:start position:0% + +so in particular + + align:start position:0% + + + + align:start position:0% + +then since + + align:start position:0% + + + + align:start position:0% + +we're all X and E + + align:start position:0% +we're all X and E + + + align:start position:0% +we're all X and E +I have a + + align:start position:0% + + + + align:start position:0% + +equals f of x + + align:start position:0% +equals f of x + + + align:start position:0% +equals f of x +this implies that every X must + + align:start position:0% +this implies that every X must + + + align:start position:0% +this implies that every X must +eventually lie in one of these e sub NS + + align:start position:0% +eventually lie in one of these e sub NS + + + align:start position:0% +eventually lie in one of these e sub NS +right because 1 minus Epsilon Phi of X + + align:start position:0% +right because 1 minus Epsilon Phi of X + + + align:start position:0% +right because 1 minus Epsilon Phi of X +is less than f of x the FNS are + + align:start position:0% +is less than f of x the FNS are + + + align:start position:0% +is less than f of x the FNS are +approaching f of x so it must pass up + + align:start position:0% +approaching f of x so it must pass up + + + align:start position:0% +approaching f of x so it must pass up +this value at some point in its quest to + + align:start position:0% +this value at some point in its quest to + + + align:start position:0% +this value at some point in its quest to +get to f of x or at least close to f of + + align:start position:0% +get to f of x or at least close to f of + + + align:start position:0% +get to f of x or at least close to f of +x okay so simply from this fact + + align:start position:0% +x okay so simply from this fact + + + align:start position:0% +x okay so simply from this fact +this implies that uh the union Over N + + align:start position:0% +this implies that uh the union Over N + + + align:start position:0% +this implies that uh the union Over N +equals 1 to Infinity of the ens + + align:start position:0% +equals 1 to Infinity of the ens + + + align:start position:0% +equals 1 to Infinity of the ens +gives me e + + align:start position:0% +gives me e + + + align:start position:0% +gives me e +okay let me highlight this + + align:start position:0% + + + + align:start position:0% + +now since these functions are increasing + + align:start position:0% +now since these functions are increasing + + + align:start position:0% +now since these functions are increasing +I should say the their point wise + + align:start position:0% +I should say the their point wise + + + align:start position:0% +I should say the their point wise +increasing not that they are increasing + + align:start position:0% +increasing not that they are increasing + + + align:start position:0% +increasing not that they are increasing +functions but they are pointwise + + align:start position:0% +functions but they are pointwise + + + align:start position:0% +functions but they are pointwise +increasing so F1 is less than or equal + + align:start position:0% +increasing so F1 is less than or equal + + + align:start position:0% +increasing so F1 is less than or equal +to f 2 is less than or equal to F3 and + + align:start position:0% +to f 2 is less than or equal to F3 and + + + align:start position:0% +to f 2 is less than or equal to F3 and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +this implies that E1 + + align:start position:0% +this implies that E1 + + + align:start position:0% +this implies that E1 +is contained in E2 is contained in E3 + + align:start position:0% +is contained in E2 is contained in E3 + + + align:start position:0% +is contained in E2 is contained in E3 +and so on right if I have some n so that + + align:start position:0% +and so on right if I have some n so that + + + align:start position:0% +and so on right if I have some n so that +X is in this set so FN of X is bigger + + align:start position:0% +X is in this set so FN of X is bigger + + + align:start position:0% +X is in this set so FN of X is bigger +than or equal to 1 minus Epsilon V of X + + align:start position:0% +than or equal to 1 minus Epsilon V of X + + + align:start position:0% +than or equal to 1 minus Epsilon V of X +then F of n plus 1 of X is bigger than + + align:start position:0% +then F of n plus 1 of X is bigger than + + + align:start position:0% +then F of n plus 1 of X is bigger than +or equal to FN of X which is bigger than + + align:start position:0% +or equal to FN of X which is bigger than + + + align:start position:0% +or equal to FN of X which is bigger than +or equal to 1 minus Epsilon Phi of X and + + align:start position:0% +or equal to 1 minus Epsilon Phi of X and + + + align:start position:0% +or equal to 1 minus Epsilon Phi of X and +therefore that X is in e n plus one okay + + align:start position:0% +therefore that X is in e n plus one okay + + + align:start position:0% +therefore that X is in e n plus one okay +so this is not only a sequence of sets + + align:start position:0% +so this is not only a sequence of sets + + + align:start position:0% +so this is not only a sequence of sets +that whose Union gives me either an + + align:start position:0% +that whose Union gives me either an + + + align:start position:0% +that whose Union gives me either an +increasing sequence of sets + + align:start position:0% +increasing sequence of sets + + + align:start position:0% +increasing sequence of sets +increasing in the sense of inclusion + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now we're going to use these two uh + + align:start position:0% +now we're going to use these two uh + + + align:start position:0% +now we're going to use these two uh +highlighted things in just a minute + + align:start position:0% +highlighted things in just a minute + + + align:start position:0% +highlighted things in just a minute +along with continuity of the bag measure + + align:start position:0% +along with continuity of the bag measure + + + align:start position:0% +along with continuity of the bag measure +to get what we want + + align:start position:0% +to get what we want + + + align:start position:0% +to get what we want +so we have + + align:start position:0% +so we have + + + align:start position:0% +so we have +um + + align:start position:0% + + + + align:start position:0% + +the integral of e + + align:start position:0% +the integral of e + + + align:start position:0% +the integral of e +f n + + align:start position:0% +f n + + + align:start position:0% +f n +this is less than or equal to the + + align:start position:0% +this is less than or equal to the + + + align:start position:0% +this is less than or equal to the +integral of FN over a smaller set so e + + align:start position:0% +integral of FN over a smaller set so e + + + align:start position:0% +integral of FN over a smaller set so e +sub n + + align:start position:0% +sub n + + + align:start position:0% +sub n +okay now on E sub n remember the E sub + + align:start position:0% +okay now on E sub n remember the E sub + + + align:start position:0% +okay now on E sub n remember the E sub +n's are defined as where FN is bigger + + align:start position:0% +n's are defined as where FN is bigger + + + align:start position:0% +n's are defined as where FN is bigger +than or equal to 1 minus Epsilon Phi of + + align:start position:0% +than or equal to 1 minus Epsilon Phi of + + + align:start position:0% +than or equal to 1 minus Epsilon Phi of +X so uh this is bigger than or equal to + + align:start position:0% +X so uh this is bigger than or equal to + + + align:start position:0% +X so uh this is bigger than or equal to +e sub n 1 minus Phi + + align:start position:0% +e sub n 1 minus Phi + + + align:start position:0% +e sub n 1 minus Phi +East sorry what am I doing minus Epsilon + + align:start position:0% +East sorry what am I doing minus Epsilon + + + align:start position:0% +East sorry what am I doing minus Epsilon +Phi + + align:start position:0% + + + + align:start position:0% + +which uh is equal to 1 minus Epsilon + + align:start position:0% +which uh is equal to 1 minus Epsilon + + + align:start position:0% +which uh is equal to 1 minus Epsilon +times the integral of e sub n + + align:start position:0% +times the integral of e sub n + + + align:start position:0% +times the integral of e sub n +over Phi and this is by definition + + align:start position:0% +over Phi and this is by definition + + + align:start position:0% +over Phi and this is by definition +equal to uh + + align:start position:0% +equal to uh + + + align:start position:0% +equal to uh +sum from J equals 1 to n now over the + + align:start position:0% +sum from J equals 1 to n now over the + + + align:start position:0% +sum from J equals 1 to n now over the +set e sub N I get integral A J measure + + align:start position:0% +set e sub N I get integral A J measure + + + align:start position:0% +set e sub N I get integral A J measure +of + + align:start position:0% +of + + + align:start position:0% +of +A J intersect + + align:start position:0% +A J intersect + + + align:start position:0% +A J intersect +he's have been and I made a small uh + + align:start position:0% +he's have been and I made a small uh + + + align:start position:0% +he's have been and I made a small uh +notation notational error + + align:start position:0% +notation notational error + + + align:start position:0% +notation notational error +let's change + + align:start position:0% + + + + align:start position:0% + +this into an m + + align:start position:0% +this into an m + + + align:start position:0% +this into an m +since we have n already denoting the + + align:start position:0% +since we have n already denoting the + + + align:start position:0% +since we have n already denoting the +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +indexing the functions we do not want + + align:start position:0% +indexing the functions we do not want + + + align:start position:0% +indexing the functions we do not want +this in right here so that should be an + + align:start position:0% +this in right here so that should be an + + + align:start position:0% +this in right here so that should be an +M it's just a fixed finite number + + align:start position:0% +M it's just a fixed finite number + + + align:start position:0% +M it's just a fixed finite number +depending on the simple function + + align:start position:0% +depending on the simple function + + + align:start position:0% +depending on the simple function +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so I have this for all in + + align:start position:0% +so I have this for all in + + + align:start position:0% +so I have this for all in +okay and therefore + + align:start position:0% + + + + align:start position:0% + +the limit as n goes to Infinity + + align:start position:0% +the limit as n goes to Infinity + + + align:start position:0% +the limit as n goes to Infinity +of the integral over e of f sub n is + + align:start position:0% +of the integral over e of f sub n is + + + align:start position:0% +of the integral over e of f sub n is +less than or equal to + + align:start position:0% +less than or equal to + + + align:start position:0% +less than or equal to +limit as n goes to Infinity of one minus + + align:start position:0% +limit as n goes to Infinity of one minus + + + align:start position:0% +limit as n goes to Infinity of one minus +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +times sum from J equals one to m + + align:start position:0% +times sum from J equals one to m + + + align:start position:0% +times sum from J equals one to m +A J measure of + + align:start position:0% + + + + align:start position:0% + +AJ + + align:start position:0% +AJ + + + align:start position:0% +AJ +e sub n + + align:start position:0% +e sub n + + + align:start position:0% +e sub n +now + + align:start position:0% +now + + + align:start position:0% +now +the E sub n's are increasing + + align:start position:0% +the E sub n's are increasing + + + align:start position:0% +the E sub n's are increasing +to e and therefore for itch for each + + align:start position:0% +to e and therefore for itch for each + + + align:start position:0% +to e and therefore for itch for each +fixed J so + + align:start position:0% +fixed J so + + + align:start position:0% +fixed J so +um in fact let's let's pause on this + + align:start position:0% +um in fact let's let's pause on this + + + align:start position:0% +um in fact let's let's pause on this +real quick and + + align:start position:0% + + + + align:start position:0% + +come back to this this thing we're going + + align:start position:0% +come back to this this thing we're going + + + align:start position:0% +come back to this this thing we're going +to eventually take the limit as n goes + + align:start position:0% +to eventually take the limit as n goes + + + align:start position:0% +to eventually take the limit as n goes +to Infinity of this quantity so let's + + align:start position:0% +to Infinity of this quantity so let's + + + align:start position:0% +to Infinity of this quantity so let's +look at what this does as n goes to + + align:start position:0% +look at what this does as n goes to + + + align:start position:0% +look at what this does as n goes to +Infinity uh + + align:start position:0% +Infinity uh + + + align:start position:0% +Infinity uh +since by those two things that I + + align:start position:0% +since by those two things that I + + + align:start position:0% +since by those two things that I +highlighted that eons are increasing C + + align:start position:0% +highlighted that eons are increasing C + + + align:start position:0% +highlighted that eons are increasing C +increasing subsets of e whose Union + + align:start position:0% +increasing subsets of e whose Union + + + align:start position:0% +increasing subsets of e whose Union +gives me E I get since + + align:start position:0% +gives me E I get since + + + align:start position:0% +gives me E I get since +E1 AJ so + + align:start position:0% +E1 AJ so + + + align:start position:0% +E1 AJ so +it's a subset of E2 + + align:start position:0% +it's a subset of E2 + + + align:start position:0% +it's a subset of E2 +8 J + + align:start position:0% +8 J + + + align:start position:0% +8 J +subset of e3 and so on + + align:start position:0% +subset of e3 and so on + + + align:start position:0% +subset of e3 and so on +and the Union + + align:start position:0% +and the Union + + + align:start position:0% +and the Union +n equals 1 to Infinity + + align:start position:0% +n equals 1 to Infinity + + + align:start position:0% +n equals 1 to Infinity +of e sub n intersect A J equals + + align:start position:0% +of e sub n intersect A J equals + + + align:start position:0% +of e sub n intersect A J equals +AJ + + align:start position:0% + + + + align:start position:0% + +because then this is just going to be + + align:start position:0% +because then this is just going to be + + + align:start position:0% +because then this is just going to be +equal to the union of the E sub n's + + align:start position:0% +equal to the union of the E sub n's + + + align:start position:0% +equal to the union of the E sub n's +intersect AJ that just gives me e + + align:start position:0% +intersect AJ that just gives me e + + + align:start position:0% +intersect AJ that just gives me e +intersect A J which is just AJ we get by + + align:start position:0% +intersect A J which is just AJ we get by + + + align:start position:0% +intersect A J which is just AJ we get by +the continuity of a lebeg measure + + align:start position:0% +the continuity of a lebeg measure + + + align:start position:0% +the continuity of a lebeg measure +and flies for all J and at the limit + + align:start position:0% +and flies for all J and at the limit + + + align:start position:0% +and flies for all J and at the limit +as n goes to Infinity of + + align:start position:0% +as n goes to Infinity of + + + align:start position:0% +as n goes to Infinity of +the measure of + + align:start position:0% +the measure of + + + align:start position:0% +the measure of +A J intersect e n is equal to the + + align:start position:0% +A J intersect e n is equal to the + + + align:start position:0% +A J intersect e n is equal to the +measure + + align:start position:0% +measure + + + align:start position:0% +measure +of + + align:start position:0% + + + + align:start position:0% + +A J which as we just said this uh + + align:start position:0% + + + + align:start position:0% + +n intersect AJ which remember this set + + align:start position:0% +n intersect AJ which remember this set + + + align:start position:0% +n intersect AJ which remember this set +is equal to AJ so this is measure of AJ + + align:start position:0% +is equal to AJ so this is measure of AJ + + + align:start position:0% +is equal to AJ so this is measure of AJ +okay so from the two Yellow Boxes we had + + align:start position:0% +okay so from the two Yellow Boxes we had + + + align:start position:0% +okay so from the two Yellow Boxes we had +before + + align:start position:0% +before + + + align:start position:0% +before +we get + + align:start position:0% +we get + + + align:start position:0% +we get +this useful one for all J we have the + + align:start position:0% +this useful one for all J we have the + + + align:start position:0% +this useful one for all J we have the +limit as n goes to Infinity of the + + align:start position:0% +limit as n goes to Infinity of the + + + align:start position:0% +limit as n goes to Infinity of the +measure of AJ intersect e n is equal to + + align:start position:0% +measure of AJ intersect e n is equal to + + + align:start position:0% +measure of AJ intersect e n is equal to +the measure of AJ Okay so now we'll + + align:start position:0% +the measure of AJ Okay so now we'll + + + align:start position:0% +the measure of AJ Okay so now we'll +stick this + + align:start position:0% +stick this + + + align:start position:0% +stick this +uh into this inequality after we take + + align:start position:0% +uh into this inequality after we take + + + align:start position:0% +uh into this inequality after we take +the limit + + align:start position:0% +the limit + + + align:start position:0% +the limit +so I got ahead of myself a minute ago + + align:start position:0% +so I got ahead of myself a minute ago + + + align:start position:0% +so I got ahead of myself a minute ago +thus limit as n goes to Infinity of the + + align:start position:0% +thus limit as n goes to Infinity of the + + + align:start position:0% +thus limit as n goes to Infinity of the +in of the integral over e of f in this + + align:start position:0% +in of the integral over e of f in this + + + align:start position:0% +in of the integral over e of f in this +is bigger than or equal to uh + + align:start position:0% + + + + align:start position:0% + +limit as n goes to Infinity + + align:start position:0% +limit as n goes to Infinity + + + align:start position:0% +limit as n goes to Infinity +1 minus Epsilon + + align:start position:0% + + + + align:start position:0% + +M now + + align:start position:0% +M now + + + align:start position:0% +M now +AJ measure of + + align:start position:0% +AJ measure of + + + align:start position:0% +AJ measure of +AJ intersect e in + + align:start position:0% +AJ intersect e in + + + align:start position:0% +AJ intersect e in +now these numbers here all converge to + + align:start position:0% +now these numbers here all converge to + + + align:start position:0% +now these numbers here all converge to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +each of these numbers here for each J + + align:start position:0% +each of these numbers here for each J + + + align:start position:0% +each of these numbers here for each J +converges as n goes to Infinity to the + + align:start position:0% +converges as n goes to Infinity to the + + + align:start position:0% +converges as n goes to Infinity to the +measure of a sub J + + align:start position:0% +measure of a sub J + + + align:start position:0% +measure of a sub J +so + + align:start position:0% +so + + + align:start position:0% +so +the limit is in equal to 1 minus Epsilon + + align:start position:0% +the limit is in equal to 1 minus Epsilon + + + align:start position:0% +the limit is in equal to 1 minus Epsilon +times the integral of J equals one to M + + align:start position:0% +times the integral of J equals one to M + + + align:start position:0% +times the integral of J equals one to M +times + + align:start position:0% +times + + + align:start position:0% +times +um + + align:start position:0% + + + + align:start position:0% + +am I writing the integral for AJ measure + + align:start position:0% +am I writing the integral for AJ measure + + + align:start position:0% +am I writing the integral for AJ measure +of + + align:start position:0% +of + + + align:start position:0% +of +a j and this is just equal to + + align:start position:0% +a j and this is just equal to + + + align:start position:0% +a j and this is just equal to +1 minus integral by definition + + align:start position:0% +1 minus integral by definition + + + align:start position:0% +1 minus integral by definition +integral of Phi + + align:start position:0% +integral of Phi + + + align:start position:0% +integral of Phi +okay so I've shown uh + + align:start position:0% +okay so I've shown uh + + + align:start position:0% +okay so I've shown uh +that for all Epsilon between 0 and 1 + + align:start position:0% +that for all Epsilon between 0 and 1 + + + align:start position:0% +that for all Epsilon between 0 and 1 +this + + align:start position:0% + + + + align:start position:0% + +1 minus Epsilon times the integral of p + + align:start position:0% +1 minus Epsilon times the integral of p + + + align:start position:0% +1 minus Epsilon times the integral of p +is less than or equal to + + align:start position:0% + + + + align:start position:0% + +this number over here which may be + + align:start position:0% +this number over here which may be + + + align:start position:0% +this number over here which may be +infinite maybe finite + + align:start position:0% +infinite maybe finite + + + align:start position:0% +infinite maybe finite +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and since this hold for all Epsilon I + + align:start position:0% +and since this hold for all Epsilon I + + + align:start position:0% +and since this hold for all Epsilon I +can send Epsilon to zero + + align:start position:0% + + + + align:start position:0% + +so I have this inequality between now + + align:start position:0% +so I have this inequality between now + + + align:start position:0% +so I have this inequality between now +fixed things along with an Epsilon here + + align:start position:0% +fixed things along with an Epsilon here + + + align:start position:0% +fixed things along with an Epsilon here +so I can send Epsilon to zero and I get + + align:start position:0% +so I can send Epsilon to zero and I get + + + align:start position:0% +so I can send Epsilon to zero and I get +the integral of Phi is less than or + + align:start position:0% +the integral of Phi is less than or + + + align:start position:0% +the integral of Phi is less than or +equal to the Limit + + align:start position:0% +equal to the Limit + + + align:start position:0% +equal to the Limit +as n goes to Infinity of + + align:start position:0% + + + + align:start position:0% + +and since Phi is an arbitrary simple + + align:start position:0% +and since Phi is an arbitrary simple + + + align:start position:0% +and since Phi is an arbitrary simple +function that's less than or equal to F + + align:start position:0% +function that's less than or equal to F + + + align:start position:0% +function that's less than or equal to F +the soup over all of these which is by + + align:start position:0% +the soup over all of these which is by + + + align:start position:0% +the soup over all of these which is by +definition the integral of f + + align:start position:0% +definition the integral of f + + + align:start position:0% +definition the integral of f +is less than or equal to + + align:start position:0% + + + + align:start position:0% + +the integral of the limit of the + + align:start position:0% +the integral of the limit of the + + + align:start position:0% +the integral of the limit of the +integrals + + align:start position:0% +integrals + + + align:start position:0% +integrals +okay + + align:start position:0% +okay + + + align:start position:0% +okay +foreign + + align:start position:0% + + + + align:start position:0% + +that's the end of the proof + + align:start position:0% + + + + align:start position:0% + +so monotone convergence theorem + + align:start position:0% +so monotone convergence theorem + + + align:start position:0% +so monotone convergence theorem +very + + align:start position:0% +very + + + align:start position:0% +very +um + + align:start position:0% + + + + align:start position:0% + +useful theorem important theorem + + align:start position:0% +useful theorem important theorem + + + align:start position:0% +useful theorem important theorem +throughout all of this + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +uh okay so let's uh + + align:start position:0% +uh okay so let's uh + + + align:start position:0% +uh okay so let's uh +let's + + align:start position:0% +let's + + + align:start position:0% +let's +get a few applications from this just + + align:start position:0% +get a few applications from this just + + + align:start position:0% +get a few applications from this just +from + + align:start position:0% +from + + + align:start position:0% +from +so this first one you know is kind of a + + align:start position:0% +so this first one you know is kind of a + + + align:start position:0% +so this first one you know is kind of a +way how would you evaluate now this + + align:start position:0% +way how would you evaluate now this + + + align:start position:0% +way how would you evaluate now this +integral remember the integral which I + + align:start position:0% +integral remember the integral which I + + + align:start position:0% +integral remember the integral which I +just erased is defined as a soup over + + align:start position:0% +just erased is defined as a soup over + + + align:start position:0% +just erased is defined as a soup over +all integrals of simple functions right + + align:start position:0% +all integrals of simple functions right + + + align:start position:0% +all integrals of simple functions right +so in order to actually compute the + + align:start position:0% +so in order to actually compute the + + + align:start position:0% +so in order to actually compute the +integral of a non-negative measurable + + align:start position:0% +integral of a non-negative measurable + + + align:start position:0% +integral of a non-negative measurable +function I would have to take I would + + align:start position:0% +function I would have to take I would + + + align:start position:0% +function I would have to take I would +have to find out the integral of every + + align:start position:0% +have to find out the integral of every + + + align:start position:0% +have to find out the integral of every +simple function less than or equal to it + + align:start position:0% +simple function less than or equal to it + + + align:start position:0% +simple function less than or equal to it +and take the soup over that whole set + + align:start position:0% +and take the soup over that whole set + + + align:start position:0% +and take the soup over that whole set +which is kind of a useless uh + + align:start position:0% +which is kind of a useless uh + + + align:start position:0% +which is kind of a useless uh +or impossible way of of computing the + + align:start position:0% +or impossible way of of computing the + + + align:start position:0% +or impossible way of of computing the +integral it's as if you know + + align:start position:0% +integral it's as if you know + + + align:start position:0% +integral it's as if you know +it's similar to when you know you come + + align:start position:0% +it's similar to when you know you come + + + align:start position:0% +it's similar to when you know you come +across Riemann integration and the + + align:start position:0% +across Riemann integration and the + + + align:start position:0% +across Riemann integration and the +Riemann integral is defined as + + align:start position:0% +Riemann integral is defined as + + + align:start position:0% +Riemann integral is defined as +uh you know the limit of Riemann sums + + align:start position:0% +uh you know the limit of Riemann sums + + + align:start position:0% +uh you know the limit of Riemann sums +you know nobody it's you can compute + + align:start position:0% +you know nobody it's you can compute + + + align:start position:0% +you know nobody it's you can compute +maybe three integrals just from Riemann + + align:start position:0% +maybe three integrals just from Riemann + + + align:start position:0% +maybe three integrals just from Riemann +sum so + + align:start position:0% +sum so + + + align:start position:0% +sum so +uh we need a more efficient way of being + + align:start position:0% +uh we need a more efficient way of being + + + align:start position:0% +uh we need a more efficient way of being +able to compute the lebag integral in + + align:start position:0% +able to compute the lebag integral in + + + align:start position:0% +able to compute the lebag integral in +the monotone convergence theorem gives + + align:start position:0% +the monotone convergence theorem gives + + + align:start position:0% +the monotone convergence theorem gives +us that + + align:start position:0% +us that + + + align:start position:0% +us that +kind of for free so uh + + align:start position:0% +kind of for free so uh + + + align:start position:0% +kind of for free so uh +we have the following if f is + + align:start position:0% + + + + align:start position:0% + +a non-negative measurable function + + align:start position:0% + + + + align:start position:0% + +and VN is a sequence + + align:start position:0% + + + + align:start position:0% + +of simple functions + + align:start position:0% + + + + align:start position:0% + +which are all non-negative + + align:start position:0% + + + + align:start position:0% + +and point wise increasing + + align:start position:0% + + + + align:start position:0% + +and converging Point wise to f + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the integral + + align:start position:0% +the integral + + + align:start position:0% +the integral +over e + + align:start position:0% +over e + + + align:start position:0% +over e +of f is equal to + + align:start position:0% +of f is equal to + + + align:start position:0% +of f is equal to +the limit as n goes to Infinity of + + align:start position:0% +the limit as n goes to Infinity of + + + align:start position:0% +the limit as n goes to Infinity of +the interval of the simple functions + + align:start position:0% +the interval of the simple functions + + + align:start position:0% +the interval of the simple functions +okay so you know back when we discussed + + align:start position:0% +okay so you know back when we discussed + + + align:start position:0% +okay so you know back when we discussed +measurable functions we actually + + align:start position:0% +measurable functions we actually + + + align:start position:0% +measurable functions we actually +constructed such a sequence of simple + + align:start position:0% +constructed such a sequence of simple + + + align:start position:0% +constructed such a sequence of simple +functions that satisfies the hypotheses + + align:start position:0% +functions that satisfies the hypotheses + + + align:start position:0% +functions that satisfies the hypotheses +of this theorem so this is not a vacuous + + align:start position:0% +of this theorem so this is not a vacuous + + + align:start position:0% +of this theorem so this is not a vacuous +theorem but this theorem tells you that + + align:start position:0% +theorem but this theorem tells you that + + + align:start position:0% +theorem but this theorem tells you that +if you want to compute the integral of f + + align:start position:0% +if you want to compute the integral of f + + + align:start position:0% +if you want to compute the integral of f +just take any sequence of simple + + align:start position:0% +just take any sequence of simple + + + align:start position:0% +just take any sequence of simple +functions increasing up to F and compute + + align:start position:0% +functions increasing up to F and compute + + + align:start position:0% +functions increasing up to F and compute +the limit of the intervals and that will + + align:start position:0% +the limit of the intervals and that will + + + align:start position:0% +the limit of the intervals and that will +give you the the integral of f + + align:start position:0% +give you the the integral of f + + + align:start position:0% +give you the the integral of f +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now they're just this just follows + + align:start position:0% +now they're just this just follows + + + align:start position:0% +now they're just this just follows +immediately from the monotone + + align:start position:0% +immediately from the monotone + + + align:start position:0% +immediately from the monotone +convergence serum I have the taking FNS + + align:start position:0% +convergence serum I have the taking FNS + + + align:start position:0% +convergence serum I have the taking FNS +equal to the fee ends okay so there's no + + align:start position:0% +equal to the fee ends okay so there's no + + + align:start position:0% +equal to the fee ends okay so there's no +there's no proof to go with that + + align:start position:0% + + + + align:start position:0% + +the next theorem is uh linearity of the + + align:start position:0% +the next theorem is uh linearity of the + + + align:start position:0% +the next theorem is uh linearity of the +integral so + + align:start position:0% +integral so + + + align:start position:0% +integral so +if f and g are + + align:start position:0% +if f and g are + + + align:start position:0% +if f and g are +two non-negative measurable functions + + align:start position:0% +two non-negative measurable functions + + + align:start position:0% +two non-negative measurable functions +then + + align:start position:0% +then + + + align:start position:0% +then +the integral of f plus G + + align:start position:0% +the integral of f plus G + + + align:start position:0% +the integral of f plus G +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +um + + align:start position:0% +um + + + align:start position:0% +um +the integral of f + + align:start position:0% +the integral of f + + + align:start position:0% +the integral of f +plus the integral of G + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now note there's no ambiguity with how + + align:start position:0% +now note there's no ambiguity with how + + + align:start position:0% +now note there's no ambiguity with how +to define so we kind of had a you know + + align:start position:0% +to define so we kind of had a you know + + + align:start position:0% +to define so we kind of had a you know +there's some touchy business about + + align:start position:0% +there's some touchy business about + + + align:start position:0% +there's some touchy business about +um adding and subtracting two extended + + align:start position:0% +um adding and subtracting two extended + + + align:start position:0% +um adding and subtracting two extended +real valued measurable functions but + + align:start position:0% +real valued measurable functions but + + + align:start position:0% +real valued measurable functions but +there's none of that here since these + + align:start position:0% +there's none of that here since these + + + align:start position:0% +there's none of that here since these +are both non-negative measurable + + align:start position:0% +are both non-negative measurable + + + align:start position:0% +are both non-negative measurable +extended real valued functions so this + + align:start position:0% +extended real valued functions so this + + + align:start position:0% +extended real valued functions so this +will always only be able to form + + align:start position:0% +will always only be able to form + + + align:start position:0% +will always only be able to form +infinity plus infinity which we Define + + align:start position:0% +infinity plus infinity which we Define + + + align:start position:0% +infinity plus infinity which we Define +to be Infinity so just let me make that + + align:start position:0% +to be Infinity so just let me make that + + + align:start position:0% +to be Infinity so just let me make that +small note + + align:start position:0% +small note + + + align:start position:0% +small note +so the integral is linear + + align:start position:0% +so the integral is linear + + + align:start position:0% +so the integral is linear +so what's the proof + + align:start position:0% + + + + align:start position:0% + +let fee in + + align:start position:0% + + + + align:start position:0% + +and sign in + + align:start position:0% +and sign in + + + align:start position:0% +and sign in +be + + align:start position:0% + + + + align:start position:0% + +two sequences of + + align:start position:0% +two sequences of + + + align:start position:0% +two sequences of +simple functions + + align:start position:0% + + + + align:start position:0% + +such that they're increasing to f and g + + align:start position:0% +such that they're increasing to f and g + + + align:start position:0% +such that they're increasing to f and g +respectively so + + align:start position:0% +respectively so + + + align:start position:0% +respectively so +0 is less than or equal to + + align:start position:0% +0 is less than or equal to + + + align:start position:0% +0 is less than or equal to +B1 is less than or equal to feed two and + + align:start position:0% +B1 is less than or equal to feed two and + + + align:start position:0% +B1 is less than or equal to feed two and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +and BN converges to f + + align:start position:0% +and BN converges to f + + + align:start position:0% +and BN converges to f +Point wise + + align:start position:0% +Point wise + + + align:start position:0% +Point wise +on E + + align:start position:0% +on E + + + align:start position:0% +on E +okay so I should have you know + + align:start position:0% +okay so I should have you know + + + align:start position:0% +okay so I should have you know +everything's happening on this set e + + align:start position:0% +everything's happening on this set e + + + align:start position:0% +everything's happening on this set e +and the same for the size + + align:start position:0% + + + + align:start position:0% + +and PSI n converging to G + + align:start position:0% + + + + align:start position:0% + +pointwise + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +uh if I take the sum of these two simple + + align:start position:0% +uh if I take the sum of these two simple + + + align:start position:0% +uh if I take the sum of these two simple +functions or sequences of simple + + align:start position:0% +functions or sequences of simple + + + align:start position:0% +functions or sequences of simple +functions I get an increasing + + align:start position:0% + + + + align:start position:0% + +sequence of simple functions + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +uh p n plus PSI n converges to f plus G + + align:start position:0% +uh p n plus PSI n converges to f plus G + + + align:start position:0% +uh p n plus PSI n converges to f plus G +pointwise + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and by this theorem that followed + + align:start position:0% +and by this theorem that followed + + + align:start position:0% +and by this theorem that followed +immediately from the monotone + + align:start position:0% +immediately from the monotone + + + align:start position:0% +immediately from the monotone +convergence theorem + + align:start position:0% + + + + align:start position:0% + +uh I get that the integral + + align:start position:0% +uh I get that the integral + + + align:start position:0% +uh I get that the integral +of f plus G + + align:start position:0% +of f plus G + + + align:start position:0% +of f plus G +uh over e this is equal to the Limit + + align:start position:0% +uh over e this is equal to the Limit + + + align:start position:0% +uh over e this is equal to the Limit +as n goes to Infinity of the integral of + + align:start position:0% +as n goes to Infinity of the integral of + + + align:start position:0% +as n goes to Infinity of the integral of +e of Phi n plus PSI n and now we've + + align:start position:0% +e of Phi n plus PSI n and now we've + + + align:start position:0% +e of Phi n plus PSI n and now we've +proved linearity of the integral for + + align:start position:0% +proved linearity of the integral for + + + align:start position:0% +proved linearity of the integral for +simple functions + + align:start position:0% +simple functions + + + align:start position:0% +simple functions +okay so this is equal to + + align:start position:0% +okay so this is equal to + + + align:start position:0% +okay so this is equal to +the limit as n goes to Infinity of the + + align:start position:0% +the limit as n goes to Infinity of the + + + align:start position:0% +the limit as n goes to Infinity of the +integral of e of B in plus the integral + + align:start position:0% +integral of e of B in plus the integral + + + align:start position:0% +integral of e of B in plus the integral +of e of PSI n + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +Again by the theorem that I just stated + + align:start position:0% +Again by the theorem that I just stated + + + align:start position:0% +Again by the theorem that I just stated +a minute ago the monotone by the + + align:start position:0% +a minute ago the monotone by the + + + align:start position:0% +a minute ago the monotone by the +monotone convergence theorem this + + align:start position:0% +monotone convergence theorem this + + + align:start position:0% +monotone convergence theorem this +converges to the integral of F this + + align:start position:0% +converges to the integral of F this + + + align:start position:0% +converges to the integral of F this +converges to the integral of G so the + + align:start position:0% +converges to the integral of G so the + + + align:start position:0% +converges to the integral of G so the +limit of the sum is the sum of the + + align:start position:0% +limit of the sum is the sum of the + + + align:start position:0% +limit of the sum is the sum of the +limits and I get + + align:start position:0% + + + + align:start position:0% + +G + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um you know using the same kind of + + align:start position:0% +um you know using the same kind of + + + align:start position:0% +um you know using the same kind of +argument if you like except now not for + + align:start position:0% +argument if you like except now not for + + + align:start position:0% +argument if you like except now not for +you know two functions but for one + + align:start position:0% +you know two functions but for one + + + align:start position:0% +you know two functions but for one +function uh you can show that the + + align:start position:0% +function uh you can show that the + + + align:start position:0% +function uh you can show that the +integral of a function + + align:start position:0% +integral of a function + + + align:start position:0% +integral of a function +um + + align:start position:0% +um + + + align:start position:0% +um +over a union of two disjoint sets is the + + align:start position:0% +over a union of two disjoint sets is the + + + align:start position:0% +over a union of two disjoint sets is the +sum of the integrals this is something + + align:start position:0% +sum of the integrals this is something + + + align:start position:0% +sum of the integrals this is something +that I uh pointed to but didn't prove + + align:start position:0% +that I uh pointed to but didn't prove + + + align:start position:0% +that I uh pointed to but didn't prove +and at the very beginning of this + + align:start position:0% +and at the very beginning of this + + + align:start position:0% +and at the very beginning of this +lecture but uh you know using that that + + align:start position:0% +lecture but uh you know using that that + + + align:start position:0% +lecture but uh you know using that that +is true for simple functions and this + + align:start position:0% +is true for simple functions and this + + + align:start position:0% +is true for simple functions and this +argument using the monotone convergence + + align:start position:0% +argument using the monotone convergence + + + align:start position:0% +argument using the monotone convergence +theorem which didn't require you know + + align:start position:0% +theorem which didn't require you know + + + align:start position:0% +theorem which didn't require you know +what I approved earlier so this is not a + + align:start position:0% +what I approved earlier so this is not a + + + align:start position:0% +what I approved earlier so this is not a +circular argument + + align:start position:0% +circular argument + + + align:start position:0% +circular argument +um + + align:start position:0% +um + + + align:start position:0% +um +you can prove that the integral of a + + align:start position:0% +you can prove that the integral of a + + + align:start position:0% +you can prove that the integral of a +non-negative measurable function over a + + align:start position:0% +non-negative measurable function over a + + + align:start position:0% +non-negative measurable function over a +union of two disjoint sets is the sum of + + align:start position:0% +union of two disjoint sets is the sum of + + + align:start position:0% +union of two disjoint sets is the sum of +the integrals one over the first set one + + align:start position:0% +the integrals one over the first set one + + + align:start position:0% +the integrals one over the first set one +over the second set + + align:start position:0% +over the second set + + + align:start position:0% +over the second set +okay + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% + + + + align:start position:0% + +that's cool this integral is + + align:start position:0% +that's cool this integral is + + + align:start position:0% +that's cool this integral is +linear over so + + align:start position:0% +linear over so + + + align:start position:0% +linear over so +the integral of uh sum of two measurable + + align:start position:0% +the integral of uh sum of two measurable + + + align:start position:0% +the integral of uh sum of two measurable +functions is the sum of the integrals + + align:start position:0% +functions is the sum of the integrals + + + align:start position:0% +functions is the sum of the integrals +what's even better is that the integral + + align:start position:0% +what's even better is that the integral + + + align:start position:0% +what's even better is that the integral +over an infinite sum is equal to the + + align:start position:0% +over an infinite sum is equal to the + + + align:start position:0% +over an infinite sum is equal to the +infinite sum of the integrals + + align:start position:0% +infinite sum of the integrals + + + align:start position:0% +infinite sum of the integrals +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +actually let me State uh + + align:start position:0% +actually let me State uh + + + align:start position:0% +actually let me State uh +or let's just do this + + align:start position:0% +or let's just do this + + + align:start position:0% +or let's just do this +um + + align:start position:0% + + + + align:start position:0% + +FN is + + align:start position:0% + + + + align:start position:0% + +a sequence + + align:start position:0% +a sequence + + + align:start position:0% +a sequence +and of non-negative measurable functions + + align:start position:0% + + + + align:start position:0% + +then the integral + + align:start position:0% +then the integral + + + align:start position:0% +then the integral +of the sum of e is equal to uh + + align:start position:0% + + + + align:start position:0% + +the infinite sum of the integrals + + align:start position:0% + + + + align:start position:0% + +now first off this is a well-defined + + align:start position:0% +now first off this is a well-defined + + + align:start position:0% +now first off this is a well-defined +function because it's a sum of + + align:start position:0% +function because it's a sum of + + + align:start position:0% +function because it's a sum of +non-negative so Point wise for each X + + align:start position:0% +non-negative so Point wise for each X + + + align:start position:0% +non-negative so Point wise for each X +this is a sum of non-negative real + + align:start position:0% +this is a sum of non-negative real + + + align:start position:0% +this is a sum of non-negative real +numbers so that's either going to be a + + align:start position:0% +numbers so that's either going to be a + + + align:start position:0% +numbers so that's either going to be a +finite number if this series converges + + align:start position:0% +finite number if this series converges + + + align:start position:0% +finite number if this series converges +or it's going to be infinite all right + + align:start position:0% +or it's going to be infinite all right + + + align:start position:0% +or it's going to be infinite all right +remember we're allowing uh you know + + align:start position:0% +remember we're allowing uh you know + + + align:start position:0% +remember we're allowing uh you know +extended real valued non-negative + + align:start position:0% +extended real valued non-negative + + + align:start position:0% +extended real valued non-negative +measurable functions in our in our + + align:start position:0% +measurable functions in our in our + + + align:start position:0% +measurable functions in our in our +framework for now so this is Meaningful + + align:start position:0% +framework for now so this is Meaningful + + + align:start position:0% +framework for now so this is Meaningful +and it's a measurable function by you + + align:start position:0% +and it's a measurable function by you + + + align:start position:0% +and it's a measurable function by you +know stuff we proved in in the section + + align:start position:0% +know stuff we proved in in the section + + + align:start position:0% +know stuff we proved in in the section +on measurable functions + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +the proof is pretty short + + align:start position:0% +the proof is pretty short + + + align:start position:0% +the proof is pretty short +um + + align:start position:0% + + + + align:start position:0% + +by an induction argument + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +the previous theorem for + + align:start position:0% +the previous theorem for + + + align:start position:0% +the previous theorem for +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the sum of two functions + + align:start position:0% + + + + align:start position:0% + +we have the statement that + + align:start position:0% +we have the statement that + + + align:start position:0% +we have the statement that +for every fixed natural number capital N + + align:start position:0% +for every fixed natural number capital N + + + align:start position:0% +for every fixed natural number capital N +the integral of + + align:start position:0% +the integral of + + + align:start position:0% +the integral of +sum n equals 1 to capital n f n + + align:start position:0% +sum n equals 1 to capital n f n + + + align:start position:0% +sum n equals 1 to capital n f n +e is equal to + + align:start position:0% + + + + align:start position:0% + +the finite sum of the integrals + + align:start position:0% + + + + align:start position:0% + +so if you can do something for + + align:start position:0% +so if you can do something for + + + align:start position:0% +so if you can do something for +two usually you can do something for n + + align:start position:0% +two usually you can do something for n + + + align:start position:0% +two usually you can do something for n +by an induction argument right so I'll + + align:start position:0% +by an induction argument right so I'll + + + align:start position:0% +by an induction argument right so I'll +leave the these details of this to you + + align:start position:0% +leave the these details of this to you + + + align:start position:0% +leave the these details of this to you +or you can just believe it based on how + + align:start position:0% +or you can just believe it based on how + + + align:start position:0% +or you can just believe it based on how +many induction arguments you've done in + + align:start position:0% +many induction arguments you've done in + + + align:start position:0% +many induction arguments you've done in +your life + + align:start position:0% +your life + + + align:start position:0% +your life +um + + align:start position:0% +um + + + align:start position:0% +um +so we have this + + align:start position:0% +so we have this + + + align:start position:0% +so we have this +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +n equals one one FN is less than or + + align:start position:0% +n equals one one FN is less than or + + + align:start position:0% +n equals one one FN is less than or +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +sum from n equals one to two of FN is + + align:start position:0% +sum from n equals one to two of FN is + + + align:start position:0% +sum from n equals one to two of FN is +less than or equal to some from equals + + align:start position:0% +less than or equal to some from equals + + + align:start position:0% +less than or equal to some from equals +one to three F in because these are all + + align:start position:0% +one to three F in because these are all + + + align:start position:0% +one to three F in because these are all +all non-negative functions so adding + + align:start position:0% +all non-negative functions so adding + + + align:start position:0% +all non-negative functions so adding +non-negative functions to something only + + align:start position:0% +non-negative functions to something only + + + align:start position:0% +non-negative functions to something only +increasing increases it + + align:start position:0% +increasing increases it + + + align:start position:0% +increasing increases it +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% + + + + align:start position:0% + +sum from n equals one to n + + align:start position:0% +sum from n equals one to n + + + align:start position:0% +sum from n equals one to n +converges to + + align:start position:0% + + + + align:start position:0% + +Point wise + + align:start position:0% +Point wise + + + align:start position:0% +Point wise +simply by you know defining this to be + + align:start position:0% +simply by you know defining this to be + + + align:start position:0% +simply by you know defining this to be +the limit as capital N goes to Infinity + + align:start position:0% +the limit as capital N goes to Infinity + + + align:start position:0% +the limit as capital N goes to Infinity +of FN of X Point wise + + align:start position:0% +of FN of X Point wise + + + align:start position:0% +of FN of X Point wise +um + + align:start position:0% + + + + align:start position:0% + +all right since I have these two things + + align:start position:0% +all right since I have these two things + + + align:start position:0% +all right since I have these two things +then by + + align:start position:0% +then by + + + align:start position:0% +then by +monotone convergence theorem I get that + + align:start position:0% +monotone convergence theorem I get that + + + align:start position:0% +monotone convergence theorem I get that +the integral of n equals 1 to Infinity + + align:start position:0% +the integral of n equals 1 to Infinity + + + align:start position:0% +the integral of n equals 1 to Infinity +of f n of e this is equal to + + align:start position:0% +of f n of e this is equal to + + + align:start position:0% +of f n of e this is equal to +the limit as + + align:start position:0% +the limit as + + + align:start position:0% +the limit as +capital N goes to Infinity of + + align:start position:0% +capital N goes to Infinity of + + + align:start position:0% +capital N goes to Infinity of +the integral of e sum from n equals 1 to + + align:start position:0% +the integral of e sum from n equals 1 to + + + align:start position:0% +the integral of e sum from n equals 1 to +capital n + + align:start position:0% + + + + align:start position:0% + +which + + align:start position:0% +which + + + align:start position:0% +which +by what we have right here + + align:start position:0% +by what we have right here + + + align:start position:0% +by what we have right here +is equal to the Limit as + + align:start position:0% +is equal to the Limit as + + + align:start position:0% +is equal to the Limit as +capital N goes to Infinity of now the + + align:start position:0% +capital N goes to Infinity of now the + + + align:start position:0% +capital N goes to Infinity of now the +finite sum + + align:start position:0% +finite sum + + + align:start position:0% +finite sum +comes out + + align:start position:0% + + + + align:start position:0% + +and this is by definition + + align:start position:0% + + + + align:start position:0% + +this infinite sum + + align:start position:0% + + + + align:start position:0% + +okay so for uh + + align:start position:0% + + + + align:start position:0% + +non-negative measurable functions + + align:start position:0% + + + + align:start position:0% + +the integral of the sum is equal to the + + align:start position:0% +the integral of the sum is equal to the + + + align:start position:0% +the integral of the sum is equal to the +sum of the integrals even for a infinite + + align:start position:0% +sum of the integrals even for a infinite + + + align:start position:0% +sum of the integrals even for a infinite +sum + + align:start position:0% +sum + + + align:start position:0% +sum +okay + + align:start position:0% + + + + align:start position:0% + +so again + + align:start position:0% +so again + + + align:start position:0% +so again +um you know this is simply false for if + + align:start position:0% +um you know this is simply false for if + + + align:start position:0% +um you know this is simply false for if +I replace everything by Riemann + + align:start position:0% +I replace everything by Riemann + + + align:start position:0% +I replace everything by Riemann +integration because in fact I can come + + align:start position:0% +integration because in fact I can come + + + align:start position:0% +integration because in fact I can come +up with a sequence of functions FN whose + + align:start position:0% +up with a sequence of functions FN whose + + + align:start position:0% +up with a sequence of functions FN whose +Riemann integral is always zero but the + + align:start position:0% +Riemann integral is always zero but the + + + align:start position:0% +Riemann integral is always zero but the +sum is not Riemann integrable think of + + align:start position:0% +sum is not Riemann integrable think of + + + align:start position:0% +sum is not Riemann integrable think of +you know taking F in to be the function + + align:start position:0% +you know taking F in to be the function + + + align:start position:0% +you know taking F in to be the function +which is 0 off of uh you know a rational + + align:start position:0% +which is 0 off of uh you know a rational + + + align:start position:0% +which is 0 off of uh you know a rational +number + + align:start position:0% +number + + + align:start position:0% +number +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and then so first enumerate the + + align:start position:0% +and then so first enumerate the + + + align:start position:0% +and then so first enumerate the +rationals q1 Q2 Q3 Q4 and so on + + align:start position:0% +rationals q1 Q2 Q3 Q4 and so on + + + align:start position:0% +rationals q1 Q2 Q3 Q4 and so on +and take FN to be the function that is 0 + + align:start position:0% +and take FN to be the function that is 0 + + + align:start position:0% +and take FN to be the function that is 0 +when X is not equal to qn and one when X + + align:start position:0% +when X is not equal to qn and one when X + + + align:start position:0% +when X is not equal to qn and one when X +is equal to q n then the infinite sum is + + align:start position:0% +is equal to q n then the infinite sum is + + + align:start position:0% +is equal to q n then the infinite sum is +just going to be the indicator function + + align:start position:0% +just going to be the indicator function + + + align:start position:0% +just going to be the indicator function +of the rational say in 0 1. uh that's + + align:start position:0% +of the rational say in 0 1. uh that's + + + align:start position:0% +of the rational say in 0 1. uh that's +not Riemann integrable but the sum of + + align:start position:0% +not Riemann integrable but the sum of + + + align:start position:0% +not Riemann integrable but the sum of +these integrals is just zero okay so + + align:start position:0% +these integrals is just zero okay so + + + align:start position:0% +these integrals is just zero okay so +this is not true for Riemann integrals + + align:start position:0% +this is not true for Riemann integrals + + + align:start position:0% +this is not true for Riemann integrals +again so we're doing something much more + + align:start position:0% +again so we're doing something much more + + + align:start position:0% +again so we're doing something much more +powerful here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +let's + + align:start position:0% +let's + + + align:start position:0% +let's +do some more properties of + + align:start position:0% + + + + align:start position:0% + +the integral + + align:start position:0% +the integral + + + align:start position:0% +the integral +now back to + + align:start position:0% +now back to + + + align:start position:0% +now back to +properties of the integral + + align:start position:0% + + + + align:start position:0% + +so uh + + align:start position:0% + + + + align:start position:0% + +if I have a non-negative measurable + + align:start position:0% +if I have a non-negative measurable + + + align:start position:0% +if I have a non-negative measurable +function + + align:start position:0% +function + + + align:start position:0% +function +then + + align:start position:0% +then + + + align:start position:0% +then +the integral + + align:start position:0% +the integral + + + align:start position:0% +the integral +of + + align:start position:0% +of + + + align:start position:0% +of +f equals zero + + align:start position:0% +f equals zero + + + align:start position:0% +f equals zero +if and only if + + align:start position:0% +if and only if + + + align:start position:0% +if and only if +x equals 0 almost everywhere on E + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +now what's uh it's a two-way street so + + align:start position:0% +now what's uh it's a two-way street so + + + align:start position:0% +now what's uh it's a two-way street so +One Direction uh if f is equal to zero + + align:start position:0% +One Direction uh if f is equal to zero + + + align:start position:0% +One Direction uh if f is equal to zero +almost everywhere then it's less than or + + align:start position:0% +almost everywhere then it's less than or + + + align:start position:0% +almost everywhere then it's less than or +equal to zero almost everywhere and + + align:start position:0% +equal to zero almost everywhere and + + + align:start position:0% +equal to zero almost everywhere and +therefore the integral of f is less than + + align:start position:0% +therefore the integral of f is less than + + + align:start position:0% +therefore the integral of f is less than +or equal to the integral of zero + + align:start position:0% +or equal to the integral of zero + + + align:start position:0% +or equal to the integral of zero +and the integral of zero is zero so + + align:start position:0% +and the integral of zero is zero so + + + align:start position:0% +and the integral of zero is zero so +um + + align:start position:0% +um + + + align:start position:0% +um +you know this direction uh follows + + align:start position:0% + + + + align:start position:0% + +from + + align:start position:0% +from + + + align:start position:0% +from +the fact that + + align:start position:0% +the fact that + + + align:start position:0% +the fact that +f is less than or equal to zero almost + + align:start position:0% +f is less than or equal to zero almost + + + align:start position:0% +f is less than or equal to zero almost +everywhere which implies that + + align:start position:0% +everywhere which implies that + + + align:start position:0% +everywhere which implies that +the integral of f over e is less than or + + align:start position:0% +the integral of f over e is less than or + + + align:start position:0% +the integral of f over e is less than or +equal to the integral of zero which you + + align:start position:0% +equal to the integral of zero which you + + + align:start position:0% +equal to the integral of zero which you +can check is zero + + align:start position:0% + + + + align:start position:0% + +and you know this is a non-negative + + align:start position:0% +and you know this is a non-negative + + + align:start position:0% +and you know this is a non-negative +quantity so + + align:start position:0% +quantity so + + + align:start position:0% +quantity so +okay so now how about the other + + align:start position:0% +okay so now how about the other + + + align:start position:0% +okay so now how about the other +direction that the integral of f being 0 + + align:start position:0% +direction that the integral of f being 0 + + + align:start position:0% +direction that the integral of f being 0 +for a non-negative measurable function + + align:start position:0% +for a non-negative measurable function + + + align:start position:0% +for a non-negative measurable function +implies f is 0 almost everywhere + + align:start position:0% + + + + align:start position:0% + +so let's + + align:start position:0% + + + + align:start position:0% + +let F in to be the set of all + + align:start position:0% +let F in to be the set of all + + + align:start position:0% +let F in to be the set of all +X is in E such that + + align:start position:0% +X is in E such that + + + align:start position:0% +X is in E such that +um + + align:start position:0% +um + + + align:start position:0% +um +f of x is bigger than 1 over n + + align:start position:0% + + + + align:start position:0% + +and let's let + + align:start position:0% +and let's let + + + align:start position:0% +and let's let +F be the set of all X's such that + + align:start position:0% +F be the set of all X's such that + + + align:start position:0% +F be the set of all X's such that +f of x is bigger than zero + + align:start position:0% +f of x is bigger than zero + + + align:start position:0% +f of x is bigger than zero +okay now if x is so this is X and E I + + align:start position:0% +okay now if x is so this is X and E I + + + align:start position:0% +okay now if x is so this is X and E I +should say + + align:start position:0% + + + + align:start position:0% + +now if I have an X where f of x is + + align:start position:0% +now if I have an X where f of x is + + + align:start position:0% +now if I have an X where f of x is +bigger than 0 then at least for some + + align:start position:0% +bigger than 0 then at least for some + + + align:start position:0% +bigger than 0 then at least for some +large n f of x will be bigger than 1 + + align:start position:0% +large n f of x will be bigger than 1 + + + align:start position:0% +large n f of x will be bigger than 1 +over n Okay so + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +the union of + + align:start position:0% +the union of + + + align:start position:0% +the union of +from n equals 1 to Infinity of the FNS + + align:start position:0% +from n equals 1 to Infinity of the FNS + + + align:start position:0% +from n equals 1 to Infinity of the FNS +equals f + + align:start position:0% + + + + align:start position:0% + +okay I mean each of these is a subset of + + align:start position:0% +okay I mean each of these is a subset of + + + align:start position:0% +okay I mean each of these is a subset of +capital F so their Union is contained in + + align:start position:0% +capital F so their Union is contained in + + + align:start position:0% +capital F so their Union is contained in +capital F and I've just the argument I + + align:start position:0% +capital F and I've just the argument I + + + align:start position:0% +capital F and I've just the argument I +gave a minute ago shows you that F + + align:start position:0% +gave a minute ago shows you that F + + + align:start position:0% +gave a minute ago shows you that F +capital F is contained in the union so + + align:start position:0% +capital F is contained in the union so + + + align:start position:0% +capital F is contained in the union so +uh this Union equals f + + align:start position:0% +uh this Union equals f + + + align:start position:0% +uh this Union equals f +and just by how it's defined + + align:start position:0% +and just by how it's defined + + + align:start position:0% +and just by how it's defined +uh you know one is bigger than or equal + + align:start position:0% +uh you know one is bigger than or equal + + + align:start position:0% +uh you know one is bigger than or equal +to a half which is bigger bigger than or + + align:start position:0% +to a half which is bigger bigger than or + + + align:start position:0% +to a half which is bigger bigger than or +equal to a third or which is bigger than + + align:start position:0% +equal to a third or which is bigger than + + + align:start position:0% +equal to a third or which is bigger than +a third F1 is contained in F2 it's + + align:start position:0% +a third F1 is contained in F2 it's + + + align:start position:0% +a third F1 is contained in F2 it's +contained in F3 + + align:start position:0% +contained in F3 + + + align:start position:0% +contained in F3 +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +right if f of x is bigger than a half + + align:start position:0% +right if f of x is bigger than a half + + + align:start position:0% +right if f of x is bigger than a half +it's certainly bigger than a third Okay + + align:start position:0% +it's certainly bigger than a third Okay + + + align:start position:0% +it's certainly bigger than a third Okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +right so now we'll use again + + align:start position:0% +right so now we'll use again + + + align:start position:0% +right so now we'll use again +continuity of + + align:start position:0% +continuity of + + + align:start position:0% +continuity of +lebeg measure so + + align:start position:0% + + + + align:start position:0% + +and for all n + + align:start position:0% +and for all n + + + align:start position:0% +and for all n +0 Which is less than or equal to + + align:start position:0% +0 Which is less than or equal to + + + align:start position:0% +0 Which is less than or equal to +1 over n times the measure of F and this + + align:start position:0% +1 over n times the measure of F and this + + + align:start position:0% +1 over n times the measure of F and this +is uh + + align:start position:0% + + + + align:start position:0% + +like equal to the integral over e of 1 + + align:start position:0% +like equal to the integral over e of 1 + + + align:start position:0% +like equal to the integral over e of 1 +over n times the indicator function of F + + align:start position:0% +over n times the indicator function of F + + + align:start position:0% +over n times the indicator function of F +N now on + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this set + + align:start position:0% +this set + + + align:start position:0% +this set +or what am I saying + + align:start position:0% +or what am I saying + + + align:start position:0% +or what am I saying +um + + align:start position:0% +um + + + align:start position:0% +um +yeah let's write it this way + + align:start position:0% + + + + align:start position:0% + +this is equal to + + align:start position:0% + + + + align:start position:0% + +over n + + align:start position:0% + + + + align:start position:0% + +and now on F in 1 over n is less than or + + align:start position:0% +and now on F in 1 over n is less than or + + + align:start position:0% +and now on F in 1 over n is less than or +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +f of x so this is less than or equal to + + align:start position:0% +f of x so this is less than or equal to + + + align:start position:0% +f of x so this is less than or equal to +the integral of FN F and capital F of N + + align:start position:0% +the integral of FN F and capital F of N + + + align:start position:0% +the integral of FN F and capital F of N +is a subset of capital E so this is + + align:start position:0% +is a subset of capital E so this is + + + align:start position:0% +is a subset of capital E so this is +less than or equal to the integral of e + + align:start position:0% +less than or equal to the integral of e + + + align:start position:0% +less than or equal to the integral of e +over e of f but by assumption this is + + align:start position:0% +over e of f but by assumption this is + + + align:start position:0% +over e of f but by assumption this is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +right + + align:start position:0% +right + + + align:start position:0% +right +and sandwiched in between 0 and 0 is 1 + + align:start position:0% +and sandwiched in between 0 and 0 is 1 + + + align:start position:0% +and sandwiched in between 0 and 0 is 1 +over n times the measure of f sub n and + + align:start position:0% +over n times the measure of f sub n and + + + align:start position:0% +over n times the measure of f sub n and +therefore for all n + + align:start position:0% +therefore for all n + + + align:start position:0% +therefore for all n +measure of f sub n equals zero + + align:start position:0% +measure of f sub n equals zero + + + align:start position:0% +measure of f sub n equals zero +which tells me that the measure + + align:start position:0% +which tells me that the measure + + + align:start position:0% +which tells me that the measure +of f which is equal to that Union + + align:start position:0% +of f which is equal to that Union + + + align:start position:0% +of f which is equal to that Union +uh + + align:start position:0% + + + + align:start position:0% + +which is equal to this increasing Union + + align:start position:0% +which is equal to this increasing Union + + + align:start position:0% +which is equal to this increasing Union +is by the continuity of the big measure + + align:start position:0% +is by the continuity of the big measure + + + align:start position:0% +is by the continuity of the big measure +equal to the Limit as n goes to Infinity + + align:start position:0% +equal to the Limit as n goes to Infinity + + + align:start position:0% +equal to the Limit as n goes to Infinity +of the measure of f sub n which equals + + align:start position:0% +of the measure of f sub n which equals + + + align:start position:0% +of the measure of f sub n which equals +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay and therefore the set of all X's + + align:start position:0% +okay and therefore the set of all X's + + + align:start position:0% +okay and therefore the set of all X's +where f of x is positive has a + + align:start position:0% +where f of x is positive has a + + + align:start position:0% +where f of x is positive has a +label measures zero + + align:start position:0% + + + + align:start position:0% + +and f equals zero almost everywhere + + align:start position:0% + + + + align:start position:0% + +Now using what we've done here and the + + align:start position:0% +Now using what we've done here and the + + + align:start position:0% +Now using what we've done here and the +monotone convergence theorem we can + + align:start position:0% +monotone convergence theorem we can + + + align:start position:0% +monotone convergence theorem we can +slightly relax + + align:start position:0% +slightly relax + + + align:start position:0% +slightly relax +um + + align:start position:0% +um + + + align:start position:0% +um +the assumptions in the monotone + + align:start position:0% +the assumptions in the monotone + + + align:start position:0% +the assumptions in the monotone +convergence theorem + + align:start position:0% + + + + align:start position:0% + +so we have the following theorem if FN + + align:start position:0% +so we have the following theorem if FN + + + align:start position:0% +so we have the following theorem if FN +uh + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +sequence in + + align:start position:0% +sequence in + + + align:start position:0% +sequence in +uh + + align:start position:0% +uh + + + align:start position:0% +uh +non-negative measurable functions + + align:start position:0% +non-negative measurable functions + + + align:start position:0% +non-negative measurable functions +such that + + align:start position:0% +such that + + + align:start position:0% +such that +um + + align:start position:0% + + + + align:start position:0% + +now for almost every X + + align:start position:0% +now for almost every X + + + align:start position:0% +now for almost every X +in E we have + + align:start position:0% +in E we have + + + align:start position:0% +in E we have +F1 of X is less than or equal to F2 of X + + align:start position:0% +F1 of X is less than or equal to F2 of X + + + align:start position:0% +F1 of X is less than or equal to F2 of X +is less than or equal to F3 of x + + align:start position:0% +is less than or equal to F3 of x + + + align:start position:0% +is less than or equal to F3 of x +and so on and + + align:start position:0% +and so on and + + + align:start position:0% +and so on and +limit as n goes to Infinity of f n of x + + align:start position:0% +limit as n goes to Infinity of f n of x + + + align:start position:0% +limit as n goes to Infinity of f n of x +equals a function f of x + + align:start position:0% +equals a function f of x + + + align:start position:0% +equals a function f of x +so remember in the statement of the + + align:start position:0% +so remember in the statement of the + + + align:start position:0% +so remember in the statement of the +monotone convergence theorem we assume + + align:start position:0% +monotone convergence theorem we assume + + + align:start position:0% +monotone convergence theorem we assume +these two things for every X now we're + + align:start position:0% +these two things for every X now we're + + + align:start position:0% +these two things for every X now we're +just assuming them for almost every X in + + align:start position:0% +just assuming them for almost every X in + + + align:start position:0% +just assuming them for almost every X in +e + + align:start position:0% +e + + + align:start position:0% +e +then we get the same conclusion then + + align:start position:0% +then we get the same conclusion then + + + align:start position:0% +then we get the same conclusion then +the integral of e + + align:start position:0% +the integral of e + + + align:start position:0% +the integral of e +of f is equal to + + align:start position:0% +of f is equal to + + + align:start position:0% +of f is equal to +the limit as n goes to Infinity of the + + align:start position:0% +the limit as n goes to Infinity of the + + + align:start position:0% +the limit as n goes to Infinity of the +integral of e + + align:start position:0% +integral of e + + + align:start position:0% +integral of e +over e of uh F sub n + + align:start position:0% +over e of uh F sub n + + + align:start position:0% +over e of uh F sub n +okay + + align:start position:0% + + + + align:start position:0% + +okay so uh + + align:start position:0% + + + + align:start position:0% + +we call these two condition star + + align:start position:0% +we call these two condition star + + + align:start position:0% +we call these two condition star +uh + + align:start position:0% + + + + align:start position:0% + +let capital f + + align:start position:0% +let capital f + + + align:start position:0% +let capital f +be the set + + align:start position:0% +be the set + + + align:start position:0% +be the set +while X is in E such that + + align:start position:0% +while X is in E such that + + + align:start position:0% +while X is in E such that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +F ends are increasing to F so star holds + + align:start position:0% + + + + align:start position:0% + +then the measure of the complement + + align:start position:0% + + + + align:start position:0% + +is by assumption equal to zero + + align:start position:0% +is by assumption equal to zero + + + align:start position:0% +is by assumption equal to zero +and I should say here the complement in + + align:start position:0% +and I should say here the complement in + + + align:start position:0% +and I should say here the complement in +E so I should say e take away F uh + + align:start position:0% +E so I should say e take away F uh + + + align:start position:0% +E so I should say e take away F uh +so let me um + + align:start position:0% + + + + align:start position:0% + +and and that should have been in the + + align:start position:0% + + + + align:start position:0% + +so if I write compliment you should + + align:start position:0% +so if I write compliment you should + + + align:start position:0% +so if I write compliment you should +interpret that as the complement within + + align:start position:0% +interpret that as the complement within + + + align:start position:0% +interpret that as the complement within +e so e take away f + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +um + + align:start position:0% +um + + + align:start position:0% +um +F minus Chi sub f + + align:start position:0% +F minus Chi sub f + + + align:start position:0% +F minus Chi sub f +uh so this is the indicator function + + align:start position:0% +uh so this is the indicator function + + + align:start position:0% +uh so this is the indicator function +over capital F this equals zero + + align:start position:0% +over capital F this equals zero + + + align:start position:0% +over capital F this equals zero +almost everywhere + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +FN minus Chi sub f f n + + align:start position:0% +FN minus Chi sub f f n + + + align:start position:0% +FN minus Chi sub f f n +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +almost everywhere + + align:start position:0% +almost everywhere + + + align:start position:0% +almost everywhere +for all n + + align:start position:0% +for all n + + + align:start position:0% +for all n +right + + align:start position:0% + + + + align:start position:0% + +these equal zero when X is in F which uh + + align:start position:0% +these equal zero when X is in F which uh + + + align:start position:0% +these equal zero when X is in F which uh +the complement is has measure zero which + + align:start position:0% +the complement is has measure zero which + + + align:start position:0% +the complement is has measure zero which +I didn't finish writing down + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +Now by + + align:start position:0% +Now by + + + align:start position:0% +Now by +monotone convergence theorem uh applied + + align:start position:0% +monotone convergence theorem uh applied + + + align:start position:0% +monotone convergence theorem uh applied +now to these + + align:start position:0% +now to these + + + align:start position:0% +now to these +Parts if you like + + align:start position:0% + + + + align:start position:0% + +in the previous theorem + + align:start position:0% + + + + align:start position:0% + +we have that + + align:start position:0% +we have that + + + align:start position:0% +we have that +um + + align:start position:0% + + + + align:start position:0% + +the integral of f + + align:start position:0% +the integral of f + + + align:start position:0% +the integral of f +of e this is equal to uh + + align:start position:0% + + + + align:start position:0% + +Chi sub f + + align:start position:0% +Chi sub f + + + align:start position:0% +Chi sub f +okay + + align:start position:0% + + + + align:start position:0% + +and okay so this is uh equal to + + align:start position:0% +and okay so this is uh equal to + + + align:start position:0% +and okay so this is uh equal to +so since F minus F uh + + align:start position:0% +so since F minus F uh + + + align:start position:0% +so since F minus F uh +wait + + align:start position:0% + + + + align:start position:0% + +yes so okay so since f equals F times + + align:start position:0% +yes so okay so since f equals F times + + + align:start position:0% +yes so okay so since f equals F times +Chi sub F almost everywhere the + + align:start position:0% +Chi sub F almost everywhere the + + + align:start position:0% +Chi sub F almost everywhere the +integrals uh equal and so this is equal + + align:start position:0% +integrals uh equal and so this is equal + + + align:start position:0% +integrals uh equal and so this is equal +to the integral over capital F of little + + align:start position:0% +to the integral over capital F of little + + + align:start position:0% +to the integral over capital F of little +F and by the monotone convergence + + align:start position:0% +F and by the monotone convergence + + + align:start position:0% +F and by the monotone convergence +theorem applied here this is equal to + + align:start position:0% +theorem applied here this is equal to + + + align:start position:0% +theorem applied here this is equal to +limit as n goes to Infinity of + + align:start position:0% + + + + align:start position:0% + +the FNS because there are pointwise + + align:start position:0% +the FNS because there are pointwise + + + align:start position:0% +the FNS because there are pointwise +increasing on capital F to little F and + + align:start position:0% +increasing on capital F to little F and + + + align:start position:0% +increasing on capital F to little F and +this is equal to so you know okay so I + + align:start position:0% +this is equal to so you know okay so I + + + align:start position:0% +this is equal to so you know okay so I +really didn't need the previous theorem + + align:start position:0% +really didn't need the previous theorem + + + align:start position:0% +really didn't need the previous theorem +I could have used what I had earlier + + align:start position:0% +I could have used what I had earlier + + + align:start position:0% +I could have used what I had earlier +that if I have uh two functions which + + align:start position:0% +that if I have uh two functions which + + + align:start position:0% +that if I have uh two functions which +equal + + align:start position:0% +equal + + + align:start position:0% +equal +each other almost everywhere so this is + + align:start position:0% +each other almost everywhere so this is + + + align:start position:0% +each other almost everywhere so this is +this previous theorem should not be + + align:start position:0% +this previous theorem should not be + + + align:start position:0% +this previous theorem should not be +referring to what I just proved a minute + + align:start position:0% +referring to what I just proved a minute + + + align:start position:0% +referring to what I just proved a minute +ago but really to the theorem at the + + align:start position:0% +ago but really to the theorem at the + + + align:start position:0% +ago but really to the theorem at the +beginning of lecture that if I have two + + align:start position:0% +beginning of lecture that if I have two + + + align:start position:0% +beginning of lecture that if I have two +functions that equaled each other almost + + align:start position:0% +functions that equaled each other almost + + + align:start position:0% +functions that equaled each other almost +everywhere then their integrals uh equal + + align:start position:0% +everywhere then their integrals uh equal + + + align:start position:0% +everywhere then their integrals uh equal +each other + + align:start position:0% +each other + + + align:start position:0% +each other +um + + align:start position:0% + + + + align:start position:0% + +although maybe I didn't state that I + + align:start position:0% +although maybe I didn't state that I + + + align:start position:0% +although maybe I didn't state that I +just stated the less than or equal to + + align:start position:0% +just stated the less than or equal to + + + align:start position:0% +just stated the less than or equal to +but you know if they're equal almost + + align:start position:0% +but you know if they're equal almost + + + align:start position:0% +but you know if they're equal almost +everywhere they're less than or equal to + + align:start position:0% +everywhere they're less than or equal to + + + align:start position:0% +everywhere they're less than or equal to +each other almost everywhere anyways + + align:start position:0% +each other almost everywhere anyways + + + align:start position:0% +each other almost everywhere anyways +back to this this is equal to the Limit + + align:start position:0% + + + + align:start position:0% + +okay so the whole point is is that uh + + align:start position:0% +okay so the whole point is is that uh + + + align:start position:0% +okay so the whole point is is that uh +sets of measure zero don't affect uh + + align:start position:0% +sets of measure zero don't affect uh + + + align:start position:0% +sets of measure zero don't affect uh +statements that involve integrals okay + + align:start position:0% +statements that involve integrals okay + + + align:start position:0% +statements that involve integrals okay +that should be the take home + + align:start position:0% +that should be the take home + + + align:start position:0% +that should be the take home +all right that uh + + align:start position:0% +all right that uh + + + align:start position:0% +all right that uh +you know if your conclusions are in + + align:start position:0% +you know if your conclusions are in + + + align:start position:0% +you know if your conclusions are in +terms of integrals + + align:start position:0% +terms of integrals + + + align:start position:0% +terms of integrals +conditions holding almost everywhere + + align:start position:0% +conditions holding almost everywhere + + + align:start position:0% +conditions holding almost everywhere +suffice typically + + align:start position:0% +suffice typically + + + align:start position:0% +suffice typically +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so for example the simplest one we had + + align:start position:0% +so for example the simplest one we had + + + align:start position:0% +so for example the simplest one we had +earlier was that you know if f is less + + align:start position:0% +earlier was that you know if f is less + + + align:start position:0% +earlier was that you know if f is less +than or equal to G then the integral of + + align:start position:0% +than or equal to G then the integral of + + + align:start position:0% +than or equal to G then the integral of +f is less than or equal to G we can + + align:start position:0% +f is less than or equal to G we can + + + align:start position:0% +f is less than or equal to G we can +relax that to the integral that if f is + + align:start position:0% +relax that to the integral that if f is + + + align:start position:0% +relax that to the integral that if f is +less than or equal to G almost + + align:start position:0% +less than or equal to G almost + + + align:start position:0% +less than or equal to G almost +everywhere then the conclusion which is + + align:start position:0% +everywhere then the conclusion which is + + + align:start position:0% +everywhere then the conclusion which is +stated in terms of integral still holds + + align:start position:0% +stated in terms of integral still holds + + + align:start position:0% +stated in terms of integral still holds +the integral of f is less than or equal + + align:start position:0% +the integral of f is less than or equal + + + align:start position:0% +the integral of f is less than or equal +to the integral of G + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +Okay so + + align:start position:0% + + + + align:start position:0% + +now we'll do the second big + + align:start position:0% +now we'll do the second big + + + align:start position:0% +now we'll do the second big +uh + + align:start position:0% + + + + align:start position:0% + +convergence of intervals or + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +this one's actually an inequality + + align:start position:0% +this one's actually an inequality + + + align:start position:0% +this one's actually an inequality +between intervals but it's still + + align:start position:0% +between intervals but it's still + + + align:start position:0% +between intervals but it's still +extremely useful in fact it's equivalent + + align:start position:0% +extremely useful in fact it's equivalent + + + align:start position:0% +extremely useful in fact it's equivalent +to the monotone convergence theorem + + align:start position:0% +to the monotone convergence theorem + + + align:start position:0% +to the monotone convergence theorem +so it is neither stronger nor weaker + + align:start position:0% + + + + align:start position:0% + +so we have uh Fat Tuesdays + + align:start position:0% + + + + align:start position:0% + +Lima + + align:start position:0% +Lima + + + align:start position:0% +Lima +stated as a theorem of course + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +which states that if F in + + align:start position:0% + + + + align:start position:0% + +is a sequence in L plus of E + + align:start position:0% +is a sequence in L plus of E + + + align:start position:0% +is a sequence in L plus of E +then + + align:start position:0% + + + + align:start position:0% + +integral of e of + + align:start position:0% + + + + align:start position:0% + +the limb imp + + align:start position:0% +the limb imp + + + align:start position:0% +the limb imp +this n goes to Infinity of f n of x + + align:start position:0% +this n goes to Infinity of f n of x + + + align:start position:0% +this n goes to Infinity of f n of x +this is a function + + align:start position:0% +this is a function + + + align:start position:0% +this is a function +okay for each X I take the limb imp as n + + align:start position:0% +okay for each X I take the limb imp as n + + + align:start position:0% +okay for each X I take the limb imp as n +goes to Infinity of f n of x + + align:start position:0% +goes to Infinity of f n of x + + + align:start position:0% +goes to Infinity of f n of x +this is less than or equal to + + align:start position:0% +this is less than or equal to + + + align:start position:0% +this is less than or equal to +the limit as n goes to Infinity of + + align:start position:0% + + + + align:start position:0% + +the integrals of f in so let me + + align:start position:0% +the integrals of f in so let me + + + align:start position:0% +the integrals of f in so let me +state it this way + + align:start position:0% +state it this way + + + align:start position:0% +state it this way +okay so uh the limb imp of f sub n this + + align:start position:0% +okay so uh the limb imp of f sub n this + + + align:start position:0% +okay so uh the limb imp of f sub n this +is + + align:start position:0% +is + + + align:start position:0% +is +let me just recall + + align:start position:0% +let me just recall + + + align:start position:0% +let me just recall +what is the limb imp + + align:start position:0% + + + + align:start position:0% + +this is equal to the soup over + + align:start position:0% + + + + align:start position:0% + +n equals one + + align:start position:0% +n equals one + + + align:start position:0% +n equals one +nth over + + align:start position:0% +nth over + + + align:start position:0% +nth over +K bigger than or equal to n f k + + align:start position:0% +K bigger than or equal to n f k + + + align:start position:0% +K bigger than or equal to n f k +of x + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that is the definition of the limb + + align:start position:0% +so that is the definition of the limb + + + align:start position:0% +so that is the definition of the limb +soup if you like if in fact let me not + + align:start position:0% +soup if you like if in fact let me not + + + align:start position:0% +soup if you like if in fact let me not +just be specific to FN of X just of a + + align:start position:0% +just be specific to FN of X just of a + + + align:start position:0% +just be specific to FN of X just of a +sequence of real numbers + + align:start position:0% +sequence of real numbers + + + align:start position:0% +sequence of real numbers +the limit of a sub n + + align:start position:0% +the limit of a sub n + + + align:start position:0% +the limit of a sub n +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +this thing on the right hand side + + align:start position:0% +this thing on the right hand side + + + align:start position:0% +this thing on the right hand side +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so this follows uh pretty easily from + + align:start position:0% +so this follows uh pretty easily from + + + align:start position:0% +so this follows uh pretty easily from +the monotone convergence theorem uh you + + align:start position:0% +the monotone convergence theorem uh you + + + align:start position:0% +the monotone convergence theorem uh you +know I said a minute ago that it's in + + align:start position:0% +know I said a minute ago that it's in + + + align:start position:0% +know I said a minute ago that it's in +fact equivalent to the monotone + + align:start position:0% +fact equivalent to the monotone + + + align:start position:0% +fact equivalent to the monotone +convergence serum you can prove + + align:start position:0% +convergence serum you can prove + + + align:start position:0% +convergence serum you can prove +if you so we're going to use the + + align:start position:0% +if you so we're going to use the + + + align:start position:0% +if you so we're going to use the +monotone convergence theorem to prove it + + align:start position:0% +monotone convergence theorem to prove it + + + align:start position:0% +monotone convergence theorem to prove it +you can also assume Fat Tuesday Limba + + align:start position:0% +you can also assume Fat Tuesday Limba + + + align:start position:0% +you can also assume Fat Tuesday Limba +holds and then prove + + align:start position:0% +holds and then prove + + + align:start position:0% +holds and then prove +um the monotone convergence theorem from + + align:start position:0% +um the monotone convergence theorem from + + + align:start position:0% +um the monotone convergence theorem from +it + + align:start position:0% +it + + + align:start position:0% +it +you can also prove it + + align:start position:0% + + + + align:start position:0% + +independently from the monotone + + align:start position:0% +independently from the monotone + + + align:start position:0% +independently from the monotone +convergence theorem I mean using + + align:start position:0% +convergence theorem I mean using + + + align:start position:0% +convergence theorem I mean using +essentially what's a similar argument to + + align:start position:0% +essentially what's a similar argument to + + + align:start position:0% +essentially what's a similar argument to +how you prove the monotone convergence + + align:start position:0% +how you prove the monotone convergence + + + align:start position:0% +how you prove the monotone convergence +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% +um + + + align:start position:0% +um +first off + + align:start position:0% + + + + align:start position:0% + +so we have + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +Lim imp f n of x + + align:start position:0% +Lim imp f n of x + + + align:start position:0% +Lim imp f n of x +which is Again by what I've written up + + align:start position:0% +which is Again by what I've written up + + + align:start position:0% +which is Again by what I've written up +here soup in + + align:start position:0% +here soup in + + + align:start position:0% +here soup in +bigger than or equal to one + + align:start position:0% +bigger than or equal to one + + + align:start position:0% +bigger than or equal to one +if + + align:start position:0% +if + + + align:start position:0% +if +K bigger than or equal to n + + align:start position:0% +K bigger than or equal to n + + + align:start position:0% +K bigger than or equal to n +F K of x + + align:start position:0% +F K of x + + + align:start position:0% +F K of x +this is now + + align:start position:0% +this is now + + + align:start position:0% +this is now +for a fixed in + + align:start position:0% +for a fixed in + + + align:start position:0% +for a fixed in +or + + align:start position:0% +or + + + align:start position:0% +or +um + + align:start position:0% +um + + + align:start position:0% +um +what happens to what's in the brackets + + align:start position:0% +what happens to what's in the brackets + + + align:start position:0% +what happens to what's in the brackets +as n is increasing well this F is being + + align:start position:0% +as n is increasing well this F is being + + + align:start position:0% +as n is increasing well this F is being +taken over a smaller set and the Imp of + + align:start position:0% +taken over a smaller set and the Imp of + + + align:start position:0% +taken over a smaller set and the Imp of +a smaller set is bigger than or equal to + + align:start position:0% +a smaller set is bigger than or equal to + + + align:start position:0% +a smaller set is bigger than or equal to +the emph of the larger set so this imp + + align:start position:0% +the emph of the larger set so this imp + + + align:start position:0% +the emph of the larger set so this imp +uh here this thing in Brackets is + + align:start position:0% +uh here this thing in Brackets is + + + align:start position:0% +uh here this thing in Brackets is +increasing in N okay so this soup is in + + align:start position:0% +increasing in N okay so this soup is in + + + align:start position:0% +increasing in N okay so this soup is in +fact the limit + + align:start position:0% + + + + align:start position:0% + +as n goes to Infinity + + align:start position:0% +as n goes to Infinity + + + align:start position:0% +as n goes to Infinity +of + + align:start position:0% +of + + + align:start position:0% +of +this + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +increasing sequence of real numbers + + align:start position:0% +increasing sequence of real numbers + + + align:start position:0% +increasing sequence of real numbers +defined as the M over K bigger than or + + align:start position:0% +defined as the M over K bigger than or + + + align:start position:0% +defined as the M over K bigger than or +equal to n of f k of X okay + + align:start position:0% +equal to n of f k of X okay + + + align:start position:0% +equal to n of f k of X okay +and so what I just told you is not + + align:start position:0% +and so what I just told you is not + + + align:start position:0% +and so what I just told you is not +specific to FK if x is specific to + + align:start position:0% +specific to FK if x is specific to + + + align:start position:0% +specific to FK if x is specific to +um AK for a sequence AK okay + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% + + + + align:start position:0% + +so since + + align:start position:0% +so since + + + align:start position:0% +so since +basically I'm going to write down what I + + align:start position:0% +basically I'm going to write down what I + + + align:start position:0% +basically I'm going to write down what I +said a minute ago since f + + align:start position:0% +said a minute ago since f + + + align:start position:0% +said a minute ago since f +K bigger than or equal to one + + align:start position:0% +K bigger than or equal to one + + + align:start position:0% +K bigger than or equal to one +K of X is less than or equal to m + + align:start position:0% +K of X is less than or equal to m + + + align:start position:0% +K of X is less than or equal to m +a bigger than or equal to two so F K of + + align:start position:0% +a bigger than or equal to two so F K of + + + align:start position:0% +a bigger than or equal to two so F K of +x + + align:start position:0% +x + + + align:start position:0% +x +less than or equal to now changes to + + align:start position:0% +less than or equal to now changes to + + + align:start position:0% +less than or equal to now changes to +three and so on + + align:start position:0% + + + + align:start position:0% + +this implies by uh the monotone + + align:start position:0% +this implies by uh the monotone + + + align:start position:0% +this implies by uh the monotone +convergence theorem + + align:start position:0% + + + + align:start position:0% + +that the integral + + align:start position:0% +that the integral + + + align:start position:0% +that the integral +of + + align:start position:0% +of + + + align:start position:0% +of +the limph of f in + + align:start position:0% + + + + align:start position:0% + +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +the limit as n goes to Infinity of the + + align:start position:0% +the limit as n goes to Infinity of the + + + align:start position:0% +the limit as n goes to Infinity of the +integral over e of the m + + align:start position:0% +integral over e of the m + + + align:start position:0% +integral over e of the m +a bigger than or equal to n + + align:start position:0% +a bigger than or equal to n + + + align:start position:0% +a bigger than or equal to n +F K okay so I have this function here + + align:start position:0% +F K okay so I have this function here + + + align:start position:0% +F K okay so I have this function here +which is defined in this way + + align:start position:0% +which is defined in this way + + + align:start position:0% +which is defined in this way +so for each N I get a function here + + align:start position:0% +so for each N I get a function here + + + align:start position:0% +so for each N I get a function here +okay + + align:start position:0% + + + + align:start position:0% + +all right now + + align:start position:0% + + + + align:start position:0% + +for all J bigger than or equal to m + + align:start position:0% +for all J bigger than or equal to m + + + align:start position:0% +for all J bigger than or equal to m +dysfunction + + align:start position:0% +dysfunction + + + align:start position:0% +dysfunction +uh given by the INF over K bigger than + + align:start position:0% +uh given by the INF over K bigger than + + + align:start position:0% +uh given by the INF over K bigger than +or equal to + + align:start position:0% +or equal to + + + align:start position:0% +or equal to +so let's uh one more quantifier in here + + align:start position:0% +so let's uh one more quantifier in here + + + align:start position:0% +so let's uh one more quantifier in here +so for all J bigger than or equal to n + + align:start position:0% +so for all J bigger than or equal to n + + + align:start position:0% +so for all J bigger than or equal to n +for all X and E + + align:start position:0% +for all X and E + + + align:start position:0% +for all X and E +I have that the M over + + align:start position:0% +I have that the M over + + + align:start position:0% +I have that the M over +K bigger than or equal to n + + align:start position:0% +K bigger than or equal to n + + + align:start position:0% +K bigger than or equal to n +of f k of X this is certainly less than + + align:start position:0% +of f k of X this is certainly less than + + + align:start position:0% +of f k of X this is certainly less than +or equal to + + align:start position:0% +or equal to + + + align:start position:0% +or equal to +f j of x + + align:start position:0% + + + + align:start position:0% + +right this is the info for all FK of X + + align:start position:0% +right this is the info for all FK of X + + + align:start position:0% +right this is the info for all FK of X +for K bigger than or equal to n and for + + align:start position:0% +for K bigger than or equal to n and for + + + align:start position:0% +for K bigger than or equal to n and for +any fixed J bigger than or equal to n + + align:start position:0% +any fixed J bigger than or equal to n + + + align:start position:0% +any fixed J bigger than or equal to n +that's certainly less than or equal to f + + align:start position:0% +that's certainly less than or equal to f + + + align:start position:0% +that's certainly less than or equal to f +j of X because this is a lower Bound for + + align:start position:0% +j of X because this is a lower Bound for + + + align:start position:0% +j of X because this is a lower Bound for +all of these guys for all J bigger than + + align:start position:0% +all of these guys for all J bigger than + + + align:start position:0% +all of these guys for all J bigger than +or equal to n + + align:start position:0% +or equal to n + + + align:start position:0% +or equal to n +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +since this function here sits below this + + align:start position:0% +since this function here sits below this + + + align:start position:0% +since this function here sits below this +function uh + + align:start position:0% +function uh + + + align:start position:0% +function uh +I have for all J bigger than or equal to + + align:start position:0% +I have for all J bigger than or equal to + + + align:start position:0% +I have for all J bigger than or equal to +n the integral of e of M + + align:start position:0% + + + + align:start position:0% + +of f k is less than or equal to + + align:start position:0% +of f k is less than or equal to + + + align:start position:0% +of f k is less than or equal to +the integral of + + align:start position:0% +the integral of + + + align:start position:0% +the integral of +f j + + align:start position:0% + + + + align:start position:0% + +so I have this number here sits below + + align:start position:0% +so I have this number here sits below + + + align:start position:0% +so I have this number here sits below +this number here for all J + + align:start position:0% +this number here for all J + + + align:start position:0% +this number here for all J +okay this is a fixed number depending on + + align:start position:0% +okay this is a fixed number depending on + + + align:start position:0% +okay this is a fixed number depending on +N this is a fixed number depending on J + + align:start position:0% +N this is a fixed number depending on J + + + align:start position:0% +N this is a fixed number depending on J +and this holds for all J bigger than or + + align:start position:0% +and this holds for all J bigger than or + + + align:start position:0% +and this holds for all J bigger than or +equal to n so this thing has to be a + + align:start position:0% +equal to n so this thing has to be a + + + align:start position:0% +equal to n so this thing has to be a +lower Bound for the set of all numbers + + align:start position:0% +lower Bound for the set of all numbers + + + align:start position:0% +lower Bound for the set of all numbers +of this form for J bigger than or equal + + align:start position:0% +of this form for J bigger than or equal + + + align:start position:0% +of this form for J bigger than or equal +to n and therefore the integral of e of + + align:start position:0% +to n and therefore the integral of e of + + + align:start position:0% +to n and therefore the integral of e of +M + + align:start position:0% +M + + + align:start position:0% +M +K bigger than or equal to n of f k is + + align:start position:0% +K bigger than or equal to n of f k is + + + align:start position:0% +K bigger than or equal to n of f k is +less than or equal to the nth over all J + + align:start position:0% +less than or equal to the nth over all J + + + align:start position:0% +less than or equal to the nth over all J +bigger than or equal to n of + + align:start position:0% + + + + align:start position:0% + +the integral of + + align:start position:0% +the integral of + + + align:start position:0% +the integral of +F sub J over e + + align:start position:0% +F sub J over e + + + align:start position:0% +F sub J over e +okay now we're going to take this and + + align:start position:0% +okay now we're going to take this and + + + align:start position:0% +okay now we're going to take this and +stick it into + + align:start position:0% +stick it into + + + align:start position:0% +stick it into +this inequality here + + align:start position:0% +this inequality here + + + align:start position:0% +this inequality here +[Applause] + + align:start position:0% + + + + align:start position:0% + +thus what we had before which was that + + align:start position:0% +thus what we had before which was that + + + align:start position:0% +thus what we had before which was that +the limb imp + + align:start position:0% + + + + align:start position:0% + +of f n over e which is equal to the + + align:start position:0% +of f n over e which is equal to the + + + align:start position:0% +of f n over e which is equal to the +Limit as + + align:start position:0% +Limit as + + + align:start position:0% +Limit as +n goes to Infinity of the Imp + + align:start position:0% +n goes to Infinity of the Imp + + + align:start position:0% +n goes to Infinity of the Imp +K bigger than or equal to n + + align:start position:0% +K bigger than or equal to n + + + align:start position:0% +K bigger than or equal to n +f k + + align:start position:0% +f k + + + align:start position:0% +f k +this is by what we've just shown is less + + align:start position:0% +this is by what we've just shown is less + + + align:start position:0% +this is by what we've just shown is less +than or equal to the Limit as n goes to + + align:start position:0% +than or equal to the Limit as n goes to + + + align:start position:0% +than or equal to the Limit as n goes to +Infinity of the Imp over J bigger than + + align:start position:0% +Infinity of the Imp over J bigger than + + + align:start position:0% +Infinity of the Imp over J bigger than +or equal to n + + align:start position:0% + + + + align:start position:0% + +of f j + + align:start position:0% + + + + align:start position:0% + +but this is just by definition equal to + + align:start position:0% +but this is just by definition equal to + + + align:start position:0% +but this is just by definition equal to +the limb + + align:start position:0% + + + + align:start position:0% + +of the integrals of the FNS + + align:start position:0% +of the integrals of the FNS + + + align:start position:0% +of the integrals of the FNS +okay + + align:start position:0% +okay + + + align:start position:0% +okay +which is fat two's Lima + + align:start position:0% + + + + align:start position:0% + +okay so one more + + align:start position:0% +okay so one more + + + align:start position:0% +okay so one more +um + + align:start position:0% +um + + + align:start position:0% +um +one more theorem about uh + + align:start position:0% +one more theorem about uh + + + align:start position:0% +one more theorem about uh +uh the lebeg integral + + align:start position:0% +uh the lebeg integral + + + align:start position:0% +uh the lebeg integral +which is a very useful one you know + + align:start position:0% +which is a very useful one you know + + + align:start position:0% +which is a very useful one you know +throughout all this we have had + + align:start position:0% +throughout all this we have had + + + align:start position:0% +throughout all this we have had +functions that are extended real valued + + align:start position:0% +functions that are extended real valued + + + align:start position:0% +functions that are extended real valued +so + + align:start position:0% +so + + + align:start position:0% +so +you know we're dealing with non-negative + + align:start position:0% +you know we're dealing with non-negative + + + align:start position:0% +you know we're dealing with non-negative +functions which which can equal Infinity + + align:start position:0% +functions which which can equal Infinity + + + align:start position:0% +functions which which can equal Infinity +um at points and maybe that makes you + + align:start position:0% +um at points and maybe that makes you + + + align:start position:0% +um at points and maybe that makes you +nervous but uh + + align:start position:0% +nervous but uh + + + align:start position:0% +nervous but uh +I'm going to tell you that as long as + + align:start position:0% +I'm going to tell you that as long as + + + align:start position:0% +I'm going to tell you that as long as +the integral is finite you don't have to + + align:start position:0% +the integral is finite you don't have to + + + align:start position:0% +the integral is finite you don't have to +be nervous + + align:start position:0% +be nervous + + + align:start position:0% +be nervous +too often so + + align:start position:0% + + + + align:start position:0% + +f is + + align:start position:0% +f is + + + align:start position:0% +f is +a non-negative measurable function over + + align:start position:0% +a non-negative measurable function over + + + align:start position:0% +a non-negative measurable function over +a measurable set e + + align:start position:0% +a measurable set e + + + align:start position:0% +a measurable set e +and the integral is finite + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +the set of x's where f of x is infinite + + align:start position:0% + + + + align:start position:0% + +is the set of measure zero okay + + align:start position:0% +is the set of measure zero okay + + + align:start position:0% +is the set of measure zero okay +so the measure of the set where it's + + align:start position:0% +so the measure of the set where it's + + + align:start position:0% +so the measure of the set where it's +infinite is zero + + align:start position:0% +infinite is zero + + + align:start position:0% +infinite is zero +so what's the proof + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +it's kind of how uh you know if we did + + align:start position:0% +it's kind of how uh you know if we did + + + align:start position:0% +it's kind of how uh you know if we did +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in spirit the proof that um + + align:start position:0% +in spirit the proof that um + + + align:start position:0% +in spirit the proof that um +if the interval is zero then then the + + align:start position:0% +if the interval is zero then then the + + + align:start position:0% +if the interval is zero then then the +function is zero almost everywhere so + + align:start position:0% +function is zero almost everywhere so + + + align:start position:0% +function is zero almost everywhere so +let f + + align:start position:0% +let f + + + align:start position:0% +let f +be the set of all X and E + + align:start position:0% +be the set of all X and E + + + align:start position:0% +be the set of all X and E +such that + + align:start position:0% +such that + + + align:start position:0% +such that +f of x equals infinity + + align:start position:0% +f of x equals infinity + + + align:start position:0% +f of x equals infinity +and F in + + align:start position:0% + + + + align:start position:0% + +be the set of all x's in e + + align:start position:0% +be the set of all x's in e + + + align:start position:0% +be the set of all x's in e +such that + + align:start position:0% +such that + + + align:start position:0% +such that +f of x is bigger than n + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +oh well + + align:start position:0% +oh well + + + align:start position:0% +oh well +that's what I had in my mind but what I + + align:start position:0% +that's what I had in my mind but what I + + + align:start position:0% +that's what I had in my mind but what I +wrote in my notes was a little bit + + align:start position:0% +wrote in my notes was a little bit + + + align:start position:0% +wrote in my notes was a little bit +different than the proof I had in my + + align:start position:0% +different than the proof I had in my + + + align:start position:0% +different than the proof I had in my +mind just now so let's go with what's uh + + align:start position:0% +mind just now so let's go with what's uh + + + align:start position:0% +mind just now so let's go with what's uh +in my notes that's a little + + align:start position:0% +in my notes that's a little + + + align:start position:0% +in my notes that's a little +more cautious okay + + align:start position:0% + + + + align:start position:0% + +then we're all in a natural number + + align:start position:0% + + + + align:start position:0% + +n times Chi f is less than or equal to F + + align:start position:0% +n times Chi f is less than or equal to F + + + align:start position:0% +n times Chi f is less than or equal to F +times Chi f where this is the indicator + + align:start position:0% +times Chi f where this is the indicator + + + align:start position:0% +times Chi f where this is the indicator +function where of capital F right + + align:start position:0% +function where of capital F right + + + align:start position:0% +function where of capital F right +because F on capital F is just infinite + + align:start position:0% +because F on capital F is just infinite + + + align:start position:0% +because F on capital F is just infinite +so this is this always holds right + + align:start position:0% +so this is this always holds right + + + align:start position:0% +so this is this always holds right +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +n times the measure + + align:start position:0% +n times the measure + + + align:start position:0% +n times the measure +of f + + align:start position:0% +of f + + + align:start position:0% +of f +so + + align:start position:0% +so + + + align:start position:0% +so +we're all n n times the measure of f is + + align:start position:0% +we're all n n times the measure of f is + + + align:start position:0% +we're all n n times the measure of f is +less than or equal to the integral over + + align:start position:0% +less than or equal to the integral over + + + align:start position:0% +less than or equal to the integral over +e times + + align:start position:0% +e times + + + align:start position:0% +e times +f + + align:start position:0% +f + + + align:start position:0% +f +i f Which is less than or equal to the + + align:start position:0% +i f Which is less than or equal to the + + + align:start position:0% +i f Which is less than or equal to the +interval of e of f + + align:start position:0% +interval of e of f + + + align:start position:0% +interval of e of f +which is finite + + align:start position:0% +which is finite + + + align:start position:0% +which is finite +right that's a fixed number + + align:start position:0% + + + + align:start position:0% + +then for all n + + align:start position:0% +then for all n + + + align:start position:0% +then for all n +measure of f + + align:start position:0% +measure of f + + + align:start position:0% +measure of f +is less than or equal to one over n + + align:start position:0% +is less than or equal to one over n + + + align:start position:0% +is less than or equal to one over n +times + + align:start position:0% +times + + + align:start position:0% +times +the integral of f over e again this is a + + align:start position:0% +the integral of f over e again this is a + + + align:start position:0% +the integral of f over e again this is a +fixed finite number + + align:start position:0% +fixed finite number + + + align:start position:0% +fixed finite number +which goes to zero as n goes to Infinity + + align:start position:0% +which goes to zero as n goes to Infinity + + + align:start position:0% +which goes to zero as n goes to Infinity +this is just a fixed number as well + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +thus + + align:start position:0% +thus + + + align:start position:0% +thus +measure of f + + align:start position:0% +measure of f + + + align:start position:0% +measure of f +equals zero + + align:start position:0% + + + + align:start position:0% + +okay so that seems like a good place to + + align:start position:0% +okay so that seems like a good place to + + + align:start position:0% +okay so that seems like a good place to +stop next time uh so we've defined the + + align:start position:0% +stop next time uh so we've defined the + + + align:start position:0% +stop next time uh so we've defined the +big integral of a non-negative + + align:start position:0% +big integral of a non-negative + + + align:start position:0% +big integral of a non-negative +measurable function + + align:start position:0% +measurable function + + + align:start position:0% +measurable function +we will then Define the class of label + + align:start position:0% +we will then Define the class of label + + + align:start position:0% +we will then Define the class of label +integrable functions and extend the + + align:start position:0% +integrable functions and extend the + + + align:start position:0% +integrable functions and extend the +definition of integral to those + + align:start position:0% +definition of integral to those + + + align:start position:0% +definition of integral to those +functions + + align:start position:0% +functions + + + align:start position:0% +functions +in a fairly straightforward way + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +prove some simple properties of + + align:start position:0% +prove some simple properties of + + + align:start position:0% +prove some simple properties of +the labic integral + + align:start position:0% +the labic integral + + + align:start position:0% +the labic integral +the last and also the last big + + align:start position:0% +the last and also the last big + + + align:start position:0% +the last and also the last big +convergence theorem which is the + + align:start position:0% +convergence theorem which is the + + + align:start position:0% +convergence theorem which is the +dominated convergence theorem and we may + + align:start position:0% +dominated convergence theorem and we may + + + align:start position:0% +dominated convergence theorem and we may +or may not + + align:start position:0% +or may not + + + align:start position:0% +or may not +finish by the end of next lecture the + + align:start position:0% +finish by the end of next lecture the + + + align:start position:0% +finish by the end of next lecture the +proof that + + align:start position:0% +proof that + + + align:start position:0% +proof that +um + + align:start position:0% +um + + + align:start position:0% +um +LP + + align:start position:0% +LP + + + align:start position:0% +LP +spaces which are based on the label + + align:start position:0% +spaces which are based on the label + + + align:start position:0% +spaces which are based on the label +integral so we built the bag integral to + + align:start position:0% +integral so we built the bag integral to + + + align:start position:0% +integral so we built the bag integral to +have you know + + align:start position:0% +have you know + + + align:start position:0% +have you know +a space of functions that are + + align:start position:0% +a space of functions that are + + + align:start position:0% +a space of functions that are +um + + align:start position:0% + + + + align:start position:0% + +for which kind of + + align:start position:0% +for which kind of + + + align:start position:0% +for which kind of +okay so let me stop that that alarm kind + + align:start position:0% +okay so let me stop that that alarm kind + + + align:start position:0% +okay so let me stop that that alarm kind +of threw me off + + align:start position:0% +of threw me off + + + align:start position:0% +of threw me off +um + + align:start position:0% +um + + + align:start position:0% +um +so it's not too difficult to show prove + + align:start position:0% +so it's not too difficult to show prove + + + align:start position:0% +so it's not too difficult to show prove +or you can just accept for now and we'll + + align:start position:0% +or you can just accept for now and we'll + + + align:start position:0% +or you can just accept for now and we'll +actually see why this is the case soon + + align:start position:0% +actually see why this is the case soon + + + align:start position:0% +actually see why this is the case soon +that the space of continuous functions + + align:start position:0% +that the space of continuous functions + + + align:start position:0% +that the space of continuous functions +with Norm being the integral so the norm + + align:start position:0% +with Norm being the integral so the norm + + + align:start position:0% +with Norm being the integral so the norm +of f being let's say the integral of the + + align:start position:0% +of f being let's say the integral of the + + + align:start position:0% +of f being let's say the integral of the +absolute value of f is a norm space but + + align:start position:0% +absolute value of f is a norm space but + + + align:start position:0% +absolute value of f is a norm space but +it's not a bonox space + + align:start position:0% +it's not a bonox space + + + align:start position:0% +it's not a bonox space +um + + align:start position:0% +um + + + align:start position:0% +um +or you could change you know the + + align:start position:0% +or you could change you know the + + + align:start position:0% +or you could change you know the +integral of f the absolute value of F2 + + align:start position:0% +integral of f the absolute value of F2 + + + align:start position:0% +integral of f the absolute value of F2 +what's called a big LP Norm the integral + + align:start position:0% +what's called a big LP Norm the integral + + + align:start position:0% +what's called a big LP Norm the integral +of f raised to the P all raised to the + + align:start position:0% +of f raised to the P all raised to the + + + align:start position:0% +of f raised to the P all raised to the +one over P so the analog of the little + + align:start position:0% +one over P so the analog of the little + + + align:start position:0% +one over P so the analog of the little +LP Norms which we encounter a few weeks + + align:start position:0% +LP Norms which we encounter a few weeks + + + align:start position:0% +LP Norms which we encounter a few weeks +ago okay not none of those are bondoc + + align:start position:0% +ago okay not none of those are bondoc + + + align:start position:0% +ago okay not none of those are bondoc +spaces when restricted to continuous + + align:start position:0% +spaces when restricted to continuous + + + align:start position:0% +spaces when restricted to continuous +functions or even Riemann interval + + align:start position:0% +functions or even Riemann interval + + + align:start position:0% +functions or even Riemann interval +functions + + align:start position:0% +functions + + + align:start position:0% +functions +so + + align:start position:0% +so + + + align:start position:0% +so +our goal at least uh is a while back + + align:start position:0% +our goal at least uh is a while back + + + align:start position:0% +our goal at least uh is a while back +when we started this sections this big + + align:start position:0% +when we started this sections this big + + + align:start position:0% +when we started this sections this big +section on lebeg integration was to + + align:start position:0% +section on lebeg integration was to + + + align:start position:0% +section on lebeg integration was to +um build uh or at least come upon a + + align:start position:0% +um build uh or at least come upon a + + + align:start position:0% +um build uh or at least come upon a +space where the resulting integrable + + align:start position:0% +space where the resulting integrable + + + align:start position:0% +space where the resulting integrable +functions form a bonus space okay and so + + align:start position:0% +functions form a bonus space okay and so + + + align:start position:0% +functions form a bonus space okay and so +we may or may not by the end of next + + align:start position:0% +we may or may not by the end of next + + + align:start position:0% +we may or may not by the end of next +lecture introduce those but uh + + align:start position:0% +lecture introduce those but uh + + + align:start position:0% +lecture introduce those but uh +um + + align:start position:0% +um + + + align:start position:0% +um +that's where we're headed that's where + + align:start position:0% +that's where we're headed that's where + + + align:start position:0% +that's where we're headed that's where +we're almost at and you know these + + align:start position:0% +we're almost at and you know these + + + align:start position:0% +we're almost at and you know these +spaces + + align:start position:0% +spaces + + + align:start position:0% +spaces +arose because one wants to apply you + + align:start position:0% +arose because one wants to apply you + + + align:start position:0% +arose because one wants to apply you +know functional analysis uh facts tools + + align:start position:0% +know functional analysis uh facts tools + + + align:start position:0% +know functional analysis uh facts tools +to concrete questions such as you know + + align:start position:0% +to concrete questions such as you know + + + align:start position:0% +to concrete questions such as you know +questions about convergence the Fourier + + align:start position:0% +questions about convergence the Fourier + + + align:start position:0% +questions about convergence the Fourier +series + + align:start position:0% +series + + + align:start position:0% +series +um + + align:start position:0% +um + + + align:start position:0% +um +which you know + + align:start position:0% +which you know + + + align:start position:0% +which you know +arose immediately after Fourier said + + align:start position:0% +arose immediately after Fourier said + + + align:start position:0% +arose immediately after Fourier said +that any periodic function can be + + align:start position:0% +that any periodic function can be + + + align:start position:0% +that any periodic function can be +um expanded as a Fourier Series so a lot + + align:start position:0% +um expanded as a Fourier Series so a lot + + + align:start position:0% +um expanded as a Fourier Series so a lot +of people went to a lot of trouble to to + + align:start position:0% +of people went to a lot of trouble to to + + + align:start position:0% +of people went to a lot of trouble to to +fill in + + align:start position:0% +fill in + + + align:start position:0% +fill in +um + + align:start position:0% +um + + + align:start position:0% +um +precisely what it means expanded as you + + align:start position:0% +precisely what it means expanded as you + + + align:start position:0% +precisely what it means expanded as you +know expanded as you know Point wise + + align:start position:0% +know expanded as you know Point wise + + + align:start position:0% +know expanded as you know Point wise +does this uh + + align:start position:0% +does this uh + + + align:start position:0% +does this uh +you know four-year series converge to + + align:start position:0% +you know four-year series converge to + + + align:start position:0% +you know four-year series converge to +the function + + align:start position:0% +the function + + + align:start position:0% +the function +um + + align:start position:0% +um + + + align:start position:0% +um +that was kind of hard to do on average + + align:start position:0% +that was kind of hard to do on average + + + align:start position:0% +that was kind of hard to do on average +do you mean average as in measured with + + align:start position:0% +do you mean average as in measured with + + + align:start position:0% +do you mean average as in measured with +respect to some Norm that's you know + + align:start position:0% +respect to some Norm that's you know + + + align:start position:0% +respect to some Norm that's you know +integrated that involves integration so + + align:start position:0% +integrated that involves integration so + + + align:start position:0% +integrated that involves integration so +which is why we're we're coming here + + align:start position:0% +which is why we're we're coming here + + + align:start position:0% +which is why we're we're coming here +um + + align:start position:0% +um + + + align:start position:0% +um +but uh we'll see that next time or we'll + + align:start position:0% +but uh we'll see that next time or we'll + + + align:start position:0% +but uh we'll see that next time or we'll +see you know the applications of this uh + + align:start position:0% +see you know the applications of this uh + + + align:start position:0% +see you know the applications of this uh +integration Theory along with the + + align:start position:0% +integration Theory along with the + + + align:start position:0% +integration Theory along with the +functional analysis later in the course + + align:start position:0% +functional analysis later in the course + + + align:start position:0% +functional analysis later in the course +when we when we circle around to Fourier + + align:start position:0% +when we when we circle around to Fourier + + + align:start position:0% +when we when we circle around to Fourier +series all right so we'll stop there \ No newline at end of file diff --git a/_LJnCFFyF-M.txt b/_LJnCFFyF-M.txt new file mode 100644 index 0000000000000000000000000000000000000000..23f4ee4381186107cc5e7a657e456c3d58ae868c --- /dev/null +++ b/_LJnCFFyF-M.txt @@ -0,0 +1,17147 @@ +align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um i'm going to get started this is + + align:start position:0% +um i'm going to get started this is + + + align:start position:0% +um i'm going to get started this is +lecture 22 on uh 1413 on happiness and + + align:start position:0% +lecture 22 on uh 1413 on happiness and + + + align:start position:0% +lecture 22 on uh 1413 on happiness and +mental health okay so what are we going + + align:start position:0% +mental health okay so what are we going + + + align:start position:0% +mental health okay so what are we going +to talk about + + align:start position:0% +to talk about + + + align:start position:0% +to talk about +uh today happiness and subjective + + align:start position:0% +uh today happiness and subjective + + + align:start position:0% +uh today happiness and subjective +well-being a little bit on mental health + + align:start position:0% +well-being a little bit on mental health + + + align:start position:0% +well-being a little bit on mental health +um so you talk about rationality and + + align:start position:0% +um so you talk about rationality and + + + align:start position:0% +um so you talk about rationality and +reveal preferences and what can we learn + + align:start position:0% +reveal preferences and what can we learn + + + align:start position:0% +reveal preferences and what can we learn +from choices + + align:start position:0% +from choices + + + align:start position:0% +from choices +and what does that tell us about + + align:start position:0% +and what does that tell us about + + + align:start position:0% +and what does that tell us about +happiness uh we also talk about some + + align:start position:0% +happiness uh we also talk about some + + + align:start position:0% +happiness uh we also talk about some +futility and how do we measure utility + + align:start position:0% +futility and how do we measure utility + + + align:start position:0% +futility and how do we measure utility +um in particular how do we measure + + align:start position:0% +um in particular how do we measure + + + align:start position:0% +um in particular how do we measure +happiness and is that a good or bad idea + + align:start position:0% +happiness and is that a good or bad idea + + + align:start position:0% +happiness and is that a good or bad idea +um and then at the very end we'll have a + + align:start position:0% +um and then at the very end we'll have a + + + align:start position:0% +um and then at the very end we'll have a +hopefully a llama + + align:start position:0% +hopefully a llama + + + align:start position:0% +hopefully a llama +or which will uh at least improve my + + align:start position:0% +or which will uh at least improve my + + + align:start position:0% +or which will uh at least improve my +happiness uh + + align:start position:0% +happiness uh + + + align:start position:0% +happiness uh +hopefully yours too i've had some uh + + align:start position:0% +hopefully yours too i've had some uh + + + align:start position:0% +hopefully yours too i've had some uh +trouble + + align:start position:0% +trouble + + + align:start position:0% +trouble +uh communicating by email with the llama + + align:start position:0% +uh communicating by email with the llama + + + align:start position:0% +uh communicating by email with the llama +goat + + align:start position:0% +goat + + + align:start position:0% +goat +uh and their sort of keepers um + + align:start position:0% +uh and their sort of keepers um + + + align:start position:0% +uh and their sort of keepers um +so i'm not exactly sure when they're + + align:start position:0% +so i'm not exactly sure when they're + + + align:start position:0% +so i'm not exactly sure when they're +gonna show up so they're scheduled + + align:start position:0% +gonna show up so they're scheduled + + + align:start position:0% +gonna show up so they're scheduled +um the problem is like so they have like + + align:start position:0% +um the problem is like so they have like + + + align:start position:0% +um the problem is like so they have like +only different certain time slots + + align:start position:0% +only different certain time slots + + + align:start position:0% +only different certain time slots +the the only time slot that was + + align:start position:0% +the the only time slot that was + + + align:start position:0% +the the only time slot that was +available was at 2 30 + + align:start position:0% +available was at 2 30 + + + align:start position:0% +available was at 2 30 +so i asked them to show up earlier on uh + + align:start position:0% +so i asked them to show up earlier on uh + + + align:start position:0% +so i asked them to show up earlier on uh +so 220 or + + align:start position:0% +so 220 or + + + align:start position:0% +so 220 or +or so i hope uh that's actually gonna + + align:start position:0% +or so i hope uh that's actually gonna + + + align:start position:0% +or so i hope uh that's actually gonna +happen + + align:start position:0% +happen + + + align:start position:0% +happen +uh but i haven't heard back so i'm not + + align:start position:0% +uh but i haven't heard back so i'm not + + + align:start position:0% +uh but i haven't heard back so i'm not +exactly i'm sure so it might have to be + + align:start position:0% +exactly i'm sure so it might have to be + + + align:start position:0% +exactly i'm sure so it might have to be +like 2 30 i hope you don't have to + + align:start position:0% +like 2 30 i hope you don't have to + + + align:start position:0% +like 2 30 i hope you don't have to +to to run uh there was also some + + align:start position:0% +to to run uh there was also some + + + align:start position:0% +to to run uh there was also some +confusion about like which zoom room the + + align:start position:0% +confusion about like which zoom room the + + + align:start position:0% +confusion about like which zoom room the +llama should go into and hopefully they + + align:start position:0% +llama should go into and hopefully they + + + align:start position:0% +llama should go into and hopefully they +find our room + + align:start position:0% +find our room + + + align:start position:0% +find our room +um uh even though they don't have an mit + + align:start position:0% +um uh even though they don't have an mit + + + align:start position:0% +um uh even though they don't have an mit +id + + align:start position:0% +id + + + align:start position:0% +id +uh so anyway that's that uh and then on + + align:start position:0% +uh so anyway that's that uh and then on + + + align:start position:0% +uh so anyway that's that uh and then on +monday um we're gonna talk about policy + + align:start position:0% +monday um we're gonna talk about policy + + + align:start position:0% +monday um we're gonna talk about policy +with behavioral agents which is very + + align:start position:0% +with behavioral agents which is very + + + align:start position:0% +with behavioral agents which is very +much the + + align:start position:0% +much the + + + align:start position:0% +much the +the idea that well now if people are + + align:start position:0% +the idea that well now if people are + + + align:start position:0% +the idea that well now if people are +potentially making mistakes or have + + align:start position:0% +potentially making mistakes or have + + + align:start position:0% +potentially making mistakes or have +uh certain biases and we might sort of + + align:start position:0% +uh certain biases and we might sort of + + + align:start position:0% +uh certain biases and we might sort of +think that we know about it then perhaps + + align:start position:0% +think that we know about it then perhaps + + + align:start position:0% +think that we know about it then perhaps +you can do policies to improve their um + + align:start position:0% +you can do policies to improve their um + + + align:start position:0% +you can do policies to improve their um +behaviors + + align:start position:0% +behaviors + + + align:start position:0% +behaviors +and uh in some cases that's + + align:start position:0% +and uh in some cases that's + + + align:start position:0% +and uh in some cases that's +straightforward if you sort of think you + + align:start position:0% +straightforward if you sort of think you + + + align:start position:0% +straightforward if you sort of think you +know people have + + align:start position:0% +know people have + + + align:start position:0% +know people have +uh biased beliefs such as wrong + + align:start position:0% +uh biased beliefs such as wrong + + + align:start position:0% +uh biased beliefs such as wrong +information based on which they make + + align:start position:0% +information based on which they make + + + align:start position:0% +information based on which they make +information + + align:start position:0% +information + + + align:start position:0% +information +then you might say well let's sort of + + align:start position:0% +then you might say well let's sort of + + + align:start position:0% +then you might say well let's sort of +just improve their information and then + + align:start position:0% +just improve their information and then + + + align:start position:0% +just improve their information and then +they make better choices + + align:start position:0% +they make better choices + + + align:start position:0% +they make better choices +in other situations it's much trickier + + align:start position:0% +in other situations it's much trickier + + + align:start position:0% +in other situations it's much trickier +because hey you know people might have + + align:start position:0% +because hey you know people might have + + + align:start position:0% +because hey you know people might have +certain preferences that are not stable + + align:start position:0% +certain preferences that are not stable + + + align:start position:0% +certain preferences that are not stable +over time and so then it's very + + align:start position:0% +over time and so then it's very + + + align:start position:0% +over time and so then it's very +tricky to figure out what is even the + + align:start position:0% +tricky to figure out what is even the + + + align:start position:0% +tricky to figure out what is even the +objective function that we should + + align:start position:0% +objective function that we should + + + align:start position:0% +objective function that we should +maximize + + align:start position:0% +maximize + + + align:start position:0% +maximize +um uh it might be tricky because + + align:start position:0% +um uh it might be tricky because + + + align:start position:0% +um uh it might be tricky because +who knows what we know versus what + + align:start position:0% +who knows what we know versus what + + + align:start position:0% +who knows what we know versus what +people know + + align:start position:0% +people know + + + align:start position:0% +people know +so who knows that the government or + + align:start position:0% +so who knows that the government or + + + align:start position:0% +so who knows that the government or +anybody else knows actually better + + align:start position:0% +anybody else knows actually better + + + align:start position:0% +anybody else knows actually better +uh what other what's good for other + + align:start position:0% +uh what other what's good for other + + + align:start position:0% +uh what other what's good for other +people and so in some sense if you want + + align:start position:0% +people and so in some sense if you want + + + align:start position:0% +people and so in some sense if you want +to intervene + + align:start position:0% +to intervene + + + align:start position:0% +to intervene +you better be reasonably confident that + + align:start position:0% +you better be reasonably confident that + + + align:start position:0% +you better be reasonably confident that +like what you're doing + + align:start position:0% +like what you're doing + + + align:start position:0% +like what you're doing +uh is actually well-founded and you know + + align:start position:0% +uh is actually well-founded and you know + + + align:start position:0% +uh is actually well-founded and you know +better on what's good for people than + + align:start position:0% +better on what's good for people than + + + align:start position:0% +better on what's good for people than +they know + + align:start position:0% +they know + + + align:start position:0% +they know +themselves and that gets you in tricky + + align:start position:0% +themselves and that gets you in tricky + + + align:start position:0% +themselves and that gets you in tricky +situations + + align:start position:0% +situations + + + align:start position:0% +situations +because potentially if you sort of get + + align:start position:0% +because potentially if you sort of get + + + align:start position:0% +because potentially if you sort of get +wrong or people if you just + + align:start position:0% +wrong or people if you just + + + align:start position:0% +wrong or people if you just +misunderstand people's preferences or + + align:start position:0% +misunderstand people's preferences or + + + align:start position:0% +misunderstand people's preferences or +their voices or behaviors + + align:start position:0% +their voices or behaviors + + + align:start position:0% +their voices or behaviors +then you might intervene and make things + + align:start position:0% +then you might intervene and make things + + + align:start position:0% +then you might intervene and make things +actually + + align:start position:0% +actually + + + align:start position:0% +actually +uh because you just misunderstood like + + align:start position:0% +uh because you just misunderstood like + + + align:start position:0% +uh because you just misunderstood like +to do + + align:start position:0% +to do + + + align:start position:0% +to do +okay so uh what is rationality + + align:start position:0% +okay so uh what is rationality + + + align:start position:0% +okay so uh what is rationality +in uh our classical um economics how do + + align:start position:0% +in uh our classical um economics how do + + + align:start position:0% +in uh our classical um economics how do +we thoughts right + + align:start position:0% +we thoughts right + + + align:start position:0% +we thoughts right +so broadly we think that beliefs + + align:start position:0% +so broadly we think that beliefs + + + align:start position:0% +so broadly we think that beliefs +preferences and actions are rational if + + align:start position:0% +preferences and actions are rational if + + + align:start position:0% +preferences and actions are rational if +they are + + align:start position:0% +they are + + + align:start position:0% +they are +uh mutually consistent what do we + + align:start position:0% +uh mutually consistent what do we + + + align:start position:0% +uh mutually consistent what do we +mean by that well we mean by that that + + align:start position:0% +mean by that well we mean by that that + + + align:start position:0% +mean by that well we mean by that that +we see certain + + align:start position:0% +we see certain + + + align:start position:0% +we see certain +behavior certain actions we can measure + + align:start position:0% +behavior certain actions we can measure + + + align:start position:0% +behavior certain actions we can measure +people's beliefs in certain ways and + + align:start position:0% +people's beliefs in certain ways and + + + align:start position:0% +people's beliefs in certain ways and +then we essentially can sort of find + + align:start position:0% +then we essentially can sort of find + + + align:start position:0% +then we essentially can sort of find +preferences that can rationalize these + + align:start position:0% +preferences that can rationalize these + + + align:start position:0% +preferences that can rationalize these +actions + + align:start position:0% +actions + + + align:start position:0% +actions +and so that's a very sort of hot + + align:start position:0% +and so that's a very sort of hot + + + align:start position:0% +and so that's a very sort of hot +definition and sort of without that kind + + align:start position:0% +definition and sort of without that kind + + + align:start position:0% +definition and sort of without that kind +of definition we can essentially + + align:start position:0% +of definition we can essentially + + + align:start position:0% +of definition we can essentially +say it's possible to be a rational + + align:start position:0% +say it's possible to be a rational + + + align:start position:0% +say it's possible to be a rational +cocaine addict it's + + align:start position:0% +cocaine addict it's + + + align:start position:0% +cocaine addict it's +possible to rationally commit suicide + + align:start position:0% +possible to rationally commit suicide + + + align:start position:0% +possible to rationally commit suicide +it's possible to rationally marry + + align:start position:0% +it's possible to rationally marry + + + align:start position:0% +it's possible to rationally marry +somebody + + align:start position:0% +somebody + + + align:start position:0% +somebody +who whom you met six hours ago it's also + + align:start position:0% +who whom you met six hours ago it's also + + + align:start position:0% +who whom you met six hours ago it's also +possible to be a rational violent + + align:start position:0% +possible to be a rational violent + + + align:start position:0% +possible to be a rational violent +defender if there's certain preferences + + align:start position:0% +defender if there's certain preferences + + + align:start position:0% +defender if there's certain preferences +that people have you can sort of write + + align:start position:0% +that people have you can sort of write + + + align:start position:0% +that people have you can sort of write +down some preferences that + + align:start position:0% +down some preferences that + + + align:start position:0% +down some preferences that +rationalize all of those things and so + + align:start position:0% +rationalize all of those things and so + + + align:start position:0% +rationalize all of those things and so +the fact that + + align:start position:0% +the fact that + + + align:start position:0% +the fact that +uh in mainstream economics are very much + + align:start position:0% +uh in mainstream economics are very much + + + align:start position:0% +uh in mainstream economics are very much +the main + + align:start position:0% +the main + + + align:start position:0% +the main +assumption so the researchers jobs is to + + align:start position:0% +assumption so the researchers jobs is to + + + align:start position:0% +assumption so the researchers jobs is to +identify + + align:start position:0% +identify + + + align:start position:0% +identify +this that are consistent with observed + + align:start position:0% +this that are consistent with observed + + + align:start position:0% +this that are consistent with observed +human behavior + + align:start position:0% +human behavior + + + align:start position:0% +human behavior +right so you see people being wise then + + align:start position:0% +right so you see people being wise then + + + align:start position:0% +right so you see people being wise then +the question is like + + align:start position:0% +the question is like + + + align:start position:0% +the question is like +what are practices that um + + align:start position:0% +what are practices that um + + + align:start position:0% +what are practices that um +that behavior now what's the idea we + + align:start position:0% +that behavior now what's the idea we + + + align:start position:0% +that behavior now what's the idea we +talked about this already before so + + align:start position:0% +talked about this already before so + + + align:start position:0% +talked about this already before so +actors make choices + + align:start position:0% +actors make choices + + + align:start position:0% +actors make choices +economists observe their choices and + + align:start position:0% +economists observe their choices and + + + align:start position:0% +economists observe their choices and +then + + align:start position:0% +then + + + align:start position:0% +then +generate these choices uh if + + align:start position:0% +generate these choices uh if + + + align:start position:0% +generate these choices uh if +um actor were perfectly right right the + + align:start position:0% +um actor were perfectly right right the + + + align:start position:0% +um actor were perfectly right right the +content to sort of give these imputed + + align:start position:0% +content to sort of give these imputed + + + align:start position:0% +content to sort of give these imputed +preferences normative meaning + + align:start position:0% +preferences normative meaning + + + align:start position:0% +preferences normative meaning +that's essentially if i know your + + align:start position:0% +that's essentially if i know your + + + align:start position:0% +that's essentially if i know your +preferences that + + align:start position:0% +preferences that + + + align:start position:0% +preferences that +that's what you should be uh doing isn't + + align:start position:0% +that's what you should be uh doing isn't + + + align:start position:0% +that's what you should be uh doing isn't +like if you prefer + + align:start position:0% +like if you prefer + + + align:start position:0% +like if you prefer +b i should be helping you to do that + + align:start position:0% +b i should be helping you to do that + + + align:start position:0% +b i should be helping you to do that +that would be a good thing + + align:start position:0% +that would be a good thing + + + align:start position:0% +that would be a good thing +for you now + + align:start position:0% +for you now + + + align:start position:0% +for you now +just give you an example of like what + + align:start position:0% +just give you an example of like what + + + align:start position:0% +just give you an example of like what +this sort of could let you potentially + + align:start position:0% +this sort of could let you potentially + + + align:start position:0% +this sort of could let you potentially +sort of astray you're like where you + + align:start position:0% +sort of astray you're like where you + + + align:start position:0% +sort of astray you're like where you +you might sort of argue well is that + + align:start position:0% +you might sort of argue well is that + + + align:start position:0% +you might sort of argue well is that +really sort of rational versus not + + align:start position:0% +really sort of rational versus not + + + align:start position:0% +really sort of rational versus not +for example uh jake jack who prefers + + align:start position:0% +for example uh jake jack who prefers + + + align:start position:0% +for example uh jake jack who prefers +taking cocaine + + align:start position:0% +taking cocaine + + + align:start position:0% +taking cocaine +over quitting jacks um have lots of + + align:start position:0% +over quitting jacks um have lots of + + + align:start position:0% +over quitting jacks um have lots of +speeches about wanting to quit but in a + + align:start position:0% +speeches about wanting to quit but in a + + + align:start position:0% +speeches about wanting to quit but in a +way as you can actually act on it that's + + align:start position:0% +way as you can actually act on it that's + + + align:start position:0% +way as you can actually act on it that's +just + + align:start position:0% +just + + + align:start position:0% +just +cheap talk um jack might in fact be if + + align:start position:0% +cheap talk um jack might in fact be if + + + align:start position:0% +cheap talk um jack might in fact be if +you were clean i + + align:start position:0% +you were clean i + + + align:start position:0% +you were clean i +bet it getting clean is too costly + + align:start position:0% +bet it getting clean is too costly + + + align:start position:0% +bet it getting clean is too costly +because their withdrawal costs + + align:start position:0% +because their withdrawal costs + + + align:start position:0% +because their withdrawal costs +um jack probably didn't to be on an + + align:start position:0% +um jack probably didn't to be on an + + + align:start position:0% +um jack probably didn't to be on an +untried cocaine + + align:start position:0% +untried cocaine + + + align:start position:0% +untried cocaine +but this battle was officially unlikely + + align:start position:0% +but this battle was officially unlikely + + + align:start position:0% +but this battle was officially unlikely +that his early experiments would + + align:start position:0% +that his early experiments would + + + align:start position:0% +that his early experiments would +make sense so finally a sort of cocaine + + align:start position:0% +make sense so finally a sort of cocaine + + + align:start position:0% +make sense so finally a sort of cocaine +should be legalized unless it generates + + align:start position:0% +should be legalized unless it generates + + + align:start position:0% +should be legalized unless it generates +externalities that's essentially that + + align:start position:0% +externalities that's essentially that + + + align:start position:0% +externalities that's essentially that +will make choices + + align:start position:0% +will make choices + + + align:start position:0% +will make choices +um they make uh if jack started taking + + align:start position:0% +um they make uh if jack started taking + + + align:start position:0% +um they make uh if jack started taking +that must have been that like he + + align:start position:0% +that must have been that like he + + + align:start position:0% +that must have been that like he +hurt uh we're not taking cocaine even + + align:start position:0% +hurt uh we're not taking cocaine even + + + align:start position:0% +hurt uh we're not taking cocaine even +though there's a chance that + + align:start position:0% +though there's a chance that + + + align:start position:0% +though there's a chance that +it really addicted and really be + + align:start position:0% +it really addicted and really be + + + align:start position:0% +it really addicted and really be +miserable now + + align:start position:0% +miserable now + + + align:start position:0% +miserable now +and now even if he uh keeps taking + + align:start position:0% +and now even if he uh keeps taking + + + align:start position:0% +and now even if he uh keeps taking +cocaine + + align:start position:0% +cocaine + + + align:start position:0% +cocaine +and it's a quit well if he doesn't do it + + align:start position:0% +and it's a quit well if he doesn't do it + + + align:start position:0% +and it's a quit well if he doesn't do it +well then it must be a rational choice + + align:start position:0% +well then it must be a rational choice + + + align:start position:0% +well then it must be a rational choice +for him to to uh + + align:start position:0% +for him to to uh + + + align:start position:0% +for him to to uh +uh not because it must be that the + + align:start position:0% +uh not because it must be that the + + + align:start position:0% +uh not because it must be that the +withdrawal costs are really high + + align:start position:0% +withdrawal costs are really high + + + align:start position:0% +withdrawal costs are really high +now we talked a little bit about this uh + + align:start position:0% +now we talked a little bit about this uh + + + align:start position:0% +now we talked a little bit about this uh +theory of rational + + align:start position:0% +theory of rational + + + align:start position:0% +theory of rational +addiction much about becker and murphy + + align:start position:0% +addiction much about becker and murphy + + + align:start position:0% +addiction much about becker and murphy +we talked about already + + align:start position:0% +we talked about already + + + align:start position:0% +we talked about already +that you know there's present bias there + + align:start position:0% +that you know there's present bias there + + + align:start position:0% +that you know there's present bias there +are + + align:start position:0% +are + + + align:start position:0% +are +factors involved including biased + + align:start position:0% +factors involved including biased + + + align:start position:0% +factors involved including biased +beliefs that might not be the case + + align:start position:0% +beliefs that might not be the case + + + align:start position:0% +beliefs that might not be the case +important to sort of understand that + + align:start position:0% +important to sort of understand that + + + align:start position:0% +important to sort of understand that +like traditional economic links until + + align:start position:0% +like traditional economic links until + + + align:start position:0% +like traditional economic links until +very recently would sort of say + + align:start position:0% +very recently would sort of say + + + align:start position:0% +very recently would sort of say +definitely um rational thing to do um + + align:start position:0% +definitely um rational thing to do um + + + align:start position:0% +definitely um rational thing to do um +here in fact no good reason um + + align:start position:0% +here in fact no good reason um + + + align:start position:0% +here in fact no good reason um +to to to make + + align:start position:0% +to to to make + + + align:start position:0% +to to to make +certain or any drugs illegal unlocks + + align:start position:0% +certain or any drugs illegal unlocks + + + align:start position:0% +certain or any drugs illegal unlocks +analogies right so externalities would + + align:start position:0% +analogies right so externalities would + + + align:start position:0% +analogies right so externalities would +be like if jack causes like behavior + + align:start position:0% +be like if jack causes like behavior + + + align:start position:0% +be like if jack causes like behavior +that's bad for others + + align:start position:0% +that's bad for others + + + align:start position:0% +that's bad for others +then we shouldn't let him do that + + align:start position:0% +then we shouldn't let him do that + + + align:start position:0% +then we shouldn't let him do that +because you know other people are harmed + + align:start position:0% +because you know other people are harmed + + + align:start position:0% +because you know other people are harmed +and he might not internalize + + align:start position:0% +and he might not internalize + + + align:start position:0% +and he might not internalize +the bodies but unless that's the case um + + align:start position:0% +the bodies but unless that's the case um + + + align:start position:0% +the bodies but unless that's the case um +we should + + align:start position:0% +we should + + + align:start position:0% +we should +intervene in any ways + + align:start position:0% +intervene in any ways + + + align:start position:0% +intervene in any ways +but so now you might sort of say but but + + align:start position:0% +but so now you might sort of say but but + + + align:start position:0% +but so now you might sort of say but but +but you know + + align:start position:0% +but you know + + + align:start position:0% +but you know +what are we talking about in all of the + + align:start position:0% +what are we talking about in all of the + + + align:start position:0% +what are we talking about in all of the +thought like how is that sort of + + align:start position:0% +thought like how is that sort of + + + align:start position:0% +thought like how is that sort of +consistent with what we talked about + + align:start position:0% +consistent with what we talked about + + + align:start position:0% +consistent with what we talked about +before + + align:start position:0% +before + + + align:start position:0% +before +and at the key of that question is the + + align:start position:0% +and at the key of that question is the + + + align:start position:0% +and at the key of that question is the +question of do people act in their best + + align:start position:0% +question of do people act in their best + + + align:start position:0% +question of do people act in their best +interest and so um what we sort of + + align:start position:0% +interest and so um what we sort of + + + align:start position:0% +interest and so um what we sort of +essentially assume + + align:start position:0% +essentially assume + + + align:start position:0% +essentially assume +often is that there's sort of a rational + + align:start position:0% +often is that there's sort of a rational + + + align:start position:0% +often is that there's sort of a rational +relationship between people's choices + + align:start position:0% +relationship between people's choices + + + align:start position:0% +relationship between people's choices +what they actually do + + align:start position:0% +what they actually do + + + align:start position:0% +what they actually do +and sort of the hedonic consequences of + + align:start position:0% +and sort of the hedonic consequences of + + + align:start position:0% +and sort of the hedonic consequences of +those choices which is sort of true + + align:start position:0% +those choices which is sort of true + + + align:start position:0% +those choices which is sort of true +well-being and so what we assume is + + align:start position:0% +well-being and so what we assume is + + + align:start position:0% +well-being and so what we assume is +essentially that + + align:start position:0% +essentially that + + + align:start position:0% +essentially that +you make certain choices that maximize + + align:start position:0% +you make certain choices that maximize + + + align:start position:0% +you make certain choices that maximize +your well-being essentially what you + + align:start position:0% +your well-being essentially what you + + + align:start position:0% +your well-being essentially what you +learned in like 1401 or 1403 is + + align:start position:0% +learned in like 1401 or 1403 is + + + align:start position:0% +learned in like 1401 or 1403 is +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +utility maximization and that's at the + + align:start position:0% +utility maximization and that's at the + + + align:start position:0% +utility maximization and that's at the +heart of like uh sort of the rationale + + align:start position:0% +heart of like uh sort of the rationale + + + align:start position:0% +heart of like uh sort of the rationale +the + + align:start position:0% +the + + + align:start position:0% +the +assumptions so economists then tend to + + align:start position:0% +assumptions so economists then tend to + + + align:start position:0% +assumptions so economists then tend to +believe that most of the time people act + + align:start position:0% +believe that most of the time people act + + + align:start position:0% +believe that most of the time people act +at least approximately in their best + + align:start position:0% +at least approximately in their best + + + align:start position:0% +at least approximately in their best +interest + + align:start position:0% +interest + + + align:start position:0% +interest +um now um as we talked about already and + + align:start position:0% +um now um as we talked about already and + + + align:start position:0% +um now um as we talked about already and +this is sort of the + + align:start position:0% +this is sort of the + + + align:start position:0% +this is sort of the +our previous lecture about misfit and + + align:start position:0% +our previous lecture about misfit and + + + align:start position:0% +our previous lecture about misfit and +wilson um + + align:start position:0% +wilson um + + + align:start position:0% +wilson um +telling more than we can know we should + + align:start position:0% +telling more than we can know we should + + + align:start position:0% +telling more than we can know we should +be actually quite skeptical about the + + align:start position:0% +be actually quite skeptical about the + + + align:start position:0% +be actually quite skeptical about the +fact that people actually know what + + align:start position:0% +fact that people actually know what + + + align:start position:0% +fact that people actually know what +they're doing and why they're doing it + + align:start position:0% +they're doing and why they're doing it + + + align:start position:0% +they're doing and why they're doing it +because you + + align:start position:0% +because you + + + align:start position:0% +because you +know as i showed you last time in some + + align:start position:0% +know as i showed you last time in some + + + align:start position:0% +know as i showed you last time in some +sense people often seem to have like + + align:start position:0% +sense people often seem to have like + + + align:start position:0% +sense people often seem to have like +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +a clue of why they do what they do so it + + align:start position:0% +a clue of why they do what they do so it + + + align:start position:0% +a clue of why they do what they do so it +seems like a bit of an odd assumption to + + align:start position:0% +seems like a bit of an odd assumption to + + + align:start position:0% +seems like a bit of an odd assumption to +sort of say well + + align:start position:0% +sort of say well + + + align:start position:0% +sort of say well +people are maximizing what's best + + align:start position:0% +people are maximizing what's best + + + align:start position:0% +people are maximizing what's best +for them so now how can we check whether + + align:start position:0% +for them so now how can we check whether + + + align:start position:0% +for them so now how can we check whether +this assumption is appropriate what + + align:start position:0% +this assumption is appropriate what + + + align:start position:0% +this assumption is appropriate what +would you do so i'm telling you here's + + align:start position:0% +would you do so i'm telling you here's + + + align:start position:0% +would you do so i'm telling you here's +certain behaviors how can we actually + + align:start position:0% +certain behaviors how can we actually + + + align:start position:0% +certain behaviors how can we actually +check whether this assumption is an + + align:start position:0% +check whether this assumption is an + + + align:start position:0% +check whether this assumption is an +appropriate one + + align:start position:0% + + + + align:start position:0% + +uh lauren we could check kind of like + + align:start position:0% +uh lauren we could check kind of like + + + align:start position:0% +uh lauren we could check kind of like +their well-being + + align:start position:0% +their well-being + + + align:start position:0% +their well-being +after um they make these decisions and + + align:start position:0% +after um they make these decisions and + + + align:start position:0% +after um they make these decisions and +if they're better + + align:start position:0% +if they're better + + + align:start position:0% +if they're better +or worse off yeah we have to sort of + + align:start position:0% +or worse off yeah we have to sort of + + + align:start position:0% +or worse off yeah we have to sort of +like somehow + + align:start position:0% +like somehow + + + align:start position:0% +like somehow +figure out some situations where we can + + align:start position:0% +figure out some situations where we can + + + align:start position:0% +figure out some situations where we can +track people's well-being + + align:start position:0% +track people's well-being + + + align:start position:0% +track people's well-being +um ideally we would have sort of some + + align:start position:0% +um ideally we would have sort of some + + + align:start position:0% +um ideally we would have sort of some +sort of experiment + + align:start position:0% +sort of experiment + + + align:start position:0% +sort of experiment +uh you know there's group a b and then + + align:start position:0% +uh you know there's group a b and then + + + align:start position:0% +uh you know there's group a b and then +group a i want + + align:start position:0% +group a i want + + + align:start position:0% +group a i want +you to let them choose and then in the + + align:start position:0% +you to let them choose and then in the + + + align:start position:0% +you to let them choose and then in the +other groups we or maybe there's + + align:start position:0% +other groups we or maybe there's + + + align:start position:0% +other groups we or maybe there's +a group c in some group we essentially + + align:start position:0% +a group c in some group we essentially + + + align:start position:0% +a group c in some group we essentially +tell people + + align:start position:0% +tell people + + + align:start position:0% +tell people +you should be doing a uh doing one thing + + align:start position:0% +you should be doing a uh doing one thing + + + align:start position:0% +you should be doing a uh doing one thing +and another group we say you should do + + align:start position:0% +and another group we say you should do + + + align:start position:0% +and another group we say you should do +another thing and then there's another + + align:start position:0% +another thing and then there's another + + + align:start position:0% +another thing and then there's another +group where we have people essentially + + align:start position:0% +group where we have people essentially + + + align:start position:0% +group where we have people essentially +choose and then you can look at like + + align:start position:0% +choose and then you can look at like + + + align:start position:0% +choose and then you can look at like +track people's well-being + + align:start position:0% +track people's well-being + + + align:start position:0% +track people's well-being +and then we could sort of figure out is + + align:start position:0% +and then we could sort of figure out is + + + align:start position:0% +and then we could sort of figure out is +the group that gets to choose actually + + align:start position:0% +the group that gets to choose actually + + + align:start position:0% +the group that gets to choose actually +doing better than maybe some groups so + + align:start position:0% +doing better than maybe some groups so + + + align:start position:0% +doing better than maybe some groups so +we actually just tell them + + align:start position:0% +we actually just tell them + + + align:start position:0% +we actually just tell them +what to do if in some ways or the + + align:start position:0% +what to do if in some ways or the + + + align:start position:0% +what to do if in some ways or the +[Music] + + align:start position:0% + + + + align:start position:0% + +if i can essentially manipulate you into + + align:start position:0% +if i can essentially manipulate you into + + + align:start position:0% +if i can essentially manipulate you into +making very drastically different + + align:start position:0% +making very drastically different + + + align:start position:0% +making very drastically different +choices by changing like small things + + align:start position:0% +choices by changing like small things + + + align:start position:0% +choices by changing like small things +that really arguably should be + + align:start position:0% +that really arguably should be + + + align:start position:0% +that really arguably should be +irrelevant for your choice + + align:start position:0% +irrelevant for your choice + + + align:start position:0% +irrelevant for your choice +like for example the social security + + align:start position:0% +like for example the social security + + + align:start position:0% +like for example the social security +number like for example + + align:start position:0% +number like for example + + + align:start position:0% +number like for example +if i could manipulate you with like + + align:start position:0% +if i could manipulate you with like + + + align:start position:0% +if i could manipulate you with like +anchoring you with your social security + + align:start position:0% +anchoring you with your social security + + + align:start position:0% +anchoring you with your social security +number and then say + + align:start position:0% +number and then say + + + align:start position:0% +number and then say +would you like to purchase this item for + + align:start position:0% +would you like to purchase this item for + + + align:start position:0% +would you like to purchase this item for +ten dollars yes or no + + align:start position:0% +ten dollars yes or no + + + align:start position:0% +ten dollars yes or no +and that affects your choice well then + + align:start position:0% +and that affects your choice well then + + + align:start position:0% +and that affects your choice well then +presumably that's a clue in some ways + + align:start position:0% +presumably that's a clue in some ways + + + align:start position:0% +presumably that's a clue in some ways +that like + + align:start position:0% +that like + + + align:start position:0% +that like +that something is not going right and so + + align:start position:0% +that something is not going right and so + + + align:start position:0% +that something is not going right and so +you're you're not necessarily optimizing + + align:start position:0% +you're you're not necessarily optimizing + + + align:start position:0% +you're you're not necessarily optimizing +because precisely because + + align:start position:0% +because precisely because + + + align:start position:0% +because precisely because +the social security number really should + + align:start position:0% +the social security number really should + + + align:start position:0% +the social security number really should +be entirely irrelevant arguably + + align:start position:0% +be entirely irrelevant arguably + + + align:start position:0% +be entirely irrelevant arguably +some forms of who we talked about like + + align:start position:0% +some forms of who we talked about like + + + align:start position:0% +some forms of who we talked about like +preference reversal or some form of like + + align:start position:0% +preference reversal or some form of like + + + align:start position:0% +preference reversal or some form of like +demand from commitment or like + + align:start position:0% +demand from commitment or like + + + align:start position:0% +demand from commitment or like +if that's the case it seems to be that + + align:start position:0% +if that's the case it seems to be that + + + align:start position:0% +if that's the case it seems to be that +then there's self-control problems + + align:start position:0% +then there's self-control problems + + + align:start position:0% +then there's self-control problems +involved or like biased beliefs in + + align:start position:0% +involved or like biased beliefs in + + + align:start position:0% +involved or like biased beliefs in +various ways that we all talked about + + align:start position:0% +various ways that we all talked about + + + align:start position:0% +various ways that we all talked about +which should have seems then to say well + + align:start position:0% +which should have seems then to say well + + + align:start position:0% +which should have seems then to say well +you keep saying you want one thing you + + align:start position:0% +you keep saying you want one thing you + + + align:start position:0% +you keep saying you want one thing you +keep even like spending money on like + + align:start position:0% +keep even like spending money on like + + + align:start position:0% +keep even like spending money on like +say healthy eating but then like you + + align:start position:0% +say healthy eating but then like you + + + align:start position:0% +say healthy eating but then like you +never uh + + align:start position:0% +never uh + + + align:start position:0% +never uh +the food all goes bad in your fridge and + + align:start position:0% +the food all goes bad in your fridge and + + + align:start position:0% +the food all goes bad in your fridge and +you keep eating like donuts + + align:start position:0% +you keep eating like donuts + + + align:start position:0% +you keep eating like donuts +that seems to be something that's not + + align:start position:0% +that seems to be something that's not + + + align:start position:0% +that seems to be something that's not +quite you don't seem to be maximizing uh + + align:start position:0% +quite you don't seem to be maximizing uh + + + align:start position:0% +quite you don't seem to be maximizing uh +your utility but in general it would be + + align:start position:0% +your utility but in general it would be + + + align:start position:0% +your utility but in general it would be +great if you could measure behavior and + + align:start position:0% +great if you could measure behavior and + + + align:start position:0% +great if you could measure behavior and +then the addonic consequences of those + + align:start position:0% +then the addonic consequences of those + + + align:start position:0% +then the addonic consequences of those +behaviors people's well-being + + align:start position:0% +behaviors people's well-being + + + align:start position:0% +behaviors people's well-being +and if you can then could say well + + align:start position:0% +and if you can then could say well + + + align:start position:0% +and if you can then could say well +option a or option b is better + + align:start position:0% +option a or option b is better + + + align:start position:0% +option a or option b is better +for people in general or specifically + + align:start position:0% +for people in general or specifically + + + align:start position:0% +for people in general or specifically +when you ask them to choose they can + + align:start position:0% +when you ask them to choose they can + + + align:start position:0% +when you ask them to choose they can +sort of figure out what's best + + align:start position:0% +sort of figure out what's best + + + align:start position:0% +sort of figure out what's best +for them notice that you need to know + + align:start position:0% +for them notice that you need to know + + + align:start position:0% +for them notice that you need to know +sort of become a factual here + + align:start position:0% +sort of become a factual here + + + align:start position:0% +sort of become a factual here +you can't like if i see you doing one + + align:start position:0% +you can't like if i see you doing one + + + align:start position:0% +you can't like if i see you doing one +thing and then track your well-being + + align:start position:0% +thing and then track your well-being + + + align:start position:0% +thing and then track your well-being +that doesn't it's not enough because you + + align:start position:0% +that doesn't it's not enough because you + + + align:start position:0% +that doesn't it's not enough because you +know i don't know the kind of actual + + align:start position:0% +know i don't know the kind of actual + + + align:start position:0% +know i don't know the kind of actual +whether you would be happy otherwise if + + align:start position:0% +whether you would be happy otherwise if + + + align:start position:0% +whether you would be happy otherwise if +you were not to choose that + + align:start position:0% +you were not to choose that + + + align:start position:0% +you were not to choose that +okay so so um a great idea + + align:start position:0% +okay so so um a great idea + + + align:start position:0% +okay so so um a great idea +um so now how do we actually do that so + + align:start position:0% +um so now how do we actually do that so + + + align:start position:0% +um so now how do we actually do that so +uh it's useful to have some terminology + + align:start position:0% +uh it's useful to have some terminology + + + align:start position:0% +uh it's useful to have some terminology +here + + align:start position:0% +here + + + align:start position:0% +here +um uh uh that in particular then + + align:start position:0% +um uh uh that in particular then + + + align:start position:0% +um uh uh that in particular then +mccanniman + + align:start position:0% +mccanniman + + + align:start position:0% +mccanniman +and others have introduced it and kind + + align:start position:0% +and others have introduced it and kind + + + align:start position:0% +and others have introduced it and kind +of one remember this is from + + align:start position:0% +of one remember this is from + + + align:start position:0% +of one remember this is from +tourist bin first skin condiment the + + align:start position:0% +tourist bin first skin condiment the + + + align:start position:0% +tourist bin first skin condiment the +nobel prize winner um + + align:start position:0% +nobel prize winner um + + + align:start position:0% +nobel prize winner um +who worked a lot on uh uh lots of + + align:start position:0% +who worked a lot on uh uh lots of + + + align:start position:0% +who worked a lot on uh uh lots of +version prospect theory that we talked + + align:start position:0% +version prospect theory that we talked + + + align:start position:0% +version prospect theory that we talked +about + + align:start position:0% +about + + + align:start position:0% +about +the economy and also has quite a bit of + + align:start position:0% +the economy and also has quite a bit of + + + align:start position:0% +the economy and also has quite a bit of +work on well-being and happiness + + align:start position:0% +work on well-being and happiness + + + align:start position:0% +work on well-being and happiness +and so on so and he introduced this very + + align:start position:0% +and so on so and he introduced this very + + + align:start position:0% +and so on so and he introduced this very +useful technology terminology which is + + align:start position:0% +useful technology terminology which is + + + align:start position:0% +useful technology terminology which is +they call like + + align:start position:0% +they call like + + + align:start position:0% +they call like +uh decision utility and experience + + align:start position:0% +uh decision utility and experience + + + align:start position:0% +uh decision utility and experience +utility so now what's decision utility + + align:start position:0% +utility so now what's decision utility + + + align:start position:0% +utility so now what's decision utility +so economists tend to use the word + + align:start position:0% +so economists tend to use the word + + + align:start position:0% +so economists tend to use the word +utility or utility function + + align:start position:0% +utility or utility function + + + align:start position:0% +utility or utility function +to describe the preferences that + + align:start position:0% +to describe the preferences that + + + align:start position:0% +to describe the preferences that +rationalize observed choices right + + align:start position:0% +rationalize observed choices right + + + align:start position:0% +rationalize observed choices right +that's essentially if you took 1401 1423 + + align:start position:0% +that's essentially if you took 1401 1423 + + + align:start position:0% +that's essentially if you took 1401 1423 +etc + + align:start position:0% +etc + + + align:start position:0% +etc +people talk about the utility function + + align:start position:0% +people talk about the utility function + + + align:start position:0% +people talk about the utility function +essentially it's the function + + align:start position:0% +essentially it's the function + + + align:start position:0% +essentially it's the function +that you write down that sort of maps + + align:start position:0% +that you write down that sort of maps + + + align:start position:0% +that you write down that sort of maps +your + + align:start position:0% +your + + + align:start position:0% +your +um choices into well-being + + align:start position:0% +um choices into well-being + + + align:start position:0% +um choices into well-being +and the function that you maximize or by + + align:start position:0% +and the function that you maximize or by + + + align:start position:0% +and the function that you maximize or by +maximizing essentially say + + align:start position:0% +maximizing essentially say + + + align:start position:0% +maximizing essentially say +well given this utility function um + + align:start position:0% +well given this utility function um + + + align:start position:0% +well given this utility function um +given your behavior it must be sort of + + align:start position:0% +given your behavior it must be sort of + + + align:start position:0% +given your behavior it must be sort of +this utility function is that or that + + align:start position:0% +this utility function is that or that + + + align:start position:0% +this utility function is that or that +utility function allows me to + + align:start position:0% +utility function allows me to + + + align:start position:0% +utility function allows me to +rationalize what you're doing + + align:start position:0% +rationalize what you're doing + + + align:start position:0% +rationalize what you're doing +and that allows me then sort of to + + align:start position:0% +and that allows me then sort of to + + + align:start position:0% +and that allows me then sort of to +explain where you choose apple silver + + align:start position:0% +explain where you choose apple silver + + + align:start position:0% +explain where you choose apple silver +bananas + + align:start position:0% +bananas + + + align:start position:0% +bananas +and um so kind of one calls these + + align:start position:0% +and um so kind of one calls these + + + align:start position:0% +and um so kind of one calls these +revealed preferences this decision + + align:start position:0% +revealed preferences this decision + + + align:start position:0% +revealed preferences this decision +utility + + align:start position:0% +utility + + + align:start position:0% +utility +that's essentially the preferences that + + align:start position:0% +that's essentially the preferences that + + + align:start position:0% +that's essentially the preferences that +rationalize decisions when people make + + align:start position:0% +rationalize decisions when people make + + + align:start position:0% +rationalize decisions when people make +choices + + align:start position:0% +choices + + + align:start position:0% +choices +uh that's the utility that they perceive + + align:start position:0% +uh that's the utility that they perceive + + + align:start position:0% +uh that's the utility that they perceive +or that they think they will perceive + + align:start position:0% +or that they think they will perceive + + + align:start position:0% +or that they think they will perceive +or receive as a consequence of their + + align:start position:0% +or receive as a consequence of their + + + align:start position:0% +or receive as a consequence of their +choices + + align:start position:0% +choices + + + align:start position:0% +choices +that's essentially uh you might call it + + align:start position:0% +that's essentially uh you might call it + + + align:start position:0% +that's essentially uh you might call it +like wanting or + + align:start position:0% +like wanting or + + + align:start position:0% +like wanting or +um choosing so + + align:start position:0% +um choosing so + + + align:start position:0% +um choosing so +concretely for an addict the decision + + align:start position:0% +concretely for an addict the decision + + + align:start position:0% +concretely for an addict the decision +utility of drug consumption exceeds the + + align:start position:0% +utility of drug consumption exceeds the + + + align:start position:0% +utility of drug consumption exceeds the +um decision utility of quitting so uh + + align:start position:0% +um decision utility of quitting so uh + + + align:start position:0% +um decision utility of quitting so uh +if that person makes the decision of of + + align:start position:0% +if that person makes the decision of of + + + align:start position:0% +if that person makes the decision of of +taking drugs um + + align:start position:0% +taking drugs um + + + align:start position:0% +taking drugs um +it must be that uh their decision + + align:start position:0% +it must be that uh their decision + + + align:start position:0% +it must be that uh their decision +utility is is higher when making those + + align:start position:0% +utility is is higher when making those + + + align:start position:0% +utility is is higher when making those +choices + + align:start position:0% +choices + + + align:start position:0% +choices +um uh uh uh they prefer one option over + + align:start position:0% +um uh uh uh they prefer one option over + + + align:start position:0% +um uh uh uh they prefer one option over +the other + + align:start position:0% +the other + + + align:start position:0% +the other +which again doesn't necessarily then + + align:start position:0% +which again doesn't necessarily then + + + align:start position:0% +which again doesn't necessarily then +mean that like afterwards the experience + + align:start position:0% +mean that like afterwards the experience + + + align:start position:0% +mean that like afterwards the experience +is actually better but when making the + + align:start position:0% +is actually better but when making the + + + align:start position:0% +is actually better but when making the +choice of taking the dog they think + + align:start position:0% +choice of taking the dog they think + + + align:start position:0% +choice of taking the dog they think +that's a better option + + align:start position:0% +that's a better option + + + align:start position:0% +that's a better option +for them now uh in contrast hanuman also + + align:start position:0% +for them now uh in contrast hanuman also + + + align:start position:0% +for them now uh in contrast hanuman also +talks about + + align:start position:0% +talks about + + + align:start position:0% +talks about +experience utility which toxic which + + align:start position:0% +experience utility which toxic which + + + align:start position:0% +experience utility which toxic which +sort of implies or talks about the + + align:start position:0% +sort of implies or talks about the + + + align:start position:0% +sort of implies or talks about the +hedonic consequences of choices + + align:start position:0% +hedonic consequences of choices + + + align:start position:0% +hedonic consequences of choices +uh he calls these hedonic experiences uh + + align:start position:0% +uh he calls these hedonic experiences uh + + + align:start position:0% +uh he calls these hedonic experiences uh +experience utility that's essentially + + align:start position:0% +experience utility that's essentially + + + align:start position:0% +experience utility that's essentially +the the preferences that coincide with + + align:start position:0% +the the preferences that coincide with + + + align:start position:0% +the the preferences that coincide with +doing so while you actually sort of + + align:start position:0% +doing so while you actually sort of + + + align:start position:0% +doing so while you actually sort of +experience the whole consequences of + + align:start position:0% +experience the whole consequences of + + + align:start position:0% +experience the whole consequences of +your choice + + align:start position:0% +your choice + + + align:start position:0% +your choice +what experience do you have a good + + align:start position:0% +what experience do you have a good + + + align:start position:0% +what experience do you have a good +utility or what's your well-being during + + align:start position:0% +utility or what's your well-being during + + + align:start position:0% +utility or what's your well-being during +that + + align:start position:0% +that + + + align:start position:0% +that +that's actually going back a long time + + align:start position:0% +that's actually going back a long time + + + align:start position:0% +that's actually going back a long time +ago if you look at sort of some of the + + align:start position:0% +ago if you look at sort of some of the + + + align:start position:0% +ago if you look at sort of some of the +important economics or bentham and + + align:start position:0% +important economics or bentham and + + + align:start position:0% +important economics or bentham and +others so if they thought that they talk + + align:start position:0% +others so if they thought that they talk + + + align:start position:0% +others so if they thought that they talk +a lot about pleasure and pain + + align:start position:0% +a lot about pleasure and pain + + + align:start position:0% +a lot about pleasure and pain +which is very much about the experience + + align:start position:0% +which is very much about the experience + + + align:start position:0% +which is very much about the experience +people have in their life + + align:start position:0% +people have in their life + + + align:start position:0% +people have in their life +as opposed to utility which is again the + + align:start position:0% +as opposed to utility which is again the + + + align:start position:0% +as opposed to utility which is again the +construct that you have + + align:start position:0% +construct that you have + + + align:start position:0% +construct that you have +at the time of um business um + + align:start position:0% +at the time of um business um + + + align:start position:0% +at the time of um business um +how do we measure sort of these sadonic + + align:start position:0% +how do we measure sort of these sadonic + + + align:start position:0% +how do we measure sort of these sadonic +experiences so well being + + align:start position:0% +experiences so well being + + + align:start position:0% +experiences so well being +um and then so there's two questions i + + align:start position:0% +um and then so there's two questions i + + + align:start position:0% +um and then so there's two questions i +guess one is how can we measure this + + align:start position:0% +guess one is how can we measure this + + + align:start position:0% +guess one is how can we measure this +if i wanted to know what is your hedonic + + align:start position:0% +if i wanted to know what is your hedonic + + + align:start position:0% +if i wanted to know what is your hedonic +experiences of this lecture right now + + align:start position:0% +experiences of this lecture right now + + + align:start position:0% +experiences of this lecture right now +how would i do this uh like how do you + + align:start position:0% +how would i do this uh like how do you + + + align:start position:0% +how would i do this uh like how do you +enjoy how much do you enjoy things and + + align:start position:0% +enjoy how much do you enjoy things and + + + align:start position:0% +enjoy how much do you enjoy things and +then second + + align:start position:0% +then second + + + align:start position:0% +then second +well i can sort of measure your + + align:start position:0% +well i can sort of measure your + + + align:start position:0% +well i can sort of measure your +experience right now maybe this moment + + align:start position:0% +experience right now maybe this moment + + + align:start position:0% +experience right now maybe this moment +maybe this hour + + align:start position:0% +maybe this hour + + + align:start position:0% +maybe this hour +but somehow i need to aggregate this + + align:start position:0% +but somehow i need to aggregate this + + + align:start position:0% +but somehow i need to aggregate this +over time right i need to know + + align:start position:0% +over time right i need to know + + + align:start position:0% +over time right i need to know +like you took class a versus class b + + align:start position:0% +like you took class a versus class b + + + align:start position:0% +like you took class a versus class b +now i can measure you at different + + align:start position:0% +now i can measure you at different + + + align:start position:0% +now i can measure you at different +points in time but somehow then i need + + align:start position:0% +points in time but somehow then i need + + + align:start position:0% +points in time but somehow then i need +to sort of aggregate this overall + + align:start position:0% +to sort of aggregate this overall + + + align:start position:0% +to sort of aggregate this overall +experience + + align:start position:0% +experience + + + align:start position:0% +experience +and how people are doing that separate + + align:start position:0% +and how people are doing that separate + + + align:start position:0% +and how people are doing that separate +questions let's start with the first + + align:start position:0% +questions let's start with the first + + + align:start position:0% +questions let's start with the first +question + + align:start position:0% +question + + + align:start position:0% +question +how do we measure people's um well-being + + align:start position:0% +how do we measure people's um well-being + + + align:start position:0% +how do we measure people's um well-being +if you wanted to like learn about your + + align:start position:0% +if you wanted to like learn about your + + + align:start position:0% +if you wanted to like learn about your +classmates uh experience in any + + align:start position:0% +classmates uh experience in any + + + align:start position:0% +classmates uh experience in any +type of situations what would you do + + align:start position:0% +type of situations what would you do + + + align:start position:0% +type of situations what would you do +what would you measure + + align:start position:0% +what would you measure + + + align:start position:0% +what would you measure +one is you could ask them verbally like + + align:start position:0% +one is you could ask them verbally like + + + align:start position:0% +one is you could ask them verbally like +uh how did you like activity a + + align:start position:0% +uh how did you like activity a + + + align:start position:0% +uh how did you like activity a +how do you like b or like you feel now + + align:start position:0% +how do you like b or like you feel now + + + align:start position:0% +how do you like b or like you feel now +right so this is like asking what people + + align:start position:0% +right so this is like asking what people + + + align:start position:0% +right so this is like asking what people +want you could also just look at + + align:start position:0% +want you could also just look at + + + align:start position:0% +want you could also just look at +um their facial features or they like + + align:start position:0% +um their facial features or they like + + + align:start position:0% +um their facial features or they like +um and try to see how uh + + align:start position:0% +um and try to see how uh + + + align:start position:0% +um and try to see how uh +how much they're smiling or or like + + align:start position:0% +how much they're smiling or or like + + + align:start position:0% +how much they're smiling or or like +notice that that you need to sort of map + + align:start position:0% +notice that that you need to sort of map + + + align:start position:0% +notice that that you need to sort of map +into some happiness as well + + align:start position:0% +into some happiness as well + + + align:start position:0% +into some happiness as well +right in some sense i could be smiling + + align:start position:0% +right in some sense i could be smiling + + + align:start position:0% +right in some sense i could be smiling +but be deeply unhappy + + align:start position:0% +but be deeply unhappy + + + align:start position:0% +but be deeply unhappy +um and if you would sort of misinterpret + + align:start position:0% +um and if you would sort of misinterpret + + + align:start position:0% +um and if you would sort of misinterpret +that so you'd have to sort of have some + + align:start position:0% +that so you'd have to sort of have some + + + align:start position:0% +that so you'd have to sort of have some +function + + align:start position:0% +function + + + align:start position:0% +function +from facial feature to sort of some + + align:start position:0% +from facial feature to sort of some + + + align:start position:0% +from facial feature to sort of some +underlying well-being that's + + align:start position:0% +underlying well-being that's + + + align:start position:0% +underlying well-being that's +somewhat grounded in some assumptions it + + align:start position:0% +somewhat grounded in some assumptions it + + + align:start position:0% +somewhat grounded in some assumptions it +seems like reasonable to think that when + + align:start position:0% +seems like reasonable to think that when + + + align:start position:0% +seems like reasonable to think that when +people are smiling they're happy and + + align:start position:0% +people are smiling they're happy and + + + align:start position:0% +people are smiling they're happy and +when they're crying they're unhappy + + align:start position:0% +when they're crying they're unhappy + + + align:start position:0% +when they're crying they're unhappy +but but i'm just sort of pointing out + + align:start position:0% +but but i'm just sort of pointing out + + + align:start position:0% +but but i'm just sort of pointing out +that that's that + + align:start position:0% +that that's that + + + align:start position:0% +that that's that +requires some underlying data to be able + + align:start position:0% +requires some underlying data to be able + + + align:start position:0% +requires some underlying data to be able +to map those things one is + + align:start position:0% +to map those things one is + + + align:start position:0% +to map those things one is +um this sort of physicological measures + + align:start position:0% +um this sort of physicological measures + + + align:start position:0% +um this sort of physicological measures +such as heart rates + + align:start position:0% +such as heart rates + + + align:start position:0% +such as heart rates +uh uh et cetera or and so there + + align:start position:0% +uh uh et cetera or and so there + + + align:start position:0% +uh uh et cetera or and so there +um again i think some common sensical + + align:start position:0% +um again i think some common sensical + + + align:start position:0% +um again i think some common sensical +stuff like if you're hardcore + + align:start position:0% +stuff like if you're hardcore + + + align:start position:0% +stuff like if you're hardcore +if you're really afraid and like your + + align:start position:0% +if you're really afraid and like your + + + align:start position:0% +if you're really afraid and like your +heart rate goes up presumably that's not + + align:start position:0% +heart rate goes up presumably that's not + + + align:start position:0% +heart rate goes up presumably that's not +a good thing + + align:start position:0% +a good thing + + + align:start position:0% +a good thing +but if you're really excited and your + + align:start position:0% +but if you're really excited and your + + + align:start position:0% +but if you're really excited and your +heart rate goes up um i presume that's a + + align:start position:0% +heart rate goes up um i presume that's a + + + align:start position:0% +heart rate goes up um i presume that's a +good thing so one has to sort of + + align:start position:0% +good thing so one has to sort of + + + align:start position:0% +good thing so one has to sort of +add some assumptions or some structure + + align:start position:0% +add some assumptions or some structure + + + align:start position:0% +add some assumptions or some structure +on sort of these measures and sometimes + + align:start position:0% +on sort of these measures and sometimes + + + align:start position:0% +on sort of these measures and sometimes +you're sort of just + + align:start position:0% +you're sort of just + + + align:start position:0% +you're sort of just +measuring them by themselves uh in + + align:start position:0% +measuring them by themselves uh in + + + align:start position:0% +measuring them by themselves uh in +general it might + + align:start position:0% +general it might + + + align:start position:0% +general it might +be misleading but with some structures + + align:start position:0% +be misleading but with some structures + + + align:start position:0% +be misleading but with some structures +really one could sort of uh + + align:start position:0% +really one could sort of uh + + + align:start position:0% +really one could sort of uh +use that well the other part is + + align:start position:0% +use that well the other part is + + + align:start position:0% +use that well the other part is +measuring there's lots of neuroscience + + align:start position:0% +measuring there's lots of neuroscience + + + align:start position:0% +measuring there's lots of neuroscience +and other + + align:start position:0% +and other + + + align:start position:0% +and other +work on this measuring people's brain + + align:start position:0% +work on this measuring people's brain + + + align:start position:0% +work on this measuring people's brain +and parts of the brain and seeing sort + + align:start position:0% +and parts of the brain and seeing sort + + + align:start position:0% +and parts of the brain and seeing sort +of which parts light up + + align:start position:0% +of which parts light up + + + align:start position:0% +of which parts light up +at which times um uh it could be another + + align:start position:0% +at which times um uh it could be another + + + align:start position:0% +at which times um uh it could be another +option + + align:start position:0% +option + + + align:start position:0% +option +of course again there you need to sort + + align:start position:0% +of course again there you need to sort + + + align:start position:0% +of course again there you need to sort +of map that into something else + + align:start position:0% +of map that into something else + + + align:start position:0% +of map that into something else +right so you need to be able to say + + align:start position:0% +right so you need to be able to say + + + align:start position:0% +right so you need to be able to say +suppose i do something nice for you + + align:start position:0% +suppose i do something nice for you + + + align:start position:0% +suppose i do something nice for you +or there's just something mean i can + + align:start position:0% +or there's just something mean i can + + + align:start position:0% +or there's just something mean i can +then sort of + + align:start position:0% +then sort of + + + align:start position:0% +then sort of +figure out which parts of the brain are + + align:start position:0% +figure out which parts of the brain are + + + align:start position:0% +figure out which parts of the brain are +are um affected + + align:start position:0% +are um affected + + + align:start position:0% +are um affected +and then i could sort of use that then + + align:start position:0% +and then i could sort of use that then + + + align:start position:0% +and then i could sort of use that then +just sort of later now if i wanted to + + align:start position:0% +just sort of later now if i wanted to + + + align:start position:0% +just sort of later now if i wanted to +figure out whether + + align:start position:0% +figure out whether + + + align:start position:0% +figure out whether +suppose i could measure your uh brains + + align:start position:0% +suppose i could measure your uh brains + + + align:start position:0% +suppose i could measure your uh brains +during lecture if i figured out earlier + + align:start position:0% +during lecture if i figured out earlier + + + align:start position:0% +during lecture if i figured out earlier +which parts of the brain are associated + + align:start position:0% +which parts of the brain are associated + + + align:start position:0% +which parts of the brain are associated +with happy versus unhappy things and now + + align:start position:0% +with happy versus unhappy things and now + + + align:start position:0% +with happy versus unhappy things and now +i could see like what your brains are + + align:start position:0% +i could see like what your brains are + + + align:start position:0% +i could see like what your brains are +doing during lecture i could then figure + + align:start position:0% +doing during lecture i could then figure + + + align:start position:0% +doing during lecture i could then figure +out whether you're happy or unhappy + + align:start position:0% +out whether you're happy or unhappy + + + align:start position:0% +out whether you're happy or unhappy +but notice you need to have some mapping + + align:start position:0% +but notice you need to have some mapping + + + align:start position:0% +but notice you need to have some mapping +because otherwise uh it's hard to + + align:start position:0% +because otherwise uh it's hard to + + + align:start position:0% +because otherwise uh it's hard to +interpret + + align:start position:0% +interpret + + + align:start position:0% +interpret +um what's going on but of course people + + align:start position:0% +um what's going on but of course people + + + align:start position:0% +um what's going on but of course people +have um + + align:start position:0% +have um + + + align:start position:0% +have um +already worked a lot on that that kind + + align:start position:0% +already worked a lot on that that kind + + + align:start position:0% +already worked a lot on that that kind +of mapping just to be clear so the + + align:start position:0% +of mapping just to be clear so the + + + align:start position:0% +of mapping just to be clear so the +the real preference measures + + align:start position:0% +the real preference measures + + + align:start position:0% +the real preference measures +are um let me just + + align:start position:0% +are um let me just + + + align:start position:0% +are um let me just +show you what i have here but the real + + align:start position:0% +show you what i have here but the real + + + align:start position:0% +show you what i have here but the real +preference measures are + + align:start position:0% +preference measures are + + + align:start position:0% +preference measures are +useful for some things but in a way if + + align:start position:0% +useful for some things but in a way if + + + align:start position:0% +useful for some things but in a way if +you wanted to sort of + + align:start position:0% +you wanted to sort of + + + align:start position:0% +you wanted to sort of +measure whether revealed preferences + + align:start position:0% +measure whether revealed preferences + + + align:start position:0% +measure whether revealed preferences +give you a good answer then of course + + align:start position:0% +give you a good answer then of course + + + align:start position:0% +give you a good answer then of course +the real preference measure + + align:start position:0% +the real preference measure + + + align:start position:0% +the real preference measure +uh uh is not helpful or but differently + + align:start position:0% +uh uh is not helpful or but differently + + + align:start position:0% +uh uh is not helpful or but differently +like + + align:start position:0% +like + + + align:start position:0% +like +you kind of want to check precisely like + + align:start position:0% +you kind of want to check precisely like + + + align:start position:0% +you kind of want to check precisely like +if i get you suppose i + + align:start position:0% +if i get you suppose i + + + align:start position:0% +if i get you suppose i +ask you like do you want lecture a or + + align:start position:0% +ask you like do you want lecture a or + + + align:start position:0% +ask you like do you want lecture a or +lecture b um + + align:start position:0% +lecture b um + + + align:start position:0% +lecture b um +and then you everybody says they want + + align:start position:0% +and then you everybody says they want + + + align:start position:0% +and then you everybody says they want +lecture a or like whatever but a or good + + align:start position:0% +lecture a or like whatever but a or good + + + align:start position:0% +lecture a or like whatever but a or good +b and everybody says they want good a + + align:start position:0% +b and everybody says they want good a + + + align:start position:0% +b and everybody says they want good a +uh the econ assumption is by real + + align:start position:0% +uh the econ assumption is by real + + + align:start position:0% +uh the econ assumption is by real +preference + + align:start position:0% +preference + + + align:start position:0% +preference +they must be that a makes you happier + + align:start position:0% +they must be that a makes you happier + + + align:start position:0% +they must be that a makes you happier +than b + + align:start position:0% +than b + + + align:start position:0% +than b +but if i wanted to test is that actually + + align:start position:0% +but if i wanted to test is that actually + + + align:start position:0% +but if i wanted to test is that actually +true + + align:start position:0% +true + + + align:start position:0% +true +then i need to have your revealed + + align:start position:0% +then i need to have your revealed + + + align:start position:0% +then i need to have your revealed +preference but then you also need to + + align:start position:0% +preference but then you also need to + + + align:start position:0% +preference but then you also need to +know your counter factual in some sense + + align:start position:0% +know your counter factual in some sense + + + align:start position:0% +know your counter factual in some sense +once i give you a good a and i give you + + align:start position:0% +once i give you a good a and i give you + + + align:start position:0% +once i give you a good a and i give you +good b + + align:start position:0% +good b + + + align:start position:0% +good b +how'd that make you and then i can sort + + align:start position:0% +how'd that make you and then i can sort + + + align:start position:0% +how'd that make you and then i can sort +of so i need the measures that here have + + align:start position:0% +of so i need the measures that here have + + + align:start position:0% +of so i need the measures that here have +here in the slides a version of that + + align:start position:0% +here in the slides a version of that + + + align:start position:0% +here in the slides a version of that +sort of say okay i'm going to look at + + align:start position:0% +sort of say okay i'm going to look at + + + align:start position:0% +sort of say okay i'm going to look at +your facial expression and see how happy + + align:start position:0% +your facial expression and see how happy + + + align:start position:0% +your facial expression and see how happy +you look when i give you good a versus + + align:start position:0% +you look when i give you good a versus + + + align:start position:0% +you look when i give you good a versus +could be + + align:start position:0% +could be + + + align:start position:0% +could be +or look at your brain and see which + + align:start position:0% +or look at your brain and see which + + + align:start position:0% +or look at your brain and see which +parts do the pleasure parts of your + + align:start position:0% +parts do the pleasure parts of your + + + align:start position:0% +parts do the pleasure parts of your +brain + + align:start position:0% +brain + + + align:start position:0% +brain +light up and if that's the case i'm + + align:start position:0% +light up and if that's the case i'm + + + align:start position:0% +light up and if that's the case i'm +going to conclude that you're happier + + align:start position:0% +going to conclude that you're happier + + + align:start position:0% +going to conclude that you're happier +with good a + + align:start position:0% +with good a + + + align:start position:0% +with good a +versus good b or that's more so the case + + align:start position:0% +versus good b or that's more so the case + + + align:start position:0% +versus good b or that's more so the case +for good a + + align:start position:0% +for good a + + + align:start position:0% +for good a +and then i can look at like you reveal + + align:start position:0% +and then i can look at like you reveal + + + align:start position:0% +and then i can look at like you reveal +preference is it really the case that + + align:start position:0% +preference is it really the case that + + + align:start position:0% +preference is it really the case that +like you choose a + + align:start position:0% +like you choose a + + + align:start position:0% +like you choose a +over b if the uh sort of experienced + + align:start position:0% +over b if the uh sort of experienced + + + align:start position:0% +over b if the uh sort of experienced +utility sort of says + + align:start position:0% +utility sort of says + + + align:start position:0% +utility sort of says +um a makes you happier than b does that + + align:start position:0% +um a makes you happier than b does that + + + align:start position:0% +um a makes you happier than b does that +make sense + + align:start position:0% + + + + align:start position:0% + +okay so what are the what are these uh + + align:start position:0% +okay so what are the what are these uh + + + align:start position:0% +okay so what are the what are these uh +techniques + + align:start position:0% +techniques + + + align:start position:0% +techniques +i think we covered most of there's the + + align:start position:0% +i think we covered most of there's the + + + align:start position:0% +i think we covered most of there's the +observer ratings facial men + + align:start position:0% +observer ratings facial men + + + align:start position:0% +observer ratings facial men +uh uh reports of mood pain pleasure + + align:start position:0% +uh uh reports of mood pain pleasure + + + align:start position:0% +uh uh reports of mood pain pleasure +happiness and so on this is what + + align:start position:0% +happiness and so on this is what + + + align:start position:0% +happiness and so on this is what +saying that uh uh + + align:start position:0% +saying that uh uh + + + align:start position:0% +saying that uh uh +autonomic measures with you know is uh + + align:start position:0% +autonomic measures with you know is uh + + + align:start position:0% +autonomic measures with you know is uh +the respiratory concealer your blood + + align:start position:0% +the respiratory concealer your blood + + + align:start position:0% +the respiratory concealer your blood +pressure or like your sorry your pulse + + align:start position:0% +pressure or like your sorry your pulse + + + align:start position:0% +pressure or like your sorry your pulse +and so on and so forth + + align:start position:0% +and so on and so forth + + + align:start position:0% +and so on and so forth +sweat um there's vocal measures as well + + align:start position:0% +sweat um there's vocal measures as well + + + align:start position:0% +sweat um there's vocal measures as well +which is like pitch loudness tone and + + align:start position:0% +which is like pitch loudness tone and + + + align:start position:0% +which is like pitch loudness tone and +you can probably detect whether somebody + + align:start position:0% +you can probably detect whether somebody + + + align:start position:0% +you can probably detect whether somebody +is angry you're excited and so on and + + align:start position:0% +is angry you're excited and so on and + + + align:start position:0% +is angry you're excited and so on and +again you can sort of write some mapping + + align:start position:0% +again you can sort of write some mapping + + + align:start position:0% +again you can sort of write some mapping +here you can look at people's brains + + align:start position:0% +here you can look at people's brains + + + align:start position:0% +here you can look at people's brains +um there's also some responses to + + align:start position:0% +um there's also some responses to + + + align:start position:0% +um there's also some responses to +emotion sensitive + + align:start position:0% +emotion sensitive + + + align:start position:0% +emotion sensitive +tasks so if i ask you you know do you + + align:start position:0% +tasks so if i ask you you know do you + + + align:start position:0% +tasks so if i ask you you know do you +want to uh + + align:start position:0% +want to uh + + + align:start position:0% +want to uh +talk to a friend um or like do you want + + align:start position:0% +talk to a friend um or like do you want + + + align:start position:0% +talk to a friend um or like do you want +us to do something nice and if the + + align:start position:0% +us to do something nice and if the + + + align:start position:0% +us to do something nice and if the +answer is like no absolutely not + + align:start position:0% +answer is like no absolutely not + + + align:start position:0% +answer is like no absolutely not +it could obviously be busy but like when + + align:start position:0% +it could obviously be busy but like when + + + align:start position:0% +it could obviously be busy but like when +people are in a bad mood + + align:start position:0% +people are in a bad mood + + + align:start position:0% +people are in a bad mood +they tend to sort of not want to do + + align:start position:0% +they tend to sort of not want to do + + + align:start position:0% +they tend to sort of not want to do +things that arguably should make them + + align:start position:0% +things that arguably should make them + + + align:start position:0% +things that arguably should make them +happy okay so we can sort of try to do + + align:start position:0% +happy okay so we can sort of try to do + + + align:start position:0% +happy okay so we can sort of try to do +that + + align:start position:0% +that + + + align:start position:0% +that +now why my decision utility and + + align:start position:0% +now why my decision utility and + + + align:start position:0% +now why my decision utility and +experience utility differ that's of + + align:start position:0% +experience utility differ that's of + + + align:start position:0% +experience utility differ that's of +course what we discussed in + + align:start position:0% +course what we discussed in + + + align:start position:0% +course what we discussed in +in at length in the class class already + + align:start position:0% +in at length in the class class already + + + align:start position:0% +in at length in the class class already +um there's sort of various uh different + + align:start position:0% +um there's sort of various uh different + + + align:start position:0% +um there's sort of various uh different +um + + align:start position:0% +um + + + align:start position:0% +um +explanations one is um we're going to + + align:start position:0% +explanations one is um we're going to + + + align:start position:0% +explanations one is um we're going to +talk about this a little bit which is + + align:start position:0% +talk about this a little bit which is + + + align:start position:0% +talk about this a little bit which is +inaccurate memories of past + + align:start position:0% +inaccurate memories of past + + + align:start position:0% +inaccurate memories of past +experiences you might just misremember + + align:start position:0% +experiences you might just misremember + + + align:start position:0% +experiences you might just misremember +um + + align:start position:0% +um + + + align:start position:0% +um +your past experiences and based on that + + align:start position:0% +your past experiences and based on that + + + align:start position:0% +your past experiences and based on that +you might have like sort of + + align:start position:0% +you might have like sort of + + + align:start position:0% +you might have like sort of +poor forecasts of your future + + align:start position:0% +poor forecasts of your future + + + align:start position:0% +poor forecasts of your future +preferences or sort of your + + align:start position:0% +preferences or sort of your + + + align:start position:0% +preferences or sort of your +uh utility so this is essentially saying + + align:start position:0% +uh utility so this is essentially saying + + + align:start position:0% +uh utility so this is essentially saying +like + + align:start position:0% +like + + + align:start position:0% +like +people's um beliefs might be wrong in + + align:start position:0% +people's um beliefs might be wrong in + + + align:start position:0% +people's um beliefs might be wrong in +various ways perhaps + + align:start position:0% +various ways perhaps + + + align:start position:0% +various ways perhaps +because people's memories are um uh + + align:start position:0% +because people's memories are um uh + + + align:start position:0% +because people's memories are um uh +tricking them in some ways + + align:start position:0% +tricking them in some ways + + + align:start position:0% +tricking them in some ways +um people might also have like wrong + + align:start position:0% +um people might also have like wrong + + + align:start position:0% +um people might also have like wrong +beliefs because they're gonna fail that + + align:start position:0% +beliefs because they're gonna fail that + + + align:start position:0% +beliefs because they're gonna fail that +there's some failures + + align:start position:0% +there's some failures + + + align:start position:0% +there's some failures +to to anticipate adaptation which is + + align:start position:0% +to to anticipate adaptation which is + + + align:start position:0% +to to anticipate adaptation which is +very much like sort of projection bias + + align:start position:0% +very much like sort of projection bias + + + align:start position:0% +very much like sort of projection bias +that we talked about already previously + + align:start position:0% +that we talked about already previously + + + align:start position:0% +that we talked about already previously +i'm going to talk about this a little + + align:start position:0% +i'm going to talk about this a little + + + align:start position:0% +i'm going to talk about this a little +bit more + + align:start position:0% +bit more + + + align:start position:0% +bit more +um it could be things like emotions + + align:start position:0% +um it could be things like emotions + + + align:start position:0% +um it could be things like emotions +which again are sort of in some ways + + align:start position:0% +which again are sort of in some ways + + + align:start position:0% +which again are sort of in some ways +often like + + align:start position:0% +often like + + + align:start position:0% +often like +um production bias which is about like + + align:start position:0% +um production bias which is about like + + + align:start position:0% +um production bias which is about like +uh uh you know things like + + align:start position:0% +uh uh you know things like + + + align:start position:0% +uh uh you know things like +people might be really angry or people + + align:start position:0% +people might be really angry or people + + + align:start position:0% +people might be really angry or people +might be uh + + align:start position:0% +might be uh + + + align:start position:0% +might be uh +um as hungry and well essentially + + align:start position:0% +um as hungry and well essentially + + + align:start position:0% +um as hungry and well essentially +they're it's very hard for to make + + align:start position:0% +they're it's very hard for to make + + + align:start position:0% +they're it's very hard for to make +certain choices + + align:start position:0% +certain choices + + + align:start position:0% +certain choices +um failing to anticipate their anger or + + align:start position:0% +um failing to anticipate their anger or + + + align:start position:0% +um failing to anticipate their anger or +their hunger or other sort of + + align:start position:0% +their hunger or other sort of + + + align:start position:0% +their hunger or other sort of +uh impulses way over time + + align:start position:0% +uh impulses way over time + + + align:start position:0% +uh impulses way over time +uh sort of other plenty of other reasons + + align:start position:0% +uh sort of other plenty of other reasons + + + align:start position:0% +uh sort of other plenty of other reasons +but we talked about this + + align:start position:0% +but we talked about this + + + align:start position:0% +but we talked about this +quite a lot and so you can think about a + + align:start position:0% +quite a lot and so you can think about a + + + align:start position:0% +quite a lot and so you can think about a +lot of what we discussed in the course + + align:start position:0% +lot of what we discussed in the course + + + align:start position:0% +lot of what we discussed in the course +about + + align:start position:0% +about + + + align:start position:0% +about +disconnects between decision utility and + + align:start position:0% +disconnects between decision utility and + + + align:start position:0% +disconnects between decision utility and +um + + align:start position:0% +um + + + align:start position:0% +um +experience utility now + + align:start position:0% +experience utility now + + + align:start position:0% +experience utility now +uh i mentioned this already a little bit + + align:start position:0% +uh i mentioned this already a little bit + + + align:start position:0% +uh i mentioned this already a little bit +um sort of the the + + align:start position:0% +um sort of the the + + + align:start position:0% +um sort of the the +third part in people's utility is what + + align:start position:0% +third part in people's utility is what + + + align:start position:0% +third part in people's utility is what +um kahneman would call remember to tell + + align:start position:0% +um kahneman would call remember to tell + + + align:start position:0% +um kahneman would call remember to tell +rv which essentially is to say + + align:start position:0% +rv which essentially is to say + + + align:start position:0% +rv which essentially is to say +well when you think about like a past + + align:start position:0% +well when you think about like a past + + + align:start position:0% +well when you think about like a past +experience + + align:start position:0% +experience + + + align:start position:0% +experience +um you might not actually evaluate it + + align:start position:0% +um you might not actually evaluate it + + + align:start position:0% +um you might not actually evaluate it +correctly + + align:start position:0% +correctly + + + align:start position:0% +correctly +in the sense you might sort of as i said + + align:start position:0% +in the sense you might sort of as i said + + + align:start position:0% +in the sense you might sort of as i said +you know you you i might + + align:start position:0% +you know you you i might + + + align:start position:0% +you know you you i might +i i might look at your experience + + align:start position:0% +i i might look at your experience + + + align:start position:0% +i i might look at your experience +utility using these kinds of features + + align:start position:0% +utility using these kinds of features + + + align:start position:0% +utility using these kinds of features +and then i might ask you afterwards how + + align:start position:0% +and then i might ask you afterwards how + + + align:start position:0% +and then i might ask you afterwards how +did you like certain experiences and + + align:start position:0% +did you like certain experiences and + + + align:start position:0% +did you like certain experiences and +then i can sort of test + + align:start position:0% +then i can sort of test + + + align:start position:0% +then i can sort of test +in a way are you how are you aggregating + + align:start position:0% +in a way are you how are you aggregating + + + align:start position:0% +in a way are you how are you aggregating +or how appropriately are you aggregating + + align:start position:0% +or how appropriately are you aggregating + + + align:start position:0% +or how appropriately are you aggregating +uh your experience utility when i just + + align:start position:0% +uh your experience utility when i just + + + align:start position:0% +uh your experience utility when i just +asked you afterwards how did you like + + align:start position:0% +asked you afterwards how did you like + + + align:start position:0% +asked you afterwards how did you like +certain + + align:start position:0% +certain + + + align:start position:0% +certain +um experiences and one quite interesting + + align:start position:0% +um experiences and one quite interesting + + + align:start position:0% +um experiences and one quite interesting +feature is + + align:start position:0% +feature is + + + align:start position:0% +feature is +uh and people's remember the terminality + + align:start position:0% +uh and people's remember the terminality + + + align:start position:0% +uh and people's remember the terminality +is what's called um excuse me uh + + align:start position:0% +is what's called um excuse me uh + + + align:start position:0% +is what's called um excuse me uh +duration neglect people tend to remember + + align:start position:0% +duration neglect people tend to remember + + + align:start position:0% +duration neglect people tend to remember +the quality + + align:start position:0% +the quality + + + align:start position:0% +the quality +rather than the length of the experience + + align:start position:0% +rather than the length of the experience + + + align:start position:0% +rather than the length of the experience +and it seems to be also what's called + + align:start position:0% +and it seems to be also what's called + + + align:start position:0% +and it seems to be also what's called +the peak end + + align:start position:0% +the peak end + + + align:start position:0% +the peak end +rule which essentially uh a sense that + + align:start position:0% +rule which essentially uh a sense that + + + align:start position:0% +rule which essentially uh a sense that +retrospective elevations are + + align:start position:0% +retrospective elevations are + + + align:start position:0% +retrospective elevations are +very much predicted by two things or an + + align:start position:0% +very much predicted by two things or an + + + align:start position:0% +very much predicted by two things or an +average of + + align:start position:0% +average of + + + align:start position:0% +average of +the peak effect of response recorded + + align:start position:0% +the peak effect of response recorded + + + align:start position:0% +the peak effect of response recorded +during an + + align:start position:0% +during an + + + align:start position:0% +during an +episode and the end value recorded just + + align:start position:0% +episode and the end value recorded just + + + align:start position:0% +episode and the end value recorded just +before the termination of the episode + + align:start position:0% +before the termination of the episode + + + align:start position:0% +before the termination of the episode +and how do i think about this well + + align:start position:0% +and how do i think about this well + + + align:start position:0% +and how do i think about this well +mostly uh + + align:start position:0% +mostly uh + + + align:start position:0% +mostly uh +uh i think about this is like being very + + align:start position:0% +uh i think about this is like being very + + + align:start position:0% +uh i think about this is like being very +salient + + align:start position:0% +salient + + + align:start position:0% +salient +so when you think about an asking about + + align:start position:0% +so when you think about an asking about + + + align:start position:0% +so when you think about an asking about +like a semester or like a certain + + align:start position:0% +like a semester or like a certain + + + align:start position:0% +like a semester or like a certain +lecture or a certain experience + + align:start position:0% +lecture or a certain experience + + + align:start position:0% +lecture or a certain experience +that you had maybe a tv show or the like + + align:start position:0% +that you had maybe a tv show or the like + + + align:start position:0% +that you had maybe a tv show or the like +when you + + align:start position:0% +when you + + + align:start position:0% +when you +think about it and try to remember how + + align:start position:0% +think about it and try to remember how + + + align:start position:0% +think about it and try to remember how +much you enjoy that experience + + align:start position:0% +much you enjoy that experience + + + align:start position:0% +much you enjoy that experience +well what's most salient of course is + + align:start position:0% +well what's most salient of course is + + + align:start position:0% +well what's most salient of course is +like is your latest experience right + + align:start position:0% +like is your latest experience right + + + align:start position:0% +like is your latest experience right +that's what comes to mind like the last + + align:start position:0% +that's what comes to mind like the last + + + align:start position:0% +that's what comes to mind like the last +thing you remember is like the last + + align:start position:0% +thing you remember is like the last + + + align:start position:0% +thing you remember is like the last +thing you experienced + + align:start position:0% +thing you experienced + + + align:start position:0% +thing you experienced +and um if the last episode of a tv show + + align:start position:0% +and um if the last episode of a tv show + + + align:start position:0% +and um if the last episode of a tv show +was terrible + + align:start position:0% +was terrible + + + align:start position:0% +was terrible +um that's what comes to mind and you + + align:start position:0% +um that's what comes to mind and you + + + align:start position:0% +um that's what comes to mind and you +might say well the whole series was + + align:start position:0% +might say well the whole series was + + + align:start position:0% +might say well the whole series was +really bad + + align:start position:0% +really bad + + + align:start position:0% +really bad +even though maybe previously it was + + align:start position:0% +even though maybe previously it was + + + align:start position:0% +even though maybe previously it was +quite good and then what + + align:start position:0% +quite good and then what + + + align:start position:0% +quite good and then what +the other thing i guess that seems to be + + align:start position:0% +the other thing i guess that seems to be + + + align:start position:0% +the other thing i guess that seems to be +really uh important is sort of the the + + align:start position:0% +really uh important is sort of the the + + + align:start position:0% +really uh important is sort of the the +peak + + align:start position:0% +peak + + + align:start position:0% +peak +um uh both positive and negative so if + + align:start position:0% +um uh both positive and negative so if + + + align:start position:0% +um uh both positive and negative so if +something was really really great or + + align:start position:0% +something was really really great or + + + align:start position:0% +something was really really great or +really really bad + + align:start position:0% +really really bad + + + align:start position:0% +really really bad +people really really remember that as + + align:start position:0% +people really really remember that as + + + align:start position:0% +people really really remember that as +opposed to like + + align:start position:0% +opposed to like + + + align:start position:0% +opposed to like +um stuff in between and again i think + + align:start position:0% +um stuff in between and again i think + + + align:start position:0% +um stuff in between and again i think +that's something that's just very + + align:start position:0% +that's something that's just very + + + align:start position:0% +that's something that's just very +salient in people's minds + + align:start position:0% +salient in people's minds + + + align:start position:0% +salient in people's minds +and then sort of then thinking about uh + + align:start position:0% +and then sort of then thinking about uh + + + align:start position:0% +and then sort of then thinking about uh +these experiences that's what comes to + + align:start position:0% +these experiences that's what comes to + + + align:start position:0% +these experiences that's what comes to +mind and in studies that + + align:start position:0% +mind and in studies that + + + align:start position:0% +mind and in studies that +so what what are these studies doing + + align:start position:0% +so what what are these studies doing + + + align:start position:0% +so what what are these studies doing +well these studies that that tend to + + align:start position:0% +well these studies that that tend to + + + align:start position:0% +well these studies that that tend to +measure experience utility in certain + + align:start position:0% +measure experience utility in certain + + + align:start position:0% +measure experience utility in certain +ways either through + + align:start position:0% + + + + align:start position:0% + +just measuring people's um tracking + + align:start position:0% +just measuring people's um tracking + + + align:start position:0% +just measuring people's um tracking +people's + + align:start position:0% +people's + + + align:start position:0% +people's +well-being over time and then sort of + + align:start position:0% +well-being over time and then sort of + + + align:start position:0% +well-being over time and then sort of +trying to predict + + align:start position:0% +trying to predict + + + align:start position:0% +trying to predict +uh they remembered utility how did you + + align:start position:0% +uh they remembered utility how did you + + + align:start position:0% +uh they remembered utility how did you +like that experience that's one version + + align:start position:0% +like that experience that's one version + + + align:start position:0% +like that experience that's one version +another version is um + + align:start position:0% +another version is um + + + align:start position:0% +another version is um +uh let me show you uh one second is um + + align:start position:0% +uh let me show you uh one second is um + + + align:start position:0% +uh let me show you uh one second is um +where people do + + align:start position:0% +where people do + + + align:start position:0% +where people do +certain tasks specifically and they + + align:start position:0% +certain tasks specifically and they + + + align:start position:0% +certain tasks specifically and they +manipulate the experience + + align:start position:0% +manipulate the experience + + + align:start position:0% +manipulate the experience +deliberately for example they're these + + align:start position:0% +deliberately for example they're these + + + align:start position:0% +deliberately for example they're these +tasks which is called a cold presser + + align:start position:0% +tasks which is called a cold presser + + + align:start position:0% +tasks which is called a cold presser +task which is + + align:start position:0% +task which is + + + align:start position:0% +task which is +they ask people to put their hands in + + align:start position:0% +they ask people to put their hands in + + + align:start position:0% +they ask people to put their hands in +the cold water and then vary kind of the + + align:start position:0% +the cold water and then vary kind of the + + + align:start position:0% +the cold water and then vary kind of the +temperature or they vary uh the duration + + align:start position:0% +temperature or they vary uh the duration + + + align:start position:0% +temperature or they vary uh the duration +and then essentially you can you can + + align:start position:0% +and then essentially you can you can + + + align:start position:0% +and then essentially you can you can +then try to predict um + + align:start position:0% +then try to predict um + + + align:start position:0% +then try to predict um +people's remember the child id and then + + align:start position:0% +people's remember the child id and then + + + align:start position:0% +people's remember the child id and then +show things such as + + align:start position:0% +show things such as + + + align:start position:0% +show things such as +duration neglect or they like and let me + + align:start position:0% +duration neglect or they like and let me + + + align:start position:0% +duration neglect or they like and let me +sort of show you what that looks like + + align:start position:0% +sort of show you what that looks like + + + align:start position:0% +sort of show you what that looks like +for example um this is a famous study by + + align:start position:0% +for example um this is a famous study by + + + align:start position:0% +for example um this is a famous study by +um schreiber and conomon + + align:start position:0% +um schreiber and conomon + + + align:start position:0% +um schreiber and conomon +they did a short trial which as you put + + align:start position:0% +they did a short trial which as you put + + + align:start position:0% +they did a short trial which as you put +your hand into 14 degree + + align:start position:0% +your hand into 14 degree + + + align:start position:0% +your hand into 14 degree +water + + align:start position:0% + + + + align:start position:0% + +for 60 seconds which is very cold or a + + align:start position:0% +for 60 seconds which is very cold or a + + + align:start position:0% +for 60 seconds which is very cold or a +long trial where you put it into + + align:start position:0% +long trial where you put it into + + + align:start position:0% +long trial where you put it into +water for 60 seconds and then the + + align:start position:0% +water for 60 seconds and then the + + + align:start position:0% +water for 60 seconds and then the +temperature rises to 15 + + align:start position:0% +temperature rises to 15 + + + align:start position:0% +temperature rises to 15 +degrees i think this is a celsius it's + + align:start position:0% +degrees i think this is a celsius it's + + + align:start position:0% +degrees i think this is a celsius it's +not far night but anyway it's cold + + align:start position:0% +not far night but anyway it's cold + + + align:start position:0% +not far night but anyway it's cold +um uh uh but so the point here is that + + align:start position:0% +um uh uh but so the point here is that + + + align:start position:0% +um uh uh but so the point here is that +like putting your hand in the 14 + + align:start position:0% +like putting your hand in the 14 + + + align:start position:0% +like putting your hand in the 14 +uh for 60 seconds into 14 degree water + + align:start position:0% +uh for 60 seconds into 14 degree water + + + align:start position:0% +uh for 60 seconds into 14 degree water +and then another 30 seconds into 15 + + align:start position:0% +and then another 30 seconds into 15 + + + align:start position:0% +and then another 30 seconds into 15 +degree water these are both + + align:start position:0% +degree water these are both + + + align:start position:0% +degree water these are both +unpleasant experiences so if you did + + align:start position:0% +unpleasant experiences so if you did + + + align:start position:0% +unpleasant experiences so if you did +each of these things in separation + + align:start position:0% +each of these things in separation + + + align:start position:0% +each of these things in separation +people would say i went into 60 + + align:start position:0% +people would say i went into 60 + + + align:start position:0% +people would say i went into 60 +seconds of cold water i also don't like + + align:start position:0% +seconds of cold water i also don't like + + + align:start position:0% +seconds of cold water i also don't like +30 seconds of 15 degree water these are + + align:start position:0% +30 seconds of 15 degree water these are + + + align:start position:0% +30 seconds of 15 degree water these are +both unpleasant experiences + + align:start position:0% +both unpleasant experiences + + + align:start position:0% +both unpleasant experiences +um so neither of them are actually + + align:start position:0% +um so neither of them are actually + + + align:start position:0% +um so neither of them are actually +desirable and sort of if you ask people + + align:start position:0% +desirable and sort of if you ask people + + + align:start position:0% +desirable and sort of if you ask people +do you give people uh this explanation + + align:start position:0% +do you give people uh this explanation + + + align:start position:0% +do you give people uh this explanation +you want to experience + + align:start position:0% +you want to experience + + + align:start position:0% +you want to experience +again people say hell no i really don't + + align:start position:0% +again people say hell no i really don't + + + align:start position:0% +again people say hell no i really don't +like this and for both of these like in + + align:start position:0% +like this and for both of these like in + + + align:start position:0% +like this and for both of these like in +separation + + align:start position:0% +separation + + + align:start position:0% +separation +but once you put them together the 30 + + align:start position:0% +but once you put them together the 30 + + + align:start position:0% +but once you put them together the 30 +seconds of + + align:start position:0% +seconds of + + + align:start position:0% +seconds of +15 degree water is more pleasant than + + align:start position:0% +15 degree water is more pleasant than + + + align:start position:0% +15 degree water is more pleasant than +the 14 degree water + + align:start position:0% +the 14 degree water + + + align:start position:0% +the 14 degree water +so when you do that people sort of say + + align:start position:0% +so when you do that people sort of say + + + align:start position:0% +so when you do that people sort of say +they prefer the long trial + + align:start position:0% +they prefer the long trial + + + align:start position:0% +they prefer the long trial +over um the shorts trial and the reason + + align:start position:0% +over um the shorts trial and the reason + + + align:start position:0% +over um the shorts trial and the reason +being and what they remember + + align:start position:0% +being and what they remember + + + align:start position:0% +being and what they remember +is like the last experience which was + + align:start position:0% +is like the last experience which was + + + align:start position:0% +is like the last experience which was +not that painful + + align:start position:0% +not that painful + + + align:start position:0% +not that painful +where things got better over time so + + align:start position:0% +where things got better over time so + + + align:start position:0% +where things got better over time so +people's remembered utility is + + align:start position:0% +people's remembered utility is + + + align:start position:0% +people's remembered utility is +is sort of violating any sort of like uh + + align:start position:0% +is sort of violating any sort of like uh + + + align:start position:0% +is sort of violating any sort of like uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +rules like what would you really think + + align:start position:0% +rules like what would you really think + + + align:start position:0% +rules like what would you really think +in terms of nationality and + + align:start position:0% +in terms of nationality and + + + align:start position:0% +in terms of nationality and +economics which is precisely because + + align:start position:0% +economics which is precisely because + + + align:start position:0% +economics which is precisely because +they remember uh the end + + align:start position:0% +they remember uh the end + + + align:start position:0% +they remember uh the end +rather than the overall duration so + + align:start position:0% +rather than the overall duration so + + + align:start position:0% +rather than the overall duration so +essentially the utility does not + + align:start position:0% +essentially the utility does not + + + align:start position:0% +essentially the utility does not +aggregate in the way we would think they + + align:start position:0% +aggregate in the way we would think they + + + align:start position:0% +aggregate in the way we would think they +input because the experience at each + + align:start position:0% +input because the experience at each + + + align:start position:0% +input because the experience at each +point in time is + + align:start position:0% +point in time is + + + align:start position:0% +point in time is +negative there's difference there's a + + align:start position:0% +negative there's difference there's a + + + align:start position:0% +negative there's difference there's a +pleasant studies uh for a colonoscopy + + align:start position:0% +pleasant studies uh for a colonoscopy + + + align:start position:0% +pleasant studies uh for a colonoscopy +don't ask me about how they got ethical + + align:start position:0% +don't ask me about how they got ethical + + + align:start position:0% +don't ask me about how they got ethical +approval for those things + + align:start position:0% +approval for those things + + + align:start position:0% +approval for those things +but anyways uh uh studies could be where + + align:start position:0% +but anyways uh uh studies could be where + + + align:start position:0% +but anyways uh uh studies could be where +um getting um extra um + + align:start position:0% +um getting um extra um + + + align:start position:0% +um getting um extra um +um a minute uh where nothing bad happens + + align:start position:0% +um a minute uh where nothing bad happens + + + align:start position:0% +um a minute uh where nothing bad happens +and essentially the treatment group has + + align:start position:0% +and essentially the treatment group has + + + align:start position:0% +and essentially the treatment group has +better um experience and memories of + + align:start position:0% +better um experience and memories of + + + align:start position:0% +better um experience and memories of +those kinds of + + align:start position:0% +those kinds of + + + align:start position:0% +those kinds of +uh of the overall experience now that + + align:start position:0% +uh of the overall experience now that + + + align:start position:0% +uh of the overall experience now that +sounds kind of like you're torturing + + align:start position:0% +sounds kind of like you're torturing + + + align:start position:0% +sounds kind of like you're torturing +people but in fact + + align:start position:0% +people but in fact + + + align:start position:0% +people but in fact +you think about it well if + + align:start position:0% +you think about it well if + + + align:start position:0% +you think about it well if +in particular medical procedures that + + align:start position:0% +in particular medical procedures that + + + align:start position:0% +in particular medical procedures that +are unpleasant + + align:start position:0% +are unpleasant + + + align:start position:0% +are unpleasant +overall if we can help people + + align:start position:0% +overall if we can help people + + + align:start position:0% +overall if we can help people +have better memories of those + + align:start position:0% +have better memories of those + + + align:start position:0% +have better memories of those +experiences + + align:start position:0% +experiences + + + align:start position:0% +experiences +maybe they will be a lot likely to come + + align:start position:0% +maybe they will be a lot likely to come + + + align:start position:0% +maybe they will be a lot likely to come +back and get future treatments or delay + + align:start position:0% +back and get future treatments or delay + + + align:start position:0% +back and get future treatments or delay +so in a way you might sort of say what + + align:start position:0% +so in a way you might sort of say what + + + align:start position:0% +so in a way you might sort of say what +are these studies why are people + + align:start position:0% +are these studies why are people + + + align:start position:0% +are these studies why are people +torturing people uh or whether + + align:start position:0% +torturing people uh or whether + + + align:start position:0% +torturing people uh or whether +researchers torture people + + align:start position:0% +researchers torture people + + + align:start position:0% +researchers torture people +uh uh i agree with that notion but in + + align:start position:0% +uh uh i agree with that notion but in + + + align:start position:0% +uh uh i agree with that notion but in +fact + + align:start position:0% +fact + + + align:start position:0% +fact +if you think about if you wanted to + + align:start position:0% +if you think about if you wanted to + + + align:start position:0% +if you think about if you wanted to +design if you think people are under + + align:start position:0% +design if you think people are under + + + align:start position:0% +design if you think people are under +um using certain medical procedures or + + align:start position:0% +um using certain medical procedures or + + + align:start position:0% +um using certain medical procedures or +certain medical tests that you should be + + align:start position:0% +certain medical tests that you should be + + + align:start position:0% +certain medical tests that you should be +doing + + align:start position:0% +doing + + + align:start position:0% +doing +you would think of dentists if there's + + align:start position:0% +you would think of dentists if there's + + + align:start position:0% +you would think of dentists if there's +some + + align:start position:0% +some + + + align:start position:0% +some +people's overall memory or memory of + + align:start position:0% +people's overall memory or memory of + + + align:start position:0% +people's overall memory or memory of +their overall experience better by sort + + align:start position:0% +their overall experience better by sort + + + align:start position:0% +their overall experience better by sort +of having the end + + align:start position:0% +of having the end + + + align:start position:0% +of having the end +of that experience slightly better than + + align:start position:0% +of that experience slightly better than + + + align:start position:0% +of that experience slightly better than +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +uh then the previous parts + + align:start position:0% +uh then the previous parts + + + align:start position:0% +uh then the previous parts +uh that i couldn't hope for in uh + + align:start position:0% +uh that i couldn't hope for in uh + + + align:start position:0% +uh that i couldn't hope for in uh +sort of a behavior that's good for + + align:start position:0% +sort of a behavior that's good for + + + align:start position:0% +sort of a behavior that's good for +people in terms of + + align:start position:0% +people in terms of + + + align:start position:0% +people in terms of +health even though of course the last + + align:start position:0% +health even though of course the last + + + align:start position:0% +health even though of course the last +minute of the actual + + align:start position:0% +minute of the actual + + + align:start position:0% +minute of the actual +experience would not be pleasant nobody + + align:start position:0% +experience would not be pleasant nobody + + + align:start position:0% +experience would not be pleasant nobody +wants to say like would you rather have + + align:start position:0% +wants to say like would you rather have + + + align:start position:0% +wants to say like would you rather have +like + + align:start position:0% +like + + + align:start position:0% +like +another minute of colonoscopy absolutely + + align:start position:0% +another minute of colonoscopy absolutely + + + align:start position:0% +another minute of colonoscopy absolutely +not but like maybe the overall + + align:start position:0% +not but like maybe the overall + + + align:start position:0% +not but like maybe the overall +experience + + align:start position:0% +experience + + + align:start position:0% +experience +remember uh is in fact better than um if + + align:start position:0% +remember uh is in fact better than um if + + + align:start position:0% +remember uh is in fact better than um if +not + + align:start position:0% +not + + + align:start position:0% +not +so there's other types of experience + + align:start position:0% +so there's other types of experience + + + align:start position:0% +so there's other types of experience +that shows this um + + align:start position:0% +that shows this um + + + align:start position:0% +that shows this um +duration neglect and pete peak and + + align:start position:0% +duration neglect and pete peak and + + + align:start position:0% +duration neglect and pete peak and +evaluations people have shown like + + align:start position:0% +evaluations people have shown like + + + align:start position:0% +evaluations people have shown like +pleasant and unpleasant + + align:start position:0% +pleasant and unpleasant + + + align:start position:0% +pleasant and unpleasant +uh + + align:start position:0% + + + + align:start position:0% + +movies or contents of movies um they've + + align:start position:0% +movies or contents of movies um they've + + + align:start position:0% +movies or contents of movies um they've +done these experiments with like + + align:start position:0% +done these experiments with like + + + align:start position:0% +done these experiments with like +uh with sounds or noise of various + + align:start position:0% +uh with sounds or noise of various + + + align:start position:0% +uh with sounds or noise of various +loudness and duration + + align:start position:0% +loudness and duration + + + align:start position:0% +loudness and duration +there's also where essentially animals + + align:start position:0% +there's also where essentially animals + + + align:start position:0% +there's also where essentially animals +are + + align:start position:0% +are + + + align:start position:0% +are +are uh given unpleasant experiences and + + align:start position:0% +are uh given unpleasant experiences and + + + align:start position:0% +are uh given unpleasant experiences and +then you look at like what + + align:start position:0% +then you look at like what + + + align:start position:0% +then you look at like what +what these are different types of + + align:start position:0% +what these are different types of + + + align:start position:0% +what these are different types of +experiences where like the animal can go + + align:start position:0% +experiences where like the animal can go + + + align:start position:0% +experiences where like the animal can go +into like one direction or the other + + align:start position:0% +into like one direction or the other + + + align:start position:0% +into like one direction or the other +or press on level versus another and + + align:start position:0% +or press on level versus another and + + + align:start position:0% +or press on level versus another and +then bad stuff happens in both of them + + align:start position:0% +then bad stuff happens in both of them + + + align:start position:0% +then bad stuff happens in both of them +and one of them is worse than the other + + align:start position:0% +and one of them is worse than the other + + + align:start position:0% +and one of them is worse than the other +and then you can look at essentially do + + align:start position:0% +and then you can look at essentially do + + + align:start position:0% +and then you can look at essentially do +animals of similarly uh + + align:start position:0% +animals of similarly uh + + + align:start position:0% +animals of similarly uh +duration or other uh uh peak end + + align:start position:0% +duration or other uh uh peak end + + + align:start position:0% +duration or other uh uh peak end +evaluations + + align:start position:0% +evaluations + + + align:start position:0% +evaluations +of experiences and it seems to be very + + align:start position:0% +of experiences and it seems to be very + + + align:start position:0% +of experiences and it seems to be very +much like a + + align:start position:0% +much like a + + + align:start position:0% +much like a +um phenomenon that's also true for + + align:start position:0% +um phenomenon that's also true for + + + align:start position:0% +um phenomenon that's also true for +for animals any questions on this + + align:start position:0% + + + + align:start position:0% + +okay so then of course if that's the + + align:start position:0% +okay so then of course if that's the + + + align:start position:0% +okay so then of course if that's the +case if people's + + align:start position:0% +case if people's + + + align:start position:0% +case if people's +um if people remember + + align:start position:0% +um if people remember + + + align:start position:0% +um if people remember +things differently that will lead to um + + align:start position:0% +things differently that will lead to um + + + align:start position:0% +things differently that will lead to um +that will lead to violations of the + + align:start position:0% +that will lead to violations of the + + + align:start position:0% +that will lead to violations of the +decision utility + + align:start position:0% +decision utility + + + align:start position:0% +decision utility +maximizing the experience utility right + + align:start position:0% +maximizing the experience utility right + + + align:start position:0% +maximizing the experience utility right +if you think about the experience + + align:start position:0% +if you think about the experience + + + align:start position:0% +if you think about the experience +utility or like the overall experience + + align:start position:0% +utility or like the overall experience + + + align:start position:0% +utility or like the overall experience +uh the utility overlaps experience + + align:start position:0% +uh the utility overlaps experience + + + align:start position:0% +uh the utility overlaps experience +utility of a certain + + align:start position:0% +utility of a certain + + + align:start position:0% +utility of a certain +choice that you make in this case i + + align:start position:0% +choice that you make in this case i + + + align:start position:0% +choice that you make in this case i +guess the cold presser pass + + align:start position:0% +guess the cold presser pass + + + align:start position:0% +guess the cold presser pass +think about this like sort of the + + align:start position:0% +think about this like sort of the + + + align:start position:0% +think about this like sort of the +integral over like say in this case i + + align:start position:0% +integral over like say in this case i + + + align:start position:0% +integral over like say in this case i +guess 90 seconds + + align:start position:0% +guess 90 seconds + + + align:start position:0% +guess 90 seconds +in the first case it's 60 seconds plus + + align:start position:0% +in the first case it's 60 seconds plus + + + align:start position:0% +in the first case it's 60 seconds plus +30 seconds uh + + align:start position:0% +30 seconds uh + + + align:start position:0% +30 seconds uh +60 seconds feeling bad versus 30 seconds + + align:start position:0% +60 seconds feeling bad versus 30 seconds + + + align:start position:0% +60 seconds feeling bad versus 30 seconds +of like + + align:start position:0% +of like + + + align:start position:0% +of like +putting your hand out which is something + + align:start position:0% +putting your hand out which is something + + + align:start position:0% +putting your hand out which is something +like a neutral experience + + align:start position:0% +like a neutral experience + + + align:start position:0% +like a neutral experience +if you're sort of integrating that + + align:start position:0% +if you're sort of integrating that + + + align:start position:0% +if you're sort of integrating that +presumably um the short trial will give + + align:start position:0% +presumably um the short trial will give + + + align:start position:0% +presumably um the short trial will give +you like a higher + + align:start position:0% +you like a higher + + + align:start position:0% +you like a higher +valuation of like higher better a more + + align:start position:0% +valuation of like higher better a more + + + align:start position:0% +valuation of like higher better a more +positive sort of experience + + align:start position:0% +positive sort of experience + + + align:start position:0% +positive sort of experience +overall right but then if you ask people + + align:start position:0% +overall right but then if you ask people + + + align:start position:0% +overall right but then if you ask people +which one do you want because people + + align:start position:0% +which one do you want because people + + + align:start position:0% +which one do you want because people +remember the long trial as being less + + align:start position:0% +remember the long trial as being less + + + align:start position:0% +remember the long trial as being less +bad + + align:start position:0% +bad + + + align:start position:0% +bad +uh people might sort of choose um the + + align:start position:0% +uh people might sort of choose um the + + + align:start position:0% +uh people might sort of choose um the +long trial over the + + align:start position:0% +long trial over the + + + align:start position:0% +long trial over the +short trial overall so then that leads + + align:start position:0% +short trial overall so then that leads + + + align:start position:0% +short trial overall so then that leads +to essential violations of the decision + + align:start position:0% +to essential violations of the decision + + + align:start position:0% +to essential violations of the decision +utility maximizing the experience + + align:start position:0% +utility maximizing the experience + + + align:start position:0% +utility maximizing the experience +utility because essentially people + + align:start position:0% +utility because essentially people + + + align:start position:0% +utility because essentially people +remember things + + align:start position:0% +remember things + + + align:start position:0% +remember things +uh in a biased way + + align:start position:0% +uh in a biased way + + + align:start position:0% +uh in a biased way +okay so then uh uh we talked about this + + align:start position:0% +okay so then uh uh we talked about this + + + align:start position:0% +okay so then uh uh we talked about this +very briefly and so far we talked about + + align:start position:0% +very briefly and so far we talked about + + + align:start position:0% +very briefly and so far we talked about +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +uh different ways imagine one specific + + align:start position:0% +uh different ways imagine one specific + + + align:start position:0% +uh different ways imagine one specific +thing that people have done um a lot + + align:start position:0% +thing that people have done um a lot + + + align:start position:0% +thing that people have done um a lot +is just asking people simply about um + + align:start position:0% +is just asking people simply about um + + + align:start position:0% +is just asking people simply about um +their happiness and life satisfaction um + + align:start position:0% +their happiness and life satisfaction um + + + align:start position:0% +their happiness and life satisfaction um +so + + align:start position:0% +so + + + align:start position:0% +so +simply you ask people there's different + + align:start position:0% +simply you ask people there's different + + + align:start position:0% +simply you ask people there's different +ways um um + + align:start position:0% +ways um um + + + align:start position:0% +ways um um +are there sort of these types of latter + + align:start position:0% +are there sort of these types of latter + + + align:start position:0% +are there sort of these types of latter +questions how satisfied are you with + + align:start position:0% +questions how satisfied are you with + + + align:start position:0% +questions how satisfied are you with +your life as a whole these days + + align:start position:0% +your life as a whole these days + + + align:start position:0% +your life as a whole these days +um there's also like affect questions + + align:start position:0% +um there's also like affect questions + + + align:start position:0% +um there's also like affect questions +about like did you experience certain + + align:start position:0% +about like did you experience certain + + + align:start position:0% +about like did you experience certain +emotions yesterday did you feel angry + + align:start position:0% +emotions yesterday did you feel angry + + + align:start position:0% +emotions yesterday did you feel angry +did you feel happy did you feel sad and + + align:start position:0% +did you feel happy did you feel sad and + + + align:start position:0% +did you feel happy did you feel sad and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +the latter question um is sort of a + + align:start position:0% +the latter question um is sort of a + + + align:start position:0% +the latter question um is sort of a +mixture of some people + + align:start position:0% +mixture of some people + + + align:start position:0% +mixture of some people +think of this as like life satisfaction + + align:start position:0% +think of this as like life satisfaction + + + align:start position:0% +think of this as like life satisfaction +some people interpret it as happiness + + align:start position:0% +some people interpret it as happiness + + + align:start position:0% +some people interpret it as happiness +others would sort of argue that it's + + align:start position:0% +others would sort of argue that it's + + + align:start position:0% +others would sort of argue that it's +rather about social comparisons + + align:start position:0% +rather about social comparisons + + + align:start position:0% +rather about social comparisons +so the latter question has noticed and + + align:start position:0% +so the latter question has noticed and + + + align:start position:0% +so the latter question has noticed and +i'm going to show you the definition in + + align:start position:0% +i'm going to show you the definition in + + + align:start position:0% +i'm going to show you the definition in +a second or in a bit + + align:start position:0% +a second or in a bit + + + align:start position:0% +a second or in a bit +the latter definition is very much just + + align:start position:0% +the latter definition is very much just + + + align:start position:0% +the latter definition is very much just +like on a a + + align:start position:0% +like on a a + + + align:start position:0% +like on a a +on a ladder from one to ten how great + + align:start position:0% +on a ladder from one to ten how great + + + align:start position:0% +on a ladder from one to ten how great +could your life be + + align:start position:0% +could your life be + + + align:start position:0% +could your life be +um where are you in this ladder so it + + align:start position:0% +um where are you in this ladder so it + + + align:start position:0% +um where are you in this ladder so it +has very much sort of this flavor of + + align:start position:0% +has very much sort of this flavor of + + + align:start position:0% +has very much sort of this flavor of +some social comparison + + align:start position:0% +some social comparison + + + align:start position:0% +some social comparison +which i you know is not quite ideal + + align:start position:0% +which i you know is not quite ideal + + + align:start position:0% +which i you know is not quite ideal +because it + + align:start position:0% +because it + + + align:start position:0% +because it +makes it like well on the ladder like + + align:start position:0% +makes it like well on the ladder like + + + align:start position:0% +makes it like well on the ladder like +how far and low are you at the ladder it + + align:start position:0% +how far and low are you at the ladder it + + + align:start position:0% +how far and low are you at the ladder it +makes it very salient that some people + + align:start position:0% +makes it very salient that some people + + + align:start position:0% +makes it very salient that some people +are higher or lower than others + + align:start position:0% +are higher or lower than others + + + align:start position:0% +are higher or lower than others +so some of the responses that you see in + + align:start position:0% +so some of the responses that you see in + + + align:start position:0% +so some of the responses that you see in +those kinds of lateral questions + + align:start position:0% +those kinds of lateral questions + + + align:start position:0% +those kinds of lateral questions +are about sort of happiness but they + + align:start position:0% +are about sort of happiness but they + + + align:start position:0% +are about sort of happiness but they +potentially are also about + + align:start position:0% +potentially are also about + + + align:start position:0% +potentially are also about +people comparing each other um to others + + align:start position:0% +people comparing each other um to others + + + align:start position:0% +people comparing each other um to others +in society and so on which + + align:start position:0% +in society and so on which + + + align:start position:0% +in society and so on which +which might not be necessarily the same + + align:start position:0% +which might not be necessarily the same + + + align:start position:0% +which might not be necessarily the same +as like how happy are you uh right now + + align:start position:0% +as like how happy are you uh right now + + + align:start position:0% +as like how happy are you uh right now +it could be now what's problematic about + + align:start position:0% +it could be now what's problematic about + + + align:start position:0% +it could be now what's problematic about +these happiness questions or what's like + + align:start position:0% +these happiness questions or what's like + + + align:start position:0% +these happiness questions or what's like +a + + align:start position:0% +a + + + align:start position:0% +a +why are economists um skeptical or + + align:start position:0% +why are economists um skeptical or + + + align:start position:0% +why are economists um skeptical or +what instances do we about + + align:start position:0% + + + + align:start position:0% + +so just to be clear so some people would + + align:start position:0% +so just to be clear so some people would + + + align:start position:0% +so just to be clear so some people would +argue like we should have like a world + + align:start position:0% +argue like we should have like a world + + + align:start position:0% +argue like we should have like a world +happiness report and gdp + + align:start position:0% +happiness report and gdp + + + align:start position:0% +happiness report and gdp +uh we should not maximize sort of gdp or + + align:start position:0% +uh we should not maximize sort of gdp or + + + align:start position:0% +uh we should not maximize sort of gdp or +like uh + + align:start position:0% +like uh + + + align:start position:0% +like uh +look at like gdp growth as like an + + align:start position:0% +look at like gdp growth as like an + + + align:start position:0% +look at like gdp growth as like an +overall performance of society + + align:start position:0% +overall performance of society + + + align:start position:0% +overall performance of society +instead we should measure subjective + + align:start position:0% +instead we should measure subjective + + + align:start position:0% +instead we should measure subjective +well-being and that that's what we + + align:start position:0% +well-being and that that's what we + + + align:start position:0% +well-being and that that's what we +should essentially maximize and policy + + align:start position:0% +should essentially maximize and policy + + + align:start position:0% +should essentially maximize and policy +should be + + align:start position:0% +should be + + + align:start position:0% +should be +the objective should be to to to + + align:start position:0% +the objective should be to to to + + + align:start position:0% +the objective should be to to to +maximize that + + align:start position:0% +maximize that + + + align:start position:0% +maximize that +so what's the pushback on that so so + + align:start position:0% +so what's the pushback on that so so + + + align:start position:0% +so what's the pushback on that so so +part of that is + + align:start position:0% +part of that is + + + align:start position:0% +part of that is +people and stuff that we talked already + + align:start position:0% +people and stuff that we talked already + + + align:start position:0% +people and stuff that we talked already +about about + + align:start position:0% +about about + + + align:start position:0% +about about +um you know uh remember utility or + + align:start position:0% +um you know uh remember utility or + + + align:start position:0% +um you know uh remember utility or +people just might not know + + align:start position:0% +people just might not know + + + align:start position:0% +people just might not know +what's what's good for them but what's + + align:start position:0% +what's what's good for them but what's + + + align:start position:0% +what's what's good for them but what's +wrong with just asking people how happy + + align:start position:0% +wrong with just asking people how happy + + + align:start position:0% +wrong with just asking people how happy +are you and like are people are just + + align:start position:0% +are you and like are people are just + + + align:start position:0% +are you and like are people are just +going to tell you or like what's the + + align:start position:0% +going to tell you or like what's the + + + align:start position:0% +going to tell you or like what's the +problem with that + + align:start position:0% +problem with that + + + align:start position:0% +problem with that +so one problem broadly speaking is + + align:start position:0% +so one problem broadly speaking is + + + align:start position:0% +so one problem broadly speaking is +when you look at different countries + + align:start position:0% +when you look at different countries + + + align:start position:0% +when you look at different countries +different societies particularly for + + align:start position:0% +different societies particularly for + + + align:start position:0% +different societies particularly for +example if you look at germans germans + + align:start position:0% +example if you look at germans germans + + + align:start position:0% +example if you look at germans germans +tend to be pretty grumpy and not super + + align:start position:0% +tend to be pretty grumpy and not super + + + align:start position:0% +tend to be pretty grumpy and not super +happy so when you ask a german how are + + align:start position:0% +happy so when you ask a german how are + + + align:start position:0% +happy so when you ask a german how are +you doing the typical german would sort + + align:start position:0% +you doing the typical german would sort + + + align:start position:0% +you doing the typical german would sort +of say okay + + align:start position:0% +of say okay + + + align:start position:0% +of say okay +by which they mean actually pretty good + + align:start position:0% +by which they mean actually pretty good + + + align:start position:0% +by which they mean actually pretty good +if you talk + + align:start position:0% +if you talk + + + align:start position:0% +if you talk +alaska a typical american how are you + + align:start position:0% +alaska a typical american how are you + + + align:start position:0% +alaska a typical american how are you +doing they say amazing they probably + + align:start position:0% +doing they say amazing they probably + + + align:start position:0% +doing they say amazing they probably +mean like + + align:start position:0% +mean like + + + align:start position:0% +mean like +pretty good um so uh when people + + align:start position:0% +pretty good um so uh when people + + + align:start position:0% +pretty good um so uh when people +give you certain statements there's lots + + align:start position:0% +give you certain statements there's lots + + + align:start position:0% +give you certain statements there's lots +of cultural and other sort of aspect + + align:start position:0% +of cultural and other sort of aspect + + + align:start position:0% +of cultural and other sort of aspect +that made comparison + + align:start position:0% +that made comparison + + + align:start position:0% +that made comparison +particularly across society is kind of + + align:start position:0% +particularly across society is kind of + + + align:start position:0% +particularly across society is kind of +tricky + + align:start position:0% +tricky + + + align:start position:0% +tricky +like you might think people in latin + + align:start position:0% +like you might think people in latin + + + align:start position:0% +like you might think people in latin +america tend to report higher levels of + + align:start position:0% +america tend to report higher levels of + + + align:start position:0% +america tend to report higher levels of +happiness + + align:start position:0% +happiness + + + align:start position:0% +happiness +because that's sort of a cultural thing + + align:start position:0% +because that's sort of a cultural thing + + + align:start position:0% +because that's sort of a cultural thing +which might be that they're actually + + align:start position:0% +which might be that they're actually + + + align:start position:0% +which might be that they're actually +happy or it might be that that's + + align:start position:0% +happy or it might be that that's + + + align:start position:0% +happy or it might be that that's +just the thing that you're supposed to + + align:start position:0% +just the thing that you're supposed to + + + align:start position:0% +just the thing that you're supposed to +exhibit + + align:start position:0% +exhibit + + + align:start position:0% +exhibit +while people in some other states uh + + align:start position:0% +while people in some other states uh + + + align:start position:0% +while people in some other states uh +scandinavia germany etc might sort of be + + align:start position:0% +scandinavia germany etc might sort of be + + + align:start position:0% +scandinavia germany etc might sort of be +in fact quite happy but like what they + + align:start position:0% +in fact quite happy but like what they + + + align:start position:0% +in fact quite happy but like what they +report to you was just + + align:start position:0% +report to you was just + + + align:start position:0% +report to you was just +some moderate uh level of enthusiasm uh + + align:start position:0% +some moderate uh level of enthusiasm uh + + + align:start position:0% +some moderate uh level of enthusiasm uh +overall so one sort of + + align:start position:0% +overall so one sort of + + + align:start position:0% +overall so one sort of +cultural uh comparison is quite hard um + + align:start position:0% +cultural uh comparison is quite hard um + + + align:start position:0% +cultural uh comparison is quite hard um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +using those types of questions there's + + align:start position:0% +using those types of questions there's + + + align:start position:0% +using those types of questions there's +lots of gallup surveys that people have + + align:start position:0% +lots of gallup surveys that people have + + + align:start position:0% +lots of gallup surveys that people have +done + + align:start position:0% +done + + + align:start position:0% +done +uh at large scales it's like the gallup + + align:start position:0% +uh at large scales it's like the gallup + + + align:start position:0% +uh at large scales it's like the gallup +world + + align:start position:0% +world + + + align:start position:0% +world +happiness whatever surveys there's like + + align:start position:0% +happiness whatever surveys there's like + + + align:start position:0% +happiness whatever surveys there's like +huge amounts of data that are being + + align:start position:0% +huge amounts of data that are being + + + align:start position:0% +huge amounts of data that are being +collected they're nationally + + align:start position:0% +collected they're nationally + + + align:start position:0% +collected they're nationally +representative surveys and so on and so + + align:start position:0% +representative surveys and so on and so + + + align:start position:0% +representative surveys and so on and so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +so that those data are available of + + align:start position:0% +so that those data are available of + + + align:start position:0% +so that those data are available of +course there's questions and like + + align:start position:0% +course there's questions and like + + + align:start position:0% +course there's questions and like +you know uh in some places it's much + + align:start position:0% +you know uh in some places it's much + + + align:start position:0% +you know uh in some places it's much +harder to collect these than + + align:start position:0% +harder to collect these than + + + align:start position:0% +harder to collect these than +others and so on and so forth and you + + align:start position:0% +others and so on and so forth and you + + + align:start position:0% +others and so on and so forth and you +know some people don't reply to surveys + + align:start position:0% +know some people don't reply to surveys + + + align:start position:0% +know some people don't reply to surveys +and so on and so forth for example + + align:start position:0% +and so on and so forth for example + + + align:start position:0% +and so on and so forth for example +the elderly might be much less likely to + + align:start position:0% +the elderly might be much less likely to + + + align:start position:0% +the elderly might be much less likely to +answer certain surveys or like some + + align:start position:0% +answer certain surveys or like some + + + align:start position:0% +answer certain surveys or like some +people without phones or internet and so + + align:start position:0% +people without phones or internet and so + + + align:start position:0% +people without phones or internet and so +on and so forth you might not be able to + + align:start position:0% +on and so forth you might not be able to + + + align:start position:0% +on and so forth you might not be able to +reach them but in principle you can + + align:start position:0% +reach them but in principle you can + + + align:start position:0% +reach them but in principle you can +solve all of those issues + + align:start position:0% +solve all of those issues + + + align:start position:0% +solve all of those issues +but i think that's it just costly to use + + align:start position:0% +but i think that's it just costly to use + + + align:start position:0% +but i think that's it just costly to use +it the reference dependence is a very + + align:start position:0% +it the reference dependence is a very + + + align:start position:0% +it the reference dependence is a very +interesting issue + + align:start position:0% +interesting issue + + + align:start position:0% +interesting issue +because in some ways you might say well + + align:start position:0% +because in some ways you might say well + + + align:start position:0% +because in some ways you might say well +now your income but + + align:start position:0% +now your income but + + + align:start position:0% +now your income but +then your reference point goes up + + align:start position:0% +then your reference point goes up + + + align:start position:0% +then your reference point goes up +nothing happens to your reported + + align:start position:0% +nothing happens to your reported + + + align:start position:0% +nothing happens to your reported +happiness but presumably you're happier + + align:start position:0% +happiness but presumably you're happier + + + align:start position:0% +happiness but presumably you're happier +than before + + align:start position:0% +than before + + + align:start position:0% +than before +so that went somewhere on the other hand + + align:start position:0% +so that went somewhere on the other hand + + + align:start position:0% +so that went somewhere on the other hand +um utility might in fact be very much + + align:start position:0% +um utility might in fact be very much + + + align:start position:0% +um utility might in fact be very much +reference dependent for example + + align:start position:0% +reference dependent for example + + + align:start position:0% +reference dependent for example +um you might compare yourself to words + + align:start position:0% +um you might compare yourself to words + + + align:start position:0% +um you might compare yourself to words +and then + + align:start position:0% +and then + + + align:start position:0% +and then +inequality for example might be + + align:start position:0% +inequality for example might be + + + align:start position:0% +inequality for example might be +extremely important for + + align:start position:0% +extremely important for + + + align:start position:0% +extremely important for +people's happiness and sort of one of + + align:start position:0% +people's happiness and sort of one of + + + align:start position:0% +people's happiness and sort of one of +the things that people argue is that + + align:start position:0% +the things that people argue is that + + + align:start position:0% +the things that people argue is that +for example the gdp also including in + + align:start position:0% +for example the gdp also including in + + + align:start position:0% +for example the gdp also including in +the us gdp in many places has gone up + + align:start position:0% +the us gdp in many places has gone up + + + align:start position:0% +the us gdp in many places has gone up +quite a bit but happiness has not + + align:start position:0% +quite a bit but happiness has not + + + align:start position:0% +quite a bit but happiness has not +increased + + align:start position:0% +increased + + + align:start position:0% +increased +but often that's people argue that's + + align:start position:0% +but often that's people argue that's + + + align:start position:0% +but often that's people argue that's +because in part + + align:start position:0% +because in part + + + align:start position:0% +because in part +inequality also went up a lot and if + + align:start position:0% +inequality also went up a lot and if + + + align:start position:0% +inequality also went up a lot and if +that inequality really makes people + + align:start position:0% +that inequality really makes people + + + align:start position:0% +that inequality really makes people +deeply unhappy + + align:start position:0% +deeply unhappy + + + align:start position:0% +deeply unhappy +well that is important and we should you + + align:start position:0% +well that is important and we should you + + + align:start position:0% +well that is important and we should you +should incorporate that in some ways in + + align:start position:0% +should incorporate that in some ways in + + + align:start position:0% +should incorporate that in some ways in +our considerations overall + + align:start position:0% +our considerations overall + + + align:start position:0% +our considerations overall +but you see that causes tricky issues + + align:start position:0% +but you see that causes tricky issues + + + align:start position:0% +but you see that causes tricky issues +because in one case + + align:start position:0% +because in one case + + + align:start position:0% +because in one case +i'm doubling everybody's income and + + align:start position:0% +i'm doubling everybody's income and + + + align:start position:0% +i'm doubling everybody's income and +presumably people should be happier + + align:start position:0% +presumably people should be happier + + + align:start position:0% +presumably people should be happier +because their living standard goes up + + align:start position:0% +because their living standard goes up + + + align:start position:0% +because their living standard goes up +um so presumably there even if happiness + + align:start position:0% +um so presumably there even if happiness + + + align:start position:0% +um so presumably there even if happiness +doesn't go up presumably those living + + align:start position:0% +doesn't go up presumably those living + + + align:start position:0% +doesn't go up presumably those living +standards have gone up and something is + + align:start position:0% +standards have gone up and something is + + + align:start position:0% +standards have gone up and something is +going wrong if i don't see increased + + align:start position:0% +going wrong if i don't see increased + + + align:start position:0% +going wrong if i don't see increased +happiness in terms of measurement + + align:start position:0% +happiness in terms of measurement + + + align:start position:0% +happiness in terms of measurement +on the other hand there might be very + + align:start position:0% +on the other hand there might be very + + + align:start position:0% +on the other hand there might be very +much real issues about + + align:start position:0% +much real issues about + + + align:start position:0% +much real issues about +inequality is quite important and + + align:start position:0% +inequality is quite important and + + + align:start position:0% +inequality is quite important and +reference dependent + + align:start position:0% +reference dependent + + + align:start position:0% +reference dependent +matters for people's happiness and + + align:start position:0% +matters for people's happiness and + + + align:start position:0% +matters for people's happiness and +well-being in the sense that like + + align:start position:0% +well-being in the sense that like + + + align:start position:0% +well-being in the sense that like +what really might matter a lot is + + align:start position:0% +what really might matter a lot is + + + align:start position:0% +what really might matter a lot is +relative income rather than absolute + + align:start position:0% +relative income rather than absolute + + + align:start position:0% +relative income rather than absolute +income and we should + + align:start position:0% +income and we should + + + align:start position:0% +income and we should +capture that in some uh meaningful way + + align:start position:0% +capture that in some uh meaningful way + + + align:start position:0% +capture that in some uh meaningful way +um + + align:start position:0% +um + + + align:start position:0% +um +uh oops sorry um in particular there's + + align:start position:0% +uh oops sorry um in particular there's + + + align:start position:0% +uh oops sorry um in particular there's +lots of issues with like + + align:start position:0% +lots of issues with like + + + align:start position:0% +lots of issues with like +depending on what i focus you on when i + + align:start position:0% +depending on what i focus you on when i + + + align:start position:0% +depending on what i focus you on when i +ask certain questions i can get very + + align:start position:0% +ask certain questions i can get very + + + align:start position:0% +ask certain questions i can get very +very different answers and one for + + align:start position:0% +very different answers and one for + + + align:start position:0% +very different answers and one for +example + + align:start position:0% +example + + + align:start position:0% +example +uh example of this is uh there's a + + align:start position:0% +uh example of this is uh there's a + + + align:start position:0% +uh example of this is uh there's a +people that struck it out that looked at + + align:start position:0% +people that struck it out that looked at + + + align:start position:0% +people that struck it out that looked at +the correlation between general + + align:start position:0% +the correlation between general + + + align:start position:0% +the correlation between general +happiness and happiness with dating + + align:start position:0% +happiness and happiness with dating + + + align:start position:0% +happiness and happiness with dating +and so what they did is very simple + + align:start position:0% +and so what they did is very simple + + + align:start position:0% +and so what they did is very simple +thing they essentially just manipulated + + align:start position:0% +thing they essentially just manipulated + + + align:start position:0% +thing they essentially just manipulated +the order of questions the first they + + align:start position:0% +the order of questions the first they + + + align:start position:0% +the order of questions the first they +asked people about how happy are you in + + align:start position:0% +asked people about how happy are you in + + + align:start position:0% +asked people about how happy are you in +general + + align:start position:0% +general + + + align:start position:0% +general +um and then they ask people how happy + + align:start position:0% +um and then they ask people how happy + + + align:start position:0% +um and then they ask people how happy +are you with your dating life + + align:start position:0% +are you with your dating life + + + align:start position:0% +are you with your dating life +and a different sub sample they ask + + align:start position:0% +and a different sub sample they ask + + + align:start position:0% +and a different sub sample they ask +people how happy are you with the date + + align:start position:0% +people how happy are you with the date + + + align:start position:0% +people how happy are you with the date +of day in life and then ask people about + + align:start position:0% +of day in life and then ask people about + + + align:start position:0% +of day in life and then ask people about +the general happiness and what that does + + align:start position:0% +the general happiness and what that does + + + align:start position:0% +the general happiness and what that does +essentially it focuses people very much + + align:start position:0% +essentially it focuses people very much + + + align:start position:0% +essentially it focuses people very much +about dating + + align:start position:0% +about dating + + + align:start position:0% +about dating +as part of their life being important + + align:start position:0% +as part of their life being important + + + align:start position:0% +as part of their life being important +and for their happiness + + align:start position:0% +and for their happiness + + + align:start position:0% +and for their happiness +and similarly i think this is exactly + + align:start position:0% +and similarly i think this is exactly + + + align:start position:0% +and similarly i think this is exactly +what maya was saying as well we just + + align:start position:0% +what maya was saying as well we just + + + align:start position:0% +what maya was saying as well we just +asked + + align:start position:0% +asked + + + align:start position:0% +asked +you about the lateral question versus + + align:start position:0% +you about the lateral question versus + + + align:start position:0% +you about the lateral question versus +about two other questions about + + align:start position:0% +about two other questions about + + + align:start position:0% +about two other questions about +uh depending on our phrase the question + + align:start position:0% +uh depending on our phrase the question + + + align:start position:0% +uh depending on our phrase the question +i can get very different answers + + align:start position:0% +i can get very different answers + + + align:start position:0% +i can get very different answers +um and what you're saying so that makes + + align:start position:0% +um and what you're saying so that makes + + + align:start position:0% +um and what you're saying so that makes +it very tricky to figure out like which + + align:start position:0% +it very tricky to figure out like which + + + align:start position:0% +it very tricky to figure out like which +question should we use how much weight + + align:start position:0% +question should we use how much weight + + + align:start position:0% +question should we use how much weight +should we put on it + + align:start position:0% +should we put on it + + + align:start position:0% +should we put on it +and even like things like the order of + + align:start position:0% +and even like things like the order of + + + align:start position:0% +and even like things like the order of +questions + + align:start position:0% +questions + + + align:start position:0% +questions +matter matters quite a bit which makes + + align:start position:0% +matter matters quite a bit which makes + + + align:start position:0% +matter matters quite a bit which makes +economists very um nervous and so on and + + align:start position:0% +economists very um nervous and so on and + + + align:start position:0% +economists very um nervous and so on and +that's why in part economists would + + align:start position:0% +that's why in part economists would + + + align:start position:0% +that's why in part economists would +argue that we really should have a real + + align:start position:0% +argue that we really should have a real + + + align:start position:0% +argue that we really should have a real +preference and choices + + align:start position:0% +preference and choices + + + align:start position:0% +preference and choices +now on the other hand um i very much + + align:start position:0% +now on the other hand um i very much + + + align:start position:0% +now on the other hand um i very much +think + + align:start position:0% +think + + + align:start position:0% +think +the questions when you just ask people + + align:start position:0% +the questions when you just ask people + + + align:start position:0% +the questions when you just ask people +and say i'm deeply unhappy + + align:start position:0% +and say i'm deeply unhappy + + + align:start position:0% +and say i'm deeply unhappy +that has some content and so if there's + + align:start position:0% +that has some content and so if there's + + + align:start position:0% +that has some content and so if there's +there's information there and so + + align:start position:0% +there's information there and so + + + align:start position:0% +there's information there and so +then the question is well how do we how + + align:start position:0% +then the question is well how do we how + + + align:start position:0% +then the question is well how do we how +do we weigh these considerations on the + + align:start position:0% +do we weigh these considerations on the + + + align:start position:0% +do we weigh these considerations on the +one hand the survey instrument is + + align:start position:0% +one hand the survey instrument is + + + align:start position:0% +one hand the survey instrument is +really just very fragile and we don't + + align:start position:0% +really just very fragile and we don't + + + align:start position:0% +really just very fragile and we don't +measure very much on the other hand + + align:start position:0% +measure very much on the other hand + + + align:start position:0% +measure very much on the other hand +um there's useful information here that + + align:start position:0% +um there's useful information here that + + + align:start position:0% +um there's useful information here that +we should be incorporating + + align:start position:0% +we should be incorporating + + + align:start position:0% +we should be incorporating +uh somehow so i just wanted to sort of + + align:start position:0% +uh somehow so i just wanted to sort of + + + align:start position:0% +uh somehow so i just wanted to sort of +have you + + align:start position:0% +have you + + + align:start position:0% +have you +that have that in mind and so let's now + + align:start position:0% +that have that in mind and so let's now + + + align:start position:0% +that have that in mind and so let's now +look at some data that people have + + align:start position:0% +look at some data that people have + + + align:start position:0% +look at some data that people have +collected + + align:start position:0% +collected + + + align:start position:0% +collected +so what's a very nice source overall is + + align:start position:0% +so what's a very nice source overall is + + + align:start position:0% +so what's a very nice source overall is +what's called the + + align:start position:0% +what's called the + + + align:start position:0% +what's called the +um our world and data which uh + + align:start position:0% +um our world and data which uh + + + align:start position:0% +um our world and data which uh +has lots of interesting graphs and + + align:start position:0% +has lots of interesting graphs and + + + align:start position:0% +has lots of interesting graphs and +figures where you can look at happiness + + align:start position:0% +figures where you can look at happiness + + + align:start position:0% +figures where you can look at happiness +and all sorts of things + + align:start position:0% +and all sorts of things + + + align:start position:0% +and all sorts of things +uh data in the world and when you look + + align:start position:0% +uh data in the world and when you look + + + align:start position:0% +uh data in the world and when you look +at life satisfaction around the + + align:start position:0% +at life satisfaction around the + + + align:start position:0% +at life satisfaction around the +the globe this is very much the uh + + align:start position:0% +the globe this is very much the uh + + + align:start position:0% +the globe this is very much the uh +latter question here which you see + + align:start position:0% +latter question here which you see + + + align:start position:0% +latter question here which you see +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +uh uh as they were saying there's sort + + align:start position:0% +uh uh as they were saying there's sort + + + align:start position:0% +uh uh as they were saying there's sort +of the + + align:start position:0% +of the + + + align:start position:0% +of the +the latter from zero to ten and again + + align:start position:0% +the latter from zero to ten and again + + + align:start position:0% +the latter from zero to ten and again +the latter question is very much + + align:start position:0% +the latter question is very much + + + align:start position:0% +the latter question is very much +something hierarchical and makes it + + align:start position:0% +something hierarchical and makes it + + + align:start position:0% +something hierarchical and makes it +makes inequality or relative comparisons + + align:start position:0% +makes inequality or relative comparisons + + + align:start position:0% +makes inequality or relative comparisons +quite silly even if it only asks you + + align:start position:0% +quite silly even if it only asks you + + + align:start position:0% +quite silly even if it only asks you +about like your worst + + align:start position:0% +about like your worst + + + align:start position:0% +about like your worst +best possible life for yourself it does + + align:start position:0% +best possible life for yourself it does + + + align:start position:0% +best possible life for yourself it does +have + + align:start position:0% +have + + + align:start position:0% +have +the the feeling that really it's about + + align:start position:0% +the the feeling that really it's about + + + align:start position:0% +the the feeling that really it's about +comparing yourself to others + + align:start position:0% +comparing yourself to others + + + align:start position:0% +comparing yourself to others +but anyway that's very much used in many + + align:start position:0% +but anyway that's very much used in many + + + align:start position:0% +but anyway that's very much used in many +uh cases often people call it life + + align:start position:0% +uh cases often people call it life + + + align:start position:0% +uh cases often people call it life +satisfaction but even here they also + + align:start position:0% +satisfaction but even here they also + + + align:start position:0% +satisfaction but even here they also +call it like happiness + + align:start position:0% +call it like happiness + + + align:start position:0% +call it like happiness +overall this is from the world happiness + + align:start position:0% +overall this is from the world happiness + + + align:start position:0% +overall this is from the world happiness +report and what you see is that + + align:start position:0% +report and what you see is that + + + align:start position:0% +report and what you see is that +in general rich countries tend to be uh + + align:start position:0% +in general rich countries tend to be uh + + + align:start position:0% +in general rich countries tend to be uh +report higher happiness scandinavian + + align:start position:0% +report higher happiness scandinavian + + + align:start position:0% +report higher happiness scandinavian +countries in particular the u.s is like + + align:start position:0% +countries in particular the u.s is like + + + align:start position:0% +countries in particular the u.s is like +reasonably happy + + align:start position:0% +reasonably happy + + + align:start position:0% +reasonably happy +europe is quite happy um and then if you + + align:start position:0% +europe is quite happy um and then if you + + + align:start position:0% +europe is quite happy um and then if you +go to like poorer countries in + + align:start position:0% +go to like poorer countries in + + + align:start position:0% +go to like poorer countries in +particular in africa + + align:start position:0% +particular in africa + + + align:start position:0% +particular in africa +they tend to be uh report a lot lower + + align:start position:0% +they tend to be uh report a lot lower + + + align:start position:0% +they tend to be uh report a lot lower +happiness level + + align:start position:0% +happiness level + + + align:start position:0% +happiness level +when you look at comparisons across + + align:start position:0% +when you look at comparisons across + + + align:start position:0% +when you look at comparisons across +countries you see like a very + + align:start position:0% +countries you see like a very + + + align:start position:0% +countries you see like a very +clear relationship rich countries + + align:start position:0% +clear relationship rich countries + + + align:start position:0% +clear relationship rich countries +tend to be a lot report much higher + + align:start position:0% +tend to be a lot report much higher + + + align:start position:0% +tend to be a lot report much higher +on life satisfaction uh compared to poor + + align:start position:0% +on life satisfaction uh compared to poor + + + align:start position:0% +on life satisfaction uh compared to poor +countries that's a very clear + + align:start position:0% +countries that's a very clear + + + align:start position:0% +countries that's a very clear +association that's true both across + + align:start position:0% +association that's true both across + + + align:start position:0% +association that's true both across +countries + + align:start position:0% +countries + + + align:start position:0% +countries +but also to within countries so what + + align:start position:0% +but also to within countries so what + + + align:start position:0% +but also to within countries so what +this graph here shows you is + + align:start position:0% +this graph here shows you is + + + align:start position:0% +this graph here shows you is +the average income in a country and then + + align:start position:0% +the average income in a country and then + + + align:start position:0% +the average income in a country and then +these arrows show you + + align:start position:0% +these arrows show you + + + align:start position:0% +these arrows show you +the gradient within the slope of the + + align:start position:0% +the gradient within the slope of the + + + align:start position:0% +the gradient within the slope of the +arrows is the gradient within countries + + align:start position:0% +arrows is the gradient within countries + + + align:start position:0% +arrows is the gradient within countries +and what you see is essentially + + align:start position:0% +and what you see is essentially + + + align:start position:0% +and what you see is essentially +uh so this is like comparing people + + align:start position:0% +uh so this is like comparing people + + + align:start position:0% +uh so this is like comparing people +within countries rich versus poor + + align:start position:0% +within countries rich versus poor + + + align:start position:0% +within countries rich versus poor +countries + + align:start position:0% +countries + + + align:start position:0% +countries +uh what is security sort of increase + + align:start position:0% +uh what is security sort of increase + + + align:start position:0% +uh what is security sort of increase +income within a country by like a + + align:start position:0% +income within a country by like a + + + align:start position:0% +income within a country by like a +thousand or something dollars how much + + align:start position:0% +thousand or something dollars how much + + + align:start position:0% +thousand or something dollars how much +does + + align:start position:0% +does + + + align:start position:0% +does +uh people's um happiness go up and what + + align:start position:0% +uh people's um happiness go up and what + + + align:start position:0% +uh people's um happiness go up and what +you see is all of those countries have + + align:start position:0% +you see is all of those countries have + + + align:start position:0% +you see is all of those countries have +like + + align:start position:0% +like + + + align:start position:0% +like +uh almost all countries have like + + align:start position:0% +uh almost all countries have like + + + align:start position:0% +uh almost all countries have like +increasing gradients which tells you + + align:start position:0% +increasing gradients which tells you + + + align:start position:0% +increasing gradients which tells you +that both within and across countries + + align:start position:0% +that both within and across countries + + + align:start position:0% +that both within and across countries +richer + + align:start position:0% +richer + + + align:start position:0% +richer +people report higher life satisfactions + + align:start position:0% +people report higher life satisfactions + + + align:start position:0% +people report higher life satisfactions +compared to poorer people similarly + + align:start position:0% +compared to poorer people similarly + + + align:start position:0% +compared to poorer people similarly +um that's also true for mental health so + + align:start position:0% +um that's also true for mental health so + + + align:start position:0% +um that's also true for mental health so +these are all questions about + + align:start position:0% +these are all questions about + + + align:start position:0% +these are all questions about +subjective well-being how happy are you + + align:start position:0% +subjective well-being how happy are you + + + align:start position:0% +subjective well-being how happy are you +overall asking the overall + + align:start position:0% +overall asking the overall + + + align:start position:0% +overall asking the overall +population but if you try to look at + + align:start position:0% +population but if you try to look at + + + align:start position:0% +population but if you try to look at +mental health + + align:start position:0% +mental health + + + align:start position:0% +mental health +conditions in terms of particularly + + align:start position:0% +conditions in terms of particularly + + + align:start position:0% +conditions in terms of particularly +depression and anxiety + + align:start position:0% +depression and anxiety + + + align:start position:0% +depression and anxiety +so techniques so using + + align:start position:0% +so techniques so using + + + align:start position:0% +so techniques so using +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +clear definitions on uh psychiatric + + align:start position:0% +clear definitions on uh psychiatric + + + align:start position:0% +clear definitions on uh psychiatric +disorders + + align:start position:0% +disorders + + + align:start position:0% +disorders +for depression and anxiety and also for + + align:start position:0% +for depression and anxiety and also for + + + align:start position:0% +for depression and anxiety and also for +other completions + + align:start position:0% +other completions + + + align:start position:0% +other completions +you find that the poor in any given + + align:start position:0% +you find that the poor in any given + + + align:start position:0% +you find that the poor in any given +location are more likely to suffer from + + align:start position:0% +location are more likely to suffer from + + + align:start position:0% +location are more likely to suffer from +depression and or + + align:start position:0% +depression and or + + + align:start position:0% +depression and or +anxiety interestingly the prevalence of + + align:start position:0% +anxiety interestingly the prevalence of + + + align:start position:0% +anxiety interestingly the prevalence of +depression + + align:start position:0% +depression + + + align:start position:0% +depression +uh um in fact also anxiety is higher in + + align:start position:0% +uh um in fact also anxiety is higher in + + + align:start position:0% +uh um in fact also anxiety is higher in +rich countries + + align:start position:0% +rich countries + + + align:start position:0% +rich countries +um there's some there's a lot of + + align:start position:0% +um there's some there's a lot of + + + align:start position:0% +um there's some there's a lot of +questions about measurement problems + + align:start position:0% +questions about measurement problems + + + align:start position:0% +questions about measurement problems +it's like it's + + align:start position:0% +it's like it's + + + align:start position:0% +it's like it's +really measuring the same thing and so + + align:start position:0% +really measuring the same thing and so + + + align:start position:0% +really measuring the same thing and so +on and so forth but it could also be + + align:start position:0% +on and so forth but it could also be + + + align:start position:0% +on and so forth but it could also be +there's other factors involved in + + align:start position:0% +there's other factors involved in + + + align:start position:0% +there's other factors involved in +particular issues such as inequality + + align:start position:0% +particular issues such as inequality + + + align:start position:0% +particular issues such as inequality +and it could just be that really what's + + align:start position:0% +and it could just be that really what's + + + align:start position:0% +and it could just be that really what's +really important is relative income as + + align:start position:0% +really important is relative income as + + + align:start position:0% +really important is relative income as +opposed to absolute income + + align:start position:0% +opposed to absolute income + + + align:start position:0% +opposed to absolute income +now we know also that anti-poverty + + align:start position:0% +now we know also that anti-poverty + + + align:start position:0% +now we know also that anti-poverty +programs uh + + align:start position:0% +programs uh + + + align:start position:0% +programs uh +improve mental health in various ways so + + align:start position:0% +improve mental health in various ways so + + + align:start position:0% +improve mental health in various ways so +including things like + + align:start position:0% +including things like + + + align:start position:0% +including things like +cash transfers and + + align:start position:0% +cash transfers and + + + align:start position:0% +cash transfers and +other anti-poverty programs so this is + + align:start position:0% +other anti-poverty programs so this is + + + align:start position:0% +other anti-poverty programs so this is +an overview of studies + + align:start position:0% +an overview of studies + + + align:start position:0% +an overview of studies +this is essentially a recent + + align:start position:0% +this is essentially a recent + + + align:start position:0% +this is essentially a recent +meta-analysis that we did for some + + align:start position:0% +meta-analysis that we did for some + + + align:start position:0% +meta-analysis that we did for some +overview paper + + align:start position:0% +overview paper + + + align:start position:0% +overview paper +of mine and what you see here is a + + align:start position:0% +of mine and what you see here is a + + + align:start position:0% +of mine and what you see here is a +number of different interventions + + align:start position:0% +number of different interventions + + + align:start position:0% +number of different interventions +both cash transfers and other + + align:start position:0% +both cash transfers and other + + + align:start position:0% +both cash transfers and other +anti-poverty programs which + + align:start position:0% +anti-poverty programs which + + + align:start position:0% +anti-poverty programs which +are more broader programs and what you + + align:start position:0% +are more broader programs and what you + + + align:start position:0% +are more broader programs and what you +see here is the treatment effect + + align:start position:0% +see here is the treatment effect + + + align:start position:0% +see here is the treatment effect +estimated in the different studies these + + align:start position:0% +estimated in the different studies these + + + align:start position:0% +estimated in the different studies these +are + + align:start position:0% +are + + + align:start position:0% +are +overall property anti-poverty programs + + align:start position:0% +overall property anti-poverty programs + + + align:start position:0% +overall property anti-poverty programs +these are cash transfer programs + + align:start position:0% +these are cash transfer programs + + + align:start position:0% +these are cash transfer programs +but overall essentially the overwhelming + + align:start position:0% +but overall essentially the overwhelming + + + align:start position:0% +but overall essentially the overwhelming +um answer is that once you give people + + align:start position:0% +um answer is that once you give people + + + align:start position:0% +um answer is that once you give people +cash or reduce their poverty + + align:start position:0% +cash or reduce their poverty + + + align:start position:0% +cash or reduce their poverty +that improves their mental health as + + align:start position:0% +that improves their mental health as + + + align:start position:0% +that improves their mental health as +measured by different + + align:start position:0% +measured by different + + + align:start position:0% +measured by different +uh these are pwb means psychological + + align:start position:0% +uh these are pwb means psychological + + + align:start position:0% +uh these are pwb means psychological +well-being indices + + align:start position:0% +well-being indices + + + align:start position:0% +well-being indices +this is also like depression screening + + align:start position:0% +this is also like depression screening + + + align:start position:0% +this is also like depression screening +scores and so on so by various measures + + align:start position:0% +scores and so on so by various measures + + + align:start position:0% +scores and so on so by various measures +of people's mental health + + align:start position:0% +of people's mental health + + + align:start position:0% +of people's mental health +giving people more money improves their + + align:start position:0% +giving people more money improves their + + + align:start position:0% +giving people more money improves their +mental health so that's true at the + + align:start position:0% +mental health so that's true at the + + + align:start position:0% +mental health so that's true at the +extreme in terms of like + + align:start position:0% +extreme in terms of like + + + align:start position:0% +extreme in terms of like +really sort of mental illness depressive + + align:start position:0% +really sort of mental illness depressive + + + align:start position:0% +really sort of mental illness depressive +um and anxiety disorders it's also true + + align:start position:0% +um and anxiety disorders it's also true + + + align:start position:0% +um and anxiety disorders it's also true +for + + align:start position:0% +for + + + align:start position:0% +for +other measures of psychological + + align:start position:0% +other measures of psychological + + + align:start position:0% +other measures of psychological +well-being if you just give people a + + align:start position:0% +well-being if you just give people a + + + align:start position:0% +well-being if you just give people a +cash they report + + align:start position:0% +cash they report + + + align:start position:0% +cash they report +higher happiness in addition to what i + + align:start position:0% +higher happiness in addition to what i + + + align:start position:0% +higher happiness in addition to what i +told you before + + align:start position:0% +told you before + + + align:start position:0% +told you before +this being true in the cross section + + align:start position:0% +this being true in the cross section + + + align:start position:0% +this being true in the cross section +now interestingly uh we also tend to + + align:start position:0% +now interestingly uh we also tend to + + + align:start position:0% +now interestingly uh we also tend to +think that others are less happy than + + align:start position:0% +think that others are less happy than + + + align:start position:0% +think that others are less happy than +they say they are so if you just ask + + align:start position:0% +they say they are so if you just ask + + + align:start position:0% +they say they are so if you just ask +people + + align:start position:0% +people + + + align:start position:0% +people +um how happy are other people in your + + align:start position:0% +um how happy are other people in your + + + align:start position:0% +um how happy are other people in your +country in almost every country in the + + align:start position:0% +country in almost every country in the + + + align:start position:0% +country in almost every country in the +world what you find is that people tend + + align:start position:0% +world what you find is that people tend + + + align:start position:0% +world what you find is that people tend +to say + + align:start position:0% +to say + + + align:start position:0% +to say +the fraction that people actually say + + align:start position:0% +the fraction that people actually say + + + align:start position:0% +the fraction that people actually say +that they're very happy or rather happy + + align:start position:0% +that they're very happy or rather happy + + + align:start position:0% +that they're very happy or rather happy +is is lower than they actually say they + + align:start position:0% +is is lower than they actually say they + + + align:start position:0% +is is lower than they actually say they +are which is kind of an interesting + + align:start position:0% + + + + align:start position:0% + +fact now um this is we talked about this + + align:start position:0% +fact now um this is we talked about this + + + align:start position:0% +fact now um this is we talked about this +already a little bit how is life + + align:start position:0% +already a little bit how is life + + + align:start position:0% +already a little bit how is life +satisfaction happiness related to life + + align:start position:0% +satisfaction happiness related to life + + + align:start position:0% +satisfaction happiness related to life +events + + align:start position:0% +events + + + align:start position:0% +events +it turns out when you look at different + + align:start position:0% +it turns out when you look at different + + + align:start position:0% +it turns out when you look at different +life events and that's quite interesting + + align:start position:0% +life events and that's quite interesting + + + align:start position:0% +life events and that's quite interesting +that + + align:start position:0% +that + + + align:start position:0% +that +a lot of life events tend to affect + + align:start position:0% +a lot of life events tend to affect + + + align:start position:0% +a lot of life events tend to affect +people's um + + align:start position:0% +people's um + + + align:start position:0% +people's um +uh reported well-being or life + + align:start position:0% +uh reported well-being or life + + + align:start position:0% +uh reported well-being or life +satisfaction + + align:start position:0% +satisfaction + + + align:start position:0% +satisfaction +a lot for many events including stuff + + align:start position:0% +a lot for many events including stuff + + + align:start position:0% +a lot for many events including stuff +like + + align:start position:0% +like + + + align:start position:0% +like +widowhood or divorce or marriage and + + align:start position:0% +widowhood or divorce or marriage and + + + align:start position:0% +widowhood or divorce or marriage and +other + + align:start position:0% +other + + + align:start position:0% +other +sort of types of events or winning the + + align:start position:0% +sort of types of events or winning the + + + align:start position:0% +sort of types of events or winning the +lottery these effects are very much + + align:start position:0% +lottery these effects are very much + + + align:start position:0% +lottery these effects are very much +transitory which is to say like when + + align:start position:0% +transitory which is to say like when + + + align:start position:0% +transitory which is to say like when +somebody when something really bad or + + align:start position:0% +somebody when something really bad or + + + align:start position:0% +somebody when something really bad or +somebody happens their happiness goes + + align:start position:0% +somebody happens their happiness goes + + + align:start position:0% +somebody happens their happiness goes +down a lot + + align:start position:0% +down a lot + + + align:start position:0% +down a lot +but it tends to recover um quite a bit + + align:start position:0% +but it tends to recover um quite a bit + + + align:start position:0% +but it tends to recover um quite a bit +this is what we talked about before + + align:start position:0% +this is what we talked about before + + + align:start position:0% +this is what we talked about before +people are quite adaptive to many + + align:start position:0% +people are quite adaptive to many + + + align:start position:0% +people are quite adaptive to many +changes and they adjust + + align:start position:0% +changes and they adjust + + + align:start position:0% +changes and they adjust +quite well this is what people call the + + align:start position:0% +quite well this is what people call the + + + align:start position:0% +quite well this is what people call the +psychological immune system + + align:start position:0% +psychological immune system + + + align:start position:0% +psychological immune system +except for a few things including + + align:start position:0% +except for a few things including + + + align:start position:0% +except for a few things including +unemployment and one potential reason is + + align:start position:0% +unemployment and one potential reason is + + + align:start position:0% +unemployment and one potential reason is +that for example unemployment might also + + align:start position:0% +that for example unemployment might also + + + align:start position:0% +that for example unemployment might also +cause + + align:start position:0% +cause + + + align:start position:0% +cause +cause things like depression and once + + align:start position:0% +cause things like depression and once + + + align:start position:0% +cause things like depression and once +you're really depressed that doesn't + + align:start position:0% +you're really depressed that doesn't + + + align:start position:0% +you're really depressed that doesn't +really go back over + + align:start position:0% +really go back over + + + align:start position:0% +really go back over +that easily that's true for women it's + + align:start position:0% +that easily that's true for women it's + + + align:start position:0% +that easily that's true for women it's +also true for + + align:start position:0% +also true for + + + align:start position:0% +also true for +men overall there's also some other + + align:start position:0% +men overall there's also some other + + + align:start position:0% +men overall there's also some other +issues which you want to be careful with + + align:start position:0% +issues which you want to be careful with + + + align:start position:0% +issues which you want to be careful with +and interpret some of this data which is + + align:start position:0% +and interpret some of this data which is + + + align:start position:0% +and interpret some of this data which is +this is called like this evolution of + + align:start position:0% +this is called like this evolution of + + + align:start position:0% +this is called like this evolution of +latent situations which is + + align:start position:0% +latent situations which is + + + align:start position:0% +latent situations which is +when you look at um things like divorce + + align:start position:0% +when you look at um things like divorce + + + align:start position:0% +when you look at um things like divorce +uh it tends to be that people + + align:start position:0% +uh it tends to be that people + + + align:start position:0% +uh it tends to be that people +that um people is the worst you might + + align:start position:0% +that um people is the worst you might + + + align:start position:0% +that um people is the worst you might +say well divorce makes them happier in + + align:start position:0% +say well divorce makes them happier in + + + align:start position:0% +say well divorce makes them happier in +some ways + + align:start position:0% +some ways + + + align:start position:0% +some ways +but really what seems to be or that that + + align:start position:0% +but really what seems to be or that that + + + align:start position:0% +but really what seems to be or that that +or you would look at this and say + + align:start position:0% +or you would look at this and say + + + align:start position:0% +or you would look at this and say +marriage makes people less happy + + align:start position:0% +marriage makes people less happy + + + align:start position:0% +marriage makes people less happy +but really what seems to be the case + + align:start position:0% +but really what seems to be the case + + + align:start position:0% +but really what seems to be the case +that you know people build up to like a + + align:start position:0% +that you know people build up to like a + + + align:start position:0% +that you know people build up to like a +positive event and then that sort of + + align:start position:0% +positive event and then that sort of + + + align:start position:0% +positive event and then that sort of +peaks uh positive or negatively + + align:start position:0% +peaks uh positive or negatively + + + align:start position:0% +peaks uh positive or negatively +and then essentially go back goes back + + align:start position:0% +and then essentially go back goes back + + + align:start position:0% +and then essentially go back goes back +to to what's before for example + + align:start position:0% +to to what's before for example + + + align:start position:0% +to to what's before for example +unemployment + + align:start position:0% +unemployment + + + align:start position:0% +unemployment +things tend to go worse even before + + align:start position:0% +things tend to go worse even before + + + align:start position:0% +things tend to go worse even before +people become unemployed + + align:start position:0% +people become unemployed + + + align:start position:0% +people become unemployed +um um uh so which seems to say there's + + align:start position:0% +um um uh so which seems to say there's + + + align:start position:0% +um um uh so which seems to say there's +people tend to these underlying events + + align:start position:0% +people tend to these underlying events + + + align:start position:0% +people tend to these underlying events +people tend to anticipate them already + + align:start position:0% +people tend to anticipate them already + + + align:start position:0% +people tend to anticipate them already +um psychologically in some ways + + align:start position:0% +um psychologically in some ways + + + align:start position:0% +um psychologically in some ways +now um this is what i was saying before + + align:start position:0% +now um this is what i was saying before + + + align:start position:0% +now um this is what i was saying before +when you look at + + align:start position:0% +when you look at + + + align:start position:0% +when you look at +uh comparisons over time um you get + + align:start position:0% +uh comparisons over time um you get + + + align:start position:0% +uh comparisons over time um you get +sometimes these + + align:start position:0% +sometimes these + + + align:start position:0% +sometimes these +situations were in particular in places + + align:start position:0% +situations were in particular in places + + + align:start position:0% +situations were in particular in places +including china but also in the u.s + + align:start position:0% +including china but also in the u.s + + + align:start position:0% +including china but also in the u.s +where real income has risen on a lot in + + align:start position:0% +where real income has risen on a lot in + + + align:start position:0% +where real income has risen on a lot in +many places but yet + + align:start position:0% +many places but yet + + + align:start position:0% +many places but yet +people's life satisfaction does not tend + + align:start position:0% +people's life satisfaction does not tend + + + align:start position:0% +people's life satisfaction does not tend +to increase + + align:start position:0% +to increase + + + align:start position:0% +to increase +why is that well that's in part i think + + align:start position:0% +why is that well that's in part i think + + + align:start position:0% +why is that well that's in part i think +because of inequality going up + + align:start position:0% +because of inequality going up + + + align:start position:0% +because of inequality going up +into the upward inequality staying the + + align:start position:0% +into the upward inequality staying the + + + align:start position:0% +into the upward inequality staying the +same and relative income really being + + align:start position:0% +same and relative income really being + + + align:start position:0% +same and relative income really being +important + + align:start position:0% +important + + + align:start position:0% +important +could be other things going on for + + align:start position:0% +could be other things going on for + + + align:start position:0% +could be other things going on for +example pollution is really bad for + + align:start position:0% +example pollution is really bad for + + + align:start position:0% +example pollution is really bad for +people's health + + align:start position:0% +people's health + + + align:start position:0% +people's health +mental health but also their happiness + + align:start position:0% +mental health but also their happiness + + + align:start position:0% +mental health but also their happiness +and so on it could also just be that + + align:start position:0% +and so on it could also just be that + + + align:start position:0% +and so on it could also just be that +people's + + align:start position:0% +people's + + + align:start position:0% +people's +reference points adjust which is just to + + align:start position:0% +reference points adjust which is just to + + + align:start position:0% +reference points adjust which is just to +make everybody twice as happy and now + + align:start position:0% +make everybody twice as happy and now + + + align:start position:0% +make everybody twice as happy and now +everybody's the reference point goes up + + align:start position:0% +everybody's the reference point goes up + + + align:start position:0% +everybody's the reference point goes up +even though their overall sort of + + align:start position:0% +even though their overall sort of + + + align:start position:0% +even though their overall sort of +objective for being standards in terms + + align:start position:0% +objective for being standards in terms + + + align:start position:0% +objective for being standards in terms +of like how much can they consume etc + + align:start position:0% +of like how much can they consume etc + + + align:start position:0% +of like how much can they consume etc +has gone up + + align:start position:0% +has gone up + + + align:start position:0% +has gone up +a lot now um + + align:start position:0% +a lot now um + + + align:start position:0% +a lot now um +this is quite interesting data now on uh + + align:start position:0% +this is quite interesting data now on uh + + + align:start position:0% +this is quite interesting data now on uh +ceiling effects + + align:start position:0% +ceiling effects + + + align:start position:0% +ceiling effects +so people uh so there's some controversy + + align:start position:0% +so people uh so there's some controversy + + + align:start position:0% +so people uh so there's some controversy +over this there was like some people + + align:start position:0% +over this there was like some people + + + align:start position:0% +over this there was like some people +were arguing that + + align:start position:0% +were arguing that + + + align:start position:0% +were arguing that +when you give people more money at some + + align:start position:0% +when you give people more money at some + + + align:start position:0% +when you give people more money at some +point there's a ceiling in fact + + align:start position:0% +point there's a ceiling in fact + + + align:start position:0% +point there's a ceiling in fact +it doesn't really make them happier + + align:start position:0% +it doesn't really make them happier + + + align:start position:0% +it doesn't really make them happier +anymore now um when you look at this + + align:start position:0% +anymore now um when you look at this + + + align:start position:0% +anymore now um when you look at this +graph here let me go back for a second + + align:start position:0% +graph here let me go back for a second + + + align:start position:0% +graph here let me go back for a second +when you look at + + align:start position:0% +when you look at + + + align:start position:0% +when you look at +um these graphs + + align:start position:0% +um these graphs + + + align:start position:0% +um these graphs +here this oops sorry + + align:start position:0% + + + + align:start position:0% + +when you look at this graph here it just + + align:start position:0% +when you look at this graph here it just + + + align:start position:0% +when you look at this graph here it just +doesn't look at all like ceiling effects + + align:start position:0% +doesn't look at all like ceiling effects + + + align:start position:0% +doesn't look at all like ceiling effects +looks like essentially + + align:start position:0% +looks like essentially + + + align:start position:0% +looks like essentially +self-reported uh life satisfaction as + + align:start position:0% +self-reported uh life satisfaction as + + + align:start position:0% +self-reported uh life satisfaction as +measured by these kinds of + + align:start position:0% +measured by these kinds of + + + align:start position:0% +measured by these kinds of +latter question essentially is like + + align:start position:0% +latter question essentially is like + + + align:start position:0% +latter question essentially is like +increasing and there seems to be no + + align:start position:0% +increasing and there seems to be no + + + align:start position:0% +increasing and there seems to be no +ceiling or doesn't seem to be flattening + + align:start position:0% +ceiling or doesn't seem to be flattening + + + align:start position:0% +ceiling or doesn't seem to be flattening +in any way you look at this one as well + + align:start position:0% +in any way you look at this one as well + + + align:start position:0% +in any way you look at this one as well +it seems to be like + + align:start position:0% +it seems to be like + + + align:start position:0% +it seems to be like +once you if you increase income by like + + align:start position:0% +once you if you increase income by like + + + align:start position:0% +once you if you increase income by like +a thousand dollars + + align:start position:0% +a thousand dollars + + + align:start position:0% +a thousand dollars +at any level it seems to be that like + + align:start position:0% +at any level it seems to be that like + + + align:start position:0% +at any level it seems to be that like +the reported life satisfaction goes up + + align:start position:0% +the reported life satisfaction goes up + + + align:start position:0% +the reported life satisfaction goes up +so again that doesn't look like they're + + align:start position:0% +so again that doesn't look like they're + + + align:start position:0% +so again that doesn't look like they're +assuming effects + + align:start position:0% +assuming effects + + + align:start position:0% +assuming effects +and that's true um as well if you look + + align:start position:0% +and that's true um as well if you look + + + align:start position:0% +and that's true um as well if you look +at + + align:start position:0% +at + + + align:start position:0% +at +these questions here this is a + + align:start position:0% +these questions here this is a + + + align:start position:0% +these questions here this is a +done these service in the u.s when you + + align:start position:0% +done these service in the u.s when you + + + align:start position:0% +done these service in the u.s when you +look at the lateral question which is + + align:start position:0% +look at the lateral question which is + + + align:start position:0% +look at the lateral question which is +this one here when you look at annual + + align:start position:0% +this one here when you look at annual + + + align:start position:0% +this one here when you look at annual +income in the u.s once you increase + + align:start position:0% +income in the u.s once you increase + + + align:start position:0% +income in the u.s once you increase +people's income + + align:start position:0% +people's income + + + align:start position:0% +people's income +their um mean ladder score which is here + + align:start position:0% +their um mean ladder score which is here + + + align:start position:0% +their um mean ladder score which is here +on the + + align:start position:0% +on the + + + align:start position:0% +on the +axis on the right tends to go up pretty + + align:start position:0% +axis on the right tends to go up pretty + + + align:start position:0% +axis on the right tends to go up pretty +much like monotonically maybe it's a + + align:start position:0% +much like monotonically maybe it's a + + + align:start position:0% +much like monotonically maybe it's a +little bit flattening but essentially it + + align:start position:0% +little bit flattening but essentially it + + + align:start position:0% +little bit flattening but essentially it +goes up so people report + + align:start position:0% +goes up so people report + + + align:start position:0% +goes up so people report +higher life satisfaction when they have + + align:start position:0% +higher life satisfaction when they have + + + align:start position:0% +higher life satisfaction when they have +higher income + + align:start position:0% +higher income + + + align:start position:0% +higher income +but when you look at people's affects + + align:start position:0% +but when you look at people's affects + + + align:start position:0% +but when you look at people's affects +both things like positive affect which + + align:start position:0% +both things like positive affect which + + + align:start position:0% +both things like positive affect which +is like happiness smiling enjoyment + + align:start position:0% +is like happiness smiling enjoyment + + + align:start position:0% +is like happiness smiling enjoyment +not being blue being stress-free and so + + align:start position:0% +not being blue being stress-free and so + + + align:start position:0% +not being blue being stress-free and so +long what you see is in particular this + + align:start position:0% +long what you see is in particular this + + + align:start position:0% +long what you see is in particular this +is for the us + + align:start position:0% +is for the us + + + align:start position:0% +is for the us +uh when you go from like something like + + align:start position:0% +uh when you go from like something like + + + align:start position:0% +uh when you go from like something like +ten thousand to twenty thousand to forty + + align:start position:0% +ten thousand to twenty thousand to forty + + + align:start position:0% +ten thousand to twenty thousand to forty +thousand dollars + + align:start position:0% +thousand dollars + + + align:start position:0% +thousand dollars +per uh year of income uh there's a clear + + align:start position:0% +per uh year of income uh there's a clear + + + align:start position:0% +per uh year of income uh there's a clear +increase over time so being poor is + + align:start position:0% +increase over time so being poor is + + + align:start position:0% +increase over time so being poor is +really + + align:start position:0% +really + + + align:start position:0% +really +like poor like um you know + + align:start position:0% + + + + align:start position:0% + +in the u.s it's really really bad for + + align:start position:0% +in the u.s it's really really bad for + + + align:start position:0% +in the u.s it's really really bad for +your + + align:start position:0% +your + + + align:start position:0% +your +affect and for your reported + + align:start position:0% +affect and for your reported + + + align:start position:0% +affect and for your reported +well-being overall but once you reach + + align:start position:0% +well-being overall but once you reach + + + align:start position:0% +well-being overall but once you reach +something like 50 60 70 000 in the u.s + + align:start position:0% +something like 50 60 70 000 in the u.s + + + align:start position:0% +something like 50 60 70 000 in the u.s +it seems to me that there's not no no + + align:start position:0% +it seems to me that there's not no no + + + align:start position:0% +it seems to me that there's not no no +effect on positive effects feeling blue + + align:start position:0% +effect on positive effects feeling blue + + + align:start position:0% +effect on positive effects feeling blue +stress free and so on + + align:start position:0% +stress free and so on + + + align:start position:0% +stress free and so on +so one interpretation of that is that + + align:start position:0% +so one interpretation of that is that + + + align:start position:0% +so one interpretation of that is that +if we take these affect questions as + + align:start position:0% +if we take these affect questions as + + + align:start position:0% +if we take these affect questions as +more like a measure of + + align:start position:0% +more like a measure of + + + align:start position:0% +more like a measure of +experience utility and happiness in any + + align:start position:0% +experience utility and happiness in any + + + align:start position:0% +experience utility and happiness in any +given life + + align:start position:0% +given life + + + align:start position:0% +given life +essentially having something like + + align:start position:0% +essentially having something like + + + align:start position:0% +essentially having something like +seventy eighty thousand dollars per year + + align:start position:0% +seventy eighty thousand dollars per year + + + align:start position:0% +seventy eighty thousand dollars per year +and you ask this is + + align:start position:0% +and you ask this is + + + align:start position:0% +and you ask this is +granted this is like from 2009 so maybe + + align:start position:0% +granted this is like from 2009 so maybe + + + align:start position:0% +granted this is like from 2009 so maybe +this number is not a little bit higher + + align:start position:0% +this number is not a little bit higher + + + align:start position:0% +this number is not a little bit higher +uh but that number is sufficient to make + + align:start position:0% +uh but that number is sufficient to make + + + align:start position:0% +uh but that number is sufficient to make +people sufficiently happy and beyond + + align:start position:0% +people sufficiently happy and beyond + + + align:start position:0% +people sufficiently happy and beyond +that + + align:start position:0% +that + + + align:start position:0% +that +um doubling lincoln will not do very + + align:start position:0% +um doubling lincoln will not do very + + + align:start position:0% +um doubling lincoln will not do very +much unlike how much you smile every day + + align:start position:0% +much unlike how much you smile every day + + + align:start position:0% +much unlike how much you smile every day +and how happy you are as measured with + + align:start position:0% +and how happy you are as measured with + + + align:start position:0% +and how happy you are as measured with +those things + + align:start position:0% +those things + + + align:start position:0% +those things +in contrast if i ask you the latter + + align:start position:0% +in contrast if i ask you the latter + + + align:start position:0% +in contrast if i ask you the latter +question which again is very much about + + align:start position:0% +question which again is very much about + + + align:start position:0% +question which again is very much about +comparison about how you feel yourself + + align:start position:0% +comparison about how you feel yourself + + + align:start position:0% +comparison about how you feel yourself +compared to somebody else in society + + align:start position:0% +compared to somebody else in society + + + align:start position:0% +compared to somebody else in society +uh going from hundred thousand between a + + align:start position:0% +uh going from hundred thousand between a + + + align:start position:0% +uh going from hundred thousand between a +thousand will um + + align:start position:0% +thousand will um + + + align:start position:0% +thousand will um +will make potentially um uh still quite + + align:start position:0% +will make potentially um uh still quite + + + align:start position:0% +will make potentially um uh still quite +a big difference + + align:start position:0% +a big difference + + + align:start position:0% +a big difference +any questions on on that + + align:start position:0% + + + + align:start position:0% + +okay so then let me uh this is among the + + align:start position:0% +okay so then let me uh this is among the + + + align:start position:0% +okay so then let me uh this is among the +most interesting + + align:start position:0% +most interesting + + + align:start position:0% +most interesting +parts of this kinds of these kinds of + + align:start position:0% +parts of this kinds of these kinds of + + + align:start position:0% +parts of this kinds of these kinds of +studies is the question about what in + + align:start position:0% +studies is the question about what in + + + align:start position:0% +studies is the question about what in +fact so if not just income so you know + + align:start position:0% +fact so if not just income so you know + + + align:start position:0% +fact so if not just income so you know +income essentially or overall if you're + + align:start position:0% +income essentially or overall if you're + + + align:start position:0% +income essentially or overall if you're +rich + + align:start position:0% +rich + + + align:start position:0% +rich +you're going to be happier compared to + + align:start position:0% +you're going to be happier compared to + + + align:start position:0% +you're going to be happier compared to +if you're poor but again + + align:start position:0% +if you're poor but again + + + align:start position:0% +if you're poor but again +um uh it seems to be like really if you + + align:start position:0% +um uh it seems to be like really if you + + + align:start position:0% +um uh it seems to be like really if you +want to sort of not be + + align:start position:0% +want to sort of not be + + + align:start position:0% +want to sort of not be +uh unhappy having income about 50 000 + + align:start position:0% +uh unhappy having income about 50 000 + + + align:start position:0% +uh unhappy having income about 50 000 +in the u.s is really important beyond + + align:start position:0% +in the u.s is really important beyond + + + align:start position:0% +in the u.s is really important beyond +that it doesn't seem to do very much + + align:start position:0% +that it doesn't seem to do very much + + + align:start position:0% +that it doesn't seem to do very much +um anymore but now what other things + + align:start position:0% +um anymore but now what other things + + + align:start position:0% +um anymore but now what other things +matter quite a bit and this is a very + + align:start position:0% +matter quite a bit and this is a very + + + align:start position:0% +matter quite a bit and this is a very +simple exercise + + align:start position:0% +simple exercise + + + align:start position:0% +simple exercise +so what they did is um this is um that + + align:start position:0% +so what they did is um this is um that + + + align:start position:0% +so what they did is um this is um that +he was supposed to read + + align:start position:0% +he was supposed to read + + + align:start position:0% +he was supposed to read +um they looked at the gallup survey + + align:start position:0% +um they looked at the gallup survey + + + align:start position:0% +um they looked at the gallup survey +questions from 40 or 450 000 americans + + align:start position:0% +questions from 40 or 450 000 americans + + + align:start position:0% +questions from 40 or 450 000 americans +and what they did is for each of these + + align:start position:0% +and what they did is for each of these + + + align:start position:0% +and what they did is for each of these +four measures of + + align:start position:0% +four measures of + + + align:start position:0% +four measures of +of um psychological well-being which is + + align:start position:0% +of um psychological well-being which is + + + align:start position:0% +of um psychological well-being which is +you know bcr positive affect not blue + + align:start position:0% +you know bcr positive affect not blue + + + align:start position:0% +you know bcr positive affect not blue +stress free and the latter questions + + align:start position:0% +stress free and the latter questions + + + align:start position:0% +stress free and the latter questions +um they were first just trying to + + align:start position:0% +um they were first just trying to + + + align:start position:0% +um they were first just trying to +predict + + align:start position:0% +predict + + + align:start position:0% +predict +uh what is the regression coefficient of + + align:start position:0% +uh what is the regression coefficient of + + + align:start position:0% +uh what is the regression coefficient of +high income so if you just put the + + align:start position:0% +high income so if you just put the + + + align:start position:0% +high income so if you just put the +sample in two and look at high income + + align:start position:0% +sample in two and look at high income + + + align:start position:0% +sample in two and look at high income +versus low income + + align:start position:0% +versus low income + + + align:start position:0% +versus low income +uh what is the regression coefficients + + align:start position:0% +uh what is the regression coefficients + + + align:start position:0% +uh what is the regression coefficients +of that they find as a + + align:start position:0% +of that they find as a + + + align:start position:0% +of that they find as a +interpreter that has causal effects + + align:start position:0% +interpreter that has causal effects + + + align:start position:0% +interpreter that has causal effects +which of course is um + + align:start position:0% +which of course is um + + + align:start position:0% +which of course is um +uh is a little uh problematic but you + + align:start position:0% +uh is a little uh problematic but you + + + align:start position:0% +uh is a little uh problematic but you +can think of this as the question if + + align:start position:0% +can think of this as the question if + + + align:start position:0% +can think of this as the question if +i wanted to try to predict how happy you + + align:start position:0% +i wanted to try to predict how happy you + + + align:start position:0% +i wanted to try to predict how happy you +are what do i + + align:start position:0% +are what do i + + + align:start position:0% +are what do i +need to know about you what are the what + + align:start position:0% +need to know about you what are the what + + + align:start position:0% +need to know about you what are the what +are the factors that i need to know + + align:start position:0% +are the factors that i need to know + + + align:start position:0% +are the factors that i need to know +about you if i wanted to predict how + + align:start position:0% +about you if i wanted to predict how + + + align:start position:0% +about you if i wanted to predict how +happy you are in your life on an even 20 + + align:start position:0% +happy you are in your life on an even 20 + + + align:start position:0% +happy you are in your life on an even 20 +times you wanted to know + + align:start position:0% +times you wanted to know + + + align:start position:0% +times you wanted to know +in 20 years from now are you going to be + + align:start position:0% +in 20 years from now are you going to be + + + align:start position:0% +in 20 years from now are you going to be +happy or not what are the things that + + align:start position:0% +happy or not what are the things that + + + align:start position:0% +happy or not what are the things that +you need to know about yourself and so + + align:start position:0% +you need to know about yourself and so + + + align:start position:0% +you need to know about yourself and so +it turns out that high income is + + align:start position:0% +it turns out that high income is + + + align:start position:0% +it turns out that high income is +predictive for this uncoefficient + + align:start position:0% +predictive for this uncoefficient + + + align:start position:0% +predictive for this uncoefficient +that says if you have higher income + + align:start position:0% +that says if you have higher income + + + align:start position:0% +that says if you have higher income +you're somewhat more likely to have + + align:start position:0% +you're somewhat more likely to have + + + align:start position:0% +you're somewhat more likely to have +positive affect + + align:start position:0% +positive affect + + + align:start position:0% +positive affect +less likely to to feel blue less likely + + align:start position:0% +less likely to to feel blue less likely + + + align:start position:0% +less likely to to feel blue less likely +to be stressed and a lot more likely to + + align:start position:0% +to be stressed and a lot more likely to + + + align:start position:0% +to be stressed and a lot more likely to +answer a higher qua give a higher answer + + align:start position:0% +answer a higher qua give a higher answer + + + align:start position:0% +answer a higher qua give a higher answer +in the latter question so in some sense + + align:start position:0% +in the latter question so in some sense + + + align:start position:0% +in the latter question so in some sense +higher income + + align:start position:0% +higher income + + + align:start position:0% +higher income +is good and then what the table does is + + align:start position:0% +is good and then what the table does is + + + align:start position:0% +is good and then what the table does is +it looks at + + align:start position:0% +it looks at + + + align:start position:0% +it looks at +it normalizes high income to one and + + align:start position:0% +it normalizes high income to one and + + + align:start position:0% +it normalizes high income to one and +then shows you other + + align:start position:0% +then shows you other + + + align:start position:0% +then shows you other +characteristics and says okay um if i + + align:start position:0% +characteristics and says okay um if i + + + align:start position:0% +characteristics and says okay um if i +knew another characteristic + + align:start position:0% +knew another characteristic + + + align:start position:0% +knew another characteristic +about you i you religious versus not and + + align:start position:0% +about you i you religious versus not and + + + align:start position:0% +about you i you religious versus not and +so on what is the relative + + align:start position:0% +so on what is the relative + + + align:start position:0% +so on what is the relative +uh coefficient of that compared to a + + align:start position:0% +uh coefficient of that compared to a + + + align:start position:0% +uh coefficient of that compared to a +high versus low income + + align:start position:0% +high versus low income + + + align:start position:0% +high versus low income +okay so for example if you're old you're + + align:start position:0% +okay so for example if you're old you're + + + align:start position:0% +okay so for example if you're old you're +um + + align:start position:0% +um + + + align:start position:0% +um +uh positive coefficient means like + + align:start position:0% +uh positive coefficient means like + + + align:start position:0% +uh positive coefficient means like +you're you're happier + + align:start position:0% +you're you're happier + + + align:start position:0% +you're you're happier +or more likely to have positive affect + + align:start position:0% +or more likely to have positive affect + + + align:start position:0% +or more likely to have positive affect +here and a negative the opposite + + align:start position:0% +here and a negative the opposite + + + align:start position:0% +here and a negative the opposite +um i guess for positive affect here so + + align:start position:0% +um i guess for positive affect here so + + + align:start position:0% +um i guess for positive affect here so +if you're old for example older people + + align:start position:0% +if you're old for example older people + + + align:start position:0% +if you're old for example older people +at least in the us tend to report + + align:start position:0% +at least in the us tend to report + + + align:start position:0% +at least in the us tend to report +higher um a positive affect + + align:start position:0% +higher um a positive affect + + + align:start position:0% +higher um a positive affect +so that's good news for you on 20 30 + + align:start position:0% +so that's good news for you on 20 30 + + + align:start position:0% +so that's good news for you on 20 30 +years you'll be likely to be + + align:start position:0% +years you'll be likely to be + + + align:start position:0% +years you'll be likely to be +to be happier um it turns out that + + align:start position:0% +to be happier um it turns out that + + + align:start position:0% +to be happier um it turns out that +religious people for example + + align:start position:0% +religious people for example + + + align:start position:0% +religious people for example +tend to be more more uh report more + + align:start position:0% +tend to be more more uh report more + + + align:start position:0% +tend to be more more uh report more +positive affects compared to + + align:start position:0% +positive affects compared to + + + align:start position:0% +positive affects compared to +non-religious people + + align:start position:0% +non-religious people + + + align:start position:0% +non-religious people +uh and the magnitude of these effects is + + align:start position:0% +uh and the magnitude of these effects is + + + align:start position:0% +uh and the magnitude of these effects is +pretty large + + align:start position:0% +pretty large + + + align:start position:0% +pretty large +that is to say one point one six is sort + + align:start position:0% +that is to say one point one six is sort + + + align:start position:0% +that is to say one point one six is sort +of to say + + align:start position:0% +of to say + + + align:start position:0% +of to say +uh if you compare religious if i knew + + align:start position:0% +uh if you compare religious if i knew + + + align:start position:0% +uh if you compare religious if i knew +about you are you religious versus not + + align:start position:0% +about you are you religious versus not + + + align:start position:0% +about you are you religious versus not +that is as predictive as knowing about + + align:start position:0% +that is as predictive as knowing about + + + align:start position:0% +that is as predictive as knowing about +you are you rich versus not are you in + + align:start position:0% +you are you rich versus not are you in + + + align:start position:0% +you are you rich versus not are you in +the upper lower half of this income + + align:start position:0% +the upper lower half of this income + + + align:start position:0% +the upper lower half of this income +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +so that's quite important in terms of + + align:start position:0% +so that's quite important in terms of + + + align:start position:0% +so that's quite important in terms of +like trying to predict whether people + + align:start position:0% +like trying to predict whether people + + + align:start position:0% +like trying to predict whether people +are happy + + align:start position:0% +are happy + + + align:start position:0% +are happy +now what's particularly striking here is + + align:start position:0% +now what's particularly striking here is + + + align:start position:0% +now what's particularly striking here is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +when you look at this here is alone uh a + + align:start position:0% +when you look at this here is alone uh a + + + align:start position:0% +when you look at this here is alone uh a +smoker + + align:start position:0% +smoker + + + align:start position:0% +smoker +uh and headache particularly um i + + align:start position:0% +uh and headache particularly um i + + + align:start position:0% +uh and headache particularly um i +i wanna sort of emphasize the alone here + + align:start position:0% +i wanna sort of emphasize the alone here + + + align:start position:0% +i wanna sort of emphasize the alone here +sort of social relationships or + + align:start position:0% +sort of social relationships or + + + align:start position:0% +sort of social relationships or +people um being in relationships with + + align:start position:0% +people um being in relationships with + + + align:start position:0% +people um being in relationships with +friends or and family + + align:start position:0% +friends or and family + + + align:start position:0% +friends or and family +or with partners is extremely predictive + + align:start position:0% +or with partners is extremely predictive + + + align:start position:0% +or with partners is extremely predictive +of people's um well-being this is what i + + align:start position:0% +of people's um well-being this is what i + + + align:start position:0% +of people's um well-being this is what i +was talking about before when it came to + + align:start position:0% +was talking about before when it came to + + + align:start position:0% +was talking about before when it came to +social preferences + + align:start position:0% +social preferences + + + align:start position:0% +social preferences +sort of investing in social + + align:start position:0% +sort of investing in social + + + align:start position:0% +sort of investing in social +relationships seems in one way is a way + + align:start position:0% +relationships seems in one way is a way + + + align:start position:0% +relationships seems in one way is a way +of of course making other people happy + + align:start position:0% +of of course making other people happy + + + align:start position:0% +of of course making other people happy +of the ignitions is good + + align:start position:0% +of the ignitions is good + + + align:start position:0% +of the ignitions is good +but in a way about uh investing or + + align:start position:0% +but in a way about uh investing or + + + align:start position:0% +but in a way about uh investing or +being nice to us and investing in social + + align:start position:0% +being nice to us and investing in social + + + align:start position:0% +being nice to us and investing in social +relationships is very much an investment + + align:start position:0% +relationships is very much an investment + + + align:start position:0% +relationships is very much an investment +in your + + align:start position:0% +in your + + + align:start position:0% +in your +future lobbying + + align:start position:0% +future lobbying + + + align:start position:0% +future lobbying +and the magnitudes here are like sort of + + align:start position:0% +and the magnitudes here are like sort of + + + align:start position:0% +and the magnitudes here are like sort of +enormous now another way you could do + + align:start position:0% +enormous now another way you could do + + + align:start position:0% +enormous now another way you could do +is uh so here you could say well + + align:start position:0% +is uh so here you could say well + + + align:start position:0% +is uh so here you could say well +what should i do to make me happier um + + align:start position:0% +what should i do to make me happier um + + + align:start position:0% +what should i do to make me happier um +in the future so one thing + + align:start position:0% +in the future so one thing + + + align:start position:0% +in the future so one thing +you could do is just look at data so one + + align:start position:0% +you could do is just look at data so one + + + align:start position:0% +you could do is just look at data so one +thing you can do is look at data + + align:start position:0% +thing you can do is look at data + + + align:start position:0% +thing you can do is look at data +and while what is it what are these + + align:start position:0% +and while what is it what are these + + + align:start position:0% +and while what is it what are these +predictor people happy + + align:start position:0% +predictor people happy + + + align:start position:0% +predictor people happy +these are all correlations you want to + + align:start position:0% +these are all correlations you want to + + + align:start position:0% +these are all correlations you want to +be careful + + align:start position:0% +be careful + + + align:start position:0% +be careful +it's going to tell you something about + + align:start position:0% +it's going to tell you something about + + + align:start position:0% +it's going to tell you something about +like if you want to be happy in 20 years + + align:start position:0% +like if you want to be happy in 20 years + + + align:start position:0% +like if you want to be happy in 20 years +things you want to invest in + + align:start position:0% +things you want to invest in + + + align:start position:0% +things you want to invest in +these numbers are probably like a pretty + + align:start position:0% +these numbers are probably like a pretty + + + align:start position:0% +these numbers are probably like a pretty +good um + + align:start position:0% +good um + + + align:start position:0% +good um +uh um your health seems to be like quite + + align:start position:0% +uh um your health seems to be like quite + + + align:start position:0% +uh um your health seems to be like quite +a good idea + + align:start position:0% +a good idea + + + align:start position:0% +a good idea +smoking for example um not so much + + align:start position:0% +smoking for example um not so much + + + align:start position:0% +smoking for example um not so much +now another thing you could do is ask + + align:start position:0% +now another thing you could do is ask + + + align:start position:0% +now another thing you could do is ask +people + + align:start position:0% +people + + + align:start position:0% +people +um at the above and just about saying + + align:start position:0% +um at the above and just about saying + + + align:start position:0% +um at the above and just about saying +um about what they should ever could + + align:start position:0% +um about what they should ever could + + + align:start position:0% +um about what they should ever could +have done in their life + + align:start position:0% +have done in their life + + + align:start position:0% +have done in their life +what do you think people said so this is + + align:start position:0% +what do you think people said so this is + + + align:start position:0% +what do you think people said so this is +an australian nurse who recorded the + + align:start position:0% +an australian nurse who recorded the + + + align:start position:0% +an australian nurse who recorded the +experience from palliative + + align:start position:0% +experience from palliative + + + align:start position:0% +experience from palliative +as end-of-life experiences and asked + + align:start position:0% +as end-of-life experiences and asked + + + align:start position:0% +as end-of-life experiences and asked +people about like + + align:start position:0% +people about like + + + align:start position:0% +people about like +uh or she didn't necessarily ask but she + + align:start position:0% +uh or she didn't necessarily ask but she + + + align:start position:0% +uh or she didn't necessarily ask but she +was just recording what people are + + align:start position:0% +was just recording what people are + + + align:start position:0% +was just recording what people are +saying + + align:start position:0% +saying + + + align:start position:0% +saying +what are the top five um regrets what + + align:start position:0% +what are the top five um regrets what + + + align:start position:0% +what are the top five um regrets what +would you think they are + + align:start position:0% + + + + align:start position:0% + +not spending enough time with family + + align:start position:0% + + + + align:start position:0% + +wish to have worked less manila says + + align:start position:0% + + + + align:start position:0% + +good enough so essentially what people + + align:start position:0% +good enough so essentially what people + + + align:start position:0% +good enough so essentially what people +tend to say + + align:start position:0% +tend to say + + + align:start position:0% +tend to say +is a combination of like they wish they + + align:start position:0% +is a combination of like they wish they + + + align:start position:0% +is a combination of like they wish they +had done been more + + align:start position:0% +had done been more + + + align:start position:0% +had done been more +social they had been i wish they had + + align:start position:0% +social they had been i wish they had + + + align:start position:0% +social they had been i wish they had +expressed their feelings more that had + + align:start position:0% +expressed their feelings more that had + + + align:start position:0% +expressed their feelings more that had +been more + + align:start position:0% +been more + + + align:start position:0% +been more +uh true to themselves in some ways and + + align:start position:0% +uh true to themselves in some ways and + + + align:start position:0% +uh true to themselves in some ways and +sort of not done things that others + + align:start position:0% +sort of not done things that others + + + align:start position:0% +sort of not done things that others +wanted them to do but rather + + align:start position:0% + + + + align:start position:0% + +spend more time with their friends and + + align:start position:0% +spend more time with their friends and + + + align:start position:0% +spend more time with their friends and +family and so on now you want to be a + + align:start position:0% +family and so on now you want to be a + + + align:start position:0% +family and so on now you want to be a +little bit careful with this this is + + align:start position:0% +little bit careful with this this is + + + align:start position:0% +little bit careful with this this is +again sort of there's issues but + + align:start position:0% +again sort of there's issues but + + + align:start position:0% +again sort of there's issues but +remember utilities also issues with like + + align:start position:0% +remember utilities also issues with like + + + align:start position:0% +remember utilities also issues with like +if you are um alone at the end of your + + align:start position:0% +if you are um alone at the end of your + + + align:start position:0% +if you are um alone at the end of your +life + + align:start position:0% +life + + + align:start position:0% +life +you might be quite um unhappy because of + + align:start position:0% +you might be quite um unhappy because of + + + align:start position:0% +you might be quite um unhappy because of +that be careful um + + align:start position:0% +that be careful um + + + align:start position:0% +that be careful um +but i think we can actually learn quite + + align:start position:0% +but i think we can actually learn quite + + + align:start position:0% +but i think we can actually learn quite +a bit about this so in some ways if you + + align:start position:0% +a bit about this so in some ways if you + + + align:start position:0% +a bit about this so in some ways if you +think about sort of certain choices you + + align:start position:0% +think about sort of certain choices you + + + align:start position:0% +think about sort of certain choices you +make in life + + align:start position:0% +make in life + + + align:start position:0% +make in life +um understanding kind of um some of + + align:start position:0% +um understanding kind of um some of + + + align:start position:0% +um understanding kind of um some of +these issues seem to be quite important + + align:start position:0% +these issues seem to be quite important + + + align:start position:0% +these issues seem to be quite important +um uh overall and think about like what + + align:start position:0% +um uh overall and think about like what + + + align:start position:0% +um uh overall and think about like what +should you maximize + + align:start position:0% +should you maximize + + + align:start position:0% +should you maximize +it seems to me that maximizing sort of + + align:start position:0% +it seems to me that maximizing sort of + + + align:start position:0% +it seems to me that maximizing sort of +income uh if that comes at the + + align:start position:0% +income uh if that comes at the + + + align:start position:0% +income uh if that comes at the +uh uh at the cost of like not having + + align:start position:0% +uh uh at the cost of like not having + + + align:start position:0% +uh uh at the cost of like not having +friends seems to be like not a good idea + + align:start position:0% +friends seems to be like not a good idea + + + align:start position:0% +friends seems to be like not a good idea +um if you want to be happy + + align:start position:0% +um if you want to be happy + + + align:start position:0% +um if you want to be happy +in the long run another thing that + + align:start position:0% +in the long run another thing that + + + align:start position:0% +in the long run another thing that +people by the way here this is not in + + align:start position:0% +people by the way here this is not in + + + align:start position:0% +people by the way here this is not in +here tend to + + align:start position:0% +here tend to + + + align:start position:0% +here tend to +to emphasize but a lot is um having a + + align:start position:0% +to emphasize but a lot is um having a + + + align:start position:0% +to emphasize but a lot is um having a +meaningful job or having work that they + + align:start position:0% +meaningful job or having work that they + + + align:start position:0% +meaningful job or having work that they +believe in terms of uh + + align:start position:0% +believe in terms of uh + + + align:start position:0% +believe in terms of uh +something meaningful as opposed to + + align:start position:0% +something meaningful as opposed to + + + align:start position:0% +something meaningful as opposed to +maximizing um income + + align:start position:0% +maximizing um income + + + align:start position:0% +maximizing um income +which you know um uh + + align:start position:0% +which you know um uh + + + align:start position:0% +which you know um uh +seems quite important okay so then um + + align:start position:0% +seems quite important okay so then um + + + align:start position:0% +seems quite important okay so then um +what kinds of things then could you do + + align:start position:0% +what kinds of things then could you do + + + align:start position:0% +what kinds of things then could you do +to make yourself happier and have a few + + align:start position:0% +to make yourself happier and have a few + + + align:start position:0% +to make yourself happier and have a few +things + + align:start position:0% +things + + + align:start position:0% +things +um uh written down here so one thing + + align:start position:0% +um uh written down here so one thing + + + align:start position:0% +um uh written down here so one thing +that i already said is invest in and + + align:start position:0% +that i already said is invest in and + + + align:start position:0% +that i already said is invest in and +maintain social relationships + + align:start position:0% +maintain social relationships + + + align:start position:0% +maintain social relationships +um small acts can make big differences + + align:start position:0% +um small acts can make big differences + + + align:start position:0% +um small acts can make big differences +um + + align:start position:0% +um + + + align:start position:0% +um +as we um talked about of letters of + + align:start position:0% +as we um talked about of letters of + + + align:start position:0% +as we um talked about of letters of +gratitude random acts of kindness these + + align:start position:0% +gratitude random acts of kindness these + + + align:start position:0% +gratitude random acts of kindness these +are very small things + + align:start position:0% +are very small things + + + align:start position:0% +are very small things +um that you could do of course you could + + align:start position:0% +um that you could do of course you could + + + align:start position:0% +um that you could do of course you could +do also like a really + + align:start position:0% +do also like a really + + + align:start position:0% +do also like a really +really important things that matters + + align:start position:0% +really important things that matters + + + align:start position:0% +really important things that matters +quite a lot how much you help your + + align:start position:0% +quite a lot how much you help your + + + align:start position:0% +quite a lot how much you help your +friends how much you sort of invest in + + align:start position:0% +friends how much you sort of invest in + + + align:start position:0% +friends how much you sort of invest in +um + + align:start position:0% +um + + + align:start position:0% +um +in others again that's partially + + align:start position:0% +in others again that's partially + + + align:start position:0% +in others again that's partially +reflective of just being pro-social and + + align:start position:0% +reflective of just being pro-social and + + + align:start position:0% +reflective of just being pro-social and +being nice to others + + align:start position:0% +being nice to others + + + align:start position:0% +being nice to others +but you can think of this as very much + + align:start position:0% +but you can think of this as very much + + + align:start position:0% +but you can think of this as very much +as like ironically in some ways you can + + align:start position:0% +as like ironically in some ways you can + + + align:start position:0% +as like ironically in some ways you can +think of this + + align:start position:0% +think of this + + + align:start position:0% +think of this +also as like investing in your own + + align:start position:0% +also as like investing in your own + + + align:start position:0% +also as like investing in your own +happiness in the future + + align:start position:0% +happiness in the future + + + align:start position:0% +happiness in the future +uh choosing meaningful work over money + + align:start position:0% +uh choosing meaningful work over money + + + align:start position:0% +uh choosing meaningful work over money +seems really important um + + align:start position:0% + + + + align:start position:0% + +if you think about what you do with your + + align:start position:0% +if you think about what you do with your + + + align:start position:0% +if you think about what you do with your +life there's so much talent at mit and i + + align:start position:0% +life there's so much talent at mit and i + + + align:start position:0% +life there's so much talent at mit and i +um i sometimes wish you know that talent + + align:start position:0% +um i sometimes wish you know that talent + + + align:start position:0% +um i sometimes wish you know that talent +would go more into more meaningful + + align:start position:0% +would go more into more meaningful + + + align:start position:0% +would go more into more meaningful +things + + align:start position:0% +things + + + align:start position:0% +things +or because of uh society or like making + + align:start position:0% +or because of uh society or like making + + + align:start position:0% +or because of uh society or like making +society better overall as opposed to + + align:start position:0% +society better overall as opposed to + + + align:start position:0% +society better overall as opposed to +like uh + + align:start position:0% +like uh + + + align:start position:0% +like uh +um some perhaps potentially social + + align:start position:0% +um some perhaps potentially social + + + align:start position:0% +um some perhaps potentially social +weight cities that pay you a lot + + align:start position:0% +weight cities that pay you a lot + + + align:start position:0% +weight cities that pay you a lot +of money um that's in something sort of + + align:start position:0% +of money um that's in something sort of + + + align:start position:0% +of money um that's in something sort of +potentially socially optimal in terms of + + align:start position:0% +potentially socially optimal in terms of + + + align:start position:0% +potentially socially optimal in terms of +use mit's talents or mit students + + align:start position:0% +use mit's talents or mit students + + + align:start position:0% +use mit's talents or mit students +talents for useful things in the world + + align:start position:0% +talents for useful things in the world + + + align:start position:0% +talents for useful things in the world +but if you're just selfish and want to + + align:start position:0% +but if you're just selfish and want to + + + align:start position:0% +but if you're just selfish and want to +make yourself happy in 20 years from now + + align:start position:0% +make yourself happy in 20 years from now + + + align:start position:0% +make yourself happy in 20 years from now +it seems to me that just maximizing + + align:start position:0% +it seems to me that just maximizing + + + align:start position:0% +it seems to me that just maximizing +income is just not what's going to get + + align:start position:0% +income is just not what's going to get + + + align:start position:0% +income is just not what's going to get +you there so it seems to be like like + + align:start position:0% +you there so it seems to be like like + + + align:start position:0% +you there so it seems to be like like +being rich is really uh + + align:start position:0% +being rich is really uh + + + align:start position:0% +being rich is really uh +glamorous and exciting but in fact if + + align:start position:0% +glamorous and exciting but in fact if + + + align:start position:0% +glamorous and exciting but in fact if +that comes at the cost of your health + + align:start position:0% + + + + align:start position:0% + +and your friendships most likely or + + align:start position:0% +and your friendships most likely or + + + align:start position:0% +and your friendships most likely or +happen or the cost of having a + + align:start position:0% +happen or the cost of having a + + + align:start position:0% +happen or the cost of having a +meaningful job that you + + align:start position:0% +meaningful job that you + + + align:start position:0% +meaningful job that you +actually believe in and i think is + + align:start position:0% +actually believe in and i think is + + + align:start position:0% +actually believe in and i think is +useful that's not gonna make you happy + + align:start position:0% +useful that's not gonna make you happy + + + align:start position:0% +useful that's not gonna make you happy +in the long run so + + align:start position:0% +in the long run so + + + align:start position:0% +in the long run so +for those of you thinking about what + + align:start position:0% +for those of you thinking about what + + + align:start position:0% +for those of you thinking about what +kind of work to pursue in the future + + align:start position:0% +kind of work to pursue in the future + + + align:start position:0% +kind of work to pursue in the future +uh uh keep that in mind uh and then i + + align:start position:0% +uh uh keep that in mind uh and then i + + + align:start position:0% +uh uh keep that in mind uh and then i +have two more things uh here on my list + + align:start position:0% +have two more things uh here on my list + + + align:start position:0% +have two more things uh here on my list +which is + + align:start position:0% +which is + + + align:start position:0% +which is +support to improve your mental health + + align:start position:0% +support to improve your mental health + + + align:start position:0% +support to improve your mental health +and reduce social media usage + + align:start position:0% +and reduce social media usage + + + align:start position:0% +and reduce social media usage +so what do i mean by that so + + align:start position:0% +so what do i mean by that so + + + align:start position:0% +so what do i mean by that so +psychotherapies have very much been + + align:start position:0% +psychotherapies have very much been + + + align:start position:0% +psychotherapies have very much been +shown + + align:start position:0% +shown + + + align:start position:0% +shown +uh to be effective in reducing + + align:start position:0% +uh to be effective in reducing + + + align:start position:0% +uh to be effective in reducing +depression anxiety and so on + + align:start position:0% +depression anxiety and so on + + + align:start position:0% +depression anxiety and so on +yet people tend to not make use of those + + align:start position:0% +yet people tend to not make use of those + + + align:start position:0% +yet people tend to not make use of those +services now why is that + + align:start position:0% +services now why is that + + + align:start position:0% +services now why is that +there's sort of obvious reasons which is + + align:start position:0% +there's sort of obvious reasons which is + + + align:start position:0% +there's sort of obvious reasons which is +stigma shame and so on there's also + + align:start position:0% +stigma shame and so on there's also + + + align:start position:0% +stigma shame and so on there's also +potentially misperceptions + + align:start position:0% +potentially misperceptions + + + align:start position:0% +potentially misperceptions +projection bias also like depression + + align:start position:0% +projection bias also like depression + + + align:start position:0% +projection bias also like depression +itself for example could precisely + + align:start position:0% +itself for example could precisely + + + align:start position:0% +itself for example could precisely +generate these kinds of beliefs + + align:start position:0% +generate these kinds of beliefs + + + align:start position:0% +generate these kinds of beliefs +there could also be other behavioral + + align:start position:0% +there could also be other behavioral + + + align:start position:0% +there could also be other behavioral +biases like other health conditions you + + align:start position:0% +biases like other health conditions you + + + align:start position:0% +biases like other health conditions you +know people just don't like to see + + align:start position:0% +know people just don't like to see + + + align:start position:0% +know people just don't like to see +doctors and so on + + align:start position:0% +doctors and so on + + + align:start position:0% +doctors and so on +now another way to view this is to say + + align:start position:0% +now another way to view this is to say + + + align:start position:0% +now another way to view this is to say +well you might think that psychotherapy + + align:start position:0% +well you might think that psychotherapy + + + align:start position:0% +well you might think that psychotherapy +is really important for depression and + + align:start position:0% +is really important for depression and + + + align:start position:0% +is really important for depression and +anxiety but psychotherapy could also be + + align:start position:0% +anxiety but psychotherapy could also be + + + align:start position:0% +anxiety but psychotherapy could also be +viewed as like sort of a coach to make + + align:start position:0% +viewed as like sort of a coach to make + + + align:start position:0% +viewed as like sort of a coach to make +you happiness think about this as like a + + align:start position:0% +you happiness think about this as like a + + + align:start position:0% +you happiness think about this as like a +happiness coach + + align:start position:0% +happiness coach + + + align:start position:0% +happiness coach +it might help you figure out your + + align:start position:0% +it might help you figure out your + + + align:start position:0% +it might help you figure out your +objective function in life what really + + align:start position:0% +objective function in life what really + + + align:start position:0% +objective function in life what really +makes you happy and how to pursue that + + align:start position:0% +makes you happy and how to pursue that + + + align:start position:0% +makes you happy and how to pursue that +and that sort of regardless of + + align:start position:0% +and that sort of regardless of + + + align:start position:0% +and that sort of regardless of +depression anxiety or any mental + + align:start position:0% +depression anxiety or any mental + + + align:start position:0% +depression anxiety or any mental +disorders that's to say like + + align:start position:0% +disorders that's to say like + + + align:start position:0% +disorders that's to say like +think about like sports in sports like + + align:start position:0% +think about like sports in sports like + + + align:start position:0% +think about like sports in sports like +you get a coach to be a better tennis + + align:start position:0% +you get a coach to be a better tennis + + + align:start position:0% +you get a coach to be a better tennis +player + + align:start position:0% +player + + + align:start position:0% +player +or whatever like soccer or whatever you + + align:start position:0% +or whatever like soccer or whatever you + + + align:start position:0% +or whatever like soccer or whatever you +sports you do that's very natural thing + + align:start position:0% +sports you do that's very natural thing + + + align:start position:0% +sports you do that's very natural thing +to do people helped you to do better + + align:start position:0% +to do people helped you to do better + + + align:start position:0% +to do people helped you to do better +now why not have a coach for many other + + align:start position:0% +now why not have a coach for many other + + + align:start position:0% +now why not have a coach for many other +things in life including like how to be + + align:start position:0% +things in life including like how to be + + + align:start position:0% +things in life including like how to be +happier on how to lead your life that + + align:start position:0% +happier on how to lead your life that + + + align:start position:0% +happier on how to lead your life that +sort of makes you + + align:start position:0% +sort of makes you + + + align:start position:0% +sort of makes you +uh satisfies you and i think that's + + align:start position:0% +uh satisfies you and i think that's + + + align:start position:0% +uh satisfies you and i think that's +in some sense if you're maximizing your + + align:start position:0% +in some sense if you're maximizing your + + + align:start position:0% +in some sense if you're maximizing your +wrong objective function which again + + align:start position:0% +wrong objective function which again + + + align:start position:0% +wrong objective function which again +could be like you just + + align:start position:0% +could be like you just + + + align:start position:0% +could be like you just +maximize money over certain other things + + align:start position:0% +maximize money over certain other things + + + align:start position:0% +maximize money over certain other things +if the therapist help you + + align:start position:0% +if the therapist help you + + + align:start position:0% +if the therapist help you +do that or help you correct that that + + align:start position:0% +do that or help you correct that that + + + align:start position:0% +do that or help you correct that that +could be extremely valuable um + + align:start position:0% +could be extremely valuable um + + + align:start position:0% +could be extremely valuable um +and helpful um uh and again that's sort + + align:start position:0% +and helpful um uh and again that's sort + + + align:start position:0% +and helpful um uh and again that's sort +of in the absence of any sort of + + align:start position:0% +of in the absence of any sort of + + + align:start position:0% +of in the absence of any sort of +uh serious mental illnesses that's just + + align:start position:0% +uh serious mental illnesses that's just + + + align:start position:0% +uh serious mental illnesses that's just +for like the average person having + + align:start position:0% +for like the average person having + + + align:start position:0% +for like the average person having +somebody to talk to to help you optimize + + align:start position:0% +somebody to talk to to help you optimize + + + align:start position:0% +somebody to talk to to help you optimize +your life + + align:start position:0% +your life + + + align:start position:0% +your life +uh and your mental well-being seems to + + align:start position:0% +uh and your mental well-being seems to + + + align:start position:0% +uh and your mental well-being seems to +be extremely important + + align:start position:0% +be extremely important + + + align:start position:0% +be extremely important +and worth trying um second about uh + + align:start position:0% +and worth trying um second about uh + + + align:start position:0% +and worth trying um second about uh +social media so + + align:start position:0% +social media so + + + align:start position:0% +social media so +uh this is a recent paper that's quite + + align:start position:0% +uh this is a recent paper that's quite + + + align:start position:0% +uh this is a recent paper that's quite +intriguing and there's actually a couple + + align:start position:0% +intriguing and there's actually a couple + + + align:start position:0% +intriguing and there's actually a couple +papers but let me just mention one + + align:start position:0% +papers but let me just mention one + + + align:start position:0% +papers but let me just mention one +which is by al qaeda um that um randomly + + align:start position:0% +which is by al qaeda um that um randomly + + + align:start position:0% +which is by al qaeda um that um randomly +uh randomizes paying students to stay + + align:start position:0% +uh randomizes paying students to stay + + + align:start position:0% +uh randomizes paying students to stay +off facebook for + + align:start position:0% +off facebook for + + + align:start position:0% +off facebook for +a month this was before the 2018 + + align:start position:0% +a month this was before the 2018 + + + align:start position:0% +a month this was before the 2018 +election which in election + + align:start position:0% +election which in election + + + align:start position:0% +election which in election +uh which is in since it's perhaps + + align:start position:0% +uh which is in since it's perhaps + + + align:start position:0% +uh which is in since it's perhaps +relevant in some ways + + align:start position:0% +relevant in some ways + + + align:start position:0% +relevant in some ways +like the timing might matter um for some + + align:start position:0% +like the timing might matter um for some + + + align:start position:0% +like the timing might matter um for some +of these results + + align:start position:0% +of these results + + + align:start position:0% +of these results +but so what they find is that sort of + + align:start position:0% +but so what they find is that sort of + + + align:start position:0% +but so what they find is that sort of +getting people to a you have to pay + + align:start position:0% +getting people to a you have to pay + + + align:start position:0% +getting people to a you have to pay +students quite a lot to do this so + + align:start position:0% +students quite a lot to do this so + + + align:start position:0% +students quite a lot to do this so +students have to pay them like 50 + + align:start position:0% +students have to pay them like 50 + + + align:start position:0% +students have to pay them like 50 +and otherwise you know they're not + + align:start position:0% +and otherwise you know they're not + + + align:start position:0% +and otherwise you know they're not +willing to do this when you do that + + align:start position:0% +willing to do this when you do that + + + align:start position:0% +willing to do this when you do that +people reduce their online activities + + align:start position:0% +people reduce their online activities + + + align:start position:0% +people reduce their online activities +um they also you reduce their factual uh + + align:start position:0% +um they also you reduce their factual uh + + + align:start position:0% +um they also you reduce their factual uh +news knowledge political polarization + + align:start position:0% +news knowledge political polarization + + + align:start position:0% +news knowledge political polarization +and so on all kinds of things that you + + align:start position:0% +and so on all kinds of things that you + + + align:start position:0% +and so on all kinds of things that you +might expect + + align:start position:0% +might expect + + + align:start position:0% +might expect +then you see um increased subjective + + align:start position:0% +then you see um increased subjective + + + align:start position:0% +then you see um increased subjective +well-being both happiness but also like + + align:start position:0% +well-being both happiness but also like + + + align:start position:0% +well-being both happiness but also like +reduced depression so + + align:start position:0% +reduced depression so + + + align:start position:0% +reduced depression so +students are happier uh uh and quite a + + align:start position:0% +students are happier uh uh and quite a + + + align:start position:0% +students are happier uh uh and quite a +bit happier by + + align:start position:0% +bit happier by + + + align:start position:0% +bit happier by +doing that moreover there seem to be + + align:start position:0% +doing that moreover there seem to be + + + align:start position:0% +doing that moreover there seem to be +large persistent + + align:start position:0% +large persistent + + + align:start position:0% +large persistent +uh reductions in post experiment phase + + align:start position:0% +uh reductions in post experiment phase + + + align:start position:0% +uh reductions in post experiment phase +drop usage that is to say one to + + align:start position:0% +drop usage that is to say one to + + + align:start position:0% +drop usage that is to say one to +experiment is over + + align:start position:0% +experiment is over + + + align:start position:0% +experiment is over +lots of students who have been paid to + + align:start position:0% +lots of students who have been paid to + + + align:start position:0% +lots of students who have been paid to +stay on facebook uh uh + + align:start position:0% +stay on facebook uh uh + + + align:start position:0% +stay on facebook uh uh +tend to do that or to continue doing + + align:start position:0% +tend to do that or to continue doing + + + align:start position:0% +tend to do that or to continue doing +that which very much sort of seems to + + align:start position:0% +that which very much sort of seems to + + + align:start position:0% +that which very much sort of seems to +say that + + align:start position:0% +say that + + + align:start position:0% +say that +uh it's a habit good perhaps there's + + align:start position:0% +uh it's a habit good perhaps there's + + + align:start position:0% +uh it's a habit good perhaps there's +also some learning involved it's + + align:start position:0% +also some learning involved it's + + + align:start position:0% +also some learning involved it's +like students learn that they're now + + align:start position:0% +like students learn that they're now + + + align:start position:0% +like students learn that they're now +happier + + align:start position:0% +happier + + + align:start position:0% +happier +overall now that always leads to the + + align:start position:0% +overall now that always leads to the + + + align:start position:0% +overall now that always leads to the +question well why are people then on + + align:start position:0% +question well why are people then on + + + align:start position:0% +question well why are people then on +facebook if it doesn't make them + + align:start position:0% +facebook if it doesn't make them + + + align:start position:0% +facebook if it doesn't make them +happy and does it have to do with like + + align:start position:0% +happy and does it have to do with like + + + align:start position:0% +happy and does it have to do with like +peer pressure does it have to do with + + align:start position:0% +peer pressure does it have to do with + + + align:start position:0% +peer pressure does it have to do with +like habit formation does it have to do + + align:start position:0% +like habit formation does it have to do + + + align:start position:0% +like habit formation does it have to do +with like um + + align:start position:0% +with like um + + + align:start position:0% +with like um +self-control problems so that would have + + align:start position:0% +self-control problems so that would have + + + align:start position:0% +self-control problems so that would have +to do with bias beliefs and so on + + align:start position:0% +to do with bias beliefs and so on + + + align:start position:0% +to do with bias beliefs and so on +but overall in some ways i think the the + + align:start position:0% +but overall in some ways i think the the + + + align:start position:0% +but overall in some ways i think the the +reason why i shoot this evidence is like + + align:start position:0% +reason why i shoot this evidence is like + + + align:start position:0% +reason why i shoot this evidence is like +when you think about your life or things + + align:start position:0% +when you think about your life or things + + + align:start position:0% +when you think about your life or things +that you do in your life you kind of + + align:start position:0% +that you do in your life you kind of + + + align:start position:0% +that you do in your life you kind of +want to think about like + + align:start position:0% +want to think about like + + + align:start position:0% +want to think about like +what are the things that you do in your + + align:start position:0% +what are the things that you do in your + + + align:start position:0% +what are the things that you do in your +life what are the things that make you + + align:start position:0% +life what are the things that make you + + + align:start position:0% +life what are the things that make you +happy uh + + align:start position:0% +happy uh + + + align:start position:0% +happy uh +or or not and perhaps experimenting with + + align:start position:0% +or or not and perhaps experimenting with + + + align:start position:0% +or or not and perhaps experimenting with +those kinds of things or just looking at + + align:start position:0% +those kinds of things or just looking at + + + align:start position:0% +those kinds of things or just looking at +data from studies + + align:start position:0% +data from studies + + + align:start position:0% +data from studies +um seems to be like a very reasonable + + align:start position:0% +um seems to be like a very reasonable + + + align:start position:0% +um seems to be like a very reasonable +thing to do so it could well be that + + align:start position:0% +thing to do so it could well be that + + + align:start position:0% +thing to do so it could well be that +social media makes you really happy and + + align:start position:0% +social media makes you really happy and + + + align:start position:0% +social media makes you really happy and +connecting with your friends in + + align:start position:0% +connecting with your friends in + + + align:start position:0% +connecting with your friends in +particular right now that's really you + + align:start position:0% +particular right now that's really you + + + align:start position:0% +particular right now that's really you +think that's really helpful because you + + align:start position:0% +think that's really helpful because you + + + align:start position:0% +think that's really helpful because you +know you can stay in touch + + align:start position:0% +know you can stay in touch + + + align:start position:0% +know you can stay in touch +you like talk online and so on and so + + align:start position:0% +you like talk online and so on and so + + + align:start position:0% +you like talk online and so on and so +forth and that's truly like i think + + align:start position:0% +forth and that's truly like i think + + + align:start position:0% +forth and that's truly like i think +that's worth worth doing + + align:start position:0% +that's worth worth doing + + + align:start position:0% +that's worth worth doing +so that could really be very beneficial + + align:start position:0% +so that could really be very beneficial + + + align:start position:0% +so that could really be very beneficial +for your um + + align:start position:0% +for your um + + + align:start position:0% +for your um +happiness overall but it might also be + + align:start position:0% +happiness overall but it might also be + + + align:start position:0% +happiness overall but it might also be +that uh there's large + + align:start position:0% +that uh there's large + + + align:start position:0% +that uh there's large +uh costs in that coming from perhaps + + align:start position:0% +uh costs in that coming from perhaps + + + align:start position:0% +uh costs in that coming from perhaps +like social comparison + + align:start position:0% +like social comparison + + + align:start position:0% +like social comparison +or like just seeing everybody happy on + + align:start position:0% +or like just seeing everybody happy on + + + align:start position:0% +or like just seeing everybody happy on +facebook or whatever people post + + align:start position:0% +facebook or whatever people post + + + align:start position:0% +facebook or whatever people post +selectively makes + + align:start position:0% +selectively makes + + + align:start position:0% +selectively makes +it look like people are are way happier + + align:start position:0% +it look like people are are way happier + + + align:start position:0% +it look like people are are way happier +than they actually are + + align:start position:0% +than they actually are + + + align:start position:0% +than they actually are +and then that makes people feel bad + + align:start position:0% +and then that makes people feel bad + + + align:start position:0% +and then that makes people feel bad +about themselves seeing others sort of + + align:start position:0% +about themselves seeing others sort of + + + align:start position:0% +about themselves seeing others sort of +posed overall + + align:start position:0% +posed overall + + + align:start position:0% +posed overall +but i think what i the reason why i + + align:start position:0% +but i think what i the reason why i + + + align:start position:0% +but i think what i the reason why i +actually do this is i want you to think + + align:start position:0% +actually do this is i want you to think + + + align:start position:0% +actually do this is i want you to think +about or be more conscious about + + align:start position:0% +about or be more conscious about + + + align:start position:0% +about or be more conscious about +uh what are the things that do make you + + align:start position:0% +uh what are the things that do make you + + + align:start position:0% +uh what are the things that do make you +in fact happier and try to + + align:start position:0% +in fact happier and try to + + + align:start position:0% +in fact happier and try to +invest in those that seem to make + + align:start position:0% +invest in those that seem to make + + + align:start position:0% +invest in those that seem to make +you happier overall so some of these + + align:start position:0% +you happier overall so some of these + + + align:start position:0% +you happier overall so some of these +things you can obviously experiment with + + align:start position:0% +things you can obviously experiment with + + + align:start position:0% +things you can obviously experiment with +for example you can obviously turn off + + align:start position:0% +for example you can obviously turn off + + + align:start position:0% +for example you can obviously turn off +your facebook or instagram whatever um + + align:start position:0% +your facebook or instagram whatever um + + + align:start position:0% +your facebook or instagram whatever um +very quickly and easily other things of + + align:start position:0% +very quickly and easily other things of + + + align:start position:0% +very quickly and easily other things of +course the stuff that i showed you um + + align:start position:0% +course the stuff that i showed you um + + + align:start position:0% +course the stuff that i showed you um +in the very long run um like you know + + align:start position:0% +in the very long run um like you know + + + align:start position:0% +in the very long run um like you know +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +the kanaman data here + + align:start position:0% + + + + align:start position:0% + +these kinds of data of course it's much + + align:start position:0% +these kinds of data of course it's much + + + align:start position:0% +these kinds of data of course it's much +harder to experiment with that like it's + + align:start position:0% +harder to experiment with that like it's + + + align:start position:0% +harder to experiment with that like it's +hard to just say i'm going to be + + align:start position:0% +hard to just say i'm going to be + + + align:start position:0% +hard to just say i'm going to be +religious for a month and uh from now on + + align:start position:0% +religious for a month and uh from now on + + + align:start position:0% +religious for a month and uh from now on +and then so see how you're happier + + align:start position:0% +and then so see how you're happier + + + align:start position:0% +and then so see how you're happier +um but it is worse to think about kind + + align:start position:0% +um but it is worse to think about kind + + + align:start position:0% +um but it is worse to think about kind +of what are the things that you're + + align:start position:0% +of what are the things that you're + + + align:start position:0% +of what are the things that you're +really pursuing + + align:start position:0% +really pursuing + + + align:start position:0% +really pursuing +and are these things going to be making + + align:start position:0% +and are these things going to be making + + + align:start position:0% +and are these things going to be making +you happy not just right now and this is + + align:start position:0% +you happy not just right now and this is + + + align:start position:0% +you happy not just right now and this is +just because you're doing some things + + align:start position:0% +just because you're doing some things + + + align:start position:0% +just because you're doing some things +because your friends want it or like + + align:start position:0% +because your friends want it or like + + + align:start position:0% +because your friends want it or like +some other influence that you have + + align:start position:0% +some other influence that you have + + + align:start position:0% +some other influence that you have +as opposed to like what are the things + + align:start position:0% +as opposed to like what are the things + + + align:start position:0% +as opposed to like what are the things +that you really want and what are the + + align:start position:0% +that you really want and what are the + + + align:start position:0% +that you really want and what are the +things that are gonna make you happy + + align:start position:0% +things that are gonna make you happy + + + align:start position:0% +things that are gonna make you happy +not just like uh this month or next + + align:start position:0% +not just like uh this month or next + + + align:start position:0% +not just like uh this month or next +month but like five ten + + align:start position:0% +month but like five ten + + + align:start position:0% +month but like five ten +twenty years um from now because a lot + + align:start position:0% +twenty years um from now because a lot + + + align:start position:0% +twenty years um from now because a lot +of choices that you make + + align:start position:0% +of choices that you make + + + align:start position:0% +of choices that you make +uh uh in the next couple or three years + + align:start position:0% +uh uh in the next couple or three years + + + align:start position:0% +uh uh in the next couple or three years +uh will be very persistent in terms of + + align:start position:0% +uh will be very persistent in terms of + + + align:start position:0% +uh will be very persistent in terms of +like depending on what jobs you choose + + align:start position:0% +like depending on what jobs you choose + + + align:start position:0% +like depending on what jobs you choose +what kinds of um friendships you have + + align:start position:0% +what kinds of um friendships you have + + + align:start position:0% +what kinds of um friendships you have +what kind of partners you have and so on + + align:start position:0% +what kind of partners you have and so on + + + align:start position:0% +what kind of partners you have and so on +will be very much persistent for a long + + align:start position:0% +will be very much persistent for a long + + + align:start position:0% +will be very much persistent for a long +time in terms of determining + + align:start position:0% +time in terms of determining + + + align:start position:0% +time in terms of determining +um your long run happiness and so that's + + align:start position:0% +um your long run happiness and so that's + + + align:start position:0% +um your long run happiness and so that's +a very useful thing to + + align:start position:0% +a very useful thing to + + + align:start position:0% +a very useful thing to +think about um let me see + + align:start position:0% +think about um let me see + + + align:start position:0% +think about um let me see +so what what do people think um um + + align:start position:0% +so what what do people think um um + + + align:start position:0% +so what what do people think um um +and i guess um at some point hopefully + + align:start position:0% +and i guess um at some point hopefully + + + align:start position:0% +and i guess um at some point hopefully +uh so if you look is monitoring the + + align:start position:0% +uh so if you look is monitoring the + + + align:start position:0% +uh so if you look is monitoring the +llama situation i hope um + + align:start position:0% +llama situation i hope um + + + align:start position:0% +llama situation i hope um +uh uh uh uh we'll see how that goes + + align:start position:0% +uh uh uh uh we'll see how that goes + + + align:start position:0% +uh uh uh uh we'll see how that goes +hopefully that makes people happier + + align:start position:0% +hopefully that makes people happier + + + align:start position:0% +hopefully that makes people happier +but um what what do people think is why + + align:start position:0% +but um what what do people think is why + + + align:start position:0% +but um what what do people think is why +why are people on facebook if it doesn't + + align:start position:0% +why are people on facebook if it doesn't + + + align:start position:0% +why are people on facebook if it doesn't +make them happy + + align:start position:0% +make them happy + + + align:start position:0% +make them happy +so there could be essentially issues + + align:start position:0% +so there could be essentially issues + + + align:start position:0% +so there could be essentially issues +with uh present bias or the like that + + align:start position:0% +with uh present bias or the like that + + + align:start position:0% +with uh present bias or the like that +like any point in time + + align:start position:0% +like any point in time + + + align:start position:0% +like any point in time +it's it's kind of the some temptations + + align:start position:0% +it's it's kind of the some temptations + + + align:start position:0% +it's it's kind of the some temptations +of perhaps posting or the like and then + + align:start position:0% +of perhaps posting or the like and then + + + align:start position:0% +of perhaps posting or the like and then +you know + + align:start position:0% +you know + + + align:start position:0% +you know +uh that makes you happy in the very + + align:start position:0% +uh that makes you happy in the very + + + align:start position:0% +uh that makes you happy in the very +short run but in the long run overall + + align:start position:0% +short run but in the long run overall + + + align:start position:0% +short run but in the long run overall +then + + align:start position:0% +then + + + align:start position:0% +then +that's not really um helping you uh + + align:start position:0% +that's not really um helping you uh + + + align:start position:0% +that's not really um helping you uh +overall there's some so it's actually + + align:start position:0% +overall there's some so it's actually + + + align:start position:0% +overall there's some so it's actually +some self-control problems in some + + align:start position:0% +some self-control problems in some + + + align:start position:0% +some self-control problems in some +some some ways um in particular right + + align:start position:0% +some some ways um in particular right + + + align:start position:0% +some some ways um in particular right +now and so to be clear the study + + align:start position:0% +now and so to be clear the study + + + align:start position:0% +now and so to be clear the study +that was done here and i actually talked + + align:start position:0% +that was done here and i actually talked + + + align:start position:0% +that was done here and i actually talked +to honda alcohol she was one of the + + align:start position:0% +to honda alcohol she was one of the + + + align:start position:0% +to honda alcohol she was one of the +authors of the study + + align:start position:0% +authors of the study + + + align:start position:0% +authors of the study +who would also tell me like look uh uh + + align:start position:0% +who would also tell me like look uh uh + + + align:start position:0% +who would also tell me like look uh uh +if you did the study right now maybe you + + align:start position:0% +if you did the study right now maybe you + + + align:start position:0% +if you did the study right now maybe you +would find the opposite + + align:start position:0% +would find the opposite + + + align:start position:0% +would find the opposite +because you know now in fact facebook or + + align:start position:0% +because you know now in fact facebook or + + + align:start position:0% +because you know now in fact facebook or +any other so social media helps people + + align:start position:0% +any other so social media helps people + + + align:start position:0% +any other so social media helps people +stay in touch and there's some positive + + align:start position:0% +stay in touch and there's some positive + + + align:start position:0% +stay in touch and there's some positive +benefits + + align:start position:0% +benefits + + + align:start position:0% +benefits +and so what you're saying is well + + align:start position:0% +and so what you're saying is well + + + align:start position:0% +and so what you're saying is well +presumably facebook was + + align:start position:0% +presumably facebook was + + + align:start position:0% +presumably facebook was +uh you know uh uh um developed + + align:start position:0% +uh you know uh uh um developed + + + align:start position:0% +uh you know uh uh um developed +early on or reason why it's successful + + align:start position:0% +early on or reason why it's successful + + + align:start position:0% +early on or reason why it's successful +because it really helped people connect + + align:start position:0% +because it really helped people connect + + + align:start position:0% +because it really helped people connect +to each other in some ways + + align:start position:0% +to each other in some ways + + + align:start position:0% +to each other in some ways +and people thought there were some + + align:start position:0% +and people thought there were some + + + align:start position:0% +and people thought there were some +benefits from that and that's + + align:start position:0% +benefits from that and that's + + + align:start position:0% +benefits from that and that's +particularly true + + align:start position:0% +particularly true + + + align:start position:0% +particularly true +if you're sort of not at the same place + + align:start position:0% +if you're sort of not at the same place + + + align:start position:0% +if you're sort of not at the same place +uh physically and sort of + + align:start position:0% +uh physically and sort of + + + align:start position:0% +uh physically and sort of +particularly right now then there are + + align:start position:0% +particularly right now then there are + + + align:start position:0% +particularly right now then there are +these benefits + + align:start position:0% +these benefits + + + align:start position:0% +these benefits +overall and then there's a question of + + align:start position:0% +overall and then there's a question of + + + align:start position:0% +overall and then there's a question of +well what are the costs and benefits of + + align:start position:0% +well what are the costs and benefits of + + + align:start position:0% +well what are the costs and benefits of +that + + align:start position:0% +that + + + align:start position:0% +that +and you know + + align:start position:0% +and you know + + + align:start position:0% +and you know +maybe people misperceive some of these + + align:start position:0% +maybe people misperceive some of these + + + align:start position:0% +maybe people misperceive some of these +or or or the like + + align:start position:0% +or or or the like + + + align:start position:0% +or or or the like +i'm trying to encourage you is to sort + + align:start position:0% +i'm trying to encourage you is to sort + + + align:start position:0% +i'm trying to encourage you is to sort +of say well uh + + align:start position:0% +of say well uh + + + align:start position:0% +of say well uh +there's ways to learn about this and + + align:start position:0% +there's ways to learn about this and + + + align:start position:0% +there's ways to learn about this and +facebook is actually a very good example + + align:start position:0% +facebook is actually a very good example + + + align:start position:0% +facebook is actually a very good example +uh where you could learn very easily + + align:start position:0% +uh where you could learn very easily + + + align:start position:0% +uh where you could learn very easily +where you say let's turn it off for a + + align:start position:0% +where you say let's turn it off for a + + + align:start position:0% +where you say let's turn it off for a +month and see what happens + + align:start position:0% +month and see what happens + + + align:start position:0% +month and see what happens +you could also there's some other + + align:start position:0% +you could also there's some other + + + align:start position:0% +you could also there's some other +activities where you say let's do more + + align:start position:0% +activities where you say let's do more + + + align:start position:0% +activities where you say let's do more +sports so let's + + align:start position:0% +sports so let's + + + align:start position:0% +sports so let's +get up early in the morning or sleep + + align:start position:0% +get up early in the morning or sleep + + + align:start position:0% +get up early in the morning or sleep +more at night there's some things we're + + align:start position:0% +more at night there's some things we're + + + align:start position:0% +more at night there's some things we're +like that are + + align:start position:0% +like that are + + + align:start position:0% +like that are +quite easy to experiment with other + + align:start position:0% +quite easy to experiment with other + + + align:start position:0% +quite easy to experiment with other +stuff as i said you know becoming + + align:start position:0% +stuff as i said you know becoming + + + align:start position:0% +stuff as i said you know becoming +religious was just not as much + + align:start position:0% +religious was just not as much + + + align:start position:0% +religious was just not as much +trickier to to experiment with or like + + align:start position:0% +trickier to to experiment with or like + + + align:start position:0% +trickier to to experiment with or like +being healthy versus not in some sense + + align:start position:0% +being healthy versus not in some sense + + + align:start position:0% +being healthy versus not in some sense +it's just a very much long one uh + + align:start position:0% +it's just a very much long one uh + + + align:start position:0% +it's just a very much long one uh +uh uh the fact um but exactly as you + + align:start position:0% +uh uh the fact um but exactly as you + + + align:start position:0% +uh uh the fact um but exactly as you +said people have + + align:start position:0% +said people have + + + align:start position:0% +said people have +never actually experienced any of this + + align:start position:0% +never actually experienced any of this + + + align:start position:0% +never actually experienced any of this +so how would you know + + align:start position:0% +so how would you know + + + align:start position:0% +so how would you know +how you're going to be happier there's + + align:start position:0% +how you're going to be happier there's + + + align:start position:0% +how you're going to be happier there's +also some + + align:start position:0% +also some + + + align:start position:0% +also some +uh you know public goods issues or some + + align:start position:0% +uh you know public goods issues or some + + + align:start position:0% +uh you know public goods issues or some +issues of um + + align:start position:0% +issues of um + + + align:start position:0% +issues of um +externalities and some more if all of + + align:start position:0% +externalities and some more if all of + + + align:start position:0% +externalities and some more if all of +you are on social media and you're not + + align:start position:0% +you are on social media and you're not + + + align:start position:0% +you are on social media and you're not +you're kind of a bit of a + + align:start position:0% +you're kind of a bit of a + + + align:start position:0% +you're kind of a bit of a +outsider and that sort of will make you + + align:start position:0% +outsider and that sort of will make you + + + align:start position:0% +outsider and that sort of will make you +likely very um + + align:start position:0% +likely very um + + + align:start position:0% +likely very um +or likely not increase your happiness + + align:start position:0% +or likely not increase your happiness + + + align:start position:0% +or likely not increase your happiness +but it might well be + + align:start position:0% +but it might well be + + + align:start position:0% +but it might well be +that like if everybody decides um uh + + align:start position:0% +that like if everybody decides um uh + + + align:start position:0% +that like if everybody decides um uh +go off social media then everybody + + align:start position:0% +go off social media then everybody + + + align:start position:0% +go off social media then everybody +sometimes then you don't rely + + align:start position:0% +sometimes then you don't rely + + + align:start position:0% +sometimes then you don't rely +on social media to like go to parties or + + align:start position:0% +on social media to like go to parties or + + + align:start position:0% +on social media to like go to parties or +whatever and so on + + align:start position:0% +whatever and so on + + + align:start position:0% +whatever and so on +and so there might be also some + + align:start position:0% +and so there might be also some + + + align:start position:0% +and so there might be also some +coordination issues potentially so + + align:start position:0% +coordination issues potentially so + + + align:start position:0% +coordination issues potentially so +conditional on everybody being on + + align:start position:0% +conditional on everybody being on + + + align:start position:0% +conditional on everybody being on +facebook around you you might want to be + + align:start position:0% +facebook around you you might want to be + + + align:start position:0% +facebook around you you might want to be +on facebook or whatever other social + + align:start position:0% +on facebook or whatever other social + + + align:start position:0% +on facebook or whatever other social +media + + align:start position:0% +media + + + align:start position:0% +media +but if that's not the case when uh so it + + align:start position:0% +but if that's not the case when uh so it + + + align:start position:0% +but if that's not the case when uh so it +could be for every single person + + align:start position:0% +could be for every single person + + + align:start position:0% +could be for every single person +every single person could be happier if + + align:start position:0% +every single person could be happier if + + + align:start position:0% +every single person could be happier if +everybody else were not on social media + + align:start position:0% +everybody else were not on social media + + + align:start position:0% +everybody else were not on social media +but conditional that everybody is on + + align:start position:0% +but conditional that everybody is on + + + align:start position:0% +but conditional that everybody is on +social media + + align:start position:0% +social media + + + align:start position:0% +social media +that's not the case and sort of but what + + align:start position:0% +that's not the case and sort of but what + + + align:start position:0% +that's not the case and sort of but what +i'm saying here is we tend to do the + + align:start position:0% +i'm saying here is we tend to do the + + + align:start position:0% +i'm saying here is we tend to do the +same things over and over again as maya + + align:start position:0% +same things over and over again as maya + + + align:start position:0% +same things over and over again as maya +was saying as well + + align:start position:0% +was saying as well + + + align:start position:0% +was saying as well +but why don't we just experiment more um + + align:start position:0% +but why don't we just experiment more um + + + align:start position:0% +but why don't we just experiment more um +often there's immediate cost + + align:start position:0% +often there's immediate cost + + + align:start position:0% +often there's immediate cost +but perhaps like long-run benefits + + align:start position:0% +but perhaps like long-run benefits + + + align:start position:0% +but perhaps like long-run benefits +there's default effects + + align:start position:0% +there's default effects + + + align:start position:0% +there's default effects +of course and so on that keep us from + + align:start position:0% +of course and so on that keep us from + + + align:start position:0% +of course and so on that keep us from +experimenting but if you think about it + + align:start position:0% +experimenting but if you think about it + + + align:start position:0% +experimenting but if you think about it +if you could make yourself just a little + + align:start position:0% +if you could make yourself just a little + + + align:start position:0% +if you could make yourself just a little +bit happier every day for like many many + + align:start position:0% +bit happier every day for like many many + + + align:start position:0% +bit happier every day for like many many +years it seems to be worth experimenting + + align:start position:0% +years it seems to be worth experimenting + + + align:start position:0% +years it seems to be worth experimenting +a lot + + align:start position:0% +a lot + + + align:start position:0% +a lot +i would sort of very much encourage you + + align:start position:0% +i would sort of very much encourage you + + + align:start position:0% +i would sort of very much encourage you +to go and try out new things in life + + align:start position:0% +to go and try out new things in life + + + align:start position:0% +to go and try out new things in life +that + + align:start position:0% +that + + + align:start position:0% +that +potentially make you happier um + + align:start position:0% +potentially make you happier um + + + align:start position:0% +potentially make you happier um +assemblable and often has a nice uh + + align:start position:0% +assemblable and often has a nice uh + + + align:start position:0% +assemblable and often has a nice uh +uh i hope this is still working the link + + align:start position:0% +uh i hope this is still working the link + + + align:start position:0% +uh i hope this is still working the link +but has a very nice new york times + + align:start position:0% +but has a very nice new york times + + + align:start position:0% +but has a very nice new york times +article that argues that + + align:start position:0% +article that argues that + + + align:start position:0% +article that argues that +what do we do um um experiment more and + + align:start position:0% +what do we do um um experiment more and + + + align:start position:0% +what do we do um um experiment more and +try to figure out what makes us + + align:start position:0% +try to figure out what makes us + + + align:start position:0% +try to figure out what makes us +um happier uh any other thoughts on on + + align:start position:0% +um happier uh any other thoughts on on + + + align:start position:0% +um happier uh any other thoughts on on +social media or facebook + + align:start position:0% + + + + align:start position:0% + +okay so uh that's all i have + + align:start position:0% +okay so uh that's all i have + + + align:start position:0% +okay so uh that's all i have +for for for now um + + align:start position:0% +for for for now um + + + align:start position:0% +for for for now um +uh next time we're gonna talk about um + + align:start position:0% +uh next time we're gonna talk about um + + + align:start position:0% +uh next time we're gonna talk about um +policy that's the last lecture + + align:start position:0% +policy that's the last lecture + + + align:start position:0% +policy that's the last lecture +please do read um um uh uh + + align:start position:0% +please do read um um uh uh + + + align:start position:0% +please do read um um uh uh +thaler and sunstein tells me the llama + + align:start position:0% +thaler and sunstein tells me the llama + + + align:start position:0% +thaler and sunstein tells me the llama +is not not here yet neither into the + + align:start position:0% +is not not here yet neither into the + + + align:start position:0% +is not not here yet neither into the +uh the the my + + align:start position:0% +uh the the my + + + align:start position:0% +uh the the my +private room where the llama might be + + align:start position:0% +private room where the llama might be + + + align:start position:0% +private room where the llama might be +otherwise uh also + + align:start position:0% +otherwise uh also + + + align:start position:0% +otherwise uh also +here there's a wait i think the the + + align:start position:0% +here there's a wait i think the the + + + align:start position:0% +here there's a wait i think the the +announce time is like 2 30 so that's in + + align:start position:0% +announce time is like 2 30 so that's in + + + align:start position:0% +announce time is like 2 30 so that's in +four minutes + + align:start position:0% +four minutes + + + align:start position:0% +four minutes +so if you have to run of course that's + + align:start position:0% +so if you have to run of course that's + + + align:start position:0% +so if you have to run of course that's +fine otherwise i'm just going to + + align:start position:0% +fine otherwise i'm just going to + + + align:start position:0% +fine otherwise i'm just going to +stick around and wait if you want to + + align:start position:0% +stick around and wait if you want to + + + align:start position:0% +stick around and wait if you want to +talk about more i'd love to sort of know + + align:start position:0% +talk about more i'd love to sort of know + + + align:start position:0% +talk about more i'd love to sort of know +more about why people are + + align:start position:0% +more about why people are + + + align:start position:0% +more about why people are +experimenting more i also would love to + + align:start position:0% +experimenting more i also would love to + + + align:start position:0% +experimenting more i also would love to +know more about + + align:start position:0% +know more about + + + align:start position:0% +know more about +um how people think so so one thing i + + align:start position:0% +um how people think so so one thing i + + + align:start position:0% +um how people think so so one thing i +was mentioning here is that well social + + align:start position:0% +was mentioning here is that well social + + + align:start position:0% +was mentioning here is that well social +media might be better than the + + align:start position:0% +media might be better than the + + + align:start position:0% +media might be better than the +detrimental effects + + align:start position:0% +detrimental effects + + + align:start position:0% +detrimental effects +in particular coming from social + + align:start position:0% +in particular coming from social + + + align:start position:0% +in particular coming from social +comparisons which is to say look + + align:start position:0% +comparisons which is to say look + + + align:start position:0% +comparisons which is to say look +uh you see everybody on instagram looks + + align:start position:0% +uh you see everybody on instagram looks + + + align:start position:0% +uh you see everybody on instagram looks +like they have a glamour glamorous life + + align:start position:0% +like they have a glamour glamorous life + + + align:start position:0% +like they have a glamour glamorous life +and are happy all the time + + align:start position:0% +and are happy all the time + + + align:start position:0% +and are happy all the time +you see that and that might make you + + align:start position:0% +you see that and that might make you + + + align:start position:0% +you see that and that might make you +feel depressed which by the way that + + align:start position:0% +feel depressed which by the way that + + + align:start position:0% +feel depressed which by the way that +might not + + align:start position:0% +might not + + + align:start position:0% +might not +lead you to a bit of glamorous pictures + + align:start position:0% +lead you to a bit of glamorous pictures + + + align:start position:0% +lead you to a bit of glamorous pictures +yourself it might reinforce the whole + + align:start position:0% +yourself it might reinforce the whole + + + align:start position:0% +yourself it might reinforce the whole +issue overall + + align:start position:0% +issue overall + + + align:start position:0% +issue overall +there surely are some downs actually but + + align:start position:0% +there surely are some downs actually but + + + align:start position:0% +there surely are some downs actually but +there's also potential upsides of + + align:start position:0% +there's also potential upsides of + + + align:start position:0% +there's also potential upsides of +connecting people online on + + align:start position:0% +connecting people online on + + + align:start position:0% +connecting people online on +a project that i'm trying to work on + + align:start position:0% +a project that i'm trying to work on + + + align:start position:0% +a project that i'm trying to work on +i think europosta anybody has some + + align:start position:0% +i think europosta anybody has some + + + align:start position:0% +i think europosta anybody has some +things one could do right now online + + align:start position:0% +things one could do right now online + + + align:start position:0% +things one could do right now online +to help people be more connected and + + align:start position:0% +to help people be more connected and + + + align:start position:0% +to help people be more connected and +less lonely and more depressed and less + + align:start position:0% + + + + align:start position:0% + +depressed \ No newline at end of file diff --git a/_OcgtpQvrVs.txt b/_OcgtpQvrVs.txt new file mode 100644 index 0000000000000000000000000000000000000000..c97844512a9aadf38670287d146d708d216a6d84 --- /dev/null +++ b/_OcgtpQvrVs.txt @@ -0,0 +1,4701 @@ +PROFESSOR: All right, welcome. + +We have some fun origami +topics today, mostly + +related to a topic +called pleat folding. + +General idea of pleat +folding is to fold + +alternating mountains and +valleys back and forth. + +And you can do a lot of cool +things with pleat folding, + +and that's what I want +to talk about today. + +In particular, this +model is usually + +called the hyperbolic +paraboloid. + +It's pretty simple. + +You start with a square paper. + +You fold this crease +pattern, which + +is concentric squares +alternating mountain + +and valley, and you +fold the diagonals, + +alternating mountain and valley. + +You crush it all +together, you'll + +get this sort of x-shape. + +And you sort of let +go, give it a twist, + +and it pops into this +saddle form, which + +looks a lot like a +hyperbolic paraboloid, which + +is one of the standard +saddle surfaces. + +It's approximating a hyperbolic +paraboloid, we think, + +or we thought, and that's +why it's called that. + +So you should all +try this at home. + +It's a great model. + +It's very cool. + +It's an example of +something I like + +to call self-folding origami +because the paper basically + +folds itself. + +You put in a very simple crease +pattern, concentric squares. + +What could be simpler than that? + +And yet you get this really +cool 3D form automatically. + +Physics, in some sense, is +finding this form for us. + +You can take this +pleating idea and apply it + +to many different +crease patterns. + +Another fun one if you have +a compass lying around, + +to score circles is you just +crease concentric circles, + +alternating mountain and valley. + +In this case, you +also need to cut out + +a circular hole in the center. + +Then you get a +different saddle form, + +which we don't know +exactly what it is. + +Let's see, I have some various +fun things to talk about here. + +So what's going on with paper-- +if I take a piece of paper, + +paper is an elastic material. + +It remembers that +it was made flat. + +It likes to be flat. + +If I curl a paper a +little bit, for example, + +it flattens back out. + +That's elastic memory. + +If however, I crease +a piece of paper, + +then that's called a +plastic deformation + +beyond the yield +point of the material. + +This works in sheet metal +also, lots of materials. + +I've effectively changed +the memory of the paper. + +It now wants to stay bent. + +If I try to unfold it, it +goes back to some angle. + +Depending on how +hard I crease it, + +it will go to a sharper angle. + +So that's basically +what's going on. + +In these surfaces, where +we crease the paper, + +it wants to stay bent. + +Where we don't crease the +paper, it wants to stay flat. + +It can't do all of those +things, but physics + +finds an equilibrium +among all those forces. + +So we simulated +that some years ago. + +This is with architecture +undergrad Jenna Fizel + +and Professor John +Ochsendorf, architecture. + +So on the right of +each of these examples, + +we have photographs of real +models, pleated foldings, + +a hyperbolic paraboloid, +squares, hexagon, + +octagon, just not so pretty. + +But we re-created that physical +model with a virtual model + +just using some +spring approximation + +to the forces I described. + +And here's an approximation +to a circle, where we just + +took a really big regular n-gon. + +This is real circles +and the simulation. + +So this confirms that what +I said is actually true. + +Those are the only +forces you need to model, + +and you get an +approximation of what + +really happens in real life. + +So instead of folding +real paper in this way, + +you could simulate it. + +Cool. + +Here is that simulator in +action with pleated hexagons, + +just to show you +what it looks like. + +So the creases are trying +to become more bent, + +at this point have +reached equilibrium, + +and you get your 3D form. + +Once you have that +3D form, so you + +have a virtual model of a +physical piece of paper, + +the natural thing to do +is build a physical model + +of the virtual model of the +physical piece of paper. + +And you've seen this +on the mailing list. + +This is what we're +calling origami skeletons. + +Here the vertices, which +you can see bigger here, + +are 3D printed plastic spheres, +and there's aluminum rods. + +The spheres have holes +at just the right angles + +to make exactly the 3D form +that was made by that simulator. + +So this is something you +could really only build + +if you had a virtual +model of that thing. + +So this is a fun example +of taking mathematics + +and our sort of the +computational understanding + +of how paper folds +and turning it + +into sculpture that requires +that mathematical basis. + +On the topic of sculpture, +at the very beginning-- + +so this is early on in my PhD, +with my dad and my PhD advisor + +Anna Lubiw, same authors as +like the folding problem, + +one of our early explorations on +the mathematical sculpture side + +was to take +hyperbolic paraboloids + +and take a lot of them +and join them together + +to make polyhedral surfaces. + +These are what we +call hyperhedra + +because hyperbolic paraboloids +are also called hypars, + +I think, originally by +the architect community. + +So these are +algorithmically-generated + +sculpture. + +The input to the algorithm is +a polyhedron, like the cube, + +and the output is a way +to join hypars together + +to represent that cube. + +And the algorithm +is very simple. + +For each face of the +polyhedron-- so here it + +has four sides, you take +four hyperbolic paraboloids + +and join them together in a +cycle just sharing one edge. + +So you do that for each of +the six faces, so in all + +you have 24 hyperbolic +paraboloids. + +Then to join two +faces together, you + +join them along a pair +of edges like this. + +And when you do that, +you get an enclosure. + +It's a closed solid. + +And you can do that +for every-- here + +we're doing it for all +the Platonic solids. + +You can do it with any +polyhedron in theory. + +So it's like an infinite +family of sculptures here, + +which is kind of fun. + +Here is a simulation of +that cube just for fun. + +That works, too. + +And back to the curve creases. + +These are some examples I +showed way back in lecture 1. + +These are sculptures in the +permanent collection at MOMA. + +And the idea here +is instead of taking + +just one concentric circle +which goes around 360 degrees, + +we take a circular ramp +which goes around twice, + +and then join the ends. + +So we have 720 +degrees of material + +there, which you might think +of as negative curvature. + +But it's a little +weird because there's + +the hole cut out in the center. + +So it's a little hard +to measure curvature, + +but you can actually define it. + +And these are three +different foldings + +with the same idea, slightly +different parameters + +in how big those ramps are, and +different numbers of creases. + +And you get very different +equilibrium forms. + +Again, this all sort +of self-folding paper + +wants to live in these +three configurations. + +Here's some that you +may not have seen. + +They're on the web. + +But these are taking +regular 360-degree circles + +but taking two or +three or four of them + +and joining them at a +couple of key points, + +and the rest is self-folding. + +So the big-- I mean, the sort of +powerful scientific engineering + +idea here is that you +could deploy complicated + +3D structures just +by manufacturing + +very simple flat +structures, maybe + +joining a few points together, +and then just say go. + +If you can manufacture +these things + +so that every crease +locally wants to bend, + +then you'll get these +3D forms automatically. + +This is especially powerful +at the nano scale, where + +you can't have your fingers +moving around and pressing + +things. + +But you can probably +use materials + +that, say, when heated +or you add some chemical, + +cause everything to fold. + +It's very easy for us from +all the chip fabrication + +we do to manufacture +flat crease patterns, + +and that will let us manufacture +3D things at the nano scale. + +You could also imagine it a +much larger scale like a space + +station-- like a space +station that looks like that. + +That would be pretty +cool-- and something + +where you don't want +to have to physically + +fold everything by hand. + +But if it could be +done automatically, + +life would be good. + +Now, we don't have +any algorithms + +for the reverse +engineering problem-- + +If I give you a 3D +curved surface like this, + +find the crease pattern and +the joins that make it happen. + +But that's the goal. + +And towards that goal, +we make sculpture + +to explore the space +of what you can make. + +All right. + +I think I have one more +sculptural example here, + +which is combining these curve +creases with glassblowing. + +And to make glassblowing +more tactical, + +Marty here, our cameraman, +is blowing glass blindfold. + +Don't try this at home. + +So paper folding is a +very tactile experience. + +To make glassblowing more about +touching the material, which + +you're not usually supposed +to do because it's over 1,000 + +degrees Fahrenheit-- blindfolds. + +AUDIENCE: 1,000 +degrees Centigrade. + +PROFESSOR: 1,000 +degrees centigrade. + +Wow. + +The temperature of +an erupting volcano. + +[MUSIC PLAYING] + +This is in the glassblowing +studio in 4.003 near here. + +He's made a whole +bunch of those. + +And here's what it looks like to +fold from scratch, so to speak, + +a concentric circle model. + +Of course, it's +accelerated in movie time. + +It only takes 10 seconds. + +In reality, it takes 10 minutes +after pre-scoring, maybe more. + +And now we get some +ship-in-the-bottle action. + +And this is a lot of fun +for us because not only + +do you have the +self-folding constraint, + +but you have this +enclosure constraint. + +These forms would +not look as exciting + +if they could +sprawl out, and they + +didn't have any constraints +to live inside these bubbles. + +So you get yet +another collection + +of forms from that glass. + +All right. + +I think that's the end of +our little sculpture tour. + +We'll come back to sculpture +at the end of this lecture. + +But I want to talk more +about-- oh, question. + +AUDIENCE: What was the +idea behind the blindfold? + +PROFESSOR: What was the +idea behind the blindfold? + +So paper folding is all +about touching material. + +Glassblowing is +usually very visual. + +It's about you look +at the material, + +and you don't usually touch it. + +So we wanted to unify the two +in order to put them together. + +Plus it was just a crazy idea. + +I think what happened +is I was in my office. + +My dad calls me up. + +He's blowing glass. + +He's like, I got +this great idea. + +Come over with a camera. + +So in that video, I +was the cameraman. + +And I was like, +all right, you want + +to burn yourself blowing glass. + +He didn't actually burn himself. + +Usually, he does. + +But blindfold, he +was more careful. + +Yeah, blindfold glassblowing, +it's pretty crazy. + +That was his first +try ever blindfold + +glassblowing in that video. + +All right. + +So this hyperbolic +paraboloid, it's + +been around for a long time. + +I didn't mention the history. + +It goes back to the +Bauhaus in the late '20s. + +Albers, who I'm sure +many of you know of, + +taught a class about design. + +And he liked using +paper as a material that + +would force you to focus-- +not worry about material + +in the sort of architectural +scale and what would stand up-- + +and just think about design. + +And paper folding was really +tactile and good for that. + +And I'm not sure exactly +whether it was him + +or a student of his, it's +somebody in that period, 1927, + +'28, came up with this +model and the circular one. + +And then it's been taught +many times since then. + +Then it really hit it big in the +origami community in the 1980s + +by [INAUDIBLE], and since then +everybody's been folding it. + +Question? + +AUDIENCE: Is it not rigid, +but paper [INAUDIBLE]? + +PROFESSOR: Ah, you made one. + +Can I show it? + +Thanks, [INAUDIBLE]. + +Simple little example, but +here is concentric squares, + +and you crease it down. + +Normally you get this +kind of X. You let go, + +and it pops into +a little saddle. + +So this is a sort of +low-resolution one. + +If you spend twice +as much time, you + +can double the +resolution and so on. + +Your question, is it rigid? + +Probably not rigid. + +There's like this +degree of freedom. + +AUDIENCE: Rigid in +the sense of that + +between creases [INAUDIBLE]. + +PROFESSOR: Yeah. + +What's happening in +between the creases? + +AUDIENCE: Exactly. + +PROFESSOR: That is exactly +the topic of today's lecture. + +In fact, we have a paper called +"How Does Paper Fold Between + +Creases" to address +exactly this question. + +I'm going to hang +onto it, if you + +don't mind because it'll +be useful to point at. + +In fact, it is +completely impossible + +to fold that crease +pattern into this shape. + +And so your idea that there's +something weird going on + +is an idea-- we've +known for a long time + +that these faces +could not stay planar. + +I mean, at least visually it's +hard to see unless you stare + +at it with all the right angles. + +But the faces look +like they twist. + +Now, that's OK. + +Paper can do all sorts of +curving stuff without creasing. + +I mean, this is sort of like +a twist, no creases involved. + +So we thought this was +possible, but in fact, it's not. + +So this is the big surprise. + +It's something we +discovered just last year, + +and I'm going to prove +that to you today. + +So the theorem is, if I have +this concentric square crease + +pattern, even ignoring +the mountains and valleys, + +it is impossible to +fold that crease pattern + +into anything that is not flat. + +So you can, of course, +not fold it at all, + +then none of the +creases get folded. + +You can collapse it +all the way down. + +That probably +isn't even allowed. + +But never mind. + +But what we really +want is a 3D form + +where every crease is +bent by a non-zero angle + +and also not by 180 degrees. + +So we'll call that a +proper folding, something + +where every crease is +strictly between 0 and 180, + +which is what we want +in these 3D forms. + +And the theorem is, +that is impossible + +for the hyperbolic paraboloid. + +There is none. + +So that's weird because +we fold them all the time. + +We've been folding +them for like 11 years, + +and other people have been +folding them for 80 years. + +What's happening with +the real piece of paper? + +Well, one possible answer +is that there's more creases + +that you don't +see in this model. + +And if you add +more creases, it is + +possible to fold +something that looks + +like a hyperbolic paraboloid. + +So here we have the regular +crease pattern in black, + +and then I've added +some purple diagonals. + +Wherever we had a +black trapezoid, + +I've added one purple +diagonal to triangulate + +the crease pattern. + +And here I've chosen what +seems to be an especially + +good triangulation +where I zigzag + +back and forth +within one quarter. + +And then also from around a +ring, I zigzag back and forth. + +So that triangulation +folds into this. + +That's another theorem. + +This is construction on a +computer, obviously, where + +we have 16 rings, and +the central crease here + +is folded by an +angle of 30 degrees. + +That's the theta. + +Notice I also had to +remove part of a diagonal. + +That's also necessary. + +In the center, you +can't crease both + +of those, the folds in an +X, by a non-zero amount. + +Those are all things we're +going to prove today. + +But before we prove +the negative things, + +I want to prove +the positive thing, + +that this thing can +actually be built. + +That may seem obvious +because here it is. + +I built one. + +But because there's all these +arguments of, well, here it + +is, I built one, we've got to +be especially careful about, + +does this thing +really truly exist? + +So let me tell you +how it's constructed + +and how we can actually prove +not only can we build it + +approximately on a computer, +but we can prove there really + +is one there even though +we don't have it exactly. + +So it's actually pretty +cool and pretty easy. + +So this is the triangulated +hyperbolic paraboloid. + +So the idea is to work +from the inside out. + +We're going to start +with this central square + +here-- and let me draw +it over here-- fold it + +by some angle theta. + +That, I think, we +all know how to do. + +It's some rotation matrix. + +And then I want to +work my way out. + +So at this point, +I know the location + +of these four vertices. + +In general, I know some +square and everything inside. + +I want to figure out +everything in the next square. + +And the creases are going to +look like this, from my zigzag + +pattern. + +So there's stuff in +here, which is known. + +So I already have figured out +the location of these vertices. + +And I want to know, +how do I figure out + +these vertices on the outside? + +If I can do that, I just repeat, +and I get a bigger and bigger + +hyperbolic paraboloid. + +So what I do is pretty easy. + +I'm going to look at this +vertex first and say, + +well, I have these +three points, and I + +have known distances +between those three points. + +I'm going to assume here, +and we'll see why later, + +that each of these +creases remains + +a straight line in +three dimensions. + +It's not obvious, because +creases might bend around. + +But let's assume +that we were going + +to fold it in a simple way. + +These triangles are going +to remain triangles. + +These edges will +remain straight. + +And they have to +remain the same length + +because we're paper folding. + +You can't stretch. + +And so I know these +three points in 3D, + +and I know these +three distances, just + +measuring them on the crease +pattern, flat crease pattern. + +So this point is on the +intersection of three spheres, + +and the centers of the +spheres are not collinear. + +This is a trick we used last +class but in two dimensions. + +So I have three +non-collinear points. + +I have three spheres-- +little hard to draw-- + +centered at them. + +The intersection of +two of the spheres + +is going to be a circle, +and the intersection + +with the third sphere is going +to be actually two points. + +So the intersection of +three spheres is two points. + +So a little bit of ambiguity. + +But it turns out +one of these points + +will set the mountain-valley +assignment correctly, + +and the other one will +set it incorrectly. + +Like if I want this to be +a mountain, one of them + +will be inside and one +of them will be outside. + +One of them will +make this mountain, + +one will make it valley. + +So it turns out if +you actually do this, + +it's uniquely determined +at every step of the way. + +Because you know what +mountain-valley assignment + +you're aiming for, you uniquely +figure out what this point is. + +By the same reasoning, +you can figure out + +what this point is, intersect +these three spheres. + +And then once I know +those two points, + +I can figure out this +point because it's + +the intersection of +these three spheres, + +with now these points are known. + +And then I can figure out this +point in the symmetric way. + +OK? + +That's how you do it. + +We repeat. + +And that is exactly how +this model is built. + +Now, this is still not a +proof that it really folds. + +It's a construction method. + +I'd say it's an algorithm. + +If I start out with +the inner thing here + +and I give you some angle, +I can approximate where + +these vertices are. + +And then I can keep going +and, at each step of the way, + +approximate where +the vertices are. + +The worry is the approximation +gets worse and worse because I + +have this propagating +error effect. + +The larger n is, +the number of rings + +in my hyperbolic paraboloid, +the lower the accuracy will be. + +But I get to +choose, at each step + +of the way, how +much precision I use + +to compute all of these numbers. + +Let me tell you how this +computation actually works. + +I did this in Mathematica, or +we did this in Mathematica. + +Here's Mathematica. + +And I asked +Mathematica, well, here + +is the equations for the +intersection of three spheres. + +I say, well, squared Euclidean +distance between this point + +and some unknown thing x, y, +z is this distance squared. + +And here's the second one, +and here's the third one. + +It's kind of tiny. + +And then here's the answer. + +It's a little messy. + +In fact, you can ask how +many terms are in this thing. + +It's 444,000 terms +in the solution. + +Don't try this at +home, I guess, by hand. + +Intersection of three +spheres is a bit messy. + +There's probably a cleaner way +than what Mathematica does, + +but this is an easy +way to get it in. + +Now, in theory-- so if you +look at all of this stuff, + +all that's happening +is you have all + +the various inputs, x1, +y1, x2, z2, and so on. + +You have some numbers +like 4 and minus and 2. + +All you're doing is +taking these numbers, + +adding them, multiplying them, +dividing them, squaring them, + +subtracting them. + +And at some point, +taking square roots. + +I don't know if +we'll ever see that. + +I mean, if we search through, +there are some square roots, + +but they're going to be +in very specific places. + +Yeah, so I probably +won't find one instantly. + +Oh, there's one, square root. + +So all I'm claiming +at this point + +is you can compute the +intersection of three + +spheres just using basic +arithmetic and square roots. + +This is called a +radical expression, + +not because it's so +amazing and controversial. + +But it's radical because that +symbol is called rad, I guess, + +and radical refers +to square roots. + +I guess they were +crazy at the time. + +All right. + +Actually, I want to +stay with Mathematica. + +So that's the idea. + +Still not a proof, just +a construction method. + +But here's a trick, +which you can + +use to turn a construction +into an actual proof + +that this thing exists. + +It's called interval arithmetic, +little computer science lesson. + +How many people have heard +of interval arithmetic? + +No one-- one person, all right. + +Yeah, even computer scientists +probably don't necessarily + +know this unless they've +seen some numerical analysis. + +So it's an idea that +instead of computing + +an approximate location +for this point, + +I want to get not only an +approximate location, but also + +an error bound on how +much I don't know it. + +So there are three +coordinates to every point. + +For each coordinate, every +number I want to represent I'm + +going to represent +as an interval + +from some lower bound +to some upper bound. + +So say, well, I don't +know what the value is, + +but I know that it is somewhere +in between these two numbers. + +So represent every +number like this. + +And then you just need +to define, how do I + +add numbers, subtract them, +multiply them, divide them, + +and take square roots? + +And the answer is carefully. + +I'll show you one example. + +If I have two numbers, +L1, U1, and L2, U2, + +and I want to add +them together, then I + +believe it's pretty simple. + +It's just L1 plus +L2, and U1 plus U2. + +This is in perfect +mathematical world + +where there's no round off. + +In reality, when +you add two numbers, + +you lose a bit of precision. + +And you make sure that +when you add these numbers, + +you always round down, and +when you add these numbers + +you always round up. + +So that way, these intervals, +the accumulation error + +is realized by these +intervals getting wider. + +You can start with +them super tiny, + +maybe, in fact, 0 +length because you + +know exactly where these points +are, so they're 0 intervals. + +But then, because of the +error in every operation + +you do on the computer, +the intervals will widen. + +But as long as you +do this computation + +with enough bits of precision, +they'll widen slowly. + +If you do it slowly +enough-- if you do it + +with enough precision, and +the errors accumulate slowly + +enough, you can build your +n-ring hyperbolic paraboloid + +without any error, or +without too much error + +to make things go wrong. + +What could go wrong is that +these three spheres might not + +intersect. + +That's really the worry here. + +There are two things +that could go wrong. + +One is that the spheres +don't intersect. + +The other is that the +surface intersects itself. + +Both would be bad. + +How do you tell when the +spheres don't intersect? + +Well, we have this formula, +this ginormous formula. + +The only thing +that could go wrong + +is that you take a square +root of a negative number. + +Now, hopefully that +never happens in reality. + +But what could +happen for us is we + +have such a poor +approximation of our numbers. + +And we try to take the +square root of some interval, + +and L is less than 0. + +Now, probably the actual +number is more than 0, + +but we can't tell, +and we just know + +the number is somewhere +in this interval. + +If the lower bound +is negative, then we + +can't take the square root. + +We don't know what the +right answer would be. + +So Mathematica conveniently +can do all of this for you. + +If you just plug in +intervals instead of numbers, + +it will do interval +arithmetic correctly, + +and you can tell it +what precision to do. + +And that is how we +found this example. + +In fact, I will show +you the notebook, + +and there's all this +computation and stuff. + +This is all, I believe, +it's in our paper, + +so if you want the code. + +So we compute the +crease patterns + +so I can measure +all the distances. + +And there's some collision +detection and stuff + +to make sure +everything's working. + +And it computes some rings. + +And then, actually, the one I +want to show you is this one. + +This is model we've +been looking at, + +and here it is in +three dimensions. + +The way it's being rendered is +a bit odd, but you get the idea. + +That is the hyperbolic +paraboloid we construct. + +Now, in reality, +each of these points + +is actually a little interval. + +It's hard to draw +that because it's + +smaller than the +resolution of the screen. + +I think I compute +up here the-- this + +is like how much we've +messed up the edge lengths. + +It's like all of +these 9's, and then + +this little area at the end. + +OK. + +Cool. + +So the point is, you just do +this with enough precision. + +As long as you don't +end up computing + +any negative square +roots, you get a surface + +where every point is +actually a little box. + +You don't know where the +point is exactly in that box. + +Then you check for +collision, just knowing + +that the points are +somewhere in those boxes. + +You try to intersect +two triangles. + +As long as they intersect away +from the boxes, you're OK. + +Then you know there's +no actual intersection. + +And we have done that +for this triangulation up + +to-- get it right-- +up to n equals + +100, 100 rings, and where +the theta angle here + +is any even number between 2 +and 178 degrees, so 2 degrees, + +4 degrees, up to 178 degrees. + +We're not interested in 180 +because that would be flat. + +That's not interesting. + +We're not interested in 0. + +Every even number of +degrees in between. + +Why even? + +Just because of +the representation. + +I'm sure it works for the odd. + +In fact, I'm pretty +sure it should + +work for any theta and any n. + +But this technique will +only let us to prove it + +for specific theta +and specific n. + +Because we're just +using a computer, + +it's only going to +check one example. + +We don't have a nice way +to do them all at once. + +In case you're +interested-- oh, here I've + +built it out of sheet +aluminum, I think? + +AUDIENCE: Galvanized-- + +PROFESSOR: Galvanized steel? + +All right. + +Water jet cut along the creases. + +Now, steel's a little tricky +to not add extra pieces + +by accident, so +there's a few defects. + +But this is also some kind of +verification that it works. + +In the computer here, the +number of digits of precision. + +So for whatever +reason, Mathematica + +speaks base 10 +instead of base 2. + +Which is weird to me, but maybe +intuitive to everyone else, + +non-computer scientist, I guess. + +So there's normal sort +of floating points + +like 16 digits of +precision or so. + +And there you can build this +thing up to n equals 3, 3 + +rings. + +But you go up to about +1,000 digits of precision, + +and then we can get beyond 100. + +It depends, though, on what +the angle is that you fold. + +So for angles that are +very big, close to 90, + +we had to go up to 2,000 +digits of precision. + +And I don't know how +far n can go here. + +I think maybe a couple 100, +but I'm not sure exactly. + +The larger n is, of course, +the more accumulation you have, + +and so you have to +do every operation + +with more digits of precision. + +But the conjecture would be, +any specific data and n, there's + +some precision for which +this approach will work, + +but we don't actually +know how to prove that. + +All right. + +So that's a triangulated hypar. + +Here's another +triangulation, which we also + +studied in this paper, where +instead of zigzagging up + +one quarter of the +square, we just + +do all the diagonals +in the same direction. + +We still zigzag around a +ring but not between rings. + +And this can also fold, +as the other model + +that was in the +Mathematica file. + +I won't bother going there. + +This is for a small fold angle +of just 8 degrees in here, + +n equals 16. + +And there's a reason I +did it for a small angle, + +because it doesn't +work for large angles. + +So that triangulation we +started with was a good one. + +It's actually not the +first one we tried, + +but it is sort of natural. + +If you fold by a +very small amount, + +you can get all the +way up to 133 rings, + +but then it fails after that. + +The spheres just don't +intersect anymore. + +Depending on how much you fold, +like if I fold by 22 degrees, + +I can get up to 13 rings. + +But here I wanted +to get to 16 rings + +so I only went up to, what was +it, 8 degrees or something. + +I could have gotten a +little beyond but not a lot. + +And up at 178, you can +still get three rings, + +but it doesn't fold after that. + +So triangulation matters, +which triangulation you do. + +Going back to the +one that works well, + +natural question +is, is it actually + +a hyperbolic paraboloid? + +It's called a hyperbolic +paraboloid because-- + +or there is a surface called +a hyperbolic paraboloid, where + +if you take a cross-section +this way, you get a parabola. + +That's the paraboloid part. + +And if you take a cross-section +this way, you get a hyperbola. + +That's a little +harder to draw, but it + +goes around here +and around here. + +Hyperbolas have two +connecting components. + +So let's look at the +parabolic part here. + +We're supposed to be +approximating a parabola if we + +look at all the points on +the top here and also maybe + +on the bottom. + +So that's what I've drawn. + +The green lines, which +are very light so a little + +tricky to see, they +zigzag back and forth, + +and that is what we compute. + +Again, it's approximate, but +it's so close to accurate + +that I just draw them +as single points. + +The error is much smaller than +the thickness of these lines. + +And then the blue +and purple lines + +here are fits of +the best parabola + +that matches these points. + +Actually, it's not +even the best parabola. + +It's kind of funny. + +I just take the last three +points-- three points + +determine a parabola. + +I take the parabola that +fits through those three + +points and bam! + +It is almost a perfect fit. + +These are the error +charts, I guess. + +This is relative errors, +probably the most informative. + +Or actually, it's the ratio-- +it's not really an error-- + +the fit value over +the actual value. + +So when it's 1, that +means it's perfect. + +And yeah, this is at the end +of the chain where I fit it, + +so of course it's going +to be perfect out here. + +At the center, at +the very beginning-- + +so I'm only looking at one +quarter of this thing-- yeah, + +the error is a little bit. + +The ratio is not 1, +but it's 0.9997 or so, + +maybe a little bit less, so +that I had to write it down. + +It's like 0.003% error, +if I got it right, + +maybe just 0.03% error. + +Fix the notes. + +Something like that. + +It's very small is the point. + +But it is non-zero. + +I mean, initially +we thought, well, + +maybe if you increase +the resolution-- you + +make a finer and finer +hyperbolic paraboloid-- + +it will more closely approximate +a hyperbolic paraboloid. + +That does not seem to +be true because, really, + +making it finer is really +just like making it bigger. + +You never really change +the center behavior. + +It's always the same. + +And this construction proves it. + +We build the center, and we +can go as far out as we want. + +It's just changing the +scale of the thing. + +But the center will +always remain the same, + +and it will always +remain off the parabola, + +but super, super close. + +Really, it's all right to call +this a hyperbolic paraboloid, + +but you should +triangulate, especially + +if you're making something +out of more rigid material. + +Cool. + +Let's go on. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah, question. + +AUDIENCE: Do the creases +have to be uniform? + +I mean, could you +tighten up inside? + +PROFESSOR: The creases do +not have to be uniform. + +Most of the hyperbolic +paraboloids we've made, + +we do evenly space +all the squares, + +but they don't have to be. + +I say that in that we've +made them out of paper, + +and they fold to +something, and you + +get other kinds of surfaces. + +Probably not going to be a +hyperbolic paraboloid anymore. + +I have not done it +with Mathematica + +and checked that it really is +possible, but it should be. + +That would be a fun thing +to explore at some point. + +Other questions? + +All right. + +So this is the end +of the positive news + +for hyperbolic paraboloids. + +Now we're going to go +to the negative stuff, + +showing that it is +impossible to fold + +this with this crease pattern. + +Hyperbolic paraboloids don't +exist without triangulation. + +For this we need a +little bit of math tools + +in this paper, "How Paper +Folds Between Creases." + +So in the study +that we just did, + +I assumed that all of the +creases stayed straight. + +And therefore that all +of the faces-- therefore? + +Yeah, I guess, because +triangles are rigid. + +If I forced the edges of the +triangle to stay straight, + +then the interior +of the triangle + +must stay flat just +to preserve distances. + +So I assumed that every face of +the piece of paper stayed flat. + +Why did I assume that? + +Because paper, real +paper, does not + +have to stay flat in +between the creases. + +This is real stuff here. + +But paper is constrained on how +it can curve without creases, + +and that is the purpose of this +little mathematical endeavour. + +There's some technical stuff, +and I want to get to the meat + +as quickly as possible. + +But I'll just mention +some assumptions. + +We assume that the +thing that we fold, + +the folding of our piece +of paper, is piecewise C2. + +C2 means you can +take two derivatives, + +and it's still good and +continuous and sort of smooth + +up to the second level. + +Piecewise means, of +course, we have creases. + +Those are not C2, not even C1. + +So we have some crease +pattern on our piece of paper. + +It's whatever. + +And what we mean is that inside +one of these regions, it's C2. + +On the creases, it's nothing. + +It's C0. + +It's continuous. + +We don't rip the paper. + +But we don't necessarily +have derivatives everywhere. + +So that's the assumption. + +Now, one annoying +thing here is you + +can have something called +a semi-crease, something + +we call a semi-crease, +which is C1 but not C2. + +Yeah. + +So you have to +divide into pieces, + +but it's not +technically a crease. + +And this is some of the worry +of what might be happening. + +Maybe you don't +need creases here, + +you only need semi-creases. + +Maybe you only need to violate +the second derivative, not + +the first. + +Creases should be violation +of first derivative. + +Those are sharp things. + +Semi-creases are just +kind of little sharp. + +It's like-- what's a good +example of a semi-sharp thing? + +I guess if I take a +parabola, and then + +I take a more shallow +parabola, then at this point + +there's no second derivative +because the first derivatives + +don't meet. + +This one has a first +derivative of this. + +This one has a first +derivative of that. + +They're not the same. + +Is that true? + +Parabolas maybe not. + +But you get the idea. + +This is a discontinuity +in the second derivative, + +not the first. + +All right. + +I'm going to basically +ignore semi-creases here, + +though, because they're +just kind of a technicality. + +They don't end up mattering. + +So we have piecewise C2. + +And we assume that our +surface is intrinsically flat, + +meaning it came from a +piece of paper-- trinsic-- + +oh, boy, intrinsically flat. + +Now this is something we +know as curvature zero. + +And I want to tell you a little +bit more about curvature. + +We have defined curvature +in a few different-- well, + +I guess in one +particular way, which + +is you add up the material, +and you take 360 minus that. + +So curvature zero +means you have 360 + +of material, which is good news. + +But there are other +ways to define it, + +in particular, the +way Gauss defined it. + +This is usually called +Gaussian curvature + +because he invented it. + +Gauss defined curvature +of a 3D surface. + +You have some weird +curved 3D thing, + +like this shape, +the orange part. + +And there's actually a lot of +natural notions of curvature + +here. + +Gaussian curvature +is just one of them. + +So let me tell you a +little bit about that. + +We're looking at +this point, and I + +want to compute the +curvature of this point. + +Well, if I look +in any direction, + +like say this red +direction-- so it's + +like I slice this world with +a plane, this blue plane, + +I get a nice +one-dimensional curve. + +Then the curvature is how bent +that curve is at that point. + +That's like a +directional curvature. + +In this direction, how bent +is-- what does how bent mean? + +It just means you try to +nestle a circle in there, + +in that plane, and you +take 1 over the radius. + +That's a curvature. + +OK? + +So if it's flat, the radius +could be infinite, and so + +curvature zero. + +If it's very sharp, then +the radius is very small. + +And so 1 over the radius is +very large, big curvature. + +So it's some thing here. + +Let's say it's a +positive number. + +And then if I take, for example, +this other blue plane, so + +this cross-section, +in that direction + +the curvature is +bent the other way. + +So you say, well, there +the directional curvature + +is negative. + +It depends which way is up. + +One of them is positive, +one of them is negative. + +Somewhere in between +it's going to be 0. + +But you have all these different +directional curvatures. + +The Gaussian curvature, +which is the one + +that we sort of know and love +and have used a lot, mostly + +for polyhedra, is the +min directional curvature + +times the max +directional curvature. + +Now, I really mean min and max. + +So the smallest one, in +this case, is negative. + +The largest one is positive. + +You take the product, and +that's the Gaussian curvature. + +It's a weird thing. + +But in particular, +because there's + +a negative one and +a positive one here, + +that means the +product is negative, + +and that's because +this is a saddle. + +Still the case, negative +Gaussian curvature + +means saddle. + +Positive means a convex cone. + +0 means intrinsically flat. + +So this is still +the thing we know, + +but this is a weird way +of thinking about it. + +This is how Gauss defined it. + +And he proved that even +if you fold the surface, + +the Gaussian curvature +never changes. + +That is called the +theorema egregium. + +Cool name. + +So Gaussian curvature +doesn't change under folding. + +We start with something +that's flat, zero curvature. + +Because if you +take a flat plane, + +you take any directional +curvature, everything's 0. + +So it's the product +of min and mix. + +They're both 0. + +So we start with something zero +curvature, it will remain so. + +Now, if I have a +product of two things, + +and I know this is +equal to 0, that + +means one of the two +things is 0, maybe both. + +If it's still a plane, +both of them will be 0. + +But one of them +still has to be 0. + +What this means is, basically, +locally at any point, + +we have a cylinder, some +kind of generalized cylinder. + +But it really only +curves in one direction + +because there's some direction +where it doesn't curve at all. + +Everything's straight. + +In all the other +directions, yeah, it + +curves different amounts. + +The orthogonal direction will +be where it curves the most. + +That will be the max, I +guess, and the min will be 0. + +So that is what a +folded sheet looks like. + +And it's maybe not +so obvious, but when + +I did all this +contorting and what not, + +really I was only bending in +one dimension, like a cylinder. + +That's not exactly +a cylinder because I + +can change the radius of the +cylinder all over the place, + +but I'm really only +bending in one direction. + +I was reading on Wikipedia, +this explains how we eat pizza. + +Because you take +a piece of pizza, + +which is basically +like a piece of paper, + +and if you bend it a little +bit, like you push in the center + +and push up on the +sides, you give it + +some curvature in one direction. + +And therefore it has to +remain straight in the other, + +so it kind of supports +the piece of pizza. + +Never thought of it +that way, but there you + +go, practical applications +for this stuff. + +All right. + +These things we +call planar points. + +If I have a point p and it's +locally flat like a plane, + +call it planar. + +These things, for some crazy +reason, we call parabolic. + +This is to be consistent +with other notation. + +I know it looks-- cylindrical +would be another fine term. + +But there's a third +kind called a elliptic, + +which would be like this stuff. + +That doesn't happen. + +So we just worry about +locally cylinder, which + +we're going to call parabolic +because it's also like locally + +a parabola, doesn't +matter, and locally planar. + +Those are the two kinds +of points we can have. + +Now, I'm going to give you some +accelerated facts we're just + +going to take as given +from differential geometry. + +Well, really, we had +to take some facts that + +were about differential +geometry and sort of port + +them to our context. + +They didn't give us +exactly what we wanted. + +We had to generalize +them a little. + +Differential geometry, if you +were at Sunday's lectures, + +that was one of the main +tools being used there. + +Differential geometry is about +smooth things, like C4 usually. + +Now, sometimes about C2 things. + +It is almost never about +piecewise C2 things. + +So you got to worry +about the pieces. + +Now, most the time, +we're thinking + +about one little region +here, and that's nice in C2. + +And you can check. + +Most of the differential +geometry still applies there. + +Blah, blah, blah. + +Let me tell you some facts. + +If I take a smooth point, so +that means not on a crease + +and not a semi-crease, +then it lies on something + +called a rule segment, +which is a line segment, + +also called a rule line. + +And the endpoints +of that segment, + +here's the interesting part, +are on creases or the boundary. + +So we already know +from this picture + +that any point +lies on a segment, + +like an actual 3D +line segment, because + +of this parabolic nature. + +What's interesting is that +segment, it can't stop. + +Just keeps on going, +like the Energizer bunny, + +until it hits a crease. + +At that point, +things aren't smooth. + +We don't know what happens. + +But really, these +creases go straight. + +Those are rule lines. + +And here, actually, we have +a choice, many different rule + +lines. + +But in the parabolic case, +that rule line is unique. + +It's going to be unique +for parabolic points. + +And so we get what's called a +ruled surface, which is just + +the union of a whole bunch +of line segments, rule lines, + +around any point. + +Maybe any smooth +point, just to be safe. + +So you may have heard +of ruled surfaces. + +They're quite common. + +They're fun because you can +build them out of strings. + +So each string, if you hold +taut, it's a line segment. + +Take a whole bunch of them +and just imagine the envelope + +there. + +That is a 3D surface, and +that's a ruled surface. + +Now this one does not +have zero curvature. + +It has negative +curvature everywhere. + +So that can't happen. + +This actually can happen. + +This is like you take +a helix, and so there's + +a blue curve in +3D, a space curve. + +And then you imagine taking +the tangent at every point. + +So just like if you just went +straight at every point instead + +of turning, then you +get a bunch of lines. + +Those are rule lines. + +And you get this cool surface. + +Now, that is a valid +folding of a piece of paper. + +Doesn't look like a +cylinder, does it? + +But locally, each of these +lines looks like a cylinder. + +It's just the radius +of the cylinder + +is changing all over the place. + +But that's a valid folding +of a piece of paper, I think. + +Has zero curvature +everywhere, if I did it right. + +Or I didn't do it, but if +I imagine it correctly. + +All right. + +So it's a ruled surface, great. + +I mean, I can really create +my whole surface locally + +around a point by a whole +bunch of rule segments. + +They're not all going to be +parallel or anything, which + +is what we imagined +from the cylinder. + +They can turn around. + +But these segments do keep going +until they hit another crease. + +Maybe the blue line's a crease. + +And the boundary here could +be the boundary of the paper, + +could be a crease boundary. + +But that's what they look like. + +Now, it's also what we +call torsal, torsal ruled. + +Here we get to somewhat +more obscure terminology + +but some useful things. + +It's quite restricted. + +I want to have a common +tangent plane throughout a rule + +segment. + +So if I look at any one +of these rule segments, + +there's one plane, +which is going + +to be like this, that is tangent +to the surface at every point + +along that segment. + +So in general, you might +imagine that the tangent + +plane turns as we go along. + +But these segments are kind of-- +they're locally cylindrical. + +So you can really make a +tangent plane all the way along. + +Whereas here, that's +probably not true. + +Imagine the tangent plane +starts-- can you see my hand? + +It starts to bend +like this, and it's + +going to bend around like that. + +It twists along a single line. + +In our case where we +have zero curvature, + +it's actually going +to be torsal ruled, + +meaning the tangent plane +just goes straight along each + +of these lines. + +We're going to need this, +that's why I mention it. + +Another fun fact +along the same spirit + +is that the points +along a rule line + +are all the same in +terms of whether they + +are planar or parabolic. + +So I'll call them uniformly +planar slash parabolic. + +Remember, planar just +means it lies in a plane. + +Parabolic is the other case. + +So here everything's parabolic. + +But you can't like suddenly +switch in the middle + +and become flat. + +That's not allowed, +not possible. + +So those are some fun facts. + +We're not going to prove them. + +If you want to see the proofs, +they're a bit technical. + +You have to read our paper, and +then the differential geometry + +books we cite. + +But a bunch of these things, you +can understand the proofs just + +assuming a little bit of +differential geometry, + +and it's not too hard. + +It's in our paper, but it's +a little bit technical. + +So I want to look at the +things that are more related + +to paper folding, +how paper folds. + +This is obviously +related, but it's + +like the foundation on which +we build what I care about. + +What I care about +most-- all right, + +let me tell you a fun fact, +what we're going to prove. + +We want this nice proper folding +of the hyperbolic paraboloid, + +meaning every crease is bent +by a non-zero angle and not 180 + +degrees. + +In that situation, +first claim is + +every crease remains straight. + +Second claim is every +face remains rigid, + +can't bend anywhere-- +every interior face. + +These guys on the boundary, +they can do crazy things. + +And you see that +in the model, where + +the outside gets +kind of all wiggly. + +That's allowed. + +The outside faces, +the ones that share + +the boundary with the paper, +can wiggle, can curve. + +But everything else +has to remain flat + +if there are no +creases in there. + +And that's not at all obvious. + +So we're going to prove it. + +And I need some water. + +All right. + +First claim, I'll call it +polygonal implies flat. + +So what I mean is, suppose +I have some region of paper. + +It's in the middle somewhere. + +Let's say it's smooth. + +And I look at the +boundary of the region. + +Doesn't actually +have to be smooth. + +It could have semi-creases. + +But it has no creases inside. + +Suppose the boundary +in 3D is a polygon, + +so it's piecewise straight. + +I don't know how that +corresponds to anything, + +but say the boundary +is straight. + +Then the inside must be planar. + +So if I have a +polygonal boundary, + +then I have a flat +planar inside. + +This is assuming no creases. + +OK? + +So what that means is that +every point inside this region + +must be planar, not parabolic. + +That's what we want to prove. + +So let's do a proof +by contradiction, + +and suppose that we +have a parabolic point. + +So we have some point, +and locally it is curved, + +and we know there's a +rule line through it. + +I know by smoothness, +by continuity, + +that if this guy is parabolic, +it's bent, then, in fact, + +all the points nearby +should also be bent, + +because you can't go instantly +from bent to straight. + +You've got to do that slowly. + +So there's some +little region-- we + +call this a neighborhood-- +around the point that + +is all parabolic. + +So I'll call this +parabolic neighborhood. + +All right. + +All of those points +have unique rule lines. + +That's what we've been saying. + +So I take this +little neighborhood, + +and each one of them +defines some rule line. + +Those rule lines +go all the way out + +to the boundary +something like this. + +Now, this boundary +is the boundary. + +That means it's polygonal, +can't be curved like this. + +In fact, it looks +something like this. + +Maybe this is straight. + +Maybe this has two segments. + +We don't know how many segments. + +I just want to look at +one of these segments here + +and all the rule lines +coming out of it. + +So what I have is I have +the boundary of the paper. + +That's a poor imitation +of a straight line. + +Straight line. + +I have some rule +lines coming out. + +Now, I don't really know +what they look like. + +I want to understand +what they look like. + +This is in 3D. + +Imagine. + +OK, this is straight. + +First thing I want to look at +is the normal to the surface. + +So normal is like +perpendicular to the surface. + +It's easy to define normals in +the interior of the surface, + +but I can actually extend +that out to the boundary. + +So I want to look +at a normal here. + +Maybe let me put it here, +something like that. + +If I took normals really +close to the boundary, + +I just took the limit +out to the boundary, + +I'll get some normal vector. + +And by smoothness, that exists. + +Just wave my hands +there, but that's true. + +OK, what's true +about this normal? + +Well, it's perpendicular +to the surface. + +Now locally, the +surface here, it's + +defined by the plane of this +line segment and this line + +segment. + +So in fact, it's +perpendicular to the boundary, + +and it's perpendicular +here to the rule line. + +Buy that? + +If I take some other normal, +like this one-- sorry, + +like that, it's also +perpendicular to this, + +but it's perpendicular to +some other rule line now. + +So these guys are +perpendicular to a common line, + +but they may not be +the same direction. + +What we do know, though, +is that it's torsal. + +There is a single +tangent plane that's + +perpendicular to this +entire rule line, which + +means the normal is +the thing perpendicular + +to that tangent plane. + +So in fact, all of the +normals along this line + +are identical, which +is kind of neat. + +These guys are all parallel. + +Same thing here. + +I won't draw that. + +It's going to get too messy. + +So what? + +All right. + +Well, here's a crazy +thing to imagine. + +I will look at the +derivative of the normal. + +So I have this point p. + +Imagine you have a point p, and +it's moving along this curve + +continuously. + +Sorry-- not curve. + +This is a straight line. + +It's moving along this edge +of the boundary just once. + +It goes like this. + +And I'm going to define n of +p is the normal at that point. + +So it starts at something, +and then maybe it's changing. + +I get to this normal, +then I get to this normal, + +and then who knows +what it looks like. + +I want to understand, +can it change at all? + +So to understand its +change, I'm going + +to take the derivative, +n prime of p. + +So this is as p +moves along here, + +how does the normal change? + +I claim, in fact, it +can't change at all. + +Why? + +Well, the derivative of +the normal, first of all, + +must be perpendicular to-- I +haven't given anything a name + +here. + +This thing is the boundary edge. + +So here's my boundary edge. + +Every single normal here-- +I didn't draw the greatest + +picture-- of those have to +be perpendicular to this one + +common edge. + +Here's the fact where we use +that this is a straight line. + +If it curves, then this +is not a consistent thing. + +But because it's straight for +a while, all of these guys + +are perpendicular +to the same thing. + +All of the ends are +perpendicular to the boundary + +edge. + +This is just little +perpendicular notation. + +And if all of the n's are +perpendicular to the boundary + +edge, the change in n must +also be perpendicular. + +Otherwise, it would +change in such in a way + +it's longer perpendicular. + +OK? + +So that's just +sort of intuitive. + +Great. + +What else? + +I need it to be perpendicular +to something else. + +I claim that n +prime of p is also + +perpendicular to the rule line. + +Ah, yes. + +Because this normal-- all of +these points along a rule line + +have the same normal direction. + +These guys were all parallel. + +And so if I look +at the change in n, + +in order to make all +these guys be the same, + +I also cannot change n in such a +way that it has a non-trivial-- + +I'm not going to +say this too well. + +Do you believe it, more or less? + +Let me try to say it once. + +I'm looking at the +change in the normal. + +I don't want the normal +to change in such a way + +that it will change +along this axis. + +So for that to be true, +the change in the normal + +must be perpendicular +to this direction. + +This is kind of weird +because the normal is also + +perpendicular to this direction. + +I mean, the normal +satisfies the same things. + +It's perpendicular +to the boundary edge. + +It's also perpendicular +to the rule line. + +That means that n, the +normal, and its derivative, + +they have the same direction. + +That's weird. + +In fact, it means that +the derivative must be 0. + +Because the normal is +always unit length. + +So this would be saying that +the normal is getting bigger + +or shorter, but it +can't do either. + +So in fact, normal's +not changing at all. + +So in fact, all of +these guys are parallel + +along the whole segment. + +That means this +whole region is flat, + +and that's a contradiction. + +All right? + +So I waved my hands a little +bit, especially on this step, + +but believe me. + +All right. + +That's one fun fact, +but we want more. + +Because how do we know that the +boundary would be polygonal? + +For that we need that straight +creases remain straight. + +And something's not true +when you have curve creases. + +Curve creases obviously +don't remain curved. + +But curve creases don't +even remain planar. + +I mean, they can +do crazy things. + +But straight creases +stay straight. + +So what I mean is, I have +my flat piece of paper. + +I take a straight line +in the piece of paper, + +and I say that's +going to be a crease. + +It has no first derivative +along the crease. + +Then when I fold that, +I get a straight line + +and some crazy stuff +on the other side, + +but that crease +remains straight. + +So I was in the +middle of the paper, + +so it actually looks like this. + +Remains a straight segment, +obviously of the same length. + +But the point is it can't +curl, and it can't even kink. + +Now, just any good theorem +needs a counter-example. + +So if we take a piece of paper +and we make a straight crease, + +look, I can curl that crease. + +So this theorem is +not true unless I + +say that the crease is proper. + +So here I had to make the crease +all the way to 180 degrees, + +then I can curl it. + +Also, if I don't fold it +at all, then I can curl it. + +But if it's folded something +in the middle, I cannot curl. + +Paper will not be happy with me. + +I need extra creases +in order to curl. + +Well, yeah, it's +just not possible. + +So proper crease, which +means the fold angle + +is not equal to 0 or +plus or minus 180. + +So that's the theorem. + +Let's prove it. + +Maybe go a little faster. + +All right. + +So we have our crease, +and in three dimensions + +it might look curved. + +We take some point. + +We know that the paper is flat. + +So if you look at the left +side and the right side + +of the piece of paper, +locally, at least, it's flat. + +And I want to think +of there being + +some tangent plane +on the right side + +and some tangent plane +on the left side. + +Wow, that's not a good picture. + +Let me draw the planes first. + +So here's two planes, and +then here's my point p. + +And locally the surface actually +lies in these two planes + +and kinks here. + +The surface kinks. + +We want the crease +to be straight here, + +but maybe the crease is +bent something like that. + +All right. + +Here's what we do. + +Again, I want to think +of-- in this case, + +I'm going to look at +tangents, not normals. + +So I'm going to say, well, +every point on the curve + +here has some tangent. + +In fact, the tangent +at this point + +must lie right along +the intersection + +of these two planes. + +I'm going to give +these planes names. + +This is p. + +This is going to be +tangent plane Tp, + +and this is going to be +other tangent plane Sp, + +so on the left and +the right side. + +So the normal at p-- sorry, not +the normal, the tangent at p-- + +did I give it a name-- p prime. + +That's what you'd +normally call it. + +That's the derivative. + +Tangent of p lies +along the intersection + +of those two planes. + +We don't really need +that, but it's true. + +Give you some intuition. + +Now, what I'm +really going to use + +is the second derivative, +little more extreme here. + +Second derivative is +curvature on the curve. + +Now, we know that in +the unfolded surface, + +there's exactly 180 +degrees of material here. + +Here's some point p. + +We know there's 180 +degrees of material. + +I mean, locally, everything's +flat in terms of the surface. + +So here's where I'm going to +wave my hands a little bit. + +I claim that the +curvature vector + +must be perpendicular to +Tp and perpendicular to Sp. + +Because if I take this +curve, and I project it + +into one of these +planes, say Tp, + +it should be straight +at p in projection. + +It also must be straight +when I project into Sp. + +And that actually means +that it's straight + +in three dimensions also. + +So the straightness +and projection + +corresponds to straightness +when flattened basically. + +I'm waving my +hands a little bit. + +But if I need the +curvature vector + +to be perpendicular +to this plane-- + +so it's something like this. + +It's coming straight +out of this plane. + +But that uniquely +determines its direction. + +It also needs to be +perpendicular to Sp. + +These two vectors can't +be the same thing, + +and yet they have to be, unless +these planes are the same. + +So it could be there's a zero +fold angle, then it's fine. + +Or it could be it's +180-degree fold angle, + +then again the +planes are the same. + +Can go in one +direction or the other. + +But if I have a proper crease, +then there's no such vector. + +And so we're done. + +That proves straight +creases stay straight. + +Cool. + +Any questions about that? + +So I'm trying to hit a +middle ground of not too + +technical but also +not too shallow. + +And so you're left in the middle +state of sort of make sense. + +But I did wave my hands, +and it's not super rigorous. + +Because to be rigorous +it would take forever, + +and I need to teach you +differential geometry and so + +on. + +But now that we are +armed with these tools-- + +straight creases stay straight +and any polygonal boundary + +stays flat, planar-- +that tells us + +that if we have +some crease pattern, + +any crease pattern made +out of straight edges, + +so no curve creases allowed, +if I make straight creases, + +every single interior +face must stay rigid + +in any proper folding. + +That's pretty cool. + +Because we've talked about +rigid origami and said not much + +is known about rigid origami. + +It's tough. + +But in fact, you really need +to understand rigid origami + +if you want to fold something +like a hyperbolic paraboloid. + +Now, when you do flat +folding stuff-- well, + +I guess those are +kind of rigid also. + +But any kind of +3-dimensional folding, + +where you fold every crease +somewhat but not all the way, + +all the faces need to be +rigid in the final form. + +Now, you could get there +by all sorts of means. + +But we want the +hyperbolic paraboloid + +to exist with creases +only along these lines. + +And now we know each of these +trapezoids must remain planar. + +Also, each of these +triangles must remain planar. + +Now, now we get to +the contradictions. + +If you have this piece +of paper and those + +are your only creases, +you can fold along + +one of the creases or +the other, but not both. + +Unless you fold one crease +all the way to 180-- here, + +we can do it. + +I have one diagonal, and +I have another diagonal. + +So everything's +meeting at 180 degrees. + +I can fold one and +then the other. + +I can fold one, or I +can fold the other. + +But I cannot fold a +little bit of one, + +and then try to +fold the other too. + +It's not possible. + +Therefore, this crease +pattern doesn't fold at all. + +OK? + +Kind of trivial. + +The center is messed up. + +But keep in mind, +again, these faces + +we don't know anything about +because this edge could + +do crazy things. + +But the interior faces +of the crease pattern + +must all stay flat +and stay exactly + +as they were in the original. + +So it's really like we +have rigid panels here + +and hinges between them. + +The outside, though, we +have no idea what happens. + +OK. + +So the inside sucks. + +So I think, at this point, +we get to this picture. + +Here's the regular +crease pattern. + +So let's just make life +easier and say, well, we'll + +cut out a hole in the center. + +That surely-- that +must be better. + +But it's no better. + +That thing still +can't fold because you + +take any of the rings +that goes around, + +like a square annulus-- +here's a ring. + +The creases in that ring +are just those four. + +So I'm just looking at +these four trapezoids. + +Again, each one +must stay planar. + +And these are the +only hinges I have. + +It's actually really +just like this. + +I've cut a hole in the +center, but it won't really + +matter because the extension +of these lines meet at a point. + +So effectively, you are +folding this whole triangle. + +You can fold just the trapezoid. + +But however you +fold the trapezoid, + +you could just extend it +and make the triangle, + +and these triangles +will remain meeting. + +So it's actually the same +thing as the center diagram. + +Because this doesn't fold, +this also won't fold. + +It doesn't matter how +many layers you cut out. + +As long as there's one +interior layer that + +doesn't touch the boundary, +it's going to be screwed. + +OK. + +That is why +hyperbolic paraboloid + +doesn't fold without diagonals. + +Once you know the creases are +straight, it's kind of obvious. + +But let me give you a +more general picture. + +This makes things a little +more interesting and tells you, + +really, all those +straight crease + +pleatings that I've shown you, +like hexagons and octagons, + +none of them are possible, +which was a surprise. + +So here I'm taking concentric +shapes in such a way + +that the diagonals +meet at a point. + +I still need that fact. + +If they don't, in fact, +it's possible to fold. + +And we have a little +example of that. + +OK, now I actually +need two interior rings + +to get a contradiction. + +So I take some ring like +this, and I take another ring, + +and I suppose none of +them touch the boundary. + +As long as I know +there's at least four, + +there's going to be two +consecutive rings like this. + +And the hinges are the diagonals +and the inner ring boundaries. + +OK. + +If I just look locally at +this, I claim it must be + +mountain-mountain-mountain-valley + or the reverse. + +This is something we would +normally prove by saying, + +OK, this is locally smallest, +therefore these guys + +are different. + +And this is also +locally smallest, + +therefore these guys are +different, and so on. + +Except that only works +for flat folding. + +Here I need to prove +it for 3D folding. + +I'm not going to bother, +but you can do it. + +So in fact, let's say this is + mountain-mountain-mountain-valley, + +then this must be +mountain, this must, + +all the way around +must be mountain. + +OK? + +That's not such a big deal. + +This must all be valley, +and this must all + +be mountain, or +the entire reverse. + +But the point is, +all of these guys + +out here must be mountains. + +So really if I extend +all of these guys + +and they meet at a single +point, if I was lucky, + +that's what I'm supposed to +assume, really what I'm doing + +is folding a whole +bunch of triangles + +where all of the +creases are mountains. + +That's not possible. + +So if you didn't +believe this thing, + +it follows from +the same argument. + +They can't all be mountains, +and therefore some crease + +is not getting folded. + +So it's the same +argument again, you just + +have to be a little +more precise. + +And that is not folding +hyperbolic paraboloids + +and things like that. + +But if you had +diagonals, it all works. + +Now, in the last few minutes, I +want to show you some more fun + +things, in particular, pillows. + +Everybody likes pillows. + +But how are they made? + +Well, it's like two +squares of material joined + +along the edges, and then +you stuff stuff inside. + +That kind of weird, because +doubly-covered square I + +think of as flat, and yet +you can put material inside. + +What is the maximum volume +you can stuff into a pillow? + +This is called the +tea bag problem + +because it also works +for square tea bags. + +Open. + +We don't know. + +Lots of practical +explorations, but open. + +Another version of +this is Mylar balloons. + +Mylar balloons can't +stretch, more or less. + +And here is two +circles glued together. + +Again flat, but you +can pump air into them. + +You get this weird behavior, +these ripples on the outside. + +That's real stuff. + +But we don't know what the +maximum volume shape is, + +but it should look something +like what we see in reality. + +Let me tell you +some fun theorems. + +If you take any convex +polyhedron, like say a cube, + +you can inflate it and +increase its volume. + +Also, I guess, works for +a doubly-covered square. + +This is the tea +bag open problem, + +where these edges are joined. + +How do you do it? + +I'm going to quote +from the paper-- + +"by simultaneously +delivering karate chops + +to the edges of the polyhedron." + +That's in the abstract. + +So you take an edge like +this-- here's an edge + +and the two incident +faces-- and I go like this. + +Wow, that was exciting. + +So what happens when you go like +this-- the whole board shakes, + +I'll probably break +it eventually-- + +you get something like that. + +So there's a valley +here, and then + +mountains there to +replace this mountain. + +And you can prove, if you do +that with suitable parameters + +here, at every edge +simultaneously you + +increase the volume, +which is pretty neat. + +Now, how far can you go? + +What happens when you keep +increasing the volume? + +Is the limit polyhedral, or +is it smooth with ripples? + +Conjecture is it's +smooth with ripples. + +In fact, you can prove +it's not polyhedral. + +Because not only for +convex polyhedral, + +you take any polyhedron, it +is possible to inflate it + +by at least some volume. + +So the limit has to be curvy. + +It's not going to be polyhedral. + +Now, exactly what +it looks like we + +don't know, but lots of +experiments to that effect. + +A big open question in this +field is, does this exist? + +We think so. + +It seems curve creases-- +none of this stuff + +works for curve creases. + +Curve creases seem +a lot more powerful. + +We haven't been able +to prove this exists + +because it seems very flexible. + +There's a lot of +degrees of freedom. + +It's hard to figure out +where the rule lines are. + +But we think so. + +So what about curved creases? + +I haven't talked +about curve creases + +really at all +until this lecture. + +I would say the most seminal +work in curve creases + +was done by David Huffman. + +Huffman is super famous. + +He was a grad student +and a professor + +here at MIT for many years. + +In particular, when +he was a grad student + +he came up with +these Huffman codes, + +which are used in +every MP3 player. + +Every device you use that +uses any kind of compression + +has Huffman codes in it. + +Super cool from the '60s. + +But he also did a lot +of curve crease origami, + +curve crease folding. + +And over the last +couple of years, + +we've been working with +his family, so his wife + +and two daughters, +Linda and Elise. + +And this is me, +that's Marty, and this + +is Duks Koschitz, +who many of you + +know is a PhD student +in architecture. + +And we were visiting there +back in May in particular. + +And what we're doing is +taking his work, which + +is all in their houses and +almost no one has seen, + +and figuring out +how he made them. + +What is the underlying +mathematics? + +What are the crease patterns +that make it possible? + +And then recreating them to +check that we did it right. + +So what I have here are just a +few examples of our recreations + +so far. + +So these are not +the original models, + +but they look just like +the original models, + +made out of the same material +and more or less the same way. + +Although we do it a little +more high-tech than he + +did because we want to draw +perfect computational diagrams + +in CAD, and then +reproduce them exactly + +on the paper with no +reproduction errors. + +So we use fancy +robotically-controlled devices + +to do that. + +So there's some +fun curve creases. + +You get some really +nice shadow patterns. + +All of those are circular +arcs, all the creases. + +Here are some more. + +These are actually parabolic +arcs and some straight creases + +in between. + +Get some cool 3D relief effect. + +These are like +tessellations like Tom Hull + +was talking about but +with curve creases. + +This is pretty awesome. + +Here the creases are quite +complicated to figure out. + +But what's happening is +you're taking a cone like this + +and pleating it back and forth +but with different angles, + +and so the whole thing twists. + +We have a physical one +of these in our offices. + +But this is the 3D model +of what's going on. + +Here's some particularly +awesome crease patterns. + +David Huffman made a +whole variety of these. + +These are just a +couple of examples. + +Got some crazy circular arcs. + +You've got some-- I +guess these are also + +circular arcs and some +straight segments. + +And then you wrap this +around to make a cylinder, + +and you get this. + +That one-- there's a bunch of +photos of the original David + +Huffman model on the web +if you Google around. + +Not looking exactly like that, +but there's a whole variety. + +Here's another one, +a bit of a maybe + +surprise what it looks like. + +Most of the center just gets +eaten away from these creases. + +Here the creases are +elliptical, and you + +get something like that. + +So there's some hidden +structure beneath. + +I think just one more example. + +This is probably the +most coolest puzzle. + +You say, well, you float along +these parabolas, just one + +valley and one mountain. + +But you fold them a +lot, you get that. + +And Huffman composed +these to make + +various kinds of tubes +and really cool things. + +So this is work in progress. + +Just wanted to +give you a sample. + +There's a paper about this +which shows more examples. + +But our goal is to recreate +all or most of them + +and document how he +did it and figure out + +how he designed these models. + +He had mathematical +tools to do this, + +and we're still figuring +out what they are. + +The hope is it will lead to +more great mathematics and art + +about curve creases. + +And that is it. + +This is my last lecture. + +Next class we have-- or +next three classes we + +have a whole bunch of +student presentations. + +Please come. + +There will be lots of +awesome things there. + +Send me your slides +ahead of time, + +and you'll have 10 minutes +to do it, to give a talk. + +And then the last lecture, +Wednesday two weeks from now, + +is Tomohiro Tachi. + +And thanks very much. + +It's been a lot of +fun doing this class + +and having you all as students. + +[APPLAUSE] \ No newline at end of file diff --git a/_RIqn1c_BY8.txt b/_RIqn1c_BY8.txt new file mode 100644 index 0000000000000000000000000000000000000000..61a0aafb95534b1555ce30d1baa5c01ebf9e5664 --- /dev/null +++ b/_RIqn1c_BY8.txt @@ -0,0 +1,5971 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +today's uh topic is going to be biogas + + align:start position:0% +today's uh topic is going to be biogas + + + align:start position:0% +today's uh topic is going to be biogas +digestors + + align:start position:0% +digestors + + + align:start position:0% +digestors +um so our objectives for the class or + + align:start position:0% +um so our objectives for the class or + + + align:start position:0% +um so our objectives for the class or +this session are going to be to learn + + align:start position:0% +this session are going to be to learn + + + align:start position:0% +this session are going to be to learn +how biogas digestors work when and where + + align:start position:0% +how biogas digestors work when and where + + + align:start position:0% +how biogas digestors work when and where +they're appropriate um some important + + align:start position:0% +they're appropriate um some important + + + align:start position:0% +they're appropriate um some important +design considerations when you're + + align:start position:0% +design considerations when you're + + + align:start position:0% +design considerations when you're +building biogas digestors and then we're + + align:start position:0% +building biogas digestors and then we're + + + align:start position:0% +building biogas digestors and then we're +going to build a small scale one in lab + + align:start position:0% +going to build a small scale one in lab + + + align:start position:0% +going to build a small scale one in lab +um so you get to play with some of the + + align:start position:0% +um so you get to play with some of the + + + align:start position:0% +um so you get to play with some of the +stuff um oops I slip slides so these are + + align:start position:0% +stuff um oops I slip slides so these are + + + align:start position:0% +stuff um oops I slip slides so these are +some pictures of biogas digestors + + align:start position:0% +some pictures of biogas digestors + + + align:start position:0% +some pictures of biogas digestors +they've been around for a couple hundred + + align:start position:0% +they've been around for a couple hundred + + + align:start position:0% +they've been around for a couple hundred +years uh or maybe 150 years + + align:start position:0% +years uh or maybe 150 years + + + align:start position:0% +years uh or maybe 150 years +um there are lots of different forms for + + align:start position:0% +um there are lots of different forms for + + + align:start position:0% +um there are lots of different forms for +them as you can see they're they scale + + align:start position:0% +them as you can see they're they scale + + + align:start position:0% +them as you can see they're they scale +up they can be anywhere from large + + align:start position:0% +up they can be anywhere from large + + + align:start position:0% +up they can be anywhere from large +industrial ones like that one or they + + align:start position:0% +industrial ones like that one or they + + + align:start position:0% +industrial ones like that one or they +can be smaller scale ones for just a + + align:start position:0% +can be smaller scale ones for just a + + + align:start position:0% +can be smaller scale ones for just a +single farmer or single + + align:start position:0% +single farmer or single + + + align:start position:0% +single farmer or single +family um and what what is a biogas + + align:start position:0% +family um and what what is a biogas + + + align:start position:0% +family um and what what is a biogas +digestor is a question that you may be + + align:start position:0% +digestor is a question that you may be + + + align:start position:0% +digestor is a question that you may be +asking so a biogas digestor is something + + align:start position:0% +asking so a biogas digestor is something + + + align:start position:0% +asking so a biogas digestor is something +that + + align:start position:0% +that + + + align:start position:0% +that +takes organic matter normally Animal + + align:start position:0% +takes organic matter normally Animal + + + align:start position:0% +takes organic matter normally Animal +Human uh vegetable waste and turns it + + align:start position:0% +Human uh vegetable waste and turns it + + + align:start position:0% +Human uh vegetable waste and turns it +into gas for cooking and also turns it + + align:start position:0% +into gas for cooking and also turns it + + + align:start position:0% +into gas for cooking and also turns it +into fertilizer for crops um so it's + + align:start position:0% +into fertilizer for crops um so it's + + + align:start position:0% +into fertilizer for crops um so it's +basically taking organic matter and + + align:start position:0% +basically taking organic matter and + + + align:start position:0% +basically taking organic matter and +putting it through a process and you get + + align:start position:0% +putting it through a process and you get + + + align:start position:0% +putting it through a process and you get +gas and fertilizer from that um the + + align:start position:0% +gas and fertilizer from that um the + + + align:start position:0% +gas and fertilizer from that um the +process that breaks down the organic + + align:start position:0% +process that breaks down the organic + + + align:start position:0% +process that breaks down the organic +matter is anerobic digestion so you have + + align:start position:0% +matter is anerobic digestion so you have + + + align:start position:0% +matter is anerobic digestion so you have +bacteria which are found in the organic + + align:start position:0% +bacteria which are found in the organic + + + align:start position:0% +bacteria which are found in the organic +waste um and when you put this when you + + align:start position:0% +waste um and when you put this when you + + + align:start position:0% +waste um and when you put this when you +put them under anerobic conditions which + + align:start position:0% +put them under anerobic conditions which + + + align:start position:0% +put them under anerobic conditions which +means that they're not exposed to oxygen + + align:start position:0% +means that they're not exposed to oxygen + + + align:start position:0% +means that they're not exposed to oxygen +they break down these they break down + + align:start position:0% +they break down these they break down + + + align:start position:0% +they break down these they break down +all the organic waste and form methane + + align:start position:0% +all the organic waste and form methane + + + align:start position:0% +all the organic waste and form methane +gas um and carbon + + align:start position:0% +gas um and carbon + + + align:start position:0% +gas um and carbon +dioxide and and so you basically have a + + align:start position:0% +dioxide and and so you basically have a + + + align:start position:0% +dioxide and and so you basically have a +giant chamber I guess and in this + + align:start position:0% +giant chamber I guess and in this + + + align:start position:0% +giant chamber I guess and in this +chamber you have your + + align:start position:0% +chamber you have your + + + align:start position:0% +chamber you have your +your waist here with your bacteria in it + + align:start position:0% +your waist here with your bacteria in it + + + align:start position:0% +your waist here with your bacteria in it +and you let it sit for a while uh it + + align:start position:0% +and you let it sit for a while uh it + + + align:start position:0% +and you let it sit for a while uh it +takes about two weeks for them to start + + align:start position:0% +takes about two weeks for them to start + + + align:start position:0% +takes about two weeks for them to start +working once you get them going and they + + align:start position:0% +working once you get them going and they + + + align:start position:0% +working once you get them going and they +produce they break down the materi they + + align:start position:0% +produce they break down the materi they + + + align:start position:0% +produce they break down the materi they +break down the organic matter in here + + align:start position:0% +break down the organic matter in here + + + align:start position:0% +break down the organic matter in here +and produce gas and you normally have an + + align:start position:0% +and produce gas and you normally have an + + + align:start position:0% +and produce gas and you normally have an +inlet and an outlet and what happens is + + align:start position:0% +inlet and an outlet and what happens is + + + align:start position:0% +inlet and an outlet and what happens is +you put in more organic matter through + + align:start position:0% +you put in more organic matter through + + + align:start position:0% +you put in more organic matter through +the inlet and it pushes out some of this + + align:start position:0% +the inlet and it pushes out some of this + + + align:start position:0% +the inlet and it pushes out some of this +slurry or whatever's left over and so + + align:start position:0% +slurry or whatever's left over and so + + + align:start position:0% +slurry or whatever's left over and so +you get fertilizer from this end and the + + align:start position:0% +you get fertilizer from this end and the + + + align:start position:0% +you get fertilizer from this end and the +enti enre time you're producing gas + + align:start position:0% +enti enre time you're producing gas + + + align:start position:0% +enti enre time you're producing gas +which you can extract from + + align:start position:0% +which you can extract from + + + align:start position:0% +which you can extract from +there + + align:start position:0% + + + + align:start position:0% + +um so about biog + + align:start position:0% +um so about biog + + + align:start position:0% +um so about biog +gas the composition of biogas is mostly + + align:start position:0% +gas the composition of biogas is mostly + + + align:start position:0% +gas the composition of biogas is mostly +methane and carbon dioxide so you have + + align:start position:0% +methane and carbon dioxide so you have + + + align:start position:0% +methane and carbon dioxide so you have +about 60% methane about 40% carbon + + align:start position:0% +about 60% methane about 40% carbon + + + align:start position:0% +about 60% methane about 40% carbon +dioxide and then their Trace Amounts of + + align:start position:0% +dioxide and then their Trace Amounts of + + + align:start position:0% +dioxide and then their Trace Amounts of +nitrogen hydrogen hydrogen sulfide and + + align:start position:0% +nitrogen hydrogen hydrogen sulfide and + + + align:start position:0% +nitrogen hydrogen hydrogen sulfide and +oxygen + + align:start position:0% +oxygen + + + align:start position:0% +oxygen +and yeah and the amount of energy you + + align:start position:0% +and yeah and the amount of energy you + + + align:start position:0% +and yeah and the amount of energy you +can extract + + align:start position:0% +can extract + + + align:start position:0% +can extract +from biog gas is 20 megga per cubic + + align:start position:0% + + + + align:start position:0% + +meter um which is a fair bit + + align:start position:0% + + + + align:start position:0% + +yes uh I'm not exactly sure right + + align:start position:0% + + + + align:start position:0% + +now I yeah I'll got back to you on that + + align:start position:0% +now I yeah I'll got back to you on that + + + align:start position:0% +now I yeah I'll got back to you on that +I had a chart with how it compares to + + align:start position:0% +I had a chart with how it compares to + + + align:start position:0% +I had a chart with how it compares to +what like what how we can light things + + align:start position:0% +what like what how we can light things + + + align:start position:0% +what like what how we can light things +but I didn't put it on here because + + align:start position:0% +but I didn't put it on here because + + + align:start position:0% +but I didn't put it on here because +yeah um and so so the parts of the + + align:start position:0% +yeah um and so so the parts of the + + + align:start position:0% +yeah um and so so the parts of the +biogas digestor + + align:start position:0% +biogas digestor + + + align:start position:0% +biogas digestor +are kind of like what I drew here but + + align:start position:0% +are kind of like what I drew here but + + + align:start position:0% +are kind of like what I drew here but +better in this picture you have a you + + align:start position:0% +better in this picture you have a you + + + align:start position:0% +better in this picture you have a you +have a trench where you put the biogas + + align:start position:0% +have a trench where you put the biogas + + + align:start position:0% +have a trench where you put the biogas +digestor you have the biogas digestor + + align:start position:0% +digestor you have the biogas digestor + + + align:start position:0% +digestor you have the biogas digestor +bag which is what contains all of the + + align:start position:0% +bag which is what contains all of the + + + align:start position:0% +bag which is what contains all of the +manure and the slurry and the gas then + + align:start position:0% +manure and the slurry and the gas then + + + align:start position:0% +manure and the slurry and the gas then +you have your Inlet and outet let and + + align:start position:0% +you have your Inlet and outet let and + + + align:start position:0% +you have your Inlet and outet let and +you have a security + + align:start position:0% +you have a security + + + align:start position:0% +you have a security +valve um and you have a gas Reservoir as + + align:start position:0% +valve um and you have a gas Reservoir as + + + align:start position:0% +valve um and you have a gas Reservoir as +well um so we're going to talk a little + + align:start position:0% +well um so we're going to talk a little + + + align:start position:0% +well um so we're going to talk a little +bit now about why you would have a + + align:start position:0% +bit now about why you would have a + + + align:start position:0% +bit now about why you would have a +biogas digestor what are the advantages + + align:start position:0% +biogas digestor what are the advantages + + + align:start position:0% +biogas digestor what are the advantages +and what are disadvantages so now that + + align:start position:0% +and what are disadvantages so now that + + + align:start position:0% +and what are disadvantages so now that +you learned a little bit about it um can + + align:start position:0% +you learned a little bit about it um can + + + align:start position:0% +you learned a little bit about it um can +we We can brainstorm some ideas about + + align:start position:0% +we We can brainstorm some ideas about + + + align:start position:0% +we We can brainstorm some ideas about +why you would use it or where you would + + align:start position:0% +why you would use it or where you would + + + align:start position:0% +why you would use it or where you would +use + + align:start position:0% +use + + + align:start position:0% +use +it yeah + + align:start position:0% + + + + align:start position:0% + +do you + + align:start position:0% +do you + + + align:start position:0% +do you +add + + align:start position:0% +add + + + align:start position:0% +add +it uh you you add water to it uh to make + + align:start position:0% +it uh you you add water to it uh to make + + + align:start position:0% +it uh you you add water to it uh to make +a slurry um so you mix manure and water + + align:start position:0% +a slurry um so you mix manure and water + + + align:start position:0% +a slurry um so you mix manure and water +and you get the slurry and then you put + + align:start position:0% +and you get the slurry and then you put + + + align:start position:0% +and you get the slurry and then you put +it into the system you guys will be + + align:start position:0% +it into the system you guys will be + + + align:start position:0% +it into the system you guys will be +doing that later today too so uh I went + + align:start position:0% +doing that later today too so uh I went + + + align:start position:0% +doing that later today too so uh I went +to a farm and got some fresh cow manure + + align:start position:0% +to a farm and got some fresh cow manure + + + align:start position:0% +to a farm and got some fresh cow manure +for you to work with + + align:start position:0% +for you to work with + + + align:start position:0% +for you to work with +so + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yeah uh + + align:start position:0% + + + + align:start position:0% + +if you want a ballpark size I guess + + align:start position:0% +if you want a ballpark size I guess + + + align:start position:0% +if you want a ballpark size I guess +would be maybe + + align:start position:0% +would be maybe + + + align:start position:0% +would be maybe +like 10 or 15 feet does that seem + + align:start position:0% +like 10 or 15 feet does that seem + + + align:start position:0% +like 10 or 15 feet does that seem +right 15 feet long maybe like this size + + align:start position:0% +right 15 feet long maybe like this size + + + align:start position:0% +right 15 feet long maybe like this size +diameter like the trench would be kind + + align:start position:0% +diameter like the trench would be kind + + + align:start position:0% +diameter like the trench would be kind +of like this Corridor between the two + + align:start position:0% +of like this Corridor between the two + + + align:start position:0% +of like this Corridor between the two +tables that's about the size that you're + + align:start position:0% +tables that's about the size that you're + + + align:start position:0% +tables that's about the size that you're +looking + + align:start position:0% +looking + + + align:start position:0% +looking +at for yeah for like a family a + + align:start position:0% +at for yeah for like a family a + + + align:start position:0% +at for yeah for like a family a +household one but they can they can + + align:start position:0% +household one but they can they can + + + align:start position:0% +household one but they can they can +range from like small to large as well + + align:start position:0% +range from like small to large as well + + + align:start position:0% +range from like small to large as well +um so if you look at this there's + + align:start position:0% +um so if you look at this there's + + + align:start position:0% +um so if you look at this there's +there's actually a lot of design that + + align:start position:0% +there's actually a lot of design that + + + align:start position:0% +there's actually a lot of design that +went into the specific biogas digestor + + align:start position:0% +went into the specific biogas digestor + + + align:start position:0% +went into the specific biogas digestor +and so we can look at the individual + + align:start position:0% +and so we can look at the individual + + + align:start position:0% +and so we can look at the individual +components of it and figure out why uh + + align:start position:0% +components of it and figure out why uh + + + align:start position:0% +components of it and figure out why uh +and try to look through the design + + align:start position:0% +and try to look through the design + + + align:start position:0% +and try to look through the design +process and thought process that they + + align:start position:0% +process and thought process that they + + + align:start position:0% +process and thought process that they +used to come up with this design because + + align:start position:0% +used to come up with this design because + + + align:start position:0% +used to come up with this design because +this is actually a pretty clever design + + align:start position:0% +this is actually a pretty clever design + + + align:start position:0% +this is actually a pretty clever design +for a biogas + + align:start position:0% +for a biogas + + + align:start position:0% +for a biogas +digester + + align:start position:0% +digester + + + align:start position:0% +digester +um so does anyone notice anything about + + align:start position:0% +um so does anyone notice anything about + + + align:start position:0% +um so does anyone notice anything about +this diagram that + + align:start position:0% +this diagram that + + + align:start position:0% +this diagram that +seems like a cool like a a good idea for + + align:start position:0% +seems like a cool like a a good idea for + + + align:start position:0% +seems like a cool like a a good idea for +them to have + + align:start position:0% + + + + align:start position:0% + +done yeah the security valve is + + align:start position:0% +done yeah the security valve is + + + align:start position:0% +done yeah the security valve is +important um you don't want your thing + + align:start position:0% +important um you don't want your thing + + + align:start position:0% +important um you don't want your thing +blowing + + align:start position:0% +blowing + + + align:start position:0% +blowing +up + + align:start position:0% + + + + align:start position:0% + +um yeah Reservoir is also good because + + align:start position:0% +um yeah Reservoir is also good because + + + align:start position:0% +um yeah Reservoir is also good because +with this because storing gas is also + + align:start position:0% +with this because storing gas is also + + + align:start position:0% +with this because storing gas is also +somewhat of a problem + + align:start position:0% +somewhat of a problem + + + align:start position:0% +somewhat of a problem +and if you don't have access like if you + + align:start position:0% +and if you don't have access like if you + + + align:start position:0% +and if you don't have access like if you +don't have a place to store the gas and + + align:start position:0% +don't have a place to store the gas and + + + align:start position:0% +don't have a place to store the gas and +access it pretty easily then you're not + + align:start position:0% +access it pretty easily then you're not + + + align:start position:0% +access it pretty easily then you're not +going to have + + align:start position:0% +going to have + + + align:start position:0% +going to have +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um can you guys think about the + + align:start position:0% +um can you guys think about the + + + align:start position:0% +um can you guys think about the +fence I don't know if you can see it in + + align:start position:0% +fence I don't know if you can see it in + + + align:start position:0% +fence I don't know if you can see it in +there but but there's a fence around + + align:start position:0% +there but but there's a fence around + + + align:start position:0% +there but but there's a fence around +this specific design um and the problem + + align:start position:0% +this specific design um and the problem + + + align:start position:0% +this specific design um and the problem +like one of the things with this design + + align:start position:0% +like one of the things with this design + + + align:start position:0% +like one of the things with this design +is that the bag the biogas digestor bag + + align:start position:0% +is that the bag the biogas digestor bag + + + align:start position:0% +is that the bag the biogas digestor bag +for this is it's a big plastic bag um + + align:start position:0% +for this is it's a big plastic bag um + + + align:start position:0% +for this is it's a big plastic bag um +that's covered in tarp that's sewn + + align:start position:0% +that's covered in tarp that's sewn + + + align:start position:0% +that's covered in tarp that's sewn +together and so you have this sort of + + align:start position:0% +together and so you have this sort of + + + align:start position:0% +together and so you have this sort of +like Giant + + align:start position:0% +like Giant + + + align:start position:0% +like Giant +uh plastic bag that's sitting outside + + align:start position:0% +uh plastic bag that's sitting outside + + + align:start position:0% +uh plastic bag that's sitting outside +and one of the cool things about it is + + align:start position:0% +and one of the cool things about it is + + + align:start position:0% +and one of the cool things about it is +it's really cheap because you don't have + + align:start position:0% +it's really cheap because you don't have + + + align:start position:0% +it's really cheap because you don't have +to build an external construction for it + + align:start position:0% +to build an external construction for it + + + align:start position:0% +to build an external construction for it +but it's also like if you have cattle + + align:start position:0% +but it's also like if you have cattle + + + align:start position:0% +but it's also like if you have cattle +which I which a lot of times you will + + align:start position:0% +which I which a lot of times you will + + + align:start position:0% +which I which a lot of times you will +have for something like this and your + + align:start position:0% +have for something like this and your + + + align:start position:0% +have for something like this and your +cow steps on this bag it's pretty much + + align:start position:0% +cow steps on this bag it's pretty much + + + align:start position:0% +cow steps on this bag it's pretty much +ruined you're ruining your like + + align:start position:0% +ruined you're ruining your like + + + align:start position:0% +ruined you're ruining your like +$300 uh biogas digestor + + align:start position:0% +$300 uh biogas digestor + + + align:start position:0% +$300 uh biogas digestor +so um so that's why they put a fence + + align:start position:0% +so um so that's why they put a fence + + + align:start position:0% +so um so that's why they put a fence +there + + align:start position:0% +there + + + align:start position:0% +there +there um can you think of other + + align:start position:0% +there um can you think of other + + + align:start position:0% +there um can you think of other +advantages to having a bag other than + + align:start position:0% +advantages to having a bag other than + + + align:start position:0% +advantages to having a bag other than +just the fact that it's + + align:start position:0% + + + + align:start position:0% + +cheaper + + align:start position:0% + + + + align:start position:0% + +yes it's not really transportable + + align:start position:0% + + + + align:start position:0% + +but uh you can't you can't really move + + align:start position:0% +but uh you can't you can't really move + + + align:start position:0% +but uh you can't you can't really move +well maybe I mean it might it's easier + + align:start position:0% +well maybe I mean it might it's easier + + + align:start position:0% +well maybe I mean it might it's easier +to transport to the site you're + + align:start position:0% +to transport to the site you're + + + align:start position:0% +to transport to the site you're +installing to so you can make one of + + align:start position:0% +installing to so you can make one of + + + align:start position:0% +installing to so you can make one of +these and I guess transport them to the + + align:start position:0% +these and I guess transport them to the + + + align:start position:0% +these and I guess transport them to the +location I haven't actually seen that + + align:start position:0% +location I haven't actually seen that + + + align:start position:0% +location I haven't actually seen that +done I've seen most of them being + + align:start position:0% +done I've seen most of them being + + + align:start position:0% +done I've seen most of them being +installed on site uh from the raw + + align:start position:0% +installed on site uh from the raw + + + align:start position:0% +installed on site uh from the raw +materials but it's definitely easier to + + align:start position:0% +materials but it's definitely easier to + + + align:start position:0% +materials but it's definitely easier to +get a long large plastic bag than it is + + align:start position:0% +get a long large plastic bag than it is + + + align:start position:0% +get a long large plastic bag than it is +to get all like the bricks you would + + align:start position:0% +to get all like the bricks you would + + + align:start position:0% +to get all like the bricks you would +need to build a giant biogas digestor + + align:start position:0% +need to build a giant biogas digestor + + + align:start position:0% +need to build a giant biogas digestor +and seal + + align:start position:0% +and seal + + + align:start position:0% +and seal +it + + align:start position:0% +it + + + align:start position:0% +it +yeah you want it you want you want to be + + align:start position:0% +yeah you want it you want you want to be + + + align:start position:0% +yeah you want it you want you want to be +able to control the seal on it but have + + align:start position:0% +able to control the seal on it but have + + + align:start position:0% +able to control the seal on it but have +a bag the volume + + align:start position:0% + + + + align:start position:0% + +can doesn't + + align:start position:0% +can doesn't + + + align:start position:0% +can doesn't +yeah so that's actually a pretty cool + + align:start position:0% +yeah so that's actually a pretty cool + + + align:start position:0% +yeah so that's actually a pretty cool +thing about this design is uh your your + + align:start position:0% +thing about this design is uh your your + + + align:start position:0% +thing about this design is uh your your +bag can get bigger and smaller depending + + align:start position:0% +bag can get bigger and smaller depending + + + align:start position:0% +bag can get bigger and smaller depending +on how much gas is being produced um + + align:start position:0% +on how much gas is being produced um + + + align:start position:0% +on how much gas is being produced um +because say you have if you have a rigid + + align:start position:0% +because say you have if you have a rigid + + + align:start position:0% +because say you have if you have a rigid +structure kind of + + align:start position:0% +structure kind of + + + align:start position:0% +structure kind of +like okay so you have I'm just going to + + align:start position:0% +like okay so you have I'm just going to + + + align:start position:0% +like okay so you have I'm just going to +redraw what I just had so you have a box + + align:start position:0% +redraw what I just had so you have a box + + + align:start position:0% +redraw what I just had so you have a box +right and it's say it's made out of + + align:start position:0% +right and it's say it's made out of + + + align:start position:0% +right and it's say it's made out of +bricks you somehow manage to seal it + + align:start position:0% +bricks you somehow manage to seal it + + + align:start position:0% +bricks you somehow manage to seal it +from the inside so there's no air loss + + align:start position:0% +from the inside so there's no air loss + + + align:start position:0% +from the inside so there's no air loss +or gas loss um which isn't trivial for a + + align:start position:0% +or gas loss um which isn't trivial for a + + + align:start position:0% +or gas loss um which isn't trivial for a +while + + align:start position:0% +while + + + align:start position:0% +while +um but you man to do that you put biogas + + align:start position:0% +um but you man to do that you put biogas + + + align:start position:0% +um but you man to do that you put biogas +in here and it's filling + + align:start position:0% +in here and it's filling + + + align:start position:0% +in here and it's filling +up um and it's producing methane and or + + align:start position:0% +up um and it's producing methane and or + + + align:start position:0% +up um and it's producing methane and or +I guess it's producing biog + + align:start position:0% + + + + align:start position:0% + +gas uh what happens as you produce more + + align:start position:0% +gas uh what happens as you produce more + + + align:start position:0% +gas uh what happens as you produce more +and more gas in this sort of + + align:start position:0% + + + + align:start position:0% + +design um you start you start getting a + + align:start position:0% +design um you start you start getting a + + + align:start position:0% +design um you start you start getting a +pressure buildup of gas in here and if + + align:start position:0% +pressure buildup of gas in here and if + + + align:start position:0% +pressure buildup of gas in here and if +you're outputting it into say a stove + + align:start position:0% + + + + align:start position:0% + +here um if you're putting it into a + + align:start position:0% +here um if you're putting it into a + + + align:start position:0% +here um if you're putting it into a +stove there depending on what the + + align:start position:0% +stove there depending on what the + + + align:start position:0% +stove there depending on what the +pressure is of the bio gas in this + + align:start position:0% +pressure is of the bio gas in this + + + align:start position:0% +pressure is of the bio gas in this +chamber you're going to get a + + align:start position:0% +chamber you're going to get a + + + align:start position:0% +chamber you're going to get a +fluctuation in your stove temperature or + + align:start position:0% +fluctuation in your stove temperature or + + + align:start position:0% +fluctuation in your stove temperature or +your flame front which is kind of + + align:start position:0% +your flame front which is kind of + + + align:start position:0% +your flame front which is kind of +annoying and tricky to work with um so + + align:start position:0% +annoying and tricky to work with um so + + + align:start position:0% +annoying and tricky to work with um so +if you have if you have something that + + align:start position:0% +if you have if you have something that + + + align:start position:0% +if you have if you have something that +expands like a bag it's better like + + align:start position:0% +expands like a bag it's better like + + + align:start position:0% +expands like a bag it's better like +you'll have more of a constant pressure + + align:start position:0% +you'll have more of a constant pressure + + + align:start position:0% +you'll have more of a constant pressure +there are some other designs that also + + align:start position:0% +there are some other designs that also + + + align:start position:0% +there are some other designs that also +try to regulate the temperature um not + + align:start position:0% +try to regulate the temperature um not + + + align:start position:0% +try to regulate the temperature um not +the temperature I'm + + align:start position:0% +the temperature I'm + + + align:start position:0% +the temperature I'm +the the volume of the chamber for the + + align:start position:0% +the the volume of the chamber for the + + + align:start position:0% +the the volume of the chamber for the +gas um there's one called a floating + + align:start position:0% +gas um there's one called a floating + + + align:start position:0% +gas um there's one called a floating +Dome one which is actually what you'll + + align:start position:0% +Dome one which is actually what you'll + + + align:start position:0% +Dome one which is actually what you'll +be making and what it is is you have a + + align:start position:0% +be making and what it is is you have a + + + align:start position:0% +be making and what it is is you have a +giant thing here you have uh you have + + align:start position:0% +giant thing here you have uh you have + + + align:start position:0% +giant thing here you have uh you have +your container which is + + align:start position:0% +your container which is + + + align:start position:0% +your container which is +solid in this case you have + + align:start position:0% +solid in this case you have + + + align:start position:0% +solid in this case you have +your your slurry here and then you have + + align:start position:0% +your your slurry here and then you have + + + align:start position:0% +your your slurry here and then you have +a dome like this that has + + align:start position:0% +a dome like this that has + + + align:start position:0% +a dome like this that has +your pipe coming out and what happens is + + align:start position:0% +your pipe coming out and what happens is + + + align:start position:0% +your pipe coming out and what happens is +this can move up and down inside of your + + align:start position:0% +this can move up and down inside of your + + + align:start position:0% +this can move up and down inside of your +shamber and so as you produce more + + align:start position:0% +shamber and so as you produce more + + + align:start position:0% +shamber and so as you produce more +methane gas or bio gas + + align:start position:0% +methane gas or bio gas + + + align:start position:0% +methane gas or bio gas +rather um as the pressure builds up it + + align:start position:0% +rather um as the pressure builds up it + + + align:start position:0% +rather um as the pressure builds up it +pushes up on the Dome so you're creating + + align:start position:0% +pushes up on the Dome so you're creating + + + align:start position:0% +pushes up on the Dome so you're creating +more of a space and regulating pressure + + align:start position:0% +more of a space and regulating pressure + + + align:start position:0% +more of a space and regulating pressure +with the size of the chamber which is a + + align:start position:0% +with the size of the chamber which is a + + + align:start position:0% +with the size of the chamber which is a +pretty cool design and the ones you guys + + align:start position:0% +pretty cool design and the ones you guys + + + align:start position:0% +pretty cool design and the ones you guys +are going to be making are kind of + + align:start position:0% +are going to be making are kind of + + + align:start position:0% +are going to be making are kind of +similar to this um but somewh with an + + align:start position:0% +similar to this um but somewh with an + + + align:start position:0% +similar to this um but somewh with an +adaptation they're going to be you're + + align:start position:0% +adaptation they're going to be you're + + + align:start position:0% +adaptation they're going to be you're +going to take the bottom of a coke + + align:start position:0% +going to take the bottom of a coke + + + align:start position:0% +going to take the bottom of a coke +bottle it's kind of like that and then + + align:start position:0% +bottle it's kind of like that and then + + + align:start position:0% +bottle it's kind of like that and then +you're going to fill it with water and + + align:start position:0% +you're going to fill it with water and + + + align:start position:0% +you're going to fill it with water and +you're going to have well you're going + + align:start position:0% +you're going to have well you're going + + + align:start position:0% +you're going to have well you're going +to have you're going to have one biogas + + align:start position:0% +to have you're going to have one biogas + + + align:start position:0% +to have you're going to have one biogas +CH you're going to have your chamber + + align:start position:0% +CH you're going to have your chamber + + + align:start position:0% +CH you're going to have your chamber +with slurry and then you're going to + + align:start position:0% +with slurry and then you're going to + + + align:start position:0% +with slurry and then you're going to +have a valve coming into here and coming + + align:start position:0% +have a valve coming into here and coming + + + align:start position:0% +have a valve coming into here and coming +out of the water and going up into that + + align:start position:0% +out of the water and going up into that + + + align:start position:0% +out of the water and going up into that +chamber so this will be able to um to + + align:start position:0% +chamber so this will be able to um to + + + align:start position:0% +chamber so this will be able to um to +move based on how much gas you have in + + align:start position:0% +move based on how much gas you have in + + + align:start position:0% +move based on how much gas you have in +there can can you guys think of any + + align:start position:0% +there can can you guys think of any + + + align:start position:0% +there can can you guys think of any +other advantages to having this sort of + + align:start position:0% + + + + align:start position:0% + +design other than being able to regulate + + align:start position:0% +design other than being able to regulate + + + align:start position:0% +design other than being able to regulate +a constant + + align:start position:0% +a constant + + + align:start position:0% +a constant +amount + + align:start position:0% +amount + + + align:start position:0% +amount +um so how would I know how much methane + + align:start position:0% +um so how would I know how much methane + + + align:start position:0% +um so how would I know how much methane +or bio gas I'm gonna have in this + + align:start position:0% +or bio gas I'm gonna have in this + + + align:start position:0% +or bio gas I'm gonna have in this +chamber with this + + align:start position:0% +chamber with this + + + align:start position:0% +chamber with this +design I like I would have to put + + align:start position:0% +design I like I would have to put + + + align:start position:0% +design I like I would have to put +basically a pressure valve on here and + + align:start position:0% +basically a pressure valve on here and + + + align:start position:0% +basically a pressure valve on here and +read pressure which is kind of annoying + + align:start position:0% +read pressure which is kind of annoying + + + align:start position:0% +read pressure which is kind of annoying +um and expensive + + align:start position:0% +um and expensive + + + align:start position:0% +um and expensive +and yeah and it's not it's not really + + align:start position:0% +and yeah and it's not it's not really + + + align:start position:0% +and yeah and it's not it's not really +like easy to get a pressure valve in a + + align:start position:0% +like easy to get a pressure valve in a + + + align:start position:0% +like easy to get a pressure valve in a +lot of places um but with a design like + + align:start position:0% +lot of places um but with a design like + + + align:start position:0% +lot of places um but with a design like +this if you let it float the amount of + + align:start position:0% +this if you let it float the amount of + + + align:start position:0% +this if you let it float the amount of +you can measure just the height of this + + align:start position:0% +you can measure just the height of this + + + align:start position:0% +you can measure just the height of this +chamber because the higher the chamber + + align:start position:0% +chamber because the higher the chamber + + + align:start position:0% +chamber because the higher the chamber +the more + + align:start position:0% +the more + + + align:start position:0% +the more +volume of biogas you have so it's almost + + align:start position:0% +volume of biogas you have so it's almost + + + align:start position:0% +volume of biogas you have so it's almost +like an indicator that tells you how + + align:start position:0% +like an indicator that tells you how + + + align:start position:0% +like an indicator that tells you how +much you have as well which is also + + align:start position:0% +much you have as well which is also + + + align:start position:0% +much you have as well which is also +pretty cool + + align:start position:0% +pretty cool + + + align:start position:0% +pretty cool +um but I've talked a lot + + align:start position:0% +um but I've talked a lot + + + align:start position:0% +um but I've talked a lot +about how biogas digestors work in sort + + align:start position:0% +about how biogas digestors work in sort + + + align:start position:0% +about how biogas digestors work in sort +of the design sense but we haven't + + align:start position:0% +of the design sense but we haven't + + + align:start position:0% +of the design sense but we haven't +really got into why they're used or + + align:start position:0% +really got into why they're used or + + + align:start position:0% +really got into why they're used or +where they would be + + align:start position:0% +where they would be + + + align:start position:0% +where they would be +applicable um so so let's think about + + align:start position:0% +applicable um so so let's think about + + + align:start position:0% +applicable um so so let's think about +some of some of when these what are the + + align:start position:0% +some of some of when these what are the + + + align:start position:0% +some of some of when these what are the +advantages of biogas to other + + align:start position:0% +advantages of biogas to other + + + align:start position:0% +advantages of biogas to other +alternative cooking fuels we can start + + align:start position:0% +alternative cooking fuels we can start + + + align:start position:0% +alternative cooking fuels we can start +by naming other sources of + + align:start position:0% + + + + align:start position:0% + +fuel someone want to throw out other + + align:start position:0% +fuel someone want to throw out other + + + align:start position:0% +fuel someone want to throw out other +sources of fuel that people use you have + + align:start position:0% + + + + align:start position:0% + +charcoal you have + + align:start position:0% + + + + align:start position:0% + +wood uh um anyone seen other techniques + + align:start position:0% +wood uh um anyone seen other techniques + + + align:start position:0% +wood uh um anyone seen other techniques +that they + + align:start position:0% +that they + + + align:start position:0% +that they +use gas natural + + align:start position:0% + + + + align:start position:0% + +gas um I've seen in parts of other parts + + align:start position:0% +gas um I've seen in parts of other parts + + + align:start position:0% +gas um I've seen in parts of other parts +of the world people actually just + + align:start position:0% +of the world people actually just + + + align:start position:0% +of the world people actually just +burn a manure straight + + align:start position:0% + + + + align:start position:0% + +um if you also have + + align:start position:0% + + + + align:start position:0% + +electricity + + align:start position:0% + + + + align:start position:0% + +yeah um in places they just take like + + align:start position:0% +yeah um in places they just take like + + + align:start position:0% +yeah um in places they just take like +cow dong and just burn it as a fuel + + align:start position:0% +cow dong and just burn it as a fuel + + + align:start position:0% +cow dong and just burn it as a fuel +source just yeah they just take it and + + align:start position:0% +source just yeah they just take it and + + + align:start position:0% +source just yeah they just take it and +burn it and then you cook your food over + + align:start position:0% +burn it and then you cook your food over + + + align:start position:0% +burn it and then you cook your food over +over + + align:start position:0% + + + + align:start position:0% + +it so yeah you like you let it sit out + + align:start position:0% +it so yeah you like you let it sit out + + + align:start position:0% +it so yeah you like you let it sit out +in the sun it dries out it forms sort of + + align:start position:0% +in the sun it dries out it forms sort of + + + align:start position:0% +in the sun it dries out it forms sort of +a brickette and you can just burn this + + align:start position:0% +a brickette and you can just burn this + + + align:start position:0% +a brickette and you can just burn this +briquette and then it produces I mean it + + align:start position:0% +briquette and then it produces I mean it + + + align:start position:0% +briquette and then it produces I mean it +releases energy when you burn it + + align:start position:0% +releases energy when you burn it + + + align:start position:0% +releases energy when you burn it +um + + align:start position:0% +um + + + align:start position:0% +um +yeah yeah it gives off a lot of bad + + align:start position:0% +yeah yeah it gives off a lot of bad + + + align:start position:0% +yeah yeah it gives off a lot of bad +smoke bad smell too + + align:start position:0% +smoke bad smell too + + + align:start position:0% +smoke bad smell too +um and the other thing about burning + + align:start position:0% +um and the other thing about burning + + + align:start position:0% +um and the other thing about burning +manure directly is that it's kind of + + align:start position:0% +manure directly is that it's kind of + + + align:start position:0% +manure directly is that it's kind of +taking a product that's very rich in + + align:start position:0% +taking a product that's very rich in + + + align:start position:0% +taking a product that's very rich in +like resources like there's a lot of + + align:start position:0% +like resources like there's a lot of + + + align:start position:0% +like resources like there's a lot of +organic matter in there that could be + + align:start position:0% +organic matter in there that could be + + + align:start position:0% +organic matter in there that could be +used as fertilizer and instead of using + + align:start position:0% +used as fertilizer and instead of using + + + align:start position:0% +used as fertilizer and instead of using +the like these good properties of that + + align:start position:0% +the like these good properties of that + + + align:start position:0% +the like these good properties of that +you're just combusting it and um so it's + + align:start position:0% +you're just combusting it and um so it's + + + align:start position:0% +you're just combusting it and um so it's +a waste of resources basically to burn + + align:start position:0% +a waste of resources basically to burn + + + align:start position:0% +a waste of resources basically to burn +manure + + align:start position:0% +manure + + + align:start position:0% +manure +directly um all right what what about + + align:start position:0% +directly um all right what what about + + + align:start position:0% +directly um all right what what about +wood and charcoal what are + + align:start position:0% +wood and charcoal what are + + + align:start position:0% +wood and charcoal what are +disadvantages of + + align:start position:0% + + + + align:start position:0% + +that okay that's definitely a big + + align:start position:0% +that okay that's definitely a big + + + align:start position:0% +that okay that's definitely a big +concern like if you look at Haiti so + + align:start position:0% +concern like if you look at Haiti so + + + align:start position:0% +concern like if you look at Haiti so +much of Haiti is deforested um and in + + align:start position:0% +much of Haiti is deforested um and in + + + align:start position:0% +much of Haiti is deforested um and in +places where you don't have access to + + align:start position:0% +places where you don't have access to + + + align:start position:0% +places where you don't have access to +like if like in a lot of parts of I + + align:start position:0% +like if like in a lot of parts of I + + + align:start position:0% +like if like in a lot of parts of I +guess um India and Nepal you'll have + + align:start position:0% +guess um India and Nepal you'll have + + + align:start position:0% +guess um India and Nepal you'll have +areas that have heavily deforested + + align:start position:0% +areas that have heavily deforested + + + align:start position:0% +areas that have heavily deforested +already and so they don't have access to + + align:start position:0% +already and so they don't have access to + + + align:start position:0% +already and so they don't have access to +Wood and charcoal even and charcoal is + + align:start position:0% +Wood and charcoal even and charcoal is + + + align:start position:0% +Wood and charcoal even and charcoal is +expensive there and um in places like + + align:start position:0% +expensive there and um in places like + + + align:start position:0% +expensive there and um in places like +that where people are farmers or cattle + + align:start position:0% +that where people are farmers or cattle + + + align:start position:0% +that where people are farmers or cattle +Farmers a technology like biogas + + align:start position:0% +Farmers a technology like biogas + + + align:start position:0% +Farmers a technology like biogas +digestors makes sense um + + align:start position:0% + + + + align:start position:0% + +any + + align:start position:0% +any + + + align:start position:0% +any +other disadvantages to Wood maybe have + + align:start position:0% +other disadvantages to Wood maybe have + + + align:start position:0% +other disadvantages to Wood maybe have +you ever + + align:start position:0% +you ever + + + align:start position:0% +you ever +tried what + + align:start position:0% + + + + align:start position:0% + +um just as a sense if any of you been to + + align:start position:0% +um just as a sense if any of you been to + + + align:start position:0% +um just as a sense if any of you been to +developing world places where you've + + align:start position:0% +developing world places where you've + + + align:start position:0% +developing world places where you've +seen people cook on three stone wood + + align:start position:0% +seen people cook on three stone wood + + + align:start position:0% +seen people cook on three stone wood +fires or anything like + + align:start position:0% +fires or anything like + + + align:start position:0% +fires or anything like +that um what did you notice about the + + align:start position:0% +that um what did you notice about the + + + align:start position:0% +that um what did you notice about the +the cooking + + align:start position:0% + + + + align:start position:0% + +process do you want to do you want to + + align:start position:0% +process do you want to do you want to + + + align:start position:0% +process do you want to do you want to +tell people about how they cooked there + + align:start position:0% + + + + align:start position:0% + +okay when they did cook how did they + + align:start position:0% +okay when they did cook how did they + + + align:start position:0% +okay when they did cook how did they +what was the process that they used for + + align:start position:0% +what was the process that they used for + + + align:start position:0% +what was the process that they used for +cooking with the fire or with the wood + + align:start position:0% +cooking with the fire or with the wood + + + align:start position:0% +cooking with the fire or with the wood +because it varies depending on where you + + align:start position:0% +because it varies depending on where you + + + align:start position:0% +because it varies depending on where you +are like a lot of different ways of + + align:start position:0% +are like a lot of different ways of + + + align:start position:0% +are like a lot of different ways of +combusting wood and using it in the + + align:start position:0% +combusting wood and using it in the + + + align:start position:0% +combusting wood and using it in the +stove what did the stove look like + + align:start position:0% + + + + align:start position:0% + +okay you yeah I'm not sure what you're + + align:start position:0% +okay you yeah I'm not sure what you're + + + align:start position:0% +okay you yeah I'm not sure what you're +getting + + align:start position:0% +getting + + + align:start position:0% +getting +likeor yeah okay well + + align:start position:0% + + + + align:start position:0% + +uh yeah and and I mean like one of the + + align:start position:0% +uh yeah and and I mean like one of the + + + align:start position:0% +uh yeah and and I mean like one of the +biggest problems with it is also just + + align:start position:0% +biggest problems with it is also just + + + align:start position:0% +biggest problems with it is also just +the smoke that it releases and the fumes + + align:start position:0% +the smoke that it releases and the fumes + + + align:start position:0% +the smoke that it releases and the fumes +from that uh which are both pretty bad + + align:start position:0% +from that uh which are both pretty bad + + + align:start position:0% +from that uh which are both pretty bad +like uh wood fires cause a lot of + + align:start position:0% +like uh wood fires cause a lot of + + + align:start position:0% +like uh wood fires cause a lot of +pollution and most people cook with wood + + align:start position:0% +pollution and most people cook with wood + + + align:start position:0% +pollution and most people cook with wood +fires inside their houses and indoor air + + align:start position:0% +fires inside their houses and indoor air + + + align:start position:0% +fires inside their houses and indoor air +pollution is a really big problem + + align:start position:0% +pollution is a really big problem + + + align:start position:0% +pollution is a really big problem +throughout the developing world and so + + align:start position:0% +throughout the developing world and so + + + align:start position:0% +throughout the developing world and so +biogas has the advantage where it + + align:start position:0% +biogas has the advantage where it + + + align:start position:0% +biogas has the advantage where it +doesn't release any of these toxic + + align:start position:0% +doesn't release any of these toxic + + + align:start position:0% +doesn't release any of these toxic +fumes yeah complain about taste I'm not + + align:start position:0% +fumes yeah complain about taste I'm not + + + align:start position:0% +fumes yeah complain about taste I'm not +saying that I know + + align:start position:0% +saying that I know + + + align:start position:0% +saying that I know +a + + align:start position:0% + + + + align:start position:0% + +lot uh I haven't seen have you seen that + + align:start position:0% +lot uh I haven't seen have you seen that + + + align:start position:0% +lot uh I haven't seen have you seen that +a concern I think the way a lot of + + align:start position:0% +a concern I think the way a lot of + + + align:start position:0% +a concern I think the way a lot of +people like a lot of people I've seen + + align:start position:0% +people like a lot of people I've seen + + + align:start position:0% +people like a lot of people I've seen +use are you talking how are you talking + + align:start position:0% +use are you talking how are you talking + + + align:start position:0% +use are you talking how are you talking +about them using the wood are you + + align:start position:0% +about them using the wood are you + + + align:start position:0% +about them using the wood are you +talking about them like barbecuing + + align:start position:0% +talking about them like barbecuing + + + align:start position:0% +talking about them like barbecuing +something or grilling + + align:start position:0% +something or grilling + + + align:start position:0% +something or grilling +I + + align:start position:0% + + + + align:start position:0% + +remember uh yeah I don't have much + + align:start position:0% +remember uh yeah I don't have much + + + align:start position:0% +remember uh yeah I don't have much +experience with that so sorry help do + + align:start position:0% +experience with that so sorry help do + + + align:start position:0% +experience with that so sorry help do +you I mean I think is a + + align:start position:0% + + + + align:start position:0% + +behavioral okay um what about natural + + align:start position:0% + + + + align:start position:0% + +gas what are some of the problem s + + align:start position:0% +gas what are some of the problem s + + + align:start position:0% +gas what are some of the problem s +associated with natural + + align:start position:0% + + + + align:start position:0% + +gas um yes + + align:start position:0% + + + + align:start position:0% + +it's I don't know I don't I don't think + + align:start position:0% +it's I don't know I don't I don't think + + + align:start position:0% +it's I don't know I don't I don't think +if it is particularly dangerous it's + + align:start position:0% +if it is particularly dangerous it's + + + align:start position:0% +if it is particularly dangerous it's +just you need a lot of infrastructure to + + align:start position:0% +just you need a lot of infrastructure to + + + align:start position:0% +just you need a lot of infrastructure to +be able to provide natural gas to people + + align:start position:0% +be able to provide natural gas to people + + + align:start position:0% +be able to provide natural gas to people +and uh some places it's it's available + + align:start position:0% +and uh some places it's it's available + + + align:start position:0% +and uh some places it's it's available +and not too bad like when I was working + + align:start position:0% +and not too bad like when I was working + + + align:start position:0% +and not too bad like when I was working +in a favella in Brazil over this I AP + + align:start position:0% +in a favella in Brazil over this I AP + + + align:start position:0% +in a favella in Brazil over this I AP +they had a truck come in with natural + + align:start position:0% +they had a truck come in with natural + + + align:start position:0% +they had a truck come in with natural +gas or LPG and they would bring it every + + align:start position:0% +gas or LPG and they would bring it every + + + align:start position:0% +gas or LPG and they would bring it every +couple days and at the same time and + + align:start position:0% +couple days and at the same time and + + + align:start position:0% +couple days and at the same time and +pick up old containers and give people + + align:start position:0% +pick up old containers and give people + + + align:start position:0% +pick up old containers and give people +new containers for a certain price and + + align:start position:0% +new containers for a certain price and + + + align:start position:0% +new containers for a certain price and +that seemed like it was great but you + + align:start position:0% +that seemed like it was great but you + + + align:start position:0% +that seemed like it was great but you +can't really have that same sort of + + align:start position:0% +can't really have that same sort of + + + align:start position:0% +can't really have that same sort of +infrastructure in a more rural place for + + align:start position:0% +infrastructure in a more rural place for + + + align:start position:0% +infrastructure in a more rural place for +example um manure we already talked + + align:start position:0% +example um manure we already talked + + + align:start position:0% +example um manure we already talked +about and electricity + + align:start position:0% +about and electricity + + + align:start position:0% +about and electricity +is I mean in places people don't really + + align:start position:0% +is I mean in places people don't really + + + align:start position:0% +is I mean in places people don't really +cook with electricity that much in the + + align:start position:0% +cook with electricity that much in the + + + align:start position:0% +cook with electricity that much in the +developing world like that I've seen + + align:start position:0% +developing world like that I've seen + + + align:start position:0% +developing world like that I've seen +um so yeah bias has a lot of advantages + + align:start position:0% +um so yeah bias has a lot of advantages + + + align:start position:0% +um so yeah bias has a lot of advantages +in + + align:start position:0% +in + + + align:start position:0% +in +in to these other cooking methods but it + + align:start position:0% +in to these other cooking methods but it + + + align:start position:0% +in to these other cooking methods but it +also need it also requires certain + + align:start position:0% +also need it also requires certain + + + align:start position:0% +also need it also requires certain +things you need uh like you basically + + align:start position:0% +things you need uh like you basically + + + align:start position:0% +things you need uh like you basically +need a lot of manure or waste to go into + + align:start position:0% +need a lot of manure or waste to go into + + + align:start position:0% +need a lot of manure or waste to go into +this biogas digestor every day I think + + align:start position:0% +this biogas digestor every day I think + + + align:start position:0% +this biogas digestor every day I think +the minimum recommendations are having + + align:start position:0% +the minimum recommendations are having + + + align:start position:0% +the minimum recommendations are having +maybe two cows or something like that um + + align:start position:0% +maybe two cows or something like that um + + + align:start position:0% +maybe two cows or something like that um +or a few pigs and if you don't have if + + align:start position:0% +or a few pigs and if you don't have if + + + align:start position:0% +or a few pigs and if you don't have if +you don't sort of meet + + align:start position:0% +you don't sort of meet + + + align:start position:0% +you don't sort of meet +these conditions you're not going to be + + align:start position:0% +these conditions you're not going to be + + + align:start position:0% +these conditions you're not going to be +able to have a biogas digestor that + + align:start position:0% +able to have a biogas digestor that + + + align:start position:0% +able to have a biogas digestor that +produces that much fuel for you to cook + + align:start position:0% +produces that much fuel for you to cook + + + align:start position:0% +produces that much fuel for you to cook +off of and the investment for building + + align:start position:0% +off of and the investment for building + + + align:start position:0% +off of and the investment for building +one isn't isn't um paid back over a + + align:start position:0% +one isn't isn't um paid back over a + + + align:start position:0% +one isn't isn't um paid back over a +reasonable period of + + align:start position:0% +reasonable period of + + + align:start position:0% +reasonable period of +time the the other thing that's cool + + align:start position:0% +time the the other thing that's cool + + + align:start position:0% +time the the other thing that's cool +about biogas is that when you when you + + align:start position:0% +about biogas is that when you when you + + + align:start position:0% +about biogas is that when you when you +pass your if I think if you're not using + + align:start position:0% +pass your if I think if you're not using + + + align:start position:0% +pass your if I think if you're not using +human waste if you're using manure and + + align:start position:0% +human waste if you're using manure and + + + align:start position:0% +human waste if you're using manure and +you're using agricultural waste if you + + align:start position:0% +you're using agricultural waste if you + + + align:start position:0% +you're using agricultural waste if you +or an organic waste if you pass it + + align:start position:0% +or an organic waste if you pass it + + + align:start position:0% +or an organic waste if you pass it +through the biogas digestor at the end + + align:start position:0% +through the biogas digestor at the end + + + align:start position:0% +through the biogas digestor at the end +of it you get fertilizer which is really + + align:start position:0% +of it you get fertilizer which is really + + + align:start position:0% +of it you get fertilizer which is really +good because you're taking a waste + + align:start position:0% +good because you're taking a waste + + + align:start position:0% +good because you're taking a waste +product right now which is animal waste + + align:start position:0% +product right now which is animal waste + + + align:start position:0% +product right now which is animal waste +and it smells bad and people try to + + align:start position:0% +and it smells bad and people try to + + + align:start position:0% +and it smells bad and people try to +dispose of it as in ways where they're + + align:start position:0% +dispose of it as in ways where they're + + + align:start position:0% +dispose of it as in ways where they're +not utilizing any value from it and + + align:start position:0% +not utilizing any value from it and + + + align:start position:0% +not utilizing any value from it and +you're you're get you're getting value + + align:start position:0% +you're you're get you're getting value + + + align:start position:0% +you're you're get you're getting value +from this product which is like which is + + align:start position:0% +from this product which is like which is + + + align:start position:0% +from this product which is like which is +trash right now which is a really cool + + align:start position:0% +trash right now which is a really cool + + + align:start position:0% +trash right now which is a really cool +idea plus when you pass uh when you pass + + align:start position:0% +idea plus when you pass uh when you pass + + + align:start position:0% +idea plus when you pass uh when you pass +the waste through the biogas digestor a + + align:start position:0% +the waste through the biogas digestor a + + + align:start position:0% +the waste through the biogas digestor a +lot of the harmful bacteria get killed + + align:start position:0% +lot of the harmful bacteria get killed + + + align:start position:0% +lot of the harmful bacteria get killed +off in the process of producing or like + + align:start position:0% +off in the process of producing or like + + + align:start position:0% +off in the process of producing or like +when it goes into anerobic conditions a + + align:start position:0% +when it goes into anerobic conditions a + + + align:start position:0% +when it goes into anerobic conditions a +lot of the harmful bacteria get killed + + align:start position:0% +lot of the harmful bacteria get killed + + + align:start position:0% +lot of the harmful bacteria get killed +off um so what you're left with + + align:start position:0% +off um so what you're left with + + + align:start position:0% +off um so what you're left with +is good fertilizer that you can use to + + align:start position:0% +is good fertilizer that you can use to + + + align:start position:0% +is good fertilizer that you can use to +grow your uh to grow crops with and and + + align:start position:0% +grow your uh to grow crops with and and + + + align:start position:0% +grow your uh to grow crops with and and +yeah so it's it's really just taking a + + align:start position:0% +yeah so it's it's really just taking a + + + align:start position:0% +yeah so it's it's really just taking a +waste product and turning and getting + + align:start position:0% +waste product and turning and getting + + + align:start position:0% +waste product and turning and getting +value from + + align:start position:0% +value from + + + align:start position:0% +value from +there + + align:start position:0% +there + + + align:start position:0% +there +um what + + align:start position:0% +um what + + + align:start position:0% +um what +are what are some of the problems you + + align:start position:0% +are what are some of the problems you + + + align:start position:0% +are what are some of the problems you +can see with biogas + + align:start position:0% +can see with biogas + + + align:start position:0% +can see with biogas +digestors based off of this cursory + + align:start position:0% +digestors based off of this cursory + + + align:start position:0% +digestors based off of this cursory +introduction to + + align:start position:0% + + + + align:start position:0% + +them + + align:start position:0% + + + + align:start position:0% + +yeah yeah um but I guess I just discuss + + align:start position:0% +yeah yeah um but I guess I just discuss + + + align:start position:0% +yeah yeah um but I guess I just discuss +about or I think the cheapest ones I've + + align:start position:0% +about or I think the cheapest ones I've + + + align:start position:0% +about or I think the cheapest ones I've +seen around $300 to + + align:start position:0% +seen around $300 to + + + align:start position:0% +seen around $300 to +build um but they're on the order of + + align:start position:0% +build um but they're on the order of + + + align:start position:0% +build um but they're on the order of +hundreds of dollars and so it's pretty + + align:start position:0% +hundreds of dollars and so it's pretty + + + align:start position:0% +hundreds of dollars and so it's pretty +expensive to Shell out at once to build + + align:start position:0% +expensive to Shell out at once to build + + + align:start position:0% +expensive to Shell out at once to build +one of + + align:start position:0% +one of + + + align:start position:0% +one of +these um + + align:start position:0% +these um + + + align:start position:0% +these um +another big thing again were you gonna + + align:start position:0% +another big thing again were you gonna + + + align:start position:0% +another big thing again were you gonna +say + + align:start position:0% + + + + align:start position:0% + +something yeah the maintenance costs are + + align:start position:0% +something yeah the maintenance costs are + + + align:start position:0% +something yeah the maintenance costs are +pretty big as well and the problem with + + align:start position:0% +pretty big as well and the problem with + + + align:start position:0% +pretty big as well and the problem with +this is uh there's so many parts as well + + align:start position:0% +this is uh there's so many parts as well + + + align:start position:0% +this is uh there's so many parts as well +that are very critical to the + + align:start position:0% +that are very critical to the + + + align:start position:0% +that are very critical to the +functionality of it that if one of them + + align:start position:0% +functionality of it that if one of them + + + align:start position:0% +functionality of it that if one of them +breaks you have to fix it otherwise your + + align:start position:0% +breaks you have to fix it otherwise your + + + align:start position:0% +breaks you have to fix it otherwise your +entire thing stops like if your bag gets + + align:start position:0% +entire thing stops like if your bag gets + + + align:start position:0% +entire thing stops like if your bag gets +a hole in it all of your gas is going to + + align:start position:0% +a hole in it all of your gas is going to + + + align:start position:0% +a hole in it all of your gas is going to +leak out + + align:start position:0% +leak out + + + align:start position:0% +leak out +so um you have to carefully design it + + align:start position:0% +so um you have to carefully design it + + + align:start position:0% +so um you have to carefully design it +and make it so that and you have to + + align:start position:0% +and make it so that and you have to + + + align:start position:0% +and make it so that and you have to +really take care of this because if you + + align:start position:0% +really take care of this because if you + + + align:start position:0% +really take care of this because if you +don't then + + align:start position:0% +don't then + + + align:start position:0% +don't then +um then it's just not going to work + + align:start position:0% +um then it's just not going to work + + + align:start position:0% +um then it's just not going to work +anymore there there are few things that + + align:start position:0% +anymore there there are few things that + + + align:start position:0% +anymore there there are few things that +in particular go or there some common + + align:start position:0% +in particular go or there some common + + + align:start position:0% +in particular go or there some common +sources of problems that you're going to + + align:start position:0% +sources of problems that you're going to + + + align:start position:0% +sources of problems that you're going to +that biog digestors have over time + + align:start position:0% +that biog digestors have over time + + + align:start position:0% +that biog digestors have over time +and um those are just leaks temperature + + align:start position:0% +and um those are just leaks temperature + + + align:start position:0% +and um those are just leaks temperature +and pH + + align:start position:0% + + + + align:start position:0% + +um so last year we did this lab in dlab + + align:start position:0% +um so last year we did this lab in dlab + + + align:start position:0% +um so last year we did this lab in dlab +energy as well where we made biogas + + align:start position:0% +energy as well where we made biogas + + + align:start position:0% +energy as well where we made biogas +digesters and none of them produced any + + align:start position:0% +digesters and none of them produced any + + + align:start position:0% +digesters and none of them produced any +methane gas or biog gas and it was + + align:start position:0% +methane gas or biog gas and it was + + + align:start position:0% +methane gas or biog gas and it was +because last year unlike this year dlab + + align:start position:0% +because last year unlike this year dlab + + + align:start position:0% +because last year unlike this year dlab +was very very cold it was like you + + align:start position:0% +was very very cold it was like you + + + align:start position:0% +was very very cold it was like you +needed to wear jackets around or you + + align:start position:0% +needed to wear jackets around or you + + + align:start position:0% +needed to wear jackets around or you +just wouldn't be able to walk around + + align:start position:0% +just wouldn't be able to walk around + + + align:start position:0% +just wouldn't be able to walk around +here and biogas digestors need a warm + + align:start position:0% +here and biogas digestors need a warm + + + align:start position:0% +here and biogas digestors need a warm +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +um I think around + + align:start position:0% +um I think around + + + align:start position:0% +um I think around +50° uh + + align:start position:0% +50° uh + + + align:start position:0% +50° uh +Celsius though that seems high now no + + align:start position:0% +Celsius though that seems high now no + + + align:start position:0% +Celsius though that seems high now no +that seems + + align:start position:0% +that seems + + + align:start position:0% +that seems +high I I'll get back to you on the + + align:start position:0% +high I I'll get back to you on the + + + align:start position:0% +high I I'll get back to you on the +temperature but they need a they have a + + align:start position:0% +temperature but they need a they have a + + + align:start position:0% +temperature but they need a they have a +pretty high operational temperature and + + align:start position:0% +pretty high operational temperature and + + + align:start position:0% +pretty high operational temperature and +if they're in that range then they work + + align:start position:0% +if they're in that range then they work + + + align:start position:0% +if they're in that range then they work +well and if they're not in that range + + align:start position:0% +well and if they're not in that range + + + align:start position:0% +well and if they're not in that range +they don't work well so if you're in an + + align:start position:0% +they don't work well so if you're in an + + + align:start position:0% +they don't work well so if you're in an +area that gets cold a lot or has like + + align:start position:0% +area that gets cold a lot or has like + + + align:start position:0% +area that gets cold a lot or has like +huge temperature shifts then your + + align:start position:0% +huge temperature shifts then your + + + align:start position:0% +huge temperature shifts then your +bacteria that are producing methane + + align:start position:0% +bacteria that are producing methane + + + align:start position:0% +bacteria that are producing methane +under anerobic conditions are going to + + align:start position:0% +under anerobic conditions are going to + + + align:start position:0% +under anerobic conditions are going to +die out um because of the cold and + + align:start position:0% +die out um because of the cold and + + + align:start position:0% +die out um because of the cold and +you have to you might have to come up + + align:start position:0% +you have to you might have to come up + + + align:start position:0% +you have to you might have to come up +with some sort of heating uh device for + + align:start position:0% +with some sort of heating uh device for + + + align:start position:0% +with some sort of heating uh device for +your biogas digestor to keep it warm um + + align:start position:0% +your biogas digestor to keep it warm um + + + align:start position:0% +your biogas digestor to keep it warm um +the last thing is pH uh you want you + + align:start position:0% +the last thing is pH uh you want you + + + align:start position:0% +the last thing is pH uh you want you +really need or for these bacteria to + + align:start position:0% +really need or for these bacteria to + + + align:start position:0% +really need or for these bacteria to +survive you need to have them at + + align:start position:0% +survive you need to have them at + + + align:start position:0% +survive you need to have them at +around um a pH that's like around seven + + align:start position:0% +around um a pH that's like around seven + + + align:start position:0% +around um a pH that's like around seven +so I think 6 to8 is reasonable and if + + align:start position:0% +so I think 6 to8 is reasonable and if + + + align:start position:0% +so I think 6 to8 is reasonable and if +your pH drops below that or gets raised + + align:start position:0% +your pH drops below that or gets raised + + + align:start position:0% +your pH drops below that or gets raised +above that then you also have problems + + align:start position:0% +above that then you also have problems + + + align:start position:0% +above that then you also have problems +with biogas digestors + + align:start position:0% +with biogas digestors + + + align:start position:0% +with biogas digestors +working + + align:start position:0% +working + + + align:start position:0% +working +um so yeah + + align:start position:0% + + + + align:start position:0% + +uh I guess that's pretty much all I had + + align:start position:0% +uh I guess that's pretty much all I had + + + align:start position:0% +uh I guess that's pretty much all I had +prepared for the biogas just like for + + align:start position:0% +prepared for the biogas just like for + + + align:start position:0% +prepared for the biogas just like for +the lectur part of this uh so do you + + align:start position:0% +the lectur part of this uh so do you + + + align:start position:0% +the lectur part of this uh so do you +have any + + align:start position:0% +have any + + + align:start position:0% +have any +questions yes + + align:start position:0% + + + + align:start position:0% + +the no they're found I mean the bacteria + + align:start position:0% +the no they're found I mean the bacteria + + + align:start position:0% +the no they're found I mean the bacteria +that are in the biogas digestors are the + + align:start position:0% +that are in the biogas digestors are the + + + align:start position:0% +that are in the biogas digestors are the +same bacteria that are going to be in + + align:start position:0% +same bacteria that are going to be in + + + align:start position:0% +same bacteria that are going to be in +your stomach or cow's stomachs or and + + align:start position:0% +your stomach or cow's stomachs or and + + + align:start position:0% +your stomach or cow's stomachs or and +yeah so they're just introduced or not + + align:start position:0% +yeah so they're just introduced or not + + + align:start position:0% +yeah so they're just introduced or not +introduced they're just found in the + + align:start position:0% +introduced they're just found in the + + + align:start position:0% +introduced they're just found in the +manure + + align:start position:0% + + + + align:start position:0% + +so uh so it needs to be separated at + + align:start position:0% +so uh so it needs to be separated at + + + align:start position:0% +so uh so it needs to be separated at +least because there's sort of like the + + align:start position:0% +least because there's sort of like the + + + align:start position:0% +least because there's sort of like the +liquid part and the hard part or like + + align:start position:0% +liquid part and the hard part or like + + + align:start position:0% +liquid part and the hard part or like +there's the liquid part and the solid + + align:start position:0% +there's the liquid part and the solid + + + align:start position:0% +there's the liquid part and the solid +matter part and the solid matter part is + + align:start position:0% +matter part and the solid matter part is + + + align:start position:0% +matter part and the solid matter part is +generally composted and the liquid part + + align:start position:0% +generally composted and the liquid part + + + align:start position:0% +generally composted and the liquid part +is used as fertilizer + + align:start position:0% + + + + align:start position:0% + +um any other questions + + align:start position:0% + + + + align:start position:0% + +Yes actually put a a cow or like what do + + align:start position:0% +Yes actually put a a cow or like what do + + + align:start position:0% +Yes actually put a a cow or like what do +they do I don't actually know that works + + align:start position:0% +they do I don't actually know that works + + + align:start position:0% +they do I don't actually know that works +um I think they just scoop it up after + + align:start position:0% +um I think they just scoop it up after + + + align:start position:0% +um I think they just scoop it up after +afterwards + + align:start position:0% + + + + align:start position:0% + +yeah I think they're usually tied up + + align:start position:0% +yeah I think they're usually tied up + + + align:start position:0% +yeah I think they're usually tied up +though + + align:start position:0% +though + + + align:start position:0% +though +so + + align:start position:0% +so + + + align:start position:0% +so +sometimes I'm just curious yeah but it's + + align:start position:0% +sometimes I'm just curious yeah but it's + + + align:start position:0% +sometimes I'm just curious yeah but it's +you you don't put the diaper on the cow + + align:start position:0% +you you don't put the diaper on the cow + + + align:start position:0% +you you don't put the diaper on the cow +generally you I I don't think I've ever + + align:start position:0% +generally you I I don't think I've ever + + + align:start position:0% +generally you I I don't think I've ever +seen that actually but you just collect + + align:start position:0% +seen that actually but you just collect + + + align:start position:0% +seen that actually but you just collect +it off the + + align:start position:0% + + + + align:start position:0% + +ground before the stove right you can + + align:start position:0% +ground before the stove right you can + + + align:start position:0% +ground before the stove right you can +like around yeah and so there must be + + align:start position:0% +like around yeah and so there must be + + + align:start position:0% +like around yeah and so there must be +like that gas resir g + + align:start position:0% +like that gas resir g + + + align:start position:0% +like that gas resir g +what you're not using but like pressure + + align:start position:0% +what you're not using but like pressure + + + align:start position:0% +what you're not using but like pressure +build there so then if there's a + + align:start position:0% +build there so then if there's a + + + align:start position:0% +build there so then if there's a +pressure build there I'm not sure what + + align:start position:0% +pressure build there I'm not sure what + + + align:start position:0% +pressure build there I'm not sure what +the function of the main Val and + + align:start position:0% +the function of the main Val and + + + align:start position:0% +the function of the main Val and +gas + + align:start position:0% +gas + + + align:start position:0% +gas +and + + align:start position:0% + + + + align:start position:0% + +issue um yeah so that's a good question + + align:start position:0% +issue um yeah so that's a good question + + + align:start position:0% +issue um yeah so that's a good question +uh I think there there there are other + + align:start position:0% +uh I think there there there are other + + + align:start position:0% +uh I think there there there are other +designs of bias digesters that don't + + align:start position:0% +designs of bias digesters that don't + + + align:start position:0% +designs of bias digesters that don't +have all of these security things + + align:start position:0% +have all of these security things + + + align:start position:0% +have all of these security things +necessarily built into them as well this + + align:start position:0% +necessarily built into them as well this + + + align:start position:0% +necessarily built into them as well this +is a this is a design that Victor + + align:start position:0% +is a this is a design that Victor + + + align:start position:0% +is a this is a design that Victor +presented I don't know if you know + + align:start position:0% +presented I don't know if you know + + + align:start position:0% +presented I don't know if you know +Victor uh but he's one of the dlab + + align:start position:0% +Victor uh but he's one of the dlab + + + align:start position:0% +Victor uh but he's one of the dlab +instructors + + align:start position:0% +instructors + + + align:start position:0% +instructors +um and so this was one of the designs + + align:start position:0% +um and so this was one of the designs + + + align:start position:0% +um and so this was one of the designs +that he presented and so I don't know + + align:start position:0% +that he presented and so I don't know + + + align:start position:0% +that he presented and so I don't know +the specifics about the difference + + align:start position:0% +the specifics about the difference + + + align:start position:0% +the specifics about the difference +different valves but I can find out for + + align:start position:0% +different valves but I can find out for + + + align:start position:0% +different valves but I can find out for +you and get back to next week + + align:start position:0% + + + + align:start position:0% + +yeah it just it + + align:start position:0% +yeah it just it + + + align:start position:0% +yeah it just it +regulates um it makes it so that if + + align:start position:0% +regulates um it makes it so that if + + + align:start position:0% +regulates um it makes it so that if +there's too much of a buildup of gas + + align:start position:0% +there's too much of a buildup of gas + + + align:start position:0% +there's too much of a buildup of gas +that the gas can escape somewhere and it + + align:start position:0% +that the gas can escape somewhere and it + + + align:start position:0% +that the gas can escape somewhere and it +you don't just have pipes like shooting + + align:start position:0% +you don't just have pipes like shooting + + + align:start position:0% +you don't just have pipes like shooting +off because of high + + align:start position:0% + + + + align:start position:0% + +pressure does that make + + align:start position:0% + + + + align:start position:0% + +sense so so you have your security valve + + align:start position:0% +sense so so you have your security valve + + + align:start position:0% +sense so so you have your security valve +here + + align:start position:0% +here + + + align:start position:0% +here +um so that that chamber right uh is + + align:start position:0% +um so that that chamber right uh is + + + align:start position:0% +um so that that chamber right uh is +going to get bigger okay so you have you + + align:start position:0% +going to get bigger okay so you have you + + + align:start position:0% +going to get bigger okay so you have you +have your bag here then you have your + + align:start position:0% +have your bag here then you have your + + + align:start position:0% +have your bag here then you have your +thing going out to security valve here + + align:start position:0% +thing going out to security valve here + + + align:start position:0% +thing going out to security valve here +um and then you have your main valve + + align:start position:0% +um and then you have your main valve + + + align:start position:0% +um and then you have your main valve +here and so when your main valve is + + align:start position:0% +here and so when your main valve is + + + align:start position:0% +here and so when your main valve is +off + + align:start position:0% +off + + + align:start position:0% +off +um this is sort of a closed system and + + align:start position:0% +um this is sort of a closed system and + + + align:start position:0% +um this is sort of a closed system and +so no gas can escape out of this + + align:start position:0% +so no gas can escape out of this + + + align:start position:0% +so no gas can escape out of this +like because you have uh like this is + + align:start position:0% +like because you have uh like this is + + + align:start position:0% +like because you have uh like this is +filled up to here + + align:start position:0% +filled up to here + + + align:start position:0% +filled up to here +or I'm drawing this wrong + + align:start position:0% +or I'm drawing this wrong + + + align:start position:0% +or I'm drawing this wrong +but um so you'll normally have + + align:start position:0% + + + + align:start position:0% + +like okay so you normally have like your + + align:start position:0% +like okay so you normally have like your + + + align:start position:0% +like okay so you normally have like your +sewage level something like + + align:start position:0% +sewage level something like + + + align:start position:0% +sewage level something like +this + + align:start position:0% +this + + + align:start position:0% +this +um and so your gas is all your gas is + + align:start position:0% +um and so your gas is all your gas is + + + align:start position:0% +um and so your gas is all your gas is +contained within + + align:start position:0% +contained within + + + align:start position:0% +contained within +within like this region of your biogas + + align:start position:0% +within like this region of your biogas + + + align:start position:0% +within like this region of your biogas +digestor right now and so if this valve + + align:start position:0% +digestor right now and so if this valve + + + align:start position:0% +digestor right now and so if this valve +is off and you keep producing more and + + align:start position:0% +is off and you keep producing more and + + + align:start position:0% +is off and you keep producing more and +more gas your bag is going to get bigger + + align:start position:0% +more gas your bag is going to get bigger + + + align:start position:0% +more gas your bag is going to get bigger +and bigger and at some point it's just + + align:start position:0% +and bigger and at some point it's just + + + align:start position:0% +and bigger and at some point it's just +going to explode because of the excess + + align:start position:0% +going to explode because of the excess + + + align:start position:0% +going to explode because of the excess +methane gas and so what the security + + align:start position:0% +methane gas and so what the security + + + align:start position:0% +methane gas and so what the security +valve does is it'll let out that excess + + align:start position:0% +valve does is it'll let out that excess + + + align:start position:0% +valve does is it'll let out that excess +gas to prevent your system from breaking + + align:start position:0% +gas to prevent your system from breaking + + + align:start position:0% +gas to prevent your system from breaking +that the one that + + align:start position:0% + + + + align:start position:0% + +control generally there's a second + + align:start position:0% +control generally there's a second + + + align:start position:0% +control generally there's a second +switch at the stoven + + align:start position:0% +switch at the stoven + + + align:start position:0% +switch at the stoven +too + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +um I'm not + + align:start position:0% +um I'm not + + + align:start position:0% +um I'm not +sure yeah I'm not sure about the + + align:start position:0% +sure yeah I'm not sure about the + + + align:start position:0% +sure yeah I'm not sure about the +specific design + + align:start position:0% + + + + align:start position:0% + +yeah out + + align:start position:0% + + + + align:start position:0% + +yeah but the other thing is you also + + align:start position:0% +yeah but the other thing is you also + + + align:start position:0% +yeah but the other thing is you also +don't want to have a fully like open + + align:start position:0% +don't want to have a fully like open + + + align:start position:0% +don't want to have a fully like open +system like one full close system + + align:start position:0% +system like one full close system + + + align:start position:0% +system like one full close system +because if there's like a spark or + + align:start position:0% +because if there's like a spark or + + + align:start position:0% +because if there's like a spark or +something like that the entire thing's + + align:start position:0% +something like that the entire thing's + + + align:start position:0% +something like that the entire thing's +just going to blow up uh + + align:start position:0% +just going to blow up uh + + + align:start position:0% +just going to blow up uh +and + + align:start position:0% + + + + align:start position:0% + +you I've I've seen lots of different + + align:start position:0% +you I've I've seen lots of different + + + align:start position:0% +you I've I've seen lots of different +types of gas reservoirs um I think the + + align:start position:0% +types of gas reservoirs um I think the + + + align:start position:0% +types of gas reservoirs um I think the +cheapest one you can do is you can just + + align:start position:0% +cheapest one you can do is you can just + + + align:start position:0% +cheapest one you can do is you can just +take another second smaller bag and seal + + align:start position:0% +take another second smaller bag and seal + + + align:start position:0% +take another second smaller bag and seal +it and then put an inlet and an outlet + + align:start position:0% +it and then put an inlet and an outlet + + + align:start position:0% +it and then put an inlet and an outlet +on that and then this bag just fills up + + align:start position:0% +on that and then this bag just fills up + + + align:start position:0% +on that and then this bag just fills up +and yeah expands as I + + align:start position:0% + + + + align:start position:0% + +yeah com + + align:start position:0% + + + + align:start position:0% + +I'm I'm pretty sure it is possible to do + + align:start position:0% +I'm I'm pretty sure it is possible to do + + + align:start position:0% +I'm I'm pretty sure it is possible to do +that but it's a pretty like + + align:start position:0% +that but it's a pretty like + + + align:start position:0% +that but it's a pretty like +sophisticated process and I've never + + align:start position:0% +sophisticated process and I've never + + + align:start position:0% +sophisticated process and I've never +seen it done on like in the actual like + + align:start position:0% +seen it done on like in the actual like + + + align:start position:0% +seen it done on like in the actual like +on in rural developing world I've only + + align:start position:0% +on in rural developing world I've only + + + align:start position:0% +on in rural developing world I've only +seen it done or heard of it being done + + align:start position:0% +seen it done or heard of it being done + + + align:start position:0% +seen it done or heard of it being done +in like on the industrial scale + + align:start position:0% + + + + align:start position:0% + +um I'm trying to think I mean there's + + align:start position:0% +um I'm trying to think I mean there's + + + align:start position:0% +um I'm trying to think I mean there's +probably the user end of it where if you + + align:start position:0% +probably the user end of it where if you + + + align:start position:0% +probably the user end of it where if you +see the reservoir it's easier to know + + align:start position:0% +see the reservoir it's easier to know + + + align:start position:0% +see the reservoir it's easier to know +how full it is and things like that + + align:start position:0% +how full it is and things like that + + + align:start position:0% +how full it is and things like that +um it's also a second part that needs to + + align:start position:0% +um it's also a second part that needs to + + + align:start position:0% +um it's also a second part that needs to +be protected if you're using a bag to + + align:start position:0% +be protected if you're using a bag to + + + align:start position:0% +be protected if you're using a bag to +make it and so if you're leaving It + + align:start position:0% +make it and so if you're leaving It + + + align:start position:0% +make it and so if you're leaving It +Outdoors like right next to your gas + + align:start position:0% +Outdoors like right next to your gas + + + align:start position:0% +Outdoors like right next to your gas +your bio gas digestor maybe it's uh more + + align:start position:0% +your bio gas digestor maybe it's uh more + + + align:start position:0% +your bio gas digestor maybe it's uh more +likely to get damaged and if you're + + align:start position:0% +likely to get damaged and if you're + + + align:start position:0% +likely to get damaged and if you're +putting this inside your house or + + align:start position:0% +putting this inside your house or + + + align:start position:0% +putting this inside your house or +something like that or in like a more + + align:start position:0% +something like that or in like a more + + + align:start position:0% +something like that or in like a more +protected area that would make it easier + + align:start position:0% + + + + align:start position:0% + +uh but + + align:start position:0% + + + + align:start position:0% + +yeah if you have a + + align:start position:0% +yeah if you have a + + + align:start position:0% +yeah if you have a +so Victor is actually like really + + align:start position:0% +so Victor is actually like really + + + align:start position:0% +so Victor is actually like really +experienced with biogas digesters so if + + align:start position:0% +experienced with biogas digesters so if + + + align:start position:0% +experienced with biogas digesters so if +we have more questions we can have him + + align:start position:0% +we have more questions we can have him + + + align:start position:0% +we have more questions we can have him +come in and talk a little bit about it + + align:start position:0% +come in and talk a little bit about it + + + align:start position:0% +come in and talk a little bit about it +if we have time um and if you guys are + + align:start position:0% +if we have time um and if you guys are + + + align:start position:0% +if we have time um and if you guys are +doing a biogas project for uh for your + + align:start position:0% +doing a biogas project for uh for your + + + align:start position:0% +doing a biogas project for uh for your +specific projects or related to it then + + align:start position:0% +specific projects or related to it then + + + align:start position:0% +specific projects or related to it then +you can also you should also talk to + + align:start position:0% +you can also you should also talk to + + + align:start position:0% +you can also you should also talk to +Victor about it to get more + + align:start position:0% +Victor about it to get more + + + align:start position:0% +Victor about it to get more +information and I'm trying to give you + + align:start position:0% +information and I'm trying to give you + + + align:start position:0% +information and I'm trying to give you +more of a general idea of how they work + + align:start position:0% +more of a general idea of how they work + + + align:start position:0% +more of a general idea of how they work +and what things to take into + + align:start position:0% +and what things to take into + + + align:start position:0% +and what things to take into +consideration when building one or + + align:start position:0% +consideration when building one or + + + align:start position:0% +consideration when building one or +looking it + + align:start position:0% +looking it + + + align:start position:0% +looking it +uh an existing design and not I mean + + align:start position:0% +uh an existing design and not I mean + + + align:start position:0% +uh an existing design and not I mean +yeah more so than like a very in-depth + + align:start position:0% +yeah more so than like a very in-depth + + + align:start position:0% +yeah more so than like a very in-depth +thing + + align:start position:0% +thing + + + align:start position:0% +thing +because um there are people in dlab who + + align:start position:0% +because um there are people in dlab who + + + align:start position:0% +because um there are people in dlab who +know a lot more about biogas digesters + + align:start position:0% +know a lot more about biogas digesters + + + align:start position:0% +know a lot more about biogas digesters +than I + + align:start position:0% + + + + align:start position:0% + +do + + align:start position:0% +do + + + align:start position:0% +do +um so I guess if there are no other + + align:start position:0% +um so I guess if there are no other + + + align:start position:0% +um so I guess if there are no other +questions uh before we go down I'm going + + align:start position:0% +questions uh before we go down I'm going + + + align:start position:0% +questions uh before we go down I'm going +to go through the muddy card questions + + align:start position:0% +to go through the muddy card questions + + + align:start position:0% +to go through the muddy card questions +from last week's lab most of the + + align:start position:0% +from last week's lab most of the + + + align:start position:0% +from last week's lab most of the +questions were all about the guts of how + + align:start position:0% +questions were all about the guts of how + + + align:start position:0% +questions were all about the guts of how +a PV + + align:start position:0% +a PV + + + align:start position:0% +a PV +panel works and photo voltaics work + + align:start position:0% +panel works and photo voltaics work + + + align:start position:0% +panel works and photo voltaics work +um yeah we're going to we're going to do + + align:start position:0% +um yeah we're going to we're going to do + + + align:start position:0% +um yeah we're going to we're going to do +a solar cell lab next week and the point + + align:start position:0% +a solar cell lab next week and the point + + + align:start position:0% +a solar cell lab next week and the point +like the first half of that is just + + align:start position:0% +like the first half of that is just + + + align:start position:0% +like the first half of that is just +going to be talking to you about how PV + + align:start position:0% +going to be talking to you about how PV + + + align:start position:0% +going to be talking to you about how PV +systems work so you guys can wait + + align:start position:0% +systems work so you guys can wait + + + align:start position:0% +systems work so you guys can wait +another week for that then you'll have + + align:start position:0% +another week for that then you'll have + + + align:start position:0% +another week for that then you'll have +it presented to you and then one person + + align:start position:0% +it presented to you and then one person + + + align:start position:0% +it presented to you and then one person +asked about why you shouldn't spot weld + + align:start position:0% +asked about why you shouldn't spot weld + + + align:start position:0% +asked about why you shouldn't spot weld +galvanized steel um and when anything's + + align:start position:0% +galvanized steel um and when anything's + + + align:start position:0% +galvanized steel um and when anything's +galvanized what you're doing is you're + + align:start position:0% +galvanized what you're doing is you're + + + align:start position:0% +galvanized what you're doing is you're +coding it with zinc so that it doesn't + + align:start position:0% +coding it with zinc so that it doesn't + + + align:start position:0% +coding it with zinc so that it doesn't +um um it doesn't rust and when you try + + align:start position:0% +um um it doesn't rust and when you try + + + align:start position:0% +um um it doesn't rust and when you try +to weld anything with zinc coatings on + + align:start position:0% +to weld anything with zinc coatings on + + + align:start position:0% +to weld anything with zinc coatings on +it the you vaporize the zinc coating and + + align:start position:0% +it the you vaporize the zinc coating and + + + align:start position:0% +it the you vaporize the zinc coating and +it's pretty toxic to you so if you're + + align:start position:0% +it's pretty toxic to you so if you're + + + align:start position:0% +it's pretty toxic to you so if you're +doing it in a really well ventilated + + align:start position:0% +doing it in a really well ventilated + + + align:start position:0% +doing it in a really well ventilated +area or you're doing it Outdoors it's + + align:start position:0% +area or you're doing it Outdoors it's + + + align:start position:0% +area or you're doing it Outdoors it's +not a big deal but if you're doing it + + align:start position:0% +not a big deal but if you're doing it + + + align:start position:0% +not a big deal but if you're doing it +indoors it's toxic so you want to make + + align:start position:0% +indoors it's toxic so you want to make + + + align:start position:0% +indoors it's toxic so you want to make +sure you avoid welding galvanized + + align:start position:0% + + + + align:start position:0% + +materials um so now what we're going to + + align:start position:0% +materials um so now what we're going to + + + align:start position:0% +materials um so now what we're going to +do is we're going to break up + + align:start position:0% +do is we're going to break up + + + align:start position:0% +do is we're going to break up +into two groups um um well first off + + align:start position:0% +into two groups um um well first off + + + align:start position:0% +into two groups um um well first off +we're going to be doing we're going to + + align:start position:0% +we're going to be doing we're going to + + + align:start position:0% +we're going to be doing we're going to +be building five biogas digestors little + + align:start position:0% +be building five biogas digestors little + + + align:start position:0% +be building five biogas digestors little +modules so you should group up into + + align:start position:0% +modules so you should group up into + + + align:start position:0% +modules so you should group up into +groups + + align:start position:0% + + + + align:start position:0% + +of three no two or three uh until we get + + align:start position:0% +of three no two or three uh until we get + + + align:start position:0% +of three no two or three uh until we get +five of them + + align:start position:0% +five of them + + + align:start position:0% +five of them +since yeah so let's let's break actually + + align:start position:0% +since yeah so let's let's break actually + + + align:start position:0% +since yeah so let's let's break actually +let's just do two let's do four biogas + + align:start position:0% +let's just do two let's do four biogas + + + align:start position:0% +let's just do two let's do four biogas +digestor things today uh so we'll break + + align:start position:0% +digestor things today uh so we'll break + + + align:start position:0% +digestor things today uh so we'll break +up into groups of threes and four and um + + align:start position:0% +up into groups of threes and four and um + + + align:start position:0% +up into groups of threes and four and um +and then two of those groups are going + + align:start position:0% +and then two of those groups are going + + + align:start position:0% +and then two of those groups are going +to go with Becca and she's going to + + align:start position:0% +to go with Becca and she's going to + + + align:start position:0% +to go with Becca and she's going to +teach you about plastic ceiling and how + + align:start position:0% +teach you about plastic ceiling and how + + + align:start position:0% +teach you about plastic ceiling and how +to make biogas slurry from or biogas + + align:start position:0% +to make biogas slurry from or biogas + + + align:start position:0% +to make biogas slurry from or biogas +digestor slurry from manure and water + + align:start position:0% +digestor slurry from manure and water + + + align:start position:0% +digestor slurry from manure and water +and the other group is going to go with + + align:start position:0% +and the other group is going to go with + + + align:start position:0% +and the other group is going to go with +me and I'll we'll I'll walk you through + + align:start position:0% +me and I'll we'll I'll walk you through + + + align:start position:0% +me and I'll we'll I'll walk you through +building the like cutting the wood and + + align:start position:0% +building the like cutting the wood and + + + align:start position:0% +building the like cutting the wood and +putting it together to build the biogas + + align:start position:0% +putting it together to build the biogas + + + align:start position:0% +putting it together to build the biogas +digestor \ No newline at end of file diff --git a/aAlR3cezPJg.txt b/aAlR3cezPJg.txt new file mode 100644 index 0000000000000000000000000000000000000000..a61652da5f7978aa7add2d89826b0b988f27e78f --- /dev/null +++ b/aAlR3cezPJg.txt @@ -0,0 +1,11299 @@ +align:start position:0% + +well today we're going to learn about + + align:start position:0% +well today we're going to learn about + + + align:start position:0% +well today we're going to learn about +something quite amazing we're going to + + align:start position:0% +something quite amazing we're going to + + + align:start position:0% +something quite amazing we're going to +sort of understand what we mean by a + + align:start position:0% +sort of understand what we mean by a + + + align:start position:0% +sort of understand what we mean by a +program a little bit more profoundly + + align:start position:0% +program a little bit more profoundly + + + align:start position:0% +program a little bit more profoundly +than we have up till now up till now + + align:start position:0% +than we have up till now up till now + + + align:start position:0% +than we have up till now up till now +we've been thinking of programs as + + align:start position:0% +we've been thinking of programs as + + + align:start position:0% +we've been thinking of programs as +describing machines so for example + + align:start position:0% +describing machines so for example + + + align:start position:0% +describing machines so for example +looking at this this still store what we + + align:start position:0% +looking at this this still store what we + + + align:start position:0% +looking at this this still store what we +see here is a program for factorial and + + align:start position:0% +see here is a program for factorial and + + + align:start position:0% +see here is a program for factorial and +what it is is a character string + + align:start position:0% +what it is is a character string + + + align:start position:0% +what it is is a character string +description if you will of a wiring + + align:start position:0% +description if you will of a wiring + + + align:start position:0% +description if you will of a wiring +diagram of a potentially infinite + + align:start position:0% +diagram of a potentially infinite + + + align:start position:0% +diagram of a potentially infinite +machine and we can look at that a little + + align:start position:0% +machine and we can look at that a little + + + align:start position:0% +machine and we can look at that a little +bit and just see the idea that this is a + + align:start position:0% +bit and just see the idea that this is a + + + align:start position:0% +bit and just see the idea that this is a +sort of compact notation which says if n + + align:start position:0% +sort of compact notation which says if n + + + align:start position:0% +sort of compact notation which says if n +is 0 the result is 1 well here comes n + + align:start position:0% +is 0 the result is 1 well here comes n + + + align:start position:0% +is 0 the result is 1 well here comes n +coming into this machine and if it's 0 + + align:start position:0% +coming into this machine and if it's 0 + + + align:start position:0% +coming into this machine and if it's 0 +then I control this switch in such a way + + align:start position:0% +then I control this switch in such a way + + + align:start position:0% +then I control this switch in such a way +that the switch allows the output to be + + align:start position:0% +that the switch allows the output to be + + + align:start position:0% +that the switch allows the output to be +1 otherwise it's n times factorial of n + + align:start position:0% +1 otherwise it's n times factorial of n + + + align:start position:0% +1 otherwise it's n times factorial of n +minus 1 well I'm computing factorial of + + align:start position:0% +minus 1 well I'm computing factorial of + + + align:start position:0% +minus 1 well I'm computing factorial of +n minus 1 and multiplying that by n and + + align:start position:0% +n minus 1 and multiplying that by n and + + + align:start position:0% +n minus 1 and multiplying that by n and +in the case that it's not 0 the switch + + align:start position:0% +in the case that it's not 0 the switch + + + align:start position:0% +in the case that it's not 0 the switch +makes the output come from there of + + align:start position:0% +makes the output come from there of + + + align:start position:0% +makes the output come from there of +course this is a machine with a + + align:start position:0% +course this is a machine with a + + + align:start position:0% +course this is a machine with a +potentially infinite number of parts + + align:start position:0% +potentially infinite number of parts + + + align:start position:0% +potentially infinite number of parts +because factorial occurs within + + align:start position:0% +because factorial occurs within + + + align:start position:0% +because factorial occurs within +factorial so we don't know how deep it + + align:start position:0% +factorial so we don't know how deep it + + + align:start position:0% +factorial so we don't know how deep it +has to be but that's basically what our + + align:start position:0% +has to be but that's basically what our + + + align:start position:0% +has to be but that's basically what our +notation for programs really means to us + + align:start position:0% +notation for programs really means to us + + + align:start position:0% +notation for programs really means to us +at this point it's a character string + + align:start position:0% +at this point it's a character string + + + align:start position:0% +at this point it's a character string +description if you will of a wiring + + align:start position:0% +description if you will of a wiring + + + align:start position:0% +description if you will of a wiring +diagram that could be also drawn some + + align:start position:0% +diagram that could be also drawn some + + + align:start position:0% +diagram that could be also drawn some +other way and in fact many people are + + align:start position:0% +other way and in fact many people are + + + align:start position:0% +other way and in fact many people are +proposed to make programming languages + + align:start position:0% +proposed to make programming languages + + + align:start position:0% +proposed to make programming languages +look graphical like this I'm not sure I + + align:start position:0% +look graphical like this I'm not sure I + + + align:start position:0% +look graphical like this I'm not sure I +believe that there are many advantages + + align:start position:0% +believe that there are many advantages + + + align:start position:0% +believe that there are many advantages +the major disadvantage of course is that + + align:start position:0% +the major disadvantage of course is that + + + align:start position:0% +the major disadvantage of course is that +it takes up more space on a page and + + align:start position:0% +it takes up more space on a page and + + + align:start position:0% +it takes up more space on a page and +therefore it's harder to pack into a + + align:start position:0% +therefore it's harder to pack into a + + + align:start position:0% +therefore it's harder to pack into a +listing or to edit very well but in any + + align:start position:0% +listing or to edit very well but in any + + + align:start position:0% +listing or to edit very well but in any +case you know there's something very + + align:start position:0% +case you know there's something very + + + align:start position:0% +case you know there's something very +remarkable that can happen in the + + align:start position:0% +remarkable that can happen in the + + + align:start position:0% +remarkable that can happen in the +computation world which is that you can + + align:start position:0% +computation world which is that you can + + + align:start position:0% +computation world which is that you can +have something called a universal + + align:start position:0% +have something called a universal + + + align:start position:0% +have something called a universal +machine if we look at the second slide + + align:start position:0% +machine if we look at the second slide + + + align:start position:0% +machine if we look at the second slide +what we see is a special machine called + + align:start position:0% +what we see is a special machine called + + + align:start position:0% +what we see is a special machine called +eval there is a machine called eval and + + align:start position:0% +eval there is a machine called eval and + + + align:start position:0% +eval there is a machine called eval and +I'm going to show it to you today + + align:start position:0% +I'm going to show it to you today + + + align:start position:0% +I'm going to show it to you today +it's very simple + + align:start position:0% +it's very simple + + + align:start position:0% +it's very simple +is remarkable is that it will fit on the + + align:start position:0% +is remarkable is that it will fit on the + + + align:start position:0% +is remarkable is that it will fit on the +blackboard however eval if the machine + + align:start position:0% +blackboard however eval if the machine + + + align:start position:0% +blackboard however eval if the machine +which takes as input a description of + + align:start position:0% +which takes as input a description of + + + align:start position:0% +which takes as input a description of +another machine it could take the wiring + + align:start position:0% +another machine it could take the wiring + + + align:start position:0% +another machine it could take the wiring +diagram of the factorial machine as + + align:start position:0% +diagram of the factorial machine as + + + align:start position:0% +diagram of the factorial machine as +input having done so it becomes a + + align:start position:0% +input having done so it becomes a + + + align:start position:0% +input having done so it becomes a +simulator for the factorial machine such + + align:start position:0% +simulator for the factorial machine such + + + align:start position:0% +simulator for the factorial machine such +that if you put a 6 in out comes a 720 + + align:start position:0% +that if you put a 6 in out comes a 720 + + + align:start position:0% +that if you put a 6 in out comes a 720 +that's a very remarkable sort of machine + + align:start position:0% +that's a very remarkable sort of machine + + + align:start position:0% +that's a very remarkable sort of machine +and the most amazing part of it is that + + align:start position:0% +and the most amazing part of it is that + + + align:start position:0% +and the most amazing part of it is that +it fits on a blackboard by contrast one + + align:start position:0% +it fits on a blackboard by contrast one + + + align:start position:0% +it fits on a blackboard by contrast one +could imagine in the analog electronics + + align:start position:0% +could imagine in the analog electronics + + + align:start position:0% +could imagine in the analog electronics +world a very different machine a machine + + align:start position:0% +world a very different machine a machine + + + align:start position:0% +world a very different machine a machine +where a machine which also was in some + + align:start position:0% +where a machine which also was in some + + + align:start position:0% +where a machine which also was in some +sense Universal where you gave a circuit + + align:start position:0% +sense Universal where you gave a circuit + + + align:start position:0% +sense Universal where you gave a circuit +diagram as one of the inputs for example + + align:start position:0% +diagram as one of the inputs for example + + + align:start position:0% +diagram as one of the inputs for example +of this little low-pass filter one pole + + align:start position:0% +of this little low-pass filter one pole + + + align:start position:0% +of this little low-pass filter one pole +low-pass filter and you could imagine + + align:start position:0% +low-pass filter and you could imagine + + + align:start position:0% +low-pass filter and you could imagine +that you could for example scan this out + + align:start position:0% +that you could for example scan this out + + + align:start position:0% +that you could for example scan this out +the scan lines right are the signal that + + align:start position:0% +the scan lines right are the signal that + + + align:start position:0% +the scan lines right are the signal that +the score that's describing what this + + align:start position:0% +the score that's describing what this + + + align:start position:0% +the score that's describing what this +machine is to simulate then the analog + + align:start position:0% +machine is to simulate then the analog + + + align:start position:0% +machine is to simulate then the analog +eval which is made out of electrical + + align:start position:0% +eval which is made out of electrical + + + align:start position:0% +eval which is made out of electrical +circuits should configure itself into a + + align:start position:0% +circuits should configure itself into a + + + align:start position:0% +circuits should configure itself into a +filter that has the frequency response + + align:start position:0% +filter that has the frequency response + + + align:start position:0% +filter that has the frequency response +specified by the circuit diagram that's + + align:start position:0% +specified by the circuit diagram that's + + + align:start position:0% +specified by the circuit diagram that's +a very hard machine to make and surely + + align:start position:0% +a very hard machine to make and surely + + + align:start position:0% +a very hard machine to make and surely +there's no chance that I could put it on + + align:start position:0% +there's no chance that I could put it on + + + align:start position:0% +there's no chance that I could put it on +a black board so we're gonna see an + + align:start position:0% +a black board so we're gonna see an + + + align:start position:0% +a black board so we're gonna see an +amazing thing today we're going to see + + align:start position:0% +amazing thing today we're going to see + + + align:start position:0% +amazing thing today we're going to see +on the blackboard the universal machine + + align:start position:0% +on the blackboard the universal machine + + + align:start position:0% +on the blackboard the universal machine +I don't see it wrong other things it's + + align:start position:0% +I don't see it wrong other things it's + + + align:start position:0% +I don't see it wrong other things it's +extremely simple now we're getting very + + align:start position:0% +extremely simple now we're getting very + + + align:start position:0% +extremely simple now we're getting very +close to the real spirit in the computer + + align:start position:0% +close to the real spirit in the computer + + + align:start position:0% +close to the real spirit in the computer +at this point so I have to show a + + align:start position:0% +at this point so I have to show a + + + align:start position:0% +at this point so I have to show a +certain amount of reverence and respect + + align:start position:0% +certain amount of reverence and respect + + + align:start position:0% +certain amount of reverence and respect +so I'm going to wear a suit jacket for + + align:start position:0% +so I'm going to wear a suit jacket for + + + align:start position:0% +so I'm going to wear a suit jacket for +the only time you'll ever see me wear a + + align:start position:0% +the only time you'll ever see me wear a + + + align:start position:0% +the only time you'll ever see me wear a +suit jacket here okay and I think I'm + + align:start position:0% +suit jacket here okay and I think I'm + + + align:start position:0% +suit jacket here okay and I think I'm +also going to put on an appropriate hat + + align:start position:0% +also going to put on an appropriate hat + + + align:start position:0% +also going to put on an appropriate hat +for the occasion okay now this is a + + align:start position:0% +for the occasion okay now this is a + + + align:start position:0% +for the occasion okay now this is a +lecture which I have to warn you + + align:start position:0% + + + + align:start position:0% + +let's see normally people under 40 and + + align:start position:0% +let's see normally people under 40 and + + + align:start position:0% +let's see normally people under 40 and +who don't have several children are + + align:start position:0% +who don't have several children are + + + align:start position:0% +who don't have several children are +advised to be careful if they're really + + align:start position:0% +advised to be careful if they're really + + + align:start position:0% +advised to be careful if they're really +worried they should + + align:start position:0% +worried they should + + + align:start position:0% +worried they should +because there's a certain amount of + + align:start position:0% +because there's a certain amount of + + + align:start position:0% +because there's a certain amount of +mysticism that will appear here which + + align:start position:0% +mysticism that will appear here which + + + align:start position:0% +mysticism that will appear here which +may be disturbing and cause trouble in + + align:start position:0% +may be disturbing and cause trouble in + + + align:start position:0% +may be disturbing and cause trouble in +your minds well in any case let's say I + + align:start position:0% +your minds well in any case let's say I + + + align:start position:0% +your minds well in any case let's say I +wish to write for you the evaluator for + + align:start position:0% +wish to write for you the evaluator for + + + align:start position:0% +wish to write for you the evaluator for +for Lisp now the evaluator isn't very + + align:start position:0% +for Lisp now the evaluator isn't very + + + align:start position:0% +for Lisp now the evaluator isn't very +complicated it's very much like all the + + align:start position:0% +complicated it's very much like all the + + + align:start position:0% +complicated it's very much like all the +programs we've seen already that's the + + align:start position:0% +programs we've seen already that's the + + + align:start position:0% +programs we've seen already that's the +amazing part of it it's going to be I'm + + align:start position:0% +amazing part of it it's going to be I'm + + + align:start position:0% +amazing part of it it's going to be I'm +gonna write it right here it's a program + + align:start position:0% +gonna write it right here it's a program + + + align:start position:0% +gonna write it right here it's a program +called eval and it's a procedure of two + + align:start position:0% +called eval and it's a procedure of two + + + align:start position:0% +called eval and it's a procedure of two +arguments an expression and an + + align:start position:0% +arguments an expression and an + + + align:start position:0% +arguments an expression and an +environment and like every interesting + + align:start position:0% +environment and like every interesting + + + align:start position:0% +environment and like every interesting +procedure it's a case analysis but + + align:start position:0% +procedure it's a case analysis but + + + align:start position:0% +procedure it's a case analysis but +before I start on this I want to tell + + align:start position:0% +before I start on this I want to tell + + + align:start position:0% +before I start on this I want to tell +you some things the program I'm gonna + + align:start position:0% +you some things the program I'm gonna + + + align:start position:0% +you some things the program I'm gonna +write on the blackboard is ugly dirty + + align:start position:0% +write on the blackboard is ugly dirty + + + align:start position:0% +write on the blackboard is ugly dirty +disgusting not the way I would write + + align:start position:0% +disgusting not the way I would write + + + align:start position:0% +disgusting not the way I would write +this as a professional okay it is + + align:start position:0% +this as a professional okay it is + + + align:start position:0% +this as a professional okay it is +written with concrete syntax meaning I'm + + align:start position:0% +written with concrete syntax meaning I'm + + + align:start position:0% +written with concrete syntax meaning I'm +going to use lots of cars and critters + + align:start position:0% +going to use lots of cars and critters + + + align:start position:0% +going to use lots of cars and critters +which is exactly what I told you not to + + align:start position:0% +which is exactly what I told you not to + + + align:start position:0% +which is exactly what I told you not to +do that's on purpose in this case + + align:start position:0% +do that's on purpose in this case + + + align:start position:0% +do that's on purpose in this case +because I want it to be small compact + + align:start position:0% +because I want it to be small compact + + + align:start position:0% +because I want it to be small compact +fit on the blackboard so you can get the + + align:start position:0% +fit on the blackboard so you can get the + + + align:start position:0% +fit on the blackboard so you can get the +whole thing so I don't want to use long + + align:start position:0% +whole thing so I don't want to use long + + + align:start position:0% +whole thing so I don't want to use long +names like I'd normally use okay I want + + align:start position:0% +names like I'd normally use okay I want + + + align:start position:0% +names like I'd normally use okay I want +to use call cooter because it's short + + align:start position:0% +to use call cooter because it's short + + + align:start position:0% +to use call cooter because it's short +okay I want to there's a hole but that's + + align:start position:0% +okay I want to there's a hole but that's + + + align:start position:0% +okay I want to there's a hole but that's +a trade-off I don't want you writing + + align:start position:0% +a trade-off I don't want you writing + + + align:start position:0% +a trade-off I don't want you writing +programs like this this is purely for an + + align:start position:0% +programs like this this is purely for an + + + align:start position:0% +programs like this this is purely for an +effect okay now you're gonna have to + + align:start position:0% +effect okay now you're gonna have to + + + align:start position:0% +effect okay now you're gonna have to +work a little harder to read it but I'm + + align:start position:0% +work a little harder to read it but I'm + + + align:start position:0% +work a little harder to read it but I'm +gonna try to make it clear as I'm + + align:start position:0% +gonna try to make it clear as I'm + + + align:start position:0% +gonna try to make it clear as I'm +writing it I'm also this is a pretty + + align:start position:0% +writing it I'm also this is a pretty + + + align:start position:0% +writing it I'm also this is a pretty +much complete interpreter but there's + + align:start position:0% +much complete interpreter but there's + + + align:start position:0% +much complete interpreter but there's +gonna be room for putting in more things + + align:start position:0% +gonna be room for putting in more things + + + align:start position:0% +gonna be room for putting in more things +I'm gonna leave out definition and + + align:start position:0% +I'm gonna leave out definition and + + + align:start position:0% +I'm gonna leave out definition and +assignment just because they're + + align:start position:0% +assignment just because they're + + + align:start position:0% +assignment just because they're +essentially they're not essential at a + + align:start position:0% +essentially they're not essential at a + + + align:start position:0% +essentially they're not essential at a +and a math for a mathematical reason + + align:start position:0% +and a math for a mathematical reason + + + align:start position:0% +and a math for a mathematical reason +that I'll show you later and also there + + align:start position:0% +that I'll show you later and also there + + + align:start position:0% +that I'll show you later and also there +they take up more space but in any case + + align:start position:0% +they take up more space but in any case + + + align:start position:0% +they take up more space but in any case +what do we have to do what we have to do + + align:start position:0% +what do we have to do what we have to do + + + align:start position:0% +what do we have to do what we have to do +a + + align:start position:0% +a + + + align:start position:0% +a +dispatch which breaks the types of + + align:start position:0% +dispatch which breaks the types of + + + align:start position:0% +dispatch which breaks the types of +expressions up into particular classes + + align:start position:0% +expressions up into particular classes + + + align:start position:0% +expressions up into particular classes +mmm so that's what we're going to have + + align:start position:0% +mmm so that's what we're going to have + + + align:start position:0% +mmm so that's what we're going to have +here + + align:start position:0% +here + + + align:start position:0% +here +well what expressions are there let's + + align:start position:0% +well what expressions are there let's + + + align:start position:0% +well what expressions are there let's +look at the kinds of expressions we can + + align:start position:0% +look at the kinds of expressions we can + + + align:start position:0% +look at the kinds of expressions we can +have things like then the numeral 3 what + + align:start position:0% +have things like then the numeral 3 what + + + align:start position:0% +have things like then the numeral 3 what +I want that to do I can make choices but + + align:start position:0% +I want that to do I can make choices but + + + align:start position:0% +I want that to do I can make choices but +I think right now I want it to be a 3 + + align:start position:0% +I think right now I want it to be a 3 + + + align:start position:0% +I think right now I want it to be a 3 +that's what I want that's easy enough + + align:start position:0% +that's what I want that's easy enough + + + align:start position:0% +that's what I want that's easy enough +that means I want if the thing is a + + align:start position:0% +that means I want if the thing is a + + + align:start position:0% +that means I want if the thing is a +number the expression then I want the + + align:start position:0% +number the expression then I want the + + + align:start position:0% +number the expression then I want the +expression itself as the answer okay now + + align:start position:0% +expression itself as the answer okay now + + + align:start position:0% +expression itself as the answer okay now +the next possibility is things that we + + align:start position:0% +the next possibility is things that we + + + align:start position:0% +the next possibility is things that we +represent as symbols examples of symbols + + align:start position:0% +represent as symbols examples of symbols + + + align:start position:0% +represent as symbols examples of symbols +are things like X and eval number X what + + align:start position:0% +are things like X and eval number X what + + + align:start position:0% +are things like X and eval number X what +do I mean them to be those are things + + align:start position:0% +do I mean them to be those are things + + + align:start position:0% +do I mean them to be those are things +that stand for other things those are + + align:start position:0% +that stand for other things those are + + + align:start position:0% +that stand for other things those are +the variables of our language okay so I + + align:start position:0% +the variables of our language okay so I + + + align:start position:0% +the variables of our language okay so I +want to be able to say for example that + + align:start position:0% +want to be able to say for example that + + + align:start position:0% +want to be able to say for example that +X for example transforms to its value + + align:start position:0% +X for example transforms to its value + + + align:start position:0% +X for example transforms to its value +which might be 3 anywhere I might ask + + align:start position:0% +which might be 3 anywhere I might ask + + + align:start position:0% +which might be 3 anywhere I might ask +something like like car I want to have + + align:start position:0% +something like like car I want to have + + + align:start position:0% +something like like car I want to have +as its value be something like some + + align:start position:0% +as its value be something like some + + + align:start position:0% +as its value be something like some +procedure I don't know what it is inside + + align:start position:0% +procedure I don't know what it is inside + + + align:start position:0% +procedure I don't know what it is inside +there perhaps some machine language code + + align:start position:0% +there perhaps some machine language code + + + align:start position:0% +there perhaps some machine language code +or something like that ok so well that's + + align:start position:0% +or something like that ok so well that's + + + align:start position:0% +or something like that ok so well that's +easy enough I'm gonna push that off I'm + + align:start position:0% +easy enough I'm gonna push that off I'm + + + align:start position:0% +easy enough I'm gonna push that off I'm +on someone else if something's a symbol + + align:start position:0% +on someone else if something's a symbol + + + align:start position:0% +on someone else if something's a symbol +if the expression is a symbol then I + + align:start position:0% +if the expression is a symbol then I + + + align:start position:0% +if the expression is a symbol then I +want the answer to be the result of + + align:start position:0% +want the answer to be the result of + + + align:start position:0% +want the answer to be the result of +looking up the expression in the + + align:start position:0% +looking up the expression in the + + + align:start position:0% +looking up the expression in the +environment + + align:start position:0% + + + + align:start position:0% + +now the environment is a dictionary + + align:start position:0% +now the environment is a dictionary + + + align:start position:0% +now the environment is a dictionary +which maps the symbol names to their + + align:start position:0% +which maps the symbol names to their + + + align:start position:0% +which maps the symbol names to their +values and that's all it is how it's + + align:start position:0% +values and that's all it is how it's + + + align:start position:0% +values and that's all it is how it's +done well we'll see that later it's very + + align:start position:0% +done well we'll see that later it's very + + + align:start position:0% +done well we'll see that later it's very +easy it's easy to make data structures + + align:start position:0% +easy it's easy to make data structures + + + align:start position:0% +easy it's easy to make data structures +of their tables of various sorts but + + align:start position:0% +of their tables of various sorts but + + + align:start position:0% +of their tables of various sorts but +it's only a table and this is the access + + align:start position:0% +it's only a table and this is the access + + + align:start position:0% +it's only a table and this is the access +routine for some table okay well the + + align:start position:0% +routine for some table okay well the + + + align:start position:0% +routine for some table okay well the +next thing another kind of expression + + align:start position:0% +next thing another kind of expression + + + align:start position:0% +next thing another kind of expression +you have things that are described + + align:start position:0% +you have things that are described + + + align:start position:0% +you have things that are described +constants that are not numbers like boom + + align:start position:0% +constants that are not numbers like boom + + + align:start position:0% +constants that are not numbers like boom +well for my convenience I want to send + + align:start position:0% +well for my convenience I want to send + + + align:start position:0% +well for my convenience I want to send +tactically transform that into a list + + align:start position:0% +tactically transform that into a list + + + align:start position:0% +tactically transform that into a list +structure which is quote boom or it's a + + align:start position:0% +structure which is quote boom or it's a + + + align:start position:0% +structure which is quote boom or it's a +coded sent a quoted object whatever it + + align:start position:0% +coded sent a quoted object whatever it + + + align:start position:0% +coded sent a quoted object whatever it +is is going to be actually an + + align:start position:0% +is is going to be actually an + + + align:start position:0% +is is going to be actually an +abbreviation which is not part of the + + align:start position:0% +abbreviation which is not part of the + + + align:start position:0% +abbreviation which is not part of the +evaluator okay what happens somewhere + + align:start position:0% +evaluator okay what happens somewhere + + + align:start position:0% +evaluator okay what happens somewhere +else + + align:start position:0% +else + + + align:start position:0% +else +an abbreviation for an expression that + + align:start position:0% +an abbreviation for an expression that + + + align:start position:0% +an abbreviation for an expression that +looks like this this way I can test for + + align:start position:0% +looks like this this way I can test for + + + align:start position:0% +looks like this this way I can test for +the type of the expression as being a + + align:start position:0% +the type of the expression as being a + + + align:start position:0% +the type of the expression as being a +quotation by examining the car of the + + align:start position:0% +quotation by examining the car of the + + + align:start position:0% +quotation by examining the car of the +expression okay so I'm not going to + + align:start position:0% +expression okay so I'm not going to + + + align:start position:0% +expression okay so I'm not going to +worry about that in the evaluator that's + + align:start position:0% +worry about that in the evaluator that's + + + align:start position:0% +worry about that in the evaluator that's +happening somewhere earlier in the + + align:start position:0% +happening somewhere earlier in the + + + align:start position:0% +happening somewhere earlier in the +reader or something if the expression of + + align:start position:0% +reader or something if the expression of + + + align:start position:0% +reader or something if the expression of +the expression is quote and what I want + + align:start position:0% +the expression is quote and what I want + + + align:start position:0% +the expression is quote and what I want +I want the I want code foo to itself the + + align:start position:0% +I want the I want code foo to itself the + + + align:start position:0% +I want the I want code foo to itself the +value a to foo it's a constant this is + + align:start position:0% +value a to foo it's a constant this is + + + align:start position:0% +value a to foo it's a constant this is +just a way of saying that this evaluates + + align:start position:0% +just a way of saying that this evaluates + + + align:start position:0% +just a way of saying that this evaluates +to itself okay so that's the what is + + align:start position:0% +to itself okay so that's the what is + + + align:start position:0% +to itself okay so that's the what is +that that's the first of the second of + + align:start position:0% +that that's the first of the second of + + + align:start position:0% +that that's the first of the second of +the list it's the second element the + + align:start position:0% +the list it's the second element the + + + align:start position:0% +the list it's the second element the +list okay but the second element list is + + align:start position:0% +list okay but the second element list is + + + align:start position:0% +list okay but the second element list is +it scatter so I'm just going right here + + align:start position:0% +it scatter so I'm just going right here + + + align:start position:0% +it scatter so I'm just going right here +quatre + + align:start position:0% + + + + align:start position:0% + +okay what else do we have here we have + + align:start position:0% +okay what else do we have here we have + + + align:start position:0% +okay what else do we have here we have +lambda expressions for example lambda of + + align:start position:0% +lambda expressions for example lambda of + + + align:start position:0% +lambda expressions for example lambda of +X lambda X plus XY well I'm going to + + align:start position:0% +X lambda X plus XY well I'm going to + + + align:start position:0% +X lambda X plus XY well I'm going to +have to have some representation for the + + align:start position:0% +have to have some representation for the + + + align:start position:0% +have to have some representation for the +procedure which is the value of an + + align:start position:0% +procedure which is the value of an + + + align:start position:0% +procedure which is the value of an +expression of a lambda expression the + + align:start position:0% +expression of a lambda expression the + + + align:start position:0% +expression of a lambda expression the +procedure is not the expression lambda X + + align:start position:0% +procedure is not the expression lambda X + + + align:start position:0% +procedure is not the expression lambda X +that's the description of it the textual + + align:start position:0% +that's the description of it the textual + + + align:start position:0% +that's the description of it the textual +description however what I'm going to + + align:start position:0% +description however what I'm going to + + + align:start position:0% +description however what I'm going to +expect to see here is something which + + align:start position:0% +expect to see here is something which + + + align:start position:0% +expect to see here is something which +contains their environment is one of its + + align:start position:0% +contains their environment is one of its + + + align:start position:0% +contains their environment is one of its +parts if I'm implementing a lexical + + align:start position:0% +parts if I'm implementing a lexical + + + align:start position:0% +parts if I'm implementing a lexical +language and so and so what I'd like to + + align:start position:0% +language and so and so what I'd like to + + + align:start position:0% +language and so and so what I'd like to +see is some type flag because I'm going + + align:start position:0% +see is some type flag because I'm going + + + align:start position:0% +see is some type flag because I'm going +to have to be able to distinguish + + align:start position:0% +to have to be able to distinguish + + + align:start position:0% +to have to be able to distinguish +procedures later procedures which were + + align:start position:0% +procedures later procedures which were + + + align:start position:0% +procedures later procedures which were +produced by lambdas from ones that may + + align:start position:0% +produced by lambdas from ones that may + + + align:start position:0% +produced by lambdas from ones that may +be primitive and so I'm going to have + + align:start position:0% +be primitive and so I'm going to have + + + align:start position:0% +be primitive and so I'm going to have +some two flag which I'll just + + align:start position:0% +some two flag which I'll just + + + align:start position:0% +some two flag which I'll just +arbitrarily call closure just for + + align:start position:0% +arbitrarily call closure just for + + + align:start position:0% +arbitrarily call closure just for +historical region reasons not to say + + align:start position:0% +historical region reasons not to say + + + align:start position:0% +historical region reasons not to say +what parts of this are important I'm + + align:start position:0% +what parts of this are important I'm + + + align:start position:0% +what parts of this are important I'm +going to need to know the bound variable + + align:start position:0% +going to need to know the bound variable + + + align:start position:0% +going to need to know the bound variable +list and the body well that's the cooter + + align:start position:0% +list and the body well that's the cooter + + + align:start position:0% +list and the body well that's the cooter +of this so that's going to be X and plus + + align:start position:0% +of this so that's going to be X and plus + + + align:start position:0% +of this so that's going to be X and plus +X Y and some environment now this is not + + align:start position:0% +X Y and some environment now this is not + + + align:start position:0% +X Y and some environment now this is not +something a user should ever should ever + + align:start position:0% +something a user should ever should ever + + + align:start position:0% +something a user should ever should ever +see this is purely a representation + + align:start position:0% +see this is purely a representation + + + align:start position:0% +see this is purely a representation +internally for a for a procedure object + + align:start position:0% +internally for a for a procedure object + + + align:start position:0% +internally for a for a procedure object +it contains a bound variable list a body + + align:start position:0% +it contains a bound variable list a body + + + align:start position:0% +it contains a bound variable list a body +and an environment and some type tag + + align:start position:0% +and an environment and some type tag + + + align:start position:0% +and an environment and some type tag +saying I am a procedure I'm going to + + align:start position:0% +saying I am a procedure I'm going to + + + align:start position:0% +saying I am a procedure I'm going to +make one now so if if the car of the + + align:start position:0% +make one now so if if the car of the + + + align:start position:0% +make one now so if if the car of the +expression is quote lambda + + align:start position:0% + + + + align:start position:0% + +then what I'm going to put here is I'm + + align:start position:0% +then what I'm going to put here is I'm + + + align:start position:0% +then what I'm going to put here is I'm +gonna make a list of closure the cutter + + align:start position:0% +gonna make a list of closure the cutter + + + align:start position:0% +gonna make a list of closure the cutter +of the the cutter of the procedure + + align:start position:0% +of the the cutter of the procedure + + + align:start position:0% +of the the cutter of the procedure +description which is everything except + + align:start position:0% +description which is everything except + + + align:start position:0% +description which is everything except +the lambda and the current environment + + align:start position:0% +the lambda and the current environment + + + align:start position:0% +the lambda and the current environment +this implements the rule for + + align:start position:0% +this implements the rule for + + + align:start position:0% +this implements the rule for +environments in the environment model + + align:start position:0% +environments in the environment model + + + align:start position:0% +environments in the environment model +asked to do with construction of + + align:start position:0% +asked to do with construction of + + + align:start position:0% +asked to do with construction of +procedures from lambda expressions the + + align:start position:0% +procedures from lambda expressions the + + + align:start position:0% +procedures from lambda expressions the +environment that was around at the time + + align:start position:0% +environment that was around at the time + + + align:start position:0% +environment that was around at the time +the evaluator encountered the lambda + + align:start position:0% +the evaluator encountered the lambda + + + align:start position:0% +the evaluator encountered the lambda +expression is the as the environment + + align:start position:0% +expression is the as the environment + + + align:start position:0% +expression is the as the environment +where the lambda expression gets where + + align:start position:0% +where the lambda expression gets where + + + align:start position:0% +where the lambda expression gets where +the procedure resulting interprets its + + align:start position:0% +the procedure resulting interprets its + + + align:start position:0% +the procedure resulting interprets its +free variables so that's part of that + + align:start position:0% +free variables so that's part of that + + + align:start position:0% +free variables so that's part of that +and so we have to capture that + + align:start position:0% +and so we have to capture that + + + align:start position:0% +and so we have to capture that +environment as part of the procedure + + align:start position:0% +environment as part of the procedure + + + align:start position:0% +environment as part of the procedure +object and we'll see how that gets used + + align:start position:0% +object and we'll see how that gets used + + + align:start position:0% +object and we'll see how that gets used +later + + align:start position:0% +later + + + align:start position:0% +later +there are also conditional expressions + + align:start position:0% +there are also conditional expressions + + + align:start position:0% +there are also conditional expressions +things like cond I'll say p1 p1 p2 e to + + align:start position:0% +things like cond I'll say p1 p1 p2 e to + + + align:start position:0% +things like cond I'll say p1 p1 p2 e to +where there's a predicate and this is a + + align:start position:0% +where there's a predicate and this is a + + + align:start position:0% +where there's a predicate and this is a +predicate is the thing that's either + + align:start position:0% +predicate is the thing that's either + + + align:start position:0% +predicate is the thing that's either +true or false and an expression to be + + align:start position:0% +true or false and an expression to be + + + align:start position:0% +true or false and an expression to be +evaluated if the predicate is true a set + + align:start position:0% +evaluated if the predicate is true a set + + + align:start position:0% +evaluated if the predicate is true a set +of clauses if you will s some names such + + align:start position:0% +of clauses if you will s some names such + + + align:start position:0% +of clauses if you will s some names such +thing so I'm gonna let them put that + + align:start position:0% +thing so I'm gonna let them put that + + + align:start position:0% +thing so I'm gonna let them put that +somewhere else we're gonna worry about + + align:start position:0% +somewhere else we're gonna worry about + + + align:start position:0% +somewhere else we're gonna worry about +that in another piece of code so EQ if + + align:start position:0% +that in another piece of code so EQ if + + + align:start position:0% +that in another piece of code so EQ if +the car the expression e is cond then + + align:start position:0% +the car the expression e is cond then + + + align:start position:0% +the car the expression e is cond then +I'm going to do nothing more then + + align:start position:0% +I'm going to do nothing more then + + + align:start position:0% +I'm going to do nothing more then +evaluate the cond the critter of the + + align:start position:0% +evaluate the cond the critter of the + + + align:start position:0% +evaluate the cond the critter of the +expression + + align:start position:0% + + + + align:start position:0% + +with all the only all the clauses in the + + align:start position:0% +with all the only all the clauses in the + + + align:start position:0% +with all the only all the clauses in the +environment that I'm giving well there's + + align:start position:0% +environment that I'm giving well there's + + + align:start position:0% +environment that I'm giving well there's +one more case arbitrary thing like the + + align:start position:0% +one more case arbitrary thing like the + + + align:start position:0% +one more case arbitrary thing like the +sum of X and three where this is a an + + align:start position:0% +sum of X and three where this is a an + + + align:start position:0% +sum of X and three where this is a an +operator applied to operands and there's + + align:start position:0% +operator applied to operands and there's + + + align:start position:0% +operator applied to operands and there's +nothing special about it + + align:start position:0% +nothing special about it + + + align:start position:0% +nothing special about it +it's not one of the special cases the + + align:start position:0% +it's not one of the special cases the + + + align:start position:0% +it's not one of the special cases the +special forms these are the special + + align:start position:0% +special forms these are the special + + + align:start position:0% +special forms these are the special +forms and if I were writing here a + + align:start position:0% +forms and if I were writing here a + + + align:start position:0% +forms and if I were writing here a +professional program again I would + + align:start position:0% +professional program again I would + + + align:start position:0% +professional program again I would +somehow make this data directed so there + + align:start position:0% +somehow make this data directed so there + + + align:start position:0% +somehow make this data directed so there +wouldn't be a sequence of conditionals + + align:start position:0% +wouldn't be a sequence of conditionals + + + align:start position:0% +wouldn't be a sequence of conditionals +here there'd be a dispatch on some bits + + align:start position:0% +here there'd be a dispatch on some bits + + + align:start position:0% +here there'd be a dispatch on some bits +if I were trying to do this in work in a + + align:start position:0% +if I were trying to do this in work in a + + + align:start position:0% +if I were trying to do this in work in a +more professional way so that in fact I + + align:start position:0% +more professional way so that in fact I + + + align:start position:0% +more professional way so that in fact I +could add to the thing without changing + + align:start position:0% +could add to the thing without changing + + + align:start position:0% +could add to the thing without changing +my program much so for example the thing + + align:start position:0% +my program much so for example the thing + + + align:start position:0% +my program much so for example the thing +would run fast but I'm not worried about + + align:start position:0% +would run fast but I'm not worried about + + + align:start position:0% +would run fast but I'm not worried about +that here we're trying to look at this + + align:start position:0% +that here we're trying to look at this + + + align:start position:0% +that here we're trying to look at this +you know it's at entirety + + align:start position:0% +you know it's at entirety + + + align:start position:0% +you know it's at entirety +so that's else well what do we do in + + align:start position:0% +so that's else well what do we do in + + + align:start position:0% +so that's else well what do we do in +this case I have to somehow do an + + align:start position:0% +this case I have to somehow do an + + + align:start position:0% +this case I have to somehow do an +addition well I have to find out what + + align:start position:0% +addition well I have to find out what + + + align:start position:0% +addition well I have to find out what +the plus is and I have to find out what + + align:start position:0% +the plus is and I have to find out what + + + align:start position:0% +the plus is and I have to find out what +the X and the three are and then I have + + align:start position:0% +the X and the three are and then I have + + + align:start position:0% +the X and the three are and then I have +to apply the result of finding out what + + align:start position:0% +to apply the result of finding out what + + + align:start position:0% +to apply the result of finding out what +the pluses to the result of finding out + + align:start position:0% +the pluses to the result of finding out + + + align:start position:0% +the pluses to the result of finding out +what the X and the three are okay we'll + + align:start position:0% +what the X and the three are okay we'll + + + align:start position:0% +what the X and the three are okay we'll +have name for that so I'm going to apply + + align:start position:0% + + + + align:start position:0% + +the result of evaluating the car of the + + align:start position:0% +the result of evaluating the car of the + + + align:start position:0% +the result of evaluating the car of the +expression the car of the expression is + + align:start position:0% +expression the car of the expression is + + + align:start position:0% +expression the car of the expression is +the operator in the environment giving + + align:start position:0% +the operator in the environment giving + + + align:start position:0% +the operator in the environment giving +so evaluating the operator gets me the + + align:start position:0% +so evaluating the operator gets me the + + + align:start position:0% +so evaluating the operator gets me the +procedure and now I have to evaluate all + + align:start position:0% +procedure and now I have to evaluate all + + + align:start position:0% +procedure and now I have to evaluate all +the operands to get the arguments I'll + + align:start position:0% +the operands to get the arguments I'll + + + align:start position:0% +the operands to get the arguments I'll +call that AB list the footer that's the + + align:start position:0% +call that AB list the footer that's the + + + align:start position:0% +call that AB list the footer that's the +operands of the expression with respect + + align:start position:0% +operands of the expression with respect + + + align:start position:0% +operands of the expression with respect +to the environment + + align:start position:0% +to the environment + + + align:start position:0% +to the environment +we have list will come up later have + + align:start position:0% +we have list will come up later have + + + align:start position:0% +we have list will come up later have +list a fly con pair conned lambda define + + align:start position:0% +list a fly con pair conned lambda define + + + align:start position:0% +list a fly con pair conned lambda define +okay so that way you're seeing here now + + align:start position:0% +okay so that way you're seeing here now + + + align:start position:0% +okay so that way you're seeing here now +is pretty much all there is in the + + align:start position:0% +is pretty much all there is in the + + + align:start position:0% +is pretty much all there is in the +evaluator itself it's the case dispatch + + align:start position:0% +evaluator itself it's the case dispatch + + + align:start position:0% +evaluator itself it's the case dispatch +on the on the type of the expression + + align:start position:0% +on the on the type of the expression + + + align:start position:0% +on the on the type of the expression +with the default being a general + + align:start position:0% +with the default being a general + + + align:start position:0% +with the default being a general +application or a combination now there + + align:start position:0% +application or a combination now there + + + align:start position:0% +application or a combination now there +are lots of things we haven't defined + + align:start position:0% +are lots of things we haven't defined + + + align:start position:0% +are lots of things we haven't defined +yet let's just look at them and see what + + align:start position:0% +yet let's just look at them and see what + + + align:start position:0% +yet let's just look at them and see what +they are we're gonna have to do this + + align:start position:0% +they are we're gonna have to do this + + + align:start position:0% +they are we're gonna have to do this +later + + align:start position:0% +later + + + align:start position:0% +later +f cond we have to write apply I'm gonna + + align:start position:0% +f cond we have to write apply I'm gonna + + + align:start position:0% +f cond we have to write apply I'm gonna +have to write ever list I'm gonna have + + align:start position:0% +have to write ever list I'm gonna have + + + align:start position:0% +have to write ever list I'm gonna have +to look right look up I think that's + + align:start position:0% +to look right look up I think that's + + + align:start position:0% +to look right look up I think that's +everything isn't there everything else + + align:start position:0% +everything isn't there everything else + + + align:start position:0% +everything isn't there everything else +is something which is simple or + + align:start position:0% +is something which is simple or + + + align:start position:0% +is something which is simple or +primitive or something like that okay + + align:start position:0% +primitive or something like that okay + + + align:start position:0% +primitive or something like that okay +and of course we could put much many + + align:start position:0% +and of course we could put much many + + + align:start position:0% +and of course we could put much many +more special forms here but that would + + align:start position:0% +more special forms here but that would + + + align:start position:0% +more special forms here but that would +be a bad idea in general in the language + + align:start position:0% +be a bad idea in general in the language + + + align:start position:0% +be a bad idea in general in the language +you make a language very complicated by + + align:start position:0% +you make a language very complicated by + + + align:start position:0% +you make a language very complicated by +putting a lot of things in there the + + align:start position:0% +putting a lot of things in there the + + + align:start position:0% +putting a lot of things in there the +number of reserved words that should + + align:start position:0% +number of reserved words that should + + + align:start position:0% +number of reserved words that should +exist in a language should be no more + + align:start position:0% +exist in a language should be no more + + + align:start position:0% +exist in a language should be no more +than a person Korean member on his + + align:start position:0% +than a person Korean member on his + + + align:start position:0% +than a person Korean member on his +fingers and toes and I get very upset + + align:start position:0% +fingers and toes and I get very upset + + + align:start position:0% +fingers and toes and I get very upset +with languages with that we should have + + align:start position:0% +with languages with that we should have + + + align:start position:0% +with languages with that we should have +hundreds of reserved words but that's + + align:start position:0% +hundreds of reserved words but that's + + + align:start position:0% +hundreds of reserved words but that's +where the reserved words go okay well + + align:start position:0% +where the reserved words go okay well + + + align:start position:0% +where the reserved words go okay well +now let's get to the next part of this + + align:start position:0% +now let's get to the next part of this + + + align:start position:0% +now let's get to the next part of this +the kernel apply okay what else is this + + align:start position:0% +the kernel apply okay what else is this + + + align:start position:0% +the kernel apply okay what else is this +doing well applies job needs to take a + + align:start position:0% +doing well applies job needs to take a + + + align:start position:0% +doing well applies job needs to take a +procedure and apply it to its arguments + + align:start position:0% +procedure and apply it to its arguments + + + align:start position:0% +procedure and apply it to its arguments +after both have been evaluated to come + + align:start position:0% +after both have been evaluated to come + + + align:start position:0% +after both have been evaluated to come +up with a procedure and the arguments + + align:start position:0% +up with a procedure and the arguments + + + align:start position:0% +up with a procedure and the arguments +rather than the operator symbols and the + + align:start position:0% +rather than the operator symbols and the + + + align:start position:0% +rather than the operator symbols and the +operand symbols whatever they are + + align:start position:0% +operand symbols whatever they are + + + align:start position:0% +operand symbols whatever they are +symbolic expressions so we will define + + align:start position:0% +symbolic expressions so we will define + + + align:start position:0% +symbolic expressions so we will define +apply + + align:start position:0% + + + + align:start position:0% + +to be a procedure of two arguments a + + align:start position:0% +to be a procedure of two arguments a + + + align:start position:0% +to be a procedure of two arguments a +procedure and arguments and what does it + + align:start position:0% +procedure and arguments and what does it + + + align:start position:0% +procedure and arguments and what does it +do it does nothing very complicated it's + + align:start position:0% +do it does nothing very complicated it's + + + align:start position:0% +do it does nothing very complicated it's +got two cases either the procedure is + + align:start position:0% +got two cases either the procedure is + + + align:start position:0% +got two cases either the procedure is +primitive and I don't know exactly how + + align:start position:0% +primitive and I don't know exactly how + + + align:start position:0% +primitive and I don't know exactly how +that is done it's possible there's some + + align:start position:0% +that is done it's possible there's some + + + align:start position:0% +that is done it's possible there's some +type information just like we made + + align:start position:0% +type information just like we made + + + align:start position:0% +type information just like we made +closure for here being the description + + align:start position:0% +closure for here being the description + + + align:start position:0% +closure for here being the description +of the type of a compound thing okay + + align:start position:0% +of the type of a compound thing okay + + + align:start position:0% +of the type of a compound thing okay +probably so but it's not essential how + + align:start position:0% +probably so but it's not essential how + + + align:start position:0% +probably so but it's not essential how +that works and in fact it turns out as + + align:start position:0% +that works and in fact it turns out as + + + align:start position:0% +that works and in fact it turns out as +you probably know or deduced that you + + align:start position:0% +you probably know or deduced that you + + + align:start position:0% +you probably know or deduced that you +don't need any primitives anyway you can + + align:start position:0% +don't need any primitives anyway you can + + + align:start position:0% +don't need any primitives anyway you can +give you anything because without them + + align:start position:0% +give you anything because without them + + + align:start position:0% +give you anything because without them +because some of the lambda playing that + + align:start position:0% +because some of the lambda playing that + + + align:start position:0% +because some of the lambda playing that +I've been playing with but it's nice to + + align:start position:0% +I've been playing with but it's nice to + + + align:start position:0% +I've been playing with but it's nice to +have them so here we're gonna do some + + align:start position:0% +have them so here we're gonna do some + + + align:start position:0% +have them so here we're gonna do some +magic which I'm not going to explain go + + align:start position:0% +magic which I'm not going to explain go + + + align:start position:0% +magic which I'm not going to explain go +to the machine language + + align:start position:0% +to the machine language + + + align:start position:0% +to the machine language +apply prim up here's how it adds + + align:start position:0% +apply prim up here's how it adds + + + align:start position:0% +apply prim up here's how it adds +executed add instruction however the + + align:start position:0% +executed add instruction however the + + + align:start position:0% +executed add instruction however the +interesting part of a language is the + + align:start position:0% +interesting part of a language is the + + + align:start position:0% +interesting part of a language is the +glue by which the parameters are glued + + align:start position:0% +glue by which the parameters are glued + + + align:start position:0% +glue by which the parameters are glued +together so let's look at that well the + + align:start position:0% +together so let's look at that well the + + + align:start position:0% +together so let's look at that well the +other possibility is that this is a + + align:start position:0% +other possibility is that this is a + + + align:start position:0% +other possibility is that this is a +compound made up by executing my a + + align:start position:0% +compound made up by executing my a + + + align:start position:0% +compound made up by executing my a +lambda expression to say compound + + align:start position:0% +lambda expression to say compound + + + align:start position:0% +lambda expression to say compound +procedure well we'll check its type if + + align:start position:0% +procedure well we'll check its type if + + + align:start position:0% +procedure well we'll check its type if +it is + + align:start position:0% + + + + align:start position:0% + +closure if it's one of those then I have + + align:start position:0% +closure if it's one of those then I have + + + align:start position:0% +closure if it's one of those then I have +to do an eval of the body right the way + + align:start position:0% +to do an eval of the body right the way + + + align:start position:0% +to do an eval of the body right the way +I do this the way I deal with this at + + align:start position:0% +I do this the way I deal with this at + + + align:start position:0% +I do this the way I deal with this at +all is the way I evaluate the + + align:start position:0% +all is the way I evaluate the + + + align:start position:0% +all is the way I evaluate the +application of a procedure to its + + align:start position:0% +application of a procedure to its + + + align:start position:0% +application of a procedure to its +arguments is by evaluating the body of + + align:start position:0% +arguments is by evaluating the body of + + + align:start position:0% +arguments is by evaluating the body of +the procedure in the environment + + align:start position:0% +the procedure in the environment + + + align:start position:0% +the procedure in the environment +resulting from extending the environment + + align:start position:0% +resulting from extending the environment + + + align:start position:0% +resulting from extending the environment +of the procedure with the bindings of + + align:start position:0% +of the procedure with the bindings of + + + align:start position:0% +of the procedure with the bindings of +the formal parameters of the procedure + + align:start position:0% +the formal parameters of the procedure + + + align:start position:0% +the formal parameters of the procedure +to the arguments that were passed to it + + align:start position:0% + + + + align:start position:0% + +long ago on sentence well that's easy + + align:start position:0% +long ago on sentence well that's easy + + + align:start position:0% +long ago on sentence well that's easy +enough however here's gonna be a lot of + + align:start position:0% +enough however here's gonna be a lot of + + + align:start position:0% +enough however here's gonna be a lot of +car could rain I have to get the body of + + align:start position:0% +car could rain I have to get the body of + + + align:start position:0% +car could rain I have to get the body of +the procedure where's the body of the + + align:start position:0% +the procedure where's the body of the + + + align:start position:0% +the procedure where's the body of the +procedure in here well here's the car + + align:start position:0% +procedure in here well here's the car + + + align:start position:0% +procedure in here well here's the car +here's the cooter as the whole rest of + + align:start position:0% +here's the cooter as the whole rest of + + + align:start position:0% +here's the cooter as the whole rest of +this so here's the Katter and so I see + + align:start position:0% +this so here's the Katter and so I see + + + align:start position:0% +this so here's the Katter and so I see +what I have here is the body is the + + align:start position:0% +what I have here is the body is the + + + align:start position:0% +what I have here is the body is the +second element of the second element of + + align:start position:0% +second element of the second element of + + + align:start position:0% +second element of the second element of +the procedure since the cattle of the + + align:start position:0% +the procedure since the cattle of the + + + align:start position:0% +the procedure since the cattle of the +cat or the cat and adder if they see ad + + align:start position:0% +cat or the cat and adder if they see ad + + + align:start position:0% +cat or the cat and adder if they see ad +a/d are can adder of the procedure to + + align:start position:0% +a/d are can adder of the procedure to + + + align:start position:0% +a/d are can adder of the procedure to +evaluate the body and there is a result + + align:start position:0% +evaluate the body and there is a result + + + align:start position:0% +evaluate the body and there is a result +of binding that's making up more + + align:start position:0% +of binding that's making up more + + + align:start position:0% +of binding that's making up more +environment well I need the formal + + align:start position:0% +environment well I need the formal + + + align:start position:0% +environment well I need the formal +parameters of the of the procedure what + + align:start position:0% +parameters of the of the procedure what + + + align:start position:0% +parameters of the of the procedure what +is that that's the car of the cat er any + + align:start position:0% +is that that's the car of the cat er any + + + align:start position:0% +is that that's the car of the cat er any +it's horrible isn't it of the procedure + + align:start position:0% +it's horrible isn't it of the procedure + + + align:start position:0% +it's horrible isn't it of the procedure +bind that to the arguments that were + + align:start position:0% +bind that to the arguments that were + + + align:start position:0% +bind that to the arguments that were +passed in the environment which is + + align:start position:0% +passed in the environment which is + + + align:start position:0% +passed in the environment which is +passed also as part of the procedure + + align:start position:0% +passed also as part of the procedure + + + align:start position:0% +passed also as part of the procedure +well that's the car of the cooter of the + + align:start position:0% +well that's the car of the cooter of the + + + align:start position:0% +well that's the car of the cooter of the +cutter of this Canada + + align:start position:0% + + + + align:start position:0% + +of the procedure find eval pair cond + + align:start position:0% +of the procedure find eval pair cond + + + align:start position:0% +of the procedure find eval pair cond +lambda define me now of course if I were + + align:start position:0% +lambda define me now of course if I were + + + align:start position:0% +lambda define me now of course if I were +being really a neat character and I was + + align:start position:0% +being really a neat character and I was + + + align:start position:0% +being really a neat character and I was +being picky very careful I would + + align:start position:0% +being picky very careful I would + + + align:start position:0% +being picky very careful I would +actually put in an extra case here for + + align:start position:0% +actually put in an extra case here for + + + align:start position:0% +actually put in an extra case here for +checking for certain errors like did you + + align:start position:0% +checking for certain errors like did you + + + align:start position:0% +checking for certain errors like did you +try to apply one to it to an argument + + align:start position:0% +try to apply one to it to an argument + + + align:start position:0% +try to apply one to it to an argument +you get a undefined procedure type sabe + + align:start position:0% +you get a undefined procedure type sabe + + + align:start position:0% +you get a undefined procedure type sabe +as well do that anyway else some sort of + + align:start position:0% +as well do that anyway else some sort of + + + align:start position:0% +as well do that anyway else some sort of +error okay like that now of course again + + align:start position:0% +error okay like that now of course again + + + align:start position:0% +error okay like that now of course again +in some sort of more real system written + + align:start position:0% +in some sort of more real system written + + + align:start position:0% +in some sort of more real system written +for professional reasons this would be + + align:start position:0% +for professional reasons this would be + + + align:start position:0% +for professional reasons this would be +written with a case analysis done by + + align:start position:0% +written with a case analysis done by + + + align:start position:0% +written with a case analysis done by +some sort of dispatch over here I would + + align:start position:0% +some sort of dispatch over here I would + + + align:start position:0% +some sort of dispatch over here I would +probably have other cases like is this + + align:start position:0% +probably have other cases like is this + + + align:start position:0% +probably have other cases like is this +compiled code it's very important I + + align:start position:0% +compiled code it's very important I + + + align:start position:0% +compiled code it's very important I +might have distinguished the kind of + + align:start position:0% +might have distinguished the kind of + + + align:start position:0% +might have distinguished the kind of +code that's produced by directly + + align:start position:0% +code that's produced by directly + + + align:start position:0% +code that's produced by directly +evaluating a lambda in an interpretation + + align:start position:0% +evaluating a lambda in an interpretation + + + align:start position:0% +evaluating a lambda in an interpretation +from code that was computed produced by + + align:start position:0% +from code that was computed produced by + + + align:start position:0% +from code that was computed produced by +somebody's compiler or something like + + align:start position:0% +somebody's compiler or something like + + + align:start position:0% +somebody's compiler or something like +that and we'll talk about that later or + + align:start position:0% +that and we'll talk about that later or + + + align:start position:0% +that and we'll talk about that later or +is this a piece of Fortran program I + + align:start position:0% +is this a piece of Fortran program I + + + align:start position:0% +is this a piece of Fortran program I +have to go off the next good it's + + align:start position:0% +have to go off the next good it's + + + align:start position:0% +have to go off the next good it's +perfectly possible thing at this point + + align:start position:0% +perfectly possible thing at this point + + + align:start position:0% +perfectly possible thing at this point +to do that in fact there's well in this + + align:start position:0% +to do that in fact there's well in this + + + align:start position:0% +to do that in fact there's well in this +concrete syntax evaluator I'm writing + + align:start position:0% +concrete syntax evaluator I'm writing + + + align:start position:0% +concrete syntax evaluator I'm writing +here there's a there's an assumption + + align:start position:0% +here there's a there's an assumption + + + align:start position:0% +here there's a there's an assumption +built in that this is Lisp right because + + align:start position:0% +built in that this is Lisp right because + + + align:start position:0% +built in that this is Lisp right because +I'm using cars and Cooter's car means + + align:start position:0% +I'm using cars and Cooter's car means + + + align:start position:0% +I'm using cars and Cooter's car means +the operator and cooter means the + + align:start position:0% +the operator and cooter means the + + + align:start position:0% +the operator and cooter means the +operands in the text there's an abstract + + align:start position:0% +operands in the text there's an abstract + + + align:start position:0% +operands in the text there's an abstract +syntax evaluator for which these could + + align:start position:0% +syntax evaluator for which these could + + + align:start position:0% +syntax evaluator for which these could +be they these have get argument abstract + + align:start position:0% +be they these have get argument abstract + + + align:start position:0% +be they these have get argument abstract +names like operator and operand and all + + align:start position:0% +names like operator and operand and all + + + align:start position:0% +names like operator and operand and all +these other things like that and in that + + align:start position:0% +these other things like that and in that + + + align:start position:0% +these other things like that and in that +case you could reprogram it to the algal + + align:start position:0% +case you could reprogram it to the algal + + + align:start position:0% +case you could reprogram it to the algal +with no problem okay well here we have + + align:start position:0% +with no problem okay well here we have + + + align:start position:0% +with no problem okay well here we have +added another couple of things that we + + align:start position:0% +added another couple of things that we + + + align:start position:0% +added another couple of things that we +haven't defined I don't think I'll worry + + align:start position:0% +haven't defined I don't think I'll worry + + + align:start position:0% +haven't defined I don't think I'll worry +about these at all however this one will + + align:start position:0% +about these at all however this one will + + + align:start position:0% +about these at all however this one will +be interesting later well we have let's + + align:start position:0% +be interesting later well we have let's + + + align:start position:0% +be interesting later well we have let's +just proceed through this and get it + + align:start position:0% +just proceed through this and get it + + + align:start position:0% +just proceed through this and get it +done there's only two more blackboards + + align:start position:0% +done there's only two more blackboards + + + align:start position:0% +done there's only two more blackboards +so it can't be very long + + align:start position:0% + + + + align:start position:0% + +it's carefully tailored to exactly fit + + align:start position:0% +it's carefully tailored to exactly fit + + + align:start position:0% +it's carefully tailored to exactly fit +well what do we have left we have to + + align:start position:0% +well what do we have left we have to + + + align:start position:0% +well what do we have left we have to +define ever list which is over here and + + align:start position:0% +define ever list which is over here and + + + align:start position:0% +define ever list which is over here and +Evelyn is nothing more than a map down + + align:start position:0% +Evelyn is nothing more than a map down + + + align:start position:0% +Evelyn is nothing more than a map down +the down a bunch of arguments operands + + align:start position:0% +the down a bunch of arguments operands + + + align:start position:0% +the down a bunch of arguments operands +producing op arguments but I'm going to + + align:start position:0% +producing op arguments but I'm going to + + + align:start position:0% +producing op arguments but I'm going to +write it out and one of the reasons I'm + + align:start position:0% +write it out and one of the reasons I'm + + + align:start position:0% +write it out and one of the reasons I'm +going to write this out is for a + + align:start position:0% +going to write this out is for a + + + align:start position:0% +going to write this out is for a +mystical reason which is I want to make + + align:start position:0% +mystical reason which is I want to make + + + align:start position:0% +mystical reason which is I want to make +this evaluator so simple that it can + + align:start position:0% +this evaluator so simple that it can + + + align:start position:0% +this evaluator so simple that it can +understand itself I'm gonna really worry + + align:start position:0% +understand itself I'm gonna really worry + + + align:start position:0% +understand itself I'm gonna really worry +about that a little bit so let's write + + align:start position:0% +about that a little bit so let's write + + + align:start position:0% +about that a little bit so let's write +it out completely see I don't want to + + align:start position:0% +it out completely see I don't want to + + + align:start position:0% +it out completely see I don't want to +worry about whether or not to think in + + align:start position:0% +worry about whether or not to think in + + + align:start position:0% +worry about whether or not to think in +pass functional arguments the evaluator + + align:start position:0% +pass functional arguments the evaluator + + + align:start position:0% +pass functional arguments the evaluator +is not going to use them the evaluator + + align:start position:0% +is not going to use them the evaluator + + + align:start position:0% +is not going to use them the evaluator +is not going to produce functional + + align:start position:0% +is not going to produce functional + + + align:start position:0% +is not going to produce functional +values so even if there were a different + + align:start position:0% +values so even if there were a different + + + align:start position:0% +values so even if there were a different +alternative language that were very + + align:start position:0% +alternative language that were very + + + align:start position:0% +alternative language that were very +close to this this this evaluates a + + align:start position:0% +close to this this this evaluates a + + + align:start position:0% +close to this this this evaluates a +complex language like scheme which does + + align:start position:0% +complex language like scheme which does + + + align:start position:0% +complex language like scheme which does +allow procedural arguments procedural + + align:start position:0% +allow procedural arguments procedural + + + align:start position:0% +allow procedural arguments procedural +values and procedural data but even if I + + align:start position:0% +values and procedural data but even if I + + + align:start position:0% +values and procedural data but even if I +were evaluating Algol which doesn't + + align:start position:0% +were evaluating Algol which doesn't + + + align:start position:0% +were evaluating Algol which doesn't +allow procedural values I could use this + + align:start position:0% +allow procedural values I could use this + + + align:start position:0% +allow procedural values I could use this +evaluator okay and this evaluators not + + align:start position:0% +evaluator okay and this evaluators not + + + align:start position:0% +evaluator okay and this evaluators not +making any assumptions about that and in + + align:start position:0% +making any assumptions about that and in + + + align:start position:0% +making any assumptions about that and in +fact if this value were restricted it's + + align:start position:0% +fact if this value were restricted it's + + + align:start position:0% +fact if this value were restricted it's +not being able to do that it wouldn't + + align:start position:0% +not being able to do that it wouldn't + + + align:start position:0% +not being able to do that it wouldn't +matter because it doesn't use any of + + align:start position:0% +matter because it doesn't use any of + + + align:start position:0% +matter because it doesn't use any of +those to those clever things so that's + + align:start position:0% +those to those clever things so that's + + + align:start position:0% +those to those clever things so that's +why I'm arranging this to be super + + align:start position:0% +why I'm arranging this to be super + + + align:start position:0% +why I'm arranging this to be super +simple this is sort of the kernel of all + + align:start position:0% +simple this is sort of the kernel of all + + + align:start position:0% +simple this is sort of the kernel of all +possible language evaluators how about + + align:start position:0% +possible language evaluators how about + + + align:start position:0% +possible language evaluators how about +that Evelynn well what is it it's a + + align:start position:0% +that Evelynn well what is it it's a + + + align:start position:0% +that Evelynn well what is it it's a +procedure of two arguments L and an + + align:start position:0% +procedure of two arguments L and an + + + align:start position:0% +procedure of two arguments L and an +environment where L is a list such that + + align:start position:0% +environment where L is a list such that + + + align:start position:0% +environment where L is a list such that +if if the list of arguments is the empty + + align:start position:0% +if if the list of arguments is the empty + + + align:start position:0% +if if the list of arguments is the empty +list then the result is the empty list + + align:start position:0% +list then the result is the empty list + + + align:start position:0% +list then the result is the empty list +otherwise + + align:start position:0% + + + + align:start position:0% + +I want to concept the result of + + align:start position:0% +I want to concept the result of + + + align:start position:0% +I want to concept the result of +evaluating the car of the the car of the + + align:start position:0% +evaluating the car of the the car of the + + + align:start position:0% +evaluating the car of the the car of the +list of operands when the environment so + + align:start position:0% +list of operands when the environment so + + + align:start position:0% +list of operands when the environment so +I want the first operand evaluated and + + align:start position:0% +I want the first operand evaluated and + + + align:start position:0% +I want the first operand evaluated and +I'm going to make a list of the results + + align:start position:0% +I'm going to make a list of the results + + + align:start position:0% +I'm going to make a list of the results +by Consing that on to the result of + + align:start position:0% +by Consing that on to the result of + + + align:start position:0% +by Consing that on to the result of +listing that's a critter recursion the + + align:start position:0% +listing that's a critter recursion the + + + align:start position:0% +listing that's a critter recursion the +cutter of the list relative the same + + align:start position:0% +cutter of the list relative the same + + + align:start position:0% +cutter of the list relative the same +environment + + align:start position:0% +environment + + + align:start position:0% +environment +AB List + + align:start position:0% +AB List + + + align:start position:0% +AB List +Kant's else cond lambda define okay and + + align:start position:0% +Kant's else cond lambda define okay and + + + align:start position:0% +Kant's else cond lambda define okay and +I have one more that I want to put on + + align:start position:0% +I have one more that I want to put on + + + align:start position:0% +I have one more that I want to put on +the blackboard to see essence of this + + align:start position:0% +the blackboard to see essence of this + + + align:start position:0% +the blackboard to see essence of this +whole thing and then there's some sort + + align:start position:0% +whole thing and then there's some sort + + + align:start position:0% +whole thing and then there's some sort +of next layer down conditionals + + align:start position:0% +of next layer down conditionals + + + align:start position:0% +of next layer down conditionals +conditionals are the only thing left + + align:start position:0% +conditionals are the only thing left + + + align:start position:0% +conditionals are the only thing left +that are sort of substantial then below + + align:start position:0% +that are sort of substantial then below + + + align:start position:0% +that are sort of substantial then below +that we have to worry about things like + + align:start position:0% +that we have to worry about things like + + + align:start position:0% +that we have to worry about things like +lookup and bind and will look up that + + align:start position:0% +lookup and bind and will look up that + + + align:start position:0% +lookup and bind and will look up that +we'll look at that in a second + + align:start position:0% +we'll look at that in a second + + + align:start position:0% +we'll look at that in a second +but of the substantial stuff at this + + align:start position:0% +but of the substantial stuff at this + + + align:start position:0% +but of the substantial stuff at this +level of detail the next important thing + + align:start position:0% +level of detail the next important thing + + + align:start position:0% +level of detail the next important thing +is how you deal with conditionals well + + align:start position:0% +is how you deal with conditionals well + + + align:start position:0% +is how you deal with conditionals well +how do we have a conditional thing okay + + align:start position:0% +how do we have a conditional thing okay + + + align:start position:0% +how do we have a conditional thing okay +it's a procedure of a set of clauses and + + align:start position:0% +it's a procedure of a set of clauses and + + + align:start position:0% +it's a procedure of a set of clauses and +an environment and what does it do it + + align:start position:0% +an environment and what does it do it + + + align:start position:0% +an environment and what does it do it +says if the cliff I have no more clauses + + align:start position:0% + + + + align:start position:0% + +well I have to give this a value it + + align:start position:0% +well I have to give this a value it + + + align:start position:0% +well I have to give this a value it +could be that it was an error + + align:start position:0% +could be that it was an error + + + align:start position:0% +could be that it was an error +supposing I ran and run off the end of a + + align:start position:0% +supposing I ran and run off the end of a + + + align:start position:0% +supposing I ran and run off the end of a +conditional it's a pretty arbitrary it's + + align:start position:0% +conditional it's a pretty arbitrary it's + + + align:start position:0% +conditional it's a pretty arbitrary it's +up to me as programmer to choose what I + + align:start position:0% +up to me as programmer to choose what I + + + align:start position:0% +up to me as programmer to choose what I +want happy it's convenient for me right + + align:start position:0% +want happy it's convenient for me right + + + align:start position:0% +want happy it's convenient for me right +now to write down that this has a value + + align:start position:0% +now to write down that this has a value + + + align:start position:0% +now to write down that this has a value +which is the empty list doesn't matter + + align:start position:0% +which is the empty list doesn't matter + + + align:start position:0% +which is the empty list doesn't matter +okay for error-checking some people + + align:start position:0% +okay for error-checking some people + + + align:start position:0% +okay for error-checking some people +might prefer something else but the + + align:start position:0% +might prefer something else but the + + + align:start position:0% +might prefer something else but the +interesting things are the following + + align:start position:0% +interesting things are the following + + + align:start position:0% +interesting things are the following +ones if I've got an else clause a closi + + align:start position:0% +ones if I've got an else clause a closi + + + align:start position:0% +ones if I've got an else clause a closi +if I have a list of clauses then each + + align:start position:0% +if I have a list of clauses then each + + + align:start position:0% +if I have a list of clauses then each +clause is a list and so the predicate + + align:start position:0% +clause is a list and so the predicate + + + align:start position:0% +clause is a list and so the predicate +part is the kr of the clauses it's the + + align:start position:0% +part is the kr of the clauses it's the + + + align:start position:0% +part is the kr of the clauses it's the +car which is the first part of the first + + align:start position:0% +car which is the first part of the first + + + align:start position:0% +car which is the first part of the first +clause in the list of clauses if it's an + + align:start position:0% +clause in the list of clauses if it's an + + + align:start position:0% +clause in the list of clauses if it's an +else + + align:start position:0% +else + + + align:start position:0% +else +then it means I want my result of the + + align:start position:0% +then it means I want my result of the + + + align:start position:0% +then it means I want my result of the +conditional to be the result of + + align:start position:0% +conditional to be the result of + + + align:start position:0% +conditional to be the result of +evaluating the matching expression so I + + align:start position:0% +evaluating the matching expression so I + + + align:start position:0% +evaluating the matching expression so I +eval the Katter so this is the first + + align:start position:0% +eval the Katter so this is the first + + + align:start position:0% +eval the Katter so this is the first +clause the second element of it quatre + + align:start position:0% +clause the second element of it quatre + + + align:start position:0% +clause the second element of it quatre +quatre of the car okay of the clauses + + align:start position:0% + + + + align:start position:0% + +with respect to the environment now the + + align:start position:0% +with respect to the environment now the + + + align:start position:0% +with respect to the environment now the +next possibility is more interesting if + + align:start position:0% +next possibility is more interesting if + + + align:start position:0% +next possibility is more interesting if +it's false if the first predicate in the + + align:start position:0% +it's false if the first predicate in the + + + align:start position:0% +it's false if the first predicate in the +predicate list is not an else and it's + + align:start position:0% +predicate list is not an else and it's + + + align:start position:0% +predicate list is not an else and it's +not false if it's not the word else and + + align:start position:0% +not false if it's not the word else and + + + align:start position:0% +not false if it's not the word else and +if it's not a false thing let's write + + align:start position:0% +if it's not a false thing let's write + + + align:start position:0% +if it's not a false thing let's write +down what it is if it's false thing if + + align:start position:0% +down what it is if it's false thing if + + + align:start position:0% +down what it is if it's false thing if +the result of evaluating the first + + align:start position:0% +the result of evaluating the first + + + align:start position:0% +the result of evaluating the first +Clause first predicate the clauses + + align:start position:0% +Clause first predicate the clauses + + + align:start position:0% +Clause first predicate the clauses +respect the environment if that + + align:start position:0% +respect the environment if that + + + align:start position:0% +respect the environment if that +evaluation yields false then it means I + + align:start position:0% +evaluation yields false then it means I + + + align:start position:0% +evaluation yields false then it means I +want to look at the next clause so I + + align:start position:0% +want to look at the next clause so I + + + align:start position:0% +want to look at the next clause so I +wanted to scarred the first one so we + + align:start position:0% +wanted to scarred the first one so we + + + align:start position:0% +wanted to scarred the first one so we +just go around the loop I've conned the + + align:start position:0% +just go around the loop I've conned the + + + align:start position:0% +just go around the loop I've conned the +quitter of the clause is rolled to that + + align:start position:0% +quitter of the clause is rolled to that + + + align:start position:0% +quitter of the clause is rolled to that +environment and otherwise I had a true + + align:start position:0% +environment and otherwise I had a true + + + align:start position:0% +environment and otherwise I had a true +clause in which case what I want is to + + align:start position:0% +clause in which case what I want is to + + + align:start position:0% +clause in which case what I want is to +evaluate the cat R of the clauses roll + + align:start position:0% +evaluate the cat R of the clauses roll + + + align:start position:0% +evaluate the cat R of the clauses roll +into that environment boy it's almost + + align:start position:0% +into that environment boy it's almost + + + align:start position:0% +into that environment boy it's almost +done it's quite close to done I think + + align:start position:0% +done it's quite close to done I think + + + align:start position:0% +done it's quite close to done I think +we're gonna finish that this part off + + align:start position:0% +we're gonna finish that this part off + + + align:start position:0% +we're gonna finish that this part off +instead of just buzzing through this + + align:start position:0% +instead of just buzzing through this + + + align:start position:0% +instead of just buzzing through this +evaluator but so far you're seeing + + align:start position:0% +evaluator but so far you're seeing + + + align:start position:0% +evaluator but so far you're seeing +almost everything let's look at the next + + align:start position:0% +almost everything let's look at the next + + + align:start position:0% +almost everything let's look at the next +next of transparency here and see oh yes + + align:start position:0% +next of transparency here and see oh yes + + + align:start position:0% +next of transparency here and see oh yes +here is bind bind is binds from making + + align:start position:0% +here is bind bind is binds from making + + + align:start position:0% +here is bind bind is binds from making +more table and what we're gonna do here + + align:start position:0% +more table and what we're gonna do here + + + align:start position:0% +more table and what we're gonna do here +is make a we're gonna make an O frame + + align:start position:0% +is make a we're gonna make an O frame + + + align:start position:0% +is make a we're gonna make an O frame +for an environment structure the + + align:start position:0% +for an environment structure the + + + align:start position:0% +for an environment structure the +environment structure is going to be + + align:start position:0% +environment structure is going to be + + + align:start position:0% +environment structure is going to be +represented as a list of frames so given + + align:start position:0% +represented as a list of frames so given + + + align:start position:0% +represented as a list of frames so given +an existing environment structure I'm + + align:start position:0% +an existing environment structure I'm + + + align:start position:0% +an existing environment structure I'm +going to make a new environment + + align:start position:0% +going to make a new environment + + + align:start position:0% +going to make a new environment +structure by consoling a new frame onto + + align:start position:0% +structure by consoling a new frame onto + + + align:start position:0% +structure by consoling a new frame onto +the existing environment structure where + + align:start position:0% +the existing environment structure where + + + align:start position:0% +the existing environment structure where +the new frame consists of the result of + + align:start position:0% +the new frame consists of the result of + + + align:start position:0% +the new frame consists of the result of +pairing up the variables which are the + + align:start position:0% +pairing up the variables which are the + + + align:start position:0% +pairing up the variables which are the +bound variables of the procedure I'm + + align:start position:0% +bound variables of the procedure I'm + + + align:start position:0% +bound variables of the procedure I'm +applying to the argument values which is + + align:start position:0% +applying to the argument values which is + + + align:start position:0% +applying to the argument values which is +the arguments that were passed that that + + align:start position:0% +the arguments that were passed that that + + + align:start position:0% +the arguments that were passed that that +procedure who's just making a list is + + align:start position:0% +procedure who's just making a list is + + + align:start position:0% +procedure who's just making a list is +getting adding a new element to a list + + align:start position:0% +getting adding a new element to a list + + + align:start position:0% +getting adding a new element to a list +of frames which is an environment + + align:start position:0% +of frames which is an environment + + + align:start position:0% +of frames which is an environment +structure to make a new environment + + align:start position:0% +structure to make a new environment + + + align:start position:0% +structure to make a new environment +where a pair up is very simple pair up + + align:start position:0% +where a pair up is very simple pair up + + + align:start position:0% +where a pair up is very simple pair up +is nothing more than if I have a list of + + align:start position:0% +is nothing more than if I have a list of + + + align:start position:0% +is nothing more than if I have a list of +variables and list of values well if I + + align:start position:0% +variables and list of values well if I + + + align:start position:0% +variables and list of values well if I +run out of variables and if I run out of + + align:start position:0% +run out of variables and if I run out of + + + align:start position:0% +run out of variables and if I run out of +everything's okay otherwise I've given + + align:start position:0% +everything's okay otherwise I've given + + + align:start position:0% +everything's okay otherwise I've given +too many arguments if if I've not run + + align:start position:0% +too many arguments if if I've not run + + + align:start position:0% +too many arguments if if I've not run +out of variables but I've run out of + + align:start position:0% +out of variables but I've run out of + + + align:start position:0% +out of variables but I've run out of +values then I have too few arguments and + + align:start position:0% +values then I have too few arguments and + + + align:start position:0% +values then I have too few arguments and +in the general case where I don't have + + align:start position:0% +in the general case where I don't have + + + align:start position:0% +in the general case where I don't have +any errors and I'm not done okay then I + + align:start position:0% +any errors and I'm not done okay then I + + + align:start position:0% +any errors and I'm not done okay then I +really am just adding a new pair of the + + align:start position:0% +really am just adding a new pair of the + + + align:start position:0% +really am just adding a new pair of the +first valuable with the first first + + align:start position:0% +first valuable with the first first + + + align:start position:0% +first valuable with the first first +argument okay the first value onto a + + align:start position:0% +argument okay the first value onto a + + + align:start position:0% +argument okay the first value onto a +list consisting of pairing resulting + + align:start position:0% +list consisting of pairing resulting + + + align:start position:0% +list consisting of pairing resulting +from pairing up the rest of the + + align:start position:0% +from pairing up the rest of the + + + align:start position:0% +from pairing up the rest of the +variables with the rest of the values + + align:start position:0% +variables with the rest of the values + + + align:start position:0% +variables with the rest of the values +lookup is of course equally simple right + + align:start position:0% +lookup is of course equally simple right + + + align:start position:0% +lookup is of course equally simple right +if I have to look up a symbol in an + + align:start position:0% +if I have to look up a symbol in an + + + align:start position:0% +if I have to look up a symbol in an +environment well if the environment is + + align:start position:0% +environment well if the environment is + + + align:start position:0% +environment well if the environment is +empty then I've got an unbound variable + + align:start position:0% +empty then I've got an unbound variable + + + align:start position:0% +empty then I've got an unbound variable +otherwise what I'm going to do is use a + + align:start position:0% +otherwise what I'm going to do is use a + + + align:start position:0% +otherwise what I'm going to do is use a +special pair list lookup procedure which + + align:start position:0% +special pair list lookup procedure which + + + align:start position:0% +special pair list lookup procedure which +will have very shortly of a symbol in + + align:start position:0% +will have very shortly of a symbol in + + + align:start position:0% +will have very shortly of a symbol in +the first frame of the environment since + + align:start position:0% +the first frame of the environment since + + + align:start position:0% +the first frame of the environment since +I know the environment is not empty it + + align:start position:0% +I know the environment is not empty it + + + align:start position:0% +I know the environment is not empty it +must have a first frame + + align:start position:0% +must have a first frame + + + align:start position:0% +must have a first frame +smiley look up the symbol in the first + + align:start position:0% +smiley look up the symbol in the first + + + align:start position:0% +smiley look up the symbol in the first +frame that becomes the value cell here + + align:start position:0% +frame that becomes the value cell here + + + align:start position:0% +frame that becomes the value cell here +okay and then if the value cell is empty + + align:start position:0% +okay and then if the value cell is empty + + + align:start position:0% +okay and then if the value cell is empty +okay that if there is no such value cell + + align:start position:0% +okay that if there is no such value cell + + + align:start position:0% +okay that if there is no such value cell +then I have to continue and look at the + + align:start position:0% +then I have to continue and look at the + + + align:start position:0% +then I have to continue and look at the +rest of the frames it means there was + + align:start position:0% +rest of the frames it means there was + + + align:start position:0% +rest of the frames it means there was +nothing found there so that's a property + + align:start position:0% +nothing found there so that's a property + + + align:start position:0% +nothing found there so that's a property +of ask you is it returns emptiness if it + + align:start position:0% +of ask you is it returns emptiness if it + + + align:start position:0% +of ask you is it returns emptiness if it +doesn't find something okay but if it + + align:start position:0% +doesn't find something okay but if it + + + align:start position:0% +doesn't find something okay but if it +did find something then I'm going to use + + align:start position:0% +did find something then I'm going to use + + + align:start position:0% +did find something then I'm going to use +the cutter of the value cell here which + + align:start position:0% +the cutter of the value cell here which + + + align:start position:0% +the cutter of the value cell here which +is the thing that was the pair + + align:start position:0% +is the thing that was the pair + + + align:start position:0% +is the thing that was the pair +consisting of the variable and the value + + align:start position:0% +consisting of the variable and the value + + + align:start position:0% +consisting of the variable and the value +so the color of it is the value part + + align:start position:0% +so the color of it is the value part + + + align:start position:0% +so the color of it is the value part +okay finally ask you is something you've + + align:start position:0% +okay finally ask you is something you've + + + align:start position:0% +okay finally ask you is something you've +probably seen already asked you takes a + + align:start position:0% +probably seen already asked you takes a + + + align:start position:0% +probably seen already asked you takes a +symbol and a list of pairs and if the + + align:start position:0% +symbol and a list of pairs and if the + + + align:start position:0% +symbol and a list of pairs and if the +list is empty it's empty after this if + + align:start position:0% +list is empty it's empty after this if + + + align:start position:0% +list is empty it's empty after this if +the symbol is the first thing in the + + align:start position:0% +the symbol is the first thing in the + + + align:start position:0% +the symbol is the first thing in the +list that's an error that should be K R + + align:start position:0% +list that's an error that should be K R + + + align:start position:0% +list that's an error that should be K R +CAA R everybody note that right there + + align:start position:0% +CAA R everybody note that right there + + + align:start position:0% +CAA R everybody note that right there +okay + + align:start position:0% + + + + align:start position:0% + +and in any case if this of the symbol is + + align:start position:0% +and in any case if this of the symbol is + + + align:start position:0% +and in any case if this of the symbol is +the kr of the a-list then I want the + + align:start position:0% +the kr of the a-list then I want the + + + align:start position:0% +the kr of the a-list then I want the +first the first pair in the a-list so in + + align:start position:0% +first the first pair in the a-list so in + + + align:start position:0% +first the first pair in the a-list so in +other words if this is the key matching + + align:start position:0% +other words if this is the key matching + + + align:start position:0% +other words if this is the key matching +there right the right entry otherwise I + + align:start position:0% +there right the right entry otherwise I + + + align:start position:0% +there right the right entry otherwise I +want to look up that symbol in the rest + + align:start position:0% +want to look up that symbol in the rest + + + align:start position:0% +want to look up that symbol in the rest +sorry for producing a bug any bugs + + align:start position:0% +sorry for producing a bug any bugs + + + align:start position:0% +sorry for producing a bug any bugs +appear well in any case you pretty much + + align:start position:0% +appear well in any case you pretty much + + + align:start position:0% +appear well in any case you pretty much +seen the whole thing now it's a very + + align:start position:0% +seen the whole thing now it's a very + + + align:start position:0% +seen the whole thing now it's a very +beautiful thing even though it's written + + align:start position:0% +beautiful thing even though it's written + + + align:start position:0% +beautiful thing even though it's written +in an ugly style meaning the kernel of + + align:start position:0% +in an ugly style meaning the kernel of + + + align:start position:0% +in an ugly style meaning the kernel of +every language I suggest that we must + + align:start position:0% +every language I suggest that we must + + + align:start position:0% +every language I suggest that we must +look at it for a while + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +are there any questions + + align:start position:0% + + + + align:start position:0% + +all right suppose it's time to take a + + align:start position:0% +all right suppose it's time to take a + + + align:start position:0% +all right suppose it's time to take a +small break then + + align:start position:0% +small break then + + + align:start position:0% +small break then +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay now we're just going to do a little + + align:start position:0% +okay now we're just going to do a little + + + align:start position:0% +okay now we're just going to do a little +bit of practice understanding what it is + + align:start position:0% +bit of practice understanding what it is + + + align:start position:0% +bit of practice understanding what it is +we've just shown you okay what we're + + align:start position:0% +we've just shown you okay what we're + + + align:start position:0% +we've just shown you okay what we're +gonna do is go through in detail and + + align:start position:0% +gonna do is go through in detail and + + + align:start position:0% +gonna do is go through in detail and +evaluation by informally substituting + + align:start position:0% +evaluation by informally substituting + + + align:start position:0% +evaluation by informally substituting +through the interpreter and since we + + align:start position:0% +through the interpreter and since we + + + align:start position:0% +through the interpreter and since we +have no assignments or definitions in + + align:start position:0% +have no assignments or definitions in + + + align:start position:0% +have no assignments or definitions in +this interpreter we have noticed no + + align:start position:0% +this interpreter we have noticed no + + + align:start position:0% +this interpreter we have noticed no +possible side-effects okay so the we can + + align:start position:0% +possible side-effects okay so the we can + + + align:start position:0% +possible side-effects okay so the we can +do substitution with impunity and not + + align:start position:0% +do substitution with impunity and not + + + align:start position:0% +do substitution with impunity and not +worry about results right so the + + align:start position:0% +worry about results right so the + + + align:start position:0% +worry about results right so the +particular problem I'd like to look at + + align:start position:0% +particular problem I'd like to look at + + + align:start position:0% +particular problem I'd like to look at +is a an interesting one + + align:start position:0% +is a an interesting one + + + align:start position:0% +is a an interesting one +it's the evaluation of quote open open + + align:start position:0% +it's the evaluation of quote open open + + + align:start position:0% +it's the evaluation of quote open open +open lambda of X lambda of y plus XY + + align:start position:0% + + + + align:start position:0% + +lambda lambda applied to three applied + + align:start position:0% +lambda lambda applied to three applied + + + align:start position:0% +lambda lambda applied to three applied +to four in the glut and some global + + align:start position:0% +to four in the glut and some global + + + align:start position:0% +to four in the glut and some global +environment which I'll call easier out + + align:start position:0% + + + + align:start position:0% + +so what we have here is a procedure of + + align:start position:0% +so what we have here is a procedure of + + + align:start position:0% +so what we have here is a procedure of +one argument X which produces as its + + align:start position:0% +one argument X which produces as its + + + align:start position:0% +one argument X which produces as its +value a procedure of one argument Y + + align:start position:0% +value a procedure of one argument Y + + + align:start position:0% +value a procedure of one argument Y +which adds X to Y we are applying the + + align:start position:0% +which adds X to Y we are applying the + + + align:start position:0% +which adds X to Y we are applying the +procedure of one argument X to 3 so X + + align:start position:0% +procedure of one argument X to 3 so X + + + align:start position:0% +procedure of one argument X to 3 so X +should become 3 and the result of that + + align:start position:0% +should become 3 and the result of that + + + align:start position:0% +should become 3 and the result of that +trivia procedure of one argument Y which + + align:start position:0% +trivia procedure of one argument Y which + + + align:start position:0% +trivia procedure of one argument Y which +we will then apply to four and there's a + + align:start position:0% +we will then apply to four and there's a + + + align:start position:0% +we will then apply to four and there's a +very simple case they will then add + + align:start position:0% +very simple case they will then add + + + align:start position:0% +very simple case they will then add +those results ok now in order to do that + + align:start position:0% +those results ok now in order to do that + + + align:start position:0% +those results ok now in order to do that +I want to make a very simple environment + + align:start position:0% +I want to make a very simple environment + + + align:start position:0% +I want to make a very simple environment +model and at this point you should + + align:start position:0% +model and at this point you should + + + align:start position:0% +model and at this point you should +already have in your mind the + + align:start position:0% +already have in your mind the + + + align:start position:0% +already have in your mind the +environments that this produces but + + align:start position:0% +environments that this produces but + + + align:start position:0% +environments that this produces but +we're gonna start out with a global + + align:start position:0% +we're gonna start out with a global + + + align:start position:0% +we're gonna start out with a global +environment which I'll call a zero + + align:start position:0% + + + + align:start position:0% + +which is that and it's going to have in + + align:start position:0% +which is that and it's going to have in + + + align:start position:0% +which is that and it's going to have in +it things definitions for plus and times + + align:start position:0% + + + + align:start position:0% + +and using Greek letters isn't that + + align:start position:0% +and using Greek letters isn't that + + + align:start position:0% +and using Greek letters isn't that +interesting for the objects and - and + + align:start position:0% +interesting for the objects and - and + + + align:start position:0% +interesting for the objects and - and +quotient and car and clear and haunts + + align:start position:0% +quotient and car and clear and haunts + + + align:start position:0% +quotient and car and clear and haunts +thank you everything else you might + + align:start position:0% +thank you everything else you might + + + align:start position:0% +thank you everything else you might +imagine in a global environment it's got + + align:start position:0% +imagine in a global environment it's got + + + align:start position:0% +imagine in a global environment it's got +something there for each of those things + + align:start position:0% +something there for each of those things + + + align:start position:0% +something there for each of those things +something the machine is born with + + align:start position:0% +something the machine is born with + + + align:start position:0% +something the machine is born with +that's easy row now what does it mean to + + align:start position:0% +that's easy row now what does it mean to + + + align:start position:0% +that's easy row now what does it mean to +do this evaluation well we go through + + align:start position:0% +do this evaluation well we go through + + + align:start position:0% +do this evaluation well we go through +the set of special forms first of all + + align:start position:0% +the set of special forms first of all + + + align:start position:0% +the set of special forms first of all +this is not a number this is not a + + align:start position:0% +this is not a number this is not a + + + align:start position:0% +this is not a number this is not a +symbol G it's not a quoted expression + + align:start position:0% +symbol G it's not a quoted expression + + + align:start position:0% +symbol G it's not a quoted expression +I'm this is a quoted expression but + + align:start position:0% +I'm this is a quoted expression but + + + align:start position:0% +I'm this is a quoted expression but +that's not what I'm interested in I'm + + align:start position:0% +that's not what I'm interested in I'm + + + align:start position:0% +that's not what I'm interested in I'm +mister question is whether or not the + + align:start position:0% +mister question is whether or not the + + + align:start position:0% +mister question is whether or not the +thing which is quoted is a quoted + + align:start position:0% +thing which is quoted is a quoted + + + align:start position:0% +thing which is quoted is a quoted +expression right I'm evaluating an + + align:start position:0% +expression right I'm evaluating an + + + align:start position:0% +expression right I'm evaluating an +expression this just says it's this + + align:start position:0% +expression this just says it's this + + + align:start position:0% +expression this just says it's this +particular expression this is not a + + align:start position:0% +particular expression this is not a + + + align:start position:0% +particular expression this is not a +quoted expression okay it's not it's not + + align:start position:0% +quoted expression okay it's not it's not + + + align:start position:0% +quoted expression okay it's not it's not +a thing that begins with lambda it's not + + align:start position:0% +a thing that begins with lambda it's not + + + align:start position:0% +a thing that begins with lambda it's not +a thing that begins with cond therefore + + align:start position:0% +a thing that begins with cond therefore + + + align:start position:0% +a thing that begins with cond therefore +it's an application of its procedure of + + align:start position:0% +it's an application of its procedure of + + + align:start position:0% +it's an application of its procedure of +an operated operands it's combination + + align:start position:0% +an operated operands it's combination + + + align:start position:0% +an operated operands it's combination +the combination but thus has this as the + + align:start position:0% +the combination but thus has this as the + + + align:start position:0% +the combination but thus has this as the +operator and this is the operands + + align:start position:0% + + + + align:start position:0% + +well that means that what I'm going to + + align:start position:0% +well that means that what I'm going to + + + align:start position:0% +well that means that what I'm going to +do is transform this into apply of eval + + align:start position:0% +do is transform this into apply of eval + + + align:start position:0% +do is transform this into apply of eval +of quote open open lambda of X lambda of + + align:start position:0% +of quote open open lambda of X lambda of + + + align:start position:0% +of quote open open lambda of X lambda of +Y I'm evaluating the operator plus X Y + + align:start position:0% +Y I'm evaluating the operator plus X Y + + + align:start position:0% +Y I'm evaluating the operator plus X Y +in the environment also e0 with the + + align:start position:0% +in the environment also e0 with the + + + align:start position:0% +in the environment also e0 with the +operands that I'm going to apply this to + + align:start position:0% +operands that I'm going to apply this to + + + align:start position:0% +operands that I'm going to apply this to +the arguments being the result of that + + align:start position:0% +the arguments being the result of that + + + align:start position:0% +the arguments being the result of that +list the list containing four in e0 I'm + + align:start position:0% +list the list containing four in e0 I'm + + + align:start position:0% +list the list containing four in e0 I'm +using this funny notation here for a + + align:start position:0% +using this funny notation here for a + + + align:start position:0% +using this funny notation here for a +zero because it should be the that + + align:start position:0% +zero because it should be the that + + + align:start position:0% +zero because it should be the that +environment and I don't have any I can't + + align:start position:0% +environment and I don't have any I can't + + + align:start position:0% +environment and I don't have any I can't +have a name for it to have no + + align:start position:0% +have a name for it to have no + + + align:start position:0% +have a name for it to have no +environment to name it in okay so this + + align:start position:0% +environment to name it in okay so this + + + align:start position:0% +environment to name it in okay so this +is just a representation of what would + + align:start position:0% +is just a representation of what would + + + align:start position:0% +is just a representation of what would +be a quoted expression if you will the + + align:start position:0% +be a quoted expression if you will the + + + align:start position:0% +be a quoted expression if you will the +data structure which is the which is the + + align:start position:0% +data structure which is the which is the + + + align:start position:0% +data structure which is the which is the +environment it goes there well so this + + align:start position:0% +environment it goes there well so this + + + align:start position:0% +environment it goes there well so this +is that's what we're seeing here well in + + align:start position:0% +is that's what we're seeing here well in + + + align:start position:0% +is that's what we're seeing here well in +order to do this I have to do this and I + + align:start position:0% +order to do this I have to do this and I + + + align:start position:0% +order to do this I have to do this and I +have to do that + + align:start position:0% +have to do that + + + align:start position:0% +have to do that +well this one's easy so why don't we do + + align:start position:0% +well this one's easy so why don't we do + + + align:start position:0% +well this one's easy so why don't we do +that one first okay this turns into + + align:start position:0% +that one first okay this turns into + + + align:start position:0% +that one first okay this turns into +apply of eval just copying something now + + align:start position:0% +apply of eval just copying something now + + + align:start position:0% +apply of eval just copying something now +most of the substitution rule is copying + + align:start position:0% + + + + align:start position:0% + +so I'm going to not say the words when I + + align:start position:0% +so I'm going to not say the words when I + + + align:start position:0% +so I'm going to not say the words when I +copy because it's faster and then the + + align:start position:0% +copy because it's faster and then the + + + align:start position:0% +copy because it's faster and then the +Ewa list is going to turn into a conce + + align:start position:0% +Ewa list is going to turn into a conce + + + align:start position:0% +Ewa list is going to turn into a conce +of eval for in e0 because it was not an + + align:start position:0% +of eval for in e0 because it was not an + + + align:start position:0% +of eval for in e0 because it was not an +empty list all right on to the result of + + align:start position:0% +empty list all right on to the result of + + + align:start position:0% +empty list all right on to the result of +that listing on the empty list any zero + + align:start position:0% + + + + align:start position:0% + +and I'm gonna start leaving out step + + align:start position:0% +and I'm gonna start leaving out step + + + align:start position:0% +and I'm gonna start leaving out step +soon because it's gonna get boring but + + align:start position:0% +soon because it's gonna get boring but + + + align:start position:0% +soon because it's gonna get boring but +this is basically the same thing as + + align:start position:0% +this is basically the same thing as + + + align:start position:0% +this is basically the same thing as +apply of eval I'm gonna keep doing this + + align:start position:0% +apply of eval I'm gonna keep doing this + + + align:start position:0% +apply of eval I'm gonna keep doing this +the lambda of X and lambda of y plus XY + + align:start position:0% +the lambda of X and lambda of y plus XY + + + align:start position:0% +the lambda of X and lambda of y plus XY +3 close v-0 I'm a pretty good machine + + align:start position:0% + + + + align:start position:0% + +applied well eval of floor for that's + + align:start position:0% +applied well eval of floor for that's + + + align:start position:0% +applied well eval of floor for that's +meets the question is it a number so + + align:start position:0% +meets the question is it a number so + + + align:start position:0% +meets the question is it a number so +that's Kant's right cons of four and + + align:start position:0% +that's Kant's right cons of four and + + + align:start position:0% +that's Kant's right cons of four and +ever list of the empty list is the empty + + align:start position:0% +ever list of the empty list is the empty + + + align:start position:0% +ever list of the empty list is the empty +list and that's this okay and that's + + align:start position:0% +list and that's this okay and that's + + + align:start position:0% +list and that's this okay and that's +very simple to understand because that + + align:start position:0% +very simple to understand because that + + + align:start position:0% +very simple to understand because that +means just for the list containing for + + align:start position:0% +means just for the list containing for + + + align:start position:0% +means just for the list containing for +itself so this is nothing more than + + align:start position:0% +itself so this is nothing more than + + + align:start position:0% +itself so this is nothing more than +apply of eval of quote open open lambda + + align:start position:0% +apply of eval of quote open open lambda + + + align:start position:0% +apply of eval of quote open open lambda +X lambda of y plus XY - 3 3 applied to + + align:start position:0% +X lambda of y plus XY - 3 3 applied to + + + align:start position:0% +X lambda of y plus XY - 3 3 applied to +well 0 applied to the list for bang so + + align:start position:0% +well 0 applied to the list for bang so + + + align:start position:0% +well 0 applied to the list for bang so +that's that step + + align:start position:0% +that's that step + + + align:start position:0% +that's that step +well now now let's look at the next more + + align:start position:0% +well now now let's look at the next more + + + align:start position:0% +well now now let's look at the next more +interesting thing what do I do to + + align:start position:0% +interesting thing what do I do to + + + align:start position:0% +interesting thing what do I do to +evaluate that evaluating this means I + + align:start position:0% +evaluate that evaluating this means I + + + align:start position:0% +evaluate that evaluating this means I +have to evaluate this is well it's not + + align:start position:0% +have to evaluate this is well it's not + + + align:start position:0% +have to evaluate this is well it's not +it's nothing but an application it's not + + align:start position:0% +it's nothing but an application it's not + + + align:start position:0% +it's nothing but an application it's not +one of the special things if the + + align:start position:0% +one of the special things if the + + + align:start position:0% +one of the special things if the +application of this operator which we + + align:start position:0% +application of this operator which we + + + align:start position:0% +application of this operator which we +see here here's the operator applied to + + align:start position:0% +see here here's the operator applied to + + + align:start position:0% +see here here's the operator applied to +this operands it's that combination well + + align:start position:0% +this operands it's that combination well + + + align:start position:0% +this operands it's that combination well +we know how to do that okay cuz that's + + align:start position:0% +we know how to do that okay cuz that's + + + align:start position:0% +we know how to do that okay cuz that's +the last case of the conditional so + + align:start position:0% +the last case of the conditional so + + + align:start position:0% +the last case of the conditional so +substituting in for this evaluation + + align:start position:0% +substituting in for this evaluation + + + align:start position:0% +substituting in for this evaluation +it's apply of a value of the operator in + + align:start position:0% +it's apply of a value of the operator in + + + align:start position:0% +it's apply of a value of the operator in +the ever list of the operands now let's + + align:start position:0% +the ever list of the operands now let's + + + align:start position:0% +the ever list of the operands now let's +apply on apply on eval quote open lambda + + align:start position:0% +apply on apply on eval quote open lambda + + + align:start position:0% +apply on apply on eval quote open lambda +of X plus lambda y plus XY lambda lambda + + align:start position:0% +of X plus lambda y plus XY lambda lambda + + + align:start position:0% +of X plus lambda y plus XY lambda lambda +in environment easy Rho apply that I'm + + align:start position:0% +in environment easy Rho apply that I'm + + + align:start position:0% +in environment easy Rho apply that I'm +going to short-circuit the evaluation + + align:start position:0% +going to short-circuit the evaluation + + + align:start position:0% +going to short-circuit the evaluation +the operands because they're the same as + + align:start position:0% +the operands because they're the same as + + + align:start position:0% +the operands because they're the same as +they were before I got a list containing + + align:start position:0% +they were before I got a list containing + + + align:start position:0% +they were before I got a list containing +three apply that and apply that to four + + align:start position:0% + + + + align:start position:0% + +okay well let's see eval of a lambda + + align:start position:0% +okay well let's see eval of a lambda + + + align:start position:0% +okay well let's see eval of a lambda +expression produces a procedure object + + align:start position:0% +expression produces a procedure object + + + align:start position:0% +expression produces a procedure object +okay so this is apply of apply of the + + align:start position:0% +okay so this is apply of apply of the + + + align:start position:0% +okay so this is apply of apply of the +procedure object closure which contains + + align:start position:0% +procedure object closure which contains + + + align:start position:0% +procedure object closure which contains +the body of the procedure X which is + + align:start position:0% +the body of the procedure X which is + + + align:start position:0% +the body of the procedure X which is +lambda which binds X and has the prayer + + align:start position:0% +lambda which binds X and has the prayer + + + align:start position:0% +lambda which binds X and has the prayer +the internals the body it returns the + + align:start position:0% +the internals the body it returns the + + + align:start position:0% +the internals the body it returns the +procedure of one argument Y which adds X + + align:start position:0% +procedure of one argument Y which adds X + + + align:start position:0% +procedure of one argument Y which adds X +to Y environment a zero is now captured + + align:start position:0% +to Y environment a zero is now captured + + + align:start position:0% +to Y environment a zero is now captured +in it + + align:start position:0% +in it + + + align:start position:0% +in it +because this was evaluated with respect + + align:start position:0% +because this was evaluated with respect + + + align:start position:0% +because this was evaluated with respect +to e0 e0 is part now of the closure + + align:start position:0% +to e0 e0 is part now of the closure + + + align:start position:0% +to e0 e0 is part now of the closure +object apply that to open three closed + + align:start position:0% +object apply that to open three closed + + + align:start position:0% +object apply that to open three closed +apply to open for closed fly + + align:start position:0% + + + + align:start position:0% + +so going from this step to this step + + align:start position:0% +so going from this step to this step + + + align:start position:0% +so going from this step to this step +meant that I made up a procedure object + + align:start position:0% +meant that I made up a procedure object + + + align:start position:0% +meant that I made up a procedure object +which captured in it easy row as part of + + align:start position:0% +which captured in it easy row as part of + + + align:start position:0% +which captured in it easy row as part of +the procedure object now we're going to + + align:start position:0% +the procedure object now we're going to + + + align:start position:0% +the procedure object now we're going to +pass those to apply we have to apply + + align:start position:0% +pass those to apply we have to apply + + + align:start position:0% +pass those to apply we have to apply +this procedure to that set of arguments + + align:start position:0% +this procedure to that set of arguments + + + align:start position:0% +this procedure to that set of arguments +well but that procedure is not is not + + align:start position:0% +well but that procedure is not is not + + + align:start position:0% +well but that procedure is not is not +primitive it's in fact a thing which has + + align:start position:0% +primitive it's in fact a thing which has + + + align:start position:0% +primitive it's in fact a thing which has +got the tag closure and therefore what + + align:start position:0% +got the tag closure and therefore what + + + align:start position:0% +got the tag closure and therefore what +we have to do is do a bind we have to + + align:start position:0% +we have to do is do a bind we have to + + + align:start position:0% +we have to do is do a bind we have to +bind a new environment is made at this + + align:start position:0% +bind a new environment is made at this + + + align:start position:0% +bind a new environment is made at this +point which has as its parent + + align:start position:0% +point which has as its parent + + + align:start position:0% +point which has as its parent +environment the one over here + + align:start position:0% +environment the one over here + + + align:start position:0% +environment the one over here +easy row that environment they will call + + align:start position:0% +easy row that environment they will call + + + align:start position:0% +easy row that environment they will call +this one you are now what's bound in + + align:start position:0% +this one you are now what's bound in + + + align:start position:0% +this one you are now what's bound in +there X is bound to three right so I + + align:start position:0% +there X is bound to three right so I + + + align:start position:0% +there X is bound to three right so I +have x equals three that's what's in + + align:start position:0% +have x equals three that's what's in + + + align:start position:0% +have x equals three that's what's in +there okay and we'll call that e1 so + + align:start position:0% +there okay and we'll call that e1 so + + + align:start position:0% +there okay and we'll call that e1 so +what this transforms into is an eval of + + align:start position:0% +what this transforms into is an eval of + + + align:start position:0% +what this transforms into is an eval of +the body of this which is this the body + + align:start position:0% +the body of this which is this the body + + + align:start position:0% +the body of this which is this the body +of that procedure in the environment + + align:start position:0% +of that procedure in the environment + + + align:start position:0% +of that procedure in the environment +that you just saw so that's an apply of + + align:start position:0% +that you just saw so that's an apply of + + + align:start position:0% +that you just saw so that's an apply of +eval quote open lambda of y plus XY the + + align:start position:0% +eval quote open lambda of y plus XY the + + + align:start position:0% +eval quote open lambda of y plus XY the +body in a1 and apply the result of that + + align:start position:0% +body in a1 and apply the result of that + + + align:start position:0% +body in a1 and apply the result of that +to four open clothes for list of + + align:start position:0% +to four open clothes for list of + + + align:start position:0% +to four open clothes for list of +arguments + + align:start position:0% +arguments + + + align:start position:0% +arguments +okay well that's sensible enough because + + align:start position:0% +okay well that's sensible enough because + + + align:start position:0% +okay well that's sensible enough because +evaluating a lambda I know what to do + + align:start position:0% +evaluating a lambda I know what to do + + + align:start position:0% +evaluating a lambda I know what to do +that means I apply the procedure which + + align:start position:0% +that means I apply the procedure which + + + align:start position:0% +that means I apply the procedure which +is closure + + align:start position:0% + + + + align:start position:0% + +find one argument why ads X to Y with II + + align:start position:0% +find one argument why ads X to Y with II + + + align:start position:0% +find one argument why ads X to Y with II +one captured in it and you should really + + align:start position:0% +one captured in it and you should really + + + align:start position:0% +one captured in it and you should really +see this right + + align:start position:0% +see this right + + + align:start position:0% +see this right +I somehow manufactured a closure I + + align:start position:0% +I somehow manufactured a closure I + + + align:start position:0% +I somehow manufactured a closure I +should have put this year there was one + + align:start position:0% +should have put this year there was one + + + align:start position:0% +should have put this year there was one +over here too okay well there's one here + + align:start position:0% +over here too okay well there's one here + + + align:start position:0% +over here too okay well there's one here +now I've captured a one and this is the + + align:start position:0% +now I've captured a one and this is the + + + align:start position:0% +now I've captured a one and this is the +procedure of one argument why okay + + align:start position:0% +procedure of one argument why okay + + + align:start position:0% +procedure of one argument why okay +whatever this is that's what that is + + align:start position:0% +whatever this is that's what that is + + + align:start position:0% +whatever this is that's what that is +there that closure okay I'm gonna apply + + align:start position:0% +there that closure okay I'm gonna apply + + + align:start position:0% +there that closure okay I'm gonna apply +that to four okay well that's easy + + align:start position:0% +that to four okay well that's easy + + + align:start position:0% +that to four okay well that's easy +enough that means I have to make a new + + align:start position:0% +enough that means I have to make a new + + + align:start position:0% +enough that means I have to make a new +environment by copying this pointer + + align:start position:0% +environment by copying this pointer + + + align:start position:0% +environment by copying this pointer +which is the pointer of the procedure + + align:start position:0% +which is the pointer of the procedure + + + align:start position:0% +which is the pointer of the procedure +which binds y equal four with that + + align:start position:0% +which binds y equal four with that + + + align:start position:0% +which binds y equal four with that +environment and here's my new + + align:start position:0% +environment and here's my new + + + align:start position:0% +environment and here's my new +environment which I'll call E - hmm and + + align:start position:0% +environment which I'll call E - hmm and + + + align:start position:0% +environment which I'll call E - hmm and +of course this application then is + + align:start position:0% +of course this application then is + + + align:start position:0% +of course this application then is +evaluate the body in E - okay so this is + + align:start position:0% +evaluate the body in E - okay so this is + + + align:start position:0% +evaluate the body in E - okay so this is +eval the body which is plus X Y in the + + align:start position:0% +eval the body which is plus X Y in the + + + align:start position:0% +eval the body which is plus X Y in the +environment e - oh but this is an + + align:start position:0% +environment e - oh but this is an + + + align:start position:0% +environment e - oh but this is an +application so this is the apply of eval + + align:start position:0% +application so this is the apply of eval + + + align:start position:0% +application so this is the apply of eval ++ in e to an M list + + align:start position:0% + + + + align:start position:0% + +quote open X&Y in E - okay well but + + align:start position:0% +quote open X&Y in E - okay well but + + + align:start position:0% +quote open X&Y in E - okay well but +let's see that is a fly the object which + + align:start position:0% +let's see that is a fly the object which + + + align:start position:0% +let's see that is a fly the object which +is the result of valuing + so here we + + align:start position:0% +is the result of valuing + so here we + + + align:start position:0% +is the result of valuing + so here we +are any 2 plus is not here it's not here + + align:start position:0% +are any 2 plus is not here it's not here + + + align:start position:0% +are any 2 plus is not here it's not here +oh yes but it's here or some primitive + + align:start position:0% +oh yes but it's here or some primitive + + + align:start position:0% +oh yes but it's here or some primitive +operator okay so it's the primitive + + align:start position:0% +operator okay so it's the primitive + + + align:start position:0% +operator okay so it's the primitive +operator for addition okay + + align:start position:0% +operator for addition okay + + + align:start position:0% +operator for addition okay +apply that to the result of evaluating x + + align:start position:0% +apply that to the result of evaluating x + + + align:start position:0% +apply that to the result of evaluating x +and y in e2 we can see that X is 3 and Y + + align:start position:0% +and y in e2 we can see that X is 3 and Y + + + align:start position:0% +and y in e2 we can see that X is 3 and Y +is 4 + + align:start position:0% +is 4 + + + align:start position:0% +is 4 +okay so that's a 2 3 and 4 here and that + + align:start position:0% +okay so that's a 2 3 and 4 here and that + + + align:start position:0% +okay so that's a 2 3 and 4 here and that +magically produces from the s7 I wanted + + align:start position:0% +magically produces from the s7 I wanted + + + align:start position:0% +magically produces from the s7 I wanted +to go through this so you would see + + align:start position:0% +to go through this so you would see + + + align:start position:0% +to go through this so you would see +essentially one important ingredient + + align:start position:0% +essentially one important ingredient + + + align:start position:0% +essentially one important ingredient +which is what's being passed around and + + align:start position:0% +which is what's being passed around and + + + align:start position:0% +which is what's being passed around and +who is one watt and what his job is so + + align:start position:0% +who is one watt and what his job is so + + + align:start position:0% +who is one watt and what his job is so +what do we have here we have eval now we + + align:start position:0% +what do we have here we have eval now we + + + align:start position:0% +what do we have here we have eval now we +have apply the two main players and + + align:start position:0% +have apply the two main players and + + + align:start position:0% +have apply the two main players and +there is a big loop that goes around + + align:start position:0% +there is a big loop that goes around + + + align:start position:0% +there is a big loop that goes around +like this which is eval produces + + align:start position:0% +like this which is eval produces + + + align:start position:0% +like this which is eval produces +produces a procedure and arguments for + + align:start position:0% +produces a procedure and arguments for + + + align:start position:0% +produces a procedure and arguments for +apply now about some things eval could + + align:start position:0% +apply now about some things eval could + + + align:start position:0% +apply now about some things eval could +do by itself does a little self things + + align:start position:0% +do by itself does a little self things + + + align:start position:0% +do by itself does a little self things +here they're not interesting we're also + + align:start position:0% +here they're not interesting we're also + + + align:start position:0% +here they're not interesting we're also +a valley valuates all of the arguments + + align:start position:0% +a valley valuates all of the arguments + + + align:start position:0% +a valley valuates all of the arguments +one after another that's not very + + align:start position:0% +one after another that's not very + + + align:start position:0% +one after another that's not very +interesting apply can pretty of why some + + align:start position:0% +interesting apply can pretty of why some + + + align:start position:0% +interesting apply can pretty of why some +procedures like + not very interesting + + align:start position:0% +procedures like + not very interesting + + + align:start position:0% +procedures like + not very interesting +however I can't apply a procedure like + + + align:start position:0% +however I can't apply a procedure like + + + + align:start position:0% +however I can't apply a procedure like + +it produces an expression an environment + + align:start position:0% +it produces an expression an environment + + + align:start position:0% +it produces an expression an environment +for for eval the procedure in arguments + + align:start position:0% +for for eval the procedure in arguments + + + align:start position:0% +for for eval the procedure in arguments +wrap up the state essentially the state + + align:start position:0% +wrap up the state essentially the state + + + align:start position:0% +wrap up the state essentially the state +of a computation and similarly the + + align:start position:0% +of a computation and similarly the + + + align:start position:0% +of a computation and similarly the +expression environment and so what we're + + align:start position:0% +expression environment and so what we're + + + align:start position:0% +expression environment and so what we're +actually going to do next is not the + + align:start position:0% +actually going to do next is not the + + + align:start position:0% +actually going to do next is not the +complete state because doesn't say what + + align:start position:0% +complete state because doesn't say what + + + align:start position:0% +complete state because doesn't say what +things who wants the answers but what + + align:start position:0% +things who wants the answers but what + + + align:start position:0% +things who wants the answers but what +we're going to it's always got something + + align:start position:0% +we're going to it's always got something + + + align:start position:0% +we're going to it's always got something +like in the expression and environment + + align:start position:0% +like in the expression and environment + + + align:start position:0% +like in the expression and environment +or procedure in arguments that's the + + align:start position:0% +or procedure in arguments that's the + + + align:start position:0% +or procedure in arguments that's the +main loop that we're going around there + + align:start position:0% +main loop that we're going around there + + + align:start position:0% +main loop that we're going around there +are minor little sub loops like give al + + align:start position:0% +are minor little sub loops like give al + + + align:start position:0% +are minor little sub loops like give al +through a blister or eval through F cond + + align:start position:0% +through a blister or eval through F cond + + + align:start position:0% +through a blister or eval through F cond +you know or apply through a primitive + + align:start position:0% +you know or apply through a primitive + + + align:start position:0% +you know or apply through a primitive +apply but they're not the essential + + align:start position:0% +apply but they're not the essential + + + align:start position:0% +apply but they're not the essential +things so that's what I wanted you to + + align:start position:0% +things so that's what I wanted you to + + + align:start position:0% +things so that's what I wanted you to +say are there any questions yes I'm + + align:start position:0% +say are there any questions yes I'm + + + align:start position:0% +say are there any questions yes I'm +trying to understand how X got down to + + align:start position:0% +trying to understand how X got down to + + + align:start position:0% +trying to understand how X got down to +three instead of four at the early part + + align:start position:0% +three instead of four at the early part + + + align:start position:0% +three instead of four at the early part +of the year here you want to know how X + + align:start position:0% +of the year here you want to know how X + + + align:start position:0% +of the year here you want to know how X +got down to three because X is the outer + + align:start position:0% +got down to three because X is the outer + + + align:start position:0% +got down to three because X is the outer +procedure and x and y is the inner + + align:start position:0% +procedure and x and y is the inner + + + align:start position:0% +procedure and x and y is the inner +procedure fine so I was very careful in + + align:start position:0% +procedure fine so I was very careful in + + + align:start position:0% +procedure fine so I was very careful in +mechanical name first of all I should + + align:start position:0% +mechanical name first of all I should + + + align:start position:0% +mechanical name first of all I should +write those procedures again for you + + align:start position:0% +write those procedures again for you + + + align:start position:0% +write those procedures again for you +pretty printed first order of business + + align:start position:0% +pretty printed first order of business + + + align:start position:0% +pretty printed first order of business +because you're probably not reading them + + align:start position:0% +because you're probably not reading them + + + align:start position:0% +because you're probably not reading them +well so I have here that procedure of + + align:start position:0% +well so I have here that procedure of + + + align:start position:0% +well so I have here that procedure of +was it x over there which is value is + + align:start position:0% +was it x over there which is value is + + + align:start position:0% +was it x over there which is value is +that procedure of Y which adds X to Y + + align:start position:0% +that procedure of Y which adds X to Y + + + align:start position:0% +that procedure of Y which adds X to Y +and lambda applied that to three take + + align:start position:0% +and lambda applied that to three take + + + align:start position:0% +and lambda applied that to three take +the result of that and applied that to + + align:start position:0% +the result of that and applied that to + + + align:start position:0% +the result of that and applied that to +four is that not what I wrote okay now + + align:start position:0% +four is that not what I wrote okay now + + + align:start position:0% +four is that not what I wrote okay now +you should immediately see that here is + + align:start position:0% +you should immediately see that here is + + + align:start position:0% +you should immediately see that here is +an application let me get a white piece + + align:start position:0% +an application let me get a white piece + + + align:start position:0% +an application let me get a white piece +of chalk here is an application a + + align:start position:0% +of chalk here is an application a + + + align:start position:0% +of chalk here is an application a +combination + + align:start position:0% +combination + + + align:start position:0% +combination +okay that combination has this is the + + align:start position:0% +okay that combination has this is the + + + align:start position:0% +okay that combination has this is the +operator and this is the operand the + + align:start position:0% +operator and this is the operand the + + + align:start position:0% +operator and this is the operand the +three is going in for the X here the + + align:start position:0% +three is going in for the X here the + + + align:start position:0% +three is going in for the X here the +result of this is a procedure of one + + align:start position:0% +result of this is a procedure of one + + + align:start position:0% +result of this is a procedure of one +argument Y which gets applied to four + + align:start position:0% +argument Y which gets applied to four + + + align:start position:0% +argument Y which gets applied to four +okay so you just weren't reading the + + align:start position:0% +okay so you just weren't reading the + + + align:start position:0% +okay so you just weren't reading the +expression right the way you see that + + align:start position:0% +expression right the way you see that + + + align:start position:0% +expression right the way you see that +over here okay is that here I have the + + align:start position:0% +over here okay is that here I have the + + + align:start position:0% +over here okay is that here I have the +actual procedure object X it's getting + + align:start position:0% +actual procedure object X it's getting + + + align:start position:0% +actual procedure object X it's getting +applied to three the list containing + + align:start position:0% +applied to three the list containing + + + align:start position:0% +applied to three the list containing +three what I'm left over with is + + align:start position:0% +three what I'm left over with is + + + align:start position:0% +three what I'm left over with is +something which gets applied to four + + align:start position:0% +something which gets applied to four + + + align:start position:0% +something which gets applied to four +okay are there any other questions okay + + align:start position:0% + + + + align:start position:0% + +time for our next small break then thank + + align:start position:0% +time for our next small break then thank + + + align:start position:0% +time for our next small break then thank +you + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +let's see at this point you should be + + align:start position:0% +let's see at this point you should be + + + align:start position:0% +let's see at this point you should be +getting the feeling what's this nonsense + + align:start position:0% +getting the feeling what's this nonsense + + + align:start position:0% +getting the feeling what's this nonsense +the Sussman character is feeding me + + align:start position:0% + + + + align:start position:0% + +there's an awful lot of strange nonsense + + align:start position:0% +there's an awful lot of strange nonsense + + + align:start position:0% +there's an awful lot of strange nonsense +here after all he purported to explain + + align:start position:0% +here after all he purported to explain + + + align:start position:0% +here after all he purported to explain +to me lisp + + align:start position:0% +to me lisp + + + align:start position:0% +to me lisp +they wrote me a list program on the + + align:start position:0% +they wrote me a list program on the + + + align:start position:0% +they wrote me a list program on the +blackboard this program was intended to + + align:start position:0% +blackboard this program was intended to + + + align:start position:0% +blackboard this program was intended to +be interpreter for lisp but you need a + + align:start position:0% +be interpreter for lisp but you need a + + + align:start position:0% +be interpreter for lisp but you need a +list printer patern order to understand + + align:start position:0% +list printer patern order to understand + + + align:start position:0% +list printer patern order to understand +that program how could that program have + + align:start position:0% +that program how could that program have + + + align:start position:0% +that program how could that program have +told me anything there is to be known + + align:start position:0% +told me anything there is to be known + + + align:start position:0% +told me anything there is to be known +about lisp how is that not completely + + align:start position:0% +about lisp how is that not completely + + + align:start position:0% +about lisp how is that not completely +vacuous it's a very strange thing does + + align:start position:0% +vacuous it's a very strange thing does + + + align:start position:0% +vacuous it's a very strange thing does +it tell me anything at all well you see + + align:start position:0% +it tell me anything at all well you see + + + align:start position:0% +it tell me anything at all well you see +the whole thing is sort of like these + + align:start position:0% +the whole thing is sort of like these + + + align:start position:0% +the whole thing is sort of like these +extras hands that we see on this slide + + align:start position:0% +extras hands that we see on this slide + + + align:start position:0% +extras hands that we see on this slide +okay yes eval and apply each sort of + + align:start position:0% +okay yes eval and apply each sort of + + + align:start position:0% +okay yes eval and apply each sort of +draw each other and construct construct + + align:start position:0% +draw each other and construct construct + + + align:start position:0% +draw each other and construct construct +the real thing which can sit out and + + align:start position:0% +the real thing which can sit out and + + + align:start position:0% +the real thing which can sit out and +draw itself Esther was a very brilliant + + align:start position:0% +draw itself Esther was a very brilliant + + + align:start position:0% +draw itself Esther was a very brilliant +man he just didn't know the names of + + align:start position:0% +man he just didn't know the names of + + + align:start position:0% +man he just didn't know the names of +these spirits what I'm going to do now + + align:start position:0% +these spirits what I'm going to do now + + + align:start position:0% +these spirits what I'm going to do now +because I'm going to try to convince you + + align:start position:0% +because I'm going to try to convince you + + + align:start position:0% +because I'm going to try to convince you +that both this means something and as a + + align:start position:0% +that both this means something and as a + + + align:start position:0% +that both this means something and as a +aside I'm going to show you why you + + align:start position:0% +aside I'm going to show you why you + + + align:start position:0% +aside I'm going to show you why you +don't need definitions just turns out + + align:start position:0% +don't need definitions just turns out + + + align:start position:0% +don't need definitions just turns out +that sort of falls out why definitions + + align:start position:0% +that sort of falls out why definitions + + + align:start position:0% +that sort of falls out why definitions +aren't essential in a mathematical sense + + align:start position:0% +aren't essential in a mathematical sense + + + align:start position:0% +aren't essential in a mathematical sense +for doing all the things that we need to + + align:start position:0% +for doing all the things that we need to + + + align:start position:0% +for doing all the things that we need to +do for computing well let's see here + + align:start position:0% +do for computing well let's see here + + + align:start position:0% +do for computing well let's see here +consider the following small program + + align:start position:0% +consider the following small program + + + align:start position:0% +consider the following small program +what does it mean is a program for + + align:start position:0% +what does it mean is a program for + + + align:start position:0% +what does it mean is a program for +computing Exponential's + + align:start position:0% + + + + align:start position:0% + +the exponential of X to the nth power is + + align:start position:0% +the exponential of X to the nth power is + + + align:start position:0% +the exponential of X to the nth power is +if n is zero then the result is 1 + + align:start position:0% +if n is zero then the result is 1 + + + align:start position:0% +if n is zero then the result is 1 +otherwise I want the product of X and + + align:start position:0% +otherwise I want the product of X and + + + align:start position:0% +otherwise I want the product of X and +the result of exponentiating X to the n + + align:start position:0% +the result of exponentiating X to the n + + + align:start position:0% +the result of exponentiating X to the n +minus 1 power I think I got it right now + + align:start position:0% +minus 1 power I think I got it right now + + + align:start position:0% +minus 1 power I think I got it right now +this is a recursive definition it's + + align:start position:0% +this is a recursive definition it's + + + align:start position:0% +this is a recursive definition it's +definition of the exponentiation + + align:start position:0% +definition of the exponentiation + + + align:start position:0% +definition of the exponentiation +procedure in terms of itself and as has + + align:start position:0% +procedure in terms of itself and as has + + + align:start position:0% +procedure in terms of itself and as has +been mentioned before your high school + + align:start position:0% +been mentioned before your high school + + + align:start position:0% +been mentioned before your high school +geometry teacher probably gave you a + + align:start position:0% +geometry teacher probably gave you a + + + align:start position:0% +geometry teacher probably gave you a +hard time about things like that was + + align:start position:0% +hard time about things like that was + + + align:start position:0% +hard time about things like that was +that justified why does this self + + align:start position:0% +that justified why does this self + + + align:start position:0% +that justified why does this self +referential definition make any sense + + align:start position:0% +referential definition make any sense + + + align:start position:0% +referential definition make any sense +well first of all I'm going to convince + + align:start position:0% +well first of all I'm going to convince + + + align:start position:0% +well first of all I'm going to convince +you that your high school geometry + + align:start position:0% +you that your high school geometry + + + align:start position:0% +you that your high school geometry +teacher then Sally telling you nonsense + + align:start position:0% + + + + align:start position:0% + +consider the following set of + + align:start position:0% +consider the following set of + + + align:start position:0% +consider the following set of +definitions here X plus y equals 3 and X + + align:start position:0% +definitions here X plus y equals 3 and X + + + align:start position:0% +definitions here X plus y equals 3 and X +minus y equal 1 well gee this tells you + + align:start position:0% +minus y equal 1 well gee this tells you + + + align:start position:0% +minus y equal 1 well gee this tells you +X in terms of Y and this one tells you Y + + align:start position:0% +X in terms of Y and this one tells you Y + + + align:start position:0% +X in terms of Y and this one tells you Y +in terms of X presumably and yet this + + align:start position:0% +in terms of X presumably and yet this + + + align:start position:0% +in terms of X presumably and yet this +happens to have a unique solution in X + + align:start position:0% +happens to have a unique solution in X + + + align:start position:0% +happens to have a unique solution in X +and y + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +however I could also write 2x plus 2y + + align:start position:0% +however I could also write 2x plus 2y + + + align:start position:0% +however I could also write 2x plus 2y +and six these two equations have an + + align:start position:0% +and six these two equations have an + + + align:start position:0% +and six these two equations have an +infinite number of solutions and I could + + align:start position:0% +infinite number of solutions and I could + + + align:start position:0% +infinite number of solutions and I could +write you for example X minus y equal + + align:start position:0% +write you for example X minus y equal + + + align:start position:0% +write you for example X minus y equal +two and these two equations have no + + align:start position:0% +two and these two equations have no + + + align:start position:0% +two and these two equations have no +solutions well I have here three sets of + + align:start position:0% +solutions well I have here three sets of + + + align:start position:0% +solutions well I have here three sets of +simultaneous linear equations this set + + align:start position:0% +simultaneous linear equations this set + + + align:start position:0% +simultaneous linear equations this set +this set and this set they have + + align:start position:0% +this set and this set they have + + + align:start position:0% +this set and this set they have +different numbers of solutions the + + align:start position:0% +different numbers of solutions the + + + align:start position:0% +different numbers of solutions the +number of solutions is not in the form + + align:start position:0% +number of solutions is not in the form + + + align:start position:0% +number of solutions is not in the form +of the equations they all three sets + + align:start position:0% +of the equations they all three sets + + + align:start position:0% +of the equations they all three sets +have the same form the number of + + align:start position:0% +have the same form the number of + + + align:start position:0% +have the same form the number of +solutions is in the content I can't tell + + align:start position:0% +solutions is in the content I can't tell + + + align:start position:0% +solutions is in the content I can't tell +by looking at the form of a definition + + align:start position:0% +by looking at the form of a definition + + + align:start position:0% +by looking at the form of a definition +whether it makes sense only by its + + align:start position:0% +whether it makes sense only by its + + + align:start position:0% +whether it makes sense only by its +detailed content what are the + + align:start position:0% +detailed content what are the + + + align:start position:0% +detailed content what are the +coefficients for example in the case of + + align:start position:0% +coefficients for example in the case of + + + align:start position:0% +coefficients for example in the case of +linear equations so I shouldn't expect + + align:start position:0% +linear equations so I shouldn't expect + + + align:start position:0% +linear equations so I shouldn't expect +to be able to tell looking at something + + align:start position:0% +to be able to tell looking at something + + + align:start position:0% +to be able to tell looking at something +like this from some simple thing like oh + + align:start position:0% +like this from some simple thing like oh + + + align:start position:0% +like this from some simple thing like oh +yes the X PT is the solution of this + + align:start position:0% +yes the X PT is the solution of this + + + align:start position:0% +yes the X PT is the solution of this +recursion equation the X PT is the + + align:start position:0% +recursion equation the X PT is the + + + align:start position:0% +recursion equation the X PT is the +procedure which if substituted in here + + align:start position:0% +procedure which if substituted in here + + + align:start position:0% +procedure which if substituted in here +gives me the x PT back okay I can't tell + + align:start position:0% +gives me the x PT back okay I can't tell + + + align:start position:0% +gives me the x PT back okay I can't tell +looking at this form whether or not in + + align:start position:0% +looking at this form whether or not in + + + align:start position:0% +looking at this form whether or not in +there is a single unique solution for + + align:start position:0% +there is a single unique solution for + + + align:start position:0% +there is a single unique solution for +the X BT and infinite number of + + align:start position:0% +the X BT and infinite number of + + + align:start position:0% +the X BT and infinite number of +solutions or no solutions + + align:start position:0% +solutions or no solutions + + + align:start position:0% +solutions or no solutions +it's got to be how it counts and things + + align:start position:0% +it's got to be how it counts and things + + + align:start position:0% +it's got to be how it counts and things +like that the details and it's harder in + + align:start position:0% +like that the details and it's harder in + + + align:start position:0% +like that the details and it's harder in +programming than linear algebra there + + align:start position:0% +programming than linear algebra there + + + align:start position:0% +programming than linear algebra there +are too many theorems about it in + + align:start position:0% +are too many theorems about it in + + + align:start position:0% +are too many theorems about it in +programming + + align:start position:0% + + + + align:start position:0% + +well I want to rewrite these equations a + + align:start position:0% +well I want to rewrite these equations a + + + align:start position:0% +well I want to rewrite these equations a +little bit these over here because what + + align:start position:0% +little bit these over here because what + + + align:start position:0% +little bit these over here because what +we're investigating equations like this + + align:start position:0% +we're investigating equations like this + + + align:start position:0% +we're investigating equations like this +but I want to play a little bit + + align:start position:0% +but I want to play a little bit + + + align:start position:0% +but I want to play a little bit +equations like this that we understand + + align:start position:0% +equations like this that we understand + + + align:start position:0% +equations like this that we understand +just so we get some insight into this + + align:start position:0% +just so we get some insight into this + + + align:start position:0% +just so we get some insight into this +kind of equation we could rewrite our + + align:start position:0% +kind of equation we could rewrite our + + + align:start position:0% +kind of equation we could rewrite our +equations here say these two the ones + + align:start position:0% +equations here say these two the ones + + + align:start position:0% +equations here say these two the ones +that are interesting as x equals three + + align:start position:0% +that are interesting as x equals three + + + align:start position:0% +that are interesting as x equals three +minus y and y equals x minus one what do + + align:start position:0% +minus y and y equals x minus one what do + + + align:start position:0% +minus y and y equals x minus one what do +we call this transformation there's a + + align:start position:0% +we call this transformation there's a + + + align:start position:0% +we call this transformation there's a +linear transformation T then what we're + + align:start position:0% +linear transformation T then what we're + + + align:start position:0% +linear transformation T then what we're +getting here is an equation X y equals T + + align:start position:0% +getting here is an equation X y equals T + + + align:start position:0% +getting here is an equation X y equals T +of X Y what am I looking for I'm looking + + align:start position:0% +of X Y what am I looking for I'm looking + + + align:start position:0% +of X Y what am I looking for I'm looking +for a fixed point of T that's the + + align:start position:0% +for a fixed point of T that's the + + + align:start position:0% +for a fixed point of T that's the +solution it is a fixed point no T so the + + align:start position:0% +solution it is a fixed point no T so the + + + align:start position:0% +solution it is a fixed point no T so the +methods we should have we're looking for + + align:start position:0% +methods we should have we're looking for + + + align:start position:0% +methods we should have we're looking for +solutions to equations if I can do it by + + align:start position:0% +solutions to equations if I can do it by + + + align:start position:0% +solutions to equations if I can do it by +fixed points might be applicable if I + + align:start position:0% +fixed points might be applicable if I + + + align:start position:0% +fixed points might be applicable if I +have a means of finding a solution to an + + align:start position:0% +have a means of finding a solution to an + + + align:start position:0% +have a means of finding a solution to an +equation by fixed points you just may + + align:start position:0% +equation by fixed points you just may + + + align:start position:0% +equation by fixed points you just may +not might not work but it might be + + align:start position:0% +not might not work but it might be + + + align:start position:0% +not might not work but it might be +applicable to investigating solutions of + + align:start position:0% +applicable to investigating solutions of + + + align:start position:0% +applicable to investigating solutions of +equations like this but what I want you + + align:start position:0% +equations like this but what I want you + + + align:start position:0% +equations like this but what I want you +to feel is that this is an equation it's + + align:start position:0% +to feel is that this is an equation it's + + + align:start position:0% +to feel is that this is an equation it's +an expression with several instances of + + align:start position:0% +an expression with several instances of + + + align:start position:0% +an expression with several instances of +various names which puts a constraint on + + align:start position:0% +various names which puts a constraint on + + + align:start position:0% +various names which puts a constraint on +the name saying what that name could + + align:start position:0% +the name saying what that name could + + + align:start position:0% +the name saying what that name could +have as its value rather than some sort + + align:start position:0% +have as its value rather than some sort + + + align:start position:0% +have as its value rather than some sort +of mechanical process of substitution + + align:start position:0% +of mechanical process of substitution + + + align:start position:0% +of mechanical process of substitution +right now this is an equation which I'm + + align:start position:0% +right now this is an equation which I'm + + + align:start position:0% +right now this is an equation which I'm +going to try to solve but let's play + + align:start position:0% +going to try to solve but let's play + + + align:start position:0% +going to try to solve but let's play +around and solve it first of all I want + + align:start position:0% +around and solve it first of all I want + + + align:start position:0% +around and solve it first of all I want +to write down the function which + + align:start position:0% +to write down the function which + + + align:start position:0% +to write down the function which +corresponds to T + + align:start position:0% +corresponds to T + + + align:start position:0% +corresponds to T +first I want to write down the function + + align:start position:0% +first I want to write down the function + + + align:start position:0% +first I want to write down the function +which corresponds to T whose fixed point + + align:start position:0% +which corresponds to T whose fixed point + + + align:start position:0% +which corresponds to T whose fixed point +is the answer to this question okay + + align:start position:0% +is the answer to this question okay + + + align:start position:0% +is the answer to this question okay +let's consider the following procedure + + align:start position:0% +let's consider the following procedure + + + align:start position:0% +let's consider the following procedure +app I claim to compute to that function + + align:start position:0% +app I claim to compute to that function + + + align:start position:0% +app I claim to compute to that function +f is that procedure of one argument G + + align:start position:0% +f is that procedure of one argument G + + + align:start position:0% +f is that procedure of one argument G +which is that procedure of two arguments + + align:start position:0% +which is that procedure of two arguments + + + align:start position:0% +which is that procedure of two arguments +X and n which have the property that if + + align:start position:0% + + + + align:start position:0% + +n is zero then the result is one + + align:start position:0% +n is zero then the result is one + + + align:start position:0% +n is zero then the result is one +otherwise the result is the product of X + + align:start position:0% +otherwise the result is the product of X + + + align:start position:0% +otherwise the result is the product of X +and G applied to X and minus and one G + + align:start position:0% +and G applied to X and minus and one G + + + align:start position:0% +and G applied to X and minus and one G +times else cond lambda lambda okay here + + align:start position:0% +times else cond lambda lambda okay here + + + align:start position:0% +times else cond lambda lambda okay here +F is a procedure which I had a solution + + align:start position:0% +F is a procedure which I had a solution + + + align:start position:0% +F is a procedure which I had a solution +to that equation if i had a good + + align:start position:0% +to that equation if i had a good + + + align:start position:0% +to that equation if i had a good +exponentiation procedure and I applied F + + align:start position:0% +exponentiation procedure and I applied F + + + align:start position:0% +exponentiation procedure and I applied F +to that procedure then the result would + + align:start position:0% +to that procedure then the result would + + + align:start position:0% +to that procedure then the result would +be a good exponentiation procedure + + align:start position:0% + + + + align:start position:0% + +because what does it do well all it is + + align:start position:0% +because what does it do well all it is + + + align:start position:0% +because what does it do well all it is +is exposing gee we're a good + + align:start position:0% +is exposing gee we're a good + + + align:start position:0% +is exposing gee we're a good +exponentiation procedure well then this + + align:start position:0% +exponentiation procedure well then this + + + align:start position:0% +exponentiation procedure well then this +would produce as its value a procedure + + align:start position:0% +would produce as its value a procedure + + + align:start position:0% +would produce as its value a procedure +of two arguments X and n such that if n + + align:start position:0% +of two arguments X and n such that if n + + + align:start position:0% +of two arguments X and n such that if n +were 0 the result would be 1 which + + align:start position:0% +were 0 the result would be 1 which + + + align:start position:0% +were 0 the result would be 1 which +certainly true of exponentiation + + align:start position:0% +certainly true of exponentiation + + + align:start position:0% +certainly true of exponentiation +otherwise it would be the result of + + align:start position:0% +otherwise it would be the result of + + + align:start position:0% +otherwise it would be the result of +multiplying X by the exponentiation + + align:start position:0% +multiplying X by the exponentiation + + + align:start position:0% +multiplying X by the exponentiation +procedure given to me with x and n minus + + align:start position:0% +procedure given to me with x and n minus + + + align:start position:0% +procedure given to me with x and n minus +1 as arguments so if this computed the + + align:start position:0% +1 as arguments so if this computed the + + + align:start position:0% +1 as arguments so if this computed the +correct exponentiation for n minus 1 + + align:start position:0% +correct exponentiation for n minus 1 + + + align:start position:0% +correct exponentiation for n minus 1 +then this would be the correct + + align:start position:0% +then this would be the correct + + + align:start position:0% +then this would be the correct +exponentiation for a 3 exponent n so + + align:start position:0% +exponentiation for a 3 exponent n so + + + align:start position:0% +exponentiation for a 3 exponent n so +this would have been the right + + align:start position:0% +this would have been the right + + + align:start position:0% +this would have been the right +exponentiation procedure so what I + + align:start position:0% +exponentiation procedure so what I + + + align:start position:0% +exponentiation procedure so what I +really want to say here is e x PT is a + + align:start position:0% +really want to say here is e x PT is a + + + align:start position:0% +really want to say here is e x PT is a +fixed point now now our problem is there + + align:start position:0% +fixed point now now our problem is there + + + align:start position:0% +fixed point now now our problem is there +might be more than one fixed point there + + align:start position:0% +might be more than one fixed point there + + + align:start position:0% +might be more than one fixed point there +might be no fixed points I have to go + + align:start position:0% +might be no fixed points I have to go + + + align:start position:0% +might be no fixed points I have to go +hunting for the fixed points I solve + + align:start position:0% +hunting for the fixed points I solve + + + align:start position:0% +hunting for the fixed points I solve +this equation well there are various + + align:start position:0% +this equation well there are various + + + align:start position:0% +this equation well there are various +ways to hunt for fixed points of course + + align:start position:0% +ways to hunt for fixed points of course + + + align:start position:0% +ways to hunt for fixed points of course +the one we played with at the beginning + + align:start position:0% +the one we played with at the beginning + + + align:start position:0% +the one we played with at the beginning +of this term worked for a cosine going + + align:start position:0% +of this term worked for a cosine going + + + align:start position:0% +of this term worked for a cosine going +to go into radians mode on your + + align:start position:0% +to go into radians mode on your + + + align:start position:0% +to go into radians mode on your +calculator and push cosine just keep + + align:start position:0% +calculator and push cosine just keep + + + align:start position:0% +calculator and push cosine just keep +doing it and you get the sum number + + align:start position:0% +doing it and you get the sum number + + + align:start position:0% +doing it and you get the sum number +which is about 0.73 0.74 I can't + + align:start position:0% +which is about 0.73 0.74 I can't + + + align:start position:0% +which is about 0.73 0.74 I can't +remember which by iterating a procedure + + align:start position:0% +remember which by iterating a procedure + + + align:start position:0% +remember which by iterating a procedure +which has by iterating a function whose + + align:start position:0% +which has by iterating a function whose + + + align:start position:0% +which has by iterating a function whose +fixed point I'm searching for it is + + align:start position:0% +fixed point I'm searching for it is + + + align:start position:0% +fixed point I'm searching for it is +sometimes the case now that function + + align:start position:0% +sometimes the case now that function + + + align:start position:0% +sometimes the case now that function +will converge and produce me the fixed + + align:start position:0% +will converge and produce me the fixed + + + align:start position:0% +will converge and produce me the fixed +point I think we luck out in this case + + align:start position:0% +point I think we luck out in this case + + + align:start position:0% +point I think we luck out in this case +so let's look for it let's look at this + + align:start position:0% +so let's look for it let's look at this + + + align:start position:0% +so let's look for it let's look at this +overhead + + align:start position:0% +overhead + + + align:start position:0% +overhead +it's a slot of the slide consider the + + align:start position:0% +it's a slot of the slide consider the + + + align:start position:0% +it's a slot of the slide consider the +following sequence of procedures easy + + align:start position:0% +following sequence of procedures easy + + + align:start position:0% +following sequence of procedures easy +row over here is the procedure which + + align:start position:0% +row over here is the procedure which + + + align:start position:0% +row over here is the procedure which +does nothing at all + + align:start position:0% +does nothing at all + + + align:start position:0% +does nothing at all +it's the procedure which produces an + + align:start position:0% +it's the procedure which produces an + + + align:start position:0% +it's the procedure which produces an +error for any arguments you give it it's + + align:start position:0% +error for any arguments you give it it's + + + align:start position:0% +error for any arguments you give it it's +basically useless + + align:start position:0% + + + + align:start position:0% + +well however I can make an approximation + + align:start position:0% +well however I can make an approximation + + + align:start position:0% +well however I can make an approximation +let's consider it the worst possible + + align:start position:0% +let's consider it the worst possible + + + align:start position:0% +let's consider it the worst possible +approximation to exponentiation because + + align:start position:0% +approximation to exponentiation because + + + align:start position:0% +approximation to exponentiation because +it does nothing well supposing I + + align:start position:0% +it does nothing well supposing I + + + align:start position:0% +it does nothing well supposing I +substitute it easy Rho for G by calling + + align:start position:0% +substitute it easy Rho for G by calling + + + align:start position:0% +substitute it easy Rho for G by calling +F as you see over here on easy row so + + align:start position:0% +F as you see over here on easy row so + + + align:start position:0% +F as you see over here on easy row so +you see over here have a zero there then + + align:start position:0% +you see over here have a zero there then + + + align:start position:0% +you see over here have a zero there then +G what's a one any one is a procedure + + align:start position:0% +G what's a one any one is a procedure + + + align:start position:0% +G what's a one any one is a procedure +which will exponentiate things to the + + align:start position:0% +which will exponentiate things to the + + + align:start position:0% +which will exponentiate things to the +zeroth power with no trouble it gets the + + align:start position:0% +zeroth power with no trouble it gets the + + + align:start position:0% +zeroth power with no trouble it gets the +right answer anything through the zero + + align:start position:0% +right answer anything through the zero + + + align:start position:0% +right answer anything through the zero +is one and it makes an error on anything + + align:start position:0% +is one and it makes an error on anything + + + align:start position:0% +is one and it makes an error on anything +else + + align:start position:0% + + + + align:start position:0% + +well now what if I take e one and + + align:start position:0% +well now what if I take e one and + + + align:start position:0% +well now what if I take e one and +substitute it for G by calling F on e + + align:start position:0% +substitute it for G by calling F on e + + + align:start position:0% +substitute it for G by calling F on e +one okay oh gosh I have here a procedure + + align:start position:0% +one okay oh gosh I have here a procedure + + + align:start position:0% +one okay oh gosh I have here a procedure +of two arguments now remember e one was + + align:start position:0% +of two arguments now remember e one was + + + align:start position:0% +of two arguments now remember e one was +appropriate for taking exponentiation x' + + align:start position:0% +appropriate for taking exponentiation x' + + + align:start position:0% +appropriate for taking exponentiation x' +of zero for x bo ready to the zero + + align:start position:0% +of zero for x bo ready to the zero + + + align:start position:0% +of zero for x bo ready to the zero +exponent so here if n is zero the result + + align:start position:0% +exponent so here if n is zero the result + + + align:start position:0% +exponent so here if n is zero the result +is one so this guy's good for that too + + align:start position:0% +is one so this guy's good for that too + + + align:start position:0% +is one so this guy's good for that too +however I can use something for raising + + align:start position:0% +however I can use something for raising + + + align:start position:0% +however I can use something for raising +to the zeroth power to multiply it by X + + align:start position:0% +to the zeroth power to multiply it by X + + + align:start position:0% +to the zeroth power to multiply it by X +to raise something to the first power so + + align:start position:0% +to raise something to the first power so + + + align:start position:0% +to raise something to the first power so +e1 e2 is good for both power 0 and 1 ok + + align:start position:0% +e1 e2 is good for both power 0 and 1 ok + + + align:start position:0% +e1 e2 is good for both power 0 and 1 ok +and III is constructed from e2 in the + + align:start position:0% +and III is constructed from e2 in the + + + align:start position:0% +and III is constructed from e2 in the +same way and III of course by the same + + align:start position:0% +same way and III of course by the same + + + align:start position:0% +same way and III of course by the same +argument is good for powers 0 1 & 2 ok + + align:start position:0% +argument is good for powers 0 1 & 2 ok + + + align:start position:0% +argument is good for powers 0 1 & 2 ok +so I will assert for you without proof + + align:start position:0% +so I will assert for you without proof + + + align:start position:0% +so I will assert for you without proof +because the proof is horribly difficult + + align:start position:0% +because the proof is horribly difficult + + + align:start position:0% +because the proof is horribly difficult +and that's the sort of thing that people + + align:start position:0% +and that's the sort of thing that people + + + align:start position:0% +and that's the sort of thing that people +call denotational semantics it's too I + + align:start position:0% +call denotational semantics it's too I + + + align:start position:0% +call denotational semantics it's too I +suppose it was invented this a great + + align:start position:0% +suppose it was invented this a great + + + align:start position:0% +suppose it was invented this a great +idea was invented by Scott and strachey + + align:start position:0% +idea was invented by Scott and strachey + + + align:start position:0% +idea was invented by Scott and strachey +sort of their very famous mathematician + + align:start position:0% +sort of their very famous mathematician + + + align:start position:0% +sort of their very famous mathematician +types who invented the interpretation + + align:start position:0% +types who invented the interpretation + + + align:start position:0% +types who invented the interpretation +for these programs that we have that I'm + + align:start position:0% +for these programs that we have that I'm + + + align:start position:0% +for these programs that we have that I'm +talking to you about right now and they + + align:start position:0% +talking to you about right now and they + + + align:start position:0% +talking to you about right now and they +proved by topology that there is + + align:start position:0% +proved by topology that there is + + + align:start position:0% +proved by topology that there is +such a fixed point in the cases that we + + align:start position:0% +such a fixed point in the cases that we + + + align:start position:0% +such a fixed point in the cases that we +want but the assertion is P X P T is + + align:start position:0% +want but the assertion is P X P T is + + + align:start position:0% +want but the assertion is P X P T is +limit as n goes to infinity of e n and + + align:start position:0% +limit as n goes to infinity of e n and + + + align:start position:0% +limit as n goes to infinity of e n and +that we've constructed this by the + + align:start position:0% +that we've constructed this by the + + + align:start position:0% +that we've constructed this by the +following way is well it's F of F F F F + + align:start position:0% + + + + align:start position:0% + +applied to the anything at all it didn't + + align:start position:0% +applied to the anything at all it didn't + + + align:start position:0% +applied to the anything at all it didn't +matter what that was because in fact it + + align:start position:0% +matter what that was because in fact it + + + align:start position:0% +matter what that was because in fact it +always produces an error applied to this + + align:start position:0% + + + + align:start position:0% + +that's by infant nesting of s so now my + + align:start position:0% +that's by infant nesting of s so now my + + + align:start position:0% +that's by infant nesting of s so now my +problem is to make some infinite things + + align:start position:0% + + + + align:start position:0% + +we need some infinite things how am I + + align:start position:0% +we need some infinite things how am I + + + align:start position:0% +we need some infinite things how am I +going to guest up an F an infinite + + align:start position:0% +going to guest up an F an infinite + + + align:start position:0% +going to guest up an F an infinite +number of times + + align:start position:0% +number of times + + + align:start position:0% +number of times +I better construct this well I don't + + align:start position:0% +I better construct this well I don't + + + align:start position:0% +I better construct this well I don't +know how would I make an infinite loop + + align:start position:0% +know how would I make an infinite loop + + + align:start position:0% +know how would I make an infinite loop +at all let's take a very simple infinite + + align:start position:0% +at all let's take a very simple infinite + + + align:start position:0% +at all let's take a very simple infinite +loop the simplest infinite loop + + align:start position:0% +loop the simplest infinite loop + + + align:start position:0% +loop the simplest infinite loop +imaginable if I were to take that + + align:start position:0% +imaginable if I were to take that + + + align:start position:0% +imaginable if I were to take that +procedure of one argument X which + + align:start position:0% +procedure of one argument X which + + + align:start position:0% +procedure of one argument X which +applies X to X ok and apply that to the + + align:start position:0% +applies X to X ok and apply that to the + + + align:start position:0% +applies X to X ok and apply that to the +procedure of one argument X which + + align:start position:0% +procedure of one argument X which + + + align:start position:0% +procedure of one argument X which +applies X to X then this is an infinite + + align:start position:0% +applies X to X then this is an infinite + + + align:start position:0% +applies X to X then this is an infinite +loop now the reason why this is an + + align:start position:0% +loop now the reason why this is an + + + align:start position:0% +loop now the reason why this is an +infinite loop is as follows the way I + + align:start position:0% +infinite loop is as follows the way I + + + align:start position:0% +infinite loop is as follows the way I +understand this is I substitute the + + align:start position:0% +understand this is I substitute the + + + align:start position:0% +understand this is I substitute the +argument for the formal parameter in the + + align:start position:0% +argument for the formal parameter in the + + + align:start position:0% +argument for the formal parameter in the +body but if I do that I take each of + + align:start position:0% +body but if I do that I take each of + + + align:start position:0% +body but if I do that I take each of +these X's I substitute one of these + + align:start position:0% +these X's I substitute one of these + + + align:start position:0% +these X's I substitute one of these +making a copy of the original expression + + align:start position:0% +making a copy of the original expression + + + align:start position:0% +making a copy of the original expression +I just started with simplest infinite + + align:start position:0% +I just started with simplest infinite + + + align:start position:0% +I just started with simplest infinite +loop + + align:start position:0% + + + + align:start position:0% + +now I want to tell you about a + + align:start position:0% +now I want to tell you about a + + + align:start position:0% +now I want to tell you about a +particular operator which is constructed + + align:start position:0% +particular operator which is constructed + + + align:start position:0% +particular operator which is constructed +by a perturbation from this infinite + + align:start position:0% +by a perturbation from this infinite + + + align:start position:0% +by a perturbation from this infinite +loop I'll call it why me why this is + + align:start position:0% +loop I'll call it why me why this is + + + align:start position:0% +loop I'll call it why me why this is +called Curry's paradoxical Combinator + + align:start position:0% +called Curry's paradoxical Combinator + + + align:start position:0% +called Curry's paradoxical Combinator +why after a fella by bukhari who is a + + align:start position:0% +why after a fella by bukhari who is a + + + align:start position:0% +why after a fella by bukhari who is a +logician of the 1930s also and if I have + + align:start position:0% +logician of the 1930s also and if I have + + + align:start position:0% +logician of the 1930s also and if I have +a procedure of one argument F what's it + + align:start position:0% +a procedure of one argument F what's it + + + align:start position:0% +a procedure of one argument F what's it +going to have in it it's going to have a + + align:start position:0% +going to have in it it's going to have a + + + align:start position:0% +going to have in it it's going to have a +kind of infinite loop in it which is + + align:start position:0% +kind of infinite loop in it which is + + + align:start position:0% +kind of infinite loop in it which is +that procedure of one argument X which + + align:start position:0% +that procedure of one argument X which + + + align:start position:0% +that procedure of one argument X which +applies F to X of X applied to that + + align:start position:0% +applies F to X of X applied to that + + + align:start position:0% +applies F to X of X applied to that +procedure of one argument X which + + align:start position:0% +procedure of one argument X which + + + align:start position:0% +procedure of one argument X which +applies F to X of X now what's this do + + align:start position:0% +applies F to X of X now what's this do + + + align:start position:0% +applies F to X of X now what's this do +suppose we apply y to F ok that's easy + + align:start position:0% +suppose we apply y to F ok that's easy + + + align:start position:0% +suppose we apply y to F ok that's easy +enough + + align:start position:0% +enough + + + align:start position:0% +enough +that's this capital F over here hmm well + + align:start position:0% +that's this capital F over here hmm well + + + align:start position:0% +that's this capital F over here hmm well +the easiest thing to say there is I + + align:start position:0% +the easiest thing to say there is I + + + align:start position:0% +the easiest thing to say there is I +substitute F for here ok + + align:start position:0% +substitute F for here ok + + + align:start position:0% +substitute F for here ok +ah so that's going to give me basically + + align:start position:0% +ah so that's going to give me basically + + + align:start position:0% +ah so that's going to give me basically +because then I'm going to put substitute + + align:start position:0% +because then I'm going to put substitute + + + align:start position:0% +because then I'm going to put substitute +this for X in here so that's F of + + align:start position:0% + + + + align:start position:0% + +let me actually do it in steps so you + + align:start position:0% +let me actually do it in steps so you + + + align:start position:0% +let me actually do it in steps so you +can see it completely I'm gonna be very + + align:start position:0% +can see it completely I'm gonna be very + + + align:start position:0% +can see it completely I'm gonna be very +careful okay this is open open lambda of + + align:start position:0% +careful okay this is open open lambda of + + + align:start position:0% +careful okay this is open open lambda of +X capital F X X applied to itself f of X + + align:start position:0% +X capital F X X applied to itself f of X + + + align:start position:0% +X capital F X X applied to itself f of X +of X substituting this for this in here + + align:start position:0% +of X substituting this for this in here + + + align:start position:0% +of X substituting this for this in here +this is f applied to what is it + + align:start position:0% +this is f applied to what is it + + + align:start position:0% +this is f applied to what is it +substituting this in here open open + + align:start position:0% +substituting this in here open open + + + align:start position:0% +substituting this in here open open +lambda of X f of X of X applied to + + align:start position:0% +lambda of X f of X of X applied to + + + align:start position:0% +lambda of X f of X of X applied to +lambda of X f of X of X F lambda pair oh + + align:start position:0% +lambda of X f of X of X F lambda pair oh + + + align:start position:0% +lambda of X f of X of X F lambda pair oh +but what is this this thing over here + + align:start position:0% +but what is this this thing over here + + + align:start position:0% +but what is this this thing over here +that I just computed is this thing over + + align:start position:0% +that I just computed is this thing over + + + align:start position:0% +that I just computed is this thing over +here but I just wrapped another F around + + align:start position:0% +here but I just wrapped another F around + + + align:start position:0% +here but I just wrapped another F around +it so by applying why to F I make an + + align:start position:0% +it so by applying why to F I make an + + + align:start position:0% +it so by applying why to F I make an +infinite series of X now if I just let + + align:start position:0% +infinite series of X now if I just let + + + align:start position:0% +infinite series of X now if I just let +this run forever I'll just be paying + + align:start position:0% +this run forever I'll just be paying + + + align:start position:0% +this run forever I'll just be paying +more and more FS outside around an + + align:start position:0% +more and more FS outside around an + + + align:start position:0% +more and more FS outside around an +infinite loop which is abuse less but it + + align:start position:0% +infinite loop which is abuse less but it + + + align:start position:0% +infinite loop which is abuse less but it +doesn't matter the inside is useless + + align:start position:0% +doesn't matter the inside is useless + + + align:start position:0% +doesn't matter the inside is useless +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so Y of F is f applied to Y of F so Y is + + align:start position:0% +so Y of F is f applied to Y of F so Y is + + + align:start position:0% +so Y of F is f applied to Y of F so Y is +a magical thing which when applied to + + align:start position:0% +a magical thing which when applied to + + + align:start position:0% +a magical thing which when applied to +some function produces the object which + + align:start position:0% +some function produces the object which + + + align:start position:0% +some function produces the object which +is the fixed point of that function if + + align:start position:0% +is the fixed point of that function if + + + align:start position:0% +is the fixed point of that function if +it exists and if this all works + + align:start position:0% + + + + align:start position:0% + +because indeed if I take why if I can + + align:start position:0% +because indeed if I take why if I can + + + align:start position:0% +because indeed if I take why if I can +put it into F I get Y of F out okay now + + align:start position:0% +put it into F I get Y of F out okay now + + + align:start position:0% +put it into F I get Y of F out okay now +I want you to think about this in terms + + align:start position:0% +I want you to think about this in terms + + + align:start position:0% +I want you to think about this in terms +of the eval apply interpreter for a bit + + align:start position:0% +of the eval apply interpreter for a bit + + + align:start position:0% +of the eval apply interpreter for a bit +I wrote down a whole bunch of recursion + + align:start position:0% +I wrote down a whole bunch of recursion + + + align:start position:0% +I wrote down a whole bunch of recursion +equations out there they're simultaneous + + align:start position:0% +equations out there they're simultaneous + + + align:start position:0% +equations out there they're simultaneous +in the same way these are simultaneous + + align:start position:0% +in the same way these are simultaneous + + + align:start position:0% +in the same way these are simultaneous +equations exponentiation was not a + + align:start position:0% +equations exponentiation was not a + + + align:start position:0% +equations exponentiation was not a +simultaneous equation it was only one + + align:start position:0% +simultaneous equation it was only one + + + align:start position:0% +simultaneous equation it was only one +variable I was looking for a meaning for + + align:start position:0% +variable I was looking for a meaning for + + + align:start position:0% +variable I was looking for a meaning for +but what Lisp is is the fixed point of + + align:start position:0% +but what Lisp is is the fixed point of + + + align:start position:0% +but what Lisp is is the fixed point of +the process which says if I knew what + + align:start position:0% +the process which says if I knew what + + + align:start position:0% +the process which says if I knew what +list was and substituted in for eval and + + align:start position:0% +list was and substituted in for eval and + + + align:start position:0% +list was and substituted in for eval and +apply and so on on the right-hand sides + + align:start position:0% +apply and so on on the right-hand sides + + + align:start position:0% +apply and so on on the right-hand sides +of all those recursion equations then if + + align:start position:0% +of all those recursion equations then if + + + align:start position:0% +of all those recursion equations then if +it was a real good Lisp it was a real + + align:start position:0% +it was a real good Lisp it was a real + + + align:start position:0% +it was a real good Lisp it was a real +one then the left hand side would also + + align:start position:0% +one then the left hand side would also + + + align:start position:0% +one then the left hand side would also +be Lisp so I made sense of that + + align:start position:0% +be Lisp so I made sense of that + + + align:start position:0% +be Lisp so I made sense of that +definition now whether or not there's an + + align:start position:0% +definition now whether or not there's an + + + align:start position:0% +definition now whether or not there's an +answer isn't so obvious + + align:start position:0% +answer isn't so obvious + + + align:start position:0% +answer isn't so obvious +I can't attack that now these arguments + + align:start position:0% +I can't attack that now these arguments + + + align:start position:0% +I can't attack that now these arguments +that we have giving you now are quite + + align:start position:0% +that we have giving you now are quite + + + align:start position:0% +that we have giving you now are quite +dangerous let's look over here on the + + align:start position:0% +dangerous let's look over here on the + + + align:start position:0% +dangerous let's look over here on the +these are limit arguments we're talking + + align:start position:0% +these are limit arguments we're talking + + + align:start position:0% +these are limit arguments we're talking +about limits and it's really calculus or + + align:start position:0% +about limits and it's really calculus or + + + align:start position:0% +about limits and it's really calculus or +topology or something like that a kind + + align:start position:0% +topology or something like that a kind + + + align:start position:0% +topology or something like that a kind +of analysis okay here's an argument that + + align:start position:0% +of analysis okay here's an argument that + + + align:start position:0% +of analysis okay here's an argument that +you all believe and I want to make sure + + align:start position:0% +you all believe and I want to make sure + + + align:start position:0% +you all believe and I want to make sure +you realize that I could be bullying + + align:start position:0% +you realize that I could be bullying + + + align:start position:0% +you realize that I could be bullying +bullying or bullshitting you right what + + align:start position:0% +bullying or bullshitting you right what + + + align:start position:0% +bullying or bullshitting you right what +is this U is the sum of a half and a + + align:start position:0% +is this U is the sum of a half and a + + + align:start position:0% +is this U is the sum of a half and a +quarter in an eighth and so on + + align:start position:0% +quarter in an eighth and so on + + + align:start position:0% +quarter in an eighth and so on +the sum of the geometric series and of + + align:start position:0% +the sum of the geometric series and of + + + align:start position:0% +the sum of the geometric series and of +course I could play a game here you + + align:start position:0% +course I could play a game here you + + + align:start position:0% +course I could play a game here you +minus 1 is 1/2 plus 1/4 plus 1/8 and so + + align:start position:0% +minus 1 is 1/2 plus 1/4 plus 1/8 and so + + + align:start position:0% +minus 1 is 1/2 plus 1/4 plus 1/8 and so +on okay but now if I multiply what I + + align:start position:0% +on okay but now if I multiply what I + + + align:start position:0% +on okay but now if I multiply what I +could do here oops + + align:start position:0% +could do here oops + + + align:start position:0% +could do here oops +there's a parentheses error here but I + + align:start position:0% +there's a parentheses error here but I + + + align:start position:0% +there's a parentheses error here but I +could put here two times u minus 1 is 1 + + align:start position:0% +could put here two times u minus 1 is 1 + + + align:start position:0% +could put here two times u minus 1 is 1 +plus 1/2 plus 1/4 plus 1/8 can I fix + + align:start position:0% +plus 1/2 plus 1/4 plus 1/8 can I fix + + + align:start position:0% +plus 1/2 plus 1/4 plus 1/8 can I fix +that + + align:start position:0% + + + + align:start position:0% + +yes Wow okay + + align:start position:0% +yes Wow okay + + + align:start position:0% +yes Wow okay +but that gives me back you to two times + + align:start position:0% +but that gives me back you to two times + + + align:start position:0% +but that gives me back you to two times +u minus one is you therefore we conclude + + align:start position:0% +u minus one is you therefore we conclude + + + align:start position:0% +u minus one is you therefore we conclude +that U is two and this actually is true + + align:start position:0% +that U is two and this actually is true + + + align:start position:0% +that U is two and this actually is true +there's no problem like that but + + align:start position:0% +there's no problem like that but + + + align:start position:0% +there's no problem like that but +supposing I did something different + + align:start position:0% +supposing I did something different + + + align:start position:0% +supposing I did something different +supposing I started up with something + + align:start position:0% +supposing I started up with something + + + align:start position:0% +supposing I started up with something +which manifestly has no some the V is + + align:start position:0% +which manifestly has no some the V is + + + align:start position:0% +which manifestly has no some the V is +one plus two plus four plus eight plus + + align:start position:0% +one plus two plus four plus eight plus + + + align:start position:0% +one plus two plus four plus eight plus +dot dot dot + + align:start position:0% +dot dot dot + + + align:start position:0% +dot dot dot +okay well V minus one is surely two plus + + align:start position:0% +okay well V minus one is surely two plus + + + align:start position:0% +okay well V minus one is surely two plus +four plus eight plus started I write V + + align:start position:0% +four plus eight plus started I write V + + + align:start position:0% +four plus eight plus started I write V +minus one of two over two + + align:start position:0% +minus one of two over two + + + align:start position:0% +minus one of two over two +gee that looks like V again from that I + + align:start position:0% +gee that looks like V again from that I + + + align:start position:0% +gee that looks like V again from that I +should be able to conclude that that's + + align:start position:0% +should be able to conclude that that's + + + align:start position:0% +should be able to conclude that that's +also wrong apparently the equals minus + + align:start position:0% +also wrong apparently the equals minus + + + align:start position:0% +also wrong apparently the equals minus +one let's see + + align:start position:0% + + + + align:start position:0% + +that should be a minus 1 and that's + + align:start position:0% +that should be a minus 1 and that's + + + align:start position:0% +that should be a minus 1 and that's +certainly a false conclusion so when you + + align:start position:0% +certainly a false conclusion so when you + + + align:start position:0% +certainly a false conclusion so when you +play with limits arguments that may work + + align:start position:0% +play with limits arguments that may work + + + align:start position:0% +play with limits arguments that may work +in one case they may not work in some + + align:start position:0% +in one case they may not work in some + + + align:start position:0% +in one case they may not work in some +other case you would be very careful the + + align:start position:0% +other case you would be very careful the + + + align:start position:0% +other case you would be very careful the +arguments have to be well-formed and I + + align:start position:0% +arguments have to be well-formed and I + + + align:start position:0% +arguments have to be well-formed and I +don't know in general what the story is + + align:start position:0% +don't know in general what the story is + + + align:start position:0% +don't know in general what the story is +about arguments like this we could read + + align:start position:0% +about arguments like this we could read + + + align:start position:0% +about arguments like this we could read +a pile of topology and find out but + + align:start position:0% +a pile of topology and find out but + + + align:start position:0% +a pile of topology and find out but +surely at least you understand now why + + align:start position:0% +surely at least you understand now why + + + align:start position:0% +surely at least you understand now why +it might be some meaning to the things + + align:start position:0% +it might be some meaning to the things + + + align:start position:0% +it might be some meaning to the things +we've been writing on the blackboard and + + align:start position:0% +we've been writing on the blackboard and + + + align:start position:0% +we've been writing on the blackboard and +you understand that what that might mean + + align:start position:0% +you understand that what that might mean + + + align:start position:0% +you understand that what that might mean +so I suppose it's almost about time for + + align:start position:0% +so I suppose it's almost about time for + + + align:start position:0% +so I suppose it's almost about time for +you to merit being made a member of the + + align:start position:0% +you to merit being made a member of the + + + align:start position:0% +you to merit being made a member of the +grand recursive order of lambda calculus + + align:start position:0% +grand recursive order of lambda calculus + + + align:start position:0% +grand recursive order of lambda calculus +hackers with this is the badge because + + align:start position:0% +hackers with this is the badge because + + + align:start position:0% +hackers with this is the badge because +you now understand for example what it + + align:start position:0% +you now understand for example what it + + + align:start position:0% +you now understand for example what it +says at the very top why F equals F Y F + + align:start position:0% +says at the very top why F equals F Y F + + + align:start position:0% +says at the very top why F equals F Y F +thank you are there any questions + + align:start position:0% +thank you are there any questions + + + align:start position:0% +thank you are there any questions +yes Lee now with this it seems that then + + align:start position:0% +yes Lee now with this it seems that then + + + align:start position:0% +yes Lee now with this it seems that then +there's no need to define as you as you + + align:start position:0% +there's no need to define as you as you + + + align:start position:0% +there's no need to define as you as you +imply to just a member of value to apply + + align:start position:0% +imply to just a member of value to apply + + + align:start position:0% +imply to just a member of value to apply +it later + + align:start position:0% +it later + + + align:start position:0% +it later +yeah defines were kind of a side effect + + align:start position:0% +yeah defines were kind of a side effect + + + align:start position:0% +yeah defines were kind of a side effect +it seemed in the language the way their + + align:start position:0% +it seemed in the language the way their + + + align:start position:0% +it seemed in the language the way their +order dependent does this resist + + align:start position:0% +order dependent does this resist + + + align:start position:0% +order dependent does this resist +eliminate the last side effect well the + + align:start position:0% +eliminate the last side effect well the + + + align:start position:0% +eliminate the last side effect well the +answer is this is not the way these + + align:start position:0% +answer is this is not the way these + + + align:start position:0% +answer is this is not the way these +things are implemented okay define + + align:start position:0% +things are implemented okay define + + + align:start position:0% +things are implemented okay define +indeed is implemented as an operation + + align:start position:0% +indeed is implemented as an operation + + + align:start position:0% +indeed is implemented as an operation +that actually modifies an environment + + align:start position:0% +that actually modifies an environment + + + align:start position:0% +that actually modifies an environment +structure okay change is the frame that + + align:start position:0% +structure okay change is the frame that + + + align:start position:0% +structure okay change is the frame that +the define is is executed in and there + + align:start position:0% +the define is is executed in and there + + + align:start position:0% +the define is is executed in and there +are many reasons for that but a lot of + + align:start position:0% +are many reasons for that but a lot of + + + align:start position:0% +are many reasons for that but a lot of +this has to do with making an + + align:start position:0% +this has to do with making an + + + align:start position:0% +this has to do with making an +interactive system what this is saying + + align:start position:0% +interactive system what this is saying + + + align:start position:0% +interactive system what this is saying +is that if you've made a system and you + + align:start position:0% +is that if you've made a system and you + + + align:start position:0% +is that if you've made a system and you +know every you're not gonna do any + + align:start position:0% +know every you're not gonna do any + + + align:start position:0% +know every you're not gonna do any +debugging or anything like that + + align:start position:0% +debugging or anything like that + + + align:start position:0% +debugging or anything like that +and you know everything there is all at + + align:start position:0% +and you know everything there is all at + + + align:start position:0% +and you know everything there is all at +once and you want to say what is the + + align:start position:0% +once and you want to say what is the + + + align:start position:0% +once and you want to say what is the +meaning for the final set of equations + + align:start position:0% +meaning for the final set of equations + + + align:start position:0% +meaning for the final set of equations +this gives you a meaning for it + + align:start position:0% +this gives you a meaning for it + + + align:start position:0% +this gives you a meaning for it +but in order to make an interactive + + align:start position:0% +but in order to make an interactive + + + align:start position:0% +but in order to make an interactive +system where you can change the meaning + + align:start position:0% +system where you can change the meaning + + + align:start position:0% +system where you can change the meaning +of one thing without changing everything + + align:start position:0% +of one thing without changing everything + + + align:start position:0% +of one thing without changing everything +else incremental II uh you can't do that + + align:start position:0% +else incremental II uh you can't do that + + + align:start position:0% +else incremental II uh you can't do that +by implementing it this way yes on this + + align:start position:0% +by implementing it this way yes on this + + + align:start position:0% +by implementing it this way yes on this +you're dangerous slide it seems the t2 + + align:start position:0% +you're dangerous slide it seems the t2 + + + align:start position:0% +you're dangerous slide it seems the t2 +completely two examples that you gave + + align:start position:0% +completely two examples that you gave + + + align:start position:0% +completely two examples that you gave +had to do with convergence and not + + align:start position:0% +had to do with convergence and not + + + align:start position:0% +had to do with convergence and not +submergence right and that may or may + + align:start position:0% +submergence right and that may or may + + + align:start position:0% +submergence right and that may or may +not have something to do with the + + align:start position:0% +not have something to do with the + + + align:start position:0% +not have something to do with the +function theory in a way which would + + align:start position:0% +function theory in a way which would + + + align:start position:0% +function theory in a way which would +lead you to think of it in terms of + + align:start position:0% +lead you to think of it in terms of + + + align:start position:0% +lead you to think of it in terms of +linear systems or not only existence but + + align:start position:0% +linear systems or not only existence but + + + align:start position:0% +linear systems or not only existence but +it how does this convergence relate to + + align:start position:0% +it how does this convergence relate to + + + align:start position:0% +it how does this convergence relate to +being able to see a priori what + + align:start position:0% +being able to see a priori what + + + align:start position:0% +being able to see a priori what +properties that might be violated I + + align:start position:0% +properties that might be violated I + + + align:start position:0% +properties that might be violated I +don't know the answer is I don't know + + align:start position:0% +don't know the answer is I don't know + + + align:start position:0% +don't know the answer is I don't know +under what circumstances and I don't + + align:start position:0% +under what circumstances and I don't + + + align:start position:0% +under what circumstances and I don't +know how to translate that into less and + + align:start position:0% +know how to translate that into less and + + + align:start position:0% +know how to translate that into less and +less than an hour of talk more what are + + align:start position:0% +less than an hour of talk more what are + + + align:start position:0% +less than an hour of talk more what are +the conditions under which for which we + + align:start position:0% +the conditions under which for which we + + + align:start position:0% +the conditions under which for which we +know that these things converge and II + + align:start position:0% +know that these things converge and II + + + align:start position:0% +know that these things converge and II +all I was showing is that that arguments + + align:start position:0% +all I was showing is that that arguments + + + align:start position:0% +all I was showing is that that arguments +that are based on convergence are flaky + + align:start position:0% +that are based on convergence are flaky + + + align:start position:0% +that are based on convergence are flaky +if you don't know the convergence + + align:start position:0% +if you don't know the convergence + + + align:start position:0% +if you don't know the convergence +beforehand you can make wrong arguments + + align:start position:0% +beforehand you can make wrong arguments + + + align:start position:0% +beforehand you can make wrong arguments +you can make deductions that is if you + + align:start position:0% +you can make deductions that is if you + + + align:start position:0% +you can make deductions that is if you +know the answer and not be stopped + + align:start position:0% +know the answer and not be stopped + + + align:start position:0% +know the answer and not be stopped +somewhere by some obvious contradiction + + align:start position:0% +somewhere by some obvious contradiction + + + align:start position:0% +somewhere by some obvious contradiction +so can we say them that if F is a + + align:start position:0% +so can we say them that if F is a + + + align:start position:0% +so can we say them that if F is a +convergent mathematical expression then + + align:start position:0% +convergent mathematical expression then + + + align:start position:0% +convergent mathematical expression then +the recursion property can be well I + + align:start position:0% +the recursion property can be well I + + + align:start position:0% +the recursion property can be well I +think there is a there is a technical + + align:start position:0% +think there is a there is a technical + + + align:start position:0% +think there is a there is a technical +kind of F okay then there is a technical + + align:start position:0% +kind of F okay then there is a technical + + + align:start position:0% +kind of F okay then there is a technical +description of those F's that have the + + align:start position:0% +description of those F's that have the + + + align:start position:0% +description of those F's that have the +property that when you when you + + align:start position:0% +property that when you when you + + + align:start position:0% +property that when you when you +iterative ly apply them like this you + + align:start position:0% +iterative ly apply them like this you + + + align:start position:0% +iterative ly apply them like this you +converge things that are monotonic and + + align:start position:0% +converge things that are monotonic and + + + align:start position:0% +converge things that are monotonic and +continuous okay and I forgot what else + + align:start position:0% +continuous okay and I forgot what else + + + align:start position:0% +continuous okay and I forgot what else +there's a whole bunch of little + + align:start position:0% +there's a whole bunch of little + + + align:start position:0% +there's a whole bunch of little +conditions like that okay which have + + align:start position:0% +conditions like that okay which have + + + align:start position:0% +conditions like that okay which have +this property now the real problem is + + align:start position:0% +this property now the real problem is + + + align:start position:0% +this property now the real problem is +deducing from looking at the F its + + align:start position:0% +deducing from looking at the F its + + + align:start position:0% +deducing from looking at the F its +definition here whether or not it has + + align:start position:0% +definition here whether or not it has + + + align:start position:0% +definition here whether or not it has +those properties and that's very hard + + align:start position:0% +those properties and that's very hard + + + align:start position:0% +those properties and that's very hard +the properties reason you could write + + align:start position:0% +the properties reason you could write + + + align:start position:0% +the properties reason you could write +them down look in a book by Jose stoy + + align:start position:0% +them down look in a book by Jose stoy + + + align:start position:0% +them down look in a book by Jose stoy +it's a great book + + align:start position:0% +it's a great book + + + align:start position:0% +it's a great book +stoy it's called the stress the Scott + + align:start position:0% +stoy it's called the stress the Scott + + + align:start position:0% +stoy it's called the stress the Scott +stretchy the Scott stretchy method of + + align:start position:0% +stretchy the Scott stretchy method of + + + align:start position:0% +stretchy the Scott stretchy method of +denotational semantics and it's by Joe's + + align:start position:0% +denotational semantics and it's by Joe's + + + align:start position:0% +denotational semantics and it's by Joe's +story MIT press and he works out all + + align:start position:0% +story MIT press and he works out all + + + align:start position:0% +story MIT press and he works out all +this in great detail enough to horrify + + align:start position:0% +this in great detail enough to horrify + + + align:start position:0% +this in great detail enough to horrify +you but it's really is readable + + align:start position:0% + + + + align:start position:0% + +okay well thank you time for the bigger + + align:start position:0% +okay well thank you time for the bigger + + + align:start position:0% +okay well thank you time for the bigger +break I suppose + + align:start position:0% +break I suppose + + + align:start position:0% +break I suppose +[Music] \ No newline at end of file diff --git a/aMfIs9Qmm9Q.txt b/aMfIs9Qmm9Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..c6c6142262db79f7eb3571f3a3d1f031e915472a --- /dev/null +++ b/aMfIs9Qmm9Q.txt @@ -0,0 +1,11931 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +opencourseware under a creative commons + + align:start position:0% +opencourseware under a creative commons + + + align:start position:0% +opencourseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit opencourseware in general is + + align:start position:0% +and mit opencourseware in general is + + + align:start position:0% +and mit opencourseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well even though we've been hinting at + + align:start position:0% +well even though we've been hinting at + + + align:start position:0% +well even though we've been hinting at +networks pretty heavily all the way + + align:start position:0% +networks pretty heavily all the way + + + align:start position:0% +networks pretty heavily all the way +through the course these are the three + + align:start position:0% +through the course these are the three + + + align:start position:0% +through the course these are the three +lectures where we actually take it on + + align:start position:0% +lectures where we actually take it on + + + align:start position:0% +lectures where we actually take it on +we + + align:start position:0% +we + + + align:start position:0% +we +really started this at the end of uh + + align:start position:0% +really started this at the end of uh + + + align:start position:0% +really started this at the end of uh +last week's lecture so-called protein + + align:start position:0% +last week's lecture so-called protein + + + align:start position:0% +last week's lecture so-called protein +two where in the process of talking + + align:start position:0% +two where in the process of talking + + + align:start position:0% +two where in the process of talking +about protein modifications + + align:start position:0% +about protein modifications + + + align:start position:0% +about protein modifications +and quantitative metabolites and their + + align:start position:0% +and quantitative metabolites and their + + + align:start position:0% +and quantitative metabolites and their +interactions with proteins we started + + align:start position:0% +interactions with proteins we started + + + align:start position:0% +interactions with proteins we started +talking about the sorts of sources of + + align:start position:0% +talking about the sorts of sources of + + + align:start position:0% +talking about the sorts of sources of +data that you would have + + align:start position:0% +data that you would have + + + align:start position:0% +data that you would have +that would allow you to get + + align:start position:0% +that would allow you to get + + + align:start position:0% +that would allow you to get +at + + align:start position:0% + + + + align:start position:0% + +quantitative + + align:start position:0% +quantitative + + + align:start position:0% +quantitative +analyses of protein networks such as red + + align:start position:0% +analyses of protein networks such as red + + + align:start position:0% +analyses of protein networks such as red +blood cell so we're going to + + align:start position:0% +blood cell so we're going to + + + align:start position:0% +blood cell so we're going to +pick up on that theme by talking about + + align:start position:0% +pick up on that theme by talking about + + + align:start position:0% +pick up on that theme by talking about +macroscopic + + align:start position:0% +macroscopic + + + align:start position:0% +macroscopic +continuous concentration gradients and + + align:start position:0% +continuous concentration gradients and + + + align:start position:0% +continuous concentration gradients and +contrast that with mesoscopic or + + align:start position:0% +contrast that with mesoscopic or + + + align:start position:0% +contrast that with mesoscopic or +discrete molecular numbers we're just + + align:start position:0% +discrete molecular numbers we're just + + + align:start position:0% +discrete molecular numbers we're just +going to very briefly touch upon + + align:start position:0% +going to very briefly touch upon + + + align:start position:0% +going to very briefly touch upon +the issues in discriminating between the + + align:start position:0% +the issues in discriminating between the + + + align:start position:0% +the issues in discriminating between the +stochastic modeling and the continuous + + align:start position:0% +stochastic modeling and the continuous + + + align:start position:0% +stochastic modeling and the continuous +modeling + + align:start position:0% +modeling + + + align:start position:0% +modeling +and + + align:start position:0% +and + + + align:start position:0% +and +a very interesting connection between + + align:start position:0% +a very interesting connection between + + + align:start position:0% +a very interesting connection between +the red blood cell model where you have + + align:start position:0% +the red blood cell model where you have + + + align:start position:0% +the red blood cell model where you have +a few examples of cooperativity with + + align:start position:0% +a few examples of cooperativity with + + + align:start position:0% +a few examples of cooperativity with +modest tills coefficients to take that + + align:start position:0% +modest tills coefficients to take that + + + align:start position:0% +modest tills coefficients to take that +to an extreme case where you have + + align:start position:0% +to an extreme case where you have + + + align:start position:0% +to an extreme case where you have +actually bistability where you have two + + align:start position:0% +actually bistability where you have two + + + align:start position:0% +actually bistability where you have two +stable modes which are separated + + align:start position:0% +stable modes which are separated + + + align:start position:0% +stable modes which are separated +by a very cooperative interaction + + align:start position:0% +by a very cooperative interaction + + + align:start position:0% +by a very cooperative interaction +and then we'll talk about the copy + + align:start position:0% +and then we'll talk about the copy + + + align:start position:0% +and then we'll talk about the copy +number control is another opportunity + + align:start position:0% +number control is another opportunity + + + align:start position:0% +number control is another opportunity +for doing it modeling either by continue + + align:start position:0% +for doing it modeling either by continue + + + align:start position:0% +for doing it modeling either by continue +macroscopic continuous modeling or + + align:start position:0% +macroscopic continuous modeling or + + + align:start position:0% +macroscopic continuous modeling or +this stochastic + + align:start position:0% +this stochastic + + + align:start position:0% +this stochastic +modeling and then after the break we'll + + align:start position:0% +modeling and then after the break we'll + + + align:start position:0% +modeling and then after the break we'll +talk about flux balance optimization + + align:start position:0% +talk about flux balance optimization + + + align:start position:0% +talk about flux balance optimization +which i think is a really exciting uh + + align:start position:0% +which i think is a really exciting uh + + + align:start position:0% +which i think is a really exciting uh +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +clever way of leveraging the little bits + + align:start position:0% +clever way of leveraging the little bits + + + align:start position:0% +clever way of leveraging the little bits +of information that you have about very + + align:start position:0% +of information that you have about very + + + align:start position:0% +of information that you have about very +complicated uh + + align:start position:0% +complicated uh + + + align:start position:0% +complicated uh +regulatory networks biochemical networks + + align:start position:0% +regulatory networks biochemical networks + + + align:start position:0% +regulatory networks biochemical networks +so + + align:start position:0% +so + + + align:start position:0% +so +i think we've kind of just barely + + align:start position:0% +i think we've kind of just barely + + + align:start position:0% +i think we've kind of just barely +touched upon this before why were the + + align:start position:0% +touched upon this before why were the + + + align:start position:0% +touched upon this before why were the +the particular networks that uh + + align:start position:0% +the particular networks that uh + + + align:start position:0% +the particular networks that uh +are being studied + + align:start position:0% +are being studied + + + align:start position:0% +are being studied +how did they come to be studied why + + align:start position:0% +how did they come to be studied why + + + align:start position:0% +how did they come to be studied why +and how + + align:start position:0% +and how + + + align:start position:0% +and how +and typically what they have in common + + align:start position:0% +and typically what they have in common + + + align:start position:0% +and typically what they have in common +is they have large + + align:start position:0% +is they have large + + + align:start position:0% +is they have large +genetic and + + align:start position:0% +genetic and + + + align:start position:0% +genetic and +biochemical kinetic data sets that go + + align:start position:0% +biochemical kinetic data sets that go + + + align:start position:0% +biochemical kinetic data sets that go +with and or + + align:start position:0% +with and or + + + align:start position:0% +with and or +now there's no model that it that + + align:start position:0% +now there's no model that it that + + + align:start position:0% +now there's no model that it that +describes all of the + + align:start position:0% +describes all of the + + + align:start position:0% +describes all of the +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +aspects of an entire cell or an entire + + align:start position:0% +aspects of an entire cell or an entire + + + align:start position:0% +aspects of an entire cell or an entire +organism + + align:start position:0% +organism + + + align:start position:0% +organism +usually they're little pieces of it the + + align:start position:0% +usually they're little pieces of it the + + + align:start position:0% +usually they're little pieces of it the +closest whole cell is the red blood cell + + align:start position:0% +closest whole cell is the red blood cell + + + align:start position:0% +closest whole cell is the red blood cell +and this is because there's no + + align:start position:0% +and this is because there's no + + + align:start position:0% +and this is because there's no +biopolymers + + align:start position:0% +biopolymers + + + align:start position:0% +biopolymers +components to it no biopolymer synthesis + + align:start position:0% +components to it no biopolymer synthesis + + + align:start position:0% +components to it no biopolymer synthesis +today we'll talk a little bit more about + + align:start position:0% +today we'll talk a little bit more about + + + align:start position:0% +today we'll talk a little bit more about +these two related topics which is cell + + align:start position:0% +these two related topics which is cell + + + align:start position:0% +these two related topics which is cell +division cycle and + + align:start position:0% +division cycle and + + + align:start position:0% +division cycle and +the segregation of of chromosomes during + + align:start position:0% +the segregation of of chromosomes during + + + align:start position:0% +the segregation of of chromosomes during +the cell division + + align:start position:0% +the cell division + + + align:start position:0% +the cell division +here the key point + + align:start position:0% +here the key point + + + align:start position:0% +here the key point +is + + align:start position:0% +is + + + align:start position:0% +is +the uh + + align:start position:0% + + + + align:start position:0% + +the critical nature of single molecules + + align:start position:0% +the critical nature of single molecules + + + align:start position:0% +the critical nature of single molecules +in these + + align:start position:0% +in these + + + align:start position:0% +in these +that come into play in the dividing + + align:start position:0% +that come into play in the dividing + + + align:start position:0% +that come into play in the dividing +cells + + align:start position:0% +cells + + + align:start position:0% +cells +and in this there they'll be talking + + align:start position:0% +and in this there they'll be talking + + + align:start position:0% +and in this there they'll be talking +about by stability how there's a + + align:start position:0% +about by stability how there's a + + + align:start position:0% +about by stability how there's a +decision of either to + + align:start position:0% +decision of either to + + + align:start position:0% +decision of either to +take the next step in dividing the cell + + align:start position:0% +take the next step in dividing the cell + + + align:start position:0% +take the next step in dividing the cell +or not + + align:start position:0% +or not + + + align:start position:0% +or not +and how uh that by stability can be + + align:start position:0% +and how uh that by stability can be + + + align:start position:0% +and how uh that by stability can be +achieved either stochastically where + + align:start position:0% +achieved either stochastically where + + + align:start position:0% +achieved either stochastically where +you're dealing with the fluctuations of + + align:start position:0% +you're dealing with the fluctuations of + + + align:start position:0% +you're dealing with the fluctuations of +single molecules greatly affecting a + + align:start position:0% +single molecules greatly affecting a + + + align:start position:0% +single molecules greatly affecting a +switch such as a + + align:start position:0% +switch such as a + + + align:start position:0% +switch such as a +phased lambda switch or you can have it + + align:start position:0% +phased lambda switch or you can have it + + + align:start position:0% +phased lambda switch or you can have it +involving large number of molecules + + align:start position:0% +involving large number of molecules + + + align:start position:0% +involving large number of molecules +where stochastics seems to play a less + + align:start position:0% +where stochastics seems to play a less + + + align:start position:0% +where stochastics seems to play a less +of a role + + align:start position:0% +of a role + + + align:start position:0% +of a role +and then we'll then + + align:start position:0% +and then we'll then + + + align:start position:0% +and then we'll then +at the end we'll talk about how we can + + align:start position:0% +at the end we'll talk about how we can + + + align:start position:0% +at the end we'll talk about how we can +do comparative metabolism where we + + align:start position:0% +do comparative metabolism where we + + + align:start position:0% +do comparative metabolism where we +really integrate genomics + + align:start position:0% +really integrate genomics + + + align:start position:0% +really integrate genomics +with a network model of biochemistry + + align:start position:0% +with a network model of biochemistry + + + align:start position:0% +with a network model of biochemistry +at mult many different levels of course + + align:start position:0% +at mult many different levels of course + + + align:start position:0% +at mult many different levels of course +there's the genome encoding the the + + align:start position:0% +there's the genome encoding the the + + + align:start position:0% +there's the genome encoding the the +components of that network but there's + + align:start position:0% +components of that network but there's + + + align:start position:0% +components of that network but there's +also the uh + + align:start position:0% +also the uh + + + align:start position:0% +also the uh +systematic knockouts of of genes and + + align:start position:0% +systematic knockouts of of genes and + + + align:start position:0% +systematic knockouts of of genes and +their effects on the network + + align:start position:0% +their effects on the network + + + align:start position:0% +their effects on the network +now we've also seen this is this slide + + align:start position:0% +now we've also seen this is this slide + + + align:start position:0% +now we've also seen this is this slide +is also review but it puts in context + + align:start position:0% +is also review but it puts in context + + + align:start position:0% +is also review but it puts in context +where we're mainly talking today + + align:start position:0% +where we're mainly talking today + + + align:start position:0% +where we're mainly talking today +uh we'll talk a little bit about + + align:start position:0% +uh we'll talk a little bit about + + + align:start position:0% +uh we'll talk a little bit about +ordinary differential equations both for + + align:start position:0% +ordinary differential equations both for + + + align:start position:0% +ordinary differential equations both for +at the beginning under red blood cell + + align:start position:0% +at the beginning under red blood cell + + + align:start position:0% +at the beginning under red blood cell +and and in the uh + + align:start position:0% +and and in the uh + + + align:start position:0% +and and in the uh +by stability discussion how you can get + + align:start position:0% +by stability discussion how you can get + + + align:start position:0% +by stability discussion how you can get +even with just con just concentration in + + align:start position:0% +even with just con just concentration in + + + align:start position:0% +even with just con just concentration in +time you can get these very interesting + + align:start position:0% +time you can get these very interesting + + + align:start position:0% +time you can get these very interesting +behaviors highly cooperative + + align:start position:0% +behaviors highly cooperative + + + align:start position:0% +behaviors highly cooperative +and then we'll we'll drop concentration + + align:start position:0% +and then we'll we'll drop concentration + + + align:start position:0% +and then we'll we'll drop concentration +in time by a steady state approximation + + align:start position:0% +in time by a steady state approximation + + + align:start position:0% +in time by a steady state approximation +we talk about flux balance in the second + + align:start position:0% +we talk about flux balance in the second + + + align:start position:0% +we talk about flux balance in the second +half and of course but you know + + align:start position:0% +half and of course but you know + + + align:start position:0% +half and of course but you know +before we were talking about uh + + align:start position:0% +before we were talking about uh + + + align:start position:0% +before we were talking about uh +molecular mechanics in the context of + + align:start position:0% +molecular mechanics in the context of + + + align:start position:0% +molecular mechanics in the context of +protein structure and masters equations + + align:start position:0% +protein structure and masters equations + + + align:start position:0% +protein structure and masters equations +are the way of looking at stochastic + + align:start position:0% +are the way of looking at stochastic + + + align:start position:0% +are the way of looking at stochastic +single molecules which we'll mention in + + align:start position:0% +single molecules which we'll mention in + + + align:start position:0% +single molecules which we'll mention in +passing + + align:start position:0% +passing + + + align:start position:0% +passing +eventually in the network uh discussions + + align:start position:0% +eventually in the network uh discussions + + + align:start position:0% +eventually in the network uh discussions +will get to spatially and homogeneous + + align:start position:0% +will get to spatially and homogeneous + + + align:start position:0% +will get to spatially and homogeneous +models where you actually care + + align:start position:0% +models where you actually care + + + align:start position:0% +models where you actually care +or realize the importance of where + + align:start position:0% +or realize the importance of where + + + align:start position:0% +or realize the importance of where +particular molecules lie + + align:start position:0% +particular molecules lie + + + align:start position:0% +particular molecules lie +in terms of their function + + align:start position:0% +in terms of their function + + + align:start position:0% +in terms of their function +now what are the limits + + align:start position:0% +now what are the limits + + + align:start position:0% +now what are the limits +and problems in connecting the in vitro + + align:start position:0% +and problems in connecting the in vitro + + + align:start position:0% +and problems in connecting the in vitro +ex + + align:start position:0% +ex + + + align:start position:0% +ex +parameters that were so key last time in + + align:start position:0% +parameters that were so key last time in + + + align:start position:0% +parameters that were so key last time in +this time in + + align:start position:0% +this time in + + + align:start position:0% +this time in +in developing a system model by by + + align:start position:0% +in developing a system model by by + + + align:start position:0% +in developing a system model by by +isolating particular molecules you can + + align:start position:0% +isolating particular molecules you can + + + align:start position:0% +isolating particular molecules you can +have uh you can cut off make us the + + align:start position:0% +have uh you can cut off make us the + + + align:start position:0% +have uh you can cut off make us the +system simpler + + align:start position:0% +system simpler + + + align:start position:0% +system simpler +but then there's the problem of + + align:start position:0% +but then there's the problem of + + + align:start position:0% +but then there's the problem of +reintegration and here + + align:start position:0% +reintegration and here + + + align:start position:0% +reintegration and here +this is more historical artifact than + + align:start position:0% +this is more historical artifact than + + + align:start position:0% +this is more historical artifact than +than really + + align:start position:0% +than really + + + align:start position:0% +than really +critical to this discussion and + + align:start position:0% +critical to this discussion and + + + align:start position:0% +critical to this discussion and +originally enzyme kinetics would ignore + + align:start position:0% +originally enzyme kinetics would ignore + + + align:start position:0% +originally enzyme kinetics would ignore +the products for technical mathematical + + align:start position:0% +the products for technical mathematical + + + align:start position:0% +the products for technical mathematical +reasons but as you can see from last + + align:start position:0% +reasons but as you can see from last + + + align:start position:0% +reasons but as you can see from last +time we showed that you could represent + + align:start position:0% +time we showed that you could represent + + + align:start position:0% +time we showed that you could represent +those equations quite well and measure + + align:start position:0% +those equations quite well and measure + + + align:start position:0% +those equations quite well and measure +and then even make the measurements in + + align:start position:0% +and then even make the measurements in + + + align:start position:0% +and then even make the measurements in +the presence of products it would just + + align:start position:0% +the presence of products it would just + + + align:start position:0% +the presence of products it would just +be another few terms in the + + align:start position:0% +be another few terms in the + + + align:start position:0% +be another few terms in the +rate equations + + align:start position:0% +rate equations + + + align:start position:0% +rate equations +more critical however is that the + + align:start position:0% +more critical however is that the + + + align:start position:0% +more critical however is that the +product is + + align:start position:0% +product is + + + align:start position:0% +product is +including the product along with + + align:start position:0% +including the product along with + + + align:start position:0% +including the product along with +substrate in the measurements and the + + align:start position:0% +substrate in the measurements and the + + + align:start position:0% +substrate in the measurements and the +modeling is just the first step because + + align:start position:0% +modeling is just the first step because + + + align:start position:0% +modeling is just the first step because +how many different products and + + align:start position:0% +how many different products and + + + align:start position:0% +how many different products and +substrates and and other regulatory + + align:start position:0% +substrates and and other regulatory + + + align:start position:0% +substrates and and other regulatory +molecules might be involved that you + + align:start position:0% +molecules might be involved that you + + + align:start position:0% +molecules might be involved that you +don't know about initially + + align:start position:0% +don't know about initially + + + align:start position:0% +don't know about initially +in addition uh the + + align:start position:0% +in addition uh the + + + align:start position:0% +in addition uh the +conditions for doing the in vitro + + align:start position:0% +conditions for doing the in vitro + + + align:start position:0% +conditions for doing the in vitro +measurements are really it's hard to do + + align:start position:0% +measurements are really it's hard to do + + + align:start position:0% +measurements are really it's hard to do +them at the concentrations in in cells + + align:start position:0% +them at the concentrations in in cells + + + align:start position:0% +them at the concentrations in in cells +and these co in cells they're nearly + + align:start position:0% +and these co in cells they're nearly + + + align:start position:0% +and these co in cells they're nearly +crystalline densities as i say up to 30 + + align:start position:0% +crystalline densities as i say up to 30 + + + align:start position:0% +crystalline densities as i say up to 30 +percent or so + + align:start position:0% +percent or so + + + align:start position:0% +percent or so +uh + + align:start position:0% + + + + align:start position:0% + +which is ver which is basically the the + + align:start position:0% +which is ver which is basically the the + + + align:start position:0% +which is ver which is basically the the +concentration the very high + + align:start position:0% +concentration the very high + + + align:start position:0% +concentration the very high +concentration of solute that occurs uh + + align:start position:0% +concentration of solute that occurs uh + + + align:start position:0% +concentration of solute that occurs uh +proteins and other macromolecules + + align:start position:0% +proteins and other macromolecules + + + align:start position:0% +proteins and other macromolecules +and uh some + + align:start position:0% +and uh some + + + align:start position:0% +and uh some +the the substrates the small molecules + + align:start position:0% +the the substrates the small molecules + + + align:start position:0% +the the substrates the small molecules +are typically in vast excess in vitro + + align:start position:0% +are typically in vast excess in vitro + + + align:start position:0% +are typically in vast excess in vitro +reactions but they're very close to + + align:start position:0% +reactions but they're very close to + + + align:start position:0% +reactions but they're very close to +equal molar and vevo + + align:start position:0% +equal molar and vevo + + + align:start position:0% +equal molar and vevo +because a lot of them are bound up with + + align:start position:0% +because a lot of them are bound up with + + + align:start position:0% +because a lot of them are bound up with +enzymes and you get interesting + + align:start position:0% +enzymes and you get interesting + + + align:start position:0% +enzymes and you get interesting +observations such as this one mentioned + + align:start position:0% +observations such as this one mentioned + + + align:start position:0% +observations such as this one mentioned +at the bottom where a chemical reaction + + align:start position:0% +at the bottom where a chemical reaction + + + align:start position:0% +at the bottom where a chemical reaction +which is spontaneous in solution which + + align:start position:0% +which is spontaneous in solution which + + + align:start position:0% +which is spontaneous in solution which +is the + + align:start position:0% + + + + align:start position:0% + +epimerization of galactose + + align:start position:0% +epimerization of galactose + + + align:start position:0% +epimerization of galactose +does not occur in normal cells + + align:start position:0% +does not occur in normal cells + + + align:start position:0% +does not occur in normal cells +on + + align:start position:0% +on + + + align:start position:0% +on +e coli unless they have an enzyme that + + align:start position:0% +e coli unless they have an enzyme that + + + align:start position:0% +e coli unless they have an enzyme that +that catalyzes this normally spontaneous + + align:start position:0% +that catalyzes this normally spontaneous + + + align:start position:0% +that catalyzes this normally spontaneous +reaction so this is curious that it + + align:start position:0% +reaction so this is curious that it + + + align:start position:0% +reaction so this is curious that it +happens in solution doesn't happen in + + align:start position:0% +happens in solution doesn't happen in + + + align:start position:0% +happens in solution doesn't happen in +the cell unless you + + align:start position:0% +the cell unless you + + + align:start position:0% +the cell unless you +have the enzyme + + align:start position:0% + + + + align:start position:0% + +okay so with all those caveats in mind + + align:start position:0% +okay so with all those caveats in mind + + + align:start position:0% +okay so with all those caveats in mind +and recognizing them that even though + + align:start position:0% +and recognizing them that even though + + + align:start position:0% +and recognizing them that even though +this model has more measured parameters + + align:start position:0% +this model has more measured parameters + + + align:start position:0% +this model has more measured parameters +than almost any other cellular model + + align:start position:0% +than almost any other cellular model + + + align:start position:0% +than almost any other cellular model +they were all measured in vitro with the + + align:start position:0% +they were all measured in vitro with the + + + align:start position:0% +they were all measured in vitro with the +caveats that we just mentioned + + align:start position:0% +caveats that we just mentioned + + + align:start position:0% +caveats that we just mentioned +and uh this the cell is aimed the + + align:start position:0% +and uh this the cell is aimed the + + + align:start position:0% +and uh this the cell is aimed the +function of all this network is mainly + + align:start position:0% +function of all this network is mainly + + + align:start position:0% +function of all this network is mainly +to provide the the redox that keeps the + + align:start position:0% +to provide the the redox that keeps the + + + align:start position:0% +to provide the the redox that keeps the +hemoglobin reduced and the atp that + + align:start position:0% +hemoglobin reduced and the atp that + + + align:start position:0% +hemoglobin reduced and the atp that +keeps the osmotic pressure under control + + align:start position:0% + + + + align:start position:0% + +so you have it and also the cell is even + + align:start position:0% +so you have it and also the cell is even + + + align:start position:0% +so you have it and also the cell is even +though we've shown a little structure in + + align:start position:0% +though we've shown a little structure in + + + align:start position:0% +though we've shown a little structure in +this network that this structure is + + align:start position:0% +this network that this structure is + + + align:start position:0% +this network that this structure is +assumed to be fairly continuous within + + align:start position:0% +assumed to be fairly continuous within + + + align:start position:0% +assumed to be fairly continuous within +the cell + + align:start position:0% +the cell + + + align:start position:0% +the cell +which is a fairly good approximation in + + align:start position:0% +which is a fairly good approximation in + + + align:start position:0% +which is a fairly good approximation in +this case + + align:start position:0% +this case + + + align:start position:0% +this case +so this is not merely the stapling + + align:start position:0% +so this is not merely the stapling + + + align:start position:0% +so this is not merely the stapling +together of some kinetic in vitro + + align:start position:0% +together of some kinetic in vitro + + + align:start position:0% +together of some kinetic in vitro +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +we have + + align:start position:0% + + + + align:start position:0% + +other considerations in a real cell we + + align:start position:0% +other considerations in a real cell we + + + align:start position:0% +other considerations in a real cell we +have + + align:start position:0% +have + + + align:start position:0% +have +the + + align:start position:0% +the + + + align:start position:0% +the +sort of physical parameters of the + + align:start position:0% +sort of physical parameters of the + + + align:start position:0% +sort of physical parameters of the +mass balance + + align:start position:0% +mass balance + + + align:start position:0% +mass balance +energy balance and redox balance we've + + align:start position:0% +energy balance and redox balance we've + + + align:start position:0% +energy balance and redox balance we've +already mentioned energy and redox + + align:start position:0% +already mentioned energy and redox + + + align:start position:0% +already mentioned energy and redox +but that you have to have conservation + + align:start position:0% +but that you have to have conservation + + + align:start position:0% +but that you have to have conservation +of mass as we'll see develop + + align:start position:0% +of mass as we'll see develop + + + align:start position:0% +of mass as we'll see develop +quite a bit more in the second half of + + align:start position:0% +quite a bit more in the second half of + + + align:start position:0% +quite a bit more in the second half of +this thought + + align:start position:0% +this thought + + + align:start position:0% +this thought +in addition their physics + + align:start position:0% +in addition their physics + + + align:start position:0% +in addition their physics +such as the osmotic pressure and electro + + align:start position:0% +such as the osmotic pressure and electro + + + align:start position:0% +such as the osmotic pressure and electro +neutrality there are cells which do + + align:start position:0% +neutrality there are cells which do + + + align:start position:0% +neutrality there are cells which do +uh you know have transients of + + align:start position:0% +uh you know have transients of + + + align:start position:0% +uh you know have transients of +non-electro neutrality for the red blood + + align:start position:0% +non-electro neutrality for the red blood + + + align:start position:0% +non-electro neutrality for the red blood +cells certainly one of the + + align:start position:0% +cells certainly one of the + + + align:start position:0% +cells certainly one of the +the goals is to maintain very close to + + align:start position:0% +the goals is to maintain very close to + + + align:start position:0% +the goals is to maintain very close to +electro neutrality and osmotically + + align:start position:0% +electro neutrality and osmotically + + + align:start position:0% +electro neutrality and osmotically +stable + + align:start position:0% +stable + + + align:start position:0% +stable +you want to have as many non-adjustable + + align:start position:0% +you want to have as many non-adjustable + + + align:start position:0% +you want to have as many non-adjustable +constraints as possible + + align:start position:0% +constraints as possible + + + align:start position:0% +constraints as possible +as in other modeling systems + + align:start position:0% +as in other modeling systems + + + align:start position:0% +as in other modeling systems +these non-if these are measurements + + align:start position:0% +these non-if these are measurements + + + align:start position:0% +these non-if these are measurements +rather than mod adjustable model + + align:start position:0% +rather than mod adjustable model + + + align:start position:0% +rather than mod adjustable model +parameters uh then it then allows you to + + align:start position:0% +parameters uh then it then allows you to + + + align:start position:0% +parameters uh then it then allows you to +to + + align:start position:0% +to + + + align:start position:0% +to +test + + align:start position:0% +test + + + align:start position:0% +test +the few hypotheses you have and have + + align:start position:0% +the few hypotheses you have and have + + + align:start position:0% +the few hypotheses you have and have +them over determined and look for + + align:start position:0% +them over determined and look for + + + align:start position:0% +them over determined and look for +contradictions + + align:start position:0% +contradictions + + + align:start position:0% +contradictions +outliers + + align:start position:0% +outliers + + + align:start position:0% +outliers +and then we can uh eventually we'll see + + align:start position:0% +and then we can uh eventually we'll see + + + align:start position:0% +and then we can uh eventually we'll see +advantages to knowing what the maximum + + align:start position:0% +advantages to knowing what the maximum + + + align:start position:0% +advantages to knowing what the maximum +flux is the maximum rates you can have + + align:start position:0% +flux is the maximum rates you can have + + + align:start position:0% +flux is the maximum rates you can have +in these complex networks + + align:start position:0% +in these complex networks + + + align:start position:0% +in these complex networks +and we can incorporate gene regulation + + align:start position:0% +and we can incorporate gene regulation + + + align:start position:0% +and we can incorporate gene regulation +as we've seen lots of wholesale + + align:start position:0% +as we've seen lots of wholesale + + + align:start position:0% +as we've seen lots of wholesale +uh + + align:start position:0% +uh + + + align:start position:0% +uh +increasingly accurate + + align:start position:0% +increasingly accurate + + + align:start position:0% +increasingly accurate +data on gene regulation is becoming + + align:start position:0% +data on gene regulation is becoming + + + align:start position:0% +data on gene regulation is becoming +available it would be nice to integrate + + align:start position:0% +available it would be nice to integrate + + + align:start position:0% +available it would be nice to integrate +these + + align:start position:0% +these + + + align:start position:0% +these +because the the expression of the + + align:start position:0% +because the the expression of the + + + align:start position:0% +because the the expression of the +proteins affects their activity the + + align:start position:0% +proteins affects their activity the + + + align:start position:0% +proteins affects their activity the +activity affects these fluxes + + align:start position:0% +activity affects these fluxes + + + align:start position:0% +activity affects these fluxes +these fluxes are represented here in + + align:start position:0% +these fluxes are represented here in + + + align:start position:0% +these fluxes are represented here in +slide number eight as dx dt where each + + align:start position:0% +slide number eight as dx dt where each + + + align:start position:0% +slide number eight as dx dt where each +of the x sub i's represents one of these + + align:start position:0% +of the x sub i's represents one of these + + + align:start position:0% +of the x sub i's represents one of these +blue dots a node in the network + + align:start position:0% +blue dots a node in the network + + + align:start position:0% +blue dots a node in the network +where you have + + align:start position:0% +where you have + + + align:start position:0% +where you have +four basic processes that affect it at + + align:start position:0% +four basic processes that affect it at + + + align:start position:0% +four basic processes that affect it at +up to four you can have synthesis steps + + align:start position:0% +up to four you can have synthesis steps + + + align:start position:0% +up to four you can have synthesis steps +degradation steps so synthesis produces + + align:start position:0% +degradation steps so synthesis produces + + + align:start position:0% +degradation steps so synthesis produces +transport can bring it into + + align:start position:0% +transport can bring it into + + + align:start position:0% +transport can bring it into +the cell degradation removes it and it + + align:start position:0% +the cell degradation removes it and it + + + align:start position:0% +the cell degradation removes it and it +can be utilized incorporated into the + + align:start position:0% +can be utilized incorporated into the + + + align:start position:0% +can be utilized incorporated into the +body of the cell and this is essentially + + align:start position:0% +body of the cell and this is essentially + + + align:start position:0% +body of the cell and this is essentially +you can think of this as a sink removing + + align:start position:0% +you can think of this as a sink removing + + + align:start position:0% +you can think of this as a sink removing +it from the free population of the the + + align:start position:0% +it from the free population of the the + + + align:start position:0% +it from the free population of the the +each free text molecule and this can be + + align:start position:0% +each free text molecule and this can be + + + align:start position:0% +each free text molecule and this can be +restated as a stoichiometric matrix s of + + align:start position:0% +restated as a stoichiometric matrix s of + + + align:start position:0% +restated as a stoichiometric matrix s of +i j where you basically that's mainly + + align:start position:0% +i j where you basically that's mainly + + + align:start position:0% +i j where you basically that's mainly +uh + + align:start position:0% +uh + + + align:start position:0% +uh +ones and minus ones you can see in front + + align:start position:0% +ones and minus ones you can see in front + + + align:start position:0% +ones and minus ones you can see in front +of each of these + + align:start position:0% + + + + align:start position:0% + +fluxes + + align:start position:0% +fluxes + + + align:start position:0% +fluxes +of synthesis degradation so forth will + + align:start position:0% +of synthesis degradation so forth will + + + align:start position:0% +of synthesis degradation so forth will +be ones and minus ones that refer to uh + + align:start position:0% +be ones and minus ones that refer to uh + + + align:start position:0% +be ones and minus ones that refer to uh +the stoichiometry and sometimes twos and + + align:start position:0% +the stoichiometry and sometimes twos and + + + align:start position:0% +the stoichiometry and sometimes twos and +zeros + + align:start position:0% +zeros + + + align:start position:0% +zeros +and then there's an uh then the + + align:start position:0% +and then there's an uh then the + + + align:start position:0% +and then there's an uh then the +transport is its own vector + + align:start position:0% + + + + align:start position:0% + +and you'll see the utility of the + + align:start position:0% +and you'll see the utility of the + + + align:start position:0% +and you'll see the utility of the +stoichiometric matrix where i is the + + align:start position:0% +stoichiometric matrix where i is the + + + align:start position:0% +stoichiometric matrix where i is the +metabolite number and j is the reaction + + align:start position:0% +metabolite number and j is the reaction + + + align:start position:0% +metabolite number and j is the reaction +number or the enzyme number + + align:start position:0% +number or the enzyme number + + + align:start position:0% +number or the enzyme number +for all the possible reactions that can + + align:start position:0% +for all the possible reactions that can + + + align:start position:0% +for all the possible reactions that can +occur in a cell + + align:start position:0% + + + + align:start position:0% + +these can be all possible reactions and + + align:start position:0% +these can be all possible reactions and + + + align:start position:0% +these can be all possible reactions and +you can toggle them on and off with + + align:start position:0% +you can toggle them on and off with + + + align:start position:0% +you can toggle them on and off with +mutations or changing different cell + + align:start position:0% +mutations or changing different cell + + + align:start position:0% +mutations or changing different cell +types + + align:start position:0% +types + + + align:start position:0% +types +now + + align:start position:0% +now + + + align:start position:0% +now +this particular + + align:start position:0% +this particular + + + align:start position:0% +this particular +particularly rich system the red blood + + align:start position:0% +particularly rich system the red blood + + + align:start position:0% +particularly rich system the red blood +cell has been modeled + + align:start position:0% +cell has been modeled + + + align:start position:0% +cell has been modeled +many times and continues to be modeled + + align:start position:0% +many times and continues to be modeled + + + align:start position:0% +many times and continues to be modeled +since the mid 70s and now into the + + align:start position:0% +since the mid 70s and now into the + + + align:start position:0% +since the mid 70s and now into the +2000s starting originally just with + + align:start position:0% +2000s starting originally just with + + + align:start position:0% +2000s starting originally just with +glycolysis later adding + + align:start position:0% +glycolysis later adding + + + align:start position:0% +glycolysis later adding +pentose phosphate nucleotide metabolism + + align:start position:0% +pentose phosphate nucleotide metabolism + + + align:start position:0% +pentose phosphate nucleotide metabolism +various pumps osmotic consideration + + align:start position:0% + + + + align:start position:0% + +hemoglobin ligands have been treated + + align:start position:0% +hemoglobin ligands have been treated + + + align:start position:0% +hemoglobin ligands have been treated +from time to time and less so + + align:start position:0% +from time to time and less so + + + align:start position:0% +from time to time and less so +issues having to do with calcium and + + align:start position:0% +issues having to do with calcium and + + + align:start position:0% +issues having to do with calcium and +shape + + align:start position:0% +shape + + + align:start position:0% +shape +no model includes all of these in one + + align:start position:0% +no model includes all of these in one + + + align:start position:0% +no model includes all of these in one +model although it + + align:start position:0% +model although it + + + align:start position:0% +model although it +it's very really very close but there + + align:start position:0% +it's very really very close but there + + + align:start position:0% +it's very really very close but there +are models that that include + + align:start position:0% +are models that that include + + + align:start position:0% +are models that that include +all the metabolism that we know and the + + align:start position:0% +all the metabolism that we know and the + + + align:start position:0% +all the metabolism that we know and the +transport + + align:start position:0% +transport + + + align:start position:0% +transport +osmotic + + align:start position:0% +osmotic + + + align:start position:0% +osmotic +properties um + + align:start position:0% +properties um + + + align:start position:0% +properties um +relatively few of those are available + + align:start position:0% +relatively few of those are available + + + align:start position:0% +relatively few of those are available +but were made available uh + + align:start position:0% +but were made available uh + + + align:start position:0% +but were made available uh +broadly but now now more they're + + align:start position:0% +broadly but now now more they're + + + align:start position:0% +broadly but now now more they're +increasingly being made available freely + + align:start position:0% +increasingly being made available freely + + + align:start position:0% +increasingly being made available freely +on the web + + align:start position:0% +on the web + + + align:start position:0% +on the web +as models should be + + align:start position:0% +as models should be + + + align:start position:0% +as models should be +the assumptions behind this + + align:start position:0% +the assumptions behind this + + + align:start position:0% +the assumptions behind this +is that + + align:start position:0% + + + + align:start position:0% + +like i said not everything is is modeled + + align:start position:0% +like i said not everything is is modeled + + + align:start position:0% +like i said not everything is is modeled +some of it from mathematical convenience + + align:start position:0% +some of it from mathematical convenience + + + align:start position:0% +some of it from mathematical convenience +you will be you will typically in order + + align:start position:0% +you will be you will typically in order + + + align:start position:0% +you will be you will typically in order +to differential equations since there's + + align:start position:0% +to differential equations since there's + + + align:start position:0% +to differential equations since there's +vast ranges of time constants from + + align:start position:0% +vast ranges of time constants from + + + align:start position:0% +vast ranges of time constants from +things that happen + + align:start position:0% +things that happen + + + align:start position:0% +things that happen +extremely + + align:start position:0% +extremely + + + align:start position:0% +extremely +quickly to things that happen extremely + + align:start position:0% +quickly to things that happen extremely + + + align:start position:0% +quickly to things that happen extremely +slowly typically what you do is you'll + + align:start position:0% +slowly typically what you do is you'll + + + align:start position:0% +slowly typically what you do is you'll +model a window in the middle where + + align:start position:0% +model a window in the middle where + + + align:start position:0% +model a window in the middle where +you'll say + + align:start position:0% +you'll say + + + align:start position:0% +you'll say +things that happen very quickly can be + + align:start position:0% +things that happen very quickly can be + + + align:start position:0% +things that happen very quickly can be +treated as a pseudoequilibrium as we've + + align:start position:0% +treated as a pseudoequilibrium as we've + + + align:start position:0% +treated as a pseudoequilibrium as we've +listed this middle line here + + align:start position:0% +listed this middle line here + + + align:start position:0% +listed this middle line here +on slide 10. + + align:start position:0% +on slide 10. + + + align:start position:0% +on slide 10. +things that happen extremely slowly can + + align:start position:0% +things that happen extremely slowly can + + + align:start position:0% +things that happen extremely slowly can +be treated as a constant if they happen + + align:start position:0% +be treated as a constant if they happen + + + align:start position:0% +be treated as a constant if they happen +over the period of you know years then + + align:start position:0% +over the period of you know years then + + + align:start position:0% +over the period of you know years then +in the course of an experiment that + + align:start position:0% +in the course of an experiment that + + + align:start position:0% +in the course of an experiment that +might be hours they can be treated as a + + align:start position:0% +might be hours they can be treated as a + + + align:start position:0% +might be hours they can be treated as a +constant + + align:start position:0% +constant + + + align:start position:0% +constant +or something that you systematically + + align:start position:0% +or something that you systematically + + + align:start position:0% +or something that you systematically +explore + + align:start position:0% + + + + align:start position:0% + +we will uh although we typically + + align:start position:0% +we will uh although we typically + + + align:start position:0% +we will uh although we typically +uh be ignoring little pieces of the + + align:start position:0% +uh be ignoring little pieces of the + + + align:start position:0% +uh be ignoring little pieces of the +metabolism like winding metabolism + + align:start position:0% +metabolism like winding metabolism + + + align:start position:0% +metabolism like winding metabolism +calcium + + align:start position:0% +calcium + + + align:start position:0% +calcium +uh + + align:start position:0% +uh + + + align:start position:0% +uh +these + + align:start position:0% +these + + + align:start position:0% +these +as either as data comes in from other + + align:start position:0% +as either as data comes in from other + + + align:start position:0% +as either as data comes in from other +systems and you treat it try to treat it + + align:start position:0% +systems and you treat it try to treat it + + + align:start position:0% +systems and you treat it try to treat it +by homology or analogy + + align:start position:0% +by homology or analogy + + + align:start position:0% +by homology or analogy +in addition when we talk about a typical + + align:start position:0% +in addition when we talk about a typical + + + align:start position:0% +in addition when we talk about a typical +cell this can mean that + + align:start position:0% +cell this can mean that + + + align:start position:0% +cell this can mean that +we have we assume homogeneous + + align:start position:0% +we have we assume homogeneous + + + align:start position:0% +we have we assume homogeneous +distribution of molecules within the + + align:start position:0% +distribution of molecules within the + + + align:start position:0% +distribution of molecules within the +cell and homogeneity from cell to cell + + align:start position:0% +cell and homogeneity from cell to cell + + + align:start position:0% +cell and homogeneity from cell to cell +within a particular organism it also + + align:start position:0% +within a particular organism it also + + + align:start position:0% +within a particular organism it also +means there's a tendency to model a a + + align:start position:0% +means there's a tendency to model a a + + + align:start position:0% +means there's a tendency to model a a +wild type without + + align:start position:0% +wild type without + + + align:start position:0% +wild type without +respect to polymorphism although in + + align:start position:0% +respect to polymorphism although in + + + align:start position:0% +respect to polymorphism although in +human population with red blood cell + + align:start position:0% +human population with red blood cell + + + align:start position:0% +human population with red blood cell +function in particular there's quite a + + align:start position:0% +function in particular there's quite a + + + align:start position:0% +function in particular there's quite a +quite a + + align:start position:0% +quite a + + + align:start position:0% +quite a +literature on + + align:start position:0% +literature on + + + align:start position:0% +literature on +mutations that affect the functioning of + + align:start position:0% +mutations that affect the functioning of + + + align:start position:0% +mutations that affect the functioning of +the + + align:start position:0% +the + + + align:start position:0% +the +of the proteins within the red blood + + align:start position:0% +of the proteins within the red blood + + + align:start position:0% +of the proteins within the red blood +cells probably one of the best + + align:start position:0% +cells probably one of the best + + + align:start position:0% +cells probably one of the best +studied human bi + + align:start position:0% +studied human bi + + + align:start position:0% +studied human bi +genetic systems + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +surface area is not absolutely constant + + align:start position:0% +surface area is not absolutely constant + + + align:start position:0% +surface area is not absolutely constant +although for the time being it's modeled + + align:start position:0% +although for the time being it's modeled + + + align:start position:0% +although for the time being it's modeled +as such + + align:start position:0% +as such + + + align:start position:0% +as such +this is some examples of a subset of it + + align:start position:0% +this is some examples of a subset of it + + + align:start position:0% +this is some examples of a subset of it +this is a subset that refers to + + align:start position:0% +this is a subset that refers to + + + align:start position:0% +this is a subset that refers to +glycolysis + + align:start position:0% +glycolysis + + + align:start position:0% +glycolysis +it is + + align:start position:0% +it is + + + align:start position:0% +it is +you can see they all have the same form + + align:start position:0% +you can see they all have the same form + + + align:start position:0% +you can see they all have the same form +where you have a change in a + + align:start position:0% +where you have a change in a + + + align:start position:0% +where you have a change in a +concentration in moles per liter with + + align:start position:0% +concentration in moles per liter with + + + align:start position:0% +concentration in moles per liter with +respect to time of some small molecule + + align:start position:0% +respect to time of some small molecule + + + align:start position:0% +respect to time of some small molecule +here glucose 6-phosphate is some + + align:start position:0% +here glucose 6-phosphate is some + + + align:start position:0% +here glucose 6-phosphate is some +synthesis rate + + align:start position:0% +synthesis rate + + + align:start position:0% +synthesis rate +with the subscript being hexakinase + + align:start position:0% +with the subscript being hexakinase + + + align:start position:0% +with the subscript being hexakinase +this is the upper left-hand + + align:start position:0% +this is the upper left-hand + + + align:start position:0% +this is the upper left-hand +corner + + align:start position:0% +corner + + + align:start position:0% +corner +and then that's the synthesis minus the + + align:start position:0% +and then that's the synthesis minus the + + + align:start position:0% +and then that's the synthesis minus the +the sinks the degradation rates which go + + align:start position:0% +the sinks the degradation rates which go + + + align:start position:0% +the sinks the degradation rates which go +through two other enzymes + + align:start position:0% +through two other enzymes + + + align:start position:0% +through two other enzymes +uh + + align:start position:0% + + + + align:start position:0% + +again a reminder at the bottom you'll + + align:start position:0% +again a reminder at the bottom you'll + + + align:start position:0% +again a reminder at the bottom you'll +see this come up a few times just a + + align:start position:0% +see this come up a few times just a + + + align:start position:0% +see this come up a few times just a +reminder it's the chain each of these is + + align:start position:0% +reminder it's the chain each of these is + + + align:start position:0% +reminder it's the chain each of these is +a form of change in the concentration of + + align:start position:0% +a form of change in the concentration of + + + align:start position:0% +a form of change in the concentration of +some + + align:start position:0% +some + + + align:start position:0% +some +small molecule respect to time is this + + align:start position:0% +small molecule respect to time is this + + + align:start position:0% +small molecule respect to time is this +is a + + align:start position:0% +is a + + + align:start position:0% +is a +sum of the synthesis + + align:start position:0% +sum of the synthesis + + + align:start position:0% +sum of the synthesis +uh subtracting the degradation + + align:start position:0% +uh subtracting the degradation + + + align:start position:0% +uh subtracting the degradation +transport + + align:start position:0% +transport + + + align:start position:0% +transport +utilization + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now remember we focused in on one little + + align:start position:0% +now remember we focused in on one little + + + align:start position:0% +now remember we focused in on one little +piece of this a couple of times now this + + align:start position:0% +piece of this a couple of times now this + + + align:start position:0% +piece of this a couple of times now this +is this is a step that happens to be + + align:start position:0% +is this is a step that happens to be + + + align:start position:0% +is this is a step that happens to be +allosteric that means that depending on + + align:start position:0% +allosteric that means that depending on + + + align:start position:0% +allosteric that means that depending on +the concentration of the + + align:start position:0% + + + + align:start position:0% + +the the the uh the numerator here tends + + align:start position:0% +the the the uh the numerator here tends + + + align:start position:0% +the the the uh the numerator here tends +to be uh + + align:start position:0% +to be uh + + + align:start position:0% +to be uh +composed of uh + + align:start position:0% +composed of uh + + + align:start position:0% +composed of uh +for the top part of this formula tends + + align:start position:0% +for the top part of this formula tends + + + align:start position:0% +for the top part of this formula tends +to be composed of substrates and + + align:start position:0% +to be composed of substrates and + + + align:start position:0% +to be composed of substrates and +products having an effect and then down + + align:start position:0% +products having an effect and then down + + + align:start position:0% +products having an effect and then down +this this + + align:start position:0% +this this + + + align:start position:0% +this this +term in the denominator has a fourth + + align:start position:0% +term in the denominator has a fourth + + + align:start position:0% +term in the denominator has a fourth +power dependence on a variety of other + + align:start position:0% +power dependence on a variety of other + + + align:start position:0% +power dependence on a variety of other +site effectors including amp and you can + + align:start position:0% +site effectors including amp and you can + + + align:start position:0% +site effectors including amp and you can +see that uh + + align:start position:0% +see that uh + + + align:start position:0% +see that uh +that the the velocity is either + + align:start position:0% +that the the velocity is either + + + align:start position:0% +that the the velocity is either +hyperbolic which is the uh sort of the + + align:start position:0% +hyperbolic which is the uh sort of the + + + align:start position:0% +hyperbolic which is the uh sort of the +upper curve which kind of goes + + align:start position:0% +upper curve which kind of goes + + + align:start position:0% +upper curve which kind of goes +smoothly up in plateaus while sigmoid + + align:start position:0% +smoothly up in plateaus while sigmoid + + + align:start position:0% +smoothly up in plateaus while sigmoid +curve implies greater cooperativity + + align:start position:0% +curve implies greater cooperativity + + + align:start position:0% +curve implies greater cooperativity +which can be affected by some of these + + align:start position:0% +which can be affected by some of these + + + align:start position:0% +which can be affected by some of these +other site effectors which is more + + align:start position:0% +other site effectors which is more + + + align:start position:0% +other site effectors which is more +sigmoid in shape and we'll + + align:start position:0% +sigmoid in shape and we'll + + + align:start position:0% +sigmoid in shape and we'll +we'll use this as a stepping stone to + + align:start position:0% +we'll use this as a stepping stone to + + + align:start position:0% +we'll use this as a stepping stone to +talking about how do you what are the + + align:start position:0% +talking about how do you what are the + + + align:start position:0% +talking about how do you what are the +various ways of getting that sigmoid + + align:start position:0% +various ways of getting that sigmoid + + + align:start position:0% +various ways of getting that sigmoid +shape we've already talked about how + + align:start position:0% +shape we've already talked about how + + + align:start position:0% +shape we've already talked about how +proteins can be multimers dimers + + align:start position:0% +proteins can be multimers dimers + + + align:start position:0% +proteins can be multimers dimers +tetramers and so forth that can be one + + align:start position:0% +tetramers and so forth that can be one + + + align:start position:0% +tetramers and so forth that can be one +way of achieving the sigmoid shape by a + + align:start position:0% +way of achieving the sigmoid shape by a + + + align:start position:0% +way of achieving the sigmoid shape by a +a conformation change which senses the + + align:start position:0% +a conformation change which senses the + + + align:start position:0% +a conformation change which senses the +second site but we'll talk about another + + align:start position:0% +second site but we'll talk about another + + + align:start position:0% +second site but we'll talk about another +way just a couple of slides + + align:start position:0% +way just a couple of slides + + + align:start position:0% +way just a couple of slides +when we have the kinetic expressions + + align:start position:0% +when we have the kinetic expressions + + + align:start position:0% +when we have the kinetic expressions +here + + align:start position:0% +here + + + align:start position:0% +here +we uh + + align:start position:0% +we uh + + + align:start position:0% +we uh +they have the form of the previous one + + align:start position:0% +they have the form of the previous one + + + align:start position:0% +they have the form of the previous one +most of them are simpler than the one in + + align:start position:0% +most of them are simpler than the one in + + + align:start position:0% +most of them are simpler than the one in +the in slide 12. + + align:start position:0% + + + + align:start position:0% + +the model has a total of 44 rate + + align:start position:0% +the model has a total of 44 rate + + + align:start position:0% +the model has a total of 44 rate +expressions they have about five + + align:start position:0% +expressions they have about five + + + align:start position:0% +expressions they have about five +constants + + align:start position:0% +constants + + + align:start position:0% +constants +uh on average so about 200 + + align:start position:0% +uh on average so about 200 + + + align:start position:0% +uh on average so about 200 +parameters these are not truly + + align:start position:0% +parameters these are not truly + + + align:start position:0% +parameters these are not truly +adjustable in the sense that that + + align:start position:0% +adjustable in the sense that that + + + align:start position:0% +adjustable in the sense that that +they're you know they're + + align:start position:0% +they're you know they're + + + align:start position:0% +they're you know they're +determined from the in vitro reactions + + align:start position:0% +determined from the in vitro reactions + + + align:start position:0% +determined from the in vitro reactions +so what kind of assumptions + + align:start position:0% +so what kind of assumptions + + + align:start position:0% +so what kind of assumptions +uh we've already mentioned the + + align:start position:0% +uh we've already mentioned the + + + align:start position:0% +uh we've already mentioned the +difference between in vitro and vivo + + align:start position:0% +difference between in vitro and vivo + + + align:start position:0% +difference between in vitro and vivo +we have the lingering + + align:start position:0% +we have the lingering + + + align:start position:0% +we have the lingering +question of how many effectors might + + align:start position:0% +question of how many effectors might + + + align:start position:0% +question of how many effectors might +there be that we don't know about + + align:start position:0% +there be that we don't know about + + + align:start position:0% +there be that we don't know about +typically these in vitro experiments + + align:start position:0% +typically these in vitro experiments + + + align:start position:0% +typically these in vitro experiments +were done with a small number of + + align:start position:0% +were done with a small number of + + + align:start position:0% +were done with a small number of +substrates and products that you know + + align:start position:0% +substrates and products that you know + + + align:start position:0% +substrates and products that you know +about + + align:start position:0% +about + + + align:start position:0% +about +but as a worst case scenario mike savage + + align:start position:0% +but as a worst case scenario mike savage + + + align:start position:0% +but as a worst case scenario mike savage +oh likes to trot out uh glutamine + + align:start position:0% +oh likes to trot out uh glutamine + + + align:start position:0% +oh likes to trot out uh glutamine +synthase which fortunately is not in + + align:start position:0% +synthase which fortunately is not in + + + align:start position:0% +synthase which fortunately is not in +this particular model but it but it + + align:start position:0% +this particular model but it but it + + + align:start position:0% +this particular model but it but it +could be there's a an enzyme that's just + + align:start position:0% +could be there's a an enzyme that's just + + + align:start position:0% +could be there's a an enzyme that's just +as complicated but hasn't been studied + + align:start position:0% +as complicated but hasn't been studied + + + align:start position:0% +as complicated but hasn't been studied +as much in case of glutamine synthase + + align:start position:0% +as much in case of glutamine synthase + + + align:start position:0% +as much in case of glutamine synthase +there are three substrates remember the + + align:start position:0% +there are three substrates remember the + + + align:start position:0% +there are three substrates remember the +previous example there were only two + + align:start position:0% +previous example there were only two + + + align:start position:0% +previous example there were only two +substrates and two products gluten + + align:start position:0% +substrates and two products gluten + + + align:start position:0% +substrates and two products gluten +synthesis three substitutes three + + align:start position:0% +synthesis three substitutes three + + + align:start position:0% +synthesis three substitutes three +products and has nine allosteric + + align:start position:0% +products and has nine allosteric + + + align:start position:0% +products and has nine allosteric +effectors rather than the + + align:start position:0% +effectors rather than the + + + align:start position:0% +effectors rather than the +you know + + align:start position:0% +you know + + + align:start position:0% +you know +three or so in the previous example so + + align:start position:0% +three or so in the previous example so + + + align:start position:0% +three or so in the previous example so +this gives a grand total of 15 different + + align:start position:0% +this gives a grand total of 15 different + + + align:start position:0% +this gives a grand total of 15 different +molecules you need to track + + align:start position:0% +molecules you need to track + + + align:start position:0% +molecules you need to track +so if + + align:start position:0% +so if + + + align:start position:0% +so if +the number of different + + align:start position:0% +the number of different + + + align:start position:0% +the number of different +measurements you might have to make + + align:start position:0% +measurements you might have to make + + + align:start position:0% +measurements you might have to make +hypothetically this is no one's actually + + align:start position:0% +hypothetically this is no one's actually + + + align:start position:0% +hypothetically this is no one's actually +made this number of measurements but + + align:start position:0% +made this number of measurements but + + + align:start position:0% +made this number of measurements but +mike savage likes to + + align:start position:0% +mike savage likes to + + + align:start position:0% +mike savage likes to +point out that even if you only did four + + align:start position:0% +point out that even if you only did four + + + align:start position:0% +point out that even if you only did four +concentration points in this + + align:start position:0% +concentration points in this + + + align:start position:0% +concentration points in this +multi-dimensional + + align:start position:0% +multi-dimensional + + + align:start position:0% +multi-dimensional +space you would have four to the 15th + + align:start position:0% +space you would have four to the 15th + + + align:start position:0% +space you would have four to the 15th +measurements or billion measurements + + align:start position:0% +measurements or billion measurements + + + align:start position:0% +measurements or billion measurements +a billion isn't nearly as intimidating + + align:start position:0% +a billion isn't nearly as intimidating + + + align:start position:0% +a billion isn't nearly as intimidating +as it was when he made this statement in + + align:start position:0% +as it was when he made this statement in + + + align:start position:0% +as it was when he made this statement in +76 but it still is uh not not something + + align:start position:0% +76 but it still is uh not not something + + + align:start position:0% +76 but it still is uh not not something +that's routinely done + + align:start position:0% + + + + align:start position:0% + +what other constraints are these + + align:start position:0% +what other constraints are these + + + align:start position:0% +what other constraints are these +physical chemical constraints of osmotic + + align:start position:0% +physical chemical constraints of osmotic + + + align:start position:0% +physical chemical constraints of osmotic +pressure and electroneutrality here + + align:start position:0% +pressure and electroneutrality here + + + align:start position:0% +pressure and electroneutrality here +stated a little more explicitly you have + + align:start position:0% +stated a little more explicitly you have + + + align:start position:0% +stated a little more explicitly you have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +pi i equal to pi e that means the out + + align:start position:0% +pi i equal to pi e that means the out + + + align:start position:0% +pi i equal to pi e that means the out +the pressure on the inside is equal to + + align:start position:0% +the pressure on the inside is equal to + + + align:start position:0% +the pressure on the inside is equal to +the pressure on the outside that sounds + + align:start position:0% +the pressure on the outside that sounds + + + align:start position:0% +the pressure on the outside that sounds +like a good way to balance things out so + + align:start position:0% +like a good way to balance things out so + + + align:start position:0% +like a good way to balance things out so +the cell doesn't explode and explicitly + + align:start position:0% +the cell doesn't explode and explicitly + + + align:start position:0% +the cell doesn't explode and explicitly +what that means is these uh gas constant + + align:start position:0% +what that means is these uh gas constant + + + align:start position:0% +what that means is these uh gas constant +r times the + + align:start position:0% +r times the + + + align:start position:0% +r times the +absolute temperature + + align:start position:0% +absolute temperature + + + align:start position:0% +absolute temperature +degrees kelvin times the sum + + align:start position:0% +degrees kelvin times the sum + + + align:start position:0% +degrees kelvin times the sum +of + + align:start position:0% +of + + + align:start position:0% +of +the + + align:start position:0% +the + + + align:start position:0% +the +pressure components for the j + + align:start position:0% +pressure components for the j + + + align:start position:0% +pressure components for the j +molecule going up to m chemical species + + align:start position:0% +molecule going up to m chemical species + + + align:start position:0% +molecule going up to m chemical species +for i interior standing for interior + + align:start position:0% +for i interior standing for interior + + + align:start position:0% +for i interior standing for interior +is equal to the same sum equivalent sum + + align:start position:0% +is equal to the same sum equivalent sum + + + align:start position:0% +is equal to the same sum equivalent sum +for the + + align:start position:0% +for the + + + align:start position:0% +for the +subscript e for exterior + + align:start position:0% +subscript e for exterior + + + align:start position:0% +subscript e for exterior +electroneutrality has the same set of + + align:start position:0% +electroneutrality has the same set of + + + align:start position:0% +electroneutrality has the same set of +concentrations for the + + align:start position:0% +concentrations for the + + + align:start position:0% +concentrations for the +i interior and j molecules + + align:start position:0% +i interior and j molecules + + + align:start position:0% +i interior and j molecules +where now z is the charge for charge is + + align:start position:0% +where now z is the charge for charge is + + + align:start position:0% +where now z is the charge for charge is +the same z that we had in m over z for + + align:start position:0% +the same z that we had in m over z for + + + align:start position:0% +the same z that we had in m over z for +the mass spectrometer + + align:start position:0% +the mass spectrometer + + + align:start position:0% +the mass spectrometer +so okay + + align:start position:0% +so okay + + + align:start position:0% +so okay +and each + + align:start position:0% +and each + + + align:start position:0% +and each +each model i give you + + align:start position:0% +each model i give you + + + align:start position:0% +each model i give you +or some of the models i give you today + + align:start position:0% +or some of the models i give you today + + + align:start position:0% +or some of the models i give you today +we will compare it uh to the the + + align:start position:0% +we will compare it uh to the the + + + align:start position:0% +we will compare it uh to the the +calculated and observed as we have done + + align:start position:0% +calculated and observed as we have done + + + align:start position:0% +calculated and observed as we have done +before + + align:start position:0% +before + + + align:start position:0% +before +and here is shown a little bit + + align:start position:0% +and here is shown a little bit + + + align:start position:0% +and here is shown a little bit +differently than how i've done it before + + align:start position:0% +differently than how i've done it before + + + align:start position:0% +differently than how i've done it before +and how we'll do it later on + + align:start position:0% +and how we'll do it later on + + + align:start position:0% +and how we'll do it later on +typically we would have + + align:start position:0% +typically we would have + + + align:start position:0% +typically we would have +observed on one axis and calculated on + + align:start position:0% +observed on one axis and calculated on + + + align:start position:0% +observed on one axis and calculated on +the other in this case we're we're + + align:start position:0% +the other in this case we're we're + + + align:start position:0% +the other in this case we're we're +sorting them + + align:start position:0% +sorting them + + + align:start position:0% +sorting them +in general we're looking for outliers + + align:start position:0% +in general we're looking for outliers + + + align:start position:0% +in general we're looking for outliers +and here we're sorting by the degree to + + align:start position:0% +and here we're sorting by the degree to + + + align:start position:0% +and here we're sorting by the degree to +which they deviate from + + align:start position:0% +which they deviate from + + + align:start position:0% +which they deviate from +uh observation and so we could the dv + + align:start position:0% +uh observation and so we could the dv + + + align:start position:0% +uh observation and so we could the dv +the deviation is going to be observation + + align:start position:0% +the deviation is going to be observation + + + align:start position:0% +the deviation is going to be observation +minus + + align:start position:0% +minus + + + align:start position:0% +minus +calculated and + + align:start position:0% +calculated and + + + align:start position:0% +calculated and +the degree of deviation can either be + + align:start position:0% +the degree of deviation can either be + + + align:start position:0% +the degree of deviation can either be +normalized to the standard deviation + + align:start position:0% +normalized to the standard deviation + + + align:start position:0% +normalized to the standard deviation +which is basically normalizing it to how + + align:start position:0% +which is basically normalizing it to how + + + align:start position:0% +which is basically normalizing it to how +confident we are in the + + align:start position:0% +confident we are in the + + + align:start position:0% +confident we are in the +experimental measure or it can be + + align:start position:0% +experimental measure or it can be + + + align:start position:0% +experimental measure or it can be +normalized to the average value which uh + + align:start position:0% +normalized to the average value which uh + + + align:start position:0% +normalized to the average value which uh +then becomes less dependent upon the + + align:start position:0% +then becomes less dependent upon the + + + align:start position:0% +then becomes less dependent upon the +accuracy of the experiment and more + + align:start position:0% +accuracy of the experiment and more + + + align:start position:0% +accuracy of the experiment and more +dependent you know with a fraction of + + align:start position:0% +dependent you know with a fraction of + + + align:start position:0% +dependent you know with a fraction of +the and so we've sorted it on the ladder + + align:start position:0% +the and so we've sorted it on the ladder + + + align:start position:0% +the and so we've sorted it on the ladder +uh and you can see that + + align:start position:0% +uh and you can see that + + + align:start position:0% +uh and you can see that +most of them are less than two standard + + align:start position:0% +most of them are less than two standard + + + align:start position:0% +most of them are less than two standard +deviation sorry + + align:start position:0% +deviation sorry + + + align:start position:0% +deviation sorry +deviation is + + align:start position:0% +deviation is + + + align:start position:0% +deviation is +less than two-fold the average value + + align:start position:0% +less than two-fold the average value + + + align:start position:0% +less than two-fold the average value +and less than seven standard deviations + + align:start position:0% +and less than seven standard deviations + + + align:start position:0% +and less than seven standard deviations +in terms of the measurements + + align:start position:0% +in terms of the measurements + + + align:start position:0% +in terms of the measurements +but the ones that are furthest to the + + align:start position:0% +but the ones that are furthest to the + + + align:start position:0% +but the ones that are furthest to the +right + + align:start position:0% +right + + + align:start position:0% +right +are clearly the ones that require the + + align:start position:0% +are clearly the ones that require the + + + align:start position:0% +are clearly the ones that require the +most attention either in the + + align:start position:0% +most attention either in the + + + align:start position:0% +most attention either in the +experimental measurements or in the + + align:start position:0% +experimental measurements or in the + + + align:start position:0% +experimental measurements or in the +modeling these are steady state measures + + align:start position:0% +modeling these are steady state measures + + + align:start position:0% +modeling these are steady state measures +this is kind of an abuse of a beautiful + + align:start position:0% +this is kind of an abuse of a beautiful + + + align:start position:0% +this is kind of an abuse of a beautiful +kinetic model + + align:start position:0% +kinetic model + + + align:start position:0% +kinetic model +but it's it reflects the the + + align:start position:0% +but it's it reflects the the + + + align:start position:0% +but it's it reflects the the +limited data that exists and it's much + + align:start position:0% +limited data that exists and it's much + + + align:start position:0% +limited data that exists and it's much +easier to collect steady state data + + align:start position:0% +easier to collect steady state data + + + align:start position:0% +easier to collect steady state data +where basically the red blood cell any + + align:start position:0% +where basically the red blood cell any + + + align:start position:0% +where basically the red blood cell any +every particular molecule even though + + align:start position:0% +every particular molecule even though + + + align:start position:0% +every particular molecule even though +the flux is in and out of every molecule + + align:start position:0% +the flux is in and out of every molecule + + + align:start position:0% +the flux is in and out of every molecule +the molecule concentration itself is + + align:start position:0% +the molecule concentration itself is + + + align:start position:0% +the molecule concentration itself is +staying constant + + align:start position:0% +staying constant + + + align:start position:0% +staying constant +now if you so that's how you uh + + align:start position:0% +now if you so that's how you uh + + + align:start position:0% +now if you so that's how you uh +if you're assuming each molecular + + align:start position:0% +if you're assuming each molecular + + + align:start position:0% +if you're assuming each molecular +concentration is staying constantly + + align:start position:0% +concentration is staying constantly + + + align:start position:0% +concentration is staying constantly +fractions with respect to time you're + + align:start position:0% +fractions with respect to time you're + + + align:start position:0% +fractions with respect to time you're +just measuring + + align:start position:0% +just measuring + + + align:start position:0% +just measuring +steady state levels but if you're more + + align:start position:0% +steady state levels but if you're more + + + align:start position:0% +steady state levels but if you're more +interested in + + align:start position:0% +interested in + + + align:start position:0% +interested in +looking at the dynamics the movie of how + + align:start position:0% +looking at the dynamics the movie of how + + + align:start position:0% +looking at the dynamics the movie of how +molecules will change if you perturb + + align:start position:0% +molecules will change if you perturb + + + align:start position:0% +molecules will change if you perturb +the + + align:start position:0% +the + + + align:start position:0% +the +the system + + align:start position:0% +the system + + + align:start position:0% +the system +you can think of a wide variety of + + align:start position:0% +you can think of a wide variety of + + + align:start position:0% +you can think of a wide variety of +different curves that this the time + + align:start position:0% +different curves that this the time + + + align:start position:0% +different curves that this the time +courses can take and one way and and + + align:start position:0% +courses can take and one way and and + + + align:start position:0% +courses can take and one way and and +then the challenge is how do you + + align:start position:0% +then the challenge is how do you + + + align:start position:0% +then the challenge is how do you +represent them you have 40 some + + align:start position:0% +represent them you have 40 some + + + align:start position:0% +represent them you have 40 some +different small molecules you're + + align:start position:0% +different small molecules you're + + + align:start position:0% +different small molecules you're +tracking the concentrations and then the + + align:start position:0% +tracking the concentrations and then the + + + align:start position:0% +tracking the concentrations and then the +time force can range over hours + + align:start position:0% +time force can range over hours + + + align:start position:0% +time force can range over hours +but here one way of doing it is doing + + align:start position:0% +but here one way of doing it is doing + + + align:start position:0% +but here one way of doing it is doing +pairs of + + align:start position:0% +pairs of + + + align:start position:0% +pairs of +substrates at a time such a and b + + align:start position:0% +substrates at a time such a and b + + + align:start position:0% +substrates at a time such a and b +and uh and then monitoring the time + + align:start position:0% +and uh and then monitoring the time + + + align:start position:0% +and uh and then monitoring the time +force as a vector think of these as a + + align:start position:0% +force as a vector think of these as a + + + align:start position:0% +force as a vector think of these as a +series of little points along here um + + align:start position:0% +series of little points along here um + + + align:start position:0% +series of little points along here um +and if + + align:start position:0% +and if + + + align:start position:0% +and if +let's look in the uh + + align:start position:0% +let's look in the uh + + + align:start position:0% +let's look in the uh +slide 17 look in the upper left number + + align:start position:0% +slide 17 look in the upper left number + + + align:start position:0% +slide 17 look in the upper left number +one if let's say a is converted to b + + align:start position:0% +one if let's say a is converted to b + + + align:start position:0% +one if let's say a is converted to b +or uh so that a plus b is equal to some + + align:start position:0% +or uh so that a plus b is equal to some + + + align:start position:0% +or uh so that a plus b is equal to some +constant you can see this + + align:start position:0% +constant you can see this + + + align:start position:0% +constant you can see this +this um + + align:start position:0% +this um + + + align:start position:0% +this um +slope of negative one this is + + align:start position:0% +slope of negative one this is + + + align:start position:0% +slope of negative one this is +exactly negative one because every every + + align:start position:0% +exactly negative one because every every + + + align:start position:0% +exactly negative one because every every +for every molecule of a that's consumed + + align:start position:0% +for every molecule of a that's consumed + + + align:start position:0% +for every molecule of a that's consumed +the molecule b is produced + + align:start position:0% +the molecule b is produced + + + align:start position:0% +the molecule b is produced +and so when you see this perfect slope + + align:start position:0% +and so when you see this perfect slope + + + align:start position:0% +and so when you see this perfect slope +of negative one and that's the kind of + + align:start position:0% +of negative one and that's the kind of + + + align:start position:0% +of negative one and that's the kind of +relationship you expect between those + + align:start position:0% +relationship you expect between those + + + align:start position:0% +relationship you expect between those +two + + align:start position:0% +two + + + align:start position:0% +two +um even if this even if you're sort of + + align:start position:0% +um even if this even if you're sort of + + + align:start position:0% +um even if this even if you're sort of +randomly sampling a dynamic system here + + align:start position:0% +randomly sampling a dynamic system here + + + align:start position:0% +randomly sampling a dynamic system here +you're taking a time course + + align:start position:0% +you're taking a time course + + + align:start position:0% +you're taking a time course +number two is a pair of concentrations + + align:start position:0% +number two is a pair of concentrations + + + align:start position:0% +number two is a pair of concentrations +of equilibrium you get an equilibrium + + align:start position:0% +of equilibrium you get an equilibrium + + + align:start position:0% +of equilibrium you get an equilibrium +constant and the ratios here will not be + + align:start position:0% +constant and the ratios here will not be + + + align:start position:0% +constant and the ratios here will not be +uh negative one they will be some + + align:start position:0% +uh negative one they will be some + + + align:start position:0% +uh negative one they will be some +constant which determines uh that + + align:start position:0% +constant which determines uh that + + + align:start position:0% +constant which determines uh that +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +you have two + + align:start position:0% + + + + align:start position:0% + +dynamically independent metabolites as + + align:start position:0% +dynamically independent metabolites as + + + align:start position:0% +dynamically independent metabolites as +in + + align:start position:0% +in + + + align:start position:0% +in +quadrant three here + + align:start position:0% +quadrant three here + + + align:start position:0% +quadrant three here +basically as you march through + + align:start position:0% + + + + align:start position:0% + +increasing b a can stay constant because + + align:start position:0% +increasing b a can stay constant because + + + align:start position:0% +increasing b a can stay constant because +it doesn't really care it doesn't + + align:start position:0% +it doesn't really care it doesn't + + + align:start position:0% +it doesn't really care it doesn't +responding to changes that in b or + + align:start position:0% +responding to changes that in b or + + + align:start position:0% +responding to changes that in b or +changes that result in b changing and + + align:start position:0% +changes that result in b changing and + + + align:start position:0% +changes that result in b changing and +then maybe some other set of + + align:start position:0% +then maybe some other set of + + + align:start position:0% +then maybe some other set of +dynamics will cause a to change and b + + align:start position:0% +dynamics will cause a to change and b + + + align:start position:0% +dynamics will cause a to change and b +stays constant and if you and if you + + align:start position:0% +stays constant and if you and if you + + + align:start position:0% +stays constant and if you and if you +sample enough time force you may find + + align:start position:0% +sample enough time force you may find + + + align:start position:0% +sample enough time force you may find +that this + + align:start position:0% +that this + + + align:start position:0% +that this +fills up the entire space uh + + align:start position:0% +fills up the entire space uh + + + align:start position:0% +fills up the entire space uh +concentrations available to a and b + + align:start position:0% +concentrations available to a and b + + + align:start position:0% +concentrations available to a and b +showing no correlation + + align:start position:0% +showing no correlation + + + align:start position:0% +showing no correlation +another interesting type of phenomena + + align:start position:0% +another interesting type of phenomena + + + align:start position:0% +another interesting type of phenomena +you can see is that uh not every + + align:start position:0% +you can see is that uh not every + + + align:start position:0% +you can see is that uh not every +possible concentration of a + + align:start position:0% +possible concentration of a + + + align:start position:0% +possible concentration of a +is not completely independent of b as as + + align:start position:0% +is not completely independent of b as as + + + align:start position:0% +is not completely independent of b as as +you might start at a particular point in + + align:start position:0% +you might start at a particular point in + + + align:start position:0% +you might start at a particular point in +a time series at this gap here in the + + align:start position:0% +a time series at this gap here in the + + + align:start position:0% +a time series at this gap here in the +lower right and you start increase the + + align:start position:0% +lower right and you start increase the + + + align:start position:0% +lower right and you start increase the +decreasing b and increasing a and then + + align:start position:0% +decreasing b and increasing a and then + + + align:start position:0% +decreasing b and increasing a and then +at some point the dynamics the entire + + align:start position:0% +at some point the dynamics the entire + + + align:start position:0% +at some point the dynamics the entire +network not just a and b contribute to + + align:start position:0% +network not just a and b contribute to + + + align:start position:0% +network not just a and b contribute to +now a taking a dive down and b + + align:start position:0% +now a taking a dive down and b + + + align:start position:0% +now a taking a dive down and b +increasing and eventually you return to + + align:start position:0% +increasing and eventually you return to + + + align:start position:0% +increasing and eventually you return to +that steady state point and you've + + align:start position:0% +that steady state point and you've + + + align:start position:0% +that steady state point and you've +described all the conditions that that + + align:start position:0% +described all the conditions that that + + + align:start position:0% +described all the conditions that that +that you might be able to achieve in + + align:start position:0% +that you might be able to achieve in + + + align:start position:0% +that you might be able to achieve in +this closed loop + + align:start position:0% +this closed loop + + + align:start position:0% +this closed loop +so we're going to look at these kind of + + align:start position:0% +so we're going to look at these kind of + + + align:start position:0% +so we're going to look at these kind of +phase diagrams the concentration of a + + align:start position:0% +phase diagrams the concentration of a + + + align:start position:0% +phase diagrams the concentration of a +versus concentration of b + + align:start position:0% +versus concentration of b + + + align:start position:0% +versus concentration of b +where a time a series of time points + + align:start position:0% +where a time a series of time points + + + align:start position:0% +where a time a series of time points +would be color coded these can be either + + align:start position:0% +would be color coded these can be either + + + align:start position:0% +would be color coded these can be either +lumped as they are in this diagram or in + + align:start position:0% +lumped as they are in this diagram or in + + + align:start position:0% +lumped as they are in this diagram or in +the next + + align:start position:0% +the next + + + align:start position:0% +the next +slide we'll see them separated out one + + align:start position:0% +slide we'll see them separated out one + + + align:start position:0% +slide we'll see them separated out one +metabolite at a time but it's the same + + align:start position:0% +metabolite at a time but it's the same + + + align:start position:0% +metabolite at a time but it's the same +concept whether you've got a group of + + align:start position:0% +concept whether you've got a group of + + + align:start position:0% +concept whether you've got a group of +metabolites involved in glycolysis + + align:start position:0% +metabolites involved in glycolysis + + + align:start position:0% +metabolites involved in glycolysis +lumped together + + align:start position:0% +lumped together + + + align:start position:0% +lumped together +uh compared to say a group that are + + align:start position:0% +uh compared to say a group that are + + + align:start position:0% +uh compared to say a group that are +redox you have in the lower left of + + align:start position:0% +redox you have in the lower left of + + + align:start position:0% +redox you have in the lower left of +each of these uh quadrants + + align:start position:0% +each of these uh quadrants + + + align:start position:0% +each of these uh quadrants +is this time series that we've been + + align:start position:0% +is this time series that we've been + + + align:start position:0% +is this time series that we've been +looking at and the upper + + align:start position:0% +looking at and the upper + + + align:start position:0% +looking at and the upper +part is a is the correlation coefficient + + align:start position:0% +part is a is the correlation coefficient + + + align:start position:0% +part is a is the correlation coefficient +is color-coded so that blue is a + + align:start position:0% +is color-coded so that blue is a + + + align:start position:0% +is color-coded so that blue is a +negative correlation and gray is very + + align:start position:0% +negative correlation and gray is very + + + align:start position:0% +negative correlation and gray is very +significant positive correlation and + + align:start position:0% +significant positive correlation and + + + align:start position:0% +significant positive correlation and +everything else is something in between + + align:start position:0% +everything else is something in between + + + align:start position:0% +everything else is something in between +so what you see from these is you see + + align:start position:0% +so what you see from these is you see + + + align:start position:0% +so what you see from these is you see +for example here's this a curve that's + + align:start position:0% +for example here's this a curve that's + + + align:start position:0% +for example here's this a curve that's +very close to the negative one curve as + + align:start position:0% +very close to the negative one curve as + + + align:start position:0% +very close to the negative one curve as +if there's a conservation reaction here + + align:start position:0% +if there's a conservation reaction here + + + align:start position:0% +if there's a conservation reaction here +between glycolysis and the adjacent + + align:start position:0% +between glycolysis and the adjacent + + + align:start position:0% +between glycolysis and the adjacent +steps + + align:start position:0% +steps + + + align:start position:0% +steps +uh you see little + + align:start position:0% +uh you see little + + + align:start position:0% +uh you see little +uh + + align:start position:0% +uh + + + align:start position:0% +uh +loops for example the lower left adenine + + align:start position:0% +loops for example the lower left adenine + + + align:start position:0% +loops for example the lower left adenine +biosynthesis + + align:start position:0% +biosynthesis + + + align:start position:0% +biosynthesis +and + + align:start position:0% + + + + align:start position:0% + +in that row + + align:start position:0% +in that row + + + align:start position:0% +in that row +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and so on you see examples of each of + + align:start position:0% +and so on you see examples of each of + + + align:start position:0% +and so on you see examples of each of +these kind of behaviors here where + + align:start position:0% +these kind of behaviors here where + + + align:start position:0% +these kind of behaviors here where +you're going from the red point + + align:start position:0% +you're going from the red point + + + align:start position:0% +you're going from the red point +these little dots in red to green to + + align:start position:0% +these little dots in red to green to + + + align:start position:0% +these little dots in red to green to +blue to the yellow to the end gray + + align:start position:0% +blue to the yellow to the end gray + + + align:start position:0% +blue to the yellow to the end gray +in increasing time coarseness from + + align:start position:0% +in increasing time coarseness from + + + align:start position:0% +in increasing time coarseness from +starting with 0.1 hour resolution and + + align:start position:0% +starting with 0.1 hour resolution and + + + align:start position:0% +starting with 0.1 hour resolution and +ending with 300 hour + + align:start position:0% +ending with 300 hour + + + align:start position:0% +ending with 300 hour +resolution + + align:start position:0% +resolution + + + align:start position:0% +resolution +okay this is lumping where we're kind of + + align:start position:0% +okay this is lumping where we're kind of + + + align:start position:0% +okay this is lumping where we're kind of +looking at things like atp and redox + + align:start position:0% +looking at things like atp and redox + + + align:start position:0% +looking at things like atp and redox +loads now if we look at it one molecule + + align:start position:0% +loads now if we look at it one molecule + + + align:start position:0% +loads now if we look at it one molecule +at a time you obviously get a more + + align:start position:0% +at a time you obviously get a more + + + align:start position:0% +at a time you obviously get a more +complex you get every possible pairwise + + align:start position:0% +complex you get every possible pairwise + + + align:start position:0% +complex you get every possible pairwise +combination of molecules + + align:start position:0% +combination of molecules + + + align:start position:0% +combination of molecules +and you can see this full dynamics now + + align:start position:0% +and you can see this full dynamics now + + + align:start position:0% +and you can see this full dynamics now +these are not these are not data these + + align:start position:0% +these are not these are not data these + + + align:start position:0% +these are not these are not data these +are all simulations and unfortunately we + + align:start position:0% +are all simulations and unfortunately we + + + align:start position:0% +are all simulations and unfortunately we +don't have + + align:start position:0% +don't have + + + align:start position:0% +don't have +that kind of dynamic resolution and + + align:start position:0% +that kind of dynamic resolution and + + + align:start position:0% +that kind of dynamic resolution and +experimental data just yet but this + + align:start position:0% +experimental data just yet but this + + + align:start position:0% +experimental data just yet but this +gives you some idea if you see some + + align:start position:0% +gives you some idea if you see some + + + align:start position:0% +gives you some idea if you see some +particularly interesting phenomena in + + align:start position:0% +particularly interesting phenomena in + + + align:start position:0% +particularly interesting phenomena in +here then it might be a motivation for + + align:start position:0% +here then it might be a motivation for + + + align:start position:0% +here then it might be a motivation for +going in and looking at + + align:start position:0% +going in and looking at + + + align:start position:0% +going in and looking at +the data in more detail + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +we mentioned this this difference + + align:start position:0% +we mentioned this this difference + + + align:start position:0% +we mentioned this this difference +between the + + align:start position:0% +between the + + + align:start position:0% +between the +um + + align:start position:0% +um + + + align:start position:0% +um +sort of ordinary + + align:start position:0% +sort of ordinary + + + align:start position:0% +sort of ordinary +uh hyperbolic curve in the upper left of + + align:start position:0% +uh hyperbolic curve in the upper left of + + + align:start position:0% +uh hyperbolic curve in the upper left of +the actual + + align:start position:0% +the actual + + + align:start position:0% +the actual +lower right of this whole slide the + + align:start position:0% +lower right of this whole slide the + + + align:start position:0% +lower right of this whole slide the +upper left of the insert + + align:start position:0% +upper left of the insert + + + align:start position:0% +upper left of the insert +and the sigmoid curve that you get from + + align:start position:0% +and the sigmoid curve that you get from + + + align:start position:0% +and the sigmoid curve that you get from +a + + align:start position:0% + + + + align:start position:0% + +allosteric interaction and this trend + + align:start position:0% +allosteric interaction and this trend + + + align:start position:0% +allosteric interaction and this trend +and within the + + align:start position:0% +and within the + + + align:start position:0% +and within the +this whole cell is set up for + + align:start position:0% +this whole cell is set up for + + + align:start position:0% +this whole cell is set up for +transporting oxygen as oxygen + + align:start position:0% +transporting oxygen as oxygen + + + align:start position:0% +transporting oxygen as oxygen +concentration increases + + align:start position:0% +concentration increases + + + align:start position:0% +concentration increases +for hemoglobin you either get this + + align:start position:0% +for hemoglobin you either get this + + + align:start position:0% +for hemoglobin you either get this +hyperbolic or sigmoid curve as it gets + + align:start position:0% +hyperbolic or sigmoid curve as it gets + + + align:start position:0% +hyperbolic or sigmoid curve as it gets +increasingly sigmoid increasingly + + align:start position:0% +increasingly sigmoid increasingly + + + align:start position:0% +increasingly sigmoid increasingly +cooperative + + align:start position:0% +cooperative + + + align:start position:0% +cooperative +with increasing amounts of of one of the + + align:start position:0% +with increasing amounts of of one of the + + + align:start position:0% +with increasing amounts of of one of the +intermediate metabolites + + align:start position:0% +intermediate metabolites + + + align:start position:0% +intermediate metabolites +2 3 diphosphoglycerate + + align:start position:0% +2 3 diphosphoglycerate + + + align:start position:0% +2 3 diphosphoglycerate +and this you can see this is now the + + align:start position:0% +and this you can see this is now the + + + align:start position:0% +and this you can see this is now the +connection between the glycolytic + + align:start position:0% +connection between the glycolytic + + + align:start position:0% +connection between the glycolytic +pathway the regula the regulation is + + align:start position:0% +pathway the regula the regulation is + + + align:start position:0% +pathway the regula the regulation is +sensing the state of the glycolytic + + align:start position:0% +sensing the state of the glycolytic + + + align:start position:0% +sensing the state of the glycolytic +pathway and the + + align:start position:0% + + + + align:start position:0% + +hemoglobin in addition their connections + + align:start position:0% +hemoglobin in addition their connections + + + align:start position:0% +hemoglobin in addition their connections +with the ph which is also regulated in + + align:start position:0% +with the ph which is also regulated in + + + align:start position:0% +with the ph which is also regulated in +this + + align:start position:0% +this + + + align:start position:0% +this +and the redox you can see just above it + + align:start position:0% +and the redox you can see just above it + + + align:start position:0% +and the redox you can see just above it +here the hemoglobin going to the + + align:start position:0% +here the hemoglobin going to the + + + align:start position:0% +here the hemoglobin going to the +unproductive net hemoglobin state so you + + align:start position:0% +unproductive net hemoglobin state so you + + + align:start position:0% +unproductive net hemoglobin state so you +can see their connections uh in the + + align:start position:0% +can see their connections uh in the + + + align:start position:0% +can see their connections uh in the +network between its ultimate function + + align:start position:0% +network between its ultimate function + + + align:start position:0% +network between its ultimate function +which is transporting oxygen and all + + align:start position:0% +which is transporting oxygen and all + + + align:start position:0% +which is transporting oxygen and all +these intermediate uh metabolism + + align:start position:0% +these intermediate uh metabolism + + + align:start position:0% +these intermediate uh metabolism +components and it also brings us to this + + align:start position:0% +components and it also brings us to this + + + align:start position:0% +components and it also brings us to this +topic again of this cooperativity and + + align:start position:0% +topic again of this cooperativity and + + + align:start position:0% +topic again of this cooperativity and +how it what how does it arise here in + + align:start position:0% +how it what how does it arise here in + + + align:start position:0% +how it what how does it arise here in +the hemoglobin has a tetrameric + + align:start position:0% +the hemoglobin has a tetrameric + + + align:start position:0% +the hemoglobin has a tetrameric +confirmation state change which is yeah + + align:start position:0% +confirmation state change which is yeah + + + align:start position:0% +confirmation state change which is yeah +there's a second site that binds this + + align:start position:0% +there's a second site that binds this + + + align:start position:0% +there's a second site that binds this +organic + + align:start position:0% +organic + + + align:start position:0% +organic +diphosphoglycerate + + align:start position:0% + + + + align:start position:0% + +but another direction we can take this + + align:start position:0% +but another direction we can take this + + + align:start position:0% +but another direction we can take this +so in the lower left-hand corner of uh + + align:start position:0% +so in the lower left-hand corner of uh + + + align:start position:0% +so in the lower left-hand corner of uh +slide 21 is the same icon again of how + + align:start position:0% +slide 21 is the same icon again of how + + + align:start position:0% +slide 21 is the same icon again of how +we get increasingly cooperative from + + align:start position:0% +we get increasingly cooperative from + + + align:start position:0% +we get increasingly cooperative from +hyperbolic to sigmoidal + + align:start position:0% +hyperbolic to sigmoidal + + + align:start position:0% +hyperbolic to sigmoidal +to the point where this becomes almost + + align:start position:0% +to the point where this becomes almost + + + align:start position:0% +to the point where this becomes almost +vertical and this and displaced from the + + align:start position:0% +vertical and this and displaced from the + + + align:start position:0% +vertical and this and displaced from the +origin so that the cell at a at a + + align:start position:0% +origin so that the cell at a at a + + + align:start position:0% +origin so that the cell at a at a +good point in response to a stimulus + + align:start position:0% +good point in response to a stimulus + + + align:start position:0% +good point in response to a stimulus +will make a decision to commit to the + + align:start position:0% +will make a decision to commit to the + + + align:start position:0% +will make a decision to commit to the +next phase in cell division just as we + + align:start position:0% +next phase in cell division just as we + + + align:start position:0% +next phase in cell division just as we +had this this is similar to the cell + + align:start position:0% +had this this is similar to the cell + + + align:start position:0% +had this this is similar to the cell +division that we talked about earlier in + + align:start position:0% +division that we talked about earlier in + + + align:start position:0% +division that we talked about earlier in +the context of the microarray analysis + + align:start position:0% +the context of the microarray analysis + + + align:start position:0% +the context of the microarray analysis +of yeast cell division here we're + + align:start position:0% +of yeast cell division here we're + + + align:start position:0% +of yeast cell division here we're +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +xenopus amphibian oocyte which has nice + + align:start position:0% +xenopus amphibian oocyte which has nice + + + align:start position:0% +xenopus amphibian oocyte which has nice +large cells to do this kind of study + + align:start position:0% +large cells to do this kind of study + + + align:start position:0% +large cells to do this kind of study +where where you need to decide to come + + align:start position:0% +where where you need to decide to come + + + align:start position:0% +where where you need to decide to come +out of g1 and commit to synthesizing dna + + align:start position:0% +out of g1 and commit to synthesizing dna + + + align:start position:0% +out of g1 and commit to synthesizing dna +in the s phase in the lower portion of + + align:start position:0% +in the s phase in the lower portion of + + + align:start position:0% +in the s phase in the lower portion of +the circle where you get now two dna + + align:start position:0% +the circle where you get now two dna + + + align:start position:0% +the circle where you get now two dna +molecules and once you're convinced that + + align:start position:0% +molecules and once you're convinced that + + + align:start position:0% +molecules and once you're convinced that +you've made rep finished replicating all + + align:start position:0% +you've made rep finished replicating all + + + align:start position:0% +you've made rep finished replicating all +your dna + + align:start position:0% +your dna + + + align:start position:0% +your dna +only at that point think can you commit + + align:start position:0% +only at that point think can you commit + + + align:start position:0% +only at that point think can you commit +to mitosis another deficient decision + + align:start position:0% +to mitosis another deficient decision + + + align:start position:0% +to mitosis another deficient decision +major decision and then you get two + + align:start position:0% +major decision and then you get two + + + align:start position:0% +major decision and then you get two +cells and you go back and you complete + + align:start position:0% +cells and you go back and you complete + + + align:start position:0% +cells and you go back and you complete +the cell cycle the little time force at + + align:start position:0% +the cell cycle the little time force at + + + align:start position:0% +the cell cycle the little time force at +the bottom here this should be + + align:start position:0% +the bottom here this should be + + + align:start position:0% +the bottom here this should be +reminiscent for you of the time force we + + align:start position:0% +reminiscent for you of the time force we + + + align:start position:0% +reminiscent for you of the time force we +had of rna synthesis of you know various + + align:start position:0% +had of rna synthesis of you know various + + + align:start position:0% +had of rna synthesis of you know various +clusters rna here it's the dna synthesis + + align:start position:0% +clusters rna here it's the dna synthesis + + + align:start position:0% +clusters rna here it's the dna synthesis +you can see it ramps up in the in the + + align:start position:0% +you can see it ramps up in the in the + + + align:start position:0% +you can see it ramps up in the in the +red s phase and then ramps down in the + + align:start position:0% +red s phase and then ramps down in the + + + align:start position:0% +red s phase and then ramps down in the +metaphase due to the creation of two new + + align:start position:0% +metaphase due to the creation of two new + + + align:start position:0% +metaphase due to the creation of two new +cells + + align:start position:0% +cells + + + align:start position:0% +cells +we want to talk about how do we make + + align:start position:0% +we want to talk about how do we make + + + align:start position:0% +we want to talk about how do we make +this as + + align:start position:0% +this as + + + align:start position:0% +this as +you know + + align:start position:0% +you know + + + align:start position:0% +you know +responses to say progesterone is + + align:start position:0% +responses to say progesterone is + + + align:start position:0% +responses to say progesterone is +something that that is signaling cells + + align:start position:0% +something that that is signaling cells + + + align:start position:0% +something that that is signaling cells +that might be waiting + + align:start position:0% +that might be waiting + + + align:start position:0% +that might be waiting +uh for long periods of time + + align:start position:0% +uh for long periods of time + + + align:start position:0% +uh for long periods of time +to complete the next step in a division + + align:start position:0% +to complete the next step in a division + + + align:start position:0% +to complete the next step in a division +cycle for an external hormone stimulus + + align:start position:0% +cycle for an external hormone stimulus + + + align:start position:0% +cycle for an external hormone stimulus +that it's time to start + + align:start position:0% + + + + align:start position:0% + +the next step in cell cycle we want this + + align:start position:0% +the next step in cell cycle we want this + + + align:start position:0% +the next step in cell cycle we want this +to be displaced from the origin you + + align:start position:0% +to be displaced from the origin you + + + align:start position:0% +to be displaced from the origin you +don't want it to be just flipping on and + + align:start position:0% +don't want it to be just flipping on and + + + align:start position:0% +don't want it to be just flipping on and +on off irrespective of the stimulus but + + align:start position:0% +on off irrespective of the stimulus but + + + align:start position:0% +on off irrespective of the stimulus but +you well it does flip you want it to go + + align:start position:0% +you well it does flip you want it to go + + + align:start position:0% +you well it does flip you want it to go +very quickly so how would we model this + + align:start position:0% +very quickly so how would we model this + + + align:start position:0% +very quickly so how would we model this +and what what so look at the upper right + + align:start position:0% +and what what so look at the upper right + + + align:start position:0% +and what what so look at the upper right +hand + + align:start position:0% +hand + + + align:start position:0% +hand +uh + + align:start position:0% +uh + + + align:start position:0% +uh +diagram of slide 22 + + align:start position:0% +diagram of slide 22 + + + align:start position:0% +diagram of slide 22 +and you have + + align:start position:0% +and you have + + + align:start position:0% +and you have +a set of these oocytes kind of + + align:start position:0% +a set of these oocytes kind of + + + align:start position:0% +a set of these oocytes kind of +diagrammatic diagrammatically indicating + + align:start position:0% +diagrammatic diagrammatically indicating + + + align:start position:0% +diagrammatic diagrammatically indicating +their state their state determined by to + + align:start position:0% +their state their state determined by to + + + align:start position:0% +their state their state determined by to +what extent are they ready to + + align:start position:0% + + + + align:start position:0% + +commit to + + align:start position:0% +commit to + + + align:start position:0% +commit to +the next division state here we can + + align:start position:0% +the next division state here we can + + + align:start position:0% +the next division state here we can +think of it as the biomarker is the + + align:start position:0% +think of it as the biomarker is the + + + align:start position:0% +think of it as the biomarker is the +state of phosphorylation of a protein + + align:start position:0% +state of phosphorylation of a protein + + + align:start position:0% +state of phosphorylation of a protein +map kinase + + align:start position:0% +map kinase + + + align:start position:0% +map kinase +if it's phosphorylated + + align:start position:0% +if it's phosphorylated + + + align:start position:0% +if it's phosphorylated +then it's committed to this division and + + align:start position:0% +then it's committed to this division and + + + align:start position:0% +then it's committed to this division and +we can think of this as the black + + align:start position:0% +we can think of this as the black + + + align:start position:0% +we can think of this as the black +side of this gradient going from white + + align:start position:0% +side of this gradient going from white + + + align:start position:0% +side of this gradient going from white +to black but + + align:start position:0% +to black but + + + align:start position:0% +to black but +if you grind up a whole population these + + align:start position:0% +if you grind up a whole population these + + + align:start position:0% +if you grind up a whole population these +oocytes and measure the total map kinase + + align:start position:0% +oocytes and measure the total map kinase + + + align:start position:0% +oocytes and measure the total map kinase +phosphorylation as a function of + + align:start position:0% +phosphorylation as a function of + + + align:start position:0% +phosphorylation as a function of +increasing stimulus s + + align:start position:0% +increasing stimulus s + + + align:start position:0% +increasing stimulus s +in this case progesterone the response + + align:start position:0% +in this case progesterone the response + + + align:start position:0% +in this case progesterone the response +that is to say the phosphorylated state + + align:start position:0% +that is to say the phosphorylated state + + + align:start position:0% +that is to say the phosphorylated state +and the commitment to mitosis + + align:start position:0% +and the commitment to mitosis + + + align:start position:0% +and the commitment to mitosis +will gradually increase as indicated in + + align:start position:0% +will gradually increase as indicated in + + + align:start position:0% +will gradually increase as indicated in +the kind of the gradient model but + + align:start position:0% +the kind of the gradient model but + + + align:start position:0% +the kind of the gradient model but +that's if you ground up all the cells + + align:start position:0% +that's if you ground up all the cells + + + align:start position:0% +that's if you ground up all the cells +but what if you asked + + align:start position:0% +but what if you asked + + + align:start position:0% +but what if you asked +the other way of obtaining that result + + align:start position:0% +the other way of obtaining that result + + + align:start position:0% +the other way of obtaining that result +would be if each each cell is making a + + align:start position:0% +would be if each each cell is making a + + + align:start position:0% +would be if each each cell is making a +all or none decision and what happens is + + align:start position:0% +all or none decision and what happens is + + + align:start position:0% +all or none decision and what happens is +the probability of a cell being in that + + align:start position:0% +the probability of a cell being in that + + + align:start position:0% +the probability of a cell being in that +all or none state changes with + + align:start position:0% +all or none state changes with + + + align:start position:0% +all or none state changes with +increasing stimulus to progesterone and + + align:start position:0% +increasing stimulus to progesterone and + + + align:start position:0% +increasing stimulus to progesterone and +that is the lower model and is in in + + align:start position:0% +that is the lower model and is in in + + + align:start position:0% +that is the lower model and is in in +fact closer to reality as indicated by + + align:start position:0% +fact closer to reality as indicated by + + + align:start position:0% +fact closer to reality as indicated by +the experiment at the at the bottom uh + + align:start position:0% +the experiment at the at the bottom uh + + + align:start position:0% +the experiment at the at the bottom uh +part of the slide here where you have + + align:start position:0% +part of the slide here where you have + + + align:start position:0% +part of the slide here where you have +at a you you'll have this is a part of a + + align:start position:0% +at a you you'll have this is a part of a + + + align:start position:0% +at a you you'll have this is a part of a +concentration curve where you're + + align:start position:0% +concentration curve where you're + + + align:start position:0% +concentration curve where you're +increasing the stimulus progesterone but + + align:start position:0% +increasing the stimulus progesterone but + + + align:start position:0% +increasing the stimulus progesterone but +at this particular stimulus you can + + align:start position:0% +at this particular stimulus you can + + + align:start position:0% +at this particular stimulus you can +sample individual cells there's enough + + align:start position:0% +sample individual cells there's enough + + + align:start position:0% +sample individual cells there's enough +of the cell that you can actually do + + align:start position:0% +of the cell that you can actually do + + + align:start position:0% +of the cell that you can actually do +proteomics + + align:start position:0% +proteomics + + + align:start position:0% +proteomics +on individual cells and the proteomics + + align:start position:0% +on individual cells and the proteomics + + + align:start position:0% +on individual cells and the proteomics +here is a western blot we mentioned this + + align:start position:0% +here is a western blot we mentioned this + + + align:start position:0% +here is a western blot we mentioned this +a couple of + + align:start position:0% +a couple of + + + align:start position:0% +a couple of +lectures back and here each + + align:start position:0% +lectures back and here each + + + align:start position:0% +lectures back and here each +you can see the two states of the map + + align:start position:0% +you can see the two states of the map + + + align:start position:0% +you can see the two states of the map +kinase the phosphorylated state is the + + align:start position:0% +kinase the phosphorylated state is the + + + align:start position:0% +kinase the phosphorylated state is the +slower electrophoretically it's the + + align:start position:0% +slower electrophoretically it's the + + + align:start position:0% +slower electrophoretically it's the +upper band in this diagram and + + align:start position:0% +upper band in this diagram and + + + align:start position:0% +upper band in this diagram and +the lower band is the unpossible release + + align:start position:0% +the lower band is the unpossible release + + + align:start position:0% +the lower band is the unpossible release +state and you can see there's no example + + align:start position:0% +state and you can see there's no example + + + align:start position:0% +state and you can see there's no example +here of a of a cell which is an + + align:start position:0% +here of a of a cell which is an + + + align:start position:0% +here of a of a cell which is an +intermediate state where it has sort of + + align:start position:0% +intermediate state where it has sort of + + + align:start position:0% +intermediate state where it has sort of +half and half or 40 60 of the two + + align:start position:0% +half and half or 40 60 of the two + + + align:start position:0% +half and half or 40 60 of the two +different + + align:start position:0% +different + + + align:start position:0% +different +protein forms + + align:start position:0% +protein forms + + + align:start position:0% +protein forms +however if you + + align:start position:0% +however if you + + + align:start position:0% +however if you +as a thought experiment took all those + + align:start position:0% +as a thought experiment took all those + + + align:start position:0% +as a thought experiment took all those +cells and mushed them up and took + + align:start position:0% +cells and mushed them up and took + + + align:start position:0% +cells and mushed them up and took +this and ran it all in one lane you + + align:start position:0% +this and ran it all in one lane you + + + align:start position:0% +this and ran it all in one lane you +would see a mixture you would see all + + align:start position:0% +would see a mixture you would see all + + + align:start position:0% +would see a mixture you would see all +the intermediate states and that would + + align:start position:0% +the intermediate states and that would + + + align:start position:0% +the intermediate states and that would +be a function of + + align:start position:0% +be a function of + + + align:start position:0% +be a function of +progesterone so this is a + + align:start position:0% +progesterone so this is a + + + align:start position:0% +progesterone so this is a +warning + + align:start position:0% +warning + + + align:start position:0% +warning +similar to the ones i said before that + + align:start position:0% +similar to the ones i said before that + + + align:start position:0% +similar to the ones i said before that +when you grind everything up and mix + + align:start position:0% +when you grind everything up and mix + + + align:start position:0% +when you grind everything up and mix +populations of cells or molecules + + align:start position:0% +populations of cells or molecules + + + align:start position:0% +populations of cells or molecules +you need to be careful that because + + align:start position:0% +you need to be careful that because + + + align:start position:0% +you need to be careful that because +different cells may be in different + + align:start position:0% +different cells may be in different + + + align:start position:0% +different cells may be in different +states different molecules many + + align:start position:0% +states different molecules many + + + align:start position:0% +states different molecules many +different states and the average + + align:start position:0% +different states and the average + + + align:start position:0% +different states and the average +behavior is not the same as individual + + align:start position:0% +behavior is not the same as individual + + + align:start position:0% +behavior is not the same as individual +so here is so but now that's only part + + align:start position:0% +so here is so but now that's only part + + + align:start position:0% +so here is so but now that's only part +of the + + align:start position:0% +of the + + + align:start position:0% +of the +the lesson here the cells are going + + align:start position:0% +the lesson here the cells are going + + + align:start position:0% +the lesson here the cells are going +through this all or none uh + + align:start position:0% +through this all or none uh + + + align:start position:0% +through this all or none uh +process we can monitor it by single cell + + align:start position:0% +process we can monitor it by single cell + + + align:start position:0% +process we can monitor it by single cell +proteomics + + align:start position:0% +proteomics + + + align:start position:0% +proteomics +but how do we model it + + align:start position:0% +but how do we model it + + + align:start position:0% +but how do we model it +well in very abstract terms the response + + align:start position:0% +well in very abstract terms the response + + + align:start position:0% +well in very abstract terms the response +here can be modeled as uh in this hill + + align:start position:0% +here can be modeled as uh in this hill + + + align:start position:0% +here can be modeled as uh in this hill +coefficient where you have a stimulus s + + align:start position:0% +coefficient where you have a stimulus s + + + align:start position:0% +coefficient where you have a stimulus s +some + + align:start position:0% +some + + + align:start position:0% +some +uh kinetic constant k kind of like a + + align:start position:0% +uh kinetic constant k kind of like a + + + align:start position:0% +uh kinetic constant k kind of like a +michaelis constant where whereas + + align:start position:0% +michaelis constant where whereas + + + align:start position:0% +michaelis constant where whereas +basically as s gets closer to k it has a + + align:start position:0% +basically as s gets closer to k it has a + + + align:start position:0% +basically as s gets closer to k it has a +larger um + + align:start position:0% +larger um + + + align:start position:0% +larger um +response here + + align:start position:0% +response here + + + align:start position:0% +response here +effect on the response and the and the + + align:start position:0% +effect on the response and the and the + + + align:start position:0% +effect on the response and the and the +uh and that's non-linear because you + + align:start position:0% +uh and that's non-linear because you + + + align:start position:0% +uh and that's non-linear because you +have the exponent h + + align:start position:0% +have the exponent h + + + align:start position:0% +have the exponent h +and the more the large larger h is the + + align:start position:0% +and the more the large larger h is the + + + align:start position:0% +and the more the large larger h is the +more non-linear it is so let's say the h + + align:start position:0% +more non-linear it is so let's say the h + + + align:start position:0% +more non-linear it is so let's say the h +is one in this little uh schematic to + + align:start position:0% +is one in this little uh schematic to + + + align:start position:0% +is one in this little uh schematic to +the right here it's hyperbolic + + align:start position:0% +the right here it's hyperbolic + + + align:start position:0% +the right here it's hyperbolic +um + + align:start position:0% +um + + + align:start position:0% +um +no sigmoid character at all in the case + + align:start position:0% +no sigmoid character at all in the case + + + align:start position:0% +no sigmoid character at all in the case +of hemoglobin and uh phosphate kinase + + align:start position:0% +of hemoglobin and uh phosphate kinase + + + align:start position:0% +of hemoglobin and uh phosphate kinase +that we talked about in the red blood + + align:start position:0% +that we talked about in the red blood + + + align:start position:0% +that we talked about in the red blood +cell it's more sigmoidal like a + + align:start position:0% +cell it's more sigmoidal like a + + + align:start position:0% +cell it's more sigmoidal like a +an h of 2.8 almost uh cube law there + + align:start position:0% +an h of 2.8 almost uh cube law there + + + align:start position:0% +an h of 2.8 almost uh cube law there +and in fact even within this system one + + align:start position:0% +and in fact even within this system one + + + align:start position:0% +and in fact even within this system one +of the steps we'll talk about in the + + align:start position:0% +of the steps we'll talk about in the + + + align:start position:0% +of the steps we'll talk about in the +next slide + + align:start position:0% + + + + align:start position:0% + +it has a a where you have a stimulus of + + align:start position:0% +it has a a where you have a stimulus of + + + align:start position:0% +it has a a where you have a stimulus of +a moss protein and a response of the + + align:start position:0% +a moss protein and a response of the + + + align:start position:0% +a moss protein and a response of the +same kinase phosphorylation response it + + align:start position:0% +same kinase phosphorylation response it + + + align:start position:0% +same kinase phosphorylation response it +has a modest + + align:start position:0% +has a modest + + + align:start position:0% +has a modest +sigmoid hill coefficient of three just + + align:start position:0% +sigmoid hill coefficient of three just + + + align:start position:0% +sigmoid hill coefficient of three just +like hemoglobin but the overall response + + align:start position:0% +like hemoglobin but the overall response + + + align:start position:0% +like hemoglobin but the overall response +of map kinase to progesterone has an + + align:start position:0% +of map kinase to progesterone has an + + + align:start position:0% +of map kinase to progesterone has an +enormous + + align:start position:0% +enormous + + + align:start position:0% +enormous +exponent of 42. that means it's all it's + + align:start position:0% +exponent of 42. that means it's all it's + + + align:start position:0% +exponent of 42. that means it's all it's +almost vertical and it's displaced from + + align:start position:0% +almost vertical and it's displaced from + + + align:start position:0% +almost vertical and it's displaced from +the origin + + align:start position:0% +the origin + + + align:start position:0% +the origin +how do we get that + + align:start position:0% +how do we get that + + + align:start position:0% +how do we get that +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +oops + + align:start position:0% + + + + align:start position:0% + +so here is a a proposed model and it's + + align:start position:0% +so here is a a proposed model and it's + + + align:start position:0% +so here is a a proposed model and it's +an interesting snapshot in the + + align:start position:0% +an interesting snapshot in the + + + align:start position:0% +an interesting snapshot in the +inevitable + + align:start position:0% +inevitable + + + align:start position:0% +inevitable +evolution of a mod model from something + + align:start position:0% +evolution of a mod model from something + + + align:start position:0% +evolution of a mod model from something +very primitive which might have just + + align:start position:0% +very primitive which might have just + + + align:start position:0% +very primitive which might have just +been the moss to + + align:start position:0% +been the moss to + + + align:start position:0% +been the moss to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +moss effects on map kinase kind of as a + + align:start position:0% +moss effects on map kinase kind of as a + + + align:start position:0% +moss effects on map kinase kind of as a +direct effect here + + align:start position:0% +direct effect here + + + align:start position:0% +direct effect here +which as we said has a health + + align:start position:0% +which as we said has a health + + + align:start position:0% +which as we said has a health +coefficient of about three-fold + + align:start position:0% +coefficient of about three-fold + + + align:start position:0% +coefficient of about three-fold +uh sorry yeah total coefficient of three + + align:start position:0% +uh sorry yeah total coefficient of three + + + align:start position:0% +uh sorry yeah total coefficient of three +a three-fold because that's an + + align:start position:0% +a three-fold because that's an + + + align:start position:0% +a three-fold because that's an +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +but overall combination of two other + + align:start position:0% +but overall combination of two other + + + align:start position:0% +but overall combination of two other +factors that you have a chain of + + align:start position:0% +factors that you have a chain of + + + align:start position:0% +factors that you have a chain of +modifiers + + align:start position:0% +modifiers + + + align:start position:0% +modifiers +each close to saturation meaning that + + align:start position:0% +each close to saturation meaning that + + + align:start position:0% +each close to saturation meaning that +each one has a slight sigmoid uh + + align:start position:0% +each one has a slight sigmoid uh + + + align:start position:0% +each one has a slight sigmoid uh +behavior and that's and you've got + + align:start position:0% +behavior and that's and you've got + + + align:start position:0% +behavior and that's and you've got +a + + align:start position:0% +a + + + align:start position:0% +a +um sorry + + align:start position:0% +um sorry + + + align:start position:0% +um sorry +it could be a hyperbolic function such + + align:start position:0% +it could be a hyperbolic function such + + + align:start position:0% +it could be a hyperbolic function such +as let's just say this dotted line + + align:start position:0% +as let's just say this dotted line + + + align:start position:0% +as let's just say this dotted line +that's going up smoothly from zero where + + align:start position:0% +that's going up smoothly from zero where + + + align:start position:0% +that's going up smoothly from zero where +it says neither that would be the effect + + align:start position:0% +it says neither that would be the effect + + + align:start position:0% +it says neither that would be the effect +of if you just have a normal + + align:start position:0% +of if you just have a normal + + + align:start position:0% +of if you just have a normal +enzymatic reaction with no alice theory + + align:start position:0% +enzymatic reaction with no alice theory + + + align:start position:0% +enzymatic reaction with no alice theory +no feedback no ultra sensitivity + + align:start position:0% +no feedback no ultra sensitivity + + + align:start position:0% +no feedback no ultra sensitivity +if each of those has a component and + + align:start position:0% +if each of those has a component and + + + align:start position:0% +if each of those has a component and +you're close to saturation meaning your + + align:start position:0% +you're close to saturation meaning your + + + align:start position:0% +you're close to saturation meaning your +substrate is very high so you're going + + align:start position:0% +substrate is very high so you're going + + + align:start position:0% +substrate is very high so you're going +as fast as the enzyme will go you have a + + align:start position:0% +as fast as the enzyme will go you have a + + + align:start position:0% +as fast as the enzyme will go you have a +chain of those you can show + + align:start position:0% +chain of those you can show + + + align:start position:0% +chain of those you can show +through kinetic modeling that that will + + align:start position:0% +through kinetic modeling that that will + + + align:start position:0% +through kinetic modeling that that will +create a very high sensitivity to the + + align:start position:0% +create a very high sensitivity to the + + + align:start position:0% +create a very high sensitivity to the +reaction and that's what uh + + align:start position:0% +reaction and that's what uh + + + align:start position:0% +reaction and that's what uh +the furthest dotted curve uh close to + + align:start position:0% +the furthest dotted curve uh close to + + + align:start position:0% +the furthest dotted curve uh close to +the axis um is ultra sensitivity alone + + align:start position:0% +the axis um is ultra sensitivity alone + + + align:start position:0% +the axis um is ultra sensitivity alone +and then this + + align:start position:0% +and then this + + + align:start position:0% +and then this +here you have progesterone going in in + + align:start position:0% +here you have progesterone going in in + + + align:start position:0% +here you have progesterone going in in +the + + align:start position:0% +the + + + align:start position:0% +the +upper left + + align:start position:0% +upper left + + + align:start position:0% +upper left +affecting + + align:start position:0% +affecting + + + align:start position:0% +affecting +a complicated rate now these rate + + align:start position:0% +a complicated rate now these rate + + + align:start position:0% +a complicated rate now these rate +constants don't necessarily + + align:start position:0% +constants don't necessarily + + + align:start position:0% +constants don't necessarily +mean + + align:start position:0% +mean + + + align:start position:0% +mean +a unitary simple kinetic + + align:start position:0% +a unitary simple kinetic + + + align:start position:0% +a unitary simple kinetic +step they can represent something as + + align:start position:0% +step they can represent something as + + + align:start position:0% +step they can represent something as +complicated as going from amino acids a + + align:start position:0% +complicated as going from amino acids a + + + align:start position:0% +complicated as going from amino acids a +to a particular protein moss + + align:start position:0% +to a particular protein moss + + + align:start position:0% +to a particular protein moss +and then the reverse reaction k minus + + align:start position:0% +and then the reverse reaction k minus + + + align:start position:0% +and then the reverse reaction k minus +case of -1 is the degradation of moss + + align:start position:0% +case of -1 is the degradation of moss + + + align:start position:0% +case of -1 is the degradation of moss +back to amino acids which is not + + align:start position:0% +back to amino acids which is not + + + align:start position:0% +back to amino acids which is not +you know a reverse of the same enzyme + + align:start position:0% +you know a reverse of the same enzyme + + + align:start position:0% +you know a reverse of the same enzyme +set by any means + + align:start position:0% +set by any means + + + align:start position:0% +set by any means +um the next step k2 is simpler it's just + + align:start position:0% +um the next step k2 is simpler it's just + + + align:start position:0% +um the next step k2 is simpler it's just +moss being phosphorylated by actually + + align:start position:0% +moss being phosphorylated by actually + + + align:start position:0% +moss being phosphorylated by actually +our friend that kinase + + align:start position:0% +our friend that kinase + + + align:start position:0% +our friend that kinase +um in his phosphorous state + + align:start position:0% +um in his phosphorous state + + + align:start position:0% +um in his phosphorous state +for producing the catalyzing autocad you + + align:start position:0% +for producing the catalyzing autocad you + + + align:start position:0% +for producing the catalyzing autocad you +know forward uh catalyzing the mos + + align:start position:0% +know forward uh catalyzing the mos + + + align:start position:0% +know forward uh catalyzing the mos +phosphorylation which catalyzes another + + align:start position:0% +phosphorylation which catalyzes another + + + align:start position:0% +phosphorylation which catalyzes another +phosphorylation of another protein which + + align:start position:0% +phosphorylation of another protein which + + + align:start position:0% +phosphorylation of another protein which +then + + align:start position:0% +then + + + align:start position:0% +then +positively stimulates mapkins itself + + align:start position:0% +positively stimulates mapkins itself + + + align:start position:0% +positively stimulates mapkins itself +so this whole thing is a set of positive + + align:start position:0% +so this whole thing is a set of positive + + + align:start position:0% +so this whole thing is a set of positive +reactions each each of the phosphate + + align:start position:0% +reactions each each of the phosphate + + + align:start position:0% +reactions each each of the phosphate +proteins increases + + align:start position:0% +proteins increases + + + align:start position:0% +proteins increases +uh the the + + align:start position:0% +uh the the + + + align:start position:0% +uh the the +enzymatic uh tendency + + align:start position:0% +enzymatic uh tendency + + + align:start position:0% +enzymatic uh tendency +to uh for each of the other phosphate + + align:start position:0% +to uh for each of the other phosphate + + + align:start position:0% +to uh for each of the other phosphate +proteins to be produced so you can see + + align:start position:0% +proteins to be produced so you can see + + + align:start position:0% +proteins to be produced so you can see +that this is kind of on a hair trigger + + align:start position:0% +that this is kind of on a hair trigger + + + align:start position:0% +that this is kind of on a hair trigger +if any one of these fossil proteins gets + + align:start position:0% +if any one of these fossil proteins gets + + + align:start position:0% +if any one of these fossil proteins gets +produced then it'll increase all the + + align:start position:0% +produced then it'll increase all the + + + align:start position:0% +produced then it'll increase all the +other ones and it'll + + align:start position:0% +other ones and it'll + + + align:start position:0% +other ones and it'll +be a very cooperative procedure and + + align:start position:0% +be a very cooperative procedure and + + + align:start position:0% +be a very cooperative procedure and +that's what this furthest towards the + + align:start position:0% +that's what this furthest towards the + + + align:start position:0% +that's what this furthest towards the +axis in the lower left-hand corner where + + align:start position:0% +axis in the lower left-hand corner where + + + align:start position:0% +axis in the lower left-hand corner where +you have this positive feedback uh alone + + align:start position:0% +you have this positive feedback uh alone + + + align:start position:0% +you have this positive feedback uh alone +causes this very uh + + align:start position:0% +causes this very uh + + + align:start position:0% +causes this very uh +great tendency to to just jump up from + + align:start position:0% +great tendency to to just jump up from + + + align:start position:0% +great tendency to to just jump up from +zero to very high uh response + + align:start position:0% +zero to very high uh response + + + align:start position:0% +zero to very high uh response +uh + + align:start position:0% +uh + + + align:start position:0% +uh +with very little + + align:start position:0% +with very little + + + align:start position:0% +with very little +stimulus well that's dangerous you don't + + align:start position:0% +stimulus well that's dangerous you don't + + + align:start position:0% +stimulus well that's dangerous you don't +you want it to be + + align:start position:0% +you want it to be + + + align:start position:0% +you want it to be +nearly vertical but you don't want to be + + align:start position:0% +nearly vertical but you don't want to be + + + align:start position:0% +nearly vertical but you don't want to be +nearly vertical at zero stimulus because + + align:start position:0% +nearly vertical at zero stimulus because + + + align:start position:0% +nearly vertical at zero stimulus because +that's unstable so you want to move it + + align:start position:0% +that's unstable so you want to move it + + + align:start position:0% +that's unstable so you want to move it +over and that's where the ultra + + align:start position:0% +over and that's where the ultra + + + align:start position:0% +over and that's where the ultra +sensitivity comes in when you have this + + align:start position:0% +sensitivity comes in when you have this + + + align:start position:0% +sensitivity comes in when you have this +chain of modifiers putting both together + + align:start position:0% +chain of modifiers putting both together + + + align:start position:0% +chain of modifiers putting both together +as a solid black line where it shifted + + align:start position:0% +as a solid black line where it shifted + + + align:start position:0% +as a solid black line where it shifted +over so you have uh + + align:start position:0% +over so you have uh + + + align:start position:0% +over so you have uh +this actually this assay was done with + + align:start position:0% +this actually this assay was done with + + + align:start position:0% +this actually this assay was done with +moss rather than progesterone as the + + align:start position:0% +moss rather than progesterone as the + + + align:start position:0% +moss rather than progesterone as the +input + + align:start position:0% +input + + + align:start position:0% +input +but + + align:start position:0% +but + + + align:start position:0% +but +but you can see the overall + + align:start position:0% + + + + align:start position:0% + +increased cooperativity and shifting to + + align:start position:0% +increased cooperativity and shifting to + + + align:start position:0% +increased cooperativity and shifting to +the to the right + + align:start position:0% +the to the right + + + align:start position:0% +the to the right +so that's an example of how you can get + + align:start position:0% +so that's an example of how you can get + + + align:start position:0% +so that's an example of how you can get +this very high hill coefficient + + align:start position:0% +this very high hill coefficient + + + align:start position:0% +this very high hill coefficient +and where you can get by stability + + align:start position:0% +and where you can get by stability + + + align:start position:0% +and where you can get by stability +without + + align:start position:0% +without + + + align:start position:0% +without +stochastic you can imagine that you can + + align:start position:0% +stochastic you can imagine that you can + + + align:start position:0% +stochastic you can imagine that you can +have stochastic bistability if you have + + align:start position:0% +have stochastic bistability if you have + + + align:start position:0% +have stochastic bistability if you have +one molecule in the cell and either it's + + align:start position:0% +one molecule in the cell and either it's + + + align:start position:0% +one molecule in the cell and either it's +there or it's not then you have + + align:start position:0% +there or it's not then you have + + + align:start position:0% +there or it's not then you have +bistability you have two states for the + + align:start position:0% +bistability you have two states for the + + + align:start position:0% +bistability you have two states for the +cell either this is the cell with the + + align:start position:0% +cell either this is the cell with the + + + align:start position:0% +cell either this is the cell with the +molecule or without + + align:start position:0% +molecule or without + + + align:start position:0% +molecule or without +but here you can see that even with a + + align:start position:0% +but here you can see that even with a + + + align:start position:0% +but here you can see that even with a +very large cell xenopus oocytes being + + align:start position:0% +very large cell xenopus oocytes being + + + align:start position:0% +very large cell xenopus oocytes being +one of the largest cells and and very + + align:start position:0% +one of the largest cells and and very + + + align:start position:0% +one of the largest cells and and very +large amounts of proteins enough that + + align:start position:0% +large amounts of proteins enough that + + + align:start position:0% +large amounts of proteins enough that +you can easily see them in proteomics + + align:start position:0% +you can easily see them in proteomics + + + align:start position:0% +you can easily see them in proteomics +you can still achieve by stability with + + align:start position:0% +you can still achieve by stability with + + + align:start position:0% +you can still achieve by stability with +the right kinetic model not every random + + align:start position:0% +the right kinetic model not every random + + + align:start position:0% +the right kinetic model not every random +model would + + align:start position:0% +model would + + + align:start position:0% +model would +achieve that high health coefficient + + align:start position:0% +achieve that high health coefficient + + + align:start position:0% +achieve that high health coefficient +okay so what you can briefly mention the + + align:start position:0% +okay so what you can briefly mention the + + + align:start position:0% +okay so what you can briefly mention the +other way of getting by stability which + + align:start position:0% +other way of getting by stability which + + + align:start position:0% +other way of getting by stability which +is via stochastics of small molecules + + align:start position:0% +is via stochastics of small molecules + + + align:start position:0% +is via stochastics of small molecules +and here uh the + + align:start position:0% + + + + align:start position:0% + +an example so instead of dealing with + + align:start position:0% +an example so instead of dealing with + + + align:start position:0% +an example so instead of dealing with +very large cells with very large numbers + + align:start position:0% +very large cells with very large numbers + + + align:start position:0% +very large cells with very large numbers +of molecules involved here in in uh say + + align:start position:0% +of molecules involved here in in uh say + + + align:start position:0% +of molecules involved here in in uh say +bacteria in particular phage infected + + align:start position:0% +bacteria in particular phage infected + + + align:start position:0% +bacteria in particular phage infected +bacteria you often have the case + + align:start position:0% +bacteria you often have the case + + + align:start position:0% +bacteria you often have the case +generally have the case of very small + + align:start position:0% +generally have the case of very small + + + align:start position:0% +generally have the case of very small +bursts of activity a transcription + + align:start position:0% +bursts of activity a transcription + + + align:start position:0% +bursts of activity a transcription +factor will bind to a promoter + + align:start position:0% +factor will bind to a promoter + + + align:start position:0% +factor will bind to a promoter +it will cause + + align:start position:0% +it will cause + + + align:start position:0% +it will cause +before the transcription factor comes + + align:start position:0% +before the transcription factor comes + + + align:start position:0% +before the transcription factor comes +off it may cause a small burst of a + + align:start position:0% +off it may cause a small burst of a + + + align:start position:0% +off it may cause a small burst of a +couple of rna transcripts being made by + + align:start position:0% +couple of rna transcripts being made by + + + align:start position:0% +couple of rna transcripts being made by +a couple of + + align:start position:0% +a couple of + + + align:start position:0% +a couple of +rna polymerases seeing those + + align:start position:0% +rna polymerases seeing those + + + align:start position:0% +rna polymerases seeing those +transcription factors + + align:start position:0% +transcription factors + + + align:start position:0% +transcription factors +then each of those rnas cause its own + + align:start position:0% +then each of those rnas cause its own + + + align:start position:0% +then each of those rnas cause its own +bursts of protein synthesis where a + + align:start position:0% +bursts of protein synthesis where a + + + align:start position:0% +bursts of protein synthesis where a +whole series of ribosomes will bind + + align:start position:0% +whole series of ribosomes will bind + + + align:start position:0% +whole series of ribosomes will bind +in a polysome and you'll get this double + + align:start position:0% +in a polysome and you'll get this double + + + align:start position:0% +in a polysome and you'll get this double +burst of rna and protein + + align:start position:0% +burst of rna and protein + + + align:start position:0% +burst of rna and protein +and + + align:start position:0% +and + + + align:start position:0% +and +and + + align:start position:0% +and + + + align:start position:0% +and +this the stochastic binding of that + + align:start position:0% +this the stochastic binding of that + + + align:start position:0% +this the stochastic binding of that +transcription factor that starts that + + align:start position:0% +transcription factor that starts that + + + align:start position:0% +transcription factor that starts that +burst + + align:start position:0% +burst + + + align:start position:0% +burst +is modeled can be modeled by reasonable + + align:start position:0% +is modeled can be modeled by reasonable + + + align:start position:0% +is modeled can be modeled by reasonable +measured parameters for each of these + + align:start position:0% +measured parameters for each of these + + + align:start position:0% +measured parameters for each of these +steps and you can see that cells one two + + align:start position:0% +steps and you can see that cells one two + + + align:start position:0% +steps and you can see that cells one two +and three in the lower left of slide 25 + + align:start position:0% +and three in the lower left of slide 25 + + + align:start position:0% +and three in the lower left of slide 25 +or time is a horizontal axis up to say + + align:start position:0% +or time is a horizontal axis up to say + + + align:start position:0% +or time is a horizontal axis up to say +45 minutes or a cell division or two + + align:start position:0% +45 minutes or a cell division or two + + + align:start position:0% +45 minutes or a cell division or two +while + + align:start position:0% +while + + + align:start position:0% +while +the number of product proteins here + + align:start position:0% +the number of product proteins here + + + align:start position:0% +the number of product proteins here +measured in dimers of protein + + align:start position:0% +measured in dimers of protein + + + align:start position:0% +measured in dimers of protein +fluctuates for cell one takes gets an + + align:start position:0% +fluctuates for cell one takes gets an + + + align:start position:0% +fluctuates for cell one takes gets an +early start early burst and cell three + + align:start position:0% +early start early burst and cell three + + + align:start position:0% +early start early burst and cell three +hasn't quite hit its burst yet + + align:start position:0% +hasn't quite hit its burst yet + + + align:start position:0% +hasn't quite hit its burst yet +so you can see there's a lot of + + align:start position:0% +so you can see there's a lot of + + + align:start position:0% +so you can see there's a lot of +variation and this is one way of + + align:start position:0% +variation and this is one way of + + + align:start position:0% +variation and this is one way of +achieving a bi-stable switch + + align:start position:0% +achieving a bi-stable switch + + + align:start position:0% +achieving a bi-stable switch +but as you've seen not the only way you + + align:start position:0% +but as you've seen not the only way you + + + align:start position:0% +but as you've seen not the only way you +can also do it where all the proteins + + align:start position:0% +can also do it where all the proteins + + + align:start position:0% +can also do it where all the proteins +are present in all large amounts if you + + align:start position:0% +are present in all large amounts if you + + + align:start position:0% +are present in all large amounts if you +do choose to go the stochastic group + + align:start position:0% +do choose to go the stochastic group + + + align:start position:0% +do choose to go the stochastic group +this might be an interesting project for + + align:start position:0% +this might be an interesting project for + + + align:start position:0% +this might be an interesting project for +some of you it's by no means shown to be + + align:start position:0% +some of you it's by no means shown to be + + + align:start position:0% +some of you it's by no means shown to be +mission critical for + + align:start position:0% +mission critical for + + + align:start position:0% +mission critical for +a community + + align:start position:0% +a community + + + align:start position:0% +a community +of uh systems modelers but it is + + align:start position:0% +of uh systems modelers but it is + + + align:start position:0% +of uh systems modelers but it is +many people believe it is a way to go + + align:start position:0% + + + + align:start position:0% + +there has been great progress since 1977 + + align:start position:0% +there has been great progress since 1977 + + + align:start position:0% +there has been great progress since 1977 +when uh gillespie proposed the the uh + + align:start position:0% +when uh gillespie proposed the the uh + + + align:start position:0% +when uh gillespie proposed the the uh +the the algorithm named after him for uh + + align:start position:0% +the the algorithm named after him for uh + + + align:start position:0% +the the algorithm named after him for uh +stochastic simulation a couple of + + align:start position:0% +stochastic simulation a couple of + + + align:start position:0% +stochastic simulation a couple of +chemical reactions in general not just + + align:start position:0% +chemical reactions in general not just + + + align:start position:0% +chemical reactions in general not just +biological biochemical reactions uh + + align:start position:0% +biological biochemical reactions uh + + + align:start position:0% +biological biochemical reactions uh +since then gibson and brock in the uh + + align:start position:0% + + + + align:start position:0% + +within the last couple of years has come + + align:start position:0% +within the last couple of years has come + + + align:start position:0% +within the last couple of years has come +up with an algorithm which is now + + align:start position:0% +up with an algorithm which is now + + + align:start position:0% +up with an algorithm which is now +time proportional to logarithmic number + + align:start position:0% +time proportional to logarithmic number + + + align:start position:0% +time proportional to logarithmic number +of reactions rather than the number of + + align:start position:0% +of reactions rather than the number of + + + align:start position:0% +of reactions rather than the number of +reactions any time you go from n to log + + align:start position:0% +reactions any time you go from n to log + + + align:start position:0% +reactions any time you go from n to log +n this is a big progress + + align:start position:0% +n this is a big progress + + + align:start position:0% +n this is a big progress +and this is done by um + + align:start position:0% +and this is done by um + + + align:start position:0% +and this is done by um +better tracking of calculations that you + + align:start position:0% +better tracking of calculations that you + + + align:start position:0% +better tracking of calculations that you +can reuse and that's uh so i encourage + + align:start position:0% +can reuse and that's uh so i encourage + + + align:start position:0% +can reuse and that's uh so i encourage +you to take a look at this + + align:start position:0% +you to take a look at this + + + align:start position:0% +you to take a look at this +aspect of stochastics another aspect is + + align:start position:0% +aspect of stochastics another aspect is + + + align:start position:0% +aspect of stochastics another aspect is +people often think of the stochastics as + + align:start position:0% +people often think of the stochastics as + + + align:start position:0% +people often think of the stochastics as +kind of a nuisance they increase the + + align:start position:0% +kind of a nuisance they increase the + + + align:start position:0% +kind of a nuisance they increase the +computer time that it takes to do + + align:start position:0% +computer time that it takes to do + + + align:start position:0% +computer time that it takes to do +simulations they increase your + + align:start position:0% +simulations they increase your + + + align:start position:0% +simulations they increase your +uncertainty about the simulations that + + align:start position:0% +uncertainty about the simulations that + + + align:start position:0% +uncertainty about the simulations that +you then produce + + align:start position:0% +you then produce + + + align:start position:0% +you then produce +but there is an aspect of it which is + + align:start position:0% +but there is an aspect of it which is + + + align:start position:0% +but there is an aspect of it which is +just beginning to be harnessed in + + align:start position:0% +just beginning to be harnessed in + + + align:start position:0% +just beginning to be harnessed in +various fields of engineering and + + align:start position:0% +various fields of engineering and + + + align:start position:0% +various fields of engineering and +biological engineering is no exception + + align:start position:0% +biological engineering is no exception + + + align:start position:0% +biological engineering is no exception +and i give you two examples here to just + + align:start position:0% +and i give you two examples here to just + + + align:start position:0% +and i give you two examples here to just +wet your appetite again i'm not going to + + align:start position:0% +wet your appetite again i'm not going to + + + align:start position:0% +wet your appetite again i'm not going to +go through them but you can see that + + align:start position:0% +go through them but you can see that + + + align:start position:0% +go through them but you can see that +that you can actually + + align:start position:0% +that you can actually + + + align:start position:0% +that you can actually +make + + align:start position:0% +make + + + align:start position:0% +make +switches and amplifiers for gene + + align:start position:0% +switches and amplifiers for gene + + + align:start position:0% +switches and amplifiers for gene +expression gene expression being one of + + align:start position:0% +expression gene expression being one of + + + align:start position:0% +expression gene expression being one of +our favorite topics in this course which + + align:start position:0% +our favorite topics in this course which + + + align:start position:0% +our favorite topics in this course which +are based on noise + + align:start position:0% +are based on noise + + + align:start position:0% +are based on noise +and where you can get by stability as uh + + align:start position:0% +and where you can get by stability as uh + + + align:start position:0% +and where you can get by stability as uh +using these fluctuations + + align:start position:0% +using these fluctuations + + + align:start position:0% +using these fluctuations +but + + align:start position:0% +but + + + align:start position:0% +but +and that's not too unexpected based on + + align:start position:0% +and that's not too unexpected based on + + + align:start position:0% +and that's not too unexpected based on +what we've just been saying but in + + align:start position:0% +what we've just been saying but in + + + align:start position:0% +what we've just been saying but in +addition you can get stochastic + + align:start position:0% +addition you can get stochastic + + + align:start position:0% +addition you can get stochastic +focusing where fluctuation allows uh + + align:start position:0% +focusing where fluctuation allows uh + + + align:start position:0% +focusing where fluctuation allows uh +enhanced sensitivity + + align:start position:0% +enhanced sensitivity + + + align:start position:0% +enhanced sensitivity +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i encourage you to look at that + + align:start position:0% +so i encourage you to look at that + + + align:start position:0% +so i encourage you to look at that +now a particular place where you might + + align:start position:0% +now a particular place where you might + + + align:start position:0% +now a particular place where you might +worry that stochastics is coming into + + align:start position:0% +worry that stochastics is coming into + + + align:start position:0% +worry that stochastics is coming into +play quite a bit is in chromosome copy + + align:start position:0% +play quite a bit is in chromosome copy + + + align:start position:0% +play quite a bit is in chromosome copy +number whether this is eukaryotic + + align:start position:0% +number whether this is eukaryotic + + + align:start position:0% +number whether this is eukaryotic +chromosomes or in the case we'll + + align:start position:0% +chromosomes or in the case we'll + + + align:start position:0% +chromosomes or in the case we'll +illustrate very simple case of plasma + + align:start position:0% +illustrate very simple case of plasma + + + align:start position:0% +illustrate very simple case of plasma +chromosomes + + align:start position:0% +chromosomes + + + align:start position:0% +chromosomes +now the interesting thing about plasmids + + align:start position:0% +now the interesting thing about plasmids + + + align:start position:0% +now the interesting thing about plasmids +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +they can either be in lockstep with cell + + align:start position:0% +they can either be in lockstep with cell + + + align:start position:0% +they can either be in lockstep with cell +division the way that eukaryotic + + align:start position:0% +division the way that eukaryotic + + + align:start position:0% +division the way that eukaryotic +chromosomes are in cases of + + align:start position:0% +chromosomes are in cases of + + + align:start position:0% +chromosomes are in cases of +xenophobicity we just talked about where + + align:start position:0% +xenophobicity we just talked about where + + + align:start position:0% +xenophobicity we just talked about where +it makes it a big decision + + align:start position:0% +it makes it a big decision + + + align:start position:0% +it makes it a big decision +and that's the case the r1 plasmas or it + + align:start position:0% +and that's the case the r1 plasmas or it + + + align:start position:0% +and that's the case the r1 plasmas or it +can be more of a kind of a cloud of copy + + align:start position:0% +can be more of a kind of a cloud of copy + + + align:start position:0% +can be more of a kind of a cloud of copy +number where they're trying to be close + + align:start position:0% +number where they're trying to be close + + + align:start position:0% +number where they're trying to be close +to + + align:start position:0% +to + + + align:start position:0% +to +a + + align:start position:0% +a + + + align:start position:0% +a +target number where you have more copies + + align:start position:0% +target number where you have more copies + + + align:start position:0% +target number where you have more copies +than one per cell and so uh as the cell + + align:start position:0% +than one per cell and so uh as the cell + + + align:start position:0% +than one per cell and so uh as the cell +divides it kind of randomly takes a + + align:start position:0% +divides it kind of randomly takes a + + + align:start position:0% +divides it kind of randomly takes a +partition of that + + align:start position:0% +partition of that + + + align:start position:0% +partition of that +of that number of + + align:start position:0% +of that number of + + + align:start position:0% +of that number of +plasmids and coli 1 is an example of + + align:start position:0% +plasmids and coli 1 is an example of + + + align:start position:0% +plasmids and coli 1 is an example of +that + + align:start position:0% +that + + + align:start position:0% +that +and we want to you know you model it in + + align:start position:0% +and we want to you know you model it in + + + align:start position:0% +and we want to you know you model it in +order to determine + + align:start position:0% +order to determine + + + align:start position:0% +order to determine +the factors that govern it + + align:start position:0% +the factors that govern it + + + align:start position:0% +the factors that govern it +this has implication + + align:start position:0% +this has implication + + + align:start position:0% +this has implication +that the copy number + + align:start position:0% +that the copy number + + + align:start position:0% +that the copy number +will affect the ex the expression levels + + align:start position:0% +will affect the ex the expression levels + + + align:start position:0% +will affect the ex the expression levels +and the expression levels are of + + align:start position:0% +and the expression levels are of + + + align:start position:0% +and the expression levels are of +importance to biotechnology and plasmids + + align:start position:0% +importance to biotechnology and plasmids + + + align:start position:0% +importance to biotechnology and plasmids +are of course also important in + + align:start position:0% +are of course also important in + + + align:start position:0% +are of course also important in +pathogenesis copy number affects + + align:start position:0% +pathogenesis copy number affects + + + align:start position:0% +pathogenesis copy number affects +pathogenesis + + align:start position:0% +pathogenesis + + + align:start position:0% +pathogenesis +uh since plasmids are a major way that + + align:start position:0% +uh since plasmids are a major way that + + + align:start position:0% +uh since plasmids are a major way that +drug resistance elements are passed + + align:start position:0% +drug resistance elements are passed + + + align:start position:0% +drug resistance elements are passed +around so let's take a look at one + + align:start position:0% +around so let's take a look at one + + + align:start position:0% +around so let's take a look at one +highly hopefully highly oversimplified + + align:start position:0% +highly hopefully highly oversimplified + + + align:start position:0% +highly hopefully highly oversimplified +version of this + + align:start position:0% +version of this + + + align:start position:0% +version of this +here you have two rnas + + align:start position:0% +here you have two rnas + + + align:start position:0% +here you have two rnas +imaginably called rna1 and rna2 the star + + align:start position:0% +imaginably called rna1 and rna2 the star + + + align:start position:0% +imaginably called rna1 and rna2 the star +rna2 is transcribed here from + + align:start position:0% +rna2 is transcribed here from + + + align:start position:0% +rna2 is transcribed here from +on the bottom strand from right to left + + align:start position:0% +on the bottom strand from right to left + + + align:start position:0% +on the bottom strand from right to left +and when it is + + align:start position:0% +and when it is + + + align:start position:0% +and when it is +so actually look at the very bottom of + + align:start position:0% +so actually look at the very bottom of + + + align:start position:0% +so actually look at the very bottom of +slide 30 uh the the magenta rna + + align:start position:0% +slide 30 uh the the magenta rna + + + align:start position:0% +slide 30 uh the the magenta rna +polymerase is making rna2 + + align:start position:0% +polymerase is making rna2 + + + align:start position:0% +polymerase is making rna2 +and + + align:start position:0% +and + + + align:start position:0% +and +if + + align:start position:0% +if + + + align:start position:0% +if +nothing binds to rna2 + + align:start position:0% +nothing binds to rna2 + + + align:start position:0% +nothing binds to rna2 +no if rna1 does not bind to it rna-h + + align:start position:0% +no if rna1 does not bind to it rna-h + + + align:start position:0% +no if rna1 does not bind to it rna-h +will cleave it it will then bind the + + align:start position:0% +will cleave it it will then bind the + + + align:start position:0% +will cleave it it will then bind the +blue dna polymerase and we'll start + + align:start position:0% +blue dna polymerase and we'll start + + + align:start position:0% +blue dna polymerase and we'll start +replicating the plasmid + + align:start position:0% +replicating the plasmid + + + align:start position:0% +replicating the plasmid +on the other hand if rna1 which is on it + + align:start position:0% +on the other hand if rna1 which is on it + + + align:start position:0% +on the other hand if rna1 which is on it +made on the opposite strand of rna2 this + + align:start position:0% +made on the opposite strand of rna2 this + + + align:start position:0% +made on the opposite strand of rna2 this +is an antisense story it will then come + + align:start position:0% +is an antisense story it will then come + + + align:start position:0% +is an antisense story it will then come +and bind to rna2 sort of in trans it + + align:start position:0% +and bind to rna2 sort of in trans it + + + align:start position:0% +and bind to rna2 sort of in trans it +acts as a transacting inhibitor it's + + align:start position:0% +acts as a transacting inhibitor it's + + + align:start position:0% +acts as a transacting inhibitor it's +aided embedded by the rom protein and + + align:start position:0% +aided embedded by the rom protein and + + + align:start position:0% +aided embedded by the rom protein and +now you don't get cleavage of rnsh and + + align:start position:0% +now you don't get cleavage of rnsh and + + + align:start position:0% +now you don't get cleavage of rnsh and +so dna polymerase doesn't have a primer + + align:start position:0% +so dna polymerase doesn't have a primer + + + align:start position:0% +so dna polymerase doesn't have a primer +upon which to act and you don't get + + align:start position:0% +upon which to act and you don't get + + + align:start position:0% +upon which to act and you don't get +replication and this is of course not + + align:start position:0% +replication and this is of course not + + + align:start position:0% +replication and this is of course not +just a yes or no thing this is something + + align:start position:0% +just a yes or no thing this is something + + + align:start position:0% +just a yes or no thing this is something +that's regulated and allows it to to + + align:start position:0% +that's regulated and allows it to to + + + align:start position:0% +that's regulated and allows it to to +feedback to get the right copy number + + align:start position:0% +feedback to get the right copy number + + + align:start position:0% +feedback to get the right copy number +you don't want it to get an infinite + + align:start position:0% +you don't want it to get an infinite + + + align:start position:0% +you don't want it to get an infinite +copy number it also choke the cell + + align:start position:0% +copy number it also choke the cell + + + align:start position:0% +copy number it also choke the cell +that's harboring it + + align:start position:0% +that's harboring it + + + align:start position:0% +that's harboring it +but you'll want it to drop down low + + align:start position:0% +but you'll want it to drop down low + + + align:start position:0% +but you'll want it to drop down low +enough so then many cells will segregate + + align:start position:0% +enough so then many cells will segregate + + + align:start position:0% +enough so then many cells will segregate +with no + + align:start position:0% +with no + + + align:start position:0% +with no +uh + + align:start position:0% +uh + + + align:start position:0% +uh +copies of the plasmid + + align:start position:0% +copies of the plasmid + + + align:start position:0% +copies of the plasmid +so you want to have a mass balance you + + align:start position:0% +so you want to have a mass balance you + + + align:start position:0% +so you want to have a mass balance you +have to have conservation of mass + + align:start position:0% + + + + align:start position:0% + +you want to be able to model + + align:start position:0% +you want to be able to model + + + align:start position:0% +you want to be able to model +both the uh + + align:start position:0% +both the uh + + + align:start position:0% +both the uh +initiation and degradation and + + align:start position:0% +initiation and degradation and + + + align:start position:0% +initiation and degradation and +inhibition so you do this by making some + + align:start position:0% +inhibition so you do this by making some + + + align:start position:0% +inhibition so you do this by making some +simplifications that the rna h rate is + + align:start position:0% +simplifications that the rna h rate is + + + align:start position:0% +simplifications that the rna h rate is +fast remember we had slow and fast + + align:start position:0% +fast remember we had slow and fast + + + align:start position:0% +fast remember we had slow and fast +reactions that we would eliminate + + align:start position:0% +reactions that we would eliminate + + + align:start position:0% +reactions that we would eliminate +um uh so so too with the dna + + align:start position:0% +um uh so so too with the dna + + + align:start position:0% +um uh so so too with the dna +polymerization + + align:start position:0% +polymerization + + + align:start position:0% +polymerization +uh + + align:start position:0% +uh + + + align:start position:0% +uh +by subsuming the rna2 concentration in + + align:start position:0% +by subsuming the rna2 concentration in + + + align:start position:0% +by subsuming the rna2 concentration in +an rna1 based model you can simplify it + + align:start position:0% +an rna1 based model you can simplify it + + + align:start position:0% +an rna1 based model you can simplify it +so that you're really only considering + + align:start position:0% +so that you're really only considering + + + align:start position:0% +so that you're really only considering +two species rna1 and the plasma dna + + align:start position:0% +two species rna1 and the plasma dna + + + align:start position:0% +two species rna1 and the plasma dna +itself we'll call these r and n + + align:start position:0% +itself we'll call these r and n + + + align:start position:0% +itself we'll call these r and n +for + + align:start position:0% +for + + + align:start position:0% +for +for the two different + + align:start position:0% +for the two different + + + align:start position:0% +for the two different +molecules so this is + + align:start position:0% +molecules so this is + + + align:start position:0% +molecules so this is +just a way of introducing a two species + + align:start position:0% +just a way of introducing a two species + + + align:start position:0% +just a way of introducing a two species +model we're going to come up with a rate + + align:start position:0% +model we're going to come up with a rate + + + align:start position:0% +model we're going to come up with a rate +equation for change in rna with respect + + align:start position:0% +equation for change in rna with respect + + + align:start position:0% +equation for change in rna with respect +of rna 1 with respect to time and then + + align:start position:0% +of rna 1 with respect to time and then + + + align:start position:0% +of rna 1 with respect to time and then +the next slide will show the change in + + align:start position:0% +the next slide will show the change in + + + align:start position:0% +the next slide will show the change in +the concentration of the plasmid + + align:start position:0% +the concentration of the plasmid + + + align:start position:0% +the concentration of the plasmid +concentration the rna is + + align:start position:0% +concentration the rna is + + + align:start position:0% +concentration the rna is +is r concentrates the plasmid is n we + + align:start position:0% +is r concentrates the plasmid is n we + + + align:start position:0% +is r concentrates the plasmid is n we +have dr dt and d and dt + + align:start position:0% +have dr dt and d and dt + + + align:start position:0% +have dr dt and d and dt +and this is very simple it's just like + + align:start position:0% +and this is very simple it's just like + + + align:start position:0% +and this is very simple it's just like +the what we're talking about with the + + align:start position:0% +the what we're talking about with the + + + align:start position:0% +the what we're talking about with the +metabolites + + align:start position:0% +metabolites + + + align:start position:0% +metabolites +you synthesize the rna + + align:start position:0% +you synthesize the rna + + + align:start position:0% +you synthesize the rna +that's a positive term you degrade it or + + align:start position:0% +that's a positive term you degrade it or + + + align:start position:0% +that's a positive term you degrade it or +you dilute it out the dilution is based + + align:start position:0% +you dilute it out the dilution is based + + + align:start position:0% +you dilute it out the dilution is based +on the growth rate mu is a typical it's + + align:start position:0% +on the growth rate mu is a typical it's + + + align:start position:0% +on the growth rate mu is a typical it's +a used in growth rates and population + + align:start position:0% +a used in growth rates and population + + + align:start position:0% +a used in growth rates and population +genetics and here it's using chemical + + align:start position:0% +genetics and here it's using chemical + + + align:start position:0% +genetics and here it's using chemical +kinetics in fact this is in a certain + + align:start position:0% +kinetics in fact this is in a certain + + + align:start position:0% +kinetics in fact this is in a certain +sense one an example a very exciting + + align:start position:0% +sense one an example a very exciting + + + align:start position:0% +sense one an example a very exciting +field we bring together population + + align:start position:0% +field we bring together population + + + align:start position:0% +field we bring together population +genetics and uh + + align:start position:0% + + + + align:start position:0% + +chemical kinetics into one place + + align:start position:0% + + + + align:start position:0% + +and population genetics and chemical + + align:start position:0% +and population genetics and chemical + + + align:start position:0% +and population genetics and chemical +kinetics when they come together + + align:start position:0% +kinetics when they come together + + + align:start position:0% +kinetics when they come together +unites some of the most disparate parts + + align:start position:0% +unites some of the most disparate parts + + + align:start position:0% +unites some of the most disparate parts +of this course + + align:start position:0% +of this course + + + align:start position:0% +of this course +okay so now we've got an equation here + + align:start position:0% +okay so now we've got an equation here + + + align:start position:0% +okay so now we've got an equation here +where the positive term is k1 the rate + + align:start position:0% +where the positive term is k1 the rate + + + align:start position:0% +where the positive term is k1 the rate +of of initiation of rna synthesis + + align:start position:0% +of of initiation of rna synthesis + + + align:start position:0% +of of initiation of rna synthesis +and it's of course the more molecules + + align:start position:0% +and it's of course the more molecules + + + align:start position:0% +and it's of course the more molecules +in the higher the concentration of the + + align:start position:0% +in the higher the concentration of the + + + align:start position:0% +in the higher the concentration of the +plasmid then the more rna you're going + + align:start position:0% +plasmid then the more rna you're going + + + align:start position:0% +plasmid then the more rna you're going +to make so that makes sense that you + + align:start position:0% +to make so that makes sense that you + + + align:start position:0% +to make so that makes sense that you +have the product the rate constant times + + align:start position:0% +have the product the rate constant times + + + align:start position:0% +have the product the rate constant times +the number of plasmids + + align:start position:0% +the number of plasmids + + + align:start position:0% +the number of plasmids +similarly the the loss of it is going to + + align:start position:0% +similarly the the loss of it is going to + + + align:start position:0% +similarly the the loss of it is going to +be related to the number of rna more + + align:start position:0% +be related to the number of rna more + + + align:start position:0% +be related to the number of rna more +rnas you have the more that you're going + + align:start position:0% +rnas you have the more that you're going + + + align:start position:0% +rnas you have the more that you're going +to lose more that you have to lose + + align:start position:0% +to lose more that you have to lose + + + align:start position:0% +to lose more that you have to lose +and this is now that's the rna this is + + align:start position:0% +and this is now that's the rna this is + + + align:start position:0% +and this is now that's the rna this is +for the dna + + align:start position:0% +for the dna + + + align:start position:0% +for the dna +here + + align:start position:0% +here + + + align:start position:0% +here +you have dependence + + align:start position:0% +you have dependence + + + align:start position:0% +you have dependence +on the rna + + align:start position:0% +on the rna + + + align:start position:0% +on the rna +rna1 remember is the thing that we + + align:start position:0% +rna1 remember is the thing that we + + + align:start position:0% +rna1 remember is the thing that we +modeled in the previous slide is uh an + + align:start position:0% +modeled in the previous slide is uh an + + + align:start position:0% +modeled in the previous slide is uh an +inhibitor and so it's going to when it + + align:start position:0% +inhibitor and so it's going to when it + + + align:start position:0% +inhibitor and so it's going to when it +binds + + align:start position:0% +binds + + + align:start position:0% +binds +to rna2 which is not ex which is + + align:start position:0% +to rna2 which is not ex which is + + + align:start position:0% +to rna2 which is not ex which is +implicitly modeled here it's going to + + align:start position:0% +implicitly modeled here it's going to + + + align:start position:0% +implicitly modeled here it's going to +have this inhibitory uh constant in the + + align:start position:0% +have this inhibitory uh constant in the + + + align:start position:0% +have this inhibitory uh constant in the +denominator um and so as the + + align:start position:0% +denominator um and so as the + + + align:start position:0% +denominator um and so as the +inhibitor rna goes up this this + + align:start position:0% +inhibitor rna goes up this this + + + align:start position:0% +inhibitor rna goes up this this +inhibitory term goes up and the rate the + + align:start position:0% +inhibitory term goes up and the rate the + + + align:start position:0% +inhibitory term goes up and the rate the +forward rate goes down um and it's of + + align:start position:0% +forward rate goes down um and it's of + + + align:start position:0% +forward rate goes down um and it's of +course depend the before the rate of + + align:start position:0% +course depend the before the rate of + + + align:start position:0% +course depend the before the rate of +replication is going to be also + + align:start position:0% +replication is going to be also + + + align:start position:0% +replication is going to be also +dependent on plasma copy number so it + + align:start position:0% +dependent on plasma copy number so it + + + align:start position:0% +dependent on plasma copy number so it +goes up within it's dilute the dilution + + align:start position:0% +goes up within it's dilute the dilution + + + align:start position:0% +goes up within it's dilute the dilution +rate is of course dependent on n as well + + align:start position:0% +rate is of course dependent on n as well + + + align:start position:0% +rate is of course dependent on n as well +so the idea of this in the next slide is + + align:start position:0% +so the idea of this in the next slide is + + + align:start position:0% +so the idea of this in the next slide is +going to be to solve the plasma number + + align:start position:0% +going to be to solve the plasma number + + + align:start position:0% +going to be to solve the plasma number +so in slide 34 + + align:start position:0% +so in slide 34 + + + align:start position:0% +so in slide 34 +we have how you would implement + + align:start position:0% +we have how you would implement + + + align:start position:0% +we have how you would implement +those two equations that we had in the + + align:start position:0% +those two equations that we had in the + + + align:start position:0% +those two equations that we had in the +last two slides + + align:start position:0% +last two slides + + + align:start position:0% +last two slides +uh are shown on the very top + + align:start position:0% +uh are shown on the very top + + + align:start position:0% +uh are shown on the very top +left part of the slide + + align:start position:0% +left part of the slide + + + align:start position:0% +left part of the slide +dr + + align:start position:0% +dr + + + align:start position:0% +dr +drdt is abbreviated dr here um in + + align:start position:0% +drdt is abbreviated dr here um in + + + align:start position:0% +drdt is abbreviated dr here um in +mathematica format it's that same k1 + + align:start position:0% +mathematica format it's that same k1 + + + align:start position:0% +mathematica format it's that same k1 +constant times n is the the + + align:start position:0% +constant times n is the the + + + align:start position:0% +constant times n is the the +concentration of plasma molecules then + + align:start position:0% +concentration of plasma molecules then + + + align:start position:0% +concentration of plasma molecules then +the negative is the is the degradation + + align:start position:0% +the negative is the is the degradation + + + align:start position:0% +the negative is the is the degradation +rate + + align:start position:0% +rate + + + align:start position:0% +rate +and the dilution by cell division mu + + align:start position:0% +and the dilution by cell division mu + + + align:start position:0% +and the dilution by cell division mu +and that's times r which is the + + align:start position:0% +and that's times r which is the + + + align:start position:0% +and that's times r which is the +concentration of the inhibitory rna rna1 + + align:start position:0% +concentration of the inhibitory rna rna1 + + + align:start position:0% +concentration of the inhibitory rna rna1 +and then the an analysis equation which + + align:start position:0% +and then the an analysis equation which + + + align:start position:0% +and then the an analysis equation which +we've already seen before for the plasma + + align:start position:0% +we've already seen before for the plasma + + + align:start position:0% +we've already seen before for the plasma +molecules in + + align:start position:0% +molecules in + + + align:start position:0% +molecules in +the change in concentration of n as a + + align:start position:0% +the change in concentration of n as a + + + align:start position:0% +the change in concentration of n as a +function of time dn + + align:start position:0% +function of time dn + + + align:start position:0% +function of time dn +dt here abbreviated the end + + align:start position:0% +dt here abbreviated the end + + + align:start position:0% +dt here abbreviated the end +is there + + align:start position:0% +is there + + + align:start position:0% +is there +and and then uh + + align:start position:0% +and and then uh + + + align:start position:0% +and and then uh +we're going to solve it so these first + + align:start position:0% +we're going to solve it so these first + + + align:start position:0% +we're going to solve it so these first +three things are setting it up and + + align:start position:0% +three things are setting it up and + + + align:start position:0% +three things are setting it up and +asking the program to solve it + + align:start position:0% +asking the program to solve it + + + align:start position:0% +asking the program to solve it +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and we're do it under the constraints if + + align:start position:0% +and we're do it under the constraints if + + + align:start position:0% +and we're do it under the constraints if +the rdt is equal to zero the dndt is + + align:start position:0% +the rdt is equal to zero the dndt is + + + align:start position:0% +the rdt is equal to zero the dndt is +equal to zero you will recognize this is + + align:start position:0% +equal to zero you will recognize this is + + + align:start position:0% +equal to zero you will recognize this is +the steady state assumption even though + + align:start position:0% +the steady state assumption even though + + + align:start position:0% +the steady state assumption even though +their flux is in and out of that that + + align:start position:0% +their flux is in and out of that that + + + align:start position:0% +their flux is in and out of that that +are non-zero the net effect is is zero + + align:start position:0% +are non-zero the net effect is is zero + + + align:start position:0% +are non-zero the net effect is is zero +and so that's the formula for steady + + align:start position:0% +and so that's the formula for steady + + + align:start position:0% +and so that's the formula for steady +state we're going to start at a dilution + + align:start position:0% +state we're going to start at a dilution + + + align:start position:0% +state we're going to start at a dilution +rate of one + + align:start position:0% +rate of one + + + align:start position:0% +rate of one +where you'll have some steady state + + align:start position:0% +where you'll have some steady state + + + align:start position:0% +where you'll have some steady state +level and then we're going to watch the + + align:start position:0% +level and then we're going to watch the + + + align:start position:0% +level and then we're going to watch the +dynamics as it goes to a dilution rate + + align:start position:0% +dynamics as it goes to a dilution rate + + + align:start position:0% +dynamics as it goes to a dilution rate +that's slower if that is to say the + + align:start position:0% +that's slower if that is to say the + + + align:start position:0% +that's slower if that is to say the +growth rate is slower and as you go + + align:start position:0% +growth rate is slower and as you go + + + align:start position:0% +growth rate is slower and as you go +through the slower + + align:start position:0% +through the slower + + + align:start position:0% +through the slower +you expect maybe to accumulate more + + align:start position:0% +you expect maybe to accumulate more + + + align:start position:0% +you expect maybe to accumulate more +plasma molecules because they're not in + + align:start position:0% +plasma molecules because they're not in + + + align:start position:0% +plasma molecules because they're not in +lock step with the the cell division + + align:start position:0% +lock step with the the cell division + + + align:start position:0% +lock step with the the cell division +rate itself + + align:start position:0% +rate itself + + + align:start position:0% +rate itself +grows more slowly there's not some other + + align:start position:0% +grows more slowly there's not some other + + + align:start position:0% +grows more slowly there's not some other +feedback and we haven't put any other + + align:start position:0% +feedback and we haven't put any other + + + align:start position:0% +feedback and we haven't put any other +feedback in this model then it should uh + + align:start position:0% +feedback in this model then it should uh + + + align:start position:0% +feedback in this model then it should uh +go to about twice the level and so + + align:start position:0% +go to about twice the level and so + + + align:start position:0% +go to about twice the level and so +basically + + align:start position:0% +basically + + + align:start position:0% +basically +as you if you now do so you do the + + align:start position:0% +as you if you now do so you do the + + + align:start position:0% +as you if you now do so you do the +the + + align:start position:0% + + + + align:start position:0% + +uh symbolic solver in the top here and + + align:start position:0% +uh symbolic solver in the top here and + + + align:start position:0% +uh symbolic solver in the top here and +you get this symbolic solution here + + align:start position:0% +you get this symbolic solution here + + + align:start position:0% +you get this symbolic solution here +and if you do the numeric solver and d + + align:start position:0% +and if you do the numeric solver and d + + + align:start position:0% +and if you do the numeric solver and d +solve + + align:start position:0% +solve + + + align:start position:0% +solve +then you can + + align:start position:0% +then you can + + + align:start position:0% +then you can +you get a very similar + + align:start position:0% +you get a very similar + + + align:start position:0% +you get a very similar +solution and you could plot it here + + align:start position:0% +solution and you could plot it here + + + align:start position:0% +solution and you could plot it here +you're plotting y which is a plasma copy + + align:start position:0% +you're plotting y which is a plasma copy + + + align:start position:0% +you're plotting y which is a plasma copy +number + + align:start position:0% +number + + + align:start position:0% +number +from + + align:start position:0% +from + + + align:start position:0% +from +over a time range of zero to three and + + align:start position:0% +over a time range of zero to three and + + + align:start position:0% +over a time range of zero to three and +you can see it goes up from slightly + + align:start position:0% +you can see it goes up from slightly + + + align:start position:0% +you can see it goes up from slightly +over one to slightly over two in terms + + align:start position:0% +over one to slightly over two in terms + + + align:start position:0% +over one to slightly over two in terms +of a concentration of the plasmid + + align:start position:0% +of a concentration of the plasmid + + + align:start position:0% +of a concentration of the plasmid +as you might expect from lowering the + + align:start position:0% + + + + align:start position:0% + +dilution curve just as we had stochastic + + align:start position:0% +dilution curve just as we had stochastic + + + align:start position:0% +dilution curve just as we had stochastic +models for the bistability that we + + align:start position:0% +models for the bistability that we + + + align:start position:0% +models for the bistability that we +talked about earlier you know the + + align:start position:0% +talked about earlier you know the + + + align:start position:0% +talked about earlier you know the +xenopus by stability could be continuous + + align:start position:0% +xenopus by stability could be continuous + + + align:start position:0% +xenopus by stability could be continuous +and the landis + + align:start position:0% +and the landis + + + align:start position:0% +and the landis +could be lambda model could be + + align:start position:0% +could be lambda model could be + + + align:start position:0% +could be lambda model could be +stochastic here there are stochastic + + align:start position:0% +stochastic here there are stochastic + + + align:start position:0% +stochastic here there are stochastic +models for copy number control c and c + + align:start position:0% +models for copy number control c and c + + + align:start position:0% +models for copy number control c and c +which are very interesting i urge you to + + align:start position:0% +which are very interesting i urge you to + + + align:start position:0% +which are very interesting i urge you to +look at them + + align:start position:0% +look at them + + + align:start position:0% +look at them +where you can have basically + + align:start position:0% +where you can have basically + + + align:start position:0% +where you can have basically +using stochastic modeling to do + + align:start position:0% +using stochastic modeling to do + + + align:start position:0% +using stochastic modeling to do +molecular clocks or you can reduce the + + align:start position:0% +molecular clocks or you can reduce the + + + align:start position:0% +molecular clocks or you can reduce the +rate at plasma loss you can see in that + + align:start position:0% +rate at plasma loss you can see in that + + + align:start position:0% +rate at plasma loss you can see in that +last one if you had a very small number + + align:start position:0% +last one if you had a very small number + + + align:start position:0% +last one if you had a very small number +of molecules you would have a a loss + + align:start position:0% +of molecules you would have a a loss + + + align:start position:0% +of molecules you would have a a loss +in some of the + + align:start position:0% +in some of the + + + align:start position:0% +in some of the +cells that would be more accurately + + align:start position:0% +cells that would be more accurately + + + align:start position:0% +cells that would be more accurately +modeled in a stochastic + + align:start position:0% +modeled in a stochastic + + + align:start position:0% +modeled in a stochastic +model now we want to go + + align:start position:0% +model now we want to go + + + align:start position:0% +model now we want to go +from + + align:start position:0% +from + + + align:start position:0% +from +these + + align:start position:0% +these + + + align:start position:0% +these +models of red blood cell where you have + + align:start position:0% +models of red blood cell where you have + + + align:start position:0% +models of red blood cell where you have +metabolism without polymer synthesis + + align:start position:0% +metabolism without polymer synthesis + + + align:start position:0% +metabolism without polymer synthesis +and a cnc model where you have polymer + + align:start position:0% +and a cnc model where you have polymer + + + align:start position:0% +and a cnc model where you have polymer +synthesis of rna and dna + + align:start position:0% +synthesis of rna and dna + + + align:start position:0% +synthesis of rna and dna +but without metabolism + + align:start position:0% +but without metabolism + + + align:start position:0% +but without metabolism +to a more integrated cell where you have + + align:start position:0% +to a more integrated cell where you have + + + align:start position:0% +to a more integrated cell where you have +both going on + + align:start position:0% +both going on + + + align:start position:0% +both going on +and you want to represent the full + + align:start position:0% +and you want to represent the full + + + align:start position:0% +and you want to represent the full +optimization that must occur getting + + align:start position:0% +optimization that must occur getting + + + align:start position:0% +optimization that must occur getting +metabolism optimally + + align:start position:0% +metabolism optimally + + + align:start position:0% +metabolism optimally +suited so that you get the right kinds + + align:start position:0% +suited so that you get the right kinds + + + align:start position:0% +suited so that you get the right kinds +of macromolecules made + + align:start position:0% +of macromolecules made + + + align:start position:0% +of macromolecules made +in a complicated cell like you call it + + align:start position:0% +in a complicated cell like you call it + + + align:start position:0% +in a complicated cell like you call it +which can adjust to a wide variety of + + align:start position:0% +which can adjust to a wide variety of + + + align:start position:0% +which can adjust to a wide variety of +different growth conditions so what are + + align:start position:0% +different growth conditions so what are + + + align:start position:0% +different growth conditions so what are +the problems here the number of + + align:start position:0% +the problems here the number of + + + align:start position:0% +the problems here the number of +parameters that we that we needed and + + align:start position:0% +parameters that we that we needed and + + + align:start position:0% +parameters that we that we needed and +had for the red blood cell was enormous + + align:start position:0% +had for the red blood cell was enormous + + + align:start position:0% +had for the red blood cell was enormous +it was 200 it was a tour de force to get + + align:start position:0% +it was 200 it was a tour de force to get + + + align:start position:0% +it was 200 it was a tour de force to get +those for e coli + + align:start position:0% +those for e coli + + + align:start position:0% +those for e coli +it's orders of magnitude more that are + + align:start position:0% +it's orders of magnitude more that are + + + align:start position:0% +it's orders of magnitude more that are +needed because instead of 40 + + align:start position:0% +needed because instead of 40 + + + align:start position:0% +needed because instead of 40 +enzymes we have + + align:start position:0% +enzymes we have + + + align:start position:0% +enzymes we have +you know + + align:start position:0% +you know + + + align:start position:0% +you know +somewhere between four hundred and four + + align:start position:0% +somewhere between four hundred and four + + + align:start position:0% +somewhere between four hundred and four +thousand + + align:start position:0% +thousand + + + align:start position:0% +thousand +so measuring parameters is a problem and + + align:start position:0% +so measuring parameters is a problem and + + + align:start position:0% +so measuring parameters is a problem and +we have the same problem about in vitro + + align:start position:0% +we have the same problem about in vitro + + + align:start position:0% +we have the same problem about in vitro +versus in vivo we have the same set of + + align:start position:0% +versus in vivo we have the same set of + + + align:start position:0% +versus in vivo we have the same set of +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +and we want to focus our more of our + + align:start position:0% +and we want to focus our more of our + + + align:start position:0% +and we want to focus our more of our +attention now on the on the flux + + align:start position:0% +attention now on the on the flux + + + align:start position:0% +attention now on the on the flux +constraints + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +after a short break we're going to come + + align:start position:0% +after a short break we're going to come + + + align:start position:0% +after a short break we're going to come +back and talk about the flux balance as + + align:start position:0% +back and talk about the flux balance as + + + align:start position:0% +back and talk about the flux balance as +a solution to this + + align:start position:0% +a solution to this + + + align:start position:0% +a solution to this +and just as we had uh + + align:start position:0% +and just as we had uh + + + align:start position:0% +and just as we had uh +with + + align:start position:0% +with + + + align:start position:0% +with +the red blood cell we're going to be + + align:start position:0% +the red blood cell we're going to be + + + align:start position:0% +the red blood cell we're going to be +focusing in on ways to to to re-look at + + align:start position:0% +focusing in on ways to to to re-look at + + + align:start position:0% +focusing in on ways to to to re-look at +the way we think about the synthesis and + + align:start position:0% +the way we think about the synthesis and + + + align:start position:0% +the way we think about the synthesis and +degradation of the of the molecules in + + align:start position:0% +degradation of the of the molecules in + + + align:start position:0% +degradation of the of the molecules in +the in this network to see if we can + + align:start position:0% +the in this network to see if we can + + + align:start position:0% +the in this network to see if we can +rephrase in a way where we can ask quite + + align:start position:0% +rephrase in a way where we can ask quite + + + align:start position:0% +rephrase in a way where we can ask quite +interesting questions about the + + align:start position:0% +interesting questions about the + + + align:start position:0% +interesting questions about the +optimization of these simple systems + + align:start position:0% +optimization of these simple systems + + + align:start position:0% +optimization of these simple systems +so um take a quick break and we'll we'll + + align:start position:0% +so um take a quick break and we'll we'll + + + align:start position:0% +so um take a quick break and we'll we'll +the second half we'll talk about flux + + align:start position:0% +the second half we'll talk about flux + + + align:start position:0% +the second half we'll talk about flux +balance \ No newline at end of file diff --git a/bA5_-EvxnL4.txt b/bA5_-EvxnL4.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1e3af820a3d6a04e2e444827574ad0fa4449fda --- /dev/null +++ b/bA5_-EvxnL4.txt @@ -0,0 +1,8163 @@ +align:start position:0% + +we're still on this first topic + + align:start position:0% +we're still on this first topic + + + align:start position:0% +we're still on this first topic +primitive cellular mechanisms + + align:start position:0% +primitive cellular mechanisms + + + align:start position:0% + +and we'll be on that + + align:start position:0% +and we'll be on that + + + align:start position:0% +and we'll be on that +for the entire session today + + align:start position:0% +for the entire session today + + + align:start position:0% +for the entire session today +talking mainly about secretion in + + align:start position:0% +talking mainly about secretion in + + + align:start position:0% +talking mainly about secretion in +neurons + + align:start position:0% +neurons + + + align:start position:0% +neurons +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we started that before when we talked + + align:start position:0% +we started that before when we talked + + + align:start position:0% +we started that before when we talked +about + + align:start position:0% +about + + + align:start position:0% +about +excitatory and inhibitory postsynaptic + + align:start position:0% +excitatory and inhibitory postsynaptic + + + align:start position:0% +excitatory and inhibitory postsynaptic +potentials + + align:start position:0% +potentials + + + align:start position:0% +potentials +and summation effects + + align:start position:0% + + + + align:start position:0% + +is action at a synapse always one way + + align:start position:0% + + + + align:start position:0% + +well if it's a chemical synapse + + align:start position:0% +well if it's a chemical synapse + + + align:start position:0% +well if it's a chemical synapse +it's most the information flow is always + + align:start position:0% +it's most the information flow is always + + + align:start position:0% +it's most the information flow is always +in one direction it doesn't mean there's + + align:start position:0% +in one direction it doesn't mean there's + + + align:start position:0% +in one direction it doesn't mean there's +there's nothing that goes the other + + align:start position:0% +there's nothing that goes the other + + + align:start position:0% +there's nothing that goes the other +direction + + align:start position:0% +direction + + + align:start position:0% +direction +there is some communication but the + + align:start position:0% +there is some communication but the + + + align:start position:0% +there is some communication but the +electrical changes generally go in one + + align:start position:0% +electrical changes generally go in one + + + align:start position:0% +electrical changes generally go in one +direction + + align:start position:0% +direction + + + align:start position:0% +direction +there are such things as electrical + + align:start position:0% +there are such things as electrical + + + align:start position:0% +there are such things as electrical +synapses they're not very common + + align:start position:0% +synapses they're not very common + + + align:start position:0% +synapses they're not very common +in the mammalian nervous system + + align:start position:0% +in the mammalian nervous system + + + align:start position:0% +in the mammalian nervous system +where the action can go on both ways + + align:start position:0% +where the action can go on both ways + + + align:start position:0% + +okay we talked about aldoloe + + align:start position:0% +okay we talked about aldoloe + + + align:start position:0% +okay we talked about aldoloe +and what + + align:start position:0% +and what + + + align:start position:0% +and what +remember remember + + align:start position:0% +remember remember + + + align:start position:0% +remember remember +he discovered some pretty good evidence + + align:start position:0% +he discovered some pretty good evidence + + + align:start position:0% +he discovered some pretty good evidence +for chemical transmission at synapses he + + align:start position:0% +for chemical transmission at synapses he + + + align:start position:0% +for chemical transmission at synapses he +was in the + + align:start position:0% +was in the + + + align:start position:0% +was in the +peripheral nervous system the autonomic + + align:start position:0% +peripheral nervous system the autonomic + + + align:start position:0% +peripheral nervous system the autonomic +nervous system working with the + + align:start position:0% +nervous system working with the + + + align:start position:0% +nervous system working with the +innervation of the frog heart + + align:start position:0% + + + + align:start position:0% + +and what was that acceleron stuff the + + align:start position:0% +and what was that acceleron stuff the + + + align:start position:0% +and what was that acceleron stuff the +accelerator substance + + align:start position:0% +accelerator substance + + + align:start position:0% +accelerator substance +norepinephrine and what was the + + align:start position:0% +norepinephrine and what was the + + + align:start position:0% +norepinephrine and what was the +vagus substance + + align:start position:0% +vagus substance + + + align:start position:0% +vagus substance +acetylcholine okay + + align:start position:0% +acetylcholine okay + + + align:start position:0% +acetylcholine okay +those were the first two transmitters + + align:start position:0% +those were the first two transmitters + + + align:start position:0% +those were the first two transmitters +discovered + + align:start position:0% + + + + align:start position:0% + +okay so now let's talk about synapses + + align:start position:0% +okay so now let's talk about synapses + + + align:start position:0% +okay so now let's talk about synapses +and we're really dealing not just with + + align:start position:0% +and we're really dealing not just with + + + align:start position:0% +and we're really dealing not just with +secretion but with membrane + + align:start position:0% +secretion but with membrane + + + align:start position:0% +secretion but with membrane +specializations for irritability as well + + align:start position:0% + + + + align:start position:0% + +so these will be the topics now under + + align:start position:0% +so these will be the topics now under + + + align:start position:0% +so these will be the topics now under +secretion and + + align:start position:0% +secretion and + + + align:start position:0% +secretion and +i've taken some pictures from the book + + align:start position:0% + + + + align:start position:0% + +at the left there they show + + align:start position:0% +at the left there they show + + + align:start position:0% +at the left there they show +one neuron connected to another sort of + + align:start position:0% +one neuron connected to another sort of + + + align:start position:0% +one neuron connected to another sort of +a cartoon and then they enlarge it to + + align:start position:0% +a cartoon and then they enlarge it to + + + align:start position:0% +a cartoon and then they enlarge it to +show the little + + align:start position:0% +show the little + + + align:start position:0% +show the little +uh + + align:start position:0% + + + + align:start position:0% + +terminals that are usually enlarged + + align:start position:0% +terminals that are usually enlarged + + + align:start position:0% +terminals that are usually enlarged +where they make a contact and at the far + + align:start position:0% +where they make a contact and at the far + + + align:start position:0% +where they make a contact and at the far +right you have a picture + + align:start position:0% +right you have a picture + + + align:start position:0% +right you have a picture +somewhat like you can + + align:start position:0% +somewhat like you can + + + align:start position:0% +somewhat like you can +the cartoon based on the electron + + align:start position:0% +the cartoon based on the electron + + + align:start position:0% +the cartoon based on the electron +micrograph studies + + align:start position:0% +micrograph studies + + + align:start position:0% +micrograph studies +of what a synapse looks like and it + + align:start position:0% +of what a synapse looks like and it + + + align:start position:0% +of what a synapse looks like and it +shows the little vesicles containing + + align:start position:0% +shows the little vesicles containing + + + align:start position:0% +shows the little vesicles containing +neurotransmitter in the terminal + + align:start position:0% + + + + align:start position:0% + +and it shows some of them + + align:start position:0% +and it shows some of them + + + align:start position:0% +and it shows some of them +releasing neurotransmitter into the + + align:start position:0% +releasing neurotransmitter into the + + + align:start position:0% +releasing neurotransmitter into the +synaptic cleft + + align:start position:0% + + + + align:start position:0% + +how big is the synaptic cleft if you're + + align:start position:0% +how big is the synaptic cleft if you're + + + align:start position:0% +how big is the synaptic cleft if you're +looking with electron microscope and you + + align:start position:0% +looking with electron microscope and you + + + align:start position:0% +looking with electron microscope and you +can measure it + + align:start position:0% + + + + align:start position:0% + +anybody know + + align:start position:0% + + + + align:start position:0% + +it was initially given in angstrom units + + align:start position:0% +it was initially given in angstrom units + + + align:start position:0% +it was initially given in angstrom units +200 angstroms about 20 nanometers + + align:start position:0% +200 angstroms about 20 nanometers + + + align:start position:0% +200 angstroms about 20 nanometers +if i'm + + align:start position:0% +if i'm + + + align:start position:0% +if i'm +converting that right + + align:start position:0% + + + + align:start position:0% + +okay so here's the book cartoon of a + + align:start position:0% +okay so here's the book cartoon of a + + + align:start position:0% +okay so here's the book cartoon of a +chemical synapse showing + + align:start position:0% +chemical synapse showing + + + align:start position:0% +chemical synapse showing +the actions when at the arrival of an + + align:start position:0% +the actions when at the arrival of an + + + align:start position:0% +the actions when at the arrival of an +action potential + + align:start position:0% + + + + align:start position:0% + +it shows other things arriving there too + + align:start position:0% +it shows other things arriving there too + + + align:start position:0% +it shows other things arriving there too +you see that + + align:start position:0% +you see that + + + align:start position:0% +you see that +it shows us an app vesicle + + align:start position:0% + + + + align:start position:0% + +well it's just to point out that + + align:start position:0% +well it's just to point out that + + + align:start position:0% +well it's just to point out that +the + + align:start position:0% +the + + + align:start position:0% +the +terminals are constantly being + + align:start position:0% +terminals are constantly being + + + align:start position:0% +terminals are constantly being +replenished with materials from the cell + + align:start position:0% +replenished with materials from the cell + + + align:start position:0% +replenished with materials from the cell +body these are being these things are + + align:start position:0% +body these are being these things are + + + align:start position:0% +body these are being these things are +being transported + + align:start position:0% +being transported + + + align:start position:0% +being transported +by anterograde transport + + align:start position:0% + + + + align:start position:0% + +but that is not + + align:start position:0% + + + + align:start position:0% + +related to what happens when an action + + align:start position:0% +related to what happens when an action + + + align:start position:0% +related to what happens when an action +potential arrives + + align:start position:0% +potential arrives + + + align:start position:0% +potential arrives +okay the action potential arrives and + + align:start position:0% +okay the action potential arrives and + + + align:start position:0% +okay the action potential arrives and +depolarizes the membrane + + align:start position:0% +depolarizes the membrane + + + align:start position:0% +depolarizes the membrane +of the synaptic terminal + + align:start position:0% + + + + align:start position:0% + +and that causes an influx of calcium + + align:start position:0% +and that causes an influx of calcium + + + align:start position:0% +and that causes an influx of calcium +ions + + align:start position:0% + + + + align:start position:0% + +which you see there + + align:start position:0% + + + + align:start position:0% + +and the influx of calcium ions causes a + + align:start position:0% +and the influx of calcium ions causes a + + + align:start position:0% +and the influx of calcium ions causes a +molecular cascade that causes these + + align:start position:0% +molecular cascade that causes these + + + align:start position:0% +molecular cascade that causes these +vesicles + + align:start position:0% +vesicles + + + align:start position:0% +vesicles +to bind to the presynaptic membrane + + align:start position:0% + + + + align:start position:0% + +and release the their neurotransmitter + + align:start position:0% +and release the their neurotransmitter + + + align:start position:0% +and release the their neurotransmitter +into the synaptic cleft so then what + + align:start position:0% +into the synaptic cleft so then what + + + align:start position:0% +into the synaptic cleft so then what +happens so they diffuse the molecules + + align:start position:0% +happens so they diffuse the molecules + + + align:start position:0% +happens so they diffuse the molecules +diffuse across that little + + align:start position:0% +diffuse across that little + + + align:start position:0% +diffuse across that little +gap + + align:start position:0% +gap + + + align:start position:0% +gap +and some of them will bind then to + + align:start position:0% +and some of them will bind then to + + + align:start position:0% +and some of them will bind then to +receptors in the postsynaptic membrane + + align:start position:0% +receptors in the postsynaptic membrane + + + align:start position:0% +receptors in the postsynaptic membrane +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yes + + align:start position:0% + + + + align:start position:0% + +again sorry in what + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% +that's + + + align:start position:0% +that's +there's usually so much material that + + align:start position:0% +there's usually so much material that + + + align:start position:0% +there's usually so much material that +you can get + + align:start position:0% +you can get + + + align:start position:0% +you can get +that doesn't happen very much but yes in + + align:start position:0% +that doesn't happen very much but yes in + + + align:start position:0% +that doesn't happen very much but yes in +studies of motor neurons they have been + + align:start position:0% +studies of motor neurons they have been + + + align:start position:0% +studies of motor neurons they have been +able to deplete the terminals that way + + align:start position:0% + + + + align:start position:0% + +there's a few other now what happens so + + align:start position:0% +there's a few other now what happens so + + + align:start position:0% +there's a few other now what happens so +it + + align:start position:0% +it + + + align:start position:0% +it +binds to a receptor + + align:start position:0% +binds to a receptor + + + align:start position:0% +binds to a receptor +well when it binds the receptor it + + align:start position:0% +well when it binds the receptor it + + + align:start position:0% +well when it binds the receptor it +causes changes in the receptor what is a + + align:start position:0% +causes changes in the receptor what is a + + + align:start position:0% +causes changes in the receptor what is a +receptor + + align:start position:0% + + + + align:start position:0% + +it's a protein embedded in the membrane + + align:start position:0% +it's a protein embedded in the membrane + + + align:start position:0% +it's a protein embedded in the membrane +postsynaptic membrane + + align:start position:0% +postsynaptic membrane + + + align:start position:0% +postsynaptic membrane +when it binds to + + align:start position:0% +when it binds to + + + align:start position:0% +when it binds to +a ligand + + align:start position:0% +a ligand + + + align:start position:0% +a ligand +which in this case would be + + align:start position:0% +which in this case would be + + + align:start position:0% +which in this case would be +the neurotransmitter + + align:start position:0% +the neurotransmitter + + + align:start position:0% +the neurotransmitter +released at that terminal it causes a + + align:start position:0% +released at that terminal it causes a + + + align:start position:0% +released at that terminal it causes a +conformational change which will cause + + align:start position:0% +conformational change which will cause + + + align:start position:0% +conformational change which will cause +the a channel to open up and + + align:start position:0% +the a channel to open up and + + + align:start position:0% +the a channel to open up and +result in either hyperpolarization or + + align:start position:0% +result in either hyperpolarization or + + + align:start position:0% +result in either hyperpolarization or +depolarization of the membrane depending + + align:start position:0% +depolarization of the membrane depending + + + align:start position:0% +depolarization of the membrane depending +on + + align:start position:0% +on + + + align:start position:0% +on +on the receptor molecule + + align:start position:0% + + + + align:start position:0% + +now it also shows a few other things + + align:start position:0% +now it also shows a few other things + + + align:start position:0% +now it also shows a few other things +there + + align:start position:0% +there + + + align:start position:0% +there +it shows a + + align:start position:0% +it shows a + + + align:start position:0% +it shows a +transporter here + + align:start position:0% +transporter here + + + align:start position:0% +transporter here +with that it's just a means for re + + align:start position:0% +with that it's just a means for re + + + align:start position:0% +with that it's just a means for re +collecting some of the transmitter + + align:start position:0% +collecting some of the transmitter + + + align:start position:0% +collecting some of the transmitter +molecules and the synaptic cleft + + align:start position:0% +molecules and the synaptic cleft + + + align:start position:0% +molecules and the synaptic cleft +reforming + + align:start position:0% +reforming + + + align:start position:0% +reforming +sort of recycling that membrane forming + + align:start position:0% +sort of recycling that membrane forming + + + align:start position:0% +sort of recycling that membrane forming +new + + align:start position:0% +new + + + align:start position:0% +new +vesicles + + align:start position:0% +vesicles + + + align:start position:0% +vesicles +they're also sometimes + + align:start position:0% +they're also sometimes + + + align:start position:0% +they're also sometimes +autoreceptors + + align:start position:0% +autoreceptors + + + align:start position:0% +autoreceptors +for reuptake now this will vary + + align:start position:0% +for reuptake now this will vary + + + align:start position:0% +for reuptake now this will vary +depending on the type of synapse in the + + align:start position:0% +depending on the type of synapse in the + + + align:start position:0% +depending on the type of synapse in the +neurotransmitter + + align:start position:0% +neurotransmitter + + + align:start position:0% +neurotransmitter +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in the case of acetylcholine + + align:start position:0% +in the case of acetylcholine + + + align:start position:0% +in the case of acetylcholine +uh most of the acetylcholine is actually + + align:start position:0% +uh most of the acetylcholine is actually + + + align:start position:0% +uh most of the acetylcholine is actually +destroyed + + align:start position:0% +destroyed + + + align:start position:0% +destroyed +by an + + align:start position:0% +by an + + + align:start position:0% +by an +enzyme acetylcholinesterase + + align:start position:0% +enzyme acetylcholinesterase + + + align:start position:0% +enzyme acetylcholinesterase +after it's released and that's what + + align:start position:0% +after it's released and that's what + + + align:start position:0% +after it's released and that's what +stops the action + + align:start position:0% +stops the action + + + align:start position:0% +stops the action +the synapse + + align:start position:0% +the synapse + + + align:start position:0% +the synapse +in the case of other molecules like + + align:start position:0% +in the case of other molecules like + + + align:start position:0% +in the case of other molecules like +norepinephrine there's a lot of reuptake + + align:start position:0% +norepinephrine there's a lot of reuptake + + + align:start position:0% +norepinephrine there's a lot of reuptake +the terminals take the transmitter up + + align:start position:0% +the terminals take the transmitter up + + + align:start position:0% +the terminals take the transmitter up +again and then it + + align:start position:0% +again and then it + + + align:start position:0% +again and then it +through these transporter molecules gets + + align:start position:0% +through these transporter molecules gets + + + align:start position:0% +through these transporter molecules gets +inside the + + align:start position:0% +inside the + + + align:start position:0% +inside the +the vesicles again + + align:start position:0% +the vesicles again + + + align:start position:0% +the vesicles again +as they reform + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +now this just shows a + + align:start position:0% +now this just shows a + + + align:start position:0% +now this just shows a +cartoon of the + + align:start position:0% +cartoon of the + + + align:start position:0% +cartoon of the +of receptors in the membrane and look at + + align:start position:0% +of receptors in the membrane and look at + + + align:start position:0% +of receptors in the membrane and look at +the one on the left + + align:start position:0% +the one on the left + + + align:start position:0% +the one on the left +okay this is a + + align:start position:0% + + + + align:start position:0% + +ligand-gated ion channel the high end + + align:start position:0% +ligand-gated ion channel the high end + + + align:start position:0% +ligand-gated ion channel the high end +channel + + align:start position:0% +channel + + + align:start position:0% +channel +that is + + align:start position:0% +that is + + + align:start position:0% +that is +changed gated by + + align:start position:0% +changed gated by + + + align:start position:0% +changed gated by +when it binds to a ligand which has + + align:start position:0% +when it binds to a ligand which has + + + align:start position:0% +when it binds to a ligand which has +beaten our transmitter + + align:start position:0% +beaten our transmitter + + + align:start position:0% +beaten our transmitter +okay the little neurotransmitter there + + align:start position:0% +okay the little neurotransmitter there + + + align:start position:0% +okay the little neurotransmitter there +is shown in green and when it binds to + + align:start position:0% +is shown in green and when it binds to + + + align:start position:0% +is shown in green and when it binds to +that protein + + align:start position:0% +that protein + + + align:start position:0% +that protein +you get a change so that + + align:start position:0% +you get a change so that + + + align:start position:0% +you get a change so that +ions can pass through the membrane so + + align:start position:0% +ions can pass through the membrane so + + + align:start position:0% +ions can pass through the membrane so +ions flow across the membrane and cause + + align:start position:0% +ions flow across the membrane and cause + + + align:start position:0% +ions flow across the membrane and cause +the membrane to depolarize or + + align:start position:0% +the membrane to depolarize or + + + align:start position:0% +the membrane to depolarize or +hyperpolarize + + align:start position:0% +hyperpolarize + + + align:start position:0% +hyperpolarize +there are other kinds of receptors that + + align:start position:0% +there are other kinds of receptors that + + + align:start position:0% +there are other kinds of receptors that +act a little differently where + + align:start position:0% +act a little differently where + + + align:start position:0% +act a little differently where +the neurotransmitter + + align:start position:0% +the neurotransmitter + + + align:start position:0% +the neurotransmitter +doesn't bind to a channel molecule + + align:start position:0% +doesn't bind to a channel molecule + + + align:start position:0% +doesn't bind to a channel molecule +okay + + align:start position:0% +okay + + + align:start position:0% +okay +this is the g protein coupled receptor a + + align:start position:0% +this is the g protein coupled receptor a + + + align:start position:0% +this is the g protein coupled receptor a +slower it has slower action + + align:start position:0% +slower it has slower action + + + align:start position:0% +slower it has slower action +sometimes called a metabotropic receptor + + align:start position:0% +sometimes called a metabotropic receptor + + + align:start position:0% +sometimes called a metabotropic receptor +noted that note there that they show a g + + align:start position:0% +noted that note there that they show a g + + + align:start position:0% +noted that note there that they show a g +protein bound to the receptor molecule + + align:start position:0% +protein bound to the receptor molecule + + + align:start position:0% +protein bound to the receptor molecule +and when the transmitter binds okay + + align:start position:0% +and when the transmitter binds okay + + + align:start position:0% +and when the transmitter binds okay +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +they call it here an activation + + align:start position:0% +they call it here an activation + + + align:start position:0% +they call it here an activation +of the g protein that actually + + align:start position:0% +of the g protein that actually + + + align:start position:0% +of the g protein that actually +dissociates and a piece of it then can + + align:start position:0% +dissociates and a piece of it then can + + + align:start position:0% +dissociates and a piece of it then can +diffuse and bind to nearby + + align:start position:0% +diffuse and bind to nearby + + + align:start position:0% +diffuse and bind to nearby +channel molecules and when it does so + + align:start position:0% +channel molecules and when it does so + + + align:start position:0% +channel molecules and when it does so +then the ion channel will open + + align:start position:0% +then the ion channel will open + + + align:start position:0% +then the ion channel will open +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that molecule that + + align:start position:0% +that molecule that + + + align:start position:0% +that molecule that +moves through the cell like that is + + align:start position:0% +moves through the cell like that is + + + align:start position:0% +moves through the cell like that is +often called an intracellular messenger + + align:start position:0% +often called an intracellular messenger + + + align:start position:0% +often called an intracellular messenger +okay + + align:start position:0% +okay + + + align:start position:0% +okay +communicating the information that the + + align:start position:0% +communicating the information that the + + + align:start position:0% +communicating the information that the +neurotransmitter has been bound and the + + align:start position:0% +neurotransmitter has been bound and the + + + align:start position:0% +neurotransmitter has been bound and the +channel should open + + align:start position:0% +channel should open + + + align:start position:0% +channel should open +okay the end result is similar + + align:start position:0% + + + + align:start position:0% + +the flow of ions through the membrane + + align:start position:0% +the flow of ions through the membrane + + + align:start position:0% +the flow of ions through the membrane +okay so let's just now review some of + + align:start position:0% +okay so let's just now review some of + + + align:start position:0% +okay so let's just now review some of +these things we've been talking about + + align:start position:0% +these things we've been talking about + + + align:start position:0% +these things we've been talking about +i'm going to put some of these questions + + align:start position:0% +i'm going to put some of these questions + + + align:start position:0% +i'm going to put some of these questions +a little bit differently + + align:start position:0% +a little bit differently + + + align:start position:0% +a little bit differently +first of all + + align:start position:0% +first of all + + + align:start position:0% +first of all +these are all about electrical + + align:start position:0% +these are all about electrical + + + align:start position:0% +these are all about electrical +properties of the neural membrane + + align:start position:0% +properties of the neural membrane + + + align:start position:0% +properties of the neural membrane +so what are the forces acting on ions at + + align:start position:0% +so what are the forces acting on ions at + + + align:start position:0% +so what are the forces acting on ions at +the cell membrane + + align:start position:0% +the cell membrane + + + align:start position:0% +the cell membrane +electrostatic forces + + align:start position:0% +electrostatic forces + + + align:start position:0% +electrostatic forces +and + + align:start position:0% + + + + align:start position:0% + +concentration gradient + + align:start position:0% + + + + align:start position:0% + +the concentrations are very different + + align:start position:0% +the concentrations are very different + + + align:start position:0% +the concentrations are very different +you'll again have forces on these ions + + align:start position:0% +you'll again have forces on these ions + + + align:start position:0% +you'll again have forces on these ions +these are the forces acting on the ions + + align:start position:0% +these are the forces acting on the ions + + + align:start position:0% +these are the forces acting on the ions +so how do they pass through the cell + + align:start position:0% +so how do they pass through the cell + + + align:start position:0% +so how do they pass through the cell +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +well they need these channels they need + + align:start position:0% +well they need these channels they need + + + align:start position:0% +well they need these channels they need +ion channels to go through + + align:start position:0% +ion channels to go through + + + align:start position:0% +ion channels to go through +because the membrane is otherwise not + + align:start position:0% +because the membrane is otherwise not + + + align:start position:0% +because the membrane is otherwise not +very permeable behind + + align:start position:0% + + + + align:start position:0% + +okay what are some of the measures of + + align:start position:0% +okay what are some of the measures of + + + align:start position:0% +okay what are some of the measures of +electrical properties + + align:start position:0% +electrical properties + + + align:start position:0% +electrical properties +i asked for four of them here + + align:start position:0% + + + + align:start position:0% + +one of them of course would just be the + + align:start position:0% +one of them of course would just be the + + + align:start position:0% +one of them of course would just be the +potential difference between inside and + + align:start position:0% +potential difference between inside and + + + align:start position:0% +potential difference between inside and +outside you can measure that with an + + align:start position:0% +outside you can measure that with an + + + align:start position:0% +outside you can measure that with an +electro tiny electrode + + align:start position:0% +electro tiny electrode + + + align:start position:0% +electro tiny electrode +what are other things that are + + align:start position:0% +what are other things that are + + + align:start position:0% +what are other things that are +electrical properties remember when we + + align:start position:0% +electrical properties remember when we + + + align:start position:0% +electrical properties remember when we +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +properties that affect + + align:start position:0% +properties that affect + + + align:start position:0% +properties that affect +speed of decremental conduction + + align:start position:0% +speed of decremental conduction + + + align:start position:0% +speed of decremental conduction +the membrane has capacitance + + align:start position:0% +the membrane has capacitance + + + align:start position:0% +the membrane has capacitance +and this resistance across the membrane + + align:start position:0% +and this resistance across the membrane + + + align:start position:0% +and this resistance across the membrane +that you can measure in a wrist + + align:start position:0% +that you can measure in a wrist + + + align:start position:0% +that you can measure in a wrist +resistance along + + align:start position:0% + + + + align:start position:0% + +the axial direction of an axon + + align:start position:0% +the axial direction of an axon + + + align:start position:0% +the axial direction of an axon +these are all measures of electrical + + align:start position:0% +these are all measures of electrical + + + align:start position:0% +these are all measures of electrical +properties that affect how the membrane + + align:start position:0% +properties that affect how the membrane + + + align:start position:0% +properties that affect how the membrane +behaves + + align:start position:0% +behaves + + + align:start position:0% +behaves +so how are these things different from + + align:start position:0% +so how are these things different from + + + align:start position:0% +so how are these things different from +copper wires it conducts right + + align:start position:0% +copper wires it conducts right + + + align:start position:0% +copper wires it conducts right +which conducts faster + + align:start position:0% + + + + align:start position:0% + +copper wires + + align:start position:0% +copper wires + + + align:start position:0% +copper wires +much faster when dealing with electrons + + align:start position:0% +much faster when dealing with electrons + + + align:start position:0% +much faster when dealing with electrons +not with these ions and the slower + + align:start position:0% +not with these ions and the slower + + + align:start position:0% +not with these ions and the slower +processes involving diffusion of ions + + align:start position:0% +processes involving diffusion of ions + + + align:start position:0% +processes involving diffusion of ions +through the membrane + + align:start position:0% + + + + align:start position:0% + +so how fast is conduction + + align:start position:0% +so how fast is conduction + + + align:start position:0% +so how fast is conduction +see if i ask the question like that + + align:start position:0% +see if i ask the question like that + + + align:start position:0% +see if i ask the question like that +you've got to ask me a question + + align:start position:0% +you've got to ask me a question + + + align:start position:0% +you've got to ask me a question +or you've got to get a pretty give a + + align:start position:0% +or you've got to get a pretty give a + + + align:start position:0% +or you've got to get a pretty give a +pretty elaborate answer how fast is + + align:start position:0% +pretty elaborate answer how fast is + + + align:start position:0% +pretty elaborate answer how fast is +conduction + + align:start position:0% +conduction + + + align:start position:0% +conduction +well depends on what kind of conduction + + align:start position:0% +well depends on what kind of conduction + + + align:start position:0% +well depends on what kind of conduction +we're talking about detrimental + + align:start position:0% +we're talking about detrimental + + + align:start position:0% +we're talking about detrimental +conduction + + align:start position:0% +conduction + + + align:start position:0% +conduction +and we know that the speed of + + align:start position:0% +and we know that the speed of + + + align:start position:0% +and we know that the speed of +decremental conduction can vary a lot + + align:start position:0% +decremental conduction can vary a lot + + + align:start position:0% +decremental conduction can vary a lot +depending on resistance and capacitance + + align:start position:0% +depending on resistance and capacitance + + + align:start position:0% +depending on resistance and capacitance +of the membrane + + align:start position:0% +of the membrane + + + align:start position:0% +of the membrane +when we talked about + + align:start position:0% +when we talked about + + + align:start position:0% +when we talked about +the effects of myelin + + align:start position:0% +the effects of myelin + + + align:start position:0% +the effects of myelin +what about non-detrimental conduction + + align:start position:0% +what about non-detrimental conduction + + + align:start position:0% +what about non-detrimental conduction +how fast is that the action potential + + align:start position:0% +how fast is that the action potential + + + align:start position:0% +how fast is that the action potential +what does it depend on + + align:start position:0% +what does it depend on + + + align:start position:0% +what does it depend on +two things + + align:start position:0% +two things + + + align:start position:0% +two things +what + + align:start position:0% + + + + align:start position:0% + +what affects rate of conduction of the + + align:start position:0% +what affects rate of conduction of the + + + align:start position:0% +what affects rate of conduction of the +action potential in an accident + + align:start position:0% + + + + align:start position:0% + +size of the axon + + align:start position:0% + + + + align:start position:0% + +and myeloma + + align:start position:0% + + + + align:start position:0% + +so if you're an invertebrate and you + + align:start position:0% +so if you're an invertebrate and you + + + align:start position:0% +so if you're an invertebrate and you +don't have myelin like a squid + + align:start position:0% +don't have myelin like a squid + + + align:start position:0% +don't have myelin like a squid +how fast you think + + align:start position:0% +how fast you think + + + align:start position:0% +how fast you think +the action potential can + + align:start position:0% +the action potential can + + + align:start position:0% +the action potential can +can go we'll make the axon really big + + align:start position:0% +can go we'll make the axon really big + + + align:start position:0% +can go we'll make the axon really big +the squid giant accent can be a + + align:start position:0% +the squid giant accent can be a + + + align:start position:0% +the squid giant accent can be a +millimeter in diameter how fast can the + + align:start position:0% +millimeter in diameter how fast can the + + + align:start position:0% +millimeter in diameter how fast can the +action potential go down that memory + + align:start position:0% + + + + align:start position:0% + +about 20 meters a second + + align:start position:0% +about 20 meters a second + + + align:start position:0% +about 20 meters a second +well + + align:start position:0% +well + + + align:start position:0% +well +we don't have one millimeter thick axons + + align:start position:0% +we don't have one millimeter thick axons + + + align:start position:0% +we don't have one millimeter thick axons +in us + + align:start position:0% +in us + + + align:start position:0% +in us +and yet we have much faster conduction + + align:start position:0% +and yet we have much faster conduction + + + align:start position:0% +and yet we have much faster conduction +because of myelin + + align:start position:0% +because of myelin + + + align:start position:0% +because of myelin +what would be the conduction of the are + + align:start position:0% +what would be the conduction of the are + + + align:start position:0% +what would be the conduction of the are +the large axons largest axons we have + + align:start position:0% +the large axons largest axons we have + + + align:start position:0% +the large axons largest axons we have +with myelin + + align:start position:0% + + + + align:start position:0% + +according to your text + + align:start position:0% + + + + align:start position:0% + +about 120 meters a second + + align:start position:0% +about 120 meters a second + + + align:start position:0% +about 120 meters a second +according to the text about six times + + align:start position:0% +according to the text about six times + + + align:start position:0% +according to the text about six times +the speed of a squid giant accent + + align:start position:0% +the speed of a squid giant accent + + + align:start position:0% +the speed of a squid giant accent +so how far do they conduct + + align:start position:0% +so how far do they conduct + + + align:start position:0% +so how far do they conduct +what's the answer to that one + + align:start position:0% + + + + align:start position:0% + +well if it's non-decrement if it's + + align:start position:0% +well if it's non-decrement if it's + + + align:start position:0% +well if it's non-decrement if it's +decremental conduction + + align:start position:0% +decremental conduction + + + align:start position:0% +decremental conduction +not very far because it gets weaker and + + align:start position:0% +not very far because it gets weaker and + + + align:start position:0% +not very far because it gets weaker and +weaker the further you go + + align:start position:0% +weaker the further you go + + + align:start position:0% +weaker the further you go +until it peters out what about a + + align:start position:0% +until it peters out what about a + + + align:start position:0% +until it peters out what about a +the axon + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +as far as the axon goes that's right + + align:start position:0% +as far as the axon goes that's right + + + align:start position:0% +as far as the axon goes that's right +goes all parts of the axon + + align:start position:0% + + + + align:start position:0% + +it's non-detrimental it goes everywhere + + align:start position:0% +it's non-detrimental it goes everywhere + + + align:start position:0% +it's non-detrimental it goes everywhere +so what would be the longest axon + + align:start position:0% +so what would be the longest axon + + + align:start position:0% +so what would be the longest axon +well in the periphery probably from your + + align:start position:0% +well in the periphery probably from your + + + align:start position:0% +well in the periphery probably from your +big toe to the spinal cord + + align:start position:0% + + + + align:start position:0% + +the central nervous system probably from + + align:start position:0% +the central nervous system probably from + + + align:start position:0% +the central nervous system probably from +your motor cortex + + align:start position:0% +your motor cortex + + + align:start position:0% +your motor cortex +to the lower enlargement the lumbar + + align:start position:0% +to the lower enlargement the lumbar + + + align:start position:0% +to the lower enlargement the lumbar +enlargement of your spinal cord to the + + align:start position:0% +enlargement of your spinal cord to the + + + align:start position:0% +enlargement of your spinal cord to the +motor neurons that are controlling the + + align:start position:0% +motor neurons that are controlling the + + + align:start position:0% +motor neurons that are controlling the +feet + + align:start position:0% + + + + align:start position:0% + +okay next question triggering up spikes + + align:start position:0% +okay next question triggering up spikes + + + align:start position:0% +okay next question triggering up spikes +how does that happen and where does it + + align:start position:0% +how does that happen and where does it + + + align:start position:0% +how does that happen and where does it +happen + + align:start position:0% + + + + align:start position:0% + +first of all where are spikes normally + + align:start position:0% +first of all where are spikes normally + + + align:start position:0% +first of all where are spikes normally +triggered + + align:start position:0% +triggered + + + align:start position:0% +triggered +we can trigger them artificially + + align:start position:0% +we can trigger them artificially + + + align:start position:0% +we can trigger them artificially +anywhere there's an axon + + align:start position:0% +anywhere there's an axon + + + align:start position:0% +anywhere there's an axon +by tweaking the axon mechanically or + + align:start position:0% +by tweaking the axon mechanically or + + + align:start position:0% +by tweaking the axon mechanically or +electrically + + align:start position:0% +electrically + + + align:start position:0% +electrically +where is it normally triggered + + align:start position:0% +where is it normally triggered + + + align:start position:0% +where is it normally triggered +at the axon hillick the initial + + align:start position:0% +at the axon hillick the initial + + + align:start position:0% +at the axon hillick the initial +segment of the axon + + align:start position:0% + + + + align:start position:0% + +and what causes it to be triggered + + align:start position:0% + + + + align:start position:0% + +depolarization that reaches the + + align:start position:0% +depolarization that reaches the + + + align:start position:0% +depolarization that reaches the +threshold + + align:start position:0% +threshold + + + align:start position:0% +threshold +for triggering the all or none response + + align:start position:0% + + + + align:start position:0% + +okay a few more questions there i didn't + + align:start position:0% +okay a few more questions there i didn't + + + align:start position:0% +okay a few more questions there i didn't +discuss the refractory period before + + align:start position:0% + + + + align:start position:0% + +what's the refractory period of an axon + + align:start position:0% +what's the refractory period of an axon + + + align:start position:0% +what's the refractory period of an axon +yes + + align:start position:0% + + + + align:start position:0% + +okay right after an action potential + + align:start position:0% +okay right after an action potential + + + align:start position:0% +okay right after an action potential +fires there's a little time period when + + align:start position:0% +fires there's a little time period when + + + align:start position:0% +fires there's a little time period when +it can't fire another action potential + + align:start position:0% +it can't fire another action potential + + + align:start position:0% +it can't fire another action potential +that's correct it takes a little bit of + + align:start position:0% +that's correct it takes a little bit of + + + align:start position:0% +that's correct it takes a little bit of +time to recover + + align:start position:0% +time to recover + + + align:start position:0% +time to recover +so at the time when it can't fire an + + align:start position:0% +so at the time when it can't fire an + + + align:start position:0% +so at the time when it can't fire an +action potential it's called a + + align:start position:0% +action potential it's called a + + + align:start position:0% +action potential it's called a +refractory period we talk about a + + align:start position:0% +refractory period we talk about a + + + align:start position:0% +refractory period we talk about a +relative refractory period when it + + align:start position:0% +relative refractory period when it + + + align:start position:0% +relative refractory period when it +the threshold it can fire but the + + align:start position:0% +the threshold it can fire but the + + + align:start position:0% +the threshold it can fire but the +threshold isn't just as high + + align:start position:0% +threshold isn't just as high + + + align:start position:0% +threshold isn't just as high +and then + + align:start position:0% +and then + + + align:start position:0% +and then +when it's completely recovered + + align:start position:0% + + + + align:start position:0% + +antidramic activation + + align:start position:0% +antidramic activation + + + align:start position:0% +antidramic activation +or antidramic conduction + + align:start position:0% +or antidramic conduction + + + align:start position:0% +or antidramic conduction +question in the back + + align:start position:0% + + + + align:start position:0% + +opposite of the normal direction so how + + align:start position:0% +opposite of the normal direction so how + + + align:start position:0% +opposite of the normal direction so how +could that happen + + align:start position:0% + + + + align:start position:0% + +okay like it's often due to mechanical + + align:start position:0% +okay like it's often due to mechanical + + + align:start position:0% +okay like it's often due to mechanical +it can be due to electrical stimulation + + align:start position:0% +it can be due to electrical stimulation + + + align:start position:0% +it can be due to electrical stimulation +we can + + align:start position:0% +we can + + + align:start position:0% +we can +we can stimulate an axon right in the + + align:start position:0% +we can stimulate an axon right in the + + + align:start position:0% +we can stimulate an axon right in the +middle of its course + + align:start position:0% +middle of its course + + + align:start position:0% +middle of its course +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you hit your elbow hard here and + + align:start position:0% +so you hit your elbow hard here and + + + align:start position:0% +so you hit your elbow hard here and +you've we call it your funny bone + + align:start position:0% +you've we call it your funny bone + + + align:start position:0% +you've we call it your funny bone +because the way it feels you're + + align:start position:0% +because the way it feels you're + + + align:start position:0% +because the way it feels you're +triggering action potentials in the + + align:start position:0% +triggering action potentials in the + + + align:start position:0% +triggering action potentials in the +nerve + + align:start position:0% +nerve + + + align:start position:0% +nerve +okay from your forearm and hand + + align:start position:0% +okay from your forearm and hand + + + align:start position:0% +okay from your forearm and hand +okay and that's why it feels so weird in + + align:start position:0% +okay and that's why it feels so weird in + + + align:start position:0% +okay and that's why it feels so weird in +your forearm and hand it's not that + + align:start position:0% +your forearm and hand it's not that + + + align:start position:0% +your forearm and hand it's not that +you've changed the form and hand at all + + align:start position:0% +you've changed the form and hand at all + + + align:start position:0% +you've changed the form and hand at all +you've just affected the nerves there + + align:start position:0% +you've just affected the nerves there + + + align:start position:0% +you've just affected the nerves there +okay but you've caused action potentials + + align:start position:0% +okay but you've caused action potentials + + + align:start position:0% +okay but you've caused action potentials +to go in both directions orthodontic + + align:start position:0% +to go in both directions orthodontic + + + align:start position:0% +to go in both directions orthodontic +towards the central nervous system and + + align:start position:0% +towards the central nervous system and + + + align:start position:0% +towards the central nervous system and +anti-dramatically back to the to the + + align:start position:0% +anti-dramatically back to the to the + + + align:start position:0% +anti-dramatically back to the to the +sites of origin of the accents yes + + align:start position:0% + + + + align:start position:0% + +which question + + align:start position:0% +which question + + + align:start position:0% +which question +louder please + + align:start position:0% + + + + align:start position:0% + +oh the four measures + + align:start position:0% +oh the four measures + + + align:start position:0% +oh the four measures +these are just the measures we talked + + align:start position:0% +these are just the measures we talked + + + align:start position:0% +these are just the measures we talked +about when we gave when we talked + + align:start position:0% +about when we gave when we talked + + + align:start position:0% +about when we gave when we talked +earlier about + + align:start position:0% +earlier about + + + align:start position:0% +earlier about +membrane properties potential difference + + align:start position:0% +membrane properties potential difference + + + align:start position:0% +membrane properties potential difference +across the membrane capacitance of the + + align:start position:0% +across the membrane capacitance of the + + + align:start position:0% +across the membrane capacitance of the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +resistance across the membrane and the + + align:start position:0% +resistance across the membrane and the + + + align:start position:0% +resistance across the membrane and the +axial resistance along the axon + + align:start position:0% + + + + align:start position:0% + +okay now this last question i'm going to + + align:start position:0% +okay now this last question i'm going to + + + align:start position:0% +okay now this last question i'm going to +spend a little more time on i want you + + align:start position:0% +spend a little more time on i want you + + + align:start position:0% +spend a little more time on i want you +to understand + + align:start position:0% +to understand + + + align:start position:0% +to understand +all these questions from the answers + + align:start position:0% +all these questions from the answers + + + align:start position:0% +all these questions from the answers +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's why i've given it to you + + align:start position:0% +that's why i've given it to you + + + align:start position:0% +that's why i've given it to you +and going over it + + align:start position:0% +and going over it + + + align:start position:0% +and going over it +a little bit quickly + + align:start position:0% +a little bit quickly + + + align:start position:0% +a little bit quickly +what influences the potency of synaptic + + align:start position:0% +what influences the potency of synaptic + + + align:start position:0% +what influences the potency of synaptic +input + + align:start position:0% +input + + + align:start position:0% +input +that is what are the conditions that + + align:start position:0% +that is what are the conditions that + + + align:start position:0% +that is what are the conditions that +favor the triggering of an action + + align:start position:0% +favor the triggering of an action + + + align:start position:0% +favor the triggering of an action +potential + + align:start position:0% +potential + + + align:start position:0% +potential +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you look there in the next + + align:start position:0% + + + + align:start position:0% + +picture proximity + + align:start position:0% +picture proximity + + + align:start position:0% +picture proximity +of an excitatory synapse to the axon + + align:start position:0% +of an excitatory synapse to the axon + + + align:start position:0% +of an excitatory synapse to the axon +hillock + + align:start position:0% +hillock + + + align:start position:0% +hillock +because of decremental conduction the + + align:start position:0% +because of decremental conduction the + + + align:start position:0% +because of decremental conduction the +closer that synapse is to the axon + + align:start position:0% +closer that synapse is to the axon + + + align:start position:0% +closer that synapse is to the axon +hillock the more likely it an excitatory + + align:start position:0% +hillock the more likely it an excitatory + + + align:start position:0% +hillock the more likely it an excitatory +postsynaptic potential is to trigger an + + align:start position:0% +postsynaptic potential is to trigger an + + + align:start position:0% +postsynaptic potential is to trigger an +action potential + + align:start position:0% +action potential + + + align:start position:0% +action potential +the number of synaptic concepts contacts + + align:start position:0% +the number of synaptic concepts contacts + + + align:start position:0% +the number of synaptic concepts contacts +form by one accent because you can have + + align:start position:0% +form by one accent because you can have + + + align:start position:0% +form by one accent because you can have +one axon that's forming multiple + + align:start position:0% +one axon that's forming multiple + + + align:start position:0% +one axon that's forming multiple +synapses on a cell okay and the more it + + align:start position:0% +synapses on a cell okay and the more it + + + align:start position:0% +synapses on a cell okay and the more it +forms then the more likely an action + + align:start position:0% +forms then the more likely an action + + + align:start position:0% +forms then the more likely an action +potential arriving over that axon will + + align:start position:0% +potential arriving over that axon will + + + align:start position:0% +potential arriving over that axon will +have in triggering an action potential + + align:start position:0% +have in triggering an action potential + + + align:start position:0% +have in triggering an action potential +in the next cell that's because of the + + align:start position:0% +in the next cell that's because of the + + + align:start position:0% +in the next cell that's because of the +spatial summation + + align:start position:0% +spatial summation + + + align:start position:0% +spatial summation +and of course because of temporal + + align:start position:0% +and of course because of temporal + + + align:start position:0% +and of course because of temporal +summation the rate at which they arrive + + align:start position:0% +summation the rate at which they arrive + + + align:start position:0% +summation the rate at which they arrive +will also affect it + + align:start position:0% +will also affect it + + + align:start position:0% +will also affect it +okay so let's just draw a couple of + + align:start position:0% +okay so let's just draw a couple of + + + align:start position:0% +okay so let's just draw a couple of +cells now to illustrate this + + align:start position:0% + + + + align:start position:0% + +let's draw a pyramidal cell + + align:start position:0% +let's draw a pyramidal cell + + + align:start position:0% +let's draw a pyramidal cell +remember the bet cell here's the nucleus + + align:start position:0% +remember the bet cell here's the nucleus + + + align:start position:0% +remember the bet cell here's the nucleus +and here's a long dendrite + + align:start position:0% + + + + align:start position:0% + +with some + + align:start position:0% +with some + + + align:start position:0% +with some +various branches and here's the axon + + align:start position:0% +various branches and here's the axon + + + align:start position:0% +various branches and here's the axon +okay we'll + + align:start position:0% +okay we'll + + + align:start position:0% +okay we'll +draw the axon he'll look like that and + + align:start position:0% +draw the axon he'll look like that and + + + align:start position:0% +draw the axon he'll look like that and +we want to know + + align:start position:0% +we want to know + + + align:start position:0% +we want to know +now what + + align:start position:0% +now what + + + align:start position:0% +now what +let's say we have a terminal here + + align:start position:0% +let's say we have a terminal here + + + align:start position:0% +let's say we have a terminal here +another terminal here + + align:start position:0% +another terminal here + + + align:start position:0% +another terminal here +another terminal here + + align:start position:0% +another terminal here + + + align:start position:0% +another terminal here +okay now if we have one action potential + + align:start position:0% +okay now if we have one action potential + + + align:start position:0% +okay now if we have one action potential +arriving over each those terminals + + align:start position:0% + + + + align:start position:0% + +the one that's closest this one + + align:start position:0% +the one that's closest this one + + + align:start position:0% +the one that's closest this one +is going to be most likely to + + align:start position:0% +is going to be most likely to + + + align:start position:0% +is going to be most likely to +cause an extra potential because it's so + + align:start position:0% +cause an extra potential because it's so + + + align:start position:0% +cause an extra potential because it's so +much closer + + align:start position:0% +much closer + + + align:start position:0% +much closer +okay + + align:start position:0% + + + + align:start position:0% + +we might be able to make + + align:start position:0% +we might be able to make + + + align:start position:0% +we might be able to make +one that's further out + + align:start position:0% +one that's further out + + + align:start position:0% +one that's further out +just as likely + + align:start position:0% +just as likely + + + align:start position:0% +just as likely +if it in fact has many terminals + + align:start position:0% + + + + align:start position:0% + +and that can happen + + align:start position:0% +and that can happen + + + align:start position:0% +and that can happen +because that'll give us more spatial + + align:start position:0% +because that'll give us more spatial + + + align:start position:0% +because that'll give us more spatial +summation + + align:start position:0% +summation + + + align:start position:0% +summation +because now + + align:start position:0% +because now + + + align:start position:0% +because now +one action potential + + align:start position:0% +one action potential + + + align:start position:0% +one action potential +coming over that axon is going to travel + + align:start position:0% +coming over that axon is going to travel + + + align:start position:0% +coming over that axon is going to travel +down all those little branches + + align:start position:0% +down all those little branches + + + align:start position:0% +down all those little branches +in most cases anyway + + align:start position:0% +in most cases anyway + + + align:start position:0% +in most cases anyway +and caused the excitatory synaptic + + align:start position:0% +and caused the excitatory synaptic + + + align:start position:0% +and caused the excitatory synaptic +potential at every one of the terminals + + align:start position:0% + + + + align:start position:0% + +well is it possible + + align:start position:0% +well is it possible + + + align:start position:0% +well is it possible +to get really reliable + + align:start position:0% +to get really reliable + + + align:start position:0% +to get really reliable +transmission at a synapse so that every + + align:start position:0% +transmission at a synapse so that every + + + align:start position:0% +transmission at a synapse so that every +time an action potential arrives that + + align:start position:0% +time an action potential arrives that + + + align:start position:0% +time an action potential arrives that +triggers an action potential in the + + align:start position:0% +triggers an action potential in the + + + align:start position:0% +triggers an action potential in the +postsynaptic cell + + align:start position:0% +postsynaptic cell + + + align:start position:0% +postsynaptic cell +with this kind of arrangement of a + + align:start position:0% +with this kind of arrangement of a + + + align:start position:0% +with this kind of arrangement of a +pyramidal cell in the cortex that's + + align:start position:0% +pyramidal cell in the cortex that's + + + align:start position:0% +pyramidal cell in the cortex that's +very unlikely + + align:start position:0% +very unlikely + + + align:start position:0% +very unlikely +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but there are + + align:start position:0% +but there are + + + align:start position:0% +but there are +cells + + align:start position:0% +cells + + + align:start position:0% +cells +where there is + + align:start position:0% +where there is + + + align:start position:0% +where there is +where you get one-to-one transmission + + align:start position:0% +where you get one-to-one transmission + + + align:start position:0% +where you get one-to-one transmission +for example + + align:start position:0% +for example + + + align:start position:0% +for example +in the auditory system + + align:start position:0% +in the auditory system + + + align:start position:0% +in the auditory system +in the cochlear nucleus this one cell + + align:start position:0% +in the cochlear nucleus this one cell + + + align:start position:0% +in the cochlear nucleus this one cell +type there + + align:start position:0% +type there + + + align:start position:0% +type there +which gets input from large axons coming + + align:start position:0% +which gets input from large axons coming + + + align:start position:0% +which gets input from large axons coming +from the cochlea + + align:start position:0% +from the cochlea + + + align:start position:0% +from the cochlea +where we want to preserve the timing + + align:start position:0% +where we want to preserve the timing + + + align:start position:0% +where we want to preserve the timing +really precisely + + align:start position:0% +really precisely + + + align:start position:0% +really precisely +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +these cells + + align:start position:0% +these cells + + + align:start position:0% +these cells +are often called magnus cellular nucleus + + align:start position:0% +are often called magnus cellular nucleus + + + align:start position:0% +are often called magnus cellular nucleus +cells + + align:start position:0% +cells + + + align:start position:0% +cells +and here's a big axon the auditory nerve + + align:start position:0% +and here's a big axon the auditory nerve + + + align:start position:0% +and here's a big axon the auditory nerve +coming in and here's what it does it + + align:start position:0% +coming in and here's what it does it + + + align:start position:0% +coming in and here's what it does it +forms a terminal like this + + align:start position:0% + + + + align:start position:0% + +so the action potential is coming here + + align:start position:0% +so the action potential is coming here + + + align:start position:0% +so the action potential is coming here +well so what is forming the big terminal + + align:start position:0% +well so what is forming the big terminal + + + align:start position:0% +well so what is forming the big terminal +well + + align:start position:0% +well + + + align:start position:0% +well +many + + align:start position:0% +many + + + align:start position:0% +many +synapses there + + align:start position:0% +synapses there + + + align:start position:0% +synapses there +and this is just a cross section and we + + align:start position:0% +and this is just a cross section and we + + + align:start position:0% +and this is just a cross section and we +can see many synaptic specializations at + + align:start position:0% +can see many synaptic specializations at + + + align:start position:0% +can see many synaptic specializations at +each one of them we have synaptic + + align:start position:0% +each one of them we have synaptic + + + align:start position:0% +each one of them we have synaptic +vesicles + + align:start position:0% + + + + align:start position:0% + +you can always identify the synapse and + + align:start position:0% +you can always identify the synapse and + + + align:start position:0% +you can always identify the synapse and +the electron micrograph by these little + + align:start position:0% +the electron micrograph by these little + + + align:start position:0% +the electron micrograph by these little +collections of synaptic vessel vesicles + + align:start position:0% +collections of synaptic vessel vesicles + + + align:start position:0% +collections of synaptic vessel vesicles +and also by thickening of the membrane + + align:start position:0% +and also by thickening of the membrane + + + align:start position:0% +and also by thickening of the membrane +okay so you can one + + align:start position:0% +okay so you can one + + + align:start position:0% +okay so you can one +terminal can have many synapses + + align:start position:0% +terminal can have many synapses + + + align:start position:0% +terminal can have many synapses +and if we looked at this we did a + + align:start position:0% +and if we looked at this we did a + + + align:start position:0% +and if we looked at this we did a +three-dimensional reconstruction we'd + + align:start position:0% +three-dimensional reconstruction we'd + + + align:start position:0% +three-dimensional reconstruction we'd +probably find would could find over 100 + + align:start position:0% +probably find would could find over 100 + + + align:start position:0% +probably find would could find over 100 +synapses + + align:start position:0% +synapses + + + align:start position:0% +synapses +the result is + + align:start position:0% +the result is + + + align:start position:0% +the result is +that when one action potential arrives + + align:start position:0% +that when one action potential arrives + + + align:start position:0% +that when one action potential arrives +there's so many synapses that are + + align:start position:0% +there's so many synapses that are + + + align:start position:0% +there's so many synapses that are +activated that it triggers + + align:start position:0% +activated that it triggers + + + align:start position:0% +activated that it triggers +enough and notice that the cell here is + + align:start position:0% +enough and notice that the cell here is + + + align:start position:0% +enough and notice that the cell here is +sort of a little + + align:start position:0% +sort of a little + + + align:start position:0% +sort of a little +bare cell without dendrites it had + + align:start position:0% +bare cell without dendrites it had + + + align:start position:0% +bare cell without dendrites it had +dendrites when it was developing + + align:start position:0% +dendrites when it was developing + + + align:start position:0% +dendrites when it was developing +that was discovered at harvard a few + + align:start position:0% +that was discovered at harvard a few + + + align:start position:0% +that was discovered at harvard a few +years ago + + align:start position:0% + + + + align:start position:0% + +by dr javari who works in the building + + align:start position:0% +by dr javari who works in the building + + + align:start position:0% +by dr javari who works in the building +sometimes here + + align:start position:0% +sometimes here + + + align:start position:0% +sometimes here +you get so much basal summation that + + align:start position:0% +you get so much basal summation that + + + align:start position:0% +you get so much basal summation that +every time an action potential arrives + + align:start position:0% +every time an action potential arrives + + + align:start position:0% +every time an action potential arrives +over the presynaptic cell it will + + align:start position:0% +over the presynaptic cell it will + + + align:start position:0% +over the presynaptic cell it will +trigger an action potential here + + align:start position:0% +trigger an action potential here + + + align:start position:0% +trigger an action potential here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so those are the extremes + + align:start position:0% +so those are the extremes + + + align:start position:0% +so those are the extremes +extremes then would be + + align:start position:0% +extremes then would be + + + align:start position:0% +extremes then would be +this cell + + align:start position:0% +this cell + + + align:start position:0% +this cell +and say an action potential here + + align:start position:0% +and say an action potential here + + + align:start position:0% +and say an action potential here +way out on the tip of the dendrite + + align:start position:0% +way out on the tip of the dendrite + + + align:start position:0% +way out on the tip of the dendrite +having very little effect + + align:start position:0% +having very little effect + + + align:start position:0% +having very little effect +by itself + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now let's talk a little bit about + + align:start position:0% +now let's talk a little bit about + + + align:start position:0% +now let's talk a little bit about +neural home neural hormones + + align:start position:0% +neural home neural hormones + + + align:start position:0% +neural home neural hormones +you know what hormones are + + align:start position:0% +you know what hormones are + + + align:start position:0% +you know what hormones are +at least by endocrine glands well then + + align:start position:0% +at least by endocrine glands well then + + + align:start position:0% +at least by endocrine glands well then +what are neural neural hormones + + align:start position:0% +what are neural neural hormones + + + align:start position:0% +what are neural neural hormones +okay + + align:start position:0% + + + + align:start position:0% + +can be illustrated + + align:start position:0% +can be illustrated + + + align:start position:0% +can be illustrated +by discussing this reflex + + align:start position:0% +by discussing this reflex + + + align:start position:0% +by discussing this reflex +the milk let down reflex + + align:start position:0% + + + + align:start position:0% + +when the baby starts to suckle + + align:start position:0% +when the baby starts to suckle + + + align:start position:0% +when the baby starts to suckle +milk does not come out immediately + + align:start position:0% +milk does not come out immediately + + + align:start position:0% +milk does not come out immediately +the reason is + + align:start position:0% +the reason is + + + align:start position:0% +the reason is +that a reflex has to be triggered and + + align:start position:0% +that a reflex has to be triggered and + + + align:start position:0% +that a reflex has to be triggered and +that's a bit that it's an unusual reflex + + align:start position:0% +that's a bit that it's an unusual reflex + + + align:start position:0% +that's a bit that it's an unusual reflex +sensory input from the nipple reaches + + align:start position:0% +sensory input from the nipple reaches + + + align:start position:0% +sensory input from the nipple reaches +the hypothalamus by a polysynaptic + + align:start position:0% +the hypothalamus by a polysynaptic + + + align:start position:0% +the hypothalamus by a polysynaptic +pathway + + align:start position:0% +pathway + + + align:start position:0% +pathway +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in the hypothalamus + + align:start position:0% +in the hypothalamus + + + align:start position:0% +in the hypothalamus +there are neurons + + align:start position:0% +there are neurons + + + align:start position:0% +there are neurons +that rather than + + align:start position:0% +that rather than + + + align:start position:0% +that rather than +exciting other cells with action + + align:start position:0% +exciting other cells with action + + + align:start position:0% +exciting other cells with action +potentials secrete + + align:start position:0% +potentials secrete + + + align:start position:0% +potentials secrete +a substance into the bloodstream + + align:start position:0% + + + + align:start position:0% + +oxytocin which then + + align:start position:0% +oxytocin which then + + + align:start position:0% +oxytocin which then +affects the smooth muscle + + align:start position:0% +affects the smooth muscle + + + align:start position:0% +affects the smooth muscle +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and oxytocin does several things + + align:start position:0% +and oxytocin does several things + + + align:start position:0% +and oxytocin does several things +it will cause the milk to be released it + + align:start position:0% +it will cause the milk to be released it + + + align:start position:0% +it will cause the milk to be released it +also causes uterine contractions and is + + align:start position:0% +also causes uterine contractions and is + + + align:start position:0% +also causes uterine contractions and is +involved in the birth process this is an + + align:start position:0% +involved in the birth process this is an + + + align:start position:0% +involved in the birth process this is an +enlargement of the + + align:start position:0% +enlargement of the + + + align:start position:0% +enlargement of the +posterior pituitaries often called the + + align:start position:0% +posterior pituitaries often called the + + + align:start position:0% +posterior pituitaries often called the +neural hypothesis + + align:start position:0% + + + + align:start position:0% + +the very base of the tween brain or + + align:start position:0% +the very base of the tween brain or + + + align:start position:0% +the very base of the tween brain or +base of the hypothalamus + + align:start position:0% + + + + align:start position:0% + +its location is defined here by the + + align:start position:0% +its location is defined here by the + + + align:start position:0% +its location is defined here by the +optic chisum but that has nothing to do + + align:start position:0% +optic chisum but that has nothing to do + + + align:start position:0% +optic chisum but that has nothing to do +with the function + + align:start position:0% +with the function + + + align:start position:0% +with the function +okay it just gives you the location + + align:start position:0% +okay it just gives you the location + + + align:start position:0% +okay it just gives you the location +that's where the fibers coming from the + + align:start position:0% +that's where the fibers coming from the + + + align:start position:0% +that's where the fibers coming from the +eyes or many of them are crossing over + + align:start position:0% + + + + align:start position:0% + +right near that structure there are two + + align:start position:0% +right near that structure there are two + + + align:start position:0% +right near that structure there are two +nuclei + + align:start position:0% +nuclei + + + align:start position:0% +nuclei +the superoptic nucleus and the + + align:start position:0% +the superoptic nucleus and the + + + align:start position:0% +the superoptic nucleus and the +paraventricular nucleus where there are + + align:start position:0% +paraventricular nucleus where there are + + + align:start position:0% +paraventricular nucleus where there are +neurons whose axons + + align:start position:0% +neurons whose axons + + + align:start position:0% +neurons whose axons +go down this little stalk + + align:start position:0% +go down this little stalk + + + align:start position:0% +go down this little stalk +to the posterior part of the pituitary + + align:start position:0% +to the posterior part of the pituitary + + + align:start position:0% +to the posterior part of the pituitary +gland the anterior part of the pituitary + + align:start position:0% +gland the anterior part of the pituitary + + + align:start position:0% +gland the anterior part of the pituitary +this part the anterior pituitary is a + + align:start position:0% +this part the anterior pituitary is a + + + align:start position:0% +this part the anterior pituitary is a +gland and isn't part of the brain at all + + align:start position:0% +gland and isn't part of the brain at all + + + align:start position:0% +gland and isn't part of the brain at all +it's gland tissue + + align:start position:0% +it's gland tissue + + + align:start position:0% +it's gland tissue +like other endocrine organs + + align:start position:0% +like other endocrine organs + + + align:start position:0% +like other endocrine organs +but the posterior part is part of the + + align:start position:0% +but the posterior part is part of the + + + align:start position:0% +but the posterior part is part of the +brain + + align:start position:0% +brain + + + align:start position:0% +brain +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the axons from these two nuclei + + align:start position:0% +and the axons from these two nuclei + + + align:start position:0% +and the axons from these two nuclei +terminate not on neurons there but they + + align:start position:0% +terminate not on neurons there but they + + + align:start position:0% +terminate not on neurons there but they +terminate on + + align:start position:0% +terminate on + + + align:start position:0% +terminate on +capillaries and blood vessels okay and + + align:start position:0% +capillaries and blood vessels okay and + + + align:start position:0% +capillaries and blood vessels okay and +they re they release + + align:start position:0% + + + + align:start position:0% + +some of them release oxytocin some of + + align:start position:0% +some of them release oxytocin some of + + + align:start position:0% +some of them release oxytocin some of +them release vasopressin okay + + align:start position:0% +them release vasopressin okay + + + align:start position:0% +them release vasopressin okay +in the case the milk let down reflex + + align:start position:0% +in the case the milk let down reflex + + + align:start position:0% +in the case the milk let down reflex +they're releasing + + align:start position:0% +they're releasing + + + align:start position:0% +they're releasing +the axons involved are releasing + + align:start position:0% +the axons involved are releasing + + + align:start position:0% +the axons involved are releasing +oxytocin sometimes called pitocin + + align:start position:0% +oxytocin sometimes called pitocin + + + align:start position:0% +oxytocin sometimes called pitocin +and that causes the milk let down and + + align:start position:0% +and that causes the milk let down and + + + align:start position:0% +and that causes the milk let down and +also can cause urine contractions many + + align:start position:0% +also can cause urine contractions many + + + align:start position:0% +also can cause urine contractions many +women when they're nursing can feel that + + align:start position:0% +women when they're nursing can feel that + + + align:start position:0% +women when they're nursing can feel that +can actually give them a sexual + + align:start position:0% +can actually give them a sexual + + + align:start position:0% +can actually give them a sexual +experience + + align:start position:0% +experience + + + align:start position:0% +experience +at least feel similar + + align:start position:0% + + + + align:start position:0% + +and that's because of this neural + + align:start position:0% +and that's because of this neural + + + align:start position:0% +and that's because of this neural +hormonal reflex + + align:start position:0% +hormonal reflex + + + align:start position:0% +hormonal reflex +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but that's not the way of course most + + align:start position:0% +but that's not the way of course most + + + align:start position:0% +but that's not the way of course most +reflexes work + + align:start position:0% + + + + align:start position:0% + +you could say the synaptic gap is rather + + align:start position:0% +you could say the synaptic gap is rather + + + align:start position:0% +you could say the synaptic gap is rather +large in that case + + align:start position:0% +large in that case + + + align:start position:0% +large in that case +okay so let's talk a little bit about + + align:start position:0% +okay so let's talk a little bit about + + + align:start position:0% +okay so let's talk a little bit about +a little more about + + align:start position:0% +a little more about + + + align:start position:0% +a little more about +other kinds of synapses + + align:start position:0% + + + + align:start position:0% + +there are multiple types + + align:start position:0% +there are multiple types + + + align:start position:0% +there are multiple types +okay + + align:start position:0% + + + + align:start position:0% + +we've been + + align:start position:0% +we've been + + + align:start position:0% +we've been +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +axosomatic and accidentaritic terminals + + align:start position:0% +axosomatic and accidentaritic terminals + + + align:start position:0% +axosomatic and accidentaritic terminals +where axon terminates + + align:start position:0% +where axon terminates + + + align:start position:0% +where axon terminates +on + + align:start position:0% +on + + + align:start position:0% +on +the usual receptive surface of neurons + + align:start position:0% +the usual receptive surface of neurons + + + align:start position:0% +the usual receptive surface of neurons +the dendrites or cell body + + align:start position:0% + + + + align:start position:0% + +and those can be either excitatory + + align:start position:0% +and those can be either excitatory + + + align:start position:0% +and those can be either excitatory +inhibitory depending on whether they're + + align:start position:0% +inhibitory depending on whether they're + + + align:start position:0% +inhibitory depending on whether they're +causing + + align:start position:0% +causing + + + align:start position:0% +causing +depolarization or hyperpolarization + + align:start position:0% + + + + align:start position:0% + +but there's other types of synapses as + + align:start position:0% +but there's other types of synapses as + + + align:start position:0% +but there's other types of synapses as +well + + align:start position:0% +well + + + align:start position:0% +well +all these other types listed + + align:start position:0% +all these other types listed + + + align:start position:0% +all these other types listed +so let's talk here about + + align:start position:0% +so let's talk here about + + + align:start position:0% +so let's talk here about +the exo-axonal synapses first of all + + align:start position:0% +the exo-axonal synapses first of all + + + align:start position:0% +the exo-axonal synapses first of all +so you can see how these can have a + + align:start position:0% +so you can see how these can have a + + + align:start position:0% +so you can see how these can have a +somewhat different kind of function + + align:start position:0% + + + + align:start position:0% + +we know a little more about the axoxonal + + align:start position:0% +we know a little more about the axoxonal + + + align:start position:0% +we know a little more about the axoxonal +synapses than we know about some of + + align:start position:0% +synapses than we know about some of + + + align:start position:0% +synapses than we know about some of +these others they're synapses between + + align:start position:0% +these others they're synapses between + + + align:start position:0% +these others they're synapses between +dendrites and other dendrites there are + + align:start position:0% +dendrites and other dendrites there are + + + align:start position:0% +dendrites and other dendrites there are +synapses between dendrites and axons + + align:start position:0% +synapses between dendrites and axons + + + align:start position:0% +synapses between dendrites and axons +we know not very much about them + + align:start position:0% +we know not very much about them + + + align:start position:0% +we know not very much about them +we'll say a little more about the + + align:start position:0% +we'll say a little more about the + + + align:start position:0% +we'll say a little more about the +reciprocal synapses and serial synapses + + align:start position:0% +reciprocal synapses and serial synapses + + + align:start position:0% +reciprocal synapses and serial synapses +and synapses saw the postsynaptic site + + align:start position:0% +and synapses saw the postsynaptic site + + + align:start position:0% +and synapses saw the postsynaptic site +in a minute + + align:start position:0% + + + + align:start position:0% + +in this picture i'm showing + + align:start position:0% + + + + align:start position:0% + +a little diagram of a cell in black + + align:start position:0% +a little diagram of a cell in black + + + align:start position:0% +a little diagram of a cell in black +there + + align:start position:0% + + + + align:start position:0% + +that is synaptically connected to a + + align:start position:0% +that is synaptically connected to a + + + align:start position:0% +that is synaptically connected to a +another cell through this green axon + + align:start position:0% +another cell through this green axon + + + align:start position:0% +another cell through this green axon +okay + + align:start position:0% + + + + align:start position:0% + +and i'm showing that if an action + + align:start position:0% +and i'm showing that if an action + + + align:start position:0% +and i'm showing that if an action +potential arrives over the green axon + + align:start position:0% +potential arrives over the green axon + + + align:start position:0% +potential arrives over the green axon +i've shown the actual potential in green + + align:start position:0% +i've shown the actual potential in green + + + align:start position:0% +i've shown the actual potential in green +there on the graph + + align:start position:0% +there on the graph + + + align:start position:0% +there on the graph +i'm showing the triggering + + align:start position:0% +i'm showing the triggering + + + align:start position:0% +i'm showing the triggering +of a slight depolarization so it's an + + align:start position:0% +of a slight depolarization so it's an + + + align:start position:0% +of a slight depolarization so it's an +excitatory postsynaptic potential + + align:start position:0% + + + + align:start position:0% + +now i've in addition i've shown another + + align:start position:0% +now i've in addition i've shown another + + + align:start position:0% +now i've in addition i've shown another +axon + + align:start position:0% +axon + + + align:start position:0% +axon +in red + + align:start position:0% +in red + + + align:start position:0% +in red +that's terminating + + align:start position:0% +that's terminating + + + align:start position:0% +that's terminating +on the terminal of the first accent + + align:start position:0% +on the terminal of the first accent + + + align:start position:0% +on the terminal of the first accent +okay + + align:start position:0% + + + + align:start position:0% + +and then in the graph i'm showing what + + align:start position:0% +and then in the graph i'm showing what + + + align:start position:0% +and then in the graph i'm showing what +would happen if an action potential + + align:start position:0% +would happen if an action potential + + + align:start position:0% +would happen if an action potential +arrives over the red axon + + align:start position:0% +arrives over the red axon + + + align:start position:0% +arrives over the red axon +just in advance of the action potential + + align:start position:0% +just in advance of the action potential + + + align:start position:0% +just in advance of the action potential +arriving over the green accent + + align:start position:0% + + + + align:start position:0% + +and it's also causing depolarization in + + align:start position:0% +and it's also causing depolarization in + + + align:start position:0% +and it's also causing depolarization in +this case the depolarization is of the + + align:start position:0% +this case the depolarization is of the + + + align:start position:0% +this case the depolarization is of the +presynaptic membrane of the green axon + + align:start position:0% +presynaptic membrane of the green axon + + + align:start position:0% +presynaptic membrane of the green axon +okay + + align:start position:0% + + + + align:start position:0% + +so the result and you see that + + align:start position:0% +so the result and you see that + + + align:start position:0% +so the result and you see that +right here + + align:start position:0% + + + + align:start position:0% + +so now when the action potential arrives + + align:start position:0% +so now when the action potential arrives + + + align:start position:0% +so now when the action potential arrives +over the green accent + + align:start position:0% +over the green accent + + + align:start position:0% +over the green accent +note that instead of this big action + + align:start position:0% +note that instead of this big action + + + align:start position:0% +note that instead of this big action +potential it's now a smaller action + + align:start position:0% +potential it's now a smaller action + + + align:start position:0% +potential it's now a smaller action +potential smaller action + + align:start position:0% +potential smaller action + + + align:start position:0% +potential smaller action +action potential because it started from + + align:start position:0% +action potential because it started from + + + align:start position:0% +action potential because it started from +a different point + + align:start position:0% +a different point + + + align:start position:0% +a different point +the result will be + + align:start position:0% + + + + align:start position:0% + +because the membrane potential changes + + align:start position:0% +because the membrane potential changes + + + align:start position:0% +because the membrane potential changes +less + + align:start position:0% +less + + + align:start position:0% +less +there will be less release of + + align:start position:0% +there will be less release of + + + align:start position:0% +there will be less release of +neurotransmitter and you'll have a + + align:start position:0% +neurotransmitter and you'll have a + + + align:start position:0% +neurotransmitter and you'll have a +smaller epsp + + align:start position:0% +smaller epsp + + + align:start position:0% +smaller epsp +and because of that effect + + align:start position:0% + + + + align:start position:0% + +it's + + align:start position:0% +it's + + + align:start position:0% +it's +called presynaptic inhibition + + align:start position:0% +called presynaptic inhibition + + + align:start position:0% +called presynaptic inhibition +it's a different use of the term + + align:start position:0% +it's a different use of the term + + + align:start position:0% +it's a different use of the term +inhibition it's called an inhibition + + align:start position:0% +inhibition it's called an inhibition + + + align:start position:0% +inhibition it's called an inhibition +because it's reducing the effect + + align:start position:0% + + + + align:start position:0% + +of the other axons terminals + + align:start position:0% +of the other axons terminals + + + align:start position:0% +of the other axons terminals +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +my question then is + + align:start position:0% +my question then is + + + align:start position:0% +my question then is +could you get + + align:start position:0% +could you get + + + align:start position:0% +could you get +pre-synaptic facilitation what would be + + align:start position:0% +pre-synaptic facilitation what would be + + + align:start position:0% +pre-synaptic facilitation what would be +required for that + + align:start position:0% +required for that + + + align:start position:0% +required for that +just using the same logic + + align:start position:0% +just using the same logic + + + align:start position:0% +just using the same logic +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what we described here + + align:start position:0% +what we described here + + + align:start position:0% +what we described here +you can imagine that if this red axon + + align:start position:0% +you can imagine that if this red axon + + + align:start position:0% +you can imagine that if this red axon +here caused a hyperpolarization + + align:start position:0% +here caused a hyperpolarization + + + align:start position:0% +here caused a hyperpolarization +increase the membrane polarization of + + align:start position:0% +increase the membrane polarization of + + + align:start position:0% +increase the membrane polarization of +the green axon + + align:start position:0% +the green axon + + + align:start position:0% +the green axon +then the actual potential + + align:start position:0% +then the actual potential + + + align:start position:0% +then the actual potential +when it arrives would be bigger + + align:start position:0% +when it arrives would be bigger + + + align:start position:0% +when it arrives would be bigger +because more neurotransmitter would be + + align:start position:0% +because more neurotransmitter would be + + + align:start position:0% +because more neurotransmitter would be +released and you could get larger epsps + + align:start position:0% +released and you could get larger epsps + + + align:start position:0% +released and you could get larger epsps +so that would be pre-synaptic + + align:start position:0% +so that would be pre-synaptic + + + align:start position:0% +so that would be pre-synaptic +facilitation + + align:start position:0% +facilitation + + + align:start position:0% +facilitation +and there is evidence + + align:start position:0% +and there is evidence + + + align:start position:0% +and there is evidence +for these things particularly for + + align:start position:0% +for these things particularly for + + + align:start position:0% +for these things particularly for +presynaptic inhibition + + align:start position:0% +presynaptic inhibition + + + align:start position:0% +presynaptic inhibition +in the dorsal horn of the spinal cord + + align:start position:0% + + + + align:start position:0% + +i know a lot of people get confused with + + align:start position:0% +i know a lot of people get confused with + + + align:start position:0% +i know a lot of people get confused with +pre-synaptic inhibition + + align:start position:0% +pre-synaptic inhibition + + + align:start position:0% +pre-synaptic inhibition +but study those pictures and + + align:start position:0% +but study those pictures and + + + align:start position:0% +but study those pictures and +try to understand it + + align:start position:0% +try to understand it + + + align:start position:0% +try to understand it +what's critical is to realize that + + align:start position:0% +what's critical is to realize that + + + align:start position:0% +what's critical is to realize that +what's causing the release of + + align:start position:0% +what's causing the release of + + + align:start position:0% +what's causing the release of +neurotransmitter is the membrane + + align:start position:0% +neurotransmitter is the membrane + + + align:start position:0% +neurotransmitter is the membrane +potential change + + align:start position:0% +potential change + + + align:start position:0% +potential change +happening when the active potential + + align:start position:0% +happening when the active potential + + + align:start position:0% +happening when the active potential +arrives so if it's a smaller action + + align:start position:0% +arrives so if it's a smaller action + + + align:start position:0% +arrives so if it's a smaller action +potential you'll get less release + + align:start position:0% +potential you'll get less release + + + align:start position:0% +potential you'll get less release +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and we can make the action potential + + align:start position:0% +and we can make the action potential + + + align:start position:0% +and we can make the action potential +smaller by deporsing the membrane a + + align:start position:0% +smaller by deporsing the membrane a + + + align:start position:0% +smaller by deporsing the membrane a +little bit + + align:start position:0% + + + + align:start position:0% + +so that + + align:start position:0% +so that + + + align:start position:0% +so that +the axon causing the presynaptic + + align:start position:0% +the axon causing the presynaptic + + + align:start position:0% +the axon causing the presynaptic +inhibition you see is not directly + + align:start position:0% +inhibition you see is not directly + + + align:start position:0% +inhibition you see is not directly +affecting + + align:start position:0% +affecting + + + align:start position:0% +affecting +that cell sitting there it's affecting + + align:start position:0% +that cell sitting there it's affecting + + + align:start position:0% +that cell sitting there it's affecting +just the axon just another axon + + align:start position:0% +just the axon just another axon + + + align:start position:0% +just the axon just another axon +and its effects + + align:start position:0% +and its effects + + + align:start position:0% +and its effects +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's say a little bit more now about + + align:start position:0% +so let's say a little bit more now about + + + align:start position:0% +so let's say a little bit more now about +these other types of synapses + + align:start position:0% +these other types of synapses + + + align:start position:0% +these other types of synapses +i'll draw them here + + align:start position:0% +i'll draw them here + + + align:start position:0% +i'll draw them here +first of all the reciprocal synapse + + align:start position:0% + + + + align:start position:0% + +let's say we're looking at a pre and a + + align:start position:0% +let's say we're looking at a pre and a + + + align:start position:0% +let's say we're looking at a pre and a +post-synaptic membrane here + + align:start position:0% +post-synaptic membrane here + + + align:start position:0% +post-synaptic membrane here +and we can see a + + align:start position:0% + + + + align:start position:0% + +the synapse here + + align:start position:0% +the synapse here + + + align:start position:0% +the synapse here +we know that this synapse + + align:start position:0% +we know that this synapse + + + align:start position:0% +we know that this synapse +okay would be going in this direction + + align:start position:0% +okay would be going in this direction + + + align:start position:0% +okay would be going in this direction +because we see where the + + align:start position:0% +because we see where the + + + align:start position:0% +because we see where the +synaptic vesicles are + + align:start position:0% +synaptic vesicles are + + + align:start position:0% +synaptic vesicles are +also there's often asymmetry in those + + align:start position:0% +also there's often asymmetry in those + + + align:start position:0% +also there's often asymmetry in those +thickenings + + align:start position:0% +thickenings + + + align:start position:0% +thickenings +the membrane but sometimes + + align:start position:0% +the membrane but sometimes + + + align:start position:0% +the membrane but sometimes +nearby you find + + align:start position:0% + + + + align:start position:0% + +another synapse + + align:start position:0% +another synapse + + + align:start position:0% +another synapse +that seems to be polarized in the + + align:start position:0% +that seems to be polarized in the + + + align:start position:0% +that seems to be polarized in the +opposite direction + + align:start position:0% +opposite direction + + + align:start position:0% +opposite direction +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but that would be called a reciprocal + + align:start position:0% +but that would be called a reciprocal + + + align:start position:0% +but that would be called a reciprocal +synapse + + align:start position:0% + + + + align:start position:0% + +one thing to understand here + + align:start position:0% +one thing to understand here + + + align:start position:0% +one thing to understand here +is that + + align:start position:0% +is that + + + align:start position:0% +is that +let's say that + + align:start position:0% + + + + align:start position:0% + +this is number one and that's where the + + align:start position:0% +this is number one and that's where the + + + align:start position:0% +this is number one and that's where the +an action potential first arrives + + align:start position:0% +an action potential first arrives + + + align:start position:0% +an action potential first arrives +when you get depolarization of that + + align:start position:0% +when you get depolarization of that + + + align:start position:0% +when you get depolarization of that +other membrane + + align:start position:0% +other membrane + + + align:start position:0% +other membrane +you could get if + + align:start position:0% +you could get if + + + align:start position:0% +you could get if +you could get released neurotransmitter + + align:start position:0% +you could get released neurotransmitter + + + align:start position:0% +you could get released neurotransmitter +in the nearby synapse even without an + + align:start position:0% +in the nearby synapse even without an + + + align:start position:0% +in the nearby synapse even without an +action potential + + align:start position:0% +action potential + + + align:start position:0% +action potential +i think that's important to understand + + align:start position:0% +i think that's important to understand + + + align:start position:0% +i think that's important to understand +when you're dealing with some of these + + align:start position:0% + + + + align:start position:0% + +synaptic configurations + + align:start position:0% +synaptic configurations + + + align:start position:0% +synaptic configurations +synapses don't require + + align:start position:0% +synapses don't require + + + align:start position:0% +synapses don't require +action potentials so normally + + align:start position:0% +action potentials so normally + + + align:start position:0% +action potentials so normally +many axons of course + + align:start position:0% +many axons of course + + + align:start position:0% +many axons of course +they release their neurotransmitter when + + align:start position:0% +they release their neurotransmitter when + + + align:start position:0% +they release their neurotransmitter when +an action potential rise but any + + align:start position:0% +an action potential rise but any + + + align:start position:0% +an action potential rise but any +sudden potential change can cause + + align:start position:0% +sudden potential change can cause + + + align:start position:0% +sudden potential change can cause +release + + align:start position:0% +release + + + align:start position:0% +release +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in this case you could have + + align:start position:0% + + + + align:start position:0% + +the action potential arriving from here + + align:start position:0% +the action potential arriving from here + + + align:start position:0% +the action potential arriving from here +causes depolarization that could then + + align:start position:0% +causes depolarization that could then + + + align:start position:0% +causes depolarization that could then +depolarize that membrane and keep it + + align:start position:0% +depolarize that membrane and keep it + + + align:start position:0% +depolarize that membrane and keep it +affect that terminal + + align:start position:0% +affect that terminal + + + align:start position:0% +affect that terminal +immediately afterwards so it's like an + + align:start position:0% +immediately afterwards so it's like an + + + align:start position:0% +immediately afterwards so it's like an +immediate feedback + + align:start position:0% +immediate feedback + + + align:start position:0% +immediate feedback +affecting their + + align:start position:0% +affecting their + + + align:start position:0% +affecting their +further action of the preset on that + + align:start position:0% +further action of the preset on that + + + align:start position:0% +further action of the preset on that +originally presynaptic side + + align:start position:0% +originally presynaptic side + + + align:start position:0% +originally presynaptic side +what about a serial synapse + + align:start position:0% +what about a serial synapse + + + align:start position:0% +what about a serial synapse +sometimes in the electromicroscope we + + align:start position:0% +sometimes in the electromicroscope we + + + align:start position:0% +sometimes in the electromicroscope we +see a dendrite + + align:start position:0% + + + + align:start position:0% + +sandwiched between two other cells and + + align:start position:0% +sandwiched between two other cells and + + + align:start position:0% +sandwiched between two other cells and +we'll see a synapse here + + align:start position:0% + + + + align:start position:0% + +and then we'll see another synapse here + + align:start position:0% + + + + align:start position:0% + +so this synapse is polarized this way + + align:start position:0% +so this synapse is polarized this way + + + align:start position:0% +so this synapse is polarized this way +the synapse polarized this way + + align:start position:0% +the synapse polarized this way + + + align:start position:0% +the synapse polarized this way +the dendrites we would call that a + + align:start position:0% +the dendrites we would call that a + + + align:start position:0% +the dendrites we would call that a +serial synapse + + align:start position:0% +serial synapse + + + align:start position:0% +serial synapse +there's a number of examples of it + + align:start position:0% +there's a number of examples of it + + + align:start position:0% +there's a number of examples of it +not always very well understood but we + + align:start position:0% +not always very well understood but we + + + align:start position:0% +not always very well understood but we +can say something + + align:start position:0% +can say something + + + align:start position:0% +can say something +about how that might work + + align:start position:0% + + + + align:start position:0% + +we know the effect of the first synapse + + align:start position:0% +we know the effect of the first synapse + + + align:start position:0% +we know the effect of the first synapse +there + + align:start position:0% + + + + align:start position:0% + +on the way that second one is operating + + align:start position:0% +on the way that second one is operating + + + align:start position:0% +on the way that second one is operating +will depend on + + align:start position:0% +will depend on + + + align:start position:0% +will depend on +membrane polarization in that dendrite + + align:start position:0% +membrane polarization in that dendrite + + + align:start position:0% +membrane polarization in that dendrite +okay so other influences on the dendrite + + align:start position:0% +okay so other influences on the dendrite + + + align:start position:0% +okay so other influences on the dendrite +coming from outside this little local + + align:start position:0% +coming from outside this little local + + + align:start position:0% +coming from outside this little local +area + + align:start position:0% +area + + + align:start position:0% +area +will affect + + align:start position:0% +will affect + + + align:start position:0% +will affect +the action + + align:start position:0% + + + + align:start position:0% + +of now if we let this 1 2 and 3 be the + + align:start position:0% +of now if we let this 1 2 and 3 be the + + + align:start position:0% +of now if we let this 1 2 and 3 be the +three cells involved the effect of cell + + align:start position:0% +three cells involved the effect of cell + + + align:start position:0% +three cells involved the effect of cell +1 on cell 3 will be influenced by + + align:start position:0% + + + + align:start position:0% + +the amount of polars at the + + align:start position:0% +the amount of polars at the + + + align:start position:0% +the amount of polars at the +level of polar polarization of that + + align:start position:0% +level of polar polarization of that + + + align:start position:0% +level of polar polarization of that +dendrite in between + + align:start position:0% +dendrite in between + + + align:start position:0% +dendrite in between +which could be affected of course by a + + align:start position:0% +which could be affected of course by a + + + align:start position:0% +which could be affected of course by a +number of factors + + align:start position:0% +number of factors + + + align:start position:0% +number of factors +from outside so it's a kind of very + + align:start position:0% +from outside so it's a kind of very + + + align:start position:0% +from outside so it's a kind of very +local gating mechanism + + align:start position:0% +local gating mechanism + + + align:start position:0% +local gating mechanism +okay + + align:start position:0% +okay + + + align:start position:0% +okay +very difficult to study because these + + align:start position:0% +very difficult to study because these + + + align:start position:0% +very difficult to study because these +this is happening at such a microscopic + + align:start position:0% +this is happening at such a microscopic + + + align:start position:0% +this is happening at such a microscopic +level + + align:start position:0% + + + + align:start position:0% + +in addition we see + + align:start position:0% +in addition we see + + + align:start position:0% +in addition we see +these are two + + align:start position:0% +these are two + + + align:start position:0% +these are two +of the + + align:start position:0% +of the + + + align:start position:0% +of the +extra kinds of synapse you can see we + + align:start position:0% +extra kinds of synapse you can see we + + + align:start position:0% +extra kinds of synapse you can see we +also find + + align:start position:0% +also find + + + align:start position:0% +also find +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we'll sometimes see a terminal + + align:start position:0% + + + + align:start position:0% + +that has an ending + + align:start position:0% + + + + align:start position:0% + +and we won't see any + + align:start position:0% + + + + align:start position:0% + +membrane on the other side + + align:start position:0% +membrane on the other side + + + align:start position:0% +membrane on the other side +it'll end + + align:start position:0% +it'll end + + + align:start position:0% +it'll end +it won't have any membrane immediately + + align:start position:0% +it won't have any membrane immediately + + + align:start position:0% +it won't have any membrane immediately +opposed to it + + align:start position:0% +opposed to it + + + align:start position:0% +opposed to it +at first it was thought these were just + + align:start position:0% +at first it was thought these were just + + + align:start position:0% +at first it was thought these were just +artifacts the methods but + + align:start position:0% +artifacts the methods but + + + align:start position:0% +artifacts the methods but +coloniae in canada is an anatomist who + + align:start position:0% +coloniae in canada is an anatomist who + + + align:start position:0% +coloniae in canada is an anatomist who +kept seeing them and he identified them + + align:start position:0% +kept seeing them and he identified them + + + align:start position:0% +kept seeing them and he identified them +in the neocortex frequently being + + align:start position:0% +in the neocortex frequently being + + + align:start position:0% +in the neocortex frequently being +axons of using norepinephrine + + align:start position:0% +axons of using norepinephrine + + + align:start position:0% +axons of using norepinephrine +to abbreviate any as a transmitter + + align:start position:0% +to abbreviate any as a transmitter + + + align:start position:0% +to abbreviate any as a transmitter +and he + + align:start position:0% +and he + + + align:start position:0% +and he +postulated that these were + + align:start position:0% +postulated that these were + + + align:start position:0% +postulated that these were +this were a way that you could get + + align:start position:0% +this were a way that you could get + + + align:start position:0% +this were a way that you could get +norepinephrine released into the + + align:start position:0% +norepinephrine released into the + + + align:start position:0% +norepinephrine released into the +extracellular space and it was not + + align:start position:0% +extracellular space and it was not + + + align:start position:0% +extracellular space and it was not +destroyed right away + + align:start position:0% +destroyed right away + + + align:start position:0% +destroyed right away +and we don't know the enzyme that does + + align:start position:0% +and we don't know the enzyme that does + + + align:start position:0% +and we don't know the enzyme that does +destroy it so it would diffuse through + + align:start position:0% +destroy it so it would diffuse through + + + align:start position:0% +destroy it so it would diffuse through +the exerciser space and be taken up by + + align:start position:0% +the exerciser space and be taken up by + + + align:start position:0% +the exerciser space and be taken up by +cells it could influence many cells in + + align:start position:0% +cells it could influence many cells in + + + align:start position:0% +cells it could influence many cells in +the vicinity okay they could modulate + + align:start position:0% +the vicinity okay they could modulate + + + align:start position:0% +the vicinity okay they could modulate +their action + + align:start position:0% +their action + + + align:start position:0% +their action +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we know that kind of synapse also + + align:start position:0% +so we know that kind of synapse also + + + align:start position:0% +so we know that kind of synapse also +exists + + align:start position:0% +exists + + + align:start position:0% +exists +synapses without a specific postsynaptic + + align:start position:0% +synapses without a specific postsynaptic + + + align:start position:0% +synapses without a specific postsynaptic +site + + align:start position:0% +site + + + align:start position:0% +site +yes + + align:start position:0% + + + + align:start position:0% + +they have they have vesicles + + align:start position:0% +they have they have vesicles + + + align:start position:0% +they have they have vesicles +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and they often have a thickening as well + + align:start position:0% +and they often have a thickening as well + + + align:start position:0% +and they often have a thickening as well +that has to do with the molecules needed + + align:start position:0% +that has to do with the molecules needed + + + align:start position:0% +that has to do with the molecules needed +to bind to the the vesicles cause the + + align:start position:0% +to bind to the the vesicles cause the + + + align:start position:0% +to bind to the the vesicles cause the +release of transmitter + + align:start position:0% + + + + align:start position:0% + +i can't tell you for sure whether + + align:start position:0% +i can't tell you for sure whether + + + align:start position:0% +i can't tell you for sure whether +they're right they really look identical + + align:start position:0% +they're right they really look identical + + + align:start position:0% +they're right they really look identical +to these other synapses okay + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +when we look consider this variety of + + align:start position:0% +when we look consider this variety of + + + align:start position:0% +when we look consider this variety of +terminals + + align:start position:0% + + + + align:start position:0% + +some people have + + align:start position:0% +some people have + + + align:start position:0% +some people have +begun to think that we should really + + align:start position:0% +begun to think that we should really + + + align:start position:0% +begun to think that we should really +think of these complexes of synapses as + + align:start position:0% +think of these complexes of synapses as + + + align:start position:0% +think of these complexes of synapses as +the functional units + + align:start position:0% +the functional units + + + align:start position:0% +the functional units +realizing that quite a lot of + + align:start position:0% +realizing that quite a lot of + + + align:start position:0% +realizing that quite a lot of +computation is happening at these in + + align:start position:0% +computation is happening at these in + + + align:start position:0% +computation is happening at these in +complexes of synapse + + align:start position:0% +complexes of synapse + + + align:start position:0% +complexes of synapse +sometimes we have a + + align:start position:0% +sometimes we have a + + + align:start position:0% +sometimes we have a +synaptic arrangement that's enclosed in + + align:start position:0% +synaptic arrangement that's enclosed in + + + align:start position:0% +synaptic arrangement that's enclosed in +wheel cells + + align:start position:0% +wheel cells + + + align:start position:0% +wheel cells +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +sometimes it's difficult to figure out + + align:start position:0% +sometimes it's difficult to figure out + + + align:start position:0% +sometimes it's difficult to figure out +exactly what it's doing our models have + + align:start position:0% +exactly what it's doing our models have + + + align:start position:0% +exactly what it's doing our models have +lagged behind the anatomy in this case + + align:start position:0% +lagged behind the anatomy in this case + + + align:start position:0% +lagged behind the anatomy in this case +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's still true most of the models + + align:start position:0% +and that's still true most of the models + + + align:start position:0% +and that's still true most of the models +deal only with the + + align:start position:0% +deal only with the + + + align:start position:0% +deal only with the +standard + + align:start position:0% +standard + + + align:start position:0% +standard +exosomatic and extra dendritic synapses + + align:start position:0% +exosomatic and extra dendritic synapses + + + align:start position:0% +exosomatic and extra dendritic synapses +and not these other types + + align:start position:0% +and not these other types + + + align:start position:0% +and not these other types +and yet there's many places in the + + align:start position:0% +and yet there's many places in the + + + align:start position:0% +and yet there's many places in the +nervous system where we see a great many + + align:start position:0% +nervous system where we see a great many + + + align:start position:0% +nervous system where we see a great many +of these other + + align:start position:0% +of these other + + + align:start position:0% +of these other +terminals + + align:start position:0% +terminals + + + align:start position:0% +terminals +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so any questions + + align:start position:0% + + + + align:start position:0% + +you think you understand pre-synaptic + + align:start position:0% +you think you understand pre-synaptic + + + align:start position:0% +you think you understand pre-synaptic +inhibition + + align:start position:0% + + + + align:start position:0% + +you have to know something about how + + align:start position:0% +you have to know something about how + + + align:start position:0% +you have to know something about how +transmitters released and know that + + align:start position:0% +transmitters released and know that + + + align:start position:0% +transmitters released and know that +we're using inhibition in a slightly + + align:start position:0% +we're using inhibition in a slightly + + + align:start position:0% +we're using inhibition in a slightly +different way yes + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +first of all make sure you know what i'm + + align:start position:0% +first of all make sure you know what i'm + + + align:start position:0% +first of all make sure you know what i'm +showing here just this could be a + + align:start position:0% +showing here just this could be a + + + align:start position:0% +showing here just this could be a +dendrite or it could be a cell + + align:start position:0% +dendrite or it could be a cell + + + align:start position:0% +dendrite or it could be a cell +with a terminal and we have to assume + + align:start position:0% +with a terminal and we have to assume + + + align:start position:0% +with a terminal and we have to assume +there's a synapse there + + align:start position:0% +there's a synapse there + + + align:start position:0% +there's a synapse there +i'm not showing the actual synapse + + align:start position:0% +i'm not showing the actual synapse + + + align:start position:0% +i'm not showing the actual synapse +and then we have another axon + + align:start position:0% +and then we have another axon + + + align:start position:0% +and then we have another axon +terminating on the first axon with an + + align:start position:0% +terminating on the first axon with an + + + align:start position:0% +terminating on the first axon with an +axo axonal contact okay + + align:start position:0% +axo axonal contact okay + + + align:start position:0% +axo axonal contact okay +i'm assuming that the synapses in either + + align:start position:0% +i'm assuming that the synapses in either + + + align:start position:0% +i'm assuming that the synapses in either +case here cause depolarization + + align:start position:0% +case here cause depolarization + + + align:start position:0% +case here cause depolarization +now before i remember we always said + + align:start position:0% +now before i remember we always said + + + align:start position:0% +now before i remember we always said +that + + align:start position:0% +that + + + align:start position:0% +that +depolarization + + align:start position:0% +depolarization + + + align:start position:0% +depolarization +was excitatory + + align:start position:0% +was excitatory + + + align:start position:0% +was excitatory +okay but that's because we were talking + + align:start position:0% +okay but that's because we were talking + + + align:start position:0% +okay but that's because we were talking +about an axon terminating on a dendrite + + align:start position:0% +about an axon terminating on a dendrite + + + align:start position:0% +about an axon terminating on a dendrite +or a cell we weren't talking about + + align:start position:0% +or a cell we weren't talking about + + + align:start position:0% +or a cell we weren't talking about +axoxonal synapses okay + + align:start position:0% +axoxonal synapses okay + + + align:start position:0% +axoxonal synapses okay +we have to use our terms a little bit + + align:start position:0% +we have to use our terms a little bit + + + align:start position:0% +we have to use our terms a little bit +differently when we're talking about + + align:start position:0% +differently when we're talking about + + + align:start position:0% +differently when we're talking about +exo-external synapses so just think + + align:start position:0% +exo-external synapses so just think + + + align:start position:0% +exo-external synapses so just think +you've got to think about what's + + align:start position:0% +you've got to think about what's + + + align:start position:0% +you've got to think about what's +happening when you get these changes so + + align:start position:0% +happening when you get these changes so + + + align:start position:0% +happening when you get these changes so +i'm showing there the action potential + + align:start position:0% +i'm showing there the action potential + + + align:start position:0% +i'm showing there the action potential +arriving and causing any psp in the + + align:start position:0% +arriving and causing any psp in the + + + align:start position:0% +arriving and causing any psp in the +this dendrite or cell okay that's what + + align:start position:0% +this dendrite or cell okay that's what + + + align:start position:0% +this dendrite or cell okay that's what +this shows + + align:start position:0% +this shows + + + align:start position:0% +this shows +now i'm showing that + + align:start position:0% +now i'm showing that + + + align:start position:0% +now i'm showing that +if an action potential arrives here it + + align:start position:0% +if an action potential arrives here it + + + align:start position:0% +if an action potential arrives here it +likewise causes a depolarization + + align:start position:0% +likewise causes a depolarization + + + align:start position:0% +likewise causes a depolarization +but if that depolarization and if i + + align:start position:0% +but if that depolarization and if i + + + align:start position:0% +but if that depolarization and if i +didn't have the other action potential + + align:start position:0% +didn't have the other action potential + + + align:start position:0% +didn't have the other action potential +it would look just like that it would be + + align:start position:0% +it would look just like that it would be + + + align:start position:0% +it would look just like that it would be +a little deportation it would disappear + + align:start position:0% +a little deportation it would disappear + + + align:start position:0% +a little deportation it would disappear +okay but now if it arrives just before + + align:start position:0% +okay but now if it arrives just before + + + align:start position:0% +okay but now if it arrives just before +the other action potential arrives + + align:start position:0% +the other action potential arrives + + + align:start position:0% +the other action potential arrives +you'll see + + align:start position:0% +you'll see + + + align:start position:0% +you'll see +that + + align:start position:0% + + + + align:start position:0% + +the amount of + + align:start position:0% +the amount of + + + align:start position:0% +the amount of +change in membrane polarity when the ash + + align:start position:0% +change in membrane polarity when the ash + + + align:start position:0% +change in membrane polarity when the ash +potential rises less because it started + + align:start position:0% +potential rises less because it started + + + align:start position:0% +potential rises less because it started +out + + align:start position:0% +out + + + align:start position:0% +out +in a more depolarized state + + align:start position:0% +in a more depolarized state + + + align:start position:0% +in a more depolarized state +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that + + align:start position:0% +that + + + align:start position:0% +that +causes less release of neurotransmitter + + align:start position:0% +causes less release of neurotransmitter + + + align:start position:0% +causes less release of neurotransmitter +at the synapse there between the green + + align:start position:0% +at the synapse there between the green + + + align:start position:0% +at the synapse there between the green +axon and + + align:start position:0% +axon and + + + align:start position:0% +axon and +the black cell + + align:start position:0% +the black cell + + + align:start position:0% +the black cell +so the apsp is smaller and that's why we + + align:start position:0% +so the apsp is smaller and that's why we + + + align:start position:0% +so the apsp is smaller and that's why we +say it's an inhibition + + align:start position:0% + + + + align:start position:0% + +okay if it's then i'm saying if you use + + align:start position:0% +okay if it's then i'm saying if you use + + + align:start position:0% +okay if it's then i'm saying if you use +the same logic + + align:start position:0% +the same logic + + + align:start position:0% +the same logic +and we say that this is not causing + + align:start position:0% +and we say that this is not causing + + + align:start position:0% +and we say that this is not causing +depolarization + + align:start position:0% +depolarization + + + align:start position:0% +depolarization +i should have drawn another color okay + + align:start position:0% +i should have drawn another color okay + + + align:start position:0% +i should have drawn another color okay +and + + align:start position:0% +and + + + align:start position:0% +and +if you have + + align:start position:0% +if you have + + + align:start position:0% +if you have +your notes there and you take let's say + + align:start position:0% +your notes there and you take let's say + + + align:start position:0% +your notes there and you take let's say +uh + + align:start position:0% + + + + align:start position:0% + +we'll just show another one here + + align:start position:0% +we'll just show another one here + + + align:start position:0% +we'll just show another one here +and we'll say that the blue one causes + + align:start position:0% +and we'll say that the blue one causes + + + align:start position:0% +and we'll say that the blue one causes +hyperpolarization rather than + + align:start position:0% +hyperpolarization rather than + + + align:start position:0% +hyperpolarization rather than +depolarization + + align:start position:0% +depolarization + + + align:start position:0% +depolarization +okay + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +that action potential arrives okay just + + align:start position:0% +that action potential arrives okay just + + + align:start position:0% +that action potential arrives okay just +like this one + + align:start position:0% +like this one + + + align:start position:0% +like this one +now what does the green one do + + align:start position:0% +now what does the green one do + + + align:start position:0% +now what does the green one do +okay + + align:start position:0% + + + + align:start position:0% + +it's it starts out like this + + align:start position:0% +it's it starts out like this + + + align:start position:0% +it's it starts out like this +and then + + align:start position:0% +and then + + + align:start position:0% +and then +shows the action potential okay + + align:start position:0% +shows the action potential okay + + + align:start position:0% +shows the action potential okay +the height is greater + + align:start position:0% +the height is greater + + + align:start position:0% +the height is greater +it'll release more neurotransmitter i + + align:start position:0% +it'll release more neurotransmitter i + + + align:start position:0% +it'll release more neurotransmitter i +shouldn't have drawn it higher there but + + align:start position:0% +shouldn't have drawn it higher there but + + + align:start position:0% +shouldn't have drawn it higher there but +the point is it starts out lower point + + align:start position:0% +the point is it starts out lower point + + + align:start position:0% +the point is it starts out lower point +so now you get a + + align:start position:0% +so now you get a + + + align:start position:0% +so now you get a +larger effect at that synapse + + align:start position:0% +larger effect at that synapse + + + align:start position:0% +larger effect at that synapse +okay so that's facilitation + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +that's right the height of the spike is + + align:start position:0% +that's right the height of the spike is + + + align:start position:0% +that's right the height of the spike is +affecting the amount of release + + align:start position:0% +affecting the amount of release + + + align:start position:0% +affecting the amount of release +of neurotransmitter + + align:start position:0% + + + + align:start position:0% + +why + + align:start position:0% +why + + + align:start position:0% +why +because + + align:start position:0% +because + + + align:start position:0% +because +more calcium comes in + + align:start position:0% + + + + align:start position:0% + +alright well that's all we have time for \ No newline at end of file diff --git a/dNl22h1kW1k.txt b/dNl22h1kW1k.txt new file mode 100644 index 0000000000000000000000000000000000000000..3b53b8ee204acf623b22ac99c0d42b9c9a0cdf70 --- /dev/null +++ b/dNl22h1kW1k.txt @@ -0,0 +1,5100 @@ +The following content is +proved under a Creative Commons + +license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Today we're going +to talk about privilege + +separation, so we're done with +buffer overflows at some level, + +but will keep +coming back as being + +a problem that we +want to deal with, + +so we'll not talk about the +details of how to exploit them, + +now we'll switch more into +mitigation, if you will, + +or prevention techniques of how +do you design a system where + +buffer overflows aren't such a +huge problem for you, perhaps, + +as well as other +security vulnerabilities. + +So for today we're going to +talk about privilege separation + +as a general purpose +technique for how + +to build a more secure system, +and the particular paper + +we assigned for you today is +this web server called OKWS. + +It's not necessarily the biggest +example of privilege separation + +on there, but it's a reasonably +well described system + +that we can actually read +and really understand + +how all the pieces work, +and you should really + +think of it more as a +case study of how to do + +privilege separation right. + +Not necessarily you should +go and download OKWS + +to run your website right now. + +So before we dive into +the details of OKWS + +and Unix permissions, +let's just see + +what is privilege separation, +why is it such a good idea? + +And then, last +week's lecture, James + +showed you that if you +write a program in C, + +then it's almost inevitable +you'll have something bad + +go wrong in that +program, and the problem, + +at some level is that if +you have a large application + +and there's any kind +of all vulnerability + +in this application, then +adversaries can connect + +and send requests +for this application, + +might be able to trick +it into doing bad things. + +And the application is +presumably privileged, + +meaning there is probably +lots of data sitting + +behind the application that +it can access and maybe delete + +files, like you guys +are going in Lab I now, + +read sensitive data, +install back doors. + +And the problem is +that a vulnerability + +in this large +application can allow + +it to modify any of +this data, or basically + +exercise all of the privileges +this application has, + +and it probably has +lots of privileges, + +unless you're careful about it. + +And what privilege +separation tries to do, + +and what we'll look +at in this lecture, + +is to take the +application and chop it up + +into different +pieces and make sure + +that each piece has only +the necessary privileges + +to do its job correctly. + +So you could imagine +maybe all the privileges + +you care about are access +to data in the back end, + +then all of this data, maybe +you can slice it up in some way, + +give this access to +this piece of data, + +this piece access to this +piece of data, and so on. + +So then, if you find a bug +here, then maybe this data + +is kind of compromised, +but hopefully + +whatever slicing +you've done is going + +to enforce the separation +so that a vulnerability here + +doesn't allow the +attacker to go and access + +these other pieces of +data, or, more generally, + +other privileges of the +application has access to. + +So this is the big idea +behind privilege separation, + +and it's hugely powerful. + +It actually doesn't really +rely on buffer overflows + +or other kinds of +vulnerabilities being present. + +It's just a general +architecture for making sure + +that vulnerabilities +in one place + +don't affect as much as +possible your system. + +This turns out to be +used pretty widely. + +Virtual machines often are +used for enforcing isolation + +within components. + +Maybe you'll take +your large system + +and break it up into a +bunch of DMs for isolation, + +but you could also use +Unix to actually perform + +this isolation with slicing. + +And as we'll talk +about in a second, + +Unix does provide you quite +a number of mechanisms + +that OKWS does actually use to +achieve privilege separation. + +And then many +applications actually + +use privilege +separation practice. + +You guys are probably +using SSH quite often. + +That uses privilege separation +in many of its components + +to make sure its +keys are not leaked + +and the server doesn't +get compromised + +or the effect of our server +compromise is reduced. + +And perhaps more relevant to you +guys, Chrome, the web browser, + +actually does +privilege separation + +quite extensively as well. + +So that if there's a bug +in Chrome's implementation, + +the adversary doesn't get full +control of your computer, which + +is a great property to have. + +So that's just a +very quick summary + +of what privilege +separation is about + +and why maybe OKWS is an +interesting case study. + +I guess we can add +it to this list, + +but it is more of an +illustrative example + +rather than an important piece +of software in its own right. + +Make sense? + +Any questions before we dive in? + +All right. + +So OKWS, as I +mentioned, it's going + +to use Unix permissions +and sort of Unix mechanisms + +to achieve the +separation between + +its different components. + +So as a result, it's +going to be important + +for us to understand how Unix +protection mechanisms work. + +And Unix isn't in some +way crucial to OKWS + +at some level for +privilege separation, + +but for any isolation +mechanism you're + +going to use, whether it's Unix, +uid, these other mechanisms, + +or virtual machines +or containers + +or any other technology, it's +really important to understand + +the details of how the +isolation mechanism works, + +because there's a lot of +tricky pieces to get right, + +because you're dealing +with some attacker that + +can exploit any [INAUDIBLE]. + +So as a result, +we'll look at Unix + +in a fair amount of +detail just to see + +what it's like, how +should we approach + +thinking about a particular +security mechanism. + +Let's look at Unix. + +So Unix historically-- well, +it's not necessarily the best + +example of how to build +a security mechanism, + +because its security +mechanism came about + +from a fairly utilitarian +need of needing + +to separate different users on +a single Unix system from one + +another, so they +weren't thinking + +of it as a general +purpose mechanism + +that applications +like OKWS are going + +to use to implement +privilege separation. + +They're just thinking, +we have a bunch + +of users that are using +the same computer, + +we need to keep them +from each other. + +So it's not necessarily a +general purpose mechanism + +but still one that is fairly +prevalent and, as a result, + +widely used. + +Chrome tries to use many +if these Unix mechanisms. + +So what does Unix have? + +So, in general, when you're +thinking about protection + +mechanism, you should +be thinking, well, + +what are the principals, meaning +what are the entities that + +have privileges or rights, +and in Unix these principals + +are typically invoked, or +sort of held, by a process. + +So I guess the subject, if you +will, in Unix is a process, so + +every operation or request that +we can think about in terms + +of security, whether something +should be allowed or not, + +is probably going +to be an operation + +that a process invokes +by making a system call. + +And the principal is +how we describe what + +privileges that process has. + +Conversely, there's also what +we can think about as objects, + +and these are the +things that a process + +might act on that try to modify, +read, observe in some way. + +There are actually a +lot of different kinds + +of objects you might worry +about protecting in an operating + +system. + +What do you guys think? + +What should we worry +about protecting? + +AUDIENCE: Files. + +PROFESSOR: Files. + +Yeah, great. + +That's a big one. + +That's where all of +our data lives, right? + +There's a closely +related thing we + +might worry about-- directories. + +Turns out to be +pretty important also + +from a security standpoint. + +Anything else? + +AUDIENCE: Networking sockets. + +PROFESSOR: Yeah, great. + +Networking sockets. + +Anything else going on? + +AUDIENCE: Other processes. + +PROFESSOR: Oh, yeah. + +Actually, this is like +stuff that the application + +or the user might care +about, but then there's + +all kinds of internal stuff that +you have to protect as well, + +so a process is not just the +subject that's making a system + +call, but a process +is also something + +that another process +can act upon. + +It can kill it or +create a new one. + +You have to figure out, what +are the rules for thinking + +about process as an +object you can manipulate. + +Other things we +might care about? + +AUDIENCE: Environment variables. + +PROFESSOR: I guess +they're probably + +not an entity you can +modify, in the sense + +of being managed by an iOS and +having some sort of a security + +policy. + +I guess I sort of think +of environment variables + +as just being some state a +process maintains in memory. + +But, I guess more +generally, we do + +care about maybe +part of a process + +is all this stuff in memory. + +So there's going to be +environment variables there, + +there's a stack, +there's arguments, + +and this also turns out +to be quite important. + +Presumably lots +of sensitive data + +lives in processor's memory. + +Other things? + +AUDIENCE: File +descriptors in general. + +PROFESSOR: There's like +another sort of internal detail + +that matters a lot. + +So files are the stuff we +might care about on disk, + +and there's this operational +thing, the file descriptor, + +that OKWS makes quite +extensive use of, + +and we'll see what +file descriptors are + +in a little bit. + +Any other stuff you guys want to +protect in an operating system? + +AUDIENCE: Hardware. + +PROFESSOR: Hardware? + +Yeah, I guess in many +ways hardware is-- well, + +hardware is, in some ways, +not really an abstraction + +that the iOS provides to you. + +I guess you run +a process, so you + +might want to make sure +the CPU doesn't get stuck. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Oh, yeah, yeah. + +So, like, extra +devices, Yeah, you're + +right, especially on +a desktop machine, + +there's lots of extra stuff. + +So there's your USB drive you +plug in, your webcam, probably + +your display itself is something +you'll want to protect, + +like an application shouldn't +draw all over your screen + +anywhere. + +So, yes, actually I +guess this isn't really + +on a server side view of +things, where there's just + +a server somewhere in a +closet, but on your phone, + +your microphone probably, +is a hugely important object + +that you want to protect, +yeah, but I will also leave it + +off this list, +because we're going + +to talk much more about +server applications for now, + +but you're absolutely right. + +I think for OKWS, +this is probably + +a more or less +exhaustive list of things + +we might care about protecting, +or, at least that OKWS uses. + +So let's talk about +how does the OS kernel + +decide when a process +can do something + +to any of these objects? + +So the [INAUDIBLE], I guess is, +we mostly think of a process + +as having the privileges +represented by this principal, + +and the principal +in a Unix system + +is this slightly +complicated thing. + +There is something +called a userid, + +which is just a 32-bit integer. + +There's also a group ID, which +is also a 32-bit integer. + +And there's not really a great +reason why they're different. + +It would've been nice +if they were just + +a uniform set of 32-bit +integer principal numbers, + +but unfortunately Unix +sort of splits them + +into two categories. + +There's userid integers and then +there are group ID integers. + +When we talk about a process +having certain privileges, + +we typically think of a +process being associated + +with a particular uid value. + +The process, for the most +part, has a single uid. + +As with almost +everything else, there's + +complications +everywhere in Unix, + +but I'll simplify it for now. + +A process has one +uid, and there's + +also a list of group +IDs that a process has. + +For historical +reasons, the group IDs + +are split into one and +then a list of others. + +Roughly, a process +can then exercise + +the privileges represented +by all of these identifiers. + +So if there's something +accessible to this userid + +a process can do stuff with it. + +That's how we think about +what privileges a process + +has, so now let's talk +about files, directories + +and other kinds of objects. + +So what happens with files, +or how do Unix permissions + +for files work? + +Well, in Unix, every +file has-- actually, + +maybe a better way to +start is to think of what + +operations do we care about? + +For files, things are +relatively straightforward. + +For files, you probably +care about read, write, + +maybe things like +execute as well, + +change permissions, maybe change +other security properties. + +AUDIENCE: Unlink. + +PROFESSOR: Unlink. + +Well, so is unlink a +property of a file itself + +or is it a directory thing? + +Actually a little not clear. + +At least, the way Unix +thinks of deleting a file, + +is that it's really a +directory kind of thing, + +because in Unix you can have-- +a file is really an inode, + +and in Unix you could have +multiple hard links to an inode + +and when you unlink a particular +name of a Unix file, what + +you're really doing is killing +one of the names for that file, + +but it might have other +names, other links to it. + +So what actually +matters is whether you + +are allowed to modify the +directory pointing at the file + +and not do something to +the file's inode itself. + +So typically, unlink +and link and rename, + +create, are operations +that we sort of think + +of as being associated +with the directory, + +although, they are actually +related, so "create" affects + +both the directory and +a new file as well, + +so we have to figure out +what are the rules there. + +OK, so what are the rules? + +In order to help us decide +when someone can read or write + +a file, we're going to stick +some permission stuff, or bits, + +in the file inode. + +In Unix, every inode, +meaning something + +that ends up being +the file or directory, + +has a couple of interesting +fields for security purposes. + +There's a userid and a group +that we say owns the file + +or owns the directory. + +So you might have all the +files in your home directory + +are probably owned by +your on your Unix system. + +There's also a set of +permission bits in Unix + +that you can sort of think +of as a bit of a matrix, + +so we want to have-- well +in Unix there's basically + +the basic design, +there's read, write + +and x for execute permissions. + +We can specify these permissions +for different entities, + +and in Unix these are +specified for the owner, + +meaning for the +uid of the inode, + +for the group that owns the +file, this gid and everyone + +else, other. + +You can sort of fill in +this 3 by 3 binary matrix. + +You might say, well, I can read +and write and maybe not execute + +this file. + +People in that gid might +be able to read but not + +write this file, and +everyone else-- or maybe they + +can also read it-- but not +do anything else with it. + +So this is the way Unix +stores permissions. + +There's some baroque way +of encoding these things + +that you'll see often that's +probably worth mentioning. + +In Unix, you encode this +matrix as an octal number, + +so you treat each row here as +a base 8 number, so r is bit 4, + +w is bit 2, x is bit +1, so this ends up + +being 6, 4, 4, so you'll +sort of say-- well, + +you'll often see this +notation, even in this paper. + +You'll say, well, this +file has permission 6, 4, + +4, meaning the owner can +read and write this file, + +the group owner can read it and +everyone else can also read it. + +Does that make sense? + +This tells us when you can +read, write and execute a file. + +What about changing +permissions on a file? + +This is not entirely a fair +question, but what do you + +guys think? + +How should we +decide when someone + +should be able to change +these permissions, + +because that's also something +to try to do, at least. + +Any guesses? + +Yeah. + +AUDIENCE: If they +have [INAUDIBLE]. + +PROFESSOR: Maybe, yeah. + +It depends. + +On the other hand, you might +create a overwritable file + +that I just want to share +with anyone, that you + +can read and write +and modify my file, + +but then this also means +that you'll all of a sudden + +be able to change +permissions, so you'll + +be able to take my file and +make it not overwritable + +or take it over. + +That seems not +necessarily great, so + +in Unix, what are +the designers chose, + +is that, well, if +you own the file, + +meaning if you have the +same uid as the file, + +then you can change permissions. + +Otherwise, you cannot. + +So even if you're in the gid +here and that group has all + +the permissions in the file, +you still cannot really change + +the permissions on that file. + +You can just read, +write, execute, + +whatever to get that solved. + +Make sense? + +Then directories +actually in Unix + +follow a pretty similar story. + +So unlinking and linking +entries in a directory + +means having write +permission on that directory, + +and if you want +to rename a file, + +then you probably need +to have write permissions + +on both the directory +you're moving it from + +and the directory +you're moving it to. + +A fairly natural plan. + +There are some corner cases with +hard links, as it turns out. + +Lecture notes have some +details but, more or less, + +that's how it works. + +There's actually another +interesting operation + +on directory that you might +care about, which is lookup. + +So you might want to just +look up a file in a directory. + +And Unix sort of encodes +execute permissions + +as implementing lookup +for directories, + +so what it means to have execute +permissions on a directory + +is just being able to look +up a certain name there. + +Might be that you don't actually +have to execute permission + +on a directory so you +can look up a name, + +but you don't don't +have read permission, + +so you can't list the +contents of a directory. + +It turns out to be +useful in some situations + +if you really want to +restrict what someone + +could do with those +files, or sort of hide + +the files from a user. + +Let's just work +through an example. + +What happens on Unix if I +call open("/etc/password")? + +What checks is the kernel +going to perform on my behalf + +when I issue this system call? + +AUDIENCE: It checks whether +you have execute permissions + +on etc? + +PROFESSOR: Yeah, that +will happen somewhere. + +I need to execute on etc. + +AUDIENCE: And then +execute on slash. + +PROFESSOR: Yes, actually, I need +to look up what does /etc even + +point to? + +So if I don't have look +up permissions on root, + +then that's not going to work. + +AUDIENCE: Then you need +read on /etc/password. + +PROFESSOR: Make sense, roughly? + +Here's a small puzzle. + +Suppose that MIT sets up a group +for all the people associated + +with 6.858 and another group +in the Unix sets of gids + +for all the TAs at MIT, but they +don't have a group four 6.858 + +TAs for some silly reason. + +Could I create a file that's +only accessible to 6.858 TAs? + +If I have a 6.858 group, +or some gid, and a TAs gid. + +So there's only one gid +that I can stick in a file. + +Any guesses? + +AUDIENCE: Well, you couldn't +anyway because you might + +have TAs that and not 858 TAs. + +PROFESSOR: That's true, yeah. + +Suppose they want to-- +you're right, yeah, + +so there are students in 858 +that are TAs of other classes, + +so that's maybe not great. + +But, still, lets try to +do intersections somehow. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yes, so you +can actually play tricks + +with this mechanism. + +It's not perfect, +but you can sort of + +use it to encode more +interesting things. + +You could actually do something +like create /foo/bar/grades + +file, and what I'll do is +I'll actually make foo owned + +by-- or set the gid to 6.858 +and only make it executable + +for the group. + +So unless you're in this group, +you can't even look things up + +in /foo, and then I could +set the permissions on bar + +so the gid is for TAs and +then it's executable for group + +as well and not others. + +So unless you can actually +traverse this path, + +you can't get to +this grades file. + +It's kind of, you know, +a cute hack, if you will, + +but these kinds of +tricks are things + +you end up doing with whatever +the base primitives are, + +the isolation mechanism +provides to you. + +And even OKWS plays all these +tricks as well in their design. + +Make sense? + +Questions? + +Yeah. + +AUDIENCE: If, like, the +permissions on the grades + +file itself, were let's +say-- the QID was 6.858, + +could a TA, like, link it +to some other directory + +and allow anybody in +6.858 to access it? + +PROFESSOR: Yeah, +potentially, right? + +So you might worry about +other things like leakage now, + +so Unix in general +doesn't try to enforce + +these kinds of transitive +security properties, + +meaning that once a process +has access to some data, + +or has some privileges, +it can basically delegate + +those privileges +to anyone it wants. + +There are other kinds of systems +called mandatory access control + +systems. + +We'll perhaps talk +about them later, + +but those try to +actually enforce + +this transitive property that, +if I give it to you, then + +you can't give to other people. + +You're basically stuck. + +It sort of taints you and +you can't go anywhere else. + +In Unix, this is +generally not the case, + +and a TA probably could not +hard link this file because + +of another silly rule that Unix +enforces for hard links, which + +is that only the owner +of a file can hard + +link it somewhere else. + +And this is partly +because of the way + +Unix does quotas, +because in Unix quotas + +are by who owns the file. + +So if you create +some giant file, + +I can hard link a copy +over to my directory, + +then you maybe delete the +file, but I still have it, + +and the file system thinks, +yep, that's the owner, + +but you can't even +delete it, because I + +have the reference to it. + +So that would be a bit of +an unfortunate combination + +of Unix mechanisms there. + +But in general, you should +worry about such things + +like transitivity, +like could someone-- + +or maybe a better problem +is, maybe someone was a TA + +and then we remove him. + +But maybe they can still sort +of stash away a reference + +somewhere, so this is maybe +not a perfect solution + +for this problem +for many reasons, + +including the fact that +there's non-858 TAs taking 858. + +Are there questions? + +OK, so that's files and +directories in Unix, + +so how security works for them. + +A closely related thing in +Unix are file descriptors. + +The file descriptors are used +fairly pretty widely in OKWS + +and what a file descriptor +represents in Unix + +is basically an open file. + +So in Unix in +particular, it turns out + +that the security checks on +opening a file are performed-- + +or security checks +for accessing a file-- + +are performed when you open +the file in the first place. + +And from there on, you +have basically a handle + +on the file, where +anyone with that handle + +can now perform +operations on that file. + +So the rules for basically +accessing a file descriptor + +are, if you have an open file +descriptor in your process, + +then you can access it. + +And security checks +don't apply in the sense + +that, to get that +file descriptor, + +you could have just opened +the file, in which case + +these regular checks +would have applied, + +or some other process +might have passed the file + +descriptor to you, so you +can pass file descriptors + +by inheriting from a +parent, so a parent + +can pass a file descriptor +to a child process + +or you can pass file descriptors +through sockets in Unix, + +but however you manage +to get a file descriptor, + +you can read and write the +file descriptor all you want, + +because the security +checks have already + +been done when the file +descriptor was initially + +created. + +So that's actually +a nice way in Unix + +to give someone privileges +that they don't otherwise have. + +So in OKWS there's probably +many components that + +need to act as a +certain socket or file, + +or whatever you +have it, and one way + +to implement this without +giving them direct access + +to read and write the +file in the file system, + +is to have someone else open the +file, create a file descriptor + +and then pass it to +this extra component. + +This way, you can +really precisely say, + +that's the only file +descriptor you'll ever have. + +And there's nothing +else they can + +try to do in the file +system that might be funny. + +Make sense? + +So in fact, it has fairly +simple rules, I guess. + +If you have a file +descriptor, you + +can do whatever +you want with It. + +OK, so what about processes? + +What are the rules there? + +I guess, what can +you do to a process? + +In Unix it's fairly simple. + +You could, I guess, +create a process. + +You could kill it. + +You could debug it. + +There's this mechanism +called ptrace in Unix, + +and probably a couple +of other things. + +And the rules are +relatively straightforward. + +So you can always create +a process, more or less, + +except that the child +process is going + +to get the same userid as +you, so you can't create + +a process with some other userid +by default. So you can't say, + +well, I'd like to +create a process running + +as "web," one of my TAs. + +The operating system kernel +will not let you do that. + +If you want to kill a +process, you basically + +have to have the same userid +as that process as well. + +It's kind of nice. + +All the things with +a single userid + +are isolated from things +with other userids. + +And more or less, the same +rule applies to ptrace as well. + +The process with the same +uid can debug processes + +with the same uid. + +As with everything, it turns out +race conditions show up often + +and can cause +problems, but there + +have been actually +some interesting bugs + +in the ptrace mechanism in Linux +where, if you debug a process + +and then it switches and gets +more privileges, then maybe you + +could somehow trick the +kernel into letting you retain + +this debug privilege +on this process, + +even after it becomes +more privileged. + +Then you can monkey with +its memory and take it over. + +But at least the basic +design that you probably + +want to enforce is roughly +a process with the same uid + +can act on each +other, otherwise not. + +And I guess, OK, so what else +did we have on this list? + +Processes. + +Memory sort of goes +along with the process. + +So, unless you're +in that process + +you can't access +the process memory. + +Virtual memory nicely enforces +this isolation for us. + +Except this debug +mechanism lets you + +poke in another +process's memory if you + +happen to have the same userid. + +And then, I guess the +other remaining thing + +for us is networking, +and networking in Unix + +doesn't really fall +in the same model, + +partly because of +it came about later. + +You know, the Unix operating +system was designed first + +and then networking came +along and became popular. + +It has a slightly +different set of rules. + +So I guess the operations +we really care about + +on the network is, presumably, +connecting somewhere or maybe + +listening actually for +connections as well. + +So you might want to +connect to some web server + +or you might want to run a +web server yourself and listen + +on a particular port. + +Maybe you want to actually +read data from a connection, + +or read/write data on +some existing connection, + +or you want to send the +raw packets or receive. + +So in Unix the network +stuff basically has + +no relation to userids, +the first approximation. + +The rule is anyone +can always connect + +to any machine or +any IP address, + +can always open a connection. + +If you want to listen +on a port, that's + +where one difference +shows up, which + +is that most users +are prohibited + +from listening on ports +below a magic value of 1024. + +Basically, if you listen and +the port is less than 1024, + +then you have to be +a special user called + +"super user" with a uid of 0. + +And in general, Unix has this +notion of an administrator, + +or super user, which is +represented by having uid of 0, + +which can bypass pretty +much all these checks, + +so if you're running as root, +then none of this applies. + +You can read/write files, +you can change permissions + +on anyone's files and +the operating system + +will let you do that +because it thinks you + +should have all the privileges. + +And one thing you +really need it for + +is for listening on +ports below 1024. + +Any idea why this +weird restriction? + +Who cares about +your port number? + +AUDIENCE: Would they define +specific port numbers + +to be certain things, +like HTTP is like 80. + +PROFESSOR: Yeah, it's +like HTTP is 80 here. + +On the other hand, other +services might be above 1024, + +so why this restriction? + +Why is this useful? + +Seems to complicate my +life more, after you. + +AUDIENCE: Since you don't want +random searches just listening + +on your HTTP. + +PROFESSOR: Yes. + +I think the reason +for this is that it + +used to be the case, +at least, that you'd + +have these machines where +there's lots of things running, + +there's users logging in, +there's services running, + +and you want to make sure +that some random user + +logging into our machine doesn't +all of sudden take over the web + +server running on that machine, +because people connecting + +from outside don't really know +who is running on that port. + +They just connect to port 80. + +And if I want to log +into that machine + +and start my own +web server, then I + +would just take over all the web +server traffic to that machine. + +That is probably +not a great plan. + +So this is one way that the +networking subsystem in Unix + +prevents arbitrary +users from impersonating + +what are called well-known +services running + +on these low port numbers. + +So that's sort of one +rationale for this restriction. + +And then, in terms of +reading and writing data + +on a connection, well, if +you have a file descriptor + +for a particular socket, then +Unix lets you read and write + +any data you want on that +TCP or uTP connection. + +And then for +sending raw packets, + +Unix is actually pretty +paranoid about this, + +so it actually will not +let you send arbitrary + +packets over the network. + +It has to be in the context +of a particular connection, + +except if you're +root, of course, + +then you can do +whatever you want. + +That make sense? + +Somewhat? + +Any other questions about +all this Unix machinery? + +OK, so one interesting +question we could try to ask, + +is where do these +userids come from? + +So, when we talk about +processes having a userid + +or having a groupid, and if +you run PS on your machine, + +you probably see lots of +processes with different uid + +values. + +Where do these guys come from? + +We need some sort of +a mechanism really + +to bootstrap all of +these userid values, + +and the way it works in Unix, +at least at the mechanism level, + +is that there's several +system calls for doing this. + +So initially to bootstrap +these uid values, + +there's a system called setuid() +that you that you can pass some + +sort of a uid number to, +and it'll set the userid + +of the current +process to this value. + +This is actually a dangerous +operation, of course, + +so in sort of Unix tradition, +you can only do this + +if you're uid is equal to 0. + +Well, must have. + +So if you are this +root user with uid 0, + +then you can call setuid() and +switch your user to anything + +else. + +There's a couple +other similar system + +calls for initializing the gids +associated with the process. + +It's setgid and setgroups. + +So these system +calls together let + +you configure the privileges +that a process has. + +So typically, when you go +and log into a Unix machine, + +the way that your processes +get the right privileges, + +is that you're +initially actually + +not talking to a process +running as your uid, + +partly because the system +doesn't know who you are yet. + +Instead, what you +initially talk to in Unix + +is some sort of a login +process, so maybe SSH + +runs a process for anyone +that connects to it + +and tries to +authenticate the user. + +So this login process runs with +uid=0 as root and then when + +the supply username +and password, + +it's actually going to check +it against its own database + +of accounts and, +typically in Unix, + +this get stored in two +files, /etc/password, which, + +for historical reasons, no +longer stores the password. + +And there's another +file, /etc/shadow, + +which does store the password, +but in /etc/password, + +there is actually a table +mapping every username + +in the system to +these integer values. + +So your username gets mapped +to a particular integer number + +in this /etc/password file, and +then login will check whether + +your password is correct, +according to this file, + +and if it is, it'll find your +integer uid and then call + +setuid on your uid value +and then execute your shell. + +Whatever, (den/sh) And now +you can actually interact with + +the shell, but it's running as +your uid so you cannot do any + +arbitrary damage +to this machine. + +Question? + +AUDIENCE: Is it possible to +start a new process with uid 0 + +if you have some non-0 uid? + +For example, if you +want [INAUDIBLE]. + +PROFESSOR: Yeah, so this sort of +lets you go down, if you will, + +so with your root, you +can restrict yourself down + +to a different uid, but +the rule we set so far + +is you can only create a process +with the same uid as yourself. + +But, of course, you want +to elevate your privileges + +for various reasons. + +You want to, I don't know, +install a package now + +and you need root privileges. + +So, Unix has +basically two ways you + +could think about doing this. + +One way we already +mentioned, this file + +descriptor passing thing. + +So if you really want to +elevate your privileges, + +maybe you can talk +to some helper, + +and the helper is +running as root. + +You can ask it, hey, can +you open this file for me? + +And maybe you like define +some new interface, + +and that helper opens the +file and gives you back + +the file descriptor +through fd passing. + +That's one way you could +elevate your privileges, + +but it's kind of awkward, +because what you really + +want in some cases is a process +running with more privileges. + +So in order to do this, Unix +has this sort of clever, + +sort of problematic mechanism +called setuid binaries. + +So setuid binaries are just +regular executables in a Unix + +file system, except +that when you run them, + +when you sort of co-exec on a +setuid binary-- one example is, + +for example, is /bin/su on +most machines, or sudo as well. + +There's a bunch of setuid +binaries on a typical Unix + +system. + +The difference is that when you +execute one of these binaries, + +it actually switches the +userid of the process + +to the owner of this binary. + +It's a little bit of a weird +mechanism when you first + +see it. + +Typically the way it is used +is that this binary probably + +has an owner uid of +0, because you really + +want to regain lots of +privileges-- you want to regain + +root privileges-- so you +can run this su command, + +and the kernel, when +you exec this binary, + +will switch the uid +of the process to 0, + +so this program will now +do some privileged stuff. + +That make sense? + +AUDIENCE: If you +have uid 0 and you + +change the uid of all +of those setuid binaries + +to something non-0 and then +you could start [INAUDIBLE]. + +PROFESSOR: Well, many +processes will not + +be able to regain +privileges later. + +You might be kind of stuck. + +It'll still boot probably, +but maybe some things + +will not work. + +This mechanism is +not tied to uid 0. + +In fact, "I" as a user on a Unix +system can create any binary. + +I can build some +program, compile it, + +and I can set this setuid +bit on that program itself. + +It's owned by me, +the user, my userid. + +And what this means is, +anyone executing my program + +will run that code +with my userid. + +Is that problematic? + +Should I do this? + +AUDIENCE:So, if there was +a bug in your application + +and suddenly someone +could do anything as you, + +not just with the program +that's assigned to you. + +PROFESSOR: Right. + +But yes, so that's right. + +If my application +is buggy, or if it + +allows you to run +anything you want, + +well, I could copy +the system shell + +and make its setuid +to me, then anyone + +can run a shell +under my account. + +That would probably not +be a best plan of action. + +But a system mechanism, +well, this is not necessarily + +problematic, because the only +person that can set the setuid + +bit on a binary is +the owner of the file, + +and owner of the file +has that uid privilege, + +so I can basically give away +my account to other people if I + +want, but someone else cannot +create a setuid binary with + +my userid. + +That make sense? + +And the setuid bit +is sort of stored + +alongside these permission bits. + +So somewhere there +is also a setuid bit + +in every inode that says whether +this executable or this program + +should be switched to the +owner's uid on execution. + +Does that make sense as sort +of a privilege estimation + +mechanism? + +It turns out that this is +a very tricky mechanism + +to use correctly. + +So the kernel +implements it correctly. + +It's actually a fairly +easy thing to do. + +It's just one check. + +If there is [INAUDIBLE], +switch the uid. + +Easy enough. + +But using it safely turns out +to be very tricky because, + +as was just pointed out, if +this program has bugs in it + +or does something +unexpected, then + +you might be able to do +arbitrary things uid 0 + +or whatever the other uid is. + +And it turns out in Unix, the +way you execute a program, + +you inherit a lot of stuff +from your parent process. + +For example, you can pass +environment variables + +to the setuid binaries, and +it used to be the case that-- + +well, in Unix, you can specify +what shared library should be + +used for a process by setting +an environment variable, + +and it used to be that the +setuid binaries weren't careful + +about filtering out these +environment variables, + +so you could run +bin/su, but say, well, + +use my shared library +for things like printf(), + +so your printf() is going to +run when bin/su prints something + +out, and you can get it to run +a shell instead of printing + +stuff. + +So there's many +other subtle things + +that you have to get right +in terms of this program + +not trusting the user +input, and this is actually + +quite different +from how you think + +of writing most Unix programs. + +You generally do trust +the user input a lot, + +so for this reason, +the setuid mechanism + +hasn't been the most +secure part, in some sense, + +of the overall Unix system. + +All right. + +Any questions about this stuff? + +Yeah. + +AUDIENCE: Does setuid +apply to groups as well, + +or just the user? + +PROFESSOR: There is actually +a symmetric setgid bit + +you could set. + +Why not. + +And you could-- well, the +same thing happens, right? + +If the file has a particular +gid and that setgid bit + +is set when you run the +program, you get that group. + +It's not used a lot, but +it is useful in cases + +where you want to give +very specific privileges. + +So here, like bin/su probably +needs a lot of privileges, + +but it might be that +there's some program that + +needs a little bit +of extra privileges, + +like maybe to write something +to a special log file. + +So you probably want +to give it some group + +and make that log file +writable by that group. + +So even if the program is +buggy, which is likely the case, + +then, well, you lose +that group, sort of, + +privileges but not much else. + +It is sort of useful +as a mechanism, + +but it doesn't show up often, +because it's-- I don't why. + +People should use root more. + +Yeah. + +AUDIENCE: What are the +restrictions on who + +can change the [INAUDIBLE]? + +AUDIENCE: Yes. + +Different Unix implementations +have slightly different checks + +for this. + +The general rule of thumb +is, only root can change + +the owner of a file, +because you don't + +want to create files +owned by someone else, + +and you don't want to take +over other people's files, + +of course, either. + +So, in general, if you're +a particular non-0 uid, + +then you're stuck. + +You can't change +owner of any file. + +If you're a root, you can +change it to anything you want. + +There are some complications +if you're a setuid binary + +and you switch from +one uid to another-- + +it's a little bit tricky-- +but for the most part + +you basically can't +change the owner of a file + +unless you're a root. + +Make sense? + +Other questions +about this machinery? + +It is, admittedly, a +slightly baroque system. + +You could probably imagine +lots of ways in which you could + +simplify this but, in fact, +most successful systems sort of + +look like this as +they evolve over time. + +As it turns out, you +can make some good use + +of these sandboxing mechanisms. + +These are just sort of the basic +Unix primitives that show up + +in pretty much every +Unix-like operating systems, + +so Mac OS X has this, Linux +has this, FreeBSD has this, + +Solaris-- if anyone's +still runs this, et cetera. + +But in every one of these, there +is actually more sophisticated + +mechanisms that you +might use, so Linux + +has something called set COMP +for sandboxing processes, + +Mac OS X has its own +thing called Seatbelt, + +and there's all +kinds of extensions. + +We'll at one extension actually +next week, just to see, + +but this is just to get you +familiar with the basics + +that every Unix system has. + +So one sort of last +bit of machinery + +we want to look at +before diving into OKWS, + +is how do you deal +with setuid binaries? + +How do you protect yourself +from these security holes, + +if you will. + +So the problem is that +inevitably you'll have some + +setuid binaries in your +system like /bin/su, or sudo, + +or what have you, and there's +probably bugs in these + +programs, so if someone can +execute the setuid binary, + +then that process +might get root access, + +so you don't want to do that-- +or don't want to allow that. + +The mechanism in +Unix that is often + +used to prevent a +potentially malicious process + +from exploiting +setuid binaries is + +to use the file system +namespace to modify it, + +using the chroot system call. + +OKWS uses this +pretty extensively. + +So in Unix, what you can +do is you can call chroot + +on a particular directory. + +So maybe you can chroot("/foo") +and there's actually two + +explanations I want to +give to what chroot does. + +The first one is just intuitive. + +What it does is it means +that after you run chroot, + +the root directory or slash +basically is equal to what /foo + +used to be before +you called chroot. + +So it kind restricts your +namespace down /foo so it looks + +like that's all +the stuff you have. + +So if you have a file that +used to be called /foo/x, + +after calling chroot, you +can get at that file by just + +opening /x. + +So just restrict your namespace +down to a subdirectory. + +So this is the +intuitive version. + +Of course, in +security, what matters + +is not the intuitive version, +but what is the kernel exactly + +doing with this system call? + +What the kernel does is +basically two things. + +So when you call chroot +a particular directory, + +it does two things. + +One, it changes +what slash means, + +so whenever you access-- +whenever you start a path + +name with slash, the kernel will +now plug in whatever the file + +you gave to chroot. + +It's roughly the /foo file +from before you called chroot. + +The other thing the kernel does, +is it tries to prevent you from + +escaping out of your / by doing +/../ because you could imagine + +in Unix, I could ask for, you +know, give me /../etcpassword. + +So if I just prepended /foo, +then this would not be good, + +because I can just sort of +walk out of /foo and go get + +/etc/password. + +So the other thing +the Unix kernel does, + +when you call chroot, is +for that particular process, + +it changes how it evaluates +/../ in this directory, + +so it basically changes /../ +in /foo to point to itself, + +so it doesn't let you do +this kind of escaping, + +and this change only applies to +this process and not everyone + +else. + +Does that roughly make sense? + +So do you guys have +any ideas about how + +you could escape a chroot +environment because of the way + +it's implemented? + +Yeah. + +AUDIENCE: So if +you're [INAUDIBLE], + +you can make a directory and +then bring that directory, + +and then go back to your +directory and [INAUDIBLE]. + +PROFESSOR: Yeah. + +So, the interesting +thing-- so the kernel + +only keeps track of +one chroot directory. + +And I'll explain sort of the +answer that I gave in a second. + +So what you could do is, +maybe your chroot'd into /foo. + +You're sort of stuck. + +You want to get +at /etc/password, + +but how do you do it? + +Well, what you could +do is you can actually + +open the root directory now. + +That will give you a file +descriptor for effectively what + +is /foo. + +Then you could +call chroot again. + +Maybe you can chroot into /bar. + +So now the kernel changes plan. + +Root is no longer /foo but +it's /foo/bar and this /../ + +redirection only +applies to /foo/bar/.. + +But know that you still have +the file descriptor for /foo. + +So now what you could do is +you could change directories + +into that file descriptor, +fchdir(fd) from this open call, + +and now you chdir(..) And at +this point, you were in /foo, + +you go to /../ from foo. + +It's no longer looped +back to /foo itself, + +because you now have a different +route and now you can escape, + +so this is perhaps a good +illustration for why the exact + +mechanism matters a lot. + +It's not, sort of, the intuitive +explanation that matters. + +And partly as a result, +in Unix only the root user + +can invoke chroot, +because otherwise chroot + +would be fairly +pointless, in some ways. + +So in Unix, you basically +have to have uid 0 in order + +to chroot a process. + +It's a little bit of a +disappointment in some ways, + +because if you wanted to +build a really privileged + +separated system +where everyone had + +just the minimum set of +privileges necessary, + +you would probably +need to use chroot, + +you would need to create +new userids, et cetera, + +but in order to do +that in Unix, you + +have to have a process +running as root, + +which has lots of privileges. + +So it's a little bit of +an unfortunate trade off, + +but it's probably one you could +make some reasonable design + +decisions on. + +Question. + +AUDIENCE: If in the [INAUDIBLE] +directory, so [INAUDIBLE] + +to a file that's in [INAUDIBLE]. + +PROFESSOR: No, actually, +unless you do this trick, + +the kernel evaluates symlinks in +your root context, if you will. + +So if you have a symlink +to /etc/password, + +it'll evaluate as if it is +similar to /foo/etc/password. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: A hard link +would not be protected. + +Yeah. + +So one way to set up a chroot +environment without creating + +lots of copies of +files is to, in fact, + +create a directory and hard +link all these things back. + +That's fairly cheap +and then use it. + +AUDIENCE: If a program gradually +generates inodes and, like, + +actually not to give you +the file descriptor-- + +PROFESSOR: Right. + +So it's like a huge +important detail here, is you + +can only access a file by +path name, not by saying, + +I want to open inode number 23. + +This might be some weird file +out there outside of my chroot. + +So in Unix you cannot open an +inode by inode number unless + +you're root, of course. + +Other questions? + +All right. + +So I think we have sort +of enough machinery + +now to see what these +OKWS guys do, and probably + +a useful, quick +introduction is by contrast + +to what everyone else does. + +So what is it that everyone else +is doing that the OKWS guys are + +afraid of? + +So the alternative design +that pretty much every web + +server follows, is like the +unprivileged separating picture + +above there, so you might +have web browsers out there + +on the internet, these guys are +going to connect to your server + +and, inside of your server, +you're basically going to have, + +basically one process, httpd, +well, Apache, let's say. + +And this is one process running +as a single userid called www + +in /etc/password. + +It takes all your +connections, does everything + +with your process, including +doing SSL processing maybe, + +including running +application code and PHP, + +et cetera, all part +of the same process. + +And if need be, this process +will typically connect back + +to some database +server, maybe MySQL + +could be running on +the same machine, + +could be running elsewhere. + +And this MySQL process +actually writes data to disk. + +But to connect to this +MySQL, you probably + +have to provide a +username and password + +but, typically, the way +applications are written + +or, at least, not very security +conscious applications are + +written, is that there's a +single account on the MySQL + +server that the application +knows the username and password + +for, so you just connect +and you have access + +to all of your data. + +So it's super +convenient to write, + +because you just write +whatever code you want. + +You can access whatever data +in the database you want. + +There's no real +isolation, but it + +has security problems that +these guys worry about, + +namely if there's bugs in +Apache, maybe in SSL, maybe + +in the application code +or in the PHP interpreter, + +then inevitably the answer +is, if there's a bug + +and you can exploit +it, then, yep, + +you get the whole +application data contents. + +Does that make sense? + +You had some questions before. + +No? + +AUDIENCE: Oh. + +Uh, yeah, it's fine. + +Thank you. + +PROFESSOR: All right. + +No worries. + +OK. + +So this is sort of state of +art what these guys really + +wanted to protect against. + +And in their case, I guess they +worried a lot because they were + +thinking, well, they're building +basically a dating website, + +okcupid.com and +they really wanted + +to make sure their, +I guess reputation, + +wouldn't be damaged by +these data disclosures. + +So in fact, I +guess-- from talking + +to the guy that +wrote this paper, + +it seems like they actually +haven't been compromised-- + +or, at least, not +that they know of-- + +or their data wasn't leaked. + +And it seems to be partly +as a result of running OKWS, + +partly as a result of maybe more +proactive monitoring that they + +do, et cetera, but it seems +to have worked out reasonably + +well for them, to +some extent, I guess, + +because of this +architecture that we have. + +OK. + +So the reason that +people, I guess, + +don't break up their +applications into smaller + +components is +because it actually + +takes quite a bit of effort to +separate out all their pieces + +of code and define clean +interfaces between them, + +decide which data +every component + +should have access to, or +if you decide to implement + +new feature, you're +going to have + +to change the data that every +component has access to give it + +new privileges or take +some away, et cetera. + +So it's a bit of some overhead +for separating application, + +but in their case I +guess they decided + +it was worth the effort. + +Let's try to understand how +their web server design works, + +and perhaps one way to do +it is to trace out roughly + +how http request gets +processed by an OKWS server. + +So, similarly to +that picture, there's + +probably a web browser +out there somewhere + +that wants to go to +okcupid.com, and in their design + +they sort of imagined +they're going + +to have a bunch of machines, +but we'll just look at probably + +just one front-end +machine that is + +going to be running OKWS +here and then another machine + +behind the scenes +that's going to be + +storing the database somewhere. + +And I sort of imagine they're +probably also using MySQL, + +because it's a nice piece +of software in many ways. + +They don't want to re-implement +this functionality, + +but they want to really +protect this data, so + +that it's really hard +to get to the raw disk + +or the raw database. + +So how does a +request work, or how + +does a request get +handled by OKWS? + +Well, the request +first comes in and gets + +handled by this +process they call + +okd for the OKWS dispatcher. + +So those guys look at what +the request is asking for + +and then actually +does a couple things. + +So first it might need +to log the request, + +so it forwards it to this +component called oklogd, + +then it might need to +generate some templates, + +maybe before the +request came in even. + +And this is handled by +another component called pubd. + +And finally, there's +a particular service + +that this request +is being sent to, + +so okd has a table of a bunch +of services it supports. + +This request is presumably +going to one of them, + +and, as a result, okd +will forward this request + +to a particular service process. + +And the job of the service +is to actually do something + +with this request, +like subscribe + +the guy to a newsletter +or to match him + +to whoever else is using +OkCupid, using the database. + +And in order to do this, +the service presumably + +might need to log some +information about the request + +as well by talking to +this oklogd component. + +And at the end of the day it's +got to talk to this database. + +So the way these +this guys actually + +implement talking +to the database + +is that, unlike that Apache +picture where you just + +talk to the database and +issue arbitrary SQL queries, + +these guys come up with this +notion of a database proxy that + +sits in front of +the MySQL database + +and accepts requests from the +service to do some queries, + +and I think that's most +of the picture for OKWS. + +There's another component +in this whole picture that + +sparks this whole mess, so +they have another component + +called okld, for the +ok launcher demon, + +and this guy is responsible for +starting all these processes + +on this front end +web server machine. + +Hopefully some of +these things actually + +look familiar, because +this is exactly + +the architecture of [INAUDIBLE] +for your lab assignment, + +so this is basically what +our design is all based on. + +It seems like a nice +design, actually. + +Well, we don't +have pubd or logd, + +but we have these two +guys and a service. + +No database proxy either. + +All right, so any +questions about OKWS? + +Yes. + +AUDIENCE: Dbproxy does +not accept SQL queries, + +it accepts some sort + +PROFESSOR: Yes. + +What does this +interface look like? + +They don't really describe +it in a lot of detail, + +but one thing I sort of imagine +you could do in this database + +proxy is basically +have this supply + +a bunch of arguments +for SQL query templates. + +So it might be +that this dbproxy, + +this one in particular, +maybe is for finding, + +I don't know, your +friends or something, + +so inside of the +dbproxy maybe there's + +a template query like select +ID from friends, where user-- I + +guess this is like +the ID of the friend, + +and this is the ID of the +person who is the friend of. + +The user equals, I don't +know, person D here, + +or something, or +person S here, right? + +And they sort of +sanitize this string, + +and I imagine this RPC +request here sort of looks + +like do query one, and the +argument is, I don't know, + +"Alice." + +I sort of imagine this +RPC interface looks + +like this, where the +application knows ahead of time + +that this database +proxy is willing to run + +three kinds of +queries on its behalf, + +and now I want to +run query number one + +and the argument is Alice. + +And that's sort of +the way I get access + +to any data in the database. + +Does this make sense? + +AUDIENCE: Could an external +user at the web browser level + +send the request like +that to the database + +or is that all internal? + +PROFESSOR: Well, yeah. + +So, how does this work? + +It's actually kind +of weird, that this + +is a separate machine, +because now it seems like, + +why don't just connect to +the database proxy yourself, + +or to the MySQL server, right? + +So what prevents +this in their design? + +AUDIENCE: Fire wall? + +PROFESSOR: Yeah, +probably at some level. + +They don't really describe +this in too much detail, + +but probably this is some +internal network, where there's + +like a switch here, +and this machine + +is connected to the +switch, this machine + +is connected to the +switch, but the switch + +is not reachable from +the outside world. + +It's like there is an +internet connection here + +and those guys are +some back-end network. + +Or maybe they're actually +on the same network, + +but there's a firewall here that +has rules that say, well, you + +can only connect to this +front-end machine on port 80. + +You cannot talk to +the back-end server. + +So that's one plan. + +I guess the other +plan they have in mind + +is that actually when you +connect to this database proxy, + +you have to supply this +20 byte token thing, + +and unless you supply +it, the dbproxy + +will reject your connection. + +So the rule is you open +the TCP connection, + +you send your 20 bytes. + +If they're not the +right 20 bytes, + +your connection gets +closed, and hopefully this + +is something that's relatively +easy for the database proxy + +to implement, so +that there's probably + +low probability of a bug in +that token checking logic that's + +right up front. + +And unless you +have the token, you + +will not be able to do +anything else of interest + +to the database server. + +That's, I think, their +sort of design goal here. + +Make sense? + +All right. + +So, let's try to +figure out, I guess, + +how these guys isolate +these different processes. + +So how do they make sure +that all these components + +don't trample on each other? + +What's the plan? + +AUDIENCE: Different roots +and different userids? + +PROFESSOR: Yeah, so pretty much +every one of these components + +runs as a difference uid, so +they have this whole table + +in the paper that describes, +for every component, + +where is it running +and what's the uid. + +So we can write this out, +so okd has its own uid, + +pubd has its own uid, the +logger has its own uid. + +okld runs as root, which +is kind of unfortunate, + +but may be all right. + +Then, there's a whole bunch of +dynamically assigned userids + +for every service. + +I sort of imagine +he has ID 51001. + +So this makes sure that +every service cannot poke + +at the processes +of other services, + +and they also use chroot +pretty extensively, + +so every one of these guys is +chroot-ed into some directory. + +They sort of initially +say, well, you + +should really chroot everyone +into a separate directory. + +As it turns out, +in that table, it + +turns out that okd +and all the services + +basically share a +chroot directory. + +It's kind of weird. + +Why do you guys think they +put okd and the services + +into a single chroot and not +give them their own chroots? + +Weird. + +Yeah. + +AUDIENCE: okd is not root. + +PROFESSOR: Well, yeah, +but like why don't they + +put pubd and oklogd and +everyone else in the same + +chroot as well? + +AUDIENCE: Okld [INAUDIBLE]. + +PROFESSOR: okld is +actually sitting out here + +in a separate chroot. + +This guy, this guy. + +Actually okld is not chroot. + +I'm sorry about that. + +These guys are chroot. + +Does it matter? + +AUDIENCE: I was thinking, +if the services have + +to share a lot of data, where's +the [INAUDIBLE] isolate them? + +PROFESSOR: Maybe. + +Actually, I think +what's going on + +is they have to share some +data, but none of this data + +actually lives in the file, +so they pass a lot of data + +through sockets from +okd to the services. + +But in fact, none of these +guys store anything of interest + +at all in the file system. + +So as a result, there's pretty +much nothing interesting + +in the chroot directory, so +I imagine the OKWS guys just + +decided, well, there's +probably some overhead + +to creating a +chroot, like you have + +to create a copy +of the directory, + +there is maybe some management +overhead for every chroot. + +Whereas, for this, there's +no real files here, + +so maybe that's all right. + +I mean, there's not +a clear, sort of, + +cut trade off here, or +not a clear-cut argument + +which way you should go, +but certainly prevents + +from setuid binaries. + +The reason that these guys are +probably in different chroots + +is because there is actually +some interesting stuff there. + +There's maybe the +templates here, + +maybe there's a log +file here, so you + +don't want these guys +accidentally reading + +the log file for some +reason, but there's + +no real mutable state +inside of the chroot shared + +by all okd and the services. + +AUDIENCE: Don't the services +have, like, two files + +or, I don't know, aspx files. + +PROFESSOR: Well, at least +the way they describe it + +in the paper, the service is +a single C++ compiled binary, + +so there's actually no extra +files, and there are templates, + +but those actually get passed +in through this weird mechanism, + +where pubd has the +templates in its directory, + +it renders them-- or sort +of pre-computes them-- + +sends them to okd and okd +gives the templates to all + +the services through RPC calls. + +So they sit in memory, +but they're actually not + +directly accessible +through the file system. + +It's a somewhat +paranoid design here. + +Can't even read the templates. + +So what's the point of having +all these components split up? + +So I guess let's talk +about maybe oklogd, + +so why do you have +a separate oklogd? + +Yeah. + +AUDIENCE: Because if +you had [INAUDIBLE], + +you could overwrite +logs, or truncate log. + +PROFESSOR: Yeah, +so we really want + +to make sure that if something +goes wrong, the log, at least, + +is intact. + +So there's a separate +log file that + +is only writable by this +uid, and all the log messages + +are sent as RPCs to +this log service, + +and even if everything else +gets compromised-- well, + +except for okld-- then +the log is still intact, + +because they talk about the +process of appending noise + +to this log. + +So what is this about? + +Does this matter? + +Should we worry +about this noise? + +Yeah. + +AUDIENCE: If somehow +you accidentally find + +a way to read the log +and you can't see what + +everyone else has been doing? + +PROFESSOR: No, I think this +noise thing they are actually + +worried about is that, +suppose you compromise + +a service or you compromise +pubd or something, + +you all of a sudden might +be able to write log + +messages to the log, +and you can actually + +write whatever you want +to the log at that point. + +So the only guarantee they claim +to provide is that, I guess, + +before the point of the +compromise, all the log entries + +are intact, and afterwards +there is sort of legitimate log + +entries interspersed +with whatever + +else the attacker wants to log. + +One actually cool thing about +having oklogd be a separate + +process instead of it just +being an append-only file, + +is that oklogd cannot add some +extra information to each log + +entry, because you could imagine +maybe the operating system + +supports an append-only file, +but then you don't actually + +know who wrote anything +to a file, when that was, + +whereas oklogd, +for every message, + +it can actually maybe time +stamp it and say, actually, + +I know this came from this +service, or this came from okd, + +so you actually get extra +information in that log file + +because it's a +separate service here. + +Make sense? + +So what's the point +of this okld guy? + +Why do we need this guy +to be running as root? + +I guess a couple reasons. + +AUDIENCE: If you want no +one else to run as root, + +then you need okld to +delegate who it is. + +PROFESSOR: Yes. + +So someone needs to set up +this whole uid chroot thing, + +and you need root for this +in Unix, so okld is it. + +That's one reason. + +Anything else? + +AUDIENCE: To define 80? + +PROFESSOR: Oh, yeah, yeah. + +This like whole listening +on a port business, + +you have to bind on port 80, so +okld does that as well for us. + +Anything else? + +AUDIENCE: Complete to +open the log file oklogd. + +You don't want to open oklogd +to have access to open the file. + +You want to open +it for [INAUDIBLE]. + +PROFESSOR: Maybe. + +Actually, yeah. + +I don't know. + +I forget this from +the source code + +whether they actually +do this or not. + +You could imagine absolutley-- + +AUDIENCE: I think they write +it in the paper as well. + +PROFESSOR: I see. + +So okld opens the log +file and passes it in? + +Could be. + +AUDIENCE: Because +otherwise an attacker + +that compromised oklogd would +be able to erase the entire log. + +PROFESSOR: That's right, yeah. + +So maybe you want to +open in append-only mode + +and then pass it +to oklogd and then + +you have more security +guarantees for the log. + +Yeah, that's +actually pretty cool. + +I missed that on the paper, +but makes a lot of sense, yeah. + +Any other things +okld is doing for us? + +I think that's basically it. + +These are the main +things that you + +can't do unless +you're root, and okld + +is sort of the component +that ends up having + +to do all these operations. + +So I guess we had +this homework question + +about what happens +if you leak this 20 + +byte database token thing. + +So what do you guys think? + +What's the damage? + +Should we leak these guys? + +Should we worry about it? + +Anything else? + +AUDIENCE: The +attacker can pretend + +to be that specific +service [INAUDIBLE]. + +PROFESSOR: That's right, yeah. + +So, you might be able to +now connect and issue, + +of course, all these +template queries. + +That actually seems fairly +straightforward, I guess, + +from this picture. + +You probably need to compromise +one of these components + +to be able to connect +to the database + +server in the first place. + +So I guess if you +have this token + +and you manage to compromise one +of these pieces in the picture, + +then you could run all +these queries as well. + +Make sense? + +Fairly straightforward stuff. + +OK, I guess let's look +at, could you do better? + +Could you do better +than this OKWS design? + +Except for make this +whole argument about, + +well, we might be able to do +even better, like allocating + +a separate unit uid +per user in this design + +instead of per service. + +But here, every service, like +newsletters or friend matching + +or account sign up +is a separate userid, + +but every OKWS user isn't really +represented by a Unix uid. + +There's not really userids, +they're service IDs. + +So, would it make sense to have +different uids for every OKWS + +customer? + +Is there a reason for that? + +Yeah. + +AUDIENCE: So at the moment, +if one user compromises + +the service, then they can get +access to all the other user's + +data for that same server. + +PROFESSOR: That's right, yeah. + +AUDIENCE: Whereas, if you +had a separate-- essentially + +a separate service +and a separate dbproxy + +for every user, +there's no way you + +could access anyone +else's data either. + +PROFESSOR: Right, but could it +be actually a stronger model? + +So especially +for-- well, I guess + +there's really two reasons why +I think the OKWS guys don't + +go to that extreme model. + +One of them is-- they make +a big deal in this paper-- + +is performance, right? + +So if you have, I +don't know, a couple + +million users on OkCupid, +then all of a sudden you + +have a couple of million +processes running here, + +or maybe a couple +million dbproxies, + +or maybe you can optimize +something on the dbproxy side, + +but here, yeah, you have +a couple million userids + +and either you have a lot of +processes running all the time + +or you're starting these +processes on demand. + +And starting a process +involves some nontrivial amount + +of overhead, so you +probably wouldn't + +be able to get as good +of performance numbers + +as these guys are able +to show with OKWS. + +There's a performance argument. + +Question. + +AUDIENCE: Yeah, I +was just reading + +in the paper that said the +performance of the system + +was better than others? + +PROFESSOR: Yeah. + +AUDIENCE: How come? + +PROFESSOR: Well, I think it's +partly because they fine tuned + +their design to their particular +workload and it's also they + +write their whole thing in C++. + +The alternative is you're +writing some stuff in PHP, + +then you're probably going +to win on that front. + +It's also the case +that they don't + +have nearly as many features +as, let's say, Apache has. + +Apache has a very +general purpose design, + +so it has lots of +processes running, + +it restarts them +every once in awhile. + +It actually has +every ttp connection + +tying up a process for the +duration of that connection. + +They do keep-alives. + +That also increases the +number of processes you + +have to run for their design. + +So all those things +just add up in terms + +of overhead for +Apache, because it + +wants to handle +anything possibly + +you could do with a web server. + +Whereas these guys, I +think, are very specific. + +We're just going to run these +services, very quick requests, + +and no even static file +serving, if they can help it. + +But I think there's actually +other web servers out there + +these days that probably can +match the performance of OKWS + +if you really wanted to. + +So, for example, Nginx is +a very optimized web server + +you can run these days. + +If you want fast application +performance on the server side, + +you probably want to keep a +long running process very much + +like the OKWS service +thing, and the fast cgi + +is a common mechanism, +or sort of protocol, + +that you could use +on the server side + +to implement this even in +Apache or Nginx as well. + +So I think many of +these performance ideas + +aren't exclusive to OKWS. + +You couldn't perform the +same performance tricks + +in other services as well. + +They just show that +better security + +doesn't preclude these tricks. + +You could still get +the performance. + +I guess for them, they were +just initially starting out + +with an Apache-like +design, where + +they were willing to pay the +price if it was easy to program + +and secure, but it just +wasn't secure, so they said, + +OK, well we'll do +this, and I don't + +think the performance +was as necessarily + +a big of a goal for them. + +I guess they wanted to-- +well, at the time they + +had some problems in terms +of performance as well, + +so I think they really +wanted good performance. + +Any other questions +about this stuff? + +OK. + +So I guess it was +saying, one reason + +why these guys don't want to +run a separate service per user + +is the fact that there's +performance overheads + +in doing that. + +The other reason is that +their full application model + +sort of hinges around a +service having to get access + +to every user's data, like +finding your friends on OkCupid + +or someone to go +out on a date with. + +And as a result, this +per user isolation model + +might not make a lot of sense, +because ultimately there + +has to be a service that you're +going to send a request to, + +and it's going to look +at everyone else's data + +to find your match. + +So that's probably, as a result, +not really amenable, like, + +even if you had user IDs or +some sort of per user isolation + +mechanism, you would +have to give that service + +access to every userid anyway. + +So for other services like +maybe Gmail or Dropbox, + +where it's much +more user focused + +and no sharing, then +a per user isolation + +might make more sense +in terms of the benefits + +you could get out of +it, because if there's + +a userid on the Dropbox server +for every Dropbox customer, + +then, well, there's a +process running for you + +and there's a process +running for someone else, + +and if you exploit +a bug, then you + +can't touch other people's data. + +But could be cool, I don't know. + +Dropbox probably doesn't do +this for performance reasons, + +but you could get +some security benefit. + +Whereas, for OKWS guys, and +even functionality-wise, + +they wouldn't be able +to take advantage + +as much of this model. + +So maybe for your +profile editing service, + +maybe that could +be run per user, + +but the matching thing +would still be shared. + +Make sense? + +All right. + +So let's look at whether +OKWS actually manages + +to improve security here. + +So when we do think of whether +a system is secure or not + +is to look at all the components +and see, well, first of all, + +what's the attack surface? + +Meaning, how would +you try to compromise + +that component, +or how hard is it, + +and second what's the damage? + +So let's go through this list. + +Let's start with okd, so +what's the attack surface? + +What kinds of things could +you use to attack it? + +[INAUDIBLE], like +all these requests + +coming from the browser. + +That seems pretty good. + +You can control it +probably in lots of ways, + +you can send lots +of strange input. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah, +so maybe there is-- + +this thing is written in C++, +so probably these guys were + +sloppy. + +I think this guy's +a good programmer, + +but if he was not very +careful somewhere, + +could be easily exploitable. + +So what's the damage? + +Suppose you find a buffer +overflow or some other bug + +in okd? + +How bad is this? + +Yeah. + +AUDIENCE: You can call basically +any service on that machine? + +PROFESSOR: Yeah, OK, so +you could call any service. + +Is that bad? + +How should we think of this? + +AUDIENCE: You can call it +whatever input you want. + +PROFESSOR: That's true, yeah. + +But you could probably have done +that even without compromising, + +because you can send any +http request you want, + +which is basically what these +service requests end up being. + +Maybe that's +actually not so bad. + +Yeah. + +AUDIENCE: Could it route all the +traffic for maybe OK website? + +PROFESSOR: Yes. + +That actually seems a +little more damaging, right? + +You can all of a sudden +take over the whole website + +and serve your pages +instead of sending + +a request to the services. + +You could redirect all +the people to match.com + +or whoever else you +want to, I don't know. + +I guess now they bought out +OkCupid but, before, who knows. + +OK, anything else? + +Could you leak data in any way? + +Yeah. + +AUDIENCE: Well, it +depends on, like if you + +use any authentication in okd. + +Instead of any SVC, +you could potentially + +just do unauthorized requests, +like in the database? + +PROFESSOR: Right. + +In their case, this guy just +parses and forwards the request + +on. + +AUDIENCE: Could it [INAUDIBLE]? + +PROFESSOR: Yeah. + +Not only can you +redirect it first, + +you could actually look for all +the subsequent requests, which + +probably includes passwords +of other users connecting + +to the site, and you +could save their passwords + +or modify their requests +or see what they're doing + +or fetch things on their behalf. + +That seems damaging potentially. + +That's probably +the biggest leak. + +If you compromise okd, you can +probably watch other requests + +and steal people's credential +passwords, steal their data + +as it flows by. + +Make sense? + +AUDIENCE: Could you do some sort +of denial of service with just + +with sending a whole-- + +PROFESSOR: Yeah, so you could +probably chew up the CPU + +or send lots of requests +to this, fill up database + +with lots of data, but +that you could probably + +do even by just sending lots +of requests in the first place. + +So now [INAUDIBLE] are somewhat +complicated-- well, different. + +Yeah. + +AUDIENCE: So, the goal +here is not to leak data-- + +PROFESSOR: Yeah. + +AUDIENCE: --from +different services. + +If you have access to +okd, presumably you + +could read the responses +that are being sent-- + +PROFESSOR: Yeah, exactly. + +So in fact, okd is has +to be pretty trustworthy, + +because the responses don't +go directly back through okd + +in the normal operation, because +you just pass off the fd, + +and the service directly +writes to the fd. + +But you could totally fake it +and create your own fd here. + +So if you compromise +this, you could basically + +watch all the traffic and +steal people's passwords there. + +AUDIENCE: But, the other way-- + +PROFESSOR: And the response is-- + +AUDIENCE: --to the output, which +means that essentially you get + +access-- + +PROFESSOR: That's right. + +Yeah, so you could-- +If okd was compromised + +and I happened to +log into that site, + +you could probably +look at my responses + +and you could probably +even take my password + +and send other requests +with my credentials + +and get data from there as well. + +Yeah. + +AUDIENCE:And then essentially +reconstruct the entire + +database. + +PROFESSOR: Exactly. + +Yeah, or at least +for users who were + +logged in at the time and +things you could reconstruct. + +This is pretty damaging, right? + +So this component is actually +a bit troublesome here. + +What happens if we +compromise, let's say, oklogd? + +How bad is that? + +Yeah. + +AUDIENCE: [INAUDIBLE] +pretty bad. + +PROFESSOR: Yeah, so there's +like all this confidential data + +in the log entries, then +that's probably not good, + +but otherwise you can't probably +access the database directly, + +right? + +Pubd, I guess you might +corrupt templates, or something + +like this, send out different +requests and responses, I mean. + +Yeah. + +AUDIENCE: So this +is about the logd. + +Presumably okdlogd doesn't +have access to read the log. + +It just needs-- + +PROFESSOR: Ah, yeah, yeah. + +Good point. + +Well, it depends on +how they do it, right? + +If they really have +this append-only file, + +then it might be that you +can't even read the log, so-- + +AUDIENCE: All you could +do is append garbage. + +PROFESSOR:That's right, yeah. + +So you could write +a lot of garbage, + +but if they were using the OS +to enforce the append-only log, + +and no reading, then +you might be actually + +in good shape for +the log contents. + +Yeah. + +AUDIENCE: Well, I guess +also, you can not append. + +So when a valid log comes in-- + +PROFESSOR: Right, so you could +probably block real entries, + +fill it up with garbage. + +You could also watch new entries +and at least compromise them. + +AUDIENCE: Or if you're +relying on a rate + +limit for number of logins. + +PROFESSOR: That's right, yeah. + +You could probably do that. + +OK. + +So what about the services? + +That's, I think, their +main attack factor, + +because-- actually, in most +of these systems, what you're + +really worried about is +the one-off components, + +because even in Apache, +the Apache code is probably + +pretty good. + +Like millions people +are running it, + +everyone's looking +for bugs in it. + +Probably [INAUDIBLE] not that +many bugs in Apache itself + +or, well, even in SSL, for all +the hoopla we've heard recently + +about [INAUDIBLE] and still +bugs probably not as bad + +as the application code that +you write for a particular site, + +because no one else +has reviewed that code. + +You just wrote it, +you haven't really + +tested it very thoroughly. + +That's probably where most of +the bugs in a complex system + +actually lie. + +So the service code is probably +the equivalent for OKWS. + +These components are +written by Max Krohn. + +He was careful to make sure +there's no buffer overflows. + +This component is written +by some web developer who + +wants to deploy the next +feature as fast as possible, + +so this is the part +where I think they really + +worry about bugs being sort +of exploitable and potentially + +damaging. + +But hopefully the damage here +is not too big, in the sense + +that you can only issue +whatever queries you are allowed + +to do by the database proxy. + +Make sense? + +So what about okld? + +This is a bit of +a sore thumb here. + +It's, like, running as root. + +How much should +we worry about it? + +Of course, the damage is +pretty big if we compromise it. + +You get access to everything +on the machine and all + +the database proxy tokens. + +How hard is it to +compromise okld? + +What signals-- what +could you poke it with? + +Does it take input? + +AUDIENCE: [INAUDIBLE] in +a very specific pattern. + +PROFESSOR: Yeah, so pretty +much the only input it takes + +is when a child exits and +it gets a notification + +that a child process +exited and then maybe it + +responds it, or not, +if it is rate limited. + +So if there's some +sort of erase condition + +or a bug with handling +exactly-- it's + +interesting-- lots of +exits at the same time, + +then maybe you could +trigger something bad, + +but even then it +seems hard to imagine + +injecting some sort of shell +code through the exit pattern. + +So it's probably a reasonable +thing to have to run as root, + +because it doesn't take +a whole lot of input. + +Make sense? + +Other questions? + +AUDIENCE: So presumably +a big concern + +would be if you managed to +somehow exploit the dbproxy. + +PROFESSOR: Uh-huh. + +AUDIENCE: If it turns out +that it doesn't, like, + +it provides an RPC +that's limited in scope, + +but if there is some input you +can give that, that turns out + +to run in different +query than it + +was expecting to run, +presumably that could + +be a big [INAUDIBLE]. + +PROFESSOR: That could +be a bit of a problem. + +So what's the attack vector +though on this database proxy? + +I think you have to +have access to one + +of these other components +in the first place. + +So at least you have to +now compromise both-- + +you have to find a bug both in +the dbproxy and somewhere else, + +so-- + +AUDIENCE: So not necessarily, +because the SVC is already + +forwarding-- + +PROFESSOR: Right. + +So as the SVC passes +through great query + +is largely unchecked-- + +AUDIENCE: Well, so, +I mean, let's say + +you're trying to log in, right? + +It will pass. + +PROFESSOR: Yeah, like your +Alice name goes in the template, + +and yeah. + +AUDIENCE: Alice is straight +to the dbproxy, in theory. + +PROFESSOR: Absolutely. + +So, there might be +some dbproxy bugs here + +that are also exploitable. + +Anyway, this hopefully +gives you guys + +some sense of how do you +think of privileged separating + +application. + +And as we see, it's not perfect. + +There are still many +things that could go wrong. + +But it seems much better than +the nonprivileged separated + +design that we started out with. \ No newline at end of file diff --git a/ddtobc-AOK4.txt b/ddtobc-AOK4.txt new file mode 100644 index 0000000000000000000000000000000000000000..f92bcf257d569510c814b10220ef611d62407430 --- /dev/null +++ b/ddtobc-AOK4.txt @@ -0,0 +1,1964 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: All right. + +Today I want to spend a few more +minutes on plotting, and + +then return to a subject that +will occupy us for a couple of + +weeks, which is the use of + +randomness in solving problems. + +Don't save. + +All right, so let's +first look at one + +more example of plotting. + +It's simple. + +It's so simple you'll find +it's not in your handout. + +So here it is to start with. + +PROFESSOR: All I'm doing here is +I wrote a little program to + +show the effect of compound +interest, nothing very + +sophisticated. + +We start with some principal and +an interest rate, and then + +we just apply it over +and over again. + +And then we're going to plot to +show what the principal has + +become if we just keep +compounding the interest. + +So it is kind of what +you'd expect. + +Compound interest is +a nice formula. + +You can actually get rich +applying it, and we see this + +nice little graph. + +On the other hand, we can't +really tell what it is. + +And this is the sort of thing +that I see all too often, + +including my graduate +students produce it. + +They come to my office, they +show me a graph, and they + +start explaining it. + +And I usually refuse to look at +it if it looks like this. + +There is no point in ever, and I +mean ever, producing a graph + +that does not have a title +and labeled axes. + +And in particular, you have +to label the axes to + +say what they mean. + +Fortunately, it's easy +enough to do. + +And here, I've just done that. + +So I'm going to run the same +code to compute the interest, + +but I'm going to put a +title on the graph. + +You've seen this before, +I just want to + +remind you how it works. + +PyLab.title And then I'm +going to label the + +x-axis and the y-axis. + +And that gives me a much +more useful graph. + +Nothing magical here, it's +just a reminder that you + +really need to do +these things. + +You'll notice here I've not only +told you that this is the + +years of compounding and that +this is the principal but I've + +measured it in dollars. + +Maybe I should have been even +more explicit and said, well, + +US dollars, whatever. + +One of the things I did want +to point out is you saw the + +two of these various icons that +will let you do things + +like zoom in on a graph +and save a graph. + +Here's this icon that I think +Professor Grimson mentioned, + +in fact, I know he did. + +It's a floppy disk, just in case +you've never seen one, I + +brought a floppy disk +to show you. + +This is one of the older +floppy disks. + +These were invented +in 1971 by IBM. + +They were originally 8 inches in +diameter and held all of 80 + +kilobytes of data. + +And as you can see, unlike +later floppy disks, they + +actually flopped. + +Eventually, Apple and others +pioneered a non-floppy floppy + +disk, that was in the '80s. + +The interesting thing today is I +typically carry around a USB + +stick with me about that big +that holds roughly 400,000 + +times more data than +this floppy. + +And so it's just quite +incredible how things have + +gone along. + +All right. + +I now want to return to what +will be the main theme for, as + +I said, a couple of weeks +which is randomness. + +And in order to talk about +randomness we have to talk + +about probability. + +And I know that Professor +Grimson started down that path + +just before spring break, but +if you're anything like me + +your mind kind of deteriorated +a little bit over spring + +break, and your head isn't +quite into things. + +And so, I'm just going to back +up a tiny bit and start over + +to get our heads into it, and +then fairly quickly move on to + +new things. + +So let's start by asking +a simple question. + +You can tell my head isn't +quite yet back to things + +because I forgot that I needed +to begin by gathering chalk. + +I've now got it. + +And we'll come over here and +take a look at some examples. + +All right. + +So the first question I want +to ask is, suppose I take a + +6-sided die, a fair one, and I +roll it 10 times, what's the + +probability of not getting a +single 1, out of that die? + +Well, how do we go about +answering this? + +Well, there is a wrong way to +do it, which is sort of the + +obvious way, and many people +will start down this path. + +They'll say, well the +probability of + +rolling a 1 on the-- + +not rolling a 1 on the first +try is 1 over 6. + +Right? + +That's true? + +That's not true. + +What's the probability of not +rolling a 1 the first time? + +5 over 6. + +All right. + +What's the probability of not +rolling a 1 on the second try? + +5 over 6. + +Well, the wrong thing to do, of +course, would be to start + +adding them up. + +We say, well, OK, we'll +just add these up. + +Well, one way we can tell that's +wrong is if we add up + +10 of these, we get +more than 1. + +Probabilities can never be +more than 1 as we'll see. + +So let's now try and think +of the right way to + +look at this problem. + +So you can think about it. + +If we roll these-- + +a die 10 times, each time +I'll get a number. + +So I might get a 3, and then +a 4, and then a 2. + +How many possible 10-digit +numbers are there? + +On a 6-sided die, if +I roll it 10 times? + +How many? + +AUDIENCE: 6 to the 10th? + +PROFESSOR: 6 to the 10th. + +Exactly Just when we look at +binary numbers, if I take a + +10-digit binary number, and ask +how many different numbers + +can I represent in 10 binary +digits, it's going + +to be 2 to the 10th. + +Here we're base 6. + +So it's going to be +6 to the 10th. + +Pretty big number. + +Now I can say, how many +of those numbers + +don't contain a 1? + +All right. + +So that's really the question +I'm now asking. + +How many of these don't +contain a 1? + +So as we said, if I look at the +first roll the odds of not + +getting a one the first time +is 5 over 6 Now what's the + +odds of not getting 1 the first +or the second time? + +It's 5 over 6 times 5 over 6. + +That makes sense? + +Because these are independent +events. + +And that's a key notion here. + +I'm assuming that whether I get +a 1 on the second roll is + +independent of whether I got +a 1 on the first roll. + +It should be true, assuming +my dice-- + +die is fair. + +Similarly, I can do this for +the third roll et cetera. + +So the probability of not +getting a 1 in 10 rolls is + +going to be (5 over +6) to the 10th. + +That makes sense? + +If not, speak up, because things +are going to get more + +complicated quickly. + +All right. + +So that's pretty simple. + +You-- + +you all-- are you all +with me on that? + +Now, suppose I ask you +the inverse question. + +What is the probability of +getting at least one 1 if I + +roll the die 10 times? + +So here I've given you how to +compute the probability of not + +getting any 1's. + +Suppose I asked you the +probability of at least one 1? + +Yeah? + +AUDIENCE: [INAUDIBLE] + +1 minus not having a 1? + +PROFESSOR: Exactly. + +Thank you. + +So that would be 1 minus because +we know that the + +probability, the sum of all the +possible things that we + +can do when we do a probability + +always has to be 1. + +It was a good effort. + +That's it. + +If you take-- + +if you want to get something +where everything is covered, + +the probabilities always +have to sum to 1. + +And so now, there are only +two possibilities here. + +One possibility is I +don't get any 1's. + +One possibility is I +get at least one 1. + +So if I take all of the +possibilities, and I subtract + +the possibilities of not getting +any 1's, the result + +must be the probability of +getting at least one 1. + +This is a very common trick in +computing probabilities. + +Very often when I ask or +somebody says, what's the + +probability of x? + +The simplest way to compute +it, is to compute the + +probability of not x and +subtract it from 1. + +OK. + +Again, heading down a wrong +track for this, one might have + +said, well all right, the +probability of getting a 1 on + +the first roll is 1 over 6. + +The probability of getting +a 1 on the second + +roll is 1 over 6. + +The probability of getting +a third roll is 1 over 6. + +I'll just add them up, and +that will give me the + +probability of getting +at least one one. + +How do I-- + +how can I be sure +that's wrong? + +Well when I'm done, I would +claim the probability is + +something like that. + +And we know that +can't be true. + +Because a probability always +has to be less + +than or equal to 1. + +So this is a good trick to keep +in mind, whenever you're + +given a probability problem, try +and figure out whether you + +have a good way to compute it +directly, or whether it's + +simpler to compute the not of +the probability, and then + +subtract it from 1. + +Probability is really +a fun field. + +It's interesting, it's history, +it's intimately + +connected with the history +of gambling. + +And, in fact, almost all of +early probability theory owes + +its existence to gamblers. + +People like Cardano, Pascal, +Fermat, Bernoulli, de Moivre, + +Laplace, all famous names you've +heard, were motivated + +by desire to understand +games of chance. + +Mostly, it started with dice. + +I've been talking about dice. + +And in fact, dice are probably +the human race's oldest + +gambling implement. + +They date at least, +archaeologically, to about 600 + +BC, where a pair of dice was +found in Egyptian tombs, + +actually longer than that. + +Two millennia before the birth +of Christ, people found dice + +in Egyptian tombs. + +Typically, they were made +from animal bones, but + +that doesn't matter. + +Pascal's interest in it, and +Pascal is really considered + +the founder of probability +theory, came when a friend + +asked him to solve the following +problem which I want + +to work out with you. + +Is it profitable to bet that +given 24 rolls of a pair of + +fair dice, you would +roll a double 6? + +He actually had a friend who +was in the business of + +gambling, making these bets. + +So he said, you've got a pair of +dice, you roll it 24 times + +and ask the question, what is +the probability of getting + +what we call today "box cars", +in those days they + +just called two 6's. + +This was considered a really +hard problem in + +the mid-17th century. + +And in fact, Pascal and Fermat, +two pretty smart guys + +as it happens, debated this. + +They exchanged letters with each +other trying to figure + +out how to solve this problem. + +It shows how math has advanced +because, in fact, today, it's + +quite an easy problem. + +So let's work it through +and think how would + +we answer this question. + +So what's the probability of +rolling, of not rolling, a + +double 6 on the first try? + +Well, the probability of +not rolling a 6 on one + +die is a sixth -- + +1 over 6. + +The probability of not rolling +a one with the next die is + +also 1 over 6. + +So the probability of not +getting a die in the first + +roll, first double 6's is-- + +the probability of getting +a double 6 is 1/36. + +So the probability of not +getting a double 6 is 35/36. + +Right? + +So now we know that the +probability of not + +getting it is that. + +What's the probability of not +getting it 24 times in a row? + +It's that. + +Which is approximately +equal to 0.51. + +So you can see why the answer +was not obvious just by + +experience. + +But there is a slight edge in +betting that you will not get + +a double 6 in 24 times. + +Again, assuming you +have fair dice. + +As old as dice is, people have +built cheater's dice. + +The excavation of Pompeii, for +example, they discovered a + +pair of loaded dice, dice with +a little weight in it so one + +number would come up more +often than it should. + +And in fact, if you look at the +internet today, you will + +find many sites where you can, +let's see, the one I found + +this morning says quote, "Are +you on unusually unlucky when + +it comes to rolling dice? + +Investing in a pair of dice +that's more reliable might be + +just what you need." And then +it says, "Of course for + +amusement only." Yeah, +we believe that. + +All right. + +As much as I trust probability +theory, I don't trust my + +ability to use it. + +And so what I did is wrote a +little simulation to see if + +Pascal was right when +he did this. + +So I've got the first-- just +this little test roll, which + +rolls a dice number of times, +gets the result. + +Now, then I decided +to check Pascal. + +So I was going to run 100,000 +trials, and keep track of the + +number of times it worked. + +So what you'll see I'm doing +here is for i in the range + +number of trials, and this is +the way we'll do a lot of + +these simulations. + +And in fact, as we deal with +probability, we'll be dealing + +a lot with the notion of +simulation, as you are doing + +in your current problem set. + +So for i in range number of +trials, for j in range 24, + +because that was Pascal's +friend's game, I'll roll the + +first die, I'll roll +the second die. + +If they're both 6's I'll +say, yes equals 1. + +And I'll break and then I'll +compute the probability of + +winning or losing. + +OK? + +So let's let it rip. + +So now let's let it rip. + +There it is. + +And we can see that it actually +comes out pretty + +close to what Pascal +predicted. + +Should we be surprised that it +didn't come out to exactly? + +Well let's see, is it exactly? + +What is 35/36 to the 24th? + +So that's the-- + +well, to 17 digits of precision, +the exact answer. + +And you can see we came up with +something close to that. + +Not exactly that, and we +wouldn't expect to. + +Now I only did 100,000 trials. + +If I did a million trials, +I'd probably come up with + +something even closer, but if I +did 2 trials, who knows what + +I get-- come up with it, right? + +Could be-- + +I could get 1, I could get lucky +both times, or unlucky. + +Later on, we'll talk more about +the question, how do we + +know how many trials to run? + +Now, the interesting thing is +I'm sure it took me less time + +to write this program +than it took Pascal + +to solve the problem. + +Now the truth is, I had several +hundred years of other + +people's work to build on. + +But in general, I think one of +the questions you'll find is, + +is it easier sometimes to write +a simulation, than it is + +to do the probabilities? + +What I often do in +practice is both. + +I'll scratch my head and figure +out how to figure out + +the answer analytically, and +then if it's easy, I'll write + +some code to simulate the +problem, and expect to get + +roughly the same answer, giving +me confidence I've done + +it correctly. + +On the other hand, if I've done +the simulation and it had + +come up with something totally +bogus, or totally different, + +then I would have had to work +hard to figure out which was + +right, the code or the math. + +Same sort of thing you saw when +you looked at the random + +walk, and the first time it was +done an answer showed up + +that was just wrong. + +But, you need to have some +intuition about a problem, so + +that you can look at +it and say, yeah, + +that's in the ballpark. + +And if it's not, it's +time to worry. + +This kind of simulation that +I've just done for the dice + +game is what's called a "Monte +Carlo simulation". + +It is the most popular kind of +simulation named after a + +Casino on the Riviera, in the +small principality of Monaco. + +This was back in the time when +it was hard to find a place + +you could gamble, and this +happened to be one of the + +places you could. + +The term was coined in 1949 by +Stanislaw Ulam and Nicholas + +Metropolis, two very well-known +mathematicians. + +Ulam, who later became famous +for designing the hydrogen + +bomb with Teller, invented the +method in 1946, and I'm going + +to quote from his description +of how he invented it. + +"The first thoughts and attempts +I made to practice + +the Monte Carlo method, were +suggested by a question which + +occurred to me in 1946, as I +was convalescing from an + +illness and playing +solitaires. + +The question was, what are the +chances that a canfield + +solitaire laid out with +52 cards will come out + +successfully? + +After spending a lot of time +trying to estimate them by + +pure combinatorial calculations, +I wondered + +whether a more practical method +than quote 'abstract + +thinking' end quote, might not +be to lay it out, say, 100 + +times, and simply observe +and count the number + +of successful plays. + +This was already possible to +envision with the beginning of + +the new era of fast computers. + +And I immediately thought of +problems, as you would, I'm + +sure, immediately thought of +problems of neutron diffusion + +and other questions of +mathematical physics. + +And more generally, how to +change processes described by + +certain differential equations +into an equivalent form + +interpretable as a succession +of random operations. + +Later, I described the idea to +John von Neumann, and we began + +to plan actual calculations." + +So as early as 1946, people +were thinking about the + +question of moving away from +solving systems of equations, + +to using randomized techniques +to simulate things and try to + +find out what the actual +answer was that way. + +Now of course "fast" +is a relative term. + +Ulam was probably referring to +the ENIAC computer, which + +could perform about 10 to the +3 additions a second. + +Not very many, 1,000 operations +a second, and + +weighed approximately 25 tons. + +Now today's computers, by +comparison, perform 10 to the + +9th additions and weigh about +10 to the minus 3 tons. + +All right. + +This technique was used during +the Manhattan Project to + +predict what would +happen doing-- + +during nuclear fission +and worked. + +Monte Carlo simulations are an +example of what's called + +"inferential statistics". + +In brief, and I'm going to be +brief because this is not a + +statistics, course, inferential +statistics is + +based upon one guiding +principle. + +And that principle is that a +random sample tends to exhibit + +the same properties +as the population + +from which it is drawn. + +So if I try and sample people, +say, for predicting an + +election, the notion is if I go +and I asked a 1,000 people + +at random in Massachusetts who +they're going to vote for, the + +average will be about the same +as if I looked at the whole + +population. + +So whenever we use a statistical +method like this, + +so for example, we assumed here, +is those 100,000 times I + +threw the pair of dice, that +that would be representative + +of all possible throws of the +dice, the infinite number of + +possible throws. + +One always has to ask the +question whether this is true, + +or whether one has a sampling +technique that is, for + +example, giving you +a biased sample. + +Little later in the term, we'll +talk about many ways in + +which you can get fooled here +and think you're doing a fair + +statistical analysis, and get +all the math right, and still + +come up with the wrong answer +because this assumption + +doesn't actually hold. + +All right. + +Let's think about it now in +terms of coins, a little + +simpler than dice, where you +can flip a coin and you get + +either a head or a tail. + +Suppose Harvey Dent, for +example, flipped a coin and it + +came up heads. + +Would you feel good inferring +from that that the next time + +he flipped a coin it would +also come up heads? + +I wouldn't. + +Suppose he flipped it +heads and it came up + +heads twice, in a row. + +Would you feel comfortable +with the third + +flip would be a head? + +Probably not. + +But suppose he flipped it a 100 +times in a row, and it was + +a head each time. + +What would you infer? + +I would infer that the coin +two-headed And, in fact, every + +time it was going to come up +heads, because it is so + +improbable that if it +was a fair coin-- + +what's the probability of having +a 100 heads in a row + +with a fair coin? + +1 over what? + +AUDIENCE: 1 over 100-- + +1 over 2 to the 100th. + +Right? + +PROFESSOR: A half the +first time times a + +half times a half. + +A huge number, a very small +number rather, right? + +So the probability and a fair +coin of getting hundred heads + +in a row is so low with just 100 +flips, that I would begin + +to think that the coin +was not fair. + +All right. + +Suppose, however, I flipped it +100 times and I got 52 heads + +and 48 tails. + +Well, I wouldn't assume +anything from that. + +Would I assume that the next +time I flipped it a 100 times + +I'd get the same +52 to 48 ratio? + +Probably not, right? + +Your common sense tells +you you wouldn't. + +All right. + +Probably, it tells you, you +wouldn't even feel comfortable + +guessing that there would +be more heads than + +tails the next time. + +So when we think about these +things, we have to think about + +the number of tests and how +close the answer is to what + +you would get if you did +things at random. + +This is sort of comparing-- + +this is technically called +comparing something to the + +null hypothesis. + +The null hypothesis is +what you would get + +with a random event. + +And when you do a simulation, +if you get something that is + +far from that, or when you +sample a population, you get + +something that's distant from +the null hypothesis, you can + +assume that maybe you're +seeing something real. + +All right. + +Let's look at this in a little +less abstract way. + +So let's go look at +some coin flips. + +So I wrote a simple +program, flip. + +Just flip the coin some number +of times and tells me what + +fraction came up heads. + +So we can run it, and +let's look at a-- + +suppose I flip a 100, +I get 0.55. + +If I flip 10, I get 0.4. + +If I flip 10 again, I get 0.5. + +Now look at that, the same +thing twice in a row + +but now I get 0.2. + +So obviously, I shouldn't infer +too much from 10 flips + +and even from 100 where +I got 0.55. + +Let's see what happens if I +flip 100 again, 0.41, big + +difference. + +So this is suggesting that we +can't feel very good about + +what happens here. + +Now if I do the following, well +I'm feeling a little bit + +better about this, well +for one bad reason + +and one good reason. + +The bad reason is, I know the +answers 0.5, and these are + +both close to 0.5, so I +feel warm and fuzzy. + +But that's cheating. + +I wouldn't need to write +the simulation + +If I knew the answer. + +But mostly I feel good about it +because I'm getting kind of + +the same answer every time. + +OK, and that's important. + +The more I do, the more stable +it gets with the larger the + +number of trials. + +This is an example of what's +called "the law of large + +numbers", also known as +Bernoulli's Law, after one of + +the Bernoulli family of +mathematicians, and I can't + +for the life of me remember +which Bernoulli. + +There are a whole +bunch of them. + +Anyway the law states, and it's +important to understand + +this because again it underlies +the inferential + +statistics, that in repeated +independent tests, and it's + +important to note the word +"independent", each test has + +to be independent of +the earlier test. + +In this case, the tests are +flips of the coin with the + +same actual probability we'll +call it p, often used to + +represent probability, of an +outcome for each test, the + +chance that the fraction of +times that outcome occurs the + +outcome that with probability, +p, converges to p as number of + +trials goes to infinity. + +All right. + +So if I did an infinite number +of trials, the fraction of + +heads I would get in this case +would be exactly 0.5. + +Of course I can't do an infinite +number of trials. + +But that's the law of large +numbers that says the-- + +Now, it's worth noting that this +law does not imply that + +if I start out with deviations +from the expected behavior, + +those deviations are likely to +be quote "evened out" by + +opposite deviations +in the future. + +So if I happen to start by +getting a whole bunch of heads + +in a row, it does not mean that +I'm more likely to get + +tails in a subsequent trial. + +All right. + +Because if I were-- + +if that were true, then they +wouldn't be independent. + +Independent means memoryless. + +So if I have an independent +process, what happens in the + +future cannot be affected +by the past. + +And therefore, I don't +get this business + +of "they even out". + +Now people refuse +to believe this. + +If you go to any gambling place, +you'll discover that if + +people threw the roulette wheel, +if black comes up 20 + +times in a row, they'll be +a rush to bet on red. + +Because everyone will say, red +is do, red is do, red is do. + +And every psychologist who has +ever done this experiment, + +finds that people don't +believe it. + +That it's not true. + +People just don't get +probability, and it happens so + +often it's got a name called +"the gambler's fallacy". + +And there's been great examples +of people going broke + +doing this. + +Now notice that the law of large +numbers here is about + +the fraction of times +I get an outcome. + +It does not imply for example, +that the absolute difference + +between the number of heads and +the number of tails will + +get smaller as I run +more trials. + +Right? + +It doesn't say anything +at all about that. + +It says the ratio of head to +tails will approach 1, but not + +that the difference +between them. + +All right, let's look at an +example showing that off. + +So what I've got here is this +program called "flip plot". + +This is on your hand out. + +This is just going to run this +business of flipping coins. + +I should point out just-- + +I did it this way just +to show you. + +What I'm doing is each flip-- if +random.random is less than + +5, I'll call it a head, +0.5, I'll call it + +heads, otherwise a tails. + +You'll notice that it appears +that maybe I'm biasing a + +little bit, because I'm +giving 0.5 a value. + +But there are so many floating +point numbers between 0 and 1, + +that the probability of getting +exactly 0.5 is so + +small that I can ignore it. + +It isn't going to really make a +difference Random.random is + +the key issue, the key function +that's used to + +implement all the other random +functions that we + +have in that package. + +All right. + +So I'm going to do it, and +I'm going to do it + +over a range of values. + +The minimum exponent to the +maximum exponent and for + +exponent in range min x to max +x plus 1, I'm going to choose + +an x value that is 2 to that. + +So this lets me go +over a big range. + +So I'll see what happens if I +get 1 flip, and 2 flips, and 4 + +and 8 and 16 and 32 et cetera. + +And then I'm going to +just do some plots. + +I'm going to plot the absolute +difference between heads and + +tails and the ratio +of heads to tails. + +Let's see what happens +when we run that. + +Actually, probably nothing +because I didn't uncomment the + +run part of it. + +Let's do that. + +So I'm going to call flip plot +with 4 and 20, running from + +four trials 2 to the +4 to 2 to the 20. + +Let's see what we get. + +Now, you may get different +things when you run at + +different times. + +In fact, you will. + +So here we see something +kind of uninteresting. + +Let's cheat and see what we got +the first time I ran it, + +which is on your hand out, and +I have a PowerPoint with it. + +I was-- + +I knew this might happen. + +Doesn't usually, but sometimes +when you run it you get + +surprising results. + +So here's what happened +when I first ran it. + +Here was the difference between +heads and tails. + +And it seems that, OK, the +difference was low, it went + +up, it went down, it went +up, it went down. + +It seemed to go down +dramatically. + +If you remember what we just saw +when I ran it, we also saw + +something where it went up a +little bit then it went down + +and then shot up dramatically at +the end, which was why that + +scale is so funny. + +And if we look at the ratio, +what we see is it seems to + +start above 1, drop below +1, and then seems to + +converge towards 1. + +Now, I show this because I +want to make a couple of + +points of plotting. + +Let's look at this out here. + +Looks like we have a pretty +dramatic trend + +of this linear drop. + +Do we? + +Do we actually have +a trend here? + +Well let's think about it. + +The default behavior of the plot +command in PyLab is to + +connect points by lines. + +How many points do I actually +have out here? + +Well, you saw the code. + +You have the code +in the hand out. + +How many points do you think +there are out here? + +A 1,000? + +A 100? + +3? + +2? + +2 to 3. + +Right? + +Depending on what I mean +by "out here". + +So what we see here is something +that happens a lot. + +People plot a small number of +points, connect them by a + +line, and mislead the audience +into thinking there's a trend + +when, in fact, maybe all +you have is an outlier. + +So it's problematical here +to do it that way. + +So let's see what happens +if we change the code. + +And what I'm going to do is +change it in two ways. + +Well, maybe I'll change +it in one way first. + +Uncomment. + +Uncomment. + +So what I'm doing here is I am +plotting in a different way. + +This quote "BO" says, don't +connect it by lines but just + +put a dot as an "O" and +B says, make it blue. + +I used blue because it's +my favorite color. + +So now if we look at these +things, we'll see something + +pretty different. + +So that's the difference between +heads and tails, + +that's the ratio. + +But now, if we look at the +difference between heads and + +tails here, what we see +is it's pretty sparse. + +So yeah, maybe there's a trend, +but maybe not, right? + +Because way out here I'm only +connecting two points, giving + +an illusion that there is a +trend but, in fact, no reason + +to believe it. + +So I always think if you're +plotting a small number of + +points, you're much better off +just plotting the points, than + +you are trying to +connect them. + +Now if we look at this one, +again, maybe we'd feel kind of + +comfortable if there is a trend +here, that there are + +several points on this line. + +We can't see much of what's +going on over here, which gets + +me to the next thing I want +to do is I'm going to use + +logarithmic axes here. + +So PyLab.semilogx says make +the x-axis logarithmic. + +PyLab.semilogy the y-axis. + +And so in the case of the +absolute difference, I'm going + +to make both logarithmic. + +Why am I doing that? + +Because both have a large +range, and by making it + +logarithmic, I can see what's +happening at the left side in + +this case where things +are changing. + +When I look at the ratios, the +y-axis does not have a very + +large range, and so there's no +need to make it logarithmic. + +We'll run it. + +So here, we can see +the difference + +between heads and tails. + +And now we can see what's going +on at the left as we can + +in Figure (4). + +And we can see things +much more clearly. + +So log scales can be +enormously useful. + +And in fact, I use them a lot, +everyone uses them a lot but, + +again, it's very important to +observe the fact that it's + +logarithmic and not +get fooled. + +All right. + +So I talked about linear +scaling, logarithmic scaling + +and we now have charts where I +can, perhaps, actually reach + +some conclusion about +what's going on. + +The next question is, how +certain can I be? + +Can I really be certain that, +indeed, this should be + +converging to 1? + +Here, if I sort of look at it, +it does look like there's kind + +of a linear trend of the +absolute difference growing as + +the number of trials grows. + +How certain can I be of that? + +You can never get absolute +certainty from sampling, + +because you could never be +sure if you haven't been + +vastly lucky or unlucky. + +That's not to say you +can't get the + +absolute correct answer. + +Maybe I could get 0.5, which +is the correct answer. + +But I can't know that that's +the correct answer. + +So now the question I want to +pursue, and it's what we'll + +cover on Thursday, is what +techniques can I use to make a + +statement of the form, I'm +certain within the following + +range that I have the +right answer. + +That I know the right answer +is highly likely to be this + +close to the answer my +simulation is giving me. + +And we'll look at how we can +make those statements and + +actually believe them. + +OK, see you on Thursday. \ No newline at end of file diff --git a/e124JF_DHCQ.txt b/e124JF_DHCQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..f296db96e04d93aac25fc9b8ec4612b20e191f9b --- /dev/null +++ b/e124JF_DHCQ.txt @@ -0,0 +1,1897 @@ +The following content is +provided under a creative + +commons license. + +Your support will help mit +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses visit +MIT OpenCourseWare at + +ocw.mit.edu + +PROFESSOR NELSON: So last time +we just about finished up the + +discussion of thermochemisty, +and we went through a + +description of calorimetry, +how we actually make + +measurements of thermodynamic +a quantities. + +I should mention, which I didn't +last time, that you + +know a calorimeter, apart from +measuring heats of formation + +also is used to measure +standard thermodynamic + +quantities like heat +capacities. + +You know how much heat does it +take to raise the temperature + +of something by a degree? + +Well, you put the material +inside the calorimeter, and + +you have a heater and it's +connected up to current + +source, and you can accurately +measure how much heat you're + +putting in, because you can +measure how much current is + +going into it, and you +separately are measuring the + +temperature of the material, so +it's a straightforward way + +of measuring the heat +capacities, thermodynamic data + +of this sort. + +So work on phase transitions, +just ordinary + +properties of material. + +Chemical reactions, all the +thermochemistry involved is + +done using constant pressure or +constant volume calorimetry + +in a pretty routine way. + +So we talked about how to use +the results of measurements + +like that to calculate +reaction energetics, + +enthalpies of reaction. + +And I just want to end the unit +on thermochemistry with a + +real brief discussion of an +approximate way of formulating + +heats of reaction, and that is +in terms of bond energies. + +Now you know you're probably +never going to sit down and do + +a series of thermodynamic + +calculations using bond energies. + +You could always look up heats +of formation of compounds and + +from those determine very +accurately heats of reaction, + +by looking at the heats of +formation of products and the + +heats of formation +of the reactants + +and subtracting them. + +And since that data is available +for a really wide + +range of materials, that's sort +of the simplest approach + +and the most accurate one to +determine reaction energetics. + +On the other hand, if you just +want to think about molecules, + +you know, you think +about bonds. + +You know if you say I've got +methane or ethane, I'm going + +to use a fuel and burn it +and capture the energy. + +How much energy do +we have in there? + +Well the way you want to be +thinking about that is all + +right, I'm going to take the +starting material, the fuel, + +I'm going to break bonds, and +I'm going to form some final + +product with new bonds. + +Roughly what kinds +of energetics + +are we talking about? + +In biological systems, it's +also super important. + +You know you think about +ordinary biochemical + +energetics, what's used is fuel +in biology and what are + +the products that are formed? + +And again, it's just super +important to be able to think + +sort of semi-quantitatively +in terms of bond energies, + +because you don't want to always +be going and looking up + +everything in tables. + +If you need to do an extensive +series of calculations, it's + +very useful to have +the tables. + +But if you just want to think +about how something is + +working, you know biological +or system or an engine or + +another application, it's very +useful to just be able to + +think in terms of +bond energies. + +So let's just go over +bond energies. + +And you've seen this in 5.111 +and 2, so I'm not going to + +belabor it but they're just a +little bit of examples that I + +want to go through, just so +it's fresh on your mind. + +So the idea, of course, is to be +able to have an idea of how + +much energy is involved +in forming or + +breaking a single bond. + +So, if we just do this by +example, we can take methane + +so it's a real simple case +because we know it's just got + +four identical carbon hydrogen +bonds, and we could say OK, + +let's just break them. + +So we'll start with methane +gas and go to one atom of + +carbon in the gas phase, +plus four atoms of + +hydrogen in the gas phase. + +The energetics in this case +aren't given by the usual + +heats of formation. + +You'd just say, if I want to +know about methane, I can look + +up its heat of formation from +the elements in their + +standards states. but the +difference here is these + +elements aren't in their +standard states. + +Carbon in its standard state +at room temperature and + +pressure is graphite, a solid, +it's not carbon atoms in the + +gas phase, and hydrogen in the +standard state is hydrogen + +molecules H2, not individual +atoms. + +All right, so we'd like to +have this bond energy for + +these things. + +So let's just to make a cycle +that will allow us to + +determine this. + +So this'll be our first step in +that cycle, or one way of + +getting there. + +And this delta H of reaction is +going to be by definition + +four times our bond energy for +a carbon hydrogen bond. + +Now let's go to be elements that +are in their standards + +states at room temperature +and pressure. + +So let's go to carbon +as graphite. + +And let's go to two molecules of +hydrogen gas, so this will + +be step two and this +will be step three. + +And this will allow us to work +because now we're starting in + +standard states, so +we can just use + +regular heats of formation. + +And that's the key. + +So if we look at step one +delta H1 there as we've + +defined it, four times +our bond energy. + +Two, this is just negative heat +of formation of methane, + +which we can look up. + +And three, is similar. + +Essentially it's the heat of +formation of carbon in the gas + +phase and hydrogen atoms in the +gas phase, commonly called + +heats of atomization, but these +are also tabulated just + +like heats of formation +of ordinary compounds. + +In fact, in the appendix +to your book that has + +thermodynamic data, you can find +carbon gas phase atoms + +including heat of formation, +and same with individual + +hydrogen atom as opposed +to hydrogen + +molecules in the gas phase. + +So those data are available. + +So we can write delta Hc from +atomization, and two times + +delta H of H2. + +This is the way this is +tabulated and this is molar. + +And of course now we've +written a cycle. + +So we know that to get from here +to here is the same as to + +go through these two steps. + +In other words delta H1 is the +sum of delta H2 and delta H3. + +And so this says that our four +times the carbon hydrogen bond + +energy is just given by minus +the heat of formation of + +methane plus the heat of +atomization of carbon, plus + +the two times the heat +of atomization + +for hydrogen molecules. + +And if we look up the numbers +that are tabulated, what we + +discover is that our carbon +hydrogen bond energy is 416.2 + +kilojoules per mole. + +Very useful to have numbers like +that stored in your head. + +To have some basic idea of +just ordinary chemical + +energetics in terms +of bond energies. + +Hydrogen bonds, you know roughly +20 kilojoules per + +mole, and so forth. + +Just having those kinds of +energetic enables you to think + +in a qualitative way about +what's likely to happen in an + +ordinary chemical or biochemical +situation. + +OK, so this is in a sense the +simplest case, because we've + +talked about the dissociation of +a molecule that consists of + +all identical bonds. + +But it's straightforward +to go from there to + +additional bond energies. + +So from this we've got a value +for a sort of typical carbon + +hydrogen bond, right. + +We can do the same thing now for +ethane, and that's got a + +single carbon carbon bond, as +well as a bunch of carbon + +hydrogen bonds, but now the we +know the carbon hydrogen bond + +energy, we can use that number +plus the relevant heats of + +formation to determine the +carbon carbon bond energy. + +And we can keep going and extend +this to essentially + +tabulate bond energies for a +very large number of different + +sorts of bonds. + +So just as an example, ethane, +so now we're going to have -- + +this I'll write it all out just +some we can keep proper + +track of all the bonds that +we're going to be breaking. + +So C2H6 goes to two carbon +gas phase atoms, and + +six hydrogen atoms. + +So in this case, our, I can +write this again as one delta + +H1 is six times the carbon +hydrogen bond energy plus the + +carbon carbon bond energy that +we'd like to determine. + +And again we can go through +now a similar cycle. + +So again this now can be +equilibrated with carbon + +graphite plus three molecules of +hydrogen in the gas phase, + +just like before. + +And so from that we can see +that we'll end up with an + +equality between these, and +negative delta H naught + +formation for C2H6 or ethane, +plus two delta H of carbon + +atomization, plus three +delta H for + +atomization hydrogen molecule. + +So we've already seen we could +look up these numbers and + +this, and we've already +determined a carbon hydrogen + +bond energy. + +So again, if we find all the +relevant values, we can + +determine that our carbon carbon +bond energy is 342 + +kilojoules. + +And so on. + +So we can keep going and again +build up a bigger and bigger + +inventory of bond energies just +to provide us with the + +kind of intuition that we'd +like to have to be able to + +think about ordinary molecular +energetics. + +Any questions about +bond energies? + +All right. + +Of course, if we know bond +energies, we also could make + +estimates of heats +of formation. + +So if we have some new compound, +we don't know its + +heat of formation, we +know its structure. + +We know what bonds +are involved. + +We could get an estimate for +what we might expect for its + +heat of formation if we know +those, and I think I'll just + +write this out on the board by +example, but not work through + +the numbers explicitly. + +You know, let's say we were +going to make, you know, n + +pentane C5H12. + +And of course again keeping +proper track of all the carbon + +carbon and carbon +hydrogen bonds. + +But now in principle we know +the carbon carbon bond + +energies and the carbon hydrogen +bond energies. + +So we should be able to figure +out the heat of formation of a + +compound like this, even if we +don't know it from a table. + +And it's again through a similar +sort of cycle so if we + +start with the atoms in the gas + +phase, and go to n pentane. + +So this is now the bond +energies which + +we basically know. + +And again make our cycle of +involving the elements in + +their stable form at standard +temperature and pressure. + +Then again, here's our +one, two, three. + +Here's our minus delta H of +atomization, and here's our + +heat of formation. + +And that's the point, is that +now we can use what we've + +already elaborated for the bond +energies and the known + +enthalpies of atomization, +and we could + +determine the heat of formation. + +If we do that, we wind up with +a value of minus 152.6 + +kilojoules. + +If we measure it. + +If we look up in a table what +the actual value is, we + +discover it's minus +146.4 kilojoules. + +So it's a few percent off. + +Why is it off? + +Why isn't it right? + +STUDENT: [UNINTELLIGIBLE] + +PROFESSOR NELSON: +Yes, exactly. + +You know you can't use the C-H +bonds from methane for every + +C-H bond, or the C-C bond in +ethane for every carbon carbon + +single bond. + +There'll be variations, usually +of modest magnitude, + +in the values. + +So this isn't going to be an +exact calculation, but + +certainly this is close enough +for allowing us to think + +qualitatively and +semi-quantitatively about + +ordinary energetics. + +Another illustration of it is if +we look at neopentane -- so + +same chemical formula. + +Same number of carbon carbon +and carbon hydrogen bonds. + +So according to the way we've +done this calculation, we + +should get exactly the same +number, because all we're + +doing is adding up the total +number of bonds, + +and it's the same. + +But what we discover is that +for neopentane, delta H of + +formation, neopentane is +minus 166.1 kilojoules. + +So again it's different +in this case + +in the other direction. + +But certainly close enough +that allows us to think + +reasonably about what might +happen in ordinary situations. + +Any questions about +bond energies? + +OK, now we're going to go to a +new topic, and let me say, the + +topic we're going to start now, +the second law, is really + +in a sense, this is the start of +the whole rest of the term. + +So far, what we've covered +essentially is conservation of + +energy, how you think about +energetics and what + +contributes to them. + +That is heat and work. + +How to account for them +all properly. + +What happens under constant +volume or constant pressure + +conditions that led us to the +definition of enthalpy right + +and so forth. + +And once you get your arms +around these ideas, and it + +takes some work to do that, but +once you do, the actual + +execution of things can be +pretty straightforward, and + +some of this can seem like +just you know a lot of + +accounting. + +It's not. + +It takes some effort to become +accustomed to it and familiar + +with how to properly think about +heat and work and how + +they contribute to energy +and so forth. + +But given that amount of effort, +a lot of this can be + +reduced to fairly +straightforward + +calculational stuff. + +What we're about to start is a +little different from that in + +some sense, and really in some +ways more difficult because + +what we're going to try to +understand starting with this + +next set of topics is what +determines whether something + +happens spontaneously? + +We haven't really talked about +that in any of this. + +We've talked about whether +reactions are endothermic or + +exothermic. + +But as you're going to see that +doesn't determine what + +happens spontaneously. + +It certainly is one of the +factors, but by no + +means the only one. + +What determines what happens +just by itself? + +Or another way of saying that +is, if I have some sort of + +system, it could be an engine. + +It could be a chemical +reaction. + +It could be a biochemical system +or some part of it. + +What determines where the +equilibrium is and the + +direction that things would have +to go in order to reach + +or approach the equilibrium? + +What is the equilibrium +state of something? + +Actually, what we've discussed +so far really doesn't allow us + +to determine that, and there are +a few easy ways to sort of + +bring that out. + +One is you can imagine +constructing some kind of + +cyclic process that you know +it could remove heat like a + +refrigerator does from a cool +region and export the heat to + +a hotter region, like the room, +or outside a window if + +it's an air conditioner or +something like that. + +Just move the heat. + +That's it. + +Why not? + +I mean you could do that +and not necessarily + +violate the first law. + +Or what about, here's +a simpler case. + +What if I just have a chamber +with a divider, and I pump out + +half of it, and I put gas in +this half, so there's gas and + +there's vacuum, and then +I remove the divider. + +So I certainly expect that what +happens is the gas fills + +the volume. + +Why? + +The first law didn't tell me +that that needs to happen. + +Why doesn't it go back the +other way, anyway, even + +without the barrier? + +Why doesn't the gas just by +itself all wind up over here? + +Let's say it's a pretty dilute +gas, so even if it does all + +end up in this half, you know +the energy of any sort of + +unfavorable repulsions between +molecules is negligible. + +Maybe they even have +weak attractions? + +Why doesn't that happened? + +It's a good thing for us +that it doesn't happen. + +Why in this room doesn't the air +all just sort of collect + +over there somewhere? + +Or just the oxygen molecules +in the air and + +suffocate all of us. + +The first law doesn't +have anything to + +say about that actually. + +Whatever the reason it doesn't +happen, we're not going to + +find the answer to that +in the first law. + +So that's what the second law +of thermodynamics and the + +development of entropy +is all about. + +It's to help us understand +what is the direction of + +spontaneous change? + +What governs that, and what's +the equilibrium state that is + +reached when the spontaneous +change occurs? + +OK? + +So the second law is going to +give us basically a principle + +that'll tell us the direction +of spontaneous change. + +One way of thinking about that +is it's going to allow it to + +sort of determine the +direction of time. + +You know if we see initial or if +we see one state and we see + +another state, we'll be able or +know, time must have been + +going this way, right because +the spontaneous change would + +happen in this direction. + +So, I'm going to put up a couple +of just statements of + +the second law of +thermodynamics. + +I'll start with kind +of an easy one. + +So maybe I'll start +with that here. + +Here's a statement +by Clausius. + +The first law says that +the energy of + +the universe is constant. + +We're always conserving +in one way or another. + +And the second law is that the +entropy of the universe is + +increasing. + +Now we're going to define +entropy presently. + +But I'm writing this up just to +give you some foreshadowing + +of how we're going to try to +guide our thinking about + +spontaneous processes. + +This tells us about conservation +of energy. + +This tells us about which +direction things move in + +spontaneously, namely the +direction that leads to an + +increase in this soon to be +defined quantity entropy. + +It's going to turn out to be a +state function, and it'll help + +us understand the direction +of spontaneous change. + +You know, like the first law +the second law too was + +developed before there was +a very well defined + +understanding of the molecular +nature of matter. + +We're going to talk about the +second law and entropy in + +macroscopic terms. + +Later on in the semester we'll +also discuss them in + +microscopic terms. + +We'll do a little bit of what's +called statistical + +mechanics, of microscopic, +basically discussing the + +microscopic origins of +entropy in terms + +of disorder of molecules. + +But really, the thermodynamics +of entropy and the second law + +evolved because people were +trying to build things. + +It was the Industrial +Revolution. people were trying + +to build engines, steam engines, +and other kinds of + +devices, refrigerators +other things. + +And they couldn't understand -- +first of all, why couldn't + +you make it perfectly +efficient? + +You know, you'd have +a steam engine. + +There'd be a source of heat. + +You could extract work. + +Never seemed like you +could get it all and + +turn it all into work. + +Why not? + +And if not, what were the +limitations on it? + +What was the best efficiency +you could achieve? + +So in a very practical way +people were motivated to think + +very hard about these +kinds of questions. + +So let's just look at some of +the things that brought out + +the need for this kind +of consideration. + +So let me start by drawing one +of the impossibilities. + +We could try to build +a heat engine. + +Where we've got some temperature +T1 which is hot, + +and some amount of heat, q1 goes +into our system, and our + +system runs as a cycle. + +It goes around and around, +because in any practical + +situation we're going to need +to keep going and repeating + +the process. + +Some amount of work comes out. + +We'll call it minus w, because +work is always defined as the + +work that's done by the +environment on the system. + +So if I'm drawing the arrow this +way, then I want to write + +it as minus w. + +Now this would be just swell. + +This is it. + +That's the whole heat engine. + +This is running in a cycle. + +So we know that, delta +u is zero. + +So that would mean that, you +know, the amount of work out + +would just equal the heat +in every time around. + +Never happens. + +Can't make it happen. + +The only way it works is +if instead there's + +an additional part. + +Somewhere heat is also lost +to a cold reservoir. + +In other words, you know +I burned some fuel. + +I consumed something to produce +my hot source, and I'm + +going to then try to turn it +into work, which I can, but + +only partly. + +There's going to be heat loss +somewhere to a colder region, + +and I can't avoid it. + +And it was discovered that +this was always the case. + +So this can be built where, just +to be clear on these. q1 + +is a positive number, because +again that's heat going from + +the environment to the system. + +This is our system running +in a cycle. + +So q1 is positive, minus w is +positive, that is work is + +being done on the environment +by the engine. + +And minus q2 is positive. + +And T1 is greater than T2. + +That I can build. + +Here's another thing +we could try to do. + +It's sort of the opposite. + +We could try to produce a +refrigerator but not have to + +do any work. + +So let's go the other way, in +other words, let's go from T2 + +which is cold we're going to +go in this direction now, + +which means q2 will be a +positive number and here's our + +system running in a cycle. + +And now here's minus q1 now is +going to be our positive + +number, and we're going to +remove heat from q2 and move + +it, or from T2 a cold region +and move it to some place + +that's hotter. + +Also a pretty nice idea. + +And also obviously impossible. + +It only works if I put work in +there to make it happen, then + +yes I can take heat out of a +cold body and move it up into + +a hotter reservoir +of some sort. + +So here's a refrigerator. + +Again T1 is greater than T2, +and in this case q2 is + +greater than zero. + +I'm removing heat, minus q1 is +greater than zero, that is + +heat is going up this way. + +Work is greater than zero. + +Has to be. + +Of course the thing is running +in a cycle. delta u is zero. + +So that means that work must +be minus q1 plus q2, right? + +And work is greater than zero, +so that's saying minus q1 + +right that's a positive +number, must + +be bigger than q2. + +In other words, I am taking +some heat away + +from the cold region. + +The heat I'm dumping into the +hotter region is bigger than + +the amount that I taking away +here, because it's also got + +this amount. + +That's why, you know, if it's +a humid or warm summer + +afternoon and you think oh what +I a great idea, I've got + +this little fridge in my room. + +I'm going to open it up +and cool the room off. + +Turns out not to +work too well. + +Because of course what +the fridge is + +doing, it's cold inside. + +So it's a machine that's +removing heat from the inside + +and dumping it outside. + +There are coils in the back of +the fridge, and if you touch + +them they're a little +bit warm and so on. + +The heat is being lost +to the room. + +How much heat? + +Well, the work that goes +in is also added. + +So the amount of heat that +goes out into the room is + +bigger than the amount of +heat that you're taking + +away from the space. + +That's bad. + +So if you try opening the +refrigerator door to cool off + +your room at the same time as +you're dumping heat into your + +room, all you discover is +the net effect is to + +heat up your room. + +Because you know the amount +of heat that the thing is + +removing from somewhere on the +inside there and struggling to + +do that because you've left the +door to the fridge open, + +right, is not as big as the +amount out heat that's coming + +out in those coils +on the back. + +It's not as big because that +heat has not only the heat + +that you're removing from +the inside, but also + +this amount of work. + +It's all conserved because +delta u is zero. + +The thing is running +in a cycle. + +Try it sometime. + +You can verify this +experimentally in a very + +simple way. + +It's not a very effective way +to work, and it wastes a + +little bit of energy, but +could be worth it in the + +interest of knowledge +and discovery. + +Let me write an alternate +statement of the + +second law of Clausius. + +All spontaneous processes +are irreversible. + +When I open that panel in the +container, I've got gas on one + +side and vacuum in the other +and it expands in there, it + +happens spontaneously, and +it's irreversible. + +It's not just going +to go back. + +And now let me write a +mathematical statement of the + +second law. + +And we'll celebrate +it's importance + +by using this color. + +Going around in a cycle, if I +integrate the quantity dq + +reversible over T, I get zero. + +Remember this, this is +our special function. + +Let me just keep going +a little more though. + +Let me also write +another version. + +If I write dq for an +irreversible path over T, + +right, less than zero. + +It's not the same. + +This is a state function. + +This isn't. + +Remember of course that the heat +that's exchange between + +the system and the environment +depends on the path. + +If there is a reversible path, +and you see how much heat was + +exchange with the environment, +and you look at that divided + +by temperature integrate over +the whole thing, you discover + +that as long as the path is +reversible, it only depends on + +the states at the beginning +and the end of the path. + +In other words if you have +various ways you can go from + +state one to two that +are reversible, + +it's always the same. + +We saw that for just a +couple of examples, a + +couple lectures back. + +Remember, we looked at these +thermodynamic cycles and just + +said, well let's just +calculate those. + +And those were, those all +involved reversible processes. + +So, in effect, we looked at +different paths to go from one + +state to another. + +We had a cycle, and one path +went to here, and the other + +path went back. + +We discovered that, in fact, +this one zero around the cycle + +or the way we expressed it at +the time is the value of this + +was the same regardless of the +way we got from one state to + +the other, whether we took a +straightforward route or a + +more circuitous route, as long +as they were reversible. + +We're going to define dS as dq +reversible over T, and since + +we're dealing with a state +function delta S going from + +state one to two of dq +reversible over T is S2 minus + +S1 state function. + +And S as state function is the +entropy, and of course the us, + +it will always be special. + +All right, now, the second law, +you know it's difficult + +to understand and to get your +arms around, because you know, + +do I really calculate this? + +I actually have to find a +reversible path in order to do + +the calculation. + +Normally, you know, when you +calculate delta u and delta h + +and so forth, you have various +ways to calculate them that + +can be pretty straightforward. + +But here, you actually have to +determine the heat exchanged + +between the system and the +environment, and you know that + +does, in general, depend +on the path. + +But it turns out that this +quantity, you know, the + +differential of that heat over +the temperature, also depends + +on path unless it's +a reversible pass. + +Any reversible path will lead +to the same results. + +It doesn't depend on path +among reversible paths. + +What that means in practice is +if we say OK, start here and + +end here and calculate the +entropy, you actually have to + +sort of figure out a reversible +way of getting from + +here to here so that you can +do that calculation. + +So it's really very different +from ordinary functions that + +you've been dealing with. + +A lot of people, you know, +because the second law is + +difficult to understand, you +know you can easily go online + +and see thousands of violations +of the second law. + +It's still easy to look, to go +find claims of perpetual + +motion machines. + +Some of them cost +a lot of money. + +You can buy them, see +how they work. + +But and also, all sorts of +schemes for producing energy. + +Go online and see, right. + +You're just, they're just crazy +ideas about getting + +energy from nothing. + +Getting energy from the heat +that's just already + +present in the air. + +I mean there's heat in the air, +all this motion, it must + +have energy. + +We should be able to extract +it and use it. + +Turns out we can't do that. + +It has to look something +like this. + +OK. + +I want to look at some more +statements of the second law. + +To do that I just want to +indicate one definition which + +is just to be clear what +these things mean. + +These are what I've called +heat reservoirs + +or hot or cold bodies. + +Here's what I mean to +be more specific. + +A heat reservoir is basically +a very large thermal mass at + +the same temperature. + +And the real idea is that you +can bring heat out of it as + +much as you want and the +temperature won't change. + +It's an idealization. right If +you have something that's big + +enough, and it's at a constant +temperature, of course you can + +take heat away, but it's just +so enormous that you won't + +measurably change it's +temperature. + +In practice you might be able +or approach that limit. + +OK, now let's look at some more +definitions or statements + +of the second law. + +This is from Kelvin of Kelvin +temperature scale fame. + +It's impossible to convert heat +into work with a system + +that operates in a cycle. + +I'm going to write +this all out. + +I know you've got it +in your notes too, + +but it's super important. + +To convert heat into work with +a system that operates in a + +cycle, without at the same time +transferring some heat to + +a colder reservoir. + +OK, a couple of things +to notice. + +One is, you know, in some sense +the second law is kind + +of negative, right? + +Must not have been done +in the new age. + +It tells us what we can't do. + +And that really is in a sense +what it's all about. + +It's telling us what are our +limitations of what can be + +accomplished. + +Very important part of this +statement -- in a cycle. + +Of course any practical engine +has to keep going, so there's + +going to be a cycle in some +way or another, but it's + +important because, you know, +there are some -- if I'm not + +operating in a cycle, +I can convert heat + +into work just fine. + +You know, I could have a heat +source, got a candle, and I've + +got a piston, maybe I've +got a weight on it. + +I've got something +stopping it. + +And then I remove the stoppers +and let it go, and because of + +the heat, there's expansion. + +It pushes up, right, and it'll +be up higher somewhere. + +Worked! + +Heat turned into work. + +I don't have a cold +body somewhere. + +But I only did this once. + +There was just one stroke +of the piston. + +If I want to continue it and run +in a cycle, somehow I've + +got to have a place where +the heat goes. + +So this sort of diagram +describes effectively the way + +the Kelvin statement works. + +This works fine and like we +illustrated before, it doesn't + +work fine if I don't have +this part of it. + +I won't be able to just take all +the heat and convert it to + +work, like I, in principle, +could do, if I don't need to + +run it in a cycle. + +Here is yet another statement +by Clausius And we'll + +end with that one. + +Maybe I'll just read +this one, so we can + +not go over the time. + +So, it's impossible for any +system to operate in a cycle + +that takes heat from a colder +reservoir, transfers it to a + +hotter reservoir, without at the +same time converting some + +work into heat. + +In other words, it's a statement +kind of similar to + +the Kelvin statement, but +applying to the case of moving + +heat from a colder to +a hotter region. + +Can't do it, unless some work is +also converted to the heat + +that gets released into +the hot region. + +I think we'll stop there. + +Next time what we'll do is lay +out a very well-defined kind + +of engine called Carnot cycle +that allows us to very + +explicitly go through and say +OK, let's just work out the + +steps of isothermal and +adiabatic expansions and + +contractions. + +In other words, how does +the engine really work? + +And just calculate it going +around in a cycle and see + +exactly how all this +is born out. + +And we'll see that next time. \ No newline at end of file diff --git a/eZzBK3oy-08.txt b/eZzBK3oy-08.txt new file mode 100644 index 0000000000000000000000000000000000000000..ccca147a1bd98c49a18e3d3e44f21bf7169a35d5 --- /dev/null +++ b/eZzBK3oy-08.txt @@ -0,0 +1,3061 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Last time we +talked about the spin operator + +pointing in some +particular direction. + +There were questions. + +In fact, there was +a useful question + +that I think I want to begin +the lecture by going back to it. + +And this, you received +an email from me. + +The notes have an extra section +added to it that is stuff + +that I didn't do +in class last time, + +but I was told in fact some +of the recitation instructors + +did discuss this +matter And I'm going + +to say a few words about it. + +Now, I do expect you +to read the notes. + +So things that you will need for +the homework, all the material + +that is in the notes is +material that I kind of + +assume you're familiar with. + +And you've read it +and understood it. + +And I probably don't cover +all what is in the notes, + +especially examples +or some things + +don't go into so much detail. + +But the notes should really be +helping you understand things + +well. + +So the remark I want to make +is that-- there was a question + +last time that better that +we think about it more + +deliberately in which we saw +there that Pauli matrices, + +sigma 1 squared was equal +to sigma 2 squared equal + +to 2 sigma 3 squared +was equal to 1. + +Well, that, indeed, +tells you something + +important about the +eigenvalues of this matrices. + +And it's a general fact. + +If you have some matrix M +that satisfies an equation. + +Now, let me write an equation. + +The matrix M squared plus alpha +M plus beta times the identity + +is equal to 0. + +This is a matrix equation. + +It takes the whole matrix, +square it, add alpha times + +the matrix, and then beta +times the identity matrix + +is equal to 0. + +Suppose you discover that +such an equation holds + +for that matrix M. Then, +suppose you are also + +asked to find eigenvalues +of this matrix M. So suppose + +there is a vector-- +that is, an eigenvector + +with eigenvalue lambda. + +That's what having +an eigenvector + +with eigenvalue lambda means. + +And you're supposed to calculate +these values of lambda. + +So what you do here +is let this equation, + +this matrix on the left, +act on the vector v. + +So you have M squared plus +alpha M plus beta 1 act + +on v. Since the matrix +is 0, it should be 0. + +And now you come and +say, well, let's see. + +Beta times 1 on v. Well, +that's just beta times + +v, the vector v. + +Alpha M on v, but M on +v is lambda v. So this + +is alpha lambda v. And M squared +on v, as you can imagine, + +you act with another M here. + +Then you go to this side. + +You get lambda Mv, which +is, again, another lambda + +times v. So M squared +on v is lambda squared + +v. If acts two times on v. + +Therefore, this is 0. + +And here you have, for +example, that lambda + +squared plus alpha lambda +plus beta on v is equal to 0. + +Well, v cannot be 0. + +Any eigenvector-- by definition, +eigenvectors are not 0 vectors. + +You can have 0 eigenvalues +but not 0 eigenvectors. + +That doesn't exist. + +An eigenvector that +is 0 is a crazy thing + +because this would +be 0, and then it + +would be-- the eigenvalue +would not be determined. + +It just makes no sense. + +So v is different from 0. + +So you see that lambda squared +plus alpha lambda plus beta is + +equal to 0. + +And the eigenvalues, any +eigenvalue of this matrix, + +must satisfy this equation. + +So the eigenvalues +of sigma 1, you + +have sigma 1 squared, for +example, is equal to 1. + +So the eigenvalues, +any lambda squared + +must be equal to +1, the number 1. + +And therefore, the +eigenvalues of sigma 1 + +are possibly plus or minus 1. + +We don't know yet. + +Could be two 1's, 2 minus +1's, one 1 and one minus 1. + +But there's another nice +thing, the trace of sigma 1. + +We'll study more the +trace, don't worry. + +If you are not that +familiar with it, + +it will become +more familiar soon. + +The trace of sigma +1 or any matrix + +is the sum of elements +in the diagonal. + +Sigma 1, if you remember, +was of this form. + +Therefore, the trace is 0. + +And in fact, the traces of any +of the Pauli matrices are 0. + +Another little theorem +of linear algebra + +shows that the +trace of a matrix is + +equal to the sum of eigenvalues. + +So whatever two +eigenvlaues sigma 1 has, + +they must add up to 0. + +Because the trace is 0 +and it's equal to the sum + +of eigenvalues. + +And therefore, if the +eigenvalues can only + +be plus or minus 1, +you have the result + +that one eigenvalue +must be plus 1. + +The other eigenvalue +must be minus 1, + +is the only way you +can get that to work. + +So two sigma 1 eigenvalues of +sigma 1 are plus 1 and minus 1. + +Those are the two eigenvalues. + +So in that section +as well, there's + +some discussion about properties +of the Pauli matrices. + +And two basic properties +of Pauli matrices + +are the following. + +Remember that the spin +matrices, the spin operators, + +are h bar over 2 times +the Pauli matrices. + +And the spin operators had the +algebra for angular momentum. + +So from the algebra +of angular momentum + +that says that Si Sj is equal +to i h bar epsilon i j k Sk, + +you deduce after plugging +this that sigma i sigma + +j is 2i epsilon i j k sigma k. + +Moreover, there's +another nice property + +of the Pauli matrices having +to deal with anticommutators. + +If you do experimentally +try multiplying + +Pauli matrices, +sigma 1 and sigma 2, + +you will find out that if you +compare it with sigma 2 sigma + +1, it's different. + +Of course, it's not the same. + +These matrices don't commute. + +But they actually-- while +they fail to commute, + +they still fail to +commute in a nice way. + +Actually, these are +minus each other. + +So in fact, sigma 1 sigma 2 plus +sigma 2 sigma 1 is equal to 0. + +And by this, we mean +that they anticommute. + +And we have a brief +way of calling this. + +When this sign was a minus, +it was called the commutator. + +When this is a plus, it's +called an anticommutator. + +So the anticommutator of sigma +1 with sigma 2 is equal to 0. + +Anticommutator defined +in general by A, + +B. Two operators is AB plus BA. + +And as you will +read in the notes, + +a little more analysis +shows that, in fact, + +the anticommutator of +sigma i and sigma j + +has a nice formula, +which is 2 delta ij times + +the unit matrix, the +2 by 2 unit matrix. + +With this result, you +get a general formula. + +Any product of two operators, +AB, you can write as 1/2 + +of the anticommutator plus +1-- no, 1/2 of the commutator + +plus 1/2 of the anticommutator. + +Expand it out, that +right-hand side, + +and you will see +quite quickly this + +is true for any two operators. + +This has AB minus BA +and this has AB plus BA. + +The BA term cancels and the +AB terms are [INAUDIBLE]. + +So sigma i sigma j +would be equal to 1/2. + +And then they put down +the anticommutator first. + +So you get delta ij +times the identity, which + +is 1/2 of the +anticommutator plus 1/2 + +of the commutator, which +is i epsilon i j k sigma k. + +It's a very useful formula. + +In order to make those +formulas look neater, + +we invent a notation in which +we think of sigma as a triplet-- + +sigma 1, sigma 2, and sigma 3. + +And then we have vectors, +like a-- normal vectors, + +components a1, a2, a3. + +And then we have a dot +sigma must be defined. + +Well, there's an +obvious definition + +of what this should +mean, but it's not + +something you're accustomed to. + +And one should pause +before saying this. + +You're having a normal +vector, a triplet of numbers, + +multiplied by a +triplet of matrices, + +or a triplet of operators. + +Since numbers commute +with matrices, + +the order in which you +write this doesn't matter. + +But this is defined +to be a1 sigma 1 + +plus a2 sigma 2 plus a3 sigma 3. + +This can be written as ai +sigma i with our repeated index + +convention that you sum +over the possibilities. + +So here is what you're +supposed to do here + +to maybe interpret +this equation nicely. + +You multiply this +equation n by ai bj. + +Now, these are numbers. + +These are matrices. + +I better not change this +order, but I can certainly, + +by multiplying that way, I +have ai sigma i bj sigma j + +equals 2 ai bj delta ij +times the matrix 1 plus i + +epsilon i j k ai bj sigma k. + +Now, what? + +Well, write it in terms +of things that look neat. + +a dot sigma, that's a matrix. + +This whole thing is a matrix +multiplied by the matrix + +b dot sigma gives you-- + +Well, ai bj delta ij, this +delta ij forces j to become i. + +In other words, you can replace +these two terms by just bi. + +And then you have ai bi. + +So this is twice. + +I don't know why I have a 2. + +No 2. + +There was no 2 there, sorry. + +So what do we get here? + +We get a dot b, the dot product. + +This is a normal dot product. + +This is just a number +times 1 plus i. + +Now, what is this thing? + +You should try to remember +how the epsilon tensor can + +be used to do cross products. + +This, there's just one +free index, the index k. + +So this must be +some sort of vector. + +And in fact, if you try the +definition of epsilon and look + +in detail what this +is, you will find + +that this is nothing but +the k component of a dot b. + +The k-- so I'll write it here. + +This is a cross b sub k. + +But now you have a cross +b sub k times sigma k. + +So this is the same as +a cross b dot sigma. + +And here you got a pretty nice +equation for Pauli matrices. + +It expresses the general +product of Pauli matrices + +in somewhat geometric terms. + +So if you take, for +example here, an operator. + +No. + +If you take, for +example, a equals + +b equal to a unit vector, +then what do we get? + +You get n dot sigma squared. + +And here you have +the dot product of n + +with n, which is 1. + +So this is 1. + +And the cross product of two +equal vectors, of course, + +is 0 so you get +this, which is nice. + +Why is this useful? + +It's because with this identity, +you can understand better + +the operator S hat +n that we introduced + +last time, which was n +dot the spin triplet. + +So nx, sx, ny, sy, nz, sc. + +So what is this? + +This is h bar over +2 and dot sigma. + +And let's square this. + +So Sn vector squared. + +This matrix squared would be +h bar over 2 squared times + +n dot sigma squared, which is 1. + +And sigma squared is 1. + +Therefore, this spin operator +along the n direction squares + +to h bar r squared +over 2 times 1. + +Now, the trace of this +Sn operator is also 0. + +Why? + +Because the trace +means that you're + +going to sum the +elements in the diagonal. + +Well, you have a sum +of matrices here. + +And therefore, you will have +to sum the diagonals of each. + +But each of the +sigmas has 0 trace. + +We wrote it there. + +Trace of sigma 1 is 0. + +All the Pauli matrices have +0 trace, so this has 0 trace. + +So you have these two relations. + +And again, this tells you that +the eigenvalues of this matrix + +can be plus minus h bar over 2. + +Because the eigenvalues +satisfy the same equation + +as the matrix. + +Therefor,e plus +minus h bar over 2. + +And this one says that the +eigenvalues add up to 0. + +So the eigenvalues of S hat n +vector are plus h bar over 2 + +and minus h bar over 2. + +We did that last time, but we do +that by just taking that matrix + +and finding the eigenvalues. + +But this shows that its +property is almost manifest. + +And this is fundamental +for the interpretation + +of this operator. + +Why? + +Well, we saw that if n +points along the z-direction, + +it becomes the operator sz. + +If it points about +the x-direction, + +it becomes the operator sx. + +If it points along +y, it becomes sy. + +But in an arbitrary +direction, it's a funny thing. + +But it still has +the key property. + +If you measured the spin +along an arbitrary direction, + +you should find only plus h bar +over 2 or minus h bar over 2. + +Because after all, the +universe is isotopic. + +It doesn't depend on direction. + +So a spin one-half particle. + +If you find out that whenever +you measure the z component, + +it's either plus +minus h bar over 2. + +Well, when you +measure any direction, + +it should be plus +minus h bar over 2. + +And this shows that this +operator has those eigenvalues. + +And therefore, it makes sense +that this is the operator + +that measures spins in +an arbitrary direction. + +There's a little more +of an aside in there, + +in the notes about +something that + +will be useful and fun to do. + +And it corresponds to +the case in which you + +have two triplets of +operators-- x1, x2, x3. + +These are operators now. + +And y equal y1, y2, y3. + +Two triplets of operators. + +So you define the dot +product of these two triplets + +as xi yi summed. + +That's the definition. + +Now, the dot product of +two triplets of operators + +defined that way +may not commute. + +Because the operators x +and y may not commute. + +So this new dot product +of both phase operators + +is not commutative-- probably. + +It may happen that +these operators commute, + +in which case x dot y +is equal to y dot x. + +Similarly, you can +define the cross product + +of these two things. + +And the k-th component is +epsilon i j k xi yj like this. + +Just like you would define +it for two number vectors. + +Now, what do you know about +the cross product in general? + +It's anti-symmetric. + +A cross B is equal +to minus B cross A. + +But this one won't be +because the operators x and y + +may not commute. + +Even x cross x may be nonzero. + +So one thing I will ask you +to compute in the homework + +is not a long calculation. + +It's three lines. + +But what is S cross S equal to? + +Question there? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yes, it's +the sum [INAUDIBLE]. + +Just in the same +way that here you're + +summing over i's and j's to +produce the cross product. + +So whenever an +index is repeated, + +we'll assume it's summed. + +And when it is not summed, +I will put to the right, + +not summed explicitly-- +the words-. + +Because in some +occasions, it matters. + +So how much is this? + +It will involve i, h +bar, and something. + +And you will try to +find out what this is. + +It's a cute thing. + +All right, any other questions? + +More questions? + +Nope. + +OK. + +So now, finally, +we get to that part + +of the course that has to +do with linear algebra. + +And I'm going to +do an experiment. + +I'm going to do it +differently than I did it + +in the previous years. + +There is this nice book. + +It's here. + +I don't know if you +can read from that far, + +but it has a pretty-- you might +almost say an arrogant title. + +It says, Linear Algebra +Done Right by Sheldon Axler. + +This is the book, actually, +MIT's course 18.700 of linear + +algebra uses. + +And when you first get the +book that looks like that, + +you read it and open-- +I'm going to show you + +that this is not that well done. + +But actually, I think +it's actually true. + +The title is not a lie. + +It's really done right. + +I actually wish I had learned +linear algebra this way. + +It may be a little +difficult if you've never + +done any linear algebra. + +You don't know what +the matrix is-- + +I don't think that's +the case anybody here. + +A determinant, or eigenvalue. + +If you never heard +any of those words, + +this might be a little hard. + +But if you've heard +those words and you've + +had a little linear +algebra, this is quite nice. + +Now, this book has +also a small problem. + +Unless you study +it seriously, it's + +not all that easy to grab +results that you need from it. + +You have to study it. + +So I don't know if +it might help you + +or not during this semester. + +It may. + +It's not necessary to get it. + +Absolutely not. + +But it is quite lovely. + +And the emphasis is +quite interesting. + +It really begins from +very basic things + +and logically +develops everything + +and asks at every point +the right questions. + +It's quite nice. + +So what I'm going to do +is-- inspired by that, + +I want to introduce some of +the linear algebra little + +by little. + +And I don't know very +well how this will go. + +Maybe there's too much detail. + +Maybe it's a lot of +detail, but not enough so + +it's not all that great. + +I don't know, you +will have to tell me. + +But we'll try to get +some ideas clear. + +And the reason I want +to get some ideas clear + +is that good books +on this subject + +allow you to understand +how much structure you + +have to put in a vector space +to define certain things. + +And unless you do +this carefully, + +you probably miss some +of the basic things. + +Like many physicists +don't quite realize + +that talking about the +matrix representation, + +you don't need brass +and [INAUDIBLE] + +to talk about the matrix +representation of an operator. + +At first sight, it seems +like you'd need it, + +but you actually don't. + +Then, the differences between +a complex and a vector space-- + +complex and a real vector +space become much clearer + +if you take your time +to understand it. + +They are very different. + +And in a sense, +complex vector spaces + +are more powerful, more +elegant, have stronger results. + +So anyway, it's enough +of an introduction. + +Let's see how we do. + +And let's just begin +there for our story. + +So we begin with vector +spaces and dimensionality. + +Yes. + +AUDIENCE: Quick question. + +The length between +the trace of matrix + +equals 0 and [INAUDIBLE] is +proportional to the identity. + +One is the product of +the eigenvalues is 1 + +and the other one was +the sum is equal to 0. + +Are those two statements +related causally, + +or are they just separate +statements [INAUDIBLE]? + +PROFESSOR: OK, the +question is, what + +is the relation between +these two statements? + +Those are separate observations. + +One does not imply the other. + +You can have matrices that +square to the identity, + +like the identity itself, +and don't have 0 trace. + +So these are +separate properties. + +This tells us that +the eigenvalue squared + +are h bar over 2. + +And this one tells me that +lambda 1 plus lambda 2-- + +there are two +eigenvalues-- are 0. + +So from here, you deduce +that the eigenvalues + +could be plus +minus h bar over 2. + +And in fact, have to be +plus minus h bar over 2. + +All right, so let's +talk about vector spaces + +and dimensionality. + +Spaces and dimensionality. + +So why do we care about this? + +Because the end result +of our discussion + +is that the states +of a physical system + +are vectors in a +complex vector space. + +That's, in a sense, the +result we're going to get. + +Observables, moreover, +are linear operators + +on those vector spaces. + +So we need to understand what +are complex vector spaces, what + +linear operators on them mean. + +So as I said, +complex vector spaces + +have subtle properties that make +them different from real vector + +spaces and we want +to appreciate that. + +In a vector space, +what do you have? + +You have vectors and +you have numbers. + +So the two things must exist. + +The numbers could be the +real numbers, in which case + +we're talking about +the real vector space. + +And the numbers could be +complex numbers, in which case + +we're talking about the +complex vector space. + +We don't say the vectors are +real, or complex, or imaginary. + +We just say there are vectors +and there are numbers. + +Now, the vectors can be +added and the numbers + +can be multiplied by +vectors to give vectors. + +That's basically +what is happening. + +Now, these numbers can +be real or complex. + +And the numbers-- so there +are vectors and numbers. + +And we will focus on +just either real numbers + +or complex numbers, +but either one. + +So these sets of +numbers form what + +is called in +mathematics a field. + +So I will not define the field. + +But a field-- use the +letter F for field. + +And our results. + +I will state results whenever-- +it doesn't matter whether it's + +real or complex, I +may use the letter F + +to say the numbers are in F. +And you say real or complex. + +What is a vector space? + +So the vector space, +V. Vector space, V, + +is a set of vectors with an +operation called addition-- + +and we represent it as plus-- +that assigns a vector u plus v + +in the vector space when u and +v belong to the vector space. + +So for any u and v +in the vector space, + +there's a rule called addition +that assigns another vector. + +This also means that this +space is closed under addition. + +That is, you cannot get out +of the vector space by adding + +vectors. + +The vector space must +contain a set that + +is consistent in that +you can add vectors + +and you're always there. + +And there's a multiplication. + +And a scalar +multiplication by elements + +of the numbers of F such +that a, which is a number, + +times v belongs to +the vector space + +when a belongs to the numbers +and v belongs to the vectors. + +So every time you +have a vector, you + +can multiply by those +numbers and the result + +of that multiplication +is another vector. + +So we say the space is also +closed under multiplication. + +Now, these properties +exist, but they + +must-- these operations +exist, but they + +must satisfy the +following properties. + +So the definition +is not really over. + +These operations satisfy-- + +1. + +u plus v is equal to v plus u. + +The order doesn't matter +how you sum vectors. + +And here, u and v in V. + +2. + +Associative. + +So u plus v plus w is +equal to u plus v plus w. + +Moreover, two numbers a times b +times v is the same as a times + +bv. + +You can add with the +first number on the vector + +and you add with the second. + +3. + +There is an additive identity. + +And that is what? + +It's a vector 0 belonging +to the vector space. + +I could write an arrow. + +But actually, for +some reason they just + +don't like to write +it because they say + +it's always ambiguous +whether you're + +talking about the 0 +number or the 0 vector. + +We do have that problem +also in the notation + +in quantum mechanics. + +But here it is, here is +a 0 vector such that 0 + +plus any vector v is equal to v. + +4. + +Well, in the field, +in the set of numbers, + +there's the number 1, which +multiplied by any other number + +keeps that number. + +So the number 1 that +belongs to the field + +satisfies that 1 times any +vector is equal to the vector. + +So we declare that that number +multiplied by other numbers + +is an identity. + +[INAUDIBLE] identity +also multiplying vectors. + +Yes, there was a question. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: There is +an additive identity. + +Additive identity, the 0 vector. + +Finally, distributive laws. + +No. + +One second. + +One, two, three-- +the zero vector. + +Oh, actually in my list I +put them in different orders + +in the notes, but never mind. + +5. + +There's an additive inverse +in the vector space. + +So for each v belonging +to the vector space, + +there is a u belonging +to the vector space such + +that v plus u is equal to 0. + +So additive identity +you can find + +for every element +its opposite vector. + +It always can be found. + +And last is this +[INAUDIBLE] which + +says that a times u plus +v is equal to au plus av, + +and a plus b on v is +equal to av plus bv. + +And a's and b's +belong to the numbers. + +a and b's belong to the field. + +And u and v belong +to the vector space. + +OK. + +It's a little disconcerting. + +There's a lot of things. + +But actually, they +are quite minimal. + +It's well done, this definition. + +They're all kind +of things that you + +know that follow quite +immediately by little proofs. + +You will see more in +the notes, but let + +me just say briefly +a few of them. + +So here is the additive +identity, the vector 0. + +It's easy to prove that +this vector 0 is unique. + +If you find another 0 prime that +also satisfies this property, + +0 is equal to 0 prime. + +So it's unique. + +You can also show that 0 times +any vector is equal to 0. + +And here, this 0 +belongs to the field + +and this 0 belongs +to the vector space. + +So the 0-- you had to postulate +that the 1 in the field + +does the right thing, but +you don't need to postulate + +that 0, the number 0, +multiplied by a vector is 0. + +You can prove that. + +And these are not +difficult to prove. + +All of them are +one-line exercises. + +They're done in that book. + +You can look at them. + +Moreover, another one. + +a any number times the 0 vector +is equal to the 0 vector. + +So in this case, those +both are vectors. + +That's also another property. + +So the 0 vector and the 0 number +really do the right thing. + +Then, another property, +the additive inverse. + +This is sort of interesting. + +So the additive inverse, +you can prove it's unique. + +So the additive +inverse is unique. + +And it's called-- for v, it's +called minus v, just a name. + +And actually, you can prove +it's equal to the number minus 1 + +times the vector. + +Might sound totally trivial +but try to prove them. + +They're all simple, but they're +not trivial, all these things. + +So you call it minus v, but +it's actually-- this is a proof. + +OK. + +So examples. + +Let's do a few examples. + +I'll have five examples +that we're going to use. + +So I think the main thing for +a physicist that I remember + +being confused about +is the statement + +that there's no characterization +that the vectors are + +real or complex. + +The vectors are +the vectors and you + +multiply by a real +or complex numbers. + +So I will have one example +that makes that very dramatic. + +As dramatic as it can be. + +So one example of vector spaces, +the set of N component vectors. + +So here it is, +a1, a2, up to a n. + +For example, with capital N. +With a i belongs to the real + +and i going from 1 up +to N is a vector space + +over r, the real numbers. + +So people use that +terminology, a vector space + +over the kind of numbers. + +You could call it +also a real vector + +space, that would be the same. + +You see, these +components are real. + +And you have to +think for a second + +if you believe all of them are +true or how would you do it. + +Well, if I would +be really precise, + +I would have to tell +you a lot of things + +that you would find boring. + +That, for example, you have +this vector and you add a set + +of b's. + +Well, you add the components. + +That's the definition of plus. + +And what's the definition +of multiplying by a number? + +Well, if a number is +multiplied by this vector, + +it goes in and +multiplies everybody. + +Those are implicit, or you +can fill-in the details. + +But if you define +them that way, it + +will satisfy all the properties. + +What is the 0 vector? + +It must be the one +with all entries 0. + +What is the additive inverse? + +Well, change the sign +of all these things. + +So it's kind of obvious that +this satisfies everything, + +if you understand how the sum +and the multiplication goes. + +Another one, it's +kind of similar. + +2. + +The set of M cross N matrices +with complex entries. + +Complex entries. + +So here you have it, +a1 1, a1 2, a1 N. + +And here it goes up +to aM1, aM2, aMN. + +With all the a i j's belonging +to the complex numbers, + +then-- I'll erase here. + +Then you have that this +is a complex vector space. + +Is a complex vector space. + +How do you multiply by a number? + +You multiply a number times +every entry of the matrices. + +How do sum two matrices? + +They have the same size, so +you sum each element the way + +it should be. + +And that should +be a vector space. + +Here is an example +that is, perhaps, + +a little more surprising. + +So the space of 2 by +2 Hermitian matrices + +is a real vector space. + +You see, this can be easily +thought [INAUDIBLE] naturally + +thought as a real vector space. + +This is a little surprising +because Hermitian matrices have + +i's. + +You remember the most +general Hermitian matrix + +was of the form-- +well, a plus-- no, + +c plus d, c minus d, +a plus ib, a minus ib, + +with all these numbers +c, d, b in real. + +But they're complex numbers. + +Why is this naturally +a real vector space? + +The problem is that if +you multiply by a number, + +it should still be a +Hermitian matrix in order + +for it to be a vector space. + +It should be in the vector. + +But if you multiply by a real +number, there's no problem. + +The matrix remains Hermitian. + +You multiplied by +a complex number, + +you use the Hermiticity. + +But an i somewhere here +for all the factors and it + +will not be Hermitian. + +So this is why it's +a real vector space. + +Multiplication by real +numbers preserves Hermiticity. + +So that's surprising. + +So again, illustrates +that nobody + +would say this is a real vector. + +But it really should be thought +as a vector over real numbers. + +Vector space over real numbers. + +Two more examples. + +And they are kind +of interesting. + +So the next example is the set +of polynomials as vector space. + +So that, again, is sort of +a very imaginative thing. + +The set of polynomials p of z. + +Here, z belongs to some +field and p of z, which + +is a function of z, also +belongs to the same field. + +And each polynomial +has coefficient. + +So any p of z is a0 +plus a1 z plus a2 z + +squared plus-- up to some an zn. + +A polynomial is +supposed to end That's + +pretty important +about polynomials. + +So the dots don't go up forever. + +So here it is, the a i's +also belong to the field. + +So looked at this polynomials. + +We have the letter z and +they have these coefficients + +which are numbers. + +So a real polynomial-- you +know 2 plus x plus x squared. + +So you have your real numbers +times this general variable + +that it's also +supposed to be real. + +So you could have it real. + +You could have it complex. + +So that's a polynomial. + +How is that a vector space? + +Well, it's a vector +space-- the space + +p of F of those polynomials-- +of all polynomials + +is a vector space over +F. And why is that? + +Well, you can take-- +again, there's + +some implicit definitions. + +How do you sum polynomials? + +Well, you sum the +independent coefficients. + +You just sum them +and factor out. + +So there's an obvious +definition of sum. + +How do you multiply a +polynomial by a number? + +Obvious definition, you +multiply everything by a number. + +If you sum polynomials, +you get polynomials. + +Given a polynomial, there +is a negative polynomial + +that adds up to 0. + +There's a 0 when all +the coefficients is 0. + +And it has all the +nice properties. + +Now, this example +is more nontrivial + +because you would +think, as opposed + +to the previous examples, +that this is probably + +infinite dimensional because +it has the linear polynomial, + +the quadratic, the cubic, +the quartic, the quintic, all + +of them together. + +And yes, we'll see +that in a second. + +So set of polynomials. + +5. + +Another example, 5. + +The set F infinity of +infinite sequences. + +Sequences x1, x2, infinite +sequences where the x i's + +are in the field. + +So you've got an +infinite sequence + +and you want to add +another infinite sequence. + +Well, you add the first +element, the second elements. + +It's like an infinite +column vector. + +Sometimes mathematicians like to +write column vectors like that + +because it's practical. + +It saves space on a page. + +The vertical one, you +start writing and the pages + +grow very fast. + +So here's an infinite sequence. + +And think of it as a +vertical one if you wish. + +And all elements +are here, but there + +are infinitely many +in every sequence. + +And of course, the set of all +infinite sequences is infinite. + +So this is a vector +space over F. + +Again, because all +the numbers are here, + +so it's a vector space over F. + +And last example. + +Our last example is a +familiar one in physics, + +is the set of complex +functions in an interval. + +Set of complex functions on +an interval x from 0 to L. + +So a set of complex +functions f of x + +I could put here on an +interval [INAUDIBLE]. + +So this is a complex +vector space. + +Vector space. + +The last three +examples, probably you + +would agree that there +are infinite dimensional, + +even though I've not defined +what that means very precisely. + +But that's what we're going +to try to understand now. + +We're supposed to understand +the concept of dimensionality. + +So let's get to +that concept now. + +So in terms of dimensionality, +to build this idea + +you need a definition. + +You need to know the term +subspace of a vector space. + +What is a subspace +of a vector space? + +A subspace of a vector space +is a subset of the vector space + +that is still a vector space. + +So that's why it's +called subspace. + +It's different from subset. + +So a subspace of V is a subset +of V that is a vector space. + +So in particular, it +must contain the vector 0 + +because any vector space +contains the vector 0. + +One of the ways you sometimes +want to understand the vector + +space is by representing it as +a sum of smaller vector spaces. + +And we will do that when +we consider, for example, + +angular momentum in detail. + +So you want to write a vector +space as a sum of subspaces. + +So what is that called? + +It's called a direct sum. + +So if you can write-- +here is the equation. + +You say V is equal to u1 +direct sum with u2 direct sum + +with u3 direct sum with u m. + +When we say this, we +mean the following. + +That the ui's are +subspaces of V. + +And any V in the +vector space can + +be written uniquely as a1 +u1 plus a2 u2 plus a n u + +n with ui [INAUDIBLE] +capital Ui. + +So let me review +what we just said. + +So you have a +vector space and you + +want to decompose it in +sort of basic ingredients. + +This is called a direct sum. + +V is a direct sum of subspaces. + +Direct sum. + +And the Ui's are +subspaces of V. But what + +must happen for +this to be true is + +that once you take +any vector here, + +you can write it as +a sum of a vector + +here, a vector here, a vector +here, a vector everywhere. + +And it must be done uniquely. + +If you can do this +in more than one way, + +this is not a direct sum. + +These subspaces kind of overlap. + +They're not doing the +decomposition in a minimal way. + +Yes. + +AUDIENCE: Does the expression +of V have to be a linear + +combination of the +vectors of the U, + +or just sums of the U sub i's? + +PROFESSOR: It's some +linear combination. + +Look, the interpretation, +for example, R2. + +The normal vector space R2. + +You have an intuition quite +clearly that any vector here + +is a unique sum of this +component along this subspace + +and this component +along this subspace. + +So it's a trivial example, +but the vector space R2 + +has a vector subspace R1 here +and a vector subspace R1. + +Any vector in R2 +is uniquely written + +as a sum of these two vectors. + +That means that R2 +is really R1 plus R1. + +Yes. + +AUDIENCE: [INAUDIBLE]. + +Is it redundant to say that +that-- because a1 u1 is also + +in big U sub 1. + +PROFESSOR: Oh. + +Oh, yes. + +You're right. + +No, I'm sorry. + +I shouldn't write those. + +I'm sorry. + +That's absolutely right. + +If I had that in my +notes, it was a mistake. + +Thank you. + +That was very good. + +Did I have that in my notes? + +No, I had it as you said it. + +True. + +So can be written +uniquely as a vector in + +first, a vector in the second. + +And the a's are +absolutely not necessary. + +OK. + +So let's go ahead then and +say the following things. + +So here we're +going to try to get + +to the concept of +dimensionality in a precise way. + +Yes. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Right, +the last one is m. + +Thank you. + +All right. + +The concept of dimensionality +of a vector space + +is something that you +intuitively understand. + +It's sort of how many +linearly independent vectors + +you need to describe the +whole set of vectors. + +So that is the number +you're trying to get to. + +I'll follow it up in a +slightly rigorous way + +to be able to do infinite +dimensional space as well. + +So we will consider something +called a list of vectors. + +List of vectors. + +And that will be something +like v1, v2 vectors in a vector + +space up to vn. + +Any list of vectors +has finite length. + +So we don't accept infinite +lists by definition. + +You can ask, once you +have a list of vectors, + +what is the vector subspace +spanned by this list? + +How much do you +reach with that list? + +So we call it the +span of the list. + +The span of the list, vn. + +And it's the set of all linear +combinations a1 v1 plus a2 v2 + +plus a n vn for ai in the field. + +So the span of the list +is all possible products + +of your vectors on the list +are-- and put like that. + +So if we say that the +list spans a vector space, + +if the span of the list +is the vector space. + +So that's natural language. + +We say, OK, this list +spans the vector space. + +Why? + +Because if you produce +the span of the list, + +it fills a vector space. + +OK, so I could say it that way. + +So here is the definition, +V is finite dimensional + +if it's spanned by some list. + +If V is spanned by some list. + +So why is that? + +Because if the list is-- a +definition, finite dimensional. + +If it's spanned by some list. + +If you got your list, by +definition it's finite length. + +And with some set of +vectors, you span everything. + +And moreover, it's +infinite dimensional + +if it's not finite dimensional. + +It's kind of silly, +but infinite-- a space + +V is infinite dimensional if +it is not finite dimensional. + +Which is to say that there is +no list that spans the space. + +So for example, this definition +is tailored in a nice way. + +Like let's think +of the polynomials. + +And we want to see if it's +finite dimensional or infinite + +dimensional. + +So you claim it's +finite dimensional. + +Let's see if it's +finite dimensional. + +So we make a list +of polynomials. + +The list must have some length, +at least, that spans it. + +You put all these +730 polynomials + +that you think span the list, +span the space, in this list. + +Now, if you look at +the list, it's 720. + +You can check one +by one until you + +find what is the one +of highest order, + +the polynomial of +highest degree. + +But if the highest degree +is say, z to the 1 million, + +then any polynomial that has +a z to the 2 million cannot be + +spanned by this one. + +So there's no finite +list that can span this, + +so this set-- the +example in 4 is + +infinite dimensional for sure. + +Example 4 is +infinite dimensional. + +Well, example one is +finite dimensional. + +You can see that +because we can produce + +a list that spans the space. + +So look at the example 1. + +It's there. + +Well, what would be the list? + +The list would be-- list. + +You would put a vector +e1, e2, up to en. + +And the vector e1 +would be 1, 0, 0, 0, 0. + +The vector e2 would +be 0, 1, 0, 0, 0. + +And go on like that. + +So you put 1's and 0's. + +And you have n of them. + +And certainly, the most general +one is a1 times e1 a2 times e2. + +And you got the list. + +So example 1 is +finite dimensional. + +A list of vectors is +linearly independent. + +A list is linearly independent +if a list v1 up to vn + +is linearly independent, If +a1 v1 plus a2 v2 plus a n vn + +is equal to 0 has the unique +solution a1 equal a2 equal + +all of them equal 0. + +So that is to mean that +whenever this list satisfies + +this property-- if you want +to represent the vector + +0 with this list, you +must set all of them + +equal to 0, all +the coefficients. + +That's clear as well +in this example. + +If you want to +represent the 0 vector, + +you must have 0 component +against the basis vector x + +and basis vector y. + +So the list of this +vector and this vector + +is linearly independent +because the 0 vector + +must have 0 numbers +multiplying each of them. + +So finally, we define +what is a basis. + +A basis of V is a +list of vectors in V + +that spans V and is +linearly independent. + +So what is a basis? + +Well, you should +have enough vectors + +to represent every vector. + +So it must span V. And +what else should it have? + +It shouldn't have extra +vectors that you don't need. + +It should be minimal. + +It should be all +linearly independent. + +You shouldn't have +added more stuff to it. + +So any finite dimensional +vector space has a basis. + +It's easy to do it. + +There's another thing +that one can prove. + +It may look kind of obvious, +but it requires a small proof + +that if you have-- the +bases are not unique. + +It's something we're going +to exploit all the time. + +One basis, another +basis, a third basis. + +We're going to change +basis all the time. + +Well, the bases are not +unique, but the length + +of the bases of a vector +space is always the same. + +So the length of the +list is-- a number + +is the same whatever +base you choose. + +And that length +is what is called + +the dimension of +the vector space. + +So the dimension +of a vector space + +is the length of any +bases of V. And therefore, + +it's a well-defined concept. + +Any base of a finite vector +space has the same length, + +and the dimension +is that number. + +So there was a question. + +Yes? + +AUDIENCE: Is there +any difference + +between bases [INAUDIBLE]? + +PROFESSOR: No, absolutely not. + +You could have a +basis, for example, + +of R2, which is this vector. + +The first and the +second is this vector. + +And any vector is a +linear superposition + +of these two vectors with some +coefficients and it's unique. + +You can find the coefficients. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yes. + +But you see, here is exactly +what I wanted to make clear. + +We're putting the +vector space and we're + +putting the least +possible structure. + +I didn't say how to take the +inner product of two vectors. + +It's not a definition +of a vector space. + +It's something we'll put later. + +And then, we will be able +to ask whether the basis is + +orthonormal or not. + +But the basis exists. + +Even though you have no +definition of an inner product, + +you can talk about basis +without any confusion. + +You can also talk about +the matrix representation + +of an operator. + +And you don't need +an inner product, + +which is sometimes very unclear. + +You can talk about the +trace of an operator + +and you don't need +an inner product. + +You can talk about +eigenvectors and eigenvalues + +and you don't need +an inner product. + +The only thing you +need the inner product + +is to get numbers. + +And we'll use them to use +[INAUDIBLE] to get numbers. + +But it can wait. + +It's better than +you see all that you + +can do without +introducing more things, + +and then introduce them. + +So let me explain a +little more this concept. + +We were talking about this +base, this vector space 1, + +for example. + +And we produced a list that +spans e1, e2, up to en. + +And those were these vectors. + +Now, this list not +only spans, but they + +are linearly independent. + +If you put a1 times +this plus a2 times + +this and you set +it all equal to 0. + +Well, each entry will be +0, and all the a's are 0. + +So these e's that you put +here on that list is actually + +a basis. + +Therefore, the length of that +basis is the dimensionality. + +And this space has +dimension N. You + +should be able to prove that +this space has been dimension + +m times N. Now, let me do the +Hermitian-- these matrices. + +And try to figure out +the dimensionality + +of the space of +Hermitian matrices. + +So here they are. + +This is the most general +Hermitian matrix. + +And I'm going to produce for +you a list of four vectors. + +Vectors-- yes, they're matrices, +but we call them vectors. + +So here is the list. + +The unit matrix, the first +Pauli matrix, the second Pauli + +matrix, and the +third Pauli matrix. + +All right, let's see how +far do we get from there. + +OK, this is a list of +vectors in the vector space + +because all of +them are Hermitian. + +Good. + +Do they span? + +Well, you calculate the most +general Hermitian matrix + +of this form. + +You just put arbitrary +complex numbers + +and require that the matrix +be equal to its matrix complex + +conjugate and transpose. + +So this is the most general one. + +Do I obtain this +matrix from this one's? + +Yes I just have to put 1 times +c plus a times sigma 1 plus b + +times sigma 2 plus +d times sigma 3. + +So any Hermitian +matrix can be obtained + +as the span of this list. + +Is this list +linearly independent? + +So I have to go here +and set this equal to 0 + +and see if it sets to 0 +all these coefficients. + +Well, it's the same thing as +setting to 0 all this matrix. + +Well, if c plus d and c minus +d are 0, then c and d are 0. + +If this is 0, it must be a 0 +and b 0, so all of them are 0. + +So yes, it's +linearly independent. + +It spans. + +Therefore, you've proven +completely rigorously + +that this vector +space is dimension 4. + +This vector space-- +I will actually + +leave it as an exercise for +you to show that this vector + +space is infinite dimensional. + +You say, of course, it's +infinite dimensional. + +It has infinite sequences. + +Well, you have to +show that if you + +have a finite list of +those infinite sequences, + +like 300 sequences, +they span that. + +They cannot span that. + +So it takes a little work. + +It's interesting +to think about it. + +I think you will enjoy trying +to think about this stuff. + +So that's our discussion +of dimensionality. + +So this one is a little +harder to make sure + +it's infinite dimensional. + +And this one is, yet, a +bit harder than that one + +but it can also be done. + +This is infinite dimensional. + +And this is infinite +dimensional. + +In the last two minute, I want +to tell you a little bit-- one + +definition and let +you go with that, + +is the definition of +a linear operator. + +So here is one thing. + +So you can be more general, +and we won't be that general. + +But when you talk +about linear maps, + +you have one vector space and +another vector space, v and w. + +This is a vector space and +this is a vector space. + +And in general, a map from +here is sometimes called, + +if it satisfies the +property, a linear map. + +And the key thing is +that in all generality, + +these two vector spaces may +not have the same dimension. + +It might be one vector space and +another very different vector + +space. + +You go from one to the other. + +Now, when you have +a vector space v + +and you map to the +same vector space, + +this is also a +linear map, but this + +is called an operator +or a linear operator. + +And what is a linear +operator therefore? + +A linear operator is +a function T. Let's + +call the linear operator T. +It takes v to v. In which way? + +Well, T acting u plus v, +on the sum of vectors, + +is Tu plus T v. And T +acting on a times a vector + +is a times T of the vector. + +These two things make +it into something + +we call a linear operator. + +It acts on the sum +of vectors linearly + +and on a number times a vector. + +The number goes out and +you act on the vector. + +So all you need to know for +what a linear operator is, + +is how it acts on basis vectors. + +Because any vector +on the vector space + +is a superposition +of basis vectors. + +So if you tell me how it +acts on the basis vectors, + +you know everything. + +So we will figure out how +the matrix representation + +of the operators arises from how +it acts on the basis vectors. + +And you don't need +an inner product. + +The reason people think +of this is they say, + +oh, the T i j +matrix element of T + +is the inner product of the +operator between i and j. + +And this is true. + +But for that you +need [? brass ?] + +and inner product, +all these things. + +And they're not necessary. + +We'll define this without that. + +We don't need it. + +So see you next time, +and we'll continue that. + +[APPLAUSE] + +Thank you. \ No newline at end of file diff --git a/f-bMQdul6xI.txt b/f-bMQdul6xI.txt new file mode 100644 index 0000000000000000000000000000000000000000..f77e77a5e174b27fb9ef48aac0113576683a0642 --- /dev/null +++ b/f-bMQdul6xI.txt @@ -0,0 +1,1459 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +in this session we're going to be + + align:start position:0% +in this session we're going to be + + + align:start position:0% +in this session we're going to be +looking at carbohydrate biosynthesis + + align:start position:0% +looking at carbohydrate biosynthesis + + + align:start position:0% +looking at carbohydrate biosynthesis +please look at storyboard 29 looking at + + align:start position:0% +please look at storyboard 29 looking at + + + align:start position:0% +please look at storyboard 29 looking at +panel a the next set of pathways on + + align:start position:0% +panel a the next set of pathways on + + + align:start position:0% +panel a the next set of pathways on +which we're going to focus concerns + + align:start position:0% +which we're going to focus concerns + + + align:start position:0% +which we're going to focus concerns +carbohydrate biosynthesis first we're + + align:start position:0% +carbohydrate biosynthesis first we're + + + align:start position:0% +carbohydrate biosynthesis first we're +going to look at the pathway by which + + align:start position:0% +going to look at the pathway by which + + + align:start position:0% +going to look at the pathway by which +glycogen is made as you know glycogen is + + align:start position:0% +glycogen is made as you know glycogen is + + + align:start position:0% +glycogen is made as you know glycogen is +the polymeric form of glucose that's + + align:start position:0% +the polymeric form of glucose that's + + + align:start position:0% +the polymeric form of glucose that's +very readily available for energy + + align:start position:0% +very readily available for energy + + + align:start position:0% +very readily available for energy +production the second pathway is + + align:start position:0% +production the second pathway is + + + align:start position:0% +production the second pathway is +gluconeogenesis the organs that utilize + + align:start position:0% +gluconeogenesis the organs that utilize + + + align:start position:0% +gluconeogenesis the organs that utilize +glucose as their metabolic fuel prefer + + align:start position:0% +glucose as their metabolic fuel prefer + + + align:start position:0% +glucose as their metabolic fuel prefer +to have glucose at a concentration of + + align:start position:0% +to have glucose at a concentration of + + + align:start position:0% +to have glucose at a concentration of +about 100 milligrams per deciliter in + + align:start position:0% +about 100 milligrams per deciliter in + + + align:start position:0% +about 100 milligrams per deciliter in +the blood the challenge comes from the + + align:start position:0% +the blood the challenge comes from the + + + align:start position:0% +the blood the challenge comes from the +fact that we eat only sporadically and + + align:start position:0% +fact that we eat only sporadically and + + + align:start position:0% +fact that we eat only sporadically and +thus levels of glucose will go up and + + align:start position:0% +thus levels of glucose will go up and + + + align:start position:0% +thus levels of glucose will go up and +down depending upon the time that has + + align:start position:0% +down depending upon the time that has + + + align:start position:0% +down depending upon the time that has +passed since our last meal when glucose + + align:start position:0% +passed since our last meal when glucose + + + align:start position:0% +passed since our last meal when glucose +levels drop gluconeogenesis is the + + align:start position:0% +levels drop gluconeogenesis is the + + + align:start position:0% +levels drop gluconeogenesis is the +pathway that's activated it takes non + + align:start position:0% +pathway that's activated it takes non + + + align:start position:0% +pathway that's activated it takes non +carbohydrate precursors converts them to + + align:start position:0% +carbohydrate precursors converts them to + + + align:start position:0% +carbohydrate precursors converts them to +glucose and then secretes the glucose + + align:start position:0% +glucose and then secretes the glucose + + + align:start position:0% +glucose and then secretes the glucose +into the blood ultimately to help + + align:start position:0% +into the blood ultimately to help + + + align:start position:0% +into the blood ultimately to help +maintain a constant glucose + + align:start position:0% +maintain a constant glucose + + + align:start position:0% +maintain a constant glucose +concentration looking at panel B our + + align:start position:0% +concentration looking at panel B our + + + align:start position:0% +concentration looking at panel B our +first topic is the synthesis of glycogen + + align:start position:0% +first topic is the synthesis of glycogen + + + align:start position:0% +first topic is the synthesis of glycogen +if you look back at my first two + + align:start position:0% +if you look back at my first two + + + align:start position:0% +if you look back at my first two +lectures I described the structure of + + align:start position:0% +lectures I described the structure of + + + align:start position:0% +lectures I described the structure of +glycogen which is also shown here the + + align:start position:0% +glycogen which is also shown here the + + + align:start position:0% +glycogen which is also shown here the +piece of glycogen that I've shown + + align:start position:0% +piece of glycogen that I've shown + + + align:start position:0% +piece of glycogen that I've shown +consists of a linear chain of glucose + + align:start position:0% +consists of a linear chain of glucose + + + align:start position:0% +consists of a linear chain of glucose +molecules connected together through the + + align:start position:0% +molecules connected together through the + + + align:start position:0% +molecules connected together through the +1 in 4 carbons chemically we call this + + align:start position:0% +1 in 4 carbons chemically we call this + + + align:start position:0% +1 in 4 carbons chemically we call this +an alpha 1 4 linkage to the left of the + + align:start position:0% +an alpha 1 4 linkage to the left of the + + + align:start position:0% +an alpha 1 4 linkage to the left of the +glycogen molecule is the non-reducing + + align:start position:0% +glycogen molecule is the non-reducing + + + align:start position:0% +glycogen molecule is the non-reducing +end and to the right is the reducing end + + align:start position:0% +end and to the right is the reducing end + + + align:start position:0% +end and to the right is the reducing end +which is connected by a tyrosine residue + + align:start position:0% +which is connected by a tyrosine residue + + + align:start position:0% +which is connected by a tyrosine residue +to a protein called glycogenin + + align:start position:0% +to a protein called glycogenin + + + align:start position:0% +to a protein called glycogenin +glycogenin is a variant of the glycogen + + align:start position:0% +glycogenin is a variant of the glycogen + + + align:start position:0% +glycogenin is a variant of the glycogen +synthase enzyme we'll talk about later + + align:start position:0% +synthase enzyme we'll talk about later + + + align:start position:0% +synthase enzyme we'll talk about later +glycogenin has the property that it can + + align:start position:0% +glycogenin has the property that it can + + + align:start position:0% +glycogenin has the property that it can +synthesize a polymeric glucose chain + + align:start position:0% +synthesize a polymeric glucose chain + + + align:start position:0% +synthesize a polymeric glucose chain +such as the one shown to boot up the + + align:start position:0% +such as the one shown to boot up the + + + align:start position:0% +such as the one shown to boot up the +synthesis of glycogen in effect + + align:start position:0% +synthesis of glycogen in effect + + + align:start position:0% +synthesis of glycogen in effect +glycogenin forms a primer molecule such + + align:start position:0% +glycogenin forms a primer molecule such + + + align:start position:0% +glycogenin forms a primer molecule such +as the one shown that provides a + + align:start position:0% +as the one shown that provides a + + + align:start position:0% +as the one shown that provides a +non-reducing end that can be extended by + + align:start position:0% +non-reducing end that can be extended by + + + align:start position:0% +non-reducing end that can be extended by +its sister in + + align:start position:0% +its sister in + + + align:start position:0% +its sister in +I'm glycogen synthase while I've drawn a + + align:start position:0% +I'm glycogen synthase while I've drawn a + + + align:start position:0% +I'm glycogen synthase while I've drawn a +linear glucose I want you to keep in + + align:start position:0% +linear glucose I want you to keep in + + + align:start position:0% +linear glucose I want you to keep in +mind that branches off of the six carbon + + align:start position:0% +mind that branches off of the six carbon + + + align:start position:0% +mind that branches off of the six carbon +of the glucoses in the chain are + + align:start position:0% +of the glucoses in the chain are + + + align:start position:0% +of the glucoses in the chain are +possible as I mentioned earlier glycogen + + align:start position:0% +possible as I mentioned earlier glycogen + + + align:start position:0% +possible as I mentioned earlier glycogen +is designed for fast break down this + + align:start position:0% +is designed for fast break down this + + + align:start position:0% +is designed for fast break down this +glucose units will quickly enter the + + align:start position:0% +glucose units will quickly enter the + + + align:start position:0% +glucose units will quickly enter the +pathway of glycolysis and generate ATP s + + align:start position:0% +pathway of glycolysis and generate ATP s + + + align:start position:0% +pathway of glycolysis and generate ATP s +in a matter of seconds + + align:start position:0% +in a matter of seconds + + + align:start position:0% +in a matter of seconds +let's now look at panels see it's useful + + align:start position:0% +let's now look at panels see it's useful + + + align:start position:0% +let's now look at panels see it's useful +to review the biochemical steps by which + + align:start position:0% +to review the biochemical steps by which + + + align:start position:0% +to review the biochemical steps by which +glycogen is broken down because the + + align:start position:0% +glycogen is broken down because the + + + align:start position:0% +glycogen is broken down because the +exact same intermediates appear in the + + align:start position:0% +exact same intermediates appear in the + + + align:start position:0% +exact same intermediates appear in the +reverse order in the synthesis of + + align:start position:0% +reverse order in the synthesis of + + + align:start position:0% +reverse order in the synthesis of +glycogen the key enzyme for glycogen + + align:start position:0% +glycogen the key enzyme for glycogen + + + align:start position:0% +glycogen the key enzyme for glycogen +breakdown or glycogenolysis is glycogen + + align:start position:0% +breakdown or glycogenolysis is glycogen + + + align:start position:0% +breakdown or glycogenolysis is glycogen +phosphorylase glycogen phosphorylase + + align:start position:0% +phosphorylase glycogen phosphorylase + + + align:start position:0% +phosphorylase glycogen phosphorylase +progressively will nip off the + + align:start position:0% +progressively will nip off the + + + align:start position:0% +progressively will nip off the +non-reducing end that is the leftmost + + align:start position:0% +non-reducing end that is the leftmost + + + align:start position:0% +non-reducing end that is the leftmost +sugar as shown producing an oxonium ion + + align:start position:0% +sugar as shown producing an oxonium ion + + + align:start position:0% +sugar as shown producing an oxonium ion +intermediate and as we saw in my first + + align:start position:0% +intermediate and as we saw in my first + + + align:start position:0% +intermediate and as we saw in my first +lecture glycogen phosphorylase stereo + + align:start position:0% +lecture glycogen phosphorylase stereo + + + align:start position:0% +lecture glycogen phosphorylase stereo +specifically adds inorganic phosphate to + + align:start position:0% +specifically adds inorganic phosphate to + + + align:start position:0% +specifically adds inorganic phosphate to +the bottom phase that is the alpha phase + + align:start position:0% +the bottom phase that is the alpha phase + + + align:start position:0% +the bottom phase that is the alpha phase +of the oxonium ion to give glucose + + align:start position:0% +of the oxonium ion to give glucose + + + align:start position:0% +of the oxonium ion to give glucose +1-phosphate + + align:start position:0% +1-phosphate + + + align:start position:0% +1-phosphate +with the stereochemistry shown once + + align:start position:0% +with the stereochemistry shown once + + + align:start position:0% +with the stereochemistry shown once +again these same intermediates are going + + align:start position:0% +again these same intermediates are going + + + align:start position:0% +again these same intermediates are going +to appear in the synthesis of glycogen + + align:start position:0% +to appear in the synthesis of glycogen + + + align:start position:0% +to appear in the synthesis of glycogen +now let's take a look at the way that + + align:start position:0% +now let's take a look at the way that + + + align:start position:0% +now let's take a look at the way that +glucose 1-phosphate interfaces with the + + align:start position:0% +glucose 1-phosphate interfaces with the + + + align:start position:0% +glucose 1-phosphate interfaces with the +other biosynthetic and catabolic + + align:start position:0% +other biosynthetic and catabolic + + + align:start position:0% +other biosynthetic and catabolic +pathways let's look at panel D this + + align:start position:0% +pathways let's look at panel D this + + + align:start position:0% +pathways let's look at panel D this +metabolic map shows glycogen in the + + align:start position:0% +metabolic map shows glycogen in the + + + align:start position:0% +metabolic map shows glycogen in the +lower right hand corner we can see how + + align:start position:0% +lower right hand corner we can see how + + + align:start position:0% +lower right hand corner we can see how +glycogen alysus results in glycogen + + align:start position:0% +glycogen alysus results in glycogen + + + align:start position:0% +glycogen alysus results in glycogen +breakdown to glucose 1-phosphate + + align:start position:0% +breakdown to glucose 1-phosphate + + + align:start position:0% +breakdown to glucose 1-phosphate +and in the reverse direction we can see + + align:start position:0% +and in the reverse direction we can see + + + align:start position:0% +and in the reverse direction we can see +how glucose 1-phosphate can be used to + + align:start position:0% +how glucose 1-phosphate can be used to + + + align:start position:0% +how glucose 1-phosphate can be used to +make glycogen by way of two enzymes UDP + + align:start position:0% +make glycogen by way of two enzymes UDP + + + align:start position:0% +make glycogen by way of two enzymes UDP +glucose pyro phosphorylase ugp and + + align:start position:0% +glucose pyro phosphorylase ugp and + + + align:start position:0% +glucose pyro phosphorylase ugp and +glycogen synthase GS let's look a little + + align:start position:0% +glycogen synthase GS let's look a little + + + align:start position:0% +glycogen synthase GS let's look a little +deeper at other pathways with which + + align:start position:0% +deeper at other pathways with which + + + align:start position:0% +deeper at other pathways with which +glucose 1-phosphate + + align:start position:0% +glucose 1-phosphate + + + align:start position:0% +glucose 1-phosphate +interfaces this schematic shows that + + align:start position:0% +interfaces this schematic shows that + + + align:start position:0% +interfaces this schematic shows that +glucose 1-phosphate + + align:start position:0% +glucose 1-phosphate + + + align:start position:0% +glucose 1-phosphate +can be converted to glucose 6-phosphate + + align:start position:0% +can be converted to glucose 6-phosphate + + + align:start position:0% +can be converted to glucose 6-phosphate +by phosphoglucomutase PGM in this case + + align:start position:0% +by phosphoglucomutase PGM in this case + + + align:start position:0% +by phosphoglucomutase PGM in this case +the phosphate is moved from the one + + align:start position:0% +the phosphate is moved from the one + + + align:start position:0% +the phosphate is moved from the one +carbon to the sixths to the six carbon + + align:start position:0% +carbon to the sixths to the six carbon + + + align:start position:0% +carbon to the sixths to the six carbon +of the glucose moiety the opposite + + align:start position:0% +of the glucose moiety the opposite + + + align:start position:0% +of the glucose moiety the opposite +reaction also occurs that is if you have + + align:start position:0% +reaction also occurs that is if you have + + + align:start position:0% +reaction also occurs that is if you have +glucose 6-phosphate phosphoglucomutase + + align:start position:0% +glucose 6-phosphate phosphoglucomutase + + + align:start position:0% +glucose 6-phosphate phosphoglucomutase +will convert it to glucose 1-phosphate + + align:start position:0% +will convert it to glucose 1-phosphate + + + align:start position:0% +will convert it to glucose 1-phosphate +glucose 6-phosphate is an intermediate + + align:start position:0% +glucose 6-phosphate is an intermediate + + + align:start position:0% +glucose 6-phosphate is an intermediate +in glycolysis gluconeogenesis which is + + align:start position:0% +in glycolysis gluconeogenesis which is + + + align:start position:0% +in glycolysis gluconeogenesis which is +the + + align:start position:0% +the + + + align:start position:0% +the +next pathway we're going to look at and + + align:start position:0% +next pathway we're going to look at and + + + align:start position:0% +next pathway we're going to look at and +another future pathway the pentose + + align:start position:0% +another future pathway the pentose + + + align:start position:0% +another future pathway the pentose +phosphate pathway all of this shows us + + align:start position:0% +phosphate pathway all of this shows us + + + align:start position:0% +phosphate pathway all of this shows us +that glucose 6-phosphate is a crossroads + + align:start position:0% +that glucose 6-phosphate is a crossroads + + + align:start position:0% +that glucose 6-phosphate is a crossroads +and one of the branches that leads from + + align:start position:0% +and one of the branches that leads from + + + align:start position:0% +and one of the branches that leads from +it and to it is by way of glucose + + align:start position:0% +it and to it is by way of glucose + + + align:start position:0% +it and to it is by way of glucose +1-phosphate + + align:start position:0% +1-phosphate + + + align:start position:0% +1-phosphate +let's imagine a scenario in which we eat + + align:start position:0% +let's imagine a scenario in which we eat + + + align:start position:0% +let's imagine a scenario in which we eat +a meal glucose appears in the blood is + + align:start position:0% +a meal glucose appears in the blood is + + + align:start position:0% +a meal glucose appears in the blood is +shown it is taken into the cell the + + align:start position:0% +shown it is taken into the cell the + + + align:start position:0% +shown it is taken into the cell the +enzymes hexokinase or glucokinase will + + align:start position:0% +enzymes hexokinase or glucokinase will + + + align:start position:0% +enzymes hexokinase or glucokinase will +phosphorylate the glucose into glucose + + align:start position:0% +phosphorylate the glucose into glucose + + + align:start position:0% +phosphorylate the glucose into glucose +6-phosphate if the glucose is not needed + + align:start position:0% +6-phosphate if the glucose is not needed + + + align:start position:0% +6-phosphate if the glucose is not needed +for glycolysis or the other pathways I + + align:start position:0% +for glycolysis or the other pathways I + + + align:start position:0% +for glycolysis or the other pathways I +mentioned phosphoglucomutase will + + align:start position:0% +mentioned phosphoglucomutase will + + + align:start position:0% +mentioned phosphoglucomutase will +convert the glucose 6-phosphate to + + align:start position:0% +convert the glucose 6-phosphate to + + + align:start position:0% +convert the glucose 6-phosphate to +glucose 1-phosphate and then in the + + align:start position:0% +glucose 1-phosphate and then in the + + + align:start position:0% +glucose 1-phosphate and then in the +pathway of glycogen synthesis glucose + + align:start position:0% +pathway of glycogen synthesis glucose + + + align:start position:0% +pathway of glycogen synthesis glucose +1-phosphate will be polymerized into + + align:start position:0% +1-phosphate will be polymerized into + + + align:start position:0% +1-phosphate will be polymerized into +glycogen for energy storage at this + + align:start position:0% +glycogen for energy storage at this + + + align:start position:0% +glycogen for energy storage at this +point let's turn to storyboard 30 and + + align:start position:0% +point let's turn to storyboard 30 and + + + align:start position:0% +point let's turn to storyboard 30 and +look at panel a now let's take a look at + + align:start position:0% +look at panel a now let's take a look at + + + align:start position:0% +look at panel a now let's take a look at +the detailed pathway by which glucose + + align:start position:0% +the detailed pathway by which glucose + + + align:start position:0% +the detailed pathway by which glucose +1-phosphate + + align:start position:0% +1-phosphate + + + align:start position:0% +1-phosphate +is converted to glycogen at the left is + + align:start position:0% +is converted to glycogen at the left is + + + align:start position:0% +is converted to glycogen at the left is +the structure of glucose 1-phosphate + + align:start position:0% +the structure of glucose 1-phosphate + + + align:start position:0% +the structure of glucose 1-phosphate +the first enzyme involved is UDP glucose + + align:start position:0% +the first enzyme involved is UDP glucose + + + align:start position:0% +the first enzyme involved is UDP glucose +pyro phosphorylase or ugp the second + + align:start position:0% +pyro phosphorylase or ugp the second + + + align:start position:0% +pyro phosphorylase or ugp the second +substrate in this reaction is UTP + + align:start position:0% +substrate in this reaction is UTP + + + align:start position:0% +substrate in this reaction is UTP +uridine triphosphate the UDP glucose + + align:start position:0% +uridine triphosphate the UDP glucose + + + align:start position:0% +uridine triphosphate the UDP glucose +pyro phosphorylase catalyzes attack by + + align:start position:0% +pyro phosphorylase catalyzes attack by + + + align:start position:0% +pyro phosphorylase catalyzes attack by +the phosphate on the 1 carbon of glucose + + align:start position:0% +the phosphate on the 1 carbon of glucose + + + align:start position:0% +the phosphate on the 1 carbon of glucose +1-phosphate on the alpha phosphorus of + + align:start position:0% +1-phosphate on the alpha phosphorus of + + + align:start position:0% +1-phosphate on the alpha phosphorus of +UTP the two products are pyrophosphate + + align:start position:0% +UTP the two products are pyrophosphate + + + align:start position:0% +UTP the two products are pyrophosphate +and UDP glucose the reaction is made + + align:start position:0% +and UDP glucose the reaction is made + + + align:start position:0% +and UDP glucose the reaction is made +thermodynamically irreversible by + + align:start position:0% +thermodynamically irreversible by + + + align:start position:0% +thermodynamically irreversible by +hydrolysis of pyrophosphate by inorganic + + align:start position:0% +hydrolysis of pyrophosphate by inorganic + + + align:start position:0% +hydrolysis of pyrophosphate by inorganic +pyro phosphatase into two molecules of + + align:start position:0% +pyro phosphatase into two molecules of + + + align:start position:0% +pyro phosphatase into two molecules of +inorganic phosphate the UDP glucose is + + align:start position:0% +inorganic phosphate the UDP glucose is + + + align:start position:0% +inorganic phosphate the UDP glucose is +the substrate for the next enzyme in the + + align:start position:0% +the substrate for the next enzyme in the + + + align:start position:0% +the substrate for the next enzyme in the +sequence glycogen synthase I'm going to + + align:start position:0% +sequence glycogen synthase I'm going to + + + align:start position:0% +sequence glycogen synthase I'm going to +divide the glycogen synthase reaction + + align:start position:0% +divide the glycogen synthase reaction + + + align:start position:0% +divide the glycogen synthase reaction +into two parts in the first we see + + align:start position:0% +into two parts in the first we see + + + align:start position:0% +into two parts in the first we see +cleavage of the bond between the 1 + + align:start position:0% +cleavage of the bond between the 1 + + + align:start position:0% +cleavage of the bond between the 1 +carbon of the glucose and the beta + + align:start position:0% +carbon of the glucose and the beta + + + align:start position:0% +carbon of the glucose and the beta +phosphate of the UDP this reaction + + align:start position:0% +phosphate of the UDP this reaction + + + align:start position:0% +phosphate of the UDP this reaction +liberate s' the UDP and generates the + + align:start position:0% +liberate s' the UDP and generates the + + + align:start position:0% +liberate s' the UDP and generates the +oxonium ion shown in the brackets + + align:start position:0% +oxonium ion shown in the brackets + + + align:start position:0% +oxonium ion shown in the brackets +structurally this oxonium ion is the + + align:start position:0% +structurally this oxonium ion is the + + + align:start position:0% +structurally this oxonium ion is the +same intermediate we saw in glycogen + + align:start position:0% +same intermediate we saw in glycogen + + + align:start position:0% +same intermediate we saw in glycogen +breakdown but here we're using it as a + + align:start position:0% +breakdown but here we're using it as a + + + align:start position:0% +breakdown but here we're using it as a +biosynthetic reagent let's look at panel + + align:start position:0% +biosynthetic reagent let's look at panel + + + align:start position:0% +biosynthetic reagent let's look at panel +B in this panel we continue the glycogen + + align:start position:0% +B in this panel we continue the glycogen + + + align:start position:0% +B in this panel we continue the glycogen +synthase reaction in panel a + + align:start position:0% +synthase reaction in panel a + + + align:start position:0% +synthase reaction in panel a +generated the oxonium ion of glucose + + align:start position:0% +generated the oxonium ion of glucose + + + align:start position:0% +generated the oxonium ion of glucose +which is shown here in panel B in the + + align:start position:0% +which is shown here in panel B in the + + + align:start position:0% +which is shown here in panel B in the +lower-left glycogen synthase activates + + align:start position:0% +lower-left glycogen synthase activates + + + align:start position:0% +lower-left glycogen synthase activates +the hydroxyl group on the 4 carbon of + + align:start position:0% +the hydroxyl group on the 4 carbon of + + + align:start position:0% +the hydroxyl group on the 4 carbon of +the terminal sugar residue that is the + + align:start position:0% +the terminal sugar residue that is the + + + align:start position:0% +the terminal sugar residue that is the +sugar on the non-reducing end the oxygen + + align:start position:0% +sugar on the non-reducing end the oxygen + + + align:start position:0% +sugar on the non-reducing end the oxygen +on the non reducing sugar residue of + + align:start position:0% +on the non reducing sugar residue of + + + align:start position:0% +on the non reducing sugar residue of +glycogen then it taps the bottom of face + + align:start position:0% +glycogen then it taps the bottom of face + + + align:start position:0% +glycogen then it taps the bottom of face +of the oxonium ion to give rise to a + + align:start position:0% +of the oxonium ion to give rise to a + + + align:start position:0% +of the oxonium ion to give rise to a +glycogen unit that has been extended by + + align:start position:0% +glycogen unit that has been extended by + + + align:start position:0% +glycogen unit that has been extended by +one glucose residue I have put an + + align:start position:0% +one glucose residue I have put an + + + align:start position:0% +one glucose residue I have put an +asterisk on the six carbon of the + + align:start position:0% +asterisk on the six carbon of the + + + align:start position:0% +asterisk on the six carbon of the +glucose residue that's been added to the + + align:start position:0% +glucose residue that's been added to the + + + align:start position:0% +glucose residue that's been added to the +growing glycogen chain \ No newline at end of file diff --git a/f6Z99Gu6XEE.txt b/f6Z99Gu6XEE.txt new file mode 100644 index 0000000000000000000000000000000000000000..3bbff1ce02e58faa2bce63c30508b818678d1b7d --- /dev/null +++ b/f6Z99Gu6XEE.txt @@ -0,0 +1,7099 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right sell potential + + align:start position:0% +ocw.mit.edu all right sell potential + + + align:start position:0% +ocw.mit.edu all right sell potential +cell potential potential Delta e cell + + align:start position:0% +cell potential potential Delta e cell + + + align:start position:0% +cell potential potential Delta e cell +and we're going to relate this back to + + align:start position:0% +and we're going to relate this back to + + + align:start position:0% +and we're going to relate this back to +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +G so as we saw with these cells you have + + align:start position:0% +G so as we saw with these cells you have + + + align:start position:0% +G so as we saw with these cells you have +this flow of electrons through this + + align:start position:0% +this flow of electrons through this + + + align:start position:0% +this flow of electrons through this +circuit they're generated at the anode + + align:start position:0% +circuit they're generated at the anode + + + align:start position:0% +circuit they're generated at the anode +from the oxidation reaction and they go + + align:start position:0% +from the oxidation reaction and they go + + + align:start position:0% +from the oxidation reaction and they go +over to the + + align:start position:0% +over to the + + + align:start position:0% +over to the +cathode and when your cell is running + + align:start position:0% +cathode and when your cell is running + + + align:start position:0% +cathode and when your cell is running +it'll generate a potential difference + + align:start position:0% +it'll generate a potential difference + + + align:start position:0% +it'll generate a potential difference +this Delta e Cell between those two + + align:start position:0% +this Delta e Cell between those two + + + align:start position:0% +this Delta e Cell between those two +electrodes in the cell + + align:start position:0% +electrodes in the cell + + + align:start position:0% +electrodes in the cell +so Delta e cell has a lot of different + + align:start position:0% +so Delta e cell has a lot of different + + + align:start position:0% +so Delta e cell has a lot of different +names um it's called cell potential cell + + align:start position:0% +names um it's called cell potential cell + + + align:start position:0% +names um it's called cell potential cell +voltage electron motive Force EMF all of + + align:start position:0% +voltage electron motive Force EMF all of + + + align:start position:0% +voltage electron motive Force EMF all of +these names are valid can be used I'm + + align:start position:0% +these names are valid can be used I'm + + + align:start position:0% +these names are valid can be used I'm +going to try to call it cell potential + + align:start position:0% +going to try to call it cell potential + + + align:start position:0% +going to try to call it cell potential +hopefully I'm not going to switch up but + + align:start position:0% +hopefully I'm not going to switch up but + + + align:start position:0% +hopefully I'm not going to switch up but +if you see any of these it's talking + + align:start position:0% +if you see any of these it's talking + + + align:start position:0% +if you see any of these it's talking +about the same + + align:start position:0% + + + + align:start position:0% + +thing so overall then if we know this + + align:start position:0% +thing so overall then if we know this + + + align:start position:0% +thing so overall then if we know this +cell potential we can relate this back + + align:start position:0% +cell potential we can relate this back + + + align:start position:0% +cell potential we can relate this back +to Delta G and so that will then be able + + align:start position:0% +to Delta G and so that will then be able + + + align:start position:0% +to Delta G and so that will then be able +to tell us whether the reaction is + + align:start position:0% +to tell us whether the reaction is + + + align:start position:0% +to tell us whether the reaction is +spontaneous or not so the overall free + + align:start position:0% +spontaneous or not so the overall free + + + align:start position:0% +spontaneous or not so the overall free +energy Gibs free energy of the cell is + + align:start position:0% +energy Gibs free energy of the cell is + + + align:start position:0% +energy Gibs free energy of the cell is +related to the cell potential by the + + align:start position:0% +related to the cell potential by the + + + align:start position:0% +related to the cell potential by the +following equation so Delta G for the + + align:start position:0% +following equation so Delta G for the + + + align:start position:0% +following equation so Delta G for the +cell minus n the number of moles of + + align:start position:0% +cell minus n the number of moles of + + + align:start position:0% +cell minus n the number of moles of +electrons that pass through the system + + align:start position:0% +electrons that pass through the system + + + align:start position:0% +electrons that pass through the system +uh Faraday constant and that cell + + align:start position:0% +uh Faraday constant and that cell + + + align:start position:0% +uh Faraday constant and that cell +potential all right so we can think + + align:start position:0% +potential all right so we can think + + + align:start position:0% +potential all right so we can think +about this at particular time we can + + align:start position:0% +about this at particular time we can + + + align:start position:0% +about this at particular time we can +also think about this equation in the + + align:start position:0% +also think about this equation in the + + + align:start position:0% +also think about this equation in the +standard States so let's just uh think + + align:start position:0% +standard States so let's just uh think + + + align:start position:0% +standard States so let's just uh think +again about standard States so we can + + align:start position:0% +again about standard States so we can + + + align:start position:0% +again about standard States so we can +talk about Delta G KN for the cell and + + align:start position:0% +talk about Delta G KN for the cell and + + + align:start position:0% +talk about Delta G KN for the cell and +Delta e KN for the cell so Delta e not + + align:start position:0% +Delta e KN for the cell so Delta e not + + + align:start position:0% +Delta e KN for the cell so Delta e not +the cell potential cell voltage EMF for + + align:start position:0% +the cell potential cell voltage EMF for + + + align:start position:0% +the cell potential cell voltage EMF for +the cell um in which the products and + + align:start position:0% +the cell um in which the products and + + + align:start position:0% +the cell um in which the products and +the reactants are in their standard + + align:start position:0% +the reactants are in their standard + + + align:start position:0% +the reactants are in their standard +State and the unit here is bolts so we + + align:start position:0% +State and the unit here is bolts so we + + + align:start position:0% +State and the unit here is bolts so we +have a new unit that we haven't used + + align:start position:0% +have a new unit that we haven't used + + + align:start position:0% +have a new unit that we haven't used +before I think volts all right so let's + + align:start position:0% +before I think volts all right so let's + + + align:start position:0% +before I think volts all right so let's +look at an example of how we would then + + align:start position:0% +look at an example of how we would then + + + align:start position:0% +look at an example of how we would then +calculate our Delta e KN for a cell and + + align:start position:0% +calculate our Delta e KN for a cell and + + + align:start position:0% +calculate our Delta e KN for a cell and +we'll do the cell we've been using this + + align:start position:0% +we'll do the cell we've been using this + + + align:start position:0% +we'll do the cell we've been using this +whole time um our cell with zinc at the + + align:start position:0% +whole time um our cell with zinc at the + + + align:start position:0% +whole time um our cell with zinc at the +anode and copper at the cathode and so + + align:start position:0% +anode and copper at the cathode and so + + + align:start position:0% +anode and copper at the cathode and so +we have our anode reaction and again + + align:start position:0% +we have our anode reaction and again + + + align:start position:0% +we have our anode reaction and again +this is our oxidation and + + align:start position:0% +this is our oxidation and + + + align:start position:0% +this is our oxidation and +ox and our cathode reaction cath r + + align:start position:0% +ox and our cathode reaction cath r + + + align:start position:0% +ox and our cathode reaction cath r +so we can write it out as the reduction + + align:start position:0% +so we can write it out as the reduction + + + align:start position:0% +so we can write it out as the reduction +reaction happening at the + + align:start position:0% +reaction happening at the + + + align:start position:0% +reaction happening at the +cathode and the equation we're going to + + align:start position:0% +cathode and the equation we're going to + + + align:start position:0% +cathode and the equation we're going to +use for this is the following so Delta e + + align:start position:0% +use for this is the following so Delta e + + + align:start position:0% +use for this is the following so Delta e +of the cell the cell potential equals e + + align:start position:0% +of the cell the cell potential equals e + + + align:start position:0% +of the cell the cell potential equals e +and e here is the standard reduction + + align:start position:0% +and e here is the standard reduction + + + align:start position:0% +and e here is the standard reduction +potential and this is a standard + + align:start position:0% +potential and this is a standard + + + align:start position:0% +potential and this is a standard +reduction potential for the couple the + + align:start position:0% +reduction potential for the couple the + + + align:start position:0% +reduction potential for the couple the +reaction that's happening at the cathode + + align:start position:0% +reaction that's happening at the cathode + + + align:start position:0% +reaction that's happening at the cathode +minus the standard reduction potential + + align:start position:0% +minus the standard reduction potential + + + align:start position:0% +minus the standard reduction potential +for the reaction that's happening at the + + align:start position:0% +for the reaction that's happening at the + + + align:start position:0% +for the reaction that's happening at the +anode + + align:start position:0% +anode + + + align:start position:0% +anode +so now we can look up those values in + + align:start position:0% +so now we can look up those values in + + + align:start position:0% +so now we can look up those values in +the back of the book so we have for zinc + + align:start position:0% +the back of the book so we have for zinc + + + align:start position:0% +the back of the book so we have for zinc +the standard reduction potential minus + + align:start position:0% +the standard reduction potential minus + + + align:start position:0% +the standard reduction potential minus +7628 and this the standard reduction + + align:start position:0% +7628 and this the standard reduction + + + align:start position:0% +7628 and this the standard reduction +potential for the copper plus two two + + align:start position:0% +potential for the copper plus two two + + + align:start position:0% +potential for the copper plus two two +electrons to Copper solid reaction Plus + + align:start position:0% +electrons to Copper solid reaction Plus + + + align:start position:0% +electrons to Copper solid reaction Plus +3402 volts so now clicker question why + + align:start position:0% +3402 volts so now clicker question why + + + align:start position:0% +3402 volts so now clicker question why +don't you calculate for me what the cell + + align:start position:0% +don't you calculate for me what the cell + + + align:start position:0% +don't you calculate for me what the cell +potential is for this type of + + align:start position:0% + + + + align:start position:0% + +cell all right so 10 more seconds + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +81% that's right so let's take a look at + + align:start position:0% +81% that's right so let's take a look at + + + align:start position:0% +81% that's right so let's take a look at +that over here so the correct answer + + align:start position:0% +that over here so the correct answer + + + align:start position:0% +that over here so the correct answer +involved putting the standard reduction + + align:start position:0% +involved putting the standard reduction + + + align:start position:0% +involved putting the standard reduction +potential for the reaction at the + + align:start position:0% +potential for the reaction at the + + + align:start position:0% +potential for the reaction at the +cathode with the sign without changing + + align:start position:0% +cathode with the sign without changing + + + align:start position:0% +cathode with the sign without changing +it as plus over here + + align:start position:0% +it as plus over here + + + align:start position:0% +it as plus over here +0.342 and then it's minus and then you + + align:start position:0% +0.342 and then it's minus and then you + + + align:start position:0% +0.342 and then it's minus and then you +put the standard reduction potential in + + align:start position:0% +put the standard reduction potential in + + + align:start position:0% +put the standard reduction potential in +there and this is a minus value minus. + + align:start position:0% +there and this is a minus value minus. + + + align:start position:0% +there and this is a minus value minus. +7628 and minus a minus we get a plus and + + align:start position:0% +7628 and minus a minus we get a plus and + + + align:start position:0% +7628 and minus a minus we get a plus and +so our answer is one + + align:start position:0% +so our answer is one + + + align:start position:0% +so our answer is one +1.13 volts and this is very + + align:start position:0% +1.13 volts and this is very + + + align:start position:0% +1.13 volts and this is very +important um and it's important to think + + align:start position:0% +important um and it's important to think + + + align:start position:0% +important um and it's important to think +about the reaction at the cathode which + + align:start position:0% +about the reaction at the cathode which + + + align:start position:0% +about the reaction at the cathode which +is the copper reaction the reaction at + + align:start position:0% +is the copper reaction the reaction at + + + align:start position:0% +is the copper reaction the reaction at +the anode is the zinc reaction and a lot + + align:start position:0% +the anode is the zinc reaction and a lot + + + align:start position:0% +the anode is the zinc reaction and a lot +of people + + align:start position:0% +of people + + + align:start position:0% +of people +um try to be too clever with these and + + align:start position:0% +um try to be too clever with these and + + + align:start position:0% +um try to be too clever with these and +they're like okay but this one this this + + align:start position:0% +they're like okay but this one this this + + + align:start position:0% +they're like okay but this one this this +one is uh going to be this one's the one + + align:start position:0% +one is uh going to be this one's the one + + + align:start position:0% +one is uh going to be this one's the one +that's being oxidized so I'll switch the + + align:start position:0% +that's being oxidized so I'll switch the + + + align:start position:0% +that's being oxidized so I'll switch the +sign and then put it in the equation and + + align:start position:0% +sign and then put it in the equation and + + + align:start position:0% +sign and then put it in the equation and +end up getting it wrong so if you always + + align:start position:0% +end up getting it wrong so if you always + + + align:start position:0% +end up getting it wrong so if you always +remember standard reduction potential + + align:start position:0% +remember standard reduction potential + + + align:start position:0% +remember standard reduction potential +put here standard reduction potential + + align:start position:0% +put here standard reduction potential + + + align:start position:0% +put here standard reduction potential +put here the equation already takes care + + align:start position:0% +put here the equation already takes care + + + align:start position:0% +put here the equation already takes care +of the sign issue for you so don't do + + align:start position:0% +of the sign issue for you so don't do + + + align:start position:0% +of the sign issue for you so don't do +anything with the sign other people say + + align:start position:0% +anything with the sign other people say + + + align:start position:0% +anything with the sign other people say +I looked through pages and pages of + + align:start position:0% +I looked through pages and pages of + + + align:start position:0% +I looked through pages and pages of +these Potentials in the book and the + + align:start position:0% +these Potentials in the book and the + + + align:start position:0% +these Potentials in the book and the +reaction I'm looking for isn't listed + + align:start position:0% +reaction I'm looking for isn't listed + + + align:start position:0% +reaction I'm looking for isn't listed +because they're looking for an oxidation + + align:start position:0% +because they're looking for an oxidation + + + align:start position:0% +because they're looking for an oxidation +they're not going to find the reaction + + align:start position:0% +they're not going to find the reaction + + + align:start position:0% +they're not going to find the reaction +written as an oxidation in a table of + + align:start position:0% +written as an oxidation in a table of + + + align:start position:0% +written as an oxidation in a table of +reduction potentials so all of these are + + align:start position:0% +reduction potentials so all of these are + + + align:start position:0% +reduction potentials so all of these are +listed as reduction potentials that's + + align:start position:0% +listed as reduction potentials that's + + + align:start position:0% +listed as reduction potentials that's +what you will find the trick is to + + align:start position:0% +what you will find the trick is to + + + align:start position:0% +what you will find the trick is to +remember which is happening at the + + align:start position:0% +remember which is happening at the + + + align:start position:0% +remember which is happening at the +cathode which is happening at the anode + + align:start position:0% +cathode which is happening at the anode + + + align:start position:0% +cathode which is happening at the anode +and then you will always get this + + align:start position:0% +and then you will always get this + + + align:start position:0% +and then you will always get this +problem right and it's good to get this + + align:start position:0% +problem right and it's good to get this + + + align:start position:0% +problem right and it's good to get this +right because as you'll see later on + + align:start position:0% +right because as you'll see later on + + + align:start position:0% +right because as you'll see later on +this can be step one in a multi-art + + align:start position:0% +this can be step one in a multi-art + + + align:start position:0% +this can be step one in a multi-art +problem all right so when we + + align:start position:0% +problem all right so when we + + + align:start position:0% +problem all right so when we +successfully calculated um Delta e of + + align:start position:0% +successfully calculated um Delta e of + + + align:start position:0% +successfully calculated um Delta e of +the cell the cell potential then we can + + align:start position:0% +the cell the cell potential then we can + + + align:start position:0% +the cell the cell potential then we can +ask is the flow of electrons going to be + + align:start position:0% +ask is the flow of electrons going to be + + + align:start position:0% +ask is the flow of electrons going to be +spontaneous for this will + + align:start position:0% +spontaneous for this will + + + align:start position:0% +spontaneous for this will +it it will be and the way we know that + + align:start position:0% +it it will be and the way we know that + + + align:start position:0% +it it will be and the way we know that +is that we can always come back to Delta + + align:start position:0% +is that we can always come back to Delta + + + align:start position:0% +is that we can always come back to Delta +G so whenever you're ask if something is + + align:start position:0% +G so whenever you're ask if something is + + + align:start position:0% +G so whenever you're ask if something is +spontaneous or not you always want to + + align:start position:0% +spontaneous or not you always want to + + + align:start position:0% +spontaneous or not you always want to +think Del Delta G that's what I'm going + + align:start position:0% +think Del Delta G that's what I'm going + + + align:start position:0% +think Del Delta G that's what I'm going +to go for I'm going to think about Delta + + align:start position:0% +to go for I'm going to think about Delta + + + align:start position:0% +to go for I'm going to think about Delta +G so here Delta g equals minus n number + + align:start position:0% +G so here Delta g equals minus n number + + + align:start position:0% +G so here Delta g equals minus n number +of moles of electrons Faraday constant + + align:start position:0% +of moles of electrons Faraday constant + + + align:start position:0% +of moles of electrons Faraday constant +times that cell potential so if the cell + + align:start position:0% +times that cell potential so if the cell + + + align:start position:0% +times that cell potential so if the cell +potential is positive Delta G will be + + align:start position:0% +potential is positive Delta G will be + + + align:start position:0% +potential is positive Delta G will be +negative and is a reaction spontaneous + + align:start position:0% +negative and is a reaction spontaneous + + + align:start position:0% +negative and is a reaction spontaneous +when Delta G is + + align:start position:0% + + + + align:start position:0% + +negative just I it's easy to answer it's + + align:start position:0% +negative just I it's easy to answer it's + + + align:start position:0% +negative just I it's easy to answer it's +on my shirt today giving it all away yes + + align:start position:0% +on my shirt today giving it all away yes + + + align:start position:0% +on my shirt today giving it all away yes +so when Delta G is is negative then you + + align:start position:0% +so when Delta G is is negative then you + + + align:start position:0% +so when Delta G is is negative then you +can be feeling spontaneous it's a + + align:start position:0% +can be feeling spontaneous it's a + + + align:start position:0% +can be feeling spontaneous it's a +spontaneous reaction so Delta e positive + + align:start position:0% +spontaneous reaction so Delta e positive + + + align:start position:0% +spontaneous reaction so Delta e positive +means Delta G negative reaction is + + align:start position:0% +means Delta G negative reaction is + + + align:start position:0% +means Delta G negative reaction is +spontaneous all right so now let's have + + align:start position:0% +spontaneous all right so now let's have + + + align:start position:0% +spontaneous all right so now let's have +a little uh reminder review of what + + align:start position:0% +a little uh reminder review of what + + + align:start position:0% +a little uh reminder review of what +types of cells have spontaneous + + align:start position:0% +types of cells have spontaneous + + + align:start position:0% +types of cells have spontaneous +reactions and what kind involve + + align:start position:0% +reactions and what kind involve + + + align:start position:0% +reactions and what kind involve +non-spontaneous reaction + + align:start position:0% + + + + align:start position:0% + +all right 10 more + + align:start position:0% + + + + align:start position:0% + +seconds can anyone uh tell me what the + + align:start position:0% +seconds can anyone uh tell me what the + + + align:start position:0% +seconds can anyone uh tell me what the +correct name is of the cell that + + align:start position:0% +correct name is of the cell that + + + align:start position:0% +correct name is of the cell that +involves a instantaneous + + align:start position:0% +involves a instantaneous + + + align:start position:0% +involves a instantaneous +reaction electrolytic + + align:start position:0% + + + + align:start position:0% + +cell + + align:start position:0% + + + + align:start position:0% + +yeah all right so if we look over + + align:start position:0% +yeah all right so if we look over + + + align:start position:0% +yeah all right so if we look over +here so people knew about the uh + + align:start position:0% +here so people knew about the uh + + + align:start position:0% +here so people knew about the uh +galvanic that's good right so a reaction + + align:start position:0% +galvanic that's good right so a reaction + + + align:start position:0% +galvanic that's good right so a reaction +if it's a spontaneous reaction that will + + align:start position:0% +if it's a spontaneous reaction that will + + + align:start position:0% +if it's a spontaneous reaction that will +produce an electric current that's + + align:start position:0% +produce an electric current that's + + + align:start position:0% +produce an electric current that's +called a galvanic cell if it's a + + align:start position:0% +called a galvanic cell if it's a + + + align:start position:0% +called a galvanic cell if it's a +non-spontaneous reaction that has to be + + align:start position:0% +non-spontaneous reaction that has to be + + + align:start position:0% +non-spontaneous reaction that has to be +driven by applying a current that's + + align:start position:0% +driven by applying a current that's + + + align:start position:0% +driven by applying a current that's +called an electrolytic cell so I just + + align:start position:0% +called an electrolytic cell so I just + + + align:start position:0% +called an electrolytic cell so I just +threw up another random name um and uh + + align:start position:0% +threw up another random name um and uh + + + align:start position:0% +threw up another random name um and uh +to see to see if people would go for it + + align:start position:0% +to see to see if people would go for it + + + align:start position:0% +to see to see if people would go for it +all right so it's important to keep + + align:start position:0% +all right so it's important to keep + + + align:start position:0% +all right so it's important to keep +these in mind because a lot of the + + align:start position:0% +these in mind because a lot of the + + + align:start position:0% +these in mind because a lot of the +problems will say things like um in this + + align:start position:0% +problems will say things like um in this + + + align:start position:0% +problems will say things like um in this +galvanic cell and you seem like you + + align:start position:0% +galvanic cell and you seem like you + + + align:start position:0% +galvanic cell and you seem like you +don't have enough information to solve + + align:start position:0% +don't have enough information to solve + + + align:start position:0% +don't have enough information to solve +the problem because the the problem + + align:start position:0% +the problem because the the problem + + + align:start position:0% +the problem because the the problem +didn't tell you which reaction was at + + align:start position:0% +didn't tell you which reaction was at + + + align:start position:0% +didn't tell you which reaction was at +the anode or which reaction was at the + + align:start position:0% +the anode or which reaction was at the + + + align:start position:0% +the anode or which reaction was at the +cathode so how do you do the problem + + align:start position:0% +cathode so how do you do the problem + + + align:start position:0% +cathode so how do you do the problem +well the fact they told you it was a + + align:start position:0% +well the fact they told you it was a + + + align:start position:0% +well the fact they told you it was a +galvanic cell there's only one way to + + align:start position:0% +galvanic cell there's only one way to + + + align:start position:0% +galvanic cell there's only one way to +put the reactions in order for it to be + + align:start position:0% +put the reactions in order for it to be + + + align:start position:0% +put the reactions in order for it to be +spontaneous so that's part of the + + align:start position:0% +spontaneous so that's part of the + + + align:start position:0% +spontaneous so that's part of the +problem figuring out which is at the + + align:start position:0% +problem figuring out which is at the + + + align:start position:0% +problem figuring out which is at the +anode and which is at the cathode based + + align:start position:0% +anode and which is at the cathode based + + + align:start position:0% +anode and which is at the cathode based +on the fact that it has to be a + + align:start position:0% +on the fact that it has to be a + + + align:start position:0% +on the fact that it has to be a +spontaneous reaction so knowing these + + align:start position:0% +spontaneous reaction so knowing these + + + align:start position:0% +spontaneous reaction so knowing these +terms is really important it's hard to + + align:start position:0% +terms is really important it's hard to + + + align:start position:0% +terms is really important it's hard to +do the problems without them all right + + align:start position:0% +do the problems without them all right + + + align:start position:0% +do the problems without them all right +summary of this part then so a cell + + align:start position:0% +summary of this part then so a cell + + + align:start position:0% +summary of this part then so a cell +operates spontaneously whether it does + + align:start position:0% +operates spontaneously whether it does + + + align:start position:0% +operates spontaneously whether it does +or not can be determined by um your cell + + align:start position:0% +or not can be determined by um your cell + + + align:start position:0% +or not can be determined by um your cell +potential if it's positive it's + + align:start position:0% +potential if it's positive it's + + + align:start position:0% +potential if it's positive it's +spontaneous and that's because if it's + + align:start position:0% +spontaneous and that's because if it's + + + align:start position:0% +spontaneous and that's because if it's +positive Delta G is negative and Delta G + + align:start position:0% +positive Delta G is negative and Delta G + + + align:start position:0% +positive Delta G is negative and Delta G +is really what tells you about + + align:start position:0% +is really what tells you about + + + align:start position:0% +is really what tells you about +spontaneity and you can calculate your + + align:start position:0% +spontaneity and you can calculate your + + + align:start position:0% +spontaneity and you can calculate your +cell Potential from your standard + + align:start position:0% +cell Potential from your standard + + + align:start position:0% +cell Potential from your standard +reduction potentials that you will find + + align:start position:0% +reduction potentials that you will find + + + align:start position:0% +reduction potentials that you will find +in your book all right so now let's + + align:start position:0% +in your book all right so now let's + + + align:start position:0% +in your book all right so now let's +think think about the meaning of the + + align:start position:0% +think think about the meaning of the + + + align:start position:0% +think think about the meaning of the +standard reduction potential what's true + + align:start position:0% +standard reduction potential what's true + + + align:start position:0% +standard reduction potential what's true +if it's a large positive value what's + + align:start position:0% +if it's a large positive value what's + + + align:start position:0% +if it's a large positive value what's +true if it is a large negative value + + align:start position:0% +true if it is a large negative value + + + align:start position:0% +true if it is a large negative value +what we can look at these values and + + align:start position:0% +what we can look at these values and + + + align:start position:0% +what we can look at these values and +know something about the reactions so + + align:start position:0% +know something about the reactions so + + + align:start position:0% +know something about the reactions so +meaning of standard prod production + + align:start position:0% +meaning of standard prod production + + + align:start position:0% +meaning of standard prod production +potentials what do the values tell us so + + align:start position:0% +potentials what do the values tell us so + + + align:start position:0% +potentials what do the values tell us so +a large positive standard reduction + + align:start position:0% +a large positive standard reduction + + + align:start position:0% +a large positive standard reduction +potential means that the element is easy + + align:start position:0% +potential means that the element is easy + + + align:start position:0% +potential means that the element is easy +to reduce so let's look at an example so + + align:start position:0% +to reduce so let's look at an example so + + + align:start position:0% +to reduce so let's look at an example so +we have um Florine F2 gas plus two + + align:start position:0% +we have um Florine F2 gas plus two + + + align:start position:0% +we have um Florine F2 gas plus two +electrons going to two Florine minus + + align:start position:0% +electrons going to two Florine minus + + + align:start position:0% +electrons going to two Florine minus +ions and this has a standard reduction + + align:start position:0% +ions and this has a standard reduction + + + align:start position:0% +ions and this has a standard reduction +potential of plus + + align:start position:0% +potential of plus + + + align:start position:0% +potential of plus +2.87 volts so large positive number + + align:start position:0% +2.87 volts so large positive number + + + align:start position:0% +2.87 volts so large positive number +means that it's easy to add electrons + + align:start position:0% +means that it's easy to add electrons + + + align:start position:0% +means that it's easy to add electrons +and we can think about this in terms of + + align:start position:0% +and we can think about this in terms of + + + align:start position:0% +and we can think about this in terms of +what we know about these reactions so + + align:start position:0% +what we know about these reactions so + + + align:start position:0% +what we know about these reactions so +again if it's a positive standard + + align:start position:0% +again if it's a positive standard + + + align:start position:0% +again if it's a positive standard +reduction potential e not that's going + + align:start position:0% +reduction potential e not that's going + + + align:start position:0% +reduction potential e not that's going +to mean a negative Delta the G for this + + align:start position:0% +to mean a negative Delta the G for this + + + align:start position:0% +to mean a negative Delta the G for this +reaction is written written as the + + align:start position:0% +reaction is written written as the + + + align:start position:0% +reaction is written written as the +reduction reaction and so it's favorable + + align:start position:0% +reduction reaction and so it's favorable + + + align:start position:0% +reduction reaction and so it's favorable +or spontaneous in that direction so the + + align:start position:0% +or spontaneous in that direction so the + + + align:start position:0% +or spontaneous in that direction so the +reduction is spontaneous or favorable so + + align:start position:0% +reduction is spontaneous or favorable so + + + align:start position:0% +reduction is spontaneous or favorable so +when you have a large positive value + + align:start position:0% +when you have a large positive value + + + align:start position:0% +when you have a large positive value +here you can think about yes Florine + + align:start position:0% +here you can think about yes Florine + + + align:start position:0% +here you can think about yes Florine +wants those electrons it spontaneously + + align:start position:0% +wants those electrons it spontaneously + + + align:start position:0% +wants those electrons it spontaneously +will grab those electrons and become F + + align:start position:0% +will grab those electrons and become F + + + align:start position:0% +will grab those electrons and become F +minus and this also makes sense to you + + align:start position:0% +minus and this also makes sense to you + + + align:start position:0% +minus and this also makes sense to you +if you think about your periodic table + + align:start position:0% +if you think about your periodic table + + + align:start position:0% +if you think about your periodic table +Trends you have Florine wants to be F + + align:start position:0% +Trends you have Florine wants to be F + + + align:start position:0% +Trends you have Florine wants to be F +minus it will have its noble gas + + align:start position:0% +minus it will have its noble gas + + + align:start position:0% +minus it will have its noble gas +configuration then it likes getting an + + align:start position:0% +configuration then it likes getting an + + + align:start position:0% +configuration then it likes getting an +extra electron so this should make sense + + align:start position:0% +extra electron so this should make sense + + + align:start position:0% +extra electron so this should make sense +from other things that we've talked + + align:start position:0% +from other things that we've talked + + + align:start position:0% +from other things that we've talked +about so now I could ask the question + + align:start position:0% +about so now I could ask the question + + + align:start position:0% +about so now I could ask the question +and I will and it's a clicker question + + align:start position:0% +and I will and it's a clicker question + + + align:start position:0% +and I will and it's a clicker question +does that make F2 a good oxidizing agent + + align:start position:0% +does that make F2 a good oxidizing agent + + + align:start position:0% +does that make F2 a good oxidizing agent +or + + align:start position:0% + + + + align:start position:0% + +not all right 10 more seconds + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +right so the answer is yes F2 is easy to + + align:start position:0% +right so the answer is yes F2 is easy to + + + align:start position:0% +right so the answer is yes F2 is easy to +reduce which makes it a good oxidizing + + align:start position:0% +reduce which makes it a good oxidizing + + + align:start position:0% +reduce which makes it a good oxidizing +agent remember it's an agent of + + align:start position:0% +agent remember it's an agent of + + + align:start position:0% +agent remember it's an agent of +oxidation it wants to go out there and + + align:start position:0% +oxidation it wants to go out there and + + + align:start position:0% +oxidation it wants to go out there and +oxidize other things it wants to self be + + align:start position:0% +oxidize other things it wants to self be + + + align:start position:0% +oxidize other things it wants to self be +reduced so something that's a good + + align:start position:0% +reduced so something that's a good + + + align:start position:0% +reduced so something that's a good +oxidizing agent is easy to reduce it + + align:start position:0% +oxidizing agent is easy to reduce it + + + align:start position:0% +oxidizing agent is easy to reduce it +wants to be reduced it wants to be an + + align:start position:0% +wants to be reduced it wants to be an + + + align:start position:0% +wants to be reduced it wants to be an +agent of oxidation bringing oxidation to + + align:start position:0% +agent of oxidation bringing oxidation to + + + align:start position:0% +agent of oxidation bringing oxidation to +the world so it's easy to reduce it's a + + align:start position:0% +the world so it's easy to reduce it's a + + + align:start position:0% +the world so it's easy to reduce it's a +good oxidizing + + align:start position:0% +good oxidizing + + + align:start position:0% +good oxidizing +agent so in general you can think about + + align:start position:0% +agent so in general you can think about + + + align:start position:0% +agent so in general you can think about +this the following way let's just like + + align:start position:0% +this the following way let's just like + + + align:start position:0% +this the following way let's just like +Bring the Noise down a little bit know + + align:start position:0% +Bring the Noise down a little bit know + + + align:start position:0% +Bring the Noise down a little bit know +it's a clicker competition day so we + + align:start position:0% +it's a clicker competition day so we + + + align:start position:0% +it's a clicker competition day so we +have a large positive value here for a + + align:start position:0% +have a large positive value here for a + + + align:start position:0% +have a large positive value here for a +reaction for a reduction reaction + + align:start position:0% +reaction for a reduction reaction + + + align:start position:0% +reaction for a reduction reaction +reaction is written large positive + + align:start position:0% +reaction is written large positive + + + align:start position:0% +reaction is written large positive +standard reduction + + align:start position:0% +standard reduction + + + align:start position:0% +standard reduction +potential and the couple here F2 to F + + align:start position:0% +potential and the couple here F2 to F + + + align:start position:0% +potential and the couple here F2 to F +minus is the couple we're talking about + + align:start position:0% +minus is the couple we're talking about + + + align:start position:0% +minus is the couple we're talking about +and we'll say that the oxidized species + + align:start position:0% +and we'll say that the oxidized species + + + align:start position:0% +and we'll say that the oxidized species +of that couple is very oxidizing and + + align:start position:0% +of that couple is very oxidizing and + + + align:start position:0% +of that couple is very oxidizing and +again F2 here is the oxidized + + align:start position:0% + + + + align:start position:0% + +species so the oxidized species F2 is a + + align:start position:0% +species so the oxidized species F2 is a + + + align:start position:0% +species so the oxidized species F2 is a +good oxidizing agent it's very oxidizing + + align:start position:0% +good oxidizing agent it's very oxidizing + + + align:start position:0% +good oxidizing agent it's very oxidizing +if because it has a large positive stand + + align:start position:0% +if because it has a large positive stand + + + align:start position:0% +if because it has a large positive stand +standard reduction + + align:start position:0% +standard reduction + + + align:start position:0% +standard reduction +potential all right so I don't know how + + align:start position:0% +potential all right so I don't know how + + + align:start position:0% +potential all right so I don't know how +well this copied um but here are some + + align:start position:0% +well this copied um but here are some + + + align:start position:0% +well this copied um but here are some +standard reduction potentials they're + + align:start position:0% +standard reduction potentials they're + + + align:start position:0% +standard reduction potentials they're +all in your book so it's okay if they + + align:start position:0% +all in your book so it's okay if they + + + align:start position:0% +all in your book so it's okay if they +look terrible um but the important Point + + align:start position:0% +look terrible um but the important Point + + + align:start position:0% +look terrible um but the important Point +here is at the top we have po large + + align:start position:0% +here is at the top we have po large + + + align:start position:0% +here is at the top we have po large +positive Valu so if you can see that in + + align:start position:0% +positive Valu so if you can see that in + + + align:start position:0% +positive Valu so if you can see that in +your handout this is the reaction we + + align:start position:0% +your handout this is the reaction we + + + align:start position:0% +your handout this is the reaction we +just talked about or the couple we just + + align:start position:0% +just talked about or the couple we just + + + align:start position:0% +just talked about or the couple we just +talked about F2 um f minus and so large + + align:start position:0% +talked about F2 um f minus and so large + + + align:start position:0% +talked about F2 um f minus and so large +positive and then there's a gap here + + align:start position:0% +positive and then there's a gap here + + + align:start position:0% +positive and then there's a gap here +there are pages in pages and pages of + + align:start position:0% +there are pages in pages and pages of + + + align:start position:0% +there are pages in pages and pages of +these standard reduction potentials and + + align:start position:0% +these standard reduction potentials and + + + align:start position:0% +these standard reduction potentials and +at the very bottom you have a large + + align:start position:0% +at the very bottom you have a large + + + align:start position:0% +at the very bottom you have a large +negative number so large positive on the + + align:start position:0% +negative number so large positive on the + + + align:start position:0% +negative number so large positive on the +top large negative on the bottom so at + + align:start position:0% +top large negative on the bottom so at + + + align:start position:0% +top large negative on the bottom so at +the very top the oxidized species of + + align:start position:0% +the very top the oxidized species of + + + align:start position:0% +the very top the oxidized species of +that couple is very oxidizing and we'll + + align:start position:0% +that couple is very oxidizing and we'll + + + align:start position:0% +that couple is very oxidizing and we'll +see at the in a minute that at the + + align:start position:0% +see at the in a minute that at the + + + align:start position:0% +see at the in a minute that at the +bottom the reduced species when it's a + + align:start position:0% +bottom the reduced species when it's a + + + align:start position:0% +bottom the reduced species when it's a +there a negative number here the reduced + + align:start position:0% +there a negative number here the reduced + + + align:start position:0% +there a negative number here the reduced +species is very + + align:start position:0% +species is very + + + align:start position:0% +species is very +reducing all right so so let's look at + + align:start position:0% +reducing all right so so let's look at + + + align:start position:0% +reducing all right so so let's look at +the reduced species and this is lithium + + align:start position:0% +the reduced species and this is lithium + + + align:start position:0% +the reduced species and this is lithium +on the bottom so a large negative + + align:start position:0% +on the bottom so a large negative + + + align:start position:0% +on the bottom so a large negative +standard reduction potential means that + + align:start position:0% +standard reduction potential means that + + + align:start position:0% +standard reduction potential means that +the element is hard to reduce so example + + align:start position:0% +the element is hard to reduce so example + + + align:start position:0% +the element is hard to reduce so example +lithium + one plus one electron going to + + align:start position:0% +lithium + one plus one electron going to + + + align:start position:0% +lithium + one plus one electron going to +lithium solid the standard reduction + + align:start position:0% +lithium solid the standard reduction + + + align:start position:0% +lithium solid the standard reduction +potential for this reaction is minus + + align:start position:0% +potential for this reaction is minus + + + align:start position:0% +potential for this reaction is minus +3.45 volts so it's hard to add electrons + + align:start position:0% +3.45 volts so it's hard to add electrons + + + align:start position:0% +3.45 volts so it's hard to add electrons +to lithium plus we have a negative + + align:start position:0% +to lithium plus we have a negative + + + align:start position:0% +to lithium plus we have a negative +standard reduction potential which means + + align:start position:0% +standard reduction potential which means + + + align:start position:0% +standard reduction potential which means +a positive Delta G for the reaction is + + align:start position:0% +a positive Delta G for the reaction is + + + align:start position:0% +a positive Delta G for the reaction is +written for the reduction reaction so + + align:start position:0% +written for the reduction reaction so + + + align:start position:0% +written for the reduction reaction so +it's not favorable lithium plus does not + + align:start position:0% +it's not favorable lithium plus does not + + + align:start position:0% +it's not favorable lithium plus does not +want electrons it doesn't want to go to + + align:start position:0% +want electrons it doesn't want to go to + + + align:start position:0% +want electrons it doesn't want to go to +lithium solid so lithium plus if it + + align:start position:0% +lithium solid so lithium plus if it + + + align:start position:0% +lithium solid so lithium plus if it +loses an electron it gets its nice noble + + align:start position:0% +loses an electron it gets its nice noble + + + align:start position:0% +loses an electron it gets its nice noble +gas configuration it's a group one + + align:start position:0% +gas configuration it's a group one + + + align:start position:0% +gas configuration it's a group one +element it likes to be in the plus one + + align:start position:0% +element it likes to be in the plus one + + + align:start position:0% +element it likes to be in the plus one +oxidation state it doesn't want to be + + align:start position:0% +oxidation state it doesn't want to be + + + align:start position:0% +oxidation state it doesn't want to be +reduced so is lithium plus one a good o + + align:start position:0% +reduced so is lithium plus one a good o + + + align:start position:0% +reduced so is lithium plus one a good o +izing + + align:start position:0% +izing + + + align:start position:0% +izing +agent no it's not it does not want to be + + align:start position:0% +agent no it's not it does not want to be + + + align:start position:0% +agent no it's not it does not want to be +reduced + + align:start position:0% +reduced + + + align:start position:0% +reduced +but lithium + + align:start position:0% +but lithium + + + align:start position:0% +but lithium +solid is a good reducing agent it's a + + align:start position:0% +solid is a good reducing agent it's a + + + align:start position:0% +solid is a good reducing agent it's a +good reducing agent because it wants to + + align:start position:0% +good reducing agent because it wants to + + + align:start position:0% +good reducing agent because it wants to +reduce other things it wants to itself + + align:start position:0% +reduce other things it wants to itself + + + align:start position:0% +reduce other things it wants to itself +become + + align:start position:0% +become + + + align:start position:0% +become +oxidized so lithium solid will reduce + + align:start position:0% +oxidized so lithium solid will reduce + + + align:start position:0% +oxidized so lithium solid will reduce +other things lithium solid wants to be + + align:start position:0% +other things lithium solid wants to be + + + align:start position:0% +other things lithium solid wants to be +oxidized it wants to be lithium + + + align:start position:0% +oxidized it wants to be lithium + + + + align:start position:0% +oxidized it wants to be lithium + +one so the rule here for those large + + align:start position:0% +one so the rule here for those large + + + align:start position:0% +one so the rule here for those large +negative standard reduction potential uh + + align:start position:0% +negative standard reduction potential uh + + + align:start position:0% +negative standard reduction potential uh +couples is that with a large negative + + align:start position:0% +couples is that with a large negative + + + align:start position:0% +couples is that with a large negative +standard reduction potential the reduced + + align:start position:0% +standard reduction potential the reduced + + + align:start position:0% +standard reduction potential the reduced +species is very reducing the reduced + + align:start position:0% +species is very reducing the reduced + + + align:start position:0% +species is very reducing the reduced +species here is lithium so lithium is + + align:start position:0% +species here is lithium so lithium is + + + align:start position:0% +species here is lithium so lithium is +reduced compared to lithium plus one + + align:start position:0% +reduced compared to lithium plus one + + + align:start position:0% +reduced compared to lithium plus one +this then is very reducing it is a good + + align:start position:0% +this then is very reducing it is a good + + + align:start position:0% +this then is very reducing it is a good +reducing agent do you think lithium + + + align:start position:0% +reducing agent do you think lithium + + + + align:start position:0% +reducing agent do you think lithium + +one would be good reducing + + align:start position:0% +one would be good reducing + + + align:start position:0% +one would be good reducing +agent what do you + + align:start position:0% + + + + align:start position:0% + +think so if it was a good reducing agent + + align:start position:0% +think so if it was a good reducing agent + + + align:start position:0% +think so if it was a good reducing agent +it wants to reduce other things and + + align:start position:0% +it wants to reduce other things and + + + align:start position:0% +it wants to reduce other things and +become oxidized you think lithium plus + + align:start position:0% +become oxidized you think lithium plus + + + align:start position:0% +become oxidized you think lithium plus +two is a good + + align:start position:0% +two is a good + + + align:start position:0% +two is a good +thing no so again it's the in this + + align:start position:0% +thing no so again it's the in this + + + align:start position:0% +thing no so again it's the in this +couple it's the reduced species that's + + align:start position:0% +couple it's the reduced species that's + + + align:start position:0% +couple it's the reduced species that's +very reducing and so people have to you + + align:start position:0% +very reducing and so people have to you + + + align:start position:0% +very reducing and so people have to you +have to think about this a little bit + + align:start position:0% +have to think about this a little bit + + + align:start position:0% +have to think about this a little bit +make sure that you pick the right one + + align:start position:0% +make sure that you pick the right one + + + align:start position:0% +make sure that you pick the right one +often you'll ask about you know the + + align:start position:0% +often you'll ask about you know the + + + align:start position:0% +often you'll ask about you know the +order of these as as reducing agents and + + align:start position:0% +order of these as as reducing agents and + + + align:start position:0% +order of these as as reducing agents and +people understand remember this but + + align:start position:0% +people understand remember this but + + + align:start position:0% +people understand remember this but +don't remember which species of the + + align:start position:0% +don't remember which species of the + + + align:start position:0% +don't remember which species of the +couple is going to be doing the thing so + + align:start position:0% +couple is going to be doing the thing so + + + align:start position:0% +couple is going to be doing the thing so +think about what's happening lithium + + align:start position:0% +think about what's happening lithium + + + align:start position:0% +think about what's happening lithium +solid does it want to uh become lithium + + align:start position:0% +solid does it want to uh become lithium + + + align:start position:0% +solid does it want to uh become lithium +plus one it sure does does lithium plus + + align:start position:0% +plus one it sure does does lithium plus + + + align:start position:0% +plus one it sure does does lithium plus +one want to become lithium plus two + + align:start position:0% +one want to become lithium plus two + + + align:start position:0% +one want to become lithium plus two +no so again back to just our table just + + align:start position:0% +no so again back to just our table just + + + align:start position:0% +no so again back to just our table just +for a second on the top large positive + + align:start position:0% +for a second on the top large positive + + + align:start position:0% +for a second on the top large positive +oxidize species very oxidizing negative + + align:start position:0% +oxidize species very oxidizing negative + + + align:start position:0% +oxidize species very oxidizing negative +value reduced species very reducing + + align:start position:0% +value reduced species very reducing + + + align:start position:0% +value reduced species very reducing +and now if we look at this I don't know + + align:start position:0% +and now if we look at this I don't know + + + align:start position:0% +and now if we look at this I don't know +how well this came out in your handout + + align:start position:0% +how well this came out in your handout + + + align:start position:0% +how well this came out in your handout +either but um part of the periodic table + + align:start position:0% +either but um part of the periodic table + + + align:start position:0% +either but um part of the periodic table +for you kind of compressed over here we + + align:start position:0% +for you kind of compressed over here we + + + align:start position:0% +for you kind of compressed over here we +have these e Florine large positive um + + align:start position:0% +have these e Florine large positive um + + + align:start position:0% +have these e Florine large positive um +standard reduction potential easy to + + align:start position:0% +standard reduction potential easy to + + + align:start position:0% +standard reduction potential easy to +reduce over here good oxidizing agents + + align:start position:0% +reduce over here good oxidizing agents + + + align:start position:0% +reduce over here good oxidizing agents +if they get an electron if they're + + align:start position:0% +if they get an electron if they're + + + align:start position:0% +if they get an electron if they're +reduced they get their noble gas + + align:start position:0% +reduced they get their noble gas + + + align:start position:0% +reduced they get their noble gas +configuration over here we have these + + align:start position:0% +configuration over here we have these + + + align:start position:0% +configuration over here we have these +negative big negative numbers easy to + + align:start position:0% +negative big negative numbers easy to + + + align:start position:0% +negative big negative numbers easy to +oxidize the solid or the neutral to + + align:start position:0% +oxidize the solid or the neutral to + + + align:start position:0% +oxidize the solid or the neutral to +their plus one um so they would be good + + align:start position:0% +their plus one um so they would be good + + + align:start position:0% +their plus one um so they would be good +reducing agents and so this all makes + + align:start position:0% +reducing agents and so this all makes + + + align:start position:0% +reducing agents and so this all makes +sense when you think about Trends in the + + align:start position:0% +sense when you think about Trends in the + + + align:start position:0% +sense when you think about Trends in the +periodic table all right so today we're + + align:start position:0% +periodic table all right so today we're + + + align:start position:0% +periodic table all right so today we're +going to have two examples of um why all + + align:start position:0% +going to have two examples of um why all + + + align:start position:0% +going to have two examples of um why all +of this is in important um across + + align:start position:0% +of this is in important um across + + + align:start position:0% +of this is in important um across +disciplines so often these units are + + align:start position:0% +disciplines so often these units are + + + align:start position:0% +disciplines so often these units are +really talked you talk about making + + align:start position:0% +really talked you talk about making + + + align:start position:0% +really talked you talk about making +batteries and things like that and that + + align:start position:0% +batteries and things like that and that + + + align:start position:0% +batteries and things like that and that +is important in fact with energy + + align:start position:0% +is important in fact with energy + + + align:start position:0% +is important in fact with energy +initiatives that's become making + + align:start position:0% +initiatives that's become making + + + align:start position:0% +initiatives that's become making +batteries is a really hot area right now + + align:start position:0% +batteries is a really hot area right now + + + align:start position:0% +batteries is a really hot area right now +but all these things you're learning are + + align:start position:0% +but all these things you're learning are + + + align:start position:0% +but all these things you're learning are +also related to biology and to medicine + + align:start position:0% +also related to biology and to medicine + + + align:start position:0% +also related to biology and to medicine +as well and so we have uh one more of + + align:start position:0% +as well and so we have uh one more of + + + align:start position:0% +as well and so we have uh one more of +the in the own word segment and John + + align:start position:0% +the in the own word segment and John + + + align:start position:0% +the in the own word segment and John +Igman studies um DNA damage um as + + align:start position:0% +Igman studies um DNA damage um as + + + align:start position:0% +Igman studies um DNA damage um as +related to cancer and um people are like + + align:start position:0% +related to cancer and um people are like + + + align:start position:0% +related to cancer and um people are like +what does you know DNA damage and cancer + + align:start position:0% +what does you know DNA damage and cancer + + + align:start position:0% +what does you know DNA damage and cancer +have to do with oxidation reduction + + align:start position:0% +have to do with oxidation reduction + + + align:start position:0% +have to do with oxidation reduction +potentials but it's all about oxidation + + align:start position:0% +potentials but it's all about oxidation + + + align:start position:0% +potentials but it's all about oxidation +reduction that's what a lot of the + + align:start position:0% +reduction that's what a lot of the + + + align:start position:0% +reduction that's what a lot of the +damage is all right so why don't you + + align:start position:0% +damage is all right so why don't you + + + align:start position:0% +damage is all right so why don't you +hear from uh from John + + align:start position:0% + + + + align:start position:0% + +Igman that's weird it was starting to my + + align:start position:0% +Igman that's weird it was starting to my + + + align:start position:0% +Igman that's weird it was starting to my +name John I'm in the Department of + + align:start position:0% +name John I'm in the Department of + + + align:start position:0% +name John I'm in the Department of +Chemistry and biological engineering MIT + + align:start position:0% +Chemistry and biological engineering MIT + + + align:start position:0% +Chemistry and biological engineering MIT +I'm a toxicologist by training so I + + align:start position:0% +I'm a toxicologist by training so I + + + align:start position:0% +I'm a toxicologist by training so I +study how cells respond to toxins and in + + align:start position:0% +study how cells respond to toxins and in + + + align:start position:0% +study how cells respond to toxins and in +particular the kinds of toxins that + + align:start position:0% +particular the kinds of toxins that + + + align:start position:0% +particular the kinds of toxins that +cause nucleic acid + + align:start position:0% +cause nucleic acid + + + align:start position:0% +cause nucleic acid +damage some of these are chemicals from + + align:start position:0% +damage some of these are chemicals from + + + align:start position:0% +damage some of these are chemicals from +out in the envir organic compounds that + + align:start position:0% +out in the envir organic compounds that + + + align:start position:0% +out in the envir organic compounds that +cause DNA damage but I'm also interested + + align:start position:0% +cause DNA damage but I'm also interested + + + align:start position:0% +cause DNA damage but I'm also interested +in how chemicals inside our body for + + align:start position:0% +in how chemicals inside our body for + + + align:start position:0% +in how chemicals inside our body for +example reactive forms of oxygen the + + align:start position:0% +example reactive forms of oxygen the + + + align:start position:0% +example reactive forms of oxygen the +molecule that we breathe also cause + + align:start position:0% +molecule that we breathe also cause + + + align:start position:0% +molecule that we breathe also cause +nucleic acid + + align:start position:0% +nucleic acid + + + align:start position:0% +nucleic acid +damage oxidation is the process by which + + align:start position:0% +damage oxidation is the process by which + + + align:start position:0% +damage oxidation is the process by which +we convert our metabolic fuels into + + align:start position:0% +we convert our metabolic fuels into + + + align:start position:0% +we convert our metabolic fuels into +energy this is a gummy bear being + + align:start position:0% +energy this is a gummy bear being + + + align:start position:0% +energy this is a gummy bear being +oxidized by potassium chlorate this is + + align:start position:0% +oxidized by potassium chlorate this is + + + align:start position:0% +oxidized by potassium chlorate this is +exactly the kind of chemical reaction + + align:start position:0% +exactly the kind of chemical reaction + + + align:start position:0% +exactly the kind of chemical reaction +that goes on in your bodies but in your + + align:start position:0% +that goes on in your bodies but in your + + + align:start position:0% +that goes on in your bodies but in your +body it goes on at a much slower rate + + align:start position:0% +body it goes on at a much slower rate + + + align:start position:0% +body it goes on at a much slower rate +oxygen is a double-edged + + align:start position:0% +oxygen is a double-edged + + + align:start position:0% +oxygen is a double-edged +sword there are two aspects to its use + + align:start position:0% +sword there are two aspects to its use + + + align:start position:0% +sword there are two aspects to its use +that is good for + + align:start position:0% + + + + align:start position:0% + +us the first one is by acting as an + + align:start position:0% +us the first one is by acting as an + + + align:start position:0% +us the first one is by acting as an +electron acceptor sort of like the anode + + align:start position:0% +electron acceptor sort of like the anode + + + align:start position:0% +electron acceptor sort of like the anode +in a battery it completes the circuit + + align:start position:0% +in a battery it completes the circuit + + + align:start position:0% +in a battery it completes the circuit +and allows us to be able to generate + + align:start position:0% +and allows us to be able to generate + + + align:start position:0% +and allows us to be able to generate +free energy that we can use to power + + align:start position:0% +free energy that we can use to power + + + align:start position:0% +free energy that we can use to power +vital processes that's good the second + + align:start position:0% +vital processes that's good the second + + + align:start position:0% +vital processes that's good the second +good thing is that it's the um it's sort + + align:start position:0% +good thing is that it's the um it's sort + + + align:start position:0% +good thing is that it's the um it's sort +of the ammunition of our inate immune + + align:start position:0% + + + + align:start position:0% + +system oxygen is used to charge the + + align:start position:0% +system oxygen is used to charge the + + + align:start position:0% +system oxygen is used to charge the +system to produce one two or three + + align:start position:0% +system to produce one two or three + + + align:start position:0% +system to produce one two or three +electron reduced species that themselves + + align:start position:0% +electron reduced species that themselves + + + align:start position:0% +electron reduced species that themselves +can react with reactive nitrogen species + + align:start position:0% +can react with reactive nitrogen species + + + align:start position:0% +can react with reactive nitrogen species +to create a host of very damaging + + align:start position:0% +to create a host of very damaging + + + align:start position:0% +to create a host of very damaging +oxidants our Nate immune system uses + + align:start position:0% +oxidants our Nate immune system uses + + + align:start position:0% +oxidants our Nate immune system uses +these to protect us against Invaders and + + align:start position:0% +these to protect us against Invaders and + + + align:start position:0% +these to protect us against Invaders and +often times we believe developing cancer + + align:start position:0% +often times we believe developing cancer + + + align:start position:0% +often times we believe developing cancer +cells the bad thing is that the second + + align:start position:0% +cells the bad thing is that the second + + + align:start position:0% +cells the bad thing is that the second +system I described doesn't have a lot of + + align:start position:0% +system I described doesn't have a lot of + + + align:start position:0% +system I described doesn't have a lot of +accuracy in how it focuses that chemical + + align:start position:0% +accuracy in how it focuses that chemical + + + align:start position:0% +accuracy in how it focuses that chemical +warfare so not only are the let's say + + align:start position:0% +warfare so not only are the let's say + + + align:start position:0% +warfare so not only are the let's say +invading bacterial cells or the cancer + + align:start position:0% +invading bacterial cells or the cancer + + + align:start position:0% +invading bacterial cells or the cancer +cells hit but surrounding cells as well + + align:start position:0% +cells hit but surrounding cells as well + + + align:start position:0% +cells hit but surrounding cells as well +and that creates oxidative damage in the + + align:start position:0% +and that creates oxidative damage in the + + + align:start position:0% +and that creates oxidative damage in the +genomes of those cells those innocent + + align:start position:0% +genomes of those cells those innocent + + + align:start position:0% +genomes of those cells those innocent +bystanders + + align:start position:0% +bystanders + + + align:start position:0% +bystanders +if those cells divide the oxidative + + align:start position:0% +if those cells divide the oxidative + + + align:start position:0% +if those cells divide the oxidative +damage that's in them can cause + + align:start position:0% +damage that's in them can cause + + + align:start position:0% +damage that's in them can cause +mutations and that sets the cell along a + + align:start position:0% +mutations and that sets the cell along a + + + align:start position:0% +mutations and that sets the cell along a +path accumulate enough + + align:start position:0% +path accumulate enough + + + align:start position:0% +path accumulate enough +mutations in enough genes you're going + + align:start position:0% +mutations in enough genes you're going + + + align:start position:0% +mutations in enough genes you're going +to convert that normal cell into a + + align:start position:0% +to convert that normal cell into a + + + align:start position:0% +to convert that normal cell into a +cancer cell that will grow out into a + + align:start position:0% + + + + align:start position:0% + +tumor so that was one of I think the + + align:start position:0% +tumor so that was one of I think the + + + align:start position:0% +tumor so that was one of I think the +only video besides mine that involved a + + align:start position:0% +only video besides mine that involved a + + + align:start position:0% +only video besides mine that involved a +faculty member but I thought it was uh + + align:start position:0% +faculty member but I thought it was uh + + + align:start position:0% +faculty member but I thought it was uh +it's nice to have a sort of a colle + + align:start position:0% +it's nice to have a sort of a colle + + + align:start position:0% +it's nice to have a sort of a colle +ction of of different uh folks talking + + align:start position:0% +ction of of different uh folks talking + + + align:start position:0% +ction of of different uh folks talking +about their research and this relates to + + align:start position:0% +about their research and this relates to + + + align:start position:0% +about their research and this relates to +free radical species as well as to + + align:start position:0% +free radical species as well as to + + + align:start position:0% +free radical species as well as to +oxidation and + + align:start position:0% +oxidation and + + + align:start position:0% +oxidation and +reduction all right so now um I have + + align:start position:0% +reduction all right so now um I have + + + align:start position:0% +reduction all right so now um I have +another bio example which hopefully + + align:start position:0% +another bio example which hopefully + + + align:start position:0% +another bio example which hopefully +we'll get to at the end but I want to + + align:start position:0% +we'll get to at the end but I want to + + + align:start position:0% +we'll get to at the end but I want to +introduce a very important equation uh + + align:start position:0% +introduce a very important equation uh + + + align:start position:0% +introduce a very important equation uh +for this unit in oxidation reduction + + align:start position:0% +for this unit in oxidation reduction + + + align:start position:0% +for this unit in oxidation reduction +which is the nerst equation so um here + + align:start position:0% +which is the nerst equation so um here + + + align:start position:0% +which is the nerst equation so um here +and this uh happens I think to all of us + + align:start position:0% +and this uh happens I think to all of us + + + align:start position:0% +and this uh happens I think to all of us +all the time um our exhausted batteries + + align:start position:0% +all the time um our exhausted batteries + + + align:start position:0% +all the time um our exhausted batteries +um so when you have a battery or you go + + align:start position:0% +um so when you have a battery or you go + + + align:start position:0% +um so when you have a battery or you go +to turn on your headphones or uh use + + align:start position:0% +to turn on your headphones or uh use + + + align:start position:0% +to turn on your headphones or uh use +your laser pointer or things like that + + align:start position:0% +your laser pointer or things like that + + + align:start position:0% +your laser pointer or things like that +and the battery doesn't work anymore + + align:start position:0% +and the battery doesn't work anymore + + + align:start position:0% +and the battery doesn't work anymore +it's because the cell reaction has + + align:start position:0% +it's because the cell reaction has + + + align:start position:0% +it's because the cell reaction has +reached equilibrium so equilibrium is a + + align:start position:0% +reached equilibrium so equilibrium is a + + + align:start position:0% +reached equilibrium so equilibrium is a +state of calmness it's also a state of + + align:start position:0% +state of calmness it's also a state of + + + align:start position:0% +state of calmness it's also a state of +batteries not working anymore um and so + + align:start position:0% +batteries not working anymore um and so + + + align:start position:0% +batteries not working anymore um and so +what we want to uh at this point when + + align:start position:0% +what we want to uh at this point when + + + align:start position:0% +what we want to uh at this point when +it's at equilibrium um the cell + + align:start position:0% +it's at equilibrium um the cell + + + align:start position:0% +it's at equilibrium um the cell +generates zero potential across its + + align:start position:0% +generates zero potential across its + + + align:start position:0% +generates zero potential across its +electrodes it's not working anymore more + + align:start position:0% +electrodes it's not working anymore more + + + align:start position:0% +electrodes it's not working anymore more +um it is a dead battery and we need to + + align:start position:0% +um it is a dead battery and we need to + + + align:start position:0% +um it is a dead battery and we need to +think about when it reaches equilibrium + + align:start position:0% +think about when it reaches equilibrium + + + align:start position:0% +think about when it reaches equilibrium +what state it's in at any given time + + align:start position:0% +what state it's in at any given time + + + align:start position:0% +what state it's in at any given time +compared to its equilibrium state so + + align:start position:0% +compared to its equilibrium state so + + + align:start position:0% +compared to its equilibrium state so +this really brings us back to some of + + align:start position:0% +this really brings us back to some of + + + align:start position:0% +this really brings us back to some of +the ideas that we had in the chemical + + align:start position:0% +the ideas that we had in the chemical + + + align:start position:0% +the ideas that we had in the chemical +equilibrium unit where we were thinking + + align:start position:0% +equilibrium unit where we were thinking + + + align:start position:0% +equilibrium unit where we were thinking +about composition of of a reaction at + + align:start position:0% +about composition of of a reaction at + + + align:start position:0% +about composition of of a reaction at +any given time compared to the + + align:start position:0% +any given time compared to the + + + align:start position:0% +any given time compared to the +equilibrium state so how does cell + + align:start position:0% +equilibrium state so how does cell + + + align:start position:0% +equilibrium state so how does cell +potential change with cell + + align:start position:0% +potential change with cell + + + align:start position:0% +potential change with cell +composition so again we know a lot about + + align:start position:0% +composition so again we know a lot about + + + align:start position:0% +composition so again we know a lot about +this and uh exam 3 on Friday has + + align:start position:0% +this and uh exam 3 on Friday has + + + align:start position:0% +this and uh exam 3 on Friday has +equilibrium on it so we already know a + + align:start position:0% +equilibrium on it so we already know a + + + align:start position:0% +equilibrium on it so we already know a +lot about what happens in relationships + + align:start position:0% +lot about what happens in relationships + + + align:start position:0% +lot about what happens in relationships +between + + align:start position:0% +between + + + align:start position:0% +between +equilibrium and we know that Delta G + + align:start position:0% +equilibrium and we know that Delta G + + + align:start position:0% +equilibrium and we know that Delta G +changes that's the composition changes + + align:start position:0% +changes that's the composition changes + + + align:start position:0% +changes that's the composition changes +in the cell and until equilibrium is + + align:start position:0% +in the cell and until equilibrium is + + + align:start position:0% +in the cell and until equilibrium is +reached so again reactions going forward + + align:start position:0% +reached so again reactions going forward + + + align:start position:0% +reached so again reactions going forward +and back in equilibrium the forward + + align:start position:0% +and back in equilibrium the forward + + + align:start position:0% +and back in equilibrium the forward +Direction equals the reverse Direction + + align:start position:0% +Direction equals the reverse Direction + + + align:start position:0% +Direction equals the reverse Direction +but at some given time um that is not + + align:start position:0% +but at some given time um that is not + + + align:start position:0% +but at some given time um that is not +always the case so the equation that we + + align:start position:0% +always the case so the equation that we + + + align:start position:0% +always the case so the equation that we +know from before is that Delta g equals + + align:start position:0% +know from before is that Delta g equals + + + align:start position:0% +know from before is that Delta g equals +Delta G Plus RT natural log of Q and so + + align:start position:0% +Delta G Plus RT natural log of Q and so + + + align:start position:0% +Delta G Plus RT natural log of Q and so +we know Delta if you know Delta G and Q + + align:start position:0% +we know Delta if you know Delta G and Q + + + align:start position:0% +we know Delta if you know Delta G and Q +you can talk about what the Delta G is + + align:start position:0% +you can talk about what the Delta G is + + + align:start position:0% +you can talk about what the Delta G is +going to be at a particular composition + + align:start position:0% +going to be at a particular composition + + + align:start position:0% +going to be at a particular composition +of the cell with a particular value of + + align:start position:0% +of the cell with a particular value of + + + align:start position:0% +of the cell with a particular value of +Q so now we can think well okay here's + + align:start position:0% +Q so now we can think well okay here's + + + align:start position:0% +Q so now we can think well okay here's +what we know about q that reaction + + align:start position:0% +what we know about q that reaction + + + align:start position:0% +what we know about q that reaction +quotient and Delta G what do we know + + align:start position:0% +quotient and Delta G what do we know + + + align:start position:0% +quotient and Delta G what do we know +about Delta G and and E the standard + + align:start position:0% +about Delta G and and E the standard + + + align:start position:0% +about Delta G and and E the standard +or the cell potential and we just talked + + align:start position:0% +or the cell potential and we just talked + + + align:start position:0% +or the cell potential and we just talked +about that so we know that Delta g + + align:start position:0% +about that so we know that Delta g + + + align:start position:0% +about that so we know that Delta g +equals minus n the number of moles of + + align:start position:0% +equals minus n the number of moles of + + + align:start position:0% +equals minus n the number of moles of +electrons Faraday constant times that + + align:start position:0% +electrons Faraday constant times that + + + align:start position:0% +electrons Faraday constant times that +cell potential so now we can do a + + align:start position:0% +cell potential so now we can do a + + + align:start position:0% +cell potential so now we can do a +rearrangement of terms we can combine + + align:start position:0% +rearrangement of terms we can combine + + + align:start position:0% +rearrangement of terms we can combine +and come up with the nerst equation so + + align:start position:0% +and come up with the nerst equation so + + + align:start position:0% +and come up with the nerst equation so +here are the two equations one we knew + + align:start position:0% +here are the two equations one we knew + + + align:start position:0% +here are the two equations one we knew +before one we just learned about today + + align:start position:0% +before one we just learned about today + + + align:start position:0% +before one we just learned about today +and we can put those together we can + + align:start position:0% +and we can put those together we can + + + align:start position:0% +and we can put those together we can +plug in for Delta G here um without the + + align:start position:0% +plug in for Delta G here um without the + + + align:start position:0% +plug in for Delta G here um without the +knot and for Delta G knot with the knot + + align:start position:0% +knot and for Delta G knot with the knot + + + align:start position:0% +knot and for Delta G knot with the knot +over here and then we can divide both + + align:start position:0% +over here and then we can divide both + + + align:start position:0% +over here and then we can divide both +sides by minus the number of moles of + + align:start position:0% +sides by minus the number of moles of + + + align:start position:0% +sides by minus the number of moles of +electrons and feraday constant to come + + align:start position:0% +electrons and feraday constant to come + + + align:start position:0% +electrons and feraday constant to come +up with the nerst equation so the nerst + + align:start position:0% +up with the nerst equation so the nerst + + + align:start position:0% +up with the nerst equation so the nerst +equation um Compares our cell potential + + align:start position:0% +equation um Compares our cell potential + + + align:start position:0% +equation um Compares our cell potential +under standard conditions with our cell + + align:start position:0% +under standard conditions with our cell + + + align:start position:0% +under standard conditions with our cell +potential at any given time based on + + align:start position:0% +potential at any given time based on + + + align:start position:0% +potential at any given time based on +that reaction quotient + + align:start position:0% +that reaction quotient + + + align:start position:0% +that reaction quotient +Q so let's do an example with the Nur + + align:start position:0% +Q so let's do an example with the Nur + + + align:start position:0% +Q so let's do an example with the Nur +equation so let's calculate + + align:start position:0% +equation so let's calculate + + + align:start position:0% +equation so let's calculate +um the cell potential at a particular + + align:start position:0% +um the cell potential at a particular + + + align:start position:0% +um the cell potential at a particular +time when the zinc plus two ions are 0.1 + + align:start position:0% +time when the zinc plus two ions are 0.1 + + + align:start position:0% +time when the zinc plus two ions are 0.1 +and copper plus two is + + align:start position:0% +and copper plus two is + + + align:start position:0% +and copper plus two is +.10 molar and we're same cell as we've + + align:start position:0% +.10 molar and we're same cell as we've + + + align:start position:0% +.10 molar and we're same cell as we've +done before so step one very easy we + + align:start position:0% +done before so step one very easy we + + + align:start position:0% +done before so step one very easy we +want to calculate the cell potential + + align:start position:0% +want to calculate the cell potential + + + align:start position:0% +want to calculate the cell potential +under standard conditions and this is + + align:start position:0% +under standard conditions and this is + + + align:start position:0% +under standard conditions and this is +particularly easy because we already did + + align:start position:0% +particularly easy because we already did + + + align:start position:0% +particularly easy because we already did +this today so you already told me it's + + align:start position:0% +this today so you already told me it's + + + align:start position:0% +this today so you already told me it's +plus one + + align:start position:0% +plus one + + + align:start position:0% +plus one +1.13 volts so we could look up our + + align:start position:0% +1.13 volts so we could look up our + + + align:start position:0% +1.13 volts so we could look up our +standard reduction potentials for our + + align:start position:0% +standard reduction potentials for our + + + align:start position:0% +standard reduction potentials for our +copper couple and our zinc couple and + + align:start position:0% +copper couple and our zinc couple and + + + align:start position:0% +copper couple and our zinc couple and +calculate this so we already did this + + align:start position:0% +calculate this so we already did this + + + align:start position:0% +calculate this so we already did this +and that's why I said you want to make + + align:start position:0% +and that's why I said you want to make + + + align:start position:0% +and that's why I said you want to make +sure you get this right because it's + + align:start position:0% +sure you get this right because it's + + + align:start position:0% +sure you get this right because it's +often just step one of a multi-art + + align:start position:0% +often just step one of a multi-art + + + align:start position:0% +often just step one of a multi-art +problem so we want to get that right + + align:start position:0% +problem so we want to get that right + + + align:start position:0% +problem so we want to get that right +okay step two is calculating Q so and + + align:start position:0% +okay step two is calculating Q so and + + + align:start position:0% +okay step two is calculating Q so and +this is a clicker question + + align:start position:0% + + + + align:start position:0% + +all right 10 more seconds + + align:start position:0% + + + + align:start position:0% + +all right try to make the math not that + + align:start position:0% +all right try to make the math not that + + + align:start position:0% +all right try to make the math not that +hard okay so Q products over + + align:start position:0% +hard okay so Q products over + + + align:start position:0% +hard okay so Q products over +reactants so one thing you want to do is + + align:start position:0% +reactants so one thing you want to do is + + + align:start position:0% +reactants so one thing you want to do is +make sure you have the reaction written + + align:start position:0% +make sure you have the reaction written + + + align:start position:0% +make sure you have the reaction written +correctly so you know what the products + + align:start position:0% +correctly so you know what the products + + + align:start position:0% +correctly so you know what the products +are and what the reactants are and here + + align:start position:0% +are and what the reactants are and here + + + align:start position:0% +are and what the reactants are and here +we have zinc ions over copper copper + + align:start position:0% +we have zinc ions over copper copper + + + align:start position:0% +we have zinc ions over copper copper +solid and zinc solid don't appear in the + + align:start position:0% +solid and zinc solid don't appear in the + + + align:start position:0% +solid and zinc solid don't appear in the +equilibrium expression or in the Q + + align:start position:0% +equilibrium expression or in the Q + + + align:start position:0% +equilibrium expression or in the Q +expression also because they're solids + + align:start position:0% +expression also because they're solids + + + align:start position:0% +expression also because they're solids +and their concentration is not changing + + align:start position:0% +and their concentration is not changing + + + align:start position:0% +and their concentration is not changing +so there is enough information that was + + align:start position:0% +so there is enough information that was + + + align:start position:0% +so there is enough information that was +given because we don't include the + + align:start position:0% +given because we don't include the + + + align:start position:0% +given because we don't include the +solids so it's just the concentration of + + align:start position:0% +solids so it's just the concentration of + + + align:start position:0% +solids so it's just the concentration of +zinc over the con zinc ions over the + + align:start position:0% +zinc over the con zinc ions over the + + + align:start position:0% +zinc over the con zinc ions over the +concentration of copper ions or 1.0 * 10 + + align:start position:0% +concentration of copper ions or 1.0 * 10 + + + align:start position:0% +concentration of copper ions or 1.0 * 10 +2 all right now we need to know n so n + + align:start position:0% +2 all right now we need to know n so n + + + align:start position:0% +2 all right now we need to know n so n +is the number of moles of electrons that + + align:start position:0% +is the number of moles of electrons that + + + align:start position:0% +is the number of moles of electrons that +are involved in this reaction this + + align:start position:0% +are involved in this reaction this + + + align:start position:0% +are involved in this reaction this +reaction involves how many electrons + + align:start position:0% + + + + align:start position:0% + +how many it involves two right so the + + align:start position:0% +how many it involves two right so the + + + align:start position:0% +how many it involves two right so the +zinc to zinc plus to zinc plus two + + align:start position:0% +zinc to zinc plus to zinc plus two + + + align:start position:0% +zinc to zinc plus to zinc plus two +copper plus two to Copper so it involves + + align:start position:0% +copper plus two to Copper so it involves + + + align:start position:0% +copper plus two to Copper so it involves +two electrons so this is two and + + align:start position:0% +two electrons so this is two and + + + align:start position:0% +two electrons so this is two and +sometimes you can just look at this and + + align:start position:0% +sometimes you can just look at this and + + + align:start position:0% +sometimes you can just look at this and +realize it's two electrons involved + + align:start position:0% +realize it's two electrons involved + + + align:start position:0% +realize it's two electrons involved +other times you have to balance the + + align:start position:0% +other times you have to balance the + + + align:start position:0% +other times you have to balance the +reaction to figure out how many um + + align:start position:0% +reaction to figure out how many um + + + align:start position:0% +reaction to figure out how many um +electrons are involved it's not obvious + + align:start position:0% +electrons are involved it's not obvious + + + align:start position:0% +electrons are involved it's not obvious +by looking at the reaction this is a + + align:start position:0% +by looking at the reaction this is a + + + align:start position:0% +by looking at the reaction this is a +simple one but some of them are not so + + align:start position:0% +simple one but some of them are not so + + + align:start position:0% +simple one but some of them are not so +that's where balancing reactions comes + + align:start position:0% +that's where balancing reactions comes + + + align:start position:0% +that's where balancing reactions comes +in handy all right so now we have + + align:start position:0% +in handy all right so now we have + + + align:start position:0% +in handy all right so now we have +everything we need to plug it into the + + align:start position:0% +everything we need to plug it into the + + + align:start position:0% +everything we need to plug it into the +nerst equation so we can put it in we + + align:start position:0% +nerst equation so we can put it in we + + + align:start position:0% +nerst equation so we can put it in we +calculated the standard um cell + + align:start position:0% +calculated the standard um cell + + + align:start position:0% +calculated the standard um cell +potential um over here the + + + align:start position:0% +potential um over here the + + + + align:start position:0% +potential um over here the + +1.1 value we can look up R everything + + align:start position:0% +1.1 value we can look up R everything + + + align:start position:0% +1.1 value we can look up R everything +again room temperature natural log of Q + + align:start position:0% +again room temperature natural log of Q + + + align:start position:0% +again room temperature natural log of Q +we calculated Q we have two electrons + + align:start position:0% +we calculated Q we have two electrons + + + align:start position:0% +we calculated Q we have two electrons +and Faraday + + align:start position:0% +and Faraday + + + align:start position:0% +and Faraday +constant and we can uh multiply this out + + align:start position:0% +constant and we can uh multiply this out + + + align:start position:0% +constant and we can uh multiply this out +get this value in terms of significant + + align:start position:0% +get this value in terms of significant + + + align:start position:0% +get this value in terms of significant +figures this also is a lot of fun we + + align:start position:0% +figures this also is a lot of fun we + + + align:start position:0% +figures this also is a lot of fun we +have log rules of significant figures + + align:start position:0% +have log rules of significant figures + + + align:start position:0% +have log rules of significant figures +multiplication and division rules of + + align:start position:0% +multiplication and division rules of + + + align:start position:0% +multiplication and division rules of +significant figures and adding and + + align:start position:0% +significant figures and adding and + + + align:start position:0% +significant figures and adding and +subtracting rules of significant figures + + align:start position:0% +subtracting rules of significant figures + + + align:start position:0% +subtracting rules of significant figures +um and also in terms of units all of a + + align:start position:0% +um and also in terms of units all of a + + + align:start position:0% +um and also in terms of units all of a +sudden vaults appeared that was nice + + align:start position:0% +sudden vaults appeared that was nice + + + align:start position:0% +sudden vaults appeared that was nice +because our anwers should be in vaults + + align:start position:0% +because our anwers should be in vaults + + + align:start position:0% +because our anwers should be in vaults +but where did they come from um so we + + align:start position:0% +but where did they come from um so we + + + align:start position:0% +but where did they come from um so we +had our Kelvin are going to cancel out + + align:start position:0% +had our Kelvin are going to cancel out + + + align:start position:0% +had our Kelvin are going to cancel out +and but we have jewels and uh over here + + align:start position:0% +and but we have jewels and uh over here + + + align:start position:0% +and but we have jewels and uh over here +and we have kums but luckily a jewel per + + align:start position:0% +and we have kums but luckily a jewel per + + + align:start position:0% +and we have kums but luckily a jewel per +Kum equals a volt so we're all set to + + align:start position:0% +Kum equals a volt so we're all set to + + + align:start position:0% +Kum equals a volt so we're all set to +get our appropriate + + align:start position:0% +get our appropriate + + + align:start position:0% +get our appropriate +units all right so just a couple things + + align:start position:0% +units all right so just a couple things + + + align:start position:0% +units all right so just a couple things +that I'll mention about this as well um + + align:start position:0% +that I'll mention about this as well um + + + align:start position:0% +that I'll mention about this as well um +since almost all these problems are at + + align:start position:0% +since almost all these problems are at + + + align:start position:0% +since almost all these problems are at +room temperature I try to make your + + align:start position:0% +room temperature I try to make your + + + align:start position:0% +room temperature I try to make your +lives a little bit easier on the exam um + + align:start position:0% +lives a little bit easier on the exam um + + + align:start position:0% +lives a little bit easier on the exam um +and multiply this out for you because + + align:start position:0% +and multiply this out for you because + + + align:start position:0% +and multiply this out for you because +these are all constants and they're big + + align:start position:0% +these are all constants and they're big + + + align:start position:0% +these are all constants and they're big +constants that involve plugging a lot of + + align:start position:0% +constants that involve plugging a lot of + + + align:start position:0% +constants that involve plugging a lot of +numbers in um so I will give you this uh + + align:start position:0% +numbers in um so I will give you this uh + + + align:start position:0% +numbers in um so I will give you this uh +combined value and if you use log + + align:start position:0% +combined value and if you use log + + + align:start position:0% +combined value and if you use log +instead of natural log you need to + + align:start position:0% +instead of natural log you need to + + + align:start position:0% +instead of natural log you need to +change that value here and so what I + + align:start position:0% +change that value here and so what I + + + align:start position:0% +change that value here and so what I +actually put on equation sheets are + + align:start position:0% +actually put on equation sheets are + + + align:start position:0% +actually put on equation sheets are +these equations I'll also put the full + + align:start position:0% +these equations I'll also put the full + + + align:start position:0% +these equations I'll also put the full +equation there as well um but just to + + align:start position:0% +equation there as well um but just to + + + align:start position:0% +equation there as well um but just to +make your lives a little bit easier it's + + align:start position:0% +make your lives a little bit easier it's + + + align:start position:0% +make your lives a little bit easier it's +horrible to make mistakes up there all + + align:start position:0% +horrible to make mistakes up there all + + + align:start position:0% +horrible to make mistakes up there all +right so just + + align:start position:0% +right so just + + + align:start position:0% +right so just +briefly what about an equilibrium what + + align:start position:0% +briefly what about an equilibrium what + + + align:start position:0% +briefly what about an equilibrium what +does q + + align:start position:0% +does q + + + align:start position:0% +does q +equal qal K Delta g + + align:start position:0% +equal qal K Delta g + + + align:start position:0% +equal qal K Delta g +equals + + align:start position:0% +equals + + + align:start position:0% +equals +Zer and so we can uh rewrite this + + align:start position:0% +Zer and so we can uh rewrite this + + + align:start position:0% +Zer and so we can uh rewrite this +expression again which we've done before + + align:start position:0% +expression again which we've done before + + + align:start position:0% +expression again which we've done before +and if we take this and and look at this + + align:start position:0% +and if we take this and and look at this + + + align:start position:0% +and if we take this and and look at this +expression now we can again combine + + align:start position:0% +expression now we can again combine + + + align:start position:0% +expression now we can again combine +these we have two expressions for Delta + + align:start position:0% +these we have two expressions for Delta + + + align:start position:0% +these we have two expressions for Delta +G KN and combine them and solve and you + + align:start position:0% +G KN and combine them and solve and you + + + align:start position:0% +G KN and combine them and solve and you +can see that you can also calculate K + + align:start position:0% +can see that you can also calculate K + + + align:start position:0% +can see that you can also calculate K +from standard reduction potentials so + + align:start position:0% +from standard reduction potentials so + + + align:start position:0% +from standard reduction potentials so +all the things that we have been + + align:start position:0% +all the things that we have been + + + align:start position:0% +all the things that we have been +learning here we can always come back to + + align:start position:0% +learning here we can always come back to + + + align:start position:0% +learning here we can always come back to +chemical equilibrium all right so I'm + + align:start position:0% +chemical equilibrium all right so I'm + + + align:start position:0% +chemical equilibrium all right so I'm +done with everything but my second bio + + align:start position:0% +done with everything but my second bio + + + align:start position:0% +done with everything but my second bio +example so you'll have to wait until + + align:start position:0% +example so you'll have to wait until + + + align:start position:0% +example so you'll have to wait until +next week to find out how Vitamin B12 + + align:start position:0% +next week to find out how Vitamin B12 + + + align:start position:0% +next week to find out how Vitamin B12 +gets reduced in the + + align:start position:0% +gets reduced in the + + + align:start position:0% +gets reduced in the +body + + align:start position:0% + + + + align:start position:0% + +okay all right let's just take 10 more + + align:start position:0% +okay all right let's just take 10 more + + + align:start position:0% +okay all right let's just take 10 more +seconds on the clicker question + + align:start position:0% + + + + align:start position:0% + +okay does someone want a nice uh t-shirt + + align:start position:0% +okay does someone want a nice uh t-shirt + + + align:start position:0% +okay does someone want a nice uh t-shirt +to tell me how they got the right + + align:start position:0% + + + + align:start position:0% + +answer + + align:start position:0% + + + + align:start position:0% + +okay pass this + + align:start position:0% + + + + align:start position:0% + +back so when you're looking at um the + + align:start position:0% +back so when you're looking at um the + + + align:start position:0% +back so when you're looking at um the +all quiet down and zinc + + align:start position:0% +all quiet down and zinc + + + align:start position:0% +all quiet down and zinc +um zinc is going to reduce um let's + + align:start position:0% +um zinc is going to reduce um let's + + + align:start position:0% +um zinc is going to reduce um let's +quiet + + align:start position:0% +quiet + + + align:start position:0% +quiet +down uh PB because it goes from a two + + align:start position:0% +down uh PB because it goes from a two + + + align:start position:0% +down uh PB because it goes from a two +plus charge to no charge at all so + + align:start position:0% +plus charge to no charge at all so + + + align:start position:0% +plus charge to no charge at all so +that's reducing its charge and then in + + align:start position:0% +that's reducing its charge and then in + + + align:start position:0% +that's reducing its charge and then in +the reverse reaction PB does the same + + align:start position:0% +the reverse reaction PB does the same + + + align:start position:0% +the reverse reaction PB does the same +thing to zinc 2+ and takes it from 2+ to + + align:start position:0% +thing to zinc 2+ and takes it from 2+ to + + + align:start position:0% +thing to zinc 2+ and takes it from 2+ to +uh a neutral charge so yep + + align:start position:0% +uh a neutral charge so yep + + + align:start position:0% +uh a neutral charge so yep +great so trick to this is just look at + + align:start position:0% +great so trick to this is just look at + + + align:start position:0% +great so trick to this is just look at +the equations and figur out what is + + align:start position:0% +the equations and figur out what is + + + align:start position:0% +the equations and figur out what is +being oxidized and what is being reduced + + align:start position:0% +being oxidized and what is being reduced + + + align:start position:0% +being oxidized and what is being reduced +in both + + align:start position:0% + + + + align:start position:0% + +directions all right oxidation + + align:start position:0% +directions all right oxidation + + + align:start position:0% +directions all right oxidation +reduction it's not just about batteries + + align:start position:0% +reduction it's not just about batteries + + + align:start position:0% +reduction it's not just about batteries +batteries of course are very important + + align:start position:0% +batteries of course are very important + + + align:start position:0% +batteries of course are very important +there's a lot of active research right + + align:start position:0% +there's a lot of active research right + + + align:start position:0% +there's a lot of active research right +now trying to make better batteries um + + align:start position:0% +now trying to make better batteries um + + + align:start position:0% +now trying to make better batteries um +that are more environmentally friendly + + align:start position:0% +that are more environmentally friendly + + + align:start position:0% +that are more environmentally friendly +have uh just solving the energy problem + + align:start position:0% +have uh just solving the energy problem + + + align:start position:0% +have uh just solving the energy problem +every single uh possible way but even if + + align:start position:0% +every single uh possible way but even if + + + align:start position:0% +every single uh possible way but even if +you're not interested in solving the + + align:start position:0% +you're not interested in solving the + + + align:start position:0% +you're not interested in solving the +energy problem oxidation reduction is + + align:start position:0% +energy problem oxidation reduction is + + + align:start position:0% +energy problem oxidation reduction is +really important in medicine so I'm just + + align:start position:0% +really important in medicine so I'm just + + + align:start position:0% +really important in medicine so I'm just +going to give you another bio example + + align:start position:0% +going to give you another bio example + + + align:start position:0% +going to give you another bio example +for this so there's a vitamin in your + + align:start position:0% +for this so there's a vitamin in your + + + align:start position:0% +for this so there's a vitamin in your +body vitamin B12 it has one of the + + align:start position:0% +body vitamin B12 it has one of the + + + align:start position:0% +body vitamin B12 it has one of the +largest negative reduction potentials of + + align:start position:0% +largest negative reduction potentials of + + + align:start position:0% +largest negative reduction potentials of +any biological molecule so we ask the + + align:start position:0% +any biological molecule so we ask the + + + align:start position:0% +any biological molecule so we ask the +question how can something like that be + + align:start position:0% +question how can something like that be + + + align:start position:0% +question how can something like that be +reduced in the body so let me introduce + + align:start position:0% +reduced in the body so let me introduce + + + align:start position:0% +reduced in the body so let me introduce +you to vitamin B12 you're going to see + + align:start position:0% +you to vitamin B12 you're going to see + + + align:start position:0% +you to vitamin B12 you're going to see +this a couple times today so vitamin B12 + + align:start position:0% +this a couple times today so vitamin B12 + + + align:start position:0% +this a couple times today so vitamin B12 +needs to be reduced to be active but it + + align:start position:0% +needs to be reduced to be active but it + + + align:start position:0% +needs to be reduced to be active but it +has a low reduction + + align:start position:0% +has a low reduction + + + align:start position:0% +has a low reduction +potential you need to have this is the + + align:start position:0% +potential you need to have this is the + + + align:start position:0% +potential you need to have this is the +vitamin B12 and you'll see several more + + align:start position:0% +vitamin B12 and you'll see several more + + + align:start position:0% +vitamin B12 and you'll see several more +views of it and it's in uh pictures in + + align:start position:0% +views of it and it's in uh pictures in + + + align:start position:0% +views of it and it's in uh pictures in +your handout of today's lecture there's + + align:start position:0% +your handout of today's lecture there's + + + align:start position:0% +your handout of today's lecture there's +an enzyme that requires vitamin B12 and + + align:start position:0% +an enzyme that requires vitamin B12 and + + + align:start position:0% +an enzyme that requires vitamin B12 and +another B vitamin called folic acid and + + align:start position:0% +another B vitamin called folic acid and + + + align:start position:0% +another B vitamin called folic acid and +if this enzyme is not functioning + + align:start position:0% +if this enzyme is not functioning + + + align:start position:0% +if this enzyme is not functioning +properly in your body it leads to all + + align:start position:0% +properly in your body it leads to all + + + align:start position:0% +properly in your body it leads to all +sorts of things it's connected to heart + + align:start position:0% +sorts of things it's connected to heart + + + align:start position:0% +sorts of things it's connected to heart +disease um if women don't have folic + + align:start position:0% +disease um if women don't have folic + + + align:start position:0% +disease um if women don't have folic +acid while they're pregnant it can lead + + align:start position:0% +acid while they're pregnant it can lead + + + align:start position:0% +acid while they're pregnant it can lead +to birth effects neural tube disease + + align:start position:0% +to birth effects neural tube disease + + + align:start position:0% +to birth effects neural tube disease +where the brain doesn't form properly um + + align:start position:0% +where the brain doesn't form properly um + + + align:start position:0% +where the brain doesn't form properly um +also there is rising evidence connecting + + align:start position:0% +also there is rising evidence connecting + + + align:start position:0% +also there is rising evidence connecting +a vitamin B12 deficiency with bringing + + align:start position:0% +a vitamin B12 deficiency with bringing + + + align:start position:0% +a vitamin B12 deficiency with bringing +on Alzheimer's disease and some people + + align:start position:0% +on Alzheimer's disease and some people + + + align:start position:0% +on Alzheimer's disease and some people +actually buy little B12 squirt bottles + + align:start position:0% +actually buy little B12 squirt bottles + + + align:start position:0% +actually buy little B12 squirt bottles +and squirt it into their nose before + + align:start position:0% +and squirt it into their nose before + + + align:start position:0% +and squirt it into their nose before +exams I'm not sure that helps but as you + + align:start position:0% +exams I'm not sure that helps but as you + + + align:start position:0% +exams I'm not sure that helps but as you +get older I would seriously consider + + align:start position:0% +get older I would seriously consider + + + align:start position:0% +get older I would seriously consider +taking extra vitam B12 all right so + + align:start position:0% +taking extra vitam B12 all right so + + + align:start position:0% +taking extra vitam B12 all right so +since we're talking about this we'll + + align:start position:0% +since we're talking about this we'll + + + align:start position:0% +since we're talking about this we'll +have a little nutrition quiz um where do + + align:start position:0% +have a little nutrition quiz um where do + + + align:start position:0% +have a little nutrition quiz um where do +you get vitamin B12 and folic acid in + + align:start position:0% +you get vitamin B12 and folic acid in + + + align:start position:0% +you get vitamin B12 and folic acid in +your diet first let's think about + + align:start position:0% +your diet first let's think about + + + align:start position:0% +your diet first let's think about +vitamin B12 does anyone know where you + + align:start position:0% +vitamin B12 does anyone know where you + + + align:start position:0% +vitamin B12 does anyone know where you +get this besides vitamin pills in food + + align:start position:0% +get this besides vitamin pills in food + + + align:start position:0% +get this besides vitamin pills in food +where do you get vitamin B12 in food + + align:start position:0% +where do you get vitamin B12 in food + + + align:start position:0% +where do you get vitamin B12 in food +yeah broccoli broccoli + + align:start position:0% + + + + align:start position:0% + +nope I have some we had a hand up there + + align:start position:0% +nope I have some we had a hand up there + + + align:start position:0% +nope I have some we had a hand up there +anyone else yeah me meat Yes red meat + + align:start position:0% +anyone else yeah me meat Yes red meat + + + align:start position:0% +anyone else yeah me meat Yes red meat +actually any kind of meat but hardly + + align:start position:0% +actually any kind of meat but hardly + + + align:start position:0% +actually any kind of meat but hardly +ever is red meat the answer to a + + align:start position:0% +ever is red meat the answer to a + + + align:start position:0% +ever is red meat the answer to a +nutritional question so I thought I'd + + align:start position:0% +nutritional question so I thought I'd + + + align:start position:0% +nutritional question so I thought I'd +put it up there in big bold red letters + + align:start position:0% +put it up there in big bold red letters + + + align:start position:0% +put it up there in big bold red letters +yeah you get B12 in meat plants don't + + align:start position:0% +yeah you get B12 in meat plants don't + + + align:start position:0% +yeah you get B12 in meat plants don't +use vitamin B12 so you can eat as many + + align:start position:0% +use vitamin B12 so you can eat as many + + + align:start position:0% +use vitamin B12 so you can eat as many +plants as you want unless they're + + align:start position:0% +plants as you want unless they're + + + align:start position:0% +plants as you want unless they're +covered with bacteria that do use B12 + + align:start position:0% +covered with bacteria that do use B12 + + + align:start position:0% +covered with bacteria that do use B12 +you will not get any in your diet so if + + align:start position:0% +you will not get any in your diet so if + + + align:start position:0% +you will not get any in your diet so if +you're vegetarian you should take a + + align:start position:0% +you're vegetarian you should take a + + + align:start position:0% +you're vegetarian you should take a +tablet you don't need much so it's not + + align:start position:0% +tablet you don't need much so it's not + + + align:start position:0% +tablet you don't need much so it's not +really a problem but it does come from + + align:start position:0% +really a problem but it does come from + + + align:start position:0% +really a problem but it does come from +red meat what about folic acid any + + align:start position:0% +red meat what about folic acid any + + + align:start position:0% +red meat what about folic acid any +guesses where folic acid comes + + align:start position:0% +guesses where folic acid comes + + + align:start position:0% +guesses where folic acid comes +from + + align:start position:0% +from + + + align:start position:0% +from +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +so very good so it's the fall in New + + align:start position:0% +so very good so it's the fall in New + + + align:start position:0% +so very good so it's the fall in New +England and hopefully some of you have + + align:start position:0% +England and hopefully some of you have + + + align:start position:0% +England and hopefully some of you have +gone out and seen the foliage um so + + align:start position:0% +gone out and seen the foliage um so + + + align:start position:0% +gone out and seen the foliage um so +folic acid does come from green leafy + + align:start position:0% +folic acid does come from green leafy + + + align:start position:0% +folic acid does come from green leafy +things and if you're Norwegian you will + + align:start position:0% +things and if you're Norwegian you will + + + align:start position:0% +things and if you're Norwegian you will +also say the following um so Norwegian + + align:start position:0% +also say the following um so Norwegian + + + align:start position:0% +also say the following um so Norwegian +scientists claim that the great + + align:start position:0% +scientists claim that the great + + + align:start position:0% +scientists claim that the great +longevity of Norwegians has to do with + + align:start position:0% +longevity of Norwegians has to do with + + + align:start position:0% +longevity of Norwegians has to do with +the fact that their beer is rich in + + align:start position:0% +the fact that their beer is rich in + + + align:start position:0% +the fact that their beer is rich in +folic acid and somehow they even got a + + align:start position:0% +folic acid and somehow they even got a + + + align:start position:0% +folic acid and somehow they even got a +grant from the Norwegian government to + + align:start position:0% +grant from the Norwegian government to + + + align:start position:0% +grant from the Norwegian government to +study the correlation between beer and + + align:start position:0% +study the correlation between beer and + + + align:start position:0% +study the correlation between beer and +uh health so that's probably like + + align:start position:0% +uh health so that's probably like + + + align:start position:0% +uh health so that's probably like +everyone signed up for that study I'm + + align:start position:0% +everyone signed up for that study I'm + + + align:start position:0% +everyone signed up for that study I'm +sure so red meat and beer um for good + + align:start position:0% +sure so red meat and beer um for good + + + align:start position:0% +sure so red meat and beer um for good +health but yes um leafy green vegetables + + align:start position:0% +health but yes um leafy green vegetables + + + align:start position:0% +health but yes um leafy green vegetables +yes folic acid foliage also orange juice + + align:start position:0% +yes folic acid foliage also orange juice + + + align:start position:0% +yes folic acid foliage also orange juice +is really high and at one point um they + + align:start position:0% +is really high and at one point um they + + + align:start position:0% +is really high and at one point um they +had this commercial for orange juice you + + align:start position:0% +had this commercial for orange juice you + + + align:start position:0% +had this commercial for orange juice you +know it's not just for breakfast anymore + + align:start position:0% +know it's not just for breakfast anymore + + + align:start position:0% +know it's not just for breakfast anymore +it's good for your heart well that was + + align:start position:0% +it's good for your heart well that was + + + align:start position:0% +it's good for your heart well that was +because of the folic acid in there and + + align:start position:0% +because of the folic acid in there and + + + align:start position:0% +because of the folic acid in there and +that's actually true so there was a + + align:start position:0% +that's actually true so there was a + + + align:start position:0% +that's actually true so there was a +commercial that actually provided you + + align:start position:0% +commercial that actually provided you + + + align:start position:0% +commercial that actually provided you +with valuable nutritional advice not so + + align:start position:0% +with valuable nutritional advice not so + + + align:start position:0% +with valuable nutritional advice not so +sure about the beer but I go by the the + + align:start position:0% +sure about the beer but I go by the the + + + align:start position:0% +sure about the beer but I go by the the +leafy greens and the orange juice all + + align:start position:0% +leafy greens and the orange juice all + + + align:start position:0% +leafy greens and the orange juice all +right so you need both of these to be + + align:start position:0% +right so you need both of these to be + + + align:start position:0% +right so you need both of these to be +healthy but again we have this problem + + align:start position:0% +healthy but again we have this problem + + + align:start position:0% +healthy but again we have this problem +that vitamin B12 has this low negative + + align:start position:0% +that vitamin B12 has this low negative + + + align:start position:0% +that vitamin B12 has this low negative +Redux potential so how is it reduced + + align:start position:0% +Redux potential so how is it reduced + + + align:start position:0% +Redux potential so how is it reduced +well in the body it's re it's reduced by + + align:start position:0% +well in the body it's re it's reduced by + + + align:start position:0% +well in the body it's re it's reduced by +a protein called flavodoxin which has a + + align:start position:0% +a protein called flavodoxin which has a + + + align:start position:0% +a protein called flavodoxin which has a +Flavin which is another B vitamin so + + align:start position:0% +Flavin which is another B vitamin so + + + align:start position:0% +Flavin which is another B vitamin so +there's lots of B vitamins going on here + + align:start position:0% +there's lots of B vitamins going on here + + + align:start position:0% +there's lots of B vitamins going on here +so the standard reduction potential for + + align:start position:0% +so the standard reduction potential for + + + align:start position:0% +so the standard reduction potential for +vitamin B12 is minus 526 that's a really + + align:start position:0% +vitamin B12 is minus 526 that's a really + + + align:start position:0% +vitamin B12 is minus 526 that's a really +low number for biology and for + + align:start position:0% +low number for biology and for + + + align:start position:0% +low number for biology and for +flavodoxin it's minus 2 three so we ask + + align:start position:0% +flavodoxin it's minus 2 three so we ask + + + align:start position:0% +flavodoxin it's minus 2 three so we ask +which is the better reducing agent and + + align:start position:0% +which is the better reducing agent and + + + align:start position:0% +which is the better reducing agent and +that's a clicker + + align:start position:0% + + + + align:start position:0% + +question all right let's just do 10 more + + align:start position:0% +question all right let's just do 10 more + + + align:start position:0% +question all right let's just do 10 more +seconds + + align:start position:0% + + + + align:start position:0% + +yep so the better reducing agent wants + + align:start position:0% +yep so the better reducing agent wants + + + align:start position:0% +yep so the better reducing agent wants +to reduce other things and get oxidized + + align:start position:0% +to reduce other things and get oxidized + + + align:start position:0% +to reduce other things and get oxidized +itself so vitamin B12 with its low + + align:start position:0% +itself so vitamin B12 with its low + + + align:start position:0% +itself so vitamin B12 with its low +negative potential is very reducing it + + align:start position:0% +negative potential is very reducing it + + + align:start position:0% +negative potential is very reducing it +wants to reduce other things it wants to + + align:start position:0% +wants to reduce other things it wants to + + + align:start position:0% +wants to reduce other things it wants to +be an agent of reduction all right so + + align:start position:0% +be an agent of reduction all right so + + + align:start position:0% +be an agent of reduction all right so +but that's not what's supposed to happen + + align:start position:0% +but that's not what's supposed to happen + + + align:start position:0% +but that's not what's supposed to happen +it's not supposed to reduce flavodoxin + + align:start position:0% +it's not supposed to reduce flavodoxin + + + align:start position:0% +it's not supposed to reduce flavodoxin +it's supposed to happen the other way + + align:start position:0% +it's supposed to happen the other way + + + align:start position:0% +it's supposed to happen the other way +around so um is we could ask is the + + align:start position:0% +around so um is we could ask is the + + + align:start position:0% +around so um is we could ask is the +reduction then of vitamin B12 by + + align:start position:0% +reduction then of vitamin B12 by + + + align:start position:0% +reduction then of vitamin B12 by +flavodoxin spontaneous if this is the + + align:start position:0% +flavodoxin spontaneous if this is the + + + align:start position:0% +flavodoxin spontaneous if this is the +case yes or + + align:start position:0% +case yes or + + + align:start position:0% +case yes or +no no shouldn't it shouldn't be + + align:start position:0% +no no shouldn't it shouldn't be + + + align:start position:0% +no no shouldn't it shouldn't be +spontaneous it's not going the way that + + align:start position:0% +spontaneous it's not going the way that + + + align:start position:0% +spontaneous it's not going the way that +it should go so we can just calculate + + align:start position:0% +it should go so we can just calculate + + + align:start position:0% +it should go so we can just calculate +how exactly non-spontaneous it is so we + + align:start position:0% +how exactly non-spontaneous it is so we + + + align:start position:0% +how exactly non-spontaneous it is so we +can + + align:start position:0% +can + + + align:start position:0% +can +calculate both what the uh change in + + align:start position:0% +calculate both what the uh change in + + + align:start position:0% +calculate both what the uh change in +potential is and we can also calculate + + align:start position:0% +potential is and we can also calculate + + + align:start position:0% +potential is and we can also calculate +Delta G KN from this so we saw how to do + + align:start position:0% +Delta G KN from this so we saw how to do + + + align:start position:0% +Delta G KN from this so we saw how to do +this um before but we were talking about + + align:start position:0% +this um before but we were talking about + + + align:start position:0% +this um before but we were talking about +uh different kinds of galvanic or + + align:start position:0% +uh different kinds of galvanic or + + + align:start position:0% +uh different kinds of galvanic or +electrolytic cells but now we can talk + + align:start position:0% +electrolytic cells but now we can talk + + + align:start position:0% +electrolytic cells but now we can talk +about use the same equation that we saw + + align:start position:0% +about use the same equation that we saw + + + align:start position:0% +about use the same equation that we saw +before but talk about it in terms of a + + align:start position:0% +before but talk about it in terms of a + + + align:start position:0% +before but talk about it in terms of a +biological system so before we saw to + + align:start position:0% +biological system so before we saw to + + + align:start position:0% +biological system so before we saw to +calculate e not of the cell the cell + + align:start position:0% +calculate e not of the cell the cell + + + align:start position:0% +calculate e not of the cell the cell +potential we had the standard reduction + + align:start position:0% +potential we had the standard reduction + + + align:start position:0% +potential we had the standard reduction +potential for the couple at the anode + + align:start position:0% +potential for the couple at the anode + + + align:start position:0% +potential for the couple at the anode +minus the standard reduction potential + + align:start position:0% +minus the standard reduction potential + + + align:start position:0% +minus the standard reduction potential +for the couple at the cathode we can do + + align:start position:0% +for the couple at the cathode we can do + + + align:start position:0% +for the couple at the cathode we can do +the same thing here but just put + + align:start position:0% +the same thing here but just put + + + align:start position:0% +the same thing here but just put +reduction and oxidation over here so we + + align:start position:0% +reduction and oxidation over here so we + + + align:start position:0% +reduction and oxidation over here so we +can make this a generic equation and we + + align:start position:0% +can make this a generic equation and we + + + align:start position:0% +can make this a generic equation and we +can plug our values in so the thing + + align:start position:0% +can plug our values in so the thing + + + align:start position:0% +can plug our values in so the thing +being reduced is vitamin B12 so we want + + align:start position:0% +being reduced is vitamin B12 so we want + + + align:start position:0% +being reduced is vitamin B12 so we want +to put the reduction potential of B12 in + + align:start position:0% +to put the reduction potential of B12 in + + + align:start position:0% +to put the reduction potential of B12 in +there and the thing being oxidized is + + align:start position:0% +there and the thing being oxidized is + + + align:start position:0% +there and the thing being oxidized is +the + + align:start position:0% +the + + + align:start position:0% +the +flavodoxin and so minus5 526 for the B12 + + align:start position:0% +flavodoxin and so minus5 526 for the B12 + + + align:start position:0% +flavodoxin and so minus5 526 for the B12 +standard reduction potential of B12 + + align:start position:0% +standard reduction potential of B12 + + + align:start position:0% +standard reduction potential of B12 +minus the standard reduction potential + + align:start position:0% +minus the standard reduction potential + + + align:start position:0% +minus the standard reduction potential +of flavodoxin and we get a negative + + align:start position:0% +of flavodoxin and we get a negative + + + align:start position:0% +of flavodoxin and we get a negative +number minus. 296 + + align:start position:0% +number minus. 296 + + + align:start position:0% +number minus. 296 +volts so then we have a negative value + + align:start position:0% +volts so then we have a negative value + + + align:start position:0% +volts so then we have a negative value +which should tell us that Delta G is + + align:start position:0% +which should tell us that Delta G is + + + align:start position:0% +which should tell us that Delta G is +going to be positive but we can also + + align:start position:0% +going to be positive but we can also + + + align:start position:0% +going to be positive but we can also +calculate that value from the equation + + align:start position:0% +calculate that value from the equation + + + align:start position:0% +calculate that value from the equation +you saw before so just because we were + + align:start position:0% +you saw before so just because we were + + + align:start position:0% +you saw before so just because we were +talking about these equations in terms + + align:start position:0% +talking about these equations in terms + + + align:start position:0% +talking about these equations in terms +of cells before we can also talk about + + align:start position:0% +of cells before we can also talk about + + + align:start position:0% +of cells before we can also talk about +it's the same exact equation that we use + + align:start position:0% +it's the same exact equation that we use + + + align:start position:0% +it's the same exact equation that we use +in biology so minus n number of moles of + + align:start position:0% +in biology so minus n number of moles of + + + align:start position:0% +in biology so minus n number of moles of +electrons this is a one electron process + + align:start position:0% +electrons this is a one electron process + + + align:start position:0% +electrons this is a one electron process +I would have had to tell you that you + + align:start position:0% +I would have had to tell you that you + + + align:start position:0% +I would have had to tell you that you +wouldn't necessarily have known it's one + + align:start position:0% +wouldn't necessarily have known it's one + + + align:start position:0% +wouldn't necessarily have known it's one +electron but that's our one um what is + + align:start position:0% +electron but that's our one um what is + + + align:start position:0% +electron but that's our one um what is +this term here this kind of weird + + align:start position:0% +this term here this kind of weird + + + align:start position:0% +this term here this kind of weird +looking F term what is that again + + align:start position:0% +looking F term what is that again + + + align:start position:0% +looking F term what is that again +Faraday constant then we plug in our + + align:start position:0% +Faraday constant then we plug in our + + + align:start position:0% +Faraday constant then we plug in our +cell potential or potential difference + + align:start position:0% +cell potential or potential difference + + + align:start position:0% +cell potential or potential difference +and we get out a value positive 28.6 + + align:start position:0% +and we get out a value positive 28.6 + + + align:start position:0% +and we get out a value positive 28.6 +kilog per mole big positive number so is + + align:start position:0% +kilog per mole big positive number so is + + + align:start position:0% +kilog per mole big positive number so is +this + + align:start position:0% +this + + + align:start position:0% +this +spontaneous um why don't we all have + + align:start position:0% +spontaneous um why don't we all have + + + align:start position:0% +spontaneous um why don't we all have +heart disease it is not a spontaneous + + align:start position:0% +heart disease it is not a spontaneous + + + align:start position:0% +heart disease it is not a spontaneous +reaction so how is it driven forward + + align:start position:0% +reaction so how is it driven forward + + + align:start position:0% +reaction so how is it driven forward +this happens in our body this reaction + + align:start position:0% +this happens in our body this reaction + + + align:start position:0% +this happens in our body this reaction +happens so clearly something has to + + align:start position:0% +happens so clearly something has to + + + align:start position:0% +happens so clearly something has to +happen to make it + + align:start position:0% +happen to make it + + + align:start position:0% +happen to make it +spontaneous so when we were talking + + align:start position:0% +spontaneous so when we were talking + + + align:start position:0% +spontaneous so when we were talking +about the different kinds of cells we an + + align:start position:0% +about the different kinds of cells we an + + + align:start position:0% +about the different kinds of cells we an +electrolytic cell where we could put in + + align:start position:0% +electrolytic cell where we could put in + + + align:start position:0% +electrolytic cell where we could put in +a current to drive a non-spontaneous + + align:start position:0% +a current to drive a non-spontaneous + + + align:start position:0% +a current to drive a non-spontaneous +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +same thing happens in biology and the + + align:start position:0% +same thing happens in biology and the + + + align:start position:0% +same thing happens in biology and the +current in this particular case is a + + align:start position:0% +current in this particular case is a + + + align:start position:0% +current in this particular case is a +molecule known as acenil methionine so + + align:start position:0% +molecule known as acenil methionine so + + + align:start position:0% +molecule known as acenil methionine so +it's the methionine amino acid with an + + align:start position:0% +it's the methionine amino acid with an + + + align:start position:0% +it's the methionine amino acid with an +adeny group attached to it and the + + align:start position:0% +adeny group attached to it and the + + + align:start position:0% +adeny group attached to it and the +cleavage of this molecule is very + + align:start position:0% +cleavage of this molecule is very + + + align:start position:0% +cleavage of this molecule is very +spontaneous it has a Delta G of minus + + align:start position:0% +spontaneous it has a Delta G of minus + + + align:start position:0% +spontaneous it has a Delta G of minus +37.6 K which is greater than what we + + align:start position:0% +37.6 K which is greater than what we + + + align:start position:0% +37.6 K which is greater than what we +need and we can even calculate the net + + align:start position:0% +need and we can even calculate the net + + + align:start position:0% +need and we can even calculate the net +Delta G for this reaction the coupled + + align:start position:0% +Delta G for this reaction the coupled + + + align:start position:0% +Delta G for this reaction the coupled +reaction of the cleavage with the + + align:start position:0% +reaction of the cleavage with the + + + align:start position:0% +reaction of the cleavage with the +reduction and if we do that we have- + + align:start position:0% +reduction and if we do that we have- + + + align:start position:0% +reduction and if we do that we have- +37.6 plus + + align:start position:0% +37.6 plus + + + align:start position:0% +37.6 plus +28.6 so + + align:start position:0% +28.6 so + + + align:start position:0% +28.6 so +-9.0 K per mole so we can drive this + + align:start position:0% +-9.0 K per mole so we can drive this + + + align:start position:0% +-9.0 K per mole so we can drive this +unfavorable reduction reaction with a + + align:start position:0% +unfavorable reduction reaction with a + + + align:start position:0% +unfavorable reduction reaction with a +very favorable reaction the cleavage of + + align:start position:0% +very favorable reaction the cleavage of + + + align:start position:0% +very favorable reaction the cleavage of +acenil methionine and that's how it + + align:start position:0% +acenil methionine and that's how it + + + align:start position:0% +acenil methionine and that's how it +works that's why we're all + + align:start position:0% +works that's why we're all + + + align:start position:0% +works that's why we're all +healthy all right so this is the end of + + align:start position:0% +healthy all right so this is the end of + + + align:start position:0% +healthy all right so this is the end of +our oxidation reduction example will + + align:start position:0% +our oxidation reduction example will + + + align:start position:0% +our oxidation reduction example will +transition to transition metals but + + align:start position:0% +transition to transition metals but + + + align:start position:0% +transition to transition metals but +we're not moving very far away from + + align:start position:0% +we're not moving very far away from + + + align:start position:0% +we're not moving very far away from +oxidation reduction because to do + + align:start position:0% +oxidation reduction because to do + + + align:start position:0% +oxidation reduction because to do +problems that are affect transition + + align:start position:0% +problems that are affect transition + + + align:start position:0% +problems that are affect transition +metals you have to know how to determine + + align:start position:0% +metals you have to know how to determine + + + align:start position:0% +metals you have to know how to determine +oxidation numbers and all sorts of + + align:start position:0% +oxidation numbers and all sorts of + + + align:start position:0% +oxidation numbers and all sorts of +things \ No newline at end of file diff --git a/fuUC0WVeKsg.txt b/fuUC0WVeKsg.txt new file mode 100644 index 0000000000000000000000000000000000000000..32c21a09083b078c81dd7af540f7919f19582498 --- /dev/null +++ b/fuUC0WVeKsg.txt @@ -0,0 +1,723 @@ +align:start position:0% + +in this video we'll discuss the method + + align:start position:0% +in this video we'll discuss the method + + + align:start position:0% +in this video we'll discuss the method +of hierarchical clustering in + + align:start position:0% +of hierarchical clustering in + + + align:start position:0% +of hierarchical clustering in +hierarchical clustering the clusters are + + align:start position:0% +hierarchical clustering the clusters are + + + align:start position:0% +hierarchical clustering the clusters are +formed by each data point starting in + + align:start position:0% +formed by each data point starting in + + + align:start position:0% +formed by each data point starting in +its own cluster as a small example + + align:start position:0% +its own cluster as a small example + + + align:start position:0% +its own cluster as a small example +suppose we have five data points each + + align:start position:0% +suppose we have five data points each + + + align:start position:0% +suppose we have five data points each +data point is labelled as belonging in + + align:start position:0% +data point is labelled as belonging in + + + align:start position:0% +data point is labelled as belonging in +its own cluster so this data points in + + align:start position:0% +its own cluster so this data points in + + + align:start position:0% +its own cluster so this data points in +the red cluster this one's in the blue + + align:start position:0% +the red cluster this one's in the blue + + + align:start position:0% +the red cluster this one's in the blue +cluster this one's in the purple cluster + + align:start position:0% +cluster this one's in the purple cluster + + + align:start position:0% +cluster this one's in the purple cluster +this one's in the green cluster and this + + align:start position:0% +this one's in the green cluster and this + + + align:start position:0% +this one's in the green cluster and this +one's in the yellow cluster then + + align:start position:0% +one's in the yellow cluster then + + + align:start position:0% +one's in the yellow cluster then +hierarchical clustering combines the two + + align:start position:0% +hierarchical clustering combines the two + + + align:start position:0% +hierarchical clustering combines the two +nearest clusters into one cluster will + + align:start position:0% +nearest clusters into one cluster will + + + align:start position:0% +nearest clusters into one cluster will +use Euclidean and centroid distances to + + align:start position:0% +use Euclidean and centroid distances to + + + align:start position:0% +use Euclidean and centroid distances to +decide which two clusters are the + + align:start position:0% +decide which two clusters are the + + + align:start position:0% +decide which two clusters are the +closest in our example the green and + + align:start position:0% +closest in our example the green and + + + align:start position:0% +closest in our example the green and +yellow clusters are closest together so + + align:start position:0% +yellow clusters are closest together so + + + align:start position:0% +yellow clusters are closest together so +we would combine these two clusters into + + align:start position:0% +we would combine these two clusters into + + + align:start position:0% +we would combine these two clusters into +one cluster so now the green cluster has + + align:start position:0% +one cluster so now the green cluster has + + + align:start position:0% +one cluster so now the green cluster has +two points and the yellow cluster is + + align:start position:0% +two points and the yellow cluster is + + + align:start position:0% +two points and the yellow cluster is +gone now this process repeats we again + + align:start position:0% +gone now this process repeats we again + + + align:start position:0% +gone now this process repeats we again +find the two nearest clusters which this + + align:start position:0% +find the two nearest clusters which this + + + align:start position:0% +find the two nearest clusters which this +time are the green cluster and the + + align:start position:0% +time are the green cluster and the + + + align:start position:0% +time are the green cluster and the +purple cluster and we combined them into + + align:start position:0% +purple cluster and we combined them into + + + align:start position:0% +purple cluster and we combined them into +one cluster now the green cluster has + + align:start position:0% +one cluster now the green cluster has + + + align:start position:0% +one cluster now the green cluster has +three points and the purple cluster is + + align:start position:0% +three points and the purple cluster is + + + align:start position:0% +three points and the purple cluster is +gone now the two nearest clusters are + + align:start position:0% +gone now the two nearest clusters are + + + align:start position:0% +gone now the two nearest clusters are +the red and blue clusters so we will + + align:start position:0% +the red and blue clusters so we will + + + align:start position:0% +the red and blue clusters so we will +combine these two clusters into one + + align:start position:0% +combine these two clusters into one + + + align:start position:0% +combine these two clusters into one +cluster the red cluster so now we have + + align:start position:0% +cluster the red cluster so now we have + + + align:start position:0% +cluster the red cluster so now we have +just two clusters the red one and the + + align:start position:0% +just two clusters the red one and the + + + align:start position:0% +just two clusters the red one and the +green one so now the final step is to + + align:start position:0% +green one so now the final step is to + + + align:start position:0% +green one so now the final step is to +combine these two clusters into one + + align:start position:0% +combine these two clusters into one + + + align:start position:0% +combine these two clusters into one +cluster so at the end of hierarchical + + align:start position:0% +cluster so at the end of hierarchical + + + align:start position:0% +cluster so at the end of hierarchical +clustering all of our data points are in + + align:start position:0% +clustering all of our data points are in + + + align:start position:0% +clustering all of our data points are in +a single cluster the hierarchical + + align:start position:0% +a single cluster the hierarchical + + + align:start position:0% +a single cluster the hierarchical +cluster process can be displayed through + + align:start position:0% +cluster process can be displayed through + + + align:start position:0% +cluster process can be displayed through +what's called a dendrogram the data + + align:start position:0% +what's called a dendrogram the data + + + align:start position:0% +what's called a dendrogram the data +points are listed along the bottom and + + align:start position:0% +points are listed along the bottom and + + + align:start position:0% +points are listed along the bottom and +the line show how the clusters were + + align:start position:0% +the line show how the clusters were + + + align:start position:0% +the line show how the clusters were +combined the height of the lines + + align:start position:0% +combined the height of the lines + + + align:start position:0% +combined the height of the lines +represents how far apart the clusters + + align:start position:0% +represents how far apart the clusters + + + align:start position:0% +represents how far apart the clusters +were when they were combined so points 1 + + align:start position:0% +were when they were combined so points 1 + + + align:start position:0% +were when they were combined so points 1 +and 4 were pretty close together when + + align:start position:0% +and 4 were pretty close together when + + + align:start position:0% +and 4 were pretty close together when +they were combined but when we combined + + align:start position:0% +they were combined but when we combined + + + align:start position:0% +they were combined but when we combined +the two clusters at the end they were + + align:start position:0% +the two clusters at the end they were + + + align:start position:0% +the two clusters at the end they were +significantly farther apart we can use a + + align:start position:0% +significantly farther apart we can use a + + + align:start position:0% +significantly farther apart we can use a +dendrogram to decide how many + + align:start position:0% +dendrogram to decide how many + + + align:start position:0% +dendrogram to decide how many +Buster's we won for our final clustering + + align:start position:0% +Buster's we won for our final clustering + + + align:start position:0% +Buster's we won for our final clustering +model this dendrogram shows the + + align:start position:0% +model this dendrogram shows the + + + align:start position:0% +model this dendrogram shows the +clustering process with ten data points + + align:start position:0% +clustering process with ten data points + + + align:start position:0% +clustering process with ten data points +the easiest way to pick the number of + + align:start position:0% +the easiest way to pick the number of + + + align:start position:0% +the easiest way to pick the number of +clusters you want is to draw a + + align:start position:0% +clusters you want is to draw a + + + align:start position:0% +clusters you want is to draw a +horizontal line across the dendrogram + + align:start position:0% +horizontal line across the dendrogram + + + align:start position:0% +horizontal line across the dendrogram +the number of vertical lines that line + + align:start position:0% +the number of vertical lines that line + + + align:start position:0% +the number of vertical lines that line +crosses is the number of clusters that + + align:start position:0% +crosses is the number of clusters that + + + align:start position:0% +crosses is the number of clusters that +will be in this case our line crosses + + align:start position:0% +will be in this case our line crosses + + + align:start position:0% +will be in this case our line crosses +two vertical lines meaning that we will + + align:start position:0% +two vertical lines meaning that we will + + + align:start position:0% +two vertical lines meaning that we will +have two clusters one cluster with + + align:start position:0% +have two clusters one cluster with + + + align:start position:0% +have two clusters one cluster with +points five two and seven and one + + align:start position:0% +points five two and seven and one + + + align:start position:0% +points five two and seven and one +cluster with the remaining points the + + align:start position:0% +cluster with the remaining points the + + + align:start position:0% +cluster with the remaining points the +farthest this horizontal line can move + + align:start position:0% +farthest this horizontal line can move + + + align:start position:0% +farthest this horizontal line can move +up and down in the dendrogram without + + align:start position:0% +up and down in the dendrogram without + + + align:start position:0% +up and down in the dendrogram without +hitting one of the horizontal lines of + + align:start position:0% +hitting one of the horizontal lines of + + + align:start position:0% +hitting one of the horizontal lines of +the dendrogram the better that choice of + + align:start position:0% +the dendrogram the better that choice of + + + align:start position:0% +the dendrogram the better that choice of +the number of clusters is if we instead + + align:start position:0% +the number of clusters is if we instead + + + align:start position:0% +the number of clusters is if we instead +selected three clusters this line can't + + align:start position:0% +selected three clusters this line can't + + + align:start position:0% +selected three clusters this line can't +move as far up and down without hitting + + align:start position:0% +move as far up and down without hitting + + + align:start position:0% +move as far up and down without hitting +horizontal lines in the dendrogram this + + align:start position:0% +horizontal lines in the dendrogram this + + + align:start position:0% +horizontal lines in the dendrogram this +probably means that the two cluster + + align:start position:0% +probably means that the two cluster + + + align:start position:0% +probably means that the two cluster +choice is better but when picking the + + align:start position:0% +choice is better but when picking the + + + align:start position:0% +choice is better but when picking the +number of clusters you should also + + align:start position:0% +number of clusters you should also + + + align:start position:0% +number of clusters you should also +consider how many clusters make sense + + align:start position:0% +consider how many clusters make sense + + + align:start position:0% +consider how many clusters make sense +for the particular application you're + + align:start position:0% +for the particular application you're + + + align:start position:0% +for the particular application you're +working with after selecting the number + + align:start position:0% +working with after selecting the number + + + align:start position:0% +working with after selecting the number +of clusters you want you should analyze + + align:start position:0% +of clusters you want you should analyze + + + align:start position:0% +of clusters you want you should analyze +your clusters to see if they're + + align:start position:0% +your clusters to see if they're + + + align:start position:0% +your clusters to see if they're +meaningful this can be done by looking + + align:start position:0% +meaningful this can be done by looking + + + align:start position:0% +meaningful this can be done by looking +at basic statistics in each cluster like + + align:start position:0% +at basic statistics in each cluster like + + + align:start position:0% +at basic statistics in each cluster like +the mean maximum and minimum values in + + align:start position:0% +the mean maximum and minimum values in + + + align:start position:0% +the mean maximum and minimum values in +each cluster and each variable you can + + align:start position:0% +each cluster and each variable you can + + + align:start position:0% +each cluster and each variable you can +also check to see if the clusters have a + + align:start position:0% +also check to see if the clusters have a + + + align:start position:0% +also check to see if the clusters have a +feature in common that was not used in + + align:start position:0% +feature in common that was not used in + + + align:start position:0% +feature in common that was not used in +the clustering like an outcome variable + + align:start position:0% +the clustering like an outcome variable + + + align:start position:0% +the clustering like an outcome variable +this often indicates that your clusters + + align:start position:0% +this often indicates that your clusters + + + align:start position:0% +this often indicates that your clusters +might help improve a predictive model in + + align:start position:0% +might help improve a predictive model in + + + align:start position:0% +might help improve a predictive model in +the next video we'll cluster our movies + + align:start position:0% +the next video we'll cluster our movies + + + align:start position:0% +the next video we'll cluster our movies +by genre and then analyze our clusters + + align:start position:0% +by genre and then analyze our clusters + + + align:start position:0% +by genre and then analyze our clusters +to see how they can be used to perform + + align:start position:0% +to see how they can be used to perform + + + align:start position:0% +to see how they can be used to perform +content filtering \ No newline at end of file diff --git a/gHW8ncZJhQY.txt b/gHW8ncZJhQY.txt new file mode 100644 index 0000000000000000000000000000000000000000..e89f8f197dec88226e6d107da4939fee03a9eba8 --- /dev/null +++ b/gHW8ncZJhQY.txt @@ -0,0 +1,1795 @@ +align:start position:0% + +in this section I'm going to dive into + + align:start position:0% +in this section I'm going to dive into + + + align:start position:0% +in this section I'm going to dive into +stack and Bricks which uh are we would + + align:start position:0% +stack and Bricks which uh are we would + + + align:start position:0% +stack and Bricks which uh are we would +say books of maps so just for you to + + align:start position:0% +say books of maps so just for you to + + + align:start position:0% +say books of maps so just for you to +have a good understanding of how stacks + + align:start position:0% +have a good understanding of how stacks + + + align:start position:0% +have a good understanding of how stacks +and bricks work it's like if you would + + align:start position:0% +and bricks work it's like if you would + + + align:start position:0% +and bricks work it's like if you would +have each of the map being a piece of + + align:start position:0% +have each of the map being a piece of + + + align:start position:0% +have each of the map being a piece of +paper and you would like to put them + + align:start position:0% +paper and you would like to put them + + + align:start position:0% +paper and you would like to put them +together uh in a in book form then you + + align:start position:0% +together uh in a in book form then you + + + align:start position:0% +together uh in a in book form then you +would use tag and brick and how is this + + align:start position:0% +would use tag and brick and how is this + + + align:start position:0% +would use tag and brick and how is this +helpful um this is helpful because these + + align:start position:0% +helpful um this is helpful because these + + + align:start position:0% +helpful um this is helpful because these +standardized processes that we want to + + align:start position:0% +standardized processes that we want to + + + align:start position:0% +standardized processes that we want to +we want to proceed on on the maps so + + align:start position:0% +we want to proceed on on the maps so + + + align:start position:0% +we want to proceed on on the maps so +let's say we want to chop them in the + + align:start position:0% +let's say we want to chop them in the + + + align:start position:0% +let's say we want to chop them in the +same shape or we want to transform them + + align:start position:0% +same shape or we want to transform them + + + align:start position:0% +same shape or we want to transform them +in the same resolution or we want to um + + align:start position:0% +in the same resolution or we want to um + + + align:start position:0% +in the same resolution or we want to um +calculate some results of these Maps we + + align:start position:0% +calculate some results of these Maps we + + + align:start position:0% +calculate some results of these Maps we +can do it using stack and bricks and we + + align:start position:0% +can do it using stack and bricks and we + + + align:start position:0% +can do it using stack and bricks and we +can also store stack and bricks in stack + + align:start position:0% +can also store stack and bricks in stack + + + align:start position:0% +can also store stack and bricks in stack +and brick form in our computer so first + + align:start position:0% +and brick form in our computer so first + + + align:start position:0% +and brick form in our computer so first +of all uh when we want to create stacks + + align:start position:0% +of all uh when we want to create stacks + + + align:start position:0% +of all uh when we want to create stacks +and Bricks there's a very handy way to + + align:start position:0% +and Bricks there's a very handy way to + + + align:start position:0% +and Bricks there's a very handy way to +charge these files all at once so we + + align:start position:0% +charge these files all at once so we + + + align:start position:0% +charge these files all at once so we +don't have to type the route every time + + align:start position:0% +don't have to type the route every time + + + align:start position:0% +don't have to type the route every time +in this case I'm going to use as example + + align:start position:0% +in this case I'm going to use as example + + + align:start position:0% +in this case I'm going to use as example +the world claim data that we downloaded + + align:start position:0% +the world claim data that we downloaded + + + align:start position:0% +the world claim data that we downloaded +if you've paid attention inside the + + align:start position:0% +if you've paid attention inside the + + + align:start position:0% +if you've paid attention inside the +folder it it comes with 12 different + + align:start position:0% +folder it it comes with 12 different + + + align:start position:0% +folder it it comes with 12 different +maps that are representing the average + + align:start position:0% +maps that are representing the average + + + align:start position:0% +maps that are representing the average +temperature of each month and now we are + + align:start position:0% +temperature of each month and now we are + + + align:start position:0% +temperature of each month and now we are +going to combine them into one brick so + + align:start position:0% +going to combine them into one brick so + + + align:start position:0% +going to combine them into one brick so +we can calculate calate the mean or the + + align:start position:0% +we can calculate calate the mean or the + + + align:start position:0% +we can calculate calate the mean or the +standard deviation of all of them so + + align:start position:0% +standard deviation of all of them so + + + align:start position:0% +standard deviation of all of them so +first of all we need to write the + + align:start position:0% +first of all we need to write the + + + align:start position:0% +first of all we need to write the +directory route where we have all the + + align:start position:0% +directory route where we have all the + + + align:start position:0% +directory route where we have all the +maps um also you could add in your code + + align:start position:0% +maps um also you could add in your code + + + align:start position:0% +maps um also you could add in your code +a Chun of code saying pattern TI in Cas + + align:start position:0% +a Chun of code saying pattern TI in Cas + + + align:start position:0% +a Chun of code saying pattern TI in Cas +in case you would have um some other + + align:start position:0% +in case you would have um some other + + + align:start position:0% +in case you would have um some other +files in that folder and you only wanted + + align:start position:0% +files in that folder and you only wanted + + + align:start position:0% +files in that folder and you only wanted +to upload the TF uh but in this case + + align:start position:0% +to upload the TF uh but in this case + + + align:start position:0% +to upload the TF uh but in this case +everything is CF so I I don't I don't + + align:start position:0% +everything is CF so I I don't I don't + + + align:start position:0% +everything is CF so I I don't I don't +need to do + + align:start position:0% +need to do + + + align:start position:0% +need to do +that um you charge the files which is + + align:start position:0% +that um you charge the files which is + + + align:start position:0% +that um you charge the files which is +only the name of the object that's um + + align:start position:0% +only the name of the object that's um + + + align:start position:0% +only the name of the object that's um +inside and then we want to transform all + + align:start position:0% +inside and then we want to transform all + + + align:start position:0% +inside and then we want to transform all +these routes into different rasters and + + align:start position:0% +these routes into different rasters and + + + align:start position:0% +these routes into different rasters and +to do so we are going to use the LLY + + align:start position:0% +to do so we are going to use the LLY + + + align:start position:0% +to do so we are going to use the LLY +function here using these map files and + + align:start position:0% +function here using these map files and + + + align:start position:0% +function here using these map files and +transforming them all into raster so + + align:start position:0% +transforming them all into raster so + + + align:start position:0% +transforming them all into raster so +doing + + align:start position:0% +doing + + + align:start position:0% +doing +this we'll get a list of uh these 12 + + align:start position:0% +this we'll get a list of uh these 12 + + + align:start position:0% +this we'll get a list of uh these 12 +maps and we want to um well just to + + align:start position:0% +maps and we want to um well just to + + + align:start position:0% +maps and we want to um well just to +consult one of them just going to see + + align:start position:0% +consult one of them just going to see + + + align:start position:0% +consult one of them just going to see +what we have in the number six for + + align:start position:0% +what we have in the number six for + + + align:start position:0% +what we have in the number six for +example and here we have a map this is + + align:start position:0% +example and here we have a map this is + + + align:start position:0% +example and here we have a map this is +all the information about this map so + + align:start position:0% +all the information about this map so + + + align:start position:0% +all the information about this map so +the dimensions resolution extend and so + + align:start position:0% +the dimensions resolution extend and so + + + align:start position:0% +the dimensions resolution extend and so +forth um just to see how it looks + + align:start position:0% +forth um just to see how it looks + + + align:start position:0% +forth um just to see how it looks +like just a map and we want to include + + align:start position:0% +like just a map and we want to include + + + align:start position:0% +like just a map and we want to include +all these Maps into a stack or a brick + + align:start position:0% +all these Maps into a stack or a brick + + + align:start position:0% +all these Maps into a stack or a brick +uh they are mostly the same for working + + align:start position:0% +uh they are mostly the same for working + + + align:start position:0% +uh they are mostly the same for working +purposes but um the organization of the + + align:start position:0% +purposes but um the organization of the + + + align:start position:0% +purposes but um the organization of the +data is a slightly different so + + align:start position:0% +data is a slightly different so + + + align:start position:0% +data is a slightly different so +sometimes for some process you would + + align:start position:0% +sometimes for some process you would + + + align:start position:0% +sometimes for some process you would +need to use stack or brick but the + + align:start position:0% +need to use stack or brick but the + + + align:start position:0% +need to use stack or brick but the +concept behind it's uh mostly the same + + align:start position:0% +concept behind it's uh mostly the same + + + align:start position:0% +concept behind it's uh mostly the same +so it works either way just um using the + + align:start position:0% +so it works either way just um using the + + + align:start position:0% +so it works either way just um using the +function stack or brick and they have to + + align:start position:0% +function stack or brick and they have to + + + align:start position:0% +function stack or brick and they have to +be in the same extension and resolution + + align:start position:0% +be in the same extension and resolution + + + align:start position:0% +be in the same extension and resolution +otherwise I wouldn't let you to put them + + align:start position:0% + + + + align:start position:0% + +together so here we have + + align:start position:0% +together so here we have + + + align:start position:0% +together so here we have +it you see we've created um raster briak + + align:start position:0% +it you see we've created um raster briak + + + align:start position:0% +it you see we've created um raster briak +or raster stack depending on the + + align:start position:0% +or raster stack depending on the + + + align:start position:0% +or raster stack depending on the +function that we used um and now I'm + + align:start position:0% +function that we used um and now I'm + + + align:start position:0% +function that we used um and now I'm +going to use the function calc which is + + align:start position:0% +going to use the function calc which is + + + align:start position:0% +going to use the function calc which is +a calculator that and I'm going to + + align:start position:0% +a calculator that and I'm going to + + + align:start position:0% +a calculator that and I'm going to +calculate something on the maps that we + + align:start position:0% +calculate something on the maps that we + + + align:start position:0% +calculate something on the maps that we +just uploaded in this case I'm + + align:start position:0% +just uploaded in this case I'm + + + align:start position:0% +just uploaded in this case I'm +calculating the standard deviation but I + + align:start position:0% +calculating the standard deviation but I + + + align:start position:0% +calculating the standard deviation but I +could change this for the mean for + + align:start position:0% +could change this for the mean for + + + align:start position:0% +could change this for the mean for +example um so I'm going to calculate uh + + align:start position:0% +example um so I'm going to calculate uh + + + align:start position:0% +example um so I'm going to calculate uh +inside this stack right here the + + align:start position:0% +inside this stack right here the + + + align:start position:0% +inside this stack right here the +standard deviation of all the maps there + + align:start position:0% +standard deviation of all the maps there + + + align:start position:0% +standard deviation of all the maps there +is also extra code that you can see here + + align:start position:0% +is also extra code that you can see here + + + align:start position:0% +is also extra code that you can see here +and this code is used to calculate the + + align:start position:0% +and this code is used to calculate the + + + align:start position:0% +and this code is used to calculate the +time that we are investing in processing + + align:start position:0% +time that we are investing in processing + + + align:start position:0% +time that we are investing in processing +this uh information just uh to make it + + align:start position:0% +this uh information just uh to make it + + + align:start position:0% +this uh information just uh to make it +fair we have to run it all at + + align:start position:0% +fair we have to run it all at + + + align:start position:0% +fair we have to run it all at +once it's going to run it and this is + + align:start position:0% +once it's going to run it and this is + + + align:start position:0% +once it's going to run it and this is +going to extract the the system time + + align:start position:0% +going to extract the the system time + + + align:start position:0% +going to extract the the system time +that was stored in our computer at the + + align:start position:0% +that was stored in our computer at the + + + align:start position:0% +that was stored in our computer at the +beginning of the process and it's going + + align:start position:0% +beginning of the process and it's going + + + align:start position:0% +beginning of the process and it's going +to record it again at the end of the + + align:start position:0% +to record it again at the end of the + + + align:start position:0% +to record it again at the end of the +process and then it's going to make the + + align:start position:0% +process and then it's going to make the + + + align:start position:0% +process and then it's going to make the +calculation of how much times time + + align:start position:0% +calculation of how much times time + + + align:start position:0% +calculation of how much times time +difference there's in between uh the the + + align:start position:0% +difference there's in between uh the the + + + align:start position:0% +difference there's in between uh the the +initiation and the finalization of the + + align:start position:0% +initiation and the finalization of the + + + align:start position:0% +initiation and the finalization of the +process so in this case we've calculated + + align:start position:0% +process so in this case we've calculated + + + align:start position:0% +process so in this case we've calculated +the standard deviation that took us 14 + + align:start position:0% +the standard deviation that took us 14 + + + align:start position:0% +the standard deviation that took us 14 +seconds and let's see how it looks like + + align:start position:0% +seconds and let's see how it looks like + + + align:start position:0% +seconds and let's see how it looks like +and so this is the standard deviation of + + align:start position:0% +and so this is the standard deviation of + + + align:start position:0% +and so this is the standard deviation of +the average temperatures um at global + + align:start position:0% +the average temperatures um at global + + + align:start position:0% +the average temperatures um at global +scale and that's also something we can + + align:start position:0% +scale and that's also something we can + + + align:start position:0% +scale and that's also something we can +store in our computer uh we can write + + align:start position:0% +store in our computer uh we can write + + + align:start position:0% +store in our computer uh we can write +raster um as it was only one one raster + + align:start position:0% +raster um as it was only one one raster + + + align:start position:0% +raster um as it was only one one raster +so for stacks and Bricks it works the + + align:start position:0% +so for stacks and Bricks it works the + + + align:start position:0% +so for stacks and Bricks it works the +same um so instead of having one map + + align:start position:0% +same um so instead of having one map + + + align:start position:0% +same um so instead of having one map +here we just + + align:start position:0% +here we just + + + align:start position:0% +here we just +um we could have put the the raster um + + align:start position:0% +um we could have put the the raster um + + + align:start position:0% +um we could have put the the raster um +break or stack + + align:start position:0% +break or stack + + + align:start position:0% +break or stack +uh in this case I'm just going to store + + align:start position:0% +uh in this case I'm just going to store + + + align:start position:0% +uh in this case I'm just going to store +the outcome of this calculation that + + align:start position:0% +the outcome of this calculation that + + + align:start position:0% +the outcome of this calculation that +we've made and just put the route that + + align:start position:0% +we've made and just put the route that + + + align:start position:0% +we've made and just put the route that +you that you want the things to be + + align:start position:0% +you that you want the things to be + + + align:start position:0% +you that you want the things to be +stored on + + align:start position:0% +stored on + + + align:start position:0% +stored on +and um well if you run this code you're + + align:start position:0% +and um well if you run this code you're + + + align:start position:0% +and um well if you run this code you're +going to create this map in your + + align:start position:0% +going to create this map in your + + + align:start position:0% +going to create this map in your +computer and also another way to store + + align:start position:0% +computer and also another way to store + + + align:start position:0% +computer and also another way to store +the map + + align:start position:0% +the map + + + align:start position:0% +the map +without using this function is to um so + + align:start position:0% +without using this function is to um so + + + align:start position:0% +without using this function is to um so +while you are calculating something + + align:start position:0% +while you are calculating something + + + align:start position:0% +while you are calculating something +where you are running a process in a F + + align:start position:0% +where you are running a process in a F + + + align:start position:0% +where you are running a process in a F +function um then if you specify a file + + align:start position:0% +function um then if you specify a file + + + align:start position:0% +function um then if you specify a file +name r is going to understand that while + + align:start position:0% +name r is going to understand that while + + + align:start position:0% +name r is going to understand that while +this is been processed it's going to be + + align:start position:0% +this is been processed it's going to be + + + align:start position:0% +this is been processed it's going to be +at the same time stored so only with a + + align:start position:0% +at the same time stored so only with a + + + align:start position:0% +at the same time stored so only with a +line of code you would have um the + + align:start position:0% +line of code you would have um the + + + align:start position:0% +line of code you would have um the +creation of that map plus the saving + + align:start position:0% +creation of that map plus the saving + + + align:start position:0% +creation of that map plus the saving +process in your + + align:start position:0% +process in your + + + align:start position:0% +process in your +computer also in case you would like to + + align:start position:0% +computer also in case you would like to + + + align:start position:0% +computer also in case you would like to +store a stack or a brick you would have + + align:start position:0% +store a stack or a brick you would have + + + align:start position:0% +store a stack or a brick you would have +to change from Tif extension to GR + + align:start position:0% +to change from Tif extension to GR + + + align:start position:0% +to change from Tif extension to GR +Rd um when you create this extension uh + + align:start position:0% +Rd um when you create this extension uh + + + align:start position:0% +Rd um when you create this extension uh +you would have two different files um + + align:start position:0% +you would have two different files um + + + align:start position:0% +you would have two different files um +and these two different files are well + + align:start position:0% +and these two different files are well + + + align:start position:0% +and these two different files are well +it's necessary that both would be in the + + align:start position:0% +it's necessary that both would be in the + + + align:start position:0% +it's necessary that both would be in the +same folder otherwise when you would + + align:start position:0% +same folder otherwise when you would + + + align:start position:0% +same folder otherwise when you would +read them um R would understand + + align:start position:0% +read them um R would understand + + + align:start position:0% +read them um R would understand +understand them as corrupted so make + + align:start position:0% +understand them as corrupted so make + + + align:start position:0% +understand them as corrupted so make +sure that not separating these two files + + align:start position:0% +sure that not separating these two files + + + align:start position:0% +sure that not separating these two files +in order to be able to read the the code + + align:start position:0% + + + + align:start position:0% + +appropriately + + align:start position:0% + + + + align:start position:0% + +also moving on to the next function um + + align:start position:0% +also moving on to the next function um + + + align:start position:0% +also moving on to the next function um +we're going to move to the crop function + + align:start position:0% +we're going to move to the crop function + + + align:start position:0% +we're going to move to the crop function +this can be used to crop one map or it + + align:start position:0% +this can be used to crop one map or it + + + align:start position:0% +this can be used to crop one map or it +can be used to crop a brick or a stack + + align:start position:0% +can be used to crop a brick or a stack + + + align:start position:0% +can be used to crop a brick or a stack +um and chopping them in small pieces in + + align:start position:0% +um and chopping them in small pieces in + + + align:start position:0% +um and chopping them in small pieces in +this case I'm going to use as a base + + align:start position:0% +this case I'm going to use as a base + + + align:start position:0% +this case I'm going to use as a base +this temperature map and I'm just going + + align:start position:0% +this temperature map and I'm just going + + + align:start position:0% +this temperature map and I'm just going +to chop the the latitude and longitude + + align:start position:0% +to chop the the latitude and longitude + + + align:start position:0% +to chop the the latitude and longitude +based on the S USA + + align:start position:0% +based on the S USA + + + align:start position:0% +based on the S USA +Coast so if I do this oh temperature is + + align:start position:0% +Coast so if I do this oh temperature is + + + align:start position:0% +Coast so if I do this oh temperature is +not found should go and charge it + + align:start position:0% +not found should go and charge it + + + align:start position:0% +not found should go and charge it +again here we have + + align:start position:0% + + + + align:start position:0% + +it now I should be able to crop + + align:start position:0% + + + + align:start position:0% + +it going to see how it looks + + align:start position:0% + + + + align:start position:0% + +like and this is the result of a + + align:start position:0% +like and this is the result of a + + + align:start position:0% +like and this is the result of a +cropping um this is a very handy tool in + + align:start position:0% +cropping um this is a very handy tool in + + + align:start position:0% +cropping um this is a very handy tool in +order to make experiments with your code + + align:start position:0% +order to make experiments with your code + + + align:start position:0% +order to make experiments with your code +so as you've seen before sometimes doing + + align:start position:0% +so as you've seen before sometimes doing + + + align:start position:0% +so as you've seen before sometimes doing +some processes when we are working in + + align:start position:0% +some processes when we are working in + + + align:start position:0% +some processes when we are working in +maps it can take a long time so if you + + align:start position:0% +maps it can take a long time so if you + + + align:start position:0% +maps it can take a long time so if you +want to just check that your code is + + align:start position:0% +want to just check that your code is + + + align:start position:0% +want to just check that your code is +working and that all the processes that + + align:start position:0% +working and that all the processes that + + + align:start position:0% +working and that all the processes that +has been done um are what you want it to + + align:start position:0% +has been done um are what you want it to + + + align:start position:0% +has been done um are what you want it to +be you can just cut your map in a small + + align:start position:0% +be you can just cut your map in a small + + + align:start position:0% +be you can just cut your map in a small +piece and then run everything in that + + align:start position:0% +piece and then run everything in that + + + align:start position:0% +piece and then run everything in that +small piece just to be a a sample um of + + align:start position:0% +small piece just to be a a sample um of + + + align:start position:0% +small piece just to be a a sample um of +your final code and then when you've + + align:start position:0% +your final code and then when you've + + + align:start position:0% +your final code and then when you've +made sure that everything is running + + align:start position:0% +made sure that everything is running + + + align:start position:0% +made sure that everything is running +properly you can run the process with + + align:start position:0% +properly you can run the process with + + + align:start position:0% +properly you can run the process with +the whole map so that might save you + + align:start position:0% +the whole map so that might save you + + + align:start position:0% +the whole map so that might save you +some some + + align:start position:0% +some some + + + align:start position:0% +some some +time there's also another function that + + align:start position:0% +time there's also another function that + + + align:start position:0% +time there's also another function that +I particularly think is very useful + + align:start position:0% +I particularly think is very useful + + + align:start position:0% +I particularly think is very useful +which is the m map fun mask function um + + align:start position:0% +which is the m map fun mask function um + + + align:start position:0% +which is the m map fun mask function um +here I'm going to use one of the maps + + align:start position:0% +here I'm going to use one of the maps + + + align:start position:0% +here I'm going to use one of the maps +that we've used previously up in the + + align:start position:0% +that we've used previously up in the + + + align:start position:0% +that we've used previously up in the +code which was this uh nitrogen + + align:start position:0% +code which was this uh nitrogen + + + align:start position:0% +code which was this uh nitrogen +deposition map um um just to remind you + + align:start position:0% +deposition map um um just to remind you + + + align:start position:0% +deposition map um um just to remind you +what was that just going to charge it + + align:start position:0% +what was that just going to charge it + + + align:start position:0% +what was that just going to charge it +and plot it so this is a nitrogen + + align:start position:0% +and plot it so this is a nitrogen + + + align:start position:0% +and plot it so this is a nitrogen +deposition that has happened uh in + + align:start position:0% +deposition that has happened uh in + + + align:start position:0% +deposition that has happened uh in +1901 I think um but we see that the map + + align:start position:0% +1901 I think um but we see that the map + + + align:start position:0% +1901 I think um but we see that the map +here it covers the whole surface of the + + align:start position:0% +here it covers the whole surface of the + + + align:start position:0% +here it covers the whole surface of the +Earth including water bodies uh what + + align:start position:0% +Earth including water bodies uh what + + + align:start position:0% +Earth including water bodies uh what +happen if I want to have the information + + align:start position:0% +happen if I want to have the information + + + align:start position:0% +happen if I want to have the information +only um on the ground only on the Earth + + align:start position:0% +only um on the ground only on the Earth + + + align:start position:0% +only um on the ground only on the Earth +surface so what I'm going to going to do + + align:start position:0% +surface so what I'm going to going to do + + + align:start position:0% +surface so what I'm going to going to do +is is I'm going to mask this map right + + align:start position:0% +is is I'm going to mask this map right + + + align:start position:0% +is is I'm going to mask this map right +here with the maps that we previously + + align:start position:0% +here with the maps that we previously + + + align:start position:0% +here with the maps that we previously +used that included only um with excluded + + align:start position:0% +used that included only um with excluded + + + align:start position:0% +used that included only um with excluded +water bodies let's say um so I'm going + + align:start position:0% +water bodies let's say um so I'm going + + + align:start position:0% +water bodies let's say um so I'm going +to use again this temperature map just + + align:start position:0% +to use again this temperature map just + + + align:start position:0% +to use again this temperature map just +going to plot + + align:start position:0% +going to plot + + + align:start position:0% +going to plot +it so I'm going to use it as a + + align:start position:0% +it so I'm going to use it as a + + + align:start position:0% +it so I'm going to use it as a +base so to do so there is this function + + align:start position:0% +base so to do so there is this function + + + align:start position:0% +base so to do so there is this function +right here that's called mask uh and I'm + + align:start position:0% +right here that's called mask uh and I'm + + + align:start position:0% +right here that's called mask uh and I'm +going to mask this nitrogen deposition + + align:start position:0% +going to mask this nitrogen deposition + + + align:start position:0% +going to mask this nitrogen deposition +based on this shape right here I'm going + + align:start position:0% +based on this shape right here I'm going + + + align:start position:0% +based on this shape right here I'm going +to run it going to give me an error here + + align:start position:0% +to run it going to give me an error here + + + align:start position:0% +to run it going to give me an error here +you have it this error is saying that we + + align:start position:0% +you have it this error is saying that we + + + align:start position:0% +you have it this error is saying that we +have different extent what is that let's + + align:start position:0% +have different extent what is that let's + + + align:start position:0% +have different extent what is that let's +just check the two + + align:start position:0% +just check the two + + + align:start position:0% +just check the two +maps this map and this other map it's + + align:start position:0% +maps this map and this other map it's + + + align:start position:0% +maps this map and this other map it's +complaining about the + + align:start position:0% +complaining about the + + + align:start position:0% +complaining about the +extend + + align:start position:0% +extend + + + align:start position:0% +extend +so this extent here is this one and this + + align:start position:0% +so this extent here is this one and this + + + align:start position:0% +so this extent here is this one and this +extent here is a slightly different and + + align:start position:0% +extent here is a slightly different and + + + align:start position:0% +extent here is a slightly different and +that's why we have this problem how to + + align:start position:0% +that's why we have this problem how to + + + align:start position:0% +that's why we have this problem how to +solve it well we'll need to fix this + + align:start position:0% +solve it well we'll need to fix this + + + align:start position:0% +solve it well we'll need to fix this +extend problem + + align:start position:0% +extend problem + + + align:start position:0% +extend problem +um we're going to use this resample + + align:start position:0% +um we're going to use this resample + + + align:start position:0% +um we're going to use this resample +function here that's going to transform + + align:start position:0% +function here that's going to transform + + + align:start position:0% +function here that's going to transform +both maps in the same extension + + align:start position:0% +both maps in the same extension + + + align:start position:0% +both maps in the same extension +projection and resolution all at once so + + align:start position:0% +projection and resolution all at once so + + + align:start position:0% +projection and resolution all at once so +by using this I'm going to make the + + align:start position:0% +by using this I'm going to make the + + + align:start position:0% +by using this I'm going to make the +nitrogen deposition map to have the + + align:start position:0% +nitrogen deposition map to have the + + + align:start position:0% +nitrogen deposition map to have the +same features as the other map so in + + align:start position:0% +same features as the other map so in + + + align:start position:0% +same features as the other map so in +this case um I'm going to use the second + + align:start position:0% +this case um I'm going to use the second + + + align:start position:0% +this case um I'm going to use the second +map that we produced to see if it works + + align:start position:0% +map that we produced to see if it works + + + align:start position:0% +map that we produced to see if it works +and now the the error is soft and we can + + align:start position:0% +and now the the error is soft and we can + + + align:start position:0% +and now the the error is soft and we can +see the result on how the map has + + align:start position:0% +see the result on how the map has + + + align:start position:0% +see the result on how the map has +changed and how all the water bodies has + + align:start position:0% +changed and how all the water bodies has + + + align:start position:0% +changed and how all the water bodies has +been + + align:start position:0% + + + + align:start position:0% + +masked \ No newline at end of file diff --git a/gRlrh4lRapM.txt b/gRlrh4lRapM.txt new file mode 100644 index 0000000000000000000000000000000000000000..52c3825e64b870b376f4b8b6f544cf6df2b50eba --- /dev/null +++ b/gRlrh4lRapM.txt @@ -0,0 +1,1003 @@ +align:start position:0% + +scattering so where did we get to last + + align:start position:0% +scattering so where did we get to last + + + align:start position:0% +scattering so where did we get to last +time we did the following things this is + + align:start position:0% +time we did the following things this is + + + align:start position:0% +time we did the following things this is +a recap we wrote a solution a scattering + + align:start position:0% +a recap we wrote a solution a scattering + + + align:start position:0% +a recap we wrote a solution a scattering +solution or al use R and this solution + + align:start position:0% +solution or al use R and this solution + + + align:start position:0% +solution or al use R and this solution +had a wave that represented the incoming + + align:start position:0% +had a wave that represented the incoming + + + align:start position:0% +had a wave that represented the incoming +wave and it had what we call the + + align:start position:0% +wave and it had what we call the + + + align:start position:0% +wave and it had what we call the +scattered wave so there were two pieces + + align:start position:0% +scattered wave so there were two pieces + + + align:start position:0% +scattered wave so there were two pieces +to the solution we understood that + + align:start position:0% +to the solution we understood that + + + align:start position:0% +to the solution we understood that +setting up a scattering problem with a + + align:start position:0% +setting up a scattering problem with a + + + align:start position:0% +setting up a scattering problem with a +central potential we had a wave that + + align:start position:0% +central potential we had a wave that + + + align:start position:0% +central potential we had a wave that +came in and then we had a spherical wave + + align:start position:0% + + + + align:start position:0% + +and that was an outgoing spherical wave + + align:start position:0% +and that was an outgoing spherical wave + + + align:start position:0% +and that was an outgoing spherical wave +I've added a subscript K to represent + + align:start position:0% +I've added a subscript K to represent + + + align:start position:0% +I've added a subscript K to represent +the wave number or decay of the wave + + align:start position:0% +the wave number or decay of the wave + + + align:start position:0% +the wave number or decay of the wave +this is an energy eigenstate we're + + align:start position:0% +this is an energy eigenstate we're + + + align:start position:0% +this is an energy eigenstate we're +calculating and therefore the energy is + + align:start position:0% +calculating and therefore the energy is + + + align:start position:0% +calculating and therefore the energy is +K squared H bar squared K squared over + + align:start position:0% +K squared H bar squared K squared over + + + align:start position:0% +K squared H bar squared K squared over +2m and we're writing a solution with + + align:start position:0% +2m and we're writing a solution with + + + align:start position:0% +2m and we're writing a solution with +that energy that's an energy eigenstate + + align:start position:0% +that energy that's an energy eigenstate + + + align:start position:0% +that energy that's an energy eigenstate +and this solution is as written not an + + align:start position:0% +and this solution is as written not an + + + align:start position:0% +and this solution is as written not an +exact solution of the Schrodinger + + align:start position:0% +exact solution of the Schrodinger + + + align:start position:0% +exact solution of the Schrodinger +equation but it's approximately exact + + align:start position:0% +equation but it's approximately exact + + + align:start position:0% +equation but it's approximately exact +for are much greater than a where a is + + align:start position:0% +for are much greater than a where a is + + + align:start position:0% +for are much greater than a where a is +the range of your potential so this is + + align:start position:0% +the range of your potential so this is + + + align:start position:0% +the range of your potential so this is +only valid in those cases it's not valid + + align:start position:0% +only valid in those cases it's not valid + + + align:start position:0% +only valid in those cases it's not valid +near the scattering for are near zero + + align:start position:0% +near the scattering for are near zero + + + align:start position:0% +near the scattering for are near zero +that's not true and it's not an exact + + align:start position:0% +that's not true and it's not an exact + + + align:start position:0% +that's not true and it's not an exact +solution this would have been an exact + + align:start position:0% +solution this would have been an exact + + + align:start position:0% +solution this would have been an exact +solution of the wave of the time + + align:start position:0% +solution of the wave of the time + + + align:start position:0% +solution of the wave of the time +independent Schrodinger equation and + + align:start position:0% +independent Schrodinger equation and + + + align:start position:0% +independent Schrodinger equation and +this without the F would have been an + + align:start position:0% +this without the F would have been an + + + align:start position:0% +this without the F would have been an +exact solution but with the + + align:start position:0% +exact solution but with the + + + align:start position:0% +exact solution but with the +F is an approximate solution but that's + + align:start position:0% +F is an approximate solution but that's + + + align:start position:0% +F is an approximate solution but that's +the solution that represents the physics + + align:start position:0% +the solution that represents the physics + + + align:start position:0% +the solution that represents the physics +of scattering then we also showed that + + align:start position:0% +of scattering then we also showed that + + + align:start position:0% +of scattering then we also showed that +the differential cross-section was in + + align:start position:0% +the differential cross-section was in + + + align:start position:0% +the differential cross-section was in +fact given by this function f so this + + align:start position:0% +fact given by this function f so this + + + align:start position:0% +fact given by this function f so this +function f is really what we're after + + align:start position:0% +function f is really what we're after + + + align:start position:0% +function f is really what we're after +and if we know F we know the + + align:start position:0% +and if we know F we know the + + + align:start position:0% +and if we know F we know the +differential cross-section which is + + align:start position:0% +differential cross-section which is + + + align:start position:0% +differential cross-section which is +something we measure experimentally + + align:start position:0% +something we measure experimentally + + + align:start position:0% +something we measure experimentally +we're scattering particles that we + + align:start position:0% +we're scattering particles that we + + + align:start position:0% +we're scattering particles that we +detect them and the differential + + align:start position:0% +detect them and the differential + + + align:start position:0% +detect them and the differential +cross-section tells us about our ability + + align:start position:0% +cross-section tells us about our ability + + + align:start position:0% +cross-section tells us about our ability +and the number of particles that each + + align:start position:0% +and the number of particles that each + + + align:start position:0% +and the number of particles that each +detector picks up then we've restricted + + align:start position:0% +detector picks up then we've restricted + + + align:start position:0% +detector picks up then we've restricted +ourselves to the case of central + + align:start position:0% +ourselves to the case of central + + + align:start position:0% +ourselves to the case of central +potentials and for those central + + align:start position:0% +potentials and for those central + + + align:start position:0% +potentials and for those central +potentials V of R was some function of + + align:start position:0% +potentials V of R was some function of + + + align:start position:0% +potentials V of R was some function of +just the scalar distance in such cases + + align:start position:0% +just the scalar distance in such cases + + + align:start position:0% +just the scalar distance in such cases +that cross-section would not have a fine + + align:start position:0% +that cross-section would not have a fine + + + align:start position:0% +that cross-section would not have a fine +dependence you can imagine here is the + + align:start position:0% +dependence you can imagine here is the + + + align:start position:0% +dependence you can imagine here is the +object is spherically symmetric and + + align:start position:0% +object is spherically symmetric and + + + align:start position:0% +object is spherically symmetric and +you're shooting waves and therefore the + + align:start position:0% +you're shooting waves and therefore the + + + align:start position:0% +you're shooting waves and therefore the +cross-section and the amplitude will be + + align:start position:0% +cross-section and the amplitude will be + + + align:start position:0% +cross-section and the amplitude will be +independent of the angle Phi there's + + align:start position:0% +independent of the angle Phi there's + + + align:start position:0% +independent of the angle Phi there's +already a direction picked up by the + + align:start position:0% +already a direction picked up by the + + + align:start position:0% +already a direction picked up by the +incoming wave but otherwise it's it's + + align:start position:0% +incoming wave but otherwise it's it's + + + align:start position:0% +incoming wave but otherwise it's it's +just that so we wrote solutions in those + + align:start position:0% +just that so we wrote solutions in those + + + align:start position:0% +just that so we wrote solutions in those +cases if we are gonna solve as we will + + align:start position:0% +cases if we are gonna solve as we will + + + align:start position:0% +cases if we are gonna solve as we will +today some of these problems you need to + + align:start position:0% +today some of these problems you need to + + + align:start position:0% +today some of these problems you need to +write complete solutions and + + align:start position:0% + + + + align:start position:0% + +spiracle solutions are of this form + + align:start position:0% +spiracle solutions are of this form + + + align:start position:0% +spiracle solutions are of this form +although the relevant ones that we will + + align:start position:0% +although the relevant ones that we will + + + align:start position:0% +although the relevant ones that we will +be using will have no M we'll be + + align:start position:0% +be using will have no M we'll be + + + align:start position:0% +be using will have no M we'll be +focusing in solutions that have M equals + + align:start position:0% +focusing in solutions that have M equals + + + align:start position:0% +focusing in solutions that have M equals +zero for us M will be equal to zero but + + align:start position:0% +zero for us M will be equal to zero but + + + align:start position:0% +zero for us M will be equal to zero but +these are the general solutions so of + + align:start position:0% +these are the general solutions so of + + + align:start position:0% +these are the general solutions so of +maybe I might as well constrain + + align:start position:0% +maybe I might as well constrain + + + align:start position:0% +maybe I might as well constrain +ourselves to our case already central + + align:start position:0% +ourselves to our case already central + + + align:start position:0% +ourselves to our case already central +potentials so we will have solutions of + + align:start position:0% +potentials so we will have solutions of + + + align:start position:0% +potentials so we will have solutions of +this kind and these are solutions of the + + align:start position:0% +this kind and these are solutions of the + + + align:start position:0% +this kind and these are solutions of the +radial equation we reviewed those and + + align:start position:0% +radial equation we reviewed those and + + + align:start position:0% +radial equation we reviewed those and +mention that sIFR would be given by Al + + align:start position:0% +mention that sIFR would be given by Al + + + align:start position:0% +mention that sIFR would be given by Al +JL of kr plus BL NL of kr times y l0 of + + align:start position:0% +JL of kr plus BL NL of kr times y l0 of + + + align:start position:0% +JL of kr plus BL NL of kr times y l0 of +Omega this will be our solutions these + + align:start position:0% +Omega this will be our solutions these + + + align:start position:0% +Omega this will be our solutions these +are the spherical Bessel functions and + + align:start position:0% +are the spherical Bessel functions and + + + align:start position:0% +are the spherical Bessel functions and +those were solutions that are valid as + + align:start position:0% +those were solutions that are valid as + + + align:start position:0% +those were solutions that are valid as +long as you are away from the from the + + align:start position:0% +long as you are away from the from the + + + align:start position:0% +long as you are away from the from the +scattering center so this is valid for R + + align:start position:0% +scattering center so this is valid for R + + + align:start position:0% +scattering center so this is valid for R +greater than a indeed you know that this + + align:start position:0% +greater than a indeed you know that this + + + align:start position:0% +greater than a indeed you know that this +could not be valid all the way to the + + align:start position:0% +could not be valid all the way to the + + + align:start position:0% +could not be valid all the way to the +center of the power of where the + + align:start position:0% +center of the power of where the + + + align:start position:0% +center of the power of where the +scattering is happening because ADA is + + align:start position:0% +scattering is happening because ADA is + + + align:start position:0% +scattering is happening because ADA is +divergent as R goes to zero so this is + + align:start position:0% +divergent as R goes to zero so this is + + + align:start position:0% +divergent as R goes to zero so this is +not the solution this is just the + + align:start position:0% +not the solution this is just the + + + align:start position:0% +not the solution this is just the +solution for R greater than a where a is + + align:start position:0% +solution for R greater than a where a is + + + align:start position:0% +solution for R greater than a where a is +the range of the potential imagine a + + align:start position:0% +the range of the potential imagine a + + + align:start position:0% +the range of the potential imagine a +potential that totally becomes zero + + align:start position:0% +potential that totally becomes zero + + + align:start position:0% +potential that totally becomes zero +after some distance a then that is your + + align:start position:0% +after some distance a then that is your + + + align:start position:0% +after some distance a then that is your +solution + + align:start position:0% +solution + + + align:start position:0% +solution +for our greater than a that is the most + + align:start position:0% +for our greater than a that is the most + + + align:start position:0% +for our greater than a that is the most +general solution given the spherical + + align:start position:0% +general solution given the spherical + + + align:start position:0% +general solution given the spherical +symmetry of the situation then the last + + align:start position:0% +symmetry of the situation then the last + + + align:start position:0% +symmetry of the situation then the last +thing we discussed was that one part of + + align:start position:0% +thing we discussed was that one part of + + + align:start position:0% +thing we discussed was that one part of +our solution they e to the i kz could be + + align:start position:0% +our solution they e to the i kz could be + + + align:start position:0% +our solution they e to the i kz could be +written in that way because it's a + + align:start position:0% +written in that way because it's a + + + align:start position:0% +written in that way because it's a +solution so it must admit an expansion + + align:start position:0% +solution so it must admit an expansion + + + align:start position:0% +solution so it must admit an expansion +of this form so it is like this you have + + align:start position:0% +of this form so it is like this you have + + + align:start position:0% +of this form so it is like this you have +a sum over all else with some funny + + align:start position:0% +a sum over all else with some funny + + + align:start position:0% +a sum over all else with some funny +coefficients including them i to the l + + align:start position:0% +coefficients including them i to the l + + + align:start position:0% +coefficients including them i to the l +yl0 + + align:start position:0% +yl0 + + + align:start position:0% +yl0 +of omega i might might as well now put + + align:start position:0% +of omega i might might as well now put + + + align:start position:0% +of omega i might might as well now put +veda because there's no phi dependence + + align:start position:0% +veda because there's no phi dependence + + + align:start position:0% +veda because there's no phi dependence +in yl0 jl of kr so this is a pretty + + align:start position:0% +in yl0 jl of kr so this is a pretty + + + align:start position:0% +in yl0 jl of kr so this is a pretty +remarkable expression we commented last + + align:start position:0% +remarkable expression we commented last + + + align:start position:0% +remarkable expression we commented last +time that represents your plane waves as + + align:start position:0% +time that represents your plane waves as + + + align:start position:0% +time that represents your plane waves as +spherical waves last but not least we + + align:start position:0% +spherical waves last but not least we + + + align:start position:0% +spherical waves last but not least we +have an expansion that is useful for a + + align:start position:0% +have an expansion that is useful for a + + + align:start position:0% +have an expansion that is useful for a +large argument of the spherical Bessel + + align:start position:0% +large argument of the spherical Bessel + + + align:start position:0% +large argument of the spherical Bessel +functions they both fall off like 1 over + + align:start position:0% +functions they both fall off like 1 over + + + align:start position:0% +functions they both fall off like 1 over +the argument with sines and cosines do + + align:start position:0% +the argument with sines and cosines do + + + align:start position:0% +the argument with sines and cosines do +you see a constant shift there in the + + align:start position:0% +you see a constant shift there in the + + + align:start position:0% +you see a constant shift there in the +science and closings of L PI over 2 and + + align:start position:0% +science and closings of L PI over 2 and + + + align:start position:0% +science and closings of L PI over 2 and +this is 4x much greater than 1 not exact + + align:start position:0% +this is 4x much greater than 1 not exact + + + align:start position:0% +this is 4x much greater than 1 not exact +either but approximate ok so these are + + align:start position:0% +either but approximate ok so these are + + + align:start position:0% +either but approximate ok so these are +some of our ingredients are ready + + align:start position:0% + + + + align:start position:0% + +how far we got and now we're gonna try + + align:start position:0% +how far we got and now we're gonna try + + + align:start position:0% +how far we got and now we're gonna try +to get more information and learn how to + + align:start position:0% +to get more information and learn how to + + + align:start position:0% +to get more information and learn how to +solve for FK we need to calculate FK if + + align:start position:0% +solve for FK we need to calculate FK if + + + align:start position:0% +solve for FK we need to calculate FK if +you have a given problem you want the + + align:start position:0% +you have a given problem you want the + + + align:start position:0% +you have a given problem you want the +current section you need FK now this the + + align:start position:0% +current section you need FK now this the + + + align:start position:0% +current section you need FK now this the +thing we're gonna do is a little + + align:start position:0% +thing we're gonna do is a little + + + align:start position:0% +thing we're gonna do is a little +intricate a lot of funny formula so + + align:start position:0% +intricate a lot of funny formula so + + + align:start position:0% +intricate a lot of funny formula so +let's try to keep the ideas very clear + + align:start position:0% +let's try to keep the ideas very clear + + + align:start position:0% +let's try to keep the ideas very clear +about it so \ No newline at end of file diff --git a/gl9c9qJRqcM.txt b/gl9c9qJRqcM.txt new file mode 100644 index 0000000000000000000000000000000000000000..80ca89ee414ddb0697c64dda309a9c0e0238c5aa --- /dev/null +++ b/gl9c9qJRqcM.txt @@ -0,0 +1,691 @@ +align:start position:0% + +let's consider the universal + + align:start position:0% +let's consider the universal + + + align:start position:0% +let's consider the universal +gravitational law is a little bit more + + align:start position:0% +gravitational law is a little bit more + + + align:start position:0% +gravitational law is a little bit more +let's consider two objects in space + + align:start position:0% +let's consider two objects in space + + + align:start position:0% +let's consider two objects in space +let's say this is the Sun and we have + + align:start position:0% +let's say this is the Sun and we have + + + align:start position:0% +let's say this is the Sun and we have +the earth here or the earth and the moon + + align:start position:0% +the earth here or the earth and the moon + + + align:start position:0% +the earth here or the earth and the moon +and of course they're orbiting each + + align:start position:0% +and of course they're orbiting each + + + align:start position:0% +and of course they're orbiting each +other so we can pick a coordinate system + + align:start position:0% +other so we can pick a coordinate system + + + align:start position:0% +other so we can pick a coordinate system +that goes radially and so we're going to + + align:start position:0% +that goes radially and so we're going to + + + align:start position:0% +that goes radially and so we're going to +have an R hat direction here I'm going + + align:start position:0% +have an R hat direction here I'm going + + + align:start position:0% +have an R hat direction here I'm going +to call this the R hat direction between + + align:start position:0% +to call this the R hat direction between + + + align:start position:0% +to call this the R hat direction between +objects one and two what forces are + + align:start position:0% +objects one and two what forces are + + + align:start position:0% +objects one and two what forces are +acting on this little moon here well + + align:start position:0% +acting on this little moon here well + + + align:start position:0% +acting on this little moon here well +it's the gravitational force going + + align:start position:0% +it's the gravitational force going + + + align:start position:0% +it's the gravitational force going +inward it's the force a 1/2 F 1/2 on + + align:start position:0% +inward it's the force a 1/2 F 1/2 on + + + align:start position:0% +inward it's the force a 1/2 F 1/2 on +object who due to their interaction + + align:start position:0% +object who due to their interaction + + + align:start position:0% +object who due to their interaction +between bodies 1 & 2 for that we can + + align:start position:0% +between bodies 1 & 2 for that we can + + + align:start position:0% +between bodies 1 & 2 for that we can +write down the universal gravitational + + align:start position:0% +write down the universal gravitational + + + align:start position:0% +write down the universal gravitational +law F 1/2 equals minus G the + + align:start position:0% +law F 1/2 equals minus G the + + + align:start position:0% +law F 1/2 equals minus G the +gravitational constant M 1 M 2 over R 1 + + align:start position:0% +gravitational constant M 1 M 2 over R 1 + + + align:start position:0% +gravitational constant M 1 M 2 over R 1 +2 squared that one is the distance + + align:start position:0% +2 squared that one is the distance + + + align:start position:0% +2 squared that one is the distance +between the two objects times R 1 2 hat + + align:start position:0% +between the two objects times R 1 2 hat + + + align:start position:0% +between the two objects times R 1 2 hat +and the minus goes actually with the + + align:start position:0% +and the minus goes actually with the + + + align:start position:0% +and the minus goes actually with the +unit vector here because the force goes + + align:start position:0% +unit vector here because the force goes + + + align:start position:0% +unit vector here because the force goes +in the opposite direction from our R hat + + align:start position:0% +in the opposite direction from our R hat + + + align:start position:0% +in the opposite direction from our R hat +let's now consider here is the earth + + align:start position:0% +let's now consider here is the earth + + + align:start position:0% +let's now consider here is the earth +again and we're going to move the moon + + align:start position:0% +again and we're going to move the moon + + + align:start position:0% +again and we're going to move the moon +or a little moon rock right to the + + align:start position:0% +or a little moon rock right to the + + + align:start position:0% +or a little moon rock right to the +surface of the earth and we want to now + + align:start position:0% +surface of the earth and we want to now + + + align:start position:0% +surface of the earth and we want to now +calculate and consider what kind of + + align:start position:0% +calculate and consider what kind of + + + align:start position:0% +calculate and consider what kind of +forces act on this moon rock and what is + + align:start position:0% +forces act on this moon rock and what is + + + align:start position:0% +forces act on this moon rock and what is +the gravitational acceleration that this + + align:start position:0% +the gravitational acceleration that this + + + align:start position:0% +the gravitational acceleration that this +moon rock on the surface of the earth is + + align:start position:0% +moon rock on the surface of the earth is + + + align:start position:0% +moon rock on the surface of the earth is +experiencing so here we have the earth + + align:start position:0% +experiencing so here we have the earth + + + align:start position:0% +experiencing so here we have the earth +earth has one earth radius and it has an + + align:start position:0% +earth has one earth radius and it has an + + + align:start position:0% +earth has one earth radius and it has an +earth mass and our moon rock has the the + + align:start position:0% +earth mass and our moon rock has the the + + + align:start position:0% +earth mass and our moon rock has the the +mass M and we know from this exercise + + align:start position:0% +mass M and we know from this exercise + + + align:start position:0% +mass M and we know from this exercise +here already that of course this + + align:start position:0% +here already that of course this + + + align:start position:0% +here already that of course this +gravitational force is acting on a moon + + align:start position:0% +gravitational force is acting on a moon + + + align:start position:0% +gravitational force is acting on a moon +rock as well that hasn't changed what we + + align:start position:0% +rock as well that hasn't changed what we + + + align:start position:0% +rock as well that hasn't changed what we +are now considering in addition is that + + align:start position:0% +are now considering in addition is that + + + align:start position:0% +are now considering in addition is that +this moon rock is also experiencing a + + align:start position:0% +this moon rock is also experiencing a + + + align:start position:0% +this moon rock is also experiencing a +gravitational acceleration due to this + + align:start position:0% +gravitational acceleration due to this + + + align:start position:0% +gravitational acceleration due to this +force and that goes inward as well so it + + align:start position:0% +force and that goes inward as well so it + + + align:start position:0% +force and that goes inward as well so it +is experiencing an M + + align:start position:0% +is experiencing an M + + + align:start position:0% +is experiencing an M +gee and we know that that is the same as + + align:start position:0% +gee and we know that that is the same as + + + align:start position:0% +gee and we know that that is the same as +the magnitude of this force here so we + + align:start position:0% +the magnitude of this force here so we + + + align:start position:0% +the magnitude of this force here so we +can equate that with G and then we have + + align:start position:0% +can equate that with G and then we have + + + align:start position:0% +can equate that with G and then we have +the earth mass and the mass of the moon + + align:start position:0% +the earth mass and the mass of the moon + + + align:start position:0% +the earth mass and the mass of the moon +rock times the distance squared so + + align:start position:0% +rock times the distance squared so + + + align:start position:0% +rock times the distance squared so +arrayed and earth radius squared and + + align:start position:0% +arrayed and earth radius squared and + + + align:start position:0% +arrayed and earth radius squared and +from that we already see that a we can + + align:start position:0% +from that we already see that a we can + + + align:start position:0% +from that we already see that a we can +cancel out the small M s of the moon + + align:start position:0% +cancel out the small M s of the moon + + + align:start position:0% +cancel out the small M s of the moon +rock and we'll get two G here so we can + + align:start position:0% +rock and we'll get two G here so we can + + + align:start position:0% +rock and we'll get two G here so we can +calculate the gravitational acceleration + + align:start position:0% +calculate the gravitational acceleration + + + align:start position:0% +calculate the gravitational acceleration +which is capital G earth mass / earth + + align:start position:0% +which is capital G earth mass / earth + + + align:start position:0% +which is capital G earth mass / earth +radius squared so if we have this kind + + align:start position:0% +radius squared so if we have this kind + + + align:start position:0% +radius squared so if we have this kind +of information we can determine the + + align:start position:0% +of information we can determine the + + + align:start position:0% +of information we can determine the +gravitational acceleration and of course + + align:start position:0% +gravitational acceleration and of course + + + align:start position:0% +gravitational acceleration and of course +it will change depending on which object + + align:start position:0% +it will change depending on which object + + + align:start position:0% +it will change depending on which object +we are considering it would be different + + align:start position:0% +we are considering it would be different + + + align:start position:0% +we are considering it would be different +if we plug in the solar mass and the + + align:start position:0% +if we plug in the solar mass and the + + + align:start position:0% +if we plug in the solar mass and the +solar radius or the moon mass and the + + align:start position:0% +solar radius or the moon mass and the + + + align:start position:0% +solar radius or the moon mass and the +moon radius if we consider an astronaut + + align:start position:0% +moon radius if we consider an astronaut + + + align:start position:0% +moon radius if we consider an astronaut +standing here on on the moon surface now + + align:start position:0% +standing here on on the moon surface now + + + align:start position:0% +standing here on on the moon surface now +let's put some numbers into this + + align:start position:0% +let's put some numbers into this + + + align:start position:0% +let's put some numbers into this +equation so we have G is capital G + + align:start position:0% +equation so we have G is capital G + + + align:start position:0% +equation so we have G is capital G +that's the gravitational constant we + + align:start position:0% +that's the gravitational constant we + + + align:start position:0% +that's the gravitational constant we +have six point six seven 10 to the 11 + + align:start position:0% +have six point six seven 10 to the 11 + + + align:start position:0% +have six point six seven 10 to the 11 +and then we have Newton and one over + + align:start position:0% +and then we have Newton and one over + + + align:start position:0% +and then we have Newton and one over +kilogram squared and mass squared times + + align:start position:0% +kilogram squared and mass squared times + + + align:start position:0% +kilogram squared and mass squared times +the earth mass five point nine seven 10 + + align:start position:0% +the earth mass five point nine seven 10 + + + align:start position:0% +the earth mass five point nine seven 10 +to the 24 kilograms and then we have to + + align:start position:0% +to the 24 kilograms and then we have to + + + align:start position:0% +to the 24 kilograms and then we have to +divide this over through the the earth + + align:start position:0% +divide this over through the the earth + + + align:start position:0% +divide this over through the the earth +radius six point three seven ten to the + + align:start position:0% +radius six point three seven ten to the + + + align:start position:0% +radius six point three seven ten to the +sixth and we have to square that and we + + align:start position:0% +sixth and we have to square that and we + + + align:start position:0% +sixth and we have to square that and we +have to square the the meters + + align:start position:0% + + + + align:start position:0% + +if we calculate this we get to 9.81 + + align:start position:0% +if we calculate this we get to 9.81 + + + align:start position:0% +if we calculate this we get to 9.81 +m/s^2 + + align:start position:0% +m/s^2 + + + align:start position:0% +m/s^2 +and surely you have seen this number + + align:start position:0% +and surely you have seen this number + + + align:start position:0% +and surely you have seen this number +before this number can either be + + align:start position:0% +before this number can either be + + + align:start position:0% +before this number can either be +calculated if you know capital G the + + align:start position:0% +calculated if you know capital G the + + + align:start position:0% +calculated if you know capital G the +gravitational constant or you can + + align:start position:0% +gravitational constant or you can + + + align:start position:0% +gravitational constant or you can +determine the gravitational acceleration + + align:start position:0% +determine the gravitational acceleration + + + align:start position:0% +determine the gravitational acceleration +through an experiment and together with + + align:start position:0% +through an experiment and together with + + + align:start position:0% +through an experiment and together with +the earth mass and earth radius you can + + align:start position:0% +the earth mass and earth radius you can + + + align:start position:0% +the earth mass and earth radius you can +actually calculate the gravitational + + align:start position:0% +actually calculate the gravitational + + + align:start position:0% +actually calculate the gravitational +constant there \ No newline at end of file diff --git a/gnWKpHUj11w.txt b/gnWKpHUj11w.txt new file mode 100644 index 0000000000000000000000000000000000000000..54ad5d1e92e17536ba3649e3fd14be4a47f28676 --- /dev/null +++ b/gnWKpHUj11w.txt @@ -0,0 +1,11811 @@ +align:start position:0% + +all right good afternoon + + align:start position:0% +all right good afternoon + + + align:start position:0% +all right good afternoon +so today's lecture is a particularly + + align:start position:0% +so today's lecture is a particularly + + + align:start position:0% +so today's lecture is a particularly +important one + + align:start position:0% + + + + align:start position:0% + +we are going to introduce the main + + align:start position:0% +we are going to introduce the main + + + align:start position:0% +we are going to introduce the main +physical principle that underlies + + align:start position:0% +physical principle that underlies + + + align:start position:0% +physical principle that underlies +general relativity we'll be spending a + + align:start position:0% +general relativity we'll be spending a + + + align:start position:0% +general relativity we'll be spending a +bunch of time + + align:start position:0% +bunch of time + + + align:start position:0% +bunch of time +connecting that principle to the + + align:start position:0% +connecting that principle to the + + + align:start position:0% +connecting that principle to the +mathematics as the rest of the term + + align:start position:0% +mathematics as the rest of the term + + + align:start position:0% +mathematics as the rest of the term +unwinds + + align:start position:0% +unwinds + + + align:start position:0% +unwinds +but today is where we're going to really + + align:start position:0% +but today is where we're going to really + + + align:start position:0% +but today is where we're going to really +lay out where the physics is + + align:start position:0% +lay out where the physics is + + + align:start position:0% +lay out where the physics is +in what is known as the principle of + + align:start position:0% +in what is known as the principle of + + + align:start position:0% +in what is known as the principle of +equivalence so before i get into that + + align:start position:0% +equivalence so before i get into that + + + align:start position:0% +equivalence so before i get into that +just a quick recap so in terms of + + align:start position:0% +just a quick recap so in terms of + + + align:start position:0% +just a quick recap so in terms of +technical stuff we did last time + + align:start position:0% +technical stuff we did last time + + + align:start position:0% +technical stuff we did last time +the most important thing we did was to + + align:start position:0% +the most important thing we did was to + + + align:start position:0% +the most important thing we did was to +introduce these mathematical objects + + align:start position:0% +introduce these mathematical objects + + + align:start position:0% +introduce these mathematical objects +called christophel symbols + + align:start position:0% +called christophel symbols + + + align:start position:0% +called christophel symbols +so the christopher symbols are those + + align:start position:0% +so the christopher symbols are those + + + align:start position:0% +so the christopher symbols are those +capital gammas + + align:start position:0% +capital gammas + + + align:start position:0% +capital gammas +we began by thinking of them as just + + align:start position:0% +we began by thinking of them as just + + + align:start position:0% +we began by thinking of them as just +what you get when you look at the + + align:start position:0% +what you get when you look at the + + + align:start position:0% +what you get when you look at the +derivative of your basis objects + + align:start position:0% +derivative of your basis objects + + + align:start position:0% +derivative of your basis objects +pardon me a second i just there was a + + align:start position:0% +pardon me a second i just there was a + + + align:start position:0% +pardon me a second i just there was a +lot of chalk on the chalkboard and i + + align:start position:0% +lot of chalk on the chalkboard and i + + + align:start position:0% +lot of chalk on the chalkboard and i +think i + + align:start position:0% +think i + + + align:start position:0% +think i +inhaled half of it while i was cleaning + + align:start position:0% +inhaled half of it while i was cleaning + + + align:start position:0% +inhaled half of it while i was cleaning +it uh so take derivatives your basis + + align:start position:0% +it uh so take derivatives your basis + + + align:start position:0% +it uh so take derivatives your basis +vectors and their release you get + + align:start position:0% +vectors and their release you get + + + align:start position:0% +vectors and their release you get +something that's linearly + + align:start position:0% +something that's linearly + + + align:start position:0% +something that's linearly +linearly related to your basis objects + + align:start position:0% +linearly related to your basis objects + + + align:start position:0% +linearly related to your basis objects +and the gamma is the set of + + align:start position:0% +and the gamma is the set of + + + align:start position:0% +and the gamma is the set of +it's a set of mathematical quantities + + align:start position:0% +it's a set of mathematical quantities + + + align:start position:0% +it's a set of mathematical quantities +that sets that linear relationship + + align:start position:0% +that sets that linear relationship + + + align:start position:0% +that sets that linear relationship +between the derivatives and the objects + + align:start position:0% +between the derivatives and the objects + + + align:start position:0% +between the derivatives and the objects +themselves + + align:start position:0% +themselves + + + align:start position:0% +themselves +one can build under the demand so we + + align:start position:0% +one can build under the demand so we + + + align:start position:0% +one can build under the demand so we +recall how we did this + + align:start position:0% +recall how we did this + + + align:start position:0% +recall how we did this +we have a physical argument that tells + + align:start position:0% +we have a physical argument that tells + + + align:start position:0% +we have a physical argument that tells +us that a quantity we call the covariant + + align:start position:0% +us that a quantity we call the covariant + + + align:start position:0% +us that a quantity we call the covariant +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +which is a way of using these + + align:start position:0% +which is a way of using these + + + align:start position:0% +which is a way of using these +christopher symbols + + align:start position:0% +christopher symbols + + + align:start position:0% +christopher symbols +in order to get tensorial derivatives so + + align:start position:0% +in order to get tensorial derivatives so + + + align:start position:0% +in order to get tensorial derivatives so +if i + + align:start position:0% +if i + + + align:start position:0% +if i +look at just the partial derivative of a + + align:start position:0% +look at just the partial derivative of a + + + align:start position:0% +look at just the partial derivative of a +tensor + + align:start position:0% +tensor + + + align:start position:0% +tensor +if i'm working in a general curvilinear + + align:start position:0% +if i'm working in a general curvilinear + + + align:start position:0% +if i'm working in a general curvilinear +coordinate system those the the set of + + align:start position:0% +coordinate system those the the set of + + + align:start position:0% +coordinate system those the the set of +partial derivatives do not constitute + + align:start position:0% +partial derivatives do not constitute + + + align:start position:0% +partial derivatives do not constitute +components of a tensor okay i posted + + align:start position:0% +components of a tensor okay i posted + + + align:start position:0% +components of a tensor okay i posted +some no + + align:start position:0% +some no + + + align:start position:0% +some no +some notes online demonstrating + + align:start position:0% +some notes online demonstrating + + + align:start position:0% +some notes online demonstrating +explicitly why that is + + align:start position:0% +explicitly why that is + + + align:start position:0% +explicitly why that is +but in a nutshell the main reason is + + align:start position:0% +but in a nutshell the main reason is + + + align:start position:0% +but in a nutshell the main reason is +that when you try to work this out + + align:start position:0% +that when you try to work this out + + + align:start position:0% +that when you try to work this out +when when you go and you work this out + + align:start position:0% +when when you go and you work this out + + + align:start position:0% +when when you go and you work this out +you will find that there are additional + + align:start position:0% +you will find that there are additional + + + align:start position:0% +you will find that there are additional +terms it looks like the derivative + + align:start position:0% +terms it looks like the derivative + + + align:start position:0% +terms it looks like the derivative +of the transformation matrix that come + + align:start position:0% +of the transformation matrix that come + + + align:start position:0% +of the transformation matrix that come +in and that spoil the tensoriality of + + align:start position:0% +in and that spoil the tensoriality of + + + align:start position:0% +in and that spoil the tensoriality of +this relationship + + align:start position:0% +this relationship + + + align:start position:0% +this relationship +and what the christopher symbol does as + + align:start position:0% +and what the christopher symbol does as + + + align:start position:0% +and what the christopher symbol does as +you guys are going to prove on pset + + align:start position:0% +you guys are going to prove on pset + + + align:start position:0% +you guys are going to prove on pset +three + + align:start position:0% +three + + + align:start position:0% +three +is it introduces terms that are exactly + + align:start position:0% +is it introduces terms that are exactly + + + align:start position:0% +is it introduces terms that are exactly +the same but with the opposite sign + + align:start position:0% +the same but with the opposite sign + + + align:start position:0% +the same but with the opposite sign +and cancel those things out so that the + + align:start position:0% +and cancel those things out so that the + + + align:start position:0% +and cancel those things out so that the +covariant derivative is what i get when + + align:start position:0% +covariant derivative is what i get when + + + align:start position:0% +covariant derivative is what i get when +i sort of correct each index with an + + align:start position:0% +i sort of correct each index with an + + + align:start position:0% +i sort of correct each index with an +appropriate factor of the christopher + + align:start position:0% +appropriate factor of the christopher + + + align:start position:0% +appropriate factor of the christopher +symbol + + align:start position:0% +symbol + + + align:start position:0% +symbol +it is something that is a component of a + + align:start position:0% +it is something that is a component of a + + + align:start position:0% +it is something that is a component of a +tensor + + align:start position:0% +tensor + + + align:start position:0% +tensor +in other words it obeys the + + align:start position:0% +in other words it obeys the + + + align:start position:0% +in other words it obeys the +transformation laws that tensors must + + align:start position:0% +transformation laws that tensors must + + + align:start position:0% +transformation laws that tensors must +have + + align:start position:0% +have + + + align:start position:0% +have +we have a physical argument that + + align:start position:0% +we have a physical argument that + + + align:start position:0% +we have a physical argument that +essentially is + + align:start position:0% +essentially is + + + align:start position:0% +essentially is +something that is tensorial in other + + align:start position:0% +something that is tensorial in other + + + align:start position:0% +something that is tensorial in other +words both sides of the equations are + + align:start position:0% +words both sides of the equations are + + + align:start position:0% +words both sides of the equations are +good tensor + + align:start position:0% +good tensor + + + align:start position:0% +good tensor +good tensor quantities in one + + align:start position:0% +good tensor quantities in one + + + align:start position:0% +good tensor quantities in one +representation has to be tensorial in + + align:start position:0% +representation has to be tensorial in + + + align:start position:0% +representation has to be tensorial in +any other representation and from that + + align:start position:0% +any other representation and from that + + + align:start position:0% +any other representation and from that +we deduce that the covariant derivative + + align:start position:0% +we deduce that the covariant derivative + + + align:start position:0% +we deduce that the covariant derivative +of the metric + + align:start position:0% +of the metric + + + align:start position:0% +of the metric +must always be zero and by taking + + align:start position:0% +must always be zero and by taking + + + align:start position:0% +must always be zero and by taking +appropriate covariant derivatives of the + + align:start position:0% +appropriate covariant derivatives of the + + + align:start position:0% +appropriate covariant derivatives of the +metric + + align:start position:0% +metric + + + align:start position:0% +metric +sort of doing a bit of gymnastics with + + align:start position:0% +sort of doing a bit of gymnastics with + + + align:start position:0% +sort of doing a bit of gymnastics with +indices and sort of wiggling things + + align:start position:0% +indices and sort of wiggling things + + + align:start position:0% +indices and sort of wiggling things +around a little bit + + align:start position:0% +around a little bit + + + align:start position:0% +around a little bit +we found that the christopher symbol can + + align:start position:0% +we found that the christopher symbol can + + + align:start position:0% +we found that the christopher symbol can +itself be built out of + + align:start position:0% +itself be built out of + + + align:start position:0% +itself be built out of +derivatives partial derivatives of the + + align:start position:0% +derivatives partial derivatives of the + + + align:start position:0% +derivatives partial derivatives of the +metric and the result looks like this + + align:start position:0% +metric and the result looks like this + + + align:start position:0% +metric and the result looks like this +so that was that's a little bit more of + + align:start position:0% +so that was that's a little bit more of + + + align:start position:0% +so that was that's a little bit more of +an in-depth uh recap than i typically do + + align:start position:0% +an in-depth uh recap than i typically do + + + align:start position:0% +an in-depth uh recap than i typically do +um but i really wanted to hammer that + + align:start position:0% +um but i really wanted to hammer that + + + align:start position:0% +um but i really wanted to hammer that +home because this is an important point + + align:start position:0% +home because this is an important point + + + align:start position:0% +home because this is an important point +we then began switching gears and we're + + align:start position:0% +we then began switching gears and we're + + + align:start position:0% +we then began switching gears and we're +going to do something so i + + align:start position:0% +going to do something so i + + + align:start position:0% +going to do something so i +introduced at the end of the previous + + align:start position:0% +introduced at the end of the previous + + + align:start position:0% +introduced at the end of the previous +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +a fairly silly argument uh which i + + align:start position:0% +a fairly silly argument uh which i + + + align:start position:0% +a fairly silly argument uh which i +nonetheless + + align:start position:0% +nonetheless + + + align:start position:0% +nonetheless +has an important physical concept to it + + align:start position:0% +has an important physical concept to it + + + align:start position:0% +has an important physical concept to it +so where we were going with was the fact + + align:start position:0% +so where we were going with was the fact + + + align:start position:0% +so where we were going with was the fact +that + + align:start position:0% +that + + + align:start position:0% +that +when we have gravity + + align:start position:0% +when we have gravity + + + align:start position:0% +when we have gravity +we cannot cover + + align:start position:0% +we cannot cover + + + align:start position:0% +we cannot cover +all of space-time + + align:start position:0% + + + + align:start position:0% + +with inertial frames + + align:start position:0% + + + + align:start position:0% + +or i should say i should watch my + + align:start position:0% +or i should say i should watch my + + + align:start position:0% +or i should say i should watch my +wording here with + + align:start position:0% +wording here with + + + align:start position:0% +wording here with +n inertial frame okay we're in fact want + + align:start position:0% +n inertial frame okay we're in fact want + + + align:start position:0% +n inertial frame okay we're in fact want +to see that you can sort of have + + align:start position:0% +to see that you can sort of have + + + align:start position:0% +to see that you can sort of have +a sequence of them and we're going to + + align:start position:0% +a sequence of them and we're going to + + + align:start position:0% +a sequence of them and we're going to +find ways of sort of linking them up but + + align:start position:0% +find ways of sort of linking them up but + + + align:start position:0% +find ways of sort of linking them up but +for now if you sort of think of special + + align:start position:0% +for now if you sort of think of special + + + align:start position:0% +for now if you sort of think of special +relativity as the theory of physics + + align:start position:0% +relativity as the theory of physics + + + align:start position:0% +relativity as the theory of physics +in which we can have lorentz coordinates + + align:start position:0% +in which we can have lorentz coordinates + + + align:start position:0% +in which we can have lorentz coordinates +that cover the entire universe + + align:start position:0% +that cover the entire universe + + + align:start position:0% +that cover the entire universe +that's out the window okay and so i'm + + align:start position:0% +that's out the window okay and so i'm + + + align:start position:0% +that's out the window okay and so i'm +going to skip my silly derivation + + align:start position:0% +going to skip my silly derivation + + + align:start position:0% +going to skip my silly derivation +part one of it is essentially just a + + align:start position:0% +part one of it is essentially just a + + + align:start position:0% +part one of it is essentially just a +motivation that a gravitational redshift + + align:start position:0% +motivation that a gravitational redshift + + + align:start position:0% +motivation that a gravitational redshift +exists + + align:start position:0% + + + + align:start position:0% + +okay so i gave a silly little + + align:start position:0% +okay so i gave a silly little + + + align:start position:0% +okay so i gave a silly little +demonstration where you imagine dropping + + align:start position:0% +demonstration where you imagine dropping + + + align:start position:0% +demonstration where you imagine dropping +a rock off of a + + align:start position:0% +a rock off of a + + + align:start position:0% +a rock off of a +tower you had some kind of a magical + + align:start position:0% +tower you had some kind of a magical + + + align:start position:0% +tower you had some kind of a magical +device that converts it into a photon + + align:start position:0% +device that converts it into a photon + + + align:start position:0% +device that converts it into a photon +that shoots it back up and then converts + + align:start position:0% +that shoots it back up and then converts + + + align:start position:0% +that shoots it back up and then converts +it back into a rock + + align:start position:0% +it back into a rock + + + align:start position:0% +it back into a rock +and you showed that as it climbed out of + + align:start position:0% +and you showed that as it climbed out of + + + align:start position:0% +and you showed that as it climbed out of +the gravitational potential + + align:start position:0% +the gravitational potential + + + align:start position:0% +the gravitational potential +it had to lose some of its energy or + + align:start position:0% +it had to lose some of its energy or + + + align:start position:0% +it had to lose some of its energy or +else you would get more energy at the + + align:start position:0% +else you would get more energy at the + + + align:start position:0% +else you would get more energy at the +top + + align:start position:0% +top + + + align:start position:0% +top +than you put in when you initially + + align:start position:0% +than you put in when you initially + + + align:start position:0% +than you put in when you initially +dropped it's a way of preventing you + + align:start position:0% +dropped it's a way of preventing you + + + align:start position:0% +dropped it's a way of preventing you +from making + + align:start position:0% +from making + + + align:start position:0% +from making +perpetual motion machines that is + + align:start position:0% +perpetual motion machines that is + + + align:start position:0% +perpetual motion machines that is +without a doubt a flaky argument it can + + align:start position:0% +without a doubt a flaky argument it can + + + align:start position:0% +without a doubt a flaky argument it can +be made a little bit more rigorous but + + align:start position:0% +be made a little bit more rigorous but + + + align:start position:0% +be made a little bit more rigorous but +i didn't want to and i will justify the + + align:start position:0% +i didn't want to and i will justify the + + + align:start position:0% +i didn't want to and i will justify the +reason i can do this + + align:start position:0% +reason i can do this + + + align:start position:0% +reason i can do this +is that this is in fact a + + align:start position:0% + + + + align:start position:0% + +highly tested experimental fact + + align:start position:0% + + + + align:start position:0% + +every single one of you has probably + + align:start position:0% +every single one of you has probably + + + align:start position:0% +every single one of you has probably +used this if you've ever used gps + + align:start position:0% +used this if you've ever used gps + + + align:start position:0% +used this if you've ever used gps +to find your way to some location where + + align:start position:0% +to find your way to some location where + + + align:start position:0% +to find your way to some location where +you're supposed to meet a friend + + align:start position:0% +you're supposed to meet a friend + + + align:start position:0% +you're supposed to meet a friend +and what this basically tells me is that + + align:start position:0% +and what this basically tells me is that + + + align:start position:0% +and what this basically tells me is that +if i imagine a tower of height h + + align:start position:0% + + + + align:start position:0% + +if i shoot light + + align:start position:0% + + + + align:start position:0% + +with frequency at the bottom omega b + + align:start position:0% +with frequency at the bottom omega b + + + align:start position:0% +with frequency at the bottom omega b +when it reaches the top and has it'll + + align:start position:0% +when it reaches the top and has it'll + + + align:start position:0% +when it reaches the top and has it'll +have a different frequency omega t where + + align:start position:0% +have a different frequency omega t where + + + align:start position:0% +have a different frequency omega t where +these are related by + + align:start position:0% +these are related by + + + align:start position:0% +these are related by +omega t equals + + align:start position:0% + + + + align:start position:0% + +and i'm going to put my c squareds back + + align:start position:0% +and i'm going to put my c squareds back + + + align:start position:0% +and i'm going to put my c squareds back +in there just to keep it all complete + + align:start position:0% +in there just to keep it all complete + + + align:start position:0% +in there just to keep it all complete +okay so this is like i emphasize a + + align:start position:0% +okay so this is like i emphasize a + + + align:start position:0% +okay so this is like i emphasize a +very precisely calibrated experimental + + align:start position:0% +very precisely calibrated experimental + + + align:start position:0% +very precisely calibrated experimental +result + + align:start position:0% +result + + + align:start position:0% +result +uh there are many ways of doing it some + + align:start position:0% +uh there are many ways of doing it some + + + align:start position:0% +uh there are many ways of doing it some +silly some serious + + align:start position:0% +silly some serious + + + align:start position:0% +silly some serious +the silly one is sort of fun but it does + + align:start position:0% +the silly one is sort of fun but it does + + + align:start position:0% +the silly one is sort of fun but it does +actually capture the experimental fact + + align:start position:0% +actually capture the experimental fact + + + align:start position:0% +actually capture the experimental fact +okay the key experimental fact + + align:start position:0% +okay the key experimental fact + + + align:start position:0% +okay the key experimental fact +is that it's necessary for lights to uh + + align:start position:0% +is that it's necessary for lights to uh + + + align:start position:0% +is that it's necessary for lights to uh +lose energy as it climbs out of the + + align:start position:0% +lose energy as it climbs out of the + + + align:start position:0% +lose energy as it climbs out of the +gravitational field + + align:start position:0% +gravitational field + + + align:start position:0% +gravitational field +in essence because it's possible uh + + align:start position:0% +in essence because it's possible uh + + + align:start position:0% +in essence because it's possible uh +thanks to quantum field theory to + + align:start position:0% +thanks to quantum field theory to + + + align:start position:0% +thanks to quantum field theory to +convert photons into particles + + align:start position:0% +convert photons into particles + + + align:start position:0% +convert photons into particles +um and particles into photons this is a + + align:start position:0% +um and particles into photons this is a + + + align:start position:0% +um and particles into photons this is a +way of conserving energy + + align:start position:0% + + + + align:start position:0% + +okay so this is just part one of this + + align:start position:0% +okay so this is just part one of this + + + align:start position:0% +okay so this is just part one of this +argument that we cannot cover + + align:start position:0% +argument that we cannot cover + + + align:start position:0% +argument that we cannot cover +all of space time with an inertial frame + + align:start position:0% + + + + align:start position:0% + +so here's part two of the argument + + align:start position:0% + + + + align:start position:0% + +suppose there was in fact a very large + + align:start position:0% +suppose there was in fact a very large + + + align:start position:0% +suppose there was in fact a very large +region of spacetime let's say it's near + + align:start position:0% +region of spacetime let's say it's near + + + align:start position:0% +region of spacetime let's say it's near +the earth's surface + + align:start position:0% +the earth's surface + + + align:start position:0% +the earth's surface +that could be covered by a single lorenz + + align:start position:0% + + + + align:start position:0% + +frame + + align:start position:0% + + + + align:start position:0% + +okay so i want you to imagine that + + align:start position:0% +okay so i want you to imagine that + + + align:start position:0% +okay so i want you to imagine that +you're sending your beam of light up + + align:start position:0% +you're sending your beam of light up + + + align:start position:0% +you're sending your beam of light up +and we're going to take advantage of the + + align:start position:0% +and we're going to take advantage of the + + + align:start position:0% +and we're going to take advantage of the +fact that light is wave + + align:start position:0% +fact that light is wave + + + align:start position:0% +fact that light is wave +so what would you do is think of the + + align:start position:0% +so what would you do is think of the + + + align:start position:0% +so what would you do is think of the +space-time trajectory of successive + + align:start position:0% +space-time trajectory of successive + + + align:start position:0% +space-time trajectory of successive +crests of this wave + + align:start position:0% +crests of this wave + + + align:start position:0% +crests of this wave +as it climbs out of the gravitational + + align:start position:0% + + + + align:start position:0% + +potential + + align:start position:0% + + + + align:start position:0% + +so i'm going to make my space-time + + align:start position:0% +so i'm going to make my space-time + + + align:start position:0% +so i'm going to make my space-time +diagram the way we like to do it + + align:start position:0% +diagram the way we like to do it + + + align:start position:0% +diagram the way we like to do it +with time running up and so + + align:start position:0% +with time running up and so + + + align:start position:0% +with time running up and so +this direction represents height + + align:start position:0% +this direction represents height + + + align:start position:0% +this direction represents height +so down here is the bottom of the tower + + align:start position:0% +so down here is the bottom of the tower + + + align:start position:0% +so down here is the bottom of the tower +so let's just make the drawing clear + + align:start position:0% +so let's just make the drawing clear + + + align:start position:0% +so let's just make the drawing clear +let's let this tick be the bottom of the + + align:start position:0% +let's let this tick be the bottom of the + + + align:start position:0% +let's let this tick be the bottom of the +tower + + align:start position:0% + + + + align:start position:0% + +this tick over here will be the top + + align:start position:0% +this tick over here will be the top + + + align:start position:0% +this tick over here will be the top +if we were just in special relativity + + align:start position:0% +if we were just in special relativity + + + align:start position:0% +if we were just in special relativity +there was no gravity we know light would + + align:start position:0% +there was no gravity we know light would + + + align:start position:0% +there was no gravity we know light would +just move on a 45 degree angle on this + + align:start position:0% +just move on a 45 degree angle on this + + + align:start position:0% +just move on a 45 degree angle on this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +we don't know yet what gravity is going + + align:start position:0% +we don't know yet what gravity is going + + + align:start position:0% +we don't know yet what gravity is going +to do to this light + + align:start position:0% +to do to this light + + + align:start position:0% +to do to this light +okay but you sort of can imagine that + + align:start position:0% +okay but you sort of can imagine that + + + align:start position:0% +okay but you sort of can imagine that +whatever it's going to do is going to + + align:start position:0% +whatever it's going to do is going to + + + align:start position:0% +whatever it's going to do is going to +sort of bend it away + + align:start position:0% +sort of bend it away + + + align:start position:0% +sort of bend it away +in some way from the trajectory that + + align:start position:0% +in some way from the trajectory that + + + align:start position:0% +in some way from the trajectory that +special relativity would predict + + align:start position:0% +special relativity would predict + + + align:start position:0% +special relativity would predict +so let's just imagine that crest one + + align:start position:0% +so let's just imagine that crest one + + + align:start position:0% +so let's just imagine that crest one +of this light it follows some trajectory + + align:start position:0% +of this light it follows some trajectory + + + align:start position:0% +of this light it follows some trajectory +in space time that maybe looks like this + + align:start position:0% + + + + align:start position:0% + +okay so here is the world line + + align:start position:0% + + + + align:start position:0% + +of crest one + + align:start position:0% +of crest one + + + align:start position:0% +of crest one +so what about the world line of crest 2 + + align:start position:0% + + + + align:start position:0% + +so let's think about what the world line + + align:start position:0% +so let's think about what the world line + + + align:start position:0% +so let's think about what the world line +of crest 2 must be + + align:start position:0% +of crest 2 must be + + + align:start position:0% +of crest 2 must be +under this assumption that we can in + + align:start position:0% +under this assumption that we can in + + + align:start position:0% +under this assumption that we can in +fact cover all of space time with a + + align:start position:0% +fact cover all of space time with a + + + align:start position:0% +fact cover all of space time with a +single lorenz frame + + align:start position:0% +single lorenz frame + + + align:start position:0% +single lorenz frame +okay if that is the case + + align:start position:0% + + + + align:start position:0% + +so if that is the case no position + + align:start position:0% +so if that is the case no position + + + align:start position:0% +so if that is the case no position +and no moment is special okay everything + + align:start position:0% +and no moment is special okay everything + + + align:start position:0% +and no moment is special okay everything +is actually translation invariant in + + align:start position:0% +is actually translation invariant in + + + align:start position:0% +is actually translation invariant in +both time and space + + align:start position:0% + + + + align:start position:0% + +so the second crest is going to be + + align:start position:0% +so the second crest is going to be + + + align:start position:0% +so the second crest is going to be +emitted one + + align:start position:0% +emitted one + + + align:start position:0% +emitted one +wave period later but you know there's + + align:start position:0% +wave period later but you know there's + + + align:start position:0% +wave period later but you know there's +absolutely nothing special about space + + align:start position:0% +absolutely nothing special about space + + + align:start position:0% +absolutely nothing special about space +time one wave period later and as it + + align:start position:0% +time one wave period later and as it + + + align:start position:0% +time one wave period later and as it +moves along + + align:start position:0% +moves along + + + align:start position:0% +moves along +there can't be anything special about + + align:start position:0% +there can't be anything special about + + + align:start position:0% +there can't be anything special about +this if it is to be a global lorenz + + align:start position:0% +this if it is to be a global lorenz + + + align:start position:0% +this if it is to be a global lorenz +frame + + align:start position:0% +frame + + + align:start position:0% +frame +whatever the trajectory is that the + + align:start position:0% +whatever the trajectory is that the + + + align:start position:0% +whatever the trajectory is that the +crest 2 follows through space time + + align:start position:0% +crest 2 follows through space time + + + align:start position:0% +crest 2 follows through space time +it's got to be congruent with the + + align:start position:0% +it's got to be congruent with the + + + align:start position:0% +it's got to be congruent with the +trajectory of crest one i've got to be + + align:start position:0% +trajectory of crest one i've got to be + + + align:start position:0% +trajectory of crest one i've got to be +able to just simply + + align:start position:0% +able to just simply + + + align:start position:0% +able to just simply +slide them on top of each other okay + + align:start position:0% +slide them on top of each other okay + + + align:start position:0% +slide them on top of each other okay +that is what this assumption demands + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +this is going to look something like + + align:start position:0% +this is going to look something like + + + align:start position:0% +this is going to look something like +this okay artwork a little bit off + + align:start position:0% +this okay artwork a little bit off + + + align:start position:0% +this okay artwork a little bit off +the key thing which i want to emphasize + + align:start position:0% +the key thing which i want to emphasize + + + align:start position:0% +the key thing which i want to emphasize +though + + align:start position:0% +though + + + align:start position:0% +though +is that if this guy is congruent + + align:start position:0% +is that if this guy is congruent + + + align:start position:0% +is that if this guy is congruent +the spacing between crest one and crest + + align:start position:0% +the spacing between crest one and crest + + + align:start position:0% +the spacing between crest one and crest +two at the bottom let's call it delta t + + align:start position:0% +two at the bottom let's call it delta t + + + align:start position:0% +two at the bottom let's call it delta t +b there'll be some spacing between the + + align:start position:0% +b there'll be some spacing between the + + + align:start position:0% +b there'll be some spacing between the +two + + align:start position:0% +two + + + align:start position:0% +two +at the top we'll call it delta t t + + align:start position:0% +at the top we'll call it delta t t + + + align:start position:0% +at the top we'll call it delta t t +they must be the same + + align:start position:0% + + + + align:start position:0% + +but that's spacing that is just a period + + align:start position:0% +but that's spacing that is just a period + + + align:start position:0% +but that's spacing that is just a period +of the wave + + align:start position:0% +of the wave + + + align:start position:0% +of the wave +and that's just up to a factor of 2 pi + + align:start position:0% +and that's just up to a factor of 2 pi + + + align:start position:0% +and that's just up to a factor of 2 pi +that's 1 over the p 1 over the frequency + + align:start position:0% + + + + align:start position:0% + +so this implies delta t b + + align:start position:0% +so this implies delta t b + + + align:start position:0% +so this implies delta t b +is not equal to delta t + + align:start position:0% +is not equal to delta t + + + align:start position:0% +is not equal to delta t +at the top delta so a frequency at the + + align:start position:0% +at the top delta so a frequency at the + + + align:start position:0% +at the top delta so a frequency at the +top is smaller + + align:start position:0% +top is smaller + + + align:start position:0% +top is smaller +so the period will actually be a little + + align:start position:0% +so the period will actually be a little + + + align:start position:0% +so the period will actually be a little +bit larger + + align:start position:0% +bit larger + + + align:start position:0% +bit larger +so when you think about this argument + + align:start position:0% +so when you think about this argument + + + align:start position:0% +so when you think about this argument +carefully + + align:start position:0% +carefully + + + align:start position:0% +carefully +the weak point is this assumption that + + align:start position:0% +the weak point is this assumption that + + + align:start position:0% +the weak point is this assumption that +i'm can actually cover the region with a + + align:start position:0% +i'm can actually cover the region with a + + + align:start position:0% +i'm can actually cover the region with a +large lawrence frame remember what this + + align:start position:0% +large lawrence frame remember what this + + + align:start position:0% +large lawrence frame remember what this +is telling me + + align:start position:0% +is telling me + + + align:start position:0% +is telling me +is that uh essentially there's there's + + align:start position:0% +is that uh essentially there's there's + + + align:start position:0% +is that uh essentially there's there's +no + + align:start position:0% +no + + + align:start position:0% +no +special direction right i can do + + align:start position:0% +special direction right i can do + + + align:start position:0% +special direction right i can do +translation variance and time and space + + align:start position:0% +translation variance and time and space + + + align:start position:0% +translation variance and time and space +and they're all the same + + align:start position:0% +and they're all the same + + + align:start position:0% +and they're all the same +but that's actually completely + + align:start position:0% +but that's actually completely + + + align:start position:0% +but that's actually completely +contradicted by common sense if there + + align:start position:0% +contradicted by common sense if there + + + align:start position:0% +contradicted by common sense if there +were no special direction + + align:start position:0% +were no special direction + + + align:start position:0% +were no special direction +why did it go down there's obviously + + align:start position:0% +why did it go down there's obviously + + + align:start position:0% +why did it go down there's obviously +something special about down + + align:start position:0% +something special about down + + + align:start position:0% +something special about down +right + + align:start position:0% + + + + align:start position:0% + +so we conclude we cannot have a global + + align:start position:0% +so we conclude we cannot have a global + + + align:start position:0% +so we conclude we cannot have a global +lorenz frame when we've got gravity + + align:start position:0% + + + + align:start position:0% + +and in case you want to read a little + + align:start position:0% +and in case you want to read a little + + + align:start position:0% +and in case you want to read a little +bit more about it + + align:start position:0% +bit more about it + + + align:start position:0% +bit more about it +i'll just give a highlight that this + + align:start position:0% +i'll just give a highlight that this + + + align:start position:0% +i'll just give a highlight that this +argument was originally developed + + align:start position:0% + + + + align:start position:0% + +by a gentleman named alfred + + align:start position:0% +by a gentleman named alfred + + + align:start position:0% +by a gentleman named alfred +alfred shield + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +that's unfortunate okay from sort of a + + align:start position:0% +that's unfortunate okay from sort of a + + + align:start position:0% +that's unfortunate okay from sort of a +philosophical perspective because + + align:start position:0% +philosophical perspective because + + + align:start position:0% +philosophical perspective because +the fact that the fact that we don't + + align:start position:0% +the fact that the fact that we don't + + + align:start position:0% +the fact that the fact that we don't +have a global rents frame + + align:start position:0% +have a global rents frame + + + align:start position:0% +have a global rents frame +kind of makes you think oh crap what are + + align:start position:0% +kind of makes you think oh crap what are + + + align:start position:0% +kind of makes you think oh crap what are +we going to do with that framework we + + align:start position:0% +we going to do with that framework we + + + align:start position:0% +we going to do with that framework we +spent + + align:start position:0% +spent + + + align:start position:0% +spent +all this time developing okay we the + + align:start position:0% +all this time developing okay we the + + + align:start position:0% +all this time developing okay we the +the existence of a lorenz frame and many + + align:start position:0% +the existence of a lorenz frame and many + + + align:start position:0% +the existence of a lorenz frame and many +of the mathematics we've been developing + + align:start position:0% +of the mathematics we've been developing + + + align:start position:0% +of the mathematics we've been developing +for the past + + align:start position:0% +for the past + + + align:start position:0% +for the past +few few lectures they all center around + + align:start position:0% +few few lectures they all center around + + + align:start position:0% +few few lectures they all center around +things you can do + + align:start position:0% +things you can do + + + align:start position:0% +things you can do +in lorenz frames so it's kind of like + + align:start position:0% +in lorenz frames so it's kind of like + + + align:start position:0% +in lorenz frames so it's kind of like +okay so we just throw all that out + + align:start position:0% + + + + align:start position:0% + +well here is where + + align:start position:0% +well here is where + + + align:start position:0% +well here is where +einstein's key physical insight came in + + align:start position:0% +einstein's key physical insight came in + + + align:start position:0% +einstein's key physical insight came in +and gave us the physical tools that + + align:start position:0% +and gave us the physical tools that + + + align:start position:0% +and gave us the physical tools that +then needed to be coupled to some + + align:start position:0% +then needed to be coupled to some + + + align:start position:0% +then needed to be coupled to some +mathematics in order to turn it into + + align:start position:0% +mathematics in order to turn it into + + + align:start position:0% +mathematics in order to turn it into +something that could be worked with + + align:start position:0% +something that could be worked with + + + align:start position:0% +something that could be worked with +but nonetheless really saved the day + + align:start position:0% + + + + align:start position:0% + +so the key insight has a there's a few + + align:start position:0% +so the key insight has a there's a few + + + align:start position:0% +so the key insight has a there's a few +steps in it so first thing + + align:start position:0% +steps in it so first thing + + + align:start position:0% +steps in it so first thing +i keep i was very careful to use the + + align:start position:0% +i keep i was very careful to use the + + + align:start position:0% +i keep i was very careful to use the +word global when i ruled out the + + align:start position:0% +word global when i ruled out the + + + align:start position:0% +word global when i ruled out the +existence of lorenz frames + + align:start position:0% + + + + align:start position:0% + +but i'm allowed to have local lorenz + + align:start position:0% +but i'm allowed to have local lorenz + + + align:start position:0% +but i'm allowed to have local lorenz +frames + + align:start position:0% +frames + + + align:start position:0% +frames +let's see what does that actually mean + + align:start position:0% + + + + align:start position:0% + +so i'll remind you that a lorentz frame + + align:start position:0% +so i'll remind you that a lorentz frame + + + align:start position:0% +so i'll remind you that a lorentz frame +is a tool that we use to describe + + align:start position:0% +is a tool that we use to describe + + + align:start position:0% +is a tool that we use to describe +inertial observers in fact + + align:start position:0% +inertial observers in fact + + + align:start position:0% +inertial observers in fact +we often call them inertial frames + + align:start position:0% +we often call them inertial frames + + + align:start position:0% +we often call them inertial frames +because they're sort of the constant + + align:start position:0% +because they're sort of the constant + + + align:start position:0% +because they're sort of the constant +coordinates they represent the + + align:start position:0% +coordinates they represent the + + + align:start position:0% +coordinates they represent the +coordinates of an inertial observer who + + align:start position:0% +coordinates of an inertial observer who + + + align:start position:0% +coordinates of an inertial observer who +happens to be at rest + + align:start position:0% +happens to be at rest + + + align:start position:0% +happens to be at rest +in that lorentz coordinate system so + + align:start position:0% +in that lorentz coordinate system so + + + align:start position:0% +in that lorentz coordinate system so +let's switch over let's start calling + + align:start position:0% +let's switch over let's start calling + + + align:start position:0% +let's switch over let's start calling +them inertial frames for just a moment + + align:start position:0% + + + + align:start position:0% + +so an inertial frame + + align:start position:0% +so an inertial frame + + + align:start position:0% +so an inertial frame +means that there is nothing accelerating + + align:start position:0% + + + + align:start position:0% + +so no accelerations + + align:start position:0% + + + + align:start position:0% + +on observers or objects at rest in that + + align:start position:0% +on observers or objects at rest in that + + + align:start position:0% +on observers or objects at rest in that +frame + + align:start position:0% + + + + align:start position:0% + +in other words no forces are acting + + align:start position:0% + + + + align:start position:0% + +einstein's insight + + align:start position:0% + + + + align:start position:0% + +was to recognize that the next best + + align:start position:0% +was to recognize that the next best + + + align:start position:0% +was to recognize that the next best +thing + + align:start position:0% + + + + align:start position:0% + +is a freely falling frame + + align:start position:0% + + + + align:start position:0% + +okay if you are in a freely + + align:start position:0% +okay if you are in a freely + + + align:start position:0% +okay if you are in a freely +falling frame to you + + align:start position:0% +falling frame to you + + + align:start position:0% +falling frame to you +sure as hell seems like there's a force + + align:start position:0% +sure as hell seems like there's a force + + + align:start position:0% +sure as hell seems like there's a force +acting on it and there's some + + align:start position:0% +acting on it and there's some + + + align:start position:0% +acting on it and there's some +accelerations acting upon you + + align:start position:0% +accelerations acting upon you + + + align:start position:0% +accelerations acting upon you +but let's imagine you're in this freely + + align:start position:0% +but let's imagine you're in this freely + + + align:start position:0% +but let's imagine you're in this freely +falling frame + + align:start position:0% +falling frame + + + align:start position:0% +falling frame +and you know you have a bunch of small + + align:start position:0% +and you know you have a bunch of small + + + align:start position:0% +and you know you have a bunch of small +objects that you release near you + + align:start position:0% +objects that you release near you + + + align:start position:0% +objects that you release near you +see if i can find some bits of broken + + align:start position:0% +see if i can find some bits of broken + + + align:start position:0% +see if i can find some bits of broken +chalk + + align:start position:0% + + + + align:start position:0% + +so when you're in this freely falling + + align:start position:0% +so when you're in this freely falling + + + align:start position:0% +so when you're in this freely falling +frame + + align:start position:0% + + + + align:start position:0% + +this is a lot easier when i was younger + + align:start position:0% +this is a lot easier when i was younger + + + align:start position:0% +this is a lot easier when i was younger +all right when you're in this freely + + align:start position:0% +all right when you're in this freely + + + align:start position:0% +all right when you're in this freely +falling frame + + align:start position:0% +falling frame + + + align:start position:0% +falling frame +okay and these objects are all falling + + align:start position:0% +okay and these objects are all falling + + + align:start position:0% +okay and these objects are all falling +there is no acceleration of these + + align:start position:0% +there is no acceleration of these + + + align:start position:0% +there is no acceleration of these +objects relative + + align:start position:0% +objects relative + + + align:start position:0% +objects relative +to you + + align:start position:0% + + + + align:start position:0% + +the reason for this is that the + + align:start position:0% +the reason for this is that the + + + align:start position:0% +the reason for this is that the +gravitational force + + align:start position:0% +gravitational force + + + align:start position:0% +gravitational force +is proportional to the mass and so + + align:start position:0% +is proportional to the mass and so + + + align:start position:0% +is proportional to the mass and so +the fact + + align:start position:0% + + + + align:start position:0% + +that we have f + + align:start position:0% +that we have f + + + align:start position:0% +that we have f +equals m a and f + + align:start position:0% +equals m a and f + + + align:start position:0% +equals m a and f +g proportional to mass + + align:start position:0% + + + + align:start position:0% + +means that all objects + + align:start position:0% +means that all objects + + + align:start position:0% +means that all objects +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +in that freely falling frame + + align:start position:0% +in that freely falling frame + + + align:start position:0% +in that freely falling frame +is the term i'm going to start using a + + align:start position:0% +is the term i'm going to start using a + + + align:start position:0% +is the term i'm going to start using a +lot + + align:start position:0% + + + + align:start position:0% + +so i'm just going to abbreviate it ffff + + align:start position:0% +so i'm just going to abbreviate it ffff + + + align:start position:0% +so i'm just going to abbreviate it ffff +if i get really lazy i might call it an + + align:start position:0% +if i get really lazy i might call it an + + + align:start position:0% +if i get really lazy i might call it an +f cubed anyway all objects that are in + + align:start position:0% +f cubed anyway all objects that are in + + + align:start position:0% +f cubed anyway all objects that are in +that freely falling frame + + align:start position:0% +that freely falling frame + + + align:start position:0% +that freely falling frame +they're experiencing the same + + align:start position:0% +they're experiencing the same + + + align:start position:0% +they're experiencing the same +acceleration and so they experience + + align:start position:0% +acceleration and so they experience + + + align:start position:0% +acceleration and so they experience +zero relative acceleration + + align:start position:0% + + + + align:start position:0% + +at least in the absence of other forces + + align:start position:0% +at least in the absence of other forces + + + align:start position:0% +at least in the absence of other forces +okay perhaps one of them is charged and + + align:start position:0% +okay perhaps one of them is charged and + + + align:start position:0% +okay perhaps one of them is charged and +there's an electric force + + align:start position:0% +there's an electric force + + + align:start position:0% +there's an electric force +okay well then it sort of suggests that + + align:start position:0% +okay well then it sort of suggests that + + + align:start position:0% +okay well then it sort of suggests that +the interesting force + + align:start position:0% +the interesting force + + + align:start position:0% +the interesting force +is the uh the extra force provided to + + align:start position:0% +is the uh the extra force provided to + + + align:start position:0% +is the uh the extra force provided to +that + + align:start position:0% +that + + + align:start position:0% +that +relative to what we call the + + align:start position:0% +relative to what we call the + + + align:start position:0% +relative to what we call the +gravitational force that is driving this + + align:start position:0% +gravitational force that is driving this + + + align:start position:0% +gravitational force that is driving this +free fall + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +i urge you to start getting comfortable + + align:start position:0% +i urge you to start getting comfortable + + + align:start position:0% +i urge you to start getting comfortable +with this idea + + align:start position:0% +with this idea + + + align:start position:0% +with this idea +because we're going to find this to be + + align:start position:0% +because we're going to find this to be + + + align:start position:0% +because we're going to find this to be +so one thing which i'm going to do in a + + align:start position:0% +so one thing which i'm going to do in a + + + align:start position:0% +so one thing which i'm going to do in a +couple minutes + + align:start position:0% + + + + align:start position:0% + +is actually a little calculation that + + align:start position:0% +is actually a little calculation that + + + align:start position:0% +is actually a little calculation that +shows me + + align:start position:0% +shows me + + + align:start position:0% +shows me +i can in fact always + + align:start position:0% + + + + align:start position:0% + +find a lorentz + + align:start position:0% +find a lorentz + + + align:start position:0% +find a lorentz +frame in the vicinity of any point in + + align:start position:0% +frame in the vicinity of any point in + + + align:start position:0% +frame in the vicinity of any point in +space time + + align:start position:0% +space time + + + align:start position:0% +space time +okay and so we're going to actually + + align:start position:0% +okay and so we're going to actually + + + align:start position:0% +okay and so we're going to actually +regard that lorenz frame + + align:start position:0% +regard that lorenz frame + + + align:start position:0% +regard that lorenz frame +as being the preferred coordinate system + + align:start position:0% +as being the preferred coordinate system + + + align:start position:0% +as being the preferred coordinate system +of a freely flowing observer one who is + + align:start position:0% +of a freely flowing observer one who is + + + align:start position:0% +of a freely flowing observer one who is +not accelerated + + align:start position:0% +not accelerated + + + align:start position:0% +not accelerated +relative to free fall at that point okay + + align:start position:0% +relative to free fall at that point okay + + + align:start position:0% +relative to free fall at that point okay +we are not in free fall right now the + + align:start position:0% +we are not in free fall right now the + + + align:start position:0% +we are not in free fall right now the +damn floor is pushing us out of the way + + align:start position:0% +damn floor is pushing us out of the way + + + align:start position:0% +damn floor is pushing us out of the way +but in this way of doing things + + align:start position:0% +but in this way of doing things + + + align:start position:0% +but in this way of doing things +we would actually regard us as being + + align:start position:0% +we would actually regard us as being + + + align:start position:0% +we would actually regard us as being +sort of the complicated people + + align:start position:0% +sort of the complicated people + + + align:start position:0% +sort of the complicated people +okay someone who is merely plumbing to + + align:start position:0% +okay someone who is merely plumbing to + + + align:start position:0% +okay someone who is merely plumbing to +their deaths + + align:start position:0% +their deaths + + + align:start position:0% +their deaths +they are actually the simple observers + + align:start position:0% +they are actually the simple observers + + + align:start position:0% +they are actually the simple observers +who are sort of doing what they should + + align:start position:0% +who are sort of doing what they should + + + align:start position:0% +who are sort of doing what they should +be doing in some sense + + align:start position:0% + + + + align:start position:0% + +so the key thing uh uh a way of saying + + align:start position:0% +so the key thing uh uh a way of saying + + + align:start position:0% +so the key thing uh uh a way of saying +this so coming back to this and + + align:start position:0% +this so coming back to this and + + + align:start position:0% +this so coming back to this and +just one more point about that because + + align:start position:0% +just one more point about that because + + + align:start position:0% +just one more point about that because +there are no + + align:start position:0% +there are no + + + align:start position:0% +there are no +relative accelerations + + align:start position:0% + + + + align:start position:0% + +within this frame + + align:start position:0% + + + + align:start position:0% + +objects maintain their relative + + align:start position:0% + + + + align:start position:0% + +velocities + + align:start position:0% + + + + align:start position:0% + +that's basically the definition of + + align:start position:0% +that's basically the definition of + + + align:start position:0% +that's basically the definition of +something that is inertial if i have a + + align:start position:0% +something that is inertial if i have a + + + align:start position:0% +something that is inertial if i have a +frame where everything + + align:start position:0% +frame where everything + + + align:start position:0% +frame where everything +is you know two objects are moving with + + align:start position:0% +is you know two objects are moving with + + + align:start position:0% +is you know two objects are moving with +respect to each other at one meter per + + align:start position:0% +respect to each other at one meter per + + + align:start position:0% +respect to each other at one meter per +second they're always moving at one + + align:start position:0% +second they're always moving at one + + + align:start position:0% +second they're always moving at one +meter per second + + align:start position:0% +meter per second + + + align:start position:0% +meter per second +that's inertial and so this sort of + + align:start position:0% +that's inertial and so this sort of + + + align:start position:0% +that's inertial and so this sort of +demands that we do all of our + + align:start position:0% +demands that we do all of our + + + align:start position:0% +demands that we do all of our +experiments in plummeting elevators or + + align:start position:0% +experiments in plummeting elevators or + + + align:start position:0% +experiments in plummeting elevators or +in space right okay obviously you can't + + align:start position:0% +in space right okay obviously you can't + + + align:start position:0% +in space right okay obviously you can't +do that so there's some complications + + align:start position:0% +do that so there's some complications + + + align:start position:0% +do that so there's some complications +we're gonna have to learn the math to + + align:start position:0% +we're gonna have to learn the math to + + + align:start position:0% +we're gonna have to learn the math to +learn the math to describe uh but this + + align:start position:0% +learn the math to describe uh but this + + + align:start position:0% +learn the math to describe uh but this +is the way we're going to from now on + + align:start position:0% +is the way we're going to from now on + + + align:start position:0% +is the way we're going to from now on +think about things is that the freely + + align:start position:0% +think about things is that the freely + + + align:start position:0% +think about things is that the freely +falling frame + + align:start position:0% +falling frame + + + align:start position:0% +falling frame +is the most natural generalization of an + + align:start position:0% +is the most natural generalization of an + + + align:start position:0% +is the most natural generalization of an +inertial frame that we describe + + align:start position:0% +inertial frame that we describe + + + align:start position:0% +inertial frame that we describe +using lorentz coordinates now before i + + align:start position:0% +using lorentz coordinates now before i + + + align:start position:0% +using lorentz coordinates now before i +discuss a few details about this an + + align:start position:0% +discuss a few details about this an + + + align:start position:0% +discuss a few details about this an +important thing that is worth noting + + align:start position:0% +important thing that is worth noting + + + align:start position:0% +important thing that is worth noting +is that a very important aspect of any + + align:start position:0% +is that a very important aspect of any + + + align:start position:0% +is that a very important aspect of any +realistic source of gravity + + align:start position:0% +realistic source of gravity + + + align:start position:0% +realistic source of gravity +is that it is not uniform okay + + align:start position:0% +is that it is not uniform okay + + + align:start position:0% +is that it is not uniform okay +gravity here is a little bit stronger + + align:start position:0% +gravity here is a little bit stronger + + + align:start position:0% +gravity here is a little bit stronger +than gravity on the ceiling okay and + + align:start position:0% +than gravity on the ceiling okay and + + + align:start position:0% +than gravity on the ceiling okay and +it's a lot stronger + + align:start position:0% +it's a lot stronger + + + align:start position:0% +it's a lot stronger +than gravity in geostationary orbit + + align:start position:0% +than gravity in geostationary orbit + + + align:start position:0% +than gravity in geostationary orbit +the reason we we call this variation in + + align:start position:0% +the reason we we call this variation in + + + align:start position:0% +the reason we we call this variation in +gravity + + align:start position:0% +gravity + + + align:start position:0% +gravity +tides + + align:start position:0% + + + + align:start position:0% + +so tides break down + + align:start position:0% + + + + align:start position:0% + +the notion of + + align:start position:0% + + + + align:start position:0% + +uniform freely falling frames + + align:start position:0% + + + + align:start position:0% + +what this is telling us is that this + + align:start position:0% +what this is telling us is that this + + + align:start position:0% +what this is telling us is that this +idea if i'm going to create this + + align:start position:0% +idea if i'm going to create this + + + align:start position:0% +idea if i'm going to create this +inertial frame that is you know + + align:start position:0% +inertial frame that is you know + + + align:start position:0% +inertial frame that is you know +essentially a freely falling frame + + align:start position:0% +essentially a freely falling frame + + + align:start position:0% +essentially a freely falling frame +it will have to be of finite size hence + + align:start position:0% +it will have to be of finite size hence + + + align:start position:0% +it will have to be of finite size hence +it's local + + align:start position:0% +it's local + + + align:start position:0% +it's local +and not global okay physically this is + + align:start position:0% +and not global okay physically this is + + + align:start position:0% +and not global okay physically this is +sort of telling me + + align:start position:0% +sort of telling me + + + align:start position:0% +sort of telling me +that if i have a really tall + + align:start position:0% +that if i have a really tall + + + align:start position:0% +that if i have a really tall +freely falling elevator + + align:start position:0% +freely falling elevator + + + align:start position:0% +freely falling elevator +and i'm here + + align:start position:0% + + + + align:start position:0% + +i have one friend here and one friend + + align:start position:0% +i have one friend here and one friend + + + align:start position:0% +i have one friend here and one friend +down there + + align:start position:0% +down there + + + align:start position:0% +down there +even if we start absolutely at rest + + align:start position:0% +even if we start absolutely at rest + + + align:start position:0% +even if we start absolutely at rest +let's say we're at rest we measure rest + + align:start position:0% +let's say we're at rest we measure rest + + + align:start position:0% +let's say we're at rest we measure rest +with respect to the walls of this + + align:start position:0% +with respect to the walls of this + + + align:start position:0% +with respect to the walls of this +elevator it's a very stiff elevator + + align:start position:0% +elevator it's a very stiff elevator + + + align:start position:0% +elevator it's a very stiff elevator +we will see the three of us diverge away + + align:start position:0% +we will see the three of us diverge away + + + align:start position:0% +we will see the three of us diverge away +from each other with time + + align:start position:0% +from each other with time + + + align:start position:0% +from each other with time +okay because this person let's say earth + + align:start position:0% +okay because this person let's say earth + + + align:start position:0% +okay because this person let's say earth +is down here this person's feeling + + align:start position:0% +is down here this person's feeling + + + align:start position:0% +is down here this person's feeling +the you know in using newtonian + + align:start position:0% +the you know in using newtonian + + + align:start position:0% +the you know in using newtonian +intuition gravity is a little stronger + + align:start position:0% +intuition gravity is a little stronger + + + align:start position:0% +intuition gravity is a little stronger +gravity is medium gravity is weak and so + + align:start position:0% +gravity is medium gravity is weak and so + + + align:start position:0% +gravity is medium gravity is weak and so +as viewed in that freely falling frame + + align:start position:0% +as viewed in that freely falling frame + + + align:start position:0% +as viewed in that freely falling frame +let's say we center it on me + + align:start position:0% +let's say we center it on me + + + align:start position:0% +let's say we center it on me +here in the middle i will see the person + + align:start position:0% +here in the middle i will see the person + + + align:start position:0% +here in the middle i will see the person +the top go up + + align:start position:0% +the top go up + + + align:start position:0% +the top go up +the person at the bottom go down + + align:start position:0% + + + + align:start position:0% + +another way of saying this + + align:start position:0% + + + + align:start position:0% + +so let me just say that so a very tall + + align:start position:0% +so let me just say that so a very tall + + + align:start position:0% +so let me just say that so a very tall +elevator + + align:start position:0% +elevator + + + align:start position:0% +elevator +will see a separation + + align:start position:0% + + + + align:start position:0% + +of free fall + + align:start position:0% + + + + align:start position:0% + +since gravity is not uniform + + align:start position:0% + + + + align:start position:0% + +there's another way of saying this + + align:start position:0% +there's another way of saying this + + + align:start position:0% +there's another way of saying this +and what this is telling me is imagine i + + align:start position:0% +and what this is telling me is imagine i + + + align:start position:0% +and what this is telling me is imagine i +made a space-time diagram + + align:start position:0% +made a space-time diagram + + + align:start position:0% +made a space-time diagram +that shows trajectories of the three of + + align:start position:0% +that shows trajectories of the three of + + + align:start position:0% +that shows trajectories of the three of +us + + align:start position:0% + + + + align:start position:0% + +so the three of us are plummeting in + + align:start position:0% +so the three of us are plummeting in + + + align:start position:0% +so the three of us are plummeting in +this elevator okay + + align:start position:0% + + + + align:start position:0% + +what we would find if we make our + + align:start position:0% +what we would find if we make our + + + align:start position:0% +what we would find if we make our +trajectories as we fall let's just go + + align:start position:0% +trajectories as we fall let's just go + + + align:start position:0% +trajectories as we fall let's just go +ahead and make a little sketch of this + + align:start position:0% +ahead and make a little sketch of this + + + align:start position:0% +ahead and make a little sketch of this +okay so let's say here is the middle + + align:start position:0% + + + + align:start position:0% + +here is the top here is the bottom and + + align:start position:0% +here is the top here is the bottom and + + + align:start position:0% +here is the top here is the bottom and +i'm going to draw this in coordinates + + align:start position:0% +i'm going to draw this in coordinates + + + align:start position:0% +i'm going to draw this in coordinates +that are fixed on the person in the + + align:start position:0% +that are fixed on the person in the + + + align:start position:0% +that are fixed on the person in the +middle + + align:start position:0% +middle + + + align:start position:0% +middle +so the person in the middle in their + + align:start position:0% +so the person in the middle in their + + + align:start position:0% +so the person in the middle in their +freely falling frame + + align:start position:0% +freely falling frame + + + align:start position:0% +freely falling frame +they think they're standing still + + align:start position:0% + + + + align:start position:0% + +they see the person at the top moving up + + align:start position:0% +they see the person at the top moving up + + + align:start position:0% +they see the person at the top moving up +and away + + align:start position:0% +and away + + + align:start position:0% +and away +person at the bottom moving up and away + + align:start position:0% + + + + align:start position:0% + +it's a very similar story to the little + + align:start position:0% +it's a very similar story to the little + + + align:start position:0% +it's a very similar story to the little +parable i sketched of that light poles + + align:start position:0% +parable i sketched of that light poles + + + align:start position:0% +parable i sketched of that light poles +moving up + + align:start position:0% +moving up + + + align:start position:0% +moving up +these are not congruent trajectories + + align:start position:0% + + + + align:start position:0% + +another way to say this is that at any + + align:start position:0% +another way to say this is that at any + + + align:start position:0% +another way to say this is that at any +moment i think of these as + + align:start position:0% +moment i think of these as + + + align:start position:0% +moment i think of these as +world lines i can at any moment along + + align:start position:0% +world lines i can at any moment along + + + align:start position:0% +world lines i can at any moment along +the world line + + align:start position:0% +the world line + + + align:start position:0% +the world line +i can draw its tangent vector + + align:start position:0% + + + + align:start position:0% + +the tangents do not + + align:start position:0% +the tangents do not + + + align:start position:0% +the tangents do not +remain parallel + + align:start position:0% + + + + align:start position:0% + +now i'm going to take you back to + + align:start position:0% + + + + align:start position:0% + +probably first i don't know when you + + align:start position:0% +probably first i don't know when you + + + align:start position:0% +probably first i don't know when you +guys all learned this but when you first + + align:start position:0% +guys all learned this but when you first + + + align:start position:0% +guys all learned this but when you first +started learning about geometry for me + + align:start position:0% +started learning about geometry for me + + + align:start position:0% +started learning about geometry for me +it was in middle school + + align:start position:0% +it was in middle school + + + align:start position:0% +it was in middle school +and when you first started learning + + align:start position:0% +and when you first started learning + + + align:start position:0% +and when you first started learning +about geometry you were usually doing + + align:start position:0% +about geometry you were usually doing + + + align:start position:0% +about geometry you were usually doing +geometry on the plane + + align:start position:0% +geometry on the plane + + + align:start position:0% +geometry on the plane +and they gave you various axioms about + + align:start position:0% +and they gave you various axioms about + + + align:start position:0% +and they gave you various axioms about +the way things behaved + + align:start position:0% +the way things behaved + + + align:start position:0% +the way things behaved +one of them is now known as euclid's + + align:start position:0% +one of them is now known as euclid's + + + align:start position:0% +one of them is now known as euclid's +parallelism axiom + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +and it states that if i have two lines + + align:start position:0% +and it states that if i have two lines + + + align:start position:0% +and it states that if i have two lines +that start + + align:start position:0% +that start + + + align:start position:0% +that start +parallel they remain parallel + + align:start position:0% + + + + align:start position:0% + +if you dig into the history of + + align:start position:0% +if you dig into the history of + + + align:start position:0% +if you dig into the history of +mathematics this axiom + + align:start position:0% +mathematics this axiom + + + align:start position:0% +mathematics this axiom +bugged the crap out of people for + + align:start position:0% +bugged the crap out of people for + + + align:start position:0% +bugged the crap out of people for +many many years okay uh because it's + + align:start position:0% +many many years okay uh because it's + + + align:start position:0% +many many years okay uh because it's +you know when you look at pictures on a + + align:start position:0% +you know when you look at pictures on a + + + align:start position:0% +you know when you look at pictures on a +piece of paper or on a chalkboard or + + align:start position:0% +piece of paper or on a chalkboard or + + + align:start position:0% +piece of paper or on a chalkboard or +something like that it seems + + align:start position:0% +something like that it seems + + + align:start position:0% +something like that it seems +right okay but it really can't be + + align:start position:0% +right okay but it really can't be + + + align:start position:0% +right okay but it really can't be +justified quite as rigorously as many + + align:start position:0% +justified quite as rigorously as many + + + align:start position:0% +justified quite as rigorously as many +other + + align:start position:0% +other + + + align:start position:0% +other +axioms that euclid wrote down and it + + align:start position:0% +axioms that euclid wrote down and it + + + align:start position:0% +axioms that euclid wrote down and it +turns out there's an underlying + + align:start position:0% +turns out there's an underlying + + + align:start position:0% +turns out there's an underlying +assumption + + align:start position:0% +assumption + + + align:start position:0% +assumption +the assumption is that you are drawing + + align:start position:0% +the assumption is that you are drawing + + + align:start position:0% +the assumption is that you are drawing +your lines + + align:start position:0% +your lines + + + align:start position:0% +your lines +on a flat manifold + + align:start position:0% + + + + align:start position:0% + +there's a ready counter example + + align:start position:0% + + + + align:start position:0% + +go to the earth's equator + + align:start position:0% +go to the earth's equator + + + align:start position:0% +go to the earth's equator +you start say somewhere in brazil your + + align:start position:0% +you start say somewhere in brazil your + + + align:start position:0% +you start say somewhere in brazil your +friends start somewhere in africa + + align:start position:0% +friends start somewhere in africa + + + align:start position:0% +friends start somewhere in africa +both of you stand on the equator and go + + align:start position:0% +both of you stand on the equator and go + + + align:start position:0% +both of you stand on the equator and go +due north you are moving on parallel + + align:start position:0% +due north you are moving on parallel + + + align:start position:0% +due north you are moving on parallel +trajectories + + align:start position:0% +trajectories + + + align:start position:0% +trajectories +you will intersect at the north pole + + align:start position:0% +you will intersect at the north pole + + + align:start position:0% +you will intersect at the north pole +okay well guess what you ain't moving on + + align:start position:0% +okay well guess what you ain't moving on + + + align:start position:0% +okay well guess what you ain't moving on +a flat manifold you're moving on the + + align:start position:0% +a flat manifold you're moving on the + + + align:start position:0% +a flat manifold you're moving on the +surface of a sphere + + align:start position:0% +surface of a sphere + + + align:start position:0% +surface of a sphere +okay curvature causes initially parallel + + align:start position:0% +okay curvature causes initially parallel + + + align:start position:0% +okay curvature causes initially parallel +trajectories to become non-cur + + align:start position:0% +trajectories to become non-cur + + + align:start position:0% +trajectories to become non-cur +non-parallel what this is telling us + + align:start position:0% +non-parallel what this is telling us + + + align:start position:0% +non-parallel what this is telling us +is that the manifold i'm going to want + + align:start position:0% +is that the manifold i'm going to want + + + align:start position:0% +is that the manifold i'm going to want +to use + + align:start position:0% +to use + + + align:start position:0% +to use +to describe events when i have gravity + + align:start position:0% +to describe events when i have gravity + + + align:start position:0% +to describe events when i have gravity +cannot be flat i'm going to have to + + align:start position:0% +cannot be flat i'm going to have to + + + align:start position:0% +cannot be flat i'm going to have to +introduce curvature into it + + align:start position:0% +introduce curvature into it + + + align:start position:0% +introduce curvature into it +take us a little while to unpack + + align:start position:0% +take us a little while to unpack + + + align:start position:0% +take us a little while to unpack +precisely mathematically what that means + + align:start position:0% +precisely mathematically what that means + + + align:start position:0% +precisely mathematically what that means +uh but this is sort of a sign that + + align:start position:0% +uh but this is sort of a sign that + + + align:start position:0% +uh but this is sort of a sign that +things got + + align:start position:0% +things got + + + align:start position:0% +things got +more complicated okay and tides are the + + align:start position:0% +more complicated okay and tides are the + + + align:start position:0% +more complicated okay and tides are the +way in which + + align:start position:0% +way in which + + + align:start position:0% +way in which +that complication is being introduced + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let me switch pages here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so what we have sort of been uh what + + align:start position:0% +so what we have sort of been uh what + + + align:start position:0% +so what we have sort of been uh what +we've basically danced around and put + + align:start position:0% +we've basically danced around and put + + + align:start position:0% +we've basically danced around and put +together here + + align:start position:0% +together here + + + align:start position:0% +together here +is one formulation of what is known as + + align:start position:0% + + + + align:start position:0% + +the principle of equivalence + + align:start position:0% + + + + align:start position:0% + +principal equivalents or one formulation + + align:start position:0% +principal equivalents or one formulation + + + align:start position:0% +principal equivalents or one formulation +of it + + align:start position:0% +of it + + + align:start position:0% +of it +tells me that + + align:start position:0% + + + + align:start position:0% + +over + + align:start position:0% +over + + + align:start position:0% +over +sufficiently small + + align:start position:0% + + + + align:start position:0% + +regions + + align:start position:0% +regions + + + align:start position:0% +regions +the motion of freely falling + + align:start position:0% + + + + align:start position:0% + +particles due + + align:start position:0% + + + + align:start position:0% + +to gravity + + align:start position:0% + + + + align:start position:0% + +cannot be distinguished + + align:start position:0% + + + + align:start position:0% + +from uniform acceleration + + align:start position:0% + + + + align:start position:0% + +the physical manifestation of this is if + + align:start position:0% +the physical manifestation of this is if + + + align:start position:0% +the physical manifestation of this is if +you're an observer who is in that freely + + align:start position:0% +you're an observer who is in that freely + + + align:start position:0% +you're an observer who is in that freely +falling frame + + align:start position:0% +falling frame + + + align:start position:0% +falling frame +moving due to gravity you are also + + align:start position:0% +moving due to gravity you are also + + + align:start position:0% +moving due to gravity you are also +experiencing that uniform acceleration + + align:start position:0% +experiencing that uniform acceleration + + + align:start position:0% +experiencing that uniform acceleration +so you see no net acceleration + + align:start position:0% +so you see no net acceleration + + + align:start position:0% +so you see no net acceleration +this particular formulation of it is + + align:start position:0% +this particular formulation of it is + + + align:start position:0% +this particular formulation of it is +known as the weak equivalence principle + + align:start position:0% + + + + align:start position:0% + +i'm going to give you a couple + + align:start position:0% +i'm going to give you a couple + + + align:start position:0% +i'm going to give you a couple +variations in this in just a second + + align:start position:0% + + + + align:start position:0% + +one thing that's important about it + + align:start position:0% +one thing that's important about it + + + align:start position:0% +one thing that's important about it +is essentially + + align:start position:0% +is essentially + + + align:start position:0% +is essentially +it's a statement that + + align:start position:0% +it's a statement that + + + align:start position:0% +it's a statement that +if you think about uh newton's laws the + + align:start position:0% +if you think about uh newton's laws the + + + align:start position:0% +if you think about uh newton's laws the +idea that f + + align:start position:0% +idea that f + + + align:start position:0% +idea that f +equals m a and the force of gravity is + + align:start position:0% +equals m a and the force of gravity is + + + align:start position:0% +equals m a and the force of gravity is +proportional to m + + align:start position:0% +proportional to m + + + align:start position:0% +proportional to m +it's a fairly precise statement that the + + align:start position:0% +it's a fairly precise statement that the + + + align:start position:0% +it's a fairly precise statement that the +you know think of that m as the + + align:start position:0% +you know think of that m as the + + + align:start position:0% +you know think of that m as the +gravitational charge + + align:start position:0% +gravitational charge + + + align:start position:0% +gravitational charge +it's saying that the gravitational + + align:start position:0% +it's saying that the gravitational + + + align:start position:0% +it's saying that the gravitational +charge the gravitational mass + + align:start position:0% +charge the gravitational mass + + + align:start position:0% +charge the gravitational mass +and the inertial mass are the same thing + + align:start position:0% +and the inertial mass are the same thing + + + align:start position:0% +and the inertial mass are the same thing +that's actually + + align:start position:0% +that's actually + + + align:start position:0% +that's actually +a testable statement what you can do is + + align:start position:0% +a testable statement what you can do is + + + align:start position:0% +a testable statement what you can do is +look at materials that have very + + align:start position:0% +look at materials that have very + + + align:start position:0% +look at materials that have very +different compositions particularly what + + align:start position:0% +different compositions particularly what + + + align:start position:0% +different compositions particularly what +you want to do is look at things that + + align:start position:0% +you want to do is look at things that + + + align:start position:0% +you want to do is look at things that +maybe have + + align:start position:0% +maybe have + + + align:start position:0% +maybe have +different ratios of neutrons to protons + + align:start position:0% +different ratios of neutrons to protons + + + align:start position:0% +different ratios of neutrons to protons +or + + align:start position:0% +or + + + align:start position:0% +or +have highly bound nuclei with lots of + + align:start position:0% +have highly bound nuclei with lots of + + + align:start position:0% +have highly bound nuclei with lots of +gluons in them or various kinds of + + align:start position:0% +gluons in them or various kinds of + + + align:start position:0% +gluons in them or various kinds of +fields that you can imagine perhaps + + align:start position:0% +fields that you can imagine perhaps + + + align:start position:0% +fields that you can imagine perhaps +coupled to gravity differently than the + + align:start position:0% +coupled to gravity differently than the + + + align:start position:0% +coupled to gravity differently than the +corkstome + + align:start position:0% +corkstome + + + align:start position:0% +corkstome +and so there are what are called free + + align:start position:0% +and so there are what are called free + + + align:start position:0% +and so there are what are called free +fall experiments to test this + + align:start position:0% + + + + align:start position:0% + +which really it basically just boils + + align:start position:0% +which really it basically just boils + + + align:start position:0% +which really it basically just boils +down to dropping + + align:start position:0% +down to dropping + + + align:start position:0% +down to dropping +lots of different elements of the + + align:start position:0% +lots of different elements of the + + + align:start position:0% +lots of different elements of the +periodic table and making sure they all + + align:start position:0% +periodic table and making sure they all + + + align:start position:0% +periodic table and making sure they all +fall at the same rate + + align:start position:0% +fall at the same rate + + + align:start position:0% +fall at the same rate +and the answer is that they are all + + align:start position:0% +and the answer is that they are all + + + align:start position:0% +and the answer is that they are all +they fall at exactly the same rate + + align:start position:0% +they fall at exactly the same rate + + + align:start position:0% +they fall at exactly the same rate +within experimental precision + + align:start position:0% +within experimental precision + + + align:start position:0% +within experimental precision +and the last time i looked it up + + align:start position:0% +and the last time i looked it up + + + align:start position:0% +and the last time i looked it up +well what these do is they demonstrate + + align:start position:0% +well what these do is they demonstrate + + + align:start position:0% +well what these do is they demonstrate +uh the wep the weak equivalence + + align:start position:0% +uh the wep the weak equivalence + + + align:start position:0% +uh the wep the weak equivalence +principle + + align:start position:0% + + + + align:start position:0% + +is valid to about i believe it's about a + + align:start position:0% +is valid to about i believe it's about a + + + align:start position:0% +is valid to about i believe it's about a +part in 10 to minus 13. might be a + + align:start position:0% +part in 10 to minus 13. might be a + + + align:start position:0% +part in 10 to minus 13. might be a +little bit better now + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +bear with me just one second here + + align:start position:0% + + + + align:start position:0% + +uh okay so good so we've got this notion + + align:start position:0% +uh okay so good so we've got this notion + + + align:start position:0% +uh okay so good so we've got this notion +here + + align:start position:0% +here + + + align:start position:0% +here +and you know you might now think okay + + align:start position:0% +and you know you might now think okay + + + align:start position:0% +and you know you might now think okay +great i have a new i have a way of + + align:start position:0% +great i have a new i have a way of + + + align:start position:0% +great i have a new i have a way of +generalizing what the notion of an + + align:start position:0% +generalizing what the notion of an + + + align:start position:0% +generalizing what the notion of an +inertial frame is + + align:start position:0% +inertial frame is + + + align:start position:0% +inertial frame is +is this enough for me to move forward + + align:start position:0% +is this enough for me to move forward + + + align:start position:0% +is this enough for me to move forward +can we now + + align:start position:0% + + + + align:start position:0% + +do all of physics + + align:start position:0% + + + + align:start position:0% + +by just applying the laws of special + + align:start position:0% +by just applying the laws of special + + + align:start position:0% +by just applying the laws of special +relativity + + align:start position:0% +relativity + + + align:start position:0% +relativity +in freely falling frames + + align:start position:0% +in freely falling frames + + + align:start position:0% +in freely falling frames +or putting it this way our new notion of + + align:start position:0% +or putting it this way our new notion of + + + align:start position:0% +or putting it this way our new notion of +an inertial frame + + align:start position:0% + + + + align:start position:0% + +for two reasons that are closely related + + align:start position:0% +for two reasons that are closely related + + + align:start position:0% +for two reasons that are closely related +this doesn't quite work + + align:start position:0% +this doesn't quite work + + + align:start position:0% +this doesn't quite work +and it comes down to the fact that + + align:start position:0% +and it comes down to the fact that + + + align:start position:0% +and it comes down to the fact that +because of tides + + align:start position:0% + + + + align:start position:0% + +we can't do that + + align:start position:0% + + + + align:start position:0% + +what this basically means is that the + + align:start position:0% +what this basically means is that the + + + align:start position:0% +what this basically means is that the +transformation that puts you into a + + align:start position:0% +transformation that puts you into a + + + align:start position:0% +transformation that puts you into a +freely falling frame + + align:start position:0% +freely falling frame + + + align:start position:0% +freely falling frame +here is not the same as a transformation + + align:start position:0% +here is not the same as a transformation + + + align:start position:0% +here is not the same as a transformation +that puts you into a freely falling + + align:start position:0% +that puts you into a freely falling + + + align:start position:0% +that puts you into a freely falling +frame + + align:start position:0% +frame + + + align:start position:0% +frame +ten thousand miles over the earth's + + align:start position:0% +ten thousand miles over the earth's + + + align:start position:0% +ten thousand miles over the earth's +surface okay there are different + + align:start position:0% +surface okay there are different + + + align:start position:0% +surface okay there are different +transformations at different locations + + align:start position:0% +transformations at different locations + + + align:start position:0% +transformations at different locations +in space time we do not + + align:start position:0% +in space time we do not + + + align:start position:0% +in space time we do not +this comes down the idea that it's not a + + align:start position:0% +this comes down the idea that it's not a + + + align:start position:0% +this comes down the idea that it's not a +global lorenz frame okay we have a + + align:start position:0% +global lorenz frame okay we have a + + + align:start position:0% +global lorenz frame okay we have a +sequence of local lorenz frames + + align:start position:0% +sequence of local lorenz frames + + + align:start position:0% +sequence of local lorenz frames +that we have to link up + + align:start position:0% + + + + align:start position:0% + +so i'm going to do a calculation in just + + align:start position:0% +so i'm going to do a calculation in just + + + align:start position:0% +so i'm going to do a calculation in just +a moment where we explicitly show + + align:start position:0% +a moment where we explicitly show + + + align:start position:0% +a moment where we explicitly show +that we can always go into a frame that + + align:start position:0% +that we can always go into a frame that + + + align:start position:0% +that we can always go into a frame that +is locally lorenz + + align:start position:0% +is locally lorenz + + + align:start position:0% +is locally lorenz +but that there's a term that i'm going + + align:start position:0% +but that there's a term that i'm going + + + align:start position:0% +but that there's a term that i'm going +to very strongly argue is essentially + + align:start position:0% +to very strongly argue is essentially + + + align:start position:0% +to very strongly argue is essentially +the curvature associated with the space + + align:start position:0% +the curvature associated with the space + + + align:start position:0% +the curvature associated with the space +time metric + + align:start position:0% +time metric + + + align:start position:0% +time metric +that sets the size of what that region + + align:start position:0% +that sets the size of what that region + + + align:start position:0% +that sets the size of what that region +actually is + + align:start position:0% + + + + align:start position:0% + +so what we are going to do um + + align:start position:0% +so what we are going to do um + + + align:start position:0% +so what we are going to do um +what is going to guide our physics as we + + align:start position:0% +what is going to guide our physics as we + + + align:start position:0% +what is going to guide our physics as we +move forward + + align:start position:0% + + + + align:start position:0% + +is essentially a we're going to take + + align:start position:0% +is essentially a we're going to take + + + align:start position:0% +is essentially a we're going to take +advantage of a reformulation + + align:start position:0% +advantage of a reformulation + + + align:start position:0% +advantage of a reformulation +reform you + + align:start position:0% +reform you + + + align:start position:0% +reform you +there we go of + + align:start position:0% +there we go of + + + align:start position:0% +there we go of +the equivalence principle + + align:start position:0% + + + + align:start position:0% + +which i'm going to word as follows + + align:start position:0% + + + + align:start position:0% + +in sufficiently small regions + + align:start position:0% +in sufficiently small regions + + + align:start position:0% +in sufficiently small regions +of space time + + align:start position:0% + + + + align:start position:0% + +we can find a representation or a + + align:start position:0% +we can find a representation or a + + + align:start position:0% +we can find a representation or a +coordinate system + + align:start position:0% + + + + align:start position:0% + +such that i don't want to cram this into + + align:start position:0% +such that i don't want to cram this into + + + align:start position:0% +such that i don't want to cram this into +the margin so i'll switch boards + + align:start position:0% + + + + align:start position:0% + +the laws of physics + + align:start position:0% + + + + align:start position:0% + +reduce + + align:start position:0% +reduce + + + align:start position:0% +reduce +to those of special relativity + + align:start position:0% +to those of special relativity + + + align:start position:0% +to those of special relativity +this is known as the einstein + + align:start position:0% +this is known as the einstein + + + align:start position:0% +this is known as the einstein +equivalence principle at least that's + + align:start position:0% +equivalence principle at least that's + + + align:start position:0% +equivalence principle at least that's +the name that carol + + align:start position:0% +the name that carol + + + align:start position:0% +the name that carol +uses in his textbook a couple books use + + align:start position:0% +uses in his textbook a couple books use + + + align:start position:0% +uses in his textbook a couple books use +different ones this is a very nice one + + align:start position:0% +different ones this is a very nice one + + + align:start position:0% +different ones this is a very nice one +because it really is + + align:start position:0% +because it really is + + + align:start position:0% +because it really is +the principle by which uh einstein + + align:start position:0% +the principle by which uh einstein + + + align:start position:0% +the principle by which uh einstein +guided us + + align:start position:0% +guided us + + + align:start position:0% +guided us +to rewriting the laws of physics + + align:start position:0% +to rewriting the laws of physics + + + align:start position:0% +to rewriting the laws of physics +so we've got a weak equivalence + + align:start position:0% +so we've got a weak equivalence + + + align:start position:0% +so we've got a weak equivalence +principle and einstein equivalence + + align:start position:0% +principle and einstein equivalence + + + align:start position:0% +principle and einstein equivalence +principle + + align:start position:0% +principle + + + align:start position:0% +principle +just as an aside there is something + + align:start position:0% +just as an aside there is something + + + align:start position:0% +just as an aside there is something +called a strong equivalence principle + + align:start position:0% + + + + align:start position:0% + +we're not going to talk about this very + + align:start position:0% +we're not going to talk about this very + + + align:start position:0% +we're not going to talk about this very +much but i'm going to give it to you + + align:start position:0% +much but i'm going to give it to you + + + align:start position:0% +much but i'm going to give it to you +because it's just kind of cool + + align:start position:0% + + + + align:start position:0% + +it tells me that gravity falls + + align:start position:0% +it tells me that gravity falls + + + align:start position:0% +it tells me that gravity falls +in a gravitational field + + align:start position:0% + + + + align:start position:0% + +in a way that is indistinguishable from + + align:start position:0% + + + + align:start position:0% + +mass + + align:start position:0% + + + + align:start position:0% + +okay that's a little weird um + + align:start position:0% +okay that's a little weird um + + + align:start position:0% +okay that's a little weird um +i'm not going to explain it very much + + align:start position:0% +i'm not going to explain it very much + + + align:start position:0% +i'm not going to explain it very much +right now + + align:start position:0% +right now + + + align:start position:0% +right now +a way to think about it will become + + align:start position:0% +a way to think about it will become + + + align:start position:0% +a way to think about it will become +clearer in some future problem sets + + align:start position:0% +clearer in some future problem sets + + + align:start position:0% +clearer in some future problem sets +basically what it's telling us is that + + align:start position:0% +basically what it's telling us is that + + + align:start position:0% +basically what it's telling us is that +when you make very strong grab when you + + align:start position:0% +when you make very strong grab when you + + + align:start position:0% +when you make very strong grab when you +make any kind of a bound object + + align:start position:0% +make any kind of a bound object + + + align:start position:0% +make any kind of a bound object +some of the mass of that object in the + + align:start position:0% +some of the mass of that object in the + + + align:start position:0% +some of the mass of that object in the +sense of the mass that is measured by + + align:start position:0% +sense of the mass that is measured by + + + align:start position:0% +sense of the mass that is measured by +orbits can be thought of as + + align:start position:0% +orbits can be thought of as + + + align:start position:0% +orbits can be thought of as +gravitational energy okay + + align:start position:0% +gravitational energy okay + + + align:start position:0% +gravitational energy okay +energy and mass are equivalent to one + + align:start position:0% +energy and mass are equivalent to one + + + align:start position:0% +energy and mass are equivalent to one +another so that gravitational energy + + align:start position:0% +another so that gravitational energy + + + align:start position:0% +another so that gravitational energy +should respond to gravity and in fact it + + align:start position:0% +should respond to gravity and in fact it + + + align:start position:0% +should respond to gravity and in fact it +falls just like any other mass + + align:start position:0% +falls just like any other mass + + + align:start position:0% +falls just like any other mass +okay this is another one this is + + align:start position:0% +okay this is another one this is + + + align:start position:0% +okay this is another one this is +actually very well + + align:start position:0% +actually very well + + + align:start position:0% +actually very well +prior to uh prior to september + + align:start position:0% +prior to uh prior to september + + + align:start position:0% +prior to uh prior to september +2015 this was very difficult to test + + align:start position:0% +2015 this was very difficult to test + + + align:start position:0% +2015 this was very difficult to test +uh there were some very precise + + align:start position:0% +uh there were some very precise + + + align:start position:0% +uh there were some very precise +measurements of the moon's orbit that + + align:start position:0% +measurements of the moon's orbit that + + + align:start position:0% +measurements of the moon's orbit that +were done to test this + + align:start position:0% +were done to test this + + + align:start position:0% +were done to test this +um and there were observations of binary + + align:start position:0% +um and there were observations of binary + + + align:start position:0% +um and there were observations of binary +pulsar systems were done to test this + + align:start position:0% + + + + align:start position:0% + +now every time ligo measures a pair of + + align:start position:0% +now every time ligo measures a pair of + + + align:start position:0% +now every time ligo measures a pair of +binary black holes + + align:start position:0% +binary black holes + + + align:start position:0% +binary black holes +which are nothing but gravitational + + align:start position:0% +which are nothing but gravitational + + + align:start position:0% +which are nothing but gravitational +energy and our theoretical models match + + align:start position:0% +energy and our theoretical models match + + + align:start position:0% +energy and our theoretical models match +the waveforms + + align:start position:0% +the waveforms + + + align:start position:0% +the waveforms +sort of like boom equivalence principle + + align:start position:0% +sort of like boom equivalence principle + + + align:start position:0% +sort of like boom equivalence principle +drop mike leave + + align:start position:0% +drop mike leave + + + align:start position:0% +drop mike leave +room all right + + align:start position:0% + + + + align:start position:0% + +so let's get precise + + align:start position:0% +so let's get precise + + + align:start position:0% +so let's get precise +what i want to do + + align:start position:0% + + + + align:start position:0% + +is show that we can always + + align:start position:0% +is show that we can always + + + align:start position:0% +is show that we can always +find a local lorenz frame + + align:start position:0% + + + + align:start position:0% + +and what i mean by that is that i want + + align:start position:0% +and what i mean by that is that i want + + + align:start position:0% +and what i mean by that is that i want +to be able to show + + align:start position:0% +to be able to show + + + align:start position:0% +to be able to show +that i can always do a + + align:start position:0% +that i can always do a + + + align:start position:0% +that i can always do a +change of my coordinates a change of my + + align:start position:0% +change of my coordinates a change of my + + + align:start position:0% +change of my coordinates a change of my +representation + + align:start position:0% +representation + + + align:start position:0% +representation +such that at some point i can convert + + align:start position:0% +such that at some point i can convert + + + align:start position:0% +such that at some point i can convert +the metric + + align:start position:0% +the metric + + + align:start position:0% +the metric +the metric of space time into the metric + + align:start position:0% +the metric of space time into the metric + + + align:start position:0% +the metric of space time into the metric +we used in special relativity + + align:start position:0% +we used in special relativity + + + align:start position:0% +we used in special relativity +at least over some finite region + + align:start position:0% + + + + align:start position:0% + +so let me define a couple of quantities + + align:start position:0% +so let me define a couple of quantities + + + align:start position:0% +so let me define a couple of quantities +and then let me formulate the way this + + align:start position:0% +and then let me formulate the way this + + + align:start position:0% +and then let me formulate the way this +calculation is going to work + + align:start position:0% +calculation is going to work + + + align:start position:0% +calculation is going to work +let us let + + align:start position:0% + + + + align:start position:0% + +coordinates with unbarred greek indices + + align:start position:0% +coordinates with unbarred greek indices + + + align:start position:0% +coordinates with unbarred greek indices +be the coordinate system that we start + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +and let's say that in this + + align:start position:0% +and let's say that in this + + + align:start position:0% +and let's say that in this +representation + + align:start position:0% + + + + align:start position:0% + +the metric is g + + align:start position:0% +the metric is g + + + align:start position:0% +the metric is g +alpha beta + + align:start position:0% +alpha beta + + + align:start position:0% +alpha beta +let us demand that there exists a set of + + align:start position:0% +let us demand that there exists a set of + + + align:start position:0% +let us demand that there exists a set of +coordinates that i will represent + + align:start position:0% +coordinates that i will represent + + + align:start position:0% +coordinates that i will represent +with bars on the indices + + align:start position:0% + + + + align:start position:0% + +when we transform to these coordinates i + + align:start position:0% +when we transform to these coordinates i + + + align:start position:0% +when we transform to these coordinates i +want space time to be + + align:start position:0% + + + + align:start position:0% + +lorentz + + align:start position:0% + + + + align:start position:0% + +at least in the vicinity of some point + + align:start position:0% +at least in the vicinity of some point + + + align:start position:0% +at least in the vicinity of some point +or some event + + align:start position:0% + + + + align:start position:0% + +i'll call that event pay + + align:start position:0% + + + + align:start position:0% + +uh so we will assume that there is some + + align:start position:0% +uh so we will assume that there is some + + + align:start position:0% +uh so we will assume that there is some +mapping between these coordinates + + align:start position:0% +mapping between these coordinates + + + align:start position:0% +mapping between these coordinates +so there's no nasty singularities there + + align:start position:0% +so there's no nasty singularities there + + + align:start position:0% +so there's no nasty singularities there +at least nothing that we can't deal with + + align:start position:0% + + + + align:start position:0% + +so we can do it in either direction but + + align:start position:0% +so we can do it in either direction but + + + align:start position:0% +so we can do it in either direction but +let's just say + + align:start position:0% +let's just say + + + align:start position:0% +let's just say +x alpha is x alpha of + + align:start position:0% +x alpha is x alpha of + + + align:start position:0% +x alpha is x alpha of +can be written as some function of these + + align:start position:0% +can be written as some function of these + + + align:start position:0% +can be written as some function of these +guys and so there's a transformation + + align:start position:0% +guys and so there's a transformation + + + align:start position:0% +guys and so there's a transformation +matrix between the two of them + + align:start position:0% +matrix between the two of them + + + align:start position:0% +matrix between the two of them +it takes the usual form + + align:start position:0% +it takes the usual form + + + align:start position:0% +it takes the usual form +okay so mathematically the way i'm going + + align:start position:0% +okay so mathematically the way i'm going + + + align:start position:0% +okay so mathematically the way i'm going +to show this + + align:start position:0% +to show this + + + align:start position:0% +to show this +is i want to show that we can find + + align:start position:0% + + + + align:start position:0% + +a coordinate system + + align:start position:0% + + + + align:start position:0% + +such that if i compute + + align:start position:0% +such that if i compute + + + align:start position:0% +such that if i compute +the space-time metric in the new the + + align:start position:0% +the space-time metric in the new the + + + align:start position:0% +the space-time metric in the new the +bard representation + + align:start position:0% +bard representation + + + align:start position:0% +bard representation +and that is always going to be given by + + align:start position:0% +and that is always going to be given by + + + align:start position:0% +and that is always going to be given by +doing + + align:start position:0% +doing + + + align:start position:0% +doing +this coordinate transformation + + align:start position:0% + + + + align:start position:0% + +then i get the metric of flat space time + + align:start position:0% +then i get the metric of flat space time + + + align:start position:0% +then i get the metric of flat space time +over as large a region as possible + + align:start position:0% + + + + align:start position:0% + +okay we know we're not going to be able + + align:start position:0% +okay we know we're not going to be able + + + align:start position:0% +okay we know we're not going to be able +to do it everywhere what i want to show + + align:start position:0% +to do it everywhere what i want to show + + + align:start position:0% +to do it everywhere what i want to show +is that i can make that happen at the + + align:start position:0% +is that i can make that happen at the + + + align:start position:0% +is that i can make that happen at the +point p and that the functional behavior + + align:start position:0% +point p and that the functional behavior + + + align:start position:0% +point p and that the functional behavior +of this thing is sufficiently flat that + + align:start position:0% +of this thing is sufficiently flat that + + + align:start position:0% +of this thing is sufficiently flat that +it remains + + align:start position:0% +it remains + + + align:start position:0% +it remains +at this over some region so let me just + + align:start position:0% +at this over some region so let me just + + + align:start position:0% +at this over some region so let me just +sketch what the logic of this + + align:start position:0% +sketch what the logic of this + + + align:start position:0% +sketch what the logic of this +calculation is going to be + + align:start position:0% + + + + align:start position:0% + +so what we're going to do is expand + + align:start position:0% + + + + align:start position:0% + +so remember + + align:start position:0% + + + + align:start position:0% + +g is a function all of these l's are + + align:start position:0% +g is a function all of these l's are + + + align:start position:0% +g is a function all of these l's are +functions + + align:start position:0% +functions + + + align:start position:0% +functions +so what i'm going to do is i'm going to + + align:start position:0% +so what i'm going to do is i'm going to + + + align:start position:0% +so what i'm going to do is i'm going to +think of this whole thing + + align:start position:0% +think of this whole thing + + + align:start position:0% +think of this whole thing +as itself being some kind of a function + + align:start position:0% +as itself being some kind of a function + + + align:start position:0% +as itself being some kind of a function +i'm going to expand in the taylor series + + align:start position:0% + + + + align:start position:0% + +there's something really cool that we're + + align:start position:0% +there's something really cool that we're + + + align:start position:0% +there's something really cool that we're +gonna be able to do with this i mean if + + align:start position:0% +gonna be able to do with this i mean if + + + align:start position:0% +gonna be able to do with this i mean if +i do this in general + + align:start position:0% +i do this in general + + + align:start position:0% +i do this in general +you're gonna get something pretty vomit + + align:start position:0% +you're gonna get something pretty vomit + + + align:start position:0% +you're gonna get something pretty vomit +okay it's gonna be just a giant giant + + align:start position:0% +okay it's gonna be just a giant giant + + + align:start position:0% +okay it's gonna be just a giant giant +mess okay you might worry what the hell + + align:start position:0% +mess okay you might worry what the hell + + + align:start position:0% +mess okay you might worry what the hell +we're gonna do with this + + align:start position:0% +we're gonna do with this + + + align:start position:0% +we're gonna do with this +okay but there's something really cool + + align:start position:0% +okay but there's something really cool + + + align:start position:0% +okay but there's something really cool +that we can do so we are + + align:start position:0% +that we can do so we are + + + align:start position:0% +that we can do so we are +given the metric g but we are free to + + align:start position:0% +given the metric g but we are free to + + + align:start position:0% +given the metric g but we are free to +pick our coordinate transformation to be + + align:start position:0% +pick our coordinate transformation to be + + + align:start position:0% +pick our coordinate transformation to be +whatever we want it to be + + align:start position:0% +whatever we want it to be + + + align:start position:0% +whatever we want it to be +so what we are going to do is compare + + align:start position:0% + + + + align:start position:0% + +the degrees of freedom + + align:start position:0% + + + + align:start position:0% + +offered by the coordinate transformation + + align:start position:0% +offered by the coordinate transformation + + + align:start position:0% +offered by the coordinate transformation +which again i emphasize we are free to + + align:start position:0% +which again i emphasize we are free to + + + align:start position:0% +which again i emphasize we are free to +make that whatever we need it to be + + align:start position:0% + + + + align:start position:0% + +so the coordinate transformation and its + + align:start position:0% +so the coordinate transformation and its + + + align:start position:0% +so the coordinate transformation and its +derivatives right we're free to sort of + + align:start position:0% +derivatives right we're free to sort of + + + align:start position:0% +derivatives right we're free to sort of +play around with this thing + + align:start position:0% +play around with this thing + + + align:start position:0% +play around with this thing +it's under our control + + align:start position:0% + + + + align:start position:0% + +to the constraints that are imposed by + + align:start position:0% +to the constraints that are imposed by + + + align:start position:0% +to the constraints that are imposed by +the metric and its derivatives which we + + align:start position:0% +the metric and its derivatives which we + + + align:start position:0% +the metric and its derivatives which we +are given + + align:start position:0% + + + + align:start position:0% + +so what we're essentially going to do + + align:start position:0% + + + + align:start position:0% + +so in a moment or two i'm going to write + + align:start position:0% +so in a moment or two i'm going to write + + + align:start position:0% +so in a moment or two i'm going to write +out this i'm going to write out very + + align:start position:0% +out this i'm going to write out very + + + align:start position:0% +out this i'm going to write out very +schematically + + align:start position:0% +schematically + + + align:start position:0% +schematically +what this uh coordinate transformation + + align:start position:0% +what this uh coordinate transformation + + + align:start position:0% +what this uh coordinate transformation +is going to look like when i do the + + align:start position:0% +is going to look like when i do the + + + align:start position:0% +is going to look like when i do the +taylor expansion + + align:start position:0% +taylor expansion + + + align:start position:0% +taylor expansion +and uh what i want to do is essentially + + align:start position:0% +and uh what i want to do is essentially + + + align:start position:0% +and uh what i want to do is essentially +just count up + + align:start position:0% +just count up + + + align:start position:0% +just count up +how many degrees of freedom the + + align:start position:0% +how many degrees of freedom the + + + align:start position:0% +how many degrees of freedom the +coordinate system offers me + + align:start position:0% +coordinate system offers me + + + align:start position:0% +coordinate system offers me +count up the number of constraints that + + align:start position:0% +count up the number of constraints that + + + align:start position:0% +count up the number of constraints that +need to be matched in order to affect + + align:start position:0% +need to be matched in order to affect + + + align:start position:0% +need to be matched in order to affect +this transformation + + align:start position:0% +this transformation + + + align:start position:0% +this transformation +see whether i've got enough assess what + + align:start position:0% +see whether i've got enough assess what + + + align:start position:0% +see whether i've got enough assess what +we learned from that + + align:start position:0% +we learned from that + + + align:start position:0% +we learned from that +okay + + align:start position:0% + + + + align:start position:0% + +so we just set up with a few more things + + align:start position:0% +so we just set up with a few more things + + + align:start position:0% +so we just set up with a few more things +to help define the logic + + align:start position:0% + + + + align:start position:0% + +so i'm going to write g alpha beta + + align:start position:0% + + + + align:start position:0% + +as g alpha beta at the point p + + align:start position:0% +as g alpha beta at the point p + + + align:start position:0% +as g alpha beta at the point p +plus x gamma + + align:start position:0% +plus x gamma + + + align:start position:0% +plus x gamma +and you know what let's do the expansion + + align:start position:0% +and you know what let's do the expansion + + + align:start position:0% +and you know what let's do the expansion +in the bar coordinate + + align:start position:0% + + + + align:start position:0% + +minus x gamma bar at the point p + + align:start position:0% + + + + align:start position:0% + +times the derivative at point p + + align:start position:0% + + + + align:start position:0% + +and then i'm going to get something that + + align:start position:0% +and then i'm going to get something that + + + align:start position:0% +and then i'm going to get something that +involves + + align:start position:0% + + + + align:start position:0% + +sort of a complicated form of x squared + + align:start position:0% + + + + align:start position:0% + +and second derivative okay this can keep + + align:start position:0% +and second derivative okay this can keep + + + align:start position:0% +and second derivative okay this can keep +going but this is going to be enough for + + align:start position:0% +going but this is going to be enough for + + + align:start position:0% +going but this is going to be enough for +our purposes + + align:start position:0% +our purposes + + + align:start position:0% +our purposes +i am likewise + + align:start position:0% + + + + align:start position:0% + +going to expand my coordinate + + align:start position:0% +going to expand my coordinate + + + align:start position:0% +going to expand my coordinate +transformation matrix + + align:start position:0% + + + + align:start position:0% + +make sure i got all my bars in place + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so let me go over to another board just + + align:start position:0% +so let me go over to another board just + + + align:start position:0% +so let me go over to another board just +write down a few more important things + + align:start position:0% +write down a few more important things + + + align:start position:0% +write down a few more important things +and then we'll start counting + + align:start position:0% + + + + align:start position:0% + +so first key thing which i want to note + + align:start position:0% +so first key thing which i want to note + + + align:start position:0% +so first key thing which i want to note +before i + + align:start position:0% +before i + + + align:start position:0% +before i +dig into the calculation + + align:start position:0% + + + + align:start position:0% + +is the metric at this point + + align:start position:0% + + + + align:start position:0% + +its derivative + + align:start position:0% + + + + align:start position:0% + +its second derivative + + align:start position:0% + + + + align:start position:0% + +these have been handed to us okay so + + align:start position:0% +these have been handed to us okay so + + + align:start position:0% +these have been handed to us okay so +we have no freedom to play with these + + align:start position:0% +we have no freedom to play with these + + + align:start position:0% +we have no freedom to play with these +these are going to give us constraints + + align:start position:0% +these are going to give us constraints + + + align:start position:0% +these are going to give us constraints +that we need to satisfy + + align:start position:0% + + + + align:start position:0% + +the coordinate transformation and its + + align:start position:0% +the coordinate transformation and its + + + align:start position:0% +the coordinate transformation and its +various derivatives + + align:start position:0% + + + + align:start position:0% + +we are free to specify these + + align:start position:0% +we are free to specify these + + + align:start position:0% +we are free to specify these +these are our degrees of freedom + + align:start position:0% + + + + align:start position:0% + +okay so let me just restate the + + align:start position:0% +okay so let me just restate the + + + align:start position:0% +okay so let me just restate the +calculation that we are going to do + + align:start position:0% +calculation that we are going to do + + + align:start position:0% +calculation that we are going to do +basically we want to do this + + align:start position:0% +basically we want to do this + + + align:start position:0% +basically we want to do this +schematically here's what this + + align:start position:0% +schematically here's what this + + + align:start position:0% +schematically here's what this +calculation is going to look like + + align:start position:0% + + + + align:start position:0% + +and if you look at this right now you + + align:start position:0% +and if you look at this right now you + + + align:start position:0% +and if you look at this right now you +might think this is going to be horrible + + align:start position:0% +might think this is going to be horrible + + + align:start position:0% +might think this is going to be horrible +but we don't need to + + align:start position:0% +but we don't need to + + + align:start position:0% +but we don't need to +specify every step of this thing in + + align:start position:0% +specify every step of this thing in + + + align:start position:0% +specify every step of this thing in +absolutely gory detail + + align:start position:0% + + + + align:start position:0% + +what we want to do is make + + align:start position:0% + + + + align:start position:0% + +this which i can write as + + align:start position:0% + + + + align:start position:0% + +this guy at point p + + align:start position:0% + + + + align:start position:0% + +this guy at point p + + align:start position:0% + + + + align:start position:0% + +is this guy at point p plus + + align:start position:0% + + + + align:start position:0% + +a term that is going to be linear + + align:start position:0% +a term that is going to be linear + + + align:start position:0% +a term that is going to be linear +in the distance from the space time + + align:start position:0% +in the distance from the space time + + + align:start position:0% +in the distance from the space time +displacement away from point p + + align:start position:0% + + + + align:start position:0% + +if you want to go and multiply this out + + align:start position:0% +if you want to go and multiply this out + + + align:start position:0% +if you want to go and multiply this out +knock yourself out but it suffices to + + align:start position:0% +knock yourself out but it suffices to + + + align:start position:0% +knock yourself out but it suffices to +know that + + align:start position:0% +know that + + + align:start position:0% +know that +you are going to get some new things + + align:start position:0% +you are going to get some new things + + + align:start position:0% +you are going to get some new things +that involve first derivatives of all + + align:start position:0% +that involve first derivatives of all + + + align:start position:0% +that involve first derivatives of all +these quantities so this will involve + + align:start position:0% + + + + align:start position:0% + +these two things + + align:start position:0% + + + + align:start position:0% + +and this will involve + + align:start position:0% +and this will involve + + + align:start position:0% +and this will involve +second derivative of all these things + + align:start position:0% + + + + align:start position:0% + +now what we're going to do is we're + + align:start position:0% +now what we're going to do is we're + + + align:start position:0% +now what we're going to do is we're +going to try to make what we would get + + align:start position:0% +going to try to make what we would get + + + align:start position:0% +going to try to make what we would get +multiplying all this out look as much + + align:start position:0% +multiplying all this out look as much + + + align:start position:0% +multiplying all this out look as much +like + + align:start position:0% +like + + + align:start position:0% +like +one one one one of the diagonal as + + align:start position:0% +one one one one of the diagonal as + + + align:start position:0% +one one one one of the diagonal as +possible + + align:start position:0% +possible + + + align:start position:0% +possible +and like i said it really just involves + + align:start position:0% +and like i said it really just involves + + + align:start position:0% +and like i said it really just involves +a counting argument + + align:start position:0% +a counting argument + + + align:start position:0% +a counting argument +it's actually one of my favorite little + + align:start position:0% +it's actually one of my favorite little + + + align:start position:0% +it's actually one of my favorite little +calculations we do in this class because + + align:start position:0% +calculations we do in this class because + + + align:start position:0% +calculations we do in this class because +it's sort of + + align:start position:0% +it's sort of + + + align:start position:0% +it's sort of +you know my favorite word for this is it + + align:start position:0% +you know my favorite word for this is it + + + align:start position:0% +you know my favorite word for this is it +really looks vomitous but + + align:start position:0% +really looks vomitous but + + + align:start position:0% +really looks vomitous but +it's quite elegant + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +you know i have an eight-year-old kid + + align:start position:0% +you know i have an eight-year-old kid + + + align:start position:0% +you know i have an eight-year-old kid +and i'm constantly trying to teach her + + align:start position:0% +and i'm constantly trying to teach her + + + align:start position:0% +and i'm constantly trying to teach her +math is just all about counting this is + + align:start position:0% +math is just all about counting this is + + + align:start position:0% +math is just all about counting this is +a perfect example this is really just + + align:start position:0% +a perfect example this is really just + + + align:start position:0% +a perfect example this is really just +about + + align:start position:0% +about + + + align:start position:0% +about +counting so let's look at this thing at + + align:start position:0% +counting so let's look at this thing at + + + align:start position:0% +counting so let's look at this thing at +zeroth order + + align:start position:0% + + + + align:start position:0% + +so what i'm trying to do is guarantee + + align:start position:0% +so what i'm trying to do is guarantee + + + align:start position:0% +so what i'm trying to do is guarantee +that i've got + + align:start position:0% +that i've got + + + align:start position:0% +that i've got +some l which i can choose which will + + align:start position:0% +some l which i can choose which will + + + align:start position:0% +some l which i can choose which will +make the components of the g + + align:start position:0% +make the components of the g + + + align:start position:0% +make the components of the g +at that point b minus 1 1 1 1. + + align:start position:0% +at that point b minus 1 1 1 1. + + + align:start position:0% +at that point b minus 1 1 1 1. +so my constraints + + align:start position:0% + + + + align:start position:0% + +the conditions i must satisfy + + align:start position:0% +the conditions i must satisfy + + + align:start position:0% +the conditions i must satisfy +involve things that hit these + + align:start position:0% +involve things that hit these + + + align:start position:0% +involve things that hit these +four by four symmetric tensor components + + align:start position:0% +four by four symmetric tensor components + + + align:start position:0% +four by four symmetric tensor components +so this guy is something that is + + align:start position:0% +so this guy is something that is + + + align:start position:0% +so this guy is something that is +symmetric + + align:start position:0% + + + + align:start position:0% + +nature has just handed me a symmetric + + align:start position:0% +nature has just handed me a symmetric + + + align:start position:0% +nature has just handed me a symmetric +tensor with a symmetric 4x4 + + align:start position:0% +tensor with a symmetric 4x4 + + + align:start position:0% +tensor with a symmetric 4x4 +object those are 10 constraints that my + + align:start position:0% +object those are 10 constraints that my + + + align:start position:0% +object those are 10 constraints that my +transformation must satisfy + + align:start position:0% + + + + align:start position:0% + +what i'm going to use to do this is + + align:start position:0% +what i'm going to use to do this is + + + align:start position:0% +what i'm going to use to do this is +this matrix at the point p + + align:start position:0% +this matrix at the point p + + + align:start position:0% +this matrix at the point p +and i'll remind you this matrix is just + + align:start position:0% + + + + align:start position:0% + +following set of partial derivatives at + + align:start position:0% +following set of partial derivatives at + + + align:start position:0% +following set of partial derivatives at +that point p + + align:start position:0% +that point p + + + align:start position:0% +that point p +this is also four by four it is not + + align:start position:0% +this is also four by four it is not + + + align:start position:0% +this is also four by four it is not +symmetric so this + + align:start position:0% +symmetric so this + + + align:start position:0% +symmetric so this +actually gives me 16 degrees of freedom + + align:start position:0% + + + + align:start position:0% + +to satisfy these constraints + + align:start position:0% + + + + align:start position:0% + +ta-da we can easily make this thing look + + align:start position:0% +ta-da we can easily make this thing look + + + align:start position:0% +ta-da we can easily make this thing look +lorencian at the point p + + align:start position:0% +lorencian at the point p + + + align:start position:0% +lorencian at the point p +in fact we can do so and have six + + align:start position:0% +in fact we can do so and have six + + + align:start position:0% +in fact we can do so and have six +degrees of freedom left over + + align:start position:0% +degrees of freedom left over + + + align:start position:0% +degrees of freedom left over +any idea what those six degrees of + + align:start position:0% +any idea what those six degrees of + + + align:start position:0% +any idea what those six degrees of +freedom are + + align:start position:0% +freedom are + + + align:start position:0% +freedom are +remember you're going into a low rent + + align:start position:0% +remember you're going into a low rent + + + align:start position:0% +remember you're going into a low rent +frame + + align:start position:0% +frame + + + align:start position:0% +frame +yeah three rotations three boosts + + align:start position:0% +yeah three rotations three boosts + + + align:start position:0% +yeah three rotations three boosts +exactly right + + align:start position:0% + + + + align:start position:0% + +boom so not only does it work + + align:start position:0% +boom so not only does it work + + + align:start position:0% +boom so not only does it work +mathematically + + align:start position:0% +mathematically + + + align:start position:0% +mathematically +but there's a little bit of leftover + + align:start position:0% +but there's a little bit of leftover + + + align:start position:0% +but there's a little bit of leftover +stuff which hopefully hits our intuition + + align:start position:0% +stuff which hopefully hits our intuition + + + align:start position:0% +stuff which hopefully hits our intuition +as to how things should behave in + + align:start position:0% +as to how things should behave in + + + align:start position:0% +as to how things should behave in +special relativity + + align:start position:0% + + + + align:start position:0% + +okay that's not really good enough + + align:start position:0% +okay that's not really good enough + + + align:start position:0% +okay that's not really good enough +though right so i just showed that i can + + align:start position:0% +though right so i just showed that i can + + + align:start position:0% +though right so i just showed that i can +do it at this point + + align:start position:0% +do it at this point + + + align:start position:0% +do it at this point +and if i move a centimeter away from + + align:start position:0% +and if i move a centimeter away from + + + align:start position:0% +and if i move a centimeter away from +that point + + align:start position:0% +that point + + + align:start position:0% +that point +suppose you know there's some really + + align:start position:0% +suppose you know there's some really + + + align:start position:0% +suppose you know there's some really +steep gradient that goes ah completely + + align:start position:0% +steep gradient that goes ah completely + + + align:start position:0% +steep gradient that goes ah completely +to hell okay then we're in trouble + + align:start position:0% +to hell okay then we're in trouble + + + align:start position:0% +to hell okay then we're in trouble +so we have to keep going we have to look + + align:start position:0% +so we have to keep going we have to look + + + align:start position:0% +so we have to keep going we have to look +at the additional terms in this + + align:start position:0% +at the additional terms in this + + + align:start position:0% +at the additional terms in this +expansion + + align:start position:0% + + + + align:start position:0% + +so when we do things at zeroth order we + + align:start position:0% +so when we do things at zeroth order we + + + align:start position:0% +so when we do things at zeroth order we +have now + + align:start position:0% +have now + + + align:start position:0% +have now +so g has been handed to us we have now + + align:start position:0% +so g has been handed to us we have now + + + align:start position:0% +so g has been handed to us we have now +specified behavior of + + align:start position:0% +specified behavior of + + + align:start position:0% +specified behavior of +l at that point so l has been + + align:start position:0% +l at that point so l has been + + + align:start position:0% +l at that point so l has been +completely completely soaked up i don't + + align:start position:0% +completely completely soaked up i don't + + + align:start position:0% +completely completely soaked up i don't +have any more freedom to sort of mess + + align:start position:0% +have any more freedom to sort of mess + + + align:start position:0% +have any more freedom to sort of mess +around with it + + align:start position:0% +around with it + + + align:start position:0% +around with it +when i go to the next order + + align:start position:0% + + + + align:start position:0% + +okay so the quantity that is setting my + + align:start position:0% +okay so the quantity that is setting my + + + align:start position:0% +okay so the quantity that is setting my +constraints + + align:start position:0% + + + + align:start position:0% + +is the first derivative of this so these + + align:start position:0% +is the first derivative of this so these + + + align:start position:0% +is the first derivative of this so these +are four derivatives + + align:start position:0% +are four derivatives + + + align:start position:0% +are four derivatives +of my ten metric functions + + align:start position:0% + + + + align:start position:0% + +so four by four symmetric by + + align:start position:0% + + + + align:start position:0% + +four components + + align:start position:0% + + + + align:start position:0% + +so i have got 40 constraints i must + + align:start position:0% + + + + align:start position:0% + +satisfy + + align:start position:0% + + + + align:start position:0% + +okay well the tool that i have available + + align:start position:0% +okay well the tool that i have available + + + align:start position:0% +okay well the tool that i have available +i am free to specify the matrix + + align:start position:0% +i am free to specify the matrix + + + align:start position:0% +i am free to specify the matrix +the derivatives at this point + + align:start position:0% + + + + align:start position:0% + +again remember this is itself a partial + + align:start position:0% +again remember this is itself a partial + + + align:start position:0% +again remember this is itself a partial +derivative + + align:start position:0% + + + + align:start position:0% + +so i've got four components alpha + + align:start position:0% + + + + align:start position:0% + +four derivatives with gamma bar four + + align:start position:0% +four derivatives with gamma bar four + + + align:start position:0% +four derivatives with gamma bar four +derivatives with mu bar + + align:start position:0% +derivatives with mu bar + + + align:start position:0% +derivatives with mu bar +partial derivatives it should not order + + align:start position:0% +partial derivatives it should not order + + + align:start position:0% +partial derivatives it should not order +should not matter what the order is + + align:start position:0% +should not matter what the order is + + + align:start position:0% +should not matter what the order is +so this needs to be symmetric on mu and + + align:start position:0% + + + + align:start position:0% + +gamma + + align:start position:0% + + + + align:start position:0% + +so i in fact have 40 degrees of freedom + + align:start position:0% +so i in fact have 40 degrees of freedom + + + align:start position:0% +so i in fact have 40 degrees of freedom +at first order + + align:start position:0% + + + + align:start position:0% + +perfect match okay so i can make my + + align:start position:0% +perfect match okay so i can make my + + + align:start position:0% +perfect match okay so i can make my +coordinate system not only can i make it + + align:start position:0% +coordinate system not only can i make it + + + align:start position:0% +coordinate system not only can i make it +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +uh the lorentz form at i can make the + + align:start position:0% +uh the lorentz form at i can make the + + + align:start position:0% +uh the lorentz form at i can make the +spacetime metric lorentz at the point p + + align:start position:0% +spacetime metric lorentz at the point p + + + align:start position:0% +spacetime metric lorentz at the point p +i can also make it flat at that point + + align:start position:0% +i can also make it flat at that point + + + align:start position:0% +i can also make it flat at that point +pay + + align:start position:0% +pay + + + align:start position:0% +pay +all right now we're feeling cocky so + + align:start position:0% +all right now we're feeling cocky so + + + align:start position:0% +all right now we're feeling cocky so +let's move on + + align:start position:0% + + + + align:start position:0% + +how far can i go + + align:start position:0% + + + + align:start position:0% + +i lost the page i need + + align:start position:0% + + + + align:start position:0% + +okay so now you have a flavor for what + + align:start position:0% +okay so now you have a flavor for what + + + align:start position:0% +okay so now you have a flavor for what +we're doing okay i want to count up the + + align:start position:0% +we're doing okay i want to count up the + + + align:start position:0% +we're doing okay i want to count up the +number of degrees of + + align:start position:0% +number of degrees of + + + align:start position:0% +number of degrees of +uh sorry the the number of constraints + + align:start position:0% +uh sorry the the number of constraints + + + align:start position:0% +uh sorry the the number of constraints +that are + + align:start position:0% +that are + + + align:start position:0% +that are +in the metric object the new metric + + align:start position:0% +in the metric object the new metric + + + align:start position:0% +in the metric object the new metric +object i work with at this order + + align:start position:0% +object i work with at this order + + + align:start position:0% +object i work with at this order +and compare it to the degrees of freedom + + align:start position:0% +and compare it to the degrees of freedom + + + align:start position:0% +and compare it to the degrees of freedom +in the coordinate transformation at this + + align:start position:0% +in the coordinate transformation at this + + + align:start position:0% +in the coordinate transformation at this +order + + align:start position:0% + + + + align:start position:0% + +so when i go to second order my new + + align:start position:0% +so when i go to second order my new + + + align:start position:0% +so when i go to second order my new +metric thing that i'm going to be + + align:start position:0% +metric thing that i'm going to be + + + align:start position:0% +metric thing that i'm going to be +messing around with + + align:start position:0% +messing around with + + + align:start position:0% +messing around with +is the second derivative so i take two + + align:start position:0% +is the second derivative so i take two + + + align:start position:0% +is the second derivative so i take two +derivatives + + align:start position:0% + + + + align:start position:0% + +of g alpha beta at the point p + + align:start position:0% + + + + align:start position:0% + +so this again needs to be symmetric in + + align:start position:0% +so this again needs to be symmetric in + + + align:start position:0% +so this again needs to be symmetric in +the derivative so i have a symmetric 4x4 + + align:start position:0% + + + + align:start position:0% + +on these two guys and the metric is + + align:start position:0% +on these two guys and the metric is + + + align:start position:0% +on these two guys and the metric is +itself + + align:start position:0% +itself + + + align:start position:0% +itself +four by four on alpha and beta + + align:start position:0% +four by four on alpha and beta + + + align:start position:0% +four by four on alpha and beta +so there's a hundred conditions 100 + + align:start position:0% +so there's a hundred conditions 100 + + + align:start position:0% +so there's a hundred conditions 100 +constraints that we must satisfy + + align:start position:0% + + + + align:start position:0% + +so let's look at the second derivative + + align:start position:0% + + + + align:start position:0% + +of this okay so let me move this down a + + align:start position:0% +of this okay so let me move this down a + + + align:start position:0% +of this okay so let me move this down a +little bit + + align:start position:0% + + + + align:start position:0% + +this is now going to look like the third + + align:start position:0% +this is now going to look like the third + + + align:start position:0% +this is now going to look like the third +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +when i do this transformation so it's + + align:start position:0% +when i do this transformation so it's + + + align:start position:0% +when i do this transformation so it's +going to be the third derivative of x + + align:start position:0% +going to be the third derivative of x + + + align:start position:0% +going to be the third derivative of x +alpha + + align:start position:0% + + + + align:start position:0% + +with respect to mu bar + + align:start position:0% + + + + align:start position:0% + +delta bar and gamma bar + + align:start position:0% + + + + align:start position:0% + +so i've got four degrees of freedom + + align:start position:0% +so i've got four degrees of freedom + + + align:start position:0% +so i've got four degrees of freedom +for my alpha + + align:start position:0% +for my alpha + + + align:start position:0% +for my alpha +and this must be perfectly + + align:start position:0% +and this must be perfectly + + + align:start position:0% +and this must be perfectly +perfectly symmetric under the any + + align:start position:0% +perfectly symmetric under the any + + + align:start position:0% +perfectly symmetric under the any +interchange of the indices mu bar + + align:start position:0% +interchange of the indices mu bar + + + align:start position:0% +interchange of the indices mu bar +delta bar and gamma bar okay + + align:start position:0% +delta bar and gamma bar okay + + + align:start position:0% +delta bar and gamma bar okay +this is a little exercise in + + align:start position:0% +this is a little exercise in + + + align:start position:0% +this is a little exercise in +combinatorics + + align:start position:0% +combinatorics + + + align:start position:0% +combinatorics +so the number of ways that the number of + + align:start position:0% +so the number of ways that the number of + + + align:start position:0% +so the number of ways that the number of +equivalent ways of arranging this + + align:start position:0% +equivalent ways of arranging this + + + align:start position:0% +equivalent ways of arranging this +turns out to be n times m plus 1 + + align:start position:0% +turns out to be n times m plus 1 + + + align:start position:0% +turns out to be n times m plus 1 +times n plus 2 over + + align:start position:0% +times n plus 2 over + + + align:start position:0% +times n plus 2 over +three factorial and i'm in four + + align:start position:0% +three factorial and i'm in four + + + align:start position:0% +three factorial and i'm in four +dimensions for n equals four + + align:start position:0% + + + + align:start position:0% + +work that out and you will find that you + + align:start position:0% +work that out and you will find that you + + + align:start position:0% +work that out and you will find that you +have + + align:start position:0% + + + + align:start position:0% + +eighty + + align:start position:0% +eighty + + + align:start position:0% +eighty +degrees of freedom + + align:start position:0% + + + + align:start position:0% + +so what we can do is we can always find + + align:start position:0% +so what we can do is we can always find + + + align:start position:0% +so what we can do is we can always find +a coordinate transformation that makes + + align:start position:0% +a coordinate transformation that makes + + + align:start position:0% +a coordinate transformation that makes +it flat + + align:start position:0% +it flat + + + align:start position:0% +it flat +it makes it laurencian at point p it is + + align:start position:0% +it makes it laurencian at point p it is + + + align:start position:0% +it makes it laurencian at point p it is +flat in that region in other words there + + align:start position:0% +flat in that region in other words there + + + align:start position:0% +flat in that region in other words there +is no first derivative there + + align:start position:0% +is no first derivative there + + + align:start position:0% +is no first derivative there +uh it's sort of you know sorry flat's + + align:start position:0% +uh it's sort of you know sorry flat's + + + align:start position:0% +uh it's sort of you know sorry flat's +not really the right word there's it's + + align:start position:0% +not really the right word there's it's + + + align:start position:0% +not really the right word there's it's +it's + + align:start position:0% +it's + + + align:start position:0% +it's +there is no slope right at that at that + + align:start position:0% +there is no slope right at that at that + + + align:start position:0% +there is no slope right at that at that +point + + align:start position:0% +point + + + align:start position:0% +point +but we cannot transform away the second + + align:start position:0% +but we cannot transform away the second + + + align:start position:0% +but we cannot transform away the second +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +and so what this tells me is + + align:start position:0% + + + + align:start position:0% + +the coordinate freedom that we have + + align:start position:0% +the coordinate freedom that we have + + + align:start position:0% +the coordinate freedom that we have +means that we can always put our metric + + align:start position:0% +means that we can always put our metric + + + align:start position:0% +means that we can always put our metric +into the following form + + align:start position:0% + + + + align:start position:0% + +i'm just gonna write this schematically + + align:start position:0% +i'm just gonna write this schematically + + + align:start position:0% +i'm just gonna write this schematically +second derivative of the metric + + align:start position:0% + + + + align:start position:0% + +i'm sort of a quadratic separation in + + align:start position:0% +i'm sort of a quadratic separation in + + + align:start position:0% +i'm sort of a quadratic separation in +space-time coordinate + + align:start position:0% + + + + align:start position:0% + +so a couple things about this are pretty + + align:start position:0% +so a couple things about this are pretty + + + align:start position:0% +so a couple things about this are pretty +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +um so you know this is basically telling + + align:start position:0% +um so you know this is basically telling + + + align:start position:0% +um so you know this is basically telling +me that we can make it lorenz only up to + + align:start position:0% +me that we can make it lorenz only up to + + + align:start position:0% +me that we can make it lorenz only up to +uh terms that look essentially like the + + align:start position:0% +uh terms that look essentially like the + + + align:start position:0% +uh terms that look essentially like the +second derivative of the metric + + align:start position:0% +second derivative of the metric + + + align:start position:0% +second derivative of the metric +well the second derivative of any + + align:start position:0% +well the second derivative of any + + + align:start position:0% +well the second derivative of any +function tells you about the curvature + + align:start position:0% +function tells you about the curvature + + + align:start position:0% +function tells you about the curvature +of that function + + align:start position:0% +of that function + + + align:start position:0% +of that function +so this word curvature is going to be + + align:start position:0% +so this word curvature is going to be + + + align:start position:0% +so this word curvature is going to be +coming up over and over and over again + + align:start position:0% +coming up over and over and over again + + + align:start position:0% +coming up over and over and over again +we are in fact because you know this is + + align:start position:0% +we are in fact because you know this is + + + align:start position:0% +we are in fact because you know this is +general relativity we can't do + + align:start position:0% +general relativity we can't do + + + align:start position:0% +general relativity we can't do +everything simply we're + + align:start position:0% +everything simply we're + + + align:start position:0% +everything simply we're +going to actually find that there is a + + align:start position:0% +going to actually find that there is a + + + align:start position:0% +going to actually find that there is a +rigorous way to define a notion of + + align:start position:0% +rigorous way to define a notion of + + + align:start position:0% +rigorous way to define a notion of +curvature + + align:start position:0% +curvature + + + align:start position:0% +curvature +uh that we're going to play with which + + align:start position:0% +uh that we're going to play with which + + + align:start position:0% +uh that we're going to play with which +indeed looks like two derivatives + + align:start position:0% +indeed looks like two derivatives + + + align:start position:0% +indeed looks like two derivatives +of the space-time metric and we are + + align:start position:0% +of the space-time metric and we are + + + align:start position:0% +of the space-time metric and we are +going to find + + align:start position:0% +going to find + + + align:start position:0% +going to find +it has i mean it's actually going to end + + align:start position:0% +it has i mean it's actually going to end + + + align:start position:0% +it has i mean it's actually going to end +up looking like a four + + align:start position:0% +up looking like a four + + + align:start position:0% +up looking like a four +four index tensor okay so it's going to + + align:start position:0% +four index tensor okay so it's going to + + + align:start position:0% +four index tensor okay so it's going to +be an object that's got four indices on + + align:start position:0% +be an object that's got four indices on + + + align:start position:0% +be an object that's got four indices on +it + + align:start position:0% +it + + + align:start position:0% +it +um each of those indices can goes over + + align:start position:0% +um each of those indices can goes over + + + align:start position:0% +um each of those indices can goes over +the four space-time + + align:start position:0% +the four space-time + + + align:start position:0% +the four space-time +uh coordinates and so naively it looks + + align:start position:0% +uh coordinates and so naively it looks + + + align:start position:0% +uh coordinates and so naively it looks +like it's got two hundred and four to + + align:start position:0% +like it's got two hundred and four to + + + align:start position:0% +like it's got two hundred and four to +the fourth power independent components + + align:start position:0% +the fourth power independent components + + + align:start position:0% +the fourth power independent components +256. it has certain symmetries we're + + align:start position:0% +256. it has certain symmetries we're + + + align:start position:0% +256. it has certain symmetries we're +going to see though + + align:start position:0% +going to see though + + + align:start position:0% +going to see though +and when you take into account those + + align:start position:0% +and when you take into account those + + + align:start position:0% +and when you take into account those +symmetries and you count up how many of + + align:start position:0% +symmetries and you count up how many of + + + align:start position:0% +symmetries and you count up how many of +those + + align:start position:0% +those + + + align:start position:0% +those +components are actually independent and + + align:start position:0% +components are actually independent and + + + align:start position:0% +components are actually independent and +any guesses what the number is going to + + align:start position:0% +any guesses what the number is going to + + + align:start position:0% +any guesses what the number is going to +turn out to be + + align:start position:0% +turn out to be + + + align:start position:0% +turn out to be +20. yes it exactly compensates for + + align:start position:0% +20. yes it exactly compensates for + + + align:start position:0% +20. yes it exactly compensates for +you know the the number that cannot be + + align:start position:0% +you know the the number that cannot be + + + align:start position:0% +you know the the number that cannot be +zeroed out by this coordinate + + align:start position:0% +zeroed out by this coordinate + + + align:start position:0% +zeroed out by this coordinate +transformation it's called the riemann + + align:start position:0% +transformation it's called the riemann + + + align:start position:0% +transformation it's called the riemann +curvature tensor + + align:start position:0% +curvature tensor + + + align:start position:0% +curvature tensor +and we will get to that fairly actually + + align:start position:0% +and we will get to that fairly actually + + + align:start position:0% +and we will get to that fairly actually +really just in a couple lectures + + align:start position:0% +really just in a couple lectures + + + align:start position:0% +really just in a couple lectures +the other thing which this is useful for + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +in all of my discussion of the + + align:start position:0% +in all of my discussion of the + + + align:start position:0% +in all of my discussion of the +equivalence principle up till now + + align:start position:0% +equivalence principle up till now + + + align:start position:0% +equivalence principle up till now +there's been a weasel word that i've + + align:start position:0% +there's been a weasel word that i've + + + align:start position:0% +there's been a weasel word that i've +inserted into much of the physics i + + align:start position:0% +inserted into much of the physics i + + + align:start position:0% +inserted into much of the physics i +always said over + + align:start position:0% +always said over + + + align:start position:0% +always said over +sufficiently small regions okay i say + + align:start position:0% +sufficiently small regions okay i say + + + align:start position:0% +sufficiently small regions okay i say +that + + align:start position:0% +that + + + align:start position:0% +that +trajectories begin to deviate from one + + align:start position:0% +trajectories begin to deviate from one + + + align:start position:0% +trajectories begin to deviate from one +another when they get sufficiently far + + align:start position:0% +another when they get sufficiently far + + + align:start position:0% +another when they get sufficiently far +away from one another + + align:start position:0% +away from one another + + + align:start position:0% +away from one another +okay and you should sort of be going + + align:start position:0% +okay and you should sort of be going + + + align:start position:0% +okay and you should sort of be going +what the hell is sufficiently small it's + + align:start position:0% +what the hell is sufficiently small it's + + + align:start position:0% +what the hell is sufficiently small it's +efficiently far away what do all these + + align:start position:0% +efficiently far away what do all these + + + align:start position:0% +efficiently far away what do all these +things mean + + align:start position:0% +things mean + + + align:start position:0% +things mean +okay and the issue is you need to have a + + align:start position:0% +okay and the issue is you need to have a + + + align:start position:0% +okay and the issue is you need to have a +scale well + + align:start position:0% + + + + align:start position:0% + +this scale is going to be set by the + + align:start position:0% +this scale is going to be set by the + + + align:start position:0% +this scale is going to be set by the +second derivative of the metric + + align:start position:0% + + + + align:start position:0% + +so the size of the region + + align:start position:0% + + + + align:start position:0% + +over which space time + + align:start position:0% +over which space time + + + align:start position:0% +over which space time +is inertial in this coordinate system in + + align:start position:0% +is inertial in this coordinate system in + + + align:start position:0% +is inertial in this coordinate system in +this representation + + align:start position:0% +this representation + + + align:start position:0% +this representation +it's approximately sort of imagine it's + + align:start position:0% +it's approximately sort of imagine it's + + + align:start position:0% +it's approximately sort of imagine it's +one over you can sort of think of d2g + + align:start position:0% +one over you can sort of think of d2g + + + align:start position:0% +one over you can sort of think of d2g +as being one over a length squared + + align:start position:0% +as being one over a length squared + + + align:start position:0% +as being one over a length squared +so one over the square root of that + + align:start position:0% +so one over the square root of that + + + align:start position:0% +so one over the square root of that +gives me a rough idea of how long the + + align:start position:0% +gives me a rough idea of how long the + + + align:start position:0% +gives me a rough idea of how long the +curvature scale associated with your + + align:start position:0% +curvature scale associated with your + + + align:start position:0% +curvature scale associated with your +space time actually is and it tells you + + align:start position:0% +space time actually is and it tells you + + + align:start position:0% +space time actually is and it tells you +how big your inertial region actually is + + align:start position:0% + + + + align:start position:0% + +so we're going to make this notion of + + align:start position:0% +so we're going to make this notion of + + + align:start position:0% +so we're going to make this notion of +curvature rigorous very very + + align:start position:0% +curvature rigorous very very + + + align:start position:0% +curvature rigorous very very +soon as a prelude to this + + align:start position:0% +soon as a prelude to this + + + align:start position:0% +soon as a prelude to this +we now need to start thinking about how + + align:start position:0% +we now need to start thinking about how + + + align:start position:0% +we now need to start thinking about how +we do mathematics and physics + + align:start position:0% +we do mathematics and physics + + + align:start position:0% +we do mathematics and physics +on a curved manifold + + align:start position:0% + + + + align:start position:0% + +so i'm going to start to set up + + align:start position:0% +so i'm going to start to set up + + + align:start position:0% +so i'm going to start to set up +some of the issues that we need to face + + align:start position:0% + + + + align:start position:0% + +so we're going to define what i mean by + + align:start position:0% +so we're going to define what i mean by + + + align:start position:0% +so we're going to define what i mean by +a manifold that is curved + + align:start position:0% +a manifold that is curved + + + align:start position:0% +a manifold that is curved +so a curved manifold is going to simply + + align:start position:0% +so a curved manifold is going to simply + + + align:start position:0% +so a curved manifold is going to simply +be one + + align:start position:0% +be one + + + align:start position:0% +be one +in which initially parallel + + align:start position:0% +in which initially parallel + + + align:start position:0% +in which initially parallel +trajectories do not remain parallel + + align:start position:0% + + + + align:start position:0% + +so an example is the surface of a sphere + + align:start position:0% +so an example is the surface of a sphere + + + align:start position:0% +so an example is the surface of a sphere +as i sort of illustrated + + align:start position:0% +as i sort of illustrated + + + align:start position:0% +as i sort of illustrated +you start somewhere on the equator in + + align:start position:0% +you start somewhere on the equator in + + + align:start position:0% +you start somewhere on the equator in +brazil your friend starts somewhere on + + align:start position:0% +brazil your friend starts somewhere on + + + align:start position:0% +brazil your friend starts somewhere on +the equator + + align:start position:0% +the equator + + + align:start position:0% +the equator +in africa the two of you start working + + align:start position:0% +in africa the two of you start working + + + align:start position:0% +in africa the two of you start working +walking north you are exactly parallel + + align:start position:0% +walking north you are exactly parallel + + + align:start position:0% +walking north you are exactly parallel +when you take that first step off of the + + align:start position:0% +when you take that first step off of the + + + align:start position:0% +when you take that first step off of the +equator + + align:start position:0% +equator + + + align:start position:0% +equator +but your trajectories cross at the north + + align:start position:0% +but your trajectories cross at the north + + + align:start position:0% +but your trajectories cross at the north +pole + + align:start position:0% + + + + align:start position:0% + +interestingly an example that looks + + align:start position:0% +interestingly an example that looks + + + align:start position:0% +interestingly an example that looks +curved but is not + + align:start position:0% + + + + align:start position:0% + +the surface of a cylinder + + align:start position:0% + + + + align:start position:0% + +okay if i take two lines okay i'm going + + align:start position:0% +okay if i take two lines okay i'm going + + + align:start position:0% +okay if i take two lines okay i'm going +to imagine that this sort of region + + align:start position:0% +to imagine that this sort of region + + + align:start position:0% +to imagine that this sort of region +continues all the way up here + + align:start position:0% +continues all the way up here + + + align:start position:0% +continues all the way up here +i make two lines that are parallel to + + align:start position:0% +i make two lines that are parallel to + + + align:start position:0% +i make two lines that are parallel to +each other here and i have them sort of + + align:start position:0% +each other here and i have them sort of + + + align:start position:0% +each other here and i have them sort of +extend around this thing + + align:start position:0% +extend around this thing + + + align:start position:0% +extend around this thing +they would remain parallel the entire + + align:start position:0% +they would remain parallel the entire + + + align:start position:0% +they would remain parallel the entire +way out okay + + align:start position:0% +way out okay + + + align:start position:0% +way out okay +another way of stating that is that you + + align:start position:0% +another way of stating that is that you + + + align:start position:0% +another way of stating that is that you +can always take a cylinder + + align:start position:0% +can always take a cylinder + + + align:start position:0% +can always take a cylinder +and with an appropriate cut but without + + align:start position:0% +and with an appropriate cut but without + + + align:start position:0% +and with an appropriate cut but without +tearing it you can flatten it out and + + align:start position:0% +tearing it you can flatten it out and + + + align:start position:0% +tearing it you can flatten it out and +make it into a simple + + align:start position:0% +make it into a simple + + + align:start position:0% +make it into a simple +sheet of a perfectly sheet flat sheet + + align:start position:0% +sheet of a perfectly sheet flat sheet + + + align:start position:0% +sheet of a perfectly sheet flat sheet +you cannot do that with a sphere without + + align:start position:0% +you cannot do that with a sphere without + + + align:start position:0% +you cannot do that with a sphere without +tearing it in some places + + align:start position:0% + + + + align:start position:0% + +so what is going to begin to complicate + + align:start position:0% +so what is going to begin to complicate + + + align:start position:0% +so what is going to begin to complicate +things + + align:start position:0% + + + + align:start position:0% + +is that we want to work with vectors and + + align:start position:0% +is that we want to work with vectors and + + + align:start position:0% +is that we want to work with vectors and +tensors + + align:start position:0% +tensors + + + align:start position:0% +tensors +that live in this curved manifold + + align:start position:0% + + + + align:start position:0% + +we haven't really thought too carefully + + align:start position:0% +we haven't really thought too carefully + + + align:start position:0% +we haven't really thought too carefully +yet about the + + align:start position:0% +yet about the + + + align:start position:0% +yet about the +space and let's let's just focus on + + align:start position:0% +space and let's let's just focus on + + + align:start position:0% +space and let's let's just focus on +vectors for now we haven't thought too + + align:start position:0% +vectors for now we haven't thought too + + + align:start position:0% +vectors for now we haven't thought too +carefully about the space + + align:start position:0% +carefully about the space + + + align:start position:0% +carefully about the space +in which the vectors actually live so + + align:start position:0% +in which the vectors actually live so + + + align:start position:0% +in which the vectors actually live so +implicit to everything we have talked + + align:start position:0% +implicit to everything we have talked + + + align:start position:0% +implicit to everything we have talked +about up until now + + align:start position:0% +about up until now + + + align:start position:0% +about up until now +so we often regard vectors + + align:start position:0% +so we often regard vectors + + + align:start position:0% +so we often regard vectors +as objects that themselves reside in a + + align:start position:0% +as objects that themselves reside in a + + + align:start position:0% +as objects that themselves reside in a +tangent space + + align:start position:0% + + + + align:start position:0% + +okay if i'm working in a manifold that + + align:start position:0% +okay if i'm working in a manifold that + + + align:start position:0% +okay if i'm working in a manifold that +is flat say it's the surface of this + + align:start position:0% +is flat say it's the surface of this + + + align:start position:0% +is flat say it's the surface of this +board okay in this two dimensions + + align:start position:0% +board okay in this two dimensions + + + align:start position:0% +board okay in this two dimensions +every point on this board has the same + + align:start position:0% +every point on this board has the same + + + align:start position:0% +every point on this board has the same +tangent right so if i draw a vector here + + align:start position:0% +tangent right so if i draw a vector here + + + align:start position:0% +tangent right so if i draw a vector here +and i draw another vector over here it's + + align:start position:0% +and i draw another vector over here it's + + + align:start position:0% +and i draw another vector over here it's +really easy for me to compare them + + align:start position:0% +really easy for me to compare them + + + align:start position:0% +really easy for me to compare them +because they actually live in the same + + align:start position:0% +because they actually live in the same + + + align:start position:0% +because they actually live in the same +space that is tangent to this board + + align:start position:0% +space that is tangent to this board + + + align:start position:0% +space that is tangent to this board +if i'm on the surface of a sphere + + align:start position:0% +if i'm on the surface of a sphere + + + align:start position:0% +if i'm on the surface of a sphere +points that are tangent to the sphere at + + align:start position:0% +points that are tangent to the sphere at + + + align:start position:0% +points that are tangent to the sphere at +the north pole are very different + + align:start position:0% +the north pole are very different + + + align:start position:0% +the north pole are very different +from points that are tangent to the + + align:start position:0% +from points that are tangent to the + + + align:start position:0% +from points that are tangent to the +sphere on the equator + + align:start position:0% +sphere on the equator + + + align:start position:0% +sphere on the equator +so it becomes difficult for me to + + align:start position:0% +so it becomes difficult for me to + + + align:start position:0% +so it becomes difficult for me to +actually compare fields when they are + + align:start position:0% +actually compare fields when they are + + + align:start position:0% +actually compare fields when they are +defined on a curved surface like this + + align:start position:0% + + + + align:start position:0% + +so this makes it a little bit and so i'm + + align:start position:0% +so this makes it a little bit and so i'm + + + align:start position:0% +so this makes it a little bit and so i'm +just going to set up this problem + + align:start position:0% +just going to set up this problem + + + align:start position:0% +just going to set up this problem +and i will sort of sketch the issue and + + align:start position:0% +and i will sort of sketch the issue and + + + align:start position:0% +and i will sort of sketch the issue and +then we will resolve it + + align:start position:0% +then we will resolve it + + + align:start position:0% +then we will resolve it +in our lecture on tuesday this makes it + + align:start position:0% +in our lecture on tuesday this makes it + + + align:start position:0% +in our lecture on tuesday this makes it +a little bit complicated for me to take + + align:start position:0% +a little bit complicated for me to take + + + align:start position:0% +a little bit complicated for me to take +derivatives of things like + + align:start position:0% +derivatives of things like + + + align:start position:0% +derivatives of things like +vectors when i'm on when i'm working in + + align:start position:0% +vectors when i'm on when i'm working in + + + align:start position:0% +vectors when i'm on when i'm working in +a curved manifold + + align:start position:0% +a curved manifold + + + align:start position:0% +a curved manifold +so let's consider the following + + align:start position:0% +so let's consider the following + + + align:start position:0% +so let's consider the following +situation + + align:start position:0% + + + + align:start position:0% + +so i'm going to define some curve which + + align:start position:0% +so i'm going to define some curve which + + + align:start position:0% +so i'm going to define some curve which +i would just call + + align:start position:0% +i would just call + + + align:start position:0% +i would just call +gamma + + align:start position:0% + + + + align:start position:0% + +that lives in a curved space of some sun + + align:start position:0% + + + + align:start position:0% + +okay i'm going to draw it here on the + + align:start position:0% +okay i'm going to draw it here on the + + + align:start position:0% +okay i'm going to draw it here on the +board + + align:start position:0% +board + + + align:start position:0% +board +but imagine that this is like on the + + align:start position:0% +but imagine that this is like on the + + + align:start position:0% +but imagine that this is like on the +surface of a sphere + + align:start position:0% +surface of a sphere + + + align:start position:0% +surface of a sphere +okay so here's + + align:start position:0% +okay so here's + + + align:start position:0% +okay so here's +the curve gamma let's say + + align:start position:0% + + + + align:start position:0% + +this point p here has coordinates x + + align:start position:0% +this point p here has coordinates x + + + align:start position:0% +this point p here has coordinates x +alpha and this point q + + align:start position:0% +alpha and this point q + + + align:start position:0% +alpha and this point q +here has coordinates + + align:start position:0% +here has coordinates + + + align:start position:0% +here has coordinates +x alpha plus dx alpha + + align:start position:0% +x alpha plus dx alpha + + + align:start position:0% +x alpha plus dx alpha +suppose there's some vector field that + + align:start position:0% +suppose there's some vector field that + + + align:start position:0% +suppose there's some vector field that +fills all this manifold + + align:start position:0% +fills all this manifold + + + align:start position:0% +fills all this manifold +okay and so let's say the vector a + + align:start position:0% + + + + align:start position:0% + +looks like this here at the point p + + align:start position:0% +looks like this here at the point p + + + align:start position:0% +looks like this here at the point p +and it looks like this here at the point + + align:start position:0% +and it looks like this here at the point + + + align:start position:0% +and it looks like this here at the point +q + + align:start position:0% + + + + align:start position:0% + +how do i take the derivative of the + + align:start position:0% +how do i take the derivative of the + + + align:start position:0% +how do i take the derivative of the +vector field as i go from point p to + + align:start position:0% +vector field as i go from point p to + + + align:start position:0% +vector field as i go from point p to +point q + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% + + + + align:start position:0% + +your first guess should basically just + + align:start position:0% +your first guess should basically just + + + align:start position:0% +your first guess should basically just +be you know do what you do or + + align:start position:0% +be you know do what you do or + + + align:start position:0% +be you know do what you do or +always do when you first learn how to + + align:start position:0% +always do when you first learn how to + + + align:start position:0% +always do when you first learn how to +take a derivative + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +okay so that would be a notion of a + + align:start position:0% +okay so that would be a notion of a + + + align:start position:0% +okay so that would be a notion of a +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +there's nothing mathematically wrong + + align:start position:0% +there's nothing mathematically wrong + + + align:start position:0% +there's nothing mathematically wrong +with that okay but we're going to find + + align:start position:0% +with that okay but we're going to find + + + align:start position:0% +with that okay but we're going to find +that it gives us problems + + align:start position:0% +that it gives us problems + + + align:start position:0% +that it gives us problems +for the same reason that we ran into + + align:start position:0% +for the same reason that we ran into + + + align:start position:0% +for the same reason that we ran into +problems when we began working with + + align:start position:0% +problems when we began working with + + + align:start position:0% +problems when we began working with +vector spaces in curvilinear coordinates + + align:start position:0% +vector spaces in curvilinear coordinates + + + align:start position:0% +vector spaces in curvilinear coordinates +okay + + align:start position:0% +okay + + + align:start position:0% +okay +if i want this to be a tensorial object + + align:start position:0% +if i want this to be a tensorial object + + + align:start position:0% +if i want this to be a tensorial object +in the same way that we have been + + align:start position:0% +in the same way that we have been + + + align:start position:0% +in the same way that we have been +defining tensors all along here i'm + + align:start position:0% +defining tensors all along here i'm + + + align:start position:0% +defining tensors all along here i'm +going to run into problems let me just + + align:start position:0% +going to run into problems let me just + + + align:start position:0% +going to run into problems let me just +actually + + align:start position:0% +actually + + + align:start position:0% +actually +demonstrate what happens if i if i try + + align:start position:0% +demonstrate what happens if i if i try + + + align:start position:0% +demonstrate what happens if i if i try +to do this + + align:start position:0% +to do this + + + align:start position:0% +to do this +so the key bit the way we want to think + + align:start position:0% +so the key bit the way we want to think + + + align:start position:0% +so the key bit the way we want to think +about it is that the points p + + align:start position:0% +about it is that the points p + + + align:start position:0% +about it is that the points p +and q don't have the same tans in space + + align:start position:0% + + + + align:start position:0% + +which is a fancy way of saying that as i + + align:start position:0% +which is a fancy way of saying that as i + + + align:start position:0% +which is a fancy way of saying that as i +move from point p + + align:start position:0% +move from point p + + + align:start position:0% +move from point p +to point q the basis vectors are moving + + align:start position:0% +to point q the basis vectors are moving + + + align:start position:0% +to point q the basis vectors are moving +they're starting to point in different + + align:start position:0% + + + + align:start position:0% + +directions + + align:start position:0% + + + + align:start position:0% + +so if this were to be like i said + + align:start position:0% +so if this were to be like i said + + + align:start position:0% +so if this were to be like i said +mathematically if you just want to get + + align:start position:0% +mathematically if you just want to get + + + align:start position:0% +mathematically if you just want to get +that derivative that is a quantity which + + align:start position:0% +that derivative that is a quantity which + + + align:start position:0% +that derivative that is a quantity which +has a mathematical meaning + + align:start position:0% +has a mathematical meaning + + + align:start position:0% +has a mathematical meaning +okay but it's not the component of a + + align:start position:0% +okay but it's not the component of a + + + align:start position:0% +okay but it's not the component of a +tensor which we have called out as + + align:start position:0% +tensor which we have called out as + + + align:start position:0% +tensor which we have called out as +having a particularly important meaning + + align:start position:0% +having a particularly important meaning + + + align:start position:0% +having a particularly important meaning +in this geometric construction of + + align:start position:0% +in this geometric construction of + + + align:start position:0% +in this geometric construction of +physics that we are doing and so + + align:start position:0% +physics that we are doing and so + + + align:start position:0% +physics that we are doing and so +if this were to be tensorial then i + + align:start position:0% +if this were to be tensorial then i + + + align:start position:0% +if this were to be tensorial then i +should be able to switch to new + + align:start position:0% +should be able to switch to new + + + align:start position:0% +should be able to switch to new +coordinates which i'll designate with + + align:start position:0% +coordinates which i'll designate with + + + align:start position:0% +coordinates which i'll designate with +primes + + align:start position:0% +primes + + + align:start position:0% +primes +such that + + align:start position:0% + + + + align:start position:0% + +the following was true + + align:start position:0% + + + + align:start position:0% + +the reason why this doesn't actually + + align:start position:0% +the reason why this doesn't actually + + + align:start position:0% +the reason why this doesn't actually +work + + align:start position:0% + + + + align:start position:0% + +is i'm going to demand that alpha excuse + + align:start position:0% +is i'm going to demand that alpha excuse + + + align:start position:0% +is i'm going to demand that alpha excuse +me that a + + align:start position:0% +me that a + + + align:start position:0% +me that a +is in fact actually already tensorial + + align:start position:0% +is in fact actually already tensorial + + + align:start position:0% +is in fact actually already tensorial +okay it's the component of a vector + + align:start position:0% +okay it's the component of a vector + + + align:start position:0% +okay it's the component of a vector +which is a + + align:start position:0% +which is a + + + align:start position:0% +which is a +particular kind of tensor + + align:start position:0% + + + + align:start position:0% + +so i'm going to demand + + align:start position:0% + + + + align:start position:0% + +that the following be true + + align:start position:0% + + + + align:start position:0% + +and i'm going to demand that my + + align:start position:0% +and i'm going to demand that my + + + align:start position:0% +and i'm going to demand that my +derivatives + + align:start position:0% + + + + align:start position:0% + +you know they are just they're just + + align:start position:0% +you know they are just they're just + + + align:start position:0% +you know they are just they're just +derivatives they do the usual rule of + + align:start position:0% +derivatives they do the usual rule of + + + align:start position:0% +derivatives they do the usual rule of +usual jacobian rule when i + + align:start position:0% +usual jacobian rule when i + + + align:start position:0% +usual jacobian rule when i +switch coordinate systems and so + + align:start position:0% +switch coordinate systems and so + + + align:start position:0% +switch coordinate systems and so +skipping a line of algebra which you can + + align:start position:0% +skipping a line of algebra which you can + + + align:start position:0% +skipping a line of algebra which you can +get in my notes this is actually very + + align:start position:0% +get in my notes this is actually very + + + align:start position:0% +get in my notes this is actually very +similar to the notes i've already posted + + align:start position:0% +similar to the notes i've already posted + + + align:start position:0% +similar to the notes i've already posted +when you work this out you're going to + + align:start position:0% + + + + align:start position:0% + +find + + align:start position:0% + + + + align:start position:0% + +you get one term that's correct + + align:start position:0% + + + + align:start position:0% + +but you get another term that involves + + align:start position:0% +but you get another term that involves + + + align:start position:0% +but you get another term that involves +a derivative of your coordinate + + align:start position:0% +a derivative of your coordinate + + + align:start position:0% +a derivative of your coordinate +transformation matrix + + align:start position:0% +transformation matrix + + + align:start position:0% +transformation matrix +and this extra term spoils the + + align:start position:0% +and this extra term spoils the + + + align:start position:0% +and this extra term spoils the +tensorialness + + align:start position:0% +tensorialness + + + align:start position:0% +tensorialness +of this quantity + + align:start position:0% + + + + align:start position:0% + +the way we are going to cure this + + align:start position:0% +the way we are going to cure this + + + align:start position:0% +the way we are going to cure this +we are going to demand that be if we + + align:start position:0% +we are going to demand that be if we + + + align:start position:0% +we are going to demand that be if we +want our our derivatives to be + + align:start position:0% +want our our derivatives to be + + + align:start position:0% +want our our derivatives to be +derivatives that + + align:start position:0% +derivatives that + + + align:start position:0% +derivatives that +comport with a notion of taking tensor + + align:start position:0% +comport with a notion of taking tensor + + + align:start position:0% +comport with a notion of taking tensor +objects and getting + + align:start position:0% +objects and getting + + + align:start position:0% +objects and getting +other tensor objects out of them before + + align:start position:0% +other tensor objects out of them before + + + align:start position:0% +other tensor objects out of them before +we take the derivative we have to have + + align:start position:0% +we take the derivative we have to have + + + align:start position:0% +we take the derivative we have to have +some way of transporting + + align:start position:0% +some way of transporting + + + align:start position:0% +some way of transporting +the objects to the same location in the + + align:start position:0% +the objects to the same location in the + + + align:start position:0% +the objects to the same location in the +manifold where i can + + align:start position:0% +manifold where i can + + + align:start position:0% +manifold where i can +then compare them + + align:start position:0% + + + + align:start position:0% + +so here's one + + align:start position:0% +so here's one + + + align:start position:0% +so here's one +example of a notion of transport that we + + align:start position:0% +example of a notion of transport that we + + + align:start position:0% +example of a notion of transport that we +could use + + align:start position:0% + + + + align:start position:0% + +so here's a at point q + + align:start position:0% +so here's a at point q + + + align:start position:0% +so here's a at point q +there's a at point p notion one that + + align:start position:0% +there's a at point p notion one that + + + align:start position:0% +there's a at point p notion one that +we'll talk about + + align:start position:0% +we'll talk about + + + align:start position:0% +we'll talk about +is known as parallel transport what + + align:start position:0% +is known as parallel transport what + + + align:start position:0% +is known as parallel transport what +that's essentially going to mean + + align:start position:0% +that's essentially going to mean + + + align:start position:0% +that's essentially going to mean +is i'm going to say well let's take one + + align:start position:0% +is i'm going to say well let's take one + + + align:start position:0% +is i'm going to say well let's take one +of these guys either q or p + + align:start position:0% +of these guys either q or p + + + align:start position:0% +of these guys either q or p +the way it's drawn in my notes i've used + + align:start position:0% +the way it's drawn in my notes i've used + + + align:start position:0% +the way it's drawn in my notes i've used +q but it could be either + + align:start position:0% +q but it could be either + + + align:start position:0% +q but it could be either +and let's imagine i sort of slide it + + align:start position:0% +and let's imagine i sort of slide it + + + align:start position:0% +and let's imagine i sort of slide it +parallel to itself + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +until + + align:start position:0% + + + + align:start position:0% + +this gives me a alpha + + align:start position:0% +this gives me a alpha + + + align:start position:0% +this gives me a alpha +from q transported to p + + align:start position:0% +from q transported to p + + + align:start position:0% +from q transported to p +and then i define a derivative with that + + align:start position:0% +and then i define a derivative with that + + + align:start position:0% +and then i define a derivative with that +transported notion of the vector + + align:start position:0% +transported notion of the vector + + + align:start position:0% +transported notion of the vector +now notice i've called this notion one + + align:start position:0% +now notice i've called this notion one + + + align:start position:0% +now notice i've called this notion one +you can take from that this idea of how + + align:start position:0% +you can take from that this idea of how + + + align:start position:0% +you can take from that this idea of how +i transport the vector from one place to + + align:start position:0% +i transport the vector from one place to + + + align:start position:0% +i transport the vector from one place to +the other to do this comparison + + align:start position:0% +the other to do this comparison + + + align:start position:0% +the other to do this comparison +i cannot uniquely define it okay there + + align:start position:0% +i cannot uniquely define it okay there + + + align:start position:0% +i cannot uniquely define it okay there +are in fact multiple ways we can do this + + align:start position:0% +are in fact multiple ways we can do this + + + align:start position:0% +are in fact multiple ways we can do this +we're going to talk about two + + align:start position:0% +we're going to talk about two + + + align:start position:0% +we're going to talk about two +that are useful uh at the level of eight + + align:start position:0% +that are useful uh at the level of eight + + + align:start position:0% +that are useful uh at the level of eight +962. + + align:start position:0% +962. + + + align:start position:0% +962. +uh in principle i imagine you could + + align:start position:0% +uh in principle i imagine you could + + + align:start position:0% +uh in principle i imagine you could +probably come up with you know a whole + + align:start position:0% +probably come up with you know a whole + + + align:start position:0% +probably come up with you know a whole +buttload of these things + + align:start position:0% +buttload of these things + + + align:start position:0% +buttload of these things +these are two that the physics picks out + + align:start position:0% +these are two that the physics picks out + + + align:start position:0% +these are two that the physics picks out +as being particularly useful for us + + align:start position:0% +as being particularly useful for us + + + align:start position:0% +as being particularly useful for us +for the analysis that we are going to do + + align:start position:0% +for the analysis that we are going to do + + + align:start position:0% +for the analysis that we are going to do +okay so we'll pick it up there on + + align:start position:0% +okay so we'll pick it up there on + + + align:start position:0% +okay so we'll pick it up there on +tuesday we're going to start by coming + + align:start position:0% +tuesday we're going to start by coming + + + align:start position:0% +tuesday we're going to start by coming +back to this notion of if i want to + + align:start position:0% +back to this notion of if i want to + + + align:start position:0% +back to this notion of if i want to +differentiate a vector field and a curve + + align:start position:0% +differentiate a vector field and a curve + + + align:start position:0% +differentiate a vector field and a curve +manifold + + align:start position:0% +manifold + + + align:start position:0% +manifold +and let me just state before before we + + align:start position:0% +and let me just state before before we + + + align:start position:0% +and let me just state before before we +conclude now that i've transported + + align:start position:0% +conclude now that i've transported + + + align:start position:0% +conclude now that i've transported +a from q to p they share the same + + align:start position:0% +a from q to p they share the same + + + align:start position:0% +a from q to p they share the same +tangent space + + align:start position:0% +tangent space + + + align:start position:0% +tangent space +since they share the same tangent space + + align:start position:0% +since they share the same tangent space + + + align:start position:0% +since they share the same tangent space +i can compare them more easily that + + align:start position:0% +i can compare them more easily that + + + align:start position:0% +i can compare them more easily that +allows me to make a sensible derivative + + align:start position:0% +allows me to make a sensible derivative + + + align:start position:0% +allows me to make a sensible derivative +that respects all the notions of what a + + align:start position:0% +that respects all the notions of what a + + + align:start position:0% +that respects all the notions of what a +tensor should be we'll pick it up from + + align:start position:0% +tensor should be we'll pick it up from + + + align:start position:0% +tensor should be we'll pick it up from +there on tuesday \ No newline at end of file diff --git a/h1dWUja7_5A.txt b/h1dWUja7_5A.txt new file mode 100644 index 0000000000000000000000000000000000000000..ee0e794d54bee3a2177743a266d12b22df2ee7b5 --- /dev/null +++ b/h1dWUja7_5A.txt @@ -0,0 +1,3066 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK, OK. + +Let's get started. + +Going to go right +into the lesson. + +Last day we started looking +at kinetics, which was the + +description of rate and + +mechanism of chemical reactions. + +We looked at the general rate +law, which shows us that the + +instant change in concentration +of species i + +goes as the instant +concentration. + +So rate is proportional +to concentration. + +And the order of reaction +is shown here as n and + +proportionality constant +is the rate constant k. + +So we saw that we can make the +rate of reaction increase by + +increasing the concentration +in the reactor. + +We saw there was a second way +to increase the rate of + +reaction, and that was to +raise the temperature. + +And this is the Arrhenius +relationship that shows that + +the rate constant changes with +temperature according to this + +exponential relationship. + +In the denominator, we have the +product of the Boltzmann + +constant and the absolute +temperature, which is a + +measure of the ambient thermal +energy that's available to + +promote reaction. + +And in the numerator we have a +barrier energy, which we call + +the activation energy. + +We'll say a little bit more +about that today. + +And the constant of +proportionality out here is A, + +which is in honor of Arrhenius, +who first + +annunciated the law. + +So what I want to do today is to +look at some common orders + +of reactions. + +So we're going to look at +the values of n that are + +encountered in not + +insignificant number of reactions. + +So let's start with +the simplest one. + +The simplest one +is first order. + +First order reactions. + +That means n equals 1 in this +rate law expression. + +And here's an example of +something that we could use. + +The decomposition of +N2O5 into NO2. + +And gives us half a +mole of oxygen. + +And we can write this rate law +in terms of the rate of + +disappearance of N2O5. + +So I can write minus +d by dt of-- + +I'm going to use square brackets +to indicate the + +concentration-- + +of N2O5. + +And this has been measured. + +You can't predict this from the + +stoichiometry of the equation. + +You have to measure this, and +on the basis of measurements + +it's found that the rate of +change of N2O5 goes as the + +concentration of N2O5. + +And there's a constant +out here. + +The rate constant. + +So just to make the point, I'm +going to put a 1 here. + +Meaning that n equals 1 and +that's why this is a + +first-order reaction. + +But this is messy. + +There's too many characters +here. + +So I'm going to compress this +and give myself a nicer font, + +so I'm going to let the +concentration of N2O5, just in + +this expression, just be c. + +Lowercase c. + +That way I can speed +this thing up. + +So I can rewrite this expression +here as minus dc by + +dt equals k times c. + +All right. + +And so we know what this +is going to look like. + +They all look like this. + +If we plot concentration versus +temperature we expect + +to have the maximum value +of this at time zero. + +So at time zero I +start off with-- + +if you want c-star or c max-- + +and you know, this +thing attenuates. + +But I can't look at that and +decide whether it's first + +order or not. + +The only thing the eye +can really tell + +is a straight line. + +So what I want to do is I want +to modify this thing. + +I want to map c into +some f of c. + +And I want to map t +into some g of t. + +So that if I plot f versus +g, I get a straight line. + +And then I can take one look at +that and go, bingo, this is + +first order. + +Or not. + +Or maybe it's first order and +the data are very noisy. + +So what we'll do is +we're going to + +integrate that equation. + +So I'm going to play with +this a little bit. + +So I'm going to transpose. + +I'll get minus dc over +c equals kdt. + +And then I can integrate this +because I know at time 0, t + +equals 0, c equals +some value-- + +I can call it c-star +or c naught-- + +and at any arbitrary time later, +I can go down that + +curve and put some value of time +and then I'll end up with + +some arbitrary value +of concentration c. + +And I know there's some math +people in the audience who are + +probably horrified that the +limits and the integrand are + +both the same. + +So I'll put a little tilde +here that way I + +don't go to math jail. + +So now I'm not integrating c. + +If I wanted to be a pedant and +really make the math instead + +of me enslaving the math, the +math enslaving me, watch this. + +What I could do is I +could make this a + +carrier variable, s. + +You know what I'm talking +about now, right? + +But let's get really crazy. + +This is how bad the +math can get. + +You can do this in +a chemistry book. + +Let's use some Greek. + +So I'll make this +d xi over xi. + +Now I've totally left the +class behind, but it's + +mathematically correct. + +What we will do is we'll +put the t back and put + +a tilde over it. + +And now everybody is happy, and +heaven forbid, the student + +might even understand +the lesson. + +All right. + +So we do that and +what do we get? + +The integral of dc over c +is a natural log of c. + +This'll be natural log of c +equals natural log of c + +naught minus kt. + +OK, so integrating this thing +gives us this expression. + +And that means if I plot the +natural log of c versus time I + +should get a straight line. + +And furthermore, the slope +is equal to minus k. + +So here's an example that's +taken from your book. + +It happens to be another +first-order reaction and it + +shows the decomposition +of cisplatin. + +This is a compound that's used +in certain cancer treatments. + +And you can cisplatin hydrolyzes +to form this + +monster cation plus +a chloride. + +And it turns out that the rate +of decomposition of cisplatin + +is first order. + +Will you look at that curve? + +That purple line? + +I don't know what that means. + +But watch. + +If I instead plot the natural +logarithm of the concentration + +of cisplatin as a function of +time, you get a nice straight + +line, and furthermore, +the value of k is + +obvious from the slope. + +So this is an indication of the +power of taking the proper + +order of reaction and +then using it in-- + +if you'll pardon the pun-- +straightening things out. + +And a couple other things +worth noting. + +I mentioned at the end of last +day, radioactive decay. + +Even though radioactive decay +is not a chemical reaction-- + +it has to do with nuclear +phenomena-- and we know + +chemistry is restricted to +the life and times of the + +electron, we don't go +into the nucleus. + +We simply know there's something +in there, there's + +neutrons, protons, and a whole +bunch of other particles. + +But chemistry is about +the life and + +times of the electron. + +Radioactive decay turns +out to be first order. + +It's good to know that +because then you can + +appreciate what goes on. + +So for example, you could +take something like the + +decomposition of uranium-238. + +One of its decompositions +gives you + +thorium-234 plus helium. + +And it turns out that this is +first order, which means that + +if you were to take a plot +of the natural log of the + +concentration of uranium +versus time, you get a + +straight line. + +And this slope would be the +k, the rate constant. + +But it turns out that the +nuclear chemists, nuclear + +engineers, prefer not to talk +about the rate of reaction in + +terms of k. + +But instead, they like to +use the inverse of k, + +which is the half-life. + +So instead, express k +through half-life. + +And the half-life, as the name +implies, is the time it takes + +to decrease the concentration +of the species by half. + +So if I start off here at c1 and +down here I have c2 equals + +1/2 c1, then this is the time +it takes to cut the + +concentration in half. + +So through half-life-- + +and we can go through this +equation here, just put c + +naught over 2 and do a little +bit of manipulation, you'll + +end up with the natural log +of 2 divided by the rate + +constant, which is 0.693 +divided by k. + +So you can see that there's +a direct relationship. + +It turns out that the half-life +for this reaction is + +4 1/2 billion years. + +4 1/2 billion years. + +So that means after 4 1/2 +billion years the + +concentration has gone down to +a half, but even then it's + +probably not safe for the +kids to go out and play. + +So you really need to think +about it in this way. + +So here it is shown +in your textbook. + +Concentration as a +function of time. + +They could have plotted it log +linear, then you would have + +ended up with this. + +But anyways, they're chemists, +so what can you expect. + +So here it is. + +Here it goes down to a half, and +then this is a half of a + +half as a quarter. + +It's the same time interval. + +And then half of a quarter is +an eighth, and it's the same + +time interval. + +So you get the sense. + +And the most important thing +is the half-life is + +independent of concentration. + +It doesn't matter what the +starting concentration is-- if + +you know what the half-life is, +you know how much time it + +takes to get to a half. + +And you know enough math. + +What if I said, well, what if I +didn't want to go to a half? + +What if I wanted to go to 10%? + +Well, you can figure out how +to modulate half-life into + +tenth-life. + +That's trivial. + +But the book, being a chemistry +book, will show you + +a table in which they give +half-life values for orders of + +reactions other than 1. + +And it's stupid because except +in the case of first order + +reactions, the value the +half-life is a function of the + +concentration. + +So what good is a constant +that's variable? + +I don't know, but I didn't +write the book. + +The only time I care about +half-life is in the case of a + +first order reaction, which +is when you have + +nuclear decay for sure. + +All right. + +So that's enough about +first order. + +Let's go look at second-order +reactions. + +So here's an example also +taken from the book. + +So second-order reaction, which +means that n equals 2 in + +the rate law expression. + +n equals 2 in the rate +law expression. + +And the example that +they gave was NO2. + +See, look. + +We went from N2O5 to NO2. + +And then we can keep the +decomposition going. + +NO2 goes to NO plus O2. + +And again, I'm going to let, in +this case, c will equal the + +concentration of NO2. + +And what you end up with in +this case is, if you go + +through the similar analysis, +you get minus dc by dt. + +It's been measured that the rate +of loss of NO2 goes as + +the square of its +concentration. + +So this is based on experimental +evidence. + +It's not because this is a 2. + +This is not. + +Please pay attention here. + +This 2 is not the consequences +of the stoichiometry. + +This 2 was determined +experimentally. + +I could have just written +this reaction NO2 goes + +to NO plus 1/2 O2. + +That doesn't make this +first order, does it? + +Experimentally in +the laboratory. + +All right. + +So now what we can do is we +can integrate this thing. + +And so we'll get minus the-- + +let's do it this way. + +Boards are cheap, so let's jump +down to the next one. + +So now I can then put minus +the integral of dc tilde-- + +cross multiply-- + +so dc tilde over c tilde +squared equals k, + +the integral dt tilde. + +And we can integrate this from +zero to some time, and this + +will go from c naught to +some concentration. + +And that will give us 1 +over c equals 1 over + +c naught plus kt. + +So this is now the new, improved +way of mapping c + +versus t into f of +c versus g of t. + +So f of c as 1 over c, which +means now if I plot 1 over c + +versus time, I'll get +a straight line. + +In this case, it's got +positive slope. + +It's got positive slope, +so that's what it's + +going to look like. + +And this is k. + +So if I take our data set and +I plot it like this, then I + +can make sense of it. + +And I think we've got +some data here. + +So here's the data from +this decomposition. + +And again, what do you see? + +A line that attenuates. + +Can you look at that line? + +Can you tell that line is second +order, whereas the + +other one that looks like +this was first order? + +Of course not. + +The only way you can tell +his to fit it into some + +linearizing function. + +So look at that. + +What they've done, that's +the least squares fit. + +They plugged it into a least +squares fitting equation. + +You can fit a straight line +through anything. + +It doesn't matter. + +But what's that mean? + +I don't know. + +So here's the log. + +This is really important-- + +look carefully. + +So somebody took these data and +then plotted them as the + +natural log, which is what you +do if it's first order. + +And look at what happens-- + +it gets a lot better but it's +still not a straight line. + +But if you were in a hurry, +you'd just say, force the fit. + +You'll get a straight line and +you'll assigned the value of k + +to it and party on. + +And it's wrong. + +So now let's try this. + +Beta. + +1 over c versus time. + +So what do we get from that? + +I get two things. + +First of all, the fact that +it's a straight line means + +that it confirms n equals 2 and +the slope of that line is + +the value of k. + +So in point of fact, what I've +been doing here is teaching + +you how to determine the +rate of reaction. + +So let's do it. + +Let's codify this. + +So determination of +order of reaction. + +So in other words, the way the +story goes is I give you a + +data set that looks +like this-- + +pardon me. + +I give you a data set that looks +like this and I say, + +determine the order +of reaction. + +So there's two general +ways to do this. + +The first one is called +the integral method. + +And that's what we've been +doing up until now. + +The integral method, it's called +the integral method + +because it's using the +integrated form + +of the radio question. + +See? + +This is the integrative form. + +This is the integrative form. + +Hence, the integral method, +and it's trial and error. + +That's what we did. + +Trial and error. + +But we don't say trial and error +because we're at MIT. + +So what do we say? + +We have a lofty way. + +What's the lofty way of saying +trial and error? + +By inspection. + +By inspection. + +Never tell anybody you do things +by trial and error. + +We don't do trial and error. + +By inspection. + +It's $50,000 a year. + +It's what you get. + +OK, so here's what I do. + +I'm impatient, so I +try n equals 1. + +If I get a straight line +on the log plot, good. + +If not, I try n equals 2. + +If I got a straight line +on 1 over c, good. + +If not, go to the second +way of determining. + +I give up. + +Won't waste my time. + +It's a two strikes and +you're out thing. + +So what's the second method? + +The second method is called +the differential method. + +The differential method. + +And this is fun because it's +data fitting and it gets into + +some nice detail. + +So what I want to do is +to define the rate. + +What's the rate? + +The rate is over here. + +Minus dc by dt, right? + +You see up in the top left +corner the rate law. + +Minus dc by dt. + +I'm going to call +that positive r. + +I'm just compress-- this +is like French cooking. + +I started with this. + +Look at all those fonts. + +Then I compressed it down +to c, and now I + +compressed it even more. + +It's just so much information +compressed in + +that little r there. + +Poor little r. + +All right. + +So now, let's rewrite the +rate law expression. + +So that's r equals +kc to the n. + +There's the rate law expression + +written very compact. + +And now I'm going to take the +logarithm of both sides. + +So taking the log of both sides, +I can write natural log + +of r, the log of a product +is the sum of the log. + +So that's going to be natural +log of k plus the + +log of, da, da, da. + +n log c. + +n log c. + +And I don't care what kind +of logarithms you use. + +You can make this log base c. + +You can make it log base 10. + +If you're feeling like you +want solidarity with the + +Mayans, you can make +it log base 5. + +I don't care. + +But make them the same. + +Make them the same. + +And then what happens? + +Well, let me show you. + +So let's say we've got our data, +start off with this data + +set like so. + +So this is concentration +versus time and + +we end up with this. + +It comes down, down, +down, attenuates. + +Remember, what are we +trying to do here? + +We're trying to take this data +set and figure out, what is + +the value of n? + +We're trying to determine n. + +So what this thing says is. + +if I make a plot of r versus c +so that it's on a log scale, + +so if I plot log r versus log c, +the slope is going to be n. + +So how do I take c versus +t and construct log + +r verses log c? + +That's what we're going to do. + +So here we are and I can start +here that at time zero. + +This is time zero. + +That's the slope, right? + +The slope here is the rate. + +So slope, I'm going to +call it r naught. + +Because that's the time-- + +it's dc by dt r naught +at t equals t naught. + +But there's no t on here. + +So what am I going to put? + +It's when t equals t naught +and c equals c naught. + +So now I'm going to take some +colored chalk and we're going + +to show you how to +construct this. + +So I've got the slope by taking +minus dc by dt here. + +So I'm going to take this value, +r naught, and this + +value, c naught-- + +I want to gang them together, +I'll bring over here and put + +them right out here-- so +now I've got r naught. + +Well, actually I should put the +abscissa first. So this is + +going to be c naught r naught. + +And now let's do it again. + +So we'll come down here +to some later time. + +Let's call this t1. + +And at t1 the concentration has +fallen to c1, and I take + +the slope of this. + +Why am I taking the slope? + +Because it's dc by dt. + +That's what the rate is. + +So here now I've got slope +r1 at c equals c1. + +r versus c. + +Forget time. + +Time doesn't belong here. + +So take those. + +It's a lower concentration, +so it's kind of + +like a lower energy. + +So we'll take a lower +wavelength here. + +So r1 and c1 come over here. + +c1, r1. + +We'll do one more. + +Three's a charm. + +Come up to here. + +This is t2. + +Concentration has fallen to +c2, and I've got a slope. + +You see how the slope is getting +less and less steep? + +Because the rate loss says +the concentration + +falls, the rate falls. + +So this is slope r2 +at c equals c2. + +That's lower energy. + +So I'll get the orange. + +Or maybe this is fuchsia. + +So we'll take this one. + +And this will put these +two together and bring + +them in like so. + +And this is now c2, r2. too +And what's this thing say? + +Take the slope. + +Look, it's a log, log plot. + +If you've got physical data and +you don't get a straight + +line on a log, log plot, +you're incompetent. + +You're a complete idiot. + +All right? + +There it is. + +And the slope here is n. + +And where it intersection, +obviously I can't get a + +negative number, so just allow +me to fix this just a wee bit. + +So there's the axis, and where +it hits the axis, this is now + +log k isn't it? + +So I determine the order +of reaction. + +Good. + +So now you know how to do it and +you'll get some practice + +if you work the homework. + +All right. + +A couple more things to say +and then we're done. + +So last thing, we talked about +increasing the rate of + +reaction by increasing the +temperature and increasing the + +concentration. + +There's one more thing +we can do. + +And what we can do is use a +catalyst. Increase rate by use + +of + +catalyst. OK. + +How does the catalyst work? + +How does the catalyst work? + +Well, let's go back to +this diagram here. + +Where we've got, this is called +the extent of reaction. + +Some kind of reaction +coordinate. + +And over here we had some kind +of energy coordinate. + +We had this energy coordinate. + +Remember, we had this thing? + +This silly thing here? + +So this is the reactions. + +And this is the product. + +And we reasoned that the +activation energy ea is + +sitting here. + +And we saw with the box, you had +to get a box up onto its + +ear, otherwise it wouldn't +fall over and so on. + +And there's a finite amount, +finite fraction of the + +Maxwell-Boltzmann +distribution. + +So if we plot energy and the +number of particles in the + +distribution have of given +energy, we get something that + +looks like this. + +Tails off. + +And we said that out +here we have the + +fracture under this line. + +This is the fraction that has +the energy to jump over the + +activation barrier. + +So fa is the-- + +f is the activated, is the +fraction activated. + +And those are the only +ones that can + +participate in the reaction. + +These other ones can't surmount + +the activation barrier. + +Now, what the catalyst +does is it lowers + +the activation barrier. + +Catalyst lowers the activation +barrier. + +It doesn't change +the n points. + +The n points represent the +energy state of the reactants + +and the energy state +of the products. + +What the catalyst does +is it finds a + +low-energy barrier pathway. + +A low-energy barrier pathway, +which on this curve would mean + +that if this energy is lower, +then the fraction of any + +distribution that has the +requisite amount of energy is + +much higher. + +Can you see the area? + +The blue area is much, much +greater than the white area. + +So that means that this +fa catalyzed-- + +I'm just going to +write cat here-- + +fa catalyzed is much greater +than fa in the absence of a + +catalyst. And that promotes. + +What's an example of it? + +Well, in an automobile +catalyst one of their + +reactions we're trying to +promote is unburned + +hydrocarbons. + +There's some unburned gasoline +that comes out in the form of + +carbon monoxide. + +What we want to do is +convert the carbon + +monoxide to carbon dioxide. + +And this occurs on the catalyst +and I'll show you + +more of this at the end +of the lecture. + +But these are both gas molecules +and they're zooming + +through space. + +And if they're going to react +with one another, they really + +need to somehow move almost on +parallel lines so they get + +close enough to each other for +a long enough period of time + +that they can start thinking +about lower energy state. + +And say, well, gee, if we break +this bond and form a new + +bond, it's going to go to-- + +you've got to get to know each +other, go have a few drinks, + +and da, da, da. + +So it's not happening. + +In the gas phase it +doesn't happen. + +So what we do instead is +we provide a service. + +This is the catalyst. The +catalyst is a solid surface + +and the CO sits down +next to another CO. + +They sit down and now they're +in place long enough in the + +right orientation to then form +CO2 and then desorb. + +So this is how the +catalyst assists. + +We call this-- especially, +imagine if + +it's the other way-- + +what if this carbon monoxide +molecule is turn around so + +that the two carbons +are side by side. + +That's not going to promote the +reaction at all because + +this thing's got to whip +around and so on. + +This is a. + +Bad orientation + +And what's the Greek idea +for orientation? + +It's stereos. + +That's what stereophonic +sound is. + +If I close my eyes, +the two speakers + +give me spatial rendition. + +So this concept here, where +things are backwards and + +they're not the right place. + +It's called steric hindrance. + +This is steric hindrance. + +One of the functions of a +catalyst is to combat steric + +hindrance and put things +in their most favorable + +orientation to facilitate +reaction. + +So what are characteristics +of the catalyst? + +The catalyst needs to have the +following characteristics-- + +first of all, it has to have an +affinity for the reactants. + +In this case, the CO. + +It has to have an affinity +for carbon monoxide. + +Affinity for reactants, so +they'll be attracted to the + +catalyst. + +But there's a second +piece here. + +If the catalyst doesn't get rid +of the CO2, can you see + +that after a very short period +of time, the surface of the + +catalyst will be covered with +carbon dioxide and then the + +reaction starves. + +It's choked. + +So it has to have a disaffinity +for the products. + +Disaffinity for the products. + +And in the real world, such as +in the gas exhaust stream of a + +car, it's not just +carbon monoxide. + +There's all kinds of other stuff +going on in there, and + +so the third thing that the +catalyst needs to have is + +selectivity. + +So it doesn't get distracted +by other reactions. + +And selectivity, most important +when you have a + +mixture of all sorts +of other species. + +So that's what the +catalyst does. + +Now there's one more thing. + +Just one second. + +Perfect. + +Gotcha just in time. + +So one more thing here. + +One more thing. + +We've shown what happens +when you catalyze. + +So I'm going to put this. + +This is ea under the influence +of catalysis. + +OK. + +This is the e of the catalyst. + +There are other substances that +can retard the reaction. + +These are called inhibitors. + +And what's an inhibitor do? + +It does the complimentary +action. + +So it raises the activation +barrier. + +So this is ea under the +influence of inhibitor. + +And what's the value of that? + +Well, if you buy some antifreeze +for use in the + +automobile cooling system. + +If you read carefully the label, +it's not just ethylene + +glycol, and water, 50/50 +volume percent. + +There are other additives. + +What are those additives? + +Some of them are called +inhibitors. + +Oh, I didn't spell this right. + +No wonder you looked +so puzzled. + +I thought you didn't understand +the concept. + +Inhibitor. + +So it inhibits the reaction. + +What's going on? + +You've got the iron or aluminum +block of the engine, + +you got the water pump. + +It's taking heat away from the +engine, you're heating + +everything up, stirring +it around. + +It's a perfect environment +for enhancing corrosion. + +And we don't want the cooling +system to act as the corrosion + +system for the engine. + +And so we add components to the +antifreeze too reduce the + +rate of corrosion, to +lengthen the service + +lifetime of the vehicle. + +And so what does the +inhibitor do? + +It raises the activation barrier +for the corrosion + +reaction and thereby reduces +its rate of reaction + +substantially. + +So this is inhibited. + +OK, so this is catalyzed, this +is inhibited, and you can see + +that the fraction of active +species over the activation + +barrier, under the influence +of inhibition, is much less + +than the fraction otherwise. + +There's a time and a place for +all of these wonderful things. + +So that's the story +of kinetics. + +That's the story of kinetics, +but it's 11:35 and it's time + +to start a new topic. + +And now, we can erase. + +Thanks. + +OK. + +So let's talk about +something else. + +Let's talk about +something else. + +What I want to talk about today +is another topic that + +comes from the general area +of rate phenomena. + +I want to talk about something +else in rate phenomena. + +We're going to talk +about diffusion. + +And that's from the general +class of rate phenomena. + +That's why it appears with +chemical kinetics. + +And what do I mean by +rate phenomena? + +Rate phenomena means d +by dt is in the room. + +All right? + +We're looking at time, +domain processes. + +You know, chemistry, before you +came into this class, you + +probably thought, I know +what chemistry is. + +Chemistry is chemicals +reacting. + +That's what people think. + +Isn't that what the ancient +Egyptians said? + +khemia That's where the guys +knew how to embalm + +the dead and so on. + +It was about chemical +reactions. + +We've been talking about +structure, properties, all + +sorts of things. + +Well, now we're talking about +rates of reaction. + +If we want to run a reaction, +there's two things that we + +need to move around to +sustain a reaction. + +So transport of two important +quantities. + +One is matter and the +other is energy. + +We star something for energy. + +As we just saw, the +thing doesn't go. + +And if we starve it for +matter it doesn't go. + +So energy in motion is +under the general + +rubric of heat transfer. + +But we won't talk about heat +transfer because we've only + +got 14 weeks. + +I'd love to talk about it, +but we're out of time. + +So instead, we will talk +about mass transport. + +And mass transport in solids +occurs by diffusion. + +And we know what's critical. + +For example, we know in the case +of the Hindenburg, the + +Hindenburg didn't explode. + +Why didn't the Hindenburg +explode? + +Because there were 7 million +cubic feet of hydrogen, but we + +couldn't get 7 million cubic +feet of oxygen to the site. + +Because of the limitations of +mass transport, 2/3 of the + +people walked off +of that vessel. + +It was on fire, and many of +them died because they + +panicked and they jumped +to their deaths. + +Very few people were actually +affected by the fire. + +So it's a good example of mass +transport, negating the rate + +of what otherwise could have +been an explosive reaction. + +So I'm going to look at a +simple example today. + +And what I want to do is +look at the doping of + +semiconductors. + +You know, we've studied +semiconductors. + +Dave, could we cut to the +document camera, please? + +So what I've got here +is I'm going to show + +you a silicon wafer. + +And the silicon wafer has +got some features on it. + +So it's already been doped. + +Oh, that's pretty, isn't it? + +So cute. + +All right. + +So what we've got here, remember +this is the 8-inch + +diameter single crystal. + +So this was cut from a single +piece of silicon 8 inches in + +diameter, about 2 meters long. + +How did they make a +single crystal? + +They immersed the tiny single +crystal into the melt and + +gradually pulled the +single crystal out. + +Sort of the way you can grow +rock mountain candy. + +And if you're really careful, +the entire giant, 2 meter + +length, 8 inches in diameter, +is one single crystal. + +And then we take this and we cut +it with a diamond saw into + +wafers, Each of them about a +millimeter in thickness. + +And, of course, the width of +the saw turns into dust So + +your yield [SNAPS] + +right off the bat +is about 50%. + +Because [SAW SOUND] + +it's all gone. + +[SAW SOUND] + +it's all gone. + +And now what we're going to +do, is we want to dope it. + +So how do I get the +boron in here? + +We say, why don't we add the +boron to the melt, but what if + +I want to make pn-junctions? + +So I want to get some boron +and some phosphorous. + +If I add the boron and +the phosphorous, + +it then goes nuts. + +I need to have p-type +against n-type. + +So how do I get it in here? + +That's we're going +to talk about. + +We're going to talk about how +we make those features. + +See those features? + +Because if you're really good, +you start with those features + +and you cut them up and +then you end up with + +this, which is this. + +This is a Pentium chip. + +The amount of material science, +physical chemistry in + +that device is absolutely +phenomenal. + +What lies underneath this piece +of gold is absolutely + +phenomenal. + +It's what powers the +information age. + +And it all starts with +this stuff here. + +It's that simple. + +So how do we get the boron in? + +Dave, let's leave this up. + +It's a pretty image. + +It might soothe the natives, +so let's just leave it up. + +By the way, that spider network +is all the gold wires + +that are addressing. + +It doesn't do you any good to +have a gazillion features + +there but you can't get +information in and out. + +So if you've got a gazillion +features, you need a gazillion + +leads to take information +in and out. + +That's very, very thin gold. + +How do you do that? + +Not with a paint brush. + +It's all with this stuff. + +That's why I teach you +this instead some + +of the other stuff. + +OK. + +So now we're going to dope. + +We're going to dope the +silicon with boron. + +Number one point to remember-- +we're going to dope the + +silicon in the solid state. + +We do not add boron +to molten silicon. + +We're going to add boron +to the silicon + +in the solid state. + +So I'm going to draw +this wafer. + +Only it's not to scale. + +It's going to look more like a +hockey puck than a thin wafer. + +Anyways, imagine it's this. + +OK? + +So this is the silicon wafer, +the silicon wafer on edge. + +And this is where all +the features were + +that I showed you. + +So we're going to do is +we're going to try + +to introduce boron. + +We want to get boron into the +silicon, we're going to bring + +it in from the surface. + +So this is a silicon +wafer, which means + +it's a single crystal. + +It's a single crystal. + +And we could use Laue methods +to figure out + +which is the face. + +Is that cut on the 0 1 1? + +Is it cut on a 1 1 1? + +And so on. + +So now we're going to +dope with boron. + +How do we do it? + +We decompose diborane. + +We introduce diborane, +it's a gas. + +B2H6. + +And we flow diborane over the +surface at some constant + +concentration. + +And what happens is that the +diborane decomposes. + +B2H6 on silicon. + +And I'm going to write +silicon with an x. + +What's the x mean? + +Crystalline. + +Single crystal. + +Make sure no one is thinking +this is being performed in the + +liquid phase. + +And this diborane decomposes +to elemental boron plus + +hydrogen gas. + +So hydrogen is a gas, and the +boron goes into the silicon. + +Boron goes into the silicon +where it goes on to the + +silicon sites. + +I could just write a rate +constant for this. + +We just studied kinetics. + +I don't know. + +What is it? + +Second order? + +You know, it doesn't have to be +integral order, by the way. + +It could be of order 1.5. + +Nothing is saying it has +to be integral order. + +OK. + +So now what I want to do is I +want to ask, what happens as + +the boron goes in? + +So that's the next question. + +As it diffuses in. + +So what I'm going to do is I'm +going to draw this little + +cartoon here. + +So I want to look at here's the +surface of the silicon. + +So I've got a gas phase here and +I've got boron going into + +the silicon crystal. + +So I'm going to now get a little +bit quantitative, if + +you'll permit. + +And so it's going to +look like this. + +And put it right underneath +here. + +So this is x. this +is depth from the + +surface of the silicon. + +So this is the free surface +of the silicon. + +And I start off with some +concentration surface + +value, c sub s. + +Meaning concentration +at the surface. + +And that's fixed. + +So cs fixed by B2H6 + +concentration in the gas phase. + +So that's fixed. + +Now, question is, what +does it look like? + +The advance of the boron? + +So this is now the + +concentration of boron in silicon. + +This is the silicon +crystal here. + +So what does it look like? + +Well, one possibility is it goes +in like this as a front. + +See if I wait, goes in farther +and farther and farther. + +That doesn't happen. + +Sorry. + +Take that off. + +You know what happens? + +Same thing we've been +looking at all day. + +So now what's the question? + +Question is, what's the +functionality of this? + +Is this 1 over c? + +Is this log c? + +Is this some other +function of c? + +I want to map this into some f +of c versus g of x so I can + +get a straight line. + +Why do I want a straight line? + +Because I want to +be quantitative. + +Because you are in charge of +designing a fab line and they + +want to know what the resonance +time of a silicon + +wafer is supposed to be at +billion dollars multiples. + +You know, the units are in +billions of dollars. + +So you don't want to make the +fab line any bigger than it + +needs to be, the resident's +time any longer. + +This is only way you're going +to be able to design it. + +You have to understand this +because the design + +specification is going to +be dope to a certain + +concentration of a +certain depth. + +So how long does it take +to get boron in? + +You can tell me. + +Set the concentration here +and wait 5 minutes, + +10 minutes, 30 minutes. + +Two companies. + +One takes 30 minutes to process +the wafer, the other + +takes 10 minutes to +process the wafer. + +Guess which company is going +to be in business + +two years from now? + +It's not going to be the one +that takes a long time. + +Hint. + +So we need to know what +the rules are here. + +And the mathematical +formulation was + +set by Adolf Fick. + +Adolf Fick, 1855, answered +the question, what is the + +form of that line? + +He's an interesting guy. + +He was at the University +of Zurich. + +And it's sort of like +the Balmer story. + +Remember J.J. + +Balmer was the school teacher +in Switzerland. + +This guy was in Switzerland, +too. + +Something going on there in +Switzerland in the late + +eighteen hundreds. + +So remember J.J. + +Balmer? + +He fit not his own data, he +fit the data of Angstrom. + +Angstrom made the measurements, + +Balmer fit the data. + +Well, same thing here. + +Fick did not make the +measurements. + +He looked at some data that had +been taken back in 1833 by + +Thomas Graham. + +Thomas Graham had been making +measurements back in the 1830s + +of gases diffusing through +porous membranes. + +Or just say, through +membranes. + +Obviously, if they +weren't porous + +they wouldn't be diffusing. + +Redundancy. + +Department of Redundancy. + +This is diffusing through +membranes. + +So what happened was +that he modeled it. + +And here's what he +came up with. + +He came up with-- + +oh, by the way. + +I didn't mention what he was. + +He was a physiologist. He +was a medical doctor. + +He just poured through the +scientific literature for + +amusement, evidently. + +OK. + +So this is what Fick gave us +as the model for the data. + +He gave us what we know as +Fick's First Law, Fick's First + +Law of Diffusion. + +And we'll just call it FFL, +Fick's First Law of Diffusion. + +And we'll write Ficks' +First Law J. + +J, which is the flux. + +This is the unit of measure of +mass transport, the flux, + +which obviously is the +mass flow rate. + +We said this is mass transport, +so this is the mass + +flow right of species i, OK? + +And we're going to say in the +x-direction because things + +diffuse in all directions, +right? + +If I open a perfume bottle here, +the diffusion will take + +place in all directions. + +So I'm going to make +this one dimension. + +So the flux is a mass flow rate +of i in the x-direction. + +J sub i in the x-direction. + +Remember we said the +Chemical Rate Law? + +We said the Chemical Rate Law +was that the rate of progress + +of a chemical reaction goes +as the concentration. + +Well, Fick studied Graham's +data and he said, the flux + +doesn't go as the +concentration. + +It goes as the gradient +in the concentration. + +That's how you linearize +those data. + +So you take the concentration +gradient, which is dc by dx. + +OK. + +So that's the concentration +gradient. + +Gradient in concentration +of i in the x-direction. + +You could write this as-- + +make this vector-- + +but we're not going +to do that. + +It would make it one-dimensional +here. + +And the constant of +proportionality is d sub i, + +which is called the diffusivity +or the diffusion + +coefficient. + +And puts the minus sign. + +Why? + +Well, you know things move from +high concentration to low + +concentration, right? + +So I open the perfume bottle, +the odor gets-- + +the odor, pardon me-- the +fragrance gets stronger as you + +get closer to the bottle. + +Things move from high +concentration the low + +concentration. + +So if I gave you this +concentration profile-- + +what's profile mean? + +Profile means-- + +this is a concentration +profile-- + +if I draw someone like this, +this is head on, right? + +And if I do the right view like + +this, this is the profile. + +Profile. + +Side view. + +This is profile. + +Concentration profile, +obviously, the concentration + +is higher to the left. + +So things are moving +from left to right. + +But look at the slope. + +The slope is a negative +number. + +So if the slope is a negative +number, but I want to get a + +positive flux, I need to have +the minus sign in here. + +Diffusivity is a physical +constant. + +It has to be a positive +number. + +So this is Fick's First Law. + +I'll just give you the units +and then we'll stop. + +So what are the units? + +Well, the units in flux are in +SI units kilograms per second. + +And we're going in one +direction, and so as we're + +trying to diffuse into this +piece of silicon, we have to + +normalize it per unit area. + +So it's kilograms per meter +squared per second. + +You know that concentration is +kilograms per cubic meter. + +d by dx is 1 over meter, which +means then that the diffuse + +coefficient or the diffusivity +has units of length squared + +per unit time. + +This is the units of the +diffusion coefficient. + +And we'll get back to +business next day. + +David, may we cut to the +slides again, please? + +OK. + +So I talked to you about-- + +oh, yeah. + +There's all this. + +You see they give +you a half-life? + +Crazy. + +Forget it. + +OK. + +There's the book talking about +activated catalog, da, da, da. + +This is Fick's First Law. + +This is the paper from 1855. + +Go ahead. "On the Influence of +Diffusion" by Dr. Adolph Fick. + +So the number one catalyst +in the world, number one + +application is automotive +catalysts for exhaust. So + +gasoline is octane. + +C8H18, which we burn in air. + +We burn it in air, we +make hydrocarbons. + +Pardon me, we burn hydrocarbons, +which obviously + +means the carbon goes to +CO2, ideally, and the + +hydrogen goes to H2O. + +But sometimes you get incomplete +combustion. + +I already showed you that. + +Maybe we stop it CO. + +But remember, air +is 4/5 nitrogen. + +So when you burn hydrocarbons +you also, at these high + +temperatures, mix nitrogen +and oxygen and make NOx. + +And is was actually the +precursor to smog. + +So what we want to do is to +eliminate these imperfect + +combustions. + +So we want to convert the +unburned hydrocarbons. + +There's actually some of the CH +compounds, volatile, then + +don't get burned. + +We want to burn those +to H2O in water-- + +pardon me, H2O in CO2. + +The unburned CO has +to go to CO2. + +You might say, but isn't +CO2 a greenhouse gas? + +Yeah, it is. + +But you know, given the choice +of carbon monoxide and carbon + +dioxide, my advice is go +with carbon dioxide. + +Carbon monoxide will +kill you at about + +200 parts per million. + +And then NOx, we +want to convert + +that to carbon dioxide. + +So GM alone tried over +1,500 catalysts. + +Why GM? + +Why not the auto industry? + +Because the U.S. Government, +in its wisdom back in the + +1970s, invoked the Sherman +Antitrust Act and forbid the + +automobile industry to +collaborate in the search for + +a catalyst. And since they +didn't understand the science + +of catalysis it was +trial and error. + +By inspection. + +And it's a huge space, +trying things. + +But they eventually found, +after 1,500 tests, + +platinum-palladium works for +hydrocarbons and CO, and + +rhodium works for NOx. + +It's almost as though mother +nature said, I'll give you a + +catalyst and it's going to be +the most expensive part of the + +Periodic Table. + +You buy this stuff at the +jewelry store, you see. + +Furthermore, this is an +oxidation reaction. + +This is an oxidation reaction. + +This is a reduction reaction. + +So if I told you I want you in +the same place at the same + +time on a vehicle moving 80 +miles an hour to conduct + +simultaneous oxidation and +reduction reactions with no + +intervention, you'd +say impossible. + +They did it. + +They did it. + +This is the power of selectivity +of the catalyst. + +So this is an old diagram +from GM literature. + +Now we have fuel injectors, +here, but fuel goes into the + +engine, out to the exhaust. +There's an oxygen sensor, + +which I'll show you next day. + +Oxygen sensor measures what +composition of the output gas + +is, sends it to an electronic +control module, which then + +goes back into the carburetor. + +And the catalytic convert +is right here. + +And Dave, if you show +the document camera. + +This is the monolith. + +This is a piece of ceramic +because platinum and rhodium + +and all of these other elements +are so expensive. + +See, this thing's having +a hard time. + +So we'll cheat a little bit. + +We'll put this here and +then it'll focus. + +All right. + +So what you're looking at, +these are long channels. + +And just to give you a scale, +this is about a half of a + +millimeter. + +This is about a half a +millimeter square and they go + +all the way down for a length +of about eight inches. + +And then the walls, the interior +walls, are coated + +with a very, very thin +layer of platinum, + +palladium, and rhodium. + +Because these are expensive +metals. + +And it's a surface effect. + +So you get no value if you have +an inch deep of platinum. + +The only stuff that works +is the free surface. + +What you'd really like +is a monolayer. + +But a monolayer of platinum has +no mechanical strength. + +So you put the platinum, +palladium, and rhodium down on + +a catalyst support. and this +stuff is made of a ceramic, + +it's magnesia, alumina silica +that's been extruded like + +pasta, and then fired. + +The technology is absolutely +phenomenal. + +Goes into this. + +And then to get the +platinum-palladium-rhodium + +they have a very +thin acid wash. + +chloroplatinic, chlororhodic +acid, wash, little bit of + +surface tension, holds just a +little bit of water, fire, out + +comes the metal. + +Just thick enough. + +If it's too thick, dilute the +concentration of the acid. + +But use that precious +metal sparingly. + +Platinum hit $2,000 an +ounce last year. + +$2,000 an ounce. + +You steal a car, throw +the car away, and get + +the catalytic converter. + +So anyway, that's underneath. + +That's what's going on +underneath the car. + +And actually, I'm holding for +you the elements of clean air, + +the catalytic converter. + +But the catalytic converter +can't work unless we control + +the air to fuel ratio, +which we have to do + +with an oxygen sensor. + +I'll show you next day. + +And you've got to feed +it into a CPU. + +If you don't have a CPU, it +can't make rapid feedback to + +keep adjusting the air-to-fuel +ratio. + +All right, Dave. Let's +cut to slides and + +we'll get out of here. + +So I'll show you what +else is in here. + +OK, there's that. + +So there's the old thing. + +There's the engine, +da, da, da. + +Exhaust, the control module. + +And look, in the old days +they actually had-- + +they look like little +ball bearings-- + +cost of these things +was phenomenal. + +So last thing, we had to +go to unleaded gas. + +Unleaded gas was brought in +because the lead would be + +broken down into elemental lead +because lead is volatile + +as an oxide. + +The lead alloys with +the platinum. + +Turns it into a lead +platinum alloy. + +Lead has no catalytic value. + +Because if it did, we would +use lead and not platinum. + +OK. + +We'll see you on Friday. \ No newline at end of file diff --git a/jsoD3oZAAXI.txt b/jsoD3oZAAXI.txt new file mode 100644 index 0000000000000000000000000000000000000000..818a55c31c96568e497bc8f1e2b8086a6d6ac6bb --- /dev/null +++ b/jsoD3oZAAXI.txt @@ -0,0 +1,1636 @@ +The following content is +provided under a creative + +commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu + +PROFESSOR NELSON: So, over the +last few lectures we've worked + +and struggled so formulate the +second and third laws of + +thermodynamics in addition +to the first. + +Last time we reach the third law +which is telling us that + +we can't quite get to zero +degrees Kelvin, but that as + +the temperature approaches +zero degrees Kelvin, the + +absolute entropy of a pure +substance in perfect + +crystalline form is zero. + +And what that corresponds to, +if you recall, is the idea + +that in a perfect crystal at +zero degrees Kelvin then you + +have no disorder at all. + +You have a perfectly +ordered system. + +And in that case, the entropy +is absolutely zero. + +And the bigger lesson from that +is that entropy, unlike + +energy u or enthalpy H, we could +define an absolutely + +number for it. + +The zero of it wasn't +arbitrary. + +Unlike the case for energy like +you've seen in lots and + +lots of disciplines, where you +can arbitrarily set the zero + +in a way that makes it +convenient for you. + +Entropy really is +not like that. + +There is an absolute zero of +entropy, and that's really + +what we learn. + +So now, now that we've got all +three of the major laws of + +thermodynamics, what I want to +start in on is a discussion of + +what happens spontaneously. + +We've seen that in just one +specialized case so far, but + +we should in a more general way +be able to tell when is a + +system at equilibrium, where +there's no net change taking + +place, and when is it still +undergoing spontaneous change + +towards some other state, +presumably toward an + +equilibrium state. + +How do we tell? + +So that's the topic that I'd +like to address today. + +So, that's the big +question, right? + +So let's say that we've got +our stuff in some state. + +A, whatever it is. + +And there's some other +possible state, + +B, whatever it is. + +And maybe if it some +well-defined + +temperature and pressure. + +What do we do to tell whether +that change will happen + +spontaneously? + +Do we calculate, you know, delta +S, delta u, delta H? + +What tells us whether or +not the change happens? + +Certainly in principle we know +how to calculate this and + +other stuff for a change in +state of this sort, for lots + +of changes of state. + +But calculating it alone doesn't +necessarily tell us + +whether or not it will just +happened of its own accord. + +And that's the issue that we'd +like to be able to address. + +Now, we have addressed +this in some cases. + +So, for example, we know that +if we take, you know, gas A + +and gas B with a barrier between +them, and we remove + +the barrier, they're +going to mix. + +And we saw that and went through +it somewhat carefully + +and saw that if the system is +isolated, for that case we do + +have a criterion that tells +us whether change happens + +spontaneously. + +Namely, it's delta S is +greater than zero. + +That tells us whether the +change is spontaneous. + +And we saw that in fact in this +case delta S of mixing, + +we calculated it, saw +that it is positive. + +So, clearly, if we remove this +barrier mixing takes place, + +and obviously you know that +that happens from lots of + +experience. + +In general, the second law +gave us the Clausius + +inequality for spontaneous +change. + +Namely dS is greater than dq +over T. I suppose we could + +specify the surroundings +temperature. + +We saw that in general dS is +greater than or equal to dq + +over T. if it's a reversible +process then the equality + +holds, but if it's irreversible, +which means it + +happens spontaneously, then +dS is greater than this. + +Just to illustrate the kind of +issues that we're up against + +here, let me just consider +a few different chemical + +reactions, all of which +happen spontaneously. + +So, I just want to write a few +examples down with a few + +values for delta u or delta H or +delta S, and see whether we + +can get any clues from +what we see. + +So here are some spontaneous +chemical changes. + +Here's one. + +If we take hydrogen peroxide +in the liquid state, it can + +break down to form +water and oxygen. + +If we look at the thermodynamic +quantities, the + +enthalpy and the entropy of the +reaction, what we find is + +delta H is minus 209 kiloJoules +and delta S is plus + +132 joules per Kelvin. + +So it seems like there's a +favorable change in entropy + +going this way. + +That is, you've got lower energy +on the right and also + +higher entropy. + +Higher entropy basically +because you're forming + +molecules of gas where there +weren't any before, and + +there's more disorder in the gas +phase than in the liquid. + +That is, the gas phase +molecules have + +more freedom to roam. + +Okay, that's one example. + +Here's another. + +Let's just take hydrogen and +nitrogen in the gas phase and + +form ammonia. + +Well, here we get, we find that +delta H is negative 92 + +kiloJoules. + +Delta S is negative 198 +joules per Kelvin. + +This one also happens +spontaneously. + +One thing that makes it pretty +clear is that certainly delta + +S or the sign of +it alone is not + +dictating the outcome here. + +All right, here's +a third example. + +Let's take salt, solid, and +dissolve it in a bunch of + +liquid water. + +Hopefully you've got experience +saying that this + +happens, of course it does. + +If we measure the +thermodynamics, we discover + +that delta H is 4 kiloJoules, +plus 4 kiloJoules. + +Delta S is 45 joules +per Kelvin. + +So now we have a different sign +for delta H and it still + +happens spontaneously. + +So clearly, we've got signs and +magnitudes of delta H and + +delta S, and if we wanted to +put delta u there, similar + +things would happen. + +They're all over the map. + +And yet, these things are all +spontaneous processes. + +And I didn't specify the +conditions, but if we were to + +do this under ordinary chemical +conditions of some, + +you'd say room temperature and +pressure, right, they all + +happen spontaneously. + +OK, clearly we'd be much better +off if we had some + +systematic quantitative way to +tell whether something would + +happen spontaneously. + +In other words, we need criteria +for equilibrium under + +more general conditions than the +ones that we've dealt with + +so far, than the one set of +conditions that we've dealt + +with so far, which is +isolated system. + +Most chemical changes, most +physical changes don't happen + +in isolated systems. + +So let's start by writing down +our definition of equilibrium. + +It's very simple. + +The equilibrium state is the +one, and it's just one, in + +which there are no spontaneous +changes that can take place to + +any other state. + +Now that's under whatever +constraints there are. + +There's a box around it. + +The temperature or +the pressure are + +fixed, what have you. + +But the point is, no spontaneous +changes can occur + +to any other state. + +So for example, when we remove +the barrier and the gases mix, + +you know it's over. + +Once the gases are mixed, +there's not going to be any + +further net change +in the system. + +It's at equilibrium, under the +new condition, that is with + +the barrier removed. + +OK, so now let's try to +formulate how to describe the + +equilibrium state and what +dictates spontaneity. + +So what we're going to +do is consider the + +first and second laws. + +So our first law, du +is dq plus dw. + +And our second law, dS is +greater than dq over the + +temperature of surroundings +for a change that happens + +spontaneously. + +And now, I want to combine +these two, which I + +of course can do. + +I can substitute dq from this +expression in here. + +I also want to assume for our +present purposes that there's + +only pressure volume work going +on, which is to say I + +want to put p dV in here +minus p dV for dw. + +So for combining for p V work, +what we see then is du has to + +be less than T surroundings +dS minus p external dV. + +Or we can rewrite this as du +plus external pressure dV + +minus T surroundings dS +is less than zero. + +Now this is fundamentally +important, and as you know + +that means that it warrants +the exalted distinction of + +being put up in colored chalk. + +And, in fact, since we're going +to reuse this again and + +again during today's lecture, +I'm going to put it over here + +and leave it sacrosanct for +our further use. du plus p + +external dV minus T +surroundings dS + +is less than zero. + +This Is our condition for +spontaneous change. + +Now this is a really quite +useful expression. + +For one thing what we have +here are all functions of + +state and parameters that we can +control like temperature + +and pressure. + +So that's a big help. + +And equilibrium happens when +there isn't any possible + +change of state that +would satisfy this. + +In other words, you've got your +system in some state. + +You know it's in some state +A, there are some + +other states around. + +Here is what we calculate to +tell whether it happens + +spontaneously. + +So we now have a real usable +criterion to help guide our + +understanding of whether things +happen by themselves of + +their own accord or not. + +Now, this is still a little +bit cumbersome, in part + +because of the variables +involved, including S. That + +is, most processes that we're +concerned with, they'll happen + +with something held constant +like pressure or temperature + +or maybe volume. + +So this isn't the most useful +form that we can have, but + +what we'll see shortly is that +from this, we can then derive + +further criteria for essentially +any set of + +variables or any set of external +constraints, like + +constant temperature or pressure +or volume and so + +forth that we might set. + +And so that's what +I now want to do. + +So I just want to use that again +and again, starting from + +that, for various different +sorts of conditions and derive + +the criterion for equilibrium +in each set of conditions. + +So first, let's start with the +one that we already know, and + +make sure that it still works, +starting from here, mainly our + +isolated system. + +So remember what that means? + +It means no heat, no work. + +Delta V is zero. + +Delta u is zero. + +So looking at this, du +is zero. dV is zero. + +So all that's left is negative +T dS is less than zero. + +In other words, T surrounding +dS has to be greater than + +zero, and of course + +temperature is always positive. + +So dS for u and V fixed +is greater than zero. + +All right, so that's +sounds right. + +That's what we saw before. + +When we have an isolated system, +the criterion that + +determines whether something +happens spontaneously is the + +entropy has to increase. + +Now, what this means too is +if we imagine a bunch of + +different states, and this is +the entropy of them, so this + +could be any sort of variable +but the point is there are a + +bunch of possible states around, +whichever one has the + +maximum entropy, that's +the equilibrium state. + +In other words, you know we've +got the two gases on either + +side of that partition. + +We remove the partition, +and they mix. + +Well, the equilibrium state +is the one with the gases + +completely mixed. + +Of course there are lots of +states that would have maybe + +local pockets of one substance +in excess and another + +substance in excess +somewhere else. + +In other words, there would be +lots of states nearby to the + +equilibrium state. + +That is, the chain, they could +they could be approached with + +very little change from +the equilibrium state. + +They aren't the equilibrium +state. + +The entropy in all of those +states will be lower than the + +entropy of the fully +mixed state. + +So the point is, once you're +at equilibrium none of the + +other states, they're +accessible, the system could + +rearrange itself to form them, +but there is no accessible + +state that has higher entropy +than the equilibrium state. + +OK, that's our familiar +isolated system. + +Now let's try moving to +unfamiliar territory and + +extending what we know. + +So, let's try constant +entropy and volume. + +And the motivation for choosing +a pair like that is + +easy to see, if we look at our +condition for spontaneous + +change or general condition. + +Well, entropy and volume +constant means dV and dS are + +equal to zero. + +What does that say? + +It means du is less than zero. + +That's our condition. + +So we immediately get du +at constant S and V + +is less than zero. + +That's our condition for +spontaneous change. + +In other words, if we don't have +to worry about entropy or + +volume equilibrium is achieved +when energy is at a minimum. + +Now this is what you learn in +elementary physics and in + +mechanics, right. + +You're not worried +about entropy. + +So, you know, if you've got a +hill or valley and there's a + +cart on wheels, it's going +to go down to the bottom. + +The spontaneous change +lowers the potential + +energy in that case. + +So this is a simple condition +that's very familiar. + +Now, the reason this condition +always holds in ordinary + +mechanics is because you're +never, in that case, concerned + +with a huge statistical +population of particles where + +the disorder among +them is an issue. + +We're not worrying then about +the fact that, well like in + +the case of gas molecules +mixing, the macroscopic state + +of the whole thing, all those +molecules, how many different + +microscopic configurations +are there? + +Remember, I mentioned then we'll +go further later on into + +this, that entropy +can be related to + +the extent of disorder. + +That is, how many different +possible configurations of all + +those molecules there would +be for a particular state. + +The reason the entropy of the +mixed gases is the highest is + +because that has the most +possible configurations. + +If you start segregating the +gases, there are fewer + +possible configurations that +the whole system can be in + +because you're forcing +a particular set of + +circumstances. + +When you don't have to worry +about criteria like that, + +ordinary, mechanical energy +rules supreme, and that's + +dictating where equilibrium +lies. + +But of course, most chemical and +biological systems aren't + +that simple precisely because +you have to worry about many + +particles and their statistics +and the way they might order + +or disorder. + +So, and of course, you know, +keeping entropy as a fixed + +variable for a system like that +is extremely cumbersome. + +As soon as you allow anything to +mix, like you might if you + +want to do any chemistry, +entropy changes. + +If you change the temperature +entropy changes and so on. + +So let's go on. + +Let's consider a few +other examples. + +Let's hang on for a little +while longer to a set of + +conditions where we will +maintain constant entropy, + +namely constant entropy +and pressure. + +So, the dS term is zero, but +the other two are not. + +So, du plus p dV is +less than zero. + +I can write this as d(u ++ pV) less than zero. + +Normally I couldn't do that +because this term would have p + +dV plus V dp, but we've +specified the pressure is + +constant, so the dp +part is zero. + +And this is a quantity +that you know, right? + +What's u plus pV? + +STUDENT: dH. + +PROFESSOR NELSON: dH less +than zero, criterion for + +spontaneous change. + +In the case where S and +p are held constant. + +Now, once again, like I +illustrated for entropy, and I + +could have done the same for +energy here, you know, if we + +again look at a bunch of +different states, and look at + +their enthalpy, well, like +before, they'll be invariably + +lots of possible states. + +And now, what is this saying, +the equilibrium state is the + +one with the lowest +possible enthalpy. + +In the case here, that I just +illustrated with the little + +cart going down the valley, +would be exactly the same with + +regular energy, the equilibrium +state is one of + +lowest energy, right. + +And of course there are +lots of nearby states. + +The cart could be a little ways +up the hill, and in this + +case, it's enthalpy, but again, +there would be lots of + +accessible states. + +But if the system is in +equilibrium, none of those + +states has lower enthalpy. + +It's already in the lowest +enthalpy state. + +That is the equilibrium state. + +OK, well, now, let's get +to the big ones. + +That is, in real life, the +variables that you'd normally + +control aren't some combination +of entropy and + +these variables, but really +their temperature, volume and + +pressure, any couple of those, +might be what you'd really + +have under experimental +control. + +So now let's go to them. + +Let's control T and V. +So, all right, so now + +we're getting serious. + +All right, well, there's our +equilibrium criterion. + +We're still going back to it. + +It still holds. + +So we've now got the dV +part equal to zero. + +So what this says is that du +minus T dS is less than zero, + +and we can combine those +to say d(u - TS) + +is less than zero. + +And again, just like before, we +can do that although this + +normally would say this has +T dS and also minus S dT. + +T is fixed. + +So that part is zero. + +So this is really the +equivalent of this. + +So when we did this here, we +conveniently found that that + +quantity u plus pV is something +we know and love, + +and we're familiar with it. + +It's our enthalpy H. So we could +write that criterion as + +dH less than zero. + +So here, let's combine these +to define a new quantity. + +It obviously has importance +because what it's going to say + +is that that's the quantity that +defines equilibrium, that + +tells us about equilibrium, +under the very important + +practical constraints +of having fixed + +temperature and volume. + +Realistically, the more +likely constraints + +than either of those. + +So let's -- we'll go to a +brand new color, define + +A as u minus TS. + +it's called the Helmholtz +free energy. + +OK, and then our criterion for +equilibrium under these + +conditions is dA, V and T equal +to the temperature of + +the surroundings, is +less than zero. + +OK, and once again, you know +if we wanted to look at a + +bunch of states that could be +accessed, well, we would find + +lots of states near by, +in character to + +the equilibrium state. + +The one that is at equilibrium, +there is only one + +macroscopic state +at equilibrium. + +It has the lowest A. + +In some sense, that's one reason +to associate this as a + +kind of energy, just like +mechanical energy u or + +enthalpy H, it's the minimum +free energy state that is the + +equilibrium state under the +relevant conditions. + +Now, let's take the step +to the biggest set of + +conditions of all. + +What is it when you run a +chemical reaction under + +ordinary circumstances, +what's constant? + +STUDENT: [UNINTELLIGIBLE] + +PROFESSOR NELSON: +A little louder. + +STUDENT: Pressure +and temperature. + +PROFESSOR NELSON: Pressure +and temperature, right. + +You're running, you're shaking +a beaker up here at room + +temperature. + +So let's look at that +set of conditions. + +All right, there it is. + +This is the condition for really +the lion's share of + +chemistry, biology, and other +kinds of changes we'll be + +concerned with. + +So, there's our condition +for equilibrium. + +We don't get to set any of +them to zero, right? + +So, okay and we can handle that. +du plus p dV minus T dS + +is less than zero, but we do +get to simplify in writing + +this as d(u + pV - TS) is less +than zero, and just like we've + +seen before, yes, this has p +dV and V dp, but the dp is + +zero because we're at +constant pressure. + +This has minus T dS minus S dT, +but the dT part is zero + +because we're at constant +temperature. + +So the result is we can combine +all of these as a + +single differential, and just +like we've seen before, what + +that suggests is that we define +another new quantity + +given by this expression. + +And that is the last one we're +going to describe. + +And that is G, u plus +pV minus TS. + +The Gibbs free energy. + +Notice, we could also write, +let's rewrite that. + +G is u plus the pV minus TS, but +u plus pV is H. So we also + +can write this as H minus TS and +u minus TS is what we just + +defined a minute ago as A. +So we can also write + +this as A plus pV. + +And the main thing of crucial +importance is what, by + +defining this in the way we +have, what that's saying is + +that dG at constant p and +T is less than zero. + +There's our condition for +equilibrium at constant + +temperature and pressure. + +Boy, is that going to be +important for the whole rest + +of the course. + +So, and of course, I hardly need +to emphasize further, but + +we could do the exact same +consideration that we have for + +H and A, there's G. There's +our equilibrium state. + +It's the state that has the +lowest Gibbs free energy. + +All these things though +are incredibly + +practical, useful criteria. + +This is only defined in terms +of state functions. + +And just like we saw before for +the case of entropy in an + +isolated system, now we have +something we can calculate. + +It's a state function, so we're +at constant temperature + +and pressure, and now we want +to consider some chemical + +change or a phase transition +or you name it. + +Does it happen of +its own accord? + +Well now we know what needs to +be calculated in order to + +determine that. + +So this one is so uniquely +pervasive, let's just really + +explicitly write it all out. + +For constant pressure and +temperature delta G is less + +than zero, means A going to B +is, all right, let's consider + +some process state A and state +B. If delta G is less than + +zero, it happens +spontaneously. + +If delta G equals zero, then +we're already in equilibrium. + +And if delta G is greater +than zero, then it goes + +spontaneously in the +other direction. + +Any questions about +any of this? + +Let me just give a couple +of examples. + +If we go back to any of those +chemical reactions that I + +wrote on the board before, +right, well certainly we can + +calculate what delta G would +be for each one of them. + +Because we know how to calculate +all the parts of it. + +It's state functions, it's +composed of state functions + +that we know how to calculate. + +So we could tell. + +When delta G is zero, you know, +it doesn't mean that + +you've got all of one side, +all reactants and zero + +products or all products +and zero reactants. + +There is some mixture of them. + +What this will tell us +is what mixture. + +You know the stuff is in there +in equilibrium, you know the + +hydrogen and nitrogen that +will form ammonia. + +And in the end, when it's at +equilibrium, and you look and + +you'd make a measurement, +right, you could do + +spectroscopy. + +You could easily see how much +of each thing is there. + +It doesn't go all the way to +absolutely 100 percent + +ammonia, zero hydrogen zero +nitrogen if they were mixed + +together with the +right ratios. + +Doesn't happen. + +There would be some +of the reactants + +and some of the products. + +In the biochemical reactions +that are taking place in your + +body, there is equilibrium +between a whole myriad of + +reactants and products, and +thank heavens that gets + +maintained. + +So that's what this will guide +us through, and of course + +that's incredibly, incredibly +important. + +Here's another thing that's +worth thinking about. + +There's a balance here between +ordinary energy or enthalpy + +and entropy. + +Energy means, you know, chemical +reactions happen, and + +you end up with something that +might be exothermic, that is, + +the products are more stable +then the reactants. + +You burn methane, and it +combines with oxygen to form + +water, to form CO2. + +And if you work out the +energetics as we've gone with + +thermochemistry, you discover +there's a huge negative delta + +H. In other words, the bonds +are much stronger. + +CO2 is really a stable +molecule. + +Methane, there are certainly +some solid bonds there, but + +breaking those to form CO2 and +water, well it's worth it, + +right, energetically. + +Still, the actual equilibrium +depends on entropy also, not + +only on the energy. + +And that's why, when I put +up those three different + +reactions, and we saw the +signs could vary. + +It's because there's a balance +between the two. + +Energy may be favoring reaction +in one direction, + +toward let's say products +that have lower energy. + +But at the same time, entropy +is going to be favoring + +whichever side has higher +entropy, has more disorder, + +and there's a balance +that's achieved. + +And that's why all those +reactions, first of all, in + +some sense what I put up was +kind of a trivial statement in + +actual fact saying they all +happen spontaneously, because + +I didn't specify what we were +starting with exactly, what + +concentrations we were +starting with. + +Even something quite unfavorable +might happen at + +least a little bit +spontaneously. + +You'll have equilibrium. + +In those cases, though, you'd +have quite a reasonable + +equilibrium, spontaneously, that +is there would be a lot + +of reaction that went if you +simply started under practical + +conditions and let it go. + +Even though the signs of the +enthalpy changed, and the + +signs of the entropy changed +because it's a combination of + +the two that matters. + +Here's a really simple +example. + +Mixing of oil and water. + +You know from experience if +you've ever mixed them to make + +salad dressing, they +don't mix too well. + +And you may know that +if you heat them up, + +they mix much better. + +Why? + +You know, we've done a bunch of +thermochemistry, and we've + +kind of seen that the energy +of mixing, your energetics + +don't change too much as a +function of temperature. + +What's changing? + +Why does it mix better +when you warm it up? + +But, you know, looking at our +definition of Gibbs free + +energy, here it is, +right, or here. + +Let me just say, actually if you +calculated delta S for the + +mixing as a function of +temperature, it doesn't change + +all that much. + +You know, the amount of disorder +upon mixing is not + +really sensitive +to temperature. + +What does change though? + +T, and the entropy is weighted +by the temperature, so the + +entropy matters more and more +the hotter it gets. + +And that's consistent +with other things + +that we've seen, right? + +Remember the whole thing about +the perfect crystal at zero + +degrees Kelvin has +zero entropy. + +It's completely ordered. + +Entropy doesn't matter +anymore. + +It'll go to the lowest +energy state. + +Raise the temperature, and now +entropy plays a bigger role. + +So the point is, this balance +between energy that you could + +think of as say bond energies +in chemical reactions, and + +entropy that you can think of in +terms of disorder, how many + +different possible combinations +or configurations + +of something wrong, +will dictate where + +the equilibrium lies. + +And knowing now how to calculate +these free energies + +especially the Helmholtz and +the Gibbs free energies, + +that's what's going to guide +us in really calculating + +quantitatively, OK, where +will equilibrium lie. + +And before long, we'll start +in on discussing chemical + +equilibrium, does deriving +where they lie phase + +equilibrium? + +Does stuff change phase to go +from liquid to solid and so + +forth, right? + +And where does that happen, at +what temperature and pressure + +and so forth. + +And it's always going to come +down to calculating the + +appropriate free energy, and how +it changes in the process. + +So this is going to be a guide +for us for essentially all + +that we're going to do in +the rest of the term. \ No newline at end of file diff --git a/k0X7iSaPM38.txt b/k0X7iSaPM38.txt new file mode 100644 index 0000000000000000000000000000000000000000..5e525bfc6cd4edb7b9055cad43075b64401faea1 --- /dev/null +++ b/k0X7iSaPM38.txt @@ -0,0 +1,4118 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So good afternoon. + +Our main topic today +is to understand + +light forces, in particular +the stimulated force using + +the dressed atom picture. + +And I hope once you understand +how light forces can + +be described in the +dressed atom picture + +you will love the +dressed atom picture, + +as most atomic physicists do. + +It is really the +language we use, + +the intuition we apply +to atomic systems. + +Whenever we have a laser +beam which drives the atom + +it is, in most situations, +more appropriate + +and better to use dressed +states as your basis states + +and not the naked, +the bare states, which + +are ground and excited state. + +Now I know last +week I quickly went + +though the dressed atom picture. + +Let me sort of go +through it in a fly-over + +by not doing any +of the derivation, + +but making a few +comments here and there. + +Also, because I want +that some of the results + +are fresh in your +head when we apply it + +to mechanical forces of light. + +So I told you that in +the dressed atom picture + +we have two kinds of +interactions, the atom + +interact with a vacuum, +with a reservoir + +of empty modes with +spontaneous emission. + +And we also interact +with a laser field. + +And the new feature about +the dressed atom picture + +is that we first +solve this exactly, + +we rediagonalize the Hamiltonian +for that Hilbert space, + +and then we allow spontaneous +emission to happen. + +Now the derivation is +pretty straightforward. + +After a number of +assumptions, we simply + +came to the two-by-two +matrix, where + +we have two levels of the +atoms coupled with the Rabi + +frequency. + +I derived it here for you using +the quantized electromagnetic + +field. + +But in your homework you derive +the same two-by-two matrix + +using a classical +electromagnetic field, + +which drives the atoms. + +And we've talked about the +similarities and differences + +last week. + +If you have any questions, +please raise your hand + +or interrupt me. + +Now two-by-two matrix +is fairly trivial. + +We can immediately +diagonalize it. + +And we find +Eigensolutions, which + +are just sine theta, +cosine theta, amplitude, + +linear superpositions +of the naked states. + +And the naked states are ground +and excited states, state A + +and state B, with N or N plus +1 photons in the laser field. + +So it's simple. + +It's just a two-by-two matrix. + +But the insight we +can get out of it + +is pretty profound +and pretty subtle. + +So what we first +discussed is-- and we + +will need that to +understand forces and energy + +conservation-- we can now +look at spontaneous emission. + +Spontaneous emission coupling +to the empty modes of the vacuum + +can only connect an excited +state B with a ground state A. + +And therefore, we +have diachromatically + +those four combinations, +represented here + +by those four arrows. + +And if you look for +the matrix element, + +you collect cosine theta +and sine theta factors. + +And that's what we did here. + +So we immediately get in +the dressed atom picture, + +an expression +which tells us what + +are the matrix elements for +the carrier, for the blue + +and for the red detuned +sideband of the Mollow triplet. + +But then there's +something else, and I + +edit this with the +lecture notes in green. + +We can also, now, if you know +what the transition rates are, + +we can set up rate equations +and can solve them. + +And once you solve a set of +differential equations for rate + +equations, you know what +the populations are. + +But now, today, I want to +tell you one more subtlety. + +You know already +that you cannot, + +in the most general situation, +formulate an equation with just + +a population. + +You know that we have +the master equation, + +we have the Optical +Bloch Equation. + +This is an equation +for the density matrix. + +And usually we get equations +where the populations + +are mixed with coherences. + +In other words, you cannot just +say the diagonal matrix element + +of the density matrix +is a population, + +and the change of population +is what goes out of this state + +and what arrives in this state. + +Coherences play a role. + +But, and this is what the +dressed atom picture does + +for you, in the limit that we +have a strong Rabi frequency-- + +and this is the limit you +want to consider here-- + +the matrix equation +decouples into an equation + +for populations and an +equation for coherences. + +And if something decouples +that should tell you we + +all on the right track, we +have the right description. + +In this description things +decouple, things are simpler. + +And that means +this description is + +most appropriate for the +physics we want to understand. + +Or, to say it more +specifically-- and all + +the details of course +are in the book + +Atom Photon Interaction-- you +can rewrite the Optical Bloch + +Equations not in the bare bases +but in the dressed atom basis. + +And in the dressed +atom basis you + +find this wonderful +separation between populations + +and coherences. + +So we have the simple +rate equations. + +By setting the +left hand side to 0 + +we find the steady +state populations. + +This will be very important to +understand the light forces. + +But you should just remember +the steady state solution such + +as we know them. + +They're just exactly given +by this angle theta, which + +tells us what kind +of superposition + +of the bare states from +the dressed states. + +Remember in the case of +theta equals 45 degrees, + +the dressed states are just +symmetric and antisymmetric + +superposition of +the naked states. + +Now what is also important +is those rate equations, + +or those rate equations +have a time constant. + +The time constant is +here, the relaxation time + +for populations. + +And we know exactly what it is. + +It's a little bit more +complicated to find + +the equivalent equation +for the coherences. + +But just take my word, +the density matrix + +in the dressed atom basis +decouples into equation + +for population, which is +simple, equation for coherences, + +little bit harder to +derive but looks the same. + +And from this equation we have +now an expression for what + +is the relaxation +time for coherences. + +And just to show you +one non-trivial example, + +if you add up cosine square +plus sine square you get 1. + +But based on what +we derived we have + +to take cosine to the power +of 4, sine to the power of 4. + +And this gives us effect of +1/2, which will appear somewhere + +in an important place +in a few minutes. + +So with that we can now +address, we know now something + +about the intensities +of this Mollow triplet, + +because the intensity is nothing +else than the population, + +what is the population in +the initial state times + +the matrix element squared. + +But what is also-- what +comes out very naturally-- + +is that we have +different widths. + +The features have +different widths. + +The sidebands have +a different width + +from the central part +of the Mollow triplet. + +And well, this is now +very naturally interpreted + +at one has a width, +which is a relaxation + +rate for the population. + +The other one, is the +sidebands have a width + +which is a relaxation +rate for the coherences. + +I showed you, and this was just +a reminder of a few weeks ago, + +that when we looked at the +linear matrix equation, which + +are the Optical +Bloch Equation, we + +discussed complex +eigenvalues mathematically. + +And those complex eigenvalues, +the imaginary part + +is the sideband frequency. + +And the real part +was the widths. + +What I have now, sort +of-- I can get everything + +from the dressed atom picture. + +But what I've gotten in a +very natural and simple way + +is this case, which is the +case where the dressed atom + +picture is particularly simple. + +It's called the +secular case, where + +the population and +coherences decouple. + +And so, what I just showed you, +that the population relaxation + +time is gamma over 2. + +This explains now +why, in this case, + +the widths of the +central feature + +is 1/2 of what it is +when we're on resonance. + +So everything is sort of +nicely playing out here. + +OK, any questions about +dressed level populations, + +rate equations, +the Mollow triplet? + +Because we want to apply +it now, in a few minutes, + +to the stimulated light force. + +But before I do +that, let me show you + +one nice piece of physics, +which can be formulated + +both in the bare, +in the uncoupled, + +and in the dressed state basis. + +And this is the process +of spontaneous emission. + +If an atom is in +the laser field, + +it just emits photon, +rapid fire photons. + +And I want to show you now, +how we would describe it + +in the bare basis, +how we describe it + +in the dressed basis. + +And we get two very different +physical pictures out of it. + +Well, in the bare +basis, maybe just + +think of quantum Monte +Carlo simulation, + +a photon has been +emitted, and that + +means we are in +the ground state. + +Now it takes a Rabi cycle +before the ground state + +atom is in the excited state. + +And when it is in the excited +state, it can emit again + +and goes back to +the ground state. + +And then things start over. + +So the picture you obtain here +is the picture of antibunching, + +that the atom emits +a photon, but then it + +takes the inverse Rabi +frequency to load the gun again. + +And then it can fire again +and emit the next photon. + +So therefore, the probability +of getting another photon right + +after you've observed the +first photon is reduced, + +or T equals 0, it is exactly 0. + +And this is antibunching, +the photons are antibunched. + +So this is how we would describe +the radiative cascade, how + +we go from N to N minus 1, to +N minus 2, how we lose photons + +from the laser +field and dump them + +into the empty +modes of the vacuum. + +That's how we describe it +in the uncoupled basis. + +Well in the dressed +basis we have sort of + +diagonalized the +atoms interacting + +with the strong laser field. + +And now we would have +the following picture. + +We have this manifold here. + +We can emit from this manifold. + +And we can go to the upper +or lower dressed state. + +And then, the next +thing will happen again. + +But what we realize here, if we +are in the upper dressed state, + +we can either emit +on the carrier + +or we can emit a +blue detune sideband. + +But once we have emitted +a blue detune sideband, + +the next sideband has to be +red detuned because we are now + +in the lower dressed state, +and we need a lower sideband + +to go back to the +upper dressed state. + +So what this picture gives +us, it gives us the sidebands + +because we are resolving the +splitting in this picture. + +And secondly, it +tells us that there + +is an alternation between +the blue detuned photons + +and the red detuned photon. + +Now you would say, well +aren't those two pictures + +really different? + +In one case we +have antibunching, + +and all of the +photons are the same. + +And over here I talk +about an alternation + +between the blue and +the red sideband. + +Well again, the two +pictures are complementary. + +In this case, if I want to +resolve the antibunching + +I need a temporal +resolution which + +is better than the +inverse Rabi frequency. + +But if my temporal resolution +is better than the inverse Rabi + +frequency then I don't have +the spectral resolution + +to observe the sidebands, +and vice versa. + +If I want to resolve +the sidebands, + +if I want to distinguish the red +from the blue detuned sideband + +of the Mollow triplet I +cannot run the experiment with + +the spectral resolution, which +would be required to observe + +the antibunching. + +So these are sort of +two different pictures. + +One is sort of in terms +of energy eigenstates + +when we have +spectral resolution. + +And this other picture +is more appropriate + +when we're interested in +the short time domain. + +So in that sense, you need both. + +You need the bare basis. + +You need to dressed basis. + +And you have to just know for +which physical process, which + +of them allows the more +direct description. + +Questions? + +OK, so this was partly +review, partly preparation + +for the next big +chapter, namely we + +want to understand the dipole +forces within the dressed atom + +picture. + +The book Atom Photon Interaction +has a nice summary of it. + +But the more detailed picture, +and I heavily draw from this, + +is in the truly seminal article +by Jean Dalibard and Claude + +Cohen-Tannoudji. + +I've linked this +article to our website. + +So I've summarized here pretty +much what I just told you. + +This is sort of the summary +from the previous section. + +What we have to know is +to understand light forces + +in the dressed atom +picture is number one, + +the energy speaking +between the two. + +The splitting between the two is +the generalized Rabi frequency. + +If there's anything +which is not-- + +well I shouldn't say 100%-- +but at least 90% clear to you, + +ask me question. + +I mean these are the +results we really + +need for the +following discussion. + +So number one is +the dressed energy + +levels are split by the +generalized Rabi frequency. + +Number two is with +this angle theta, which + +came from the solution +of diagonalizing + +the two-by-two matrix, we +have now the steady state + +populations in the upper and +in the lower dressed state. + +And the third thing is when +we have a population when + +we are not in steady state, then +the steady state populations + +are obtained with the time +constant, which is given here. + +The time constant +is not just gamma, + +it's gamma times these +trigonometric functions. + +So these are simple ingredients. + +But by using those +ingredients we + +can get a very nice formulation +for the stimulated force. + +So what I've shown +here is, and this + +is the situation we want +to focus on for a while. + +Assume you focus a laser beam. + +Then plot it as a +function of position. + +The atom is outside +the laser beam, + +it goes into the +laser beam where + +it experiences the +electromagnetic field. + +And if it goes further it +has crossed the laser beam + +and is out of the +laser beam again. + +So what happens is the splitting +between the two dressed + +energy levels is the +generalized Rabi frequency. + +And this is outside the laser +beam, simply the detuning. + +But then when the +laser beam is on, + +the generalized Rabi +frequency gets larger. + +We have a larger lar splitting +between the dressed energy + +levels, and so on. + +What is also important +is that if the laser is + +red detuned, which is here, the +lower dressed level correlates, + +corresponds to the ground state. + +Whereas for blue detuning the +ground state in this limit, + +the ground state correlates +with the upper dressed level. + +So it's important. + +So therefore an atom in this +situation-- because atoms + +are always more in +the ground state + +than in the excited +state-- an atom + +will have more population +in the upper dressed level. + +And here it will have more +population the lower dressed + +level. + +So what we want to +do now is we want + +to rewrite the stimulated light +force, or the dipole force, + +as we want to express it +through the forces acting + +on the dressed atom level. + +Well, I told you that we have a +splitting of the dressed energy + +levels by the generalized +Rabi frequency. + +So therefore, if +I just cover that, + +the energy level +of the two dressed + +levels is h bar over 2 plus +minus the generalized Rabi + +frequency. + +And the force if an atom is +in one of the dressed levels + +is simply the gradient of that. + +So therefore we have the picture +that the two dressed energy + +levels, atoms in those +two dressed levels, + +always experience +opposite forces. + +Then an expression +for the net force + +is that the average +dipole force is + +the force in dressed +level one times + +the probability that the +atom is in dressed level one. + +And the same for two. + +And if you sum it up we +get exactly the expression + +we have derived earlier for +the stimulated light force. + +But let's just sort of look at +it in the following picture. + +If we are blue detuned, +and let's assume + +we are not saturating +the transition, + +so therefore the atom will be +mainly in the ground state. + +So you have more +population in that state. + +But, well, if the +laser power is 0, + +we have 100% population here. + +But when the atom moves +into the laser beam + +there is a superposition of +ground and excited state. + +But that also means +there's a superposition + +of upper and lower +dressed level. + +But we have always, of +course, more population + +in the dressed level which +connects to the ground state + +because an atom will-- well, it +also comes out of the solution. + +But it's natural, just assume +you make the laser beam weak, + +you start in the ground +state and everything + +is sort of connected. + +The ground state +is simply dressed + +by a small excited +state contribution. + +So that explains it, why +for blue detuned light, + +the physics is mainly in +the upper dressed level. + +And we see the repulsive dipole +force of a blue detuned laser. + +Whereas, for red detuned +light, the dominant population + +is in the lower +dressed level, and we + +have an attractive force. + +Well that's simple. + +We haven't gained so +much, but you'll see, + +we can now rapidly gain insight +by take it to the next level. + +Let me first mention +a trivial example. + +And this is when we +are on resonance. + +When we are on resonance we +have equal population in the two + +dressed states, they +are resonantly mixed. + +And therefore if the +population in the two + +dressed states is the same, +but the atoms experience + +opposite forces, that means the +dipole force average out to 0. + +In a few minutes I want +to calculate for you + +what the heating is. + +The dipole force is 0. + +But you know the atom in +this radiative cascade + +is making transitions between +upper and lower dressed level. + +So what does it +mean for the atom? + +When it is in one dressed +level it experience the force + +from this side. + +If the atom is in the +other dressed level, + +it's experience a +force from that side. + +So the atom is actually subject +to an average force which is 0. + +But if you take these picture +literally, and you can, + +the atom is really whacked +left, right, left, right, left, + +right. + +And there is fluctuations. + +And we can use those fluctuating +forces to immediately calculate + +what is the heating. + +The force average is 0, but +the fluctuations of the force + +cause heating. + +So that's immediately the +next step of physical insight + +we will get out of this picture. + +But before I do that I +want to do something else. + +I want to discuss +what happens now + +to the force when the +atom is slowly moving. + +Remember, there is +still one phenomenon + +which I owe you an +explanation for. + +And this is when we +discussed molasses. + +We always had the effect +in optical molasses + +with a spontaneous +light force that we + +need red detuning of the +laser beam to get cooling. + +The simple picture is the atom +absorbs a red detuned photon + +and emits away a +resonant photon. + +And then that energy +difference is taken away + +from the kinetic energy, +and this is cooling. + +But then I told +you that when you + +go to higher power +of the standing wave, + +the sine of alpha of the +friction coefficient reverses. + +And that means cooling is now +done by blue detuned light, + +heating is done by +red detuned light. + +And that's what we +want to understand. + +So in order to get any cooling +effect, or heating effect, + +we have to now +change the equation + +we had for the +average dipole force. + +Remember also, the +average dipole force, + +we did that earlier, can be +derived from a potential. + +It's a gradient over potential. + +So therefore, when you +fly through a laser beam + +you go down and up or up +and down the potential, + +but nothing has happened to you. + +But the assumption +we had for that + +is that the dipole force was +calculated with a steady state + +population. + +So now we want to say +if the atom is slowly + +moving it may not +be fully adiabatic, + +and we want to calculate +the first correction + +to the non-adiabaticity. + +So in other words, we have +the following picture. + +When an atom flies +through the laser beam + +it needs a certain time +to adjust its population. + +And the question, +what is this time? + +Well, it is the relaxation +time for the populations + +among the dressed +states to adjust. + +And this is exactly the +inverse of the rate gamma + +pop, which we have +calculated earlier. + +So the physical picture now +is that in the dressed level + +one and two, the population +at any given moment + +is almost the steady state. + +But there is a time +lag, a time lag + +by the time it takes to relax. + +So in other words, the +atom is always a little bit + +behind in adjusting +to the laser field + +because it takes a +finite amount of time. + +So let's now try to understand, +in this picture which + +we have obtained +with a laser beam + +the two dressed levels and +the atom flying through, + +let's try to understand what +this extra lag time means. + +So the atom is flying +into the laser beam. + +It starts out in +the ground state, + +which means 100% in the +upper dressed energy level. + +Now, in the laser beam the +higher the laser power is, + +the more there is a mixture of +the other dressed energy level. + +But what happens is, +when the atom is here, + +when it just assume it flies in, +and there was not enough time + +to adjust the +population, that would + +mean that the atom-- and this +is indicated with the red dots-- + +that the atom has a +little bit of more + +population in the +upper dressed level + +than it would have +in equilibrium + +But what does it +mean for the force + +now, if there is more +population here than there? + +Well, the more population +you have in the upper state, + +the more you're +climbing up a hill, + +the more you get a +force to the left. + +So this red arrow shows due +to the non-adiabaticity, + +due to the time lag, there +is a little extra force + +to the left hand side. + +So this is on the up hill. + +Let's now understand what +happens on the down hill. + +Well, we just have to +keep track of signs. + +Here, the atom, in a +fairly high laser field, + +is in the upper dressed level +with a mixture in the lower + +dressed level. + +But now it flies out +of the laser beam, + +but it cannot immediately +adjust its population. + +And that means it +wants to have now + +more population in the +upper dressed level + +but it hasn't fully adjusted. + +So therefore, instead of +having the blue bullet, which + +represents equilibrium, the +atom has the red bullet. + +It has a little bit +lower population in that, + +and higher population there. + +But lower population here +and hire population here + +means-- if you have a little +bit higher population than you + +should have here it means +you are climbing up the hill, + +and there is an extra force, +which is again, to the left. + +So we realize the +n the time lag, + +means when an atom goes up +the hill there's a little bit + +extra force to the left. + +And when it goes +down the hill there + +is a little bit extra +force to the left. + +And after it has flown +through the steady state + +part of the force roller +coaster up down, which + +can be derived from a +potential, has integrated to 0. + +But what is left is this +non-adiabatic component + +of the force which is +slowing down the atom. + +In other words, I have shown +you in this simple picture + +that the time lag in adjusting +the dressed energy population + +means that there is a small +differential force which + +is slowing down the atom. + +And what I assumed +here was blue detuning. + +So we have cooling, we have +friction for blue detuned light + +when it comes to the +stimulated force. + +Now this picture, this +equation that the population is + +a steady state at the +given position minus a time + +lag, we can solve it. + +And I'm not doing +it here because it + +involves a few +mathematical equations. + +But by just using these answers, +and the rest is straight + +forward, you can then +arrive at an expression + +for the stimulated +for the dipole force. + +Colin? + +AUDIENCE: So, in the +spirit of last time, + +keeping track of the +energy, the energy here + +would be going into +the fact that now I + +have-- if the atom's +a harmonic oscillator + +it's a little behind +the drive field? + +PROFESSOR: Yes. + +AUDIENCE: So you imprint some +fluctuation on the laser beam, + +and that's where the +energy's being carried off, + +in the laser beam? + +PROFESSOR: Well the energy's +carried off by the laser beam. + +I have actually +prepared something + +which I want to +show you in 10 or 15 + +minutes, where the energy goes. + +So let's maybe do +that in a moment. + +So this is a physical picture. + +And I think what is also +important I want to later tell + +you, for other laser +cooling mechanisms, which + +are too complicated to describe, +but they also have a time lag. + +And I think, I try to +teach you basic concepts + +by using this simplest +physical picture I can have. + +And what can be simpler than two +levels of an atom and one laser + +beam? + +But what you understand here +with this stimulated force, + +which is also called +blue molasses, + +is for the first +time how a time lag + +in adjusting to the +local laser field, + +how that leads to cooling. + +I'm summarizing +here, simply taking + +this picture, this +equation, and you + +know, turning the crank on it. + +The paper by Jean Dalibard +and Claude Cohen-Tannoudji + +calculates what is the +dipole force in steady state. + +We get almost the same +result with the Optical Bloch + +Equations, but we +are discussing here + +the limit that the Rabi +frequency is larger than gamma. + +So therefore, if you're +missing occurrences of gamma, + +they don't appear here +because we've always + +assumed omega is larger +than gamma in this picture. + +Now I want to apply +this picture now, + +not just going through one +hump of the laser field, + +but going through +a standing wave. + +So we have a standing wave of +light, which is blue detuned. + +Of course, in a +standing wave of light, + +if you ever reach over +one optical wavelengths, + +you go up the hill, +you go down the hill, + +the lambda average +dipole force is 0. + +But now you find that if +you put in this time lag, + +you find a friction force, with +a friction coefficient alpha. + +And this friction coefficient is +cooling for blue detuned light. + +Now I don't want to +elaborate on this expression. + +But if you take the treatment +of Jean Dalibard and Claude + +Cohen-Tonnoudji, which +is very transparent. + +It reads wonderfully easily, +as the book Atom Photon + +Interaction. + +In the limit of large +detuning, which is the simplest + +possibly limit, you find +the friction coefficient + +which looks highly nontrivial. + +It depends to the sixth power +of the Rabi frequency and such. + +The only reason why I put +it here, in 20 minutes + +I want to give you a very, +very simple picture where + +I derive that for you. + +So that's just a check mark. + +Any questions right +now about-- because I + +want to go on-- about +the stimulated force + +in the dressed atom picture? + +And if we allowed deviations +from the steady state + +population we get +a cooling effect, + +and this explains the +effect of blue molasses. + +And we've applied it +to a standing wave. + +Cody? + +AUDIENCE: Just [INAUDIBLE] +the upper alpha + +are a friction constant +and the lower one + +is the polarizability? + +Or, something. + +PROFESSOR: No, oh, +thanks for asking. + +Alpha, yeah, we [INAUDIBLE]. + +Here it's the +friction coefficient. + +Here, remember when we +had the light force-- + +the spontaneous light force and +the stimulated light force-- + +one was directed +along a vector alpha, + +and the other one +along a vector beta. + +Alpha was pointing +into the direction + +of the gradient of +the laser intensity, + +and beta was the phase +gradient of the laser beam. + +So those two have +nothing to do-- + +this is friction coefficient. + +This is the direction for +the stimulated light force. + +And yes, a little +bit later today, + +I will use alpha again, +but for the polarizability. + +Yes. + +AUDIENCE: The [INAUDIBLE] +track the atoms + +in the [INAUDIBLE] +standing wave, [INAUDIBLE]. + +PROFESSOR: You're talking +about trap in here, + +that if you have a standing +wave of blue detuned light-- + +well if the standing wave +is infinitely extended then + +the atom is always +in the standing wave. + +But if you use two Gaussian +laser beams to form a standing + +wave, there is +always a net force + +to expel the atoms away +from blue detuned light, + +because blue detuned light +has an average dipole + +force which is repulsive. + +So whenever you want +to manipulate atoms + +with blue detuned light you need +an additional magnetic trap, + +or an additional red +detuned optical trap. + +Because whatever you want to +do with atoms, if you want + +to do it with atoms +in steady state + +you have to keep +the atoms together. + +And what keeps +the atoms together + +is red detuned optical +traps, or magnetic traps. + +The blue detuned +light can be used + +to create a blue +detuned lattice. + +Or it can be used +at least, if you + +want to do laser cooling with +blue detuned light it can + +be used for laser +cooling, as I've + +started to describe for you now. + +But yes, I mean, in that +sense as an experimentalist, + +you can run experiments where +you have only red detuned + +light-- red detuned +light for trapping, + +red detuned light for cooling. + +But if you use blue detuned +light for a standing wave + +or for blue +molasses, in addition + +you will always use +red detuned light + +to keep the clouds together. + +So pretty much every +experiment usually + +has some red detuned +light for confinement. + +And you have to then +match blue detuned light + +with red detuned light to +get the two things you want. + +We can now use the +dressed atom picture + +to calculate the heating. + +Remember the final +temperature you can reach + +was always the ratio between +a heating coefficient, which + +is actually the momentum +diffusion coefficient, + +over alpha. + +So right now we have +understood the alpha part. + +We know the physical +picture, why alpha + +provides cooling, why +we have a friction + +force for blue detuned light. + +But let's now take +it to the next step, + +and calculate what +is the heating. + +And I mentioned it already in +the context of simple molasses, + +which we discussed, I +think, two weeks ago, + +that we describe heating by the +momentum diffusion coefficient. + +Well the momentum +diffusion coefficient + +tells you that P +square is simply + +growing as a function of time. + +If you have a cold cloud +and you heat it up, + +you can describe the heating +by the temporal growth + +of P square. + +If you don't like +momentum, divide P + +squared by 2m you have +the kinetic energy, which + +increases. + +So it is this momentum +diffusion coefficient. + +And if you have a cloud which +moves with an average momentum, + +you only want to have the P +square minus P average square. + +But if you think about a +cloud which is being cooled, + +the second term is 0. + +So the momentum +diffusion coefficient + +is the derivative of P square. + +But the derivative of +P is simply the force. + +So therefore we can absorb the +derivative by replacing P-- + +at least one of the +P's-- by the force. + +And we can now get +rid of to second P + +of the second +occurrence of momentum + +by saying well momentum +is derivative of force. + +Sorry, derivative of +momentum is force, + +or momentum is the +integral of force. + +So we can exactly rewrite that +momentum diffusion coefficient + +by an integral over +correlation function of forces. + +And then we have the +nice physical picture + +that with increase +of kinetic energy, + +the momentum +diffusion coefficient + +comes because we have +fluctuations of the force. + +Yes? + +AUDIENCE: With the last +time, the previous page + +the factor [INAUDIBLE]. + +PROFESSOR: The factor of 2 here? + +AUDIENCE: No, the next slide. + +PROFESSOR: Here is 2. + +AUDIENCE: For both terms. + +PROFESSOR: Here is 2. + +And here it disappears, +because we have a factor of 2 + +and a factor of 2, and +the two cancel each other. + +AUDIENCE: No, I meant, there's a +2 multiplied the first average. + +And there's a 2 +for the second one. + +Are those for the first term? + +PROFESSOR: I think +this is correct. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: What happens +is P-- you use-- + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: No, it's +supposed to be-- + +PROFESSOR: Wait, is one missing? + +Maybe [INAUDIBLE]. + +I think you're right. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Let's assume +this is what it should be. + +So here is the reminder, +the kinetic energy. + +If you have a process which +causes momentum diffusion, + +the momentum +diffusion coefficient + +gives you the heating rate. + +And the cooling rate is given by +our friction coefficient alpha. + +And as we discussed in +the context of molasses-- + +of red detuned molasses, but it +applies to any cooling scheme-- + +the finite temperature +is when you + +have detail balance +between heating and cooling + +And therefore its ratio +of the momentum diffusion + +coefficient over the +friction coefficient. + +Kensie? + +AUDIENCE: In the +previous step, what + +was the significance of +choosing f of 0 basically? + +Like, the time arguments were +0 and D. So we said that f of 0 + +was DPDT? + +PROFESSOR: Oh, we assumed that +the laser beam's Hamiltonian is + +invariant against +time translation, + +and we simply evaluate +that at T equals 0. + +I mean, that's of the argument +you have fluctuating forces. + +And you could have +fluctuating forces + +at time T and time T prime. + +But then you use the augment +that in a steady state solution + +the correlation +function does not + +depend on T and T prime +separately, but only + +on the difference. + +And then you simply +set one argument to 0, + +and the other argument +becomes a time difference. + +Other questions? + +So now, by understanding +that momentum diffusion is + +nothing else than the integral +over the force fluctuation, + +we can now use this physical +picture which I gave you + +earlier that an +atom which cascades + +through upper, lower, +upper, lower dressed states + +will experience opposite but +equal forces, form the right + +and from the left. + +So I can simply evaluate that +by assuming we are on resonance. + +On resonance the force is h +bar over 2 times the derivative + +of the generalized +Rabi frequency. + +And the force +correlation, what is it? + +Well, it's the force +f of 0 times f of T. + +But as long as the atom +is in one dressed state + +the force doesn't change. + +So I simply take here the +force, I take the force squared, + +and then when I integrate over +that, well the moment the atom + +makes a transition +there is no longer + +any correlation +between the force. + +Everything becomes random and +the integral averages out to 0. + +So in other words, +that's the way + +how you should look +at this integral. + +You start with the +force f0, as long + +as the force is correlated. + +Because the atom hasn't +done spontaneous emission, + +you have sort of f of 0, f of 0. + +And you integrate it, +nominally to infinity. + +But you simply integrate it +until some spontaneous emission + +randomizes the system. + +So therefore, this integral +over the correlation function + +is nothing else then the force +squared times the typical time + +scale for a transition. + +So if you put that +in on resonance, + +we have the force here, +we square the force. + +And then we multiply with the +spontaneous emission rate, + +which for resonance +system is gamma over 2. + +And with that we get now +the heating coefficient, + +the momentum +diffusion coefficient + +for an atom which is +exposed to resonant light + +due to the stimulated +light force. + +The paper, the references +I've given you, + +is simply taking this +augment and extending that + +to arbitrary detuning. + +For arbitrary detuning, I told +you what happens on resonance. + +The atom spends equal amount +in each dressed state. + +If you detune the atom spends +more time in one dressed state, + +then quickly in the +other dressed state, + +and then more time in the +other dressed state again. + +So you can, by +simply understanding + +what are the rates for cascading +between the dressed levels, + +you could pretty much write +down the expression, find it, + +and here is the solution +taken out of the paper. + +So we have to correct +prefactor, but then + +if the detuning is +non-vanishing we + +get a contribution +from the second factor. + +Colin? + +AUDIENCE: Are you assuming +the exponential correlation-- + +exponential behavior +to the correlation. + +Because then you might +have different prefactors, + +if it were something like if +you were in a [INAUDIBLE]. + +PROFESSOR: Well what +happens is the following. + +I think if you're +in one dressed state + +and the force pushes +you in one direction + +and you integrate over it you +have an exponential decay. + +But instead of integrating +over the exponential decay + +you can just take +the force squared + +and multiply it with the +average time the atom stays. + +In other words, if I have an +exponentially decaying function + +I can always approximate it +by the function of T equals + +0 times the time. + +And what you are +asking me now is + +is the time the one over E +time, or is it an average time? + +What is the correct +time to use here? + +AUDIENCE: I guess when +the time scale depends + +on how the correlations decay +for [INAUDIBLE] different. + +PROFESSOR: Yes, OK, I agree. + +The shape of the decay of +the correlation function + +would matter. + +I'm not going into that. + +But what I'm sort +of assuming here + +is that the correlation +function indicated with time + +is the correlation function of +T equals 0 times the correlation + +time. + +And how the correlation +time is related + +to the exponential +time, or if there's + +a small prefactor and such, +that may depend on details. + +Yes, you're right. + +I've swept this under the rug. + +How are we doing? + +Good. + +Let me just summarize. + +The dressed atom +picture has given us + +two pieces of major insight +into the stimulated force. + +The first one is that the +atom experience is always + +opposite forces in the +two dressed levels. + +And it is the +population imbalance + +between the two dressed levels +which results in a net force. + +And this requires +either red detuning, + +then the force is +repulsive, or blue + +detuning-- sorry, +red detuning then + +the force is attractive, +or blue detuning then it's + +a force repulsive. + +Second, with this +time lag thing, + +we understand that time +lag, non-adiabaticity, + +is the way to get cooling. + +And the third thing we have +learned, when the atom does + +a radiative cascade the force-- +when it goes from the upper + +to the lower dressed +level-- the force + +is suddenly reversing it's sign. + +And this causes fluctuations, +this shakes up atom, + +and this causes heating. + +And this has nothing to do with +the other heating mechanism we + +discussed earlier, +namely every time there + +is spontaneous emission +there's a random recoil. + +In strong laser fields +the fluctuations + +of the stimulated +force, which has + +nothing to do with +spontaneous emission, + +are much, much larger +than the photon recoil. + +So therefore for +strong laser fields, + +it is this alternation +of the force when + +atoms switch dressed +energy levels, which + +is responsible for +most of the heating. + +I want to come now to another +physical situation, which + +is actually wonderful. + +You learn about +Sisyphus cooling. + +Everybody in cold atoms +speaks about Sisyphus + +cooling because it's a very, +very elegant cooling scheme. + +We usually apply in the +laboratory Sisyphus cooling + +when we do polarization +gradient cooling. + +I will say you a +few things later. + +But this is much, much harder +to understand than the Sisyphus + +cooling, which takes place +for a two level atom moving + +through a blue +detuned standing wave. + +So in other words, +I try to explain now + +to you what Sisyphus cooling is. + +The relevant application +is multi-level polarization + +gradient cooling, which +I give you an idea, + +but it's hard to fully describe. + +But here, in our current +discussion on the two level + +atom interacting with one laser +beam, or one standing wave, + +we find the simplest +physical realization + +of Sisyphus cooling. + +So just to make sure that you +are following the argument, + +I have so far explained to you +why blue detuned light cools + +in the limit of very +small velocities. + +Very small velocity means +we did a first order Taylor + +expansion in this lag time. + +But now I want to discuss with +you a different regime, namely + +that the atom moves +with a velocity such + +that it can go up and down +several periods of the standing + +wave before it does +spontaneous emission. + +So before when we discussed +the friction coefficient, + +the velocity was infinitesimal. + +But now I assume that +the velocity is such + +that the atom can +surf a few waves + +and then it will +spontaneously emit. + +And let me assume that +we are blue detuned. + +So the atom, let's say here, +where the splitting is minimum, + +well this is where +we don't have light. + +The generalized Rabi frequency +is just the detuning. + +So we are in a node +of the standing wave. + +And then the atom starts +in the ground state, + +and it experiences +the periodic potential + +due to the standing wave. + +But we want to now ask, OK, +when will spontaneous emission + +happen in this picture? + +Well, it cannot happen here, +when the atom is in the ground + +state, when there is not light. + +But where there is light, when +the atoms move to an anti-node, + +there is a mixture, indicated +in red, of the excited state. + +So in other words, when an +atom does this roller coaster, + +it will most likely emit a +photon-- either the carrier + +or one of the +sidebands-- when it + +is at the maximum of the +potential corresponding + +to an anti-node where it +experiences the light. + +OK, when the atom +emits on the carrier + +it goes from the +upper dressed level + +to the upper dressed level. + +Then sort of +nothing has happened + +because the atom is in +the same dressed level. + +Let me now discuss the case +when something happens. + +And this is when the atom decays +from the upper dressed level + +to the lower dressed level. + +And at least for weak excitation +the lower dressed level + +corresponds to +the excited state. + +In other words, when +there is no light, + +the upper dressed +level was ground state, + +the lower dressed +level is excited state. + +But what happens now is +actually interesting, + +the atom had to +climb up the hill. + +But the spontaneous emission +to the lower dressed level + +takes the atom to the bottom. + +So you can see, on average, +it has climbed a hill here, + +but now it is at the bottom. + +And now we're going to ask +how does the atom get out + +of the lower dressed level? + +Well, the lower +dressed level is mainly + +excited-- is 100% excited +if there is no light. + +But if there is light, and +light means the generalized Rabi + +frequency is larger, the +excited state has now in it + +mixture of the ground +state because the light + +mixes ground and excited state. + +So now, of course, +whenever there is red + +you can spontaneously emit. + +But there is a +probability that the atom + +is more likely to emit when you +are in a purely excited state, + +and not in a mixed state. + +So now, talking about +the lower manifold, + +the atom does it's +roller coaster. + +It has a velocity +that it can cover + +several periods of the +standing wave in one lifetime. + +But there is a higher +probability for the atom + +now to emit when it +is on top of the hill. + +So that's remarkable. + +We have the upper dressed level. + +We have the lower dressed level. + +The atom is doing +the roller coaster. + +But whenever it emits a +sideband, whenever it switches + +state, it mainly +does it by emitting + +at the top of the hill. + +And after the +spontaneous emission + +it finds itself at the +bottom of the hill. + +So on average the atom +is climbing more up hills + +than down hills. + +And this is called +Sisyphus cooling. + +I think you've all heard +about the Greek myth of King + +Sisyphus, who was condemned. + +He challenged the gods +and he got his punishment. + +And his punishment +was that he always + +has to roll a stone up the hill. + +And when he's done +the stone falls down + +and he has to roll the stone up. + +So in other words, we +have condemned the atoms + +to the same verdict. + +They always have to +go up hill to work. + +Then they fall down +hill with the help + +of a spontaneous photon. + +But then they have +to climb up hill. + +And it is the uphill climb where +the experience and net friction + +force, which cools the +atoms down and reduces + +their kinetic energy. + +So this is Sisyphus cooling. + +And since I need it +in a few minutes, + +I just wrote down for you, based +on this simple and wonderfully + +elegant picture, +how much energy does + +the atom lose per unit time? + +What is the cooling rate? + +Well it's clear that +the cooling rate + +comes when the atom switches +from one dressed energy + +level to the next, because +nothing happens on the carrier. + +So it is the transition state +between dressed level one + +and dressed level two. + +And then we multiply +with mu naught + +the depths of the optical +lattice, because it + +is this energy difference which +is extracted from the atom. + +You may ask, OK what +is time limiting? + +It's really the transition rate +form the first dressed level, + +which is mainly ground state, to +the other dressed level, which + +is mainly exciting state. + +Because once the atom is in +this level, which is mainly + +the excited state, +it will pretty much + +do the next transition +at a rate which + +corresponds to the +spontaneous emission rate. + +So in other words, if you're +not fully on resonance, + +or if you're not +situated in laser power, + +the rate, one, two, is slower +than the rate two, one. + +And therefore this rate +is the rate limiting step. + +Let me show you +just a few pictures. + +What I'm just explaining to +you was explored very early on, + +just have to sort of put you +back that it was in the mid + +'80s, '82, '83, '84, that people +developed [INAUDIBLE] slowing. + +It was in '85 that optical +molasses with red detuned light + +was demonstrated +for the first time. + +It was in '86 that +the dipole trap + +was demonstrated by Steve Chu. + +And in '87 that Steve +Chu and Dave Pritchard + +introduced the +magneto optic trap. + +So the mid to late '80s +were fantastic times, + +where one important technique +was realized and demonstrated. + +And this was actually the +first major experimental paper + +of a new laser +cooling group, which + +was founded by Claude +Cohen-Tonnoudji at the Ecole + +Normale Superieure in Paris. + +And it was exactly about cooling +atoms with stimulated emission, + +and this is blue molasses. + +And, I mean, you exactly +see here out of this paper, + +the Sisyphus cooling mechanism. + +And addressing the question +about red detuned light here, + +this was actually +beam experiment. + +You head a blue +detuned standing wave, + +and you were sending +an atomic beam through. + +And if this atomic +beam was cooled, + +the divergence of the +atomic beam was reduced. + +So this experiment had only +one blue detuned standing wave + +and nothing else, because it +was not a trapping experiment. + +It was a beam +collimation experiment. + +And what is shown +here is that you + +have the original +atomic beam profile. + +And for blue detuned light +you make it narrower, + +so this is cooling. + +Whereas for red detuned +light you have a defocusing, + +which corresponds to heating. + +Any question? + +I want to wrap up the discussion +of the stimulated light force + +by discussing pretty +much everything again, + +but in the simplest +possibly limit. + +That's actually +something I haven't + +found in any text books. + +But when I derived +it for myself it + +helped me to really +understand it. + +It's sort of the perturbative +result of the dressed atom + +picture. + +So everything is simple. + +And by telling +you, look at this. + +You know this is +just EC stock shift. + +But in the dressed +atom picture it's + +a generalized Rabi +frequency, you suddenly + +understand the trivial +perturbative result + +and how it translates into +the dressed atom picture. + +So what I'm presenting you +now in the next 10 minutes, + +it provides a lot of +insight because it + +connects simple pictures. + +So I'm discussing +things here in the limit + +that the detuning is large. + +The detuning is larger +than the Rabi frequency, + +and spontaneous emission +rate is the smallest + +of the three rates. + +In that case, I can simply +do perturbation theory, + +and I want to show you. + +Also, because this +is pedagogical, + +I just want to show you how +the effects come together. + +I neglect all factors +on the order of unity. + +And I set h bar to 1. + +So let's assume we +have a standing wave. + +A standing wave is cosine KX. + +So we have an electric field. + +But we describe the electric +field with a Rabi frequency. + +So the Rabi frequency +forms a standing wave. + +Now what are the +two dressed states? + +The dressed states 1 and +2 are the bare states, + +ground and excited state. + +And then there a +perturbative mixture. + +And in first order +perturbation theory + +we take the matrix +element over the detuning. + +So one dressed +state is the ground + +state with a little bit +of excited stated mixed. + +The other dressed state is +the excited state, minus sign, + +little bit of ground stated mix. + +These are our two dressed +states in the trivial limit + +that we can apply +perturbation theory. + +What are now the +transition rates + +between the two dressed states? + +Well, we want to make +spontaneous emission + +from dressed state 1 +to dressed state 2. + +We have to go from this small +mixture, which is the excited + +stated mixture, to +the ground state here. + +So therefore we get the +product of the two amplitudes, + +and then we multiply with gamma. + +Of course, most of-- yeah. + +So this is the rate to +go from dressed state + +1 to dressed state 2. + +What is the inverse rate to +go back from dressed state + +2 to dressed state 1? + +Well, you go from the excited +state to the ground state, + +multiply with gamma, +and that's what you get. + +Sure we have, in perturbation +theory, the coefficient is 1. + +It's only in higher +order perturbation theory + +that the coefficient of the +bare state becomes less than 1. + +So isn't that simple? + +We just discussed it with +all the cosine to the 4, + +sine to the 4. + +But now in perturbation +theory this + +is the rate for going +from dressed state 1 to 2. + +And this is the rate to +go the other way around. + +So what is our dressed +state potential? + +Well, the dressed +state potential + +is simply the EC +stock shift, which + +is opposite for the ground +and for the excited state. + +And the EC stock shift +in perturbation theory + +is nothing else than matrix +elements squared over detuning. + +So this is mu naught. + +This is the potential of the +standing wave experienced + +by the atom. + +Now we want to do +Sisyphus cooling. + +What is the cooling rate +in Sisyphus cooling? + +Well, remember, +Sisyphus cooling we + +assume that the +atom is fast enough + +to go over several +hills and valleys. + +The cooling rate is determined +by the rate at which the atoms + +switch dressed levels +times mu naught. + +And I can scroll back, but mu +naught was the EC stock effect, + +and gamma one, two was this +expression we had before. + +So therefore, in +the simple picture, + +while everything +is perturbative, + +we have a nice expression +for the cooling rate. + +Well, now let's get something +non-trivial out of it. + +What is the friction +coefficient? + +Well, in many +situations I've plotted + +for you, the force +versus velocity. + +Now I want to plot for you the +cooling rate versus velocity. + +That means its force +times velocity. + +And as we just discussed, when +the velocity is sufficiently + +fast that the atom can go +over several hills and valleys + +in a spontaneous +lifetime, the cooling rate + +will saturate +because it is limited + +by the rate at which +the atom switches + +between dressed levels. + +But now the question +is, if we want + +to understand what +happens at low velocities, + +how should we connect the two? + +Well, you can say we know, +for analytical reasons, + +that the force versus +velocity has to be linear. + +So the cooling rate, which +is another power of velocity, + +should be quadratic. + +And since I neglect all +factors on the order of unity, + +this is now the force is +friction coefficient times V. + +So therefore, what +I do in red here + +is a parabolic +approximation, which + +is alpha the cooling +rate times V squared. + +And now, if I want to +know what is alpha, + +I just sort of +connect this parabola + +with the saturated +value, which I know. + +And I know the transition +happens at the velocity when + +the atom moves further +than one wavelength in one + +spontaneous emission time. + +So therefore, based on +this very physical picture, + +and on the inside how low +velocities and high velocities + +connect together, I can actually +obtain the friction coefficient + +in this blue detuned standing +wave by taking the cooling rate + +and dividing it by the velocity +at which the atom moves + +one wavelength per +spontaneous emission time. + +And if I do that, I +obtain this result, + +which I have already +quoted earlier to you + +from the paper of +Cohen-Tonnoudji and Jean + +Dalibard. + +It looks fairly non-trivial with +power to the 6, power to the 5. + +But this is now the simple +perturbative results + +for the friction coefficient. + +Now we have the +friction coefficient. + +Let's take it further. + +I want to give you, in +this perturbative limit, + +I want to give you the +momentum diffusion coefficient. + +And then we will find in +the perturbative limit what + +is the lowest temperature +to which we can cool. + +So pretty much +I'll do everything + +as we've done before, but I use +the simple perturbative limit. + +So again, in order to calculate +the diffusion coefficient-- + +the momentum diffusion +coefficient-- and the heating + +we need the fluctuations +of the force. + +And now, just remember, we +are in the perturbative limit. + +The atom is mainly +in the ground state, + +which is the upper +dressed level. + +It has only a little +excited stated mixture, + +so it will mainly +stay in this state. + +But then with this excited +stated mixture and this, + +power of the Rabi frequency, +it makes the transition + +to the other dressed state. + +But the other dressed state +is almost 100% excited state. + +So it will leave the +other dressed state + +almost immediately. + +So this could be a Quantum +Monte Carlo wave function result + +that the atom +experiences the force + +in the upper dressed level. + +Then it goes to the lower +dressed level, which is mainly + +the excited state, just +4 times 1 over gamma. + +And then it returns. + +So the picture now is that the +atom for almost all the time + +experiences the steady +state force, which + +is the blue dashed line. + +And there are only, when it +goes to the other dressed state, + +these small spikes where +the force has changed sign. + +And if you now calculate the +fluctuations of the force-- + +the integral of f square-- +once we calculate the square + +the small deviations +from the average force + +does not contribute. + +What contributes are the spikes. + +So all I do is now I take the +4 square in one of the spikes. + +And the force is nothing else +than the derivat-- remember + +we have a standing +wave a mu naught. + +The derivative of the +standing wave is the force. + +But if you have a +sinusoid lattice + +the force is K times the +amplitude of the lattice. + +I square it, so this +is the spike squared. + +Then I have to multiply +with the time 1 + +over gamma, over which +the force stays the same. + +So this is, you can see, the +correlation time of the force. + +But then I have +to multiply, also, + +when I do an average over +many, sort of, you can see, + +trajectories, I have to +average over the probability + +that-- I have to multiply +with the probability + +that the atom is in +the dressed state + +1 and not in the +dressed state 2. + +It may take you a +few minutes just + +to think about +the combinatorics. + +But in the end all I do +is I take the 4 square, + +I multiply with correlation time +when the atom is in state 2, + +and get the probability +that the atom is in state 2. + +And when the atom is in +state 1, in my ensemble, + +it doesn't contribute at +all, because in state 1 + +you're so close to +the average force + +that it doesn't contribute +with the fluctuation. + +Anyway, it's simple but subtle. + +But it's a one-liner. + +And now based on +this perturbative + +picture we have perturbatively +exact an expression + +for the heating rate. + +But now it's +interesting, the rate + +gamma one, two, the rate to +switch between dressed energy + +levels always also appears in +the expression for the friction + +coefficient. + +So therefore, if +you're now asking + +what is the ultimate temperature +to which we can cool the atom? + +It is the ratio of this +analytic result for the heating + +coefficient divided +by the analytic result + +for the friction coefficient. + +Pretty much everything +cancels out, and what remains + +is mu naught. + +And this is a remarkable result. + +It's highly non-trivial, and I +really enjoyed showing to you + +how simply it can be +derived by-- it's really + +just perturbation theory. + +But you have to put in the right +concepts from the dressed atom + +picture. + +So what we learn +is the following. + +If you have a +standing wave, and we + +cool with a stimulated +force, the lowest temperature + +is-- with a prefactor, +which I haven't calculated-- + +the amplitude of +the standing wave. + +And that means that it is +impossible to ever localize + +atoms within a standing wave. + +Laser cooling cannot be used +to create atoms in an optical + +lattice. + +The temperature of +the atoms is always + +comparable to the +depths of the lattice. + +So therefore the +atoms will never + +be localized in one +well of the lattice. + +And this is generally valid. + +The assumption we +have made here is + +that we have a two level atom. + +A lot of you work with +atoms to optical lattices. + +And you often use evaporative +cooling, take a Bose Einstein + +condensate, which is pretty much +a [INAUDIBLE] temperature put + +it in optical lattice. + +But before '95, people studied +laser cooling and atoms + +in optical lattices. + +And this was only +possible because atoms + +can be cooled to +lower temperatures + +than we have derived here +because they are not two level + +atoms. + +So laser cooling +in a standing wave, + +localization of atoms in a +standing wave by laser cooling, + +is only possibly by physics +beyond what we have discussed. + +Colin? + +AUDIENCE: If you use something +like Raman's sideband cooling, + +you could-- like, yeah, +you'd kind of need + +three levels for that, but +you eliminated the third. + +Really, it's just that +it's two levels, right? + +PROFESSOR: If you do +Raman's sideband cooling, + +he posted-- I think, +in the next 10 minutes, + +I cover what you want to see. + +Because now it involves +two ground states. + +And I want to show you, if +you have two ground states, + +to Hyper fine-- Raman's +sideband cooling-- if you have + +two different ground +states there is no physics. + +And I briefly want +to touch upon that. + +We'll just kind of +fill in one thing here, + +and it is, well, if +you take everything + +I've told you seriously, +you would say OK, too bad. + +We cannot localize atoms +in an optical lattice + +because the temperature +is always comparable + +to the amplitude of the lattice. + +But by making the lattice +smaller and smaller and smaller + +I can reach lower and +lower temperatures. + +Well, yes, the some +extent that's possible. + +But what we have done here +is we've done approximations. + +We've only focused on +the stimulated force. + +We have not looked +at the recoil which + +comes in spontaneous emission. + +And therefore, the moment we +would make the optical lattice + +smaller than gamma then +we have to include heating + +by the spontaneous light force. + +And the result will be that +blue molasses cannot reach lower + +temperatures than +red detuned molasses. + +And for red detuned +molasses we have already + +discussed the famous Doppler +limit, which is gamma over 2. + +So that's what I +wanted to present + +to you with the +stimulated force. + +First, a more general +discussion using the real + +dressed atom picture. + +But now in the end, to fly +over using sort of the baby + +dressed atom picture, which +is simple perturbation theory. + +OK, so we've done the hard work. + +Now we want to have some +fun discussing the physics. + +And I'm realizing I've only +five, six, seven minutes left. + +I want to discuss three points. + +One is I want to give you all +the different pictures to find + +the potential of a dipole +trap, because we've + +encountered several. + +The second thing is I want +to have a discussion with you + +if the stimulated force is due +to electric or magnetic forces. + +And eventually, and we'll +be running out of time, + +I have to do that on +Wednesday to discuss + +the question of +energy conservation. + +If you cool the atoms +where does the energy go? + +So if you use the +stimulated force, + +it gives rise to +dipole potential. + +And using the Optical Bloch +Equations or the dressed atom + +picture, we found +this expression + +for the dipole potential. + +And there are at least four ways +how we could have derived it. + +One is the Optical Bloch +Equations, we did that. + +The dressed atom picture, +we did that today. + +Another picture is very +straightforward and simple. + +It just says that +the potential is + +the electric +potential of a dipole. + +And then all you have to know +is from the EC polarizability, + +if you drive an atom +with a laser field + +below resonance-- +I mean that's just + +harmonic oscillator-- +below resonance + +the harmonic oscillator is +in phase with the force. + +Above resonance, if you drive +a harmonic oscillator fast, + +the response of the harmonic +oscillator is in opposite, + +it's out of phase. + +So therefore, if your +potential is minus the E, + +you are in phase-- it is a +negative attractive potential. + +If the harmonic oscillator +is driven above resonance + +there is another +minus sign, you get + +plus the E, which becomes +a repulsive potential. + +So it's, look and +say, just the physics + +of a harmonic oscillator. + +There's one thing I like, +which is sometimes not + +taught in an atomic +physics course + +because it is the force on a +macroscopic dielectric object. + +So let's assume we +have an atom-- no, we + +don't have an atom. + +We have something +which is bigger. + +Let's assume a tiny +polystyrenes sphere. + +You can assume a +small sphere of glass. + +What happens if I +shine a laser beam + +on a small sphere of glass? + +Well, let me assume that +the laser beam is-- well, + +if the laser beam hits +this sphere right on, + +it's symmetric, +there is no force. + +So what we want to do is we +want to have a laser beam, shown + +here by this arrow, +which has a maximum here + +so the profile is like this. + +And we want to discuss +whether this sphere is sucked + +into the laser beam, this +would be an attractive force, + +or whether this +sphere is repelled. + +And all we want +to use is optics, + +the optics of refraction. + +When we have a laser beam +which is weak, medium, strong, + +strong here, and +for red detuning + +we have an index of refraction +which is larger than 1. + +So the sphere acts like a lens. + +So that leaves those +photons up and in, + +and those photons up and in. + +And when a photon is bent in, +the momentum of the photon + +has changed. + +And the momentum, of course, +the opposite momentum transfer, + +is imparted to the sphere. + +So in this case, we +have sort of-- we + +have more photons in this +part of the laser beam, which + +are bent up, than +photons are bent down. + +And this means the net +force is that the sphere is + +sucked into the laser beam. + +And if you go for +blue detuned light, + +where the index of +refraction is smaller than 1, + +it is the opposite. + +So the picture which +we have discussed here + +was for atoms form +microscopic objects. + +But you have, actually, +similar physics + +of a stimulated force for +mesoscopic and macroscopic + +objects. + +And then what matters whether +you trap or anti-trap, + +is whether the index of +refraction is larger than 1 + +or smaller than one. + +And you know, two level +system for blue detuned light + +has an index of refraction +which is smaller than 1. + +And for red detuned +light our atomic clouds + +have an index of refraction +which is larger than 1. + +But this picture that you +can use the same set up, + +the same focus beam +and a similar dipole + +force to trap larger +objects is actually + +exploited in a different +field of physics, + +in biology, in the form +of optical tweezers. + +When actually in +the early '80s, when + +Steve Chu came to Bell Labs +and had discussions with Art + +Ashkin, they actually discussed +optical trapping, both of atoms + +and both of biological objects, +little microspheres, or cells. + +And it's sort of remarkable +that both approaches + +were realized within +the same year. + +So atoms were trapped in '86. + +And macroscopic objects +were manipulated, + +I think it's exactly +the same year. + +And as you know, +the optical tweezers + +is now an important technology +in biology and biophysics. + +For instance, you can +focus a laser beam + +and manipulate objects +within a living cell. + +So I think I should stop here, +but maybe take your questions. + +Then let me conclude +with an outlook. + +We have this week and next week, +and then the semester is over. + +So this week we have +one class on Wednesday. + +I want to finish this +discussion and teach + +about magnetic trapping +and evaporative cooling. + +And the last week, because +of a makeup class on Friday, + +we have three more classes, +Monday, Wednesday, Friday. + +By the way, I just learned +that the Friday class + +is in these room. + +And on Monday, +Wednesday, Friday we + +talk about, well, +it's really featured + +pick about Bose gasses, lecture +one, Fermi gasses, lecture two. + +And the third lecture is +about quantum logic with ions. + +OK, see you Wednesday. \ No newline at end of file diff --git a/lazME0LEUzA.txt b/lazME0LEUzA.txt new file mode 100644 index 0000000000000000000000000000000000000000..cab3908ccdcae9e55b047cab1d68103e8adec341 --- /dev/null +++ b/lazME0LEUzA.txt @@ -0,0 +1,2451 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so our topic was holographic + + align:start position:0% +ocw.mit.edu so our topic was holographic + + + align:start position:0% +ocw.mit.edu so our topic was holographic +partical image Velo symetry also known + + align:start position:0% +partical image Velo symetry also known + + + align:start position:0% +partical image Velo symetry also known +as hpiv for short um so basically what + + align:start position:0% +as hpiv for short um so basically what + + + align:start position:0% +as hpiv for short um so basically what +is hpiv and it's this really nice + + align:start position:0% +is hpiv and it's this really nice + + + align:start position:0% +is hpiv and it's this really nice +technique that allows you to + + align:start position:0% +technique that allows you to + + + align:start position:0% +technique that allows you to +simultaneously capture the information + + align:start position:0% +simultaneously capture the information + + + align:start position:0% +simultaneously capture the information +about velocity vectors in a + + align:start position:0% +about velocity vectors in a + + + align:start position:0% +about velocity vectors in a +three-dimensional flow which is really + + align:start position:0% +three-dimensional flow which is really + + + align:start position:0% +three-dimensional flow which is really +hard with conventional PIV because it's + + align:start position:0% +hard with conventional PIV because it's + + + align:start position:0% +hard with conventional PIV because it's +two-dimensional and there's a lot of + + align:start position:0% +two-dimensional and there's a lot of + + + align:start position:0% +two-dimensional and there's a lot of +limitations on it um so we have some + + align:start position:0% +limitations on it um so we have some + + + align:start position:0% +limitations on it um so we have some +nice examples of what you can get from + + align:start position:0% +nice examples of what you can get from + + + align:start position:0% +nice examples of what you can get from +hpiv on the top left is the near field + + align:start position:0% +hpiv on the top left is the near field + + + align:start position:0% +hpiv on the top left is the near field +of a laminer jet and you can see that + + align:start position:0% +of a laminer jet and you can see that + + + align:start position:0% +of a laminer jet and you can see that +there's velocity vectors pointing up in + + align:start position:0% +there's velocity vectors pointing up in + + + align:start position:0% +there's velocity vectors pointing up in +the jet Direction on the bottom we have + + align:start position:0% +the jet Direction on the bottom we have + + + align:start position:0% +the jet Direction on the bottom we have +a turbulent flow in a square duct and + + align:start position:0% +a turbulent flow in a square duct and + + + align:start position:0% +a turbulent flow in a square duct and +the uh intensity of velocity is + + align:start position:0% +the uh intensity of velocity is + + + align:start position:0% +the uh intensity of velocity is +represented by the different colors um + + align:start position:0% +represented by the different colors um + + + align:start position:0% +represented by the different colors um +so so how does hpiv do this basic idea + + align:start position:0% +so so how does hpiv do this basic idea + + + align:start position:0% +so so how does hpiv do this basic idea +is that first you have to record a + + align:start position:0% +is that first you have to record a + + + align:start position:0% +is that first you have to record a +hologram and then you can reconstruct it + + align:start position:0% +hologram and then you can reconstruct it + + + align:start position:0% +hologram and then you can reconstruct it +so when you record your hologram you're + + align:start position:0% +so when you record your hologram you're + + + align:start position:0% +so when you record your hologram you're +uh interfering a coherent reference wave + + align:start position:0% +uh interfering a coherent reference wave + + + align:start position:0% +uh interfering a coherent reference wave +with the light that's scattered from a + + align:start position:0% +with the light that's scattered from a + + + align:start position:0% +with the light that's scattered from a +particle field of interest and then + + align:start position:0% +particle field of interest and then + + + align:start position:0% +particle field of interest and then +you're capturing the intensity at the + + align:start position:0% +you're capturing the intensity at the + + + align:start position:0% +you're capturing the intensity at the +plane of the Hologram um and then this + + align:start position:0% +plane of the Hologram um and then this + + + align:start position:0% +plane of the Hologram um and then this +is really important because what you're + + align:start position:0% +is really important because what you're + + + align:start position:0% +is really important because what you're +doing here essentially is you're taking + + align:start position:0% +doing here essentially is you're taking + + + align:start position:0% +doing here essentially is you're taking +your 3D information and you're storing + + align:start position:0% +your 3D information and you're storing + + + align:start position:0% +your 3D information and you're storing +it in a two dimensional form then when + + align:start position:0% +it in a two dimensional form then when + + + align:start position:0% +it in a two dimensional form then when +you want to reconstruct and get your 3D + + align:start position:0% +you want to reconstruct and get your 3D + + + align:start position:0% +you want to reconstruct and get your 3D +information back out you'll take your + + align:start position:0% +information back out you'll take your + + + align:start position:0% +information back out you'll take your +hologram and if you illuminate it with + + align:start position:0% +hologram and if you illuminate it with + + + align:start position:0% +hologram and if you illuminate it with +the conjugate of the reference wave + + align:start position:0% +the conjugate of the reference wave + + + align:start position:0% +the conjugate of the reference wave +you'll get out a real image and uh for + + align:start position:0% +you'll get out a real image and uh for + + + align:start position:0% +you'll get out a real image and uh for +hpiv you have to do this at discrete zps + + align:start position:0% +hpiv you have to do this at discrete zps + + + align:start position:0% +hpiv you have to do this at discrete zps +which we'll go into + + align:start position:0% +which we'll go into + + + align:start position:0% +which we'll go into +later so there's two basic ways that you + + align:start position:0% +later so there's two basic ways that you + + + align:start position:0% +later so there's two basic ways that you +can illuminate your um system the first + + align:start position:0% +can illuminate your um system the first + + + align:start position:0% +can illuminate your um system the first +is inline when you have the particle + + align:start position:0% +is inline when you have the particle + + + align:start position:0% +is inline when you have the particle +field in line with your reference beam + + align:start position:0% +field in line with your reference beam + + + align:start position:0% +field in line with your reference beam +this is really nice because it's a + + align:start position:0% +this is really nice because it's a + + + align:start position:0% +this is really nice because it's a +relatively simple setup but it has some + + align:start position:0% +relatively simple setup but it has some + + + align:start position:0% +relatively simple setup but it has some +limitations because you need to make + + align:start position:0% +limitations because you need to make + + + align:start position:0% +limitations because you need to make +sure that your particles have a small + + align:start position:0% +sure that your particles have a small + + + align:start position:0% +sure that your particles have a small +diameter so that they're not interfering + + align:start position:0% +diameter so that they're not interfering + + + align:start position:0% +diameter so that they're not interfering +with the reference beam too much um and + + align:start position:0% +with the reference beam too much um and + + + align:start position:0% +with the reference beam too much um and +you can see an image of it here the + + align:start position:0% +you can see an image of it here the + + + align:start position:0% +you can see an image of it here the +other main technique is off axis so here + + align:start position:0% +other main technique is off axis so here + + + align:start position:0% +other main technique is off axis so here +you'll have like an obliquely incident + + align:start position:0% +you'll have like an obliquely incident + + + align:start position:0% +you'll have like an obliquely incident +reference beam and there's several + + align:start position:0% +reference beam and there's several + + + align:start position:0% +reference beam and there's several +advantages to this in that you can have + + align:start position:0% +advantages to this in that you can have + + + align:start position:0% +advantages to this in that you can have +the real and virtual images separate + + align:start position:0% +the real and virtual images separate + + + align:start position:0% +the real and virtual images separate +when you're reconstructing your images + + align:start position:0% +when you're reconstructing your images + + + align:start position:0% +when you're reconstructing your images +and you can also have much higher + + align:start position:0% +and you can also have much higher + + + align:start position:0% +and you can also have much higher +seating densities for your particles but + + align:start position:0% +seating densities for your particles but + + + align:start position:0% +seating densities for your particles but +if you're using digital holography then + + align:start position:0% +if you're using digital holography then + + + align:start position:0% +if you're using digital holography then +your incident angle needs to be less + + align:start position:0% +your incident angle needs to be less + + + align:start position:0% +your incident angle needs to be less +than 2° which is pretty tight + + align:start position:0% +than 2° which is pretty tight + + + align:start position:0% +than 2° which is pretty tight +restrictions it makes it kind of + + align:start position:0% +restrictions it makes it kind of + + + align:start position:0% +restrictions it makes it kind of +difficult so when you're designing an + + align:start position:0% +difficult so when you're designing an + + + align:start position:0% +difficult so when you're designing an +hpiv experiment there's a bunch of + + align:start position:0% +hpiv experiment there's a bunch of + + + align:start position:0% +hpiv experiment there's a bunch of +considerations that you need to worry + + align:start position:0% +considerations that you need to worry + + + align:start position:0% +considerations that you need to worry +about the first is recording distance + + align:start position:0% +about the first is recording distance + + + align:start position:0% +about the first is recording distance +because if your CCD is really far away + + align:start position:0% +because if your CCD is really far away + + + align:start position:0% +because if your CCD is really far away +from the field that you're studying then + + align:start position:0% +from the field that you're studying then + + + align:start position:0% +from the field that you're studying then +it's essentially running a low pass + + align:start position:0% +it's essentially running a low pass + + + align:start position:0% +it's essentially running a low pass +filter on your system but if it's too + + align:start position:0% +filter on your system but if it's too + + + align:start position:0% +filter on your system but if it's too +close then you're going to limit your + + align:start position:0% +close then you're going to limit your + + + align:start position:0% +close then you're going to limit your +field of view and you make it aliasing + + align:start position:0% +field of view and you make it aliasing + + + align:start position:0% +field of view and you make it aliasing +which is definitely a problem another + + align:start position:0% +which is definitely a problem another + + + align:start position:0% +which is definitely a problem another +consideration is the concentration of + + align:start position:0% +consideration is the concentration of + + + align:start position:0% +consideration is the concentration of +particles if you have too many particles + + align:start position:0% +particles if you have too many particles + + + align:start position:0% +particles if you have too many particles +you'll get a lot of speckle noise which + + align:start position:0% +you'll get a lot of speckle noise which + + + align:start position:0% +you'll get a lot of speckle noise which +is basically interference from the + + align:start position:0% +is basically interference from the + + + align:start position:0% +is basically interference from the +different particles um but if you don't + + align:start position:0% +different particles um but if you don't + + + align:start position:0% +different particles um but if you don't +have enough then you won't really + + align:start position:0% +have enough then you won't really + + + align:start position:0% +have enough then you won't really +recover all of your flow information + + align:start position:0% +recover all of your flow information + + + align:start position:0% +recover all of your flow information +which is the whole point of this that's + + align:start position:0% +which is the whole point of this that's + + + align:start position:0% +which is the whole point of this that's +problematic and finally if you're doing + + align:start position:0% +problematic and finally if you're doing + + + align:start position:0% +problematic and finally if you're doing +digital holography then you need to + + align:start position:0% +digital holography then you need to + + + align:start position:0% +digital holography then you need to +worry about the physical size of your + + align:start position:0% +worry about the physical size of your + + + align:start position:0% +worry about the physical size of your +CCD and the pixel size um so next we're + + align:start position:0% +CCD and the pixel size um so next we're + + + align:start position:0% +CCD and the pixel size um so next we're +going to talk about an experiment and + + align:start position:0% +going to talk about an experiment and + + + align:start position:0% +going to talk about an experiment and +that's + + align:start position:0% + + + + align:start position:0% + +Mike I'll do it thank you + + align:start position:0% +Mike I'll do it thank you + + + align:start position:0% +Mike I'll do it thank you +Anna okay so here's a photograph of our + + align:start position:0% +Anna okay so here's a photograph of our + + + align:start position:0% +Anna okay so here's a photograph of our +experimental setup we have a laser an ND + + align:start position:0% +experimental setup we have a laser an ND + + + align:start position:0% +experimental setup we have a laser an ND +filter spatial filter Iris and cating + + align:start position:0% +filter spatial filter Iris and cating + + + align:start position:0% +filter spatial filter Iris and cating +lens and the basic point of that part of + + align:start position:0% +lens and the basic point of that part of + + + align:start position:0% +lens and the basic point of that part of +the setup is just to get a nice plain + + align:start position:0% +the setup is just to get a nice plain + + + align:start position:0% +the setup is just to get a nice plain +wave to alum at our area of Interest + + align:start position:0% +wave to alum at our area of Interest + + + align:start position:0% +wave to alum at our area of Interest +what we're interested in it's a little + + align:start position:0% +what we're interested in it's a little + + + align:start position:0% +what we're interested in it's a little +difficult to see here but there's a tiny + + align:start position:0% +difficult to see here but there's a tiny + + + align:start position:0% +difficult to see here but there's a tiny +cylinder inside of this flow channel uh + + align:start position:0% +cylinder inside of this flow channel uh + + + align:start position:0% +cylinder inside of this flow channel uh +and we want to look at the flow around + + align:start position:0% +and we want to look at the flow around + + + align:start position:0% +and we want to look at the flow around +that cylinder um it's water flowing past + + align:start position:0% +that cylinder um it's water flowing past + + + align:start position:0% +that cylinder um it's water flowing past +there seated with spherical particles + + align:start position:0% +there seated with spherical particles + + + align:start position:0% +there seated with spherical particles +and we're going to use this camera with + + align:start position:0% +and we're going to use this camera with + + + align:start position:0% +and we're going to use this camera with +no lenses to uh capture the interaction + + align:start position:0% +no lenses to uh capture the interaction + + + align:start position:0% +no lenses to uh capture the interaction +between those spherical particles and + + align:start position:0% +between those spherical particles and + + + align:start position:0% +between those spherical particles and +the uh and the incoming plane wave + + align:start position:0% + + + + align:start position:0% + +okay so this is a typical raw hologram + + align:start position:0% +okay so this is a typical raw hologram + + + align:start position:0% +okay so this is a typical raw hologram +that we would get taking uh images of + + align:start position:0% +that we would get taking uh images of + + + align:start position:0% +that we would get taking uh images of +that flow pattern um you can see our + + align:start position:0% +that flow pattern um you can see our + + + align:start position:0% +that flow pattern um you can see our +flow obstruction the cylinder and the + + align:start position:0% +flow obstruction the cylinder and the + + + align:start position:0% +flow obstruction the cylinder and the +flow Direction in our case is from left + + align:start position:0% +flow Direction in our case is from left + + + align:start position:0% +flow Direction in our case is from left +to right notice also that you get the + + align:start position:0% +to right notice also that you get the + + + align:start position:0% +to right notice also that you get the +nice these nice defraction rings around + + align:start position:0% +nice these nice defraction rings around + + + align:start position:0% +nice these nice defraction rings around +the uh particles and even though this is + + align:start position:0% +the uh particles and even though this is + + + align:start position:0% +the uh particles and even though this is +a 2D image we're able to um we're able + + align:start position:0% +a 2D image we're able to um we're able + + + align:start position:0% +a 2D image we're able to um we're able +to extract + + align:start position:0% + + + + align:start position:0% + +the I + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% + + + + align:start position:0% + +I I + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +um okay so as Anna mentioned the main + + align:start position:0% +um okay so as Anna mentioned the main + + + align:start position:0% +um okay so as Anna mentioned the main +use of hpiv is to get instantaneous 3D + + align:start position:0% +use of hpiv is to get instantaneous 3D + + + align:start position:0% +use of hpiv is to get instantaneous 3D +velocity Maps so I'm going to go into + + align:start position:0% +velocity Maps so I'm going to go into + + + align:start position:0% +velocity Maps so I'm going to go into +how that's done uh in practice today um + + align:start position:0% +how that's done uh in practice today um + + + align:start position:0% +how that's done uh in practice today um +so some of you might be familiar with + + align:start position:0% +so some of you might be familiar with + + + align:start position:0% +so some of you might be familiar with +PIV and you might know that they + + align:start position:0% +PIV and you might know that they + + + align:start position:0% +PIV and you might know that they +typically use image correlation + + align:start position:0% +typically use image correlation + + + align:start position:0% +typically use image correlation +techniques uh the problem with that is + + align:start position:0% +techniques uh the problem with that is + + + align:start position:0% +techniques uh the problem with that is +that hpiv since it's three-dimensional + + align:start position:0% +that hpiv since it's three-dimensional + + + align:start position:0% +that hpiv since it's three-dimensional +information is very memory intensive so + + align:start position:0% +information is very memory intensive so + + + align:start position:0% +information is very memory intensive so +for example if you take all the + + align:start position:0% +for example if you take all the + + + align:start position:0% +for example if you take all the +reconstructed images from our example + + align:start position:0% +reconstructed images from our example + + + align:start position:0% +reconstructed images from our example +it's 1 second at 500 frames per second + + align:start position:0% +it's 1 second at 500 frames per second + + + align:start position:0% +it's 1 second at 500 frames per second +um it was 9 96 GB of data so imagine + + align:start position:0% +um it was 9 96 GB of data so imagine + + + align:start position:0% +um it was 9 96 GB of data so imagine +processing that um so instead what + + align:start position:0% +processing that um so instead what + + + align:start position:0% +processing that um so instead what +people do is use the 3D coordinates as + + align:start position:0% +people do is use the 3D coordinates as + + + align:start position:0% +people do is use the 3D coordinates as +the data so which is why as Mike + + align:start position:0% +the data so which is why as Mike + + + align:start position:0% +the data so which is why as Mike +described we need to be able to know + + align:start position:0% +described we need to be able to know + + + align:start position:0% +described we need to be able to know +exactly where everything is in 3D so + + align:start position:0% +exactly where everything is in 3D so + + + align:start position:0% +exactly where everything is in 3D so +there are two main categories of um + + align:start position:0% +there are two main categories of um + + + align:start position:0% +there are two main categories of um +algorithms for creating the velocity + + align:start position:0% +algorithms for creating the velocity + + + align:start position:0% +algorithms for creating the velocity +maps and I'm going to go over an example + + align:start position:0% +maps and I'm going to go over an example + + + align:start position:0% +maps and I'm going to go over an example +of each of those in a sec so the first + + align:start position:0% +of each of those in a sec so the first + + + align:start position:0% +of each of those in a sec so the first +one is correlation which is a most + + align:start position:0% +one is correlation which is a most + + + align:start position:0% +one is correlation which is a most +statistical method and the second is + + align:start position:0% +statistical method and the second is + + + align:start position:0% +statistical method and the second is +particle tracking uh which follows + + align:start position:0% +particle tracking uh which follows + + + align:start position:0% +particle tracking uh which follows +individual particles and is nicer for + + align:start position:0% +individual particles and is nicer for + + + align:start position:0% +individual particles and is nicer for +more complex + + align:start position:0% + + + + align:start position:0% + +flows okay so here's an example of a + + align:start position:0% +flows okay so here's an example of a + + + align:start position:0% +flows okay so here's an example of a +correlation + + align:start position:0% +correlation + + + align:start position:0% +correlation +algorithm uh basically what you have is + + align:start position:0% +algorithm uh basically what you have is + + + align:start position:0% +algorithm uh basically what you have is +you take two um images a Time sequence + + align:start position:0% +you take two um images a Time sequence + + + align:start position:0% +you take two um images a Time sequence +and so the the particles in green + + align:start position:0% +and so the the particles in green + + + align:start position:0% +and so the the particles in green +represent maybe what the particles look + + align:start position:0% +represent maybe what the particles look + + + align:start position:0% +represent maybe what the particles look +like at time one and a purple you have + + align:start position:0% +like at time one and a purple you have + + + align:start position:0% +like at time one and a purple you have +time two so so the goal is to uh shift + + align:start position:0% +time two so so the goal is to uh shift + + + align:start position:0% +time two so so the goal is to uh shift +these particles around you just keep + + align:start position:0% +these particles around you just keep + + + align:start position:0% +these particles around you just keep +clicking um and so I should mention that + + align:start position:0% +clicking um and so I should mention that + + + align:start position:0% +clicking um and so I should mention that +these particles the way you can do a + + align:start position:0% +these particles the way you can do a + + + align:start position:0% +these particles the way you can do a +correlation on coordinates is by + + align:start position:0% +correlation on coordinates is by + + + align:start position:0% +correlation on coordinates is by +representing each particle as a gaussian + + align:start position:0% +representing each particle as a gaussian + + + align:start position:0% +representing each particle as a gaussian +so then if you shift it around until you + + align:start position:0% +so then if you shift it around until you + + + align:start position:0% +so then if you shift it around until you +get the best correlation what you can + + align:start position:0% +get the best correlation what you can + + + align:start position:0% +get the best correlation what you can +get is a mean displacement Vector of + + align:start position:0% +get is a mean displacement Vector of + + + align:start position:0% +get is a mean displacement Vector of +your uh particles in time now if you + + align:start position:0% +your uh particles in time now if you + + + align:start position:0% +your uh particles in time now if you +look at small interrogation Windows what + + align:start position:0% +look at small interrogation Windows what + + + align:start position:0% +look at small interrogation Windows what +you can compare uh from Time 1 to time + + align:start position:0% +you can compare uh from Time 1 to time + + + align:start position:0% +you can compare uh from Time 1 to time +two + + align:start position:0% +two + + + align:start position:0% +two +is um so assuming you have the best + + align:start position:0% +is um so assuming you have the best + + + align:start position:0% +is um so assuming you have the best +correlation you can not only compare the + + align:start position:0% +correlation you can not only compare the + + + align:start position:0% +correlation you can not only compare the +minimum distance but the change in what + + align:start position:0% +minimum distance but the change in what + + + align:start position:0% +minimum distance but the change in what +people call group morphology so you can + + align:start position:0% +people call group morphology so you can + + + align:start position:0% +people call group morphology so you can +see you know maybe due to local velocity + + align:start position:0% +see you know maybe due to local velocity + + + align:start position:0% +see you know maybe due to local velocity +gradients the particles have shifted + + align:start position:0% +gradients the particles have shifted + + + align:start position:0% +gradients the particles have shifted +relative to each other at time two so + + align:start position:0% +relative to each other at time two so + + + align:start position:0% +relative to each other at time two so +you know optimizing these two things + + align:start position:0% +you know optimizing these two things + + + align:start position:0% +you know optimizing these two things +this minimum distance and the group + + align:start position:0% +this minimum distance and the group + + + align:start position:0% +this minimum distance and the group +morphology you can pair the particles + + align:start position:0% +morphology you can pair the particles + + + align:start position:0% +morphology you can pair the particles +from one time step to another and with + + align:start position:0% +from one time step to another and with + + + align:start position:0% +from one time step to another and with +that along with the overall main + + align:start position:0% +that along with the overall main + + + align:start position:0% +that along with the overall main +displacement you can get a velocity map + + align:start position:0% +displacement you can get a velocity map + + + align:start position:0% +displacement you can get a velocity map +so the next thing is particle tracking + + align:start position:0% +so the next thing is particle tracking + + + align:start position:0% +so the next thing is particle tracking +uh and like I said this is useful in + + align:start position:0% +uh and like I said this is useful in + + + align:start position:0% +uh and like I said this is useful in +complex flows or with lower seating + + align:start position:0% +complex flows or with lower seating + + + align:start position:0% +complex flows or with lower seating +densities um and again you might have a + + align:start position:0% +densities um and again you might have a + + + align:start position:0% +densities um and again you might have a +lower seating density to reduce speckle + + align:start position:0% +lower seating density to reduce speckle + + + align:start position:0% +lower seating density to reduce speckle +noise uh what you do is in two or more + + align:start position:0% +noise uh what you do is in two or more + + + align:start position:0% +noise uh what you do is in two or more +time steps you trace numbers of + + align:start position:0% +time steps you trace numbers of + + + align:start position:0% +time steps you trace numbers of +particles and you can fit what the most + + align:start position:0% +particles and you can fit what the most + + + align:start position:0% +particles and you can fit what the most +probable or best or smoothest velocity + + align:start position:0% +probable or best or smoothest velocity + + + align:start position:0% +probable or best or smoothest velocity +function is so you typically have some + + align:start position:0% +function is so you typically have some + + + align:start position:0% +function is so you typically have some +knowledge about what the flow should + + align:start position:0% +knowledge about what the flow should + + + align:start position:0% +knowledge about what the flow should +look like um so if you take X ofi being + + align:start position:0% +look like um so if you take X ofi being + + + align:start position:0% +look like um so if you take X ofi being +uh the locations of the particles at + + align:start position:0% +uh the locations of the particles at + + + align:start position:0% +uh the locations of the particles at +time x in frame I then you can just you + + align:start position:0% +time x in frame I then you can just you + + + align:start position:0% +time x in frame I then you can just you +know using you you know they might + + align:start position:0% +know using you you know they might + + + align:start position:0% +know using you you know they might +translate due to vorticity I mean sorry + + align:start position:0% +translate due to vorticity I mean sorry + + + align:start position:0% +translate due to vorticity I mean sorry +transform due to foric or there's a + + align:start position:0% +transform due to foric or there's a + + + align:start position:0% +transform due to foric or there's a +translation due to flow and you'll get + + align:start position:0% +translation due to flow and you'll get + + + align:start position:0% +translation due to flow and you'll get +what it looks like at the next time step + + align:start position:0% +what it looks like at the next time step + + + align:start position:0% +what it looks like at the next time step +Y and then so for example in this paper + + align:start position:0% +Y and then so for example in this paper + + + align:start position:0% +Y and then so for example in this paper +they assigned a cost function that + + align:start position:0% +they assigned a cost function that + + + align:start position:0% +they assigned a cost function that +looked like + + align:start position:0% +looked like + + + align:start position:0% +looked like +this um and if you recognize compare + + align:start position:0% +this um and if you recognize compare + + + align:start position:0% +this um and if you recognize compare +this equation to this equation this is + + align:start position:0% +this equation to this equation this is + + + align:start position:0% +this equation to this equation this is +basically the predicted position of of a + + align:start position:0% +basically the predicted position of of a + + + align:start position:0% +basically the predicted position of of a +set of particles at the next time step + + align:start position:0% +set of particles at the next time step + + + align:start position:0% +set of particles at the next time step +so you're you're basically minimizing uh + + align:start position:0% +so you're you're basically minimizing uh + + + align:start position:0% +so you're you're basically minimizing uh +an error the distance between two times + + align:start position:0% +an error the distance between two times + + + align:start position:0% +an error the distance between two times +um and I'll skip the math basically + + align:start position:0% +um and I'll skip the math basically + + + align:start position:0% +um and I'll skip the math basically +these are some other mathematically + + align:start position:0% +these are some other mathematically + + + align:start position:0% +these are some other mathematically +necessary terms so you're minimizing + + align:start position:0% +necessary terms so you're minimizing + + + align:start position:0% +necessary terms so you're minimizing +this cause function and again in the end + + align:start position:0% +this cause function and again in the end + + + align:start position:0% +this cause function and again in the end +you end up with a list of particle Pairs + + align:start position:0% +you end up with a list of particle Pairs + + + align:start position:0% +you end up with a list of particle Pairs +and you can create velocity + + align:start position:0% +and you can create velocity + + + align:start position:0% +and you can create velocity +Maps um okay yeah so just a few other + + align:start position:0% +Maps um okay yeah so just a few other + + + align:start position:0% +Maps um okay yeah so just a few other +neat techniques I won't go into really + + align:start position:0% +neat techniques I won't go into really + + + align:start position:0% +neat techniques I won't go into really +great detail one of them was really cool + + align:start position:0% +great detail one of them was really cool + + + align:start position:0% +great detail one of them was really cool +basically what they do is generate the + + align:start position:0% +basically what they do is generate the + + + align:start position:0% +basically what they do is generate the +lists of all possible particle pairings + + align:start position:0% +lists of all possible particle pairings + + + align:start position:0% +lists of all possible particle pairings +and call those chromosomes and based on + + align:start position:0% +and call those chromosomes and based on + + + align:start position:0% +and call those chromosomes and based on +uh fit functions similar to the cost + + align:start position:0% +uh fit functions similar to the cost + + + align:start position:0% +uh fit functions similar to the cost +function used in particle detection they + + align:start position:0% +function used in particle detection they + + + align:start position:0% +function used in particle detection they +sort of um generate parents and + + align:start position:0% +sort of um generate parents and + + + align:start position:0% +sort of um generate parents and +offsprings and they keep iterating until + + align:start position:0% +offsprings and they keep iterating until + + + align:start position:0% +offsprings and they keep iterating until +they have the best most evolutionarily + + align:start position:0% +they have the best most evolutionarily + + + align:start position:0% +they have the best most evolutionarily +fit particle pair um and again Optical + + align:start position:0% +fit particle pair um and again Optical + + + align:start position:0% +fit particle pair um and again Optical +correlation I said is not typically used + + align:start position:0% +correlation I said is not typically used + + + align:start position:0% +correlation I said is not typically used +but with some data compression + + align:start position:0% +but with some data compression + + + align:start position:0% +but with some data compression +techniques some people have used them so + + align:start position:0% +techniques some people have used them so + + + align:start position:0% +techniques some people have used them so +in the end what you end up with is a + + align:start position:0% +in the end what you end up with is a + + + align:start position:0% +in the end what you end up with is a +velocity map like we showed in the + + align:start position:0% +velocity map like we showed in the + + + align:start position:0% +velocity map like we showed in the +beginning unfortunately our attempts at + + align:start position:0% +beginning unfortunately our attempts at + + + align:start position:0% +beginning unfortunately our attempts at +a velocity map on hours didn't work out + + align:start position:0% +a velocity map on hours didn't work out + + + align:start position:0% +a velocity map on hours didn't work out +but um you could see in the video that + + align:start position:0% +but um you could see in the video that + + + align:start position:0% +but um you could see in the video that +you could see the flow and track the + + align:start position:0% +you could see the flow and track the + + + align:start position:0% +you could see the flow and track the +particles and whatnot so you get the + + align:start position:0% +particles and whatnot so you get the + + + align:start position:0% +particles and whatnot so you get the +general idea that's all any questions + + align:start position:0% + + + + align:start position:0% + +so all of this is based on the idea that + + align:start position:0% +so all of this is based on the idea that + + + align:start position:0% +so all of this is based on the idea that +you put a + + align:start position:0% +you put a + + + align:start position:0% +you put a +might you put particles inside the fluid + + align:start position:0% +might you put particles inside the fluid + + + align:start position:0% +might you put particles inside the fluid +is there any way that you could do this + + align:start position:0% +is there any way that you could do this + + + align:start position:0% +is there any way that you could do this +without changing the characteristics of + + align:start position:0% +without changing the characteristics of + + + align:start position:0% +without changing the characteristics of +by adding particles in is it solely + + align:start position:0% +by adding particles in is it solely + + + align:start position:0% +by adding particles in is it solely +having these likees in there particles + + align:start position:0% +having these likees in there particles + + + align:start position:0% +having these likees in there particles +in yeah you you definitely need + + align:start position:0% +in yeah you you definitely need + + + align:start position:0% +in yeah you you definitely need +particles it's holographic particle + + align:start position:0% +particles it's holographic particle + + + align:start position:0% +particles it's holographic particle +image symmetry um I think but as far as + + align:start position:0% +image symmetry um I think but as far as + + + align:start position:0% +image symmetry um I think but as far as +from the fluid mean point of view small + + align:start position:0% +from the fluid mean point of view small + + + align:start position:0% +from the fluid mean point of view small +enough particles are assume yeah + + align:start position:0% +enough particles are assume yeah + + + align:start position:0% +enough particles are assume yeah +neutrally buoyant particles are assumed + + align:start position:0% +neutrally buoyant particles are assumed + + + align:start position:0% +neutrally buoyant particles are assumed +not to disturb the flow so it's not a + + align:start position:0% + + + + align:start position:0% + +problem in the papers in the literature + + align:start position:0% +problem in the papers in the literature + + + align:start position:0% +problem in the papers in the literature +do they discuss um quantitative analysis + + align:start position:0% +do they discuss um quantitative analysis + + + align:start position:0% +do they discuss um quantitative analysis +of the error that may be in the + + align:start position:0% +of the error that may be in the + + + align:start position:0% +of the error that may be in the +experiments that they do they so great + + align:start position:0% +experiments that they do they so great + + + align:start position:0% +experiments that they do they so great +velocity vectors right do they discuss + + align:start position:0% +velocity vectors right do they discuss + + + align:start position:0% +velocity vectors right do they discuss +how one could make a ground truth + + align:start position:0% +how one could make a ground truth + + + align:start position:0% +how one could make a ground truth +measurement um the error in the velocity + + align:start position:0% +measurement um the error in the velocity + + + align:start position:0% +measurement um the error in the velocity +vector + + align:start position:0% +vector + + + align:start position:0% +vector +M yeah I mean there were discussions + + align:start position:0% +M yeah I mean there were discussions + + + align:start position:0% +M yeah I mean there were discussions +about the errors of each compon each + + align:start position:0% +about the errors of each compon each + + + align:start position:0% +about the errors of each compon each +step of the process so errors in + + align:start position:0% +step of the process so errors in + + + align:start position:0% +step of the process so errors in +locating particles aism but I haven't I + + align:start position:0% +locating particles aism but I haven't I + + + align:start position:0% +locating particles aism but I haven't I +don't know if you guys saw an in-depth + + align:start position:0% + + + + align:start position:0% + +M well like she said there's they + + align:start position:0% +M well like she said there's they + + + align:start position:0% +M well like she said there's they +definitely talk about the errors in + + align:start position:0% +definitely talk about the errors in + + + align:start position:0% +definitely talk about the errors in +terms of uh the steps of the the + + align:start position:0% +terms of uh the steps of the the + + + align:start position:0% +terms of uh the steps of the the +different steps of reconstructing and + + align:start position:0% +different steps of reconstructing and + + + align:start position:0% +different steps of reconstructing and +especially the errors in the Z Dimension + + align:start position:0% +especially the errors in the Z Dimension + + + align:start position:0% +especially the errors in the Z Dimension +so you have um one of the problems with + + align:start position:0% +so you have um one of the problems with + + + align:start position:0% +so you have um one of the problems with +holography is you have a depth of focus + + align:start position:0% +holography is you have a depth of focus + + + align:start position:0% +holography is you have a depth of focus +where a depth of focus issue where that + + align:start position:0% +where a depth of focus issue where that + + + align:start position:0% +where a depth of focus issue where that +um we we're testing spheres here but + + align:start position:0% +um we we're testing spheres here but + + + align:start position:0% +um we we're testing spheres here but +it's going to actually look kind of like + + align:start position:0% +it's going to actually look kind of like + + + align:start position:0% +it's going to actually look kind of like +an elongated ellipse with that um extra + + align:start position:0% +an elongated ellipse with that um extra + + + align:start position:0% +an elongated ellipse with that um extra +with the length Dimension being in that + + align:start position:0% +with the length Dimension being in that + + + align:start position:0% +with the length Dimension being in that +Z depth just as a an artifact of the + + align:start position:0% +Z depth just as a an artifact of the + + + align:start position:0% +Z depth just as a an artifact of the +Reconstruction so there are errors in + + align:start position:0% +Reconstruction so there are errors in + + + align:start position:0% +Reconstruction so there are errors in +terms of everyone has to make some kind + + align:start position:0% +terms of everyone has to make some kind + + + align:start position:0% +terms of everyone has to make some kind +of assumption so you need to um you need + + align:start position:0% +of assumption so you need to um you need + + + align:start position:0% +of assumption so you need to um you need +to say well I know there's spherical so + + align:start position:0% +to say well I know there's spherical so + + + align:start position:0% +to say well I know there's spherical so +if I get an ellipse I can find the + + align:start position:0% +if I get an ellipse I can find the + + + align:start position:0% +if I get an ellipse I can find the +centroid of that and then pick it out + + align:start position:0% +centroid of that and then pick it out + + + align:start position:0% +centroid of that and then pick it out +but based on your particular program + + align:start position:0% +but based on your particular program + + + align:start position:0% +but based on your particular program +how you're calculating it you could get + + align:start position:0% +how you're calculating it you could get + + + align:start position:0% +how you're calculating it you could get +different errors based on those + + align:start position:0% +different errors based on those + + + align:start position:0% +different errors based on those +assumptions and also um one thing based + + align:start position:0% +assumptions and also um one thing based + + + align:start position:0% +assumptions and also um one thing based +on the technique that you use there are + + align:start position:0% +on the technique that you use there are + + + align:start position:0% +on the technique that you use there are +different tradeoffs I don't know if it's + + align:start position:0% +different tradeoffs I don't know if it's + + + align:start position:0% +different tradeoffs I don't know if it's +called um so like I said with + + align:start position:0% +called um so like I said with + + + align:start position:0% +called um so like I said with +correlation small velocity gradients so + + align:start position:0% +correlation small velocity gradients so + + + align:start position:0% +correlation small velocity gradients so +maybe the Edie currents behind the + + align:start position:0% +maybe the Edie currents behind the + + + align:start position:0% +maybe the Edie currents behind the +cylinder are going to introduce errors + + align:start position:0% +cylinder are going to introduce errors + + + align:start position:0% +cylinder are going to introduce errors +um because the morphol + + align:start position:0% +um because the morphol + + + align:start position:0% +um because the morphol +changes and that's kind of detrimental + + align:start position:0% +changes and that's kind of detrimental + + + align:start position:0% +changes and that's kind of detrimental +to the algorithm um so that's you know + + align:start position:0% +to the algorithm um so that's you know + + + align:start position:0% +to the algorithm um so that's you know +depending on the technique I don't think + + align:start position:0% +depending on the technique I don't think + + + align:start position:0% +depending on the technique I don't think +you can do an overall study + + align:start position:0% + + + + align:start position:0% + +that okay thank you \ No newline at end of file diff --git a/nhGA_iLfKA8.txt b/nhGA_iLfKA8.txt new file mode 100644 index 0000000000000000000000000000000000000000..824be34766179ce4f01ffa8acacb1766d3ebebb4 --- /dev/null +++ b/nhGA_iLfKA8.txt @@ -0,0 +1,109 @@ +PHIL: Finally. + +FEMALE SPEAKER: MIT grad +student, food lover, fitness + +enthusiast, literature buff, +organic chemist by day, super + +hero by night. + +PHIL: Soon as my mother had +me, I was ready to go. + +Came out of there, running +and jumping. + +I haven't chewed gum since +I'm a role model. + +What's that stupid train +in Harry Potter? + +FEMALE SPEAKER: Hogwarts +Express. + +PHIL: It's a Hogwarts Express. + +I just took my sweatshirt off +and it cut my forehead. + +I found the photo of +Natalie Portman. + +FEMALE SPEAKER: I think +Phil is weird. + +PHIL: You know that Paula Deen +was married to James Dean. + +FEMALE SPEAKER: What? + +PHIL: A lot of people +don't know that. + +You know what my favorite +dance move is? + +Slapping people with my tie. + +This is my hood. + +Don't take my advice. + +IKE: I want to take it. + +PHIL: I'm going to sign up +for ChristianMingle.com. + +The commercial says, find +God's match for you on + +ChristianMingle.com or at +Starbucks like every other + +self-respecting American. + +MALE SPEAKER: Did you seriously +just end your + +sentence with a preposition? + +PHIL: I can't talk about +my personal life in + +front of the students. + +MALE SPEAKER: I love +you, Phil. + +MALE SPEAKER: We +love you, Phil. + +PHIL: OK. + +PHIL: Tom Cruise says I'm +silently judging you. + +There's a girl that was picking +on me at school, and + +on the way to school I remember +trying to make up my + +mind as to whether I was going +to stick my tongue out at her + +or hit her with my bag. + +I never felt so close to dying +in my entire life. + +MALE SPEAKER: It's +a sticky bun. + +PHIL: I can't. + +I really can't + +[MUSIC PLAYING] \ No newline at end of file diff --git a/nukI0huUEiM.txt b/nukI0huUEiM.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b5fdfb5710505896e5e95467d66da79fb7f2d2e --- /dev/null +++ b/nukI0huUEiM.txt @@ -0,0 +1,5478 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Welcome, everybody. + +So this is the one group meeting +that we'll have with + +all you folks. + +We really appreciate your +willingness to come and help + +us teach 6-172. + +Saman will explain what the +course is all about, and then + +I will give a presentation, +a little bit, of what your + +expected responsibilities are, +and then Eric, who is one of + +our TAs, will present what the +first project that they've + +been working on is all about. + +We think we have a pretty good +acronym, OK, MIT POSSE. + +Masters in the Practice of +Software Systems Engineering, + +OK, and it is very much like a +posse, in that we're trying to + +sort of deputizing you folks to +help us deal with this mass + +of students that we deal with. + +There's no way, given the +resources that we have + +available at MIT, that we +could possibly give the + +attention to each of the +students examples of code, and + +so our strategy is to go out +and deputize some people to + +help us teach. + +As we'll discuss your +responsibility is not to do + +any grading, OK, or even any +understanding of the course + +content, OK? + +But rather to ask good questions +of the students so + +that they understand what +it's like to do software + +development, and you'll see that +most of the students are + +very immature when it comes +to coding practices. + +They have taken a minimum of +one systems course before + +this, basically. + +SAMAN AMARASINGHE: Probably two +classes where they write + +very small programs-- + +PROFESSOR: Where they write a +very small programs, so they + +have no sort of sense +of writing scale. + +Moreover the class that we're +teaching because it's on the + +topic of performance +engineering, they are inclined + +to break all the rules in +order to get the best + +performance. + +And that's part of our game but +of course what we want is, + +we want the countervailing-- + +you still have to make things +maintainable, you really + +should do it this way, yeah +it's fine to violate some + +abstractions here and there, but +then you should document + +that you're violating those +abstractions and so forth. + +And that's what we're counting +on you for, is to insert some + +experience and common sense. + +So, Saman, take it away. + +SAMAN AMARASINGHE: OK, good, +so to add to what Charles + +said, when I was an undergrad, +when I took something like a + +science class, or a physics +class, or engineering class, + +most of the problems had kind +of right answer and a wrong + +answer and then it's very easy +to grade those things. + +But when I took something like +an English class, all the + +papers I wrote, somebody really +went through carefully + +and graded it and gave me lot +of insightful comments so I + +can kind of develop my +own style of writing. + +And what happens in software is +the programming there's a + +style that each individual has +to develop their style, but + +they can't develop a very +haphazard style so there's a + +certain set of good styles, +certain bad styles. + +And the problem that is in a +large class we can grade for + +correctness very easily, we can +also look at the programs + +and have a very fast thing, +okay, saying, here are no + +comments, or your comment +doesn't seem to be, it's too + +verbose, or some very high level +feedback, but it's very + +hard to help somebody +build their style. + +And so what you guys are coming +into is to help us get + +these young students create +their own style of + +programming. + +The nice thing about +this class-- + +and also sometimes last year the +masters found it a little + +bit hard was, we are giving +them small amount of code. + +They are doing performance +engineering on a maximum + +couple of hundred +lines of code. + +There's no very complicated +class structures or + +something like that. + +So we are not looking at the +style and software engineering + +in the macro level, how to +structure large classes but + +more at the micro level. + +In each method do they +have right style? + +Are they is it clean? + +Are they commenting +them properly, or + +can they do it better? + +So at that level at least the +building blocks that they're-- + +as they go build a larger and +larger program they can + +hopefully use. + +So that's what we're looking at, +and it helps to instead of + +dumping you ten thousand lines +of code, you only get a couple + +of hundred lines of code, so you +can actually go through it + +a lot more carefully, +and help them out. + +So this is starting with a crazy +eye chart that is our + +new curriculum that we +introduced in the department. + +So what you have is some early +courses in here, these are + +basically very general +math courses, early + +courses that do-- + +they probably write about ten +lines of code type thing in + +these courses, and then we feed +into these foundation + +courses and then after that +we sit at, this says 197, + +actually what should be 172. + +We sit at that level, so we are +sitting at that level, and + +then the prerequisite for people +who are coming is that + +they're taking a computer +architecture course so they + +know a little bit about +architecture. + +They have taken this +introductory software course, + +so they have written some Java +programs, and so they know a + +little bit about software +engineering from that course, + +and they have taken algorithms +course, so they understand + +algorithms somewhat, so this +is the background of the + +people are coming in. + +At the low end there might be +some people who have only + +written couple of thousand lines +of code in their lives, + +and there are other people who +are, written half probably-- + +the Linux kernel. + +So there are kind of very +diversified group of people. + +But there's some people who it's +really new to them, and + +they don't even understand why +you had to do good nice + +programming, why do you have +to document these things. + +I mean, for them it's a very +new concept, because they + +haven't seen that. + +So OK, if you're writing ten +lines, OK, why do you need + +document that, I know +how to do this. + +So part of that is this is, +for a lot of them it's eye + +opening, and in last year also +we talked to students, they + +actually gained a lot from +talking to you guys. + +It's easy for us to tell them +do it, a lot of them say OK, + +just to get the grade, I will +do it, but after that I'm + +never going to do these things, +and they just go off + +in very like, mad at us for +asking them to do it, but when + +you guys say this is what +happens in industry, there's a + +lot more impact on what +they're going to do. + +And so I would go through very +fast, so we have done case + +study on Matrix Multiply show +doing how you can basically do + +things like algorithmic tricks, +architecture tricks, + +and stuff like that +get really good + +performance on Matrix Multiply. + +So we started with doing very +object oriented, immutable + +type matrices, Matrix +Multiply and then go + +down to doing blast. + +How much a performance gap +do you think that has? + +AUDIENCE: It probably depends +on how big the + +matrices are because-- + +SAMAN AMARASINGHE: Yeah +it is 2k by a 2k + +matrix so it is, yeah-- + +So somebody said 200x. + +AUDIENCE: 10x + +SAMAN AMARASINGHE: Yeah 10x, +so actually, in fact we've + +been-- since I started with +the immutable matrix, very + +object oriented stuff like +that, and then did all to + +optimize I could, +I got 300,000x. + +So this is kind of extreme case, +but it illustrates how + +much, kind of, performance +sometimes is hidden in these + +applications. + +And then we talk bunch about, +these are done lectures, talk + +about some very simple things +in performance engineering, + +how to optimize loops, things +like how to get the compiler + +to do certain things. + +Some basic facts, we have bunch +of rules in there that + +we went through fast. + +And we are going to do introduce +them to performance + +analysis for a lot +of these people. + +First of all, they don't even +know their code is running + +bad, because they don't know how +to look at it other than + +getting one number then. + +Even if they know that their +code is running bad, how do + +you go about figuring +out what's going on? + +They know a little bit about +GDB but they don't know + +anything about performance +analysis, so we are + +introducing them to +tools in here. + +And we are talking about C to +Machine Code, lot of them are + +Java programmers, we already +gave them a C primer, saying + +if you're Java what does C +mean, kind of a thing. + +And I actually talk about +computer architecture today + +and talk about the entire +process they're going to use. + +They're using this Nehalem +processor and all of the + +interesting things that happen +inside the processor that they + +had to be aware of. + +And the same, maybe I will talk +about the memory system + +optimization, and then Charles +is going to talk about + +algorithms and data structures +for caches in there and some + +about storage allocation. + +We'll have a bunch of lectures +on parallelism that Charles is + +going to use Cilk Language to +illustrate how to write + +parallel programs, that's +what we are going + +to use in this class. + +And then more on parallelism, +some things like data + +synchronization issues, dig deep +into other performance + +issues in parallelism +in there. + +And then since their final +project is on Ray Tracing, + +we'll introduce them to a Ray +Tracing primer, and see how + +Ray Tracing is done +and so they can go + +into their final project. + +Then I'm going to talk a little +bit about compile + +optimization, what compilers can +do for you, and how to get + +compilers to do those +things for you. + +And a little bit about +distributed systems, so how + +can you scale out +on this point? + +It's about getting a small piece +of code to run fast, now + +how do we get millions of users +go to this very large + +scale system, and get +them to work, and + +what issues are involved. + +And then we are going to also +have about three or four case + +studies sprinkled around. + +We'll get someone from +University come and talk + +specific problems, OK, look I +had this problem, and at the + +beginning it was bad. + +Here's how I went about figuring +out why and here are + +the things I tried, these are +things worked, these didn't + +work, and how we went go. + +So kind of a very hands on +case studies about doing + +performance because what these +people has to do is develop a + +methodology. + +Their own methodology of how +to go about solving these + +problems, and then looking at +these case studies will give + +them a feel how a very +experienced person will go + +about looking at some +of those problems. + +So these are the kind +of lectures we + +are doing in a nutshell. + +So the projects we are doing. + +So students' mission, what +we do is we write some + +inefficient piece of code, not +that long, and we give them + +the specific, here so this is +functionally correct but it + +runs darn slow. + +And what you can say is, OK, +take advantage of right now, + +the first project is basically +looking at algorithmic and + +data structure inefficiencies. + +So OK, trying to find better +ways of doing that and change + +this program to run faster. + +So that's their thing, so they +don't have deal with thousands + +of lines of code. + +Small program, it's correct, to +run them faster, and this + +we'll also be asking them to +write tests, so you can + +actually test their +implementation, and make sure + +that implementation +are also correct. + +And basically there's +no right answer. + +This drives students crazy +because they are like, "When + +am I done?" I'm like, "You're +never done until the + +deadline," because you can keep +doing more and more and + +you could keep increasing +performance in there, and of + +course if you hit very marginal +returns and at some + +point and you might decide, +OK, that's good enough. + +And also more times +the journey is as + +important as the outcome. + +So at the end of the day you +can say I got it very fast, + +but how did you get there? + +What's the process +you followed? + +Some of these programs are easy +to get there, but if you + +haven't learned that process +you can't scale it out. + +And so, a lot of times your part +is to talk to them and + +say, "What did you do?" And say, +"Okay look why did you + +skip that stage, why didn't you +profile it?" And get them + +to get do that. + +And some will say, "Yeah, I +just look at it, I realize + +what it is." Like, no just do +something there might be + +something hidden in there, so +get through the process, + +understand the process, +that's the important. + +So the way the project works is, +we give them a project, we + +start them the project, and +there might be, some projects + +have two parts in there, and +final and a project request + +design document for them to +give us, saying what they + +figure out what's bad and what +kind of optimizing they are + +thinking of doing +in this project. + +And then we have a thing +called a beta turn-in. + +They said OK look we ran this, +we got the project and turned + +the product in, an we call +it a beta, because + +I'll tell you why. + +And then what we do is, we run +everybody's project against + +everybody, basically we run +every project, and we figure + +out who got the fastest +implementation. + +And we said OK, we announced +this and said this is the + +fastest implementation, and then +we figure out how off are + +you from the fastest, and we +have a proportion of the grade + +that's basically computer +graded. + +So we figure the fastest, you'll +get 100% for something + +that on the other hand if you +are 10x slower you get 10%. + +Except, the first time we tried, +the fastest was 1,000x + +better than the slowest, so +somebody got like 0.1%, that + +didn't work, so we are doing +square root of the former so + +they'll be little +bit more, in the + +somebody, got 1,000x there. + +So sometimes it's because +somebody just missed one + +critical insight and so and also +they might not have done + +the test properly and stuff +like this, so we give them + +opportunity. + +And then after this beta turn-in +you get this code, and + +the TAs get this code to run and +do a very fast check over + +that and that, and then they +are going to have a week to + +find a time with you, sit down +for hour or 90 minutes, and go + +through this code. + +And then they will get all the +feedback, the performance + +feedback, and they can talk to +people and figure out what + +they missed and they get another +chance to fix all + +those things, get the +performance up to turn in, and + +there'll be another performance +measurement, but + +now if they match up to that +point, they can get a full + +amount so of course, if people +exceed they don't get extra, + +because we want to limit the +competition, but at least you + +get a chance to kind of match +up the best code. + +So, what you have is this design +review week, that they + +get to talk to you, and get +feedback and, then after that, + +they fix everything up +and then resubmit it. + +PROFESSOR: You should mention +the beta tests. + +SAMAN AMARASINGHE: Yes, so what +also we do in this is + +we're asking them also to create +a test suite, and we + +are going to run everybody's +programs against everybody's + +test suite, and also give them +points on coverage of their + +suite, and also how well +their program does + +against everybody else. + +So if somebody finds lot of +bugs in other programs, or + +some there's a test that founds +couple of bugs that + +nobody else found we will give +a lot of points for that + +person, because that means they +went and did a really + +good job in creating +a test suite. + +So we are actually using that +to basically emphasize on + +testing and testability +issues in there. + +And then final, when you're turn +in, then the TAs will, at + +that point, will grade for +performance and also the + +coding style. + +So that time they will go to the +code and assign the grade. + +And so if the students have +listened to you, and carried + +out what you said, they should +get really good grades on that + +part, and then they had +to also provide + +a write up in that. + +So this is kind of the flow +of the projects we have. + +And the project one is a simple +algorithmic and data + +structure trick. + +So we did things like data +rotator, bit flip counter, and + +this Pentominoes Puzzle +that he's going to + +explain a little bit. + +So we give these things, that +we have a pretty inefficient + +representation, where most of +them has a much better bit + +representation, and you can do +bit tricks to basically get + +good performance. + +So these are algorithmic and +data structure representations + +that can have huge performance +gains. + +So this is the first project +and this is what next week + +you're going to get. + +So project two is more about +memory system performance, + +things like image rotator +and number sorting. + +We have two parts, the first +part is we give them these + +problems, and they're supposed +to run with different data set + +sizes, look at performance +counter results and identify + +what's going on with +these programs. + +So there's one thing that +we'll give them bunch of + +source compiled, and they have +to figure out which sort is + +which by looking at performance +counters and + +different ones. + +So you had to identify, so +basically give them idea to + +basically observe a program +behavior, and then we ask them + +to go and fix some of +the performance + +issues as a second part. + +So this is a lot about basically +getting performance + +information, understanding a lot +of hardware, what's going + +on and then going and doing +some performance fixes. + +So there'll be two parts, +to this project. + +And the project three +is implementing + +efficient storage allocator. + +Most of these students find +after they've done the Java + +and Python, they come thinking +there are these objects + +running in memory, with a thing +called pointer that + +points to, and to understand +what a pointer is + +is sometimes hard. + +And this is an interesting +example that they actually do + +a lot of pointer manipulations, +and you have to + +get a lot of those things right +and you have to have + +good discipline to do that, +as well as getting some + +performance, so this is +interesting project in there. + +Here you don't get too much of +performance variance but + +students have to think very +carefully about basically + +aliasing data structures +and stuff like that. + +So getting some of this dirty +little things you have to do, + +and learning how do it right. + +And then we go into parallel +programming. + +So first part is introducing +the concept of parallelism + +giving them some simple +programs to basically + +parallelize, and then the second +part is we give them + +insertion detection we're +inserting a bunch of lines + +into a image and then they have +to figure out when these + +lines move when they actually +intersect, and so it's not + +embracing a parallel, you +have to actually do by + +intersegmenting the data into +regions and basically figuring + +out where communication is. + +So there's a lot of issue +in there to get it done. + +It's a fairly complex program +that they have to to deal with + +and so they're going to have +to think through a lot of + +parallelism issues, +synchronization issues, + +communication issues, all +those things come + +into play in here. + +And then project 5 is just a +problem set because we want to + +get to make sure that they +understood some basic material + +we did, so you don't have +to deal with that. + +We give them, actually, a write +up they don't have to do + +any coding in there and they +turn that in as a normal + +problem set. + +And the project six also you +don't have time to critique + +that because it is delivered the +last day of class, but if + +you're interested in basically +giving them some feedback, or, + +just come in to the finals +and see how they do. + +So there what they do is, this +is a really fun project, we + +give them a very unoptimized ray +tracer, and we okay here's + +an image that it can generate. + +If you generate image that +looks the same to + +us, you'll be OK. + +So you can change the algorithms +you are doing, come + +up with other things you can +do, where you can still + +maintain the visual equivalence +and then you can + +do that, you can optimize, you +can parallelize, you can do + +anything you want and +build a ray tracer. + +So they go and then we explain +to them the basics of ray + +tracing and they do lot of cool +things and a lot of these + +kids actually really change, +think through algorithmic + +issues, even look at a lot of +graphics and find different + +ways, or better ways of doing +things, and come up with + +really cool tricks and +then do really well. + +So for that we will invite +you guys to come to the-- + +then we will have basically a +bake off, everyone will come + +and figure out who has the +fastest ray tracer, and they + +have the bragging rights, as +well as the grade of having + +the fastest ray tracer, so-- + +PROFESSOR: I'm going +to go through this. + +SAMAN AMARASINGHE: Okay, you +go through-- we have the + +schedule here. + +So the most programs are done in +C, and very little C++, not + +very complex C++ classes, +or anything like that. + +We want them to be very +close to the metal. + +They have been trained in a lot +of abstract programming in + +Java, Python and stuff like +that, now they're going to get + +to the metal, and understand +things like pointers, malloc + +and free, native data types +and stuff like that. + +We're not dealing with things +like dealing in garbage + +collection and bound checks, and +all the other things, so + +they're really seeing what's +going close to the metal, and + +sometimes we are even +encouraging to look at at a + +little bit of assembly work, +that's not really required. + +AUDIENCE: Have these students +had exposure to any kind of + +assembly language programing? + +SAMAN AMARASINGHE: In 004, they +are using some assembly + +programming for in the +architecture class, but I + +think it's a very simple, I +think RISC machine inspection + +they're doing. + +And then we will have our course +website as you go about + +you can look at what the course +is doing and also if + +you change this F10 to a F09 you +will see last year's code. + +So you can actually even see +into the future what we have + +been doing. + +So if you want to kind of +preface from the front. + +AUDIENCE: I took a look at this +website and found that + +most of it was unavailable +because of-- + +SAMAN AMARASINGHE: We should +have Word readable we need to + +make it if it's not +Word readable-- + +AUDIENCE: It says it's +Word readable. + +To us. + +GUEST SPEAKER: Some of it is a +lot of it was not I've said + +you need to, I mean it's +all available for- + +AUDIENCE: Certificate? + +SAMAN AMARASINGHE: We will check +that, because all this + +things that we have set up +in the background to get + +everything Word-- we want to +make everything Word readable, + +so we'll make sure +that happens. + +So, OK, so that's all I have +about the class and one thing + +interesting more so this +projects, the best to worst + +can sometimes be 1,000x +difference. + +So what that means, even for the +people who are struggling, + +they can get something +out of the class. + +But unlike other classes where +you just read the limit and + +then you're bored, you can +really keep pushing the limit, + +especially things like the final +product, the people who + +did well really pushed the +limits, they could have done + +that for a graphics +class type thing. + +I mean they pushed algorithms +changes, did amazing + +parallelization techniques, data +partitioning, everything. + +And where some people just kind +of stayed within that and + +did some small parallelization +got some like low hanging + +fruit in there. + +I mean what we're trying to do +is, computer science these + +days, we get some students, as +I said, their first time + +they're coding anything more +than ten lines and other + +people who are already a +submitter for open source + +projects, who have written +millions of lines of code, we + +have these two. + +And these codes, I think we +are trying to cater to at + +every level, and keep everybody +basically very + +motivated, and excited +to be in there. + +And I think the last year it +was a pretty good success. + +And they really enjoy meeting +masters last year, and after + +we go to discussion we can talk +about that a little bit. + +PROFESSOR: So we have two +websites, as Saman mentioned + +before, so here they are, and +then here's the schedule. + +So we'll run through this, in +more detail for what is + +expected of you, in a moment, +but basically there's four + +projects that's sort of are +organized along here. + +Oops, that typo didn't +get fixed. + +That's should be November 19 +obviously there, instead of + +October 19 if you +want to correct + +that on your calendars. + +OK, so in general it begins with +an information session + +which you're allowed to attend +in person but most people just + +dial in, it's more convenient. + +Then we will provide you with +the beta code submitted by + +your four students and then +you'll have two meetings that + +typically are 60 to 90 minutes +with each of your two pairs. + +OK, so let's go through +how this is working. + +So the first thing is just to +make sure you folks recognize + +that you're making +a commitment. + +It's very difficult for us, and +it's even more difficult + +for the students, to cope with +something that happens + +mid-term, OK? + +Where suddenly their master +disappeared, or whatever, so + +we're very big on +anti-flakiness, if you will. + +And so if you believe that +there's going to be a problem + +please let us know as much +in advance as you can. + +Sometimes things are +unavoidable, they come up, we + +don't fault you for that +or anything, OK? + +Just let us know, we'll try to +deal with the situation. + +But for the most part we're +really asking you to make a + +strong commitment to the +class, and so if your + +situation is such that you're +unsure it's best to talk with + +us or politely decline to +participate, rather than + +putting on the rosy glasses, +say, "Oh yeah I think I can do + +this, even though I know that +I've got a major deadline that + +conflicts with one of these +projects," or whatever. + +It's just really difficult +on the + +students when things change. + +They are sort of going I don't +know if you remember what it's + +like being in school as an +undergraduate, but pretty much + +the students go sort of hand +to mouth, in terms of like, + +they look and they say, OK I got +this deadline this week I + +better work on that one. + +They don't really look ahead and +so forth, and so it's up + +to us, to some extent, to +recognize that they're in that + +mode and that we need +to do things to make + +that easy for them. + +When they get sick or something +mid-term it can + +really throw a student way off +for the term, and so certainly + +when something happens to the +staff, that sort of, at that + +caliber, can really knock them +off their trajectory. + +The design and code reviews +should normally be held at + +MIT, and the students will +have some locations. + +If you are within walking +distance to campus however, + +you may suggest an alternative +place to meet, such as at your + +own workplace, if that's more +convenient for you, OK? + +But if a student balks at +doing that you shouldn't + +pressure them to accept. + +The content of the off campus +meetings should be + +professional, it's strictly +the review process, no lab + +tours, no free lunches, or +dinners, or what have you, OK? + +And we'll talk a little bit +more about that later. + +But the main thing about them is +that they can be scheduled + +in the evening or you know +whatever time you and your two + +students find convenient +to get together, OK? + +There's no limits as to +when you know what + +time those can be. + +They can be on the weekend they +can be, whatever you can + +work out, very flexible. + +So here's the basic guidelines, +each master is + +responsible for reviewing +the code + +produced by four students. + +The students typically will work +in teams of two or three + +for the projects, OK? + +So what you will have is your +four students will be + +organized into two review groups +of two students each, + +but none of the students will +be on the same project. + +The reason for that is that we +want to make sure that every + +student who goes to represent +their project can represent + +the whole project. + +So they're responsible for +the whole project. + +They don't have a buddy there +on the same team, who can + +cover for them when you're +asking them questions about + +their project. + +You ask them questions they've +got to be able to answer about + +the whole thing, even +if they didn't code + +every piece of that. + +We're encouraging them generally +to do things like + +pair programming, so they +really should understand + +what's going on throughout. + +The reason for having two +groups, rather than meeting + +them individually, it turns out +there's actually some good + +knowledge of one of them sort of +being able to see what the + +other teams are doing. + +So generally they're not +allowed to share their + +solutions, et cetera, with +other teams, but in this + +meeting that's OK. + +The ideas and so forth can come +but they shouldn't be + +making copies for each +other of the code + +of the other group. + +But they can say, oh is that +what the other team did, And + +so forth, and there can be +some learning for them to + +submit the final project. + +SAMAN AMARASINGHE: Also last +year, lot of masters very + +successfully used the other team +members to kind critique + +each other. + +So showing something do you +understand this, and then they + +can look at it and say, "Yeah, +I can see what's going on, + +that's very useful," also when +we go to masters we can talk + +about of that type of thing. + +PROFESSOR: Also things +like documentation. + +You can look at the code there +and ask the other one, "Do you + +understand what that +documentation + +says?" And so forth. + +It turns out it's actually +easier than that, because + +usually if the documentation +is inadequate, the student + +himself has trouble remembering + +what they did, right? + +I mean you know how this +works with code, so. + +So consequently you're +responsible for generally for + +two review meetings for each +of the four projects. + +Now as it turns out we'll assign +things, we're going to + +have things like students +dropping the class, and so + +there will be some minor +reshuffling as we go on. + +Some of you may end up with only +one team of two students. + +Some of you may find that you're +reconstituting it. + +In some cases if we end up-- + +we may ask somebody, "Can you +cover an extra team this time + +because somebody is going +to be out of town?" Or + +something like that. + +So there may be some variations +on this, but this + +is basically how things go. + +Now, one thing you should +understand is that you are not + +going to grade the students. + +So, one of the things I learned +long ago was that when + +you grade somebody they behave +differently than if you don't. + +So you're not grading them that +has a plus and a minus. + +The plus is that then this is +really pure feedback for them. + +This is to help them, they know +that you're supposed to + +have read it. + +The downside is some students +will say, "Eh, then I don't + +need to listen, because nobody's +holding a stick over + +my head." But the reason +we do that is twofold. + +One is because we think that the +quality of interaction is + +better, and the second reason +is because you're not + +empowered by MIT +to give grades. + +So you won't be grading them. + +You're also not responsible +for the technical + +content of the class. + +We're going to be teaching +stuff, hopefully which is + +sufficiently new, some of it, +that some of you may not know + +all of what we're teaching with +respect to parallelism, + +and so forth. + +Some of you may that's great, +but that's not the role. + +We will take responsibility +for teaching the + +content of the class. + +What we're really after here +is for you to listen as an + +experienced program developer, +and provide feedback to the + +students about software +engineering. + +In other words explained to +them what's going on. "Why + +didn't you write that in +your documentation? + +How come all your variables +have only one letter? + +Why is this stuff wrapping +around three + +lines before you-- + +why no white space?" +This kind of stuff. + +So, remember they're very smart +students, but they're + +also very immature +many of them. + +Some of them you'll discover +are like way mature, but + +there's going to be some of them +that are just absolutely + +this is new to them, and +what they need is some + +encouragement and some +suggestions as to what they + +can do to improve the quality +of their code. + +And since we're not in a +position to review it, why + +we're deputizing you as members +of the MIT POSSE, is + +to deputize you to help them +produce better quality code, + +which is not something that's +easy for us either to give + +feedback on, or to grade. + +So hopefully when we are grading +them in the end on + +their final submission and the +quality of things, it reflects + +that they've learned something +from you folks about + +producing good code. + +Also you want to be careful, +this is one of the bugs I have + +when I interact with the +students is, I tend to do most + +of the talking if I don't +check myself. + +And one of the really good +things is to have a guideline + +that they I don't know how many +of you have teenage kids, + +and if you lecture them how +quickly they learn right? + +No, they don't. + +So the goal here is to +help them learn. + +And so lecturing usually +doesn't work. + +What works generally is getting + +them to do the talking. + +And then it's great +to pepper your + +interactions with anecdotes. + +I work with one person who did +this, or early in my career I + +did this and here's how +it blew up in my face, + +that kind of thing. + +Excellent to have anecdotes that +you can give with real + +world experience. + +Why you might think it's like +this, but in fact, if you do + +it that way you're headed +down a very bad path. + +Let me tell you story +about that. + +That's fine, OK. + +SAMAN AMARASINGHE: Or if you +find a very stubborn person + +saying, "If you do that +I won't hire you." + +PROFESSOR: That counts too. + +You would never get a job here +if you coded like that. + +And in fact that's actually +what Saman says, that's + +actually one of the big benefits +of having folks from + +industry providing that +feedback, because we can say + +that, if you do it like that you +wouldn't be hired by XYZ + +corporation. + +You can say that, but if you +say, I wouldn't hire you, if + +you did that, that has +a, it's like, oh! + +It has a big impact, whereas +when we do it it's + +like eh, you know. + +It's like what do they know? + +So the guideline is make them +do a lot of the talking, so + +that they're trying to explain +and you teach them a little + +bit what a design and +code review is. + +Now, in fact what your +review is, is both + +design and code review. + +SAMAN AMARASINGHE: To add to +that, what we have told them + +is to prepare for what a filing +statement type thing, + +to walk through and explain +what they did to you guys. + +So they will come with some +preparations stuff that they + +can do that, let them, both of +them kind of do that, and then + +start them off the +instructive part. + +PROFESSOR: And maybe +they'll do that. + +But that's the goal is, you +should say, "Look, when you + +come you should prepare +something that brings me up to + +speed," and teach them a +little bit about what's + +expected of them when +you have a design or + +code review in industry. + +So for each of the projects, as +we mentioned, there will be + +a short information session, +typically by dialing + +conferencing, except +for this one, which + +we'll do in a minute. + +After the students have +submitted their beta releases + +we will get the code to you. + +Last year we had the students +responsible for getting the + +code to the MIT POSSE, and that +was basically a nightmare + +for everybody involved. + +So this time we will make sure +that we get you their code, + +and I hope that way the +unreliability-- + +I don't know if you remember +but like, these are mostly + +like juniors and seniors, and +when you're juniors and + +seniors you're not 100% reliable +in everything you do + +and your word is your bond is +not necessarily, oh I forgot + +that my word is my bond, +kind of thing, right? + +So by us getting it to you, +we'll remove one layer + +hopefully of flakiness. + +Next what you'll do is, you'll +coordinate to meet with a + +mutually agreeable time, and +then after the review you're + +going to provide us with a +little bit of feed back, it + +doesn't have to be long, just a +short email, not as a grade + +or evaluation, but to help us +understand where the student's + +are doing well, and what +they're missing. + +So what we may need to stress +in class and so forth. + +And then, of course, after +the review, they have the + +opportunity to make changes to +their code before they submit + +their final revision. + +Now, that's a little bit +different from industry where + +you would go through typically +some kind of feature freeze, + +and code freeze, and so forth. + +Our beta is beta sort of in +name, but not necessarily in + +all aspects, in that they can +actually completely rewrite + +their code between the beta +and the final version. + +SAMAN AMARASINGHE: So in your +feedback you can also tell a + +little bit about in your +interactions what worked and + +what didn't. + +This is the first time, as far +as we know anybody's doing + +this kind of a thing anywhere. + +We are also developing +a process so + +good practice is very-- + +PROFESSOR: And since your email +will go to MIT POSSE and + +everybody will read it, what +hopefully you can do is, some + +of the practices that you find +useful, I tried this at work, + +I tried this, it didn't work. + +That starts to get spread out +among you and is becomes very + +helpful for each other to say, +"Oh, well that was an + +interesting idea let me try +that." And so we hopefully + +we'll be able then to start +compiling some best practices. + +AUDIENCE: Will we be identifying +students by name + +in those broadcasting minutes? + +PROFESSOR: Yes, yes, in fact +here's the thing is, what + +you're going to do is give, +well it one, names the + +students who attended, and that +helps us keep track of + +who's actually going to +these and who isn't. + +The strengths and weaknesses in +the student presentations. + +Some suggestions for improving +the assignment. + +That's suggestions for us to +improve the assignment for + +them, and any other comments. + +So we got some really good +feedback last year that, "Hey + +the code you're handing out as +the initial code that was + +really sloppily documented." +Last year we were much more + +behind the eight-ball in terms +of trying to do this. + +This time we've had more time, +and in particular we also have + +some really outstanding TAs +who've worked very hard on the + +software engineering +of the project. + +So I think that we'll be better +in that regard, this + +year, than we were last year. + +AUDIENCE: I just +had a question + +PROFESSOR: Yeah, sure. + +AUDIENCE: You mentioned that +they're going to give to you + +and you're going to +pass the code out. + +PROFESSOR: Yes. + +AUDIENCE: Do you mean just the +code or are you thinking + +structured more as a design +review, they really will be + +talking about, a +review package. + +It would be the code plus I +don't know whether you're + +doing documentation generation +or any sort of an intro or + +front matter? + +PROFESSOR: Yeah, so the +question is whether in + +addition to the code there +should there's going to be any + +other documentation, or +package, or whatever. + +In fact, most of the final +documentation is going to be + +for the final project and not +for the beta, and so they + +should have things well +documented within the code, + +for example about what their +strategies are, and how they + +work, and so forth, but there +won't generally be a write up. + +They should be providing you at +your meeting with a brief + +outline of what's going on, and +you can ask them after the + +first meeting for any other +thing that you think would be + +helpful to them and to you in +making the design meeting more + +productive. + +One of the things always in +these things is how much do + +you require out of the students +and at which time. + +They have in this project, we're +on a relentless series + +of deadlines for them. + +And so we've tried to do as +much as we can while being + +still relatively minimalistic +in asking for too + +much stuff too early. + +And so it would be great if they +had a complete package of + +here's what's going on, the +fact is that they were up + +really late the night before +trying to get this stuff done, + +they've also had to submit beta +tests and so we decided + +that the final write up of how +their project worked, et + +cetera, we would save for the +final, and it won't be + +something, in English written +like that will only be in the + +code, it won't be as +a separate package. + +AUDIENCE: Right. + +PROFESSOR: Any other questions +about that? + +OK, so one final word, +relationships with students. + +So one of the things that MIT +has, and many other places + +have, I'm sure that you're +aware, that if you're in a + +power position with somebody, +and this in particular applies + +at MIT with students, you must +ensure that all your + +relationships are strictly +educational. + +And what that means is like +a, no romance, OK, duh. + +But it also means in this +context, no recruiting, hints + +at job opportunities, offers +of summer internships, lab + +tours, et cetera, free dinners, +and so forth. + +Your job has to be completely +educational. + +However when the term is over +you're welcome to continue + +your friendship in a non-power +relationship. + +There's no longer a power +relationship you're welcome to + +start a romance with one of the +students if you will, but + +in particular, allowed to seduce +them to come to your + +company as a summer intern, +or a job or what have you. + +So you're welcome to do that but +not during the term, those + +sorts of things are absolutely +off bounds. + +Now the students themselves may +say, "Hey do you guys have + +summer internships, and so +forth?" And it's up to you + +folks to draw the line and say +something like, "Yes, we do, + +but if you're interested in +that, we can talk about that + +after the term is over," +for example. + +So, put them off in some way, +and return the conversation to + +the educational mission +for the term. + +Yeah? + +AUDIENCE: So what if the +students do a good job? + +PROFESSOR: Yes, but then you +run the risk of it being + +interpreted as a quid pro quo +for employment, which is + +exactly the thing that we're +trying to steer away from. + +They're smart MIT students, I +think they'll figure out that + +if they're interested in a +summer internship they should + +be impressing their mentor. + +Not all of them figure +this out, by the way. + +AUDIENCE: So just to clarify. + +Just to clarify, it's okay to +say, "If you write your code + +this way, I won't hire you." +But it's not OK to say, "I + +wouldn't hire you." I just +want to clarify. + +PROFESSOR: You'd say I wouldn't +hire you, OK, my + +company would not hire +somebody who wrote + +their code like this. + +You could say that. + +AUDIENCE: But it's not okay to +say my company looks for + +people who would write +code this way? + +PROFESSOR: No, I think +that would be OK too. + +No, the issue is whether you +personalize it, right? + +If you're interested in a summer +job, I can get you a + +summer job, all you have to do +is, dadadadadadadaaa, and now + +they feel like there's another +master to serve. + +So what we want to avoid is +having them feel like there's + +another obligation on top +of the obligation + +they have to the class. + +They should not feel that in +some ways they're obliged to + +do something for you in order, +for example, to get a job. + +SAMAN AMARASINGHE: Or +get a good grade. + +PROFESSOR: Or get a +good grade, or-- + +SAMAN AMARASINGHE: If I say no +to the summer job they're + +going to badmouth me and I will +fail this class or get a + +bad grade, and then. + +So, that put them in a binding +situation that they won't work + +for the class, but they'll +feel obliged + +to something else. + +PROFESSOR: You're in a power +situation, and you're in a + +situation where you must not let +them have any sense that + +there's any power relationship +there, if you + +will, in other words-- + +AUDIENCE: We shouldn't try to +extort meals from them. + +PROFESSOR: For example. + +Exactly, exactly. + +Also if you feel anything +awkward is developing, let + +Saman, or me, this is something +for which the staff + +only email is better than +probably the MIT POSSE one. + +SAMAN AMARASINGHE: Or +even to us directly. + +PROFESSOR: Or even to us +directly, although I actually + +think it better to go +via the staff only. + +It really is much better to go +get via staff only, because + +the TAs need to know what's +going on with all the students + +in class as well. + +Question back here. + +AUDIENCE: Two logistical +questions but I don't want to + +interrupt you before +you finish. + +PROFESSOR: No, that's fine. + +AUDIENCE: Okay, it's not clear +to me do we meet with the same + +four students throughout +the term? + +PROFESSOR: If possible +we will do that. + +Because otherwise what happens +is, they hear it from one and + +then they go to another. + +So this way there's some amount +of continuity, but that + +won't happen perfectly because +students will drop and we'll + +have to reconstitute +groups and things. + +GUEST SPEAKER: The winners get +David and the losers get me. + +That's OK. + +I just wanted to be clear. + +Also you e-mail the code +to us before we do + +the sit down session? + +PROFESSOR: Yes. + +GUEST SPEAKER: Are we expected +to review it by ourselves + +beforehand? + +PROFESSOR: I think it helps +to take a look at it, yes. + +GUEST SPEAKER: As opposed +to walk in cold + +and doing just that. + +PROFESSOR: Yeah, yes, that's +right, I mean I think you do a + +better job if you have looked at +the code beforehand to see, + +oh my goodness this is, +and take a few notes. + +But for this we're relying on +you to use your best judgment + +for what's the best +way of giving + +feedback to the students. + +But I think generally the reason +we email it to you in + +advance is specifically so you +have a chance to look it over. + +Once again we're not so +concerned about whether the + +content of what they're learning +in it as much as-- + +you look at it, it will take you +two seconds as soon as you + +see one piece of undergraduate +code, it'll take you two + +seconds to say, I don't care +what this thing does this + +student needs to learn X. +I mean you will see. + +Is that the feedback, from +people who took this-- + +AUDIENCE: You'll know +it when you see it. + +PROFESSOR: Any other comments +from people + +from last year what-- + +AUDIENCE: Yeah, a +couple comments. + +One very minor sort of +procedural things. + +Personally, I found it a lot +more useful to me to show up + +in person for the information +sessions than do it by + +conference call, if for no other +reason then a lot of + +people who called in had issues +with voice quality. + +You know, just getting +a good quality voice + +signal over the phone. + +Also I found it very helpful +to have each student review + +the other one's code. + +So I would just do that to start +with, just hand it to + +each other and here, +what do you think? + +That also gives them some +experience of actually doing a + +review, as well as being +the person who's + +work is being reviewed. + +PROFESSOR: That's a great +technique just because one of + +the things that you want them +to do is empathize with the + +person who's going to read the +code, and so, by putting them + +in the situation where they have +to read somebody else's + +code they very quickly learn +oh, this is, my goodness + +that's exactly what I did to +the other one, so that is a + +great technique. + +AUDIENCE: The reference +implementations are we going + +to get those-- + +PROFESSOR: Yes. + +AUDIENCE: Soon? + +Early? + +PROFESSOR: Yes, those generally +we will be able to + +give you the reference +implementations at the + +information session. + +Or actually, we should probably +get it to them before + +the information session. + +AUDIENCE: I would suggest +before the-- + +PROFESSOR: Yeah, let's get those +make sure we get those + +to you before the information +session. + +We'll get you a reference +implementation at least a few + +days in advance. + +AUDIENCE: OK, also something +that was a recurring issue + +last year regarding the +reference supplementations + +which was the... + +there was some issues with +some of the reference + +implementation-- + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: --software +engineering. + +AUDIENCE: In particular things +like functions that should + +have been local to a file they +were not declared static or, + +that kind of thing, or macros +that should have been used or + +that were used and shouldn't +have been. + +PROFESSOR: Last year we were +running with a much larger + +class than we expected, with no +infrastructure to speak of, + +and we had two TAs who were flat +out, and so we definitely + +cut corners. + +This year the department has +been good to us, we have four + +TAs, and so I think that the +quality is going to be higher. + +That doesn't mean that the TAs +are seasoned 20 years of + +software development experience +or more, either. + +So they have some things to +learn too, but already based + +on the first project we're +ahead of the game. + +AUDIENCE: OK, also if from time +to time one of us wants + +to attend the class? + +PROFESSOR: Feel free to +attend the class. + +AUDIENCE: OK, where's +the schedule? + +PROFESSOR: It is Tuesdays and +Thursdays in 26-100 at-- + +AUDIENCE: Is it on +the website? + +PROFESSOR: It's on the website +at 2:30 to 4:00. + +So Tuesdays and Thursdays 2:30 +to 4:00, you're welcome to + +come and learn all about +performance engineering. + +Reed, did you have a question? + +AUDIENCE: No, I guess I was +just going to say that in + +regard to the feedback, we +TAs here have got that. + +SAMAN AMARASINGHE: During class +last week most of the + +TAs were students last year, +so they aren't learning + +anything new. + +AUDIENCE: I'm sorry, +where is the class? + +PROFESSOR: It's in 26-100 + +AUDIENCE: So it's not here? + +PROFESSOR: No. + +So this is the situation, we +outgrew our classroom which + +seated 60, and we had 85 or 90 +students, so they put us into + +the next smaller classroom +that we would fit into. + +That was 26-100 which +fits 500. + +Then we found that in 26-100 +you needed a microphone for + +the students to hear you, even +though we had them all crowded + +into one quarter of the +auditorium, you still then-- + +just the structure of it-- you +needed a microphone, so they + +said, "That will be $85 a +lecture." And you say, "What + +do you mean $85 a lecture?" + +SAMAN AMARASINGHE: Someone has +to walk in just to turn on-- + +PROFESSOR: To turn +on thing thing. + +So, anyway we sorted all this +out OK, but it was sort of + +funny that you're charging us +for being in a room that we + +have no choice as to be in? + +Anyway it was very funny. + +AUDIENCE: Are your lectures +video taped are they + +available-- + +PROFESSOR: They are +videotaped. + +We are not planning to put them +up quick because what + +that does is discourages +students from attending the + +lectures, as you can imagine. + +SAMAN AMARASINGHE: Mainly for +OCW OpenCourseWare So they + +basically they could go to +OpenCourseWare they will + +process it and they have to go +through a lot of legal stuff + +and make sure the +named are right. + +PROFESSOR: Are right +and so forth, yeah. + +There is a bunch +of stuff there. + +Good, so it says final words +here but they aren't really + +final, because we still +have Eric to talk + +about the first project. + +But the feedback from the +students last year was that + +the MIT POSSE was one thing that +made this one of their + +favorite classes. + +It was getting that kind of +seasoned feedback in a very + +small group setting when you +look at the student faculty + +ratio, that's one thing you're +always battling. + +especially at MIT, where we are +in a very popular major, + +and so the ability to recruit +all you folks to help that + +ratio in favor of the students +is really very much + +appreciated by students and +by us, so enjoy the term. + +This is really rewarding the +people who have done it before + +we had just tremendously +positive feedback from them + +about just how rewarding it was +to work with these young + +programmers. + +SAMAN AMARASINGHE: They are very +smart people, you can see + +the changes, you will see +the you impact on them. + +You will see you're molding +these people into better + +programmers, so that's +the fun part. + +PROFESSOR: So Eric is now going +to talk a little bit + +about project one, and this is +similar to what we will do, + +although most of you will +probably be on the phone + +unless you heed Barry's advice, +for the future one. + +So I'll get out of your way. + +ERIC: So the project one this +is, I think, the one project + +that was substantially different +from last year. + +So, the code for this +project we, the TAs, + +coded up this semester. + +Did we give out the hand outs, +Saman, or Charles? + +Yeah so these are the-- + +PROFESSOR: So this is the actual +assignment and we'll + +share this with you, +plus the reference + +implementation, I think. + +ERIC: Well we'll send out the +reference implementation + +tonight then. + +In fact, now people have already +done their betas for + +project one. + +Project one has two parts, it's +a part called Every Bit + +Counts and a part called +Tiling a Torus with + +Pentominoes. + +So the first part it's an +abstract data types of + +modeling and bit array, packed +bit array and they are a given + +a couple of tasks to do on +long strings of bits. + +So you might have eight million +bits and there are two + +functions to rotate the +substring of the bits by some + +amount to the left or right, and +the other operation is to + +count how many flipped +bits there + +are in a given substring. + +So the specific interface for +this, this an excerpt without + +the comments from the header +file of this C module. + +There is a couple of accessors +which accesses bits + +individually those are not, +well those accessors are + +currently used to implement, +in the reference + +implementation, the rotate and +count flips operations. + +So what they will need to do +is to go into the C module, + +the implementation, and change +these functions, to basically + +be 10,000 times faster, or +whatever, I can't remember + +what they actually got. + +In particular the rotate +operation is incredibly slow, + +there's one constraint for them +and we're saying that, + +well imagine that this is on the +cell phone or something, + +where you have a really big +bit array, but you don't + +really have very much more +memory to consume beyond that + +big bit array. + +So we're asking them to only +do this using a constant + +amount of memory. + +So that's the first problem +with these two parts, the + +rotate and the count flips. + +Any problem, questions about +that particular part? + +Does it seem clear what? + +AUDIENCE: What does the +count flips do? + +ERIC: Oh yeah, so I should've +swap those two slides. + +So, if you have a bit string, +suppose nine bits or + +something, 1, 2, 3, 4, 5, 6, 7, +8, that would have to be 8. + +If this is the substring you +want to count, then you count + +transitions from zero to +one, or one to zero. + +And there's some new tricks you +can do by for instance, + +considering six-- + +AUDIENCE: Count the number of +runs, of consecutive value. + +ERIC: Yeah, the number +of runs. + +AUDIENCE: Plus plus one-- + +or minus one, yeah. + +ERIC: That's right. + +And you don't count the +beginning or the end as a + +transition, so in this +particular substring there is + +one there, one there, +and one there. + +And it's not a substrings, it's +always substrings, it's + +not the entire string, and you +can see that for instance, you + +give us an argument, the bit +array and you say where the + +starting offset and the number +of bits that the substring + +that the substring is +and that's where the + +operation is done. + +So our testing routines will +do lots of rotations in + +different parts of +that substring. + +AUDIENCE: For the memory +constraint, do you have a + +fixed size that they're +allowed to use or? + +ERIC: We decided against +the fixed size. + +We just say don't use malloc, +and you can allocate constant + +amounts of memory, and the thing +is if they choose to + +have a 16 megabyte or four +gigabyte lookup table then + +their performance will +suffer anyway. + +So yep? + +AUDIENCE: What is the computer +architecture? + +ERIC: What's that? + +AUDIENCE: What is the computer +architecture? + +SAMAN AMARASINGHE: We +are running on-- + +we got this donation from both +Intel and Dell, we have 16 + +machine-segments, each with two +six core processors and 48 + +gigs of memory. + +So they're doing it on 12 +cores so it becomes + +interesting, and you got a +parallel 740 gigs, so we have + +a lot of memory in these kinds +of things and we'll be asking + +them to run through that. + +So these were the latest +what's the word? + +PROFESSOR: Core i7. + +SAMAN AMARASINGHE: Core i7s. + +PROFESSOR: Nehalem. + +ERIC: For this first project, +we're asking them specifically + +not to parallelize. + +AUDIENCE: It's all on +Windows or Linux? + +ERIC: Linux. + +AUDIENCE: Linux? + +ERIC: Yeah. + +So the idea here is to exploit +bit operation and in + +particular in rotates. + +The reference implementation +does the really stupid thing + +of you want sort of 4,000 bits +to the right rotates, well + +I'll do it one at a time, +that's the reference + +implementation. + +But they're only allowed to us +a constant amount of memory, + +so there is certain amount of +tricks you have to do to do it + +in a more efficient way. + +AUDIENCE: Do you stress in the +course about portable data + +code from one operating +system to another, one + +machine to the other. + +PROFESSOR: This is where we +want you to stress the + +importance of it, because that's +not something that + +we're in a position to do or +enforce, or what have you, OK? + +We let them assume for this +problem, for example, that the + +machine they're working +on is Little Endian. + +We talked about the issue, but +we did not insist that they + +wrote code that would be that +would port to a Big Endian + +machine, because they're running +on the Intel machines. + +But this is exactly the kind +of thing where code quality + +would say, portability, +maintainability, readability, + +all these kinds of things, this +is exactly the kind of + +thing we want you to say. + +You say "Hey, you did it like +this, in fact did you know + +that without sacrificing +anything in performance, you + +could have made it portable from +one operating system to + +another?" And then you could +talk about those issues, and + +that's absolutely super, +to do that. + +But we are not spending a lot +of class time doing that, + +we're really focusing on the +performance engineering part + +of the course. + +ERIC: The reference +implementation should be + +portable, so this should be +portable, although we did make + +sure here, for instance, in the +reference representation + +of bit array here, that the +order of the bits within each + +bite happened to coincide +with the low end + +ideas of these machines. + +So that if you happen to cast it +to a 64-bit integer on each + +of the bytes in the array then +you would get something that + +was easy to work with on a +low end in architecture. + +But the reference implementation +is portable + +itself, or should be, so tell +us any kind of problems with + +the reference implementation +like that. + +The next problem is based +on the puzzle, + +it's a puzzle solver. + +It's this puzzle that I'd +never heard of before. + +Apparently, if you generalize +dominoes you get Pentominoes + +and the five end cases. + +So there are this many +configurations of dominoes + +with five squares on +them, I guess. + +And the pentominoes puzzle is +you're given an eight by eight + +board with four squares crossed +out, and now you're + +supposed to arrange these so +that the entire board is + +filled up, and only-- + +what's that? + +SAMAN AMARASINGHE: You can +do flips of these-- + +ERIC: Oh, right. + +You can do flips, you rotate + +SAMAN AMARASINGHE: And +they will dissipate + +and all those things. + +ERIC: Right so the task is +find all the solutions, + +although I believe in our +reference implementation that + +was too fast, so we decided to +generalize the puzzle to the + +toroidal case, where the board +wraps around the edges, just + +to make it take a little +longer, to do. + +PROFESSOR: Like space +boards right? + +You go off the right edge you +come in the left edge. + +AUDIENCE: Top and bottom also? + +PROFESSOR: Top and bottom +also, yeah. + +ERIC: So these two are +both examples of + +solutions to this puzzle. + +AUDIENCE: I've got +a question here. + +ERIC: Yep. + +AUDIENCE: Are you allowed +to put the empty space + +where ever you want? + +ERIC: Well, that's the +input to the solver. + +SAMAN AMARASINGHE: Given +these empty spaces-- + +AUDIENCE: OK, and then +it fills in the rest. + +ERIC: That's right. + +Of course you can put +empty spaces so + +that it can't solved. + +And then they have to correctly +determine that + +there's no answer. + +PROFESSOR: That there's +no answer. + +AUDIENCE: Right. + +ERIC: And, also I believe the +reference solution takes days, + +for certain. + +To find all the solutions of +certain configurations of the + +initial four dots. + +So there's an option to the +program we give them, to just + +find the first 2,000 +or something. + +PROFESSOR: So once again you can +see this is conducive to + +bit tricks, where you represent +the board as a + +64-bit word and then do masking +operations, and so + +forth, to determine whether +a piece fits + +and do clever shifting. + +It's easy to shift a piece down +one row, where you're + +trying it out, because that's +just a shift by eight, but how + +do you shift it horizontally, to +come around on the other-- + +So they have to do some +shifting, some masking-- + +So anyway, the first project +is all about thinking about + +bit representations of +things, and so forth. + +ERIC: In fact, we give them a +solver that we don't really-- + +well, a searcher, routine to +search the space of possible + +solutions, that we don't really +expect them to change, + +but they can change it +if they want to do. + +So, the interface here is +basically a board data + +structure that they're free +to change the internal + +representations of. + +Or did we somehow prohibit +that due to testing? + +No? + +No, no, no, that's the +whole point, right. + +So again, you have this basic +accessor for use by the + +testing routines. + +But then what you really need +to, well, you need to change + +basically the entire +implementation of all of this, + +if you're changing the +representation of the board, + +for instance. + +But this is the function that +should be running faster after + +you're done, so I guess that +comment is misleading. + +This is the function that is +supposed to run a lot faster + +when you're done. + +There is actual comments +in the header file. + +So right, you give +it a function + +pointer to a call back. + +PROFESSOR: Now, one sort of +standard thing we decided + +we're doing is, we're not trying +to write both 32 and + +64-bit code in the classroom, +we're just going to do 64-bit. + +So just one more level. + +In practice you would want to +have stuff that runs both on + +32 and 64, but for the most part +it's fine if they just + +have it running on 64-bit. + +ERIC: Right, so these by the +way are the initial four + +points that are the input +to the puzzle. + +I believe that's the +problem set one. + +Questions about, yeah? + +AUDIENCE: Can students submit +more than one answer? + +PROFESSOR: No. + +Nope, they got to decide +what they're doing. + +AUDIENCE: I guess I have a +question about the answer. + +ERIC: Yeah. + +AUDIENCE: Is an answer that is +probabilistically correct, I + +mean like, it will sometimes +when you test it, you have it + +pass all the test cases, but +mine isn't guaranteed to + +necessarily always solve all +test cases is that OK? + +ERIC: If they can conceal that +to us, then I think they-- + +PROFESSOR: They deserve +credit. + +ERIC: Keep in mind that the +other half of the problem set + +is to write test cases that +will catch as many obscure + +bugs in the other students' +code as possible. + +So they run the risk of +competing against-- + +PROFESSOR: They lose extra +points if they don't pass + +their own tests. + +AUDIENCE: They each need +to write some tests + +that will be as-- + +PROFESSOR: Yeah, +so then they-- + +AUDIENCE: They exercise +somebody else's. + +PROFESSOR: --to somebody +else's, yeah. + +SAMAN AMARASINGHE: We are +running all the tests against + +everybody else. + +PROFESSOR: And then for the +final version we give them the + +full regression suite of the +whole class, so they have very + +good confidence, and we good +confidence that they're + +handing in something +that is correct. + +SAMAN AMARASINGHE: OK, so you +want to open up for-- + +PROFESSOR: For questions +or comments. + +SAMAN AMARASINGHE: Especially, +I won't even mind the people + +who did it last time, last time +to provide some of your + +feedback on how we can... + +[BUZZING NOISE] + +PROFESSOR: Don't want +to do that? + +SAMAN AMARASINGHE: Yeah, + +PROFESSOR: I was trying +to turn on the lights. + +Do we have more lights +we can turn on? + +SAMAN AMARASINGHE: Also, if you +could turn these on, too? + +PROFESSOR: Good. + +Yeah, so comments? + +AUDIENCE: I want to say that's +why I was a master last year, + +and I had a great time, but +I figured I'd stay-- + +[INTERPOSING VOICES] + +PROFESSOR: Yeah, could +you stand up so + +people can hear you? + +Thanks. + +SAMAN AMARASINGHE: +Give him a mic. + +Give him a mic because I +think it'll be good-- + +PROFESSOR: It'll be good +to have these-- yeah. + +All right? + +AUDIENCE: All right. + +Thank you. + +So the first thing I found +really helpful was to take the + +reference solution and actually +diff what the student + +provide because they often just +provided a solution, and + +if you don't know what they +started from, it was hard to + +tell what they'd +actually done. + +So diffing the two, that was +a good place to start. + +And then I found incredibly +helpful just to spend 15 or 20 + +minutes prior to actually +meeting with them, looking at + +the code and writing like two +or three or four things to + +talk to them about. + +And it might sound like it's +going to be highfalutin and + +stuff, but it was like they're +using their returning function + +pointers to local variables, +stuff like that. + +It was really like what the hell +the makefiles were doing, + +for example, is something +that I think they really + +appreciated me telling +them that didn't get + +talked about in class. + +Especially once I got a good +rapport with them, they just + +ask questions, and I spent the +whole time answering more + +practical stuff about +the problem. + +We had a good discussion, so +that's what I would suggest. + +PROFESSOR: Thank you, that's +great feedback. + +Yeah, as I say, don't +underestimate-- + +I mean, most people learn the +kinds of things you're saying, + +but somebody told them that, +hey, these are practices that + +really don't make sense in +a real software system. + +AUDIENCE: People were, by the +time we got to the projects, + +your standard pattern was highly +representative, a bunch + +of flags you want to encode in +a bunch of fields, right? + +And you've seen them a +couple times, it's + +just a standard pattern. + +PROFESSOR: Yeah, so one of the +things you'll find in this + +first one is that they're very +confused about the difference + +between unsigned and signed, and +how shifts work, and what + +happens when, you know, how come +I shifted this thing left + +33 bits and I got a zero. + +Why? + +I thought I was shifting a +64-bit value, but in fact, + +they hadn't done 1LL, +they just did 1. + +And so there are things like +that, where they don't-- + +very low hanging fruit, if +you will, to talk about. + +AUDIENCE: Did you tell them +about valgrind by the way? + +Like, why would programs crash +when they said they spent a + +huge amount of time debugging +these crazy C programs when + +they're not used to the compiler +not protecting them. + +PROFESSOR: Actually, that's a +good point because we were + +going to try to introduce-- +maybe we should do that as + +part of the next lecture, +spend a little + +bit of time on valgrind. + +SAMAN AMARASINGHE: Yeah. + +PROFESSOR: Because the memory +checker there is really a + +pretty useful tool for them +to get correct code. + +AUDIENCE: I second that. + +That thing has saved my +butt so many times. + +PROFESSOR: So many +times, exactly. + +AUDIENCE: I've heard that, but +more low-hanging fruit for + +valgrind is to always compile a +-w all to just cache all the + +warning and declare all warnings +as errors, and it + +just makes-- + +PROFESSOR: I think that +we have that as a + +default in our makefile. + +Is that right? + +ERIC: At least for the +first project. + +PROFESSOR: The first project? + +AUDIENCE: I think they should +understand that in industry + +practice, if you don't do +that, you're a schmuck. + +PROFESSOR: Right. + +Yep. + +Good, so that's good, and why, +in particular, the valgrind-- + +we discussed that last year, +and really actually, the + +upcoming lecture's exactly +when we should do that. + +SAMAN AMARASINGHE: Because +there's also another tool + +called Dr. Memory. + +PROFESSOR: OK, which +makes sense, yeah. + +AUDIENCE: One issue that I +experienced a little last year + +was that people they +specifically intend to write a + +little test for their code. + +They've mostly relied on a few +runs by hand, then they wrote + +a progression producing things +that they ran earlier. + +I guess that now you're actually +encouraging them to + +actually have a test suite. + +PROFESSOR: Yeah, well, now they +get points off if they + +didn't write enough test that +somebody else's code passed it + +that had a bug. + +AUDIENCE: And in this case the +testing run will be as far as + +the first turn in, and then the +second turn in is just you + +have a version to run +against and then + +just need to optimize. + +PROFESSOR: Right, +that's right. + +SAMAN AMARASINGHE: So first, +about the actual tests they + +have write a lot of tests +because that will help, and + +the second, then you give +them all the tests. + +So they will have a lot of test +suite to run and then of + +course we have a lot of number +of points we'll deduct of you + +actually fail those test. + +Because they have no excuse. + +PROFESSOR: There's no excuse +at that point, it's just a + +question of having-- + +AUDIENCE: What performance and +measurement tools are you + +going to be using this year? + +SAMAN AMARASINGHE: So, right +now, we are going to give them + +perf because what we found was, +the process of ECUT is so + +new a lot of performance tools +don't have-- like OperaFile + +didn't work, because they +haven't been ported properly. + +There's no port for it yet. + +So perf we are going to use, and +we are thinking of giving + +them gprof in there. + +And then last year gave them +couple Pintools we didn't ask + +them to write anything but for +example, account number + +instruction or couple of +tools they do that. + +Those are main tools you get, +and also we need to go to + +Cilk, you'll do a bunch of +Cilk tools in there. + +AUDIENCE: Everyone last year, +they were given VTune, I think + +it was, it was too hard +for them to use. + +PROFESSOR: Yeah, that was too +hard for them to use because + +they have to use the machines +remotely, and VTune and is an + +interactive tool, and so that +just made it very complicated + +to do things. + +So instead we're going to go +with a something that has + +textual output, and is easy, +therefore, to run from command + +line and has all the advantages +of running things + +that you get when you run things +from command line. + +AUDIENCE: So a logistical +question so, meeting on MIT is + +fine, but where are there +designated places to meet? + +SAMAN AMARASINGHE: We will +work with student to find + +places for them. + +For example, there are locations +for PSS students to + +meet, and we are going +to get them arranged. + +So if in the organizing you guys +can create probably an + +online scheduling something. + +What's that website? + +Online is, online +scheduling is-- + +PROFESSOR: Doodle. + +SAMAN AMARASINGHE: Doodle, +Doodle or something like that, + +and get their times and then +they'll work with us to figure + +out the place to meet, and then +they can send it out. + +One thing we will have to do +is, between four students, + +because every project we are +chaining the pairings, so + +sometimes we might end up in a +way that, two of your students + +are paired together, and then +we will tell you don't put + +them together in the same group, +you'll basically have + +to mix them in the other way. + +If they are not in any kind +of a pairing, then you can + +organize the four in +any way you want. + +PROFESSOR: Actually I don't even +want of the four of them, + +I don't even want us pairing. + +That shouldn't be. + +But we'll see what happens. + +Barry? + +AUDIENCE: Last year of course +was in classroom downstairs + +and I just met them just +outside the classroom. + +There's plenty of +little space. + +PROFESSOR: Also the first floor +of STATA, I mean we've + +had a lot of people just +using the first + +floor of this building. + +There's lots of cafe and place +there, and so forth, to sit + +there, get a coffee, +and so forth. + +So some people just did +something that informally, + +other people wanted a more quiet +private place to talk. + +And I think that we'll help the +students facilitate that. + +SAMAN AMARASINGHE: And the key +thing is, especially if any + +students are flaking out, for +example, doesn't answer your + +email, or missed the meeting, +or something like that, or + +late to the meeting, +let us know. + +Because that's part of their +grade, even though you're not + +grading them, if they are not +participating in working with + +you guys, they will get +points deducted. + +So we really want to know that, +and we have tried to + +emphasize that they have to act, +and actually do it right. + +So we really need to know that, +if the students are not + +actually cooperating +with you guys. + +PROFESSOR: So I hope that this +year will have a better-- + +So the vast majority of people +last year had no trouble, but + +we did have a couple of people +for whom it was one or two + +students who just made life a +little bit miserable for their + +master, and so hopefully we'll +provide a few more incentives + +this year to avoid +that situation. + +But they're students +and so they-- + +AUDIENCE: When do we find +out which students + +are assigned to us? + +SAMAN AMARASINGHE: Probably +the next two days. + +OK, and then who's responsible +for contacting whom? + +That's a good question. + +Who should we contact? + +PROFESSOR: We decided that, +didn't we, at the meeting? + +What did we decide? + +AUDIENCE: This is what happens +when you don't + +write things down. + +SAMAN AMARASINGHE: You have +to cover the old stuff. + +PROFESSOR: Let's see, so last +time I think we had it that + +the students contacted the +mentor, and then-- + +SAMAN AMARASINGHE: What we will +do is we will set up, + +we'll send the intro email to +everybody, we'll send the + +intro email to the mentor, Cc +the student then saying I am + +introducing you to each other. + +And then one thing you can do +is immediately reply and, if + +you have Peter Doodle Paul, +or something like that. + +And then say, OK, look, do +you know your students? + +So you can reply to that and +hopefully they will reply + +back, and proceed. + +So when we send you the names +you will also see the emails + +of students. + +PROFESSOR: Are people familiar +with doodle? + +Anybody not familiar +with doodle? + +So doodle is a website where +you can basically enter a + +whole bunch of times, and then +people enter their names and + +mark off which times they +can make things. + +It's a poll source. + +SAMAN AMARASINGHE: Don't do what +I did the last time, I + +marked off all the times that I +cannot participate, so I was + +basically the exact opposite. + +PROFESSOR: It's green and red, +is what the colors they use. + +So green means you can make it, +and red means you can't. + +So, anyway you don't have to use +that facility, but it is a + +convenient one to use. + +AUDIENCE: Can we expect students +to be dropping? + +SAMAN AMARASINGHE: There will +be people dropping. + +They just started. + +This is also a group project +and at 2:00 AM we got mails + +saying OK, I'm dropping the +class, and we had to scramble + +trying to add a 3:00 AM +to create another + +group, and so, Yeah. + +AUDIENCE: You shouldn't +take dropping as a + +reflection on our end. + +People drop out. + +SAMAN AMARASINGHE: You +have to know that. + +PROFESSOR: You can +if you want. + +AUDIENCE: I had like +three people drop + +PROFESSOR: No, that +tends to be more-- + +AUDIENCE: I had one student, +it was awesome. + +So easy. + +PROFESSOR: Yeah. + +AUDIENCE: To get an idea of the +mindset the students are + +going to be in this sort of a +really tough 6-170 type thing, + +or is this one of the +easier classes. + +PROFESSOR: No this is +a challenging class. + +SAMAN AMARASINGHE: So +you take 6-170 that + +has about four projects. + +We doubled the number of +turn-ins because each project + +has beta and a final, and +some projects has + +two turn-ins in there. + +So basically, they have all +their big projects going on, + +because they are doing the +new project and they have + +submitted final on the +previous project. + +And they're already completed +project zero that was-- + +PROFESSOR: Just like +real life huh? + +SAMAN AMARASINGHE: We gave +them project zero. + +That was built to to get used to +the system and we can help + +them with the class, they +have to finish this one. + +So this class just screams +excess very, very-- + +PROFESSOR: Yeah, and of course +they're students, some of them + +have learned you put off things +to the end, and haven't + +learned the lessons of +well not always. + +So as I said, as a group they're +relatively immature + +when it comes to some of these +things, but there's a large + +fraction of them who are +incredibly mature about these + +kinds of things. + +So our job is as lecturers in +the class is to make it so + +that the students +who start work + +early don't get penalized. + +And that's probably the hardest +thing in the software + +related class because, the +classic thing is that they + +want to get started, they +find all the bugs right? + +And they waste their time doing +it, and if you do it + +later, then the TAs have worked +all the bugs out. + +So one of our challenges is to +make it so that students who + +start early are rewarded by +being able to have more time + +not wasting their time. + +SAMAN AMARASINGHE: And today was +the day that they turn in + +the project and by looking at +the class, you realize they + +haven't gone to sleep, and I +asked and most people haven't + +slept in about 30 hours. + +They have been up entire +last night and an email + +conversation when I went +to sleep there was + +an email train going. + +Every five minutes, +something pop up. + +When I woke up, the train was +still going, and amazingly, + +there were a couple of TAs up +and answering all through the + +night, and that kept +continuing. + +So these kids they can be flaky +sometimes, but they're + +amazingly hard working. + +And this is only one class +they're taking. + +They might be taking four +classes like that. + +And I have seen people +scheduling their schedule as + +by hour, scheduling and they +say, OK, look I can do the + +problems set or I have +one hour of sleep. + +And a lot of times that's +their thing, and then + +sometimes they triage. + +That's why sometimes they miss +classes, they realize, OK, I + +can do the problem set, I can +sleep, I came do that. + +So I think these kids +work amazingly hard. + +PROFESSOR: I do think it's +helpful to also counsel them + +on, hey, you can't do everything +on a death march. + +You got to learn at some point +what you're capable of, and + +manage your own time resources +and so forth. + +Because the joke at +MIT is, classes, + +friends, sleep, pick two. + +The other thing, let me just +say, is that despite the + +obvious sleep deprivation we +saw in the class today the + +number of students who came up +after class so charged about + +working on this first project +was really quite amazing. + +They were all very, +very excited. + +And very excited we also gave +them the initial feedback on + +the performance, and you could +see, there's one group of + +students who clearly got it, and +then there's another tier + +of students who didn't get it +quite this much, and then + +there's the ones who their code +has errors and stuff. + +There's no doubt that there are +a lot of students who are + +very charged about this. + +This is a fun class but +it's a hard class. + +SAMAN AMARASINGHE: I think +you'll find this is true. + +They will be, probably tired, +but they will be soaking up + +this information like a +sieve, and sometimes + +I found last year's-- + +After the looking at the first +set of code, some of those the + +masters were really upset. + +How can you teach you guys, +these guys write this kind of + +bad code, but when they realized +after they said + +something, this is getting +into their heads. + +I mean, they're improving +they're actually changing. + +These guys are very smart, +and they're looking + +for you guys for-- + +They're basically sponge, +really empty sponge. + +They're going absorb a +lot in this class. + +PROFESSOR: I have a 2 and 1/2 +year old at home, and it's + +amazing what the progress is +she's made in six months. + +She talking now in complete +sentences, and so forth, it's + +just really amazing how how +she does it, and these + +students are like that. + +They start out and you say, oh +my God, they have no skills + +whatsoever. + +By the end of the term the +progress that they've made is + +really astounding. + +You just say, gee if you could +just keep on that trajectory + +your whole life. + +But really, they really are very +smart, and they come up + +to speed very, very fast, +especially given good + +counseling. + +The main thing that they need +right now is just the + +attention so somebody actually +can look at their code and + +say, you know you did it like +this it would be better code. + +Any other questions or issues? + +This is lots of fun. + +If you run into any troubles, +we're right here, + +just send us email. + +And as I say they're young and +immature, but then you get to + +see them grow, of course some of +them will flake out on you, + +but the vast majority, you'll +see, are really very dedicated + +and well meaning. + +They really want to do a good +job in the class, and really, + +really find the class +very exciting. + +Our numbers, in fact, almost +doubled for last year. + +So the reputation got around +that this was a + +good class to be doing. + +And the other thing is, right +now what I really like about + +the class, the students right +now compared with + +say 10 years ago. + +So 10 years ago we had the +Internet boom, and there were + +all kinds of students taking +computer science because they + +thought it was a ticket to +fortune and so forth. + +And now we're back to what it +was pre-2000, 1998, whatever. + +Where the vast majority of +students who are taking the + +class really enjoy +engineering. + +They really enjoy +the software. + +They really enjoy +the engineering. + +The fact that you end up with +a pretty good job and + +opportunity sometimes to do +entrepreneurship, and + +opportunity to explore things, +it's sort of like, oh that's a + +fringe benefit. + +But what they're really after +is just the intellectual + +excitement and so forth. + +So it's really quite fun to +work with the students and + +quite rewarding. + +Really very nice type of class +to have right now, where the + +students taking it because +they're actually interested in + +the material, not because it +buys them a bread ticket, meal + +ticket, whatever. + +Yeah, question? + +AUDIENCE: The standard, is the +coding standard in the + +reference, the standard is to +consider for them provided? + +SAMAN AMARASINGHE: I don't +think we have set up a + +standard, per se. + +What we want them +to do is kind of + +create their own style. + +It's like in a writing class, +you don't give them a standard + +writing guideline is to follow +this one, you don't constrain + +them to that. + +We want to give them the +opportunity to grow into their + +style, but kind of guide them, +so that they don't make the + +classic mistakes. + +That's why we need you guys, I +mean, if there's a standard, + +we can come up with a standard, +create a script to + +actually check the standard, and +then say, OK, thou shall + +follow the standard. + +And you can do that and +everybody will hate it. + +You can't make that +bad happen. + +One thing you want to do is +make them lifelong good + +coders, not something they +realize OK, I need to do this + +to get this grade, and I'm going +to abandon everything + +and convince myself never +to that again. + +And we have had sometimes, like +when we needed all this + +software engineering. + +We went through things like +thou shall write all the + +preconditions and +postconditions, and everything + +will be graded. + +And people did it, but half of +them got into them and said + +this is good things. + +Other half, they didn't realize +why they're doing it, + +they just hated it. + +And I don't think they +left assuming I would + +never do this again. + +So the key thing here is, +we don't want force + +something on to them. + +We want them to come through a +natural process, and I think a + +lot of them, can, when they +understand what they're doing, + +they'll develop a really +good kind of practice. + +PROFESSOR: It's also the case, I +think, that coding standards + +vary culturally from place to +place, and the what people + +expect in one place is different +from what thing. + +So being too prescriptive means, +as Saman is saying, + +that it becomes a grammatical +thing, rather than is this + +code organized. + +The real thing, coding standards +are very important, + +especially in large software +organizations of course, so + +that everybody can tell what's +going on in any particular + +piece of code without having +been the author. + +But in this kind of thing where +we have something that's + +relatively small, what we're +mostly interested in is the + +organizational aspects of coding +style, as opposed to + +the grammatical ones. + +SAMAN AMARASINGHE: So also don't +impose your standard and + +say, my company this is what we +do, I want to follow that. + +Just figure out and kind of +guide them towards something + +while they're maturing, and +try to make it better. + +That's the thing. + +That's why you cannot have +a cookie-cutter model. + +PROFESSOR: And why it's good +to have senior software + +engineers who understand what's +really important, as + +opposed to what might be +required in any particular + +individual situation. + +SAMAN AMARASINGHE: One other +topic I want to add is + +sometimes when you have two +students, there might be a + +case that one person might be +very talkative and dominating, + +and one person might be just a +listener, and so you have to + +keep an eye on that and make +sure that you give the other + +person opportunities to talk, +and because it might + +be just like that. + +Encouragement and stuff like +that, so make sure that you + +get both of them to talk. + +And also the are supposed to be + +responsible for all the code. + +You should not let them get away +by saying, oh my partner + +wrote it, so I don't +understand. + +So that's not a good answer. + +So get them to actually go +through that, and if they + +don't come prepared tell them +that, and you can give them + +some feedback, as a next +time can you please + +do, this and this. + +Because they also don't know +what to expect, and we give + +them a little bit of guideline, +but it'll be good, + +also for you, the first time +around, if you find some + +mistakes also for the next code +review you can encourage + +them what to do, how to prepare +and what to do. + +Don't give them too much work, +because we're already giving + +them enough work. + +Don't ask them to write extra +documentation, but you can say + +it would have been nice if you +had this level of preparation, + +if you could have explained to +me, or given me a summary, or + +something like that. + +So something like that is +something you can expect. + +And the other thing is if you +had to figure out how we want + +to do code review. + +So, for example, you might want +to bring your laptop, or + +ask them to bring a laptop in +there, if you want each other + +to look at the code on the +computer, so ask them to bring + +the laptops or something. + +So think about the logistics +of how you're going to do + +that, and that'll be useful. + +PROFESSOR: And I think any other +sort of expectations you + +have, in your email to them +the first time say, here's + +what I'd like you. + +I think it's helpful to say I'd +like you to come prepared + +to give me a five minute update +on how you did each of + +the problems, for example. + +We will be telling them that, +but to have it come directly + +from you means-- + +The difference if I say go do +this to that person, versus + +you're coming to me +and expecting it. + +Good. + +So, I want to once again, I +can't thank you folks enough + +for being willing to +give your time. + +Time is the stuff life is made +out of, so I really appreciate + +your willingness to volunteer +your time for these students, + +and I really think you have a +dramatically meaningful impact + +on the students. + +The students may or may not +fully appreciate that, OK, but + +Saman and I really appreciate +that, and we will make sure + +the students appreciate it. + +AUDIENCE: Yeah. + +I just have one. + +What what are the guidelines for +a contact outside of the + +code reviews with +the students. + +I mean are they, can we have +them email us with questions + +about the process and just +kind of general guidance + +PROFESSOR: It's your level of +tolerance we don't want you to + +have to commit more than about +20 hours across the term, + +because then it becomes +onerous. + +But if you're willing I think +it's completely open ended, in + +terms of how much else. + +I mean it's one thing if you go +into solving their problems + +for them, that we don't want you +doing, but when it comes + +to, especially the quality, and +non-metrical aspects of + +programming, the more you can +give them the better, OK? + +Because it's only making them +be better programmers. + +And I think the fact that there +may be some unevenness + +in that across the masters +is irrelevant. + +Really, I do not want to hold +back some students from + +getting good mentorship because +somebody else is not + +getting the same level of +attention, et cetera. + +But really, no expectation +there, on our part, to do more + +than the code reviews +themselves. + +SAMAN AMARASINGHE: So, that said +I want to make sure that + +you aren't answering their +question, at some point I + +don't want to be a +crutch for them. + +For example, if they say, OK, +before prebeta, they say OK, + +this is my next problem, can you +on a little bit, I didn't + +understand. + +If you have that, so they're +trying to get too much into + +that level, kind of making you +their programmer, or something + +like that, just let us know. + +A lot of these things, there +will be a lot of cases that + +arise that we haven't +thought through. + +The students are ingenious +enough they will find a lot of + +loopholes, a lot of kind of +interesting things that we + +never thought through. + +So if you find something that +you're not feeling comfortable + +just send a mail and say +OK, take a look. + +PROFESSOR: It really is, if +their questions are about + +course content it's not +appropriate for you folks to + +be dealing with, really. + +OK, that's what our TAs are +for, and course staff. + +If it's about coding style and +engineering practice, and even + +time management, or anything +that's sort of the + +non-technical aspects, but +things that have a strong + +impact on technical, that yes. + +Anything you can provide +there is great. + +SAMAN AMARASINGHE: So if you +find anything that's outside + +the norm of what we discussed +if you feel a little bit + +uncomfortable, just +send email. + +Send an email, and say, +hey, can I do this? + +Is it OK, for me to do this? + +And then we can always provide +guidance, so we are + +responsible. + +PROFESSOR: --do something and +say after the fact, oh, it + +went past, let us know. + +There's rarely anything you can +do on one shot basis that + +is heinous or unrecoverable +from, or whatever, so. + +SAMAN AMARASINGHE: It +is always good, + +I mean that's why-- + +since we see everybody able to +and we have done these kind of + +situation before. + +We can just easily +tell you what. + +PROFESSOR: But, mentor them, +for sure, mentor them. + +SAMAN AMARASINGHE: I think a lot +of times, when you talk to + +students last time they got a +lot more information out from + +the masters, other than +just the coding style. + +I mean, they talk about what is +it like to be an engineer + +in a company, what +are the things? + +And so they get a good feel. + +I mean, some of them might +not have done a + +internship in a company. + +So they don't know. + +I mean, they're just green, and +talking to you guys they + +get a feel for what it's like. + +And also from a non-marketing +situation too. + +I mean you might have ulterior +motives to market your company + +to them, and stuff, but this is +not that they're going into + +a job interview. + +So, for a lot of +them it's rare. + +I mean they might not have +retinues of friends that they + +can go and talk at that +kind of casual level. + +Most of the time they're on +guard because they're on an + +interview or they assume that +information coming to them + +will be sugar-coated, and here +is a way that they can get-- + +I think it's very +good for them. + +PROFESSOR: Eight minutes +over time. + +SAMAN AMARASINGHE: OK, +I think we should. + +PROFESSOR: So, any last +final comments? + +Saman and I will hang around for +a few minutes, for anybody + +wants to chat more one one. + +And one and once again I thank +you for all the time that + +you're planning to put into +the 6-172, thanks. + +AUDIENCE: Thank you. \ No newline at end of file diff --git a/oFL2Hxqg7eo.txt b/oFL2Hxqg7eo.txt new file mode 100644 index 0000000000000000000000000000000000000000..277d2388378aeded2704ce61a9998c56b7c8c03f --- /dev/null +++ b/oFL2Hxqg7eo.txt @@ -0,0 +1,8923 @@ +align:start position:0% + +um okay I want to talk today about um + + align:start position:0% +um okay I want to talk today about um + + + align:start position:0% +um okay I want to talk today about um +continue our discussion of oligopoly + + align:start position:0% +continue our discussion of oligopoly + + + align:start position:0% +continue our discussion of oligopoly +last time we talked about + + align:start position:0% +last time we talked about + + + align:start position:0% +last time we talked about +non-cooperative equilibria but we in the + + align:start position:0% +non-cooperative equilibria but we in the + + + align:start position:0% +non-cooperative equilibria but we in the +start we said gee life would just be + + align:start position:0% +start we said gee life would just be + + + align:start position:0% +start we said gee life would just be +better off everyone would just cooperate + + align:start position:0% +better off everyone would just cooperate + + + align:start position:0% +better off everyone would just cooperate +and someone even asked me well why don't + + align:start position:0% +and someone even asked me well why don't + + + align:start position:0% +and someone even asked me well why don't +they just cooperate so let's talk about + + align:start position:0% +they just cooperate so let's talk about + + + align:start position:0% +they just cooperate so let's talk about +that let's talk about cartels what + + align:start position:0% +that let's talk about cartels what + + + align:start position:0% +that let's talk about cartels what +happens when firms try to cooperate + + align:start position:0% +happens when firms try to cooperate + + + align:start position:0% +happens when firms try to cooperate +achieve the cooperative equilibrium in + + align:start position:0% +achieve the cooperative equilibrium in + + + align:start position:0% +achieve the cooperative equilibrium in +oligopolies now clearly this is gonna be + + align:start position:0% +oligopolies now clearly this is gonna be + + + align:start position:0% +oligopolies now clearly this is gonna be +the best outcome so to fix examples + + align:start position:0% +the best outcome so to fix examples + + + align:start position:0% +the best outcome so to fix examples +let's go back to our example of last + + align:start position:0% +let's go back to our example of last + + + align:start position:0% +let's go back to our example of last +time American united recall last time we + + align:start position:0% +time American united recall last time we + + + align:start position:0% +time American united recall last time we +said the demand was of the form 339 + + align:start position:0% +said the demand was of the form 339 + + + align:start position:0% +said the demand was of the form 339 +minus Q prices 339 minus Q and that the + + align:start position:0% +minus Q prices 339 minus Q and that the + + + align:start position:0% +minus Q prices 339 minus Q and that the +marginal cost was 147 okay now we talked + + align:start position:0% +marginal cost was 147 okay now we talked + + + align:start position:0% +marginal cost was 147 okay now we talked +about the fact that if American was a + + align:start position:0% +about the fact that if American was a + + + align:start position:0% +about the fact that if American was a +monopoly in this market they would + + align:start position:0% +monopoly in this market they would + + + align:start position:0% +monopoly in this market they would +simply solve the monopolist problem they + + align:start position:0% +simply solve the monopolist problem they + + + align:start position:0% +simply solve the monopolist problem they +would set marginal revenue which is 339 + + align:start position:0% +would set marginal revenue which is 339 + + + align:start position:0% +would set marginal revenue which is 339 +minus 2q equal to marginal cost which is + + align:start position:0% +minus 2q equal to marginal cost which is + + + align:start position:0% +minus 2q equal to marginal cost which is +147 and they would get that the optimal + + align:start position:0% +147 and they would get that the optimal + + + align:start position:0% +147 and they would get that the optimal +Q would be 96 and then reading back off + + align:start position:0% +Q would be 96 and then reading back off + + + align:start position:0% +Q would be 96 and then reading back off +the demand curve that in place imply an + + align:start position:0% +the demand curve that in place imply an + + + align:start position:0% +the demand curve that in place imply an +optimal quantity of two hundred and + + align:start position:0% +optimal quantity of two hundred and + + + align:start position:0% +optimal quantity of two hundred and +forty three dollars okay so that was + + align:start position:0% +forty three dollars okay so that was + + + align:start position:0% +forty three dollars okay so that was +what we got last time + + align:start position:0% +what we got last time + + + align:start position:0% +what we got last time +now imagine that Americans not a + + align:start position:0% +now imagine that Americans not a + + + align:start position:0% +now imagine that Americans not a +monopoly but American United cooperate + + align:start position:0% +monopoly but American United cooperate + + + align:start position:0% +monopoly but American United cooperate +what if they got to goodness said you + + align:start position:0% +what if they got to goodness said you + + + align:start position:0% +what if they got to goodness said you +know what let's behave as if we're one + + align:start position:0% +know what let's behave as if we're one + + + align:start position:0% +know what let's behave as if we're one +monopolist flying 96 flights and just + + align:start position:0% +monopolist flying 96 flights and just + + + align:start position:0% +monopolist flying 96 flights and just +splitting them equally we'll do forty + + align:start position:0% +splitting them equally we'll do forty + + + align:start position:0% +splitting them equally we'll do forty +eight you do 48 so let's cartelize let's + + align:start position:0% +eight you do 48 so let's cartelize let's + + + align:start position:0% +eight you do 48 so let's cartelize let's +achieve the monopoly outcome and those + + align:start position:0% +achieve the monopoly outcome and those + + + align:start position:0% +achieve the monopoly outcome and those +two share 5050 the fruits of that + + align:start position:0% +two share 5050 the fruits of that + + + align:start position:0% +two share 5050 the fruits of that +outcome so in that case each firm would + + align:start position:0% +outcome so in that case each firm would + + + align:start position:0% +outcome so in that case each firm would +fly 48 flights at a price of 243 dollars + + align:start position:0% +fly 48 flights at a price of 243 dollars + + + align:start position:0% +fly 48 flights at a price of 243 dollars +okay and total profits in the market + + align:start position:0% +okay and total profits in the market + + + align:start position:0% +okay and total profits in the market +each firm would then make profits of 48 + + align:start position:0% +each firm would then make profits of 48 + + + align:start position:0% +each firm would then make profits of 48 +times price minus average cost which is + + align:start position:0% +times price minus average cost which is + + + align:start position:0% +times price minus average cost which is +marginal costs because it's flat times + + align:start position:0% +marginal costs because it's flat times + + + align:start position:0% +marginal costs because it's flat times +to 43 minus 147 or so it's like I'm not + + align:start position:0% +to 43 minus 147 or so it's like I'm not + + + align:start position:0% +to 43 minus 147 or so it's like I'm not +like you guys can do that my head + + align:start position:0% +like you guys can do that my head + + + align:start position:0% +like you guys can do that my head +4608 per firm okay so each firm would + + align:start position:0% +4608 per firm okay so each firm would + + + align:start position:0% +4608 per firm okay so each firm would +achieve profits of forty states take the + + align:start position:0% +achieve profits of forty states take the + + + align:start position:0% +achieve profits of forty states take the +ninety six flights split them in half + + align:start position:0% +ninety six flights split them in half + + + align:start position:0% +ninety six flights split them in half +and then achieved profits of 4608 now + + align:start position:0% +and then achieved profits of 4608 now + + + align:start position:0% +and then achieved profits of 4608 now +what we can see is that these profits + + align:start position:0% +what we can see is that these profits + + + align:start position:0% +what we can see is that these profits +are much higher than what they got in + + align:start position:0% +are much higher than what they got in + + + align:start position:0% +are much higher than what they got in +the non cooperative equilibrium + + align:start position:0% +the non cooperative equilibrium + + + align:start position:0% +the non cooperative equilibrium +remember the non-cooperative equilibrium + + align:start position:0% +remember the non-cooperative equilibrium + + + align:start position:0% +remember the non-cooperative equilibrium +they were each doing sixty-four flights + + align:start position:0% +they were each doing sixty-four flights + + + align:start position:0% +they were each doing sixty-four flights +at a price of the you chewing sixty-four + + align:start position:0% +at a price of the you chewing sixty-four + + + align:start position:0% +at a price of the you chewing sixty-four +flights at a price of 211 we solved that + + align:start position:0% +flights at a price of 211 we solved that + + + align:start position:0% +flights at a price of 211 we solved that +last time so what were their non + + align:start position:0% +last time so what were their non + + + align:start position:0% +last time so what were their non +cooperative profits they're non + + align:start position:0% +cooperative profits they're non + + + align:start position:0% +cooperative profits they're non +cooperative profits for each firm was 64 + + align:start position:0% +cooperative profits for each firm was 64 + + + align:start position:0% +cooperative profits for each firm was 64 +times the 211 they were charging minus + + align:start position:0% +times the 211 they were charging minus + + + align:start position:0% +times the 211 they were charging minus +the 147 in marginal costs or their + + align:start position:0% +the 147 in marginal costs or their + + + align:start position:0% +the 147 in marginal costs or their +former prophets were 4096 so their + + align:start position:0% +former prophets were 4096 so their + + + align:start position:0% +former prophets were 4096 so their +profits used to be 4,000 ices when they + + align:start position:0% +profits used to be 4,000 ices when they + + + align:start position:0% +profits used to be 4,000 ices when they +weren't cooperating they've gone up by + + align:start position:0% +weren't cooperating they've gone up by + + + align:start position:0% +weren't cooperating they've gone up by +12.5 percent to 46 Oh eight by + + align:start position:0% +12.5 percent to 46 Oh eight by + + + align:start position:0% +12.5 percent to 46 Oh eight by +cooperating so simply by getting + + align:start position:0% +cooperating so simply by getting + + + align:start position:0% +cooperating so simply by getting +together saying don't be an + + align:start position:0% +together saying don't be an + + + align:start position:0% +together saying don't be an +let's cooperate let's figure how to make + + align:start position:0% +let's cooperate let's figure how to make + + + align:start position:0% +let's cooperate let's figure how to make +the most money getting together they + + align:start position:0% +the most money getting together they + + + align:start position:0% +the most money getting together they +solve the prisoner's dilemma get to the + + align:start position:0% +solve the prisoner's dilemma get to the + + + align:start position:0% +solve the prisoner's dilemma get to the +best outcome and make a lot more money + + align:start position:0% +best outcome and make a lot more money + + + align:start position:0% +best outcome and make a lot more money +okay so the question is why don't they + + align:start position:0% +okay so the question is why don't they + + + align:start position:0% +okay so the question is why don't they +always do this in oligopolistic markets + + align:start position:0% +always do this in oligopolistic markets + + + align:start position:0% +always do this in oligopolistic markets +and fundamentally there's two reasons + + align:start position:0% +and fundamentally there's two reasons + + + align:start position:0% +and fundamentally there's two reasons +now normal people you see when I'm done + + align:start position:0% +now normal people you see when I'm done + + + align:start position:0% +now normal people you see when I'm done +normal people will teach them in a + + align:start position:0% +normal people will teach them in a + + + align:start position:0% +normal people will teach them in a +different order than I will but let me + + align:start position:0% +different order than I will but let me + + + align:start position:0% +different order than I will but let me +start with the two reasons in the + + align:start position:0% +start with the two reasons in the + + + align:start position:0% +start with the two reasons in the +ordering Connors would teach them the + + align:start position:0% +ordering Connors would teach them the + + + align:start position:0% +ordering Connors would teach them the +first reason why cartels don't form is + + align:start position:0% +first reason why cartels don't form is + + + align:start position:0% +first reason why cartels don't form is +that they're fundamentally fundamentally + + align:start position:0% +that they're fundamentally fundamentally + + + align:start position:0% +that they're fundamentally fundamentally +unstable cartels are fundamentally + + align:start position:0% +unstable cartels are fundamentally + + + align:start position:0% +unstable cartels are fundamentally +unstable as long as firms are + + align:start position:0% +unstable as long as firms are + + + align:start position:0% +unstable as long as firms are +self-interested each individual firm in + + align:start position:0% +self-interested each individual firm in + + + align:start position:0% +self-interested each individual firm in +a cartel has an incentive to cheat and + + align:start position:0% +a cartel has an incentive to cheat and + + + align:start position:0% +a cartel has an incentive to cheat and +that's because they essentially could + + align:start position:0% +that's because they essentially could + + + align:start position:0% +that's because they essentially could +solve the monopoly problem of poisoning + + align:start position:0% +solve the monopoly problem of poisoning + + + align:start position:0% +solve the monopoly problem of poisoning +by cheating let me explain how that + + align:start position:0% +by cheating let me explain how that + + + align:start position:0% +by cheating let me explain how that +works this best sees through numbers + + align:start position:0% +works this best sees through numbers + + + align:start position:0% +works this best sees through numbers +let's imagine that we start in this + + align:start position:0% +let's imagine that we start in this + + + align:start position:0% +let's imagine that we start in this +cooperative equilibrium forty eight + + align:start position:0% +cooperative equilibrium forty eight + + + align:start position:0% +cooperative equilibrium forty eight +flights each improv so 4608 and now + + align:start position:0% +flights each improv so 4608 and now + + + align:start position:0% +flights each improv so 4608 and now +let's imagine in the middle that quietly + + align:start position:0% +let's imagine in the middle that quietly + + + align:start position:0% +let's imagine in the middle that quietly +American increases its number of flights + + align:start position:0% +American increases its number of flights + + + align:start position:0% +American increases its number of flights +from forty to fifty American says well I + + align:start position:0% +from forty to fifty American says well I + + + align:start position:0% +from forty to fifty American says well I +know agreed forty eight but on the slime + + align:start position:0% +know agreed forty eight but on the slime + + + align:start position:0% +know agreed forty eight but on the slime +and I fly two more flights and hope they + + align:start position:0% +and I fly two more flights and hope they + + + align:start position:0% +and I fly two more flights and hope they +don't catch me okay well what's + + align:start position:0% +don't catch me okay well what's + + + align:start position:0% +don't catch me okay well what's +Americans profits + + align:start position:0% +Americans profits + + + align:start position:0% +Americans profits +well their quantity is 50 Q sub a is now + + align:start position:0% +well their quantity is 50 Q sub a is now + + + align:start position:0% +well their quantity is 50 Q sub a is now +50 what's the price if they can do 50 + + align:start position:0% +50 what's the price if they can do 50 + + + align:start position:0% +50 what's the price if they can do 50 +flights what's the price yeah + + align:start position:0% +flights what's the price yeah + + + align:start position:0% +flights what's the price yeah +I'm sorry it's 280 it's the price is + + align:start position:0% +I'm sorry it's 280 it's the price is + + + align:start position:0% +I'm sorry it's 280 it's the price is +let's see we got that right go check my + + align:start position:0% +let's see we got that right go check my + + + align:start position:0% +let's see we got that right go check my +notes no no if the price was 243 when + + align:start position:0% +notes no no if the price was 243 when + + + align:start position:0% +notes no no if the price was 243 when +they're monopoly now they're doing two + + align:start position:0% +they're monopoly now they're doing two + + + align:start position:0% +they're monopoly now they're doing two +more flights remember they're adding two + + align:start position:0% +more flights remember they're adding two + + + align:start position:0% +more flights remember they're adding two +flights to the total there used to be + + align:start position:0% +flights to the total there used to be + + + align:start position:0% +flights to the total there used to be +there used to be 96 flights now goes to + + align:start position:0% +there used to be 96 flights now goes to + + + align:start position:0% +there used to be 96 flights now goes to +98 flights so price falls to 241 okay so + + align:start position:0% +98 flights so price falls to 241 okay so + + + align:start position:0% +98 flights so price falls to 241 okay so +you were thinking about them as a loan + + align:start position:0% +you were thinking about them as a loan + + + align:start position:0% +you were thinking about them as a loan +but remember there's still united doing + + align:start position:0% +but remember there's still united doing + + + align:start position:0% +but remember there's still united doing +the flights - they're still doing 48 + + align:start position:0% +the flights - they're still doing 48 + + + align:start position:0% +the flights - they're still doing 48 +flights so there are 96 flights total + + align:start position:0% +flights so there are 96 flights total + + + align:start position:0% +flights so there are 96 flights total +now it goes to 98 so the price falls to + + align:start position:0% +now it goes to 98 so the price falls to + + + align:start position:0% +now it goes to 98 so the price falls to +241 okay + + align:start position:0% +241 okay + + + align:start position:0% +241 okay +so what's their profits their profits + + align:start position:0% +so what's their profits their profits + + + align:start position:0% +so what's their profits their profits +are now 50 times 241 - 147 or 4,700 + + align:start position:0% +are now 50 times 241 - 147 or 4,700 + + + align:start position:0% +are now 50 times 241 - 147 or 4,700 +their profits have gone up okay let me + + align:start position:0% +their profits have gone up okay let me + + + align:start position:0% +their profits have gone up okay let me +back up and do it again because I went + + align:start position:0% +back up and do it again because I went + + + align:start position:0% +back up and do it again because I went +fast okay they saving in two more + + align:start position:0% +fast okay they saving in two more + + + align:start position:0% +fast okay they saving in two more +flights we have to respect to demand + + align:start position:0% +flights we have to respect to demand + + + align:start position:0% +flights we have to respect to demand +curve so there could be two more flights + + align:start position:0% +curve so there could be two more flights + + + align:start position:0% +curve so there could be two more flights +the price has to fall if the price falls + + align:start position:0% +the price has to fall if the price falls + + + align:start position:0% +the price has to fall if the price falls +then the price has to fall 241 they now + + align:start position:0% +then the price has to fall 241 they now + + + align:start position:0% +then the price has to fall 241 they now +make profits of 4700 okay well if United + + align:start position:0% +make profits of 4700 okay well if United + + + align:start position:0% +make profits of 4700 okay well if United +is caught with their pants down and + + align:start position:0% +is caught with their pants down and + + + align:start position:0% +is caught with their pants down and +continues to forty eight flights what is + + align:start position:0% +continues to forty eight flights what is + + + align:start position:0% +continues to forty eight flights what is +United make well United still doing 48 + + align:start position:0% +United make well United still doing 48 + + + align:start position:0% +United make well United still doing 48 +flights so the profits have United are + + align:start position:0% +flights so the profits have United are + + + align:start position:0% +flights so the profits have United are +48 times 241 - 147 or 45 12 so Americans + + align:start position:0% +48 times 241 - 147 or 45 12 so Americans + + + align:start position:0% +48 times 241 - 147 or 45 12 so Americans +profits are up and United profits are + + align:start position:0% +profits are up and United profits are + + + align:start position:0% +profits are up and United profits are +down through American cheating what + + align:start position:0% +down through American cheating what + + + align:start position:0% +down through American cheating what +happened + + align:start position:0% +happened + + + align:start position:0% +happened +how by cheating did they draw what's the + + align:start position:0% +how by cheating did they draw what's the + + + align:start position:0% +how by cheating did they draw what's the +intuition of why them cheating drove + + align:start position:0% +intuition of why them cheating drove + + + align:start position:0% +intuition of why them cheating drove +their profits up and is down and in fact + + align:start position:0% +their profits up and is down and in fact + + + align:start position:0% +their profits up and is down and in fact +if you add these up lowered total + + align:start position:0% +if you add these up lowered total + + + align:start position:0% +if you add these up lowered total +profits in the market what's going on + + align:start position:0% +profits in the market what's going on + + + align:start position:0% +profits in the market what's going on +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +see my quantity you're lowering the + + align:start position:0% +see my quantity you're lowering the + + + align:start position:0% +see my quantity you're lowering the +price that you can sell each unit for + + align:start position:0% +price that you can sell each unit for + + + align:start position:0% +price that you can sell each unit for +but for American because they're + + align:start position:0% +but for American because they're + + + align:start position:0% +but for American because they're +increasing the number of units they're + + align:start position:0% +increasing the number of units they're + + + align:start position:0% +increasing the number of units they're +selling they still make a great profit + + align:start position:0% +selling they still make a great profit + + + align:start position:0% +selling they still make a great profit +whereas United States and because each + + align:start position:0% +whereas United States and because each + + + align:start position:0% +whereas United States and because each +unit be sold for less and again that's + + align:start position:0% +unit be sold for less and again that's + + + align:start position:0% +unit be sold for less and again that's +that's almost right you got most of it + + align:start position:0% +that's almost right you got most of it + + + align:start position:0% +that's almost right you got most of it +but there's one key wrinkle that's + + align:start position:0% +but there's one key wrinkle that's + + + align:start position:0% +but there's one key wrinkle that's +important which is a monopolist would + + align:start position:0% +important which is a monopolist would + + + align:start position:0% +important which is a monopolist would +have the same argument the the key thing + + align:start position:0% +have the same argument the the key thing + + + align:start position:0% +have the same argument the the key thing +is why doesn't what stops the monopolist + + align:start position:0% +is why doesn't what stops the monopolist + + + align:start position:0% +is why doesn't what stops the monopolist +from raising the price from where he is + + align:start position:0% +from raising the price from where he is + + + align:start position:0% +from raising the price from where he is +yeah the poisoning effect but think + + align:start position:0% +yeah the poisoning effect but think + + + align:start position:0% +yeah the poisoning effect but think +about the poisoning effect who's the + + align:start position:0% +about the poisoning effect who's the + + + align:start position:0% +about the poisoning effect who's the +poisoning effect affect everyone in the + + align:start position:0% +poisoning effect affect everyone in the + + + align:start position:0% +poisoning effect affect everyone in the +market everyone sees a lower price but + + align:start position:0% +market everyone sees a lower price but + + + align:start position:0% +market everyone sees a lower price but +only American gets more flights so they + + align:start position:0% +only American gets more flights so they + + + align:start position:0% +only American gets more flights so they +essentially get the benefit it's like + + align:start position:0% +essentially get the benefit it's like + + + align:start position:0% +essentially get the benefit it's like +you said they get the benefit the extra + + align:start position:0% +you said they get the benefit the extra + + + align:start position:0% +you said they get the benefit the extra +flights but only half the penalty of the + + align:start position:0% +flights but only half the penalty of the + + + align:start position:0% +flights but only half the penalty of the +poison effect so for them it is optimal + + align:start position:0% +poison effect so for them it is optimal + + + align:start position:0% +poison effect so for them it is optimal +to rich to lower the price and sell more + + align:start position:0% +to rich to lower the price and sell more + + + align:start position:0% +to rich to lower the price and sell more +because they share the negative effect + + align:start position:0% +because they share the negative effect + + + align:start position:0% +because they share the negative effect +the negative part with United but they + + align:start position:0% +the negative part with United but they + + + align:start position:0% +the negative part with United but they +get all the positive part once again a + + align:start position:0% +get all the positive part once again a + + + align:start position:0% +get all the positive part once again a +monopolist when you rip when you try to + + align:start position:0% +monopolist when you rip when you try to + + + align:start position:0% +monopolist when you rip when you try to +sell more and lower the price there's a + + align:start position:0% +sell more and lower the price there's a + + + align:start position:0% +sell more and lower the price there's a +positive approach to sell more units but + + align:start position:0% +positive approach to sell more units but + + + align:start position:0% +positive approach to sell more units but +a negative part which is the poisoning + + align:start position:0% +a negative part which is the poisoning + + + align:start position:0% +a negative part which is the poisoning +effect well here American gets all the + + align:start position:0% +effect well here American gets all the + + + align:start position:0% +effect well here American gets all the +positive part only half the negative + + align:start position:0% +positive part only half the negative + + + align:start position:0% +positive part only half the negative +part so they make money by cheating okay + + align:start position:0% +part so they make money by cheating okay + + + align:start position:0% +part so they make money by cheating okay +well of course United knows this they + + align:start position:0% +well of course United knows this they + + + align:start position:0% +well of course United knows this they +saw the place go down they know + + align:start position:0% +saw the place go down they know + + + align:start position:0% +saw the place go down they know +Americans cheating + + align:start position:0% +Americans cheating + + + align:start position:0% +Americans cheating +so United wants to cheat and the whole + + align:start position:0% +so United wants to cheat and the whole + + + align:start position:0% +so United wants to cheat and the whole +thing breaks apart sort cartels are + + align:start position:0% +thing breaks apart sort cartels are + + + align:start position:0% +thing breaks apart sort cartels are +unstable because by cheating you get all + + align:start position:0% +unstable because by cheating you get all + + + align:start position:0% +unstable because by cheating you get all +the benefit but only part of the cost + + align:start position:0% +the benefit but only part of the cost + + + align:start position:0% +the benefit but only part of the cost +and since so cheating is incentivized at + + align:start position:0% +and since so cheating is incentivized at + + + align:start position:0% +and since so cheating is incentivized at +a cartel and therefore cartels will + + align:start position:0% +a cartel and therefore cartels will + + + align:start position:0% +a cartel and therefore cartels will +break down they're not stable okay so + + align:start position:0% +break down they're not stable okay so + + + align:start position:0% +break down they're not stable okay so +that's the primary reason economists say + + align:start position:0% +that's the primary reason economists say + + + align:start position:0% +that's the primary reason economists say +we don't see cartels the other reason + + align:start position:0% +we don't see cartels the other reason + + + align:start position:0% +we don't see cartels the other reason +people like to bring up is this little + + align:start position:0% +people like to bring up is this little + + + align:start position:0% +people like to bring up is this little +thing they're illegal but you know we + + align:start position:0% +thing they're illegal but you know we + + + align:start position:0% +thing they're illegal but you know we +don't let stuff like that bothers + + align:start position:0% +don't let stuff like that bothers + + + align:start position:0% +don't let stuff like that bothers +economists but they are illegal that's + + align:start position:0% +economists but they are illegal that's + + + align:start position:0% +economists but they are illegal that's +another reason why we don't see cartels + + align:start position:0% +another reason why we don't see cartels + + + align:start position:0% +another reason why we don't see cartels +in the late 1800 cartels were quite + + align:start position:0% +in the late 1800 cartels were quite + + + align:start position:0% +in the late 1800 cartels were quite +common in late 1800s big industries like + + align:start position:0% +common in late 1800s big industries like + + + align:start position:0% +common in late 1800s big industries like +oil and railroad industries came to be + + align:start position:0% +oil and railroad industries came to be + + + align:start position:0% +oil and railroad industries came to be +dominated by a few large firms and they + + align:start position:0% +dominated by a few large firms and they + + + align:start position:0% +dominated by a few large firms and they +tried to become cartels but it kept + + align:start position:0% +tried to become cartels but it kept + + + align:start position:0% +tried to become cartels but it kept +breaking down so its fatal eighteen + + align:start position:0% +breaking down so its fatal eighteen + + + align:start position:0% +breaking down so its fatal eighteen +hundreds with oil company Standard Oil + + align:start position:0% +hundreds with oil company Standard Oil + + + align:start position:0% +hundreds with oil company Standard Oil +and the big + + align:start position:0% +and the big + + + align:start position:0% +and the big +companies they kept trying to have + + align:start position:0% +companies they kept trying to have + + + align:start position:0% +companies they kept trying to have +cartels and a cape breaking down say + + align:start position:0% +cartels and a cape breaking down say + + + align:start position:0% +cartels and a cape breaking down say +couples idea + + align:start position:0% +couples idea + + + align:start position:0% +couples idea +they basically arm said look we can't + + align:start position:0% +they basically arm said look we can't + + + align:start position:0% +they basically arm said look we can't +trust each other so we're gonna every + + align:start position:0% +trust each other so we're gonna every + + + align:start position:0% +trust each other so we're gonna every +firm is gonna turn over all its + + align:start position:0% +firm is gonna turn over all its + + + align:start position:0% +firm is gonna turn over all its +decisions to a common trust and there'll + + align:start position:0% +decisions to a common trust and there'll + + + align:start position:0% +decisions to a common trust and there'll +be a trust that's got representatives + + align:start position:0% +be a trust that's got representatives + + + align:start position:0% +be a trust that's got representatives +for every fern on the board but we will + + align:start position:0% +for every fern on the board but we will + + + align:start position:0% +for every fern on the board but we will +publicly commit to what we're gonna + + align:start position:0% +publicly commit to what we're gonna + + + align:start position:0% +publicly commit to what we're gonna +Bruce at what price and therefore we can + + align:start position:0% +Bruce at what price and therefore we can + + + align:start position:0% +Bruce at what price and therefore we can +make sure there's no cheating so + + align:start position:0% +make sure there's no cheating so + + + align:start position:0% +make sure there's no cheating so +essentially every firm still involved + + align:start position:0% +essentially every firm still involved + + + align:start position:0% +essentially every firm still involved +they're all in this trust board but + + align:start position:0% +they're all in this trust board but + + + align:start position:0% +they're all in this trust board but +they're making that decision in a in a + + align:start position:0% +they're making that decision in a in a + + + align:start position:0% +they're making that decision in a in a +in a way that's at least public to them + + align:start position:0% +in a way that's at least public to them + + + align:start position:0% +in a way that's at least public to them +not public to the public but public to + + align:start position:0% +not public to the public but public to + + + align:start position:0% +not public to the public but public to +them so they can make sure they're not + + align:start position:0% +them so they can make sure they're not + + + align:start position:0% +them so they can make sure they're not +cheating they form these trusts and + + align:start position:0% +cheating they form these trusts and + + + align:start position:0% +cheating they form these trusts and +essentially Carter lies they made huge + + align:start position:0% +essentially Carter lies they made huge + + + align:start position:0% +essentially Carter lies they made huge +profits and it worked + + align:start position:0% +profits and it worked + + + align:start position:0% +profits and it worked +it's all the stability problem because + + align:start position:0% +it's all the stability problem because + + + align:start position:0% +it's all the stability problem because +cheating could be observed more readily + + align:start position:0% +cheating could be observed more readily + + + align:start position:0% +cheating could be observed more readily +now what a solved it very long we don't + + align:start position:0% +now what a solved it very long we don't + + + align:start position:0% +now what a solved it very long we don't +know because the government the public + + align:start position:0% +know because the government the public + + + align:start position:0% +know because the government the public +are pissed and the government came in + + align:start position:0% +are pissed and the government came in + + + align:start position:0% +are pissed and the government came in +and passed what's called antitrust laws + + align:start position:0% +and passed what's called antitrust laws + + + align:start position:0% +and passed what's called antitrust laws +and antitrust laws are laws which do not + + align:start position:0% +and antitrust laws are laws which do not + + + align:start position:0% +and antitrust laws are laws which do not +permit the Cardinal is a ssin of India + + align:start position:0% +permit the Cardinal is a ssin of India + + + align:start position:0% +permit the Cardinal is a ssin of India +of oligopolistic industries in this way + + align:start position:0% +of oligopolistic industries in this way + + + align:start position:0% +of oligopolistic industries in this way +so let's talk about antitrust laws and + + align:start position:0% +so let's talk about antitrust laws and + + + align:start position:0% +so let's talk about antitrust laws and +how they work or how they don't work I + + align:start position:0% +how they work or how they don't work I + + + align:start position:0% +how they work or how they don't work I +want to do a couple examples what + + align:start position:0% +want to do a couple examples what + + + align:start position:0% +want to do a couple examples what +examples the movie industry now the + + align:start position:0% +examples the movie industry now the + + + align:start position:0% +examples the movie industry now the +movie distri you know is a classic + + align:start position:0% +movie distri you know is a classic + + + align:start position:0% +movie distri you know is a classic +oligopolistic industry you know there's + + align:start position:0% +oligopolistic industry you know there's + + + align:start position:0% +oligopolistic industry you know there's +a few players there's new players 8:24 + + align:start position:0% +a few players there's new players 8:24 + + + align:start position:0% +a few players there's new players 8:24 +is huge now what didn't exist 15 years + + align:start position:0% +is huge now what didn't exist 15 years + + + align:start position:0% +is huge now what didn't exist 15 years +ago but by and large is sort of a few + + align:start position:0% +ago but by and large is sort of a few + + + align:start position:0% +ago but by and large is sort of a few +players you've heard of which dominate + + align:start position:0% +players you've heard of which dominate + + + align:start position:0% +players you've heard of which dominate +the industry + + align:start position:0% +the industry + + + align:start position:0% +the industry +okay these and the way the industry + + align:start position:0% +okay these and the way the industry + + + align:start position:0% +okay these and the way the industry +works is movie companies make and they + + align:start position:0% +works is movie companies make and they + + + align:start position:0% +works is movie companies make and they +produce the movies and then sell them to + + align:start position:0% +produce the movies and then sell them to + + + align:start position:0% +produce the movies and then sell them to +movie theaters that show the movies they + + align:start position:0% +movie theaters that show the movies they + + + align:start position:0% +movie theaters that show the movies they +show a variety movies at any one time + + align:start position:0% +show a variety movies at any one time + + + align:start position:0% +show a variety movies at any one time +well what happened was in the 30s and + + align:start position:0% +well what happened was in the 30s and + + + align:start position:0% +well what happened was in the 30s and +40s + + align:start position:0% +40s + + + align:start position:0% +40s +the production company started buying up + + align:start position:0% +the production company started buying up + + + align:start position:0% +the production company started buying up +the movie theaters and what they do when + + align:start position:0% +the movie theaters and what they do when + + + align:start position:0% +the movie theaters and what they do when +they bought the movie is a movie theater + + align:start position:0% +they bought the movie is a movie theater + + + align:start position:0% +they bought the movie is a movie theater +we now own you and you will only show + + align:start position:0% +we now own you and you will only show + + + align:start position:0% +we now own you and you will only show +our movies so I say the movie theater we + + align:start position:0% +our movies so I say the movie theater we + + + align:start position:0% +our movies so I say the movie theater we +now own you you know movie theater on + + align:start position:0% +now own you you know movie theater on + + + align:start position:0% +now own you you know movie theater on +the corner of you know Lincoln and + + align:start position:0% +the corner of you know Lincoln and + + + align:start position:0% +the corner of you know Lincoln and +Kennedy streets and we're MGM and you + + align:start position:0% +Kennedy streets and we're MGM and you + + + align:start position:0% +Kennedy streets and we're MGM and you +only show MGM movies and essentially + + align:start position:0% +only show MGM movies and essentially + + + align:start position:0% +only show MGM movies and essentially +what that meant was essentially they + + align:start position:0% +what that meant was essentially they + + + align:start position:0% +what that meant was essentially they +were taking over monopolizing a given + + align:start position:0% +were taking over monopolizing a given + + + align:start position:0% +were taking over monopolizing a given +distribution network and they + + align:start position:0% +distribution network and they + + + align:start position:0% +distribution network and they +essentially carved it up they agreed + + align:start position:0% +essentially carved it up they agreed + + + align:start position:0% +essentially carved it up they agreed +okay you get these theaters we'll take + + align:start position:0% +okay you get these theaters we'll take + + + align:start position:0% +okay you get these theaters we'll take +these theaters and it said + + align:start position:0% +these theaters and it said + + + align:start position:0% +these theaters and it said +that was the way they formed their + + align:start position:0% +that was the way they formed their + + + align:start position:0% +that was the way they formed their +cartel was through distribution and the + + align:start position:0% +cartel was through distribution and the + + + align:start position:0% +cartel was through distribution and the +federal government jumped in and said + + align:start position:0% +federal government jumped in and said + + + align:start position:0% +federal government jumped in and said +that that was an antitrust violation the + + align:start position:0% +that that was an antitrust violation the + + + align:start position:0% +that that was an antitrust violation the +federal government sued and won and so + + align:start position:0% +federal government sued and won and so + + + align:start position:0% +federal government sued and won and so +that industry that that um that was + + align:start position:0% +that industry that that um that was + + + align:start position:0% +that industry that that um that was +broken up but did that mean that didn't + + align:start position:0% +broken up but did that mean that didn't + + + align:start position:0% +broken up but did that mean that didn't +mean folks stopped trying to Carta lies + + align:start position:0% +mean folks stopped trying to Carta lies + + + align:start position:0% +mean folks stopped trying to Carta lies +it just meant they stopped being so + + align:start position:0% +it just meant they stopped being so + + + align:start position:0% +it just meant they stopped being so +obvious about it + + align:start position:0% +obvious about it + + + align:start position:0% +obvious about it +so later moves to Carta lies were more + + align:start position:0% +so later moves to Carta lies were more + + + align:start position:0% +so later moves to Carta lies were more +hidden so for example in the early 2000s + + align:start position:0% +hidden so for example in the early 2000s + + + align:start position:0% +hidden so for example in the early 2000s +airline industries were in big trouble + + align:start position:0% +airline industries were in big trouble + + + align:start position:0% +airline industries were in big trouble +because oil prices were going way up due + + align:start position:0% +because oil prices were going way up due + + + align:start position:0% +because oil prices were going way up due +to the Iraq war and other factors oil + + align:start position:0% +to the Iraq war and other factors oil + + + align:start position:0% +to the Iraq war and other factors oil +prices were going way up and the airline + + align:start position:0% +prices were going way up and the airline + + + align:start position:0% +prices were going way up and the airline +industry was in trouble so in 2004 + + align:start position:0% +industry was in trouble so in 2004 + + + align:start position:0% +industry was in trouble so in 2004 +British Airlines and Virgin Atlantic had + + align:start position:0% +British Airlines and Virgin Atlantic had + + + align:start position:0% +British Airlines and Virgin Atlantic had +secret talks about essentially carta + + align:start position:0% +secret talks about essentially carta + + + align:start position:0% +secret talks about essentially carta +lies in the cross atlantic market from + + align:start position:0% +lies in the cross atlantic market from + + + align:start position:0% +lies in the cross atlantic market from +the east coast to to london and what + + align:start position:0% +the east coast to to london and what + + + align:start position:0% +the east coast to to london and what +they did is they said look if we sort of + + align:start position:0% +they did is they said look if we sort of + + + align:start position:0% +they did is they said look if we sort of +obviously set our prices together people + + align:start position:0% +obviously set our prices together people + + + align:start position:0% +obviously set our prices together people +are gonna notice so you do is instead is + + align:start position:0% +are gonna notice so you do is instead is + + + align:start position:0% +are gonna notice so you do is instead is +we're gonna add fuel surcharges to the + + align:start position:0% +we're gonna add fuel surcharges to the + + + align:start position:0% +we're gonna add fuel surcharges to the +bill we're gonna say oh gasket oils + + align:start position:0% +bill we're gonna say oh gasket oils + + + align:start position:0% +bill we're gonna say oh gasket oils +getting more expensive your price + + align:start position:0% +getting more expensive your price + + + align:start position:0% +getting more expensive your price +haven't changed but there's now a fuel + + align:start position:0% +haven't changed but there's now a fuel + + + align:start position:0% +haven't changed but there's now a fuel +surcharge on your bill and that fuel + + align:start position:0% +surcharge on your bill and that fuel + + + align:start position:0% +surcharge on your bill and that fuel +surcharge is going to be suddenly won't + + align:start position:0% +surcharge is going to be suddenly won't + + + align:start position:0% +surcharge is going to be suddenly won't +pay attention just they won't notice + + align:start position:0% +pay attention just they won't notice + + + align:start position:0% +pay attention just they won't notice +that we're rising it together and these + + align:start position:0% +that we're rising it together and these + + + align:start position:0% +that we're rising it together and these +fuel surcharges rose quickly from ten + + align:start position:0% +fuel surcharges rose quickly from ten + + + align:start position:0% +fuel surcharges rose quickly from ten +dollars to 120 dollars per flight and + + align:start position:0% +dollars to 120 dollars per flight and + + + align:start position:0% +dollars to 120 dollars per flight and +essentially rose in lockstep they + + align:start position:0% +essentially rose in lockstep they + + + align:start position:0% +essentially rose in lockstep they +essentially coordinated but tried to + + align:start position:0% +essentially coordinated but tried to + + + align:start position:0% +essentially coordinated but tried to +hide it by making the coordination not + + align:start position:0% +hide it by making the coordination not + + + align:start position:0% +hide it by making the coordination not +over the sticker price but over this + + align:start position:0% +over the sticker price but over this + + + align:start position:0% +over the sticker price but over this +thing it's sort of the bottom of your + + align:start position:0% +thing it's sort of the bottom of your + + + align:start position:0% +thing it's sort of the bottom of your +ticket which was the fuel surcharge so + + align:start position:0% +ticket which was the fuel surcharge so + + + align:start position:0% +ticket which was the fuel surcharge so +this worked for a while but then what + + align:start position:0% +this worked for a while but then what + + + align:start position:0% +this worked for a while but then what +happened well what happened with the + + align:start position:0% +happened well what happened with the + + + align:start position:0% +happened well what happened with the +prisoner's dilemma was that lawyers for + + align:start position:0% +prisoner's dilemma was that lawyers for + + + align:start position:0% +prisoner's dilemma was that lawyers for +lawyers for virgin airlines started + + align:start position:0% +lawyers for virgin airlines started + + + align:start position:0% +lawyers for virgin airlines started +worrying they were to get busted and + + align:start position:0% +worrying they were to get busted and + + + align:start position:0% +worrying they were to get busted and +they said well if we go to the feds + + align:start position:0% +they said well if we go to the feds + + + align:start position:0% +they said well if we go to the feds +first and bust British Airlines + + align:start position:0% +first and bust British Airlines + + + align:start position:0% +first and bust British Airlines +maybe we'll get a better deal so they + + align:start position:0% +maybe we'll get a better deal so they + + + align:start position:0% +maybe we'll get a better deal so they +were essentially the prisoner that + + align:start position:0% +were essentially the prisoner that + + + align:start position:0% +were essentially the prisoner that +ratted the Virgin Atlantic went was the + + align:start position:0% +ratted the Virgin Atlantic went was the + + + align:start position:0% +ratted the Virgin Atlantic went was the +prisoner that ratted and the whole thing + + align:start position:0% +prisoner that ratted and the whole thing + + + align:start position:0% +prisoner that ratted and the whole thing +broke down there were penalties more on + + align:start position:0% +broke down there were penalties more on + + + align:start position:0% +broke down there were penalties more on +British Air Lines cos Virgin Atlantic + + align:start position:0% +British Air Lines cos Virgin Atlantic + + + align:start position:0% +British Air Lines cos Virgin Atlantic +ratted on them but just like the + + align:start position:0% +ratted on them but just like the + + + align:start position:0% +ratted on them but just like the +prisoner's dilemma breaks down it broke + + align:start position:0% +prisoner's dilemma breaks down it broke + + + align:start position:0% +prisoner's dilemma breaks down it broke +down in reality and so that was + + align:start position:0% +down in reality and so that was + + + align:start position:0% +down in reality and so that was +something not where the law really + + align:start position:0% +something not where the law really + + + align:start position:0% +something not where the law really +worked but where the the cartel was + + align:start position:0% +worked but where the the cartel was + + + align:start position:0% +worked but where the the cartel was +unstable + + align:start position:0% +unstable + + + align:start position:0% +unstable +and the end result was Virgin Atlantic + + align:start position:0% +and the end result was Virgin Atlantic + + + align:start position:0% +and the end result was Virgin Atlantic +paid no fees paid no penalty and British + + align:start position:0% +paid no fees paid no penalty and British + + + align:start position:0% +paid no fees paid no penalty and British +Airlines paid more than five hundred + + align:start position:0% +Airlines paid more than five hundred + + + align:start position:0% +Airlines paid more than five hundred +million dollars so British Airlines + + align:start position:0% +million dollars so British Airlines + + + align:start position:0% +million dollars so British Airlines +coolly did not study the prisoners + + align:start position:0% +coolly did not study the prisoners + + + align:start position:0% +coolly did not study the prisoners +dilemma + + align:start position:0% +dilemma + + + align:start position:0% +dilemma +did not realize that they should have + + align:start position:0% +did not realize that they should have + + + align:start position:0% +did not realize that they should have +gone first and ratting out Virgin Virgin + + align:start position:0% +gone first and ratting out Virgin Virgin + + + align:start position:0% +gone first and ratting out Virgin Virgin +Atlantic now that said sometimes cartels + + align:start position:0% +Atlantic now that said sometimes cartels + + + align:start position:0% +Atlantic now that said sometimes cartels +open operate openly in the public and + + align:start position:0% +open operate openly in the public and + + + align:start position:0% +open operate openly in the public and +get away with it ok let's talk about + + align:start position:0% +get away with it ok let's talk about + + + align:start position:0% +get away with it ok let's talk about +probably the biggest open cartel in + + align:start position:0% +probably the biggest open cartel in + + + align:start position:0% +probably the biggest open cartel in +American perhaps in America today the + + align:start position:0% +American perhaps in America today the + + + align:start position:0% +American perhaps in America today the +National Football League + + align:start position:0% +National Football League + + + align:start position:0% +National Football League +ok the National Football League football + + align:start position:0% +ok the National Football League football + + + align:start position:0% +ok the National Football League football +is the most popular sport in America the + + align:start position:0% +is the most popular sport in America the + + + align:start position:0% +is the most popular sport in America the +most profitable sport in America there + + align:start position:0% +most profitable sport in America there + + + align:start position:0% +most profitable sport in America there +are 32 teams and they're essentially 32 + + align:start position:0% +are 32 teams and they're essentially 32 + + + align:start position:0% +are 32 teams and they're essentially 32 +businesses whose job it is to produce + + align:start position:0% +businesses whose job it is to produce + + + align:start position:0% +businesses whose job it is to produce +football wins okay now these businesses + + align:start position:0% +football wins okay now these businesses + + + align:start position:0% +football wins okay now these businesses +have a huge incentive to collude with + + align:start position:0% +have a huge incentive to collude with + + + align:start position:0% +have a huge incentive to collude with +their fellow business however because + + align:start position:0% +their fellow business however because + + + align:start position:0% +their fellow business however because +because they can because of television + + align:start position:0% +because they can because of television + + + align:start position:0% +because they can because of television +rights so the New York Giants of the New + + align:start position:0% +rights so the New York Giants of the New + + + align:start position:0% +rights so the New York Giants of the New +York Jets competed over the television + + align:start position:0% +York Jets competed over the television + + + align:start position:0% +York Jets competed over the television +rights for their area they would compete + + align:start position:0% +rights for their area they would compete + + + align:start position:0% +rights for their area they would compete +away the profits that could be made by + + align:start position:0% +away the profits that could be made by + + + align:start position:0% +away the profits that could be made by +getting a big contract if they collude + + align:start position:0% +getting a big contract if they collude + + + align:start position:0% +getting a big contract if they collude +and say no you can only we will only + + align:start position:0% +and say no you can only we will only + + + align:start position:0% +and say no you can only we will only +agree to a contract together they can + + align:start position:0% +agree to a contract together they can + + + align:start position:0% +agree to a contract together they can +get a higher price for that contract + + align:start position:0% +get a higher price for that contract + + + align:start position:0% +get a higher price for that contract +because it's either you give them the + + align:start position:0% +because it's either you give them the + + + align:start position:0% +because it's either you give them the +contract you're out if they competed TV + + align:start position:0% +contract you're out if they competed TV + + + align:start position:0% +contract you're out if they competed TV +covers for P because each other and + + align:start position:0% +covers for P because each other and + + + align:start position:0% +covers for P because each other and +fight the price down okay + + align:start position:0% +fight the price down okay + + + align:start position:0% +fight the price down okay +and in general access goes more than + + align:start position:0% +and in general access goes more than + + + align:start position:0% +and in general access goes more than +this the league sells the rights to + + align:start position:0% +this the league sells the rights to + + + align:start position:0% +this the league sells the rights to +televise games as a package so in fact + + align:start position:0% +televise games as a package so in fact + + + align:start position:0% +televise games as a package so in fact +the National Football League literally + + align:start position:0% +the National Football League literally + + + align:start position:0% +the National Football League literally +sells explicitly says we have a cartel + + align:start position:0% +sells explicitly says we have a cartel + + + align:start position:0% +sells explicitly says we have a cartel +of 32 teams we are selling the monopoly + + align:start position:0% +of 32 teams we are selling the monopoly + + + align:start position:0% +of 32 teams we are selling the monopoly +right to televise these games + + align:start position:0% +right to televise these games + + + align:start position:0% +right to televise these games +somebody's got Sunday somebody's got + + align:start position:0% +somebody's got Sunday somebody's got + + + align:start position:0% +somebody's got Sunday somebody's got +Thursday somebody's gots Monday night + + align:start position:0% +Thursday somebody's gots Monday night + + + align:start position:0% +Thursday somebody's gots Monday night +etc but it's a monopoly product they're + + align:start position:0% +etc but it's a monopoly product they're + + + align:start position:0% +etc but it's a monopoly product they're +selling now how did they get away with + + align:start position:0% +selling now how did they get away with + + + align:start position:0% +selling now how did they get away with +that + + align:start position:0% +that + + + align:start position:0% +that +well basically actually in 1957 they + + align:start position:0% +well basically actually in 1957 they + + + align:start position:0% +well basically actually in 1957 they +were busted that's a long time ago it's + + align:start position:0% +were busted that's a long time ago it's + + + align:start position:0% +were busted that's a long time ago it's +even before I was born that long ago + + align:start position:0% +even before I was born that long ago + + + align:start position:0% +even before I was born that long ago +okay they were busted and the court + + align:start position:0% +okay they were busted and the court + + + align:start position:0% +okay they were busted and the court +ruled that the NFL was violating + + align:start position:0% +ruled that the NFL was violating + + + align:start position:0% +ruled that the NFL was violating +antitrust laws okay now that was fought + + align:start position:0% +antitrust laws okay now that was fought + + + align:start position:0% +antitrust laws okay now that was fought +in 1957 that was 60 years ago the NFL + + align:start position:0% +in 1957 that was 60 years ago the NFL + + + align:start position:0% +in 1957 that was 60 years ago the NFL +would still makes about 40 billion + + align:start position:0% +would still makes about 40 billion + + + align:start position:0% +would still makes about 40 billion +dollars on his television contract what + + align:start position:0% +dollars on his television contract what + + + align:start position:0% +dollars on his television contract what +happened + + align:start position:0% +happened + + + align:start position:0% +happened +Congress just exempted them Congress + + align:start position:0% +Congress just exempted them Congress + + + align:start position:0% +Congress just exempted them Congress +said well you know what we know they're + + align:start position:0% +said well you know what we know they're + + + align:start position:0% +said well you know what we know they're +violent I trust but we're gonna pass a + + align:start position:0% +violent I trust but we're gonna pass a + + + align:start position:0% +violent I trust but we're gonna pass a +law which exempts them from antitrust + + align:start position:0% +law which exempts them from antitrust + + + align:start position:0% +law which exempts them from antitrust +law and let them do it + + align:start position:0% +law and let them do it + + + align:start position:0% +law and let them do it +so proves basically that Americans like + + align:start position:0% +so proves basically that Americans like + + + align:start position:0% +so proves basically that Americans like +football more than free markets and + + align:start position:0% +football more than free markets and + + + align:start position:0% +football more than free markets and +basically we now have a Cardinal eyes + + align:start position:0% +basically we now have a Cardinal eyes + + + align:start position:0% +basically we now have a Cardinal eyes +football industry that because Congress + + align:start position:0% +football industry that because Congress + + + align:start position:0% +football industry that because Congress +basically exempt them from the laws + + align:start position:0% +basically exempt them from the laws + + + align:start position:0% +basically exempt them from the laws +okay so those are some examples yeah + + align:start position:0% + + + + align:start position:0% + +other sports teams + + align:start position:0% +other sports teams + + + align:start position:0% +other sports teams +it is not add there are it's largely + + align:start position:0% +it is not add there are it's largely + + + align:start position:0% +it is not add there are it's largely +true for other sports leaks it's largely + + align:start position:0% +true for other sports leaks it's largely + + + align:start position:0% +true for other sports leaks it's largely +true the the some of the versions aren't + + align:start position:0% +true the the some of the versions aren't + + + align:start position:0% +true the the some of the versions aren't +explicit football but it's largely true + + align:start position:0% +explicit football but it's largely true + + + align:start position:0% +explicit football but it's largely true +for other sports leagues as well it's + + align:start position:0% +for other sports leagues as well it's + + + align:start position:0% +for other sports leagues as well it's +simple I mean I don't know I don't know + + align:start position:0% +simple I mean I don't know I don't know + + + align:start position:0% +simple I mean I don't know I don't know +that you have international antitrust + + align:start position:0% +that you have international antitrust + + + align:start position:0% +that you have international antitrust +laws I'm not sure how that works with + + align:start position:0% +laws I'm not sure how that works with + + + align:start position:0% +laws I'm not sure how that works with +international league it's a good + + align:start position:0% +international league it's a good + + + align:start position:0% +international league it's a good +question um okay now another form of + + align:start position:0% +question um okay now another form of + + + align:start position:0% +question um okay now another form of +cartels we talked about cartels and how + + align:start position:0% +cartels we talked about cartels and how + + + align:start position:0% +cartels we talked about cartels and how +companies instead of to put them + + align:start position:0% +companies instead of to put them + + + align:start position:0% +companies instead of to put them +together actually sometimes the federal + + align:start position:0% +together actually sometimes the federal + + + align:start position:0% +together actually sometimes the federal +government can make a cartel yeah OPEC + + align:start position:0% +government can make a cartel yeah OPEC + + + align:start position:0% +government can make a cartel yeah OPEC +so OPEC is as I mentioned the first + + align:start position:0% +so OPEC is as I mentioned the first + + + align:start position:0% +so OPEC is as I mentioned the first +lecture a series of countries that get + + align:start position:0% +lecture a series of countries that get + + + align:start position:0% +lecture a series of countries that get +together produce oil it's not working as + + align:start position:0% +together produce oil it's not working as + + + align:start position:0% +together produce oil it's not working as +well as it was when I was a kid we're + + align:start position:0% +well as it was when I was a kid we're + + + align:start position:0% +well as it was when I was a kid we're +really well because more countries a + + align:start position:0% +really well because more countries a + + + align:start position:0% +really well because more countries a +more countries are cheating and more + + align:start position:0% +more countries are cheating and more + + + align:start position:0% +more countries are cheating and more +countries there's more oil being found + + align:start position:0% +countries there's more oil being found + + + align:start position:0% +countries there's more oil being found +outside OPEC but it still works it's + + align:start position:0% +outside OPEC but it still works it's + + + align:start position:0% +outside OPEC but it still works it's +sort of a partially functioning cartel + + align:start position:0% +sort of a partially functioning cartel + + + align:start position:0% +sort of a partially functioning cartel +as I think the way to think about it um + + align:start position:0% +as I think the way to think about it um + + + align:start position:0% +as I think the way to think about it um +okay so let me um let me actually let me + + align:start position:0% +okay so let me um let me actually let me + + + align:start position:0% +okay so let me um let me actually let me +go on and talk about lesson do one more + + align:start position:0% +go on and talk about lesson do one more + + + align:start position:0% +go on and talk about lesson do one more +example about a time when a government + + align:start position:0% +example about a time when a government + + + align:start position:0% +example about a time when a government +made a cartel here's a one more + + align:start position:0% +made a cartel here's a one more + + + align:start position:0% +made a cartel here's a one more +interesting example so in the early + + align:start position:0% +interesting example so in the early + + + align:start position:0% +interesting example so in the early +1980s before the early nineties the US + + align:start position:0% +1980s before the early nineties the US + + + align:start position:0% +1980s before the early nineties the US +dominated the car production business + + align:start position:0% +dominated the car production business + + + align:start position:0% +dominated the car production business +starting in the late 70s Japan started + + align:start position:0% +starting in the late 70s Japan started + + + align:start position:0% +starting in the late 70s Japan started +making huge inroads into car production + + align:start position:0% +making huge inroads into car production + + + align:start position:0% +making huge inroads into car production +and by the early 1980s we're in + + align:start position:0% +and by the early 1980s we're in + + + align:start position:0% +and by the early 1980s we're in +recession and car manufacturers in the + + align:start position:0% +recession and car manufacturers in the + + + align:start position:0% +recession and car manufacturers in the +u.s. are really pissed that Japan was + + align:start position:0% +u.s. are really pissed that Japan was + + + align:start position:0% +u.s. are really pissed that Japan was +taking so much of our market and we'll + + align:start position:0% +taking so much of our market and we'll + + + align:start position:0% +taking so much of our market and we'll +talk it a couple election about + + align:start position:0% +talk it a couple election about + + + align:start position:0% +talk it a couple election about +international trade and all those set of + + align:start position:0% +international trade and all those set of + + + align:start position:0% +international trade and all those set of +issues but put those issues aside right + + align:start position:0% +issues but put those issues aside right + + + align:start position:0% +issues but put those issues aside right +now you just have this issue that car + + align:start position:0% +now you just have this issue that car + + + align:start position:0% +now you just have this issue that car +manufacturers wanted to limit the amount + + align:start position:0% +manufacturers wanted to limit the amount + + + align:start position:0% +manufacturers wanted to limit the amount +of Japanese cars come into America now + + align:start position:0% +of Japanese cars come into America now + + + align:start position:0% +of Japanese cars come into America now +you guys have been reading in the paper + + align:start position:0% +you guys have been reading in the paper + + + align:start position:0% +you guys have been reading in the paper +about international trade and why + + align:start position:0% +about international trade and why + + + align:start position:0% +about international trade and why +economists typically don't like limiting + + align:start position:0% +economists typically don't like limiting + + + align:start position:0% +economists typically don't like limiting +limiting international trade and Reagan + + align:start position:0% +limiting international trade and Reagan + + + align:start position:0% +limiting international trade and Reagan +was you know a standard Republican part + + align:start position:0% +was you know a standard Republican part + + + align:start position:0% +was you know a standard Republican part +of the party of free trade so Reagan + + align:start position:0% +of the party of free trade so Reagan + + + align:start position:0% +of the party of free trade so Reagan +said well we're not gonna limit the cars + + align:start position:0% +said well we're not gonna limit the cars + + + align:start position:0% +said well we're not gonna limit the cars +that Japan wants to send in but we're + + align:start position:0% +that Japan wants to send in but we're + + + align:start position:0% +that Japan wants to send in but we're +gonna tell Japan if you guys were + + align:start position:0% +gonna tell Japan if you guys were + + + align:start position:0% +gonna tell Japan if you guys were +willing to agree to a voluntary export + + align:start position:0% +willing to agree to a voluntary export + + + align:start position:0% +willing to agree to a voluntary export +restraints + + align:start position:0% +restraints + + + align:start position:0% +restraints +we wouldn't mind so what he said to + + align:start position:0% +we wouldn't mind so what he said to + + + align:start position:0% +we wouldn't mind so what he said to +Japan + + align:start position:0% +Japan + + + align:start position:0% +Japan +something called a voluntary export + + align:start position:0% +something called a voluntary export + + + align:start position:0% +something called a voluntary export +constraint which basically said you we + + align:start position:0% +constraint which basically said you we + + + align:start position:0% +constraint which basically said you we +will negotiate deal with you where you + + align:start position:0% +will negotiate deal with you where you + + + align:start position:0% +will negotiate deal with you where you +will voluntarily agree + + align:start position:0% +will voluntarily agree + + + align:start position:0% +will voluntarily agree +to reduce the number of cars you send to + + align:start position:0% +to reduce the number of cars you send to + + + align:start position:0% +to reduce the number of cars you send to +America okay it's not a government + + align:start position:0% +America okay it's not a government + + + align:start position:0% +America okay it's not a government +policies isn't big government this is + + align:start position:0% +policies isn't big government this is + + + align:start position:0% +policies isn't big government this is +pride negotiations of private company + + align:start position:0% +pride negotiations of private company + + + align:start position:0% +pride negotiations of private company +voluntary agreement okay Japanese to + + align:start position:0% +voluntary agreement okay Japanese to + + + align:start position:0% +voluntary agreement okay Japanese to +this why yeah because because you need a + + align:start position:0% +this why yeah because because you need a + + + align:start position:0% +this why yeah because because you need a +cartel yes the Japanese companies used + + align:start position:0% +cartel yes the Japanese companies used + + + align:start position:0% +cartel yes the Japanese companies used +to have to compete with each other sell + + align:start position:0% +to have to compete with each other sell + + + align:start position:0% +to have to compete with each other sell +the cars in America now it's like okay + + align:start position:0% +the cars in America now it's like okay + + + align:start position:0% +the cars in America now it's like okay +you guys get together and limit how many + + align:start position:0% +you guys get together and limit how many + + + align:start position:0% +you guys get together and limit how many +cars you send they're like great + + align:start position:0% +cars you send they're like great + + + align:start position:0% +cars you send they're like great +you've given us an ability to form a + + align:start position:0% +you've given us an ability to form a + + + align:start position:0% +you've given us an ability to form a +cartel by central telling us get + + align:start position:0% +cartel by central telling us get + + + align:start position:0% +cartel by central telling us get +together and figure out how you gonna + + align:start position:0% +together and figure out how you gonna + + + align:start position:0% +together and figure out how you gonna +sell as many cars to America so + + align:start position:0% +sell as many cars to America so + + + align:start position:0% +sell as many cars to America so +essentially this voluntary export + + align:start position:0% +essentially this voluntary export + + + align:start position:0% +essentially this voluntary export +strains essentially cartelized and no + + align:start position:0% +strains essentially cartelized and no + + + align:start position:0% +strains essentially cartelized and no +company could cheat so if you had a + + align:start position:0% +company could cheat so if you had a + + + align:start position:0% +company could cheat so if you had a +cartel any cup and tried to cheat they + + align:start position:0% +cartel any cup and tried to cheat they + + + align:start position:0% +cartel any cup and tried to cheat they +couldn't sell the cars to you just + + align:start position:0% +couldn't sell the cars to you just + + + align:start position:0% +couldn't sell the cars to you just +wouldn't let them come into the US so + + align:start position:0% +wouldn't let them come into the US so + + + align:start position:0% +wouldn't let them come into the US so +essentially the u.s. provided them a + + align:start position:0% +essentially the u.s. provided them a + + + align:start position:0% +essentially the u.s. provided them a +wave and forcing their cartel what + + align:start position:0% +wave and forcing their cartel what + + + align:start position:0% +wave and forcing their cartel what +happened well um the average price of a + + align:start position:0% +happened well um the average price of a + + + align:start position:0% +happened well um the average price of a +Japanese car in America went up by + + align:start position:0% +Japanese car in America went up by + + + align:start position:0% +Japanese car in America went up by +$1,200 okay + + align:start position:0% +$1,200 okay + + + align:start position:0% +$1,200 okay +u.s. Auto profits did go up but US + + align:start position:0% +u.s. Auto profits did go up but US + + + align:start position:0% +u.s. Auto profits did go up but US +consumers lost out by way more than + + align:start position:0% +consumers lost out by way more than + + + align:start position:0% +consumers lost out by way more than +producers gained and on that the + + align:start position:0% +producers gained and on that the + + + align:start position:0% +producers gained and on that the +estimates are that US consumers about + + align:start position:0% +estimates are that US consumers about + + + align:start position:0% +estimates are that US consumers about +three billion overall u.s. about three + + align:start position:0% +three billion overall u.s. about three + + + align:start position:0% +three billion overall u.s. about three +billion dollars worse because of this + + align:start position:0% +billion dollars worse because of this + + + align:start position:0% +billion dollars worse because of this +policy + + align:start position:0% +policy + + + align:start position:0% +policy +it's just examples of how different way + + align:start position:0% +it's just examples of how different way + + + align:start position:0% +it's just examples of how different way +different government policies can + + align:start position:0% +different government policies can + + + align:start position:0% +different government policies can +interact with the cardinal's ation of + + align:start position:0% +interact with the cardinal's ation of + + + align:start position:0% +interact with the cardinal's ation of +industries yeah company like price + + align:start position:0% +industries yeah company like price + + + align:start position:0% +industries yeah company like price +matches isn't that sort of like making a + + align:start position:0% +matches isn't that sort of like making a + + + align:start position:0% +matches isn't that sort of like making a +cartel like because that other company + + align:start position:0% +cartel like because that other company + + + align:start position:0% +cartel like because that other company +would see it they're gonna price it + + align:start position:0% +would see it they're gonna price it + + + align:start position:0% +would see it they're gonna price it +actually I wouldn't want to set a price + + align:start position:0% +actually I wouldn't want to set a price + + + align:start position:0% +actually I wouldn't want to set a price +lower than that well it's a great + + align:start position:0% +lower than that well it's a great + + + align:start position:0% +lower than that well it's a great +question and you're pointing out this is + + align:start position:0% +question and you're pointing out this is + + + align:start position:0% +question and you're pointing out this is +not a solid line and in some sense the + + align:start position:0% +not a solid line and in some sense the + + + align:start position:0% +not a solid line and in some sense the +question is if it's true that so for + + align:start position:0% +question is if it's true that so for + + + align:start position:0% +question is if it's true that so for +many years tobacco industry worked this + + align:start position:0% +many years tobacco industry worked this + + + align:start position:0% +many years tobacco industry worked this +way + + align:start position:0% +way + + + align:start position:0% +way +there was one large player Philip Morris + + align:start position:0% +there was one large player Philip Morris + + + align:start position:0% +there was one large player Philip Morris +Philip Morris would sort of raise the + + align:start position:0% +Philip Morris would sort of raise the + + + align:start position:0% +Philip Morris would sort of raise the +price that ever would match now as long + + align:start position:0% +price that ever would match now as long + + + align:start position:0% +price that ever would match now as long +as there's no evidence that they agreed + + align:start position:0% +as there's no evidence that they agreed + + + align:start position:0% +as there's no evidence that they agreed +to do that that is not illegal if + + align:start position:0% +to do that that is not illegal if + + + align:start position:0% +to do that that is not illegal if +there's evidence they agree to that's + + align:start position:0% +there's evidence they agree to that's + + + align:start position:0% +there's evidence they agree to that's +illegal but as long as it's just like no + + align:start position:0% +illegal but as long as it's just like no + + + align:start position:0% +illegal but as long as it's just like no +we're just this is the way it's going to + + align:start position:0% +we're just this is the way it's going to + + + align:start position:0% +we're just this is the way it's going to +work then that's not illegal so + + align:start position:0% +work then that's not illegal so + + + align:start position:0% +work then that's not illegal so +basically that's sort of an implicit + + align:start position:0% +basically that's sort of an implicit + + + align:start position:0% +basically that's sort of an implicit +cartel now once again what's holding it + + align:start position:0% +cartel now once again what's holding it + + + align:start position:0% +cartel now once again what's holding it +together nothing a company could cheat + + align:start position:0% +together nothing a company could cheat + + + align:start position:0% +together nothing a company could cheat +and try to be + + align:start position:0% +and try to be + + + align:start position:0% +and try to be +try to charge less but basically that + + align:start position:0% +try to charge less but basically that + + + align:start position:0% +try to charge less but basically that +essentially they figured they're working + + align:start position:0% +essentially they figured they're working + + + align:start position:0% +essentially they figured they're working +better as a cartel and essentially was + + align:start position:0% +better as a cartel and essentially was + + + align:start position:0% +better as a cartel and essentially was +hard - there was no way to bust it yeah + + align:start position:0% +hard - there was no way to bust it yeah + + + align:start position:0% +hard - there was no way to bust it yeah +I mean like if a company says to + + align:start position:0% +I mean like if a company says to + + + align:start position:0% +I mean like if a company says to +consumers like if you can bring in a + + align:start position:0% +consumers like if you can bring in a + + + align:start position:0% +consumers like if you can bring in a +lower price we'll sell it for that price + + align:start position:0% +lower price we'll sell it for that price + + + align:start position:0% +lower price we'll sell it for that price +that's sort of a different I mean you + + align:start position:0% +that's sort of a different I mean you + + + align:start position:0% +that's sort of a different I mean you +could imagine you would need every + + align:start position:0% +could imagine you would need every + + + align:start position:0% +could imagine you would need every +company do that that would be a cartel + + align:start position:0% +company do that that would be a cartel + + + align:start position:0% +company do that that would be a cartel +enforcing way if every company had that + + align:start position:0% +enforcing way if every company had that + + + align:start position:0% +enforcing way if every company had that +deal in a market but one company of that + + align:start position:0% +deal in a market but one company of that + + + align:start position:0% +deal in a market but one company of that +deal doesn't doesn't enforce the cartel + + align:start position:0% +deal doesn't doesn't enforce the cartel + + + align:start position:0% +deal doesn't doesn't enforce the cartel +every company need to have that deal and + + align:start position:0% +every company need to have that deal and + + + align:start position:0% +every company need to have that deal and +so the question is if every company if + + align:start position:0% +so the question is if every company if + + + align:start position:0% +so the question is if every company if +every company on their own or gainfully + + align:start position:0% +every company on their own or gainfully + + + align:start position:0% +every company on their own or gainfully +sited we're gonna have that deal that + + align:start position:0% +sited we're gonna have that deal that + + + align:start position:0% +sited we're gonna have that deal that +would essentially be a way of trying to + + align:start position:0% +would essentially be a way of trying to + + + align:start position:0% +would essentially be a way of trying to +bring in force the cartel but I think + + align:start position:0% +bring in force the cartel but I think + + + align:start position:0% +bring in force the cartel but I think +that would be hard to say was an anti + + align:start position:0% +that would be hard to say was an anti + + + align:start position:0% +that would be hard to say was an anti +truck wasn't antitrust violation it's + + align:start position:0% +truck wasn't antitrust violation it's + + + align:start position:0% +truck wasn't antitrust violation it's +good good questions other questions okay + + align:start position:0% +good good questions other questions okay + + + align:start position:0% +good good questions other questions okay +so now let's ask why do we care about + + align:start position:0% +so now let's ask why do we care about + + + align:start position:0% +so now let's ask why do we care about +all this we care about all this because + + align:start position:0% +all this we care about all this because + + + align:start position:0% +all this we care about all this because +it matters for ultimately what matters + + align:start position:0% +it matters for ultimately what matters + + + align:start position:0% +it matters for ultimately what matters +to us in this class which is economic + + align:start position:0% +to us in this class which is economic + + + align:start position:0% +to us in this class which is economic +welfare okay so now let's go to the + + align:start position:0% +welfare okay so now let's go to the + + + align:start position:0% +welfare okay so now let's go to the +second thing I want to cover which is + + align:start position:0% +second thing I want to cover which is + + + align:start position:0% +second thing I want to cover which is +comparing the equilibria we've now + + align:start position:0% +comparing the equilibria we've now + + + align:start position:0% +comparing the equilibria we've now +covered three types of market structures + + align:start position:0% +covered three types of market structures + + + align:start position:0% +covered three types of market structures +perfect competition Monopoly and + + align:start position:0% +perfect competition Monopoly and + + + align:start position:0% +perfect competition Monopoly and +oligopoly now let's compare them and I + + align:start position:0% +oligopoly now let's compare them and I + + + align:start position:0% +oligopoly now let's compare them and I +compare them in two ways quantity sold + + align:start position:0% +compare them in two ways quantity sold + + + align:start position:0% +compare them in two ways quantity sold +and profits and profits profits per firm + + align:start position:0% + + + + align:start position:0% + +profits earned per firm and we're gonna + + align:start position:0% +profits earned per firm and we're gonna + + + align:start position:0% +profits earned per firm and we're gonna +stick with this United American market + + align:start position:0% +stick with this United American market + + + align:start position:0% +stick with this United American market +okay we know if there's a monopoly if + + align:start position:0% +okay we know if there's a monopoly if + + + align:start position:0% +okay we know if there's a monopoly if +this is a monopoly if they can car + + align:start position:0% +this is a monopoly if they can car + + + align:start position:0% +this is a monopoly if they can car +perfectly cartelize then there'll be + + align:start position:0% +perfectly cartelize then there'll be + + + align:start position:0% +perfectly cartelize then there'll be +ninety six flights total each one fly + + align:start position:0% +ninety six flights total each one fly + + + align:start position:0% +ninety six flights total each one fly +forty eight flights and profits per firm + + align:start position:0% +forty eight flights and profits per firm + + + align:start position:0% +forty eight flights and profits per firm +will be forty six owing and we solve + + align:start position:0% +will be forty six owing and we solve + + + align:start position:0% +will be forty six owing and we solve +that already that's the cartel outcome + + align:start position:0% +that already that's the cartel outcome + + + align:start position:0% +that already that's the cartel outcome +the non cooperative outcome which we'll + + align:start position:0% +the non cooperative outcome which we'll + + + align:start position:0% +the non cooperative outcome which we'll +call the oligopoly outcome is they each + + align:start position:0% +call the oligopoly outcome is they each + + + align:start position:0% +call the oligopoly outcome is they each +sell sixty four flights we saw that last + + align:start position:0% +sell sixty four flights we saw that last + + + align:start position:0% +sell sixty four flights we saw that last +time and as we saw here they each make + + align:start position:0% +time and as we saw here they each make + + + align:start position:0% +time and as we saw here they each make +profits a fourth for no nine six what's + + align:start position:0% +profits a fourth for no nine six what's + + + align:start position:0% +profits a fourth for no nine six what's +the competitive outcome in this market + + align:start position:0% + + + + align:start position:0% + +what's the competitive outcome in this + + align:start position:0% +what's the competitive outcome in this + + + align:start position:0% +what's the competitive outcome in this +market first of all what's the price + + align:start position:0% +market first of all what's the price + + + align:start position:0% +market first of all what's the price +somebody raise their hand and tell me if + + align:start position:0% +somebody raise their hand and tell me if + + + align:start position:0% +somebody raise their hand and tell me if +this is a perfectly competitive market + + align:start position:0% +this is a perfectly competitive market + + + align:start position:0% +this is a perfectly competitive market +with the price beat and well and then + + align:start position:0% +with the price beat and well and then + + + align:start position:0% +with the price beat and well and then +what would the quantity yeah price new + + align:start position:0% +what would the quantity yeah price new + + + align:start position:0% +what would the quantity yeah price new +147 because a perfectly competitive + + align:start position:0% +147 because a perfectly competitive + + + align:start position:0% +147 because a perfectly competitive +market price of marginal cost so profits + + align:start position:0% +market price of marginal cost so profits + + + align:start position:0% +market price of marginal cost so profits +would be zero and quantity would be 339 + + align:start position:0% +would be zero and quantity would be 339 + + + align:start position:0% +would be zero and quantity would be 339 +minus 147 or 192 okay so here we have + + align:start position:0% +minus 147 or 192 okay so here we have + + + align:start position:0% +minus 147 or 192 okay so here we have +for a given market a nice table which + + align:start position:0% +for a given market a nice table which + + + align:start position:0% +for a given market a nice table which +lets us compare the three different + + align:start position:0% +lets us compare the three different + + + align:start position:0% +lets us compare the three different +possible outcomes and what you see is + + align:start position:0% +possible outcomes and what you see is + + + align:start position:0% +possible outcomes and what you see is +essentially the more you can monopolize + + align:start position:0% +essentially the more you can monopolize + + + align:start position:0% +essentially the more you can monopolize +the higher your profits but the smaller + + align:start position:0% +the higher your profits but the smaller + + + align:start position:0% +the higher your profits but the smaller +the market okay so basically three + + align:start position:0% +the market okay so basically three + + + align:start position:0% +the market okay so basically three +lessons here first of all + + align:start position:0% +lessons here first of all + + + align:start position:0% +lessons here first of all +generally speaking the oligopoly outcome + + align:start position:0% +generally speaking the oligopoly outcome + + + align:start position:0% +generally speaking the oligopoly outcome +is somewhere between the monopoly and + + align:start position:0% +is somewhere between the monopoly and + + + align:start position:0% +is somewhere between the monopoly and +perfectly competitive outcome where in + + align:start position:0% +perfectly competitive outcome where in + + + align:start position:0% +perfectly competitive outcome where in +between take 1412 what 1412 was about is + + align:start position:0% +between take 1412 what 1412 was about is + + + align:start position:0% +between take 1412 what 1412 was about is +how you figure out where in between this + + align:start position:0% +how you figure out where in between this + + + align:start position:0% +how you figure out where in between this +outcome comes between these two it's all + + align:start position:0% +outcome comes between these two it's all + + + align:start position:0% +outcome comes between these two it's all +about game theory okay so that's what's + + align:start position:0% +about game theory okay so that's what's + + + align:start position:0% +about game theory okay so that's what's +exciting about game theory is this is a + + align:start position:0% +exciting about game theory is this is a + + + align:start position:0% +exciting about game theory is this is a +wide range and game theory as it says + + align:start position:0% +wide range and game theory as it says + + + align:start position:0% +wide range and game theory as it says +sophisticated tools that let us pin down + + align:start position:0% +sophisticated tools that let us pin down + + + align:start position:0% +sophisticated tools that let us pin down +we're in this range companies will end + + align:start position:0% +we're in this range companies will end + + + align:start position:0% +we're in this range companies will end +up in the realistic case point to is the + + align:start position:0% +up in the realistic case point to is the + + + align:start position:0% +up in the realistic case point to is the +more you can monopolize the higher your + + align:start position:0% +more you can monopolize the higher your + + + align:start position:0% +more you can monopolize the higher your +profits will be but let us come to + + align:start position:0% +profits will be but let us come to + + + align:start position:0% +profits will be but let us come to +welfare now having computed SERP social + + align:start position:0% +welfare now having computed SERP social + + + align:start position:0% +welfare now having computed SERP social +surplus here but here's the cheat I + + align:start position:0% +surplus here but here's the cheat I + + + align:start position:0% +surplus here but here's the cheat I +don't really need to I don't need to + + align:start position:0% +don't really need to I don't need to + + + align:start position:0% +don't really need to I don't need to +because essentially roughly speaking + + align:start position:0% +because essentially roughly speaking + + + align:start position:0% +because essentially roughly speaking +social welfare is proportional to the + + align:start position:0% +social welfare is proportional to the + + + align:start position:0% +social welfare is proportional to the +quantity sold in the Lord's we know that + + align:start position:0% +quantity sold in the Lord's we know that + + + align:start position:0% +quantity sold in the Lord's we know that +in a perfectly competitive market this + + align:start position:0% +in a perfectly competitive market this + + + align:start position:0% +in a perfectly competitive market this +is the welfare maximizing qualities 192 + + align:start position:0% +is the welfare maximizing qualities 192 + + + align:start position:0% +is the welfare maximizing qualities 192 +we know that there's a hundred ninety + + align:start position:0% +we know that there's a hundred ninety + + + align:start position:0% +we know that there's a hundred ninety +two flights that maximize welfare cuz + + align:start position:0% +two flights that maximize welfare cuz + + + align:start position:0% +two flights that maximize welfare cuz +that's the competitive outcome what + + align:start position:0% +that's the competitive outcome what + + + align:start position:0% +that's the competitive outcome what +we're saying is the more all this + + align:start position:0% +we're saying is the more all this + + + align:start position:0% +we're saying is the more all this +shouldn't be 64 128 that's my bet 64 we + + align:start position:0% +shouldn't be 64 128 that's my bet 64 we + + + align:start position:0% +shouldn't be 64 128 that's my bet 64 we +know that as we monopolize the market + + align:start position:0% +know that as we monopolize the market + + + align:start position:0% +know that as we monopolize the market +there are fewer and fewer flights + + align:start position:0% +there are fewer and fewer flights + + + align:start position:0% +there are fewer and fewer flights +therefore we're creating a deadweight + + align:start position:0% +therefore we're creating a deadweight + + + align:start position:0% +therefore we're creating a deadweight +loss essentially deadweight loss is + + align:start position:0% +loss essentially deadweight loss is + + + align:start position:0% +loss essentially deadweight loss is +proportional actually it's sort of + + align:start position:0% +proportional actually it's sort of + + + align:start position:0% +proportional actually it's sort of +exponentially proportional to the gap + + align:start position:0% +exponentially proportional to the gap + + + align:start position:0% +exponentially proportional to the gap +between the quality sold and the + + align:start position:0% +between the quality sold and the + + + align:start position:0% +between the quality sold and the +competitive quantity + + align:start position:0% +competitive quantity + + + align:start position:0% +competitive quantity +welfare's maximize here by definition we + + align:start position:0% +welfare's maximize here by definition we + + + align:start position:0% +welfare's maximize here by definition we +prove that so any reduction from that + + align:start position:0% +prove that so any reduction from that + + + align:start position:0% +prove that so any reduction from that +means that increased deadweight lost so + + align:start position:0% +means that increased deadweight lost so + + + align:start position:0% +means that increased deadweight lost so +the more you reduce quantity the more + + align:start position:0% +the more you reduce quantity the more + + + align:start position:0% +the more you reduce quantity the more +you lower welfare so essentially as we + + align:start position:0% +you lower welfare so essentially as we + + + align:start position:0% +you lower welfare so essentially as we +go down the down the column we lower + + align:start position:0% +go down the down the column we lower + + + align:start position:0% +go down the down the column we lower +profits but raise social welfare yeah + + align:start position:0% + + + + align:start position:0% + +yeah you know cartel / monopoly yes but + + align:start position:0% +yeah you know cartel / monopoly yes but + + + align:start position:0% +yeah you know cartel / monopoly yes but +all the way to 96 you prosper beaten + + align:start position:0% +all the way to 96 you prosper beaten + + + align:start position:0% +all the way to 96 you prosper beaten +would be twice that but the bottom line + + align:start position:0% +would be twice that but the bottom line + + + align:start position:0% +would be twice that but the bottom line +is that essentially you've got you + + align:start position:0% +is that essentially you've got you + + + align:start position:0% +is that essentially you've got you +you've got essentially more profits in + + align:start position:0% +you've got essentially more profits in + + + align:start position:0% +you've got essentially more profits in +this market ok other questions about + + align:start position:0% +this market ok other questions about + + + align:start position:0% +this market ok other questions about +that so the bottom line is the more + + align:start position:0% +that so the bottom line is the more + + + align:start position:0% +that so the bottom line is the more +competitive the market the higher the + + align:start position:0% +competitive the market the higher the + + + align:start position:0% +competitive the market the higher the +welfare but the lower the profits okay + + align:start position:0% +welfare but the lower the profits okay + + + align:start position:0% +welfare but the lower the profits okay +so that's kind of our bottom line of how + + align:start position:0% +so that's kind of our bottom line of how + + + align:start position:0% +so that's kind of our bottom line of how +we think about this questions about that + + align:start position:0% +we think about this questions about that + + + align:start position:0% +we think about this questions about that +ok next thing I want to cover we've only + + align:start position:0% +ok next thing I want to cover we've only + + + align:start position:0% +ok next thing I want to cover we've only +covered the case of two firms what if + + align:start position:0% +covered the case of two firms what if + + + align:start position:0% +covered the case of two firms what if +there are many firms after all most + + align:start position:0% +there are many firms after all most + + + align:start position:0% +there are many firms after all most +oligopoly markets are not just two firms + + align:start position:0% +oligopoly markets are not just two firms + + + align:start position:0% +oligopoly markets are not just two firms +Karm are we talking about cars and movie + + align:start position:0% +Karm are we talking about cars and movie + + + align:start position:0% +Karm are we talking about cars and movie +producing studios there are many firms + + align:start position:0% +producing studios there are many firms + + + align:start position:0% +producing studios there are many firms +ok + + align:start position:0% +ok + + + align:start position:0% +ok +well the cournot model is super hard to + + align:start position:0% +well the cournot model is super hard to + + + align:start position:0% +well the cournot model is super hard to +do when there's more firms but there's + + align:start position:0% +do when there's more firms but there's + + + align:start position:0% +do when there's more firms but there's +no reason you can't it's literally just + + align:start position:0% +no reason you can't it's literally just + + + align:start position:0% +no reason you can't it's literally just +becomes three equations and three + + align:start position:0% +becomes three equations and three + + + align:start position:0% +becomes three equations and three +unknowns or four equations and four + + align:start position:0% +unknowns or four equations and four + + + align:start position:0% +unknowns or four equations and four +unknowns little as you can see you could + + align:start position:0% +unknowns little as you can see you could + + + align:start position:0% +unknowns little as you can see you could +simply see as you take that model and + + align:start position:0% +simply see as you take that model and + + + align:start position:0% +simply see as you take that model and +add more firms it just expands the state + + align:start position:0% +add more firms it just expands the state + + + align:start position:0% +add more firms it just expands the state +space it becomes impossible to graph but + + align:start position:0% +space it becomes impossible to graph but + + + align:start position:0% +space it becomes impossible to graph but +you could solve it eventually we've got + + align:start position:0% +you could solve it eventually we've got + + + align:start position:0% +you could solve it eventually we've got +n equations in n unknowns the key bottom + + align:start position:0% +n equations in n unknowns the key bottom + + + align:start position:0% +n equations in n unknowns the key bottom +line result is that as the core note as + + align:start position:0% +line result is that as the core note as + + + align:start position:0% +line result is that as the core note as +the number of firms gets large they're + + align:start position:0% +the number of firms gets large they're + + + align:start position:0% +the number of firms gets large they're +cournot equilibrium approaches the + + align:start position:0% +cournot equilibrium approaches the + + + align:start position:0% +cournot equilibrium approaches the +competitive equilibrium that is + + align:start position:0% +competitive equilibrium that is + + + align:start position:0% +competitive equilibrium that is +mathematically if you solve this you + + align:start position:0% +mathematically if you solve this you + + + align:start position:0% +mathematically if you solve this you +don't have to solve this but the bottom + + align:start position:0% +don't have to solve this but the bottom + + + align:start position:0% +don't have to solve this but the bottom +line condition is the mark-up that Ferns + + align:start position:0% +line condition is the mark-up that Ferns + + + align:start position:0% +line condition is the mark-up that Ferns +earned is equal to minus 1 over N times + + align:start position:0% +earned is equal to minus 1 over N times + + + align:start position:0% +earned is equal to minus 1 over N times +the elasticity and instead of a market + + align:start position:0% +the elasticity and instead of a market + + + align:start position:0% +the elasticity and instead of a market +this is sort of in a symmetric cournot + + align:start position:0% +this is sort of in a symmetric cournot + + + align:start position:0% +this is sort of in a symmetric cournot +market of the kind we've been working + + align:start position:0% +market of the kind we've been working + + + align:start position:0% +market of the kind we've been working +with + + align:start position:0% + + + + align:start position:0% + +the mark-up is one over the number of + + align:start position:0% +the mark-up is one over the number of + + + align:start position:0% +the mark-up is one over the number of +firm sons the elasticity of x the + + align:start position:0% +firm sons the elasticity of x the + + + align:start position:0% +firm sons the elasticity of x the +elasticity of demand so think about this + + align:start position:0% +elasticity of demand so think about this + + + align:start position:0% +elasticity of demand so think about this +for a second imagine there is one firm + + align:start position:0% +for a second imagine there is one firm + + + align:start position:0% +for a second imagine there is one firm +then this equation says the markup is + + align:start position:0% +then this equation says the markup is + + + align:start position:0% +then this equation says the markup is +equal to minus one over the last two see + + align:start position:0% +equal to minus one over the last two see + + + align:start position:0% +equal to minus one over the last two see +demand where have we seen that before + + align:start position:0% +demand where have we seen that before + + + align:start position:0% +demand where have we seen that before +that's the monopoly condition that's the + + align:start position:0% +that's the monopoly condition that's the + + + align:start position:0% +that's the monopoly condition that's the +monopoly markup condition so an N equals + + align:start position:0% +monopoly markup condition so an N equals + + + align:start position:0% +monopoly markup condition so an N equals +1 this is an equation we've seen before + + align:start position:0% +1 this is an equation we've seen before + + + align:start position:0% +1 this is an equation we've seen before +the monopoly markup condition when N + + align:start position:0% +the monopoly markup condition when N + + + align:start position:0% +the monopoly markup condition when N +equals 2 the firms are making half as + + align:start position:0% +equals 2 the firms are making half as + + + align:start position:0% +equals 2 the firms are making half as +much when a equals 3 a third it goes in + + align:start position:0% +much when a equals 3 a third it goes in + + + align:start position:0% +much when a equals 3 a third it goes in +fact factor third etc what this says as + + align:start position:0% +fact factor third etc what this says as + + + align:start position:0% +fact factor third etc what this says as +n approaches infinity we approach the + + align:start position:0% +n approaches infinity we approach the + + + align:start position:0% +n approaches infinity we approach the +competitive outcome ok we'll never get + + align:start position:0% +competitive outcome ok we'll never get + + + align:start position:0% +competitive outcome ok we'll never get +there but we're asymptoting towards the + + align:start position:0% +there but we're asymptoting towards the + + + align:start position:0% +there but we're asymptoting towards the +competitive outcome which basically says + + align:start position:0% +competitive outcome which basically says + + + align:start position:0% +competitive outcome which basically says +you know it's sort of like my point + + align:start position:0% +you know it's sort of like my point + + + align:start position:0% +you know it's sort of like my point +about catastro markets you get a market + + align:start position:0% +about catastro markets you get a market + + + align:start position:0% +about catastro markets you get a market +that's sort of competitive enough you're + + align:start position:0% +that's sort of competitive enough you're + + + align:start position:0% +that's sort of competitive enough you're +gonna shrink + + align:start position:0% +gonna shrink + + + align:start position:0% +gonna shrink +you're gonna shrink the mark up as more + + align:start position:0% +you're gonna shrink the mark up as more + + + align:start position:0% +you're gonna shrink the mark up as more +and more firms enter ok so that's sort + + align:start position:0% +and more firms enter ok so that's sort + + + align:start position:0% +and more firms enter ok so that's sort +of a general condition that we could + + align:start position:0% +of a general condition that we could + + + align:start position:0% +of a general condition that we could +derive that shows that um as more firms + + align:start position:0% +derive that shows that um as more firms + + + align:start position:0% +derive that shows that um as more firms +as more firms are in then you get a + + align:start position:0% +as more firms are in then you get a + + + align:start position:0% +as more firms are in then you get a +lower markup um now I wanna make there's + + align:start position:0% +lower markup um now I wanna make there's + + + align:start position:0% +lower markup um now I wanna make there's +actually but this actually understates + + align:start position:0% +actually but this actually understates + + + align:start position:0% +actually but this actually understates +the case for an important strategic + + align:start position:0% +the case for an important strategic + + + align:start position:0% +the case for an important strategic +reason which is more firms lowers the + + align:start position:0% +reason which is more firms lowers the + + + align:start position:0% +reason which is more firms lowers the +markup in a in a more firm lows of our + + align:start position:0% +markup in a in a more firm lows of our + + + align:start position:0% +markup in a in a more firm lows of our +company cournot non-cooperative model + + align:start position:0% +company cournot non-cooperative model + + + align:start position:0% +company cournot non-cooperative model +but more firms also makes a cooperative + + align:start position:0% +but more firms also makes a cooperative + + + align:start position:0% +but more firms also makes a cooperative +model harder so this is for the non + + align:start position:0% +model harder so this is for the non + + + align:start position:0% +model harder so this is for the non +cooperative model the non cooperative + + align:start position:0% +cooperative model the non cooperative + + + align:start position:0% +cooperative model the non cooperative +model your profits follows they're more + + align:start position:0% +model your profits follows they're more + + + align:start position:0% +model your profits follows they're more +firms but it also gets harder to + + align:start position:0% +firms but it also gets harder to + + + align:start position:0% +firms but it also gets harder to +cooperate as they're more firms because + + align:start position:0% +cooperate as they're more firms because + + + align:start position:0% +cooperate as they're more firms because +they're more people they're more people + + align:start position:0% +they're more people they're more people + + + align:start position:0% +they're more people they're more people +you have to trust more people you have + + align:start position:0% +you have to trust more people you have + + + align:start position:0% +you have to trust more people you have +to keep hold of it's a great example of + + align:start position:0% +to keep hold of it's a great example of + + + align:start position:0% +to keep hold of it's a great example of +this actually for a long time + + align:start position:0% +this actually for a long time + + + align:start position:0% +this actually for a long time +mercury just stuff we using thermometers + + align:start position:0% +mercury just stuff we using thermometers + + + align:start position:0% +mercury just stuff we using thermometers +and such only was found in Italy in + + align:start position:0% +and such only was found in Italy in + + + align:start position:0% +and such only was found in Italy in +Spain in the mines in Italy in Spain and + + align:start position:0% +Spain in the mines in Italy in Spain and + + + align:start position:0% +Spain in the mines in Italy in Spain and +they had a cartel between the two + + align:start position:0% +they had a cartel between the two + + + align:start position:0% +they had a cartel between the two +countries to sell mercury what happened + + align:start position:0% +countries to sell mercury what happened + + + align:start position:0% +countries to sell mercury what happened +other countries discovered mercury and + + align:start position:0% +other countries discovered mercury and + + + align:start position:0% +other countries discovered mercury and +they couldn't keep the cartel together + + align:start position:0% +they couldn't keep the cartel together + + + align:start position:0% +they couldn't keep the cartel together +and the price of mercury fell a lot with + + align:start position:0% +and the price of mercury fell a lot with + + + align:start position:0% +and the price of mercury fell a lot with +the question about OPEC similar thing + + align:start position:0% +the question about OPEC similar thing + + + align:start position:0% +the question about OPEC similar thing +OPEC was much more successful in the + + align:start position:0% +OPEC was much more successful in the + + + align:start position:0% +OPEC was much more successful in the +1970s when essentially the only source + + align:start position:0% +1970s when essentially the only source + + + align:start position:0% +1970s when essentially the only source +of oil were basically these Arab nations + + align:start position:0% +of oil were basically these Arab nations + + + align:start position:0% +of oil were basically these Arab nations +that form OPEC + + align:start position:0% +that form OPEC + + + align:start position:0% +that form OPEC +what happened over time as you + + align:start position:0% +what happened over time as you + + + align:start position:0% +what happened over time as you +discovered more oil around the world in + + align:start position:0% +discovered more oil around the world in + + + align:start position:0% +discovered more oil around the world in +particular in Russia and in the US which + + align:start position:0% +particular in Russia and in the US which + + + align:start position:0% +particular in Russia and in the US which +is sort of broken the power of this + + align:start position:0% +is sort of broken the power of this + + + align:start position:0% +is sort of broken the power of this +cartel to a large extent so the reason + + align:start position:0% +cartel to a large extent so the reason + + + align:start position:0% +cartel to a large extent so the reason +why a bigger market moves us towards the + + align:start position:0% +why a bigger market moves us towards the + + + align:start position:0% +why a bigger market moves us towards the +competitive equilibrium is that it makes + + align:start position:0% +competitive equilibrium is that it makes + + + align:start position:0% +competitive equilibrium is that it makes +it harder to maintain a cartel okay now + + align:start position:0% +it harder to maintain a cartel okay now + + + align:start position:0% +it harder to maintain a cartel okay now +let's actually the other issue I want to + + align:start position:0% +let's actually the other issue I want to + + + align:start position:0% +let's actually the other issue I want to +cover here is I want to talk about what + + align:start position:0% +cover here is I want to talk about what + + + align:start position:0% +cover here is I want to talk about what +is what does all this teach us about a + + align:start position:0% +is what does all this teach us about a + + + align:start position:0% +is what does all this teach us about a +key policy issue which is the issue of + + align:start position:0% +key policy issue which is the issue of + + + align:start position:0% +key policy issue which is the issue of +mergers + + align:start position:0% +mergers + + + align:start position:0% +mergers +what does everything we've learned here + + align:start position:0% +what does everything we've learned here + + + align:start position:0% +what does everything we've learned here +tell us about thinking about mergers ok + + align:start position:0% +tell us about thinking about mergers ok + + + align:start position:0% +tell us about thinking about mergers ok +we know about mergers happens all the + + align:start position:0% +we know about mergers happens all the + + + align:start position:0% +we know about mergers happens all the +time two companies merge well it turns + + align:start position:0% +time two companies merge well it turns + + + align:start position:0% +time two companies merge well it turns +out when companies merge and they're + + align:start position:0% +out when companies merge and they're + + + align:start position:0% +out when companies merge and they're +large enough the federal government + + align:start position:0% +large enough the federal government + + + align:start position:0% +large enough the federal government +regulates that the federal government + + align:start position:0% +regulates that the federal government + + + align:start position:0% +regulates that the federal government +gets a vote on whether that merger is + + align:start position:0% +gets a vote on whether that merger is + + + align:start position:0% +gets a vote on whether that merger is +going to be allowed to go forward either + + align:start position:0% +going to be allowed to go forward either + + + align:start position:0% +going to be allowed to go forward either +the Department of Justice the Federal + + align:start position:0% +the Department of Justice the Federal + + + align:start position:0% +the Department of Justice the Federal +Trade Commission depending on what kind + + align:start position:0% +Trade Commission depending on what kind + + + align:start position:0% +Trade Commission depending on what kind +what industry it is so the federal + + align:start position:0% +what industry it is so the federal + + + align:start position:0% +what industry it is so the federal +government has to decide how do you + + align:start position:0% +government has to decide how do you + + + align:start position:0% +government has to decide how do you +evaluate whether two firms merging is a + + align:start position:0% +evaluate whether two firms merging is a + + + align:start position:0% +evaluate whether two firms merging is a +good idea or not and essentially what it + + align:start position:0% +good idea or not and essentially what it + + + align:start position:0% +good idea or not and essentially what it +comes down to is a simple trade off + + align:start position:0% +comes down to is a simple trade off + + + align:start position:0% +comes down to is a simple trade off +economies of scale versus market power + + align:start position:0% + + + + align:start position:0% + +the benefit of two firms merging these + + align:start position:0% +the benefit of two firms merging these + + + align:start position:0% +the benefit of two firms merging these +economies of scale if two firms have + + align:start position:0% +economies of scale if two firms have + + + align:start position:0% +economies of scale if two firms have +sort of redundant production processes + + align:start position:0% +sort of redundant production processes + + + align:start position:0% +sort of redundant production processes +and they merge they can be more + + align:start position:0% +and they merge they can be more + + + align:start position:0% +and they merge they can be more +efficient there can be positive + + align:start position:0% +efficient there can be positive + + + align:start position:0% +efficient there can be positive +economies of scale for merging firms + + align:start position:0% +economies of scale for merging firms + + + align:start position:0% +economies of scale for merging firms +okay so there's cost efficiencies + + align:start position:0% +okay so there's cost efficiencies + + + align:start position:0% +okay so there's cost efficiencies +basically connie's of scale deliver cost + + align:start position:0% +basically connie's of scale deliver cost + + + align:start position:0% +basically connie's of scale deliver cost +efficiencies on the other hand the more + + align:start position:0% +efficiencies on the other hand the more + + + align:start position:0% +efficiencies on the other hand the more +firms merge the more this end goes down + + align:start position:0% +firms merge the more this end goes down + + + align:start position:0% +firms merge the more this end goes down +and the more markets go up and the worse + + align:start position:0% +and the more markets go up and the worse + + + align:start position:0% +and the more markets go up and the worse +it is for consumers so the trade-off is + + align:start position:0% +it is for consumers so the trade-off is + + + align:start position:0% +it is for consumers so the trade-off is +do you want to reduce it's reducing n + + align:start position:0% +do you want to reduce it's reducing n + + + align:start position:0% +do you want to reduce it's reducing n +worth it in terms of the kinds of scale + + align:start position:0% +worth it in terms of the kinds of scale + + + align:start position:0% +worth it in terms of the kinds of scale +or in other words does the producer + + align:start position:0% +or in other words does the producer + + + align:start position:0% +or in other words does the producer +efficiency go up enough to make up for + + align:start position:0% +efficiency go up enough to make up for + + + align:start position:0% +efficiency go up enough to make up for +the potential loss to consumers of this + + align:start position:0% +the potential loss to consumers of this + + + align:start position:0% +the potential loss to consumers of this +less competitive market okay + + align:start position:0% +less competitive market okay + + + align:start position:0% +less competitive market okay +people understand that now interesting + + align:start position:0% +people understand that now interesting + + + align:start position:0% +people understand that now interesting +case of this which has been got very big + + align:start position:0% +case of this which has been got very big + + + align:start position:0% +case of this which has been got very big +implications for all of us in America is + + align:start position:0% +implications for all of us in America is + + + align:start position:0% +implications for all of us in America is +hospital mergers during the decade of + + align:start position:0% +hospital mergers during the decade of + + + align:start position:0% +hospital mergers during the decade of +the 2000s there was a rash of hospital + + align:start position:0% +the 2000s there was a rash of hospital + + + align:start position:0% +the 2000s there was a rash of hospital +mergers + + align:start position:0% +mergers + + + align:start position:0% +mergers +we're Hospital said look here's a + + align:start position:0% +we're Hospital said look here's a + + + align:start position:0% +we're Hospital said look here's a +classic case recon as a scale because + + align:start position:0% +classic case recon as a scale because + + + align:start position:0% +classic case recon as a scale because +hospitals have what's called a peak load + + align:start position:0% +hospitals have what's called a peak load + + + align:start position:0% +hospitals have what's called a peak load +problem they have to have empty beds + + align:start position:0% +problem they have to have empty beds + + + align:start position:0% +problem they have to have empty beds +hostels can't be full all the time + + align:start position:0% +hostels can't be full all the time + + + align:start position:0% +hostels can't be full all the time +because there might be a car accident + + align:start position:0% +because there might be a car accident + + + align:start position:0% +because there might be a car accident +and people need beds so by definition + + align:start position:0% +and people need beds so by definition + + + align:start position:0% +and people need beds so by definition +it's inefficient for hospitals to be a + + align:start position:0% +it's inefficient for hospitals to be a + + + align:start position:0% +it's inefficient for hospitals to be a +hundred percent capacity hospitals one + + align:start position:0% +hundred percent capacity hospitals one + + + align:start position:0% +hundred percent capacity hospitals one +of xmx is capacity the problem that + + align:start position:0% +of xmx is capacity the problem that + + + align:start position:0% +of xmx is capacity the problem that +there's two hospitals next to each other + + align:start position:0% +there's two hospitals next to each other + + + align:start position:0% +there's two hospitals next to each other +each of the excess capacity that's + + align:start position:0% +each of the excess capacity that's + + + align:start position:0% +each of the excess capacity that's +inefficient it'd be more efficient to + + align:start position:0% +inefficient it'd be more efficient to + + + align:start position:0% +inefficient it'd be more efficient to +have one hospital one merge hospital + + align:start position:0% +have one hospital one merge hospital + + + align:start position:0% +have one hospital one merge hospital +then they just managed a proper amount + + align:start position:0% +then they just managed a proper amount + + + align:start position:0% +then they just managed a proper amount +of excess capacity and hospitals made + + align:start position:0% +of excess capacity and hospitals made + + + align:start position:0% +of excess capacity and hospitals made +this argument and we basically approved + + align:start position:0% +this argument and we basically approved + + + align:start position:0% +this argument and we basically approved +any household merger that they wanted in + + align:start position:0% +any household merger that they wanted in + + + align:start position:0% +any household merger that they wanted in +the 2000s well what happened what + + align:start position:0% +the 2000s well what happened what + + + align:start position:0% +the 2000s well what happened what +happened is the hospitals lied they kept + + align:start position:0% +happened is the hospitals lied they kept + + + align:start position:0% +happened is the hospitals lied they kept +both hospitals open kept all the empty + + align:start position:0% +both hospitals open kept all the empty + + + align:start position:0% +both hospitals open kept all the empty +beds and just raised prices so + + align:start position:0% +beds and just raised prices so + + + align:start position:0% +beds and just raised prices so +essentially the hospital mergers did not + + align:start position:0% +essentially the hospital mergers did not + + + align:start position:0% +essentially the hospital mergers did not +deliver any of the economies of scale + + align:start position:0% +deliver any of the economies of scale + + + align:start position:0% +deliver any of the economies of scale +they promised but did deliver a lot of + + align:start position:0% +they promised but did deliver a lot of + + + align:start position:0% +they promised but did deliver a lot of +the market power we feared so a huge + + align:start position:0% +the market power we feared so a huge + + + align:start position:0% +the market power we feared so a huge +cause of the increase in medical + + align:start position:0% +cause of the increase in medical + + + align:start position:0% +cause of the increase in medical +spending in the 2000s was these hospital + + align:start position:0% +spending in the 2000s was these hospital + + + align:start position:0% +spending in the 2000s was these hospital +mergers which essentially took a lot of + + align:start position:0% +mergers which essentially took a lot of + + + align:start position:0% +mergers which essentially took a lot of +the competitive pressure out of the + + align:start position:0% +the competitive pressure out of the + + + align:start position:0% +the competitive pressure out of the +medical market and didn't really deliver + + align:start position:0% +medical market and didn't really deliver + + + align:start position:0% +medical market and didn't really deliver +economies of scale and this is the hard + + align:start position:0% +economies of scale and this is the hard + + + align:start position:0% +economies of scale and this is the hard +part about being a regulator most of + + align:start position:0% +part about being a regulator most of + + + align:start position:0% +part about being a regulator most of +what public policy economists do in the + + align:start position:0% +what public policy economists do in the + + + align:start position:0% +what public policy economists do in the +world is regulate all over the world + + align:start position:0% +world is regulate all over the world + + + align:start position:0% +world is regulate all over the world +there are thousands of economists + + align:start position:0% +there are thousands of economists + + + align:start position:0% +there are thousands of economists +employed all over the world hundreds of + + align:start position:0% +employed all over the world hundreds of + + + align:start position:0% +employed all over the world hundreds of +that tens of thousands whose job it is + + align:start position:0% +that tens of thousands whose job it is + + + align:start position:0% +that tens of thousands whose job it is +to make regulatory decisions of this + + align:start position:0% +to make regulatory decisions of this + + + align:start position:0% +to make regulatory decisions of this +nature and they're really hard because + + align:start position:0% +nature and they're really hard because + + + align:start position:0% +nature and they're really hard because +we've drawn nice clean theoretical + + align:start position:0% +we've drawn nice clean theoretical + + + align:start position:0% +we've drawn nice clean theoretical +models here but we have to know what's + + align:start position:0% +models here but we have to know what's + + + align:start position:0% +models here but we have to know what's +Epsilon you know how much wit what's + + align:start position:0% +Epsilon you know how much wit what's + + + align:start position:0% +Epsilon you know how much wit what's +epsilon to figure out the effect to + + align:start position:0% +epsilon to figure out the effect to + + + align:start position:0% +epsilon to figure out the effect to +consumers what are the economies of + + align:start position:0% +consumers what are the economies of + + + align:start position:0% +consumers what are the economies of +scale will they actually split those + + align:start position:0% +scale will they actually split those + + + align:start position:0% +scale will they actually split those +economies of scale etc so these are + + align:start position:0% +economies of scale etc so these are + + + align:start position:0% +economies of scale etc so these are +really hard and interesting decisions + + align:start position:0% +really hard and interesting decisions + + + align:start position:0% +really hard and interesting decisions +now let's go on to the last topic I want + + align:start position:0% +now let's go on to the last topic I want + + + align:start position:0% +now let's go on to the last topic I want +to cover today which is price + + align:start position:0% +to cover today which is price + + + align:start position:0% +to cover today which is price +competition price competition now the + + align:start position:0% +competition price competition now the + + + align:start position:0% +competition price competition now the +models we've been discussing so far have + + align:start position:0% +models we've been discussing so far have + + + align:start position:0% +models we've been discussing so far have +been what we call quantity competition + + align:start position:0% +been what we call quantity competition + + + align:start position:0% +been what we call quantity competition +the United American compete on how many + + align:start position:0% +the United American compete on how many + + + align:start position:0% +the United American compete on how many +flights descend and then the demand + + align:start position:0% +flights descend and then the demand + + + align:start position:0% +flights descend and then the demand +curve tells them what they can charge + + align:start position:0% +curve tells them what they can charge + + + align:start position:0% +curve tells them what they can charge +but in fact in many markets that's not + + align:start position:0% +but in fact in many markets that's not + + + align:start position:0% +but in fact in many markets that's not +how firms compete in fact we even + + align:start position:0% +how firms compete in fact we even + + + align:start position:0% +how firms compete in fact we even +mentioned it + + align:start position:0% +mentioned it + + + align:start position:0% +mentioned it +I mentioned about best price offers etc + + align:start position:0% +I mentioned about best price offers etc + + + align:start position:0% +I mentioned about best price offers etc +they don't compete on quantity compete + + align:start position:0% +they don't compete on quantity compete + + + align:start position:0% +they don't compete on quantity compete +on price and that's a different model + + align:start position:0% +on price and that's a different model + + + align:start position:0% +on price and that's a different model +named after another French economist + + align:start position:0% +named after another French economist + + + align:start position:0% +named after another French economist +portraying a model of Bertrand + + align:start position:0% +portraying a model of Bertrand + + + align:start position:0% +portraying a model of Bertrand +competition is the model of price + + align:start position:0% +competition is the model of price + + + align:start position:0% +competition is the model of price +competition as a model we call + + align:start position:0% +competition as a model we call + + + align:start position:0% +competition as a model we call +portraying competition this model says + + align:start position:0% +portraying competition this model says + + + align:start position:0% +portraying competition this model says +that basically two firms compete over + + align:start position:0% +that basically two firms compete over + + + align:start position:0% +that basically two firms compete over +what price to set and then the quantity + + align:start position:0% +what price to set and then the quantity + + + align:start position:0% +what price to set and then the quantity +is determined by by the price that + + align:start position:0% +is determined by by the price that + + + align:start position:0% +is determined by by the price that +results from that competition so to + + align:start position:0% +results from that competition so to + + + align:start position:0% +results from that competition so to +compete over quantity to compete over + + align:start position:0% +compete over quantity to compete over + + + align:start position:0% +compete over quantity to compete over +price and the main curve then tells you + + align:start position:0% +price and the main curve then tells you + + + align:start position:0% +price and the main curve then tells you +the quantity okay now in this case + + align:start position:0% +the quantity okay now in this case + + + align:start position:0% +the quantity okay now in this case +what's really striking about Bertrand + + align:start position:0% +what's really striking about Bertrand + + + align:start position:0% +what's really striking about Bertrand +competition is that unlike the cournot + + align:start position:0% +competition is that unlike the cournot + + + align:start position:0% +competition is that unlike the cournot +model under Bertrand competition two + + align:start position:0% +model under Bertrand competition two + + + align:start position:0% +model under Bertrand competition two +firms can be enough to get us to the + + align:start position:0% +firms can be enough to get us to the + + + align:start position:0% +firms can be enough to get us to the +competitive equilibrium why why do we + + align:start position:0% +competitive equilibrium why why do we + + + align:start position:0% +competitive equilibrium why why do we +only potentially two firms to get the + + align:start position:0% +only potentially two firms to get the + + + align:start position:0% +only potentially two firms to get the +competitive equilibrium yeah why don't + + align:start position:0% +competitive equilibrium yeah why don't + + + align:start position:0% +competitive equilibrium yeah why don't +you explain a little bit more you mean + + align:start position:0% + + + + align:start position:0% + +exactly as long as there's profits to be + + align:start position:0% +exactly as long as there's profits to be + + + align:start position:0% +exactly as long as there's profits to be +made it's like our entry exit decisions + + align:start position:0% +made it's like our entry exit decisions + + + align:start position:0% +made it's like our entry exit decisions +right as long as his profits to be made + + align:start position:0% +right as long as his profits to be made + + + align:start position:0% +right as long as his profits to be made +I'm gonna come in at a price one penny + + align:start position:0% +I'm gonna come in at a price one penny + + + align:start position:0% +I'm gonna come in at a price one penny +below you make one penny less profits + + align:start position:0% +below you make one penny less profits + + + align:start position:0% +below you make one penny less profits +and steal all the business from you so + + align:start position:0% +and steal all the business from you so + + + align:start position:0% +and steal all the business from you so +if there's perfect competition between + + align:start position:0% +if there's perfect competition between + + + align:start position:0% +if there's perfect competition between +firms in a poor Tran sense then you only + + align:start position:0% +firms in a poor Tran sense then you only + + + align:start position:0% +firms in a poor Tran sense then you only +need two firms to get to the competitive + + align:start position:0% +need two firms to get to the competitive + + + align:start position:0% +need two firms to get to the competitive +equilibrium in theory okay so it's a + + align:start position:0% +equilibrium in theory okay so it's a + + + align:start position:0% +equilibrium in theory okay so it's a +very different idea that cournot + + align:start position:0% +very different idea that cournot + + + align:start position:0% +very different idea that cournot +competition where you need many many + + align:start position:0% +competition where you need many many + + + align:start position:0% +competition where you need many many +firms to get close to the competitive + + align:start position:0% +firms to get close to the competitive + + + align:start position:0% +firms to get close to the competitive +outcome with price competition because + + align:start position:0% +outcome with price competition because + + + align:start position:0% +outcome with price competition because +firms are always kind of competing to go + + align:start position:0% +firms are always kind of competing to go + + + align:start position:0% +firms are always kind of competing to go +one penny below each other in a market + + align:start position:0% +one penny below each other in a market + + + align:start position:0% +one penny below each other in a market +that's otherwise competitive you could + + align:start position:0% +that's otherwise competitive you could + + + align:start position:0% +that's otherwise competitive you could +actually drive the price to competitive + + align:start position:0% +actually drive the price to competitive + + + align:start position:0% +actually drive the price to competitive +price through essentially you can + + align:start position:0% +price through essentially you can + + + align:start position:0% +price through essentially you can +actually drive the price down to + + align:start position:0% +actually drive the price down to + + + align:start position:0% +actually drive the price down to +marginal cost it's sort of like I talked + + align:start position:0% +marginal cost it's sort of like I talked + + + align:start position:0% +marginal cost it's sort of like I talked +about contestable markets and as long as + + align:start position:0% +about contestable markets and as long as + + + align:start position:0% +about contestable markets and as long as +a profit we made some would enter here + + align:start position:0% +a profit we made some would enter here + + + align:start position:0% +a profit we made some would enter here +as long as those profits we made someone + + align:start position:0% +as long as those profits we made someone + + + align:start position:0% +as long as those profits we made someone +or lower their price and that'll keep + + align:start position:0% +or lower their price and that'll keep + + + align:start position:0% +or lower their price and that'll keep +happening until price equals marginal + + align:start position:0% +happening until price equals marginal + + + align:start position:0% +happening until price equals marginal +cost + + align:start position:0% +cost + + + align:start position:0% +cost +so I'm Bertrand competition you actually + + align:start position:0% +so I'm Bertrand competition you actually + + + align:start position:0% +so I'm Bertrand competition you actually +can get close to where at to the + + align:start position:0% +can get close to where at to the + + + align:start position:0% +can get close to where at to the +competitive outcome with a small number + + align:start position:0% +competitive outcome with a small number + + + align:start position:0% +competitive outcome with a small number +of firms now two points to make about + + align:start position:0% +of firms now two points to make about + + + align:start position:0% +of firms now two points to make about +this your first point is well holy + + align:start position:0% +this your first point is well holy + + + align:start position:0% +this your first point is well holy +how do i side which one of these to use + + align:start position:0% +how do i side which one of these to use + + + align:start position:0% +how do i side which one of these to use +you've just taught me you've just spent + + align:start position:0% +you've just taught me you've just spent + + + align:start position:0% +you've just taught me you've just spent +you know lecture and half of this fancy + + align:start position:0% +you know lecture and half of this fancy + + + align:start position:0% +you know lecture and half of this fancy +model spent our 37 seconds on this model + + align:start position:0% +model spent our 37 seconds on this model + + + align:start position:0% +model spent our 37 seconds on this model +how do I know which one to use you + + align:start position:0% +how do I know which one to use you + + + align:start position:0% +how do I know which one to use you +didn't write down any math so I'm gonna + + align:start position:0% +didn't write down any math so I'm gonna + + + align:start position:0% +didn't write down any math so I'm gonna +do I'm freaking out okay how do I know + + align:start position:0% +do I'm freaking out okay how do I know + + + align:start position:0% +do I'm freaking out okay how do I know +which one to use well the bottom line is + + align:start position:0% +which one to use well the bottom line is + + + align:start position:0% +which one to use well the bottom line is +we're not going to ask you do much math + + align:start position:0% +we're not going to ask you do much math + + + align:start position:0% +we're not going to ask you do much math +about portraying competition other than + + align:start position:0% +about portraying competition other than + + + align:start position:0% +about portraying competition other than +sort of the intuition the competing over + + align:start position:0% +sort of the intuition the competing over + + + align:start position:0% +sort of the intuition the competing over +price the more relevant question is how + + align:start position:0% +price the more relevant question is how + + + align:start position:0% +price the more relevant question is how +do you think about the situation's + + align:start position:0% +do you think about the situation's + + + align:start position:0% +do you think about the situation's +workwear cournot competition is more + + align:start position:0% +workwear cournot competition is more + + + align:start position:0% +workwear cournot competition is more +likely and Bertrand competition more + + align:start position:0% +likely and Bertrand competition more + + + align:start position:0% +likely and Bertrand competition more +likely so what do you think and what + + align:start position:0% +likely so what do you think and what + + + align:start position:0% +likely so what do you think and what +types of markets unique or no + + align:start position:0% +types of markets unique or no + + + align:start position:0% +types of markets unique or no +competition be more likely and what + + align:start position:0% +competition be more likely and what + + + align:start position:0% +competition be more likely and what +kinds of markets do you think Bertrand + + align:start position:0% +kinds of markets do you think Bertrand + + + align:start position:0% +kinds of markets do you think Bertrand +competition will be more likely yeah + + align:start position:0% + + + + align:start position:0% + +well elasticity is the same so basically + + align:start position:0% +well elasticity is the same so basically + + + align:start position:0% +well elasticity is the same so basically +elasticity is gonna have a similar + + align:start position:0% +elasticity is gonna have a similar + + + align:start position:0% +elasticity is gonna have a similar +effect in both it's gonna basically + + align:start position:0% +effect in both it's gonna basically + + + align:start position:0% +effect in both it's gonna basically +drive the price down in both okay + + align:start position:0% +drive the price down in both okay + + + align:start position:0% +drive the price down in both okay +because he less does he's higher droves + + align:start position:0% +because he less does he's higher droves + + + align:start position:0% +because he less does he's higher droves +to mark up for a trend it's gonna its + + align:start position:0% +to mark up for a trend it's gonna its + + + align:start position:0% +to mark up for a trend it's gonna its +drive you less to drive it down in both + + align:start position:0% +drive you less to drive it down in both + + + align:start position:0% +drive you less to drive it down in both +so it's not a silly about eliciting it's + + align:start position:0% +so it's not a silly about eliciting it's + + + align:start position:0% +so it's not a silly about eliciting it's +something about production processes + + align:start position:0% +something about production processes + + + align:start position:0% +something about production processes +what type of production processes are + + align:start position:0% +what type of production processes are + + + align:start position:0% +what type of production processes are +gonna lend themselves to price + + align:start position:0% +gonna lend themselves to price + + + align:start position:0% +gonna lend themselves to price +competition versus quantity competition + + align:start position:0% +competition versus quantity competition + + + align:start position:0% +competition versus quantity competition +think about this way if I offer a price + + align:start position:0% +think about this way if I offer a price + + + align:start position:0% +think about this way if I offer a price +what do I have to do that's roughly + + align:start position:0% +what do I have to do that's roughly + + + align:start position:0% +what do I have to do that's roughly +speaking right basically if there's long + + align:start position:0% +speaking right basically if there's long + + + align:start position:0% +speaking right basically if there's long +lags in production I can't do price + + align:start position:0% +lags in production I can't do price + + + align:start position:0% +lags in production I can't do price +competition so if I say I'm gonna + + align:start position:0% +competition so if I say I'm gonna + + + align:start position:0% +competition so if I say I'm gonna +compete people say great I want all your + + align:start position:0% +compete people say great I want all your + + + align:start position:0% +compete people say great I want all your +product I'm like great you could have it + + align:start position:0% +product I'm like great you could have it + + + align:start position:0% +product I'm like great you could have it +in a year that doesn't work so things + + align:start position:0% +in a year that doesn't work so things + + + align:start position:0% +in a year that doesn't work so things +like auto companies are gonna have a + + align:start position:0% +like auto companies are gonna have a + + + align:start position:0% +like auto companies are gonna have a +hard time with pure price competition + + align:start position:0% +hard time with pure price competition + + + align:start position:0% +hard time with pure price competition +because if Toyota says okay I'm a dollar + + align:start position:0% +because if Toyota says okay I'm a dollar + + + align:start position:0% +because if Toyota says okay I'm a dollar +less someone says okay great + + align:start position:0% +less someone says okay great + + + align:start position:0% +less someone says okay great +we want a million Toyota's tomorrow they + + align:start position:0% +we want a million Toyota's tomorrow they + + + align:start position:0% +we want a million Toyota's tomorrow they +can't do it so things which are capital + + align:start position:0% +can't do it so things which are capital + + + align:start position:0% +can't do it so things which are capital +intensive lagged production processes + + align:start position:0% +intensive lagged production processes + + + align:start position:0% +intensive lagged production processes +it's gonna be hard to have pure reality + + align:start position:0% +it's gonna be hard to have pure reality + + + align:start position:0% +it's gonna be hard to have pure reality +life of course could be some mix of + + align:start position:0% +life of course could be some mix of + + + align:start position:0% +life of course could be some mix of +these but it'll tend more towards + + align:start position:0% +these but it'll tend more towards + + + align:start position:0% +these but it'll tend more towards +quantity competition because you're + + align:start position:0% +quantity competition because you're + + + align:start position:0% +quantity competition because you're +really going to peter --what unicel + + align:start position:0% +really going to peter --what unicel + + + align:start position:0% +really going to peter --what unicel +because that's sort of you can't just + + align:start position:0% +because that's sort of you can't just + + + align:start position:0% +because that's sort of you can't just +infinitely supply it whereas other + + align:start position:0% +infinitely supply it whereas other + + + align:start position:0% +infinitely supply it whereas other +things like cereal sales where you could + + align:start position:0% +things like cereal sales where you could + + + align:start position:0% +things like cereal sales where you could +sort of immediately crank up a million + + align:start position:0% +sort of immediately crank up a million + + + align:start position:0% +sort of immediately crank up a million +more box of cereal in like a day out of + + align:start position:0% +more box of cereal in like a day out of + + + align:start position:0% +more box of cereal in like a day out of +your production process that will be + + align:start position:0% +your production process that will be + + + align:start position:0% +your production process that will be +more likely to be price calm + + align:start position:0% +more likely to be price calm + + + align:start position:0% +more likely to be price calm +things with small production lags then + + align:start position:0% +things with small production lags then + + + align:start position:0% +things with small production lags then +you'd be more like to that price + + align:start position:0% +you'd be more like to that price + + + align:start position:0% +you'd be more like to that price +competition because if you lower the + + align:start position:0% +competition because if you lower the + + + align:start position:0% +competition because if you lower the +price all the sudden you dominate the + + align:start position:0% +price all the sudden you dominate the + + + align:start position:0% +price all the sudden you dominate the +market you can meet that demand okay so + + align:start position:0% +market you can meet that demand okay so + + + align:start position:0% +market you can meet that demand okay so +essentially we could think about price + + align:start position:0% +essentially we could think about price + + + align:start position:0% +essentially we could think about price +competition as being more likely they + + align:start position:0% +competition as being more likely they + + + align:start position:0% +competition as being more likely they +small the production lag or maybe the + + align:start position:0% +small the production lag or maybe the + + + align:start position:0% +small the production lag or maybe the +less capital and it's not really by + + align:start position:0% +less capital and it's not really by + + + align:start position:0% +less capital and it's not really by +capital density because you can have a + + align:start position:0% +capital density because you can have a + + + align:start position:0% +capital density because you can have a +capital hence addition you can create + + align:start position:0% +capital hence addition you can create + + + align:start position:0% +capital hence addition you can create +things quickly it's more about + + align:start position:0% +things quickly it's more about + + + align:start position:0% +things quickly it's more about +production lags now we're never gonna + + align:start position:0% +production lags now we're never gonna + + + align:start position:0% +production lags now we're never gonna +ask you to tell us which is right and of + + align:start position:0% +ask you to tell us which is right and of + + + align:start position:0% +ask you to tell us which is right and of +course in reality life somewhere in + + align:start position:0% +course in reality life somewhere in + + + align:start position:0% +course in reality life somewhere in +between but this just gives you a sense + + align:start position:0% +between but this just gives you a sense + + + align:start position:0% +between but this just gives you a sense +of kind of when more one type of + + align:start position:0% +of kind of when more one type of + + + align:start position:0% +of kind of when more one type of +competition is more likely than the + + align:start position:0% +competition is more likely than the + + + align:start position:0% +competition is more likely than the +other yeah great segue you've jumped + + align:start position:0% +other yeah great segue you've jumped + + + align:start position:0% +other yeah great segue you've jumped +ahead to the last point I want to make + + align:start position:0% +ahead to the last point I want to make + + + align:start position:0% +ahead to the last point I want to make +which is imagine you're in a Bertrand + + align:start position:0% +which is imagine you're in a Bertrand + + + align:start position:0% +which is imagine you're in a Bertrand +competition world like with cereal + + align:start position:0% +competition world like with cereal + + + align:start position:0% +competition world like with cereal +that's a pretty awful world if you're a + + align:start position:0% +that's a pretty awful world if you're a + + + align:start position:0% +that's a pretty awful world if you're a +producer okay basically that's where + + align:start position:0% +producer okay basically that's where + + + align:start position:0% +producer okay basically that's where +your markups tiny because any time try + + align:start position:0% +your markups tiny because any time try + + + align:start position:0% +your markups tiny because any time try +to raise the price you get undercut what + + align:start position:0% +to raise the price you get undercut what + + + align:start position:0% +to raise the price you get undercut what +can you do well we've already gotten the + + align:start position:0% +can you do well we've already gotten the + + + align:start position:0% +can you do well we've already gotten the +answer what you can do you can engage in + + align:start position:0% +answer what you can do you can engage in + + + align:start position:0% +answer what you can do you can engage in +product differentiation you can engage + + align:start position:0% +product differentiation you can engage + + + align:start position:0% +product differentiation you can engage +in product differentiation okay so + + align:start position:0% +in product differentiation okay so + + + align:start position:0% +in product differentiation okay so +basically the reason why you're in + + align:start position:0% +basically the reason why you're in + + + align:start position:0% +basically the reason why you're in +Bertrand competition is because you're + + align:start position:0% +Bertrand competition is because you're + + + align:start position:0% +Bertrand competition is because you're +selling the same thing once I'm selling + + align:start position:0% +selling the same thing once I'm selling + + + align:start position:0% +selling the same thing once I'm selling +something different I take on the + + align:start position:0% +something different I take on the + + + align:start position:0% +something different I take on the +features of monopolist again + + align:start position:0% +features of monopolist again + + + align:start position:0% +features of monopolist again +so if I could get sumers to not think of + + align:start position:0% +so if I could get sumers to not think of + + + align:start position:0% +so if I could get sumers to not think of +my good as identical to my competitors + + align:start position:0% +my good as identical to my competitors + + + align:start position:0% +my good as identical to my competitors +then I can price above marginal cost and + + align:start position:0% +then I can price above marginal cost and + + + align:start position:0% +then I can price above marginal cost and +people still buy it the reason Bertrand + + align:start position:0% +people still buy it the reason Bertrand + + + align:start position:0% +people still buy it the reason Bertrand +competition drives price to marginal + + align:start position:0% +competition drives price to marginal + + + align:start position:0% +competition drives price to marginal +cost because people who used the goods + + align:start position:0% +cost because people who used the goods + + + align:start position:0% +cost because people who used the goods +is identical but if they don't view the + + align:start position:0% +is identical but if they don't view the + + + align:start position:0% +is identical but if they don't view the +goods identical then I can keep price + + align:start position:0% +goods identical then I can keep price + + + align:start position:0% +goods identical then I can keep price +above marginal cost okay + + align:start position:0% +above marginal cost okay + + + align:start position:0% +above marginal cost okay +and the example of breakfast cereals is + + align:start position:0% +and the example of breakfast cereals is + + + align:start position:0% +and the example of breakfast cereals is +the perfect way to illustrate this so + + align:start position:0% +the perfect way to illustrate this so + + + align:start position:0% +the perfect way to illustrate this so +back around World War two they were + + align:start position:0% +back around World War two they were + + + align:start position:0% +back around World War two they were +essentially basically like three types + + align:start position:0% +essentially basically like three types + + + align:start position:0% +essentially basically like three types +of cereal okay + + align:start position:0% +of cereal okay + + + align:start position:0% +of cereal okay +there was Cheerios there was corn flakes + + align:start position:0% +there was Cheerios there was corn flakes + + + align:start position:0% +there was Cheerios there was corn flakes +and Quaker Oats + + align:start position:0% +and Quaker Oats + + + align:start position:0% +and Quaker Oats +okay that's basically what cereal was + + align:start position:0% +okay that's basically what cereal was + + + align:start position:0% +okay that's basically what cereal was +not very exciting now by the night but + + align:start position:0% +not very exciting now by the night but + + + align:start position:0% +not very exciting now by the night but +by 1970 there were more than a hundred + + align:start position:0% +by 1970 there were more than a hundred + + + align:start position:0% +by 1970 there were more than a hundred +and fifty breakfast cereals to choose + + align:start position:0% +and fifty breakfast cereals to choose + + + align:start position:0% +and fifty breakfast cereals to choose +from + + align:start position:0% +from + + + align:start position:0% +from +including some which are variations of + + align:start position:0% +including some which are variations of + + + align:start position:0% +including some which are variations of +Cheerios in variation of cornflakes in + + align:start position:0% +Cheerios in variation of cornflakes in + + + align:start position:0% +Cheerios in variation of cornflakes in +fact you could all say in some sense all + + align:start position:0% +fact you could all say in some sense all + + + align:start position:0% +fact you could all say in some sense all +cereals variation of Shiro's and + + align:start position:0% +cereals variation of Shiro's and + + + align:start position:0% +cereals variation of Shiro's and +cornflakes and oats and then um and + + align:start position:0% +cornflakes and oats and then um and + + + align:start position:0% +cornflakes and oats and then um and +moreover now if you go to store today + + align:start position:0% +moreover now if you go to store today + + + align:start position:0% +moreover now if you go to store today +you can actually buy generic versions of + + align:start position:0% +you can actually buy generic versions of + + + align:start position:0% +you can actually buy generic versions of +brand-name cereals so you can buy OD O's + + align:start position:0% +brand-name cereals so you can buy OD O's + + + align:start position:0% +brand-name cereals so you can buy OD O's +or marshmallow matey's which are Lucky + + align:start position:0% +or marshmallow matey's which are Lucky + + + align:start position:0% +or marshmallow matey's which are Lucky +Charms or what are they what's the other + + align:start position:0% +Charms or what are they what's the other + + + align:start position:0% +Charms or what are they what's the other +one I love buying these big bags you + + align:start position:0% +one I love buying these big bags you + + + align:start position:0% +one I love buying these big bags you +guys are buy these generic lectrons + + align:start position:0% +guys are buy these generic lectrons + + + align:start position:0% +guys are buy these generic lectrons +marshmallow matey's generic Captain + + align:start position:0% +marshmallow matey's generic Captain + + + align:start position:0% +marshmallow matey's generic Captain +Crunch is like you know ahoy matey or + + align:start position:0% +Crunch is like you know ahoy matey or + + + align:start position:0% +Crunch is like you know ahoy matey or +something I don't know they got these + + align:start position:0% +something I don't know they got these + + + align:start position:0% +something I don't know they got these +generic things which you can buy which + + align:start position:0% +generic things which you can buy which + + + align:start position:0% +generic things which you can buy which +are really just the same so essentially + + align:start position:0% +are really just the same so essentially + + + align:start position:0% +are really just the same so essentially +what you do what companies want to + + align:start position:0% +what you do what companies want to + + + align:start position:0% +what you do what companies want to +always do whichever trend competition is + + align:start position:0% +always do whichever trend competition is + + + align:start position:0% +always do whichever trend competition is +always try to proc differentiate always + + align:start position:0% +always try to proc differentiate always + + + align:start position:0% +always try to proc differentiate always +try to figure out a way they can create + + align:start position:0% +try to figure out a way they can create + + + align:start position:0% +try to figure out a way they can create +a market where they can price above + + align:start position:0% +a market where they can price above + + + align:start position:0% +a market where they can price above +marginal cost okay so for example let's + + align:start position:0% +marginal cost okay so for example let's + + + align:start position:0% +marginal cost okay so for example let's +take General Mills a company that makes + + align:start position:0% +take General Mills a company that makes + + + align:start position:0% +take General Mills a company that makes +Cheerios okay they're making Cheerios + + align:start position:0% +Cheerios okay they're making Cheerios + + + align:start position:0% +Cheerios okay they're making Cheerios +and then they and then also an OD O's + + align:start position:0% +and then they and then also an OD O's + + + align:start position:0% +and then they and then also an OD O's +and stuff started coming along and they + + align:start position:0% +and stuff started coming along and they + + + align:start position:0% +and stuff started coming along and they +weren't making money what do they do + + align:start position:0% +weren't making money what do they do + + + align:start position:0% +weren't making money what do they do +they created different kinds of Cheerios + + align:start position:0% +they created different kinds of Cheerios + + + align:start position:0% +they created different kinds of Cheerios +like Apple Cinnamon Cheerios General + + align:start position:0% +like Apple Cinnamon Cheerios General + + + align:start position:0% +like Apple Cinnamon Cheerios General +Mills do not create Apple Cinnamon + + align:start position:0% +Mills do not create Apple Cinnamon + + + align:start position:0% +Mills do not create Apple Cinnamon +Cheerios out of the goodness of their + + align:start position:0% +Cheerios out of the goodness of their + + + align:start position:0% +Cheerios out of the goodness of their +heart General Mills created Apple + + align:start position:0% +heart General Mills created Apple + + + align:start position:0% +heart General Mills created Apple +Cinnamon Cheerios because they were + + align:start position:0% +Cinnamon Cheerios because they were + + + align:start position:0% +Cinnamon Cheerios because they were +getting killed in the cheerio market and + + align:start position:0% +getting killed in the cheerio market and + + + align:start position:0% +getting killed in the cheerio market and +so they tried to differentiate by having + + align:start position:0% +so they tried to differentiate by having + + + align:start position:0% +so they tried to differentiate by having +a new product that on which they could + + align:start position:0% +a new product that on which they could + + + align:start position:0% +a new product that on which they could +charge a higher price which was Apple + + align:start position:0% +charge a higher price which was Apple + + + align:start position:0% +charge a higher price which was Apple +Cinnamon Cheerios now how do we feel + + align:start position:0% +Cinnamon Cheerios now how do we feel + + + align:start position:0% +Cinnamon Cheerios now how do we feel +about this well it's not clear on the + + align:start position:0% +about this well it's not clear on the + + + align:start position:0% +about this well it's not clear on the +one hand by introducing Apple Cinnamon + + align:start position:0% +one hand by introducing Apple Cinnamon + + + align:start position:0% +one hand by introducing Apple Cinnamon +Cheerios General Mills was able to push + + align:start position:0% +Cheerios General Mills was able to push + + + align:start position:0% +Cheerios General Mills was able to push +its price greater than marginal cost and + + align:start position:0% +its price greater than marginal cost and + + + align:start position:0% +its price greater than marginal cost and +when as price pushed above marginal cost + + align:start position:0% +when as price pushed above marginal cost + + + align:start position:0% +when as price pushed above marginal cost +quantity sold in the market Falls it + + align:start position:0% +quantity sold in the market Falls it + + + align:start position:0% +quantity sold in the market Falls it +created deadweight loss quantity fell + + align:start position:0% +created deadweight loss quantity fell + + + align:start position:0% +created deadweight loss quantity fell +and that's bad + + align:start position:0% +and that's bad + + + align:start position:0% +and that's bad +okay on the other hand Apple Cinnamon + + align:start position:0% +okay on the other hand Apple Cinnamon + + + align:start position:0% +okay on the other hand Apple Cinnamon +chairs are quite good ok so this + + align:start position:0% +chairs are quite good ok so this + + + align:start position:0% +chairs are quite good ok so this +actually ends up being much like our + + align:start position:0% +actually ends up being much like our + + + align:start position:0% +actually ends up being much like our +patent discussion which is essentially + + align:start position:0% +patent discussion which is essentially + + + align:start position:0% +patent discussion which is essentially +by differentiating they've had two + + align:start position:0% +by differentiating they've had two + + + align:start position:0% +by differentiating they've had two +effects they've lowered consumer surplus + + align:start position:0% +effects they've lowered consumer surplus + + + align:start position:0% +effects they've lowered consumer surplus +in welfare by pricing about marginal + + align:start position:0% +in welfare by pricing about marginal + + + align:start position:0% +in welfare by pricing about marginal +cost but raised it by shifting out the + + align:start position:0% +cost but raised it by shifting out the + + + align:start position:0% +cost but raised it by shifting out the +demand curve by creating a new good that + + align:start position:0% +demand curve by creating a new good that + + + align:start position:0% +demand curve by creating a new good that +people want + + align:start position:0% +people want + + + align:start position:0% +people want +yeah that's okay another way stating my + + align:start position:0% +yeah that's okay another way stating my + + + align:start position:0% +yeah that's okay another way stating my +point even if the demand curve razzle + + align:start position:0% +point even if the demand curve razzle + + + align:start position:0% +point even if the demand curve razzle +let's say there's a new demand curve for + + align:start position:0% +let's say there's a new demand curve for + + + align:start position:0% +let's say there's a new demand curve for +Apple cinema shows its way out okay + + align:start position:0% +Apple cinema shows its way out okay + + + align:start position:0% +Apple cinema shows its way out okay +that's great okay but still the fact + + align:start position:0% +that's great okay but still the fact + + + align:start position:0% +that's great okay but still the fact +that their pricing above marginal cost + + align:start position:0% +that their pricing above marginal cost + + + align:start position:0% +that their pricing above marginal cost +means they'll sell fewer than they would + + align:start position:0% +means they'll sell fewer than they would + + + align:start position:0% +means they'll sell fewer than they would +in a competitive market if they had + + align:start position:0% +in a competitive market if they had + + + align:start position:0% +in a competitive market if they had +invented out certain shows and sold on + + align:start position:0% +invented out certain shows and sold on + + + align:start position:0% +invented out certain shows and sold on +marginal cost who still be way better + + align:start position:0% +marginal cost who still be way better + + + align:start position:0% +marginal cost who still be way better +off so the trade-off is essentially how + + align:start position:0% +off so the trade-off is essentially how + + + align:start position:0% +off so the trade-off is essentially how +far out do we shift demand by cratons + + align:start position:0% +far out do we shift demand by cratons + + + align:start position:0% +far out do we shift demand by cratons +new product versus how much you restrict + + align:start position:0% +new product versus how much you restrict + + + align:start position:0% +new product versus how much you restrict +sales by pricing it above marginal cost + + align:start position:0% +sales by pricing it above marginal cost + + + align:start position:0% +sales by pricing it above marginal cost +so essentially um now and now what we + + align:start position:0% +so essentially um now and now what we + + + align:start position:0% +so essentially um now and now what we +have is a market with about five firms + + align:start position:0% +have is a market with about five firms + + + align:start position:0% +have is a market with about five firms +that dominated at about five thousand + + align:start position:0% +that dominated at about five thousand + + + align:start position:0% +that dominated at about five thousand +brands of cereal okay so it's constant + + align:start position:0% +brands of cereal okay so it's constant + + + align:start position:0% +brands of cereal okay so it's constant +product differentiation and essentially + + align:start position:0% +product differentiation and essentially + + + align:start position:0% +product differentiation and essentially +this is the trade-off with product + + align:start position:0% +this is the trade-off with product + + + align:start position:0% +this is the trade-off with product +differentiation which is we get reduced + + align:start position:0% +differentiation which is we get reduced + + + align:start position:0% +differentiation which is we get reduced +sale we get a deadweight loss because + + align:start position:0% +sale we get a deadweight loss because + + + align:start position:0% +sale we get a deadweight loss because +they're not pricing at marginal cost but + + align:start position:0% +they're not pricing at marginal cost but + + + align:start position:0% +they're not pricing at marginal cost but +we get new products that people might + + align:start position:0% +we get new products that people might + + + align:start position:0% +we get new products that people might +like yeah imitation + + align:start position:0% + + + + align:start position:0% + +well actually that's really interesting + + align:start position:0% +well actually that's really interesting + + + align:start position:0% +well actually that's really interesting +it depends on whether that brand loyalty + + align:start position:0% +it depends on whether that brand loyalty + + + align:start position:0% +it depends on whether that brand loyalty +is based on innovation or blind or blind + + align:start position:0% +is based on innovation or blind or blind + + + align:start position:0% +is based on innovation or blind or blind +faith so it says that this is this is + + align:start position:0% +faith so it says that this is this is + + + align:start position:0% +faith so it says that this is this is +once again this gets into the deep + + align:start position:0% +once again this gets into the deep + + + align:start position:0% +once again this gets into the deep +interesting issues of industrial + + align:start position:0% +interesting issues of industrial + + + align:start position:0% +interesting issues of industrial +organization you talk about game theory + + align:start position:0% +organization you talk about game theory + + + align:start position:0% +organization you talk about game theory +which is if I can create brand loyalty + + align:start position:0% +which is if I can create brand loyalty + + + align:start position:0% +which is if I can create brand loyalty +by in a way that makes you slightly + + align:start position:0% +by in a way that makes you slightly + + + align:start position:0% +by in a way that makes you slightly +better off but keeps you in my brain + + align:start position:0% +better off but keeps you in my brain + + + align:start position:0% +better off but keeps you in my brain +forever then that might be worse if I + + align:start position:0% +forever then that might be worse if I + + + align:start position:0% +forever then that might be worse if I +create in a way that makes you much + + align:start position:0% +create in a way that makes you much + + + align:start position:0% +create in a way that makes you much +better off that might be better so + + align:start position:0% +better off that might be better so + + + align:start position:0% +better off that might be better so +essentially that's why for example you + + align:start position:0% +essentially that's why for example you + + + align:start position:0% +essentially that's why for example you +may have noticed you may be getting one + + align:start position:0% +may have noticed you may be getting one + + + align:start position:0% +may have noticed you may be getting one +or two credit card mailers that's it you + + align:start position:0% +or two credit card mailers that's it you + + + align:start position:0% +or two credit card mailers that's it you +guys are you guys getting inundated with + + align:start position:0% +guys are you guys getting inundated with + + + align:start position:0% +guys are you guys getting inundated with +credit card offers okay it's not because + + align:start position:0% +credit card offers okay it's not because + + + align:start position:0% +credit card offers okay it's not because +they love you guys it's because if they + + align:start position:0% +they love you guys it's because if they + + + align:start position:0% +they love you guys it's because if they +hook you now then you might stick with + + align:start position:0% +hook you now then you might stick with + + + align:start position:0% +hook you now then you might stick with +that credit card later so try and + + align:start position:0% +that credit card later so try and + + + align:start position:0% +that credit card later so try and +exploit trying to get you they're trying + + align:start position:0% +exploit trying to get you they're trying + + + align:start position:0% +exploit trying to get you they're trying +to give you a good deal now to get you + + align:start position:0% +to give you a good deal now to get you + + + align:start position:0% +to give you a good deal now to get you +hooked later second charge them closer + + align:start position:0% +hooked later second charge them closer + + + align:start position:0% +hooked later second charge them closer +to monopoly price later on so + + align:start position:0% +to monopoly price later on so + + + align:start position:0% +to monopoly price later on so +essentially there's a trade-off which is + + align:start position:0% +essentially there's a trade-off which is + + + align:start position:0% +essentially there's a trade-off which is +if that loyalty is based on real + + align:start position:0% +if that loyalty is based on real + + + align:start position:0% +if that loyalty is based on real +differences in quality that might be + + align:start position:0% +differences in quality that might be + + + align:start position:0% +differences in quality that might be +good if it's not it might not be but the + + align:start position:0% +good if it's not it might not be but the + + + align:start position:0% +good if it's not it might not be but the +welfare gets very murky it's a good + + align:start position:0% +welfare gets very murky it's a good + + + align:start position:0% +welfare gets very murky it's a good +question other questions okay + + align:start position:0% +question other questions okay + + + align:start position:0% +question other questions okay +these are exciting real world topics + + align:start position:0% +these are exciting real world topics + + + align:start position:0% +these are exciting real world topics +it's more reasons to go on and study + + align:start position:0% +it's more reasons to go on and study + + + align:start position:0% +it's more reasons to go on and study +more in economics but let's stop now + + align:start position:0% +more in economics but let's stop now + + + align:start position:0% +more in economics but let's stop now +we'll come back and we'll start talking + + align:start position:0% +we'll come back and we'll start talking + + + align:start position:0% +we'll come back and we'll start talking +about factor markets on Monday \ No newline at end of file diff --git a/oiKLWa_0dhs.txt b/oiKLWa_0dhs.txt new file mode 100644 index 0000000000000000000000000000000000000000..19b7937f4818b35954c0d8d349d92cb5b80a9e2b --- /dev/null +++ b/oiKLWa_0dhs.txt @@ -0,0 +1,8791 @@ +align:start position:0% + +so we've been discussing similarities + + align:start position:0% +so we've been discussing similarities + + + align:start position:0% +so we've been discussing similarities +regularity lemma for the past couple of + + align:start position:0% +regularity lemma for the past couple of + + + align:start position:0% +regularity lemma for the past couple of +lectures and one of the theorems that we + + align:start position:0% +lectures and one of the theorems that we + + + align:start position:0% +lectures and one of the theorems that we +proved was Ross theorem which tells us + + align:start position:0% +proved was Ross theorem which tells us + + + align:start position:0% +proved was Ross theorem which tells us +how large can a subset of 1 to M be if + + align:start position:0% +how large can a subset of 1 to M be if + + + align:start position:0% +how large can a subset of 1 to M be if +it has no three term arithmetic + + align:start position:0% +it has no three term arithmetic + + + align:start position:0% +it has no three term arithmetic +progressions and I mentioned at the end + + align:start position:0% +progressions and I mentioned at the end + + + align:start position:0% +progressions and I mentioned at the end +of last time that we can construct + + align:start position:0% +of last time that we can construct + + + align:start position:0% +of last time that we can construct +fairly large subsets of 1 to N without + + align:start position:0% +fairly large subsets of 1 to N without + + + align:start position:0% +fairly large subsets of 1 to N without +three term automatic progressions I want + + align:start position:0% +three term automatic progressions I want + + + align:start position:0% +three term automatic progressions I want +to begin today's lecture worth showing + + align:start position:0% +to begin today's lecture worth showing + + + align:start position:0% +to begin today's lecture worth showing +you that example showing that + + align:start position:0% +you that example showing that + + + align:start position:0% +you that example showing that +construction but first let's try to do + + align:start position:0% +construction but first let's try to do + + + align:start position:0% +construction but first let's try to do +something that is somewhat more naive + + align:start position:0% +something that is somewhat more naive + + + align:start position:0% +something that is somewhat more naive +some more more straightforward to try to + + align:start position:0% +some more more straightforward to try to + + + align:start position:0% +some more more straightforward to try to +just construct greedily + + align:start position:0% +just construct greedily + + + align:start position:0% +just construct greedily +383 steps and recall from last time we + + align:start position:0% +383 steps and recall from last time we + + + align:start position:0% +383 steps and recall from last time we +showed Ross theorem that such a set must + + align:start position:0% +showed Ross theorem that such a set must + + + align:start position:0% +showed Ross theorem that such a set must +have size not all of em ok so what's one + + align:start position:0% +have size not all of em ok so what's one + + + align:start position:0% +have size not all of em ok so what's one +thing you might do well you can try to + + align:start position:0% +thing you might do well you can try to + + + align:start position:0% +thing you might do well you can try to +greedily construct such a set it will + + align:start position:0% +greedily construct such a set it will + + + align:start position:0% +greedily construct such a set it will +just make our life a little bit easier + + align:start position:0% +just make our life a little bit easier + + + align:start position:0% +just make our life a little bit easier +if we start with 0 instead of 1 so now + + align:start position:0% +if we start with 0 instead of 1 so now + + + align:start position:0% +if we start with 0 instead of 1 so now +you put one element in and you keep + + align:start position:0% +you put one element in and you keep + + + align:start position:0% +you put one element in and you keep +putting in the next integer as long as + + align:start position:0% +putting in the next integer as long as + + + align:start position:0% +putting in the next integer as long as +it doesn't create a three-term + + align:start position:0% +it doesn't create a three-term + + + align:start position:0% +it doesn't create a three-term +arithmetic progression ok so you keep + + align:start position:0% +arithmetic progression ok so you keep + + + align:start position:0% +arithmetic progression ok so you keep +doing this well you can put two in so + + align:start position:0% +doing this well you can put two in so + + + align:start position:0% +doing this well you can put two in so +let's skip to so we go to the next one 3 + + align:start position:0% +let's skip to so we go to the next one 3 + + + align:start position:0% +let's skip to so we go to the next one 3 +okay so four is okay so skip 5 we have + + align:start position:0% +okay so four is okay so skip 5 we have + + + align:start position:0% +okay so four is okay so skip 5 we have +to skip 6 as well because 0 3 6 that's a + + align:start position:0% +to skip 6 as well because 0 3 6 that's a + + + align:start position:0% +to skip 6 as well because 0 3 6 that's a + + align:start position:0% + + + align:start position:0% +keep going so what's the next number we + + align:start position:0% +keep going so what's the next number we + + + align:start position:0% +keep going so what's the next number we +can put in + + align:start position:0% + + + + align:start position:0% + +go to nine okay then the next one is ten + + align:start position:0% +go to nine okay then the next one is ten + + + align:start position:0% +go to nine okay then the next one is ten +okay what's the next one we can put him + + align:start position:0% +okay what's the next one we can put him + + + align:start position:0% +okay what's the next one we can put him +okay so you can play this game right so + + align:start position:0% +okay so you can play this game right so + + + align:start position:0% +okay so you can play this game right so +find out what is the next number that + + align:start position:0% +find out what is the next number that + + + align:start position:0% +find out what is the next number that +you can put in greedily if you can put + + align:start position:0% +you can put in greedily if you can put + + + align:start position:0% +you can put in greedily if you can put +it in put it in in a way that generates + + align:start position:0% +it in put it in in a way that generates + + + align:start position:0% +it in put it in in a way that generates +a subset of integers without three term + + align:start position:0% +a subset of integers without three term + + + align:start position:0% +a subset of integers without three term +arithmetic progressions so this section + + align:start position:0% +arithmetic progressions so this section + + + align:start position:0% +arithmetic progressions so this section +has a name so this is called a Stanley + + align:start position:0% +has a name so this is called a Stanley + + + align:start position:0% +has a name so this is called a Stanley +sequence and there's an easier way to + + align:start position:0% +sequence and there's an easier way to + + + align:start position:0% +sequence and there's an easier way to +see what the sequence is namely if you + + align:start position:0% +see what the sequence is namely if you + + + align:start position:0% +see what the sequence is namely if you +write the sequence in page three you + + align:start position:0% + + + + align:start position:0% + +find that these numbers are 0 0 1 1 0 1 + + align:start position:0% +find that these numbers are 0 0 1 1 0 1 + + + align:start position:0% +find that these numbers are 0 0 1 1 0 1 +1 1 0 0 1 0 1 1 1 0 so these are just + + align:start position:0% +1 1 0 0 1 0 1 1 1 0 so these are just + + + align:start position:0% +1 1 0 0 1 0 1 1 1 0 so these are just +numbers whose phase 3 representation + + align:start position:0% + + + + align:start position:0% + +consists of zeros and ones + + align:start position:0% +consists of zeros and ones + + + align:start position:0% +consists of zeros and ones +ok so I'll leave it to you as an + + align:start position:0% +ok so I'll leave it to you as an + + + align:start position:0% +ok so I'll leave it to you as an +exercise to figure out why this is the + + align:start position:0% +exercise to figure out why this is the + + + align:start position:0% +exercise to figure out why this is the +case if you generate the sequence greedy + + align:start position:0% +case if you generate the sequence greedy + + + align:start position:0% +case if you generate the sequence greedy +list greedily this way this is exactly + + align:start position:0% +list greedily this way this is exactly + + + align:start position:0% +list greedily this way this is exactly +the sequence that you obtain but once + + align:start position:0% +the sequence that you obtain but once + + + align:start position:0% +the sequence that you obtain but once +you know that it's not too hard to find + + align:start position:0% +you know that it's not too hard to find + + + align:start position:0% +you know that it's not too hard to find +out how many numbers you generate so up + + align:start position:0% +out how many numbers you generate so up + + + align:start position:0% +out how many numbers you generate so up +to suppose n is equal to 3 to the K we + + align:start position:0% +to suppose n is equal to 3 to the K we + + + align:start position:0% +to suppose n is equal to 3 to the K we +get 2 to the K terms which gives you n + + align:start position:0% +get 2 to the K terms which gives you n + + + align:start position:0% +get 2 to the K terms which gives you n +raised to the power of log base 3 of 2 + + align:start position:0% + + + + align:start position:0% + +so you can figure out what that number + + align:start position:0% +so you can figure out what that number + + + align:start position:0% +so you can figure out what that number +is but some number is strictly less than + + align:start position:0% +is but some number is strictly less than + + + align:start position:0% +is but some number is strictly less than + + align:start position:0% + + + + align:start position:0% + +and actually for a very long time people + + align:start position:0% +and actually for a very long time people + + + align:start position:0% +and actually for a very long time people +thought this was the best construction + + align:start position:0% +thought this was the best construction + + + align:start position:0% +thought this was the best construction +so this construction was known even + + align:start position:0% +so this construction was known even + + + align:start position:0% +so this construction was known even +before Stanley if there was something + + align:start position:0% +before Stanley if there was something + + + align:start position:0% +before Stanley if there was something +that it's very natural to come up with + + align:start position:0% +that it's very natural to come up with + + + align:start position:0% +that it's very natural to come up with +and it was somewhat of a surprise when + + align:start position:0% +and it was somewhat of a surprise when + + + align:start position:0% +and it was somewhat of a surprise when +in the 40s it was discovered that you + + align:start position:0% +in the 40s it was discovered that you + + + align:start position:0% +in the 40s it was discovered that you +can create much larger subsets or the + + align:start position:0% +can create much larger subsets or the + + + align:start position:0% +can create much larger subsets or the +positive integers without arithmetic + + align:start position:0% +positive integers without arithmetic + + + align:start position:0% +positive integers without arithmetic +progressions so that's the first thing I + + align:start position:0% +progressions so that's the first thing I + + + align:start position:0% +progressions so that's the first thing I +want to show you today so these sets + + align:start position:0% +want to show you today so these sets + + + align:start position:0% +want to show you today so these sets +were first discovered by Salem and + + align:start position:0% +were first discovered by Salem and + + + align:start position:0% +were first discovered by Salem and +Spencer back in the 40s and a few years + + align:start position:0% +Spencer back in the 40s and a few years + + + align:start position:0% +Spencer back in the 40s and a few years +later a parent gave a somewhat improved + + align:start position:0% +later a parent gave a somewhat improved + + + align:start position:0% +later a parent gave a somewhat improved +and simplified version of the Salem + + align:start position:0% +and simplified version of the Salem + + + align:start position:0% +and simplified version of the Salem +Spencer construction so these were all + + align:start position:0% +Spencer construction so these were all + + + align:start position:0% +Spencer construction so these were all +back in the 40s so these days we usually + + align:start position:0% +back in the 40s so these days we usually + + + align:start position:0% +back in the 40s so these days we usually +refer at least in the additive + + align:start position:0% +refer at least in the additive + + + align:start position:0% +refer at least in the additive +combinatorics community to this + + align:start position:0% +combinatorics community to this + + + align:start position:0% +combinatorics community to this +construction as parens construction in + + align:start position:0% +construction as parens construction in + + + align:start position:0% +construction as parens construction in +this indeed what I will show you is due + + align:start position:0% +this indeed what I will show you is due + + + align:start position:0% +this indeed what I will show you is due +to parent but somehow the Salem Spencer + + align:start position:0% +to parent but somehow the Salem Spencer + + + align:start position:0% +to parent but somehow the Salem Spencer +name has been forgotten and I just want + + align:start position:0% +name has been forgotten and I just want + + + align:start position:0% +name has been forgotten and I just want +to point out that it was Salem and + + align:start position:0% +to point out that it was Salem and + + + align:start position:0% +to point out that it was Salem and +Spencer who first demonstrated that + + align:start position:0% +Spencer who first demonstrated that + + + align:start position:0% +Spencer who first demonstrated that +there exists a subset of 1 to n that is + + align:start position:0% +there exists a subset of 1 to n that is + + + align:start position:0% +there exists a subset of 1 to n that is +3 AP free and has size and to the one - + + align:start position:0% +3 AP free and has size and to the one - + + + align:start position:0% +3 AP free and has size and to the one - +little one that there's no power saving + + align:start position:0% +little one that there's no power saving + + + align:start position:0% +little one that there's no power saving +so there exists examples with no power + + align:start position:0% +so there exists examples with no power + + + align:start position:0% +so there exists examples with no power +saving and and this is important because + + align:start position:0% +saving and and this is important because + + + align:start position:0% +saving and and this is important because +as we saw last time the proof of roster + + align:start position:0% +as we saw last time the proof of roster + + + align:start position:0% +as we saw last time the proof of roster +I mean we basically spend two full + + align:start position:0% +I mean we basically spend two full + + + align:start position:0% +I mean we basically spend two full +lectures proving Ross theorem and it's + + align:start position:0% +lectures proving Ross theorem and it's + + + align:start position:0% +lectures proving Ross theorem and it's +someone involved right it wasn't this + + align:start position:0% +someone involved right it wasn't this + + + align:start position:0% +someone involved right it wasn't this +one line of inequality you can just use + + align:start position:0% +one line of inequality you can just use + + + align:start position:0% +one line of inequality you can just use +to deduce the result and that is part of + + align:start position:0% +to deduce the result and that is part of + + + align:start position:0% +to deduce the result and that is part of +the difficulty so having such an example + + align:start position:0% +the difficulty so having such an example + + + align:start position:0% +the difficulty so having such an example +is indication that graph theorem should + + align:start position:0% +is indication that graph theorem should + + + align:start position:0% +is indication that graph theorem should +not be so easy it's not a rigorous + + align:start position:0% +not be so easy it's not a rigorous + + + align:start position:0% +not be so easy it's not a rigorous +demonstration but it's some indication + + align:start position:0% +demonstration but it's some indication + + + align:start position:0% +demonstration but it's some indication +of the difficulty of Ross theorem + + align:start position:0% +of the difficulty of Ross theorem + + + align:start position:0% +of the difficulty of Ross theorem +okay so let's see this construction due + + align:start position:0% +okay so let's see this construction due + + + align:start position:0% +okay so let's see this construction due +to parent so let me write down the + + align:start position:0% +to parent so let me write down the + + + align:start position:0% +to parent so let me write down the +precise statement there exists a + + align:start position:0% +precise statement there exists a + + + align:start position:0% +precise statement there exists a +constant C such that there exists a + + align:start position:0% +constant C such that there exists a + + + align:start position:0% +constant C such that there exists a +subset of 1 through n that is 3 AP free + + align:start position:0% +subset of 1 through n that is 3 AP free + + + align:start position:0% +subset of 1 through n that is 3 AP free +and has size at least n times e to the + + align:start position:0% +and has size at least n times e to the + + + align:start position:0% +and has size at least n times e to the +minus c root log n perhaps somewhat + + align:start position:0% +minus c root log n perhaps somewhat + + + align:start position:0% +minus c root log n perhaps somewhat +amazingly enough this bound is still the + + align:start position:0% +amazingly enough this bound is still the + + + align:start position:0% +amazingly enough this bound is still the +current best known we do not know any + + align:start position:0% +current best known we do not know any + + + align:start position:0% +current best known we do not know any +constructions that is essentially better + + align:start position:0% +constructions that is essentially better + + + align:start position:0% +constructions that is essentially better +than barons construction from the 40's + + align:start position:0% +than barons construction from the 40's + + + align:start position:0% +than barons construction from the 40's +there were some small recent + + align:start position:0% +there were some small recent + + + align:start position:0% +there were some small recent +improvements that clarified what the C + + align:start position:0% +improvements that clarified what the C + + + align:start position:0% +improvements that clarified what the C +could be but in this form we do not know + + align:start position:0% +could be but in this form we do not know + + + align:start position:0% +could be but in this form we do not know +anything better than what was known back + + align:start position:0% +anything better than what was known back + + + align:start position:0% +anything better than what was known back +in the 40s and the construction I will + + align:start position:0% +in the 40s and the construction I will + + + align:start position:0% +in the 40s and the construction I will +show you hopefully it's you should + + align:start position:0% +show you hopefully it's you should + + + align:start position:0% +show you hopefully it's you should +believe that it's quite simple so I'll + + align:start position:0% +believe that it's quite simple so I'll + + + align:start position:0% +believe that it's quite simple so I'll +show you what the construction is it's + + align:start position:0% +show you what the construction is it's + + + align:start position:0% +show you what the construction is it's +clever but it's not complicated and it's + + align:start position:0% +clever but it's not complicated and it's + + + align:start position:0% +clever but it's not complicated and it's +a really interesting direction to figure + + align:start position:0% +a really interesting direction to figure + + + align:start position:0% +a really interesting direction to figure +out is this really the best construction + + align:start position:0% +out is this really the best construction + + + align:start position:0% +out is this really the best construction +out there can you do better + + align:start position:0% + + + + align:start position:0% + +so let's see we're going to set some + + align:start position:0% +so let's see we're going to set some + + + align:start position:0% +so let's see we're going to set some +parameters to be decided later mnd let + + align:start position:0% +parameters to be decided later mnd let + + + align:start position:0% +parameters to be decided later mnd let +me consider X to be this discrete box in + + align:start position:0% +me consider X to be this discrete box in + + + align:start position:0% +me consider X to be this discrete box in +P dimensions so this is the the box of + + align:start position:0% +P dimensions so this is the the box of + + + align:start position:0% +P dimensions so this is the the box of +lattice points in D dimensions 1 through + + align:start position:0% +lattice points in D dimensions 1 through + + + align:start position:0% +lattice points in D dimensions 1 through +m raised to D and let me consider a + + align:start position:0% +m raised to D and let me consider a + + + align:start position:0% +m raised to D and let me consider a +intersection of this box by a sphere of + + align:start position:0% +intersection of this box by a sphere of + + + align:start position:0% +intersection of this box by a sphere of +radius root L we look at points in this + + align:start position:0% +radius root L we look at points in this + + + align:start position:0% +radius root L we look at points in this +X such that the sum of their squares is + + align:start position:0% +X such that the sum of their squares is + + + align:start position:0% +X such that the sum of their squares is +equal to exactly L you take a bunch of + + align:start position:0% +equal to exactly L you take a bunch of + + + align:start position:0% +equal to exactly L you take a bunch of +these spheres they partition your set X + + align:start position:0% + + + + align:start position:0% + +smallest possible sum of squares largest + + align:start position:0% +smallest possible sum of squares largest + + + align:start position:0% +smallest possible sum of squares largest +possible sum of squares so in particular + + align:start position:0% +possible sum of squares so in particular + + + align:start position:0% +possible sum of squares so in particular +there exists some L such that X sub L is + + align:start position:0% +there exists some L such that X sub L is + + + align:start position:0% +there exists some L such that X sub L is +large + + align:start position:0% + + + + align:start position:0% + +just by pigeonhole principle you can + + align:start position:0% +just by pigeonhole principle you can + + + align:start position:0% +just by pigeonhole principle you can +probably do this step a little with a + + align:start position:0% +probably do this step a little with a + + + align:start position:0% +probably do this step a little with a +bit more finesse but it's not going to + + align:start position:0% +bit more finesse but it's not going to + + + align:start position:0% +bit more finesse but it's not going to +change any of the asymptotics okay the + + align:start position:0% +change any of the asymptotics okay the + + + align:start position:0% +change any of the asymptotics okay the +intuition here and we'll come back to + + align:start position:0% +intuition here and we'll come back to + + + align:start position:0% +intuition here and we'll come back to +this in a second is that X lies XL lies + + align:start position:0% +this in a second is that X lies XL lies + + + align:start position:0% +this in a second is that X lies XL lies +on a sphere so this is the set of + + align:start position:0% +on a sphere so this is the set of + + + align:start position:0% +on a sphere so this is the set of +lattice points that lies on a given + + align:start position:0% +lattice points that lies on a given + + + align:start position:0% +lattice points that lies on a given +sphere and because you are looking at a + + align:start position:0% +sphere and because you are looking at a + + + align:start position:0% +sphere and because you are looking at a +sphere it has no three term a piece so + + align:start position:0% +sphere it has no three term a piece so + + + align:start position:0% +sphere it has no three term a piece so +we're going to use that property but + + align:start position:0% +we're going to use that property but + + + align:start position:0% +we're going to use that property but +right now it's not yet a subset of the + + align:start position:0% +right now it's not yet a subset of the + + + align:start position:0% +right now it's not yet a subset of the +integers so what we're going to do is to + + align:start position:0% +integers so what we're going to do is to + + + align:start position:0% +integers so what we're going to do is to +take this section of a sphere and I'm + + align:start position:0% +take this section of a sphere and I'm + + + align:start position:0% +take this section of a sphere and I'm +projected through one dimension so that + + align:start position:0% +projected through one dimension so that + + + align:start position:0% +projected through one dimension so that +it is now going to be a sub set of + + align:start position:0% +it is now going to be a sub set of + + + align:start position:0% +it is now going to be a sub set of +integers + + align:start position:0% +integers + + + align:start position:0% +integers +and we're going to do this in such a way + + align:start position:0% +and we're going to do this in such a way + + + align:start position:0% +and we're going to do this in such a way +that it does not affect the presence of + + align:start position:0% +that it does not affect the presence of + + + align:start position:0% +that it does not affect the presence of +three-term LPS so let us map X to the + + align:start position:0% +three-term LPS so let us map X to the + + + align:start position:0% +three-term LPS so let us map X to the +integers by base expansion so this is + + align:start position:0% +integers by base expansion so this is + + + align:start position:0% +integers by base expansion so this is +base 2m expansion all right so what's + + align:start position:0% +base 2m expansion all right so what's + + + align:start position:0% +base 2m expansion all right so what's +the point of this construction here so + + align:start position:0% +the point of this construction here so + + + align:start position:0% +the point of this construction here so +far + + align:start position:0% +far + + + align:start position:0% +far +well you verify a couple of properties + + align:start position:0% +well you verify a couple of properties + + + align:start position:0% +well you verify a couple of properties +the first thing that this construction + + align:start position:0% +the first thing that this construction + + + align:start position:0% +the first thing that this construction +here is injective this map so if you + + align:start position:0% +here is injective this map so if you + + + align:start position:0% +here is injective this map so if you +call this map think of this fee is + + align:start position:0% +call this map think of this fee is + + + align:start position:0% +call this map think of this fee is +injective or space expansion so it's + + align:start position:0% +injective or space expansion so it's + + + align:start position:0% +injective or space expansion so it's +it's injective but also somewhat + + align:start position:0% +it's injective but also somewhat + + + align:start position:0% +it's injective but also somewhat +stronger claim is that if you have three + + align:start position:0% +stronger claim is that if you have three + + + align:start position:0% +stronger claim is that if you have three +points so if you have three points in X + + align:start position:0% +points so if you have three points in X + + + align:start position:0% +points so if you have three points in X +that map to a three ap in integers then + + align:start position:0% +that map to a three ap in integers then + + + align:start position:0% +that map to a three ap in integers then +the three points originally must be a + + align:start position:0% +the three points originally must be a + + + align:start position:0% +the three points originally must be a +three ap in X okay this is not a hard + + align:start position:0% +three ap in X okay this is not a hard + + + align:start position:0% +three ap in X okay this is not a hard +time just think about it here because + + align:start position:0% +time just think about it here because + + + align:start position:0% +time just think about it here because +we're using to base to M expansion and + + align:start position:0% +we're using to base to M expansion and + + + align:start position:0% +we're using to base to M expansion and +you only allowed to use digits up to M + + align:start position:0% +you only allowed to use digits up to M + + + align:start position:0% +you only allowed to use digits up to M +you don't have any wraparound effects + + align:start position:0% +you don't have any wraparound effects + + + align:start position:0% +you don't have any wraparound effects +you don't have any carry overs when you + + align:start position:0% +you don't have any carry overs when you + + + align:start position:0% +you don't have any carry overs when you +do the addition so combining these two + + align:start position:0% +do the addition so combining these two + + + align:start position:0% +do the addition so combining these two +observations + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +we find that the image of Excel is a CA + + align:start position:0% +we find that the image of Excel is a CA + + + align:start position:0% +we find that the image of Excel is a CA +P 3 set 1 2 and okay so one is and I can + + align:start position:0% +P 3 set 1 2 and okay so one is and I can + + + align:start position:0% +P 3 set 1 2 and okay so one is and I can +take em to be for instance to M raised + + align:start position:0% +take em to be for instance to M raised + + + align:start position:0% +take em to be for instance to M raised +to power D so all the numbers up there + + align:start position:0% +to power D so all the numbers up there + + + align:start position:0% +to power D so all the numbers up there +are less than this quantity and the size + + align:start position:0% +are less than this quantity and the size + + + align:start position:0% +are less than this quantity and the size +is the size of except L which is M to + + align:start position:0% +is the size of except L which is M to + + + align:start position:0% +is the size of except L which is M to +the D divided by D M squared and now you + + align:start position:0% +the D divided by D M squared and now you + + + align:start position:0% +the D divided by D M squared and now you +just need to find the appropriate + + align:start position:0% +just need to find the appropriate + + + align:start position:0% +just need to find the appropriate +choices of the parameters m and D to + + align:start position:0% +choices of the parameters m and D to + + + align:start position:0% +choices of the parameters m and D to +maximize the size of XML and and that's + + align:start position:0% +maximize the size of XML and and that's + + + align:start position:0% +maximize the size of XML and and that's +that's an exercise and so for instance + + align:start position:0% +that's an exercise and so for instance + + + align:start position:0% +that's an exercise and so for instance +if you take M to be e to the root log N + + align:start position:0% +if you take M to be e to the root log N + + + align:start position:0% +if you take M to be e to the root log N +and D to be good log n then you find + + align:start position:0% +and D to be good log n then you find + + + align:start position:0% +and D to be good log n then you find +that the size here is the bound that we + + align:start position:0% +that the size here is the bound that we + + + align:start position:0% +that the size here is the bound that we +claim and that finishes the construction + + align:start position:0% +claim and that finishes the construction + + + align:start position:0% +claim and that finishes the construction +of parent giving you a fairly large + + align:start position:0% +of parent giving you a fairly large + + + align:start position:0% +of parent giving you a fairly large +subset of 1 through n without three term + + align:start position:0% +subset of 1 through n without three term + + + align:start position:0% +subset of 1 through n without three term +arithmetic progressions and the idea + + align:start position:0% +arithmetic progressions and the idea + + + align:start position:0% +arithmetic progressions and the idea +here is you look at a higher dimensional + + align:start position:0% +here is you look at a higher dimensional + + + align:start position:0% +here is you look at a higher dimensional +object namely a higher dimensional + + align:start position:0% +object namely a higher dimensional + + + align:start position:0% +object namely a higher dimensional +sphere which has this property of being + + align:start position:0% +sphere which has this property of being + + + align:start position:0% +sphere which has this property of being +383 and are you projected onto the + + align:start position:0% +383 and are you projected onto the + + + align:start position:0% +383 and are you projected onto the +integers any questions so far + + align:start position:0% + + + + align:start position:0% + +okay so we have some proof do we have + + align:start position:0% +okay so we have some proof do we have + + + align:start position:0% +okay so we have some proof do we have +some examples so now let's go on to + + align:start position:0% +some examples so now let's go on to + + + align:start position:0% +some examples so now let's go on to +variations of Ross theorem and I want to + + align:start position:0% +variations of Ross theorem and I want to + + + align:start position:0% +variations of Ross theorem and I want to +show you a higher dimensional version of + + align:start position:0% +show you a higher dimensional version of + + + align:start position:0% +show you a higher dimensional version of +Ross theorem so I mentioned in very + + align:start position:0% +Ross theorem so I mentioned in very + + + align:start position:0% +Ross theorem so I mentioned in very +first lecture so you have this whole + + align:start position:0% +first lecture so you have this whole + + + align:start position:0% +first lecture so you have this whole +host of theorems in additive + + align:start position:0% +host of theorems in additive + + + align:start position:0% +host of theorems in additive +combinatorics rough + + align:start position:0% +combinatorics rough + + + align:start position:0% +combinatorics rough +similarly multi-dimensional similarity + + align:start position:0% +similarly multi-dimensional similarity + + + align:start position:0% +similarly multi-dimensional similarity +okay so this is in some sense the + + align:start position:0% +okay so this is in some sense the + + + align:start position:0% +okay so this is in some sense the +simplest example of multi-dimensional + + align:start position:0% +simplest example of multi-dimensional + + + align:start position:0% +simplest example of multi-dimensional +similarity theorem and this example is + + align:start position:0% +similarity theorem and this example is + + + align:start position:0% +similarity theorem and this example is +known as corners okay so what's a corner + + align:start position:0% +known as corners okay so what's a corner + + + align:start position:0% +known as corners okay so what's a corner +a corner is what we're working inside + + align:start position:0% +a corner is what we're working inside + + + align:start position:0% +a corner is what we're working inside +two dimensions so Corner is simply three + + align:start position:0% +two dimensions so Corner is simply three + + + align:start position:0% +two dimensions so Corner is simply three +points such that the two throat their + + align:start position:0% +points such that the two throat their + + + align:start position:0% +points such that the two throat their +position like that such that these two + + align:start position:0% +position like that such that these two + + + align:start position:0% +position like that such that these two +segments they are parallel to the axis + + align:start position:0% +segments they are parallel to the axis + + + align:start position:0% +segments they are parallel to the axis +and they are the same length okay so + + align:start position:0% +and they are the same length okay so + + + align:start position:0% +and they are the same length okay so +that's by definition where the corner is + + align:start position:0% +that's by definition where the corner is + + + align:start position:0% +that's by definition where the corner is +and the question is if you give me a + + align:start position:0% +and the question is if you give me a + + + align:start position:0% +and the question is if you give me a +subset of a grid that is Corner free how + + align:start position:0% +subset of a grid that is Corner free how + + + align:start position:0% +subset of a grid that is Corner free how +large can this subset theorem so if a is + + align:start position:0% +large can this subset theorem so if a is + + + align:start position:0% +large can this subset theorem so if a is +a subset of 1 to M with no corners + + align:start position:0% +a subset of 1 to M with no corners + + + align:start position:0% +a subset of 1 to M with no corners +particular no three points of the form X + + align:start position:0% +particular no three points of the form X + + + align:start position:0% +particular no three points of the form X +comma Y X plus T comma Y and X comma y + + align:start position:0% +comma Y X plus T comma Y and X comma y + + + align:start position:0% +comma Y X plus T comma Y and X comma y +plus D where D is some positive integer + + align:start position:0% +plus D where D is some positive integer + + + align:start position:0% +plus D where D is some positive integer +then the size of a has to be little o of + + align:start position:0% +then the size of a has to be little o of + + + align:start position:0% +then the size of a has to be little o of +N squared question + + align:start position:0% + + + + align:start position:0% + +okay good question so that's one of the + + align:start position:0% +okay good question so that's one of the + + + align:start position:0% +okay good question so that's one of the +first things we will address in this + + align:start position:0% +first things we will address in this + + + align:start position:0% +first things we will address in this +proof so your question was do we only + + align:start position:0% +proof so your question was do we only + + + align:start position:0% +proof so your question was do we only +care about corners oriented in the + + align:start position:0% +care about corners oriented in the + + + align:start position:0% +care about corners oriented in the +positive direction so you can have a + + align:start position:0% +positive direction so you can have a + + + align:start position:0% +positive direction so you can have a +more relaxed version of this problem + + align:start position:0% +more relaxed version of this problem + + + align:start position:0% +more relaxed version of this problem +where you allow D to be negative as well + + align:start position:0% +where you allow D to be negative as well + + + align:start position:0% +where you allow D to be negative as well +I look the first step in the proof is so + + align:start position:0% +I look the first step in the proof is so + + + align:start position:0% +I look the first step in the proof is so +we'll see that that constraint doesn't + + align:start position:0% +we'll see that that constraint doesn't + + + align:start position:0% +we'll see that that constraint doesn't +actually matter yes okay great let's get + + align:start position:0% +actually matter yes okay great let's get + + + align:start position:0% +actually matter yes okay great let's get +started so as Michael mentioned we do + + align:start position:0% +started so as Michael mentioned we do + + + align:start position:0% +started so as Michael mentioned we do +have this constraint in this over here + + align:start position:0% +have this constraint in this over here + + + align:start position:0% +have this constraint in this over here +that D is positive and somewhat annoying + + align:start position:0% +that D is positive and somewhat annoying + + + align:start position:0% +that D is positive and somewhat annoying +because if you remember in our proof of + + align:start position:0% +because if you remember in our proof of + + + align:start position:0% +because if you remember in our proof of +Ross theorem they are positive negative + + align:start position:0% +Ross theorem they are positive negative + + + align:start position:0% +Ross theorem they are positive negative +they don't play a role so let's try to + + align:start position:0% +they don't play a role so let's try to + + + align:start position:0% +they don't play a role so let's try to +find a way to get rid of this constraint + + align:start position:0% +find a way to get rid of this constraint + + + align:start position:0% +find a way to get rid of this constraint +so that we are in a more flexible + + align:start position:0% +so that we are in a more flexible + + + align:start position:0% +so that we are in a more flexible +situation all right so first step is + + align:start position:0% +situation all right so first step is + + + align:start position:0% +situation all right so first step is +that well get rid of this D being + + align:start position:0% +that well get rid of this D being + + + align:start position:0% +that well get rid of this D being +positive requirement okay so here is a + + align:start position:0% +positive requirement okay so here is a + + + align:start position:0% +positive requirement okay so here is a +trick let's consider the sum set a plus + + align:start position:0% +trick let's consider the sum set a plus + + + align:start position:0% +trick let's consider the sum set a plus +a okay so some set here means and + + align:start position:0% +a okay so some set here means and + + + align:start position:0% +a okay so some set here means and +looking at all pairwise sums as a set so + + align:start position:0% +looking at all pairwise sums as a set so + + + align:start position:0% +looking at all pairwise sums as a set so +you don't keep track of you don't keep + + align:start position:0% +you don't keep track of you don't keep + + + align:start position:0% +you don't keep track of you don't keep +track of duplicates all right so you + + align:start position:0% +track of duplicates all right so you + + + align:start position:0% +track of duplicates all right so you +keep it as a set and we're living inside + + align:start position:0% +keep it as a set and we're living inside + + + align:start position:0% +keep it as a set and we're living inside +the squid but now somewhat wider and + + align:start position:0% +the squid but now somewhat wider and + + + align:start position:0% +the squid but now somewhat wider and +with okay + + align:start position:0% +with okay + + + align:start position:0% +with okay +then there exists a element in this + + align:start position:0% +then there exists a element in this + + + align:start position:0% +then there exists a element in this +domain of the subset by pigeonhole + + align:start position:0% +domain of the subset by pigeonhole + + + align:start position:0% +domain of the subset by pigeonhole +that's represented in many different + + align:start position:0% +that's represented in many different + + + align:start position:0% +that's represented in many different +ways so there exists a Z represented as + + align:start position:0% +ways so there exists a Z represented as + + + align:start position:0% +ways so there exists a Z represented as +a plus B in at least size of a squared + + align:start position:0% +a plus B in at least size of a squared + + + align:start position:0% +a plus B in at least size of a squared +divided by size of 2n squared + + align:start position:0% +divided by size of 2n squared + + + align:start position:0% +divided by size of 2n squared +different ways just because if you look + + align:start position:0% +different ways just because if you look + + + align:start position:0% +different ways just because if you look +at how many things come up in that + + align:start position:0% +at how many things come up in that + + + align:start position:0% +at how many things come up in that +representation okay just use pigeonhole + + align:start position:0% + + + + align:start position:0% + +and now let's take a prime to be a + + align:start position:0% +and now let's take a prime to be a + + + align:start position:0% +and now let's take a prime to be a +intersect Z minus a alright so what's + + align:start position:0% +intersect Z minus a alright so what's + + + align:start position:0% +intersect Z minus a alright so what's +happening here so you have this set a + + align:start position:0% +happening here so you have this set a + + + align:start position:0% +happening here so you have this set a +and basically what I want to do is look + + align:start position:0% +and basically what I want to do is look + + + align:start position:0% +and basically what I want to do is look +at the look at minus a and then shift + + align:start position:0% +at the look at minus a and then shift + + + align:start position:0% +at the look at minus a and then shift +minus a over so that the intersect in as + + align:start position:0% +minus a over so that the intersect in as + + + align:start position:0% +minus a over so that the intersect in as +many elements as you can and by + + align:start position:0% +many elements as you can and by + + + align:start position:0% +many elements as you can and by +pigeonhole I can guarantee that their + + align:start position:0% +pigeonhole I can guarantee that their + + + align:start position:0% +pigeonhole I can guarantee that their +intersection is fairly large because + + align:start position:0% +intersection is fairly large because + + + align:start position:0% +intersection is fairly large because +size of a prime is essentially the + + align:start position:0% +size of a prime is essentially the + + + align:start position:0% +size of a prime is essentially the +number of ways that Z can be represented + + align:start position:0% +number of ways that Z can be represented + + + align:start position:0% +number of ways that Z can be represented +in the aforementioned manner so it's the + + align:start position:0% +in the aforementioned manner so it's the + + + align:start position:0% +in the aforementioned manner so it's the +physis to show that a prime yes and + + align:start position:0% +physis to show that a prime yes and + + + align:start position:0% +physis to show that a prime yes and +squared if you show that and you + + align:start position:0% +squared if you show that and you + + + align:start position:0% +squared if you show that and you +automatically show a lot o of N squared + + align:start position:0% +automatically show a lot o of N squared + + + align:start position:0% +automatically show a lot o of N squared +but now a prime is symmetric it's a + + align:start position:0% +but now a prime is symmetric it's a + + + align:start position:0% +but now a prime is symmetric it's a +prime is symmetric around Z over 2 + + align:start position:0% + + + + align:start position:0% + +so this is centrally symmetric about 0 / + + align:start position:0% +so this is centrally symmetric about 0 / + + + align:start position:0% +so this is centrally symmetric about 0 / +2 meaning that a prime equals to Z minus + + align:start position:0% +2 meaning that a prime equals to Z minus + + + align:start position:0% +2 meaning that a prime equals to Z minus +a prime and so you see now we've gotten + + align:start position:0% +a prime and so you see now we've gotten + + + align:start position:0% +a prime and so you see now we've gotten +rid of this deep positive requirement + + align:start position:0% +rid of this deep positive requirement + + + align:start position:0% +rid of this deep positive requirement +because if a prime had a positive corner + + align:start position:0% +because if a prime had a positive corner + + + align:start position:0% +because if a prime had a positive corner +then has a negative corner and vice + + align:start position:0% +then has a negative corner and vice + + + align:start position:0% +then has a negative corner and vice +versa so no corner in a prime with the + + align:start position:0% +versa so no corner in a prime with the + + + align:start position:0% +versa so no corner in a prime with the +positive implies that no corner with be + + align:start position:0% +positive implies that no corner with be + + + align:start position:0% +positive implies that no corner with be +negative okay so now let's forget about + + align:start position:0% +negative okay so now let's forget about + + + align:start position:0% +negative okay so now let's forget about +a and a prime and just replace a by a + + align:start position:0% +a and a prime and just replace a by a + + + align:start position:0% +a and a prime and just replace a by a +prime and forget about this the positive + + align:start position:0% +prime and forget about this the positive + + + align:start position:0% +prime and forget about this the positive +condition so let's forget about this + + align:start position:0% +condition so let's forget about this + + + align:start position:0% +condition so let's forget about this +part and but I do want B not equal to 0 + + align:start position:0% +part and but I do want B not equal to 0 + + + align:start position:0% +part and but I do want B not equal to 0 +otherwise you have trivial corners of + + align:start position:0% +otherwise you have trivial corners of + + + align:start position:0% +otherwise you have trivial corners of +course you always have trivial corners + + align:start position:0% +course you always have trivial corners + + + align:start position:0% +course you always have trivial corners +all right + + align:start position:0% + + + + align:start position:0% + +so remember how the proof of Ross + + align:start position:0% +so remember how the proof of Ross + + + align:start position:0% +so remember how the proof of Ross +theorem went and this relates to the + + align:start position:0% +theorem went and this relates to the + + + align:start position:0% +theorem went and this relates to the +very first lecture where I show you this + + align:start position:0% +very first lecture where I show you this + + + align:start position:0% +very first lecture where I show you this +connection between additive + + align:start position:0% +connection between additive + + + align:start position:0% +connection between additive +combinatorics on one hand and graph + + align:start position:0% +combinatorics on one hand and graph + + + align:start position:0% +combinatorics on one hand and graph +theory on the other hand or you take + + align:start position:0% +theory on the other hand or you take + + + align:start position:0% +theory on the other hand or you take +some arithmetic pattern and you try to + + align:start position:0% +some arithmetic pattern and you try to + + + align:start position:0% +some arithmetic pattern and you try to +encode it in a graph so that the + + align:start position:0% +encode it in a graph so that the + + + align:start position:0% +encode it in a graph so that the +patterns in your automatic set + + align:start position:0% +patterns in your automatic set + + + align:start position:0% +patterns in your automatic set +correspond to patterns in the graph so + + align:start position:0% +correspond to patterns in the graph so + + + align:start position:0% +correspond to patterns in the graph so +we're going to do the same thing here so + + align:start position:0% +we're going to do the same thing here so + + + align:start position:0% +we're going to do the same thing here so +we're going to encode the subset of the + + align:start position:0% +we're going to encode the subset of the + + + align:start position:0% +we're going to encode the subset of the +grid as a tripartite graph in such a way + + align:start position:0% +grid as a tripartite graph in such a way + + + align:start position:0% +grid as a tripartite graph in such a way +that the corners correspond to triangles + + align:start position:0% +that the corners correspond to triangles + + + align:start position:0% +that the corners correspond to triangles +in the graph + + align:start position:0% +in the graph + + + align:start position:0% +in the graph +okay so I'll show you how to do this and + + align:start position:0% +okay so I'll show you how to do this and + + + align:start position:0% +okay so I'll show you how to do this and +it will be fairly simple but and in + + align:start position:0% +it will be fairly simple but and in + + + align:start position:0% +it will be fairly simple but and in +general I mean sometimes it takes a + + align:start position:0% +general I mean sometimes it takes a + + + align:start position:0% +general I mean sometimes it takes a +little bit ingenuity to figure out what + + align:start position:0% +little bit ingenuity to figure out what + + + align:start position:0% +little bit ingenuity to figure out what +is the right way to set up the graph so + + align:start position:0% +is the right way to set up the graph so + + + align:start position:0% +is the right way to set up the graph so +one of an upcoming homework problem will + + align:start position:0% +one of an upcoming homework problem will + + + align:start position:0% +one of an upcoming homework problem will +be for you to figure out how to set up a + + align:start position:0% +be for you to figure out how to set up a + + + align:start position:0% +be for you to figure out how to set up a +corresponding graph when the pattern is + + align:start position:0% +corresponding graph when the pattern is + + + align:start position:0% +corresponding graph when the pattern is +not a corner but a square right if I add + + align:start position:0% +not a corner but a square right if I add + + + align:start position:0% +not a corner but a square right if I add +one extra point up there how would you + + align:start position:0% +one extra point up there how would you + + + align:start position:0% +one extra point up there how would you +do that + + align:start position:0% +do that + + + align:start position:0% +do that +so okay okay so what does this graph + + align:start position:0% +so okay okay so what does this graph + + + align:start position:0% +so okay okay so what does this graph +look like + + align:start position:0% +look like + + + align:start position:0% +look like +let's build a graph where so this should + + align:start position:0% +let's build a graph where so this should + + + align:start position:0% +let's build a graph where so this should +be somewhat reminiscent of the proof of + + align:start position:0% +be somewhat reminiscent of the proof of + + + align:start position:0% +be somewhat reminiscent of the proof of +Ross theorem where I give you three sets + + align:start position:0% +Ross theorem where I give you three sets + + + align:start position:0% +Ross theorem where I give you three sets +XY and z and x and y are both going to + + align:start position:0% +XY and z and x and y are both going to + + + align:start position:0% +XY and z and x and y are both going to +have n elements and Z is now going to + + align:start position:0% +have n elements and Z is now going to + + + align:start position:0% +have n elements and Z is now going to +have two n elements + + align:start position:0% + + + + align:start position:0% + +X they're supposed to enumerate or index + + align:start position:0% +X they're supposed to enumerate or index + + + align:start position:0% +X they're supposed to enumerate or index +all the vertical lines in your grid so + + align:start position:0% +all the vertical lines in your grid so + + + align:start position:0% +all the vertical lines in your grid so +you have this grid n by n so exercise + + align:start position:0% +you have this grid n by n so exercise + + + align:start position:0% +you have this grid n by n so exercise +for each vertex in X corresponds to a + + align:start position:0% +for each vertex in X corresponds to a + + + align:start position:0% +for each vertex in X corresponds to a +vertical line y corresponds to the + + align:start position:0% +vertical line y corresponds to the + + + align:start position:0% +vertical line y corresponds to the +horizontal lines and thee corresponds to + + align:start position:0% +horizontal lines and thee corresponds to + + + align:start position:0% +horizontal lines and thee corresponds to +these negatively sloped diagonal lines + + align:start position:0% +these negatively sloped diagonal lines + + + align:start position:0% +these negatively sloped diagonal lines +slope -1 lines of course you should only + + align:start position:0% +slope -1 lines of course you should only + + + align:start position:0% +slope -1 lines of course you should only +take lines that affect you are n by n + + align:start position:0% +take lines that affect you are n by n + + + align:start position:0% +take lines that affect you are n by n +grid so that's why there there's many of + + align:start position:0% +grid so that's why there there's many of + + + align:start position:0% +grid so that's why there there's many of +them for each direction okay so what's + + align:start position:0% +them for each direction okay so what's + + + align:start position:0% +them for each direction okay so what's +the graph I join two vertices if there + + align:start position:0% +the graph I join two vertices if there + + + align:start position:0% +the graph I join two vertices if there +are corresponding lines meet in a point + + align:start position:0% +are corresponding lines meet in a point + + + align:start position:0% +are corresponding lines meet in a point +of it + + align:start position:0% + + + + align:start position:0% + +so I might have this might be a a point + + align:start position:0% +so I might have this might be a a point + + + align:start position:0% +so I might have this might be a a point +of a so I put an edge between those two + + align:start position:0% +of a so I put an edge between those two + + + align:start position:0% +of a so I put an edge between those two +lines 1/4 X 1/4 Z because the + + align:start position:0% +lines 1/4 X 1/4 Z because the + + + align:start position:0% +lines 1/4 X 1/4 Z because the +intersection lies in a and more + + align:start position:0% +intersection lies in a and more + + + align:start position:0% +intersection lies in a and more +explicitly I mean that is pretty + + align:start position:0% +explicitly I mean that is pretty + + + align:start position:0% +explicitly I mean that is pretty +explicit and alternatively you could + + align:start position:0% +explicit and alternatively you could + + + align:start position:0% +explicit and alternatively you could +also write this graph by telling us how + + align:start position:0% +also write this graph by telling us how + + + align:start position:0% +also write this graph by telling us how +to put in the edge between X and Z + + align:start position:0% +to put in the edge between X and Z + + + align:start position:0% +to put in the edge between X and Z +namely you do this if X comma Z minus X + + align:start position:0% +namely you do this if X comma Z minus X + + + align:start position:0% +namely you do this if X comma Z minus X +nicing a you put an edge between x and y + + align:start position:0% +nicing a you put an edge between x and y + + + align:start position:0% +nicing a you put an edge between x and y +if X comma Y lies in a and likewise + + align:start position:0% +if X comma Y lies in a and likewise + + + align:start position:0% +if X comma Y lies in a and likewise +you're putting final edge if Z minus y + + align:start position:0% +you're putting final edge if Z minus y + + + align:start position:0% +you're putting final edge if Z minus y +comma y lies in a so to equivalent + + align:start position:0% +comma y lies in a so to equivalent + + + align:start position:0% +comma y lies in a so to equivalent +descriptions of the same graph any + + align:start position:0% +descriptions of the same graph any + + + align:start position:0% +descriptions of the same graph any +questions all right + + align:start position:0% +questions all right + + + align:start position:0% +questions all right +so the rest of the proof is more or less + + align:start position:0% +so the rest of the proof is more or less + + + align:start position:0% +so the rest of the proof is more or less +the same as the proof of Ross theorem we + + align:start position:0% +the same as the proof of Ross theorem we + + + align:start position:0% +the same as the proof of Ross theorem we +saw last time so we need to figure out + + align:start position:0% +saw last time so we need to figure out + + + align:start position:0% +saw last time so we need to figure out +how many edges are there every element + + align:start position:0% +how many edges are there every element + + + align:start position:0% +how many edges are there every element +of a gives you 3 edges that's one of you + + align:start position:0% +of a gives you 3 edges that's one of you + + + align:start position:0% +of a gives you 3 edges that's one of you +I just correspond the element the other + + align:start position:0% +I just correspond the element the other + + + align:start position:0% +I just correspond the element the other +two pairs or two other edges and most + + align:start position:0% +two pairs or two other edges and most + + + align:start position:0% +two pairs or two other edges and most +importantly the triangles in this graph + + align:start position:0% +importantly the triangles in this graph + + + align:start position:0% +importantly the triangles in this graph +I claimed correspond to corners so what + + align:start position:0% +I claimed correspond to corners so what + + + align:start position:0% +I claimed correspond to corners so what +is the triangle a triangle corresponds + + align:start position:0% +is the triangle a triangle corresponds + + + align:start position:0% +is the triangle a triangle corresponds +to a horizontal line a vertical line + + align:start position:0% +to a horizontal line a vertical line + + + align:start position:0% +to a horizontal line a vertical line +slope one minus one line that pairwise + + align:start position:0% +slope one minus one line that pairwise + + + align:start position:0% +slope one minus one line that pairwise +intersect in elements of a if you look + + align:start position:0% +intersect in elements of a if you look + + + align:start position:0% +intersect in elements of a if you look +at their intersections that's a corner + + align:start position:0% +at their intersections that's a corner + + + align:start position:0% +at their intersections that's a corner +if you have a corner you build a + + align:start position:0% +if you have a corner you build a + + + align:start position:0% +if you have a corner you build a +triangle and because your graph your set + + align:start position:0% +triangle and because your graph your set + + + align:start position:0% +triangle and because your graph your set +is corner free well you don't have any + + align:start position:0% +is corner free well you don't have any + + + align:start position:0% +is corner free well you don't have any +triangles actually no that's not true + + align:start position:0% +triangles actually no that's not true + + + align:start position:0% +triangles actually no that's not true +right so like we saw in rostrum you have + + align:start position:0% +right so like we saw in rostrum you have + + + align:start position:0% +right so like we saw in rostrum you have +some triangles but corresponding to + + align:start position:0% +some triangles but corresponding to + + + align:start position:0% +some triangles but corresponding to +trivial corners triangles correspond to + + align:start position:0% +trivial corners triangles correspond to + + + align:start position:0% +trivial corners triangles correspond to +trivial corners because you're set a is + + align:start position:0% +trivial corners because you're set a is + + + align:start position:0% +trivial corners because you're set a is +tri this corner free trivial corners + + align:start position:0% +tri this corner free trivial corners + + + align:start position:0% +tri this corner free trivial corners +meaning the same point with D equals to + + align:start position:0% +meaning the same point with D equals to + + + align:start position:0% +meaning the same point with D equals to +zero so it's not a genuine corner like + + align:start position:0% +zero so it's not a genuine corner like + + + align:start position:0% +zero so it's not a genuine corner like +that and in particular in this in this + + align:start position:0% +that and in particular in this in this + + + align:start position:0% +that and in particular in this in this +graph every edge is in a unique triangle + + align:start position:0% + + + + align:start position:0% + +and so we're in the same situation by + + align:start position:0% +and so we're in the same situation by + + + align:start position:0% +and so we're in the same situation by +the corollary of of triangle removal + + align:start position:0% +the corollary of of triangle removal + + + align:start position:0% +the corollary of of triangle removal +lemma we find that a number of edges + + align:start position:0% + + + + align:start position:0% + +must be due to all of the number of + + align:start position:0% +must be due to all of the number of + + + align:start position:0% +must be due to all of the number of +vertices so so the number of edges must + + align:start position:0% +vertices so so the number of edges must + + + align:start position:0% +vertices so so the number of edges must +be sub-quadratic so must be little o of + + align:start position:0% +be sub-quadratic so must be little o of + + + align:start position:0% +be sub-quadratic so must be little o of +N squared and so that implies that the + + align:start position:0% +N squared and so that implies that the + + + align:start position:0% +N squared and so that implies that the +size of a is little o of N squared that + + align:start position:0% +size of a is little o of N squared that + + + align:start position:0% +size of a is little o of N squared that +proves the corners theorem any questions + + align:start position:0% + + + + align:start position:0% + +so once you set up this graph the rest + + align:start position:0% +so once you set up this graph the rest + + + align:start position:0% +so once you set up this graph the rest +is the same as trois theorem so this + + align:start position:0% +is the same as trois theorem so this + + + align:start position:0% +is the same as trois theorem so this +connection between graph theory and + + align:start position:0% +connection between graph theory and + + + align:start position:0% +connection between graph theory and +additive combinatorics well you need to + + align:start position:0% +additive combinatorics well you need to + + + align:start position:0% +additive combinatorics well you need to +figure out how to set up this graph and + + align:start position:0% +figure out how to set up this graph and + + + align:start position:0% +figure out how to set up this graph and +then sometimes it's clear but sometimes + + align:start position:0% +then sometimes it's clear but sometimes + + + align:start position:0% +then sometimes it's clear but sometimes +you have to you know really think hard + + align:start position:0% +you have to you know really think hard + + + align:start position:0% +you have to you know really think hard +about how to do this all right + + align:start position:0% +about how to do this all right + + + align:start position:0% +about how to do this all right +what does Corner have to deal with + + align:start position:0% +what does Corner have to deal with + + + align:start position:0% +what does Corner have to deal with +roster them other than that they have + + align:start position:0% +roster them other than that they have + + + align:start position:0% +roster them other than that they have +very similar-looking proofs you can + + align:start position:0% +very similar-looking proofs you can + + + align:start position:0% +very similar-looking proofs you can +deduce roster and form the corners + + align:start position:0% +deduce roster and form the corners + + + align:start position:0% +deduce roster and form the corners +theorem and two to show you this + + align:start position:0% +theorem and two to show you this + + + align:start position:0% +theorem and two to show you this +precisely + + align:start position:0% +precisely + + + align:start position:0% +precisely +so let me use R sub three of em to + + align:start position:0% +so let me use R sub three of em to + + + align:start position:0% +so let me use R sub three of em to +denote the size largest and okay so this + + align:start position:0% +denote the size largest and okay so this + + + align:start position:0% +denote the size largest and okay so this +notation R sub three is actually fairly + + align:start position:0% +notation R sub three is actually fairly + + + align:start position:0% +notation R sub three is actually fairly +standard the next one's not so standard + + align:start position:0% +standard the next one's not so standard + + + align:start position:0% +standard the next one's not so standard +but let's just do that so that's not an + + align:start position:0% +but let's just do that so that's not an + + + align:start position:0% +but let's just do that so that's not an +L but that's a corner so that is the + + align:start position:0% +L but that's a corner so that is the + + + align:start position:0% +L but that's a corner so that is the +size of the largest corner free subset + + align:start position:0% +size of the largest corner free subset + + + align:start position:0% +size of the largest corner free subset +off and squared okay so we gave bounds + + align:start position:0% +off and squared okay so we gave bounds + + + align:start position:0% +off and squared okay so we gave bounds +for both quantities but they are + + align:start position:0% +for both quantities but they are + + + align:start position:0% +for both quantities but they are +actually related to each other through + + align:start position:0% +actually related to each other through + + + align:start position:0% +actually related to each other through +this fairly simple proposition that if + + align:start position:0% +this fairly simple proposition that if + + + align:start position:0% +this fairly simple proposition that if +you have an upper bound for corners then + + align:start position:0% +you have an upper bound for corners then + + + align:start position:0% +you have an upper bound for corners then +you have an upper bound for Ross theorem + + align:start position:0% + + + + align:start position:0% + +indeed given a a 383 subset of one + + align:start position:0% +indeed given a a 383 subset of one + + + align:start position:0% +indeed given a a 383 subset of one +through n let me build for you a corner + + align:start position:0% +through n let me build for you a corner + + + align:start position:0% +through n let me build for you a corner +free subset of the grid that is a fairly + + align:start position:0% +free subset of the grid that is a fairly + + + align:start position:0% +free subset of the grid that is a fairly +large subset of that grid I can form B + + align:start position:0% +large subset of that grid I can form B + + + align:start position:0% +large subset of that grid I can form B +by setting it to be the set of pairs + + align:start position:0% + + + + align:start position:0% + +inside the squid whose difference X + + align:start position:0% +inside the squid whose difference X + + + align:start position:0% +inside the squid whose difference X +minus y lies in a so what does this look + + align:start position:0% +minus y lies in a so what does this look + + + align:start position:0% +minus y lies in a so what does this look +like this is the grid of size 2n and if + + align:start position:0% +like this is the grid of size 2n and if + + + align:start position:0% +like this is the grid of size 2n and if +I start with a that is 3 AP free what I + + align:start position:0% +I start with a that is 3 AP free what I + + + align:start position:0% +I start with a that is 3 AP free what I +can do so over here is look at the lines + + align:start position:0% + + + + align:start position:0% + +like that putting all of those points + + align:start position:0% +like that putting all of those points + + + align:start position:0% +like that putting all of those points +and you see that this set of points + + align:start position:0% +and you see that this set of points + + + align:start position:0% +and you see that this set of points +should not have any corners right + + align:start position:0% +should not have any corners right + + + align:start position:0% +should not have any corners right +because if they had corners then the + + align:start position:0% +because if they had corners then the + + + align:start position:0% +because if they had corners then the +corners would project down to a 3 AP so + + align:start position:0% +corners would project down to a 3 AP so + + + align:start position:0% +corners would project down to a 3 AP so +B is corner free + + align:start position:0% + + + + align:start position:0% + +to recap if we have upper bound on + + align:start position:0% +to recap if we have upper bound on + + + align:start position:0% +to recap if we have upper bound on +corners we have upper bound on Ross + + align:start position:0% +corners we have upper bound on Ross + + + align:start position:0% +corners we have upper bound on Ross +theorem but you also know that if you + + align:start position:0% +theorem but you also know that if you + + + align:start position:0% +theorem but you also know that if you +have lower bound on Ross theorem then + + align:start position:0% +have lower bound on Ross theorem then + + + align:start position:0% +have lower bound on Ross theorem then +you have lower bound on quarters so the + + align:start position:0% +you have lower bound on quarters so the + + + align:start position:0% +you have lower bound on quarters so the +parent construction we saw at the + + align:start position:0% +parent construction we saw at the + + + align:start position:0% +parent construction we saw at the +beginning of today extends to exactly + + align:start position:0% +beginning of today extends to exactly + + + align:start position:0% +beginning of today extends to exactly +this way to a fairly large corner free + + align:start position:0% +this way to a fairly large corner free + + + align:start position:0% +this way to a fairly large corner free +subset and that's more or less the best + + align:start position:0% +subset and that's more or less the best + + + align:start position:0% +subset and that's more or less the best +thing that we know how to do in fact + + align:start position:0% +thing that we know how to do in fact + + + align:start position:0% +thing that we know how to do in fact +there aren't that many constructions in + + align:start position:0% +there aren't that many constructions in + + + align:start position:0% +there aren't that many constructions in +additive combinatorics that's know + + align:start position:0% +additive combinatorics that's know + + + align:start position:0% +additive combinatorics that's know +almost everything that I know how to + + align:start position:0% +almost everything that I know how to + + + align:start position:0% +almost everything that I know how to +construct is fairly large come from + + align:start position:0% +construct is fairly large come from + + + align:start position:0% +construct is fairly large come from +barons construction or some variant of + + align:start position:0% +barons construction or some variant of + + + align:start position:0% +barons construction or some variant of +barons construction so it looks pretty + + align:start position:0% +barons construction so it looks pretty + + + align:start position:0% +barons construction so it looks pretty +simple comes from the 40s yeah we don't + + align:start position:0% +simple comes from the 40s yeah we don't + + + align:start position:0% +simple comes from the 40s yeah we don't +really have too many new ideas besides + + align:start position:0% +really have too many new ideas besides + + + align:start position:0% +really have too many new ideas besides +playing and massaging barons + + align:start position:0% +playing and massaging barons + + + align:start position:0% +playing and massaging barons +construction let me tell you what is the + + align:start position:0% +construction let me tell you what is the + + + align:start position:0% +construction let me tell you what is the +best don't upper bound on the corners + + align:start position:0% +best don't upper bound on the corners + + + align:start position:0% +best don't upper bound on the corners +theorem cut off so the proof using + + align:start position:0% +theorem cut off so the proof using + + + align:start position:0% +theorem cut off so the proof using +triangle removal memo it goes to + + align:start position:0% +triangle removal memo it goes to + + + align:start position:0% +triangle removal memo it goes to +similarities regularity lemma gives you + + align:start position:0% +similarities regularity lemma gives you + + + align:start position:0% +similarities regularity lemma gives you +pretty horrible bounce but you saying + + align:start position:0% +pretty horrible bounce but you saying + + + align:start position:0% +pretty horrible bounce but you saying +for you analytic methods so you see if + + align:start position:0% +for you analytic methods so you see if + + + align:start position:0% +for you analytic methods so you see if +you have upper bound on Roth it doesn't + + align:start position:0% +you have upper bound on Roth it doesn't + + + align:start position:0% +you have upper bound on Roth it doesn't +give you an upper bound on Raw on corner + + align:start position:0% +give you an upper bound on Raw on corner + + + align:start position:0% +give you an upper bound on Raw on corner +so you need to do something extra and so + + align:start position:0% +so you need to do something extra and so + + + align:start position:0% +so you need to do something extra and so +the best-known bound so far is of the + + align:start position:0% +the best-known bound so far is of the + + + align:start position:0% +the best-known bound so far is of the +form and square divided by poly log log + + align:start position:0% +form and square divided by poly log log + + + align:start position:0% +form and square divided by poly log log +M log log n raised to some small + + align:start position:0% +M log log n raised to some small + + + align:start position:0% +M log log n raised to some small +constant C any questions + + align:start position:0% + + + + align:start position:0% + +last time we discussed the triangle + + align:start position:0% +last time we discussed the triangle + + + align:start position:0% +last time we discussed the triangle +counting lemma and a triangle removal + + align:start position:0% +counting lemma and a triangle removal + + + align:start position:0% +counting lemma and a triangle removal +lemma and well it shouldn't be surprise + + align:start position:0% +lemma and well it shouldn't be surprise + + + align:start position:0% +lemma and well it shouldn't be surprise +to you that if you can do it for + + align:start position:0% +to you that if you can do it for + + + align:start position:0% +to you that if you can do it for +triangles we may be able able to do it + + align:start position:0% +triangles we may be able able to do it + + + align:start position:0% +triangles we may be able able to do it +for other sub graphs so that's the next + + align:start position:0% +for other sub graphs so that's the next + + + align:start position:0% +for other sub graphs so that's the next +thing I want to discuss how to use the + + align:start position:0% +thing I want to discuss how to use the + + + align:start position:0% +thing I want to discuss how to use the +generalize the techniques and results + + align:start position:0% +generalize the techniques and results + + + align:start position:0% +generalize the techniques and results +that we obtain for triangles to other + + align:start position:0% +that we obtain for triangles to other + + + align:start position:0% +that we obtain for triangles to other +graphs and what are some of the + + align:start position:0% +graphs and what are some of the + + + align:start position:0% +graphs and what are some of the +implications if you combine it with + + align:start position:0% +implications if you combine it with + + + align:start position:0% +implications if you combine it with +similarities regularity lemma so let's + + align:start position:0% +similarities regularity lemma so let's + + + align:start position:0% +similarities regularity lemma so let's +generalize triangle so the strategy for + + align:start position:0% +generalize triangle so the strategy for + + + align:start position:0% +generalize triangle so the strategy for +the triangle counting lemma let me + + align:start position:0% +the triangle counting lemma let me + + + align:start position:0% +the triangle counting lemma let me +remind you was that we embedded the + + align:start position:0% +remind you was that we embedded the + + + align:start position:0% +remind you was that we embedded the +vertices one by one putting a vertex and + + align:start position:0% +vertices one by one putting a vertex and + + + align:start position:0% +vertices one by one putting a vertex and +a typical vertex here should have many + + align:start position:0% +a typical vertex here should have many + + + align:start position:0% +a typical vertex here should have many +neighbors to both vertex s so these two + + align:start position:0% +neighbors to both vertex s so these two + + + align:start position:0% +neighbors to both vertex s so these two +guys should have sizes typically roughly + + align:start position:0% +guys should have sizes typically roughly + + + align:start position:0% +guys should have sizes typically roughly +the same as a fraction of them + + align:start position:0% +the same as a fraction of them + + + align:start position:0% +the same as a fraction of them +corresponding to the edge density + + align:start position:0% +corresponding to the edge density + + + align:start position:0% +corresponding to the edge density +between the vertex parts and if they're + + align:start position:0% +between the vertex parts and if they're + + + align:start position:0% +between the vertex parts and if they're +not too small then from the epsilon + + align:start position:0% +not too small then from the epsilon + + + align:start position:0% +not too small then from the epsilon +regularity of these two sets you can + + align:start position:0% +regularity of these two sets you can + + + align:start position:0% +regularity of these two sets you can +reduce the number of edges between them + + align:start position:0% +reduce the number of edges between them + + + align:start position:0% +reduce the number of edges between them +so that was the strategy for the + + align:start position:0% +so that was the strategy for the + + + align:start position:0% +so that was the strategy for the +triangle counting them so you can try to + + align:start position:0% +triangle counting them so you can try to + + + align:start position:0% +triangle counting them so you can try to +extend the same strategy for other + + align:start position:0% +extend the same strategy for other + + + align:start position:0% +extend the same strategy for other +graphs so let me show you how this would + + align:start position:0% +graphs so let me show you how this would + + + align:start position:0% +graphs so let me show you how this would +have been done but I don't want to give + + align:start position:0% +have been done but I don't want to give + + + align:start position:0% +have been done but I don't want to give +too many details because it does get + + align:start position:0% +too many details because it does get + + + align:start position:0% +too many details because it does get +somewhat hairy if you try to execute it + + align:start position:0% + + + + align:start position:0% + +so the first strategy is to embed the + + align:start position:0% +so the first strategy is to embed the + + + align:start position:0% +so the first strategy is to embed the +vertices of H one at a time so my H now + + align:start position:0% +vertices of H one at a time so my H now + + + align:start position:0% +vertices of H one at a time so my H now +is going to be lets say a k4 and I wish + + align:start position:0% +is going to be lets say a k4 and I wish + + + align:start position:0% +is going to be lets say a k4 and I wish +to embed this H in the setting where you + + align:start position:0% +to embed this H in the setting where you + + + align:start position:0% +to embed this H in the setting where you +have these four parts in a regularity + + align:start position:0% +have these four parts in a regularity + + + align:start position:0% +have these four parts in a regularity +partition and they're pairwise Epsilon + + align:start position:0% +partition and they're pairwise Epsilon + + + align:start position:0% +partition and they're pairwise Epsilon +regular with edge densities that are not + + align:start position:0% +regular with edge densities that are not + + + align:start position:0% +regular with edge densities that are not +too small + + align:start position:0% +too small + + + align:start position:0% +too small +well what you can try to do mimicking + + align:start position:0% +well what you can try to do mimicking + + + align:start position:0% +well what you can try to do mimicking +the strategy over there is to first find + + align:start position:0% +the strategy over there is to first find + + + align:start position:0% +the strategy over there is to first find +a typical image for the top vertex and a + + align:start position:0% +a typical image for the top vertex and a + + + align:start position:0% +a typical image for the top vertex and a +typical image over here - some small bad + + align:start position:0% +typical image over here - some small bad + + + align:start position:0% +typical image over here - some small bad +exceptions will have many neighbors to + + align:start position:0% +exceptions will have many neighbors to + + + align:start position:0% +exceptions will have many neighbors to +each of the three parts next I need to + + align:start position:0% +each of the three parts next I need to + + + align:start position:0% +each of the three parts next I need to +figure out where this vertex can go I'm + + align:start position:0% +figure out where this vertex can go I'm + + + align:start position:0% +figure out where this vertex can go I'm +going to embed this vertex somewhere + + align:start position:0% +going to embed this vertex somewhere + + + align:start position:0% +going to embed this vertex somewhere +here again a typical place for this + + align:start position:0% +here again a typical place for this + + + align:start position:0% +here again a typical place for this +vertex modulo some small fraction which + + align:start position:0% +vertex modulo some small fraction which + + + align:start position:0% +vertex modulo some small fraction which +I'm going to throw away so now you see + + align:start position:0% +I'm going to throw away so now you see + + + align:start position:0% +I'm going to throw away so now you see +you need somewhat stronger hypotheses on + + align:start position:0% +you need somewhat stronger hypotheses on + + + align:start position:0% +you need somewhat stronger hypotheses on +the epsilon regularity but they're still + + align:start position:0% +the epsilon regularity but they're still + + + align:start position:0% +the epsilon regularity but they're still +all polynomial dependent so it's just + + align:start position:0% +all polynomial dependent so it's just + + + align:start position:0% +all polynomial dependent so it's just +have to choose your parameters correctly + + align:start position:0% +have to choose your parameters correctly + + + align:start position:0% +have to choose your parameters correctly +so this typical green vertex should have + + align:start position:0% +so this typical green vertex should have + + + align:start position:0% +so this typical green vertex should have +lots of neighbors over here so you just + + align:start position:0% +lots of neighbors over here so you just + + + align:start position:0% +lots of neighbors over here so you just +keep embedding so it's almost this + + align:start position:0% +keep embedding so it's almost this + + + align:start position:0% +keep embedding so it's almost this +greedy strategy you keep embedding each + + align:start position:0% +greedy strategy you keep embedding each + + + align:start position:0% +greedy strategy you keep embedding each +vertex but you have to guarantee that + + align:start position:0% +vertex but you have to guarantee that + + + align:start position:0% +vertex but you have to guarantee that +there are still lots of options left + + align:start position:0% + + + + align:start position:0% + +so embed vertices one at a time and I + + align:start position:0% +so embed vertices one at a time and I + + + align:start position:0% +so embed vertices one at a time and I +want you embed each vertex so that you + + align:start position:0% +want you embed each vertex so that you + + + align:start position:0% +want you embed each vertex so that you +have to be embedded vertices have many + + align:start position:0% +have to be embedded vertices have many + + + align:start position:0% +have to be embedded vertices have many +choices left + + align:start position:0% + + + + align:start position:0% + +so epsilon regularity guarantee so you + + align:start position:0% +so epsilon regularity guarantee so you + + + align:start position:0% +so epsilon regularity guarantee so you +can always do this and you do this all + + align:start position:0% +can always do this and you do this all + + + align:start position:0% +can always do this and you do this all +the way until the end and you arrive + + align:start position:0% +the way until the end and you arrive + + + align:start position:0% +the way until the end and you arrive +some statement and depending on how you + + align:start position:0% +some statement and depending on how you + + + align:start position:0% +some statement and depending on how you +do this the exact formulation of the + + align:start position:0% +do this the exact formulation of the + + + align:start position:0% +do this the exact formulation of the +statement will be somewhat different but + + align:start position:0% +statement will be somewhat different but + + + align:start position:0% +statement will be somewhat different but +let me give you one statement which we + + align:start position:0% +let me give you one statement which we + + + align:start position:0% +let me give you one statement which we +will not prove but you can deduce using + + align:start position:0% +will not prove but you can deduce using + + + align:start position:0% +will not prove but you can deduce using +this strategy and this is known as a + + align:start position:0% +this strategy and this is known as a + + + align:start position:0% +this strategy and this is known as a +graph embedding them up and again as I + + align:start position:0% +graph embedding them up and again as I + + + align:start position:0% +graph embedding them up and again as I +mentioned when I started discussing + + align:start position:0% +mentioned when I started discussing + + + align:start position:0% +mentioned when I started discussing +similarities regularity lemma the exact + + align:start position:0% +similarities regularity lemma the exact + + + align:start position:0% +similarities regularity lemma the exact +statements are not they're fairly robust + + align:start position:0% +statements are not they're fairly robust + + + align:start position:0% +statements are not they're fairly robust +and they're not as important as the + + align:start position:0% +and they're not as important as the + + + align:start position:0% +and they're not as important as the +spirit of the ideas or so if you have + + align:start position:0% +spirit of the ideas or so if you have + + + align:start position:0% +spirit of the ideas or so if you have +some application in mind you might have + + align:start position:0% +some application in mind you might have + + + align:start position:0% +some application in mind you might have +to go into the proof tweak a thing here + + align:start position:0% +to go into the proof tweak a thing here + + + align:start position:0% +to go into the proof tweak a thing here +and there but you get what you want so + + align:start position:0% +and there but you get what you want so + + + align:start position:0% +and there but you get what you want so +the graph embedding lemma says for + + align:start position:0% +the graph embedding lemma says for + + + align:start position:0% +the graph embedding lemma says for +example that if H is bipartite and with + + align:start position:0% +example that if H is bipartite and with + + + align:start position:0% +example that if H is bipartite and with +maximum degree at most Delta so the H + + align:start position:0% +maximum degree at most Delta so the H + + + align:start position:0% +maximum degree at most Delta so the H +maximum degree is at most Delta and + + align:start position:0% +maximum degree is at most Delta and + + + align:start position:0% +maximum degree is at most Delta and +suppose you have vertex sets v1 through + + align:start position:0% +suppose you have vertex sets v1 through + + + align:start position:0% +suppose you have vertex sets v1 through +the R such that each vertex set is not + + align:start position:0% +the R such that each vertex set is not + + + align:start position:0% +the R such that each vertex set is not +too small + + align:start position:0% + + + + align:start position:0% + +and if these vertex sets are pairwise + + align:start position:0% +and if these vertex sets are pairwise + + + align:start position:0% +and if these vertex sets are pairwise +Epsilon regular and the density is not + + align:start position:0% +Epsilon regular and the density is not + + + align:start position:0% +Epsilon regular and the density is not +too small so here on doing assuming some + + align:start position:0% +too small so here on doing assuming some + + + align:start position:0% +too small so here on doing assuming some +lower bound on the density which depends + + align:start position:0% +lower bound on the density which depends + + + align:start position:0% +lower bound on the density which depends +on your epsilon then the conclusion is + + align:start position:0% +on your epsilon then the conclusion is + + + align:start position:0% +on your epsilon then the conclusion is +that G contains a copy of H okay just + + align:start position:0% +that G contains a copy of H okay just + + + align:start position:0% +that G contains a copy of H okay just +want to give a few remarks on the + + align:start position:0% +want to give a few remarks on the + + + align:start position:0% +want to give a few remarks on the +statement of this theorem again we will + + align:start position:0% +statement of this theorem again we will + + + align:start position:0% +statement of this theorem again we will +not discuss the proof so what does this + + align:start position:0% +not discuss the proof so what does this + + + align:start position:0% +not discuss the proof so what does this +hypothesis our hypothesis on G being H + + align:start position:0% +hypothesis our hypothesis on G being H + + + align:start position:0% +hypothesis our hypothesis on G being H +being our part I'd have to do with + + align:start position:0% +being our part I'd have to do with + + + align:start position:0% +being our part I'd have to do with +anything so here as an example when R + + align:start position:0% +anything so here as an example when R + + + align:start position:0% +anything so here as an example when R +equals to 4 instead of this k4 maybe I + + align:start position:0% +equals to 4 instead of this k4 maybe I + + + align:start position:0% +equals to 4 instead of this k4 maybe I +also care about that graph over there + + align:start position:0% + + + + align:start position:0% + +right or maybe some more vertices some + + align:start position:0% +right or maybe some more vertices some + + + align:start position:0% +right or maybe some more vertices some +more edges but if it's for Park height + + align:start position:0% +more edges but if it's for Park height + + + align:start position:0% +more edges but if it's for Park height +and the point is that I want to embed + + align:start position:0% +and the point is that I want to embed + + + align:start position:0% +and the point is that I want to embed +the vertices in such a way that that top + + align:start position:0% +the vertices in such a way that that top + + + align:start position:0% +the vertices in such a way that that top +vertex goes to the part that it's + + align:start position:0% +vertex goes to the part that it's + + + align:start position:0% +vertex goes to the part that it's +supposed to go into that's what I'm + + align:start position:0% +supposed to go into that's what I'm + + + align:start position:0% +supposed to go into that's what I'm +embedding this configuration you know in + + align:start position:0% +embedding this configuration you know in + + + align:start position:0% +embedding this configuration you know in +the same way that corresponds to the + + align:start position:0% +the same way that corresponds to the + + + align:start position:0% +the same way that corresponds to the +proper coloring of H okay so if you do + + align:start position:0% +proper coloring of H okay so if you do + + + align:start position:0% +proper coloring of H okay so if you do +this you can there's enough room still + + align:start position:0% +this you can there's enough room still + + + align:start position:0% +this you can there's enough room still +to go as long as you're have some lower + + align:start position:0% +to go as long as you're have some lower + + + align:start position:0% +to go as long as you're have some lower +bound on the edge density between the + + align:start position:0% +bound on the edge density between the + + + align:start position:0% +bound on the edge density between the +individual parts and you only depend + + align:start position:0% +individual parts and you only depend + + + align:start position:0% +individual parts and you only depend +really on not the number of edges of H + + align:start position:0% +really on not the number of edges of H + + + align:start position:0% +really on not the number of edges of H +but the maximum degree because if you + + align:start position:0% +but the maximum degree because if you + + + align:start position:0% +but the maximum degree because if you +look at how many times each vertex its + + align:start position:0% +look at how many times each vertex its + + + align:start position:0% +look at how many times each vertex its +possibilities can be shrunk it's at most + + align:start position:0% +possibilities can be shrunk it's at most + + + align:start position:0% +possibilities can be shrunk it's at most +Delta times you know this graphing + + align:start position:0% +Delta times you know this graphing + + + align:start position:0% +Delta times you know this graphing +bending lemma so I give you the + + align:start position:0% +bending lemma so I give you the + + + align:start position:0% +bending lemma so I give you the +statement here but it's a fairly robust + + align:start position:0% +statement here but it's a fairly robust + + + align:start position:0% +statement here but it's a fairly robust +statement and if you want to get for + + align:start position:0% +statement and if you want to get for + + + align:start position:0% +statement and if you want to get for +example not just a single copy of H if + + align:start position:0% +example not just a single copy of H if + + + align:start position:0% +example not just a single copy of H if +you want again many + + align:start position:0% +you want again many + + + align:start position:0% +you want again many +copies of H you can tweet the hypothesis + + align:start position:0% +copies of H you can tweet the hypothesis + + + align:start position:0% +copies of H you can tweet the hypothesis +you can tweet the proof somewhat to get + + align:start position:0% +you can tweet the proof somewhat to get + + + align:start position:0% +you can tweet the proof somewhat to get +you what you want again following what + + align:start position:0% +you what you want again following what + + + align:start position:0% +you what you want again following what +we did for the triangle counting them + + align:start position:0% + + + + align:start position:0% + +question maximum degree increases this + + align:start position:0% +question maximum degree increases this + + + align:start position:0% +question maximum degree increases this +number goes up okay I want to show you a + + align:start position:0% +number goes up okay I want to show you a + + + align:start position:0% +number goes up okay I want to show you a +different way to do counting that does + + align:start position:0% +different way to do counting that does + + + align:start position:0% +different way to do counting that does +not go through this embedding vertices + + align:start position:0% +not go through this embedding vertices + + + align:start position:0% +not go through this embedding vertices +one by one but instead we will try to + + align:start position:0% +one by one but instead we will try to + + + align:start position:0% +one by one but instead we will try to +analyze what happens if you take out an + + align:start position:0% +analyze what happens if you take out an + + + align:start position:0% +analyze what happens if you take out an +edge of each one by one so and that's an + + align:start position:0% +edge of each one by one so and that's an + + + align:start position:0% +edge of each one by one so and that's an +alternative approach which I like more + + align:start position:0% +alternative approach which I like more + + + align:start position:0% +alternative approach which I like more +it's somewhat less intuitive if you are + + align:start position:0% +it's somewhat less intuitive if you are + + + align:start position:0% +it's somewhat less intuitive if you are +not used to thinking about it but the + + align:start position:0% +not used to thinking about it but the + + + align:start position:0% +not used to thinking about it but the +execution works out to be much cleaner + + align:start position:0% +execution works out to be much cleaner + + + align:start position:0% +execution works out to be much cleaner +and it's also in line with some of the + + align:start position:0% +and it's also in line with some of the + + + align:start position:0% +and it's also in line with some of the +techniques that we'll see later on when + + align:start position:0% +techniques that we'll see later on when + + + align:start position:0% +techniques that we'll see later on when +we discuss graph limits so let's take a + + align:start position:0% +we discuss graph limits so let's take a + + + align:start position:0% +we discuss graph limits so let's take a +quick break any questions so far + + align:start position:0% + + + + align:start position:0% + +we will see a second strategy for + + align:start position:0% +we will see a second strategy for + + + align:start position:0% +we will see a second strategy for +proving a graph counting llama and the + + align:start position:0% +proving a graph counting llama and the + + + align:start position:0% +proving a graph counting llama and the +second strategy is more analytic in + + align:start position:0% +second strategy is more analytic in + + + align:start position:0% +second strategy is more analytic in +nature which is to embed or to + + align:start position:0% + + + + align:start position:0% + +analytically somehow will analyze what + + align:start position:0% +analytically somehow will analyze what + + + align:start position:0% +analytically somehow will analyze what +happens when we take out one edge of H + + align:start position:0% + + + + align:start position:0% + +okay so let me give you the statement + + align:start position:0% +okay so let me give you the statement + + + align:start position:0% +okay so let me give you the statement +first the graph counting lemma says that + + align:start position:0% +first the graph counting lemma says that + + + align:start position:0% +first the graph counting lemma says that +if you have a graph H worth vertex set + + align:start position:0% +if you have a graph H worth vertex set + + + align:start position:0% +if you have a graph H worth vertex set +elements of 1 through K I also have an + + align:start position:0% +elements of 1 through K I also have an + + + align:start position:0% +elements of 1 through K I also have an +epsilon parameter and I have a graph G + + align:start position:0% +epsilon parameter and I have a graph G + + + align:start position:0% +epsilon parameter and I have a graph G +and subsets B 1 through B K G such that + + align:start position:0% +and subsets B 1 through B K G such that + + + align:start position:0% +and subsets B 1 through B K G such that +VI VJ is epsilon regular whenever IJ is + + align:start position:0% +VI VJ is epsilon regular whenever IJ is + + + align:start position:0% +VI VJ is epsilon regular whenever IJ is +an edge of H so here the setup is + + align:start position:0% +an edge of H so here the setup is + + + align:start position:0% +an edge of H so here the setup is +slightly different from the picture I + + align:start position:0% +slightly different from the picture I + + + align:start position:0% +slightly different from the picture I +drew up there so what's going on here is + + align:start position:0% +drew up there so what's going on here is + + + align:start position:0% +drew up there so what's going on here is +that you have let's say H being this + + align:start position:0% +that you have let's say H being this + + + align:start position:0% +that you have let's say H being this +graph and suppose you are in a situation + + align:start position:0% +graph and suppose you are in a situation + + + align:start position:0% +graph and suppose you are in a situation +where I know that some of these + + align:start position:0% + + + + align:start position:0% + +so I know that five of these pairs are + + align:start position:0% +so I know that five of these pairs are + + + align:start position:0% +so I know that five of these pairs are +epsilon regular and what I really want + + align:start position:0% +epsilon regular and what I really want + + + align:start position:0% +epsilon regular and what I really want +to do is embed this H into this + + align:start position:0% +to do is embed this H into this + + + align:start position:0% +to do is embed this H into this +configuration so 1 2 B 1 B 2 and so on + + align:start position:0% +configuration so 1 2 B 1 B 2 and so on + + + align:start position:0% +configuration so 1 2 B 1 B 2 and so on +and I want to know how many ways can you + + align:start position:0% +and I want to know how many ways can you + + + align:start position:0% +and I want to know how many ways can you +embed this way the conclusion is that + + align:start position:0% +embed this way the conclusion is that + + + align:start position:0% +embed this way the conclusion is that +the number of couples the number of such + + align:start position:0% +the number of couples the number of such + + + align:start position:0% +the number of couples the number of such +embeddings such that the ivj is an edge + + align:start position:0% +embeddings such that the ivj is an edge + + + align:start position:0% +embeddings such that the ivj is an edge +of G for all IJ h yes so we now picture + + align:start position:0% +of G for all IJ h yes so we now picture + + + align:start position:0% +of G for all IJ h yes so we now picture +the number of such embeddings the little + + align:start position:0% +the number of such embeddings the little + + + align:start position:0% +the number of such embeddings the little +VC is within a small error which is the + + align:start position:0% +VC is within a small error which is the + + + align:start position:0% +VC is within a small error which is the +number of edges of H epsilon times the + + align:start position:0% + + + + align:start position:0% + +total of the product of these vertex set + + align:start position:0% +total of the product of these vertex set + + + align:start position:0% +total of the product of these vertex set +sizes of this number which is what you + + align:start position:0% +sizes of this number which is what you + + + align:start position:0% +sizes of this number which is what you +would predict the number of embeddings + + align:start position:0% +would predict the number of embeddings + + + align:start position:0% +would predict the number of embeddings +to be if all of your bipartite graphs + + align:start position:0% +to be if all of your bipartite graphs + + + align:start position:0% +to be if all of your bipartite graphs +were actually random + + align:start position:0% + + + + align:start position:0% + +so like in the triangle counting them up + + align:start position:0% +so like in the triangle counting them up + + + align:start position:0% +so like in the triangle counting them up +if you look at the edge densities in + + align:start position:0% +if you look at the edge densities in + + + align:start position:0% +if you look at the edge densities in +this configuration and predict how many + + align:start position:0% +this configuration and predict how many + + + align:start position:0% +this configuration and predict how many +copies of H you would get that's the + + align:start position:0% +copies of H you would get that's the + + + align:start position:0% +copies of H you would get that's the +number you should write down and this + + align:start position:0% +number you should write down and this + + + align:start position:0% +number you should write down and this +counting lemma tells you that the truth + + align:start position:0% +counting lemma tells you that the truth + + + align:start position:0% +counting lemma tells you that the truth +is not so far from the prediction any + + align:start position:0% +is not so far from the prediction any + + + align:start position:0% +is not so far from the prediction any +questions all right so we will proof the + + align:start position:0% +questions all right so we will proof the + + + align:start position:0% +questions all right so we will proof the +graph counting them up in an analytic + + align:start position:0% +graph counting them up in an analytic + + + align:start position:0% +graph counting them up in an analytic +manner + + align:start position:0% +manner + + + align:start position:0% +manner +it helps to so it will be convenient for + + align:start position:0% +it helps to so it will be convenient for + + + align:start position:0% +it helps to so it will be convenient for +me to rephrase the result just a little + + align:start position:0% +me to rephrase the result just a little + + + align:start position:0% +me to rephrase the result just a little +bit to in this probabilistic form so it + + align:start position:0% +bit to in this probabilistic form so it + + + align:start position:0% +bit to in this probabilistic form so it +has equivalent to show that if you have + + align:start position:0% +has equivalent to show that if you have + + + align:start position:0% +has equivalent to show that if you have +uniformly randomly chosen vertices you + + align:start position:0% +uniformly randomly chosen vertices you + + + align:start position:0% +uniformly randomly chosen vertices you +little V 1 in big d 1 and so on will be + + align:start position:0% +little V 1 in big d 1 and so on will be + + + align:start position:0% +little V 1 in big d 1 and so on will be +K and big be K so they're independent + + align:start position:0% +K and big be K so they're independent + + + align:start position:0% +K and big be K so they're independent +uniformly at random then the probability + + align:start position:0% +uniformly at random then the probability + + + align:start position:0% +uniformly at random then the probability +so basically I am putting down a + + align:start position:0% +so basically I am putting down a + + + align:start position:0% +so basically I am putting down a +potential image for each vertex of H and + + align:start position:0% +potential image for each vertex of H and + + + align:start position:0% +potential image for each vertex of H and +asking what's the probability that you + + align:start position:0% +asking what's the probability that you + + + align:start position:0% +asking what's the probability that you +actually have an embedding of H so the + + align:start position:0% +actually have an embedding of H so the + + + align:start position:0% +actually have an embedding of H so the +probability that little miracle VJ is an + + align:start position:0% +probability that little miracle VJ is an + + + align:start position:0% +probability that little miracle VJ is an +actual edge of G for all IJ being an + + align:start position:0% +actual edge of G for all IJ being an + + + align:start position:0% +actual edge of G for all IJ being an +edge of H this number here we're saying + + align:start position:0% +edge of H this number here we're saying + + + align:start position:0% +edge of H this number here we're saying +that it differs from the prediction + + align:start position:0% +that it differs from the prediction + + + align:start position:0% +that it differs from the prediction +which is simply multiplying all the edge + + align:start position:0% +which is simply multiplying all the edge + + + align:start position:0% +which is simply multiplying all the edge +densities together so the difference + + align:start position:0% +densities together so the difference + + + align:start position:0% +densities together so the difference +between the actual and the predicted + + align:start position:0% +between the actual and the predicted + + + align:start position:0% +between the actual and the predicted +values is fairly small so I haven't done + + align:start position:0% +values is fairly small so I haven't done + + + align:start position:0% +values is fairly small so I haven't done +anything just rephrasing the problem + + align:start position:0% +anything just rephrasing the problem + + + align:start position:0% +anything just rephrasing the problem +instead of counting now we're looking at + + align:start position:0% +instead of counting now we're looking at + + + align:start position:0% +instead of counting now we're looking at +probabilities as I mentioned we'll take + + align:start position:0% +probabilities as I mentioned we'll take + + + align:start position:0% +probabilities as I mentioned we'll take +out one edge at a time so we blabling if + + align:start position:0% +out one edge at a time so we blabling if + + + align:start position:0% +out one edge at a time so we blabling if +necessary let's assume that 1/2 is an + + align:start position:0% +necessary let's assume that 1/2 is an + + + align:start position:0% +necessary let's assume that 1/2 is an +edge of H so now we'll show the + + align:start position:0% +edge of H so now we'll show the + + + align:start position:0% +edge of H so now we'll show the +following claim so the note start that + + align:start position:0% +following claim so the note start that + + + align:start position:0% +following claim so the note start that +if you look at this quantity over here + + align:start position:0% + + + + align:start position:0% + +compared to if you take out just the + + align:start position:0% +compared to if you take out just the + + + align:start position:0% +compared to if you take out just the +edge density between v1 and v2 but now + + align:start position:0% +edge density between v1 and v2 but now + + + align:start position:0% +edge density between v1 and v2 but now +you put in a similar quantity where I'm + + align:start position:0% +you put in a similar quantity where I'm + + + align:start position:0% +you put in a similar quantity where I'm +considering all of the edges of H except + + align:start position:0% +considering all of the edges of H except + + + align:start position:0% +considering all of the edges of H except +for one two + + align:start position:0% + + + + align:start position:0% + +I claim that this difference is at most + + align:start position:0% +I claim that this difference is at most + + + align:start position:0% +I claim that this difference is at most +Epsilon + + align:start position:0% + + + + align:start position:0% + +so you can think of this quantity here + + align:start position:0% +so you can think of this quantity here + + + align:start position:0% +so you can think of this quantity here +as the same quantity as the green one + + align:start position:0% +as the same quantity as the green one + + + align:start position:0% +as the same quantity as the green one +except not on H but on H minus the edge + + align:start position:0% +except not on H but on H minus the edge + + + align:start position:0% +except not on H but on H minus the edge +want you to show this star claim + + align:start position:0% +want you to show this star claim + + + align:start position:0% +want you to show this star claim +let us couple the two random processes + + align:start position:0% +let us couple the two random processes + + + align:start position:0% +let us couple the two random processes +choosing these little V by that I mean + + align:start position:0% +choosing these little V by that I mean + + + align:start position:0% +choosing these little V by that I mean +here you have the random little V ice + + align:start position:0% +here you have the random little V ice + + + align:start position:0% +here you have the random little V ice +and here you have the random little V + + align:start position:0% +and here you have the random little V + + + align:start position:0% +and here you have the random little V +ice we use the same little V ice in both + + align:start position:0% +ice we use the same little V ice in both + + + align:start position:0% +ice we use the same little V ice in both +probabilities so in both there's two + + align:start position:0% +probabilities so in both there's two + + + align:start position:0% +probabilities so in both there's two +different random events but you use the + + align:start position:0% +different random events but you use the + + + align:start position:0% +different random events but you use the +same little V ice it suffices to show + + align:start position:0% + + + + align:start position:0% + +this inequality star with so what's this + + align:start position:0% +this inequality star with so what's this + + + align:start position:0% +this inequality star with so what's this +process this random process you pick the + + align:start position:0% +process this random process you pick the + + + align:start position:0% +process this random process you pick the +one you pick B 2 you pick these three + + align:start position:0% +one you pick B 2 you pick these three + + + align:start position:0% +one you pick B 2 you pick these three +all of them independently uniformly at + + align:start position:0% +all of them independently uniformly at + + + align:start position:0% +all of them independently uniformly at +random but if I show you the inequality + + align:start position:0% +random but if I show you the inequality + + + align:start position:0% +random but if I show you the inequality +under further constraint of arbitrary B + + align:start position:0% +under further constraint of arbitrary B + + + align:start position:0% +under further constraint of arbitrary B +3 through VN then that's even better + + align:start position:0% + + + + align:start position:0% + +so with B 3 through K fixed arbitrary + + align:start position:0% +so with B 3 through K fixed arbitrary + + + align:start position:0% +so with B 3 through K fixed arbitrary +and only little V 1 and little V 2 + + align:start position:0% +and only little V 1 and little V 2 + + + align:start position:0% +and only little V 1 and little V 2 +random ok so you can phrase this in + + align:start position:0% +random ok so you can phrase this in + + + align:start position:0% +random ok so you can phrase this in +terms of conditional probabilities if + + align:start position:0% +terms of conditional probabilities if + + + align:start position:0% +terms of conditional probabilities if +you like so you're comparing these two + + align:start position:0% +you like so you're comparing these two + + + align:start position:0% +you like so you're comparing these two +probabilities now I fix the VIII's + + align:start position:0% +probabilities now I fix the VIII's + + + align:start position:0% +probabilities now I fix the VIII's +through the case and just let B 1 and B + + align:start position:0% +through the case and just let B 1 and B + + + align:start position:0% +through the case and just let B 1 and B +2 be random and if conditioned on B 3 + + align:start position:0% +2 be random and if conditioned on B 3 + + + align:start position:0% +2 be random and if conditioned on B 3 +through VK you have this inequality then + + align:start position:0% +through VK you have this inequality then + + + align:start position:0% +through VK you have this inequality then +letting V 3 through VK go letting them + + align:start position:0% +letting V 3 through VK go letting them + + + align:start position:0% +letting V 3 through VK go letting them +be random as well by triangle inequality + + align:start position:0% +be random as well by triangle inequality + + + align:start position:0% +be random as well by triangle inequality +you obtain the bound that we're looking + + align:start position:0% +you obtain the bound that we're looking + + + align:start position:0% +you obtain the bound that we're looking +for any questions about this step if + + align:start position:0% +for any questions about this step if + + + align:start position:0% +for any questions about this step if +you're confused about what's happening + + align:start position:0% +you're confused about what's happening + + + align:start position:0% +you're confused about what's happening +here another way to bypass all the + + align:start position:0% +here another way to bypass all the + + + align:start position:0% +here another way to bypass all the +probability languages to go back to the + + align:start position:0% +probability languages to go back to the + + + align:start position:0% +probability languages to go back to the +counting language so in other words + + align:start position:0% +counting language so in other words + + + align:start position:0% +counting language so in other words +we're trying to count embeddings and I'm + + align:start position:0% +we're trying to count embeddings and I'm + + + align:start position:0% +we're trying to count embeddings and I'm +asking if you arbitrarily fix V 3 + + align:start position:0% +asking if you arbitrarily fix V 3 + + + align:start position:0% +asking if you arbitrarily fix V 3 +through VK how many different choices + + align:start position:0% +through VK how many different choices + + + align:start position:0% +through VK how many different choices +are there 2 V 1 and V 2 in the two + + align:start position:0% +are there 2 V 1 and V 2 in the two + + + align:start position:0% +are there 2 V 1 and V 2 in the two +different settings okay + + align:start position:0% +different settings okay + + + align:start position:0% +different settings okay +so let a 1 B the set of places where + + align:start position:0% +so let a 1 B the set of places where + + + align:start position:0% +so let a 1 B the set of places where +little V 1 can go if you already knew + + align:start position:0% +little V 1 can go if you already knew + + + align:start position:0% +little V 1 can go if you already knew +what the 3 through VK should be + + align:start position:0% + + + + align:start position:0% + +okay so you look at all the neighbors of + + align:start position:0% +okay so you look at all the neighbors of + + + align:start position:0% +okay so you look at all the neighbors of +V one neighbors a one in H except for + + align:start position:0% +V one neighbors a one in H except for + + + align:start position:0% +V one neighbors a one in H except for +two and I want to make sure that v1 VI + + align:start position:0% +two and I want to make sure that v1 VI + + + align:start position:0% +two and I want to make sure that v1 VI +high ranges over all such neighbors is + + align:start position:0% +high ranges over all such neighbors is + + + align:start position:0% +high ranges over all such neighbors is +indeed a valid edge in G I'll draw a + + align:start position:0% +indeed a valid edge in G I'll draw a + + + align:start position:0% +indeed a valid edge in G I'll draw a +picture in a second and a two + + align:start position:0% +picture in a second and a two + + + align:start position:0% +picture in a second and a two +likewise is the same quantity but was + + align:start position:0% +likewise is the same quantity but was + + + align:start position:0% +likewise is the same quantity but was +tuned instead of one so for example if + + align:start position:0% +tuned instead of one so for example if + + + align:start position:0% +tuned instead of one so for example if +you're in trying to embed a k4 what's + + align:start position:0% +you're in trying to embed a k4 what's + + + align:start position:0% +you're in trying to embed a k4 what's +happening here is that you have this v1 + + align:start position:0% +happening here is that you have this v1 + + + align:start position:0% +happening here is that you have this v1 +plus v2 and somebody already arbitrarily + + align:start position:0% +plus v2 and somebody already arbitrarily + + + align:start position:0% +plus v2 and somebody already arbitrarily +fixed the locations were v3 and v4 are + + align:start position:0% +fixed the locations were v3 and v4 are + + + align:start position:0% +fixed the locations were v3 and v4 are +embedded and you're asking well how many + + align:start position:0% +embedded and you're asking well how many + + + align:start position:0% +embedded and you're asking well how many +different choices are known now are now + + align:start position:0% +different choices are known now are now + + + align:start position:0% +different choices are known now are now +left for me one little v1 it's the + + align:start position:0% +left for me one little v1 it's the + + + align:start position:0% +left for me one little v1 it's the +common neighborhood of v3 and v4 so + + align:start position:0% +common neighborhood of v3 and v4 so + + + align:start position:0% +common neighborhood of v3 and v4 so +that's your a 1 and B 3 and B 4 also + + align:start position:0% +that's your a 1 and B 3 and B 4 also + + + align:start position:0% +that's your a 1 and B 3 and B 4 also +their common neighborhood in D 2 is 8 + + align:start position:0% + + + + align:start position:0% + +okay so with that notation what is is + + align:start position:0% +okay so with that notation what is is + + + align:start position:0% +okay so with that notation what is is +that we're trying to show over here so + + align:start position:0% +that we're trying to show over here so + + + align:start position:0% +that we're trying to show over here so +if you rewrite this inequality with the + + align:start position:0% +if you rewrite this inequality with the + + + align:start position:0% +if you rewrite this inequality with the +b3 through the case fixed you find that + + align:start position:0% +b3 through the case fixed you find that + + + align:start position:0% +b3 through the case fixed you find that +what we're trying to show is the + + align:start position:0% +what we're trying to show is the + + + align:start position:0% +what we're trying to show is the +following so we cling and the screen + + align:start position:0% +following so we cling and the screen + + + align:start position:0% +following so we cling and the screen +implies the start that if you look at + + align:start position:0% +implies the start that if you look at + + + align:start position:0% +implies the start that if you look at +what the first term should be so this is + + align:start position:0% +what the first term should be so this is + + + align:start position:0% +what the first term should be so this is +the number of edges between v1 and + + align:start position:0% +the number of edges between v1 and + + + align:start position:0% +the number of edges between v1 and +between a1 and a2 as a fraction of + + align:start position:0% +between a1 and a2 as a fraction of + + + align:start position:0% +between a1 and a2 as a fraction of +product of V 1 and V 2 and then the + + align:start position:0% +product of V 1 and V 2 and then the + + + align:start position:0% +product of V 1 and V 2 and then the +second guy here is if you take use the + + align:start position:0% +second guy here is if you take use the + + + align:start position:0% +second guy here is if you take use the +prediction D of V 1 and V 2 and so this + + align:start position:0% +prediction D of V 1 and V 2 and so this + + + align:start position:0% +prediction D of V 1 and V 2 and so this +is each of them each of these two + + align:start position:0% +is each of them each of these two + + + align:start position:0% +is each of them each of these two +factors is the probability that little V + + align:start position:0% +factors is the probability that little V + + + align:start position:0% +factors is the probability that little V +1 lies in a one little B tootle icing a2 + + align:start position:0% +1 lies in a one little B tootle icing a2 + + + align:start position:0% +1 lies in a one little B tootle icing a2 +and then you pack on this extra constant + + align:start position:0% +and then you pack on this extra constant + + + align:start position:0% +and then you pack on this extra constant +namely this constant yeah it's we're + + align:start position:0% +namely this constant yeah it's we're + + + align:start position:0% +namely this constant yeah it's we're +trying to show that this difference is + + align:start position:0% +trying to show that this difference is + + + align:start position:0% +trying to show that this difference is +small and the claim is that this + + align:start position:0% +small and the claim is that this + + + align:start position:0% +small and the claim is that this +difference is indeed always small it's + + align:start position:0% +difference is indeed always small it's + + + align:start position:0% +difference is indeed always small it's +always at most epsilon for every a 1 and + + align:start position:0% +always at most epsilon for every a 1 and + + + align:start position:0% +always at most epsilon for every a 1 and +V 1 and a 2 in v2 and here in particular + + align:start position:0% +V 1 and a 2 in v2 and here in particular + + + align:start position:0% +V 1 and a 2 in v2 and here in particular +so this statement looks somewhat like + + align:start position:0% +so this statement looks somewhat like + + + align:start position:0% +so this statement looks somewhat like +the definition of epsilon regularity but + + align:start position:0% +the definition of epsilon regularity but + + + align:start position:0% +the definition of epsilon regularity but +there's no restrictions on the sizes of + + align:start position:0% +there's no restrictions on the sizes of + + + align:start position:0% +there's no restrictions on the sizes of +a 1 and a 2 they don't have to be big + + align:start position:0% + + + + align:start position:0% + +and as you can imagine this statement + + align:start position:0% +and as you can imagine this statement + + + align:start position:0% +and as you can imagine this statement +we're not really using all that much + + align:start position:0% +we're not really using all that much + + + align:start position:0% +we're not really using all that much +we're only over assuming is the epsilon + + align:start position:0% +we're only over assuming is the epsilon + + + align:start position:0% +we're only over assuming is the epsilon +regularity between a 1 and between B 1 + + align:start position:0% +regularity between a 1 and between B 1 + + + align:start position:0% +regularity between a 1 and between B 1 +and B 2 so we won't reduce this + + align:start position:0% +and B 2 so we won't reduce this + + + align:start position:0% +and B 2 so we won't reduce this +inequality from the hypothesis of + + align:start position:0% +inequality from the hypothesis of + + + align:start position:0% +inequality from the hypothesis of +epsilon regularity between B 1 and B 2 + + align:start position:0% +epsilon regularity between B 1 and B 2 + + + align:start position:0% +epsilon regularity between B 1 and B 2 +so let's check okay so we know that B 1 + + align:start position:0% +so let's check okay so we know that B 1 + + + align:start position:0% +so let's check okay so we know that B 1 +and B 2 is epsilon regular by hypothesis + + align:start position:0% +and B 2 is epsilon regular by hypothesis + + + align:start position:0% +and B 2 is epsilon regular by hypothesis +so if either be either a 1 or V a 2 is + + align:start position:0% +so if either be either a 1 or V a 2 is + + + align:start position:0% +so if either be either a 1 or V a 2 is +too small right so if a 1 is too small + + align:start position:0% +too small right so if a 1 is too small + + + align:start position:0% +too small right so if a 1 is too small +or a 2 is too small then we see that + + align:start position:0% +or a 2 is too small then we see that + + + align:start position:0% +or a 2 is too small then we see that +both of these terms here are at most + + align:start position:0% +both of these terms here are at most + + + align:start position:0% +both of these terms here are at most +Epsilon + + align:start position:0% + + + + align:start position:0% + +so if the a so too small then neither of + + align:start position:0% +so if the a so too small then neither of + + + align:start position:0% +so if the a so too small then neither of +these terms can be too large here it's + + align:start position:0% +these terms can be too large here it's + + + align:start position:0% +these terms can be too large here it's +bounded by if you took a product of a1 + + align:start position:0% +bounded by if you took a product of a1 + + + align:start position:0% +bounded by if you took a product of a1 +and a2 and likewise over there so in + + align:start position:0% +and a2 and likewise over there so in + + + align:start position:0% +and a2 and likewise over there so in +this case their difference is that most + + align:start position:0% +this case their difference is that most + + + align:start position:0% +this case their difference is that most +Epsilon and we're critical otherwise if + + align:start position:0% +Epsilon and we're critical otherwise if + + + align:start position:0% +Epsilon and we're critical otherwise if +a1 and a2 are both at least an epsilon + + align:start position:0% +a1 and a2 are both at least an epsilon + + + align:start position:0% +a1 and a2 are both at least an epsilon +fraction of their mbn sets then we find + + align:start position:0% +fraction of their mbn sets then we find + + + align:start position:0% +fraction of their mbn sets then we find +that okay so what happens so here so by + + align:start position:0% +that okay so what happens so here so by + + + align:start position:0% +that okay so what happens so here so by +by the hypothesis of epsilon regularity + + align:start position:0% +by the hypothesis of epsilon regularity + + + align:start position:0% +by the hypothesis of epsilon regularity +we find that D of V 1 and V 2 differs + + align:start position:0% +we find that D of V 1 and V 2 differs + + + align:start position:0% +we find that D of V 1 and V 2 differs +from the number of edges between a1 and + + align:start position:0% +from the number of edges between a1 and + + + align:start position:0% +from the number of edges between a1 and +a2 divided by the product of their sizes + + align:start position:0% +a2 divided by the product of their sizes + + + align:start position:0% +a2 divided by the product of their sizes +so that's T of a1 and a2 so this + + align:start position:0% +so that's T of a1 and a2 so this + + + align:start position:0% +so that's T of a1 and a2 so this +difference is most epsilon which then + + align:start position:0% +difference is most epsilon which then + + + align:start position:0% +difference is most epsilon which then +implies the inequality up there so here + + align:start position:0% +implies the inequality up there so here + + + align:start position:0% +implies the inequality up there so here +we're using that size of a is at most + + align:start position:0% +we're using that size of a is at most + + + align:start position:0% +we're using that size of a is at most +the size of V + + align:start position:0% + + + + align:start position:0% + +all right so we have this claim and that + + align:start position:0% +all right so we have this claim and that + + + align:start position:0% +all right so we have this claim and that +claim proves this inequality in star and + + align:start position:0% +claim proves this inequality in star and + + + align:start position:0% +claim proves this inequality in star and +basically what we've done this we showed + + align:start position:0% +basically what we've done this we showed + + + align:start position:0% +basically what we've done this we showed +that if you took out a single edge you + + align:start position:0% +that if you took out a single edge you + + + align:start position:0% +that if you took out a single edge you +change the desired quantity by at most + + align:start position:0% +change the desired quantity by at most + + + align:start position:0% +change the desired quantity by at most +Epsilon essentially so now you do this + + align:start position:0% +Epsilon essentially so now you do this + + + align:start position:0% +Epsilon essentially so now you do this +for every edge of H alternatively you + + align:start position:0% +for every edge of H alternatively you + + + align:start position:0% +for every edge of H alternatively you +can do induction on the number of edges + + align:start position:0% +can do induction on the number of edges + + + align:start position:0% +can do induction on the number of edges +of H so to complete the proof of + + align:start position:0% +of H so to complete the proof of + + + align:start position:0% +of H so to complete the proof of +accounting memo okay so we do induction + + align:start position:0% + + + + align:start position:0% + +the number of edges of H and when H has + + align:start position:0% +the number of edges of H and when H has + + + align:start position:0% +the number of edges of H and when H has +exactly one edge that's pretty easy but + + align:start position:0% +exactly one edge that's pretty easy but + + + align:start position:0% +exactly one edge that's pretty easy but +now if you have more edges well you + + align:start position:0% +now if you have more edges well you + + + align:start position:0% +now if you have more edges well you +applied induction hypothesis to the + + align:start position:0% +applied induction hypothesis to the + + + align:start position:0% +applied induction hypothesis to the +graph which is H minus the h1 to and you + + align:start position:0% +graph which is H minus the h1 to and you + + + align:start position:0% +graph which is H minus the h1 to and you +find that this quantity here differs + + align:start position:0% +find that this quantity here differs + + + align:start position:0% +find that this quantity here differs +from + + align:start position:0% + + + + align:start position:0% + +the predicted quantity by the number of + + align:start position:0% +the predicted quantity by the number of + + + align:start position:0% +the predicted quantity by the number of +edges of H minus one times epsilon in + + align:start position:0% +edges of H minus one times epsilon in + + + align:start position:0% +edges of H minus one times epsilon in +other words you run this proof that we + + align:start position:0% +other words you run this proof that we + + + align:start position:0% +other words you run this proof that we +just did one edge at a time so each time + + align:start position:0% +just did one edge at a time so each time + + + align:start position:0% +just did one edge at a time so each time +you take out an edge you use epsilon + + align:start position:0% +you take out an edge you use epsilon + + + align:start position:0% +you take out an edge you use epsilon +regularity to show that the effect of + + align:start position:0% +regularity to show that the effect of + + + align:start position:0% +regularity to show that the effect of +taking that edge out from H does not + + align:start position:0% +taking that edge out from H does not + + + align:start position:0% +taking that edge out from H does not +have too big of an effect on the actual + + align:start position:0% +have too big of an effect on the actual + + + align:start position:0% +have too big of an effect on the actual +number of embeddings do this for one + + align:start position:0% +number of embeddings do this for one + + + align:start position:0% +number of embeddings do this for one +edge at a time and eventually you prove + + align:start position:0% +edge at a time and eventually you prove + + + align:start position:0% +edge at a time and eventually you prove +the graph counting them so this is one + + align:start position:0% +the graph counting them so this is one + + + align:start position:0% +the graph counting them so this is one +of those proofs which may be less + + align:start position:0% +of those proofs which may be less + + + align:start position:0% +of those proofs which may be less +intuitive compared to the one I showed + + align:start position:0% +intuitive compared to the one I showed + + + align:start position:0% +intuitive compared to the one I showed +earlier in the sense that you know + + align:start position:0% +earlier in the sense that you know + + + align:start position:0% +earlier in the sense that you know +there's not as nice of a story you can + + align:start position:0% +there's not as nice of a story you can + + + align:start position:0% +there's not as nice of a story you can +tell about putting in one vertex of time + + align:start position:0% +tell about putting in one vertex of time + + + align:start position:0% +tell about putting in one vertex of time +but on the other hand if you were to + + align:start position:0% +but on the other hand if you were to + + + align:start position:0% +but on the other hand if you were to +carry all this proof to bound each time + + align:start position:0% +carry all this proof to bound each time + + + align:start position:0% +carry all this proof to bound each time +how big this says have to be it gets + + align:start position:0% +how big this says have to be it gets + + + align:start position:0% +how big this says have to be it gets +much hairier over here and here the + + align:start position:0% +much hairier over here and here the + + + align:start position:0% +much hairier over here and here the +execution is much cleaner but maybe less + + align:start position:0% +execution is much cleaner but maybe less + + + align:start position:0% +execution is much cleaner but maybe less +intuitive unless you are willing to be + + align:start position:0% +intuitive unless you are willing to be + + + align:start position:0% +intuitive unless you are willing to be +comfortable with these calculations and + + align:start position:0% +comfortable with these calculations and + + + align:start position:0% +comfortable with these calculations and +it's really not so bad and the strength + + align:start position:0% +it's really not so bad and the strength + + + align:start position:0% +it's really not so bad and the strength +of these two results are somewhat + + align:start position:0% +of these two results are somewhat + + + align:start position:0% +of these two results are somewhat +different so again it's not so much the + + align:start position:0% +different so again it's not so much the + + + align:start position:0% +different so again it's not so much the +exact statements that matter but the + + align:start position:0% +exact statements that matter but the + + + align:start position:0% +exact statements that matter but the +spirit of these statements which is that + + align:start position:0% +spirit of these statements which is that + + + align:start position:0% +spirit of these statements which is that +if you have a bunch of epsilon regular + + align:start position:0% +if you have a bunch of epsilon regular + + + align:start position:0% +if you have a bunch of epsilon regular +pairs then you can embed and kind of + + align:start position:0% +pairs then you can embed and kind of + + + align:start position:0% +pairs then you can embed and kind of +pretending that everything behaved + + align:start position:0% +pretending that everything behaved + + + align:start position:0% +pretending that everything behaved +roughly like random questions + + align:start position:0% + + + + align:start position:0% + +all right so now we have some where this + + align:start position:0% +all right so now we have some where this + + + align:start position:0% +all right so now we have some where this +graph regularity lemma we have the graph + + align:start position:0% +graph regularity lemma we have the graph + + + align:start position:0% +graph regularity lemma we have the graph +counting lemma embedding llamas we can + + align:start position:0% +counting lemma embedding llamas we can + + + align:start position:0% +counting lemma embedding llamas we can +use it to derive some additional + + align:start position:0% +use it to derive some additional + + + align:start position:0% +use it to derive some additional +applications that don't just involve + + align:start position:0% +applications that don't just involve + + + align:start position:0% +applications that don't just involve +triangles so when we only had a triangle + + align:start position:0% +triangles so when we only had a triangle + + + align:start position:0% +triangles so when we only had a triangle +counting lemma we can only do the + + align:start position:0% +counting lemma we can only do the + + + align:start position:0% +counting lemma we can only do the +triangle removal lemma but now we can do + + align:start position:0% +triangle removal lemma but now we can do + + + align:start position:0% +triangle removal lemma but now we can do +other removal emma's so in particular + + align:start position:0% +other removal emma's so in particular + + + align:start position:0% +other removal emma's so in particular +there's the graph removal lemma which + + align:start position:0% +there's the graph removal lemma which + + + align:start position:0% +there's the graph removal lemma which +generalizes the triangle removal MO okay + + align:start position:0% +generalizes the triangle removal MO okay + + + align:start position:0% +generalizes the triangle removal MO okay +so in the graph removal lemma the + + align:start position:0% +so in the graph removal lemma the + + + align:start position:0% +so in the graph removal lemma the +statement is that for every H and + + align:start position:0% +statement is that for every H and + + + align:start position:0% +statement is that for every H and +epsilon there exists a delta such that + + align:start position:0% + + + + align:start position:0% + +every N vertex graph with fewer than + + align:start position:0% +every N vertex graph with fewer than + + + align:start position:0% +every N vertex graph with fewer than +Delta n to the vertex of H number of + + align:start position:0% +Delta n to the vertex of H number of + + + align:start position:0% +Delta n to the vertex of H number of +copies of H so has very few copies of H + + align:start position:0% +copies of H so has very few copies of H + + + align:start position:0% +copies of H so has very few copies of H +such graph can be made h3 by removing a + + align:start position:0% + + + + align:start position:0% + +fairly small number of edges or it's the + + align:start position:0% +fairly small number of edges or it's the + + + align:start position:0% +fairly small number of edges or it's the +same statement as the triangle removal + + align:start position:0% +same statement as the triangle removal + + + align:start position:0% +same statement as the triangle removal +Emma except now for general graph H and + + align:start position:0% +Emma except now for general graph H and + + + align:start position:0% +Emma except now for general graph H and +as you expect the proof is more or less + + align:start position:0% +as you expect the proof is more or less + + + align:start position:0% +as you expect the proof is more or less +the same as that of a triangle removal + + align:start position:0% +the same as that of a triangle removal + + + align:start position:0% +the same as that of a triangle removal +mo once we have the trial th counting + + align:start position:0% +mo once we have the trial th counting + + + align:start position:0% +mo once we have the trial th counting +lemma so let me remind you how this goes + + align:start position:0% +lemma so let me remind you how this goes + + + align:start position:0% +lemma so let me remind you how this goes +so it's really the same proof + + align:start position:0% + + + + align:start position:0% + +triangle removal where there was this + + align:start position:0% +triangle removal where there was this + + + align:start position:0% +triangle removal where there was this +recipe for applying the regularity lemma + + align:start position:0% +recipe for applying the regularity lemma + + + align:start position:0% +recipe for applying the regularity lemma +from last time so well it's a you first + + align:start position:0% + + + + align:start position:0% + +okay so what's the first step when you + + align:start position:0% +okay so what's the first step when you + + + align:start position:0% +okay so what's the first step when you +do regularity you partition so let's do + + align:start position:0% +do regularity you partition so let's do + + + align:start position:0% +do regularity you partition so let's do +partition + + align:start position:0% + + + + align:start position:0% + +okay so apply the regularity lemma to do + + align:start position:0% +okay so apply the regularity lemma to do + + + align:start position:0% +okay so apply the regularity lemma to do +partitioning and what's the second step + + align:start position:0% +partitioning and what's the second step + + + align:start position:0% +partitioning and what's the second step +okay so we clean this graph and you do + + align:start position:0% +okay so we clean this graph and you do + + + align:start position:0% +okay so we clean this graph and you do +the same cleaning procedure as in the + + align:start position:0% +the same cleaning procedure as in the + + + align:start position:0% +the same cleaning procedure as in the +triangle removal amount except maybe you + + align:start position:0% +triangle removal amount except maybe you + + + align:start position:0% +triangle removal amount except maybe you +have to adjust the parameter somewhat so + + align:start position:0% +have to adjust the parameter somewhat so + + + align:start position:0% +have to adjust the parameter somewhat so +remove edges remove no density pairs + + align:start position:0% + + + + align:start position:0% + +irregular pairs and small vertex s and + + align:start position:0% + + + + align:start position:0% + +the last step okay so what do we do now + + align:start position:0% +the last step okay so what do we do now + + + align:start position:0% +the last step okay so what do we do now +okay so you can count so if there were + + align:start position:0% +okay so you can count so if there were + + + align:start position:0% +okay so you can count so if there were +any H left then the counting lemma shows + + align:start position:0% +any H left then the counting lemma shows + + + align:start position:0% +any H left then the counting lemma shows +you that you must have lots of copies of + + align:start position:0% +you that you must have lots of copies of + + + align:start position:0% +you that you must have lots of copies of +H left okay so now let me show you how + + align:start position:0% +H left okay so now let me show you how + + + align:start position:0% +H left okay so now let me show you how +to use the strategy now that we have + + align:start position:0% +to use the strategy now that we have + + + align:start position:0% +to use the strategy now that we have +this general graph counting lemma will + + align:start position:0% +this general graph counting lemma will + + + align:start position:0% +this general graph counting lemma will +proof the error stone similar match + + align:start position:0% +proof the error stone similar match + + + align:start position:0% +proof the error stone similar match +theorem which we omitted the proof that + + align:start position:0% +theorem which we omitted the proof that + + + align:start position:0% +theorem which we omitted the proof that +we omitted from the first part of the + + align:start position:0% +we omitted from the first part of the + + + align:start position:0% +we omitted from the first part of the +course so remind you the errors stone + + align:start position:0% +course so remind you the errors stone + + + align:start position:0% +course so remind you the errors stone +romanovitch theorem says that if you + + align:start position:0% +romanovitch theorem says that if you + + + align:start position:0% +romanovitch theorem says that if you +have a graph H then the extremal number + + align:start position:0% +have a graph H then the extremal number + + + align:start position:0% +have a graph H then the extremal number +of H is equal to this quantity which + + align:start position:0% +of H is equal to this quantity which + + + align:start position:0% +of H is equal to this quantity which +depends only on the chromatic number of + + align:start position:0% +depends only on the chromatic number of + + + align:start position:0% +depends only on the chromatic number of +H + + align:start position:0% + + + + align:start position:0% + +the lower bound comes from taking the + + align:start position:0% +the lower bound comes from taking the + + + align:start position:0% +the lower bound comes from taking the +Turan graph you take the tour on graph + + align:start position:0% +Turan graph you take the tour on graph + + + align:start position:0% +Turan graph you take the tour on graph +you get this lower bound so it's really + + align:start position:0% +you get this lower bound so it's really + + + align:start position:0% +you get this lower bound so it's really +the upper bound that we need to think + + align:start position:0% +the upper bound that we need to think + + + align:start position:0% +the upper bound that we need to think +about all right so what's the strategy + + align:start position:0% +about all right so what's the strategy + + + align:start position:0% +about all right so what's the strategy +here the statement really is that if you + + align:start position:0% +here the statement really is that if you + + + align:start position:0% +here the statement really is that if you +have a graph G that's n vertex whose + + align:start position:0% +have a graph G that's n vertex whose + + + align:start position:0% +have a graph G that's n vertex whose +number of edges is at least that much + + align:start position:0% +number of edges is at least that much + + + align:start position:0% +number of edges is at least that much +okay so I fixed an epsilon bigger than 0 + + align:start position:0% +okay so I fixed an epsilon bigger than 0 + + + align:start position:0% +okay so I fixed an epsilon bigger than 0 +fix a positive epsilon so the claim what + + align:start position:0% +fix a positive epsilon so the claim what + + + align:start position:0% +fix a positive epsilon so the claim what +we're trying to show with Eddystone + + align:start position:0% +we're trying to show with Eddystone + + + align:start position:0% +we're trying to show with Eddystone +small image is that if you have a graph + + align:start position:0% +small image is that if you have a graph + + + align:start position:0% +small image is that if you have a graph +G with too many edges too many meaning + + align:start position:0% +G with too many edges too many meaning + + + align:start position:0% +G with too many edges too many meaning +this many edges then G contains a copy + + align:start position:0% +this many edges then G contains a copy + + + align:start position:0% +this many edges then G contains a copy +of H if n is sufficiently large okay so + + align:start position:0% +of H if n is sufficiently large okay so + + + align:start position:0% +of H if n is sufficiently large okay so +let's use the regularity method right so + + align:start position:0% +let's use the regularity method right so + + + align:start position:0% +let's use the regularity method right so +applying this three-step recipe first we + + align:start position:0% +applying this three-step recipe first we + + + align:start position:0% +applying this three-step recipe first we +partition so partition the vertex energy + + align:start position:0% +partition so partition the vertex energy + + + align:start position:0% +partition so partition the vertex energy +into and pieces and in such a way that + + align:start position:0% +into and pieces and in such a way that + + + align:start position:0% +into and pieces and in such a way that +it is 8 irregular and for some parameter + + align:start position:0% +it is 8 irregular and for some parameter + + + align:start position:0% +it is 8 irregular and for some parameter +theta that what decide later + + align:start position:0% + + + + align:start position:0% + +the second step is cleaning the cleaning + + align:start position:0% +the second step is cleaning the cleaning + + + align:start position:0% +the second step is cleaning the cleaning +step again the same kind of cleaning as + + align:start position:0% +step again the same kind of cleaning as + + + align:start position:0% +step again the same kind of cleaning as +we've done before so let's remove an + + align:start position:0% +we've done before so let's remove an + + + align:start position:0% +we've done before so let's remove an +edge from VI cross VJ if any of the + + align:start position:0% +edge from VI cross VJ if any of the + + + align:start position:0% +edge from VI cross VJ if any of the +following hope the VI VJ is not 8 + + align:start position:0% +following hope the VI VJ is not 8 + + + align:start position:0% +following hope the VI VJ is not 8 +irregular if the density is too small or + + align:start position:0% + + + + align:start position:0% + +either the two sets is too small so same + + align:start position:0% +either the two sets is too small so same + + + align:start position:0% +either the two sets is too small so same +cleaning as before and we can check that + + align:start position:0% +cleaning as before and we can check that + + + align:start position:0% +cleaning as before and we can check that +the number of edges removed is not too + + align:start position:0% +the number of edges removed is not too + + + align:start position:0% +the number of edges removed is not too +small so in the first case same + + align:start position:0% +small so in the first case same + + + align:start position:0% +small so in the first case same +calculation as last time in the same + + align:start position:0% +calculation as last time in the same + + + align:start position:0% +calculation as last time in the same +first case number of edges removed is + + align:start position:0% +first case number of edges removed is + + + align:start position:0% +first case number of edges removed is +that most eita and squared and we'll + + align:start position:0% +that most eita and squared and we'll + + + align:start position:0% +that most eita and squared and we'll +choose 8 huh to be less than epsilon + + align:start position:0% +choose 8 huh to be less than epsilon + + + align:start position:0% +choose 8 huh to be less than epsilon +over 8 actually significantly smaller as + + align:start position:0% +over 8 actually significantly smaller as + + + align:start position:0% +over 8 actually significantly smaller as +you will see in a second in the second + + align:start position:0% +you will see in a second in the second + + + align:start position:0% +you will see in a second in the second +step same as what happened in a triangle + + align:start position:0% +step same as what happened in a triangle + + + align:start position:0% +step same as what happened in a triangle +removal stage the number of edges + + align:start position:0% +removal stage the number of edges + + + align:start position:0% +removal stage the number of edges +removed in the second type is that most + + align:start position:0% +removed in the second type is that most + + + align:start position:0% +removed in the second type is that most +that amount still very small number and + + align:start position:0% +that amount still very small number and + + + align:start position:0% +that amount still very small number and +the third one here it's also a very + + align:start position:0% +the third one here it's also a very + + + align:start position:0% +the third one here it's also a very +small number so third type they start + + align:start position:0% +small number so third type they start + + + align:start position:0% +small number so third type they start +with one of these sets they're + + align:start position:0% +with one of these sets they're + + + align:start position:0% +with one of these sets they're +impossible ok so it's very small number + + align:start position:0% +impossible ok so it's very small number + + + align:start position:0% +impossible ok so it's very small number +and so the total + + align:start position:0% + + + + align:start position:0% + +yes and most an epsilon over 2 and + + align:start position:0% +yes and most an epsilon over 2 and + + + align:start position:0% +yes and most an epsilon over 2 and +squared okay so maybe I want epsilon + + align:start position:0% +squared okay so maybe I want epsilon + + + align:start position:0% +squared okay so maybe I want epsilon +over yeah so okay so let's say epsilon + + align:start position:0% +over yeah so okay so let's say epsilon + + + align:start position:0% +over yeah so okay so let's say epsilon +over 2 and squared number of edges like + + align:start position:0% +over 2 and squared number of edges like + + + align:start position:0% +over 2 and squared number of edges like +that be strictly okay so now after + + align:start position:0% +that be strictly okay so now after + + + align:start position:0% +that be strictly okay so now after +removing these edges from G we have this + + align:start position:0% +removing these edges from G we have this + + + align:start position:0% +removing these edges from G we have this +G prime which has strictly more than 1 + + align:start position:0% +G prime which has strictly more than 1 + + + align:start position:0% +G prime which has strictly more than 1 +minus 1 over R 1 1 minus 1 over R times + + align:start position:0% +minus 1 over R 1 1 minus 1 over R times + + + align:start position:0% +minus 1 over R 1 1 minus 1 over R times +and squared over 2 edges ok so now what + + align:start position:0% +and squared over 2 edges ok so now what + + + align:start position:0% +and squared over 2 edges ok so now what +do we do so we knew from Tehran's + + align:start position:0% +do we do so we knew from Tehran's + + + align:start position:0% +do we do so we knew from Tehran's +theorem that if your graph has strictly + + align:start position:0% +theorem that if your graph has strictly + + + align:start position:0% +theorem that if your graph has strictly +more than this number of edges you must + + align:start position:0% +more than this number of edges you must + + + align:start position:0% +more than this number of edges you must +have a K sub R plus 1 so even after the + + align:start position:0% +have a K sub R plus 1 so even after the + + + align:start position:0% +have a K sub R plus 1 so even after the +meeting all these edges G still G still + + align:start position:0% +meeting all these edges G still G still + + + align:start position:0% +meeting all these edges G still G still +has lots of edges left and in particular + + align:start position:0% +has lots of edges left and in particular + + + align:start position:0% +has lots of edges left and in particular +Terron theorem implies that G prime + + align:start position:0% +Terron theorem implies that G prime + + + align:start position:0% +Terron theorem implies that G prime +contains a click on our plus 1 vertices + + align:start position:0% +contains a click on our plus 1 vertices + + + align:start position:0% +contains a click on our plus 1 vertices +so here I should say that R is chromatic + + align:start position:0% +so here I should say that R is chromatic + + + align:start position:0% +so here I should say that R is chromatic +number of H minus 1 ok so I find one + + align:start position:0% +number of H minus 1 ok so I find one + + + align:start position:0% +number of H minus 1 ok so I find one +copy of this clique but what does that + + align:start position:0% +copy of this clique but what does that + + + align:start position:0% +copy of this clique but what does that +copy look like + + align:start position:0% +copy look like + + + align:start position:0% +copy look like +I find this one copy of a click let's + + align:start position:0% +I find this one copy of a click let's + + + align:start position:0% +I find this one copy of a click let's +say R equals to four and the point now + + align:start position:0% +say R equals to four and the point now + + + align:start position:0% +say R equals to four and the point now +is that the counting lemma will allow me + + align:start position:0% +is that the counting lemma will allow me + + + align:start position:0% +is that the counting lemma will allow me +to amplify that click into H so allow me + + align:start position:0% +to amplify that click into H so allow me + + + align:start position:0% +to amplify that click into H so allow me +to amplify this click into a copy of H + + align:start position:0% +to amplify this click into a copy of H + + + align:start position:0% +to amplify this click into a copy of H +so for example if H were this graph over + + align:start position:0% +so for example if H were this graph over + + + align:start position:0% +so for example if H were this graph over +here so then you would find a copy of H + + align:start position:0% +here so then you would find a copy of H + + + align:start position:0% +here so then you would find a copy of H +in G which is what we want so why does + + align:start position:0% +in G which is what we want so why does + + + align:start position:0% +in G which is what we want so why does +the counting lemma allow you to do this + + align:start position:0% +the counting lemma allow you to do this + + + align:start position:0% +the counting lemma allow you to do this +amplification so it's at this point the + + align:start position:0% +amplification so it's at this point the + + + align:start position:0% +amplification so it's at this point the +ideas are all there but there's there's + + align:start position:0% +ideas are all there but there's there's + + + align:start position:0% +ideas are all there but there's there's +a slight wrinkle in the calculations I + + align:start position:0% +a slight wrinkle in the calculations I + + + align:start position:0% +a slight wrinkle in the calculations I +mean there's in the executions I just + + align:start position:0% +mean there's in the executions I just + + + align:start position:0% +mean there's in the executions I just +want to point out just in case some of + + align:start position:0% +want to point out just in case some of + + + align:start position:0% +want to point out just in case some of +the vertices of H end up in the same + + align:start position:0% +the vertices of H end up in the same + + + align:start position:0% +the vertices of H end up in the same +vertex in G but that turns out not to be + + align:start position:0% +vertex in G but that turns out not to be + + + align:start position:0% +vertex in G but that turns out not to be +an issue so by counting lemma the number + + align:start position:0% +an issue so by counting lemma the number + + + align:start position:0% +an issue so by counting lemma the number +R comma morphisms from H to G prime + + align:start position:0% +R comma morphisms from H to G prime + + + align:start position:0% +R comma morphisms from H to G prime +where I'm really only considering + + align:start position:0% +where I'm really only considering + + + align:start position:0% +where I'm really only considering +homomorphisms that map each vertex and H + + align:start position:0% +homomorphisms that map each vertex and H + + + align:start position:0% +homomorphisms that map each vertex and H +2 is a sine part is at least this + + align:start position:0% +2 is a sine part is at least this + + + align:start position:0% +2 is a sine part is at least this +quantity where I'm looking at the + + align:start position:0% +quantity where I'm looking at the + + + align:start position:0% +quantity where I'm looking at the +predicted density of such homomorphisms + + align:start position:0% +predicted density of such homomorphisms + + + align:start position:0% +predicted density of such homomorphisms +and all of these edge densities are at + + align:start position:0% +and all of these edge densities are at + + + align:start position:0% +and all of these edge densities are at +least epsilon over 8 so it's at least + + align:start position:0% +least epsilon over 8 so it's at least + + + align:start position:0% +least epsilon over 8 so it's at least +that amount minus a small error that + + align:start position:0% +that amount minus a small error that + + + align:start position:0% +that amount minus a small error that +comes from the counting + + align:start position:0% + + + + align:start position:0% + +and well all of the vertex parts are + + align:start position:0% +and well all of the vertex parts are + + + align:start position:0% +and well all of the vertex parts are +quite large so all of the vertex parts + + align:start position:0% +quite large so all of the vertex parts + + + align:start position:0% +quite large so all of the vertex parts +are of size like that so that's the + + align:start position:0% +are of size like that so that's the + + + align:start position:0% +are of size like that so that's the +result of the counting lemma combined + + align:start position:0% +result of the counting lemma combined + + + align:start position:0% +result of the counting lemma combined +with information about the densities of + + align:start position:0% +with information about the densities of + + + align:start position:0% +with information about the densities of +the parts and the sizes of the parts + + align:start position:0% +the parts and the sizes of the parts + + + align:start position:0% +the parts and the sizes of the parts +that came out of cleaning so setting + + align:start position:0% +that came out of cleaning so setting + + + align:start position:0% +that came out of cleaning so setting +eita + + align:start position:0% +eita + + + align:start position:0% +eita +to be an appropriate value we see that + + align:start position:0% +to be an appropriate value we see that + + + align:start position:0% +to be an appropriate value we see that +for sufficiently large and this quantity + + align:start position:0% +for sufficiently large and this quantity + + + align:start position:0% +for sufficiently large and this quantity +here is on the order of and - the number + + align:start position:0% +here is on the order of and - the number + + + align:start position:0% +here is on the order of and - the number +of vertices of H but I'm only counting + + align:start position:0% +of vertices of H but I'm only counting + + + align:start position:0% +of vertices of H but I'm only counting +homomorphisms and so it could be that + + align:start position:0% +homomorphisms and so it could be that + + + align:start position:0% +homomorphisms and so it could be that +some of the vertices of H end up in the + + align:start position:0% +some of the vertices of H end up in the + + + align:start position:0% +some of the vertices of H end up in the +same vertex of G and those would not be + + align:start position:0% +same vertex of G and those would not be + + + align:start position:0% +same vertex of G and those would not be +genuine sub graphs so I shouldn't + + align:start position:0% +genuine sub graphs so I shouldn't + + + align:start position:0% +genuine sub graphs so I shouldn't +consider those as sub graphs because + + align:start position:0% +consider those as sub graphs because + + + align:start position:0% +consider those as sub graphs because +otherwise if you were to allow those + + align:start position:0% +otherwise if you were to allow those + + + align:start position:0% +otherwise if you were to allow those +then if you found this k4 then you found + + align:start position:0% +then if you found this k4 then you found + + + align:start position:0% +then if you found this k4 then you found +all four chromatic graphs so you + + align:start position:0% +all four chromatic graphs so you + + + align:start position:0% +all four chromatic graphs so you +shouldn't consider copies that are + + align:start position:0% +shouldn't consider copies that are + + + align:start position:0% +shouldn't consider copies that are +degenerate but that's okay because the + + align:start position:0% +degenerate but that's okay because the + + + align:start position:0% +degenerate but that's okay because the +number of maps from the vertex set of H + + align:start position:0% +number of maps from the vertex set of H + + + align:start position:0% +number of maps from the vertex set of H +to the vertex set of G that are non + + align:start position:0% +to the vertex set of G that are non + + + align:start position:0% +to the vertex set of G that are non +injective is of a lower water the number + + align:start position:0% +injective is of a lower water the number + + + align:start position:0% +injective is of a lower water the number +of non injective maps from the vertex + + align:start position:0% +of non injective maps from the vertex + + + align:start position:0% +of non injective maps from the vertex +set well you have to pick two vertices + + align:start position:0% +set well you have to pick two vertices + + + align:start position:0% +set well you have to pick two vertices +of H to map to the same vertex and then + + align:start position:0% +of H to map to the same vertex and then + + + align:start position:0% +of H to map to the same vertex and then +the number of choices you have one order + + align:start position:0% +the number of choices you have one order + + + align:start position:0% +the number of choices you have one order +less so there are a negligible fraction + + align:start position:0% +less so there are a negligible fraction + + + align:start position:0% +less so there are a negligible fraction +of these homomorphisms and the + + align:start position:0% +of these homomorphisms and the + + + align:start position:0% +of these homomorphisms and the +conclusion then is that G prime contains + + align:start position:0% +conclusion then is that G prime contains + + + align:start position:0% +conclusion then is that G prime contains +a copy of H which is what we're looking + + align:start position:0% +a copy of H which is what we're looking + + + align:start position:0% +a copy of H which is what we're looking +for G prime contains copy of H then G + + align:start position:0% +for G prime contains copy of H then G + + + align:start position:0% +for G prime contains copy of H then G +contains a copy of H and that + + align:start position:0% +contains a copy of H and that + + + align:start position:0% +contains a copy of H and that +the area stone Shimano veteran you get a + + align:start position:0% +the area stone Shimano veteran you get a + + + align:start position:0% +the area stone Shimano veteran you get a +bit more out of this proof so you see + + align:start position:0% +bit more out of this proof so you see + + + align:start position:0% +bit more out of this proof so you see +that not only does G contain one copy of + + align:start position:0% +that not only does G contain one copy of + + + align:start position:0% +that not only does G contain one copy of +H but the counting lemma actually shows + + align:start position:0% +H but the counting lemma actually shows + + + align:start position:0% +H but the counting lemma actually shows +you it contains many copies of H and + + align:start position:0% +you it contains many copies of H and + + + align:start position:0% +you it contains many copies of H and +this is a phenomenon known as super + + align:start position:0% +this is a phenomenon known as super + + + align:start position:0% +this is a phenomenon known as super +saturation which you already saw in the + + align:start position:0% +saturation which you already saw in the + + + align:start position:0% +saturation which you already saw in the +first problem set that often when you + + align:start position:0% +first problem set that often when you + + + align:start position:0% +first problem set that often when you +are beyond a certain threshold an + + align:start position:0% +are beyond a certain threshold an + + + align:start position:0% +are beyond a certain threshold an +extremal threshold you don't just gain + + align:start position:0% +extremal threshold you don't just gain + + + align:start position:0% +extremal threshold you don't just gain +one extra copy but you often gain many + + align:start position:0% +one extra copy but you often gain many + + + align:start position:0% +one extra copy but you often gain many +copies and it's you see this in this + + align:start position:0% +copies and it's you see this in this + + + align:start position:0% +copies and it's you see this in this +proof here okay so to summarize we've + + align:start position:0% +proof here okay so to summarize we've + + + align:start position:0% +proof here okay so to summarize we've +seen this proof of errors strong Chimel + + align:start position:0% +seen this proof of errors strong Chimel + + + align:start position:0% +seen this proof of errors strong Chimel +image which comes from applying + + align:start position:0% +image which comes from applying + + + align:start position:0% +image which comes from applying +regularity and then finding a single + + align:start position:0% +regularity and then finding a single + + + align:start position:0% +regularity and then finding a single +copy of a clique from Tehran's theorem + + align:start position:0% +copy of a clique from Tehran's theorem + + + align:start position:0% +copy of a clique from Tehran's theorem +and then using counting lemma to boost + + align:start position:0% +and then using counting lemma to boost + + + align:start position:0% +and then using counting lemma to boost +that copy from Tehran's theorem into an + + align:start position:0% +that copy from Tehran's theorem into an + + + align:start position:0% +that copy from Tehran's theorem into an +actual copy of H so in the second + + align:start position:0% +actual copy of H so in the second + + + align:start position:0% +actual copy of H so in the second +homework one of the problems is to come + + align:start position:0% +homework one of the problems is to come + + + align:start position:0% +homework one of the problems is to come +up with a different proof of Adderstone + + align:start position:0% +up with a different proof of Adderstone + + + align:start position:0% +up with a different proof of Adderstone +small image that is more similar to the + + align:start position:0% +small image that is more similar to the + + + align:start position:0% +small image that is more similar to the +proof of cavora shorter on more through + + align:start position:0% +proof of cavora shorter on more through + + + align:start position:0% +proof of cavora shorter on more through +double counting like arguments and that + + align:start position:0% +double counting like arguments and that + + + align:start position:0% +double counting like arguments and that +is closer in spirit although not exactly + + align:start position:0% +is closer in spirit although not exactly + + + align:start position:0% +is closer in spirit although not exactly +the same as the original proof in stone + + align:start position:0% +the same as the original proof in stone + + + align:start position:0% +the same as the original proof in stone +so this regularity proof I think it's + + align:start position:0% +so this regularity proof I think it's + + + align:start position:0% +so this regularity proof I think it's +more conceptual you get to see how to do + + align:start position:0% +more conceptual you get to see how to do + + + align:start position:0% +more conceptual you get to see how to do +this boosting but it gives you a + + align:start position:0% +this boosting but it gives you a + + + align:start position:0% +this boosting but it gives you a +terrible bound and the other proof that + + align:start position:0% +terrible bound and the other proof that + + + align:start position:0% +terrible bound and the other proof that +you see in the homework gives you a much + + align:start position:0% +you see in the homework gives you a much + + + align:start position:0% +you see in the homework gives you a much +more reasonable bound on the dependence + + align:start position:0% +more reasonable bound on the dependence + + + align:start position:0% +more reasonable bound on the dependence +between how engross versus how quickly + + align:start position:0% +between how engross versus how quickly + + + align:start position:0% +between how engross versus how quickly +this little ol has to go to zero \ No newline at end of file diff --git a/oyU5uvPqzkE.txt b/oyU5uvPqzkE.txt new file mode 100644 index 0000000000000000000000000000000000000000..2a6b08bd3acab500b053f9df0d29388df3ad6dbb --- /dev/null +++ b/oyU5uvPqzkE.txt @@ -0,0 +1,2979 @@ +align:start position:0% + +so here is a problem example based on + + align:start position:0% +so here is a problem example based on + + + align:start position:0% +so here is a problem example based on +Griffiths from 9.3 so it's a two-state + + align:start position:0% +Griffiths from 9.3 so it's a two-state + + + align:start position:0% +Griffiths from 9.3 so it's a two-state +system system and we'll call it the + + align:start position:0% +system system and we'll call it the + + + align:start position:0% +system system and we'll call it the +states a and B with energies EA and EB + + align:start position:0% +states a and B with energies EA and EB + + + align:start position:0% +states a and B with energies EA and EB +and we'll call Omega zero the difference + + align:start position:0% +and we'll call Omega zero the difference + + + align:start position:0% +and we'll call Omega zero the difference +EA minus EB over h-bar so those are + + align:start position:0% +EA minus EB over h-bar so those are + + + align:start position:0% +EA minus EB over h-bar so those are +energy eigenstates which means that h0 + + align:start position:0% +energy eigenstates which means that h0 + + + align:start position:0% +energy eigenstates which means that h0 +is really a EB we represent the first + + align:start position:0% +is really a EB we represent the first + + + align:start position:0% +is really a EB we represent the first +column vector by the state a the second + + align:start position:0% +column vector by the state a the second + + + align:start position:0% +column vector by the state a the second +state is the second column vector with + + align:start position:0% +state is the second column vector with + + + align:start position:0% +state is the second column vector with +entries 0 on one is the state B that's + + align:start position:0% +entries 0 on one is the state B that's + + + align:start position:0% +entries 0 on one is the state B that's +why the matrix looks like that + + align:start position:0% +why the matrix looks like that + + + align:start position:0% +why the matrix looks like that +and then you put a perturbation and the + + align:start position:0% +and then you put a perturbation and the + + + align:start position:0% +and then you put a perturbation and the +perturbation Delta H is going to take + + align:start position:0% +perturbation Delta H is going to take + + + align:start position:0% +perturbation Delta H is going to take +the form u delta T where u is a matrix + + align:start position:0% +the form u delta T where u is a matrix + + + align:start position:0% +the form u delta T where u is a matrix +that has you a a you a B you be a you'll + + align:start position:0% +that has you a a you a B you be a you'll + + + align:start position:0% +that has you a a you a B you be a you'll +be B the matrix elements and they're + + align:start position:0% +be B the matrix elements and they're + + + align:start position:0% +be B the matrix elements and they're +simple enough it's a 0 here and an alpha + + align:start position:0% +simple enough it's a 0 here and an alpha + + + align:start position:0% +simple enough it's a 0 here and an alpha +here and an alpha + + align:start position:0% +here and an alpha + + + align:start position:0% +here and an alpha +diagur here should be a hermitian matrix + + align:start position:0% +diagur here should be a hermitian matrix + + + align:start position:0% +diagur here should be a hermitian matrix +and that's the way it is the letter U I + + align:start position:0% +and that's the way it is the letter U I + + + align:start position:0% +and that's the way it is the letter U I +guess is not great we would suggest + + align:start position:0% +guess is not great we would suggest + + + align:start position:0% +guess is not great we would suggest +unitary but maybe I should be I'll leave + + align:start position:0% +unitary but maybe I should be I'll leave + + + align:start position:0% +unitary but maybe I should be I'll leave +it + + align:start position:0% +it + + + align:start position:0% +it +not create problems with my imitation so + + align:start position:0% +not create problems with my imitation so + + + align:start position:0% +not create problems with my imitation so +here is the question this is your + + align:start position:0% +here is the question this is your + + + align:start position:0% +here is the question this is your +perturbation Hamiltonian actually I + + align:start position:0% +perturbation Hamiltonian actually I + + + align:start position:0% +perturbation Hamiltonian actually I +wrote it wrong here it's a delta + + align:start position:0% +wrote it wrong here it's a delta + + + align:start position:0% +wrote it wrong here it's a delta +function of T that's Delta H so in terms + + align:start position:0% +function of T that's Delta H so in terms + + + align:start position:0% +function of T that's Delta H so in terms +of H zero applies everywhere H zero + + align:start position:0% +of H zero applies everywhere H zero + + + align:start position:0% +of H zero applies everywhere H zero +applies everywhere and in the middle + + align:start position:0% +applies everywhere and in the middle + + + align:start position:0% +applies everywhere and in the middle +there is a delta H for one little + + align:start position:0% +there is a delta H for one little + + + align:start position:0% +there is a delta H for one little +instant so what happens here we're going + + align:start position:0% +instant so what happens here we're going + + + align:start position:0% +instant so what happens here we're going +to try to figure out what's going on but + + align:start position:0% +to try to figure out what's going on but + + + align:start position:0% +to try to figure out what's going on but +the question will be posed as follows + + align:start position:0% +the question will be posed as follows + + + align:start position:0% +the question will be posed as follows +assume the system is in the state a for + + align:start position:0% +assume the system is in the state a for + + + align:start position:0% +assume the system is in the state a for +T less than 0 what is let's have the + + align:start position:0% +T less than 0 what is let's have the + + + align:start position:0% +T less than 0 what is let's have the +probability to be in the state B for T + + align:start position:0% +probability to be in the state B for T + + + align:start position:0% +probability to be in the state B for T +greater than zero + + align:start position:0% + + + + align:start position:0% + +find the probability find the + + align:start position:0% +find the probability find the + + + align:start position:0% +find the probability find the +probability to be and B greater than + + align:start position:0% +probability to be and B greater than + + + align:start position:0% +probability to be and B greater than +zero so what's going on here are the + + align:start position:0% +zero so what's going on here are the + + + align:start position:0% +zero so what's going on here are the +states a and B there were isin states of + + align:start position:0% +states a and B there were isin states of + + + align:start position:0% +states a and B there were isin states of +H zero if you had the system in the + + align:start position:0% +H zero if you had the system in the + + + align:start position:0% +H zero if you had the system in the +state a that's an energy eigenstate it + + align:start position:0% +state a that's an energy eigenstate it + + + align:start position:0% +state a that's an energy eigenstate it +would stay in the state a forever + + align:start position:0% +would stay in the state a forever + + + align:start position:0% +would stay in the state a forever +wouldn't do anything indeed if whoever + + align:start position:0% +wouldn't do anything indeed if whoever + + + align:start position:0% +wouldn't do anything indeed if whoever +prepared that state ever since he or she + + align:start position:0% +prepared that state ever since he or she + + + align:start position:0% +prepared that state ever since he or she +prepared it it has stayed in the state a + + align:start position:0% +prepared it it has stayed in the state a + + + align:start position:0% +prepared it it has stayed in the state a +until time equals zero but then the + + align:start position:0% +until time equals zero but then the + + + align:start position:0% +until time equals zero but then the +system is kicked and it's caked with + + align:start position:0% +system is kicked and it's caked with + + + align:start position:0% +system is kicked and it's caked with +some Delta function strength and in the + + align:start position:0% +some Delta function strength and in the + + + align:start position:0% +some Delta function strength and in the +off-diagonal terms that's pretty + + align:start position:0% +off-diagonal terms that's pretty + + + align:start position:0% +off-diagonal terms that's pretty +important it's not kicked on the + + align:start position:0% +important it's not kicked on the + + + align:start position:0% +important it's not kicked on the +diagonal terms kicked here so this term + + align:start position:0% +diagonal terms kicked here so this term + + + align:start position:0% +diagonal terms kicked here so this term +suggests the transition + + align:start position:0% +suggests the transition + + + align:start position:0% +suggests the transition +from state a to be here and presumably + + align:start position:0% +from state a to be here and presumably + + + align:start position:0% +from state a to be here and presumably +due to this the system will transition + + align:start position:0% +due to this the system will transition + + + align:start position:0% +due to this the system will transition +and when it transitions + + align:start position:0% +and when it transitions + + + align:start position:0% +and when it transitions +it must transition instantaneously in a + + align:start position:0% +it must transition instantaneously in a + + + align:start position:0% +it must transition instantaneously in a +sense because if it takes time to + + align:start position:0% +sense because if it takes time to + + + align:start position:0% +sense because if it takes time to +transition the Delta function asks for + + align:start position:0% +transition the Delta function asks for + + + align:start position:0% +transition the Delta function asks for +zero time if it takes time to transition + + align:start position:0% +zero time if it takes time to transition + + + align:start position:0% +zero time if it takes time to transition +and it would not transition because + + align:start position:0% +and it would not transition because + + + align:start position:0% +and it would not transition because +after the Delta function has come and + + align:start position:0% +after the Delta function has come and + + + align:start position:0% +after the Delta function has come and +gone the system doesn't change anymore + + align:start position:0% +gone the system doesn't change anymore + + + align:start position:0% +gone the system doesn't change anymore +so it really has to transition + + align:start position:0% +so it really has to transition + + + align:start position:0% +so it really has to transition +instantaneously so at time equals zero + + align:start position:0% +instantaneously so at time equals zero + + + align:start position:0% +instantaneously so at time equals zero +you must generate a probability or an + + align:start position:0% +you must generate a probability or an + + + align:start position:0% +you must generate a probability or an +amplitude to be in the state B already + + align:start position:0% +amplitude to be in the state B already + + + align:start position:0% +amplitude to be in the state B already +so there must be an immediate transition + + align:start position:0% +so there must be an immediate transition + + + align:start position:0% +so there must be an immediate transition +in which the state originally at time + + align:start position:0% +in which the state originally at time + + + align:start position:0% +in which the state originally at time +less than zero was the state a but at + + align:start position:0% +less than zero was the state a but at + + + align:start position:0% +less than zero was the state a but at +time a little bit after zero must be a + + align:start position:0% +time a little bit after zero must be a + + + align:start position:0% +time a little bit after zero must be a +little bit of a plus a little bit of B + + align:start position:0% +little bit of a plus a little bit of B + + + align:start position:0% +little bit of a plus a little bit of B +so this is 3 0 minus 0 minus and 0 plus + + align:start position:0% +so this is 3 0 minus 0 minus and 0 plus + + + align:start position:0% +so this is 3 0 minus 0 minus and 0 plus +at 0 minus is a and that 0 plus must be + + align:start position:0% +at 0 minus is a and that 0 plus must be + + + align:start position:0% +at 0 minus is a and that 0 plus must be +something like that because if at 0 plus + + align:start position:0% +something like that because if at 0 plus + + + align:start position:0% +something like that because if at 0 plus +is still a it's going to stay a forever + + align:start position:0% +is still a it's going to stay a forever + + + align:start position:0% +is still a it's going to stay a forever +so there must have some amplitude to be + + align:start position:0% +so there must have some amplitude to be + + + align:start position:0% +so there must have some amplitude to be +at me at 0 plus so you're having your + + align:start position:0% +at me at 0 plus so you're having your + + + align:start position:0% +at me at 0 plus so you're having your +first transition amplitude problem how + + align:start position:0% +first transition amplitude problem how + + + align:start position:0% +first transition amplitude problem how +does an interaction make you jump from + + align:start position:0% +does an interaction make you jump from + + + align:start position:0% +does an interaction make you jump from +one state to another now my letters here + + align:start position:0% +one state to another now my letters here + + + align:start position:0% +one state to another now my letters here +alpha and beta are pretty bad U and V + + align:start position:0% +alpha and beta are pretty bad U and V + + + align:start position:0% +alpha and beta are pretty bad U and V +maybe because I have an alpha where in + + align:start position:0% +maybe because I have an alpha where in + + + align:start position:0% +maybe because I have an alpha where in +the interaction and maybe if you think + + align:start position:0% +the interaction and maybe if you think + + + align:start position:0% +the interaction and maybe if you think +perturbatively you would say look if + + align:start position:0% +perturbatively you would say look if + + + align:start position:0% +perturbatively you would say look if +alpha is very small there must be a + + align:start position:0% +alpha is very small there must be a + + + align:start position:0% +alpha is very small there must be a +small transition + + align:start position:0% +small transition + + + align:start position:0% +small transition +if the perturbation is of order alpha + + align:start position:0% +if the perturbation is of order alpha + + + align:start position:0% +if the perturbation is of order alpha +maybe I expect the perturbed state to be + + align:start position:0% +maybe I expect the perturbed state to be + + + align:start position:0% +maybe I expect the perturbed state to be +of order alpha so maybe after all this + + align:start position:0% +of order alpha so maybe after all this + + + align:start position:0% +of order alpha so maybe after all this +is like alpha times B or proportional to + + align:start position:0% +is like alpha times B or proportional to + + + align:start position:0% +is like alpha times B or proportional to +alpha times B a number here and this one + + align:start position:0% +alpha times B a number here and this one + + + align:start position:0% +alpha times B a number here and this one +well if alpha is very small + + align:start position:0% +well if alpha is very small + + + align:start position:0% +well if alpha is very small +that's probably roughly about one still + + align:start position:0% +that's probably roughly about one still + + + align:start position:0% +that's probably roughly about one still +a little bit less alpha squared less for + + align:start position:0% +a little bit less alpha squared less for + + + align:start position:0% +a little bit less alpha squared less for +probability conservation but I expect an + + align:start position:0% +probability conservation but I expect an + + + align:start position:0% +probability conservation but I expect an +alpha B here so okay with you given a + + align:start position:0% +alpha B here so okay with you given a + + + align:start position:0% +alpha B here so okay with you given a +problem like that under normal + + align:start position:0% +problem like that under normal + + + align:start position:0% +problem like that under normal +conditions it's a good idea to think + + align:start position:0% +conditions it's a good idea to think + + + align:start position:0% +conditions it's a good idea to think +about it before trying to solve it and I + + align:start position:0% +about it before trying to solve it and I + + + align:start position:0% +about it before trying to solve it and I +think we've done a little bit of + + align:start position:0% +think we've done a little bit of + + + align:start position:0% +think we've done a little bit of +thinking we've realized the state stays + + align:start position:0% +thinking we've realized the state stays + + + align:start position:0% +thinking we've realized the state stays +in a after a while and immediately must + + align:start position:0% +in a after a while and immediately must + + + align:start position:0% +in a after a while and immediately must +transition into some other state and + + align:start position:0% +transition into some other state and + + + align:start position:0% +transition into some other state and +once it's in that other state is going + + align:start position:0% +once it's in that other state is going + + + align:start position:0% +once it's in that other state is going +to remain in that state forever because + + align:start position:0% +to remain in that state forever because + + + align:start position:0% +to remain in that state forever because +those are energy eigenstates so you're + + align:start position:0% +those are energy eigenstates so you're + + + align:start position:0% +those are energy eigenstates so you're +gonna get Exponential's of e to the + + align:start position:0% +gonna get Exponential's of e to the + + + align:start position:0% +gonna get Exponential's of e to the +minus IET but this is gonna be that + + align:start position:0% +minus IET but this is gonna be that + + + align:start position:0% +minus IET but this is gonna be that +okay so let's solve this here is our + + align:start position:0% +okay so let's solve this here is our + + + align:start position:0% +okay so let's solve this here is our +equation let's try to write it for this + + align:start position:0% +equation let's try to write it for this + + + align:start position:0% +equation let's try to write it for this +case so I would have I h-bar see a dot + + align:start position:0% +case so I would have I h-bar see a dot + + + align:start position:0% +case so I would have I h-bar see a dot +of T we have two states one and two but + + align:start position:0% +of T we have two states one and two but + + + align:start position:0% +of T we have two states one and two but +here is a and B so you have I Omega a of + + align:start position:0% +here is a and B so you have I Omega a of + + + align:start position:0% +here is a and B so you have I Omega a of +something T and Delta H a with something + + align:start position:0% +something T and Delta H a with something + + + align:start position:0% +something T and Delta H a with something +well the Delta H is clear that it can + + align:start position:0% +well the Delta H is clear that it can + + + align:start position:0% +well the Delta H is clear that it can +only be a Delta H from A to B because + + align:start position:0% +only be a Delta H from A to B because + + + align:start position:0% +only be a Delta H from A to B because +there's you a B there's only that + + align:start position:0% +there's you a B there's only that + + + align:start position:0% +there's you a B there's only that +transition amplitude and then it would + + align:start position:0% +transition amplitude and then it would + + + align:start position:0% +transition amplitude and then it would +be an I Omega a B quit + + align:start position:0% +be an I Omega a B quit + + + align:start position:0% +be an I Omega a B quit +was defined as Omega zero Delta H a B of + + align:start position:0% +was defined as Omega zero Delta H a B of + + + align:start position:0% +was defined as Omega zero Delta H a B of +time CB of time and that's the only term + + align:start position:0% +time CB of time and that's the only term + + + align:start position:0% +time CB of time and that's the only term +that exists here from the difference + + align:start position:0% +that exists here from the difference + + + align:start position:0% +that exists here from the difference +from the sum you could sum over a and B + + align:start position:0% +from the sum you could sum over a and B + + + align:start position:0% +from the sum you could sum over a and B +but we saw that over a you get zero so + + align:start position:0% +but we saw that over a you get zero so + + + align:start position:0% +but we saw that over a you get zero so +this is just this term and then we have + + align:start position:0% +this is just this term and then we have + + + align:start position:0% +this is just this term and then we have +I h-bar C B dot of T is equal to e to + + align:start position:0% +I h-bar C B dot of T is equal to e to + + + align:start position:0% +I h-bar C B dot of T is equal to e to +the I and now you're going to have B a + + align:start position:0% +the I and now you're going to have B a + + + align:start position:0% +the I and now you're going to have B a +so Delta H be a of T C a of T and here I + + align:start position:0% +so Delta H be a of T C a of T and here I + + + align:start position:0% +so Delta H be a of T C a of T and here I +would have Omega be a which is the + + align:start position:0% +would have Omega be a which is the + + + align:start position:0% +would have Omega be a which is the +opposite sign as Omega a B which we + + align:start position:0% +opposite sign as Omega a B which we + + + align:start position:0% +opposite sign as Omega a B which we +anyway call Omega zero so here is minus + + align:start position:0% +anyway call Omega zero so here is minus + + + align:start position:0% +anyway call Omega zero so here is minus +I Omega 0 T yes sorry + + align:start position:0% +I Omega 0 T yes sorry + + + align:start position:0% +I Omega 0 T yes sorry +right because Delta H a a is equal to 0 + + align:start position:0% +right because Delta H a a is equal to 0 + + + align:start position:0% +right because Delta H a a is equal to 0 +and therefore there's no coupling to C a + + align:start position:0% +and therefore there's no coupling to C a + + + align:start position:0% +and therefore there's no coupling to C a +and Delta H B is zero from that matrix + + align:start position:0% +and Delta H B is zero from that matrix + + + align:start position:0% +and Delta H B is zero from that matrix +element and therefore you cannot couple + + align:start position:0% +element and therefore you cannot couple + + + align:start position:0% +element and therefore you cannot couple +B to B and now I'll just write it I + + align:start position:0% +B to B and now I'll just write it I + + + align:start position:0% +B to B and now I'll just write it I +h-bar see a dot of T I h-bar C B dot of + + align:start position:0% +h-bar see a dot of T I h-bar C B dot of + + + align:start position:0% +h-bar see a dot of T I h-bar C B dot of +T is equal e to the I Omega 0 T Delta H + + align:start position:0% +T is equal e to the I Omega 0 T Delta H + + + align:start position:0% +T is equal e to the I Omega 0 T Delta H +a B was Alpha Delta of time CB of T and + + align:start position:0% +a B was Alpha Delta of time CB of T and + + + align:start position:0% +a B was Alpha Delta of time CB of T and +this is e to the minus I Omega 0 T alpha + + align:start position:0% +this is e to the minus I Omega 0 T alpha + + + align:start position:0% +this is e to the minus I Omega 0 T alpha +star Dow + + align:start position:0% +star Dow + + + align:start position:0% +star Dow +of time see a of T H be a was you be a + + align:start position:0% +of time see a of T H be a was you be a + + + align:start position:0% +of time see a of T H be a was you be a +which is alpha star type Z Delta + + align:start position:0% +which is alpha star type Z Delta + + + align:start position:0% +which is alpha star type Z Delta +function of time okay here a half of + + align:start position:0% +function of time okay here a half of + + + align:start position:0% +function of time okay here a half of +Delta function of time it says that this + + align:start position:0% +Delta function of time it says that this + + + align:start position:0% +Delta function of time it says that this +only matters from time is equal to zero + + align:start position:0% +only matters from time is equal to zero + + + align:start position:0% +only matters from time is equal to zero +so things are a little delicate here but + + align:start position:0% +so things are a little delicate here but + + + align:start position:0% +so things are a little delicate here but +let's see can I write here well if I + + align:start position:0% +let's see can I write here well if I + + + align:start position:0% +let's see can I write here well if I +have f of X times Delta of X we know + + align:start position:0% +have f of X times Delta of X we know + + + align:start position:0% +have f of X times Delta of X we know +this is f of 0 times Delta of X because + + align:start position:0% +this is f of 0 times Delta of X because + + + align:start position:0% +this is f of 0 times Delta of X because +anyway only zeros rather than two so I + + align:start position:0% +anyway only zeros rather than two so I + + + align:start position:0% +anyway only zeros rather than two so I +can put time equals zero here and forget + + align:start position:0% +can put time equals zero here and forget + + + align:start position:0% +can put time equals zero here and forget +about this exponential of alpha delta of + + align:start position:0% +about this exponential of alpha delta of + + + align:start position:0% +about this exponential of alpha delta of +t CB of T and here have alpha star Delta + + align:start position:0% +t CB of T and here have alpha star Delta + + + align:start position:0% +t CB of T and here have alpha star Delta +of T see aft everybody happy so far but + + align:start position:0% +of T see aft everybody happy so far but + + + align:start position:0% +of T see aft everybody happy so far but +here you know I have CB of T and CA of T + + align:start position:0% +here you know I have CB of T and CA of T + + + align:start position:0% +here you know I have CB of T and CA of T +and delta T so I should put alpha delta + + align:start position:0% +and delta T so I should put alpha delta + + + align:start position:0% +and delta T so I should put alpha delta +of t CB at 0 and alpha star delta of p + + align:start position:0% +of t CB at 0 and alpha star delta of p + + + align:start position:0% +of t CB at 0 and alpha star delta of p +see a at 0 right yes people look less + + align:start position:0% +see a at 0 right yes people look less + + + align:start position:0% +see a at 0 right yes people look less +convinced which I congratulate you for + + align:start position:0% +convinced which I congratulate you for + + + align:start position:0% +convinced which I congratulate you for +doubting this this would be bad it seems + + align:start position:0% +doubting this this would be bad it seems + + + align:start position:0% +doubting this this would be bad it seems +like I'm just following the logic but + + align:start position:0% +like I'm just following the logic but + + + align:start position:0% +like I'm just following the logic but +I've gone too far now why did I go too + + align:start position:0% +I've gone too far now why did I go too + + + align:start position:0% +I've gone too far now why did I go too +far + + align:start position:0% +far + + + align:start position:0% +far +first this is going to be a disaster + + align:start position:0% +first this is going to be a disaster + + + align:start position:0% +first this is going to be a disaster +because in many ways + + align:start position:0% + + + + align:start position:0% + +we don't know what these numbers are + + align:start position:0% +we don't know what these numbers are + + + align:start position:0% +we don't know what these numbers are +you see we argued that this is going to + + align:start position:0% +you see we argued that this is going to + + + align:start position:0% +you see we argued that this is going to +change this continuously those function + + align:start position:0% +change this continuously those function + + + align:start position:0% +change this continuously those function +does numbers are going to change this + + align:start position:0% +does numbers are going to change this + + + align:start position:0% +does numbers are going to change this +continuously at time equals zero before + + align:start position:0% +continuously at time equals zero before + + + align:start position:0% +continuously at time equals zero before +time equals zero ca was one and CB was + + align:start position:0% +time equals zero ca was one and CB was + + + align:start position:0% +time equals zero ca was one and CB was +zero but after time equals 0 ZB is going + + align:start position:0% +zero but after time equals 0 ZB is going + + + align:start position:0% +zero but after time equals 0 ZB is going +to be a number something that we don't + + align:start position:0% +to be a number something that we don't + + + align:start position:0% +to be a number something that we don't +know so the Delta function which does it + + align:start position:0% +know so the Delta function which does it + + + align:start position:0% +know so the Delta function which does it +hit the one before zero the one after + + align:start position:0% +hit the one before zero the one after + + + align:start position:0% +hit the one before zero the one after +zero the average was what does it do + + align:start position:0% +zero the average was what does it do + + + align:start position:0% +zero the average was what does it do +this is a case where you have a delta + + align:start position:0% +this is a case where you have a delta + + + align:start position:0% +this is a case where you have a delta +function that we don't know what it's + + align:start position:0% +function that we don't know what it's + + + align:start position:0% +function that we don't know what it's +doing so this is totally wrong so I will + + align:start position:0% +doing so this is totally wrong so I will + + + align:start position:0% +doing so this is totally wrong so I will +just stop there and I will consider + + align:start position:0% +just stop there and I will consider + + + align:start position:0% +just stop there and I will consider +however these two equations so we have + + align:start position:0% +however these two equations so we have + + + align:start position:0% +however these two equations so we have +the equations now in a nice way I'll + + align:start position:0% +the equations now in a nice way I'll + + + align:start position:0% +the equations now in a nice way I'll +reconsider them and we are facing a + + align:start position:0% +reconsider them and we are facing a + + + align:start position:0% +reconsider them and we are facing a +difficulty the difficulty of the Delta + + align:start position:0% +difficulty the difficulty of the Delta + + + align:start position:0% +difficulty the difficulty of the Delta +function not allowing us to treat nicely + + align:start position:0% +function not allowing us to treat nicely + + + align:start position:0% +function not allowing us to treat nicely +the transition so of I h-bar see a dot + + align:start position:0% +the transition so of I h-bar see a dot + + + align:start position:0% +the transition so of I h-bar see a dot +is equal to Alpha Delta of the CB and I + + align:start position:0% +is equal to Alpha Delta of the CB and I + + + align:start position:0% +is equal to Alpha Delta of the CB and I +h-bar see me dot equal alpha star Delta + + align:start position:0% +h-bar see me dot equal alpha star Delta + + + align:start position:0% +h-bar see me dot equal alpha star Delta +of the CA well now the only way to + + align:start position:0% +of the CA well now the only way to + + + align:start position:0% +of the CA well now the only way to +resolve this difficulty is to think + + align:start position:0% +resolve this difficulty is to think + + + align:start position:0% +resolve this difficulty is to think +about this physically and introduce a + + align:start position:0% +about this physically and introduce a + + + align:start position:0% +about this physically and introduce a +regulator that is physical you see no + + align:start position:0% +regulator that is physical you see no + + + align:start position:0% +regulator that is physical you see no +signal in the world really is a delta + + align:start position:0% +signal in the world really is a delta + + + align:start position:0% +signal in the world really is a delta +function it nothing becomes infinite and + + align:start position:0% +function it nothing becomes infinite and + + + align:start position:0% +function it nothing becomes infinite and +nothing lasts for zero time so this + + align:start position:0% +nothing lasts for zero time so this + + + align:start position:0% +nothing lasts for zero time so this +interaction is the + + align:start position:0% +interaction is the + + + align:start position:0% +interaction is the +the function represents a function of + + align:start position:0% +the function represents a function of + + + align:start position:0% +the function represents a function of +time Delta of time is a spike but we can + + align:start position:0% +time Delta of time is a spike but we can + + + align:start position:0% +time Delta of time is a spike but we can +think of it as a regulated thing you've + + align:start position:0% +think of it as a regulated thing you've + + + align:start position:0% +think of it as a regulated thing you've +regulated Delta functions in all kind of + + align:start position:0% +regulated Delta functions in all kind of + + + align:start position:0% +regulated Delta functions in all kind of +way it might be useful to regulate it as + + align:start position:0% +way it might be useful to regulate it as + + + align:start position:0% +way it might be useful to regulate it as +follows as a function of time that is + + align:start position:0% +follows as a function of time that is + + + align:start position:0% +follows as a function of time that is +zero before time equals zero is zero + + align:start position:0% +zero before time equals zero is zero + + + align:start position:0% +zero before time equals zero is zero +after some time T star and it has height + + align:start position:0% +after some time T star and it has height + + + align:start position:0% +after some time T star and it has height +one over T star that's a picture of a + + align:start position:0% +one over T star that's a picture of a + + + align:start position:0% +one over T star that's a picture of a +delta function it has the right area at + + align:start position:0% +delta function it has the right area at + + + align:start position:0% +delta function it has the right area at +least and we're going to think of this + + align:start position:0% +least and we're going to think of this + + + align:start position:0% +least and we're going to think of this +system as exactly doing that in between + + align:start position:0% + + + + align:start position:0% + +440 in the interval 0 to T star the + + align:start position:0% +440 in the interval 0 to T star the + + + align:start position:0% +440 in the interval 0 to T star the +Delta function is going to be replaced + + align:start position:0% +Delta function is going to be replaced + + + align:start position:0% +Delta function is going to be replaced +by this function this constant function + + align:start position:0% +by this function this constant function + + + align:start position:0% +by this function this constant function +so we'll have I h-bar H see a dot is + + align:start position:0% +so we'll have I h-bar H see a dot is + + + align:start position:0% +so we'll have I h-bar H see a dot is +equal to alpha over T star C be an I + + align:start position:0% +equal to alpha over T star C be an I + + + align:start position:0% +equal to alpha over T star C be an I +h-bar C B dot is equal to alpha star + + align:start position:0% +h-bar C B dot is equal to alpha star + + + align:start position:0% +h-bar C B dot is equal to alpha star +over T sub star now the star doesn't + + align:start position:0% +over T sub star now the star doesn't + + + align:start position:0% +over T sub star now the star doesn't +mean complex conjugation for T is just a + + align:start position:0% +mean complex conjugation for T is just a + + + align:start position:0% +mean complex conjugation for T is just a +number it could have called T naught + + align:start position:0% +number it could have called T naught + + + align:start position:0% +number it could have called T naught +something like that and this is true for + + align:start position:0% +something like that and this is true for + + + align:start position:0% +something like that and this is true for +this time interval and then you would + + align:start position:0% +this time interval and then you would + + + align:start position:0% +this time interval and then you would +say look I have two problems with this + + align:start position:0% +say look I have two problems with this + + + align:start position:0% +say look I have two problems with this +first you've introduced a T star and now + + align:start position:0% +first you've introduced a T star and now + + + align:start position:0% +first you've introduced a T star and now +your calculation is going to depend on T + + align:start position:0% +your calculation is going to depend on T + + + align:start position:0% +your calculation is going to depend on T +star that the answer is gonna depend on + + align:start position:0% +star that the answer is gonna depend on + + + align:start position:0% +star that the answer is gonna depend on +T star and what are you gonna put for T + + align:start position:0% +T star and what are you gonna put for T + + + align:start position:0% +T star and what are you gonna put for T +star well + + align:start position:0% +star well + + + align:start position:0% +star well +that better not happen we have to go on + + align:start position:0% +that better not happen we have to go on + + + align:start position:0% +that better not happen we have to go on +a limb many times when you do a + + align:start position:0% +a limb many times when you do a + + + align:start position:0% +a limb many times when you do a +calculation some of you go on a limb you + + align:start position:0% +calculation some of you go on a limb you + + + align:start position:0% +calculation some of you go on a limb you +say something and see if it works this + + align:start position:0% +say something and see if it works this + + + align:start position:0% +say something and see if it works this +seems reasonable and what we expect is + + align:start position:0% +seems reasonable and what we expect is + + + align:start position:0% +seems reasonable and what we expect is +that we will find an answer that is + + align:start position:0% +that we will find an answer that is + + + align:start position:0% +that we will find an answer that is +independent on this T star so that we + + align:start position:0% +independent on this T star so that we + + + align:start position:0% +independent on this T star so that we +can take this star to zero and make + + align:start position:0% +can take this star to zero and make + + + align:start position:0% +can take this star to zero and make +sense of it the other question that + + align:start position:0% +sense of it the other question that + + + align:start position:0% +sense of it the other question that +could come is that all that was your + + align:start position:0% +could come is that all that was your + + + align:start position:0% +could come is that all that was your +delta function so one second you you + + align:start position:0% +delta function so one second you you + + + align:start position:0% +delta function so one second you you +used Delta function for this maybe you + + align:start position:0% +used Delta function for this maybe you + + + align:start position:0% +used Delta function for this maybe you +have to put back these terms these + + align:start position:0% +have to put back these terms these + + + align:start position:0% +have to put back these terms these +Exponential's we set them to one but + + align:start position:0% +Exponential's we set them to one but + + + align:start position:0% +Exponential's we set them to one but +then you could say look I don't think I + + align:start position:0% +then you could say look I don't think I + + + align:start position:0% +then you could say look I don't think I +have to put them back + + align:start position:0% +have to put them back + + + align:start position:0% +have to put them back +why because I can choose this star as + + align:start position:0% +why because I can choose this star as + + + align:start position:0% +why because I can choose this star as +small as I want such as Omega P star + + align:start position:0% +small as I want such as Omega P star + + + align:start position:0% +small as I want such as Omega P star +which is the possible value that this + + align:start position:0% +which is the possible value that this + + + align:start position:0% +which is the possible value that this +can get and most is like ten to the + + align:start position:0% +can get and most is like ten to the + + + align:start position:0% +can get and most is like ten to the +minus six T and therefore this face is + + align:start position:0% +minus six T and therefore this face is + + + align:start position:0% +minus six T and therefore this face is +going to be zero essentially that's + + align:start position:0% +going to be zero essentially that's + + + align:start position:0% +going to be zero essentially that's +going to be one so I claim that I don't + + align:start position:0% +going to be one so I claim that I don't + + + align:start position:0% +going to be one so I claim that I don't +have to worry about this anymore + + align:start position:0% +have to worry about this anymore + + + align:start position:0% +have to worry about this anymore +so what do we have we have two simple + + align:start position:0% +so what do we have we have two simple + + + align:start position:0% +so what do we have we have two simple +differential equations like this with + + align:start position:0% +differential equations like this with + + + align:start position:0% +differential equations like this with +the conditions that see a at time equals + + align:start position:0% +the conditions that see a at time equals + + + align:start position:0% +the conditions that see a at time equals +0 is 1 and see B at time equals 0 is 0 + + align:start position:0% +0 is 1 and see B at time equals 0 is 0 + + + align:start position:0% +0 is 1 and see B at time equals 0 is 0 +the state before the Delta function hits + + align:start position:0% +the state before the Delta function hits + + + align:start position:0% +the state before the Delta function hits +is given by that and now what we want to + + align:start position:0% +is given by that and now what we want to + + + align:start position:0% +is given by that and now what we want to +know is how much is ca after the Delta + + align:start position:0% +know is how much is ca after the Delta + + + align:start position:0% +know is how much is ca after the Delta +function and see me after the Delta + + align:start position:0% +function and see me after the Delta + + + align:start position:0% +function and see me after the Delta +function + + align:start position:0% + + + + align:start position:0% + +so for that we have all the tools needed + + align:start position:0% +so for that we have all the tools needed + + + align:start position:0% +so for that we have all the tools needed +I could take this equation this is a + + align:start position:0% +I could take this equation this is a + + + align:start position:0% +I could take this equation this is a +couple system of equations a simple + + align:start position:0% +couple system of equations a simple + + + align:start position:0% +couple system of equations a simple +system I can differentiate again here + + align:start position:0% +system I can differentiate again here + + + align:start position:0% +system I can differentiate again here +and I get a CA double dot CB dot and use + + align:start position:0% +and I get a CA double dot CB dot and use + + + align:start position:0% +and I get a CA double dot CB dot and use +this equation so you get the equation if + + align:start position:0% +this equation so you get the equation if + + + align:start position:0% +this equation so you get the equation if +you differentiate again take a dot to + + align:start position:0% +you differentiate again take a dot to + + + align:start position:0% +you differentiate again take a dot to +form see a double dot you get that see a + + align:start position:0% +form see a double dot you get that see a + + + align:start position:0% +form see a double dot you get that see a +double dot is equal to minus alpha over + + align:start position:0% +double dot is equal to minus alpha over + + + align:start position:0% +double dot is equal to minus alpha over +H bar T star squared CA you can see that + + align:start position:0% +H bar T star squared CA you can see that + + + align:start position:0% +H bar T star squared CA you can see that +you put the IH bar here take the + + align:start position:0% +you put the IH bar here take the + + + align:start position:0% +you put the IH bar here take the +derivative you get an alpha times an + + align:start position:0% +derivative you get an alpha times an + + + align:start position:0% +derivative you get an alpha times an +alpha star which is length of alpha + + align:start position:0% +alpha star which is length of alpha + + + align:start position:0% +alpha star which is length of alpha +squared and the H bar appears two times + + align:start position:0% +squared and the H bar appears two times + + + align:start position:0% +squared and the H bar appears two times +these star appears two times this is an + + align:start position:0% +these star appears two times this is an + + + align:start position:0% +these star appears two times this is an +oscillating solution so + + align:start position:0% + + + + align:start position:0% + +that's simple enough so what happens + + align:start position:0% +that's simple enough so what happens + + + align:start position:0% +that's simple enough so what happens +here is that CA will oscillate in time + + align:start position:0% +here is that CA will oscillate in time + + + align:start position:0% +here is that CA will oscillate in time +and you will have a solution of the form + + align:start position:0% +and you will have a solution of the form + + + align:start position:0% +and you will have a solution of the form +C a is equal to a constant beta naught + + align:start position:0% +C a is equal to a constant beta naught + + + align:start position:0% +C a is equal to a constant beta naught +cosine of alpha H bar P star P plus beta + + align:start position:0% +cosine of alpha H bar P star P plus beta + + + align:start position:0% +cosine of alpha H bar P star P plus beta +1 sine of alpha P over H bar T star and + + align:start position:0% +1 sine of alpha P over H bar T star and + + + align:start position:0% +1 sine of alpha P over H bar T star and +if you wish C be from the first equation + + align:start position:0% +if you wish C be from the first equation + + + align:start position:0% +if you wish C be from the first equation +is proportional to C a dot and see a dot + + align:start position:0% +is proportional to C a dot and see a dot + + + align:start position:0% +is proportional to C a dot and see a dot +is going to be of the form beta naught + + align:start position:0% +is going to be of the form beta naught + + + align:start position:0% +is going to be of the form beta naught +sine of this thing plus beta 1 cosine of + + align:start position:0% +sine of this thing plus beta 1 cosine of + + + align:start position:0% +sine of this thing plus beta 1 cosine of +this thing + + align:start position:0% + + + + align:start position:0% + +okay so we've turned this into a + + align:start position:0% +okay so we've turned this into a + + + align:start position:0% +okay so we've turned this into a +tractable problem because of flattening + + align:start position:0% +tractable problem because of flattening + + + align:start position:0% +tractable problem because of flattening +the delta function and your initial + + align:start position:0% +the delta function and your initial + + + align:start position:0% +the delta function and your initial +conditions again CB must vanish at time + + align:start position:0% +conditions again CB must vanish at time + + + align:start position:0% +conditions again CB must vanish at time +equals zero so if CB must vanish at time + + align:start position:0% +equals zero so if CB must vanish at time + + + align:start position:0% +equals zero so if CB must vanish at time +equals 0 beta 1 must be 0 if beta 1 is 0 + + align:start position:0% +equals 0 beta 1 must be 0 if beta 1 is 0 + + + align:start position:0% +equals 0 beta 1 must be 0 if beta 1 is 0 +this term is gone and C a was 1 for time + + align:start position:0% +this term is gone and C a was 1 for time + + + align:start position:0% +this term is gone and C a was 1 for time +equals 0 so beta 0 is 1 therefore CA is + + align:start position:0% +equals 0 so beta 0 is 1 therefore CA is + + + align:start position:0% +equals 0 so beta 0 is 1 therefore CA is +equal to cosine alpha T over H star T + + align:start position:0% +equal to cosine alpha T over H star T + + + align:start position:0% +equal to cosine alpha T over H star T +star CA of T and CB of T you can + + align:start position:0% +star CA of T and CB of T you can + + + align:start position:0% +star CA of T and CB of T you can +calculate it from the top equation you + + align:start position:0% +calculate it from the top equation you + + + align:start position:0% +calculate it from the top equation you +take the derivative of CA and divide by + + align:start position:0% +take the derivative of CA and divide by + + + align:start position:0% +take the derivative of CA and divide by +alpha multiplied by T star let me I'll + + align:start position:0% +alpha multiplied by T star let me I'll + + + align:start position:0% +alpha multiplied by T star let me I'll +let you do it you get minus I alpha over + + align:start position:0% +let you do it you get minus I alpha over + + + align:start position:0% +let you do it you get minus I alpha over +alpha sine alpha T over H T star okay we + + align:start position:0% +alpha sine alpha T over H T star okay we + + + align:start position:0% +alpha sine alpha T over H T star okay we +solved for the functions we know what's + + align:start position:0% +solved for the functions we know what's + + + align:start position:0% +solved for the functions we know what's +gonna happen and now what did we want we + + align:start position:0% +gonna happen and now what did we want we + + + align:start position:0% +gonna happen and now what did we want we +wanted to know what are those things for + + align:start position:0% +wanted to know what are those things for + + + align:start position:0% +wanted to know what are those things for +later times 4 times T star or more now + + align:start position:0% +later times 4 times T star or more now + + + align:start position:0% +later times 4 times T star or more now +you cannot use this equations beyond + + align:start position:0% +you cannot use this equations beyond + + + align:start position:0% +you cannot use this equations beyond +time T star because they assume the + + align:start position:0% +time T star because they assume the + + + align:start position:0% +time T star because they assume the +Delta function is there so what you have + + align:start position:0% +Delta function is there so what you have + + + align:start position:0% +Delta function is there so what you have +to figure out is what are these + + align:start position:0% +to figure out is what are these + + + align:start position:0% +to figure out is what are these +coefficients at time T star and those + + align:start position:0% +coefficients at time T star and those + + + align:start position:0% +coefficients at time T star and those +would be the + + align:start position:0% +would be the + + + align:start position:0% +would be the +coefficients at any later time because + + align:start position:0% +coefficients at any later time because + + + align:start position:0% +coefficients at any later time because +there's no more Hamiltonian so CA at T + + align:start position:0% +there's no more Hamiltonian so CA at T + + + align:start position:0% +there's no more Hamiltonian so CA at T +greater than T star is in fact equal to + + align:start position:0% +greater than T star is in fact equal to + + + align:start position:0% +greater than T star is in fact equal to +ca at T star and CA at T star happily he + + align:start position:0% +ca at T star and CA at T star happily he + + + align:start position:0% +ca at T star and CA at T star happily he +said numbers a doesn't depend on T star + + align:start position:0% +said numbers a doesn't depend on T star + + + align:start position:0% +said numbers a doesn't depend on T star +cosine alpha over H bar and see me at T + + align:start position:0% +cosine alpha over H bar and see me at T + + + align:start position:0% +cosine alpha over H bar and see me at T +greater than T star is CB a T star it + + align:start position:0% +greater than T star is CB a T star it + + + align:start position:0% +greater than T star is CB a T star it +doesn't change anymore + + align:start position:0% +doesn't change anymore + + + align:start position:0% +doesn't change anymore +after the Delta function has turned off + + align:start position:0% +after the Delta function has turned off + + + align:start position:0% +after the Delta function has turned off +and CB at T star is minus I alpha over + + align:start position:0% +and CB at T star is minus I alpha over + + + align:start position:0% +and CB at T star is minus I alpha over +alpha alpha over alpha like this times + + align:start position:0% +alpha alpha over alpha like this times + + + align:start position:0% +alpha alpha over alpha like this times +sine of alpha over H bar and this is + + align:start position:0% +sine of alpha over H bar and this is + + + align:start position:0% +sine of alpha over H bar and this is +really what you wanted now you know what + + align:start position:0% +really what you wanted now you know what + + + align:start position:0% +really what you wanted now you know what +the state is doing at after the Delta + + align:start position:0% +the state is doing at after the Delta + + + align:start position:0% +the state is doing at after the Delta +function has turned down it has this + + align:start position:0% +function has turned down it has this + + + align:start position:0% +function has turned down it has this +amplitude to be in the B state and it is + + align:start position:0% +amplitude to be in the B state and it is + + + align:start position:0% +amplitude to be in the B state and it is +as we predicted remember this is like + + align:start position:0% +as we predicted remember this is like + + + align:start position:0% +as we predicted remember this is like +the face of alpha because the Alpha is + + align:start position:0% +the face of alpha because the Alpha is + + + align:start position:0% +the face of alpha because the Alpha is +alpha times its face length of alpha + + align:start position:0% +alpha times its face length of alpha + + + align:start position:0% +alpha times its face length of alpha +Terry's face and it will cancel and here + + align:start position:0% +Terry's face and it will cancel and here + + + align:start position:0% +Terry's face and it will cancel and here +you have sine of this quantity so it is + + align:start position:0% +you have sine of this quantity so it is + + + align:start position:0% +you have sine of this quantity so it is +proportional CB is proportional to alpha + + align:start position:0% +proportional CB is proportional to alpha + + + align:start position:0% +proportional CB is proportional to alpha +and that's exactly what you would expect + + align:start position:0% +and that's exactly what you would expect + + + align:start position:0% +and that's exactly what you would expect +so if just to complete the story let's + + align:start position:0% +so if just to complete the story let's + + + align:start position:0% +so if just to complete the story let's +write the answer + + align:start position:0% +write the answer + + + align:start position:0% +write the answer +[Music] + + align:start position:0% + + + + align:start position:0% + +and and what is the answer a sigh of T + + align:start position:0% +and and what is the answer a sigh of T + + + align:start position:0% +and and what is the answer a sigh of T +for T greater than zero is the + + align:start position:0% +for T greater than zero is the + + + align:start position:0% +for T greater than zero is the +coefficient C a of D which was cosine + + align:start position:0% +coefficient C a of D which was cosine + + + align:start position:0% +coefficient C a of D which was cosine +alpha over H bar times e to the minus i + + align:start position:0% +alpha over H bar times e to the minus i + + + align:start position:0% +alpha over H bar times e to the minus i +e AP over H bar a remember the solution + + align:start position:0% +e AP over H bar a remember the solution + + + align:start position:0% +e AP over H bar a remember the solution +is C a e to the minus IET a and then the + + align:start position:0% +is C a e to the minus IET a and then the + + + align:start position:0% +is C a e to the minus IET a and then the +other one which is minus I alpha over + + align:start position:0% +other one which is minus I alpha over + + + align:start position:0% +other one which is minus I alpha over +alpha sine of alpha over H bar e to the + + align:start position:0% +alpha sine of alpha over H bar e to the + + + align:start position:0% +alpha sine of alpha over H bar e to the +minus I a BT over H bar B that is the + + align:start position:0% +minus I a BT over H bar B that is the + + + align:start position:0% +minus I a BT over H bar B that is the +state after the Delta function has turn + + align:start position:0% +state after the Delta function has turn + + + align:start position:0% +state after the Delta function has turn +on and what is the probability to be + + align:start position:0% +on and what is the probability to be + + + align:start position:0% +on and what is the probability to be +found in the state B time T would be B + + align:start position:0% +found in the state B time T would be B + + + align:start position:0% +found in the state B time T would be B +times the state squared so you get B + + align:start position:0% +times the state squared so you get B + + + align:start position:0% +times the state squared so you get B +will couple just to that B with being + + align:start position:0% +will couple just to that B with being + + + align:start position:0% +will couple just to that B with being +gives you 1 this is a face this is a + + align:start position:0% +gives you 1 this is a face this is a + + + align:start position:0% +gives you 1 this is a face this is a +face sine squared of this thing sine + + align:start position:0% +face sine squared of this thing sine + + + align:start position:0% +face sine squared of this thing sine +squared of alpha over H bar what is the + + align:start position:0% +squared of alpha over H bar what is the + + + align:start position:0% +squared of alpha over H bar what is the +probability to be in a is a sigh of t + + align:start position:0% +probability to be in a is a sigh of t + + + align:start position:0% +probability to be in a is a sigh of t +and in this case it will be cosine + + align:start position:0% +and in this case it will be cosine + + + align:start position:0% +and in this case it will be cosine +squared of alpha over H bar and it's + + align:start position:0% +squared of alpha over H bar and it's + + + align:start position:0% +squared of alpha over H bar and it's +very handy that cosine squared plus sine + + align:start position:0% +very handy that cosine squared plus sine + + + align:start position:0% +very handy that cosine squared plus sine +squared is it + + align:start position:0% +squared is it + + + align:start position:0% +squared is it +to one because it has to be either in a + + align:start position:0% +to one because it has to be either in a + + + align:start position:0% +to one because it has to be either in a +or on B and it's kind of interesting + + align:start position:0% +or on B and it's kind of interesting + + + align:start position:0% +or on B and it's kind of interesting +this if you were doing this in perturb a + + align:start position:0% +this if you were doing this in perturb a + + + align:start position:0% +this if you were doing this in perturb a +we solved it exactly if you were doing + + align:start position:0% +we solved it exactly if you were doing + + + align:start position:0% +we solved it exactly if you were doing +this in perturbation theory we would + + align:start position:0% +this in perturbation theory we would + + + align:start position:0% +this in perturbation theory we would +have found P of be proportional to alpha + + align:start position:0% +have found P of be proportional to alpha + + + align:start position:0% +have found P of be proportional to alpha +squared because the first term in the + + align:start position:0% +squared because the first term in the + + + align:start position:0% +squared because the first term in the +expansion here in terms of the + + align:start position:0% +expansion here in terms of the + + + align:start position:0% +expansion here in terms of the +interaction \ No newline at end of file diff --git a/p9mFf79aWg8.txt b/p9mFf79aWg8.txt new file mode 100644 index 0000000000000000000000000000000000000000..ed164d15edb55ba233a88565c2ea8d43d9c35274 --- /dev/null +++ b/p9mFf79aWg8.txt @@ -0,0 +1,7635 @@ +align:start position:0% + +The following content is provided by MIT + + align:start position:0% +The following content is provided by MIT + + + align:start position:0% +The following content is provided by MIT +Open Courseware under a Creative Common + + align:start position:0% +Open Courseware under a Creative Common + + + align:start position:0% +Open Courseware under a Creative Common +License. Additional information about + + align:start position:0% +License. Additional information about + + + align:start position:0% +License. Additional information about +our license and MIT Open Courseware in + + align:start position:0% +our license and MIT Open Courseware in + + + align:start position:0% +our license and MIT Open Courseware in +general is available at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +So today we're going to continue with + + align:start position:0% +So today we're going to continue with + + + align:start position:0% +So today we're going to continue with +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +equilibrium and at the end of the + + align:start position:0% +equilibrium and at the end of the + + + align:start position:0% +equilibrium and at the end of the +lecture, Professor Ser will be here to + + align:start position:0% +lecture, Professor Ser will be here to + + + align:start position:0% +lecture, Professor Ser will be here to +talk about exam + + align:start position:0% +talk about exam + + + align:start position:0% +talk about exam +two. So we're going to start off where + + align:start position:0% +two. So we're going to start off where + + + align:start position:0% +two. So we're going to start off where +we left off and we are talking about + + align:start position:0% +we left off and we are talking about + + + align:start position:0% +we left off and we are talking about +Latier's principle. + + align:start position:0% +Latier's principle. + + + align:start position:0% +Latier's principle. +So, Lhat Leier had this great idea that + + align:start position:0% +So, Lhat Leier had this great idea that + + + align:start position:0% +So, Lhat Leier had this great idea that +uh systems tend to respond to stress in + + align:start position:0% +uh systems tend to respond to stress in + + + align:start position:0% +uh systems tend to respond to stress in +a particular + + align:start position:0% +a particular + + + align:start position:0% +a particular +way. That if you apply a stress to a + + align:start position:0% +way. That if you apply a stress to a + + + align:start position:0% +way. That if you apply a stress to a +system at + + align:start position:0% +system at + + + align:start position:0% +system at +equilibrium, it will respond to that + + align:start position:0% +equilibrium, it will respond to that + + + align:start position:0% +equilibrium, it will respond to that +stress by trying to minimize the stress. + + align:start position:0% +stress by trying to minimize the stress. + + + align:start position:0% +stress by trying to minimize the stress. +So the reaction will respond to adjust + + align:start position:0% +So the reaction will respond to adjust + + + align:start position:0% +So the reaction will respond to adjust +for the stress that was applied and + + align:start position:0% +for the stress that was applied and + + + align:start position:0% +for the stress that was applied and +minimize that stress. So if you consider + + align:start position:0% +minimize that stress. So if you consider + + + align:start position:0% +minimize that stress. So if you consider +what stress is applied to a reaction and + + align:start position:0% +what stress is applied to a reaction and + + + align:start position:0% +what stress is applied to a reaction and +then how that stress can be minimized, + + align:start position:0% +then how that stress can be minimized, + + + align:start position:0% +then how that stress can be minimized, +you can predict whether the reaction + + align:start position:0% +you can predict whether the reaction + + + align:start position:0% +you can predict whether the reaction +will go in the forward direction or the + + align:start position:0% +will go in the forward direction or the + + + align:start position:0% +will go in the forward direction or the +reverse direction. And so it tends to go + + align:start position:0% +reverse direction. And so it tends to go + + + align:start position:0% +reverse direction. And so it tends to go +in in one of those directions to + + align:start position:0% +in in one of those directions to + + + align:start position:0% +in in one of those directions to +minimize the stress until the stress has + + align:start position:0% +minimize the stress until the stress has + + + align:start position:0% +minimize the stress until the stress has +been minimized. and then equilibrium is + + align:start position:0% +been minimized. and then equilibrium is + + + align:start position:0% +been minimized. and then equilibrium is +reached + + align:start position:0% +reached + + + align:start position:0% +reached +again. So we talked uh last class about + + align:start position:0% +again. So we talked uh last class about + + + align:start position:0% +again. So we talked uh last class about +adding and + + align:start position:0% +adding and + + + align:start position:0% +adding and +removing products or uh reactants and + + align:start position:0% +removing products or uh reactants and + + + align:start position:0% +removing products or uh reactants and +how the system would respond. And today + + align:start position:0% +how the system would respond. And today + + + align:start position:0% +how the system would respond. And today +we're going to consider changes in uh + + align:start position:0% +we're going to consider changes in uh + + + align:start position:0% +we're going to consider changes in uh +volume to a gaseous system and also + + align:start position:0% +volume to a gaseous system and also + + + align:start position:0% +volume to a gaseous system and also +temperature and how systems respond. And + + align:start position:0% +temperature and how systems respond. And + + + align:start position:0% +temperature and how systems respond. And +at the end we'll talk about the + + align:start position:0% +at the end we'll talk about the + + + align:start position:0% +at the end we'll talk about the +relevance of this to biological systems. + + align:start position:0% +relevance of this to biological systems. + + + align:start position:0% +relevance of this to biological systems. +So again here's + + align:start position:0% +So again here's + + + align:start position:0% +So again here's +lhatier. So we can use this to predict + + align:start position:0% +lhatier. So we can use this to predict + + + align:start position:0% +lhatier. So we can use this to predict +the direction of the reaction the the + + align:start position:0% +the direction of the reaction the the + + + align:start position:0% +the direction of the reaction the the +response to the stress that is + + align:start position:0% + + + + align:start position:0% + +applied. So first let's consider what + + align:start position:0% +applied. So first let's consider what + + + align:start position:0% +applied. So first let's consider what +happens if you have a mixture of gases + + align:start position:0% +happens if you have a mixture of gases + + + align:start position:0% +happens if you have a mixture of gases +at equilibrium. They're reacting again + + align:start position:0% +at equilibrium. They're reacting again + + + align:start position:0% +at equilibrium. They're reacting again +at equilibrium. It's a dynamic process. + + align:start position:0% +at equilibrium. It's a dynamic process. + + + align:start position:0% +at equilibrium. It's a dynamic process. +So you have the reaction going in the + + align:start position:0% +So you have the reaction going in the + + + align:start position:0% +So you have the reaction going in the +forward direction and the reverse + + align:start position:0% +forward direction and the reverse + + + align:start position:0% +forward direction and the reverse +direction but the rates of those direct + + align:start position:0% +direction but the rates of those direct + + + align:start position:0% +direction but the rates of those direct +reactions are the same. So there's no + + align:start position:0% +reactions are the same. So there's no + + + align:start position:0% +reactions are the same. So there's no +net change in composition but the + + align:start position:0% +net change in composition but the + + + align:start position:0% +net change in composition but the +reaction is still happening. So now if + + align:start position:0% +reaction is still happening. So now if + + + align:start position:0% +reaction is still happening. So now if +you have a system at equilibrium a + + align:start position:0% +you have a system at equilibrium a + + + align:start position:0% +you have a system at equilibrium a +gaseous system in equilibrium and you + + align:start position:0% +gaseous system in equilibrium and you + + + align:start position:0% +gaseous system in equilibrium and you +change the volume we'll consider how the + + align:start position:0% +change the volume we'll consider how the + + + align:start position:0% +change the volume we'll consider how the +reaction will shift to compensate for + + align:start position:0% +reaction will shift to compensate for + + + align:start position:0% +reaction will shift to compensate for +this stress. + + align:start position:0% +this stress. + + + align:start position:0% +this stress. +So a decrease in volume of a gaseous + + align:start position:0% +So a decrease in volume of a gaseous + + + align:start position:0% +So a decrease in volume of a gaseous +system will cause an increase in total + + align:start position:0% +system will cause an increase in total + + + align:start position:0% +system will cause an increase in total +pressure. How do we know that? What + + align:start position:0% +pressure. How do we know that? What + + + align:start position:0% +pressure. How do we know that? What +equation tells us about pressures and + + align:start position:0% +equation tells us about pressures and + + + align:start position:0% +equation tells us about pressures and +volumes of gases? + + align:start position:0% + + + + align:start position:0% + +Yeah, ideal gas law. So PV equals + + align:start position:0% +Yeah, ideal gas law. So PV equals + + + align:start position:0% +Yeah, ideal gas law. So PV equals +NRT. So that's what we'll be considering + + align:start position:0% +NRT. So that's what we'll be considering + + + align:start position:0% +NRT. So that's what we'll be considering +today. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +Lhatier's principle would predict that + + align:start position:0% +Lhatier's principle would predict that + + + align:start position:0% +Lhatier's principle would predict that +the system will respond in such a way + + align:start position:0% +the system will respond in such a way + + + align:start position:0% +the system will respond in such a way +then to reduce the total pressure. So if + + align:start position:0% +then to reduce the total pressure. So if + + + align:start position:0% +then to reduce the total pressure. So if +you change decrease the volume increase + + align:start position:0% +you change decrease the volume increase + + + align:start position:0% +you change decrease the volume increase +the total pressure, the system's going + + align:start position:0% +the total pressure, the system's going + + + align:start position:0% +the total pressure, the system's going +to respond then to reduce that total + + align:start position:0% +to respond then to reduce that total + + + align:start position:0% +to respond then to reduce that total +pressure to minimize that stress that + + align:start position:0% +pressure to minimize that stress that + + + align:start position:0% +pressure to minimize that stress that +was added into the system. + + align:start position:0% + + + + align:start position:0% + +So let's look at an + + align:start position:0% + + + + align:start position:0% + +example. So here we have two P2 gas + + align:start position:0% +example. So here we have two P2 gas + + + align:start position:0% +example. So here we have two P2 gas +going to P4 gas. So two molecules of P2 + + align:start position:0% +going to P4 gas. So two molecules of P2 + + + align:start position:0% +going to P4 gas. So two molecules of P2 +going to one of + + align:start position:0% +going to one of + + + align:start position:0% +going to one of +P4. And in the middle one here we have + + align:start position:0% +P4. And in the middle one here we have + + + align:start position:0% +P4. And in the middle one here we have +the system at equilibrium. And we're + + align:start position:0% +the system at equilibrium. And we're + + + align:start position:0% +the system at equilibrium. And we're +going to consider both what happens when + + align:start position:0% +going to consider both what happens when + + + align:start position:0% +going to consider both what happens when +we decrease the volume and when we + + align:start position:0% +we decrease the volume and when we + + + align:start position:0% +we decrease the volume and when we +increase the + + align:start position:0% +increase the + + + align:start position:0% +increase the +volume. First let's consider this + + align:start position:0% + + + + align:start position:0% + +decrease. So what happens is that a + + align:start position:0% +decrease. So what happens is that a + + + align:start position:0% +decrease. So what happens is that a +decrease in volume shifts the reactants + + align:start position:0% +decrease in volume shifts the reactants + + + align:start position:0% +decrease in volume shifts the reactants +shifts the reactant reaction toward + + align:start position:0% +shifts the reactant reaction toward + + + align:start position:0% +shifts the reactant reaction toward +products. So why is that true? Well has + + align:start position:0% +products. So why is that true? Well has + + + align:start position:0% +products. So why is that true? Well has +to do with the stokometry of this + + align:start position:0% +to do with the stokometry of this + + + align:start position:0% +to do with the stokometry of this +equation. So for every two moles here + + align:start position:0% +equation. So for every two moles here + + + align:start position:0% +equation. So for every two moles here +that are consumed only one is + + align:start position:0% +that are consumed only one is + + + align:start position:0% +that are consumed only one is +formed. So a shift to the right toward + + align:start position:0% +formed. So a shift to the right toward + + + align:start position:0% +formed. So a shift to the right toward +products is going to reduce the number + + align:start position:0% +products is going to reduce the number + + + align:start position:0% +products is going to reduce the number +of molecules in the system and therefore + + align:start position:0% +of molecules in the system and therefore + + + align:start position:0% +of molecules in the system and therefore +reduce the total pressure. So when you + + align:start position:0% +reduce the total pressure. So when you + + + align:start position:0% +reduce the total pressure. So when you +have a decrease in volume that initially + + align:start position:0% +have a decrease in volume that initially + + + align:start position:0% +have a decrease in volume that initially +causes the total pressure to increase + + align:start position:0% +causes the total pressure to increase + + + align:start position:0% +causes the total pressure to increase +and so the system responds in such a way + + align:start position:0% +and so the system responds in such a way + + + align:start position:0% +and so the system responds in such a way +to minimize that stress and decrease the + + align:start position:0% +to minimize that stress and decrease the + + + align:start position:0% +to minimize that stress and decrease the +pressure which it can do from shift by + + align:start position:0% +pressure which it can do from shift by + + + align:start position:0% +pressure which it can do from shift by +shifting this reaction toward products + + align:start position:0% +shifting this reaction toward products + + + align:start position:0% +shifting this reaction toward products +or to the right. So this is what chat + + align:start position:0% +or to the right. So this is what chat + + + align:start position:0% +or to the right. So this is what chat +lhatier's principle would allow you to + + align:start position:0% +lhatier's principle would allow you to + + + align:start position:0% +lhatier's principle would allow you to +guess when you look at this particular + + align:start position:0% +guess when you look at this particular + + + align:start position:0% +guess when you look at this particular +reaction and you can also prove to + + align:start position:0% +reaction and you can also prove to + + + align:start position:0% +reaction and you can also prove to +yourself that this is correct by + + align:start position:0% +yourself that this is correct by + + + align:start position:0% +yourself that this is correct by +considering Q and K and delta + + align:start position:0% +considering Q and K and delta + + + align:start position:0% +considering Q and K and delta +G. So let's prove that this is this is + + align:start position:0% +G. So let's prove that this is this is + + + align:start position:0% +G. So let's prove that this is this is +what would in fact happen. So we + + align:start position:0% +what would in fact happen. So we + + + align:start position:0% +what would in fact happen. So we +consider again Q and K. Remember this is + + align:start position:0% +consider again Q and K. Remember this is + + + align:start position:0% +consider again Q and K. Remember this is +this is what's important in both of + + align:start position:0% +this is what's important in both of + + + align:start position:0% +this is what's important in both of +these two lectures. We're talking about + + align:start position:0% +these two lectures. We're talking about + + + align:start position:0% +these two lectures. We're talking about +Q, the reaction quotient, the uh ratio + + align:start position:0% +Q, the reaction quotient, the uh ratio + + + align:start position:0% +Q, the reaction quotient, the uh ratio +of products to reactants under whatever + + align:start position:0% +of products to reactants under whatever + + + align:start position:0% +of products to reactants under whatever +condition you are at that particular + + align:start position:0% +condition you are at that particular + + + align:start position:0% +condition you are at that particular +moment in time. Whereas K is our + + align:start position:0% +moment in time. Whereas K is our + + + align:start position:0% +moment in time. Whereas K is our +equilibrium constant, the ratio of + + align:start position:0% +equilibrium constant, the ratio of + + + align:start position:0% +equilibrium constant, the ratio of +products to reactions at + + align:start position:0% +products to reactions at + + + align:start position:0% +products to reactions at +equilibrium. So now to make the math + + align:start position:0% +equilibrium. So now to make the math + + + align:start position:0% +equilibrium. So now to make the math +easy, let's assume that the volume + + align:start position:0% +easy, let's assume that the volume + + + align:start position:0% +easy, let's assume that the volume +decrease happens by a factor of two. So + + align:start position:0% +decrease happens by a factor of two. So + + + align:start position:0% +decrease happens by a factor of two. So +you decrease the volume by two. + + align:start position:0% +you decrease the volume by two. + + + align:start position:0% +you decrease the volume by two. +So that's going to initially increase + + align:start position:0% +So that's going to initially increase + + + align:start position:0% +So that's going to initially increase +the pressure of both gases of P2 the + + align:start position:0% +the pressure of both gases of P2 the + + + align:start position:0% +the pressure of both gases of P2 the +reactant and P4 the product by two. So + + align:start position:0% +reactant and P4 the product by two. So + + + align:start position:0% +reactant and P4 the product by two. So +the partial pressure was going to go + + align:start position:0% +the partial pressure was going to go + + + align:start position:0% +the partial pressure was going to go +up. So now we can figure out by how much + + align:start position:0% +up. So now we can figure out by how much + + + align:start position:0% +up. So now we can figure out by how much +with this decrease uh in in volume. So Q + + align:start position:0% +with this decrease uh in in volume. So Q + + + align:start position:0% +with this decrease uh in in volume. So Q +again the reaction quotient is products + + align:start position:0% +again the reaction quotient is products + + + align:start position:0% +again the reaction quotient is products +over reactants. So our product partial + + align:start position:0% +over reactants. So our product partial + + + align:start position:0% +over reactants. So our product partial +pressure of + + align:start position:0% +pressure of + + + align:start position:0% +pressure of +P4 over the partial pressure of P2 + + align:start position:0% +P4 over the partial pressure of P2 + + + align:start position:0% +P4 over the partial pressure of P2 +raised to the 2. So again you consider + + align:start position:0% +raised to the 2. So again you consider + + + align:start position:0% +raised to the 2. So again you consider +the stochometry when you're writing your + + align:start position:0% +the stochometry when you're writing your + + + align:start position:0% +the stochometry when you're writing your +equation for Q or for K. So if we work + + align:start position:0% +equation for Q or for K. So if we work + + + align:start position:0% +equation for Q or for K. So if we work +this out we find that by decreasing the + + align:start position:0% +this out we find that by decreasing the + + + align:start position:0% +this out we find that by decreasing the +volume by a factor of two, Q is now half + + align:start position:0% +volume by a factor of two, Q is now half + + + align:start position:0% +volume by a factor of two, Q is now half +what it was. It's decreased by a factor + + align:start position:0% +what it was. It's decreased by a factor + + + align:start position:0% +what it was. It's decreased by a factor +of two. So now Q is less than K. So we + + align:start position:0% +of two. So now Q is less than K. So we + + + align:start position:0% +of two. So now Q is less than K. So we +were at equilibrium before but a stress + + align:start position:0% +were at equilibrium before but a stress + + + align:start position:0% +were at equilibrium before but a stress +was implied. The volume was decreased + + align:start position:0% +was implied. The volume was decreased + + + align:start position:0% +was implied. The volume was decreased +and now we have a situation where Q is + + align:start position:0% +and now we have a situation where Q is + + + align:start position:0% +and now we have a situation where Q is +no longer equal K. Q is less than K. And + + align:start position:0% +no longer equal K. Q is less than K. And + + + align:start position:0% +no longer equal K. Q is less than K. And +so that's going to then shift the + + align:start position:0% +so that's going to then shift the + + + align:start position:0% +so that's going to then shift the +reaction toward products. It'll be + + align:start position:0% +reaction toward products. It'll be + + + align:start position:0% +reaction toward products. It'll be +spontaneous in the forward direction. So + + align:start position:0% +spontaneous in the forward direction. So + + + align:start position:0% +spontaneous in the forward direction. So +you can just sort of rationalize what + + align:start position:0% +you can just sort of rationalize what + + + align:start position:0% +you can just sort of rationalize what +will happen. And you'll have questions + + align:start position:0% +will happen. And you'll have questions + + + align:start position:0% +will happen. And you'll have questions +on homeworks and and on exams saying + + align:start position:0% +on homeworks and and on exams saying + + + align:start position:0% +on homeworks and and on exams saying +okay if this stress is applied predict + + align:start position:0% +okay if this stress is applied predict + + + align:start position:0% +okay if this stress is applied predict +how the reaction is going to respond. + + align:start position:0% +how the reaction is going to respond. + + + align:start position:0% +how the reaction is going to respond. +You can work it out in terms of thinking + + align:start position:0% +You can work it out in terms of thinking + + + align:start position:0% +You can work it out in terms of thinking +about Q and K or just sort of + + align:start position:0% +about Q and K or just sort of + + + align:start position:0% +about Q and K or just sort of +rationalize how do you minimize minimize + + align:start position:0% +rationalize how do you minimize minimize + + + align:start position:0% +rationalize how do you minimize minimize +that stress that's been applied to the + + align:start position:0% +that stress that's been applied to the + + + align:start position:0% +that stress that's been applied to the +system. And if you're asked how much + + align:start position:0% +system. And if you're asked how much + + + align:start position:0% +system. And if you're asked how much +happens if numbers are given, you can + + align:start position:0% +happens if numbers are given, you can + + + align:start position:0% +happens if numbers are given, you can +actually work this out. What Q and now + + align:start position:0% +actually work this out. What Q and now + + + align:start position:0% +actually work this out. What Q and now +what Q is at that point and and what K + + align:start position:0% + + + + align:start position:0% + +was. Now if we increase volume, so if we + + align:start position:0% +was. Now if we increase volume, so if we + + + align:start position:0% +was. Now if we increase volume, so if we +go in in this + + align:start position:0% +go in in this + + + align:start position:0% +go in in this +direction, what's going to happen? Well, + + align:start position:0% +direction, what's going to happen? Well, + + + align:start position:0% +direction, what's going to happen? Well, +the reverse will happen in this + + align:start position:0% +the reverse will happen in this + + + align:start position:0% +the reverse will happen in this +case. So we're going to shift toward + + align:start position:0% +case. So we're going to shift toward + + + align:start position:0% +case. So we're going to shift toward +reactants. + + align:start position:0% +reactants. + + + align:start position:0% +reactants. +So for every one mole of product that + + align:start position:0% +So for every one mole of product that + + + align:start position:0% +So for every one mole of product that +goes in this direction in the reverse + + align:start position:0% +goes in this direction in the reverse + + + align:start position:0% +goes in this direction in the reverse +direction, you'll form these two moles + + align:start position:0% +direction, you'll form these two moles + + + align:start position:0% +direction, you'll form these two moles +of P2. So a shift toward the reactants, + + align:start position:0% +of P2. So a shift toward the reactants, + + + align:start position:0% +of P2. So a shift toward the reactants, +a shift to the left is going to increase + + align:start position:0% +a shift to the left is going to increase + + + align:start position:0% +a shift to the left is going to increase +the total pressure. So if you increase + + align:start position:0% +the total pressure. So if you increase + + + align:start position:0% +the total pressure. So if you increase +the volume, you're initially going to uh + + align:start position:0% +the volume, you're initially going to uh + + + align:start position:0% +the volume, you're initially going to uh +decrease the partial pressure and a + + align:start position:0% +decrease the partial pressure and a + + + align:start position:0% +decrease the partial pressure and a +shift in this direction of of the + + align:start position:0% +shift in this direction of of the + + + align:start position:0% +shift in this direction of of the +reactions will compensate. It'll + + align:start position:0% +reactions will compensate. It'll + + + align:start position:0% +reactions will compensate. It'll +increase that partial pressure until you + + align:start position:0% +increase that partial pressure until you + + + align:start position:0% +increase that partial pressure until you +reach equilibrium again because you're + + align:start position:0% +reach equilibrium again because you're + + + align:start position:0% +reach equilibrium again because you're +going from in the reverse direction from + + align:start position:0% +going from in the reverse direction from + + + align:start position:0% +going from in the reverse direction from +one to two + + align:start position:0% + + + + align:start position:0% + +moles. So again, we could work this out + + align:start position:0% +moles. So again, we could work this out + + + align:start position:0% +moles. So again, we could work this out +in Q and K. And actually we'll do this + + align:start position:0% +in Q and K. And actually we'll do this + + + align:start position:0% +in Q and K. And actually we'll do this +at a later example but again you can + + align:start position:0% +at a later example but again you can + + + align:start position:0% +at a later example but again you can +rationalize or figure it out in terms of + + align:start position:0% +rationalize or figure it out in terms of + + + align:start position:0% +rationalize or figure it out in terms of +Q and K and what delta G would be + + align:start position:0% +Q and K and what delta G would be + + + align:start position:0% +Q and K and what delta G would be +positive or negative which direction the + + align:start position:0% +positive or negative which direction the + + + align:start position:0% +positive or negative which direction the +reaction is spontaneous in the forward + + align:start position:0% +reaction is spontaneous in the forward + + + align:start position:0% +reaction is spontaneous in the forward +direction or in the reverse + + align:start position:0% +direction or in the reverse + + + align:start position:0% +direction or in the reverse +direction. All right so let's make this + + align:start position:0% +direction. All right so let's make this + + + align:start position:0% +direction. All right so let's make this +a little bit more complicated now and + + align:start position:0% +a little bit more complicated now and + + + align:start position:0% +a little bit more complicated now and +consider what happens when you add an + + align:start position:0% +consider what happens when you add an + + + align:start position:0% +consider what happens when you add an +inert gas into that into that mixture. + + align:start position:0% +inert gas into that into that mixture. + + + align:start position:0% +inert gas into that into that mixture. +So here we're adding an inert gas into + + align:start position:0% +So here we're adding an inert gas into + + + align:start position:0% +So here we're adding an inert gas into +the container and when we add it, it's + + align:start position:0% +the container and when we add it, it's + + + align:start position:0% +the container and when we add it, it's +increasing the total pressure of that + + align:start position:0% +increasing the total pressure of that + + + align:start position:0% +increasing the total pressure of that +container and temperature is + + align:start position:0% +container and temperature is + + + align:start position:0% +container and temperature is +constant. Add an inert gas, increase the + + align:start position:0% +constant. Add an inert gas, increase the + + + align:start position:0% +constant. Add an inert gas, increase the +total pressure. What's going to happen + + align:start position:0% +total pressure. What's going to happen + + + align:start position:0% +total pressure. What's going to happen +to the reaction? Will it shift to the + + align:start position:0% +to the reaction? Will it shift to the + + + align:start position:0% +to the reaction? Will it shift to the +left or the right? + + align:start position:0% +left or the right? + + + align:start position:0% +left or the right? +What's going to happen? + + align:start position:0% + + + + align:start position:0% + +So the answer is in this case nothing. + + align:start position:0% +So the answer is in this case nothing. + + + align:start position:0% +So the answer is in this case nothing. +Why why was why won't this affect the + + align:start position:0% +Why why was why won't this affect the + + + align:start position:0% +Why why was why won't this affect the +equilibrium? Why aren't we affecting Q + + align:start position:0% +equilibrium? Why aren't we affecting Q + + + align:start position:0% +equilibrium? Why aren't we affecting Q +here? And the answer is that Q depends + + align:start position:0% +here? And the answer is that Q depends + + + align:start position:0% +here? And the answer is that Q depends +on the partial pressures of the gases + + align:start position:0% +on the partial pressures of the gases + + + align:start position:0% +on the partial pressures of the gases +involved and partial pressures are not + + align:start position:0% +involved and partial pressures are not + + + align:start position:0% +involved and partial pressures are not +changing. The total pressure is changing + + align:start position:0% +changing. The total pressure is changing + + + align:start position:0% +changing. The total pressure is changing +but the partial pressure of those gases + + align:start position:0% +but the partial pressure of those gases + + + align:start position:0% +but the partial pressure of those gases +are not changing. + + align:start position:0% +are not changing. + + + align:start position:0% +are not changing. +So at this point let's review partial + + align:start position:0% +So at this point let's review partial + + + align:start position:0% +So at this point let's review partial +pressure and then I think this will make + + align:start position:0% +pressure and then I think this will make + + + align:start position:0% +pressure and then I think this will make +a lot of + + align:start position:0% +a lot of + + + align:start position:0% +a lot of +sense. So the definition of partial + + align:start position:0% +sense. So the definition of partial + + + align:start position:0% +sense. So the definition of partial +pressure is the pressure that each gas + + align:start position:0% +pressure is the pressure that each gas + + + align:start position:0% +pressure is the pressure that each gas +would exert if it were alone in the + + align:start position:0% +would exert if it were alone in the + + + align:start position:0% +would exert if it were alone in the +container. So here we have some oxygen + + align:start position:0% +container. So here we have some oxygen + + + align:start position:0% +container. So here we have some oxygen +at one atmosphere. Here we have nitrogen + + align:start position:0% +at one atmosphere. Here we have nitrogen + + + align:start position:0% +at one atmosphere. Here we have nitrogen +at one atmosphere. And here we have a + + align:start position:0% +at one atmosphere. And here we have a + + + align:start position:0% +at one atmosphere. And here we have a +mixture of the oxygen and the nitrogen. + + align:start position:0% +mixture of the oxygen and the nitrogen. + + + align:start position:0% +mixture of the oxygen and the nitrogen. +And now that we've added one gas to the + + align:start position:0% +And now that we've added one gas to the + + + align:start position:0% +And now that we've added one gas to the +other, the pressure is two atmospheres. + + align:start position:0% +other, the pressure is two atmospheres. + + + align:start position:0% +other, the pressure is two atmospheres. +So we added one atmosphere of this and + + align:start position:0% +So we added one atmosphere of this and + + + align:start position:0% +So we added one atmosphere of this and +one atmosphere of that. And we have two + + align:start position:0% +one atmosphere of that. And we have two + + + align:start position:0% +one atmosphere of that. And we have two +atmospheres total. + + align:start position:0% +atmospheres total. + + + align:start position:0% +atmospheres total. +But if you're asking about the partial + + align:start position:0% +But if you're asking about the partial + + + align:start position:0% +But if you're asking about the partial +pressure say of + + align:start position:0% +pressure say of + + + align:start position:0% +pressure say of +oxygen, the partial pressure of oxygen + + align:start position:0% +oxygen, the partial pressure of oxygen + + + align:start position:0% +oxygen, the partial pressure of oxygen +is the same here as it is in the mixture + + align:start position:0% +is the same here as it is in the mixture + + + align:start position:0% +is the same here as it is in the mixture +because partial pressure is the pressure + + align:start position:0% +because partial pressure is the pressure + + + align:start position:0% +because partial pressure is the pressure +that's due just to that particular gas + + align:start position:0% +that's due just to that particular gas + + + align:start position:0% +that's due just to that particular gas +as if it were alone in a + + align:start position:0% + + + + align:start position:0% + +container. So let's look at the the the + + align:start position:0% +container. So let's look at the the the + + + align:start position:0% +container. So let's look at the the the +equations for partial pressure. And if + + align:start position:0% +equations for partial pressure. And if + + + align:start position:0% +equations for partial pressure. And if +you haven't had partial pressure before + + align:start position:0% +you haven't had partial pressure before + + + align:start position:0% +you haven't had partial pressure before +in high school, I said this is a review, + + align:start position:0% +in high school, I said this is a review, + + + align:start position:0% +in high school, I said this is a review, +but this is actually everything you need + + align:start position:0% +but this is actually everything you need + + + align:start position:0% +but this is actually everything you need +to know about partial pressure for this + + align:start position:0% +to know about partial pressure for this + + + align:start position:0% +to know about partial pressure for this +unit. So it doesn't really matter if you + + align:start position:0% +unit. So it doesn't really matter if you + + + align:start position:0% +unit. So it doesn't really matter if you +haven't seen this + + align:start position:0% +haven't seen this + + + align:start position:0% +haven't seen this +before. So if we have our familiar ideal + + align:start position:0% +before. So if we have our familiar ideal + + + align:start position:0% +before. So if we have our familiar ideal +gas law, the partial pressure of a + + align:start position:0% +gas law, the partial pressure of a + + + align:start position:0% +gas law, the partial pressure of a +depends on just the number of molecules + + align:start position:0% +depends on just the number of molecules + + + align:start position:0% +depends on just the number of molecules +of A in that container at a given + + align:start position:0% +of A in that container at a given + + + align:start position:0% +of A in that container at a given +volume. The total pressure of a system + + align:start position:0% +volume. The total pressure of a system + + + align:start position:0% +volume. The total pressure of a system +will be the partial pressure of A plus B + + align:start position:0% +will be the partial pressure of A plus B + + + align:start position:0% +will be the partial pressure of A plus B +plus C depending on how much of a + + align:start position:0% +plus C depending on how much of a + + + align:start position:0% +plus C depending on how much of a +mixture you have. In this case, we have + + align:start position:0% +mixture you have. In this case, we have + + + align:start position:0% +mixture you have. In this case, we have +a mixture of O2 and N2. So, our total + + align:start position:0% +a mixture of O2 and N2. So, our total + + + align:start position:0% +a mixture of O2 and N2. So, our total +pressure is two. But our partial + + align:start position:0% +pressure is two. But our partial + + + align:start position:0% +pressure is two. But our partial +pressures of each of these gases in here + + align:start position:0% +pressures of each of these gases in here + + + align:start position:0% +pressures of each of these gases in here +is still one as it was before when they + + align:start position:0% +is still one as it was before when they + + + align:start position:0% +is still one as it was before when they +were + + align:start position:0% +were + + + align:start position:0% +were +alone. So, how is this all relevant? + + align:start position:0% +alone. So, how is this all relevant? + + + align:start position:0% +alone. So, how is this all relevant? +Well, it's relevant because Q depends on + + align:start position:0% +Well, it's relevant because Q depends on + + + align:start position:0% +Well, it's relevant because Q depends on +the partial pressure, not the total + + align:start position:0% +the partial pressure, not the total + + + align:start position:0% +the partial pressure, not the total +pressure. So the question you have to + + align:start position:0% +pressure. So the question you have to + + + align:start position:0% +pressure. So the question you have to +ask yourself in looking at all these + + align:start position:0% +ask yourself in looking at all these + + + align:start position:0% +ask yourself in looking at all these +problems is, is the partial pressure + + align:start position:0% +problems is, is the partial pressure + + + align:start position:0% +problems is, is the partial pressure +changing? I.e. is Q changing? Because + + align:start position:0% +changing? I.e. is Q changing? Because + + + align:start position:0% +changing? I.e. is Q changing? Because +only when Q changes will equilibrium be + + align:start position:0% +only when Q changes will equilibrium be + + + align:start position:0% +only when Q changes will equilibrium be +affected. So in the particular example + + align:start position:0% +affected. So in the particular example + + + align:start position:0% +affected. So in the particular example +that I gave you at the beginning here, + + align:start position:0% +that I gave you at the beginning here, + + + align:start position:0% +that I gave you at the beginning here, +you asked what happens if an inert gas + + align:start position:0% +you asked what happens if an inert gas + + + align:start position:0% +you asked what happens if an inert gas +is added to an ina container increasing + + align:start position:0% +is added to an ina container increasing + + + align:start position:0% +is added to an ina container increasing +the total pressure at comp at constant + + align:start position:0% +the total pressure at comp at constant + + + align:start position:0% +the total pressure at comp at constant +temperature. And so the answer was + + align:start position:0% +temperature. And so the answer was + + + align:start position:0% +temperature. And so the answer was +nothing because Q is not affected. The + + align:start position:0% +nothing because Q is not affected. The + + + align:start position:0% +nothing because Q is not affected. The +partial pressure for that for the gases + + align:start position:0% +partial pressure for that for the gases + + + align:start position:0% +partial pressure for that for the gases +is still the same. The volume hasn't + + align:start position:0% +is still the same. The volume hasn't + + + align:start position:0% +is still the same. The volume hasn't +changed any. You haven't added more of + + align:start position:0% +changed any. You haven't added more of + + + align:start position:0% +changed any. You haven't added more of +these two gases. You added an inert gas. + + align:start position:0% +these two gases. You added an inert gas. + + + align:start position:0% +these two gases. You added an inert gas. +So the number of moles of these are the + + align:start position:0% +So the number of moles of these are the + + + align:start position:0% +So the number of moles of these are the +same. the volume is the same. So the + + align:start position:0% +same. the volume is the same. So the + + + align:start position:0% +same. the volume is the same. So the +partial pressure is the same. And if + + align:start position:0% +partial pressure is the same. And if + + + align:start position:0% +partial pressure is the same. And if +partial pressures are the same, then Q + + align:start position:0% +partial pressures are the same, then Q + + + align:start position:0% +partial pressures are the same, then Q +is unaffected. So Q does not change. So + + align:start position:0% +is unaffected. So Q does not change. So + + + align:start position:0% +is unaffected. So Q does not change. So +it doesn't matter. There's no there's no + + align:start position:0% +it doesn't matter. There's no there's no + + + align:start position:0% +it doesn't matter. There's no there's no +shift. Q is still equal to K. We're + + align:start position:0% +shift. Q is still equal to K. We're + + + align:start position:0% +shift. Q is still equal to K. We're +still under these conditions. Seems like + + align:start position:0% +still under these conditions. Seems like + + + align:start position:0% +still under these conditions. Seems like +it's a stress applied, but it's not + + align:start position:0% +it's a stress applied, but it's not + + + align:start position:0% +it's a stress applied, but it's not +really a real stress, so there's no + + align:start position:0% +really a real stress, so there's no + + + align:start position:0% +really a real stress, so there's no +change. All right, let's look at another + + align:start position:0% +change. All right, let's look at another + + + align:start position:0% +change. All right, let's look at another +scenario and consider what will happen. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +now what happens if we add an inert gas + + align:start position:0% +now what happens if we add an inert gas + + + align:start position:0% +now what happens if we add an inert gas +but the total pressure and the + + align:start position:0% +but the total pressure and the + + + align:start position:0% +but the total pressure and the +temperature are kept constant. So the + + align:start position:0% +temperature are kept constant. So the + + + align:start position:0% +temperature are kept constant. So the +total pressure is not allowed to change. + + align:start position:0% +total pressure is not allowed to change. + + + align:start position:0% +total pressure is not allowed to change. +It's kept + + align:start position:0% +It's kept + + + align:start position:0% +It's kept +constant. So for this to be true for you + + align:start position:0% +constant. So for this to be true for you + + + align:start position:0% +constant. So for this to be true for you +to add two things together and the total + + align:start position:0% +to add two things together and the total + + + align:start position:0% +to add two things together and the total +pressure doesn't change what had to have + + align:start position:0% +pressure doesn't change what had to have + + + align:start position:0% +pressure doesn't change what had to have +happened. + + align:start position:0% + + + + align:start position:0% + +volume volume had to have changed here + + align:start position:0% +volume volume had to have changed here + + + align:start position:0% +volume volume had to have changed here +otherwise this wouldn't this couldn't be + + align:start position:0% +otherwise this wouldn't this couldn't be + + + align:start position:0% +otherwise this wouldn't this couldn't be +true. So the volume had to change + + align:start position:0% +true. So the volume had to change + + + align:start position:0% +true. So the volume had to change +because here we have we have t constant + + align:start position:0% +because here we have we have t constant + + + align:start position:0% +because here we have we have t constant +temperature we have uh the gas constant + + align:start position:0% +temperature we have uh the gas constant + + + align:start position:0% +temperature we have uh the gas constant +here number of moles if uh if we've + + align:start position:0% +here number of moles if uh if we've + + + align:start position:0% +here number of moles if uh if we've +increased this number of moles and then + + align:start position:0% +increased this number of moles and then + + + align:start position:0% +increased this number of moles and then +the total pressure has to be affected by + + align:start position:0% +the total pressure has to be affected by + + + align:start position:0% +the total pressure has to be affected by +it if it didn't that means volume had to + + align:start position:0% +it if it didn't that means volume had to + + + align:start position:0% +it if it didn't that means volume had to +have changed for that to be true. + + align:start position:0% +have changed for that to be true. + + + align:start position:0% +have changed for that to be true. +So for the pressure to be constant, the + + align:start position:0% +So for the pressure to be constant, the + + + align:start position:0% +So for the pressure to be constant, the +volume of the container must have + + align:start position:0% +volume of the container must have + + + align:start position:0% +volume of the container must have +increased. And so you'll notice in + + align:start position:0% +increased. And so you'll notice in + + + align:start position:0% +increased. And so you'll notice in +working a lot of these problems, often + + align:start position:0% +working a lot of these problems, often + + + align:start position:0% +working a lot of these problems, often +it won't say anything about the volume. + + align:start position:0% +it won't say anything about the volume. + + + align:start position:0% +it won't say anything about the volume. +It'll tell you about the pressure and + + align:start position:0% +It'll tell you about the pressure and + + + align:start position:0% +It'll tell you about the pressure and +you have to figure out whether that + + align:start position:0% +you have to figure out whether that + + + align:start position:0% +you have to figure out whether that +means there was a volume change because + + align:start position:0% +means there was a volume change because + + + align:start position:0% +means there was a volume change because +the volume changes are the ones that are + + align:start position:0% +the volume changes are the ones that are + + + align:start position:0% +the volume changes are the ones that are +relevant. So it's all sort of uh in in + + align:start position:0% +relevant. So it's all sort of uh in in + + + align:start position:0% +relevant. So it's all sort of uh in in +the in the wordings of these + + align:start position:0% +the in the wordings of these + + + align:start position:0% +the in the wordings of these +problems. All right. So the volume must + + align:start position:0% +problems. All right. So the volume must + + + align:start position:0% +problems. All right. So the volume must +have increased otherwise the pressure + + align:start position:0% +have increased otherwise the pressure + + + align:start position:0% +have increased otherwise the pressure +would have gone up. So then this + + align:start position:0% +would have gone up. So then this + + + align:start position:0% +would have gone up. So then this +question really is what happens when the + + align:start position:0% +question really is what happens when the + + + align:start position:0% +question really is what happens when the +volume increases and we know how to + + align:start position:0% +volume increases and we know how to + + + align:start position:0% +volume increases and we know how to +answer that question + + align:start position:0% +answer that question + + + align:start position:0% +answer that question +already. So for this particular uh + + align:start position:0% +already. So for this particular uh + + + align:start position:0% +already. So for this particular uh +reaction where you have these two uh P2s + + align:start position:0% +reaction where you have these two uh P2s + + + align:start position:0% +reaction where you have these two uh P2s +going to one P4. An increase in volume + + align:start position:0% +going to one P4. An increase in volume + + + align:start position:0% +going to one P4. An increase in volume +means that you're going to shift two + + align:start position:0% +means that you're going to shift two + + + align:start position:0% +means that you're going to shift two +reactants. You're going to go from this + + align:start position:0% +reactants. You're going to go from this + + + align:start position:0% +reactants. You're going to go from this +side that has one to this side which has + + align:start position:0% +side that has one to this side which has + + + align:start position:0% +side that has one to this side which has +two and that way when you increase the + + align:start position:0% +two and that way when you increase the + + + align:start position:0% +two and that way when you increase the +volume the partial pressure is going to + + align:start position:0% +volume the partial pressure is going to + + + align:start position:0% +volume the partial pressure is going to +drop. So you want to respond in a way to + + align:start position:0% +drop. So you want to respond in a way to + + + align:start position:0% +drop. So you want to respond in a way to +minimize that stress which means you + + align:start position:0% +minimize that stress which means you + + + align:start position:0% +minimize that stress which means you +want then an increase in uh the partial + + align:start position:0% +want then an increase in uh the partial + + + align:start position:0% +want then an increase in uh the partial +pressure and again we can think about + + align:start position:0% +pressure and again we can think about + + + align:start position:0% +pressure and again we can think about +this in terms of Q and K. And let me + + align:start position:0% +this in terms of Q and K. And let me + + + align:start position:0% +this in terms of Q and K. And let me +just uh work a little example on the + + align:start position:0% +just uh work a little example on the + + + align:start position:0% +just uh work a little example on the +board to emphasize the point. So we did + + align:start position:0% +board to emphasize the point. So we did + + + align:start position:0% +board to emphasize the point. So we did +the other example earlier but now let's + + align:start position:0% +the other example earlier but now let's + + + align:start position:0% +the other example earlier but now let's +consider + + align:start position:0% +consider + + + align:start position:0% +consider +um if your + + align:start position:0% +um if your + + + align:start position:0% +um if your +volume + + align:start position:0% +volume + + + align:start position:0% +volume +doubles and my picture doesn't make it + + align:start position:0% +doubles and my picture doesn't make it + + + align:start position:0% +doubles and my picture doesn't make it +look like it's doubling but um this + + align:start position:0% +look like it's doubling but um this + + + align:start position:0% +look like it's doubling but um this +makes the math easier. So that means if + + align:start position:0% +makes the math easier. So that means if + + + align:start position:0% +makes the math easier. So that means if +the volume doubles you're going to half + + align:start position:0% +the volume doubles you're going to half + + + align:start position:0% +the volume doubles you're going to half +the partial pressure initially of both + + align:start position:0% +the partial pressure initially of both + + + align:start position:0% +the partial pressure initially of both +gases of P2 and P4. And so now we + + align:start position:0% +gases of P2 and P4. And so now we + + + align:start position:0% +gases of P2 and P4. And so now we +consider Q because it's really all about + + align:start position:0% +consider Q because it's really all about + + + align:start position:0% +consider Q because it's really all about +the relationship between Q and K. Q is + + align:start position:0% +the relationship between Q and K. Q is + + + align:start position:0% +the relationship between Q and K. Q is +going to equal the partial pressure of + + align:start position:0% +going to equal the partial pressure of + + + align:start position:0% +going to equal the partial pressure of +the products. Products over reactants. + + align:start position:0% +the products. Products over reactants. + + + align:start position:0% +the products. Products over reactants. +And the reactant is partial pressure of + + align:start position:0% +And the reactant is partial pressure of + + + align:start position:0% +And the reactant is partial pressure of +P2. And again with the stoometry that's + + align:start position:0% +P2. And again with the stoometry that's + + + align:start position:0% +P2. And again with the stoometry that's +squared. So if the volume doubles + + align:start position:0% +squared. So if the volume doubles + + + align:start position:0% +squared. So if the volume doubles +initially the partial pressure will be + + align:start position:0% +initially the partial pressure will be + + + align:start position:0% +initially the partial pressure will be +half for this for the products and also + + align:start position:0% +half for this for the products and also + + + align:start position:0% +half for this for the products and also +half for the reactant P2 and that's + + align:start position:0% +half for the reactant P2 and that's + + + align:start position:0% +half for the reactant P2 and that's +squared. So Q is twice what it was + + align:start position:0% +squared. So Q is twice what it was + + + align:start position:0% +squared. So Q is twice what it was +before. So now Q is greater than + + align:start position:0% +before. So now Q is greater than + + + align:start position:0% +before. So now Q is greater than +K and so you will have a delta G that's + + align:start position:0% +K and so you will have a delta G that's + + + align:start position:0% +K and so you will have a delta G that's +positive which means you're going to be + + align:start position:0% +positive which means you're going to be + + + align:start position:0% +positive which means you're going to be +spontaneous in the direction toward + + align:start position:0% + + + + align:start position:0% + +reactants. And you could sort of just + + align:start position:0% +reactants. And you could sort of just + + + align:start position:0% +reactants. And you could sort of just +reason that out by looking at the number + + align:start position:0% +reason that out by looking at the number + + + align:start position:0% +reason that out by looking at the number +of moles on one side or the other. Or if + + align:start position:0% +of moles on one side or the other. Or if + + + align:start position:0% +of moles on one side or the other. Or if +you want to convince yourself you can + + align:start position:0% +you want to convince yourself you can + + + align:start position:0% +you want to convince yourself you can +look at Q and K because this is where it + + align:start position:0% +look at Q and K because this is where it + + + align:start position:0% +look at Q and K because this is where it +really comes from. So when Q equals K, + + align:start position:0% +really comes from. So when Q equals K, + + + align:start position:0% +really comes from. So when Q equals K, +you're at equilibrium. Uh if it's + + align:start position:0% +you're at equilibrium. Uh if it's + + + align:start position:0% +you're at equilibrium. Uh if it's +greater than K, then then you shift. + + align:start position:0% +greater than K, then then you shift. + + + align:start position:0% +greater than K, then then you shift. +Yeah. Question. + + align:start position:0% + + + + align:start position:0% + +Yeah. Just because it doubled. So we're + + align:start position:0% +Yeah. Just because it doubled. So we're + + + align:start position:0% +Yeah. Just because it doubled. So we're +saying that then this is so we're just + + align:start position:0% +saying that then this is so we're just + + + align:start position:0% +saying that then this is so we're just +we're there could be real numbers that + + align:start position:0% +we're there could be real numbers that + + + align:start position:0% +we're there could be real numbers that +you're looking at, but this is just + + align:start position:0% +you're looking at, but this is just + + + align:start position:0% +you're looking at, but this is just +considering if you uh if you double this + + align:start position:0% +considering if you uh if you double this + + + align:start position:0% +considering if you uh if you double this +then you're going to have a a decrease. + + align:start position:0% + + + + align:start position:0% + +Yeah. So it's the partial pressure. + + align:start position:0% +Yeah. So it's the partial pressure. + + + align:start position:0% +Yeah. So it's the partial pressure. +Yeah. The number of moles aren't + + align:start position:0% +Yeah. The number of moles aren't + + + align:start position:0% +Yeah. The number of moles aren't +changing, but the pressure partial + + align:start position:0% +changing, but the pressure partial + + + align:start position:0% +changing, but the pressure partial +pressure is changing because the volume + + align:start position:0% +pressure is changing because the volume + + + align:start position:0% +pressure is changing because the volume +is changing. + + align:start position:0% + + + + align:start position:0% + +All right. Yeah. + + align:start position:0% + + + + align:start position:0% + +So Q well at equilibrium Q is equal to + + align:start position:0% +So Q well at equilibrium Q is equal to + + + align:start position:0% +So Q well at equilibrium Q is equal to +K. So the react Q uh and K are both + + align:start position:0% +K. So the react Q uh and K are both + + + align:start position:0% +K. So the react Q uh and K are both +products over our reactants or the + + align:start position:0% +products over our reactants or the + + + align:start position:0% +products over our reactants or the +partial pressure of products over + + align:start position:0% +partial pressure of products over + + + align:start position:0% +partial pressure of products over +reactants. So when when you make some + + align:start position:0% +reactants. So when when you make some + + + align:start position:0% +reactants. So when when you make some +change like this Q was equal to K but + + align:start position:0% +change like this Q was equal to K but + + + align:start position:0% +change like this Q was equal to K but +now now you have a you have a change + + align:start position:0% +now now you have a you have a change + + + align:start position:0% +now now you have a you have a change +either if you increase or decrease then + + align:start position:0% +either if you increase or decrease then + + + align:start position:0% +either if you increase or decrease then +it changes the relationship to your + + align:start position:0% +it changes the relationship to your + + + align:start position:0% +it changes the relationship to your +equilibrium. So you're no longer in the + + align:start position:0% +equilibrium. So you're no longer in the + + + align:start position:0% +equilibrium. So you're no longer in the +equilibrium conditions. Are we given + + align:start position:0% +equilibrium conditions. Are we given + + + align:start position:0% +equilibrium conditions. Are we given +that Q is equal to K in the initial + + align:start position:0% +that Q is equal to K in the initial + + + align:start position:0% +that Q is equal to K in the initial +states? So at equilibrium Q equals K by + + align:start position:0% +states? So at equilibrium Q equals K by + + + align:start position:0% +states? So at equilibrium Q equals K by +definition that in the in the question, + + align:start position:0% +definition that in the in the question, + + + align:start position:0% +definition that in the in the question, +right? So you're always considering if + + align:start position:0% +right? So you're always considering if + + + align:start position:0% +right? So you're always considering if +you're talking about applying a stress + + align:start position:0% +you're talking about applying a stress + + + align:start position:0% +you're talking about applying a stress +to a system, you're assuming that the + + align:start position:0% +to a system, you're assuming that the + + + align:start position:0% +to a system, you're assuming that the +the system was at equilibrium and then + + align:start position:0% +the system was at equilibrium and then + + + align:start position:0% +the system was at equilibrium and then +you apply a press a stress to that that + + align:start position:0% +you apply a press a stress to that that + + + align:start position:0% +you apply a press a stress to that that +situation that is at equilibrium and ask + + align:start position:0% +situation that is at equilibrium and ask + + + align:start position:0% +situation that is at equilibrium and ask +how does the system respond. So in all + + align:start position:0% +how does the system respond. So in all + + + align:start position:0% +how does the system respond. So in all +of these questions, you're under + + align:start position:0% +of these questions, you're under + + + align:start position:0% +of these questions, you're under +equilibrium conditions and then you + + align:start position:0% +equilibrium conditions and then you + + + align:start position:0% +equilibrium conditions and then you +apply the + + align:start position:0% + + + + align:start position:0% + +stress. + + align:start position:0% +stress. + + + align:start position:0% +stress. +Okay, so that's volume. Um, and so the + + align:start position:0% +Okay, so that's volume. Um, and so the + + + align:start position:0% +Okay, so that's volume. Um, and so the +secret to these problems is is asking is + + align:start position:0% +secret to these problems is is asking is + + + align:start position:0% +secret to these problems is is asking is +the partial pressure changing under + + align:start position:0% +the partial pressure changing under + + + align:start position:0% +the partial pressure changing under +those conditions when you're talking + + align:start position:0% +those conditions when you're talking + + + align:start position:0% +those conditions when you're talking +about volume. You had ai system at + + align:start position:0% +about volume. You had ai system at + + + align:start position:0% +about volume. You had ai system at +equilibrium, then you messed up your + + align:start position:0% +equilibrium, then you messed up your + + + align:start position:0% +equilibrium, then you messed up your +system at equilibrium by compressing the + + align:start position:0% +system at equilibrium by compressing the + + + align:start position:0% +system at equilibrium by compressing the +container or increasing the container. + + align:start position:0% +container or increasing the container. + + + align:start position:0% +container or increasing the container. +And whether you added an inert gas, it + + align:start position:0% +And whether you added an inert gas, it + + + align:start position:0% +And whether you added an inert gas, it +really always falls down to those two + + align:start position:0% +really always falls down to those two + + + align:start position:0% +really always falls down to those two +possibilities that the volume was + + align:start position:0% +possibilities that the volume was + + + align:start position:0% +possibilities that the volume was +decreased or the volume was increased. + + align:start position:0% +decreased or the volume was increased. + + + align:start position:0% +decreased or the volume was increased. +So you have to look at the question and + + align:start position:0% +So you have to look at the question and + + + align:start position:0% +So you have to look at the question and +read carefully and say, okay, what's + + align:start position:0% +read carefully and say, okay, what's + + + align:start position:0% +read carefully and say, okay, what's +happening to the volume under these + + align:start position:0% +happening to the volume under these + + + align:start position:0% +happening to the volume under these +cases? And then you can figure out which + + align:start position:0% +cases? And then you can figure out which + + + align:start position:0% +cases? And then you can figure out which +direction it's going to go. And of + + align:start position:0% +direction it's going to go. And of + + + align:start position:0% +direction it's going to go. And of +course, that was all one example. You + + align:start position:0% +course, that was all one example. You + + + align:start position:0% +course, that was all one example. You +have to look at what the particular + + align:start position:0% +have to look at what the particular + + + align:start position:0% +have to look at what the particular +reaction is. How many moles of are on + + align:start position:0% +reaction is. How many moles of are on + + + align:start position:0% +reaction is. How many moles of are on +one side and how many are on the other + + align:start position:0% +one side and how many are on the other + + + align:start position:0% +one side and how many are on the other +to think about + + align:start position:0% +to think about + + + align:start position:0% +to think about +this. So lately also works for + + align:start position:0% +this. So lately also works for + + + align:start position:0% +this. So lately also works for +temperature. So + + align:start position:0% +temperature. So + + + align:start position:0% +temperature. So +um in this + + align:start position:0% +um in this + + + align:start position:0% +um in this +case you're thinking about what happens + + align:start position:0% +case you're thinking about what happens + + + align:start position:0% +case you're thinking about what happens +if you raise the temperature of an + + align:start position:0% +if you raise the temperature of an + + + align:start position:0% +if you raise the temperature of an +equilibrium mixture. So the the reaction + + align:start position:0% +equilibrium mixture. So the the reaction + + + align:start position:0% +equilibrium mixture. So the the reaction +mixture is at equilibrium delta G equals + + align:start position:0% +mixture is at equilibrium delta G equals + + + align:start position:0% +mixture is at equilibrium delta G equals +0. Q equals K. And now you're changing + + align:start position:0% +0. Q equals K. And now you're changing + + + align:start position:0% +0. Q equals K. And now you're changing +something. You're changing the + + align:start position:0% +something. You're changing the + + + align:start position:0% +something. You're changing the +temperature. So raising the + + align:start position:0% +temperature. So raising the + + + align:start position:0% +temperature. So raising the +temperature by adding heat will cause + + align:start position:0% +temperature by adding heat will cause + + + align:start position:0% +temperature by adding heat will cause +the reaction to + + align:start position:0% +the reaction to + + + align:start position:0% +the reaction to +shift so that that heat is absorbed. So + + align:start position:0% +shift so that that heat is absorbed. So + + + align:start position:0% +shift so that that heat is absorbed. So +this is the same idea. You're applying + + align:start position:0% +this is the same idea. You're applying + + + align:start position:0% +this is the same idea. You're applying +stress to the system, raising the + + align:start position:0% +stress to the system, raising the + + + align:start position:0% +stress to the system, raising the +temperature. The reaction is going to + + align:start position:0% +temperature. The reaction is going to + + + align:start position:0% +temperature. The reaction is going to +respond so that that heat that was added + + align:start position:0% +respond so that that heat that was added + + + align:start position:0% +respond so that that heat that was added +is now absorbed. So you go back to where + + align:start position:0% +is now absorbed. So you go back to where + + + align:start position:0% +is now absorbed. So you go back to where +you were when you started. So lhat leier + + align:start position:0% +you were when you started. So lhat leier + + + align:start position:0% +you were when you started. So lhat leier +works for temperature as well. It's the + + align:start position:0% +works for temperature as well. It's the + + + align:start position:0% +works for temperature as well. It's the +same idea, but here the stress is + + align:start position:0% +same idea, but here the stress is + + + align:start position:0% +same idea, but here the stress is +changing the temperature of the system, + + align:start position:0% +changing the temperature of the system, + + + align:start position:0% +changing the temperature of the system, +adding heat or removing heat from the + + align:start position:0% +adding heat or removing heat from the + + + align:start position:0% +adding heat or removing heat from the +system and thinking about how that + + align:start position:0% +system and thinking about how that + + + align:start position:0% +system and thinking about how that +reaction that was at equilibrium is + + align:start position:0% +reaction that was at equilibrium is + + + align:start position:0% +reaction that was at equilibrium is +going to respond to the + + align:start position:0% + + + + align:start position:0% + +stress. So let's consider an exothermic + + align:start position:0% +stress. So let's consider an exothermic + + + align:start position:0% +stress. So let's consider an exothermic +reaction first. + + align:start position:0% + + + + align:start position:0% + +So an exothermic reaction, if we are + + align:start position:0% +So an exothermic reaction, if we are + + + align:start position:0% +So an exothermic reaction, if we are +raising the temperature of an exothermic + + align:start position:0% +raising the temperature of an exothermic + + + align:start position:0% +raising the temperature of an exothermic +reaction, you will favor the formation + + align:start position:0% +reaction, you will favor the formation + + + align:start position:0% +reaction, you will favor the formation +of the reactants. Why is that true? + + align:start position:0% +of the reactants. Why is that true? + + + align:start position:0% +of the reactants. Why is that true? +Well, with an exothermic reaction, + + align:start position:0% +Well, with an exothermic reaction, + + + align:start position:0% +Well, with an exothermic reaction, +you're producing + + align:start position:0% +you're producing + + + align:start position:0% +you're producing +heat and in the reverse direction, you + + align:start position:0% +heat and in the reverse direction, you + + + align:start position:0% +heat and in the reverse direction, you +would be absorbing heat. So according to + + align:start position:0% +would be absorbing heat. So according to + + + align:start position:0% +would be absorbing heat. So according to +Latier's principle, you want to respond + + align:start position:0% +Latier's principle, you want to respond + + + align:start position:0% +Latier's principle, you want to respond +to minimize the stress. So if you raise + + align:start position:0% +to minimize the stress. So if you raise + + + align:start position:0% +to minimize the stress. So if you raise +temperature, you want to shift in a + + align:start position:0% +temperature, you want to shift in a + + + align:start position:0% +temperature, you want to shift in a +direction that where that heat will be + + align:start position:0% + + + + align:start position:0% + +absorbed. So shift then in the + + align:start position:0% +absorbed. So shift then in the + + + align:start position:0% +absorbed. So shift then in the +endothermic direction. And so for an + + align:start position:0% +endothermic direction. And so for an + + + align:start position:0% +endothermic direction. And so for an +endothermic reaction, it's just the + + align:start position:0% +endothermic reaction, it's just the + + + align:start position:0% +endothermic reaction, it's just the +reverse of this. For an endothermic + + align:start position:0% +reverse of this. For an endothermic + + + align:start position:0% +reverse of this. For an endothermic +reaction, you're absorbing heat toward + + align:start position:0% +reaction, you're absorbing heat toward + + + align:start position:0% +reaction, you're absorbing heat toward +products and producing heat toward + + align:start position:0% +products and producing heat toward + + + align:start position:0% +products and producing heat toward +reactants. If you raise the temperature + + align:start position:0% +reactants. If you raise the temperature + + + align:start position:0% +reactants. If you raise the temperature +of an endothermic reaction, you will + + align:start position:0% +of an endothermic reaction, you will + + + align:start position:0% +of an endothermic reaction, you will +favor the formation of products because + + align:start position:0% +favor the formation of products because + + + align:start position:0% +favor the formation of products because +again, if you're adding heat, you want + + align:start position:0% +again, if you're adding heat, you want + + + align:start position:0% +again, if you're adding heat, you want +to absorb the heat. So, it'll shift the + + align:start position:0% +to absorb the heat. So, it'll shift the + + + align:start position:0% +to absorb the heat. So, it'll shift the +reaction in a direction that absorbs the + + align:start position:0% + + + + align:start position:0% + +heat. So, let's let's consider this a + + align:start position:0% +heat. So, let's let's consider this a + + + align:start position:0% +heat. So, let's let's consider this a +bit + + align:start position:0% +bit + + + align:start position:0% +bit +further. In this case, delta H is our + + align:start position:0% +further. In this case, delta H is our + + + align:start position:0% +further. In this case, delta H is our +predictive tool. If we know delta H, + + align:start position:0% +predictive tool. If we know delta H, + + + align:start position:0% +predictive tool. If we know delta H, +we're going to we're going to be able to + + align:start position:0% +we're going to we're going to be able to + + + align:start position:0% +we're going to we're going to be able to +predict the direction that the reaction + + align:start position:0% +predict the direction that the reaction + + + align:start position:0% +predict the direction that the reaction +is going to go. Before we were talking + + align:start position:0% +is going to go. Before we were talking + + + align:start position:0% +is going to go. Before we were talking +about delta G as being our our + + align:start position:0% +about delta G as being our our + + + align:start position:0% +about delta G as being our our +indicator. So here delta H is telling us + + align:start position:0% +indicator. So here delta H is telling us + + + align:start position:0% +indicator. So here delta H is telling us +quite a bit about what's what's going to + + align:start position:0% +quite a bit about what's what's going to + + + align:start position:0% +quite a bit about what's what's going to +happen, i.e. whether the reaction is + + align:start position:0% +happen, i.e. whether the reaction is + + + align:start position:0% +happen, i.e. whether the reaction is +exothermic or + + align:start position:0% + + + + align:start position:0% + +endothermic. Let's just do a quick + + align:start position:0% +endothermic. Let's just do a quick + + + align:start position:0% +endothermic. Let's just do a quick +example. + + align:start position:0% +example. + + + align:start position:0% +example. +So um here's a + + align:start position:0% +So um here's a + + + align:start position:0% +So um here's a +reaction delta + + align:start position:0% + + + + align:start position:0% + +H197.78 kJ per mole. Is that an + + align:start position:0% +H197.78 kJ per mole. Is that an + + + align:start position:0% +H197.78 kJ per mole. Is that an +endothermic or exothermic reaction? + + align:start position:0% +endothermic or exothermic reaction? + + + align:start position:0% +endothermic or exothermic reaction? +Exothermic reaction. So if heat is added + + align:start position:0% +Exothermic reaction. So if heat is added + + + align:start position:0% +Exothermic reaction. So if heat is added +if the temperature is raised what + + align:start position:0% +if the temperature is raised what + + + align:start position:0% +if the temperature is raised what +direction will it go toward products or + + align:start position:0% +direction will it go toward products or + + + align:start position:0% +direction will it go toward products or +reactants? + + align:start position:0% + + + + align:start position:0% + +Reactants. So it'll absorb it will want + + align:start position:0% +Reactants. So it'll absorb it will want + + + align:start position:0% +Reactants. So it'll absorb it will want +to absorb that heat. So it goes in the + + align:start position:0% +to absorb that heat. So it goes in the + + + align:start position:0% +to absorb that heat. So it goes in the +endothermic direction or the reverse + + align:start position:0% +endothermic direction or the reverse + + + align:start position:0% +endothermic direction or the reverse +direction. So that's pretty simple. + + align:start position:0% +direction. So that's pretty simple. + + + align:start position:0% +direction. So that's pretty simple. +Delta H allows us to make that + + align:start position:0% + + + + align:start position:0% + +prediction. All right. So we need to + + align:start position:0% +prediction. All right. So we need to + + + align:start position:0% +prediction. All right. So we need to +think now about the relationship between + + align:start position:0% +think now about the relationship between + + + align:start position:0% +think now about the relationship between +temperature and equilibrium + + align:start position:0% +temperature and equilibrium + + + align:start position:0% +temperature and equilibrium +constants. So equilibrium + + align:start position:0% +constants. So equilibrium + + + align:start position:0% +constants. So equilibrium +constant has been constant up until this + + align:start position:0% +constant has been constant up until this + + + align:start position:0% +constant has been constant up until this +point. + + align:start position:0% +point. + + + align:start position:0% +point. +But now we see that temperature will + + align:start position:0% +But now we see that temperature will + + + align:start position:0% +But now we see that temperature will +change the equilibrium constant. The + + align:start position:0% +change the equilibrium constant. The + + + align:start position:0% +change the equilibrium constant. The +ratio of products to reactants that you + + align:start position:0% +ratio of products to reactants that you + + + align:start position:0% +ratio of products to reactants that you +have at equilibrium will depend on + + align:start position:0% +have at equilibrium will depend on + + + align:start position:0% +have at equilibrium will depend on +whether it's an exothermic endothermic + + align:start position:0% +whether it's an exothermic endothermic + + + align:start position:0% +whether it's an exothermic endothermic +reaction and how much heat is in the + + align:start position:0% +reaction and how much heat is in the + + + align:start position:0% +reaction and how much heat is in the +system. The temperature that the + + align:start position:0% +system. The temperature that the + + + align:start position:0% +system. The temperature that the +reaction is being run at. You'll get a + + align:start position:0% +reaction is being run at. You'll get a + + + align:start position:0% +reaction is being run at. You'll get a +different equilibrium constant, a + + align:start position:0% +different equilibrium constant, a + + + align:start position:0% +different equilibrium constant, a +different ratio of products to reactants + + align:start position:0% +different ratio of products to reactants + + + align:start position:0% +different ratio of products to reactants +if you're at one temperature versus + + align:start position:0% +if you're at one temperature versus + + + align:start position:0% +if you're at one temperature versus +another temperature. + + align:start position:0% + + + + align:start position:0% + +And also we'll come back to this at the + + align:start position:0% +And also we'll come back to this at the + + + align:start position:0% +And also we'll come back to this at the +end of the course. Reaction rates also + + align:start position:0% +end of the course. Reaction rates also + + + align:start position:0% +end of the course. Reaction rates also +depend on temperature. So how fast those + + align:start position:0% +depend on temperature. So how fast those + + + align:start position:0% +depend on temperature. So how fast those +reactions go depends on temperature as + + align:start position:0% + + + + align:start position:0% + +well. All right. So now we want to + + align:start position:0% +well. All right. So now we want to + + + align:start position:0% +well. All right. So now we want to +figure out exactly how equilibrium + + align:start position:0% +figure out exactly how equilibrium + + + align:start position:0% +figure out exactly how equilibrium +constants depend on temperature. And to + + align:start position:0% +constants depend on temperature. And to + + + align:start position:0% +constants depend on temperature. And to +do that we have to think about what we + + align:start position:0% +do that we have to think about what we + + + align:start position:0% +do that we have to think about what we +know uh in terms of equations that have + + align:start position:0% +know uh in terms of equations that have + + + align:start position:0% +know uh in terms of equations that have +temperature in them and have equilibrium + + align:start position:0% +temperature in them and have equilibrium + + + align:start position:0% +temperature in them and have equilibrium +constants in + + align:start position:0% +constants in + + + align:start position:0% +constants in +them. So we know that delta G KN is + + align:start position:0% +them. So we know that delta G KN is + + + align:start position:0% +them. So we know that delta G KN is +minus RT natural log of + + align:start position:0% +minus RT natural log of + + + align:start position:0% +minus RT natural log of +K. We also know that delta G KN is equal + + align:start position:0% +K. We also know that delta G KN is equal + + + align:start position:0% +K. We also know that delta G KN is equal +to delta H knus T delta S. So now if we + + align:start position:0% +to delta H knus T delta S. So now if we + + + align:start position:0% +to delta H knus T delta S. So now if we +want to take that information and + + align:start position:0% +want to take that information and + + + align:start position:0% +want to take that information and +combine it and solve for the equilibrium + + align:start position:0% +combine it and solve for the equilibrium + + + align:start position:0% +combine it and solve for the equilibrium +constant in terms of delta H and we want + + align:start position:0% +constant in terms of delta H and we want + + + align:start position:0% +constant in terms of delta H and we want +to do that we want to solve for in terms + + align:start position:0% +to do that we want to solve for in terms + + + align:start position:0% +to do that we want to solve for in terms +of delta H and in terms of temperature + + align:start position:0% +of delta H and in terms of temperature + + + align:start position:0% +of delta H and in terms of temperature +because we want to think about delta H + + align:start position:0% +because we want to think about delta H + + + align:start position:0% +because we want to think about delta H +endothermic exothermic reactions and the + + align:start position:0% +endothermic exothermic reactions and the + + + align:start position:0% +endothermic exothermic reactions and the +relationship between equilibrium + + align:start position:0% +relationship between equilibrium + + + align:start position:0% +relationship between equilibrium +constant and temperature. So if we just + + align:start position:0% +constant and temperature. So if we just + + + align:start position:0% +constant and temperature. So if we just +rearrange these equations that that you + + align:start position:0% +rearrange these equations that that you + + + align:start position:0% +rearrange these equations that that you +have already seen and uh should be + + align:start position:0% +have already seen and uh should be + + + align:start position:0% +have already seen and uh should be +reviewing now for exam two you can come + + align:start position:0% +reviewing now for exam two you can come + + + align:start position:0% +reviewing now for exam two you can come +up with + + align:start position:0% +up with + + + align:start position:0% +up with +this and now we want to think about + + align:start position:0% +this and now we want to think about + + + align:start position:0% +this and now we want to think about +which of these terms are temperature + + align:start position:0% +which of these terms are temperature + + + align:start position:0% +which of these terms are temperature +dependent so I've already told you that + + align:start position:0% +dependent so I've already told you that + + + align:start position:0% +dependent so I've already told you that +the equilibrium constant is temperature + + align:start position:0% +the equilibrium constant is temperature + + + align:start position:0% +the equilibrium constant is temperature +dependent delta H here and delta S we + + align:start position:0% +dependent delta H here and delta S we + + + align:start position:0% +dependent delta H here and delta S we +can assume uh that they're pretty much + + align:start position:0% +can assume uh that they're pretty much + + + align:start position:0% +can assume uh that they're pretty much +constant over any temperature that we're + + align:start position:0% +constant over any temperature that we're + + + align:start position:0% +constant over any temperature that we're +we would be looking at any temperature + + align:start position:0% +we would be looking at any temperature + + + align:start position:0% +we would be looking at any temperature +that a reaction would would be run. So + + align:start position:0% +that a reaction would would be run. So + + + align:start position:0% +that a reaction would would be run. So +these guys are are not really changing. + + align:start position:0% +these guys are are not really changing. + + + align:start position:0% +these guys are are not really changing. +And so if they're not really changing + + align:start position:0% +And so if they're not really changing + + + align:start position:0% +And so if they're not really changing +then we can see that the equilibrium + + align:start position:0% +then we can see that the equilibrium + + + align:start position:0% +then we can see that the equilibrium +constant is going to change with respect + + align:start position:0% +constant is going to change with respect + + + align:start position:0% +constant is going to change with respect +to the change in temperature. So as we + + align:start position:0% +to the change in temperature. So as we + + + align:start position:0% +to the change in temperature. So as we +change temperature K will vary + + align:start position:0% +change temperature K will vary + + + align:start position:0% +change temperature K will vary +here. And we can look at this for two + + align:start position:0% +here. And we can look at this for two + + + align:start position:0% +here. And we can look at this for two +different + + align:start position:0% +different + + + align:start position:0% +different +temperatures. So we look if you change + + align:start position:0% +temperatures. So we look if you change + + + align:start position:0% +temperatures. So we look if you change +the temperature of the system the first + + align:start position:0% +the temperature of the system the first + + + align:start position:0% +the temperature of the system the first +temperature and the second temperature + + align:start position:0% +temperature and the second temperature + + + align:start position:0% +temperature and the second temperature +T1 and T2 and both there'll be different + + align:start position:0% +T1 and T2 and both there'll be different + + + align:start position:0% +T1 and T2 and both there'll be different +equilibrium constants at these two + + align:start position:0% +equilibrium constants at these two + + + align:start position:0% +equilibrium constants at these two +temperatures different ratios of + + align:start position:0% +temperatures different ratios of + + + align:start position:0% +temperatures different ratios of +products uh two reactants at this at + + align:start position:0% +products uh two reactants at this at + + + align:start position:0% +products uh two reactants at this at +these different + + align:start position:0% +these different + + + align:start position:0% +these different +temperatures. So if we write out two + + align:start position:0% +temperatures. So if we write out two + + + align:start position:0% +temperatures. So if we write out two +equations then one for K2 with T2. So + + align:start position:0% +equations then one for K2 with T2. So + + + align:start position:0% +equations then one for K2 with T2. So +the uh equation for the second + + align:start position:0% +the uh equation for the second + + + align:start position:0% +the uh equation for the second +temperature and the equation for the + + align:start position:0% +temperature and the equation for the + + + align:start position:0% +temperature and the equation for the +first temperature at T1 and the first + + align:start position:0% +first temperature at T1 and the first + + + align:start position:0% +first temperature at T1 and the first +equilibrium constant for that particular + + align:start position:0% +equilibrium constant for that particular + + + align:start position:0% +equilibrium constant for that particular +temperature and then if we subtract + + align:start position:0% +temperature and then if we subtract + + + align:start position:0% +temperature and then if we subtract +these two equations. So if we uh + + align:start position:0% +these two equations. So if we uh + + + align:start position:0% +these two equations. So if we uh +subtract the natural logs of the K's we + + align:start position:0% +subtract the natural logs of the K's we + + + align:start position:0% +subtract the natural logs of the K's we +can express that in terms of natural log + + align:start position:0% +can express that in terms of natural log + + + align:start position:0% +can express that in terms of natural log +of K2 over K1. And if we subtract the + + align:start position:0% +of K2 over K1. And if we subtract the + + + align:start position:0% +of K2 over K1. And if we subtract the +second part, uh when we subtract this + + align:start position:0% +second part, uh when we subtract this + + + align:start position:0% +second part, uh when we subtract this +from from this, the delta S over R terms + + align:start position:0% +from from this, the delta S over R terms + + + align:start position:0% +from from this, the delta S over R terms +are going to cancel out. They're the + + align:start position:0% +are going to cancel out. They're the + + + align:start position:0% +are going to cancel out. They're the +same. Delta H isn't delta S is not + + align:start position:0% +same. Delta H isn't delta S is not + + + align:start position:0% +same. Delta H isn't delta S is not +changing with temperature here. And so + + align:start position:0% +changing with temperature here. And so + + + align:start position:0% +changing with temperature here. And so +those two terms would be the same. + + align:start position:0% +those two terms would be the same. + + + align:start position:0% +those two terms would be the same. +They're going to go away. And now what's + + align:start position:0% +They're going to go away. And now what's + + + align:start position:0% +They're going to go away. And now what's +different, these two temperatures, and + + align:start position:0% +different, these two temperatures, and + + + align:start position:0% +different, these two temperatures, and +we can pull out the negative delta H + + align:start position:0% +we can pull out the negative delta H + + + align:start position:0% +we can pull out the negative delta H +here. We can pull out the one over r and + + align:start position:0% +here. We can pull out the one over r and + + + align:start position:0% +here. We can pull out the one over r and +that leaves 1 over t2 minus one over + + align:start position:0% +that leaves 1 over t2 minus one over + + + align:start position:0% +that leaves 1 over t2 minus one over +t1 and it has a name. So you know this + + align:start position:0% +t1 and it has a name. So you know this + + + align:start position:0% +t1 and it has a name. So you know this +must be an important equation. That's + + align:start position:0% +must be an important equation. That's + + + align:start position:0% +must be an important equation. That's +how that's partly how you can tell is + + align:start position:0% +how that's partly how you can tell is + + + align:start position:0% +how that's partly how you can tell is +the van hoff + + align:start position:0% +the van hoff + + + align:start position:0% +the van hoff +equation. So it tells you how the + + align:start position:0% +equation. So it tells you how the + + + align:start position:0% +equation. So it tells you how the +equilibrium constants are going to + + align:start position:0% +equilibrium constants are going to + + + align:start position:0% +equilibrium constants are going to +change with temperature. + + align:start position:0% + + + + align:start position:0% + +Now let's look at how the numbers are + + align:start position:0% +Now let's look at how the numbers are + + + align:start position:0% +Now let's look at how the numbers are +going to work out. If we have a negative + + align:start position:0% +going to work out. If we have a negative + + + align:start position:0% +going to work out. If we have a negative +sign here, i.e. if it's an exothermic + + align:start position:0% +sign here, i.e. if it's an exothermic + + + align:start position:0% +sign here, i.e. if it's an exothermic +reaction or we're going to have a + + align:start position:0% +reaction or we're going to have a + + + align:start position:0% +reaction or we're going to have a +positive delta H. So that would be an + + align:start position:0% +positive delta H. So that would be an + + + align:start position:0% +positive delta H. So that would be an +endothermic reaction. And whether you're + + align:start position:0% +endothermic reaction. And whether you're + + + align:start position:0% +endothermic reaction. And whether you're +adding or removing heat, there'll be a + + align:start position:0% +adding or removing heat, there'll be a + + + align:start position:0% +adding or removing heat, there'll be a +difference in the ratios of K1 to K2. So + + align:start position:0% +difference in the ratios of K1 to K2. So + + + align:start position:0% +difference in the ratios of K1 to K2. So +let's think about what comes out of this + + align:start position:0% +let's think about what comes out of this + + + align:start position:0% +let's think about what comes out of this +equation and rationalize + + align:start position:0% +equation and rationalize + + + align:start position:0% +equation and rationalize +it. So this looks a little complicated, + + align:start position:0% +it. So this looks a little complicated, + + + align:start position:0% +it. So this looks a little complicated, +but it's actually pretty + + align:start position:0% +but it's actually pretty + + + align:start position:0% +but it's actually pretty +simple. So here all we're doing is + + align:start position:0% +simple. So here all we're doing is + + + align:start position:0% +simple. So here all we're doing is +saying what if delta h is negative? If + + align:start position:0% +saying what if delta h is negative? If + + + align:start position:0% +saying what if delta h is negative? If +delta h is negative and we have t2 + + align:start position:0% +delta h is negative and we have t2 + + + align:start position:0% +delta h is negative and we have t2 +greater than t1, well this negative sign + + align:start position:0% +greater than t1, well this negative sign + + + align:start position:0% +greater than t1, well this negative sign +here is going to be negative all the way + + align:start position:0% +here is going to be negative all the way + + + align:start position:0% +here is going to be negative all the way +through here. it's always present. + + align:start position:0% +through here. it's always present. + + + align:start position:0% +through here. it's always present. +That's part of the equation. Delta H. + + align:start position:0% +That's part of the equation. Delta H. + + + align:start position:0% +That's part of the equation. Delta H. +Now, if it's negative, you'll have a + + align:start position:0% +Now, if it's negative, you'll have a + + + align:start position:0% +Now, if it's negative, you'll have a +negative here. And then we consider the + + align:start position:0% +negative here. And then we consider the + + + align:start position:0% +negative here. And then we consider the +difference between 1 over T2 and 1 over + + align:start position:0% +difference between 1 over T2 and 1 over + + + align:start position:0% +difference between 1 over T2 and 1 over +T1. And in this case, if T2 is greater + + align:start position:0% +T1. And in this case, if T2 is greater + + + align:start position:0% +T1. And in this case, if T2 is greater +than T1, that's a negative. So when you + + align:start position:0% +than T1, that's a negative. So when you + + + align:start position:0% +than T1, that's a negative. So when you +multiplied all those out together, we + + align:start position:0% +multiplied all those out together, we + + + align:start position:0% +multiplied all those out together, we +would have a negative here. And that's + + align:start position:0% +would have a negative here. And that's + + + align:start position:0% +would have a negative here. And that's +just what's all done there. Now, let's + + align:start position:0% +just what's all done there. Now, let's + + + align:start position:0% +just what's all done there. Now, let's +let's rationalize that this makes sense. + + align:start position:0% +let's rationalize that this makes sense. + + + align:start position:0% +let's rationalize that this makes sense. +So this is just the same thing but has a + + align:start position:0% +So this is just the same thing but has a + + + align:start position:0% +So this is just the same thing but has a +little more rationalization in it. Uh + + align:start position:0% +little more rationalization in it. Uh + + + align:start position:0% +little more rationalization in it. Uh +puts things in words instead of using + + align:start position:0% +puts things in words instead of using + + + align:start position:0% +puts things in words instead of using +the uh greater and less than + + align:start position:0% +the uh greater and less than + + + align:start position:0% +the uh greater and less than +thing. So for the case where and this + + align:start position:0% +thing. So for the case where and this + + + align:start position:0% +thing. So for the case where and this +these parts aren't written in your notes + + align:start position:0% +these parts aren't written in your notes + + + align:start position:0% +these parts aren't written in your notes +but if you want to add the words to it + + align:start position:0% +but if you want to add the words to it + + + align:start position:0% +but if you want to add the words to it +that's fine on the on the handout. So + + align:start position:0% +that's fine on the on the handout. So + + + align:start position:0% +that's fine on the on the handout. So +and you can just think about this on + + align:start position:0% +and you can just think about this on + + + align:start position:0% +and you can just think about this on +your own as well. So if delta H is less + + align:start position:0% +your own as well. So if delta H is less + + + align:start position:0% +your own as well. So if delta H is less +than zero negative number you have an + + align:start position:0% +than zero negative number you have an + + + align:start position:0% +than zero negative number you have an +exothermic reaction. So what happens if + + align:start position:0% +exothermic reaction. So what happens if + + + align:start position:0% +exothermic reaction. So what happens if +you increase the temperature of an + + align:start position:0% +you increase the temperature of an + + + align:start position:0% +you increase the temperature of an +exothermic reaction and let me just uh + + align:start position:0% +exothermic reaction and let me just uh + + + align:start position:0% +exothermic reaction and let me just uh +put those back up on the board for a + + align:start position:0% +put those back up on the board for a + + + align:start position:0% +put those back up on the board for a +minute. So for an + + align:start position:0% +minute. So for an + + + align:start position:0% +minute. So for an +exothermic it's not the best chunk. + + align:start position:0% + + + + align:start position:0% + +For an exothermic reaction, we're + + align:start position:0% +For an exothermic reaction, we're + + + align:start position:0% +For an exothermic reaction, we're +talking about + + align:start position:0% + + + + align:start position:0% + +reactants going to + + align:start position:0% + + + + align:start position:0% + +products. In an exothermic reaction, + + align:start position:0% +products. In an exothermic reaction, + + + align:start position:0% +products. In an exothermic reaction, +heat is + + align:start position:0% +heat is + + + align:start position:0% +heat is +produced in the forward direction and + + align:start position:0% +produced in the forward direction and + + + align:start position:0% +produced in the forward direction and +heat is + + align:start position:0% +heat is + + + align:start position:0% +heat is +absorbed in the reverse direction. + + align:start position:0% +absorbed in the reverse direction. + + + align:start position:0% +absorbed in the reverse direction. +So if we increase the temperature, it's + + align:start position:0% +So if we increase the temperature, it's + + + align:start position:0% +So if we increase the temperature, it's +going to want to go in a direction to + + align:start position:0% +going to want to go in a direction to + + + align:start position:0% +going to want to go in a direction to +compensate for that to absorb the heat. + + align:start position:0% +compensate for that to absorb the heat. + + + align:start position:0% +compensate for that to absorb the heat. +So it's going to go toward reactants. + + align:start position:0% +So it's going to go toward reactants. + + + align:start position:0% +So it's going to go toward reactants. +And so you're going to have a K1 that's + + align:start position:0% +And so you're going to have a K1 that's + + + align:start position:0% +And so you're going to have a K1 that's +greater than K2, which means at the new + + align:start position:0% +greater than K2, which means at the new + + + align:start position:0% +greater than K2, which means at the new +temperature, you're going to have less + + align:start position:0% +temperature, you're going to have less + + + align:start position:0% +temperature, you're going to have less +products or more reactants. So we can + + align:start position:0% +products or more reactants. So we can + + + align:start position:0% +products or more reactants. So we can +rationalize what that would be true. And + + align:start position:0% +rationalize what that would be true. And + + + align:start position:0% +rationalize what that would be true. And +if you don't want to rationalize it, you + + align:start position:0% +if you don't want to rationalize it, you + + + align:start position:0% +if you don't want to rationalize it, you +can always take the Van Hoff equation + + align:start position:0% +can always take the Van Hoff equation + + + align:start position:0% +can always take the Van Hoff equation +and figure it out uh by looking at the + + align:start position:0% +and figure it out uh by looking at the + + + align:start position:0% +and figure it out uh by looking at the +at the different signs and what what it + + align:start position:0% +at the different signs and what what it + + + align:start position:0% +at the different signs and what what it +would mean what's going to happen in + + align:start position:0% +would mean what's going to happen in + + + align:start position:0% +would mean what's going to happen in +terms of that ratio of K1 to K2 when you + + align:start position:0% +terms of that ratio of K1 to K2 when you + + + align:start position:0% +terms of that ratio of K1 to K2 when you +have this particular condition. Now if + + align:start position:0% +have this particular condition. Now if + + + align:start position:0% +have this particular condition. Now if +you decrease the temperature of an + + align:start position:0% +you decrease the temperature of an + + + align:start position:0% +you decrease the temperature of an +exothermic reaction, then it wants to + + align:start position:0% +exothermic reaction, then it wants to + + + align:start position:0% +exothermic reaction, then it wants to +compensate by producing more heat. + + align:start position:0% +compensate by producing more heat. + + + align:start position:0% +compensate by producing more heat. +You've decreased the temperature. It + + align:start position:0% +You've decreased the temperature. It + + + align:start position:0% +You've decreased the temperature. It +wants to respond to the stress to + + align:start position:0% +wants to respond to the stress to + + + align:start position:0% +wants to respond to the stress to +minimize the stress. The way to minimize + + align:start position:0% +minimize the stress. The way to minimize + + + align:start position:0% +minimize the stress. The way to minimize +the stress is produce more heat. So + + align:start position:0% +the stress is produce more heat. So + + + align:start position:0% +the stress is produce more heat. So +you'll make more + + align:start position:0% +you'll make more + + + align:start position:0% +you'll make more +products. Now for the endothermic + + align:start position:0% +products. Now for the endothermic + + + align:start position:0% +products. Now for the endothermic +reaction, it's just the other way + + align:start position:0% + + + + align:start position:0% + +around. So + + align:start position:0% +around. So + + + align:start position:0% +around. So +reactants going to + + align:start position:0% + + + + align:start position:0% + +products. Here + + align:start position:0% +products. Here + + + align:start position:0% +products. Here +heat is absorbed. + + align:start position:0% +heat is absorbed. + + + align:start position:0% +heat is absorbed. +And in the reverse direction, heat is + + align:start position:0% + + + + align:start position:0% + +produced. So now if we have our + + align:start position:0% +produced. So now if we have our + + + align:start position:0% +produced. So now if we have our +endothermic reaction and we increase + + align:start position:0% +endothermic reaction and we increase + + + align:start position:0% +endothermic reaction and we increase +temperature, we're going to shift to our + + align:start position:0% +temperature, we're going to shift to our + + + align:start position:0% +temperature, we're going to shift to our +products because we're going to want to + + align:start position:0% +products because we're going to want to + + + align:start position:0% +products because we're going to want to +absorb that heat that was just added, + + align:start position:0% +absorb that heat that was just added, + + + align:start position:0% +absorb that heat that was just added, +minimize the stress. And for an + + align:start position:0% +minimize the stress. And for an + + + align:start position:0% +minimize the stress. And for an +endothermic reaction, if we decrease the + + align:start position:0% +endothermic reaction, if we decrease the + + + align:start position:0% +endothermic reaction, if we decrease the +temperature, then we're going to shift + + align:start position:0% +temperature, then we're going to shift + + + align:start position:0% +temperature, then we're going to shift +it to produce more heat, i.e. toward + + align:start position:0% +it to produce more heat, i.e. toward + + + align:start position:0% +it to produce more heat, i.e. toward +reactants. So we'll have less products + + align:start position:0% +reactants. So we'll have less products + + + align:start position:0% +reactants. So we'll have less products +and we'd have K1 that's greater than + + align:start position:0% +and we'd have K1 that's greater than + + + align:start position:0% +and we'd have K1 that's greater than +K2. So you can use the Van Hoff equation + + align:start position:0% +K2. So you can use the Van Hoff equation + + + align:start position:0% +K2. So you can use the Van Hoff equation +to rationalize the prediction of change + + align:start position:0% +to rationalize the prediction of change + + + align:start position:0% +to rationalize the prediction of change +or if you're given numbers, you can say + + align:start position:0% +or if you're given numbers, you can say + + + align:start position:0% +or if you're given numbers, you can say +the exact amount of change. If you're + + align:start position:0% +the exact amount of change. If you're + + + align:start position:0% +the exact amount of change. If you're +given a K value at one temperature and + + align:start position:0% +given a K value at one temperature and + + + align:start position:0% +given a K value at one temperature and +then said, okay, if we change this + + align:start position:0% +then said, okay, if we change this + + + align:start position:0% +then said, okay, if we change this +temperature, if we increase it, this is + + align:start position:0% +temperature, if we increase it, this is + + + align:start position:0% +temperature, if we increase it, this is +what delta H is, what is our new + + align:start position:0% +what delta H is, what is our new + + + align:start position:0% +what delta H is, what is our new +equilibrium constant? So, you can use + + align:start position:0% +equilibrium constant? So, you can use + + + align:start position:0% +equilibrium constant? So, you can use +the Vanhoff equation to come up with + + align:start position:0% +the Vanhoff equation to come up with + + + align:start position:0% +the Vanhoff equation to come up with +direct numbers, or you can use it to + + align:start position:0% +direct numbers, or you can use it to + + + align:start position:0% +direct numbers, or you can use it to +just rationalize the direction of + + align:start position:0% +just rationalize the direction of + + + align:start position:0% +just rationalize the direction of +change. Um, if you have uh less time on + + align:start position:0% +change. Um, if you have uh less time on + + + align:start position:0% +change. Um, if you have uh less time on +a test, you can also just think about + + align:start position:0% +a test, you can also just think about + + + align:start position:0% +a test, you can also just think about +what might be going on here and predict + + align:start position:0% +what might be going on here and predict + + + align:start position:0% +what might be going on here and predict +without working through the numbers. + + align:start position:0% + + + + align:start position:0% + +Okay. So, now we're going to um + + align:start position:0% +Okay. So, now we're going to um + + + align:start position:0% +Okay. So, now we're going to um +apply what we just learned to think + + align:start position:0% +apply what we just learned to think + + + align:start position:0% +apply what we just learned to think +about how it can be used. + + align:start position:0% + + + + align:start position:0% + +So you want to think + + align:start position:0% +So you want to think + + + align:start position:0% +So you want to think +about the shifts that we talked about + + align:start position:0% +about the shifts that we talked about + + + align:start position:0% +about the shifts that we talked about +last class and the ones today have + + align:start position:0% +last class and the ones today have + + + align:start position:0% +last class and the ones today have +options of adding and removing products + + align:start position:0% +options of adding and removing products + + + align:start position:0% +options of adding and removing products +or reactants, changing volumes, changing + + align:start position:0% + + + + align:start position:0% + +temperatures. This is quite an important + + align:start position:0% +temperatures. This is quite an important + + + align:start position:0% +temperatures. This is quite an important +reaction and we talked about this last + + align:start position:0% +reaction and we talked about this last + + + align:start position:0% +reaction and we talked about this last +time. Nitrogen gas plus hydrogen gas + + align:start position:0% +time. Nitrogen gas plus hydrogen gas + + + align:start position:0% +time. Nitrogen gas plus hydrogen gas +going to ammonia. It's an exothermic + + align:start position:0% +going to ammonia. It's an exothermic + + + align:start position:0% +going to ammonia. It's an exothermic +reaction. + + align:start position:0% +reaction. + + + align:start position:0% +reaction. +So, if it's + + align:start position:0% +So, if it's + + + align:start position:0% +So, if it's +exothermic and you want to drive it + + align:start position:0% +exothermic and you want to drive it + + + align:start position:0% +exothermic and you want to drive it +toward ammonia, which is what people do, + + align:start position:0% +toward ammonia, which is what people do, + + + align:start position:0% +toward ammonia, which is what people do, +they want to make ammonia. You want to + + align:start position:0% +they want to make ammonia. You want to + + + align:start position:0% +they want to make ammonia. You want to +what's called fix nitrogen. So, ammonia + + align:start position:0% +what's called fix nitrogen. So, ammonia + + + align:start position:0% +what's called fix nitrogen. So, ammonia +is used in fertilizers, lots of nitrogen + + align:start position:0% +is used in fertilizers, lots of nitrogen + + + align:start position:0% +is used in fertilizers, lots of nitrogen +in the air, but you don't want it in the + + align:start position:0% +in the air, but you don't want it in the + + + align:start position:0% +in the air, but you don't want it in the +air. You want it in your soil for + + align:start position:0% +air. You want it in your soil for + + + align:start position:0% +air. You want it in your soil for +growing better crops. So, you want to do + + align:start position:0% +growing better crops. So, you want to do + + + align:start position:0% +growing better crops. So, you want to do +this reaction. If you want to maximize + + align:start position:0% +this reaction. If you want to maximize + + + align:start position:0% +this reaction. If you want to maximize +the yield, then it seems like the low + + align:start position:0% +the yield, then it seems like the low + + + align:start position:0% +the yield, then it seems like the low +temperature would be good. It's an + + align:start position:0% +temperature would be good. It's an + + + align:start position:0% +temperature would be good. It's an +exothermic reaction. So, low temperature + + align:start position:0% +exothermic reaction. So, low temperature + + + align:start position:0% +exothermic reaction. So, low temperature +would be good. It would favor + + align:start position:0% +would be good. It would favor + + + align:start position:0% +would be good. It would favor +products. But there's a problem with + + align:start position:0% +products. But there's a problem with + + + align:start position:0% +products. But there's a problem with +that, which is that low temperature also + + align:start position:0% +that, which is that low temperature also + + + align:start position:0% +that, which is that low temperature also +slows the rate. And you usually want a + + align:start position:0% +slows the rate. And you usually want a + + + align:start position:0% +slows the rate. And you usually want a +good rate. You want to make a lot of + + align:start position:0% +good rate. You want to make a lot of + + + align:start position:0% +good rate. You want to make a lot of +products pretty quickly, make some money + + align:start position:0% +products pretty quickly, make some money + + + align:start position:0% +products pretty quickly, make some money +off of it. So, you have to balance here. + + align:start position:0% +off of it. So, you have to balance here. + + + align:start position:0% +off of it. So, you have to balance here. +So sometimes the thermodynamics and the + + align:start position:0% +So sometimes the thermodynamics and the + + + align:start position:0% +So sometimes the thermodynamics and the +kinetics are working against each other. + + align:start position:0% +kinetics are working against each other. + + + align:start position:0% +kinetics are working against each other. +Um what would favor one doesn't work so + + align:start position:0% +Um what would favor one doesn't work so + + + align:start position:0% +Um what would favor one doesn't work so +well for the other. So um they have to + + align:start position:0% +well for the other. So um they have to + + + align:start position:0% +well for the other. So um they have to +have a compromised temperature which is + + align:start position:0% +have a compromised temperature which is + + + align:start position:0% +have a compromised temperature which is +actually quite a high temperature of + + align:start position:0% +actually quite a high temperature of + + + align:start position:0% +actually quite a high temperature of +500° + + align:start position:0% +500° + + + align:start position:0% +500° +C. All right. So it's a little bit of a + + align:start position:0% +C. All right. So it's a little bit of a + + + align:start position:0% +C. All right. So it's a little bit of a +problem there. The temperature thing + + align:start position:0% +problem there. The temperature thing + + + align:start position:0% +problem there. The temperature thing +isn't working for us. What are some + + align:start position:0% +isn't working for us. What are some + + + align:start position:0% +isn't working for us. What are some +other things that they could do to drive + + align:start position:0% +other things that they could do to drive + + + align:start position:0% +other things that they could do to drive +the reaction toward products? What else + + align:start position:0% +the reaction toward products? What else + + + align:start position:0% +the reaction toward products? What else +could you do? + + align:start position:0% + + + + align:start position:0% + +Okay. What What else could you do? + + align:start position:0% + + + + align:start position:0% + +I'm hearing a couple different things. + + align:start position:0% +I'm hearing a couple different things. + + + align:start position:0% +I'm hearing a couple different things. +I'm looking for one others. What + + align:start position:0% + + + + align:start position:0% + +about So, a couple things that you could + + align:start position:0% +about So, a couple things that you could + + + align:start position:0% +about So, a couple things that you could +do that would work. I heard I think I + + align:start position:0% +do that would work. I heard I think I + + + align:start position:0% +do that would work. I heard I think I +heard most of them now. Uh remove + + align:start position:0% +heard most of them now. Uh remove + + + align:start position:0% +heard most of them now. Uh remove +products as they're formed. So if you + + align:start position:0% +products as they're formed. So if you + + + align:start position:0% +products as they're formed. So if you +remove this product, that would drive it + + align:start position:0% +remove this product, that would drive it + + + align:start position:0% +remove this product, that would drive it +toward more products. And so one thing + + align:start position:0% +toward more products. And so one thing + + + align:start position:0% +toward more products. And so one thing +that they actually do is at every once + + align:start position:0% +that they actually do is at every once + + + align:start position:0% +that they actually do is at every once +in a while to stop the reaction, cool + + align:start position:0% +in a while to stop the reaction, cool + + + align:start position:0% +in a while to stop the reaction, cool +cool it all down and liquefy the ammonia + + align:start position:0% +cool it all down and liquefy the ammonia + + + align:start position:0% +cool it all down and liquefy the ammonia +gas. The liquid pours off and then + + align:start position:0% +gas. The liquid pours off and then + + + align:start position:0% +gas. The liquid pours off and then +you've removed this product and then you + + align:start position:0% +you've removed this product and then you + + + align:start position:0% +you've removed this product and then you +make more product. So if it reaches + + align:start position:0% +make more product. So if it reaches + + + align:start position:0% +make more product. So if it reaches +equilibrium, you pull off the product + + align:start position:0% +equilibrium, you pull off the product + + + align:start position:0% +equilibrium, you pull off the product +and then it makes more. And I also heard + + align:start position:0% +and then it makes more. And I also heard + + + align:start position:0% +and then it makes more. And I also heard +about this compressing the volume of the + + align:start position:0% +about this compressing the volume of the + + + align:start position:0% +about this compressing the volume of the +container because over here the + + align:start position:0% +container because over here the + + + align:start position:0% +container because over here the +reactants there's four molecules that + + align:start position:0% +reactants there's four molecules that + + + align:start position:0% +reactants there's four molecules that +are reacting to form two and so that + + align:start position:0% +are reacting to form two and so that + + + align:start position:0% +are reacting to form two and so that +should also help shift in the correct + + align:start position:0% +should also help shift in the correct + + + align:start position:0% +should also help shift in the correct +direction to make + + align:start position:0% +direction to make + + + align:start position:0% +direction to make +product. So they actually do do these at + + align:start position:0% +product. So they actually do do these at + + + align:start position:0% +product. So they actually do do these at +this pretty high temperature and they + + align:start position:0% +this pretty high temperature and they + + + align:start position:0% +this pretty high temperature and they +have to apply a really high pressure to + + align:start position:0% +have to apply a really high pressure to + + + align:start position:0% +have to apply a really high pressure to +compress that volume. So these are this + + align:start position:0% +compress that volume. So these are this + + + align:start position:0% +compress that volume. So these are this +is expensive. It requires a lot of + + align:start position:0% +is expensive. It requires a lot of + + + align:start position:0% +is expensive. It requires a lot of +energy actually to do this reaction + + align:start position:0% +energy actually to do this reaction + + + align:start position:0% +energy actually to do this reaction +because the conditions that are required + + align:start position:0% +because the conditions that are required + + + align:start position:0% +because the conditions that are required +to maximize the + + align:start position:0% +to maximize the + + + align:start position:0% +to maximize the +yield. So again, why this is important, + + align:start position:0% +yield. So again, why this is important, + + + align:start position:0% +yield. So again, why this is important, +there's lots of nitrogen in the air. + + align:start position:0% +there's lots of nitrogen in the air. + + + align:start position:0% +there's lots of nitrogen in the air. +However, it's really stable and you + + align:start position:0% +However, it's really stable and you + + + align:start position:0% +However, it's really stable and you +could probably tell me why it's so + + align:start position:0% +could probably tell me why it's so + + + align:start position:0% +could probably tell me why it's so +stable if you uh draw a nice uh Lewis + + align:start position:0% +stable if you uh draw a nice uh Lewis + + + align:start position:0% +stable if you uh draw a nice uh Lewis +diagram of this. Um it's difficult to + + align:start position:0% +diagram of this. Um it's difficult to + + + align:start position:0% +diagram of this. Um it's difficult to +break these apart. So that's why this is + + align:start position:0% +break these apart. So that's why this is + + + align:start position:0% +break these apart. So that's why this is +a hard problem because you want to break + + align:start position:0% +a hard problem because you want to break + + + align:start position:0% +a hard problem because you want to break +this bond to have usable nitrogen and uh + + align:start position:0% +this bond to have usable nitrogen and uh + + + align:start position:0% +this bond to have usable nitrogen and uh +it's challenging to do. So the process + + align:start position:0% +it's challenging to do. So the process + + + align:start position:0% +it's challenging to do. So the process +which I just described to you is one + + align:start position:0% +which I just described to you is one + + + align:start position:0% +which I just described to you is one +that was developed um though developed + + align:start position:0% +that was developed um though developed + + + align:start position:0% +that was developed um though developed +quite a long time ago. Uh this uh this + + align:start position:0% +quite a long time ago. Uh this uh this + + + align:start position:0% +quite a long time ago. Uh this uh this +reaction is called the hover Bosch + + align:start position:0% +reaction is called the hover Bosch + + + align:start position:0% +reaction is called the hover Bosch +process and it's responsible for + + align:start position:0% +process and it's responsible for + + + align:start position:0% +process and it's responsible for +generating 1.6* 6* 10^ the 10 kilograms + + align:start position:0% +generating 1.6* 6* 10^ the 10 kilograms + + + align:start position:0% +generating 1.6* 6* 10^ the 10 kilograms +of ammonia each year in the US for + + align:start position:0% +of ammonia each year in the US for + + + align:start position:0% +of ammonia each year in the US for +fertilizers uh and and other things. And + + align:start position:0% +fertilizers uh and and other things. And + + + align:start position:0% +fertilizers uh and and other things. And +it was developed by these two men right + + align:start position:0% +it was developed by these two men right + + + align:start position:0% +it was developed by these two men right +here. Um Harbor came up with the initial + + align:start position:0% +here. Um Harbor came up with the initial + + + align:start position:0% +here. Um Harbor came up with the initial +idea and Bosch helped figure out the + + align:start position:0% +idea and Bosch helped figure out the + + + align:start position:0% +idea and Bosch helped figure out the +appropriate conditions to get the + + align:start position:0% +appropriate conditions to get the + + + align:start position:0% +appropriate conditions to get the +maximum yield. So all they're doing is + + align:start position:0% +maximum yield. So all they're doing is + + + align:start position:0% +maximum yield. So all they're doing is +basically using some of the principles + + align:start position:0% +basically using some of the principles + + + align:start position:0% +basically using some of the principles +that you've already learned in this + + align:start position:0% +that you've already learned in this + + + align:start position:0% +that you've already learned in this +course. um and they both won Nobel + + align:start position:0% +course. um and they both won Nobel + + + align:start position:0% +course. um and they both won Nobel +prizes uh for being part of of this + + align:start position:0% +prizes uh for being part of of this + + + align:start position:0% +prizes uh for being part of of this +process. Uh this one initially and this + + align:start position:0% +process. Uh this one initially and this + + + align:start position:0% +process. Uh this one initially and this +one uh later on. I'll also mention this + + align:start position:0% +one uh later on. I'll also mention this + + + align:start position:0% +one uh later on. I'll also mention this +is a interesting man if you're + + align:start position:0% +is a interesting man if you're + + + align:start position:0% +is a interesting man if you're +interested in sort of history of + + align:start position:0% +interested in sort of history of + + + align:start position:0% +interested in sort of history of +science. Um he's a a German chemist and + + align:start position:0% +science. Um he's a a German chemist and + + + align:start position:0% +science. Um he's a a German chemist and +uh during World War I he switched his + + align:start position:0% +uh during World War I he switched his + + + align:start position:0% +uh during World War I he switched his +effort from fertilizers to uh coming up + + align:start position:0% +effort from fertilizers to uh coming up + + + align:start position:0% +effort from fertilizers to uh coming up +with different kinds of poison gases + + align:start position:0% +with different kinds of poison gases + + + align:start position:0% +with different kinds of poison gases +that could be used in warfare. Um but uh + + align:start position:0% +that could be used in warfare. Um but uh + + + align:start position:0% +that could be used in warfare. Um but uh +he was not rewarded uh favorably for + + align:start position:0% +he was not rewarded uh favorably for + + + align:start position:0% +he was not rewarded uh favorably for +this later on uh because he was also + + align:start position:0% +this later on uh because he was also + + + align:start position:0% +this later on uh because he was also +Jewish. So in 1933 he had to flee + + align:start position:0% +Jewish. So in 1933 he had to flee + + + align:start position:0% +Jewish. So in 1933 he had to flee +Germany uh despite all that he had done + + align:start position:0% +Germany uh despite all that he had done + + + align:start position:0% +Germany uh despite all that he had done +for the war effort earlier on and he did + + align:start position:0% +for the war effort earlier on and he did + + + align:start position:0% +for the war effort earlier on and he did +not live too long a life after that. But + + align:start position:0% +not live too long a life after that. But + + + align:start position:0% +not live too long a life after that. But +this is this was developed a long time + + align:start position:0% +this is this was developed a long time + + + align:start position:0% +this is this was developed a long time +ago and it is still used. So some + + align:start position:0% +ago and it is still used. So some + + + align:start position:0% +ago and it is still used. So some +scientists are actually trying to figure + + align:start position:0% +scientists are actually trying to figure + + + align:start position:0% +scientists are actually trying to figure +out how to do a better job. They figure + + align:start position:0% +out how to do a better job. They figure + + + align:start position:0% +out how to do a better job. They figure +any process that was really started to + + align:start position:0% +any process that was really started to + + + align:start position:0% +any process that was really started to +be developed before in the 1800s and + + align:start position:0% +be developed before in the 1800s and + + + align:start position:0% +be developed before in the 1800s and +kind of met and and refined in the + + align:start position:0% +kind of met and and refined in the + + + align:start position:0% +kind of met and and refined in the +1900s, maybe we could do better. Again, + + align:start position:0% +1900s, maybe we could do better. Again, + + + align:start position:0% +1900s, maybe we could do better. Again, +a lot of energy is responsible high + + align:start position:0% +a lot of energy is responsible high + + + align:start position:0% +a lot of energy is responsible high +temperatures, these extreme presses + + align:start position:0% +temperatures, these extreme presses + + + align:start position:0% +temperatures, these extreme presses +pressures for the condensed volume. + + align:start position:0% +pressures for the condensed volume. + + + align:start position:0% +pressures for the condensed volume. +Maybe we could figure out a way to do + + align:start position:0% +Maybe we could figure out a way to do + + + align:start position:0% +Maybe we could figure out a way to do +that same reaction without those extreme + + align:start position:0% +that same reaction without those extreme + + + align:start position:0% +that same reaction without those extreme +conditions that require a lot of energy. + + align:start position:0% +conditions that require a lot of energy. + + + align:start position:0% +conditions that require a lot of energy. +And so a number of scientists have + + align:start position:0% +And so a number of scientists have + + + align:start position:0% +And so a number of scientists have +looked to an enzyme, a protein found in + + align:start position:0% +looked to an enzyme, a protein found in + + + align:start position:0% +looked to an enzyme, a protein found in +bacteria. It does the exact same + + align:start position:0% +bacteria. It does the exact same + + + align:start position:0% +bacteria. It does the exact same +reaction as uh what is done + + align:start position:0% +reaction as uh what is done + + + align:start position:0% +reaction as uh what is done +commercially, but it doesn't use any + + align:start position:0% +commercially, but it doesn't use any + + + align:start position:0% +commercially, but it doesn't use any +high temperatures or any high pressures. + + align:start position:0% +high temperatures or any high pressures. + + + align:start position:0% +high temperatures or any high pressures. +So a number of scientists are trying to + + align:start position:0% +So a number of scientists are trying to + + + align:start position:0% +So a number of scientists are trying to +figure out how this protein works, how + + align:start position:0% +figure out how this protein works, how + + + align:start position:0% +figure out how this protein works, how +it's able to do this reaction so + + align:start position:0% +it's able to do this reaction so + + + align:start position:0% +it's able to do this reaction so +efficiently. And here's a space filling + + align:start position:0% +efficiently. And here's a space filling + + + align:start position:0% +efficiently. And here's a space filling +um picture of the enzyme. And here are + + align:start position:0% +um picture of the enzyme. And here are + + + align:start position:0% +um picture of the enzyme. And here are +metallo clusters that do the actual + + align:start position:0% +metallo clusters that do the actual + + + align:start position:0% +metallo clusters that do the actual +chemistry. And so uh in orange is iron + + align:start position:0% +chemistry. And so uh in orange is iron + + + align:start position:0% +chemistry. And so uh in orange is iron +and yellow is sulfur. Blue is nitrogen. + + align:start position:0% +and yellow is sulfur. Blue is nitrogen. + + + align:start position:0% +and yellow is sulfur. Blue is nitrogen. +Uh red is oxygen. Gray is carbon. Uh + + align:start position:0% +Uh red is oxygen. Gray is carbon. Uh + + + align:start position:0% +Uh red is oxygen. Gray is carbon. Uh +this uh purple color here is malibdinum. + + align:start position:0% +this uh purple color here is malibdinum. + + + align:start position:0% +this uh purple color here is malibdinum. +So these are metals used in biology to + + align:start position:0% +So these are metals used in biology to + + + align:start position:0% +So these are metals used in biology to +two particular kinds of reactions. And + + align:start position:0% +two particular kinds of reactions. And + + + align:start position:0% +two particular kinds of reactions. And +uh this just uh + + align:start position:0% +uh this just uh + + + align:start position:0% +uh this just uh +shows the um a little bit more about the + + align:start position:0% +shows the um a little bit more about the + + + align:start position:0% +shows the um a little bit more about the +the cluster is sort of in the heart of + + align:start position:0% +the cluster is sort of in the heart of + + + align:start position:0% +the cluster is sort of in the heart of +this protein molecule and all the + + align:start position:0% +this protein molecule and all the + + + align:start position:0% +this protein molecule and all the +chemistry happens at the metals but it's + + align:start position:0% +chemistry happens at the metals but it's + + + align:start position:0% +chemistry happens at the metals but it's +surrounded by a lot of protein. So + + align:start position:0% +surrounded by a lot of protein. So + + + align:start position:0% +surrounded by a lot of protein. So +that's one effort that a number of + + align:start position:0% +that's one effort that a number of + + + align:start position:0% +that's one effort that a number of +scientists are venturing on. Often we + + align:start position:0% +scientists are venturing on. Often we + + + align:start position:0% +scientists are venturing on. Often we +find var forms of bacteria have proteins + + align:start position:0% +find var forms of bacteria have proteins + + + align:start position:0% +find var forms of bacteria have proteins +that do reactions that we want to do and + + align:start position:0% +that do reactions that we want to do and + + + align:start position:0% +that do reactions that we want to do and +they do it much better than we do them. + + align:start position:0% +they do it much better than we do them. + + + align:start position:0% +they do it much better than we do them. +And so we want to understand uh how that + + align:start position:0% +And so we want to understand uh how that + + + align:start position:0% +And so we want to understand uh how that +how that works. And this is this is one + + align:start position:0% +how that works. And this is this is one + + + align:start position:0% +how that works. And this is this is one +example. Turns out this is quite + + align:start position:0% +example. Turns out this is quite + + + align:start position:0% +example. Turns out this is quite +complicated and scientists still don't + + align:start position:0% +complicated and scientists still don't + + + align:start position:0% +complicated and scientists still don't +understand the exact details of the + + align:start position:0% +understand the exact details of the + + + align:start position:0% +understand the exact details of the +reaction mechanism at that metal uh + + align:start position:0% +reaction mechanism at that metal uh + + + align:start position:0% +reaction mechanism at that metal uh +site. + + align:start position:0% +site. + + + align:start position:0% +site. +Another attempt is just to pretend that + + align:start position:0% +Another attempt is just to pretend that + + + align:start position:0% +Another attempt is just to pretend that +you know to move away from nature and + + align:start position:0% +you know to move away from nature and + + + align:start position:0% +you know to move away from nature and +Dick Shrock's lab here at MIT has been + + align:start position:0% +Dick Shrock's lab here at MIT has been + + + align:start position:0% +Dick Shrock's lab here at MIT has been +able to do this reaction using a sort of + + align:start position:0% +able to do this reaction using a sort of + + + align:start position:0% +able to do this reaction using a sort of +designed catalyst that has malibdinum in + + align:start position:0% +designed catalyst that has malibdinum in + + + align:start position:0% +designed catalyst that has malibdinum in +the center and uh you probably have + + align:start position:0% +the center and uh you probably have + + + align:start position:0% +the center and uh you probably have +heard the name Dick Shrock because he + + align:start position:0% +heard the name Dick Shrock because he + + + align:start position:0% +heard the name Dick Shrock because he +won the Nobel Prize in chemistry uh just + + align:start position:0% +won the Nobel Prize in chemistry uh just + + + align:start position:0% +won the Nobel Prize in chemistry uh just +a few weeks ago. So this is he didn't + + align:start position:0% +a few weeks ago. So this is he didn't + + + align:start position:0% +a few weeks ago. So this is he didn't +win for this. This is another one of his + + align:start position:0% +win for this. This is another one of his + + + align:start position:0% +win for this. This is another one of his +uh his contributions. + + align:start position:0% + + + + align:start position:0% + +All right. So, + + align:start position:0% +All right. So, + + + align:start position:0% +All right. So, +um, okay, really quickly, I want to give + + align:start position:0% +um, okay, really quickly, I want to give + + + align:start position:0% +um, okay, really quickly, I want to give +this one more biological example and + + align:start position:0% +this one more biological example and + + + align:start position:0% +this one more biological example and +then we'll hear more about exam two. So, + + align:start position:0% +then we'll hear more about exam two. So, + + + align:start position:0% +then we'll hear more about exam two. So, +again, as I' I've try, I will emphasize + + align:start position:0% +again, as I' I've try, I will emphasize + + + align:start position:0% +again, as I' I've try, I will emphasize +in this course, all the things you learn + + align:start position:0% +in this course, all the things you learn + + + align:start position:0% +in this course, all the things you learn +can be applied to biological systems as + + align:start position:0% +can be applied to biological systems as + + + align:start position:0% +can be applied to biological systems as +well. Same basic principles. So, here we + + align:start position:0% +well. Same basic principles. So, here we + + + align:start position:0% +well. Same basic principles. So, here we +have uh + + align:start position:0% +have uh + + + align:start position:0% +have uh +hemoglobin. So, hemoglobin is the + + align:start position:0% +hemoglobin. So, hemoglobin is the + + + align:start position:0% +hemoglobin. So, hemoglobin is the +protein in your body which carries + + align:start position:0% +protein in your body which carries + + + align:start position:0% +protein in your body which carries +oxygen carries carries oxygen from the + + align:start position:0% +oxygen carries carries oxygen from the + + + align:start position:0% +oxygen carries carries oxygen from the +lungs to the cells. And you can write + + align:start position:0% +lungs to the cells. And you can write + + + align:start position:0% +lungs to the cells. And you can write +the reaction for hemoglobin and oxygen + + align:start position:0% +the reaction for hemoglobin and oxygen + + + align:start position:0% +the reaction for hemoglobin and oxygen +the way you can write any of the + + align:start position:0% +the way you can write any of the + + + align:start position:0% +the way you can write any of the +reactions we've written. So hemoglobin + + align:start position:0% +reactions we've written. So hemoglobin + + + align:start position:0% +reactions we've written. So hemoglobin +plus oxygen goes to + + align:start position:0% +plus oxygen goes to + + + align:start position:0% +plus oxygen goes to +oxyhemoglobin. So here this is just + + align:start position:0% +oxyhemoglobin. So here this is just + + + align:start position:0% +oxyhemoglobin. So here this is just +oxygen bound to the + + align:start position:0% +oxygen bound to the + + + align:start position:0% +oxygen bound to the +hemoglobin. Now let's consider what + + align:start position:0% +hemoglobin. Now let's consider what + + + align:start position:0% +hemoglobin. Now let's consider what +happens if you decide to climb a + + align:start position:0% +happens if you decide to climb a + + + align:start position:0% +happens if you decide to climb a +mountain. So the partial pressure of + + align:start position:0% +mountain. So the partial pressure of + + + align:start position:0% +mountain. So the partial pressure of +oxygen is different at sea level. It's + + align:start position:0% +oxygen is different at sea level. It's + + + align:start position:0% +oxygen is different at sea level. It's +higher than it is in the mountains. So + + align:start position:0% +higher than it is in the mountains. So + + + align:start position:0% +higher than it is in the mountains. So +as you go up higher altitudes, the + + align:start position:0% +as you go up higher altitudes, the + + + align:start position:0% +as you go up higher altitudes, the +partial pressure of the oxygen + + align:start position:0% +partial pressure of the oxygen + + + align:start position:0% +partial pressure of the oxygen +decreases. So what does this mean in + + align:start position:0% +decreases. So what does this mean in + + + align:start position:0% +decreases. So what does this mean in +terms of this equilibrium? Which + + align:start position:0% +terms of this equilibrium? Which + + + align:start position:0% +terms of this equilibrium? Which +direction would it + + align:start position:0% + + + + align:start position:0% + +shift? If this is decreased, partial + + align:start position:0% +shift? If this is decreased, partial + + + align:start position:0% +shift? If this is decreased, partial +pressure of this is + + align:start position:0% +pressure of this is + + + align:start position:0% +pressure of this is +decreased. Yeah. So, you're going to uh + + align:start position:0% +decreased. Yeah. So, you're going to uh + + + align:start position:0% +decreased. Yeah. So, you're going to uh +shift toward reactants, which means you + + align:start position:0% +shift toward reactants, which means you + + + align:start position:0% +shift toward reactants, which means you +have less oxygenated blood. You have + + align:start position:0% +have less oxygenated blood. You have + + + align:start position:0% +have less oxygenated blood. You have +less oxygen bound, and that's not good. + + align:start position:0% +less oxygen bound, and that's not good. + + + align:start position:0% +less oxygen bound, and that's not good. +Makes it much harder to uh get energy uh + + align:start position:0% +Makes it much harder to uh get energy uh + + + align:start position:0% +Makes it much harder to uh get energy uh +to uh to climb that mountain. So, that's + + align:start position:0% +to uh to climb that mountain. So, that's + + + align:start position:0% +to uh to climb that mountain. So, that's +not good. So, usually if you're going to + + align:start position:0% +not good. So, usually if you're going to + + + align:start position:0% +not good. So, usually if you're going to +go climb a mountain, you have to adjust. + + align:start position:0% +go climb a mountain, you have to adjust. + + + align:start position:0% +go climb a mountain, you have to adjust. +You have to + + align:start position:0% +You have to + + + align:start position:0% +You have to +acclimatize. And uh so, I don't know how + + align:start position:0% +acclimatize. And uh so, I don't know how + + + align:start position:0% +acclimatize. And uh so, I don't know how +many people are mountain climbers. + + align:start position:0% +many people are mountain climbers. + + + align:start position:0% +many people are mountain climbers. +anybody, a few people. So, you usually + + align:start position:0% +anybody, a few people. So, you usually + + + align:start position:0% +anybody, a few people. So, you usually +have to get up and wait for a while + + align:start position:0% +have to get up and wait for a while + + + align:start position:0% +have to get up and wait for a while +before uh before you can start climbing. + + align:start position:0% +before uh before you can start climbing. + + + align:start position:0% +before uh before you can start climbing. +And what actually happens is your body's + + align:start position:0% +And what actually happens is your body's + + + align:start position:0% +And what actually happens is your body's +making more hemoglobin. So, you have to + + align:start position:0% +making more hemoglobin. So, you have to + + + align:start position:0% +making more hemoglobin. So, you have to +wait for this to happen. And if it makes + + align:start position:0% +wait for this to happen. And if it makes + + + align:start position:0% +wait for this to happen. And if it makes +more hemoglobin, what direction does it + + align:start position:0% + + + + align:start position:0% + +go? So, it shifts toward products. So, + + align:start position:0% +go? So, it shifts toward products. So, + + + align:start position:0% +go? So, it shifts toward products. So, +then you're you're in better shape to + + align:start position:0% +then you're you're in better shape to + + + align:start position:0% +then you're you're in better shape to +climb your mountain. So again, same + + align:start position:0% +climb your mountain. So again, same + + + align:start position:0% +climb your mountain. So again, same +principles of of shifting reaction + + align:start position:0% +principles of of shifting reaction + + + align:start position:0% +principles of of shifting reaction +applying to a biological system. \ No newline at end of file diff --git a/pGpyDJwAI8A.txt b/pGpyDJwAI8A.txt new file mode 100644 index 0000000000000000000000000000000000000000..68b3633a92304eccf1c0a8471f1b57ee33a221d4 --- /dev/null +++ b/pGpyDJwAI8A.txt @@ -0,0 +1,8379 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +So there's going to be three lectures + + align:start position:0% +So there's going to be three lectures + + + align:start position:0% +So there's going to be three lectures +and these are three lectures that I + + align:start position:0% +and these are three lectures that I + + + align:start position:0% +and these are three lectures that I +don't particularly like because they're + + align:start position:0% +don't particularly like because they're + + + align:start position:0% +don't particularly like because they're +kind of uh traditional but you know I + + align:start position:0% +kind of uh traditional but you know I + + + align:start position:0% +kind of uh traditional but you know I +think we have to do it. We want to + + align:start position:0% +think we have to do it. We want to + + + align:start position:0% +think we have to do it. We want to +understand spectra. We want to be able + + align:start position:0% +understand spectra. We want to be able + + + align:start position:0% +understand spectra. We want to be able +to + + align:start position:0% +to + + + align:start position:0% +to +uh understand what's in spectra. And so + + align:start position:0% +uh understand what's in spectra. And so + + + align:start position:0% +uh understand what's in spectra. And so +the first one this one is mostly + + align:start position:0% +the first one this one is mostly + + + align:start position:0% +the first one this one is mostly +selection rules. + + align:start position:0% + + + + align:start position:0% + +In other words, what do you need in + + align:start position:0% +In other words, what do you need in + + + align:start position:0% +In other words, what do you need in +order to get a particular kind of + + align:start position:0% +order to get a particular kind of + + + align:start position:0% +order to get a particular kind of +spectrum? And the next one is about + + align:start position:0% +spectrum? And the next one is about + + + align:start position:0% +spectrum? And the next one is about +relative + + align:start position:0% + + + + align:start position:0% + +intensities. Where do they come + + align:start position:0% +intensities. Where do they come + + + align:start position:0% +intensities. Where do they come +from? Uh and uh we'll we'll touch a + + align:start position:0% +from? Uh and uh we'll we'll touch a + + + align:start position:0% +from? Uh and uh we'll we'll touch a +little bit on that. And the third, which + + align:start position:0% +little bit on that. And the third, which + + + align:start position:0% +little bit on that. And the third, which +is the nicest one, + + align:start position:0% +is the nicest one, + + + align:start position:0% +is the nicest one, +pictures of spectrum. What do they look + + align:start position:0% +pictures of spectrum. What do they look + + + align:start position:0% +pictures of spectrum. What do they look +like? So that we know you know what to + + align:start position:0% +like? So that we know you know what to + + + align:start position:0% +like? So that we know you know what to +see I mean spectra are have a lot of + + align:start position:0% +see I mean spectra are have a lot of + + + align:start position:0% +see I mean spectra are have a lot of +information but uh if once you start you + + align:start position:0% +information but uh if once you start you + + + align:start position:0% +information but uh if once you start you +need to have some kind of an idealized + + align:start position:0% +need to have some kind of an idealized + + + align:start position:0% +need to have some kind of an idealized +view of what's going to be in the + + align:start position:0% +view of what's going to be in the + + + align:start position:0% +view of what's going to be in the +spectrum. Remember we have a pretty good + + align:start position:0% +spectrum. Remember we have a pretty good + + + align:start position:0% +spectrum. Remember we have a pretty good +idea of energy level + + align:start position:0% +idea of energy level + + + align:start position:0% +idea of energy level +diagrams but spectra aren't energy level + + align:start position:0% +diagrams but spectra aren't energy level + + + align:start position:0% +diagrams but spectra aren't energy level +diagrams. They're transitions between + + align:start position:0% +diagrams. They're transitions between + + + align:start position:0% +diagrams. They're transitions between +energy levels. And so it takes the + + align:start position:0% +energy levels. And so it takes the + + + align:start position:0% +energy levels. And so it takes the +information from different energy levels + + align:start position:0% +information from different energy levels + + + align:start position:0% +information from different energy levels +and combines it in a way that you have + + align:start position:0% +and combines it in a way that you have + + + align:start position:0% +and combines it in a way that you have +to begin to learn how to take apart. And + + align:start position:0% +to begin to learn how to take apart. And + + + align:start position:0% +to begin to learn how to take apart. And +so uh I think we'll have three lectures + + align:start position:0% +so uh I think we'll have three lectures + + + align:start position:0% +so uh I think we'll have three lectures +of this type. Okay. And + + align:start position:0% +of this type. Okay. And + + + align:start position:0% +of this type. Okay. And +so one of the results of today's lecture + + align:start position:0% +so one of the results of today's lecture + + + align:start position:0% +so one of the results of today's lecture +is that you will get a deeper sense of + + align:start position:0% +is that you will get a deeper sense of + + + align:start position:0% +is that you will get a deeper sense of +the rules for the three main kinds of + + align:start position:0% +the rules for the three main kinds of + + + align:start position:0% +the rules for the three main kinds of +spectra. If you have + + align:start position:0% +spectra. If you have + + + align:start position:0% +spectra. If you have +a + + align:start position:0% +a + + + align:start position:0% +a +permanent dipole moment, you can have a + + align:start position:0% +permanent dipole moment, you can have a + + + align:start position:0% +permanent dipole moment, you can have a +pure rotation. + + align:start position:0% + + + + align:start position:0% + +If there is a + + align:start position:0% +If there is a + + + align:start position:0% +If there is a +change in you as there would be when you + + align:start position:0% +change in you as there would be when you + + + align:start position:0% +change in you as there would be when you +vibrate certain + + align:start position:0% +vibrate certain + + + align:start position:0% +vibrate certain +vibrations then you get a vibration + + align:start position:0% +vibrations then you get a vibration + + + align:start position:0% +vibrations then you get a vibration +rotation + + align:start position:0% + + + + align:start position:0% + +spectrum and + + align:start position:0% +spectrum and + + + align:start position:0% +spectrum and +uh for an electronic spectrum you have + + align:start position:0% +uh for an electronic spectrum you have + + + align:start position:0% +uh for an electronic spectrum you have +to worry about electronic symmetries. + + align:start position:0% + + + + align:start position:0% + +you're you're going to need there to be + + align:start position:0% +you're you're going to need there to be + + + align:start position:0% +you're you're going to need there to be +some electric dipole transition moment + + align:start position:0% +some electric dipole transition moment + + + align:start position:0% +some electric dipole transition moment +that's not zero and the electronic + + align:start position:0% +that's not zero and the electronic + + + align:start position:0% +that's not zero and the electronic +symmetries will tell you when that's + + align:start position:0% +symmetries will tell you when that's + + + align:start position:0% +symmetries will tell you when that's +true. So here we have a pronto dipole + + align:start position:0% +true. So here we have a pronto dipole + + + align:start position:0% +true. So here we have a pronto dipole +moment which is the m dipole moment of a + + align:start position:0% +moment which is the m dipole moment of a + + + align:start position:0% +moment which is the m dipole moment of a +state of an electronic state and here we + + align:start position:0% +state of an electronic state and here we + + + align:start position:0% +state of an electronic state and here we +have when the molecule vibrates the + + align:start position:0% +have when the molecule vibrates the + + + align:start position:0% +have when the molecule vibrates the +dipole moment might change and it turns + + align:start position:0% +dipole moment might change and it turns + + + align:start position:0% +dipole moment might change and it turns +out that that's what makes it possible + + align:start position:0% +out that that's what makes it possible + + + align:start position:0% +out that that's what makes it possible +to change the vibrational uh quantum + + align:start position:0% +to change the vibrational uh quantum + + + align:start position:0% +to change the vibrational uh quantum +number and at the same time change the + + align:start position:0% +number and at the same time change the + + + align:start position:0% +number and at the same time change the +rotational quantum number and if there + + align:start position:0% +rotational quantum number and if there + + + align:start position:0% +rotational quantum number and if there +is an nonzero electric dipole transition + + align:start position:0% +is an nonzero electric dipole transition + + + align:start position:0% +is an nonzero electric dipole transition +moment then we can change vibration and + + align:start position:0% +moment then we can change vibration and + + + align:start position:0% +moment then we can change vibration and +rotation and so this you all know. Uh, + + align:start position:0% +rotation and so this you all know. Uh, + + + align:start position:0% +rotation and so this you all know. Uh, +but I'm going to try to go a little + + align:start position:0% +but I'm going to try to go a little + + + align:start position:0% +but I'm going to try to go a little +deeper than what you probably saw + + align:start position:0% +deeper than what you probably saw + + + align:start position:0% +deeper than what you probably saw +originally. Now, I don't know whether + + align:start position:0% +originally. Now, I don't know whether + + + align:start position:0% +originally. Now, I don't know whether +the the website for Hogan's monograph is + + align:start position:0% +the the website for Hogan's monograph is + + + align:start position:0% +the the website for Hogan's monograph is +in your notes. It's on the web. Uh, and + + align:start position:0% +in your notes. It's on the web. Uh, and + + + align:start position:0% +in your notes. It's on the web. Uh, and +uh, you definitely want to + + align:start position:0% +uh, you definitely want to + + + align:start position:0% +uh, you definitely want to +read JT Hogan uh, uh, NBS Monograph 115. + + align:start position:0% +read JT Hogan uh, uh, NBS Monograph 115. + + + align:start position:0% +read JT Hogan uh, uh, NBS Monograph 115. +It is a really really beautiful + + align:start position:0% +It is a really really beautiful + + + align:start position:0% +It is a really really beautiful +introduction to the stuff you need to + + align:start position:0% +introduction to the stuff you need to + + + align:start position:0% +introduction to the stuff you need to +know about + + align:start position:0% +know about + + + align:start position:0% +know about +that. You don't need to hear it from me. + + align:start position:0% +that. You don't need to hear it from me. + + + align:start position:0% +that. You don't need to hear it from me. +You can just get it from + + align:start position:0% +You can just get it from + + + align:start position:0% +You can just get it from +him. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, we're concerned about a particular + + align:start position:0% +So, we're concerned about a particular + + + align:start position:0% +So, we're concerned about a particular +electronic property which is the + + align:start position:0% +electronic property which is the + + + align:start position:0% +electronic property which is the +electric dipole moment. And so we have + + align:start position:0% +electric dipole moment. And so we have + + + align:start position:0% +electric dipole moment. And so we have +electric dipole moment which the + + align:start position:0% +electric dipole moment which the + + + align:start position:0% +electric dipole moment which the +operator + + align:start position:0% + + + + align:start position:0% + +is this thing which + + align:start position:0% +is this thing which + + + align:start position:0% +is this thing which +is that's + + align:start position:0% +is that's + + + align:start position:0% +is that's +right. So this is the electron times the + + align:start position:0% +right. So this is the electron times the + + + align:start position:0% +right. So this is the electron times the +uh uh vector connecting the electron to + + align:start position:0% +uh uh vector connecting the electron to + + + align:start position:0% +uh uh vector connecting the electron to +the center of mass. It's a sum over the + + align:start position:0% +the center of mass. It's a sum over the + + + align:start position:0% +the center of mass. It's a sum over the +individual electrons. This is the + + align:start position:0% +individual electrons. This is the + + + align:start position:0% +individual electrons. This is the +electric dwell moment or at least this + + align:start position:0% +electric dwell moment or at least this + + + align:start position:0% +electric dwell moment or at least this +is the thing that we care + + align:start position:0% +is the thing that we care + + + align:start position:0% +is the thing that we care +about. We tend to ignore the nuclei. The + + align:start position:0% +about. We tend to ignore the nuclei. The + + + align:start position:0% +about. We tend to ignore the nuclei. The +nuclei take care of themselves and for + + align:start position:0% +nuclei take care of themselves and for + + + align:start position:0% +nuclei take care of themselves and for +rotation and vibration. I mean uh uh you + + align:start position:0% +rotation and vibration. I mean uh uh you + + + align:start position:0% +rotation and vibration. I mean uh uh you +can show the nuclear contribution but + + align:start position:0% +can show the nuclear contribution but + + + align:start position:0% +can show the nuclear contribution but +this is the the more complicated thing + + align:start position:0% +this is the the more complicated thing + + + align:start position:0% +this is the the more complicated thing +because the nuclei aren't doing much but + + align:start position:0% +because the nuclei aren't doing much but + + + align:start position:0% +because the nuclei aren't doing much but +the electrons are somehow spread. So + + align:start position:0% +the electrons are somehow spread. So + + + align:start position:0% +the electrons are somehow spread. So +this is the operator and we're going to + + align:start position:0% +this is the operator and we're going to + + + align:start position:0% +this is the operator and we're going to +want to by integrating over the + + align:start position:0% +want to by integrating over the + + + align:start position:0% +want to by integrating over the +electronic coordinates get some sort of + + align:start position:0% +electronic coordinates get some sort of + + + align:start position:0% +electronic coordinates get some sort of +a operator initial final vector + + align:start position:0% +a operator initial final vector + + + align:start position:0% +a operator initial final vector +r. So if we integrate over the electron + + align:start position:0% +r. So if we integrate over the electron + + + align:start position:0% +r. So if we integrate over the electron +coordinates, we convert this operator + + align:start position:0% +coordinates, we convert this operator + + + align:start position:0% +coordinates, we convert this operator +into a + + align:start position:0% +into a + + + align:start position:0% +into a +function a function of r which may still + + align:start position:0% +function a function of r which may still + + + align:start position:0% +function a function of r which may still +be operating between uh vibrational or + + align:start position:0% +be operating between uh vibrational or + + + align:start position:0% +be operating between uh vibrational or +vibration rotation energy levels. So the + + align:start position:0% +vibration rotation energy levels. So the + + + align:start position:0% +vibration rotation energy levels. So the +first big step is the Bopen + + align:start position:0% +first big step is the Bopen + + + align:start position:0% +first big step is the Bopen +approximation takes us from an operator + + align:start position:0% +approximation takes us from an operator + + + align:start position:0% +approximation takes us from an operator +to the electronic coordinate which is + + align:start position:0% +to the electronic coordinate which is + + + align:start position:0% +to the electronic coordinate which is +embarrassing which is something we don't + + align:start position:0% +embarrassing which is something we don't + + + align:start position:0% +embarrassing which is something we don't +particularly want to deal with is + + align:start position:0% +particularly want to deal with is + + + align:start position:0% +particularly want to deal with is +integrated away. And one of the things + + align:start position:0% +integrated away. And one of the things + + + align:start position:0% +integrated away. And one of the things +we do because we've written the wave + + align:start position:0% +we do because we've written the wave + + + align:start position:0% +we do because we've written the wave +function as a product of these three + + align:start position:0% +function as a product of these three + + + align:start position:0% +function as a product of these three +factors is that we integrate out various + + align:start position:0% +factors is that we integrate out various + + + align:start position:0% +factors is that we integrate out various +of the the variables to reduce always to + + align:start position:0% +of the the variables to reduce always to + + + align:start position:0% +of the the variables to reduce always to +the thing we want. Okay. So that's one + + align:start position:0% +the thing we want. Okay. So that's one + + + align:start position:0% +the thing we want. Okay. So that's one +of the key building blocks. Another + + align:start position:0% +of the key building blocks. Another + + + align:start position:0% +of the key building blocks. Another +thing is that we have a molecule and the + + align:start position:0% +thing is that we have a molecule and the + + + align:start position:0% +thing is that we have a molecule and the +molecule is rotating doing stuff and we + + align:start position:0% +molecule is rotating doing stuff and we + + + align:start position:0% +molecule is rotating doing stuff and we +have a laboratory where we are and where + + align:start position:0% +have a laboratory where we are and where + + + align:start position:0% +have a laboratory where we are and where +our detectors are and our lasers are. + + align:start position:0% +our detectors are and our lasers are. + + + align:start position:0% +our detectors are and our lasers are. +And so we want to know about + + align:start position:0% +And so we want to know about + + + align:start position:0% +And so we want to know about +uh uh what does the LA what what does + + align:start position:0% +uh uh what does the LA what what does + + + align:start position:0% +uh uh what does the LA what what does +the what can you do in the laboratory to + + align:start position:0% +the what can you do in the laboratory to + + + align:start position:0% +the what can you do in the laboratory to +something uh that has all of its stuff + + align:start position:0% +something uh that has all of its stuff + + + align:start position:0% +something uh that has all of its stuff +in the body frame. And so we're going to + + align:start position:0% +in the body frame. And so we're going to + + + align:start position:0% +in the body frame. And so we're going to +be concerned about the relationship + + align:start position:0% +be concerned about the relationship + + + align:start position:0% +be concerned about the relationship +between two coordinate systems + + align:start position:0% + + + + align:start position:0% + +uh both centered at the center of mass + + align:start position:0% +uh both centered at the center of mass + + + align:start position:0% +uh both centered at the center of mass +of the molecule. So we the two + + align:start position:0% +of the molecule. So we the two + + + align:start position:0% +of the molecule. So we the two +coordinate systems coincide + + align:start position:0% +coordinate systems coincide + + + align:start position:0% +coordinate systems coincide +uh at the at the origin. The origins of + + align:start position:0% +uh at the at the origin. The origins of + + + align:start position:0% +uh at the at the origin. The origins of +the two coordinate systems coincide but + + align:start position:0% +the two coordinate systems coincide but + + + align:start position:0% +the two coordinate systems coincide but +the orientations of the two coordinate + + align:start position:0% +the orientations of the two coordinate + + + align:start position:0% +the orientations of the two coordinate +systems + + align:start position:0% +systems + + + align:start position:0% +systems +are not fixed. and we're going to be + + align:start position:0% +are not fixed. and we're going to be + + + align:start position:0% +are not fixed. and we're going to be +averaging over + + align:start position:0% +averaging over + + + align:start position:0% +averaging over +uh the body fixed coordinates, but we're + + align:start position:0% +uh the body fixed coordinates, but we're + + + align:start position:0% +uh the body fixed coordinates, but we're +going to want something that describes + + align:start position:0% +going to want something that describes + + + align:start position:0% +going to want something that describes +the relationship between the lab and the + + align:start position:0% +the relationship between the lab and the + + + align:start position:0% +the relationship between the lab and the +uh body. And so we're going to use + + align:start position:0% +uh body. And so we're going to use + + + align:start position:0% +uh body. And so we're going to use +capital letters for the laboratory and + + align:start position:0% +capital letters for the laboratory and + + + align:start position:0% +capital letters for the laboratory and +lowercase letters for the body. And uh + + align:start position:0% +lowercase letters for the body. And uh + + + align:start position:0% +lowercase letters for the body. And uh +so in order to uh talk about how the + + align:start position:0% +so in order to uh talk about how the + + + align:start position:0% +so in order to uh talk about how the +body presents itself to the laboratory, + + align:start position:0% +body presents itself to the laboratory, + + + align:start position:0% +body presents itself to the laboratory, +we're going to be integrating over the + + align:start position:0% +we're going to be integrating over the + + + align:start position:0% +we're going to be integrating over the +the the coordinates that determine the + + align:start position:0% +the the coordinates that determine the + + + align:start position:0% +the the coordinates that determine the +orientation of the body relative to the + + align:start position:0% +orientation of the body relative to the + + + align:start position:0% +orientation of the body relative to the +laboratory. And uh uh crucial in that + + align:start position:0% +laboratory. And uh uh crucial in that + + + align:start position:0% +laboratory. And uh uh crucial in that +will be the direction + + align:start position:0% +will be the direction + + + align:start position:0% +will be the direction +cos. Okay. + + align:start position:0% + + + + align:start position:0% + +So last time we had some kind of exact + + align:start position:0% +So last time we had some kind of exact + + + align:start position:0% +So last time we had some kind of exact +Hamiltonian and we replaced it by a zero + + align:start position:0% +Hamiltonian and we replaced it by a zero + + + align:start position:0% +Hamiltonian and we replaced it by a zero +order + + align:start position:0% +order + + + align:start position:0% +order +Hamiltonian and some kind of a + + align:start position:0% +Hamiltonian and some kind of a + + + align:start position:0% +Hamiltonian and some kind of a +perturbation term. And then we used + + align:start position:0% +perturbation term. And then we used + + + align:start position:0% +perturbation term. And then we used +perturbation theory to get the uh energy + + align:start position:0% +perturbation theory to get the uh energy + + + align:start position:0% +perturbation theory to get the uh energy +levels electronic vibration rotation + + align:start position:0% +levels electronic vibration rotation + + + align:start position:0% +levels electronic vibration rotation +energy levels. So you sort of know about + + align:start position:0% +energy levels. So you sort of know about + + + align:start position:0% +energy levels. So you sort of know about +how to do this or that it is something + + align:start position:0% +how to do this or that it is something + + + align:start position:0% +how to do this or that it is something +to do and you also + + align:start position:0% +to do and you also + + + align:start position:0% +to do and you also +get wave functions + + align:start position:0% +get wave functions + + + align:start position:0% +get wave functions +EJ. So, you know, you start out with a a + + align:start position:0% +EJ. So, you know, you start out with a a + + + align:start position:0% +EJ. So, you know, you start out with a a +picture, a zero order picture that + + align:start position:0% +picture, a zero order picture that + + + align:start position:0% +picture, a zero order picture that +involves the the building blocks that + + align:start position:0% +involves the the building blocks that + + + align:start position:0% +involves the the building blocks that +you understand rigid rotor, + + align:start position:0% +you understand rigid rotor, + + + align:start position:0% +you understand rigid rotor, +uh, harmonic oscillator, some model for + + align:start position:0% +uh, harmonic oscillator, some model for + + + align:start position:0% +uh, harmonic oscillator, some model for +electronic and we add whatever was left + + align:start position:0% +electronic and we add whatever was left + + + align:start position:0% +electronic and we add whatever was left +out and from that we can get energy + + align:start position:0% +out and from that we can get energy + + + align:start position:0% +out and from that we can get energy +levels and wave functions. Now we want + + align:start position:0% +levels and wave functions. Now we want + + + align:start position:0% +levels and wave functions. Now we want +to use this uh to + + align:start position:0% + + + + align:start position:0% + +uh get spectra. I mean if you were + + align:start position:0% +uh get spectra. I mean if you were + + + align:start position:0% +uh get spectra. I mean if you were +quantum chemists so you would be + + align:start position:0% +quantum chemists so you would be + + + align:start position:0% +quantum chemists so you would be +satisfied with just calculating this + + align:start position:0% +satisfied with just calculating this + + + align:start position:0% +satisfied with just calculating this +stuff but we're experimentalists for the + + align:start position:0% +stuff but we're experimentalists for the + + + align:start position:0% +stuff but we're experimentalists for the +most part and we learn about the things + + align:start position:0% +most part and we learn about the things + + + align:start position:0% +most part and we learn about the things +that you use to describe these effective + + align:start position:0% +that you use to describe these effective + + + align:start position:0% +that you use to describe these effective +Hamiltonians by looking at spectra. So + + align:start position:0% +Hamiltonians by looking at spectra. So + + + align:start position:0% +Hamiltonians by looking at spectra. So +we're going to our world is the spectra + + align:start position:0% +we're going to our world is the spectra + + + align:start position:0% +we're going to our world is the spectra +not the calculations. And so we're going + + align:start position:0% +not the calculations. And so we're going + + + align:start position:0% +not the calculations. And so we're going +to find out how to get to these things + + align:start position:0% +to find out how to get to these things + + + align:start position:0% +to find out how to get to these things +from what we can observe in the + + align:start position:0% +from what we can observe in the + + + align:start position:0% +from what we can observe in the +laboratory. And so that's what we're + + align:start position:0% +laboratory. And so that's what we're + + + align:start position:0% +laboratory. And so that's what we're +going to be talking about. + + align:start position:0% +going to be talking about. + + + align:start position:0% +going to be talking about. +So the Borne offenar approximation + + align:start position:0% +So the Borne offenar approximation + + + align:start position:0% +So the Borne offenar approximation +uh enabled us to separate the energies + + align:start position:0% +uh enabled us to separate the energies + + + align:start position:0% +uh enabled us to separate the energies +into electronic + + align:start position:0% +into electronic + + + align:start position:0% +into electronic +energies, vibrational + + align:start position:0% + + + + align:start position:0% + +energies and + + align:start position:0% +energies and + + + align:start position:0% +energies and +rotational energies. + + align:start position:0% +rotational energies. + + + align:start position:0% +rotational energies. +And + + align:start position:0% + + + + align:start position:0% + +uh so this is the electronic uh + + align:start position:0% +uh so this is the electronic uh + + + align:start position:0% +uh so this is the electronic uh +transition uh operator and we write this + + align:start position:0% +transition uh operator and we write this + + + align:start position:0% +transition uh operator and we write this +as a + + align:start position:0% +as a + + + align:start position:0% +as a +vector + + align:start position:0% +vector + + + align:start position:0% +vector +I function of + + align:start position:0% +I function of + + + align:start position:0% +I function of +R. In the spirit of the Bournehoffman + + align:start position:0% +R. In the spirit of the Bournehoffman + + + align:start position:0% +R. In the spirit of the Bournehoffman +approximation the wave functions are + + align:start position:0% +approximation the wave functions are + + + align:start position:0% +approximation the wave functions are +parametrically dependent on R. So when + + align:start position:0% +parametrically dependent on R. So when + + + align:start position:0% +parametrically dependent on R. So when +we do this integral over r little r we + + align:start position:0% +we do this integral over r little r we + + + align:start position:0% +we do this integral over r little r we +still have some function of r. So this + + align:start position:0% +still have some function of r. So this + + + align:start position:0% +still have some function of r. So this +is now what's called the transition + + align:start position:0% +is now what's called the transition + + + align:start position:0% +is now what's called the transition +transition moment function initial and + + align:start position:0% +transition moment function initial and + + + align:start position:0% +transition moment function initial and +final. It's a vector. It has three + + align:start position:0% + + + + align:start position:0% + +components. Okay. The next thing we want + + align:start position:0% +components. Okay. The next thing we want + + + align:start position:0% +components. Okay. The next thing we want +to do is we want to get rid of the theta + + align:start position:0% +to do is we want to get rid of the theta + + + align:start position:0% +to do is we want to get rid of the theta +fi the orientation of the body relative + + align:start position:0% +fi the orientation of the body relative + + + align:start position:0% +fi the orientation of the body relative +to the laboratory. And so we exploit we + + align:start position:0% +to the laboratory. And so we exploit we + + + align:start position:0% +to the laboratory. And so we exploit we +have a this dot product here and we're + + align:start position:0% +have a this dot product here and we're + + + align:start position:0% +have a this dot product here and we're +going to write this uh in terms + + align:start position:0% + + + + align:start position:0% + +of how should I + + align:start position:0% + + + + align:start position:0% + +have I probably should have written this + + align:start position:0% +have I probably should have written this + + + align:start position:0% +have I probably should have written this +now + + align:start position:0% +now + + + align:start position:0% +now +instead M + + align:start position:0% + + + + align:start position:0% + +So we're interested in this dot product. + + align:start position:0% +So we're interested in this dot product. + + + align:start position:0% +So we're interested in this dot product. +And so we're going to have the electric + + align:start position:0% +And so we're going to have the electric + + + align:start position:0% +And so we're going to have the electric +field uh in the laboratory capital + + align:start position:0% +field uh in the laboratory capital + + + align:start position:0% +field uh in the laboratory capital +X unit vector + + align:start position:0% +X unit vector + + + align:start position:0% +X unit vector +X plus electric field in the laboratory + + align:start position:0% +X plus electric field in the laboratory + + + align:start position:0% +X plus electric field in the laboratory +Y unit vector + + align:start position:0% +Y unit vector + + + align:start position:0% +Y unit vector +Y etc. + + align:start position:0% +Y etc. + + + align:start position:0% +Y etc. +and dot it into m + + align:start position:0% +and dot it into m + + + align:start position:0% +and dot it into m +x little + + align:start position:0% +x little + + + align:start position:0% +x little +x + m + + align:start position:0% +x + m + + + align:start position:0% +x + m +y. Okay, so we have this dot product and + + align:start position:0% +y. Okay, so we have this dot product and + + + align:start position:0% +y. Okay, so we have this dot product and +uh x x + + align:start position:0% + + + + align:start position:0% + +um is cosine + + align:start position:0% + + + + align:start position:0% + +X. This is the direction cosine that + + align:start position:0% +X. This is the direction cosine that + + + align:start position:0% +X. This is the direction cosine that +relates X in the laboratory to X in the + + align:start position:0% +relates X in the laboratory to X in the + + + align:start position:0% +relates X in the laboratory to X in the +uh body. And we, you know, we just this + + align:start position:0% +uh body. And we, you know, we just this + + + align:start position:0% +uh body. And we, you know, we just this +way. And so we collect all of these + + align:start position:0% +way. And so we collect all of these + + + align:start position:0% +way. And so we collect all of these +combinations of unit vectors laboratory + + align:start position:0% +combinations of unit vectors laboratory + + + align:start position:0% +combinations of unit vectors laboratory +and body and we write them as this + + align:start position:0% +and body and we write them as this + + + align:start position:0% +and body and we write them as this +vector this matrix L uh alpha and it has + + align:start position:0% +vector this matrix L uh alpha and it has + + + align:start position:0% +vector this matrix L uh alpha and it has +laboratory and body components. So we + + align:start position:0% +laboratory and body components. So we + + + align:start position:0% +laboratory and body components. So we +have this is a 3x3 matrix that provides + + align:start position:0% +have this is a 3x3 matrix that provides + + + align:start position:0% +have this is a 3x3 matrix that provides +the transformation between the + + align:start position:0% +the transformation between the + + + align:start position:0% +the transformation between the +laboratory and the + + align:start position:0% +laboratory and the + + + align:start position:0% +laboratory and the +body and it's a perfectly well-known + + align:start position:0% + + + + align:start position:0% + +object and + + align:start position:0% + + + + align:start position:0% + +u + + align:start position:0% +u + + + align:start position:0% +u +So this + + align:start position:0% +So this + + + align:start position:0% +So this +uh you can write this matrix as some + + align:start position:0% +uh you can write this matrix as some + + + align:start position:0% +uh you can write this matrix as some +function of theta and phi which are the + + align:start position:0% +function of theta and phi which are the + + + align:start position:0% +function of theta and phi which are the +orientation of the + + align:start position:0% +orientation of the + + + align:start position:0% +orientation of the +z-axis the z-axis of the in the body + + align:start position:0% +z-axis the z-axis of the in the body + + + align:start position:0% +z-axis the z-axis of the in the body +frame relative to the + + align:start position:0% +frame relative to the + + + align:start position:0% +frame relative to the +laboratory. Okay. And so + + align:start position:0% +laboratory. Okay. And so + + + align:start position:0% +laboratory. Okay. And so +um and so this is this is the direction + + align:start position:0% +um and so this is this is the direction + + + align:start position:0% +um and so this is this is the direction +cosine matrix. So these are X, Y and Z. + + align:start position:0% +cosine matrix. So these are X, Y and Z. + + + align:start position:0% +cosine matrix. So these are X, Y and Z. +This is the transformation. These are + + align:start position:0% +This is the transformation. These are + + + align:start position:0% +This is the transformation. These are +body. So this matrix tells how you get + + align:start position:0% +body. So this matrix tells how you get + + + align:start position:0% +body. So this matrix tells how you get +from body fixed coordinates to + + align:start position:0% +from body fixed coordinates to + + + align:start position:0% +from body fixed coordinates to +laboratory fixed coordinates. + + align:start position:0% +laboratory fixed coordinates. + + + align:start position:0% +laboratory fixed coordinates. +And this is a function of theta and fi + + align:start position:0% +And this is a function of theta and fi + + + align:start position:0% +And this is a function of theta and fi +the orientations of the z axis the body + + align:start position:0% +the orientations of the z axis the body + + + align:start position:0% +the orientations of the z axis the body +fix z-axis relative to the xyz axis in + + align:start position:0% +fix z-axis relative to the xyz axis in + + + align:start position:0% +fix z-axis relative to the xyz axis in +the laboratory. And this is a + + align:start position:0% +the laboratory. And this is a + + + align:start position:0% +the laboratory. And this is a +trigonometric object which you could + + align:start position:0% +trigonometric object which you could + + + align:start position:0% +trigonometric object which you could +write down from what you already know. + + align:start position:0% +write down from what you already know. + + + align:start position:0% +write down from what you already know. +And I don't have room to write this + + align:start position:0% +And I don't have room to write this + + + align:start position:0% +And I don't have room to write this +here. + + align:start position:0% + + + + align:start position:0% + +So it's in the notes. It's a 3x3 matrix. + + align:start position:0% +So it's in the notes. It's a 3x3 matrix. + + + align:start position:0% +So it's in the notes. It's a 3x3 matrix. +And uh uh what we would like to do is to + + align:start position:0% +And uh uh what we would like to do is to + + + align:start position:0% +And uh uh what we would like to do is to +take this matrix and uh uh calculate + + align:start position:0% +take this matrix and uh uh calculate + + + align:start position:0% +take this matrix and uh uh calculate +these + + align:start position:0% +these + + + align:start position:0% +these +quantities. Omega I J I + + align:start position:0% +quantities. Omega I J I + + + align:start position:0% +quantities. Omega I J I +M + + align:start position:0% +M + + + align:start position:0% +M +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +LP omega + + align:start position:0% + + + + align:start position:0% + +F. Okay. So this is a these are this is + + align:start position:0% +F. Okay. So this is a these are this is + + + align:start position:0% +F. Okay. So this is a these are this is +an explicit function of the orientation + + align:start position:0% +an explicit function of the orientation + + + align:start position:0% +an explicit function of the orientation +of the laboratory uh relative to the + + align:start position:0% +of the laboratory uh relative to the + + + align:start position:0% +of the laboratory uh relative to the +body. These are state vectors. What we + + align:start position:0% +body. These are state vectors. What we + + + align:start position:0% +body. These are state vectors. What we +really ought to put in here is, you + + align:start position:0% +really ought to put in here is, you + + + align:start position:0% +really ought to put in here is, you +know, we should write these + + align:start position:0% + + + + align:start position:0% + +omega + + align:start position:0% +omega + + + align:start position:0% +omega +and then it's a + + align:start position:0% +and then it's a + + + align:start position:0% +and then it's a +function function of theta and phi and + + align:start position:0% +function function of theta and phi and + + + align:start position:0% +function function of theta and phi and +we are going to be integrating theta + + align:start position:0% +we are going to be integrating theta + + + align:start position:0% +we are going to be integrating theta +and so this this notation is a little + + align:start position:0% +and so this this notation is a little + + + align:start position:0% +and so this this notation is a little +bit awkward because we really have a + + align:start position:0% +bit awkward because we really have a + + + align:start position:0% +bit awkward because we really have a +function of theta and we have a symbol a + + align:start position:0% +function of theta and we have a symbol a + + + align:start position:0% +function of theta and we have a symbol a +state vector and we really are going to + + align:start position:0% +state vector and we really are going to + + + align:start position:0% +state vector and we really are going to +be doing an integral over it. So this is + + align:start position:0% +be doing an integral over it. So this is + + + align:start position:0% +be doing an integral over it. So this is +what we want and so this is the + + align:start position:0% +what we want and so this is the + + + align:start position:0% +what we want and so this is the +direction + + align:start position:0% +direction + + + align:start position:0% +direction +cosine and these are the direction + + align:start position:0% +cosine and these are the direction + + + align:start position:0% +cosine and these are the direction +cosine matrix + + align:start position:0% +cosine matrix + + + align:start position:0% +cosine matrix +elements and since the only thing that + + align:start position:0% +elements and since the only thing that + + + align:start position:0% +elements and since the only thing that +goes into them is geometric factors and + + align:start position:0% +goes into them is geometric factors and + + + align:start position:0% +goes into them is geometric factors and +universal + + align:start position:0% +universal + + + align:start position:0% +universal +functions they are universally + + align:start position:0% +functions they are universally + + + align:start position:0% +functions they are universally +tabulated. They are things that tell you + + align:start position:0% +tabulated. They are things that tell you + + + align:start position:0% +tabulated. They are things that tell you +everything about uh + + align:start position:0% +everything about uh + + + align:start position:0% +everything about uh +uh transition probabilities + + align:start position:0% +uh transition probabilities + + + align:start position:0% +uh transition probabilities +uh for different combinations of these + + align:start position:0% +uh for different combinations of these + + + align:start position:0% +uh for different combinations of these +quota + + align:start position:0% +quota + + + align:start position:0% +quota +numbers. Okay. So it they are things + + align:start position:0% +numbers. Okay. So it they are things + + + align:start position:0% +numbers. Okay. So it they are things +that you would expect you could write in + + align:start position:0% +that you would expect you could write in + + + align:start position:0% +that you would expect you could write in +terms of transformation coefficients + + align:start position:0% +terms of transformation coefficients + + + align:start position:0% +terms of transformation coefficients +like cleft Gordon or vector coupling + + align:start position:0% +like cleft Gordon or vector coupling + + + align:start position:0% +like cleft Gordon or vector coupling +coefficients and in fact they are uh + + align:start position:0% +coefficients and in fact they are uh + + + align:start position:0% +coefficients and in fact they are uh +this is the first time you're going to + + align:start position:0% +this is the first time you're going to + + + align:start position:0% +this is the first time you're going to +see see those things in this I'm not + + align:start position:0% +see see those things in this I'm not + + + align:start position:0% +see see those things in this I'm not +going to do it that way because that's + + align:start position:0% +going to do it that way because that's + + + align:start position:0% +going to do it that way because that's +needlessly elegant and anybody who knows + + align:start position:0% +needlessly elegant and anybody who knows + + + align:start position:0% +needlessly elegant and anybody who knows +me knows that I + + align:start position:0% + + + + align:start position:0% + +not okay + + align:start position:0% +not okay + + + align:start position:0% +not okay +So we have this this thing which tells + + align:start position:0% +So we have this this thing which tells + + + align:start position:0% +So we have this this thing which tells +us something about + + align:start position:0% +us something about + + + align:start position:0% +us something about +uh the uh the selection rules and the + + align:start position:0% +uh the uh the selection rules and the + + + align:start position:0% +uh the uh the selection rules and the +relative probabilities for transitions + + align:start position:0% +relative probabilities for transitions + + + align:start position:0% +relative probabilities for transitions +between different initial and final + + align:start position:0% + + + + align:start position:0% + +rotational. Okay. So these things are + + align:start position:0% +rotational. Okay. So these things are + + + align:start position:0% +rotational. Okay. So these things are +tabulated. You can read about them in + + align:start position:0% +tabulated. You can read about them in + + + align:start position:0% +tabulated. You can read about them in +Hogan. And + + align:start position:0% +Hogan. And + + + align:start position:0% +Hogan. And +now there are three kinds of things that + + align:start position:0% +now there are three kinds of things that + + + align:start position:0% +now there are three kinds of things that +we care about that we + + align:start position:0% +we care about that we + + + align:start position:0% +we care about that we +get + + align:start position:0% + + + + align:start position:0% + +from I didn't skip anything. I didn't + + align:start position:0% +from I didn't skip anything. I didn't + + + align:start position:0% +from I didn't skip anything. I didn't +skip anything want to. the type of band, + + align:start position:0% +skip anything want to. the type of band, + + + align:start position:0% +skip anything want to. the type of band, +the branch and + + align:start position:0% +the branch and + + + align:start position:0% +the branch and +uh the + + align:start position:0% + + + + align:start position:0% + +polarization. Okay, so the branch how + + align:start position:0% +polarization. Okay, so the branch how + + + align:start position:0% +polarization. Okay, so the branch how +does J + + align:start position:0% +does J + + + align:start position:0% +does J +change? Well, first of all, we have a + + align:start position:0% +change? Well, first of all, we have a + + + align:start position:0% +change? Well, first of all, we have a +photon. We normally think of a photon as + + align:start position:0% +photon. We normally think of a photon as + + + align:start position:0% +photon. We normally think of a photon as +having an angular momentum of + + align:start position:0% +having an angular momentum of + + + align:start position:0% +having an angular momentum of +one. Whether you believe that or not, it + + align:start position:0% +one. Whether you believe that or not, it + + + align:start position:0% +one. Whether you believe that or not, it +doesn't matter. I am going to use that + + align:start position:0% +doesn't matter. I am going to use that + + + align:start position:0% +doesn't matter. I am going to use that +idea. So a photon can transfer one unit + + align:start position:0% +idea. So a photon can transfer one unit + + + align:start position:0% +idea. So a photon can transfer one unit +of angular momentum and so delta j can + + align:start position:0% +of angular momentum and so delta j can + + + align:start position:0% +of angular momentum and so delta j can +be zero plus or minus one. And these + + align:start position:0% +be zero plus or minus one. And these + + + align:start position:0% +be zero plus or minus one. And these +direction cosine matrix elements have in + + align:start position:0% +direction cosine matrix elements have in + + + align:start position:0% +direction cosine matrix elements have in +them something that tells you the + + align:start position:0% +them something that tells you the + + + align:start position:0% +them something that tells you the +relative probabilities of for a change + + align:start position:0% +relative probabilities of for a change + + + align:start position:0% +relative probabilities of for a change +in j 0 plus or minus one. But you also + + align:start position:0% +in j 0 plus or minus one. But you also + + + align:start position:0% +in j 0 plus or minus one. But you also +have to tell it well what how would how + + align:start position:0% +have to tell it well what how would how + + + align:start position:0% +have to tell it well what how would how +did omega change and how did m change. + + align:start position:0% +did omega change and how did m change. + + + align:start position:0% +did omega change and how did m change. +So uh the type of band has to do with + + align:start position:0% +So uh the type of band has to do with + + + align:start position:0% +So uh the type of band has to do with +delta omega being zero or plus or minus + + align:start position:0% +delta omega being zero or plus or minus + + + align:start position:0% +delta omega being zero or plus or minus +one. This is called + + align:start position:0% + + + + align:start position:0% + +parallel. This is called perpendicular. + + align:start position:0% + + + + align:start position:0% + +So if omega doesn't change, there are + + align:start position:0% +So if omega doesn't change, there are + + + align:start position:0% +So if omega doesn't change, there are +certain patterns of J + + align:start position:0% +certain patterns of J + + + align:start position:0% +certain patterns of J +uh for patterns of transitions for delta + + align:start position:0% +uh for patterns of transitions for delta + + + align:start position:0% +uh for patterns of transitions for delta +J of zero versus + + align:start position:0% +J of zero versus + + + align:start position:0% +J of zero versus +one. And so there's a characteristic + + align:start position:0% +one. And so there's a characteristic + + + align:start position:0% +one. And so there's a characteristic +shape of a band if omega doesn't change + + align:start position:0% +shape of a band if omega doesn't change + + + align:start position:0% +shape of a band if omega doesn't change +or omega does + + align:start position:0% + + + + align:start position:0% + +change. And again, omega is a projection + + align:start position:0% +change. And again, omega is a projection + + + align:start position:0% +change. And again, omega is a projection +of J on the body. uh and if J can only + + align:start position:0% +of J on the body. uh and if J can only + + + align:start position:0% +of J on the body. uh and if J can only +change by one, omega can only change by + + align:start position:0% +change by one, omega can only change by + + + align:start position:0% +change by one, omega can only change by +one. But if J + + align:start position:0% +one. But if J + + + align:start position:0% +one. But if J +uh doesn't change, + + align:start position:0% +uh doesn't change, + + + align:start position:0% +uh doesn't change, +omega can still change by plus or minus + + align:start position:0% +omega can still change by plus or minus + + + align:start position:0% +omega can still change by plus or minus +one. Okay. So, and then the polarization + + align:start position:0% +one. Okay. So, and then the polarization + + + align:start position:0% +one. Okay. So, and then the polarization +has to do with delta + + align:start position:0% +has to do with delta + + + align:start position:0% +has to do with delta +M. And delta M can be 0 plus one. + + align:start position:0% +M. And delta M can be 0 plus one. + + + align:start position:0% +M. And delta M can be 0 plus one. +And this when you have delta m of zero + + align:start position:0% +And this when you have delta m of zero + + + align:start position:0% +And this when you have delta m of zero +we say we have a z + + align:start position:0% +we say we have a z + + + align:start position:0% +we say we have a z +polarized and uh when we have delta m + + align:start position:0% +polarized and uh when we have delta m + + + align:start position:0% +polarized and uh when we have delta m +plus or minus one we have x or y + + align:start position:0% +plus or minus one we have x or y + + + align:start position:0% +plus or minus one we have x or y +polarized + + align:start position:0% +polarized + + + align:start position:0% +polarized +transitions. So + + align:start position:0% +transitions. So + + + align:start position:0% +transitions. So +this controls the the orientation of + + align:start position:0% +this controls the the orientation of + + + align:start position:0% +this controls the the orientation of +well we call it parallel because the the + + align:start position:0% +well we call it parallel because the the + + + align:start position:0% +well we call it parallel because the the +transition moment is parallel to the + + align:start position:0% +transition moment is parallel to the + + + align:start position:0% +transition moment is parallel to the +interuclear axis. + + align:start position:0% +interuclear axis. + + + align:start position:0% +interuclear axis. +We call it perpendicular because the + + align:start position:0% +We call it perpendicular because the + + + align:start position:0% +We call it perpendicular because the +transition moment in the body is + + align:start position:0% +transition moment in the body is + + + align:start position:0% +transition moment in the body is +perpendicular to the interior axis for + + align:start position:0% +perpendicular to the interior axis for + + + align:start position:0% +perpendicular to the interior axis for +diatomic molecules for anything well + + align:start position:0% +diatomic molecules for anything well + + + align:start position:0% +diatomic molecules for anything well +some for for nonlinear molecules there + + align:start position:0% +some for for nonlinear molecules there + + + align:start position:0% +some for for nonlinear molecules there +are three directions rather than two but + + align:start position:0% +are three directions rather than two but + + + align:start position:0% +are three directions rather than two but +for diatomic and linear polyatomics you + + align:start position:0% +for diatomic and linear polyatomics you + + + align:start position:0% +for diatomic and linear polyatomics you +know we care about parallel and + + align:start position:0% +know we care about parallel and + + + align:start position:0% +know we care about parallel and +perpendicular and this idea of parallel + + align:start position:0% +perpendicular and this idea of parallel + + + align:start position:0% +perpendicular and this idea of parallel +versus perpendicular even for uh fairly + + align:start position:0% +versus perpendicular even for uh fairly + + + align:start position:0% +versus perpendicular even for uh fairly +complicated molecules is very important. + + align:start position:0% +complicated molecules is very important. + + + align:start position:0% +complicated molecules is very important. +because it carries with it a a + + align:start position:0% +because it carries with it a a + + + align:start position:0% +because it carries with it a a +characteristic uh feature in the + + align:start position:0% +characteristic uh feature in the + + + align:start position:0% +characteristic uh feature in the +spectrum + + align:start position:0% +spectrum + + + align:start position:0% +spectrum +par for parallel type + + align:start position:0% +par for parallel type + + + align:start position:0% +par for parallel type +transitions. J does uh uh delta J of + + align:start position:0% +transitions. J does uh uh delta J of + + + align:start position:0% +transitions. J does uh uh delta J of +zero is weak. Q branches are weak. These + + align:start position:0% +zero is weak. Q branches are weak. These + + + align:start position:0% +zero is weak. Q branches are weak. These +are called delta J of zero is called a Q + + align:start position:0% +are called delta J of zero is called a Q + + + align:start position:0% +are called delta J of zero is called a Q +branch. P delta J of plus or minus one + + align:start position:0% +branch. P delta J of plus or minus one + + + align:start position:0% +branch. P delta J of plus or minus one +is called P and R branches. So if if you + + align:start position:0% +is called P and R branches. So if if you + + + align:start position:0% +is called P and R branches. So if if you +have a parallel transition, you tend not + + align:start position:0% +have a parallel transition, you tend not + + + align:start position:0% +have a parallel transition, you tend not +to have Q branches. If you have a + + align:start position:0% +to have Q branches. If you have a + + + align:start position:0% +to have Q branches. If you have a +perpendicular transition, the Q branches + + align:start position:0% +perpendicular transition, the Q branches + + + align:start position:0% +perpendicular transition, the Q branches +are strongest. And so these are really + + align:start position:0% +are strongest. And so these are really + + + align:start position:0% +are strongest. And so these are really +really they jump out at you. These are + + align:start position:0% +really they jump out at you. These are + + + align:start position:0% +really they jump out at you. These are +features that you see in the spectrum + + align:start position:0% +features that you see in the spectrum + + + align:start position:0% +features that you see in the spectrum +and you say, "Oh my god, I can tell just + + align:start position:0% +and you say, "Oh my god, I can tell just + + + align:start position:0% +and you say, "Oh my god, I can tell just +by looking at it that uh that it's a + + align:start position:0% +by looking at it that uh that it's a + + + align:start position:0% +by looking at it that uh that it's a +parallel or perpendicular transition." + + align:start position:0% +parallel or perpendicular transition." + + + align:start position:0% +parallel or perpendicular transition." +So in nonlinear molecules is it + + align:start position:0% +So in nonlinear molecules is it + + + align:start position:0% +So in nonlinear molecules is it +empirical that if you have weak Q + + align:start position:0% +empirical that if you have weak Q + + + align:start position:0% +empirical that if you have weak Q +branches you call it parallel type and + + align:start position:0% +branches you call it parallel type and + + + align:start position:0% +branches you call it parallel type and +if you have strong Q branches you call + + align:start position:0% +if you have strong Q branches you call + + + align:start position:0% +if you have strong Q branches you call +it perpendicular type or is there a + + align:start position:0% +it perpendicular type or is there a + + + align:start position:0% +it perpendicular type or is there a +there's a little bit more to it but yes + + align:start position:0% +there's a little bit more to it but yes + + + align:start position:0% +there's a little bit more to it but yes +I mean uh you're almost always looking + + align:start position:0% +I mean uh you're almost always looking + + + align:start position:0% +I mean uh you're almost always looking +to see you see most + + align:start position:0% +to see you see most + + + align:start position:0% +to see you see most +molecules + + align:start position:0% +molecules + + + align:start position:0% +molecules +are near symmetric tops and so one + + align:start position:0% +are near symmetric tops and so one + + + align:start position:0% +are near symmetric tops and so one +quantizes is relative to the near + + align:start position:0% +quantizes is relative to the near + + + align:start position:0% +quantizes is relative to the near +symmetry axis. And so it's either the + + align:start position:0% +symmetry axis. And so it's either the + + + align:start position:0% +symmetry axis. And so it's either the +transition moment is either parallel to + + align:start position:0% +transition moment is either parallel to + + + align:start position:0% +transition moment is either parallel to +the near symmetry axis or perpendicular + + align:start position:0% +the near symmetry axis or perpendicular + + + align:start position:0% +the near symmetry axis or perpendicular +to it. And this gives rise to very + + align:start position:0% +to it. And this gives rise to very + + + align:start position:0% +to it. And this gives rise to very +dramatic changes in the profile of the + + align:start position:0% +dramatic changes in the profile of the + + + align:start position:0% +dramatic changes in the profile of the +band. So it's one of the most useful + + align:start position:0% +band. So it's one of the most useful + + + align:start position:0% +band. So it's one of the most useful +things to recognize that there are + + align:start position:0% +things to recognize that there are + + + align:start position:0% +things to recognize that there are +different orientations of the transition + + align:start position:0% +different orientations of the transition + + + align:start position:0% +different orientations of the transition +moment in the body and those translate + + align:start position:0% +moment in the body and those translate + + + align:start position:0% +moment in the body and those translate +into profound differences in the + + align:start position:0% +into profound differences in the + + + align:start position:0% +into profound differences in the +appearance of the + + align:start position:0% +appearance of the + + + align:start position:0% +appearance of the +spring. Okay. And M uh that's the + + align:start position:0% +spring. Okay. And M uh that's the + + + align:start position:0% +spring. Okay. And M uh that's the +projection of uh J in the body frame. + + align:start position:0% +projection of uh J in the body frame. + + + align:start position:0% +projection of uh J in the body frame. +And uh this is relatively unimportant. + + align:start position:0% +And uh this is relatively unimportant. + + + align:start position:0% +And uh this is relatively unimportant. +However, often uh you can use the + + align:start position:0% +However, often uh you can use the + + + align:start position:0% +However, often uh you can use the +polarization in the uh uh the + + align:start position:0% +polarization in the uh uh the + + + align:start position:0% +polarization in the uh uh the +polarization of radiation especially in + + align:start position:0% +polarization of radiation especially in + + + align:start position:0% +polarization of radiation especially in +double resonance experiments to learn + + align:start position:0% +double resonance experiments to learn + + + align:start position:0% +double resonance experiments to learn +something about what J is. So uh but + + align:start position:0% +something about what J is. So uh but + + + align:start position:0% +something about what J is. So uh but +this is a relatively + + align:start position:0% +this is a relatively + + + align:start position:0% +this is a relatively +uh minor thing. Now these direction + + align:start position:0% +uh minor thing. Now these direction + + + align:start position:0% +uh minor thing. Now these direction +cosine matrix elements are generally + + align:start position:0% +cosine matrix elements are generally + + + align:start position:0% +cosine matrix elements are generally +written can generally be expressed as + + align:start position:0% +written can generally be expressed as + + + align:start position:0% +written can generally be expressed as +you will see in hog as a product of + + align:start position:0% +you will see in hog as a product of + + + align:start position:0% +you will see in hog as a product of +three + + align:start position:0% +three + + + align:start position:0% +three +factors a factor that depends on j omega + + align:start position:0% +factors a factor that depends on j omega + + + align:start position:0% +factors a factor that depends on j omega +uh or j initial omega initial so I'm + + align:start position:0% +uh or j initial omega initial so I'm + + + align:start position:0% +uh or j initial omega initial so I'm +going to use spectroscopic + + align:start position:0% + + + + align:start position:0% + +notation so a factor that's j omega + + align:start position:0% +notation so a factor that's j omega + + + align:start position:0% +notation so a factor that's j omega +dependent + + align:start position:0% +dependent + + + align:start position:0% +dependent +a factor that's J M + + align:start position:0% +a factor that's J M + + + align:start position:0% +a factor that's J M +dependent and these two factors look the + + align:start position:0% +dependent and these two factors look the + + + align:start position:0% +dependent and these two factors look the +same they're just the symbols are + + align:start position:0% +same they're just the symbols are + + + align:start position:0% +same they're just the symbols are +different and a factor that just in the + + align:start position:0% +different and a factor that just in the + + + align:start position:0% +different and a factor that just in the +denominator involves some + + align:start position:0% +denominator involves some + + + align:start position:0% +denominator involves some +RJ okay so you these direction cosine + + align:start position:0% +RJ okay so you these direction cosine + + + align:start position:0% +RJ okay so you these direction cosine +matrix elements are a product of three + + align:start position:0% +matrix elements are a product of three + + + align:start position:0% +matrix elements are a product of three +things and generally you're interested + + align:start position:0% +things and generally you're interested + + + align:start position:0% +things and generally you're interested +in one or the other of these and this is + + align:start position:0% + + + + align:start position:0% + +Okay. So, excuse + + align:start position:0% + + + + align:start position:0% + +me. Now, um you one of the beauties of + + align:start position:0% +me. Now, um you one of the beauties of + + + align:start position:0% +me. Now, um you one of the beauties of +using bracket notation is that we tend + + align:start position:0% +using bracket notation is that we tend + + + align:start position:0% +using bracket notation is that we tend +not to look at wave functions ever. We + + align:start position:0% +not to look at wave functions ever. We + + + align:start position:0% +not to look at wave functions ever. We +we manipulate them as symbols and that's + + align:start position:0% +we manipulate them as symbols and that's + + + align:start position:0% +we manipulate them as symbols and that's +usually okay. But + + align:start position:0% +usually okay. But + + + align:start position:0% +usually okay. But +sometimes there are hidden phase + + align:start position:0% +sometimes there are hidden phase + + + align:start position:0% +sometimes there are hidden phase +convictions that cause you to make uh + + align:start position:0% +convictions that cause you to make uh + + + align:start position:0% +convictions that cause you to make uh +usually a sign error which + + align:start position:0% +usually a sign error which + + + align:start position:0% +usually a sign error which +uh often results in something which is + + align:start position:0% +uh often results in something which is + + + align:start position:0% +uh often results in something which is +supposed to be allowed being forbidden + + align:start position:0% +supposed to be allowed being forbidden + + + align:start position:0% +supposed to be allowed being forbidden +and vice versa or some kind of + + align:start position:0% +and vice versa or some kind of + + + align:start position:0% +and vice versa or some kind of +interference effect being constructed + + align:start position:0% +interference effect being constructed + + + align:start position:0% +interference effect being constructed +when it's supposed to be destroyed. And + + align:start position:0% +when it's supposed to be destroyed. And + + + align:start position:0% +when it's supposed to be destroyed. And +these are very very hard errors to find + + align:start position:0% +these are very very hard errors to find + + + align:start position:0% +these are very very hard errors to find +because you generally you know you say + + align:start position:0% +because you generally you know you say + + + align:start position:0% +because you generally you know you say +oh I understand what I'm doing and I + + align:start position:0% +oh I understand what I'm doing and I + + + align:start position:0% +oh I understand what I'm doing and I +understand how these things ought to + + align:start position:0% +understand how these things ought to + + + align:start position:0% +understand how these things ought to +behave. So if + + align:start position:0% +behave. So if + + + align:start position:0% +behave. So if +you if you just say well suppose I + + align:start position:0% +you if you just say well suppose I + + + align:start position:0% +you if you just say well suppose I +choose theta and + + align:start position:0% +choose theta and + + + align:start position:0% +choose theta and +fi zero + + align:start position:0% +fi zero + + + align:start position:0% +fi zero +uh what will happen? And what you + + align:start position:0% +uh what will happen? And what you + + + align:start position:0% +uh what will happen? And what you +normally would expect because you're + + align:start position:0% +normally would expect because you're + + + align:start position:0% +normally would expect because you're +clever people and you don't want to do a + + align:start position:0% +clever people and you don't want to do a + + + align:start position:0% +clever people and you don't want to do a +calculation. You normally expect that + + align:start position:0% +calculation. You normally expect that + + + align:start position:0% +calculation. You normally expect that +little x is going to be parallel to big + + align:start position:0% +little x is going to be parallel to big + + + align:start position:0% +little x is going to be parallel to big +x and little y is going to be parallel + + align:start position:0% +x and little y is going to be parallel + + + align:start position:0% +x and little y is going to be parallel +to big y and z is parallel. And that's + + align:start position:0% +to big y and z is parallel. And that's + + + align:start position:0% +to big y and z is parallel. And that's +not right. If you substitute in uh what + + align:start position:0% +not right. If you substitute in uh what + + + align:start position:0% +not right. If you substitute in uh what +you get with theta and phi both chosen + + align:start position:0% +you get with theta and phi both chosen + + + align:start position:0% +you get with theta and phi both chosen +to be zero, what you + + align:start position:0% +to be zero, what you + + + align:start position:0% +to be zero, what you +discover is the direction cosine + + align:start position:0% +discover is the direction cosine + + + align:start position:0% +discover is the direction cosine +matrix has the form 0 - 1 0 1 0 + + align:start position:0% +matrix has the form 0 - 1 0 1 0 + + + align:start position:0% +matrix has the form 0 - 1 0 1 0 +0 1. + + align:start position:0% +0 1. + + + align:start position:0% +0 1. +And and so you see that when this is + + align:start position:0% +And and so you see that when this is + + + align:start position:0% +And and so you see that when this is +applied to uh + + align:start position:0% +applied to uh + + + align:start position:0% +applied to uh +uh so when you take this matrix and + + align:start position:0% +uh so when you take this matrix and + + + align:start position:0% +uh so when you take this matrix and +apply it to uh + + align:start position:0% + + + + align:start position:0% + +u little x little y z. what you get + + align:start position:0% +u little x little y z. what you get + + + align:start position:0% +u little x little y z. what you get +is minus y + + align:start position:0% + + + + align:start position:0% + +uh x and + + align:start position:0% +uh x and + + + align:start position:0% +uh x and +z. So this + + align:start position:0% +z. So this + + + align:start position:0% +z. So this +matrix with this choice of + + align:start position:0% +matrix with this choice of + + + align:start position:0% +matrix with this choice of +uh theta and + + align:start position:0% +uh theta and + + + align:start position:0% +uh theta and +fi or this choice of phase. Notice + + align:start position:0% +fi or this choice of phase. Notice + + + align:start position:0% +fi or this choice of phase. Notice +normally when you have two coordinate + + align:start position:0% +normally when you have two coordinate + + + align:start position:0% +normally when you have two coordinate +systems to specify the orientation of + + align:start position:0% +systems to specify the orientation of + + + align:start position:0% +systems to specify the orientation of +one relative to the + + align:start position:0% +one relative to the + + + align:start position:0% +one relative to the +other you have three angles but we're + + align:start position:0% +other you have three angles but we're + + + align:start position:0% +other you have three angles but we're +just keeping track of the orientation of + + align:start position:0% +just keeping track of the orientation of + + + align:start position:0% +just keeping track of the orientation of +uh the the um + + align:start position:0% +uh the the um + + + align:start position:0% +uh the the um +z-axis relative to the laboratory frame. + + align:start position:0% +z-axis relative to the laboratory frame. + + + align:start position:0% +z-axis relative to the laboratory frame. +And and for this choice, what we end up + + align:start position:0% +And and for this choice, what we end up + + + align:start position:0% +And and for this choice, what we end up +getting is that uh x goes into minus y, + + align:start position:0% +getting is that uh x goes into minus y, + + + align:start position:0% +getting is that uh x goes into minus y, +y goes into x. So there's an extra + + align:start position:0% +y goes into x. So there's an extra + + + align:start position:0% +y goes into x. So there's an extra +rotation by pi / 2 that you didn't + + align:start position:0% +rotation by pi / 2 that you didn't + + + align:start position:0% +rotation by pi / 2 that you didn't +expect. And this this is a that is a + + align:start position:0% +expect. And this this is a that is a + + + align:start position:0% +expect. And this this is a that is a +face choice that + + align:start position:0% +face choice that + + + align:start position:0% +face choice that +uh can come back and burn you if you're + + align:start position:0% +uh can come back and burn you if you're + + + align:start position:0% +uh can come back and burn you if you're +not aware of it. And it turns out that + + align:start position:0% +not aware of it. And it turns out that + + + align:start position:0% +not aware of it. And it turns out that +the phase choice for direction cosiness + + align:start position:0% +the phase choice for direction cosiness + + + align:start position:0% +the phase choice for direction cosiness +uh normally used by spectroscopists and + + align:start position:0% +uh normally used by spectroscopists and + + + align:start position:0% +uh normally used by spectroscopists and +by quantum chemists are + + align:start position:0% +by quantum chemists are + + + align:start position:0% +by quantum chemists are +different. And so you can't just + + align:start position:0% +different. And so you can't just + + + align:start position:0% +different. And so you can't just +continue manipulating the symbols + + align:start position:0% +continue manipulating the symbols + + + align:start position:0% +continue manipulating the symbols +without sometimes asking well what did + + align:start position:0% +without sometimes asking well what did + + + align:start position:0% +without sometimes asking well what did +they really do? And so this is one of + + align:start position:0% +they really do? And so this is one of + + + align:start position:0% +they really do? And so this is one of +those times. Okay. So do quantum + + align:start position:0% +those times. Okay. So do quantum + + + align:start position:0% +those times. Okay. So do quantum +chemists use a phase choice that sets it + + align:start position:0% +chemists use a phase choice that sets it + + + align:start position:0% +chemists use a phase choice that sets it +to zero so there is no rotation. No, + + align:start position:0% +to zero so there is no rotation. No, + + + align:start position:0% +to zero so there is no rotation. No, +they choose this one. Okay. because of + + align:start position:0% +they choose this one. Okay. because of + + + align:start position:0% +they choose this one. Okay. because of +this. No rotation. Okay. + + align:start position:0% +this. No rotation. Okay. + + + align:start position:0% +this. No rotation. Okay. +Doesn't mean we're we're better or more + + align:start position:0% +Doesn't mean we're we're better or more + + + align:start position:0% +Doesn't mean we're we're better or more +moral or anything, but you know, it + + align:start position:0% +moral or anything, but you know, it + + + align:start position:0% +moral or anything, but you know, it +turns out that this is a source of + + align:start position:0% +turns out that this is a source of + + + align:start position:0% +turns out that this is a source of +confusion. It does seem reasonable that + + align:start position:0% +confusion. It does seem reasonable that + + + align:start position:0% +confusion. It does seem reasonable that +you would make no rotation when the + + align:start position:0% +you would make no rotation when the + + + align:start position:0% +you would make no rotation when the +angles are + + align:start position:0% +angles are + + + align:start position:0% +angles are +Yeah. coincidence. And so what is that + + align:start position:0% +Yeah. coincidence. And so what is that + + + align:start position:0% +Yeah. coincidence. And so what is that +other oiler angle? It's the rotation + + align:start position:0% +other oiler angle? It's the rotation + + + align:start position:0% +other oiler angle? It's the rotation +about Z. So, you know, you fix that. I + + align:start position:0% +about Z. So, you know, you fix that. I + + + align:start position:0% +about Z. So, you know, you fix that. I +mean, you know, I didn't say anything + + align:start position:0% +mean, you know, I didn't say anything + + + align:start position:0% +mean, you know, I didn't say anything +about that oiler angle because we didn't + + align:start position:0% +about that oiler angle because we didn't + + + align:start position:0% +about that oiler angle because we didn't +think about it. But the spectroscopists + + align:start position:0% +think about it. But the spectroscopists + + + align:start position:0% +think about it. But the spectroscopists +and the quantum chemists choose that + + align:start position:0% +and the quantum chemists choose that + + + align:start position:0% +and the quantum chemists choose that +third oiler angle so that instead of + + align:start position:0% +third oiler angle so that instead of + + + align:start position:0% +third oiler angle so that instead of +having this ridiculous result, + + align:start position:0% +having this ridiculous result, + + + align:start position:0% +having this ridiculous result, +uh, you get X, Y, and Z and + + align:start position:0% +uh, you get X, Y, and Z and + + + align:start position:0% +uh, you get X, Y, and Z and +spectroscopist use that and the quantum + + align:start position:0% +spectroscopist use that and the quantum + + + align:start position:0% +spectroscopist use that and the quantum +chemist use + + align:start position:0% +chemist use + + + align:start position:0% +chemist use +this. + + align:start position:0% +this. + + + align:start position:0% +this. +Okay. So, where are we now? + + align:start position:0% + + + + align:start position:0% + +So we're massaging our little our main + + align:start position:0% +So we're massaging our little our main + + + align:start position:0% +So we're massaging our little our main +equation down to + + align:start position:0% +equation down to + + + align:start position:0% +equation down to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +simp we have the probability for a + + align:start position:0% +simp we have the probability for a + + + align:start position:0% +simp we have the probability for a +transition that's going to be now + + align:start position:0% +transition that's going to be now + + + align:start position:0% +transition that's going to be now +proportional to a sum of stuff. Notice + + align:start position:0% +proportional to a sum of stuff. Notice + + + align:start position:0% +proportional to a sum of stuff. Notice +I'm putting it inside the absolute + + align:start position:0% +I'm putting it inside the absolute + + + align:start position:0% +I'm putting it inside the absolute +value. + + align:start position:0% +value. + + + align:start position:0% +value. +And a probability is always the square + + align:start position:0% +And a probability is always the square + + + align:start position:0% +And a probability is always the square +of uh an a matrix element or amplitude. + + align:start position:0% +of uh an a matrix element or amplitude. + + + align:start position:0% +of uh an a matrix element or amplitude. +And so the probability is going to be + + align:start position:0% +And so the probability is going to be + + + align:start position:0% +And so the probability is going to be +the sum over the + + align:start position:0% + + + + align:start position:0% + +uh the space fixed and body fixed uh + + align:start position:0% +uh the space fixed and body fixed uh + + + align:start position:0% +uh the space fixed and body fixed uh +axes. We have the uh electric field + + align:start position:0% +axes. We have the uh electric field + + + align:start position:0% +axes. We have the uh electric field +coordinates in space. We have the + + align:start position:0% +coordinates in space. We have the + + + align:start position:0% +coordinates in space. We have the +i + + align:start position:0% + + + + align:start position:0% + +M + + align:start position:0% + + + + align:start position:0% + +R F and this is integrated over R and we + + align:start position:0% +R F and this is integrated over R and we + + + align:start position:0% +R F and this is integrated over R and we +have this omega I can't write it + + align:start position:0% +have this omega I can't write it + + + align:start position:0% +have this omega I can't write it +here + + align:start position:0% +here + + + align:start position:0% +here +I al + + align:start position:0% +I al + + + align:start position:0% +I al +S space body. + + align:start position:0% + + + + align:start position:0% + +Uh, okay. So, that's all in here. And + + align:start position:0% +Uh, okay. So, that's all in here. And + + + align:start position:0% +Uh, okay. So, that's all in here. And +so, this contains everything. Now, it's + + align:start position:0% +so, this contains everything. Now, it's + + + align:start position:0% +so, this contains everything. Now, it's +set up to actually analyze the various + + align:start position:0% +set up to actually analyze the various + + + align:start position:0% +set up to actually analyze the various +cases. Is SP the same thing as LP? + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +And in fact, there's another criminal + + align:start position:0% +And in fact, there's another criminal + + + align:start position:0% +And in fact, there's another criminal +thing I often do because + + align:start position:0% +thing I often do because + + + align:start position:0% +thing I often do because +uh my co-author on the book, she refused + + align:start position:0% +uh my co-author on the book, she refused + + + align:start position:0% +uh my co-author on the book, she refused +to let me call it body fix. It's + + align:start position:0% +to let me call it body fix. It's + + + align:start position:0% +to let me call it body fix. It's +molecule fix. I don't know why uh + + align:start position:0% +molecule fix. I don't know why uh + + + align:start position:0% +molecule fix. I don't know why uh +because it may be that in French there + + align:start position:0% +because it may be that in French there + + + align:start position:0% +because it may be that in French there +was something a little bit too + + align:start position:0% +was something a little bit too + + + align:start position:0% +was something a little bit too +suggestive about that. But anyway, I + + align:start position:0% +suggestive about that. But anyway, I + + + align:start position:0% +suggestive about that. But anyway, I +don't You didn't want to get confused + + align:start position:0% +don't You didn't want to get confused + + + align:start position:0% +don't You didn't want to get confused +with your body, right? Well, that's the, + + align:start position:0% +with your body, right? Well, that's the, + + + align:start position:0% +with your body, right? Well, that's the, +you know, that's because that's the lab. + + align:start position:0% +you know, that's because that's the lab. + + + align:start position:0% +you know, that's because that's the lab. +So anyway, so sorry about the notation. + + align:start position:0% +So anyway, so sorry about the notation. + + + align:start position:0% +So anyway, so sorry about the notation. +Okay. So now we have um we have three + + align:start position:0% +Okay. So now we have um we have three + + + align:start position:0% +Okay. So now we have um we have three +different kinds of transition. So a pure + + align:start position:0% +different kinds of transition. So a pure + + + align:start position:0% +different kinds of transition. So a pure +rotation + + align:start position:0% + + + + align:start position:0% + +transition in a pure rotation + + align:start position:0% +transition in a pure rotation + + + align:start position:0% +transition in a pure rotation +transition, we're not changing + + align:start position:0% +transition, we're not changing + + + align:start position:0% +transition, we're not changing +electronic states. So uh this uh + + align:start position:0% +electronic states. So uh this uh + + + align:start position:0% +electronic states. So uh this uh +uh the for pure rotation transition the + + align:start position:0% +uh the for pure rotation transition the + + + align:start position:0% +uh the for pure rotation transition the +electronic + + align:start position:0% +electronic + + + align:start position:0% +electronic +states + + align:start position:0% +states + + + align:start position:0% +states +I I guess I have a notational problem. + + align:start position:0% + + + + align:start position:0% + +Um EI is equal to EF and VI is equal to + + align:start position:0% +Um EI is equal to EF and VI is equal to + + + align:start position:0% +Um EI is equal to EF and VI is equal to +VF. So there's no change in electronic + + align:start position:0% +VF. So there's no change in electronic + + + align:start position:0% +VF. So there's no change in electronic +and no change in + + align:start position:0% +and no change in + + + align:start position:0% +and no change in +vibrational quantum numbers. And so what + + align:start position:0% +vibrational quantum numbers. And so what + + + align:start position:0% +vibrational quantum numbers. And so what +can we immediately say about the various + + align:start position:0% +can we immediately say about the various + + + align:start position:0% +can we immediately say about the various +terms + + align:start position:0% + + + + align:start position:0% + +here? Um + + align:start position:0% + + + + align:start position:0% + +So if we're going to have delta omega + + align:start position:0% +So if we're going to have delta omega + + + align:start position:0% +So if we're going to have delta omega +equals + + align:start position:0% +equals + + + align:start position:0% +equals +z, it requires + + align:start position:0% + + + + align:start position:0% + +this not to be equal to + + align:start position:0% +this not to be equal to + + + align:start position:0% +this not to be equal to +z. If we have delta omega + + align:start position:0% + + + + align:start position:0% + +Well, we've chosen initial state is + + align:start position:0% +Well, we've chosen initial state is + + + align:start position:0% +Well, we've chosen initial state is +equal to the final state. So, omega is + + align:start position:0% + + + + align:start position:0% + +um so + + align:start position:0% +um so + + + align:start position:0% +um so +um and this also requires that uh the + + align:start position:0% +um and this also requires that uh the + + + align:start position:0% +um and this also requires that uh the +uh MX + + align:start position:0% + + + + align:start position:0% + +So if there's no change in omega, we + + align:start position:0% +So if there's no change in omega, we + + + align:start position:0% +So if there's no change in omega, we +have one component of this not zero. The + + align:start position:0% +have one component of this not zero. The + + + align:start position:0% +have one component of this not zero. The +other two are zero. Now for a diatomic + + align:start position:0% +other two are zero. Now for a diatomic + + + align:start position:0% +other two are zero. Now for a diatomic +molecule, we're talking about this + + align:start position:0% +molecule, we're talking about this + + + align:start position:0% +molecule, we're talking about this +electronic integral. Uh and so we can + + align:start position:0% +electronic integral. Uh and so we can + + + align:start position:0% +electronic integral. Uh and so we can +have a polar diatomic molecule. Um and + + align:start position:0% +have a polar diatomic molecule. Um and + + + align:start position:0% +have a polar diatomic molecule. Um and +uh uh so it's certainly possible to have + + align:start position:0% +uh uh so it's certainly possible to have + + + align:start position:0% +uh uh so it's certainly possible to have +a dipole moment along this + + align:start position:0% +a dipole moment along this + + + align:start position:0% +a dipole moment along this +direction. But suppose we look at a + + align:start position:0% +direction. But suppose we look at a + + + align:start position:0% +direction. But suppose we look at a +reflection + + align:start position:0% +reflection + + + align:start position:0% +reflection +plane. All diatomic molecules have + + align:start position:0% +plane. All diatomic molecules have + + + align:start position:0% +plane. All diatomic molecules have +reflection planes containing the two + + align:start position:0% + + + + align:start position:0% + +nuclei. And + + align:start position:0% +nuclei. And + + + align:start position:0% +nuclei. And +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so there's + + align:start position:0% +so there's + + + align:start position:0% +so there's +absolute so that's a good symmetry + + align:start position:0% +absolute so that's a good symmetry + + + align:start position:0% +absolute so that's a good symmetry +operation. Uh and so whatever you have + + align:start position:0% +operation. Uh and so whatever you have + + + align:start position:0% +operation. Uh and so whatever you have +above the reflection plane you have to + + align:start position:0% +above the reflection plane you have to + + + align:start position:0% +above the reflection plane you have to +have below the reflection plane. You + + align:start position:0% +have below the reflection plane. You + + + align:start position:0% +have below the reflection plane. You +cannot have a perpendicular dipole + + align:start position:0% +cannot have a perpendicular dipole + + + align:start position:0% +cannot have a perpendicular dipole +moment in a dipole in a diatomic + + align:start position:0% +moment in a dipole in a diatomic + + + align:start position:0% +moment in a dipole in a diatomic +molecule. So for for a transition + + align:start position:0% +molecule. So for for a transition + + + align:start position:0% +molecule. So for for a transition +uh in which the electronic state doesn't + + align:start position:0% +uh in which the electronic state doesn't + + + align:start position:0% +uh in which the electronic state doesn't +change you know the only thing that can + + align:start position:0% +change you know the only thing that can + + + align:start position:0% +change you know the only thing that can +happen is to have a nonzero Z component + + align:start position:0% +happen is to have a nonzero Z component + + + align:start position:0% +happen is to have a nonzero Z component +of the transition moment the + + align:start position:0% +of the transition moment the + + + align:start position:0% +of the transition moment the +perpendicular components are going to be + + align:start position:0% +perpendicular components are going to be + + + align:start position:0% +perpendicular components are going to be +zero certainly. Yes. Do you mean all + + align:start position:0% +zero certainly. Yes. Do you mean all + + + align:start position:0% +zero certainly. Yes. Do you mean all +those to be + + align:start position:0% +those to be + + + align:start position:0% +those to be +I MC I? + + align:start position:0% +I MC I? + + + align:start position:0% +I MC I? +It should be I if we're not changing the + + align:start position:0% +It should be I if we're not changing the + + + align:start position:0% +It should be I if we're not changing the +rotation that should be an I I and in + + align:start position:0% +rotation that should be an I I and in + + + align:start position:0% +rotation that should be an I I and in +fact it is so in my notes and so yes. + + align:start position:0% +fact it is so in my notes and so yes. + + + align:start position:0% +fact it is so in my notes and so yes. +Okay. So that's why I was confused + + align:start position:0% +Okay. So that's why I was confused + + + align:start position:0% +Okay. So that's why I was confused +because I was wondering what the hell I + + align:start position:0% +because I was wondering what the hell I + + + align:start position:0% +because I was wondering what the hell I +was doing. Okay. So now we can have a + + align:start position:0% +was doing. Okay. So now we can have a + + + align:start position:0% +was doing. Okay. So now we can have a +diatomic molecule in a state that that + + align:start position:0% +diatomic molecule in a state that that + + + align:start position:0% +diatomic molecule in a state that that +has uh uh omega not equal to zero. We + + align:start position:0% +has uh uh omega not equal to zero. We + + + align:start position:0% +has uh uh omega not equal to zero. We +can have a diatomic molecule in a + + align:start position:0% +can have a diatomic molecule in a + + + align:start position:0% +can have a diatomic molecule in a +triplet state that has several different + + align:start position:0% +triplet state that has several different + + + align:start position:0% +triplet state that has several different +omegas. But we cannot have a diatomic + + align:start position:0% +omegas. But we cannot have a diatomic + + + align:start position:0% +omegas. But we cannot have a diatomic +molecule that has a perpendicular + + align:start position:0% +molecule that has a perpendicular + + + align:start position:0% +molecule that has a perpendicular +component of the + + align:start position:0% +component of the + + + align:start position:0% +component of the +moment. And so we have strictly a delta + + align:start position:0% +moment. And so we have strictly a delta + + + align:start position:0% +moment. And so we have strictly a delta +omega equals zero selection rule. + + align:start position:0% +omega equals zero selection rule. + + + align:start position:0% +omega equals zero selection rule. +Now if we have a center of inversion + + align:start position:0% +Now if we have a center of inversion + + + align:start position:0% +Now if we have a center of inversion +symmetry + + align:start position:0% +symmetry + + + align:start position:0% +symmetry +here as you would for + + align:start position:0% +here as you would for + + + align:start position:0% +here as you would for +homonuclear then uh the electronic wave + + align:start position:0% +homonuclear then uh the electronic wave + + + align:start position:0% +homonuclear then uh the electronic wave +functions are classified either G or + + align:start position:0% + + + + align:start position:0% + +U and the transition the uh + + align:start position:0% +U and the transition the uh + + + align:start position:0% +U and the transition the uh +this is classified U in it's bundatana + + align:start position:0% +this is classified U in it's bundatana + + + align:start position:0% +this is classified U in it's bundatana +and so any nonzero integral is going to + + align:start position:0% +and so any nonzero integral is going to + + + align:start position:0% +and so any nonzero integral is going to +be between uh a g and a u + + align:start position:0% +be between uh a g and a u + + + align:start position:0% +be between uh a g and a u +state + + align:start position:0% +state + + + align:start position:0% +state +and so you cannot have a transition + + align:start position:0% +and so you cannot have a transition + + + align:start position:0% +and so you cannot have a transition +where the + + align:start position:0% +where the + + + align:start position:0% +where the +electronic you cannot have if you have a + + align:start position:0% +electronic you cannot have if you have a + + + align:start position:0% +electronic you cannot have if you have a +homonuclear molecule then there is no + + align:start position:0% +homonuclear molecule then there is no + + + align:start position:0% +homonuclear molecule then there is no +permanent dipole moment this function is + + align:start position:0% +permanent dipole moment this function is + + + align:start position:0% +permanent dipole moment this function is +rigorously zero and so you get the + + align:start position:0% +rigorously zero and so you get the + + + align:start position:0% +rigorously zero and so you get the +selection rule or the the fact that N2 + + align:start position:0% +selection rule or the the fact that N2 + + + align:start position:0% +selection rule or the the fact that N2 +has no permanent has no pure rotation + + align:start position:0% +has no permanent has no pure rotation + + + align:start position:0% +has no permanent has no pure rotation +spectrum CO does and uh there's only + + align:start position:0% +spectrum CO does and uh there's only + + + align:start position:0% +spectrum CO does and uh there's only +going to be uh transition there's only + + align:start position:0% +going to be uh transition there's only + + + align:start position:0% +going to be uh transition there's only +going to be Ztype transitions + + align:start position:0% +going to be Ztype transitions + + + align:start position:0% +going to be Ztype transitions +and you need a heteronuclear molecule. + + align:start position:0% +and you need a heteronuclear molecule. + + + align:start position:0% +and you need a heteronuclear molecule. +Now as you go to polyatomic molecules + + align:start position:0% +Now as you go to polyatomic molecules + + + align:start position:0% +Now as you go to polyatomic molecules +there's more complicated stuff going on. + + align:start position:0% +there's more complicated stuff going on. + + + align:start position:0% +there's more complicated stuff going on. +uh you can have a permanent uh you can + + align:start position:0% +uh you can have a permanent uh you can + + + align:start position:0% +uh you can have a permanent uh you can +have a a component of the dipole moment + + align:start position:0% +have a a component of the dipole moment + + + align:start position:0% +have a a component of the dipole moment +that is not along the near symmetry + + align:start position:0% +that is not along the near symmetry + + + align:start position:0% +that is not along the near symmetry +axis. And so you can uh + + align:start position:0% + + + + align:start position:0% + +um observe different kinds of uh pure + + align:start position:0% +um observe different kinds of uh pure + + + align:start position:0% +um observe different kinds of uh pure +rotation transition. So the pure + + align:start position:0% +rotation transition. So the pure + + + align:start position:0% +rotation transition. So the pure +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +transition where we've chosen the + + align:start position:0% +transition where we've chosen the + + + align:start position:0% +transition where we've chosen the +electronic state not to change and the + + align:start position:0% +electronic state not to change and the + + + align:start position:0% +electronic state not to change and the +vibrational state not to change. We have + + align:start position:0% +vibrational state not to change. We have + + + align:start position:0% +vibrational state not to change. We have +the requirement that there be a nonzero + + align:start position:0% +the requirement that there be a nonzero + + + align:start position:0% +the requirement that there be a nonzero +dipole moment and there can only be one + + align:start position:0% +dipole moment and there can only be one + + + align:start position:0% +dipole moment and there can only be one +component of a non-zero dipole moment + + align:start position:0% +component of a non-zero dipole moment + + + align:start position:0% +component of a non-zero dipole moment +along the the Z-axis and that means + + align:start position:0% +along the the Z-axis and that means + + + align:start position:0% +along the the Z-axis and that means +omega. + + align:start position:0% +omega. + + + align:start position:0% +omega. +Okay, what else do I want to + + align:start position:0% +Okay, what else do I want to + + + align:start position:0% +Okay, what else do I want to +say? That wasn't very beautiful. + + align:start position:0% + + + + align:start position:0% + +Um, so the + + align:start position:0% + + + + align:start position:0% + +next step is well suppose we want + + align:start position:0% +next step is well suppose we want + + + align:start position:0% +next step is well suppose we want +vibrations to + + align:start position:0% +vibrations to + + + align:start position:0% +vibrations to +change. So we're interested in + + align:start position:0% +change. So we're interested in + + + align:start position:0% +change. So we're interested in +vibration rotation spectrum. + + align:start position:0% +vibration rotation spectrum. + + + align:start position:0% +vibration rotation spectrum. +What does it take for that to occur? + + align:start position:0% +What does it take for that to occur? + + + align:start position:0% +What does it take for that to occur? +Well, we can write the critical thing + + align:start position:0% +Well, we can write the critical thing + + + align:start position:0% +Well, we can write the critical thing +this uh this dipole moment + + align:start position:0% +this uh this dipole moment + + + align:start position:0% +this uh this dipole moment +function as a power series. So + + align:start position:0% +function as a power series. So + + + align:start position:0% +function as a power series. So +um for a diatomic molecule it's still it + + align:start position:0% +um for a diatomic molecule it's still it + + + align:start position:0% +um for a diatomic molecule it's still it +can only be uh you can only no matter + + align:start position:0% +can only be uh you can only no matter + + + align:start position:0% +can only be uh you can only no matter +what you do even if you stretch the + + align:start position:0% +what you do even if you stretch the + + + align:start position:0% +what you do even if you stretch the +molecule you can't arrange for a dipole + + align:start position:0% +molecule you can't arrange for a dipole + + + align:start position:0% +molecule you can't arrange for a dipole +to occur perpendicular. So we're + + align:start position:0% +to occur perpendicular. So we're + + + align:start position:0% +to occur perpendicular. So we're +interested only in the Z component. + + align:start position:0% +interested only in the Z component. + + + align:start position:0% +interested only in the Z component. +We're keeping the electronic state + + align:start position:0% +We're keeping the electronic state + + + align:start position:0% +We're keeping the electronic state +fixed. We want to know uh the art of + + align:start position:0% +fixed. We want to know uh the art of + + + align:start position:0% +fixed. We want to know uh the art of +evidence and so we write + + align:start position:0% + + + + align:start position:0% + +this power series. + + align:start position:0% + + + + align:start position:0% + +You can't have a dipole moment with an + + align:start position:0% +You can't have a dipole moment with an + + + align:start position:0% +You can't have a dipole moment with an +external field perpendicular to the + + align:start position:0% +external field perpendicular to the + + + align:start position:0% +external field perpendicular to the +inter nuclear axis + + align:start position:0% +inter nuclear axis + + + align:start position:0% +inter nuclear axis +due to some polarization. You can you + + align:start position:0% +due to some polarization. You can you + + + align:start position:0% +due to some polarization. You can you +can polarize the molecule. Yeah. But + + align:start position:0% +can polarize the molecule. Yeah. But + + + align:start position:0% +can polarize the molecule. Yeah. But +again, the molecule is free to rotate. + + align:start position:0% +again, the molecule is free to rotate. + + + align:start position:0% +again, the molecule is free to rotate. +And so you apply an electric field. What + + align:start position:0% +And so you apply an electric field. What + + + align:start position:0% +And so you apply an electric field. What +is it going to do to I mean eventually + + align:start position:0% +is it going to do to I mean eventually + + + align:start position:0% +is it going to do to I mean eventually +it's going to rotate to a line, right? + + align:start position:0% +it's going to rotate to a line, right? + + + align:start position:0% +it's going to rotate to a line, right? +Minimize the energy and whatever. But + + align:start position:0% +Minimize the energy and whatever. But + + + align:start position:0% +Minimize the energy and whatever. But +certainly if you impose an external + + align:start position:0% +certainly if you impose an external + + + align:start position:0% +certainly if you impose an external +field you can you can spoil the + + align:start position:0% +field you can you can spoil the + + + align:start position:0% +field you can you can spoil the +isotropy. So the molecule is rotating + + align:start position:0% +isotropy. So the molecule is rotating + + + align:start position:0% +isotropy. So the molecule is rotating +and it it's not free to rotate + + align:start position:0% +and it it's not free to rotate + + + align:start position:0% +and it it's not free to rotate +uh it's now rotating in a uh in a in a + + align:start position:0% +uh it's now rotating in a uh in a in a + + + align:start position:0% +uh it's now rotating in a uh in a in a +potential and so there'll be splittings + + align:start position:0% +potential and so there'll be splittings + + + align:start position:0% +potential and so there'll be splittings +in the energy levels. You can make + + align:start position:0% +in the energy levels. You can make + + + align:start position:0% +in the energy levels. You can make +states of different things. Yeah. + + align:start position:0% +states of different things. Yeah. + + + align:start position:0% +states of different things. Yeah. +So, but I I have not applied an external + + align:start position:0% +So, but I I have not applied an external + + + align:start position:0% +So, but I I have not applied an external +field. I'm just uh asking well what will + + align:start position:0% +field. I'm just uh asking well what will + + + align:start position:0% +field. I'm just uh asking well what will +you observe with a weak uh field. Okay. + + align:start position:0% +you observe with a weak uh field. Okay. + + + align:start position:0% +you observe with a weak uh field. Okay. +So, we have this + + align:start position:0% +So, we have this + + + align:start position:0% +So, we have this +and this is the displacement + + align:start position:0% +and this is the displacement + + + align:start position:0% +and this is the displacement +uh for the harmonic oscillator. And we + + align:start position:0% +uh for the harmonic oscillator. And we + + + align:start position:0% +uh for the harmonic oscillator. And we +know that if we have matrix + + align:start position:0% + + + + align:start position:0% + +elements for harmonic oscillators, we + + align:start position:0% +elements for harmonic oscillators, we + + + align:start position:0% +elements for harmonic oscillators, we +know that the only non-zero ones are + + align:start position:0% +know that the only non-zero ones are + + + align:start position:0% +know that the only non-zero ones are +going to be ones that change v by plus + + align:start position:0% +going to be ones that change v by plus + + + align:start position:0% +going to be ones that change v by plus +or minus one from this term. And from + + align:start position:0% +or minus one from this term. And from + + + align:start position:0% +or minus one from this term. And from +this we have + + align:start position:0% +this we have + + + align:start position:0% +this we have +uh a selection will delta v of 0 plus or + + align:start position:0% +uh a selection will delta v of 0 plus or + + + align:start position:0% +uh a selection will delta v of 0 plus or +minus 2. So we get the sense that if the + + align:start position:0% +minus 2. So we get the sense that if the + + + align:start position:0% +minus 2. So we get the sense that if the +dipole moment changes with + + align:start position:0% +dipole moment changes with + + + align:start position:0% +dipole moment changes with +R that's what this is well then you can + + align:start position:0% +R that's what this is well then you can + + + align:start position:0% +R that's what this is well then you can +change V by one and so you get a + + align:start position:0% +change V by one and so you get a + + + align:start position:0% +change V by one and so you get a +propensity + + align:start position:0% + + + + align:start position:0% + +rule which + + align:start position:0% +rule which + + + align:start position:0% +rule which +says for a + + align:start position:0% +says for a + + + align:start position:0% +says for a +vibration if this dipole moment changes + + align:start position:0% +vibration if this dipole moment changes + + + align:start position:0% +vibration if this dipole moment changes +and you can have a vibration + + align:start position:0% +and you can have a vibration + + + align:start position:0% +and you can have a vibration +uh like in nitrogen + + align:start position:0% +uh like in nitrogen + + + align:start position:0% +uh like in nitrogen +uh the dipole moment is zero and + + align:start position:0% +uh the dipole moment is zero and + + + align:start position:0% +uh the dipole moment is zero and +stretching it doesn't do anything in + + align:start position:0% +stretching it doesn't do anything in + + + align:start position:0% +stretching it doesn't do anything in +CO the dipole moment at equilibrium is + + align:start position:0% +CO the dipole moment at equilibrium is + + + align:start position:0% +CO the dipole moment at equilibrium is +almost zero but stretching it does + + align:start position:0% +almost zero but stretching it does + + + align:start position:0% +almost zero but stretching it does +change the dip the dipole so this thing + + align:start position:0% +change the dip the dipole so this thing + + + align:start position:0% +change the dip the dipole so this thing +is the thing that makes the transitions + + align:start position:0% +is the thing that makes the transitions + + + align:start position:0% +is the thing that makes the transitions +occur and this is the the main thing + + align:start position:0% +occur and this is the the main thing + + + align:start position:0% +occur and this is the the main thing +that enables you to change the quantum + + align:start position:0% +that enables you to change the quantum + + + align:start position:0% +that enables you to change the quantum +number so this is how big how how + + align:start position:0% +number so this is how big how how + + + align:start position:0% +number so this is how big how how +probable and this is yes or no but this + + align:start position:0% +probable and this is yes or no but this + + + align:start position:0% +probable and this is yes or no but this +is a power series. It's not just two + + align:start position:0% +is a power series. It's not just two + + + align:start position:0% +is a power series. It's not just two +terms. I mean this gave rise to pure + + align:start position:0% +terms. I mean this gave rise to pure + + + align:start position:0% +terms. I mean this gave rise to pure +rotation spectra. This gives rise to + + align:start position:0% +rotation spectra. This gives rise to + + + align:start position:0% +rotation spectra. This gives rise to +vibration rotation spectrum. This gives + + align:start position:0% +vibration rotation spectrum. This gives + + + align:start position:0% +vibration rotation spectrum. This gives +rise to some weaker transitions overtone + + align:start position:0% +rise to some weaker transitions overtone + + + align:start position:0% +rise to some weaker transitions overtone +transitions. Uh and so this is not a + + align:start position:0% +transitions. Uh and so this is not a + + + align:start position:0% +transitions. Uh and so this is not a +selection rule. This is it the what you + + align:start position:0% +selection rule. This is it the what you + + + align:start position:0% +selection rule. This is it the what you +expect is for the vibrational modes + + align:start position:0% +expect is for the vibrational modes + + + align:start position:0% +expect is for the vibrational modes +where the dipole moment changes and now + + align:start position:0% +where the dipole moment changes and now + + + align:start position:0% +where the dipole moment changes and now +I'm generalizing beyond uh diatomic + + align:start position:0% +I'm generalizing beyond uh diatomic + + + align:start position:0% +I'm generalizing beyond uh diatomic +molecules because it's short step but + + align:start position:0% +molecules because it's short step but + + + align:start position:0% +molecules because it's short step but +there will be transitions where that + + align:start position:0% +there will be transitions where that + + + align:start position:0% +there will be transitions where that +mode changes by + + align:start position:0% +mode changes by + + + align:start position:0% +mode changes by +one and uh if you have a polyatomic + + align:start position:0% +one and uh if you have a polyatomic + + + align:start position:0% +one and uh if you have a polyatomic +molecule you can imagine that there will + + align:start position:0% +molecule you can imagine that there will + + + align:start position:0% +molecule you can imagine that there will +changes in the dipole moment and not + + align:start position:0% +changes in the dipole moment and not + + + align:start position:0% +changes in the dipole moment and not +just along the Z-axis but along whatever + + align:start position:0% +just along the Z-axis but along whatever + + + align:start position:0% +just along the Z-axis but along whatever +axis the vibration chooses and so you + + align:start position:0% +axis the vibration chooses and so you + + + align:start position:0% +axis the vibration chooses and so you +can get some pretty interesting + + align:start position:0% +can get some pretty interesting + + + align:start position:0% +can get some pretty interesting +phenomena. Okay. + + align:start position:0% +phenomena. Okay. + + + align:start position:0% +phenomena. Okay. +So that's + + align:start position:0% +So that's + + + align:start position:0% +So that's +uh so pure rotation spectra require a + + align:start position:0% +uh so pure rotation spectra require a + + + align:start position:0% +uh so pure rotation spectra require a +dipole moment vibrational spectra + + align:start position:0% +dipole moment vibrational spectra + + + align:start position:0% +dipole moment vibrational spectra +require a change in the dipole + + align:start position:0% +require a change in the dipole + + + align:start position:0% +require a change in the dipole +moment and electronic spectra you just + + align:start position:0% +moment and electronic spectra you just + + + align:start position:0% +moment and electronic spectra you just +have to have this initial state + + align:start position:0% +have to have this initial state + + + align:start position:0% +have to have this initial state +uh m + + align:start position:0% +uh m + + + align:start position:0% +uh m +uh + + align:start position:0% +uh + + + align:start position:0% +uh +no we need to have m i f + + align:start position:0% + + + + align:start position:0% + +are not equal to + + align:start position:0% +are not equal to + + + align:start position:0% +are not equal to +zero. So, and how do we do that? Well, + + align:start position:0% +zero. So, and how do we do that? Well, + + + align:start position:0% +zero. So, and how do we do that? Well, +we classify the initial state and the + + align:start position:0% +we classify the initial state and the + + + align:start position:0% +we classify the initial state and the +final state according to their + + align:start position:0% +final state according to their + + + align:start position:0% +final state according to their +irreducible + + align:start position:0% +irreducible + + + align:start position:0% +irreducible +representation. And the we classify the + + align:start position:0% +representation. And the we classify the + + + align:start position:0% +representation. And the we classify the +transition moment operator. And so the + + align:start position:0% +transition moment operator. And so the + + + align:start position:0% +transition moment operator. And so the +integral here has to be totally + + align:start position:0% +integral here has to be totally + + + align:start position:0% +integral here has to be totally +symmetric. And so you get electronic + + align:start position:0% +symmetric. And so you get electronic + + + align:start position:0% +symmetric. And so you get electronic +selection rules. And so you can have + + align:start position:0% +selection rules. And so you can have + + + align:start position:0% +selection rules. And so you can have +things like G sigma G+ going + + align:start position:0% +things like G sigma G+ going + + + align:start position:0% +things like G sigma G+ going +to sigma U plus you. And uh so if you + + align:start position:0% +to sigma U plus you. And uh so if you + + + align:start position:0% +to sigma U plus you. And uh so if you +have a homonuclear molecule + + align:start position:0% +have a homonuclear molecule + + + align:start position:0% +have a homonuclear molecule +uh you can go from you always go from G + + align:start position:0% +uh you can go from you always go from G + + + align:start position:0% +uh you can go from you always go from G +to U. You can go sigma to pi. You cannot + + align:start position:0% + + + + align:start position:0% + +go between plus minus. + + align:start position:0% +go between plus minus. + + + align:start position:0% +go between plus minus. +And so there's, you know, there's stuff + + align:start position:0% +And so there's, you know, there's stuff + + + align:start position:0% +And so there's, you know, there's stuff +that you can figure out from symmetry. + + align:start position:0% +that you can figure out from symmetry. + + + align:start position:0% +that you can figure out from symmetry. +So there's three kinds of transitions + + align:start position:0% +So there's three kinds of transitions + + + align:start position:0% +So there's three kinds of transitions +and many people get confused because + + align:start position:0% +and many people get confused because + + + align:start position:0% +and many people get confused because +it's not taught anymore. It's in the + + align:start position:0% +it's not taught anymore. It's in the + + + align:start position:0% +it's not taught anymore. It's in the +elementary physical chemistry course. + + align:start position:0% +elementary physical chemistry course. + + + align:start position:0% +elementary physical chemistry course. +Maybe you saw it. Uh but in America all + + align:start position:0% +Maybe you saw it. Uh but in America all + + + align:start position:0% +Maybe you saw it. Uh but in America all +the stuff about spectra of small + + align:start position:0% +the stuff about spectra of small + + + align:start position:0% +the stuff about spectra of small +molecules is gone from uh the quantum + + align:start position:0% +molecules is gone from uh the quantum + + + align:start position:0% +molecules is gone from uh the quantum +mechanics course. And so many I've asked + + align:start position:0% +mechanics course. And so many I've asked + + + align:start position:0% +mechanics course. And so many I've asked +on cubes you know what are you what do + + align:start position:0% +on cubes you know what are you what do + + + align:start position:0% +on cubes you know what are you what do +you need to have a pure rotation + + align:start position:0% +you need to have a pure rotation + + + align:start position:0% +you need to have a pure rotation +spectrum and uh I get the most amazing + + align:start position:0% +spectrum and uh I get the most amazing + + + align:start position:0% +spectrum and uh I get the most amazing +answers but it's a very simple thing so + + align:start position:0% +answers but it's a very simple thing so + + + align:start position:0% +answers but it's a very simple thing so +we have three kinds of spectrum three + + align:start position:0% +we have three kinds of spectrum three + + + align:start position:0% +we have three kinds of spectrum three +distinct things that make them possible + + align:start position:0% +distinct things that make them possible + + + align:start position:0% +distinct things that make them possible +and we have two we have symmetry and we + + align:start position:0% +and we have two we have symmetry and we + + + align:start position:0% +and we have two we have symmetry and we +have how big and uh uh usually when + + align:start position:0% +have how big and uh uh usually when + + + align:start position:0% +have how big and uh uh usually when +you're looking at the spectrum you don't + + align:start position:0% +you're looking at the spectrum you don't + + + align:start position:0% +you're looking at the spectrum you don't +care so much about how big + + align:start position:0% +care so much about how big + + + align:start position:0% +care so much about how big +you care about isn't possible. But if + + align:start position:0% +you care about isn't possible. But if + + + align:start position:0% +you care about isn't possible. But if +there's a a fundamental transition where + + align:start position:0% +there's a a fundamental transition where + + + align:start position:0% +there's a a fundamental transition where +the vibration changes by + + align:start position:0% +the vibration changes by + + + align:start position:0% +the vibration changes by +one and an overtone, you normally expect + + align:start position:0% +one and an overtone, you normally expect + + + align:start position:0% +one and an overtone, you normally expect +that the overtone will be weaker than + + align:start position:0% +that the overtone will be weaker than + + + align:start position:0% +that the overtone will be weaker than +the + + align:start position:0% +the + + + align:start position:0% +the +fundamental. By how much? Well, that + + align:start position:0% +fundamental. By how much? Well, that + + + align:start position:0% +fundamental. By how much? Well, that +depends because these transition moment + + align:start position:0% +depends because these transition moment + + + align:start position:0% +depends because these transition moment +functions or dipole moment functions are + + align:start position:0% +functions or dipole moment functions are + + + align:start position:0% +functions or dipole moment functions are +often complicated. But again there's + + align:start position:0% +often complicated. But again there's + + + align:start position:0% +often complicated. But again there's +another simple rule and that is + + align:start position:0% +another simple rule and that is + + + align:start position:0% +another simple rule and that is +that electronic properties change as a + + align:start position:0% +that electronic properties change as a + + + align:start position:0% +that electronic properties change as a +function of r slowly. + + align:start position:0% +function of r slowly. + + + align:start position:0% +function of r slowly. +If they change fast, it's because + + align:start position:0% +If they change fast, it's because + + + align:start position:0% +If they change fast, it's because +something unourred has occurred. And + + align:start position:0% +something unourred has occurred. And + + + align:start position:0% +something unourred has occurred. And +that's + + align:start position:0% +that's + + + align:start position:0% +that's +interesting. But generally, you don't + + align:start position:0% +interesting. But generally, you don't + + + align:start position:0% +interesting. But generally, you don't +expect things, you know, if they if + + align:start position:0% +expect things, you know, if they if + + + align:start position:0% +expect things, you know, if they if +they're allowed to change with R because + + align:start position:0% +they're allowed to change with R because + + + align:start position:0% +they're allowed to change with R because +of symmetry. They will, but the change + + align:start position:0% +of symmetry. They will, but the change + + + align:start position:0% +of symmetry. They will, but the change +will be slow. + + align:start position:0% +will be slow. + + + align:start position:0% +will be slow. +electronic properties are are going to + + align:start position:0% +electronic properties are are going to + + + align:start position:0% +electronic properties are are going to +change with J slowly because J + + align:start position:0% +change with J slowly because J + + + align:start position:0% +change with J slowly because J +uh affects the R + + align:start position:0% +uh affects the R + + + align:start position:0% +uh affects the R +integral. I mean if you if you have + + align:start position:0% + + + + align:start position:0% + +a potential energy curve and you're + + align:start position:0% +a potential energy curve and you're + + + align:start position:0% +a potential energy curve and you're +vibrating in this potential energy curve + + align:start position:0% +vibrating in this potential energy curve + + + align:start position:0% +vibrating in this potential energy curve +and you add to this potential energy + + align:start position:0% +and you add to this potential energy + + + align:start position:0% +and you add to this potential energy +curve a centrifugal term uh which is JJ + + align:start position:0% +curve a centrifugal term uh which is JJ + + + align:start position:0% +curve a centrifugal term uh which is JJ ++ + + align:start position:0% ++ + + + align:start position:0% ++ +one over uh 2 u r 2. So when r gets + + align:start position:0% +one over uh 2 u r 2. So when r gets + + + align:start position:0% +one over uh 2 u r 2. So when r gets +small this gets big. So you're you're + + align:start position:0% +small this gets big. So you're you're + + + align:start position:0% +small this gets big. So you're you're +you're adding something that this to the + + align:start position:0% +you're adding something that this to the + + + align:start position:0% +you're adding something that this to the +curve that does this, it shifts the + + align:start position:0% +curve that does this, it shifts the + + + align:start position:0% +curve that does this, it shifts the +amplitude + + align:start position:0% +amplitude + + + align:start position:0% +amplitude +out. And so you can have J causing a + + align:start position:0% +out. And so you can have J causing a + + + align:start position:0% +out. And so you can have J causing a +change in the R, the average value of R. + + align:start position:0% +change in the R, the average value of R. + + + align:start position:0% +change in the R, the average value of R. +And so you can have very very subtle + + align:start position:0% +And so you can have very very subtle + + + align:start position:0% +And so you can have very very subtle +changes in electronic properties with J + + align:start position:0% +changes in electronic properties with J + + + align:start position:0% +changes in electronic properties with J +that's called centrial distortion or + + align:start position:0% +that's called centrial distortion or + + + align:start position:0% +that's called centrial distortion or +whatever. And uh so you expect these + + align:start position:0% +whatever. And uh so you expect these + + + align:start position:0% +whatever. And uh so you expect these +things to be very very slow and you + + align:start position:0% +things to be very very slow and you + + + align:start position:0% +things to be very very slow and you +expect you know what the sign of these + + align:start position:0% +expect you know what the sign of these + + + align:start position:0% +expect you know what the sign of these +things will be and whenever it isn't + + align:start position:0% +things will be and whenever it isn't + + + align:start position:0% +things will be and whenever it isn't +that way it's telling you that something + + align:start position:0% +that way it's telling you that something + + + align:start position:0% +that way it's telling you that something +special has occurred that there has been + + align:start position:0% +special has occurred that there has been + + + align:start position:0% +special has occurred that there has been +an accidental degeneracy of two kinds of + + align:start position:0% +an accidental degeneracy of two kinds of + + + align:start position:0% +an accidental degeneracy of two kinds of +states something that you had neglected + + align:start position:0% +states something that you had neglected + + + align:start position:0% +states something that you had neglected +which results in something very + + align:start position:0% +which results in something very + + + align:start position:0% +which results in something very +interesting and so + + align:start position:0% +interesting and so + + + align:start position:0% +interesting and so +uh you you want to approach spectra with + + align:start position:0% +uh you you want to approach spectra with + + + align:start position:0% +uh you you want to approach spectra with +the idea of this is what I expect and + + align:start position:0% +the idea of this is what I expect and + + + align:start position:0% +the idea of this is what I expect and +it's very simple and uh many things are + + align:start position:0% +it's very simple and uh many things are + + + align:start position:0% +it's very simple and uh many things are +not supposed to happen when they do + + align:start position:0% +not supposed to happen when they do + + + align:start position:0% +not supposed to happen when they do +happen then you get excited because this + + align:start position:0% +happen then you get excited because this + + + align:start position:0% +happen then you get excited because this +is something to figure out and usually + + align:start position:0% +is something to figure out and usually + + + align:start position:0% +is something to figure out and usually +it tells you something very special + + align:start position:0% +it tells you something very special + + + align:start position:0% +it tells you something very special +about the molecule and so I think well + + align:start position:0% +about the molecule and so I think well + + + align:start position:0% +about the molecule and so I think well +in fact I've actually talked a little + + align:start position:0% +in fact I've actually talked a little + + + align:start position:0% +in fact I've actually talked a little +too long so uh I will continue with this + + align:start position:0% +too long so uh I will continue with this + + + align:start position:0% +too long so uh I will continue with this +tomorrow and I think the main subject + + align:start position:0% +tomorrow and I think the main subject + + + align:start position:0% +tomorrow and I think the main subject +will have to do with + + align:start position:0% + + + + align:start position:0% + +what goes into + + align:start position:0% +what goes into + + + align:start position:0% +what goes into +Can I ask two quick questions? No. One + + align:start position:0% +Can I ask two quick questions? No. One + + + align:start position:0% +Can I ask two quick questions? No. One +is something I'm confused about. Um, you + + align:start position:0% +is something I'm confused about. Um, you + + + align:start position:0% +is something I'm confused about. Um, you +said that even when delta J equals Z, + + align:start position:0% +said that even when delta J equals Z, + + + align:start position:0% +said that even when delta J equals Z, +delta omega can + + align:start position:0% +delta omega can + + + align:start position:0% +delta omega can +change, but delta omega is just a + + align:start position:0% +change, but delta omega is just a + + + align:start position:0% +change, but delta omega is just a +projection of J on the Z axis. + + align:start position:0% +projection of J on the Z axis. + + + align:start position:0% +projection of J on the Z axis. +Suppose you're going from J= 10 to J= + + align:start position:0% +Suppose you're going from J= 10 to J= + + + align:start position:0% +Suppose you're going from J= 10 to J= +10. + + align:start position:0% +10. + + + align:start position:0% +10. +So J can have a projection on the body + + align:start position:0% +So J can have a projection on the body + + + align:start position:0% +So J can have a projection on the body +axis + + align:start position:0% +axis + + + align:start position:0% +axis +and there's no reason why the projection + + align:start position:0% +and there's no reason why the projection + + + align:start position:0% +and there's no reason why the projection +can or cannot + + align:start position:0% +can or cannot + + + align:start position:0% +can or cannot +change. The the change in the projection + + align:start position:0% +change. The the change in the projection + + + align:start position:0% +change. The the change in the projection +quantum number has to do with + + align:start position:0% +quantum number has to do with + + + align:start position:0% +quantum number has to do with +symmetry along which axis is the the + + align:start position:0% +symmetry along which axis is the the + + + align:start position:0% +symmetry along which axis is the the +dipole. + + align:start position:0% + + + + align:start position:0% + +Oh, I see. I see. So, I mean, normally + + align:start position:0% +Oh, I see. I see. So, I mean, normally + + + align:start position:0% +Oh, I see. I see. So, I mean, normally +you think if J doesn't change, Yeah. + + align:start position:0% +you think if J doesn't change, Yeah. + + + align:start position:0% +you think if J doesn't change, Yeah. +Well, you're going J equals Z to J + + align:start position:0% +Well, you're going J equals Z to J + + + align:start position:0% +Well, you're going J equals Z to J +equals Z. And of course, well, omega is + + align:start position:0% +equals Z. And of course, well, omega is + + + align:start position:0% +equals Z. And of course, well, omega is +zero in both cases because omega has to + + align:start position:0% +zero in both cases because omega has to + + + align:start position:0% +zero in both cases because omega has to +be. So, it but J= 10 to J equals 10, you + + align:start position:0% +be. So, it but J= 10 to J equals 10, you + + + align:start position:0% +be. So, it but J= 10 to J equals 10, you +can have omega going not changing or + + align:start position:0% +can have omega going not changing or + + + align:start position:0% +can have omega going not changing or +going up or down. There's no reason. + + align:start position:0% +going up or down. There's no reason. + + + align:start position:0% +going up or down. There's no reason. +Okay. The other question I had was a + + align:start position:0% +Okay. The other question I had was a + + + align:start position:0% +Okay. The other question I had was a +little bit weirder. + + align:start position:0% +little bit weirder. + + + align:start position:0% +little bit weirder. +Um, so normally we do spectroscopy by + + align:start position:0% +Um, so normally we do spectroscopy by + + + align:start position:0% +Um, so normally we do spectroscopy by +having a laser in a laboratory or a lamp + + align:start position:0% +having a laser in a laboratory or a lamp + + + align:start position:0% +having a laser in a laboratory or a lamp +in a laboratory interacting with + + align:start position:0% +in a laboratory interacting with + + + align:start position:0% +in a laboratory interacting with +molecules that are moving sometimes very + + align:start position:0% +molecules that are moving sometimes very + + + align:start position:0% +molecules that are moving sometimes very +fast. Oh, I think this is not a quick + + align:start position:0% +fast. Oh, I think this is not a quick + + + align:start position:0% +fast. Oh, I think this is not a quick +question but well. Is this a counter + + align:start position:0% +question but well. Is this a counter + + + align:start position:0% +question but well. Is this a counter +revolutionary? Well, I mean I was going + + align:start position:0% +revolutionary? Well, I mean I was going + + + align:start position:0% +revolutionary? Well, I mean I was going +to ask so what happens a couple things. + + align:start position:0% +to ask so what happens a couple things. + + + align:start position:0% +to ask so what happens a couple things. +So first of all, what happens if you + + align:start position:0% +So first of all, what happens if you + + + align:start position:0% +So first of all, what happens if you +trap the molecules and they're not + + align:start position:0% +trap the molecules and they're not + + + align:start position:0% +trap the molecules and they're not +moving with respect to the laboratory? + + align:start position:0% +moving with respect to the laboratory? + + + align:start position:0% +moving with respect to the laboratory? +um and you know say that they're very + + align:start position:0% +um and you know say that they're very + + + align:start position:0% +um and you know say that they're very +cold also when they're trapped you know + + align:start position:0% +cold also when they're trapped you know + + + align:start position:0% +cold also when they're trapped you know +does that let you does that just + + align:start position:0% +does that let you does that just + + + align:start position:0% +does that let you does that just +simplify a little bit of algebra or does + + align:start position:0% +simplify a little bit of algebra or does + + + align:start position:0% +simplify a little bit of algebra or does +that get you something? Well, if the + + align:start position:0% +that get you something? Well, if the + + + align:start position:0% +that get you something? Well, if the +molecules are free to rotate, + + align:start position:0% +molecules are free to rotate, + + + align:start position:0% +molecules are free to rotate, +then there's nothing + + align:start position:0% +then there's nothing + + + align:start position:0% +then there's nothing +different. If you have trapped them uh + + align:start position:0% +different. If you have trapped them uh + + + align:start position:0% +different. If you have trapped them uh +in one J state, I mean, well, what you + + align:start position:0% +in one J state, I mean, well, what you + + + align:start position:0% +in one J state, I mean, well, what you +normally do, if you trap them in a + + align:start position:0% +normally do, if you trap them in a + + + align:start position:0% +normally do, if you trap them in a +particular J state, it still doesn't do + + align:start position:0% +particular J state, it still doesn't do + + + align:start position:0% +particular J state, it still doesn't do +anything because they're still But + + align:start position:0% +anything because they're still But + + + align:start position:0% +anything because they're still But +suppose you trap them in a strong + + align:start position:0% +suppose you trap them in a strong + + + align:start position:0% +suppose you trap them in a strong +electric field, then it's called + + align:start position:0% +electric field, then it's called + + + align:start position:0% +electric field, then it's called +pendular states. But what has to happen + + align:start position:0% +pendular states. But what has to happen + + + align:start position:0% +pendular states. But what has to happen +then? You've destroyed J. Mhm. So you + + align:start position:0% +then? You've destroyed J. Mhm. So you + + + align:start position:0% +then? You've destroyed J. Mhm. So you +have a molecule now that's oriented in a + + align:start position:0% +have a molecule now that's oriented in a + + + align:start position:0% +have a molecule now that's oriented in a +laboratory because you applied a strong + + align:start position:0% +laboratory because you applied a strong + + + align:start position:0% +laboratory because you applied a strong +enough field and that field achieved + + align:start position:0% +enough field and that field achieved + + + align:start position:0% +enough field and that field achieved +that by saying okay I'm mixing states of + + align:start position:0% +that by saying okay I'm mixing states of + + + align:start position:0% +that by saying okay I'm mixing states of +different J's. + + align:start position:0% +different J's. + + + align:start position:0% +different J's. +J is what makes it be able to move. If J + + align:start position:0% +J is what makes it be able to move. If J + + + align:start position:0% +J is what makes it be able to move. If J +is destroyed then you you can say it's + + align:start position:0% +is destroyed then you you can say it's + + + align:start position:0% +is destroyed then you you can say it's +project it has a projection that doesn't + + align:start position:0% +project it has a projection that doesn't + + + align:start position:0% +project it has a projection that doesn't +average to zero + + align:start position:0% +average to zero + + + align:start position:0% +average to zero +in then let me ask the opposite + + align:start position:0% +in then let me ask the opposite + + + align:start position:0% +in then let me ask the opposite +question. So what happens if you do your + + align:start position:0% +question. So what happens if you do your + + + align:start position:0% +question. So what happens if you do your +spectroscopy by using uh emission from + + align:start position:0% +spectroscopy by using uh emission from + + + align:start position:0% +spectroscopy by using uh emission from +atoms or molecules that are moving along + + align:start position:0% +atoms or molecules that are moving along + + + align:start position:0% +atoms or molecules that are moving along +with the atoms and molecules that you're + + align:start position:0% +with the atoms and molecules that you're + + + align:start position:0% +with the atoms and molecules that you're +trying to see or you mean they're + + align:start position:0% +trying to see or you mean they're + + + align:start position:0% +trying to see or you mean they're +exciting each other. They're exciting + + align:start position:0% +exciting each other. They're exciting + + + align:start position:0% +exciting each other. They're exciting +each other and then or there's there's + + align:start position:0% +each other and then or there's there's + + + align:start position:0% +each other and then or there's there's +some kind but they're + + align:start position:0% +some kind but they're + + + align:start position:0% +some kind but they're +not relative to each other. Say there's + + align:start position:0% +not relative to each other. Say there's + + + align:start position:0% +not relative to each other. Say there's +some kind of coherence between + + align:start position:0% +some kind of coherence between + + + align:start position:0% +some kind of coherence between +them that you you know something like + + align:start position:0% +them that you you know something like + + + align:start position:0% +them that you you know something like +you you have a molecule that then breaks + + align:start position:0% +you you have a molecule that then breaks + + + align:start position:0% +you you have a molecule that then breaks +and emits as it breaks and there's + + align:start position:0% +and emits as it breaks and there's + + + align:start position:0% +and emits as it breaks and there's +something we're getting to entangled + + align:start position:0% +something we're getting to entangled + + + align:start position:0% +something we're getting to entangled +states. I don't know. I I mean yes there + + align:start position:0% +states. I don't know. I I mean yes there + + + align:start position:0% +states. I don't know. I I mean yes there +are there are things you can build where + + align:start position:0% +are there are things you can build where + + + align:start position:0% +are there are things you can build where +the the two + + align:start position:0% +the the two + + + align:start position:0% +the the two +pieces came from one thing in in some + + align:start position:0% +pieces came from one thing in in some + + + align:start position:0% +pieces came from one thing in in some +organized way. And you have to be + + align:start position:0% +organized way. And you have to be + + + align:start position:0% +organized way. And you have to be +careful about saying that now they're + + align:start position:0% +careful about saying that now they're + + + align:start position:0% +careful about saying that now they're +free to move relative to each other uh + + align:start position:0% +free to move relative to each other uh + + + align:start position:0% +free to move relative to each other uh +uh randomly, right? Uh and there are + + align:start position:0% +uh randomly, right? Uh and there are + + + align:start position:0% +uh randomly, right? Uh and there are +probably some consequences in the + + align:start position:0% +probably some consequences in the + + + align:start position:0% +probably some consequences in the +laboratory associated with the + + align:start position:0% +laboratory associated with the + + + align:start position:0% +laboratory associated with the +correlated motions of two fragments. And + + align:start position:0% +correlated motions of two fragments. And + + + align:start position:0% +correlated motions of two fragments. And +uh but I'm not prepared to answer that + + align:start position:0% +uh but I'm not prepared to answer that + + + align:start position:0% +uh but I'm not prepared to answer that +question. Normally if you have two + + align:start position:0% +question. Normally if you have two + + + align:start position:0% +question. Normally if you have two +things that are uh that were not one + + align:start position:0% +things that are uh that were not one + + + align:start position:0% +things that are uh that were not one +thing initially + + align:start position:0% +thing initially + + + align:start position:0% +thing initially +They're oriented randomly and so you + + align:start position:0% +They're oriented randomly and so you + + + align:start position:0% +They're oriented randomly and so you +have body frames and laboratory frames + + align:start position:0% +have body frames and laboratory frames + + + align:start position:0% +have body frames and laboratory frames +and you you just have to do those + + align:start position:0% +and you you just have to do those + + + align:start position:0% +and you you just have to do those +transformations to to establish a + + align:start position:0% +transformations to to establish a + + + align:start position:0% +transformations to to establish a +correlation between two body frames + + align:start position:0% +correlation between two body frames + + + align:start position:0% +correlation between two body frames +requires a trick. I it might be possible + + align:start position:0% +requires a trick. I it might be possible + + + align:start position:0% +requires a trick. I it might be possible +to do this. Uh I mean I mean for example + + align:start position:0% +to do this. Uh I mean I mean for example + + + align:start position:0% +to do this. Uh I mean I mean for example +suppose you have a very short pulse + + align:start position:0% +suppose you have a very short pulse + + + align:start position:0% +suppose you have a very short pulse +uh and so this molecule got excited at + + align:start position:0% +uh and so this molecule got excited at + + + align:start position:0% +uh and so this molecule got excited at +this time this molecule got excited at + + align:start position:0% +this time this molecule got excited at + + + align:start position:0% +this time this molecule got excited at +that time uh + + align:start position:0% + + + + align:start position:0% + +and the molecules that got excited had + + align:start position:0% +and the molecules that got excited had + + + align:start position:0% +and the molecules that got excited had +their J's oriented in a in a way that is + + align:start position:0% +their J's oriented in a in a way that is + + + align:start position:0% +their J's oriented in a in a way that is +preferentially + + align:start position:0% +preferentially + + + align:start position:0% +preferentially +uh so that you have some selection on + + align:start position:0% +uh so that you have some selection on + + + align:start position:0% +uh so that you have some selection on +the orientation the body frames. these + + align:start position:0% +the orientation the body frames. these + + + align:start position:0% +the orientation the body frames. these +two things there's probably some I mean + + align:start position:0% +two things there's probably some I mean + + + align:start position:0% +two things there's probably some I mean +what if one is an ion that's out around + + align:start position:0% +what if one is an ion that's out around + + + align:start position:0% +what if one is an ion that's out around +and something else is coming into the + + align:start position:0% +and something else is coming into the + + + align:start position:0% +and something else is coming into the +ion and then they're interacting for + + align:start position:0% +ion and then they're interacting for + + + align:start position:0% +ion and then they're interacting for +some for some time + + align:start position:0% +some for some time + + + align:start position:0% +some for some time +um close to each other because this is + + align:start position:0% +um close to each other because this is + + + align:start position:0% +um close to each other because this is +something that uh you should think about + + align:start position:0% +something that uh you should think about + + + align:start position:0% +something that uh you should think about +uh and it's certainly an active area of + + align:start position:0% +uh and it's certainly an active area of + + + align:start position:0% +uh and it's certainly an active area of +you know when do you observe + + align:start position:0% +you know when do you observe + + + align:start position:0% +you know when do you observe +correlations between particles and when + + align:start position:0% +correlations between particles and when + + + align:start position:0% +correlations between particles and when +uh does the independent nature of the + + align:start position:0% +uh does the independent nature of the + + + align:start position:0% +uh does the independent nature of the +particles wash out any correlation? What + + align:start position:0% +particles wash out any correlation? What + + + align:start position:0% +particles wash out any correlation? What +do you have to do to create a coherence + + align:start position:0% +do you have to do to create a coherence + + + align:start position:0% +do you have to do to create a coherence +that can be detected in length? I mean + + align:start position:0% +that can be detected in length? I mean + + + align:start position:0% +that can be detected in length? I mean +often you can create some kind of + + align:start position:0% +often you can create some kind of + + + align:start position:0% +often you can create some kind of +coherence or + + align:start position:0% +coherence or + + + align:start position:0% +coherence or +correlation and but sometimes + + align:start position:0% +correlation and but sometimes + + + align:start position:0% +correlation and but sometimes +uh there is no observation you can make + + align:start position:0% +uh there is no observation you can make + + + align:start position:0% +uh there is no observation you can make +that doesn't destroy that but you know + + align:start position:0% +that doesn't destroy that but you know + + + align:start position:0% +that doesn't destroy that but you know +it's a very useful way of thinking okay + + align:start position:0% +it's a very useful way of thinking okay + + + align:start position:0% +it's a very useful way of thinking okay +I want to create some correlation + + align:start position:0% +I want to create some correlation + + + align:start position:0% +I want to create some correlation +somehow and then I want to read that to + + align:start position:0% +somehow and then I want to read that to + + + align:start position:0% +somehow and then I want to read that to +so that I can see how that evolves and + + align:start position:0% +so that I can see how that evolves and + + + align:start position:0% +so that I can see how that evolves and +there are some very beautiful + + align:start position:0% +there are some very beautiful + + + align:start position:0% +there are some very beautiful +uh uh studies of you you create with + + align:start position:0% +uh uh studies of you you create with + + + align:start position:0% +uh uh studies of you you create with +multiple photon, multiple steps of + + align:start position:0% +multiple photon, multiple steps of + + + align:start position:0% +multiple photon, multiple steps of +exitation uh things called uh um + + align:start position:0% +exitation uh things called uh um + + + align:start position:0% +exitation uh things called uh um +alignment and orientation and higher + + align:start position:0% +alignment and orientation and higher + + + align:start position:0% +alignment and orientation and higher +multiple moments. And so you've created + + align:start position:0% +multiple moments. And so you've created + + + align:start position:0% +multiple moments. And so you've created +something and then you have to read + + align:start position:0% +something and then you have to read + + + align:start position:0% +something and then you have to read +those things and the relaxations of the + + align:start position:0% +those things and the relaxations of the + + + align:start position:0% +those things and the relaxations of the +alignments and the orientation tell you + + align:start position:0% +alignments and the orientation tell you + + + align:start position:0% +alignments and the orientation tell you +something about + + align:start position:0% +something about + + + align:start position:0% +something about +the the + + align:start position:0% +the the + + + align:start position:0% +the the +uh TEDs or components of the + + align:start position:0% +uh TEDs or components of the + + + align:start position:0% +uh TEDs or components of the +interactions between molecules. \ No newline at end of file diff --git a/pUFSXhoazY8.txt b/pUFSXhoazY8.txt new file mode 100644 index 0000000000000000000000000000000000000000..5608cd2481745f25e1e5e4ad5fb07cba44a6053d --- /dev/null +++ b/pUFSXhoazY8.txt @@ -0,0 +1,1763 @@ +align:start position:0% + +welcome in this session we're going to + + align:start position:0% +welcome in this session we're going to + + + align:start position:0% +welcome in this session we're going to +examine pole diagrams so let's consider + + align:start position:0% +examine pole diagrams so let's consider + + + align:start position:0% +examine pole diagrams so let's consider +the poll diagrams for the linear time + + align:start position:0% +the poll diagrams for the linear time + + + align:start position:0% +the poll diagrams for the linear time +independent systems of the form bdy + + align:start position:0% +independent systems of the form bdy + + + align:start position:0% +independent systems of the form bdy +equals F so here we have a few pole + + align:start position:0% +equals F so here we have a few pole + + + align:start position:0% +equals F so here we have a few pole +diagrams to examine with the poles + + align:start position:0% +diagrams to examine with the poles + + + align:start position:0% +diagrams to examine with the poles +marked with the red crosses the axes are + + align:start position:0% +marked with the red crosses the axes are + + + align:start position:0% +marked with the red crosses the axes are +imaginary axis and the real axis and the + + align:start position:0% +imaginary axis and the real axis and the + + + align:start position:0% +imaginary axis and the real axis and the +questions are list all the stable + + align:start position:0% +questions are list all the stable + + + align:start position:0% +questions are list all the stable +systems choose the systems with the + + align:start position:0% +systems choose the systems with the + + + align:start position:0% +systems choose the systems with the +fastest Decay and last last choose + + align:start position:0% +fastest Decay and last last choose + + + align:start position:0% +fastest Decay and last last choose +fastest Decay without oscillation so you + + align:start position:0% +fastest Decay without oscillation so you + + + align:start position:0% +fastest Decay without oscillation so you +have to think of how to interpret these + + align:start position:0% +have to think of how to interpret these + + + align:start position:0% +have to think of how to interpret these +diagrams and what are the meanings of + + align:start position:0% +diagrams and what are the meanings of + + + align:start position:0% +diagrams and what are the meanings of +the position of the different poles to + + align:start position:0% +the position of the different poles to + + + align:start position:0% +the position of the different poles to +address these questions so pause the + + align:start position:0% +address these questions so pause the + + + align:start position:0% +address these questions so pause the +video take a few minutes and I'll be + + align:start position:0% +video take a few minutes and I'll be + + + align:start position:0% +video take a few minutes and I'll be +right + + align:start position:0% + + + + align:start position:0% + +back well welcome back okay so the first + + align:start position:0% +back well welcome back okay so the first + + + align:start position:0% +back well welcome back okay so the first +question asks us to list all the stable + + align:start position:0% +question asks us to list all the stable + + + align:start position:0% +question asks us to list all the stable +systems so if you recall all the stable + + align:start position:0% +systems so if you recall all the stable + + + align:start position:0% +systems so if you recall all the stable +systems would be the ones for which the + + align:start position:0% +systems would be the ones for which the + + + align:start position:0% +systems would be the ones for which the +real part of the pole are all negative + + align:start position:0% +real part of the pole are all negative + + + align:start position:0% +real part of the pole are all negative +so if we have all the + + align:start position:0% + + + + align:start position:0% + +poles with real part negative we would + + align:start position:0% +poles with real part negative we would + + + align:start position:0% +poles with real part negative we would +have a stable system for which the + + align:start position:0% +have a stable system for which the + + + align:start position:0% +have a stable system for which the +solution after a long time would Decay + + align:start position:0% +solution after a long time would Decay + + + align:start position:0% +solution after a long time would Decay +basically would be transient so here if + + align:start position:0% +basically would be transient so here if + + + align:start position:0% +basically would be transient so here if +we look our our at our pole diagrams we + + align:start position:0% +we look our our at our pole diagrams we + + + align:start position:0% +we look our our at our pole diagrams we +have diagram B for which the real part + + align:start position:0% +have diagram B for which the real part + + + align:start position:0% +have diagram B for which the real part +of the two poles are minus 3 and minus 2 + + align:start position:0% +of the two poles are minus 3 and minus 2 + + + align:start position:0% +of the two poles are minus 3 and minus 2 +so this would definitely generate a + + align:start position:0% +so this would definitely generate a + + + align:start position:0% +so this would definitely generate a +decaying a decaying exponential of + + align:start position:0% +decaying a decaying exponential of + + + align:start position:0% +decaying a decaying exponential of +exponential minus 2T exponential minus + + align:start position:0% +exponential minus 2T exponential minus + + + align:start position:0% +exponential minus 2T exponential minus +3T type functions at large time for the + + align:start position:0% +3T type functions at large time for the + + + align:start position:0% +3T type functions at large time for the +for the system uh in a we have a minus + + align:start position:0% +for the system uh in a we have a minus + + + align:start position:0% +for the system uh in a we have a minus +one and a one so the real part here + + align:start position:0% +one and a one so the real part here + + + align:start position:0% +one and a one so the real part here +would give us a Decay an exponential + + align:start position:0% +would give us a Decay an exponential + + + align:start position:0% +would give us a Decay an exponential +decay exponential minus t but we would + + align:start position:0% +decay exponential minus t but we would + + + align:start position:0% +decay exponential minus t but we would +have here a term that would diverge with + + align:start position:0% +have here a term that would diverge with + + + align:start position:0% +have here a term that would diverge with +exponential T so this would have + + align:start position:0% +exponential T so this would have + + + align:start position:0% +exponential T so this would have +basically Behavior at long time that + + align:start position:0% +basically Behavior at long time that + + + align:start position:0% +basically Behavior at long time that +diverges and doesn't go to zero so this + + align:start position:0% +diverges and doesn't go to zero so this + + + align:start position:0% +diverges and doesn't go to zero so this +would not basically be a stable + + align:start position:0% +would not basically be a stable + + + align:start position:0% +would not basically be a stable +system for C we have all the real Parts + + align:start position:0% +system for C we have all the real Parts + + + align:start position:0% +system for C we have all the real Parts +negative so we're in the stable case for + + align:start position:0% +negative so we're in the stable case for + + + align:start position:0% +negative so we're in the stable case for +D we also have the same all the real + + align:start position:0% +D we also have the same all the real + + + align:start position:0% +D we also have the same all the real +parts are negative so these are + + align:start position:0% +parts are negative so these are + + + align:start position:0% +parts are negative so these are +imaginary 3 I minus uh minus 2+ 3 I so + + align:start position:0% +imaginary 3 I minus uh minus 2+ 3 I so + + + align:start position:0% +imaginary 3 I minus uh minus 2+ 3 I so +both of them have also negative real + + align:start position:0% +both of them have also negative real + + + align:start position:0% +both of them have also negative real +part so everything is on the left side + + align:start position:0% +part so everything is on the left side + + + align:start position:0% +part so everything is on the left side +of the plane same thing for e and for f + + align:start position:0% +of the plane same thing for e and for f + + + align:start position:0% +of the plane same thing for e and for f +we are right on the uh we're right on + + align:start position:0% +we are right on the uh we're right on + + + align:start position:0% +we are right on the uh we're right on +the on the imaginary axis which means + + align:start position:0% +the on the imaginary axis which means + + + align:start position:0% +the on the imaginary axis which means +that we can't tell if it's going to be + + align:start position:0% +that we can't tell if it's going to be + + + align:start position:0% +that we can't tell if it's going to be +uh an exponential it's not going to be + + align:start position:0% +uh an exponential it's not going to be + + + align:start position:0% +uh an exponential it's not going to be +an exponential decay or or growth at + + align:start position:0% +an exponential decay or or growth at + + + align:start position:0% +an exponential decay or or growth at +this point so this to answer the first + + align:start position:0% + + + + align:start position:0% + +questions the stable systems would be + + align:start position:0% +questions the stable systems would be + + + align:start position:0% +questions the stable systems would be +b + + align:start position:0% +b + + + align:start position:0% +b +c + + align:start position:0% +c + + + align:start position:0% +c +d + + align:start position:0% +d + + + align:start position:0% +d +e and that's it + + align:start position:0% + + + + align:start position:0% + +so now for the second part choose the + + align:start position:0% +so now for the second part choose the + + + align:start position:0% +so now for the second part choose the +system with the fastest Decay so here + + align:start position:0% +system with the fastest Decay so here + + + align:start position:0% +system with the fastest Decay so here +again as we just saw the real part of + + align:start position:0% +again as we just saw the real part of + + + align:start position:0% +again as we just saw the real part of +the poles gives us the speed at which + + align:start position:0% +the poles gives us the speed at which + + + align:start position:0% +the poles gives us the speed at which +the system is going to Decay and so we + + align:start position:0% +the system is going to Decay and so we + + + align:start position:0% +the system is going to Decay and so we +have to look for a system that has the + + align:start position:0% +have to look for a system that has the + + + align:start position:0% +have to look for a system that has the +the its pole the rightmost on the + + align:start position:0% +the its pole the rightmost on the + + + align:start position:0% +the its pole the rightmost on the +rightmost part of the plane so so for + + align:start position:0% +rightmost part of the plane so so for + + + align:start position:0% +rightmost part of the plane so so for +example we restrict ourself here the + + align:start position:0% +example we restrict ourself here the + + + align:start position:0% +example we restrict ourself here the +fastest Decay here is going to be + + align:start position:0% +fastest Decay here is going to be + + + align:start position:0% +fastest Decay here is going to be +governed by the rightmost pole so the + + align:start position:0% +governed by the rightmost pole so the + + + align:start position:0% +governed by the rightmost pole so the +exponential minus 2T uh that we need to + + align:start position:0% +exponential minus 2T uh that we need to + + + align:start position:0% +exponential minus 2T uh that we need to +examine here we have an exponential + + align:start position:0% +examine here we have an exponential + + + align:start position:0% +examine here we have an exponential +minus 3T Decay type here we would have + + align:start position:0% +minus 3T Decay type here we would have + + + align:start position:0% +minus 3T Decay type here we would have +an exponential minus t Decay here we + + align:start position:0% +an exponential minus t Decay here we + + + align:start position:0% +an exponential minus t Decay here we +would have something a little bit uh uh + + align:start position:0% +would have something a little bit uh uh + + + align:start position:0% +would have something a little bit uh uh +minus 0.5t and here again this is not + + align:start position:0% +minus 0.5t and here again this is not + + + align:start position:0% +minus 0.5t and here again this is not +stable system with a Decay at large time + + align:start position:0% +stable system with a Decay at large time + + + align:start position:0% +stable system with a Decay at large time +so which of the system has the fastest + + align:start position:0% +so which of the system has the fastest + + + align:start position:0% +so which of the system has the fastest +Decay we would need to select the ones + + align:start position:0% +Decay we would need to select the ones + + + align:start position:0% +Decay we would need to select the ones +the one with the + + align:start position:0% +the one with the + + + align:start position:0% +the one with the +with the uh rightmost pole that is the + + align:start position:0% +with the uh rightmost pole that is the + + + align:start position:0% +with the uh rightmost pole that is the +most on the left so we would need to + + align:start position:0% +most on the left so we would need to + + + align:start position:0% +most on the left so we would need to +compare this minus two with this minus + + align:start position:0% +compare this minus two with this minus + + + align:start position:0% +compare this minus two with this minus +three with this minus one with this + + align:start position:0% +three with this minus one with this + + + align:start position:0% +three with this minus one with this +minus 0.5 and from all these poles the + + align:start position:0% +minus 0.5 and from all these poles the + + + align:start position:0% +minus 0.5 and from all these poles the +one that has the minus uh three here + + align:start position:0% +one that has the minus uh three here + + + align:start position:0% +one that has the minus uh three here +would be the one that would be decaying + + align:start position:0% +would be the one that would be decaying + + + align:start position:0% +would be the one that would be decaying +the fastest okay so we would have system + + align:start position:0% + + + + align:start position:0% + +C decaying + + align:start position:0% +C decaying + + + align:start position:0% +C decaying +as exponential minus 3T and I'm going to + + align:start position:0% +as exponential minus 3T and I'm going to + + + align:start position:0% +as exponential minus 3T and I'm going to +just write down the others and these + + align:start position:0% +just write down the others and these + + + align:start position:0% +just write down the others and these +would be the dominant terms that would + + align:start position:0% +would be the dominant terms that would + + + align:start position:0% +would be the dominant terms that would +basically subscribe the behavior at + + align:start position:0% +basically subscribe the behavior at + + + align:start position:0% +basically subscribe the behavior at +large T so this is the + + align:start position:0% + + + + align:start position:0% + +fastest uh for our system B which is not + + align:start position:0% +fastest uh for our system B which is not + + + align:start position:0% +fastest uh for our system B which is not +the fastest I'm just going to write it + + align:start position:0% +the fastest I'm just going to write it + + + align:start position:0% +the fastest I'm just going to write it +it's going to be dominated by minus + + align:start position:0% +it's going to be dominated by minus + + + align:start position:0% +it's going to be dominated by minus +2T uh for the system D it would be + + align:start position:0% +2T uh for the system D it would be + + + align:start position:0% +2T uh for the system D it would be +dominated + + align:start position:0% + + + + align:start position:0% + +by a minus 1T for the system + + align:start position:0% +by a minus 1T for the system + + + align:start position:0% +by a minus 1T for the system +e would be dominated by the + + align:start position:0% +e would be dominated by the + + + align:start position:0% +e would be dominated by the +minus 0.5 t Okay so the fastest Decay + + align:start position:0% +minus 0.5 t Okay so the fastest Decay + + + align:start position:0% +minus 0.5 t Okay so the fastest Decay +would definitely be system C okay so the + + align:start position:0% +would definitely be system C okay so the + + + align:start position:0% +would definitely be system C okay so the +last question choose the fastest Decay + + align:start position:0% +last question choose the fastest Decay + + + align:start position:0% +last question choose the fastest Decay +without oscillations so now we need to + + align:start position:0% +without oscillations so now we need to + + + align:start position:0% +without oscillations so now we need to +pay attention to whether the poles are + + align:start position:0% +pay attention to whether the poles are + + + align:start position:0% +pay attention to whether the poles are +on the imaginary axis on the real Axis + + align:start position:0% +on the imaginary axis on the real Axis + + + align:start position:0% +on the imaginary axis on the real Axis +or somewhere in the middle so let's + + align:start position:0% +or somewhere in the middle so let's + + + align:start position:0% +or somewhere in the middle so let's +again examine only the stable cases so + + align:start position:0% +again examine only the stable cases so + + + align:start position:0% +again examine only the stable cases so +here the two poles are on the real axis + + align:start position:0% +here the two poles are on the real axis + + + align:start position:0% +here the two poles are on the real axis +so it's going to give us a behavior that + + align:start position:0% +so it's going to give us a behavior that + + + align:start position:0% +so it's going to give us a behavior that +is only pure Decay exponential decay + + align:start position:0% +is only pure Decay exponential decay + + + align:start position:0% +is only pure Decay exponential decay +exponential minus 2T exponential minus + + align:start position:0% +exponential minus 2T exponential minus + + + align:start position:0% +exponential minus 2T exponential minus +3T with no oscillations because + + align:start position:0% +3T with no oscillations because + + + align:start position:0% +3T with no oscillations because +basically these two poles don't have any + + align:start position:0% +basically these two poles don't have any + + + align:start position:0% +basically these two poles don't have any +imaginary part here we have a term in + + align:start position:0% +imaginary part here we have a term in + + + align:start position:0% +imaginary part here we have a term in +exponential minus 3T but we would have a + + align:start position:0% +exponential minus 3T but we would have a + + + align:start position:0% +exponential minus 3T but we would have a +term that would show oscillations with + + align:start position:0% +term that would show oscillations with + + + align:start position:0% +term that would show oscillations with +with the circular frequencies of three + + align:start position:0% +with the circular frequencies of three + + + align:start position:0% +with the circular frequencies of three +so you would have an exponential minus 3 + + align:start position:0% +so you would have an exponential minus 3 + + + align:start position:0% +so you would have an exponential minus 3 +T cosine 3T plus exponential minus 3T + + align:start position:0% +T cosine 3T plus exponential minus 3T + + + align:start position:0% +T cosine 3T plus exponential minus 3T +sin 3T for example so here we would have + + align:start position:0% +sin 3T for example so here we would have + + + align:start position:0% +sin 3T for example so here we would have +system that shows oscillation so we + + align:start position:0% +system that shows oscillation so we + + + align:start position:0% +system that shows oscillation so we +don't want that for this case then would + + align:start position:0% +don't want that for this case then would + + + align:start position:0% +don't want that for this case then would +be similar so you see the pattern here + + align:start position:0% +be similar so you see the pattern here + + + align:start position:0% +be similar so you see the pattern here +we have an exponential decay here we + + align:start position:0% +we have an exponential decay here we + + + align:start position:0% +we have an exponential decay here we +would have decaying oscillations so + + align:start position:0% +would have decaying oscillations so + + + align:start position:0% +would have decaying oscillations so +there is oscillations same thing here + + align:start position:0% +there is oscillations same thing here + + + align:start position:0% +there is oscillations same thing here +and so we are left with only system B + + align:start position:0% +and so we are left with only system B + + + align:start position:0% +and so we are left with only system B +which basically does not show any + + align:start position:0% +which basically does not show any + + + align:start position:0% +which basically does not show any +oscillation but only an exponential + + align:start position:0% +oscillation but only an exponential + + + align:start position:0% +oscillation but only an exponential +decay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so pure + + align:start position:0% + + + + align:start position:0% + +Decay and it's dominated by the + + align:start position:0% +Decay and it's dominated by the + + + align:start position:0% +Decay and it's dominated by the +exponential minus + + align:start position:0% +exponential minus + + + align:start position:0% +exponential minus +2T without + + align:start position:0% + + + + align:start position:0% + +oscillations okay so that ends this + + align:start position:0% +oscillations okay so that ends this + + + align:start position:0% +oscillations okay so that ends this +first part of the problem I'm going to + + align:start position:0% +first part of the problem I'm going to + + + align:start position:0% +first part of the problem I'm going to +just take a a minute and come back to + + align:start position:0% +just take a a minute and come back to + + + align:start position:0% +just take a a minute and come back to +show you the second part of the problem + + align:start position:0% + + + + align:start position:0% + +okay welcome back for the second part of + + align:start position:0% +okay welcome back for the second part of + + + align:start position:0% +okay welcome back for the second part of +the problem so here another pole diagram + + align:start position:0% +the problem so here another pole diagram + + + align:start position:0% +the problem so here another pole diagram +that we're going to label J for this + + align:start position:0% +that we're going to label J for this + + + align:start position:0% +that we're going to label J for this +system and the polls are basically uh + + align:start position:0% +system and the polls are basically uh + + + align:start position:0% +system and the polls are basically uh +here 0.5 + 4 I 0.5 - 4 I and then here + + align:start position:0% +here 0.5 + 4 I 0.5 - 4 I and then here + + + align:start position:0% +here 0.5 + 4 I 0.5 - 4 I and then here +we have almost a minus three and here + + align:start position:0% +we have almost a minus three and here + + + align:start position:0% +we have almost a minus three and here +would be a minus 4 + + align:start position:0% +would be a minus 4 + + + align:start position:0% +would be a minus 4 +okay so the question is to consider now + + align:start position:0% +okay so the question is to consider now + + + align:start position:0% +okay so the question is to consider now +this the previous system we had P of d + + align:start position:0% +this the previous system we had P of d + + + align:start position:0% +this the previous system we had P of d +yals F of T but now with f of T equals + + align:start position:0% +yals F of T but now with f of T equals + + + align:start position:0% +yals F of T but now with f of T equals +F0 cos Omega T and Omega the the + + align:start position:0% +F0 cos Omega T and Omega the the + + + align:start position:0% +F0 cos Omega T and Omega the the +circular frequency going between one and + + align:start position:0% +circular frequency going between one and + + + align:start position:0% +circular frequency going between one and +five and the question is for which + + align:start position:0% +five and the question is for which + + + align:start position:0% +five and the question is for which +values of Omega uh do we have the + + align:start position:0% +values of Omega uh do we have the + + + align:start position:0% +values of Omega uh do we have the +largest response from the system G so + + align:start position:0% +largest response from the system G so + + + align:start position:0% +largest response from the system G so +basically we're looking at phenomenon of + + align:start position:0% +basically we're looking at phenomenon of + + + align:start position:0% +basically we're looking at phenomenon of +resonance where we want to find the + + align:start position:0% +resonance where we want to find the + + + align:start position:0% +resonance where we want to find the +frequency Omega for which the response + + align:start position:0% +frequency Omega for which the response + + + align:start position:0% +frequency Omega for which the response +of the system is going to be the biggest + + align:start position:0% +of the system is going to be the biggest + + + align:start position:0% +of the system is going to be the biggest +so you have so I give you just a few + + align:start position:0% +so you have so I give you just a few + + + align:start position:0% +so you have so I give you just a few +minutes and we we'll be right + + align:start position:0% + + + + align:start position:0% + +back okay welcome back for this second + + align:start position:0% +back okay welcome back for this second + + + align:start position:0% +back okay welcome back for this second +part so here if you + + align:start position:0% +part so here if you + + + align:start position:0% +part so here if you +recall the amplitude response from the + + align:start position:0% +recall the amplitude response from the + + + align:start position:0% +recall the amplitude response from the +previous + + align:start position:0% +previous + + + align:start position:0% +previous +recitations the amplitude is governed by + + align:start position:0% +recitations the amplitude is governed by + + + align:start position:0% +recitations the amplitude is governed by +one over the characteristic polinomial + + align:start position:0% +one over the characteristic polinomial + + + align:start position:0% +one over the characteristic polinomial +evaluated at I Omega where do I Omega + + align:start position:0% +evaluated at I Omega where do I Omega + + + align:start position:0% +evaluated at I Omega where do I Omega +come from if you recall it comes from + + align:start position:0% +come from if you recall it comes from + + + align:start position:0% +come from if you recall it comes from +the exponential response formula because + + align:start position:0% +the exponential response formula because + + + align:start position:0% +the exponential response formula because +on the right hand side here we have a + + align:start position:0% +on the right hand side here we have a + + + align:start position:0% +on the right hand side here we have a +cosine Omega T that is then then we + + align:start position:0% +cosine Omega T that is then then we + + + align:start position:0% +cosine Omega T that is then then we +complexify exponential I Omega T Etc to + + align:start position:0% +complexify exponential I Omega T Etc to + + + align:start position:0% +complexify exponential I Omega T Etc to +get the amplitude response so the + + align:start position:0% +get the amplitude response so the + + + align:start position:0% +get the amplitude response so the +amplitude is going to be the largest for + + align:start position:0% +amplitude is going to be the largest for + + + align:start position:0% +amplitude is going to be the largest for +basically values of I Omega that are the + + align:start position:0% +basically values of I Omega that are the + + + align:start position:0% +basically values of I Omega that are the +closest to the poles of the + + align:start position:0% +closest to the poles of the + + + align:start position:0% +closest to the poles of the +polinomial to the poles of this + + align:start position:0% +polinomial to the poles of this + + + align:start position:0% +polinomial to the poles of this +function right basically the poles of + + align:start position:0% +function right basically the poles of + + + align:start position:0% +function right basically the poles of +the one over characteristic polinomial + + align:start position:0% +the one over characteristic polinomial + + + align:start position:0% +the one over characteristic polinomial +is going to give us the the the one over + + align:start position:0% +is going to give us the the the one over + + + align:start position:0% +is going to give us the the the one over +zero which will give an amplitude + + align:start position:0% +zero which will give an amplitude + + + align:start position:0% +zero which will give an amplitude +response that goes to Infinity so the + + align:start position:0% +response that goes to Infinity so the + + + align:start position:0% +response that goes to Infinity so the +largest uh response so we want to choose + + align:start position:0% +largest uh response so we want to choose + + + align:start position:0% +largest uh response so we want to choose +our frequency I Omega basically we want + + align:start position:0% +our frequency I Omega basically we want + + + align:start position:0% +our frequency I Omega basically we want +to look at this diagram and look at the + + align:start position:0% +to look at this diagram and look at the + + + align:start position:0% +to look at this diagram and look at the +poles that are the + + align:start position:0% +poles that are the + + + align:start position:0% +poles that are the +closest to the values that going to give + + align:start position:0% +closest to the values that going to give + + + align:start position:0% +closest to the values that going to give +us P of s equals to zero and this is + + align:start position:0% +us P of s equals to zero and this is + + + align:start position:0% +us P of s equals to zero and this is +basically diagram that gives us the pole + + align:start position:0% +basically diagram that gives us the pole + + + align:start position:0% +basically diagram that gives us the pole +of this one over p and so we want to + + align:start position:0% +of this one over p and so we want to + + + align:start position:0% +of this one over p and so we want to +choose the Val Val for I Omega which + + align:start position:0% +choose the Val Val for I Omega which + + + align:start position:0% +choose the Val Val for I Omega which +will be on the imaginary axis that is + + align:start position:0% +will be on the imaginary axis that is + + + align:start position:0% +will be on the imaginary axis that is +the closest to one of these two poles + + align:start position:0% +the closest to one of these two poles + + + align:start position:0% +the closest to one of these two poles +given that we work with positive + + align:start position:0% +given that we work with positive + + + align:start position:0% +given that we work with positive +frequencies we would want for example to + + align:start position:0% +frequencies we would want for example to + + + align:start position:0% +frequencies we would want for example to +choose I + + align:start position:0% +choose I + + + align:start position:0% +choose I +Omega equals I4 okay so it would be here + + align:start position:0% +Omega equals I4 okay so it would be here + + + align:start position:0% +Omega equals I4 okay so it would be here +or just Omega equals to + + align:start position:0% +or just Omega equals to + + + align:start position:0% +or just Omega equals to +four and this value of Omega would get + + align:start position:0% +four and this value of Omega would get + + + align:start position:0% +four and this value of Omega would get +us very close to this pole which would + + align:start position:0% +us very close to this pole which would + + + align:start position:0% +us very close to this pole which would +mean then that we are one over a very + + align:start position:0% +mean then that we are one over a very + + + align:start position:0% +mean then that we are one over a very +small number which means that the + + align:start position:0% +small number which means that the + + + align:start position:0% +small number which means that the +amplitude response will be the biggest + + align:start position:0% +amplitude response will be the biggest + + + align:start position:0% +amplitude response will be the biggest +so that's the idea behind look behind + + align:start position:0% +so that's the idea behind look behind + + + align:start position:0% +so that's the idea behind look behind +the resonance and looking at again + + align:start position:0% +the resonance and looking at again + + + align:start position:0% +the resonance and looking at again +another the phenomenon of resonance from + + align:start position:0% +another the phenomenon of resonance from + + + align:start position:0% +another the phenomenon of resonance from +the pole diagram perspective and with + + align:start position:0% +the pole diagram perspective and with + + + align:start position:0% +the pole diagram perspective and with +the idea of uh the use of the laast + + align:start position:0% +the idea of uh the use of the laast + + + align:start position:0% +the idea of uh the use of the laast +transform behind the the whole technique + + align:start position:0% +transform behind the the whole technique + + + align:start position:0% +transform behind the the whole technique +so that ends this session and uh the + + align:start position:0% +so that ends this session and uh the + + + align:start position:0% +so that ends this session and uh the +goal was really to learn to interpret + + align:start position:0% +goal was really to learn to interpret + + + align:start position:0% +goal was really to learn to interpret +and the meaning of the polls in the pole + + align:start position:0% +and the meaning of the polls in the pole + + + align:start position:0% +and the meaning of the polls in the pole +diagrams and how that do the poles give + + align:start position:0% +diagrams and how that do the poles give + + + align:start position:0% +diagrams and how that do the poles give +us an idea and insight on the behavior + + align:start position:0% +us an idea and insight on the behavior + + + align:start position:0% +us an idea and insight on the behavior +of the the system on the long term \ No newline at end of file diff --git a/qyAoSHisZtU.txt b/qyAoSHisZtU.txt new file mode 100644 index 0000000000000000000000000000000000000000..83dd3f8e5272c4baf3c6698f66b4addb238b4852 --- /dev/null +++ b/qyAoSHisZtU.txt @@ -0,0 +1,16819 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mit.edu. + + align:start position:0% + + + + align:start position:0% + +Good morning uh everyone here in + + align:start position:0% +Good morning uh everyone here in + + + align:start position:0% +Good morning uh everyone here in +Cambridge and uh happy holidays to you + + align:start position:0% +Cambridge and uh happy holidays to you + + + align:start position:0% +Cambridge and uh happy holidays to you +guys in uh Singapore. What's the + + align:start position:0% +guys in uh Singapore. What's the + + + align:start position:0% +guys in uh Singapore. What's the +holiday? I had it on my my PDA, but I've + + align:start position:0% +holiday? I had it on my my PDA, but I've + + + align:start position:0% +holiday? I had it on my my PDA, but I've +forgotten what it is. See if I can tell + + align:start position:0% +forgotten what it is. See if I can tell + + + align:start position:0% +forgotten what it is. See if I can tell +you. Labor Day. It's Labor Day in + + align:start position:0% +you. Labor Day. It's Labor Day in + + + align:start position:0% +you. Labor Day. It's Labor Day in +Singapore. Okay. Somebody was asking me + + align:start position:0% +Singapore. Okay. Somebody was asking me + + + align:start position:0% +Singapore. Okay. Somebody was asking me +when Labor Day is in in the US. And you + + align:start position:0% +when Labor Day is in in the US. And you + + + align:start position:0% +when Labor Day is in in the US. And you +think of labor, of course, it means + + align:start position:0% +think of labor, of course, it means + + + align:start position:0% +think of labor, of course, it means +something different than this, but you + + align:start position:0% +something different than this, but you + + + align:start position:0% +something different than this, but you +think of labor something that's kind of + + align:start position:0% +think of labor something that's kind of + + + align:start position:0% +think of labor something that's kind of +ownorous and something you don't always + + align:start position:0% +ownorous and something you don't always + + + align:start position:0% +ownorous and something you don't always +look forward to doing. And that's for an + + align:start position:0% +look forward to doing. And that's for an + + + align:start position:0% +look forward to doing. And that's for an +academic at least, that's September, you + + align:start position:0% +academic at least, that's September, you + + + align:start position:0% +academic at least, that's September, you +know, when you have to go back to work. + + align:start position:0% +know, when you have to go back to work. + + + align:start position:0% +know, when you have to go back to work. +So it's in September in the US. + + align:start position:0% +So it's in September in the US. + + + align:start position:0% +So it's in September in the US. +Okay. Excuse me. Um my voice is shot. So + + align:start position:0% +Okay. Excuse me. Um my voice is shot. So + + + align:start position:0% +Okay. Excuse me. Um my voice is shot. So +uh you may be lucky and I may finish + + align:start position:0% +uh you may be lucky and I may finish + + + align:start position:0% +uh you may be lucky and I may finish +early. This never happened before but + + align:start position:0% +early. This never happened before but + + + align:start position:0% +early. This never happened before but +you know might might today. Um + + align:start position:0% +you know might might today. Um + + + align:start position:0% +you know might might today. Um +uh what I've been asked to talk about + + align:start position:0% +uh what I've been asked to talk about + + + align:start position:0% +uh what I've been asked to talk about +today is this concept of using feedback + + align:start position:0% +today is this concept of using feedback + + + align:start position:0% +today is this concept of using feedback +to uh improve the statistical + + align:start position:0% +to uh improve the statistical + + + align:start position:0% +to uh improve the statistical +performance of a process. And um it's + + align:start position:0% +performance of a process. And um it's + + + align:start position:0% +performance of a process. And um it's +got this title cycle cycle cycle to + + align:start position:0% +got this title cycle cycle cycle to + + + align:start position:0% +got this title cycle cycle cycle to +cycle control. Um just a little caveat + + align:start position:0% +cycle control. Um just a little caveat + + + align:start position:0% +cycle control. Um just a little caveat +uh this whole lecture and the material + + align:start position:0% +uh this whole lecture and the material + + + align:start position:0% +uh this whole lecture and the material +behind it and a research two research + + align:start position:0% +behind it and a research two research + + + align:start position:0% +behind it and a research two research +projects that came out of it um were + + align:start position:0% +projects that came out of it um were + + + align:start position:0% +projects that came out of it um were +spawned about eight or nine years ago + + align:start position:0% +spawned about eight or nine years ago + + + align:start position:0% +spawned about eight or nine years ago +when I was preparing a lecture for this + + align:start position:0% +when I was preparing a lecture for this + + + align:start position:0% +when I was preparing a lecture for this +class um + + align:start position:0% +class um + + + align:start position:0% +class um +pre internet transmission that kind of + + align:start position:0% +pre internet transmission that kind of + + + align:start position:0% +pre internet transmission that kind of +stuff and I I thought gee what would + + align:start position:0% +stuff and I I thought gee what would + + + align:start position:0% +stuff and I I thought gee what would +happen if we we used to do a lot of + + align:start position:0% +happen if we we used to do a lot of + + + align:start position:0% +happen if we we used to do a lot of +stuff on feedback control in the class + + align:start position:0% +stuff on feedback control in the class + + + align:start position:0% +stuff on feedback control in the class +but for a different reason I said how + + align:start position:0% +but for a different reason I said how + + + align:start position:0% +but for a different reason I said how +about if we applied it here and came up + + align:start position:0% +about if we applied it here and came up + + + align:start position:0% +about if we applied it here and came up +with this this idea of cycle cycle + + align:start position:0% +with this this idea of cycle cycle + + + align:start position:0% +with this this idea of cycle cycle +control. One of the problems was, of + + align:start position:0% +control. One of the problems was, of + + + align:start position:0% +control. One of the problems was, of +course, I found out that it was old + + align:start position:0% +course, I found out that it was old + + + align:start position:0% +course, I found out that it was old +material. It was actually hidden in + + align:start position:0% +material. It was actually hidden in + + + align:start position:0% +material. It was actually hidden in +textbooks. It was treated in a different + + align:start position:0% +textbooks. It was treated in a different + + + align:start position:0% +textbooks. It was treated in a different +way. So, um this is, let's just say, a + + align:start position:0% +way. So, um this is, let's just say, a + + + align:start position:0% +way. So, um this is, let's just say, a +different spin on a somewhat well-known + + align:start position:0% +different spin on a somewhat well-known + + + align:start position:0% +different spin on a somewhat well-known +uh topic, but usually under the heading + + align:start position:0% +uh topic, but usually under the heading + + + align:start position:0% +uh topic, but usually under the heading +of advanced material on, um the use of + + align:start position:0% +of advanced material on, um the use of + + + align:start position:0% +of advanced material on, um the use of +feedback control in the context of a + + align:start position:0% +feedback control in the context of a + + + align:start position:0% +feedback control in the context of a +statistical process control uh problem. + + align:start position:0% +statistical process control uh problem. + + + align:start position:0% +statistical process control uh problem. +Now I'm going to go through a couple + + align:start position:0% +Now I'm going to go through a couple + + + align:start position:0% +Now I'm going to go through a couple +slides which were from day one of the + + align:start position:0% +slides which were from day one of the + + + align:start position:0% +slides which were from day one of the +class. Um and uh to emphasize uh I think + + align:start position:0% +class. Um and uh to emphasize uh I think + + + align:start position:0% +class. Um and uh to emphasize uh I think +what we said back then is that in effect + + align:start position:0% +what we said back then is that in effect + + + align:start position:0% +what we said back then is that in effect +there's there's always feedback going + + align:start position:0% +there's there's always feedback going + + + align:start position:0% +there's there's always feedback going +on. Now most of the stuff we've done in + + align:start position:0% +on. Now most of the stuff we've done in + + + align:start position:0% +on. Now most of the stuff we've done in +the class so far on SPC + + align:start position:0% +the class so far on SPC + + + align:start position:0% +the class so far on SPC +uh and designed experiments has been in + + align:start position:0% +uh and designed experiments has been in + + + align:start position:0% +uh and designed experiments has been in +the classical feedback control sense + + align:start position:0% +the classical feedback control sense + + + align:start position:0% +the classical feedback control sense +open loop. you kind of do something, you + + align:start position:0% +open loop. you kind of do something, you + + + align:start position:0% +open loop. you kind of do something, you +record what happens, but there's no + + align:start position:0% +record what happens, but there's no + + + align:start position:0% +record what happens, but there's no +necessarily an algorithmic + + align:start position:0% +necessarily an algorithmic + + + align:start position:0% +necessarily an algorithmic +um approach to saying, "Okay, what if + + align:start position:0% +um approach to saying, "Okay, what if + + + align:start position:0% +um approach to saying, "Okay, what if +it's not right?" I mean, I don't know + + align:start position:0% +it's not right?" I mean, I don't know + + + align:start position:0% +it's not right?" I mean, I don't know +what Professor Bonding said about SPC, + + align:start position:0% +what Professor Bonding said about SPC, + + + align:start position:0% +what Professor Bonding said about SPC, +but you know, SPC doesn't necessarily + + align:start position:0% +but you know, SPC doesn't necessarily + + + align:start position:0% +but you know, SPC doesn't necessarily +tell you what actions to do to correct + + align:start position:0% +tell you what actions to do to correct + + + align:start position:0% +tell you what actions to do to correct +what's wrong. Uh what it does is it + + align:start position:0% +what's wrong. Uh what it does is it + + + align:start position:0% +what's wrong. Uh what it does is it +tells you the process is not following + + align:start position:0% +tells you the process is not following + + + align:start position:0% +tells you the process is not following +the model, the statistical model that + + align:start position:0% +the model, the statistical model that + + + align:start position:0% +the model, the statistical model that +you had. And our designed experiments + + align:start position:0% +you had. And our designed experiments + + + align:start position:0% +you had. And our designed experiments +and process optimization is indeed an + + align:start position:0% +and process optimization is indeed an + + + align:start position:0% +and process optimization is indeed an +falls into the larger context of + + align:start position:0% +falls into the larger context of + + + align:start position:0% +falls into the larger context of +openloop optimization. How can I run a + + align:start position:0% +openloop optimization. How can I run a + + + align:start position:0% +openloop optimization. How can I run a +process in effect unattended open loop + + align:start position:0% +process in effect unattended open loop + + + align:start position:0% +process in effect unattended open loop +um and still have it uh be robust to + + align:start position:0% +um and still have it uh be robust to + + + align:start position:0% +um and still have it uh be robust to +things trying to to uh deter it from its + + align:start position:0% +things trying to to uh deter it from its + + + align:start position:0% +things trying to to uh deter it from its +proper course. + + align:start position:0% +proper course. + + + align:start position:0% +proper course. +Um, we talked at the beginning of the + + align:start position:0% +Um, we talked at the beginning of the + + + align:start position:0% +Um, we talked at the beginning of the +term about this idea of the general + + align:start position:0% +term about this idea of the general + + + align:start position:0% +term about this idea of the general +process control problem. And uh, I'm + + align:start position:0% +process control problem. And uh, I'm + + + align:start position:0% +process control problem. And uh, I'm +sure you remember like it was yesterday + + align:start position:0% +sure you remember like it was yesterday + + + align:start position:0% +sure you remember like it was yesterday +that uh, I referred to this process + + align:start position:0% +that uh, I referred to this process + + + align:start position:0% +that uh, I referred to this process +control loop as sort of the holy grail. + + align:start position:0% +control loop as sort of the holy grail. + + + align:start position:0% +control loop as sort of the holy grail. +Boy, if we could do that, all this other + + align:start position:0% +Boy, if we could do that, all this other + + + align:start position:0% +Boy, if we could do that, all this other +stuff wouldn't matter because it would + + align:start position:0% +stuff wouldn't matter because it would + + + align:start position:0% +stuff wouldn't matter because it would +mean that I would have in some way the + + align:start position:0% +mean that I would have in some way the + + + align:start position:0% +mean that I would have in some way the +ability to interact with a process and + + align:start position:0% +ability to interact with a process and + + + align:start position:0% +ability to interact with a process and +say, "Here's what I want. Here's a + + align:start position:0% +say, "Here's what I want. Here's a + + + align:start position:0% +say, "Here's what I want. Here's a +dimension that I want. Maybe here's a + + align:start position:0% +dimension that I want. Maybe here's a + + + align:start position:0% +dimension that I want. Maybe here's a +variability that I can tolerate. uh + + align:start position:0% +variability that I can tolerate. uh + + + align:start position:0% +variability that I can tolerate. uh +here's a property strength or a + + align:start position:0% +here's a property strength or a + + + align:start position:0% +here's a property strength or a +reactivity or something I want + + align:start position:0% +reactivity or something I want + + + align:start position:0% +reactivity or something I want +that if I simply measure it and apply + + align:start position:0% +that if I simply measure it and apply + + + align:start position:0% +that if I simply measure it and apply +correctly feedback control principles + + align:start position:0% +correctly feedback control principles + + + align:start position:0% +correctly feedback control principles +compare the two somehow with the magic + + align:start position:0% +compare the two somehow with the magic + + + align:start position:0% +compare the two somehow with the magic +uh control + + align:start position:0% +uh control + + + align:start position:0% +uh control +algorithm everything will be fine okay + + align:start position:0% +algorithm everything will be fine okay + + + align:start position:0% +algorithm everything will be fine okay +and and feedback control if it's + + align:start position:0% +and and feedback control if it's + + + align:start position:0% +and and feedback control if it's +successful always seeks to make the + + align:start position:0% +successful always seeks to make the + + + align:start position:0% +successful always seeks to make the +difference between those two close to + + align:start position:0% +difference between those two close to + + + align:start position:0% +difference between those two close to +zero and as quickly as possible um so + + align:start position:0% +zero and as quickly as possible um so + + + align:start position:0% +zero and as quickly as possible um so +the concept of pro uh process output + + align:start position:0% +the concept of pro uh process output + + + align:start position:0% +the concept of pro uh process output +control or controlling the product + + align:start position:0% +control or controlling the product + + + align:start position:0% +control or controlling the product +geometry and properties was put + + align:start position:0% +geometry and properties was put + + + align:start position:0% +geometry and properties was put +forward and at the time we probably said + + align:start position:0% +forward and at the time we probably said + + + align:start position:0% +forward and at the time we probably said +but it doesn't work or it can't happen + + align:start position:0% +but it doesn't work or it can't happen + + + align:start position:0% +but it doesn't work or it can't happen +or it's very rare. So what motivates + + align:start position:0% +or it's very rare. So what motivates + + + align:start position:0% +or it's very rare. So what motivates +this this particular concept is the idea + + align:start position:0% +this this particular concept is the idea + + + align:start position:0% +this this particular concept is the idea +that um this is indeed very hard to do + + align:start position:0% +that um this is indeed very hard to do + + + align:start position:0% +that um this is indeed very hard to do +and it's very hard to do for two + + align:start position:0% +and it's very hard to do for two + + + align:start position:0% +and it's very hard to do for two +reasons. One is you seldom can find out + + align:start position:0% +reasons. One is you seldom can find out + + + align:start position:0% +reasons. One is you seldom can find out +what's wrong with the product until it's + + align:start position:0% +what's wrong with the product until it's + + + align:start position:0% +what's wrong with the product until it's +too late. When you think about most of + + align:start position:0% +too late. When you think about most of + + + align:start position:0% +too late. When you think about most of +the processes, there are a few + + align:start position:0% +the processes, there are a few + + + align:start position:0% +the processes, there are a few +exceptions to this, but most + + align:start position:0% +exceptions to this, but most + + + align:start position:0% +exceptions to this, but most +processes, semiconductor is a great + + align:start position:0% +processes, semiconductor is a great + + + align:start position:0% +processes, semiconductor is a great +example, but but uh every kind of + + align:start position:0% +example, but but uh every kind of + + + align:start position:0% +example, but but uh every kind of +mechanical and thermal process around, + + align:start position:0% +mechanical and thermal process around, + + + align:start position:0% +mechanical and thermal process around, +basically, you have to make something + + align:start position:0% +basically, you have to make something + + + align:start position:0% +basically, you have to make something +kind of put it down. Oh, we're done. + + align:start position:0% +kind of put it down. Oh, we're done. + + + align:start position:0% +kind of put it down. Oh, we're done. +Okay, let's measure it. Did it fit? Is + + align:start position:0% +Okay, let's measure it. Did it fit? Is + + + align:start position:0% +Okay, let's measure it. Did it fit? Is +it the right shape? Is it the right uh + + align:start position:0% +it the right shape? Is it the right uh + + + align:start position:0% +it the right shape? Is it the right uh +does it have the right properties? And + + align:start position:0% +does it have the right properties? And + + + align:start position:0% +does it have the right properties? And +it's too late. So, if it's wrong, what + + align:start position:0% +it's too late. So, if it's wrong, what + + + align:start position:0% +it's too late. So, if it's wrong, what +do you do? Okay, so what do you do? If + + align:start position:0% +do you do? Okay, so what do you do? If + + + align:start position:0% +do you do? Okay, so what do you do? If +you run the process, you pick up the + + align:start position:0% +you run the process, you pick up the + + + align:start position:0% +you run the process, you pick up the +product, you measure it, it's not right. + + align:start position:0% +product, you measure it, it's not right. + + + align:start position:0% +product, you measure it, it's not right. +What do you do? It's not a rhetorical + + align:start position:0% +What do you do? It's not a rhetorical + + + align:start position:0% +What do you do? It's not a rhetorical +question. It's an an it's a question. + + align:start position:0% +question. It's an an it's a question. + + + align:start position:0% +question. It's an an it's a question. +What do I do? Throw it away. + + align:start position:0% +What do I do? Throw it away. + + + align:start position:0% +What do I do? Throw it away. +Throw it + + align:start position:0% +Throw it + + + align:start position:0% +Throw it +away. Rework + + align:start position:0% +away. Rework + + + align:start position:0% +away. Rework +it. Okay. And that's what we do now, + + align:start position:0% +it. Okay. And that's what we do now, + + + align:start position:0% +it. Okay. And that's what we do now, +right? Yeah. You got past fail. Throw it + + align:start position:0% +right? Yeah. You got past fail. Throw it + + + align:start position:0% +right? Yeah. You got past fail. Throw it +away. If it's a low value added, it's a + + align:start position:0% +away. If it's a low value added, it's a + + + align:start position:0% +away. If it's a low value added, it's a +high value added thing like an airplane + + align:start position:0% +high value added thing like an airplane + + + align:start position:0% +high value added thing like an airplane +or something like that, then you uh you + + align:start position:0% +or something like that, then you uh you + + + align:start position:0% +or something like that, then you uh you +rework it. Richard, what else? Well, + + align:start position:0% +rework it. Richard, what else? Well, + + + align:start position:0% +rework it. Richard, what else? Well, +that size is big enough. big enough or + + align:start position:0% +that size is big enough. big enough or + + + align:start position:0% +that size is big enough. big enough or +the the production rate is big enough, + + align:start position:0% +the the production rate is big enough, + + + align:start position:0% +the the production rate is big enough, +you could try to adjust your process. + + align:start position:0% +you could try to adjust your process. + + + align:start position:0% +you could try to adjust your process. +For example, when you have a CNC turning + + align:start position:0% +For example, when you have a CNC turning + + + align:start position:0% +For example, when you have a CNC turning +process, you could try to make + + align:start position:0% +process, you could try to make + + + align:start position:0% +process, you could try to make +adjustments for the for the two + + align:start position:0% +adjustments for the for the two + + + align:start position:0% +adjustments for the for the two +position. Yep. Well, yeah. So, so you + + align:start position:0% +position. Yep. Well, yeah. So, so you + + + align:start position:0% +position. Yep. Well, yeah. So, so you +can do all three of those things. And + + align:start position:0% +can do all three of those things. And + + + align:start position:0% +can do all three of those things. And +what we're going to talk about today is + + align:start position:0% +what we're going to talk about today is + + + align:start position:0% +what we're going to talk about today is +more towards what Richard was saying, + + align:start position:0% +more towards what Richard was saying, + + + align:start position:0% +more towards what Richard was saying, +which is you learn, you take that as + + align:start position:0% +which is you learn, you take that as + + + align:start position:0% +which is you learn, you take that as +data and say, "Oh, something's not right + + align:start position:0% +data and say, "Oh, something's not right + + + align:start position:0% +data and say, "Oh, something's not right +here." And the question now is you know + + align:start position:0% +here." And the question now is you know + + + align:start position:0% +here." And the question now is you know +we can always take that data and and I + + align:start position:0% +we can always take that data and and I + + + align:start position:0% +we can always take that data and and I +made it sound black or white you know + + align:start position:0% +made it sound black or white you know + + + align:start position:0% +made it sound black or white you know +it's a good part or it's a bad part but + + align:start position:0% +it's a good part or it's a bad part but + + + align:start position:0% +it's a good part or it's a bad part but +indeed as you know is it uh from the + + align:start position:0% +indeed as you know is it uh from the + + + align:start position:0% +indeed as you know is it uh from the +concept of process capability is it + + align:start position:0% +concept of process capability is it + + + align:start position:0% +concept of process capability is it +falling where I expected it to is it + + align:start position:0% +falling where I expected it to is it + + + align:start position:0% +falling where I expected it to is it +falling outside there or is it tending + + align:start position:0% +falling outside there or is it tending + + + align:start position:0% +falling outside there or is it tending +there to there and how quickly do I take + + align:start position:0% +there to there and how quickly do I take + + + align:start position:0% +there to there and how quickly do I take +action now SPC in general is about you + + align:start position:0% +action now SPC in general is about you + + + align:start position:0% +action now SPC in general is about you +kind of in effect sit back measure the + + align:start position:0% +kind of in effect sit back measure the + + + align:start position:0% +kind of in effect sit back measure the +statistical performance of the process + + align:start position:0% +statistical performance of the process + + + align:start position:0% +statistical performance of the process +and say okay is this matching model. If + + align:start position:0% +and say okay is this matching model. If + + + align:start position:0% +and say okay is this matching model. If +it's not, pull the cord, make some + + align:start position:0% +it's not, pull the cord, make some + + + align:start position:0% +it's not, pull the cord, make some +changes, uh, investigate. Something's + + align:start position:0% +changes, uh, investigate. Something's + + + align:start position:0% +changes, uh, investigate. Something's +wrong. Investigate. What we're going to + + align:start position:0% +wrong. Investigate. What we're going to + + + align:start position:0% +wrong. Investigate. What we're going to +talk about today is the is extreme of + + align:start position:0% +talk about today is the is extreme of + + + align:start position:0% +talk about today is the is extreme of +that, which is to say every single part + + align:start position:0% +that, which is to say every single part + + + align:start position:0% +that, which is to say every single part +that comes out, we will assume should be + + align:start position:0% +that comes out, we will assume should be + + + align:start position:0% +that comes out, we will assume should be +correct, but uh, it will be off by some + + align:start position:0% +correct, but uh, it will be off by some + + + align:start position:0% +correct, but uh, it will be off by some +amount based on that error on a + + align:start position:0% +amount based on that error on a + + + align:start position:0% +amount based on that error on a +production cycle to cycle basis. Every + + align:start position:0% +production cycle to cycle basis. Every + + + align:start position:0% +production cycle to cycle basis. Every +time we make something, we'll measure + + align:start position:0% +time we make something, we'll measure + + + align:start position:0% +time we make something, we'll measure +it. Every time we measure it, we'll + + align:start position:0% +it. Every time we measure it, we'll + + + align:start position:0% +it. Every time we measure it, we'll +compare it to the target value and if + + align:start position:0% +compare it to the target value and if + + + align:start position:0% +compare it to the target value and if +it's wrong, we'll make an + + align:start position:0% +it's wrong, we'll make an + + + align:start position:0% +it's wrong, we'll make an +adjustment. Okay? Now, I can guarantee + + align:start position:0% +adjustment. Okay? Now, I can guarantee + + + align:start position:0% +adjustment. Okay? Now, I can guarantee +you there are a number of papers, many + + align:start position:0% +you there are a number of papers, many + + + align:start position:0% +you there are a number of papers, many +papers, probably thousands, hundreds I + + align:start position:0% +papers, probably thousands, hundreds I + + + align:start position:0% +papers, probably thousands, hundreds I +should say, uh and and uh many textbooks + + align:start position:0% +should say, uh and and uh many textbooks + + + align:start position:0% +should say, uh and and uh many textbooks +that will tell you that's crazy talk. + + align:start position:0% +that will tell you that's crazy talk. + + + align:start position:0% +that will tell you that's crazy talk. +You know, it's nuts. Should never do + + align:start position:0% +You know, it's nuts. Should never do + + + align:start position:0% +You know, it's nuts. Should never do +that because + + align:start position:0% +that because + + + align:start position:0% +that because +uh you'll never you'll never get it + + align:start position:0% +uh you'll never you'll never get it + + + align:start position:0% +uh you'll never you'll never get it +better. Okay. Now based on what you know + + align:start position:0% +better. Okay. Now based on what you know + + + align:start position:0% +better. Okay. Now based on what you know +so far about statistical processes and + + align:start position:0% +so far about statistical processes and + + + align:start position:0% +so far about statistical processes and +the nature of of these + + align:start position:0% +the nature of of these + + + align:start position:0% +the nature of of these +um techniques that we've done as well as + + align:start position:0% +um techniques that we've done as well as + + + align:start position:0% +um techniques that we've done as well as +a little bit on the physical processes. + + align:start position:0% +a little bit on the physical processes. + + + align:start position:0% +a little bit on the physical processes. +Why would why would you imagine the + + align:start position:0% +Why would why would you imagine the + + + align:start position:0% +Why would why would you imagine the +statistics community in particular would + + align:start position:0% +statistics community in particular would + + + align:start position:0% +statistics community in particular would +have that attitude towards this approach + + align:start position:0% +have that attitude towards this approach + + + align:start position:0% +have that attitude towards this approach +of what we call constant adjustment? + + align:start position:0% +of what we call constant adjustment? + + + align:start position:0% +of what we call constant adjustment? +Can you think why that's not a good + + align:start position:0% +Can you think why that's not a good + + + align:start position:0% +Can you think why that's not a good +idea? Yeah. If there is some underlying + + align:start position:0% +idea? Yeah. If there is some underlying + + + align:start position:0% +idea? Yeah. If there is some underlying +variance to the process and you + + align:start position:0% +variance to the process and you + + + align:start position:0% +variance to the process and you +continuously keep changing the mean and + + align:start position:0% +continuously keep changing the mean and + + + align:start position:0% +continuously keep changing the mean and +you're continuously changing the bounds + + align:start position:0% +you're continuously changing the bounds + + + align:start position:0% +you're continuously changing the bounds +of the of the variance unless it is + + align:start position:0% +of the of the variance unless it is + + + align:start position:0% +of the of the variance unless it is +statistically significant outside some + + align:start position:0% +statistically significant outside some + + + align:start position:0% +statistically significant outside some +bounds I guess they would object to + + align:start position:0% +bounds I guess they would object to + + + align:start position:0% +bounds I guess they would object to +making changes based on something + + align:start position:0% +making changes based on something + + + align:start position:0% +making changes based on something +that's normal expected. + + align:start position:0% +that's normal expected. + + + align:start position:0% +that's normal expected. +Yeah. Yeah. Richard same thing. Yeah. I + + align:start position:0% +Yeah. Yeah. Richard same thing. Yeah. I + + + align:start position:0% +Yeah. Yeah. Richard same thing. Yeah. I +mean that that's that's basically right. + + align:start position:0% +mean that that's that's basically right. + + + align:start position:0% +mean that that's that's basically right. +I'm going to state it a little bit + + align:start position:0% +I'm going to state it a little bit + + + align:start position:0% +I'm going to state it a little bit +differently. You know, everything could + + align:start position:0% +differently. You know, everything could + + + align:start position:0% +differently. You know, everything could +be + + align:start position:0% +be + + + align:start position:0% +be +fine and and your process is following a + + align:start position:0% +fine and and your process is following a + + + align:start position:0% +fine and and your process is following a +nice normal distribution and here's your + + align:start position:0% +nice normal distribution and here's your + + + align:start position:0% +nice normal distribution and here's your +target. I mean, basically says you will + + align:start position:0% +target. I mean, basically says you will + + + align:start position:0% +target. I mean, basically says you will +always have an error. It will always be + + align:start position:0% +always have an error. It will always be + + + align:start position:0% +always have an error. It will always be +wrong. You'll always be adjusting the + + align:start position:0% +wrong. You'll always be adjusting the + + + align:start position:0% +wrong. You'll always be adjusting the +process. So, you know, it's the concept + + align:start position:0% +process. So, you know, it's the concept + + + align:start position:0% +process. So, you know, it's the concept +of a dog chasing its tail. You know, + + align:start position:0% +of a dog chasing its tail. You know, + + + align:start position:0% +of a dog chasing its tail. You know, +you'll never how can that possibly make + + align:start position:0% +you'll never how can that possibly make + + + align:start position:0% +you'll never how can that possibly make +it better. So, they just say don't do + + align:start position:0% +it better. So, they just say don't do + + + align:start position:0% +it better. So, they just say don't do +it. And there are actually studies out + + align:start position:0% +it. And there are actually studies out + + + align:start position:0% +it. And there are actually studies out +there. There's a wonderful study that + + align:start position:0% +there. There's a wonderful study that + + + align:start position:0% +there. There's a wonderful study that +was done by uh professor at Harvard + + align:start position:0% +was done by uh professor at Harvard + + + align:start position:0% +was done by uh professor at Harvard +Business School on uh um I've forgotten + + align:start position:0% +Business School on uh um I've forgotten + + + align:start position:0% +Business School on uh um I've forgotten +what the do you know this one was um + + align:start position:0% +what the do you know this one was um + + + align:start position:0% +what the do you know this one was um +Jimdar um + + align:start position:0% +Jimdar um + + + align:start position:0% +Jimdar um +uh I think it was a big basic material + + align:start position:0% +uh I think it was a big basic material + + + align:start position:0% +uh I think it was a big basic material +basic mineral processing plant. one of + + align:start position:0% +basic mineral processing plant. one of + + + align:start position:0% +basic mineral processing plant. one of +these huge things with lots of different + + align:start position:0% +these huge things with lots of different + + + align:start position:0% +these huge things with lots of different +set points. And the operators had + + align:start position:0% +set points. And the operators had + + + align:start position:0% +set points. And the operators had +control over this thing and they were + + align:start position:0% +control over this thing and they were + + + align:start position:0% +control over this thing and they were +always looking at things and they could + + align:start position:0% +always looking at things and they could + + + align:start position:0% +always looking at things and they could +type in new numbers and change the + + align:start position:0% +type in new numbers and change the + + + align:start position:0% +type in new numbers and change the +change the set points in the plant and + + align:start position:0% +change the set points in the plant and + + + align:start position:0% +change the set points in the plant and +that sort of thing. And they all had + + align:start position:0% +that sort of thing. And they all had + + + align:start position:0% +that sort of thing. And they all had +their idea of how they could make it + + align:start position:0% +their idea of how they could make it + + + align:start position:0% +their idea of how they could make it +better. And he had this hypothesis that + + align:start position:0% +better. And he had this hypothesis that + + + align:start position:0% +better. And he had this hypothesis that +they were chasing their tail. You know, + + align:start position:0% +they were chasing their tail. You know, + + + align:start position:0% +they were chasing their tail. You know, +they were looking at these things and + + align:start position:0% +they were looking at these things and + + + align:start position:0% +they were looking at these things and +they were always adjusting the process. + + align:start position:0% +they were always adjusting the process. + + + align:start position:0% +they were always adjusting the process. +So one day with the concurrence of the + + align:start position:0% +So one day with the concurrence of the + + + align:start position:0% +So one day with the concurrence of the +management from the operator's point of + + align:start position:0% +management from the operator's point of + + + align:start position:0% +management from the operator's point of +view, everything was still the same. But + + align:start position:0% +view, everything was still the same. But + + + align:start position:0% +view, everything was still the same. But +they disconnected it. So that the + + align:start position:0% +they disconnected it. So that the + + + align:start position:0% +they disconnected it. So that the +operators were making changes to all the + + align:start position:0% +operators were making changes to all the + + + align:start position:0% +operators were making changes to all the +set points in the mach in the machines. + + align:start position:0% +set points in the mach in the machines. + + + align:start position:0% +set points in the mach in the machines. +Nothing was actually changing and guess + + align:start position:0% +Nothing was actually changing and guess + + + align:start position:0% +Nothing was actually changing and guess +what + + align:start position:0% +what + + + align:start position:0% +what +happened? It got better. The variance + + align:start position:0% +happened? It got better. The variance + + + align:start position:0% +happened? It got better. The variance +went down. And so that kind of + + align:start position:0% +went down. And so that kind of + + + align:start position:0% +went down. And so that kind of +circumstantial stuff says, okay, it is + + align:start position:0% +circumstantial stuff says, okay, it is + + + align:start position:0% +circumstantial stuff says, okay, it is +crazy talk. Why should I bother to do + + align:start position:0% +crazy talk. Why should I bother to do + + + align:start position:0% +crazy talk. Why should I bother to do +that? + + align:start position:0% +that? + + + align:start position:0% +that? +Um but there's an important butt here is + + align:start position:0% +Um but there's an important butt here is + + + align:start position:0% +Um but there's an important butt here is +that if that's all the information you + + align:start position:0% +that if that's all the information you + + + align:start position:0% +that if that's all the information you +have, if your idea is okay based on the + + align:start position:0% +have, if your idea is okay based on the + + + align:start position:0% +have, if your idea is okay based on the +error, make an + + align:start position:0% +error, make an + + + align:start position:0% +error, make an +adjustment. Um if you uh have any + + align:start position:0% +adjustment. Um if you uh have any + + + align:start position:0% +adjustment. Um if you uh have any +schooling and feedback control, you know + + align:start position:0% +schooling and feedback control, you know + + + align:start position:0% +schooling and feedback control, you know +that just closing the loop is not + + align:start position:0% +that just closing the loop is not + + + align:start position:0% +that just closing the loop is not +success. In fact, closing the loop is as + + align:start position:0% +success. In fact, closing the loop is as + + + align:start position:0% +success. In fact, closing the loop is as +I was once chastised by one of my + + align:start position:0% +I was once chastised by one of my + + + align:start position:0% +I was once chastised by one of my +professors, all that guarantees is that + + align:start position:0% +professors, all that guarantees is that + + + align:start position:0% +professors, all that guarantees is that +you can take a nice stable process and + + align:start position:0% +you can take a nice stable process and + + + align:start position:0% +you can take a nice stable process and +eventually make it go unstable. But you + + align:start position:0% +eventually make it go unstable. But you + + + align:start position:0% +eventually make it go unstable. But you +have to close the loop with a knowledge + + align:start position:0% +have to close the loop with a knowledge + + + align:start position:0% +have to close the loop with a knowledge +of what's going on and a knowledge of + + align:start position:0% +of what's going on and a knowledge of + + + align:start position:0% +of what's going on and a knowledge of +what the limits are. And in the end, + + align:start position:0% +what the limits are. And in the end, + + + align:start position:0% +what the limits are. And in the end, +what that means is you've got if you're + + align:start position:0% +what that means is you've got if you're + + + align:start position:0% +what that means is you've got if you're +going to have an operator making + + align:start position:0% +going to have an operator making + + + align:start position:0% +going to have an operator making +adjustments to the process based on + + align:start position:0% +adjustments to the process based on + + + align:start position:0% +adjustments to the process based on +measurements, they should have some uh + + align:start position:0% +measurements, they should have some uh + + + align:start position:0% +measurements, they should have some uh +um basis for f form basis for that. So + + align:start position:0% +um basis for f form basis for that. So + + + align:start position:0% +um basis for f form basis for that. So +that that's what this whole thing is + + align:start position:0% +that that's what this whole thing is + + + align:start position:0% +that that's what this whole thing is +about is what what is that basis and how + + align:start position:0% +about is what what is that basis and how + + + align:start position:0% +about is what what is that basis and how +how good could it + + align:start position:0% +how good could it + + + align:start position:0% +how good could it +be? + + align:start position:0% + + + + align:start position:0% + +Okay. Okay. wake up + + align:start position:0% + + + + align:start position:0% + +now. All right. Um, and just to just to + + align:start position:0% +now. All right. Um, and just to just to + + + align:start position:0% +now. All right. Um, and just to just to +tie this back in with what we we uh + + align:start position:0% +tie this back in with what we we uh + + + align:start position:0% +tie this back in with what we we uh +talked about in the beginning, if you + + align:start position:0% +talked about in the beginning, if you + + + align:start position:0% +talked about in the beginning, if you +look at this variability equation, which + + align:start position:0% +look at this variability equation, which + + + align:start position:0% +look at this variability equation, which +I don't know how much you've used that + + align:start position:0% +I don't know how much you've used that + + + align:start position:0% +I don't know how much you've used that +during the term, it's not not important, + + align:start position:0% +during the term, it's not not important, + + + align:start position:0% +during the term, it's not not important, +but the whole idea is that what we'd + + align:start position:0% +but the whole idea is that what we'd + + + align:start position:0% +but the whole idea is that what we'd +like to do is change the variability, + + align:start position:0% +like to do is change the variability, + + + align:start position:0% +like to do is change the variability, +reduce the variability of a process. And + + align:start position:0% +reduce the variability of a process. And + + + align:start position:0% +reduce the variability of a process. And +we'd like to do it, you know, SPC does + + align:start position:0% +we'd like to do it, you know, SPC does + + + align:start position:0% +we'd like to do it, you know, SPC does +it by reducing the uh the disturbance. + + align:start position:0% +it by reducing the uh the disturbance. + + + align:start position:0% +it by reducing the uh the disturbance. +Design experiments does it reducing the + + align:start position:0% +Design experiments does it reducing the + + + align:start position:0% +Design experiments does it reducing the +sensitivity and feedback control does it + + align:start position:0% +sensitivity and feedback control does it + + + align:start position:0% +sensitivity and feedback control does it +by trying to offset the problems. So if + + align:start position:0% +by trying to offset the problems. So if + + + align:start position:0% +by trying to offset the problems. So if +there is something that's causing a mean + + align:start position:0% +there is something that's causing a mean + + + align:start position:0% +there is something that's causing a mean +shift, you want to push it back by + + align:start position:0% +shift, you want to push it back by + + + align:start position:0% +shift, you want to push it back by +making an offset change. And that's + + align:start position:0% +making an offset change. And that's + + + align:start position:0% +making an offset change. And that's +that's all that this uh is relating to. + + align:start position:0% +that's all that this uh is relating to. + + + align:start position:0% +that's all that this uh is relating to. +And so in effect we get to the third + + align:start position:0% +And so in effect we get to the third + + + align:start position:0% +And so in effect we get to the third +level of this process control hierarchy + + align:start position:0% +level of this process control hierarchy + + + align:start position:0% +level of this process control hierarchy +that we talked about on day one which is + + align:start position:0% +that we talked about on day one which is + + + align:start position:0% +that we talked about on day one which is +the first one is basically good + + align:start position:0% +the first one is basically good + + + align:start position:0% +the first one is basically good +housekeeping standard operating + + align:start position:0% +housekeeping standard operating + + + align:start position:0% +housekeeping standard operating +procedures statistical analysis and + + align:start position:0% +procedures statistical analysis and + + + align:start position:0% +procedures statistical analysis and +identification of whether everything is + + align:start position:0% +identification of whether everything is + + + align:start position:0% +identification of whether everything is +in a in a state of sort of uh stationary + + align:start position:0% +in a in a state of sort of uh stationary + + + align:start position:0% +in a in a state of sort of uh stationary +statistical control. Second one is + + align:start position:0% +statistical control. Second one is + + + align:start position:0% +statistical control. Second one is +reducing sensitivity or increasing + + align:start position:0% +reducing sensitivity or increasing + + + align:start position:0% +reducing sensitivity or increasing +robustness. That's the whole designed + + align:start position:0% +robustness. That's the whole designed + + + align:start position:0% +robustness. That's the whole designed +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +uh area. And then finally sort of this + + align:start position:0% +uh area. And then finally sort of this + + + align:start position:0% +uh area. And then finally sort of this +gets it as as good as it can be without + + align:start position:0% +gets it as as good as it can be without + + + align:start position:0% +gets it as as good as it can be without +active manipulation. And then finally we + + align:start position:0% +active manipulation. And then finally we + + + align:start position:0% +active manipulation. And then finally we +actively manipulate um and see what we + + align:start position:0% +actively manipulate um and see what we + + + align:start position:0% +actively manipulate um and see what we +do. So I do think you know I I've come + + align:start position:0% +do. So I do think you know I I've come + + + align:start position:0% +do. So I do think you know I I've come +to firmly believe even though I I came + + align:start position:0% +to firmly believe even though I I came + + + align:start position:0% +to firmly believe even though I I came +to this whole thing from a feedback + + align:start position:0% +to this whole thing from a feedback + + + align:start position:0% +to this whole thing from a feedback +control can solve any problem in the + + align:start position:0% +control can solve any problem in the + + + align:start position:0% +control can solve any problem in the +world point of view. + + align:start position:0% +world point of view. + + + align:start position:0% +world point of view. +um this is the last thing you do after + + align:start position:0% +um this is the last thing you do after + + + align:start position:0% +um this is the last thing you do after +you've tried these far cheaper, far more + + align:start position:0% +you've tried these far cheaper, far more + + + align:start position:0% +you've tried these far cheaper, far more +robust uh and um far more in some ways + + align:start position:0% +robust uh and um far more in some ways + + + align:start position:0% +robust uh and um far more in some ways +uh in-depth knowledge of the process uh + + align:start position:0% +uh in-depth knowledge of the process uh + + + align:start position:0% +uh in-depth knowledge of the process uh +approaches. Okay. So, uh I have to take + + align:start position:0% +approaches. Okay. So, uh I have to take + + + align:start position:0% +approaches. Okay. So, uh I have to take +a moment to to just review feedback + + align:start position:0% +a moment to to just review feedback + + + align:start position:0% +a moment to to just review feedback +control. How many of you guys have had a + + align:start position:0% +control. How many of you guys have had a + + + align:start position:0% +control. How many of you guys have had a +feedback control + + align:start position:0% + + + + align:start position:0% + +course? Okay, that's pretty Hayden. + + align:start position:0% +course? Okay, that's pretty Hayden. + + + align:start position:0% +course? Okay, that's pretty Hayden. +You've never had a feedback control? + + align:start position:0% +You've never had a feedback control? + + + align:start position:0% +You've never had a feedback control? +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Okay. The TA hasn't had the course, + + align:start position:0% +Okay. The TA hasn't had the course, + + + align:start position:0% +Okay. The TA hasn't had the course, +we're in trouble. Um, uh, and you know, + + align:start position:0% +we're in trouble. Um, uh, and you know, + + + align:start position:0% +we're in trouble. Um, uh, and you know, +we often use this generic feedback + + align:start position:0% +we often use this generic feedback + + + align:start position:0% +we often use this generic feedback +control regulator um, approach. And I, I + + align:start position:0% +control regulator um, approach. And I, I + + + align:start position:0% +control regulator um, approach. And I, I +want to do this because I'm going to use + + align:start position:0% +want to do this because I'm going to use + + + align:start position:0% +want to do this because I'm going to use +a little bit of terminology. This is + + align:start position:0% +a little bit of terminology. This is + + + align:start position:0% +a little bit of terminology. This is +stuff we've already used in the class, + + align:start position:0% +stuff we've already used in the class, + + + align:start position:0% +stuff we've already used in the class, +but I want to look at it a little bit + + align:start position:0% +but I want to look at it a little bit + + + align:start position:0% +but I want to look at it a little bit +differently. So, let me just define the + + align:start position:0% +differently. So, let me just define the + + + align:start position:0% +differently. So, let me just define the +terms + + align:start position:0% +terms + + + align:start position:0% +terms +here. Whoops. This box right here, + + align:start position:0% +here. Whoops. This box right here, + + + align:start position:0% +here. Whoops. This box right here, +that's the process. That's the + + align:start position:0% +that's the process. That's the + + + align:start position:0% +that's the process. That's the +manufacturing process. That's the + + align:start position:0% +manufacturing process. That's the + + + align:start position:0% +manufacturing process. That's the +machine, the material, all that other + + align:start position:0% +machine, the material, all that other + + + align:start position:0% +machine, the material, all that other +stuff we talked about. And the input to + + align:start position:0% +stuff we talked about. And the input to + + + align:start position:0% +stuff we talked about. And the input to +that is something that I can change. + + align:start position:0% +that is something that I can change. + + + align:start position:0% +that is something that I can change. +Temperature, a pressure, a feed, a time, + + align:start position:0% +Temperature, a pressure, a feed, a time, + + + align:start position:0% +Temperature, a pressure, a feed, a time, +something like that. The output of the + + align:start position:0% +something like that. The output of the + + + align:start position:0% +something like that. The output of the +process is the output of the process. + + align:start position:0% +process is the output of the process. + + + align:start position:0% +process is the output of the process. +It's what we care + + align:start position:0% +It's what we care + + + align:start position:0% +It's what we care +about. Um, actually, I'm going to put + + align:start position:0% +about. Um, actually, I'm going to put + + + align:start position:0% +about. Um, actually, I'm going to put +the output of the process over here for + + align:start position:0% +the output of the process over here for + + + align:start position:0% +the output of the process over here for +the moment. Um, the key thing is that uh + + align:start position:0% +the moment. Um, the key thing is that uh + + + align:start position:0% +the moment. Um, the key thing is that uh +the process, there are two things that + + align:start position:0% +the process, there are two things that + + + align:start position:0% +the process, there are two things that +make the process not always do the same + + align:start position:0% +make the process not always do the same + + + align:start position:0% +make the process not always do the same +thing. In other words, if I hold the + + align:start position:0% +thing. In other words, if I hold the + + + align:start position:0% +thing. In other words, if I hold the +inputs the same all the time, the output + + align:start position:0% +inputs the same all the time, the output + + + align:start position:0% +inputs the same all the time, the output +still varies. We know that, you know, we + + align:start position:0% +still varies. We know that, you know, we + + + align:start position:0% +still varies. We know that, you know, we +know that from SPC, you know it from + + align:start position:0% +know that from SPC, you know it from + + + align:start position:0% +know that from SPC, you know it from +data that you've taken. Where is that + + align:start position:0% +data that you've taken. Where is that + + + align:start position:0% +data that you've taken. Where is that +other thing coming from? Well, in a + + align:start position:0% +other thing coming from? Well, in a + + + align:start position:0% +other thing coming from? Well, in a +control system sense, one of one of the + + align:start position:0% +control system sense, one of one of the + + + align:start position:0% +control system sense, one of one of the +sources is the disturbance. We just kind + + align:start position:0% +sources is the disturbance. We just kind + + + align:start position:0% +sources is the disturbance. We just kind +of think of it as an external factor. + + align:start position:0% +of think of it as an external factor. + + + align:start position:0% +of think of it as an external factor. +This D1 or D2 um you know, the classic + + align:start position:0% +This D1 or D2 um you know, the classic + + + align:start position:0% +This D1 or D2 um you know, the classic +example of that is a flight control + + align:start position:0% +example of that is a flight control + + + align:start position:0% +example of that is a flight control +altitude + + align:start position:0% +altitude + + + align:start position:0% +altitude +uh autopilot. You know, what's a good + + align:start position:0% +uh autopilot. You know, what's a good + + + align:start position:0% +uh autopilot. You know, what's a good +disturbance to an autopilot? Well, a + + align:start position:0% +disturbance to an autopilot? Well, a + + + align:start position:0% +disturbance to an autopilot? Well, a +wind current or something like that, you + + align:start position:0% +wind current or something like that, you + + + align:start position:0% +wind current or something like that, you +know, is external to the machine. It + + align:start position:0% +know, is external to the machine. It + + + align:start position:0% +know, is external to the machine. It +causes it to change and and uh causes + + align:start position:0% +causes it to change and and uh causes + + + align:start position:0% +causes it to change and and uh causes +the output of the flight control system + + align:start position:0% +the output of the flight control system + + + align:start position:0% +the output of the flight control system +to change. And you the purpose of the + + align:start position:0% +to change. And you the purpose of the + + + align:start position:0% +to change. And you the purpose of the +controller in that case and the purpose + + align:start position:0% +controller in that case and the purpose + + + align:start position:0% +controller in that case and the purpose +of the controller primarily for + + align:start position:0% +of the controller primarily for + + + align:start position:0% +of the controller primarily for +manufacturing is to minimize the effect + + align:start position:0% +manufacturing is to minimize the effect + + + align:start position:0% +manufacturing is to minimize the effect +of these disturbances. You'd like to + + align:start position:0% +of these disturbances. You'd like to + + + align:start position:0% +of these disturbances. You'd like to +make it look like they aren't there so + + align:start position:0% +make it look like they aren't there so + + + align:start position:0% +make it look like they aren't there so +that you're flying the plane and and + + align:start position:0% +that you're flying the plane and and + + + align:start position:0% +that you're flying the plane and and +wind's blowing up and down. It still + + align:start position:0% +wind's blowing up and down. It still + + + align:start position:0% +wind's blowing up and down. It still +keeps going level. you're machining + + align:start position:0% +keeps going level. you're machining + + + align:start position:0% +keeps going level. you're machining +something and the material gets harder + + align:start position:0% +something and the material gets harder + + + align:start position:0% +something and the material gets harder +or softer, you just keep going the same + + align:start position:0% +or softer, you just keep going the same + + + align:start position:0% +or softer, you just keep going the same +way. Um, you know, you're etching + + align:start position:0% +way. Um, you know, you're etching + + + align:start position:0% +way. Um, you know, you're etching +something and maybe your your solution + + align:start position:0% +something and maybe your your solution + + + align:start position:0% +something and maybe your your solution +is losing strength, but it still etches + + align:start position:0% +is losing strength, but it still etches + + + align:start position:0% +is losing strength, but it still etches +enough. All those sorts of things. Um, + + align:start position:0% +enough. All those sorts of things. Um, + + + align:start position:0% +enough. All those sorts of things. Um, +that's a standard way of modeling things + + align:start position:0% +that's a standard way of modeling things + + + align:start position:0% +that's a standard way of modeling things +in control and that's the way we'll do + + align:start position:0% +in control and that's the way we'll do + + + align:start position:0% +in control and that's the way we'll do +it for this for this approach. In fact, + + align:start position:0% +it for this for this approach. In fact, + + + align:start position:0% +it for this for this approach. In fact, +what happens more often than not in + + align:start position:0% +what happens more often than not in + + + align:start position:0% +what happens more often than not in +manufacturing is captured by this this + + align:start position:0% +manufacturing is captured by this this + + + align:start position:0% +manufacturing is captured by this this +crazy little arrow here, uh, the dark + + align:start position:0% +crazy little arrow here, uh, the dark + + + align:start position:0% +crazy little arrow here, uh, the dark +one, which basically says, yeah, well, + + align:start position:0% +one, which basically says, yeah, well, + + + align:start position:0% +one, which basically says, yeah, well, +this input output relationship between + + align:start position:0% +this input output relationship between + + + align:start position:0% +this input output relationship between +the the settings on the machine and the + + align:start position:0% +the the settings on the machine and the + + + align:start position:0% +the the settings on the machine and the +output of the material is in fact never + + align:start position:0% +output of the material is in fact never + + + align:start position:0% +output of the material is in fact never +a constant. We're always putting in + + align:start position:0% +a constant. We're always putting in + + + align:start position:0% +a constant. We're always putting in +different material. The machine is + + align:start position:0% +different material. The machine is + + + align:start position:0% +different material. The machine is +changing over time. This is all the + + align:start position:0% +changing over time. This is all the + + + align:start position:0% +changing over time. This is all the +stuff we talked about in the first days. + + align:start position:0% +stuff we talked about in the first days. + + + align:start position:0% +stuff we talked about in the first days. +So, in fact, we have two types of + + align:start position:0% +So, in fact, we have two types of + + + align:start position:0% +So, in fact, we have two types of +disturbances. These sort of external + + align:start position:0% +disturbances. These sort of external + + + align:start position:0% +disturbances. These sort of external +ones and these internal ones. The + + align:start position:0% +ones and these internal ones. The + + + align:start position:0% +ones and these internal ones. The +problem is that from a control system + + align:start position:0% +problem is that from a control system + + + align:start position:0% +problem is that from a control system +theory point of view, the external ones + + align:start position:0% +theory point of view, the external ones + + + align:start position:0% +theory point of view, the external ones +are easy to model and analyze. The + + align:start position:0% +are easy to model and analyze. The + + + align:start position:0% +are easy to model and analyze. The +internal ones are very uneasy to uh + + align:start position:0% +internal ones are very uneasy to uh + + + align:start position:0% +internal ones are very uneasy to uh +model and analyze. So um we will + + align:start position:0% +model and analyze. So um we will + + + align:start position:0% +model and analyze. So um we will +actually look more at this one even + + align:start position:0% +actually look more at this one even + + + align:start position:0% +actually look more at this one even +though we'll pretend that we're looking + + align:start position:0% +though we'll pretend that we're looking + + + align:start position:0% +though we'll pretend that we're looking +at uh both of these. + + align:start position:0% +at uh both of these. + + + align:start position:0% +at uh both of these. +So again the purpose of the control + + align:start position:0% +So again the purpose of the control + + + align:start position:0% +So again the purpose of the control +system is to make this output quantity + + align:start position:0% +system is to make this output quantity + + + align:start position:0% +system is to make this output quantity +stay exactly in line with what the input + + align:start position:0% +stay exactly in line with what the input + + + align:start position:0% +stay exactly in line with what the input +quantity is which of course would be + + align:start position:0% +quantity is which of course would be + + + align:start position:0% +quantity is which of course would be +some sort of a desired dimension + + align:start position:0% +some sort of a desired dimension + + + align:start position:0% +some sort of a desired dimension +something like that. + + align:start position:0% +something like that. + + + align:start position:0% +something like that. +Um so + + align:start position:0% + + + + align:start position:0% + +um when we look when again if any of you + + align:start position:0% +um when we look when again if any of you + + + align:start position:0% +um when we look when again if any of you +have studied control systems in any + + align:start position:0% +have studied control systems in any + + + align:start position:0% +have studied control systems in any +advanced way we have this one you know + + align:start position:0% +advanced way we have this one you know + + + align:start position:0% +advanced way we have this one you know +one aspect of control systems is called + + align:start position:0% +one aspect of control systems is called + + + align:start position:0% +one aspect of control systems is called +stoa stochastic control systems which is + + align:start position:0% +stoa stochastic control systems which is + + + align:start position:0% +stoa stochastic control systems which is +where the control theory actually + + align:start position:0% +where the control theory actually + + + align:start position:0% +where the control theory actually +assumes that the variables that you're + + align:start position:0% +assumes that the variables that you're + + + align:start position:0% +assumes that the variables that you're +controlling and other things have some + + align:start position:0% +controlling and other things have some + + + align:start position:0% +controlling and other things have some +randomness associated with it. Most + + align:start position:0% +randomness associated with it. Most + + + align:start position:0% +randomness associated with it. Most +control is done of course in uh for + + align:start position:0% +control is done of course in uh for + + + align:start position:0% +control is done of course in uh for +deterministic quantities but in fact + + align:start position:0% +deterministic quantities but in fact + + + align:start position:0% +deterministic quantities but in fact +most things have these random components + + align:start position:0% +most things have these random components + + + align:start position:0% +most things have these random components +and when you do that you find that um + + align:start position:0% +and when you do that you find that um + + + align:start position:0% +and when you do that you find that um +what you're taught on that is that well + + align:start position:0% +what you're taught on that is that well + + + align:start position:0% +what you're taught on that is that well +if I use feedback I can minimize mean + + align:start position:0% +if I use feedback I can minimize mean + + + align:start position:0% +if I use feedback I can minimize mean +shifts in the process or mean shifts in + + align:start position:0% +shifts in the process or mean shifts in + + + align:start position:0% +shifts in the process or mean shifts in +the disturbance and I can often reduce + + align:start position:0% +the disturbance and I can often reduce + + + align:start position:0% +the disturbance and I can often reduce +so-called dynamic disturbances if things + + align:start position:0% +so-called dynamic disturbances if things + + + align:start position:0% +so-called dynamic disturbances if things +are changing from time to time I should + + align:start position:0% +are changing from time to time I should + + + align:start position:0% +are changing from time to time I should +be able to reduce those so if I + + align:start position:0% +be able to reduce those so if I + + + align:start position:0% +be able to reduce those so if I +translate that into the the lexicon of + + align:start position:0% +translate that into the the lexicon of + + + align:start position:0% +translate that into the the lexicon of +this class that kind of means well look + + align:start position:0% +this class that kind of means well look + + + align:start position:0% +this class that kind of means well look +here here's a distribution let me + + align:start position:0% +here here's a distribution let me + + + align:start position:0% +here here's a distribution let me +drawing too many lines here hang + + align:start position:0% +drawing too many lines here hang + + + align:start position:0% +drawing too many lines here hang +on can't + + align:start position:0% + + + + align:start position:0% + +um this distribution on the left well + + align:start position:0% +um this distribution on the left well + + + align:start position:0% +um this distribution on the left well +first of all let me point out what I've + + align:start position:0% +first of all let me point out what I've + + + align:start position:0% +first of all let me point out what I've +tried to draw here you see this is your + + align:start position:0% +tried to draw here you see this is your + + + align:start position:0% +tried to draw here you see this is your +process capability window that's where + + align:start position:0% +process capability window that's where + + + align:start position:0% +process capability window that's where +you want to be so ideally we're centered + + align:start position:0% +you want to be so ideally we're centered + + + align:start position:0% +you want to be so ideally we're centered +on that and well within the bounds of + + align:start position:0% +on that and well within the bounds of + + + align:start position:0% +on that and well within the bounds of +that imagine Imagine you have a process + + align:start position:0% +that imagine Imagine you have a process + + + align:start position:0% +that imagine Imagine you have a process +that's operating over here. So, it's + + align:start position:0% +that's operating over here. So, it's + + + align:start position:0% +that's operating over here. So, it's +obviously got terrible process + + align:start position:0% +obviously got terrible process + + + align:start position:0% +obviously got terrible process +capability. Um, the mean is way over + + align:start position:0% +capability. Um, the mean is way over + + + align:start position:0% +capability. Um, the mean is way over +here. And even if I were to center it + + align:start position:0% +here. And even if I were to center it + + + align:start position:0% +here. And even if I were to center it +within the the target window, it would + + align:start position:0% +within the the target window, it would + + + align:start position:0% +within the the target window, it would +probably be outside that. I'd have a low + + align:start position:0% +probably be outside that. I'd have a low + + + align:start position:0% +probably be outside that. I'd have a low +process + + align:start position:0% +process + + + align:start position:0% +process +capability. So, wouldn't it be nice to + + align:start position:0% +capability. So, wouldn't it be nice to + + + align:start position:0% +capability. So, wouldn't it be nice to +have a controller that can take this + + align:start position:0% +have a controller that can take this + + + align:start position:0% +have a controller that can take this +distribution, center it, and even make + + align:start position:0% +distribution, center it, and even make + + + align:start position:0% +distribution, center it, and even make +it narrower? Well, there's a suggestion + + align:start position:0% +it narrower? Well, there's a suggestion + + + align:start position:0% +it narrower? Well, there's a suggestion +that feedback control can do that + + align:start position:0% +that feedback control can do that + + + align:start position:0% +that feedback control can do that +because we know we can eliminate mean + + align:start position:0% +because we know we can eliminate mean + + + align:start position:0% +because we know we can eliminate mean +errors with feedback control. The + + align:start position:0% +errors with feedback control. The + + + align:start position:0% +errors with feedback control. The +question is what happens with the + + align:start position:0% +question is what happens with the + + + align:start position:0% +question is what happens with the +variance? And you know, as we thought + + align:start position:0% +variance? And you know, as we thought + + + align:start position:0% +variance? And you know, as we thought +about this idea of chasing your + + align:start position:0% +about this idea of chasing your + + + align:start position:0% +about this idea of chasing your +tail, excuse me, + + align:start position:0% +tail, excuse me, + + + align:start position:0% +tail, excuse me, +um how can I be measuring a random + + align:start position:0% +um how can I be measuring a random + + + align:start position:0% +um how can I be measuring a random +variable, particularly an uncorrelated + + align:start position:0% +variable, particularly an uncorrelated + + + align:start position:0% +variable, particularly an uncorrelated +random variable, and use that knowledge + + align:start position:0% +random variable, and use that knowledge + + + align:start position:0% +random variable, and use that knowledge +to actually reduce the degree of + + align:start position:0% +to actually reduce the degree of + + + align:start position:0% +to actually reduce the degree of +randomness? Keep thinking about that. + + align:start position:0% +randomness? Keep thinking about that. + + + align:start position:0% +randomness? Keep thinking about that. +But we can analyze it and then of course + + align:start position:0% +But we can analyze it and then of course + + + align:start position:0% +But we can analyze it and then of course +the proof of the pudding will be to uh + + align:start position:0% +the proof of the pudding will be to uh + + + align:start position:0% +the proof of the pudding will be to uh +actually do an experiment. Let me uh + + align:start position:0% + + + + align:start position:0% + +oops. Okay. So uh what do we want to + + align:start position:0% +oops. Okay. So uh what do we want to + + + align:start position:0% +oops. Okay. So uh what do we want to +look at in trying to understand this? + + align:start position:0% +look at in trying to understand this? + + + align:start position:0% +look at in trying to understand this? +What kind of disturbances do we expect + + align:start position:0% +What kind of disturbances do we expect + + + align:start position:0% +What kind of disturbances do we expect +to see or how do we want to model + + align:start position:0% +to see or how do we want to model + + + align:start position:0% +to see or how do we want to model +disturbances? Well, we know so far that + + align:start position:0% +disturbances? Well, we know so far that + + + align:start position:0% +disturbances? Well, we know so far that +to capture the process, we're going to + + align:start position:0% +to capture the process, we're going to + + + align:start position:0% +to capture the process, we're going to +have to model disturbances as being + + align:start position:0% +have to model disturbances as being + + + align:start position:0% +have to model disturbances as being +random. Our whole premise for the stat + + align:start position:0% +random. Our whole premise for the stat + + + align:start position:0% +random. Our whole premise for the stat +statistical models is that the the + + align:start position:0% +statistical models is that the the + + + align:start position:0% +statistical models is that the the +process has some randomness associated + + align:start position:0% +process has some randomness associated + + + align:start position:0% +process has some randomness associated +with it. And then we have things like + + align:start position:0% +with it. And then we have things like + + + align:start position:0% +with it. And then we have things like +unexpected mean shifts which in control + + align:start position:0% +unexpected mean shifts which in control + + + align:start position:0% +unexpected mean shifts which in control +lexicon we call infrequent step-wise. + + align:start position:0% +lexicon we call infrequent step-wise. + + + align:start position:0% +lexicon we call infrequent step-wise. +And then we might have things like tool + + align:start position:0% +And then we might have things like tool + + + align:start position:0% +And then we might have things like tool +wear or you know just degradation of + + align:start position:0% +wear or you know just degradation of + + + align:start position:0% +wear or you know just degradation of +solutions and things over time. And so + + align:start position:0% +solutions and things over time. And so + + + align:start position:0% +solutions and things over time. And so +there's a slowly varying change + + align:start position:0% +there's a slowly varying change + + + align:start position:0% +there's a slowly varying change +uh of the process. And then of course + + align:start position:0% +uh of the process. And then of course + + + align:start position:0% +uh of the process. And then of course +cyclic you know things that are + + align:start position:0% +cyclic you know things that are + + + align:start position:0% +cyclic you know things that are +happening because of shift changes time + + align:start position:0% +happening because of shift changes time + + + align:start position:0% +happening because of shift changes time +time of day other things like that. Um + + align:start position:0% +time of day other things like that. Um + + + align:start position:0% +time of day other things like that. Um +it would be nice to deal with all those. + + align:start position:0% +it would be nice to deal with all those. + + + align:start position:0% +it would be nice to deal with all those. +For the moment we're going to deal + + align:start position:0% +For the moment we're going to deal + + + align:start position:0% +For the moment we're going to deal +primarily with infrequent stepwise + + align:start position:0% +primarily with infrequent stepwise + + + align:start position:0% +primarily with infrequent stepwise +random uh + + align:start position:0% +random uh + + + align:start position:0% +random uh +disturbances. There are there are more + + align:start position:0% +disturbances. There are there are more + + + align:start position:0% +disturbances. There are there are more +advanced topics on this that we'll deal + + align:start position:0% +advanced topics on this that we'll deal + + + align:start position:0% +advanced topics on this that we'll deal +with these two but we won't get into + + align:start position:0% +with these two but we won't get into + + + align:start position:0% +with these two but we won't get into +those today. + + align:start position:0% +those today. + + + align:start position:0% +those today. +Um okay so cycleto cycle control is is + + align:start position:0% +Um okay so cycleto cycle control is is + + + align:start position:0% +Um okay so cycleto cycle control is is +simply defined as doing the best you can + + align:start position:0% +simply defined as doing the best you can + + + align:start position:0% +simply defined as doing the best you can +with this situation that we have now. + + align:start position:0% +with this situation that we have now. + + + align:start position:0% +with this situation that we have now. +Okay so the ideal thing is to have a + + align:start position:0% +Okay so the ideal thing is to have a + + + align:start position:0% +Okay so the ideal thing is to have a +full measure of how you're doing on your + + align:start position:0% +full measure of how you're doing on your + + + align:start position:0% +full measure of how you're doing on your +production can always that make that + + align:start position:0% +production can always that make that + + + align:start position:0% +production can always that make that +measurement after the cycle of + + align:start position:0% +measurement after the cycle of + + + align:start position:0% +measurement after the cycle of +production has finished. So, I mean, uh, + + align:start position:0% +production has finished. So, I mean, uh, + + + align:start position:0% +production has finished. So, I mean, uh, +think of this maybe an injection molding + + align:start position:0% +think of this maybe an injection molding + + + align:start position:0% +think of this maybe an injection molding +machine is a good model for this or + + align:start position:0% +machine is a good model for this or + + + align:start position:0% +machine is a good model for this or +something that that happens kind of + + align:start position:0% +something that that happens kind of + + + align:start position:0% +something that that happens kind of +quick or a metal stamping operation or + + align:start position:0% +quick or a metal stamping operation or + + + align:start position:0% +quick or a metal stamping operation or +high-speed forging operation. Any of + + align:start position:0% +high-speed forging operation. Any of + + + align:start position:0% +high-speed forging operation. Any of +these things where, you know, you can't + + align:start position:0% +these things where, you know, you can't + + + align:start position:0% +these things where, you know, you can't +get in there with your gauge while it's + + align:start position:0% +get in there with your gauge while it's + + + align:start position:0% +get in there with your gauge while it's +happening unless you're crazy. And, uh, + + align:start position:0% +happening unless you're crazy. And, uh, + + + align:start position:0% +happening unless you're crazy. And, uh, +even if you did, you wouldn't it + + align:start position:0% +even if you did, you wouldn't it + + + align:start position:0% +even if you did, you wouldn't it +wouldn't tell you what you wanted to + + align:start position:0% +wouldn't tell you what you wanted to + + + align:start position:0% +wouldn't tell you what you wanted to +know. Like an injection molded part, you + + align:start position:0% +know. Like an injection molded part, you + + + align:start position:0% +know. Like an injection molded part, you +know, until it's popped out. In fact, + + align:start position:0% +know, until it's popped out. In fact, + + + align:start position:0% +know, until it's popped out. In fact, +until it's cooled off, you don't know + + align:start position:0% +until it's cooled off, you don't know + + + align:start position:0% +until it's cooled off, you don't know +how you did. + + align:start position:0% +how you did. + + + align:start position:0% +how you did. +um uh so it's finally there you measure + + align:start position:0% +um uh so it's finally there you measure + + + align:start position:0% +um uh so it's finally there you measure +it and then you say ah I have to make a + + align:start position:0% +it and then you say ah I have to make a + + + align:start position:0% +it and then you say ah I have to make a +change can I make a change and most + + align:start position:0% +change can I make a change and most + + + align:start position:0% +change can I make a change and most +machines will allow you to make a change + + align:start position:0% +machines will allow you to make a change + + + align:start position:0% +machines will allow you to make a change +somewhere and you know you did your + + align:start position:0% +somewhere and you know you did your + + + align:start position:0% +somewhere and you know you did your +designed experiments and the whole idea + + align:start position:0% +designed experiments and the whole idea + + + align:start position:0% +designed experiments and the whole idea +of that was to say what are the + + align:start position:0% +of that was to say what are the + + + align:start position:0% +of that was to say what are the +significant inputs to change + + align:start position:0% +significant inputs to change + + + align:start position:0% +significant inputs to change +significantly have a significant uh + + align:start position:0% +significantly have a significant uh + + + align:start position:0% +significantly have a significant uh +change in the output so we find out what + + align:start position:0% +change in the output so we find out what + + + align:start position:0% +change in the output so we find out what +those significant ones are and try to + + align:start position:0% +those significant ones are and try to + + + align:start position:0% +those significant ones are and try to +match them so if the dimension is wrong + + align:start position:0% +match them so if the dimension is wrong + + + align:start position:0% +match them so if the dimension is wrong +you say okay here's what I want to + + align:start position:0% +you say okay here's what I want to + + + align:start position:0% +you say okay here's what I want to +adjust uh to change + + align:start position:0% +adjust uh to change + + + align:start position:0% +adjust uh to change +Now, the key thing is this, or think of + + align:start position:0% +Now, the key thing is this, or think of + + + align:start position:0% +Now, the key thing is this, or think of +it this way. Take injection molding + + align:start position:0% +it this way. Take injection molding + + + align:start position:0% +it this way. Take injection molding +because we I'll give you some data on + + align:start position:0% +because we I'll give you some data on + + + align:start position:0% +because we I'll give you some data on +that in a moment. You set it up. You run + + align:start position:0% +that in a moment. You set it up. You run + + + align:start position:0% +that in a moment. You set it up. You run +a part. You take it onto the bench. You + + align:start position:0% +a part. You take it onto the bench. You + + + align:start position:0% +a part. You take it onto the bench. You +measure it. You say, "It's not + + align:start position:0% +measure it. You say, "It's not + + + align:start position:0% +measure it. You say, "It's not +right. How soon can I make a change in + + align:start position:0% +right. How soon can I make a change in + + + align:start position:0% +right. How soon can I make a change in +the process to improve + + align:start position:0% +the process to improve + + + align:start position:0% +the process to improve +it?" Next cycle. So, before I say go + + align:start position:0% +it?" Next cycle. So, before I say go + + + align:start position:0% +it?" Next cycle. So, before I say go +again, I make a little change. I + + align:start position:0% +again, I make a little change. I + + + align:start position:0% +again, I make a little change. I +increase the hold time. I decrease the + + align:start position:0% +increase the hold time. I decrease the + + + align:start position:0% +increase the hold time. I decrease the +pressure. Something like that. Then I + + align:start position:0% +pressure. Something like that. Then I + + + align:start position:0% +pressure. Something like that. Then I +say go and I keep doing that and it's + + align:start position:0% +say go and I keep doing that and it's + + + align:start position:0% +say go and I keep doing that and it's +cycle to cycle to cycle. But within each + + align:start position:0% +cycle to cycle to cycle. But within each + + + align:start position:0% +cycle to cycle to cycle. But within each +cycle when I say change the hold time or + + align:start position:0% +cycle when I say change the hold time or + + + align:start position:0% +cycle when I say change the hold time or +I say change the um pressure during the + + align:start position:0% +I say change the um pressure during the + + + align:start position:0% +I say change the um pressure during the +actual cycle of inje of of of melding + + align:start position:0% +actual cycle of inje of of of melding + + + align:start position:0% +actual cycle of inje of of of melding +and injecting and cooling the material + + align:start position:0% +and injecting and cooling the material + + + align:start position:0% +and injecting and cooling the material +nothing changes. So from the injection + + align:start position:0% +nothing changes. So from the injection + + + align:start position:0% +nothing changes. So from the injection +molding machine process point of view + + align:start position:0% +molding machine process point of view + + + align:start position:0% +molding machine process point of view +it's still sort of this fixed input + + align:start position:0% +it's still sort of this fixed input + + + align:start position:0% +it's still sort of this fixed input +process. + + align:start position:0% +process. + + + align:start position:0% +process. +Right? Okay. So that's the important + + align:start position:0% +Right? Okay. So that's the important + + + align:start position:0% +Right? Okay. So that's the important +thing. the dynamics occurs between the + + align:start position:0% +thing. the dynamics occurs between the + + + align:start position:0% +thing. the dynamics occurs between the +cycles not during the cycles. So what + + align:start position:0% +cycles not during the cycles. So what + + + align:start position:0% +cycles not during the cycles. So what +this allows us to do is treat this as a + + align:start position:0% +this allows us to do is treat this as a + + + align:start position:0% +this allows us to do is treat this as a +very simple digital control system or + + align:start position:0% +very simple digital control system or + + + align:start position:0% +very simple digital control system or +discrete control system. So in in + + align:start position:0% +discrete control system. So in in + + + align:start position:0% +discrete control system. So in in +discrete control theory concepts things + + align:start position:0% +discrete control theory concepts things + + + align:start position:0% +discrete control theory concepts things +only happen at an instantaneous period + + align:start position:0% +only happen at an instantaneous period + + + align:start position:0% +only happen at an instantaneous period +in time. Nothing happens in between. So + + align:start position:0% +in time. Nothing happens in between. So + + + align:start position:0% +in time. Nothing happens in between. So +we've got a nice match between the + + align:start position:0% +we've got a nice match between the + + + align:start position:0% +we've got a nice match between the +theory and what's actually + + align:start position:0% +theory and what's actually + + + align:start position:0% +theory and what's actually +happening. Okay? And so we execute this + + align:start position:0% +happening. Okay? And so we execute this + + + align:start position:0% +happening. Okay? And so we execute this +loop once every cycle. Now you may be + + align:start position:0% +loop once every cycle. Now you may be + + + align:start position:0% +loop once every cycle. Now you may be +saying, geez, you know, do we have to uh + + align:start position:0% +saying, geez, you know, do we have to uh + + + align:start position:0% +saying, geez, you know, do we have to uh +measure it after every cycle? What about + + align:start position:0% +measure it after every cycle? What about + + + align:start position:0% +measure it after every cycle? What about +every tenth cycle? You know, maybe it's + + align:start position:0% +every tenth cycle? You know, maybe it's + + + align:start position:0% +every tenth cycle? You know, maybe it's +going to take too much time to make the + + align:start position:0% +going to take too much time to make the + + + align:start position:0% +going to take too much time to make the +measurement and slow the process down + + align:start position:0% +measurement and slow the process down + + + align:start position:0% +measurement and slow the process down +and so on. Fine. We can put those + + align:start position:0% +and so on. Fine. We can put those + + + align:start position:0% +and so on. Fine. We can put those +multipliers in, but the fastest we could + + align:start position:0% +multipliers in, but the fastest we could + + + align:start position:0% +multipliers in, but the fastest we could +ever do it would be one cycle, one + + align:start position:0% +ever do it would be one cycle, one + + + align:start position:0% +ever do it would be one cycle, one +measurement per cycle. Okay. Well, this + + align:start position:0% +measurement per cycle. Okay. Well, this + + + align:start position:0% +measurement per cycle. Okay. Well, this +is where we found out that we'd + + align:start position:0% +is where we found out that we'd + + + align:start position:0% +is where we found out that we'd +reinvented the wheel or uninvented the + + align:start position:0% +reinvented the wheel or uninvented the + + + align:start position:0% +reinvented the wheel or uninvented the +wheel or something like that. Um within + + align:start position:0% +wheel or something like that. Um within + + + align:start position:0% +wheel or something like that. Um within +the semiconductor industry uh uh there's + + align:start position:0% +the semiconductor industry uh uh there's + + + align:start position:0% +the semiconductor industry uh uh there's +this concept of run by run control where + + align:start position:0% +this concept of run by run control where + + + align:start position:0% +this concept of run by run control where +you've got a recipe you run the process + + align:start position:0% +you've got a recipe you run the process + + + align:start position:0% +you've got a recipe you run the process +you make a measurement you say it's not + + align:start position:0% +you make a measurement you say it's not + + + align:start position:0% +you make a measurement you say it's not +right let's change the recipe that sort + + align:start position:0% +right let's change the recipe that sort + + + align:start position:0% +right let's change the recipe that sort +of thing it's given the title run by run + + align:start position:0% +of thing it's given the title run by run + + + align:start position:0% +of thing it's given the title run by run +control um and I think even if you look + + align:start position:0% +control um and I think even if you look + + + align:start position:0% +control um and I think even if you look +in the text on Montgomery and I don't + + align:start position:0% +in the text on Montgomery and I don't + + + align:start position:0% +in the text on Montgomery and I don't +remember what uh chapter it's in there's + + align:start position:0% +remember what uh chapter it's in there's + + + align:start position:0% +remember what uh chapter it's in there's +something in there about forgotten the + + align:start position:0% +something in there about forgotten the + + + align:start position:0% +something in there about forgotten the +term he used I think he calls it + + align:start position:0% +term he used I think he calls it + + + align:start position:0% +term he used I think he calls it +feedback control but there is some + + align:start position:0% +feedback control but there is some + + + align:start position:0% +feedback control but there is some +discussion of this uh and there are some + + align:start position:0% +discussion of this uh and there are some + + + align:start position:0% +discussion of this uh and there are some +larger theoretical uh trackcts around + + align:start position:0% +larger theoretical uh trackcts around + + + align:start position:0% +larger theoretical uh trackcts around +that talk about you know the concept of + + align:start position:0% +that talk about you know the concept of + + + align:start position:0% +that talk about you know the concept of +a discrete control system uh like + + align:start position:0% +a discrete control system uh like + + + align:start position:0% +a discrete control system uh like +this. So what is it we're really trying + + align:start position:0% +this. So what is it we're really trying + + + align:start position:0% +this. So what is it we're really trying +to do? Well to use again the terminology + + align:start position:0% +to do? Well to use again the terminology + + + align:start position:0% +to do? Well to use again the terminology +of the class we would like to reduce the + + align:start position:0% +of the class we would like to reduce the + + + align:start position:0% +of the class we would like to reduce the +expected loss function or increase a a + + align:start position:0% +expected loss function or increase a a + + + align:start position:0% +expected loss function or increase a a +measure of process capability with + + align:start position:0% +measure of process capability with + + + align:start position:0% +measure of process capability with +feedback. Okay. So ultimately as I said + + align:start position:0% +feedback. Okay. So ultimately as I said + + + align:start position:0% +feedback. Okay. So ultimately as I said +if if our goal is to go say from if we + + align:start position:0% +if if our goal is to go say from if we + + + align:start position:0% +if if our goal is to go say from if we +have + + align:start position:0% +have + + + align:start position:0% +have +a target that looks like that. And we + + align:start position:0% +a target that looks like that. And we + + + align:start position:0% +a target that looks like that. And we +have a process that's, you + + align:start position:0% +have a process that's, you + + + align:start position:0% +have a process that's, you +know, over here somewhere. Oops, it's + + align:start position:0% +know, over here somewhere. Oops, it's + + + align:start position:0% +know, over here somewhere. Oops, it's +not very gassy + + align:start position:0% + + + + align:start position:0% + +looking. If we + + align:start position:0% +looking. If we + + + align:start position:0% +looking. If we +can make the process look more like + + align:start position:0% +can make the process look more like + + + align:start position:0% +can make the process look more like +that, we will have in increased our + + align:start position:0% +that, we will have in increased our + + + align:start position:0% +that, we will have in increased our +process capability or decreased our + + align:start position:0% +process capability or decreased our + + + align:start position:0% +process capability or decreased our +process, our expected loss. And we can + + align:start position:0% +process, our expected loss. And we can + + + align:start position:0% +process, our expected loss. And we can +think of that again with our two major + + align:start position:0% +think of that again with our two major + + + align:start position:0% +think of that again with our two major +goals. One is to to reduce mean shift to + + align:start position:0% +goals. One is to to reduce mean shift to + + + align:start position:0% +goals. One is to to reduce mean shift to +zero if possible and decrease the + + align:start position:0% +zero if possible and decrease the + + + align:start position:0% +zero if possible and decrease the +variance. Now this is a bit of a + + align:start position:0% +variance. Now this is a bit of a + + + align:start position:0% +variance. Now this is a bit of a +um um high u + + align:start position:0% + + + + align:start position:0% + +um I can't think the word I'm trying to + + align:start position:0% +um I can't think the word I'm trying to + + + align:start position:0% +um I can't think the word I'm trying to +come up with. Anyway, it's uh we're + + align:start position:0% +come up with. Anyway, it's uh we're + + + align:start position:0% +come up with. Anyway, it's uh we're +looking to the future of what's going to + + align:start position:0% +looking to the future of what's going to + + + align:start position:0% +looking to the future of what's going to +happen with the results here. + + align:start position:0% +happen with the results here. + + + align:start position:0% +happen with the results here. +Um, what if I have a process that's over + + align:start position:0% +Um, what if I have a process that's over + + + align:start position:0% +Um, what if I have a process that's over +here and I'm able to recenter it without + + align:start position:0% +here and I'm able to recenter it without + + + align:start position:0% +here and I'm able to recenter it without +reducing the variance? Is that a good + + align:start position:0% +reducing the variance? Is that a good + + + align:start position:0% +reducing the variance? Is that a good +thing? Yeah. Okay. What if I have a + + align:start position:0% +thing? Yeah. Okay. What if I have a + + + align:start position:0% +thing? Yeah. Okay. What if I have a +process over here and all I can do is + + align:start position:0% +process over here and all I can do is + + + align:start position:0% +process over here and all I can do is +recenter it? I can recenter it, but at + + align:start position:0% +recenter it? I can recenter it, but at + + + align:start position:0% +recenter it? I can recenter it, but at +the cost of increasing the variance. Is + + align:start position:0% +the cost of increasing the variance. Is + + + align:start position:0% +the cost of increasing the variance. Is +that a good + + align:start position:0% +that a good + + + align:start position:0% +that a good +thing? Well, that sort of depends, + + align:start position:0% +thing? Well, that sort of depends, + + + align:start position:0% +thing? Well, that sort of depends, +right? If it I mean, if I I didn't tell + + align:start position:0% +right? If it I mean, if I I didn't tell + + + align:start position:0% +right? If it I mean, if I I didn't tell +you how much I'm going to increase it. + + align:start position:0% +you how much I'm going to increase it. + + + align:start position:0% +you how much I'm going to increase it. +If I increase it by a factor of 10, + + align:start position:0% +If I increase it by a factor of 10, + + + align:start position:0% +If I increase it by a factor of 10, +you'd probably say it's no good. And + + align:start position:0% +you'd probably say it's no good. And + + + align:start position:0% +you'd probably say it's no good. And +what if I could move it over here, + + align:start position:0% +what if I could move it over here, + + + align:start position:0% +what if I could move it over here, +center the process, and reduce the + + align:start position:0% +center the process, and reduce the + + + align:start position:0% +center the process, and reduce the +variance at the same time? Of course, + + align:start position:0% +variance at the same time? Of course, + + + align:start position:0% +variance at the same time? Of course, +why wouldn't that be great? Okay, so + + align:start position:0% +why wouldn't that be great? Okay, so + + + align:start position:0% +why wouldn't that be great? Okay, so +we're going to kind of think of those as + + align:start position:0% +we're going to kind of think of those as + + + align:start position:0% +we're going to kind of think of those as +uh as + + align:start position:0% +uh as + + + align:start position:0% +uh as +objectives. Now, we have to go through + + align:start position:0% +objectives. Now, we have to go through + + + align:start position:0% +objectives. Now, we have to go through +this to + + align:start position:0% +this to + + + align:start position:0% +this to +understand the derivation. + + align:start position:0% +understand the derivation. + + + align:start position:0% +understand the derivation. +Um, and uh I'm the punchline that I'm + + align:start position:0% +Um, and uh I'm the punchline that I'm + + + align:start position:0% +Um, and uh I'm the punchline that I'm +going to come to is, hey, we can + + align:start position:0% +going to come to is, hey, we can + + + align:start position:0% +going to come to is, hey, we can +actually do two of those three. I can + + align:start position:0% +actually do two of those three. I can + + + align:start position:0% +actually do two of those three. I can +I'm going to show you that we can center + + align:start position:0% +I'm going to show you that we can center + + + align:start position:0% +I'm going to show you that we can center +this guarantee it. I love that. Don't + + align:start position:0% +this guarantee it. I love that. Don't + + + align:start position:0% +this guarantee it. I love that. Don't +seldom get to say that. I seldom get to + + align:start position:0% +seldom get to say that. I seldom get to + + + align:start position:0% +seldom get to say that. I seldom get to +say that. But we can guarantee that we + + align:start position:0% +say that. But we can guarantee that we + + + align:start position:0% +say that. But we can guarantee that we +can center it virtually under any + + align:start position:0% +can center it virtually under any + + + align:start position:0% +can center it virtually under any +circumstance. And we can't even tell you + + align:start position:0% +circumstance. And we can't even tell you + + + align:start position:0% +circumstance. And we can't even tell you +how long it will take to center + + align:start position:0% +how long it will take to center + + + align:start position:0% +how long it will take to center +it. + + align:start position:0% +it. + + + align:start position:0% +it. +Um how many cycles can always do that + + align:start position:0% +Um how many cycles can always do that + + + align:start position:0% +Um how many cycles can always do that +and then there'll be two extremes. In + + align:start position:0% +and then there'll be two extremes. In + + + align:start position:0% +and then there'll be two extremes. In +one extreme I can center it but I will + + align:start position:0% +one extreme I can center it but I will + + + align:start position:0% +one extreme I can center it but I will +always increase the variance. + + align:start position:0% +always increase the variance. + + + align:start position:0% +always increase the variance. +but by a well established bounded + + align:start position:0% +but by a well established bounded + + + align:start position:0% +but by a well established bounded +amount. So it's not going to be one day + + align:start position:0% +amount. So it's not going to be one day + + + align:start position:0% +amount. So it's not going to be one day +20 times, another day two times, that + + align:start position:0% +20 times, another day two times, that + + + align:start position:0% +20 times, another day two times, that +sort of thing. We tell you exactly how + + align:start position:0% +sort of thing. We tell you exactly how + + + align:start position:0% +sort of thing. We tell you exactly how +much it is. And in the other case, the + + align:start position:0% +much it is. And in the other case, the + + + align:start position:0% +much it is. And in the other case, the +better one, of course, I can center it + + align:start position:0% +better one, of course, I can center it + + + align:start position:0% +better one, of course, I can center it +and reduce the + + align:start position:0% +and reduce the + + + align:start position:0% +and reduce the +variance. Okay. Now, the the naysayers + + align:start position:0% +variance. Okay. Now, the the naysayers + + + align:start position:0% +variance. Okay. Now, the the naysayers +that we talked about earlier who would + + align:start position:0% +that we talked about earlier who would + + + align:start position:0% +that we talked about earlier who would +say, "Oh, don't adjust the process. + + align:start position:0% +say, "Oh, don't adjust the process. + + + align:start position:0% +say, "Oh, don't adjust the process. +It'll only get worse." We're right in + + align:start position:0% +It'll only get worse." We're right in + + + align:start position:0% +It'll only get worse." We're right in +the sense that if I adjust the process + + align:start position:0% +the sense that if I adjust the process + + + align:start position:0% +the sense that if I adjust the process +and center the mean but increase the + + align:start position:0% +and center the mean but increase the + + + align:start position:0% +and center the mean but increase the +variance, you know, by one measure of + + align:start position:0% +variance, you know, by one measure of + + + align:start position:0% +variance, you know, by one measure of +goodness, things have gotten worse, + + align:start position:0% +goodness, things have gotten worse, + + + align:start position:0% +goodness, things have gotten worse, +right? It's it's got more variability. + + align:start position:0% +right? It's it's got more variability. + + + align:start position:0% +right? It's it's got more variability. +Um, and we can see more heristically + + align:start position:0% +Um, and we can see more heristically + + + align:start position:0% +Um, and we can see more heristically +than theoretically why that in fact has + + align:start position:0% +than theoretically why that in fact has + + + align:start position:0% +than theoretically why that in fact has +to be true. But, um, uh, again, if it's + + align:start position:0% +to be true. But, um, uh, again, if it's + + + align:start position:0% +to be true. But, um, uh, again, if it's +bounded and we know what's going on, + + align:start position:0% +bounded and we know what's going on, + + + align:start position:0% +bounded and we know what's going on, +maybe it's it's better. Maybe it's a lot + + align:start position:0% +maybe it's it's better. Maybe it's a lot + + + align:start position:0% +maybe it's it's better. Maybe it's a lot +better. Okay. So, how do we actually get + + align:start position:0% +better. Okay. So, how do we actually get + + + align:start position:0% +better. Okay. So, how do we actually get +to use this? And I'm going to go through + + align:start position:0% +to use this? And I'm going to go through + + + align:start position:0% +to use this? And I'm going to go through +this real quickly because again, if if + + align:start position:0% +this real quickly because again, if if + + + align:start position:0% +this real quickly because again, if if +you guys have seen feedback control uh + + align:start position:0% +you guys have seen feedback control uh + + + align:start position:0% +you guys have seen feedback control uh +in its basics, you probably did it for + + align:start position:0% +in its basics, you probably did it for + + + align:start position:0% +in its basics, you probably did it for +continuous systems and that doesn't + + align:start position:0% +continuous systems and that doesn't + + + align:start position:0% +continuous systems and that doesn't +really give you that much insight into + + align:start position:0% +really give you that much insight into + + + align:start position:0% +really give you that much insight into +what we're going to be doing here. So, + + align:start position:0% +what we're going to be doing here. So, + + + align:start position:0% +what we're going to be doing here. So, +uh and there's some a couple uh + + align:start position:0% +uh and there's some a couple uh + + + align:start position:0% +uh and there's some a couple uh +derivations here which I will just zip + + align:start position:0% +derivations here which I will just zip + + + align:start position:0% +derivations here which I will just zip +through and and assume if you're + + align:start position:0% +through and and assume if you're + + + align:start position:0% +through and and assume if you're +interested, you can go back and look at + + align:start position:0% +interested, you can go back and look at + + + align:start position:0% +interested, you can go back and look at +the notes. Oh, yeah. Before I + + align:start position:0% +the notes. Oh, yeah. Before I + + + align:start position:0% +the notes. Oh, yeah. Before I +forget, uh because I won't don't want to + + align:start position:0% +forget, uh because I won't don't want to + + + align:start position:0% +forget, uh because I won't don't want to +wait till the punchline at the end. Um + + align:start position:0% +wait till the punchline at the end. Um + + + align:start position:0% +wait till the punchline at the end. Um +there are two papers that I've put on + + align:start position:0% +there are two papers that I've put on + + + align:start position:0% +there are two papers that I've put on +the + + align:start position:0% +the + + + align:start position:0% +the +uh website that basically recite the + + align:start position:0% +uh website that basically recite the + + + align:start position:0% +uh website that basically recite the +what we're talking about what I'm + + align:start position:0% +what we're talking about what I'm + + + align:start position:0% +what we're talking about what I'm +talking about here. A paper that George + + align:start position:0% +talking about here. A paper that George + + + align:start position:0% +talking about here. A paper that George +Sue and and I authored u several years + + align:start position:0% +Sue and and I authored u several years + + + align:start position:0% +Sue and and I authored u several years +back. Well, George did his master's + + align:start position:0% +back. Well, George did his master's + + + align:start position:0% +back. Well, George did his master's +thesis on this whole topic. He was a + + align:start position:0% +thesis on this whole topic. He was a + + + align:start position:0% +thesis on this whole topic. He was a +2830 student the year I kind of made up + + align:start position:0% +2830 student the year I kind of made up + + + align:start position:0% +2830 student the year I kind of made up +this lecture. + + align:start position:0% +this lecture. + + + align:start position:0% +this lecture. +uh actually was a whole section of the + + align:start position:0% +uh actually was a whole section of the + + + align:start position:0% +uh actually was a whole section of the +class back then and he u he said hey + + align:start position:0% +class back then and he u he said hey + + + align:start position:0% +class back then and he u he said hey +that would be interesting can I do a + + align:start position:0% +that would be interesting can I do a + + + align:start position:0% +that would be interesting can I do a +master's thesis on I said yes and he did + + align:start position:0% +master's thesis on I said yes and he did + + + align:start position:0% +master's thesis on I said yes and he did +and that's a lot of the results I'm + + align:start position:0% +and that's a lot of the results I'm + + + align:start position:0% +and that's a lot of the results I'm +going to talk about today uh are on that + + align:start position:0% +going to talk about today uh are on that + + + align:start position:0% +going to talk about today uh are on that +and then + + align:start position:0% +and then + + + align:start position:0% +and then +um we had a particular problem in + + align:start position:0% +um we had a particular problem in + + + align:start position:0% +um we had a particular problem in +our oh great I just I just erased it + + align:start position:0% +our oh great I just I just erased it + + + align:start position:0% +our oh great I just I just erased it +well there's a second paper that's on + + align:start position:0% +well there's a second paper that's on + + + align:start position:0% +well there's a second paper that's on +there that Adam Janeski uh did with me + + align:start position:0% +there that Adam Janeski uh did with me + + + align:start position:0% +there that Adam Janeski uh did with me +based on his PhD and + + align:start position:0% +based on his PhD and + + + align:start position:0% +based on his PhD and +Um Adam was also a student in the class + + align:start position:0% +Um Adam was also a student in the class + + + align:start position:0% +Um Adam was also a student in the class +also TA in the class and he uh wanted to + + align:start position:0% +also TA in the class and he uh wanted to + + + align:start position:0% +also TA in the class and he uh wanted to +say well what happens if I have a really + + align:start position:0% +say well what happens if I have a really + + + align:start position:0% +say well what happens if I have a really +big complicated process instead of + + align:start position:0% +big complicated process instead of + + + align:start position:0% +big complicated process instead of +having one input and one output maybe it + + align:start position:0% +having one input and one output maybe it + + + align:start position:0% +having one input and one output maybe it +had um had thousand inputs and a + + align:start position:0% +had um had thousand inputs and a + + + align:start position:0% +had um had thousand inputs and a +thousand outputs because we happen to + + align:start position:0% +thousand outputs because we happen to + + + align:start position:0% +thousand outputs because we happen to +have one in our lab that fit that. We + + align:start position:0% +have one in our lab that fit that. We + + + align:start position:0% +have one in our lab that fit that. We +said maybe we could make it work for + + align:start position:0% +said maybe we could make it work for + + + align:start position:0% +said maybe we could make it work for +this. So he did the extension to that + + align:start position:0% +this. So he did the extension to that + + + align:start position:0% +this. So he did the extension to that +and that paper um is a very brief + + align:start position:0% +and that paper um is a very brief + + + align:start position:0% +and that paper um is a very brief +version of of uh what happens when you + + align:start position:0% +version of of uh what happens when you + + + align:start position:0% +version of of uh what happens when you +try to extend it beyond what I've + + align:start position:0% + + + + align:start position:0% + +done. So but it all requires that we go + + align:start position:0% +done. So but it all requires that we go + + + align:start position:0% +done. So but it all requires that we go +through a little bit of the + + align:start position:0% +through a little bit of the + + + align:start position:0% +through a little bit of the +theory. + + align:start position:0% +theory. + + + align:start position:0% +theory. +So what am I trying to represent with + + align:start position:0% +So what am I trying to represent with + + + align:start position:0% +So what am I trying to represent with +this diagram? I'll give you guys a test + + align:start position:0% +this diagram? I'll give you guys a test + + + align:start position:0% +this diagram? I'll give you guys a test +of your of your uh control background. + + align:start position:0% +of your of your uh control background. + + + align:start position:0% +of your of your uh control background. +What what what is this + + align:start position:0% + + + + align:start position:0% + +Richard response? Yeah, this is this is + + align:start position:0% +Richard response? Yeah, this is this is + + + align:start position:0% +Richard response? Yeah, this is this is +like a classical highly uh um simplified + + align:start position:0% +like a classical highly uh um simplified + + + align:start position:0% +like a classical highly uh um simplified +example of a the simplest dynamic system + + align:start position:0% +example of a the simplest dynamic system + + + align:start position:0% +example of a the simplest dynamic system +you can have. Um and in the lexicon of + + align:start position:0% +you can have. Um and in the lexicon of + + + align:start position:0% +you can have. Um and in the lexicon of +our class here, I've made a step change + + align:start position:0% +our class here, I've made a step change + + + align:start position:0% +our class here, I've made a step change +to an input. You know, I instantaneously + + align:start position:0% +to an input. You know, I instantaneously + + + align:start position:0% +to an input. You know, I instantaneously +changed a pressure, temperature, feed, + + align:start position:0% +changed a pressure, temperature, feed, + + + align:start position:0% +changed a pressure, temperature, feed, +something like that. And what does the + + align:start position:0% +something like that. And what does the + + + align:start position:0% +something like that. And what does the +output do? Well, in real systems, they + + align:start position:0% +output do? Well, in real systems, they + + + align:start position:0% +output do? Well, in real systems, they +don't change instantaneously. They they + + align:start position:0% +don't change instantaneously. They they + + + align:start position:0% +don't change instantaneously. They they +have dynamics, right? And the simplest + + align:start position:0% +have dynamics, right? And the simplest + + + align:start position:0% +have dynamics, right? And the simplest +dynamics would be something like this, a + + align:start position:0% +dynamics would be something like this, a + + + align:start position:0% +dynamics would be something like this, a +simple lag. Uh this would be a first + + align:start position:0% +simple lag. Uh this would be a first + + + align:start position:0% +simple lag. Uh this would be a first +order linear system. And it takes four + + align:start position:0% +order linear system. And it takes four + + + align:start position:0% +order linear system. And it takes four +time constants to settle out. And so + + align:start position:0% +time constants to settle out. And so + + + align:start position:0% +time constants to settle out. And so +there's an important number here, which + + align:start position:0% +there's an important number here, which + + + align:start position:0% +there's an important number here, which +is the the what I'll call the process + + align:start position:0% +is the the what I'll call the process + + + align:start position:0% +is the the what I'll call the process +time constant. How long does it take the + + align:start position:0% +time constant. How long does it take the + + + align:start position:0% +time constant. How long does it take the +process to reach steady state after + + align:start position:0% +process to reach steady state after + + + align:start position:0% +process to reach steady state after +you've made a change to it? That's going + + align:start position:0% +you've made a change to it? That's going + + + align:start position:0% +you've made a change to it? That's going +to become an important number for us. + + align:start position:0% +to become an important number for us. + + + align:start position:0% +to become an important number for us. +Um, and then we have the disturbance, + + align:start position:0% +Um, and then we have the disturbance, + + + align:start position:0% +Um, and then we have the disturbance, +which would be our randomness and that + + align:start position:0% +which would be our randomness and that + + + align:start position:0% +which would be our randomness and that +sort of thing. But, um, why do I care + + align:start position:0% +sort of thing. But, um, why do I care + + + align:start position:0% +sort of thing. But, um, why do I care +about this steady state number? Why do I + + align:start position:0% +about this steady state number? Why do I + + + align:start position:0% +about this steady state number? Why do I +put this number four times the time + + align:start position:0% +put this number four times the time + + + align:start position:0% +put this number four times the time +constant of there? Why do you think + + align:start position:0% +constant of there? Why do you think + + + align:start position:0% +constant of there? Why do you think +given given where we're going, we're + + align:start position:0% +given given where we're going, we're + + + align:start position:0% +given given where we're going, we're +only going to look at the process after + + align:start position:0% +only going to look at the process after + + + align:start position:0% +only going to look at the process after +it's done, we're only going to make a + + align:start position:0% +it's done, we're only going to make a + + + align:start position:0% +it's done, we're only going to make a +change between the + + align:start position:0% + + + + align:start position:0% + +processes. I'm only going to look at the + + align:start position:0% +processes. I'm only going to look at the + + + align:start position:0% +processes. I'm only going to look at the +output. Think of it. We're going to talk + + align:start position:0% +output. Think of it. We're going to talk + + + align:start position:0% +output. Think of it. We're going to talk +about a sampler in just a second. And + + align:start position:0% +about a sampler in just a second. And + + + align:start position:0% +about a sampler in just a second. And +sampler is an is a a a mathematical + + align:start position:0% +sampler is an is a a a mathematical + + + align:start position:0% +sampler is an is a a a mathematical +concept in effect based on a delta + + align:start position:0% +concept in effect based on a delta + + + align:start position:0% +concept in effect based on a delta +function that says here here's a + + align:start position:0% +function that says here here's a + + + align:start position:0% +function that says here here's a +continuous number. I'm going to look at + + align:start position:0% +continuous number. I'm going to look at + + + align:start position:0% +continuous number. I'm going to look at +it. I'm going to sample it and look at + + align:start position:0% +it. I'm going to sample it and look at + + + align:start position:0% +it. I'm going to sample it and look at +it for an infantessimally small period + + align:start position:0% +it for an infantessimally small period + + + align:start position:0% +it for an infantessimally small period +of time. So I'm going to do this to the + + align:start position:0% +of time. So I'm going to do this to the + + + align:start position:0% +of time. So I'm going to do this to the +output. So I'm going to make a change. + + align:start position:0% +output. So I'm going to make a change. + + + align:start position:0% +output. So I'm going to make a change. +Then I'm going to sample the output. + + align:start position:0% +Then I'm going to sample the output. + + + align:start position:0% +Then I'm going to sample the output. +When do I want to sample the output? + + align:start position:0% +When do I want to sample the output? + + + align:start position:0% +When do I want to sample the output? +After it's stabilized. Okay. All right. + + align:start position:0% +After it's stabilized. Okay. All right. + + + align:start position:0% +After it's stabilized. Okay. All right. +So conceptually if I have a process that + + align:start position:0% +So conceptually if I have a process that + + + align:start position:0% +So conceptually if I have a process that +has this speed to it and I make sure I + + align:start position:0% +has this speed to it and I make sure I + + + align:start position:0% +has this speed to it and I make sure I +always sample it after it's reached this + + align:start position:0% +always sample it after it's reached this + + + align:start position:0% +always sample it after it's reached this +steady state after a stepwise + + align:start position:0% +steady state after a stepwise + + + align:start position:0% +steady state after a stepwise +change what does the process look like + + align:start position:0% +change what does the process look like + + + align:start position:0% +change what does the process look like +from an input output point of + + align:start position:0% +from an input output point of + + + align:start position:0% +from an input output point of +view constant input gives me a constant + + align:start position:0% +view constant input gives me a constant + + + align:start position:0% +view constant input gives me a constant +output I don't see any dynamics right I + + align:start position:0% +output I don't see any dynamics right I + + + align:start position:0% +output I don't see any dynamics right I +don't see any of this stuff in between + + align:start position:0% +don't see any of this stuff in between + + + align:start position:0% +don't see any of this stuff in between +and can you see that then if I looked at + + align:start position:0% +and can you see that then if I looked at + + + align:start position:0% +and can you see that then if I looked at +a lot of different inputs let them all + + align:start position:0% +a lot of different inputs let them all + + + align:start position:0% +a lot of different inputs let them all +go to steady Let the output all go to + + align:start position:0% +go to steady Let the output all go to + + + align:start position:0% +go to steady Let the output all go to +steady state. Looks at all the sample + + align:start position:0% +steady state. Looks at all the sample + + + align:start position:0% +steady state. Looks at all the sample +ones. I'd basically have a bunch of + + align:start position:0% +ones. I'd basically have a bunch of + + + align:start position:0% +ones. I'd basically have a bunch of +inputs, a bunch of outputs. And what + + align:start position:0% +inputs, a bunch of outputs. And what + + + align:start position:0% +inputs, a bunch of outputs. And what +would be the simplest relationship + + align:start position:0% +would be the simplest relationship + + + align:start position:0% +would be the simplest relationship +between those + + align:start position:0% + + + + align:start position:0% + +two? You just did your designed + + align:start position:0% +two? You just did your designed + + + align:start position:0% +two? You just did your designed +experiments. What's the simplest + + align:start position:0% +experiments. What's the simplest + + + align:start position:0% +experiments. What's the simplest +relationship that you could have between + + align:start position:0% +relationship that you could have between + + + align:start position:0% +relationship that you could have between +a single input and a single + + align:start position:0% +a single input and a single + + + align:start position:0% +a single input and a single +output? Yeah, straight line, linear fit. + + align:start position:0% +output? Yeah, straight line, linear fit. + + + align:start position:0% +output? Yeah, straight line, linear fit. +And that's a great first place for us to + + align:start position:0% +And that's a great first place for us to + + + align:start position:0% +And that's a great first place for us to +start with this model. So the nice thing + + align:start position:0% +start with this model. So the nice thing + + + align:start position:0% +start with this model. So the nice thing +is with this cycleto cycle control I can + + align:start position:0% +is with this cycleto cycle control I can + + + align:start position:0% +is with this cycleto cycle control I can +take a process that could be in fact a + + align:start position:0% +take a process that could be in fact a + + + align:start position:0% +take a process that could be in fact a +lot more complicated by this than this + + align:start position:0% +lot more complicated by this than this + + + align:start position:0% +lot more complicated by this than this +and just say sorry I can reduce it down + + align:start position:0% +and just say sorry I can reduce it down + + + align:start position:0% +and just say sorry I can reduce it down +to I hope it's my next + + align:start position:0% +to I hope it's my next + + + align:start position:0% +to I hope it's my next +slide. I hope this thing will + + align:start position:0% + + + + align:start position:0% + +work. + + align:start position:0% +work. + + + align:start position:0% +work. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and me just I'm going to skip through + + align:start position:0% +and me just I'm going to skip through + + + align:start position:0% +and me just I'm going to skip through +all this. Um well this is just this + + align:start position:0% +all this. Um well this is just this + + + align:start position:0% +all this. Um well this is just this +diagram says that what what's in fact + + align:start position:0% +diagram says that what what's in fact + + + align:start position:0% +diagram says that what what's in fact +maybe happening with the process is that + + align:start position:0% +maybe happening with the process is that + + + align:start position:0% +maybe happening with the process is that +I make a change at a particular time it + + align:start position:0% +I make a change at a particular time it + + + align:start position:0% +I make a change at a particular time it +comes to ste up to steady state but I + + align:start position:0% +comes to ste up to steady state but I + + + align:start position:0% +comes to ste up to steady state but I +sample it here here here and here and + + align:start position:0% +sample it here here here and here and + + + align:start position:0% +sample it here here here and here and +all that mess in between I'm unaware + + align:start position:0% +all that mess in between I'm unaware + + + align:start position:0% +all that mess in between I'm unaware +of I don't care + + align:start position:0% +of I don't care + + + align:start position:0% +of I don't care +about and what I can do now is reduce + + align:start position:0% +about and what I can do now is reduce + + + align:start position:0% +about and what I can do now is reduce +the whole process down to a to a single + + align:start position:0% +the whole process down to a to a single + + + align:start position:0% +the whole process down to a to a single +number and I don't even have to worry + + align:start position:0% +number and I don't even have to worry + + + align:start position:0% +number and I don't even have to worry +the nice thing is I don't need to go + + align:start position:0% +the nice thing is I don't need to go + + + align:start position:0% +the nice thing is I don't need to go +into this right now I don't even need to + + align:start position:0% +into this right now I don't even need to + + + align:start position:0% +into this right now I don't even need to +worry about the offset. You know, you + + align:start position:0% +worry about the offset. You know, you + + + align:start position:0% +worry about the offset. You know, you +think of a of a straight line fit, you + + align:start position:0% +think of a of a straight line fit, you + + + align:start position:0% +think of a of a straight line fit, you +know, you've got the slope and the + + align:start position:0% +know, you've got the slope and the + + + align:start position:0% +know, you've got the slope and the +offset. In the approach that that we + + align:start position:0% +offset. In the approach that that we + + + align:start position:0% +offset. In the approach that that we +take here with cycle to cycle, I don't + + align:start position:0% +take here with cycle to cycle, I don't + + + align:start position:0% +take here with cycle to cycle, I don't +even care about the offset. In run by + + align:start position:0% +even care about the offset. In run by + + + align:start position:0% +even care about the offset. In run by +run, they do, but it turns turns out it + + align:start position:0% +run, they do, but it turns turns out it + + + align:start position:0% +run, they do, but it turns turns out it +comes out in the wash anyway. So now all + + align:start position:0% +comes out in the wash anyway. So now all + + + align:start position:0% +comes out in the wash anyway. So now all +I need to know about the process is an + + align:start position:0% +I need to know about the process is an + + + align:start position:0% +I need to know about the process is an +input output relationship between but + + align:start position:0% +input output relationship between but + + + align:start position:0% +input output relationship between but +it's discreet. It's between a discrete + + align:start position:0% +it's discreet. It's between a discrete + + + align:start position:0% +it's discreet. It's between a discrete +input and an infant at an instant in + + align:start position:0% +input and an infant at an instant in + + + align:start position:0% +input and an infant at an instant in +time and a discrete output. + + align:start position:0% +time and a discrete output. + + + align:start position:0% +time and a discrete output. +So that is a valid model of our process. + + align:start position:0% +So that is a valid model of our process. + + + align:start position:0% +So that is a valid model of our process. +Now the only thing that's questionable + + align:start position:0% +Now the only thing that's questionable + + + align:start position:0% +Now the only thing that's questionable +is what's this number and is it a + + align:start position:0% +is what's this number and is it a + + + align:start position:0% +is what's this number and is it a +constant? In other words, if I run the + + align:start position:0% +constant? In other words, if I run the + + + align:start position:0% +constant? In other words, if I run the +process today, is it one number? Is it + + align:start position:0% +process today, is it one number? Is it + + + align:start position:0% +process today, is it one number? Is it +is it another number? And of + + align:start position:0% +is it another number? And of + + + align:start position:0% +is it another number? And of +course, as you know, we would do a test + + align:start position:0% +course, as you know, we would do a test + + + align:start position:0% +course, as you know, we would do a test +for for uh linearity or maybe it should + + align:start position:0% +for for uh linearity or maybe it should + + + align:start position:0% +for for uh linearity or maybe it should +be maybe it would be better modeled as + + align:start position:0% +be maybe it would be better modeled as + + + align:start position:0% +be maybe it would be better modeled as +quadratic and other stuff like that. uh + + align:start position:0% +quadratic and other stuff like that. uh + + + align:start position:0% +quadratic and other stuff like that. uh +without going into it and again invoking + + align:start position:0% +without going into it and again invoking + + + align:start position:0% +without going into it and again invoking +the linearization properties of a good + + align:start position:0% +the linearization properties of a good + + + align:start position:0% +the linearization properties of a good +control system, it doesn't matter. As + + align:start position:0% +control system, it doesn't matter. As + + + align:start position:0% +control system, it doesn't matter. As +long as we have a pretty good estimate + + align:start position:0% +long as we have a pretty good estimate + + + align:start position:0% +long as we have a pretty good estimate +of it and as long as it's not rapidly + + align:start position:0% +of it and as long as it's not rapidly + + + align:start position:0% +of it and as long as it's not rapidly +changing, uh we're + + align:start position:0% + + + + align:start position:0% + +okay. Okay. So, here's here's ultimately + + align:start position:0% +okay. Okay. So, here's here's ultimately + + + align:start position:0% +okay. Okay. So, here's here's ultimately +our model. We have the process, we have + + align:start position:0% +our model. We have the process, we have + + + align:start position:0% +our model. We have the process, we have +some process uncertainty, and we're + + align:start position:0% +some process uncertainty, and we're + + + align:start position:0% +some process uncertainty, and we're +going to bring that in as a purely + + align:start position:0% +going to bring that in as a purely + + + align:start position:0% +going to bring that in as a purely +additive number because the model I just + + align:start position:0% +additive number because the model I just + + + align:start position:0% +additive number because the model I just +showed you was a deterministic model. + + align:start position:0% +showed you was a deterministic model. + + + align:start position:0% +showed you was a deterministic model. +There was no randomness in it. So it + + align:start position:0% +There was no randomness in it. So it + + + align:start position:0% +There was no randomness in it. So it +obviously doesn't capture what we care + + align:start position:0% +obviously doesn't capture what we care + + + align:start position:0% +obviously doesn't capture what we care +about and I'm going to sample that + + align:start position:0% +about and I'm going to sample that + + + align:start position:0% +about and I'm going to sample that +output compared it compare it to what I + + align:start position:0% +output compared it compare it to what I + + + align:start position:0% +output compared it compare it to what I +want and that'll be my cycle to cycle a + + align:start position:0% +want and that'll be my cycle to cycle a + + + align:start position:0% +want and that'll be my cycle to cycle a +cycle + + align:start position:0% +cycle + + + align:start position:0% +cycle +controller. Um + + align:start position:0% +controller. Um + + + align:start position:0% +controller. Um +now when you get into discrete control + + align:start position:0% +now when you get into discrete control + + + align:start position:0% +now when you get into discrete control +systems one of the things that you can + + align:start position:0% +systems one of the things that you can + + + align:start position:0% +systems one of the things that you can +easily model is the is the idea of a + + align:start position:0% +easily model is the is the idea of a + + + align:start position:0% +easily model is the is the idea of a +pure delay. Obviously if if if I've got + + align:start position:0% +pure delay. Obviously if if if I've got + + + align:start position:0% +pure delay. Obviously if if if I've got +something that happens a given cycle and + + align:start position:0% +something that happens a given cycle and + + + align:start position:0% +something that happens a given cycle and +nothing you know I don't do anything + + align:start position:0% +nothing you know I don't do anything + + + align:start position:0% +nothing you know I don't do anything +until the next cycle of time happens I + + align:start position:0% +until the next cycle of time happens I + + + align:start position:0% +until the next cycle of time happens I +can have the concept of a pure delay as + + align:start position:0% +can have the concept of a pure delay as + + + align:start position:0% +can have the concept of a pure delay as +well something happens here but there's + + align:start position:0% +well something happens here but there's + + + align:start position:0% +well something happens here but there's +no reaction until here or here or here + + align:start position:0% +no reaction until here or here or here + + + align:start position:0% +no reaction until here or here or here +and the theory of uh discrete control + + align:start position:0% +and the theory of uh discrete control + + + align:start position:0% +and the theory of uh discrete control +systems allows you to deal with delays + + align:start position:0% +systems allows you to deal with delays + + + align:start position:0% +systems allows you to deal with delays +very nicely and we have three kinds of + + align:start position:0% +very nicely and we have three kinds of + + + align:start position:0% +very nicely and we have three kinds of +delays in any control system but + + align:start position:0% +delays in any control system but + + + align:start position:0% +delays in any control system but +certainly have them here one is a + + align:start position:0% +certainly have them here one is a + + + align:start position:0% +certainly have them here one is a +measurement delay okay part comes off + + align:start position:0% +measurement delay okay part comes off + + + align:start position:0% +measurement delay okay part comes off +takes me some time to measure it to + + align:start position:0% +takes me some time to measure it to + + + align:start position:0% +takes me some time to measure it to +measure + + align:start position:0% + + + + align:start position:0% + +um because of that measurement delay, + + align:start position:0% +um because of that measurement delay, + + + align:start position:0% +um because of that measurement delay, +there's no way that I can make an + + align:start position:0% +there's no way that I can make an + + + align:start position:0% +there's no way that I can make an +adjustment before the next cycle. Okay? + + align:start position:0% +adjustment before the next cycle. Okay? + + + align:start position:0% +adjustment before the next cycle. Okay? +So, I already have a delay based on + + align:start position:0% +So, I already have a delay based on + + + align:start position:0% +So, I already have a delay based on +that. There's controller + + align:start position:0% +that. There's controller + + + align:start position:0% +that. There's controller +delay, you know, despite well, of + + align:start position:0% +delay, you know, despite well, of + + + align:start position:0% +delay, you know, despite well, of +course, if you're using uh uh fast + + align:start position:0% +course, if you're using uh uh fast + + + align:start position:0% +course, if you're using uh uh fast +computers and that sort of thing, that + + align:start position:0% +computers and that sort of thing, that + + + align:start position:0% +computers and that sort of thing, that +can be made very small, but it does take + + align:start position:0% +can be made very small, but it does take + + + align:start position:0% +can be made very small, but it does take +some time. And if it's a if it's a an + + align:start position:0% +some time. And if it's a if it's a an + + + align:start position:0% +some time. And if it's a if it's a an +operator, a human being, you know, + + align:start position:0% +operator, a human being, you know, + + + align:start position:0% +operator, a human being, you know, +measuring it and then doing a little bit + + align:start position:0% +measuring it and then doing a little bit + + + align:start position:0% +measuring it and then doing a little bit +of pencil work on a pad, there's a delay + + align:start position:0% +of pencil work on a pad, there's a delay + + + align:start position:0% +of pencil work on a pad, there's a delay +associated with that. And then there's a + + align:start position:0% +associated with that. And then there's a + + + align:start position:0% +associated with that. And then there's a +process delay. + + align:start position:0% +process delay. + + + align:start position:0% +process delay. +Uh when can I make uh when can I make + + align:start position:0% +Uh when can I make uh when can I make + + + align:start position:0% +Uh when can I make uh when can I make +the machine when when is the machine + + align:start position:0% +the machine when when is the machine + + + align:start position:0% +the machine when when is the machine +next available to be changed? Okay. So + + align:start position:0% +next available to be changed? Okay. So + + + align:start position:0% +next available to be changed? Okay. So +given all three of these, what do you + + align:start position:0% +given all three of these, what do you + + + align:start position:0% +given all three of these, what do you +think for this model? What do you think + + align:start position:0% +think for this model? What do you think + + + align:start position:0% +think for this model? What do you think +the correct model of delay is for this + + align:start position:0% +the correct model of delay is for this + + + align:start position:0% +the correct model of delay is for this +approach to to uh process control? + + align:start position:0% + + + + align:start position:0% + +Now let me let me preface this with one + + align:start position:0% +Now let me let me preface this with one + + + align:start position:0% +Now let me let me preface this with one +other comment. We have a basic unit of + + align:start position:0% +other comment. We have a basic unit of + + + align:start position:0% +other comment. We have a basic unit of +time here. + + align:start position:0% +time here. + + + align:start position:0% +time here. +Now what's the shortest time other than + + align:start position:0% +Now what's the shortest time other than + + + align:start position:0% +Now what's the shortest time other than +zero? What's the shortest time interval + + align:start position:0% +zero? What's the shortest time interval + + + align:start position:0% +zero? What's the shortest time interval +that's possible that exists in this + + align:start position:0% +that's possible that exists in this + + + align:start position:0% +that's possible that exists in this +approach to the whole uh feedback + + align:start position:0% +approach to the whole uh feedback + + + align:start position:0% +approach to the whole uh feedback +control thing? + + align:start position:0% + + + + align:start position:0% + +The fastest I can do something. + + align:start position:0% + + + + align:start position:0% + +One cycle. Yeah. One cycle. Right. That + + align:start position:0% +One cycle. Yeah. One cycle. Right. That + + + align:start position:0% +One cycle. Yeah. One cycle. Right. That +nothing because nothing exists between + + align:start position:0% +nothing because nothing exists between + + + align:start position:0% +nothing because nothing exists between +cycles. Um when something happens, the + + align:start position:0% +cycles. Um when something happens, the + + + align:start position:0% +cycles. Um when something happens, the +next chance I can do something on uh is + + align:start position:0% +next chance I can do something on uh is + + + align:start position:0% +next chance I can do something on uh is +is a cycle. So this is all kind of time + + align:start position:0% +is a cycle. So this is all kind of time + + + align:start position:0% +is a cycle. So this is all kind of time +independent in terms of real time. It's + + align:start position:0% +independent in terms of real time. It's + + + align:start position:0% +independent in terms of real time. It's +just based on the cycle time of the + + align:start position:0% +just based on the cycle time of the + + + align:start position:0% +just based on the cycle time of the +process. Okay. So given + + align:start position:0% +process. Okay. So given + + + align:start position:0% +process. Okay. So given +this go back to that other question + + align:start position:0% +this go back to that other question + + + align:start position:0% +this go back to that other question +there delays involved in all discrete + + align:start position:0% +there delays involved in all discrete + + + align:start position:0% +there delays involved in all discrete +control system there are delays in this + + align:start position:0% +control system there are delays in this + + + align:start position:0% +control system there are delays in this +conrete control + + align:start position:0% +conrete control + + + align:start position:0% +conrete control +system. How do you think we should model + + align:start position:0% +system. How do you think we should model + + + align:start position:0% +system. How do you think we should model +the delays of a manufacturing process + + align:start position:0% +the delays of a manufacturing process + + + align:start position:0% +the delays of a manufacturing process +for the con for this context of cycleto + + align:start position:0% +for the con for this context of cycleto + + + align:start position:0% +for the con for this context of cycleto +cycle + + align:start position:0% + + + + align:start position:0% + +control and I'll give you the I'll give + + align:start position:0% +control and I'll give you the I'll give + + + align:start position:0% +control and I'll give you the I'll give +you the thought experiment. run the run + + align:start position:0% +you the thought experiment. run the run + + + align:start position:0% +you the thought experiment. run the run +the injection molding machine. Put the + + align:start position:0% +the injection molding machine. Put the + + + align:start position:0% +the injection molding machine. Put the +part on the bench. Measure the part. + + align:start position:0% +part on the bench. Measure the part. + + + align:start position:0% +part on the bench. Measure the part. +Figure out the next control cycle based + + align:start position:0% +Figure out the next control cycle based + + + align:start position:0% +Figure out the next control cycle based +on the algorithm I'm going to come up + + align:start position:0% +on the algorithm I'm going to come up + + + align:start position:0% +on the algorithm I'm going to come up +with. Adjust the machine. Push the + + align:start position:0% +with. Adjust the machine. Push the + + + align:start position:0% +with. Adjust the machine. Push the +button. Run the machine + + align:start position:0% +button. Run the machine + + + align:start position:0% +button. Run the machine +again. That's the delay structure. How + + align:start position:0% +again. That's the delay structure. How + + + align:start position:0% +again. That's the delay structure. How +would you model that delay or or how + + align:start position:0% +would you model that delay or or how + + + align:start position:0% +would you model that delay or or how +many delays or how many machine cycles + + align:start position:0% +many delays or how many machine cycles + + + align:start position:0% +many delays or how many machine cycles +do I need to delay the process? + + align:start position:0% + + + + align:start position:0% + +minimum one a + + align:start position:0% +minimum one a + + + align:start position:0% +minimum one a +half one + + align:start position:0% +half one + + + align:start position:0% +half one +tenth + + align:start position:0% + + + + align:start position:0% + +10 I know I'm not making myself clear + + align:start position:0% +10 I know I'm not making myself clear + + + align:start position:0% +10 I know I'm not making myself clear +here I can see Richard well the the + + align:start position:0% +here I can see Richard well the the + + + align:start position:0% +here I can see Richard well the the +discrete points of time where you're + + align:start position:0% +discrete points of time where you're + + + align:start position:0% +discrete points of time where you're +looking at your process then that you're + + align:start position:0% +looking at your process then that you're + + + align:start position:0% +looking at your process then that you're +actually modeling + + align:start position:0% +actually modeling + + + align:start position:0% +actually modeling +um are probably right when + + align:start position:0% +um are probably right when + + + align:start position:0% +um are probably right when +uh your part comes out kind of. So + + align:start position:0% +uh your part comes out kind of. So + + + align:start position:0% +uh your part comes out kind of. So +you should probably have a delay of one + + align:start position:0% +you should probably have a delay of one + + + align:start position:0% +you should probably have a delay of one +cycle. Exactly. Exactly. If I can + + align:start position:0% +cycle. Exactly. Exactly. If I can + + + align:start position:0% +cycle. Exactly. Exactly. If I can +measure quickly, make a decision quickly + + align:start position:0% +measure quickly, make a decision quickly + + + align:start position:0% +measure quickly, make a decision quickly +and be ready to adjust the machine + + align:start position:0% +and be ready to adjust the machine + + + align:start position:0% +and be ready to adjust the machine +before it's time to push the button. + + align:start position:0% +before it's time to push the button. + + + align:start position:0% +before it's time to push the button. +Then I have built in a one cycle + + align:start position:0% +Then I have built in a one cycle + + + align:start position:0% +Then I have built in a one cycle +delay. The best I could ever do is is + + align:start position:0% +delay. The best I could ever do is is + + + align:start position:0% +delay. The best I could ever do is is +and this this is how you capture it in + + align:start position:0% +and this this is how you capture it in + + + align:start position:0% +and this this is how you capture it in +the theory at least. The whole idea of + + align:start position:0% +the theory at least. The whole idea of + + + align:start position:0% +the theory at least. The whole idea of +cycle to cycle control is I make a + + align:start position:0% +cycle to cycle control is I make a + + + align:start position:0% +cycle to cycle control is I make a +measurement the the next chance I have + + align:start position:0% +measurement the the next chance I have + + + align:start position:0% +measurement the the next chance I have +to intervene on the process is one cycle + + align:start position:0% +to intervene on the process is one cycle + + + align:start position:0% +to intervene on the process is one cycle +later. So you build in a one cycle + + align:start position:0% +later. So you build in a one cycle + + + align:start position:0% +later. So you build in a one cycle +delay. Okay. Why does this make a big + + align:start position:0% +delay. Okay. Why does this make a big + + + align:start position:0% +delay. Okay. Why does this make a big +difference? Well in looking at uh + + align:start position:0% +difference? Well in looking at uh + + + align:start position:0% +difference? Well in looking at uh +discrete time control theory the whole + + align:start position:0% +discrete time control theory the whole + + + align:start position:0% +discrete time control theory the whole +concept of a delay operator is the whole + + align:start position:0% +concept of a delay operator is the whole + + + align:start position:0% +concept of a delay operator is the whole +basis for it. + + align:start position:0% +basis for it. + + + align:start position:0% +basis for it. +Now if you if you uh dig into your deep + + align:start position:0% +Now if you if you uh dig into your deep + + + align:start position:0% +Now if you if you uh dig into your deep +dark pasts on the u uh control system + + align:start position:0% +dark pasts on the u uh control system + + + align:start position:0% +dark pasts on the u uh control system +theory you may have remembered something + + align:start position:0% +theory you may have remembered something + + + align:start position:0% +theory you may have remembered something +called the lelass transform and the + + align:start position:0% +called the lelass transform and the + + + align:start position:0% +called the lelass transform and the +applause operator and all that other + + align:start position:0% +applause operator and all that other + + + align:start position:0% +applause operator and all that other +business which was you which was a way + + align:start position:0% +business which was you which was a way + + + align:start position:0% +business which was you which was a way +of algebraically describing time + + align:start position:0% +of algebraically describing time + + + align:start position:0% +of algebraically describing time +differential equations. What you have + + align:start position:0% +differential equations. What you have + + + align:start position:0% +differential equations. What you have +with a discrete control system is time + + align:start position:0% +with a discrete control system is time + + + align:start position:0% +with a discrete control system is time +difference equations. Things are just + + align:start position:0% +difference equations. Things are just + + + align:start position:0% +difference equations. Things are just +sums of of uh inputs and outputs at + + align:start position:0% +sums of of uh inputs and outputs at + + + align:start position:0% +sums of of uh inputs and outputs at +different intervals of time. There's an + + align:start position:0% +different intervals of time. There's an + + + align:start position:0% +different intervals of time. There's an +equivalent to that operator which is + + align:start position:0% +equivalent to that operator which is + + + align:start position:0% +equivalent to that operator which is +called uh the z + + align:start position:0% +called uh the z + + + align:start position:0% +called uh the z +transform and we're not going to do z + + align:start position:0% +transform and we're not going to do z + + + align:start position:0% +transform and we're not going to do z +transforms here much as I'd love to but + + align:start position:0% +transforms here much as I'd love to but + + + align:start position:0% +transforms here much as I'd love to but +basically it's it's an operator that + + align:start position:0% +basically it's it's an operator that + + + align:start position:0% +basically it's it's an operator that +says if I I I transform everything into + + align:start position:0% +says if I I I transform everything into + + + align:start position:0% +says if I I I transform everything into +this sort of z domain and now the + + align:start position:0% +this sort of z domain and now the + + + align:start position:0% +this sort of z domain and now the +concept of an advance in time by one + + align:start position:0% +concept of an advance in time by one + + + align:start position:0% +concept of an advance in time by one +time step can be done by having by + + align:start position:0% +time step can be done by having by + + + align:start position:0% +time step can be done by having by +premultiplying by this operator z with + + align:start position:0% +premultiplying by this operator z with + + + align:start position:0% +premultiplying by this operator z with +an exponent that's the number of of + + align:start position:0% +an exponent that's the number of of + + + align:start position:0% +an exponent that's the number of of +steps ahead you want to do if I want to + + align:start position:0% +steps ahead you want to do if I want to + + + align:start position:0% +steps ahead you want to do if I want to +have a delay then I just put a negative + + align:start position:0% +have a delay then I just put a negative + + + align:start position:0% +have a delay then I just put a negative +uh exponent up here and so for example + + align:start position:0% +uh exponent up here and so for example + + + align:start position:0% +uh exponent up here and so for example +if I think of this concept of here's uh + + align:start position:0% +if I think of this concept of here's uh + + + align:start position:0% +if I think of this concept of here's uh +terminology is here's the output y at + + align:start position:0% +terminology is here's the output y at + + + align:start position:0% +terminology is here's the output y at +instant of time + + align:start position:0% +instant of time + + + align:start position:0% +instant of time +I okay not there's no there's no + + align:start position:0% +I okay not there's no there's no + + + align:start position:0% +I okay not there's no there's no +continuous variable t it's it's the + + align:start position:0% +continuous variable t it's it's the + + + align:start position:0% +continuous variable t it's it's the +sample i if you will if I multiply that + + align:start position:0% +sample i if you will if I multiply that + + + align:start position:0% +sample i if you will if I multiply that +number by z to the plus one that's the + + align:start position:0% +number by z to the plus one that's the + + + align:start position:0% +number by z to the plus one that's the +same as saying oh you mean y one time + + align:start position:0% +same as saying oh you mean y one time + + + align:start position:0% +same as saying oh you mean y one time +step ahead + + align:start position:0% +step ahead + + + align:start position:0% +step ahead +And if I multiply it by Z ^ squ, it's + + align:start position:0% +And if I multiply it by Z ^ squ, it's + + + align:start position:0% +And if I multiply it by Z ^ squ, it's +two times steps ahead. And more relevant + + align:start position:0% +two times steps ahead. And more relevant + + + align:start position:0% +two times steps ahead. And more relevant +to what we're doing here, if I say, + + align:start position:0% +to what we're doing here, if I say, + + + align:start position:0% +to what we're doing here, if I say, +okay, here's an output at the current + + align:start position:0% +okay, here's an output at the current + + + align:start position:0% +okay, here's an output at the current +time I, if I premultiply it by this + + align:start position:0% +time I, if I premultiply it by this + + + align:start position:0% +time I, if I premultiply it by this +operator Z to the minus one, I'm really + + align:start position:0% +operator Z to the minus one, I'm really + + + align:start position:0% +operator Z to the minus one, I'm really +saying, let's look at it one time step + + align:start position:0% +saying, let's look at it one time step + + + align:start position:0% +saying, let's look at it one time step +uh + + align:start position:0% +uh + + + align:start position:0% +uh +behind. Okay. + + align:start position:0% +behind. Okay. + + + align:start position:0% +behind. Okay. +Um so when we look at our process model, + + align:start position:0% +Um so when we look at our process model, + + + align:start position:0% +Um so when we look at our process model, +we have to modify it a little bit. you + + align:start position:0% +we have to modify it a little bit. you + + + align:start position:0% +we have to modify it a little bit. you +say, "Okay, um, we can do this anywhere + + align:start position:0% +say, "Okay, um, we can do this anywhere + + + align:start position:0% +say, "Okay, um, we can do this anywhere +in the loop we want, but we decided to + + align:start position:0% +in the loop we want, but we decided to + + + align:start position:0% +in the loop we want, but we decided to +do it here because it's the easiest." + + align:start position:0% +do it here because it's the easiest." + + + align:start position:0% +do it here because it's the easiest." +When I make u a change to the input + + align:start position:0% +When I make u a change to the input + + + align:start position:0% +When I make u a change to the input +conceptually, I don't get to see what + + align:start position:0% +conceptually, I don't get to see what + + + align:start position:0% +conceptually, I don't get to see what +happens to that until the cycle is over + + align:start position:0% +happens to that until the cycle is over + + + align:start position:0% +happens to that until the cycle is over +and I'm ready to do the next cycle. So, + + align:start position:0% +and I'm ready to do the next cycle. So, + + + align:start position:0% +and I'm ready to do the next cycle. So, +we're going to model the whole thing not + + align:start position:0% +we're going to model the whole thing not + + + align:start position:0% +we're going to model the whole thing not +as a simple gain, but as it's got messed + + align:start position:0% +as a simple gain, but as it's got messed + + + align:start position:0% +as a simple gain, but as it's got messed +up in + + align:start position:0% +up in + + + align:start position:0% +up in +the in this, but as as this. + + align:start position:0% +the in this, but as as this. + + + align:start position:0% +the in this, but as as this. +Or in other words, we're going to say + + align:start position:0% +Or in other words, we're going to say + + + align:start position:0% +Or in other words, we're going to say +that the current output is equal to the + + align:start position:0% +that the current output is equal to the + + + align:start position:0% +that the current output is equal to the +prior + + align:start position:0% +prior + + + align:start position:0% +prior +input times that gain. And this may seem + + align:start position:0% +input times that gain. And this may seem + + + align:start position:0% +input times that gain. And this may seem +pretty trivial to you, but this is like + + align:start position:0% +pretty trivial to you, but this is like + + + align:start position:0% +pretty trivial to you, but this is like +the basis of the whole thing. It's very + + align:start position:0% +the basis of the whole thing. It's very + + + align:start position:0% +the basis of the whole thing. It's very +simple from a discrete control system + + align:start position:0% +simple from a discrete control system + + + align:start position:0% +simple from a discrete control system +point of view, but the mere fact that + + align:start position:0% +point of view, but the mere fact that + + + align:start position:0% +point of view, but the mere fact that +you say, yeah, the input leads to the + + align:start position:0% +you say, yeah, the input leads to the + + + align:start position:0% +you say, yeah, the input leads to the +output, but a time step later, is what + + align:start position:0% +output, but a time step later, is what + + + align:start position:0% +output, but a time step later, is what +makes the whole thing. It's it's the + + align:start position:0% +makes the whole thing. It's it's the + + + align:start position:0% +makes the whole thing. It's it's the +part that makes it not work if you don't + + align:start position:0% +part that makes it not work if you don't + + + align:start position:0% +part that makes it not work if you don't +know what you're doing. And it's the + + align:start position:0% +know what you're doing. And it's the + + + align:start position:0% +know what you're doing. And it's the +part you have to analyze to be sure what + + align:start position:0% +part you have to analyze to be sure what + + + align:start position:0% +part you have to analyze to be sure what +is going on. Okay. So for the moment + + align:start position:0% +is going on. Okay. So for the moment + + + align:start position:0% +is going on. Okay. So for the moment +we've modeled the process. It's a pure + + align:start position:0% +we've modeled the process. It's a pure + + + align:start position:0% +we've modeled the process. It's a pure +gain with a one time step one cycle uh + + align:start position:0% + + + + align:start position:0% + +delay. Now if I let's take some here's + + align:start position:0% +delay. Now if I let's take some here's + + + align:start position:0% +delay. Now if I let's take some here's +some data from a process that's under + + align:start position:0% +some data from a process that's under + + + align:start position:0% +some data from a process that's under +that's that's I think this is probably + + align:start position:0% +that's that's I think this is probably + + + align:start position:0% +that's that's I think this is probably +under a state of statistical control. + + align:start position:0% +under a state of statistical control. + + + align:start position:0% +under a state of statistical control. +And you know that these lines in between + + align:start position:0% +And you know that these lines in between + + + align:start position:0% +And you know that these lines in between +here this is done on Excel. the lines in + + align:start position:0% +here this is done on Excel. the lines in + + + align:start position:0% +here this is done on Excel. the lines in +between there don't exist. You know, + + align:start position:0% +between there don't exist. You know, + + + align:start position:0% +between there don't exist. You know, +it's dots here. Here's a measurement. + + align:start position:0% +it's dots here. Here's a measurement. + + + align:start position:0% +it's dots here. Here's a measurement. +There's a measurement. So on they're + + align:start position:0% +There's a measurement. So on they're + + + align:start position:0% +There's a measurement. So on they're +just there to let you see it better. So + + align:start position:0% +just there to let you see it better. So + + + align:start position:0% +just there to let you see it better. So +that's the output of our real + + align:start position:0% +that's the output of our real + + + align:start position:0% +that's the output of our real +process. Well, how does the model I just + + align:start position:0% +process. Well, how does the model I just + + + align:start position:0% +process. Well, how does the model I just +came up with reflect this in any way? Of + + align:start position:0% +came up with reflect this in any way? Of + + + align:start position:0% +came up with reflect this in any way? Of +course, it doesn't. I I haven't included + + align:start position:0% +course, it doesn't. I I haven't included + + + align:start position:0% +course, it doesn't. I I haven't included +the randomness at all. So what we have + + align:start position:0% +the randomness at all. So what we have + + + align:start position:0% +the randomness at all. So what we have +to do is add in some randomness, then do + + align:start position:0% +to do is add in some randomness, then do + + + align:start position:0% +to do is add in some randomness, then do +our sampling, and then see if we get + + align:start position:0% +our sampling, and then see if we get + + + align:start position:0% +our sampling, and then see if we get +something that looks like uh looks like + + align:start position:0% +something that looks like uh looks like + + + align:start position:0% +something that looks like uh looks like +this. So + + align:start position:0% +this. So + + + align:start position:0% +this. So +again, we have to come up a mo with a + + align:start position:0% +again, we have to come up a mo with a + + + align:start position:0% +again, we have to come up a mo with a +model that fits what we observe in real + + align:start position:0% +model that fits what we observe in real + + + align:start position:0% +model that fits what we observe in real +life, what I just showed you, and also + + align:start position:0% +life, what I just showed you, and also + + + align:start position:0% +life, what I just showed you, and also +is amendable to our control theory. So + + align:start position:0% +is amendable to our control theory. So + + + align:start position:0% +is amendable to our control theory. So +again, as I said, here's still we're + + align:start position:0% +again, as I said, here's still we're + + + align:start position:0% +again, as I said, here's still we're +still continuous here. Now, this is + + align:start position:0% +still continuous here. Now, this is + + + align:start position:0% +still continuous here. Now, this is +before we've done the sampling. We've + + align:start position:0% +before we've done the sampling. We've + + + align:start position:0% +before we've done the sampling. We've +got this continuous random + + align:start position:0% +got this continuous random + + + align:start position:0% +got this continuous random +variable D of T. It's always there. It's + + align:start position:0% +variable D of T. It's always there. It's + + + align:start position:0% +variable D of T. It's always there. It's +always changing. Then we sample at our + + align:start position:0% +always changing. Then we sample at our + + + align:start position:0% +always changing. Then we sample at our +once every cycle and we get our discrete + + align:start position:0% +once every cycle and we get our discrete + + + align:start position:0% +once every cycle and we get our discrete +variable. Now it should include a random + + align:start position:0% +variable. Now it should include a random + + + align:start position:0% +variable. Now it should include a random +component. + + align:start position:0% +component. + + + align:start position:0% +component. +Okay. + + align:start position:0% + + + + align:start position:0% + +Um that's not exactly what it should + + align:start position:0% +Um that's not exactly what it should + + + align:start position:0% +Um that's not exactly what it should +say. So well that's jumping ahead, but + + align:start position:0% +say. So well that's jumping ahead, but + + + align:start position:0% +say. So well that's jumping ahead, but +let's go ahead and do that. So now uh in + + align:start position:0% +let's go ahead and do that. So now uh in + + + align:start position:0% +let's go ahead and do that. So now uh in +our cycleto cycle control system, we're + + align:start position:0% +our cycleto cycle control system, we're + + + align:start position:0% +our cycleto cycle control system, we're +going to add into it basically a + + align:start position:0% +going to add into it basically a + + + align:start position:0% +going to add into it basically a +sequence of numbers that follows a + + align:start position:0% +sequence of numbers that follows a + + + align:start position:0% +sequence of numbers that follows a +stationary normal uh distribution + + align:start position:0% +stationary normal uh distribution + + + align:start position:0% +stationary normal uh distribution +distribution function. Well, that's no + + align:start position:0% +distribution function. Well, that's no + + + align:start position:0% +distribution function. Well, that's no +big deal. That's what you've been doing + + align:start position:0% +big deal. That's what you've been doing + + + align:start position:0% +big deal. That's what you've been doing +all along in the terms. So that's that + + align:start position:0% +all along in the terms. So that's that + + + align:start position:0% +all along in the terms. So that's that +shouldn't be a + + align:start position:0% +shouldn't be a + + + align:start position:0% +shouldn't be a +problem. Um and this is + + align:start position:0% +problem. Um and this is + + + align:start position:0% +problem. Um and this is +just this is just a little bit of a + + align:start position:0% +just this is just a little bit of a + + + align:start position:0% +just this is just a little bit of a +connection between the continuous theory + + align:start position:0% +connection between the continuous theory + + + align:start position:0% +connection between the continuous theory +and and the discrete theory. uh a + + align:start position:0% +and and the discrete theory. uh a + + + align:start position:0% +and and the discrete theory. uh a +continuous random random number is in in + + align:start position:0% +continuous random random number is in in + + + align:start position:0% +continuous random random number is in in +fact that you know uh if you go back to + + align:start position:0% +fact that you know uh if you go back to + + + align:start position:0% +fact that you know uh if you go back to +our early stuff on statistics this is + + align:start position:0% +our early stuff on statistics this is + + + align:start position:0% +our early stuff on statistics this is +really where we started from but you + + align:start position:0% +really where we started from but you + + + align:start position:0% +really where we started from but you +know there's this number that's changing + + align:start position:0% +know there's this number that's changing + + + align:start position:0% +know there's this number that's changing +continuously and it's never the same + + align:start position:0% +continuously and it's never the same + + + align:start position:0% +continuously and it's never the same +number at any time and it's following a + + align:start position:0% +number at any time and it's following a + + + align:start position:0% +number at any time and it's following a +Gaussian distribution and it's + + align:start position:0% +Gaussian distribution and it's + + + align:start position:0% +Gaussian distribution and it's +stationary or a normal distribution I + + align:start position:0% +stationary or a normal distribution I + + + align:start position:0% +stationary or a normal distribution I +should say um at any instant in time + + align:start position:0% +should say um at any instant in time + + + align:start position:0% +should say um at any instant in time +there is no correlation meaning if I + + align:start position:0% +there is no correlation meaning if I + + + align:start position:0% +there is no correlation meaning if I +sample this this distribution right now + + align:start position:0% +sample this this distribution right now + + + align:start position:0% +sample this this distribution right now +and I get a particular number It gives + + align:start position:0% +and I get a particular number It gives + + + align:start position:0% +and I get a particular number It gives +me absolutely no information about + + align:start position:0% +me absolutely no information about + + + align:start position:0% +me absolutely no information about +what's going to happen + + align:start position:0% +what's going to happen + + + align:start position:0% +what's going to happen +next. It does it does allow me + + align:start position:0% +next. It does it does allow me + + + align:start position:0% +next. It does it does allow me +eventually with enough data to say what + + align:start position:0% +eventually with enough data to say what + + + align:start position:0% +eventually with enough data to say what +the distribution is, but it tells me + + align:start position:0% +the distribution is, but it tells me + + + align:start position:0% +the distribution is, but it tells me +nothing about what's going to happen + + align:start position:0% +nothing about what's going to happen + + + align:start position:0% +nothing about what's going to happen +next. So, it's totally uncorrelated. And + + align:start position:0% +next. So, it's totally uncorrelated. And + + + align:start position:0% +next. So, it's totally uncorrelated. And +if we sample that process, then we get + + align:start position:0% +if we sample that process, then we get + + + align:start position:0% +if we sample that process, then we get +what we've used throughout the term is + + align:start position:0% +what we've used throughout the term is + + + align:start position:0% +what we've used throughout the term is +this normal identically distributed + + align:start position:0% +this normal identically distributed + + + align:start position:0% +this normal identically distributed +independent + + align:start position:0% +independent + + + align:start position:0% +independent +random sequence. Had Dwayne have you + + align:start position:0% +random sequence. Had Dwayne have you + + + align:start position:0% +random sequence. Had Dwayne have you +used NEI? You talked about the the + + align:start position:0% +used NEI? You talked about the the + + + align:start position:0% +used NEI? You talked about the the +acronym. Uh we've used I N. Yeah. Okay. + + align:start position:0% +acronym. Uh we've used I N. Yeah. Okay. + + + align:start position:0% +acronym. Uh we've used I N. Yeah. Okay. +All the other other permutations. Okay, + + align:start position:0% +All the other other permutations. Okay, + + + align:start position:0% +All the other other permutations. Okay, +normal identically distributed + + align:start position:0% +normal identically distributed + + + align:start position:0% +normal identically distributed +independent. So it means a stationary + + align:start position:0% +independent. So it means a stationary + + + align:start position:0% +independent. So it means a stationary +random variable with no correlation from + + align:start position:0% +random variable with no correlation from + + + align:start position:0% +random variable with no correlation from +from time to time. Okay. All right. + + align:start position:0% +from time to time. Okay. All right. + + + align:start position:0% +from time to time. Okay. All right. +Here's the algebra. Um and it's the key + + align:start position:0% +Here's the algebra. Um and it's the key + + + align:start position:0% +Here's the algebra. Um and it's the key +to the whole thing, but I won't uh I + + align:start position:0% +to the whole thing, but I won't uh I + + + align:start position:0% +to the whole thing, but I won't uh I +won't go through it except to say that + + align:start position:0% +won't go through it except to say that + + + align:start position:0% +won't go through it except to say that +um if you remember your block diagram + + align:start position:0% +um if you remember your block diagram + + + align:start position:0% +um if you remember your block diagram +algebra, there's a there's a clear + + align:start position:0% +algebra, there's a there's a clear + + + align:start position:0% +algebra, there's a there's a clear +algebra that happens here. And we'll + + align:start position:0% +algebra that happens here. And we'll + + + align:start position:0% +algebra that happens here. And we'll +just take the first step here. The + + align:start position:0% +just take the first step here. The + + + align:start position:0% +just take the first step here. The +output y subi. What this diagram means + + align:start position:0% +output y subi. What this diagram means + + + align:start position:0% +output y subi. What this diagram means +is that the output y + + align:start position:0% + + + + align:start position:0% + +subi going this way is equal to that's a + + align:start position:0% +subi going this way is equal to that's a + + + align:start position:0% +subi going this way is equal to that's a +summation there. I should have put that + + align:start position:0% +summation there. I should have put that + + + align:start position:0% +summation there. I should have put that +there. It's equal to d subi plus the + + align:start position:0% +there. It's equal to d subi plus the + + + align:start position:0% +there. It's equal to d subi plus the +output of this box. And the output of + + align:start position:0% +output of this box. And the output of + + + align:start position:0% +output of this box. And the output of +this box is kp * u subi delayed by one + + align:start position:0% +this box is kp * u subi delayed by one + + + align:start position:0% +this box is kp * u subi delayed by one +time step. So that's all that that + + align:start position:0% +time step. So that's all that that + + + align:start position:0% +time step. So that's all that that +equation means right there. Then we + + align:start position:0% +equation means right there. Then we + + + align:start position:0% +equation means right there. Then we +solve backwards here. So we say okay + + align:start position:0% +solve backwards here. So we say okay + + + align:start position:0% +solve backwards here. So we say okay +well this this value right here the + + align:start position:0% +well this this value right here the + + + align:start position:0% +well this this value right here the +input to that happens to be equal to the + + align:start position:0% +input to that happens to be equal to the + + + align:start position:0% +input to that happens to be equal to the +controller gain times the difference of + + align:start position:0% +controller gain times the difference of + + + align:start position:0% +controller gain times the difference of +the reference and our + + align:start position:0% +the reference and our + + + align:start position:0% +the reference and our +feedback. You put it all together and + + align:start position:0% +feedback. You put it all together and + + + align:start position:0% +feedback. You put it all together and +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +uh the equation for this uh uh the + + align:start position:0% +uh the equation for this uh uh the + + + align:start position:0% +uh the equation for this uh uh the +output of the + + align:start position:0% +output of the + + + align:start position:0% +output of the +controller. And then here's the + + align:start position:0% +controller. And then here's the + + + align:start position:0% +controller. And then here's the +important + + align:start position:0% +important + + + align:start position:0% +important +thing. If I now say all right um I'm + + align:start position:0% +thing. If I now say all right um I'm + + + align:start position:0% +thing. If I now say all right um I'm +going to make the input my command think + + align:start position:0% +going to make the input my command think + + + align:start position:0% +going to make the input my command think +of it as a dimension or something for + + align:start position:0% +of it as a dimension or something for + + + align:start position:0% +of it as a dimension or something for +what we're doing here a constant value + + align:start position:0% +what we're doing here a constant value + + + align:start position:0% +what we're doing here a constant value +10 in never going to change + + align:start position:0% +10 in never going to change + + + align:start position:0% +10 in never going to change +um and uh and you can think of it as a + + align:start position:0% +um and uh and you can think of it as a + + + align:start position:0% +um and uh and you can think of it as a +constant oh I'm sorry back up I'm going + + align:start position:0% +constant oh I'm sorry back up I'm going + + + align:start position:0% +constant oh I'm sorry back up I'm going +to do that too but uh for the moment + + align:start position:0% +to do that too but uh for the moment + + + align:start position:0% +to do that too but uh for the moment +let's say that the disturbance is not + + align:start position:0% +let's say that the disturbance is not + + + align:start position:0% +let's say that the disturbance is not +random it's just a constant value I'm + + align:start position:0% +random it's just a constant value I'm + + + align:start position:0% +random it's just a constant value I'm +going to use the term + + align:start position:0% +going to use the term + + + align:start position:0% +going to use the term +mu, but it's a constant value. If I do + + align:start position:0% +mu, but it's a constant value. If I do + + + align:start position:0% +mu, but it's a constant value. If I do +that and put it into this equation and + + align:start position:0% +that and put it into this equation and + + + align:start position:0% +that and put it into this equation and +solve + + align:start position:0% +solve + + + align:start position:0% +solve +for y + + align:start position:0% +for y + + + align:start position:0% +for y +subi and I let time + + align:start position:0% +subi and I let time + + + align:start position:0% +subi and I let time +go forever, so it's now steady state. + + align:start position:0% +go forever, so it's now steady state. + + + align:start position:0% +go forever, so it's now steady state. +Uh, if you go through the algebra, what + + align:start position:0% +Uh, if you go through the algebra, what + + + align:start position:0% +Uh, if you go through the algebra, what +you get is that the steady state value + + align:start position:0% +you get is that the steady state value + + + align:start position:0% +you get is that the steady state value +of the output is equal to these two + + align:start position:0% +of the output is equal to these two + + + align:start position:0% +of the output is equal to these two +quantities right here. Okay? It's the + + align:start position:0% +quantities right here. Okay? It's the + + + align:start position:0% +quantities right here. Okay? It's the +disturbance divided by this quantity and + + align:start position:0% +disturbance divided by this quantity and + + + align:start position:0% +disturbance divided by this quantity and +it's the reference multiplied by that + + align:start position:0% +it's the reference multiplied by that + + + align:start position:0% +it's the reference multiplied by that +quantity. Okay, big deal. But here's + + align:start position:0% +quantity. Okay, big deal. But here's + + + align:start position:0% +quantity. Okay, big deal. But here's +here's the big + + align:start position:0% +here's the big + + + align:start position:0% +here's the big +deal. Here's the + + align:start position:0% +deal. Here's the + + + align:start position:0% +deal. Here's the +output value in steady state. Here's the + + align:start position:0% +output value in steady state. Here's the + + + align:start position:0% +output value in steady state. Here's the +disturbance. What do I want that + + align:start position:0% +disturbance. What do I want that + + + align:start position:0% +disturbance. What do I want that +quantity to be? If this is a good + + align:start position:0% +quantity to be? If this is a good + + + align:start position:0% +quantity to be? If this is a good +control + + align:start position:0% + + + + align:start position:0% + +system and oh, for the moment, imagine + + align:start position:0% +system and oh, for the moment, imagine + + + align:start position:0% +system and oh, for the moment, imagine +that that my reference is zero. + + align:start position:0% +that that my reference is zero. + + + align:start position:0% +that that my reference is zero. +Conceptually, that's an important thing. + + align:start position:0% +Conceptually, that's an important thing. + + + align:start position:0% +Conceptually, that's an important thing. +Imagine that my reference is zero. So, + + align:start position:0% +Imagine that my reference is zero. So, + + + align:start position:0% +Imagine that my reference is zero. So, +the ideal output of the process is zero. + + align:start position:0% +the ideal output of the process is zero. + + + align:start position:0% +the ideal output of the process is zero. +Now this says that the ratio of the + + align:start position:0% +Now this says that the ratio of the + + + align:start position:0% +Now this says that the ratio of the +output in steady state to the + + align:start position:0% +output in steady state to the + + + align:start position:0% +output in steady state to the +disturbance which is finite some + + align:start position:0% +disturbance which is finite some + + + align:start position:0% +disturbance which is finite some +constant value is this quantity. What + + align:start position:0% +constant value is this quantity. What + + + align:start position:0% +constant value is this quantity. What +would I like this quantity to + + align:start position:0% + + + + align:start position:0% + +be? How about + + align:start position:0% +be? How about + + + align:start position:0% +be? How about +zero? Disturbances are bad. If this + + align:start position:0% +zero? Disturbances are bad. If this + + + align:start position:0% +zero? Disturbances are bad. If this +number is anything but zero then I am + + align:start position:0% +number is anything but zero then I am + + + align:start position:0% +number is anything but zero then I am +not rejecting my disturbance. Let's jump + + align:start position:0% +not rejecting my disturbance. Let's jump + + + align:start position:0% +not rejecting my disturbance. Let's jump +ahead to say if I can't make this zero, + + align:start position:0% +ahead to say if I can't make this zero, + + + align:start position:0% +ahead to say if I can't make this zero, +I can't center this distribution because + + align:start position:0% +I can't center this distribution because + + + align:start position:0% +I can't center this distribution because +this shift is indeed that dist that it's + + align:start position:0% +this shift is indeed that dist that it's + + + align:start position:0% +this shift is indeed that dist that it's +the mean shift. Okay, how can I make + + align:start position:0% +the mean shift. Okay, how can I make + + + align:start position:0% +the mean shift. Okay, how can I make +this + + align:start position:0% + + + + align:start position:0% + +zero? Okay + + align:start position:0% +zero? Okay + + + align:start position:0% +zero? Okay +can't I how do I make this quantity + + align:start position:0% +can't I how do I make this quantity + + + align:start position:0% +can't I how do I make this quantity +zero? There it is right + + align:start position:0% +zero? There it is right + + + align:start position:0% +zero? There it is right +there. How do I make that quantity zero? + + align:start position:0% + + + + align:start position:0% + +I could do that. If I can make it an + + align:start position:0% +I could do that. If I can make it an + + + align:start position:0% +I could do that. If I can make it an +infinite gain, it would be + + align:start position:0% + + + + align:start position:0% + +zero. Tough thing to do. Okay. So, kind + + align:start position:0% +zero. Tough thing to do. Okay. So, kind + + + align:start position:0% +zero. Tough thing to do. Okay. So, kind +of say, geez, you know, we're not going + + align:start position:0% +of say, geez, you know, we're not going + + + align:start position:0% +of say, geez, you know, we're not going +to be able to do it and this means that + + align:start position:0% +to be able to do it and this means that + + + align:start position:0% +to be able to do it and this means that +I won't be able to do this and and uh + + align:start position:0% +I won't be able to do this and and uh + + + align:start position:0% +I won't be able to do this and and uh +the naysayers are right and all that + + align:start position:0% +the naysayers are right and all that + + + align:start position:0% +the naysayers are right and all that +sort of thing. So, + + align:start position:0% +sort of thing. So, + + + align:start position:0% +sort of thing. So, +um but fortunately, you'll see in a + + align:start position:0% +um but fortunately, you'll see in a + + + align:start position:0% +um but fortunately, you'll see in a +moment, there's a way we can do it. uh + + align:start position:0% +moment, there's a way we can do it. uh + + + align:start position:0% +moment, there's a way we can do it. uh +and maybe you saw this in your control + + align:start position:0% +and maybe you saw this in your control + + + align:start position:0% +and maybe you saw this in your control +system things as well. Conceptually, all + + align:start position:0% +system things as well. Conceptually, all + + + align:start position:0% +system things as well. Conceptually, all +I need is this gain to be equal infinity + + align:start position:0% +I need is this gain to be equal infinity + + + align:start position:0% +I need is this gain to be equal infinity +when things are in steady + + align:start position:0% +when things are in steady + + + align:start position:0% +when things are in steady +state. Uh that's one way to think of it. + + align:start position:0% +state. Uh that's one way to think of it. + + + align:start position:0% +state. Uh that's one way to think of it. +The other way to think of it is if you + + align:start position:0% +The other way to think of it is if you + + + align:start position:0% +The other way to think of it is if you +did your control systems theory, it said + + align:start position:0% +did your control systems theory, it said + + + align:start position:0% +did your control systems theory, it said +ah steady state error equals zero. That + + align:start position:0% +ah steady state error equals zero. That + + + align:start position:0% +ah steady state error equals zero. That +means I want an integral controller. And + + align:start position:0% +means I want an integral controller. And + + + align:start position:0% +means I want an integral controller. And +there's there's theoretical reasons for + + align:start position:0% +there's there's theoretical reasons for + + + align:start position:0% +there's there's theoretical reasons for +that. So what we can do instead of using + + align:start position:0% +that. So what we can do instead of using + + + align:start position:0% +that. So what we can do instead of using +a simple controller Oh, I I should back + + align:start position:0% +a simple controller Oh, I I should back + + + align:start position:0% +a simple controller Oh, I I should back +up here. What I did in here is I I + + align:start position:0% +up here. What I did in here is I I + + + align:start position:0% +up here. What I did in here is I I +picked our control law was simply to say + + align:start position:0% +picked our control law was simply to say + + + align:start position:0% +picked our control law was simply to say +uh that the control law was if there's + + align:start position:0% +uh that the control law was if there's + + + align:start position:0% +uh that the control law was if there's +an error make a purely proportional + + align:start position:0% +an error make a purely proportional + + + align:start position:0% +an error make a purely proportional +change in the set points. Now I'm going + + align:start position:0% +change in the set points. Now I'm going + + + align:start position:0% +change in the set points. Now I'm going +to say let's get a little bit more + + align:start position:0% +to say let's get a little bit more + + + align:start position:0% +to say let's get a little bit more +sophisticated. Let's do an integral + + align:start position:0% +sophisticated. Let's do an integral + + + align:start position:0% +sophisticated. Let's do an integral +controller. And an integral controller + + align:start position:0% +controller. And an integral controller + + + align:start position:0% +controller. And an integral controller +in discrete terms is simply a running + + align:start position:0% +in discrete terms is simply a running + + + align:start position:0% +in discrete terms is simply a running +sum of the + + align:start position:0% +sum of the + + + align:start position:0% +sum of the +errors. You know, and if you remember + + align:start position:0% +errors. You know, and if you remember + + + align:start position:0% +errors. You know, and if you remember +back to calculus 101, calculus when you + + align:start position:0% +back to calculus 101, calculus when you + + + align:start position:0% +back to calculus 101, calculus when you +when you know, typically when you derive + + align:start position:0% +when you know, typically when you derive + + + align:start position:0% +when you know, typically when you derive +an integration, you start off with a + + align:start position:0% +an integration, you start off with a + + + align:start position:0% +an integration, you start off with a +summation and then make the summation + + align:start position:0% +summation and then make the summation + + + align:start position:0% +summation and then make the summation +interval smaller and smaller till it + + align:start position:0% +interval smaller and smaller till it + + + align:start position:0% +interval smaller and smaller till it +becomes continuous. Now, we break it + + align:start position:0% +becomes continuous. Now, we break it + + + align:start position:0% +becomes continuous. Now, we break it +back the other way and say, okay, the + + align:start position:0% +back the other way and say, okay, the + + + align:start position:0% +back the other way and say, okay, the +best we can do for a discrete time + + align:start position:0% +best we can do for a discrete time + + + align:start position:0% +best we can do for a discrete time +integrator is to sum up errors. So, this + + align:start position:0% +integrator is to sum up errors. So, this + + + align:start position:0% +integrator is to sum up errors. So, this +is my new controller. It simply says the + + align:start position:0% +is my new controller. It simply says the + + + align:start position:0% +is my new controller. It simply says the +output at any time, how I'm going to + + align:start position:0% +output at any time, how I'm going to + + + align:start position:0% +output at any time, how I'm going to +change the machine is the sum of all the + + align:start position:0% +change the machine is the sum of all the + + + align:start position:0% +change the machine is the sum of all the +prior errors. Okay. Now I can do again I + + align:start position:0% +prior errors. Okay. Now I can do again I + + + align:start position:0% +prior errors. Okay. Now I can do again I +can um turn this into a recursive form. + + align:start position:0% +can um turn this into a recursive form. + + + align:start position:0% +can um turn this into a recursive form. +So you just say the the next output is + + align:start position:0% +So you just say the the next output is + + + align:start position:0% +So you just say the the next output is +the prior output plus the next uh + + align:start position:0% +the prior output plus the next uh + + + align:start position:0% +the prior output plus the next uh +error and then I can do the Z transform + + align:start position:0% +error and then I can do the Z transform + + + align:start position:0% +error and then I can do the Z transform +business on it. It comes out like this. + + align:start position:0% +business on it. It comes out like this. + + + align:start position:0% +business on it. It comes out like this. +And this is where it gets uh uh useful. + + align:start position:0% +And this is where it gets uh uh useful. + + + align:start position:0% +And this is where it gets uh uh useful. +Now my controller instead of being a + + align:start position:0% +Now my controller instead of being a + + + align:start position:0% +Now my controller instead of being a +simple gain looks like this. This Z over + + align:start position:0% +simple gain looks like this. This Z over + + + align:start position:0% +simple gain looks like this. This Z over +Z minus one which is describing this + + align:start position:0% +Z minus one which is describing this + + + align:start position:0% +Z minus one which is describing this +equation. And I can do the algebra of + + align:start position:0% +equation. And I can do the algebra of + + + align:start position:0% +equation. And I can do the algebra of +this and see what happens. Okay, so I + + align:start position:0% +this and see what happens. Okay, so I + + + align:start position:0% +this and see what happens. Okay, so I +follow the same block diagram algebra + + align:start position:0% +follow the same block diagram algebra + + + align:start position:0% +follow the same block diagram algebra +and the nice thing now is that Z is + + align:start position:0% +and the nice thing now is that Z is + + + align:start position:0% +and the nice thing now is that Z is +simply a an a multiplier. So I can treat + + align:start position:0% +simply a an a multiplier. So I can treat + + + align:start position:0% +simply a an a multiplier. So I can treat +it like any other quantity if I do that + + align:start position:0% +it like any other quantity if I do that + + + align:start position:0% +it like any other quantity if I do that +and I go through all + + align:start position:0% + + + + align:start position:0% + +this. So you know these Z's cancel out. + + align:start position:0% +this. So you know these Z's cancel out. + + + align:start position:0% +this. So you know these Z's cancel out. +I I write the equation for the + + align:start position:0% +I I write the equation for the + + + align:start position:0% +I I write the equation for the +disturbance. Um I'm assuming that R is + + align:start position:0% +disturbance. Um I'm assuming that R is + + + align:start position:0% +disturbance. Um I'm assuming that R is +equal to zero. So this is zero over + + align:start position:0% +equal to zero. So this is zero over + + + align:start position:0% +equal to zero. So this is zero over +here. Go through the block diagram + + align:start position:0% +here. Go through the block diagram + + + align:start position:0% +here. Go through the block diagram +algebra. + + align:start position:0% +algebra. + + + align:start position:0% +algebra. +get down to here. And now a couple + + align:start position:0% +get down to here. And now a couple + + + align:start position:0% +get down to here. And now a couple +things are kind of interesting. But uh + + align:start position:0% +things are kind of interesting. But uh + + + align:start position:0% +things are kind of interesting. But uh +what I can say is at steady state, we + + align:start position:0% +what I can say is at steady state, we + + + align:start position:0% +what I can say is at steady state, we +know that all of the y's in the system + + align:start position:0% +know that all of the y's in the system + + + align:start position:0% +know that all of the y's in the system +are the same. Everything's kind of + + align:start position:0% +are the same. Everything's kind of + + + align:start position:0% +are the same. Everything's kind of +settled out. And I come down here and + + align:start position:0% +settled out. And I come down here and + + + align:start position:0% +settled out. And I come down here and +say that because this disturbance is a + + align:start position:0% +say that because this disturbance is a + + + align:start position:0% +say that because this disturbance is a +constant, these two things are the same. + + align:start position:0% +constant, these two things are the same. + + + align:start position:0% +constant, these two things are the same. +You know, the disturbance at at time + + align:start position:0% +You know, the disturbance at at time + + + align:start position:0% +You know, the disturbance at at time +20,000 and time 20,000 plus one are the + + align:start position:0% +20,000 and time 20,000 plus one are the + + + align:start position:0% +20,000 and time 20,000 plus one are the +same because it's a constant. And when + + align:start position:0% +same because it's a constant. And when + + + align:start position:0% +same because it's a constant. And when +you come down here, you find out that + + align:start position:0% +you come down here, you find out that + + + align:start position:0% +you come down here, you find out that +this quantity is equal to zero + + align:start position:0% +this quantity is equal to zero + + + align:start position:0% +this quantity is equal to zero +regardless of the loop gain. In other + + align:start position:0% +regardless of the loop gain. In other + + + align:start position:0% +regardless of the loop gain. In other +words, it doesn't matter what value I + + align:start position:0% +words, it doesn't matter what value I + + + align:start position:0% +words, it doesn't matter what value I +pick for for + + align:start position:0% +pick for for + + + align:start position:0% +pick for for +KC, it's always zero. Okay? So, it's + + align:start position:0% +KC, it's always zero. Okay? So, it's + + + align:start position:0% +KC, it's always zero. Okay? So, it's +just a way of showing that with a simple + + align:start position:0% +just a way of showing that with a simple + + + align:start position:0% +just a way of showing that with a simple +integral controller, I indeed can take a + + align:start position:0% +integral controller, I indeed can take a + + + align:start position:0% +integral controller, I indeed can take a +finite constant disturbance and + + align:start position:0% +finite constant disturbance and + + + align:start position:0% +finite constant disturbance and +completely eliminate it in steady state. + + align:start position:0% +completely eliminate it in steady state. + + + align:start position:0% +completely eliminate it in steady state. +Not instantaneously, but in steady + + align:start position:0% +Not instantaneously, but in steady + + + align:start position:0% +Not instantaneously, but in steady +state. Okay. + + align:start position:0% +state. Okay. + + + align:start position:0% +state. Okay. +Um, so now here's the problem. Since KC + + align:start position:0% +Um, so now here's the problem. Since KC + + + align:start position:0% +Um, so now here's the problem. Since KC +doesn't matter, that's my controller + + align:start position:0% +doesn't matter, that's my controller + + + align:start position:0% +doesn't matter, that's my controller +gain. That's my design. Since that + + align:start position:0% +gain. That's my design. Since that + + + align:start position:0% +gain. That's my design. Since that +doesn't matter, so must matter to + + align:start position:0% +doesn't matter, so must matter to + + + align:start position:0% +doesn't matter, so must matter to +something, right? So what value do I + + align:start position:0% +something, right? So what value do I + + + align:start position:0% +something, right? So what value do I +pick for that gain of KC? What's the + + align:start position:0% +pick for that gain of KC? What's the + + + align:start position:0% +pick for that gain of KC? What's the +effect of the value of this controller + + align:start position:0% +effect of the value of this controller + + + align:start position:0% +effect of the value of this controller +gain on the performance of this system? + + align:start position:0% +gain on the performance of this system? + + + align:start position:0% +gain on the performance of this system? +You guys remember from control theory at + + align:start position:0% +You guys remember from control theory at + + + align:start position:0% +You guys remember from control theory at +all? what the effect of a controller + + align:start position:0% +all? what the effect of a controller + + + align:start position:0% +all? what the effect of a controller +gain is. + + align:start position:0% +gain is. + + + align:start position:0% +gain is. +Typically, low gain, high gain, middle + + align:start position:0% +Typically, low gain, high gain, middle + + + align:start position:0% +Typically, low gain, high gain, middle +gain, too high gain, too low a + + align:start position:0% +gain, too high gain, too low a + + + align:start position:0% +gain, too high gain, too low a +gain. Generally, what happens as you + + align:start position:0% +gain. Generally, what happens as you + + + align:start position:0% +gain. Generally, what happens as you +adjust the controller gain? + + align:start position:0% + + + + align:start position:0% + +Yeah. I mean, think of it this way. Um, + + align:start position:0% +Yeah. I mean, think of it this way. Um, + + + align:start position:0% +Yeah. I mean, think of it this way. Um, +if forget about this for a moment, this + + align:start position:0% +if forget about this for a moment, this + + + align:start position:0% +if forget about this for a moment, this +controller gain says, uh, it's how much + + align:start position:0% +controller gain says, uh, it's how much + + + align:start position:0% +controller gain says, uh, it's how much +I'm going to adjust the system based on + + align:start position:0% +I'm going to adjust the system based on + + + align:start position:0% +I'm going to adjust the system based on +the error. If I'm very conservative and + + align:start position:0% +the error. If I'm very conservative and + + + align:start position:0% +the error. If I'm very conservative and +KC is really small and I get, let's say, + + align:start position:0% +KC is really small and I get, let's say, + + + align:start position:0% +KC is really small and I get, let's say, +an error, you know, a modest error, I'm + + align:start position:0% +an error, you know, a modest error, I'm + + + align:start position:0% +an error, you know, a modest error, I'm +going to make a really modest timid + + align:start position:0% +going to make a really modest timid + + + align:start position:0% +going to make a really modest timid +change. It's a measure of timidity, I + + align:start position:0% +change. It's a measure of timidity, I + + + align:start position:0% +change. It's a measure of timidity, I +guess. Uh, I'm going to make a timid + + align:start position:0% +guess. Uh, I'm going to make a timid + + + align:start position:0% +guess. Uh, I'm going to make a timid +change on the on over here. If I'm + + align:start position:0% +change on the on over here. If I'm + + + align:start position:0% +change on the on over here. If I'm +bold and uh trusting my control system, + + align:start position:0% +bold and uh trusting my control system, + + + align:start position:0% +bold and uh trusting my control system, +small error here, large gain, I make a + + align:start position:0% +small error here, large gain, I make a + + + align:start position:0% +small error here, large gain, I make a +huge change. And obviously, huge change + + align:start position:0% +huge change. And obviously, huge change + + + align:start position:0% +huge change. And obviously, huge change +going to get the system moving faster. + + align:start position:0% +going to get the system moving faster. + + + align:start position:0% +going to get the system moving faster. +So conceptually, heruristically, however + + align:start position:0% +So conceptually, heruristically, however + + + align:start position:0% +So conceptually, heruristically, however +you want to call it, high gains will + + align:start position:0% +you want to call it, high gains will + + + align:start position:0% +you want to call it, high gains will +generally lead to faster system + + align:start position:0% +generally lead to faster system + + + align:start position:0% +generally lead to faster system +response. Low gains will lead to slower + + align:start position:0% +response. Low gains will lead to slower + + + align:start position:0% +response. Low gains will lead to slower +system response. Which ones do you think + + align:start position:0% +system response. Which ones do you think + + + align:start position:0% +system response. Which ones do you think +typically, but not always? Which ones + + align:start position:0% +typically, but not always? Which ones + + + align:start position:0% +typically, but not always? Which ones +typically do you think are the most + + align:start position:0% +typically do you think are the most + + + align:start position:0% +typically do you think are the most +dangerous with respect to things like as + + align:start position:0% +dangerous with respect to things like as + + + align:start position:0% +dangerous with respect to things like as +I mentioned earlier the property of + + align:start position:0% +I mentioned earlier the property of + + + align:start position:0% +I mentioned earlier the property of +control systems known as + + align:start position:0% +control systems known as + + + align:start position:0% +control systems known as +instability. High gains or low gains? + + align:start position:0% +instability. High gains or low gains? + + + align:start position:0% +instability. High gains or low gains? +High gains of course. Yeah. Because + + align:start position:0% +High gains of course. Yeah. Because + + + align:start position:0% +High gains of course. Yeah. Because +imagine tiny gain, tiny error here. + + align:start position:0% +imagine tiny gain, tiny error here. + + + align:start position:0% +imagine tiny gain, tiny error here. +You're almost there, huge gain. You + + align:start position:0% +You're almost there, huge gain. You + + + align:start position:0% +You're almost there, huge gain. You +whack the system with a big thing. It + + align:start position:0% +whack the system with a big thing. It + + + align:start position:0% +whack the system with a big thing. It +goes way past where you wanted it to. + + align:start position:0% +goes way past where you wanted it to. + + + align:start position:0% +goes way past where you wanted it to. +And now you say, "Oh my gosh, now it's a + + align:start position:0% +And now you say, "Oh my gosh, now it's a + + + align:start position:0% +And now you say, "Oh my gosh, now it's a +large error." And it keeps coming back + + align:start position:0% +large error." And it keeps coming back + + + align:start position:0% +large error." And it keeps coming back +and forth and next thing you know, you + + align:start position:0% +and forth and next thing you know, you + + + align:start position:0% +and forth and next thing you know, you +got a system that's uh that's + + align:start position:0% +got a system that's uh that's + + + align:start position:0% +got a system that's uh that's +unstable. Okay. So to understand this, + + align:start position:0% +unstable. Okay. So to understand this, + + + align:start position:0% +unstable. Okay. So to understand this, +you have to understand discrete time + + align:start position:0% +you have to understand discrete time + + + align:start position:0% +you have to understand discrete time +control theory. There's some wonderful + + align:start position:0% +control theory. There's some wonderful + + + align:start position:0% +control theory. There's some wonderful +books and courses and other things on + + align:start position:0% +books and courses and other things on + + + align:start position:0% +books and courses and other things on +that. We don't we don't have time for + + align:start position:0% +that. We don't we don't have time for + + + align:start position:0% +that. We don't we don't have time for +that here. We'll do it heristically. + + align:start position:0% +that here. We'll do it heristically. + + + align:start position:0% +that here. We'll do it heristically. +We'll do it just for this + + align:start position:0% +We'll do it just for this + + + align:start position:0% +We'll do it just for this +system. Here's what + + align:start position:0% +system. Here's what + + + align:start position:0% +system. Here's what +happens. Excuse me. I'm going to step + + align:start position:0% +happens. Excuse me. I'm going to step + + + align:start position:0% +happens. Excuse me. I'm going to step +through different gains. Now, I already + + align:start position:0% +through different gains. Now, I already + + + align:start position:0% +through different gains. Now, I already +knew the theory behind this. I knew what + + align:start position:0% +knew the theory behind this. I knew what + + + align:start position:0% +knew the theory behind this. I knew what +these numbers needed to be. Um, but uh + + align:start position:0% +these numbers needed to be. Um, but uh + + + align:start position:0% +these numbers needed to be. Um, but uh +here's what you get. I got to say one + + align:start position:0% +here's what you get. I got to say one + + + align:start position:0% +here's what you get. I got to say one +other thing. What I'm going to show you + + align:start position:0% +other thing. What I'm going to show you + + + align:start position:0% +other thing. What I'm going to show you +is the product of these two gains. + + align:start position:0% +is the product of these two gains. + + + align:start position:0% +is the product of these two gains. +That's what really matters because + + align:start position:0% +That's what really matters because + + + align:start position:0% +That's what really matters because +again, these you can collapse these + + align:start position:0% +again, these you can collapse these + + + align:start position:0% +again, these you can collapse these +blocks blocks together and it's just + + align:start position:0% +blocks blocks together and it's just + + + align:start position:0% +blocks blocks together and it's just +this product KC KP that matters. + + align:start position:0% +this product KC KP that matters. + + + align:start position:0% +this product KC KP that matters. +So, the so-called loop gain, if I use a + + align:start position:0% +So, the so-called loop gain, if I use a + + + align:start position:0% +So, the so-called loop gain, if I use a +loop gain of a half, here's what + + align:start position:0% +loop gain of a half, here's what + + + align:start position:0% +loop gain of a half, here's what +happens. If I make a step change in the + + align:start position:0% +happens. If I make a step change in the + + + align:start position:0% +happens. If I make a step change in the +input, it goes one, two, three, four, + + align:start position:0% +input, it goes one, two, three, four, + + + align:start position:0% +input, it goes one, two, three, four, +five, six, seven, maybe eight cycles + + align:start position:0% +five, six, seven, maybe eight cycles + + + align:start position:0% +five, six, seven, maybe eight cycles +later, it has reached the final value + + align:start position:0% +later, it has reached the final value + + + align:start position:0% +later, it has reached the final value +and the error is zero. Okay, just as I + + align:start position:0% +and the error is zero. Okay, just as I + + + align:start position:0% +and the error is zero. Okay, just as I +expected. Say, okay, that's good. What + + align:start position:0% +expected. Say, okay, that's good. What + + + align:start position:0% +expected. Say, okay, that's good. What +happens if I increase the gain? Should + + align:start position:0% +happens if I increase the gain? Should + + + align:start position:0% +happens if I increase the gain? Should +get better. Well, indeed it does. Look + + align:start position:0% +get better. Well, indeed it does. Look + + + align:start position:0% +get better. Well, indeed it does. Look +at this. If I increase the gain to 9/10, + + align:start position:0% +at this. If I increase the gain to 9/10, + + + align:start position:0% +at this. If I increase the gain to 9/10, +one, two, maybe three cycles, it's done. + + align:start position:0% +one, two, maybe three cycles, it's done. + + + align:start position:0% +one, two, maybe three cycles, it's done. +And you notice here, this is really + + align:start position:0% +And you notice here, this is really + + + align:start position:0% +And you notice here, this is really +emphasizing the discrete control aspect + + align:start position:0% +emphasizing the discrete control aspect + + + align:start position:0% +emphasizing the discrete control aspect +of it. There's a change and then, you + + align:start position:0% +of it. There's a change and then, you + + + align:start position:0% +of it. There's a change and then, you +know, who knows? And then another change + + align:start position:0% +know, who knows? And then another change + + + align:start position:0% +know, who knows? And then another change +and then who knows? Um, so 9/10 is good. + + align:start position:0% +and then who knows? Um, so 9/10 is good. + + + align:start position:0% +and then who knows? Um, so 9/10 is good. +You know, 9/10 is good. Then + + align:start position:0% +You know, 9/10 is good. Then + + + align:start position:0% +You know, 9/10 is good. Then +uh 1.510 should be good. You know, 1510 + + align:start position:0% +uh 1.510 should be good. You know, 1510 + + + align:start position:0% +uh 1.510 should be good. You know, 1510 +should be good. So I go to 15/10. And + + align:start position:0% +should be good. So I go to 15/10. And + + + align:start position:0% +should be good. So I go to 15/10. And +what happens? Well, it now takes two + + align:start position:0% +what happens? Well, it now takes two + + + align:start position:0% +what happens? Well, it now takes two +things. It took three cycles to settle + + align:start position:0% +things. It took three cycles to settle + + + align:start position:0% +things. It took three cycles to settle +here. Now, we're back out to taking + + align:start position:0% +here. Now, we're back out to taking + + + align:start position:0% +here. Now, we're back out to taking +eight cycles to settle and I got this + + align:start position:0% +eight cycles to settle and I got this + + + align:start position:0% +eight cycles to settle and I got this +oscillation. So, it seems like I kind of + + align:start position:0% +oscillation. So, it seems like I kind of + + + align:start position:0% +oscillation. So, it seems like I kind of +went through I was getting better and + + align:start position:0% +went through I was getting better and + + + align:start position:0% +went through I was getting better and +now I'm getting worse just to see what + + align:start position:0% +now I'm getting worse just to see what + + + align:start position:0% +now I'm getting worse just to see what +happens since this is simulation. + + align:start position:0% +happens since this is simulation. + + + align:start position:0% +happens since this is simulation. +Anyway, let's set the loop gain equal to + + align:start position:0% +Anyway, let's set the loop gain equal to + + + align:start position:0% +Anyway, let's set the loop gain equal to +two. And what happens? The system indeed + + align:start position:0% +two. And what happens? The system indeed + + + align:start position:0% +two. And what happens? The system indeed +is now what we call marginally stable. + + align:start position:0% +is now what we call marginally stable. + + + align:start position:0% +is now what we call marginally stable. +And I don't have it on here, but if I + + align:start position:0% +And I don't have it on here, but if I + + + align:start position:0% +And I don't have it on here, but if I +set it to 2.001, + + align:start position:0% +set it to 2.001, + + + align:start position:0% +set it to 2.001, +O1, it starts to + + align:start position:0% +O1, it starts to + + + align:start position:0% +O1, it starts to +diverge. Okay. Um, here's the cool + + align:start position:0% +diverge. Okay. Um, here's the cool + + + align:start position:0% +diverge. Okay. Um, here's the cool +thing. If I set that equal to one, how + + align:start position:0% +thing. If I set that equal to one, how + + + align:start position:0% +thing. If I set that equal to one, how +long does it take to get to the correct + + align:start position:0% + + + + align:start position:0% + +value? One time step. And this is + + align:start position:0% +value? One time step. And this is + + + align:start position:0% +value? One time step. And this is +actually a pretty well-known concept in + + align:start position:0% +actually a pretty well-known concept in + + + align:start position:0% +actually a pretty well-known concept in +discrete time control systems that if + + align:start position:0% +discrete time control systems that if + + + align:start position:0% +discrete time control systems that if +you can magically find exactly the right + + align:start position:0% +you can magically find exactly the right + + + align:start position:0% +you can magically find exactly the right +gain so that the loop gain is equal to + + align:start position:0% +gain so that the loop gain is equal to + + + align:start position:0% +gain so that the loop gain is equal to +one, you would indeed can get exactly + + align:start position:0% +one, you would indeed can get exactly + + + align:start position:0% +one, you would indeed can get exactly +there in one time step. So this is our + + align:start position:0% +there in one time step. So this is our + + + align:start position:0% +there in one time step. So this is our +goal and it says that the best control + + align:start position:0% +goal and it says that the best control + + + align:start position:0% +goal and it says that the best control +system I could have now would take a + + align:start position:0% +system I could have now would take a + + + align:start position:0% +system I could have now would take a +mean offset like this and take it to + + align:start position:0% +mean offset like this and take it to + + + align:start position:0% +mean offset like this and take it to +zero error in one time step. So this is + + align:start position:0% +zero error in one time step. So this is + + + align:start position:0% +zero error in one time step. So this is +probably the right controller for us to + + align:start position:0% +probably the right controller for us to + + + align:start position:0% +probably the right controller for us to +use. Okay. It also tells us that if I'm + + align:start position:0% +use. Okay. It also tells us that if I'm + + + align:start position:0% +use. Okay. It also tells us that if I'm +too aggressive and I use a gain a loop + + align:start position:0% +too aggressive and I use a gain a loop + + + align:start position:0% +too aggressive and I use a gain a loop +gain of two and think of the operators + + align:start position:0% +gain of two and think of the operators + + + align:start position:0% +gain of two and think of the operators +now at this cement plant that I was + + align:start position:0% +now at this cement plant that I was + + + align:start position:0% +now at this cement plant that I was +talking about and they were turning the + + align:start position:0% +talking about and they were turning the + + + align:start position:0% +talking about and they were turning the +knob a little bit too far and so they + + align:start position:0% +knob a little bit too far and so they + + + align:start position:0% +knob a little bit too far and so they +were maybe here or here and making + + align:start position:0% +were maybe here or here and making + + + align:start position:0% +were maybe here or here and making +things worse or they were here and they + + align:start position:0% +things worse or they were here and they + + + align:start position:0% +things worse or they were here and they +were being too timid and it really + + align:start position:0% +were being too timid and it really + + + align:start position:0% +were being too timid and it really +didn't have any effect over the time + + align:start position:0% +didn't have any effect over the time + + + align:start position:0% +didn't have any effect over the time +frame that they were talking about. If + + align:start position:0% +frame that they were talking about. If + + + align:start position:0% +frame that they were talking about. If +you knew what your process gains were + + align:start position:0% +you knew what your process gains were + + + align:start position:0% +you knew what your process gains were +and you knew where to set this, you + + align:start position:0% +and you knew where to set this, you + + + align:start position:0% +and you knew where to set this, you +could always guarantee that you got the + + align:start position:0% +could always guarantee that you got the + + + align:start position:0% +could always guarantee that you got the +maximum effect in the in the minimum + + align:start position:0% +maximum effect in the in the minimum + + + align:start position:0% +maximum effect in the in the minimum +amount of time. And that also the other + + align:start position:0% +amount of time. And that also the other + + + align:start position:0% +amount of time. And that also the other +thing is the operators were not using + + align:start position:0% +thing is the operators were not using + + + align:start position:0% +thing is the operators were not using +this control algorithm. They were using + + align:start position:0% +this control algorithm. They were using + + + align:start position:0% +this control algorithm. They were using +that control algorithm. So it would + + align:start position:0% +that control algorithm. So it would + + + align:start position:0% +that control algorithm. So it would +never get to zero uh + + align:start position:0% +never get to zero uh + + + align:start position:0% +never get to zero uh +error. Okay. + + align:start position:0% +error. Okay. + + + align:start position:0% +error. Okay. +So with with a fairly large gap in in + + align:start position:0% +So with with a fairly large gap in in + + + align:start position:0% +So with with a fairly large gap in in +coverage here, what I've what I'm + + align:start position:0% +coverage here, what I've what I'm + + + align:start position:0% +coverage here, what I've what I'm +purporting to show you is that if I have + + align:start position:0% +purporting to show you is that if I have + + + align:start position:0% +purporting to show you is that if I have +a random if I have an output a process + + align:start position:0% +a random if I have an output a process + + + align:start position:0% +a random if I have an output a process +whose output looks like this and I apply + + align:start position:0% +whose output looks like this and I apply + + + align:start position:0% +whose output looks like this and I apply +this simple discrete time controller + + align:start position:0% +this simple discrete time controller + + + align:start position:0% +this simple discrete time controller +which means I measure adjust but adjust + + align:start position:0% +which means I measure adjust but adjust + + + align:start position:0% +which means I measure adjust but adjust +according + + align:start position:0% + + + + align:start position:0% + +to this this algorithm here which + + align:start position:0% +to this this algorithm here which + + + align:start position:0% +to this this algorithm here which +basically + + align:start position:0% +basically + + + align:start position:0% +basically +is this is something I think is + + align:start position:0% +is this is something I think is + + + align:start position:0% +is this is something I think is +important which basically says okay I'm + + align:start position:0% +important which basically says okay I'm + + + align:start position:0% +important which basically says okay I'm +the operator I have to make an + + align:start position:0% +the operator I have to make an + + + align:start position:0% +the operator I have to make an +adjustment to the process here's the + + align:start position:0% +adjustment to the process here's the + + + align:start position:0% +adjustment to the process here's the +adjustment I'm going to make and the + + align:start position:0% +adjustment I'm going to make and the + + + align:start position:0% +adjustment I'm going to make and the +adjustment I'm going to make is whatever + + align:start position:0% +adjustment I'm going to make is whatever + + + align:start position:0% +adjustment I'm going to make is whatever +it was the last time plus this + + align:start position:0% +it was the last time plus this + + + align:start position:0% +it was the last time plus this +controller gain which you're going to + + align:start position:0% +controller gain which you're going to + + + align:start position:0% +controller gain which you're going to +tell me what it is times the current + + align:start position:0% +tell me what it is times the current + + + align:start position:0% +tell me what it is times the current +error a little bit different than what + + align:start position:0% +error a little bit different than what + + + align:start position:0% +error a little bit different than what +it might have been uh + + align:start position:0% +it might have been uh + + + align:start position:0% +it might have been uh +otherwise uh you can also notice that if + + align:start position:0% +otherwise uh you can also notice that if + + + align:start position:0% +otherwise uh you can also notice that if +I bring this over to the other side what + + align:start position:0% +I bring this over to the other side what + + + align:start position:0% +I bring this over to the other side what +it's really telling the operator is the + + align:start position:0% +it's really telling the operator is the + + + align:start position:0% +it's really telling the operator is the +increment in the adjustment should be + + align:start position:0% +increment in the adjustment should be + + + align:start position:0% +increment in the adjustment should be +proportional to the error + + align:start position:0% +proportional to the error + + + align:start position:0% +proportional to the error +not the not the absolute value of it. + + align:start position:0% +not the not the absolute value of it. + + + align:start position:0% +not the not the absolute value of it. +But anyway, you implement that + + align:start position:0% +But anyway, you implement that + + + align:start position:0% +But anyway, you implement that +controller and what that says is that if + + align:start position:0% +controller and what that says is that if + + + align:start position:0% +controller and what that says is that if +I have a random output on my process + + align:start position:0% +I have a random output on my process + + + align:start position:0% +I have a random output on my process +stationary, you know, in a state of + + align:start position:0% +stationary, you know, in a state of + + + align:start position:0% +stationary, you know, in a state of +stationary uh statistical control, but + + align:start position:0% +stationary uh statistical control, but + + + align:start position:0% +stationary uh statistical control, but +offset from here, it tells me that at + + align:start position:0% +offset from here, it tells me that at + + + align:start position:0% +offset from here, it tells me that at +least the mean value + + align:start position:0% +least the mean value + + + align:start position:0% +least the mean value +here sort of + + align:start position:0% +here sort of + + + align:start position:0% +here sort of +before will now be the mean value after. + + align:start position:0% +before will now be the mean value after. + + + align:start position:0% +before will now be the mean value after. +But the question + + align:start position:0% +But the question + + + align:start position:0% +But the question +is will the distribution look like that + + align:start position:0% +is will the distribution look like that + + + align:start position:0% +is will the distribution look like that +or will it look + + align:start position:0% +or will it look + + + align:start position:0% +or will it look +like that? So we have to look at the + + align:start position:0% +like that? So we have to look at the + + + align:start position:0% +like that? So we have to look at the +random component. This gets a lot harder + + align:start position:0% +random component. This gets a lot harder + + + align:start position:0% +random component. This gets a lot harder +to do. So I'll just kind of pop through + + align:start position:0% +to do. So I'll just kind of pop through + + + align:start position:0% +to do. So I'll just kind of pop through +it. + + align:start position:0% +it. + + + align:start position:0% +it. +Um and again more heristically than than + + align:start position:0% +Um and again more heristically than than + + + align:start position:0% +Um and again more heristically than than +mathematically. Our + + align:start position:0% +mathematically. Our + + + align:start position:0% +mathematically. Our +random model of this thing is that we + + align:start position:0% +random model of this thing is that we + + + align:start position:0% +random model of this thing is that we +have this this normally independent uh + + align:start position:0% +have this this normally independent uh + + + align:start position:0% +have this this normally independent uh +uh identically distributed independent + + align:start position:0% +uh identically distributed independent + + + align:start position:0% +uh identically distributed independent +sequence uh for D subi. So it's a bunch + + align:start position:0% +sequence uh for D subi. So it's a bunch + + + align:start position:0% +sequence uh for D subi. So it's a bunch +of numbers that are coming out and + + align:start position:0% +of numbers that are coming out and + + + align:start position:0% +of numbers that are coming out and +they're sampled from a uh a normal + + align:start position:0% +they're sampled from a uh a normal + + + align:start position:0% +they're sampled from a uh a normal +distribution. + + align:start position:0% + + + + align:start position:0% + +Um if they are totally independent what + + align:start position:0% +Um if they are totally independent what + + + align:start position:0% +Um if they are totally independent what +that means is that d there's no way that + + align:start position:0% +that means is that d there's no way that + + + align:start position:0% +that means is that d there's no way that +I can predict what the next value of the + + align:start position:0% +I can predict what the next value of the + + + align:start position:0% +I can predict what the next value of the +disturbance will be. This d + + align:start position:0% +disturbance will be. This d + + + align:start position:0% +disturbance will be. This d +subi if there were then I could write an + + align:start position:0% +subi if there were then I could write an + + + align:start position:0% +subi if there were then I could write an +equation that says okay there's some + + align:start position:0% +equation that says okay there's some + + + align:start position:0% +equation that says okay there's some +relation between the current value and + + align:start position:0% +relation between the current value and + + + align:start position:0% +relation between the current value and +all the prior values. you often see + + align:start position:0% +all the prior values. you often see + + + align:start position:0% +all the prior values. you often see +these these so-called uh time series + + align:start position:0% +these these so-called uh time series + + + align:start position:0% +these these so-called uh time series +equations or discrete time equations or + + align:start position:0% +equations or discrete time equations or + + + align:start position:0% +equations or discrete time equations or +that sort of thing. Um but since there + + align:start position:0% +that sort of thing. Um but since there + + + align:start position:0% +that sort of thing. Um but since there +isn't then it says sorry it's just not + + align:start position:0% +isn't then it says sorry it's just not + + + align:start position:0% +isn't then it says sorry it's just not +equal to any of the pri any function of + + align:start position:0% +equal to any of the pri any function of + + + align:start position:0% +equal to any of the pri any function of +any of the prior values. There's no way + + align:start position:0% +any of the prior values. There's no way + + + align:start position:0% +any of the prior values. There's no way +to predict what's going to happen next. + + align:start position:0% +to predict what's going to happen next. + + + align:start position:0% +to predict what's going to happen next. +Okay. Um, so if I do that, then you can + + align:start position:0% +Okay. Um, so if I do that, then you can + + + align:start position:0% +Okay. Um, so if I do that, then you can +I think you can see then that knowing + + align:start position:0% +I think you can see then that knowing + + + align:start position:0% +I think you can see then that knowing +this doesn't tell me doesn't give me a + + align:start position:0% +this doesn't tell me doesn't give me a + + + align:start position:0% +this doesn't tell me doesn't give me a +good idea of how to adjust it to take + + align:start position:0% +good idea of how to adjust it to take + + + align:start position:0% +good idea of how to adjust it to take +care of what the next value is going to + + align:start position:0% + + + + align:start position:0% + +be. Okay, so there's no way that knowing + + align:start position:0% +be. Okay, so there's no way that knowing + + + align:start position:0% +be. Okay, so there's no way that knowing +the prior value of the disturbance will + + align:start position:0% +the prior value of the disturbance will + + + align:start position:0% +the prior value of the disturbance will +allow me to write an equation to exactly + + align:start position:0% +allow me to write an equation to exactly + + + align:start position:0% +allow me to write an equation to exactly +cancel what the next one will be. + + align:start position:0% +cancel what the next one will be. + + + align:start position:0% +cancel what the next one will be. +Okay. Right. So again, what what I'm + + align:start position:0% +Okay. Right. So again, what what I'm + + + align:start position:0% +Okay. Right. So again, what what I'm +saying is this. + + align:start position:0% +saying is this. + + + align:start position:0% +saying is this. +Um let's imagine here that I'm at I'm at + + align:start position:0% +Um let's imagine here that I'm at I'm at + + + align:start position:0% +Um let's imagine here that I'm at I'm at +time interval + + align:start position:0% +time interval + + + align:start position:0% +time interval +subi and I have a disturbance d subi and + + align:start position:0% +subi and I have a disturbance d subi and + + + align:start position:0% +subi and I have a disturbance d subi and +I measure that and I say ah the + + align:start position:0% +I measure that and I say ah the + + + align:start position:0% +I measure that and I say ah the +disturbance at this instant is the value + + align:start position:0% +disturbance at this instant is the value + + + align:start position:0% +disturbance at this instant is the value +of d + + align:start position:0% +of d + + + align:start position:0% +of d +subi. What I need to do then is come up + + align:start position:0% +subi. What I need to do then is come up + + + align:start position:0% +subi. What I need to do then is come up +with a if you will a delta u that's + + align:start position:0% +with a if you will a delta u that's + + + align:start position:0% +with a if you will a delta u that's +equal to minus d subi for the next + + align:start position:0% +equal to minus d subi for the next + + + align:start position:0% +equal to minus d subi for the next +cycle. + + align:start position:0% +cycle. + + + align:start position:0% +cycle. +But of course that's too late. I can't + + align:start position:0% +But of course that's too late. I can't + + + align:start position:0% +But of course that's too late. I can't +cancel out the disturbance that's + + align:start position:0% +cancel out the disturbance that's + + + align:start position:0% +cancel out the disturbance that's +already happened. So I need to know what + + align:start position:0% +already happened. So I need to know what + + + align:start position:0% +already happened. So I need to know what +D subi plus one + + align:start position:0% +D subi plus one + + + align:start position:0% +D subi plus one +is. And then I could write this equation + + align:start position:0% +is. And then I could write this equation + + + align:start position:0% +is. And then I could write this equation +and I'd cancel it + + align:start position:0% +and I'd cancel it + + + align:start position:0% +and I'd cancel it +out. But I can't, right? Because I have + + align:start position:0% +out. But I can't, right? Because I have + + + align:start position:0% +out. But I can't, right? Because I have +no idea what the next one will be. So + + align:start position:0% +no idea what the next one will be. So + + + align:start position:0% +no idea what the next one will be. So +all you can imagine but but with the + + align:start position:0% +all you can imagine but but with the + + + align:start position:0% +all you can imagine but but with the +controller that I've written, there's no + + align:start position:0% +controller that I've written, there's no + + + align:start position:0% +controller that I've written, there's no +way to separate out these two functions. + + align:start position:0% +way to separate out these two functions. + + + align:start position:0% +way to separate out these two functions. +So I'm going to do this anyway. I'm + + align:start position:0% +So I'm going to do this anyway. I'm + + + align:start position:0% +So I'm going to do this anyway. I'm +going to do this knowing full well that + + align:start position:0% +going to do this knowing full well that + + + align:start position:0% +going to do this knowing full well that +it's not right because that's the only + + align:start position:0% +it's not right because that's the only + + + align:start position:0% +it's not right because that's the only +way I can implement the controller. And + + align:start position:0% +way I can implement the controller. And + + + align:start position:0% +way I can implement the controller. And +so heristically it can't be good, right? + + align:start position:0% +so heristically it can't be good, right? + + + align:start position:0% +so heristically it can't be good, right? +So it must be bad. And if you go through + + align:start position:0% +So it must be bad. And if you go through + + + align:start position:0% +So it must be bad. And if you go through +oops, if you go through the theory on + + align:start position:0% +oops, if you go through the theory on + + + align:start position:0% +oops, if you go through the theory on +this and even do simulations and things + + align:start position:0% +this and even do simulations and things + + + align:start position:0% +this and even do simulations and things +like that, indeed you find out it's bad. + + align:start position:0% +like that, indeed you find out it's bad. + + + align:start position:0% +like that, indeed you find out it's bad. +And here's here's the measure of + + align:start position:0% +And here's here's the measure of + + + align:start position:0% +And here's here's the measure of +badness. Here's a variance ratio. This + + align:start position:0% +badness. Here's a variance ratio. This + + + align:start position:0% +badness. Here's a variance ratio. This +is basically saying I've taken a random + + align:start position:0% +is basically saying I've taken a random + + + align:start position:0% +is basically saying I've taken a random +uh + + align:start position:0% +uh + + + align:start position:0% +uh +number with with a distribution and with + + align:start position:0% +number with with a distribution and with + + + align:start position:0% +number with with a distribution and with +a certain variance and that's sigma + + align:start position:0% +a certain variance and that's sigma + + + align:start position:0% +a certain variance and that's sigma +squared. This is sort of before and + + align:start position:0% +squared. This is sort of before and + + + align:start position:0% +squared. This is sort of before and +after. Let me write that down here. This + + align:start position:0% +after. Let me write that down here. This + + + align:start position:0% +after. Let me write that down here. This +is before and this is after. So this is + + align:start position:0% +is before and this is after. So this is + + + align:start position:0% +is before and this is after. So this is +how much the this ratio is how much the + + align:start position:0% +how much the this ratio is how much the + + + align:start position:0% +how much the this ratio is how much the +control system has increased or + + align:start position:0% +control system has increased or + + + align:start position:0% +control system has increased or +decreased the variance of the + + align:start position:0% +decreased the variance of the + + + align:start position:0% +decreased the variance of the +output. And this is as a function of + + align:start position:0% +output. And this is as a function of + + + align:start position:0% +output. And this is as a function of +this loop gain that we talked about. + + align:start position:0% +this loop gain that we talked about. + + + align:start position:0% +this loop gain that we talked about. +this this quantity that we'd like to + + align:start position:0% +this this quantity that we'd like to + + + align:start position:0% +this this quantity that we'd like to +have at one. Okay. So, what does this + + align:start position:0% +have at one. Okay. So, what does this + + + align:start position:0% +have at one. Okay. So, what does this +mean? Well, if I don't do any control, + + align:start position:0% +mean? Well, if I don't do any control, + + + align:start position:0% +mean? Well, if I don't do any control, +the loop gain is zero. Then I haven't + + align:start position:0% +the loop gain is zero. Then I haven't + + + align:start position:0% +the loop gain is zero. Then I haven't +increased the variance at all. And so, + + align:start position:0% +increased the variance at all. And so, + + + align:start position:0% +increased the variance at all. And so, +it's at one. That ratio is at one. Let's + + align:start position:0% +it's at one. That ratio is at one. Let's + + + align:start position:0% +it's at one. That ratio is at one. Let's +go out to our favorite number, which was + + align:start position:0% +go out to our favorite number, which was + + + align:start position:0% +go out to our favorite number, which was +one because it gave us the best + + align:start position:0% +one because it gave us the best + + + align:start position:0% +one because it gave us the best +response. And it means I've increased + + align:start position:0% +response. And it means I've increased + + + align:start position:0% +response. And it means I've increased +the variance ratio to about + + align:start position:0% +the variance ratio to about + + + align:start position:0% +the variance ratio to about +2.2. Uh, or the standard deviation + + align:start position:0% +2.2. Uh, or the standard deviation + + + align:start position:0% +2.2. Uh, or the standard deviation +u ratio. I think it comes out to about + + align:start position:0% +u ratio. I think it comes out to about + + + align:start position:0% +u ratio. I think it comes out to about +1.5. So I've taken this width and I've + + align:start position:0% +1.5. So I've taken this width and I've + + + align:start position:0% +1.5. So I've taken this width and I've +increased it by + + align:start position:0% +increased it by + + + align:start position:0% +increased it by +50%. Nothing I can do about it. Nothing + + align:start position:0% +50%. Nothing I can do about it. Nothing + + + align:start position:0% +50%. Nothing I can do about it. Nothing +I can do about it. I can run it a slower + + align:start position:0% +I can do about it. I can run it a slower + + + align:start position:0% +I can do about it. I can run it a slower +I can run a slower process. I can say + + align:start position:0% +I can run a slower process. I can say + + + align:start position:0% +I can run a slower process. I can say +okay I'll take some time steps to reach + + align:start position:0% +okay I'll take some time steps to reach + + + align:start position:0% +okay I'll take some time steps to reach +steady state and maybe bring it down to + + align:start position:0% +steady state and maybe bring it down to + + + align:start position:0% +steady state and maybe bring it down to +1.3. But you know so this is in fact a + + align:start position:0% +1.3. But you know so this is in fact a + + + align:start position:0% +1.3. But you know so this is in fact a +really good description of what I was + + align:start position:0% +really good description of what I was + + + align:start position:0% +really good description of what I was +telling you before. With this control + + align:start position:0% +telling you before. With this control + + + align:start position:0% +telling you before. With this control +system, with this type of noise, I can + + align:start position:0% +system, with this type of noise, I can + + + align:start position:0% +system, with this type of noise, I can +take a process that looks like this. I + + align:start position:0% +take a process that looks like this. I + + + align:start position:0% +take a process that looks like this. I +can guarantee to center it, but I'm + + align:start position:0% +can guarantee to center it, but I'm + + + align:start position:0% +can guarantee to center it, but I'm +going to increase the variance by some + + align:start position:0% +going to increase the variance by some + + + align:start position:0% +going to increase the variance by some +factor depending on uh what I set the + + align:start position:0% +factor depending on uh what I set the + + + align:start position:0% +factor depending on uh what I set the +gain at, probably + + align:start position:0% +gain at, probably + + + align:start position:0% +gain at, probably +50%. Is that good or is that bad? + + align:start position:0% +50%. Is that good or is that bad? + + + align:start position:0% +50%. Is that good or is that bad? +Depends. Getting rid of mean shifts is a + + align:start position:0% +Depends. Getting rid of mean shifts is a + + + align:start position:0% +Depends. Getting rid of mean shifts is a +pretty important thing. If you think + + align:start position:0% +pretty important thing. If you think + + + align:start position:0% +pretty important thing. If you think +about sort of the philosophy of six + + align:start position:0% +about sort of the philosophy of six + + + align:start position:0% +about sort of the philosophy of six +sigma, this is actually pretty good + + align:start position:0% +sigma, this is actually pretty good + + + align:start position:0% +sigma, this is actually pretty good +because six sigma once starts with + + align:start position:0% +because six sigma once starts with + + + align:start position:0% +because six sigma once starts with +narrow distributions allows for mean + + align:start position:0% +narrow distributions allows for mean + + + align:start position:0% +narrow distributions allows for mean +offsets. And if we say, okay, but we'll + + align:start position:0% +offsets. And if we say, okay, but we'll + + + align:start position:0% +offsets. And if we say, okay, but we'll +make sure you don't get mean offsets and + + align:start position:0% +make sure you don't get mean offsets and + + + align:start position:0% +make sure you don't get mean offsets and +you already have a narrow distribution, + + align:start position:0% +you already have a narrow distribution, + + + align:start position:0% +you already have a narrow distribution, +we'll only make it 50% wider. + + align:start position:0% + + + + align:start position:0% + +Okay. So, I don't want to sell it too + + align:start position:0% +Okay. So, I don't want to sell it too + + + align:start position:0% +Okay. So, I don't want to sell it too +much, but it it's it's half good, it's + + align:start position:0% +much, but it it's it's half good, it's + + + align:start position:0% +much, but it it's it's half good, it's +half bad, Richard, but if you can um + + align:start position:0% +half bad, Richard, but if you can um + + + align:start position:0% +half bad, Richard, but if you can um +adjust the loop gain at 02, we we will + + align:start position:0% +adjust the loop gain at 02, we we will + + + align:start position:0% +adjust the loop gain at 02, we we will +still arrive at our process mean, right? + + align:start position:0% +still arrive at our process mean, right? + + + align:start position:0% +still arrive at our process mean, right? +Yep. Yeah. But I'll show you an example + + align:start position:0% +Yep. Yeah. But I'll show you an example + + + align:start position:0% +Yep. Yeah. But I'll show you an example +of why that might not be a great idea uh + + align:start position:0% +of why that might not be a great idea uh + + + align:start position:0% +of why that might not be a great idea uh +when we get to the + + align:start position:0% +when we get to the + + + align:start position:0% +when we get to the +experiments. Okay. So, the conclusion + + align:start position:0% +experiments. Okay. So, the conclusion + + + align:start position:0% +experiments. Okay. So, the conclusion +cycleto cycle control for an + + align:start position:0% +cycleto cycle control for an + + + align:start position:0% +cycleto cycle control for an +uncorrelated random + + align:start position:0% +uncorrelated random + + + align:start position:0% +uncorrelated random +disturbance can do what I said. It takes + + align:start position:0% +disturbance can do what I said. It takes + + + align:start position:0% +disturbance can do what I said. It takes +this distribution, shifts it, guarantees + + align:start position:0% +this distribution, shifts it, guarantees + + + align:start position:0% +this distribution, shifts it, guarantees +that it's going to be at zero mean, but + + align:start position:0% +that it's going to be at zero mean, but + + + align:start position:0% +that it's going to be at zero mean, but +it widens the distribution. Okay, + + align:start position:0% +it widens the distribution. Okay, + + + align:start position:0% +it widens the distribution. Okay, +obviously I've I've drawn this so that + + align:start position:0% +obviously I've I've drawn this so that + + + align:start position:0% +obviously I've I've drawn this so that +it still looks fine. And the process and + + align:start position:0% +it still looks fine. And the process and + + + align:start position:0% +it still looks fine. And the process and +if and if I looked at this as CPK or + + align:start position:0% +if and if I looked at this as CPK or + + + align:start position:0% +if and if I looked at this as CPK or +expected quality loss, the way I've + + align:start position:0% +expected quality loss, the way I've + + + align:start position:0% +expected quality loss, the way I've +drawn it, I mean, this is a winner by by + + align:start position:0% +drawn it, I mean, this is a winner by by + + + align:start position:0% +drawn it, I mean, this is a winner by by +a lot, right? This has this has terrible + + align:start position:0% +a lot, right? This has this has terrible + + + align:start position:0% +a lot, right? This has this has terrible +process capability. And now this is this + + align:start position:0% +process capability. And now this is this + + + align:start position:0% +process capability. And now this is this +is really pretty good even though it got + + align:start position:0% +is really pretty good even though it got + + + align:start position:0% +is really pretty good even though it got +wider because of the mean shift. + + align:start position:0% +wider because of the mean shift. + + + align:start position:0% +wider because of the mean shift. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +However, not all processes are the same + + align:start position:0% +However, not all processes are the same + + + align:start position:0% +However, not all processes are the same +and uh there's there's a big difference + + align:start position:0% +and uh there's there's a big difference + + + align:start position:0% +and uh there's there's a big difference +in a lot of these. And so what if the + + align:start position:0% +in a lot of these. And so what if the + + + align:start position:0% +in a lot of these. And so what if the +process is not well described by a + + align:start position:0% +process is not well described by a + + + align:start position:0% +process is not well described by a +normally identically distributed + + align:start position:0% +normally identically distributed + + + align:start position:0% +normally identically distributed +independent random + + align:start position:0% +independent random + + + align:start position:0% +independent random +variable? Don't worry about what that + + align:start position:0% +variable? Don't worry about what that + + + align:start position:0% +variable? Don't worry about what that +says right there. + + align:start position:0% +says right there. + + + align:start position:0% +says right there. +Um and again think about there there's + + align:start position:0% +Um and again think about there there's + + + align:start position:0% +Um and again think about there there's +it's sometimes called the concept of + + align:start position:0% +it's sometimes called the concept of + + + align:start position:0% +it's sometimes called the concept of +history or process history or memory or + + align:start position:0% +history or process history or memory or + + + align:start position:0% +history or process history or memory or +memory or something like that. Imagine + + align:start position:0% +memory or something like that. Imagine + + + align:start position:0% +memory or something like that. Imagine +uh it would I think it would work well + + align:start position:0% +uh it would I think it would work well + + + align:start position:0% +uh it would I think it would work well +with a semiconductor process but I know + + align:start position:0% +with a semiconductor process but I know + + + align:start position:0% +with a semiconductor process but I know +it works well with injection molding + + align:start position:0% +it works well with injection molding + + + align:start position:0% +it works well with injection molding +because I'll show you in a second. + + align:start position:0% +because I'll show you in a second. + + + align:start position:0% +because I'll show you in a second. +Imagine I have an injection molding + + align:start position:0% +Imagine I have an injection molding + + + align:start position:0% +Imagine I have an injection molding +process and I decide to make these + + align:start position:0% +process and I decide to make these + + + align:start position:0% +process and I decide to make these +changes by changing the hold time. Every + + align:start position:0% +changes by changing the hold time. Every + + + align:start position:0% +changes by changing the hold time. Every +time I get an error, I change the hold + + align:start position:0% +time I get an error, I change the hold + + + align:start position:0% +time I get an error, I change the hold +time. But I change So every time I cycle + + align:start position:0% +time. But I change So every time I cycle + + + align:start position:0% +time. But I change So every time I cycle +this thing, which is pretty rapid, I + + align:start position:0% +this thing, which is pretty rapid, I + + + align:start position:0% +this thing, which is pretty rapid, I +change the hold time. Now, the hold time + + align:start position:0% +change the hold time. Now, the hold time + + + align:start position:0% +change the hold time. Now, the hold time +determines, among other things, the + + align:start position:0% +determines, among other things, the + + + align:start position:0% +determines, among other things, the +temperature at which you open the mold, + + align:start position:0% +temperature at which you open the mold, + + + align:start position:0% +temperature at which you open the mold, +how cool it is when it opens up, when + + align:start position:0% +how cool it is when it opens up, when + + + align:start position:0% +how cool it is when it opens up, when +you release the pressure. + + align:start position:0% +you release the pressure. + + + align:start position:0% +you release the pressure. +Okay. How long do you think it takes + + align:start position:0% +Okay. How long do you think it takes + + + align:start position:0% +Okay. How long do you think it takes +that mold to reach equilibrium after I + + align:start position:0% +that mold to reach equilibrium after I + + + align:start position:0% +that mold to reach equilibrium after I +change the hold time? You think it + + align:start position:0% +change the hold time? You think it + + + align:start position:0% +change the hold time? You think it +reaches equilibrium after the first + + align:start position:0% +reaches equilibrium after the first + + + align:start position:0% +reaches equilibrium after the first +cycle? Big piece of metal. I say I hold + + align:start position:0% +cycle? Big piece of metal. I say I hold + + + align:start position:0% +cycle? Big piece of metal. I say I hold +it an extra 10 + + align:start position:0% +it an extra 10 + + + align:start position:0% +it an extra 10 +seconds, you know, so it starts to cool + + align:start position:0% +seconds, you know, so it starts to cool + + + align:start position:0% +seconds, you know, so it starts to cool +off. But can you see that it's probably + + align:start position:0% +off. But can you see that it's probably + + + align:start position:0% +off. But can you see that it's probably +going to take several of those cycles + + align:start position:0% +going to take several of those cycles + + + align:start position:0% +going to take several of those cycles +before it cools off to its new + + align:start position:0% +before it cools off to its new + + + align:start position:0% +before it cools off to its new +equilibrium temperature. Does that make + + align:start position:0% +equilibrium temperature. Does that make + + + align:start position:0% +equilibrium temperature. Does that make +sense? And then if I say, let's let's + + align:start position:0% +sense? And then if I say, let's let's + + + align:start position:0% +sense? And then if I say, let's let's +open it quicker all of a sudden. I open + + align:start position:0% +open it quicker all of a sudden. I open + + + align:start position:0% +open it quicker all of a sudden. I open +it quicker, it's going to start to heat + + align:start position:0% +it quicker, it's going to start to heat + + + align:start position:0% +it quicker, it's going to start to heat +up. It's going to take a while for it to + + align:start position:0% +up. It's going to take a while for it to + + + align:start position:0% +up. It's going to take a while for it to +heat up there. So in fact, the process + + align:start position:0% +heat up there. So in fact, the process + + + align:start position:0% +heat up there. So in fact, the process +is not at steady + + align:start position:0% +is not at steady + + + align:start position:0% +is not at steady +state. At least the disturbances are not + + align:start position:0% +state. At least the disturbances are not + + + align:start position:0% +state. At least the disturbances are not +at steady state. There's a little bit of + + align:start position:0% +at steady state. There's a little bit of + + + align:start position:0% +at steady state. There's a little bit of +history and we can we can represent this + + align:start position:0% +history and we can we can represent this + + + align:start position:0% +history and we can we can represent this +uh mathematically by taking a purely + + align:start position:0% +uh mathematically by taking a purely + + + align:start position:0% +uh mathematically by taking a purely +random independent sequence and put it + + align:start position:0% +random independent sequence and put it + + + align:start position:0% +random independent sequence and put it +through a first order process and you + + align:start position:0% +through a first order process and you + + + align:start position:0% +through a first order process and you +end up with an equation that shows in + + align:start position:0% +end up with an equation that shows in + + + align:start position:0% +end up with an equation that shows in +fact the next disturbance is somewhat + + align:start position:0% +fact the next disturbance is somewhat + + + align:start position:0% +fact the next disturbance is somewhat +predicted by the prior ones. There's a + + align:start position:0% +predicted by the prior ones. There's a + + + align:start position:0% +predicted by the prior ones. There's a +little bit of memory between the two and + + align:start position:0% +little bit of memory between the two and + + + align:start position:0% +little bit of memory between the two and +this is where we get the concept of some + + align:start position:0% +this is where we get the concept of some + + + align:start position:0% +this is where we get the concept of some +process + + align:start position:0% + + + + align:start position:0% + +correlation. So what happens if there's + + align:start position:0% +correlation. So what happens if there's + + + align:start position:0% +correlation. So what happens if there's +process correlation? Well, this is a lot + + align:start position:0% +process correlation? Well, this is a lot + + + align:start position:0% +process correlation? Well, this is a lot +harder to do theoretically. So, we did + + align:start position:0% +harder to do theoretically. So, we did + + + align:start position:0% +harder to do theoretically. So, we did +it u um in simulation. I think we also + + align:start position:0% +it u um in simulation. I think we also + + + align:start position:0% +it u um in simulation. I think we also +have a theoretical one on this. But now + + align:start position:0% +have a theoretical one on this. But now + + + align:start position:0% +have a theoretical one on this. But now +look at here's the variance ratio. Same + + align:start position:0% +look at here's the variance ratio. Same + + + align:start position:0% +look at here's the variance ratio. Same +thing as before, but now with a with a a + + align:start position:0% +thing as before, but now with a with a a + + + align:start position:0% +thing as before, but now with a with a a +disturbance that has a little bit of + + align:start position:0% +disturbance that has a little bit of + + + align:start position:0% +disturbance that has a little bit of +correlation. Watch what happens as I + + align:start position:0% +correlation. Watch what happens as I + + + align:start position:0% +correlation. Watch what happens as I +increase the gain from zero up to one. + + align:start position:0% +increase the gain from zero up to one. + + + align:start position:0% +increase the gain from zero up to one. +What happens to the variance + + align:start position:0% +What happens to the variance + + + align:start position:0% +What happens to the variance +ratio? It actually goes down for a + + align:start position:0% +ratio? It actually goes down for a + + + align:start position:0% +ratio? It actually goes down for a +while. I'm not quite sure this is I'm + + align:start position:0% +while. I'm not quite sure this is I'm + + + align:start position:0% +while. I'm not quite sure this is I'm +not sure these numbers are right. This + + align:start position:0% +not sure these numbers are right. This + + + align:start position:0% +not sure these numbers are right. This +one's not right. + + align:start position:0% +one's not right. + + + align:start position:0% +one's not right. +That was not right. But anyway, it's + + align:start position:0% +That was not right. But anyway, it's + + + align:start position:0% +That was not right. But anyway, it's +going + + align:start position:0% +going + + + align:start position:0% +going +down. Actually, I'm sorry. That that can + + align:start position:0% +down. Actually, I'm sorry. That that can + + + align:start position:0% +down. Actually, I'm sorry. That that can +be right. There's another factor in + + align:start position:0% +be right. There's another factor in + + + align:start position:0% +be right. There's another factor in +here. So, why would the variance ratio + + align:start position:0% +here. So, why would the variance ratio + + + align:start position:0% +here. So, why would the variance ratio +go down? Well, it's because I now + + align:start position:0% +go down? Well, it's because I now + + + align:start position:0% +go down? Well, it's because I now +actually do get some information about + + align:start position:0% +actually do get some information about + + + align:start position:0% +actually do get some information about +what the next disturbance is going to be + + align:start position:0% +what the next disturbance is going to be + + + align:start position:0% +what the next disturbance is going to be +based on the prior one. That's + + align:start position:0% +based on the prior one. That's + + + align:start position:0% +based on the prior one. That's +essentially what correlation means. And + + align:start position:0% +essentially what correlation means. And + + + align:start position:0% +essentially what correlation means. And +it's kind of cool because, you know, we + + align:start position:0% +it's kind of cool because, you know, we + + + align:start position:0% +it's kind of cool because, you know, we +can't be much more specific than that, + + align:start position:0% +can't be much more specific than that, + + + align:start position:0% +can't be much more specific than that, +but it basically says + + align:start position:0% +but it basically says + + + align:start position:0% +but it basically says +um I can I can I'll show you this in a + + align:start position:0% +um I can I can I'll show you this in a + + + align:start position:0% +um I can I can I'll show you this in a +moment, but I can actually use this + + align:start position:0% +moment, but I can actually use this + + + align:start position:0% +moment, but I can actually use this +controller as a way of measuring + + align:start position:0% +controller as a way of measuring + + + align:start position:0% +controller as a way of measuring +correlation in a process. If the + + align:start position:0% +correlation in a process. If the + + + align:start position:0% +correlation in a process. If the +variance ratio goes down, there had to + + align:start position:0% +variance ratio goes down, there had to + + + align:start position:0% +variance ratio goes down, there had to +have been some + + align:start position:0% +have been some + + + align:start position:0% +have been some +correlation. So yeah, here's the curve I + + align:start position:0% +correlation. So yeah, here's the curve I + + + align:start position:0% +correlation. So yeah, here's the curve I +was thinking of. So you can think of it + + align:start position:0% +was thinking of. So you can think of it + + + align:start position:0% +was thinking of. So you can think of it +instead as a sort of a continuum of + + align:start position:0% +instead as a sort of a continuum of + + + align:start position:0% +instead as a sort of a continuum of +correlation. Here's zero correlation and + + align:start position:0% +correlation. Here's zero correlation and + + + align:start position:0% +correlation. Here's zero correlation and +here's large correlation, if you will. + + align:start position:0% +here's large correlation, if you will. + + + align:start position:0% +here's large correlation, if you will. +So zero correlation is the first case we + + align:start position:0% +So zero correlation is the first case we + + + align:start position:0% +So zero correlation is the first case we +had the independent random variable and + + align:start position:0% +had the independent random variable and + + + align:start position:0% +had the independent random variable and +here's that same curve that we had uh + + align:start position:0% +here's that same curve that we had uh + + + align:start position:0% +here's that same curve that we had uh +before where at one you know it was + + align:start position:0% +before where at one you know it was + + + align:start position:0% +before where at one you know it was +still uh up there as I increase the + + align:start position:0% +still uh up there as I increase the + + + align:start position:0% +still uh up there as I increase the +amount of correlation in other words as + + align:start position:0% +amount of correlation in other words as + + + align:start position:0% +amount of correlation in other words as +the memory gets stronger and stronger + + align:start position:0% +the memory gets stronger and stronger + + + align:start position:0% +the memory gets stronger and stronger +this curve starts to come down here + + align:start position:0% +this curve starts to come down here + + + align:start position:0% +this curve starts to come down here +where at very large values you can see + + align:start position:0% +where at very large values you can see + + + align:start position:0% +where at very large values you can see +that at one I could have a variance + + align:start position:0% +that at one I could have a variance + + + align:start position:0% +that at one I could have a variance +ratio as low as a + + align:start position:0% +ratio as low as a + + + align:start position:0% +ratio as low as a +Which means that depending on the + + align:start position:0% +Which means that depending on the + + + align:start position:0% +Which means that depending on the +physics of the process, I could take a + + align:start position:0% +physics of the process, I could take a + + + align:start position:0% +physics of the process, I could take a +broad shifted distribution and make it + + align:start position:0% +broad shifted distribution and make it + + + align:start position:0% +broad shifted distribution and make it +narrow and centered with this approach. + + align:start position:0% +narrow and centered with this approach. + + + align:start position:0% +narrow and centered with this approach. +And this is with exactly the same + + align:start position:0% +And this is with exactly the same + + + align:start position:0% +And this is with exactly the same +controller. Nothing different. Okay. + + align:start position:0% +controller. Nothing different. Okay. + + + align:start position:0% +controller. Nothing different. Okay. +So the cool thing is that + + align:start position:0% +So the cool thing is that + + + align:start position:0% +So the cool thing is that +um we end up with these it's actually a + + align:start position:0% +um we end up with these it's actually a + + + align:start position:0% +um we end up with these it's actually a +continuum but we can say that for a + + align:start position:0% +continuum but we can say that for a + + + align:start position:0% +continuum but we can say that for a +totally uncorrelated process here's + + align:start position:0% +totally uncorrelated process here's + + + align:start position:0% +totally uncorrelated process here's +what's going to happen mean shift + + align:start position:0% +what's going to happen mean shift + + + align:start position:0% +what's going to happen mean shift +invariance + + align:start position:0% +invariance + + + align:start position:0% +invariance +increase if we start to have some + + align:start position:0% +increase if we start to have some + + + align:start position:0% +increase if we start to have some +correlation in the process and there's + + align:start position:0% +correlation in the process and there's + + + align:start position:0% +correlation in the process and there's +some memory some reason that the that + + align:start position:0% +some memory some reason that the that + + + align:start position:0% +some memory some reason that the that +the disturbance is + + align:start position:0% +the disturbance is + + + align:start position:0% +the disturbance is +occurring we can start to actually uh + + align:start position:0% +occurring we can start to actually uh + + + align:start position:0% +occurring we can start to actually uh +get both + + align:start position:0% + + + + align:start position:0% + +Okay. So, who believes + + align:start position:0% + + + + align:start position:0% + +this? It's just simulation. It's just + + align:start position:0% +this? It's just simulation. It's just + + + align:start position:0% +this? It's just simulation. It's just +math. Who believes it? Come + + align:start position:0% +math. Who believes it? Come + + + align:start position:0% +math. Who believes it? Come +on. Abstension is not allowed. + + align:start position:0% + + + + align:start position:0% + +believers + + align:start position:0% +believers + + + align:start position:0% +believers +I don't believe in bending an injection + + align:start position:0% +I don't believe in bending an injection + + + align:start position:0% +I don't believe in bending an injection +molding but other than that + + align:start position:0% +molding but other than that + + + align:start position:0% +molding but other than that +believers agnostics okay um obviously it + + align:start position:0% +believers agnostics okay um obviously it + + + align:start position:0% +believers agnostics okay um obviously it +must work I wouldn't uh wouldn't say + + align:start position:0% +must work I wouldn't uh wouldn't say + + + align:start position:0% +must work I wouldn't uh wouldn't say +this but um so George Sue a good part of + + align:start position:0% +this but um so George Sue a good part of + + + align:start position:0% +this but um so George Sue a good part of +his thesis was to say that the theory + + align:start position:0% +his thesis was to say that the theory + + + align:start position:0% +his thesis was to say that the theory +wasn't that in the end if you'd already + + align:start position:0% +wasn't that in the end if you'd already + + + align:start position:0% +wasn't that in the end if you'd already +had the background the theory isn't that + + align:start position:0% +had the background the theory isn't that + + + align:start position:0% +had the background the theory isn't that +that extensive and it does seem too good + + align:start position:0% +that extensive and it does seem too good + + + align:start position:0% +that extensive and it does seem too good +to be true so we said let's do an + + align:start position:0% +to be true so we said let's do an + + + align:start position:0% +to be true so we said let's do an +experiment and let's try to find two + + align:start position:0% +experiment and let's try to find two + + + align:start position:0% +experiment and let's try to find two +extremes. Let's find something that we + + align:start position:0% +extremes. Let's find something that we + + + align:start position:0% +extremes. Let's find something that we +think has the least amount of + + align:start position:0% +think has the least amount of + + + align:start position:0% +think has the least amount of +correlation and something that has + + align:start position:0% +correlation and something that has + + + align:start position:0% +correlation and something that has +reasonable correlation. Let's also find + + align:start position:0% +reasonable correlation. Let's also find + + + align:start position:0% +reasonable correlation. Let's also find +something that's quick and easy to do in + + align:start position:0% +something that's quick and easy to do in + + + align:start position:0% +something that's quick and easy to do in +the lab that we have. Uh and so we + + align:start position:0% +the lab that we have. Uh and so we + + + align:start position:0% +the lab that we have. Uh and so we +decided not to do semiconductors. We + + align:start position:0% +decided not to do semiconductors. We + + + align:start position:0% +decided not to do semiconductors. We +decided to do bending and injection + + align:start position:0% +decided to do bending and injection + + + align:start position:0% +decided to do bending and injection +molding. And uh so George set up this + + align:start position:0% +molding. And uh so George set up this + + + align:start position:0% +molding. And uh so George set up this +experiment which um in fact you guys at + + align:start position:0% +experiment which um in fact you guys at + + + align:start position:0% +experiment which um in fact you guys at +Singapore when you view this will will + + align:start position:0% +Singapore when you view this will will + + + align:start position:0% +Singapore when you view this will will +recognize because you've done this in + + align:start position:0% +recognize because you've done this in + + + align:start position:0% +recognize because you've done this in +your summer experiments. Uh it's an + + align:start position:0% +your summer experiments. Uh it's an + + + align:start position:0% +your summer experiments. Uh it's an +experiment we used to do in this class + + align:start position:0% +experiment we used to do in this class + + + align:start position:0% +experiment we used to do in this class +and it's you take a simple strip of of + + align:start position:0% +and it's you take a simple strip of of + + + align:start position:0% +and it's you take a simple strip of of +sheet metal and you bend it. The input + + align:start position:0% +sheet metal and you bend it. The input + + + align:start position:0% +sheet metal and you bend it. The input +is the depth of the punch, the output is + + align:start position:0% +is the depth of the punch, the output is + + + align:start position:0% +is the depth of the punch, the output is +the angle. Pretty simple. So um and + + align:start position:0% +the angle. Pretty simple. So um and + + + align:start position:0% +the angle. Pretty simple. So um and +we're going to do injection molding. So + + align:start position:0% +we're going to do injection molding. So + + + align:start position:0% +we're going to do injection molding. So +uh this is in George's thesis. And + + align:start position:0% +uh this is in George's thesis. And + + + align:start position:0% +uh this is in George's thesis. And +here's the process model for bending. + + align:start position:0% +here's the process model for bending. + + + align:start position:0% +here's the process model for bending. +Okay, pretty simple, right? The input is + + align:start position:0% +Okay, pretty simple, right? The input is + + + align:start position:0% +Okay, pretty simple, right? The input is +the displacement of that punch. The + + align:start position:0% +the displacement of that punch. The + + + align:start position:0% +the displacement of that punch. The +output is the angle. George did a number + + align:start position:0% +output is the angle. George did a number + + + align:start position:0% +output is the angle. George did a number +of + + align:start position:0% +of + + + align:start position:0% +of +tests. He put in different punts jets. + + align:start position:0% +tests. He put in different punts jets. + + + align:start position:0% +tests. He put in different punts jets. +He measured different + + align:start position:0% +He measured different + + + align:start position:0% +He measured different +angles. Shouldn't be this straight, but + + align:start position:0% +angles. Shouldn't be this straight, but + + + align:start position:0% +angles. Shouldn't be this straight, but +he got some good results. And and so he + + align:start position:0% +he got some good results. And and so he + + + align:start position:0% +he got some good results. And and so he +came up with this number for a + + align:start position:0% +came up with this number for a + + + align:start position:0% +came up with this number for a +particular value of steel. Now, keep in + + align:start position:0% +particular value of steel. Now, keep in + + + align:start position:0% +particular value of steel. Now, keep in +mind this number will change immediately + + align:start position:0% +mind this number will change immediately + + + align:start position:0% +mind this number will change immediately +if I put different thickness material in + + align:start position:0% +if I put different thickness material in + + + align:start position:0% +if I put different thickness material in +or a different uh composition material + + align:start position:0% +or a different uh composition material + + + align:start position:0% +or a different uh composition material +because it depends on yield strengths + + align:start position:0% +because it depends on yield strengths + + + align:start position:0% +because it depends on yield strengths +and and stiffnesses and that sort of + + align:start position:0% +and and stiffnesses and that sort of + + + align:start position:0% +and and stiffnesses and that sort of +thing. But he got a nice number for + + align:start position:0% +thing. But he got a nice number for + + + align:start position:0% +thing. But he got a nice number for +this. So all he needed from that was the + + align:start position:0% +this. So all he needed from that was the + + + align:start position:0% +this. So all he needed from that was the +slope. Now he had that slope. He could + + align:start position:0% +slope. Now he had that slope. He could + + + align:start position:0% +slope. Now he had that slope. He could +tune the the loop gain knowing that + + align:start position:0% +tune the the loop gain knowing that + + + align:start position:0% +tune the the loop gain knowing that +slope to be somewhere around where we + + align:start position:0% +slope to be somewhere around where we + + + align:start position:0% +slope to be somewhere around where we +wanted it to be. So he implemented that + + align:start position:0% +wanted it to be. So he implemented that + + + align:start position:0% +wanted it to be. So he implemented that +and uh this data is a little bit weird + + align:start position:0% +and uh this data is a little bit weird + + + align:start position:0% +and uh this data is a little bit weird +because we hadn't at this point done all + + align:start position:0% +because we hadn't at this point done all + + + align:start position:0% +because we hadn't at this point done all +the theory and realized that there was + + align:start position:0% +the theory and realized that there was + + + align:start position:0% +the theory and realized that there was +only one true controller. So none of + + align:start position:0% +only one true controller. So none of + + + align:start position:0% +only one true controller. So none of +these are actually for the best + + align:start position:0% +these are actually for the best + + + align:start position:0% +these are actually for the best +controller case. So here's for a + + align:start position:0% +controller case. So here's for a + + + align:start position:0% +controller case. So here's for a +controller that is a proportional + + align:start position:0% +controller that is a proportional + + + align:start position:0% +controller that is a proportional +controller, no integral control and has + + align:start position:0% +controller, no integral control and has + + + align:start position:0% +controller, no integral control and has +a gain of a seventh. Um and what we + + align:start position:0% +a gain of a seventh. Um and what we + + + align:start position:0% +a gain of a seventh. Um and what we +wanted to look at was the uh variance + + align:start position:0% +wanted to look at was the uh variance + + + align:start position:0% +wanted to look at was the uh variance +ratio uh only and see indeed what we got + + align:start position:0% +ratio uh only and see indeed what we got + + + align:start position:0% +ratio uh only and see indeed what we got +is that + + align:start position:0% +is that + + + align:start position:0% +is that +uh here's the data beforehand here's the + + align:start position:0% +uh here's the data beforehand here's the + + + align:start position:0% +uh here's the data beforehand here's the +data afterhand and uh our variance did + + align:start position:0% +data afterhand and uh our variance did + + + align:start position:0% +data afterhand and uh our variance did +go up and it went up roughly equal to + + align:start position:0% +go up and it went up roughly equal to + + + align:start position:0% +go up and it went up roughly equal to +what we expected it uh to see. That's + + align:start position:0% +what we expected it uh to see. That's + + + align:start position:0% +what we expected it uh to see. That's +not one of the good ones. + + align:start position:0% + + + + align:start position:0% + +Um yeah. So here here was one of the + + align:start position:0% +Um yeah. So here here was one of the + + + align:start position:0% +Um yeah. So here here was one of the +cooler things that we + + align:start position:0% +cooler things that we + + + align:start position:0% +cooler things that we +did. + + align:start position:0% +did. + + + align:start position:0% +did. +Um this is now where we did integral + + align:start position:0% +Um this is now where we did integral + + + align:start position:0% +Um this is now where we did integral +control and + + align:start position:0% +control and + + + align:start position:0% +control and +uh we put in a disturbance but the + + align:start position:0% +uh we put in a disturbance but the + + + align:start position:0% +uh we put in a disturbance but the +disturbance was not a mean shift. What + + align:start position:0% +disturbance was not a mean shift. What + + + align:start position:0% +disturbance was not a mean shift. What +we did is we took material of exactly + + align:start position:0% +we did is we took material of exactly + + + align:start position:0% +we did is we took material of exactly +the same thickness. I think that's what + + align:start position:0% +the same thickness. I think that's what + + + align:start position:0% +the same thickness. I think that's what +we did here. + + align:start position:0% +we did here. + + + align:start position:0% +we did here. +Yeah, we did material of exactly the + + align:start position:0% +Yeah, we did material of exactly the + + + align:start position:0% +Yeah, we did material of exactly the +same same thickness but a different + + align:start position:0% +same same thickness but a different + + + align:start position:0% +same same thickness but a different +material. I think we put in aluminum + + align:start position:0% +material. I think we put in aluminum + + + align:start position:0% +material. I think we put in aluminum +instead of steel. So now uh the gain is + + align:start position:0% +instead of steel. So now uh the gain is + + + align:start position:0% +instead of steel. So now uh the gain is +wrong. And obviously the first time So + + align:start position:0% +wrong. And obviously the first time So + + + align:start position:0% +wrong. And obviously the first time So +right here everything's fine. The target + + align:start position:0% +right here everything's fine. The target + + + align:start position:0% +right here everything's fine. The target +is 35° and and George slips in a + + align:start position:0% +is 35° and and George slips in a + + + align:start position:0% +is 35° and and George slips in a +different material. So immediately the + + align:start position:0% +different material. So immediately the + + + align:start position:0% +different material. So immediately the +angle goes right down because he's using + + align:start position:0% +angle goes right down because he's using + + + align:start position:0% +angle goes right down because he's using +the setting from the prior cycle. Right? + + align:start position:0% +the setting from the prior cycle. Right? + + + align:start position:0% +the setting from the prior cycle. Right? +So now we've got this huge error. But + + align:start position:0% +So now we've got this huge error. But + + + align:start position:0% +So now we've got this huge error. But +what happens by following the algorithm + + align:start position:0% +what happens by following the algorithm + + + align:start position:0% +what happens by following the algorithm +in one, two, three, four time steps, + + align:start position:0% +in one, two, three, four time steps, + + + align:start position:0% +in one, two, three, four time steps, +it's back and right on the money where + + align:start position:0% +it's back and right on the money where + + + align:start position:0% +it's back and right on the money where +it should be. Now, he was using a gain + + align:start position:0% +it should be. Now, he was using a gain + + + align:start position:0% +it should be. Now, he was using a gain +that was too low. So, this took a long + + align:start position:0% +that was too low. So, this took a long + + + align:start position:0% +that was too low. So, this took a long +time to come back up. And the variance + + align:start position:0% +time to come back up. And the variance + + + align:start position:0% +time to come back up. And the variance +ratio is a little bit lower than we + + align:start position:0% +ratio is a little bit lower than we + + + align:start position:0% +ratio is a little bit lower than we +would have expected. But this is another + + align:start position:0% +would have expected. But this is another + + + align:start position:0% +would have expected. But this is another +value for this controller that that I + + align:start position:0% +value for this controller that that I + + + align:start position:0% +value for this controller that that I +wanted to point out to and why using + + align:start position:0% +wanted to point out to and why using + + + align:start position:0% +wanted to point out to and why using +higher gains is important. If something + + align:start position:0% +higher gains is important. If something + + + align:start position:0% +higher gains is important. If something +like that came along, different material + + align:start position:0% +like that came along, different material + + + align:start position:0% +like that came along, different material +or significant changes in the material, + + align:start position:0% +or significant changes in the material, + + + align:start position:0% +or significant changes in the material, +this automatically with no intervention + + align:start position:0% +this automatically with no intervention + + + align:start position:0% +this automatically with no intervention +on anybody's part, not even, you know, + + align:start position:0% +on anybody's part, not even, you know, + + + align:start position:0% +on anybody's part, not even, you know, +pulling the end on cord or or um uh + + align:start position:0% +pulling the end on cord or or um uh + + + align:start position:0% +pulling the end on cord or or um uh +having to do statistically significant + + align:start position:0% +having to do statistically significant + + + align:start position:0% +having to do statistically significant +number of measurements, just gets you + + align:start position:0% +number of measurements, just gets you + + + align:start position:0% +number of measurements, just gets you +back on track. And it's a classic + + align:start position:0% +back on track. And it's a classic + + + align:start position:0% +back on track. And it's a classic +example of of the strength of + + align:start position:0% +example of of the strength of + + + align:start position:0% +example of of the strength of +disturbance response for controllers. + + align:start position:0% +disturbance response for controllers. + + + align:start position:0% +disturbance response for controllers. +Um now sort of a + + align:start position:0% +Um now sort of a + + + align:start position:0% +Um now sort of a +a a compilation of everything that + + align:start position:0% +a a compilation of everything that + + + align:start position:0% +a a compilation of everything that +uh uh George did over all the + + align:start position:0% +uh uh George did over all the + + + align:start position:0% +uh uh George did over all the +experiments with the interal controllers + + align:start position:0% +experiments with the interal controllers + + + align:start position:0% +experiments with the interal controllers +is he just for for the bending he said + + align:start position:0% +is he just for for the bending he said + + + align:start position:0% +is he just for for the bending he said +he said let's take a uh look at this + + align:start position:0% +he said let's take a uh look at this + + + align:start position:0% +he said let's take a uh look at this +quantity V which was the expected uh + + align:start position:0% +quantity V which was the expected uh + + + align:start position:0% +quantity V which was the expected uh +quality loss and he plotted it as a + + align:start position:0% +quality loss and he plotted it as a + + + align:start position:0% +quality loss and he plotted it as a +function of the gain and indeed it goes + + align:start position:0% +function of the gain and indeed it goes + + + align:start position:0% +function of the gain and indeed it goes +through a minimum right at the gain of + + align:start position:0% +through a minimum right at the gain of + + + align:start position:0% +through a minimum right at the gain of +one and then goes back up. So, uh, that + + align:start position:0% +one and then goes back up. So, uh, that + + + align:start position:0% +one and then goes back up. So, uh, that +was a pretty good result and it said + + align:start position:0% +was a pretty good result and it said + + + align:start position:0% +was a pretty good result and it said +that, you know, indeed from no gain at + + align:start position:0% +that, you know, indeed from no gain at + + + align:start position:0% +that, you know, indeed from no gain at +all where the variance was very high and + + align:start position:0% +all where the variance was very high and + + + align:start position:0% +all where the variance was very high and +and the offsets could be very high, uh, + + align:start position:0% +and the offsets could be very high, uh, + + + align:start position:0% +and the offsets could be very high, uh, +we did a lot + + align:start position:0% +we did a lot + + + align:start position:0% +we did a lot +better. Um, excuse me. Uh, was that from + + align:start position:0% +better. Um, excuse me. Uh, was that from + + + align:start position:0% +better. Um, excuse me. Uh, was that from +from experiments? Yes. Yes. Uh, wait a + + align:start position:0% +from experiments? Yes. Yes. Uh, wait a + + + align:start position:0% +from experiments? Yes. Yes. Uh, wait a +second. Actually, no, you're right. I'm + + align:start position:0% +second. Actually, no, you're right. I'm + + + align:start position:0% +second. Actually, no, you're right. I'm +sorry. This was this was calculated. + + align:start position:0% +sorry. This was this was calculated. + + + align:start position:0% +sorry. This was this was calculated. +This was not from experiments. Yeah. But + + align:start position:0% +This was not from experiments. Yeah. But + + + align:start position:0% +This was not from experiments. Yeah. But +it suggested again that that KC should + + align:start position:0% +it suggested again that that KC should + + + align:start position:0% +it suggested again that that KC should +be one. Ah, yes. I'm sorry. So then he + + align:start position:0% +be one. Ah, yes. I'm sorry. So then he + + + align:start position:0% +be one. Ah, yes. I'm sorry. So then he +did this experiment. He increased the + + align:start position:0% +did this experiment. He increased the + + + align:start position:0% +did this experiment. He increased the +gain to one for the material shift. Uh + + align:start position:0% +gain to one for the material shift. Uh + + + align:start position:0% +gain to one for the material shift. Uh +and well there's a different material + + align:start position:0% +and well there's a different material + + + align:start position:0% +and well there's a different material +shift too. This was a change in + + align:start position:0% +shift too. This was a change in + + + align:start position:0% +shift too. This was a change in +thickness. And again change in + + align:start position:0% +thickness. And again change in + + + align:start position:0% +thickness. And again change in +thickness. It immediately goes down and + + align:start position:0% +thickness. It immediately goes down and + + + align:start position:0% +thickness. It immediately goes down and +just in two time steps it's back up uh + + align:start position:0% +just in two time steps it's back up uh + + + align:start position:0% +just in two time steps it's back up uh +to zero. So pretty cool. But so it so it + + align:start position:0% +to zero. So pretty cool. But so it so it + + + align:start position:0% +to zero. So pretty cool. But so it so it +confirms that indeed we can go from here + + align:start position:0% +confirms that indeed we can go from here + + + align:start position:0% +confirms that indeed we can go from here +to here in a predictable amount of time. + + align:start position:0% +to here in a predictable amount of time. + + + align:start position:0% +to here in a predictable amount of time. +The higher the gain, the faster it gets + + align:start position:0% +The higher the gain, the faster it gets + + + align:start position:0% +The higher the gain, the faster it gets +there. But what this doesn't show, but + + align:start position:0% +there. But what this doesn't show, but + + + align:start position:0% +there. But what this doesn't show, but +which we did have with other data, it + + align:start position:0% +which we did have with other data, it + + + align:start position:0% +which we did have with other data, it +said, "Yeah, it does increase the + + align:start position:0% +said, "Yeah, it does increase the + + + align:start position:0% +said, "Yeah, it does increase the +variance about the much the same amount + + align:start position:0% +variance about the much the same amount + + + align:start position:0% +variance about the much the same amount +we + + align:start position:0% +we + + + align:start position:0% +we +expected." Oops. Okay. So, now let's go + + align:start position:0% +expected." Oops. Okay. So, now let's go + + + align:start position:0% +expected." Oops. Okay. So, now let's go +to injection molding. Well, that got + + align:start position:0% +to injection molding. Well, that got + + + align:start position:0% +to injection molding. Well, that got +more complicated right away because the + + align:start position:0% +more complicated right away because the + + + align:start position:0% +more complicated right away because the +first thing you find out with injection + + align:start position:0% +first thing you find out with injection + + + align:start position:0% +first thing you find out with injection +molding is you're not sure which + + align:start position:0% +molding is you're not sure which + + + align:start position:0% +molding is you're not sure which +variables matter. You're not sure what + + align:start position:0% +variables matter. You're not sure what + + + align:start position:0% +variables matter. You're not sure what +the process gain is. So, he had to do a + + align:start position:0% +the process gain is. So, he had to do a + + + align:start position:0% +the process gain is. So, he had to do a +full DOE on the thing and do a + + align:start position:0% +full DOE on the thing and do a + + + align:start position:0% +full DOE on the thing and do a +significance test and find out what was + + align:start position:0% +significance test and find out what was + + + align:start position:0% +significance test and find out what was +important. And what he ended up with + + align:start position:0% +important. And what he ended up with + + + align:start position:0% +important. And what he ended up with +through the ANOVA analysis and some + + align:start position:0% +through the ANOVA analysis and some + + + align:start position:0% +through the ANOVA analysis and some +other stuff was I think that yeah that + + align:start position:0% +other stuff was I think that yeah that + + + align:start position:0% +other stuff was I think that yeah that +hold time for his particular problem + + align:start position:0% +hold time for his particular problem + + + align:start position:0% +hold time for his particular problem +hold time was the most important. He was + + align:start position:0% +hold time was the most important. He was + + + align:start position:0% +hold time was the most important. He was +molding rings simple ring test rings and + + align:start position:0% +molding rings simple ring test rings and + + + align:start position:0% +molding rings simple ring test rings and +so we came up with a model that looked + + align:start position:0% +so we came up with a model that looked + + + align:start position:0% +so we came up with a model that looked +like this uh and it was a a again that + + align:start position:0% +like this uh and it was a a again that + + + align:start position:0% +like this uh and it was a a again that +term didn't matter but it was a constant + + align:start position:0% +term didn't matter but it was a constant + + + align:start position:0% +term didn't matter but it was a constant +times x2 which was the hold time. This + + align:start position:0% +times x2 which was the hold time. This + + + align:start position:0% +times x2 which was the hold time. This +is reduced one. He started with a lot + + align:start position:0% +is reduced one. He started with a lot + + + align:start position:0% +is reduced one. He started with a lot +more variables to start with. + + align:start position:0% +more variables to start with. + + + align:start position:0% +more variables to start with. +So, here's proportional control again, + + align:start position:0% +So, here's proportional control again, + + + align:start position:0% +So, here's proportional control again, +one that we later abandoned, but it + + align:start position:0% +one that we later abandoned, but it + + + align:start position:0% +one that we later abandoned, but it +gives you a nice example of what of a + + align:start position:0% +gives you a nice example of what of a + + + align:start position:0% +gives you a nice example of what of a +bunch of things. Here's openloop. He's + + align:start position:0% +bunch of things. Here's openloop. He's + + + align:start position:0% +bunch of things. Here's openloop. He's +making these parts and noticing they're + + align:start position:0% +making these parts and noticing they're + + + align:start position:0% +making these parts and noticing they're +they're all over the place and they're + + align:start position:0% +they're all over the place and they're + + + align:start position:0% +they're all over the place and they're +kind of drifting, right? You know, + + align:start position:0% +kind of drifting, right? You know, + + + align:start position:0% +kind of drifting, right? You know, +they're not even steady. And then he + + align:start position:0% +they're not even steady. And then he + + + align:start position:0% +they're not even steady. And then he +turns on the controller with a closed + + align:start position:0% +turns on the controller with a closed + + + align:start position:0% +turns on the controller with a closed +loop gain of a half and the mean value + + align:start position:0% +loop gain of a half and the mean value + + + align:start position:0% +loop gain of a half and the mean value +is not correct, but it's + + align:start position:0% +is not correct, but it's + + + align:start position:0% +is not correct, but it's +constant. So, it's completely + + align:start position:0% +constant. So, it's completely + + + align:start position:0% +constant. So, it's completely +eliminating these shifts that were going + + align:start position:0% +eliminating these shifts that were going + + + align:start position:0% +eliminating these shifts that were going +on. uh and and the effect is quite uh + + align:start position:0% +on. uh and and the effect is quite uh + + + align:start position:0% +on. uh and and the effect is quite uh +dramatic. But let's go on to something. + + align:start position:0% +dramatic. But let's go on to something. + + + align:start position:0% +dramatic. But let's go on to something. +Oh, and the other thing is really cool + + align:start position:0% +Oh, and the other thing is really cool + + + align:start position:0% +Oh, and the other thing is really cool +is that the variance ratio was like a + + align:start position:0% +is that the variance ratio was like a + + + align:start position:0% +is that the variance ratio was like a +quarter. So you can see here that this + + align:start position:0% +quarter. So you can see here that this + + + align:start position:0% +quarter. So you can see here that this +is kind of all over the place and now + + align:start position:0% +is kind of all over the place and now + + + align:start position:0% +is kind of all over the place and now +it's it's uh greatly + + align:start position:0% +it's it's uh greatly + + + align:start position:0% +it's it's uh greatly +reduced. Um you can actually measure the + + align:start position:0% +reduced. Um you can actually measure the + + + align:start position:0% +reduced. Um you can actually measure the +correlation of these two processes by + + align:start position:0% +correlation of these two processes by + + + align:start position:0% +correlation of these two processes by +just doing uh running it through a + + align:start position:0% +just doing uh running it through a + + + align:start position:0% +just doing uh running it through a +correlation filter. And uh this doesn't + + align:start position:0% +correlation filter. And uh this doesn't + + + align:start position:0% +correlation filter. And uh this doesn't +tell you just by looking at it to use a + + align:start position:0% +tell you just by looking at it to use a + + + align:start position:0% +tell you just by looking at it to use a +mat lab function. But this basically + + align:start position:0% +mat lab function. But this basically + + + align:start position:0% +mat lab function. But this basically +means that bending was indeed + + align:start position:0% +means that bending was indeed + + + align:start position:0% +means that bending was indeed +uncorrelated and injection molding was + + align:start position:0% +uncorrelated and injection molding was + + + align:start position:0% +uncorrelated and injection molding was +had some correlation. There's a little + + align:start position:0% +had some correlation. There's a little + + + align:start position:0% +had some correlation. There's a little +bit of correlation in the bending + + align:start position:0% +bit of correlation in the bending + + + align:start position:0% +bit of correlation in the bending +because the variance comes from coupons + + align:start position:0% +because the variance comes from coupons + + + align:start position:0% +because the variance comes from coupons +that were cut from the shame sheet of + + align:start position:0% +that were cut from the shame sheet of + + + align:start position:0% +that were cut from the shame sheet of +sheet metal and that sort of + + align:start position:0% +sheet metal and that sort of + + + align:start position:0% +sheet metal and that sort of +thing. + + align:start position:0% + + + + align:start position:0% + +Um that's cool too. That's that's + + align:start position:0% +Um that's cool too. That's that's + + + align:start position:0% +Um that's cool too. That's that's +basically more the same thing. Here's + + align:start position:0% +basically more the same thing. Here's + + + align:start position:0% +basically more the same thing. Here's +the one I wanted to show you is that + + align:start position:0% +the one I wanted to show you is that + + + align:start position:0% +the one I wanted to show you is that +um the injection molding integral + + align:start position:0% +um the injection molding integral + + + align:start position:0% +um the injection molding integral +control. It just zooms right in. The the + + align:start position:0% +control. It just zooms right in. The the + + + align:start position:0% +control. It just zooms right in. The the +uh desired value was + + align:start position:0% +uh desired value was + + + align:start position:0% +uh desired value was +1.436. It just pops you right onto that. + + align:start position:0% +1.436. It just pops you right onto that. + + + align:start position:0% +1.436. It just pops you right onto that. +I guess you know the measurements uh uh + + align:start position:0% +I guess you know the measurements uh uh + + + align:start position:0% +I guess you know the measurements uh uh +have some error in but this is an inch + + align:start position:0% +have some error in but this is an inch + + + align:start position:0% +have some error in but this is an inch +is 1.438 and a variance ratio of point4. + + align:start position:0% +is 1.438 and a variance ratio of point4. + + + align:start position:0% +is 1.438 and a variance ratio of point4. +So this is the one example from his data + + align:start position:0% +So this is the one example from his data + + + align:start position:0% +So this is the one example from his data +of implementing what we consider the + + align:start position:0% +of implementing what we consider the + + + align:start position:0% +of implementing what we consider the +ideal controller and it it it you know + + align:start position:0% +ideal controller and it it it you know + + + align:start position:0% +ideal controller and it it it you know +simply put it does what we expected it + + align:start position:0% +simply put it does what we expected it + + + align:start position:0% +simply put it does what we expected it +uh to do. So from these model + + align:start position:0% +uh to do. So from these model + + + align:start position:0% +uh to do. So from these model +predictions and the assumptions that we + + align:start position:0% +predictions and the assumptions that we + + + align:start position:0% +predictions and the assumptions that we +make, we make the argument that we can + + align:start position:0% +make, we make the argument that we can + + + align:start position:0% +make, we make the argument that we can +do this discrete time control stuff that + + align:start position:0% +do this discrete time control stuff that + + + align:start position:0% +do this discrete time control stuff that +discrete time control theory will well + + align:start position:0% +discrete time control theory will well + + + align:start position:0% +discrete time control theory will well +fit what's going on and you get these + + align:start position:0% +fit what's going on and you get these + + + align:start position:0% +fit what's going on and you get these +this condition where you will always + + align:start position:0% +this condition where you will always + + + align:start position:0% +this condition where you will always +center this and you will get varying + + align:start position:0% +center this and you will get varying + + + align:start position:0% +center this and you will get varying +degrees of u either uh amplification or + + align:start position:0% +degrees of u either uh amplification or + + + align:start position:0% +degrees of u either uh amplification or +attenuation of the variance. But the + + align:start position:0% +attenuation of the variance. But the + + + align:start position:0% +attenuation of the variance. But the +thing I want to emphasize is that this + + align:start position:0% +thing I want to emphasize is that this + + + align:start position:0% +thing I want to emphasize is that this +is this is u hardcore feedback + + align:start position:0% +is this is u hardcore feedback + + + align:start position:0% +is this is u hardcore feedback +control. But the way we implemented it, + + align:start position:0% +control. But the way we implemented it, + + + align:start position:0% +control. But the way we implemented it, +the way it could be implemented is + + align:start position:0% +the way it could be implemented is + + + align:start position:0% +the way it could be implemented is +simply to have a have a pad of paper + + align:start position:0% +simply to have a have a pad of paper + + + align:start position:0% +simply to have a have a pad of paper +that says if you measure this error, do + + align:start position:0% +that says if you measure this error, do + + + align:start position:0% +that says if you measure this error, do +the following thing. If you measure that + + align:start position:0% +the following thing. If you measure that + + + align:start position:0% +the following thing. If you measure that +error, do the following thing and you + + align:start position:0% +error, do the following thing and you + + + align:start position:0% +error, do the following thing and you +will get these you will get these + + align:start position:0% +will get these you will get these + + + align:start position:0% +will get these you will get these +results. So it's it's uh highly + + align:start position:0% +results. So it's it's uh highly + + + align:start position:0% +results. So it's it's uh highly +implementable. It could be done + + align:start position:0% +implementable. It could be done + + + align:start position:0% +implementable. It could be done +automated as well, but it's highly + + align:start position:0% +automated as well, but it's highly + + + align:start position:0% +automated as well, but it's highly +implementable. And as I understand in + + align:start position:0% +implementable. And as I understand in + + + align:start position:0% +implementable. And as I understand in +the semiconductor field, the run by run + + align:start position:0% +the semiconductor field, the run by run + + + align:start position:0% +the semiconductor field, the run by run +is I guess my sense was that it when it + + align:start position:0% +is I guess my sense was that it when it + + + align:start position:0% +is I guess my sense was that it when it +first came + + align:start position:0% +first came + + + align:start position:0% +first came +out, everybody said, "Yeah, that's + + align:start position:0% +out, everybody said, "Yeah, that's + + + align:start position:0% +out, everybody said, "Yeah, that's +great, but we don't need it." And now as + + align:start position:0% +great, but we don't need it." And now as + + + align:start position:0% +great, but we don't need it." And now as +as basically the needs here and the the + + align:start position:0% +as basically the needs here and the the + + + align:start position:0% +as basically the needs here and the the +the criticality of the mean shifts have + + align:start position:0% +the criticality of the mean shifts have + + + align:start position:0% +the criticality of the mean shifts have +gotten tighter and tighter, they're + + align:start position:0% +gotten tighter and tighter, they're + + + align:start position:0% +gotten tighter and tighter, they're +saying, "Oh, geez, we do need this and + + align:start position:0% +saying, "Oh, geez, we do need this and + + + align:start position:0% +saying, "Oh, geez, we do need this and +it's starting to be used." Is that is + + align:start position:0% +it's starting to be used." Is that is + + + align:start position:0% +it's starting to be used." Is that is +that correct? Yeah. because it because I + + align:start position:0% +that correct? Yeah. because it because I + + + align:start position:0% +that correct? Yeah. because it because I +think we talked about this earlier in + + align:start position:0% +think we talked about this earlier in + + + align:start position:0% +think we talked about this earlier in +the term this whole issue when you get + + align:start position:0% +the term this whole issue when you get + + + align:start position:0% +the term this whole issue when you get +to process capability you know + + align:start position:0% +to process capability you know + + + align:start position:0% +to process capability you know +if if the state-of-the-art is uh here's + + align:start position:0% +if if the state-of-the-art is uh here's + + + align:start position:0% +if if the state-of-the-art is uh here's +the + + align:start position:0% +the + + + align:start position:0% +the +process and here's the process + + align:start position:0% +process and here's the process + + + align:start position:0% +process and here's the process +capability + + align:start position:0% +capability + + + align:start position:0% +capability +window show me the problem you have you + + align:start position:0% +window show me the problem you have you + + + align:start position:0% +window show me the problem you have you +know there's no problem but if this + + align:start position:0% +know there's no problem but if this + + + align:start position:0% +know there's no problem but if this +window all of a sudden looks like this + + align:start position:0% +window all of a sudden looks like this + + + align:start position:0% +window all of a sudden looks like this +say because you're doing + + align:start position:0% +say because you're doing + + + align:start position:0% +say because you're doing +uh tenth micron lines whereas before you + + align:start position:0% +uh tenth micron lines whereas before you + + + align:start position:0% +uh tenth micron lines whereas before you +were doing five micron lines or you're + + align:start position:0% +were doing five micron lines or you're + + + align:start position:0% +were doing five micron lines or you're +doing you know a precision machine + + align:start position:0% +doing you know a precision machine + + + align:start position:0% +doing you know a precision machine +whereas before you were doing + + align:start position:0% +whereas before you were doing + + + align:start position:0% +whereas before you were doing +non-precision you know this compared to + + align:start position:0% +non-precision you know this compared to + + + align:start position:0% +non-precision you know this compared to +this looks pretty awful and if you don't + + align:start position:0% +this looks pretty awful and if you don't + + + align:start position:0% +this looks pretty awful and if you don't +know how to go from here to here what do + + align:start position:0% +know how to go from here to here what do + + + align:start position:0% +know how to go from here to here what do +you do well again run by runner cycle to + + align:start position:0% +you do well again run by runner cycle to + + + align:start position:0% +you do well again run by runner cycle to +cycle says well one thing I can tell you + + align:start position:0% +cycle says well one thing I can tell you + + + align:start position:0% +cycle says well one thing I can tell you +is I can get that baby right over in the + + align:start position:0% +is I can get that baby right over in the + + + align:start position:0% +is I can get that baby right over in the +middle there and if I can work on the + + align:start position:0% +middle there and if I can work on the + + + align:start position:0% +middle there and if I can work on the +variance I can do + + align:start position:0% +variance I can do + + + align:start position:0% +variance I can do +more okay um so uh and the other thing + + align:start position:0% +more okay um so uh and the other thing + + + align:start position:0% +more okay um so uh and the other thing +is that correlation helps we've kind of + + align:start position:0% +is that correlation helps we've kind of + + + align:start position:0% +is that correlation helps we've kind of +avoided corl correlation because it's + + align:start position:0% +avoided corl correlation because it's + + + align:start position:0% +avoided corl correlation because it's +theoretically nasty throughout this + + align:start position:0% +theoretically nasty throughout this + + + align:start position:0% +theoretically nasty throughout this +class. But most processes do have a + + align:start position:0% +class. But most processes do have a + + + align:start position:0% +class. But most processes do have a +little bit of correlation in it. Um and + + align:start position:0% +little bit of correlation in it. Um and + + + align:start position:0% +little bit of correlation in it. Um and +if I have the correlation then indeed I + + align:start position:0% +if I have the correlation then indeed I + + + align:start position:0% +if I have the correlation then indeed I +can reduce this even more as I + + align:start position:0% +can reduce this even more as I + + + align:start position:0% +can reduce this even more as I +mentioned. And last thing I mentioned is + + align:start position:0% +mentioned. And last thing I mentioned is + + + align:start position:0% +mentioned. And last thing I mentioned is +that we have demonstrated this as well + + align:start position:0% +that we have demonstrated this as well + + + align:start position:0% +that we have demonstrated this as well +on uh a couple different processes but + + align:start position:0% +on uh a couple different processes but + + + align:start position:0% +on uh a couple different processes but +um Adam Janeski a couple years ago + + align:start position:0% +um Adam Janeski a couple years ago + + + align:start position:0% +um Adam Janeski a couple years ago +extended it to a 100 by 100 problem. Uh + + align:start position:0% +extended it to a 100 by 100 problem. Uh + + + align:start position:0% +extended it to a 100 by 100 problem. Uh +so 100 inputs, 100 outputs because we + + align:start position:0% +so 100 inputs, 100 outputs because we + + + align:start position:0% +so 100 inputs, 100 outputs because we +had this old process we've been looking + + align:start position:0% +had this old process we've been looking + + + align:start position:0% +had this old process we've been looking +at in our in our lab for years called uh + + align:start position:0% +at in our in our lab for years called uh + + + align:start position:0% +at in our in our lab for years called uh +flexible die forming. And we had a a a + + align:start position:0% +flexible die forming. And we had a a a + + + align:start position:0% +flexible die forming. And we had a a a +tool, a forming machine, full-size + + align:start position:0% +tool, a forming machine, full-size + + + align:start position:0% +tool, a forming machine, full-size +forming machine made up of a lot of + + align:start position:0% +forming machine made up of a lot of + + + align:start position:0% +forming machine made up of a lot of +elements you can move around and in this + + align:start position:0% +elements you can move around and in this + + + align:start position:0% +elements you can move around and in this +particular case there were 100 elements. + + align:start position:0% +particular case there were 100 elements. + + + align:start position:0% +particular case there were 100 elements. +We used to have a lot more but he had a + + align:start position:0% +We used to have a lot more but he had a + + + align:start position:0% +We used to have a lot more but he had a +hundred. Um and the idea is you would + + align:start position:0% +hundred. Um and the idea is you would + + + align:start position:0% +hundred. Um and the idea is you would +form something, measure it, and say + + align:start position:0% +form something, measure it, and say + + + align:start position:0% +form something, measure it, and say +there's a shape error. How do I fix it? + + align:start position:0% +there's a shape error. How do I fix it? + + + align:start position:0% +there's a shape error. How do I fix it? +And you'd like to do that as quickly as + + align:start position:0% +And you'd like to do that as quickly as + + + align:start position:0% +And you'd like to do that as quickly as +possible. And with this method, you + + align:start position:0% +possible. And with this method, you + + + align:start position:0% +possible. And with this method, you +could show that within one or two + + align:start position:0% +could show that within one or two + + + align:start position:0% +could show that within one or two +cycles, you could reduce uh reduce the + + align:start position:0% +cycles, you could reduce uh reduce the + + + align:start position:0% +cycles, you could reduce uh reduce the +error. And Adam, the extension is pretty + + align:start position:0% +error. And Adam, the extension is pretty + + + align:start position:0% +error. And Adam, the extension is pretty +complicated, but most of the results + + align:start position:0% +complicated, but most of the results + + + align:start position:0% +complicated, but most of the results +just uh just show up the same + + align:start position:0% +just uh just show up the same + + + align:start position:0% +just uh just show up the same +way. + + align:start position:0% +way. + + + align:start position:0% +way. +Okay. Labor Day well + + align:start position:0% +Okay. Labor Day well + + + align:start position:0% +Okay. Labor Day well +spent. All right. Uh if you're uh + + align:start position:0% +spent. All right. Uh if you're uh + + + align:start position:0% +spent. All right. Uh if you're uh +interested in this more, as I said, + + align:start position:0% +interested in this more, as I said, + + + align:start position:0% +interested in this more, as I said, +there are a couple papers uh that I've + + align:start position:0% +there are a couple papers uh that I've + + + align:start position:0% +there are a couple papers uh that I've +put on the web. There are two underlying + + align:start position:0% +put on the web. There are two underlying + + + align:start position:0% +put on the web. There are two underlying +thesis uh a master's thesis and a PhD + + align:start position:0% +thesis uh a master's thesis and a PhD + + + align:start position:0% +thesis uh a master's thesis and a PhD +thesis as that's just the work we've + + align:start position:0% +thesis as that's just the work we've + + + align:start position:0% +thesis as that's just the work we've +done here and then of course uh in the + + align:start position:0% +done here and then of course uh in the + + + align:start position:0% +done here and then of course uh in the +semiconductor literature primarily a + + align:start position:0% +semiconductor literature primarily a + + + align:start position:0% +semiconductor literature primarily a +little bit in the statistical control + + align:start position:0% +little bit in the statistical control + + + align:start position:0% +little bit in the statistical control +literature there's there's more under + + align:start position:0% +literature there's there's more under + + + align:start position:0% +literature there's there's more under +this idea of uh run by run control and + + align:start position:0% +this idea of uh run by run control and + + + align:start position:0% +this idea of uh run by run control and +what's the other term they use Dwayne + + align:start position:0% +what's the other term they use Dwayne + + + align:start position:0% +what's the other term they use Dwayne +that's it's in the there's run to run by + + align:start position:0% +that's it's in the there's run to run by + + + align:start position:0% +that's it's in the there's run to run by +one yeah run to run but but even in sort + + align:start position:0% +one yeah run to run but but even in sort + + + align:start position:0% +one yeah run to run but but even in sort +of the general statistics community + + align:start position:0% +of the general statistics community + + + align:start position:0% +of the general statistics community +there is a term for it they oh they call + + align:start position:0% +there is a term for it they oh they call + + + align:start position:0% +there is a term for it they oh they call +it adjustment something like continuous + + align:start position:0% +it adjustment something like continuous + + + align:start position:0% +it adjustment something like continuous +adjustment or feedback adjustment. + + align:start position:0% +adjustment or feedback adjustment. + + + align:start position:0% +adjustment or feedback adjustment. +Engineering control. Yeah, engineering + + align:start position:0% +Engineering control. Yeah, engineering + + + align:start position:0% +Engineering control. Yeah, engineering +control. Yeah, it's used a little bit + + align:start position:0% +control. Yeah, it's used a little bit + + + align:start position:0% +control. Yeah, it's used a little bit +derogatorily than there. Yeah. Right. + + align:start position:0% +derogatorily than there. Yeah. Right. + + + align:start position:0% +derogatorily than there. Yeah. Right. +Right. Um, so, uh, yeah, if you have any + + align:start position:0% +Right. Um, so, uh, yeah, if you have any + + + align:start position:0% +Right. Um, so, uh, yeah, if you have any +have any more questions about that, feel + + align:start position:0% +have any more questions about that, feel + + + align:start position:0% +have any more questions about that, feel +free to contact me. Okay. Thank you all. \ No newline at end of file diff --git a/rGYhDvz066I.txt b/rGYhDvz066I.txt new file mode 100644 index 0000000000000000000000000000000000000000..df6a88f140324b8e14ab1212bc3e3e1c2dd06398 --- /dev/null +++ b/rGYhDvz066I.txt @@ -0,0 +1,3389 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All right, +so today our topic + +is going to be depth +perception, which, + +as I have mentioned +to you before, + +is certainly one of the +most intriguing achievements + +in vision. + +Because the impressions +onto the retinal surface + +essentially two dimensional. + +And from that, somehow +the brain needs + +to reconstruct the +third dimension. + +And what is interesting +about this also, + +that even in the most primitive +animals, this is a must. + +And so annals with +tiny brains also + +have mechanisms to be +able to calculate depth + +from the information that +comes in through their eyes. + +And to demonstrate +that, I have here + +a frog, which has a tiny little +brain like that, has big eyes, + +and this frog, +for its existence, + +needs to know exactly +where things are in depth. + +Because if he doesn't, +he would starve to death. + +And so what a frog does +looks something like this, + +very crudely. + +He will stick out his +tongue, grab a flying insect + +and consume it. + +And because of this +incredible capability, + +it is a well-adjusted, +healthy animal + +in most parts of the world. + +Now the big question +then comes up, + +how do we carry out +these computations. + +What kind of +mechanisms are involved + +in being able to compute +where things are in space, + +either in absolute sense +where it is from you + +and in a relative sense +where one object is + +relative to another one. + +Now it turns out that this +became such a serious problem, + +in the course of +evolution, that actually + +several different +mechanisms have evolved + +to make possible our ability +to see things in depth. + +And so when one looks at this as +a list, as a fairly brief list, + +we can make a distinction +between so called ocular motor + +cues and visual cues. + +The ocular motor cues are +accommodation and vergence. + +So if various objects are +at a very distance from you, + +your eyes converge or diverge. + +And you your lens gets +thicker and thinner. + +And that information can be +utilized in a rather crude way + +to tell you about where things +are in that relative to you. + +Now as far as visual +cues are concerned, + +the very significant +one we are going + +to talk about quite a +bit, is a binocular cue, + +which is called stereopsis +as you all know. + +And then we have a whole +bunch of monocular cues motion + +parallax, shading, +interposition, size, + +and perspective. + +And so we will talk +about many of these + +to give you a sense +of what it is like + +and to give you a sense of what +various brain structures do + +with this as a result +of extensive research + +that had been done in this area. + +So now, first of all, let's +talk about stereopsis. + +And we talk about +stereopsis, we're + +going to talk about +the basic facts of it, + +and then we are going to +have some demonstrations. + +First of all, the so +called stereoscope, + +of whichever modern version +that has been handed out to you, + +the stereoscope was invented +in the late 19th century. + +And when that was done, the +initial approach to this + +was to be able to present +to each eye separately + +an image that was +taken by a camera that + +has two lenses, which are apart +about as much as your two eyes + +are apart. + +And each of those +created a separate image + +of what's out there. + +And, of course, each eye gets +a very slightly different + +perspective of what's there. + +And then when you +present these two images + +that you had collected +separately to each eye, + +you get a very strong +sense of real depth, + +as you will see +in just a minute. + +Now another way to do it, +which nowadays is easier + +because you can +barely ever find even + +one of these two-lens +cameras, even in stores that + +sell ancient materials, +antique stores. + +So sometimes what +you do instead, + +if you only want to take a +picture of a static image, + +that you can take a +camera, put in a track, + +and have it take two +pictures in succession. + +And then you can +do the same thing + +as you do with a serial camera. + +You can present one to each eye. + +OK, so, what we are +going to do now, + +we are going to have +a series of demos. + +And so we have a handout +for each of you, the paper. + +And that you can +keep and take home. + +But the stereoscope that +I have for each of you, + +that you're going to +have to leave behind, + +because I need to use +that in other classes. + +So what I want you +to do then, there + +are two pictures +on the first page + +that you put the stereoscope +down onto the page + +so that the vertical +line cuts it in half + +so that one goes into each eye. + +And then you put your +head right down to it + +to look into it, all right? + +And if you do that, if you +have it properly sectioned, + +you're going to have a sense +that that image is actually + +three dimensional. + +It's an ancient, ancient +old picture on purpose. + +But you should still be +able to see it in depth. + +So that's the initial thing. + +This became quite a parlor +game and for that case, + +for many, many decades, +whenever you went to a party, + +they would hand out to you a +stereoscope, a handheld one, + +and they would show you +all kinds of images. + +And you can even +do this today when + +you get on the internet +to find such displays. + +Now, then a very important +discovery was made. + +I shouldn't say +discovery, really, + +I should say an invention was +made by Bela Julesz who came up + +with a so-called +random dot stereograms. + +By the way, don't look at the +bottom one, that just tells you + +what it's going to look like. + +There's nothing to look at +the bottom, the bottom set. + +Now if you look +in the middle set, + +that looks like a +random dot stereogram. + +And the idea here was that +the only cue that you provide + +is stereo cue, nothing else. + +It's pure. + +And so what can +be done here, you + +can take a section here, +or the same on each side, + +and simply move a few pixels, +those images as a unit, over. + +And when you do that, they're +going to stick out in depth. + +So now take you stereoscope +and look in the middle display, + +and you look through it, +you should see something + +sticking out in depth. + +And the first question I'm going +to ask you is how many of you + +can see something +stick out in depth? + +What do you see? + +You see + +AUDIENCE: A square. + +PROFESSOR: A little +square sticking out? + +All right, so now, don't try +to look at the bottom one. + +That simply tells you what the +procedure was in that center + +section where you see +the square sticking out. + +The pixels were moved a few +steps inward from both the left + +and to the right creating +what is called a disparity. + +And that's what the brain +then can calculate for depth. + +So now to provide you +with the acid test, + +go to the second page. + +Now you look at the +second page, everybody + +see the letter on top? + +You don't even have to look +through the stereoscope, + +obviously you see +the letter E, right? + +That's because that +section is made darker. + +But now if you do the same thing +at the bottom, the only cue + +you have is the disparity cue. + +And the question comes up, +what letter do you see there? + +And let me just add, this can be +used as a quick, general test. + +You can present +these two subjects, + +and if it can present a whole +bunch of different letters, + +and if they can see the letters, +that means they can see stereo. + +If they cannot see the letters, +then it looks like they may not + +see stereo. + +Now let me add one +other fact here. + +As you move these progressively +closer to each other like this, + +you increase the disparity. + +And that causes the image to +be seen at increasing depths. + +Our sensitivity is +so great that when + +you look at this on a +computer, a standard computer, + +if you move those +images just one + +pixel from the left +to the right, then + +from right to the left, +you will see it in depth. + +And even monkeys can see +as small step as one pixel. + +So now how many +of you can tell me + +what was the letter +at the bottom there? + +AUDIENCE: H. + +PROFESSOR: H, H, good. + +Anybody not being able +to see the letter? + +Everybody sees it. + +Well, you guys are lucky. + +Because there are a +significant number + +of people in the world +who lack stereopsis, + +something like 5% to +10% of the population + +lacks stereopsis for +a variety of reasons. + +We'll talk about that +a bit more later. + +But one is sometimes +you're born, + +and you're amblyopic in one eye. + +Sometimes you are +strabismic, which + +means that your two +eyes are not aligned, + +which in commonplace +language is often + +called as being cross +eyed or wall eyed. + +Those types of +people very seldom + +will have stereoscopic +depth perception, + +even after it's +corrected, especially + +if the correction is made by the +time you're 8 or 10 years old, + +the correction won't help. + +It has to be done +much, much earlier. + +All right, so that then +is the very, very basics + +of the stereo procedures. + +And now another +procedure that had + +been developed more +recently is one + +which is called the +auto stereogram. + +So then if you go to the next +page, and what you want to do + +is you want to look at +this horizontally like that + +with the T on top. + +And then just look at it at +sort of, I don't know, maybe + +about 20 inches from you, +normal reading length. + +And what you want to do +is to look beyond it. + +So stare beyond it. + +And if you keep doing +that for a while, + +you will suddenly see an image, +a three-dimensional image, + +as this comes actually from +a book called The Magic Eye. + +There are several +magic eye books + +in which all kinds +of displays are + +done using these +auto stereograms. + +Does everybody see-- who +can see what's sticking out? + +OK, what do you see? + +AUDIENCE: Was it a shark? + +PROFESSOR: You see a shark? + +OK. + +Now let me see if any +of you don't see it. + +Keep staring at it. + +Look beyond it. + +Another thing that +helps, if you look at it, + +bring it a little +closer to you so you + +can look beyond it +easier, gradually + +move it back and forth. + +And if you're patient, +eventually you + +may be able to do this. + +The reason this is +difficult is because you + +have to uncouple the +vergence in your two eyes. + +You have to look +beyond it slightly. + +And, in fact, that is +one of the reasons why + +testing people for +stereopsis, an auto stereogram + +is not a very good procedure. + +Whereas virtually everybody +can use a stereoscope + +without any trouble. + +AUDIENCE: That's so cool. + +PROFESSOR: Did you +get it finally? + +AUDIENCE: Yeah, that's so cool. + +PROFESSOR: Yeah, all +right so, if anybody + +is really interested in +this auto stereograms + +is I say go to the +store, the bookstore, + +and get one of those +magic eye books. + +They're just a lot of fun. + +And you can just +leaf through it. + +You don't even have to buy +the book, just look through it + +at the store. + +And you'll see one interesting, +clever image after the next. + +All right, so that's +the stereoscope. + +And now let me +explain to, I think + +I've mentioned this briefly +before, the principles involved + +behind being able to see +stereoscopic depth perception. + +And what I've mentioned +to you before was + +that if you have the +two eyes fixating + +at a particular distance, if you +then draw a circle around that, + +that's sometimes called +a Veith-Muller circle, + +or the sometimes called a +horopter, then any target, + +like this one here, will +hit equivalent points + +on the retinal surface of +the left and right eyes. + +However, if you +do the same thing, + +and you put a target +either beyond or closer + +than the Vieth-Muller +circle, then they're + +going to hit nonequivalent +points on the retinal surface. + +So then by nonequivalency, we +can do this and calculate this + +as to where the +image falls relative + +to the central fixation +spot in the foveola. + +And so then, when these +nonequivalent points are hit, + +somehow the brain can +measure this nonequivalence. + +And that is then +converted into an estimate + +of where things are in depth. + +Now the idea behind +this was that + +these nonequivalent +points, that you + +have on the retinal surface, +can connect in the cortex + +to single cells. + +So they have a cell in the +cortex that is binocular, + +by virtue of the +fact that inputs + +from the left and right eyes. + +But they don't necessarily have +to come from equivalent points. + +They can come from +nonequivalent points. + +And that may be then +the mechanism whereby + +it can tell you the +degree of nonequivalence, + +and, therefore, convert +that into depth. + +And, therefore, there +could be single neurons + +in the brain that are +selective to certain depths. + +And so people began to do all +kinds of experiments with this. + +And the way these +experiments were done + +is you presented +images separately + +to the left eyes and right eyes. + +And you could then present them +to both eyes at the same time + +and vary the amount of +disparity systematically + +to see what kind +of tuning function + +you would get in the cortex. + +So this, some of the most +beautiful work of this + +was done by a person +called John [? Porgio ?] + +And I will tell you briefly +about some of his experiments. + +So here we go with then. + +We're going to look at +the neural responses, + +neural responses in V1 as +initially done in the monkey. + +So here's an example of a cell. + +We have here different +degrees of disparity. + +And we have the +neuron responding + +each time they're +four repeated trials. + +And you can see the action +potentials by these dark lines + +here. + +And what you do is you move +the stimuli back and forth + +across the two eyes, the +way it's actually done, + +you have a mirror. + +And then you have two +in this experiment. + +You have two monitors, one to +the left and one to the right. + +And then you can set +it up almost exactly + +the same as what you would +do with a stereoscope. + +So this particular cell, +as you can readily see, + +responds best when +there's zero disparity. + +Now by contrast, here is a +cell that responds vigorously + +at the far disparity and +not to the close one. + +So then, when you do this, you +can study hundreds of cells + +to see what kinds +of distributions + +you have in the cortex for +different degrees of disparity, + +cell activity. + +Now again, this +hearkens back to what + +I talked about with +respect to color vision + +where the question came up, +if you want to see color, + +how many receptors +would you need that peak + +at different wavelengths, right? + +And one idea was that maybe you +need as many photo receptors + +as there are colors. + +But in the end, it turned +out that we have only three + +of them. + +And on the basis of that, we +can recreate all the colors out + +there. + +Now the same thing +applies to stereopsis. + +So when this was +done systematically, + +here's an example of +the tuning functions. + +This one here is the +same, very much the same, + +as the first figure +I showed you. + +And so we have a bunch +of different ones. + +And if you then study, as +I've said hundreds of cells, + +you can come up with a +distribution of this. + +And what John +[? Porgio ?] came up with, + +he thought that there +were four major classes. + +And the relative amount +of activity of these four + +major classes then is used +to compute all the very fine + +differences in depth. + +So there's a right on one. + +This cell is right +on the fixation spot. + +And then you have +near and far cells. + +And you have some +in between cells. + +Initially he thought +there were four classes. + +Some people argue that +there may be as many as six. + +But at any rate, +there's a limited number + +on the basis of which +you can calculate + +almost an unlimited +number of depths, + +which is quite remarkable. + +All right, so now, what +you can next turn to + +is to ask the question to what +degree do various extrastriate + +areas contribute to +stereoscopic depth perception. + +And some people +thought that this + +is a unique function +for area MT, + +some people argue +that maybe it's + +area V4, and so experiments were +done in which it was examined + +to what degree stereoscopic +depth deception is altered when + +you eliminate, say, area MT +or you eliminate area V4. + +So that is what's been done. + +And you can think +about it for a minute + +and say, well, +what do you think? + +What do you think would +happen in a monkey + +once you no longer had area V4? + +What you think would happen +if the monkey no longer had + +area MT? + +Well, the results were +actually quite surprising. + +And they're shown here, +same experiment as before. + +The Bela Julesz random +dot stereograms. + +And then you're presenting +one of four locations + +of however many +little area where, + +like little square, +that's sticks out in depth + +and you vary the amount +of depth that sticks out + +by varying the +number of pixels you + +moved the images +into this place. + +And when that was +done systematically, + +this is what was found. + +It was found that neither +V4 lesion nor an MT lesion + +cause a significant deficit. + +The only deficit +that was significant + +had to do with a +response latency. + +And as I should have +mentioned earlier, + +like when we talked +about the frog, one + +of the very important things +about processing depth, + +again, is to be able +to do it quickly. + +So when you have that's frog +and the fly is flying along, + +he has to be very +quick to compute it + +so that he can catch it, +right, as you had seen. + +So in this case, +what you see here, + +that there is about a 20 +millisecond difference + +after V4 lesion, increase in +latency, and quite a bit more, + +almost 40, 30, 40 +after and MT lesion. + +So that contributes to some +aspect of depth processing + +in terms of being +able to do it quickly. + +But neither the MT or V4 +are unique in processing + +stereopsis. + +It looks like that +it is processed + +in several different +areas in the brain + +and inspire conjoint +computation that you + +can arrive at the actual depth. + +And it's by virtue of +that joint computation + +that you can do +this very quickly. + +So now you come to the +next important depth + +cue, which is called +motion parallax. + +This one is a capacity +that we had acquired + +in the course of +evolution, which + +is extremely potent +and powerful. + +And it's based on a very +simple physical fact. + +And the physical fact it that +either when you are in motion, + +or something in +the environment is + +in motion, the rate at +which these images travel + +across the retinal surface is +heavily distance dependent. + +And so let me demonstrate +this concretely for you. + +Here we have an +eye that's fixed. + +It's always looking +straight ahead. + +And we have two rods +here, sorry, just one rod, + +that we are going to move into +position gradually from here + +to here, and then back up +as shown by the arrows here. + +And we examine the +range over which + +these near and far and +middle objects move + +across the retinal surface +when you engage in this motion + +and the eye is stable. + +And you can see that +the far object moves + +over a much shorter distance +than the near object. + +This you can readily do it +yourself in an experiment. + +You can stick out your thumb and +move your head back and forth. + +And you see that your thumb will +move a lot more than the object + +that you're looking at. + +So now the same thing also +applies when you actually + +are engaged in the eye +movements, which of course you + +do all the time. + +In this case, they eye is set up +so that it's fixated initially + +on this object and +then tracks it to here + +and then tracks it back. + +And when you do that, you +get the same kind of effect, + +namely that the distance over +which a far and a near object + +move is quite different. + +The near object moves over +much, much greater distance + +than the far object, even +though the eyes are tracking. + +So this, then, being +a basic physical fact, + +was then used in the +course of evolution + +to create mechanisms that are +sensitive to this differential + +motion. + +And, of course, because +of the rate of motion + +also varies a little +bit, it became + +possible to create mechanisms +to make that computation + +to tell you where +things are in depth. + +So here I'm going to show +you an actual demo of this + +to make it clear to you. + +In this case, again, we have +a bunch of random dots, much + +like in the Bela Julesz +random dot stereograms + +but just a single one. + +And everybody agrees +there's no depth here. + +Is there any depth? + +Do you see any depth? + +So now what I'm +going to do is I'm + +going to set this image +into rocking motion. + +And when I do this, +almost instantly, you're + +going to see something in depth. + +Are you ready? + +So what you see here is +are three levels, right, + +very clearly. + +In milliseconds, in 20 +milliseconds, you can see this. + +And let me explain to +you why you see this. + +If, OK, let me go +back and do it again. + +If I keep this stable, you can +see that the dots move over + +a great distance here, +a lesser distance + +here, and practically +not at all here. + +So there is a +differential motion. + +And the greater the motion, +the closer the image + +is in your analysis. + +So that's called +motion parallax. + +And then what you +can do actually, + +you can play all kinds +of games, do experiments + +in which you can present +this kind of image. + +You can put this into each +of the eyes separately. + +And you can present +this image alone + +or you can present it paired +with disparity for stereopsis. + +And you can do each separately +or you can do the two together. + +So let's now first summarize +the essence of motion parallax. + +To derive depth information +from motion parallax, + +neurons are needed that +provide information + +about velocity and +direction of motion + +and perhaps also about +differential motion. + +Secondly, the +majority of V1 cells + +are direction and +velocity selective, + +as we had discussed before, +and some appear also + +to be selective for +differential motion, which + +I did not mention before. + +But, indeed, there are such +cells in the visual cortex. + +Now, the third +important point is + +that such cells that are +motion selective and direction + +selective and selective +for differential motion + +are very, very common area MT. + +So those are some of the +very, very basic facts. + +And now we can move on and ask +what kind of brain activation + +occurs by stereopsis +and motion parallax + +in normal and serial +blind subjects + +using a recently +developed technique, which + +is magnetic resonance imaging, +functional, functional + +magnetic resonance imaging. + +So how do you do +this kind of stuff? + +Well, what you do here, +here's an example, + +you have a very +large stereoscope + +with a mirror at the end. + +And you have a subject +who is lying down. + +And this whole unit, except +not of course that part, + +is put into the magnet. + +And we have a magnet +down here at MIT. + +Most of you probably +have seen that. + +It's on the ground floor. + +So you can do this, and then you +can present those images here. + +And so the stereoscope +will present two images + +and then you can vary this +by rocking him back and forth + +either to present +only motion parallax + +or present only stereopsis +and to present both. + +And so now the question is, this +is a very primitive question + +at this stage, where +in the brain are + +these processes analyzed? + +And so you can find out +what brain areas are + +active by doing this repeatedly +collecting the fMRI data + +and then printing +them out and looking + +at them to see what happens. + +So I'm going to show you +a couple examples of that. + +Here is the basic +figure that the person + +sees but done in such a +way that you can see it. + +Of course, he doesn't +see anything like this. + +He just sees different depths. + +There are one, two, +three, four, five, six, + +seven different depths here. + +And this rocks back and forth. + +And then you can, as I +say, present this only + +with differential motion +or you can present it only + +with disparity or you +can present it with both. + +And then finally, as a +control, what you do is + +you can do the same thing. + +But you don't have +any depth of any sort. + +You just have a flat surface +rocking back and forth. + +And then when you +do data analysis, + +you actually subtract the last +one from the rest of the data + +so that you're not looking at +the data for the activation + +just by the spots but +for the activation that's + +specific for stereopsis +or motion parallax. + +So now if you do +this experiment, + +here's an example +of a normal subject + +and a stereobind subject. + +And we have here a sagittal cut +adding up the images sideways. + +And what you see here, this is +posterior cortex, of course. + +Here in the normal subject, +when you present only motion + +parallax, you only +analyze motion parallax. + +But you have a huge amount of +activation in the visual areas. + +And then if you +do the same thing + +when you do a binocular +stereopsis only, + +you also get a great +deal of activation, + +in quite similar set of areas. + +And then the big +crucial test comes up. + +What happens if you present +the stereo under monocular + +conditions when you +don't see stereo? + +And if you do that, using this +same calculation procedures, + +there is no brain +activation here. + +And, therefore, what we see here +is due, indeed, to the analysis + +that we do for stereopsis. + +Now if you do the +same experiment + +in a stereoblind subject who +has been tested, on tests + +similar we had shown you, +when that person even + +looks at it under +binocular conditions, + +there is no brain +activation meaning + +that this person doesn't have +any mechanisms in the brain + +to analyze stereopsis. + +Now the fortunate +thing is that we + +have these several +different mechanisms + +for depth perception. + +And so people who are +stereoblind and have + +no analysis for disparity, they +can still see depth reasonably + +well. + +And, indeed, they can get +driver's license and all + +that, because we have all these +other mechanisms that include, + +that we have talked +about, motion parallax. + +So that then is one +way of looking at it. + +Now the other way to look at it, +especially when I ask as well, + +are the same brain areas +doing both or what. + +And so what you +can do is instead + +of doing a sagittal section, +you can take sections coronally + +like bang, bang, +bang, bang like that + +and see what that looks like. + +And here's an example in which +I've isolated the stereo. + +And here are a +bunch of sections. + +And this shows the +activation for stereopsis. + +You can see there are +all kinds of areas + +that are being activated. + +And then if you +do the same thing + +and just look at +the parallax alone, + +here we have the +activation for that. + +And then lastly here, +we do both of them. + +Now we can go back. + +The way to look at +the question, how + +are these two areas, these +two types of depth perception + +analyses, differently +activating in the brain. + +And so I'm going to +go back and forth + +between stereo and parallax. + +You can see, and that, you +can see the difference. + +Now some regions, +which have a perfect + +overlap, and +there's some regions + +that are quite separate. + +Notable here are +these areas here, + +which are activated by +stereo but not by parallax. + +So this then can provide +you with an initial idea + +that there are some brain +areas in which both of these + +are analyzed together. + +And there's some +brain areas in which + +are uniquely analyzed for either +stereopsis or motion parallax + +alone. + +Now this tells you where it +takes place in the brain. + +But how it takes place requires +a totally different approach. + +Namely, the most +comfortably to record + +from individual neurons +in various areas + +just like I had shown +you that nice work done + +by John [? Porgio ?] recording +from the one demonstrating + +there that there are disparity +selective neurons that + +are tuned that then provide +the hardware, if you will, + +for being able to analyze +stereoscopic depth. + +So that then summarizes +what I wanted + +to tell you about +motion parallax. + +And now we are going +to go on and talk + +about yet another +important depth + +cue that is utilized by the +brain, which is called shading. + +Now remember that our ability to +use light to illuminate things + +is something that was +practically nonexistent + +for endless millions of years. + +And so because of that, +both animals and us, + +we have to heavily +rely on information + +based on light coming from +the sun, coming from above. + +And shading is based on those +millions of years of evolution + +utilizing the fact that +most of the light that + +illuminates things +comes from above. + +So there are all kinds +of nice examples of this. + +And here is one of them. + +What you can do here is you +can take a bunch of disks + +and set them up so. + +You can do this on a computer +to make the upper part + +light and the lower part +dark or the other way + +around, the upper part +dark and lower part light. + +And all of you readily +can see that these images, + +the first and third row, seem +to be protruding towards you. + +And the images in the second and +fourth row seem to be receding. + +Now that is because the +brain is interpreting + +that on the basis of the fact +that the light at least used + +to come predominantly +from above. + +So that is the basic +arrangement for seeing depth. + +And now I'm going to give +you some demonstrations + +to indicate that this cue +is actually quite powerful, + +even when you would not +necessarily expect it to be. + +So these shading cues have +also been extensively used + +in art work to provide +an impression of depth. + +And I will show +you some examples + +that will give you a +sense of how that is done. + +So let me make one more point +before I proceed that namely it + +is, indeed, the +degree of illumination + +that's crucial here. + +We have the same change +from red to, sorry, + +from some greenish to yellowish. + +And you have no sense of +depth here whatsoever. + +In other words, you do need +the shading information, + +meaning the amount +of light that's + +being reflected from +various surfaces, that + +is crucial for perceiving depth. + +So now what we +are going to do is + +we are going to present a series +of slides that will highlight + +the power that shading has +for the perception of depth. + +So here is an example +of how we do this. + +And the reason I'm +showing this in some + +detail because if you really are +interested in stuff like this, + +you can do all this +on your own computer. + +You can play games, +endless games with it. + +You can spend hours and +hours having a lot of fun + +thinking about how depth +works on the basis of shading. + +So what you have here are +a whole bunch of disks. + +And each of these can +be shaded differently + +by many different +computer programs. + +So that's what you can do. + +That's the basics. + +So now what we can do +is we can play a game. + +And we can say, present just +two different objects here. + +But we're going to present them +repeatedly on a big display. + +And then we can shade these +differently as we please. + +So here is a whole +bunch of them. + +And all the rows, this, the +first, third, and so on rows + +are the same shape +and the second, fourth + +and so on are the other +shape, these two shapes. + +So we only have two shapes +here that are juxtapositioned. + +Now what we can do is say, well, +this is a peculiar sensation. + +I have a vague +sense that there's + +something maybe in +the third dimension. + +But it's not too well +defined, because this + +is not in accordance with +the rules and laws of shading + +of light coming from above. + +So now what we can do +instead, we can selectively + +shade these to be in accordance +with the rules of light coming + +from above to create +shading and depth. + +And when you do that, +here's an example of that. + +What you can see here is +a very compelling image + +of these protruding elements, +sort of protruding to the left, + +right? + +Everybody see, have a +strong sense of depth here? + +So now what you can do +is you can play with it + +and decide, well, +can we do something + +that, keeping the +very, very same shapes, + +shade them differently +and see what + +it does to our +perception of depth. + +And so what we are +going to do next + +is we're going to take +each of these elements + +here, the same ones +here, and we're + +going to reverse the contrast. + +You see the contrast +here on top is white + +and the bottom is black. + +So we're going to +reverse that contrast. + +And when we do so, the question +is what are you going to see. + +And if you do that, +low and behold, + +you still have a +strong sense of depth. + +But it's a very confusing sense. + +You may see sometimes these +objects pointing to the left + +and sometimes to the right. + +It's unstable, because you're +confusing those computations + +that have evolved +over millions of years + +for interpreting depth +in terms of shading. + +Now you can play also +some additional games. + +You can make this even more +complicated, make more changes, + +and here is another one. + +You still have a +feeling of depth. + +But it's totally confusing. + +It's very hard. + +You can't organize it +any way, because it + +is not in accordance +with the law of light + +coming from above +to a real object. + +And lastly, you +can also make this + +so that it would be in +accordance with the laws. + +But you can change +it around so that you + +get a completely +different perception, + +a strong sense of depth. + +It's still the very, +very same elements + +that you had seen before. + +But now the shading is +done, again, differently. + +And then now gives you, +again, a unified sense + +of a display that +is not conflicting. + +Because in this case, it's +in accordance with that + +some of the basic +principles of shading. + +So now, what we can do next, +having talked about stereo + +and we have talked +about shading, + +is to look at some +more of the demos. + +So let's go back +to the stereoscope. + +And let's go back +to the handouts. + +And so if you now come to the +next page that has a heading + +called stereo and shading. + +So, again, take the +stereoscope and we + +are going to look +at these in steps. + +So let's start by looking +at the top display + +first, which is +called stereo only. + +So if you look at +that, first of all, + +if you just look at it +without the stereoscope, + +you see pretty much a +sort of flat display + +of a truncated pyramid. + +Then if you put the stereoscope +there and look through it, + +you should see, if you look +at it for a little while, + +that one of those +sticks out towards you + +and the other one +seems to recede. + +Does everybody see that? + +So let's stop there +for a minute, because I + +want to add one more +fact here, which + +I should have mentioned earlier. + +So what you do here +is-- so you have + +these two displays like that. + +And you have one image here +and another image here. + +When you-- this is +greatly exaggerated, + +these coming together like this. + +That means it's +going to stick out + +towards you as you look at it. + +But if you do the +opposite like that, + +they're further apart +than the rest of them. + +Then actually you +see it receding. + +And that's why, if you now +take away the stereoscope + +and look at it, you can see +that the top left image is + +in each, or facing +towards each other, + +whereas the other ones are +facing away from each other. + +And that's what creates, that's +what the brain interprets, + +as protruding versus receding +using the stereoscope. + +So that is very +similar, in a way, + +to what happens with shading. + +So now if you look +at the second image + +there, first without the +stereoscope, what you see here, + +again, is one that +sticks out just + +like in the original display. + +And the rest of +them are receding. + +That's because the shading, +the one that sticks out + +is light on top and +dark on the bottom. + +And it's the obverse +for the other ones. + +Now if you do the +same thing looking + +through the stereoscope, +what you will see + +is still some degree of depth, +but it's not very pronounced. + +Because there is no +corresponding disparity + +information. + +But now if you look +at the third display, + +where stereo and shading are +in harmony, then what you see + +is an extremely +compelling dramatic sense + +of depth with the top +left one sticking out + +towards you and the +other three receding. + +So shading appeared to have +added to the compelling nature + +of the depth that you see +through the stereoscope. + +Now the last image in here is +that we put stereo and shading + +and conflict with each other. + +And when you do that, you can +look at it, first with just one + +eye, then with the other eye. + +When you look at it with both +of them, you, for a while, + +you see something unstable. + +And when you see it +well, eventually, you + +realize that there +is a conflict there + +because of the +shading and the stereo + +being in opposition +to each other. + +Now then, this kind of effect, +if you go to the next page, + +we're going to go now to +page five, six, and seven. + +Again, what you +need to do here is + +to look at it sideways +with the F's on top. + +And when you look at this, those +of you who can use your eyes so + +that they are divergent, +and you look beyond it, + +then this is very much like, +or it is the same actually, + +as an auto stereogram. + +So if you look at this for a +while, and you look beyond it, + +eventually it's going to gel. + +And when it gels, +what you should + +see is where the +F's are, the images + +are protruding towards you, +and the others are receding. + +Now it may take you awhile. + +It's much more difficult +than what we just + +did with the stereoscope. + +But you should be +able to see that. + +How many of you are able to +actually see those images? + +A little bit di-- move it back +and forth a little bit slowly. + +And maybe eventually +you manage it. + +So as I say, where +the F's are you + +see these images-- these +truncated pyramids protruding + +towards you. + +And the rest of +them are receding. + +If you have difficulty +seeing this, + +I'm not surprised, because +it takes a lot of practice. + +But once you get +a sense of it, I + +think that you will enjoy +doing this and actually + +showing it to some +of your friends. + +So then if you go +to the next page, + +there we have added shading. + +And the shearing is +the same everywhere. + +But the stereo cues are not. + +Once again, what +happens is that they + +are stereo cues where +the F's are stick out + +towards you much +greater than the others. + +They stick out a lot less +because of the added stereo. + +And then, in the last demo +there, the last page, we + +are putting, just like in that +figure with a stereoscope, + +we are putting them into +opposition with each other. + +And so when you +look at these, this + +would be very difficult +to see for a while. + +Because there's a tendency +to see it differently + +for stereo and for +motion parallax. + +And so it's going to +be an unstable percept. + +So what you can do then +is you can play around + +with this at your leisure and +especially once you become more + +proficient looking at +all the stereograms, + +if you go and get one of these +magic eye books to look at, + +you will be able to see +these displays as well. + +So now, this is the one was the +first one that I showed you. + +As I said, this one, with +the F's, are the ones + +that should stick +out closest to you. + +Once you see that, then +you can go on to the next + +to add the shading or +subtract the shading from it. + +So now, an interesting +question that arises + +is to what degree are we +able, or are animals able, + +to integrate these different +kinds of depth cues. + +And in particular, +in this case, you're + +going to ask the question, what +about integrating stereopsis, + +parallax, and shading. + +So the experiment is +one done on monkeys + +in which you can present +these cues either singly + +or in combination. + +And we can ask the +question, well, + +does the monkey do better +with one or the other, + +or does he integrate really +and does really much better + +when you provide all three cues. + +And so here is a procedure. + +What you do here, again, +you have a rocking display + +like this, and you +can present this + +either with shading +as shown here + +or with motion parallax where +it rocks back and forth, + +and lastly also with stereopsis. + +So if you do that, the results +you get are quite dramatic. + +What happens is shown here as +a percent correct performance + +and here is the latency +in milliseconds. + +And it shows that the monkey +does extremely well when + +you present-- this +is percent correct. + +This is degrees of disparity. + +The monkey does extremely well +when you present all three cues + +and does worse when you present +each of those cues alone. + +Even more dramatic +is the fact, and this + +is-- I keep coming back to +this, that the ability for us + +to respond quickly to things +is very important for survival. + +And here what we can see is +that when you present all three + +cues, performance is much, +much, much, much faster than + +when you present +each of those alone. + +And, of course, as +you might expect, + +when you present parallax +only, because that's + +motion over time, that +takes the longest to do. + +So even though motion +parallax cues are great, + +it became important in +the course of evolution + +to create mechanisms that +can detect these things more + +quickly and more efficiently. + +So now we come to +yet another cue + +that we know very little about +at the level of the brain + +or single units, because +it's so complicated, which + +is called perspective. + +But I want you to just be aware +of it and have a sense of it. + +And here is one of +those cartoon examples + +that gives you a very +strong sense of depth. + +And you almost cringe. + +If you were there, +you would worry + +that you would be falling down. + +This is done strictly by +virtue of perspective. + +It's very similar to what you +encounter all the time when + +you're driving down a road and +the road seems to converge, + +even though you're +not aware of it. + +But that's what's happening +on the rental surface. + +Because things further away +are smaller than things + +that are close by. + +And that's when you look +down a railroad track, + +the same thing happens, +even though you + +know that the railroad +track is not converging, + +it's going parallel. + +But because of the +distances involved, + +that's what falls on the retina. + +And you're smart enough to +know that even though that's + +what falls on the +retina, you can + +make the right kind +of interpretation. + +Conversely, you can +also compute the depth + +on the basis of that +kind of convergence. + +Now here's another example +of that, a much simpler way + +that people can do +with experiments. + +Here we have a bunch of dots. + +And we have two basic cues that +have to do with perspective. + +One of them is this gradually +decreasing size of these dots. + +I should say elongated +disks, if you will, + +and also that they +are converging + +much like a railroad +track converges. + +And so we have a +very strong sense + +of having a third +dimension here. + +Now the fact that +this is so strong + +can be mitigated by +adding a few things here. + +If you add some more dots, +it's not question as dramatic. + +And then if you start +mixing up the sizes, + +you are beginning to lose it. + +And then if you +totally mix it up, + +then you have no sense +of that left at all. + +So it is that progression +of steps and sizes + +and whatnot that +gives you the sense + +of the depth of the images +that you're looking at. + +Now here's another +converse example + +of this that is an illusory +effect that what you see here + +is three barrels, if you will. + +And this barrel is a lot +bigger than this barrel, right, + +or is it? + +Well, so what we're +going to do here, + +we have an inducing element here +by this hallway, if you will, + +with a door at the end. + +And we're going to +remove this hallway + +keeping the barrels +exactly as they are. + +And if you do that, +low and behold, + +those barrels are +all the same size. + +It's induced by virtue +of the surround that + +gives you a false +sense of depth. + +So now let me show you +another picture because + +of the purpose behind this. + +This a picture +that's in a museum + +in Worcester, Massachusetts. + +And it was created by a +fellow called Edward Savage. + +And it's a pretty +unpleasant picture. + +But the main reason +I'm showing this to you + +is that there seems to be +very poor sense of depth + +in this picture. + +Now the reason +this is interesting + +is because when artists +began, centuries + +ago in the 13th, 12th +centuries, draw things, + +they did not have a concept +of an understanding of how + +to create depth, a third +dimension, in their drawings. + +So what they did +eventually, they came up + +with a so-called +vanishing point, + +and they drew very much +like what we had here. + +Lines that converged +at a point and then + +scaled the images +accordingly rather + +than keeping it the same size. + +And that way you got +a good sense of depth. + +So now that has a number +of interesting stories + +about it that we +are going to discuss + +next time you talk about +the perception of shapes, + +OK, patterns. + +But I will leave that +discussion until that. + +What I'm going to do +next, however, I'm + +going to try to give you a sense +of how important stereopsis can + +be for the perception +of fine depths. + +And so to do that, what I'm +going--I'm going to show you + +actually a film. + +And here what we have is +a so-called needle test. + +What you have here is a +fine needle protruding. + +And here we have a +bunch of different size + +circular openings, a little bit +like a needle, but it's round. + +And the task is to take these +one at a time and hang them up. + +And one can time how +quickly you can do that, + +or you can make a film to +see how well you can do it. + +And then what we +can do is we can + +test the subject under +binocular conditions, + +and test them under +monocular conditions. + +So I'm going to show you a film +of this, actually two films. + +It will just take just +few seconds to do it. + +OK, be ready, it's going +to come up in a second. + +OK, here's the subject under +binocular viewing conditions. + +So that's the condition +under binocular viewing. + +And now I'm going to show it to +you, same subject, same time, + +but with one eye closed off. + +So that then just +even looking at it + +without taking any +careful measurements. + +It's obvious that +it's much, much + +more difficult to thread +a needle under monocular + +than under binocular +viewing conditions. + +And so what you can do +is when you go home, + +and next time you want +to sew something up, + +try threading the needle with +one eye closed and with the two + +eyes open. + +And you will see immediately +what a huge difference it is. + +And that difference, +therefore, is due + +to you're having the +mechanism of steropsis. + +Just a few seconds here. + +Another test that has been +used in a similar fashion which + +allows you to actually calculate +exactly what your error is + +in reaching, you +can have a subject + +sit in front of one +of these touch panels, + +and then do this experiment +either binocularly or + +monocularly. + +And after he presses +this a dot comes up, + +and then the person +has to touch it. + +And you have about 30 +or 40 trials like that. + +And then you have recorded +where the person touched. + +And, therefore, you +can calculate the error + +between where we touched +and where the dot is. + +And then, again, you +get a huge effect + +between monocular and +binocular viewing conditions. + +Now when you come to +monocular and binocular + +viewing conditions, another +thing important to test + +is to what degree a person +who does or does not + +have stereopsis is capable +of integrating information + +between the two eyes. + +So to do that, we +have here examples + +of what is called +binocular integration. + +So what we do here, again, +you can use a stereoscope. + +You look at a monitor. + +And this represent the left +eye, this is the right eye. + +And you flash these on. + +If you integrate this, +this is what you see. + +This would be actually +what you would + +show in the control +part of the experiment. + +So you see the Star of David. + +And if a subject is +shown this, and they + +don't see the Star +of David, you worry + +that their ability to integrate +the information between the two + +eyes is deficient. + +And I would say 90% of the +cases, those people who + +are deficient on this +also show major deficiency + +in stereoscopic viewing. + +Now another way to do +this is an experiment + +in which you can present +two words here, sud and try, + +so the two are separate. + +And when you present +them simultaneously, + +you actually see +the word sturdy. + +So you ask the subject, please +tell us what do you see. + +What is it word you see. + +And the subject says sud. + +And the subject +says try, then you + +know that that subject +sees, if he says try, + +he sees mostly with his +right and prefers it, + +doesn't see too well +with his left eye. + +If he says sturdy, then +he integrates the two. + +And, therefore, +you can safely say + +that this guy has very good +integration between the two + +eyes. + +So what I would +like to do next then + +is to provide you with any +questions that you have. + +This was a complicated +topic, that you have, + +and then we are +going to summarize. + +Does anybody have a question +about motion parallax, + +stereopsis, and so on? + +Let me maybe add one +more important factor. + +Your eyes are separated +only by so many centimeters. + +Now, can you think +of an animal where + +there's a much +larger separation? + +AUDIENCE: Hammerheads. + +PROFESSOR: The hammerhead shark. + +Yeah, that has a separation +of over a foot between the two + +eyes. + +And so you could ask the +question, why on earth did + +that animal evolve to such a +huge separation between the two + +eyes? + +Well, that brings one to yet +another interesting point. + +This I think may have started +during the Second World War. + +It was realized that +when you're flying + +over some territory, where +there are all kinds of weapons + +and whatnot, which +are well camouflaged, + +that just looking down at +them, you can't see them. + +But obviously if you're +going to have a tank + +or you're going to have a +gun or other that may be more + +like a cannon, it sticks +out of the ground. + +So it was discovered that +if you had in your airplane + +two lenses which +are far apart, that + +would greatly magnify the depth. + +You could defeat +that camouflage. + +And you could find +those weapons down there + +by virtue of the fact they're +sticking out of the ground. + +So the fact then is that the +more you separate the images + +from the two eyes, if you +will, or your two cameras, + +the more likely it is +that you can calculate + +the disparity of information +between the two images. + +So that then is probably +one of the reasons, not + +the sole reason, but +maybe one of the reasons + +why, in some animals, is +an excessive separation + +between the two eyes. + +And that brings me to get me +to yet another point, which + +is that stereopsis actually +works best at relatively + +short distances, like +threading a needle. + +It doesn't work too well beyond, +I don't know, 10 feet or so. + +It becomes progressively +less effective. + +But at short distance, +it's very effective. + +And so I presume +also many animals + +that have to hunt for +food are able to utilize + +the mechanism of stereopsis, +because everything + +is at a close distance when they +hunt for food on the ground. + +And by contrast, when you +talk about motion parallax, + +that works extremely well +over very long distances. + +So does anybody have any +questions about motion parallax + +or about steropsis? + +Oh, once again, I'm +crystal clear, huh? + +So, therefore, I +think it's time for us + +to summarize what we +had covered today. + +First of all, there +are numerous mechanisms + +that have emerged +for analyzing depth. + +And they include the ocular +motor cues, which are vergence + +an accommodation and then the +binocular cue of stereopsis + +and then the monocular +cues of parallax shading + +and perspective. + +Then you have several +cortical structures + +that process stereopsis. + +You don't have one +specific brain area + +that uniquely does this. + +The number of disparities that +are represented in the brain, + +as studies in the area of +the one by John [? Porgio, ?] + +is limited. + +And maybe, maybe four, +but there may be six, + +but certainly there are +not a large number of them. + +And so it's analogous +to the way things + +had been resolved for us to +be able to process color. + +Utilizing motion parallax +for depth processing + +necessitates neuron specific +for direction, velocity, + +and differential velocity. + +Several areas getting V1 and +MT process motion parallax, + +which I did not say. + +But indeed, if you make +a lesion in area MT, + +you go get a deficit in +motion parallax, even + +thought you don't get a +major deficit in steropsis. + +Now, area MT +combines the analysis + +of motion parallax, +depth, and flicker. + +However, these analyses +are also carried out + +by several other structures +as I've already said. + +And lastly, little +is know at present + +about the manner in which +information about shading + +and prospective are +analyzed in the brain. + +And hopefully, that will +be one of the future tasks + +by neuroscientists. + +And so if any of you ever +get involved in neuroscience, + +this certainly is +a big open area + +that we hope people +will start to analyze. + +So that then is the essence of +what I wanted to cover today. + +And once again, if any of +you has a question, please, + +please don't hesitate to ask. + +I'll be very happy +to answer them. + +OK, lastly then, did everybody +sign the attendance sheet? + +If not, please come up after the +class and sign your name to it. + +Very good. + +So next time then, +we are going to talk + +about pattern perception. + +And hopefully you will +find that also interesting. \ No newline at end of file diff --git a/rR8ZtI8m0Mo.txt b/rR8ZtI8m0Mo.txt new file mode 100644 index 0000000000000000000000000000000000000000..f69636795e4f3caf2e5e0b324851ad2953eac52c --- /dev/null +++ b/rR8ZtI8m0Mo.txt @@ -0,0 +1,2869 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK. + +So. + +Last day we started looking at +phase diagrams, and we looked + +at unary phase diagrams, one +component systems, and one + +component system P versus T, +pressure versus temperature. + +And this is the situation +for water. + +Water is an exception, because +it's got this negative solid + +equals liquid coexistence curve, +but otherwise, you have + +large, single-phase regions +here, which I've designated + +circle p equals 1, and then +along these lines, we have + +equilibria. + +So this is liquid goes to vapor, +this is solid goes to + +liquid, this is solid +goes to vapor. + +And we know that for water, if +we take the 1 atmosphere, if + +this is pressure in atmospheres, +the 1 atmosphere + +isobar, then that would put +this point at 100 degrees + +Celsius, and this point +at 0 Celsius. + +And then we have the triple +point, which is solid equals + +liquid equals vapor at 0.01 +degrees C, and p equals, I + +think it was 4.58 millimeters +of mercury. + +So that's the triple point. + +And we looked at a variety of +other one-component phase + +diagrams, and I think we +came to a pretty good + +understanding. + +And then up here, we have the +supercritical fluids. + +So I've got a break +in the line here. + +And for water, you reach +supercriticality at 374 + +degrees Celsius, and up here +at 218 atmospheres. + +So these are not phenomenal, +these are not geological + +pressures at all. + +And so that's if we want to +the decaffeinating of + +coffee and so on. + +And so what happens here, is you +have a highly compressed + +vapor or a highly rarefied +liquid, and you end up with + +solubilizing power of a +liquid, but transport + +properties of a gas. + +So this stuff has really +good diffusivity. + +So it can penetrate into +interstices and do its work + +very quickly, to say nothing of +the fact that you're up at + +374 degrees Celsius or higher. + +So today what I want to do, +is I want to look at + +two-component systems. So +component number is circle c, + +c equals 2. + +So that means now I have +to deal with pressure, + +temperature, and lowercase +c is composition. + +I want to know how things +vary with composition. + +So let me give you an example. + +Suppose I have two substances, +A and B. + +So here's substance A, and I've +got its one-component + +phase diagram. + +And in this case, I'm going to +put solid-liquid vapor in the + +conventional setting, where +the solid-liquid line is-- + +the coexistence curve has +a positive slope. + +So this is A, and let's say I've +got B over here, and it's + +got its solid-liquid coexistence +curve, and so + +we've got its melting +point, and whatever. + +So now the question I want +to ask is, what happens + +if I mix A and B? + +And let's just say, here's the +melting point of A, so this is + +at p equals 1 atmosphere. + +And here's the melting +point of B. + +And I want to ask the question, +how does the melting + +point of the mixture vary? + +So let's say I'm going to +connect these, and I want to + +ask, what happens if I've +got an AB mixture? + +So I'm going to put lowercase +c here, which is + +concentration. + +So at the one end, I've got 100% +A, and over here, I've + +got 100% B, and I know +those melting points. + +Question is, what happens +when I mix them? + +Does the melting point-- is +it just a straight line? + +Is it a linear variation? + +Do you go through +a local maximum? + +Do you go through +a local minimum? + +Or do you go wild? + +I mean, what happens? + +So a question you might ask +is, suppose I made a 50-50 + +alloy of 50% A and 50% B. + +If I knew the end-member +melting points, could I + +predict this? + +Or if not, do I have +an archive? + +Remember the phase diagram +compendium is an archive. + +What is the value +of the melting + +point at 50-50 or 75-25? + +So that's the question +I want to ask. + +Now this is getting really +messy, because now I have to + +plot pressure, and I have to +plot temperature, and I have + +to plot composition. + +So this is really +crazy, right? + +I've got pressure, and I'm +going to have composition + +here, and I'm going to have +to have now a third + +axis, aren't I? + +I'm going to have to +have a third axis. + +I'm going to need a +temperature axis. + +And I've got to make a +three-dimensional drawing. + +And this is messy. + +But we're in luck, because 3091 +is solid state chemistry. + +So as solid state chemists, +we're more interested in what + +happens in the solid here. + +Now, I've drawn these lines +with a slope, but they're + +really not to scale. + +It turns out that, you know, you +can move 10,000 feet up or + +down in the atmosphere and have +a huge variation in the + +boiling point because this +line is shallow. + +But this line is virtually +straight up and down. + +You have to go to geological +pressures to change the + +melting point very much. + +And so, as a result, this +is almost insensitive to + +pressure, to first +order, right? + +So we can say solid equals +liquid is almost insensitive + +to pressure, whereas liquid +equals vapor is very sensitive + +very sensitive to pressure. + +But we don't care about +this so much. + +So what I'm going to do +is throw it away. + +I'm going to throw it away, and +just say, let's look at + +just T versus C. + +Temperature versus composition +on the strength of the fact + +that the melting point and all +of these things are mildly + +dependent on pressure. + +All right. + +So now I'm going to give you +three different types. + +There's many, many different +types of binary phase diagram. + +So now we're going to be +looking at C equals 2. + +So instead of a unary, this is +going to be called binary. + +Binary phase diagrams. And they +come in all shapes and + +sizes, but they can +pretty much be + +classified in several bins. + +And I've made the +classification. + +So classify binary +phase diagrams + +according to their bonding. + +It all comes back electronic +structure and bonding. + +Vary by bonding. + +Because bonding, then, +ultimately indicates + +solubility, and that's what +we're looking at here. + +We're going to look at how well +A dissolves into B, and + +how well B dissolves into A. + +That dictates solubility. + +So it all comes full circle. + +So I've made this up. + +You're now going to find +this in the book. + +So I just decided, for ease of +teaching 3091, is I'm going to + +just give the different types. + +And so I call them type one, +type two, and type three. + +You're not going to find +that in the books. + +I made that up, because +it's simple. + +So type one. + +What's type one binary phase +diagram, according to me? + +What is the type one? + +It means complete solubility. + +So A and B are completely +soluble in one another as + +solid and liquids. + +That's the first thing +that you'll see on a + +type one phase diagram. + +And the second one is, a change +of state is present. + +And you know the only change of +state we care about here is + +solid goes to liquid. + +So we're going to show solid +goes to liquid, and the thing + +is totally, as they say in +California, totally soluble as + +liquids and solids. + +Now, here's some bonding rules +that you can think about. + +So what would be the +characteristics of two + +substances A and B that would +give complete solid + +solubility? + +Well, one thing is they'd have +to have identical crystal + +structures. + +That would heighten the +chances of this. + +Identical crystal structures. + +So if they're both FCC metals, +you've got a better chance of + +making an infinite variation in +solution composition than + +if one is an FCC metal and the +other is a BCC metal because + +FCC will just sit on +the lattice site. + +But there's more fine +structures. + +Second one is similar +atomic volumes. + +So if we're going to have a +substitutional solid solution, + +let's make sure we're replacing +oranges with + +oranges, and not trying to put +a grapefruit on a site that + +normally is occupied by a lemon, +because there's going + +to be a size restriction +there. + +And the third thing is, even if +they have identical crystal + +structures and similar atomic +volumes, you can still run + +into trouble with respect to +complete solid solubility if + +you have a large variation +in electronegativity. + +And I'll show you an +example of that. + +So if you have a small +difference in + +electronegativity, it means +there's a low propensity for + +polarity, and ultimately no +chance of electron transfer. + +So I think it's pretty cool. + +So I wrote those down, but was +disappointed to learn that for + +metals, they were enunciated +about 75 years ago by the + +British metallurgist +Hume-Rothery. + +So I can't take credit +for this. + +This is one name. + +It's one of these hyphenated +British names. + +He's Sir da-da-da-da +Hume-Rothery. + +So he has the Hume-Rothery +Rule. + +And he called such systems that +mix as binaries forming + +isomorphous, meaning they +have the same structure. + +So let's take a look at the +prototypical isomorphous phase + +diagram, and it looks +like this. + +We're plotting temperature +versus composition. + +We threw away the pressure +coordinate. + +So I got pure A on the left, +pure B on the right. + +Little c is concentration, +so it varies from + +100% A to 100% B. + +And the vertical axis +is temperature. + +So one extreme, I've got +the melting point-- + +this is a melting +point of pure A. + +And at the other extreme, +I've got the melting + +point of pure B. + +So that, we know. + +And now the question is, how +does melting point vary as a + +function of composition? + +And for an isomorphous phase +diagram, it looks like this: + +lens-shaped. + +Up here is all liquid. + +You see A and B mix in +all proportions. + +And down here is all solid. + +And furthermore, it's an +all-liquid solution. + +It's a mixture. + +And this is an all-solid +solution. + +And then comes the piece +that if you take enough + +thermodynamics, you'll be +able to rationalize. + +I'm simply going to tell you +without proof that when you + +have a multicomponent system, +when c is greater than 1-- so + +we're in that situation. + +Now, c is 2. + +When c is greater than 1, it is +impossible to move from one + +field, up here, this is-- + +I'd better put the label +on it-- this is a + +single-phase field. + +So up here, p equals 1, because +it's homogeneous + +liquid solution, p equals 1. + +When you're in pure materials, +you can go + +from solid to liquid. + +But when you're in a +two-component system, you + +cannot move from one +single-phase field to a second + +single-phase field +without moving + +through a two-phase field. + +And we'll get to that, what it +means to move from one field + +of p equals 1 to another field +of p equals 1 requires + +traverse or transit across +a field of p equals 2. + +And so what's in here has +to be the end member. + +So this must be liquid +plus solid. + +So I'm going to call it slush. + +They have a slush in here. + +The other terminology that +people give this is, it's + +lens-shaped, right? + +Looks like a lens. + +So let's call this lens shape. + +So we're going to use +the Latin word for + +lens, which is lens. + +But we want to make +it adjectival. + +So we're going to use +the adjective-- + +what's the genetive +form of lens? + +Lentis? + +So we will call this +lenticular. + +This is lenticular. + +The phase diagram has +a lenticular shape. + +Looks like a lens. + +And you know, just as over here, +I showed you, every line + +represents a coexistence +curve, right? + +The lines are all coexistence +curves. + +These lines are coexistence +curves. + +The line up here is liquid +equals vapor, so this one must + +be the coexistence of the two +things on either side. + +So what do I have here? + +I have liquid. + +Here I have slush. + +So I'm going to write that. + +So I'm going to write the +equilibrium, liquid goes to + +liquid plus solid. + +And this line, this coexistence +curve, it's called + +the liquidus line. + +This is the liquidus +equilibrium, the liquidus + +coexistence curve, and so on. + +And so what's the liquidus? + +The liquidus is the lowest +temperature. + +So you pick a composition. + +The liquidus is the lowest +temperature at which you can + +have a single-phase liquid +solution, OK? + +So liquidus equilibrium. + +And the liquidus is the lowest +temperature at which all + +liquid is stable. + +You go below that temperature at +that composition, you start + +making solid, because slush +requires that there be some + +solid present. + +And then the lower line, it also +is a coexistence curve. + +So on the one side, +I've got solid. + +On the other side, +I've got slush. + +So I'm going to write +that one down. + +That solid goes to liquid +plus solid. + +And that's called the solidus +equilibrium, or that's the + +solidus line, the solidus +coexistence curve, and the + +solidus is the complement. + +The solidus is the highest +temperature at which you can + +have all solid present. + +So you pick a composition, and +I'll tell you what the highest + +temperature is at which +you'll have a + +single-phase solid solution. + +So solidus is the highest +temperature at which + +all solid is stable. + +All right. + +Good. + +And I'm going to look at +a few of these things. + +It's always fun to see if +I'm on track with the + +Hume-Rothery rule. + +So here's copper nickel. + +They're both FCC metals. + +So we've got copper melting at +about 1085, nickel melting at + +about 1455. + +And there's the phase diagram, +lenticular phase diagram. + +So up here is all liquid, +and then-- + +this is all metallurgy +terminology. + +A solid solution of A and +B, they call alpha. + +Metallurgist looks at that, goes +oh, it must be a solid + +solution, OK? + +So there's p equals +2 in between, + +p equals 1, p equals-- + +Here's a ceramic system. + +This is nickel oxide, +magnesium oxide. + +It's not metals, but they have +identical crystal structures, + +very similar atomic volumes. + +They're ions, so we have +nickel and magnesium + +substituting for one another +on the cationic sublattice. + +So they must have very +nearly equal sizes. + +If I look at this, and I see a +lenticular diagram, it means + +they must have similar atomic +volumes, which means the + +dominant defect in here must +be Schottky, not Frankel + +because Frankel needs a big +difference in atomic volume. + +If you have a big difference in +atomic volume, we wouldn't + +have a lenticular +phase diagram. + +So here's-- mag oxide melts at +2800 degrees centigrade. + +It's a great refractory. + +You can hold molten +iron in it. + +And here's nickel +oxide down here. + +All right. + +Here's an interesting one. + +This is gold nickel. + +Both FCC metals. + +Shade your eyes from +the lower part. + +Just look at the upper part. + +It looks lenticular. + +It's what you'd expect, +gold and nickel. + +They're both, you know, +card-bearing metals. + +But you've seen already, with +the cesium-gold, gold has a + +fairly high electronegativity. + +And what happens is that you +get over here, at about 33 + +atomic percent of nickel in +gold, you have an atomic ratio + +that allows to have something +that starting to approximate + +electron transfer. + +So it's almost as though you +have a lenticular phase + +diagram between pure nickel and +this nickel-gold compound. + +But up in here, it's nice +lenticular stuff. + +All right. + +What's the next one? + +Oh, yeah. + +So now I want to go in and I +want to start talking about + +what goes on inside here. + +So what I'm going to do, is +I'm going to blow this up. + +And I'm going to start at 40%, +40 weight percent nickel, and + +I'm going to say, what happens +if we take a crucible that's + +40 weight percent nickel and +copper, and we cool it from + +all liquid at 1300, down to all +solid at 1200, pausing in + +that slush zone at 1250? + +So we're going to take snapshots +and say, what's the + +contents of the crucible look +like at 1300, at 1250, and at + +1200, and come out of it, have +an appreciation for what all + +of this stuff means. + +So let's start our experiment. + +So we're going to have +three crucibles here. + +And we're going to start with +40% nickel in copper, and + +that's going to be the +experiment we'll perform. + +So I've got three crucibles. + +And so if I look at the phase +diagram, here I am. + +This was 1300 degrees C, this +was at 1250 degrees C, and + +then this was at +1200 degrees C. + +So at 1300, that's trivial. + +1300 for this thing, it should +be just all liquid. + +And maybe it's copper. + +I know at this temperature, +it's going to be blinding + +white heat. + +So it doesn't matter. + +I could use this. + +But I felt compelled, it's one +of those rare opportunities to + +use colored chalk. + +So I want this to sort +of be copper-colored. + +The meniscus is going to look +like this, because the liquid + +metals have a very high +surface tension. + +They want to ball up. + +So you're going to have a +meniscus looking like this, + +and this is all single +phase, all liquid. + +And over here, I'm going +to do the easy one. + +If we get down to 1200, it's +all solid state, right? + +At 1200, I'm going to end up +with something that's solid, + +and it's going to be +polycrystalline, and these are + +all going to be grains +of alpha. + +All solid. + +And I'm going to label all of +these as alpha solid solution. + +They all have the same +composition, which is 40% + +nickel in copper. + +And these are all 40% nickel. + +Now, according to this phase +diagram, when we get down into + +the center there, something +else happens. + +We end up in a two-phase +regime. + +And that two-phase regime is +a regime in which certain + +compositions are forbidden +because that's an equilibrium. + +It doesn't allow us to have +what's in between. + +I think the next slide +actually shows this. + +So what I've designated +as c2 is this 40%. + +So c2 is now going to park at +that point in the middle. + +Whoops! + +Want to get into that. + +So here's where we are. + +We're in the center of that +two-phase regime. + +So this is the solidus. + +This is the liquidus. + +And we're at 1250. + +t equals-- + +And we're at this value. + +We started at c2, +which is 40%. + +But in this regime, +40% is forbidden. + +If you stop at 40% at 1250, +this says that the stable + +phases are a liquid +and a solid. + +But the liquid has less nickel +in it, and the solid has more + +nickel in it. + +It's like if this is +a solubility limit. + +In other words, if you started +at pure copper, and you + +started adding nickel, you can +keep adding nickel until you + +get to this concentration. + +You try to add any more nickel, +it's like adding too + +much sugar to water. + +What do you have? + +The stuff just falls to +the bottom of the + +cup, doesn't dissolve. + +That's this. + +It's the solid. + +Only instead of being pure +nickel, it's still a copper + +nickel solution, but +kind of rich. + +So I'm going to call +this c star. + +It's the solubility limit +on the liquid side. + +And this one here I'm going to +call c star on the solid side. + +In other words, I could start +from this side, and keep + +adding copper to nickel, and I +make a homogeneous alloy until + +I get to this composition. + +If I try to add any more +copper, I jump across. + +So we're here in the middle. + +But now, isn't there something +strange here? + +It's saying I'm going to have +a liquid that's nickel-poor + +and a solid that's +nickel-rich. + +And I'm just putting up here +what the diagram says. + +And we know that FCC metals, +which is denser, the + +liquid or the solid? + +The solid. + +So down here I'm going to have +alpha, OK, a bunch of grains + +of alpha solid solution, and up +here, I'm going to have a + +liquid solution. + +And the composition here is +c star liquid, and the + +composition here is +c star solid. + +It's different composition +from this. + +Here the composition is equal +to c2, or the 40% nickel. + +So I've got disproportionation. + +But the total mass, I can't +have sources or sinks. + +So I have to conserve mass. + +So I'm going to ask you to +just do the algebra. + +You've got two equations +and two unknowns. + +I know what the n-member +concentrations are. + +They're given by the +n's of this thing + +called the tie line. + +The tie line ties the two ends +of the two-phase region + +together, and then we just +do a mass balance. + +Well, fortunately, the +metallurgists have thought + +about this for a while, so we +don't have to go through and + +figure out, well, if two +apples cost 15 cents-- + +we don't have to do that +kind of thing. + +We can just invoke the lever +rule, and it will tell us how + +much of the liquid that's +nickel-depleted and solid + +that's nickel-rich +add up to this. + +And so let's look at +the lever rule. + +Basically what's going to happen +here is that the stuff + +that started off as 40% nickel, +60% copper, that's my + +initial mix, it's going to +break into two layers. + +It's going to break into a +liquid layer, which, if you go + +to the phase diagram, looks like +it's about 38% nickel and + +68% copper, and that's +what we're going + +to call c star liquid. + +And then over here it's 45% +percent nickel and 55% copper. + +And that's what we call +c star of the solid. + +And so it's just a lever. + +So there's c star. + +This is the c2 that we want. + +And we want to ask, what's the +relative amount of the liquid + +phase and the solid phase? + +And why they call it a lever +rule is, look, if you cooled + +something that was at +this composition, it + +would be 100% liquid. + +And if you cooled something at +this composition, it will be + +100% solid. + +And so it's going +to be a constant + +variation across here. + +So you use, you take this, and +you know, and I want this + +amount, I'm taking this versus +this, kind of thing. + +It's a lever construction. + +So we'll just put it down. + +So the percent of the liquid +in the crucible at 1250-- + +and then this is a +general thing. + +Whenever p equals 2, you'll +use a lever rule. + +Percent of the liquid is +given by this one. + +The composition of the solid +at the end of the tie line + +minus the composition +that you started at. + +This is your bulk initial +concentration, divided by the + +length of that tie line. + +c star solid minus +c star liquid. + +And then multiplied by 100%. + +So you get a percent, and the +number here is going to be 45 + +minus 40 over 45 minus 32, +and that works out-- + +going to multiply by 100, or +else there will be complaints. + +And then this turns +out to be 38%. + +So what that means is that +if you take this + +amount of liquid here-- + +pardon me-- based on +conservation of mass, if you + +drop and hold at 1250, 38% of +that volume is now sitting + +here in the liquid, which means +62% of it by volume has + +turned into solid. + +And the composition here is +different from the composition + +here, but if you add up all the +nickel in the crucible and + +sum it versus all the copper in +the crucible, you still end + +up with 40% net nickel. + +So this very powerful. + +Because what you can do here +is you can separate metal. + +Because I started here with 40% +nickel, 60% copper, and + +now I've got something-- + +the liquid face, I wrote +here, the liquid + +phase is now 68% copper. + +So can you see that if I'm +clever about this, I could use + +this as a technique +for enriching. + +And if I'm thinking about +recycling metals, maybe I need + +to know something about phase +diagrams because it's a very + +simple way of concentrating +impurities or concentrating + +the desirable stuff. + +Let's look at one other thing +here that's really very + +interesting. + +Suppose I had something, instead +of c2 at 40%, suppose + +I choose a c1. + +So this is 40% nickel. + +Now what if I take something +that's 35% nickel, and I cool + +it down to 1250? + +What happens? + +If I park here at 1250 degrees, +according to the + +phase diagram, that substance +has to phase separate, and I'm + +going to end up with +the same thing. + +I'm going to end up with +liquid and solid. + +Now, isn't there a contradiction +there? + +How is it that whether I started +with 40% or 35%, I end + +up with the same end members? + +What's the missing piece? + +The relative amounts +will be different! + +The relative amounts. + +Here, look. + +As I'm getting closer to the +liquid, can you see that + +axiomatically, I'm going to +make more liquid and less + +solid if I ended up with +something over here? + +But at 1250, those are +the end members. + +That's the only stuff that's +going to be present. + +Ah! + +That's so good. + +I think I've got some +other stuff here. + +Oh yeah. + +Oh, this was-- yeah. + +So p equals 2. + +Lever rule. + +Whenever you see p equals 2, you +have two things you think + +of. p equals 2 means +phase separation. + +And that phase separation means +you're going to get + +different amounts, and +the lever rule. + +And why I have this Manchurian +Candidate-- + +it's this movie. + +I know there's a remake. + +The remake is horrible. + +The original, if you see the +original, is about some + +fellows that were brainwashed. + +They were American prisoners +of war brainwashed in North + +Korea and they're brainwashed +to become assassins on cue. + +And the cue is the Queen +of Diamonds. + +When someone shows the Queen of +Diamonds, they just go into + +automatic pilot, and they're +supposed to assassinate the + +political figure. + +So for you, your Queen of +Diamonds is p equals 2. + +When you see p equals 2, you +go, phase separation. + +Lever rule. + +All right? + +No guns, just this. + +I just want the formula. + +You go, phase separation, +lever rule. + +Whenever p equals two. + +So what happens in here? + +Phase separation. + +Boom, boom. + +Right there. + +Oh, I'm not supposed +to say boom, boom. + +Phase separation. + +Ta-da! + +You know, something. + +PC, whatever. + +OK. + +So let's keep going. + +Now I want to look at a second +type of phase diagram. + +So the first type of phase +diagram was complete + +solubility. + +Now the second type of phase +diagram has partial + +solubility. + +So let's look at that one. + +So i call this type two. + +And you don't predict +this stuff. + +We would give you the phase +diagram and simply ask you, + +you know, you're the specialist. +Tell me happens if + +I cool this to such and +such a temperature? + +You can tell me you get phase +separation, and the + +composition of the two end +members, and so on. + +So the characteristics, the +bonding characteristics here, + +are partial or limited +solubility of A and B. + +We're doing all of this for a +binary system A and B, and no + +change of state. + +So that means either always +solid, or always liquid. + +That's not to say that the A +and B never become solid. + +I'm just saying that a type two +diagram is limited to a + +single state. + +So let's take a look +at the diagram. + +The diagram looks like this. + +We're going to plot +temperature versus + +composition. + +So pure B on the right, +pure A on the left. + +Concentration is the abscissa, +and then the ordinate, of + +course, is temperature. + +And so the shape of the +diagram is this. + +There's the coexistence curve. + +It's called a synclinal +coexistence curve. + +So above, we have all solid. + +And in here, we have +two solids. + +So using the metallurgical +terms, this + +is alpha plus beta. + +Two phase regime, OK? + +So let's get those labels up +right off the bat, so we know + +who's where. + +So outside the coexistence +curve, p equals 1. + +Inside the coexistence +curve, p equals 2. + +And wherever I'm saying all +solid, alpha plus beta, I + +could write all liquid, and then +it goes to l1 plus l2. + +So maybe we should do that, to +show that we're multilingual. + +So it's either all solid, or +it could be all liquid. + +And then this would be liquid +1 plus liquid 2. + +And so why do we call +it synclinal? + +What's this? + +This is an incline. + +If I put two inclines +and I synchronize + +them, I get a syncline. + +And if I don't synchronize +them-- + +these are two ladders. + +I could prop them up. + +That's called a syncline. + +And if I put two ladders like +this, if I'm really stupid and + +I fail physics, if I do +this, they fall down. + +So this is called an +anticline, OK? + +That's an anticline. + +This is a syncline. + +It's not a U-shape, or a hump, +or something like that. + +This is 3091. + +This is a syncline. + +Synclinal coexistence curve. + +All right. + +So what's on here? + +What's this equilibrium, then? + +Well, the equilibrium must +be this equals this. + +So that would be, in the case +of the solid, it's the solid + +solution goes to alpha plus +beta, or it could be the + +liquid goes to liquid +1 plus liquid 2. + +That's the equilibrium. + +You can think about it almost +as a solubility. + +So let's start over +here on the left. + +Let's pick a temperature. + +Let's call this T1. + +So I can put B into A, and I +continue to get an all-solid + +solution, up to this +concentration here. + +What happens at this +concentration? + +I've hit a solubility limit. + +And if I try to put any more B +into A, I get a tie line-- + +lever rule. + +In here is lever rule +time, isn't it? + +Lever rule. p equals 2, OK? + +So it's solubility limits. + +Solubility limits. + +All right. + +So let's look at +some examples. + +Oh, here's this one, actually. + +That's why I had a-- + +you know, if you go to lower +temperature, gold, nickel-- + +look! + +They actually phase separate. + +That's shocking. + +I always find this one shocking, +because you think + +gold, nickel, nice FCC +metals, they should + +substitute for one another. + +Look what happens. + +If you start putting nickel into +pure gold at 700 degrees, + +you get the 10 weight percent, +you put any more in, boom. + +Right across here. + +So this is going to +be two phase. + +So if you look at the +solid, what's that + +going to look like? + +If I'm at, say, 30%, now I look +underneath and I've got a + +polygrain system, and I'm going +to have an alpha and a + +beta, and an alpha and a beta. + +I'm going to have two +different grains. + +And now, what's the relative +amount of alpha and the + +relative amount of beta? + +It's given by the lever rule. + +OK. + +Let's look at a few +other examples. + +Here's hexane nitrobenzene. + +And so they've even put +l-alpha, l-beta. + +They put the-- + +actually, that's probably a-- + +it's hard to read. + +But I think it's really an F, +but it didn't come through + +very well, so it's the beta +fraction, the alpha fraction. + +So you can see how you +use the lever rule. + +So up here it's all p. + +That's the not pressure, +that's my circle p. + +Single phase, two phase. + +Drop down to 290 degrees, it +separates into two liquids. + +With the hexane-- + +with two liquids, you'll +actually have them floating on + +top of one another, right? + +Well, maybe. + +Depending if the density +difference is tiny, you might + +get a dispersion. + +I'll show you that +in a second. + +All right. + +So p equals 2, lever rule. + +OK? + +Hexane nitrobenzene. + +Look at this one. + +This is surprising to me. + +Potassium chloride, +sodium chloride. + +It's almost lenticular with a +little bit of depression, but + +down here, it actually +separates. + +This is polymer. + +It's a polystyrene, +polybutadiene, + +depending on what the-- + +at low index, polymerization +index, they mix. + +At high polymerization index, +the two are mixing. + +You get two phase, +single phase. + +Changes the mechanical +properties, too, doesn't it? + +Now this one-- + +some systems actually have +a lower critical point. + +Oh, I meant to tell you. + +You see, there's this +temperature here. + +Above this temperature, they +mix in all proportions. + +You can ever have phase +separation. + +This is the maximum temperature +at which you have + +no phase separation. + +So this is called the consolute +temperature. + +And it's usually an +upper consolute. + +The higher you go +in temperature-- + +it's like saying, do you +dissolve more sugar in cold + +water or warm water? + +You dissolve more sugar +in warm water. + +And eventually, you get to a +temperature high enough that + +you can mix in all proportions, +right? + +That's the consolute. + +Some systems, for entropic +reasons-- and again, if you + +take 560 or some of the other +thermal classes, you'll + +understand this, but for +entropic reasons, you actually + +have homogeneous solutions at +low temperature, and at + +elevated temperature, you +get phase separation. + +That's funny, isn't it. + +So this is water triethylamine, +and they mix in + +all proportions at +this zone here. + +And then above a certain-- it's +called lower consolute + +temperature. + +It actually phase separates. + +Doesn't matter. + +All you care about is +p equals 2, phase + +separation, lever rule. + +The rest is details. + +This is a real hoot. + +This is water nicotine. + +It has a lower consolute +temperature and an upper + +consolute temperature. + +So it's got a solubility +bubble. + +You see? + +Out here, things are soluble. + +In here, they're insoluble. + +So they are emissible. + +So we call this zone, this +region here under the dome, so + +to speak, this it's called the +miscibility gap, because + +things in there are not soluble +in one another. + +But with nicotine, you have a +lower consolute and an upper + +consolute, so you have a +miscibility gap that's a + +complete ring. + +That's cool! + +I like this. + +All right. + +So now I'm going to do +a little experiment. + +We have a few minutes, so I'm +going to show you ouzo water. + +I'm going to mix it, and I'm +going to actually mix ouzo and + +water, and go into the two phase +regime, and then out. + +So this is what it +is, all right? + +It's oily stuff, you know. + +If you're of Greek ancestry, you +know what this stuff is. + +All right? + +But it's got licorice, it's got +a fair bit of oil in it. + +So what I'm going to do, is I'm +going to come in here, and + +I'm going to start adding +ouzo to water. + +And they're both clear, +colorless liquids. + +OK, Dave. Let's go to the-- + +All right. + +So what we're going to do-- +this is distilled water. + +So I'm going to put some +distilled water in here. + +A little bit of distilled +water. + +And this is ouzo. + +It's clear and colorless. + +OK. + +Can we show you this? + +Let's do this. + +OK. + +Ouzo, it comes from Greece. + +All right. + +So it's also clear +and colorless. + +That was the point. + +Not to show you the label. + +See? + +It's clear and colorless. + +So this is clear and colorless, +and the water, as + +you know, is clear +and colorless. + +So now what I'm going to do-- + +see, I don't have +to wear a smock, + +or goggles, or anything. + +This is great. + +So what I'm going to do, +is I'm going to add + +some of this stuff. + +Clear and colorless. + +OK. + +It's turned milky. + +Why has it turned milky? + +Because we've now crossed into +here, and the second phase is + +coming out. + +But the density difference and +surface tension differences + +are so slight, that instead of +having the second phase float + +on the first phase, we +have a dispersion, G. + +If you go to the dairy case, +and you look at something + +called milk, you'll have +the same thing. + +Why is milk milky? + +Because the fatty phase is a +fine dispersion, and the + +particle sizes is dadadada, +versus the wavelength of + +visible light, et cetera. + +Now if my phase diagram is +correct, and I'm in here, if I + +keep adding ouzo, I should +eventually emerge on this + +side, and instead of having a +milky dispersion, I eventually + +should come here, and now +I'll have a homogeneous, + +single-phase solution. + +But now it's going to be +ouzo-rich, instead of + +water-rich. + +You never thought phase diagrams +were interesting. + +You don't know. + +There we go. + +Je vous presente. + +There it is. + +So what we've done is, we've +come across the thing. + +Yeah, that's good. + +Just put that there. + +Now, David, please, back +to the slides. + +May I have the next +slide, please? + +That's a joke. + +When you have these terrible +speakers at conferences, they + +get up there, really nervous, +and they stand up there, and + +the first thing they say +is, may I have the + +first slide, please? + +That's sort of a gag +among scientists. + +What's your opening statement? + +May I have the first +slide, please? + +May I have the next +slide, please? + +OK. + +So we've done this. + +All right. + +Now-- + +yeah, OK, this is just more. + +All right. + +So now I'm going to +show you absinthe. + +Absinthe is the same thing. + +Absinthe also comes from +the same family. + +And there's a little +culture here. + +It contains wormwood. + +The wormwood was up at around +200, 250 parts per million. + +And what wormwood +does, it's got a + +hormone they call thujone. + +And thujone antagonizes the +gamma aminobutyric acid, which + +moderates firing of the +neural synapses. + +Basically, we've got this GABA +that regulates how-- our + +brains could work much +faster than they do, + +but the GABA regulates. + +If GABA doesn't work, you can +start moving so fast that you + +get muscle thing, and you get +epileptic, is one example. + +But anyways, what it does, is +if you drink this stuff, + +instead of being a stupid +drunk, you become a very + +high-functioning, very +alert drunk. + +And I'm going to show you what +the consequence is in art. + +Anyways, the cultural piece +here was that there was a + +destruction of the French wine +industry in the 1800s due to a + +blight called Phylloxera. + +It's like a beetle, and +it ate the vines. + +And in fact, the French wine +industry was saved by the + +American wine industry. + +Vines from New York state were +brought over, grafts were + +made, and virtually all French +wine today is on American + +stock with the exception, +occasionally you'll see + +something says vieille vin. + +Old vines. + +There was some areas +that were spared. + +So what's that have to +do with anything? + +It has to do with the fact that +when the Phylloxera hit, + +the price of wine went very +high, and the people at the + +bottom of the socioeconomic +ladder couldn't afford wine. + +So they turn to absinthe. + +Absinthe was easily produced. + +Thirty years later, when the +vines come back, the French + +wine industry wants to +recapture the market. + +So there's a Faustian bargain +between the French wine + +industry and the Women's +Temperance Union to try to + +disparage absinthe. + +And there were a few major +show trials that involved + +vicious murders in which it was +alleged that the killer + +was deranged on absinthe. + +And with this, they slandered +the name of absinthe so badly + +that it was eventually +banned and literally + +taken off the market. + +I mean-- + +you know, we had the Rosalind +Franklin commentary a few + +lectures ago. + +I hope I never read about you +doing something like this in + +order to help your +start-up company + +take over market share. + +That's not the way you're +supposed to do it. + +Anyway, so what-- + +now, how did they drink it? + +They drank it by mixing-- + +so it's now back, but it's +got very low levels + +of thujone, so it's-- + +David, may we go to this? + +So we're going to make a +mix called the louche. + +It's a-- + +OK, here it is. + +And this stuff here +is beautiful. + +Because it's a green color, +a soft green color. + +And the French even have +a name for it. + +They call it the green +fairy, la fee verte. + +So this is what absinthe +looks like. + +Beautiful. + +Very nice. + +And it's got the same kind +of licorice smell to it. + +And so you make the louche by +one part absinthe and five + +parts water. + +So this, at no upcharge, +you get this glass. + +It's a beautiful piece +of, you know, late + +Belle Epoque glassware. + +And the interesting thing is, +these people were absolutely + +crazy, scientifically. + +And so what they did is, the +markings on this glass are + +such that if you put absinthe up +to this ring here, and then + +you put water the rest of the +way, you get exactly the five + +to one ratio for louche. + +So you don't even +have to measure. + +You just put like so. + +OK. + +Let's see. + +I'm going to get this right! + +It's science. + +Here's our distilled water. + +You see how it's milky? + +So there's the louche. + +And if you wanted to be a real +hipster, you had this special + +Belle Epoque spoon. + +And what you'd put on top of +this would be a sugar cube. + +You know, this is +how it was done. + +You have to know some culture. + +You don't know. + +You've led sheltered lives. + +You pour it through +here, like this. + +So now I'm going to +show you the art. + +So David, may we cut to +the slides again? + +So there's the louche. + +All right. + +So here's the poster. + +Here's the man. + +He's pouring the water through +the slotted spoon with the + +thing, and there's a very +well-to-do lady, you can tell, + +she's got a beautiful hat, +and she's well-dressed. + +And he's inviting her to join +him for a glass of absinthe. + +L'absinthe oxygenee. + +That's the name of +the company. + +The oxygenated absinthe. + +C'est ma sante. + +This is my health. + +Van Gogh painted this. + +This is Picasso. + +The absinthe drinker. + +There's the absinthe again. + +This is Picasso after +many absinthes. + +You can see the slotted spoon +and the sugar cube. + +What else is there? + +That's up to you. + +All right. + +When you saw Moulin Rouge, you +may not have known all of this + +cultural history. + +So now let's take a look at +what's going on here. + +There's the absinthe, and I +think we've got a little-- + +[VIDEO PLAYBACK] + +-I don't even know if I am a +true Bohemian revolutionary. + +-Do you believe in beauty? + +-Yes. + +-Freedom? + +-Yes, of course. + +-Truth? + +-Yes. + +-Love? + +-Love? + +Love. + +Above all things, I +believe in love. + +Love is like oxygen. + +Love is a many-splendored +thing-- + +[END VIDEO PLAYBACK] + +Love is like oxygen. + +Chemistry is everywhere! + +All right, so this is what +happens eventually. + +This is the poster. + +This is from Switzerland. + +October 7, 1910. + +Gentleman, This Is the Hour! + +And there's the clergyman with +the Bible, and there's the + +green fairy. + +And she has a wand. + +She's been stabbed, but she's +lying here with a wand. + +The wand is an opalescent wand, +because this stuff is + +opalescent. + +Last thing I'll show you is +some really, really cool + +chemistry that you +must remember. + +When Toulouse-Lautrec drank-- + +let's go back, David, +to the thing. + +So when Toulouse-Lautrec drank +absinthe, and he drank lots of + +it, he didn't like +the milky color. + +So he wanted to make the +milky color disappear. + +So I'm in the two-phase +regime, and + +I've got an oily phase. + +And so how do I get rid +of the oily phase? + +What he did is he added cognac + +And why did he add cognac? + +Not because he was a +hard-drinking alcoholic. + +It's because if you've got a fat +phase here, and you've got + +an aqueous phase here, +and if you add + +alcohol, you've got CH3CH2OH. + +This can bond to the water by +a hydrogen bond, and this + +aliphatic tail can +stab the fat and + +bring them into solution. + +That's why you have +these recipes. + +Do you ever wonder why the +recipe says, add brandy, or + +add this, and then two steps +later, it says flame? + +You say, geez, I just put +the brandy in, now + +it's vaporizing away. + +Isn't that kind of stupid? + +No, it's not! + +This is what you're doing. + +You're cosolvating. + +If you're ever making a cream +sauce or something, and all of + +a sudden, everything +just curdles? + +First you scream. + +You go, ahhh! + +Phase separation. + +The second thing you do, is you +get some of this, and you + +cosolvate it. + +All right. + +So let's see what Lautrec did. + +Lautrec-- + +I might have to dilute +the volume here. + +We've got quite a lot in here. + +So just to make the point. + +So here's the louche, ad now +we're going to add cognac. + +He called this drink, Le +Tremblement de Terre. + +The earthquake. + +He had a walking stick a meter +long that was hollow, and it + +always had this in it. + +Look! + +Look at that. + +Isn't that something? + +So now it's this beautiful +blonde, golden color. + +It's clear. + +So this is all phase separation +and so on. + +At the end, it's all +about chemistry. + +All right. + +We'll see you on Wednesday +for our wrap-up. + +Good. \ No newline at end of file diff --git a/rd9d0WBFzt8.txt b/rd9d0WBFzt8.txt new file mode 100644 index 0000000000000000000000000000000000000000..ebc4fd467ec2cb5bc9bcd12bb59c24b38df14d3a --- /dev/null +++ b/rd9d0WBFzt8.txt @@ -0,0 +1,587 @@ +align:start position:0% + +we'd like to now calculate the angular + + align:start position:0% +we'd like to now calculate the angular + + + align:start position:0% +we'd like to now calculate the angular +momentum about an axis of rotation of a + + align:start position:0% +momentum about an axis of rotation of a + + + align:start position:0% +momentum about an axis of rotation of a +symmetric object like a ring so here's + + align:start position:0% +symmetric object like a ring so here's + + + align:start position:0% +symmetric object like a ring so here's +our axis of rotation we're gonna have + + align:start position:0% +our axis of rotation we're gonna have + + + align:start position:0% +our axis of rotation we're gonna have +Omega pointing up that means Omega Z Z + + align:start position:0% +Omega pointing up that means Omega Z Z + + + align:start position:0% +Omega pointing up that means Omega Z Z +will be positive because that's going to + + align:start position:0% +will be positive because that's going to + + + align:start position:0% +will be positive because that's going to +be our K hat axis and this is a ring of + + align:start position:0% +be our K hat axis and this is a ring of + + + align:start position:0% +be our K hat axis and this is a ring of +mass m and radius R so here's our radius + + align:start position:0% +mass m and radius R so here's our radius + + + align:start position:0% +mass m and radius R so here's our radius +now and we're gonna choose a point + + align:start position:0% +now and we're gonna choose a point + + + align:start position:0% +now and we're gonna choose a point +that's some lies somewhere on the + + align:start position:0% +that's some lies somewhere on the + + + align:start position:0% +that's some lies somewhere on the +symmetry axis of the ring and the object + + align:start position:0% +symmetry axis of the ring and the object + + + align:start position:0% +symmetry axis of the ring and the object +is rotating about that symmetry axis so + + align:start position:0% +is rotating about that symmetry axis so + + + align:start position:0% +is rotating about that symmetry axis so +it's passing through the center of mass + + align:start position:0% +it's passing through the center of mass + + + align:start position:0% +it's passing through the center of mass +now we've already the way we'll do this + + align:start position:0% +now we've already the way we'll do this + + + align:start position:0% +now we've already the way we'll do this +is we'll divide our ring up into pairs + + align:start position:0% +is we'll divide our ring up into pairs + + + align:start position:0% +is we'll divide our ring up into pairs +of symmetric objects so we have an M + + align:start position:0% +of symmetric objects so we have an M + + + align:start position:0% +of symmetric objects so we have an M +here and a little Delta M there and + + align:start position:0% +here and a little Delta M there and + + + align:start position:0% +here and a little Delta M there and +we're going to calculate the angular + + align:start position:0% +we're going to calculate the angular + + + align:start position:0% +we're going to calculate the angular +momentum first of that pair well we've + + align:start position:0% +momentum first of that pair well we've + + + align:start position:0% +momentum first of that pair well we've +already made that calculation that the + + align:start position:0% +already made that calculation that the + + + align:start position:0% +already made that calculation that the +angular momentum about S of the pair is + + align:start position:0% +angular momentum about S of the pair is + + + align:start position:0% +angular momentum about S of the pair is +twice the mass of each object that's the + + align:start position:0% +twice the mass of each object that's the + + + align:start position:0% +twice the mass of each object that's the +mass of the pair times R squared and it + + align:start position:0% +mass of the pair times R squared and it + + + align:start position:0% +mass of the pair times R squared and it +points in the Omega direction and so to + + align:start position:0% +points in the Omega direction and so to + + + align:start position:0% +points in the Omega direction and so to +get the angular momentum of the Ring + + align:start position:0% +get the angular momentum of the Ring + + + align:start position:0% +get the angular momentum of the Ring +we'll just sum up a set of symmetric + + align:start position:0% +we'll just sum up a set of symmetric + + + align:start position:0% +we'll just sum up a set of symmetric +pairs until we expand out over the + + align:start position:0% +pairs until we expand out over the + + + align:start position:0% +pairs until we expand out over the +entire ring and so L of the ring about s + + align:start position:0% +entire ring and so L of the ring about s + + + align:start position:0% +entire ring and so L of the ring about s +is just the sum over the pairs of the + + align:start position:0% +is just the sum over the pairs of the + + + align:start position:0% +is just the sum over the pairs of the +mass of the pair times R squared Omega + + align:start position:0% +mass of the pair times R squared Omega + + + align:start position:0% +mass of the pair times R squared Omega +and R squared and Omega are all + + align:start position:0% +and R squared and Omega are all + + + align:start position:0% +and R squared and Omega are all +constants the total mass of the ring is + + align:start position:0% +constants the total mass of the ring is + + + align:start position:0% +constants the total mass of the ring is +just the sum over the pairs of the mass + + align:start position:0% +just the sum over the pairs of the mass + + + align:start position:0% +just the sum over the pairs of the mass +of the pair and that's the total mass M + + align:start position:0% +of the pair and that's the total mass M + + + align:start position:0% +of the pair and that's the total mass M +of the ring and so what we get is an R + + align:start position:0% +of the ring and so what we get is an R + + + align:start position:0% +of the ring and so what we get is an R +squared Omega L of the ring s this is + + align:start position:0% +squared Omega L of the ring s this is + + + align:start position:0% +squared Omega L of the ring s this is +the moment of inertia about the axis for + + align:start position:0% +the moment of inertia about the axis for + + + align:start position:0% +the moment of inertia about the axis for +the ring because all the mass is + + align:start position:0% +the ring because all the mass is + + + align:start position:0% +the ring because all the mass is +distributed a distance R away and so we + + align:start position:0% +distributed a distance R away and so we + + + align:start position:0% +distributed a distance R away and so we +see for a continuous symmetric body like + + align:start position:0% +see for a continuous symmetric body like + + + align:start position:0% +see for a continuous symmetric body like +a ring + + align:start position:0% +a ring + + + align:start position:0% +a ring +again because it's symmetric the angular + + align:start position:0% +again because it's symmetric the angular + + + align:start position:0% +again because it's symmetric the angular +momentum only has a component along the + + align:start position:0% +momentum only has a component along the + + + align:start position:0% +momentum only has a component along the +axis of rotation now what if we had a an + + align:start position:0% +axis of rotation now what if we had a an + + + align:start position:0% +axis of rotation now what if we had a an +extended symmetric object and let's see + + align:start position:0% +extended symmetric object and let's see + + + align:start position:0% +extended symmetric object and let's see +if I can possibly draw something like + + align:start position:0% +if I can possibly draw something like + + + align:start position:0% +if I can possibly draw something like +that so we'll draw a pear-shaped object + + align:start position:0% +that so we'll draw a pear-shaped object + + + align:start position:0% +that so we'll draw a pear-shaped object +what is the moment of inertia of this + + align:start position:0% +what is the moment of inertia of this + + + align:start position:0% +what is the moment of inertia of this +pear-shaped object which is intended to + + align:start position:0% +pear-shaped object which is intended to + + + align:start position:0% +pear-shaped object which is intended to +be symmetric about the z axis well I can + + align:start position:0% +be symmetric about the z axis well I can + + + align:start position:0% +be symmetric about the z axis well I can +think of that pear-shaped object as + + align:start position:0% +think of that pear-shaped object as + + + align:start position:0% +think of that pear-shaped object as +consisting of a ring and it's a solid + + align:start position:0% +consisting of a ring and it's a solid + + + align:start position:0% +consisting of a ring and it's a solid +object this is a solid symmetric object + + align:start position:0% +object this is a solid symmetric object + + + align:start position:0% +object this is a solid symmetric object +and then inside the ring is just more + + align:start position:0% +and then inside the ring is just more + + + align:start position:0% +and then inside the ring is just more +rings so the whole disk here is just a + + align:start position:0% +rings so the whole disk here is just a + + + align:start position:0% +rings so the whole disk here is just a +superposition of rings and so the moment + + align:start position:0% +superposition of rings and so the moment + + + align:start position:0% +superposition of rings and so the moment +of inertia so the angular momentum of + + align:start position:0% +of inertia so the angular momentum of + + + align:start position:0% +of inertia so the angular momentum of +just this disk is the moment of the disk + + align:start position:0% +just this disk is the moment of the disk + + + align:start position:0% +just this disk is the moment of the disk +about the axis and now I'll just add + + align:start position:0% +about the axis and now I'll just add + + + align:start position:0% +about the axis and now I'll just add +more disks that are symmetric and so by + + align:start position:0% +more disks that are symmetric and so by + + + align:start position:0% +more disks that are symmetric and so by +exactly the same calculation as I have + + align:start position:0% +exactly the same calculation as I have + + + align:start position:0% +exactly the same calculation as I have +here the moment of this symmetric object + + align:start position:0% +here the moment of this symmetric object + + + align:start position:0% +here the moment of this symmetric object +is just the moment of inertia is more + + align:start position:0% +is just the moment of inertia is more + + + align:start position:0% +is just the moment of inertia is more +complicated for this object and it + + align:start position:0% +complicated for this object and it + + + align:start position:0% +complicated for this object and it +points in the Omega direction so again + + align:start position:0% +points in the Omega direction so again + + + align:start position:0% +points in the Omega direction so again +in conclusion a symmetric object about + + align:start position:0% +in conclusion a symmetric object about + + + align:start position:0% +in conclusion a symmetric object about +the axis of rotation only has a + + align:start position:0% +the axis of rotation only has a + + + align:start position:0% +the axis of rotation only has a +component of L pointing in the direction + + align:start position:0% +component of L pointing in the direction + + + align:start position:0% +component of L pointing in the direction +of Omega the constant of proportionality + + align:start position:0% +of Omega the constant of proportionality + + + align:start position:0% +of Omega the constant of proportionality +between the angular momentum and the + + align:start position:0% +between the angular momentum and the + + + align:start position:0% +between the angular momentum and the +angular velocity is the moment of + + align:start position:0% +angular velocity is the moment of + + + align:start position:0% +angular velocity is the moment of +inertia about that acts + + align:start position:0% +inertia about that acts + + + align:start position:0% +inertia about that acts +axis this we need to calculate for each + + align:start position:0% +axis this we need to calculate for each + + + align:start position:0% +axis this we need to calculate for each +symmetric object \ No newline at end of file diff --git a/rqI_0FNAeS0.txt b/rqI_0FNAeS0.txt new file mode 100644 index 0000000000000000000000000000000000000000..386bf4d844de2df33cb4a60dcbcb856150a566c5 --- /dev/null +++ b/rqI_0FNAeS0.txt @@ -0,0 +1,12459 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +And uh before we get into the topic + + align:start position:0% +And uh before we get into the topic + + + align:start position:0% +And uh before we get into the topic +which is educational teaching with + + align:start position:0% +which is educational teaching with + + + align:start position:0% +which is educational teaching with +educational technology um I just want to + + align:start position:0% +educational technology um I just want to + + + align:start position:0% +educational technology um I just want to +go back to some of the previous + + align:start position:0% +go back to some of the previous + + + align:start position:0% +go back to some of the previous +assignments a little bit of logistics + + align:start position:0% +assignments a little bit of logistics + + + align:start position:0% +assignments a little bit of logistics +etc. So you should have feedback on all + + align:start position:0% +etc. So you should have feedback on all + + + align:start position:0% +etc. So you should have feedback on all +the assignments that can be given that + + align:start position:0% +the assignments that can be given that + + + align:start position:0% +the assignments that can be given that +can you can be given feedback on uh the + + align:start position:0% +can you can be given feedback on uh the + + + align:start position:0% +can you can be given feedback on uh the +the assignment where you gave a + + align:start position:0% +the assignment where you gave a + + + align:start position:0% +the assignment where you gave a +presentation to a um a friend uh I can't + + align:start position:0% +presentation to a um a friend uh I can't + + + align:start position:0% +presentation to a um a friend uh I can't +really give you feedback on. I I looked + + align:start position:0% +really give you feedback on. I I looked + + + align:start position:0% +really give you feedback on. I I looked +over it. You all made nice observations + + align:start position:0% +over it. You all made nice observations + + + align:start position:0% +over it. You all made nice observations +uh good pointed observations. And I hope + + align:start position:0% +uh good pointed observations. And I hope + + + align:start position:0% +uh good pointed observations. And I hope +um that you can see how and I think I + + align:start position:0% +um that you can see how and I think I + + + align:start position:0% +um that you can see how and I think I +made this comment on the wiki that you + + align:start position:0% +made this comment on the wiki that you + + + align:start position:0% +made this comment on the wiki that you +can see how just your just your presence + + align:start position:0% +can see how just your just your presence + + + align:start position:0% +can see how just your just your presence +uh and the choice of words that you make + + align:start position:0% +uh and the choice of words that you make + + + align:start position:0% +uh and the choice of words that you make +can have a big effect. Um and that was + + align:start position:0% +can have a big effect. Um and that was + + + align:start position:0% +can have a big effect. Um and that was +the whole point of that assignment. So, + + align:start position:0% +the whole point of that assignment. So, + + + align:start position:0% +the whole point of that assignment. So, +so that's my feedback on that + + align:start position:0% +so that's my feedback on that + + + align:start position:0% +so that's my feedback on that +assignment. Um the previous one, the + + align:start position:0% +assignment. Um the previous one, the + + + align:start position:0% +assignment. Um the previous one, the +last one that I can that I feel like I + + align:start position:0% +last one that I can that I feel like I + + + align:start position:0% +last one that I can that I feel like I +can give you substantive feedback on is + + align:start position:0% +can give you substantive feedback on is + + + align:start position:0% +can give you substantive feedback on is +the active learning. How to incorporate + + align:start position:0% +the active learning. How to incorporate + + + align:start position:0% +the active learning. How to incorporate +active learning. As I mentioned last + + align:start position:0% +active learning. As I mentioned last + + + align:start position:0% +active learning. As I mentioned last +time, um you guys did such a great job + + align:start position:0% +time, um you guys did such a great job + + + align:start position:0% +time, um you guys did such a great job +of incorporating active learning in the + + align:start position:0% +of incorporating active learning in the + + + align:start position:0% +of incorporating active learning in the +first time you'd submitted that where it + + align:start position:0% +first time you'd submitted that where it + + + align:start position:0% +first time you'd submitted that where it +was just creating a course outline that + + align:start position:0% +was just creating a course outline that + + + align:start position:0% +was just creating a course outline that +there wasn't a lot extra to add, but I + + align:start position:0% +there wasn't a lot extra to add, but I + + + align:start position:0% +there wasn't a lot extra to add, but I +added whenever I added comments whenever + + align:start position:0% +added whenever I added comments whenever + + + align:start position:0% +added whenever I added comments whenever +possible. One thing that I commented on + + align:start position:0% +possible. One thing that I commented on + + + align:start position:0% +possible. One thing that I commented on +on at least two people's um homework uh + + align:start position:0% +on at least two people's um homework uh + + + align:start position:0% +on at least two people's um homework uh +the one about active learning was the + + align:start position:0% +the one about active learning was the + + + align:start position:0% +the one about active learning was the +idea uh you mentioned do you doing + + align:start position:0% +idea uh you mentioned do you doing + + + align:start position:0% +idea uh you mentioned do you doing +demos? So there's a very uh interesting + + align:start position:0% +demos? So there's a very uh interesting + + + align:start position:0% +demos? So there's a very uh interesting +piece of work out of Eric Mazzour's + + align:start position:0% +piece of work out of Eric Mazzour's + + + align:start position:0% +piece of work out of Eric Mazzour's +group at Harvard about the use of demos + + align:start position:0% +group at Harvard about the use of demos + + + align:start position:0% +group at Harvard about the use of demos +and that paper is called the crouch and + + align:start position:0% +and that paper is called the crouch and + + + align:start position:0% +and that paper is called the crouch and +mazzour paper and it's the it's a + + align:start position:0% +mazzour paper and it's the it's a + + + align:start position:0% +mazzour paper and it's the it's a +optional reading in the um I believe + + align:start position:0% +optional reading in the um I believe + + + align:start position:0% +optional reading in the um I believe +it's the active learning session. So if + + align:start position:0% +it's the active learning session. So if + + + align:start position:0% +it's the active learning session. So if +you + + align:start position:0% +you + + + align:start position:0% +you +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +look, so this is um + + align:start position:0% + + + + align:start position:0% + +the active learning class which is class + + align:start position:0% +the active learning class which is class + + + align:start position:0% +the active learning class which is class +five, right? Am I right about that? Or + + align:start position:0% +five, right? Am I right about that? Or + + + align:start position:0% +five, right? Am I right about that? Or +six? + + align:start position:0% +six? + + + align:start position:0% +six? +Six. Six. + + align:start position:0% +Six. Six. + + + align:start position:0% +Six. Six. +Yes. Six. + + align:start position:0% + + + + align:start position:0% + +Oh, okay. So, it's five. + + align:start position:0% +Oh, okay. So, it's five. + + + align:start position:0% +Oh, okay. So, it's five. +Um yeah so um that's a really + + align:start position:0% +Um yeah so um that's a really + + + align:start position:0% +Um yeah so um that's a really +interesting paper because I think + + align:start position:0% +interesting paper because I think + + + align:start position:0% +interesting paper because I think +sometimes we say I'm going to do a + + align:start position:0% +sometimes we say I'm going to do a + + + align:start position:0% +sometimes we say I'm going to do a +demo op priori a demo isn't active I + + align:start position:0% +demo op priori a demo isn't active I + + + align:start position:0% +demo op priori a demo isn't active I +mean it's active for you you're doing + + align:start position:0% +mean it's active for you you're doing + + + align:start position:0% +mean it's active for you you're doing +the demo but it's not necessarily active + + align:start position:0% +the demo but it's not necessarily active + + + align:start position:0% +the demo but it's not necessarily active +for students and if we enter into the + + align:start position:0% +for students and if we enter into the + + + align:start position:0% +for students and if we enter into the +enterprise of doing a demo thinking + + align:start position:0% +enterprise of doing a demo thinking + + + align:start position:0% +enterprise of doing a demo thinking +we're being well thinking they're being + + align:start position:0% +we're being well thinking they're being + + + align:start position:0% +we're being well thinking they're being +active um they might not be and crouch + + align:start position:0% +active um they might not be and crouch + + + align:start position:0% +active um they might not be and crouch +did an interesting um study + + align:start position:0% +did an interesting um study + + + align:start position:0% +did an interesting um study +where they looked at they were doing + + align:start position:0% +where they looked at they were doing + + + align:start position:0% +where they looked at they were doing +mechanics freshman mechanics class and + + align:start position:0% +mechanics freshman mechanics class and + + + align:start position:0% +mechanics freshman mechanics class and +they had, you know, masses on an air + + align:start position:0% +they had, you know, masses on an air + + + align:start position:0% +they had, you know, masses on an air +track, you know, when you have like a + + align:start position:0% +track, you know, when you have like a + + + align:start position:0% +track, you know, when you have like a +mass of 2M and you slam into it with a + + align:start position:0% +mass of 2M and you slam into it with a + + + align:start position:0% +mass of 2M and you slam into it with a +mass of M. What happens to the mass of + + align:start position:0% +mass of M. What happens to the mass of + + + align:start position:0% +mass of M. What happens to the mass of +2M? What happens to this mass of M that + + align:start position:0% +2M? What happens to this mass of M that + + + align:start position:0% +2M? What happens to this mass of M that +was coming in? That kind of stuff. And + + align:start position:0% +was coming in? That kind of stuff. And + + + align:start position:0% +was coming in? That kind of stuff. And +so they would show the students these + + align:start position:0% +so they would show the students these + + + align:start position:0% +so they would show the students these +demos. Oh, look what happens. Here comes + + align:start position:0% +demos. Oh, look what happens. Here comes + + + align:start position:0% +demos. Oh, look what happens. Here comes +the mass of M at a velocity d. And then + + align:start position:0% +the mass of M at a velocity d. And then + + + align:start position:0% +the mass of M at a velocity d. And then +when they ask students like in the same + + align:start position:0% +when they ask students like in the same + + + align:start position:0% +when they ask students like in the same +class at the end of the same class + + align:start position:0% +class at the end of the same class + + + align:start position:0% +class at the end of the same class +period to say what happens when a mass + + align:start position:0% +period to say what happens when a mass + + + align:start position:0% +period to say what happens when a mass +of M collides with a mass of 2 mass of M + + align:start position:0% +of M collides with a mass of 2 mass of M + + + align:start position:0% +of M collides with a mass of 2 mass of M +going X miles an hour um collides with a + + align:start position:0% +going X miles an hour um collides with a + + + align:start position:0% +going X miles an hour um collides with a +mass of 2M what happens? Students got it + + align:start position:0% +mass of 2M what happens? Students got it + + + align:start position:0% +mass of 2M what happens? Students got it +wrong. They had just seen the demo. They + + align:start position:0% +wrong. They had just seen the demo. They + + + align:start position:0% +wrong. They had just seen the demo. They +had just seen the demo and they still + + align:start position:0% +had just seen the demo and they still + + + align:start position:0% +had just seen the demo and they still +got it wrong. + + align:start position:0% +got it wrong. + + + align:start position:0% +got it wrong. +So what they found was um and that's I + + align:start position:0% +So what they found was um and that's I + + + align:start position:0% +So what they found was um and that's I +think that's a really profound finding + + align:start position:0% +think that's a really profound finding + + + align:start position:0% +think that's a really profound finding +because as experts we think of course + + align:start position:0% +because as experts we think of course + + + align:start position:0% +because as experts we think of course +they're going to see this it's going to + + align:start position:0% +they're going to see this it's going to + + + align:start position:0% +they're going to see this it's going to +be emlazed into their brain they'll + + align:start position:0% +be emlazed into their brain they'll + + + align:start position:0% +be emlazed into their brain they'll +never forget it but they never learn it + + align:start position:0% +never forget it but they never learn it + + + align:start position:0% +never forget it but they never learn it +basically. So it's more evidence for the + + align:start position:0% +basically. So it's more evidence for the + + + align:start position:0% +basically. So it's more evidence for the +for active learning for sure. But what + + align:start position:0% +for active learning for sure. But what + + + align:start position:0% +for active learning for sure. But what +they found out was they forced students + + align:start position:0% +they found out was they forced students + + + align:start position:0% +they found out was they forced students +to make a prediction to discuss that + + align:start position:0% +to make a prediction to discuss that + + + align:start position:0% +to make a prediction to discuss that +prediction with somebody else before + + align:start position:0% +prediction with somebody else before + + + align:start position:0% +prediction with somebody else before +they saw the demo. And when they did + + align:start position:0% +they saw the demo. And when they did + + + align:start position:0% +they saw the demo. And when they did +that, the the scores on these sort of + + align:start position:0% +that, the the scores on these sort of + + + align:start position:0% +that, the the scores on these sort of +post demo uh quizzes, if you will, u + + align:start position:0% +post demo uh quizzes, if you will, u + + + align:start position:0% +post demo uh quizzes, if you will, u +went way up. + + align:start position:0% +went way up. + + + align:start position:0% +went way up. +So, it's a small tweak, but it's a + + align:start position:0% +So, it's a small tweak, but it's a + + + align:start position:0% +So, it's a small tweak, but it's a +profound one because you might really + + align:start position:0% +profound one because you might really + + + align:start position:0% +profound one because you might really +just be wasting your time. Um, if you + + align:start position:0% +just be wasting your time. Um, if you + + + align:start position:0% +just be wasting your time. Um, if you +show a lot of demos and you don't ask + + align:start position:0% +show a lot of demos and you don't ask + + + align:start position:0% +show a lot of demos and you don't ask +students to make these predictions + + align:start position:0% +students to make these predictions + + + align:start position:0% +students to make these predictions +beforehand, this goes back to the + + align:start position:0% +beforehand, this goes back to the + + + align:start position:0% +beforehand, this goes back to the +mathematician uh George Pia who who + + align:start position:0% +mathematician uh George Pia who who + + + align:start position:0% +mathematician uh George Pia who who +wrote in the 50s about asking people to + + align:start position:0% +wrote in the 50s about asking people to + + + align:start position:0% +wrote in the 50s about asking people to +make predictions before you gave them + + align:start position:0% +make predictions before you gave them + + + align:start position:0% +make predictions before you gave them +the answer. Um, I'm not sure he had any + + align:start position:0% +the answer. Um, I'm not sure he had any + + + align:start position:0% +the answer. Um, I'm not sure he had any +data for it, but this was his thing. Um, + + align:start position:0% +data for it, but this was his thing. Um, + + + align:start position:0% +data for it, but this was his thing. Um, +this is pretty good data suggesting that + + align:start position:0% +this is pretty good data suggesting that + + + align:start position:0% +this is pretty good data suggesting that +you really should um should ask students + + align:start position:0% +you really should um should ask students + + + align:start position:0% +you really should um should ask students +to make predictions before showing the + + align:start position:0% +to make predictions before showing the + + + align:start position:0% +to make predictions before showing the +demo. So, that was uh just one a couple + + align:start position:0% +demo. So, that was uh just one a couple + + + align:start position:0% +demo. So, that was uh just one a couple +people brought that up. I I um and I + + align:start position:0% +people brought that up. I I um and I + + + align:start position:0% +people brought that up. I I um and I +wanted to make sure everybody heard + + align:start position:0% +wanted to make sure everybody heard + + + align:start position:0% +wanted to make sure everybody heard +that. Okay. If you can't find this + + align:start position:0% +that. Okay. If you can't find this + + + align:start position:0% +that. Okay. If you can't find this +reference um let me know. It might be + + align:start position:0% +reference um let me know. It might be + + + align:start position:0% +reference um let me know. It might be +hiding somewhere else. I'm pretty sure + + align:start position:0% +hiding somewhere else. I'm pretty sure + + + align:start position:0% +hiding somewhere else. I'm pretty sure +it's in in this um it is. Oh, + + align:start position:0% +it's in in this um it is. Oh, + + + align:start position:0% +it's in in this um it is. Oh, +great. Okay. Um so, that was that. But, + + align:start position:0% +great. Okay. Um so, that was that. But, + + + align:start position:0% +great. Okay. Um so, that was that. But, +but overall, great job on that + + align:start position:0% +but overall, great job on that + + + align:start position:0% +but overall, great job on that +assignment. Um, and then I briefly + + align:start position:0% +assignment. Um, and then I briefly + + + align:start position:0% +assignment. Um, and then I briefly +looked over the assignment that was due + + align:start position:0% +looked over the assignment that was due + + + align:start position:0% +looked over the assignment that was due +today or whenever um, uh, using moving, + + align:start position:0% +today or whenever um, uh, using moving, + + + align:start position:0% +today or whenever um, uh, using moving, +uh, creating prompts at various levels + + align:start position:0% +uh, creating prompts at various levels + + + align:start position:0% +uh, creating prompts at various levels +of Bloom's taxonomy or a taxonomy of + + align:start position:0% +of Bloom's taxonomy or a taxonomy of + + + align:start position:0% +of Bloom's taxonomy or a taxonomy of +your choosing. Again, I thought you did + + align:start position:0% +your choosing. Again, I thought you did + + + align:start position:0% +your choosing. Again, I thought you did +a great you did a great job. Um, I'd + + align:start position:0% +a great you did a great job. Um, I'd + + + align:start position:0% +a great you did a great job. Um, I'd +like to hear a little bit of reactions + + align:start position:0% +like to hear a little bit of reactions + + + align:start position:0% +like to hear a little bit of reactions +to that assignment. Was it difficult? + + align:start position:0% +to that assignment. Was it difficult? + + + align:start position:0% +to that assignment. Was it difficult? +Was it easy? Do you see how it could be + + align:start position:0% +Was it easy? Do you see how it could be + + + align:start position:0% +Was it easy? Do you see how it could be +useful? Does it seem like a waste of + + align:start position:0% + + + + align:start position:0% + +time? I think was very, very useful. + + align:start position:0% +time? I think was very, very useful. + + + align:start position:0% +time? I think was very, very useful. +Yeah, just uh um it lets you see what + + align:start position:0% +Yeah, just uh um it lets you see what + + + align:start position:0% +Yeah, just uh um it lets you see what +the students will go through when you + + align:start position:0% +the students will go through when you + + + align:start position:0% +the students will go through when you +mark that thing otherwise because it's + + align:start position:0% +mark that thing otherwise because it's + + + align:start position:0% +mark that thing otherwise because it's +like you are solving it too. So you kind + + align:start position:0% +like you are solving it too. So you kind + + + align:start position:0% +like you are solving it too. So you kind +of feel and see how what level to take + + align:start position:0% +of feel and see how what level to take + + + align:start position:0% +of feel and see how what level to take +them to. Yes. So it's very good. Great. + + align:start position:0% +them to. Yes. So it's very good. Great. + + + align:start position:0% +them to. Yes. So it's very good. Great. +Otherwise you wouldn't know you just + + align:start position:0% +Otherwise you wouldn't know you just + + + align:start position:0% +Otherwise you wouldn't know you just +said and then you don't know how much + + align:start position:0% +said and then you don't know how much + + + align:start position:0% +said and then you don't know how much +dream it really gives them. Exactly. And + + align:start position:0% +dream it really gives them. Exactly. And + + + align:start position:0% +dream it really gives them. Exactly. And +I think that happens. I mean it's + + align:start position:0% +I think that happens. I mean it's + + + align:start position:0% +I think that happens. I mean it's +happened to me when I first started + + align:start position:0% +happened to me when I first started + + + align:start position:0% +happened to me when I first started +teaching um intro materials. you know, + + align:start position:0% +teaching um intro materials. you know, + + + align:start position:0% +teaching um intro materials. you know, +you're just like, "Okay, they'll + + align:start position:0% +you're just like, "Okay, they'll + + + align:start position:0% +you're just like, "Okay, they'll +calculate the the, you know, the the + + align:start position:0% +calculate the the, you know, the the + + + align:start position:0% +calculate the the, you know, the the +stress on this plane and blah blah + + align:start position:0% +stress on this plane and blah blah + + + align:start position:0% +stress on this plane and blah blah +blah." And you're like, "Well, why are + + align:start position:0% +blah." And you're like, "Well, why are + + + align:start position:0% +blah." And you're like, "Well, why are +they doing that? What is that getting + + align:start position:0% +they doing that? What is that getting + + + align:start position:0% +they doing that? What is that getting +them?" Um, and it's just this reality + + align:start position:0% +them?" Um, and it's just this reality + + + align:start position:0% +them?" Um, and it's just this reality +check for you so that you don't go off + + align:start position:0% +check for you so that you don't go off + + + align:start position:0% +check for you so that you don't go off +into the weeds sort of. So, yeah, Tesla. + + align:start position:0% +into the weeds sort of. So, yeah, Tesla. + + + align:start position:0% +into the weeds sort of. So, yeah, Tesla. +Yeah, I think it's really very + + align:start position:0% +Yeah, I think it's really very + + + align:start position:0% +Yeah, I think it's really very +interesting. And what I noticed that by + + align:start position:0% +interesting. And what I noticed that by + + + align:start position:0% +interesting. And what I noticed that by +trying to set standard questions at + + align:start position:0% +trying to set standard questions at + + + align:start position:0% +trying to set standard questions at +those level of + + align:start position:0% +those level of + + + align:start position:0% +those level of +learning, you push yourself also to have + + align:start position:0% +learning, you push yourself also to have + + + align:start position:0% +learning, you push yourself also to have +a limit. You want to bring a question + + align:start position:0% +a limit. You want to bring a question + + + align:start position:0% +a limit. You want to bring a question +student + + align:start position:0% +student + + + align:start position:0% +student +yourself. That's number one. Number two, + + align:start position:0% +yourself. That's number one. Number two, + + + align:start position:0% +yourself. That's number one. Number two, +what I say is that most of very good + + align:start position:0% +what I say is that most of very good + + + align:start position:0% +what I say is that most of very good +questions that test high level of + + align:start position:0% +questions that test high level of + + + align:start position:0% +questions that test high level of +communicative learning is not may not + + align:start position:0% +communicative learning is not may not + + + align:start position:0% +communicative learning is not may not +test just one level. I'm setting very + + align:start position:0% +test just one level. I'm setting very + + + align:start position:0% +test just one level. I'm setting very +good questions. I might test almost all + + align:start position:0% +good questions. I might test almost all + + + align:start position:0% +good questions. I might test almost all +the level in just a simple question. + + align:start position:0% +the level in just a simple question. + + + align:start position:0% +the level in just a simple question. +Yes. Understand? You may have a + + align:start position:0% +Yes. Understand? You may have a + + + align:start position:0% +Yes. Understand? You may have a +remembering part and then you might have + + align:start position:0% +remembering part and then you might have + + + align:start position:0% +remembering part and then you might have +an application part. So for instance, + + align:start position:0% +an application part. So for instance, + + + align:start position:0% +an application part. So for instance, +what I did, I put some questions + + align:start position:0% +what I did, I put some questions + + + align:start position:0% +what I did, I put some questions +actually tested more than just one + + align:start position:0% +actually tested more than just one + + + align:start position:0% +actually tested more than just one +tested about three at the same time. So + + align:start position:0% +tested about three at the same time. So + + + align:start position:0% +tested about three at the same time. So +I think it's really very good. + + align:start position:0% +I think it's really very good. + + + align:start position:0% +I think it's really very good. +gas, right? and also to to make sure + + align:start position:0% +gas, right? and also to to make sure + + + align:start position:0% +gas, right? and also to to make sure +you're aware of that and then also + + align:start position:0% +you're aware of that and then also + + + align:start position:0% +you're aware of that and then also +decide well if they don't remember the + + align:start position:0% +decide well if they don't remember the + + + align:start position:0% +decide well if they don't remember the +value of the universal gas constant in + + align:start position:0% +value of the universal gas constant in + + + align:start position:0% +value of the universal gas constant in +this these units but they do the apply + + align:start position:0% +this these units but they do the apply + + + align:start position:0% +this these units but they do the apply +part fine they just use the so it's + + align:start position:0% +part fine they just use the so it's + + + align:start position:0% +part fine they just use the so it's +important you know we always have to + + align:start position:0% +important you know we always have to + + + align:start position:0% +important you know we always have to +think about that when we grade questions + + align:start position:0% +think about that when we grade questions + + + align:start position:0% +think about that when we grade questions +but but I think by by parsing it out + + align:start position:0% +but but I think by by parsing it out + + + align:start position:0% +but but I think by by parsing it out +like that it makes you more cognizant of + + align:start position:0% +like that it makes you more cognizant of + + + align:start position:0% +like that it makes you more cognizant of +those issues that might come up in terms + + align:start position:0% +those issues that might come up in terms + + + align:start position:0% +those issues that might come up in terms +of how the students um respond to the + + align:start position:0% +of how the students um respond to the + + + align:start position:0% +of how the students um respond to the +the question I thought it was actually + + align:start position:0% +the question I thought it was actually + + + align:start position:0% +the question I thought it was actually +difficult to make a question that only + + align:start position:0% +difficult to make a question that only + + + align:start position:0% +difficult to make a question that only +satisfied one of the criteria like apply + + align:start position:0% +satisfied one of the criteria like apply + + + align:start position:0% +satisfied one of the criteria like apply +had to be stumped for like 15 minutes + + align:start position:0% +had to be stumped for like 15 minutes + + + align:start position:0% +had to be stumped for like 15 minutes +because everything I was asking that to + + align:start position:0% +because everything I was asking that to + + + align:start position:0% +because everything I was asking that to +try to apply was also analyzed or you + + align:start position:0% +try to apply was also analyzed or you + + + align:start position:0% +try to apply was also analyzed or you +know like it was it was so I tried to I + + align:start position:0% +know like it was it was so I tried to I + + + align:start position:0% +know like it was it was so I tried to I +mean I guess I could have just made one + + align:start position:0% +mean I guess I could have just made one + + + align:start position:0% +mean I guess I could have just made one +that did both but I was sitting there + + align:start position:0% +that did both but I was sitting there + + + align:start position:0% +that did both but I was sitting there +and I was like no okay not this one okay + + align:start position:0% +and I was like no okay not this one okay + + + align:start position:0% +and I was like no okay not this one okay +that really I was I almost I almost left + + align:start position:0% +that really I was I almost I almost left + + + align:start position:0% +that really I was I almost I almost left +it blank and said I'm stuck possible I + + align:start position:0% +it blank and said I'm stuck possible I + + + align:start position:0% +it blank and said I'm stuck possible I +finally came with something that I think + + align:start position:0% +finally came with something that I think + + + align:start position:0% +finally came with something that I think +just answers the fly But it was + + align:start position:0% +just answers the fly But it was + + + align:start position:0% +just answers the fly But it was +interesting to think about. Right. + + align:start position:0% +interesting to think about. Right. + + + align:start position:0% +interesting to think about. Right. +Right. And and you don't and you know in + + align:start position:0% +Right. And and you don't and you know in + + + align:start position:0% +Right. And and you don't and you know in +real life in real life you don't have to + + align:start position:0% +real life in real life you don't have to + + + align:start position:0% +real life in real life you don't have to +you know just have one you know you can + + align:start position:0% +you know just have one you know you can + + + align:start position:0% +you know just have one you know you can +embed them together but you know recall + + align:start position:0% +embed them together but you know recall + + + align:start position:0% +embed them together but you know recall +and apply + + align:start position:0% +and apply + + + align:start position:0% +and apply +or whatever. Um but and I think in some + + align:start position:0% +or whatever. Um but and I think in some + + + align:start position:0% +or whatever. Um but and I think in some +for some topics it might be easier to to + + align:start position:0% +for some topics it might be easier to to + + + align:start position:0% +for some topics it might be easier to to +siloize it a little bit. Um you know + + align:start position:0% +siloize it a little bit. Um you know + + + align:start position:0% +siloize it a little bit. Um you know +given the data + + align:start position:0% +given the data + + + align:start position:0% +given the data +construct a whatever. So that that + + align:start position:0% +construct a whatever. So that that + + + align:start position:0% +construct a whatever. So that that +that's more of an apply. I mean, but + + align:start position:0% +that's more of an apply. I mean, but + + + align:start position:0% +that's more of an apply. I mean, but +there might be classes or subjects where + + align:start position:0% +there might be classes or subjects where + + + align:start position:0% +there might be classes or subjects where +that doesn't really you can't really do + + align:start position:0% +that doesn't really you can't really do + + + align:start position:0% +that doesn't really you can't really do +that quite the same + + align:start position:0% +that quite the same + + + align:start position:0% +that quite the same +way. Um, other + + align:start position:0% + + + + align:start position:0% + +reactions? I was also thinking of it in + + align:start position:0% +reactions? I was also thinking of it in + + + align:start position:0% +reactions? I was also thinking of it in +terms of grading like if you have a have + + align:start position:0% +terms of grading like if you have a have + + + align:start position:0% +terms of grading like if you have a have +a rubric and or you have, you + + align:start position:0% +a rubric and or you have, you + + + align:start position:0% +a rubric and or you have, you +know, assigning the number of points + + align:start position:0% +know, assigning the number of points + + + align:start position:0% +know, assigning the number of points +based on which level you were asking, + + align:start position:0% +based on which level you were asking, + + + align:start position:0% +based on which level you were asking, +right? like as opposed to saying okay + + align:start position:0% +right? like as opposed to saying okay + + + align:start position:0% +right? like as opposed to saying okay +five points for each question to say + + align:start position:0% +five points for each question to say + + + align:start position:0% +five points for each question to say +like okay you get one point for the + + align:start position:0% +like okay you get one point for the + + + align:start position:0% +like okay you get one point for the +remembering and then you get you know 10 + + align:start position:0% +remembering and then you get you know 10 + + + align:start position:0% +remembering and then you get you know 10 +points for the creative or you know + + align:start position:0% +points for the creative or you know + + + align:start position:0% +points for the creative or you know +right right I would be careful I mean I + + align:start position:0% +right right I would be careful I mean I + + + align:start position:0% +right right I would be careful I mean I +think that's a fine idea I would be + + align:start position:0% +think that's a fine idea I would be + + + align:start position:0% +think that's a fine idea I would be +careful to make sure that students know + + align:start position:0% +careful to make sure that students know + + + align:start position:0% +careful to make sure that students know +that so they don't kill themselves + + align:start position:0% +that so they don't kill themselves + + + align:start position:0% +that so they don't kill themselves +memorizing you know pi out to 25 digits + + align:start position:0% +memorizing you know pi out to 25 digits + + + align:start position:0% +memorizing you know pi out to 25 digits +or something right + + align:start position:0% +or something right + + + align:start position:0% +or something right +um um so if there are if you do have + + align:start position:0% +um um so if there are if you do have + + + align:start position:0% +um um so if there are if you do have +these sort of this is what I think is + + align:start position:0% +these sort of this is what I think is + + + align:start position:0% +these sort of this is what I think is +important you need to you'll need to + + align:start position:0% +important you need to you'll need to + + + align:start position:0% +important you need to you'll need to +specify that I mean and that a rubric + + align:start position:0% +specify that I mean and that a rubric + + + align:start position:0% +specify that I mean and that a rubric +could incorporate that for sure. But you + + align:start position:0% +could incorporate that for sure. But you + + + align:start position:0% +could incorporate that for sure. But you +do want to make sure students know what + + align:start position:0% +do want to make sure students know what + + + align:start position:0% +do want to make sure students know what +your logic is. + + align:start position:0% + + + + align:start position:0% + +I think also there are some questions + + align:start position:0% +I think also there are some questions + + + align:start position:0% +I think also there are some questions +you said uh that you give formulas the + + align:start position:0% +you said uh that you give formulas the + + + align:start position:0% +you said uh that you give formulas the +formula in the equation uh just to make + + align:start position:0% +formula in the equation uh just to make + + + align:start position:0% +formula in the equation uh just to make +sure that student won't spend all of + + align:start position:0% +sure that student won't spend all of + + + align:start position:0% +sure that student won't spend all of +their time to cram the equations. Yes. + + align:start position:0% +their time to cram the equations. Yes. + + + align:start position:0% +their time to cram the equations. Yes. +Yes. Right. And that in most classes + + align:start position:0% +Yes. Right. And that in most classes + + + align:start position:0% +Yes. Right. And that in most classes +that's totally reasonable. Right. I + + align:start position:0% +that's totally reasonable. Right. I + + + align:start position:0% +that's totally reasonable. Right. I +mean, um, you know, the joke I make + + align:start position:0% +mean, um, you know, the joke I make + + + align:start position:0% +mean, um, you know, the joke I make +about, you know, it's rare the real life + + align:start position:0% +about, you know, it's rare the real life + + + align:start position:0% +about, you know, it's rare the real life +that somebody comes in and says, "I need + + align:start position:0% +that somebody comes in and says, "I need + + + align:start position:0% +that somebody comes in and says, "I need +this answer right now. Don't look up + + align:start position:0% +this answer right now. Don't look up + + + align:start position:0% +this answer right now. Don't look up +anything." Right? I mean, it's kind of a + + align:start position:0% +anything." Right? I mean, it's kind of a + + + align:start position:0% +anything." Right? I mean, it's kind of a +weird + + align:start position:0% +weird + + + align:start position:0% +weird +um pretense. So, most most I mean, it's + + align:start position:0% +um pretense. So, most most I mean, it's + + + align:start position:0% +um pretense. So, most most I mean, it's +usually reasonable to just put the + + align:start position:0% +usually reasonable to just put the + + + align:start position:0% +usually reasonable to just put the +equations at the bottom or write it in + + align:start position:0% +equations at the bottom or write it in + + + align:start position:0% +equations at the bottom or write it in +the problem + + align:start position:0% +the problem + + + align:start position:0% +the problem +statement. Anything else on + + align:start position:0% +statement. Anything else on + + + align:start position:0% +statement. Anything else on +that? Okay. So, uh, today we're going to + + align:start position:0% +that? Okay. So, uh, today we're going to + + + align:start position:0% +that? Okay. So, uh, today we're going to +talk about teaching with educational + + align:start position:0% +talk about teaching with educational + + + align:start position:0% +talk about teaching with educational +technology. Um, if you I had written on + + align:start position:0% +technology. Um, if you I had written on + + + align:start position:0% +technology. Um, if you I had written on +the website to bring a web enabled + + align:start position:0% +the website to bring a web enabled + + + align:start position:0% +the website to bring a web enabled +device. If you didn't, I have an extra + + align:start position:0% +device. If you didn't, I have an extra + + + align:start position:0% +device. If you didn't, I have an extra +laptop and and we can share. It's not a + + align:start position:0% +laptop and and we can share. It's not a + + + align:start position:0% +laptop and and we can share. It's not a +it's not it shouldn't be a problem. + + align:start position:0% +it's not it shouldn't be a problem. + + + align:start position:0% +it's not it shouldn't be a problem. +Um, as part of this, um, I hope that + + align:start position:0% +Um, as part of this, um, I hope that + + + align:start position:0% +Um, as part of this, um, I hope that +you'll be able to identify appropriate + + align:start position:0% +you'll be able to identify appropriate + + + align:start position:0% +you'll be able to identify appropriate +educational technologies to, um, advance + + align:start position:0% +educational technologies to, um, advance + + + align:start position:0% +educational technologies to, um, advance +an intended learning outcome. And I want + + align:start position:0% +an intended learning outcome. And I want + + + align:start position:0% +an intended learning outcome. And I want +to get back to that in just a second. + + align:start position:0% +to get back to that in just a second. + + + align:start position:0% +to get back to that in just a second. +and maybe describe best practices and + + align:start position:0% +and maybe describe best practices and + + + align:start position:0% +and maybe describe best practices and +potential pitfalls of particular + + align:start position:0% +potential pitfalls of particular + + + align:start position:0% +potential pitfalls of particular +educational technologies. So somewhat + + align:start position:0% +educational technologies. So somewhat + + + align:start position:0% +educational technologies. So somewhat +modest uh modest + + align:start position:0% +modest uh modest + + + align:start position:0% +modest uh modest +goals. I think it's a really interesting + + align:start position:0% +goals. I think it's a really interesting + + + align:start position:0% +goals. I think it's a really interesting +thing to think about technology is so + + align:start position:0% +thing to think about technology is so + + + align:start position:0% +thing to think about technology is so +and I I didn't make this up. I heard + + align:start position:0% +and I I didn't make this up. I heard + + + align:start position:0% +and I I didn't make this up. I heard +this at a at a conference. So, they + + align:start position:0% +this at a at a conference. So, they + + + align:start position:0% +this at a at a conference. So, they +said, "When you walk into Home Depot or + + align:start position:0% +said, "When you walk into Home Depot or + + + align:start position:0% +said, "When you walk into Home Depot or +one of these big home improvement + + align:start position:0% +one of these big home improvement + + + align:start position:0% +one of these big home improvement +stores, um what is the if if you happen + + align:start position:0% +stores, um what is the if if you happen + + + align:start position:0% +stores, um what is the if if you happen +to be blessed by having an employee come + + align:start position:0% +to be blessed by having an employee come + + + align:start position:0% +to be blessed by having an employee come +up to you?" Because sometimes it's hard + + align:start position:0% +up to you?" Because sometimes it's hard + + + align:start position:0% +up to you?" Because sometimes it's hard +to find an employee in those stores. Um + + align:start position:0% +to find an employee in those stores. Um + + + align:start position:0% +to find an employee in those stores. Um +what do they ask you? + + align:start position:0% + + + + align:start position:0% + +Um everything okay? Is there anything I + + align:start position:0% +Um everything okay? Is there anything I + + + align:start position:0% +Um everything okay? Is there anything I +can help you with today? Right. Okay. Is + + align:start position:0% +can help you with today? Right. Okay. Is + + + align:start position:0% +can help you with today? Right. Okay. Is +there anything I can help you with? Um + + align:start position:0% +there anything I can help you with? Um + + + align:start position:0% +there anything I can help you with? Um +if and you say, "Yeah, yeah, you can." + + align:start position:0% +if and you say, "Yeah, yeah, you can." + + + align:start position:0% +if and you say, "Yeah, yeah, you can." +And then they say, + + align:start position:0% + + + + align:start position:0% + +What do you usually it's what are you + + align:start position:0% +What do you usually it's what are you + + + align:start position:0% +What do you usually it's what are you +working on, right? What are you trying + + align:start position:0% +working on, right? What are you trying + + + align:start position:0% +working on, right? What are you trying +to + + align:start position:0% +to + + + align:start position:0% +to +do? They don't say what tool do you + + align:start position:0% +do? They don't say what tool do you + + + align:start position:0% +do? They don't say what tool do you +want. I mean, they might, but if they're + + align:start position:0% +want. I mean, they might, but if they're + + + align:start position:0% +want. I mean, they might, but if they're +good, they + + align:start position:0% +good, they + + + align:start position:0% +good, they +don't. And that's a kind of an I think + + align:start position:0% +don't. And that's a kind of an I think + + + align:start position:0% +don't. And that's a kind of an I think +that's a a word to the wise when we + + align:start position:0% +that's a a word to the wise when we + + + align:start position:0% +that's a a word to the wise when we +think about educational technology. It's + + align:start position:0% +think about educational technology. It's + + + align:start position:0% +think about educational technology. It's +not what looks really cool and fun and + + align:start position:0% +not what looks really cool and fun and + + + align:start position:0% +not what looks really cool and fun and +what do I want? You know, what tool do I + + align:start position:0% +what do I want? You know, what tool do I + + + align:start position:0% +what do I want? You know, what tool do I +want? It's what am I trying to + + align:start position:0% +want? It's what am I trying to + + + align:start position:0% +want? It's what am I trying to +build? What do I want my students to + + align:start position:0% +build? What do I want my students to + + + align:start position:0% +build? What do I want my students to +build? What am I trying to build? What + + align:start position:0% +build? What am I trying to build? What + + + align:start position:0% +build? What am I trying to build? What +am I trying to accomplish? And then I + + align:start position:0% +am I trying to accomplish? And then I + + + align:start position:0% +am I trying to accomplish? And then I +can step back and say, which of these + + align:start position:0% +can step back and say, which of these + + + align:start position:0% +can step back and say, which of these +technologies is going to help me do + + align:start position:0% +technologies is going to help me do + + + align:start position:0% +technologies is going to help me do +it? And it's easy to get wrapped up. I + + align:start position:0% +it? And it's easy to get wrapped up. I + + + align:start position:0% +it? And it's easy to get wrapped up. I +mean, you know, we're all kind of techy + + align:start position:0% +mean, you know, we're all kind of techy + + + align:start position:0% +mean, you know, we're all kind of techy +geeky. I mean, that is a compliment. Um, + + align:start position:0% +geeky. I mean, that is a compliment. Um, + + + align:start position:0% +geeky. I mean, that is a compliment. Um, +but um, you know, it's kind of fun like, + + align:start position:0% +but um, you know, it's kind of fun like, + + + align:start position:0% +but um, you know, it's kind of fun like, +"Oh, cool. Look what this can do." And + + align:start position:0% +"Oh, cool. Look what this can do." And + + + align:start position:0% +"Oh, cool. Look what this can do." And +then we go walking around looking for + + align:start position:0% +then we go walking around looking for + + + align:start position:0% +then we go walking around looking for +something to do with it. Um, and that + + align:start position:0% +something to do with it. Um, and that + + + align:start position:0% +something to do with it. Um, and that +might be okay, but you have to check + + align:start position:0% +might be okay, but you have to check + + + align:start position:0% +might be okay, but you have to check +your assumption. You have to check your + + align:start position:0% +your assumption. You have to check your + + + align:start position:0% +your assumption. You have to check your +assumptions about wh why you're doing + + align:start position:0% +assumptions about wh why you're doing + + + align:start position:0% +assumptions about wh why you're doing +it. Are you doing it just to be cool or + + align:start position:0% +it. Are you doing it just to be cool or + + + align:start position:0% +it. Are you doing it just to be cool or +are you doing it because it's really + + align:start position:0% +are you doing it because it's really + + + align:start position:0% +are you doing it because it's really +going to help student learning or it's + + align:start position:0% +going to help student learning or it's + + + align:start position:0% +going to help student learning or it's +going to help some aspect of your + + align:start position:0% +going to help some aspect of your + + + align:start position:0% +going to help some aspect of your +advance a learning outcome? Um, and + + align:start position:0% +advance a learning outcome? Um, and + + + align:start position:0% +advance a learning outcome? Um, and +that's true. You know, I we can we can + + align:start position:0% +that's true. You know, I we can we can + + + align:start position:0% +that's true. You know, I we can we can +use educational technology as some kind + + align:start position:0% +use educational technology as some kind + + + align:start position:0% +use educational technology as some kind +of a scapegoat, but that's true for + + align:start position:0% +of a scapegoat, but that's true for + + + align:start position:0% +of a scapegoat, but that's true for +anything. It's true for that amazing + + align:start position:0% +anything. It's true for that amazing + + + align:start position:0% +anything. It's true for that amazing +exam question that you thought up in the + + align:start position:0% +exam question that you thought up in the + + + align:start position:0% +exam question that you thought up in the +shower like I know what I'll do. I'll do + + align:start position:0% +shower like I know what I'll do. I'll do + + + align:start position:0% +shower like I know what I'll do. I'll do +this and do that and blah blah. Like + + align:start position:0% +this and do that and blah blah. Like + + + align:start position:0% +this and do that and blah blah. Like +maybe it's cool but maybe it's not + + align:start position:0% +maybe it's cool but maybe it's not + + + align:start position:0% +maybe it's cool but maybe it's not +getting you any going to get you + + align:start position:0% +getting you any going to get you + + + align:start position:0% +getting you any going to get you +anywhere or maybe it's not consistent + + align:start position:0% +anywhere or maybe it's not consistent + + + align:start position:0% +anywhere or maybe it's not consistent +with your learning outcomes. So it + + align:start position:0% +with your learning outcomes. So it + + + align:start position:0% +with your learning outcomes. So it +doesn't have to be technology but often + + align:start position:0% +doesn't have to be technology but often + + + align:start position:0% +doesn't have to be technology but often +technology is kind of pretty shiny and + + align:start position:0% +technology is kind of pretty shiny and + + + align:start position:0% +technology is kind of pretty shiny and +um we tend to like gravitate toward it + + align:start position:0% +um we tend to like gravitate toward it + + + align:start position:0% +um we tend to like gravitate toward it +but it's remembering that we're using it + + align:start position:0% +but it's remembering that we're using it + + + align:start position:0% +but it's remembering that we're using it +to advance some particular learning + + align:start position:0% +to advance some particular learning + + + align:start position:0% +to advance some particular learning +outcome. + + align:start position:0% +outcome. + + + align:start position:0% +outcome. +Okay. So what you guys did the readings + + align:start position:0% +Okay. So what you guys did the readings + + + align:start position:0% +Okay. So what you guys did the readings +what what are educational technologies? + + align:start position:0% +what what are educational technologies? + + + align:start position:0% +what what are educational technologies? +What's what what is that? What does it + + align:start position:0% +What's what what is that? What does it + + + align:start position:0% +What's what what is that? What does it +mean? Can we come up with the + + align:start position:0% +mean? Can we come up with the + + + align:start position:0% +mean? Can we come up with the +definition? + + align:start position:0% +definition? + + + align:start position:0% +definition? +Yeah, I think I from what I can + + align:start position:0% +Yeah, I think I from what I can + + + align:start position:0% +Yeah, I think I from what I can +understand an educational technology + + align:start position:0% +understand an educational technology + + + align:start position:0% +understand an educational technology +uh is a tool. Now I didn't want to use + + align:start position:0% +uh is a tool. Now I didn't want to use + + + align:start position:0% +uh is a tool. Now I didn't want to use +that word is a tool which helps the + + align:start position:0% +that word is a tool which helps the + + + align:start position:0% +that word is a tool which helps the +student and also help the the teacher. + + align:start position:0% +student and also help the the teacher. + + + align:start position:0% +student and also help the the teacher. +So that means something that can enable + + align:start position:0% +So that means something that can enable + + + align:start position:0% +So that means something that can enable +uh intercommunication between the + + align:start position:0% +uh intercommunication between the + + + align:start position:0% +uh intercommunication between the +teacher and the student. Okay. And then + + align:start position:0% +teacher and the student. Okay. And then + + + align:start position:0% +teacher and the student. Okay. And then +the student and the student. Okay. So we + + align:start position:0% +the student and the student. Okay. So we + + + align:start position:0% +the student and the student. Okay. So we +have a lot of ideas in that statement. + + align:start position:0% +have a lot of ideas in that statement. + + + align:start position:0% +have a lot of ideas in that statement. +Um so it's a tool. Yeah. + + align:start position:0% +Um so it's a tool. Yeah. + + + align:start position:0% +Um so it's a tool. Yeah. +So so + + align:start position:0% + + + + align:start position:0% + +a tool. Um you said it enables + + align:start position:0% +a tool. Um you said it enables + + + align:start position:0% +a tool. Um you said it enables +communication. Yeah. Student student and + + align:start position:0% +communication. Yeah. Student student and + + + align:start position:0% +communication. Yeah. Student student and +then the + + align:start position:0% + + + + align:start position:0% + +Um, and I think you had something else + + align:start position:0% +Um, and I think you had something else + + + align:start position:0% +Um, and I think you had something else +in + + align:start position:0% +in + + + align:start position:0% +in +there. Did you or No, did + + align:start position:0% + + + + align:start position:0% + +Something + + align:start position:0% +Something + + + align:start position:0% +Something +else is a education technology is like a + + align:start position:0% +else is a education technology is like a + + + align:start position:0% +else is a education technology is like a +tool to enhance students learning, + + align:start position:0% +tool to enhance students learning, + + + align:start position:0% +tool to enhance students learning, +enhancement of student + + align:start position:0% +enhancement of student + + + align:start position:0% +enhancement of student +learning and uh enhancement of + + align:start position:0% +learning and uh enhancement of + + + align:start position:0% +learning and uh enhancement of +instructors teaching as well. + + align:start position:0% + + + + align:start position:0% + +The technology part is like a electronic + + align:start position:0% +The technology part is like a electronic + + + align:start position:0% +The technology part is like a electronic +device. So it has to have electricity. + + align:start position:0% + + + + align:start position:0% + +Has to involve electrons. No, that's + + align:start position:0% +Has to involve electrons. No, that's + + + align:start position:0% +Has to involve electrons. No, that's +everything. + + align:start position:0% +everything. + + + align:start position:0% +everything. +Wait, let's let Michelle What? What + + align:start position:0% +Wait, let's let Michelle What? What + + + align:start position:0% +Wait, let's let Michelle What? What +should we say about that? + + align:start position:0% + + + + align:start position:0% + +I think that's kind of correct to say it + + align:start position:0% +I think that's kind of correct to say it + + + align:start position:0% +I think that's kind of correct to say it +has to be an electronic device, right? + + align:start position:0% +has to be an electronic device, right? + + + align:start position:0% +has to be an electronic device, right? +Like if it's a clicker or if it's a + + align:start position:0% +Like if it's a clicker or if it's a + + + align:start position:0% +Like if it's a clicker or if it's a +web + + align:start position:0% + + + + align:start position:0% + +must be electronic. It sounds so like + + align:start position:0% +must be electronic. It sounds so like + + + align:start position:0% +must be electronic. It sounds so like +1950s. Um I think we had Yeah, Gordon. + + align:start position:0% +1950s. Um I think we had Yeah, Gordon. + + + align:start position:0% +1950s. Um I think we had Yeah, Gordon. +Yeah. Um I'll just adjust a little bit + + align:start position:0% +Yeah. Um I'll just adjust a little bit + + + align:start position:0% +Yeah. Um I'll just adjust a little bit +and add in front of the two + + align:start position:0% +and add in front of the two + + + align:start position:0% +and add in front of the two +productivity is kind of + + align:start position:0% + + + + align:start position:0% + +a kind of two + + align:start position:0% +a kind of two + + + align:start position:0% +a kind of two +that create a community of l that will + + align:start position:0% +that create a community of l that will + + + align:start position:0% +that create a community of l that will +not be constrained or restricted by time + + align:start position:0% +not be constrained or restricted by time + + + align:start position:0% +not be constrained or restricted by time +or place. So it uh lends itself to + + align:start position:0% +or place. So it uh lends itself to + + + align:start position:0% +or place. So it uh lends itself to +asynchronicity. + + align:start position:0% + + + + align:start position:0% + +Yes. + + align:start position:0% + + + + align:start position:0% + +Anything else? I think it's also + + align:start position:0% +Anything else? I think it's also + + + align:start position:0% +Anything else? I think it's also +enhancer is easier + + align:start position:0% +enhancer is easier + + + align:start position:0% +enhancer is easier +is use of materials or is facilitates + + align:start position:0% +is use of materials or is facilitates + + + align:start position:0% +is use of materials or is facilitates +um + + align:start position:0% +um + + + align:start position:0% +um +materials um it helps + + align:start position:0% +materials um it helps + + + align:start position:0% +materials um it helps +to I can give the same material to um + + align:start position:0% +to I can give the same material to um + + + align:start position:0% +to I can give the same material to um +students at the same time right a + + align:start position:0% +students at the same time right a + + + align:start position:0% +students at the same time right a +distribution aids distribution yeah + + align:start position:0% +distribution aids distribution yeah + + + align:start position:0% +distribution aids distribution yeah +learning materials can be easily + + align:start position:0% +learning materials can be easily + + + align:start position:0% +learning materials can be easily +accessed + + align:start position:0% + + + + align:start position:0% + +Did I hear something else? Is it that is + + align:start position:0% +Did I hear something else? Is it that is + + + align:start position:0% +Did I hear something else? Is it that is +efficient? + + align:start position:0% + + + + align:start position:0% + +Efficient. That's a loaded + + align:start position:0% + + + + align:start position:0% + +word. + + align:start position:0% + + + + align:start position:0% + +Anybody have anything else or do you + + align:start position:0% +Anybody have anything else or do you + + + align:start position:0% +Anybody have anything else or do you +want to make a somebody want to make a + + align:start position:0% +want to make a somebody want to make a + + + align:start position:0% +want to make a somebody want to make a +comment on this collection of + + align:start position:0% +comment on this collection of + + + align:start position:0% +comment on this collection of +attributes? It prepared the student to + + align:start position:0% +attributes? It prepared the student to + + + align:start position:0% +attributes? It prepared the student to +be continuous learners. + + align:start position:0% + + + + align:start position:0% + +I don't think I have any cynics in this. + + align:start position:0% +I don't think I have any cynics in this. + + + align:start position:0% +I don't think I have any cynics in this. +Well, the cynics haven't said anything. + + align:start position:0% +Well, the cynics haven't said anything. + + + align:start position:0% +Well, the cynics haven't said anything. +I think all of the comments are positive + + align:start position:0% +I think all of the comments are positive + + + align:start position:0% +I think all of the comments are positive +things like if you're doing it well what + + align:start position:0% +things like if you're doing it well what + + + align:start position:0% +things like if you're doing it well what +should happen but they aren't + + align:start position:0% +should happen but they aren't + + + align:start position:0% +should happen but they aren't +necessarily what actually happens + + align:start position:0% +necessarily what actually happens + + + align:start position:0% +necessarily what actually happens +because most of the time it's probably + + align:start position:0% +because most of the time it's probably + + + align:start position:0% +because most of the time it's probably +not done well using a technology is + + align:start position:0% +not done well using a technology is + + + align:start position:0% +not done well using a technology is +not + + align:start position:0% + + + + align:start position:0% + +optimal. Okay, that's one observation. + + align:start position:0% +optimal. Okay, that's one observation. + + + align:start position:0% +optimal. Okay, that's one observation. +And it's sort of um you know that rhyme. + + align:start position:0% +And it's sort of um you know that rhyme. + + + align:start position:0% +And it's sort of um you know that rhyme. +There was a little girl who had a little + + align:start position:0% +There was a little girl who had a little + + + align:start position:0% +There was a little girl who had a little +curl right in the middle of her + + align:start position:0% +curl right in the middle of her + + + align:start position:0% +curl right in the middle of her +forehead. And when she was good, she was + + align:start position:0% +forehead. And when she was good, she was + + + align:start position:0% +forehead. And when she was good, she was +very very good. And when she was bad, + + align:start position:0% +very very good. And when she was bad, + + + align:start position:0% +very very good. And when she was bad, +she was horrid. So it's a little bit + + align:start position:0% +she was horrid. So it's a little bit + + + align:start position:0% +she was horrid. So it's a little bit +like this, right? When it's good, it's + + align:start position:0% +like this, right? When it's good, it's + + + align:start position:0% +like this, right? When it's good, it's +very very good. And when it's bad, maybe + + align:start position:0% +very very good. And when it's bad, maybe + + + align:start position:0% +very very good. And when it's bad, maybe +it's even worse than if you hadn't + + align:start position:0% +it's even worse than if you hadn't + + + align:start position:0% +it's even worse than if you hadn't +bothered. But um uh Alex, you had + + align:start position:0% +bothered. But um uh Alex, you had + + + align:start position:0% +bothered. But um uh Alex, you had +something to say. No. Well, on the side + + align:start position:0% +something to say. No. Well, on the side + + + align:start position:0% +something to say. No. Well, on the side +of cynics, I I thought of the comment + + align:start position:0% +of cynics, I I thought of the comment + + + align:start position:0% +of cynics, I I thought of the comment +that students are often disinterested + + align:start position:0% +that students are often disinterested + + + align:start position:0% +that students are often disinterested +when they don't see the point or don't + + align:start position:0% +when they don't see the point or don't + + + align:start position:0% +when they don't see the point or don't +see them using it later, but um it's not + + align:start position:0% +see them using it later, but um it's not + + + align:start position:0% +see them using it later, but um it's not +necessarily a definition of it. Right. + + align:start position:0% +necessarily a definition of it. Right. + + + align:start position:0% +necessarily a definition of it. Right. +Right. No, but that's a very good point. + + align:start position:0% +Right. No, but that's a very good point. + + + align:start position:0% +Right. No, but that's a very good point. +And somebody had quoted um this idea of + + align:start position:0% +And somebody had quoted um this idea of + + + align:start position:0% +And somebody had quoted um this idea of +an app that if if an app doesn't load in + + align:start position:0% +an app that if if an app doesn't load in + + + align:start position:0% +an app that if if an app doesn't load in +something like seven seconds, people + + align:start position:0% +something like seven seconds, people + + + align:start position:0% +something like seven seconds, people +stop using it. Like if you try to get an + + align:start position:0% +stop using it. Like if you try to get an + + + align:start position:0% +stop using it. Like if you try to get an +app to open on your phone and you're + + align:start position:0% +app to open on your phone and you're + + + align:start position:0% +app to open on your phone and you're +like, "What's going on here? Come on. 1 + + align:start position:0% +like, "What's going on here? Come on. 1 + + + align:start position:0% +like, "What's going on here? Come on. 1 +2 3 4. Okay, forget it." Um and that's a + + align:start position:0% +2 3 4. Okay, forget it." Um and that's a + + + align:start position:0% +2 3 4. Okay, forget it." Um and that's a +similar idea that if you if you if it + + align:start position:0% +similar idea that if you if you if it + + + align:start position:0% +similar idea that if you if you if it +doesn't look like it's going to help + + align:start position:0% +doesn't look like it's going to help + + + align:start position:0% +doesn't look like it's going to help +you, um and whatever that means, help + + align:start position:0% +you, um and whatever that means, help + + + align:start position:0% +you, um and whatever that means, help +you. It's self self-defined help. But if + + align:start position:0% +you. It's self self-defined help. But if + + + align:start position:0% +you. It's self self-defined help. But if +it doesn't look like it's going to help + + align:start position:0% +it doesn't look like it's going to help + + + align:start position:0% +it doesn't look like it's going to help +you, you're not going to buy into it. + + align:start position:0% +you, you're not going to buy into it. + + + align:start position:0% +you, you're not going to buy into it. +Um, some other thoughts about this list. + + align:start position:0% + + + + align:start position:0% + +I don't think I mean personally I don't + + align:start position:0% +I don't think I mean personally I don't + + + align:start position:0% +I don't think I mean personally I don't +think that that to be an uh educational + + align:start position:0% +think that that to be an uh educational + + + align:start position:0% +think that that to be an uh educational +technology has to meet all these + + align:start position:0% +technology has to meet all these + + + align:start position:0% +technology has to meet all these +criteria at once right I mean that's an + + align:start position:0% +criteria at once right I mean that's an + + + align:start position:0% +criteria at once right I mean that's an +important thing to note that it might + + align:start position:0% +important thing to note that it might + + + align:start position:0% +important thing to note that it might +you know it might improve productivity I + + align:start position:0% +you know it might improve productivity I + + + align:start position:0% +you know it might improve productivity I +mean a learning management system the + + align:start position:0% +mean a learning management system the + + + align:start position:0% +mean a learning management system the +old old school learning management + + align:start position:0% +old old school learning management + + + align:start position:0% +old old school learning management +systems that just put up you put up + + align:start position:0% +systems that just put up you put up + + + align:start position:0% +systems that just put up you put up +problem sets and you put up the the + + align:start position:0% +problem sets and you put up the the + + + align:start position:0% +problem sets and you put up the the +gradebook was in one place and that kind + + align:start position:0% +gradebook was in one place and that kind + + + align:start position:0% +gradebook was in one place and that kind +of thing that might help your prod + + align:start position:0% +of thing that might help your prod + + + align:start position:0% +of thing that might help your prod +productivity. You're not looking around + + align:start position:0% +productivity. You're not looking around + + + align:start position:0% +productivity. You're not looking around +for stuff, but it's not necessarily + + align:start position:0% +for stuff, but it's not necessarily + + + align:start position:0% +for stuff, but it's not necessarily +promoting learning at any level. It's a + + align:start position:0% +promoting learning at any level. It's a + + + align:start position:0% +promoting learning at any level. It's a +delivery system, a materials delivery + + align:start position:0% +delivery system, a materials delivery + + + align:start position:0% +delivery system, a materials delivery +system. So, it kind of does this and it + + align:start position:0% +system. So, it kind of does this and it + + + align:start position:0% +system. So, it kind of does this and it +does this, but it might not really be + + align:start position:0% +does this, but it might not really be + + + align:start position:0% +does this, but it might not really be +part of the learning enterprise. It's a + + align:start position:0% +part of the learning enterprise. It's a + + + align:start position:0% +part of the learning enterprise. It's a +store. It's a repository. And that's + + align:start position:0% +store. It's a repository. And that's + + + align:start position:0% +store. It's a repository. And that's +fine. I mean, there's nothing wrong with + + align:start position:0% +fine. I mean, there's nothing wrong with + + + align:start position:0% +fine. I mean, there's nothing wrong with +that, but that's that's one type. Um, if + + align:start position:0% +that, but that's that's one type. Um, if + + + align:start position:0% +that, but that's that's one type. Um, if +you're saying that it's um, you know, it + + align:start position:0% +you're saying that it's um, you know, it + + + align:start position:0% +you're saying that it's um, you know, it +enables communication, well, that might + + align:start position:0% +enables communication, well, that might + + + align:start position:0% +enables communication, well, that might +be part of this, but it might be + + align:start position:0% +be part of this, but it might be + + + align:start position:0% +be part of this, but it might be +something else, right? If I say, "All + + align:start position:0% +something else, right? If I say, "All + + + align:start position:0% +something else, right? If I say, "All +right, you know, I want you guys to read + + align:start position:0% +right, you know, I want you guys to read + + + align:start position:0% +right, you know, I want you guys to read +everybody's it's a wiki and I want you + + align:start position:0% +everybody's it's a wiki and I want you + + + align:start position:0% +everybody's it's a wiki and I want you +guys to read what everybody else wrote + + align:start position:0% +guys to read what everybody else wrote + + + align:start position:0% +guys to read what everybody else wrote +and to make a comment on at least one + + align:start position:0% +and to make a comment on at least one + + + align:start position:0% +and to make a comment on at least one +other person's posting." Well, I + + align:start position:0% +other person's posting." Well, I + + + align:start position:0% +other person's posting." Well, I +facilitated communication between you in + + align:start position:0% +facilitated communication between you in + + + align:start position:0% +facilitated communication between you in +an asynchronous way. I I didn't tell + + align:start position:0% +an asynchronous way. I I didn't tell + + + align:start position:0% +an asynchronous way. I I didn't tell +everybody to do it at, you know, noon on + + align:start position:0% +everybody to do it at, you know, noon on + + + align:start position:0% +everybody to do it at, you know, noon on +on the 29th of October. Um, but but it + + align:start position:0% +on the 29th of October. Um, but but it + + + align:start position:0% +on the 29th of October. Um, but but it +it does facilitate it facilitates + + align:start position:0% +it does facilitate it facilitates + + + align:start position:0% +it does facilitate it facilitates +communication. + + align:start position:0% +communication. + + + align:start position:0% +communication. +Um, I think this one is the is a loaded + + align:start position:0% +Um, I think this one is the is a loaded + + + align:start position:0% +Um, I think this one is the is a loaded +one for sure and it gets to Michelle's + + align:start position:0% +one for sure and it gets to Michelle's + + + align:start position:0% +one for sure and it gets to Michelle's +comment about when it if you did it + + align:start position:0% +comment about when it if you did it + + + align:start position:0% +comment about when it if you did it +right, it would do that. Um, but if you + + align:start position:0% +right, it would do that. Um, but if you + + + align:start position:0% +right, it would do that. Um, but if you +did it wrong, it probably wouldn't do + + align:start position:0% +did it wrong, it probably wouldn't do + + + align:start position:0% +did it wrong, it probably wouldn't do +that at all. I mean, it's likely to not + + align:start position:0% +that at all. I mean, it's likely to not + + + align:start position:0% +that at all. I mean, it's likely to not +do that at + + align:start position:0% +do that at + + + align:start position:0% +do that at +all. Um, so these are attributes that + + align:start position:0% +all. Um, so these are attributes that + + + align:start position:0% +all. Um, so these are attributes that +could could um that you could use to + + align:start position:0% +could could um that you could use to + + + align:start position:0% +could could um that you could use to +describe some educational technologies. + + align:start position:0% +describe some educational technologies. + + + align:start position:0% +describe some educational technologies. +Um I do have a definition from the + + align:start position:0% +Um I do have a definition from the + + + align:start position:0% +Um I do have a definition from the +reading but before I put that up um any + + align:start position:0% +reading but before I put that up um any + + + align:start position:0% +reading but before I put that up um any +any other thing you want to add? It's + + align:start position:0% +any other thing you want to add? It's + + + align:start position:0% +any other thing you want to add? It's +interesting to think about it like does + + align:start position:0% +interesting to think about it like does + + + align:start position:0% +interesting to think about it like does +it have to be electronic? So I have had + + align:start position:0% +it have to be electronic? So I have had + + + align:start position:0% +it have to be electronic? So I have had +classes in the past where people argue + + align:start position:0% +classes in the past where people argue + + + align:start position:0% +classes in the past where people argue +okay well a blackboard is an electronic + + align:start position:0% +okay well a blackboard is an electronic + + + align:start position:0% +okay well a blackboard is an electronic +is a educational technology right I mean + + align:start position:0% +is a educational technology right I mean + + + align:start position:0% +is a educational technology right I mean +you couldn't do that without some sort + + align:start position:0% +you couldn't do that without some sort + + + align:start position:0% +you couldn't do that without some sort +of + + align:start position:0% +of + + + align:start position:0% +of +human-made product and without it I + + align:start position:0% +human-made product and without it I + + + align:start position:0% +human-made product and without it I +would have to be walking around you know + + align:start position:0% +would have to be walking around you know + + + align:start position:0% +would have to be walking around you know +speaking very slowly and hoping you took + + align:start position:0% +speaking very slowly and hoping you took + + + align:start position:0% +speaking very slowly and hoping you took +notes or walking around with I don't + + align:start position:0% +notes or walking around with I don't + + + align:start position:0% +notes or walking around with I don't +know a piece of paper or a that I wrote + + align:start position:0% +know a piece of paper or a that I wrote + + + align:start position:0% +know a piece of paper or a that I wrote +on and sharing it with you or something. + + align:start position:0% +on and sharing it with you or something. + + + align:start position:0% +on and sharing it with you or something. +So, so it does it certainly does a + + align:start position:0% +So, so it does it certainly does a + + + align:start position:0% +So, so it does it certainly does a +blackboard does fit a lot of these + + align:start position:0% +blackboard does fit a lot of these + + + align:start position:0% +blackboard does fit a lot of these +categories, right? It it it's an + + align:start position:0% +categories, right? It it it's an + + + align:start position:0% +categories, right? It it it's an +efficient delivery system. Um, at some + + align:start position:0% +efficient delivery system. Um, at some + + + align:start position:0% +efficient delivery system. Um, at some +level it enables communication. Um, it's + + align:start position:0% +level it enables communication. Um, it's + + + align:start position:0% +level it enables communication. Um, it's +uh aids distribution of learning + + align:start position:0% +uh aids distribution of learning + + + align:start position:0% +uh aids distribution of learning +materials. Um, so so we want to think + + align:start position:0% +materials. Um, so so we want to think + + + align:start position:0% +materials. Um, so so we want to think +about whether we really if if it means + + align:start position:0% +about whether we really if if it means + + + align:start position:0% +about whether we really if if it means +it has to be electronic. Um, but that's + + align:start position:0% +it has to be electronic. Um, but that's + + + align:start position:0% +it has to be electronic. Um, but that's +a and you may have guessed by now there + + align:start position:0% +a and you may have guessed by now there + + + align:start position:0% +a and you may have guessed by now there +is not a de single definition. That's + + align:start position:0% +is not a de single definition. That's + + + align:start position:0% +is not a de single definition. That's +the other issue comment. Yes, just a + + align:start position:0% +the other issue comment. Yes, just a + + + align:start position:0% +the other issue comment. Yes, just a +comment. What about um if it's not well + + align:start position:0% +comment. What about um if it's not well + + + align:start position:0% +comment. What about um if it's not well +moderated + + align:start position:0% + + + + align:start position:0% + +ser the efficient one that you know + + align:start position:0% +ser the efficient one that you know + + + align:start position:0% +ser the efficient one that you know +we've all gotten sucked into websites or + + align:start position:0% +we've all gotten sucked into websites or + + + align:start position:0% +we've all gotten sucked into websites or +or sucked into perhaps an online + + align:start position:0% +or sucked into perhaps an online + + + align:start position:0% +or sucked into perhaps an online +discussion or or commenting on something + + align:start position:0% +discussion or or commenting on something + + + align:start position:0% +discussion or or commenting on something +and it might be interesting. You might + + align:start position:0% +and it might be interesting. You might + + + align:start position:0% +and it might be interesting. You might +learn, but it it may not be efficient at + + align:start position:0% +learn, but it it may not be efficient at + + + align:start position:0% +learn, but it it may not be efficient at +all. Or you might just be on the, you + + align:start position:0% +all. Or you might just be on the, you + + + align:start position:0% +all. Or you might just be on the, you +know, the screed end of things where + + align:start position:0% +know, the screed end of things where + + + align:start position:0% +know, the screed end of things where +you're just people are just either + + align:start position:0% +you're just people are just either + + + align:start position:0% +you're just people are just either +ranting or they're not they're + + align:start position:0% +ranting or they're not they're + + + align:start position:0% +ranting or they're not they're +reinforcing kind of misconceptions or or + + align:start position:0% +reinforcing kind of misconceptions or or + + + align:start position:0% +reinforcing kind of misconceptions or or +whatever. So yeah, you do have to you do + + align:start position:0% +whatever. So yeah, you do have to you do + + + align:start position:0% +whatever. So yeah, you do have to you do +have to kind of make sure people are + + align:start position:0% +have to kind of make sure people are + + + align:start position:0% +have to kind of make sure people are +using it carefully, but that's true for + + align:start position:0% +using it carefully, but that's true for + + + align:start position:0% +using it carefully, but that's true for +virtually anything you do, + + align:start position:0% +virtually anything you do, + + + align:start position:0% +virtually anything you do, +right? Any other comments? + + align:start position:0% +right? Any other comments? + + + align:start position:0% +right? Any other comments? +And I I think as well that + + align:start position:0% +And I I think as well that + + + align:start position:0% +And I I think as well that +um the the fact that uh this tool is + + align:start position:0% +um the the fact that uh this tool is + + + align:start position:0% +um the the fact that uh this tool is +available. I mean the student can you + + align:start position:0% +available. I mean the student can you + + + align:start position:0% +available. I mean the student can you +know decide to stay home you know in the + + align:start position:0% +know decide to stay home you know in the + + + align:start position:0% +know decide to stay home you know in the +bad weather start stay at home since he + + align:start position:0% +bad weather start stay at home since he + + + align:start position:0% +bad weather start stay at home since he +knows this is available then he can + + align:start position:0% +knows this is available then he can + + + align:start position:0% +knows this is available then he can +go and then I mean that could that that + + align:start position:0% +go and then I mean that could that that + + + align:start position:0% +go and then I mean that could that that +could uh it could be good and bad + + align:start position:0% +could uh it could be good and bad + + + align:start position:0% +could uh it could be good and bad +because the students would continue to + + align:start position:0% +because the students would continue to + + + align:start position:0% +because the students would continue to +learn on his own and become a good you + + align:start position:0% +learn on his own and become a good you + + + align:start position:0% +learn on his own and become a good you +know student and then he could miss out + + align:start position:0% +know student and then he could miss out + + + align:start position:0% +know student and then he could miss out +on + + align:start position:0% +on + + + align:start position:0% +on +uh critical points as well. Right. + + align:start position:0% +uh critical points as well. Right. + + + align:start position:0% +uh critical points as well. Right. +Right. So So that and but that implies + + align:start position:0% +Right. So So that and but that implies + + + align:start position:0% +Right. So So that and but that implies +some sort of like web um housed + + align:start position:0% +some sort of like web um housed + + + align:start position:0% +some sort of like web um housed +delivered um repository of content or of + + align:start position:0% +delivered um repository of content or of + + + align:start position:0% +delivered um repository of content or of +lecture video lectures or whatever. We + + align:start position:0% +lecture video lectures or whatever. We + + + align:start position:0% +lecture video lectures or whatever. We +don't have to only have I mean that you + + align:start position:0% +don't have to only have I mean that you + + + align:start position:0% +don't have to only have I mean that you +could have a course that used clickers + + align:start position:0% +could have a course that used clickers + + + align:start position:0% +could have a course that used clickers +let's say that didn't even have a + + align:start position:0% +let's say that didn't even have a + + + align:start position:0% +let's say that didn't even have a +website but they used clickers. So that + + align:start position:0% +website but they used clickers. So that + + + align:start position:0% +website but they used clickers. So that +course might be using educational + + align:start position:0% +course might be using educational + + + align:start position:0% +course might be using educational +technology pro maybe in a very very good + + align:start position:0% +technology pro maybe in a very very good + + + align:start position:0% +technology pro maybe in a very very good +way in the + + align:start position:0% +way in the + + + align:start position:0% +way in the +classroom but they don't even bother + + align:start position:0% +classroom but they don't even bother + + + align:start position:0% +classroom but they don't even bother +with a website. So in that case the + + align:start position:0% +with a website. So in that case the + + + align:start position:0% +with a website. So in that case the +student has to come to class if they + + align:start position:0% +student has to come to class if they + + + align:start position:0% +student has to come to class if they +want to experience that particular use + + align:start position:0% +want to experience that particular use + + + align:start position:0% +want to experience that particular use +of technology. Um, I think you're right + + align:start position:0% +of technology. Um, I think you're right + + + align:start position:0% +of technology. Um, I think you're right +that that if you do have a website or + + align:start position:0% +that that if you do have a website or + + + align:start position:0% +that that if you do have a website or +you do have lectures online or you do + + align:start position:0% +you do have lectures online or you do + + + align:start position:0% +you do have lectures online or you do +have rich content online, then then it + + align:start position:0% +have rich content online, then then it + + + align:start position:0% +have rich content online, then then it +does sort of perhaps make learn make + + align:start position:0% +does sort of perhaps make learn make + + + align:start position:0% +does sort of perhaps make learn make +being in the classroom a little bit less + + align:start position:0% +being in the classroom a little bit less + + + align:start position:0% +being in the classroom a little bit less +necessary. I will say if you employ + + align:start position:0% +necessary. I will say if you employ + + + align:start position:0% +necessary. I will say if you employ +active learning methods in class, group + + align:start position:0% +active learning methods in class, group + + + align:start position:0% +active learning methods in class, group +discussions, etc. um that being in the + + align:start position:0% +discussions, etc. um that being in the + + + align:start position:0% +discussions, etc. um that being in the +classroom is certainly I would argue is + + align:start position:0% +classroom is certainly I would argue is + + + align:start position:0% +classroom is certainly I would argue is +value added for the student. So it's not + + align:start position:0% +value added for the student. So it's not + + + align:start position:0% +value added for the student. So it's not +the same ex it's not a replacement + + align:start position:0% +the same ex it's not a replacement + + + align:start position:0% +the same ex it's not a replacement +experience but it might be better than + + align:start position:0% +experience but it might be better than + + + align:start position:0% +experience but it might be better than +nothing let's say it might not. + + align:start position:0% +nothing let's say it might not. + + + align:start position:0% +nothing let's say it might not. +Yes. Go ahead. Yeah. I found something + + align:start position:0% +Yes. Go ahead. Yeah. I found something + + + align:start position:0% +Yes. Go ahead. Yeah. I found something +in the reading very interesting. Um + + align:start position:0% +in the reading very interesting. Um + + + align:start position:0% +in the reading very interesting. Um +where they said that if you use + + align:start position:0% +where they said that if you use + + + align:start position:0% +where they said that if you use +clickers, I mean I I I I would love to + + align:start position:0% +clickers, I mean I I I I would love to + + + align:start position:0% +clickers, I mean I I I I would love to +do that. I mean to take the attendance + + align:start position:0% +do that. I mean to take the attendance + + + align:start position:0% +do that. I mean to take the attendance +of the students + + align:start position:0% +of the students + + + align:start position:0% +of the students +that it + + align:start position:0% +that it + + + align:start position:0% +that it +might discourage the students from using + + align:start position:0% +might discourage the students from using + + + align:start position:0% +might discourage the students from using +technology but I don't know I mean in + + align:start position:0% +technology but I don't know I mean in + + + align:start position:0% +technology but I don't know I mean in +some environments it might actually be + + align:start position:0% +some environments it might actually be + + + align:start position:0% +some environments it might actually be +good to have technology that you can use + + align:start position:0% +good to have technology that you can use + + + align:start position:0% +good to have technology that you can use +nonvasively to find out if the students + + align:start position:0% +nonvasively to find out if the students + + + align:start position:0% +nonvasively to find out if the students +coming to you. + + align:start position:0% +coming to you. + + + align:start position:0% +coming to you. +Yeah, matter. It's true. + + align:start position:0% +Yeah, matter. It's true. + + + align:start position:0% +Yeah, matter. It's true. +One person will come with five friends + + align:start position:0% +One person will come with five friends + + + align:start position:0% +One person will come with five friends +clickers and click them all. No, but if + + align:start position:0% +clickers and click them all. No, but if + + + align:start position:0% +clickers and click them all. No, but if +if you have like RFID technology or + + align:start position:0% +if you have like RFID technology or + + + align:start position:0% +if you have like RFID technology or +something like that that you can use to + + align:start position:0% +something like that that you can use to + + + align:start position:0% +something like that that you can use to +um authenticate first when you come to + + align:start position:0% +um authenticate first when you come to + + + align:start position:0% +um authenticate first when you come to +the class to know that okay this person + + align:start position:0% +the class to know that okay this person + + + align:start position:0% +the class to know that okay this person +is the one using this particular thumb + + align:start position:0% +is the one using this particular thumb + + + align:start position:0% +is the one using this particular thumb +print or something like that. I mean + + align:start position:0% +print or something like that. I mean + + + align:start position:0% +print or something like that. I mean +scam then nobody's going to register for + + align:start position:0% +scam then nobody's going to register for + + + align:start position:0% +scam then nobody's going to register for +your class. + + align:start position:0% +your class. + + + align:start position:0% +your class. +Yeah. my in my in my country the classes + + align:start position:0% +Yeah. my in my in my country the classes + + + align:start position:0% +Yeah. my in my in my country the classes +are composed and what I mean is you + + align:start position:0% +are composed and what I mean is you + + + align:start position:0% +are composed and what I mean is you +don't have the option of choosing like + + align:start position:0% +don't have the option of choosing like + + + align:start position:0% +don't have the option of choosing like +over + + align:start position:0% +over + + + align:start position:0% +over +here to it's + + align:start position:0% +here to it's + + + align:start position:0% +here to it's +not just I don't want to do + + align:start position:0% +not just I don't want to do + + + align:start position:0% +not just I don't want to do +this you just have to do all so certain + + align:start position:0% +this you just have to do all so certain + + + align:start position:0% +this you just have to do all so certain +courses you have to do yeah you must do + + align:start position:0% +courses you have to do yeah you must do + + + align:start position:0% +courses you have to do yeah you must do +them you have to show up yeah you must + + align:start position:0% +them you have to show up yeah you must + + + align:start position:0% +them you have to show up yeah you must +yeah you should show up but then the + + align:start position:0% +yeah you should show up but then the + + + align:start position:0% +yeah you should show up but then the +size is too big it's difficult to take + + align:start position:0% +size is too big it's difficult to take + + + align:start position:0% +size is too big it's difficult to take +the attendance and if you have this + + align:start position:0% +the attendance and if you have this + + + align:start position:0% +the attendance and if you have this +wonderful way of getting the students + + align:start position:0% + + + + align:start position:0% + +actually love. + + align:start position:0% +actually love. + + + align:start position:0% +actually love. +I think + + align:start position:0% +I think + + + align:start position:0% +I think +something shed more light on when does + + align:start position:0% +something shed more light on when does + + + align:start position:0% +something shed more light on when does +it become problem? Something that + + align:start position:0% +it become problem? Something that + + + align:start position:0% +it become problem? Something that +promotes independent learning. When does + + align:start position:0% +promotes independent learning. When does + + + align:start position:0% +promotes independent learning. When does +it become problem? Well, I'm I don't + + align:start position:0% +it become problem? Well, I'm I don't + + + align:start position:0% +it become problem? Well, I'm I don't +know if there's an answer to that. I + + align:start position:0% +know if there's an answer to that. I + + + align:start position:0% +know if there's an answer to that. I +mean, for some students, it's never a + + align:start position:0% +mean, for some students, it's never a + + + align:start position:0% +mean, for some students, it's never a +problem. For some students, it's + + align:start position:0% +problem. For some students, it's + + + align:start position:0% +problem. For some students, it's +awesome. For some students, they it's + + align:start position:0% +awesome. For some students, they it's + + + align:start position:0% +awesome. For some students, they it's +just more information and it's just + + align:start position:0% +just more information and it's just + + + align:start position:0% +just more information and it's just +another path and they're learning and + + align:start position:0% +another path and they're learning and + + + align:start position:0% +another path and they're learning and +they're learning and they're learning + + align:start position:0% +they're learning and they're learning + + + align:start position:0% +they're learning and they're learning +and it's supplementing what they're + + align:start position:0% +and it's supplementing what they're + + + align:start position:0% +and it's supplementing what they're +learning in the + + align:start position:0% +learning in the + + + align:start position:0% +learning in the +class. Um because it kind of depends on + + align:start position:0% +class. Um because it kind of depends on + + + align:start position:0% +class. Um because it kind of depends on +attendance that Dr. is talking about. + + align:start position:0% +attendance that Dr. is talking about. + + + align:start position:0% +attendance that Dr. is talking about. +Well, I so is will it be necessary? + + align:start position:0% +Well, I so is will it be necessary? + + + align:start position:0% +Well, I so is will it be necessary? +Well, yeah. And actually that's a any + + align:start position:0% +Well, yeah. And actually that's a any + + + align:start position:0% +Well, yeah. And actually that's a any +problem. Uh that's a uh important point + + align:start position:0% +problem. Uh that's a uh important point + + + align:start position:0% +problem. Uh that's a uh important point +is that I think I showed these slides + + align:start position:0% +is that I think I showed these slides + + + align:start position:0% +is that I think I showed these slides +about clicker use um in 511 showed it + + align:start position:0% +about clicker use um in 511 showed it + + + align:start position:0% +about clicker use um in 511 showed it +when we did the clicker when we did + + align:start position:0% +when we did the clicker when we did + + + align:start position:0% +when we did the clicker when we did +active learning. Um, and what the first + + align:start position:0% +active learning. Um, and what the first + + + align:start position:0% +active learning. Um, and what the first +year they used them, they actually did + + align:start position:0% +year they used them, they actually did + + + align:start position:0% +year they used them, they actually did +they used them more or less to take + + align:start position:0% +they used them more or less to take + + + align:start position:0% +they used them more or less to take +attendance. And students figured that + + align:start position:0% +attendance. And students figured that + + + align:start position:0% +attendance. And students figured that +out pretty quickly. Um, they did all + + align:start position:0% +out pretty quickly. Um, they did all + + + align:start position:0% +out pretty quickly. Um, they did all +sorts of things, sharing clickers, + + align:start position:0% +sorts of things, sharing clickers, + + + align:start position:0% +sorts of things, sharing clickers, +clicking and then leaving, right? Um, or + + align:start position:0% +clicking and then leaving, right? Um, or + + + align:start position:0% +clicking and then leaving, right? Um, or +coming in at the end and clicking, um, + + align:start position:0% +coming in at the end and clicking, um, + + + align:start position:0% +coming in at the end and clicking, um, +but not being there the whole time. Uh, + + align:start position:0% +but not being there the whole time. Uh, + + + align:start position:0% +but not being there the whole time. Uh, +and if you ask students, well, what do + + align:start position:0% +and if you ask students, well, what do + + + align:start position:0% +and if you ask students, well, what do +you think about the clickers? They're + + align:start position:0% +you think about the clickers? They're + + + align:start position:0% +you think about the clickers? They're +like, I don't this is this is + + align:start position:0% +like, I don't this is this is + + + align:start position:0% +like, I don't this is this is +crappy. You know, this didn't help me. + + align:start position:0% +crappy. You know, this didn't help me. + + + align:start position:0% +crappy. You know, this didn't help me. +This was terrible. and probably it + + align:start position:0% +This was terrible. and probably it + + + align:start position:0% +This was terrible. and probably it +didn't. I mean, there's an attitudinal + + align:start position:0% +didn't. I mean, there's an attitudinal + + + align:start position:0% +didn't. I mean, there's an attitudinal +thing that says at some point if you + + align:start position:0% +thing that says at some point if you + + + align:start position:0% +thing that says at some point if you +think it's not helping, it's not + + align:start position:0% +think it's not helping, it's not + + + align:start position:0% +think it's not helping, it's not +helping. Um, so the next year they made + + align:start position:0% +helping. Um, so the next year they made + + + align:start position:0% +helping. Um, so the next year they made +it a point to really incorporate it into + + align:start position:0% +it a point to really incorporate it into + + + align:start position:0% +it a point to really incorporate it into +the class to ask good questions, rich + + align:start position:0% +the class to ask good questions, rich + + + align:start position:0% +the class to ask good questions, rich +questions, questions that had um um + + align:start position:0% +questions, questions that had um um + + + align:start position:0% +questions, questions that had um um +interesting distra interesting and and + + align:start position:0% +interesting distra interesting and and + + + align:start position:0% +interesting distra interesting and and +informative distractors. So the wrong + + align:start position:0% +informative distractors. So the wrong + + + align:start position:0% +informative distractors. So the wrong +answers told the instructors what what + + align:start position:0% +answers told the instructors what what + + + align:start position:0% +answers told the instructors what what +the problems and misconceptions were. + + align:start position:0% +the problems and misconceptions were. + + + align:start position:0% +the problems and misconceptions were. +And um this was made clear to the + + align:start position:0% +And um this was made clear to the + + + align:start position:0% +And um this was made clear to the +students and in that way the if you ask + + align:start position:0% +students and in that way the if you ask + + + align:start position:0% +students and in that way the if you ask +students what they thought about the + + align:start position:0% +students what they thought about the + + + align:start position:0% +students what they thought about the +clickers they they were they were not at + + align:start position:0% +clickers they they were they were not at + + + align:start position:0% +clickers they they were they were not at +all resentful of the use of clickers and + + align:start position:0% +all resentful of the use of clickers and + + + align:start position:0% +all resentful of the use of clickers and +they did not see them as a way of just + + align:start position:0% +they did not see them as a way of just + + + align:start position:0% +they did not see them as a way of just +taking attendance. They didn't think + + align:start position:0% +taking attendance. They didn't think + + + align:start position:0% +taking attendance. They didn't think +they were sort of you know baby or + + align:start position:0% +they were sort of you know baby or + + + align:start position:0% +they were sort of you know baby or +whatever. Um and they were more they + + align:start position:0% +whatever. Um and they were more they + + + align:start position:0% +whatever. Um and they were more they +were therefore more effective. Um Rachel + + align:start position:0% +were therefore more effective. Um Rachel + + + align:start position:0% +were therefore more effective. Um Rachel +you had a comment. Yeah, I was just + + align:start position:0% +you had a comment. Yeah, I was just + + + align:start position:0% +you had a comment. Yeah, I was just +gonna say when I took 802 that's the ENM + + align:start position:0% +gonna say when I took 802 that's the ENM + + + align:start position:0% +gonna say when I took 802 that's the ENM +electricity magnetism freshman year the + + align:start position:0% +electricity magnetism freshman year the + + + align:start position:0% +electricity magnetism freshman year the +class I + + align:start position:0% +class I + + + align:start position:0% +class I +took and it was piloted. + + align:start position:0% +took and it was piloted. + + + align:start position:0% +took and it was piloted. +So we did all the online course and then + + align:start position:0% +So we did all the online course and then + + + align:start position:0% +So we did all the online course and then +the idea was come to class and we just + + align:start position:0% +the idea was come to class and we just + + + align:start position:0% +the idea was come to class and we just +like learn for two hours from the + + align:start position:0% +like learn for two hours from the + + + align:start position:0% +like learn for two hours from the +teacher using like group discussions and + + align:start position:0% +teacher using like group discussions and + + + align:start position:0% +teacher using like group discussions and +all these different things and it was + + align:start position:0% +all these different things and it was + + + align:start position:0% +all these different things and it was +one of the worst classes I've + + align:start position:0% +one of the worst classes I've + + + align:start position:0% +one of the worst classes I've +ever professor wasn't prepared to do + + align:start position:0% +ever professor wasn't prepared to do + + + align:start position:0% +ever professor wasn't prepared to do +these like these twoour + + align:start position:0% +these like these twoour + + + align:start position:0% +these like these twoour +discussions and like group discussions + + align:start position:0% +discussions and like group discussions + + + align:start position:0% +discussions and like group discussions +and like group work and all these like + + align:start position:0% +and like group work and all these like + + + align:start position:0% +and like group work and all these like +different things that like you could + + align:start position:0% +different things that like you could + + + align:start position:0% +different things that like you could +tell he just like wasn't used to doing + + align:start position:0% +tell he just like wasn't used to doing + + + align:start position:0% +tell he just like wasn't used to doing +and like it was a giant mess because of + + align:start position:0% +and like it was a giant mess because of + + + align:start position:0% +and like it was a giant mess because of +it. So, it's just like I think they're + + align:start position:0% +it. So, it's just like I think they're + + + align:start position:0% +it. So, it's just like I think they're +really useful tools, but it also + + align:start position:0% +really useful tools, but it also + + + align:start position:0% +really useful tools, but it also +requires the professor to like really + + align:start position:0% +requires the professor to like really + + + align:start position:0% +requires the professor to like really +like put something into it for the + + align:start position:0% +like put something into it for the + + + align:start position:0% +like put something into it for the +students to get something out of it. + + align:start position:0% +students to get something out of it. + + + align:start position:0% +students to get something out of it. +Right. Right. And that's a that's a + + align:start position:0% +Right. Right. And that's a that's a + + + align:start position:0% +Right. Right. And that's a that's a +consideration. I mean, for some things + + align:start position:0% +consideration. I mean, for some things + + + align:start position:0% +consideration. I mean, for some things +you can adopt them. There's kind of a + + align:start position:0% +you can adopt them. There's kind of a + + + align:start position:0% +you can adopt them. There's kind of a +low bar for adoption and a low bar for + + align:start position:0% +low bar for adoption and a low bar for + + + align:start position:0% +low bar for adoption and a low bar for +for solid use, right? Maybe not + + align:start position:0% +for solid use, right? Maybe not + + + align:start position:0% +for solid use, right? Maybe not +innovative, maybe not groundbreaking, + + align:start position:0% +innovative, maybe not groundbreaking, + + + align:start position:0% +innovative, maybe not groundbreaking, +but solid pedagogical use. Um, for + + align:start position:0% +but solid pedagogical use. Um, for + + + align:start position:0% +but solid pedagogical use. Um, for +others, if you're going to use them + + align:start position:0% +others, if you're going to use them + + + align:start position:0% +others, if you're going to use them +effectively in the classroom, you're + + align:start position:0% +effectively in the classroom, you're + + + align:start position:0% +effectively in the classroom, you're +going to have to spend some time + + align:start position:0% +going to have to spend some time + + + align:start position:0% +going to have to spend some time +engaging with the technology, making + + align:start position:0% +engaging with the technology, making + + + align:start position:0% +engaging with the technology, making +sure you understand it, making sure you + + align:start position:0% +sure you understand it, making sure you + + + align:start position:0% +sure you understand it, making sure you +understand what what you can do with it. + + align:start position:0% +understand what what you can do with it. + + + align:start position:0% +understand what what you can do with it. +Um, otherwise, it's not going to work. + + align:start position:0% +Um, otherwise, it's not going to work. + + + align:start position:0% +Um, otherwise, it's not going to work. +Um, a couple stories. One is, + + align:start position:0% +Um, a couple stories. One is, + + + align:start position:0% +Um, a couple stories. One is, +um, the idea + + align:start position:0% +um, the idea + + + align:start position:0% +um, the idea +of Well, maybe I'll hold that one. I'll + + align:start position:0% +of Well, maybe I'll hold that one. I'll + + + align:start position:0% +of Well, maybe I'll hold that one. I'll +hold that one. Any other I'll bring it + + align:start position:0% +hold that one. Any other I'll bring it + + + align:start position:0% +hold that one. Any other I'll bring it +up later. Remind me. Um any other + + align:start position:0% +up later. Remind me. Um any other + + + align:start position:0% +up later. Remind me. Um any other +comments about this? So this is a + + align:start position:0% +comments about this? So this is a + + + align:start position:0% +comments about this? So this is a +definition that I got um that in I think + + align:start position:0% +definition that I got um that in I think + + + align:start position:0% +definition that I got um that in I think +from one of the reasons. So + + align:start position:0% +from one of the reasons. So + + + align:start position:0% +from one of the reasons. So +technological processes and resources + + align:start position:0% +technological processes and resources + + + align:start position:0% +technological processes and resources +that are used, created or managed for + + align:start position:0% +that are used, created or managed for + + + align:start position:0% +that are used, created or managed for +learning and or improving + + align:start position:0% +learning and or improving + + + align:start position:0% +learning and or improving +performance. So that's crazy broad. Um, + + align:start position:0% +performance. So that's crazy broad. Um, + + + align:start position:0% +performance. So that's crazy broad. Um, +and then in that definition, there's + + align:start position:0% +and then in that definition, there's + + + align:start position:0% +and then in that definition, there's +this technological which gets around the + + align:start position:0% +this technological which gets around the + + + align:start position:0% +this technological which gets around the +electronic, but brings back the idea, + + align:start position:0% +electronic, but brings back the idea, + + + align:start position:0% +electronic, but brings back the idea, +well, a blackboard is probably a + + align:start position:0% +well, a blackboard is probably a + + + align:start position:0% +well, a blackboard is probably a +technology at some level, or at least it + + align:start position:0% +technology at some level, or at least it + + + align:start position:0% +technology at some level, or at least it +was at some point. So, it's a it's it's + + align:start position:0% +was at some point. So, it's a it's it's + + + align:start position:0% +was at some point. So, it's a it's it's +admittedly an incredibly + + align:start position:0% +admittedly an incredibly + + + align:start position:0% +admittedly an incredibly +um incredibly difficult concept to pin + + align:start position:0% +um incredibly difficult concept to pin + + + align:start position:0% +um incredibly difficult concept to pin +down. And maybe at some point, you don't + + align:start position:0% +down. And maybe at some point, you don't + + + align:start position:0% +down. And maybe at some point, you don't +necessarily have to, you have to decide + + align:start position:0% +necessarily have to, you have to decide + + + align:start position:0% +necessarily have to, you have to decide +which slice of it you want to deal with. + + align:start position:0% +which slice of it you want to deal with. + + + align:start position:0% +which slice of it you want to deal with. +Uh and + + align:start position:0% +Uh and + + + align:start position:0% +Uh and +um so the other important thing is that + + align:start position:0% +um so the other important thing is that + + + align:start position:0% +um so the other important thing is that +it's and it doesn't have to be but it + + align:start position:0% +it's and it doesn't have to be but it + + + align:start position:0% +it's and it doesn't have to be but it +can be an integral part or it should + + align:start position:0% +can be an integral part or it should + + + align:start position:0% +can be an integral part or it should +it's well be well integrated if not an + + align:start position:0% +it's well be well integrated if not an + + + align:start position:0% +it's well be well integrated if not an +integral it should be well integrated + + align:start position:0% +integral it should be well integrated + + + align:start position:0% +integral it should be well integrated +within the course. Um uh and and or it + + align:start position:0% +within the course. Um uh and and or it + + + align:start position:0% +within the course. Um uh and and or it +could be a supplemental learning aid. So + + align:start position:0% +could be a supplemental learning aid. So + + + align:start position:0% +could be a supplemental learning aid. So +it could be a way of delivering content + + align:start position:0% +it could be a way of delivering content + + + align:start position:0% +it could be a way of delivering content +outside of class or kind of the idea of + + align:start position:0% +outside of class or kind of the idea of + + + align:start position:0% +outside of class or kind of the idea of +an enrichment an enrichment of the + + align:start position:0% +an enrichment an enrichment of the + + + align:start position:0% +an enrichment an enrichment of the +material and it could be something like + + align:start position:0% +material and it could be something like + + + align:start position:0% +material and it could be something like +hardware really just just like + + align:start position:0% +hardware really just just like + + + align:start position:0% +hardware really just just like +hardware. Um I'm going to come back to + + align:start position:0% +hardware. Um I'm going to come back to + + + align:start position:0% +hardware. Um I'm going to come back to +how we parse how we chop this up in just + + align:start position:0% +how we parse how we chop this up in just + + + align:start position:0% +how we parse how we chop this up in just +a + + align:start position:0% +a + + + align:start position:0% +a +second. + + align:start position:0% +second. + + + align:start position:0% +second. +Remember that we don't want to do + + align:start position:0% +Remember that we don't want to do + + + align:start position:0% +Remember that we don't want to do +anything. This is the idea about walking + + align:start position:0% +anything. This is the idea about walking + + + align:start position:0% +anything. This is the idea about walking +into Home Depot. We don't want to do + + align:start position:0% +into Home Depot. We don't want to do + + + align:start position:0% +into Home Depot. We don't want to do +anything without thinking first about + + align:start position:0% +anything without thinking first about + + + align:start position:0% +anything without thinking first about +our intended learning outcomes. What + + align:start position:0% +our intended learning outcomes. What + + + align:start position:0% +our intended learning outcomes. What +intended learning outcome is the + + align:start position:0% +intended learning outcome is the + + + align:start position:0% +intended learning outcome is the +technology going to advance? Not what am + + align:start position:0% +technology going to advance? Not what am + + + align:start position:0% +technology going to advance? Not what am +I going to do with this + + align:start position:0% +I going to do with this + + + align:start position:0% +I going to do with this +technology? And um so in terms of + + align:start position:0% +technology? And um so in terms of + + + align:start position:0% +technology? And um so in terms of +categorization um this is something that + + align:start position:0% +categorization um this is something that + + + align:start position:0% +categorization um this is something that +I came up with just after grappling with + + align:start position:0% +I came up with just after grappling with + + + align:start position:0% +I came up with just after grappling with +things. So this is just my thing um and + + align:start position:0% +things. So this is just my thing um and + + + align:start position:0% +things. So this is just my thing um and +we're going to talk more about different + + align:start position:0% +we're going to talk more about different + + + align:start position:0% +we're going to talk more about different +ways to think about it. So this is just + + align:start position:0% +ways to think about it. So this is just + + + align:start position:0% +ways to think about it. So this is just +one slice of it. You could think about + + align:start position:0% +one slice of it. You could think about + + + align:start position:0% +one slice of it. You could think about +technologies that you use in the + + align:start position:0% +technologies that you use in the + + + align:start position:0% +technologies that you use in the +classroom. So that would be, you know, + + align:start position:0% +classroom. So that would be, you know, + + + align:start position:0% +classroom. So that would be, you know, +clickers, that would be using some sort + + align:start position:0% +clickers, that would be using some sort + + + align:start position:0% +clickers, that would be using some sort +of projection system, using a + + align:start position:0% +of projection system, using a + + + align:start position:0% +of projection system, using a +Smartboard, using some sort of, uh, + + align:start position:0% +Smartboard, using some sort of, uh, + + + align:start position:0% +Smartboard, using some sort of, uh, +simulations that you show students, um, + + align:start position:0% +simulations that you show students, um, + + + align:start position:0% +simulations that you show students, um, +etc. like, uh, virtual demos. Um, it + + align:start position:0% +etc. like, uh, virtual demos. Um, it + + + align:start position:0% +etc. like, uh, virtual demos. Um, it +could be a way for students to engage + + align:start position:0% +could be a way for students to engage + + + align:start position:0% +could be a way for students to engage +with the content, with the content and + + align:start position:0% +with the content, with the content and + + + align:start position:0% +with the content, with the content and +with other students outside of the + + align:start position:0% +with other students outside of the + + + align:start position:0% +with other students outside of the +classroom. So it could be some sort of a + + align:start position:0% +classroom. So it could be some sort of a + + + align:start position:0% +classroom. So it could be some sort of a +a a wiki, some other collaboration tool. + + align:start position:0% +a a wiki, some other collaboration tool. + + + align:start position:0% +a a wiki, some other collaboration tool. +Um or and or it could be something that + + align:start position:0% +Um or and or it could be something that + + + align:start position:0% +Um or and or it could be something that +delivers the content to the student + + align:start position:0% +delivers the content to the student + + + align:start position:0% +delivers the content to the student +outside of + + align:start position:0% + + + + align:start position:0% + +class. Um and that and there may be an + + align:start position:0% +class. Um and that and there may be an + + + align:start position:0% +class. Um and that and there may be an +overlap, right? You may show a + + align:start position:0% +overlap, right? You may show a + + + align:start position:0% +overlap, right? You may show a +simulation in class and then decide + + align:start position:0% +simulation in class and then decide + + + align:start position:0% +simulation in class and then decide +students should have access to it + + align:start position:0% +students should have access to it + + + align:start position:0% +students should have access to it +outside of class. So they're not + + align:start position:0% +outside of class. So they're not + + + align:start position:0% +outside of class. So they're not +mutually exclusive. Um and so this the + + align:start position:0% +mutually exclusive. Um and so this the + + + align:start position:0% +mutually exclusive. Um and so this the +engagement with the content can co uh + + align:start position:0% +engagement with the content can co uh + + + align:start position:0% +engagement with the content can co uh +include these collaboration tools, extra + + align:start position:0% +include these collaboration tools, extra + + + align:start position:0% +include these collaboration tools, extra +materials, content enrichment materials. + + align:start position:0% +materials, content enrichment materials. + + + align:start position:0% +materials, content enrichment materials. +Um and then the third one might be um + + align:start position:0% +Um and then the third one might be um + + + align:start position:0% +Um and then the third one might be um +student assignments. So the idea maybe + + align:start position:0% +student assignments. So the idea maybe + + + align:start position:0% +student assignments. So the idea maybe +you're going to + + align:start position:0% +you're going to + + + align:start position:0% +you're going to +use a technology say to the students + + align:start position:0% +use a technology say to the students + + + align:start position:0% +use a technology say to the students +okay I want you to create a website for + + align:start position:0% +okay I want you to create a website for + + + align:start position:0% +okay I want you to create a website for +a company that you're going to create + + align:start position:0% +a company that you're going to create + + + align:start position:0% +a company that you're going to create +and this is this parameters and you want + + align:start position:0% +and this is this parameters and you want + + + align:start position:0% +and this is this parameters and you want +to make sure you you you're explicit + + align:start position:0% +to make sure you you you're explicit + + + align:start position:0% +to make sure you you you're explicit +about what the company sells and how you + + align:start position:0% +about what the company sells and how you + + + align:start position:0% +about what the company sells and how you +deal with customers or whatever the + + align:start position:0% +deal with customers or whatever the + + + align:start position:0% +deal with customers or whatever the +assignment involves the technology. go + + align:start position:0% +assignment involves the technology. go + + + align:start position:0% +assignment involves the technology. go +out and make an audio recording of of + + align:start position:0% +out and make an audio recording of of + + + align:start position:0% +out and make an audio recording of of +people using a particular technology or + + align:start position:0% +people using a particular technology or + + + align:start position:0% +people using a particular technology or +interview interview people in the + + align:start position:0% +interview interview people in the + + + align:start position:0% +interview interview people in the +community. If you're going to design + + align:start position:0% +community. If you're going to design + + + align:start position:0% +community. If you're going to design +something for use in some community, + + align:start position:0% +something for use in some community, + + + align:start position:0% +something for use in some community, +interview the people in the community + + align:start position:0% +interview the people in the community + + + align:start position:0% +interview the people in the community +and submit this audio recording. So, it + + align:start position:0% +and submit this audio recording. So, it + + + align:start position:0% +and submit this audio recording. So, it +could be the technology could be used in + + align:start position:0% +could be the technology could be used in + + + align:start position:0% +could be the technology could be used in +the student assignments and that and you + + align:start position:0% +the student assignments and that and you + + + align:start position:0% +the student assignments and that and you +could back that all the way up to online + + align:start position:0% +could back that all the way up to online + + + align:start position:0% +could back that all the way up to online +problems, you know, as they use in edex + + align:start position:0% +problems, you know, as they use in edex + + + align:start position:0% +problems, you know, as they use in edex +and + + align:start position:0% +and + + + align:start position:0% +and +MITx. Um and then for assessment and + + align:start position:0% +MITx. Um and then for assessment and + + + align:start position:0% +MITx. Um and then for assessment and +feedback, the idea that um uh you can + + align:start position:0% +feedback, the idea that um uh you can + + + align:start position:0% +feedback, the idea that um uh you can +either use clicker questions, which + + align:start position:0% +either use clicker questions, which + + + align:start position:0% +either use clicker questions, which +would be for the formative feedback, or + + align:start position:0% +would be for the formative feedback, or + + + align:start position:0% +would be for the formative feedback, or +you can use you can use it as some sort + + align:start position:0% +you can use you can use it as some sort + + + align:start position:0% +you can use you can use it as some sort +of a a quiz, an online quiz or um some + + align:start position:0% +of a a quiz, an online quiz or um some + + + align:start position:0% +of a a quiz, an online quiz or um some +other way of giving feedback to the + + align:start position:0% +other way of giving feedback to the + + + align:start position:0% +other way of giving feedback to the +students. So that gets to the + + align:start position:0% +students. So that gets to the + + + align:start position:0% +students. So that gets to the +summitative and the formative idea. Um + + align:start position:0% +summitative and the formative idea. Um + + + align:start position:0% +summitative and the formative idea. Um +and then the idea of just using a + + align:start position:0% +and then the idea of just using a + + + align:start position:0% +and then the idea of just using a +learning management system just to + + align:start position:0% +learning management system just to + + + align:start position:0% +learning management system just to +administrator administrate the + + align:start position:0% +administrator administrate the + + + align:start position:0% +administrator administrate the +course. That's one + + align:start position:0% +course. That's one + + + align:start position:0% +course. That's one +slice. + + align:start position:0% +slice. + + + align:start position:0% +slice. +Um, there's another very interesting + + align:start position:0% +Um, there's another very interesting + + + align:start position:0% +Um, there's another very interesting +couple other very interesting ways to + + align:start position:0% +couple other very interesting ways to + + + align:start position:0% +couple other very interesting ways to +slice this up and I have a hand out here + + align:start position:0% +slice this up and I have a hand out here + + + align:start position:0% +slice this up and I have a hand out here +because these are woefully + + align:start position:0% +because these are woefully + + + align:start position:0% +because these are woefully +tiny these + + align:start position:0% +tiny these + + + align:start position:0% +tiny these +schematics. So, if you could just take + + align:start position:0% +schematics. So, if you could just take + + + align:start position:0% +schematics. So, if you could just take +one and pass it along. One is called the + + align:start position:0% +one and pass it along. One is called the + + + align:start position:0% +one and pass it along. One is called the +sections framework and the other is + + align:start position:0% +sections framework and the other is + + + align:start position:0% +sections framework and the other is +called um the backwards edte tool + + align:start position:0% +called um the backwards edte tool + + + align:start position:0% +called um the backwards edte tool +flowchart. + + align:start position:0% +flowchart. + + + align:start position:0% +flowchart. +So these are different these are not + + align:start position:0% +So these are different these are not + + + align:start position:0% +So these are different these are not +mine and these are different ways oh + + align:start position:0% +mine and these are different ways oh + + + align:start position:0% +mine and these are different ways oh +sorry different ways of um thinking + + align:start position:0% +sorry different ways of um thinking + + + align:start position:0% +sorry different ways of um thinking +about thinking about + + align:start position:0% +about thinking about + + + align:start position:0% +about thinking about +technology so let + + align:start position:0% +technology so let + + + align:start position:0% +technology so let +me so the first one is this edtech chart + + align:start position:0% +me so the first one is this edtech chart + + + align:start position:0% +me so the first one is this edtech chart +and I know you can't read that here so + + align:start position:0% +and I know you can't read that here so + + + align:start position:0% +and I know you can't read that here so +that's why you have the handout + + align:start position:0% + + + + align:start position:0% + +um and I like it because it it it kind + + align:start position:0% +um and I like it because it it it kind + + + align:start position:0% +um and I like it because it it it kind +of starts with the the activity that you + + align:start position:0% +of starts with the the activity that you + + + align:start position:0% +of starts with the the activity that you +want students to use. So it starts with + + align:start position:0% +want students to use. So it starts with + + + align:start position:0% +want students to use. So it starts with +this what do you want students to do and + + align:start position:0% +this what do you want students to do and + + + align:start position:0% +this what do you want students to do and +that's what the purple box are the + + align:start position:0% +that's what the purple box are the + + + align:start position:0% +that's what the purple box are the +student + + align:start position:0% +student + + + align:start position:0% +student +tasks and then it kind of creates these + + align:start position:0% +tasks and then it kind of creates these + + + align:start position:0% +tasks and then it kind of creates these +sort of guiding questions that sort of + + align:start position:0% +sort of guiding questions that sort of + + + align:start position:0% +sort of guiding questions that sort of +rerout route you um and then it gives + + align:start position:0% +rerout route you um and then it gives + + + align:start position:0% +rerout route you um and then it gives +you a suggestion for a tech tool. So I'm + + align:start position:0% +you a suggestion for a tech tool. So I'm + + + align:start position:0% +you a suggestion for a tech tool. So I'm +going to just let you I'm going to give + + align:start position:0% +going to just let you I'm going to give + + + align:start position:0% +going to just let you I'm going to give +you a few minutes just to parse that um + + align:start position:0% +you a few minutes just to parse that um + + + align:start position:0% +you a few minutes just to parse that um +just to engage with it a little bit. + + align:start position:0% +just to engage with it a little bit. + + + align:start position:0% +just to engage with it a little bit. +It's very beautiful. It's it I like this + + align:start position:0% +It's very beautiful. It's it I like this + + + align:start position:0% +It's very beautiful. It's it I like this +one. I like this one. I I think it's + + align:start position:0% +one. I like this one. I I think it's + + + align:start position:0% +one. I like this one. I I think it's +very It's very useful. Um any other any + + align:start position:0% +very It's very useful. Um any other any + + + align:start position:0% +very It's very useful. Um any other any +comments or thoughts about it? + + align:start position:0% + + + + align:start position:0% + +Yeah. Gordon, I don't get it. Okay. Uh + + align:start position:0% +Yeah. Gordon, I don't get it. Okay. Uh + + + align:start position:0% +Yeah. Gordon, I don't get it. Okay. Uh +Gordon doesn't get it. Somebody want to + + align:start position:0% +Gordon doesn't get it. Somebody want to + + + align:start position:0% +Gordon doesn't get it. Somebody want to +uh maybe nobody gets it, but do you want + + align:start position:0% +uh maybe nobody gets it, but do you want + + + align:start position:0% +uh maybe nobody gets it, but do you want +to explain it a little bit out loud, + + align:start position:0% +to explain it a little bit out loud, + + + align:start position:0% +to explain it a little bit out loud, +David, please? Yeah. For example, um but + + align:start position:0% +David, please? Yeah. For example, um but + + + align:start position:0% +David, please? Yeah. For example, um but +can you explain to everybody? You might + + align:start position:0% +can you explain to everybody? You might + + + align:start position:0% +can you explain to everybody? You might +let's say first I'll just take the first + + align:start position:0% +let's say first I'll just take the first + + + align:start position:0% +let's say first I'll just take the first +um could you go to the slide oh sure + + align:start position:0% + + + + align:start position:0% + +okay say what you want students to do + + align:start position:0% +okay say what you want students to do + + + align:start position:0% +okay say what you want students to do +okay then if you take the extreme to the + + align:start position:0% +okay then if you take the extreme to the + + + align:start position:0% +okay then if you take the extreme to the +left to create analyze data that's what + + align:start position:0% +left to create analyze data that's what + + + align:start position:0% +left to create analyze data that's what +I want the students to do and so doing + + align:start position:0% +I want the students to do and so doing + + + align:start position:0% +I want the students to do and so doing +that what you find out is it kind of a + + align:start position:0% +that what you find out is it kind of a + + + align:start position:0% +that what you find out is it kind of a +sol you want them to apply to it if it + + align:start position:0% +sol you want them to apply to it if it + + + align:start position:0% +sol you want them to apply to it if it +is Yes, then you can create forms so + + align:start position:0% +is Yes, then you can create forms so + + + align:start position:0% +is Yes, then you can create forms so +that they can carry out the survey. If + + align:start position:0% +that they can carry out the survey. If + + + align:start position:0% +that they can carry out the survey. If +it is not, you find out is it a group + + align:start position:0% +it is not, you find out is it a group + + + align:start position:0% +it is not, you find out is it a group +effort that you want them to use. Now if + + align:start position:0% +effort that you want them to use. Now if + + + align:start position:0% +effort that you want them to use. Now if +it is a yes, then again there no greater + + align:start position:0% +it is a yes, then again there no greater + + + align:start position:0% +it is a yes, then again there no greater +you know. So that's one branch of that. + + align:start position:0% +you know. So that's one branch of that. + + + align:start position:0% +you know. So that's one branch of that. +So similarly then you can use other keys + + align:start position:0% +So similarly then you can use other keys + + + align:start position:0% +So similarly then you can use other keys +on top, blue, orange and green and then + + align:start position:0% +on top, blue, orange and green and then + + + align:start position:0% +on top, blue, orange and green and then +you see that actually + + align:start position:0% + + + + align:start position:0% + +it's certainly not exclusive. I mean, + + align:start position:0% +it's certainly not exclusive. I mean, + + + align:start position:0% +it's certainly not exclusive. I mean, +it's certainly not it doesn't have + + align:start position:0% +it's certainly not it doesn't have + + + align:start position:0% +it's certainly not it doesn't have +everything on here, but it kind of gives + + align:start position:0% +everything on here, but it kind of gives + + + align:start position:0% +everything on here, but it kind of gives +you, I think, a way of thinking about, + + align:start position:0% +you, I think, a way of thinking about, + + + align:start position:0% +you, I think, a way of thinking about, +okay, I start with what I want students + + align:start position:0% +okay, I start with what I want students + + + align:start position:0% +okay, I start with what I want students +to do, which most of us have a pretty + + align:start position:0% +to do, which most of us have a pretty + + + align:start position:0% +to do, which most of us have a pretty +good handle on. Um, and then it helps + + align:start position:0% +good handle on. Um, and then it helps + + + align:start position:0% +good handle on. Um, and then it helps +you just think backwards to the + + align:start position:0% +you just think backwards to the + + + align:start position:0% +you just think backwards to the +technology. Um, Teslim, yes, I just want + + align:start position:0% +technology. Um, Teslim, yes, I just want + + + align:start position:0% +technology. Um, Teslim, yes, I just want +to add that it's all about what do you + + align:start position:0% +to add that it's all about what do you + + + align:start position:0% +to add that it's all about what do you +want to do and how do you how can you do + + align:start position:0% +want to do and how do you how can you do + + + align:start position:0% +want to do and how do you how can you do +it? Yes, that's that's what it's all + + align:start position:0% +it? Yes, that's that's what it's all + + + align:start position:0% +it? Yes, that's that's what it's all +about. And secondly, it it actually + + align:start position:0% +about. And secondly, it it actually + + + align:start position:0% +about. And secondly, it it actually +looks at the the levels of person as + + align:start position:0% +looks at the the levels of person as + + + align:start position:0% +looks at the the levels of person as +well. For instance, collect analyze + + align:start position:0% +well. For instance, collect analyze + + + align:start position:0% +well. For instance, collect analyze +data. That's an part. If you don't go to + + align:start position:0% +data. That's an part. If you don't go to + + + align:start position:0% +data. That's an part. If you don't go to +the right parts, you see memorize and + + align:start position:0% +the right parts, you see memorize and + + + align:start position:0% +the right parts, you see memorize and +repetition. So you have all the levels + + align:start position:0% +repetition. So you have all the levels + + + align:start position:0% +repetition. So you have all the levels +of toning there. So how do you want them + + align:start position:0% +of toning there. So how do you want them + + + align:start position:0% +of toning there. So how do you want them +to do it? What do you want them to do? + + align:start position:0% +to do it? What do you want them to do? + + + align:start position:0% +to do it? What do you want them to do? +And how do you how do you help them + + align:start position:0% +And how do you how do you help them + + + align:start position:0% +And how do you how do you help them +doing it? That's that's what + + align:start position:0% + + + + align:start position:0% + +Yeah. Yeah. No, it's it is great. Um, + + align:start position:0% +Yeah. Yeah. No, it's it is great. Um, + + + align:start position:0% +Yeah. Yeah. No, it's it is great. Um, +uh, other other thoughts and yeah, we're + + align:start position:0% +uh, other other thoughts and yeah, we're + + + align:start position:0% +uh, other other thoughts and yeah, we're +going to get back to the idea of the + + align:start position:0% +going to get back to the idea of the + + + align:start position:0% +going to get back to the idea of the +taxonomy + + align:start position:0% +taxonomy + + + align:start position:0% +taxonomy +shortly. Other other + + align:start position:0% + + + + align:start position:0% + +thoughts? Um, let's see. There's a + + align:start position:0% +thoughts? Um, let's see. There's a + + + align:start position:0% +thoughts? Um, let's see. There's a +second one, um, which is on the other + + align:start position:0% +second one, um, which is on the other + + + align:start position:0% +second one, um, which is on the other +side of your handout. It's the And so, + + align:start position:0% +side of your handout. It's the And so, + + + align:start position:0% +side of your handout. It's the And so, +these are just I know you can't see + + align:start position:0% +these are just I know you can't see + + + align:start position:0% +these are just I know you can't see +this. That's why you have the handout. + + align:start position:0% +this. That's why you have the handout. + + + align:start position:0% +this. That's why you have the handout. +Um, these are just ideas. Again, there + + align:start position:0% +Um, these are just ideas. Again, there + + + align:start position:0% +Um, these are just ideas. Again, there +there's no rules really, but it's just + + align:start position:0% +there's no rules really, but it's just + + + align:start position:0% +there's no rules really, but it's just +it depending on what you're trying to + + align:start position:0% +it depending on what you're trying to + + + align:start position:0% +it depending on what you're trying to +do. It just may help you start to think + + align:start position:0% +do. It just may help you start to think + + + align:start position:0% +do. It just may help you start to think +about how to get the right tool for the + + align:start position:0% +about how to get the right tool for the + + + align:start position:0% +about how to get the right tool for the +job. Um, so it's called sections because + + align:start position:0% +job. Um, so it's called sections because + + + align:start position:0% +job. Um, so it's called sections because +each of the bo each of those boxes with + + align:start position:0% +each of the bo each of those boxes with + + + align:start position:0% +each of the bo each of those boxes with +the red outline, S E C T I O Ns, the S + + align:start position:0% +the red outline, S E C T I O Ns, the S + + + align:start position:0% +the red outline, S E C T I O Ns, the S +is student characteristics, the E is + + align:start position:0% +is student characteristics, the E is + + + align:start position:0% +is student characteristics, the E is +ease of use, C is cost, teaching and + + align:start position:0% +ease of use, C is cost, teaching and + + + align:start position:0% +ease of use, C is cost, teaching and +learning, interse um interaction to + + align:start position:0% +learning, interse um interaction to + + + align:start position:0% +learning, interse um interaction to +promote active learning, organization, + + align:start position:0% +promote active learning, organization, + + + align:start position:0% +promote active learning, organization, +novelty, and speed. Um, and this chart I + + align:start position:0% +novelty, and speed. Um, and this chart I + + + align:start position:0% +novelty, and speed. Um, and this chart I +think just I'm going to let you engage + + align:start position:0% +think just I'm going to let you engage + + + align:start position:0% +think just I'm going to let you engage +with it for just a minute, but it brings + + align:start position:0% +with it for just a minute, but it brings + + + align:start position:0% +with it for just a minute, but it brings +up the idea of the the learning curve + + align:start position:0% +up the idea of the the learning curve + + + align:start position:0% +up the idea of the the learning curve +for the + + align:start position:0% +for the + + + align:start position:0% +for the +instructor, which you don't want to lose + + align:start position:0% +instructor, which you don't want to lose + + + align:start position:0% +instructor, which you don't want to lose +sight of that you want to factor that + + align:start position:0% +sight of that you want to factor that + + + align:start position:0% +sight of that you want to factor that +into your choices about what + + align:start position:0% +into your choices about what + + + align:start position:0% +into your choices about what +technologies to use. So, again, I'm + + align:start position:0% +technologies to use. So, again, I'm + + + align:start position:0% +technologies to use. So, again, I'm +going to shut up for a minute or so. So, + + align:start position:0% +going to shut up for a minute or so. So, + + + align:start position:0% +going to shut up for a minute or so. So, +you can look at this + + align:start position:0% + + + + align:start position:0% + +This is + + align:start position:0% +This is + + + align:start position:0% +This is +just the choices of + + align:start position:0% +just the choices of + + + align:start position:0% +just the choices of +selecting L technologies which depends + + align:start position:0% +selecting L technologies which depends + + + align:start position:0% +selecting L technologies which depends +on the student the ease of use of that + + align:start position:0% +on the student the ease of use of that + + + align:start position:0% +on the student the ease of use of that +technology. Then what the posifications + + align:start position:0% +technology. Then what the posifications + + + align:start position:0% +technology. Then what the posifications +are and then what kind of teaching or + + align:start position:0% +are and then what kind of teaching or + + + align:start position:0% +are and then what kind of teaching or +learning environment or kind of that + + align:start position:0% +learning environment or kind of that + + + align:start position:0% +learning environment or kind of that +will be and then what is the interaction + + align:start position:0% +will be and then what is the interaction + + + align:start position:0% +will be and then what is the interaction +know so those are properties that + + align:start position:0% +know so those are properties that + + + align:start position:0% +know so those are properties that +determines the technologies that we want + + align:start position:0% +determines the technologies that we want + + + align:start position:0% +determines the technologies that we want +to choose right right but what's the + + align:start position:0% +to choose right right but what's the + + + align:start position:0% +to choose right right but what's the +difference between this one and I mean + + align:start position:0% +difference between this one and I mean + + + align:start position:0% +difference between this one and I mean +there's many differences obviously but + + align:start position:0% +there's many differences obviously but + + + align:start position:0% +there's many differences obviously but +what's a kind of a use definition a + + align:start position:0% +what's a kind of a use definition a + + + align:start position:0% +what's a kind of a use definition a +utility definition + + align:start position:0% +utility definition + + + align:start position:0% +utility definition +utility difference. One's one one's a + + align:start position:0% +utility difference. One's one one's a + + + align:start position:0% +utility difference. One's one one's a +flowchart that points you to the answer. + + align:start position:0% +flowchart that points you to the answer. + + + align:start position:0% +flowchart that points you to the answer. +So it asks the yes or no questions. The + + align:start position:0% +So it asks the yes or no questions. The + + + align:start position:0% +So it asks the yes or no questions. The +other just gives you the then you have + + align:start position:0% +other just gives you the then you have + + + align:start position:0% +other just gives you the then you have +to select from a doesn't guide you + + align:start position:0% +to select from a doesn't guide you + + + align:start position:0% +to select from a doesn't guide you +directly. Right. It kind of it exactly + + align:start position:0% +directly. Right. It kind of it exactly + + + align:start position:0% +directly. Right. It kind of it exactly +it it kind of helps you think about it. + + align:start position:0% +it it kind of helps you think about it. + + + align:start position:0% +it it kind of helps you think about it. +Oh my gosh, I have, you know, I have no + + align:start position:0% +Oh my gosh, I have, you know, I have no + + + align:start position:0% +Oh my gosh, I have, you know, I have no +money. Right. So that's certainly that's + + align:start position:0% +money. Right. So that's certainly that's + + + align:start position:0% +money. Right. So that's certainly that's +going to rule out a whole c a whole, you + + align:start position:0% +going to rule out a whole c a whole, you + + + align:start position:0% +going to rule out a whole c a whole, you +know, set of of uh options for you. Um + + align:start position:0% +know, set of of uh options for you. Um + + + align:start position:0% +know, set of of uh options for you. Um +but it doesn't say oh you have no money. + + align:start position:0% +but it doesn't say oh you have no money. + + + align:start position:0% +but it doesn't say oh you have no money. +uh think about these right I mean it + + align:start position:0% +uh think about these right I mean it + + + align:start position:0% +uh think about these right I mean it +doesn't um it doesn't it's not a + + align:start position:0% +doesn't um it doesn't it's not a + + + align:start position:0% +doesn't um it doesn't it's not a +flowchart it doesn't point you to to an + + align:start position:0% +flowchart it doesn't point you to to an + + + align:start position:0% +flowchart it doesn't point you to to an +end result but it it if you if you went + + align:start position:0% +end result but it it if you if you went + + + align:start position:0% +end result but it it if you if you went +through this exercise and answered these + + align:start position:0% +through this exercise and answered these + + + align:start position:0% +through this exercise and answered these +questions I think you would have a + + align:start position:0% +questions I think you would have a + + + align:start position:0% +questions I think you would have a +better you'd be in a better place with + + align:start position:0% +better you'd be in a better place with + + + align:start position:0% +better you'd be in a better place with +respect to choosing the particular + + align:start position:0% +respect to choosing the particular + + + align:start position:0% +respect to choosing the particular +technology yeah also I think that the + + align:start position:0% +technology yeah also I think that the + + + align:start position:0% +technology yeah also I think that the +second one is not aimed at directing you + + align:start position:0% +second one is not aimed at directing you + + + align:start position:0% +second one is not aimed at directing you +towards any type of choice it doesn't + + align:start position:0% +towards any type of choice it doesn't + + + align:start position:0% +towards any type of choice it doesn't +aim that at all for instance if you want + + align:start position:0% +aim that at all for instance if you want + + + align:start position:0% +aim that at all for instance if you want +to + + align:start position:0% +to + + + align:start position:0% +to +use the + + align:start position:0% +use the + + + align:start position:0% +use the +Then you see the properties of when it + + align:start position:0% +Then you see the properties of when it + + + align:start position:0% +Then you see the properties of when it +comes to + + align:start position:0% +comes to + + + align:start position:0% +comes to +money you can think about because if you + + align:start position:0% +money you can think about because if you + + + align:start position:0% +money you can think about because if you +don't think about everything you might + + align:start position:0% +don't think about everything you might + + + align:start position:0% +don't think about everything you might +end up missing some of it + + align:start position:0% +end up missing some of it + + + align:start position:0% +end up missing some of it +just + + align:start position:0% +just + + + align:start position:0% +just +such you know + + align:start position:0% + + + + align:start position:0% + +right it's it's some things to just keep + + align:start position:0% +right it's it's some things to just keep + + + align:start position:0% +right it's it's some things to just keep +in your head when you're making these + + align:start position:0% +in your head when you're making these + + + align:start position:0% +in your head when you're making these +choices. it's not necessarily a + + align:start position:0% +choices. it's not necessarily a + + + align:start position:0% +choices. it's not necessarily a +formalism for making a + + align:start position:0% +formalism for making a + + + align:start position:0% +formalism for making a +choice. + + align:start position:0% +choice. + + + align:start position:0% +choice. +Um, so one other slice of all this + + align:start position:0% +Um, so one other slice of all this + + + align:start position:0% +Um, so one other slice of all this +technology is is this um it's kind of a + + align:start position:0% +technology is is this um it's kind of a + + + align:start position:0% +technology is is this um it's kind of a +classic I I would say classic model + + align:start position:0% +classic I I would say classic model + + + align:start position:0% +classic I I would say classic model +which is called the Samur model. SAM R. + + align:start position:0% +which is called the Samur model. SAM R. + + + align:start position:0% +which is called the Samur model. SAM R. +I know I'm throwing a lot of models at + + align:start position:0% +I know I'm throwing a lot of models at + + + align:start position:0% +I know I'm throwing a lot of models at +you but but you have to kind of find the + + align:start position:0% +you but but you have to kind of find the + + + align:start position:0% +you but but you have to kind of find the +slice that that works for you. Um the + + align:start position:0% +slice that that works for you. Um the + + + align:start position:0% +slice that that works for you. Um the +samur model I think is very is very + + align:start position:0% +samur model I think is very is very + + + align:start position:0% +samur model I think is very is very +useful to keep in mind when you're + + align:start position:0% +useful to keep in mind when you're + + + align:start position:0% +useful to keep in mind when you're +deciding why you're using a techn why + + align:start position:0% +deciding why you're using a techn why + + + align:start position:0% +deciding why you're using a techn why +you're gravitating to a particular + + align:start position:0% +you're gravitating to a particular + + + align:start position:0% +you're gravitating to a particular +technology and it's this idea of um of + + align:start position:0% +technology and it's this idea of um of + + + align:start position:0% +technology and it's this idea of um of +it being is the is the technology just a + + align:start position:0% +it being is the is the technology just a + + + align:start position:0% +it being is the is the technology just a +substitution. So back in the day when + + align:start position:0% +substitution. So back in the day when + + + align:start position:0% +substitution. So back in the day when +when everybody said oh courses need web + + align:start position:0% +when everybody said oh courses need web + + + align:start position:0% +when everybody said oh courses need web +pages you have to have a course web + + align:start position:0% +pages you have to have a course web + + + align:start position:0% +pages you have to have a course web +page. Well what was a course web page? + + align:start position:0% +page. Well what was a course web page? + + + align:start position:0% +page. Well what was a course web page? +It was an electronic version of your + + align:start position:0% +It was an electronic version of your + + + align:start position:0% +It was an electronic version of your +syllabus basically. I mean it was sort + + align:start position:0% +syllabus basically. I mean it was sort + + + align:start position:0% +syllabus basically. I mean it was sort +of it had the name of the course. It had + + align:start position:0% +of it had the name of the course. It had + + + align:start position:0% +of it had the name of the course. It had +some picture and then it was there was a + + align:start position:0% +some picture and then it was there was a + + + align:start position:0% +some picture and then it was there was a +link and you could click on it and the + + align:start position:0% +link and you could click on it and the + + + align:start position:0% +link and you could click on it and the +students got the syllabus. They got a + + align:start position:0% +students got the syllabus. They got a + + + align:start position:0% +students got the syllabus. They got a +like a you know a text version of the + + align:start position:0% +like a you know a text version of the + + + align:start position:0% +like a you know a text version of the +syllabus. I mean a soft copy of the + + align:start position:0% +syllabus. I mean a soft copy of the + + + align:start position:0% +syllabus. I mean a soft copy of the +syllabus that then they printed out and + + align:start position:0% +syllabus that then they printed out and + + + align:start position:0% +syllabus that then they printed out and +brought to class. So it was really it + + align:start position:0% +brought to class. So it was really it + + + align:start position:0% +brought to class. So it was really it +was a onetoone substitution. Instead of + + align:start position:0% +was a onetoone substitution. Instead of + + + align:start position:0% +was a onetoone substitution. Instead of +seeing the syllabus uh in a in a piece + + align:start position:0% +seeing the syllabus uh in a in a piece + + + align:start position:0% +seeing the syllabus uh in a in a piece +of paper they see it online. It was + + align:start position:0% +of paper they see it online. It was + + + align:start position:0% +of paper they see it online. It was +complete substitution. it didn't do + + align:start position:0% +complete substitution. it didn't do + + + align:start position:0% +complete substitution. it didn't do +anything extra except maybe made it a + + align:start position:0% +anything extra except maybe made it a + + + align:start position:0% +anything extra except maybe made it a +little easier for students not to lose + + align:start position:0% +little easier for students not to lose + + + align:start position:0% +little easier for students not to lose +the syllabus but it didn't really have + + align:start position:0% +the syllabus but it didn't really have + + + align:start position:0% +the syllabus but it didn't really have +any functional difference. Um then the + + align:start position:0% +any functional difference. Um then the + + + align:start position:0% +any functional difference. Um then the +next level that's the S the A is that it + + align:start position:0% +next level that's the S the A is that it + + + align:start position:0% +next level that's the S the A is that it +it's a there's an augmentation. So um + + align:start position:0% +it's a there's an augmentation. So um + + + align:start position:0% +it's a there's an augmentation. So um +there's a substitute but with a tra with + + align:start position:0% +there's a substitute but with a tra with + + + align:start position:0% +there's a substitute but with a tra with +a little bit of an improvement. So maybe + + align:start position:0% +a little bit of an improvement. So maybe + + + align:start position:0% +a little bit of an improvement. So maybe +um students could hand the homework in + + align:start position:0% +um students could hand the homework in + + + align:start position:0% +um students could hand the homework in +online, right? They're still handing + + align:start position:0% +online, right? They're still handing + + + align:start position:0% +online, right? They're still handing +homework in. They're still probably + + align:start position:0% +homework in. They're still probably + + + align:start position:0% +homework in. They're still probably +writing their homework out, scanning it, + + align:start position:0% +writing their homework out, scanning it, + + + align:start position:0% +writing their homework out, scanning it, +and handing it in, but it's a little + + align:start position:0% +and handing it in, but it's a little + + + align:start position:0% +and handing it in, but it's a little +easier. It's a little bit easier. Maybe + + align:start position:0% +easier. It's a little bit easier. Maybe + + + align:start position:0% +easier. It's a little bit easier. Maybe +you don't lose the you don't lose their + + align:start position:0% +you don't lose the you don't lose their + + + align:start position:0% +you don't lose the you don't lose their +homeworks, that kind of thing. So, + + align:start position:0% +homeworks, that kind of thing. So, + + + align:start position:0% +homeworks, that kind of thing. So, +that's the augmentation. Um, the next + + align:start position:0% +that's the augmentation. Um, the next + + + align:start position:0% +that's the augmentation. Um, the next +level would be a modification. So, some + + align:start position:0% +level would be a modification. So, some + + + align:start position:0% +level would be a modification. So, some +sort of like serious redesign of a task + + align:start position:0% +sort of like serious redesign of a task + + + align:start position:0% +sort of like serious redesign of a task +that you couldn't do before that + + align:start position:0% +that you couldn't do before that + + + align:start position:0% +that you couldn't do before that +technology. And then the final would be + + align:start position:0% +technology. And then the final would be + + + align:start position:0% +technology. And then the final would be +it just redefineses the the tasks that + + align:start position:0% +it just redefineses the the tasks that + + + align:start position:0% +it just redefineses the the tasks that +you do, the tasks that students do. + + align:start position:0% +you do, the tasks that students do. + + + align:start position:0% +you do, the tasks that students do. +um in a way that's completely + + align:start position:0% +um in a way that's completely + + + align:start position:0% +um in a way that's completely +different. So, I'm going to ask you to + + align:start position:0% +different. So, I'm going to ask you to + + + align:start position:0% +different. So, I'm going to ask you to +think about that for your own courses in + + align:start position:0% +think about that for your own courses in + + + align:start position:0% +think about that for your own courses in +about two minutes. + + align:start position:0% +about two minutes. + + + align:start position:0% +about two minutes. +Um just there's a little bit of a um + + align:start position:0% +Um just there's a little bit of a um + + + align:start position:0% +Um just there's a little bit of a um +schematic here that might help. These + + align:start position:0% +schematic here that might help. These + + + align:start position:0% +schematic here that might help. These +are sort of a little bit baby but the + + align:start position:0% +are sort of a little bit baby but the + + + align:start position:0% +are sort of a little bit baby but the +idea of um + + align:start position:0% +idea of um + + + align:start position:0% +idea of um +substitution. Um so the idea of using a + + align:start position:0% +substitution. Um so the idea of using a + + + align:start position:0% +substitution. Um so the idea of using a +word processor instead of a typewriter + + align:start position:0% +word processor instead of a typewriter + + + align:start position:0% +word processor instead of a typewriter +that was substit that was a + + align:start position:0% +that was substit that was a + + + align:start position:0% +that was substit that was a +substitutional + + align:start position:0% +substitutional + + + align:start position:0% +substitutional +technology. Um so then augmentation you + + align:start position:0% +technology. Um so then augmentation you + + + align:start position:0% +technology. Um so then augmentation you +get spell check right once you're in a + + align:start position:0% +get spell check right once you're in a + + + align:start position:0% +get spell check right once you're in a +computer you get to have spellch check + + align:start position:0% +computer you get to have spellch check + + + align:start position:0% +computer you get to have spellch check +and and formatting and cutting and + + align:start position:0% +and and formatting and cutting and + + + align:start position:0% +and and formatting and cutting and +pasting and that's different than what + + align:start position:0% +pasting and that's different than what + + + align:start position:0% +pasting and that's different than what +you can do on a typewriter. Um and then + + align:start position:0% +you can do on a typewriter. Um and then + + + align:start position:0% +you can do on a typewriter. Um and then +so modification. Well, there was like an + + align:start position:0% +so modification. Well, there was like an + + + align:start position:0% +so modification. Well, there was like an +email or you could put graphs and images + + align:start position:0% +email or you could put graphs and images + + + align:start position:0% +email or you could put graphs and images +into the right into the document was a + + align:start position:0% +into the right into the document was a + + + align:start position:0% +into the right into the document was a +it was changed sort of the way we viewed + + align:start position:0% +it was changed sort of the way we viewed + + + align:start position:0% +it was changed sort of the way we viewed +um a a document like a whole document. + + align:start position:0% +um a a document like a whole document. + + + align:start position:0% +um a a document like a whole document. +Um and then the idea of having uh + + align:start position:0% +Um and then the idea of having uh + + + align:start position:0% +Um and then the idea of having uh +hypertext or a some sort of a web page + + align:start position:0% +hypertext or a some sort of a web page + + + align:start position:0% +hypertext or a some sort of a web page +that students navigated in a nonlinear + + align:start position:0% +that students navigated in a nonlinear + + + align:start position:0% +that students navigated in a nonlinear +or a non-prescribed way that would be + + align:start position:0% +or a non-prescribed way that would be + + + align:start position:0% +or a non-prescribed way that would be +the that would be the redefinition, + + align:start position:0% +the that would be the redefinition, + + + align:start position:0% +the that would be the redefinition, +let's say. + + align:start position:0% +let's say. + + + align:start position:0% +let's say. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +um, so that's kind of a that's a sort of + + align:start position:0% +um, so that's kind of a that's a sort of + + + align:start position:0% +um, so that's kind of a that's a sort of +baby examples of + + align:start position:0% +baby examples of + + + align:start position:0% +baby examples of +that. Um, and then this this next one + + align:start position:0% +that. Um, and then this this next one + + + align:start position:0% +that. Um, and then this this next one +which is pretty fun is there's this + + align:start position:0% +which is pretty fun is there's this + + + align:start position:0% +which is pretty fun is there's this +woman Kathy Shrock and um, if you Google + + align:start position:0% +woman Kathy Shrock and um, if you Google + + + align:start position:0% +woman Kathy Shrock and um, if you Google +Kathy Shrock, it comes up. She comes up + + align:start position:0% +Kathy Shrock, it comes up. She comes up + + + align:start position:0% +Kathy Shrock, it comes up. She comes up +got a ton of stuff. But um she's done + + align:start position:0% +got a ton of stuff. But um she's done + + + align:start position:0% +got a ton of stuff. But um she's done +and this to get back to Bloom's taxonomy + + align:start position:0% +and this to get back to Bloom's taxonomy + + + align:start position:0% +and this to get back to Bloom's taxonomy +there is that she's taken Bloom's + + align:start position:0% +there is that she's taken Bloom's + + + align:start position:0% +there is that she's taken Bloom's +taxonomy remember understand apply + + align:start position:0% +taxonomy remember understand apply + + + align:start position:0% +taxonomy remember understand apply +analyze evaluate create and then she + + align:start position:0% +analyze evaluate create and then she + + + align:start position:0% +analyze evaluate create and then she +said okay well here's some apps that can + + align:start position:0% +said okay well here's some apps that can + + + align:start position:0% +said okay well here's some apps that can +facilitate those + + align:start position:0% +facilitate those + + + align:start position:0% +facilitate those +things facilitate the act of remembering + + align:start position:0% +things facilitate the act of remembering + + + align:start position:0% +things facilitate the act of remembering +or facilitate the act of evaluating or + + align:start position:0% +or facilitate the act of evaluating or + + + align:start position:0% +or facilitate the act of evaluating or +creating. So it's not mutually + + align:start position:0% +creating. So it's not mutually + + + align:start position:0% +creating. So it's not mutually +exclusive. It's not it's not, you know, + + align:start position:0% +exclusive. It's not it's not, you know, + + + align:start position:0% +exclusive. It's not it's not, you know, +it's not um exhaustive, but it is + + align:start position:0% +it's not um exhaustive, but it is + + + align:start position:0% +it's not um exhaustive, but it is +important to remember that some things + + align:start position:0% +important to remember that some things + + + align:start position:0% +important to remember that some things +really are lending some of these tools + + align:start position:0% +really are lending some of these tools + + + align:start position:0% +really are lending some of these tools +are supporting remembering or they're + + align:start position:0% +are supporting remembering or they're + + + align:start position:0% +are supporting remembering or they're +supporting uh some other level + + align:start position:0% +supporting uh some other level + + + align:start position:0% +supporting uh some other level +understanding, but they're not + + align:start position:0% +understanding, but they're not + + + align:start position:0% +understanding, but they're not +necessarily, you know, at the highest + + align:start position:0% +necessarily, you know, at the highest + + + align:start position:0% +necessarily, you know, at the highest +level or they're not at the lowest + + align:start position:0% +level or they're not at the lowest + + + align:start position:0% +level or they're not at the lowest +level. They it's good to be aware of + + align:start position:0% + + + + align:start position:0% + +that. Before I charge you with your your + + align:start position:0% +that. Before I charge you with your your + + + align:start position:0% +that. Before I charge you with your your +assignment, I did want to + + align:start position:0% +assignment, I did want to + + + align:start position:0% +assignment, I did want to +um demo a few other technologies just + + align:start position:0% +um demo a few other technologies just + + + align:start position:0% +um demo a few other technologies just +just so you could take a look at them. + + align:start position:0% +just so you could take a look at them. + + + align:start position:0% +just so you could take a look at them. +And there was that list in the reading + + align:start position:0% +And there was that list in the reading + + + align:start position:0% +And there was that list in the reading +which I hope you checked out. + + align:start position:0% +which I hope you checked out. + + + align:start position:0% +which I hope you checked out. +Um I invited you to this + + align:start position:0% +Um I invited you to this + + + align:start position:0% +Um I invited you to this +um I thought I invited you. Oh, wait a + + align:start position:0% +um I thought I invited you. Oh, wait a + + + align:start position:0% +um I thought I invited you. Oh, wait a +minute. + + align:start position:0% +minute. + + + align:start position:0% +minute. +Huh? Hang on. It's on the Well, let's + + align:start position:0% +Huh? Hang on. It's on the Well, let's + + + align:start position:0% +Huh? Hang on. It's on the Well, let's +just start up a new one. + + align:start position:0% + + + + align:start position:0% + +Um, so I can create this this uh picture + + align:start position:0% + + + + align:start position:0% + +here and I can share this then with you. + + align:start position:0% +here and I can share this then with you. + + + align:start position:0% +here and I can share this then with you. +Um, + + align:start position:0% + + + + align:start position:0% + +um, and I can invite the + + align:start position:0% +um, and I can invite the + + + align:start position:0% +um, and I can invite the +board. And so this is the link and if + + align:start position:0% +board. And so this is the link and if + + + align:start position:0% +board. And so this is the link and if +you have a device and want to log in + + align:start position:0% +you have a device and want to log in + + + align:start position:0% +you have a device and want to log in +there, you can check it + + align:start position:0% +there, you can check it + + + align:start position:0% +there, you can check it +out and then you can write on + + align:start position:0% +out and then you can write on + + + align:start position:0% +out and then you can write on +it. Oh, somebody wrote on it. Somebody + + align:start position:0% +it. Oh, somebody wrote on it. Somebody + + + align:start position:0% +it. Oh, somebody wrote on it. Somebody +erased my + + align:start position:0% + + + + align:start position:0% + +picture. I don't know who that was. + + align:start position:0% + + + + align:start position:0% + +Is that a UP? + + align:start position:0% +Is that a UP? + + + align:start position:0% +Is that a UP? +U QPL. + + align:start position:0% + + + + align:start position:0% + +Anybody? That's different from the link + + align:start position:0% +Anybody? That's different from the link + + + align:start position:0% +Anybody? That's different from the link +that was in the wiki. I I know. I just + + align:start position:0% +that was in the wiki. I I know. I just + + + align:start position:0% +that was in the wiki. I I know. I just +created a new one because I didn't want + + align:start position:0% +created a new one because I didn't want + + + align:start position:0% +created a new one because I didn't want +to go look for the wiki link. + + align:start position:0% + + + + align:start position:0% + +So, this is free. This is free. Yeah. + + align:start position:0% +So, this is free. This is free. Yeah. + + + align:start position:0% +So, this is free. This is free. Yeah. +Um, so we're working a little backwards + + align:start position:0% +Um, so we're working a little backwards + + + align:start position:0% +Um, so we're working a little backwards +here. I'm showing you the tool and now + + align:start position:0% +here. I'm showing you the tool and now + + + align:start position:0% +here. I'm showing you the tool and now +I'm asking you what you might want to do + + align:start position:0% +I'm asking you what you might want to do + + + align:start position:0% +I'm asking you what you might want to do +with it, which I is not necessarily best + + align:start position:0% +with it, which I is not necessarily best + + + align:start position:0% +with it, which I is not necessarily best +practice, but um I have a use that I + + align:start position:0% +practice, but um I have a use that I + + + align:start position:0% +practice, but um I have a use that I +um you can change the color. This thing, + + align:start position:0% +um you can change the color. This thing, + + + align:start position:0% +um you can change the color. This thing, +this pen here changes the color. Uh no, + + align:start position:0% +this pen here changes the color. Uh no, + + + align:start position:0% +this pen here changes the color. Uh no, +something changes the color. + + align:start position:0% + + + + align:start position:0% + +Maybe not. Um + + align:start position:0% +Maybe not. Um + + + align:start position:0% +Maybe not. Um +Oh, somebody got blue. Um uh I teach + + align:start position:0% +Oh, somebody got blue. Um uh I teach + + + align:start position:0% +Oh, somebody got blue. Um uh I teach +when I taught thermodynamics we would + + align:start position:0% +when I taught thermodynamics we would + + + align:start position:0% +when I taught thermodynamics we would +often do sketches. I'd say okay sketch + + align:start position:0% +often do sketches. I'd say okay sketch + + + align:start position:0% +often do sketches. I'd say okay sketch +the Gibbs free + + align:start position:0% +the Gibbs free + + + align:start position:0% +the Gibbs free +energy versus temperature gives energy + + align:start position:0% +energy versus temperature gives energy + + + align:start position:0% +energy versus temperature gives energy +versus pressure. Tell me what the what's + + align:start position:0% +versus pressure. Tell me what the what's + + + align:start position:0% +versus pressure. Tell me what the what's +the uh you know tell me what the uh the + + align:start position:0% +the uh you know tell me what the uh the + + + align:start position:0% +the uh you know tell me what the uh the +first derivative of of G with respect to + + align:start position:0% +first derivative of of G with respect to + + + align:start position:0% +first derivative of of G with respect to +T is things like that. Sketch sketch the + + align:start position:0% +T is things like that. Sketch sketch the + + + align:start position:0% +T is things like that. Sketch sketch the +slope catch sketch the curvature etc. + + align:start position:0% +slope catch sketch the curvature etc. + + + align:start position:0% +slope catch sketch the curvature etc. +And so this kind of application is you + + align:start position:0% +And so this kind of application is you + + + align:start position:0% +And so this kind of application is you +could have a student you could have + + align:start position:0% +could have a student you could have + + + align:start position:0% +could have a student you could have +students log in do that kind of a sketch + + align:start position:0% +students log in do that kind of a sketch + + + align:start position:0% +students log in do that kind of a sketch +and then people can people can evaluate + + align:start position:0% +and then people can people can evaluate + + + align:start position:0% +and then people can people can evaluate +it. It's anonymous. You can see I can't + + align:start position:0% +it. It's anonymous. You can see I can't + + + align:start position:0% +it. It's anonymous. You can see I can't +tell who said what except David who + + align:start position:0% +tell who said what except David who + + + align:start position:0% +tell who said what except David who +wrote his name. Um but um I can't see + + align:start position:0% +wrote his name. Um but um I can't see + + + align:start position:0% +wrote his name. Um but um I can't see +who did what. So so that it could work + + align:start position:0% +who did what. So so that it could work + + + align:start position:0% +who did what. So so that it could work +pretty well in a in a small class. If + + align:start position:0% +pretty well in a in a small class. If + + + align:start position:0% +pretty well in a in a small class. If +you had a class of 400 people, I'd be + + align:start position:0% +you had a class of 400 people, I'd be + + + align:start position:0% +you had a class of 400 people, I'd be +afraid, + + align:start position:0% +afraid, + + + align:start position:0% +afraid, +right? I'd be very afraid. But um but in + + align:start position:0% +right? I'd be very afraid. But um but in + + + align:start position:0% +right? I'd be very afraid. But um but in +a in a small class, you can come up with + + align:start position:0% +a in a small class, you can come up with + + + align:start position:0% +a in a small class, you can come up with +with some interesting uses of it. It it + + align:start position:0% +with some interesting uses of it. It it + + + align:start position:0% +with some interesting uses of it. It it +the good thing about it is that you + + align:start position:0% +the good thing about it is that you + + + align:start position:0% +the good thing about it is that you +don't have students coming up to the + + align:start position:0% +don't have students coming up to the + + + align:start position:0% +don't have students coming up to the +board. There's a it minimizes that + + align:start position:0% +board. There's a it minimizes that + + + align:start position:0% +board. There's a it minimizes that +motion, the sort of getting everybody + + align:start position:0% +motion, the sort of getting everybody + + + align:start position:0% +motion, the sort of getting everybody +unsettled and settled again. Um it's not + + align:start position:0% +unsettled and settled again. Um it's not + + + align:start position:0% +unsettled and settled again. Um it's not +a cure. I wouldn't say this is this + + align:start position:0% +a cure. I wouldn't say this is this + + + align:start position:0% +a cure. I wouldn't say this is this +redefineses anything in terms of the SAM + + align:start position:0% +redefineses anything in terms of the SAM + + + align:start position:0% +redefineses anything in terms of the SAM +model. I'd say it's probably a + + align:start position:0% +model. I'd say it's probably a + + + align:start position:0% +model. I'd say it's probably a +modification, maybe an augmentation, + + align:start position:0% +modification, maybe an augmentation, + + + align:start position:0% +modification, maybe an augmentation, +maybe. I don't know. But it's certainly + + align:start position:0% +maybe. I don't know. But it's certainly + + + align:start position:0% +maybe. I don't know. But it's certainly +not um it's certainly not an + + align:start position:0% +not um it's certainly not an + + + align:start position:0% +not um it's certainly not an +R. Um so I wanted to just demo that + + align:start position:0% +R. Um so I wanted to just demo that + + + align:start position:0% +R. Um so I wanted to just demo that +because it's kind of fun. Um the other + + align:start position:0% +because it's kind of fun. Um the other + + + align:start position:0% +because it's kind of fun. Um the other +thing I wanted to do is I think you guys + + align:start position:0% +thing I wanted to do is I think you guys + + + align:start position:0% +thing I wanted to do is I think you guys +saw this list. Did you see this list on + + align:start position:0% +saw this list. Did you see this list on + + + align:start position:0% +saw this list. Did you see this list on +the from the + + align:start position:0% +the from the + + + align:start position:0% +the from the +readings? This is just some things that + + align:start position:0% +readings? This is just some things that + + + align:start position:0% +readings? This is just some things that +I've compiled. It's kind of a mishmash, + + align:start position:0% +I've compiled. It's kind of a mishmash, + + + align:start position:0% +I've compiled. It's kind of a mishmash, +but um there's some interesting things + + align:start position:0% +but um there's some interesting things + + + align:start position:0% +but um there's some interesting things +on here that you might want to explore + + align:start position:0% +on here that you might want to explore + + + align:start position:0% +on here that you might want to explore +depending on your um on your teaching + + align:start position:0% +depending on your um on your teaching + + + align:start position:0% +depending on your um on your teaching +what on your learning outcomes. Uh, and + + align:start position:0% +what on your learning outcomes. Uh, and + + + align:start position:0% +what on your learning outcomes. Uh, and +we've used back channel. Today's meet is + + align:start position:0% +we've used back channel. Today's meet is + + + align:start position:0% +we've used back channel. Today's meet is +pretty similar to back channel. Um, back + + align:start position:0% +pretty similar to back channel. Um, back + + + align:start position:0% +pretty similar to back channel. Um, back +channel chat is pretty similar to back + + align:start position:0% +channel chat is pretty similar to back + + + align:start position:0% +channel chat is pretty similar to back +channel. So, those are some things that + + align:start position:0% +channel. So, those are some things that + + + align:start position:0% +channel. So, those are some things that +are are pretty similar. We just looked + + align:start position:0% +are are pretty similar. We just looked + + + align:start position:0% +are are pretty similar. We just looked +at um the web app. We've used clickers. + + align:start position:0% +at um the web app. We've used clickers. + + + align:start position:0% +at um the web app. We've used clickers. +Um, we've talked about Siccat, which is + + align:start position:0% +Um, we've talked about Siccat, which is + + + align:start position:0% +Um, we've talked about Siccat, which is +this uh just a cell phone based + + align:start position:0% +this uh just a cell phone based + + + align:start position:0% +this uh just a cell phone based +clicker. Um, but there's a lot of a lot + + align:start position:0% +clicker. Um, but there's a lot of a lot + + + align:start position:0% +clicker. Um, but there's a lot of a lot +of interesting uh uses and you you might + + align:start position:0% +of interesting uh uses and you you might + + + align:start position:0% +of interesting uh uses and you you might +want to just play around with them. Um + + align:start position:0% +want to just play around with them. Um + + + align:start position:0% +want to just play around with them. Um +there's also and I'll augment this list. + + align:start position:0% +there's also and I'll augment this list. + + + align:start position:0% +there's also and I'll augment this list. +So when you go if you click it again + + align:start position:0% +So when you go if you click it again + + + align:start position:0% +So when you go if you click it again +from the from the wiki you'll get a + + align:start position:0% +from the from the wiki you'll get a + + + align:start position:0% +from the from the wiki you'll get a +augmented list of things. A few things I + + align:start position:0% +augmented list of things. A few things I + + + align:start position:0% +augmented list of things. A few things I +want to add to it. Um so + + align:start position:0% + + + + align:start position:0% + +now given your experience in life and + + align:start position:0% +now given your experience in life and + + + align:start position:0% +now given your experience in life and +the readings etc is that I'd like for + + align:start position:0% +the readings etc is that I'd like for + + + align:start position:0% +the readings etc is that I'd like for +you to think about um think about a + + align:start position:0% +you to think about um think about a + + + align:start position:0% +you to think about um think about a +technology that you haven't used before. + + align:start position:0% +technology that you haven't used before. + + + align:start position:0% +technology that you haven't used before. +Actually, what you want to do first is + + align:start position:0% +Actually, what you want to do first is + + + align:start position:0% +Actually, what you want to do first is +think about a learning outcome. Um, but + + align:start position:0% +think about a learning outcome. Um, but + + + align:start position:0% +think about a learning outcome. Um, but +um, you want to think about a learning + + align:start position:0% +um, you want to think about a learning + + + align:start position:0% +um, you want to think about a learning +outcome. You want to think about um, a + + align:start position:0% +outcome. You want to think about um, a + + + align:start position:0% +outcome. You want to think about um, a +technology that might advance that + + align:start position:0% +technology that might advance that + + + align:start position:0% +technology that might advance that +learning outcome. And then just jot down + + align:start position:0% +learning outcome. And then just jot down + + + align:start position:0% +learning outcome. And then just jot down +why you chose this + + align:start position:0% +why you chose this + + + align:start position:0% +why you chose this +technology, where does it fit in the SAM + + align:start position:0% +technology, where does it fit in the SAM + + + align:start position:0% +technology, where does it fit in the SAM +model, + + align:start position:0% +model, + + + align:start position:0% +model, +um, how you would use it in your class, + + align:start position:0% +um, how you would use it in your class, + + + align:start position:0% +um, how you would use it in your class, +any kind of difficulties, and then + + align:start position:0% +any kind of difficulties, and then + + + align:start position:0% +any kind of difficulties, and then +there's a Google doc. I'm pretty sure + + align:start position:0% +there's a Google doc. I'm pretty sure + + + align:start position:0% +there's a Google doc. I'm pretty sure +everybody can access it. We can only + + align:start position:0% +everybody can access it. We can only + + + align:start position:0% +everybody can access it. We can only +hope. Um, and if you can type your + + align:start position:0% +hope. Um, and if you can type your + + + align:start position:0% +hope. Um, and if you can type your +responses into that. So, I'm going to + + align:start position:0% +responses into that. So, I'm going to + + + align:start position:0% +responses into that. So, I'm going to +give you about five, seven minutes for + + align:start position:0% +give you about five, seven minutes for + + + align:start position:0% +give you about five, seven minutes for +that activity and then we're going to do + + align:start position:0% +that activity and then we're going to do + + + align:start position:0% +that activity and then we're going to do +a lightning round based on it. So, so + + align:start position:0% +a lightning round based on it. So, so + + + align:start position:0% +a lightning round based on it. So, so +use whatever um use the handouts, use + + align:start position:0% +use whatever um use the handouts, use + + + align:start position:0% +use whatever um use the handouts, use +your knowledge, use etc. But um and then + + align:start position:0% +your knowledge, use etc. But um and then + + + align:start position:0% +your knowledge, use etc. But um and then +somebody can tell me really quickly if + + align:start position:0% +somebody can tell me really quickly if + + + align:start position:0% +somebody can tell me really quickly if +they can get into the Google doc. So, + + align:start position:0% +they can get into the Google doc. So, + + + align:start position:0% +they can get into the Google doc. So, +yeah, you guys are good. I I was going + + align:start position:0% +yeah, you guys are good. I I was going + + + align:start position:0% +yeah, you guys are good. I I was going +to say write your name down, but it + + align:start position:0% +to say write your name down, but it + + + align:start position:0% +to say write your name down, but it +doesn't really matter whether your + + align:start position:0% +doesn't really matter whether your + + + align:start position:0% +doesn't really matter whether your +name's up or not. So, um, so I want to + + align:start position:0% +name's up or not. So, um, so I want to + + + align:start position:0% +name's up or not. So, um, so I want to +make sure that you take a look at + + align:start position:0% +make sure that you take a look at + + + align:start position:0% +make sure that you take a look at +everybody else's some of the learning + + align:start position:0% +everybody else's some of the learning + + + align:start position:0% +everybody else's some of the learning +outcomes. We're going to do this + + align:start position:0% +outcomes. We're going to do this + + + align:start position:0% +outcomes. We're going to do this +lightning round where you're going to be + + align:start position:0% +lightning round where you're going to be + + + align:start position:0% +lightning round where you're going to be +talking to other people about their + + align:start position:0% +talking to other people about their + + + align:start position:0% +talking to other people about their +about the technology they chose, their + + align:start position:0% +about the technology they chose, their + + + align:start position:0% +about the technology they chose, their +learning outcome, why they chose it, + + align:start position:0% +learning outcome, why they chose it, + + + align:start position:0% +learning outcome, why they chose it, +etc. and you're going to be trying to + + align:start position:0% +etc. and you're going to be trying to + + + align:start position:0% +etc. and you're going to be trying to +help your partner uh troubleshoot or + + align:start position:0% +help your partner uh troubleshoot or + + + align:start position:0% +help your partner uh troubleshoot or +perhaps implement the technology in a + + align:start position:0% +perhaps implement the technology in a + + + align:start position:0% +perhaps implement the technology in a +better way, solve some of their problems + + align:start position:0% +better way, solve some of their problems + + + align:start position:0% +better way, solve some of their problems +uh with the implementation process or + + align:start position:0% +uh with the implementation process or + + + align:start position:0% +uh with the implementation process or +perhaps think about a different + + align:start position:0% +perhaps think about a different + + + align:start position:0% +perhaps think about a different +technology al together given their + + align:start position:0% +technology al together given their + + + align:start position:0% +technology al together given their +desired learning outcomes. So we let's + + align:start position:0% +desired learning outcomes. So we let's + + + align:start position:0% +desired learning outcomes. So we let's +just take a minute and either read it on + + align:start position:0% +just take a minute and either read it on + + + align:start position:0% +just take a minute and either read it on +your own device or read it up here so + + align:start position:0% +your own device or read it up here so + + + align:start position:0% +your own device or read it up here so +that we can so that you kind of get a + + align:start position:0% +that we can so that you kind of get a + + + align:start position:0% +that we can so that you kind of get a +sense for what we're um what you're + + align:start position:0% +sense for what we're um what you're + + + align:start position:0% +sense for what we're um what you're +going to be talking about. Okay. And if + + align:start position:0% +going to be talking about. Okay. And if + + + align:start position:0% +going to be talking about. Okay. And if +Yeah, that's okay. Okay. And if you + + align:start position:0% +Yeah, that's okay. Okay. And if you + + + align:start position:0% +Yeah, that's okay. Okay. And if you +haven't read it, + + align:start position:0% +haven't read it, + + + align:start position:0% +haven't read it, +um, if you haven't read over it, please + + align:start position:0% +um, if you haven't read over it, please + + + align:start position:0% +um, if you haven't read over it, please +do that + + align:start position:0% + + + + align:start position:0% + +now. So, there's some really interesting + + align:start position:0% +now. So, there's some really interesting + + + align:start position:0% +now. So, there's some really interesting +ideas up here, I think. Um, and a big a + + align:start position:0% +ideas up here, I think. Um, and a big a + + + align:start position:0% +ideas up here, I think. Um, and a big a +broad spectrum of of + + align:start position:0% +broad spectrum of of + + + align:start position:0% +broad spectrum of of +uh of + + align:start position:0% +uh of + + + align:start position:0% +uh of +ambition, right? right? We have some + + align:start position:0% +ambition, right? right? We have some + + + align:start position:0% +ambition, right? right? We have some +pretty small tech like assignment one + + align:start position:0% +pretty small tech like assignment one + + + align:start position:0% +pretty small tech like assignment one +assignments worth of technology perhaps + + align:start position:0% +assignments worth of technology perhaps + + + align:start position:0% +assignments worth of technology perhaps +and then we also have kind of a whole + + align:start position:0% +and then we also have kind of a whole + + + align:start position:0% +and then we also have kind of a whole +course uh + + align:start position:0% +course uh + + + align:start position:0% +course uh +design. So So that's another thing we + + align:start position:0% +design. So So that's another thing we + + + align:start position:0% +design. So So that's another thing we +didn't really talk about. I mean I + + align:start position:0% +didn't really talk about. I mean I + + + align:start position:0% +didn't really talk about. I mean I +didn't narrow the scope in any in any + + align:start position:0% +didn't narrow the scope in any in any + + + align:start position:0% +didn't narrow the scope in any in any +way or define the scope in any way. So + + align:start position:0% +way or define the scope in any way. So + + + align:start position:0% +way or define the scope in any way. So +could be for a whole class, it could be + + align:start position:0% +could be for a whole class, it could be + + + align:start position:0% +could be for a whole class, it could be +for um one particular assignment or one + + align:start position:0% +for um one particular assignment or one + + + align:start position:0% +for um one particular assignment or one +particular course activi class activity + + align:start position:0% +particular course activi class activity + + + align:start position:0% +particular course activi class activity +and that's fine. That's okay. + + align:start position:0% +and that's fine. That's okay. + + + align:start position:0% +and that's fine. That's okay. +Um, so does everybody did everybody get + + align:start position:0% +Um, so does everybody did everybody get + + + align:start position:0% +Um, so does everybody did everybody get +a chance to look over the other posts? + + align:start position:0% +a chance to look over the other posts? + + + align:start position:0% +a chance to look over the other posts? +I'll + + align:start position:0% +I'll + + + align:start position:0% +I'll +say I have had the past two things. So + + align:start position:0% +say I have had the past two things. So + + + align:start position:0% +say I have had the past two things. So +here's a pitfall of of all these things + + align:start position:0% +here's a pitfall of of all these things + + + align:start position:0% +here's a pitfall of of all these things +that I when the um the the AWW where + + align:start position:0% +that I when the um the the AWW where + + + align:start position:0% +that I when the um the the AWW where +everyone was drawing um I could draw + + align:start position:0% +everyone was drawing um I could draw + + + align:start position:0% +everyone was drawing um I could draw +here but it was never showing up there. + + align:start position:0% +here but it was never showing up there. + + + align:start position:0% +here but it was never showing up there. +Interesting. Oh yeah. My thing never + + align:start position:0% +Interesting. Oh yeah. My thing never + + + align:start position:0% +Interesting. Oh yeah. My thing never +showed up. Yeah. And then the other + + align:start position:0% +showed up. Yeah. And then the other + + + align:start position:0% +showed up. Yeah. And then the other +thing with this now um with the Google + + align:start position:0% +thing with this now um with the Google + + + align:start position:0% +thing with this now um with the Google +doc I tried to um edit it and it doesn't + + align:start position:0% +doc I tried to um edit it and it doesn't + + + align:start position:0% +doc I tried to um edit it and it doesn't +let me click on it says do you want to + + align:start position:0% +let me click on it says do you want to + + + align:start position:0% +let me click on it says do you want to +use the app? So then I had to download + + align:start position:0% +use the app? So then I had to download + + + align:start position:0% +use the app? So then I had to download +the app and now I say yes use the app + + align:start position:0% +the app and now I say yes use the app + + + align:start position:0% +the app and now I say yes use the app +and then it says um something about the + + align:start position:0% +and then it says um something about the + + + align:start position:0% +and then it says um something about the +server not being recognized. But then if + + align:start position:0% +server not being recognized. But then if + + + align:start position:0% +server not being recognized. But then if +I go back and say no thanks and I try to + + align:start position:0% +I go back and say no thanks and I try to + + + align:start position:0% +I go back and say no thanks and I try to +use it um use it without the app, then I + + align:start position:0% +use it um use it without the app, then I + + + align:start position:0% +use it um use it without the app, then I +can't put anything in. Interesting. + + align:start position:0% +can't put anything in. Interesting. + + + align:start position:0% +can't put anything in. Interesting. +Okay. So who had trouble? Yeah, I + + align:start position:0% +Okay. So who had trouble? Yeah, I + + + align:start position:0% +Okay. So who had trouble? Yeah, I +downloaded the app. I'm using that. All + + align:start position:0% +downloaded the app. I'm using that. All + + + align:start position:0% +downloaded the app. I'm using that. All +right. And is that Did anybody that was + + align:start position:0% +right. And is that Did anybody that was + + + align:start position:0% +right. And is that Did anybody that was +using a smartphone uh have tr not have + + align:start position:0% +using a smartphone uh have tr not have + + + align:start position:0% +using a smartphone uh have tr not have +trouble? I didn't have trouble. You + + align:start position:0% +trouble? I didn't have trouble. You + + + align:start position:0% +trouble? I didn't have trouble. You +didn't have trouble? I know that I'm + + align:start position:0% +didn't have trouble? I know that I'm + + + align:start position:0% +didn't have trouble? I know that I'm +using Oh, yeah. Okay. And uh I were you + + align:start position:0% +using Oh, yeah. Okay. And uh I were you + + + align:start position:0% +using Oh, yeah. Okay. And uh I were you +on I an Android or Android? It's + + align:start position:0% +on I an Android or Android? It's + + + align:start position:0% +on I an Android or Android? It's +Android. Android. iPhone. + + align:start position:0% +Android. Android. iPhone. + + + align:start position:0% +Android. Android. iPhone. +iPhone. + + align:start position:0% +iPhone. + + + align:start position:0% +iPhone. +Who else had trouble? + + align:start position:0% +Who else had trouble? + + + align:start position:0% +Who else had trouble? +It was more than just the two of you, + + align:start position:0% +It was more than just the two of you, + + + align:start position:0% +It was more than just the two of you, +right? With this one. + + align:start position:0% +right? With this one. + + + align:start position:0% +right? With this one. +With this one, with this particular one, + + align:start position:0% +With this one, with this particular one, + + + align:start position:0% +With this one, with this particular one, +Rachel had problems with it. Um, so for + + align:start position:0% +Rachel had problems with it. Um, so for + + + align:start position:0% +Rachel had problems with it. Um, so for +now, if you wouldn't mind, just + + align:start position:0% +now, if you wouldn't mind, just + + + align:start position:0% +now, if you wouldn't mind, just +um, uh, let's see. I'd like to We don't + + align:start position:0% +um, uh, let's see. I'd like to We don't + + + align:start position:0% +um, uh, let's see. I'd like to We don't +have to complete this right now, but + + align:start position:0% +have to complete this right now, but + + + align:start position:0% +have to complete this right now, but +maybe if there's a lull, just come on + + align:start position:0% +maybe if there's a lull, just come on + + + align:start position:0% +maybe if there's a lull, just come on +over here and you can type your your app + + align:start position:0% +over here and you can type your your app + + + align:start position:0% +over here and you can type your your app +in just so we have a complete record, + + align:start position:0% +in just so we have a complete record, + + + align:start position:0% +in just so we have a complete record, +your uh, technology in. But that's an + + align:start position:0% +your uh, technology in. But that's an + + + align:start position:0% +your uh, technology in. But that's an +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +um it's a good thing to keep in mind + + align:start position:0% +um it's a good thing to keep in mind + + + align:start position:0% +um it's a good thing to keep in mind +that access might be an issue. I did try + + align:start position:0% +that access might be an issue. I did try + + + align:start position:0% +that access might be an issue. I did try +this out on two computers, but I tried + + align:start position:0% +this out on two computers, but I tried + + + align:start position:0% +this out on two computers, but I tried +them out on two computers and I didn't + + align:start position:0% +them out on two computers and I didn't + + + align:start position:0% +them out on two computers and I didn't +try phone. + + align:start position:0% +try phone. + + + align:start position:0% +try phone. +Do it after. Yeah, after is fine. + + align:start position:0% +Do it after. Yeah, after is fine. + + + align:start position:0% +Do it after. Yeah, after is fine. +Um so if we could get up and anybody + + align:start position:0% +Um so if we could get up and anybody + + + align:start position:0% +Um so if we could get up and anybody +else that didn't didn't wasn't able to + + align:start position:0% +else that didn't didn't wasn't able to + + + align:start position:0% +else that didn't didn't wasn't able to +input their ideas, if you can, we'll do + + align:start position:0% +input their ideas, if you can, we'll do + + + align:start position:0% +input their ideas, if you can, we'll do +it later. That's fine. + + align:start position:0% +it later. That's fine. + + + align:start position:0% +it later. That's fine. +So, we're going to do the lightning + + align:start position:0% +So, we're going to do the lightning + + + align:start position:0% +So, we're going to do the lightning +round. And if I could get um you + + align:start position:0% +round. And if I could get um you + + + align:start position:0% +round. And if I could get um you +gentlemen to come around and fill in the + + align:start position:0% +gentlemen to come around and fill in the + + + align:start position:0% +gentlemen to come around and fill in the +back. Just fill in up to + + align:start position:0% +back. Just fill in up to + + + align:start position:0% +back. Just fill in up to +here. Um great. So, what we're going to + + align:start position:0% +here. Um great. So, what we're going to + + + align:start position:0% +here. Um great. So, what we're going to +do is I'm going to ask the row in the + + align:start position:0% +do is I'm going to ask the row in the + + + align:start position:0% +do is I'm going to ask the row in the +back, this row to um share their + + align:start position:0% +back, this row to um share their + + + align:start position:0% +back, this row to um share their +technology, their their their intended + + align:start position:0% +technology, their their their intended + + + align:start position:0% +technology, their their their intended +learning outcome, their concern. Uh, and + + align:start position:0% +learning outcome, their concern. Uh, and + + + align:start position:0% +learning outcome, their concern. Uh, and +then the other the this row will give + + align:start position:0% +then the other the this row will give + + + align:start position:0% +then the other the this row will give +their advice and it's two minutes for + + align:start position:0% +their advice and it's two minutes for + + + align:start position:0% +their advice and it's two minutes for +the whole process and then we'll switch. + + align:start position:0% +the whole process and then we'll switch. + + + align:start position:0% +the whole process and then we'll switch. +Okay. So, what do I do? So, you just + + align:start position:0% +Okay. So, what do I do? So, you just + + + align:start position:0% +Okay. So, what do I do? So, you just +have to tell me what you're going to + + align:start position:0% +have to tell me what you're going to + + + align:start position:0% +have to tell me what you're going to +tell me more or less what you wrote on + + align:start position:0% +tell me more or less what you wrote on + + + align:start position:0% +tell me more or less what you wrote on +the screen. Okay. But hold on. I got to + + align:start position:0% +the screen. Okay. But hold on. I got to + + + align:start position:0% +the screen. Okay. But hold on. I got to +set the timer. + + align:start position:0% + + + + align:start position:0% + +Okay. Go. All right. Now the kind of + + align:start position:0% +Okay. Go. All right. Now the kind of + + + align:start position:0% +Okay. Go. All right. Now the kind of +technology that I pick to use is called + + align:start position:0% +technology that I pick to use is called + + + align:start position:0% +technology that I pick to use is called +entry point. The department pays + + align:start position:0% +entry point. The department pays + + + align:start position:0% +entry point. The department pays +subscription for it annually. So it's + + align:start position:0% +subscription for it annually. So it's + + + align:start position:0% +subscription for it annually. So it's +not very it's not available like free + + align:start position:0% +not very it's not available like free + + + align:start position:0% +not very it's not available like free +going to um is going to share their um + + align:start position:0% +going to um is going to share their um + + + align:start position:0% +going to um is going to share their um +ideas with the other with the other + + align:start position:0% + + + + align:start position:0% + +side. I guess my only constraint would + + align:start position:0% +side. I guess my only constraint would + + + align:start position:0% +side. I guess my only constraint would +be not everyone. + + align:start position:0% + + + + align:start position:0% + +All right. So, so that's a very good + + align:start position:0% +All right. So, so that's a very good + + + align:start position:0% +All right. So, so that's a very good +idea. But what do you see as a + + align:start position:0% +idea. But what do you see as a + + + align:start position:0% +idea. But what do you see as a +difference between the tool you want to + + align:start position:0% +difference between the tool you want to + + + align:start position:0% +difference between the tool you want to +use and the one the professor is using? + + align:start position:0% +use and the one the professor is using? + + + align:start position:0% +use and the one the professor is using? +Dave, + + align:start position:0% +Dave, + + + align:start position:0% +Dave, +it's the moment you've been waiting for. + + align:start position:0% +it's the moment you've been waiting for. + + + align:start position:0% +it's the moment you've been waiting for. +Okay. So, we're going to do this this + + align:start position:0% +Okay. So, we're going to do this this + + + align:start position:0% +Okay. So, we're going to do this this +two more times. This time and one more + + align:start position:0% +two more times. This time and one more + + + align:start position:0% +two more times. This time and one more +time. Okay. + + align:start position:0% +time. Okay. + + + align:start position:0% +time. Okay. +All right. Now + + align:start position:0% + + + + align:start position:0% + +for for the course which I want to teach + + align:start position:0% +for for the course which I want to teach + + + align:start position:0% +for for the course which I want to teach +using uh uh educational technology. So + + align:start position:0% +using uh uh educational technology. So + + + align:start position:0% +using uh uh educational technology. So +it was a big challenge because the head + + align:start position:0% +it was a big challenge because the head + + + align:start position:0% +it was a big challenge because the head +of department wanted to say no but then + + align:start position:0% +of department wanted to say no but then + + + align:start position:0% +of department wanted to say no but then +it continued because many of the + + align:start position:0% +it continued because many of the + + + align:start position:0% +it continued because many of the +professor already prefer it. So does it + + align:start position:0% +professor already prefer it. So does it + + + align:start position:0% +professor already prefer it. So does it +like input equations like easy? Yeah. + + align:start position:0% +like input equations like easy? Yeah. + + + align:start position:0% +like input equations like easy? Yeah. +enable you to do anything and and and + + align:start position:0% +enable you to do anything and and and + + + align:start position:0% +enable you to do anything and and and +it's you can reconfigure it. Al if you + + align:start position:0% +it's you can reconfigure it. Al if you + + + align:start position:0% +it's you can reconfigure it. Al if you +come around + + align:start position:0% +come around + + + align:start position:0% +come around +and then uh Tessine yes if you come + + align:start position:0% +and then uh Tessine yes if you come + + + align:start position:0% +and then uh Tessine yes if you come +around please everybody slide down uh we + + align:start position:0% +around please everybody slide down uh we + + + align:start position:0% +around please everybody slide down uh we +already went that way or you went that + + align:start position:0% +already went that way or you went that + + + align:start position:0% +already went that way or you went that +way. We already saw those people. Okay, + + align:start position:0% +way. We already saw those people. Okay, + + + align:start position:0% +way. We already saw those people. Okay, +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +for seen I haven't seen right um anyone. + + align:start position:0% +for seen I haven't seen right um anyone. + + + align:start position:0% +for seen I haven't seen right um anyone. +Okay, please come on over. This is more + + align:start position:0% +Okay, please come on over. This is more + + + align:start position:0% +Okay, please come on over. This is more +difficult. Okay, so my or my intended + + align:start position:0% +difficult. Okay, so my or my intended + + + align:start position:0% +difficult. Okay, so my or my intended +learning outcome in general was for + + align:start position:0% +learning outcome in general was for + + + align:start position:0% +learning outcome in general was for +students to better understand and be + + align:start position:0% +students to better understand and be + + + align:start position:0% +students to better understand and be +able to explain the 20 people sitting on + + align:start position:0% +able to explain the 20 people sitting on + + + align:start position:0% +able to explain the 20 people sitting on +a computer talking to the to the message + + align:start position:0% +a computer talking to the to the message + + + align:start position:0% +a computer talking to the to the message +board instead of them just talking to + + align:start position:0% +board instead of them just talking to + + + align:start position:0% +board instead of them just talking to +each other. So I think it's got + + align:start position:0% + + + + align:start position:0% + +access + + align:start position:0% +access + + + align:start position:0% +access +money. I I think it cost like $15. I'm + + align:start position:0% +money. I I think it cost like $15. I'm + + + align:start position:0% +money. I I think it cost like $15. I'm +not sure if that's pretty. + + align:start position:0% +not sure if that's pretty. + + + align:start position:0% +not sure if that's pretty. +So I know in my uh in my conversations I + + align:start position:0% +So I know in my uh in my conversations I + + + align:start position:0% +So I know in my uh in my conversations I +I heard some really interesting ideas, + + align:start position:0% +I heard some really interesting ideas, + + + align:start position:0% +I heard some really interesting ideas, +some some uh fascinating uh uses and + + align:start position:0% +some some uh fascinating uh uses and + + + align:start position:0% +some some uh fascinating uh uses and +some incredible obstacles. Um, I'll just + + align:start position:0% +some incredible obstacles. Um, I'll just + + + align:start position:0% +some incredible obstacles. Um, I'll just +point out David's obstacle. It's on the + + align:start position:0% +point out David's obstacle. It's on the + + + align:start position:0% +point out David's obstacle. It's on the +It's on the spreadsheet, but he wants to + + align:start position:0% +It's on the spreadsheet, but he wants to + + + align:start position:0% +It's on the spreadsheet, but he wants to +use this piece of software and it cost + + align:start position:0% +use this piece of software and it cost + + + align:start position:0% +use this piece of software and it cost +$12,000 a + + align:start position:0% +$12,000 a + + + align:start position:0% +$12,000 a +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +year. So, it sounds fabulous. Sounds + + align:start position:0% +year. So, it sounds fabulous. Sounds + + + align:start position:0% +year. So, it sounds fabulous. Sounds +really fabulous. Um, and your department + + align:start position:0% +really fabulous. Um, and your department + + + align:start position:0% +really fabulous. Um, and your department +actually bought it for you. Yeah. Have + + align:start position:0% +actually bought it for you. Yeah. Have + + + align:start position:0% +actually bought it for you. Yeah. Have +it for all the faculty, all the faculty. + + align:start position:0% +it for all the faculty, all the faculty. + + + align:start position:0% +it for all the faculty, all the faculty. +Yeah. So, that's great. But that that's + + align:start position:0% +Yeah. So, that's great. But that that's + + + align:start position:0% +Yeah. So, that's great. But that that's +a huge hurdle. I mean, that so there's + + align:start position:0% +a huge hurdle. I mean, that so there's + + + align:start position:0% +a huge hurdle. I mean, that so there's +an example of of, you know, like + + align:start position:0% +an example of of, you know, like + + + align:start position:0% +an example of of, you know, like +trade-offs that you might not always be + + align:start position:0% +trade-offs that you might not always be + + + align:start position:0% +trade-offs that you might not always be +able to make. Um so um that was my + + align:start position:0% +able to make. Um so um that was my + + + align:start position:0% +able to make. Um so um that was my +interesting um so u but I did hear some + + align:start position:0% +interesting um so u but I did hear some + + + align:start position:0% +interesting um so u but I did hear some +other wonderful ones too. So I hope that + + align:start position:0% +other wonderful ones too. So I hope that + + + align:start position:0% +other wonderful ones too. So I hope that +you take a look at it. You'll note that + + align:start position:0% +you take a look at it. You'll note that + + + align:start position:0% +you take a look at it. You'll note that +I always give you time after this this + + align:start position:0% +I always give you time after this this + + + align:start position:0% +I always give you time after this this +this uh lightning round because it's a + + align:start position:0% +this uh lightning round because it's a + + + align:start position:0% +this uh lightning round because it's a +noisy it's a very noisy kind of little + + align:start position:0% +noisy it's a very noisy kind of little + + + align:start position:0% +noisy it's a very noisy kind of little +crazy exercise and I always like to give + + align:start position:0% +crazy exercise and I always like to give + + + align:start position:0% +crazy exercise and I always like to give +you a few minutes of silence afterwards + + align:start position:0% +you a few minutes of silence afterwards + + + align:start position:0% +you a few minutes of silence afterwards +to sort of process it a little bit + + align:start position:0% +to sort of process it a little bit + + + align:start position:0% +to sort of process it a little bit +because it can be a bit of an overload. + + align:start position:0% +because it can be a bit of an overload. + + + align:start position:0% +because it can be a bit of an overload. +So that's that's sort of the part of the + + align:start position:0% +So that's that's sort of the part of the + + + align:start position:0% +So that's that's sort of the part of the +design or the planning for this + + align:start position:0% +design or the planning for this + + + align:start position:0% +design or the planning for this +exercise. Um any anything anybody want + + align:start position:0% +exercise. Um any anything anybody want + + + align:start position:0% +exercise. Um any anything anybody want +to share about something they learned or + + align:start position:0% +to share about something they learned or + + + align:start position:0% +to share about something they learned or +some issue or problem that was solved or + + align:start position:0% +some issue or problem that was solved or + + + align:start position:0% +some issue or problem that was solved or +still + + align:start position:0% + + + + align:start position:0% + +unsolved? All right. Um I see some + + align:start position:0% +unsolved? All right. Um I see some + + + align:start position:0% +unsolved? All right. Um I see some +people are still typing. + + align:start position:0% +people are still typing. + + + align:start position:0% +people are still typing. +Um I'm going to I'm going to go on. Feel + + align:start position:0% +Um I'm going to I'm going to go on. Feel + + + align:start position:0% +Um I'm going to I'm going to go on. Feel +free to keep adding to this. Um, and + + align:start position:0% +free to keep adding to this. Um, and + + + align:start position:0% +free to keep adding to this. Um, and +again, please take a look at it because + + align:start position:0% +again, please take a look at it because + + + align:start position:0% +again, please take a look at it because +we only got so many pairings and you can + + align:start position:0% +we only got so many pairings and you can + + + align:start position:0% +we only got so many pairings and you can +see virtually everything from the Google + + align:start position:0% +see virtually everything from the Google + + + align:start position:0% +see virtually everything from the Google +doc, assuming everybody gets + + align:start position:0% +doc, assuming everybody gets + + + align:start position:0% +doc, assuming everybody gets +in. + + align:start position:0% + + + + align:start position:0% + +Um, so what I wanted to do is flash back + + align:start position:0% +Um, so what I wanted to do is flash back + + + align:start position:0% +Um, so what I wanted to do is flash back +a little bit to what what we talked + + align:start position:0% +a little bit to what what we talked + + + align:start position:0% +a little bit to what what we talked +about the second day, the second class + + align:start position:0% +about the second day, the second class + + + align:start position:0% +about the second day, the second class +that we met. We talked about all these + + align:start position:0% +that we met. We talked about all these + + + align:start position:0% +that we met. We talked about all these +different learning theories about + + align:start position:0% +different learning theories about + + + align:start position:0% +different learning theories about +behaviorism, cognitivism, + + align:start position:0% +behaviorism, cognitivism, + + + align:start position:0% +behaviorism, cognitivism, +constructivism, and I think we've done + + align:start position:0% +constructivism, and I think we've done + + + align:start position:0% +constructivism, and I think we've done +some other exercise with these three + + align:start position:0% +some other exercise with these three + + + align:start position:0% +some other exercise with these three +three learning theories before, but it's + + align:start position:0% +three learning theories before, but it's + + + align:start position:0% +three learning theories before, but it's +a good chance for you to reflect back to + + align:start position:0% +a good chance for you to reflect back to + + + align:start position:0% +a good chance for you to reflect back to +do a little um backward transfer uh and + + align:start position:0% +do a little um backward transfer uh and + + + align:start position:0% +do a little um backward transfer uh and +to reinforce some of the concepts from + + align:start position:0% +to reinforce some of the concepts from + + + align:start position:0% +to reinforce some of the concepts from +the beginning of the semester and to + + align:start position:0% +the beginning of the semester and to + + + align:start position:0% +the beginning of the semester and to +also think about how technologies might + + align:start position:0% +also think about how technologies might + + + align:start position:0% +also think about how technologies might +be. So we talked about how technologies + + align:start position:0% +be. So we talked about how technologies + + + align:start position:0% +be. So we talked about how technologies +might fit at different levels of blooms + + align:start position:0% +might fit at different levels of blooms + + + align:start position:0% +might fit at different levels of blooms +or supports different levels of blooms + + align:start position:0% +or supports different levels of blooms + + + align:start position:0% +or supports different levels of blooms +but also different different + + align:start position:0% +but also different different + + + align:start position:0% +but also different different +technologies different any anything you + + align:start position:0% +technologies different any anything you + + + align:start position:0% +technologies different any anything you +do in the classroom but different the + + align:start position:0% +do in the classroom but different the + + + align:start position:0% +do in the classroom but different the +different use of different technologies + + align:start position:0% +different use of different technologies + + + align:start position:0% +different use of different technologies +can actually be more behaviorist + + align:start position:0% +can actually be more behaviorist + + + align:start position:0% +can actually be more behaviorist +cognitivist or constructivist in nature. + + align:start position:0% +cognitivist or constructivist in nature. + + + align:start position:0% +cognitivist or constructivist in nature. +So I think it's useful for you to think + + align:start position:0% +So I think it's useful for you to think + + + align:start position:0% +So I think it's useful for you to think +about that um just as a way of just + + align:start position:0% +about that um just as a way of just + + + align:start position:0% +about that um just as a way of just +getting a bit of a marker about again + + align:start position:0% +getting a bit of a marker about again + + + align:start position:0% +getting a bit of a marker about again +it's this idea about what are we trying + + align:start position:0% +it's this idea about what are we trying + + + align:start position:0% +it's this idea about what are we trying +to do with this with this tool. Um and + + align:start position:0% +to do with this with this tool. Um and + + + align:start position:0% +to do with this with this tool. Um and +so I'm going to divide you up and we + + align:start position:0% +so I'm going to divide you up and we + + + align:start position:0% +so I'm going to divide you up and we +have nine people left. So three groups + + align:start position:0% +have nine people left. So three groups + + + align:start position:0% +have nine people left. So three groups +of three which works absolutely + + align:start position:0% +of three which works absolutely + + + align:start position:0% +of three which works absolutely +perfectly. Um yes three groups of three + + align:start position:0% +perfectly. Um yes three groups of three + + + align:start position:0% +perfectly. Um yes three groups of three +and we're going to have the behaviorist + + align:start position:0% +and we're going to have the behaviorist + + + align:start position:0% +and we're going to have the behaviorist +group, the cognitivist group and the and + + align:start position:0% +group, the cognitivist group and the and + + + align:start position:0% +group, the cognitivist group and the and +the constructivist group. + + align:start position:0% +the constructivist group. + + + align:start position:0% +the constructivist group. +What I want you to do is think about a + + align:start position:0% +What I want you to do is think about a + + + align:start position:0% +What I want you to do is think about a +particular technology that is um that + + align:start position:0% +particular technology that is um that + + + align:start position:0% +particular technology that is um that +sort of would be consistent with this. + + align:start position:0% +sort of would be consistent with this. + + + align:start position:0% +sort of would be consistent with this. +Okay, one group will have four um uh a + + align:start position:0% +Okay, one group will have four um uh a + + + align:start position:0% +Okay, one group will have four um uh a +particular technology that's be that's + + align:start position:0% +particular technology that's be that's + + + align:start position:0% +particular technology that's be that's +uh consistent with that particular + + align:start position:0% +uh consistent with that particular + + + align:start position:0% +uh consistent with that particular +theory learning theory. Um and so this + + align:start position:0% +theory learning theory. Um and so this + + + align:start position:0% +theory learning theory. Um and so this +will take about maybe four + + align:start position:0% +will take about maybe four + + + align:start position:0% +will take about maybe four +minutes and think about perhaps even + + align:start position:0% +minutes and think about perhaps even + + + align:start position:0% +minutes and think about perhaps even +think of a learning outcome that that + + align:start position:0% +think of a learning outcome that that + + + align:start position:0% +think of a learning outcome that that +tool advances but at that level. So, at + + align:start position:0% +tool advances but at that level. So, at + + + align:start position:0% +tool advances but at that level. So, at +the behaviorist level, let's say. Um, + + align:start position:0% +the behaviorist level, let's say. Um, + + + align:start position:0% +the behaviorist level, let's say. Um, +and then what I'm going to do is the + + align:start position:0% +and then what I'm going to do is the + + + align:start position:0% +and then what I'm going to do is the +activity is called a + + align:start position:0% +activity is called a + + + align:start position:0% +activity is called a +jigsaw. And so, first you're going to be + + align:start position:0% +jigsaw. And so, first you're going to be + + + align:start position:0% +jigsaw. And so, first you're going to be +in these homogeneous groups. So, + + align:start position:0% +in these homogeneous groups. So, + + + align:start position:0% +in these homogeneous groups. So, +everybody talks about one group talks + + align:start position:0% +everybody talks about one group talks + + + align:start position:0% +everybody talks about one group talks +about constructivism, one group group + + align:start position:0% +about constructivism, one group group + + + align:start position:0% +about constructivism, one group group +talks about behaviorism, and one group + + align:start position:0% +talks about behaviorism, and one group + + + align:start position:0% +talks about behaviorism, and one group +talks about + + align:start position:0% +talks about + + + align:start position:0% +talks about +cognitivism. And then I'm going to mix + + align:start position:0% +cognitivism. And then I'm going to mix + + + align:start position:0% +cognitivism. And then I'm going to mix +you up. So, each group then has one + + align:start position:0% +you up. So, each group then has one + + + align:start position:0% +you up. So, each group then has one +cognitivist, one constructivist, and one + + align:start position:0% +cognitivist, one constructivist, and one + + + align:start position:0% +cognitivist, one constructivist, and one +behaviorist in it. So, this is this is + + align:start position:0% +behaviorist in it. So, this is this is + + + align:start position:0% +behaviorist in it. So, this is this is +an active learning technique, and I + + align:start position:0% +an active learning technique, and I + + + align:start position:0% +an active learning technique, and I +wanted to model it for you. So, let's + + align:start position:0% +wanted to model it for you. So, let's + + + align:start position:0% +wanted to model it for you. So, let's +get um let's let's just create some + + align:start position:0% +get um let's let's just create some + + + align:start position:0% +get um let's let's just create some +groups. + + align:start position:0% + + + + align:start position:0% + +Nobody wants cognitive. + + align:start position:0% +Nobody wants cognitive. + + + align:start position:0% +Nobody wants cognitive. +Open it. Yes. Open it up. + + align:start position:0% + + + + align:start position:0% + +How you perceive things, how you + + align:start position:0% +How you perceive things, how you + + + align:start position:0% +How you perceive things, how you +interpret information. So, it's all + + align:start position:0% +interpret information. So, it's all + + + align:start position:0% +interpret information. So, it's all +about like sensory Yeah. All right, + + align:start position:0% +about like sensory Yeah. All right, + + + align:start position:0% +about like sensory Yeah. All right, +folks. I don't know how far you got + + align:start position:0% +folks. I don't know how far you got + + + align:start position:0% +folks. I don't know how far you got +here, but um now each one of you is + + align:start position:0% +here, but um now each one of you is + + + align:start position:0% +here, but um now each one of you is +going to be the expert in your + + align:start position:0% +going to be the expert in your + + + align:start position:0% +going to be the expert in your +particular + + align:start position:0% +particular + + + align:start position:0% +particular +um he's going to be an expert in your + + align:start position:0% +um he's going to be an expert in your + + + align:start position:0% +um he's going to be an expert in your +particular + + align:start position:0% + + + + align:start position:0% + +field. So, um so I'm going to take and + + align:start position:0% +field. So, um so I'm going to take and + + + align:start position:0% +field. So, um so I'm going to take and +this is the constructivist + + align:start position:0% +this is the constructivist + + + align:start position:0% +this is the constructivist +constructivist. So, here's three + + align:start position:0% +constructivist. So, here's three + + + align:start position:0% +constructivist. So, here's three +constructivists. I'd like one + + align:start position:0% +constructivists. I'd like one + + + align:start position:0% +constructivists. I'd like one +cognitivist and one behaviorist to find + + align:start position:0% +cognitivist and one behaviorist to find + + + align:start position:0% +cognitivist and one behaviorist to find +a constructivist and to make a new + + align:start position:0% +a constructivist and to make a new + + + align:start position:0% +a constructivist and to make a new +group. All right. So now each one of you + + align:start position:0% +group. All right. So now each one of you + + + align:start position:0% +group. All right. So now each one of you +is the content expert for your + + align:start position:0% +is the content expert for your + + + align:start position:0% +is the content expert for your +particular theory and just sort of + + align:start position:0% +particular theory and just sort of + + + align:start position:0% +particular theory and just sort of +explain what you came up with to your + + align:start position:0% +explain what you came up with to your + + + align:start position:0% +explain what you came up with to your +peers. So just you'll just go around the + + align:start position:0% +peers. So just you'll just go around the + + + align:start position:0% +peers. So just you'll just go around the +table and talk about it. Kids get to go + + align:start position:0% +table and talk about it. Kids get to go + + + align:start position:0% +table and talk about it. Kids get to go +around and like pick what station they + + align:start position:0% +around and like pick what station they + + + align:start position:0% +around and like pick what station they +want to learn + + align:start position:0% +want to learn + + + align:start position:0% +want to learn +about. It's like they're still learning, + + align:start position:0% +about. It's like they're still learning, + + + align:start position:0% +about. It's like they're still learning, +but they're having an active role in + + align:start position:0% +but they're having an active role in + + + align:start position:0% +but they're having an active role in +like participating on what they're going + + align:start position:0% +like participating on what they're going + + + align:start position:0% +like participating on what they're going +to learn about rather than just like + + align:start position:0% +to learn about rather than just like + + + align:start position:0% +to learn about rather than just like +being passively taught. And that's + + align:start position:0% +being passively taught. And that's + + + align:start position:0% +being passively taught. And that's +constructivist. Okay. So, what + + align:start position:0% +constructivist. Okay. So, what + + + align:start position:0% +constructivist. Okay. So, what +technology you + + align:start position:0% +technology you + + + align:start position:0% +technology you +Well, I think that um like a cool way to + + align:start position:0% +Well, I think that um like a cool way to + + + align:start position:0% +Well, I think that um like a cool way to +do it is to have like computers set up + + align:start position:0% +do it is to have like computers set up + + + align:start position:0% +do it is to have like computers set up +throughout the room that have like + + align:start position:0% +throughout the room that have like + + + align:start position:0% +throughout the room that have like +internet access and like So, the class + + align:start position:0% +internet access and like So, the class + + + align:start position:0% +internet access and like So, the class +is officially over. I mean, it's it's + + align:start position:0% +is officially over. I mean, it's it's + + + align:start position:0% +is officially over. I mean, it's it's +five of I don't know if people have to + + align:start position:0% +five of I don't know if people have to + + + align:start position:0% +five of I don't know if people have to +go other places or not. Um, so we can um + + align:start position:0% +go other places or not. Um, so we can um + + + align:start position:0% +go other places or not. Um, so we can um +we can take this up beginning of class + + align:start position:0% +we can take this up beginning of class + + + align:start position:0% +we can take this up beginning of class +next time if there's things you want to + + align:start position:0% +next time if there's things you want to + + + align:start position:0% +next time if there's things you want to +finish up. I'd like to hear I'd like to + + align:start position:0% +finish up. I'd like to hear I'd like to + + + align:start position:0% +finish up. I'd like to hear I'd like to +hear some of your uh what you came up + + align:start position:0% +hear some of your uh what you came up + + + align:start position:0% +hear some of your uh what you came up +with for sure. So, and we just plan to + + align:start position:0% +with for sure. So, and we just plan to + + + align:start position:0% +with for sure. So, and we just plan to +do that and uh and just tie it tie up + + align:start position:0% +do that and uh and just tie it tie up + + + align:start position:0% +do that and uh and just tie it tie up +the exercise. Not the best um not the + + align:start position:0% +the exercise. Not the best um not the + + + align:start position:0% +the exercise. Not the best um not the +best pedagogical strategy to you know + + align:start position:0% +best pedagogical strategy to you know + + + align:start position:0% +best pedagogical strategy to you know +make it make you wait a week um but it + + align:start position:0% +make it make you wait a week um but it + + + align:start position:0% +make it make you wait a week um but it +is what it is. So, um, okay. Thanks very + + align:start position:0% +is what it is. So, um, okay. Thanks very + + + align:start position:0% +is what it is. So, um, okay. Thanks very +much and I look forward to seeing your + + align:start position:0% +much and I look forward to seeing your + + + align:start position:0% +much and I look forward to seeing your +post session assignments. \ No newline at end of file diff --git a/sSWHT2kbkvc.txt b/sSWHT2kbkvc.txt new file mode 100644 index 0000000000000000000000000000000000000000..8f6612bb6cc5ae5c23dd2d7c4c25a14458aa6b3f --- /dev/null +++ b/sSWHT2kbkvc.txt @@ -0,0 +1,915 @@ +align:start position:0% + +in this segment we will derive a formula + + align:start position:0% +in this segment we will derive a formula + + + align:start position:0% +in this segment we will derive a formula +for the variance of the geometric PMF + + align:start position:0% +for the variance of the geometric PMF + + + align:start position:0% +for the variance of the geometric PMF +the argument will be very much similar + + align:start position:0% +the argument will be very much similar + + + align:start position:0% +the argument will be very much similar +to the argument that we use to derive + + align:start position:0% +to the argument that we use to derive + + + align:start position:0% +to the argument that we use to derive +the expected value of the geometric PMF + + align:start position:0% +the expected value of the geometric PMF + + + align:start position:0% +the expected value of the geometric PMF +and it relies on the memorylessness + + align:start position:0% +and it relies on the memorylessness + + + align:start position:0% +and it relies on the memorylessness +properties of geometric random variables + + align:start position:0% +properties of geometric random variables + + + align:start position:0% +properties of geometric random variables +so let X be a geometric random variable + + align:start position:0% +so let X be a geometric random variable + + + align:start position:0% +so let X be a geometric random variable +with some parameter P the way to think + + align:start position:0% +with some parameter P the way to think + + + align:start position:0% +with some parameter P the way to think +about X is like the number of coin flips + + align:start position:0% +about X is like the number of coin flips + + + align:start position:0% +about X is like the number of coin flips +that it takes until we obtain heads for + + align:start position:0% +that it takes until we obtain heads for + + + align:start position:0% +that it takes until we obtain heads for +the first time where P is the + + align:start position:0% +the first time where P is the + + + align:start position:0% +the first time where P is the +probability of heads at each toss recall + + align:start position:0% +probability of heads at each toss recall + + + align:start position:0% +probability of heads at each toss recall +now the memorylessness property if I + + align:start position:0% +now the memorylessness property if I + + + align:start position:0% +now the memorylessness property if I +tell you that X is bigger than 1 which + + align:start position:0% +tell you that X is bigger than 1 which + + + align:start position:0% +tell you that X is bigger than 1 which +means that the first trial was a failure + + align:start position:0% +means that the first trial was a failure + + + align:start position:0% +means that the first trial was a failure +we obtained tails giving that event the + + align:start position:0% +we obtained tails giving that event the + + + align:start position:0% +we obtained tails giving that event the +remaining number of tosses has the same + + align:start position:0% +remaining number of tosses has the same + + + align:start position:0% +remaining number of tosses has the same +geometric PMF as if we were just + + align:start position:0% +geometric PMF as if we were just + + + align:start position:0% +geometric PMF as if we were just +starting at this time so it has the same + + align:start position:0% +starting at this time so it has the same + + + align:start position:0% +starting at this time so it has the same +geometric PMF as the unconditional PMF + + align:start position:0% +geometric PMF as the unconditional PMF + + + align:start position:0% +geometric PMF as the unconditional PMF +of X and this is the property that we + + align:start position:0% +of X and this is the property that we + + + align:start position:0% +of X and this is the property that we +exploited in order to find the expected + + align:start position:0% +exploited in order to find the expected + + + align:start position:0% +exploited in order to find the expected +value of x now let us take this + + align:start position:0% +value of x now let us take this + + + align:start position:0% +value of x now let us take this +observation and add one to the random + + align:start position:0% +observation and add one to the random + + + align:start position:0% +observation and add one to the random +variables involved and turned this + + align:start position:0% +variables involved and turned this + + + align:start position:0% +variables involved and turned this +statement to the following version the + + align:start position:0% +statement to the following version the + + + align:start position:0% +statement to the following version the +conditional PMF of X which is this + + align:start position:0% +conditional PMF of X which is this + + + align:start position:0% +conditional PMF of X which is this +random variable plus 1 is the same as + + align:start position:0% +random variable plus 1 is the same as + + + align:start position:0% +random variable plus 1 is the same as +the unconditional PMF of this random + + align:start position:0% +the unconditional PMF of this random + + + align:start position:0% +the unconditional PMF of this random +variable plus 1 so it's the same + + align:start position:0% +variable plus 1 so it's the same + + + align:start position:0% +variable plus 1 so it's the same +statement as before except that we added + + align:start position:0% +statement as before except that we added + + + align:start position:0% +statement as before except that we added +1 1 consequence of the memorylessness + + align:start position:0% +1 1 consequence of the memorylessness + + + align:start position:0% +1 1 consequence of the memorylessness +that we have already seen and exploited + + align:start position:0% +that we have already seen and exploited + + + align:start position:0% +that we have already seen and exploited +is that the expected value of x in the + + align:start position:0% +is that the expected value of x in the + + + align:start position:0% +is that the expected value of x in the +conditional universe where the first + + align:start position:0% +conditional universe where the first + + + align:start position:0% +conditional universe where the first +coin flip was wasted is equal to 1 + + align:start position:0% +coin flip was wasted is equal to 1 + + + align:start position:0% +coin flip was wasted is equal to 1 +that's the wasted coin flip plus how + + align:start position:0% +that's the wasted coin flip plus how + + + align:start position:0% +that's the wasted coin flip plus how +long you expect to have to flip the coin + + align:start position:0% +long you expect to have to flip the coin + + + align:start position:0% +long you expect to have to flip the coin +until you obtain heads for the first + + align:start position:0% +until you obtain heads for the first + + + align:start position:0% +until you obtain heads for the first +time starting from the second flip since + + align:start position:0% +time starting from the second flip since + + + align:start position:0% +time starting from the second flip since +the conditional distribution of X in + + align:start position:0% +the conditional distribution of X in + + + align:start position:0% +the conditional distribution of X in +this universe is the same as the + + align:start position:0% +this universe is the same as the + + + align:start position:0% +this universe is the same as the +unconditional distribution of this + + align:start position:0% +unconditional distribution of this + + + align:start position:0% +unconditional distribution of this +random variable it means that the + + align:start position:0% +random variable it means that the + + + align:start position:0% +random variable it means that the +corresponding expected value in this + + align:start position:0% +corresponding expected value in this + + + align:start position:0% +corresponding expected value in this +universe is going to be equal to the + + align:start position:0% +universe is going to be equal to the + + + align:start position:0% +universe is going to be equal to the +expected value of this random variable + + align:start position:0% +expected value of this random variable + + + align:start position:0% +expected value of this random variable +which is 1 plus + + align:start position:0% +which is 1 plus + + + align:start position:0% +which is 1 plus +expected value of X and buy exactly the + + align:start position:0% +expected value of X and buy exactly the + + + align:start position:0% +expected value of X and buy exactly the +same argument the random variable x + + align:start position:0% +same argument the random variable x + + + align:start position:0% +same argument the random variable x +squared has the same distribution in the + + align:start position:0% +squared has the same distribution in the + + + align:start position:0% +squared has the same distribution in the +conditional universe as the random + + align:start position:0% +conditional universe as the random + + + align:start position:0% +conditional universe as the random +variable X plus 1 squared in the + + align:start position:0% +variable X plus 1 squared in the + + + align:start position:0% +variable X plus 1 squared in the +unconditional universe so since X in the + + align:start position:0% +unconditional universe so since X in the + + + align:start position:0% +unconditional universe so since X in the +conditional universe has the same + + align:start position:0% +conditional universe has the same + + + align:start position:0% +conditional universe has the same +distribution as X plus 1 it means that X + + align:start position:0% +distribution as X plus 1 it means that X + + + align:start position:0% +distribution as X plus 1 it means that X +square in the conditional universe has + + align:start position:0% +square in the conditional universe has + + + align:start position:0% +square in the conditional universe has +the same distribution as X plus 1 + + align:start position:0% +the same distribution as X plus 1 + + + align:start position:0% +the same distribution as X plus 1 +squared in the unconditional universe so + + align:start position:0% +squared in the unconditional universe so + + + align:start position:0% +squared in the unconditional universe so +now let us take those facts and use a + + align:start position:0% +now let us take those facts and use a + + + align:start position:0% +now let us take those facts and use a +divide and conquer method to calculate + + align:start position:0% +divide and conquer method to calculate + + + align:start position:0% +divide and conquer method to calculate +the expected value of x squared we will + + align:start position:0% +the expected value of x squared we will + + + align:start position:0% +the expected value of x squared we will +use exactly the same method that we we + + align:start position:0% +use exactly the same method that we we + + + align:start position:0% +use exactly the same method that we we +used in order to calculate the expected + + align:start position:0% +used in order to calculate the expected + + + align:start position:0% +used in order to calculate the expected +value we separate into two scenarios in + + align:start position:0% +value we separate into two scenarios in + + + align:start position:0% +value we separate into two scenarios in +one scenario X is equal to 1 and then we + + align:start position:0% +one scenario X is equal to 1 and then we + + + align:start position:0% +one scenario X is equal to 1 and then we +have the expected value of x squared + + align:start position:0% +have the expected value of x squared + + + align:start position:0% +have the expected value of x squared +given that X is equal to 1 and then we + + align:start position:0% +given that X is equal to 1 and then we + + + align:start position:0% +given that X is equal to 1 and then we +have another scenario the scenario that + + align:start position:0% +have another scenario the scenario that + + + align:start position:0% +have another scenario the scenario that +X is bigger than 1 and then we have the + + align:start position:0% +X is bigger than 1 and then we have the + + + align:start position:0% +X is bigger than 1 and then we have the +expected value of x squared + + align:start position:0% +expected value of x squared + + + align:start position:0% +expected value of x squared +even that X is bigger than 1 so this is + + align:start position:0% +even that X is bigger than 1 so this is + + + align:start position:0% +even that X is bigger than 1 so this is +just the total expectation theorem now + + align:start position:0% +just the total expectation theorem now + + + align:start position:0% +just the total expectation theorem now +let us calculate terms the probability + + align:start position:0% +let us calculate terms the probability + + + align:start position:0% +let us calculate terms the probability +that the first toss results in success + + align:start position:0% +that the first toss results in success + + + align:start position:0% +that the first toss results in success +that X is equal to 1 this is P and if X + + align:start position:0% +that X is equal to 1 this is P and if X + + + align:start position:0% +that X is equal to 1 this is P and if X +is equal to 1 then the value of x + + align:start position:0% +is equal to 1 then the value of x + + + align:start position:0% +is equal to 1 then the value of x +squared is also equal to 1 and then + + align:start position:0% +squared is also equal to 1 and then + + + align:start position:0% +squared is also equal to 1 and then +there is probability 1 minus P that the + + align:start position:0% +there is probability 1 minus P that the + + + align:start position:0% +there is probability 1 minus P that the +first trial was not a success so we get + + align:start position:0% +first trial was not a success so we get + + + align:start position:0% +first trial was not a success so we get +to continue we have this conditional + + align:start position:0% +to continue we have this conditional + + + align:start position:0% +to continue we have this conditional +expectation here but it is equal to this + + align:start position:0% +expectation here but it is equal to this + + + align:start position:0% +expectation here but it is equal to this +unconditional expectation up there and + + align:start position:0% +unconditional expectation up there and + + + align:start position:0% +unconditional expectation up there and +now let us expand the terms in this + + align:start position:0% +now let us expand the terms in this + + + align:start position:0% +now let us expand the terms in this +quadratic and write this as expected + + align:start position:0% +quadratic and write this as expected + + + align:start position:0% +quadratic and write this as expected +value of x squared plus twice the + + align:start position:0% +value of x squared plus twice the + + + align:start position:0% +value of x squared plus twice the +expected value of x plus 1 now we know + + align:start position:0% +expected value of x plus 1 now we know + + + align:start position:0% +expected value of x plus 1 now we know +what this expected value here is the + + align:start position:0% +what this expected value here is the + + + align:start position:0% +what this expected value here is the +expected value of a geometric is just 1 + + align:start position:0% +expected value of a geometric is just 1 + + + align:start position:0% +expected value of a geometric is just 1 +over P + + align:start position:0% +over P + + + align:start position:0% +over P +and what we're left with is an equation + + align:start position:0% +and what we're left with is an equation + + + align:start position:0% +and what we're left with is an equation +that involves a single unknown namely + + align:start position:0% +that involves a single unknown namely + + + align:start position:0% +that involves a single unknown namely +this quantity is the unknown and we can + + align:start position:0% +this quantity is the unknown and we can + + + align:start position:0% +this quantity is the unknown and we can +solve this linear equation for this + + align:start position:0% +solve this linear equation for this + + + align:start position:0% +solve this linear equation for this +unknown we carry out some algebra which + + align:start position:0% +unknown we carry out some algebra which + + + align:start position:0% +unknown we carry out some algebra which +is not so interesting by itself and + + align:start position:0% +is not so interesting by itself and + + + align:start position:0% +is not so interesting by itself and +after we carry out the algebra what we + + align:start position:0% +after we carry out the algebra what we + + + align:start position:0% +after we carry out the algebra what we +obtain is that the expected value of x + + align:start position:0% +obtain is that the expected value of x + + + align:start position:0% +obtain is that the expected value of x +squared is equal to 2 over P squared + + align:start position:0% +squared is equal to 2 over P squared + + + align:start position:0% +squared is equal to 2 over P squared +minus 1 over P and then we use the + + align:start position:0% +minus 1 over P and then we use the + + + align:start position:0% +minus 1 over P and then we use the +formula that the variance of the run of + + align:start position:0% +formula that the variance of the run of + + + align:start position:0% +formula that the variance of the run of +a random variable is equal to the + + align:start position:0% +a random variable is equal to the + + + align:start position:0% +a random variable is equal to the +expected value of the square of that + + align:start position:0% +expected value of the square of that + + + align:start position:0% +expected value of the square of that +random variable minus the square of the + + align:start position:0% +random variable minus the square of the + + + align:start position:0% +random variable minus the square of the +expected value we already know what that + + align:start position:0% +expected value we already know what that + + + align:start position:0% +expected value we already know what that +expected value is we found the expected + + align:start position:0% +expected value is we found the expected + + + align:start position:0% +expected value is we found the expected +value of the square and putting all that + + align:start position:0% +value of the square and putting all that + + + align:start position:0% +value of the square and putting all that +together we obtain a final answer and + + align:start position:0% +together we obtain a final answer and + + + align:start position:0% +together we obtain a final answer and +this is the expression for the variance + + align:start position:0% +this is the expression for the variance + + + align:start position:0% +this is the expression for the variance +of a geometric random variable it goes + + align:start position:0% +of a geometric random variable it goes + + + align:start position:0% +of a geometric random variable it goes +without saying that for this calculation + + align:start position:0% +without saying that for this calculation + + + align:start position:0% +without saying that for this calculation +to make sense we need to assume that the + + align:start position:0% +to make sense we need to assume that the + + + align:start position:0% +to make sense we need to assume that the +parameter that we're dealing with is + + align:start position:0% +parameter that we're dealing with is + + + align:start position:0% +parameter that we're dealing with is +positive \ No newline at end of file diff --git a/sh3EPjhhd40.txt b/sh3EPjhhd40.txt new file mode 100644 index 0000000000000000000000000000000000000000..5ba2eaa5eb516bb4deacb4bb4793fb6e3a653a0c --- /dev/null +++ b/sh3EPjhhd40.txt @@ -0,0 +1,2377 @@ +PROFESSOR PATRICK WINSTON: +You know, some + +of you who for instance-- + +I don't know, Sonya, +Krishna, Shoshana-- + +some of you I can count on +being here every time. + +Some of you show up +once in a while. + +The ones of you who show up once +in a while happen to be + +very lucky if you picked today, +because what we're + +going to do today is I'm going +to tell you stuff that might + +make a big difference +in your whole life. + +Because I'm going to tell +you how you can + +make yourself smarter. + +No kidding. + +And I'm also going to tell you +how you can package your ideas + +so you'll be the one that's +picked instead + +of some other slug. + +So that's what we're +going to do today. + +It's the most important lecture +of the semester. + +The sleep lecture is only the +second most important. + +This is the most important. + +Now the vehicle that's going +to get us there is a + +discussion about how it's +possible to learn in a way + +that is a little reminiscent +of what we + +talked about last time. + +Because last time we learned +something very definite from a + +small number of examples. + +This takes it one step further +and shows how it's possible to + +learn in a human-like way from +a single example in one shot. + +So it's extremely different, +very different from everything + +you've seen before. + +Everything that involves +learning from thousands of + +trials and gazillions of +examples and only learning a + +little tiny bit, if anything, +from each of them. + +This is going to +learn something + +definite from every example. + +So here's the classroom +example. + +What's this? + +It's an arch. + +I know the architects are +complaining that it's not an + +arch in architecture land. + +It's a post and lintel +construction. + +But for us today it's +going to be an arch. + +Now if you were from Mars and +didn't know what an arch was, + +I might present this to you and +you'd get a general idea + +of some things that might be +factors, but you'd have no + +idea what's really important. + +So then I would say, +that's not an arch. + +And you would learn something +very definite from that. + +And then I would shove these +together and put this back on, + +and I would say, that's +not an arch either. + +And you'd learn something +very definite from that. + +And then I could paint the top +one blue, and you'd learn + +something very different +from that. + +And how can that happen +is the question? + +How can that happen in detail, +and what might it mean for + +human learning and how you can +make yourself smarter? + +And that's where we're +going to go. + +All right? + +So how can we make a program +that's a smart as a martian + +about learning things +like that? + +Well, if you were writing that +program, surely the first + +thing you would do is you'd try +to get off the picture as + +quickly as possible and into +symbol land where things are + +clearer about what the +important parts are. + +So you'd be presented with an +initial example that might + +look like this. + +We'll call that an example. + +And it's more than +just an example. + +It's the initial model. + +That's the starting point. + +And now we're going to couple +that with something that's not + +actually an arch but looks a +whole lot like one, at least + +on the descriptive level to +which we're about to go. + +So here's something that's not +an arch, but its description + +doesn't differ from that +of an arch very much. + +In fact, if we were to draw this +out in a kind of network, + +we would have a description +that looks like this, and + +these relations would be +support relations. + +And this would be drawn +out like so. + +And the only difference +would be-- + +the only difference would be +that those support relations + +that we had in the +initial model-- + +the example-- + +have disappeared down out here +in this configuration. + +But since it's not very +different from the model, + +we're going to call +this a near miss. + +And now, you see, we've +abstracted away from all the + +details that don't +matter to us. + +Last time we talked about a +good representation having + +certain qualities-- + +qualities like making the +right things explicit. + +Well, this makes the structure +explicit, and it suppresses + +information about blemishes +on the surface. + +We don't care much about how +tall the objects are. + +We don't think it matters +what they're made of. + +So this is a representation that +satisfies the first of + +the criteria from last time. + +It makes the right +things explicit. + +And by making the right things +explicit, it's exposing some + +constraint here with +respect to what it + +takes to be an arch. + +And we see that if those support +relations are missing, + +it's not an arch. + +So we ought to be able to learn +something from that. + +What we're going to do is we're +going to put these two + +things together. + +We're going to describe the +difference between the two. + +And we're going to reach the +conclusion that since there's + +only one difference-- + +one kind of difference with +two manifestations to + +disappearing support relations, +we're going to + +conclude that those support +relations are important. + +And we're going to +turn them red + +because they're so important. + +And we're going to change the +name from "support" to "must + +support." + +So this is our new model. + +This is an evolving model that +now is decorated with + +information about what's +important. + +So if you're going to match +something against this model, + +it must be the case that those +support relations are there. + +If it's not there-- if they're +not there, it's not an arch. + +All right? + +So we've learned something +definite + +from a single example. + +This is not 10,000 trials. + +This is a teacher presenting +something to the student and + +the student learning something +immediately in one step about + +what's important in an arch. + +So let's do it again. + +That was so much fun. + +Let's do this one. + +Same as before except that now +when we describe this thing, + +there are some additional +relations-- + +these relations, and those +are touch relations. + +So now when we compare that-- + +is that an arch? + +No. + +It's a near miss. + +When we compare that near miss +with our evolving model, we + +see immediately that once again +there's exactly one + +difference, two + +manifestations, the touch relations. + +So we can immediately conclude +that these touch relations are + +interfering with our belief that +this could be an arch. + +So what do we do with that? + +We put those together +again and we build + +ourselves a new model. + +It's much like the old model. + +It still has the imperatives +up here. + +We have to have the +support relations. + +But now down here-- and we draw +not signs through there-- + +these are must not +touch relations. + +So now you can't match against +that model if those two side + +supports are touching +each other. + +So in just two steps, we've +learned two important things + +about what has to be in place in +order for this thing to be + +construed to be an arch. + +So our martian is making +great progress. + +But our martian isn't through, +because there's some more + +things we might want +it to know about + +the nature of arches. + +For example, we might present +it with this one. + +Well, that looks just like +our initial example. + +It's an example just like +our initial example. + +But this time the top has +been painted red. + +And I'm still saying that +that's an arch. + +So once again, there's only +one difference and that + +difference is that in the +description of this object, we + +have the additional information +that the color of + +the top is red. + +And we've been carrying along +without saying so, that the + +color of the top in the evolving +model is white. + +So now we know that the top +doesn't have to be white. + +It can be either red or white. + +So we'll put those +two together and + +we'll get a new model. + +And that new model this +time once again + +will have three parts. + +It will have the relations, an +imperative form that we've + +been carrying along now, the +must support and the must not + +touch, but now we're going to +turn that color relation + +itself into an imperative. + +And we're going to say that +the top has to be + +either red or white. + +So now, once again, in one step +we've learned something + +definite about archness. + +Two more steps. + +Suppose now we present +it with this example. + +It's an example. + +And this time there's going +to be a little paint + +added here as well. + +This time we're going to have +the top painted blue like so. + +So the description +will be like so. + +And now we have to somehow put +that together with our + +evolving model to make +a new model. + +And there's some choices here. + +And our choice depends somewhat +on the nature of the + +world that we're working in. + +So suppose we're working +in flag world. + +There are only three colors-- + +red, white, and blue. + +Now we've seen them all. + +If we've seen them all, then +what we're going to do is + +we're going to say that the +evolving model now is adjusted + +yet again like so. + +Oh-- but those are imperatives +still. + +Let me carry that along. + +At this time, this guy-- + +the color relation-- + +goes out here to anything +at all. + +So we could have just not drawn +it at all, but then we + +would have lost track of the +fact that we've actually + +learned that anything +can be there. + +So we're going to retain the +relation but have it point to + +the "anything goes" marker. + +Well, we're making great +progress and I said there's + +just one more thing to go. + +So let me compress that +into this area here. + +What I'm going to add this time +is I'm going to say that + +the example is like everything +you've seen before except that + +the top is now one of those +kinds of child's bricks. + +So you have a choice actually +about whether this + +is an arch or not. + +But if I say, yeah, it's still +an arch, then we'd add a + +little something to +its description. + +So this description would +look like this. + +Same things that we've seen +before in terms of support, + +but now we'd have a relation +that says that + +this top is a wedge. + +And over here-- + +something we've been carrying +along but not writing down-- + +this top is a block. + +A brick, I guess in the +language of the day. + +So if we say that it can be +either a wedge or a brick on + +top, what do we do with that? + +Once again, it depends on the +nature of representation, but + +if we say that we have a +representation, that has a + +hierarchy of parts. + +So bricks and wedges are both +children's blocks and + +children's box or toys. + +Then we can think of drawing +in a little bit of that + +hierarchy right here and +saying well, let's see. + +Immediately above that we've +got the brick or wedge. + +And a little bit above +that we've got block. + +And a little bit above +that we've got toy. + +And a little bit above that +we eventually get to + +any physical object. + +So what does it do in response +to that kind of situation? + +You have the choice. + +But what the program I'm +speaking of actually did was + +to make a conservative +generalization up here just to + +say that it's one +of those guys. + +So once again it's learned +something definite. + +Let me see. + +Let me count the steps. + +One, two, three, four, five. + +And I just learned +four things. + +So the generalization of a +color, it took two steps to + +get all the way up +to "don't care." + +So note how it contrasts with +anything you've seen in a + +neural net. + +Or anything you will see +downstream in some of the + +other learning techniques that +we'll be talking about that + +involve using thousands of +samples to learn what it is-- + +to learn whatever it is that +is intended to be learned. + +Let me show you another +example of how these + +heuristics can be put to work. + +So there are two sets +of drawings. + +We have the upper set +and the lower set. + +And your task, you smart +humans working in vast + +parallelism, your task is to +give me a description of the + +top trains that distinguishes +and separates them from the + +trains on the bottom. + +You got it? + +Nobody's got it? + +Well, let me try one on you. + +The top trains all have a short +car with a closed top. + +So how is it possible that +a computer could have + +figured that out? + +It turns out that it figured +it out with much the same + +apparatus that I've shown you +here in connection with the + +arches, just deployed in a +somewhat different manner. + +In this particular case, the +examples are presented one at + +a time by a teacher +who's eager for + +the student to learn. + +In this case, the examples are +presented all at once and the + +machine is expected to figure +out a description that + +separates the two groups. + +And here's how it works. + +What you do is you start +with one of them. + +But you have a lot of them. + +You have some examples-- + +we'll call the examples on top +the "plus examples" and the + +examples on the bottom the +"negative examples." So the + +first thing that you do is you +pick one of the positive + +examples to work with. + +Anybody got any good guesses +about what we're + +going to call that? + +Yeah, you do. + +We're going to call +that the seed. + +It's just highly reminiscent of +what we did last time when + +we were doing [? phonology ?] + +but now at a much +different level. + +We're going to pick one of those +guys to be the seed, and + +then we're going to take these +heuristics and we're going to + +search for one that loosens this +description so that it + +covers more of the positives. + +You see, if you have a seed that +is exactly a description + +of a particular thing and you +insist that everything be just + +like that, then nothing will +match except itself. + +But you can use these heuristics +to expand the + +coverage of the description, to +loosen it so that it covers + +more of the positives. + +So in your first step you might +cover, for example, that + +group of objects. + +Too bad for your side, you've +also in that particular case + +included a negative example in +your description, but perhaps + +in this next step beyond that +you'll get to the point where + +you've eliminated all of those +negative examples and zeroed + +in on all the positive +examples. + +So how might a program be +constructed that would do that + +sort of thing? + +Well, think about the choices. + +The first choice that you have +it is to pick a positive + +example to be the seed. + +And once you've picked a +particular example to be the + +seed, then you can apply +heuristics, all of them that + +you have, to make a new +description that may cover the + +data better. + +It may have more of the +positives and fewer of the + +negatives than in your +previous step. + +But this, if you have a lot of +heuristics, and these are a + +lot of heuristics because +there's a lot of description + +in that set of trains, there +are lots of possible things + +that you could do with those +heuristics because you could + +apply them anywhere. + +So this tree is extremely +large. + +So what do you do to keep +it under control? + +Well, now you have answers +to questions like that by + +knee-jerk, right? + +The branching factor +is too big. + +You want to keep a few +solutions going. + +You have some way of measuring +how well you're doing so you + +can use a beam search. + +This piece here was originally +worked out by a friend of + +mine, now, alas, deceased, +[? Rashad ?] + +[? Malkowski ?] + +when he was at the University +of Illinois. + +And of course, he wasn't +interested in toy trains, he + +was just interested in +soybean diseases. + +And so this exact program was +used to build descriptions of + +soybean diseases. + +It turned out to be +better than the + +plant pathology books. + +We now have two ways of +deploying the same heuristics. + +But my vocabulary is in need +of enrichment, because I'm + +talking about "those" +heuristics. + +And one of the nice things +that [? Malkowski ?] + +did for me a long time ago is +give each of them a name. + +So here are the names that +were developed by + +[? Malkowski. ?] + +What's happening here? + +You're going from an original +model to an understanding-- + +some things are essential. + +So he called this the "require +link" heuristic. + +And here in the next step, we're +forbidding some things + +from being there. + +So [? Malkowski ?] + +called that heuristic the +"forbid link" heuristic. + +And in the next step, we're +saying it can be + +either red or white. + +So we have a set of colors +and we're extending it. + +And over here in this heuristic, +going from red or + +white to anything goes, that's +essentially forgetting about + +color altogether, so we're going +to call that "drop link" + +even though for reasons of +keeping track, we don't + +actually get rid of it. + +We just have it pointing to +the "anything" marker. + +And finally, in this last step, +what we're doing with + +this tree of categories is we're +climbing up it one step. + +So he called that the "climb +tree" heuristic. + +So now we have a vocabulary +of things we can do in the + +learning process, and having +that vocabulary gives us power + +over it, right? + +Because those are names. + +We can now say, well, what +you need here is + +the "drop link" heuristic. + +And what you need over there is +the "extend set" heuristic. + +So now I want to back up +yet another time and + +say, well, let's see. + +When we were working with that +phonology stuff, all I did was + +generalize. + +Are we just generalizing here? + +No. + +We're both generalizing +and specializing. + +So when I say that the links +over here that are developed + +in our first step are +essential, this is a + +specialization step. + +And when I say they can't be-- + +they cannot be touch +relations, that's a + +specialization step. + +Because we're able to match +fewer and fewer things when we + +say you can't have +touch relations. + +But over here, when I go here +and say, well, it doesn't have + +to be white. + +It can also be red. + +That's a generalization. + +Now we can match more things. + +And when I drop the link +altogether, that's a + +generalization. + +And when I climb the tree, +that's a generalization. + +And that's why when I do this +notional picture of what + +happens when [? Malkowski ?] + +program does a tree search to +find a solution to the train + +problem, they're both +specialization steps which + +draw in the number of things +that can be matched, and + +generalization steps that +make it broader. + +So, let's see. + +We've also got the notion +of near miss. + +And we've got the notion +of example-- + +some of these things +are examples, + +some are near misses. + +We've got generalization +specialization. + +Does one go with one or the +other, or are they all mixed + +up in their relationship +to each other? + +Can you generalize and +specialize with near misses? + +What do you think? + +You think-- + +you don't think so, +[INAUDIBLE]? + +What do you think? + +STUDENT: [INAUDIBLE] + +specialization. + +PROFESSOR PATRICK WINSTON: +[INAUDIBLE] lead to + +specialization. + +Let's see if that's right. + +So we've got specialization +here, and that's a near miss. + +We've got specialization here, +and that's a near miss. + +We've got generalization here, +and that's an example. + +And we've got generalization +here, and that's an example. + +And we've got generalization +here, and that's an example. + +So [INAUDIBLE] has got +that one nailed. + +The examples always generalize, +and the near + +misses always specialize. + +So we've got apparatuses in +place that allow us to both + +expand what we could match and +shrink what we could match. + +So what has this got +to do anything? + +Well, which one of these methods +is better, by the way? + +This one-- + +this one requires a teacher +to organize everything up. + +This one can handle +it in batch mode. + +This one is the sort of thing +you would need to do with a + +human because we don't +have much memory. + +That one is the sort of thing +that a computer's good at + +because it has lots of memory. + +So which one's better? + +Well, it depends on what +you're trying to do. + +If you're trying to build a +machine that analyzes the + +stock market, you might +want to go that way. + +Or soybean diseases, or +any one of a variety + +of practical problems. + +If you're trying to model +people, then maybe this is a + +way that deserves additional +merit. + +How do you get all +that sorted out? + +Well, one way to get it all +sorted out is to talk in terms + +of what are sometimes called +"felicity conditions." So when + +I talk about felicity +conditions, I'm talking about + +a teacher and a student +and covenants that + +hold between them. + +So here's the teacher. + +That's me. + +And here's the student. + +That's you. + +And the objective of interaction +is to transform an + +initial state of knowledge into +a new state of knowledge + +so that the student is smarter +and able to make use of that + +new knowledge to do things that +couldn't be done before + +by the student. + +So the student over here +has a learner. + +And he has something that +uses what is learned. + +And the teacher over +here has a style. + +So if any learning is to take +place, one side has to know + +something about the +other side. + +For example, it's helpful if +the teacher understands the + +initial state of the student. + +And here's one way of +thinking about that. + +You can think of what you know +as forming a kind of network. + +So initially, you don't +know anything. + +But as you learn, you start + +developing quanta of knowledge. + +And these quanta of knowledge +are all linked together by + +prerequisite relationships that +might indicate how you + +get from one quantum +to another. + +So maybe you have generalization +links, maybe + +you have specialization links, +maybe you have combination + +links, but you can think of what +you know as forming this + +kind of network. + +Now your state of knowledge at +any particular time can then + +be viewed as a kind of wavefront +in that space. + +So if I, the teacher, know where +your wavefront is, can I + +do a better job of teaching +you stuff? + +Sure, for this reason. + +Suppose you make a mistake, +m1, that depends on q1. + +Way, way behind your +wavefront. + +What do I do if I know +that you made a + +mistake of that kind? + +Oh, I just say, oh, you forgot +you need a semicolon after + +that kind of statement. + +I just remind you of something +that you certainly know, you + +just overlooked. + +Right? + +On the other hand, suppose you +make a mistake that depends on + +a piece of knowledge +way out here. + +That kind of mistake, m2. + +What do I say to you then? + +What do you think, Patrick? + +What do you think I would +say if you made + +that kind of mistake? + +STUDENT: [INAUDIBLE]. + +PROFESSOR PATRICK WINSTON: No. + +That's not what I would +say [INAUDIBLE]. + +STUDENT: You'd tell us that +we don't know that yet. + +PROFESSOR PATRICK WINSTON: I +would say something like that. + +What [INAUDIBLE] suggested +I would say. + +Oh, don't worry about that. + +We'll get to it. + +We're not ready for it yet. + +So in this case, I remind +somebody of something they + +already know. + +In this case, I tell them +they'll learn about it later. + +So what do I do with mistake +number three? + +That's the learning moment. + +That's where I can push +the wavefront out. + +Because everything's in +place to learn the + +stuff at the next radius. + +So if I know that the student +has made a mistake on that + +wavefront, that's when I say, +this is the teaching moment. + +This is when I explain +something. + +So that's why it's important for +the teacher to have a good + +model of where the +student is in the + +initial state of knowledge. + +Next thing that's important for +the teacher to know is the + +way that the student learns. + +Because if the student is a +computer, they can handle the + +stuff in batch. + +That's one thing. + +If the student is a third +grader who has a limited + +capacity to store stuff, then +that makes a difference in how + +you teach it. + +You might teach it that way to +the third grader, and that + +way, buried underneath this +board, to a computer. + +So you need to understand the +way that the learner-- + +the computational capacity +of the learner. + +And there's also a need to +understand the computational + +capacity of the user box down +there, because sometimes you + +can be taught stuff that +you can't actually use. + +So by now, most of you have +attempted to read that + +sentence up there, right? + +And it seems screwy, right? + +It seems unintelligible, +perhaps? + +It's a garden path sentence. + +It makes perfectly good English, +but the way you + +generally read it, it doesn't, +because you have a limited + +buffer in your language +processor. + +What does this mean? + +You're expecting this to +be "to." Question. + +But it's actually a command. + +Here's the deal. + +Somebody's got to give the +students their grades. + +Well, we can have their +parents do it. + +Have the grades given +to their students by + +their parents, then. + +So it's a command. + +And you garden path on it, +because you have limited + +buffer space in your +language processor. + +So with parentheses you +can understand it. + +You can learn about it. + +You can see that it's good +English, but you can't + +generally process that kind of +sentence without going back + +and starting over. + +And what about going +the other way? + +Are there covenants that we have +to have here that involve + +the student understanding some +things about the teacher? + +Well, first thing there +is is trust. + +The student has to presume that +the teacher is teaching + +the student correct +information, + +not lying to student. + +Ratified that you're all here +because presumably you all + +think that I'm not trying to +screw you by telling you stuff + +that's a lie. + +There's also this sort +of thing down here. + +Understanding of the +teacher's style. + +So you might say, well, +professor x, all he does is + +read slides to us in +class, so why go? + +You wouldn't be entirely +misadvised. + +That's an understanding +of one kind of style. + +Or you can say, well, old +Winston, he tries to tell us + +something definite and convey a +family of powerful ideas in + +every class. + +So maybe it's worth dragging +yourself out of bed at 10 + +o'clock in the morning. + +Those are style issues, and +those are things that the + +student uses to determine how +to match the student's style + +against that of the +instructor. + +So that helps us to interpret or +think about differences in + +style so that we can appreciate +whether we ought to + +be learning that way, where +that way is the way that's + +underneath down here, the way +you would teach a computer, + +the way [? Malkowski ?] + +taught a computer about +soybean diseases. + +We can do it that way, or we +can do it this way with a + +teacher who deliberately +organizes and shapes the + +learning sequence for the +benefit of a student who has a + +limited processing capability. + +Now you're humans, right? + +So think about what the machine +has to do here. + +The machine-- + +in order to learn anything +definite in each of those + +steps, the machine has to +build a description. + +So it has to describe the +examples to itself. + +That's unquestioned, right? + +Because what it's doing is +looking at the differences. + +So it can't look at the +differences unless it's got + +descriptions of things. + +So if you're like the machine, +then you can't learn anything + +unless you build descriptions. + +Unless you talk to yourself. + +And if you talk to yourself, +you're building the kind of + +descriptions that make +it possible for + +you to do the learning. + +And you say to me, I'm +an MIT student. + +I want to see the numbers. + +So let me show you +the numbers. + +And when I'm going +to show numbers-- + +the numbers that I'm going to +show you show you the virtues + +of talking to yourself. + +So here's the experiment. + +The experiment was done by a +friend of mine, Michelene Chi. + +Always seems to go by +the name Mickey Chi. + +There he is. + +So here's the deal. + +The students that she worked +with were expected to learn + +about elementary physics. + +801 type stuff. + +And she took eight subjects, +and she had them-- + +she took them through a bunch of +examples and then she gave + +them an examination. + +So eight subjects, and so they +divide into two groups. + +The bottom half and +the top half. + +The ones who did better than +average and the ones who did + +worse than average. + +So then you can say, well, +OK, what did that mean? + +You can say, how much did +they talk to themselves? + +Well, that was measured by +having them talk out loud as + +they solved the problems +on an examination. + +So we could ask how much self +explanation was done by the + +smart ones versus the +less smart ones? + +And here are the results. + +The worst ones-- the worst four +said about 10 things to + +themselves. + +The best four said about 35 +things to themselves. + +That's a pretty dramatic +difference. + +Here's the data in a more +straightforward form. + +This, by the way, points out +that the smart ones scored + +twice as high as the +less smart ones. + +And when we look at the number +of explanations they gave + +themselves in two categories, +smart ones said three times as + +much stuff to themselves +as the less smart ones. + +So, as you can see, the +explanations break down into + +two groups. + +Some have to do with monitoring +and not with + +physics at all. + +They're things like, +oh hell, I'm stuck. + +Or, I don't know what to do. + +And the others have to +do with physics. + +Things like, well, maybe I +should draw a force diagram. + +Or let me write down f equals +ma, or something like that, as + +physics knowledge. + +I think it's interesting that +this average score is + +different by a factor of two, +and the average talking to + +oneself differed by +a factor of three. + +Now this isn't quite there, +because what's not clear is if + +you encourage somebody to talk +to themself, and they talk to + +themselves more than they would +have ordinarily, does + +that make them score better? + +All we know is that the ones who +talk to themselves more do + +score better. + +But anecdotally, talking to +some veterans of 6.034, + +they've started talking to +themselves more when they + +solve problems, and they think +that it makes them smarter. + +Now I would caution you not to +do this too much in public. + +Because people can get the +wrong idea if you talk to + +yourself too much. + +But it does seem-- + +it does, in fact, +seem to help. + +Now what I did last time +is I told you how + +to be a good scientist. + +What I'm telling you now is how +to make yourself smarter. + +And I want to conclude this hour +by telling you about how + +you can package your ideas so +that they have greater impact. + +So I guess I could have said, +how to make yourself more + +famous, but I've limited +myself to saying how to + +package your ideas better. + +And the reason you want to +package your ideas better is + +because if you package your +ideas better than the next + +slug, then you're going to get +the faculty position and + +they're not. + +If you say to me, I'm +going to be an + +entrepreneur, same thing. + +You're going to get the venture +capitalist money and + +the next slug won't if you +package your ideas better. + +So this little piece of work +on the arch business got a + +whole lot more famous than +I ever expected. + +I did it when I was young and +stupid, and didn't have any + +idea what qualities might emerge +from a piece of work + +that would make it well known. + +I only figured it +out much later. + +But in retrospect, it has five +qualities that you can think + +about when you're deciding +whether your packaging of your + +idea is in a form that will +lead to that idea becoming + +well known. + +And since there are five of +them, it's convenient to put + +them all on the points +of a star like so. + +So quality number one. + +I've made these all into s-words +just to make them + +easier to remember. + +Quality number one is that +there's some kind of symbol + +associated with a work. + +Some kind of visual handle +that people will use to + +remember your idea. + +So what's the visual +symbol here? + +Well, that's astonishingly easy +to figure out, right? + +That's the arch. + +For years without my +intending it, this + +was called arch learning. + +So you need a symbol. + +Then you also need a slogan. + +That's a kind of +verbal handle. + +It doesn't explain the idea, +but it's enough of a handle + +to, as Minsky would say, put you +back in the mental state + +you were in when you understood +the idea in the + +first place. + +So what is the slogan +for this work? + +Anybody have any ideas? + +Pretty obvious. + +What's essential to this +process working? + +The ability to present an +example is very similar + +[INAUDIBLE], that constitutes +a model but + +isn't one of those. + +STUDENT: [INAUDIBLE]. + +PROFESSOR PATRICK WINSTON: +So it's a near miss. + +The next thing you need if your +work is going to become + +well known is a surprise. + +What's the surprise +with this stuff? + +Well, the surprise-- + +everything that had been done +in artificial intelligence + +having to do with learning +before this time was + +precursors to neural nets. + +Thousands of examples +to learn anything. + +So the big surprise was that it +was possible for a machine + +to learn something definite +from each of the examples. + +So that now goes by the name +of one shot learning. + +That was the surprise, that a +computer could learn something + +definite from a single +example. + +So let's see. + +We've almost completed +our star. + +But there are more +points on it. + +So this point is the salient. + +What's a salient-- + +what's a salient idea? + +Jose, do you know what +a salient idea is? + +He's too shy to tell me. + +What's a salient idea? + +Ah, who said important? + +Wrong answer, but very good. + +You're not shy. + +So what does it really mean? + +Yes. + +STUDENT: Relative to +what somebody's + +already thinking about? + +PROFESSOR PATRICK WINSTON: +Relative to what somebody's + +thinking about. + +Not quite. + +If you have a-- + +if you're an expert in-- + +yes? + +STUDENT: [INAUDIBLE]. + +PROFESSOR PATRICK WINSTON: +Really close. + +We're getting closer. + +[INAUDIBLE]. + +Yes? + +STUDENT: Maybe an idea that +wasn't obviously apparent, but + +becomes apparent gradually as +somebody starts to understand? + +PROFESSOR PATRICK WINSTON: We're +zeroing-- we're circling + +the wagons here and +zeroing in on it. + +Yes? + +STUDENT: If I'm preempting what +you're about to say, it + +has sort of a doorway of how you +can understand the idea. + +PROFESSOR PATRICK WINSTON: +It's what? + +Sorry. + +STUDENT: It's sort of like +a doorway of how you + +can grasp the idea. + +PROFESSOR PATRICK WINSTON: +That's sort if it, too, but if + +you study military history, +what's the salient on a fort? + +Well, this is a good word to +have in your vocabulary + +because it sort of means all of +those things, but what it + +really means is something +that sticks out. + +So on a fort, if this were a +fort, these would all be + +salients because +they stick out. + +So the salient idea is +usually important + +because it sticks out. + +But it's not-- the meaning is +not "important," the meaning + +is "stick out." + +So a piece of work becomes +more famous if it has + +something that sticks out. + +It's interesting. + +There are theses that have been +written at MIT that have + +too many good ideas. + +And how can have too +many good ideas? + +Well, you can have too many +good ideas if no one idea + +rises above and becomes the idea +that people think about + +when they think about you. + +We have people on the faculty +who would have been more + +famous if their theses +had fewer ideas. + +It's amazing. + +So this piece of work +did have a salient. + +And the salient idea was that +you could get one shot + +learning via the use +of near misses. + +That was the salient idea. + +The fifth thing, ah. + +Talk more about this +in my "How to + +Speak" lecture in January. + +The fifth thing I like people +to try to incorporate into + +their presentations +is a story. + +Because we humans somehow +love stories. + +We love people to +tell us stories. + +We love things to be packaged +in stories. + +And believe me, I think all of +education is essentially about + +storytelling and story +understanding. + +So if you want your idea to +be sold to the venture + +capitalist, if you want to get +the faculty job, if you want + +to get your book sold to a +publisher, if you want to sell + +something to a customer, ask +yourself if your presentation + +has these qualities in it. + +And if it has all of those +things, it's a lot more likely + +to be effective than +it doesn't. + +And you'll end up +being famous. + +Now you say to me, well, being +famous-- that sounds like the + +Sloan School type of concept. + +Isn't it immoral to +want to be famous? + +Maybe that's a decision +you can make. + +But whenever I think about the +question, I somehow think of + +the idea that your ideas +are like your children. + +You want to be sure that they +have the best life possible. + +So if they're not packaged +well, they won't. + +I'm also reminded of an evening +I spent at a soiree + +with Julia Child. + +Julia, and there's me. + +And I have no idea how +come I got to sit + +next to Julia Child. + +I think they thought I was +one of the rich Winstons. + +The Winston flowers, or the +Harry Winston diamonds or + +something like that. + +There I was, sitting next +to Julia Child. + +And the interesting thing-- + +by the way, did you notice +I'm now telling a story? + +The interesting thing about this +experience was that there + +was a constant flow +of people-- + +happened to be all women-- + +people going past Ms. Child +saying how wonderful she was + +to have made such an enormous +change in their life. + +Must have been 10 of them. + +It was amazing. + +Just steady flow. + +So eventually I leaned over to +her and I said, Ms. Child, is + +it fun to be famous? + +And she thought about it +a second and said, + +you get used to it. + +And that had a profound effect +on me, because you always say, + +well, what's the +opposite like? + +Is it fun to be ignored? + +And the answer is, no, it's not +much fun to be ignored. + +So yeah, it's something you can +get used to, but you can + +never get used to having your +stuff ignored, especially if + +it's good stuff. + +So that's why I commend +to you this business + +about packaging ideas. + +And now you see that 6034 +is not just about AI. + +It's about how to +do good science. + +It's how to make yourself +smarter, and how to make + +yourself more famous. \ No newline at end of file diff --git a/tR-mj5pYNSs.txt b/tR-mj5pYNSs.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7d8508df887dc9013971609007344f8fa767dbc --- /dev/null +++ b/tR-mj5pYNSs.txt @@ -0,0 +1,15387 @@ +align:start position:0% + +okay so we talked about perometry we had + + align:start position:0% +okay so we talked about perometry we had + + + align:start position:0% +okay so we talked about perometry we had +some sort of plasma like this and we had + + align:start position:0% +some sort of plasma like this and we had + + + align:start position:0% +some sort of plasma like this and we had +a clothing laser beam that went through + + align:start position:0% +a clothing laser beam that went through + + + align:start position:0% +a clothing laser beam that went through +the plasma and we split off a fraction + + align:start position:0% +the plasma and we split off a fraction + + + align:start position:0% +the plasma and we split off a fraction +that probing laser beam and sent it + + align:start position:0% +that probing laser beam and sent it + + + align:start position:0% +that probing laser beam and sent it +around the plasma which meant that when + + align:start position:0% +around the plasma which meant that when + + + align:start position:0% +around the plasma which meant that when +the two beams + + align:start position:0% +the two beams + + + align:start position:0% +the two beams +recombined we got some interference + + align:start position:0% +recombined we got some interference + + + align:start position:0% +recombined we got some interference +effect between them and we call these + + align:start position:0% +effect between them and we call these + + + align:start position:0% +effect between them and we call these +beams the + + align:start position:0% + + + + align:start position:0% + +probe and the + + align:start position:0% + + + + align:start position:0% + +reference and we said or we found that + + align:start position:0% +reference and we said or we found that + + + align:start position:0% +reference and we said or we found that +the phase difference between these two + + align:start position:0% +the phase difference between these two + + + align:start position:0% +the phase difference between these two +beams Delta F which is the phase + + align:start position:0% +beams Delta F which is the phase + + + align:start position:0% +beams Delta F which is the phase +accumulated by the probe beam minus the + + align:start position:0% +accumulated by the probe beam minus the + + + align:start position:0% +accumulated by the probe beam minus the +phase accumulated by the reference beam + + align:start position:0% +phase accumulated by the reference beam + + + align:start position:0% +phase accumulated by the reference beam +that is going to be minus Omega over 2 C + + align:start position:0% +that is going to be minus Omega over 2 C + + + align:start position:0% +that is going to be minus Omega over 2 C +* the critical density which is itself a + + align:start position:0% +* the critical density which is itself a + + + align:start position:0% +* the critical density which is itself a +function of the wavelength of the laser + + align:start position:0% +function of the wavelength of the laser + + + align:start position:0% +function of the wavelength of the laser +times the integral of the line + + align:start position:0% +times the integral of the line + + + align:start position:0% +times the integral of the line +integrated electron density so the + + align:start position:0% +integrated electron density so the + + + align:start position:0% +integrated electron density so the +electron density inside this plasma n e + + align:start position:0% +electron density inside this plasma n e + + + align:start position:0% +electron density inside this plasma n e +over some plasma length scale L like + + align:start position:0% +over some plasma length scale L like + + + align:start position:0% +over some plasma length scale L like +that and so this is a phase difference + + align:start position:0% +that and so this is a phase difference + + + align:start position:0% +that and so this is a phase difference +between the probe and the reference we + + align:start position:0% +between the probe and the reference we + + + align:start position:0% +between the probe and the reference we +want to measure that we came up with a + + align:start position:0% +want to measure that we came up with a + + + align:start position:0% +want to measure that we came up with a +simple system system uh where the + + align:start position:0% +simple system system uh where the + + + align:start position:0% +simple system system uh where the +intensity on our detector was just going + + align:start position:0% +intensity on our detector was just going + + + align:start position:0% +intensity on our detector was just going +to be equal to 1 plus the coine of this + + align:start position:0% +to be equal to 1 plus the coine of this + + + align:start position:0% +to be equal to 1 plus the coine of this +phase here and we realize very quickly + + align:start position:0% +phase here and we realize very quickly + + + align:start position:0% +phase here and we realize very quickly +that this causes us some problems + + align:start position:0% +that this causes us some problems + + + align:start position:0% +that this causes us some problems +because if we have a signal on our + + align:start position:0% +because if we have a signal on our + + + align:start position:0% +because if we have a signal on our +detector of 1 plus cos Delta pi and that + + align:start position:0% +detector of 1 plus cos Delta pi and that + + + align:start position:0% +detector of 1 plus cos Delta pi and that +signal looks + + align:start position:0% +signal looks + + + align:start position:0% +signal looks +like something like this so some sort of + + align:start position:0% +like something like this so some sort of + + + align:start position:0% +like something like this so some sort of +uh 1 plus cosine of some constant a t + + align:start position:0% +uh 1 plus cosine of some constant a t + + + align:start position:0% +uh 1 plus cosine of some constant a t +like that something is oscillating then + + align:start position:0% +like that something is oscillating then + + + align:start position:0% +like that something is oscillating then +we have a lot of phase ambiguity in the + + align:start position:0% +we have a lot of phase ambiguity in the + + + align:start position:0% +we have a lot of phase ambiguity in the +sense that we don't know when the phase + + align:start position:0% +sense that we don't know when the phase + + + align:start position:0% +sense that we don't know when the phase +is going up and down we also can't + + align:start position:0% +is going up and down we also can't + + + align:start position:0% +is going up and down we also can't +measure the phase more than modulo 2 pi + + align:start position:0% +measure the phase more than modulo 2 pi + + + align:start position:0% +measure the phase more than modulo 2 pi +and for this example here we had a look + + align:start position:0% +and for this example here we had a look + + + align:start position:0% +and for this example here we had a look +at what possible paths we could take in + + align:start position:0% +at what possible paths we could take in + + + align:start position:0% +at what possible paths we could take in +our little Delta 5 space that would give + + align:start position:0% +our little Delta 5 space that would give + + + align:start position:0% +our little Delta 5 space that would give +us exactly the same signal we said we + + align:start position:0% +us exactly the same signal we said we + + + align:start position:0% +us exactly the same signal we said we +could have one that ramps up like this + + align:start position:0% +could have one that ramps up like this + + + align:start position:0% +could have one that ramps up like this +we could also have a Delta 5 that goes + + align:start position:0% +we could also have a Delta 5 that goes + + + align:start position:0% +we could also have a Delta 5 that goes +down like that and then every time we + + align:start position:0% +down like that and then every time we + + + align:start position:0% +down like that and then every time we +get to some multiple of Pi um we lose + + align:start position:0% +get to some multiple of Pi um we lose + + + align:start position:0% +get to some multiple of Pi um we lose +track of whether we are going up or down + + align:start position:0% +track of whether we are going up or down + + + align:start position:0% +track of whether we are going up or down +and so we start having these multiple + + align:start position:0% +and so we start having these multiple + + + align:start position:0% +and so we start having these multiple +ranching Pathways and any possible path + + align:start position:0% +ranching Pathways and any possible path + + + align:start position:0% +ranching Pathways and any possible path +through this space is a + + align:start position:0% +through this space is a + + + align:start position:0% +through this space is a +valid uh we produce the same signal on + + align:start position:0% +valid uh we produce the same signal on + + + align:start position:0% +valid uh we produce the same signal on +our tectum we can't tell the difference + + align:start position:0% +our tectum we can't tell the difference + + + align:start position:0% +our tectum we can't tell the difference +between them so this we then recen a + + align:start position:0% +between them so this we then recen a + + + align:start position:0% +between them so this we then recen a +homod technique and then we looked at + + align:start position:0% +homod technique and then we looked at + + + align:start position:0% +homod technique and then we looked at +rodine techniques + + align:start position:0% +rodine techniques + + + align:start position:0% +rodine techniques +instead so when we started working with + + align:start position:0% +instead so when we started working with + + + align:start position:0% +instead so when we started working with +our Hine + + align:start position:0% + + + + align:start position:0% + +Technique we borrowed some tricks from + + align:start position:0% +Technique we borrowed some tricks from + + + align:start position:0% +Technique we borrowed some tricks from +FM radio transmission and we now have + + align:start position:0% +FM radio transmission and we now have + + + align:start position:0% +FM radio transmission and we now have +going through our plasma some radiation + + align:start position:0% +going through our plasma some radiation + + + align:start position:0% +going through our plasma some radiation +source which has got a frequency Omega + + align:start position:0% +source which has got a frequency Omega + + + align:start position:0% +source which has got a frequency Omega +one and now our reference beam has + + align:start position:0% +one and now our reference beam has + + + align:start position:0% +one and now our reference beam has +frequency Omega 2 so they've got some + + align:start position:0% +frequency Omega 2 so they've got some + + + align:start position:0% +frequency Omega 2 so they've got some +frequency shift between them we talked + + align:start position:0% +frequency shift between them we talked + + + align:start position:0% +frequency shift between them we talked +about techniques for doing that we put + + align:start position:0% +about techniques for doing that we put + + + align:start position:0% +about techniques for doing that we put +in some recombining beam splitter here + + align:start position:0% +in some recombining beam splitter here + + + align:start position:0% +in some recombining beam splitter here +and we put it through to our detector + + align:start position:0% +and we put it through to our detector + + + align:start position:0% +and we put it through to our detector +and we said if Omega 1 is equal to Omega + + align:start position:0% +and we said if Omega 1 is equal to Omega + + + align:start position:0% +and we said if Omega 1 is equal to Omega +2 we just get back our homine system + + align:start position:0% +2 we just get back our homine system + + + align:start position:0% +2 we just get back our homine system +which is kind of obvious because here we + + align:start position:0% +which is kind of obvious because here we + + + align:start position:0% +which is kind of obvious because here we +split it so they will have the same + + align:start position:0% +split it so they will have the same + + + align:start position:0% +split it so they will have the same +frequency but in the more interesting + + align:start position:0% +frequency but in the more interesting + + + align:start position:0% +frequency but in the more interesting +case where Omega one is not equal to + + align:start position:0% +case where Omega one is not equal to + + + align:start position:0% +case where Omega one is not equal to +Omega 2 uh we'll end up with um two + + align:start position:0% +Omega 2 uh we'll end up with um two + + + align:start position:0% +Omega 2 uh we'll end up with um two +frequencies present in our final signal + + align:start position:0% +frequencies present in our final signal + + + align:start position:0% +frequencies present in our final signal +we'll have a signal that on our detector + + align:start position:0% +we'll have a signal that on our detector + + + align:start position:0% +we'll have a signal that on our detector +even the absence of any plasma so if we + + align:start position:0% +even the absence of any plasma so if we + + + align:start position:0% +even the absence of any plasma so if we +just leave the system running we'll have + + align:start position:0% +just leave the system running we'll have + + + align:start position:0% +just leave the system running we'll have +a signal that looks a little + + align:start position:0% +a signal that looks a little + + + align:start position:0% +a signal that looks a little +bit like + + align:start position:0% +bit like + + + align:start position:0% +bit like +this and there will be two frequencies + + align:start position:0% +this and there will be two frequencies + + + align:start position:0% +this and there will be two frequencies +inside this there'll be this envelope + + align:start position:0% +inside this there'll be this envelope + + + align:start position:0% +inside this there'll be this envelope +frequency called the beat + + align:start position:0% +frequency called the beat + + + align:start position:0% +frequency called the beat +frequency which oscillates at the + + align:start position:0% +frequency which oscillates at the + + + align:start position:0% +frequency which oscillates at the +difference between the two Omega 1 minus + + align:start position:0% +difference between the two Omega 1 minus + + + align:start position:0% +difference between the two Omega 1 minus +Omega 2 and then there'll also be this + + align:start position:0% +Omega 2 and then there'll also be this + + + align:start position:0% +Omega 2 and then there'll also be this +fast frequency within it at Omega 1 plus + + align:start position:0% +fast frequency within it at Omega 1 plus + + + align:start position:0% +fast frequency within it at Omega 1 plus +Omega 2 now these frequencies for any + + align:start position:0% +Omega 2 now these frequencies for any + + + align:start position:0% +Omega 2 now these frequencies for any +radiation we're likely to use are very + + align:start position:0% +radiation we're likely to use are very + + + align:start position:0% +radiation we're likely to use are very +high so it's very hard to get a detector + + align:start position:0% +high so it's very hard to get a detector + + + align:start position:0% +high so it's very hard to get a detector +to work at these frequencies so we won't + + align:start position:0% +to work at these frequencies so we won't + + + align:start position:0% +to work at these frequencies so we won't +actually see this at all our detector + + align:start position:0% +actually see this at all our detector + + + align:start position:0% +actually see this at all our detector +will just average this out and what will + + align:start position:0% +will just average this out and what will + + + align:start position:0% +will just average this out and what will +see is this slow beat frequency instead + + align:start position:0% +see is this slow beat frequency instead + + + align:start position:0% +see is this slow beat frequency instead +and we can dtune Omega one from Omega 2 + + align:start position:0% +and we can dtune Omega one from Omega 2 + + + align:start position:0% +and we can dtune Omega one from Omega 2 +to get a beat frequency that nicely + + align:start position:0% +to get a beat frequency that nicely + + + align:start position:0% +to get a beat frequency that nicely +Falls within our detector + + align:start position:0% +Falls within our detector + + + align:start position:0% +Falls within our detector +range so far so good but there's no + + align:start position:0% +range so far so good but there's no + + + align:start position:0% +range so far so good but there's no +plasma physics in here um what we'll end + + align:start position:0% +plasma physics in here um what we'll end + + + align:start position:0% +plasma physics in here um what we'll end +up then is measuring something that + + align:start position:0% +up then is measuring something that + + + align:start position:0% +up then is measuring something that +looks + + align:start position:0% +looks + + + align:start position:0% +looks +like I over I is equal to one plus + + align:start position:0% +like I over I is equal to one plus + + + align:start position:0% +like I over I is equal to one plus +cosine of Omega 1 minus Omega 2 T that's + + align:start position:0% +cosine of Omega 1 minus Omega 2 T that's + + + align:start position:0% +cosine of Omega 1 minus Omega 2 T that's +the beat frequency but we will also have + + align:start position:0% +the beat frequency but we will also have + + + align:start position:0% +the beat frequency but we will also have +an additional phase term Delta f as we + + align:start position:0% +an additional phase term Delta f as we + + + align:start position:0% +an additional phase term Delta f as we +had before because that's what + + align:start position:0% +had before because that's what + + + align:start position:0% +had before because that's what +represents the phase of going through + + align:start position:0% +represents the phase of going through + + + align:start position:0% +represents the phase of going through +this plasma here Delta 5 and when we + + align:start position:0% +this plasma here Delta 5 and when we + + + align:start position:0% +this plasma here Delta 5 and when we +looked at this we said H that's + + align:start position:0% +looked at this we said H that's + + + align:start position:0% +looked at this we said H that's +interesting we've got frequencies times + + align:start position:0% +interesting we've got frequencies times + + + align:start position:0% +interesting we've got frequencies times +time and now we've just got this other + + align:start position:0% +time and now we've just got this other + + + align:start position:0% +time and now we've just got this other +term Delta which means that if Delta + + align:start position:0% +term Delta which means that if Delta + + + align:start position:0% +term Delta which means that if Delta +changes in time we have a change in + + align:start position:0% +changes in time we have a change in + + + align:start position:0% +changes in time we have a change in +Delta Pi with respect to time that's + + align:start position:0% +Delta Pi with respect to time that's + + + align:start position:0% +Delta Pi with respect to time that's +going to look like an + + align:start position:0% +going to look like an + + + align:start position:0% +going to look like an +effective frequency inside here and then + + align:start position:0% +effective frequency inside here and then + + + align:start position:0% +effective frequency inside here and then +we can rewrite this + + align:start position:0% +we can rewrite this + + + align:start position:0% +we can rewrite this +as 1 plus cosine of Omega 1 minus Omega + + align:start position:0% +as 1 plus cosine of Omega 1 minus Omega + + + align:start position:0% +as 1 plus cosine of Omega 1 minus Omega +2 plus partial of Delta pi partial T + + align:start position:0% +2 plus partial of Delta pi partial T + + + align:start position:0% +2 plus partial of Delta pi partial T +times time like that and what we + + align:start position:0% +times time like that and what we + + + align:start position:0% +times time like that and what we +actually measure on our detector at the + + align:start position:0% +actually measure on our detector at the + + + align:start position:0% +actually measure on our detector at the +end of the day is a signal which is + + align:start position:0% +end of the day is a signal which is + + + align:start position:0% +end of the day is a signal which is +oscillating with some frequency which + + align:start position:0% +oscillating with some frequency which + + + align:start position:0% +oscillating with some frequency which +I'll call Omega Prime which is a sum of + + align:start position:0% +I'll call Omega Prime which is a sum of + + + align:start position:0% +I'll call Omega Prime which is a sum of +these three different frequencies here + + align:start position:0% +these three different frequencies here + + + align:start position:0% +these three different frequencies here +which means that if we see a change in + + align:start position:0% +which means that if we see a change in + + + align:start position:0% +which means that if we see a change in +the frequency Omega Prime we know that + + align:start position:0% +the frequency Omega Prime we know that + + + align:start position:0% +the frequency Omega Prime we know that +that change is due to a change in Delta + + align:start position:0% +that change is due to a change in Delta + + + align:start position:0% +that change is due to a change in Delta +F in the phase and so now we can measure + + align:start position:0% +F in the phase and so now we can measure + + + align:start position:0% +F in the phase and so now we can measure +the temporal change in Phase which is + + align:start position:0% +the temporal change in Phase which is + + + align:start position:0% +the temporal change in Phase which is +the temporal + + align:start position:0% +the temporal + + + align:start position:0% +the temporal +in the electron density the nice thing + + align:start position:0% +in the electron density the nice thing + + + align:start position:0% +in the electron density the nice thing +about this technique is that we found + + align:start position:0% +about this technique is that we found + + + align:start position:0% +about this technique is that we found +that now we can distinguish between the + + align:start position:0% +that now we can distinguish between the + + + align:start position:0% +that now we can distinguish between the +phase going up in + + align:start position:0% +phase going up in + + + align:start position:0% +phase going up in +time from the phase going down in + + align:start position:0% +time from the phase going down in + + + align:start position:0% +time from the phase going down in +time which we were aren't able to do + + align:start position:0% +time which we were aren't able to do + + + align:start position:0% +time which we were aren't able to do +with this technique that's why we got + + align:start position:0% +with this technique that's why we got + + + align:start position:0% +with this technique that's why we got +this ambiguity every time we went past + + align:start position:0% +this ambiguity every time we went past + + + align:start position:0% +this ambiguity every time we went past +Pi whether we were going up or down with + + align:start position:0% +Pi whether we were going up or down with + + + align:start position:0% +Pi whether we were going up or down with +this technique it was resolved and we + + align:start position:0% +this technique it was resolved and we + + + align:start position:0% +this technique it was resolved and we +saw that we resolved that by looking at + + align:start position:0% +saw that we resolved that by looking at + + + align:start position:0% +saw that we resolved that by looking at +this in foror space + + align:start position:0% + + + + align:start position:0% + +so in the case for the homod + + align:start position:0% +so in the case for the homod + + + align:start position:0% +so in the case for the homod +technique we were detecting + + align:start position:0% +technique we were detecting + + + align:start position:0% +technique we were detecting +effectively this frequency here at some + + align:start position:0% +effectively this frequency here at some + + + align:start position:0% +effectively this frequency here at some +positive Omega so + + align:start position:0% +positive Omega so + + + align:start position:0% +positive Omega so +that's partial Delta FTI T but that gave + + align:start position:0% +that's partial Delta FTI T but that gave + + + align:start position:0% +that's partial Delta FTI T but that gave +exactly the same result as some negative + + align:start position:0% +exactly the same result as some negative + + + align:start position:0% +exactly the same result as some negative +frequency here so we couldn't tell the + + align:start position:0% +frequency here so we couldn't tell the + + + align:start position:0% +frequency here so we couldn't tell the +difference between the negative version + + align:start position:0% +difference between the negative version + + + align:start position:0% +difference between the negative version +of this in the positive version when we + + align:start position:0% +of this in the positive version when we + + + align:start position:0% +of this in the positive version when we +moved the hetr + + align:start position:0% +moved the hetr + + + align:start position:0% +moved the hetr +technique because we are effectively + + align:start position:0% +technique because we are effectively + + + align:start position:0% +technique because we are effectively +encoding our fluctuation quantity around + + align:start position:0% +encoding our fluctuation quantity around + + + align:start position:0% +encoding our fluctuation quantity around +some frequency Omega 1 minus Omega + + align:start position:0% + + + + align:start position:0% + +2 now we can tell the difference between + + align:start position:0% +2 now we can tell the difference between + + + align:start position:0% +2 now we can tell the difference between +whether we're in the negative side of + + align:start position:0% +whether we're in the negative side of + + + align:start position:0% +whether we're in the negative side of +that or the positive side of that so if + + align:start position:0% +that or the positive side of that so if + + + align:start position:0% +that or the positive side of that so if +we've shifted this frequency a small + + align:start position:0% +we've shifted this frequency a small + + + align:start position:0% +we've shifted this frequency a small +Distance by changing the phase by having + + align:start position:0% +Distance by changing the phase by having + + + align:start position:0% +Distance by changing the phase by having +some time changing electron density so + + align:start position:0% +some time changing electron density so + + + align:start position:0% +some time changing electron density so +this enabled us to resolve the ambiguity + + align:start position:0% +this enabled us to resolve the ambiguity + + + align:start position:0% +this enabled us to resolve the ambiguity +between these two and G this technique + + align:start position:0% +between these two and G this technique + + + align:start position:0% +between these two and G this technique +in general helps resolve a lot of the + + align:start position:0% +in general helps resolve a lot of the + + + align:start position:0% +in general helps resolve a lot of the +ambiguities associated with homod intry + + align:start position:0% +ambiguities associated with homod intry + + + align:start position:0% +ambiguities associated with homod intry +as I mentioned in the problem set you'll + + align:start position:0% +as I mentioned in the problem set you'll + + + align:start position:0% +as I mentioned in the problem set you'll +come across a couple of other techniques + + align:start position:0% +come across a couple of other techniques + + + align:start position:0% +come across a couple of other techniques +which can do this in a slightly cheaper + + align:start position:0% +which can do this in a slightly cheaper + + + align:start position:0% +which can do this in a slightly cheaper +but more ambiguous way so we got through + + align:start position:0% +but more ambiguous way so we got through + + + align:start position:0% +but more ambiguous way so we got through +all of that and I just want to pause + + align:start position:0% +all of that and I just want to pause + + + align:start position:0% +all of that and I just want to pause +here and see if there are any questions + + align:start position:0% +here and see if there are any questions + + + align:start position:0% +here and see if there are any questions +on that material before we go on and + + align:start position:0% +on that material before we go on and + + + align:start position:0% +on that material before we go on and +finish off the spatially petrine + + align:start position:0% +finish off the spatially petrine + + + align:start position:0% +finish off the spatially petrine +finishing where we do this as an Imaging + + align:start position:0% +finishing where we do this as an Imaging + + + align:start position:0% +finishing where we do this as an Imaging +technique so questions + + align:start position:0% + + + + align:start position:0% + +yeah so I understand the detector not + + align:start position:0% +yeah so I understand the detector not + + + align:start position:0% +yeah so I understand the detector not +able to resolve + + align:start position:0% +able to resolve + + + align:start position:0% +able to resolve +theega but does the time change in the + + align:start position:0% +theega but does the time change in the + + + align:start position:0% +theega but does the time change in the +phase difference contribute to that + + align:start position:0% +phase difference contribute to that + + + align:start position:0% +phase difference contribute to that +oscillation as well if you + + align:start position:0% +oscillation as well if you + + + align:start position:0% +oscillation as well if you +worble yes but it would if we look at it + + align:start position:0% +worble yes but it would if we look at it + + + align:start position:0% +worble yes but it would if we look at it +in a f + + align:start position:0% + + + + align:start position:0% + +domain I'll just use this one + + align:start position:0% + + + + align:start position:0% + +briefly Okay so + + align:start position:0% + + + + align:start position:0% + +exaggerate + + align:start position:0% +exaggerate + + + align:start position:0% +exaggerate +this let's say we've got our two + + align:start position:0% +this let's say we've got our two + + + align:start position:0% +this let's say we've got our two +frequencies Omega one and Omega 2 close + + align:start position:0% +frequencies Omega one and Omega 2 close + + + align:start position:0% +frequencies Omega one and Omega 2 close +together Omega one Omega 2 like that the + + align:start position:0% +together Omega one Omega 2 like that the + + + align:start position:0% +together Omega one Omega 2 like that the +difference between them is down here + + align:start position:0% +difference between them is down here + + + align:start position:0% +difference between them is down here +this is the be frequency Omega 1 minus + + align:start position:0% +this is the be frequency Omega 1 minus + + + align:start position:0% +this is the be frequency Omega 1 minus +Omega 2 and indeed we have some shift to + + align:start position:0% +Omega 2 and indeed we have some shift to + + + align:start position:0% +Omega 2 and indeed we have some shift to +this to higher or lower frequencies and + + align:start position:0% +this to higher or lower frequencies and + + + align:start position:0% +this to higher or lower frequencies and +that shift is due to the change in the + + align:start position:0% +that shift is due to the change in the + + + align:start position:0% +that shift is due to the change in the +phase in time the sum frequency is up + + align:start position:0% +phase in time the sum frequency is up + + + align:start position:0% +phase in time the sum frequency is up +here right this is Omega one plus Omega + + align:start position:0% +here right this is Omega one plus Omega + + + align:start position:0% +here right this is Omega one plus Omega +2 and indeed it will also be shifted by + + align:start position:0% +2 and indeed it will also be shifted by + + + align:start position:0% +2 and indeed it will also be shifted by +the same amount here but it would be at + + align:start position:0% +the same amount here but it would be at + + + align:start position:0% +the same amount here but it would be at +such a high frequency still that + + align:start position:0% +such a high frequency still that + + + align:start position:0% +such a high frequency still that +there'll be no way to measure it if you + + align:start position:0% +there'll be no way to measure it if you + + + align:start position:0% +there'll be no way to measure it if you +happen to have a system where your phase + + align:start position:0% +happen to have a system where your phase + + + align:start position:0% +happen to have a system where your phase +changes so much that you can shift this + + align:start position:0% +changes so much that you can shift this + + + align:start position:0% +changes so much that you can shift this +one down into the range you can + + align:start position:0% +one down into the range you can + + + align:start position:0% +one down into the range you can +measure + + align:start position:0% +measure + + + align:start position:0% +measure +then I don't think you need to technique + + align:start position:0% +then I don't think you need to technique + + + align:start position:0% +then I don't think you need to technique +at all at that point but anyway um + + align:start position:0% +at all at that point but anyway um + + + align:start position:0% +at all at that point but anyway um +certainly if that happens you should + + align:start position:0% +certainly if that happens you should + + + align:start position:0% +certainly if that happens you should +make omega 1 and Omega 2 larger until it + + align:start position:0% +make omega 1 and Omega 2 larger until it + + + align:start position:0% +make omega 1 and Omega 2 larger until it +doesn't happen because you remember that + + align:start position:0% +doesn't happen because you remember that + + + align:start position:0% +doesn't happen because you remember that +we have this condition that you only + + align:start position:0% +we have this condition that you only + + + align:start position:0% +we have this condition that you only +really get good results of this if Delta + + align:start position:0% +really get good results of this if Delta + + + align:start position:0% +really get good results of this if Delta +5 delta T is much much less than Omega 1 + + align:start position:0% +5 delta T is much much less than Omega 1 + + + align:start position:0% +5 delta T is much much less than Omega 1 +minus Omega 2 which necessarily means + + align:start position:0% +minus Omega 2 which necessarily means + + + align:start position:0% +minus Omega 2 which necessarily means +it's m less than Omega 1 plus Omega 2 + + align:start position:0% +it's m less than Omega 1 plus Omega 2 + + + align:start position:0% +it's m less than Omega 1 plus Omega 2 +you don't want your shifted frequency + + align:start position:0% +you don't want your shifted frequency + + + align:start position:0% +you don't want your shifted frequency +getting anyway close to zero because + + align:start position:0% +getting anyway close to zero because + + + align:start position:0% +getting anyway close to zero because +then you Alize it aliz it again and you + + align:start position:0% +then you Alize it aliz it again and you + + + align:start position:0% +then you Alize it aliz it again and you +won't be able to measure it so + + align:start position:0% +won't be able to measure it so + + + align:start position:0% +won't be able to measure it so +yeah good + + align:start position:0% +yeah good + + + align:start position:0% +yeah good +question any other + + align:start position:0% + + + + align:start position:0% + +questions well have either taught it + + align:start position:0% +questions well have either taught it + + + align:start position:0% +questions well have either taught it +very well or you're going to find the + + align:start position:0% +very well or you're going to find the + + + align:start position:0% +very well or you're going to find the +homework very + + align:start position:0% +homework very + + + align:start position:0% +homework very +fast right let's go on to spatially hetr + + align:start position:0% + + + + align:start position:0% + +techniques so here is the idea that we + + align:start position:0% +techniques so here is the idea that we + + + align:start position:0% +techniques so here is the idea that we +actually put an expanded + + align:start position:0% +actually put an expanded + + + align:start position:0% +actually put an expanded +beam through our plasma so we take our + + align:start position:0% +beam through our plasma so we take our + + + align:start position:0% +beam through our plasma so we take our +laser beam which maybe is initially + + align:start position:0% +laser beam which maybe is initially + + + align:start position:0% +laser beam which maybe is initially +relatively small and through some beam + + align:start position:0% +relatively small and through some beam + + + align:start position:0% +relatively small and through some beam +expander we get out a large laser beam + + align:start position:0% +expander we get out a large laser beam + + + align:start position:0% +expander we get out a large laser beam +and we pass that we've expanded our beam + + align:start position:0% +and we pass that we've expanded our beam + + + align:start position:0% +and we pass that we've expanded our beam +enough that our plasma is maybe slightly + + align:start position:0% +enough that our plasma is maybe slightly + + + align:start position:0% +enough that our plasma is maybe slightly +smaller than the beam diameter so there + + align:start position:0% +smaller than the beam diameter so there + + + align:start position:0% +smaller than the beam diameter so there +are some regions outside the plasma that + + align:start position:0% +are some regions outside the plasma that + + + align:start position:0% +are some regions outside the plasma that +we can still image where there won't be + + align:start position:0% +we can still image where there won't be + + + align:start position:0% +we can still image where there won't be +any phase shifts this turns out to be + + align:start position:0% +any phase shifts this turns out to be + + + align:start position:0% +any phase shifts this turns out to be +useful for zeroing our system talk about + + align:start position:0% +useful for zeroing our system talk about + + + align:start position:0% +useful for zeroing our system talk about +that in a little bit later on + + align:start position:0% +that in a little bit later on + + + align:start position:0% +that in a little bit later on +and what we said is this beam of course + + align:start position:0% +and what we said is this beam of course + + + align:start position:0% +and what we said is this beam of course +consists of some wave fronts like this + + align:start position:0% +consists of some wave fronts like this + + + align:start position:0% +consists of some wave fronts like this +and these wave fronts as they go through + + align:start position:0% +and these wave fronts as they go through + + + align:start position:0% +and these wave fronts as they go through +the plasma are going to advance because + + align:start position:0% +the plasma are going to advance because + + + align:start position:0% +the plasma are going to advance because +the phase speed in the plasma is faster + + align:start position:0% +the phase speed in the plasma is faster + + + align:start position:0% +the phase speed in the plasma is faster +than the speed of light and so the phase + + align:start position:0% +than the speed of light and so the phase + + + align:start position:0% +than the speed of light and so the phase +actually advances inside the plasma and + + align:start position:0% +actually advances inside the plasma and + + + align:start position:0% +actually advances inside the plasma and +so the wavefront that comes out is also + + align:start position:0% +so the wavefront that comes out is also + + + align:start position:0% +so the wavefront that comes out is also +going to be Advanced with respect the + + align:start position:0% +going to be Advanced with respect the + + + align:start position:0% +going to be Advanced with respect the +plasma we want to measure the change in + + align:start position:0% +plasma we want to measure the change in + + + align:start position:0% +plasma we want to measure the change in +this wavefront so one thing we could do + + align:start position:0% +this wavefront so one thing we could do + + + align:start position:0% +this wavefront so one thing we could do +is we could interfere it with a a set + + align:start position:0% +is we could interfere it with a a set + + + align:start position:0% +is we could interfere it with a a set +of plane waves that we derived from the + + align:start position:0% +of plane waves that we derived from the + + + align:start position:0% +of plane waves that we derived from the +same laser beam we'll put a beam + + align:start position:0% +same laser beam we'll put a beam + + + align:start position:0% +same laser beam we'll put a beam +splitter in somewhere down here send + + align:start position:0% +splitter in somewhere down here send + + + align:start position:0% +splitter in somewhere down here send +these around the + + align:start position:0% +these around the + + + align:start position:0% +these around the +plasma send it back in here and then + + align:start position:0% +plasma send it back in here and then + + + align:start position:0% +plasma send it back in here and then +we'll have another beam splitter as we + + align:start position:0% +we'll have another beam splitter as we + + + align:start position:0% +we'll have another beam splitter as we +normally do that recombines these and + + align:start position:0% +normally do that recombines these and + + + align:start position:0% +normally do that recombines these and +then we would have this nice flat phase + + align:start position:0% +then we would have this nice flat phase + + + align:start position:0% +then we would have this nice flat phase +front and we would now have from the + + align:start position:0% +front and we would now have from the + + + align:start position:0% +front and we would now have from the +prob beam some phase front which is + + align:start position:0% +prob beam some phase front which is + + + align:start position:0% +prob beam some phase front which is +Advanced a little bit and if we put all + + align:start position:0% +Advanced a little bit and if we put all + + + align:start position:0% +Advanced a little bit and if we put all +of this image onto a detector + + align:start position:0% + + + + align:start position:0% + +our camera like this we get a series of + + align:start position:0% +our camera like this we get a series of + + + align:start position:0% +our camera like this we get a series of +constructive and destructive + + align:start position:0% +constructive and destructive + + + align:start position:0% +constructive and destructive +interference fringes that you know maybe + + align:start position:0% +interference fringes that you know maybe + + + align:start position:0% +interference fringes that you know maybe +look like + + align:start position:0% +look like + + + align:start position:0% +look like +this just drawing a set of nested condol + + align:start position:0% +this just drawing a set of nested condol + + + align:start position:0% +this just drawing a set of nested condol +here we assume we've got some sort of + + align:start position:0% +here we assume we've got some sort of + + + align:start position:0% +here we assume we've got some sort of +Pete Central structure here now the + + align:start position:0% +Pete Central structure here now the + + + align:start position:0% +Pete Central structure here now the +trouble with this is if this is still a + + align:start position:0% +trouble with this is if this is still a + + + align:start position:0% +trouble with this is if this is still a +homod + + align:start position:0% +homod + + + align:start position:0% +homod +system uh in the sense that we can't + + align:start position:0% +system uh in the sense that we can't + + + align:start position:0% +system uh in the sense that we can't +tell whether these density consol are + + align:start position:0% +tell whether these density consol are + + + align:start position:0% +tell whether these density consol are +going up or down if I draw like a random + + align:start position:0% +going up or down if I draw like a random + + + align:start position:0% +going up or down if I draw like a random +line out across this my density could + + align:start position:0% +line out across this my density could + + + align:start position:0% +line out across this my density could +look like a peak structure maybe I've + + align:start position:0% +look like a peak structure maybe I've + + + align:start position:0% +look like a peak structure maybe I've +got a prior that that's true um but I + + align:start position:0% +got a prior that that's true um but I + + + align:start position:0% +got a prior that that's true um but I +can't prove to you that my density + + align:start position:0% +can't prove to you that my density + + + align:start position:0% +can't prove to you that my density +doesn't look + + align:start position:0% +doesn't look + + + align:start position:0% +doesn't look +like that instead or any number of other + + align:start position:0% +like that instead or any number of other + + + align:start position:0% +like that instead or any number of other +different paths through phas space that + + align:start position:0% +different paths through phas space that + + + align:start position:0% +different paths through phas space that +would give us the same Fringe pattern + + align:start position:0% +would give us the same Fringe pattern + + + align:start position:0% +would give us the same Fringe pattern +and so this is still problematic so what + + align:start position:0% +and so this is still problematic so what + + + align:start position:0% +and so this is still problematic so what +we what is a spatially hrod version of + + align:start position:0% +we what is a spatially hrod version of + + + align:start position:0% +we what is a spatially hrod version of +our temporary hrod system that we had up + + align:start position:0% +our temporary hrod system that we had up + + + align:start position:0% +our temporary hrod system that we had up +there and we do our spatial hrod dining + + align:start position:0% +there and we do our spatial hrod dining + + + align:start position:0% +there and we do our spatial hrod dining +by tilting these fringes that literally + + align:start position:0% +by tilting these fringes that literally + + + align:start position:0% +by tilting these fringes that literally +means slightly adjusting this mirror + + align:start position:0% +means slightly adjusting this mirror + + + align:start position:0% +means slightly adjusting this mirror +here so that the fringes come through at + + align:start position:0% +here so that the fringes come through at + + + align:start position:0% +here so that the fringes come through at +an absolutely tiny angles we're not + + align:start position:0% +an absolutely tiny angles we're not + + + align:start position:0% +an absolutely tiny angles we're not +talking about 10 degrees here we're + + align:start position:0% +talking about 10 degrees here we're + + + align:start position:0% +talking about 10 degrees here we're +talking about like much less than a + + align:start position:0% +talking about like much less than a + + + align:start position:0% +talking about like much less than a +degree and that means that our phase + + align:start position:0% +degree and that means that our phase + + + align:start position:0% +degree and that means that our phase +fronts are now coming at some slight + + align:start position:0% +fronts are now coming at some slight + + + align:start position:0% +fronts are now coming at some slight +tilt here and as opposed to having Omega + + align:start position:0% +tilt here and as opposed to having Omega + + + align:start position:0% +tilt here and as opposed to having Omega +one minus Omega 2 we now have an inbuilt + + align:start position:0% +one minus Omega 2 we now have an inbuilt + + + align:start position:0% +one minus Omega 2 we now have an inbuilt +phase pattern that looks like K1 + + align:start position:0% +phase pattern that looks like K1 + + + align:start position:0% +phase pattern that looks like K1 +minus K2 and these are vectors in the XY + + align:start position:0% +minus K2 and these are vectors in the XY + + + align:start position:0% +minus K2 and these are vectors in the XY +flame here we don't care about their Z + + align:start position:0% +flame here we don't care about their Z + + + align:start position:0% +flame here we don't care about their Z +components where this is X and this is y + + align:start position:0% +components where this is X and this is y + + + align:start position:0% +components where this is X and this is y +and by convention we usually have the Z + + align:start position:0% +and by convention we usually have the Z + + + align:start position:0% +and by convention we usually have the Z +coordinate going the direction of our + + align:start position:0% +coordinate going the direction of our + + + align:start position:0% +coordinate going the direction of our +Rays here so we're obviously putting a + + align:start position:0% +Rays here so we're obviously putting a + + + align:start position:0% +Rays here so we're obviously putting a +camera here we don't measure anything in + + align:start position:0% +camera here we don't measure anything in + + + align:start position:0% +camera here we don't measure anything in +Zed we're measure in y and x and we're + + align:start position:0% +Zed we're measure in y and x and we're + + + align:start position:0% +Zed we're measure in y and x and we're +interested in the misalignment of these + + align:start position:0% +interested in the misalignment of these + + + align:start position:0% +interested in the misalignment of these +wave fronts in X and Y so in the absence + + align:start position:0% +wave fronts in X and Y so in the absence + + + align:start position:0% +wave fronts in X and Y so in the absence +of any plasma + + align:start position:0% + + + + align:start position:0% + +this misalignment is simply going to + + align:start position:0% +this misalignment is simply going to + + + align:start position:0% +this misalignment is simply going to +give you a series of straight fringes + + align:start position:0% +give you a series of straight fringes + + + align:start position:0% +give you a series of straight fringes +evenly spaced like this and so that is + + align:start position:0% +evenly spaced like this and so that is + + + align:start position:0% +evenly spaced like this and so that is +like the signal that you have your beat + + align:start position:0% +like the signal that you have your beat + + + align:start position:0% +like the signal that you have your beat +signal here the green line in the + + align:start position:0% +signal here the green line in the + + + align:start position:0% +signal here the green line in the +absence of any plasma this signal just + + align:start position:0% +absence of any plasma this signal just + + + align:start position:0% +absence of any plasma this signal just +goes on and on and on but when we + + align:start position:0% +goes on and on and on but when we + + + align:start position:0% +goes on and on and on but when we +introduce the plasma into our system + + align:start position:0% +introduce the plasma into our system + + + align:start position:0% +introduce the plasma into our system +each of these fringes will get distorted + + align:start position:0% +each of these fringes will get distorted + + + align:start position:0% +each of these fringes will get distorted +and they'll get distorted by amount that + + align:start position:0% +and they'll get distorted by amount that + + + align:start position:0% +and they'll get distorted by amount that +corresponds to the line integrated + + align:start position:0% +corresponds to the line integrated + + + align:start position:0% +corresponds to the line integrated +electron density + + align:start position:0% + + + + align:start position:0% + +and by looking at the shift between + + align:start position:0% +and by looking at the shift between + + + align:start position:0% +and by looking at the shift between +where The Fringe was before we added the + + align:start position:0% +where The Fringe was before we added the + + + align:start position:0% +where The Fringe was before we added the +plasma and where The Fringe is + + align:start position:0% +plasma and where The Fringe is + + + align:start position:0% +plasma and where The Fringe is +afterwards we can then calculate the + + align:start position:0% +afterwards we can then calculate the + + + align:start position:0% +afterwards we can then calculate the +amount of density that's been added + + align:start position:0% +amount of density that's been added + + + align:start position:0% +amount of density that's been added +because we know that the Fringe shift is + + align:start position:0% +because we know that the Fringe shift is + + + align:start position:0% +because we know that the Fringe shift is +really fortal to the density here and + + align:start position:0% +really fortal to the density here and + + + align:start position:0% +really fortal to the density here and +once again because we've got a hring + + align:start position:0% +once again because we've got a hring + + + align:start position:0% +once again because we've got a hring +technique + + align:start position:0% + + + + align:start position:0% + +here we have avoided this ambiguity um + + align:start position:0% +here we have avoided this ambiguity um + + + align:start position:0% +here we have avoided this ambiguity um +even if these fringes overlap even if we + + align:start position:0% +even if these fringes overlap even if we + + + align:start position:0% +even if these fringes overlap even if we +have a distortion so large that this + + align:start position:0% +have a distortion so large that this + + + align:start position:0% +have a distortion so large that this +Fringe goes above this one when we go + + align:start position:0% +Fringe goes above this one when we go + + + align:start position:0% +Fringe goes above this one when we go +out to the edge of the plasma where The + + align:start position:0% +out to the edge of the plasma where The + + + align:start position:0% +out to the edge of the plasma where The +Fringe Shi is zero out here we can still + + align:start position:0% +Fringe Shi is zero out here we can still + + + align:start position:0% +Fringe Shi is zero out here we can still +uniquely identify each Fringe with its + + align:start position:0% +uniquely identify each Fringe with its + + + align:start position:0% +uniquely identify each Fringe with its +background Fringe and so we can track + + align:start position:0% +background Fringe and so we can track + + + align:start position:0% +background Fringe and so we can track +them along and we can say aha this one's + + align:start position:0% +them along and we can say aha this one's + + + align:start position:0% +them along and we can say aha this one's +done two Fringe shifts or four + + align:start position:0% +done two Fringe shifts or four + + + align:start position:0% +done two Fringe shifts or four +FRS and there is a for transform way to + + align:start position:0% +FRS and there is a for transform way to + + + align:start position:0% +FRS and there is a for transform way to +think about this as well but now we need + + align:start position:0% +think about this as well but now we need + + + align:start position:0% +think about this as well but now we need +to have a two-dimensional Foria + + align:start position:0% +to have a two-dimensional Foria + + + align:start position:0% +to have a two-dimensional Foria +transform and what we're looking at here + + align:start position:0% +transform and what we're looking at here + + + align:start position:0% +transform and what we're looking at here +are now a x and + + align:start position:0% +are now a x and + + + align:start position:0% +are now a x and +KY and so originally your K1 minus K2 + + align:start position:0% +KY and so originally your K1 minus K2 + + + align:start position:0% +KY and so originally your K1 minus K2 +beat frequency is maybe up here and by + + align:start position:0% +beat frequency is maybe up here and by + + + align:start position:0% +beat frequency is maybe up here and by +symmetry because our signal is + + align:start position:0% +symmetry because our signal is + + + align:start position:0% +symmetry because our signal is +submission down here so this is the + + align:start position:0% +submission down here so this is the + + + align:start position:0% +submission down here so this is the +negative number as well + + align:start position:0% +negative number as well + + + align:start position:0% +negative number as well +and now we've distorted these fringes + + align:start position:0% +and now we've distorted these fringes + + + align:start position:0% +and now we've distorted these fringes +it's taken this initial beat frequency + + align:start position:0% +it's taken this initial beat frequency + + + align:start position:0% +it's taken this initial beat frequency +and maybe we now have for components + + align:start position:0% +and maybe we now have for components + + + align:start position:0% +and maybe we now have for components +that look a little bit like this or they + + align:start position:0% +that look a little bit like this or they + + + align:start position:0% +that look a little bit like this or they +could look like that and moving around + + align:start position:0% +could look like that and moving around + + + align:start position:0% +could look like that and moving around +in Foria space changes what the shape of + + align:start position:0% +in Foria space changes what the shape of + + + align:start position:0% +in Foria space changes what the shape of +your background trend is look like this + + align:start position:0% +your background trend is look like this + + + align:start position:0% +your background trend is look like this +here where my components are roughly + + align:start position:0% +here where my components are roughly + + + align:start position:0% +here where my components are roughly +equal in KX and KY that will correspond + + align:start position:0% +equal in KX and KY that will correspond + + + align:start position:0% +equal in KX and KY that will correspond +to fringes which are 45 degrees if I had + + align:start position:0% +to fringes which are 45 degrees if I had + + + align:start position:0% +to fringes which are 45 degrees if I had +my V frequency down here this would cor + + align:start position:0% +my V frequency down here this would cor + + + align:start position:0% +my V frequency down here this would cor +fringes with the K Vector in that + + align:start position:0% +fringes with the K Vector in that + + + align:start position:0% +fringes with the K Vector in that +direction that like + + align:start position:0% +direction that like + + + align:start position:0% +direction that like +that so you can choose what your carrier + + align:start position:0% +that so you can choose what your carrier + + + align:start position:0% +that so you can choose what your carrier +frequency is and there was a good + + align:start position:0% +frequency is and there was a good + + + align:start position:0% +frequency is and there was a good +question in the last lecture about your + + align:start position:0% +question in the last lecture about your + + + align:start position:0% +question in the last lecture about your +sensitivity to different density + + align:start position:0% +sensitivity to different density + + + align:start position:0% +sensitivity to different density +gradients in different directions and + + align:start position:0% +gradients in different directions and + + + align:start position:0% +gradients in different directions and +indeed you have more sensitivity uh in + + align:start position:0% +indeed you have more sensitivity uh in + + + align:start position:0% +indeed you have more sensitivity uh in +the Direction perpendicular to where + + align:start position:0% +the Direction perpendicular to where + + + align:start position:0% +the Direction perpendicular to where +your carrier frequency spatial + + align:start position:0% +your carrier frequency spatial + + + align:start position:0% +your carrier frequency spatial +frequency okay there's a lot going on + + align:start position:0% +frequency okay there's a lot going on + + + align:start position:0% +frequency okay there's a lot going on +there I actually have a load of slides + + align:start position:0% +there I actually have a load of slides + + + align:start position:0% +there I actually have a load of slides +of pictures of real data on this that + + align:start position:0% +of pictures of real data on this that + + + align:start position:0% +of pictures of real data on this that +might make it a little bit clearer but + + align:start position:0% +might make it a little bit clearer but + + + align:start position:0% +might make it a little bit clearer but +before we get on to that are there any + + align:start position:0% + + + + align:start position:0% + +questions yeah + + align:start position:0% +questions yeah + + + align:start position:0% +questions yeah +uh I might have answered this but so by + + align:start position:0% +uh I might have answered this but so by + + + align:start position:0% +uh I might have answered this but so by +by + + align:start position:0% +by + + + align:start position:0% +by +tilting the wave FRS of the reference + + align:start position:0% +tilting the wave FRS of the reference + + + align:start position:0% +tilting the wave FRS of the reference +beam what in essence we're doing is + + align:start position:0% +beam what in essence we're doing is + + + align:start position:0% +beam what in essence we're doing is +we're changing + + align:start position:0% +we're changing + + + align:start position:0% +we're changing +the the wave Vector component that is + + align:start position:0% +the the wave Vector component that is + + + align:start position:0% +the the wave Vector component that is +interfering with what's coming through + + align:start position:0% +interfering with what's coming through + + + align:start position:0% +interfering with what's coming through +the p i mean we're trying to create some + + align:start position:0% +the p i mean we're trying to create some + + + align:start position:0% +the p i mean we're trying to create some +beat interference here so I guess you + + align:start position:0% +beat interference here so I guess you + + + align:start position:0% +beat interference here so I guess you +know technically we're not changing the + + align:start position:0% +know technically we're not changing the + + + align:start position:0% +know technically we're not changing the +magnitude of K no because because in + + align:start position:0% +magnitude of K no because because in + + + align:start position:0% +magnitude of K no because because in +free space the magnitude of K is fixed + + align:start position:0% +free space the magnitude of K is fixed + + + align:start position:0% +free space the magnitude of K is fixed +precisely because the dispersion + + align:start position:0% +precisely because the dispersion + + + align:start position:0% +precisely because the dispersion +relationship The Wave in free space not + + align:start position:0% +relationship The Wave in free space not + + + align:start position:0% +relationship The Wave in free space not +in a plasma is Omega CK and so what + + align:start position:0% +in a plasma is Omega CK and so what + + + align:start position:0% +in a plasma is Omega CK and so what +we've done by tilting the wave is we've + + align:start position:0% +we've done by tilting the wave is we've + + + align:start position:0% +we've done by tilting the wave is we've +changed the distribution of the of that + + align:start position:0% +changed the distribution of the of that + + + align:start position:0% +changed the distribution of the of that +magnitude in either Dimension so what + + align:start position:0% +magnitude in either Dimension so what + + + align:start position:0% +magnitude in either Dimension so what +say well so now the component of K that + + align:start position:0% +say well so now the component of K that + + + align:start position:0% +say well so now the component of K that +is interfering with the wave front is + + align:start position:0% +is interfering with the wave front is + + + align:start position:0% +is interfering with the wave front is +slightly different yeah so K2 here is + + align:start position:0% +slightly different yeah so K2 here is + + + align:start position:0% +slightly different yeah so K2 here is +the is for example the reference beam + + align:start position:0% +the is for example the reference beam + + + align:start position:0% +the is for example the reference beam +here and K1 + + align:start position:0% +here and K1 + + + align:start position:0% +here and K1 +is this beam coming through for example + + align:start position:0% +is this beam coming through for example + + + align:start position:0% +is this beam coming through for example +yeah so K1 is exclusively an X I guess + + align:start position:0% +yeah so K1 is exclusively an X I guess + + + align:start position:0% +yeah so K1 is exclusively an X I guess +think about that if we align our if we + + align:start position:0% +think about that if we align our if we + + + align:start position:0% +think about that if we align our if we +aligned it in this way but if I align + + align:start position:0% +aligned it in this way but if I align + + + align:start position:0% +aligned it in this way but if I align +the fringes if I rotate the fringes I + + align:start position:0% +the fringes if I rotate the fringes I + + + align:start position:0% +the fringes if I rotate the fringes I +can measure other components of it as + + align:start position:0% +can measure other components of it as + + + align:start position:0% +can measure other components of it as +well and it turns out as I'll show you + + align:start position:0% +well and it turns out as I'll show you + + + align:start position:0% +well and it turns out as I'll show you +you still get to measure some of the Y + + align:start position:0% +you still get to measure some of the Y + + + align:start position:0% +you still get to measure some of the Y +components and things like that even if + + align:start position:0% +components and things like that even if + + + align:start position:0% +components and things like that even if +you're in this setup which is most + + align:start position:0% +you're in this setup which is most + + + align:start position:0% +you're in this setup which is most +sensitive to X component but you're + + align:start position:0% +sensitive to X component but you're + + + align:start position:0% +sensitive to X component but you're +right yeah was there another question + + align:start position:0% +right yeah was there another question + + + align:start position:0% +right yeah was there another question +yeah so as the + + align:start position:0% +yeah so as the + + + align:start position:0% +yeah so as the +prob uh light proes through the plasma + + align:start position:0% +prob uh light proes through the plasma + + + align:start position:0% +prob uh light proes through the plasma +it'll refract and bend around and all + + align:start position:0% +it'll refract and bend around and all + + + align:start position:0% +it'll refract and bend around and all +this why don't you get het hoding for + + align:start position:0% +this why don't you get het hoding for + + + align:start position:0% +this why don't you get het hoding for +free from sort of changes to the wave + + align:start position:0% +free from sort of changes to the wave + + + align:start position:0% +free from sort of changes to the wave +propagation as it transs the + + align:start position:0% +propagation as it transs the + + + align:start position:0% +propagation as it transs the +plasma so those yeah so the question was + + align:start position:0% +plasma so those yeah so the question was + + + align:start position:0% +plasma so those yeah so the question was +why didn't you get hring for free as you + + align:start position:0% +why didn't you get hring for free as you + + + align:start position:0% +why didn't you get hring for free as you +sort of get K changing within the plasma + + align:start position:0% +sort of get K changing within the plasma + + + align:start position:0% +sort of get K changing within the plasma +here I mean that's effectively you're + + align:start position:0% +here I mean that's effectively you're + + + align:start position:0% +here I mean that's effectively you're +measuring here with these phase Contours + + align:start position:0% +measuring here with these phase Contours + + + align:start position:0% +measuring here with these phase Contours +it's just that they're still ambiguous + + align:start position:0% +it's just that they're still ambiguous + + + align:start position:0% +it's just that they're still ambiguous +um you need to shift them so that + + align:start position:0% +um you need to shift them so that + + + align:start position:0% +um you need to shift them so that +they're as we did in frequency space for + + align:start position:0% +they're as we did in frequency space for + + + align:start position:0% +they're as we did in frequency space for +the hrod temporary hrod version you need + + align:start position:0% +the hrod temporary hrod version you need + + + align:start position:0% +the hrod temporary hrod version you need +to shift them into such a direction that + + align:start position:0% +to shift them into such a direction that + + + align:start position:0% +to shift them into such a direction that +they're completely unambiguous whether + + align:start position:0% +they're completely unambiguous whether + + + align:start position:0% +they're completely unambiguous whether +your phase shift is up or down and here + + align:start position:0% +your phase shift is up or down and here + + + align:start position:0% +your phase shift is up or down and here +at the moment even with this you're + + align:start position:0% +at the moment even with this you're + + + align:start position:0% +at the moment even with this you're +going to get these ambiguous + + align:start position:0% +going to get these ambiguous + + + align:start position:0% +going to get these ambiguous +fringes um I'll show you some pictures + + align:start position:0% +fringes um I'll show you some pictures + + + align:start position:0% +fringes um I'll show you some pictures +that maybe will make it a bit clear in a + + align:start position:0% +that maybe will make it a bit clear in a + + + align:start position:0% +that maybe will make it a bit clear in a +moment but yeah were there any questions + + align:start position:0% +moment but yeah were there any questions + + + align:start position:0% +moment but yeah were there any questions +online + + align:start position:0% + + + + align:start position:0% + +um hi yeah yeah um so how uh how like + + align:start position:0% +um hi yeah yeah um so how uh how like + + + align:start position:0% +um hi yeah yeah um so how uh how like +fine can you get for like the amount of + + align:start position:0% +fine can you get for like the amount of + + + align:start position:0% +fine can you get for like the amount of +like X components or Y components in + + align:start position:0% +like X components or Y components in + + + align:start position:0% +like X components or Y components in +your uh your scan like how detailed can + + align:start position:0% +your uh your scan like how detailed can + + + align:start position:0% +your uh your scan like how detailed can +you get because I'm assuming because the + + align:start position:0% +you get because I'm assuming because the + + + align:start position:0% +you get because I'm assuming because the +wave front is continuous but I'm + + align:start position:0% +wave front is continuous but I'm + + + align:start position:0% +wave front is continuous but I'm +assuming you can't get like perfectly + + align:start position:0% +assuming you can't get like perfectly + + + align:start position:0% +assuming you can't get like perfectly +granular like understanding of the + + align:start position:0% +granular like understanding of the + + + align:start position:0% +granular like understanding of the +Plasma's density just from this even did + + align:start position:0% +Plasma's density just from this even did + + + align:start position:0% +Plasma's density just from this even did +everyone in the room hear the question + + align:start position:0% +everyone in the room hear the question + + + align:start position:0% +everyone in the room hear the question +like what's it sort of limits on + + align:start position:0% +like what's it sort of limits on + + + align:start position:0% +like what's it sort of limits on +resolution in a way so I'll spal + + align:start position:0% +resolution in a way so I'll spal + + + align:start position:0% +resolution in a way so I'll spal +resolution is set by our Fringe spacing + + align:start position:0% +resolution is set by our Fringe spacing + + + align:start position:0% +resolution is set by our Fringe spacing +right so we can usually we can say this + + align:start position:0% +right so we can usually we can say this + + + align:start position:0% +right so we can usually we can say this +is a dark destructive interference and + + align:start position:0% +is a dark destructive interference and + + + align:start position:0% +is a dark destructive interference and +this is a light constructive + + align:start position:0% +this is a light constructive + + + align:start position:0% +this is a light constructive +interference and theoretically you could + + align:start position:0% +interference and theoretically you could + + + align:start position:0% +interference and theoretically you could +identify like the gray point halfway + + align:start position:0% +identify like the gray point halfway + + + align:start position:0% +identify like the gray point halfway +between light and dark but it starts + + align:start position:0% +between light and dark but it starts + + + align:start position:0% +between light and dark but it starts +getting a bit ambiguous there dark and + + align:start position:0% +getting a bit ambiguous there dark and + + + align:start position:0% +getting a bit ambiguous there dark and +light are pretty obvious and that means + + align:start position:0% +light are pretty obvious and that means + + + align:start position:0% +light are pretty obvious and that means +that your spatial resolution is of set + + align:start position:0% +that your spatial resolution is of set + + + align:start position:0% +that your spatial resolution is of set +by the spacing between your fringes and + + align:start position:0% +by the spacing between your fringes and + + + align:start position:0% +by the spacing between your fringes and +if I choose to have my fringes closer + + align:start position:0% +if I choose to have my fringes closer + + + align:start position:0% +if I choose to have my fringes closer +together so I choose a K1 minus K2 which + + align:start position:0% +together so I choose a K1 minus K2 which + + + align:start position:0% +together so I choose a K1 minus K2 which +is a larger number so a higher beat + + align:start position:0% +is a larger number so a higher beat + + + align:start position:0% +is a larger number so a higher beat +frequency then I would have my fringes + + align:start position:0% +frequency then I would have my fringes + + + align:start position:0% +frequency then I would have my fringes +closed together like this I would gain + + align:start position:0% +closed together like this I would gain + + + align:start position:0% +closed together like this I would gain +spatial resolution and I'd be able to + + align:start position:0% +spatial resolution and I'd be able to + + + align:start position:0% +spatial resolution and I'd be able to +keep playing that game down to the + + align:start position:0% +keep playing that game down to the + + + align:start position:0% +keep playing that game down to the +resolution of my camera where I like + + align:start position:0% +resolution of my camera where I like + + + align:start position:0% +resolution of my camera where I like +need certain number of pixels to be able + + align:start position:0% +need certain number of pixels to be able + + + align:start position:0% +need certain number of pixels to be able +to difference tell the difference + + align:start position:0% +to difference tell the difference + + + align:start position:0% +to difference tell the difference +between light and dark the trouble is as + + align:start position:0% +between light and dark the trouble is as + + + align:start position:0% +between light and dark the trouble is as +I shrink this down I am gaining spatial + + align:start position:0% +I shrink this down I am gaining spatial + + + align:start position:0% +I shrink this down I am gaining spatial +resolution but I am losing a resolution + + align:start position:0% +resolution but I am losing a resolution + + + align:start position:0% +resolution but I am losing a resolution +of the density because these Fringe + + align:start position:0% +of the density because these Fringe + + + align:start position:0% +of the density because these Fringe +shifts are now smaller and smaller you + + align:start position:0% +shifts are now smaller and smaller you + + + align:start position:0% +shifts are now smaller and smaller you +know The Fringe is now only moving a + + align:start position:0% +know The Fringe is now only moving a + + + align:start position:0% +know The Fringe is now only moving a +very small distance maybe it's only + + align:start position:0% +very small distance maybe it's only + + + align:start position:0% +very small distance maybe it's only +moving two pixels or one one pixel now + + align:start position:0% +moving two pixels or one one pixel now + + + align:start position:0% +moving two pixels or one one pixel now +I've got a 50% error right because I + + align:start position:0% +I've got a 50% error right because I + + + align:start position:0% +I've got a 50% error right because I +don't know whether it's two or one + + align:start position:0% +don't know whether it's two or one + + + align:start position:0% +don't know whether it's two or one +pixels so there is a tradeoff directly + + align:start position:0% +pixels so there is a tradeoff directly + + + align:start position:0% +pixels so there is a tradeoff directly +between the density resolution of this + + align:start position:0% +between the density resolution of this + + + align:start position:0% +between the density resolution of this +Diagnostic and the spatial resolution so + + align:start position:0% +Diagnostic and the spatial resolution so + + + align:start position:0% +Diagnostic and the spatial resolution so +that's a very good question and that is + + align:start position:0% +that's a very good question and that is + + + align:start position:0% +that's a very good question and that is +the same it's always the same because + + align:start position:0% +the same it's always the same because + + + align:start position:0% +the same it's always the same because +mathematically it's the same it's the + + align:start position:0% +mathematically it's the same it's the + + + align:start position:0% +mathematically it's the same it's the +same for the temporary hetr version as + + align:start position:0% +same for the temporary hetr version as + + + align:start position:0% +same for the temporary hetr version as +well so you can have time resolution or + + align:start position:0% +well so you can have time resolution or + + + align:start position:0% +well so you can have time resolution or +you can have density resolution but you + + align:start position:0% +you can have density resolution but you + + + align:start position:0% +you can have density resolution but you +can't have both they trade off against + + align:start position:0% +can't have both they trade off against + + + align:start position:0% +can't have both they trade off against +each other I see that makes sense all + + align:start position:0% +each other I see that makes sense all + + + align:start position:0% +each other I see that makes sense all +right thank you thank you yeah can this + + align:start position:0% +right thank you thank you yeah can this + + + align:start position:0% +right thank you thank you yeah can this +be used for temporal measurements as + + align:start position:0% +be used for temporal measurements as + + + align:start position:0% +be used for temporal measurements as +well you can just keep you know rolling + + align:start position:0% +well you can just keep you know rolling + + + align:start position:0% +well you can just keep you know rolling +Imaging yeah so can this be used for + + align:start position:0% +Imaging yeah so can this be used for + + + align:start position:0% +Imaging yeah so can this be used for +temporal measurements as well yes if you + + align:start position:0% +temporal measurements as well yes if you + + + align:start position:0% +temporal measurements as well yes if you +have a fast camera uh you can do this + + align:start position:0% +have a fast camera uh you can do this + + + align:start position:0% +have a fast camera uh you can do this +for example I know a guy who used a a CW + + align:start position:0% +for example I know a guy who used a a CW + + + align:start position:0% +for example I know a guy who used a a CW +laser beam so basically continuous wave + + align:start position:0% +laser beam so basically continuous wave + + + align:start position:0% +laser beam so basically continuous wave +laser beam at like 30 Watts or something + + align:start position:0% +laser beam at like 30 Watts or something + + + align:start position:0% +laser beam at like 30 Watts or something +terrifying and he had a fast camera and + + align:start position:0% +terrifying and he had a fast camera and + + + align:start position:0% +terrifying and he had a fast camera and +so he took you know the fast camera + + align:start position:0% +so he took you know the fast camera + + + align:start position:0% +so he took you know the fast camera +could take 12 pictures one every five + + align:start position:0% +could take 12 pictures one every five + + + align:start position:0% +could take 12 pictures one every five +NCS and you would be able to make a + + align:start position:0% +NCS and you would be able to make a + + + align:start position:0% +NCS and you would be able to make a +little movie and depending on the speed + + align:start position:0% +little movie and depending on the speed + + + align:start position:0% +little movie and depending on the speed +of your PL plasma you know if you don't + + align:start position:0% +of your PL plasma you know if you don't + + + align:start position:0% +of your PL plasma you know if you don't +need every five NCS but you working with + + align:start position:0% +need every five NCS but you working with + + + align:start position:0% +need every five NCS but you working with +a plasma where the time scale is + + align:start position:0% +a plasma where the time scale is + + + align:start position:0% +a plasma where the time scale is +milliseconds then you can actually just + + align:start position:0% +milliseconds then you can actually just + + + align:start position:0% +milliseconds then you can actually just +have a continuous cam so you need a nice + + align:start position:0% +have a continuous cam so you need a nice + + + align:start position:0% +have a continuous cam so you need a nice +bright light source that is continuous + + align:start position:0% +bright light source that is continuous + + + align:start position:0% +bright light source that is continuous +enough and you need a camera which is + + align:start position:0% +enough and you need a camera which is + + + align:start position:0% +enough and you need a camera which is +fast enough and that's you know what + + align:start position:0% +fast enough and that's you know what + + + align:start position:0% +fast enough and that's you know what +sets the resolution so you could make a + + align:start position:0% +sets the resolution so you could make a + + + align:start position:0% +sets the resolution so you could make a +2d movie of the density Evolution time + + align:start position:0% +2d movie of the density Evolution time + + + align:start position:0% +2d movie of the density Evolution time +so yes limitation here is just + + align:start position:0% +so yes limitation here is just + + + align:start position:0% +so yes limitation here is just +technological yes yeah yeah yeah this + + align:start position:0% +technological yes yeah yeah yeah this + + + align:start position:0% +technological yes yeah yeah yeah this +technique is I mean that that that is + + align:start position:0% +technique is I mean that that that is + + + align:start position:0% +technique is I mean that that that is +time resolved spatially hetr intry I + + align:start position:0% +time resolved spatially hetr intry I + + + align:start position:0% +time resolved spatially hetr intry I +don't think you can do temporary and + + align:start position:0% +don't think you can do temporary and + + + align:start position:0% +don't think you can do temporary and +spatially hetr front between the same + + align:start position:0% +spatially hetr front between the same + + + align:start position:0% +spatially hetr front between the same +diagnostic if you work out a way of + + align:start position:0% +diagnostic if you work out a way of + + + align:start position:0% +diagnostic if you work out a way of +doing it let me know uh that + + align:start position:0% +doing it let me know uh that + + + align:start position:0% +doing it let me know uh that +sounds hard maybe not + + align:start position:0% +sounds hard maybe not + + + align:start position:0% +sounds hard maybe not +necessary because you've already got + + align:start position:0% +necessary because you've already got + + + align:start position:0% +necessary because you've already got +around the ambiguity in one way so I + + align:start position:0% +around the ambiguity in one way so I + + + align:start position:0% +around the ambiguity in one way so I +don't know if you need both and if you + + align:start position:0% +don't know if you need both and if you + + + align:start position:0% +don't know if you need both and if you +had a homod system in one sense I think + + align:start position:0% +had a homod system in one sense I think + + + align:start position:0% +had a homod system in one sense I think +You' be able to use lack of phase + + align:start position:0% +You' be able to use lack of phase + + + align:start position:0% +You' be able to use lack of phase +ambiguity from the hrod par system to + + align:start position:0% +ambiguity from the hrod par system to + + + align:start position:0% +ambiguity from the hrod par system to +get over that but I haven't really + + align:start position:0% +get over that but I haven't really + + + align:start position:0% +get over that but I haven't really +thought about it that much interesting + + align:start position:0% +thought about it that much interesting + + + align:start position:0% +thought about it that much interesting +question yeah could be a fun diagnostic + + align:start position:0% +question yeah could be a fun diagnostic + + + align:start position:0% +question yeah could be a fun diagnostic +very + + align:start position:0% +very + + + align:start position:0% +very +expensive so yeah cool any other + + align:start position:0% +expensive so yeah cool any other + + + align:start position:0% +expensive so yeah cool any other +questions yeah so so this case it's + + align:start position:0% +questions yeah so so this case it's + + + align:start position:0% +questions yeah so so this case it's +we're not it's not just we're measuring + + align:start position:0% +we're not it's not just we're measuring + + + align:start position:0% +we're not it's not just we're measuring +the K factor of um how we're measuring + + align:start position:0% +the K factor of um how we're measuring + + + align:start position:0% +the K factor of um how we're measuring +the wave we're actually we're actually + + align:start position:0% +the wave we're actually we're actually + + + align:start position:0% +the wave we're actually we're actually +deflecting the probe wave a little oh so + + align:start position:0% +deflecting the probe wave a little oh so + + + align:start position:0% +deflecting the probe wave a little oh so +the question is is the probe wave + + align:start position:0% +the question is is the probe wave + + + align:start position:0% +the question is is the probe wave +actually being deflected as it goes + + align:start position:0% +actually being deflected as it goes + + + align:start position:0% +actually being deflected as it goes +through Plaza well done to stoping that + + align:start position:0% +through Plaza well done to stoping that + + + align:start position:0% +through Plaza well done to stoping that +I was going to have that as a question + + align:start position:0% +I was going to have that as a question + + + align:start position:0% +I was going to have that as a question +later on when we looked at some data but + + align:start position:0% +later on when we looked at some data but + + + align:start position:0% +later on when we looked at some data but +as you pointed out you've ruin the game + + align:start position:0% +as you pointed out you've ruin the game + + + align:start position:0% +as you pointed out you've ruin the game +so I told you earlier that rays are + + align:start position:0% +so I told you earlier that rays are + + + align:start position:0% +so I told you earlier that rays are +always perpendicular to the phase front + + align:start position:0% +always perpendicular to the phase front + + + align:start position:0% +always perpendicular to the phase front +right and so as I drawing this the rays + + align:start position:0% +right and so as I drawing this the rays + + + align:start position:0% +right and so as I drawing this the rays +are like this fine the phase fronts are + + align:start position:0% +are like this fine the phase fronts are + + + align:start position:0% +are like this fine the phase fronts are +flat but you can see here that if I drew + + align:start position:0% +flat but you can see here that if I drew + + + align:start position:0% +flat but you can see here that if I drew +those lines like this I would start to + + align:start position:0% +those lines like this I would start to + + + align:start position:0% +those lines like this I would start to +get deflection and so you will have shog + + align:start position:0% +get deflection and so you will have shog + + + align:start position:0% +get deflection and so you will have shog +graphy effects overlaid on top of your + + align:start position:0% +graphy effects overlaid on top of your + + + align:start position:0% +graphy effects overlaid on top of your +interferometry signal it turns out the + + align:start position:0% +interferometry signal it turns out the + + + align:start position:0% +interferometry signal it turns out the +modulation from interferometry is + + align:start position:0% +modulation from interferometry is + + + align:start position:0% +modulation from interferometry is +usually stronger and so you see that + + align:start position:0% +usually stronger and so you see that + + + align:start position:0% +usually stronger and so you see that +more strongly but if these are very big + + align:start position:0% +more strongly but if these are very big + + + align:start position:0% +more strongly but if these are very big +you may actually just lose the light + + align:start position:0% +you may actually just lose the light + + + align:start position:0% +you may actually just lose the light +because your lens will be + + align:start position:0% +because your lens will be + + + align:start position:0% +because your lens will be +this big and your rays will exit it now + + align:start position:0% +this big and your rays will exit it now + + + align:start position:0% +this big and your rays will exit it now +in general inry is so sensitive that + + align:start position:0% +in general inry is so sensitive that + + + align:start position:0% +in general inry is so sensitive that +I've drawn this in a very exaggerated + + align:start position:0% +I've drawn this in a very exaggerated + + + align:start position:0% +I've drawn this in a very exaggerated +way the the phase fronts can be almost + + align:start position:0% +way the the phase fronts can be almost + + + align:start position:0% +way the the phase fronts can be almost +perfectly pler still and I'll still get + + align:start position:0% +perfectly pler still and I'll still get + + + align:start position:0% +perfectly pler still and I'll still get +really nice inry patterns but it won't + + align:start position:0% +really nice inry patterns but it won't + + + align:start position:0% +really nice inry patterns but it won't +be so distorted that the light will all + + align:start position:0% +be so distorted that the light will all + + + align:start position:0% +be so distorted that the light will all +be spreading outwards and I won't be + + align:start position:0% +be spreading outwards and I won't be + + + align:start position:0% +be spreading outwards and I won't be +able to do anything about it so yeah + + align:start position:0% +able to do anything about it so yeah + + + align:start position:0% +able to do anything about it so yeah +you're quite right like in this picture + + align:start position:0% +you're quite right like in this picture + + + align:start position:0% +you're quite right like in this picture +we should have shog graphy and and all + + align:start position:0% +we should have shog graphy and and all + + + align:start position:0% +we should have shog graphy and and all +sorts of things like that as + + align:start position:0% +sorts of things like that as + + + align:start position:0% +sorts of things like that as +well okay any other questions we show + + align:start position:0% +well okay any other questions we show + + + align:start position:0% +well okay any other questions we show +some pictures at the moment otherwise um + + align:start position:0% +some pictures at the moment otherwise um + + + align:start position:0% +some pictures at the moment otherwise um +a question yes pleas um could because of + + align:start position:0% +a question yes pleas um could because of + + + align:start position:0% +a question yes pleas um could because of +the shifting of the wave fronts could is + + align:start position:0% +the shifting of the wave fronts could is + + + align:start position:0% +the shifting of the wave fronts could is +there possibility for inter uh + + align:start position:0% +there possibility for inter uh + + + align:start position:0% +there possibility for inter uh +interference within the same wfront so + + align:start position:0% +interference within the same wfront so + + + align:start position:0% +interference within the same wfront so +like would K1 could interfere with + + align:start position:0% +like would K1 could interfere with + + + align:start position:0% +like would K1 could interfere with +itself if there's enough of a shift in + + align:start position:0% +itself if there's enough of a shift in + + + align:start position:0% +itself if there's enough of a shift in +the density plasma yeah and in fact that + + align:start position:0% +the density plasma yeah and in fact that + + + align:start position:0% +the density plasma yeah and in fact that +that's when we were talking about shodog + + align:start position:0% +that's when we were talking about shodog + + + align:start position:0% +that's when we were talking about shodog +graphy and I said we don't really want a + + align:start position:0% +graphy and I said we don't really want a + + + align:start position:0% +graphy and I said we don't really want a +coherent light source for shodog graphy + + align:start position:0% +coherent light source for shodog graphy + + + align:start position:0% +coherent light source for shodog graphy +so even if you like take out the + + align:start position:0% +so even if you like take out the + + + align:start position:0% +so even if you like take out the +reference beam and the question is can + + align:start position:0% +reference beam and the question is can + + + align:start position:0% +reference beam and the question is can +this shift so much that it actually + + align:start position:0% +this shift so much that it actually + + + align:start position:0% +this shift so much that it actually +interferes with itself yes that happens + + align:start position:0% +interferes with itself yes that happens + + + align:start position:0% +interferes with itself yes that happens +and you can see that in shog graphy and + + align:start position:0% +and you can see that in shog graphy and + + + align:start position:0% +and you can see that in shog graphy and +it's bad because it's really hard to + + align:start position:0% +it's bad because it's really hard to + + + align:start position:0% +it's bad because it's really hard to +interpret but there is a + + align:start position:0% +interpret but there is a + + + align:start position:0% +interpret but there is a +technique I I should have read up on + + align:start position:0% +technique I I should have read up on + + + align:start position:0% +technique I I should have read up on +this more before saying this but it is a + + align:start position:0% +this more before saying this but it is a + + + align:start position:0% +this more before saying this but it is a +technique called phase contrast Imaging + + align:start position:0% +technique called phase contrast Imaging + + + align:start position:0% +technique called phase contrast Imaging +which is used in uh with x-rays and that + + align:start position:0% +which is used in uh with x-rays and that + + + align:start position:0% +which is used in uh with x-rays and that +actually exploits the interference of + + align:start position:0% +actually exploits the interference of + + + align:start position:0% +actually exploits the interference of +the X-ray which is just radiation like + + align:start position:0% +the X-ray which is just radiation like + + + align:start position:0% +the X-ray which is just radiation like +all this other stuff with itself to make + + align:start position:0% +all this other stuff with itself to make + + + align:start position:0% +all this other stuff with itself to make +very very precise measurements of sharp + + align:start position:0% +very very precise measurements of sharp + + + align:start position:0% +very very precise measurements of sharp +density gradients so there in general + + align:start position:0% +density gradients so there in general + + + align:start position:0% +density gradients so there in general +you want to avoid coherence in shog + + align:start position:0% +you want to avoid coherence in shog + + + align:start position:0% +you want to avoid coherence in shog +graphy because it messes up your your + + align:start position:0% +graphy because it messes up your your + + + align:start position:0% +graphy because it messes up your your +data and it's hard to interpret but if + + align:start position:0% +data and it's hard to interpret but if + + + align:start position:0% +data and it's hard to interpret but if +you can do it very precisely uh you can + + align:start position:0% +you can do it very precisely uh you can + + + align:start position:0% +you can do it very precisely uh you can +do some very nice techniques with it so + + align:start position:0% +do some very nice techniques with it so + + + align:start position:0% +do some very nice techniques with it so +it's it's not always a curse in general + + align:start position:0% +it's it's not always a curse in general + + + align:start position:0% +it's it's not always a curse in general +all of these effects will be overlaid on + + align:start position:0% +all of these effects will be overlaid on + + + align:start position:0% +all of these effects will be overlaid on +top of each other I've just been + + align:start position:0% +top of each other I've just been + + + align:start position:0% +top of each other I've just been +presenting them one at a time but + + align:start position:0% +presenting them one at a time but + + + align:start position:0% +presenting them one at a time but +they're all present in the same system + + align:start position:0% +they're all present in the same system + + + align:start position:0% +they're all present in the same system +okay so this is a very biased sample of + + align:start position:0% +okay so this is a very biased sample of + + + align:start position:0% +okay so this is a very biased sample of +uh interferograms and it's biased in the + + align:start position:0% +uh interferograms and it's biased in the + + + align:start position:0% +uh interferograms and it's biased in the +sense that I just went through quite a + + align:start position:0% +sense that I just went through quite a + + + align:start position:0% +sense that I just went through quite a +lot of papers I've written and tried to + + align:start position:0% +lot of papers I've written and tried to + + + align:start position:0% +lot of papers I've written and tried to +grab them because I was in a hurry but + + align:start position:0% +grab them because I was in a hurry but + + + align:start position:0% +grab them because I was in a hurry but +hopefully some of these will be + + align:start position:0% +hopefully some of these will be + + + align:start position:0% +hopefully some of these will be +informative I tried very hard to find + + align:start position:0% +informative I tried very hard to find + + + align:start position:0% +informative I tried very hard to find +some uh temporally hrod interferometry + + align:start position:0% +some uh temporally hrod interferometry + + + align:start position:0% +some uh temporally hrod interferometry +and it's actually quite hard to do find + + align:start position:0% +and it's actually quite hard to do find + + + align:start position:0% +and it's actually quite hard to do find +where they show the raw signal because + + align:start position:0% +where they show the raw signal because + + + align:start position:0% +where they show the raw signal because +we have such good electronics for this + + align:start position:0% +we have such good electronics for this + + + align:start position:0% +we have such good electronics for this +stuff these days that mostly you just do + + align:start position:0% +stuff these days that mostly you just do + + + align:start position:0% +stuff these days that mostly you just do +the signal processing on a chip and give + + align:start position:0% +the signal processing on a chip and give + + + align:start position:0% +the signal processing on a chip and give +the output of it so you don't really + + align:start position:0% +the output of it so you don't really + + + align:start position:0% +the output of it so you don't really +digitize the raw signal so this is my + + align:start position:0% +digitize the raw signal so this is my + + + align:start position:0% +digitize the raw signal so this is my +best attempt so far this was a Heeney + + align:start position:0% +best attempt so far this was a Heeney + + + align:start position:0% +best attempt so far this was a Heeney +laser beam so that's a green laser beam + + align:start position:0% +laser beam so that's a green laser beam + + + align:start position:0% +laser beam so that's a green laser beam +on azdc upgrade and uh this is from + + align:start position:0% +on azdc upgrade and uh this is from + + + align:start position:0% +on azdc upgrade and uh this is from +paper from 2017 so it's relatively + + align:start position:0% +paper from 2017 so it's relatively + + + align:start position:0% +paper from 2017 so it's relatively +recent uh they had the heene is + + align:start position:0% +recent uh they had the heene is + + + align:start position:0% +recent uh they had the heene is +obviously green but they use the hrod + + align:start position:0% +obviously green but they use the hrod + + + align:start position:0% +obviously green but they use the hrod +technique to produce a probe of 40 mehz + + align:start position:0% +technique to produce a probe of 40 mehz + + + align:start position:0% +technique to produce a probe of 40 mehz +so that's the beat frequency there that + + align:start position:0% +so that's the beat frequency there that + + + align:start position:0% +so that's the beat frequency there that +effectively sets the temporal resolution + + align:start position:0% +effectively sets the temporal resolution + + + align:start position:0% +effectively sets the temporal resolution +of this and they actually did something + + align:start position:0% +of this and they actually did something + + + align:start position:0% +of this and they actually did something +even more complicated than we've + + align:start position:0% +even more complicated than we've + + + align:start position:0% +even more complicated than we've +discussed where they hrod the system and + + align:start position:0% +discussed where they hrod the system and + + + align:start position:0% +discussed where they hrod the system and +then interfered the hrod probe as the + + align:start position:0% +then interfered the hrod probe as the + + + align:start position:0% +then interfered the hrod probe as the +hrod reference which is very weird and + + align:start position:0% +hrod reference which is very weird and + + + align:start position:0% +hrod reference which is very weird and +they did it was a quadr system where + + align:start position:0% +they did it was a quadr system where + + + align:start position:0% +they did it was a quadr system where +they shifted one of the signals out of + + align:start position:0% +they shifted one of the signals out of + + + align:start position:0% +they shifted one of the signals out of +phase by 90 degrees and you'll learn + + align:start position:0% +phase by 90 degrees and you'll learn + + + align:start position:0% +phase by 90 degrees and you'll learn +about quadrature in the problem set and + + align:start position:0% +about quadrature in the problem set and + + + align:start position:0% +about quadrature in the problem set and +then they digitized those two signals + + align:start position:0% +then they digitized those two signals + + + align:start position:0% +then they digitized those two signals +and so what they saw was these signals + + align:start position:0% +and so what they saw was these signals + + + align:start position:0% +and so what they saw was these signals +here and if you look at this carefully + + align:start position:0% +here and if you look at this carefully + + + align:start position:0% +here and if you look at this carefully +which you can't do right now but I'll + + align:start position:0% +which you can't do right now but I'll + + + align:start position:0% +which you can't do right now but I'll +put the slides up later you'll find out + + align:start position:0% +put the slides up later you'll find out + + + align:start position:0% +put the slides up later you'll find out +that these signals are actually 90° out + + align:start position:0% +that these signals are actually 90° out + + + align:start position:0% +that these signals are actually 90° out +of phase which is really really cool uh + + align:start position:0% +of phase which is really really cool uh + + + align:start position:0% +of phase which is really really cool uh +and then they were able to process those + + align:start position:0% +and then they were able to process those + + + align:start position:0% +and then they were able to process those +together and they could get out of phase + + align:start position:0% +together and they could get out of phase + + + align:start position:0% +together and they could get out of phase +shift and you can see the time on the + + align:start position:0% +shift and you can see the time on the + + + align:start position:0% +shift and you can see the time on the +bottom here is sort of in millisecond is + + align:start position:0% +bottom here is sort of in millisecond is + + + align:start position:0% +bottom here is sort of in millisecond is +time scale so this is pretty fast for a + + align:start position:0% +time scale so this is pretty fast for a + + + align:start position:0% +time scale so this is pretty fast for a +toac and you can see that the phase + + align:start position:0% +toac and you can see that the phase + + + align:start position:0% +toac and you can see that the phase +shift is going multiples of two Pi so + + align:start position:0% +shift is going multiples of two Pi so + + + align:start position:0% +shift is going multiples of two Pi so +they've resolved that ambiguity so + + align:start position:0% +they've resolved that ambiguity so + + + align:start position:0% +they've resolved that ambiguity so +they're saying look the density went up + + align:start position:0% +they're saying look the density went up + + + align:start position:0% +they're saying look the density went up +and then it came down then it went up + + align:start position:0% +and then it came down then it went up + + + align:start position:0% +and then it came down then it went up +again then it went down so they have + + align:start position:0% +again then it went down so they have + + + align:start position:0% +again then it went down so they have +some confidence that this is this is + + align:start position:0% +some confidence that this is this is + + + align:start position:0% +some confidence that this is this is +real uh so this was quite a nice example + + align:start position:0% +real uh so this was quite a nice example + + + align:start position:0% +real uh so this was quite a nice example +um another example is from the pulse + + align:start position:0% +um another example is from the pulse + + + align:start position:0% +um another example is from the pulse +power world this was on the Z machine + + align:start position:0% +power world this was on the Z machine + + + align:start position:0% +power world this was on the Z machine +Sandia um where they uh actually show + + align:start position:0% +Sandia um where they uh actually show + + + align:start position:0% +Sandia um where they uh actually show +the raw data not quite the world data + + align:start position:0% +the raw data not quite the world data + + + align:start position:0% +the raw data not quite the world data +what they show is a spectrogram so this + + align:start position:0% +what they show is a spectrogram so this + + + align:start position:0% +what they show is a spectrogram so this +is like if you do a very short time + + align:start position:0% +is like if you do a very short time + + + align:start position:0% +is like if you do a very short time +window fer transform on your temporal + + align:start position:0% +window fer transform on your temporal + + + align:start position:0% +window fer transform on your temporal +signal and you plot what frequency + + align:start position:0% +signal and you plot what frequency + + + align:start position:0% +signal and you plot what frequency +components there are at a single time so + + align:start position:0% +components there are at a single time so + + + align:start position:0% +components there are at a single time so +if I take a slice at a certain time here + + align:start position:0% +if I take a slice at a certain time here + + + align:start position:0% +if I take a slice at a certain time here +I can see a dominant frequency component + + align:start position:0% +I can see a dominant frequency component + + + align:start position:0% +I can see a dominant frequency component +down here and you can see that dominant + + align:start position:0% +down here and you can see that dominant + + + align:start position:0% +down here and you can see that dominant +frequency component change in time and + + align:start position:0% +frequency component change in time and + + + align:start position:0% +frequency component change in time and +they've shifted this so the beat + + align:start position:0% +they've shifted this so the beat + + + align:start position:0% +they've shifted this so the beat +frequency is at zero but you know that + + align:start position:0% +frequency is at zero but you know that + + + align:start position:0% +frequency is at zero but you know that +would actually be gigahertz or something + + align:start position:0% +would actually be gigahertz or something + + + align:start position:0% +would actually be gigahertz or something +like that and this would be a shift from + + align:start position:0% +like that and this would be a shift from + + + align:start position:0% +like that and this would be a shift from +that beat frequency of of gigahertz and + + align:start position:0% +that beat frequency of of gigahertz and + + + align:start position:0% +that beat frequency of of gigahertz and +they've done a technique where they + + align:start position:0% +they've done a technique where they + + + align:start position:0% +they've done a technique where they +shift the beat frequency in each window + + align:start position:0% +shift the beat frequency in each window + + + align:start position:0% +shift the beat frequency in each window +a different amount and this gives a much + + align:start position:0% +a different amount and this gives a much + + + align:start position:0% +a different amount and this gives a much +higher dynamic range but effectively + + align:start position:0% +higher dynamic range but effectively + + + align:start position:0% +higher dynamic range but effectively +this is looking at an increase in Phase + + align:start position:0% +this is looking at an increase in Phase + + + align:start position:0% +this is looking at an increase in Phase +that's chirped in time and the time + + align:start position:0% +that's chirped in time and the time + + + align:start position:0% +that's chirped in time and the time +scale on the bottom here is nanc so over + + align:start position:0% +scale on the bottom here is nanc so over + + + align:start position:0% +scale on the bottom here is nanc so over +about 100 nanc they've measured a + + align:start position:0% +about 100 nanc they've measured a + + + align:start position:0% +about 100 nanc they've measured a +significant phase shift now what they're + + align:start position:0% +significant phase shift now what they're + + + align:start position:0% +significant phase shift now what they're +doing with this technique is not + + align:start position:0% +doing with this technique is not + + + align:start position:0% +doing with this technique is not +actually measuring a plasma they're + + align:start position:0% +actually measuring a plasma they're + + + align:start position:0% +actually measuring a plasma they're +measuring the motion of a conductor um + + align:start position:0% +measuring the motion of a conductor um + + + align:start position:0% +measuring the motion of a conductor um +so this is this is photonic doit of + + align:start position:0% +so this is this is photonic doit of + + + align:start position:0% +so this is this is photonic doit of +symmetry for the HD kids who've heard + + align:start position:0% +symmetry for the HD kids who've heard + + + align:start position:0% +symmetry for the HD kids who've heard +about that before um and they're doing + + align:start position:0% +about that before um and they're doing + + + align:start position:0% +about that before um and they're doing +that to measure all sorts of cool like + + align:start position:0% +that to measure all sorts of cool like + + + align:start position:0% +that to measure all sorts of cool like +squishing metal type things but exactly + + align:start position:0% +squishing metal type things but exactly + + + align:start position:0% +squishing metal type things but exactly +the same physics that play because that + + align:start position:0% +the same physics that play because that + + + align:start position:0% +the same physics that play because that +moving conductor um just gives you a + + align:start position:0% +moving conductor um just gives you a + + + align:start position:0% +moving conductor um just gives you a +phase shift uh and that phase shift + + align:start position:0% +phase shift uh and that phase shift + + + align:start position:0% +phase shift uh and that phase shift +could be density or it could be some + + align:start position:0% +could be density or it could be some + + + align:start position:0% +could be density or it could be some +moving conductor so it's up to you + + align:start position:0% +moving conductor so it's up to you + + + align:start position:0% +moving conductor so it's up to you +afterwards to interpret what the data + + align:start position:0% +afterwards to interpret what the data + + + align:start position:0% +afterwards to interpret what the data +looks like and they run out of bandwidth + + align:start position:0% +looks like and they run out of bandwidth + + + align:start position:0% +looks like and they run out of bandwidth +up here so 25 GHz they can't sample any + + align:start position:0% +up here so 25 GHz they can't sample any + + + align:start position:0% +up here so 25 GHz they can't sample any +faster because that's already a very + + align:start position:0% +faster because that's already a very + + + align:start position:0% +faster because that's already a very +expensive digitizer which is why they + + align:start position:0% +expensive digitizer which is why they + + + align:start position:0% +expensive digitizer which is why they +have this clever technique which + + align:start position:0% +have this clever technique which + + + align:start position:0% +have this clever technique which +effectively adizes the signal so it goes + + align:start position:0% +effectively adizes the signal so it goes + + + align:start position:0% +effectively adizes the signal so it goes +up on one and the beat frequency appears + + align:start position:0% +up on one and the beat frequency appears + + + align:start position:0% +up on one and the beat frequency appears +to go down on the other and then when it + + align:start position:0% +to go down on the other and then when it + + + align:start position:0% +to go down on the other and then when it +hits this point here it starts going + + align:start position:0% +hits this point here it starts going + + + align:start position:0% +hits this point here it starts going +back up and they do the same trick + + align:start position:0% +back up and they do the same trick + + + align:start position:0% +back up and they do the same trick +several times and by sort of + + align:start position:0% +several times and by sort of + + + align:start position:0% +several times and by sort of +appropriately flipping and splicing + + align:start position:0% +appropriately flipping and splicing + + + align:start position:0% +appropriately flipping and splicing +these signals together they'll actually + + align:start position:0% +these signals together they'll actually + + + align:start position:0% +these signals together they'll actually +get a signal that just keeps going up + + align:start position:0% +get a signal that just keeps going up + + + align:start position:0% +get a signal that just keeps going up +and up and up and then they can measure + + align:start position:0% +and up and up and then they can measure + + + align:start position:0% +and up and up and then they can measure +this motion of this conductor a very + + align:start position:0% +this motion of this conductor a very + + + align:start position:0% +this motion of this conductor a very +long time scale so there's some very + + align:start position:0% +long time scale so there's some very + + + align:start position:0% +long time scale so there's some very +cool Advanced Techniques and electronics + + align:start position:0% +cool Advanced Techniques and electronics + + + align:start position:0% +cool Advanced Techniques and electronics +involved in all of this but this at + + align:start position:0% +involved in all of this but this at + + + align:start position:0% +involved in all of this but this at +least is closest the world data and + + align:start position:0% +least is closest the world data and + + + align:start position:0% +least is closest the world data and +again to the P set you'll be making your + + align:start position:0% +again to the P set you'll be making your + + + align:start position:0% +again to the P set you'll be making your +own world data so you can see what it + + align:start position:0% +own world data so you can see what it + + + align:start position:0% +own world data so you can see what it +looks like there any questions on these + + align:start position:0% +looks like there any questions on these + + + align:start position:0% +looks like there any questions on these +two temporary resolve + + align:start position:0% + + + + align:start position:0% + +techniques in the + + align:start position:0% +techniques in the + + + align:start position:0% +techniques in the +aade example they have any kind of spal + + align:start position:0% +aade example they have any kind of spal + + + align:start position:0% +aade example they have any kind of spal +resolution no it's just a cord so it's a + + align:start position:0% +resolution no it's just a cord so it's a + + + align:start position:0% +resolution no it's just a cord so it's a +laser beam through the plasma and that's + + align:start position:0% +laser beam through the plasma and that's + + + align:start position:0% +laser beam through the plasma and that's +pretty typical for toac plasmas one + + align:start position:0% +pretty typical for toac plasmas one + + + align:start position:0% +pretty typical for toac plasmas one +reason for that which doesn't apply here + + align:start position:0% +reason for that which doesn't apply here + + + align:start position:0% +reason for that which doesn't apply here +is that you often want to use like + + align:start position:0% +is that you often want to use like + + + align:start position:0% +is that you often want to use like +microwave waves because the density is + + align:start position:0% +microwave waves because the density is + + + align:start position:0% +microwave waves because the density is +more appropriate for microwaves than for + + align:start position:0% +more appropriate for microwaves than for + + + align:start position:0% +more appropriate for microwaves than for +lasers and so that means it's actually + + align:start position:0% +lasers and so that means it's actually + + + align:start position:0% +lasers and so that means it's actually +quite hard to do like Imaging with + + align:start position:0% +quite hard to do like Imaging with + + + align:start position:0% +quite hard to do like Imaging with +microwaves right we tend to just have an + + align:start position:0% +microwaves right we tend to just have an + + + align:start position:0% +microwaves right we tend to just have an +antenna which launches microwaves and + + align:start position:0% +antenna which launches microwaves and + + + align:start position:0% +antenna which launches microwaves and +antenna which collects them so you tend + + align:start position:0% +antenna which collects them so you tend + + + align:start position:0% +antenna which collects them so you tend +to just have a line with a heene that's + + align:start position:0% +to just have a line with a heene that's + + + align:start position:0% +to just have a line with a heene that's +not a limitation but um obviously they + + align:start position:0% +not a limitation but um obviously they + + + align:start position:0% +not a limitation but um obviously they +probably couldn't do a camera that is + + align:start position:0% +probably couldn't do a camera that is + + + align:start position:0% +probably couldn't do a camera that is +resolving on this time scale maybe they + + align:start position:0% +resolving on this time scale maybe they + + + align:start position:0% +resolving on this time scale maybe they +don't want to uh they certainly couldn't + + align:start position:0% +don't want to uh they certainly couldn't + + + align:start position:0% +don't want to uh they certainly couldn't +have a camera that covered the entire + + align:start position:0% +have a camera that covered the entire + + + align:start position:0% +have a camera that covered the entire +toat cross-section on that time scale so + + align:start position:0% +toat cross-section on that time scale so + + + align:start position:0% +toat cross-section on that time scale so +I think they went for this sort of + + align:start position:0% +I think they went for this sort of + + + align:start position:0% +I think they went for this sort of +resolved but just one point in space + + align:start position:0% +resolved but just one point in space + + + align:start position:0% +resolved but just one point in space +technique instead we'll talk a little + + align:start position:0% +technique instead we'll talk a little + + + align:start position:0% +technique instead we'll talk a little +bit about how many chords like that you + + align:start position:0% +bit about how many chords like that you + + + align:start position:0% +bit about how many chords like that you +need in order to do some sort of + + align:start position:0% +need in order to do some sort of + + + align:start position:0% +need in order to do some sort of +reconstruction uh later on in the + + align:start position:0% +reconstruction uh later on in the + + + align:start position:0% +reconstruction uh later on in the +lecture other + + align:start position:0% + + + + align:start position:0% + +questions anything + + align:start position:0% + + + + align:start position:0% + +online + + align:start position:0% +online + + + align:start position:0% +online +okay so these are examples of spatially + + align:start position:0% +okay so these are examples of spatially + + + align:start position:0% +okay so these are examples of spatially +hetr interferograms this is the case + + align:start position:0% +hetr interferograms this is the case + + + align:start position:0% +hetr interferograms this is the case +with no plasma you see you got these + + align:start position:0% +with no plasma you see you got these + + + align:start position:0% +with no plasma you see you got these +nice uniformly spaced fringes here and + + align:start position:0% +nice uniformly spaced fringes here and + + + align:start position:0% +nice uniformly spaced fringes here and +some of them are light that's + + align:start position:0% +some of them are light that's + + + align:start position:0% +some of them are light that's +constructive interference some of them + + align:start position:0% +constructive interference some of them + + + align:start position:0% +constructive interference some of them +are Dark that's destructive interference + + align:start position:0% +are Dark that's destructive interference + + + align:start position:0% +are Dark that's destructive interference +so the prob beam is going straight into + + align:start position:0% +so the prob beam is going straight into + + + align:start position:0% +so the prob beam is going straight into +the page like this and the reference + + align:start position:0% +the page like this and the reference + + + align:start position:0% +the page like this and the reference +beam is tilted at a tiny angle upwards + + align:start position:0% +beam is tilted at a tiny angle upwards + + + align:start position:0% +beam is tilted at a tiny angle upwards +and we've chosen that angle to give us + + align:start position:0% +and we've chosen that angle to give us + + + align:start position:0% +and we've chosen that angle to give us +this nice Fringe pattern here because + + align:start position:0% +this nice Fringe pattern here because + + + align:start position:0% +this nice Fringe pattern here because +when we put a plasma in the way we have + + align:start position:0% +when we put a plasma in the way we have + + + align:start position:0% +when we put a plasma in the way we have +plasma flows coming from the left and + + align:start position:0% +plasma flows coming from the left and + + + align:start position:0% +plasma flows coming from the left and +the right and we can see that all these + + align:start position:0% +the right and we can see that all these + + + align:start position:0% +the right and we can see that all these +fringes are just thed you can see most + + align:start position:0% +fringes are just thed you can see most + + + align:start position:0% +fringes are just thed you can see most +prominently the fringes all tick up in + + align:start position:0% +prominently the fringes all tick up in + + + align:start position:0% +prominently the fringes all tick up in +the center here and and that corresponds + + align:start position:0% +the center here and and that corresponds + + + align:start position:0% +the center here and and that corresponds +to an increase in the line integrated + + align:start position:0% +to an increase in the line integrated + + + align:start position:0% +to an increase in the line integrated +electron density you can also see there + + align:start position:0% +electron density you can also see there + + + align:start position:0% +electron density you can also see there +are regions where there's quite large + + align:start position:0% +are regions where there's quite large + + + align:start position:0% +are regions where there's quite large +Fring shift distortions around here + + align:start position:0% +Fring shift distortions around here + + + align:start position:0% +Fring shift distortions around here +these are actually Four plasma sources + + align:start position:0% +these are actually Four plasma sources + + + align:start position:0% +these are actually Four plasma sources +on either side here um and you can see + + align:start position:0% +on either side here um and you can see + + + align:start position:0% +on either side here um and you can see +that some of the distortions are so + + align:start position:0% +that some of the distortions are so + + + align:start position:0% +that some of the distortions are so +large we've actually formed closed + + align:start position:0% +large we've actually formed closed + + + align:start position:0% +large we've actually formed closed +fringes again so in that place we have + + align:start position:0% +fringes again so in that place we have + + + align:start position:0% +fringes again so in that place we have +violated the condition that K1 minus K2 + + align:start position:0% +violated the condition that K1 minus K2 + + + align:start position:0% +violated the condition that K1 minus K2 +has to be much much larger than the + + align:start position:0% +has to be much much larger than the + + + align:start position:0% +has to be much much larger than the +spatial derivative of the phase we've + + align:start position:0% +spatial derivative of the phase we've + + + align:start position:0% +spatial derivative of the phase we've +effectively recovered by accident the L + + align:start position:0% +effectively recovered by accident the L + + + align:start position:0% +effectively recovered by accident the L +system because we weren't able to keep + + align:start position:0% +system because we weren't able to keep + + + align:start position:0% +system because we weren't able to keep +our Fringe spacing close enough together + + align:start position:0% +our Fringe spacing close enough together + + + align:start position:0% +our Fringe spacing close enough together +we made this Fringe spacing even closer + + align:start position:0% +we made this Fringe spacing even closer + + + align:start position:0% +we made this Fringe spacing even closer +these closed fringes would go away and + + align:start position:0% +these closed fringes would go away and + + + align:start position:0% +these closed fringes would go away and +we lose that ambiguity but we'd also be + + align:start position:0% +we lose that ambiguity but we'd also be + + + align:start position:0% +we lose that ambiguity but we'd also be +sacrificing our Dynamic resolution of + + align:start position:0% +sacrificing our Dynamic resolution of + + + align:start position:0% +sacrificing our Dynamic resolution of +the electron density so for an interfer + + align:start position:0% +the electron density so for an interfer + + + align:start position:0% +the electron density so for an interfer +like this I have very strong priers that + + align:start position:0% +like this I have very strong priers that + + + align:start position:0% +like this I have very strong priers that +the density is going to be higher here + + align:start position:0% +the density is going to be higher here + + + align:start position:0% +the density is going to be higher here +than here and so I can just um when I'm + + align:start position:0% +than here and so I can just um when I'm + + + align:start position:0% +than here and so I can just um when I'm +doing the processing on this data um + + align:start position:0% +doing the processing on this data um + + + align:start position:0% +doing the processing on this data um +make sure the density goes up here + + align:start position:0% +make sure the density goes up here + + + align:start position:0% +make sure the density goes up here +instead of down ially making choices on + + align:start position:0% +instead of down ially making choices on + + + align:start position:0% +instead of down ially making choices on +that decision tree uh we had before and + + align:start position:0% +that decision tree uh we had before and + + + align:start position:0% +that decision tree uh we had before and +if you spend a little while processing + + align:start position:0% +if you spend a little while processing + + + align:start position:0% +if you spend a little while processing +these interferograms this is the raw + + align:start position:0% +these interferograms this is the raw + + + align:start position:0% +these interferograms this is the raw +data and this is the line integrated + + align:start position:0% +data and this is the line integrated + + + align:start position:0% +data and this is the line integrated +electron density here and for this the + + align:start position:0% +electron density here and for this the + + + align:start position:0% +electron density here and for this the +electron density is in units of + + align:start position:0% +electron density is in units of + + + align:start position:0% +electron density is in units of +techically 18 per cm cubed so + + align:start position:0% +techically 18 per cm cubed so + + + align:start position:0% +techically 18 per cm cubed so +technically the thing that you get out + + align:start position:0% +technically the thing that you get out + + + align:start position:0% +technically the thing that you get out +of this is line integrated electron + + align:start position:0% +of this is line integrated electron + + + align:start position:0% +of this is line integrated electron +density so that's per centimeter squared + + align:start position:0% +density so that's per centimeter squared + + + align:start position:0% +density so that's per centimeter squared +in this system we had a lot of symmetry + + align:start position:0% +in this system we had a lot of symmetry + + + align:start position:0% +in this system we had a lot of symmetry +in this out of plane Direction and we + + align:start position:0% +in this out of plane Direction and we + + + align:start position:0% +in this out of plane Direction and we +knew how long the plasma in that + + align:start position:0% +knew how long the plasma in that + + + align:start position:0% +knew how long the plasma in that +direction so we just divided by that + + align:start position:0% +direction so we just divided by that + + + align:start position:0% +direction so we just divided by that +length to get the line averaged plasma + + align:start position:0% +length to get the line averaged plasma + + + align:start position:0% +length to get the line averaged plasma +density and you can see again although + + align:start position:0% +density and you can see again although + + + align:start position:0% +density and you can see again although +we did have these homod regions here + + align:start position:0% +we did have these homod regions here + + + align:start position:0% +we did have these homod regions here +where we have some ambiguity about the + + align:start position:0% +where we have some ambiguity about the + + + align:start position:0% +where we have some ambiguity about the +phase because we had strong priors we're + + align:start position:0% +phase because we had strong priors we're + + + align:start position:0% +phase because we had strong priors we're +able to assign the correct electron + + align:start position:0% +able to assign the correct electron + + + align:start position:0% +able to assign the correct electron +density and if we' assigned it + + align:start position:0% +density and if we' assigned it + + + align:start position:0% +density and if we' assigned it +incorrectly if we said it's going down + + align:start position:0% +incorrectly if we said it's going down + + + align:start position:0% +incorrectly if we said it's going down +we would see like a weird hole here that + + align:start position:0% +we would see like a weird hole here that + + + align:start position:0% +we would see like a weird hole here that +wasn't on the other side so it also + + align:start position:0% +wasn't on the other side so it also + + + align:start position:0% +wasn't on the other side so it also +helps to have a bit of symmetry in your + + align:start position:0% +helps to have a bit of symmetry in your + + + align:start position:0% +helps to have a bit of symmetry in your +system as well to check that you're + + align:start position:0% +system as well to check that you're + + + align:start position:0% +system as well to check that you're +assigning things correctly um so I won't + + align:start position:0% +assigning things correctly um so I won't + + + align:start position:0% +assigning things correctly um so I won't +go into the details of how you process + + align:start position:0% +go into the details of how you process + + + align:start position:0% +go into the details of how you process +these there are some vaguely involved + + align:start position:0% +these there are some vaguely involved + + + align:start position:0% +these there are some vaguely involved +techniques um but you can take data like + + align:start position:0% +techniques um but you can take data like + + + align:start position:0% +techniques um but you can take data like +that and get out some really nice + + align:start position:0% +that and get out some really nice + + + align:start position:0% +that and get out some really nice +pictures of the electron Den in your + + align:start position:0% +pictures of the electron Den in your + + + align:start position:0% +pictures of the electron Den in your +plasma so that was quite a nice one you + + align:start position:0% +plasma so that was quite a nice one you + + + align:start position:0% +plasma so that was quite a nice one you +can see all the fringes are still + + align:start position:0% +can see all the fringes are still + + + align:start position:0% +can see all the fringes are still +roughly parallel they only move a little + + align:start position:0% +roughly parallel they only move a little + + + align:start position:0% +roughly parallel they only move a little +bit here's some interferograms of + + align:start position:0% +bit here's some interferograms of + + + align:start position:0% +bit here's some interferograms of +slightly more Twisted fringes you can + + align:start position:0% +slightly more Twisted fringes you can + + + align:start position:0% +slightly more Twisted fringes you can +see the background fringes are like this + + align:start position:0% +see the background fringes are like this + + + align:start position:0% +see the background fringes are like this +on this image and they're like this on + + align:start position:0% +on this image and they're like this on + + + align:start position:0% +on this image and they're like this on +this image it's just how it was set up + + align:start position:0% +this image it's just how it was set up + + + align:start position:0% +this image it's just how it was set up +in the two experiments and you can see + + align:start position:0% +in the two experiments and you can see + + + align:start position:0% +in the two experiments and you can see +that this is an example I used earlier + + align:start position:0% +that this is an example I used earlier + + + align:start position:0% +that this is an example I used earlier +of a b do probe sticking in a plasma and + + align:start position:0% +of a b do probe sticking in a plasma and + + + align:start position:0% +of a b do probe sticking in a plasma and +a bowel shock is forming around it and + + align:start position:0% +a bowel shock is forming around it and + + + align:start position:0% +a bowel shock is forming around it and +you can see strong distortions of the + + align:start position:0% +you can see strong distortions of the + + + align:start position:0% +you can see strong distortions of the +interference fringes especially very + + align:start position:0% +interference fringes especially very + + + align:start position:0% +interference fringes especially very +close to the bow shock where in fact the + + align:start position:0% +close to the bow shock where in fact the + + + align:start position:0% +close to the bow shock where in fact the +deflections of the rays are so large + + align:start position:0% +deflections of the rays are so large + + + align:start position:0% +deflections of the rays are so large +from the density gradiance that they're + + align:start position:0% +from the density gradiance that they're + + + align:start position:0% +from the density gradiance that they're +lost from our Imaging system and so we + + align:start position:0% +lost from our Imaging system and so we + + + align:start position:0% +lost from our Imaging system and so we +don't have interference fringes here + + align:start position:0% +don't have interference fringes here + + + align:start position:0% +don't have interference fringes here +because they've been refracted out of + + align:start position:0% +because they've been refracted out of + + + align:start position:0% +because they've been refracted out of +our system we no longer can do + + align:start position:0% +our system we no longer can do + + + align:start position:0% +our system we no longer can do +interferometry so when the density + + align:start position:0% +interferometry so when the density + + + align:start position:0% +interferometry so when the density +gradient gets too large it's very hard + + align:start position:0% +gradient gets too large it's very hard + + + align:start position:0% +gradient gets too large it's very hard +to tr and again these images were + + align:start position:0% +to tr and again these images were + + + align:start position:0% +to tr and again these images were +processed and you get out nice pictures + + align:start position:0% +processed and you get out nice pictures + + + align:start position:0% +processed and you get out nice pictures +of the bow shock in these two cases here + + align:start position:0% +of the bow shock in these two cases here + + + align:start position:0% +of the bow shock in these two cases here +and this paper was comparing bow shocks + + align:start position:0% +and this paper was comparing bow shocks + + + align:start position:0% +and this paper was comparing bow shocks +with magnetic fields aligned uh with + + align:start position:0% +with magnetic fields aligned uh with + + + align:start position:0% +with magnetic fields aligned uh with +with the field of view and perpendicular + + align:start position:0% +with the field of view and perpendicular + + + align:start position:0% +with the field of view and perpendicular +the field of view we have very different + + align:start position:0% +the field of view we have very different + + + align:start position:0% +the field of view we have very different +batt shot geometries there so those are + + align:start position:0% +batt shot geometries there so those are + + + align:start position:0% +batt shot geometries there so those are +quite complicated but probably the most + + align:start position:0% +quite complicated but probably the most + + + align:start position:0% +quite complicated but probably the most +complicated one I've ever seen traced + + align:start position:0% +complicated one I've ever seen traced + + + align:start position:0% +complicated one I've ever seen traced +was this one V swaddling 2013 so this + + align:start position:0% +was this one V swaddling 2013 so this + + + align:start position:0% +was this one V swaddling 2013 so this +was a 32 wire imploding aluminium Z + + align:start position:0% +was a 32 wire imploding aluminium Z + + + align:start position:0% +was a 32 wire imploding aluminium Z +pinch there a scale bar up there which + + align:start position:0% +pinch there a scale bar up there which + + + align:start position:0% +pinch there a scale bar up there which +is actually wrong that's a millimeter + + align:start position:0% +is actually wrong that's a millimeter + + + align:start position:0% +is actually wrong that's a millimeter +says a centimeter should be a millimeter + + align:start position:0% +says a centimeter should be a millimeter + + + align:start position:0% +says a centimeter should be a millimeter +no one's ever noticed that before um and + + align:start position:0% +no one's ever noticed that before um and + + + align:start position:0% +no one's ever noticed that before um and +so these that are positions of the 32 + + align:start position:0% +so these that are positions of the 32 + + + align:start position:0% +so these that are positions of the 32 +wires here and there's plasma flowing + + align:start position:0% +wires here and there's plasma flowing + + + align:start position:0% +wires here and there's plasma flowing +inwards and as the plasma flows inwards + + align:start position:0% +inwards and as the plasma flows inwards + + + align:start position:0% +inwards and as the plasma flows inwards +it collides with the plasma flows from + + align:start position:0% +it collides with the plasma flows from + + + align:start position:0% +it collides with the plasma flows from +adjacent streams and it forms a network + + align:start position:0% +adjacent streams and it forms a network + + + align:start position:0% +adjacent streams and it forms a network +of oblique shocks so this is two wires + + align:start position:0% +of oblique shocks so this is two wires + + + align:start position:0% +of oblique shocks so this is two wires +here the first oblique shock is out of + + align:start position:0% +here the first oblique shock is out of + + + align:start position:0% +here the first oblique shock is out of +the field here and forms a plasma here + + align:start position:0% +the field here and forms a plasma here + + + align:start position:0% +the field here and forms a plasma here +and then these two plasmas interact they + + align:start position:0% +and then these two plasmas interact they + + + align:start position:0% +and then these two plasmas interact they +form another oblique shock structure and + + align:start position:0% +form another oblique shock structure and + + + align:start position:0% +form another oblique shock structure and +then these two interact and they put + + align:start position:0% +then these two interact and they put + + + align:start position:0% +then these two interact and they put +enough structure and there may even be + + align:start position:0% +enough structure and there may even be + + + align:start position:0% +enough structure and there may even be +like a fourth or a fifth generation in + + align:start position:0% +like a fourth or a fifth generation in + + + align:start position:0% +like a fourth or a fifth generation in +here so this is a complete mess right + + align:start position:0% +here so this is a complete mess right + + + align:start position:0% +here so this is a complete mess right +this is extremely complicated but + + align:start position:0% +this is extremely complicated but + + + align:start position:0% +this is extremely complicated but +because the interr is very high quality + + align:start position:0% +because the interr is very high quality + + + align:start position:0% +because the interr is very high quality +with a great deal of patience you can + + align:start position:0% +with a great deal of patience you can + + + align:start position:0% +with a great deal of patience you can +follow each interference Fringe all the + + align:start position:0% +follow each interference Fringe all the + + + align:start position:0% +follow each interference Fringe all the +way around and you can work out its + + align:start position:0% +way around and you can work out its + + + align:start position:0% +way around and you can work out its +displacement and you get out this rather + + align:start position:0% +displacement and you get out this rather + + + align:start position:0% +displacement and you get out this rather +nice map of the electron density and we + + align:start position:0% +nice map of the electron density and we + + + align:start position:0% +nice map of the electron density and we +see that there is still sufficient + + align:start position:0% +see that there is still sufficient + + + align:start position:0% +see that there is still sufficient +spatial resolution despite the fact that + + align:start position:0% +spatial resolution despite the fact that + + + align:start position:0% +spatial resolution despite the fact that +we're using interference fringes which + + align:start position:0% +we're using interference fringes which + + + align:start position:0% +we're using interference fringes which +limit our spatial resolution there's + + align:start position:0% +limit our spatial resolution there's + + + align:start position:0% +limit our spatial resolution there's +still sufficient spatial resolution to + + align:start position:0% +still sufficient spatial resolution to + + + align:start position:0% +still sufficient spatial resolution to +resolve these very sharp shock features + + align:start position:0% +resolve these very sharp shock features + + + align:start position:0% +resolve these very sharp shock features +here so this is a nice piece of + + align:start position:0% +here so this is a nice piece of + + + align:start position:0% +here so this is a nice piece of +work okay + + align:start position:0% +work okay + + + align:start position:0% +work okay +uh and then my final + + align:start position:0% +uh and then my final + + + align:start position:0% +uh and then my final +example uh for this batch here was + + align:start position:0% +example uh for this batch here was + + + align:start position:0% +example uh for this batch here was +actually showing something we've already + + align:start position:0% +actually showing something we've already + + + align:start position:0% +actually showing something we've already +discussed this is this is where we had + + align:start position:0% +discussed this is this is where we had + + + align:start position:0% +discussed this is this is where we had +plasma flows from the left and the right + + align:start position:0% +plasma flows from the left and the right + + + align:start position:0% +plasma flows from the left and the right +colliding here and as opposed to seeing + + align:start position:0% +colliding here and as opposed to seeing + + + align:start position:0% +colliding here and as opposed to seeing +interference fringes we just see this + + align:start position:0% +interference fringes we just see this + + + align:start position:0% +interference fringes we just see this +Dark Void and you can see the fringes + + align:start position:0% +Dark Void and you can see the fringes + + + align:start position:0% +Dark Void and you can see the fringes +are beginning to bend up downwards here + + align:start position:0% +are beginning to bend up downwards here + + + align:start position:0% +are beginning to bend up downwards here +which will indicate enhanced electron + + align:start position:0% +which will indicate enhanced electron + + + align:start position:0% +which will indicate enhanced electron +density but um because the density + + align:start position:0% +density but um because the density + + + align:start position:0% +density but um because the density +gradient is too large the prob beam has + + align:start position:0% +gradient is too large the prob beam has + + + align:start position:0% +gradient is too large the prob beam has +being refracted out of our collection + + align:start position:0% +being refracted out of our collection + + + align:start position:0% +being refracted out of our collection +Optics but we don't get to see anything + + align:start position:0% +Optics but we don't get to see anything + + + align:start position:0% +Optics but we don't get to see anything +now you could say well perhaps it's + + align:start position:0% +now you could say well perhaps it's + + + align:start position:0% +now you could say well perhaps it's +because the plasma is too dense right if + + align:start position:0% +because the plasma is too dense right if + + + align:start position:0% +because the plasma is too dense right if +we got to the critical density the laser + + align:start position:0% +we got to the critical density the laser + + + align:start position:0% +we got to the critical density the laser +beam going through the plasma will be + + align:start position:0% +beam going through the plasma will be + + + align:start position:0% +beam going through the plasma will be +reflected and so that could be the case + + align:start position:0% +reflected and so that could be the case + + + align:start position:0% +reflected and so that could be the case +it's just that density is really really + + align:start position:0% +it's just that density is really really + + + align:start position:0% +it's just that density is really really +high and very hard to reach whereas we + + align:start position:0% +high and very hard to reach whereas we + + + align:start position:0% +high and very hard to reach whereas we +know that in this system that density + + align:start position:0% +know that in this system that density + + + align:start position:0% +know that in this system that density +gradient is very easy to reach and so + + align:start position:0% +gradient is very easy to reach and so + + + align:start position:0% +gradient is very easy to reach and so +we're pretty certain that in these + + align:start position:0% +we're pretty certain that in these + + + align:start position:0% +we're pretty certain that in these +experiments it was the um density + + align:start position:0% +experiments it was the um density + + + align:start position:0% +experiments it was the um density +gradient rather than the absolute + + align:start position:0% +gradient rather than the absolute + + + align:start position:0% +gradient rather than the absolute +density that caused us to lose our + + align:start position:0% +density that caused us to lose our + + + align:start position:0% +density that caused us to lose our +probing in the center here and there's + + align:start position:0% +probing in the center here and there's + + + align:start position:0% +probing in the center here and there's +not really much you can do about that + + align:start position:0% +not really much you can do about that + + + align:start position:0% +not really much you can do about that +you can go to a shorter wavelength if + + align:start position:0% +you can go to a shorter wavelength if + + + align:start position:0% +you can go to a shorter wavelength if +you've got one so that your beam doesn't + + align:start position:0% +you've got one so that your beam doesn't + + + align:start position:0% +you've got one so that your beam doesn't +get deflected so much um you can use a + + align:start position:0% +get deflected so much um you can use a + + + align:start position:0% +get deflected so much um you can use a +bigger lens so you collect more light + + align:start position:0% +bigger lens so you collect more light + + + align:start position:0% +bigger lens so you collect more light +but there's only so big a lens they'll + + align:start position:0% +but there's only so big a lens they'll + + + align:start position:0% +but there's only so big a lens they'll +sell you uh and so you know sometimes + + align:start position:0% +sell you uh and so you know sometimes + + + align:start position:0% +sell you uh and so you know sometimes +you just have to deal with the fact that + + align:start position:0% +you just have to deal with the fact that + + + align:start position:0% +you just have to deal with the fact that +your data has got holes in the middle + + align:start position:0% +your data has got holes in the middle + + + align:start position:0% +your data has got holes in the middle +and when this image was processed in + + align:start position:0% +and when this image was processed in + + + align:start position:0% +and when this image was processed in +these paper he just mask this region but + + align:start position:0% +these paper he just mask this region but + + + align:start position:0% +these paper he just mask this region but +the data are off and he said we don't + + align:start position:0% +the data are off and he said we don't + + + align:start position:0% +the data are off and he said we don't +have any data that really the only thing + + align:start position:0% +have any data that really the only thing + + + align:start position:0% +have any data that really the only thing +you can + + align:start position:0% +you can + + + align:start position:0% +you can +do okay any questions on the spatially + + align:start position:0% +do okay any questions on the spatially + + + align:start position:0% +do okay any questions on the spatially +hetr + + align:start position:0% +hetr + + + align:start position:0% +hetr +inry yes so I think is sort of AUD to + + align:start position:0% +inry yes so I think is sort of AUD to + + + align:start position:0% +inry yes so I think is sort of AUD to +just to make sure I understand in order + + align:start position:0% +just to make sure I understand in order + + + align:start position:0% +just to make sure I understand in order +to extract useful information from one + + align:start position:0% +to extract useful information from one + + + align:start position:0% +to extract useful information from one +of these pictures you need to be able to + + align:start position:0% +of these pictures you need to be able to + + + align:start position:0% +of these pictures you need to be able to +trace each Fringe from edge to edge of + + align:start position:0% +trace each Fringe from edge to edge of + + + align:start position:0% +trace each Fringe from edge to edge of +the picture + + align:start position:0% +the picture + + + align:start position:0% +the picture +and if you lose that you're in trouble + + align:start position:0% +and if you lose that you're in trouble + + + align:start position:0% +and if you lose that you're in trouble +so then how do you I mean is this all + + align:start position:0% +so then how do you I mean is this all + + + align:start position:0% +so then how do you I mean is this all +done with computer image processing for + + align:start position:0% +done with computer image processing for + + + align:start position:0% +done with computer image processing for +your ability to to say continually Trace + + align:start position:0% +your ability to to say continually Trace + + + align:start position:0% +your ability to to say continually Trace +all of these fringes and so you don't + + align:start position:0% +all of these fringes and so you don't + + + align:start position:0% +all of these fringes and so you don't +have to be able to trace each Fringe + + align:start position:0% +have to be able to trace each Fringe + + + align:start position:0% +have to be able to trace each Fringe +from side to side but you + + align:start position:0% +from side to side but you + + + align:start position:0% +from side to side but you +do ideally You' be able to assign say + + align:start position:0% +do ideally You' be able to assign say + + + align:start position:0% +do ideally You' be able to assign say +you numbered each of the fringes from + + align:start position:0% +you numbered each of the fringes from + + + align:start position:0% +you numbered each of the fringes from +the bottom to the top of the image here + + align:start position:0% +the bottom to the top of the image here + + + align:start position:0% +the bottom to the top of the image here +you'd like to be able to assign numbers + + align:start position:0% +you'd like to be able to assign numbers + + + align:start position:0% +you'd like to be able to assign numbers +to the fringes in the image without a + + align:start position:0% +to the fringes in the image without a + + + align:start position:0% +to the fringes in the image without a +plasma so you need a reference + + align:start position:0% +plasma so you need a reference + + + align:start position:0% +plasma so you need a reference +interferogram so you always have to have + + align:start position:0% +interferogram so you always have to have + + + align:start position:0% +interferogram so you always have to have +two pictures right because that + + align:start position:0% +two pictures right because that + + + align:start position:0% +two pictures right because that +reference interferogram gives you the + + align:start position:0% +reference interferogram gives you the + + + align:start position:0% +reference interferogram gives you the +background signal that you're + + align:start position:0% +background signal that you're + + + align:start position:0% +background signal that you're +effectively modulating here so like in + + align:start position:0% +effectively modulating here so like in + + + align:start position:0% +effectively modulating here so like in +temporal hrod infmetry you'll have to + + align:start position:0% +temporal hrod infmetry you'll have to + + + align:start position:0% +temporal hrod infmetry you'll have to +measure the beat frequency for some time + + align:start position:0% +measure the beat frequency for some time + + + align:start position:0% +measure the beat frequency for some time +before the plasma arrives okay the + + align:start position:0% +before the plasma arrives okay the + + + align:start position:0% +before the plasma arrives okay the +Trouble Comes um that actually you don't + + align:start position:0% +Trouble Comes um that actually you don't + + + align:start position:0% +Trouble Comes um that actually you don't +need to be able to uniquely uh allocate + + align:start position:0% +need to be able to uniquely uh allocate + + + align:start position:0% +need to be able to uniquely uh allocate +each of these fringes to a fringe in the + + align:start position:0% +each of these fringes to a fringe in the + + + align:start position:0% +each of these fringes to a fringe in the +reference interferogram you'd like to if + + align:start position:0% +reference interferogram you'd like to if + + + align:start position:0% +reference interferogram you'd like to if +you can't do that then there's some + + align:start position:0% +you can't do that then there's some + + + align:start position:0% +you can't do that then there's some +offset constant that you of density that + + align:start position:0% +offset constant that you of density that + + + align:start position:0% +offset constant that you of density that +you can't get rid of so you that's + + align:start position:0% +you can't get rid of so you that's + + + align:start position:0% +you can't get rid of so you that's +ambiguous so you're like my you can say + + align:start position:0% +ambiguous so you're like my you can say + + + align:start position:0% +ambiguous so you're like my you can say +that my density is going to change from + + align:start position:0% +that my density is going to change from + + + align:start position:0% +that my density is going to change from +here to Here by tally 18 but it may also + + align:start position:0% +here to Here by tally 18 but it may also + + + align:start position:0% +here to Here by tally 18 but it may also +be like tally 18 plus 10 to 18 or 10 to + + align:start position:0% +be like tally 18 plus 10 to 18 or 10 to + + + align:start position:0% +be like tally 18 plus 10 to 18 or 10 to +17 plus 10 to 18 something like that so + + align:start position:0% +17 plus 10 to 18 something like that so + + + align:start position:0% +17 plus 10 to 18 something like that so +there's some ambiguity there if the + + align:start position:0% +there's some ambiguity there if the + + + align:start position:0% +there's some ambiguity there if the +fringes are broken so in this case uh + + align:start position:0% +fringes are broken so in this case uh + + + align:start position:0% +fringes are broken so in this case uh +some of the fringes well actually this + + align:start position:0% +some of the fringes well actually this + + + align:start position:0% +some of the fringes well actually this +one is simpler to see in this case some + + align:start position:0% +one is simpler to see in this case some + + + align:start position:0% +one is simpler to see in this case some +of the fringes on this side here you + + align:start position:0% +of the fringes on this side here you + + + align:start position:0% +of the fringes on this side here you +can't actually follow them through on + + align:start position:0% +can't actually follow them through on + + + align:start position:0% +can't actually follow them through on +the other side but you can make some + + align:start position:0% +the other side but you can make some + + + align:start position:0% +the other side but you can make some +pretty good guesses in the absence of + + align:start position:0% +pretty good guesses in the absence of + + + align:start position:0% +pretty good guesses in the absence of +the plasma because there'll be nice + + align:start position:0% +the plasma because there'll be nice + + + align:start position:0% +the plasma because there'll be nice +straight lines and you can trace them + + align:start position:0% +straight lines and you can trace them + + + align:start position:0% +straight lines and you can trace them +cross like that so for these complicated + + align:start position:0% +cross like that so for these complicated + + + align:start position:0% +cross like that so for these complicated +interferograms uh the best process we've + + align:start position:0% +interferograms uh the best process we've + + + align:start position:0% +interferograms uh the best process we've +found is grad students um but lots of + + align:start position:0% +found is grad students um but lots of + + + align:start position:0% +found is grad students um but lots of +people say oh I'm going to write an + + align:start position:0% +people say oh I'm going to write an + + + align:start position:0% +people say oh I'm going to write an +image processing algorithm and a DDOS in + + align:start position:0% +image processing algorithm and a DDOS in + + + align:start position:0% +image processing algorithm and a DDOS in +students from the psfc who were doing a + + align:start position:0% +students from the psfc who were doing a + + + align:start position:0% +students from the psfc who were doing a +machine learning course who tried to do + + align:start position:0% +machine learning course who tried to do + + + align:start position:0% +machine learning course who tried to do +this the trouble is humans have + + align:start position:0% +this the trouble is humans have + + + align:start position:0% +this the trouble is humans have +incredible visual processing so when you + + align:start position:0% +incredible visual processing so when you + + + align:start position:0% +incredible visual processing so when you +look at this you can work out where all + + align:start position:0% +look at this you can work out where all + + + align:start position:0% +look at this you can work out where all +these lines are perfectly every single + + align:start position:0% +these lines are perfectly every single + + + align:start position:0% +these lines are perfectly every single +algorithm I've seen to try to do this + + align:start position:0% +algorithm I've seen to try to do this + + + align:start position:0% +algorithm I've seen to try to do this +automatically starts getting hung up on + + align:start position:0% +automatically starts getting hung up on + + + align:start position:0% +automatically starts getting hung up on +like the little fuzziness on this line + + align:start position:0% +like the little fuzziness on this line + + + align:start position:0% +like the little fuzziness on this line +here and it's like oh I think that's + + align:start position:0% +here and it's like oh I think that's + + + align:start position:0% +here and it's like oh I think that's +really so I'm going to spend all my time + + align:start position:0% +really so I'm going to spend all my time + + + align:start position:0% +really so I'm going to spend all my time +trying to fit that perfectly and so + + align:start position:0% +trying to fit that perfectly and so + + + align:start position:0% +trying to fit that perfectly and so +there may be techniques which can do it + + align:start position:0% +there may be techniques which can do it + + + align:start position:0% +there may be techniques which can do it +automatically but at the end of the day + + align:start position:0% +automatically but at the end of the day + + + align:start position:0% +automatically but at the end of the day +um it really requires a human to look at + + align:start position:0% +um it really requires a human to look at + + + align:start position:0% +um it really requires a human to look at +this region where there's no fringes and + + align:start position:0% +this region where there's no fringes and + + + align:start position:0% +this region where there's no fringes and +say ah we've lost the fringes because I + + align:start position:0% +say ah we've lost the fringes because I + + + align:start position:0% +say ah we've lost the fringes because I +know that density is really high there + + align:start position:0% +know that density is really high there + + + align:start position:0% +know that density is really high there +or in fact round in these regions here + + align:start position:0% +or in fact round in these regions here + + + align:start position:0% +or in fact round in these regions here +it's hard to see but there's actually + + align:start position:0% +it's hard to see but there's actually + + + align:start position:0% +it's hard to see but there's actually +some very strong shog graphy effects + + align:start position:0% +some very strong shog graphy effects + + + align:start position:0% +some very strong shog graphy effects +there's some like brightness in this + + align:start position:0% +there's some like brightness in this + + + align:start position:0% +there's some like brightness in this +region here uh and that looks like + + align:start position:0% +region here uh and that looks like + + + align:start position:0% +region here uh and that looks like +additional interference fringes but if + + align:start position:0% +additional interference fringes but if + + + align:start position:0% +additional interference fringes but if +youve looked at these enough you'll know + + align:start position:0% +youve looked at these enough you'll know + + + align:start position:0% +youve looked at these enough you'll know +that it's theography so it seems to be + + align:start position:0% +that it's theography so it seems to be + + + align:start position:0% +that it's theography so it seems to be +very hard to train a computer to do so + + align:start position:0% +very hard to train a computer to do so + + + align:start position:0% +very hard to train a computer to do so +not saying it's impossible I just + + align:start position:0% +not saying it's impossible I just + + + align:start position:0% +not saying it's impossible I just +haven't seen a realistic program yet if + + align:start position:0% +haven't seen a realistic program yet if + + + align:start position:0% +haven't seen a realistic program yet if +you have an interferogram where all the + + align:start position:0% +you have an interferogram where all the + + + align:start position:0% +you have an interferogram where all the +Fringe shifts are relatively small and + + align:start position:0% +Fringe shifts are relatively small and + + + align:start position:0% +Fringe shifts are relatively small and +well behaved you can do this using for + + align:start position:0% +well behaved you can do this using for + + + align:start position:0% +well behaved you can do this using for +transforms uh so there are techniques + + align:start position:0% +transforms uh so there are techniques + + + align:start position:0% +transforms uh so there are techniques +which are for transform based uh which + + align:start position:0% +which are for transform based uh which + + + align:start position:0% +which are for transform based uh which +basically do a wavel look transform so + + align:start position:0% +basically do a wavel look transform so + + + align:start position:0% +basically do a wavel look transform so +it's like a small region for a + + align:start position:0% +it's like a small region for a + + + align:start position:0% +it's like a small region for a +transformation and looks at the local + + align:start position:0% +transformation and looks at the local + + + align:start position:0% +transformation and looks at the local +frequencies there uh and that's like + + align:start position:0% +frequencies there uh and that's like + + + align:start position:0% +frequencies there uh and that's like +those spectrograms that I showed + + align:start position:0% +those spectrograms that I showed + + + align:start position:0% +those spectrograms that I showed +you that's the 2D equivalent of the + + align:start position:0% +you that's the 2D equivalent of the + + + align:start position:0% +you that's the 2D equivalent of the +spectrograms I showed you here where we + + align:start position:0% +spectrograms I showed you here where we + + + align:start position:0% +spectrograms I showed you here where we +have the Spectra each time you want the + + align:start position:0% +have the Spectra each time you want the + + + align:start position:0% +have the Spectra each time you want the +K Spectra at each position and those do + + align:start position:0% +K Spectra at each position and those do + + + align:start position:0% +K Spectra at each position and those do +an okay job but as soon as there starts + + align:start position:0% +an okay job but as soon as there starts + + + align:start position:0% +an okay job but as soon as there starts +being any ambiguous feature or even some + + align:start position:0% +being any ambiguous feature or even some + + + align:start position:0% +being any ambiguous feature or even some +relatively large FR distortions they + + align:start position:0% +relatively large FR distortions they + + + align:start position:0% +relatively large FR distortions they +also fall over really badly so it seems + + align:start position:0% +also fall over really badly so it seems + + + align:start position:0% +also fall over really badly so it seems +like a hard problem to automate so that + + align:start position:0% +like a hard problem to automate so that + + + align:start position:0% +like a hard problem to automate so that +was a long answer to your question I'm + + align:start position:0% +was a long answer to your question I'm + + + align:start position:0% +was a long answer to your question I'm +sorry okay other + + align:start position:0% +sorry okay other + + + align:start position:0% +sorry okay other +questions yeah so the image processing + + align:start position:0% +questions yeah so the image processing + + + align:start position:0% +questions yeah so the image processing +it seems like choosing which areas to + + align:start position:0% +it seems like choosing which areas to + + + align:start position:0% +it seems like choosing which areas to +mask and which areas to not mask is + + align:start position:0% +mask and which areas to not mask is + + + align:start position:0% +mask and which areas to not mask is +important yes is there any clear like + + align:start position:0% +important yes is there any clear like + + + align:start position:0% +important yes is there any clear like +cut dry rules for that or it + + align:start position:0% +cut dry rules for that or it + + + align:start position:0% +cut dry rules for that or it +all inition at least the way that I do + + align:start position:0% +all inition at least the way that I do + + + align:start position:0% +all inition at least the way that I do +it it seems to be very like intuitive + + align:start position:0% +it it seems to be very like intuitive + + + align:start position:0% +it it seems to be very like intuitive +yes exactly you sort of have to know + + align:start position:0% +yes exactly you sort of have to know + + + align:start position:0% +yes exactly you sort of have to know +what you expect to see uh and then sort + + align:start position:0% +what you expect to see uh and then sort + + + align:start position:0% +what you expect to see uh and then sort +of work with that + + align:start position:0% +of work with that + + + align:start position:0% +of work with that +yeah other questions the side of the + + align:start position:0% +yeah other questions the side of the + + + align:start position:0% +yeah other questions the side of the +room is much more questioning than the + + align:start position:0% +room is much more questioning than the + + + align:start position:0% +room is much more questioning than the +side of the room okay next one a from a + + align:start position:0% +side of the room okay next one a from a + + + align:start position:0% +side of the room okay next one a from a +practical standpoint how U how many time + + align:start position:0% +practical standpoint how U how many time + + + align:start position:0% +practical standpoint how U how many time +points can you resolve with Dios + + align:start position:0% + + + + align:start position:0% + +yeah so you you know if your plasma is + + align:start position:0% +yeah so you you know if your plasma is + + + align:start position:0% +yeah so you you know if your plasma is +uh the question was what's the sort of + + align:start position:0% +uh the question was what's the sort of + + + align:start position:0% +uh the question was what's the sort of +temporal resolution of something like + + align:start position:0% +temporal resolution of something like + + + align:start position:0% +temporal resolution of something like +this if your plasma is only lasting for + + align:start position:0% +this if your plasma is only lasting for + + + align:start position:0% +this if your plasma is only lasting for +a few hundred NCS then it depends + + align:start position:0% +a few hundred NCS then it depends + + + align:start position:0% +a few hundred NCS then it depends +whether you can afford a camera that can + + align:start position:0% +whether you can afford a camera that can + + + align:start position:0% +whether you can afford a camera that can +take more than one picture in few + + align:start position:0% +take more than one picture in few + + + align:start position:0% +take more than one picture in few +hundred NCS these were taken with uh + + align:start position:0% +hundred NCS these were taken with uh + + + align:start position:0% +hundred NCS these were taken with uh +offthe shelf Canon DSLR cameras uh + + align:start position:0% +offthe shelf Canon DSLR cameras uh + + + align:start position:0% +offthe shelf Canon DSLR cameras uh +bought in 2006 and there the shutter was + + align:start position:0% +bought in 2006 and there the shutter was + + + align:start position:0% +bought in 2006 and there the shutter was +actually open for one second but the + + align:start position:0% +actually open for one second but the + + + align:start position:0% +actually open for one second but the +laser pulse is only a nanc long and that + + align:start position:0% +laser pulse is only a nanc long and that + + + align:start position:0% +laser pulse is only a nanc long and that +sets the time resolution yeah so you can + + align:start position:0% +sets the time resolution yeah so you can + + + align:start position:0% +sets the time resolution yeah so you can +get one picture uh uh in an experiment + + align:start position:0% +get one picture uh uh in an experiment + + + align:start position:0% +get one picture uh uh in an experiment +with this and then you do the experiment + + align:start position:0% +with this and then you do the experiment + + + align:start position:0% +with this and then you do the experiment +again and you hope it's reproducible + + align:start position:0% +again and you hope it's reproducible + + + align:start position:0% +again and you hope it's reproducible +enough and you move the laser later in + + align:start position:0% +enough and you move the laser later in + + + align:start position:0% +enough and you move the laser later in +time you take another picture you keep + + align:start position:0% +time you take another picture you keep + + + align:start position:0% +time you take another picture you keep +doing that yes it's hard yeah this be a + + align:start position:0% +doing that yes it's hard yeah this be a + + + align:start position:0% +doing that yes it's hard yeah this be a +silly question but what are those circle + + align:start position:0% +silly question but what are those circle + + + align:start position:0% +silly question but what are those circle +of fringes that are here yeah so this is + + align:start position:0% +of fringes that are here yeah so this is + + + align:start position:0% +of fringes that are here yeah so this is +what I was saying where we've + + align:start position:0% +what I was saying where we've + + + align:start position:0% +what I was saying where we've +effectively + + align:start position:0% +effectively + + + align:start position:0% +effectively +violated like the they're very light in + + align:start position:0% +violated like the they're very light in + + + align:start position:0% +violated like the they're very light in +the backround these are defraction + + align:start position:0% +the backround these are defraction + + + align:start position:0% +the backround these are defraction +patterns of dust spots dust spot that + + align:start position:0% +patterns of dust spots dust spot that + + + align:start position:0% +patterns of dust spots dust spot that +like there's dust on an optic somewhere + + align:start position:0% +like there's dust on an optic somewhere + + + align:start position:0% +like there's dust on an optic somewhere +it creates a defraction pattern it's out + + align:start position:0% +it creates a defraction pattern it's out + + + align:start position:0% +it creates a defraction pattern it's out +of focus it modulates the intensity of + + align:start position:0% +of focus it modulates the intensity of + + + align:start position:0% +of focus it modulates the intensity of +the laser be it's another thing that + + align:start position:0% +the laser be it's another thing that + + + align:start position:0% +the laser be it's another thing that +makes it hard for an automated algorithm + + align:start position:0% +makes it hard for an automated algorithm + + + align:start position:0% +makes it hard for an automated algorithm +to work we tend to normalize those out + + align:start position:0% +to work we tend to normalize those out + + + align:start position:0% +to work we tend to normalize those out +but I'm showing you this is the actual + + align:start position:0% +but I'm showing you this is the actual + + + align:start position:0% +but I'm showing you this is the actual +Law data from the account I haven't done + + align:start position:0% +Law data from the account I haven't done + + + align:start position:0% +Law data from the account I haven't done +anything to it um but you can do tricks + + align:start position:0% +anything to it um but you can do tricks + + + align:start position:0% +anything to it um but you can do tricks +to get rid of those because it's like a + + align:start position:0% +to get rid of those because it's like a + + + align:start position:0% +to get rid of those because it's like a +slow moving slow changing effect you can + + align:start position:0% +slow moving slow changing effect you can + + + align:start position:0% +slow moving slow changing effect you can +do like a low pass + + align:start position:0% +do like a low pass + + + align:start position:0% +do like a low pass +filter yeah in these sort of papers how + + align:start position:0% +filter yeah in these sort of papers how + + + align:start position:0% +filter yeah in these sort of papers how +is uncertainty communicated with the + + align:start position:0% +is uncertainty communicated with the + + + align:start position:0% +is uncertainty communicated with the +result yeah so we tend to we you tend to + + align:start position:0% +result yeah so we tend to we you tend to + + + align:start position:0% +result yeah so we tend to we you tend to +estimate something like your uncertainty + + align:start position:0% +estimate something like your uncertainty + + + align:start position:0% +estimate something like your uncertainty +and density is going to be about a + + align:start position:0% +and density is going to be about a + + + align:start position:0% +and density is going to be about a +quarter of a fringe shift and we'll talk + + align:start position:0% +quarter of a fringe shift and we'll talk + + + align:start position:0% +quarter of a fringe shift and we'll talk +about I'll talk about what that means + + align:start position:0% +about I'll talk about what that means + + + align:start position:0% +about I'll talk about what that means +actually in the next uh bit of the + + align:start position:0% +actually in the next uh bit of the + + + align:start position:0% +actually in the next uh bit of the +chalkboard talk so yeah you can you can + + align:start position:0% +chalkboard talk so yeah you can you can + + + align:start position:0% +chalkboard talk so yeah you can you can +estimate uncertainty by saying how + + align:start position:0% +estimate uncertainty by saying how + + + align:start position:0% +estimate uncertainty by saying how +certain are you that The Fringe has + + align:start position:0% +certain are you that The Fringe has + + + align:start position:0% +certain are you that The Fringe has +shifted up this far versus this far so + + align:start position:0% +shifted up this far versus this far so + + + align:start position:0% +shifted up this far versus this far so +there's sort like a pixel uncertainty + + align:start position:0% +there's sort like a pixel uncertainty + + + align:start position:0% +there's sort like a pixel uncertainty +and also how well good you are at + + align:start position:0% +and also how well good you are at + + + align:start position:0% +and also how well good you are at +assigning this is the lightest part of + + align:start position:0% +assigning this is the lightest part of + + + align:start position:0% +assigning this is the lightest part of +The Fringe this is the darkest part + + align:start position:0% +The Fringe this is the darkest part + + + align:start position:0% +The Fringe this is the darkest part +because effectively you're you're + + align:start position:0% +because effectively you're you're + + + align:start position:0% +because effectively you're you're +looking for the light parts and the dark + + align:start position:0% +looking for the light parts and the dark + + + align:start position:0% +looking for the light parts and the dark +Parts but there's several pixels which + + align:start position:0% +Parts but there's several pixels which + + + align:start position:0% +Parts but there's several pixels which +will be equally light because it's near + + align:start position:0% +will be equally light because it's near + + + align:start position:0% +will be equally light because it's near +a Maxima or a Minima so so you you tend + + align:start position:0% +a Maxima or a Minima so so you you tend + + + align:start position:0% +a Maxima or a Minima so so you you tend +to whack a relatively High uncertainty + + align:start position:0% +to whack a relatively High uncertainty + + + align:start position:0% +to whack a relatively High uncertainty +on it and just call it a + + align:start position:0% +on it and just call it a + + + align:start position:0% +on it and just call it a +day in the field in this field you know + + align:start position:0% +day in the field in this field you know + + + align:start position:0% +day in the field in this field you know +if we get measurements right with in + + align:start position:0% +if we get measurements right with in + + + align:start position:0% +if we get measurements right with in +about 20% we're pretty happy so this is + + align:start position:0% +about 20% we're pretty happy so this is + + + align:start position:0% +about 20% we're pretty happy so this is +very different from other parts of plas + + align:start position:0% +very different from other parts of plas + + + align:start position:0% +very different from other parts of plas +physics + + align:start position:0% +physics + + + align:start position:0% +physics +so okay were there any questions online + + align:start position:0% +so okay were there any questions online + + + align:start position:0% +so okay were there any questions online +I'm sorry I can't see Hands online at + + align:start position:0% +I'm sorry I can't see Hands online at + + + align:start position:0% +I'm sorry I can't see Hands online at +the moment because I hid that little bar + + align:start position:0% +the moment because I hid that little bar + + + align:start position:0% +the moment because I hid that little bar +and I don't know how to get it back so + + align:start position:0% +and I don't know how to get it back so + + + align:start position:0% +and I don't know how to get it back so +if you have put your hand up or + + align:start position:0% +if you have put your hand up or + + + align:start position:0% +if you have put your hand up or +something like that I can't see + + align:start position:0% + + + + align:start position:0% + +it assume I'm still on Zoom somewhere no + + align:start position:0% +it assume I'm still on Zoom somewhere no + + + align:start position:0% +it assume I'm still on Zoom somewhere no +idea how to get back there + + align:start position:0% +idea how to get back there + + + align:start position:0% +idea how to get back there +Escape FL ah okay there was something in + + align:start position:0% +Escape FL ah okay there was something in + + + align:start position:0% +Escape FL ah okay there was something in +the chat no questions here all right + + align:start position:0% +the chat no questions here all right + + + align:start position:0% +the chat no questions here all right +well that was easy thank + + align:start position:0% +well that was easy thank + + + align:start position:0% +well that was easy thank +you I think we'll go back to the + + align:start position:0% +you I think we'll go back to the + + + align:start position:0% +you I think we'll go back to the +chalkboard for the moment then I've got + + align:start position:0% +chalkboard for the moment then I've got + + + align:start position:0% +chalkboard for the moment then I've got +a few more pictures depending on uh how + + align:start position:0% +a few more pictures depending on uh how + + + align:start position:0% +a few more pictures depending on uh how +we do for time so + + align:start position:0% + + + + align:start position:0% + +gu I should look down here for the + + align:start position:0% +gu I should look down here for the + + + align:start position:0% +gu I should look down here for the +remote controll some + + align:start position:0% + + + + align:start position:0% + +so maybe just a little bit more + + align:start position:0% +so maybe just a little bit more + + + align:start position:0% +so maybe just a little bit more +practical stuff you know one thing that + + align:start position:0% +practical stuff you know one thing that + + + align:start position:0% +practical stuff you know one thing that +really matters is your choice of your + + align:start position:0% +really matters is your choice of your + + + align:start position:0% +really matters is your choice of your +probe wavelength I've been talking a lot + + align:start position:0% +probe wavelength I've been talking a lot + + + align:start position:0% +probe wavelength I've been talking a lot +about frequency it turns out that a lot + + align:start position:0% +about frequency it turns out that a lot + + + align:start position:0% +about frequency it turns out that a lot +of the time people quote their + + align:start position:0% +of the time people quote their + + + align:start position:0% +of the time people quote their +frequencies in terms of wavelengths and + + align:start position:0% +frequencies in terms of wavelengths and + + + align:start position:0% +frequencies in terms of wavelengths and +obviously they're very intimately linked + + align:start position:0% +obviously they're very intimately linked + + + align:start position:0% +obviously they're very intimately linked +so if you remember we had our phase + + align:start position:0% +so if you remember we had our phase + + + align:start position:0% +so if you remember we had our phase +shift was minus Omega over 2 C and crial + + align:start position:0% +shift was minus Omega over 2 C and crial + + + align:start position:0% +shift was minus Omega over 2 C and crial +any + + align:start position:0% +any + + + align:start position:0% +any +any like that we often Define a quantity + + align:start position:0% +any like that we often Define a quantity + + + align:start position:0% +any like that we often Define a quantity +called a fringe shift which I'm going to + + align:start position:0% +called a fringe shift which I'm going to + + + align:start position:0% +called a fringe shift which I'm going to +write as capital F and a fringe shift is + + align:start position:0% +write as capital F and a fringe shift is + + + align:start position:0% +write as capital F and a fringe shift is +just a shift of an intensity maximum or + + align:start position:0% +just a shift of an intensity maximum or + + + align:start position:0% +just a shift of an intensity maximum or +Minima by an amount in time or space + + align:start position:0% +Minima by an amount in time or space + + + align:start position:0% +Minima by an amount in time or space +that makes it look like another + + align:start position:0% +that makes it look like another + + + align:start position:0% +that makes it look like another +intensity Maxima or Minima having said + + align:start position:0% +intensity Maxima or Minima having said + + + align:start position:0% +intensity Maxima or Minima having said +that out loud I realize it's pretty + + align:start position:0% +that out loud I realize it's pretty + + + align:start position:0% +that out loud I realize it's pretty +incomprehensible so let me draw the + + align:start position:0% +incomprehensible so let me draw the + + + align:start position:0% +incomprehensible so let me draw the +picture um let's say that this is space + + align:start position:0% +picture um let's say that this is space + + + align:start position:0% +picture um let's say that this is space +or time doesn't really matter and you've + + align:start position:0% +or time doesn't really matter and you've + + + align:start position:0% +or time doesn't really matter and you've +got some intensity here and some + + align:start position:0% +got some intensity here and some + + + align:start position:0% +got some intensity here and some +background Fringe pattern like this so + + align:start position:0% +background Fringe pattern like this so + + + align:start position:0% +background Fringe pattern like this so +this is the beat frequency that you're + + align:start position:0% +this is the beat frequency that you're + + + align:start position:0% +this is the beat frequency that you're +measuring either in space or time in the + + align:start position:0% +measuring either in space or time in the + + + align:start position:0% +measuring either in space or time in the +absence of any plasma and then say that + + align:start position:0% +absence of any plasma and then say that + + + align:start position:0% +absence of any plasma and then say that +you have some plasma + + align:start position:0% +you have some plasma + + + align:start position:0% +you have some plasma +signal uh I'm going to draw this wrong I + + align:start position:0% +signal uh I'm going to draw this wrong I + + + align:start position:0% +signal uh I'm going to draw this wrong I +don't I know give me a + + align:start position:0% + + + + align:start position:0% + +moment okay so in the presence of a + + align:start position:0% +moment okay so in the presence of a + + + align:start position:0% +moment okay so in the presence of a +plasma your Fringe pattern has been + + align:start position:0% +plasma your Fringe pattern has been + + + align:start position:0% +plasma your Fringe pattern has been +distorted I got that wrong + + align:start position:0% + + + + align:start position:0% + +Twi there we go I consider it so this + + align:start position:0% +Twi there we go I consider it so this + + + align:start position:0% +Twi there we go I consider it so this +BRD here you would think should line up + + align:start position:0% +BRD here you would think should line up + + + align:start position:0% +BRD here you would think should line up +with this one but in fact it's been + + align:start position:0% +with this one but in fact it's been + + + align:start position:0% +with this one but in fact it's been +shifted all the way so it lines up was + + align:start position:0% +shifted all the way so it lines up was + + + align:start position:0% +shifted all the way so it lines up was +this one instead so this is the case + + align:start position:0% +this one instead so this is the case + + + align:start position:0% +this one instead so this is the case +with plasma and this is the case with no + + align:start position:0% +with plasma and this is the case with no + + + align:start position:0% +with plasma and this is the case with no +plasma and that is the definition of one + + align:start position:0% +plasma and that is the definition of one + + + align:start position:0% +plasma and that is the definition of one +Fringe shift so it's effectively Delta 5 + + align:start position:0% +Fringe shift so it's effectively Delta 5 + + + align:start position:0% +Fringe shift so it's effectively Delta 5 +over 2 pi we're just count counting the + + align:start position:0% +over 2 pi we're just count counting the + + + align:start position:0% +over 2 pi we're just count counting the +motion of Minima and Maxima here and we + + align:start position:0% +motion of Minima and Maxima here and we + + + align:start position:0% +motion of Minima and Maxima here and we +can write that in Practical units as 4 + + align:start position:0% +can write that in Practical units as 4 + + + align:start position:0% +can write that in Practical units as 4 +5 * 10 + + align:start position:0% +5 * 10 + + + align:start position:0% +5 * 10 +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +16 Lambda + + align:start position:0% +16 Lambda + + + align:start position:0% +16 Lambda +time the line integrated electron + + align:start position:0% +time the line integrated electron + + + align:start position:0% +time the line integrated electron +density so people often + + align:start position:0% +density so people often + + + align:start position:0% +density so people often +write this quantity here like this I + + align:start position:0% +write this quantity here like this I + + + align:start position:0% +write this quantity here like this I +think because it looks nicer on one line + + align:start position:0% +think because it looks nicer on one line + + + align:start position:0% +think because it looks nicer on one line +uh in a an equation right because you + + align:start position:0% +uh in a an equation right because you + + + align:start position:0% +uh in a an equation right because you +don't have that big integral side but + + align:start position:0% +don't have that big integral side but + + + align:start position:0% +don't have that big integral side but +effectively it just means the average + + align:start position:0% +effectively it just means the average + + + align:start position:0% +effectively it just means the average +electral density average over some + + align:start position:0% +electral density average over some + + + align:start position:0% +electral density average over some +distance L like that and all of these + + align:start position:0% +distance L like that and all of these + + + align:start position:0% +distance L like that and all of these +units here are + + align:start position:0% + + + + align:start position:0% + +SI and so that means you can then work + + align:start position:0% +SI and so that means you can then work + + + align:start position:0% +SI and so that means you can then work +out what your line integrated electron + + align:start position:0% +out what your line integrated electron + + + align:start position:0% +out what your line integrated electron +density is in terms of fringes it's 2.2 + + align:start position:0% +density is in terms of fringes it's 2.2 + + + align:start position:0% +density is in terms of fringes it's 2.2 +10 to the that a minus 16 here 10 plus + + align:start position:0% +10 to the that a minus 16 here 10 plus + + + align:start position:0% +10 to the that a minus 16 here 10 plus +15 over Lambda times the number of Fring + + align:start position:0% +15 over Lambda times the number of Fring + + + align:start position:0% +15 over Lambda times the number of Fring +shifts and that's in units of a meter + + align:start position:0% +shifts and that's in units of a meter + + + align:start position:0% +shifts and that's in units of a meter +squar and so now I'm just going to give + + align:start position:0% +squar and so now I'm just going to give + + + align:start position:0% +squar and so now I'm just going to give +you um for different Lambda what this + + align:start position:0% +you um for different Lambda what this + + + align:start position:0% +you um for different Lambda what this +number actually is so we can have a look + + align:start position:0% +number actually is so we can have a look + + + align:start position:0% +number actually is so we can have a look +at some different sources so I have a + + align:start position:0% +at some different sources so I have a + + + align:start position:0% +at some different sources so I have a +little table where I have wavelength of + + align:start position:0% +little table where I have wavelength of + + + align:start position:0% +little table where I have wavelength of +the source and then I have any l + + align:start position:0% +the source and then I have any l + + + align:start position:0% +the source and then I have any l +or FAL one that's a units of me squared + + align:start position:0% +or FAL one that's a units of me squared + + + align:start position:0% +or FAL one that's a units of me squared +I'm just going to go down a list of + + align:start position:0% +I'm just going to go down a list of + + + align:start position:0% +I'm just going to go down a list of +sources so if for example we're in the + + align:start position:0% +sources so if for example we're in the + + + align:start position:0% +sources so if for example we're in the +microwave range here + + align:start position:0% + + + + align:start position:0% + +this might be a wavelength of 3.3 + + align:start position:0% +this might be a wavelength of 3.3 + + + align:start position:0% +this might be a wavelength of 3.3 +millimeters so that would be a 90 gahz + + align:start position:0% +millimeters so that would be a 90 gahz + + + align:start position:0% +millimeters so that would be a 90 gahz +source so this is relatively low density + + align:start position:0% +source so this is relatively low density + + + align:start position:0% +source so this is relatively low density +plasmas here and that density here will + + align:start position:0% +plasmas here and that density here will + + + align:start position:0% +plasmas here and that density here will +be 6.7 10 + + align:start position:0% +be 6.7 10 + + + align:start position:0% +be 6.7 10 +1 we could jump quite a bit and go to a + + align:start position:0% +1 we could jump quite a bit and go to a + + + align:start position:0% +1 we could jump quite a bit and go to a +CO2 laser this is a nice infrared laser + + align:start position:0% +CO2 laser this is a nice infrared laser + + + align:start position:0% +CO2 laser this is a nice infrared laser +and you can make right powerful CO2 + + align:start position:0% +and you can make right powerful CO2 + + + align:start position:0% +and you can make right powerful CO2 +lasers so they're quite popular on + + align:start position:0% +lasers so they're quite popular on + + + align:start position:0% +lasers so they're quite popular on +diagnostics as uh yeah alator had a CO2 + + align:start position:0% +diagnostics as uh yeah alator had a CO2 + + + align:start position:0% +diagnostics as uh yeah alator had a CO2 +ineter so this is + + align:start position:0% +ineter so this is + + + align:start position:0% +ineter so this is +10.6 micrometers here so I've dropped a + + align:start position:0% +10.6 micrometers here so I've dropped a + + + align:start position:0% +10.6 micrometers here so I've dropped a +couple of orders of magnitude from the + + align:start position:0% +couple of orders of magnitude from the + + + align:start position:0% +couple of orders of magnitude from the +microwaves and you can + + align:start position:0% + + + + align:start position:0% + +see that the densities that we're + + align:start position:0% +see that the densities that we're + + + align:start position:0% +see that the densities that we're +measuring here have gone up quite a bit + + align:start position:0% +measuring here have gone up quite a bit + + + align:start position:0% +measuring here have gone up quite a bit +by similar amounts + + align:start position:0% +by similar amounts + + + align:start position:0% +by similar amounts +20 and then something like a neod Demian + + align:start position:0% +20 and then something like a neod Demian + + + align:start position:0% +20 and then something like a neod Demian +yag laser + + align:start position:0% +yag laser + + + align:start position:0% +yag laser +this is the sort of thing I use if we + + align:start position:0% +this is the sort of thing I use if we + + + align:start position:0% +this is the sort of thing I use if we +use the second harmonic that would be + + align:start position:0% +use the second harmonic that would be + + + align:start position:0% +use the second harmonic that would be +532 nanometers that will make those + + align:start position:0% +532 nanometers that will make those + + + align:start position:0% +532 nanometers that will make those +beautiful green images that we looked at + + align:start position:0% +beautiful green images that we looked at + + + align:start position:0% +beautiful green images that we looked at +and that is 4.2 * 10 the 21 hit so if I + + align:start position:0% +and that is 4.2 * 10 the 21 hit so if I + + + align:start position:0% +and that is 4.2 * 10 the 21 hit so if I +see a Fring shift of one and on those + + align:start position:0% +see a Fring shift of one and on those + + + align:start position:0% +see a Fring shift of one and on those +images that I showed you first The + + align:start position:0% +images that I showed you first The + + + align:start position:0% +images that I showed you first The +Fringe shift was maybe two or three + + align:start position:0% +Fringe shift was maybe two or three + + + align:start position:0% +Fringe shift was maybe two or three +fringes each of those corresponds to + + align:start position:0% +fringes each of those corresponds to + + + align:start position:0% +fringes each of those corresponds to +electron density 4.2 * 10 21 so just by + + align:start position:0% +electron density 4.2 * 10 21 so just by + + + align:start position:0% +electron density 4.2 * 10 21 so just by +looking at the image and by eyeballing + + align:start position:0% +looking at the image and by eyeballing + + + align:start position:0% +looking at the image and by eyeballing +it you can start estimating the line + + align:start position:0% +it you can start estimating the line + + + align:start position:0% +it you can start estimating the line +integrated electron density and then if + + align:start position:0% +integrated electron density and then if + + + align:start position:0% +integrated electron density and then if +you have some idea of how long your + + align:start position:0% +you have some idea of how long your + + + align:start position:0% +you have some idea of how long your +plasma is you can then get a rough + + align:start position:0% +plasma is you can then get a rough + + + align:start position:0% +plasma is you can then get a rough +estimate of the electron density itself + + align:start position:0% +estimate of the electron density itself + + + align:start position:0% +estimate of the electron density itself +I think what's very interesting about + + align:start position:0% +I think what's very interesting about + + + align:start position:0% +I think what's very interesting about +this which I worked this out just before + + align:start position:0% +this which I worked this out just before + + + align:start position:0% +this which I worked this out just before +the lecture and I hope I'm right because + + align:start position:0% +the lecture and I hope I'm right because + + + align:start position:0% +the lecture and I hope I'm right because +I was very surprised by it if we take + + align:start position:0% +I was very surprised by it if we take + + + align:start position:0% +I was very surprised by it if we take +for example a wavelength of 1064 + + align:start position:0% +for example a wavelength of 1064 + + + align:start position:0% +for example a wavelength of 1064 +nanometers so this is an infrared ndag + + align:start position:0% +nanometers so this is an infrared ndag + + + align:start position:0% +nanometers so this is an infrared ndag +Glazer and we take a length of 10us 2 + + align:start position:0% +Glazer and we take a length of 10us 2 + + + align:start position:0% +Glazer and we take a length of 10us 2 +met so a centimeter so this is the sort + + align:start position:0% +met so a centimeter so this is the sort + + + align:start position:0% +met so a centimeter so this is the sort +of experiment that I might do one + + align:start position:0% +of experiment that I might do one + + + align:start position:0% +of experiment that I might do one +Fringe would then correspond to a + + align:start position:0% +Fringe would then correspond to a + + + align:start position:0% +Fringe would then correspond to a +density + + align:start position:0% +density + + + align:start position:0% +density +of 2 * 10 + + align:start position:0% +of 2 * 10 + + + align:start position:0% +of 2 * 10 +23 per met squ okay not that + + align:start position:0% +23 per met squ okay not that + + + align:start position:0% +23 per met squ okay not that +interesting so far meter + + align:start position:0% +interesting so far meter + + + align:start position:0% +interesting so far meter +cubed but then you ask yourself what is + + align:start position:0% +cubed but then you ask yourself what is + + + align:start position:0% +cubed but then you ask yourself what is +the critical density here this is turns + + align:start position:0% +the critical density here this is turns + + + align:start position:0% +the critical density here this is turns +out to be 10 + + align:start position:0% +out to be 10 + + + align:start position:0% +out to be 10 +28 per me cubed so what is the + + align:start position:0% +28 per me cubed so what is the + + + align:start position:0% +28 per me cubed so what is the +refractive index we've been saying that + + align:start position:0% +refractive index we've been saying that + + + align:start position:0% +refractive index we've been saying that +it's + + align:start position:0% +it's + + + align:start position:0% +it's +1us NE 2 + + align:start position:0% +1us NE 2 + + + align:start position:0% +1us NE 2 +NC this is a very small number this is + + align:start position:0% +NC this is a very small number this is + + + align:start position:0% +NC this is a very small number this is +now well it's almost close it's one + + align:start position:0% +now well it's almost close it's one + + + align:start position:0% +now well it's almost close it's one +minus 10 minus 5 so all of these + + align:start position:0% +minus 10 minus 5 so all of these + + + align:start position:0% +minus 10 minus 5 so all of these +interprom effects we're looking at are + + align:start position:0% +interprom effects we're looking at are + + + align:start position:0% +interprom effects we're looking at are +to do with changes in the refractive + + align:start position:0% +to do with changes in the refractive + + + align:start position:0% +to do with changes in the refractive +index on the order of 10us 5 or so I + + align:start position:0% +index on the order of 10us 5 or so I + + + align:start position:0% +index on the order of 10us 5 or so I +kind of find that remarkable we're able + + align:start position:0% +kind of find that remarkable we're able + + + align:start position:0% +kind of find that remarkable we're able +to measure very very very small changes + + align:start position:0% +to measure very very very small changes + + + align:start position:0% +to measure very very very small changes +in ref index it's not like n ever gets + + align:start position:0% +in ref index it's not like n ever gets + + + align:start position:0% +in ref index it's not like n ever gets +close to zero or two or something + + align:start position:0% +close to zero or two or something + + + align:start position:0% +close to zero or two or something +bizarre like that anyway I thought that + + align:start position:0% +bizarre like that anyway I thought that + + + align:start position:0% +bizarre like that anyway I thought that +was + + align:start position:0% + + + + align:start position:0% + +interesting okay so you will pick your + + align:start position:0% +interesting okay so you will pick your + + + align:start position:0% +interesting okay so you will pick your +source to match your plasma right if + + align:start position:0% +source to match your plasma right if + + + align:start position:0% +source to match your plasma right if +you're doing low density plasmas then if + + align:start position:0% +you're doing low density plasmas then if + + + align:start position:0% +you're doing low density plasmas then if +you use a 532 nanometer in prometer you + + align:start position:0% +you use a 532 nanometer in prometer you + + + align:start position:0% +you use a 532 nanometer in prometer you +won't see any Fringe shift the fringes + + align:start position:0% +won't see any Fringe shift the fringes + + + align:start position:0% +won't see any Fringe shift the fringes +won't move at all you won't be able to + + align:start position:0% +won't move at all you won't be able to + + + align:start position:0% +won't move at all you won't be able to +measure any plasma so you need to use a + + align:start position:0% +measure any plasma so you need to use a + + + align:start position:0% +measure any plasma so you need to use a +long wavelength source that is more + + align:start position:0% +long wavelength source that is more + + + align:start position:0% +long wavelength source that is more +sensitive those lower densities um + + align:start position:0% +sensitive those lower densities um + + + align:start position:0% +sensitive those lower densities um +conversely if you try to use a long + + align:start position:0% +conversely if you try to use a long + + + align:start position:0% +conversely if you try to use a long +wavelength Source on a nice dense plasma + + align:start position:0% +wavelength Source on a nice dense plasma + + + align:start position:0% +wavelength Source on a nice dense plasma +first of all the beam may just get + + align:start position:0% +first of all the beam may just get + + + align:start position:0% +first of all the beam may just get +absorbed because it will hit the + + align:start position:0% +absorbed because it will hit the + + + align:start position:0% +absorbed because it will hit the +critical density or it might get + + align:start position:0% +critical density or it might get + + + align:start position:0% +critical density or it might get +refracted out and even if it doesn't do + + align:start position:0% +refracted out and even if it doesn't do + + + align:start position:0% +refracted out and even if it doesn't do +any of those you'll have such huge phase + + align:start position:0% +any of those you'll have such huge phase + + + align:start position:0% +any of those you'll have such huge phase +shifts you won't be able to meet that + + align:start position:0% +shifts you won't be able to meet that + + + align:start position:0% +shifts you won't be able to meet that +hrod Criterion and you'll just have like + + align:start position:0% +hrod Criterion and you'll just have like + + + align:start position:0% +hrod Criterion and you'll just have like +very complicated Fringe patterns and no + + align:start position:0% +very complicated Fringe patterns and no + + + align:start position:0% +very complicated Fringe patterns and no +chance of processing so you've got to + + align:start position:0% +chance of processing so you've got to + + + align:start position:0% +chance of processing so you've got to +pick very carefully um what sort of + + align:start position:0% +pick very carefully um what sort of + + + align:start position:0% +pick very carefully um what sort of +source you have and there are other ones + + align:start position:0% +source you have and there are other ones + + + align:start position:0% +source you have and there are other ones +out here as well but I just s of picked + + align:start position:0% +out here as well but I just s of picked + + + align:start position:0% +out here as well but I just s of picked +a range that might be relevant to some + + align:start position:0% +a range that might be relevant to some + + + align:start position:0% +a range that might be relevant to some +of the people in this group any + + align:start position:0% +of the people in this group any + + + align:start position:0% +of the people in this group any +questions on that before we move + + align:start position:0% + + + + align:start position:0% + +on so I want to talk about a few + + align:start position:0% +on so I want to talk about a few + + + align:start position:0% +on so I want to talk about a few +extensions to this technique and the + + align:start position:0% +extensions to this technique and the + + + align:start position:0% +extensions to this technique and the +first one we're going to talk about is + + align:start position:0% +first one we're going to talk about is + + + align:start position:0% +first one we're going to talk about is +called twocc + + align:start position:0% +called twocc + + + align:start position:0% +called twocc +color + + align:start position:0% + + + + align:start position:0% + +in there are two reasons to do two color + + align:start position:0% +in there are two reasons to do two color + + + align:start position:0% +in there are two reasons to do two color +deometry conveniently one is to handle + + align:start position:0% + + + + align:start position:0% + +vibrations and the other one is to + + align:start position:0% +vibrations and the other one is to + + + align:start position:0% +vibrations and the other one is to +handle + + align:start position:0% + + + + align:start position:0% + +neutrals so let's have a little talk + + align:start position:0% +neutrals so let's have a little talk + + + align:start position:0% +neutrals so let's have a little talk +about vibrations first of + + align:start position:0% +about vibrations first of + + + align:start position:0% +about vibrations first of +all your system is made up of lots of + + align:start position:0% +all your system is made up of lots of + + + align:start position:0% +all your system is made up of lots of +mirrors and other Optics and there are + + align:start position:0% +mirrors and other Optics and there are + + + align:start position:0% +mirrors and other Optics and there are +vibrations everywhere and so all these + + align:start position:0% +vibrations everywhere and so all these + + + align:start position:0% +vibrations everywhere and so all these +mirrors and Optics will be vibrating + + align:start position:0% +mirrors and Optics will be vibrating + + + align:start position:0% +mirrors and Optics will be vibrating +slightly which means their path length + + align:start position:0% +slightly which means their path length + + + align:start position:0% +slightly which means their path length +will be changing by a small amount how + + align:start position:0% +will be changing by a small amount how + + + align:start position:0% +will be changing by a small amount how +big a deal is this well if we imagine + + align:start position:0% +big a deal is this well if we imagine + + + align:start position:0% +big a deal is this well if we imagine +that you've + + align:start position:0% +that you've + + + align:start position:0% +that you've +got some mirror for example here and we + + align:start position:0% +got some mirror for example here and we + + + align:start position:0% +got some mirror for example here and we +bounce our beam off it like that and the + + align:start position:0% +bounce our beam off it like that and the + + + align:start position:0% +bounce our beam off it like that and the +mirror is oscillating with an amplitude + + align:start position:0% +mirror is oscillating with an amplitude + + + align:start position:0% +mirror is oscillating with an amplitude +little L here we're going to get a phase + + align:start position:0% +little L here we're going to get a phase + + + align:start position:0% +little L here we're going to get a phase +change very simply just by looking at + + align:start position:0% +change very simply just by looking at + + + align:start position:0% +change very simply just by looking at +the distance that this moves on the + + align:start position:0% +the distance that this moves on the + + + align:start position:0% +the distance that this moves on the +order of 2 pi little L upon Lambda + + align:start position:0% +order of 2 pi little L upon Lambda + + + align:start position:0% +order of 2 pi little L upon Lambda +so + + align:start position:0% +so + + + align:start position:0% +so +if the phase if the amplitude of these + + align:start position:0% +if the phase if the amplitude of these + + + align:start position:0% +if the phase if the amplitude of these +vibrations is on the order of the + + align:start position:0% +vibrations is on the order of the + + + align:start position:0% +vibrations is on the order of the +wavelength you're going to get phase + + align:start position:0% +wavelength you're going to get phase + + + align:start position:0% +wavelength you're going to get phase +shift of 2 pi which is actually already + + align:start position:0% +shift of 2 pi which is actually already + + + align:start position:0% +shift of 2 pi which is actually already +pretty huge that's one frint + + align:start position:0% +pretty huge that's one frint + + + align:start position:0% +pretty huge that's one frint +shift but this is a tiny number I mean + + align:start position:0% +shift but this is a tiny number I mean + + + align:start position:0% +shift but this is a tiny number I mean +if I'm working with green light this + + align:start position:0% +if I'm working with green light this + + + align:start position:0% +if I'm working with green light this +means I am sensitive to vibrations on + + align:start position:0% +means I am sensitive to vibrations on + + + align:start position:0% +means I am sensitive to vibrations on +the order of 532 nanometers right so + + align:start position:0% +the order of 532 nanometers right so + + + align:start position:0% +the order of 532 nanometers right so +this is extremely hard to avoid you + + align:start position:0% +this is extremely hard to avoid you + + + align:start position:0% +this is extremely hard to avoid you +can't get rid of vibrations at SW very + + align:start position:0% +can't get rid of vibrations at SW very + + + align:start position:0% +can't get rid of vibrations at SW very +easily so you're gonna have big problems + + align:start position:0% +easily so you're gonna have big problems + + + align:start position:0% +easily so you're gonna have big problems +with these vibrations and if your whole + + align:start position:0% +with these vibrations and if your whole + + + align:start position:0% +with these vibrations and if your whole +toac is vibrating so you got all these + + align:start position:0% +toac is vibrating so you got all these + + + align:start position:0% +toac is vibrating so you got all these +cryopumps and neutral beams and exciting + + align:start position:0% +cryopumps and neutral beams and exciting + + + align:start position:0% +cryopumps and neutral beams and exciting +things going on this is going to be an + + align:start position:0% +things going on this is going to be an + + + align:start position:0% +things going on this is going to be an +absolute nightmare turns out not to be a + + align:start position:0% +absolute nightmare turns out not to be a + + + align:start position:0% +absolute nightmare turns out not to be a +huge nightmare for my stuff because + + align:start position:0% +huge nightmare for my stuff because + + + align:start position:0% +huge nightmare for my stuff because +although these very sensitive to + + align:start position:0% +although these very sensitive to + + + align:start position:0% +although these very sensitive to +vibrations the time scale over which our + + align:start position:0% +vibrations the time scale over which our + + + align:start position:0% +vibrations the time scale over which our +experiment takes place a nanc or a laser + + align:start position:0% +experiment takes place a nanc or a laser + + + align:start position:0% +experiment takes place a nanc or a laser +pulse the vibrations are not at + + align:start position:0% +pulse the vibrations are not at + + + align:start position:0% +pulse the vibrations are not at +gigahertz you don't have mechanical + + align:start position:0% +gigahertz you don't have mechanical + + + align:start position:0% +gigahertz you don't have mechanical +vibrations out those frequencies so we + + align:start position:0% +vibrations out those frequencies so we + + + align:start position:0% +vibrations out those frequencies so we +can ignore it but if you have vibrations + + align:start position:0% +can ignore it but if you have vibrations + + + align:start position:0% +can ignore it but if you have vibrations +at kohtz or even Hertz from people + + align:start position:0% +at kohtz or even Hertz from people + + + align:start position:0% +at kohtz or even Hertz from people +walking around this will ruin your nice + + align:start position:0% +walking around this will ruin your nice + + + align:start position:0% +walking around this will ruin your nice +more steady state + + align:start position:0% +more steady state + + + align:start position:0% +more steady state +experiment and what we want to notice is + + align:start position:0% +experiment and what we want to notice is + + + align:start position:0% +experiment and what we want to notice is +this phase + + align:start position:0% +this phase + + + align:start position:0% +this phase +shift in + + align:start position:0% +shift in + + + align:start position:0% +shift in +particular as I've just sort of alluded + + align:start position:0% +particular as I've just sort of alluded + + + align:start position:0% +particular as I've just sort of alluded +to is + + align:start position:0% +to is + + + align:start position:0% +to is +large or + + align:start position:0% +large or + + + align:start position:0% +large or +small wavelengths and this already + + align:start position:0% +small wavelengths and this already + + + align:start position:0% +small wavelengths and this already +suggests the beginnings of a scheme that + + align:start position:0% +suggests the beginnings of a scheme that + + + align:start position:0% +suggests the beginnings of a scheme that +we're going to use especially ex I call + + align:start position:0% +we're going to use especially ex I call + + + align:start position:0% +we're going to use especially ex I call +the two-color in barometry to deal with + + align:start position:0% +the two-color in barometry to deal with + + + align:start position:0% +the two-color in barometry to deal with +this so the + + align:start position:0% + + + + align:start position:0% + +solution is we run two incomers down the + + align:start position:0% +solution is we run two incomers down the + + + align:start position:0% +solution is we run two incomers down the +same line of sight with two different + + align:start position:0% +same line of sight with two different + + + align:start position:0% +same line of sight with two different +wavelengths okay one of these + + align:start position:0% +wavelengths okay one of these + + + align:start position:0% +wavelengths okay one of these +wavelengths is + + align:start position:0% +wavelengths is + + + align:start position:0% +wavelengths is +short and so that could be something + + align:start position:0% +short and so that could be something + + + align:start position:0% +short and so that could be something +like on a toat a laser so it could just + + align:start position:0% +like on a toat a laser so it could just + + + align:start position:0% +like on a toat a laser so it could just +be a hey laser be goes straight through + + align:start position:0% +be a hey laser be goes straight through + + + align:start position:0% +be a hey laser be goes straight through +the plasma doesn't see it at all because + + align:start position:0% +the plasma doesn't see it at all because + + + align:start position:0% +the plasma doesn't see it at all because +it's not dense enough but that short + + align:start position:0% +it's not dense enough but that short + + + align:start position:0% +it's not dense enough but that short +wavelength is very sensitive to + + align:start position:0% + + + + align:start position:0% + +vibrations those are vibrations + + align:start position:0% +vibrations those are vibrations + + + align:start position:0% +vibrations those are vibrations +proportional + + align:start position:0% +proportional + + + align:start position:0% +proportional +five Vib should we call it for vibration + + align:start position:0% +five Vib should we call it for vibration + + + align:start position:0% +five Vib should we call it for vibration +proportional to one over Lambda so this + + align:start position:0% +proportional to one over Lambda so this + + + align:start position:0% +proportional to one over Lambda so this +will be a very good diagnostic not of + + align:start position:0% +will be a very good diagnostic not of + + + align:start position:0% +will be a very good diagnostic not of +plasma it won't see the plasma but it be + + align:start position:0% +plasma it won't see the plasma but it be + + + align:start position:0% +plasma it won't see the plasma but it be +a very good diagnostic of vibrations + + align:start position:0% +a very good diagnostic of vibrations + + + align:start position:0% +a very good diagnostic of vibrations +okay and the other one a long wavelength + + align:start position:0% +okay and the other one a long wavelength + + + align:start position:0% +okay and the other one a long wavelength +here which might be on a toac something + + align:start position:0% +here which might be on a toac something + + + align:start position:0% +here which might be on a toac something +like you know a microwave source so many + + align:start position:0% +like you know a microwave source so many + + + align:start position:0% +like you know a microwave source so many +many many differences in wavelength by + + align:start position:0% +many many differences in wavelength by + + + align:start position:0% +many many differences in wavelength by +two or three ORS of magnitude that long + + align:start position:0% +two or three ORS of magnitude that long + + + align:start position:0% +two or three ORS of magnitude that long +wavelength will be very sensitive to the + + align:start position:0% +wavelength will be very sensitive to the + + + align:start position:0% +wavelength will be very sensitive to the +plasma because by plasma is proportional + + align:start position:0% +plasma because by plasma is proportional + + + align:start position:0% +plasma because by plasma is proportional +to + + align:start position:0% + + + + align:start position:0% + +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +here and so what you can do when you + + align:start position:0% +here and so what you can do when you + + + align:start position:0% +here and so what you can do when you +measure the overall f with these two + + align:start position:0% +measure the overall f with these two + + + align:start position:0% +measure the overall f with these two +devices well I'm not going to do it + + align:start position:0% +devices well I'm not going to do it + + + align:start position:0% +devices well I'm not going to do it +explicitly you're going to have two uh + + align:start position:0% +explicitly you're going to have two uh + + + align:start position:0% +explicitly you're going to have two uh +two sources of uh phase one of them is + + align:start position:0% +two sources of uh phase one of them is + + + align:start position:0% +two sources of uh phase one of them is +going to be the standard plasma here NL + + align:start position:0% +going to be the standard plasma here NL + + + align:start position:0% +going to be the standard plasma here NL +and the other one is going to be the + + align:start position:0% +and the other one is going to be the + + + align:start position:0% +and the other one is going to be the +vibrations due to L so you'll have two + + align:start position:0% +vibrations due to L so you'll have two + + + align:start position:0% +vibrations due to L so you'll have two +unknowns and now you've got two + + align:start position:0% +unknowns and now you've got two + + + align:start position:0% +unknowns and now you've got two +measurements and so you can use a system + + align:start position:0% +measurements and so you can use a system + + + align:start position:0% +measurements and so you can use a system +of equation to solve for that and if + + align:start position:0% +of equation to solve for that and if + + + align:start position:0% +of equation to solve for that and if +you're very very quick you can even use + + align:start position:0% +you're very very quick you can even use + + + align:start position:0% +you're very very quick you can even use +the short + + align:start position:0% + + + + align:start position:0% + +wavelength uh to feedback into your + + align:start position:0% +wavelength uh to feedback into your + + + align:start position:0% +wavelength uh to feedback into your +mirrors with the PA Zone and stabilize + + align:start position:0% +mirrors with the PA Zone and stabilize + + + align:start position:0% +mirrors with the PA Zone and stabilize +the mirrors so you can do like vibration + + align:start position:0% +the mirrors so you can do like vibration + + + align:start position:0% +the mirrors so you can do like vibration +stabilization + + align:start position:0% +stabilization + + + align:start position:0% +stabilization +uh feedback mirrors so you can use this + + align:start position:0% +uh feedback mirrors so you can use this + + + align:start position:0% +uh feedback mirrors so you can use this +very + + align:start position:0% +very + + + align:start position:0% +very +fast short wavelength into perometer to + + align:start position:0% +fast short wavelength into perometer to + + + align:start position:0% +fast short wavelength into perometer to +vibration stabilize all your mirrors I + + align:start position:0% +vibration stabilize all your mirrors I + + + align:start position:0% +vibration stabilize all your mirrors I +don't know if anyone's actually done + + align:start position:0% +don't know if anyone's actually done + + + align:start position:0% +don't know if anyone's actually done +this it's in hutson's book so presumably + + align:start position:0% +this it's in hutson's book so presumably + + + align:start position:0% +this it's in hutson's book so presumably +someone tried it sounds like it would + + align:start position:0% +someone tried it sounds like it would + + + align:start position:0% +someone tried it sounds like it would +work but I guess uh it could be very + + align:start position:0% +work but I guess uh it could be very + + + align:start position:0% +work but I guess uh it could be very +very effective so this is maybe more of + + align:start position:0% +very effective so this is maybe more of + + + align:start position:0% +very effective so this is maybe more of +a question mark rather than something + + align:start position:0% +a question mark rather than something + + + align:start position:0% +a question mark rather than something +that everyone does it's pretty clear + + align:start position:0% +that everyone does it's pretty clear + + + align:start position:0% +that everyone does it's pretty clear +that if you digitize both these signals + + align:start position:0% +that if you digitize both these signals + + + align:start position:0% +that if you digitize both these signals +you should be able to work out what was + + align:start position:0% +you should be able to work out what was + + + align:start position:0% +you should be able to work out what was +vibration and what was plasma of course + + align:start position:0% +vibration and what was plasma of course + + + align:start position:0% +vibration and what was plasma of course +of the vibrations are huge it might + + align:start position:0% +of the vibrations are huge it might + + + align:start position:0% +of the vibrations are huge it might +still Ru your measurement so it might be + + align:start position:0% +still Ru your measurement so it might be + + + align:start position:0% +still Ru your measurement so it might be +worth doing this feedback system so + + align:start position:0% +worth doing this feedback system so + + + align:start position:0% +worth doing this feedback system so +that's one use for two color + + align:start position:0% +that's one use for two color + + + align:start position:0% +that's one use for two color +interferometry just in case you're + + align:start position:0% +interferometry just in case you're + + + align:start position:0% +interferometry just in case you're +trying to work it out the two colors is + + align:start position:0% +trying to work it out the two colors is + + + align:start position:0% +trying to work it out the two colors is +because we have two wavelengths so we + + align:start position:0% +because we have two wavelengths so we + + + align:start position:0% +because we have two wavelengths so we +tend to associate with like color okay + + align:start position:0% +tend to associate with like color okay + + + align:start position:0% +tend to associate with like color okay +any questions on + + align:start position:0% + + + + align:start position:0% + +next okay the second thing I want to + + align:start position:0% +next okay the second thing I want to + + + align:start position:0% +next okay the second thing I want to +deal with is + + align:start position:0% + + + + align:start position:0% + +neutrals so far our refractive index has + + align:start position:0% +neutrals so far our refractive index has + + + align:start position:0% +neutrals so far our refractive index has +been derived assuming a fully ionized + + align:start position:0% +been derived assuming a fully ionized + + + align:start position:0% +been derived assuming a fully ionized +plas + + align:start position:0% +plas + + + align:start position:0% +plas +right and so in that fully ionized + + align:start position:0% +right and so in that fully ionized + + + align:start position:0% +right and so in that fully ionized +plasma we just have + + align:start position:0% +plasma we just have + + + align:start position:0% +plasma we just have +ions and we have electrons now these + + align:start position:0% +ions and we have electrons now these + + + align:start position:0% +ions and we have electrons now these +have Associated frequencies with them + + align:start position:0% +have Associated frequencies with them + + + align:start position:0% +have Associated frequencies with them +the ion frequency which is much much + + align:start position:0% +the ion frequency which is much much + + + align:start position:0% +the ion frequency which is much much +less than the electron frequency and so + + align:start position:0% +less than the electron frequency and so + + + align:start position:0% +less than the electron frequency and so +when we write down the refractive index + + align:start position:0% +when we write down the refractive index + + + align:start position:0% +when we write down the refractive index +we just have one this is refractive + + align:start position:0% +we just have one this is refractive + + + align:start position:0% +we just have one this is refractive +index squar one minus Omega s over Omega + + align:start position:0% +index squar one minus Omega s over Omega + + + align:start position:0% +index squar one minus Omega s over Omega +e e 2 need to tr + + align:start position:0% +e e 2 need to tr + + + align:start position:0% +e e 2 need to tr +that there's technically another term in + + align:start position:0% +that there's technically another term in + + + align:start position:0% +that there's technically another term in +here 1us Omega 2 Omega p i s but because + + align:start position:0% +here 1us Omega 2 Omega p i s but because + + + align:start position:0% +here 1us Omega 2 Omega p i s but because +the arms are so much more massive we + + align:start position:0% +the arms are so much more massive we + + + align:start position:0% +the arms are so much more massive we +always just ignore this term and we + + align:start position:0% +always just ignore this term and we + + + align:start position:0% +always just ignore this term and we +subtly drop the subscript on the plasma + + align:start position:0% +subtly drop the subscript on the plasma + + + align:start position:0% +subtly drop the subscript on the plasma +frequency here so this is the reflective + + align:start position:0% +frequency here so this is the reflective + + + align:start position:0% +frequency here so this is the reflective +index we've been using so far however + + align:start position:0% +index we've been using so far however + + + align:start position:0% +index we've been using so far however +when you've also got + + align:start position:0% + + + + align:start position:0% + +neutrals you've got some density of + + align:start position:0% +neutrals you've got some density of + + + align:start position:0% +neutrals you've got some density of +these as well and I'm going to write + + align:start position:0% +these as well and I'm going to write + + + align:start position:0% +these as well and I'm going to write +that n Alpha because no not alpha n + + align:start position:0% +that n Alpha because no not alpha n + + + align:start position:0% +that n Alpha because no not alpha n +a the a sort of being atoms okay so + + align:start position:0% +a the a sort of being atoms okay so + + + align:start position:0% +a the a sort of being atoms okay so +let's go for that now neutrals are much + + align:start position:0% +let's go for that now neutrals are much + + + align:start position:0% +let's go for that now neutrals are much +more complicated in fact because they + + align:start position:0% +more complicated in fact because they + + + align:start position:0% +more complicated in fact because they +have Atomic transitions inside them and + + align:start position:0% +have Atomic transitions inside them and + + + align:start position:0% +have Atomic transitions inside them and +those atomic transitions change + + align:start position:0% +those atomic transitions change + + + align:start position:0% +those atomic transitions change +refractive index if you're close to + + align:start position:0% +refractive index if you're close to + + + align:start position:0% +refractive index if you're close to +Atomic transition you have very + + align:start position:0% +Atomic transition you have very + + + align:start position:0% +Atomic transition you have very +different effects like absorption than + + align:start position:0% +different effects like absorption than + + + align:start position:0% +different effects like absorption than +you do if you're far from Atomic + + align:start position:0% +you do if you're far from Atomic + + + align:start position:0% +you do if you're far from Atomic +transition and so your Spectra or your + + align:start position:0% +transition and so your Spectra or your + + + align:start position:0% +transition and so your Spectra or your +your + + align:start position:0% + + + + align:start position:0% + +of refractive index for your neutrals + + align:start position:0% +of refractive index for your neutrals + + + align:start position:0% +of refractive index for your neutrals +here against frequency will look like + + align:start position:0% +here against frequency will look like + + + align:start position:0% +here against frequency will look like +some sort + + align:start position:0% +some sort + + + align:start position:0% +some sort +of spiky Minefield of + + align:start position:0% +of spiky Minefield of + + + align:start position:0% +of spiky Minefield of +lines something like that you know it + + align:start position:0% +lines something like that you know it + + + align:start position:0% +lines something like that you know it +will depend exactly on the atomic + + align:start position:0% +will depend exactly on the atomic + + + align:start position:0% +will depend exactly on the atomic +physics and in general we can write down + + align:start position:0% +physics and in general we can write down + + + align:start position:0% +physics and in general we can write down +this refractive index as equal to one + + align:start position:0% +this refractive index as equal to one + + + align:start position:0% +this refractive index as equal to one +always a good start uh Plus + + align:start position:0% +always a good start uh Plus + + + align:start position:0% +always a good start uh Plus +2 pi + + align:start position:0% +2 pi + + + align:start position:0% +2 pi +e^2 M ignore that it's just some + + align:start position:0% +e^2 M ignore that it's just some + + + align:start position:0% +e^2 M ignore that it's just some +constant that they're normalizing by and + + align:start position:0% +constant that they're normalizing by and + + + align:start position:0% +constant that they're normalizing by and +then we sum over every single Atomic + + align:start position:0% +then we sum over every single Atomic + + + align:start position:0% +then we sum over every single Atomic +transition in this neutral gas so first + + align:start position:0% +transition in this neutral gas so first + + + align:start position:0% +transition in this neutral gas so first +of all we want to sum over all of + + align:start position:0% +of all we want to sum over all of + + + align:start position:0% +of all we want to sum over all of +the atoms in + + align:start position:0% +the atoms in + + + align:start position:0% +the atoms in +state I here so for example there may be + + align:start position:0% +state I here so for example there may be + + + align:start position:0% +state I here so for example there may be +atoms which are partially ionized they + + align:start position:0% +atoms which are partially ionized they + + + align:start position:0% +atoms which are partially ionized they +lost one electron and and so then they + + align:start position:0% +lost one electron and and so then they + + + align:start position:0% +lost one electron and and so then they +have different uh refractive index here + + align:start position:0% +have different uh refractive index here + + + align:start position:0% +have different uh refractive index here +so all the atoms in a certain State I + + align:start position:0% +so all the atoms in a certain State I + + + align:start position:0% +so all the atoms in a certain State I +and then all of the transitions between + + align:start position:0% +and then all of the transitions between + + + align:start position:0% +and then all of the transitions between +that state I and some other + + align:start position:0% +that state I and some other + + + align:start position:0% +that state I and some other +state + + align:start position:0% +state + + + align:start position:0% +state +K and this is divided by the transition + + align:start position:0% +K and this is divided by the transition + + + align:start position:0% +K and this is divided by the transition +frequency which is one of these lines + + align:start position:0% +frequency which is one of these lines + + + align:start position:0% +frequency which is one of these lines +here by between I and K + + align:start position:0% +here by between I and K + + + align:start position:0% +here by between I and K +minus Omega squ here so in this case + + align:start position:0% +minus Omega squ here so in this case + + + align:start position:0% +minus Omega squ here so in this case +fi is the strength of of these + + align:start position:0% +fi is the strength of of these + + + align:start position:0% +fi is the strength of of these +transitions which determines How likely + + align:start position:0% +transitions which determines How likely + + + align:start position:0% +transitions which determines How likely +it is to happen and so how strongly it + + align:start position:0% +it is to happen and so how strongly it + + + align:start position:0% +it is to happen and so how strongly it +shows up and this is the frequency of + + align:start position:0% +shows up and this is the frequency of + + + align:start position:0% +shows up and this is the frequency of +one of these + + align:start position:0% + + + + align:start position:0% + +transitions I misspoke earli I spoke + + align:start position:0% +transitions I misspoke earli I spoke + + + align:start position:0% +transitions I misspoke earli I spoke +about this being through uh ionization + + align:start position:0% +about this being through uh ionization + + + align:start position:0% +about this being through uh ionization +it's just to do as excitation so it's to + + align:start position:0% +it's just to do as excitation so it's to + + + align:start position:0% +it's just to do as excitation so it's to +do with whether your atom is in like its + + align:start position:0% +do with whether your atom is in like its + + + align:start position:0% +do with whether your atom is in like its +ground state or some other state or + + align:start position:0% +ground state or some other state or + + + align:start position:0% +ground state or some other state or +something else like that now this + + align:start position:0% +something else like that now this + + + align:start position:0% +something else like that now this +formula is intensely complicated right + + align:start position:0% +formula is intensely complicated right + + + align:start position:0% +formula is intensely complicated right +and you can spend a very long time doing + + align:start position:0% +and you can spend a very long time doing + + + align:start position:0% +and you can spend a very long time doing +quantum mechanics calculations try and + + align:start position:0% +quantum mechanics calculations try and + + + align:start position:0% +quantum mechanics calculations try and +work out both of these two teres and of + + align:start position:0% +work out both of these two teres and of + + + align:start position:0% +work out both of these two teres and of +course as soon as you go to something + + align:start position:0% +course as soon as you go to something + + + align:start position:0% +course as soon as you go to something +above hydrogen becomes very complicated + + align:start position:0% +above hydrogen becomes very complicated + + + align:start position:0% +above hydrogen becomes very complicated +even for hydrogen it's pretty + + align:start position:0% +even for hydrogen it's pretty + + + align:start position:0% +even for hydrogen it's pretty +complicated but above hydrogen it's + + align:start position:0% +complicated but above hydrogen it's + + + align:start position:0% +complicated but above hydrogen it's +extremely complicated because there are + + align:start position:0% +extremely complicated because there are + + + align:start position:0% +extremely complicated because there are +multiple electrons interacting here so + + align:start position:0% +multiple electrons interacting here so + + + align:start position:0% +multiple electrons interacting here so +you don't actually stand a chance of + + align:start position:0% +you don't actually stand a chance of + + + align:start position:0% +you don't actually stand a chance of +solving this + + align:start position:0% +solving this + + + align:start position:0% +solving this +directly your best bet is the fact that + + align:start position:0% +directly your best bet is the fact that + + + align:start position:0% +directly your best bet is the fact that +if you look at some path of the spectrum + + align:start position:0% +if you look at some path of the spectrum + + + align:start position:0% +if you look at some path of the spectrum +or some part reflective index that's + + align:start position:0% +or some part reflective index that's + + + align:start position:0% +or some part reflective index that's +away from one of these lines so this is + + align:start position:0% +away from one of these lines so this is + + + align:start position:0% +away from one of these lines so this is +for + + align:start position:0% +for + + + align:start position:0% +for +Omega not equal + + align:start position:0% +Omega not equal + + + align:start position:0% +Omega not equal +to any of these transitions here there's + + align:start position:0% +to any of these transitions here there's + + + align:start position:0% +to any of these transitions here there's +a general formula that works pretty well + + align:start position:0% +a general formula that works pretty well + + + align:start position:0% +a general formula that works pretty well +which says the reflective index is just + + align:start position:0% +which says the reflective index is just + + + align:start position:0% +which says the reflective index is just +equal to 1+ 2 + + align:start position:0% +equal to 1+ 2 + + + align:start position:0% +equal to 1+ 2 +pi + + align:start position:0% +pi + + + align:start position:0% +pi +alpha n where this na here is still the + + align:start position:0% +alpha n where this na here is still the + + + align:start position:0% +alpha n where this na here is still the +number density of + + align:start position:0% + + + + align:start position:0% + +neutrals and this new Alpha is a + + align:start position:0% +neutrals and this new Alpha is a + + + align:start position:0% +neutrals and this new Alpha is a +quantity called the + + align:start position:0% + + + + align:start position:0% + +polarizability + + align:start position:0% + + + + align:start position:0% + +polariz which is easy to calculate and + + align:start position:0% +polariz which is easy to calculate and + + + align:start position:0% +polariz which is easy to calculate and +also very easy to measure so you can + + align:start position:0% +also very easy to measure so you can + + + align:start position:0% +also very easy to measure so you can +measure this for your different gases + + align:start position:0% +measure this for your different gases + + + align:start position:0% +measure this for your different gases +and so for example is little table of + + align:start position:0% +and so for example is little table of + + + align:start position:0% +and so for example is little table of +different gases if we have it for helium + + align:start position:0% +different gases if we have it for helium + + + align:start position:0% +different gases if we have it for helium +or hydrogen or argon + + align:start position:0% +or hydrogen or argon + + + align:start position:0% +or hydrogen or argon +here there 2 pi Alpha in unit + + align:start position:0% +here there 2 pi Alpha in unit + + + align:start position:0% +here there 2 pi Alpha in unit +me cubed the 2 pi is just some + + align:start position:0% +me cubed the 2 pi is just some + + + align:start position:0% +me cubed the 2 pi is just some +normalization constant that comes from + + align:start position:0% +normalization constant that comes from + + + align:start position:0% +normalization constant that comes from +somewhere else in the theory so you know + + align:start position:0% +somewhere else in the theory so you know + + + align:start position:0% +somewhere else in the theory so you know +we always quote it with the alpha I'm + + align:start position:0% +we always quote it with the alpha I'm + + + align:start position:0% +we always quote it with the alpha I'm +just going to quote you 2 pi Alpha here + + align:start position:0% +just going to quote you 2 pi Alpha here + + + align:start position:0% +just going to quote you 2 pi Alpha here +but this number is like 10us 30 a helium + + align:start position:0% +but this number is like 10us 30 a helium + + + align:start position:0% +but this number is like 10us 30 a helium +5 * 10us 30 + + align:start position:0% +5 * 10us 30 + + + align:start position:0% +5 * 10us 30 +hydrogen and 1 * 10us + + align:start position:0% +hydrogen and 1 * 10us + + + align:start position:0% +hydrogen and 1 * 10us +29 I wrote this as Aron because I missed + + align:start position:0% +29 I wrote this as Aron because I missed + + + align:start position:0% +29 I wrote this as Aron because I missed +the i in my notes it's actually air so + + align:start position:0% +the i in my notes it's actually air so + + + align:start position:0% +the i in my notes it's actually air so +there we go and and then just as a + + align:start position:0% +there we go and and then just as a + + + align:start position:0% +there we go and and then just as a +little calculation here you know Air at + + align:start position:0% +little calculation here you know Air at + + + align:start position:0% +little calculation here you know Air at +standard temperature and pressure the + + align:start position:0% +standard temperature and pressure the + + + align:start position:0% +standard temperature and pressure the +number density is round about 2.5 * 10 + + align:start position:0% +number density is round about 2.5 * 10 + + + align:start position:0% +number density is round about 2.5 * 10 +25 per met cubed and so therefore the + + align:start position:0% +25 per met cubed and so therefore the + + + align:start position:0% +25 per met cubed and so therefore the +refractive index of + + align:start position:0% +refractive index of + + + align:start position:0% +refractive index of +air is about 1 plus 2.5 * 10us 4 so once + + align:start position:0% +air is about 1 plus 2.5 * 10us 4 so once + + + align:start position:0% +air is about 1 plus 2.5 * 10us 4 so once +again the change in refractive + + align:start position:0% +again the change in refractive + + + align:start position:0% +again the change in refractive +index is very small compared to what for + + align:start position:0% +index is very small compared to what for + + + align:start position:0% +index is very small compared to what for +the neutrals it's on the same sort of + + align:start position:0% +the neutrals it's on the same sort of + + + align:start position:0% +the neutrals it's on the same sort of +order as the change of refractive index + + align:start position:0% +order as the change of refractive index + + + align:start position:0% +order as the change of refractive index +you get for a similar sort of plasma but + + align:start position:0% +you get for a similar sort of plasma but + + + align:start position:0% +you get for a similar sort of plasma but +crucially the refractive index is always + + align:start position:0% +crucially the refractive index is always + + + align:start position:0% +crucially the refractive index is always +greater than one for neutrals and is + + align:start position:0% +greater than one for neutrals and is + + + align:start position:0% +greater than one for neutrals and is +always less than one for a plasma this + + align:start position:0% +always less than one for a plasma this + + + align:start position:0% +always less than one for a plasma this +was our first hint how we're going to + + align:start position:0% +was our first hint how we're going to + + + align:start position:0% +was our first hint how we're going to +use two color interferometry here so + + align:start position:0% +use two color interferometry here so + + + align:start position:0% +use two color interferometry here so +let's have a look at how to use two + + align:start position:0% +let's have a look at how to use two + + + align:start position:0% +let's have a look at how to use two +color interferometry to determine both + + align:start position:0% +color interferometry to determine both + + + align:start position:0% +color interferometry to determine both +the number density of the neutrals and + + align:start position:0% +the number density of the neutrals and + + + align:start position:0% +the number density of the neutrals and +the number density of the electrons and + + align:start position:0% +the number density of the electrons and + + + align:start position:0% +the number density of the electrons and +you might come across this scenario + + align:start position:0% +you might come across this scenario + + + align:start position:0% +you might come across this scenario +quite a lot if you're doing low temp + + align:start position:0% +quite a lot if you're doing low temp + + + align:start position:0% +quite a lot if you're doing low temp +plasmas you always come across this + + align:start position:0% +plasmas you always come across this + + + align:start position:0% +plasmas you always come across this +scenario even if you're doing something + + align:start position:0% +scenario even if you're doing something + + + align:start position:0% +scenario even if you're doing something +in a toac maybe there's a region at the + + align:start position:0% +in a toac maybe there's a region at the + + + align:start position:0% +in a toac maybe there's a region at the +edge where there's a large number of + + align:start position:0% +edge where there's a large number of + + + align:start position:0% +edge where there's a large number of +neutrals and your beam has to go through + + align:start position:0% +neutrals and your beam has to go through + + + align:start position:0% +neutrals and your beam has to go through +that region at the edge and you you want + + align:start position:0% +that region at the edge and you you want + + + align:start position:0% +that region at the edge and you you want +to ignore it you just want to measure + + align:start position:0% +to ignore it you just want to measure + + + align:start position:0% +to ignore it you just want to measure +the core but you're still actually + + align:start position:0% +the core but you're still actually + + + align:start position:0% +the core but you're still actually +picking up a big phase shift on these + + align:start position:0% +picking up a big phase shift on these + + + align:start position:0% +picking up a big phase shift on these +neutrals at the edge so this is a big + + align:start position:0% +neutrals at the edge so this is a big + + + align:start position:0% +neutrals at the edge so this is a big +problem and this is a hard one to solve + + align:start position:0% +problem and this is a hard one to solve + + + align:start position:0% +problem and this is a hard one to solve +so let's have a look at + + align:start position:0% + + + + align:start position:0% + +this so + + align:start position:0% +this so + + + align:start position:0% +this so +remember that when we derived the phase + + align:start position:0% +remember that when we derived the phase + + + align:start position:0% +remember that when we derived the phase +shift Delta 5 I did it first of all just + + align:start position:0% +shift Delta 5 I did it first of all just + + + align:start position:0% +shift Delta 5 I did it first of all just +in terms of a generic refractive index + + align:start position:0% +in terms of a generic refractive index + + + align:start position:0% +in terms of a generic refractive index +specifying it to be u a plasma and that + + align:start position:0% +specifying it to be u a plasma and that + + + align:start position:0% +specifying it to be u a plasma and that +reflective index was just n minus + + align:start position:0% +reflective index was just n minus + + + align:start position:0% +reflective index was just n minus +one dl it's 2 pi Lambda at the front + + align:start position:0% +one dl it's 2 pi Lambda at the front + + + align:start position:0% +one dl it's 2 pi Lambda at the front +here so this is just affecting the + + align:start position:0% +here so this is just affecting the + + + align:start position:0% +here so this is just affecting the +change in the path length uh effective + + align:start position:0% +change in the path length uh effective + + + align:start position:0% +change in the path length uh effective +path length that the probing be sees + + align:start position:0% +path length that the probing be sees + + + align:start position:0% +path length that the probing be sees +okay and we also said that an a is + + align:start position:0% +okay and we also said that an a is + + + align:start position:0% +okay and we also said that an a is +greater than one and + + align:start position:0% + + + + align:start position:0% + +DNA D Lambda is equal to zero which is + + align:start position:0% +DNA D Lambda is equal to zero which is + + + align:start position:0% +DNA D Lambda is equal to zero which is +mathematically saying that in this + + align:start position:0% +mathematically saying that in this + + + align:start position:0% +mathematically saying that in this +polarizability model here we assume that + + align:start position:0% +polarizability model here we assume that + + + align:start position:0% +polarizability model here we assume that +it doesn't depend on wavelength because + + align:start position:0% +it doesn't depend on wavelength because + + + align:start position:0% +it doesn't depend on wavelength because +as long as we don't go too close to one + + align:start position:0% +as long as we don't go too close to one + + + align:start position:0% +as long as we don't go too close to one +of these transitions so the + + align:start position:0% +of these transitions so the + + + align:start position:0% +of these transitions so the +polarizability here the same as the + + align:start position:0% +polarizability here the same as the + + + align:start position:0% +polarizability here the same as the +polarizability here it's the same as the + + align:start position:0% +polarizability here it's the same as the + + + align:start position:0% +polarizability here it's the same as the +polarizability here okay so then we'll + + align:start position:0% +polarizability here okay so then we'll + + + align:start position:0% +polarizability here okay so then we'll +end up with a total Fringe shift on our + + align:start position:0% +end up with a total Fringe shift on our + + + align:start position:0% +end up with a total Fringe shift on our +ineter of minus 4.5 + + align:start position:0% +ineter of minus 4.5 + + + align:start position:0% +ineter of minus 4.5 +* 10 + + align:start position:0% +* 10 + + + align:start position:0% +* 10 +16 - 16 * Lambda the + + align:start position:0% +16 - 16 * Lambda the + + + align:start position:0% +16 - 16 * Lambda the +integral of the electron density that's + + align:start position:0% +integral of the electron density that's + + + align:start position:0% +integral of the electron density that's +the plasma component here and we will + + align:start position:0% +the plasma component here and we will + + + align:start position:0% +the plasma component here and we will +also have a term which is plus notice + + align:start position:0% +also have a term which is plus notice + + + align:start position:0% +also have a term which is plus notice +the difference in the sign here plus 2 + + align:start position:0% +the difference in the sign here plus 2 + + + align:start position:0% +the difference in the sign here plus 2 +pi Alpha upon + + align:start position:0% +pi Alpha upon + + + align:start position:0% +pi Alpha upon +Lambda integral of Na + + align:start position:0% +Lambda integral of Na + + + align:start position:0% +Lambda integral of Na +D so they will cause shift in Fringe in + + align:start position:0% +D so they will cause shift in Fringe in + + + align:start position:0% +D so they will cause shift in Fringe in +different directions so to a lower + + align:start position:0% +different directions so to a lower + + + align:start position:0% +different directions so to a lower +effective spatial or temporal frequency + + align:start position:0% +effective spatial or temporal frequency + + + align:start position:0% +effective spatial or temporal frequency +but they also have a different + + align:start position:0% +but they also have a different + + + align:start position:0% +but they also have a different +dependence + + align:start position:0% +dependence + + + align:start position:0% +dependence +on Lambda and this is key because again + + align:start position:0% +on Lambda and this is key because again + + + align:start position:0% +on Lambda and this is key because again +as we saw with the vibrations if we have + + align:start position:0% +as we saw with the vibrations if we have + + + align:start position:0% +as we saw with the vibrations if we have +different dependences on Lambda we can + + align:start position:0% +different dependences on Lambda we can + + + align:start position:0% +different dependences on Lambda we can +use a two colic technique to get around + + align:start position:0% +use a two colic technique to get around + + + align:start position:0% +use a two colic technique to get around +this so by + + align:start position:0% +this so by + + + align:start position:0% +this so by +plasma is + + align:start position:0% +plasma is + + + align:start position:0% +plasma is +big + + align:start position:0% +big + + + align:start position:0% +big +or large wavelengths + + align:start position:0% +or large wavelengths + + + align:start position:0% +or large wavelengths +and it's by neutral B shift neutrals is + + align:start position:0% +and it's by neutral B shift neutrals is + + + align:start position:0% +and it's by neutral B shift neutrals is +big or small + + align:start position:0% + + + + align:start position:0% + +wavs and again we've got two unknowns + + align:start position:0% +wavs and again we've got two unknowns + + + align:start position:0% +wavs and again we've got two unknowns +we've + + align:start position:0% +we've + + + align:start position:0% +we've +got the density of the electrons oh + + align:start position:0% +got the density of the electrons oh + + + align:start position:0% +got the density of the electrons oh +sorry and the density of the + + align:start position:0% + + + + align:start position:0% + +neutrals and if we have a two-color + + align:start position:0% +neutrals and if we have a two-color + + + align:start position:0% +neutrals and if we have a two-color +technique uh we have two equations and + + align:start position:0% +technique uh we have two equations and + + + align:start position:0% +technique uh we have two equations and +so we can solve all of that and I'm not + + align:start position:0% +so we can solve all of that and I'm not + + + align:start position:0% +so we can solve all of that and I'm not +going to write down the algebra now it's + + align:start position:0% +going to write down the algebra now it's + + + align:start position:0% +going to write down the algebra now it's +quite boring um and you can work out + + align:start position:0% +quite boring um and you can work out + + + align:start position:0% +quite boring um and you can work out +uniquely apparently what the electron + + align:start position:0% +uniquely apparently what the electron + + + align:start position:0% +uniquely apparently what the electron +and neutral densities are and I'll show + + align:start position:0% +and neutral densities are and I'll show + + + align:start position:0% +and neutral densities are and I'll show +you that this doesn't generally work in + + align:start position:0% +you that this doesn't generally work in + + + align:start position:0% +you that this doesn't generally work in +vors um so in + + align:start position:0% + + + + align:start position:0% + +practice rather than end up with + + align:start position:0% +practice rather than end up with + + + align:start position:0% +practice rather than end up with +negative predictions for your density of + + align:start position:0% +negative predictions for your density of + + + align:start position:0% +negative predictions for your density of +both the neutrals and the + + align:start position:0% +both the neutrals and the + + + align:start position:0% +both the neutrals and the +electrons and uh this tends to be as far + + align:start position:0% +electrons and uh this tends to be as far + + + align:start position:0% +electrons and uh this tends to be as far +as I can tell from reading the + + align:start position:0% +as I can tell from reading the + + + align:start position:0% +as I can tell from reading the +literature um but when we did this + + align:start position:0% +literature um but when we did this + + + align:start position:0% +literature um but when we did this +approximation of n is about 1 plus 2 pi + + align:start position:0% +approximation of n is about 1 plus 2 pi + + + align:start position:0% +approximation of n is about 1 plus 2 pi +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +here we have assumed that Alpha is + + align:start position:0% + + + + align:start position:0% + +constant but it doesn't have to be + + align:start position:0% +constant but it doesn't have to be + + + align:start position:0% +constant but it doesn't have to be +constant it could change with wavelength + + align:start position:0% +constant it could change with wavelength + + + align:start position:0% +constant it could change with wavelength +and if we're using two different + + align:start position:0% +and if we're using two different + + + align:start position:0% +and if we're using two different +wavelengths and there are two different + + align:start position:0% +wavelengths and there are two different + + + align:start position:0% +wavelengths and there are two different +values of alpha then that will cause + + align:start position:0% +values of alpha then that will cause + + + align:start position:0% +values of alpha then that will cause +chaos with your two equations two + + align:start position:0% +chaos with your two equations two + + + align:start position:0% +chaos with your two equations two +unknowns because Alpha is actually + + align:start position:0% +unknowns because Alpha is actually + + + align:start position:0% +unknowns because Alpha is actually +relatively hard to pin down in some + + align:start position:0% +relatively hard to pin down in some + + + align:start position:0% +relatively hard to pin down in some +sources you can very rarely find it the + + align:start position:0% +sources you can very rarely find it the + + + align:start position:0% +sources you can very rarely find it the +exact wavelength you're working on you + + align:start position:0% +exact wavelength you're working on you + + + align:start position:0% +exact wavelength you're working on you +may also have horrifically ended up + + align:start position:0% +may also have horrifically ended up + + + align:start position:0% +may also have horrifically ended up +using one of your wavelengths like here + + align:start position:0% +using one of your wavelengths like here + + + align:start position:0% +using one of your wavelengths like here +halfway up one of these resonances or + + align:start position:0% +halfway up one of these resonances or + + + align:start position:0% +halfway up one of these resonances or +even worse at the peak of one resonances + + align:start position:0% +even worse at the peak of one resonances + + + align:start position:0% +even worse at the peak of one resonances +and if you did that your whole model is + + align:start position:0% +and if you did that your whole model is + + + align:start position:0% +and if you did that your whole model is +completely off and I think this is what + + align:start position:0% +completely off and I think this is what + + + align:start position:0% +completely off and I think this is what +causes this and I'll show you some data + + align:start position:0% +causes this and I'll show you some data + + + align:start position:0% +causes this and I'll show you some data +that I took where we predicted negative + + align:start position:0% +that I took where we predicted negative + + + align:start position:0% +that I took where we predicted negative +densities I'll talk a little bit about + + align:start position:0% +densities I'll talk a little bit about + + + align:start position:0% +densities I'll talk a little bit about +that as well obviously negative + + align:start position:0% +that as well obviously negative + + + align:start position:0% +that as well obviously negative +densities are un phisical so uh we + + align:start position:0% +densities are un phisical so uh we + + + align:start position:0% +densities are un phisical so uh we +thought that that was probably wrong but + + align:start position:0% +thought that that was probably wrong but + + + align:start position:0% +thought that that was probably wrong but +we published it anyway because other + + align:start position:0% +we published it anyway because other + + + align:start position:0% +we published it anyway because other +people were doing the technique and not + + align:start position:0% +people were doing the technique and not + + + align:start position:0% +people were doing the technique and not +pointing out they had negative numbers + + align:start position:0% +pointing out they had negative numbers + + + align:start position:0% +pointing out they had negative numbers +and we thought it'd be nice to point out + + align:start position:0% +and we thought it'd be nice to point out + + + align:start position:0% +and we thought it'd be nice to point out +that we knew that it was wrong so okay + + align:start position:0% +that we knew that it was wrong so okay + + + align:start position:0% +that we knew that it was wrong so okay +so that was a quick round up of two + + align:start position:0% +so that was a quick round up of two + + + align:start position:0% +so that was a quick round up of two +color + + align:start position:0% +color + + + align:start position:0% +color +geometry and I have some quick slides + + align:start position:0% +geometry and I have some quick slides + + + align:start position:0% +geometry and I have some quick slides +after this showing some examples but + + align:start position:0% +after this showing some examples but + + + align:start position:0% +after this showing some examples but +I'll just pause here and see if there + + align:start position:0% +I'll just pause here and see if there + + + align:start position:0% +I'll just pause here and see if there +are any + + align:start position:0% +are any + + + align:start position:0% +are any +questions yes this technique work better + + align:start position:0% +questions yes this technique work better + + + align:start position:0% +questions yes this technique work better +for certain levels ofation like there is + + align:start position:0% +for certain levels ofation like there is + + + align:start position:0% +for certain levels ofation like there is +there a spectrum where it works better + + align:start position:0% +there a spectrum where it works better + + + align:start position:0% +there a spectrum where it works better +than others the question was does this + + align:start position:0% +than others the question was does this + + + align:start position:0% +than others the question was does this +sorry if you're using like a really + + align:start position:0% +sorry if you're using like a really + + + align:start position:0% +sorry if you're using like a really +deeply ionized plasma it's really not a + + align:start position:0% +deeply ionized plasma it's really not a + + + align:start position:0% +deeply ionized plasma it's really not a +good option as opposed to a + + align:start position:0% +good option as opposed to a + + + align:start position:0% +good option as opposed to a +more right really good question so the + + align:start position:0% +more right really good question so the + + + align:start position:0% +more right really good question so the +question was does this work better for + + align:start position:0% +question was does this work better for + + + align:start position:0% +question was does this work better for +different levels of ionization in a + + align:start position:0% +different levels of ionization in a + + + align:start position:0% +different levels of ionization in a +plasma so you might be thinking to + + align:start position:0% +plasma so you might be thinking to + + + align:start position:0% +plasma so you might be thinking to +yourself if I have a very very weakly + + align:start position:0% +yourself if I have a very very weakly + + + align:start position:0% +yourself if I have a very very weakly +ionized plasma um then it may be very + + align:start position:0% +ionized plasma um then it may be very + + + align:start position:0% +ionized plasma um then it may be very +hard to measure the electrons over the + + align:start position:0% +hard to measure the electrons over the + + + align:start position:0% +hard to measure the electrons over the +sort of overwhelming change in + + align:start position:0% +sort of overwhelming change in + + + align:start position:0% +sort of overwhelming change in +refractive index from the neutrals and + + align:start position:0% +refractive index from the neutrals and + + + align:start position:0% +refractive index from the neutrals and +that's true it's going to be hard but if + + align:start position:0% +that's true it's going to be hard but if + + + align:start position:0% +that's true it's going to be hard but if +you look at this equation here this is + + align:start position:0% +you look at this equation here this is + + + align:start position:0% +you look at this equation here this is +the thing you're measuring The Fringe + + align:start position:0% +the thing you're measuring The Fringe + + + align:start position:0% +the thing you're measuring The Fringe +shift you can choose your two + + align:start position:0% +shift you can choose your two + + + align:start position:0% +shift you can choose your two +wavelengths to optimize the wavelength + + align:start position:0% +wavelengths to optimize the wavelength + + + align:start position:0% +wavelengths to optimize the wavelength +sensitivity of one of them to the + + align:start position:0% +sensitivity of one of them to the + + + align:start position:0% +sensitivity of one of them to the +electrons and the sensitivity the other + + align:start position:0% +electrons and the sensitivity the other + + + align:start position:0% +electrons and the sensitivity the other +one to the neutrals so you're going to + + align:start position:0% +one to the neutrals so you're going to + + + align:start position:0% +one to the neutrals so you're going to +need to have some widely spaced + + align:start position:0% +need to have some widely spaced + + + align:start position:0% +need to have some widely spaced +wavelengths so if you try and do it with + + align:start position:0% +wavelengths so if you try and do it with + + + align:start position:0% +wavelengths so if you try and do it with +just like two different frequencies from + + align:start position:0% +just like two different frequencies from + + + align:start position:0% +just like two different frequencies from +the same l + + align:start position:0% +the same l + + + align:start position:0% +the same l +that's going to be really hard but if + + align:start position:0% +that's going to be really hard but if + + + align:start position:0% +that's going to be really hard but if +you have like a microwave into perometer + + align:start position:0% +you have like a microwave into perometer + + + align:start position:0% +you have like a microwave into perometer +and a Heeney green laser beam like they + + align:start position:0% +and a Heeney green laser beam like they + + + align:start position:0% +and a Heeney green laser beam like they +do on the toax for vibration + + align:start position:0% +do on the toax for vibration + + + align:start position:0% +do on the toax for vibration +stabilization that will work much better + + align:start position:0% +stabilization that will work much better + + + align:start position:0% +stabilization that will work much better +the difficulty there is then you have + + align:start position:0% +the difficulty there is then you have + + + align:start position:0% +the difficulty there is then you have +two completely different detection + + align:start position:0% +two completely different detection + + + align:start position:0% +two completely different detection +techniques and so it's not like easy to + + align:start position:0% +techniques and so it's not like easy to + + + align:start position:0% +techniques and so it's not like easy to +compare these two but that's what you + + align:start position:0% +compare these two but that's what you + + + align:start position:0% +compare these two but that's what you +probably want to do if you're dealing + + align:start position:0% +probably want to do if you're dealing + + + align:start position:0% +probably want to do if you're dealing +with like 1% ionization or something + + align:start position:0% +with like 1% ionization or something + + + align:start position:0% +with like 1% ionization or something +like that you might have to do this + + align:start position:0% +like that you might have to do this + + + align:start position:0% +like that you might have to do this +technique yeah okay were there other + + align:start position:0% +technique yeah okay were there other + + + align:start position:0% +technique yeah okay were there other +questions anything online + + align:start position:0% + + + + align:start position:0% + +what physically is the polarizability is + + align:start position:0% +what physically is the polarizability is + + + align:start position:0% +what physically is the polarizability is +that like the electric polarizability + + align:start position:0% +that like the electric polarizability + + + align:start position:0% +that like the electric polarizability +medium yeah the question was what + + align:start position:0% +medium yeah the question was what + + + align:start position:0% +medium yeah the question was what +physically is the polarizability yeah + + align:start position:0% +physically is the polarizability yeah + + + align:start position:0% +physically is the polarizability yeah +this is this polarizability is very + + align:start position:0% +this is this polarizability is very + + + align:start position:0% +this is this polarizability is very +strongly related to how the electron + + align:start position:0% +strongly related to how the electron + + + align:start position:0% +strongly related to how the electron +wave functions are distorted by the + + align:start position:0% +wave functions are distorted by the + + + align:start position:0% +wave functions are distorted by the +electric field of the electromagnetic + + align:start position:0% +electric field of the electromagnetic + + + align:start position:0% +electric field of the electromagnetic +wave okay yes which is why when you get + + align:start position:0% +wave okay yes which is why when you get + + + align:start position:0% +wave okay yes which is why when you get +close to a transition and the uh the + + align:start position:0% +close to a transition and the uh the + + + align:start position:0% +close to a transition and the uh the +frequency of the wave is now resonant + + align:start position:0% +frequency of the wave is now resonant + + + align:start position:0% +frequency of the wave is now resonant +with some Atomic transition this + + align:start position:0% +with some Atomic transition this + + + align:start position:0% +with some Atomic transition this +polarizability changes dramatically + + align:start position:0% +polarizability changes dramatically + + + align:start position:0% +polarizability changes dramatically +because oppos just going through the + + align:start position:0% +because oppos just going through the + + + align:start position:0% +because oppos just going through the +medium electromagnetic wav is absor + + align:start position:0% +medium electromagnetic wav is absor + + + align:start position:0% +medium electromagnetic wav is absor +ABB I'm saying it in a very classical + + align:start position:0% +ABB I'm saying it in a very classical + + + align:start position:0% +ABB I'm saying it in a very classical +way but of course you need to start + + align:start position:0% +way but of course you need to start + + + align:start position:0% +way but of course you need to start +doing Quantum if you want to have like + + align:start position:0% +doing Quantum if you want to have like + + + align:start position:0% +doing Quantum if you want to have like +absorption the wave field is inducing a + + align:start position:0% +absorption the wave field is inducing a + + + align:start position:0% +absorption the wave field is inducing a +small dipole moment yeah absolutely the + + align:start position:0% +small dipole moment yeah absolutely the + + + align:start position:0% +small dipole moment yeah absolutely the +wave is inducing a dipole moment and + + align:start position:0% +wave is inducing a dipole moment and + + + align:start position:0% +wave is inducing a dipole moment and +that is slowing down the wave slowing + + align:start position:0% +that is slowing down the wave slowing + + + align:start position:0% +that is slowing down the wave slowing +down the phase of the wave in a plasma + + align:start position:0% +down the phase of the wave in a plasma + + + align:start position:0% +down the phase of the wave in a plasma +remember it always speeds up the phase + + align:start position:0% +remember it always speeds up the phase + + + align:start position:0% +remember it always speeds up the phase +of the wave yeah okay any other + + align:start position:0% + + + + align:start position:0% + +questions Maybe I should have saved all + + align:start position:0% +questions Maybe I should have saved all + + + align:start position:0% +questions Maybe I should have saved all +my pictures the end + + align:start position:0% + + + + align:start position:0% + +avoided can you see this + + align:start position:0% + + + + align:start position:0% + +online okay perfect okay and it's + + align:start position:0% +online okay perfect okay and it's + + + align:start position:0% +online okay perfect okay and it's +showing up slowly + + align:start position:0% +showing up slowly + + + align:start position:0% +showing up slowly +here so this was a set of experiments we + + align:start position:0% +here so this was a set of experiments we + + + align:start position:0% +here so this was a set of experiments we +did with a very sexily named but boring + + align:start position:0% +did with a very sexily named but boring + + + align:start position:0% +did with a very sexily named but boring +device called a plasma gun which is + + align:start position:0% +device called a plasma gun which is + + + align:start position:0% +device called a plasma gun which is +actually just a bit of coax cable where + + align:start position:0% +actually just a bit of coax cable where + + + align:start position:0% +actually just a bit of coax cable where +you've chopped off the end of it and you + + align:start position:0% +you've chopped off the end of it and you + + + align:start position:0% +you've chopped off the end of it and you +pulse it with some current and the + + align:start position:0% +pulse it with some current and the + + + align:start position:0% +pulse it with some current and the +current flows up the inner conductor + + align:start position:0% +current flows up the inner conductor + + + align:start position:0% +current flows up the inner conductor +across the chopped off plastic insulator + + align:start position:0% +across the chopped off plastic insulator + + + align:start position:0% +across the chopped off plastic insulator +and back down through the outer + + align:start position:0% +and back down through the outer + + + align:start position:0% +and back down through the outer +conductor and as it flows across here it + + align:start position:0% +conductor and as it flows across here it + + + align:start position:0% +conductor and as it flows across here it +sends plumes of plasma out and they're + + align:start position:0% +sends plumes of plasma out and they're + + + align:start position:0% +sends plumes of plasma out and they're +moving you know 10 kmers a second but + + align:start position:0% +moving you know 10 kmers a second but + + + align:start position:0% +moving you know 10 kmers a second but +this only works in vacuum so it's not a + + align:start position:0% +this only works in vacuum so it's not a + + + align:start position:0% +this only works in vacuum so it's not a +very good gun um anyway this was a fun + + align:start position:0% +very good gun um anyway this was a fun + + + align:start position:0% +very good gun um anyway this was a fun +object to study because there was a grad + + align:start position:0% +object to study because there was a grad + + + align:start position:0% +object to study because there was a grad +student using it for he thesis and we + + align:start position:0% +student using it for he thesis and we + + + align:start position:0% +student using it for he thesis and we +put it on our experiment and we did two + + align:start position:0% +put it on our experiment and we did two + + + align:start position:0% +put it on our experiment and we did two +color interferometry and these + + align:start position:0% +color interferometry and these + + + align:start position:0% +color interferometry and these +interferograms were made using uh an ND + + align:start position:0% +interferograms were made using uh an ND + + + align:start position:0% +interferograms were made using uh an ND +in the Adian yag we use the second + + align:start position:0% +in the Adian yag we use the second + + + align:start position:0% +in the Adian yag we use the second +harmonic at 532 nanom which shows up as + + align:start position:0% +harmonic at 532 nanom which shows up as + + + align:start position:0% +harmonic at 532 nanom which shows up as +green here to do one of the measurements + + align:start position:0% +green here to do one of the measurements + + + align:start position:0% +green here to do one of the measurements +and simultaneously along the same line + + align:start position:0% +and simultaneously along the same line + + + align:start position:0% +and simultaneously along the same line +of sight through the same bit of plasma + + align:start position:0% +of sight through the same bit of plasma + + + align:start position:0% +of sight through the same bit of plasma +we use the third harmonic which is 355 + + align:start position:0% +we use the third harmonic which is 355 + + + align:start position:0% +we use the third harmonic which is 355 +nanometers so that's in the ultraviolet + + align:start position:0% +nanometers so that's in the ultraviolet + + + align:start position:0% +nanometers so that's in the ultraviolet +you can't see it by eye um you might be + + align:start position:0% +you can't see it by eye um you might be + + + align:start position:0% +you can't see it by eye um you might be +asking why does it show up as orange + + align:start position:0% +asking why does it show up as orange + + + align:start position:0% +asking why does it show up as orange +this is when you remove the ultraviolet + + align:start position:0% +this is when you remove the ultraviolet + + + align:start position:0% +this is when you remove the ultraviolet +filter from your offthe shelf and a DSLR + + align:start position:0% +filter from your offthe shelf and a DSLR + + + align:start position:0% +filter from your offthe shelf and a DSLR +camera uh the pixels get confused and + + align:start position:0% +camera uh the pixels get confused and + + + align:start position:0% +camera uh the pixels get confused and +think that this is orange obviously it + + align:start position:0% +think that this is orange obviously it + + + align:start position:0% +think that this is orange obviously it +can't it can see ultraviolet but what + + align:start position:0% +can't it can see ultraviolet but what + + + align:start position:0% +can't it can see ultraviolet but what +would we render it as on the screen so + + align:start position:0% +would we render it as on the screen so + + + align:start position:0% +would we render it as on the screen so +anyway um so this is uh 355 and these + + align:start position:0% +anyway um so this is uh 355 and these + + + align:start position:0% +anyway um so this is uh 355 and these +are the fringes before the plasma was + + align:start position:0% +are the fringes before the plasma was + + + align:start position:0% +are the fringes before the plasma was +there and these are the fringes after + + align:start position:0% +there and these are the fringes after + + + align:start position:0% +there and these are the fringes after +the plasma was there and you can see The + + align:start position:0% +the plasma was there and you can see The + + + align:start position:0% +the plasma was there and you can see The +Fringe shift is very small there just + + align:start position:0% +Fringe shift is very small there just + + + align:start position:0% +Fringe shift is very small there just +tiny little shifts here and here um so + + align:start position:0% +tiny little shifts here and here um so + + + align:start position:0% +tiny little shifts here and here um so +this wasn't a very uh High plasma + + align:start position:0% +this wasn't a very uh High plasma + + + align:start position:0% +this wasn't a very uh High plasma +density but what we were able to do is + + align:start position:0% +density but what we were able to do is + + + align:start position:0% +density but what we were able to do is +to infer the phase shift uh for these + + align:start position:0% +to infer the phase shift uh for these + + + align:start position:0% +to infer the phase shift uh for these +two interferograms like this and then + + align:start position:0% +two interferograms like this and then + + + align:start position:0% +two interferograms like this and then +we combined these two together using uh + + align:start position:0% +we combined these two together using uh + + + align:start position:0% +we combined these two together using uh +the simultaneous equations we also did + + align:start position:0% +the simultaneous equations we also did + + + align:start position:0% +the simultaneous equations we also did +uh an arble inversion which I'll talk + + align:start position:0% +uh an arble inversion which I'll talk + + + align:start position:0% +uh an arble inversion which I'll talk +about in the next lecture and we got out + + align:start position:0% +about in the next lecture and we got out + + + align:start position:0% +about in the next lecture and we got out +the electron density and this looks + + align:start position:0% +the electron density and this looks + + + align:start position:0% +the electron density and this looks +quite reasonable we get up to about + + align:start position:0% +quite reasonable we get up to about + + + align:start position:0% +quite reasonable we get up to about +tally 18 here and it falls off nicely in + + align:start position:0% +tally 18 here and it falls off nicely in + + + align:start position:0% +tally 18 here and it falls off nicely in +various directions but we also got a + + align:start position:0% +various directions but we also got a + + + align:start position:0% +various directions but we also got a +prediction of the um neutral density + + align:start position:0% +prediction of the um neutral density + + + align:start position:0% +prediction of the um neutral density +here and these red regions are fine + + align:start position:0% +here and these red regions are fine + + + align:start position:0% +here and these red regions are fine +these are positive numbers but in right + + align:start position:0% +these are positive numbers but in right + + + align:start position:0% +these are positive numbers but in right +in the middle here there's a big + + align:start position:0% +in the middle here there's a big + + + align:start position:0% +in the middle here there's a big +negative number in fact it's so negative + + align:start position:0% +negative number in fact it's so negative + + + align:start position:0% +negative number in fact it's so negative +we're predicting like many more absences + + align:start position:0% +we're predicting like many more absences + + + align:start position:0% +we're predicting like many more absences +of neutrals than we had electrons it's + + align:start position:0% +of neutrals than we had electrons it's + + + align:start position:0% +of neutrals than we had electrons it's +like clearly completely nonsense and so + + align:start position:0% +like clearly completely nonsense and so + + + align:start position:0% +like clearly completely nonsense and so +we went back to some of the textbooks + + align:start position:0% +we went back to some of the textbooks + + + align:start position:0% +we went back to some of the textbooks +that explain this technique for + + align:start position:0% +that explain this technique for + + + align:start position:0% +that explain this technique for +measuring neutrals and we found that the + + align:start position:0% +measuring neutrals and we found that the + + + align:start position:0% +measuring neutrals and we found that the +example data they were showing also had + + align:start position:0% +example data they were showing also had + + + align:start position:0% +example data they were showing also had +negative numbers in it's just they + + align:start position:0% +negative numbers in it's just they + + + align:start position:0% +negative numbers in it's just they +didn't bother to mention that this was a + + align:start position:0% +didn't bother to mention that this was a + + + align:start position:0% +didn't bother to mention that this was a +huge problem we think this is a huge + + align:start position:0% +huge problem we think this is a huge + + + align:start position:0% +huge problem we think this is a huge +problem um so I'm a little bit baffled + + align:start position:0% +problem um so I'm a little bit baffled + + + align:start position:0% +problem um so I'm a little bit baffled +by the fact that people people will in a + + align:start position:0% +by the fact that people people will in a + + + align:start position:0% +by the fact that people people will in a +textbook say that this technique can be + + align:start position:0% +textbook say that this technique can be + + + align:start position:0% +textbook say that this technique can be +used to measure neutrals but in reality + + align:start position:0% +used to measure neutrals but in reality + + + align:start position:0% +used to measure neutrals but in reality +it seems to be really really tricky to + + align:start position:0% +it seems to be really really tricky to + + + align:start position:0% +it seems to be really really tricky to +do it properly and I think the problem + + align:start position:0% +do it properly and I think the problem + + + align:start position:0% +do it properly and I think the problem +is the quality of the polarizability + + align:start position:0% +is the quality of the polarizability + + + align:start position:0% +is the quality of the polarizability +data that we have so we were trying to + + align:start position:0% +data that we have so we were trying to + + + align:start position:0% +data that we have so we were trying to +use the polarizability data assuming it + + align:start position:0% +use the polarizability data assuming it + + + align:start position:0% +use the polarizability data assuming it +worked at 532 and 355 nanometers but it + + align:start position:0% +worked at 532 and 355 nanometers but it + + + align:start position:0% +worked at 532 and 355 nanometers but it +was derived in the lab by some group you + + align:start position:0% +was derived in the lab by some group you + + + align:start position:0% +was derived in the lab by some group you +know in the 80s who published their + + align:start position:0% +know in the 80s who published their + + + align:start position:0% +know in the 80s who published their +paper on it and they did it like a 10.6 + + align:start position:0% +paper on it and they did it like a 10.6 + + + align:start position:0% +paper on it and they did it like a 10.6 +microns in the infrared so there's no + + align:start position:0% +microns in the infrared so there's no + + + align:start position:0% +microns in the infrared so there's no +really good reason to believe the + + align:start position:0% +really good reason to believe the + + + align:start position:0% +really good reason to believe the +polarizability is the same but it's + + align:start position:0% +polarizability is the same but it's + + + align:start position:0% +polarizability is the same but it's +really hard to get hold of this data in + + align:start position:0% +really hard to get hold of this data in + + + align:start position:0% +really hard to get hold of this data in +a consistent fashion so um if you're + + align:start position:0% +a consistent fashion so um if you're + + + align:start position:0% +a consistent fashion so um if you're +going to try and use this technique I + + align:start position:0% +going to try and use this technique I + + + align:start position:0% +going to try and use this technique I +think you should be very skeptical about + + align:start position:0% +think you should be very skeptical about + + + align:start position:0% +think you should be very skeptical about +the results especially if you start + + align:start position:0% +the results especially if you start + + + align:start position:0% +the results especially if you start +seeing negative numbers Okay so we've + + align:start position:0% +seeing negative numbers Okay so we've + + + align:start position:0% +seeing negative numbers Okay so we've +only got a couple more minutes I'll just + + align:start position:0% +only got a couple more minutes I'll just + + + align:start position:0% +only got a couple more minutes I'll just +take any questions on this and then + + align:start position:0% +take any questions on this and then + + + align:start position:0% +take any questions on this and then +we'll do other version in the next + + align:start position:0% +we'll do other version in the next + + + align:start position:0% +we'll do other version in the next +lecture but any questions yes how + + align:start position:0% + + + + align:start position:0% + +do you could use interferometry to + + align:start position:0% +do you could use interferometry to + + + align:start position:0% +do you could use interferometry to +measure the + + align:start position:0% +measure the + + + align:start position:0% +measure the +polarizability in the absence of any + + align:start position:0% +polarizability in the absence of any + + + align:start position:0% +polarizability in the absence of any +electrons right then you'd know exactly + + align:start position:0% +electrons right then you'd know exactly + + + align:start position:0% +electrons right then you'd know exactly +what you were measuring so if you were + + align:start position:0% +what you were measuring so if you were + + + align:start position:0% +what you were measuring so if you were +able to puff some gas in you need some + + align:start position:0% +able to puff some gas in you need some + + + align:start position:0% +able to puff some gas in you need some +measurement of the number density as + + align:start position:0% +measurement of the number density as + + + align:start position:0% +measurement of the number density as +well so that's but you know can imagine + + align:start position:0% +well so that's but you know can imagine + + + align:start position:0% +well so that's but you know can imagine +um if you've got a gas cell at a certain + + align:start position:0% +um if you've got a gas cell at a certain + + + align:start position:0% +um if you've got a gas cell at a certain +pressure and it's at room temperature + + align:start position:0% +pressure and it's at room temperature + + + align:start position:0% +pressure and it's at room temperature +then you from the ideal gas law you know + + align:start position:0% +then you from the ideal gas law you know + + + align:start position:0% +then you from the ideal gas law you know +the number density inside that gas cell + + align:start position:0% +the number density inside that gas cell + + + align:start position:0% +the number density inside that gas cell +and you know the size of the volume and + + align:start position:0% +and you know the size of the volume and + + + align:start position:0% +and you know the size of the volume and +you could do a perometry on that volume + + align:start position:0% +you could do a perometry on that volume + + + align:start position:0% +you could do a perometry on that volume +for example and that would give you a + + align:start position:0% +for example and that would give you a + + + align:start position:0% +for example and that would give you a +measurement of the phas shift and then + + align:start position:0% +measurement of the phas shift and then + + + align:start position:0% +measurement of the phas shift and then +you could back out what the polarizer + + align:start position:0% +you could back out what the polarizer + + + align:start position:0% +you could back out what the polarizer +ability must be maybe we should have + + align:start position:0% +ability must be maybe we should have + + + align:start position:0% +ability must be maybe we should have +done that here but we didn't so yeah + + align:start position:0% +done that here but we didn't so yeah + + + align:start position:0% +done that here but we didn't so yeah +it's just like an additional calibration + + align:start position:0% +it's just like an additional calibration + + + align:start position:0% +it's just like an additional calibration +step yes yes exactly so I think it's a + + align:start position:0% +step yes yes exactly so I think it's a + + + align:start position:0% +step yes yes exactly so I think it's a +doable Cali it's just quite hard so + + align:start position:0% +doable Cali it's just quite hard so + + + align:start position:0% +doable Cali it's just quite hard so +whereas for the electron density it's + + align:start position:0% +whereas for the electron density it's + + + align:start position:0% +whereas for the electron density it's +like that is all in terms of fundamental + + align:start position:0% +like that is all in terms of fundamental + + + align:start position:0% +like that is all in terms of fundamental +parameters like the electron charge and + + align:start position:0% +parameters like the electron charge and + + + align:start position:0% +parameters like the electron charge and +electron mass and you're like okay we + + align:start position:0% +electron mass and you're like okay we + + + align:start position:0% +electron mass and you're like okay we +know what those are so then when you're + + align:start position:0% +know what those are so then when you're + + + align:start position:0% +know what those are so then when you're +applying those formulas you have + + align:start position:0% +applying those formulas you have + + + align:start position:0% +applying those formulas you have +absolute confidence when you measure the + + align:start position:0% +absolute confidence when you measure the + + + align:start position:0% +absolute confidence when you measure the +phase change what the electron density + + align:start position:0% +phase change what the electron density + + + align:start position:0% +phase change what the electron density +is just for this the theory is a little + + align:start position:0% +is just for this the theory is a little + + + align:start position:0% +is just for this the theory is a little +bit more W yeah other questions yeah you + + align:start position:0% +bit more W yeah other questions yeah you + + + align:start position:0% +bit more W yeah other questions yeah you +good data of individual species and then + + align:start position:0% +good data of individual species and then + + + align:start position:0% +good data of individual species and then +you know you have a certain ratio in + + align:start position:0% +you know you have a certain ratio in + + + align:start position:0% +you know you have a certain ratio in +your plasma um um is is there any reason + + align:start position:0% +your plasma um um is is there any reason + + + align:start position:0% +your plasma um um is is there any reason +to think that you could just do an + + align:start position:0% +to think that you could just do an + + + align:start position:0% +to think that you could just do an +average oh if you think beforehand you + + align:start position:0% +average oh if you think beforehand you + + + align:start position:0% +average oh if you think beforehand you +somehow know for some reason the number + + align:start position:0% +somehow know for some reason the number + + + align:start position:0% +somehow know for some reason the number +of number of the electron density and + + align:start position:0% +of number of the electron density and + + + align:start position:0% +of number of the electron density and +the neutral density or oh sorry like two + + align:start position:0% +the neutral density or oh sorry like two + + + align:start position:0% +the neutral density or oh sorry like two +different neutral species yes and you + + align:start position:0% +different neutral species yes and you + + + align:start position:0% +different neutral species yes and you +have good oh we didn't even get into + + align:start position:0% +have good oh we didn't even get into + + + align:start position:0% +have good oh we didn't even get into +that that's a nightmare because then + + align:start position:0% +that that's a nightmare because then + + + align:start position:0% +that that's a nightmare because then +you'll have two different polariz + + align:start position:0% +you'll have two different polariz + + + align:start position:0% +you'll have two different polariz +abilities and even more transitions that + + align:start position:0% +abilities and even more transitions that + + + align:start position:0% +abilities and even more transitions that +you're trying to miss okay right so we + + align:start position:0% +you're trying to miss okay right so we + + + align:start position:0% +you're trying to miss okay right so we +already like oh god let's stay well away + + align:start position:0% +already like oh god let's stay well away + + + align:start position:0% +already like oh god let's stay well away +from any of these transitions but if you + + align:start position:0% +from any of these transitions but if you + + + align:start position:0% +from any of these transitions but if you +have two species you'll have even harder + + align:start position:0% +have two species you'll have even harder + + + align:start position:0% +have two species you'll have even harder +find your region with no transition so + + align:start position:0% +find your region with no transition so + + + align:start position:0% +find your region with no transition so +it'll be very hard to find a source + + align:start position:0% +it'll be very hard to find a source + + + align:start position:0% +it'll be very hard to find a source +yeah any questions + + align:start position:0% + + + + align:start position:0% + +online all right thank you very much + + align:start position:0% +online all right thank you very much + + + align:start position:0% +online all right thank you very much +everyone see you on Thursday \ No newline at end of file diff --git a/uGGTX2ypzKI.txt b/uGGTX2ypzKI.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d764c363099519798f5be794560fcc9a1b0a98f --- /dev/null +++ b/uGGTX2ypzKI.txt @@ -0,0 +1,627 @@ +align:start position:0% + +we end this lecture sequence by stepping + + align:start position:0% +we end this lecture sequence by stepping + + + align:start position:0% +we end this lecture sequence by stepping +back to discuss what probability theory + + align:start position:0% +back to discuss what probability theory + + + align:start position:0% +back to discuss what probability theory +really is and what exactly is the + + align:start position:0% +really is and what exactly is the + + + align:start position:0% +really is and what exactly is the +meaning of the word probability in the + + align:start position:0% +meaning of the word probability in the + + + align:start position:0% +meaning of the word probability in the +most narrow view probability theory is + + align:start position:0% +most narrow view probability theory is + + + align:start position:0% +most narrow view probability theory is +just a branch of mathematics we start + + align:start position:0% +just a branch of mathematics we start + + + align:start position:0% +just a branch of mathematics we start +with some axioms we consider models that + + align:start position:0% +with some axioms we consider models that + + + align:start position:0% +with some axioms we consider models that +satisfy these axioms and we establish + + align:start position:0% +satisfy these axioms and we establish + + + align:start position:0% +satisfy these axioms and we establish +some consequences which are the theorems + + align:start position:0% +some consequences which are the theorems + + + align:start position:0% +some consequences which are the theorems +of this theory you could do all that + + align:start position:0% +of this theory you could do all that + + + align:start position:0% +of this theory you could do all that +without ever asking the question of what + + align:start position:0% +without ever asking the question of what + + + align:start position:0% +without ever asking the question of what +the world probability really means yet + + align:start position:0% +the world probability really means yet + + + align:start position:0% +the world probability really means yet +one of the theorems of probability + + align:start position:0% +one of the theorems of probability + + + align:start position:0% +one of the theorems of probability +theory that we will see later in this + + align:start position:0% +theory that we will see later in this + + + align:start position:0% +theory that we will see later in this +class is that probabilities can be + + align:start position:0% +class is that probabilities can be + + + align:start position:0% +class is that probabilities can be +interpreted as frequencies very loosely + + align:start position:0% +interpreted as frequencies very loosely + + + align:start position:0% +interpreted as frequencies very loosely +speaking if I have a fair coin and I + + align:start position:0% +speaking if I have a fair coin and I + + + align:start position:0% +speaking if I have a fair coin and I +toss it infinitely many times then the + + align:start position:0% +toss it infinitely many times then the + + + align:start position:0% +toss it infinitely many times then the +fraction of heads that I will observe + + align:start position:0% +fraction of heads that I will observe + + + align:start position:0% +fraction of heads that I will observe +will be 1/2 in this sense the + + align:start position:0% +will be 1/2 in this sense the + + + align:start position:0% +will be 1/2 in this sense the +probability of an event a can be + + align:start position:0% +probability of an event a can be + + + align:start position:0% +probability of an event a can be +interpreted as the frequency with which + + align:start position:0% +interpreted as the frequency with which + + + align:start position:0% +interpreted as the frequency with which +event a will occur in an infinite number + + align:start position:0% +event a will occur in an infinite number + + + align:start position:0% +event a will occur in an infinite number +of repetitions of the experiment but is + + align:start position:0% +of repetitions of the experiment but is + + + align:start position:0% +of repetitions of the experiment but is +this all there is if we're dealing with + + align:start position:0% +this all there is if we're dealing with + + + align:start position:0% +this all there is if we're dealing with +coin tosses it makes sense to think of + + align:start position:0% +coin tosses it makes sense to think of + + + align:start position:0% +coin tosses it makes sense to think of +probabilities as frequencies but + + align:start position:0% +probabilities as frequencies but + + + align:start position:0% +probabilities as frequencies but +consider a statement such as the current + + align:start position:0% +consider a statement such as the current + + + align:start position:0% +consider a statement such as the current +president of my country will be + + align:start position:0% +president of my country will be + + + align:start position:0% +president of my country will be +reelected in the next election with + + align:start position:0% +reelected in the next election with + + + align:start position:0% +reelected in the next election with +probability 0.7 it is hard to think of + + align:start position:0% +probability 0.7 it is hard to think of + + + align:start position:0% +probability 0.7 it is hard to think of +this number 0.7 as a frequency it does + + align:start position:0% +this number 0.7 as a frequency it does + + + align:start position:0% +this number 0.7 as a frequency it does +not make sense to think of infinitely + + align:start position:0% +not make sense to think of infinitely + + + align:start position:0% +not make sense to think of infinitely +many repetitions of the next election + + align:start position:0% +many repetitions of the next election + + + align:start position:0% +many repetitions of the next election +in cases like this and in many others it + + align:start position:0% +in cases like this and in many others it + + + align:start position:0% +in cases like this and in many others it +is better to think of probabilities as + + align:start position:0% +is better to think of probabilities as + + + align:start position:0% +is better to think of probabilities as +just some way of describing our beliefs + + align:start position:0% +just some way of describing our beliefs + + + align:start position:0% +just some way of describing our beliefs +and if you're a betting person + + align:start position:0% +and if you're a betting person + + + align:start position:0% +and if you're a betting person +probabilities can be thought of as some + + align:start position:0% +probabilities can be thought of as some + + + align:start position:0% +probabilities can be thought of as some +numerical guidance into what kinds of + + align:start position:0% +numerical guidance into what kinds of + + + align:start position:0% +numerical guidance into what kinds of +bets you might be willing to make but + + align:start position:0% +bets you might be willing to make but + + + align:start position:0% +bets you might be willing to make but +now if we think of probabilities as + + align:start position:0% +now if we think of probabilities as + + + align:start position:0% +now if we think of probabilities as +beliefs you can run into the argument + + align:start position:0% +beliefs you can run into the argument + + + align:start position:0% +beliefs you can run into the argument +that well beliefs are subjective isn't + + align:start position:0% +that well beliefs are subjective isn't + + + align:start position:0% +that well beliefs are subjective isn't +probability theory supposed to be an + + align:start position:0% +probability theory supposed to be an + + + align:start position:0% +probability theory supposed to be an +objective part of math and science is + + align:start position:0% +objective part of math and science is + + + align:start position:0% +objective part of math and science is +probability theory Justin + + align:start position:0% +probability theory Justin + + + align:start position:0% +probability theory Justin +exercising subjectivity well not quite + + align:start position:0% +exercising subjectivity well not quite + + + align:start position:0% +exercising subjectivity well not quite +there is more into it probability at the + + align:start position:0% +there is more into it probability at the + + + align:start position:0% +there is more into it probability at the +minimum gives us some rules for thinking + + align:start position:0% +minimum gives us some rules for thinking + + + align:start position:0% +minimum gives us some rules for thinking +systematically about uncertain + + align:start position:0% +systematically about uncertain + + + align:start position:0% +systematically about uncertain +situations and if it happens that our + + align:start position:0% +situations and if it happens that our + + + align:start position:0% +situations and if it happens that our +probability model our subjective beliefs + + align:start position:0% +probability model our subjective beliefs + + + align:start position:0% +probability model our subjective beliefs +have some relation with the real world + + align:start position:0% +have some relation with the real world + + + align:start position:0% +have some relation with the real world +then probability theory can be a very + + align:start position:0% +then probability theory can be a very + + + align:start position:0% +then probability theory can be a very +useful tool for making predictions and + + align:start position:0% +useful tool for making predictions and + + + align:start position:0% +useful tool for making predictions and +decisions that apply to the real world + + align:start position:0% +decisions that apply to the real world + + + align:start position:0% +decisions that apply to the real world +now whether your predictions and + + align:start position:0% +now whether your predictions and + + + align:start position:0% +now whether your predictions and +decisions will be any good will depend + + align:start position:0% +decisions will be any good will depend + + + align:start position:0% +decisions will be any good will depend +on whether you have chosen a good model + + align:start position:0% +on whether you have chosen a good model + + + align:start position:0% +on whether you have chosen a good model +have you chosen a model that provides a + + align:start position:0% +have you chosen a model that provides a + + + align:start position:0% +have you chosen a model that provides a +good enough representation of the real + + align:start position:0% +good enough representation of the real + + + align:start position:0% +good enough representation of the real +world how do you make sure that this is + + align:start position:0% +world how do you make sure that this is + + + align:start position:0% +world how do you make sure that this is +the case there is a whole field the + + align:start position:0% +the case there is a whole field the + + + align:start position:0% +the case there is a whole field the +field of Statistics whose purpose is to + + align:start position:0% +field of Statistics whose purpose is to + + + align:start position:0% +field of Statistics whose purpose is to +complement probability theory by using + + align:start position:0% +complement probability theory by using + + + align:start position:0% +complement probability theory by using +data to come up with good models and so + + align:start position:0% +data to come up with good models and so + + + align:start position:0% +data to come up with good models and so +we have the following diagram that + + align:start position:0% +we have the following diagram that + + + align:start position:0% +we have the following diagram that +summarizes the relation between the real + + align:start position:0% +summarizes the relation between the real + + + align:start position:0% +summarizes the relation between the real +world statistics and probability the + + align:start position:0% +world statistics and probability the + + + align:start position:0% +world statistics and probability the +real world generates data the field of + + align:start position:0% +real world generates data the field of + + + align:start position:0% +real world generates data the field of +statistics and inference uses this data + + align:start position:0% +statistics and inference uses this data + + + align:start position:0% +statistics and inference uses this data +to come up with probabilistic models + + align:start position:0% +to come up with probabilistic models + + + align:start position:0% +to come up with probabilistic models +once we have a probabilistic model we + + align:start position:0% +once we have a probabilistic model we + + + align:start position:0% +once we have a probabilistic model we +use probability theory and the analysis + + align:start position:0% +use probability theory and the analysis + + + align:start position:0% +use probability theory and the analysis +tools that it provides to us and the + + align:start position:0% +tools that it provides to us and the + + + align:start position:0% +tools that it provides to us and the +results that we get from these analysis + + align:start position:0% +results that we get from these analysis + + + align:start position:0% +results that we get from these analysis +leads to predictions and decisions about + + align:start position:0% +leads to predictions and decisions about + + + align:start position:0% +leads to predictions and decisions about +the real world \ No newline at end of file diff --git a/v1pwYnDe7dc.txt b/v1pwYnDe7dc.txt new file mode 100644 index 0000000000000000000000000000000000000000..ce860b4ea986cc31ecfec28501d1e96d00cf2fc3 --- /dev/null +++ b/v1pwYnDe7dc.txt @@ -0,0 +1,467 @@ +align:start position:0% + +MIT recently did a uh um a study of + + align:start position:0% +MIT recently did a uh um a study of + + + align:start position:0% +MIT recently did a uh um a study of +future of MIT education and right at the + + align:start position:0% +future of MIT education and right at the + + + align:start position:0% +future of MIT education and right at the +top what we have to do is to teach + + align:start position:0% +top what we have to do is to teach + + + align:start position:0% +top what we have to do is to teach +teamwork and leadership + + align:start position:0% +teamwork and leadership + + + align:start position:0% +teamwork and leadership +uh above technical skills. And the neat + + align:start position:0% +uh above technical skills. And the neat + + + align:start position:0% +uh above technical skills. And the neat +thing about getting students to work + + align:start position:0% +thing about getting students to work + + + align:start position:0% +thing about getting students to work +with visual materials is that because + + align:start position:0% +with visual materials is that because + + + align:start position:0% +with visual materials is that because +there's so much information that you got + + align:start position:0% +there's so much information that you got + + + align:start position:0% +there's so much information that you got +to work in teams, + + align:start position:0% +to work in teams, + + + align:start position:0% +to work in teams, +uh just having one perspective is + + align:start position:0% +uh just having one perspective is + + + align:start position:0% +uh just having one perspective is +interesting, but having two perspectives + + align:start position:0% +interesting, but having two perspectives + + + align:start position:0% +interesting, but having two perspectives +is really interesting. And having + + align:start position:0% +is really interesting. And having + + + align:start position:0% +is really interesting. And having +multiple perspectives on the same + + align:start position:0% +multiple perspectives on the same + + + align:start position:0% +multiple perspectives on the same +material is is just extraordinary. And + + align:start position:0% +material is is just extraordinary. And + + + align:start position:0% +material is is just extraordinary. And +people debate. Okay, this is something + + align:start position:0% +people debate. Okay, this is something + + + align:start position:0% +people debate. Okay, this is something +else. the idea of uh critical thinking. + + align:start position:0% +else. the idea of uh critical thinking. + + + align:start position:0% +else. the idea of uh critical thinking. +You really debate based on whatever + + align:start position:0% +You really debate based on whatever + + + align:start position:0% +You really debate based on whatever +evidence you can find in the image and + + align:start position:0% +evidence you can find in the image and + + + align:start position:0% +evidence you can find in the image and +uh historical and cultural knowledge + + align:start position:0% +uh historical and cultural knowledge + + + align:start position:0% +uh historical and cultural knowledge +that you gain from uh your readings and + + align:start position:0% +that you gain from uh your readings and + + + align:start position:0% +that you gain from uh your readings and +the + + align:start position:0% +the + + + align:start position:0% +the +video. And so uh the idea of teamwork + + align:start position:0% +video. And so uh the idea of teamwork + + + align:start position:0% +video. And so uh the idea of teamwork +really comes into play. And then you can + + align:start position:0% +really comes into play. And then you can + + + align:start position:0% +really comes into play. And then you can +see people playing leadership roles and + + align:start position:0% +see people playing leadership roles and + + + align:start position:0% +see people playing leadership roles and +people uh sort of switch leaders + + align:start position:0% +people uh sort of switch leaders + + + align:start position:0% +people uh sort of switch leaders +leadership as they go from one image to + + align:start position:0% +leadership as they go from one image to + + + align:start position:0% +leadership as they go from one image to +the next depending on what they feel + + align:start position:0% +the next depending on what they feel + + + align:start position:0% +the next depending on what they feel +comfortable talking about. Here are some + + align:start position:0% +comfortable talking about. Here are some + + + align:start position:0% +comfortable talking about. Here are some +uh things to keep in mind about + + align:start position:0% +uh things to keep in mind about + + + align:start position:0% +uh things to keep in mind about +incorporating visual materials. Uh the + + align:start position:0% +incorporating visual materials. Uh the + + + align:start position:0% +incorporating visual materials. Uh the +first thing that one should know we know + + align:start position:0% +first thing that one should know we know + + + align:start position:0% +first thing that one should know we know +this already is that young people are + + align:start position:0% +this already is that young people are + + + align:start position:0% +this already is that young people are +exposed to visual materials by the + + align:start position:0% +exposed to visual materials by the + + + align:start position:0% +exposed to visual materials by the +tongue on a daily basis. uh and yet they + + align:start position:0% +tongue on a daily basis. uh and yet they + + + align:start position:0% +tongue on a daily basis. uh and yet they +are never taught how to interpret them. + + align:start position:0% +are never taught how to interpret them. + + + align:start position:0% +are never taught how to interpret them. +What happens with visual materials is + + align:start position:0% +What happens with visual materials is + + + align:start position:0% +What happens with visual materials is +that you go in, you react emotionally uh + + align:start position:0% +that you go in, you react emotionally uh + + + align:start position:0% +that you go in, you react emotionally uh +and then you you come out uh without + + align:start position:0% +and then you you come out uh without + + + align:start position:0% +and then you you come out uh without +carefully analyzing the content + + align:start position:0% +carefully analyzing the content + + + align:start position:0% +carefully analyzing the content +uh unlike written material. Written + + align:start position:0% +uh unlike written material. Written + + + align:start position:0% +uh unlike written material. Written +material you have to go through word by + + align:start position:0% +material you have to go through word by + + + align:start position:0% +material you have to go through word by +word and sort of think about what what + + align:start position:0% +word and sort of think about what what + + + align:start position:0% +word and sort of think about what what +what is this? What does this say? And so + + align:start position:0% +what is this? What does this say? And so + + + align:start position:0% +what is this? What does this say? And so +uh it's critical that we teach uh sort + + align:start position:0% +uh it's critical that we teach uh sort + + + align:start position:0% +uh it's critical that we teach uh sort +of how to read visuals. Okay. Uh that's + + align:start position:0% +of how to read visuals. Okay. Uh that's + + + align:start position:0% +of how to read visuals. Okay. Uh that's +one point. The second point is that u + + align:start position:0% +one point. The second point is that u + + + align:start position:0% +one point. The second point is that u +there's a ton of visuals out there. You + + align:start position:0% +there's a ton of visuals out there. You + + + align:start position:0% +there's a ton of visuals out there. You +have to curate them. You can't just + + align:start position:0% +have to curate them. You can't just + + + align:start position:0% +have to curate them. You can't just +throw uh students into know + + align:start position:0% +throw uh students into know + + + align:start position:0% +throw uh students into know +um this collection of visuals without + + align:start position:0% +um this collection of visuals without + + + align:start position:0% +um this collection of visuals without +some sense of uh knowing where those + + align:start position:0% +some sense of uh knowing where those + + + align:start position:0% +some sense of uh knowing where those +visuals come from. If you want students + + align:start position:0% +visuals come from. If you want students + + + align:start position:0% +visuals come from. If you want students +to publish the visuals then you have to + + align:start position:0% +to publish the visuals then you have to + + + align:start position:0% +to publish the visuals then you have to +think about + + align:start position:0% +think about + + + align:start position:0% +think about +copyright and students should be taught + + align:start position:0% +copyright and students should be taught + + + align:start position:0% +copyright and students should be taught +about copyright. Okay? What things you + + align:start position:0% +about copyright. Okay? What things you + + + align:start position:0% +about copyright. Okay? What things you +can and cannot do. So these are all like + + align:start position:0% +can and cannot do. So these are all like + + + align:start position:0% +can and cannot do. So these are all like +21st century skills that you can teach + + align:start position:0% +21st century skills that you can teach + + + align:start position:0% +21st century skills that you can teach +with visual material. \ No newline at end of file diff --git a/wEKFGdo4Sck.txt b/wEKFGdo4Sck.txt new file mode 100644 index 0000000000000000000000000000000000000000..3a902da4903f727bfe5581157287cb31e3c3f7f3 --- /dev/null +++ b/wEKFGdo4Sck.txt @@ -0,0 +1,16200 @@ +align:start position:0% + +hey everybody uh welcome back this is + + align:start position:0% +hey everybody uh welcome back this is + + + align:start position:0% +hey everybody uh welcome back this is +our + + align:start position:0% +our + + + align:start position:0% +our +last uh quiz review for the term uh quiz + + align:start position:0% +last uh quiz review for the term uh quiz + + + align:start position:0% +last uh quiz review for the term uh quiz +three we'll be talking about which will + + align:start position:0% +three we'll be talking about which will + + + align:start position:0% +three we'll be talking about which will +be the last quiz until the final + + align:start position:0% +be the last quiz until the final + + + align:start position:0% +be the last quiz until the final +uh it's on dynamic programming which you + + align:start position:0% +uh it's on dynamic programming which you + + + align:start position:0% +uh it's on dynamic programming which you +guys have been studying + + align:start position:0% +guys have been studying + + + align:start position:0% +guys have been studying +in lectures and recitations and on your + + align:start position:0% +in lectures and recitations and on your + + + align:start position:0% +in lectures and recitations and on your +problem sets seven and + + align:start position:0% +problem sets seven and + + + align:start position:0% +problem sets seven and +eight um and lectures + + align:start position:0% +eight um and lectures + + + align:start position:0% +eight um and lectures +fifteen through eighteen so four + + align:start position:0% +fifteen through eighteen so four + + + align:start position:0% +fifteen through eighteen so four +lectures uh + + align:start position:0% +lectures uh + + + align:start position:0% +lectures uh +quiz one and quiz two material on uh + + align:start position:0% +quiz one and quiz two material on uh + + + align:start position:0% +quiz one and quiz two material on uh +essentially data structures and graph + + align:start position:0% +essentially data structures and graph + + + align:start position:0% +essentially data structures and graph +algorithms aren't going to be + + align:start position:0% +algorithms aren't going to be + + + align:start position:0% +algorithms aren't going to be +explicitly test or we're not trying to + + align:start position:0% +explicitly test or we're not trying to + + + align:start position:0% +explicitly test or we're not trying to +explicitly test it + + align:start position:0% +explicitly test it + + + align:start position:0% +explicitly test it +that material on quiz 3 but uh + + align:start position:0% +that material on quiz 3 but uh + + + align:start position:0% +that material on quiz 3 but uh +you know it is fair game uh the material + + align:start position:0% +you know it is fair game uh the material + + + align:start position:0% +you know it is fair game uh the material +is cumulative and so if + + align:start position:0% +is cumulative and so if + + + align:start position:0% +is cumulative and so if +you know you have to store some stuff in + + align:start position:0% +you know you have to store some stuff in + + + align:start position:0% +you know you have to store some stuff in +the data structure that's that's fair + + align:start position:0% +the data structure that's that's fair + + + align:start position:0% +the data structure that's that's fair +game but we're not specifically trying + + align:start position:0% +game but we're not specifically trying + + + align:start position:0% +game but we're not specifically trying +to test you on that material + + align:start position:0% +to test you on that material + + + align:start position:0% +to test you on that material +okay and really we haven't learned all + + align:start position:0% +okay and really we haven't learned all + + + align:start position:0% +okay and really we haven't learned all +that much + + align:start position:0% +that much + + + align:start position:0% +that much +new material in these last four lectures + + align:start position:0% +new material in these last four lectures + + + align:start position:0% +new material in these last four lectures +or this last unit + + align:start position:0% +or this last unit + + + align:start position:0% +or this last unit +uh so right so this is scope we've got + + align:start position:0% +uh so right so this is scope we've got + + + align:start position:0% +uh so right so this is scope we've got +uh you know we're mostly handling + + align:start position:0% +uh you know we're mostly handling + + + align:start position:0% +uh you know we're mostly handling +dynamic programming + + align:start position:0% +dynamic programming + + + align:start position:0% +dynamic programming +uh on these these four lectures and + + align:start position:0% +uh on these these four lectures and + + + align:start position:0% +uh on these these four lectures and +recitations and these two problem sets + + align:start position:0% +recitations and these two problem sets + + + align:start position:0% +recitations and these two problem sets +but really the focus is going to be on + + align:start position:0% +but really the focus is going to be on + + + align:start position:0% +but really the focus is going to be on +this recursive framework + + align:start position:0% +this recursive framework + + + align:start position:0% +this recursive framework +of solving problems with a focus on + + align:start position:0% +of solving problems with a focus on + + + align:start position:0% +of solving problems with a focus on +dynamic programming specifically + + align:start position:0% +dynamic programming specifically + + + align:start position:0% +dynamic programming specifically +now the recursive framework we've we + + align:start position:0% +now the recursive framework we've we + + + align:start position:0% +now the recursive framework we've we +have + + align:start position:0% +have + + + align:start position:0% +have +i think in previous + + align:start position:0% +i think in previous + + + align:start position:0% +i think in previous +slides we use this uh sort bot notation + + align:start position:0% +slides we use this uh sort bot notation + + + align:start position:0% +slides we use this uh sort bot notation +and i think there might be a space + + align:start position:0% +and i think there might be a space + + + align:start position:0% +and i think there might be a space +there uh in in previous versions i'm + + align:start position:0% +there uh in in previous versions i'm + + + align:start position:0% +there uh in in previous versions i'm +concatenating them together here + + align:start position:0% +concatenating them together here + + + align:start position:0% +concatenating them together here +but really it's it's a framework for + + align:start position:0% +but really it's it's a framework for + + + align:start position:0% +but really it's it's a framework for +solving breaking down your problem + + align:start position:0% +solving breaking down your problem + + + align:start position:0% +solving breaking down your problem +into a set of sub-problems that can then + + align:start position:0% +into a set of sub-problems that can then + + + align:start position:0% +into a set of sub-problems that can then +be related recursively + + align:start position:0% +be related recursively + + + align:start position:0% +be related recursively +and if that relationship depends on + + align:start position:0% +and if that relationship depends on + + + align:start position:0% +and if that relationship depends on +problems in a + + align:start position:0% +problems in a + + + align:start position:0% +problems in a +decreasing or in a smaller sense right + + align:start position:0% +decreasing or in a smaller sense right + + + align:start position:0% +decreasing or in a smaller sense right +there's a directionality to + + align:start position:0% +there's a directionality to + + + align:start position:0% +there's a directionality to +which subproblems i'm reducing to each + + align:start position:0% +which subproblems i'm reducing to each + + + align:start position:0% +which subproblems i'm reducing to each +time i make a recursive call + + align:start position:0% +time i make a recursive call + + + align:start position:0% +time i make a recursive call +and that dependency graph is acyclic + + align:start position:0% +and that dependency graph is acyclic + + + align:start position:0% +and that dependency graph is acyclic +then we can solve + + align:start position:0% +then we can solve + + + align:start position:0% +then we can solve +via dynamic programming by memoizing + + align:start position:0% +via dynamic programming by memoizing + + + align:start position:0% +via dynamic programming by memoizing +from bottom up + + align:start position:0% +from bottom up + + + align:start position:0% +from bottom up +or by calling things and remembering the + + align:start position:0% +or by calling things and remembering the + + + align:start position:0% +or by calling things and remembering the +calls that we've + + align:start position:0% +calls that we've + + + align:start position:0% +calls that we've +we've called before uh via memoization + + align:start position:0% +we've called before uh via memoization + + + align:start position:0% +we've called before uh via memoization +right and the basic idea here is this + + align:start position:0% +right and the basic idea here is this + + + align:start position:0% +right and the basic idea here is this +the recursive framework + + align:start position:0% +the recursive framework + + + align:start position:0% +the recursive framework +sort bot that we established + + align:start position:0% +sort bot that we established + + + align:start position:0% +sort bot that we established +is good for any recursive algorithm + + align:start position:0% +is good for any recursive algorithm + + + align:start position:0% +is good for any recursive algorithm +but in the special case where + + align:start position:0% +but in the special case where + + + align:start position:0% +but in the special case where +subproblems made + + align:start position:0% +subproblems made + + + align:start position:0% +subproblems made +may be used more than once may be used + + align:start position:0% +may be used more than once may be used + + + align:start position:0% +may be used more than once may be used +when computing other subproblems then we + + align:start position:0% +when computing other subproblems then we + + + align:start position:0% +when computing other subproblems then we +get this really nice + + align:start position:0% +get this really nice + + + align:start position:0% +get this really nice +uh speed up by recognizing that we don't + + align:start position:0% +uh speed up by recognizing that we don't + + + align:start position:0% +uh speed up by recognizing that we don't +have to do that work more than once + + align:start position:0% +have to do that work more than once + + + align:start position:0% +have to do that work more than once +and essentially instead of looking at it + + align:start position:0% +and essentially instead of looking at it + + + align:start position:0% +and essentially instead of looking at it +as a tree of recursive calls + + align:start position:0% +as a tree of recursive calls + + + align:start position:0% +as a tree of recursive calls +that may recall the same problems more + + align:start position:0% +that may recall the same problems more + + + align:start position:0% +that may recall the same problems more +than once we look at it by collapsing + + align:start position:0% +than once we look at it by collapsing + + + align:start position:0% +than once we look at it by collapsing +those nodes of the same + + align:start position:0% +those nodes of the same + + + align:start position:0% +those nodes of the same +value down into one we get a dag + + align:start position:0% +value down into one we get a dag + + + align:start position:0% +value down into one we get a dag +and dynamic programming is is when those + + align:start position:0% +and dynamic programming is is when those + + + align:start position:0% +and dynamic programming is is when those +sub-problems overlap okay so let's take + + align:start position:0% +sub-problems overlap okay so let's take + + + align:start position:0% +sub-problems overlap okay so let's take +a look about + + align:start position:0% +a look about + + + align:start position:0% +a look about +at uh our recursive framework here + + align:start position:0% +at uh our recursive framework here + + + align:start position:0% +at uh our recursive framework here +sort bot we have the s-r-t-b-o-t + + align:start position:0% +sort bot we have the s-r-t-b-o-t + + + align:start position:0% +sort bot we have the s-r-t-b-o-t +i remembered the space this time a sub + + align:start position:0% +i remembered the space this time a sub + + + align:start position:0% +i remembered the space this time a sub +problem + + align:start position:0% +problem + + + align:start position:0% +problem +you're going to define some sub problems + + align:start position:0% +you're going to define some sub problems + + + align:start position:0% +you're going to define some sub problems +you're going to relate them recursively + + align:start position:0% +you're going to relate them recursively + + + align:start position:0% +you're going to relate them recursively +you're going to specify a topological + + align:start position:0% +you're going to specify a topological + + + align:start position:0% +you're going to specify a topological +order of those sub problems + + align:start position:0% +order of those sub problems + + + align:start position:0% +order of those sub problems +that the relation satisfies uh + + align:start position:0% +that the relation satisfies uh + + + align:start position:0% +that the relation satisfies uh +you're going to list some base cases + + align:start position:0% +you're going to list some base cases + + + align:start position:0% +you're going to list some base cases +basically wherever + + align:start position:0% +basically wherever + + + align:start position:0% +basically wherever +you could solve the sub-problem in + + align:start position:0% +you could solve the sub-problem in + + + align:start position:0% +you could solve the sub-problem in +constant time without doing any + + align:start position:0% +constant time without doing any + + + align:start position:0% +constant time without doing any +recursive work + + align:start position:0% +recursive work + + + align:start position:0% +recursive work +stating how you solve the original + + align:start position:0% +stating how you solve the original + + + align:start position:0% +stating how you solve the original +problem which + + align:start position:0% +problem which + + + align:start position:0% +problem which +might involve combining many + + align:start position:0% +might involve combining many + + + align:start position:0% +might involve combining many +sub-problems but + + align:start position:0% +sub-problems but + + + align:start position:0% +sub-problems but +frequently is just you know finding one + + align:start position:0% +frequently is just you know finding one + + + align:start position:0% +frequently is just you know finding one +sub-problem + + align:start position:0% +sub-problem + + + align:start position:0% +sub-problem +and possibly remembering storing parent + + align:start position:0% +and possibly remembering storing parent + + + align:start position:0% +and possibly remembering storing parent +pointers to return an optimal sequence + + align:start position:0% +pointers to return an optimal sequence + + + align:start position:0% +pointers to return an optimal sequence +or something like that + + align:start position:0% +or something like that + + + align:start position:0% +or something like that +and then analyze the time now the last + + align:start position:0% +and then analyze the time now the last + + + align:start position:0% +and then analyze the time now the last +one isn't really + + align:start position:0% +one isn't really + + + align:start position:0% +one isn't really +important for solving a problem + + align:start position:0% +important for solving a problem + + + align:start position:0% +important for solving a problem +recursively but in this class it's + + align:start position:0% +recursively but in this class it's + + + align:start position:0% +recursively but in this class it's +really important because we want to + + align:start position:0% +really important because we want to + + + align:start position:0% +really important because we want to +tell whether the algorithms that we make + + align:start position:0% +tell whether the algorithms that we make + + + align:start position:0% +tell whether the algorithms that we make +are efficient so + + align:start position:0% +are efficient so + + + align:start position:0% +are efficient so +let's dive a little deeper into each one + + align:start position:0% +let's dive a little deeper into each one + + + align:start position:0% +let's dive a little deeper into each one +of these things + + align:start position:0% +of these things + + + align:start position:0% +of these things +so when we approach a sub-problem + + align:start position:0% +so when we approach a sub-problem + + + align:start position:0% +so when we approach a sub-problem +really what i'm asking you for is to + + align:start position:0% +really what i'm asking you for is to + + + align:start position:0% +really what i'm asking you for is to +describe + + align:start position:0% +describe + + + align:start position:0% +describe +basically set up a set of sub-problems + + align:start position:0% +basically set up a set of sub-problems + + + align:start position:0% +basically set up a set of sub-problems +basically + + align:start position:0% +basically + + + align:start position:0% +basically +i like to use the variable x but you can + + align:start position:0% +i like to use the variable x but you can + + + align:start position:0% +i like to use the variable x but you can +use whatever variable you want + + align:start position:0% +use whatever variable you want + + + align:start position:0% +use whatever variable you want +but basically you're telling us what's + + align:start position:0% +but basically you're telling us what's + + + align:start position:0% +but basically you're telling us what's +in your memo and how big your memo is + + align:start position:0% +in your memo and how big your memo is + + + align:start position:0% +in your memo and how big your memo is +right so we we usually have x + + align:start position:0% +right so we we usually have x + + + align:start position:0% +right so we we usually have x +as a function of some variables + + align:start position:0% +as a function of some variables + + + align:start position:0% +as a function of some variables +and you're wanting to describe to me + + align:start position:0% +and you're wanting to describe to me + + + align:start position:0% +and you're wanting to describe to me +what the meaning of that sub-problem is + + align:start position:0% +what the meaning of that sub-problem is + + + align:start position:0% +what the meaning of that sub-problem is +in terms of the parameters + + align:start position:0% +in terms of the parameters + + + align:start position:0% +in terms of the parameters +now if you have parameters in your + + align:start position:0% +now if you have parameters in your + + + align:start position:0% +now if you have parameters in your +sub-problem that don't appear + + align:start position:0% +sub-problem that don't appear + + + align:start position:0% +sub-problem that don't appear +in your sub-problem definition you're + + align:start position:0% +in your sub-problem definition you're + + + align:start position:0% +in your sub-problem definition you're +doing it wrong and you're probably not + + align:start position:0% +doing it wrong and you're probably not + + + align:start position:0% +doing it wrong and you're probably not +going to get points for the problem + + align:start position:0% +going to get points for the problem + + + align:start position:0% +going to get points for the problem +because i don't know what your + + align:start position:0% +because i don't know what your + + + align:start position:0% +because i don't know what your +sub-problem means now right even if it's + + align:start position:0% +sub-problem means now right even if it's + + + align:start position:0% +sub-problem means now right even if it's +a correct sub-problem and you do the + + align:start position:0% +a correct sub-problem and you do the + + + align:start position:0% +a correct sub-problem and you do the +rest of it right + + align:start position:0% + + + + align:start position:0% + +part of this class is about + + align:start position:0% +part of this class is about + + + align:start position:0% +part of this class is about +communication and if you're not + + align:start position:0% +communication and if you're not + + + align:start position:0% +communication and if you're not +communicating to us what this + + align:start position:0% +communicating to us what this + + + align:start position:0% +communicating to us what this +thing is doing it's really difficult for + + align:start position:0% +thing is doing it's really difficult for + + + align:start position:0% +thing is doing it's really difficult for +you us to + + align:start position:0% +you us to + + + align:start position:0% +you us to +for us for you to convince us that your + + align:start position:0% +for us for you to convince us that your + + + align:start position:0% +for us for you to convince us that your +algorithm is correct + + align:start position:0% +algorithm is correct + + + align:start position:0% +algorithm is correct +right so you really want to in words + + align:start position:0% +right so you really want to in words + + + align:start position:0% +right so you really want to in words +describe + + align:start position:0% +describe + + + align:start position:0% +describe +what the output of your sub problem is + + align:start position:0% +what the output of your sub problem is + + + align:start position:0% +what the output of your sub problem is +what will the memo return to me + + align:start position:0% +what will the memo return to me + + + align:start position:0% +what will the memo return to me +and how those return values depend on + + align:start position:0% +and how those return values depend on + + + align:start position:0% +and how those return values depend on +the inputs + + align:start position:0% +the inputs + + + align:start position:0% +the inputs +right the parameters of your sub problem + + align:start position:0% +right the parameters of your sub problem + + + align:start position:0% +right the parameters of your sub problem +right so that's what in words describe + + align:start position:0% +right so that's what in words describe + + + align:start position:0% +right so that's what in words describe +what a sub problem means so that's + + align:start position:0% +what a sub problem means so that's + + + align:start position:0% +what a sub problem means so that's +that's going to be a really important + + align:start position:0% +that's going to be a really important + + + align:start position:0% +that's going to be a really important +thing for you not to + + align:start position:0% +thing for you not to + + + align:start position:0% +thing for you not to +forget on a quiz then when making sub + + align:start position:0% +forget on a quiz then when making sub + + + align:start position:0% +forget on a quiz then when making sub +problems often + + align:start position:0% +problems often + + + align:start position:0% +problems often +what we're doing is we're recursing + + align:start position:0% +what we're doing is we're recursing + + + align:start position:0% +what we're doing is we're recursing +on different values of indices in a + + align:start position:0% +on different values of indices in a + + + align:start position:0% +on different values of indices in a +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +or numbers in your problem right that's + + align:start position:0% +or numbers in your problem right that's + + + align:start position:0% +or numbers in your problem right that's +kind of what we got to in the last + + align:start position:0% +kind of what we got to in the last + + + align:start position:0% +kind of what we got to in the last +in lecture 18 i guess uh when we were + + align:start position:0% +in lecture 18 i guess uh when we were + + + align:start position:0% +in lecture 18 i guess uh when we were +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +expanding subproblems based on an + + align:start position:0% +expanding subproblems based on an + + + align:start position:0% +expanding subproblems based on an +integer in a problem now actually + + align:start position:0% +integer in a problem now actually + + + align:start position:0% +integer in a problem now actually +an integer in our problem is the number + + align:start position:0% +an integer in our problem is the number + + + align:start position:0% +an integer in our problem is the number +of things in a sequence + + align:start position:0% +of things in a sequence + + + align:start position:0% +of things in a sequence +right and so really those indices are + + align:start position:0% +right and so really those indices are + + + align:start position:0% +right and so really those indices are +integers in our problem that we're + + align:start position:0% +integers in our problem that we're + + + align:start position:0% +integers in our problem that we're +looping over except those integers + + align:start position:0% +looping over except those integers + + + align:start position:0% +looping over except those integers +happen to be the size of our subproblem + + align:start position:0% +happen to be the size of our subproblem + + + align:start position:0% +happen to be the size of our subproblem +whereas + + align:start position:0% +whereas + + + align:start position:0% +whereas +other integers might be larger which is + + align:start position:0% +other integers might be larger which is + + + align:start position:0% +other integers might be larger which is +why you might get a pseudo-polynomial + + align:start position:0% +why you might get a pseudo-polynomial + + + align:start position:0% +why you might get a pseudo-polynomial +time bound + + align:start position:0% +time bound + + + align:start position:0% +time bound +okay but in general when i have a + + align:start position:0% +okay but in general when i have a + + + align:start position:0% +okay but in general when i have a +sequence of things that i might want to + + align:start position:0% +sequence of things that i might want to + + + align:start position:0% +sequence of things that i might want to +dynamic program over common choices for + + align:start position:0% +dynamic program over common choices for + + + align:start position:0% +dynamic program over common choices for +sub-problems are preface prefixes or + + align:start position:0% +sub-problems are preface prefixes or + + + align:start position:0% +sub-problems are preface prefixes or +suffixes + + align:start position:0% +suffixes + + + align:start position:0% +suffixes +if i can kind of locally figure out to + + align:start position:0% +if i can kind of locally figure out to + + + align:start position:0% +if i can kind of locally figure out to +do with one + + align:start position:0% +do with one + + + align:start position:0% +do with one +what to do with one item and then + + align:start position:0% +what to do with one item and then + + + align:start position:0% +what to do with one item and then +recurse + + align:start position:0% +recurse + + + align:start position:0% +recurse +or if i can't kind of localize it by one + + align:start position:0% +or if i can't kind of localize it by one + + + align:start position:0% +or if i can't kind of localize it by one +choice on one side + + align:start position:0% +choice on one side + + + align:start position:0% +choice on one side +if i have to make a choice in the middle + + align:start position:0% +if i have to make a choice in the middle + + + align:start position:0% +if i have to make a choice in the middle +or i have to make a choice on both ends + + align:start position:0% +or i have to make a choice on both ends + + + align:start position:0% +or i have to make a choice on both ends +then you might want to use sub right so + + align:start position:0% +then you might want to use sub right so + + + align:start position:0% +then you might want to use sub right so +basically contiguous subsequences + + align:start position:0% +basically contiguous subsequences + + + align:start position:0% +basically contiguous subsequences +of your sequence because you might need + + align:start position:0% +of your sequence because you might need + + + align:start position:0% +of your sequence because you might need +that flexibility + + align:start position:0% +that flexibility + + + align:start position:0% +that flexibility +when recursing downward if you need to + + align:start position:0% +when recursing downward if you need to + + + align:start position:0% +when recursing downward if you need to +take something from both the front and + + align:start position:0% +take something from both the front and + + + align:start position:0% +take something from both the front and +the back for example + + align:start position:0% +the back for example + + + align:start position:0% +the back for example +right and really what's the difference + + align:start position:0% +right and really what's the difference + + + align:start position:0% +right and really what's the difference +between prefixes and suffixes + + align:start position:0% +between prefixes and suffixes + + + align:start position:0% +between prefixes and suffixes +not much okay we've been concentrating + + align:start position:0% +not much okay we've been concentrating + + + align:start position:0% +not much okay we've been concentrating +on suffixes in this class because + + align:start position:0% +on suffixes in this class because + + + align:start position:0% +on suffixes in this class because +in some sense it's easier to think about + + align:start position:0% +in some sense it's easier to think about + + + align:start position:0% +in some sense it's easier to think about +what am i doing with the first + + align:start position:0% +what am i doing with the first + + + align:start position:0% +what am i doing with the first +thing in my sequence or my you know + + align:start position:0% +thing in my sequence or my you know + + + align:start position:0% +thing in my sequence or my you know +suffix + + align:start position:0% +suffix + + + align:start position:0% +suffix +and then i can recurse on what happens + + align:start position:0% +and then i can recurse on what happens + + + align:start position:0% +and then i can recurse on what happens +later now in actuality + + align:start position:0% +later now in actuality + + + align:start position:0% +later now in actuality +when you're doing this say + + align:start position:0% +when you're doing this say + + + align:start position:0% +when you're doing this say +bottom up right the actual computation + + align:start position:0% +bottom up right the actual computation + + + align:start position:0% +bottom up right the actual computation +that is evaluated first + + align:start position:0% +that is evaluated first + + + align:start position:0% +that is evaluated first +is where in that sequence + + align:start position:0% + + + + align:start position:0% + +right i may be calling at the top level + + align:start position:0% +right i may be calling at the top level + + + align:start position:0% +right i may be calling at the top level +what happens to my first element but + + align:start position:0% +what happens to my first element but + + + align:start position:0% +what happens to my first element but +i'll actually + + align:start position:0% +i'll actually + + + align:start position:0% +i'll actually +deal with that first element last right + + align:start position:0% +deal with that first element last right + + + align:start position:0% +deal with that first element last right +because i will recursively solve + + align:start position:0% +because i will recursively solve + + + align:start position:0% +because i will recursively solve +everything below me + + align:start position:0% +everything below me + + + align:start position:0% +everything below me +right in front of me before i figure out + + align:start position:0% +right in front of me before i figure out + + + align:start position:0% +right in front of me before i figure out +what to do with this thing + + align:start position:0% +what to do with this thing + + + align:start position:0% +what to do with this thing +right so in actuality when i'm solving + + align:start position:0% +right so in actuality when i'm solving + + + align:start position:0% +right so in actuality when i'm solving +uh my recursion i will start at the end + + align:start position:0% +uh my recursion i will start at the end + + + align:start position:0% +uh my recursion i will start at the end +bottom up right because that's my base + + align:start position:0% +bottom up right because that's my base + + + align:start position:0% +bottom up right because that's my base +case + + align:start position:0% +case + + + align:start position:0% +case +and then i'll work my way back to the + + align:start position:0% +and then i'll work my way back to the + + + align:start position:0% +and then i'll work my way back to the +front whereas with prefixes + + align:start position:0% +front whereas with prefixes + + + align:start position:0% +front whereas with prefixes +you look at it the other way what do i'm + + align:start position:0% +you look at it the other way what do i'm + + + align:start position:0% +you look at it the other way what do i'm +doing with my last element + + align:start position:0% +doing with my last element + + + align:start position:0% +doing with my last element +right if i look at what i'm doing at the + + align:start position:0% +right if i look at what i'm doing at the + + + align:start position:0% +right if i look at what i'm doing at the +last time i recurse on a prefix on the + + align:start position:0% +last time i recurse on a prefix on the + + + align:start position:0% +last time i recurse on a prefix on the +stuff that's before me + + align:start position:0% +stuff that's before me + + + align:start position:0% +stuff that's before me +and then when i do bottom up i start + + align:start position:0% +and then when i do bottom up i start + + + align:start position:0% +and then when i do bottom up i start +from the front + + align:start position:0% +from the front + + + align:start position:0% +from the front +and work my way up right it's just it's + + align:start position:0% +and work my way up right it's just it's + + + align:start position:0% +and work my way up right it's just it's +two different sides of the same coin + + align:start position:0% +two different sides of the same coin + + + align:start position:0% +two different sides of the same coin +and usually these are interchangeable + + align:start position:0% +and usually these are interchangeable + + + align:start position:0% +and usually these are interchangeable +we've been doing it + + align:start position:0% +we've been doing it + + + align:start position:0% +we've been doing it +suffix wise because uh when + + align:start position:0% +suffix wise because uh when + + + align:start position:0% +suffix wise because uh when +starting to learn dynamic programming + + align:start position:0% +starting to learn dynamic programming + + + align:start position:0% +starting to learn dynamic programming +it's it's a lot + + align:start position:0% +it's it's a lot + + + align:start position:0% +it's it's a lot +we read things from left to right and + + align:start position:0% +we read things from left to right and + + + align:start position:0% +we read things from left to right and +things like that it's a lot easier to + + align:start position:0% +things like that it's a lot easier to + + + align:start position:0% +things like that it's a lot easier to +figure out what's happening with the + + align:start position:0% +figure out what's happening with the + + + align:start position:0% +figure out what's happening with the +first thing + + align:start position:0% +first thing + + + align:start position:0% +first thing +and move forward conceptually it's + + align:start position:0% +and move forward conceptually it's + + + align:start position:0% +and move forward conceptually it's +actually exactly the same thing + + align:start position:0% +actually exactly the same thing + + + align:start position:0% +actually exactly the same thing +i could just flip my sequence + + align:start position:0% +i could just flip my sequence + + + align:start position:0% +i could just flip my sequence +do the exact same thing with prefixes it + + align:start position:0% +do the exact same thing with prefixes it + + + align:start position:0% +do the exact same thing with prefixes it +would be the exact same dynamic program + + align:start position:0% +would be the exact same dynamic program + + + align:start position:0% +would be the exact same dynamic program +right so there's these things are + + align:start position:0% +right so there's these things are + + + align:start position:0% +right so there's these things are +interchangeable + + align:start position:0% +interchangeable + + + align:start position:0% +interchangeable +it's just it's really useful when + + align:start position:0% +it's just it's really useful when + + + align:start position:0% +it's just it's really useful when +learning into dynamic program + + align:start position:0% +learning into dynamic program + + + align:start position:0% +learning into dynamic program +to be able to switch back and forth + + align:start position:0% +to be able to switch back and forth + + + align:start position:0% +to be able to switch back and forth +between these things + + align:start position:0% +between these things + + + align:start position:0% +between these things +we'll be working on suffixes today on + + align:start position:0% +we'll be working on suffixes today on + + + align:start position:0% +we'll be working on suffixes today on +the problems that we do + + align:start position:0% +the problems that we do + + + align:start position:0% +the problems that we do +but these are interchangeable and + + align:start position:0% +but these are interchangeable and + + + align:start position:0% +but these are interchangeable and +sometimes it's useful to be able to + + align:start position:0% +sometimes it's useful to be able to + + + align:start position:0% +sometimes it's useful to be able to +conceptually think about it + + align:start position:0% +conceptually think about it + + + align:start position:0% +conceptually think about it +in both directions okay + + align:start position:0% + + + + align:start position:0% + +so aside from dealing with subsequences + + align:start position:0% +so aside from dealing with subsequences + + + align:start position:0% +so aside from dealing with subsequences +of sequences in particular contiguous + + align:start position:0% +of sequences in particular contiguous + + + align:start position:0% +of sequences in particular contiguous +ones + + align:start position:0% +ones + + + align:start position:0% +ones +uh we also often multiply our subsets uh + + align:start position:0% +uh we also often multiply our subsets uh + + + align:start position:0% +uh we also often multiply our subsets uh +across multiple inputs like if we have + + align:start position:0% +across multiple inputs like if we have + + + align:start position:0% +across multiple inputs like if we have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +multiple sequences we might take indices + + align:start position:0% +multiple sequences we might take indices + + + align:start position:0% +multiple sequences we might take indices +in each one of them to represent + + align:start position:0% +in each one of them to represent + + + align:start position:0% +in each one of them to represent +prefixes or suffixes + + align:start position:0% +prefixes or suffixes + + + align:start position:0% +prefixes or suffixes +and then we might have to remember + + align:start position:0% +and then we might have to remember + + + align:start position:0% +and then we might have to remember +additional information by maintaining + + align:start position:0% +additional information by maintaining + + + align:start position:0% +additional information by maintaining +some + + align:start position:0% +some + + + align:start position:0% +some +auxiliary information like am i trying + + align:start position:0% +auxiliary information like am i trying + + + align:start position:0% +auxiliary information like am i trying +to + + align:start position:0% +to + + + align:start position:0% +to +maximize or minimize my sum in a + + align:start position:0% +maximize or minimize my sum in a + + + align:start position:0% +maximize or minimize my sum in a +or evaluated expression in an arithmetic + + align:start position:0% +or evaluated expression in an arithmetic + + + align:start position:0% +or evaluated expression in an arithmetic +parenthesization + + align:start position:0% +parenthesization + + + align:start position:0% +parenthesization +or is it player one's turn or players + + align:start position:0% +or is it player one's turn or players + + + align:start position:0% +or is it player one's turn or players +two turn + + align:start position:0% +two turn + + + align:start position:0% +two turn +right uh or which finger where where was + + align:start position:0% +right uh or which finger where where was + + + align:start position:0% +right uh or which finger where where was +my finger in when i was playing piano or + + align:start position:0% +my finger in when i was playing piano or + + + align:start position:0% +my finger in when i was playing piano or +something like that right those are the + + align:start position:0% +something like that right those are the + + + align:start position:0% +something like that right those are the +kinds of things that we might + + align:start position:0% +kinds of things that we might + + + align:start position:0% +kinds of things that we might +expand our state on and in particular we + + align:start position:0% +expand our state on and in particular we + + + align:start position:0% +expand our state on and in particular we +might expand our state based on the + + align:start position:0% +might expand our state based on the + + + align:start position:0% +might expand our state based on the +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +in our problem if we're trying to for + + align:start position:0% +in our problem if we're trying to for + + + align:start position:0% +in our problem if we're trying to for +example keep track of how much space is + + align:start position:0% +example keep track of how much space is + + + align:start position:0% +example keep track of how much space is +left in a knapsack + + align:start position:0% +left in a knapsack + + + align:start position:0% +left in a knapsack +or something like that right but in + + align:start position:0% +or something like that right but in + + + align:start position:0% +or something like that right but in +general if i'm trying to + + align:start position:0% +general if i'm trying to + + + align:start position:0% +general if i'm trying to +uh say pack a set of things it's useful + + align:start position:0% +uh say pack a set of things it's useful + + + align:start position:0% +uh say pack a set of things it's useful +to know + + align:start position:0% +to know + + + align:start position:0% +to know +how much space i have left + + align:start position:0% +how much space i have left + + + align:start position:0% +how much space i have left +to pack okay so that's subproblems + + align:start position:0% +to pack okay so that's subproblems + + + align:start position:0% +to pack okay so that's subproblems +this is really the key part about + + align:start position:0% +this is really the key part about + + + align:start position:0% +this is really the key part about +dynamic programming + + align:start position:0% +dynamic programming + + + align:start position:0% +dynamic programming +is the recursive part this is what makes + + align:start position:0% +is the recursive part this is what makes + + + align:start position:0% +is the recursive part this is what makes +it hard is choosing a set of sub + + align:start position:0% +it hard is choosing a set of sub + + + align:start position:0% +it hard is choosing a set of sub +problems + + align:start position:0% +problems + + + align:start position:0% +problems +and it's often you build sub problems to + + align:start position:0% + + + + align:start position:0% + +fit well with a relation so usually the + + align:start position:0% +fit well with a relation so usually the + + + align:start position:0% +fit well with a relation so usually the +building what these sub problems are is + + align:start position:0% +building what these sub problems are is + + + align:start position:0% +building what these sub problems are is +usual + + align:start position:0% +usual + + + align:start position:0% +usual +usually closely coupled with the next + + align:start position:0% +usually closely coupled with the next + + + align:start position:0% +usually closely coupled with the next +step which is relating the sub problems + + align:start position:0% +step which is relating the sub problems + + + align:start position:0% +step which is relating the sub problems +recursively + + align:start position:0% +recursively + + + align:start position:0% +recursively +and if i relate recursively i usually + + align:start position:0% +and if i relate recursively i usually + + + align:start position:0% +and if i relate recursively i usually +what i want + + align:start position:0% +what i want + + + align:start position:0% +what i want +is an expression a mathematical + + align:start position:0% +is an expression a mathematical + + + align:start position:0% +is an expression a mathematical +expression + + align:start position:0% +expression + + + align:start position:0% +expression +relating the uh + + align:start position:0% +relating the uh + + + align:start position:0% +relating the uh +definition of a of a sub problem you had + + align:start position:0% +definition of a of a sub problem you had + + + align:start position:0% +definition of a of a sub problem you had +in the previous section + + align:start position:0% +in the previous section + + + align:start position:0% +in the previous section +relating those in math terms + + align:start position:0% +relating those in math terms + + + align:start position:0% +relating those in math terms +to the other things this is it's really + + align:start position:0% +to the other things this is it's really + + + align:start position:0% +to the other things this is it's really +important that you + + align:start position:0% +important that you + + + align:start position:0% +important that you +write this in math because it needs to + + align:start position:0% +write this in math because it needs to + + + align:start position:0% +write this in math because it needs to +be precise + + align:start position:0% +be precise + + + align:start position:0% +be precise +to communicate this thing well now you + + align:start position:0% +to communicate this thing well now you + + + align:start position:0% +to communicate this thing well now you +can write it in words + + align:start position:0% +can write it in words + + + align:start position:0% +can write it in words +but i would suggest you write it as a + + align:start position:0% +but i would suggest you write it as a + + + align:start position:0% +but i would suggest you write it as a +mathematical expression + + align:start position:0% +mathematical expression + + + align:start position:0% +mathematical expression +because it's a lot more concise for us + + align:start position:0% +because it's a lot more concise for us + + + align:start position:0% +because it's a lot more concise for us +to see what's happening + + align:start position:0% +to see what's happening + + + align:start position:0% +to see what's happening +in your recursion so relate them + + align:start position:0% +in your recursion so relate them + + + align:start position:0% +in your recursion so relate them +recursively + + align:start position:0% +recursively + + + align:start position:0% +recursively +basically i'm going to write say that x + + align:start position:0% +basically i'm going to write say that x + + + align:start position:0% +basically i'm going to write say that x +of some set of parameters + + align:start position:0% +of some set of parameters + + + align:start position:0% +of some set of parameters +equals some function usually a + + align:start position:0% +equals some function usually a + + + align:start position:0% +equals some function usually a +maximization or a minimization or a + + align:start position:0% +maximization or a minimization or a + + + align:start position:0% +maximization or a minimization or a +summation + + align:start position:0% +summation + + + align:start position:0% +summation +or an or or an and or some some other + + align:start position:0% +or an or or an and or some some other + + + align:start position:0% +or an or or an and or some some other +combinator + + align:start position:0% +combinator + + + align:start position:0% +combinator +of a bunch of choices that you might + + align:start position:0% +of a bunch of choices that you might + + + align:start position:0% +of a bunch of choices that you might +make right + + align:start position:0% +make right + + + align:start position:0% +make right +so uh or a bunch of sub-problems that + + align:start position:0% +so uh or a bunch of sub-problems that + + + align:start position:0% +so uh or a bunch of sub-problems that +you might recurse on + + align:start position:0% +you might recurse on + + + align:start position:0% +you might recurse on +basically you're going to depend on some + + align:start position:0% +basically you're going to depend on some + + + align:start position:0% +basically you're going to depend on some +other sub-problems + + align:start position:0% +other sub-problems + + + align:start position:0% +other sub-problems +that are smaller in some sense now + + align:start position:0% +that are smaller in some sense now + + + align:start position:0% +that are smaller in some sense now +actually embedded in this the idea of a + + align:start position:0% +actually embedded in this the idea of a + + + align:start position:0% +actually embedded in this the idea of a +smaller sub problem isn't really well + + align:start position:0% +smaller sub problem isn't really well + + + align:start position:0% +smaller sub problem isn't really well +defined yet + + align:start position:0% +defined yet + + + align:start position:0% +defined yet +right we haven't told you an ordering + + align:start position:0% +right we haven't told you an ordering + + + align:start position:0% +right we haven't told you an ordering +of these sub-problems to be smaller + + align:start position:0% +of these sub-problems to be smaller + + + align:start position:0% +of these sub-problems to be smaller +but that's what's going to come in the + + align:start position:0% +but that's what's going to come in the + + + align:start position:0% +but that's what's going to come in the +third step right + + align:start position:0% +third step right + + + align:start position:0% +third step right +so kind of a strategy for + + align:start position:0% +so kind of a strategy for + + + align:start position:0% +so kind of a strategy for +figuring out what these recursive + + align:start position:0% +figuring out what these recursive + + + align:start position:0% +figuring out what these recursive +relations might be is to identify some + + align:start position:0% +relations might be is to identify some + + + align:start position:0% +relations might be is to identify some +question about the subproblem solution + + align:start position:0% +question about the subproblem solution + + + align:start position:0% +question about the subproblem solution +right uh what do i do with the first + + align:start position:0% +right uh what do i do with the first + + + align:start position:0% +right uh what do i do with the first +character in this string + + align:start position:0% +character in this string + + + align:start position:0% +character in this string +or um you know + + align:start position:0% +or um you know + + + align:start position:0% +or um you know +which cage do i put this tiger in right + + align:start position:0% +which cage do i put this tiger in right + + + align:start position:0% +which cage do i put this tiger in right +to to figure out what sub problem should + + align:start position:0% +to to figure out what sub problem should + + + align:start position:0% +to to figure out what sub problem should +i recurse on later i don't know the + + align:start position:0% +i recurse on later i don't know the + + + align:start position:0% +i recurse on later i don't know the +answer to that question + + align:start position:0% +answer to that question + + + align:start position:0% +answer to that question +but if i knew the answer to that + + align:start position:0% +but if i knew the answer to that + + + align:start position:0% +but if i knew the answer to that +question then i could + + align:start position:0% +question then i could + + + align:start position:0% +question then i could +recurse on a smaller sub problem because + + align:start position:0% +recurse on a smaller sub problem because + + + align:start position:0% +recurse on a smaller sub problem because +i've figured out what to do with that + + align:start position:0% +i've figured out what to do with that + + + align:start position:0% +i've figured out what to do with that +tiger right and so + + align:start position:0% +tiger right and so + + + align:start position:0% +tiger right and so +it will let me reduce to smaller + + align:start position:0% +it will let me reduce to smaller + + + align:start position:0% +it will let me reduce to smaller +subproblems and then + + align:start position:0% +subproblems and then + + + align:start position:0% +subproblems and then +what dynamic programming does is because + + align:start position:0% +what dynamic programming does is because + + + align:start position:0% +what dynamic programming does is because +i only have a polynomial + + align:start position:0% +i only have a polynomial + + + align:start position:0% +i only have a polynomial +number of sub-problems and i've assumed + + align:start position:0% +number of sub-problems and i've assumed + + + align:start position:0% +number of sub-problems and i've assumed +i've already computed what those + + align:start position:0% +i've already computed what those + + + align:start position:0% +i've already computed what those +those are i've already already memorized + + align:start position:0% +those are i've already already memorized + + + align:start position:0% +those are i've already already memorized +memoized + + align:start position:0% +memoized + + + align:start position:0% +memoized +what the solutions to those sub-problems + + align:start position:0% +what the solutions to those sub-problems + + + align:start position:0% +what the solutions to those sub-problems +are then i can just locally brute force + + align:start position:0% +are then i can just locally brute force + + + align:start position:0% +are then i can just locally brute force +over all the possible answers to that + + align:start position:0% +over all the possible answers to that + + + align:start position:0% +over all the possible answers to that +question and that's just one way to look + + align:start position:0% +question and that's just one way to look + + + align:start position:0% +question and that's just one way to look +at dynamic programming + + align:start position:0% +at dynamic programming + + + align:start position:0% +at dynamic programming +okay so then as we were talking about + + align:start position:0% +okay so then as we were talking about + + + align:start position:0% +okay so then as we were talking about +topological order + + align:start position:0% +topological order + + + align:start position:0% +topological order +arguing that relation is a cyclic + + align:start position:0% +arguing that relation is a cyclic + + + align:start position:0% +arguing that relation is a cyclic +essentially just defining what smaller + + align:start position:0% +essentially just defining what smaller + + + align:start position:0% +essentially just defining what smaller +means + + align:start position:0% +means + + + align:start position:0% +means +when we say we're recursing on smaller + + align:start position:0% +when we say we're recursing on smaller + + + align:start position:0% +when we say we're recursing on smaller +sub-problems what a smaller mean + + align:start position:0% +sub-problems what a smaller mean + + + align:start position:0% +sub-problems what a smaller mean +usually you're saying that some + + align:start position:0% +usually you're saying that some + + + align:start position:0% +usually you're saying that some +index or some parameter of my + + align:start position:0% +index or some parameter of my + + + align:start position:0% +index or some parameter of my +sub-problem decrease always decreases or + + align:start position:0% +sub-problem decrease always decreases or + + + align:start position:0% +sub-problem decrease always decreases or +increases + + align:start position:0% +increases + + + align:start position:0% +increases +sometimes that's not always the case + + align:start position:0% +sometimes that's not always the case + + + align:start position:0% +sometimes that's not always the case +some sometimes you have to maybe add a + + align:start position:0% +some sometimes you have to maybe add a + + + align:start position:0% +some sometimes you have to maybe add a +couple + + align:start position:0% +couple + + + align:start position:0% +couple +indices and see that that always + + align:start position:0% +indices and see that that always + + + align:start position:0% +indices and see that that always +increases because + + align:start position:0% +increases because + + + align:start position:0% +increases because +one may stay the same while the other + + align:start position:0% +one may stay the same while the other + + + align:start position:0% +one may stay the same while the other +increases or something like that + + align:start position:0% +increases or something like that + + + align:start position:0% +increases or something like that +but in general as long as you argue that + + align:start position:0% +but in general as long as you argue that + + + align:start position:0% +but in general as long as you argue that +the relations are acyclic + + align:start position:0% +the relations are acyclic + + + align:start position:0% +the relations are acyclic +then the subproblem graph is a dag and + + align:start position:0% +then the subproblem graph is a dag and + + + align:start position:0% +then the subproblem graph is a dag and +you can compute in a bottom-up manner + + align:start position:0% +you can compute in a bottom-up manner + + + align:start position:0% +you can compute in a bottom-up manner +and you don't get infinite loops in your + + align:start position:0% +and you don't get infinite loops in your + + + align:start position:0% +and you don't get infinite loops in your +recursion right + + align:start position:0% +recursion right + + + align:start position:0% +recursion right +okay the last thing uh the last couple + + align:start position:0% +okay the last thing uh the last couple + + + align:start position:0% +okay the last thing uh the last couple +things are kind of bookkeeping + + align:start position:0% +things are kind of bookkeeping + + + align:start position:0% +things are kind of bookkeeping +but if you don't write these on your + + align:start position:0% +but if you don't write these on your + + + align:start position:0% +but if you don't write these on your +exam we can't give you points for them + + align:start position:0% +exam we can't give you points for them + + + align:start position:0% +exam we can't give you points for them +so write these down uh base cases + + align:start position:0% +so write these down uh base cases + + + align:start position:0% +so write these down uh base cases +if if you don't tell us base cases then + + align:start position:0% +if if you don't tell us base cases then + + + align:start position:0% +if if you don't tell us base cases then +your algorithm cannot be + + align:start position:0% +your algorithm cannot be + + + align:start position:0% +your algorithm cannot be +polynomial time it can't even be pi + + align:start position:0% +polynomial time it can't even be pi + + + align:start position:0% +polynomial time it can't even be pi +finite time because your algorithm never + + align:start position:0% +finite time because your algorithm never + + + align:start position:0% +finite time because your algorithm never +stops + + align:start position:0% +stops + + + align:start position:0% +stops +right it just continues to recurse + + align:start position:0% +right it just continues to recurse + + + align:start position:0% +right it just continues to recurse +forever and ever and ever + + align:start position:0% +forever and ever and ever + + + align:start position:0% +forever and ever and ever +and so it's hard to give us points i + + align:start position:0% +and so it's hard to give us points i + + + align:start position:0% +and so it's hard to give us points i +mean we will give you some points + + align:start position:0% +mean we will give you some points + + + align:start position:0% +mean we will give you some points +if your sub problems in relation are + + align:start position:0% +if your sub problems in relation are + + + align:start position:0% +if your sub problems in relation are +correct but + + align:start position:0% +correct but + + + align:start position:0% +correct but +really if you write code without a base + + align:start position:0% +really if you write code without a base + + + align:start position:0% +really if you write code without a base +case + + align:start position:0% +case + + + align:start position:0% +case +it's going to be wrong right so base + + align:start position:0% +it's going to be wrong right so base + + + align:start position:0% +it's going to be wrong right so base +cases are + + align:start position:0% +cases are + + + align:start position:0% +cases are +really important basically for any + + align:start position:0% +really important basically for any + + + align:start position:0% +really important basically for any +anything at the bounds of your + + align:start position:0% +anything at the bounds of your + + + align:start position:0% +anything at the bounds of your +computation wherever your recursive + + align:start position:0% +computation wherever your recursive + + + align:start position:0% +computation wherever your recursive +relation + + align:start position:0% +relation + + + align:start position:0% +relation +would essentially go outside the bounds + + align:start position:0% +would essentially go outside the bounds + + + align:start position:0% +would essentially go outside the bounds +of your memo + + align:start position:0% +of your memo + + + align:start position:0% +of your memo +right let's say i'm i'm dealing with a + + align:start position:0% +right let's say i'm i'm dealing with a + + + align:start position:0% +right let's say i'm i'm dealing with a +subsequence and at some point i'm + + align:start position:0% +subsequence and at some point i'm + + + align:start position:0% +subsequence and at some point i'm +trying to point to a state where + + align:start position:0% +trying to point to a state where + + + align:start position:0% +trying to point to a state where +i have zero or negative elements in my + + align:start position:0% +i have zero or negative elements in my + + + align:start position:0% +i have zero or negative elements in my +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +that's probably a bad thing and so i + + align:start position:0% +that's probably a bad thing and so i + + + align:start position:0% +that's probably a bad thing and so i +want to define + + align:start position:0% +want to define + + + align:start position:0% +want to define +how to compute those things in constant + + align:start position:0% +how to compute those things in constant + + + align:start position:0% +how to compute those things in constant +time + + align:start position:0% +time + + + align:start position:0% +time +so that my algorithm can terminate when + + align:start position:0% +so that my algorithm can terminate when + + + align:start position:0% +so that my algorithm can terminate when +it gets to one of those + + align:start position:0% +it gets to one of those + + + align:start position:0% +it gets to one of those +you know base cases so for + + align:start position:0% +you know base cases so for + + + align:start position:0% +you know base cases so for +it's really important that you cover all + + align:start position:0% +it's really important that you cover all + + + align:start position:0% +it's really important that you cover all +of those possible + + align:start position:0% +of those possible + + + align:start position:0% +of those possible +leaf locations where you want to be able + + align:start position:0% +leaf locations where you want to be able + + + align:start position:0% +leaf locations where you want to be able +to return in constant time and we'll + + align:start position:0% +to return in constant time and we'll + + + align:start position:0% +to return in constant time and we'll +we'll do some of that today + + align:start position:0% +we'll do some of that today + + + align:start position:0% +we'll do some of that today +uh state solutions for all reachable + + align:start position:0% +uh state solutions for all reachable + + + align:start position:0% +uh state solutions for all reachable +independent + + align:start position:0% +independent + + + align:start position:0% +independent +sub-problems where the relation breaks + + align:start position:0% +sub-problems where the relation breaks + + + align:start position:0% +sub-problems where the relation breaks +down essentially + + align:start position:0% +down essentially + + + align:start position:0% +down essentially +i would be going outside the bounds of + + align:start position:0% +i would be going outside the bounds of + + + align:start position:0% +i would be going outside the bounds of +my my thing or + + align:start position:0% +my my thing or + + + align:start position:0% +my my thing or +you know anything where like maybe if + + align:start position:0% +you know anything where like maybe if + + + align:start position:0% +you know anything where like maybe if +you've got one + + align:start position:0% +you've got one + + + align:start position:0% +you've got one +item left you might say well i have no + + align:start position:0% +item left you might say well i have no + + + align:start position:0% +item left you might say well i have no +choice on what to do with that item i + + align:start position:0% +choice on what to do with that item i + + + align:start position:0% +choice on what to do with that item i +have to pick it or something like that + + align:start position:0% +have to pick it or something like that + + + align:start position:0% +have to pick it or something like that +okay then for + + align:start position:0% +okay then for + + + align:start position:0% +okay then for +your original problem you show how to + + align:start position:0% +your original problem you show how to + + + align:start position:0% +your original problem you show how to +compute + + align:start position:0% +compute + + + align:start position:0% +compute +solution to the original problem from + + align:start position:0% +solution to the original problem from + + + align:start position:0% +solution to the original problem from +the solutions + + align:start position:0% +the solutions + + + align:start position:0% +the solutions +of your sub-problems so uh so + + align:start position:0% +of your sub-problems so uh so + + + align:start position:0% +of your sub-problems so uh so +that usually this is just here's a + + align:start position:0% +that usually this is just here's a + + + align:start position:0% +that usually this is just here's a +sub-problem + + align:start position:0% +sub-problem + + + align:start position:0% +sub-problem +it's the one that used all of the things + + align:start position:0% +it's the one that used all of the things + + + align:start position:0% +it's the one that used all of the things +and that's going to be my answer right + + align:start position:0% +and that's going to be my answer right + + + align:start position:0% +and that's going to be my answer right +that's not always the case right + + align:start position:0% +that's not always the case right + + + align:start position:0% +that's not always the case right +sometimes like in + + align:start position:0% +sometimes like in + + + align:start position:0% +sometimes like in +a longest increasing subsequence we had + + align:start position:0% +a longest increasing subsequence we had + + + align:start position:0% +a longest increasing subsequence we had +to take a max over all of our sub + + align:start position:0% +to take a max over all of our sub + + + align:start position:0% +to take a max over all of our sub +problems that we computed + + align:start position:0% +problems that we computed + + + align:start position:0% +problems that we computed +or max sub array sum we also had to do + + align:start position:0% +or max sub array sum we also had to do + + + align:start position:0% +or max sub array sum we also had to do +that + + align:start position:0% +that + + + align:start position:0% +that +right uh but uh but in general + + align:start position:0% +right uh but uh but in general + + + align:start position:0% +right uh but uh but in general +the output to our subproblems wants to + + align:start position:0% +the output to our subproblems wants to + + + align:start position:0% +the output to our subproblems wants to +be some scalar value that we're trying + + align:start position:0% +be some scalar value that we're trying + + + align:start position:0% +be some scalar value that we're trying +to optimize or a boolean or something + + align:start position:0% +to optimize or a boolean or something + + + align:start position:0% +to optimize or a boolean or something +like that right + + align:start position:0% +like that right + + + align:start position:0% +like that right +it's how we maximize or minimize + + align:start position:0% +it's how we maximize or minimize + + + align:start position:0% +it's how we maximize or minimize +uh what we're doing we're not storing + + align:start position:0% +uh what we're doing we're not storing + + + align:start position:0% +uh what we're doing we're not storing +the entire sequence of how we got there + + align:start position:0% +the entire sequence of how we got there + + + align:start position:0% +the entire sequence of how we got there +because there could be an exponential + + align:start position:0% +because there could be an exponential + + + align:start position:0% +because there could be an exponential +number of possible subsequences that got + + align:start position:0% +number of possible subsequences that got + + + align:start position:0% +number of possible subsequences that got +there + + align:start position:0% +there + + + align:start position:0% +there +that's the whole point of dynamic + + align:start position:0% +that's the whole point of dynamic + + + align:start position:0% +that's the whole point of dynamic +programming we're kind of isolating the + + align:start position:0% +programming we're kind of isolating the + + + align:start position:0% +programming we're kind of isolating the +complexity of one sub problem down to a + + align:start position:0% +complexity of one sub problem down to a + + + align:start position:0% +complexity of one sub problem down to a +single number + + align:start position:0% +single number + + + align:start position:0% +single number +right but in a lot of problems we might + + align:start position:0% +right but in a lot of problems we might + + + align:start position:0% +right but in a lot of problems we might +want to reconstruct + + align:start position:0% +want to reconstruct + + + align:start position:0% +want to reconstruct +say the placement of tigers into cages + + align:start position:0% +say the placement of tigers into cages + + + align:start position:0% +say the placement of tigers into cages +and not just uh how + + align:start position:0% +and not just uh how + + + align:start position:0% +and not just uh how +what's the minimum discomfort over all + + align:start position:0% +what's the minimum discomfort over all + + + align:start position:0% +what's the minimum discomfort over all +tigers or something like that right like + + align:start position:0% +tigers or something like that right like + + + align:start position:0% +tigers or something like that right like +you add in your problem set + + align:start position:0% +you add in your problem set + + + align:start position:0% +you add in your problem set +right so i actually want to know where + + align:start position:0% +right so i actually want to know where + + + align:start position:0% +right so i actually want to know where +to put tigers into cages + + align:start position:0% +to put tigers into cages + + + align:start position:0% +to put tigers into cages +and to do that every time i maximize a + + align:start position:0% +and to do that every time i maximize a + + + align:start position:0% +and to do that every time i maximize a +sub problem i can remember which sub + + align:start position:0% +sub problem i can remember which sub + + + align:start position:0% +sub problem i can remember which sub +problem + + align:start position:0% +problem + + + align:start position:0% +problem +or sub problems i depended on just + + align:start position:0% +or sub problems i depended on just + + + align:start position:0% +or sub problems i depended on just +like storing parent pointers in shortest + + align:start position:0% +like storing parent pointers in shortest + + + align:start position:0% +like storing parent pointers in shortest +paths + + align:start position:0% +paths + + + align:start position:0% +paths +and then using those parent pointers i + + align:start position:0% +and then using those parent pointers i + + + align:start position:0% +and then using those parent pointers i +can just walk back + + align:start position:0% +can just walk back + + + align:start position:0% +can just walk back +in my subproblem graph and and figure + + align:start position:0% +in my subproblem graph and and figure + + + align:start position:0% +in my subproblem graph and and figure +out which + + align:start position:0% +out which + + + align:start position:0% +out which +uh path to a base case lead led me to + + align:start position:0% +uh path to a base case lead led me to + + + align:start position:0% +uh path to a base case lead led me to +an optimal solution okay and then the + + align:start position:0% +an optimal solution okay and then the + + + align:start position:0% +an optimal solution okay and then the +last thing + + align:start position:0% +last thing + + + align:start position:0% +last thing +is analyzing running time generally + + align:start position:0% +is analyzing running time generally + + + align:start position:0% +is analyzing running time generally +you're just summing the work done + + align:start position:0% +you're just summing the work done + + + align:start position:0% +you're just summing the work done +by each sub problem because the + + align:start position:0% +by each sub problem because the + + + align:start position:0% +by each sub problem because the +assumption is you're calculating all of + + align:start position:0% +assumption is you're calculating all of + + + align:start position:0% +assumption is you're calculating all of +the sub problems you described to me + + align:start position:0% +the sub problems you described to me + + + align:start position:0% +the sub problems you described to me +uh and but but if the work per + + align:start position:0% +uh and but but if the work per + + + align:start position:0% +uh and but but if the work per +subproblem is bounded by + + align:start position:0% +subproblem is bounded by + + + align:start position:0% +subproblem is bounded by +the same value you can just multiply it + + align:start position:0% +the same value you can just multiply it + + + align:start position:0% +the same value you can just multiply it +out right so that's + + align:start position:0% +out right so that's + + + align:start position:0% +out right so that's +that's generally a a weaker bound but + + align:start position:0% +that's generally a a weaker bound but + + + align:start position:0% +that's generally a a weaker bound but +usually asymptotically equivalent to the + + align:start position:0% +usually asymptotically equivalent to the + + + align:start position:0% +usually asymptotically equivalent to the +stronger + + align:start position:0% +stronger + + + align:start position:0% +stronger +uh notion on the left uh + + align:start position:0% +uh notion on the left uh + + + align:start position:0% +uh notion on the left uh +and and that's basically how you do + + align:start position:0% +and and that's basically how you do + + + align:start position:0% +and and that's basically how you do +running time usually + + align:start position:0% +running time usually + + + align:start position:0% +running time usually +it's enough to how do i define to + + align:start position:0% +it's enough to how do i define to + + + align:start position:0% +it's enough to how do i define to +determine + + align:start position:0% +determine + + + align:start position:0% +determine +how many sub problems i have well i look + + align:start position:0% +how many sub problems i have well i look + + + align:start position:0% +how many sub problems i have well i look +at the possible values of each of my + + align:start position:0% +at the possible values of each of my + + + align:start position:0% +at the possible values of each of my +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +and then i multiply those numbers + + align:start position:0% +and then i multiply those numbers + + + align:start position:0% +and then i multiply those numbers +together right a lot of people will + + align:start position:0% +together right a lot of people will + + + align:start position:0% +together right a lot of people will +maybe say oh i add them together + + align:start position:0% +maybe say oh i add them together + + + align:start position:0% +maybe say oh i add them together +no because i'm able to choose each of + + align:start position:0% +no because i'm able to choose each of + + + align:start position:0% +no because i'm able to choose each of +these independently + + align:start position:0% +these independently + + + align:start position:0% +these independently +and so i multiply those things together + + align:start position:0% +and so i multiply those things together + + + align:start position:0% +and so i multiply those things together +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the the work done by each sum problem is + + align:start position:0% +the the work done by each sum problem is + + + align:start position:0% +the the work done by each sum problem is +usually + + align:start position:0% +usually + + + align:start position:0% +usually +the size of the thing i'm maximizing + + align:start position:0% +the size of the thing i'm maximizing + + + align:start position:0% +the size of the thing i'm maximizing +over or minimizing over or + + align:start position:0% +over or minimizing over or + + + align:start position:0% +over or minimizing over or +summing in my relation right it's going + + align:start position:0% +summing in my relation right it's going + + + align:start position:0% +summing in my relation right it's going +to be the size of that + + align:start position:0% +to be the size of that + + + align:start position:0% +to be the size of that +the branching that i have the number of + + align:start position:0% +the branching that i have the number of + + + align:start position:0% +the branching that i have the number of +sub problems i depend on + + align:start position:0% +sub problems i depend on + + + align:start position:0% +sub problems i depend on +and so the number of subproblems you + + align:start position:0% +and so the number of subproblems you + + + align:start position:0% +and so the number of subproblems you +probably look at your + + align:start position:0% +probably look at your + + + align:start position:0% +probably look at your +sub problem statement definition to find + + align:start position:0% +sub problem statement definition to find + + + align:start position:0% +sub problem statement definition to find +the work done + + align:start position:0% +the work done + + + align:start position:0% +the work done +by each subproblem you look at your + + align:start position:0% +by each subproblem you look at your + + + align:start position:0% +by each subproblem you look at your +recursive relation okay + + align:start position:0% +recursive relation okay + + + align:start position:0% +recursive relation okay +so with that we've got this really nice + + align:start position:0% +so with that we've got this really nice + + + align:start position:0% +so with that we've got this really nice +framework + + align:start position:0% +framework + + + align:start position:0% +framework +and we're going to use it to solve some + + align:start position:0% +and we're going to use it to solve some + + + align:start position:0% +and we're going to use it to solve some +practice problems + + align:start position:0% +practice problems + + + align:start position:0% +practice problems +happy days and these are a little bit + + align:start position:0% +happy days and these are a little bit + + + align:start position:0% +happy days and these are a little bit +longer + + align:start position:0% +longer + + + align:start position:0% +longer +in terms of uh + + align:start position:0% + + + + align:start position:0% + +description than our previous quiz 2 + + align:start position:0% +description than our previous quiz 2 + + + align:start position:0% +description than our previous quiz 2 +review + + align:start position:0% +review + + + align:start position:0% +review +so uh i'm going to go ahead and read + + align:start position:0% +so uh i'm going to go ahead and read + + + align:start position:0% +so uh i'm going to go ahead and read +them out for you + + align:start position:0% +them out for you + + + align:start position:0% +them out for you +this one's a little shorter okay tiffany + + align:start position:0% +this one's a little shorter okay tiffany + + + align:start position:0% +this one's a little shorter okay tiffany +bannon stumbles upon a lottery chart + + align:start position:0% +bannon stumbles upon a lottery chart + + + align:start position:0% +bannon stumbles upon a lottery chart +dropped by a time traveler from the + + align:start position:0% +dropped by a time traveler from the + + + align:start position:0% +dropped by a time traveler from the +future which lists winning lottery + + align:start position:0% +future which lists winning lottery + + + align:start position:0% +future which lists winning lottery +numbers and positive integer cash + + align:start position:0% +numbers and positive integer cash + + + align:start position:0% +numbers and positive integer cash +payouts for the next n days + + align:start position:0% +payouts for the next n days + + + align:start position:0% +payouts for the next n days +anyone get the reference here tiffany + + align:start position:0% +anyone get the reference here tiffany + + + align:start position:0% +anyone get the reference here tiffany +bannon + + align:start position:0% +bannon + + + align:start position:0% +bannon +biff tannen from uh some + + align:start position:0% +biff tannen from uh some + + + align:start position:0% +biff tannen from uh some +back to the future thing okay so this + + align:start position:0% +back to the future thing okay so this + + + align:start position:0% +back to the future thing okay so this +was actually + + align:start position:0% +was actually + + + align:start position:0% +was actually +i think it's the second back to the + + align:start position:0% +i think it's the second back to the + + + align:start position:0% +i think it's the second back to the +future movie where this happens + + align:start position:0% +future movie where this happens + + + align:start position:0% +future movie where this happens +um anyway tiffany wants to use this + + align:start position:0% +um anyway tiffany wants to use this + + + align:start position:0% +um anyway tiffany wants to use this +information to make money because she + + align:start position:0% +information to make money because she + + + align:start position:0% +information to make money because she +knows the future about the lottery + + align:start position:0% +knows the future about the lottery + + + align:start position:0% +knows the future about the lottery +but is worried that if she plays winning + + align:start position:0% +but is worried that if she plays winning + + + align:start position:0% +but is worried that if she plays winning +numbers every day lottery organizers + + align:start position:0% +numbers every day lottery organizers + + + align:start position:0% +numbers every day lottery organizers +will get suspicious and shut her down + + align:start position:0% +will get suspicious and shut her down + + + align:start position:0% +will get suspicious and shut her down +right so the idea here is + + align:start position:0% +right so the idea here is + + + align:start position:0% +right so the idea here is +maybe it's still suspicious but decides + + align:start position:0% +maybe it's still suspicious but decides + + + align:start position:0% +maybe it's still suspicious but decides +to play the lottery infrequently + + align:start position:0% +to play the lottery infrequently + + + align:start position:0% +to play the lottery infrequently +at most twice in any seven day period + + align:start position:0% +at most twice in any seven day period + + + align:start position:0% +at most twice in any seven day period +but an issue well she'll win right but + + align:start position:0% +but an issue well she'll win right but + + + align:start position:0% +but an issue well she'll win right but +uh it's infrequent enough that eh maybe + + align:start position:0% +uh it's infrequent enough that eh maybe + + + align:start position:0% +uh it's infrequent enough that eh maybe +that's by chance + + align:start position:0% +that's by chance + + + align:start position:0% +that's by chance +maybe not describe a linear time + + align:start position:0% +maybe not describe a linear time + + + align:start position:0% +maybe not describe a linear time +algorithm to determine the maximum + + align:start position:0% +algorithm to determine the maximum + + + align:start position:0% +algorithm to determine the maximum +amount of lottery winnings tiff + + align:start position:0% +amount of lottery winnings tiff + + + align:start position:0% +amount of lottery winnings tiff +tiffany can win in the next n days by + + align:start position:0% +tiffany can win in the next n days by + + + align:start position:0% +tiffany can win in the next n days by +playing the lottery infrequently now + + align:start position:0% +playing the lottery infrequently now + + + align:start position:0% +playing the lottery infrequently now +this was + + align:start position:0% +this was + + + align:start position:0% +this was +a particularly difficult type of pset + + align:start position:0% +a particularly difficult type of pset + + + align:start position:0% +a particularly difficult type of pset +uh or first pset on dynamic programming + + align:start position:0% +uh or first pset on dynamic programming + + + align:start position:0% +uh or first pset on dynamic programming +problem but let's try to do it together + + align:start position:0% +problem but let's try to do it together + + + align:start position:0% +problem but let's try to do it together +so this is problem one i'm gonna just + + align:start position:0% +so this is problem one i'm gonna just + + + align:start position:0% +so this is problem one i'm gonna just +call it lotto + + align:start position:0% +call it lotto + + + align:start position:0% +call it lotto +okay so how can we + + align:start position:0% +okay so how can we + + + align:start position:0% +okay so how can we +deal with subproblems here well i might + + align:start position:0% +deal with subproblems here well i might + + + align:start position:0% +deal with subproblems here well i might +wanna think about + + align:start position:0% +wanna think about + + + align:start position:0% +wanna think about +what do i do on the first day + + align:start position:0% +what do i do on the first day + + + align:start position:0% +what do i do on the first day +am i going to play the lottery or not + + align:start position:0% +am i going to play the lottery or not + + + align:start position:0% +am i going to play the lottery or not +and then recurse on the rest + + align:start position:0% +and then recurse on the rest + + + align:start position:0% +and then recurse on the rest +that sounds good right so some i might + + align:start position:0% +that sounds good right so some i might + + + align:start position:0% +that sounds good right so some i might +have something like + + align:start position:0% +have something like + + + align:start position:0% +have something like +uh well let's say that l of i + + align:start position:0% +uh well let's say that l of i + + + align:start position:0% +uh well let's say that l of i +is the uh winnings + + align:start position:0% + + + + align:start position:0% + +on day i + + align:start position:0% +on day i + + + align:start position:0% +on day i +this is kind of just like i this doesn't + + align:start position:0% +this is kind of just like i this doesn't + + + align:start position:0% +this is kind of just like i this doesn't +define me some notation on what the cash + + align:start position:0% +define me some notation on what the cash + + + align:start position:0% +define me some notation on what the cash +payouts are and so i'm + + align:start position:0% +payouts are and so i'm + + + align:start position:0% +payouts are and so i'm +making a variable to do that and + + align:start position:0% +making a variable to do that and + + + align:start position:0% +making a variable to do that and +for the sake of what's written down on + + align:start position:0% +for the sake of what's written down on + + + align:start position:0% +for the sake of what's written down on +my sheet i'm going to assume that these + + align:start position:0% +my sheet i'm going to assume that these + + + align:start position:0% +my sheet i'm going to assume that these +is one indexed i don't know why + + align:start position:0% +is one indexed i don't know why + + + align:start position:0% +is one indexed i don't know why +okay okay so i have days one to n + + align:start position:0% +okay okay so i have days one to n + + + align:start position:0% +okay okay so i have days one to n +i know what their lottery payouts are so + + align:start position:0% +i know what their lottery payouts are so + + + align:start position:0% +i know what their lottery payouts are so +i might when i'm doing my sort bot stuff + + align:start position:0% +i might when i'm doing my sort bot stuff + + + align:start position:0% +i might when i'm doing my sort bot stuff +i have + + align:start position:0% +i have + + + align:start position:0% +i have +sub problems right what i might want to + + align:start position:0% +sub problems right what i might want to + + + align:start position:0% +sub problems right what i might want to +do + + align:start position:0% +do + + + align:start position:0% +do +is see what happens on day one and + + align:start position:0% +is see what happens on day one and + + + align:start position:0% +is see what happens on day one and +recurse on what's later + + align:start position:0% +recurse on what's later + + + align:start position:0% +recurse on what's later +so i might have something like x of i + + align:start position:0% +so i might have something like x of i + + + align:start position:0% +so i might have something like x of i +is max winnings + + align:start position:0% + + + + align:start position:0% + +uh for i guess possible + + align:start position:0% + + + + align:start position:0% + +for days i + + align:start position:0% +for days i + + + align:start position:0% +for days i +to n okay anyone have a problem with + + align:start position:0% +to n okay anyone have a problem with + + + align:start position:0% +to n okay anyone have a problem with +this + + align:start position:0% +this + + + align:start position:0% +this +type of sub problem let's see let's kind + + align:start position:0% +type of sub problem let's see let's kind + + + align:start position:0% +type of sub problem let's see let's kind +of + + align:start position:0% +of + + + align:start position:0% +of +see what this type of sub problem would + + align:start position:0% +see what this type of sub problem would + + + align:start position:0% +see what this type of sub problem would +lead me to + + align:start position:0% + + + + align:start position:0% + +i can either in my relate step + + align:start position:0% +i can either in my relate step + + + align:start position:0% +i can either in my relate step +what are my choices i can either play on + + align:start position:0% +what are my choices i can either play on + + + align:start position:0% +what are my choices i can either play on +day i + + align:start position:0% +day i + + + align:start position:0% +day i +or i cannot play on day i right if i + + align:start position:0% + + + + align:start position:0% + +i'm i'm trying to maximize this thing + + align:start position:0% +i'm i'm trying to maximize this thing + + + align:start position:0% +i'm i'm trying to maximize this thing +maximize + + align:start position:0% +maximize + + + align:start position:0% +maximize +either if i play on day i get + + align:start position:0% +either if i play on day i get + + + align:start position:0% +either if i play on day i get +l i and then i can recurse on the + + align:start position:0% +l i and then i can recurse on the + + + align:start position:0% +l i and then i can recurse on the +remainder + + align:start position:0% +remainder + + + align:start position:0% +remainder +or i don't play on l i and i recurse on + + align:start position:0% +or i don't play on l i and i recurse on + + + align:start position:0% +or i don't play on l i and i recurse on +the remainder + + align:start position:0% +the remainder + + + align:start position:0% +the remainder +anyone like this recurrence why don't we + + align:start position:0% +anyone like this recurrence why don't we + + + align:start position:0% +anyone like this recurrence why don't we +like this recurrence + + align:start position:0% +like this recurrence + + + align:start position:0% +like this recurrence +i'm just always going to pick this thing + + align:start position:0% +i'm just always going to pick this thing + + + align:start position:0% +i'm just always going to pick this thing +these things are always positive i think + + align:start position:0% +these things are always positive i think + + + align:start position:0% +these things are always positive i think +it's just positive integer payouts yeah + + align:start position:0% +it's just positive integer payouts yeah + + + align:start position:0% +it's just positive integer payouts yeah +and so i'm always going to pick li and + + align:start position:0% +and so i'm always going to pick li and + + + align:start position:0% +and so i'm always going to pick li and +the problem here is that it's not + + align:start position:0% +the problem here is that it's not + + + align:start position:0% +the problem here is that it's not +obeying or dealing with this condition + + align:start position:0% +obeying or dealing with this condition + + + align:start position:0% +obeying or dealing with this condition +that i have + + align:start position:0% +that i have + + + align:start position:0% +that i have +which is i'm only allowed to play twice + + align:start position:0% +which is i'm only allowed to play twice + + + align:start position:0% +which is i'm only allowed to play twice +a week or not + + align:start position:0% +a week or not + + + align:start position:0% +a week or not +not quite twice a week it's not a fixed + + align:start position:0% +not quite twice a week it's not a fixed + + + align:start position:0% +not quite twice a week it's not a fixed +week-long period + + align:start position:0% +week-long period + + + align:start position:0% +week-long period +it's within any consecutive seven-day + + align:start position:0% +it's within any consecutive seven-day + + + align:start position:0% +it's within any consecutive seven-day +period which is a little confusing + + align:start position:0% +period which is a little confusing + + + align:start position:0% +period which is a little confusing +how can i remember what days i'm allowed + + align:start position:0% +how can i remember what days i'm allowed + + + align:start position:0% +how can i remember what days i'm allowed +to pick later on it seems + + align:start position:0% +to pick later on it seems + + + align:start position:0% +to pick later on it seems +a little daunting okay + + align:start position:0% +a little daunting okay + + + align:start position:0% +a little daunting okay +in a sense for me to know right like + + align:start position:0% +in a sense for me to know right like + + + align:start position:0% +in a sense for me to know right like +this is + + align:start position:0% +this is + + + align:start position:0% +this is +max winning possible for days i to n but + + align:start position:0% +max winning possible for days i to n but + + + align:start position:0% +max winning possible for days i to n but +in some sense it depends on + + align:start position:0% +in some sense it depends on + + + align:start position:0% +in some sense it depends on +which days i picked before right because + + align:start position:0% +which days i picked before right because + + + align:start position:0% +which days i picked before right because +if i picked i + + align:start position:0% +if i picked i + + + align:start position:0% +if i picked i +minus one right i can't + + align:start position:0% +minus one right i can't + + + align:start position:0% +minus one right i can't +pick another day for another six days + + align:start position:0% +pick another day for another six days + + + align:start position:0% +pick another day for another six days +right if i have uh + + align:start position:0% + + + + align:start position:0% + +right so i have let's do this precisely + + align:start position:0% +right so i have let's do this precisely + + + align:start position:0% +right so i have let's do this precisely +this is i minus one + + align:start position:0% +this is i minus one + + + align:start position:0% +this is i minus one +right i have seven day period one two + + align:start position:0% +right i have seven day period one two + + + align:start position:0% +right i have seven day period one two +three + + align:start position:0% +three + + + align:start position:0% +three +four five six seven + + align:start position:0% +four five six seven + + + align:start position:0% +four five six seven +right if i uh + + align:start position:0% +right if i uh + + + align:start position:0% +right if i uh +played the lottery here and i played the + + align:start position:0% +played the lottery here and i played the + + + align:start position:0% +played the lottery here and i played the +lottery here + + align:start position:0% +lottery here + + + align:start position:0% +lottery here +then i'm not allowed to play the lottery + + align:start position:0% +then i'm not allowed to play the lottery + + + align:start position:0% +then i'm not allowed to play the lottery +here i'm not allowed to play here not + + align:start position:0% +here i'm not allowed to play here not + + + align:start position:0% +here i'm not allowed to play here not +allowed to play here not allowed to play + + align:start position:0% +allowed to play here not allowed to play + + + align:start position:0% +allowed to play here not allowed to play +here + + align:start position:0% +here + + + align:start position:0% +here +not allowed to play here i am allowed to + + align:start position:0% +not allowed to play here i am allowed to + + + align:start position:0% +not allowed to play here i am allowed to +play here + + align:start position:0% + + + + align:start position:0% + +right so this is i plus 1 plus 2 plus 3 + + align:start position:0% +right so this is i plus 1 plus 2 plus 3 + + + align:start position:0% +right so this is i plus 1 plus 2 plus 3 +plus 4 plus 5 plus 6 + + align:start position:0% +plus 4 plus 5 plus 6 + + + align:start position:0% +plus 4 plus 5 plus 6 +i plus 6. + + align:start position:0% + + + + align:start position:0% + +so depending on what happened before me + + align:start position:0% +so depending on what happened before me + + + align:start position:0% +so depending on what happened before me +i might not be able to play until day i + + align:start position:0% +i might not be able to play until day i + + + align:start position:0% +i might not be able to play until day i +plus six + + align:start position:0% +plus six + + + align:start position:0% +plus six +but if i haven't played until since like + + align:start position:0% +but if i haven't played until since like + + + align:start position:0% +but if i haven't played until since like +way back here i could potentially play + + align:start position:0% +way back here i could potentially play + + + align:start position:0% +way back here i could potentially play +the next guy i don't actually know which + + align:start position:0% +the next guy i don't actually know which + + + align:start position:0% +the next guy i don't actually know which +of these i can play on next + + align:start position:0% +of these i can play on next + + + align:start position:0% +of these i can play on next +in some sense i need to remember which + + align:start position:0% +in some sense i need to remember which + + + align:start position:0% +in some sense i need to remember which +days + + align:start position:0% +days + + + align:start position:0% +days +i'm allowed to play on next and i want + + align:start position:0% +i'm allowed to play on next and i want + + + align:start position:0% +i'm allowed to play on next and i want +to be able to jet like at the beginning + + align:start position:0% +to be able to jet like at the beginning + + + align:start position:0% +to be able to jet like at the beginning +i have no restrictions i can i can just + + align:start position:0% +i have no restrictions i can i can just + + + align:start position:0% +i have no restrictions i can i can just +play on this guy + + align:start position:0% +play on this guy + + + align:start position:0% +play on this guy +next even if i if i played there + + align:start position:0% +next even if i if i played there + + + align:start position:0% +next even if i if i played there +but in general i need i i will be + + align:start position:0% +but in general i need i i will be + + + align:start position:0% +but in general i need i i will be +restricted in some way + + align:start position:0% +restricted in some way + + + align:start position:0% +restricted in some way +between being able to play on this guy + + align:start position:0% +between being able to play on this guy + + + align:start position:0% +between being able to play on this guy +and being able to play on this one guy + + align:start position:0% +and being able to play on this one guy + + + align:start position:0% +and being able to play on this one guy +and so what i'm going to do is i'm going + + align:start position:0% +and so what i'm going to do is i'm going + + + align:start position:0% +and so what i'm going to do is i'm going +to generalize my sub problems + + align:start position:0% +to generalize my sub problems + + + align:start position:0% +to generalize my sub problems +by storing additional information so + + align:start position:0% +by storing additional information so + + + align:start position:0% +by storing additional information so +that i can + + align:start position:0% +that i can + + + align:start position:0% +that i can +rely on that information when i look + + align:start position:0% +rely on that information when i look + + + align:start position:0% +rely on that information when i look +into the future + + align:start position:0% +into the future + + + align:start position:0% +into the future +and recurse okay so instead of + + align:start position:0% +and recurse okay so instead of + + + align:start position:0% +and recurse okay so instead of +uh i'm going to in some sense need to + + align:start position:0% +uh i'm going to in some sense need to + + + align:start position:0% +uh i'm going to in some sense need to +remember + + align:start position:0% +remember + + + align:start position:0% +remember +two days right + + align:start position:0% +two days right + + + align:start position:0% +two days right +where was the last two places i played + + align:start position:0% +where was the last two places i played + + + align:start position:0% +where was the last two places i played +i'm going to simplify that a little bit + + align:start position:0% +i'm going to simplify that a little bit + + + align:start position:0% +i'm going to simplify that a little bit +by saying that + + align:start position:0% +by saying that + + + align:start position:0% +by saying that +this sub problem max winnings possible + + align:start position:0% +this sub problem max winnings possible + + + align:start position:0% +this sub problem max winnings possible +for days + + align:start position:0% +for days + + + align:start position:0% +for days +i to n i'm going to + + align:start position:0% +i to n i'm going to + + + align:start position:0% +i to n i'm going to +say that i have to play on day i okay + + align:start position:0% +say that i have to play on day i okay + + + align:start position:0% +say that i have to play on day i okay +similar restriction as longest + + align:start position:0% +similar restriction as longest + + + align:start position:0% +similar restriction as longest +increasing subsequence right + + align:start position:0% +increasing subsequence right + + + align:start position:0% +increasing subsequence right +i'm definitely including this in my + + align:start position:0% +i'm definitely including this in my + + + align:start position:0% +i'm definitely including this in my +subsequence that's just going to make it + + align:start position:0% +subsequence that's just going to make it + + + align:start position:0% +subsequence that's just going to make it +easier + + align:start position:0% +easier + + + align:start position:0% +easier +for me to be like oh i definitely know i + + align:start position:0% +for me to be like oh i definitely know i + + + align:start position:0% +for me to be like oh i definitely know i +played on this day + + align:start position:0% +played on this day + + + align:start position:0% +played on this day +right it's going to be make it easier + + align:start position:0% +right it's going to be make it easier + + + align:start position:0% +right it's going to be make it easier +for my thinking so + + align:start position:0% +for my thinking so + + + align:start position:0% +for my thinking so +assuming play + + align:start position:0% +assuming play + + + align:start position:0% +assuming play +on day i + + align:start position:0% +on day i + + + align:start position:0% +on day i +and actually i need to remember what's + + align:start position:0% +and actually i need to remember what's + + + align:start position:0% +and actually i need to remember what's +the next day i can play + + align:start position:0% +the next day i can play + + + align:start position:0% +the next day i can play +okay so i'm going to expand this sub + + align:start position:0% +okay so i'm going to expand this sub + + + align:start position:0% +okay so i'm going to expand this sub +problem by + + align:start position:0% +problem by + + + align:start position:0% +problem by +another i guess this is a j + + align:start position:0% +another i guess this is a j + + + align:start position:0% +another i guess this is a j +okay assuming i play on day i + + align:start position:0% +okay assuming i play on day i + + + align:start position:0% +okay assuming i play on day i +and i'm allowed to play + + align:start position:0% + + + + align:start position:0% + +uh i guessed and next + + align:start position:0% +uh i guessed and next + + + align:start position:0% +uh i guessed and next +allowable + + align:start position:0% + + + + align:start position:0% + +play on + + align:start position:0% +play on + + + align:start position:0% +play on +day i plus j + + align:start position:0% +day i plus j + + + align:start position:0% +day i plus j +for + + align:start position:0% + + + + align:start position:0% + +what are my possible range of days for + + align:start position:0% +what are my possible range of days for + + + align:start position:0% +what are my possible range of days for +jay + + align:start position:0% + + + + align:start position:0% + +i can either play the next day + + align:start position:0% +i can either play the next day + + + align:start position:0% +i can either play the next day +but i never restricted past day i plus + + align:start position:0% +but i never restricted past day i plus + + + align:start position:0% +but i never restricted past day i plus +six right because + + align:start position:0% +six right because + + + align:start position:0% +six right because +the things before me further to the + + align:start position:0% +the things before me further to the + + + align:start position:0% +the things before me further to the +right because i haven't dealt with them + + align:start position:0% +right because i haven't dealt with them + + + align:start position:0% +right because i haven't dealt with them +yet right so + + align:start position:0% +yet right so + + + align:start position:0% +yet right so +i only have to deal with this from one + + align:start position:0% +i only have to deal with this from one + + + align:start position:0% +i only have to deal with this from one +to six + + align:start position:0% +to six + + + align:start position:0% +to six +well this is nice because it expanded my + + align:start position:0% +well this is nice because it expanded my + + + align:start position:0% +well this is nice because it expanded my +sub problems by a constant number + + align:start position:0% +sub problems by a constant number + + + align:start position:0% +sub problems by a constant number +right so i actually didn't lose anything + + align:start position:0% +right so i actually didn't lose anything + + + align:start position:0% +right so i actually didn't lose anything +asymptotically + + align:start position:0% +asymptotically + + + align:start position:0% +asymptotically +by remembering this information but i'm + + align:start position:0% +by remembering this information but i'm + + + align:start position:0% +by remembering this information but i'm +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +i'm able to remember all the things that + + align:start position:0% +i'm able to remember all the things that + + + align:start position:0% +i'm able to remember all the things that +could have happened before me + + align:start position:0% +could have happened before me + + + align:start position:0% +could have happened before me +i compress it into this one number okay + + align:start position:0% +i compress it into this one number okay + + + align:start position:0% +i compress it into this one number okay +so + + align:start position:0% + + + + align:start position:0% + +now let's rewrite our relation i'm + + align:start position:0% +now let's rewrite our relation i'm + + + align:start position:0% +now let's rewrite our relation i'm +actually going to + + align:start position:0% +actually going to + + + align:start position:0% +actually going to +go ahead and use some more board space + + align:start position:0% +go ahead and use some more board space + + + align:start position:0% +go ahead and use some more board space +because + + align:start position:0% +because + + + align:start position:0% +because +i think that's easier than erasing + + align:start position:0% + + + + align:start position:0% + +all right so we're looking at my + + align:start position:0% +all right so we're looking at my + + + align:start position:0% +all right so we're looking at my +relation + + align:start position:0% +relation + + + align:start position:0% +relation +this is a pretty complicated relation + + align:start position:0% +this is a pretty complicated relation + + + align:start position:0% +this is a pretty complicated relation +but what's happening now now + + align:start position:0% +but what's happening now now + + + align:start position:0% +but what's happening now now +uh i'm assuming i play on day i + + align:start position:0% +uh i'm assuming i play on day i + + + align:start position:0% +uh i'm assuming i play on day i +that actually simplifies things a little + + align:start position:0% +that actually simplifies things a little + + + align:start position:0% +that actually simplifies things a little +bit because no matter what + + align:start position:0% +bit because no matter what + + + align:start position:0% +bit because no matter what +i get the winnings on day i okay + + align:start position:0% +i get the winnings on day i okay + + + align:start position:0% +i get the winnings on day i okay +now when i call this sub problem i + + align:start position:0% +now when i call this sub problem i + + + align:start position:0% +now when i call this sub problem i +better make sure that it's okay that i + + align:start position:0% +better make sure that it's okay that i + + + align:start position:0% +better make sure that it's okay that i +played on day i + + align:start position:0% +played on day i + + + align:start position:0% +played on day i +but that's that's for my caller right i + + align:start position:0% +but that's that's for my caller right i + + + align:start position:0% +but that's that's for my caller right i +am locally allowed to play on day i am + + align:start position:0% +am locally allowed to play on day i am + + + align:start position:0% +am locally allowed to play on day i am +playing on day out right + + align:start position:0% +playing on day out right + + + align:start position:0% +playing on day out right +that's the definition of my sub problem + + align:start position:0% +that's the definition of my sub problem + + + align:start position:0% +that's the definition of my sub problem +so + + align:start position:0% +so + + + align:start position:0% +so +x of i is i'm going to maximize over + + align:start position:0% +x of i is i'm going to maximize over + + + align:start position:0% +x of i is i'm going to maximize over +some choice right max + + align:start position:0% + + + + align:start position:0% + +of i guess i have l i no matter what + + align:start position:0% +of i guess i have l i no matter what + + + align:start position:0% +of i guess i have l i no matter what +so this could actually come out of my + + align:start position:0% +so this could actually come out of my + + + align:start position:0% +so this could actually come out of my +max + + align:start position:0% +max + + + align:start position:0% +max +and then i'm going to choose what am i + + align:start position:0% +and then i'm going to choose what am i + + + align:start position:0% +and then i'm going to choose what am i +choosing here i'm not choosing whether + + align:start position:0% +choosing here i'm not choosing whether + + + align:start position:0% +choosing here i'm not choosing whether +i'm playing on day i + + align:start position:0% +i'm playing on day i + + + align:start position:0% +i'm playing on day i +i'm choosing what my next day i play is + + align:start position:0% +i'm choosing what my next day i play is + + + align:start position:0% +i'm choosing what my next day i play is +so that then i can recurse on that sub + + align:start position:0% +so that then i can recurse on that sub + + + align:start position:0% +so that then i can recurse on that sub +problem + + align:start position:0% + + + + align:start position:0% + +so what day can i play on well i'm kind + + align:start position:0% +so what day can i play on well i'm kind + + + align:start position:0% +so what day can i play on well i'm kind +of restricted + + align:start position:0% + + + + align:start position:0% + +by this j parameter that i didn't add + + align:start position:0% +by this j parameter that i didn't add + + + align:start position:0% +by this j parameter that i didn't add +into my sub problem + + align:start position:0% + + + + align:start position:0% + +on what possible days i can play next + + align:start position:0% +on what possible days i can play next + + + align:start position:0% +on what possible days i can play next +right + + align:start position:0% +right + + + align:start position:0% +right +i'm going to split that into a + + align:start position:0% +i'm going to split that into a + + + align:start position:0% +i'm going to split that into a +kind of compress that into one thing + + align:start position:0% +kind of compress that into one thing + + + align:start position:0% +kind of compress that into one thing +so x i can + + align:start position:0% +so x i can + + + align:start position:0% +so x i can +play on i have a choice of + + align:start position:0% +play on i have a choice of + + + align:start position:0% +play on i have a choice of +the next day i play somewhere between + + align:start position:0% +the next day i play somewhere between + + + align:start position:0% +the next day i play somewhere between +j which is my next allowable play and + + align:start position:0% +j which is my next allowable play and + + + align:start position:0% +j which is my next allowable play and +sometime in the future + + align:start position:0% +sometime in the future + + + align:start position:0% +sometime in the future +right so i plus + + align:start position:0% +right so i plus + + + align:start position:0% +right so i plus +k this is going to be my loop that i'm + + align:start position:0% +k this is going to be my loop that i'm + + + align:start position:0% +k this is going to be my loop that i'm +looping over in terms of my max + + align:start position:0% + + + + align:start position:0% + +and then what am i restricted on + + align:start position:0% +and then what am i restricted on + + + align:start position:0% +and then what am i restricted on +in my play right it depends on + + align:start position:0% +in my play right it depends on + + + align:start position:0% +in my play right it depends on +how far i am from i right + + align:start position:0% +how far i am from i right + + + align:start position:0% +how far i am from i right +so if i'm here + + align:start position:0% + + + + align:start position:0% + +this is i if i choose k + + align:start position:0% +this is i if i choose k + + + align:start position:0% +this is i if i choose k +to be the next day i can't play + + align:start position:0% +to be the next day i can't play + + + align:start position:0% +to be the next day i can't play +for many many times so + + align:start position:0% +for many many times so + + + align:start position:0% +for many many times so +like the sub problem i'm going to + + align:start position:0% +like the sub problem i'm going to + + + align:start position:0% +like the sub problem i'm going to +rehearse on + + align:start position:0% +rehearse on + + + align:start position:0% +rehearse on +is uh this is + + align:start position:0% +is uh this is + + + align:start position:0% +is uh this is +i plus k i'm going to recurse on i + + align:start position:0% +i plus k i'm going to recurse on i + + + align:start position:0% +i plus k i'm going to recurse on i +plus k but i'm not + + align:start position:0% +plus k but i'm not + + + align:start position:0% +plus k but i'm not +able to j needs to be the max it can be + + align:start position:0% +able to j needs to be the max it can be + + + align:start position:0% +able to j needs to be the max it can be +right because i can't play uh + + align:start position:0% +right because i can't play uh + + + align:start position:0% +right because i can't play uh +until i plus six right so this i + + align:start position:0% +until i plus six right so this i + + + align:start position:0% +until i plus six right so this i +plus k plus six is going to be my thing + + align:start position:0% +plus k plus six is going to be my thing + + + align:start position:0% +plus k plus six is going to be my thing +so + + align:start position:0% + + + + align:start position:0% + +let's see so i'm going to put + + align:start position:0% + + + + align:start position:0% + +let's see if i can unpack what i wrote + + align:start position:0% +let's see if i can unpack what i wrote + + + align:start position:0% +let's see if i can unpack what i wrote +down here + + align:start position:0% +down here + + + align:start position:0% +down here +max of 1 7 minus k + + align:start position:0% +max of 1 7 minus k + + + align:start position:0% +max of 1 7 minus k +yuck + + align:start position:0% + + + + align:start position:0% + +oh i'll put it here + + align:start position:0% + + + + align:start position:0% + +1 7 minus k okay if i + + align:start position:0% +1 7 minus k okay if i + + + align:start position:0% +1 7 minus k okay if i +if i pick k + + align:start position:0% + + + + align:start position:0% + +i'm not aggressive as toward these + + align:start position:0% +i'm not aggressive as toward these + + + align:start position:0% +i'm not aggressive as toward these +boards as justin is + + align:start position:0% +boards as justin is + + + align:start position:0% +boards as justin is +um okay so + + align:start position:0% +um okay so + + + align:start position:0% +um okay so +if i get if i pick a way down here + + align:start position:0% +if i get if i pick a way down here + + + align:start position:0% +if i get if i pick a way down here +right they're not restricted at all + + align:start position:0% +right they're not restricted at all + + + align:start position:0% +right they're not restricted at all +right and so the + + align:start position:0% +right and so the + + + align:start position:0% +right and so the +the most permissive option i have here + + align:start position:0% +the most permissive option i have here + + + align:start position:0% +the most permissive option i have here +is one + + align:start position:0% +is one + + + align:start position:0% +is one +right so i definitely can't be worse + + align:start position:0% +right so i definitely can't be worse + + + align:start position:0% +right so i definitely can't be worse +than one right + + align:start position:0% +than one right + + + align:start position:0% +than one right +but if i pick uh + + align:start position:0% + + + + align:start position:0% + +and then this needs to be some number + + align:start position:0% +and then this needs to be some number + + + align:start position:0% +and then this needs to be some number +between + + align:start position:0% +between + + + align:start position:0% +between +six and one right and so i can just + + align:start position:0% +six and one right and so i can just + + + align:start position:0% +six and one right and so i can just +check the other bound right + + align:start position:0% +check the other bound right + + + align:start position:0% +check the other bound right +if this is the most restrictive right + + align:start position:0% +if this is the most restrictive right + + + align:start position:0% +if this is the most restrictive right +then this should be uh six + + align:start position:0% +then this should be uh six + + + align:start position:0% +then this should be uh six +right so when k equals one this should + + align:start position:0% +right so when k equals one this should + + + align:start position:0% +right so when k equals one this should +be six and it decreases + + align:start position:0% +be six and it decreases + + + align:start position:0% +be six and it decreases +every time further back or further + + align:start position:0% +every time further back or further + + + align:start position:0% +every time further back or further +forward i choose this k + + align:start position:0% +forward i choose this k + + + align:start position:0% +forward i choose this k +right so that's what my sub problem is + + align:start position:0% +right so that's what my sub problem is + + + align:start position:0% +right so that's what my sub problem is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +and i'm choosing over k + + align:start position:0% +and i'm choosing over k + + + align:start position:0% +and i'm choosing over k +in uh from j + + align:start position:0% +in uh from j + + + align:start position:0% +in uh from j +j uh sorry i plus j + + align:start position:0% +j uh sorry i plus j + + + align:start position:0% +j uh sorry i plus j +so sorry j thank you + + align:start position:0% + + + + align:start position:0% + +until what + + align:start position:0% + + + + align:start position:0% + +that's the question until what do i have + + align:start position:0% +that's the question until what do i have + + + align:start position:0% +that's the question until what do i have +to + + align:start position:0% +to + + + align:start position:0% +to +loop over n if i loop over and i'm going + + align:start position:0% +loop over n if i loop over and i'm going + + + align:start position:0% +loop over n if i loop over and i'm going +to get a quadratic running time + + align:start position:0% +to get a quadratic running time + + + align:start position:0% +to get a quadratic running time +which is worse than what i'm allowed to + + align:start position:0% +which is worse than what i'm allowed to + + + align:start position:0% +which is worse than what i'm allowed to +do the assumption is + + align:start position:0% +do the assumption is + + + align:start position:0% +do the assumption is +that i only have to check a constant + + align:start position:0% +that i only have to check a constant + + + align:start position:0% +that i only have to check a constant +number of these and why might that be + + align:start position:0% +number of these and why might that be + + + align:start position:0% +number of these and why might that be +any ideas let's say i'm + + align:start position:0% + + + + align:start position:0% + +got my sub problem i'm recursing i've + + align:start position:0% +got my sub problem i'm recursing i've + + + align:start position:0% +got my sub problem i'm recursing i've +got i + + align:start position:0% +got i + + + align:start position:0% +got i +yeah i don't know where j is j is + + align:start position:0% +yeah i don't know where j is j is + + + align:start position:0% +yeah i don't know where j is j is +somewhere over here + + align:start position:0% +somewhere over here + + + align:start position:0% +somewhere over here +one two three maybe it's four or + + align:start position:0% +one two three maybe it's four or + + + align:start position:0% +one two three maybe it's four or +something like that + + align:start position:0% + + + + align:start position:0% + +let's say i pick some k down here what + + align:start position:0% +let's say i pick some k down here what + + + align:start position:0% +let's say i pick some k down here what +is this this is i + + align:start position:0% +is this this is i + + + align:start position:0% +is this this is i +plus so this is j is 4 + + align:start position:0% +plus so this is j is 4 + + + align:start position:0% +plus so this is j is 4 +5 6 7 8 9 10 11 12 13 14 15 + + align:start position:0% +5 6 7 8 9 10 11 12 13 14 15 + + + align:start position:0% +5 6 7 8 9 10 11 12 13 14 15 +15 way over here like two weeks later + + align:start position:0% +15 way over here like two weeks later + + + align:start position:0% +15 way over here like two weeks later +is it ever optimal for me to do that + + align:start position:0% +is it ever optimal for me to do that + + + align:start position:0% +is it ever optimal for me to do that +why not + + align:start position:0% +why not + + + align:start position:0% +why not +yeah i could play the lotto in the + + align:start position:0% +yeah i could play the lotto in the + + + align:start position:0% +yeah i could play the lotto in the +middle here right right i'm + + align:start position:0% +middle here right right i'm + + + align:start position:0% +middle here right right i'm +i'm within seven like from here to there + + align:start position:0% +i'm within seven like from here to there + + + align:start position:0% +i'm within seven like from here to there +that's a seven + + align:start position:0% +that's a seven + + + align:start position:0% +that's a seven +where i only played once and from here + + align:start position:0% +where i only played once and from here + + + align:start position:0% +where i only played once and from here +to here that's a seven day period where + + align:start position:0% +to here that's a seven day period where + + + align:start position:0% +to here that's a seven day period where +i only played once + + align:start position:0% +i only played once + + + align:start position:0% +i only played once +right so it's going to be more these are + + align:start position:0% +right so it's going to be more these are + + + align:start position:0% +right so it's going to be more these are +positive values so it's going to be more + + align:start position:0% +positive values so it's going to be more + + + align:start position:0% +positive values so it's going to be more +optimal for me to choose something in + + align:start position:0% +optimal for me to choose something in + + + align:start position:0% +optimal for me to choose something in +here to play + + align:start position:0% +here to play + + + align:start position:0% +here to play +right so how far i mean i could just use + + align:start position:0% +right so how far i mean i could just use + + + align:start position:0% +right so how far i mean i could just use + + align:start position:0% + + + align:start position:0% +that would satisfy right because i've + + align:start position:0% +that would satisfy right because i've + + + align:start position:0% +that would satisfy right because i've +already argued to you that it's never + + align:start position:0% +already argued to you that it's never + + + align:start position:0% +already argued to you that it's never +optimal to i can check this + + align:start position:0% +optimal to i can check this + + + align:start position:0% +optimal to i can check this +it's not going to be optimal it's going + + align:start position:0% +it's not going to be optimal it's going + + + align:start position:0% +it's not going to be optimal it's going +to be more optimal to play sometime over + + align:start position:0% +to be more optimal to play sometime over + + + align:start position:0% +to be more optimal to play sometime over +here + + align:start position:0% +here + + + align:start position:0% +here +right but how far do i have to check + + align:start position:0% + + + + align:start position:0% + +well maybe i have to check up to seven + + align:start position:0% +well maybe i have to check up to seven + + + align:start position:0% +well maybe i have to check up to seven +does that work + + align:start position:0% + + + + align:start position:0% + +not quite so let's say i played here + + align:start position:0% +not quite so let's say i played here + + + align:start position:0% +not quite so let's say i played here +and i played here + + align:start position:0% +and i played here + + + align:start position:0% +and i played here +and i played here and i played here + + align:start position:0% +and i played here and i played here + + + align:start position:0% +and i played here and i played here +right i actually + + align:start position:0% +right i actually + + + align:start position:0% +right i actually +can't play here here here + + align:start position:0% +can't play here here here + + + align:start position:0% +can't play here here here +here here right i'm not allowed to play + + align:start position:0% +here here right i'm not allowed to play + + + align:start position:0% +here here right i'm not allowed to play +those + + align:start position:0% +those + + + align:start position:0% +those +i guess these should be o's i played + + align:start position:0% +i guess these should be o's i played + + + align:start position:0% +i guess these should be o's i played +there + + align:start position:0% + + + + align:start position:0% + +and i'm not allowed to play here one two + + align:start position:0% +and i'm not allowed to play here one two + + + align:start position:0% +and i'm not allowed to play here one two +three four + + align:start position:0% +three four + + + align:start position:0% +three four +five right but i am allowed to play + + align:start position:0% +five right but i am allowed to play + + + align:start position:0% +five right but i am allowed to play +anywhere in here + + align:start position:0% +anywhere in here + + + align:start position:0% +anywhere in here +so i basically want to shrink this until + + align:start position:0% +so i basically want to shrink this until + + + align:start position:0% +so i basically want to shrink this until +these x's + + align:start position:0% + + + + align:start position:0% + +collide with each other because then it + + align:start position:0% +collide with each other because then it + + + align:start position:0% +collide with each other because then it +it's possible that an optimal solution + + align:start position:0% +it's possible that an optimal solution + + + align:start position:0% +it's possible that an optimal solution +would require me to pick these two + + align:start position:0% +would require me to pick these two + + + align:start position:0% +would require me to pick these two +and then require me to pick these two + + align:start position:0% +and then require me to pick these two + + + align:start position:0% +and then require me to pick these two +way over there right + + align:start position:0% +way over there right + + + align:start position:0% +way over there right +so this is 10 things in the middle i + + align:start position:0% +so this is 10 things in the middle i + + + align:start position:0% +so this is 10 things in the middle i +only have to go up to at most 11. + + align:start position:0% +only have to go up to at most 11. + + + align:start position:0% +only have to go up to at most 11. +okay it's 11. + + align:start position:0% +okay it's 11. + + + align:start position:0% +okay it's 11. +now you could use any constant above 11 + + align:start position:0% +now you could use any constant above 11 + + + align:start position:0% +now you could use any constant above 11 +and get the same running time bound but + + align:start position:0% +and get the same running time bound but + + + align:start position:0% +and get the same running time bound but +that's that's my analysis + + align:start position:0% +that's that's my analysis + + + align:start position:0% +that's that's my analysis +okay so we have our recursive relation + + align:start position:0% +okay so we have our recursive relation + + + align:start position:0% +okay so we have our recursive relation +uh and so what am i doing i'm just + + align:start position:0% +uh and so what am i doing i'm just + + + align:start position:0% +uh and so what am i doing i'm just +looping over my choices of next day to + + align:start position:0% +looping over my choices of next day to + + + align:start position:0% +looping over my choices of next day to +play + + align:start position:0% +play + + + align:start position:0% +play +i'm recursing on this thing where i + + align:start position:0% +i'm recursing on this thing where i + + + align:start position:0% +i'm recursing on this thing where i +actually do play on that day + + align:start position:0% +actually do play on that day + + + align:start position:0% +actually do play on that day +right but i'm remembering the + + align:start position:0% +right but i'm remembering the + + + align:start position:0% +right but i'm remembering the +information about what i'm allowed to + + align:start position:0% +information about what i'm allowed to + + + align:start position:0% +information about what i'm allowed to +play next + + align:start position:0% +play next + + + align:start position:0% +play next +by limiting based on what my previous + + align:start position:0% +by limiting based on what my previous + + + align:start position:0% +by limiting based on what my previous +value was + + align:start position:0% +value was + + + align:start position:0% +value was +okay so that's the kind of key thing i'm + + align:start position:0% +okay so that's the kind of key thing i'm + + + align:start position:0% +okay so that's the kind of key thing i'm +remembering something further in advance + + align:start position:0% +remembering something further in advance + + + align:start position:0% +remembering something further in advance +or + + align:start position:0% +or + + + align:start position:0% +or +i'm remembering what happened in the + + align:start position:0% +i'm remembering what happened in the + + + align:start position:0% +i'm remembering what happened in the +past by + + align:start position:0% +past by + + + align:start position:0% +past by +describing it as a restriction of + + align:start position:0% +describing it as a restriction of + + + align:start position:0% +describing it as a restriction of +something in the future + + align:start position:0% +something in the future + + + align:start position:0% +something in the future +okay so this was a pretty difficult + + align:start position:0% +okay so this was a pretty difficult + + + align:start position:0% +okay so this was a pretty difficult +problem i think it was one of our first + + align:start position:0% +problem i think it was one of our first + + + align:start position:0% +problem i think it was one of our first +dynamic programming problems on that + + align:start position:0% +dynamic programming problems on that + + + align:start position:0% +dynamic programming problems on that +term + + align:start position:0% +term + + + align:start position:0% +term +it was probably a little ambitious okay + + align:start position:0% + + + + align:start position:0% + +yeah yes the recurrence goes up to 11 + + align:start position:0% +yeah yes the recurrence goes up to 11 + + + align:start position:0% +yeah yes the recurrence goes up to 11 +not ten + + align:start position:0% +not ten + + + align:start position:0% +not ten +eleven okay uh + + align:start position:0% +eleven okay uh + + + align:start position:0% +eleven okay uh +so we have our topological sort + + align:start position:0% +so we have our topological sort + + + align:start position:0% +so we have our topological sort +what's a topological sort for these + + align:start position:0% +what's a topological sort for these + + + align:start position:0% +what's a topological sort for these +subproblems anybody + + align:start position:0% +subproblems anybody + + + align:start position:0% +subproblems anybody +k is always going to be a positive + + align:start position:0% +k is always going to be a positive + + + align:start position:0% +k is always going to be a positive +number right because j goes from 1 to 6. + + align:start position:0% +number right because j goes from 1 to 6. + + + align:start position:0% +number right because j goes from 1 to 6. +so i'm always going to be increasing in + + align:start position:0% +so i'm always going to be increasing in + + + align:start position:0% +so i'm always going to be increasing in +this first quantity right so + + align:start position:0% +this first quantity right so + + + align:start position:0% +this first quantity right so +for x of i j + + align:start position:0% +for x of i j + + + align:start position:0% +for x of i j +i always uh or + + align:start position:0% +i always uh or + + + align:start position:0% +i always uh or +sorry depends + + align:start position:0% + + + + align:start position:0% + +on strictly + + align:start position:0% +on strictly + + + align:start position:0% +on strictly +larger + + align:start position:0% + + + + align:start position:0% + +i right so + + align:start position:0% +i right so + + + align:start position:0% +i right so +this i when i call subproblems it always + + align:start position:0% +this i when i call subproblems it always + + + align:start position:0% +this i when i call subproblems it always +calls subproblems with a larger eye + + align:start position:0% +calls subproblems with a larger eye + + + align:start position:0% +calls subproblems with a larger eye +now this is a little weird because i + + align:start position:0% +now this is a little weird because i + + + align:start position:0% +now this is a little weird because i +wanted me to depend on + + align:start position:0% +wanted me to depend on + + + align:start position:0% +wanted me to depend on +smaller sub problems smaller + + align:start position:0% +smaller sub problems smaller + + + align:start position:0% +smaller sub problems smaller +now it is smaller because i'm taking a + + align:start position:0% +now it is smaller because i'm taking a + + + align:start position:0% +now it is smaller because i'm taking a +smaller suffix + + align:start position:0% +smaller suffix + + + align:start position:0% +smaller suffix +but it's corresponding to using a larger + + align:start position:0% +but it's corresponding to using a larger + + + align:start position:0% +but it's corresponding to using a larger +number + + align:start position:0% +number + + + align:start position:0% +number +to me that's a little confusing but + + align:start position:0% +to me that's a little confusing but + + + align:start position:0% +to me that's a little confusing but +that's okay because we're kind of + + align:start position:0% +that's okay because we're kind of + + + align:start position:0% +that's okay because we're kind of +using things that are always + + align:start position:0% +using things that are always + + + align:start position:0% +using things that are always +monotonically going in some direction + + align:start position:0% +monotonically going in some direction + + + align:start position:0% +monotonically going in some direction +so this is corresponding to a smaller + + align:start position:0% +so this is corresponding to a smaller + + + align:start position:0% +so this is corresponding to a smaller +sub problem + + align:start position:0% +sub problem + + + align:start position:0% +sub problem +in some some measure right it's the + + align:start position:0% +in some some measure right it's the + + + align:start position:0% +in some some measure right it's the +number of elements + + align:start position:0% +number of elements + + + align:start position:0% +number of elements +that we're actually recursing on in some + + align:start position:0% +that we're actually recursing on in some + + + align:start position:0% +that we're actually recursing on in some +sense if we + + align:start position:0% +sense if we + + + align:start position:0% +sense if we +wrote this as a prefix we would have + + align:start position:0% +wrote this as a prefix we would have + + + align:start position:0% +wrote this as a prefix we would have +us depending on strictly smaller i + + align:start position:0% +us depending on strictly smaller i + + + align:start position:0% +us depending on strictly smaller i +and that would be more natural in terms + + align:start position:0% +and that would be more natural in terms + + + align:start position:0% +and that would be more natural in terms +of a recursing on smaller sub-problems + + align:start position:0% +of a recursing on smaller sub-problems + + + align:start position:0% +of a recursing on smaller sub-problems +but i digress okay all right then + + align:start position:0% +but i digress okay all right then + + + align:start position:0% +but i digress okay all right then +we have our original subproblem + + align:start position:0% +we have our original subproblem + + + align:start position:0% +we have our original subproblem +i'm gonna i can't move this board + + align:start position:0% +i'm gonna i can't move this board + + + align:start position:0% +i'm gonna i can't move this board +i'll just keep going because we have + + align:start position:0% +i'll just keep going because we have + + + align:start position:0% +i'll just keep going because we have +lots of boards + + align:start position:0% +lots of boards + + + align:start position:0% +lots of boards +okay our original subproblem now + + align:start position:0% + + + + align:start position:0% + +what could i do i have to start + + align:start position:0% +what could i do i have to start + + + align:start position:0% +what could i do i have to start +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +right here my sub problems assume that + + align:start position:0% +right here my sub problems assume that + + + align:start position:0% +right here my sub problems assume that +i'm starting at i + + align:start position:0% +i'm starting at i + + + align:start position:0% +i'm starting at i +but i don't know where i start i could + + align:start position:0% +but i don't know where i start i could + + + align:start position:0% +but i don't know where i start i could +start by taking the first element but i + + align:start position:0% +start by taking the first element but i + + + align:start position:0% +start by taking the first element but i +might not + + align:start position:0% +might not + + + align:start position:0% +might not +so i could just take the max + + align:start position:0% + + + + align:start position:0% + +over all you know i + + align:start position:0% + + + + align:start position:0% + +overall i of x i + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% +what + + + align:start position:0% +what +the first one i'm not restricted on what + + align:start position:0% +the first one i'm not restricted on what + + + align:start position:0% +the first one i'm not restricted on what +i choose next + + align:start position:0% +i choose next + + + align:start position:0% +i choose next +so what's the most permissive version of + + align:start position:0% +so what's the most permissive version of + + + align:start position:0% +so what's the most permissive version of +jay + + align:start position:0% + + + + align:start position:0% + +one right i'm allowed to take the next + + align:start position:0% +one right i'm allowed to take the next + + + align:start position:0% +one right i'm allowed to take the next +today + + align:start position:0% +today + + + align:start position:0% +today +right so if i just take the max over all + + align:start position:0% +right so if i just take the max over all + + + align:start position:0% +right so if i just take the max over all +of these sub problems + + align:start position:0% +of these sub problems + + + align:start position:0% +of these sub problems +i'll get the solution now actually this + + align:start position:0% +i'll get the solution now actually this + + + align:start position:0% +i'll get the solution now actually this +is a little bit more work than i need + + align:start position:0% +is a little bit more work than i need + + + align:start position:0% +is a little bit more work than i need +this is looping over all + + align:start position:0% +this is looping over all + + + align:start position:0% +this is looping over all +n right + + align:start position:0% +n right + + + align:start position:0% +n right +it's definitely correct right because i + + align:start position:0% +it's definitely correct right because i + + + align:start position:0% +it's definitely correct right because i +have to start somewhere + + align:start position:0% +have to start somewhere + + + align:start position:0% +have to start somewhere +but will i ever start after the first i + + align:start position:0% +but will i ever start after the first i + + + align:start position:0% +but will i ever start after the first i +don't know seven + + align:start position:0% +don't know seven + + + align:start position:0% +don't know seven +no right so i could just take this max + + align:start position:0% +no right so i could just take this max + + + align:start position:0% +no right so i could just take this max +over the first some constant number + + align:start position:0% +over the first some constant number + + + align:start position:0% +over the first some constant number +and that would be fine but that's okay + + align:start position:0% +and that would be fine but that's okay + + + align:start position:0% +and that would be fine but that's okay +this is still smaller than the number of + + align:start position:0% +this is still smaller than the number of + + + align:start position:0% +this is still smaller than the number of +subproblems that we have yeah + + align:start position:0% +subproblems that we have yeah + + + align:start position:0% +subproblems that we have yeah +if i were being lazy during my exam and + + align:start position:0% +if i were being lazy during my exam and + + + align:start position:0% +if i were being lazy during my exam and +i looked over jay + + align:start position:0% +i looked over jay + + + align:start position:0% +i looked over jay +would that be correct if i looped over j + + align:start position:0% +would that be correct if i looped over j + + + align:start position:0% +would that be correct if i looped over j +for every possible thing + + align:start position:0% +for every possible thing + + + align:start position:0% +for every possible thing +took took the loop over this and j + + align:start position:0% +took took the loop over this and j + + + align:start position:0% +took took the loop over this and j +yeah that would still be fine why not + + align:start position:0% +yeah that would still be fine why not + + + align:start position:0% +yeah that would still be fine why not +it's just + + align:start position:0% +it's just + + + align:start position:0% +it's just +less it's it's it's more restrictive of + + align:start position:0% +less it's it's it's more restrictive of + + + align:start position:0% +less it's it's it's more restrictive of +sub problems + + align:start position:0% +sub problems + + + align:start position:0% +sub problems +it will never be better to do that + + align:start position:0% +it will never be better to do that + + + align:start position:0% +it will never be better to do that +but you could do that because it + + align:start position:0% +but you could do that because it + + + align:start position:0% +but you could do that because it +wouldn't change your running time + + align:start position:0% +wouldn't change your running time + + + align:start position:0% +wouldn't change your running time +uh could it change my running time if my + + align:start position:0% +uh could it change my running time if my + + + align:start position:0% +uh could it change my running time if my +j accidentally moved too far + + align:start position:0% + + + + align:start position:0% + +well j is restricted to be one to six so + + align:start position:0% +well j is restricted to be one to six so + + + align:start position:0% +well j is restricted to be one to six so +i'm not + + align:start position:0% +i'm not + + + align:start position:0% +i'm not +i i don't i don't think so but in a + + align:start position:0% +i i don't i don't think so but in a + + + align:start position:0% +i i don't i don't think so but in a +different problem in a different context + + align:start position:0% +different problem in a different context + + + align:start position:0% +different problem in a different context +it could + + align:start position:0% +it could + + + align:start position:0% +it could +okay so that's the original and then + + align:start position:0% +okay so that's the original and then + + + align:start position:0% +okay so that's the original and then +time here + + align:start position:0% + + + + align:start position:0% + +what do we got we have a linear number + + align:start position:0% +what do we got we have a linear number + + + align:start position:0% +what do we got we have a linear number +of subproblems + + align:start position:0% +of subproblems + + + align:start position:0% +of subproblems +number of sub problems we've got uh + + align:start position:0% +number of sub problems we've got uh + + + align:start position:0% +number of sub problems we've got uh +i actually like usually saying exactly + + align:start position:0% +i actually like usually saying exactly + + + align:start position:0% +i actually like usually saying exactly +how many subproblems i have + + align:start position:0% +how many subproblems i have + + + align:start position:0% +how many subproblems i have +oh we didn't do base case i missed bot + + align:start position:0% +oh we didn't do base case i missed bot + + + align:start position:0% +oh we didn't do base case i missed bot +i missed my b + + align:start position:0% + + + + align:start position:0% + +we'll do the original first and then the + + align:start position:0% +we'll do the original first and then the + + + align:start position:0% +we'll do the original first and then the +base case okay + + align:start position:0% +base case okay + + + align:start position:0% +base case okay +base case what do we have is our base + + align:start position:0% +base case what do we have is our base + + + align:start position:0% +base case what do we have is our base +case here + + align:start position:0% +case here + + + align:start position:0% +case here +well when i don't have anything to do + + align:start position:0% +well when i don't have anything to do + + + align:start position:0% +well when i don't have anything to do +right + + align:start position:0% +right + + + align:start position:0% +right +if i'm and actually + + align:start position:0% +if i'm and actually + + + align:start position:0% +if i'm and actually +if i have this situation + + align:start position:0% +if i have this situation + + + align:start position:0% +if i have this situation +for i equals + + align:start position:0% +for i equals + + + align:start position:0% +for i equals +say n + + align:start position:0% +say n + + + align:start position:0% +say n +right i've got my last thing + + align:start position:0% + + + + align:start position:0% + +i could potentially start looping over + + align:start position:0% +i could potentially start looping over + + + align:start position:0% +i could potentially start looping over +sub problems that are negative + + align:start position:0% +sub problems that are negative + + + align:start position:0% +sub problems that are negative +in terms of my index i'm not going to + + align:start position:0% +in terms of my index i'm not going to + + + align:start position:0% +in terms of my index i'm not going to +want to do that there's a couple ways i + + align:start position:0% +want to do that there's a couple ways i + + + align:start position:0% +want to do that there's a couple ways i +can deal with that + + align:start position:0% +can deal with that + + + align:start position:0% +can deal with that +i could set a value for all of my sub + + align:start position:0% +i could set a value for all of my sub + + + align:start position:0% +i could set a value for all of my sub +problems for negative ah + + align:start position:0% +problems for negative ah + + + align:start position:0% +problems for negative ah +that's one thing i could do but then i + + align:start position:0% +that's one thing i could do but then i + + + align:start position:0% +that's one thing i could do but then i +have to kind of remember + + align:start position:0% +have to kind of remember + + + align:start position:0% +have to kind of remember +or i have to figure out how far i go + + align:start position:0% +or i have to figure out how far i go + + + align:start position:0% +or i have to figure out how far i go +into the negative + + align:start position:0% +into the negative + + + align:start position:0% +into the negative +right that's one thing i could do and i + + align:start position:0% +right that's one thing i could do and i + + + align:start position:0% +right that's one thing i could do and i +give a base case for each of those cases + + align:start position:0% +give a base case for each of those cases + + + align:start position:0% +give a base case for each of those cases +i don't have anything + + align:start position:0% +i don't have anything + + + align:start position:0% +i don't have anything +so i get like a i don't know + + align:start position:0% +so i get like a i don't know + + + align:start position:0% +so i get like a i don't know +uh zero value for playing + + align:start position:0% +uh zero value for playing + + + align:start position:0% +uh zero value for playing +in the future right because i have + + align:start position:0% +in the future right because i have + + + align:start position:0% +in the future right because i have +negative things i can't do anything with + + align:start position:0% +negative things i can't do anything with + + + align:start position:0% +negative things i can't do anything with +that + + align:start position:0% +that + + + align:start position:0% +that +another way of handling that which i + + align:start position:0% +another way of handling that which i + + + align:start position:0% +another way of handling that which i +think i did in my + + align:start position:0% +think i did in my + + + align:start position:0% +think i did in my +solutions was restrict that + + align:start position:0% +solutions was restrict that + + + align:start position:0% +solutions was restrict that +k to only be i guess + + align:start position:0% +k to only be i guess + + + align:start position:0% +k to only be i guess +and restrict that i plus + + align:start position:0% +and restrict that i plus + + + align:start position:0% +and restrict that i plus +k is less than or equal to n + + align:start position:0% +k is less than or equal to n + + + align:start position:0% +k is less than or equal to n +and then i'll never go to negative sub + + align:start position:0% +and then i'll never go to negative sub + + + align:start position:0% +and then i'll never go to negative sub +problems i'll never a curse on these + + align:start position:0% +problems i'll never a curse on these + + + align:start position:0% +problems i'll never a curse on these +things + + align:start position:0% +things + + + align:start position:0% +things +but that means that when i call this on + + align:start position:0% +but that means that when i call this on + + + align:start position:0% +but that means that when i call this on +n + + align:start position:0% + + + + align:start position:0% + +right when i only have one lottery day + + align:start position:0% +right when i only have one lottery day + + + align:start position:0% +right when i only have one lottery day +left + + align:start position:0% +left + + + align:start position:0% +left +this set will be empty + + align:start position:0% +this set will be empty + + + align:start position:0% +this set will be empty +so what's the max over that thing max + + align:start position:0% +so what's the max over that thing max + + + align:start position:0% +so what's the max over that thing max +over an empty set + + align:start position:0% +over an empty set + + + align:start position:0% +over an empty set +i don't know i mean i could add on zero + + align:start position:0% +i don't know i mean i could add on zero + + + align:start position:0% +i don't know i mean i could add on zero +here that's one way i could do it or i + + align:start position:0% +here that's one way i could do it or i + + + align:start position:0% +here that's one way i could do it or i +could just say when i'm at n + + align:start position:0% +could just say when i'm at n + + + align:start position:0% +could just say when i'm at n +and that thing is empty right + + align:start position:0% +and that thing is empty right + + + align:start position:0% +and that thing is empty right +or you know whenever it's empty + + align:start position:0% +or you know whenever it's empty + + + align:start position:0% +or you know whenever it's empty +right we can say the base case x i + + align:start position:0% +right we can say the base case x i + + + align:start position:0% +right we can say the base case x i +j i guess we could put this at n + + align:start position:0% +j i guess we could put this at n + + + align:start position:0% +j i guess we could put this at n +equals zero or sorry equals + + align:start position:0% +equals zero or sorry equals + + + align:start position:0% +equals zero or sorry equals +l of i right + + align:start position:0% +l of i right + + + align:start position:0% +l of i right +l of n thank you because + + align:start position:0% +l of n thank you because + + + align:start position:0% +l of n thank you because +at the last guy i have to use ln + + align:start position:0% +at the last guy i have to use ln + + + align:start position:0% +at the last guy i have to use ln +so there it is right now in actuality + + align:start position:0% +so there it is right now in actuality + + + align:start position:0% +so there it is right now in actuality +if you write this correctly right i put + + align:start position:0% +if you write this correctly right i put + + + align:start position:0% +if you write this correctly right i put +the li + + align:start position:0% +the li + + + align:start position:0% +the li +outside and i union this with a zero + + align:start position:0% +outside and i union this with a zero + + + align:start position:0% +outside and i union this with a zero +i can actually get away with just having + + align:start position:0% +i can actually get away with just having + + + align:start position:0% +i can actually get away with just having +the relation + + align:start position:0% +the relation + + + align:start position:0% +the relation +and no base case because my relation + + align:start position:0% +and no base case because my relation + + + align:start position:0% +and no base case because my relation +actually reduces to a base case + + align:start position:0% +actually reduces to a base case + + + align:start position:0% +actually reduces to a base case +because i of the way that i wrote my + + align:start position:0% +because i of the way that i wrote my + + + align:start position:0% +because i of the way that i wrote my +relation + + align:start position:0% +relation + + + align:start position:0% +relation +but in general you'll want to write some + + align:start position:0% +but in general you'll want to write some + + + align:start position:0% +but in general you'll want to write some +kind of base case here + + align:start position:0% +kind of base case here + + + align:start position:0% +kind of base case here +to either acknowledge that your relation + + align:start position:0% +to either acknowledge that your relation + + + align:start position:0% +to either acknowledge that your relation +handles it + + align:start position:0% +handles it + + + align:start position:0% +handles it +or being specific about what happens + + align:start position:0% +or being specific about what happens + + + align:start position:0% +or being specific about what happens +when i can't do any more work right + + align:start position:0% +when i can't do any more work right + + + align:start position:0% +when i can't do any more work right +right so and the last thing time we've + + align:start position:0% +right so and the last thing time we've + + + align:start position:0% +right so and the last thing time we've +got + + align:start position:0% +got + + + align:start position:0% +got +n sub problems exactly + + align:start position:0% +n sub problems exactly + + + align:start position:0% +n sub problems exactly +times constant work per sub problem + + align:start position:0% +times constant work per sub problem + + + align:start position:0% +times constant work per sub problem +because i'm looping + + align:start position:0% +because i'm looping + + + align:start position:0% +because i'm looping +over 11 possible values actually it's + + align:start position:0% +over 11 possible values actually it's + + + align:start position:0% +over 11 possible values actually it's +up to 11 right because j could be six + + align:start position:0% + + + + align:start position:0% + +so this is order n work total + + align:start position:0% +so this is order n work total + + + align:start position:0% +so this is order n work total +okay so this is a pretty daunting first + + align:start position:0% +okay so this is a pretty daunting first + + + align:start position:0% +okay so this is a pretty daunting first +problem + + align:start position:0% +problem + + + align:start position:0% +problem +but what in in terms of what uh + + align:start position:0% +but what in in terms of what uh + + + align:start position:0% +but what in in terms of what uh +uh eric professor domain was talking + + align:start position:0% +uh eric professor domain was talking + + + align:start position:0% +uh eric professor domain was talking +about + + align:start position:0% +about + + + align:start position:0% +about +last uh lecture uh in terms of + + align:start position:0% +last uh lecture uh in terms of + + + align:start position:0% +last uh lecture uh in terms of +categorization of subproblem + + align:start position:0% +categorization of subproblem + + + align:start position:0% +categorization of subproblem +or categorization of azation of dynamic + + align:start position:0% +or categorization of azation of dynamic + + + align:start position:0% +or categorization of azation of dynamic +programs + + align:start position:0% +programs + + + align:start position:0% +programs +what do we got we've got a suffix + + align:start position:0% +what do we got we've got a suffix + + + align:start position:0% +what do we got we've got a suffix +subproblem where we expanded by some + + align:start position:0% +subproblem where we expanded by some + + + align:start position:0% +subproblem where we expanded by some +local information + + align:start position:0% +local information + + + align:start position:0% +local information +right remembering how uh when's the next + + align:start position:0% +right remembering how uh when's the next + + + align:start position:0% +right remembering how uh when's the next +time i can + + align:start position:0% +time i can + + + align:start position:0% +time i can +i can play so that's kind of a + + align:start position:0% +i can play so that's kind of a + + + align:start position:0% +i can play so that's kind of a +categorization of these sub problems + + align:start position:0% +categorization of these sub problems + + + align:start position:0% +categorization of these sub problems +the recurrence relation has + + align:start position:0% +the recurrence relation has + + + align:start position:0% +the recurrence relation has +constant branching but more than like + + align:start position:0% +constant branching but more than like + + + align:start position:0% +constant branching but more than like +two branching + + align:start position:0% +two branching + + + align:start position:0% +two branching +right and uh + + align:start position:0% +right and uh + + + align:start position:0% +right and uh +i'm combining a bunch of sub problems + + align:start position:0% +i'm combining a bunch of sub problems + + + align:start position:0% +i'm combining a bunch of sub problems +right in my original + + align:start position:0% +right in my original + + + align:start position:0% +right in my original +evaluation right and if i wanted to + + align:start position:0% +evaluation right and if i wanted to + + + align:start position:0% +evaluation right and if i wanted to +figure out what days tif should play + + align:start position:0% +figure out what days tif should play + + + align:start position:0% +figure out what days tif should play +on the lottery you can store parent + + align:start position:0% +on the lottery you can store parent + + + align:start position:0% +on the lottery you can store parent +pointers + + align:start position:0% +pointers + + + align:start position:0% +pointers +when i'm do evaluating this max + + align:start position:0% +when i'm do evaluating this max + + + align:start position:0% +when i'm do evaluating this max +right i figure out which subproblem + + align:start position:0% +right i figure out which subproblem + + + align:start position:0% +right i figure out which subproblem +x i recursed that gave me the max + + align:start position:0% +x i recursed that gave me the max + + + align:start position:0% +x i recursed that gave me the max +and i can walk back to see which choices + + align:start position:0% +and i can walk back to see which choices + + + align:start position:0% +and i can walk back to see which choices +i made + + align:start position:0% +i made + + + align:start position:0% +i made +to figure out which days i played the + + align:start position:0% +to figure out which days i played the + + + align:start position:0% +to figure out which days i played the +lottery does that make sense + + align:start position:0% + + + + align:start position:0% + +so any questions on problem one + + align:start position:0% +so any questions on problem one + + + align:start position:0% +so any questions on problem one +that's the most that was i i want to + + align:start position:0% +that's the most that was i i want to + + + align:start position:0% +that's the most that was i i want to +have the + + align:start position:0% +have the + + + align:start position:0% +have the +most complicated one first so that we + + align:start position:0% +most complicated one first so that we + + + align:start position:0% +most complicated one first so that we +could have an easier + + align:start position:0% +could have an easier + + + align:start position:0% +could have an easier +way to go in in a sense this is the most + + align:start position:0% +way to go in in a sense this is the most + + + align:start position:0% +way to go in in a sense this is the most +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +version of this kind of actually pretty + + align:start position:0% +version of this kind of actually pretty + + + align:start position:0% +version of this kind of actually pretty +simple + + align:start position:0% +simple + + + align:start position:0% +simple +dynamic programming setup why do i say + + align:start position:0% +dynamic programming setup why do i say + + + align:start position:0% +dynamic programming setup why do i say +simple dynamic programming setup + + align:start position:0% +simple dynamic programming setup + + + align:start position:0% +simple dynamic programming setup +it's just suffixes and i'm just doing a + + align:start position:0% +it's just suffixes and i'm just doing a + + + align:start position:0% +it's just suffixes and i'm just doing a +constant amount of work + + align:start position:0% +constant amount of work + + + align:start position:0% +constant amount of work +local to me it's just a very complicated + + align:start position:0% +local to me it's just a very complicated + + + align:start position:0% +local to me it's just a very complicated +local setup + + align:start position:0% +local setup + + + align:start position:0% +local setup +okay but that's what i mean by + + align:start position:0% +okay but that's what i mean by + + + align:start position:0% +okay but that's what i mean by +simple when we're designing subproblems + + align:start position:0% +simple when we're designing subproblems + + + align:start position:0% +simple when we're designing subproblems +this is one that we could + + align:start position:0% +this is one that we could + + + align:start position:0% +this is one that we could +i mean when we're designing problems for + + align:start position:0% +i mean when we're designing problems for + + + align:start position:0% +i mean when we're designing problems for +this dynamic programming setup + + align:start position:0% +this dynamic programming setup + + + align:start position:0% +this dynamic programming setup +it's one of the hardest + + align:start position:0% +it's one of the hardest + + + align:start position:0% +it's one of the hardest +from a it's one of the easiest from a + + align:start position:0% +from a it's one of the easiest from a + + + align:start position:0% +from a it's one of the easiest from a +conceptual standpoint + + align:start position:0% +conceptual standpoint + + + align:start position:0% +conceptual standpoint +but one of the hardest to actually + + align:start position:0% +but one of the hardest to actually + + + align:start position:0% +but one of the hardest to actually +implement okay + + align:start position:0% +implement okay + + + align:start position:0% +implement okay +so problem two this one's a longing + + align:start position:0% +so problem two this one's a longing + + + align:start position:0% +so problem two this one's a longing +okay a wealthy family alice bob and + + align:start position:0% +okay a wealthy family alice bob and + + + align:start position:0% +okay a wealthy family alice bob and +their young son charlie are sailing + + align:start position:0% +their young son charlie are sailing + + + align:start position:0% +their young son charlie are sailing +around the world + + align:start position:0% +around the world + + + align:start position:0% +around the world +when they encounter a massive storm + + align:start position:0% +when they encounter a massive storm + + + align:start position:0% +when they encounter a massive storm +charlie is thrown overboard + + align:start position:0% +charlie is thrown overboard + + + align:start position:0% +charlie is thrown overboard +presumed drowned okay this is very + + align:start position:0% +presumed drowned okay this is very + + + align:start position:0% +presumed drowned okay this is very +colorful language for these problem set + + align:start position:0% +colorful language for these problem set + + + align:start position:0% +colorful language for these problem set +writers + + align:start position:0% +writers + + + align:start position:0% +writers +twenty years later a man comes to alice + + align:start position:0% +twenty years later a man comes to alice + + + align:start position:0% +twenty years later a man comes to alice +and bob claiming to be charlie + + align:start position:0% +and bob claiming to be charlie + + + align:start position:0% +and bob claiming to be charlie +having maybe been marooned on an island + + align:start position:0% +having maybe been marooned on an island + + + align:start position:0% +having maybe been marooned on an island +for that long + + align:start position:0% +for that long + + + align:start position:0% +for that long +okay alice and bob are excited but + + align:start position:0% +okay alice and bob are excited but + + + align:start position:0% +okay alice and bob are excited but +skeptical and they order a dna matching + + align:start position:0% +skeptical and they order a dna matching + + + align:start position:0% +skeptical and they order a dna matching +test from the genetic + + align:start position:0% +test from the genetic + + + align:start position:0% +test from the genetic +testing company 46 and the + + align:start position:0% +testing company 46 and the + + + align:start position:0% +testing company 46 and the +uh given alice and sorry + + align:start position:0% +uh given alice and sorry + + + align:start position:0% +uh given alice and sorry +given three length n dna sequences + + align:start position:0% +given three length n dna sequences + + + align:start position:0% +given three length n dna sequences +basically strings of cgta or something + + align:start position:0% +basically strings of cgta or something + + + align:start position:0% +basically strings of cgta or something +like that + + align:start position:0% +like that + + + align:start position:0% +like that +from each of alice bob and charlie the + + align:start position:0% +from each of alice bob and charlie the + + + align:start position:0% +from each of alice bob and charlie the +testing center will determine + + align:start position:0% +testing center will determine + + + align:start position:0% +testing center will determine +three uh their answer accessory + + align:start position:0% +three uh their answer accessory + + + align:start position:0% +three uh their answer accessory +as follows if charlie's dna can be + + align:start position:0% +as follows if charlie's dna can be + + + align:start position:0% +as follows if charlie's dna can be +partitioned + + align:start position:0% +partitioned + + + align:start position:0% +partitioned +into two not necessarily contiguous + + align:start position:0% +into two not necessarily contiguous + + + align:start position:0% +into two not necessarily contiguous +subsequences of equal length + + align:start position:0% +subsequences of equal length + + + align:start position:0% +subsequences of equal length +so basically i take i can take the if i + + align:start position:0% +so basically i take i can take the if i + + + align:start position:0% +so basically i take i can take the if i +have + + align:start position:0% +have + + + align:start position:0% +have +n is a length five right or at length + + align:start position:0% +n is a length five right or at length + + + align:start position:0% +n is a length five right or at length +six it's better be even + + align:start position:0% +six it's better be even + + + align:start position:0% +six it's better be even +i need to find three characters in order + + align:start position:0% +i need to find three characters in order + + + align:start position:0% +i need to find three characters in order +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the other three characters + + align:start position:0% +the other three characters + + + align:start position:0% +the other three characters +must match to make some sub strings + + align:start position:0% +must match to make some sub strings + + + align:start position:0% +must match to make some sub strings +in some subsequences in alice and bob's + + align:start position:0% +in some subsequences in alice and bob's + + + align:start position:0% +in some subsequences in alice and bob's +dna + + align:start position:0% +dna + + + align:start position:0% +dna +okay so uh there's that's a little hard + + align:start position:0% +okay so uh there's that's a little hard + + + align:start position:0% +okay so uh there's that's a little hard +to parse so let's look at an example + + align:start position:0% +to parse so let's look at an example + + + align:start position:0% +to parse so let's look at an example +here + + align:start position:0% +here + + + align:start position:0% +here +for example alice's dna is aat + + align:start position:0% +for example alice's dna is aat + + + align:start position:0% +for example alice's dna is aat +bob's dna is ccgg + + align:start position:0% +bob's dna is ccgg + + + align:start position:0% +bob's dna is ccgg +if charlie's dna were c-a-t-g + + align:start position:0% +if charlie's dna were c-a-t-g + + + align:start position:0% +if charlie's dna were c-a-t-g +they'd be matched right because c g + + align:start position:0% +they'd be matched right because c g + + + align:start position:0% +they'd be matched right because c g +is a sub-sequence of charlie's dna and + + align:start position:0% +is a sub-sequence of charlie's dna and + + + align:start position:0% +is a sub-sequence of charlie's dna and +is a subsequence of bob's + + align:start position:0% +is a subsequence of bob's + + + align:start position:0% +is a subsequence of bob's +uh ba bob's dna + + align:start position:0% +uh ba bob's dna + + + align:start position:0% +uh ba bob's dna +and a t is a subsequence of charlie's + + align:start position:0% +and a t is a subsequence of charlie's + + + align:start position:0% +and a t is a subsequence of charlie's +dna + + align:start position:0% +dna + + + align:start position:0% +dna +and is also a subsequence of alice's dna + + align:start position:0% +and is also a subsequence of alice's dna + + + align:start position:0% +and is also a subsequence of alice's dna +and so we've partitioned them into two + + align:start position:0% +and so we've partitioned them into two + + + align:start position:0% +and so we've partitioned them into two +equal length subsequences these are not + + align:start position:0% +equal length subsequences these are not + + + align:start position:0% +equal length subsequences these are not +necessarily + + align:start position:0% +necessarily + + + align:start position:0% +necessarily +consecutive subsequences but just any + + align:start position:0% +consecutive subsequences but just any + + + align:start position:0% +consecutive subsequences but just any +subsequences + + align:start position:0% +subsequences + + + align:start position:0% +subsequences +such that uh + + align:start position:0% +such that uh + + + align:start position:0% +such that uh +that that uh they appear in alice and + + align:start position:0% +that that uh they appear in alice and + + + align:start position:0% +that that uh they appear in alice and +bob + + align:start position:0% +bob + + + align:start position:0% +bob +but if charlie would be found to be an + + align:start position:0% +but if charlie would be found to be an + + + align:start position:0% +but if charlie would be found to be an +imposter if his dna sequence were + + align:start position:0% +imposter if his dna sequence were + + + align:start position:0% +imposter if his dna sequence were +a g t c essentially it's easy to + + align:start position:0% +a g t c essentially it's easy to + + + align:start position:0% +a g t c essentially it's easy to +to realize that because g and c + + align:start position:0% +to realize that because g and c + + + align:start position:0% +to realize that because g and c +are swapped in terms of their ordering + + align:start position:0% +are swapped in terms of their ordering + + + align:start position:0% +are swapped in terms of their ordering +and g c the letters gc + + align:start position:0% +and g c the letters gc + + + align:start position:0% +and g c the letters gc +only appear in bob's dna and don't + + align:start position:0% +only appear in bob's dna and don't + + + align:start position:0% +only appear in bob's dna and don't +appear in that order + + align:start position:0% +appear in that order + + + align:start position:0% +appear in that order +right so it's easy to see that he's an + + align:start position:0% +right so it's easy to see that he's an + + + align:start position:0% +right so it's easy to see that he's an +imposter with these strings but you can + + align:start position:0% +imposter with these strings but you can + + + align:start position:0% +imposter with these strings but you can +imagine with longer strings this could + + align:start position:0% +imagine with longer strings this could + + + align:start position:0% +imagine with longer strings this could +be difficult to solve + + align:start position:0% +be difficult to solve + + + align:start position:0% +be difficult to solve +right so we want an n to the fourth time + + align:start position:0% +right so we want an n to the fourth time + + + align:start position:0% +right so we want an n to the fourth time +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +to determine whether charlie is a fraud + + align:start position:0% +to determine whether charlie is a fraud + + + align:start position:0% +to determine whether charlie is a fraud +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i actually shortened this last night + + align:start position:0% +so i actually shortened this last night + + + align:start position:0% +so i actually shortened this last night +this was like twice as long on the + + align:start position:0% +this was like twice as long on the + + + align:start position:0% +this was like twice as long on the +problem set so + + align:start position:0% +problem set so + + + align:start position:0% +problem set so +yeah anyway so how do we approach this + + align:start position:0% +yeah anyway so how do we approach this + + + align:start position:0% +yeah anyway so how do we approach this +problem yes + + align:start position:0% + + + + align:start position:0% + +no they don't have to be contiguous like + + align:start position:0% +no they don't have to be contiguous like + + + align:start position:0% +no they don't have to be contiguous like +in the example it would be matched if + + align:start position:0% +in the example it would be matched if + + + align:start position:0% +in the example it would be matched if +c and g is a subsequence not contiguous + + align:start position:0% +c and g is a subsequence not contiguous + + + align:start position:0% +c and g is a subsequence not contiguous +of c + + align:start position:0% +of c + + + align:start position:0% +of c +a t g yeah so that's an important part + + align:start position:0% +a t g yeah so that's an important part + + + align:start position:0% +a t g yeah so that's an important part +of this problem + + align:start position:0% +of this problem + + + align:start position:0% +of this problem +i'm just i'm not trying to figure out if + + align:start position:0% +i'm just i'm not trying to figure out if + + + align:start position:0% +i'm just i'm not trying to figure out if +there's + + align:start position:0% +there's + + + align:start position:0% +there's +basically there are only two sub + + align:start position:0% +basically there are only two sub + + + align:start position:0% +basically there are only two sub +contiguous subsequences of length 2n + + align:start position:0% +contiguous subsequences of length 2n + + + align:start position:0% +contiguous subsequences of length 2n +that this thing can be partitioned and i + + align:start position:0% +that this thing can be partitioned and i + + + align:start position:0% +that this thing can be partitioned and i +just look in the middle no + + align:start position:0% +just look in the middle no + + + align:start position:0% +just look in the middle no +we're looking for subsequences not sub + + align:start position:0% +we're looking for subsequences not sub + + + align:start position:0% +we're looking for subsequences not sub +strings + + align:start position:0% +strings + + + align:start position:0% +strings +so they kind of interleave like this in + + align:start position:0% +so they kind of interleave like this in + + + align:start position:0% +so they kind of interleave like this in +some way + + align:start position:0% +some way + + + align:start position:0% +some way +and there's actually a number of + + align:start position:0% +and there's actually a number of + + + align:start position:0% +and there's actually a number of +different ways i can partition that + + align:start position:0% +different ways i can partition that + + + align:start position:0% +different ways i can partition that +there's actually an exponential number + + align:start position:0% +there's actually an exponential number + + + align:start position:0% +there's actually an exponential number +of ways + + align:start position:0% +of ways + + + align:start position:0% +of ways +so that's a problem potentially yes is + + align:start position:0% +so that's a problem potentially yes is + + + align:start position:0% +so that's a problem potentially yes is +there a biological basis no there's no + + align:start position:0% +there a biological basis no there's no + + + align:start position:0% +there a biological basis no there's no +biological basis to this thing + + align:start position:0% +biological basis to this thing + + + align:start position:0% +biological basis to this thing +that i know of okay all right + + align:start position:0% +that i know of okay all right + + + align:start position:0% +that i know of okay all right +so how do we solve this problem + + align:start position:0% +so how do we solve this problem + + + align:start position:0% +so how do we solve this problem +what problem does this look like + + align:start position:0% + + + + align:start position:0% + +i mean it seems like string matching + + align:start position:0% +i mean it seems like string matching + + + align:start position:0% +i mean it seems like string matching +right so i might want to think it's + + align:start position:0% +right so i might want to think it's + + + align:start position:0% +right so i might want to think it's +something like longest common + + align:start position:0% +something like longest common + + + align:start position:0% +something like longest common +subsequence right + + align:start position:0% +subsequence right + + + align:start position:0% +subsequence right +but here i have three sequences instead + + align:start position:0% +but here i have three sequences instead + + + align:start position:0% +but here i have three sequences instead +of + + align:start position:0% +of + + + align:start position:0% +of +two sequences and we've got this other + + align:start position:0% +two sequences and we've got this other + + + align:start position:0% +two sequences and we've got this other +weird condition + + align:start position:0% +weird condition + + + align:start position:0% +weird condition +where we kind of need an exact partition + + align:start position:0% +where we kind of need an exact partition + + + align:start position:0% +where we kind of need an exact partition +of charlie + + align:start position:0% +of charlie + + + align:start position:0% +of charlie +right i need to use all of the letters + + align:start position:0% +right i need to use all of the letters + + + align:start position:0% +right i need to use all of the letters +in charlie but i don't have to use all + + align:start position:0% +in charlie but i don't have to use all + + + align:start position:0% +in charlie but i don't have to use all +of the letters in + + align:start position:0% +of the letters in + + + align:start position:0% +of the letters in +alice and bob right so let's just let's + + align:start position:0% +alice and bob right so let's just let's + + + align:start position:0% +alice and bob right so let's just let's +get some notation here + + align:start position:0% +get some notation here + + + align:start position:0% +get some notation here +you know a b and c are + + align:start position:0% +you know a b and c are + + + align:start position:0% +you know a b and c are +n length + + align:start position:0% +n length + + + align:start position:0% +n length +strings right so what could i do + + align:start position:0% +strings right so what could i do + + + align:start position:0% +strings right so what could i do +let's define some sub sub problems + + align:start position:0% +let's define some sub sub problems + + + align:start position:0% +let's define some sub sub problems +if i were to + + align:start position:0% + + + + align:start position:0% + +go via longest common subsequence + + align:start position:0% +go via longest common subsequence + + + align:start position:0% +go via longest common subsequence +i might keep track of an index of a + + align:start position:0% +i might keep track of an index of a + + + align:start position:0% +i might keep track of an index of a +suffix or prefix + + align:start position:0% +suffix or prefix + + + align:start position:0% +suffix or prefix +of each one of these strings right that + + align:start position:0% +of each one of these strings right that + + + align:start position:0% +of each one of these strings right that +kind of makes sense + + align:start position:0% +kind of makes sense + + + align:start position:0% +kind of makes sense +something like i j + + align:start position:0% +something like i j + + + align:start position:0% +something like i j +k where we're talking about the + + align:start position:0% +k where we're talking about the + + + align:start position:0% +k where we're talking about the +suffixes uh sorry + + align:start position:0% +suffixes uh sorry + + + align:start position:0% +suffixes uh sorry +that's prefixes i + + align:start position:0% +that's prefixes i + + + align:start position:0% +that's prefixes i +b j and + + align:start position:0% +b j and + + + align:start position:0% +b j and +c k right + + align:start position:0% +c k right + + + align:start position:0% +c k right +that seems reasonable at least right + + align:start position:0% +that seems reasonable at least right + + + align:start position:0% +that seems reasonable at least right +it's it's what we would do + + align:start position:0% +it's it's what we would do + + + align:start position:0% +it's it's what we would do +for longest common subsequence + + align:start position:0% + + + + align:start position:0% + +what's the problem here i mean + + align:start position:0% +what's the problem here i mean + + + align:start position:0% +what's the problem here i mean +i could match this guy with one of these + + align:start position:0% +i could match this guy with one of these + + + align:start position:0% +i could match this guy with one of these +guys + + align:start position:0% +guys + + + align:start position:0% +guys +or decide to skip it and match one of + + align:start position:0% +or decide to skip it and match one of + + + align:start position:0% +or decide to skip it and match one of +these guys and decide to skip + + align:start position:0% +these guys and decide to skip + + + align:start position:0% +these guys and decide to skip +it but if i do that + + align:start position:0% +it but if i do that + + + align:start position:0% +it but if i do that +i might get a subsequence + + align:start position:0% + + + + align:start position:0% + +but actually i always need to match all + + align:start position:0% +but actually i always need to match all + + + align:start position:0% +but actually i always need to match all +of c + + align:start position:0% + + + + align:start position:0% + +does that make sense always need to + + align:start position:0% +does that make sense always need to + + + align:start position:0% +does that make sense always need to +match + + align:start position:0% +match + + + align:start position:0% +match +all of c right + + align:start position:0% +all of c right + + + align:start position:0% +all of c right +so in a sense + + align:start position:0% +so in a sense + + + align:start position:0% +so in a sense +let's see let's see how can i do this uh + + align:start position:0% +let's see let's see how can i do this uh + + + align:start position:0% +let's see let's see how can i do this uh +i need to match all of c but i also need + + align:start position:0% +i need to match all of c but i also need + + + align:start position:0% +i need to match all of c but i also need +to make sure i'm using exactly n over + + align:start position:0% +to make sure i'm using exactly n over + + + align:start position:0% +to make sure i'm using exactly n over +two characters + + align:start position:0% +two characters + + + align:start position:0% +two characters +from c in blue and exactly n over two + + align:start position:0% +from c in blue and exactly n over two + + + align:start position:0% +from c in blue and exactly n over two +characters + + align:start position:0% +characters + + + align:start position:0% +characters +from c in a + + align:start position:0% +from c in a + + + align:start position:0% +from c in a +does that make sense how can i + + align:start position:0% +does that make sense how can i + + + align:start position:0% +does that make sense how can i +satisfy that condition now i understand + + align:start position:0% +satisfy that condition now i understand + + + align:start position:0% +satisfy that condition now i understand +why i used prefixes before + + align:start position:0% +why i used prefixes before + + + align:start position:0% +why i used prefixes before +and i swapped it to suffixes here + + align:start position:0% + + + + align:start position:0% + +but we'll make it work how can i + + align:start position:0% +but we'll make it work how can i + + + align:start position:0% +but we'll make it work how can i +remember + + align:start position:0% +remember + + + align:start position:0% +remember +how many characters i assigned from + + align:start position:0% +how many characters i assigned from + + + align:start position:0% +how many characters i assigned from +alice versus bob right as i'm + + align:start position:0% +alice versus bob right as i'm + + + align:start position:0% +alice versus bob right as i'm +matching characters in alice and bob + + align:start position:0% + + + + align:start position:0% + +i need to kind of remember where they + + align:start position:0% +i need to kind of remember where they + + + align:start position:0% +i need to kind of remember where they +point to + + align:start position:0% +point to + + + align:start position:0% +point to +or how many i've already used in in + + align:start position:0% +or how many i've already used in in + + + align:start position:0% +or how many i've already used in in +charlie so that i can give you up the + + align:start position:0% +charlie so that i can give you up the + + + align:start position:0% +charlie so that i can give you up the +remainder + + align:start position:0% +remainder + + + align:start position:0% +remainder +right in here oh actually this + + align:start position:0% +right in here oh actually this + + + align:start position:0% +right in here oh actually this +works in a different sense + + align:start position:0% +works in a different sense + + + align:start position:0% +works in a different sense +there's like 18 different ways we could + + align:start position:0% +there's like 18 different ways we could + + + align:start position:0% +there's like 18 different ways we could +do this so + + align:start position:0% +do this so + + + align:start position:0% +do this so +okay so i need to remember + + align:start position:0% +okay so i need to remember + + + align:start position:0% +okay so i need to remember +how many i've already used up so that i + + align:start position:0% +how many i've already used up so that i + + + align:start position:0% +how many i've already used up so that i +can be sure to allocate exactly that + + align:start position:0% +can be sure to allocate exactly that + + + align:start position:0% +can be sure to allocate exactly that +many characters in the future + + align:start position:0% +many characters in the future + + + align:start position:0% +many characters in the future +to either alice or bob right + + align:start position:0% +to either alice or bob right + + + align:start position:0% +to either alice or bob right +so how can i remember that + + align:start position:0% + + + + align:start position:0% + +i can just remember how many do i + + align:start position:0% + + + + align:start position:0% + +i'll do it the way that i did it before + + align:start position:0% +i'll do it the way that i did it before + + + align:start position:0% +i'll do it the way that i did it before +which is i can remember i can remember + + align:start position:0% +which is i can remember i can remember + + + align:start position:0% +which is i can remember i can remember +two different things here + + align:start position:0% +two different things here + + + align:start position:0% +two different things here +i can remember how many things i have + + align:start position:0% +i can remember how many things i have + + + align:start position:0% +i can remember how many things i have +left to match in alice + + align:start position:0% +left to match in alice + + + align:start position:0% +left to match in alice +in c where i can remember how many + + align:start position:0% +in c where i can remember how many + + + align:start position:0% +in c where i can remember how many +things i've + + align:start position:0% +things i've + + + align:start position:0% +things i've +already matched nc to alice + + align:start position:0% +already matched nc to alice + + + align:start position:0% +already matched nc to alice +okay if i talk about how many things + + align:start position:0% +okay if i talk about how many things + + + align:start position:0% +okay if i talk about how many things +i've + + align:start position:0% +i've + + + align:start position:0% +i've +already matched then i can index this + + align:start position:0% +already matched then i can index this + + + align:start position:0% +already matched then i can index this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +by the sum of those things if i talk + + align:start position:0% +by the sum of those things if i talk + + + align:start position:0% +by the sum of those things if i talk +about + + align:start position:0% +about + + + align:start position:0% +about +how many things i have yet to match i + + align:start position:0% +how many things i have yet to match i + + + align:start position:0% +how many things i have yet to match i +have to do like n + + align:start position:0% +have to do like n + + + align:start position:0% +have to do like n +minus the things okay + + align:start position:0% +minus the things okay + + + align:start position:0% +minus the things okay +so those are the different parameters we + + align:start position:0% +so those are the different parameters we + + + align:start position:0% +so those are the different parameters we +can do + + align:start position:0% +can do + + + align:start position:0% +can do +we'll do what's in my notes and i'll try + + align:start position:0% +we'll do what's in my notes and i'll try + + + align:start position:0% +we'll do what's in my notes and i'll try +to fix it + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +what we're going to do is remember or + + align:start position:0% +what we're going to do is remember or + + + align:start position:0% +what we're going to do is remember or +figure out how many things i'm still + + align:start position:0% +figure out how many things i'm still + + + align:start position:0% +figure out how many things i'm still +needing to match + + align:start position:0% +needing to match + + + align:start position:0% +needing to match +in c to alice and bob right so i'm going + + align:start position:0% +in c to alice and bob right so i'm going + + + align:start position:0% +in c to alice and bob right so i'm going +to call this + + align:start position:0% +to call this + + + align:start position:0% +to call this +k sorry + + align:start position:0% +k sorry + + + align:start position:0% +k sorry +k i i is associated with a + + align:start position:0% +k i i is associated with a + + + align:start position:0% +k i i is associated with a +and b is associated with j + + align:start position:0% +and b is associated with j + + + align:start position:0% +and b is associated with j +and k j + + align:start position:0% +and k j + + + align:start position:0% +and k j +okay this is going to be + + align:start position:0% +okay this is going to be + + + align:start position:0% +okay this is going to be +the + + align:start position:0% + + + + align:start position:0% + +i have to write this down well okay so + + align:start position:0% +i have to write this down well okay so + + + align:start position:0% +i have to write this down well okay so +this is going to be + + align:start position:0% +this is going to be + + + align:start position:0% +this is going to be +what kind of output do i want to my sub + + align:start position:0% +what kind of output do i want to my sub + + + align:start position:0% +what kind of output do i want to my sub +problem i just want to know if these + + align:start position:0% +problem i just want to know if these + + + align:start position:0% +problem i just want to know if these +things are + + align:start position:0% +things are + + + align:start position:0% +things are +if he's a fraud or not so this is going + + align:start position:0% +if he's a fraud or not so this is going + + + align:start position:0% +if he's a fraud or not so this is going +to be a boolean + + align:start position:0% +to be a boolean + + + align:start position:0% +to be a boolean +right so true if + + align:start position:0% +right so true if + + + align:start position:0% +right so true if +can match + + align:start position:0% +can match + + + align:start position:0% +can match +k i + + align:start position:0% + + + + align:start position:0% + +length + + align:start position:0% + + + + align:start position:0% + +sub sequence of + + align:start position:0% + + + + align:start position:0% + +suffix + + align:start position:0% + + + + align:start position:0% + +a suffix is this guy + + align:start position:0% + + + + align:start position:0% + +and length + + align:start position:0% + + + + align:start position:0% + +uh kj i guess + + align:start position:0% +uh kj i guess + + + align:start position:0% +uh kj i guess +kj length subsequence + + align:start position:0% +kj length subsequence + + + align:start position:0% +kj length subsequence +of suffix + + align:start position:0% +of suffix + + + align:start position:0% +of suffix +b j i + + align:start position:0% +b j i + + + align:start position:0% +b j i +or bj suffix right + + align:start position:0% +or bj suffix right + + + align:start position:0% +or bj suffix right +uh to + + align:start position:0% +uh to + + + align:start position:0% +uh to +all characters + + align:start position:0% +all characters + + + align:start position:0% +all characters +in and now what is this in this is the + + align:start position:0% +in and now what is this in this is the + + + align:start position:0% +in and now what is this in this is the +hard part + + align:start position:0% +hard part + + + align:start position:0% +hard part +do i need a separate index + + align:start position:0% +do i need a separate index + + + align:start position:0% +do i need a separate index +for c to know where i am and see + + align:start position:0% + + + + align:start position:0% + +in a sense yes i need to know where i am + + align:start position:0% +in a sense yes i need to know where i am + + + align:start position:0% +in a sense yes i need to know where i am +in c + + align:start position:0% +in c + + + align:start position:0% +in c +how much i have to match right but if i + + align:start position:0% +how much i have to match right but if i + + + align:start position:0% +how much i have to match right but if i +need to match + + align:start position:0% +need to match + + + align:start position:0% +need to match +k i to kj to all of them + + align:start position:0% +k i to kj to all of them + + + align:start position:0% +k i to kj to all of them +then there better be ki plus j things + + align:start position:0% +then there better be ki plus j things + + + align:start position:0% +then there better be ki plus j things +left in + + align:start position:0% +left in + + + align:start position:0% +left in +c right so i in a sense i don't need to + + align:start position:0% +c right so i in a sense i don't need to + + + align:start position:0% +c right so i in a sense i don't need to +remember that information again + + align:start position:0% +remember that information again + + + align:start position:0% +remember that information again +it's not independent to my other + + align:start position:0% +it's not independent to my other + + + align:start position:0% +it's not independent to my other +parameters i can compute it + + align:start position:0% +parameters i can compute it + + + align:start position:0% +parameters i can compute it +right i can throw it in but i can + + align:start position:0% +right i can throw it in but i can + + + align:start position:0% +right i can throw it in but i can +determine it from the other parameters + + align:start position:0% +determine it from the other parameters + + + align:start position:0% +determine it from the other parameters +right so i want to match it with the + + align:start position:0% +right so i want to match it with the + + + align:start position:0% +right so i want to match it with the +suffix + + align:start position:0% +suffix + + + align:start position:0% +suffix +of c of length k i plus k + + align:start position:0% +of c of length k i plus k + + + align:start position:0% +of c of length k i plus k +j so i think this is the only part that + + align:start position:0% +j so i think this is the only part that + + + align:start position:0% +j so i think this is the only part that +is going to be annoying to me okay + + align:start position:0% +is going to be annoying to me okay + + + align:start position:0% +is going to be annoying to me okay +so this should be suffix + + align:start position:0% + + + + align:start position:0% + +of all of the things + + align:start position:0% + + + + align:start position:0% + +minus k i minus kj + + align:start position:0% +minus k i minus kj + + + align:start position:0% +minus k i minus kj +minus 1. + + align:start position:0% +minus 1. + + + align:start position:0% +minus 1. +it's just this and why is that + + align:start position:0% +it's just this and why is that + + + align:start position:0% +it's just this and why is that +okay if i've matched everything + + align:start position:0% +okay if i've matched everything + + + align:start position:0% +okay if i've matched everything +k i and kj are both zero + + align:start position:0% +k i and kj are both zero + + + align:start position:0% +k i and kj are both zero +and i should have nothing in c which + + align:start position:0% +and i should have nothing in c which + + + align:start position:0% +and i should have nothing in c which +should be + + align:start position:0% +should be + + + align:start position:0% +should be +n colon okay + + align:start position:0% +n colon okay + + + align:start position:0% +n colon okay +we're zero index yes we are i use + + align:start position:0% +we're zero index yes we are i use + + + align:start position:0% +we're zero index yes we are i use +whenever i use python notation + + align:start position:0% +whenever i use python notation + + + align:start position:0% +whenever i use python notation +i better be zero index okay + + align:start position:0% +i better be zero index okay + + + align:start position:0% +i better be zero index okay +does this make sense as a sub problem i + + align:start position:0% +does this make sense as a sub problem i + + + align:start position:0% +does this make sense as a sub problem i +mean it's confusing + + align:start position:0% +mean it's confusing + + + align:start position:0% +mean it's confusing +but hopefully it makes sense right what + + align:start position:0% +but hopefully it makes sense right what + + + align:start position:0% +but hopefully it makes sense right what +i'm going to try to do is i'm going to + + align:start position:0% +i'm going to try to do is i'm going to + + + align:start position:0% +i'm going to try to do is i'm going to +match + + align:start position:0% +match + + + align:start position:0% +match +some number of characters in this subfix + + align:start position:0% +some number of characters in this subfix + + + align:start position:0% +some number of characters in this subfix +which is + + align:start position:0% +which is + + + align:start position:0% +which is +hopefully longer than kj ki right + + align:start position:0% +hopefully longer than kj ki right + + + align:start position:0% +hopefully longer than kj ki right +otherwise it's i'm going to be in a base + + align:start position:0% +otherwise it's i'm going to be in a base + + + align:start position:0% +otherwise it's i'm going to be in a base +case where this is impossible + + align:start position:0% +case where this is impossible + + + align:start position:0% +case where this is impossible +right and some subsequence of this + + align:start position:0% +right and some subsequence of this + + + align:start position:0% +right and some subsequence of this +matched completely into this all right + + align:start position:0% +matched completely into this all right + + + align:start position:0% +matched completely into this all right +so that's + + align:start position:0% + + + + align:start position:0% + +those are my sub problems i'm going to + + align:start position:0% +those are my sub problems i'm going to + + + align:start position:0% +those are my sub problems i'm going to +try to relate them + + align:start position:0% +try to relate them + + + align:start position:0% +try to relate them +now we have x + + align:start position:0% +now we have x + + + align:start position:0% +now we have x +i j + + align:start position:0% +i j + + + align:start position:0% +i j +k i k j + + align:start position:0% +k i k j + + + align:start position:0% +k i k j +what is this going to equal all right + + align:start position:0% +what is this going to equal all right + + + align:start position:0% +what is this going to equal all right +well we've got booleans so this is + + align:start position:0% +well we've got booleans so this is + + + align:start position:0% +well we've got booleans so this is +and false + + align:start position:0% +and false + + + align:start position:0% +and false +otherwise okay that's it's a problem + + align:start position:0% +otherwise okay that's it's a problem + + + align:start position:0% +otherwise okay that's it's a problem +right + + align:start position:0% +right + + + align:start position:0% +right +so i just need some sub problem i + + align:start position:0% +so i just need some sub problem i + + + align:start position:0% +so i just need some sub problem i +recurse on to be true + + align:start position:0% +recurse on to be true + + + align:start position:0% +recurse on to be true +so what's the combinator for sum + + align:start position:0% +so what's the combinator for sum + + + align:start position:0% +so what's the combinator for sum +of a bunch of choices boolean cases + + align:start position:0% +of a bunch of choices boolean cases + + + align:start position:0% +of a bunch of choices boolean cases +any one of which may be true + + align:start position:0% + + + + align:start position:0% + +i want to combine a bunch of them i just + + align:start position:0% +i want to combine a bunch of them i just + + + align:start position:0% +i want to combine a bunch of them i just +want to see if any of them are true + + align:start position:0% +want to see if any of them are true + + + align:start position:0% +want to see if any of them are true +i'm going to or over them okay + + align:start position:0% +i'm going to or over them okay + + + align:start position:0% +i'm going to or over them okay +and i'm going to or over four choices + + align:start position:0% +and i'm going to or over four choices + + + align:start position:0% +and i'm going to or over four choices +okay what are my choices + + align:start position:0% +okay what are my choices + + + align:start position:0% +okay what are my choices +either the the first thing in a + + align:start position:0% +either the the first thing in a + + + align:start position:0% +either the the first thing in a +matches with c the first thing in b + + align:start position:0% +matches with c the first thing in b + + + align:start position:0% +matches with c the first thing in b +matches with c or i don't match with + + align:start position:0% +matches with c or i don't match with + + + align:start position:0% +matches with c or i don't match with +either + + align:start position:0% +either + + + align:start position:0% +either +right so those are my four tropes + + align:start position:0% +right so those are my four tropes + + + align:start position:0% +right so those are my four tropes +so if i match with a + + align:start position:0% +so if i match with a + + + align:start position:0% +so if i match with a +i plus one i recurse on a smaller suffix + + align:start position:0% +i plus one i recurse on a smaller suffix + + + align:start position:0% +i plus one i recurse on a smaller suffix +of a + + align:start position:0% +of a + + + align:start position:0% +of a +and a + + align:start position:0% +and a + + + align:start position:0% +and a +by adding oh this all just works great + + align:start position:0% +by adding oh this all just works great + + + align:start position:0% +by adding oh this all just works great +kj this is i + + align:start position:0% + + + + align:start position:0% + +if a i + + align:start position:0% +if a i + + + align:start position:0% +if a i +equals c i + + align:start position:0% + + + + align:start position:0% + +and a i + + align:start position:0% +and a i + + + align:start position:0% +and a i +is greater than zero right so if + + align:start position:0% +is greater than zero right so if + + + align:start position:0% +is greater than zero right so if +k i is greater than zero i need to match + + align:start position:0% +k i is greater than zero i need to match + + + align:start position:0% +k i is greater than zero i need to match +an i + + align:start position:0% +an i + + + align:start position:0% +an i +right so this this conditional doesn't + + align:start position:0% +right so this this conditional doesn't + + + align:start position:0% +right so this this conditional doesn't +even make sense + + align:start position:0% +even make sense + + + align:start position:0% +even make sense +unless i've evaluated this k i to be + + align:start position:0% +unless i've evaluated this k i to be + + + align:start position:0% +unless i've evaluated this k i to be +bigger than zero otherwise i'm trying to + + align:start position:0% +bigger than zero otherwise i'm trying to + + + align:start position:0% +bigger than zero otherwise i'm trying to +access i + + align:start position:0% +access i + + + align:start position:0% +access i +of n right so i'm just putting this + + align:start position:0% +of n right so i'm just putting this + + + align:start position:0% +of n right so i'm just putting this +conditional on there + + align:start position:0% +conditional on there + + + align:start position:0% +conditional on there +same with matching b i + + align:start position:0% +same with matching b i + + + align:start position:0% +same with matching b i +j plus one k i + + align:start position:0% +j plus one k i + + + align:start position:0% +j plus one k i +k j plus one + + align:start position:0% +k j plus one + + + align:start position:0% +k j plus one +if sorry this should be minus + + align:start position:0% +if sorry this should be minus + + + align:start position:0% +if sorry this should be minus +one i'm i have fewer characters that i + + align:start position:0% +one i'm i have fewer characters that i + + + align:start position:0% +one i'm i have fewer characters that i +have to + + align:start position:0% +have to + + + align:start position:0% +have to +recurse on so that's a typo in my notes + + align:start position:0% +recurse on so that's a typo in my notes + + + align:start position:0% +recurse on so that's a typo in my notes +uh b + + align:start position:0% +uh b + + + align:start position:0% +uh b +j equals c + + align:start position:0% +j equals c + + + align:start position:0% +j equals c +oh this is not ci what is this it's + + align:start position:0% +oh this is not ci what is this it's + + + align:start position:0% +oh this is not ci what is this it's +whatever that thing is + + align:start position:0% +whatever that thing is + + + align:start position:0% +whatever that thing is +so i'm going to just say question mark + + align:start position:0% + + + + align:start position:0% + +and kj is greater than 0. + + align:start position:0% +and kj is greater than 0. + + + align:start position:0% +and kj is greater than 0. +so i'll fill that in in the notes it's + + align:start position:0% +so i'll fill that in in the notes it's + + + align:start position:0% +so i'll fill that in in the notes it's +going to be some complicated expression + + align:start position:0% +going to be some complicated expression + + + align:start position:0% +going to be some complicated expression +that looks like that + + align:start position:0% +that looks like that + + + align:start position:0% +that looks like that +okay it's exactly that expression + + align:start position:0% +okay it's exactly that expression + + + align:start position:0% +okay it's exactly that expression +yes that it is so it's it's that thing + + align:start position:0% + + + + align:start position:0% + +okay then + + align:start position:0% +okay then + + + align:start position:0% +okay then +we have two more choices either i + + align:start position:0% +we have two more choices either i + + + align:start position:0% +we have two more choices either i +if i if i didn't match a i + + align:start position:0% + + + + align:start position:0% + +i may match bj in the future so i only + + align:start position:0% +i may match bj in the future so i only + + + align:start position:0% +i may match bj in the future so i only +want to + + align:start position:0% +want to + + + align:start position:0% +want to +reduce ai so x i + + align:start position:0% +reduce ai so x i + + + align:start position:0% +reduce ai so x i +plus 1 i leave everything else the same + + align:start position:0% + + + + align:start position:0% + +assuming if i + + align:start position:0% +assuming if i + + + align:start position:0% +assuming if i +less than n right i don't want to + + align:start position:0% +less than n right i don't want to + + + align:start position:0% +less than n right i don't want to +move off the end of this thing or + + align:start position:0% +move off the end of this thing or + + + align:start position:0% +move off the end of this thing or +x i j plus 1 + + align:start position:0% +x i j plus 1 + + + align:start position:0% +x i j plus 1 +k i kj + + align:start position:0% +k i kj + + + align:start position:0% +k i kj +if j is less than n + + align:start position:0% +if j is less than n + + + align:start position:0% +if j is less than n +okay so those are my four choices if i + + align:start position:0% +okay so those are my four choices if i + + + align:start position:0% +okay so those are my four choices if i +match the letter i'm great + + align:start position:0% +match the letter i'm great + + + align:start position:0% +match the letter i'm great +otherwise i decrease the size of my sub + + align:start position:0% +otherwise i decrease the size of my sub + + + align:start position:0% +otherwise i decrease the size of my sub +problem and i recurse + + align:start position:0% +problem and i recurse + + + align:start position:0% +problem and i recurse +okay + + align:start position:0% + + + + align:start position:0% + +so fun recursion topological sort right + + align:start position:0% +so fun recursion topological sort right + + + align:start position:0% +so fun recursion topological sort right +these subproblems only + + align:start position:0% +these subproblems only + + + align:start position:0% +these subproblems only +depend on + + align:start position:0% +depend on + + + align:start position:0% +depend on +what larger i + + align:start position:0% +what larger i + + + align:start position:0% +what larger i +not quite larger j + + align:start position:0% +not quite larger j + + + align:start position:0% +not quite larger j +not quite changing + + align:start position:0% +not quite changing + + + align:start position:0% +not quite changing +k or d don't even change here + + align:start position:0% +k or d don't even change here + + + align:start position:0% +k or d don't even change here +so we're going to use depend on larger + + align:start position:0% +so we're going to use depend on larger + + + align:start position:0% +so we're going to use depend on larger +i guess strictly + + align:start position:0% +i guess strictly + + + align:start position:0% +i guess strictly +that's kind of an important thing i plus + + align:start position:0% +that's kind of an important thing i plus + + + align:start position:0% +that's kind of an important thing i plus +j + + align:start position:0% +j + + + align:start position:0% +j +right because at least one of these two + + align:start position:0% +right because at least one of these two + + + align:start position:0% +right because at least one of these two +things is increasing + + align:start position:0% +things is increasing + + + align:start position:0% +things is increasing +and then the nice thing about that is it + + align:start position:0% +and then the nice thing about that is it + + + align:start position:0% +and then the nice thing about that is it +kind of tells us when we should stop + + align:start position:0% +kind of tells us when we should stop + + + align:start position:0% +kind of tells us when we should stop +right we should stop when either i + + align:start position:0% +right we should stop when either i + + + align:start position:0% +right we should stop when either i +or j get to n we should know + + align:start position:0% +or j get to n we should know + + + align:start position:0% +or j get to n we should know +enough at that point to be able to + + align:start position:0% +enough at that point to be able to + + + align:start position:0% +enough at that point to be able to +determine + + align:start position:0% +determine + + + align:start position:0% +determine +if we succeeded or not possible + + align:start position:0% +if we succeeded or not possible + + + align:start position:0% +if we succeeded or not possible +so we have our base case + + align:start position:0% + + + + align:start position:0% + +what's the easy base case when + + align:start position:0% +what's the easy base case when + + + align:start position:0% +what's the easy base case when +we succeeded when have we succeeded + + align:start position:0% +we succeeded when have we succeeded + + + align:start position:0% +we succeeded when have we succeeded +if we have nothing left in a and b + + align:start position:0% +if we have nothing left in a and b + + + align:start position:0% +if we have nothing left in a and b +and we have nothing left in c right i + + align:start position:0% +and we have nothing left in c right i + + + align:start position:0% +and we have nothing left in c right i +have nothing left to match so i have + + align:start position:0% +have nothing left to match so i have + + + align:start position:0% +have nothing left to match so i have +n n and i don't need to match anything + + align:start position:0% +n n and i don't need to match anything + + + align:start position:0% +n n and i don't need to match anything +else + + align:start position:0% +else + + + align:start position:0% +else +that's just going to be true right + + align:start position:0% +that's just going to be true right + + + align:start position:0% +that's just going to be true right +all roads point to this sub problem + + align:start position:0% +all roads point to this sub problem + + + align:start position:0% +all roads point to this sub problem +to get to a true solution right + + align:start position:0% +to get to a true solution right + + + align:start position:0% +to get to a true solution right +otherwise we have some false space cases + + align:start position:0% +otherwise we have some false space cases + + + align:start position:0% +otherwise we have some false space cases +if you set us as + + align:start position:0% +if you set us as + + + align:start position:0% +if you set us as +something up like this and you only give + + align:start position:0% +something up like this and you only give + + + align:start position:0% +something up like this and you only give +us a base case that's true + + align:start position:0% +us a base case that's true + + + align:start position:0% +us a base case that's true +and you're oring over the things your + + align:start position:0% +and you're oring over the things your + + + align:start position:0% +and you're oring over the things your +answer will always be true so you're not + + align:start position:0% +answer will always be true so you're not + + + align:start position:0% +answer will always be true so you're not +having any discriminatory power at all + + align:start position:0% +having any discriminatory power at all + + + align:start position:0% +having any discriminatory power at all +if you give us a + + align:start position:0% +if you give us a + + + align:start position:0% +if you give us a +true base case you better be giving us + + align:start position:0% +true base case you better be giving us + + + align:start position:0% +true base case you better be giving us +some false base cases + + align:start position:0% +some false base cases + + + align:start position:0% +some false base cases +or one at least so in the case where + + align:start position:0% +or one at least so in the case where + + + align:start position:0% +or one at least so in the case where +the first one is n + + align:start position:0% +the first one is n + + + align:start position:0% +the first one is n +and we have some i kj + + align:start position:0% + + + + align:start position:0% + +this is going to be false if + + align:start position:0% +this is going to be false if + + + align:start position:0% +this is going to be false if +what + + align:start position:0% + + + + align:start position:0% + +if we have nothing left in a i + + align:start position:0% +if we have nothing left in a i + + + align:start position:0% +if we have nothing left in a i +or i o but + + align:start position:0% +or i o but + + + align:start position:0% +or i o but +this guy is positive we got problems + + align:start position:0% +this guy is positive we got problems + + + align:start position:0% +this guy is positive we got problems +right otherwise this thing is zero + + align:start position:0% +right otherwise this thing is zero + + + align:start position:0% +right otherwise this thing is zero +and we'll just try to match everything + + align:start position:0% +and we'll just try to match everything + + + align:start position:0% +and we'll just try to match everything +up here and eventually + + align:start position:0% +up here and eventually + + + align:start position:0% +up here and eventually +we'll get down to this base case or + + align:start position:0% +we'll get down to this base case or + + + align:start position:0% +we'll get down to this base case or +something where + + align:start position:0% +something where + + + align:start position:0% +something where +this thing goes to zero and we've got a + + align:start position:0% +this thing goes to zero and we've got a + + + align:start position:0% +this thing goes to zero and we've got a +problem + + align:start position:0% + + + + align:start position:0% + +it's the same goes for the other side as + + align:start position:0% +it's the same goes for the other side as + + + align:start position:0% +it's the same goes for the other side as +well if we run out of things + + align:start position:0% +well if we run out of things + + + align:start position:0% +well if we run out of things +in b + + align:start position:0% + + + + align:start position:0% + +when the number of things we need to + + align:start position:0% +when the number of things we need to + + + align:start position:0% +when the number of things we need to +match in b is greater than zero okay so + + align:start position:0% +match in b is greater than zero okay so + + + align:start position:0% +match in b is greater than zero okay so +those are our base cases + + align:start position:0% +those are our base cases + + + align:start position:0% +those are our base cases +the original problem is what + + align:start position:0% + + + + align:start position:0% + +yeah it's just gonna be one of our sub + + align:start position:0% +yeah it's just gonna be one of our sub + + + align:start position:0% +yeah it's just gonna be one of our sub +problems n n + + align:start position:0% +problems n n + + + align:start position:0% +problems n n +and then n over two and n over two right + + align:start position:0% +and then n over two and n over two right + + + align:start position:0% +and then n over two and n over two right +i'm trying to match + + align:start position:0% +i'm trying to match + + + align:start position:0% +i'm trying to match +half of the things in c with half of the + + align:start position:0% +half of the things in c with half of the + + + align:start position:0% +half of the things in c with half of the +things + + align:start position:0% +things + + + align:start position:0% +things +right + + align:start position:0% + + + + align:start position:0% + +zero thank you uh + + align:start position:0% +zero thank you uh + + + align:start position:0% +zero thank you uh +because we're zero index yes again + + align:start position:0% +because we're zero index yes again + + + align:start position:0% +because we're zero index yes again +that's + + align:start position:0% +that's + + + align:start position:0% +that's +switching from prefix suffixes in the + + align:start position:0% +switching from prefix suffixes in the + + + align:start position:0% +switching from prefix suffixes in the +middle was fun so anyway + + align:start position:0% +middle was fun so anyway + + + align:start position:0% +middle was fun so anyway +and it better be the case that n is two + + align:start position:0% +and it better be the case that n is two + + + align:start position:0% +and it better be the case that n is two +or else it's obviously false or it is + + align:start position:0% +or else it's obviously false or it is + + + align:start position:0% +or else it's obviously false or it is +even + + align:start position:0% +even + + + align:start position:0% +even +or else this is obviously false okay + + align:start position:0% + + + + align:start position:0% + +and then the last thing which i'm not + + align:start position:0% +and then the last thing which i'm not + + + align:start position:0% +and then the last thing which i'm not +going to write down + + align:start position:0% +going to write down + + + align:start position:0% +going to write down +is we have a constant work here + + align:start position:0% +is we have a constant work here + + + align:start position:0% +is we have a constant work here +right because i'm just checking the + + align:start position:0% +right because i'm just checking the + + + align:start position:0% +right because i'm just checking the +value of + + align:start position:0% +value of + + + align:start position:0% +value of +four sub-problems and a conditional for + + align:start position:0% +four sub-problems and a conditional for + + + align:start position:0% +four sub-problems and a conditional for +each + + align:start position:0% +each + + + align:start position:0% +each +and i have how many sub problems i loops + + align:start position:0% +and i have how many sub problems i loops + + + align:start position:0% +and i have how many sub problems i loops +over n + + align:start position:0% +over n + + + align:start position:0% +over n +j loops over n k and k j loop over n + + align:start position:0% +j loops over n k and k j loop over n + + + align:start position:0% +j loops over n k and k j loop over n +over two + + align:start position:0% +over two + + + align:start position:0% +over two +so i get a quartic number of sub + + align:start position:0% +so i get a quartic number of sub + + + align:start position:0% +so i get a quartic number of sub +problems + + align:start position:0% +problems + + + align:start position:0% +problems +cortic running time as desired okay so + + align:start position:0% +cortic running time as desired okay so + + + align:start position:0% +cortic running time as desired okay so +i'm not going to write that down + + align:start position:0% +i'm not going to write that down + + + align:start position:0% +i'm not going to write that down +because i'm quite a bit late + + align:start position:0% +because i'm quite a bit late + + + align:start position:0% +because i'm quite a bit late +i'm probably going to do just do one + + align:start position:0% +i'm probably going to do just do one + + + align:start position:0% +i'm probably going to do just do one +more problem which is sad because the + + align:start position:0% +more problem which is sad because the + + + align:start position:0% +more problem which is sad because the +last one is about gokimonpo + + align:start position:0% +last one is about gokimonpo + + + align:start position:0% +last one is about gokimonpo +which is a fun fun problem gokimonpo + + align:start position:0% +which is a fun fun problem gokimonpo + + + align:start position:0% +which is a fun fun problem gokimonpo +basically relies on i'm trying to catch + + align:start position:0% +basically relies on i'm trying to catch + + + align:start position:0% +basically relies on i'm trying to catch +a bunch of pocket monsters + + align:start position:0% +a bunch of pocket monsters + + + align:start position:0% +a bunch of pocket monsters +just monsters i think is in this and + + align:start position:0% +just monsters i think is in this and + + + align:start position:0% +just monsters i think is in this and +you can either go to a location + + align:start position:0% +you can either go to a location + + + align:start position:0% +you can either go to a location +and catch that monster for free + + align:start position:0% + + + + align:start position:0% + +but that costs money because i have to + + align:start position:0% +but that costs money because i have to + + + align:start position:0% +but that costs money because i have to +ride share there okay + + align:start position:0% +ride share there okay + + + align:start position:0% +ride share there okay +or i don't have to go to that location + + align:start position:0% +or i don't have to go to that location + + + align:start position:0% +or i don't have to go to that location +and i buy it on my in in-app purchase + + align:start position:0% +and i buy it on my in in-app purchase + + + align:start position:0% +and i buy it on my in in-app purchase +but that cost me a different amount of + + align:start position:0% +but that cost me a different amount of + + + align:start position:0% +but that cost me a different amount of +money okay + + align:start position:0% +money okay + + + align:start position:0% +money okay +but buying it and i mean at purchase + + align:start position:0% +but buying it and i mean at purchase + + + align:start position:0% +but buying it and i mean at purchase +kept me at the location i was previously + + align:start position:0% +kept me at the location i was previously + + + align:start position:0% +kept me at the location i was previously +wherever i was + + align:start position:0% +wherever i was + + + align:start position:0% +wherever i was +and so the the point of that problem is + + align:start position:0% +and so the the point of that problem is + + + align:start position:0% +and so the the point of that problem is +i need to remember where i was + + align:start position:0% +i need to remember where i was + + + align:start position:0% +i need to remember where i was +last so that i know how far i need to + + align:start position:0% +last so that i know how far i need to + + + align:start position:0% +last so that i know how far i need to +travel + + align:start position:0% +travel + + + align:start position:0% +travel +to get to my next monster okay so that's + + align:start position:0% +to get to my next monster okay so that's + + + align:start position:0% +to get to my next monster okay so that's +going to be the last one that i'm not + + align:start position:0% +going to be the last one that i'm not + + + align:start position:0% +going to be the last one that i'm not +going to be able to get to + + align:start position:0% +going to be able to get to + + + align:start position:0% +going to be able to get to +number three is a problem about + + align:start position:0% +number three is a problem about + + + align:start position:0% +number three is a problem about +tapas okay so + + align:start position:0% +tapas okay so + + + align:start position:0% +tapas okay so +these all come from spring 18. 18 the + + align:start position:0% +these all come from spring 18. 18 the + + + align:start position:0% +these all come from spring 18. 18 the +first two came from a problem set + + align:start position:0% +first two came from a problem set + + + align:start position:0% +first two came from a problem set +uh these next two come from the final + + align:start position:0% +uh these next two come from the final + + + align:start position:0% +uh these next two come from the final +exam that year + + align:start position:0% +exam that year + + + align:start position:0% +exam that year +okay albert ratkins + + align:start position:0% +okay albert ratkins + + + align:start position:0% +okay albert ratkins +uh he's on a diet uh but he has a + + align:start position:0% +uh he's on a diet uh but he has a + + + align:start position:0% +uh he's on a diet uh but he has a +dinner at an upscale tapas bar where he + + align:start position:0% +dinner at an upscale tapas bar where he + + + align:start position:0% +dinner at an upscale tapas bar where he +got many he's going to order many small + + align:start position:0% +got many he's going to order many small + + + align:start position:0% +got many he's going to order many small +plates + + align:start position:0% +plates + + + align:start position:0% +plates +okay there are n plates of food on the + + align:start position:0% +okay there are n plates of food on the + + + align:start position:0% +okay there are n plates of food on the +menu + + align:start position:0% +menu + + + align:start position:0% +menu +where you know each plate has a certain + + align:start position:0% +where you know each plate has a certain + + + align:start position:0% +where you know each plate has a certain +information it has a volume a number of + + align:start position:0% +information it has a volume a number of + + + align:start position:0% +information it has a volume a number of +calories in that dish + + align:start position:0% +calories in that dish + + + align:start position:0% +calories in that dish +and a sweetness label basically zero or + + align:start position:0% +and a sweetness label basically zero or + + + align:start position:0% +and a sweetness label basically zero or +one whether it's sweet or not + + align:start position:0% +one whether it's sweet or not + + + align:start position:0% +one whether it's sweet or not +okay but he's on a diet and he wants to + + align:start position:0% +okay but he's on a diet and he wants to + + + align:start position:0% +okay but he's on a diet and he wants to +eat no more than k calories during his + + align:start position:0% +eat no more than k calories during his + + + align:start position:0% +eat no more than k calories during his +meal + + align:start position:0% +meal + + + align:start position:0% +meal +but wants to fill his stomach as much as + + align:start position:0% +but wants to fill his stomach as much as + + + align:start position:0% +but wants to fill his stomach as much as +possible because he wants to feel + + align:start position:0% +possible because he wants to feel + + + align:start position:0% +possible because he wants to feel +full right so he wants to maximize the + + align:start position:0% +full right so he wants to maximize the + + + align:start position:0% +full right so he wants to maximize the +volume that he fills + + align:start position:0% +volume that he fills + + + align:start position:0% +volume that he fills +even though he wants to reduce the + + align:start position:0% +even though he wants to reduce the + + + align:start position:0% +even though he wants to reduce the +number of calories like keep restrict + + align:start position:0% +number of calories like keep restrict + + + align:start position:0% +number of calories like keep restrict +the number of calories + + align:start position:0% +the number of calories + + + align:start position:0% +the number of calories +okay he also wants to order exactly + + align:start position:0% +okay he also wants to order exactly + + + align:start position:0% +okay he also wants to order exactly +s sweet plates + + align:start position:0% +s sweet plates + + + align:start position:0% +s sweet plates +okay so we've got this other condition + + align:start position:0% +okay so we've got this other condition + + + align:start position:0% +okay so we've got this other condition +where + + align:start position:0% +where + + + align:start position:0% +where +i need to make sure i'm eating a certain + + align:start position:0% +i need to make sure i'm eating a certain + + + align:start position:0% +i need to make sure i'm eating a certain +number of sweet plates + + align:start position:0% +number of sweet plates + + + align:start position:0% +number of sweet plates +it might be useful for me to remember + + align:start position:0% +it might be useful for me to remember + + + align:start position:0% +it might be useful for me to remember +how many sweet plates i've already eaten + + align:start position:0% +how many sweet plates i've already eaten + + + align:start position:0% +how many sweet plates i've already eaten +so i make sure that i eat that number + + align:start position:0% +so i make sure that i eat that number + + + align:start position:0% +so i make sure that i eat that number +okay + + align:start position:0% +okay + + + align:start position:0% +okay +without purchasing the same dish twice + + align:start position:0% +without purchasing the same dish twice + + + align:start position:0% +without purchasing the same dish twice +okay so here's a condition + + align:start position:0% +okay so here's a condition + + + align:start position:0% +okay so here's a condition +that's similar to the knapsack 0-1 + + align:start position:0% +that's similar to the knapsack 0-1 + + + align:start position:0% +that's similar to the knapsack 0-1 +problem versus a knapsack + + align:start position:0% +problem versus a knapsack + + + align:start position:0% +problem versus a knapsack +kind of general problem am i allowed to + + align:start position:0% +kind of general problem am i allowed to + + + align:start position:0% +kind of general problem am i allowed to +take more than one of these things or + + align:start position:0% +take more than one of these things or + + + align:start position:0% +take more than one of these things or +not + + align:start position:0% +not + + + align:start position:0% +not +here it's a restriction that i'm not + + align:start position:0% +here it's a restriction that i'm not + + + align:start position:0% +here it's a restriction that i'm not +allowed to take + + align:start position:0% +allowed to take + + + align:start position:0% +allowed to take +a plate more than once okay and i'm + + align:start position:0% +a plate more than once okay and i'm + + + align:start position:0% +a plate more than once okay and i'm +going to try to describe + + align:start position:0% +going to try to describe + + + align:start position:0% +going to try to describe +a order n k s time algorithm to find the + + align:start position:0% +a order n k s time algorithm to find the + + + align:start position:0% +a order n k s time algorithm to find the +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +volume of food obert can eat given his + + align:start position:0% +volume of food obert can eat given his + + + align:start position:0% +volume of food obert can eat given his +diet + + align:start position:0% +diet + + + align:start position:0% +diet +okay so first thing i'm going to note + + align:start position:0% +okay so first thing i'm going to note + + + align:start position:0% +okay so first thing i'm going to note +here is the the + + align:start position:0% +here is the the + + + align:start position:0% +here is the the +one of the things that we talked about + + align:start position:0% +one of the things that we talked about + + + align:start position:0% +one of the things that we talked about +at the last dynamic programming lecture + + align:start position:0% +at the last dynamic programming lecture + + + align:start position:0% +at the last dynamic programming lecture +was is this a polynomial running time + + align:start position:0% +was is this a polynomial running time + + + align:start position:0% +was is this a polynomial running time +that it's asking me for right actually + + align:start position:0% +that it's asking me for right actually + + + align:start position:0% +that it's asking me for right actually +on your problem set eight + + align:start position:0% +on your problem set eight + + + align:start position:0% +on your problem set eight +you were asked on each problem to + + align:start position:0% +you were asked on each problem to + + + align:start position:0% +you were asked on each problem to +categorize whether the running time of + + align:start position:0% +categorize whether the running time of + + + align:start position:0% +categorize whether the running time of +your algorithm was polynomial or not + + align:start position:0% +your algorithm was polynomial or not + + + align:start position:0% +your algorithm was polynomial or not +and actually you don't have to solve the + + align:start position:0% +and actually you don't have to solve the + + + align:start position:0% +and actually you don't have to solve the +problem in order to answer that question + + align:start position:0% +problem in order to answer that question + + + align:start position:0% +problem in order to answer that question +if we give you the running time right if + + align:start position:0% +if we give you the running time right if + + + align:start position:0% +if we give you the running time right if +we give you the running time you can + + align:start position:0% +we give you the running time you can + + + align:start position:0% +we give you the running time you can +just take a look at that running time + + align:start position:0% +just take a look at that running time + + + align:start position:0% +just take a look at that running time +and be like + + align:start position:0% +and be like + + + align:start position:0% +and be like +oh is that polynomial in the size of my + + align:start position:0% +oh is that polynomial in the size of my + + + align:start position:0% +oh is that polynomial in the size of my +input + + align:start position:0% +input + + + align:start position:0% +input +and here it's is it all the ones + + align:start position:0% +and here it's is it all the ones + + + align:start position:0% +and here it's is it all the ones +previously + + align:start position:0% +previously + + + align:start position:0% +previously +were this one was the order n that was + + align:start position:0% +were this one was the order n that was + + + align:start position:0% +were this one was the order n that was +an order n squared because + + align:start position:0% +an order n squared because + + + align:start position:0% +an order n squared because +n was the number of things in my input + + align:start position:0% +n was the number of things in my input + + + align:start position:0% +n was the number of things in my input +the number of words + + align:start position:0% +the number of words + + + align:start position:0% +the number of words +it took to give you that input here + + align:start position:0% +it took to give you that input here + + + align:start position:0% +it took to give you that input here +what do i have i have a triple of + + align:start position:0% +what do i have i have a triple of + + + align:start position:0% +what do i have i have a triple of +numbers for each + + align:start position:0% +numbers for each + + + align:start position:0% +numbers for each +plate there are n of them so n is + + align:start position:0% +plate there are n of them so n is + + + align:start position:0% +plate there are n of them so n is +polynomial + + align:start position:0% +polynomial + + + align:start position:0% +polynomial +s is polynomial because s + + align:start position:0% +s is polynomial because s + + + align:start position:0% +s is polynomial because s +is smaller than n and it's positive + + align:start position:0% +is smaller than n and it's positive + + + align:start position:0% +is smaller than n and it's positive +number + + align:start position:0% +number + + + align:start position:0% +number +but k k is just some + + align:start position:0% +but k k is just some + + + align:start position:0% +but k k is just some +number in my input right + + align:start position:0% +number in my input right + + + align:start position:0% +number in my input right +is representable in potentially one word + + align:start position:0% +is representable in potentially one word + + + align:start position:0% +is representable in potentially one word +that's the assumption + + align:start position:0% +that's the assumption + + + align:start position:0% +that's the assumption +but it could have exponential size + + align:start position:0% +but it could have exponential size + + + align:start position:0% +but it could have exponential size +depending on the size of my word + + align:start position:0% +depending on the size of my word + + + align:start position:0% +depending on the size of my word +of my machine i don't know how big k is + + align:start position:0% +of my machine i don't know how big k is + + + align:start position:0% +of my machine i don't know how big k is +relative to n + + align:start position:0% +relative to n + + + align:start position:0% +relative to n +and so this is a pseudo-polynomial + + align:start position:0% +and so this is a pseudo-polynomial + + + align:start position:0% +and so this is a pseudo-polynomial +running time + + align:start position:0% +running time + + + align:start position:0% +running time +okay because k is just a number in my + + align:start position:0% +okay because k is just a number in my + + + align:start position:0% +okay because k is just a number in my +problem + + align:start position:0% +problem + + + align:start position:0% +problem +similar to subset sum similar to + + align:start position:0% +similar to subset sum similar to + + + align:start position:0% +similar to subset sum similar to +knapsack which you guys did in lecture + + align:start position:0% +knapsack which you guys did in lecture + + + align:start position:0% +knapsack which you guys did in lecture +and recitation and so if we ask you on + + align:start position:0% +and recitation and so if we ask you on + + + align:start position:0% +and recitation and so if we ask you on +an exam + + align:start position:0% +an exam + + + align:start position:0% +an exam +which we probably will whether certain + + align:start position:0% +which we probably will whether certain + + + align:start position:0% +which we probably will whether certain +running times are polynomial or not + + align:start position:0% +running times are polynomial or not + + + align:start position:0% +running times are polynomial or not +that's the logic that you go about it + + align:start position:0% +that's the logic that you go about it + + + align:start position:0% +that's the logic that you go about it +how big is my input + + align:start position:0% + + + + align:start position:0% + +what is my running time that i'm trying + + align:start position:0% +what is my running time that i'm trying + + + align:start position:0% +what is my running time that i'm trying +to evaluate and + + align:start position:0% +to evaluate and + + + align:start position:0% +to evaluate and +can i bound each of those terms in terms + + align:start position:0% +can i bound each of those terms in terms + + + align:start position:0% +can i bound each of those terms in terms +of the size of my input + + align:start position:0% +of the size of my input + + + align:start position:0% +of the size of my input +if not then you say it's + + align:start position:0% +if not then you say it's + + + align:start position:0% +if not then you say it's +pseudopolynomial + + align:start position:0% +pseudopolynomial + + + align:start position:0% +pseudopolynomial +okay all right so let's try to + + align:start position:0% +okay all right so let's try to + + + align:start position:0% +okay all right so let's try to +tackle this problem now already because + + align:start position:0% +tackle this problem now already because + + + align:start position:0% +tackle this problem now already because +we've got pseudopolynomial + + align:start position:0% +we've got pseudopolynomial + + + align:start position:0% +we've got pseudopolynomial +uh you're thinking maybe this is going + + align:start position:0% +uh you're thinking maybe this is going + + + align:start position:0% +uh you're thinking maybe this is going +to be knapsack-like or subset some like + + align:start position:0% +to be knapsack-like or subset some like + + + align:start position:0% +to be knapsack-like or subset some like +okay what do i need to i'm just going to + + align:start position:0% +okay what do i need to i'm just going to + + + align:start position:0% +okay what do i need to i'm just going to +go straight for sub problems here + + align:start position:0% +go straight for sub problems here + + + align:start position:0% +go straight for sub problems here +uh actually i should probably say + + align:start position:0% +uh actually i should probably say + + + align:start position:0% +uh actually i should probably say +what my things are meh this is fine + + align:start position:0% +what my things are meh this is fine + + + align:start position:0% +what my things are meh this is fine +i gave notation up there didn't i okay + + align:start position:0% +i gave notation up there didn't i okay + + + align:start position:0% +i gave notation up there didn't i okay +so + + align:start position:0% +so + + + align:start position:0% +so +we're gonna have sub problems i'm gonna + + align:start position:0% +we're gonna have sub problems i'm gonna + + + align:start position:0% +we're gonna have sub problems i'm gonna +i want to maximize the number + + align:start position:0% +i want to maximize the number + + + align:start position:0% +i want to maximize the number +the volume of food so that should + + align:start position:0% +the volume of food so that should + + + align:start position:0% +the volume of food so that should +probably be the output + + align:start position:0% +probably be the output + + + align:start position:0% +probably be the output +of my sub problem the max volume on + + align:start position:0% +of my sub problem the max volume on + + + align:start position:0% +of my sub problem the max volume on +some subset of dishes right + + align:start position:0% +some subset of dishes right + + + align:start position:0% +some subset of dishes right +i'm going to choose suffixes here + + align:start position:0% +i'm going to choose suffixes here + + + align:start position:0% +i'm going to choose suffixes here +i and some other stuff + + align:start position:0% +i and some other stuff + + + align:start position:0% +i and some other stuff +is going to be max volume + + align:start position:0% +is going to be max volume + + + align:start position:0% +is going to be max volume +of food possible + + align:start position:0% + + + + align:start position:0% + +uh for plates + + align:start position:0% + + + + align:start position:0% + +p i to p n i'm gonna assume one index + + align:start position:0% +p i to p n i'm gonna assume one index + + + align:start position:0% +p i to p n i'm gonna assume one index +here because + + align:start position:0% +here because + + + align:start position:0% +here because +why not + + align:start position:0% + + + + align:start position:0% + +but do i need to remember information + + align:start position:0% +but do i need to remember information + + + align:start position:0% +but do i need to remember information +along the way + + align:start position:0% +along the way + + + align:start position:0% +along the way +yeah just like with subset sum or + + align:start position:0% +yeah just like with subset sum or + + + align:start position:0% +yeah just like with subset sum or +knapsack + + align:start position:0% +knapsack + + + align:start position:0% +knapsack +i need i have this calorie limit + + align:start position:0% +i need i have this calorie limit + + + align:start position:0% +i need i have this calorie limit +right so it's going to be really useful + + align:start position:0% +right so it's going to be really useful + + + align:start position:0% +right so it's going to be really useful +for me to know how many calories i've + + align:start position:0% +for me to know how many calories i've + + + align:start position:0% +for me to know how many calories i've +already + + align:start position:0% +already + + + align:start position:0% +already +eaten or how many calories i have left + + align:start position:0% +eaten or how many calories i have left + + + align:start position:0% +eaten or how many calories i have left +in my budget + + align:start position:0% +in my budget + + + align:start position:0% +in my budget +right so let's say j + + align:start position:0% +right so let's say j + + + align:start position:0% +right so let's say j +uh using + + align:start position:0% +uh using + + + align:start position:0% +uh using +at most j + + align:start position:0% +at most j + + + align:start position:0% +at most j +calories right from the remaining dishes + + align:start position:0% +calories right from the remaining dishes + + + align:start position:0% +calories right from the remaining dishes +and i need to make sure that i'm eating + + align:start position:0% +and i need to make sure that i'm eating + + + align:start position:0% +and i need to make sure that i'm eating +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +some number of sweet plates in the + + align:start position:0% +some number of sweet plates in the + + + align:start position:0% +some number of sweet plates in the +future + + align:start position:0% +future + + + align:start position:0% +future +and i need to remember as i eat a sweet + + align:start position:0% +and i need to remember as i eat a sweet + + + align:start position:0% +and i need to remember as i eat a sweet +plate + + align:start position:0% +plate + + + align:start position:0% +plate +the number of sweet plates i need to eat + + align:start position:0% +the number of sweet plates i need to eat + + + align:start position:0% +the number of sweet plates i need to eat +decreases and so i want to generalize + + align:start position:0% +decreases and so i want to generalize + + + align:start position:0% +decreases and so i want to generalize +that i'm going to put + + align:start position:0% +that i'm going to put + + + align:start position:0% +that i'm going to put +an s prime here to denote eating + + align:start position:0% + + + + align:start position:0% + +exactly + + align:start position:0% + + + + align:start position:0% + +s sweet + + align:start position:0% +s sweet + + + align:start position:0% +s sweet +plates okay + + align:start position:0% +plates okay + + + align:start position:0% +plates okay +so that's my sub problem + + align:start position:0% + + + + align:start position:0% + +let's i've got tons of board space i'm + + align:start position:0% +let's i've got tons of board space i'm + + + align:start position:0% +let's i've got tons of board space i'm +going to go ahead and use it + + align:start position:0% +going to go ahead and use it + + + align:start position:0% +going to go ahead and use it +relation + + align:start position:0% + + + + align:start position:0% + +we've got x i j s + + align:start position:0% +we've got x i j s + + + align:start position:0% +we've got x i j s +prime equals okay i'm trying to maximize + + align:start position:0% +prime equals okay i'm trying to maximize + + + align:start position:0% +prime equals okay i'm trying to maximize +volume + + align:start position:0% +volume + + + align:start position:0% +volume +probably i want to be maximizing over + + align:start position:0% +probably i want to be maximizing over + + + align:start position:0% +probably i want to be maximizing over +something right + + align:start position:0% +something right + + + align:start position:0% +something right +this combinator is kind of what i like + + align:start position:0% +this combinator is kind of what i like + + + align:start position:0% +this combinator is kind of what i like +to call it + + align:start position:0% +to call it + + + align:start position:0% +to call it +right usually what you're doing in + + align:start position:0% +right usually what you're doing in + + + align:start position:0% +right usually what you're doing in +dynamic programming is making some kind + + align:start position:0% +dynamic programming is making some kind + + + align:start position:0% +dynamic programming is making some kind +of choice + + align:start position:0% +of choice + + + align:start position:0% +of choice +or common combining combinating + + align:start position:0% +or common combining combinating + + + align:start position:0% +or common combining combinating +combining some number of sub problems + + align:start position:0% +combining some number of sub problems + + + align:start position:0% +combining some number of sub problems +and choosing which one's the best right + + align:start position:0% +and choosing which one's the best right + + + align:start position:0% +and choosing which one's the best right +if you don't if you just list a bunch of + + align:start position:0% +if you don't if you just list a bunch of + + + align:start position:0% +if you don't if you just list a bunch of +options here + + align:start position:0% +options here + + + align:start position:0% +options here +and don't tell us how to combine them + + align:start position:0% +and don't tell us how to combine them + + + align:start position:0% +and don't tell us how to combine them +that's going to be a problem because we + + align:start position:0% +that's going to be a problem because we + + + align:start position:0% +that's going to be a problem because we +don't know what your dynamic program is + + align:start position:0% +don't know what your dynamic program is + + + align:start position:0% +don't know what your dynamic program is +doing at all + + align:start position:0% +doing at all + + + align:start position:0% +doing at all +so it's really useful for you to be able + + align:start position:0% +so it's really useful for you to be able + + + align:start position:0% +so it's really useful for you to be able +to tell us + + align:start position:0% +to tell us + + + align:start position:0% +to tell us +how you're combining your sub problems + + align:start position:0% +how you're combining your sub problems + + + align:start position:0% +how you're combining your sub problems +here we're doing a maximization + + align:start position:0% +here we're doing a maximization + + + align:start position:0% +here we're doing a maximization +over the different volumes possible if + + align:start position:0% +over the different volumes possible if + + + align:start position:0% +over the different volumes possible if +we + + align:start position:0% +we + + + align:start position:0% +we +decide to eat the plate i + + align:start position:0% +decide to eat the plate i + + + align:start position:0% +decide to eat the plate i +then we get v i in volume + + align:start position:0% +then we get v i in volume + + + align:start position:0% +then we get v i in volume +we fill our tummies with vi and volume + + align:start position:0% +we fill our tummies with vi and volume + + + align:start position:0% +we fill our tummies with vi and volume +but then we have to recurse on using + + align:start position:0% +but then we have to recurse on using + + + align:start position:0% +but then we have to recurse on using +one fewer plate because we can't use + + align:start position:0% +one fewer plate because we can't use + + + align:start position:0% +one fewer plate because we can't use +that plate again + + align:start position:0% +that plate again + + + align:start position:0% +that plate again +and we've decreased the amount of + + align:start position:0% +and we've decreased the amount of + + + align:start position:0% +and we've decreased the amount of +calories in our budget + + align:start position:0% +calories in our budget + + + align:start position:0% +calories in our budget +and i'm going to say s prime + + align:start position:0% +and i'm going to say s prime + + + align:start position:0% +and i'm going to say s prime +minus s i because + + align:start position:0% +minus s i because + + + align:start position:0% +minus s i because +s i is one if it's sweet + + align:start position:0% +s i is one if it's sweet + + + align:start position:0% +s i is one if it's sweet +and zero if it's not so it's kind of + + align:start position:0% +and zero if it's not so it's kind of + + + align:start position:0% +and zero if it's not so it's kind of +nice that they + + align:start position:0% +nice that they + + + align:start position:0% +nice that they +kind of gave us this notation here i can + + align:start position:0% +kind of gave us this notation here i can + + + align:start position:0% +kind of gave us this notation here i can +just subtract it off + + align:start position:0% +just subtract it off + + + align:start position:0% +just subtract it off +if it's there i don't have to do this + + align:start position:0% +if it's there i don't have to do this + + + align:start position:0% +if it's there i don't have to do this +conditional or something + + align:start position:0% +conditional or something + + + align:start position:0% +conditional or something +and i don't ever want to go below these + + align:start position:0% +and i don't ever want to go below these + + + align:start position:0% +and i don't ever want to go below these +budgets + + align:start position:0% +budgets + + + align:start position:0% +budgets +so i'm just going to say if uh + + align:start position:0% +so i'm just going to say if uh + + + align:start position:0% +so i'm just going to say if uh +c i is uh + + align:start position:0% +c i is uh + + + align:start position:0% +c i is uh +less than or equal to j and s i + + align:start position:0% +less than or equal to j and s i + + + align:start position:0% +less than or equal to j and s i +is less than or equal to s prime okay so + + align:start position:0% +is less than or equal to s prime okay so + + + align:start position:0% +is less than or equal to s prime okay so +that's going to make sure + + align:start position:0% +that's going to make sure + + + align:start position:0% +that's going to make sure +that i never have these guys go negative + + align:start position:0% +that i never have these guys go negative + + + align:start position:0% +that i never have these guys go negative +okay otherwise i don't eat the plate and + + align:start position:0% +okay otherwise i don't eat the plate and + + + align:start position:0% +okay otherwise i don't eat the plate and +that's kind of the easy case + + align:start position:0% +that's kind of the easy case + + + align:start position:0% +that's kind of the easy case +because i just go i plus 1 j + + align:start position:0% +because i just go i plus 1 j + + + align:start position:0% +because i just go i plus 1 j +s prime these things didn't change i + + align:start position:0% +s prime these things didn't change i + + + align:start position:0% +s prime these things didn't change i +just have one + + align:start position:0% +just have one + + + align:start position:0% +just have one +fewer thing left okay so i'm maximizing + + align:start position:0% +fewer thing left okay so i'm maximizing + + + align:start position:0% +fewer thing left okay so i'm maximizing +over these things + + align:start position:0% +over these things + + + align:start position:0% +over these things +this one's an always it's not in it + + align:start position:0% +this one's an always it's not in it + + + align:start position:0% +this one's an always it's not in it +right okay so + + align:start position:0% +right okay so + + + align:start position:0% +right okay so +i just have two choices and maximizing + + align:start position:0% +i just have two choices and maximizing + + + align:start position:0% +i just have two choices and maximizing +over them + + align:start position:0% +over them + + + align:start position:0% +over them +topological sort order here i'm always + + align:start position:0% +topological sort order here i'm always + + + align:start position:0% +topological sort order here i'm always +recursing + + align:start position:0% +recursing + + + align:start position:0% +recursing +on a thing with larger eye + + align:start position:0% + + + + align:start position:0% + +depends on + + align:start position:0% +depends on + + + align:start position:0% +depends on +larger eye so a cyclic + + align:start position:0% +larger eye so a cyclic + + + align:start position:0% +larger eye so a cyclic +happy okay + + align:start position:0% + + + + align:start position:0% + +base cases + + align:start position:0% + + + + align:start position:0% + +what's the good case + + align:start position:0% + + + + align:start position:0% + +i get to the end i've reached the end of + + align:start position:0% +i get to the end i've reached the end of + + + align:start position:0% +i get to the end i've reached the end of +my menu + + align:start position:0% +my menu + + + align:start position:0% +my menu +i can't look at any more plates i'm + + align:start position:0% +i can't look at any more plates i'm + + + align:start position:0% +i can't look at any more plates i'm +stuffed + + align:start position:0% + + + + align:start position:0% + +and i've already forbidden myself from + + align:start position:0% +and i've already forbidden myself from + + + align:start position:0% +and i've already forbidden myself from +going negative on the calories so that + + align:start position:0% +going negative on the calories so that + + + align:start position:0% +going negative on the calories so that +should be all good + + align:start position:0% + + + + align:start position:0% + +but what do i want on the third + + align:start position:0% +but what do i want on the third + + + align:start position:0% +but what do i want on the third +parameter + + align:start position:0% +parameter + + + align:start position:0% +parameter +zero i better a i better have eaten + + align:start position:0% +zero i better a i better have eaten + + + align:start position:0% +zero i better a i better have eaten +exactly uh s plates so i want to get + + align:start position:0% +exactly uh s plates so i want to get + + + align:start position:0% +exactly uh s plates so i want to get +down to + + align:start position:0% +down to + + + align:start position:0% +down to +x m plus + + align:start position:0% +x m plus + + + align:start position:0% +x m plus +one because i'm one indexed j for any j + + align:start position:0% +one because i'm one indexed j for any j + + + align:start position:0% +one because i'm one indexed j for any j +zero that's gonna be + + align:start position:0% +zero that's gonna be + + + align:start position:0% +zero that's gonna be +zero right i get no calories there but + + align:start position:0% +zero right i get no calories there but + + + align:start position:0% +zero right i get no calories there but +it's a good thing it's a good place + + align:start position:0% +it's a good thing it's a good place + + + align:start position:0% +it's a good thing it's a good place +it's fine zero is good all right + + align:start position:0% +it's fine zero is good all right + + + align:start position:0% +it's fine zero is good all right +this is uh + + align:start position:0% + + + + align:start position:0% + +done i don't know okay there's another + + align:start position:0% +done i don't know okay there's another + + + align:start position:0% +done i don't know okay there's another +base case right what's the bad base case + + align:start position:0% +base case right what's the bad base case + + + align:start position:0% +base case right what's the bad base case +i get to the end + + align:start position:0% +i get to the end + + + align:start position:0% +i get to the end +i'm always increasing i and so i better + + align:start position:0% +i'm always increasing i and so i better + + + align:start position:0% +i'm always increasing i and so i better +be doing something on n plus one i got + + align:start position:0% +be doing something on n plus one i got + + + align:start position:0% +be doing something on n plus one i got +to the end + + align:start position:0% + + + + align:start position:0% + +j again is going to always be + + align:start position:0% +j again is going to always be + + + align:start position:0% +j again is going to always be +non-negative + + align:start position:0% +non-negative + + + align:start position:0% +non-negative +because we we're always going to be in + + align:start position:0% +because we we're always going to be in + + + align:start position:0% +because we we're always going to be in +our in our calorie budget + + align:start position:0% +our in our calorie budget + + + align:start position:0% +our in our calorie budget +but if this is anything + + align:start position:0% +but if this is anything + + + align:start position:0% +but if this is anything +other than s prime + + align:start position:0% +other than s prime + + + align:start position:0% +other than s prime +greater than z or if it's anything but + + align:start position:0% +greater than z or if it's anything but + + + align:start position:0% +greater than z or if it's anything but +zero what is that going to be + + align:start position:0% + + + + align:start position:0% + +minus infinity right i never want to be + + align:start position:0% +minus infinity right i never want to be + + + align:start position:0% +minus infinity right i never want to be +in this situation + + align:start position:0% +in this situation + + + align:start position:0% +in this situation +if i do my dynamic program and i get a + + align:start position:0% +if i do my dynamic program and i get a + + + align:start position:0% +if i do my dynamic program and i get a +minus infinity up at the top + + align:start position:0% +minus infinity up at the top + + + align:start position:0% +minus infinity up at the top +that means there is no path to this + + align:start position:0% +that means there is no path to this + + + align:start position:0% +that means there is no path to this +subproblem here + + align:start position:0% +subproblem here + + + align:start position:0% +subproblem here +where i'm happy i'm always sad + + align:start position:0% +where i'm happy i'm always sad + + + align:start position:0% +where i'm happy i'm always sad +and so i return that the maximum value + + align:start position:0% +and so i return that the maximum value + + + align:start position:0% +and so i return that the maximum value +volume of food obert can eat and + + align:start position:0% +volume of food obert can eat and + + + align:start position:0% +volume of food obert can eat and +maintain his diet + + align:start position:0% +maintain his diet + + + align:start position:0% +maintain his diet +is not possible essentially there + + align:start position:0% +is not possible essentially there + + + align:start position:0% +is not possible essentially there +aren't s dishes sweet dishes in the + + align:start position:0% +aren't s dishes sweet dishes in the + + + align:start position:0% +aren't s dishes sweet dishes in the +thing + + align:start position:0% +thing + + + align:start position:0% +thing +whose calorie budget are below my limit + + align:start position:0% +whose calorie budget are below my limit + + + align:start position:0% +whose calorie budget are below my limit +right and that's probably an easier + + align:start position:0% +right and that's probably an easier + + + align:start position:0% +right and that's probably an easier +thing to check + + align:start position:0% +thing to check + + + align:start position:0% +thing to check +then in this bound okay so we have + + align:start position:0% +then in this bound okay so we have + + + align:start position:0% +then in this bound okay so we have +our original sub problems now solution + + align:start position:0% +our original sub problems now solution + + + align:start position:0% +our original sub problems now solution +is given by + + align:start position:0% +is given by + + + align:start position:0% +is given by +what + + align:start position:0% + + + + align:start position:0% + +just one of our sub problems right it's + + align:start position:0% +just one of our sub problems right it's + + + align:start position:0% +just one of our sub problems right it's +just seeing what's the maximum volume i + + align:start position:0% +just seeing what's the maximum volume i + + + align:start position:0% +just seeing what's the maximum volume i +don't have to + + align:start position:0% +don't have to + + + align:start position:0% +don't have to +retrace my steps to figure out my thing + + align:start position:0% +retrace my steps to figure out my thing + + + align:start position:0% +retrace my steps to figure out my thing +i just + + align:start position:0% +i just + + + align:start position:0% +i just +i say one of the sub problems it's + + align:start position:0% +i say one of the sub problems it's + + + align:start position:0% +i say one of the sub problems it's +using all of the things on my menu using + + align:start position:0% +using all of the things on my menu using + + + align:start position:0% +using all of the things on my menu using +my entire budget k + + align:start position:0% +my entire budget k + + + align:start position:0% +my entire budget k +and trying to get exactly s + + align:start position:0% +and trying to get exactly s + + + align:start position:0% +and trying to get exactly s +things that that's going to be my output + + align:start position:0% +things that that's going to be my output + + + align:start position:0% +things that that's going to be my output +to my algorithm + + align:start position:0% +to my algorithm + + + align:start position:0% +to my algorithm +and this takes what time + + align:start position:0% +and this takes what time + + + align:start position:0% +and this takes what time +how many sub problems do i have i have n + + align:start position:0% +how many sub problems do i have i have n + + + align:start position:0% +how many sub problems do i have i have n +plus one + + align:start position:0% +plus one + + + align:start position:0% +plus one +sub problems for this + + align:start position:0% +sub problems for this + + + align:start position:0% +sub problems for this +uh parameter i have a plus one + + align:start position:0% +uh parameter i have a plus one + + + align:start position:0% +uh parameter i have a plus one +possible things for this parameter and i + + align:start position:0% +possible things for this parameter and i + + + align:start position:0% +possible things for this parameter and i +have s plus one possible things for this + + align:start position:0% +have s plus one possible things for this + + + align:start position:0% +have s plus one possible things for this +parameter + + align:start position:0% +parameter + + + align:start position:0% +parameter +so i get order n k + + align:start position:0% +so i get order n k + + + align:start position:0% +so i get order n k +s sub problems + + align:start position:0% +s sub problems + + + align:start position:0% +s sub problems +sub problems + + align:start position:0% +sub problems + + + align:start position:0% +sub problems +how much work per sub problem just a max + + align:start position:0% +how much work per sub problem just a max + + + align:start position:0% +how much work per sub problem just a max +of two things + + align:start position:0% +of two things + + + align:start position:0% +of two things +so constant work per subproblem + + align:start position:0% + + + + align:start position:0% + +yields order n k s + + align:start position:0% +yields order n k s + + + align:start position:0% +yields order n k s +time total okay + + align:start position:0% +time total okay + + + align:start position:0% +time total okay +so those are three nice practice + + align:start position:0% +so those are three nice practice + + + align:start position:0% +so those are three nice practice +problems for you + + align:start position:0% +problems for you + + + align:start position:0% +problems for you +one two that are polynomial one that's + + align:start position:0% +one two that are polynomial one that's + + + align:start position:0% +one two that are polynomial one that's +pseudopolynomial you have one more + + align:start position:0% +pseudopolynomial you have one more + + + align:start position:0% +pseudopolynomial you have one more +example in there which is the goku + + align:start position:0% +example in there which is the goku + + + align:start position:0% +example in there which is the goku +non-mon po problem + + align:start position:0% +non-mon po problem + + + align:start position:0% +non-mon po problem +which is a fun problem it involves + + align:start position:0% +which is a fun problem it involves + + + align:start position:0% +which is a fun problem it involves +remembering additional information + + align:start position:0% +remembering additional information + + + align:start position:0% +remembering additional information +that's not an not really a pseudo + + align:start position:0% +that's not an not really a pseudo + + + align:start position:0% +that's not an not really a pseudo +polynomial number + + align:start position:0% +polynomial number + + + align:start position:0% +polynomial number +in your problem but it's the location of + + align:start position:0% +in your problem but it's the location of + + + align:start position:0% +in your problem but it's the location of +where i was + + align:start position:0% +where i was + + + align:start position:0% +where i was +last or uh where i was going okay + + align:start position:0% +last or uh where i was going okay + + + align:start position:0% +last or uh where i was going okay +so take a look at that problem uh is + + align:start position:0% +so take a look at that problem uh is + + + align:start position:0% +so take a look at that problem uh is +another + + align:start position:0% +another + + + align:start position:0% +another +a kind of non-trivial way of expanding + + align:start position:0% +a kind of non-trivial way of expanding + + + align:start position:0% +a kind of non-trivial way of expanding +sub-problems + + align:start position:0% +sub-problems + + + align:start position:0% +sub-problems +okay and with that good luck on your + + align:start position:0% +okay and with that good luck on your + + + align:start position:0% +okay and with that good luck on your +quiz 3. \ No newline at end of file diff --git a/wTM4v2gIeqk.txt b/wTM4v2gIeqk.txt new file mode 100644 index 0000000000000000000000000000000000000000..fa90c8b17f110607a3fa6700973466a882795469 --- /dev/null +++ b/wTM4v2gIeqk.txt @@ -0,0 +1,8099 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay. Right. Good morning. Um so we're + + align:start position:0% +Okay. Right. Good morning. Um so we're + + + align:start position:0% +Okay. Right. Good morning. Um so we're +we're uh doing finite elements uh today + + align:start position:0% +we're uh doing finite elements uh today + + + align:start position:0% +we're uh doing finite elements uh today +uh so the element that we've considered + + align:start position:0% +uh so the element that we've considered + + + align:start position:0% +uh so the element that we've considered +so far was the basic linear element + + align:start position:0% +so far was the basic linear element + + + align:start position:0% +so far was the basic linear element +uh continuous + + align:start position:0% +uh continuous + + + align:start position:0% +uh continuous +but of course the slopes had jumps. The + + align:start position:0% +but of course the slopes had jumps. The + + + align:start position:0% +but of course the slopes had jumps. The +slope was minus one over delta x and + + align:start position:0% +slope was minus one over delta x and + + + align:start position:0% +slope was minus one over delta x and +then uh for that one this one was a plus + + align:start position:0% +then uh for that one this one was a plus + + + align:start position:0% +then uh for that one this one was a plus +and then a minus. So a jump in slope but + + align:start position:0% +and then a minus. So a jump in slope but + + + align:start position:0% +and then a minus. So a jump in slope but +no jump in the function. So that + + align:start position:0% +no jump in the function. So that + + + align:start position:0% +no jump in the function. So that +actually my abbreviation for that would + + align:start position:0% +actually my abbreviation for that would + + + align:start position:0% +actually my abbreviation for that would +be C 0 saying that it's continuous + + align:start position:0% +be C 0 saying that it's continuous + + + align:start position:0% +be C 0 saying that it's continuous +but not no derivative is continuous. And + + align:start position:0% +but not no derivative is continuous. And + + + align:start position:0% +but not no derivative is continuous. And +now we'll get to some elements where the + + align:start position:0% +now we'll get to some elements where the + + + align:start position:0% +now we'll get to some elements where the +slope is continuous. It it's it's sort + + align:start position:0% +slope is continuous. It it's it's sort + + + align:start position:0% +slope is continuous. It it's it's sort +of fun to create these uh finite + + align:start position:0% +of fun to create these uh finite + + + align:start position:0% +of fun to create these uh finite +elements uh of higher degree. uh it's + + align:start position:0% +elements uh of higher degree. uh it's + + + align:start position:0% +elements uh of higher degree. uh it's +pretty straightforward in 1D and that's + + align:start position:0% +pretty straightforward in 1D and that's + + + align:start position:0% +pretty straightforward in 1D and that's +where we are now. So that's that's the + + align:start position:0% +where we are now. So that's that's the + + + align:start position:0% +where we are now. So that's that's the +we'll get second degree elements and + + align:start position:0% +we'll get second degree elements and + + + align:start position:0% +we'll get second degree elements and +third degree elements and that gives us + + align:start position:0% +third degree elements and that gives us + + + align:start position:0% +third degree elements and that gives us +as we'll see higher accuracy. So I want + + align:start position:0% +as we'll see higher accuracy. So I want + + + align:start position:0% +as we'll see higher accuracy. So I want +to connect the degree of the polomials + + align:start position:0% +to connect the degree of the polomials + + + align:start position:0% +to connect the degree of the polomials +to the accuracy of the of the + + align:start position:0% +to the accuracy of the of the + + + align:start position:0% +to the accuracy of the of the +approximation and uh then this part of + + align:start position:0% +approximation and uh then this part of + + + align:start position:0% +approximation and uh then this part of +that connection is to recognize that + + align:start position:0% +that connection is to recognize that + + + align:start position:0% +that connection is to recognize that +these problems have a strong form as we + + align:start position:0% +these problems have a strong form as we + + + align:start position:0% +these problems have a strong form as we +know the equation a weak form that's the + + align:start position:0% +know the equation a weak form that's the + + + align:start position:0% +know the equation a weak form that's the +one that has test functions and also a + + align:start position:0% +one that has test functions and also a + + + align:start position:0% +one that has test functions and also a +minimum form that we'll see. Okay. So, + + align:start position:0% +minimum form that we'll see. Okay. So, + + + align:start position:0% +minimum form that we'll see. Okay. So, +ready for how would I get some + + align:start position:0% +ready for how would I get some + + + align:start position:0% +ready for how would I get some +quadratics? So, second degree elements, + + align:start position:0% +quadratics? So, second degree elements, + + + align:start position:0% +quadratics? So, second degree elements, +parabas into the picture. Okay. So, I'm + + align:start position:0% +parabas into the picture. Okay. So, I'm + + + align:start position:0% +parabas into the picture. Okay. So, I'm +going to you you remember Gerkin's idea. + + align:start position:0% +going to you you remember Gerkin's idea. + + + align:start position:0% +going to you you remember Gerkin's idea. +Choose trial functions and we're taking + + align:start position:0% +Choose trial functions and we're taking + + + align:start position:0% +Choose trial functions and we're taking +those to be the same as the test + + align:start position:0% +those to be the same as the test + + + align:start position:0% +those to be the same as the test +function. So, these are the trial + + align:start position:0% +function. So, these are the trial + + + align:start position:0% +function. So, these are the trial +functions we've chosen. One, two, three, + + align:start position:0% +functions we've chosen. One, two, three, + + + align:start position:0% +functions we've chosen. One, two, three, +four of them. and they're linear and + + align:start position:0% +four of them. and they're linear and + + + align:start position:0% +four of them. and they're linear and +that limits the accuracy that you can + + align:start position:0% +that limits the accuracy that you can + + + align:start position:0% +that limits the accuracy that you can +get because you're your approximations + + align:start position:0% +get because you're your approximations + + + align:start position:0% +get because you're your approximations +then are combinations of those. So + + align:start position:0% +then are combinations of those. So + + + align:start position:0% +then are combinations of those. So +they're like broken line functions, + + align:start position:0% +they're like broken line functions, + + + align:start position:0% +they're like broken line functions, +linear approximations and the accuracy + + align:start position:0% +linear approximations and the accuracy + + + align:start position:0% +linear approximations and the accuracy +is + + align:start position:0% +is + + + align:start position:0% +is +not great. It's it's sort of the lowest + + align:start position:0% +not great. It's it's sort of the lowest + + + align:start position:0% +not great. It's it's sort of the lowest +level possible. So how would you get uh + + align:start position:0% +level possible. So how would you get uh + + + align:start position:0% +level possible. So how would you get uh +parabas? + + align:start position:0% +parabas? + + + align:start position:0% +parabas? +Get up. Get I would now. So this was + + align:start position:0% +Get up. Get I would now. So this was + + + align:start position:0% +Get up. Get I would now. So this was +this was first guy. The second guy is + + align:start position:0% +this was first guy. The second guy is + + + align:start position:0% +this was first guy. The second guy is +going to be continuous + + align:start position:0% + + + + align:start position:0% + +and quadratic. + + align:start position:0% + + + + align:start position:0% + +So it's going to have new trial + + align:start position:0% +So it's going to have new trial + + + align:start position:0% +So it's going to have new trial +functions. In addition to these, I'm + + align:start position:0% +functions. In addition to these, I'm + + + align:start position:0% +functions. In addition to these, I'm +going to put in some more. + + align:start position:0% +going to put in some more. + + + align:start position:0% +going to put in some more. +Gerkin's happy with that. I still + + align:start position:0% +Gerkin's happy with that. I still + + + align:start position:0% +Gerkin's happy with that. I still +proceed as usual. uh my approximation is + + align:start position:0% +proceed as usual. uh my approximation is + + + align:start position:0% +proceed as usual. uh my approximation is +some combination of those. It's only + + align:start position:0% +some combination of those. It's only + + + align:start position:0% +some combination of those. It's only +going to be continuous. So it'll just be + + align:start position:0% +going to be continuous. So it'll just be + + + align:start position:0% +going to be continuous. So it'll just be +a C0 guy. Again, that means no, that + + align:start position:0% +a C0 guy. Again, that means no, that + + + align:start position:0% +a C0 guy. Again, that means no, that +means jump in slope. The first + + align:start position:0% +means jump in slope. The first + + + align:start position:0% +means jump in slope. The first +derivative isn't there. Eventually, I + + align:start position:0% +derivative isn't there. Eventually, I + + + align:start position:0% +derivative isn't there. Eventually, I +want to get to a C1 where the slopes are + + align:start position:0% +want to get to a C1 where the slopes are + + + align:start position:0% +want to get to a C1 where the slopes are +continuous. Okay, but how would I get + + align:start position:0% +continuous. Okay, but how would I get + + + align:start position:0% +continuous. Okay, but how would I get +some quadratics? So I I all I want to + + align:start position:0% +some quadratics? So I I all I want to + + + align:start position:0% +some quadratics? So I I all I want to +know all I want now is my my functions + + align:start position:0% +know all I want now is my my functions + + + align:start position:0% +know all I want now is my my functions +my space my combinations should be the + + align:start position:0% +my space my combinations should be the + + + align:start position:0% +my space my combinations should be the +peacewise parabas instead of peacewise + + align:start position:0% +peacewise parabas instead of peacewise + + + align:start position:0% +peacewise parabas instead of peacewise +linear uh and and piece the pieces uh + + align:start position:0% +linear uh and and piece the pieces uh + + + align:start position:0% +linear uh and and piece the pieces uh +are broken at the notes. Okay. So here's + + align:start position:0% +are broken at the notes. Okay. So here's + + + align:start position:0% +are broken at the notes. Okay. So here's +a here's a way to do it. Inside each + + align:start position:0% +a here's a way to do it. Inside each + + + align:start position:0% +a here's a way to do it. Inside each +interval I'm going to add well I'll just + + align:start position:0% +interval I'm going to add well I'll just + + + align:start position:0% +interval I'm going to add well I'll just +call them bubble functions. So these + + align:start position:0% +call them bubble functions. So these + + + align:start position:0% +call them bubble functions. So these +will be new additional guys. So this + + align:start position:0% +will be new additional guys. So this + + + align:start position:0% +will be new additional guys. So this +will be my first fee. You remember that + + align:start position:0% +will be my first fee. You remember that + + + align:start position:0% +will be my first fee. You remember that +halfhat because I'm I happen to the + + align:start position:0% +halfhat because I'm I happen to the + + + align:start position:0% +halfhat because I'm I happen to the +problem I was doing was a freefixed + + align:start position:0% +problem I was doing was a freefixed + + + align:start position:0% +problem I was doing was a freefixed +problem. That's why I had uh halfhat at + + align:start position:0% +problem. That's why I had uh halfhat at + + + align:start position:0% +problem. That's why I had uh halfhat at +this end because there was no boundary + + align:start position:0% +this end because there was no boundary + + + align:start position:0% +this end because there was no boundary +condition that my functions had to + + align:start position:0% +condition that my functions had to + + + align:start position:0% +condition that my functions had to +satisfy at this end. There was it was + + align:start position:0% +satisfy at this end. There was it was + + + align:start position:0% +satisfy at this end. There was it was +fixed. So that's why the hat ended and + + align:start position:0% +fixed. So that's why the hat ended and + + + align:start position:0% +fixed. So that's why the hat ended and +there was no half hat. There's no extra + + align:start position:0% +there was no half hat. There's no extra + + + align:start position:0% +there was no half hat. There's no extra +function there. So I have right now one + + align:start position:0% +function there. So I have right now one + + + align:start position:0% +function there. So I have right now one +two three four. I'm going to add four + + align:start position:0% +two three four. I'm going to add four + + + align:start position:0% +two three four. I'm going to add four +more bubble functions. They'll be each + + align:start position:0% +more bubble functions. They'll be each + + + align:start position:0% +more bubble functions. They'll be each +one will be inside an interval. So it'll + + align:start position:0% +one will be inside an interval. So it'll + + + align:start position:0% +one will be inside an interval. So it'll +be a little parabola. This is function + + align:start position:0% +be a little parabola. This is function + + + align:start position:0% +be a little parabola. This is function +number whatever. + + align:start position:0% +number whatever. + + + align:start position:0% +number whatever. +If if if this is if I number this number + + align:start position:0% +If if if this is if I number this number + + + align:start position:0% +If if if this is if I number this number +one, let's say F1 now is that's probably + + align:start position:0% +one, let's say F1 now is that's probably + + + align:start position:0% +one, let's say F1 now is that's probably +a change in numbering. F2 is going to be + + align:start position:0% +a change in numbering. F2 is going to be + + + align:start position:0% +a change in numbering. F2 is going to be +my bubble. And do you see what my bubble + + align:start position:0% +my bubble. And do you see what my bubble + + + align:start position:0% +my bubble. And do you see what my bubble +function is? It's a function that goes + + align:start position:0% +function is? It's a function that goes + + + align:start position:0% +function is? It's a function that goes +there and straight. + + align:start position:0% +there and straight. + + + align:start position:0% +there and straight. +So it is continuous, no jumps, and it is + + align:start position:0% +So it is continuous, no jumps, and it is + + + align:start position:0% +So it is continuous, no jumps, and it is +second degree. It's a parabola. And I'll + + align:start position:0% +second degree. It's a parabola. And I'll + + + align:start position:0% +second degree. It's a parabola. And I'll +make its height one. And then there'll + + align:start position:0% +make its height one. And then there'll + + + align:start position:0% +make its height one. And then there'll +be another function. I if I had another + + align:start position:0% +be another function. I if I had another + + + align:start position:0% +be another function. I if I had another +color I could draw it. Well, I'll just + + align:start position:0% +color I could draw it. Well, I'll just + + + align:start position:0% +color I could draw it. Well, I'll just +do it with broken lines maybe. So + + align:start position:0% +do it with broken lines maybe. So + + + align:start position:0% +do it with broken lines maybe. So +there'll be another bubble function in + + align:start position:0% +there'll be another bubble function in + + + align:start position:0% +there'll be another bubble function in +here. Another a third bubble function in + + align:start position:0% +here. Another a third bubble function in + + + align:start position:0% +here. Another a third bubble function in +the third interval. And a fourth in the + + align:start position:0% +the third interval. And a fourth in the + + + align:start position:0% +the third interval. And a fourth in the +fourth interval. Do you see that? I've + + align:start position:0% +fourth interval. Do you see that? I've + + + align:start position:0% +fourth interval. Do you see that? I've +now got my old F1, F3, F5, and F7 were + + align:start position:0% +now got my old F1, F3, F5, and F7 were + + + align:start position:0% +now got my old F1, F3, F5, and F7 were +the hat functions, but now I've got a + + align:start position:0% +the hat functions, but now I've got a + + + align:start position:0% +the hat functions, but now I've got a +F2, F4, F6, and F8 that are + + align:start position:0% +F2, F4, F6, and F8 that are + + + align:start position:0% +F2, F4, F6, and F8 that are +uh these new trial functions. So part of + + align:start position:0% +uh these new trial functions. So part of + + + align:start position:0% +uh these new trial functions. So part of +the message is we can throw in + + align:start position:0% +the message is we can throw in + + + align:start position:0% +the message is we can throw in +additional functions. + + align:start position:0% +additional functions. + + + align:start position:0% +additional functions. +uh they don't have to be polomials + + align:start position:0% +uh they don't have to be polomials + + + align:start position:0% +uh they don't have to be polomials +uh but the those are the simplest + + align:start position:0% +uh but the those are the simplest + + + align:start position:0% +uh but the those are the simplest +choices. Why are they simple? Because + + align:start position:0% +choices. Why are they simple? Because + + + align:start position:0% +choices. Why are they simple? Because +you remember that in the end when I made + + align:start position:0% +you remember that in the end when I made + + + align:start position:0% +you remember that in the end when I made +the choice I have to do various + + align:start position:0% +the choice I have to do various + + + align:start position:0% +the choice I have to do various +integrations. So you remember that I + + align:start position:0% +integrations. So you remember that I + + + align:start position:0% +integrations. So you remember that I +have to integrate to find the entries ki + + align:start position:0% +have to integrate to find the entries ki + + + align:start position:0% +have to integrate to find the entries ki +j. Uh do you remember what that integral + + align:start position:0% +j. Uh do you remember what that integral + + + align:start position:0% +j. Uh do you remember what that integral +looked like? You certainly remember f I + + align:start position:0% +looked like? You certainly remember f I + + + align:start position:0% +looked like? You certainly remember f I +that was the integral of from zero to + + align:start position:0% +that was the integral of from zero to + + + align:start position:0% +that was the integral of from zero to +one of whatever function fi we had times + + align:start position:0% +one of whatever function fi we had times + + + align:start position:0% +one of whatever function fi we had times +the f ofx dx times the load right + + align:start position:0% +the f ofx dx times the load right + + + align:start position:0% +the f ofx dx times the load right +and these maybe we computed these you + + align:start position:0% +and these maybe we computed these you + + + align:start position:0% +and these maybe we computed these you +remember we computed these for the + + align:start position:0% +remember we computed these for the + + + align:start position:0% +remember we computed these for the +peacewise linear guys uh but I don't + + align:start position:0% +peacewise linear guys uh but I don't + + + align:start position:0% +peacewise linear guys uh but I don't +think I wrote down the expression that + + align:start position:0% +think I wrote down the expression that + + + align:start position:0% +think I wrote down the expression that +we we were really doing. So, let me just + + align:start position:0% +we we were really doing. So, let me just + + + align:start position:0% +we we were really doing. So, let me just +do that. It's C of X. There's a D U + + align:start position:0% +do that. It's C of X. There's a D U + + + align:start position:0% +do that. It's C of X. There's a D U +Well, yeah. D U no, DV + + align:start position:0% + + + + align:start position:0% + +J + + align:start position:0% +J + + + align:start position:0% +J +DX and a D VI + + align:start position:0% +DX and a D VI + + + align:start position:0% +DX and a D VI +DX. + + align:start position:0% +DX. + + + align:start position:0% +DX. +Those were the integrals that we had to + + align:start position:0% +Those were the integrals that we had to + + + align:start position:0% +Those were the integrals that we had to +do. And we were taking V's to be the + + align:start position:0% +do. And we were taking V's to be the + + + align:start position:0% +do. And we were taking V's to be the +same as V's. So no, + + align:start position:0% +same as V's. So no, + + + align:start position:0% +same as V's. So no, +maybe I'll just do that here because I + + align:start position:0% +maybe I'll just do that here because I + + + align:start position:0% +maybe I'll just do that here because I +don't plan to make any other choices at + + align:start position:0% +don't plan to make any other choices at + + + align:start position:0% +don't plan to make any other choices at +all. dx. + + align:start position:0% +all. dx. + + + align:start position:0% +all. dx. +So this this is it's a symmetric matrix. + + align:start position:0% +So this this is it's a symmetric matrix. + + + align:start position:0% +So this this is it's a symmetric matrix. +Now kji because uh if I if when I'm + + align:start position:0% +Now kji because uh if I if when I'm + + + align:start position:0% +Now kji because uh if I if when I'm +choosing fees the same as the v's this + + align:start position:0% +choosing fees the same as the v's this + + + align:start position:0% +choosing fees the same as the v's this +is what it looks like and I'm allowed to + + align:start position:0% +is what it looks like and I'm allowed to + + + align:start position:0% +is what it looks like and I'm allowed to +if I switch j and I I don't see any + + align:start position:0% +if I switch j and I I don't see any + + + align:start position:0% +if I switch j and I I don't see any +difference. So these are the things that + + align:start position:0% +difference. So these are the things that + + + align:start position:0% +difference. So these are the things that +have to be integrated and those are the + + align:start position:0% +have to be integrated and those are the + + + align:start position:0% +have to be integrated and those are the +ones we did integrate when f was + + align:start position:0% +ones we did integrate when f was + + + align:start position:0% +ones we did integrate when f was +peacewise linear. When f was peacewise + + align:start position:0% +peacewise linear. When f was peacewise + + + align:start position:0% +peacewise linear. When f was peacewise +linear the d the slope was peacewise + + align:start position:0% +linear the d the slope was peacewise + + + align:start position:0% +linear the d the slope was peacewise +constant and we had really easy + + align:start position:0% +constant and we had really easy + + + align:start position:0% +constant and we had really easy +integrals very easy integrals. This was + + align:start position:0% +integrals very easy integrals. This was + + + align:start position:0% +integrals very easy integrals. This was +these were constants in different. We + + align:start position:0% +these were constants in different. We + + + align:start position:0% +these were constants in different. We +had to pay attention to where where we + + align:start position:0% +had to pay attention to where where we + + + align:start position:0% +had to pay attention to where where we +were. Was the slope on a minus interval + + align:start position:0% +were. Was the slope on a minus interval + + + align:start position:0% +were. Was the slope on a minus interval +or on a plus interval, but they were + + align:start position:0% +or on a plus interval, but they were + + + align:start position:0% +or on a plus interval, but they were +easy to compute. And they led us back to + + align:start position:0% +easy to compute. And they led us back to + + + align:start position:0% +easy to compute. And they led us back to +the + + align:start position:0% +the + + + align:start position:0% +the +kind of matrix that we've seen before, + + align:start position:0% +kind of matrix that we've seen before, + + + align:start position:0% +kind of matrix that we've seen before, +the twos and minus ones. And our right + + align:start position:0% +the twos and minus ones. And our right + + + align:start position:0% +the twos and minus ones. And our right +hand sides look familiar. + + align:start position:0% +hand sides look familiar. + + + align:start position:0% +hand sides look familiar. +Now we've got new functions. + + align:start position:0% +Now we've got new functions. + + + align:start position:0% +Now we've got new functions. +We still have the same formulas. No + + align:start position:0% +We still have the same formulas. No + + + align:start position:0% +We still have the same formulas. No +change in formulas. That's the the the + + align:start position:0% +change in formulas. That's the the the + + + align:start position:0% +change in formulas. That's the the the +system is is really quite uh successful + + align:start position:0% +system is is really quite uh successful + + + align:start position:0% +system is is really quite uh successful +because these are the things that we + + align:start position:0% +because these are the things that we + + + align:start position:0% +because these are the things that we +have to compute. So now I'll have to + + align:start position:0% +have to compute. So now I'll have to + + + align:start position:0% +have to compute. So now I'll have to +integrate these parabas. + + align:start position:0% +integrate these parabas. + + + align:start position:0% +integrate these parabas. +These little parabas will be half of the + + align:start position:0% +These little parabas will be half of the + + + align:start position:0% +These little parabas will be half of the +fees will be little parabas and their + + align:start position:0% +fees will be little parabas and their + + + align:start position:0% +fees will be little parabas and their +derivatives will be linear. So you see + + align:start position:0% +derivatives will be linear. So you see + + + align:start position:0% +derivatives will be linear. So you see +I'll have more + + align:start position:0% +I'll have more + + + align:start position:0% +I'll have more +calculations to do which I don't plan to + + align:start position:0% +calculations to do which I don't plan to + + + align:start position:0% +calculations to do which I don't plan to +do but more integrations to for example + + align:start position:0% +do but more integrations to for example + + + align:start position:0% +do but more integrations to for example +the diagonal entry say 22 from which + + align:start position:0% +the diagonal entry say 22 from which + + + align:start position:0% +the diagonal entry say 22 from which +will come from the from that bubble with + + align:start position:0% +will come from the from that bubble with + + + align:start position:0% +will come from the from that bubble with +itself. + + align:start position:0% +itself. + + + align:start position:0% +itself. +K22 then will be the integral of C of X + + align:start position:0% +K22 then will be the integral of C of X + + + align:start position:0% +K22 then will be the integral of C of X +times the derivative of that bubble + + align:start position:0% +times the derivative of that bubble + + + align:start position:0% +times the derivative of that bubble +which will be a straight line times + + align:start position:0% +which will be a straight line times + + + align:start position:0% +which will be a straight line times +itself. So it' be squared uh and C is + + align:start position:0% +itself. So it' be squared uh and C is + + + align:start position:0% +itself. So it' be squared uh and C is +positive. So this this K22 is going to + + align:start position:0% +positive. So this this K22 is going to + + + align:start position:0% +positive. So this this K22 is going to +be some nice positive number. Uh but we + + align:start position:0% +be some nice positive number. Uh but we + + + align:start position:0% +be some nice positive number. Uh but we +have to figure out what it is. + + align:start position:0% +have to figure out what it is. + + + align:start position:0% +have to figure out what it is. +Maybe I'll just say one fact that we'll + + align:start position:0% +Maybe I'll just say one fact that we'll + + + align:start position:0% +Maybe I'll just say one fact that we'll +come back to and that the that this K is + + align:start position:0% +come back to and that the that this K is + + + align:start position:0% +come back to and that the that this K is +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +positive definite. It's you thought it + + align:start position:0% +positive definite. It's you thought it + + + align:start position:0% +positive definite. It's you thought it +would be by using the letter K. We kind + + align:start position:0% +would be by using the letter K. We kind + + + align:start position:0% +would be by using the letter K. We kind +of expected it to be and it will be + + align:start position:0% +of expected it to be and it will be + + + align:start position:0% +of expected it to be and it will be +it'll be symmetric because the fees and + + align:start position:0% +it'll be symmetric because the fees and + + + align:start position:0% +it'll be symmetric because the fees and +the V's are the same. So we're just + + align:start position:0% +the V's are the same. So we're just + + + align:start position:0% +the V's are the same. So we're just +doing thing and it turns out it's + + align:start position:0% +doing thing and it turns out it's + + + align:start position:0% +doing thing and it turns out it's +positive definite. So it's just great + + align:start position:0% +positive definite. So it's just great + + + align:start position:0% +positive definite. So it's just great +just great it's just we have a little + + align:start position:0% +just great it's just we have a little + + + align:start position:0% +just great it's just we have a little +more effort either to use a + + align:start position:0% +more effort either to use a + + + align:start position:0% +more effort either to use a +formula for integrating + + align:start position:0% +formula for integrating + + + align:start position:0% +formula for integrating +um polomials or using numerical + + align:start position:0% +um polomials or using numerical + + + align:start position:0% +um polomials or using numerical +integration one way or another and I + + align:start position:0% +integration one way or another and I + + + align:start position:0% +integration one way or another and I +won't concentrate now on that point we + + align:start position:0% +won't concentrate now on that point we + + + align:start position:0% +won't concentrate now on that point we +get these numbers okay oh but I here's + + align:start position:0% +get these numbers okay oh but I here's + + + align:start position:0% +get these numbers okay oh but I here's +something to concentrate on what what uh + + align:start position:0% +something to concentrate on what what uh + + + align:start position:0% +something to concentrate on what what uh +where what kind of a matrix K do we have + + align:start position:0% +where what kind of a matrix K do we have + + + align:start position:0% +where what kind of a matrix K do we have +so what what where will it be non zero + + align:start position:0% +so what what where will it be non zero + + + align:start position:0% +so what what where will it be non zero +let me so it'll be 8 by 8 right 8 by + + align:start position:0% +let me so it'll be 8 by 8 right 8 by + + + align:start position:0% +let me so it'll be 8 by 8 right 8 by +I'll I'll follow through on this uh on + + align:start position:0% +I'll I'll follow through on this uh on + + + align:start position:0% +I'll I'll follow through on this uh on +that choice just to say where will I see + + align:start position:0% +that choice just to say where will I see + + + align:start position:0% +that choice just to say where will I see +nonzeros here because if you if you get + + align:start position:0% +nonzeros here because if you if you get + + + align:start position:0% +nonzeros here because if you if you get +that point you you you see the the way + + align:start position:0% +that point you you you see the the way + + + align:start position:0% +that point you you you see the the way +things come together so + + align:start position:0% +things come together so + + + align:start position:0% +things come together so +I'll just put little x for nonzero So + + align:start position:0% +I'll just put little x for nonzero So + + + align:start position:0% +I'll just put little x for nonzero So +k11. + + align:start position:0% + + + + align:start position:0% + +So what what's that first row of k? It's + + align:start position:0% +So what what's that first row of k? It's + + + align:start position:0% +So what what's that first row of k? It's +coming from the first function + + align:start position:0% +coming from the first function + + + align:start position:0% +coming from the first function +integrated against itself k11. If for if + + align:start position:0% +integrated against itself k11. If for if + + + align:start position:0% +integrated against itself k11. If for if +for one one we'll get something there. + + align:start position:0% +for one one we'll get something there. + + + align:start position:0% +for one one we'll get something there. +Will we have something in in the one two + + align:start position:0% +Will we have something in in the one two + + + align:start position:0% +Will we have something in in the one two +position? + + align:start position:0% +position? + + + align:start position:0% +position? +So that's my question. Do we have + + align:start position:0% +So that's my question. Do we have + + + align:start position:0% +So that's my question. Do we have +something in the one two position? Uh + + align:start position:0% +something in the one two position? Uh + + + align:start position:0% +something in the one two position? Uh +what's one two? That's this function + + align:start position:0% +what's one two? That's this function + + + align:start position:0% +what's one two? That's this function +against the bubble function. Yes. Right. + + align:start position:0% +against the bubble function. Yes. Right. + + + align:start position:0% +against the bubble function. Yes. Right. +They're they're non zero at the same + + align:start position:0% +They're they're non zero at the same + + + align:start position:0% +They're they're non zero at the same +place. We can expect something there. + + align:start position:0% +place. We can expect something there. + + + align:start position:0% +place. We can expect something there. +What about K13? + + align:start position:0% +What about K13? + + + align:start position:0% +What about K13? +That's what we've done before. That's + + align:start position:0% +That's what we've done before. That's + + + align:start position:0% +That's what we've done before. That's +this one against this one. Yes, + + align:start position:0% +this one against this one. Yes, + + + align:start position:0% +this one against this one. Yes, +we expect a nonzero there. But then what + + align:start position:0% +we expect a nonzero there. But then what + + + align:start position:0% +we expect a nonzero there. But then what +after that? What am I what will the rest + + align:start position:0% +after that? What am I what will the rest + + + align:start position:0% +after that? What am I what will the rest +of that row be? zero because that first + + align:start position:0% +of that row be? zero because that first + + + align:start position:0% +of that row be? zero because that first +half hat doesn't touch + + align:start position:0% +half hat doesn't touch + + + align:start position:0% +half hat doesn't touch +any of the others. So let's let's go on. + + align:start position:0% +any of the others. So let's let's go on. + + + align:start position:0% +any of the others. So let's let's go on. +Of course, it'll be symmetric. So I know + + align:start position:0% +Of course, it'll be symmetric. So I know + + + align:start position:0% +Of course, it'll be symmetric. So I know +this I know this much. But now let me + + align:start position:0% +this I know this much. But now let me + + + align:start position:0% +this I know this much. But now let me +look. So this is the first this is the + + align:start position:0% +look. So this is the first this is the + + + align:start position:0% +look. So this is the first this is the +halfhat row + + align:start position:0% +halfhat row + + + align:start position:0% +halfhat row +and this is the first bubble row because + + align:start position:0% +and this is the first bubble row because + + + align:start position:0% +and this is the first bubble row because +that's because that was halfhat was F1 + + align:start position:0% +that's because that was halfhat was F1 + + + align:start position:0% +that's because that was halfhat was F1 +and now the first bubble is F2. What + + align:start position:0% +and now the first bubble is F2. What + + + align:start position:0% +and now the first bubble is F2. What +nonzeros do we get out of the out in the + + align:start position:0% +nonzeros do we get out of the out in the + + + align:start position:0% +nonzeros do we get out of the out in the +stiffness matrix? + + align:start position:0% +stiffness matrix? + + + align:start position:0% +stiffness matrix? +Again, we're we could + + align:start position:0% +Again, we're we could + + + align:start position:0% +Again, we're we could +I'm constructing it entry by entry. Uh + + align:start position:0% +I'm constructing it entry by entry. Uh + + + align:start position:0% +I'm constructing it entry by entry. Uh +another way to construct it will be + + align:start position:0% +another way to construct it will be + + + align:start position:0% +another way to construct it will be +element by element and stamp them in. + + align:start position:0% +element by element and stamp them in. + + + align:start position:0% +element by element and stamp them in. +You're you're beginning to see the idea + + align:start position:0% +You're you're beginning to see the idea + + + align:start position:0% +You're you're beginning to see the idea +of that. But let's So what do I get for + + align:start position:0% +of that. But let's So what do I get for + + + align:start position:0% +of that. But let's So what do I get for +that bubble? I I just look to see what + + align:start position:0% +that bubble? I I just look to see what + + + align:start position:0% +that bubble? I I just look to see what +who which elements touch that bubble and + + align:start position:0% +who which elements touch that bubble and + + + align:start position:0% +who which elements touch that bubble and +which ones do + + align:start position:0% + + + + align:start position:0% + +one two + + align:start position:0% +one two + + + align:start position:0% +one two +and three and not four right I think we + + align:start position:0% +and three and not four right I think we + + + align:start position:0% +and three and not four right I think we +only get in that row we only get so from + + align:start position:0% +only get in that row we only get so from + + + align:start position:0% +only get in that row we only get so from +that bubble I think we only get that + + align:start position:0% +that bubble I think we only get that + + + align:start position:0% +that bubble I think we only get that +much now we we're not quite seeing the + + align:start position:0% +much now we we're not quite seeing the + + + align:start position:0% +much now we we're not quite seeing the +picture yet let me go to the next hat + + align:start position:0% +picture yet let me go to the next hat + + + align:start position:0% +picture yet let me go to the next hat +the the the the the hat + + align:start position:0% +the the the the the hat + + + align:start position:0% +the the the the the hat +And then I'll do the bubble. + + align:start position:0% +And then I'll do the bubble. + + + align:start position:0% +And then I'll do the bubble. +Oh no, sorry. The hat's numbered F3. And + + align:start position:0% +Oh no, sorry. The hat's numbered F3. And + + + align:start position:0% +Oh no, sorry. The hat's numbered F3. And +then the next bubble is numbered F4. And + + align:start position:0% +then the next bubble is numbered F4. And + + + align:start position:0% +then the next bubble is numbered F4. And +let's Where do I get zeros? Yeah. Now + + align:start position:0% +let's Where do I get zeros? Yeah. Now + + + align:start position:0% +let's Where do I get zeros? Yeah. Now +you can tell me where do I get zeros + + align:start position:0% +you can tell me where do I get zeros + + + align:start position:0% +you can tell me where do I get zeros +from the from inner products from these + + align:start position:0% +from the from inner products from these + + + align:start position:0% +from the from inner products from these +guys when when I is three. So which fees + + align:start position:0% +guys when when I is three. So which fees + + + align:start position:0% +guys when when I is three. So which fees +does fee number three overlap? That's + + align:start position:0% +does fee number three overlap? That's + + + align:start position:0% +does fee number three overlap? That's +all I'm asking. + + align:start position:0% +all I'm asking. + + + align:start position:0% +all I'm asking. +Does it overlap number one? Yes. Does it + + align:start position:0% +Does it overlap number one? Yes. Does it + + + align:start position:0% +Does it overlap number one? Yes. Does it +overlap fee number two? Let's do you + + align:start position:0% +overlap fee number two? Let's do you + + + align:start position:0% +overlap fee number two? Let's do you +want to highlight? So, we're now looking + + align:start position:0% +want to highlight? So, we're now looking + + + align:start position:0% +want to highlight? So, we're now looking +at Fe3 at this hat. Oh god, where's it + + align:start position:0% +at Fe3 at this hat. Oh god, where's it + + + align:start position:0% +at Fe3 at this hat. Oh god, where's it +gone? + + align:start position:0% + + + + align:start position:0% + +That's the one we're doing now. + + align:start position:0% +That's the one we're doing now. + + + align:start position:0% +That's the one we're doing now. +So, what does it overlap? It overlaps + + align:start position:0% +So, what does it overlap? It overlaps + + + align:start position:0% +So, what does it overlap? It overlaps +the fir the half hat. Does it overlap + + align:start position:0% +the fir the half hat. Does it overlap + + + align:start position:0% +the fir the half hat. Does it overlap +the first bubble? Yes. Does it overlap + + align:start position:0% +the first bubble? Yes. Does it overlap + + + align:start position:0% +the first bubble? Yes. Does it overlap +itself? Yes. Does it overlap the second + + align:start position:0% +itself? Yes. Does it overlap the second + + + align:start position:0% +itself? Yes. Does it overlap the second +bubble? + + align:start position:0% +bubble? + + + align:start position:0% +bubble? +Yes. Does it overlap the the next hat? + + align:start position:0% +Yes. Does it overlap the the next hat? + + + align:start position:0% +Yes. Does it overlap the the next hat? +Yes. And then all zeros. Okay. And now + + align:start position:0% +Yes. And then all zeros. Okay. And now + + + align:start position:0% +Yes. And then all zeros. Okay. And now +do one more row. Bubble four. So now I'm + + align:start position:0% +do one more row. Bubble four. So now I'm + + + align:start position:0% +do one more row. Bubble four. So now I'm +looking at this guy. This next bubble. + + align:start position:0% +looking at this guy. This next bubble. + + + align:start position:0% +looking at this guy. This next bubble. +What does that overlap? + + align:start position:0% +What does that overlap? + + + align:start position:0% +What does that overlap? +Does it overlap the first uh the + + align:start position:0% +Does it overlap the first uh the + + + align:start position:0% +Does it overlap the first uh the +halfhat? + + align:start position:0% +halfhat? + + + align:start position:0% +halfhat? +Nope. Of course, symmetry told us that. + + align:start position:0% +Nope. Of course, symmetry told us that. + + + align:start position:0% +Nope. Of course, symmetry told us that. +Does it overlap the first does does the + + align:start position:0% +Does it overlap the first does does the + + + align:start position:0% +Does it overlap the first does does the +second bubble overlap the first bubble? + + align:start position:0% +second bubble overlap the first bubble? + + + align:start position:0% +second bubble overlap the first bubble? +No. Big point. Zero there. Does the + + align:start position:0% +No. Big point. Zero there. Does the + + + align:start position:0% +No. Big point. Zero there. Does the +second bubble overlap the + + align:start position:0% +second bubble overlap the + + + align:start position:0% +second bubble overlap the +the hat? Yes. Does the second bubble + + align:start position:0% +the hat? Yes. Does the second bubble + + + align:start position:0% +the hat? Yes. Does the second bubble +overlap itself? Certainly. On the + + align:start position:0% +overlap itself? Certainly. On the + + + align:start position:0% +overlap itself? Certainly. On the +diagonal, we have something. Does the + + align:start position:0% +diagonal, we have something. Does the + + + align:start position:0% +diagonal, we have something. Does the +second bubble overlap the next hat5? + + align:start position:0% +second bubble overlap the next hat5? + + + align:start position:0% +second bubble overlap the next hat5? +Yes. And that's it. + + align:start position:0% +Yes. And that's it. + + + align:start position:0% +Yes. And that's it. +Uh, I think the second bubble does not + + align:start position:0% +Uh, I think the second bubble does not + + + align:start position:0% +Uh, I think the second bubble does not +overlap the the following bubble. + + align:start position:0% +overlap the the following bubble. + + + align:start position:0% +overlap the the following bubble. +I don't know if you see what pattern + + align:start position:0% +I don't know if you see what pattern + + + align:start position:0% +I don't know if you see what pattern +we're getting here. + + align:start position:0% + + + + align:start position:0% + +The this was those were special rows + + align:start position:0% +The this was those were special rows + + + align:start position:0% +The this was those were special rows +because that was only a half hat. These + + align:start position:0% +because that was only a half hat. These + + + align:start position:0% +because that was only a half hat. These +are typical rows. A typical hat function + + align:start position:0% +are typical rows. A typical hat function + + + align:start position:0% +are typical rows. A typical hat function +has get that row is showing us five + + align:start position:0% +has get that row is showing us five + + + align:start position:0% +has get that row is showing us five +nonzeros because it overlaps itself, the + + align:start position:0% +nonzeros because it overlaps itself, the + + + align:start position:0% +nonzeros because it overlaps itself, the +neighboring hats and the neighboring + + align:start position:0% +neighboring hats and the neighboring + + + align:start position:0% +neighboring hats and the neighboring +bubbles. But the bubble row only has + + align:start position:0% +bubbles. But the bubble row only has + + + align:start position:0% +bubbles. But the bubble row only has +three because a bubble overlaps itself, + + align:start position:0% +three because a bubble overlaps itself, + + + align:start position:0% +three because a bubble overlaps itself, +the neighboring hat on each side, but + + align:start position:0% +the neighboring hat on each side, but + + + align:start position:0% +the neighboring hat on each side, but +not the ne not the neighboring bubbles. + + align:start position:0% +not the ne not the neighboring bubbles. + + + align:start position:0% +not the ne not the neighboring bubbles. +So we have only three nonzeros. Do you + + align:start position:0% +So we have only three nonzeros. Do you + + + align:start position:0% +So we have only three nonzeros. Do you +see that? The next row will have five. + + align:start position:0% +see that? The next row will have five. + + + align:start position:0% +see that? The next row will have five. +Yeah. Will I get it right? Hope so. The + + align:start position:0% +Yeah. Will I get it right? Hope so. The + + + align:start position:0% +Yeah. Will I get it right? Hope so. The +next row, I think, will have I think + + align:start position:0% +next row, I think, will have I think + + + align:start position:0% +next row, I think, will have I think +they'd be here. + + align:start position:0% + + + + align:start position:0% + +And then the next row will have only + + align:start position:0% +And then the next row will have only + + + align:start position:0% +And then the next row will have only +only three guys. Maybe here, here, here. + + align:start position:0% +only three guys. Maybe here, here, here. + + + align:start position:0% +only three guys. Maybe here, here, here. +It's uh + + align:start position:0% +It's uh + + + align:start position:0% +It's uh +well, it's certainly a band matrix. + + align:start position:0% +well, it's certainly a band matrix. + + + align:start position:0% +well, it's certainly a band matrix. +And so, so you could say, okay, it's a + + align:start position:0% +And so, so you could say, okay, it's a + + + align:start position:0% +And so, so you could say, okay, it's a +band matrix. I wouldn't call it trid + + align:start position:0% +band matrix. I wouldn't call it trid + + + align:start position:0% +band matrix. I wouldn't call it trid +diagonal anymore. What might I call the + + align:start position:0% +diagonal anymore. What might I call the + + + align:start position:0% +diagonal anymore. What might I call the +if I had if I showed you that matrix and + + align:start position:0% +if I had if I showed you that matrix and + + + align:start position:0% +if I had if I showed you that matrix and +said, what kind of a matrix? You'd say a + + align:start position:0% +said, what kind of a matrix? You'd say a + + + align:start position:0% +said, what kind of a matrix? You'd say a +band matrix. Uh, if you wanted to tell + + align:start position:0% +band matrix. Uh, if you wanted to tell + + + align:start position:0% +band matrix. Uh, if you wanted to tell +me that it had five bands, you could + + align:start position:0% +me that it had five bands, you could + + + align:start position:0% +me that it had five bands, you could +maybe say penta diagonal or something. + + align:start position:0% +maybe say penta diagonal or something. + + + align:start position:0% +maybe say penta diagonal or something. +But it's easy to work with. Of course, + + align:start position:0% +But it's easy to work with. Of course, + + + align:start position:0% +But it's easy to work with. Of course, +that's the point of finite elements is + + align:start position:0% +that's the point of finite elements is + + + align:start position:0% +that's the point of finite elements is +that everything all the functions are + + align:start position:0% +that everything all the functions are + + + align:start position:0% +that everything all the functions are +local so that we get all zeros when + + align:start position:0% +local so that we get all zeros when + + + align:start position:0% +local so that we get all zeros when +elements when when trial functions don't + + align:start position:0% +elements when when trial functions don't + + + align:start position:0% +elements when when trial functions don't +overlap. Uh my my additional point was + + align:start position:0% +overlap. Uh my my additional point was + + + align:start position:0% +overlap. Uh my my additional point was +just a small one that it's not a big + + align:start position:0% +just a small one that it's not a big + + + align:start position:0% +just a small one that it's not a big +deal but it's like a little bit worth + + align:start position:0% +deal but it's like a little bit worth + + + align:start position:0% +deal but it's like a little bit worth +noticing. these ones, these rows with + + align:start position:0% +noticing. these ones, these rows with + + + align:start position:0% +noticing. these ones, these rows with +three only three entries, three + + align:start position:0% +three only three entries, three + + + align:start position:0% +three only three entries, three +nonzeros. Uh those + + align:start position:0% + + + + align:start position:0% + +I guess what I want to say is I could + + align:start position:0% +I guess what I want to say is I could + + + align:start position:0% +I guess what I want to say is I could +eliminate I could I have to solve eight + + align:start position:0% +eliminate I could I have to solve eight + + + align:start position:0% +eliminate I could I have to solve eight +equations and eight unknowns. + + align:start position:0% +equations and eight unknowns. + + + align:start position:0% +equations and eight unknowns. +And the normal way to do it would be + + align:start position:0% +And the normal way to do it would be + + + align:start position:0% +And the normal way to do it would be +just elimination LU. That would work + + align:start position:0% +just elimination LU. That would work + + + align:start position:0% +just elimination LU. That would work +fine. Start from the top, eliminate and + + align:start position:0% +fine. Start from the top, eliminate and + + + align:start position:0% +fine. Start from the top, eliminate and +uh you got it. Uh and of course in one + + align:start position:0% +uh you got it. Uh and of course in one + + + align:start position:0% +uh you got it. Uh and of course in one +dimension that's nobody would do + + align:start position:0% +dimension that's nobody would do + + + align:start position:0% +dimension that's nobody would do +anything else. That would be simple. Uh + + align:start position:0% +anything else. That would be simple. Uh + + + align:start position:0% +anything else. That would be simple. Uh +I I I just want to say these bubbles by + + align:start position:0% +I I I just want to say these bubbles by + + + align:start position:0% +I I I just want to say these bubbles by +giving me extra zeros. + + align:start position:0% +giving me extra zeros. + + + align:start position:0% +giving me extra zeros. +I could eliminate the bubbles first. I + + align:start position:0% +I could eliminate the bubbles first. I + + + align:start position:0% +I could eliminate the bubbles first. I +I'll just can I just make this point but + + align:start position:0% +I'll just can I just make this point but + + + align:start position:0% +I'll just can I just make this point but +not labor it? Uh I could eliminate the + + align:start position:0% +not labor it? Uh I could eliminate the + + + align:start position:0% +not labor it? Uh I could eliminate the +bubbles first. I could my I could use + + align:start position:0% +bubbles first. I could my I could use + + + align:start position:0% +bubbles first. I could my I could use +this this this equation to uh express + + align:start position:0% +this this this equation to uh express + + + align:start position:0% +this this this equation to uh express +the bubble coefficient in terms of its + + align:start position:0% +the bubble coefficient in terms of its + + + align:start position:0% +the bubble coefficient in terms of its +neighbors. I could use this one to + + align:start position:0% +neighbors. I could use this one to + + + align:start position:0% +neighbors. I could use this one to +express the bubble coefficient in terms + + align:start position:0% +express the bubble coefficient in terms + + + align:start position:0% +express the bubble coefficient in terms +of its neighbors and I could plug back + + align:start position:0% +of its neighbors and I could plug back + + + align:start position:0% +of its neighbors and I could plug back +into the other equations. I could get I + + align:start position:0% +into the other equations. I could get I + + + align:start position:0% +into the other equations. I could get I +could simplify this. Um + + align:start position:0% +could simplify this. Um + + + align:start position:0% +could simplify this. Um +I could I could get the bubbles done + + align:start position:0% +I could I could get the bubbles done + + + align:start position:0% +I could I could get the bubbles done +first if I wanted. I I I can see that to + + align:start position:0% +first if I wanted. I I I can see that to + + + align:start position:0% +first if I wanted. I I I can see that to +to go into the gory details is is + + align:start position:0% +to go into the gory details is is + + + align:start position:0% +to go into the gory details is is +probably not wise. But but bubbles are + + align:start position:0% +probably not wise. But but bubbles are + + + align:start position:0% +probably not wise. But but bubbles are +easy to do. + + align:start position:0% +easy to do. + + + align:start position:0% +easy to do. +However, + + align:start position:0% + + + + align:start position:0% + +uh we can do there are better elements. + + align:start position:0% + + + + align:start position:0% + +So that's that's my discussion of + + align:start position:0% +So that's that's my discussion of + + + align:start position:0% +So that's that's my discussion of +quadratic elements almost complete. + + align:start position:0% +quadratic elements almost complete. + + + align:start position:0% +quadratic elements almost complete. +It's not a big favorite because cubics + + align:start position:0% +It's not a big favorite because cubics + + + align:start position:0% +It's not a big favorite because cubics +are better. So why are cubics better? + + align:start position:0% +are better. So why are cubics better? + + + align:start position:0% +are better. So why are cubics better? +Why are cubics better? And now so you're + + align:start position:0% +Why are cubics better? And now so you're + + + align:start position:0% +Why are cubics better? And now so you're +going to say okay upgrade to cubics. How + + align:start position:0% +going to say okay upgrade to cubics. How + + + align:start position:0% +going to say okay upgrade to cubics. How +shall I do that? And and and what's so + + align:start position:0% +shall I do that? And and and what's so + + + align:start position:0% +shall I do that? And and and what's so +and I want to say a word about the error + + align:start position:0% +and I want to say a word about the error + + + align:start position:0% +and I want to say a word about the error +here. The of course the reason + + align:start position:0% +here. The of course the reason + + + align:start position:0% +here. The of course the reason +quadratics are better than cubics and I + + align:start position:0% +quadratics are better than cubics and I + + + align:start position:0% +quadratics are better than cubics and I +mean sorry the reason quadratics are + + align:start position:0% +mean sorry the reason quadratics are + + + align:start position:0% +mean sorry the reason quadratics are +better than linear and cubics will be + + align:start position:0% +better than linear and cubics will be + + + align:start position:0% +better than linear and cubics will be +better than quadratics is I'm getting + + align:start position:0% +better than quadratics is I'm getting + + + align:start position:0% +better than quadratics is I'm getting +more accuracy I'm if I approximate yeah + + align:start position:0% +more accuracy I'm if I approximate yeah + + + align:start position:0% +more accuracy I'm if I approximate yeah +how suppose I have a my true solution + + align:start position:0% +how suppose I have a my true solution + + + align:start position:0% +how suppose I have a my true solution +may be some curve like that okay my + + align:start position:0% +may be some curve like that okay my + + + align:start position:0% +may be some curve like that okay my +peacewise linear elements suppose + + align:start position:0% +peacewise linear elements suppose + + + align:start position:0% +peacewise linear elements suppose +suppose suppose the peacewise linear + + align:start position:0% +suppose suppose the peacewise linear + + + align:start position:0% +suppose suppose the peacewise linear +element ments happen to be as they would + + align:start position:0% +element ments happen to be as they would + + + align:start position:0% +element ments happen to be as they would +in a special model problem right on the + + align:start position:0% +in a special model problem right on the + + + align:start position:0% +in a special model problem right on the +money at the nodes. + + align:start position:0% +money at the nodes. + + + align:start position:0% +money at the nodes. +Usually they won't be. But what would be + + align:start position:0% +Usually they won't be. But what would be + + + align:start position:0% +Usually they won't be. But what would be +the error in that one? Well, no error at + + align:start position:0% +the error in that one? Well, no error at + + + align:start position:0% +the error in that one? Well, no error at +all in at the nodes as I've drawn it. + + align:start position:0% +all in at the nodes as I've drawn it. + + + align:start position:0% +all in at the nodes as I've drawn it. +But that that's not what I'm interested + + align:start position:0% +But that that's not what I'm interested + + + align:start position:0% +But that that's not what I'm interested +in. I'm interested in how big is that? + + align:start position:0% +in. I'm interested in how big is that? + + + align:start position:0% +in. I'm interested in how big is that? +How far off is the displacement? Uh + + align:start position:0% +How far off is the displacement? Uh + + + align:start position:0% +How far off is the displacement? Uh +because + + align:start position:0% +because + + + align:start position:0% +because +What's the maximum error in the + + align:start position:0% +What's the maximum error in the + + + align:start position:0% +What's the maximum error in the +displacement? + + align:start position:0% +displacement? + + + align:start position:0% +displacement? +Do you have any idea if this is size h + + align:start position:0% +Do you have any idea if this is size h + + + align:start position:0% +Do you have any idea if this is size h +delta x? Shall I call delta? Should I + + align:start position:0% +delta x? Shall I call delta? Should I + + + align:start position:0% +delta x? Shall I call delta? Should I +call it delta x or h? + + align:start position:0% + + + + align:start position:0% + +If I + + align:start position:0% +If I + + + align:start position:0% +If I +how how far does a curving function + + align:start position:0% +how how far does a curving function + + + align:start position:0% +how how far does a curving function +escape from the from the I I need to + + align:start position:0% +escape from the from the I I need to + + + align:start position:0% +escape from the from the I I need to +blow that up, don't I? So I have a + + align:start position:0% +blow that up, don't I? So I have a + + + align:start position:0% +blow that up, don't I? So I have a +curving function and and a linear + + align:start position:0% +curving function and and a linear + + + align:start position:0% +curving function and and a linear +function and I want to know how far + + align:start position:0% +function and I want to know how far + + + align:start position:0% +function and I want to know how far +apart they are over a distance of length + + align:start position:0% +apart they are over a distance of length + + + align:start position:0% +apart they are over a distance of length +delta x. What what's this scale? + + align:start position:0% +delta x. What what's this scale? + + + align:start position:0% +delta x. What what's this scale? +That's that's the question I'm + + align:start position:0% +That's that's the question I'm + + + align:start position:0% +That's that's the question I'm +it's just good to it it'll have a simple + + align:start position:0% +it's just good to it it'll have a simple + + + align:start position:0% +it's just good to it it'll have a simple +answer and and it's great to know it. + + align:start position:0% +answer and and it's great to know it. + + + align:start position:0% +answer and and it's great to know it. +Anybody want to make a guess what is + + align:start position:0% +Anybody want to make a guess what is + + + align:start position:0% +Anybody want to make a guess what is +that? Is that scale of size delta x? Is + + align:start position:0% +that? Is that scale of size delta x? Is + + + align:start position:0% +that? Is that scale of size delta x? Is +it of size delta x squar? Size delta x + + align:start position:0% +it of size delta x squar? Size delta x + + + align:start position:0% +it of size delta x squar? Size delta x +cub. That's it's that exponent of delta + + align:start position:0% +cub. That's it's that exponent of delta + + + align:start position:0% +cub. That's it's that exponent of delta +x that is telling me how big is the + + align:start position:0% +x that is telling me how big is the + + + align:start position:0% +x that is telling me how big is the +error. + + align:start position:0% +error. + + + align:start position:0% +error. +And uh it's easy to find once you get + + align:start position:0% +And uh it's easy to find once you get + + + align:start position:0% +And uh it's easy to find once you get +the hang of it. Anybody want to make a + + align:start position:0% +the hang of it. Anybody want to make a + + + align:start position:0% +the hang of it. Anybody want to make a +guess? Delta x squared. Squared would be + + align:start position:0% +guess? Delta x squared. Squared would be + + + align:start position:0% +guess? Delta x squared. Squared would be +the right guess. Squared would be the + + align:start position:0% +the right guess. Squared would be the + + + align:start position:0% +the right guess. Squared would be the +right guess. Uh we could uh I could I + + align:start position:0% +right guess. Uh we could uh I could I + + + align:start position:0% +right guess. Uh we could uh I could I +could just turn that picture + + align:start position:0% +could just turn that picture + + + align:start position:0% +could just turn that picture +if if we wanted to. Uh again, this is + + align:start position:0% +if if we wanted to. Uh again, this is + + + align:start position:0% +if if we wanted to. Uh again, this is +delta x. Here's some + + align:start position:0% +delta x. Here's some + + + align:start position:0% +delta x. Here's some +now the it would look like that pretty + + align:start position:0% +now the it would look like that pretty + + + align:start position:0% +now the it would look like that pretty +much doesn't have to be symmetric of + + align:start position:0% +much doesn't have to be symmetric of + + + align:start position:0% +much doesn't have to be symmetric of +course because this could have this + + align:start position:0% +course because this could have this + + + align:start position:0% +course because this could have this +could be a complicated function. But + + align:start position:0% +could be a complicated function. But + + + align:start position:0% +could be a complicated function. But +when I focus on a little delta x + + align:start position:0% +when I focus on a little delta x + + + align:start position:0% +when I focus on a little delta x +interval + + align:start position:0% +interval + + + align:start position:0% +interval +every function uh looks like a little + + align:start position:0% +every function uh looks like a little + + + align:start position:0% +every function uh looks like a little +polomial and and this the the error + + align:start position:0% +polomial and and this the the error + + + align:start position:0% +polomial and and this the the error +there let's see what would that function + + align:start position:0% +there let's see what would that function + + + align:start position:0% +there let's see what would that function +be uh uh so + + align:start position:0% +be uh uh so + + + align:start position:0% +be uh uh so +yeah yeah what what this ah + + align:start position:0% +yeah yeah what what this ah + + + align:start position:0% +yeah yeah what what this ah +let me uh I won't uh + + align:start position:0% +let me uh I won't uh + + + align:start position:0% +let me uh I won't uh +I I could go forever on this. But look, + + align:start position:0% +I I could go forever on this. But look, + + + align:start position:0% +I I could go forever on this. But look, +if the slope is something whatever, then + + align:start position:0% +if the slope is something whatever, then + + + align:start position:0% +if the slope is something whatever, then +then it gets up to a height of + + align:start position:0% +then it gets up to a height of + + + align:start position:0% +then it gets up to a height of +let me change numbers here. Let me call + + align:start position:0% +let me change numbers here. Let me call + + + align:start position:0% +let me change numbers here. Let me call +it from zero to y. + + align:start position:0% +it from zero to y. + + + align:start position:0% +it from zero to y. +What would be a little parabola that + + align:start position:0% +What would be a little parabola that + + + align:start position:0% +What would be a little parabola that +that has a has a slope of one, let's + + align:start position:0% +that has a has a slope of one, let's + + + align:start position:0% +that has a has a slope of one, let's +say, at both ends. + + align:start position:0% +say, at both ends. + + + align:start position:0% +say, at both ends. +What would that parabola be? That's we + + align:start position:0% +What would that parabola be? That's we + + + align:start position:0% +What would that parabola be? That's we +probably have seen that before. Or if I + + align:start position:0% +probably have seen that before. Or if I + + + align:start position:0% +probably have seen that before. Or if I +wanted a slope of one at both ends, it + + align:start position:0% +wanted a slope of one at both ends, it + + + align:start position:0% +wanted a slope of one at both ends, it +would be something like the the + + align:start position:0% +would be something like the the + + + align:start position:0% +would be something like the the +polomial. Oh, + + align:start position:0% + + + + align:start position:0% + +the polomial would be something like Oh, + + align:start position:0% +the polomial would be something like Oh, + + + align:start position:0% +the polomial would be something like Oh, +what would it be? Yeah, sorry. Tell me + + align:start position:0% +what would it be? Yeah, sorry. Tell me + + + align:start position:0% +what would it be? Yeah, sorry. Tell me +that little polomial. It's a polomial in + + align:start position:0% +that little polomial. It's a polomial in + + + align:start position:0% +that little polomial. It's a polomial in +x. It's just a quadratic. It's its slope + + align:start position:0% +x. It's just a quadratic. It's its slope + + + align:start position:0% +x. It's just a quadratic. It's its slope +is one. So, it maybe starts with an x + + align:start position:0% +is one. So, it maybe starts with an x + + + align:start position:0% +is one. So, it maybe starts with an x +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +uh I've got to bring it down here. Uh + + align:start position:0% +uh I've got to bring it down here. Uh + + + align:start position:0% +uh I've got to bring it down here. Uh +yeah. Is it x times 1 - + + align:start position:0% +yeah. Is it x times 1 - + + + align:start position:0% +yeah. Is it x times 1 - +x over + + align:start position:0% +x over + + + align:start position:0% +x over +I didn't like y ever in the first place? + + align:start position:0% +I didn't like y ever in the first place? + + + align:start position:0% +I didn't like y ever in the first place? +Um + + align:start position:0% +Um + + + align:start position:0% +Um +what do I want to put there? I don't + + align:start position:0% +what do I want to put there? I don't + + + align:start position:0% +what do I want to put there? I don't +want to put a one. That's that would + + align:start position:0% +want to put a one. That's that would + + + align:start position:0% +want to put a one. That's that would +make it look big. It's really + + align:start position:0% +make it look big. It's really + + + align:start position:0% +make it look big. It's really +Ah, y is there. Okay. So I I think that + + align:start position:0% +Ah, y is there. Okay. So I I think that + + + align:start position:0% +Ah, y is there. Okay. So I I think that +quadratic + + align:start position:0% +quadratic + + + align:start position:0% +quadratic +is zero at zero because of that term. + + align:start position:0% +is zero at zero because of that term. + + + align:start position:0% +is zero at zero because of that term. +It's zero at x= y because of that term. + + align:start position:0% +It's zero at x= y because of that term. + + + align:start position:0% +It's zero at x= y because of that term. +It's second degree. And I think its + + align:start position:0% +It's second degree. And I think its + + + align:start position:0% +It's second degree. And I think its +height is a maximum right there. And + + align:start position:0% +height is a maximum right there. And + + + align:start position:0% +height is a maximum right there. And +what is that height at at y over two? + + align:start position:0% +what is that height at at y over two? + + + align:start position:0% +what is that height at at y over two? +This is y over two. This is y over two. + + align:start position:0% +This is y over two. This is y over two. + + + align:start position:0% +This is y over two. This is y over two. +That height is y^2 over 4. + + align:start position:0% +That height is y^2 over 4. + + + align:start position:0% +That height is y^2 over 4. +That's what I was shooting for the + + align:start position:0% +That's what I was shooting for the + + + align:start position:0% +That's what I was shooting for the +square that in a little interval of + + align:start position:0% +square that in a little interval of + + + align:start position:0% +square that in a little interval of +length y or length delta x if I draw a + + align:start position:0% +length y or length delta x if I draw a + + + align:start position:0% +length y or length delta x if I draw a +little parabola and I'm matching at the + + align:start position:0% +little parabola and I'm matching at the + + + align:start position:0% +little parabola and I'm matching at the +ends then the the height it reaches is + + align:start position:0% +ends then the the height it reaches is + + + align:start position:0% +ends then the the height it reaches is +like y^2 that that's the scaling right + + align:start position:0% +like y^2 that that's the scaling right + + + align:start position:0% +like y^2 that that's the scaling right +so that my conclusion is that if I use + + align:start position:0% +so that my conclusion is that if I use + + + align:start position:0% +so that my conclusion is that if I use +these basic hat function elements the + + align:start position:0% +these basic hat function elements the + + + align:start position:0% +these basic hat function elements the +error in the error I get is so can I + + align:start position:0% +error in the error I get is so can I + + + align:start position:0% +error in the error I get is so can I +list the errors the error is delta x squ + + align:start position:0% +list the errors the error is delta x squ + + + align:start position:0% +list the errors the error is delta x squ +that's the er that's the displacement + + align:start position:0% +that's the er that's the displacement + + + align:start position:0% +that's the er that's the displacement +error the error in u + + align:start position:0% +error the error in u + + + align:start position:0% +error the error in u +it's I'm not proving anything the the + + align:start position:0% +it's I'm not proving anything the the + + + align:start position:0% +it's I'm not proving anything the the +dis careful discussion of of the + + align:start position:0% +dis careful discussion of of the + + + align:start position:0% +dis careful discussion of of the +accuracy is a later section in the book + + align:start position:0% +accuracy is a later section in the book + + + align:start position:0% +accuracy is a later section in the book +but I'm trying to make the main point is + + align:start position:0% +but I'm trying to make the main point is + + + align:start position:0% +but I'm trying to make the main point is +that if We're fitting functions by + + align:start position:0% +that if We're fitting functions by + + + align:start position:0% +that if We're fitting functions by +straight lines then we have an error of + + align:start position:0% +straight lines then we have an error of + + + align:start position:0% +straight lines then we have an error of +delta x squar and we have what's the + + align:start position:0% +delta x squar and we have what's the + + + align:start position:0% +delta x squar and we have what's the +slope error? What do you think is the + + align:start position:0% +slope error? What do you think is the + + + align:start position:0% +slope error? What do you think is the +slope error but in + + align:start position:0% +slope error but in + + + align:start position:0% +slope error but in +because for us that slope is important + + align:start position:0% +because for us that slope is important + + + align:start position:0% +because for us that slope is important +that's the error in the stretching and + + align:start position:0% +that's the error in the stretching and + + + align:start position:0% +that's the error in the stretching and +the strain. So the error in the function + + align:start position:0% +the strain. So the error in the function + + + align:start position:0% +the strain. So the error in the function +is delta x squared. The error in the + + align:start position:0% +is delta x squared. The error in the + + + align:start position:0% +is delta x squared. The error in the +slope will be one order less just delta + + align:start position:0% +slope will be one order less just delta + + + align:start position:0% +slope will be one order less just delta +x. Okay, I I'll come back to all this. + + align:start position:0% +x. Okay, I I'll come back to all this. + + + align:start position:0% +x. Okay, I I'll come back to all this. +If now make a guess. + + align:start position:0% +If now make a guess. + + + align:start position:0% +If now make a guess. +Suppose I include these bubble functions + + align:start position:0% +Suppose I include these bubble functions + + + align:start position:0% +Suppose I include these bubble functions +on a on the with with delta x as my as + + align:start position:0% +on a on the with with delta x as my as + + + align:start position:0% +on a on the with with delta x as my as +my uh length scale horizontally. What + + align:start position:0% +my uh length scale horizontally. What + + + align:start position:0% +my uh length scale horizontally. What +will be the scale of the error? What do + + align:start position:0% +will be the scale of the error? What do + + + align:start position:0% +will be the scale of the error? What do +you guess is the expected error in + + align:start position:0% +you guess is the expected error in + + + align:start position:0% +you guess is the expected error in +displacement for uh um general problem + + align:start position:0% +displacement for uh um general problem + + + align:start position:0% +displacement for uh um general problem +for general c of x and f ofx uh which I + + align:start position:0% +for general c of x and f ofx uh which I + + + align:start position:0% +for general c of x and f ofx uh which I +which I won't get exactly right but how + + align:start position:0% +which I won't get exactly right but how + + + align:start position:0% +which I won't get exactly right but how +close will I come I'll I'll come within + + align:start position:0% +close will I come I'll I'll come within + + + align:start position:0% +close will I come I'll I'll come within +delta x to what power + + align:start position:0% +delta x to what power + + + align:start position:0% +delta x to what power +make a guess please + + align:start position:0% +make a guess please + + + align:start position:0% +make a guess please +four is a optimist + + align:start position:0% +four is a optimist + + + align:start position:0% +four is a optimist +well I won't get up to four cubed. I'll + + align:start position:0% +well I won't get up to four cubed. I'll + + + align:start position:0% +well I won't get up to four cubed. I'll +only get cubed. I'll get one by by + + align:start position:0% +only get cubed. I'll get one by by + + + align:start position:0% +only get cubed. I'll get one by by +increasing the the degree of the + + align:start position:0% +increasing the the degree of the + + + align:start position:0% +increasing the the degree of the +polomial by one. I'll get one degree + + align:start position:0% +polomial by one. I'll get one degree + + + align:start position:0% +polomial by one. I'll get one degree +better. + + align:start position:0% +better. + + + align:start position:0% +better. +So you you could look at it this way. + + align:start position:0% +So you you could look at it this way. + + + align:start position:0% +So you you could look at it this way. +Suppose I have a t suppose I have any + + align:start position:0% +Suppose I have a t suppose I have any + + + align:start position:0% +Suppose I have a t suppose I have any +function. + + align:start position:0% +function. + + + align:start position:0% +function. +Yeah, this is another way to think about + + align:start position:0% +Yeah, this is another way to think about + + + align:start position:0% +Yeah, this is another way to think about +the accuracy. Suppose I have any + + align:start position:0% +the accuracy. Suppose I have any + + + align:start position:0% +the accuracy. Suppose I have any +function f ofx. Okay, + + align:start position:0% +function f ofx. Okay, + + + align:start position:0% +function f ofx. Okay, +one of the things the whole whole point + + align:start position:0% +one of the things the whole whole point + + + align:start position:0% +one of the things the whole whole point +of calculus is that I could start it's + + align:start position:0% +of calculus is that I could start it's + + + align:start position:0% +of calculus is that I could start it's +if I start where it is at zero then I + + align:start position:0% +if I start where it is at zero then I + + + align:start position:0% +if I start where it is at zero then I +add in + + align:start position:0% +add in + + + align:start position:0% +add in +frime at zero the slope times x then I + + align:start position:0% +frime at zero the slope times x then I + + + align:start position:0% +frime at zero the slope times x then I +add in 12 fp prime at zero time x2 and + + align:start position:0% +add in 12 fp prime at zero time x2 and + + + align:start position:0% +add in 12 fp prime at zero time x2 and +so on right + + align:start position:0% +so on right + + + align:start position:0% +so on right +that's called the tailaylor series + + align:start position:0% +that's called the tailaylor series + + + align:start position:0% +that's called the tailaylor series +That's and we're not paying any + + align:start position:0% +That's and we're not paying any + + + align:start position:0% +That's and we're not paying any +attention about to convergence or high + + align:start position:0% +attention about to convergence or high + + + align:start position:0% +attention about to convergence or high +high order. It's the early terms that + + align:start position:0% +high order. It's the early terms that + + + align:start position:0% +high order. It's the early terms that +I'm interested in. And the point is that + + align:start position:0% +I'm interested in. And the point is that + + + align:start position:0% +I'm interested in. And the point is that +if my functions include linear + + align:start position:0% +if my functions include linear + + + align:start position:0% +if my functions include linear +functions, + + align:start position:0% +functions, + + + align:start position:0% +functions, +the hats, the hat, which the hats did, + + align:start position:0% +the hats, the hat, which the hats did, + + + align:start position:0% +the hats, the hat, which the hats did, +they will be able to get these terms + + align:start position:0% +they will be able to get these terms + + + align:start position:0% +they will be able to get these terms +right. And this will be the error that I + + align:start position:0% +right. And this will be the error that I + + + align:start position:0% +right. And this will be the error that I +I miss. I I'm just looking to see what's + + align:start position:0% +I miss. I I'm just looking to see what's + + + align:start position:0% +I miss. I I'm just looking to see what's +the first term in the tailaylor series + + align:start position:0% +the first term in the tailaylor series + + + align:start position:0% +the first term in the tailaylor series +that I will not get. And if I only have + + align:start position:0% +that I will not get. And if I only have + + + align:start position:0% +that I will not get. And if I only have +hat functions, I can't get an x squ. I + + align:start position:0% +hat functions, I can't get an x squ. I + + + align:start position:0% +hat functions, I can't get an x squ. I +can't get a parabola. But when I go here + + align:start position:0% +can't get a parabola. But when I go here + + + align:start position:0% +can't get a parabola. But when I go here +and include the the x squares, I can get + + align:start position:0% +and include the the x squares, I can get + + + align:start position:0% +and include the the x squares, I can get +that term right. So then it'll be the 16 + + align:start position:0% +that term right. So then it'll be the 16 + + + align:start position:0% +that term right. So then it'll be the 16 +f triple prime x cub that I miss. So + + align:start position:0% +f triple prime x cub that I miss. So + + + align:start position:0% +f triple prime x cub that I miss. So +it'll be the the error will be the the + + align:start position:0% +it'll be the the error will be the the + + + align:start position:0% +it'll be the the error will be the the +the the next missing term. Okay, so + + align:start position:0% +the the next missing term. Okay, so + + + align:start position:0% +the the next missing term. Okay, so +that's thoughts about the error and and + + align:start position:0% +that's thoughts about the error and and + + + align:start position:0% +that's thoughts about the error and and +of course that's why those elements are + + align:start position:0% +of course that's why those elements are + + + align:start position:0% +of course that's why those elements are +better than these. They take more work + + align:start position:0% +better than these. They take more work + + + align:start position:0% +better than these. They take more work +but they are worth it. But now I want to + + align:start position:0% +but they are worth it. But now I want to + + + align:start position:0% +but they are worth it. But now I want to +tell you about the next elements cubics + + align:start position:0% + + + + align:start position:0% + +where you're going to expect to get + + align:start position:0% +where you're going to expect to get + + + align:start position:0% +where you're going to expect to get +delta x to the 4th. + + align:start position:0% +delta x to the 4th. + + + align:start position:0% +delta x to the 4th. +So now we're getting serious accuracy. + + align:start position:0% +So now we're getting serious accuracy. + + + align:start position:0% +So now we're getting serious accuracy. +Now we're getting good accuracy. + + align:start position:0% +Now we're getting good accuracy. + + + align:start position:0% +Now we're getting good accuracy. +Of course, our problem is not the most + + align:start position:0% +Of course, our problem is not the most + + + align:start position:0% +Of course, our problem is not the most +difficult problem. It's in 1D, but this + + align:start position:0% +difficult problem. It's in 1D, but this + + + align:start position:0% +difficult problem. It's in 1D, but this +is good. Okay, + + align:start position:0% +is good. Okay, + + + align:start position:0% +is good. Okay, +here's the this was now the fun in the + + align:start position:0% +here's the this was now the fun in the + + + align:start position:0% +here's the this was now the fun in the +golden age of finite elements to + + align:start position:0% +golden age of finite elements to + + + align:start position:0% +golden age of finite elements to +construct + + align:start position:0% +construct + + + align:start position:0% +construct +cubics. + + align:start position:0% +cubics. + + + align:start position:0% +cubics. +What shall I use as basis functions for + + align:start position:0% +What shall I use as basis functions for + + + align:start position:0% +What shall I use as basis functions for +cubics? So, I want to have a cubic in + + align:start position:0% +cubics? So, I want to have a cubic in + + + align:start position:0% +cubics? So, I want to have a cubic in +each piece. Suppose first of all suppose + + align:start position:0% +each piece. Suppose first of all suppose + + + align:start position:0% +each piece. Suppose first of all suppose +I just want no more than that. I just + + align:start position:0% +I just want no more than that. I just + + + align:start position:0% +I just want no more than that. I just +I'm very suppose I'm happy with just + + align:start position:0% +I'm very suppose I'm happy with just + + + align:start position:0% +I'm very suppose I'm happy with just +continuous + + align:start position:0% + + + + align:start position:0% + +functions and I let the slope jump. + + align:start position:0% +functions and I let the slope jump. + + + align:start position:0% +functions and I let the slope jump. +What new trial functions shall I put in? + + align:start position:0% +What new trial functions shall I put in? + + + align:start position:0% +What new trial functions shall I put in? +So I'm going to put in new trial + + align:start position:0% +So I'm going to put in new trial + + + align:start position:0% +So I'm going to put in new trial +functions. What will they look like? + + align:start position:0% +functions. What will they look like? + + + align:start position:0% +functions. What will they look like? +Little cubics. little, you know, third + + align:start position:0% +Little cubics. little, you know, third + + + align:start position:0% +Little cubics. little, you know, third +degree pieces instead of parabas. + + align:start position:0% +degree pieces instead of parabas. + + + align:start position:0% +degree pieces instead of parabas. +They'll be little pieces of third degree + + align:start position:0% +They'll be little pieces of third degree + + + align:start position:0% +They'll be little pieces of third degree +and they could be more bubble. I could + + align:start position:0% +and they could be more bubble. I could + + + align:start position:0% +and they could be more bubble. I could +put in four more bubbles, + + align:start position:0% +put in four more bubbles, + + + align:start position:0% +put in four more bubbles, +four four cubic bubbles. So, I would be + + align:start position:0% +four four cubic bubbles. So, I would be + + + align:start position:0% +four four cubic bubbles. So, I would be +up to up to 12 uh degrees 12 uh + + align:start position:0% +up to up to 12 uh degrees 12 uh + + + align:start position:0% +up to up to 12 uh degrees 12 uh +12 x 12 matrices, 12 functions. And for + + align:start position:0% +12 x 12 matrices, 12 functions. And for + + + align:start position:0% +12 x 12 matrices, 12 functions. And for +that size delta x, that would give me + + align:start position:0% +that size delta x, that would give me + + + align:start position:0% +that size delta x, that would give me +delta x to the 4th. So that would be + + align:start position:0% +delta x to the 4th. So that would be + + + align:start position:0% +delta x to the 4th. So that would be +okay. + + align:start position:0% +okay. + + + align:start position:0% +okay. +There's a better idea. You can see that + + align:start position:0% +There's a better idea. You can see that + + + align:start position:0% +There's a better idea. You can see that +I left space. I'm going to call I'm + + align:start position:0% +I left space. I'm going to call I'm + + + align:start position:0% +I left space. I'm going to call I'm +going to make also the slope + + align:start position:0% +going to make also the slope + + + align:start position:0% +going to make also the slope +also continuous. + + align:start position:0% +also continuous. + + + align:start position:0% +also continuous. +I'm not going to allow jumps in slope. + + align:start position:0% +I'm not going to allow jumps in slope. + + + align:start position:0% +I'm not going to allow jumps in slope. +Think how will I do that? So and I'm + + align:start position:0% +Think how will I do that? So and I'm + + + align:start position:0% +Think how will I do that? So and I'm +going to call those C what what will I + + align:start position:0% +going to call those C what what will I + + + align:start position:0% +going to call those C what what will I +call that when the slope is continuous? + + align:start position:0% +call that when the slope is continuous? + + + align:start position:0% +call that when the slope is continuous? +the first derivative. I'll call that C1, + + align:start position:0% +the first derivative. I'll call that C1, + + + align:start position:0% +the first derivative. I'll call that C1, +continuous first derivative. + + align:start position:0% +continuous first derivative. + + + align:start position:0% +continuous first derivative. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now, I'm actually in section 3.2 where + + align:start position:0% +Now, I'm actually in section 3.2 where + + + align:start position:0% +Now, I'm actually in section 3.2 where +these better elements, these really + + align:start position:0% +these better elements, these really + + + align:start position:0% +these better elements, these really +nifty elements are constructed. Uh C1 + + align:start position:0% +nifty elements are constructed. Uh C1 + + + align:start position:0% +nifty elements are constructed. Uh C1 +continuous slope cubics. Okay, ready for + + align:start position:0% +continuous slope cubics. Okay, ready for + + + align:start position:0% +continuous slope cubics. Okay, ready for +those? What shall be my trial functions + + align:start position:0% +those? What shall be my trial functions + + + align:start position:0% +those? What shall be my trial functions +for continuous slope cubics? So, I have + + align:start position:0% +for continuous slope cubics? So, I have + + + align:start position:0% +for continuous slope cubics? So, I have +to start again. I have to start again + + align:start position:0% +to start again. I have to start again + + + align:start position:0% +to start again. I have to start again +because the hat functions are are out + + align:start position:0% +because the hat functions are are out + + + align:start position:0% +because the hat functions are are out +now. Those hat functions have a jump in + + align:start position:0% +now. Those hat functions have a jump in + + + align:start position:0% +now. Those hat functions have a jump in +slope. The bubble functions have a jump + + align:start position:0% +slope. The bubble functions have a jump + + + align:start position:0% +slope. The bubble functions have a jump +in slope. I'm not I'm not uh + + align:start position:0% +in slope. I'm not I'm not uh + + + align:start position:0% +in slope. I'm not I'm not uh +I'm uh rethinking here to create better + + align:start position:0% +I'm uh rethinking here to create better + + + align:start position:0% +I'm uh rethinking here to create better +element. Okay. So let's just think have + + align:start position:0% +element. Okay. So let's just think have + + + align:start position:0% +element. Okay. So let's just think have +we got a chance at it? + + align:start position:0% +we got a chance at it? + + + align:start position:0% +we got a chance at it? +How could this element how could these + + align:start position:0% +How could this element how could these + + + align:start position:0% +How could this element how could these +elements work? Okay. So here's the idea + + align:start position:0% +elements work? Okay. So here's the idea + + + align:start position:0% +elements work? Okay. So here's the idea +then. Here's my my my + + align:start position:0% + + + + align:start position:0% + +interval 0 to one and here's a typical + + align:start position:0% +interval 0 to one and here's a typical + + + align:start position:0% +interval 0 to one and here's a typical +interval. And now at a typical node like + + align:start position:0% +interval. And now at a typical node like + + + align:start position:0% +interval. And now at a typical node like +node one I plan to have as unknowns the + + align:start position:0% +node one I plan to have as unknowns the + + + align:start position:0% +node one I plan to have as unknowns the +height of the function as before and + + align:start position:0% +height of the function as before and + + + align:start position:0% +height of the function as before and +also the slope. So I want the function + + align:start position:0% +also the slope. So I want the function + + + align:start position:0% +also the slope. So I want the function +my trial function is going to have uh + + align:start position:0% +my trial function is going to have uh + + + align:start position:0% +my trial function is going to have uh +some height and some slope + + align:start position:0% +some height and some slope + + + align:start position:0% +some height and some slope +and at node two it's going to have some + + align:start position:0% +and at node two it's going to have some + + + align:start position:0% +and at node two it's going to have some +height and some slope and here's the + + align:start position:0% +height and some slope and here's the + + + align:start position:0% +height and some slope and here's the +question + + align:start position:0% +question + + + align:start position:0% +question +here here's the good point that those + + align:start position:0% +here here's the good point that those + + + align:start position:0% +here here's the good point that those +four numbers the two heights and the two + + align:start position:0% +four numbers the two heights and the two + + + align:start position:0% +four numbers the two heights and the two +slopes + + align:start position:0% +slopes + + + align:start position:0% +slopes +that gives me four things four four + + align:start position:0% +that gives me four things four four + + + align:start position:0% +that gives me four things four four +quantities + + align:start position:0% +quantities + + + align:start position:0% +quantities +How many quantities do I need to + + align:start position:0% +How many quantities do I need to + + + align:start position:0% +How many quantities do I need to +determine a cubic? So a cubic of course + + align:start position:0% +determine a cubic? So a cubic of course + + + align:start position:0% +determine a cubic? So a cubic of course +I mean by a cubic something like a kn + + align:start position:0% +I mean by a cubic something like a kn + + + align:start position:0% +I mean by a cubic something like a kn +plus a1x plus a2x^2 + + align:start position:0% +plus a1x plus a2x^2 + + + align:start position:0% +plus a1x plus a2x^2 +and a3x cub. It's called a cubic because + + align:start position:0% +and a3x cub. It's called a cubic because + + + align:start position:0% +and a3x cub. It's called a cubic because +it's x cub. So how many numbers here? + + align:start position:0% +it's x cub. So how many numbers here? + + + align:start position:0% +it's x cub. So how many numbers here? +Four. Perfect match. There's exactly one + + align:start position:0% +Four. Perfect match. There's exactly one + + + align:start position:0% +Four. Perfect match. There's exactly one +cubic that has a specified height and a + + align:start position:0% +cubic that has a specified height and a + + + align:start position:0% +cubic that has a specified height and a +specified slope at these two ends. It'll + + align:start position:0% +specified slope at these two ends. It'll + + + align:start position:0% +specified slope at these two ends. It'll +there there's one cubic that'll do that. + + align:start position:0% +there there's one cubic that'll do that. + + + align:start position:0% +there there's one cubic that'll do that. +And then whatever the height here is and + + align:start position:0% +And then whatever the height here is and + + + align:start position:0% +And then whatever the height here is and +and whatever the slope there is, + + align:start position:0% +and whatever the slope there is, + + + align:start position:0% +and whatever the slope there is, +there'll be one cubic with that height + + align:start position:0% +there'll be one cubic with that height + + + align:start position:0% +there'll be one cubic with that height +and that slope that comes into this one. + + align:start position:0% +and that slope that comes into this one. + + + align:start position:0% +and that slope that comes into this one. +And do you see that they will have + + align:start position:0% +And do you see that they will have + + + align:start position:0% +And do you see that they will have +continuous slope because of course the + + align:start position:0% +continuous slope because of course the + + + align:start position:0% +continuous slope because of course the +slope is continuous in between it's + + align:start position:0% +slope is continuous in between it's + + + align:start position:0% +slope is continuous in between it's +polomial the question is always at the + + align:start position:0% +polomial the question is always at the + + + align:start position:0% +polomial the question is always at the +nodes but but I use the same number + + align:start position:0% +nodes but but I use the same number + + + align:start position:0% +nodes but but I use the same number +coming from the left and from the right + + align:start position:0% +coming from the left and from the right + + + align:start position:0% +coming from the left and from the right +the slope has become an extra unknown + + align:start position:0% +the slope has become an extra unknown + + + align:start position:0% +the slope has become an extra unknown +the slope has become an extra unknown + + align:start position:0% +the slope has become an extra unknown + + + align:start position:0% +the slope has become an extra unknown +now so I have height slope at every + + align:start position:0% +now so I have height slope at every + + + align:start position:0% +now so I have height slope at every +point so that's that's one way to + + align:start position:0% +point so that's that's one way to + + + align:start position:0% +point so that's that's one way to +describe these these these trial + + align:start position:0% +describe these these these trial + + + align:start position:0% +describe these these these trial +functions. Now the trial functions have + + align:start position:0% +functions. Now the trial functions have + + + align:start position:0% +functions. Now the trial functions have +height + + align:start position:0% +height + + + align:start position:0% +height +and also + + align:start position:0% +and also + + + align:start position:0% +and also +slope at each node. + + align:start position:0% +slope at each node. + + + align:start position:0% +slope at each node. +So what does that mean? That means that + + align:start position:0% +So what does that mean? That means that + + + align:start position:0% +So what does that mean? That means that +I'm going to have two unknowns, two + + align:start position:0% +I'm going to have two unknowns, two + + + align:start position:0% +I'm going to have two unknowns, two +functions, two trial functions with each + + align:start position:0% +functions, two trial functions with each + + + align:start position:0% +functions, two trial functions with each +with its own coefficient + + align:start position:0% +with its own coefficient + + + align:start position:0% +with its own coefficient +at each node. So if if I take a typical + + align:start position:0% +at each node. So if if I take a typical + + + align:start position:0% +at each node. So if if I take a typical +node there, I want two functions. Okay, + + align:start position:0% +node there, I want two functions. Okay, + + + align:start position:0% +node there, I want two functions. Okay, +that's that's this is uh interesting. + + align:start position:0% +that's that's this is uh interesting. + + + align:start position:0% +that's that's this is uh interesting. +But you see what I'm creating? I I think + + align:start position:0% +But you see what I'm creating? I I think + + + align:start position:0% +But you see what I'm creating? I I think +I'm going to get two functions there, + + align:start position:0% +I'm going to get two functions there, + + + align:start position:0% +I'm going to get two functions there, +two functions there, two functions + + align:start position:0% +two functions there, two functions + + + align:start position:0% +two functions there, two functions +there, two functions there, right? + + align:start position:0% +there, two functions there, right? + + + align:start position:0% +there, two functions there, right? +Because nobody's constraining that. So + + align:start position:0% +Because nobody's constraining that. So + + + align:start position:0% +Because nobody's constraining that. So +I'm up to eight. And how many functions + + align:start position:0% +I'm up to eight. And how many functions + + + align:start position:0% +I'm up to eight. And how many functions +do you think I'm going to have + + align:start position:0% +do you think I'm going to have + + + align:start position:0% +do you think I'm going to have +associated with that node? + + align:start position:0% +associated with that node? + + + align:start position:0% +associated with that node? +only one. Why? Because it's because the + + align:start position:0% +only one. Why? Because it's because the + + + align:start position:0% +only one. Why? Because it's because the +the the height is is fixed. So I think + + align:start position:0% +the the height is is fixed. So I think + + + align:start position:0% +the the height is is fixed. So I think +I've got a nine nine trial functions + + align:start position:0% +I've got a nine nine trial functions + + + align:start position:0% +I've got a nine nine trial functions +here. And and if we can see what those + + align:start position:0% +here. And and if we can see what those + + + align:start position:0% +here. And and if we can see what those +are, then we can then the system will + + align:start position:0% +are, then we can then the system will + + + align:start position:0% +are, then we can then the system will +take over. They're my f1 + + align:start position:0% +take over. They're my f1 + + + align:start position:0% +take over. They're my f1 +to f9 whatever they plug in here. They + + align:start position:0% +to f9 whatever they plug in here. They + + + align:start position:0% +to f9 whatever they plug in here. They +plug in the right hand side. I'll have a + + align:start position:0% +plug in the right hand side. I'll have a + + + align:start position:0% +plug in the right hand side. I'll have a +9 by9 stiffness matrix. It'll have it'll + + align:start position:0% +9 by9 stiffness matrix. It'll have it'll + + + align:start position:0% +9 by9 stiffness matrix. It'll have it'll +be it'll be local again actually. + + align:start position:0% +be it'll be local again actually. + + + align:start position:0% +be it'll be local again actually. +Well, let's see if we can figure out + + align:start position:0% +Well, let's see if we can figure out + + + align:start position:0% +Well, let's see if we can figure out +these functions. + + align:start position:0% +these functions. + + + align:start position:0% +these functions. +Okay, so you have the idea. I'm + + align:start position:0% +Okay, so you have the idea. I'm + + + align:start position:0% +Okay, so you have the idea. I'm +expecting two trial functions. One is + + align:start position:0% +expecting two trial functions. One is + + + align:start position:0% +expecting two trial functions. One is +sort of a round hat. All right, let me + + align:start position:0% +sort of a round hat. All right, let me + + + align:start position:0% +sort of a round hat. All right, let me +draw that. The round hat function + + align:start position:0% +draw that. The round hat function + + + align:start position:0% +draw that. The round hat function +will be the function. + + align:start position:0% + + + + align:start position:0% + +These will be the round hats + + align:start position:0% + + + + align:start position:0% + +and they'll be associated with they they + + align:start position:0% +and they'll be associated with they they + + + align:start position:0% +and they'll be associated with they they +give me heights. + + align:start position:0% +give me heights. + + + align:start position:0% +give me heights. +And then I'll also have an additional + + align:start position:0% +And then I'll also have an additional + + + align:start position:0% +And then I'll also have an additional +one except at the last node. And these + + align:start position:0% +one except at the last node. And these + + + align:start position:0% +one except at the last node. And these +will be I don't know what to call them + + align:start position:0% +will be I don't know what to call them + + + align:start position:0% +will be I don't know what to call them +yet. You'll have to give me a name. + + align:start position:0% +yet. You'll have to give me a name. + + + align:start position:0% +yet. You'll have to give me a name. +These will give me the slopes. + + align:start position:0% +These will give me the slopes. + + + align:start position:0% +These will give me the slopes. +Okay. So, what does a round hat look + + align:start position:0% +Okay. So, what does a round hat look + + + align:start position:0% +Okay. So, what does a round hat look +like? Now, these have to be in my follow + + align:start position:0% +like? Now, these have to be in my follow + + + align:start position:0% +like? Now, these have to be in my follow +my rules. They have to be continuous. + + align:start position:0% +my rules. They have to be continuous. + + + align:start position:0% +my rules. They have to be continuous. +Their slope has to be continuous. And I + + align:start position:0% +Their slope has to be continuous. And I + + + align:start position:0% +Their slope has to be continuous. And I +want to take the one that has height one + + align:start position:0% +want to take the one that has height one + + + align:start position:0% +want to take the one that has height one +and zero slope there. And it has should + + align:start position:0% +and zero slope there. And it has should + + + align:start position:0% +and zero slope there. And it has should +have height zero and zero slope here. + + align:start position:0% +have height zero and zero slope here. + + + align:start position:0% +have height zero and zero slope here. +Height zero zero slope. You see it'll be + + align:start position:0% +Height zero zero slope. You see it'll be + + + align:start position:0% +Height zero zero slope. You see it'll be +a height. + + align:start position:0% +a height. + + + align:start position:0% +a height. +You see what it's it's going to be this + + align:start position:0% +You see what it's it's going to be this + + + align:start position:0% +You see what it's it's going to be this +fee. Whatever number it is, it'll be the + + align:start position:0% +fee. Whatever number it is, it'll be the + + + align:start position:0% +fee. Whatever number it is, it'll be the +fee that's that gives that whose + + align:start position:0% +fee that's that gives that whose + + + align:start position:0% +fee that's that gives that whose +coefficient tells me the height at node + + align:start position:0% +coefficient tells me the height at node + + + align:start position:0% +coefficient tells me the height at node +one. So here's node one. + + align:start position:0% +one. So here's node one. + + + align:start position:0% +one. So here's node one. +What will it look like? What will this + + align:start position:0% +What will it look like? What will this + + + align:start position:0% +What will it look like? What will this +function do? Well, there is exactly one + + align:start position:0% +function do? Well, there is exactly one + + + align:start position:0% +function do? Well, there is exactly one +cubic that starts from zero with slope + + align:start position:0% +cubic that starts from zero with slope + + + align:start position:0% +cubic that starts from zero with slope +zero and ends there ends at one with + + align:start position:0% +zero and ends there ends at one with + + + align:start position:0% +zero and ends there ends at one with +slope zero. Right? That's what we said. + + align:start position:0% +slope zero. Right? That's what we said. + + + align:start position:0% +slope zero. Right? That's what we said. +Four numbers determine a cubic + + align:start position:0% +Four numbers determine a cubic + + + align:start position:0% +Four numbers determine a cubic +in that interval. Then there's another + + align:start position:0% +in that interval. Then there's another + + + align:start position:0% +in that interval. Then there's another +cubic that uh with the those two numbers + + align:start position:0% +cubic that uh with the those two numbers + + + align:start position:0% +cubic that uh with the those two numbers +again that keeps the continuous slope + + align:start position:0% +again that keeps the continuous slope + + + align:start position:0% +again that keeps the continuous slope +and these two numbers in this interval + + align:start position:0% +and these two numbers in this interval + + + align:start position:0% +and these two numbers in this interval +and of course it'll just be symmetric. + + align:start position:0% +and of course it'll just be symmetric. + + + align:start position:0% +and of course it'll just be symmetric. +You see the round hat? So that's the + + align:start position:0% +You see the round hat? So that's the + + + align:start position:0% +You see the round hat? So that's the +that's the basis function, the trial + + align:start position:0% +that's the basis function, the trial + + + align:start position:0% +that's the basis function, the trial +function that has continuous slopes and + + align:start position:0% +function that has continuous slopes and + + + align:start position:0% +function that has continuous slopes and +heights of course and it has height one + + align:start position:0% +heights of course and it has height one + + + align:start position:0% +heights of course and it has height one +at that point. And now let me draw the + + align:start position:0% +at that point. And now let me draw the + + + align:start position:0% +at that point. And now let me draw the +one that has height zero, slope zero, + + align:start position:0% +one that has height zero, slope zero, + + + align:start position:0% +one that has height zero, slope zero, +height zero, slope zero. + + align:start position:0% +height zero, slope zero. + + + align:start position:0% +height zero, slope zero. +And what should I what do I want it to + + align:start position:0% +And what should I what do I want it to + + + align:start position:0% +And what should I what do I want it to +do there? + + align:start position:0% + + + + align:start position:0% + +What should this function be like? It + + align:start position:0% +What should this function be like? It + + + align:start position:0% +What should this function be like? It +should tell me about it should have it + + align:start position:0% +should tell me about it should have it + + + align:start position:0% +should tell me about it should have it +should be the one that that tells its + + align:start position:0% +should be the one that that tells its + + + align:start position:0% +should be the one that that tells its +coefficient will tell me the slope. So I + + align:start position:0% +coefficient will tell me the slope. So I + + + align:start position:0% +coefficient will tell me the slope. So I +want it to have a slope of one and a + + align:start position:0% +want it to have a slope of one and a + + + align:start position:0% +want it to have a slope of one and a +height of zero. + + align:start position:0% + + + + align:start position:0% + +You see that the these functions shall I + + align:start position:0% +You see that the these functions shall I + + + align:start position:0% +You see that the these functions shall I +call these the height functions? FH1 + + align:start position:0% +call these the height functions? FH1 + + + align:start position:0% +call these the height functions? FH1 +that's that's the FE that's the trial + + align:start position:0% +that's that's the FE that's the trial + + + align:start position:0% +that's that's the FE that's the trial +function that tells me the height at + + align:start position:0% +function that tells me the height at + + + align:start position:0% +function that tells me the height at +node one it it gets when I take + + align:start position:0% +node one it it gets when I take + + + align:start position:0% +node one it it gets when I take +combinations it gets multiplied by uh H1 + + align:start position:0% +combinations it gets multiplied by uh H1 + + + align:start position:0% +combinations it gets multiplied by uh H1 +a co which is exactly the height at node + + align:start position:0% +a co which is exactly the height at node + + + align:start position:0% +a co which is exactly the height at node +one now what about this guy this guy is + + align:start position:0% +one now what about this guy this guy is + + + align:start position:0% +one now what about this guy this guy is +going to have it's going to start with + + align:start position:0% +going to have it's going to start with + + + align:start position:0% +going to have it's going to start with +zero slope at zero it's going to be a + + align:start position:0% +zero slope at zero it's going to be a + + + align:start position:0% +zero slope at zero it's going to be a +cubic and there's exactly one cubic + + align:start position:0% +cubic and there's exactly one cubic + + + align:start position:0% +cubic and there's exactly one cubic +that'll do it. It'll look a little like + + align:start position:0% +that'll do it. It'll look a little like + + + align:start position:0% +that'll do it. It'll look a little like +this. Then there will be exactly one + + align:start position:0% +this. Then there will be exactly one + + + align:start position:0% +this. Then there will be exactly one +cubic that does that and gets back to + + align:start position:0% +cubic that does that and gets back to + + + align:start position:0% +cubic that does that and gets back to +gets back to zero. Do you see that? + + align:start position:0% +gets back to zero. Do you see that? + + + align:start position:0% +gets back to zero. Do you see that? +That's possible. In each interval, I've + + align:start position:0% +That's possible. In each interval, I've + + + align:start position:0% +That's possible. In each interval, I've +got four numbers, two heights, two + + align:start position:0% +got four numbers, two heights, two + + + align:start position:0% +got four numbers, two heights, two +slopes. So this would be the a picture + + align:start position:0% +slopes. So this would be the a picture + + + align:start position:0% +slopes. So this would be the a picture +of the fe slope at node one function. + + align:start position:0% +of the fe slope at node one function. + + + align:start position:0% +of the fe slope at node one function. +So that's a standard function. It's a + + align:start position:0% +So that's a standard function. It's a + + + align:start position:0% +So that's a standard function. It's a +cubic. It's a cubic pie-wise cubic local + + align:start position:0% +cubic. It's a cubic pie-wise cubic local + + + align:start position:0% +cubic. It's a cubic pie-wise cubic local +again because in all these intervals + + align:start position:0% +again because in all these intervals + + + align:start position:0% +again because in all these intervals +it's zero and it will be when I go to + + align:start position:0% +it's zero and it will be when I go to + + + align:start position:0% +it's zero and it will be when I go to +take combinations of all these guys + + align:start position:0% +take combinations of all these guys + + + align:start position:0% +take combinations of all these guys +it'll be multiplied by its coefficient u + + align:start position:0% +it'll be multiplied by its coefficient u + + + align:start position:0% +it'll be multiplied by its coefficient u +slope one and then I'll have guys I'll + + align:start position:0% +slope one and then I'll have guys I'll + + + align:start position:0% +slope one and then I'll have guys I'll +have nine altogether + + align:start position:0% +have nine altogether + + + align:start position:0% +have nine altogether +but those two are the typical ones. Do + + align:start position:0% +but those two are the typical ones. Do + + + align:start position:0% +but those two are the typical ones. Do +do you see how that's going? + + align:start position:0% +do you see how that's going? + + + align:start position:0% +do you see how that's going? +It's uh it's like one it's it's it's + + align:start position:0% +It's uh it's like one it's it's it's + + + align:start position:0% +It's uh it's like one it's it's it's +more subtle than uh hat functions. + + align:start position:0% +more subtle than uh hat functions. + + + align:start position:0% +more subtle than uh hat functions. +But what suppose so you have to + + align:start position:0% +But what suppose so you have to + + + align:start position:0% +But what suppose so you have to +or whoever's writing the finite element + + align:start position:0% +or whoever's writing the finite element + + + align:start position:0% +or whoever's writing the finite element +code gets a formula for those those uh + + align:start position:0% +code gets a formula for those those uh + + + align:start position:0% +code gets a formula for those those uh +fees + + align:start position:0% +fees + + + align:start position:0% +fees +and plugs them into the integrals. comes + + align:start position:0% +and plugs them into the integrals. comes + + + align:start position:0% +and plugs them into the integrals. comes +out with a with a stiffness matrix. + + align:start position:0% +out with a with a stiffness matrix. + + + align:start position:0% +out with a with a stiffness matrix. +Actually, we could even look at that + + align:start position:0% +Actually, we could even look at that + + + align:start position:0% +Actually, we could even look at that +stiffness matrix. What what this this is + + align:start position:0% +stiffness matrix. What what this this is + + + align:start position:0% +stiffness matrix. What what this this is +a good way to to sort of understand the + + align:start position:0% +a good way to to sort of understand the + + + align:start position:0% +a good way to to sort of understand the +picture. Now, it'll be 9 by9, right? And + + align:start position:0% +picture. Now, it'll be 9 by9, right? And + + + align:start position:0% +picture. Now, it'll be 9 by9, right? And +at a typical so here we'll have a a + + align:start position:0% +at a typical so here we'll have a a + + + align:start position:0% +at a typical so here we'll have a a +typical this will be our fee height one + + align:start position:0% +typical this will be our fee height one + + + align:start position:0% +typical this will be our fee height one +row and this will be our fee slope one + + align:start position:0% +row and this will be our fee slope one + + + align:start position:0% +row and this will be our fee slope one +row and this will be our fee height two + + align:start position:0% +row and this will be our fee height two + + + align:start position:0% +row and this will be our fee height two +row and so on. Of course I didn't leave + + align:start position:0% +row and so on. Of course I didn't leave + + + align:start position:0% +row and so on. Of course I didn't leave +room for all + + align:start position:0% +room for all + + + align:start position:0% +room for all +what will a typical row of the stiffness + + align:start position:0% +what will a typical row of the stiffness + + + align:start position:0% +what will a typical row of the stiffness +matrix have in it. + + align:start position:0% +matrix have in it. + + + align:start position:0% +matrix have in it. +It's just I'm just asking about the + + align:start position:0% +It's just I'm just asking about the + + + align:start position:0% +It's just I'm just asking about the +overlaps. Feight certainly overlaps + + align:start position:0% +overlaps. Feight certainly overlaps + + + align:start position:0% +overlaps. Feight certainly overlaps +itself. + + align:start position:0% +itself. + + + align:start position:0% +itself. +Does F1 height overlap F1 slope? + + align:start position:0% +Does F1 height overlap F1 slope? + + + align:start position:0% +Does F1 height overlap F1 slope? +Yes or no? + + align:start position:0% +Yes or no? + + + align:start position:0% +Yes or no? +Sure. Sure. They're Does F1 height + + align:start position:0% +Sure. Sure. They're Does F1 height + + + align:start position:0% +Sure. Sure. They're Does F1 height +overlap F2 height? + + align:start position:0% +overlap F2 height? + + + align:start position:0% +overlap F2 height? +Yes. Yes. Because the F1 the F2 height + + align:start position:0% +Yes. Yes. Because the F1 the F2 height + + + align:start position:0% +Yes. Yes. Because the F1 the F2 height +will go up like that. + + align:start position:0% +will go up like that. + + + align:start position:0% +will go up like that. +you see and the F2 slope. So actually + + align:start position:0% +you see and the F2 slope. So actually + + + align:start position:0% +you see and the F2 slope. So actually +we'll have + + align:start position:0% + + + + align:start position:0% + +I think we'll have six I think we'll + + align:start position:0% +I think we'll have six I think we'll + + + align:start position:0% +I think we'll have six I think we'll +have six nonzeros on a typical diagonal + + align:start position:0% +have six nonzeros on a typical diagonal + + + align:start position:0% +have six nonzeros on a typical diagonal +on a typical row. Is that right? + + align:start position:0% +on a typical row. Is that right? + + + align:start position:0% +on a typical row. Is that right? +six nonzeros because a typical H will + + align:start position:0% +six nonzeros because a typical H will + + + align:start position:0% +six nonzeros because a typical H will +a typical H this is maybe not so typical + + align:start position:0% +a typical H this is maybe not so typical + + + align:start position:0% +a typical H this is maybe not so typical +because to the left of it there's only + + align:start position:0% +because to the left of it there's only + + + align:start position:0% +because to the left of it there's only +one there's no oh there there two right + + align:start position:0% +one there's no oh there there two right + + + align:start position:0% +one there's no oh there there two right +there's a f0 f0 and a f0 sure there are + + align:start position:0% +there's a f0 f0 and a f0 sure there are + + + align:start position:0% +there's a f0 f0 and a f0 sure there are +two there are two here there two guys + + align:start position:0% +two there are two here there two guys + + + align:start position:0% +two there are two here there two guys +here there's one height guy + + align:start position:0% +here there's one height guy + + + align:start position:0% +here there's one height guy +and there's one + + align:start position:0% + + + + align:start position:0% + +What's what's cooking in that? Oh, it's + + align:start position:0% +What's what's cooking in that? Oh, it's + + + align:start position:0% +What's what's cooking in that? Oh, it's +it's got a slope of one and it gets back + + align:start position:0% +it's got a slope of one and it gets back + + + align:start position:0% +it's got a slope of one and it gets back +to zero. There's a what I'm drawing now + + align:start position:0% +to zero. There's a what I'm drawing now + + + align:start position:0% +to zero. There's a what I'm drawing now +in little dashed lines were was the fe + + align:start position:0% +in little dashed lines were was the fe + + + align:start position:0% +in little dashed lines were was the fe +slope zero. + + align:start position:0% +slope zero. + + + align:start position:0% +slope zero. +The the one that gives me a slope at at + + align:start position:0% +The the one that gives me a slope at at + + + align:start position:0% +The the one that gives me a slope at at +node zero and this is the one that gives + + align:start position:0% +node zero and this is the one that gives + + + align:start position:0% +node zero and this is the one that gives +me a height. Yeah. Do you see it? R. + + align:start position:0% + + + + align:start position:0% + +So above this was a fee slope zero and + + align:start position:0% +So above this was a fee slope zero and + + + align:start position:0% +So above this was a fee slope zero and +and stuck in there was a fee height zero + + align:start position:0% + + + + align:start position:0% + +six + + align:start position:0% + + + + align:start position:0% + +six diagonal matrix. Yeah, I think it it + + align:start position:0% +six diagonal matrix. Yeah, I think it it + + + align:start position:0% +six diagonal matrix. Yeah, I think it it +helps to draw that little uh thing with + + align:start position:0% +helps to draw that little uh thing with + + + align:start position:0% +helps to draw that little uh thing with +x's and zeros because then you sort of + + align:start position:0% +x's and zeros because then you sort of + + + align:start position:0% +x's and zeros because then you sort of +see how things are fitting together. + + align:start position:0% +see how things are fitting together. + + + align:start position:0% +see how things are fitting together. +Okay. Uh so this is the these these + + align:start position:0% +Okay. Uh so this is the these these + + + align:start position:0% +Okay. Uh so this is the these these +functions. Now I go I've gone into + + align:start position:0% +functions. Now I go I've gone into + + + align:start position:0% +functions. Now I go I've gone into +section 3.2 for that and I'll do I want + + align:start position:0% +section 3.2 for that and I'll do I want + + + align:start position:0% +section 3.2 for that and I'll do I want +to + + align:start position:0% +to + + + align:start position:0% +to +go to a slightly different topic and + + align:start position:0% +go to a slightly different topic and + + + align:start position:0% +go to a slightly different topic and +then I'll come back in section 3.2 to + + align:start position:0% +then I'll come back in section 3.2 to + + + align:start position:0% +then I'll come back in section 3.2 to +these cubics. So these are C1 cubics + + align:start position:0% +these cubics. So these are C1 cubics + + + align:start position:0% +these cubics. So these are C1 cubics +continuous slope cubics. Very + + align:start position:0% +continuous slope cubics. Very + + + align:start position:0% +continuous slope cubics. Very +interesting construction. Are are are + + align:start position:0% +interesting construction. Are are are + + + align:start position:0% +interesting construction. Are are are +you seeing what how it could go in more + + align:start position:0% +you seeing what how it could go in more + + + align:start position:0% +you seeing what how it could go in more +dimensions? I mean, yeah. Then you + + align:start position:0% +dimensions? I mean, yeah. Then you + + + align:start position:0% +dimensions? I mean, yeah. Then you +really have we'll that's what we'll see + + align:start position:0% +really have we'll that's what we'll see + + + align:start position:0% +really have we'll that's what we'll see +for Lelass's equation. How how how can + + align:start position:0% +for Lelass's equation. How how how can + + + align:start position:0% +for Lelass's equation. How how how can +you construct quadratics, cubics in a + + align:start position:0% +you construct quadratics, cubics in a + + + align:start position:0% +you construct quadratics, cubics in a +plane? It's it gets interesting. Okay, + + align:start position:0% +plane? It's it gets interesting. Okay, + + + align:start position:0% +plane? It's it gets interesting. Okay, +but that's you'll you'll get the knack + + align:start position:0% +but that's you'll you'll get the knack + + + align:start position:0% +but that's you'll you'll get the knack +of these guys. These are these are um + + align:start position:0% +of these guys. These are these are um + + + align:start position:0% +of these guys. These are these are um +pretty direct and very useful. So, + + align:start position:0% +pretty direct and very useful. So, + + + align:start position:0% +pretty direct and very useful. So, +what's the effect? The effect is that we + + align:start position:0% +what's the effect? The effect is that we + + + align:start position:0% +what's the effect? The effect is that we +get a a matrix. + + align:start position:0% +get a a matrix. + + + align:start position:0% +get a a matrix. +It looks kind of like a looks quite like + + align:start position:0% +It looks kind of like a looks quite like + + + align:start position:0% +It looks kind of like a looks quite like +a difference matrix. + + align:start position:0% +a difference matrix. + + + align:start position:0% +a difference matrix. +Uh well actually the height rows and the + + align:start position:0% +Uh well actually the height rows and the + + + align:start position:0% +Uh well actually the height rows and the +numbers in the height rows and the + + align:start position:0% +numbers in the height rows and the + + + align:start position:0% +numbers in the height rows and the +slopes rows will look different. It's + + align:start position:0% +slopes rows will look different. It's + + + align:start position:0% +slopes rows will look different. It's +you know we've getting something new + + align:start position:0% +you know we've getting something new + + + align:start position:0% +you know we've getting something new +here. + + align:start position:0% +here. + + + align:start position:0% +here. +And but we're getting a matrix + + align:start position:0% +And but we're getting a matrix + + + align:start position:0% +And but we're getting a matrix +a ku equal f that's going to give us + + align:start position:0% +a ku equal f that's going to give us + + + align:start position:0% +a ku equal f that's going to give us +fourth order accuracy. + + align:start position:0% +fourth order accuracy. + + + align:start position:0% +fourth order accuracy. +So the accuracy has moved up. Uh + + align:start position:0% +So the accuracy has moved up. Uh + + + align:start position:0% +So the accuracy has moved up. Uh +yeah. So we've got up to fourth order + + align:start position:0% +yeah. So we've got up to fourth order + + + align:start position:0% +yeah. So we've got up to fourth order +accuracy which we could get by finite + + align:start position:0% +accuracy which we could get by finite + + + align:start position:0% +accuracy which we could get by finite +differences + + align:start position:0% +differences + + + align:start position:0% +differences +by a lot of patience. + + align:start position:0% +by a lot of patience. + + + align:start position:0% +by a lot of patience. +We get them from finite elements in a + + align:start position:0% +We get them from finite elements in a + + + align:start position:0% +We get them from finite elements in a +straight way. Okay. Any question or + + align:start position:0% +straight way. Okay. Any question or + + + align:start position:0% +straight way. Okay. Any question or +discussion? I'm talking real fast to get + + align:start position:0% +discussion? I'm talking real fast to get + + + align:start position:0% +discussion? I'm talking real fast to get +these these uh this new idea of + + align:start position:0% +these these uh this new idea of + + + align:start position:0% +these these uh this new idea of +constructing finite elements here. Okay, + + align:start position:0% +constructing finite elements here. Okay, + + + align:start position:0% +constructing finite elements here. Okay, +I do want to say + + align:start position:0% + + + + align:start position:0% + +something about that line + + align:start position:0% + + + + align:start position:0% + +because that's a a part of this order of + + align:start position:0% +because that's a a part of this order of + + + align:start position:0% +because that's a a part of this order of +this business of estimating the + + align:start position:0% +this business of estimating the + + + align:start position:0% +this business of estimating the +accuracy. It's the it's the key it's a + + align:start position:0% +accuracy. It's the it's the key it's a + + + align:start position:0% +accuracy. It's the it's the key it's a +key idea in uh in the background of the + + align:start position:0% +key idea in uh in the background of the + + + align:start position:0% +key idea in uh in the background of the +Gerkin method and the the the minimum + + align:start position:0% +Gerkin method and the the the minimum + + + align:start position:0% +Gerkin method and the the the minimum +form would be associated with names like + + align:start position:0% +form would be associated with names like + + + align:start position:0% +form would be associated with names like +Ritz. + + align:start position:0% +Ritz. + + + align:start position:0% +Ritz. +All right, I I I'll just + + align:start position:0% +All right, I I I'll just + + + align:start position:0% +All right, I I I'll just +go directly to that if I may. Okay. So I + + align:start position:0% +go directly to that if I may. Okay. So I + + + align:start position:0% +go directly to that if I may. Okay. So I +I what I want to do is tell you + + align:start position:0% +I what I want to do is tell you + + + align:start position:0% +I what I want to do is tell you +for our model problem. I want to tell + + align:start position:0% +for our model problem. I want to tell + + + align:start position:0% +for our model problem. I want to tell +you the strong form. No. Yeah. Let me + + align:start position:0% +you the strong form. No. Yeah. Let me + + + align:start position:0% +you the strong form. No. Yeah. Let me +let me do it this order. I'll put I'll + + align:start position:0% +let me do it this order. I'll put I'll + + + align:start position:0% +let me do it this order. I'll put I'll +put the strong form, + + align:start position:0% +put the strong form, + + + align:start position:0% +put the strong form, +the weak form, + + align:start position:0% +the weak form, + + + align:start position:0% +the weak form, +and then I want to add in the minimum + + align:start position:0% +and then I want to add in the minimum + + + align:start position:0% +and then I want to add in the minimum +form. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So the strong form of our equation was + + align:start position:0% +So the strong form of our equation was + + + align:start position:0% +So the strong form of our equation was +minus the derivative + + align:start position:0% +minus the derivative + + + align:start position:0% +minus the derivative +of c du dx= + + align:start position:0% +of c du dx= + + + align:start position:0% +of c du dx= +f. + + align:start position:0% +f. + + + align:start position:0% +f. +Okay. + + align:start position:0% + + + + align:start position:0% + +What was the weak form? + + align:start position:0% +What was the weak form? + + + align:start position:0% +What was the weak form? +The weak form came this is an f ofx. + + align:start position:0% +The weak form came this is an f ofx. + + + align:start position:0% +The weak form came this is an f ofx. +Okay. The weak form came by how how do + + align:start position:0% +Okay. The weak form came by how how do + + + align:start position:0% +Okay. The weak form came by how how do +you get to the weak form? You multiply + + align:start position:0% +you get to the weak form? You multiply + + + align:start position:0% +you get to the weak form? You multiply +both sides by a test function. You + + align:start position:0% +both sides by a test function. You + + + align:start position:0% +both sides by a test function. You +integrate. You integrate by parts. And + + align:start position:0% +integrate. You integrate by parts. And + + + align:start position:0% +integrate. You integrate by parts. And +you get this beautifully symmetric form + + align:start position:0% +you get this beautifully symmetric form + + + align:start position:0% +you get this beautifully symmetric form +that I that we have up there. du dx + + align:start position:0% +that I that we have up there. du dx + + + align:start position:0% +that I that we have up there. du dx +dv dx dx + + align:start position:0% + + + + align:start position:0% + +equals the integral of f ofx v ofx dx. + + align:start position:0% +equals the integral of f ofx v ofx dx. + + + align:start position:0% +equals the integral of f ofx v ofx dx. +I write that again just so you see the + + align:start position:0% +I write that again just so you see the + + + align:start position:0% +I write that again just so you see the +the nice symmetry of that weak form. Uh + + align:start position:0% +the nice symmetry of that weak form. Uh + + + align:start position:0% +the nice symmetry of that weak form. Uh +and it's for all all test functions + + align:start position:0% +and it's for all all test functions + + + align:start position:0% +and it's for all all test functions +V. + + align:start position:0% +V. + + + align:start position:0% +V. +Okay, + + align:start position:0% + + + + align:start position:0% + +I'm shooting for a third description, a + + align:start position:0% +I'm shooting for a third description, a + + + align:start position:0% +I'm shooting for a third description, a +third description of the same problem. + + align:start position:0% +third description of the same problem. + + + align:start position:0% +third description of the same problem. +And it's it's really neat to see that + + align:start position:0% +And it's it's really neat to see that + + + align:start position:0% +And it's it's really neat to see that +you have that. Let me just see it first + + align:start position:0% +you have that. Let me just see it first + + + align:start position:0% +you have that. Let me just see it first +in the discrete case. The discrete case, + + align:start position:0% +in the discrete case. The discrete case, + + + align:start position:0% +in the discrete case. The discrete case, +the strong form would be a transpose c a + + align:start position:0% +the strong form would be a transpose c a + + + align:start position:0% +the strong form would be a transpose c a +u= f. That's the strong form, + + align:start position:0% +u= f. That's the strong form, + + + align:start position:0% +u= f. That's the strong form, +right? I think I always like to see the + + align:start position:0% +right? I think I always like to see the + + + align:start position:0% +right? I think I always like to see the +discrete one first and then the + + align:start position:0% +discrete one first and then the + + + align:start position:0% +discrete one first and then the +continuous. Okay. What would be the the + + align:start position:0% +continuous. Okay. What would be the the + + + align:start position:0% +continuous. Okay. What would be the the +weak form in the discrete case? I would + + align:start position:0% +weak form in the discrete case? I would + + + align:start position:0% +weak form in the discrete case? I would +multiply by a vector v + + align:start position:0% +multiply by a vector v + + + align:start position:0% +multiply by a vector v +and I would take inner products arpose c + + align:start position:0% +and I would take inner products arpose c + + + align:start position:0% +and I would take inner products arpose c +a u inner product with v equals f inner + + align:start position:0% +a u inner product with v equals f inner + + + align:start position:0% +a u inner product with v equals f inner +product with v + + align:start position:0% +product with v + + + align:start position:0% +product with v +you can use dot + + align:start position:0% +you can use dot + + + align:start position:0% +you can use dot +or or so that would be the weak form + + align:start position:0% +or or so that would be the weak form + + + align:start position:0% +or or so that would be the weak form +that that oh yes that's I've multiplied + + align:start position:0% +that that oh yes that's I've multiplied + + + align:start position:0% +that that oh yes that's I've multiplied +I've just taken the dotproduct of both + + align:start position:0% +I've just taken the dotproduct of both + + + align:start position:0% +I've just taken the dotproduct of both +sides with v + + align:start position:0% +sides with v + + + align:start position:0% +sides with v +now you'll you'll see the weak form + + align:start position:0% +now you'll you'll see the weak form + + + align:start position:0% +now you'll you'll see the weak form +better. If what should I do? What would + + align:start position:0% +better. If what should I do? What would + + + align:start position:0% +better. If what should I do? What would +make that look nice? + + align:start position:0% +make that look nice? + + + align:start position:0% +make that look nice? +So that's the the dotproduct of a + + align:start position:0% +So that's the the dotproduct of a + + + align:start position:0% +So that's the the dotproduct of a +transpose cau with v. And what do I do + + align:start position:0% +transpose cau with v. And what do I do + + + align:start position:0% +transpose cau with v. And what do I do +to make that look nice? + + align:start position:0% +to make that look nice? + + + align:start position:0% +to make that look nice? +Do you get the idea yet? It doesn't look + + align:start position:0% +Do you get the idea yet? It doesn't look + + + align:start position:0% +Do you get the idea yet? It doesn't look +pretty to me. It's every it's all + + align:start position:0% +pretty to me. It's every it's all + + + align:start position:0% +pretty to me. It's every it's all +lopsided, + + align:start position:0% +lopsided, + + + align:start position:0% +lopsided, +right? So what can I do with a + + align:start position:0% +right? So what can I do with a + + + align:start position:0% +right? So what can I do with a +transpose? What's the rule about a + + align:start position:0% +transpose? What's the rule about a + + + align:start position:0% +transpose? What's the rule about a +transpose that if I have a transpose + + align:start position:0% +transpose that if I have a transpose + + + align:start position:0% +transpose that if I have a transpose +times something dotted with something, + + align:start position:0% +times something dotted with something, + + + align:start position:0% +times something dotted with something, +what can I do? + + align:start position:0% +what can I do? + + + align:start position:0% +what can I do? +I can get I can move the aranspose over + + align:start position:0% +I can get I can move the aranspose over + + + align:start position:0% +I can get I can move the aranspose over +to the other guy. + + align:start position:0% +to the other guy. + + + align:start position:0% +to the other guy. +And what will it be when I do that? So + + align:start position:0% +And what will it be when I do that? So + + + align:start position:0% +And what will it be when I do that? So +I'll take it away from here. And what do + + align:start position:0% +I'll take it away from here. And what do + + + align:start position:0% +I'll take it away from here. And what do +I put there? + + align:start position:0% + + + + align:start position:0% + +A. + + align:start position:0% +A. + + + align:start position:0% +A. +That's the whole point of transposes. + + align:start position:0% +That's the whole point of transposes. + + + align:start position:0% +That's the whole point of transposes. +Transposes, you put them on the other + + align:start position:0% +Transposes, you put them on the other + + + align:start position:0% +Transposes, you put them on the other +side of the dotproduct. You take the + + align:start position:0% +side of the dotproduct. You take the + + + align:start position:0% +side of the dotproduct. You take the +transpose. So it would be literally + + align:start position:0% +transpose. So it would be literally + + + align:start position:0% +transpose. So it would be literally +maybe a transpose transpose which is a. + + align:start position:0% +maybe a transpose transpose which is a. + + + align:start position:0% +maybe a transpose transpose which is a. +What I just did there is integration by + + align:start position:0% +What I just did there is integration by + + + align:start position:0% +What I just did there is integration by +parts. Well, summation by parts because + + align:start position:0% +parts. Well, summation by parts because + + + align:start position:0% +parts. Well, summation by parts because +I'm in the discrete case. The whole idea + + align:start position:0% +I'm in the discrete case. The whole idea + + + align:start position:0% +I'm in the discrete case. The whole idea +of integration by parts amounted to + + align:start position:0% +of integration by parts amounted to + + + align:start position:0% +of integration by parts amounted to +taking a transpose off of you, off of + + align:start position:0% +taking a transpose off of you, off of + + + align:start position:0% +taking a transpose off of you, off of +this, and putting a over there. + + align:start position:0% +this, and putting a over there. + + + align:start position:0% +this, and putting a over there. +Isn't that neat? That's that. And do you + + align:start position:0% +Isn't that neat? That's that. And do you + + + align:start position:0% +Isn't that neat? That's that. And do you +see that this C AU AV is just what I + + align:start position:0% +see that this C AU AV is just what I + + + align:start position:0% +see that this C AU AV is just what I +have here? C A is derivative. So this is + + align:start position:0% +have here? C A is derivative. So this is + + + align:start position:0% +have here? C A is derivative. So this is +C A U AV inner product. + + align:start position:0% + + + + align:start position:0% + +That's cool. + + align:start position:0% +That's cool. + + + align:start position:0% +That's cool. +That's that's just like how it should + + align:start position:0% +That's that's just like how it should + + + align:start position:0% +That's that's just like how it should +be. I just followed that rule that a + + align:start position:0% +be. I just followed that rule that a + + + align:start position:0% +be. I just followed that rule that a +transpose times something uh so I call + + align:start position:0% +transpose times something uh so I call + + + align:start position:0% +transpose times something uh so I call +it w inner product with u is the same as + + align:start position:0% +it w inner product with u is the same as + + + align:start position:0% +it w inner product with u is the same as +w au that that if I bring an arpose over + + align:start position:0% +w au that that if I bring an arpose over + + + align:start position:0% +w au that that if I bring an arpose over +it becomes an a. If I bring an a over it + + align:start position:0% +it becomes an a. If I bring an a over it + + + align:start position:0% +it becomes an a. If I bring an a over it +would become an arpose. All right. What + + align:start position:0% +would become an arpose. All right. What + + + align:start position:0% +would become an arpose. All right. What +about the minimum form? Have I got one + + align:start position:0% +about the minimum form? Have I got one + + + align:start position:0% +about the minimum form? Have I got one +minute to do the minimum form? Yes. + + align:start position:0% +minute to do the minimum form? Yes. + + + align:start position:0% +minute to do the minimum form? Yes. +What's the min? So what's the + + align:start position:0% +What's the min? So what's the + + + align:start position:0% +What's the min? So what's the +minimization that hides that's hiding + + align:start position:0% +minimization that hides that's hiding + + + align:start position:0% +minimization that hides that's hiding +behind this the minimization + + align:start position:0% +behind this the minimization + + + align:start position:0% +behind this the minimization +in the discrete case? Do you remember + + align:start position:0% +in the discrete case? Do you remember + + + align:start position:0% +in the discrete case? Do you remember +we're we're we're looking at ku equal f + + align:start position:0% +we're we're we're looking at ku equal f + + + align:start position:0% +we're we're we're looking at ku equal f +and some some quadratic quantity from + + align:start position:0% +and some some quadratic quantity from + + + align:start position:0% +and some some quadratic quantity from +least squares has its minimum when ku + + align:start position:0% +least squares has its minimum when ku + + + align:start position:0% +least squares has its minimum when ku +equals f and and it's 12 uranspose k u + + align:start position:0% +equals f and and it's 12 uranspose k u + + + align:start position:0% +equals f and and it's 12 uranspose k u +minus uranspose f where k is arpose ca. + + align:start position:0% +minus uranspose f where k is arpose ca. + + + align:start position:0% +minus uranspose f where k is arpose ca. +This is the minimum statement of the + + align:start position:0% +This is the minimum statement of the + + + align:start position:0% +This is the minimum statement of the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +that if I look for the u that minimizes + + align:start position:0% +that if I look for the u that minimizes + + + align:start position:0% +that if I look for the u that minimizes +that quadratic, it leads me to the + + align:start position:0% +that quadratic, it leads me to the + + + align:start position:0% +that quadratic, it leads me to the +equation ku equal f. So that's the + + align:start position:0% +equation ku equal f. So that's the + + + align:start position:0% +equation ku equal f. So that's the +minimum statement. And if if we wanted + + align:start position:0% +minimum statement. And if if we wanted + + + align:start position:0% +minimum statement. And if if we wanted +to really look perfectly like the + + align:start position:0% +to really look perfectly like the + + + align:start position:0% +to really look perfectly like the +others, I would put in a transpose ca. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Can I write down next time because our + + align:start position:0% +Can I write down next time because our + + + align:start position:0% +Can I write down next time because our +time is really up. I don't It's not fair + + align:start position:0% +time is really up. I don't It's not fair + + + align:start position:0% +time is really up. I don't It's not fair +to I All I'm going to do is write down + + align:start position:0% +to I All I'm going to do is write down + + + align:start position:0% +to I All I'm going to do is write down +the same thing here. I'm minimizing a + + align:start position:0% +the same thing here. I'm minimizing a + + + align:start position:0% +the same thing here. I'm minimizing a +half. Oh, I'm going to do it anyway. C + + align:start position:0% +half. Oh, I'm going to do it anyway. C + + + align:start position:0% +half. Oh, I'm going to do it anyway. C +of X dux^2 + + align:start position:0% + + + + align:start position:0% + +minus the integral of f ofx u of x. + + align:start position:0% +minus the integral of f ofx u of x. + + + align:start position:0% +minus the integral of f ofx u of x. +So, so that's the that's the minimum + + align:start position:0% +So, so that's the that's the minimum + + + align:start position:0% +So, so that's the that's the minimum +problem. Minimize over all u + + align:start position:0% +problem. Minimize over all u + + + align:start position:0% +problem. Minimize over all u +this quadratic. This is this is like the + + align:start position:0% +this quadratic. This is this is like the + + + align:start position:0% +this quadratic. This is this is like the +right way to see these problems. You see + + align:start position:0% +right way to see these problems. You see + + + align:start position:0% +right way to see these problems. You see +a differential equation which we use for + + align:start position:0% +a differential equation which we use for + + + align:start position:0% +a differential equation which we use for +finite differences. You see a weak form + + align:start position:0% +finite differences. You see a weak form + + + align:start position:0% +finite differences. You see a weak form +which we use for finite elements. And + + align:start position:0% +which we use for finite elements. And + + + align:start position:0% +which we use for finite elements. And +now you see a minimum form. Okay, that + + align:start position:0% +now you see a minimum form. Okay, that + + + align:start position:0% +now you see a minimum form. Okay, that +gives you something to think about. And + + align:start position:0% +gives you something to think about. And + + + align:start position:0% +gives you something to think about. And +there'll be a homework on finite + + align:start position:0% +there'll be a homework on finite + + + align:start position:0% +there'll be a homework on finite +elements that'll give you a chance to + + align:start position:0% +elements that'll give you a chance to + + + align:start position:0% +elements that'll give you a chance to +use them. Okay. Thank you. \ No newline at end of file diff --git a/yYto-sIfHjo.txt b/yYto-sIfHjo.txt new file mode 100644 index 0000000000000000000000000000000000000000..aadc908ed5d45be8d431651e9fa8b655790b36c3 --- /dev/null +++ b/yYto-sIfHjo.txt @@ -0,0 +1,9963 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so as a quick review of all the + + align:start position:0% +so as a quick review of all the + + + align:start position:0% +so as a quick review of all the +different biological effects we've + + align:start position:0% +different biological effects we've + + + align:start position:0% +different biological effects we've +pretty much taken it up to here we've + + align:start position:0% +pretty much taken it up to here we've + + + align:start position:0% +pretty much taken it up to here we've +explained the physical and chemical + + align:start position:0% +explained the physical and chemical + + + align:start position:0% +explained the physical and chemical +stages of what happens when radiation + + align:start position:0% +stages of what happens when radiation + + + align:start position:0% +stages of what happens when radiation +interacts with mostly bags of water with + + align:start position:0% +interacts with mostly bags of water with + + + align:start position:0% +interacts with mostly bags of water with +some solutes and them better known as + + align:start position:0% +some solutes and them better known as + + + align:start position:0% +some solutes and them better known as +organisms at dynamic equilibrium + + align:start position:0% +organisms at dynamic equilibrium + + + align:start position:0% +organisms at dynamic equilibrium +everything from this sort of femtosecond + + align:start position:0% +everything from this sort of femtosecond + + + align:start position:0% +everything from this sort of femtosecond +level ionization of water almost + + align:start position:0% +level ionization of water almost + + + align:start position:0% +level ionization of water almost +certainly because that's most of what + + align:start position:0% +certainly because that's most of what + + + align:start position:0% +certainly because that's most of what +biological things are - the formation of + + align:start position:0% +biological things are - the formation of + + + align:start position:0% +biological things are - the formation of +many many many many many different + + align:start position:0% +many many many many many different + + + align:start position:0% +many many many many many different +radiolysis byproducts eventually that + + align:start position:0% +radiolysis byproducts eventually that + + + align:start position:0% +radiolysis byproducts eventually that +end up as just a few that we care about + + align:start position:0% +end up as just a few that we care about + + + align:start position:0% +end up as just a few that we care about +the one longer-lived radio lytic + + align:start position:0% +the one longer-lived radio lytic + + + align:start position:0% +the one longer-lived radio lytic +byproducts that will then diffuse away + + align:start position:0% +byproducts that will then diffuse away + + + align:start position:0% +byproducts that will then diffuse away +from the original damage cascades and go + + align:start position:0% +from the original damage cascades and go + + + align:start position:0% +from the original damage cascades and go +on to eat something else likely DNA or + + align:start position:0% +on to eat something else likely DNA or + + + align:start position:0% +on to eat something else likely DNA or +something that you don't want to get + + align:start position:0% +something that you don't want to get + + + align:start position:0% +something that you don't want to get +oxidized or chemically changed we talked + + align:start position:0% +oxidized or chemically changed we talked + + + align:start position:0% +oxidized or chemically changed we talked +a little bit about radiolysis in + + align:start position:0% +a little bit about radiolysis in + + + align:start position:0% +a little bit about radiolysis in +reactors and how you can actually + + align:start position:0% +reactors and how you can actually + + + align:start position:0% +reactors and how you can actually +measure it directly which was only done + + align:start position:0% +measure it directly which was only done + + + align:start position:0% +measure it directly which was only done +really a few years ago which is pretty + + align:start position:0% +really a few years ago which is pretty + + + align:start position:0% +really a few years ago which is pretty +cool just to remind you of this + + align:start position:0% +cool just to remind you of this + + + align:start position:0% +cool just to remind you of this +experiment there's a tiny high pressure + + align:start position:0% +experiment there's a tiny high pressure + + + align:start position:0% +experiment there's a tiny high pressure +cell of high pressure high temperature + + align:start position:0% +cell of high pressure high temperature + + + align:start position:0% +cell of high pressure high temperature +water there's a foil sample with a very + + align:start position:0% +water there's a foil sample with a very + + + align:start position:0% +water there's a foil sample with a very +thin region and protons firing through + + align:start position:0% +thin region and protons firing through + + + align:start position:0% +thin region and protons firing through +it so that they both are radiate the + + align:start position:0% +it so that they both are radiate the + + + align:start position:0% +it so that they both are radiate the +sample and induce radiolysis and the + + align:start position:0% +sample and induce radiolysis and the + + + align:start position:0% +sample and induce radiolysis and the +water at the same time and this way you + + align:start position:0% +water at the same time and this way you + + + align:start position:0% +water at the same time and this way you +can test the effect of radiolysis in the + + align:start position:0% +can test the effect of radiolysis in the + + + align:start position:0% +can test the effect of radiolysis in the +water here versus just plain old high + + align:start position:0% +water here versus just plain old high + + + align:start position:0% +water here versus just plain old high +pressure high temperature corrosion here + + align:start position:0% +pressure high temperature corrosion here + + + align:start position:0% +pressure high temperature corrosion here +and the results are pretty striking or + + align:start position:0% +and the results are pretty striking or + + + align:start position:0% +and the results are pretty striking or +you can clearly see the boundary where + + align:start position:0% +you can clearly see the boundary where + + + align:start position:0% +you can clearly see the boundary where +the proton beam was as well as the + + align:start position:0% +the proton beam was as well as the + + + align:start position:0% +the proton beam was as well as the +increased thickness of the oxide and + + align:start position:0% +increased thickness of the oxide and + + + align:start position:0% +increased thickness of the oxide and +corrosion layer formed when radiolysis + + align:start position:0% +corrosion layer formed when radiolysis + + + align:start position:0% +corrosion layer formed when radiolysis +is turned on so to speak we went through + + align:start position:0% +is turned on so to speak we went through + + + align:start position:0% +is turned on so to speak we went through +DNA damage and we ended with + + align:start position:0% +DNA damage and we ended with + + + align:start position:0% +DNA damage and we ended with +pseudoscience so I want to bring up a + + align:start position:0% +pseudoscience so I want to bring up a + + + align:start position:0% +pseudoscience so I want to bring up a +couple no we don't have time for that + + align:start position:0% +couple no we don't have time for that + + + align:start position:0% +couple no we don't have time for that +but we we spent the last 15 minutes of + + align:start position:0% +but we we spent the last 15 minutes of + + + align:start position:0% +but we we spent the last 15 minutes of +class railing against pseudoscience and + + align:start position:0% +class railing against pseudoscience and + + + align:start position:0% +class railing against pseudoscience and +making sure that you check your facts + + align:start position:0% +making sure that you check your facts + + + align:start position:0% +making sure that you check your facts +but we pointed out a number of things + + align:start position:0% +but we pointed out a number of things + + + align:start position:0% +but we pointed out a number of things +wrong with some of the studies so aside + + align:start position:0% +wrong with some of the studies so aside + + + align:start position:0% +wrong with some of the studies so aside +from just that guy miss reading + + align:start position:0% +from just that guy miss reading + + + align:start position:0% +from just that guy miss reading +everything on that entire blog of the + + align:start position:0% +everything on that entire blog of the + + + align:start position:0% +everything on that entire blog of the +studies that you felt weren't very + + align:start position:0% +studies that you felt weren't very + + + align:start position:0% +studies that you felt weren't very +convincing what do you remember about + + align:start position:0% +convincing what do you remember about + + + align:start position:0% +convincing what do you remember about +them some of those studies were totally + + align:start position:0% +them some of those studies were totally + + + align:start position:0% +them some of those studies were totally +fine but some of them were not + + align:start position:0% + + + + align:start position:0% + +that's what I was hoping some would say + + align:start position:0% +that's what I was hoping some would say + + + align:start position:0% +that's what I was hoping some would say +yeah the case study of four women who + + align:start position:0% +yeah the case study of four women who + + + align:start position:0% +yeah the case study of four women who +got breast cancer in the pocket where + + align:start position:0% +got breast cancer in the pocket where + + + align:start position:0% +got breast cancer in the pocket where +they held their cell phones for right or + + align:start position:0% +they held their cell phones for right or + + + align:start position:0% +they held their cell phones for right or +in a study of 29 humans 11 of them got + + align:start position:0% +in a study of 29 humans 11 of them got + + + align:start position:0% +in a study of 29 humans 11 of them got +brain tumors here it's pretty easy to + + align:start position:0% +brain tumors here it's pretty easy to + + + align:start position:0% +brain tumors here it's pretty easy to +cherry-pick small amounts of data + + align:start position:0% +cherry-pick small amounts of data + + + align:start position:0% +cherry-pick small amounts of data +I want did want to say that just because + + align:start position:0% +I want did want to say that just because + + + align:start position:0% +I want did want to say that just because +radiofrequency photons aren't ionizing + + align:start position:0% +radiofrequency photons aren't ionizing + + + align:start position:0% +radiofrequency photons aren't ionizing +doesn't mean they can't hurt you if + + align:start position:0% +doesn't mean they can't hurt you if + + + align:start position:0% +doesn't mean they can't hurt you if +you've ever no no one's ever been inside + + align:start position:0% +you've ever no no one's ever been inside + + + align:start position:0% +you've ever no no one's ever been inside +a microwave I wonder if anyone's ever + + align:start position:0% +a microwave I wonder if anyone's ever + + + align:start position:0% +a microwave I wonder if anyone's ever +felt the effects of an external + + align:start position:0% +felt the effects of an external + + + align:start position:0% +felt the effects of an external +microwave beam by something like this + + align:start position:0% +microwave beam by something like this + + + align:start position:0% +microwave beam by something like this +the Active Denial system one of my + + align:start position:0% +the Active Denial system one of my + + + align:start position:0% +the Active Denial system one of my +favorite weapons ever because it doesn't + + align:start position:0% +favorite weapons ever because it doesn't + + + align:start position:0% +favorite weapons ever because it doesn't +actually permanently hurt anyone it just + + align:start position:0% +actually permanently hurt anyone it just + + + align:start position:0% +actually permanently hurt anyone it just +heats up the outer layer of your skin it + + align:start position:0% +heats up the outer layer of your skin it + + + align:start position:0% +heats up the outer layer of your skin it +fires these non ionizing photons at RF + + align:start position:0% +fires these non ionizing photons at RF + + + align:start position:0% +fires these non ionizing photons at RF +frequency and effectively makes you feel + + align:start position:0% +frequency and effectively makes you feel + + + align:start position:0% +frequency and effectively makes you feel +like you're on fire so if there's a + + align:start position:0% +like you're on fire so if there's a + + + align:start position:0% +like you're on fire so if there's a +whole mess of troops charging at you + + align:start position:0% +whole mess of troops charging at you + + + align:start position:0% +whole mess of troops charging at you +let's say at the DMZ from North and + + align:start position:0% +let's say at the DMZ from North and + + + align:start position:0% +let's say at the DMZ from North and +South Korea all you've got to do is turn + + align:start position:0% +South Korea all you've got to do is turn + + + align:start position:0% +South Korea all you've got to do is turn +on this thing and they all think they're + + align:start position:0% +on this thing and they all think they're + + + align:start position:0% +on this thing and they all think they're +on fire because their body is sending + + align:start position:0% +on fire because their body is sending + + + align:start position:0% +on fire because their body is sending +them signals that I'm on fire and then + + align:start position:0% +them signals that I'm on fire and then + + + align:start position:0% +them signals that I'm on fire and then +you turn it off and they're okay so no + + align:start position:0% +you turn it off and they're okay so no + + + align:start position:0% +you turn it off and they're okay so no +loss of life no permanent damage a lot + + align:start position:0% +loss of life no permanent damage a lot + + + align:start position:0% +loss of life no permanent damage a lot +of maybe psychological but whatever + + align:start position:0% +of maybe psychological but whatever + + + align:start position:0% +of maybe psychological but whatever +can't see that and Active Denial system + + align:start position:0% +can't see that and Active Denial system + + + align:start position:0% +can't see that and Active Denial system +great name for it isn't it yeah I think + + align:start position:0% +great name for it isn't it yeah I think + + + align:start position:0% +great name for it isn't it yeah I think +non-lethal weapons are really the way of + + align:start position:0% +non-lethal weapons are really the way of + + + align:start position:0% +non-lethal weapons are really the way of +the future is just make it make it + + align:start position:0% +the future is just make it make it + + + align:start position:0% +the future is just make it make it +unpleasant to engage in warfare and + + align:start position:0% +unpleasant to engage in warfare and + + + align:start position:0% +unpleasant to engage in warfare and +people probably won't but then no one + + align:start position:0% +people probably won't but then no one + + + align:start position:0% +people probably won't but then no one +has to get hurt which is nice + + align:start position:0% +has to get hurt which is nice + + + align:start position:0% +has to get hurt which is nice +well then on to the sources of data + + align:start position:0% +well then on to the sources of data + + + align:start position:0% +well then on to the sources of data +because like Sarah said sample size is + + align:start position:0% +because like Sarah said sample size is + + + align:start position:0% +because like Sarah said sample size is +everything especially when you're trying + + align:start position:0% +everything especially when you're trying + + + align:start position:0% +everything especially when you're trying +to figure out our small amounts of + + align:start position:0% +to figure out our small amounts of + + + align:start position:0% +to figure out our small amounts of +radiation bad for you this simple + + align:start position:0% +radiation bad for you this simple + + + align:start position:0% +radiation bad for you this simple +question hasn't really been answered + + align:start position:0% +question hasn't really been answered + + + align:start position:0% +question hasn't really been answered +suitably yet and that's because thank + + align:start position:0% +suitably yet and that's because thank + + + align:start position:0% +suitably yet and that's because thank +God we don't have enough people exposed + + align:start position:0% +God we don't have enough people exposed + + + align:start position:0% +God we don't have enough people exposed +too small but measurable amounts of + + align:start position:0% +too small but measurable amounts of + + + align:start position:0% +too small but measurable amounts of +radiation to draw meaningful conclusions + + align:start position:0% +radiation to draw meaningful conclusions + + + align:start position:0% +radiation to draw meaningful conclusions +from this data I think that's a good + + align:start position:0% +from this data I think that's a good + + + align:start position:0% +from this data I think that's a good +thing is if we were certain about + + align:start position:0% +thing is if we were certain about + + + align:start position:0% +thing is if we were certain about +whether small amounts of radiation like + + align:start position:0% +whether small amounts of radiation like + + + align:start position:0% +whether small amounts of radiation like +1 millisievert could cause cancer then + + align:start position:0% +1 millisievert could cause cancer then + + + align:start position:0% +1 millisievert could cause cancer then +there would have been millions or + + align:start position:0% +there would have been millions or + + + align:start position:0% +there would have been millions or +billions of people exposed and so it's + + align:start position:0% +billions of people exposed and so it's + + + align:start position:0% +billions of people exposed and so it's +kind of a good thing that they weren't + + align:start position:0% +kind of a good thing that they weren't + + + align:start position:0% +kind of a good thing that they weren't +but the sources of this data the first + + align:start position:0% +but the sources of this data the first + + + align:start position:0% +but the sources of this data the first +source was radium dial workers like you + + align:start position:0% +source was radium dial workers like you + + + align:start position:0% +source was radium dial workers like you +may have heard of the folks that would + + align:start position:0% +may have heard of the folks that would + + + align:start position:0% +may have heard of the folks that would +lick the paint + + align:start position:0% +lick the paint + + + align:start position:0% +lick the paint +Rush's with glow-in-the-dark radium + + align:start position:0% +Rush's with glow-in-the-dark radium + + + align:start position:0% +Rush's with glow-in-the-dark radium +watches they ended up setting the first + + align:start position:0% +watches they ended up setting the first + + + align:start position:0% +watches they ended up setting the first +occupational limit for dose because they + + align:start position:0% +occupational limit for dose because they + + + align:start position:0% +occupational limit for dose because they +were the first large group to be exposed + + align:start position:0% +were the first large group to be exposed + + + align:start position:0% +were the first large group to be exposed +to radiation in a controlled setting + + align:start position:0% +to radiation in a controlled setting + + + align:start position:0% +to radiation in a controlled setting +things like uranium miners radon + + align:start position:0% +things like uranium miners radon + + + align:start position:0% +things like uranium miners radon +breathers better known as us but + + align:start position:0% +breathers better known as us but + + + align:start position:0% +breathers better known as us but +especially folks that smoke anything + + align:start position:0% +especially folks that smoke anything + + + align:start position:0% +especially folks that smoke anything +medical diagnostic so anyone that gets a + + align:start position:0% +medical diagnostic so anyone that gets a + + + align:start position:0% +medical diagnostic so anyone that gets a +medical procedure you can follow up with + + align:start position:0% +medical procedure you can follow up with + + + align:start position:0% +medical procedure you can follow up with +them to find out what's let's say the + + align:start position:0% +them to find out what's let's say the + + + align:start position:0% +them to find out what's let's say the +extra incidence of cancer and figure out + + align:start position:0% +extra incidence of cancer and figure out + + + align:start position:0% +extra incidence of cancer and figure out +if you have a high dose rate medical + + align:start position:0% +if you have a high dose rate medical + + + align:start position:0% +if you have a high dose rate medical +procedure does it and do secondary + + align:start position:0% +procedure does it and do secondary + + + align:start position:0% +procedure does it and do secondary +cancer down the line but like we said + + align:start position:0% +cancer down the line but like we said + + + align:start position:0% +cancer down the line but like we said +last time down the line is the key here + + align:start position:0% +last time down the line is the key here + + + align:start position:0% +last time down the line is the key here +I take a whole bunch of radiation now if + + align:start position:0% +I take a whole bunch of radiation now if + + + align:start position:0% +I take a whole bunch of radiation now if +it was going to save my life now and + + align:start position:0% +it was going to save my life now and + + + align:start position:0% +it was going to save my life now and +maybe make it messed up in 20 years + + align:start position:0% +maybe make it messed up in 20 years + + + align:start position:0% +maybe make it messed up in 20 years +because then you get 20 more years of + + align:start position:0% +because then you get 20 more years of + + + align:start position:0% +because then you get 20 more years of +life or however long you get and then + + align:start position:0% +life or however long you get and then + + + align:start position:0% +life or however long you get and then +from accidents survivors of the atomic + + align:start position:0% +from accidents survivors of the atomic + + + align:start position:0% +from accidents survivors of the atomic +bombs not just the folks at the + + align:start position:0% +bombs not just the folks at the + + + align:start position:0% +bombs not just the folks at the +epicenter but in the whole Fallout + + align:start position:0% +epicenter but in the whole Fallout + + + align:start position:0% +epicenter but in the whole Fallout +regions in nearby as well as nearby + + align:start position:0% +regions in nearby as well as nearby + + + align:start position:0% +regions in nearby as well as nearby +nuclear accidents and the criticality + + align:start position:0% +nuclear accidents and the criticality + + + align:start position:0% +nuclear accidents and the criticality +events like the diamond core that you + + align:start position:0% +events like the diamond core that you + + + align:start position:0% +events like the diamond core that you +guys analyzed on the exam luckily there + + align:start position:0% +guys analyzed on the exam luckily there + + + align:start position:0% +guys analyzed on the exam luckily there +aren't a lot of those either but they + + align:start position:0% +aren't a lot of those either but they + + + align:start position:0% +aren't a lot of those either but they +were pretty severe the ones that got + + align:start position:0% +were pretty severe the ones that got + + + align:start position:0% +were pretty severe the ones that got +exposed and speaking of accidents has + + align:start position:0% +exposed and speaking of accidents has + + + align:start position:0% +exposed and speaking of accidents has +anyone ever heard of the kyshtym + + align:start position:0% +anyone ever heard of the kyshtym + + + align:start position:0% +anyone ever heard of the kyshtym +disaster this is the third worst nuclear + + align:start position:0% +disaster this is the third worst nuclear + + + align:start position:0% +disaster this is the third worst nuclear +accident that we know of in history + + align:start position:0% +accident that we know of in history + + + align:start position:0% +accident that we know of in history +after Chernobyl and Fukushima and worse + + align:start position:0% +after Chernobyl and Fukushima and worse + + + align:start position:0% +after Chernobyl and Fukushima and worse +than Three Mile Island because Three + + align:start position:0% +than Three Mile Island because Three + + + align:start position:0% +than Three Mile Island because Three +Mile Island was an almost accident there + + align:start position:0% +Mile Island was an almost accident there + + + align:start position:0% +Mile Island was an almost accident there +was some partial melting of the core + + align:start position:0% +was some partial melting of the core + + + align:start position:0% +was some partial melting of the core +there was almost no release of + + align:start position:0% +there was almost no release of + + + align:start position:0% +there was almost no release of +radioactivity and the definition of a + + align:start position:0% +radioactivity and the definition of a + + + align:start position:0% +radioactivity and the definition of a +nuclear accident and the public sense is + + align:start position:0% +nuclear accident and the public sense is + + + align:start position:0% +nuclear accident and the public sense is +release of radioactivity there's + + align:start position:0% +release of radioactivity there's + + + align:start position:0% +release of radioactivity there's +actually two quantities that folks in PR + + align:start position:0% +actually two quantities that folks in PR + + + align:start position:0% +actually two quantities that folks in PR +a or probabilistic risk analysis are + + align:start position:0% +a or probabilistic risk analysis are + + + align:start position:0% +a or probabilistic risk analysis are +most interested in has anyone heard of + + align:start position:0% +most interested in has anyone heard of + + + align:start position:0% +most interested in has anyone heard of +these terms CDF and lourve core damage + + align:start position:0% +these terms CDF and lourve core damage + + + align:start position:0% +these terms CDF and lourve core damage +frequency and large early release + + align:start position:0% +frequency and large early release + + + align:start position:0% +frequency and large early release +frequency the all the fancy probability + + align:start position:0% +frequency the all the fancy probability + + + align:start position:0% +frequency the all the fancy probability +fault trees and everything goes into + + align:start position:0% +fault trees and everything goes into + + + align:start position:0% +fault trees and everything goes into +calculating the probability that the + + align:start position:0% +calculating the probability that the + + + align:start position:0% +calculating the probability that the +core gets damaged so that could be an + + align:start position:0% +core gets damaged so that could be an + + + align:start position:0% +core gets damaged so that could be an +accident in one write or the probability + + align:start position:0% +accident in one write or the probability + + + align:start position:0% +accident in one write or the probability +of a radioactivity release and that is + + align:start position:0% +of a radioactivity release and that is + + + align:start position:0% +of a radioactivity release and that is +an accident so if no one's ever heard of + + align:start position:0% +an accident so if no one's ever heard of + + + align:start position:0% +an accident so if no one's ever heard of +this there's a city in Russia I don't + + align:start position:0% +this there's a city in Russia I don't + + + align:start position:0% +this there's a city in Russia I don't +know why it says roofs lund maybe came + + align:start position:0% +know why it says roofs lund maybe came + + + align:start position:0% +know why it says roofs lund maybe came +from a different language called kyshtym + + align:start position:0% +from a different language called kyshtym + + + align:start position:0% +from a different language called kyshtym +where they had the Maya clear and + + align:start position:0% +where they had the Maya clear and + + + align:start position:0% +where they had the Maya clear and +reprocessing plant and there was a tank + + align:start position:0% +reprocessing plant and there was a tank + + + align:start position:0% +reprocessing plant and there was a tank +full of radioactive way + + align:start position:0% +full of radioactive way + + + align:start position:0% +full of radioactive way +that was exploded it was a chemical + + align:start position:0% +that was exploded it was a chemical + + + align:start position:0% +that was exploded it was a chemical +explosion but full of strontium all + + align:start position:0% +explosion but full of strontium all + + + align:start position:0% +explosion but full of strontium all +sorts of other radionuclides + + align:start position:0% +sorts of other radionuclides + + + align:start position:0% +sorts of other radionuclides +that blew up with about a hundred tons + + align:start position:0% +that blew up with about a hundred tons + + + align:start position:0% +that blew up with about a hundred tons +worth of TNT and ended up contaminating + + align:start position:0% +worth of TNT and ended up contaminating + + + align:start position:0% +worth of TNT and ended up contaminating +a rather large area with this plume + + align:start position:0% +a rather large area with this plume + + + align:start position:0% +a rather large area with this plume +called the I think it's called the East + + align:start position:0% +called the I think it's called the East + + + align:start position:0% +called the I think it's called the East +Chelyabinsk radioactive twice or the + + align:start position:0% +Chelyabinsk radioactive twice or the + + + align:start position:0% +Chelyabinsk radioactive twice or the +early what is it the South South + + align:start position:0% +early what is it the South South + + + align:start position:0% +early what is it the South South +something Urals radioactive trace and + + align:start position:0% +something Urals radioactive trace and + + + align:start position:0% +something Urals radioactive trace and +that area still contaminated today + + align:start position:0% +that area still contaminated today + + + align:start position:0% +that area still contaminated today +because the disaster was covered up or + + align:start position:0% +because the disaster was covered up or + + + align:start position:0% +because the disaster was covered up or +rather wasn't nothing was said these + + align:start position:0% +rather wasn't nothing was said these + + + align:start position:0% +rather wasn't nothing was said these +towns here they didn't I weren't + + align:start position:0% +towns here they didn't I weren't + + + align:start position:0% +towns here they didn't I weren't +actually towns back in 1957 when this + + align:start position:0% +actually towns back in 1957 when this + + + align:start position:0% +actually towns back in 1957 when this +happened they were just given + + align:start position:0% +happened they were just given + + + align:start position:0% +happened they were just given +designations like Chelyabinsk forty or + + align:start position:0% +designations like Chelyabinsk forty or + + + align:start position:0% +designations like Chelyabinsk forty or +chillier been sixty-five because the + + align:start position:0% +chillier been sixty-five because the + + + align:start position:0% +chillier been sixty-five because the +largest nearby city was Chelyabinsk and + + align:start position:0% +largest nearby city was Chelyabinsk and + + + align:start position:0% +largest nearby city was Chelyabinsk and +the villages nearby were just numbered + + align:start position:0% +the villages nearby were just numbered + + + align:start position:0% +the villages nearby were just numbered +so that was just the postcode for the + + align:start position:0% +so that was just the postcode for the + + + align:start position:0% +so that was just the postcode for the +secret nuclear city the US had a few + + align:start position:0% +secret nuclear city the US had a few + + + align:start position:0% +secret nuclear city the US had a few +Russia had something like a hundred + + align:start position:0% +Russia had something like a hundred + + + align:start position:0% +Russia had something like a hundred +twenty and they still have a lot of + + align:start position:0% +twenty and they still have a lot of + + + align:start position:0% +twenty and they still have a lot of +cities where entry is restricted or it's + + align:start position:0% +cities where entry is restricted or it's + + + align:start position:0% +cities where entry is restricted or it's +still awfully difficult to go there like + + align:start position:0% +still awfully difficult to go there like + + + align:start position:0% +still awfully difficult to go there like +when you have to declare we're and + + align:start position:0% +when you have to declare we're and + + + align:start position:0% +when you have to declare we're and +Russia are you going to get a visa if + + align:start position:0% +Russia are you going to get a visa if + + + align:start position:0% +Russia are you going to get a visa if +you say one of these cities there's + + align:start position:0% +you say one of these cities there's + + + align:start position:0% +you say one of these cities there's +going to be some questions and this is + + align:start position:0% +going to be some questions and this is + + + align:start position:0% +going to be some questions and this is +where I'm going best possible logo for a + + align:start position:0% +where I'm going best possible logo for a + + + align:start position:0% +where I'm going best possible logo for a +conference being held in Siberia in + + align:start position:0% +conference being held in Siberia in + + + align:start position:0% +conference being held in Siberia in +February right on the end right on the + + align:start position:0% +February right on the end right on the + + + align:start position:0% +February right on the end right on the +edge in this town called kyshtym the + + align:start position:0% +edge in this town called kyshtym the + + + align:start position:0% +edge in this town called kyshtym the +nearest town to the MIAC plant so I'll + + align:start position:0% +nearest town to the MIAC plant so I'll + + + align:start position:0% +nearest town to the MIAC plant so I'll +be taking my camera I don't know if I'll + + align:start position:0% +be taking my camera I don't know if I'll + + + align:start position:0% +be taking my camera I don't know if I'll +be allowed to use it but we're gonna + + align:start position:0% +be allowed to use it but we're gonna + + + align:start position:0% +be allowed to use it but we're gonna +find out anyway it's being held in a + + align:start position:0% +find out anyway it's being held in a + + + align:start position:0% +find out anyway it's being held in a +sanatorium and does anyone know what a + + align:start position:0% +sanatorium and does anyone know what a + + + align:start position:0% +sanatorium and does anyone know what a +sanatorium is like I'm honestly asking a + + align:start position:0% +sanatorium is like I'm honestly asking a + + + align:start position:0% +sanatorium is like I'm honestly asking a +question I don't know what a sanatorium + + align:start position:0% +question I don't know what a sanatorium + + + align:start position:0% +question I don't know what a sanatorium +is or why the nuclear conference is + + align:start position:0% +is or why the nuclear conference is + + + align:start position:0% +is or why the nuclear conference is +being held there but it should be pretty + + align:start position:0% +being held there but it should be pretty + + + align:start position:0% +being held there but it should be pretty +cool so yes Iberia in February right + + align:start position:0% +cool so yes Iberia in February right + + + align:start position:0% +cool so yes Iberia in February right +near the South Urals radioactive tracer + + align:start position:0% +near the South Urals radioactive tracer + + + align:start position:0% +near the South Urals radioactive tracer +should be interesting + + align:start position:0% +should be interesting + + + align:start position:0% +should be interesting +the first group of folks that were + + align:start position:0% +the first group of folks that were + + + align:start position:0% +the first group of folks that were +exposed were the people painting radium + + align:start position:0% +exposed were the people painting radium + + + align:start position:0% +exposed were the people painting radium +watch dials and the reason radium was so + + align:start position:0% +watch dials and the reason radium was so + + + align:start position:0% +watch dials and the reason radium was so +damaging is because radium is in the + + align:start position:0% +damaging is because radium is in the + + + align:start position:0% +damaging is because radium is in the +same column of the periodic table as + + align:start position:0% +same column of the periodic table as + + + align:start position:0% +same column of the periodic table as +calcium it's a bone seeking element so + + align:start position:0% +calcium it's a bone seeking element so + + + align:start position:0% +calcium it's a bone seeking element so +which of the tissues do you think would + + align:start position:0% +which of the tissues do you think would + + + align:start position:0% +which of the tissues do you think would +be most damaged by ingestion of radium + + align:start position:0% + + + + align:start position:0% + +bones what part of the bones + + align:start position:0% +bones what part of the bones + + + align:start position:0% +bones what part of the bones +specifically the marrow the rapidly + + align:start position:0% +specifically the marrow the rapidly + + + align:start position:0% +specifically the marrow the rapidly +dividing part of the bones if you + + align:start position:0% +dividing part of the bones if you + + + align:start position:0% +dividing part of the bones if you +remember from the I don't have it on + + align:start position:0% +remember from the I don't have it on + + + align:start position:0% +remember from the I don't have it on +this presentation but the relative + + align:start position:0% +this presentation but the relative + + + align:start position:0% +this presentation but the relative +tissue factors for different tissues the + + align:start position:0% +tissue factors for different tissues the + + + align:start position:0% +tissue factors for different tissues the +hard part of the bone is a point zero + + align:start position:0% +hard part of the bone is a point zero + + + align:start position:0% +hard part of the bone is a point zero +one it's basically like a nobody cares + + align:start position:0% +one it's basically like a nobody cares + + + align:start position:0% +one it's basically like a nobody cares +bone marrow however is a different story + + align:start position:0% +bone marrow however is a different story + + + align:start position:0% +bone marrow however is a different story +because it's always rapidly dividing + + align:start position:0% +because it's always rapidly dividing + + + align:start position:0% +because it's always rapidly dividing +producing red blood cells platelets + + align:start position:0% +producing red blood cells platelets + + + align:start position:0% +producing red blood cells platelets +lymphocytes it's it's making your blood + + align:start position:0% +lymphocytes it's it's making your blood + + + align:start position:0% +lymphocytes it's it's making your blood +the solid portion of your blood and so + + align:start position:0% +the solid portion of your blood and so + + + align:start position:0% +the solid portion of your blood and so +it's a pretty important tissue + + align:start position:0% +it's a pretty important tissue + + + align:start position:0% +it's a pretty important tissue +so get radium anyone else oh no what + + align:start position:0% +so get radium anyone else oh no what + + + align:start position:0% +so get radium anyone else oh no what +does radium tend to emit which kind of + + align:start position:0% +does radium tend to emit which kind of + + + align:start position:0% +does radium tend to emit which kind of +particles if you had to take a guess + + align:start position:0% +particles if you had to take a guess + + + align:start position:0% +particles if you had to take a guess +yeah alphas it's a pretty heavy element + + align:start position:0% +yeah alphas it's a pretty heavy element + + + align:start position:0% +yeah alphas it's a pretty heavy element +it emits alphas and alphas have that + + align:start position:0% +it emits alphas and alphas have that + + + align:start position:0% +it emits alphas and alphas have that +radiation quality factor of twenty + + align:start position:0% +radiation quality factor of twenty + + + align:start position:0% +radiation quality factor of twenty +meaning alphas have very short range but + + align:start position:0% +meaning alphas have very short range but + + + align:start position:0% +meaning alphas have very short range but +they're the most damaging type of + + align:start position:0% +they're the most damaging type of + + + align:start position:0% +they're the most damaging type of +radiation when ingested so this was + + align:start position:0% +radiation when ingested so this was + + + align:start position:0% +radiation when ingested so this was +really bad news there was a lot of + + align:start position:0% +really bad news there was a lot of + + + align:start position:0% +really bad news there was a lot of +incidence of illness and cancer from + + align:start position:0% +incidence of illness and cancer from + + + align:start position:0% +incidence of illness and cancer from +folks painting radium watch dials and + + align:start position:0% +folks painting radium watch dials and + + + align:start position:0% +folks painting radium watch dials and +then the first data from bones after + + align:start position:0% +then the first data from bones after + + + align:start position:0% +then the first data from bones after +death because there were a lot of those + + align:start position:0% +death because there were a lot of those + + + align:start position:0% +death because there were a lot of those +established how much radium were you + + align:start position:0% +established how much radium were you + + + align:start position:0% +established how much radium were you +allowed to get exposed to this came out + + align:start position:0% +allowed to get exposed to this came out + + + align:start position:0% +allowed to get exposed to this came out +to about 0.6 milligram anyone have any + + align:start position:0% +to about 0.6 milligram anyone have any + + + align:start position:0% +to about 0.6 milligram anyone have any +idea what that would be in millisieverts + + align:start position:0% +idea what that would be in millisieverts + + + align:start position:0% +idea what that would be in millisieverts +per week with a quality factor of twenty + + align:start position:0% +per week with a quality factor of twenty + + + align:start position:0% +per week with a quality factor of twenty +and a bone marrow factor of about 0.12 + + align:start position:0% + + + + align:start position:0% + +yeah on the order of like singles of + + align:start position:0% +yeah on the order of like singles of + + + align:start position:0% +yeah on the order of like singles of +millisieverts per week + + align:start position:0% +millisieverts per week + + + align:start position:0% +millisieverts per week +not bad anyone know how much dose you + + align:start position:0% +not bad anyone know how much dose you + + + align:start position:0% +not bad anyone know how much dose you +typically get in a year in background + + align:start position:0% +typically get in a year in background + + + align:start position:0% +typically get in a year in background +yeah it's few millisieverts a year yeah + + align:start position:0% +yeah it's few millisieverts a year yeah + + + align:start position:0% +yeah it's few millisieverts a year yeah +so this was the first occupational + + align:start position:0% +so this was the first occupational + + + align:start position:0% +so this was the first occupational +safety limit for radiation risk it is + + align:start position:0% +safety limit for radiation risk it is + + + align:start position:0% +safety limit for radiation risk it is +actually it comes out to larger than 50 + + align:start position:0% +actually it comes out to larger than 50 + + + align:start position:0% +actually it comes out to larger than 50 +millisieverts per year which is what the + + align:start position:0% +millisieverts per year which is what the + + + align:start position:0% +millisieverts per year which is what the +normal occupational workers are allowed + + align:start position:0% +normal occupational workers are allowed + + + align:start position:0% +normal occupational workers are allowed +how about your radiation workers what's + + align:start position:0% +how about your radiation workers what's + + + align:start position:0% +how about your radiation workers what's +your limit five REM which comes out 250 + + align:start position:0% +your limit five REM which comes out 250 + + + align:start position:0% +your limit five REM which comes out 250 +millisieverts per year okay there you go + + align:start position:0% +millisieverts per year okay there you go + + + align:start position:0% +millisieverts per year okay there you go +large population sizes that do exist + + align:start position:0% +large population sizes that do exist + + + align:start position:0% +large population sizes that do exist +that get a whole lot of radiation + + align:start position:0% +that get a whole lot of radiation + + + align:start position:0% +that get a whole lot of radiation +however is anyone that smokes and + + align:start position:0% +however is anyone that smokes and + + + align:start position:0% +however is anyone that smokes and +anything because when you take plant + + align:start position:0% +anything because when you take plant + + + align:start position:0% +anything because when you take plant +matter which has a high surface area + + align:start position:0% +matter which has a high surface area + + + align:start position:0% +matter which has a high surface area +concentrate it so anything that it + + align:start position:0% +concentrate it so anything that it + + + align:start position:0% +concentrate it so anything that it +brings up from the roots in the soil or + + align:start position:0% +brings up from the roots in the soil or + + + align:start position:0% +brings up from the roots in the soil or +that settles out on the leaves in the + + align:start position:0% +that settles out on the leaves in the + + + align:start position:0% +that settles out on the leaves in the +air gets concentrated in the dry + + align:start position:0% +air gets concentrated in the dry + + + align:start position:0% +air gets concentrated in the dry +fraction and then gets burned and + + align:start position:0% +fraction and then gets burned and + + + align:start position:0% +fraction and then gets burned and +inhaled a lot of those heavy metals that + + align:start position:0% +inhaled a lot of those heavy metals that + + + align:start position:0% +inhaled a lot of those heavy metals that +are radon byproducts and such are fairly + + align:start position:0% +are radon byproducts and such are fairly + + + align:start position:0% +are radon byproducts and such are fairly +reactive they'll stick around in your + + align:start position:0% +reactive they'll stick around in your + + + align:start position:0% +reactive they'll stick around in your +tissues and give you a whole lot of + + align:start position:0% +tissues and give you a whole lot of + + + align:start position:0% +tissues and give you a whole lot of +alpha dose so when you have populations + + align:start position:0% +alpha dose so when you have populations + + + align:start position:0% +alpha dose so when you have populations +of people who have or haven't smoked you + + align:start position:0% +of people who have or haven't smoked you + + + align:start position:0% +of people who have or haven't smoked you +actually can figure out the number of + + align:start position:0% +actually can figure out the number of + + + align:start position:0% +actually can figure out the number of +extra attributable deaths to things like + + align:start position:0% +extra attributable deaths to things like + + + align:start position:0% +extra attributable deaths to things like +indoor radon depending on if you live in + + align:start position:0% +indoor radon depending on if you live in + + + align:start position:0% +indoor radon depending on if you live in +a smoky atmosphere or not and so to + + align:start position:0% +a smoky atmosphere or not and so to + + + align:start position:0% +a smoky atmosphere or not and so to +distinguish the types of biological + + align:start position:0% +distinguish the types of biological + + + align:start position:0% +distinguish the types of biological +effects that we're worried about we can + + align:start position:0% +effects that we're worried about we can + + + align:start position:0% +effects that we're worried about we can +group these into two there's short term + + align:start position:0% +group these into two there's short term + + + align:start position:0% +group these into two there's short term +effects which manifest themselves in + + align:start position:0% +effects which manifest themselves in + + + align:start position:0% +effects which manifest themselves in +hours days or weeks we'll call that + + align:start position:0% +hours days or weeks we'll call that + + + align:start position:0% +hours days or weeks we'll call that +immediate and then there's long term + + align:start position:0% +immediate and then there's long term + + + align:start position:0% +immediate and then there's long term +effects which tend to manifest in short + + align:start position:0% +effects which tend to manifest in short + + + align:start position:0% +effects which tend to manifest in short +shortest years and longest decades so + + align:start position:0% +shortest years and longest decades so + + + align:start position:0% +shortest years and longest decades so +things like acute radiation sickness is + + align:start position:0% +things like acute radiation sickness is + + + align:start position:0% +things like acute radiation sickness is +due to rapid cell death of a few + + align:start position:0% +due to rapid cell death of a few + + + align:start position:0% +due to rapid cell death of a few +different kinds over time and which kind + + align:start position:0% +different kinds over time and which kind + + + align:start position:0% +different kinds over time and which kind +depends on the route of exposure the + + align:start position:0% +depends on the route of exposure the + + + align:start position:0% +depends on the route of exposure the +isotope the type of radiation and the + + align:start position:0% +isotope the type of radiation and the + + + align:start position:0% +isotope the type of radiation and the +total amount of dose to those tissues + + align:start position:0% +total amount of dose to those tissues + + + align:start position:0% +total amount of dose to those tissues +and if you guys of all what are some of + + align:start position:0% +and if you guys of all what are some of + + + align:start position:0% +and if you guys of all what are some of +the symptoms of acute radiation sickness + + align:start position:0% +the symptoms of acute radiation sickness + + + align:start position:0% +the symptoms of acute radiation sickness +like did anyone read what happened to + + align:start position:0% +like did anyone read what happened to + + + align:start position:0% +like did anyone read what happened to +the folks in the demon core + + align:start position:0% + + + + align:start position:0% + +hair fell out what else vomiting + + align:start position:0% +hair fell out what else vomiting + + + align:start position:0% +hair fell out what else vomiting +diarrhea all the fun ones yeah well I + + align:start position:0% +diarrhea all the fun ones yeah well I + + + align:start position:0% +diarrhea all the fun ones yeah well I +will explain why these sorts of things + + align:start position:0% +will explain why these sorts of things + + + align:start position:0% +will explain why these sorts of things +happen with acute radiation exposure now + + align:start position:0% +happen with acute radiation exposure now + + + align:start position:0% +happen with acute radiation exposure now +if you don't get that much radiation + + align:start position:0% +if you don't get that much radiation + + + align:start position:0% +if you don't get that much radiation +exposed but you do get enough to mutate + + align:start position:0% +exposed but you do get enough to mutate + + + align:start position:0% +exposed but you do get enough to mutate +cells you have what's called delayed + + align:start position:0% +cells you have what's called delayed + + + align:start position:0% +cells you have what's called delayed +somatic effects anything from cancer to + + align:start position:0% +somatic effects anything from cancer to + + + align:start position:0% +somatic effects anything from cancer to +straight-up mutations to birth defects + + align:start position:0% +straight-up mutations to birth defects + + + align:start position:0% +straight-up mutations to birth defects +any sort of permanent and reproducible + + align:start position:0% +any sort of permanent and reproducible + + + align:start position:0% +any sort of permanent and reproducible +modification to a cells DNA that can + + align:start position:0% +modification to a cells DNA that can + + + align:start position:0% +modification to a cells DNA that can +induce mutations so let's first talk + + align:start position:0% +induce mutations so let's first talk + + + align:start position:0% +induce mutations so let's first talk +about the short-term effects because + + align:start position:0% +about the short-term effects because + + + align:start position:0% +about the short-term effects because +they're a little easier to understand + + align:start position:0% +they're a little easier to understand + + + align:start position:0% +they're a little easier to understand +and because the doses were much higher + + align:start position:0% +and because the doses were much higher + + + align:start position:0% +and because the doses were much higher +you don't need as much of a population + + align:start position:0% +you don't need as much of a population + + + align:start position:0% +you don't need as much of a population +size in order to figure out did this + + align:start position:0% +size in order to figure out did this + + + align:start position:0% +size in order to figure out did this +effect did this amount of dose have an + + align:start position:0% +effect did this amount of dose have an + + + align:start position:0% +effect did this amount of dose have an +effect so for things up to a quarter of + + align:start position:0% +effect so for things up to a quarter of + + + align:start position:0% +effect so for things up to a quarter of +a gray pretty much nothing happens + + align:start position:0% +a gray pretty much nothing happens + + + align:start position:0% +a gray pretty much nothing happens +that's quite a toasty dose for gammas + + align:start position:0% +that's quite a toasty dose for gammas + + + align:start position:0% +that's quite a toasty dose for gammas +that would be like getting five times + + align:start position:0% +that would be like getting five times + + + align:start position:0% +that would be like getting five times +your occupational yearly limit + + align:start position:0% +your occupational yearly limit + + + align:start position:0% +your occupational yearly limit +instantaneously yeah this is not + + align:start position:0% +instantaneously yeah this is not + + + align:start position:0% +instantaneously yeah this is not +something you'd want to happen but it's + + align:start position:0% +something you'd want to happen but it's + + + align:start position:0% +something you'd want to happen but it's +not going to cause any significant ill + + align:start position:0% +not going to cause any significant ill + + + align:start position:0% +not going to cause any significant ill +effects up to a gray you'll start to see + + align:start position:0% +effects up to a gray you'll start to see + + + align:start position:0% +effects up to a gray you'll start to see +a few symptoms like nausea and anorexia + + align:start position:0% +a few symptoms like nausea and anorexia + + + align:start position:0% +a few symptoms like nausea and anorexia +they probably tend to go together if + + align:start position:0% +they probably tend to go together if + + + align:start position:0% +they probably tend to go together if +you're feeling gastrointestinal e + + align:start position:0% +you're feeling gastrointestinal e + + + align:start position:0% +you're feeling gastrointestinal e +horrible you probably don't want to eat + + align:start position:0% +horrible you probably don't want to eat + + + align:start position:0% +horrible you probably don't want to eat +much and you will see things like bone + + align:start position:0% +much and you will see things like bone + + + align:start position:0% +much and you will see things like bone +marrow damage like we talked about with + + align:start position:0% +marrow damage like we talked about with + + + align:start position:0% +marrow damage like we talked about with +the radium workers fewer red white blood + + align:start position:0% +the radium workers fewer red white blood + + + align:start position:0% +the radium workers fewer red white blood +cells less platelets also means easier + + align:start position:0% +cells less platelets also means easier + + + align:start position:0% +cells less platelets also means easier +to bleed so a lot of the effects of + + align:start position:0% +to bleed so a lot of the effects of + + + align:start position:0% +to bleed so a lot of the effects of +radiation damage are not primary they're + + align:start position:0% +radiation damage are not primary they're + + + align:start position:0% +radiation damage are not primary they're +secondary just like most radiation + + align:start position:0% +secondary just like most radiation + + + align:start position:0% +secondary just like most radiation +damage to cells itself is not damage to + + align:start position:0% +damage to cells itself is not damage to + + + align:start position:0% +damage to cells itself is not damage to +the DNA but it's radiolysis of the water + + align:start position:0% +the DNA but it's radiolysis of the water + + + align:start position:0% +the DNA but it's radiolysis of the water +nearby the DNA and eventual chemical + + align:start position:0% +nearby the DNA and eventual chemical + + + align:start position:0% +nearby the DNA and eventual chemical +migration to cause damage to the DNA + + align:start position:0% +migration to cause damage to the DNA + + + align:start position:0% +migration to cause damage to the DNA +chemically in this case it's not like + + align:start position:0% +chemically in this case it's not like + + + align:start position:0% +chemically in this case it's not like +radiation takes out your platelets + + align:start position:0% +radiation takes out your platelets + + + align:start position:0% +radiation takes out your platelets +radiation takes out the cells that + + align:start position:0% +radiation takes out the cells that + + + align:start position:0% +radiation takes out the cells that +create the platelets the bone marrow + + align:start position:0% +create the platelets the bone marrow + + + align:start position:0% +create the platelets the bone marrow +meaning that platelets if they live + + align:start position:0% +meaning that platelets if they live + + + align:start position:0% +meaning that platelets if they live +about three weeks you'll tend to see a + + align:start position:0% +about three weeks you'll tend to see a + + + align:start position:0% +about three weeks you'll tend to see a +drop in platelet count when your + + align:start position:0% +drop in platelet count when your + + + align:start position:0% +drop in platelet count when your +production system gets lower this should + + align:start position:0% +production system gets lower this should + + + align:start position:0% +production system gets lower this should +sound strikingly similar to series + + align:start position:0% +sound strikingly similar to series + + + align:start position:0% +sound strikingly similar to series +radioactive decay because the same + + align:start position:0% +radioactive decay because the same + + + align:start position:0% +radioactive decay because the same +equations can be used to model it let's + + align:start position:0% +equations can be used to model it let's + + + align:start position:0% +equations can be used to model it let's +say you have a normal stable platelet + + align:start position:0% +say you have a normal stable platelet + + + align:start position:0% +say you have a normal stable platelet +count I'm not gonna get on the board I + + align:start position:0% +count I'm not gonna get on the board I + + + align:start position:0% +count I'm not gonna get on the board I +told you guys we wouldn't get too + + align:start position:0% +told you guys we wouldn't get too + + + align:start position:0% +told you guys we wouldn't get too +deriving anymore but you've got some + + align:start position:0% +deriving anymore but you've got some + + + align:start position:0% +deriving anymore but you've got some +source of platelets which would be your + + align:start position:0% +source of platelets which would be your + + + align:start position:0% +source of platelets which would be your +bone marrow and you've got some sink of + + align:start position:0% +bone marrow and you've got some sink of + + + align:start position:0% +bone marrow and you've got some sink of +platelets which would be normal cell + + align:start position:0% +platelets which would be normal cell + + + align:start position:0% +platelets which would be normal cell +death so let's say there's a half-life + + align:start position:0% +death so let's say there's a half-life + + + align:start position:0% +death so let's say there's a half-life +or a lifetime of platelets if you kill a + + align:start position:0% +or a lifetime of platelets if you kill a + + + align:start position:0% +or a lifetime of platelets if you kill a +little bit of the source then you'll see + + align:start position:0% +little bit of the source then you'll see + + + align:start position:0% +little bit of the source then you'll see +the sink start to decay but the source + + align:start position:0% +the sink start to decay but the source + + + align:start position:0% +the sink start to decay but the source +will start to grow back over time from + + align:start position:0% +will start to grow back over time from + + + align:start position:0% +will start to grow back over time from +cell division and you'll see the level + + align:start position:0% +cell division and you'll see the level + + + align:start position:0% +cell division and you'll see the level +pop back up again and you can model it + + align:start position:0% +pop back up again and you can model it + + + align:start position:0% +pop back up again and you can model it +with the same first order linear + + align:start position:0% +with the same first order linear + + + align:start position:0% +with the same first order linear +ordinary differential equations same OD + + align:start position:0% +ordinary differential equations same OD + + + align:start position:0% +ordinary differential equations same OD +es as series radioactive decay you can + + align:start position:0% +es as series radioactive decay you can + + + align:start position:0% +es as series radioactive decay you can +use to guess how many platelets you + + align:start position:0% +use to guess how many platelets you + + + align:start position:0% +use to guess how many platelets you +should have in your body at any time + + align:start position:0% +should have in your body at any time + + + align:start position:0% +should have in your body at any time +following a certain dose 1 2 3 Gray's + + align:start position:0% +following a certain dose 1 2 3 Gray's + + + align:start position:0% +following a certain dose 1 2 3 Gray's +when things get bad from go too bad from + + align:start position:0% +when things get bad from go too bad from + + + align:start position:0% +when things get bad from go too bad from +worse pretty quick nausea and/or Exia + + align:start position:0% +worse pretty quick nausea and/or Exia + + + align:start position:0% +worse pretty quick nausea and/or Exia +and infection tell me why do you think + + align:start position:0% +and infection tell me why do you think + + + align:start position:0% +and infection tell me why do you think +infection results from radiation damage + + align:start position:0% +infection results from radiation damage + + + align:start position:0% +infection results from radiation damage +yeah let's say your hair everything yeah + + align:start position:0% +yeah let's say your hair everything yeah + + + align:start position:0% +yeah let's say your hair everything yeah +front to back let's hear it yep the + + align:start position:0% +front to back let's hear it yep the + + + align:start position:0% +front to back let's hear it yep the +immune system is compromised what else + + align:start position:0% +immune system is compromised what else + + + align:start position:0% +immune system is compromised what else +everyone gonna say the same thing okay I + + align:start position:0% +everyone gonna say the same thing okay I + + + align:start position:0% +everyone gonna say the same thing okay I +have another story so I agree with you + + align:start position:0% +have another story so I agree with you + + + align:start position:0% +have another story so I agree with you +guys but it also has to do with these + + align:start position:0% +guys but it also has to do with these + + + align:start position:0% +guys but it also has to do with these +platelets anytime anything happens to + + align:start position:0% +platelets anytime anything happens to + + + align:start position:0% +platelets anytime anything happens to +you ever cells tend to die you clap your + + align:start position:0% +you ever cells tend to die you clap your + + + align:start position:0% +you ever cells tend to die you clap your +hands you probably kill a few cells you + + align:start position:0% +hands you probably kill a few cells you + + + align:start position:0% +hands you probably kill a few cells you +bump into something you probably kill a + + align:start position:0% +bump into something you probably kill a + + + align:start position:0% +bump into something you probably kill a +few cells you swallow some metal + + align:start position:0% +few cells you swallow some metal + + + align:start position:0% +few cells you swallow some metal +shavings you're gonna kill a lot of + + align:start position:0% +shavings you're gonna kill a lot of + + + align:start position:0% +shavings you're gonna kill a lot of +shell cells but your body has got mucous + + align:start position:0% +shell cells but your body has got mucous + + + align:start position:0% +shell cells but your body has got mucous +membranes and all sorts of things and + + align:start position:0% +membranes and all sorts of things and + + + align:start position:0% +membranes and all sorts of things and +platelets in order to repair that damage + + align:start position:0% +platelets in order to repair that damage + + + align:start position:0% +platelets in order to repair that damage +all of a sudden if your blood thins out + + align:start position:0% +all of a sudden if your blood thins out + + + align:start position:0% +all of a sudden if your blood thins out +and can start leaking from different + + align:start position:0% +and can start leaking from different + + + align:start position:0% +and can start leaking from different +places or it's a lot harder to repair + + align:start position:0% +places or it's a lot harder to repair + + + align:start position:0% +places or it's a lot harder to repair +like physical leaks in your body + + align:start position:0% +like physical leaks in your body + + + align:start position:0% +like physical leaks in your body +bacteria can get in + + align:start position:0% +bacteria can get in + + + align:start position:0% +bacteria can get in +so the normal amount of bacteria you're + + align:start position:0% +so the normal amount of bacteria you're + + + align:start position:0% +so the normal amount of bacteria you're +exposed to every day which is enormous + + align:start position:0% +exposed to every day which is enormous + + + align:start position:0% +exposed to every day which is enormous +there's theorized to be something like + + align:start position:0% +there's theorized to be something like + + + align:start position:0% +there's theorized to be something like +ten times as many bacterial cells in + + align:start position:0% +ten times as many bacterial cells in + + + align:start position:0% +ten times as many bacterial cells in +your body as human cells they're all + + align:start position:0% +your body as human cells they're all + + + align:start position:0% +your body as human cells they're all +over the place they're just a lot + + align:start position:0% +over the place they're just a lot + + + align:start position:0% +over the place they're just a lot +smaller well they can get into places + + align:start position:0% +smaller well they can get into places + + + align:start position:0% +smaller well they can get into places +that they wouldn't normally get in so + + align:start position:0% +that they wouldn't normally get in so + + + align:start position:0% +that they wouldn't normally get in so +what would normally be a pinprick and a + + align:start position:0% +what would normally be a pinprick and a + + + align:start position:0% +what would normally be a pinprick and a +simple immune response with a suppressed + + align:start position:0% +simple immune response with a suppressed + + + align:start position:0% +simple immune response with a suppressed +immune system and a lower platelet count + + align:start position:0% +immune system and a lower platelet count + + + align:start position:0% +immune system and a lower platelet count +becomes a much more dangerous thing you + + align:start position:0% +becomes a much more dangerous thing you + + + align:start position:0% +becomes a much more dangerous thing you +could undergo something called sepsis + + align:start position:0% +could undergo something called sepsis + + + align:start position:0% +could undergo something called sepsis +that's basically blood turning to sewage + + align:start position:0% +that's basically blood turning to sewage + + + align:start position:0% +that's basically blood turning to sewage +because you get a massive blood + + align:start position:0% +because you get a massive blood + + + align:start position:0% +because you get a massive blood +infection + + align:start position:0% +infection + + + align:start position:0% +infection +this is again let's say a secondary or + + align:start position:0% +this is again let's say a secondary or + + + align:start position:0% +this is again let's say a secondary or +even a tertiary effect but very real + + align:start position:0% +even a tertiary effect but very real + + + align:start position:0% +even a tertiary effect but very real +Hamada logic damage more severe Hema + + align:start position:0% +Hamada logic damage more severe Hema + + + align:start position:0% +Hamada logic damage more severe Hema +refers to blood that's basically saying + + align:start position:0% +refers to blood that's basically saying + + + align:start position:0% +refers to blood that's basically saying +the same thing recovery probable though + + align:start position:0% +the same thing recovery probable though + + + align:start position:0% +the same thing recovery probable though +not assured why probable and why not + + align:start position:0% +not assured why probable and why not + + + align:start position:0% +not assured why probable and why not +assured that's true everyone reacts + + align:start position:0% +assured that's true everyone reacts + + + align:start position:0% +assured that's true everyone reacts +differently it also matters how much + + align:start position:0% +differently it also matters how much + + + align:start position:0% +differently it also matters how much +treatment you get so if you get a crazy + + align:start position:0% +treatment you get so if you get a crazy + + + align:start position:0% +treatment you get so if you get a crazy +compromised immune system we have + + align:start position:0% +compromised immune system we have + + + align:start position:0% +compromised immune system we have +hospitals and you know sterile bubbles + + align:start position:0% +hospitals and you know sterile bubbles + + + align:start position:0% +hospitals and you know sterile bubbles +and all sorts of things that you can be + + align:start position:0% +and all sorts of things that you can be + + + align:start position:0% +and all sorts of things that you can be +put in but if you don't get to a + + align:start position:0% +put in but if you don't get to a + + + align:start position:0% +put in but if you don't get to a +hospital in time to reduce the onset of + + align:start position:0% +hospital in time to reduce the onset of + + + align:start position:0% +hospital in time to reduce the onset of +massive infection that's what could + + align:start position:0% +massive infection that's what could + + + align:start position:0% +massive infection that's what could +happen then you go higher three to six + + align:start position:0% +happen then you go higher three to six + + + align:start position:0% +happen then you go higher three to six +gray everything is above plus diarrhea + + align:start position:0% +gray everything is above plus diarrhea + + + align:start position:0% +gray everything is above plus diarrhea +deep elation hair loss temporary + + align:start position:0% +deep elation hair loss temporary + + + align:start position:0% +deep elation hair loss temporary +sterility think the temporary sterility + + align:start position:0% +sterility think the temporary sterility + + + align:start position:0% +sterility think the temporary sterility +one's obvious why do you think diarrhea + + align:start position:0% +one's obvious why do you think diarrhea + + + align:start position:0% +one's obvious why do you think diarrhea +and hair loss would occur + + align:start position:0% + + + + align:start position:0% + +yeah exactly yeah any the most sensitive + + align:start position:0% +yeah exactly yeah any the most sensitive + + + align:start position:0% +yeah exactly yeah any the most sensitive +cells are the ones that are rapidly + + align:start position:0% +cells are the ones that are rapidly + + + align:start position:0% +cells are the ones that are rapidly +dividing to make you know villi and stem + + align:start position:0% +dividing to make you know villi and stem + + + align:start position:0% +dividing to make you know villi and stem +cells in your intestines hair follicles + + align:start position:0% +cells in your intestines hair follicles + + + align:start position:0% +cells in your intestines hair follicles +gonads anything that's dividing all the + + align:start position:0% +gonads anything that's dividing all the + + + align:start position:0% +gonads anything that's dividing all the +time is going to feel the effects of + + align:start position:0% +time is going to feel the effects of + + + align:start position:0% +time is going to feel the effects of +radiation damage much more severely and + + align:start position:0% +radiation damage much more severely and + + + align:start position:0% +radiation damage much more severely and +barring any mutation which may take a + + align:start position:0% +barring any mutation which may take a + + + align:start position:0% +barring any mutation which may take a +long time to manifest the wrong damage + + align:start position:0% +long time to manifest the wrong damage + + + align:start position:0% +long time to manifest the wrong damage +of DNA and the cell just can't divide so + + align:start position:0% +of DNA and the cell just can't divide so + + + align:start position:0% +of DNA and the cell just can't divide so +it dies and if those cells die then that + + align:start position:0% +it dies and if those cells die then that + + + align:start position:0% +it dies and if those cells die then that +means that you can't uptake nutrition + + align:start position:0% +means that you can't uptake nutrition + + + align:start position:0% +means that you can't uptake nutrition +and you just body just flushes + + align:start position:0% +and you just body just flushes + + + align:start position:0% +and you just body just flushes +everything out in diarrhea fatalities + + align:start position:0% +everything out in diarrhea fatalities + + + align:start position:0% +everything out in diarrhea fatalities +will occur in the range of three and a + + align:start position:0% +will occur in the range of three and a + + + align:start position:0% +will occur in the range of three and a +half gray without treatment and this is + + align:start position:0% +half gray without treatment and this is + + + align:start position:0% +half gray without treatment and this is +what's called the typical ld50 does + + align:start position:0% +what's called the typical ld50 does + + + align:start position:0% +what's called the typical ld50 does +anyone know what an ld50 is the lethal + + align:start position:0% +anyone know what an ld50 is the lethal + + + align:start position:0% +anyone know what an ld50 is the lethal +dose for right so about 50% of the + + align:start position:0% +dose for right so about 50% of the + + + align:start position:0% +dose for right so about 50% of the +people exposed to 3.5 grey will die this + + align:start position:0% +people exposed to 3.5 grey will die this + + + align:start position:0% +people exposed to 3.5 grey will die this +doesn't take into account difference in + + align:start position:0% +doesn't take into account difference in + + + align:start position:0% +doesn't take into account difference in +treatment difference in person or + + align:start position:0% +treatment difference in person or + + + align:start position:0% +treatment difference in person or +everything it's all together and I'll go + + align:start position:0% +everything it's all together and I'll go + + + align:start position:0% +everything it's all together and I'll go +into one and ld50 for different things + + align:start position:0% +into one and ld50 for different things + + + align:start position:0% +into one and ld50 for different things +is in a second and then over six gray + + align:start position:0% +is in a second and then over six gray + + + align:start position:0% +is in a second and then over six gray +you get immediate incapacitation hits + + align:start position:0% +you get immediate incapacitation hits + + + align:start position:0% +you get immediate incapacitation hits +the nervous system you get so many cells + + align:start position:0% +the nervous system you get so many cells + + + align:start position:0% +the nervous system you get so many cells +leaking out that the chemical signals + + align:start position:0% +leaking out that the chemical signals + + + align:start position:0% +leaking out that the chemical signals +for your neurons sodium and potassium + + align:start position:0% +for your neurons sodium and potassium + + + align:start position:0% +for your neurons sodium and potassium +and other ions well if all your cells + + align:start position:0% +and other ions well if all your cells + + + align:start position:0% +and other ions well if all your cells +die and leak out that all of a sudden + + align:start position:0% +die and leak out that all of a sudden + + + align:start position:0% +die and leak out that all of a sudden +you're flooded with the ions that are + + align:start position:0% +you're flooded with the ions that are + + + align:start position:0% +you're flooded with the ions that are +normally kept in a very careful + + align:start position:0% +normally kept in a very careful + + + align:start position:0% +normally kept in a very careful +equilibrium to signal so you can + + align:start position:0% +equilibrium to signal so you can + + + align:start position:0% +equilibrium to signal so you can +actually get sudden unconsciousness in a + + align:start position:0% +actually get sudden unconsciousness in a + + + align:start position:0% +actually get sudden unconsciousness in a +matter of seconds to minutes from doses + + align:start position:0% +matter of seconds to minutes from doses + + + align:start position:0% +matter of seconds to minutes from doses +over ten great so you just you just go + + align:start position:0% +over ten great so you just you just go + + + align:start position:0% +over ten great so you just you just go +out like a light like that and may not + + align:start position:0% +out like a light like that and may not + + + align:start position:0% +out like a light like that and may not +recover what's an ld50 it's the on it's + + align:start position:0% +recover what's an ld50 it's the on it's + + + align:start position:0% +recover what's an ld50 it's the on it's +whenever an effect gets an onset by 50 + + align:start position:0% +whenever an effect gets an onset by 50 + + + align:start position:0% +whenever an effect gets an onset by 50 +percent of the population and there are + + align:start position:0% +percent of the population and there are + + + align:start position:0% +percent of the population and there are +different something-something 50 doses + + align:start position:0% +different something-something 50 doses + + + align:start position:0% +different something-something 50 doses +depending on let's say whether + + align:start position:0% +depending on let's say whether + + + align:start position:0% +depending on let's say whether +something's therapeutic toxic or lethal + + align:start position:0% +something's therapeutic toxic or lethal + + + align:start position:0% +something's therapeutic toxic or lethal +the example I like to give is selenium + + align:start position:0% +the example I like to give is selenium + + + align:start position:0% +the example I like to give is selenium +anyone know anything about selenium in + + align:start position:0% +anyone know anything about selenium in + + + align:start position:0% +anyone know anything about selenium in +the diet it's one of those trace + + align:start position:0% +the diet it's one of those trace + + + align:start position:0% +the diet it's one of those trace +minerals that you need to survive but + + align:start position:0% +minerals that you need to survive but + + + align:start position:0% +minerals that you need to survive but +can also kill you so below if you need + + align:start position:0% +can also kill you so below if you need + + + align:start position:0% +can also kill you so below if you need +to get about on average five micrograms + + align:start position:0% +to get about on average five micrograms + + + align:start position:0% +to get about on average five micrograms +of selenium in order to produce certain + + align:start position:0% +of selenium in order to produce certain + + + align:start position:0% +of selenium in order to produce certain +enzymes that keep things going in the + + align:start position:0% +enzymes that keep things going in the + + + align:start position:0% +enzymes that keep things going in the +body five micrograms is not a lot but + + align:start position:0% +body five micrograms is not a lot but + + + align:start position:0% +body five micrograms is not a lot but +you know that in order to have a little + + align:start position:0% +you know that in order to have a little + + + align:start position:0% +you know that in order to have a little +bit of selenium it's got a therapeutic + + align:start position:0% +bit of selenium it's got a therapeutic + + + align:start position:0% +bit of selenium it's got a therapeutic +effect once you get around five + + align:start position:0% +effect once you get around five + + + align:start position:0% +effect once you get around five +micrograms + + align:start position:0% +micrograms + + + align:start position:0% +micrograms +most people will see some sort of + + align:start position:0% +most people will see some sort of + + + align:start position:0% +most people will see some sort of +biological benefit if you get five + + align:start position:0% +biological benefit if you get five + + + align:start position:0% +biological benefit if you get five +milligrams starts to become toxic this + + align:start position:0% +milligrams starts to become toxic this + + + align:start position:0% +milligrams starts to become toxic this +is the case with pretty much anything + + align:start position:0% +is the case with pretty much anything + + + align:start position:0% +is the case with pretty much anything +vitamins anyone ever had that's probably + + align:start position:0% +vitamins anyone ever had that's probably + + + align:start position:0% +vitamins anyone ever had that's probably +gonna be an O anyone ever eaten Rossi a + + align:start position:0% +gonna be an O anyone ever eaten Rossi a + + + align:start position:0% +gonna be an O anyone ever eaten Rossi a +liver before the polar bear livers I + + align:start position:0% +liver before the polar bear livers I + + + align:start position:0% +liver before the polar bear livers I +don't know no one's gone up way way up + + align:start position:0% +don't know no one's gone up way way up + + + align:start position:0% +don't know no one's gone up way way up +north anyway and you know why or indeed + + align:start position:0% +north anyway and you know why or indeed + + + align:start position:0% +north anyway and you know why or indeed +vitamin A something that you need a + + align:start position:0% +vitamin A something that you need a + + + align:start position:0% +vitamin A something that you need a +whole lot of to survive it's so + + align:start position:0% +whole lot of to survive it's so + + + align:start position:0% +whole lot of to survive it's so +concentrated in the livers of seals and + + align:start position:0% +concentrated in the livers of seals and + + + align:start position:0% +concentrated in the livers of seals and +polar bears that if you were to just eat + + align:start position:0% +polar bears that if you were to just eat + + + align:start position:0% +polar bears that if you were to just eat +a polar bear liver you would die of + + align:start position:0% +a polar bear liver you would die of + + + align:start position:0% +a polar bear liver you would die of +vitamin A poisoning so I didn't hear all + + align:start position:0% +vitamin A poisoning so I didn't hear all + + + align:start position:0% +vitamin A poisoning so I didn't hear all +those things at once one at a time just + + align:start position:0% +those things at once one at a time just + + + align:start position:0% +those things at once one at a time just +take a little taste you know it's all + + align:start position:0% +take a little taste you know it's all + + + align:start position:0% +take a little taste you know it's all +about the amount right what were you + + align:start position:0% +about the amount right what were you + + + align:start position:0% +about the amount right what were you +guys saying well no it's not like you + + align:start position:0% +guys saying well no it's not like you + + + align:start position:0% +guys saying well no it's not like you +take a taste and you die again it's all + + align:start position:0% +take a taste and you die again it's all + + + align:start position:0% +take a taste and you die again it's all +about the amount of exposure one little + + align:start position:0% +about the amount of exposure one little + + + align:start position:0% +about the amount of exposure one little +taste is not gonna flood your system + + align:start position:0% +taste is not gonna flood your system + + + align:start position:0% +taste is not gonna flood your system +with vitamin A but you eat an entire + + align:start position:0% +with vitamin A but you eat an entire + + + align:start position:0% +with vitamin A but you eat an entire +polar bears liver you're gonna have a + + align:start position:0% +polar bears liver you're gonna have a + + + align:start position:0% +polar bears liver you're gonna have a +bad day what I don't know why polar + + align:start position:0% +bad day what I don't know why polar + + + align:start position:0% +bad day what I don't know why polar +bears have so much vitamin A no idea + + align:start position:0% +bears have so much vitamin A no idea + + + align:start position:0% +bears have so much vitamin A no idea +actually but then beyond that you can + + align:start position:0% +actually but then beyond that you can + + + align:start position:0% +actually but then beyond that you can +get lethal effects where you might get + + align:start position:0% +get lethal effects where you might get + + + align:start position:0% +get lethal effects where you might get +sick from eating too much of something + + align:start position:0% +sick from eating too much of something + + + align:start position:0% +sick from eating too much of something +but then again you know anyone ever + + align:start position:0% +but then again you know anyone ever + + + align:start position:0% +but then again you know anyone ever +heard of the old hold your Wii for a + + align:start position:0% +heard of the old hold your Wii for a + + + align:start position:0% +heard of the old hold your Wii for a +week contest where we found out really + + align:start position:0% +week contest where we found out really + + + align:start position:0% +week contest where we found out really +the ld50 of water yeah so you drink way + + align:start position:0% +the ld50 of water yeah so you drink way + + + align:start position:0% +the ld50 of water yeah so you drink way +too much water without any other solutes + + align:start position:0% +too much water without any other solutes + + + align:start position:0% +too much water without any other solutes +you deplete your body from electrolytes + + align:start position:0% +you deplete your body from electrolytes + + + align:start position:0% +you deplete your body from electrolytes +and then you can also die so I ran into + + align:start position:0% +and then you can also die so I ran into + + + align:start position:0% +and then you can also die so I ran into +this experience personally I don't have + + align:start position:0% +this experience personally I don't have + + + align:start position:0% +this experience personally I don't have +to ask any of you guys went hiking with + + align:start position:0% +to ask any of you guys went hiking with + + + align:start position:0% +to ask any of you guys went hiking with +my dad in Nepal in 2009 in the last + + align:start position:0% +my dad in Nepal in 2009 in the last + + + align:start position:0% +my dad in Nepal in 2009 in the last +vacation I've taken that's a long time + + align:start position:0% +vacation I've taken that's a long time + + + align:start position:0% +vacation I've taken that's a long time +ago it's kind of cool at MIT it's fun + + align:start position:0% +ago it's kind of cool at MIT it's fun + + + align:start position:0% +ago it's kind of cool at MIT it's fun +enough here that I haven't felt like + + align:start position:0% +enough here that I haven't felt like + + + align:start position:0% +enough here that I haven't felt like +I've needed a vacation in what like + + align:start position:0% +I've needed a vacation in what like + + + align:start position:0% +I've needed a vacation in what like +seven years I'm actually kind of taking + + align:start position:0% +seven years I'm actually kind of taking + + + align:start position:0% +seven years I'm actually kind of taking +one this year because I'm going + + align:start position:0% +one this year because I'm going + + + align:start position:0% +one this year because I'm going +somewhere for research and just sticking + + align:start position:0% +somewhere for research and just sticking + + + align:start position:0% +somewhere for research and just sticking +around but when hiking in Nepal I ate + + align:start position:0% +around but when hiking in Nepal I ate + + + align:start position:0% +around but when hiking in Nepal I ate +something I probably shouldn't in fact + + align:start position:0% +something I probably shouldn't in fact + + + align:start position:0% +something I probably shouldn't in fact +everyone eventually ate something they + + align:start position:0% +everyone eventually ate something they + + + align:start position:0% +everyone eventually ate something they +probably shouldn't and I had what could + + align:start position:0% +probably shouldn't and I had what could + + + align:start position:0% +probably shouldn't and I had what could +be described as massive GI syndrome + + align:start position:0% +be described as massive GI syndrome + + + align:start position:0% +be described as massive GI syndrome +Delhi Belly whatever you want to call it + + align:start position:0% +Delhi Belly whatever you want to call it + + + align:start position:0% +Delhi Belly whatever you want to call it +my brother likes to call it poop and + + align:start position:0% +my brother likes to call it poop and + + + align:start position:0% +my brother likes to call it poop and +mouth disease + + align:start position:0% +mouth disease + + + align:start position:0% +mouth disease +because sanitation and stuff is not the + + align:start position:0% +because sanitation and stuff is not the + + + align:start position:0% +because sanitation and stuff is not the +best there and so I was in a pretty bad + + align:start position:0% +best there and so I was in a pretty bad + + + align:start position:0% +best there and so I was in a pretty bad +state and instead of drinking water to + + align:start position:0% +state and instead of drinking water to + + + align:start position:0% +state and instead of drinking water to +replenish all of the water that was + + align:start position:0% +replenish all of the water that was + + + align:start position:0% +replenish all of the water that was +leaving of every direction from the body + + align:start position:0% +leaving of every direction from the body + + + align:start position:0% +leaving of every direction from the body +drinking salt water we took tablets that + + align:start position:0% +drinking salt water we took tablets that + + + align:start position:0% +drinking salt water we took tablets that +had the same isotonic concentration of + + align:start position:0% +had the same isotonic concentration of + + + align:start position:0% +had the same isotonic concentration of +electrolytes amino acids as those being + + align:start position:0% +electrolytes amino acids as those being + + + align:start position:0% +electrolytes amino acids as those being +lost by the body because when water goes + + align:start position:0% +lost by the body because when water goes + + + align:start position:0% +lost by the body because when water goes +in the body everything + + align:start position:0% +in the body everything + + + align:start position:0% +in the body everything +osmotic aliy equilibria if you take in + + align:start position:0% +osmotic aliy equilibria if you take in + + + align:start position:0% +osmotic aliy equilibria if you take in +lots of pure water it with a little bit + + align:start position:0% +lots of pure water it with a little bit + + + align:start position:0% +lots of pure water it with a little bit +of sodium potassium other electrolytes + + align:start position:0% +of sodium potassium other electrolytes + + + align:start position:0% +of sodium potassium other electrolytes +will dissolve into that water if it's + + align:start position:0% +will dissolve into that water if it's + + + align:start position:0% +will dissolve into that water if it's +going out in any direction it's gonna + + align:start position:0% +going out in any direction it's gonna + + + align:start position:0% +going out in any direction it's gonna +leave your body depleting you of + + align:start position:0% +leave your body depleting you of + + + align:start position:0% +leave your body depleting you of +electrolytes so I had seven wonderful + + align:start position:0% +electrolytes so I had seven wonderful + + + align:start position:0% +electrolytes so I had seven wonderful +days lying in bed drinking about a liter + + align:start position:0% +days lying in bed drinking about a liter + + + align:start position:0% +days lying in bed drinking about a liter +of warm saltwater every 15 minutes or so + + align:start position:0% +of warm saltwater every 15 minutes or so + + + align:start position:0% +of warm saltwater every 15 minutes or so +in order to maintain not just the water + + align:start position:0% +in order to maintain not just the water + + + align:start position:0% +in order to maintain not just the water +but the electrolytes that your body + + align:start position:0% +but the electrolytes that your body + + + align:start position:0% +but the electrolytes that your body +needed freaky huh yeah it was a great + + align:start position:0% +needed freaky huh yeah it was a great + + + align:start position:0% +needed freaky huh yeah it was a great +vacation is there any wonder why I don't + + align:start position:0% +vacation is there any wonder why I don't + + + align:start position:0% +vacation is there any wonder why I don't +want to take another one if I go back + + align:start position:0% +want to take another one if I go back + + + align:start position:0% +want to take another one if I go back +there I'm having nothing but Clif bars + + align:start position:0% +there I'm having nothing but Clif bars + + + align:start position:0% +there I'm having nothing but Clif bars +now it's hard to say no when folks that + + align:start position:0% +now it's hard to say no when folks that + + + align:start position:0% +now it's hard to say no when folks that +live up in the mountains offer you what + + align:start position:0% +live up in the mountains offer you what + + + align:start position:0% +live up in the mountains offer you what +little food they have but you should + + align:start position:0% +little food they have but you should + + + align:start position:0% +little food they have but you should +really say no for your own safety anyway + + align:start position:0% +really say no for your own safety anyway + + + align:start position:0% +really say no for your own safety anyway +yeah there's an ld50 for water by any + + align:start position:0% +yeah there's an ld50 for water by any + + + align:start position:0% +yeah there's an ld50 for water by any +mechanism from electrolyte depletion to + + align:start position:0% +mechanism from electrolyte depletion to + + + align:start position:0% +mechanism from electrolyte depletion to +there was a contest on the radio called + + align:start position:0% +there was a contest on the radio called + + + align:start position:0% +there was a contest on the radio called +hold your Wii for a Wii when the + + align:start position:0% +hold your Wii for a Wii when the + + + align:start position:0% +hold your Wii for a Wii when the +Nintendo Wii came out they said how much + + align:start position:0% +Nintendo Wii came out they said how much + + + align:start position:0% +Nintendo Wii came out they said how much +water could you drink without going to + + align:start position:0% +water could you drink without going to + + + align:start position:0% +water could you drink without going to +the bathroom and someone's bladder + + align:start position:0% +the bathroom and someone's bladder + + + align:start position:0% +the bathroom and someone's bladder +exploded right yeah that's what I heard + + align:start position:0% +exploded right yeah that's what I heard + + + align:start position:0% +exploded right yeah that's what I heard +either it would be a bladder explosion + + align:start position:0% +either it would be a bladder explosion + + + align:start position:0% +either it would be a bladder explosion +or an electrolyte depletion so whatever + + align:start position:0% +or an electrolyte depletion so whatever + + + align:start position:0% +or an electrolyte depletion so whatever +the mechanism the ld50 just tells if + + align:start position:0% +the mechanism the ld50 just tells if + + + align:start position:0% +the mechanism the ld50 just tells if +somebody if a population in just a + + align:start position:0% +somebody if a population in just a + + + align:start position:0% +somebody if a population in just a +certain amount of something or takes in + + align:start position:0% +certain amount of something or takes in + + + align:start position:0% +certain amount of something or takes in +a certain amount of radiation how much + + align:start position:0% +a certain amount of radiation how much + + + align:start position:0% +a certain amount of radiation how much +will cause 50% to die or for much lower + + align:start position:0% +will cause 50% to die or for much lower + + + align:start position:0% +will cause 50% to die or for much lower +doses 50% will see some therapeutic + + align:start position:0% +doses 50% will see some therapeutic + + + align:start position:0% +doses 50% will see some therapeutic +effect by any mechanism it doesn't + + align:start position:0% +effect by any mechanism it doesn't + + + align:start position:0% +effect by any mechanism it doesn't +distinguish by mechanism so the four + + align:start position:0% +distinguish by mechanism so the four + + + align:start position:0% +distinguish by mechanism so the four +phases of radiation damage this is where + + align:start position:0% +phases of radiation damage this is where + + + align:start position:0% +phases of radiation damage this is where +all those Latin and bio roots really + + align:start position:0% +all those Latin and bio roots really + + + align:start position:0% +all those Latin and bio roots really +come in handy the prodromal phase is the + + align:start position:0% +come in handy the prodromal phase is the + + + align:start position:0% +come in handy the prodromal phase is the +initial symptoms of exposure which may + + align:start position:0% +initial symptoms of exposure which may + + + align:start position:0% +initial symptoms of exposure which may +or may not happen one to three days + + align:start position:0% +or may not happen one to three days + + + align:start position:0% +or may not happen one to three days +after exposure for massive exposure + + align:start position:0% +after exposure for massive exposure + + + align:start position:0% +after exposure for massive exposure +you're not going to see this because + + align:start position:0% +you're not going to see this because + + + align:start position:0% +you're not going to see this because +you're not going to live one to three + + align:start position:0% +you're not going to live one to three + + + align:start position:0% +you're not going to live one to three +days for very minor exposure you may not + + align:start position:0% +days for very minor exposure you may not + + + align:start position:0% +days for very minor exposure you may not +even see + + align:start position:0% +even see + + + align:start position:0% +even see +these prodromal effects like a drop in + + align:start position:0% +these prodromal effects like a drop in + + + align:start position:0% +these prodromal effects like a drop in +blood cell count or GI syndrome because + + align:start position:0% +blood cell count or GI syndrome because + + + align:start position:0% +blood cell count or GI syndrome because +the dose might not be severe enough for + + align:start position:0% +the dose might not be severe enough for + + + align:start position:0% +the dose might not be severe enough for +your body not to be able to cope with it + + align:start position:0% +your body not to be able to cope with it + + + align:start position:0% +your body not to be able to cope with it +the latent phase this is the tricky one + + align:start position:0% +the latent phase this is the tricky one + + + align:start position:0% +the latent phase this is the tricky one +an apparent recovery from the prodromal + + align:start position:0% +an apparent recovery from the prodromal + + + align:start position:0% +an apparent recovery from the prodromal +systems so getting a medium dose of + + align:start position:0% +systems so getting a medium dose of + + + align:start position:0% +systems so getting a medium dose of +radiation let's call that like 2 to 5 + + align:start position:0% +radiation let's call that like 2 to 5 + + + align:start position:0% +radiation let's call that like 2 to 5 +grey will cause some nausea vomiting and + + align:start position:0% +grey will cause some nausea vomiting and + + + align:start position:0% +grey will cause some nausea vomiting and +headache and then you get better and + + align:start position:0% +headache and then you get better and + + + align:start position:0% +headache and then you get better and +then you get worse in the manifest + + align:start position:0% +then you get worse in the manifest + + + align:start position:0% +then you get worse in the manifest +illness phase because a lot of the + + align:start position:0% +illness phase because a lot of the + + + align:start position:0% +illness phase because a lot of the +things that radiation will do can be + + align:start position:0% +things that radiation will do can be + + + align:start position:0% +things that radiation will do can be +immediate if you suddenly cause the body + + align:start position:0% +immediate if you suddenly cause the body + + + align:start position:0% +immediate if you suddenly cause the body +to release serotonin and induce the + + align:start position:0% +to release serotonin and induce the + + + align:start position:0% +to release serotonin and induce the +vomiting reflex that goes away once that + + align:start position:0% +vomiting reflex that goes away once that + + + align:start position:0% +vomiting reflex that goes away once that +serotonin is consumed or dealt with I + + align:start position:0% +serotonin is consumed or dealt with I + + + align:start position:0% +serotonin is consumed or dealt with I +don't know how the body would deal with + + align:start position:0% +don't know how the body would deal with + + + align:start position:0% +don't know how the body would deal with +it you might think you're getting better + + align:start position:0% +it you might think you're getting better + + + align:start position:0% +it you might think you're getting better +but the cells that divide rapidly have + + align:start position:0% +but the cells that divide rapidly have + + + align:start position:0% +but the cells that divide rapidly have +still incurred that damage and you won't + + align:start position:0% +still incurred that damage and you won't + + + align:start position:0% +still incurred that damage and you won't +see that damage until they fail to + + align:start position:0% +see that damage until they fail to + + + align:start position:0% +see that damage until they fail to +divide in their normal amount of time so + + align:start position:0% +divide in their normal amount of time so + + + align:start position:0% +divide in their normal amount of time so +gee things like GI syndrome and hair + + align:start position:0% +gee things like GI syndrome and hair + + + align:start position:0% +gee things like GI syndrome and hair +loss might not show up for a few days + + align:start position:0% +loss might not show up for a few days + + + align:start position:0% +loss might not show up for a few days +afterwards because it's not like your + + align:start position:0% +afterwards because it's not like your + + + align:start position:0% +afterwards because it's not like your +hair will just instantly fall out like + + align:start position:0% +hair will just instantly fall out like + + + align:start position:0% +hair will just instantly fall out like +there's some cell that is holding on to + + align:start position:0% +there's some cell that is holding on to + + + align:start position:0% +there's some cell that is holding on to +your hair follicle and then will just + + align:start position:0% +your hair follicle and then will just + + + align:start position:0% +your hair follicle and then will just +release it when irradiated but those + + align:start position:0% +release it when irradiated but those + + + align:start position:0% +release it when irradiated but those +follicles won't continue to produce the + + align:start position:0% +follicles won't continue to produce the + + + align:start position:0% +follicles won't continue to produce the +keratin at the same rate or in a + + align:start position:0% +keratin at the same rate or in a + + + align:start position:0% +keratin at the same rate or in a +different way or I can't speak that + + align:start position:0% +different way or I can't speak that + + + align:start position:0% +different way or I can't speak that +intelligently about exactly the + + align:start position:0% +intelligently about exactly the + + + align:start position:0% +intelligently about exactly the +mechanism of hair loss but it will take + + align:start position:0% +mechanism of hair loss but it will take + + + align:start position:0% +mechanism of hair loss but it will take +a little bit of time to get there and + + align:start position:0% +a little bit of time to get there and + + + align:start position:0% +a little bit of time to get there and +the final phase is a binary do you + + align:start position:0% +the final phase is a binary do you + + + align:start position:0% +the final phase is a binary do you +recover or do you die could take days + + align:start position:0% +recover or do you die could take days + + + align:start position:0% +recover or do you die could take days +two months two years to figure that out + + align:start position:0% +two months two years to figure that out + + + align:start position:0% +two months two years to figure that out +these weren't in the reading but I + + align:start position:0% +these weren't in the reading but I + + + align:start position:0% +these weren't in the reading but I +wanted to pull some much better tables + + align:start position:0% +wanted to pull some much better tables + + + align:start position:0% +wanted to pull some much better tables +about what happens in each of these + + align:start position:0% +about what happens in each of these + + + align:start position:0% +about what happens in each of these +phases as a function of radiation dose + + align:start position:0% +phases as a function of radiation dose + + + align:start position:0% +phases as a function of radiation dose +so when does vomiting onset there are + + align:start position:0% +so when does vomiting onset there are + + + align:start position:0% +so when does vomiting onset there are +actually patterns to be seen here so for + + align:start position:0% +actually patterns to be seen here so for + + + align:start position:0% +actually patterns to be seen here so for +mild it may take a couple of hours after + + align:start position:0% +mild it may take a couple of hours after + + + align:start position:0% +mild it may take a couple of hours after +exposure you may not stimulate the + + align:start position:0% +exposure you may not stimulate the + + + align:start position:0% +exposure you may not stimulate the +immediate release of the hormones that + + align:start position:0% +immediate release of the hormones that + + + align:start position:0% +immediate release of the hormones that +induce vomiting but then as the dose + + align:start position:0% +induce vomiting but then as the dose + + + align:start position:0% +induce vomiting but then as the dose +gets more and more severe could be + + align:start position:0% +gets more and more severe could be + + + align:start position:0% +gets more and more severe could be +anywhere from hours to less than 10 + + align:start position:0% +anywhere from hours to less than 10 + + + align:start position:0% +anywhere from hours to less than 10 +minutes so you can use the onset of + + align:start position:0% +minutes so you can use the onset of + + + align:start position:0% +minutes so you can use the onset of +things like vomiting diarrhea headache + + align:start position:0% +things like vomiting diarrhea headache + + + align:start position:0% +things like vomiting diarrhea headache +loss of consciousness and severe cases + + align:start position:0% +loss of consciousness and severe cases + + + align:start position:0% +loss of consciousness and severe cases +to gauge the amount of dose someone has + + align:start position:0% +to gauge the amount of dose someone has + + + align:start position:0% +to gauge the amount of dose someone has +absorbed in some unknown accident + + align:start position:0% +absorbed in some unknown accident + + + align:start position:0% +absorbed in some unknown accident +because it's not like if you're in some + + align:start position:0% +because it's not like if you're in some + + + align:start position:0% +because it's not like if you're in some +severe nuclear accident and you don't + + align:start position:0% +severe nuclear accident and you don't + + + align:start position:0% +severe nuclear accident and you don't +happen to be wearing a very large + + align:start position:0% +happen to be wearing a very large + + + align:start position:0% +happen to be wearing a very large +dosimeter how do you know how much dose + + align:start position:0% +dosimeter how do you know how much dose + + + align:start position:0% +dosimeter how do you know how much dose +you got and how do you know how to treat + + align:start position:0% +you got and how do you know how to treat + + + align:start position:0% +you got and how do you know how to treat +the person time can be your best weapon + + align:start position:0% +the person time can be your best weapon + + + align:start position:0% +the person time can be your best weapon +there because except for very lethal + + align:start position:0% +there because except for very lethal + + + align:start position:0% +there because except for very lethal +doses where you could go unconscious in + + align:start position:0% +doses where you could go unconscious in + + + align:start position:0% +doses where you could go unconscious in +seconds or minutes you've got some time + + align:start position:0% +seconds or minutes you've got some time + + + align:start position:0% +seconds or minutes you've got some time +hours two days to treat what happened + + align:start position:0% +hours two days to treat what happened + + + align:start position:0% +hours two days to treat what happened +and if you can say all right I know the + + align:start position:0% +and if you can say all right I know the + + + align:start position:0% +and if you can say all right I know the +time of exposure and I know the time of + + align:start position:0% +time of exposure and I know the time of + + + align:start position:0% +time of exposure and I know the time of +onset of headache of diarrhea of + + align:start position:0% +onset of headache of diarrhea of + + + align:start position:0% +onset of headache of diarrhea of +vomiting you can figure out roughly + + align:start position:0% +vomiting you can figure out roughly + + + align:start position:0% +vomiting you can figure out roughly +maybe within plus or minus a grey how + + align:start position:0% +maybe within plus or minus a grey how + + + align:start position:0% +maybe within plus or minus a grey how +much dose you had and what to treat + + align:start position:0% +much dose you had and what to treat + + + align:start position:0% +much dose you had and what to treat +there are probably smarter ways of doing + + align:start position:0% +there are probably smarter ways of doing + + + align:start position:0% +there are probably smarter ways of doing +this but with nothing else you've got + + align:start position:0% +this but with nothing else you've got + + + align:start position:0% +this but with nothing else you've got +time as a variable to help you figure + + align:start position:0% +time as a variable to help you figure + + + align:start position:0% +time as a variable to help you figure +this out why do you guys think that your + + align:start position:0% +this out why do you guys think that your + + + align:start position:0% +this out why do you guys think that your +body temperature would go up upon + + align:start position:0% +body temperature would go up upon + + + align:start position:0% +body temperature would go up upon +exposure to huge amounts of radiation + + align:start position:0% +exposure to huge amounts of radiation + + + align:start position:0% +exposure to huge amounts of radiation +what's with the fever what does a fever + + align:start position:0% +what's with the fever what does a fever + + + align:start position:0% +what's with the fever what does a fever +were a response to could it be a + + align:start position:0% +were a response to could it be a + + + align:start position:0% +were a response to could it be a +response to + + align:start position:0% +response to + + + align:start position:0% +response to +infection so any sort of sudden massive + + align:start position:0% +infection so any sort of sudden massive + + + align:start position:0% +infection so any sort of sudden massive +infection would mount an immune response + + align:start position:0% +infection would mount an immune response + + + align:start position:0% +infection would mount an immune response +and that would cause a fever because + + align:start position:0% +and that would cause a fever because + + + align:start position:0% +and that would cause a fever because +you've got all sorts of cells doing + + align:start position:0% +you've got all sorts of cells doing + + + align:start position:0% +you've got all sorts of cells doing +things expending energy trying to rid + + align:start position:0% +things expending energy trying to rid + + + align:start position:0% +things expending energy trying to rid +your body of the infection what else + + align:start position:0% + + + + align:start position:0% + +okay something for you to read up on for + + align:start position:0% +okay something for you to read up on for + + + align:start position:0% +okay something for you to read up on for +the not for the home okay for the + + align:start position:0% +the not for the home okay for the + + + align:start position:0% +the not for the home okay for the +practice homework the one that I can't + + align:start position:0% +practice homework the one that I can't + + + align:start position:0% +practice homework the one that I can't +make do because it's after the last day + + align:start position:0% +make do because it's after the last day + + + align:start position:0% +make do because it's after the last day +of classes what about let's see headache + + align:start position:0% +of classes what about let's see headache + + + align:start position:0% +of classes what about let's see headache +I don't think we've explained that well + + align:start position:0% +I don't think we've explained that well + + + align:start position:0% +I don't think we've explained that well +we'll get into the diarrhea stuff let's + + align:start position:0% +we'll get into the diarrhea stuff let's + + + align:start position:0% +we'll get into the diarrhea stuff let's +go into the latent phase what tends to + + align:start position:0% +go into the latent phase what tends to + + + align:start position:0% +go into the latent phase what tends to +happen well it looks like you get better + + align:start position:0% +happen well it looks like you get better + + + align:start position:0% +happen well it looks like you get better +but blood work will tell you otherwise + + align:start position:0% +but blood work will tell you otherwise + + + align:start position:0% +but blood work will tell you otherwise +and you can then tell how much dose you + + align:start position:0% +and you can then tell how much dose you + + + align:start position:0% +and you can then tell how much dose you +were exposed to after a certain amount + + align:start position:0% +were exposed to after a certain amount + + + align:start position:0% +were exposed to after a certain amount +of time by things like lymphocyte and + + align:start position:0% +of time by things like lymphocyte and + + + align:start position:0% +of time by things like lymphocyte and +granulocytes + + align:start position:0% +granulocytes + + + align:start position:0% +granulocytes +different immune system blood cells also + + align:start position:0% +different immune system blood cells also + + + align:start position:0% +different immune system blood cells also +platelets also all sorts of other things + + align:start position:0% +platelets also all sorts of other things + + + align:start position:0% +platelets also all sorts of other things +you can tell by a drop in certain blood + + align:start position:0% +you can tell by a drop in certain blood + + + align:start position:0% +you can tell by a drop in certain blood +cell levels how much dose you've had and + + align:start position:0% +cell levels how much dose you've had and + + + align:start position:0% +cell levels how much dose you've had and +you can sustain a certain drop in + + align:start position:0% +you can sustain a certain drop in + + + align:start position:0% +you can sustain a certain drop in +platelets and immune cells without any + + align:start position:0% +platelets and immune cells without any + + + align:start position:0% +platelets and immune cells without any +ill effects something like 30 to 40 + + align:start position:0% +ill effects something like 30 to 40 + + + align:start position:0% +ill effects something like 30 to 40 +percent your platelets could go away + + align:start position:0% +percent your platelets could go away + + + align:start position:0% +percent your platelets could go away +you're not haemophiliac temporarily + + align:start position:0% +you're not haemophiliac temporarily + + + align:start position:0% +you're not haemophiliac temporarily +you're still gonna be okay can form + + align:start position:0% +you're still gonna be okay can form + + + align:start position:0% +you're still gonna be okay can form +blood clots and result rows of what is + + align:start position:0% +blood clots and result rows of what is + + + align:start position:0% +blood clots and result rows of what is +it responds to a nosebleed or a bruise + + align:start position:0% +it responds to a nosebleed or a bruise + + + align:start position:0% +it responds to a nosebleed or a bruise +and these things aren't going to be + + align:start position:0% +and these things aren't going to be + + + align:start position:0% +and these things aren't going to be +life-threatening diarrhea for low doses + + align:start position:0% +life-threatening diarrhea for low doses + + + align:start position:0% +life-threatening diarrhea for low doses +you don't really get any so it looks + + align:start position:0% +you don't really get any so it looks + + + align:start position:0% +you don't really get any so it looks +like intestinal cells may be a little + + align:start position:0% +like intestinal cells may be a little + + + align:start position:0% +like intestinal cells may be a little +bit more robust than bone marrow except + + align:start position:0% +bit more robust than bone marrow except + + + align:start position:0% +bit more robust than bone marrow except +with really severe doses you'll start to + + align:start position:0% +with really severe doses you'll start to + + + align:start position:0% +with really severe doses you'll start to +see that pop up once those cells fail to + + align:start position:0% +see that pop up once those cells fail to + + + align:start position:0% +see that pop up once those cells fail to +divide once let's say the existing villi + + align:start position:0% +divide once let's say the existing villi + + + align:start position:0% +divide once let's say the existing villi +die-off new ones don't replace them and + + align:start position:0% +die-off new ones don't replace them and + + + align:start position:0% +die-off new ones don't replace them and +you lose your ability to uptake + + align:start position:0% +you lose your ability to uptake + + + align:start position:0% +you lose your ability to uptake +nutrition and then depilation hair loss + + align:start position:0% +nutrition and then depilation hair loss + + + align:start position:0% +nutrition and then depilation hair loss +beating you know beginning on day 15 or + + align:start position:0% +beating you know beginning on day 15 or + + + align:start position:0% +beating you know beginning on day 15 or +later you might think you're out of the + + align:start position:0% +later you might think you're out of the + + + align:start position:0% +later you might think you're out of the +woods and then all of a sudden your hair + + align:start position:0% +woods and then all of a sudden your hair + + + align:start position:0% +woods and then all of a sudden your hair +starts to fall out and that will help + + align:start position:0% +starts to fall out and that will help + + + align:start position:0% +starts to fall out and that will help +tell you about how much dose you've had + + align:start position:0% +tell you about how much dose you've had + + + align:start position:0% +tell you about how much dose you've had +once again and then the critical phase + + align:start position:0% +once again and then the critical phase + + + align:start position:0% +once again and then the critical phase +what happens when things go from bad to + + align:start position:0% +what happens when things go from bad to + + + align:start position:0% +what happens when things go from bad to +better to worse how quickly does this + + align:start position:0% +better to worse how quickly does this + + + align:start position:0% +better to worse how quickly does this +happen + + align:start position:0% +happen + + + align:start position:0% +happen +you tend to get things like infections + + align:start position:0% +you tend to get things like infections + + + align:start position:0% +you tend to get things like infections +more severe infections disorientation + + align:start position:0% +more severe infections disorientation + + + align:start position:0% +more severe infections disorientation +on longer times like seven days your + + align:start position:0% +on longer times like seven days your + + + align:start position:0% +on longer times like seven days your +platelet count + + align:start position:0% +platelet count + + + align:start position:0% +platelet count +pretty proportional to dose same thing + + align:start position:0% +pretty proportional to dose same thing + + + align:start position:0% +pretty proportional to dose same thing +with number of lymphocytes lower and + + align:start position:0% +with number of lymphocytes lower and + + + align:start position:0% +with number of lymphocytes lower and +lower and lower and then the onset time + + align:start position:0% +lower and lower and then the onset time + + + align:start position:0% +lower and lower and then the onset time +is smaller and smaller and then you can + + align:start position:0% +is smaller and smaller and then you can + + + align:start position:0% +is smaller and smaller and then you can +see the lethality of these different + + align:start position:0% +see the lethality of these different + + + align:start position:0% +see the lethality of these different +doses depending on the person the + + align:start position:0% +doses depending on the person the + + + align:start position:0% +doses depending on the person the +treatments a susceptibility any sort of + + align:start position:0% +treatments a susceptibility any sort of + + + align:start position:0% +treatments a susceptibility any sort of +pre-existing conditions which you might + + align:start position:0% +pre-existing conditions which you might + + + align:start position:0% +pre-existing conditions which you might +not know you have a question cancer yeah + + align:start position:0% +not know you have a question cancer yeah + + + align:start position:0% +not know you have a question cancer yeah +radiation doses are pretty intense + + align:start position:0% +radiation doses are pretty intense + + + align:start position:0% +radiation doses are pretty intense +so the dosed of a tumor for example in + + align:start position:0% +so the dosed of a tumor for example in + + + align:start position:0% +so the dosed of a tumor for example in +proton therapy which is the only one + + align:start position:0% +proton therapy which is the only one + + + align:start position:0% +proton therapy which is the only one +I've really read about can be in the + + align:start position:0% +I've really read about can be in the + + + align:start position:0% +I've really read about can be in the +killa grey level but the idea there is + + align:start position:0% +killa grey level but the idea there is + + + align:start position:0% +killa grey level but the idea there is +you fried the tumor you kill it soon + + align:start position:0% +you fried the tumor you kill it soon + + + align:start position:0% +you fried the tumor you kill it soon +like you go beyond the lethal dose for + + align:start position:0% +like you go beyond the lethal dose for + + + align:start position:0% +like you go beyond the lethal dose for +those cells while inducing much less + + align:start position:0% +those cells while inducing much less + + + align:start position:0% +those cells while inducing much less +damage in the rest of the rest of the + + align:start position:0% +damage in the rest of the rest of the + + + align:start position:0% +damage in the rest of the rest of the +surrounding person that's the nice cork + + align:start position:0% +surrounding person that's the nice cork + + + align:start position:0% +surrounding person that's the nice cork +of protons is you can do that in a very + + align:start position:0% +of protons is you can do that in a very + + + align:start position:0% +of protons is you can do that in a very +narrow range the straggle on 250 MeV + + align:start position:0% +narrow range the straggle on 250 MeV + + + align:start position:0% +narrow range the straggle on 250 MeV +proton beams is on the order of like you + + align:start position:0% +proton beams is on the order of like you + + + align:start position:0% +proton beams is on the order of like you +know microns less than millimeters which + + align:start position:0% +know microns less than millimeters which + + + align:start position:0% +know microns less than millimeters which +is pretty cool but a lot of the hair + + align:start position:0% +is pretty cool but a lot of the hair + + + align:start position:0% +is pretty cool but a lot of the hair +loss can come from the chemotherapy + + align:start position:0% +loss can come from the chemotherapy + + + align:start position:0% +loss can come from the chemotherapy +chemotherapy is better known as poison + + align:start position:0% +chemotherapy is better known as poison + + + align:start position:0% +chemotherapy is better known as poison +it's just a poison that effects tumor + + align:start position:0% +it's just a poison that effects tumor + + + align:start position:0% +it's just a poison that effects tumor +cells slightly more strongly than the + + align:start position:0% +cells slightly more strongly than the + + + align:start position:0% +cells slightly more strongly than the +rest of your cells but it is nasty stuff + + align:start position:0% +rest of your cells but it is nasty stuff + + + align:start position:0% +rest of your cells but it is nasty stuff +and it's the chemo that can cause the + + align:start position:0% +and it's the chemo that can cause the + + + align:start position:0% +and it's the chemo that can cause the +hair loss as well yeah so would you + + align:start position:0% +hair loss as well yeah so would you + + + align:start position:0% +hair loss as well yeah so would you +attribute the hair loss to radiation or + + align:start position:0% +attribute the hair loss to radiation or + + + align:start position:0% +attribute the hair loss to radiation or +to chemo I would say chances are it's + + align:start position:0% +to chemo I would say chances are it's + + + align:start position:0% +to chemo I would say chances are it's +chemo depending on where the tumor is I + + align:start position:0% +chemo depending on where the tumor is I + + + align:start position:0% +chemo depending on where the tumor is I +mean if you have a localized proton beam + + align:start position:0% +mean if you have a localized proton beam + + + align:start position:0% +mean if you have a localized proton beam +coming in to treat a tumor there there + + align:start position:0% +coming in to treat a tumor there there + + + align:start position:0% +coming in to treat a tumor there there +you're not gonna get much hair loss up + + align:start position:0% +you're not gonna get much hair loss up + + + align:start position:0% +you're not gonna get much hair loss up +here but chemo penetrates throughout the + + align:start position:0% +here but chemo penetrates throughout the + + + align:start position:0% +here but chemo penetrates throughout the +whole body as far as if you're getting + + align:start position:0% +whole body as far as if you're getting + + + align:start position:0% +whole body as far as if you're getting +x-ray therapy of a brain tumor that I + + align:start position:0% +x-ray therapy of a brain tumor that I + + + align:start position:0% +x-ray therapy of a brain tumor that I +don't know I really haven't looked into + + align:start position:0% +don't know I really haven't looked into + + + align:start position:0% +don't know I really haven't looked into +that so good question and then the time + + align:start position:0% +that so good question and then the time + + + align:start position:0% +that so good question and then the time +and severity of these symptoms well this + + align:start position:0% +and severity of these symptoms well this + + + align:start position:0% +and severity of these symptoms well this +is something I'd like you guys to read + + align:start position:0% +is something I'd like you guys to read + + + align:start position:0% +is something I'd like you guys to read +on your own because it's tons of words + + align:start position:0% +on your own because it's tons of words + + + align:start position:0% +on your own because it's tons of words +on a screen but it's something I suggest + + align:start position:0% +on a screen but it's something I suggest + + + align:start position:0% +on a screen but it's something I suggest +you read it's not done that carefully in + + align:start position:0% +you read it's not done that carefully in + + + align:start position:0% +you read it's not done that carefully in +the reading which is why I provided it + + align:start position:0% +the reading which is why I provided it + + + align:start position:0% +the reading which is why I provided it +here for you in the slides then going on + + align:start position:0% +here for you in the slides then going on + + + align:start position:0% +here for you in the slides then going on +to what these radiation symptoms mean I + + align:start position:0% +to what these radiation symptoms mean I + + + align:start position:0% +to what these radiation symptoms mean I +wanted to translate a little bit of the + + align:start position:0% +wanted to translate a little bit of the + + + align:start position:0% +wanted to translate a little bit of the +Latin Greek whatever routes into + + align:start position:0% +Latin Greek whatever routes into + + + align:start position:0% +Latin Greek whatever routes into +something you can understand these + + align:start position:0% +something you can understand these + + + align:start position:0% +something you can understand these +hamato poetic symptoms anything to do + + align:start position:0% +hamato poetic symptoms anything to do + + + align:start position:0% +hamato poetic symptoms anything to do +with the blood decreased platelets + + align:start position:0% +with the blood decreased platelets + + + align:start position:0% +with the blood decreased platelets +immune suppression all that kind of + + align:start position:0% +immune suppression all that kind of + + + align:start position:0% +immune suppression all that kind of +stuff and the origin is the stem cell + + align:start position:0% +stuff and the origin is the stem cell + + + align:start position:0% +stuff and the origin is the stem cell +system in your bone marrow breaks down + + align:start position:0% +system in your bone marrow breaks down + + + align:start position:0% +system in your bone marrow breaks down +and you don't make as much of all the + + align:start position:0% +and you don't make as much of all the + + + align:start position:0% +and you don't make as much of all the +components of blood as you normally + + align:start position:0% +components of blood as you normally + + + align:start position:0% +components of blood as you normally +should the gastrointestinal comes from + + align:start position:0% +should the gastrointestinal comes from + + + align:start position:0% +should the gastrointestinal comes from +the stem cells in the villi those high + + align:start position:0% +the stem cells in the villi those high + + + align:start position:0% +the stem cells in the villi those high +surface area structures in your + + align:start position:0% +surface area structures in your + + + align:start position:0% +surface area structures in your +intestines that absorb the nutrition + + align:start position:0% +intestines that absorb the nutrition + + + align:start position:0% +intestines that absorb the nutrition +which are also normally covered in a + + align:start position:0% +which are also normally covered in a + + + align:start position:0% +which are also normally covered in a +thick layer of mucus to keep all the + + align:start position:0% +thick layer of mucus to keep all the + + + align:start position:0% +thick layer of mucus to keep all the +bacteria from getting out because + + align:start position:0% +bacteria from getting out because + + + align:start position:0% +bacteria from getting out because +nutrients like let's say minerals or + + align:start position:0% +nutrients like let's say minerals or + + + align:start position:0% +nutrients like let's say minerals or +small proteins are a hell of a lot + + align:start position:0% +small proteins are a hell of a lot + + + align:start position:0% +small proteins are a hell of a lot +smaller than bacteria they can diffuse + + align:start position:0% +smaller than bacteria they can diffuse + + + align:start position:0% +smaller than bacteria they can diffuse +or transport through the mucus much + + align:start position:0% +or transport through the mucus much + + + align:start position:0% +or transport through the mucus much +faster so you can uptake the nutrition + + align:start position:0% +faster so you can uptake the nutrition + + + align:start position:0% +faster so you can uptake the nutrition +and not let the bad stuff in and the + + align:start position:0% +and not let the bad stuff in and the + + + align:start position:0% +and not let the bad stuff in and the +neuro or cerebrovascular stuff is + + align:start position:0% +neuro or cerebrovascular stuff is + + + align:start position:0% +neuro or cerebrovascular stuff is +straight up blasting of endothelial + + align:start position:0% +straight up blasting of endothelial + + + align:start position:0% +straight up blasting of endothelial +cells your let's say yeah I think that + + align:start position:0% +cells your let's say yeah I think that + + + align:start position:0% +cells your let's say yeah I think that +skin cells a term called edema which is + + align:start position:0% +skin cells a term called edema which is + + + align:start position:0% +skin cells a term called edema which is +fluid leakage has anyone ever seen + + align:start position:0% +fluid leakage has anyone ever seen + + + align:start position:0% +fluid leakage has anyone ever seen +pictures of folks with massive edema in + + align:start position:0% +pictures of folks with massive edema in + + + align:start position:0% +pictures of folks with massive edema in +the legs like folks at let's say haven't + + align:start position:0% +the legs like folks at let's say haven't + + + align:start position:0% +the legs like folks at let's say haven't +gone out of bed for years and their legs + + align:start position:0% +gone out of bed for years and their legs + + + align:start position:0% +gone out of bed for years and their legs +swell up like this + + align:start position:0% +swell up like this + + + align:start position:0% +swell up like this +that's just fluid leaking into the + + align:start position:0% +that's just fluid leaking into the + + + align:start position:0% +that's just fluid leaking into the +intracellular spaces I'd say take a look + + align:start position:0% +intracellular spaces I'd say take a look + + + align:start position:0% +intracellular spaces I'd say take a look +I don't think I'm gonna show pictures of + + align:start position:0% +I don't think I'm gonna show pictures of + + + align:start position:0% +I don't think I'm gonna show pictures of +it cuz it's kind of nasty on the screen + + align:start position:0% +it cuz it's kind of nasty on the screen + + + align:start position:0% +it cuz it's kind of nasty on the screen +but if you want to know what edema looks + + align:start position:0% +but if you want to know what edema looks + + + align:start position:0% +but if you want to know what edema looks +like then I suggest you look it up + + align:start position:0% +like then I suggest you look it up + + + align:start position:0% +like then I suggest you look it up +there's plenty of horrific stuff on + + align:start position:0% +there's plenty of horrific stuff on + + + align:start position:0% +there's plenty of horrific stuff on +Google Images and so what happens in + + align:start position:0% +Google Images and so what happens in + + + align:start position:0% +Google Images and so what happens in +these hematopoietic cells about one gray + + align:start position:0% +these hematopoietic cells about one gray + + + align:start position:0% +these hematopoietic cells about one gray +can knock out about a third of your bone + + align:start position:0% +can knock out about a third of your bone + + + align:start position:0% +can knock out about a third of your bone +marrow cells and that's actually okay + + align:start position:0% +marrow cells and that's actually okay + + + align:start position:0% +marrow cells and that's actually okay +because those surviving cells are + + align:start position:0% +because those surviving cells are + + + align:start position:0% +because those surviving cells are +redefining quite quickly and that means + + align:start position:0% +redefining quite quickly and that means + + + align:start position:0% +redefining quite quickly and that means +that you won't have that much of a drop + + align:start position:0% +that you won't have that much of a drop + + + align:start position:0% +that you won't have that much of a drop +in blood cells because let's say you + + align:start position:0% +in blood cells because let's say you + + + align:start position:0% +in blood cells because let's say you +kill off a bunch of the bone marrow + + align:start position:0% +kill off a bunch of the bone marrow + + + align:start position:0% +kill off a bunch of the bone marrow +cells but they read avise in a shorter + + align:start position:0% +cells but they read avise in a shorter + + + align:start position:0% +cells but they read avise in a shorter +life time than let's say the red blood + + align:start position:0% +life time than let's say the red blood + + + align:start position:0% +life time than let's say the red blood +cells or platelets live you're not going + + align:start position:0% +cells or platelets live you're not going + + + align:start position:0% +cells or platelets live you're not going +to see that much of a dip in the blood + + align:start position:0% +to see that much of a dip in the blood + + + align:start position:0% +to see that much of a dip in the blood +cell levels which are ultimately your + + align:start position:0% +cell levels which are ultimately your + + + align:start position:0% +cell levels which are ultimately your +main line of defense against sepsis + + align:start position:0% +main line of defense against sepsis + + + align:start position:0% +main line of defense against sepsis +things like destruction of bone marrow + + align:start position:0% +things like destruction of bone marrow + + + align:start position:0% +things like destruction of bone marrow +yeah that would that would be a bad + + align:start position:0% +yeah that would that would be a bad + + + align:start position:0% +yeah that would that would be a bad +thing there's a whole lot of words here + + align:start position:0% +thing there's a whole lot of words here + + + align:start position:0% +thing there's a whole lot of words here +I'd say this is better for you to read I + + align:start position:0% +I'd say this is better for you to read I + + + align:start position:0% +I'd say this is better for you to read I +want to go through an explanation of + + align:start position:0% +want to go through an explanation of + + + align:start position:0% +want to go through an explanation of +some pictures of what tends to happen to + + align:start position:0% +some pictures of what tends to happen to + + + align:start position:0% +some pictures of what tends to happen to +in this case mouse bone marrow tissue + + align:start position:0% +in this case mouse bone marrow tissue + + + align:start position:0% +in this case mouse bone marrow tissue +after a lethal dose 9.5 + + align:start position:0% +after a lethal dose 9.5 + + + align:start position:0% +after a lethal dose 9.5 +gray that's what it looks like + + align:start position:0% +gray that's what it looks like + + + align:start position:0% +gray that's what it looks like +beforehand that's what you're left with + + align:start position:0% +beforehand that's what you're left with + + + align:start position:0% +beforehand that's what you're left with +is very very few cells so that would be + + align:start position:0% +is very very few cells so that would be + + + align:start position:0% +is very very few cells so that would be +definitely what a lethal dose looks like + + align:start position:0% +definitely what a lethal dose looks like + + + align:start position:0% +definitely what a lethal dose looks like +because the ability to make all the + + align:start position:0% +because the ability to make all the + + + align:start position:0% +because the ability to make all the +things that bone marrow makes has been + + align:start position:0% +things that bone marrow makes has been + + + align:start position:0% +things that bone marrow makes has been +almost eliminated in this tissue so a + + align:start position:0% +almost eliminated in this tissue so a + + + align:start position:0% +almost eliminated in this tissue so a +visual of what these sorts of things + + align:start position:0% +visual of what these sorts of things + + + align:start position:0% +visual of what these sorts of things +look like for the gastrointestinal + + align:start position:0% +look like for the gastrointestinal + + + align:start position:0% +look like for the gastrointestinal +systems I'm going to skip right ahead + + align:start position:0% +systems I'm going to skip right ahead + + + align:start position:0% +systems I'm going to skip right ahead +and show you what healthy and irradiated + + align:start position:0% +and show you what healthy and irradiated + + + align:start position:0% +and show you what healthy and irradiated +villi tend to look like so I've been + + align:start position:0% +villi tend to look like so I've been + + + align:start position:0% +villi tend to look like so I've been +does anyone not know what I mean but I + + align:start position:0% +does anyone not know what I mean but I + + + align:start position:0% +does anyone not know what I mean but I +say villi okay good so the little high + + align:start position:0% +say villi okay good so the little high + + + align:start position:0% +say villi okay good so the little high +surface area structures in your + + align:start position:0% +surface area structures in your + + + align:start position:0% +surface area structures in your +intestine that are normally great + + align:start position:0% +intestine that are normally great + + + align:start position:0% +intestine that are normally great +absorbers of nutrition mostly due to + + align:start position:0% +absorbers of nutrition mostly due to + + + align:start position:0% +absorbers of nutrition mostly due to +their surface area but also due to their + + align:start position:0% +their surface area but also due to their + + + align:start position:0% +their surface area but also due to their +structure and their biological function + + align:start position:0% +structure and their biological function + + + align:start position:0% +structure and their biological function +and you tend to kill those off with a + + align:start position:0% +and you tend to kill those off with a + + + align:start position:0% +and you tend to kill those off with a +fair bit of radiation so this is what it + + align:start position:0% +fair bit of radiation so this is what it + + + align:start position:0% +fair bit of radiation so this is what it +looks like after four days and seven + + align:start position:0% +looks like after four days and seven + + + align:start position:0% +looks like after four days and seven +days and then twelve days things can + + align:start position:0% +days and then twelve days things can + + + align:start position:0% +days and then twelve days things can +recover so they don't kill all the cells + + align:start position:0% +recover so they don't kill all the cells + + + align:start position:0% +recover so they don't kill all the cells +they will divide and they will recall + + align:start position:0% +they will divide and they will recall + + + align:start position:0% +they will divide and they will recall +curve as Amanda allow for that natural + + align:start position:0% +curve as Amanda allow for that natural + + + align:start position:0% +curve as Amanda allow for that natural +healing to take place then you can + + align:start position:0% +healing to take place then you can + + + align:start position:0% +healing to take place then you can +survive an acute dose of radiation so + + align:start position:0% +survive an acute dose of radiation so + + + align:start position:0% +survive an acute dose of radiation so +when we talk about why do you need + + align:start position:0% +when we talk about why do you need + + + align:start position:0% +when we talk about why do you need +hospital treatment it's basically to + + align:start position:0% +hospital treatment it's basically to + + + align:start position:0% +hospital treatment it's basically to +stand in for your body's normal + + align:start position:0% +stand in for your body's normal + + + align:start position:0% +stand in for your body's normal +functions while your body regenerates + + align:start position:0% +functions while your body regenerates + + + align:start position:0% +functions while your body regenerates +those functions but for extremely severe + + align:start position:0% +those functions but for extremely severe + + + align:start position:0% +those functions but for extremely severe +cases let's go back to that table of + + align:start position:0% +cases let's go back to that table of + + + align:start position:0% +cases let's go back to that table of +hominid let's say leukocytes or whatnot + + align:start position:0% +hominid let's say leukocytes or whatnot + + + align:start position:0% +hominid let's say leukocytes or whatnot +you have or lymphocytes if you get down + + align:start position:0% +you have or lymphocytes if you get down + + + align:start position:0% +you have or lymphocytes if you get down +to the zero level you've completely + + align:start position:0% +to the zero level you've completely + + + align:start position:0% +to the zero level you've completely +knocked out your body's ability to + + align:start position:0% +knocked out your body's ability to + + + align:start position:0% +knocked out your body's ability to +produce those you might have a few cells + + align:start position:0% +produce those you might have a few cells + + + align:start position:0% +produce those you might have a few cells +left here there but at that point + + align:start position:0% +left here there but at that point + + + align:start position:0% +left here there but at that point +there's not much anyone can do but make + + align:start position:0% +there's not much anyone can do but make + + + align:start position:0% +there's not much anyone can do but make +you comfortable and then in this case I + + align:start position:0% +you comfortable and then in this case I + + + align:start position:0% +you comfortable and then in this case I +think this was a human one yeah okay so + + align:start position:0% +think this was a human one yeah okay so + + + align:start position:0% +think this was a human one yeah okay so +a healthy intestine from a human it's + + align:start position:0% +a healthy intestine from a human it's + + + align:start position:0% +a healthy intestine from a human it's +got a rather small whatever that part is + + align:start position:0% +got a rather small whatever that part is + + + align:start position:0% +got a rather small whatever that part is +in the submucosa level lots of villi + + align:start position:0% +in the submucosa level lots of villi + + + align:start position:0% +in the submucosa level lots of villi +lots of surface area after radiation + + align:start position:0% +lots of surface area after radiation + + + align:start position:0% +lots of surface area after radiation +damage when you have massive cell death + + align:start position:0% +damage when you have massive cell death + + + align:start position:0% +damage when you have massive cell death +notice that the structures out here are + + align:start position:0% +notice that the structures out here are + + + align:start position:0% +notice that the structures out here are +pretty much gone and there's a lot of + + align:start position:0% +pretty much gone and there's a lot of + + + align:start position:0% +pretty much gone and there's a lot of +scarring or what's the word that they + + align:start position:0% +scarring or what's the word that they + + + align:start position:0% +scarring or what's the word that they +use severe fibrosis why would your body + + align:start position:0% +use severe fibrosis why would your body + + + align:start position:0% +use severe fibrosis why would your body +make scar tissue in response to + + align:start position:0% +make scar tissue in response to + + + align:start position:0% +make scar tissue in response to +radiation damage + + align:start position:0% + + + + align:start position:0% + +so anytime your body senses that a whole + + align:start position:0% +so anytime your body senses that a whole + + + align:start position:0% +so anytime your body senses that a whole +lot of cells are dying it's going to + + align:start position:0% +lot of cells are dying it's going to + + + align:start position:0% +lot of cells are dying it's going to +respond by attempting to repair so like + + align:start position:0% +respond by attempting to repair so like + + + align:start position:0% +respond by attempting to repair so like +if you get let's say a small bit of + + align:start position:0% +if you get let's say a small bit of + + + align:start position:0% +if you get let's say a small bit of +surgery done you could be left with some + + align:start position:0% +surgery done you could be left with some + + + align:start position:0% +surgery done you could be left with some +scar tissue that's cells that have died + + align:start position:0% +scar tissue that's cells that have died + + + align:start position:0% +scar tissue that's cells that have died +and when those cell contents leak out + + align:start position:0% +and when those cell contents leak out + + + align:start position:0% +and when those cell contents leak out +they signal to the nearby cells fix + + align:start position:0% +they signal to the nearby cells fix + + + align:start position:0% +they signal to the nearby cells fix +something I can't speak any more + + align:start position:0% +something I can't speak any more + + + align:start position:0% +something I can't speak any more +intelligently about that but the body + + align:start position:0% +intelligently about that but the body + + + align:start position:0% +intelligently about that but the body +does and scar tissue is not what you + + align:start position:0% +does and scar tissue is not what you + + + align:start position:0% +does and scar tissue is not what you +want in your intestine because that + + align:start position:0% +want in your intestine because that + + + align:start position:0% +want in your intestine because that +interferes with what does that Nutrition + + align:start position:0% +interferes with what does that Nutrition + + + align:start position:0% +interferes with what does that Nutrition +uptake as well as killing the structures + + align:start position:0% +uptake as well as killing the structures + + + align:start position:0% +uptake as well as killing the structures +that are doing that uptake to begin with + + align:start position:0% +that are doing that uptake to begin with + + + align:start position:0% +that are doing that uptake to begin with +then there's the neurovascular stuff + + align:start position:0% +then there's the neurovascular stuff + + + align:start position:0% +then there's the neurovascular stuff +massive cell death from a huge amount of + + align:start position:0% +massive cell death from a huge amount of + + + align:start position:0% +massive cell death from a huge amount of +absorbed energy can just cause those + + align:start position:0% +absorbed energy can just cause those + + + align:start position:0% +absorbed energy can just cause those +cells to die and leak out causing a lot + + align:start position:0% +cells to die and leak out causing a lot + + + align:start position:0% +cells to die and leak out causing a lot +of edema that can cause a lock and a + + align:start position:0% +of edema that can cause a lock and a + + + align:start position:0% +of edema that can cause a lock and a +drop in blood pressure which is also not + + align:start position:0% +drop in blood pressure which is also not + + + align:start position:0% +drop in blood pressure which is also not +good for you + + align:start position:0% +good for you + + + align:start position:0% +good for you +this could be part of what leads to some + + align:start position:0% +this could be part of what leads to some + + + align:start position:0% +this could be part of what leads to some +of the unconsciousness if you have a + + align:start position:0% +of the unconsciousness if you have a + + + align:start position:0% +of the unconsciousness if you have a +drop in blood pressure due to any reason + + align:start position:0% +drop in blood pressure due to any reason + + + align:start position:0% +drop in blood pressure due to any reason +then that could make you go unconscious + + align:start position:0% +then that could make you go unconscious + + + align:start position:0% +then that could make you go unconscious +and there's pretty much not a prodromal + + align:start position:0% +and there's pretty much not a prodromal + + + align:start position:0% +and there's pretty much not a prodromal +or a latent phase if you hit the + + align:start position:0% +or a latent phase if you hit the + + + align:start position:0% +or a latent phase if you hit the +neurovascular syndrome you're pretty + + align:start position:0% +neurovascular syndrome you're pretty + + + align:start position:0% +neurovascular syndrome you're pretty +much gonna go to the critical phase + + align:start position:0% +much gonna go to the critical phase + + + align:start position:0% +much gonna go to the critical phase +right away within seconds minutes or + + align:start position:0% +right away within seconds minutes or + + + align:start position:0% +right away within seconds minutes or +small number of hours they're not a + + align:start position:0% +small number of hours they're not a + + + align:start position:0% +small number of hours they're not a +question why the skin lesions + + align:start position:0% +question why the skin lesions + + + align:start position:0% +question why the skin lesions +because mature skin cells live about + + align:start position:0% +because mature skin cells live about + + + align:start position:0% +because mature skin cells live about +three weeks if you kill off the skin + + align:start position:0% +three weeks if you kill off the skin + + + align:start position:0% +three weeks if you kill off the skin +cells in the dividing layer and you + + align:start position:0% +cells in the dividing layer and you + + + align:start position:0% +cells in the dividing layer and you +don't reform new ones and those skin + + align:start position:0% +don't reform new ones and those skin + + + align:start position:0% +don't reform new ones and those skin +cells die you end up with the grossest + + align:start position:0% +cells die you end up with the grossest + + + align:start position:0% +cells die you end up with the grossest +word in this class moist desquamation it + + align:start position:0% +word in this class moist desquamation it + + + align:start position:0% +word in this class moist desquamation it +kind of sounds like what it is that's + + align:start position:0% +kind of sounds like what it is that's + + + align:start position:0% +kind of sounds like what it is that's +like sloughing off of skin and leaving + + align:start position:0% +like sloughing off of skin and leaving + + + align:start position:0% +like sloughing off of skin and leaving +open sores because you don't have the + + align:start position:0% +open sores because you don't have the + + + align:start position:0% +open sores because you don't have the +ability to regenerate that skin which is + + align:start position:0% +ability to regenerate that skin which is + + + align:start position:0% +ability to regenerate that skin which is +normally your first line of defense to + + align:start position:0% +normally your first line of defense to + + + align:start position:0% +normally your first line of defense to +everything and you've got fluid leaking + + align:start position:0% +everything and you've got fluid leaking + + + align:start position:0% +everything and you've got fluid leaking +out and it's just yeah its moist + + align:start position:0% +out and it's just yeah its moist + + + align:start position:0% +out and it's just yeah its moist +desquamation why the vomiting well this + + align:start position:0% +desquamation why the vomiting well this + + + align:start position:0% +desquamation why the vomiting well this +question hasn't been fully answered yet + + align:start position:0% +question hasn't been fully answered yet + + + align:start position:0% +question hasn't been fully answered yet +as far as back and i've looked at the + + align:start position:0% +as far as back and i've looked at the + + + align:start position:0% +as far as back and i've looked at the +literature around to 2011 there is a + + align:start position:0% +literature around to 2011 there is a + + + align:start position:0% +literature around to 2011 there is a +hypothesis that intestinal cells will + + align:start position:0% +hypothesis that intestinal cells will + + + align:start position:0% +hypothesis that intestinal cells will +secrete serotonin in certain conditions + + align:start position:0% +secrete serotonin in certain conditions + + + align:start position:0% +secrete serotonin in certain conditions +including when they start dying which + + align:start position:0% +including when they start dying which + + + align:start position:0% +including when they start dying which +would then stimulate a center in your + + align:start position:0% +would then stimulate a center in your + + + align:start position:0% +would then stimulate a center in your +medulla the sort of automatic reflex + + align:start position:0% +medulla the sort of automatic reflex + + + align:start position:0% +medulla the sort of automatic reflex +center of the blank membrane to induce + + align:start position:0% +center of the blank membrane to induce + + + align:start position:0% +center of the blank membrane to induce +vomiting why might this be + + align:start position:0% +vomiting why might this be + + + align:start position:0% +vomiting why might this be +good thing we're not talking about + + align:start position:0% +good thing we're not talking about + + + align:start position:0% +good thing we're not talking about +radiation but why would you want to + + align:start position:0% +radiation but why would you want to + + + align:start position:0% +radiation but why would you want to +stimulate this vomiting reflux yeah so + + align:start position:0% +stimulate this vomiting reflux yeah so + + + align:start position:0% +stimulate this vomiting reflux yeah so +let's say you eat a a wet aged steak you + + align:start position:0% +let's say you eat a a wet aged steak you + + + align:start position:0% +let's say you eat a a wet aged steak you +know something that's left out on the + + align:start position:0% +know something that's left out on the + + + align:start position:0% +know something that's left out on the +table or in the fridge or let's say + + align:start position:0% +table or in the fridge or let's say + + + align:start position:0% +table or in the fridge or let's say +behind the fridge you're left to + + align:start position:0% +behind the fridge you're left to + + + align:start position:0% +behind the fridge you're left to +marinate in the Sun and you eat it and + + align:start position:0% +marinate in the Sun and you eat it and + + + align:start position:0% +marinate in the Sun and you eat it and +those bacteria start killing everything + + align:start position:0% +those bacteria start killing everything + + + align:start position:0% +those bacteria start killing everything +if those cells in your intestine die + + align:start position:0% +if those cells in your intestine die + + + align:start position:0% +if those cells in your intestine die +they've got to send some signal far away + + align:start position:0% +they've got to send some signal far away + + + align:start position:0% +they've got to send some signal far away +to the brain to tell you to get + + align:start position:0% +to the brain to tell you to get + + + align:start position:0% +to the brain to tell you to get +everything out of the stomach and that's + + align:start position:0% +everything out of the stomach and that's + + + align:start position:0% +everything out of the stomach and that's +what happens so the body has developed + + align:start position:0% +what happens so the body has developed + + + align:start position:0% +what happens so the body has developed +these long-distance hormonal signalling + + align:start position:0% +these long-distance hormonal signalling + + + align:start position:0% +these long-distance hormonal signalling +mechanisms to say something is going + + align:start position:0% +mechanisms to say something is going + + + align:start position:0% +mechanisms to say something is going +wrong expel everything because it's + + align:start position:0% +wrong expel everything because it's + + + align:start position:0% +wrong expel everything because it's +probably bad for you so radiation damage + + align:start position:0% +probably bad for you so radiation damage + + + align:start position:0% +probably bad for you so radiation damage +to these cells which will kill them may + + align:start position:0% +to these cells which will kill them may + + + align:start position:0% +to these cells which will kill them may +trigger the same effects if those cells + + align:start position:0% +trigger the same effects if those cells + + + align:start position:0% +trigger the same effects if those cells +have little pockets or organelles that + + align:start position:0% +have little pockets or organelles that + + + align:start position:0% +have little pockets or organelles that +contain these hormones and cause + + align:start position:0% +contain these hormones and cause + + + align:start position:0% +contain these hormones and cause +instantaneous secretion by cell death + + align:start position:0% +instantaneous secretion by cell death + + + align:start position:0% +instantaneous secretion by cell death +that might do the same thing too but as + + align:start position:0% +that might do the same thing too but as + + + align:start position:0% +that might do the same thing too but as +far as this paper it's a hypothesis it's + + align:start position:0% +far as this paper it's a hypothesis it's + + + align:start position:0% +far as this paper it's a hypothesis it's +not necessarily proven but it does + + align:start position:0% +not necessarily proven but it does + + + align:start position:0% +not necessarily proven but it does +correlate inversely with the amount of + + align:start position:0% +correlate inversely with the amount of + + + align:start position:0% +correlate inversely with the amount of +time to vomiting in terms of dose and + + align:start position:0% +time to vomiting in terms of dose and + + + align:start position:0% +time to vomiting in terms of dose and +time to vomiting so that much we do know + + align:start position:0% +time to vomiting so that much we do know + + + align:start position:0% +time to vomiting so that much we do know +and then on to the long-term effects + + align:start position:0% +and then on to the long-term effects + + + align:start position:0% +and then on to the long-term effects +there's two that are really important is + + align:start position:0% +there's two that are really important is + + + align:start position:0% +there's two that are really important is +cancer risk and birth defect risk you + + align:start position:0% +cancer risk and birth defect risk you + + + align:start position:0% +cancer risk and birth defect risk you +won't tend to see this happen despite + + align:start position:0% +won't tend to see this happen despite + + + align:start position:0% +won't tend to see this happen despite +popular media but you will see a lot of + + align:start position:0% +popular media but you will see a lot of + + + align:start position:0% +popular media but you will see a lot of +bad stuff happen these are extremely + + align:start position:0% +bad stuff happen these are extremely + + + align:start position:0% +bad stuff happen these are extremely +difficult to wrap our heads around and + + align:start position:0% +difficult to wrap our heads around and + + + align:start position:0% +difficult to wrap our heads around and +the reason for that is the population + + align:start position:0% +the reason for that is the population + + + align:start position:0% +the reason for that is the population +size required in order to do a proper + + align:start position:0% +size required in order to do a proper + + + align:start position:0% +size required in order to do a proper +study with proper statistics and give + + align:start position:0% +study with proper statistics and give + + + align:start position:0% +study with proper statistics and give +confidence to the saying let's say a + + align:start position:0% +confidence to the saying let's say a + + + align:start position:0% +confidence to the saying let's say a +dose in order to let's say a dose of 1 + + align:start position:0% +dose in order to let's say a dose of 1 + + + align:start position:0% +dose in order to let's say a dose of 1 +milligram what have some amount of + + align:start position:0% +milligram what have some amount of + + + align:start position:0% +milligram what have some amount of +excess risk you'd need to expose 60 1.8 + + align:start position:0% +excess risk you'd need to expose 60 1.8 + + + align:start position:0% +excess risk you'd need to expose 60 1.8 +million people plus a similarly sized + + align:start position:0% +million people plus a similarly sized + + + align:start position:0% +million people plus a similarly sized +control to distinguish whether or not + + align:start position:0% +control to distinguish whether or not + + + align:start position:0% +control to distinguish whether or not +point 1 mil agree has an additional + + align:start position:0% +point 1 mil agree has an additional + + + align:start position:0% +point 1 mil agree has an additional +amount of risk so let's say for game + + align:start position:0% +amount of risk so let's say for game + + + align:start position:0% +amount of risk so let's say for game +most a whole body what's point 1 + + align:start position:0% +most a whole body what's point 1 + + + align:start position:0% +most a whole body what's point 1 +milligrams of increased risk dose in + + align:start position:0% +milligrams of increased risk dose in + + + align:start position:0% +milligrams of increased risk dose in +sieverts sorry 1 mil agree + + align:start position:0% + + + + align:start position:0% + +1 millisievert you know tissue factors 1 + + align:start position:0% +1 millisievert you know tissue factors 1 + + + align:start position:0% +1 millisievert you know tissue factors 1 +gamma radiation quality factors 1 that's + + align:start position:0% +gamma radiation quality factors 1 that's + + + align:start position:0% +gamma radiation quality factors 1 that's +1 millisievert that's 20 years of + + align:start position:0% +1 millisievert that's 20 years of + + + align:start position:0% +1 millisievert that's 20 years of +exposure 20 years of allowed exposure at + + align:start position:0% +exposure 20 years of allowed exposure at + + + align:start position:0% +exposure 20 years of allowed exposure at +the same time or 10 years of exposure at + + align:start position:0% +the same time or 10 years of exposure at + + + align:start position:0% +the same time or 10 years of exposure at +the same time we're a hundred micro + + align:start position:0% +the same time we're a hundred micro + + + align:start position:0% +the same time we're a hundred micro +sievert exposure at once has been said + + align:start position:0% +sievert exposure at once has been said + + + align:start position:0% +sievert exposure at once has been said +to say maybe that's the onset of + + align:start position:0% +to say maybe that's the onset of + + + align:start position:0% +to say maybe that's the onset of +detectable amount of damage pretty + + align:start position:0% +detectable amount of damage pretty + + + align:start position:0% +detectable amount of damage pretty +difficult and our sources of data for + + align:start position:0% +difficult and our sources of data for + + + align:start position:0% +difficult and our sources of data for +these doses are a lot smaller is that + + align:start position:0% +these doses are a lot smaller is that + + + align:start position:0% +these doses are a lot smaller is that +the key with the exception of very high + + align:start position:0% +the key with the exception of very high + + + align:start position:0% +the key with the exception of very high +radiations than we need to make any real + + align:start position:0% +radiations than we need to make any real + + + align:start position:0% +radiations than we need to make any real +conclusions the largest sample size we + + align:start position:0% +conclusions the largest sample size we + + + align:start position:0% +conclusions the largest sample size we +have besides smokers would be atomic + + align:start position:0% +have besides smokers would be atomic + + + align:start position:0% +have besides smokers would be atomic +bomb survivors so folks have followed + + align:start position:0% +bomb survivors so folks have followed + + + align:start position:0% +bomb survivors so folks have followed +all of the survivors of the Hiroshima + + align:start position:0% +all of the survivors of the Hiroshima + + + align:start position:0% +all of the survivors of the Hiroshima +and Nagasaki bombings not just people + + align:start position:0% +and Nagasaki bombings not just people + + + align:start position:0% +and Nagasaki bombings not just people +nearby but in the surrounding + + align:start position:0% +nearby but in the surrounding + + + align:start position:0% +nearby but in the surrounding +countryside and tried to follow how many + + align:start position:0% +countryside and tried to follow how many + + + align:start position:0% +countryside and tried to follow how many +excess cancers were there as a result of + + align:start position:0% +excess cancers were there as a result of + + + align:start position:0% +excess cancers were there as a result of +the radiation for anyone exposed within + + align:start position:0% +the radiation for anyone exposed within + + + align:start position:0% +the radiation for anyone exposed within +3 kilometers for less than 5 milligram + + align:start position:0% + + + + align:start position:0% + +so by following this group of people and + + align:start position:0% +so by following this group of people and + + + align:start position:0% +so by following this group of people and +finding out how many of them got cancer + + align:start position:0% +finding out how many of them got cancer + + + align:start position:0% +finding out how many of them got cancer +compared to control groups you can try + + align:start position:0% +compared to control groups you can try + + + align:start position:0% +compared to control groups you can try +and figure out how much extra cancer was + + align:start position:0% +and figure out how much extra cancer was + + + align:start position:0% +and figure out how much extra cancer was +due to radiation and to graph this this + + align:start position:0% +due to radiation and to graph this this + + + align:start position:0% +due to radiation and to graph this this +is actually in the I think the ICRP + + align:start position:0% +is actually in the I think the ICRP + + + align:start position:0% +is actually in the I think the ICRP +publication graphing the amount of + + align:start position:0% +publication graphing the amount of + + + align:start position:0% +publication graphing the amount of +relative risk or to use the words from + + align:start position:0% +relative risk or to use the words from + + + align:start position:0% +relative risk or to use the words from +the last studies we saw the odds ratio + + align:start position:0% +the last studies we saw the odds ratio + + + align:start position:0% +the last studies we saw the odds ratio +the o.r of getting cancer an odds ratio + + align:start position:0% +the o.r of getting cancer an odds ratio + + + align:start position:0% +the o.r of getting cancer an odds ratio +of 1 means exactly the same amount of + + align:start position:0% +of 1 means exactly the same amount of + + + align:start position:0% +of 1 means exactly the same amount of +risk with vs. without the radiation and + + align:start position:0% +risk with vs. without the radiation and + + + align:start position:0% +risk with vs. without the radiation and +the actual raw data points are plotted + + align:start position:0% +the actual raw data points are plotted + + + align:start position:0% +the actual raw data points are plotted +here and there's a couple of lines drawn + + align:start position:0% +here and there's a couple of lines drawn + + + align:start position:0% +here and there's a couple of lines drawn +through here and this is the source of a + + align:start position:0% +through here and this is the source of a + + + align:start position:0% +through here and this is the source of a +lot of the controversy behind radiation + + align:start position:0% +lot of the controversy behind radiation + + + align:start position:0% +lot of the controversy behind radiation +damage nowadays the black line is the + + align:start position:0% +damage nowadays the black line is the + + + align:start position:0% +damage nowadays the black line is the +LNT or the linear no-threshold model + + align:start position:0% +LNT or the linear no-threshold model + + + align:start position:0% +LNT or the linear no-threshold model +which is a hypothesis that says every + + align:start position:0% +which is a hypothesis that says every + + + align:start position:0% +which is a hypothesis that says every +amount of radiation is bad and it is + + align:start position:0% +amount of radiation is bad and it is + + + align:start position:0% +amount of radiation is bad and it is +linear with dose I for one don't believe + + align:start position:0% +linear with dose I for one don't believe + + + align:start position:0% +linear with dose I for one don't believe +this model this is to me a fear-based + + align:start position:0% +this model this is to me a fear-based + + + align:start position:0% +this model this is to me a fear-based +model it's certainly easy to make policy + + align:start position:0% +model it's certainly easy to make policy + + + align:start position:0% +model it's certainly easy to make policy +based on this because you can I think + + align:start position:0% +based on this because you can I think + + + align:start position:0% +based on this because you can I think +your average congressman can understand + + align:start position:0% +your average congressman can understand + + + align:start position:0% +your average congressman can understand +a linear graph not sure whether they + + align:start position:0% +a linear graph not sure whether they + + + align:start position:0% +a linear graph not sure whether they +could understand p-values and statistics + + align:start position:0% +could understand p-values and statistics + + + align:start position:0% +could understand p-values and statistics +but there + + align:start position:0% +but there + + + align:start position:0% +but there +have to that's what they asked + + align:start position:0% +have to that's what they asked + + + align:start position:0% +have to that's what they asked +scientists to testify about when you + + align:start position:0% +scientists to testify about when you + + + align:start position:0% +scientists to testify about when you +look at the actual data there's this + + align:start position:0% +look at the actual data there's this + + + align:start position:0% +look at the actual data there's this +kind of funky shape line along with plus + + align:start position:0% +kind of funky shape line along with plus + + + align:start position:0% +kind of funky shape line along with plus +or minus 1 Sigma error bars doesn't + + align:start position:0% +or minus 1 Sigma error bars doesn't + + + align:start position:0% +or minus 1 Sigma error bars doesn't +really show a linear threshold does it + + align:start position:0% +really show a linear threshold does it + + + align:start position:0% +really show a linear threshold does it +it actually looks like it might be super + + align:start position:0% +it actually looks like it might be super + + + align:start position:0% +it actually looks like it might be super +linear for very small doses and then it + + align:start position:0% +linear for very small doses and then it + + + align:start position:0% +linear for very small doses and then it +tails off and then it picks up again but + + align:start position:0% +tails off and then it picks up again but + + + align:start position:0% +tails off and then it picks up again but +this right here is a zoom in of this + + align:start position:0% +this right here is a zoom in of this + + + align:start position:0% +this right here is a zoom in of this +data rich area of the graph it actually + + align:start position:0% +data rich area of the graph it actually + + + align:start position:0% +data rich area of the graph it actually +looks like for really high doses it + + align:start position:0% +looks like for really high doses it + + + align:start position:0% +looks like for really high doses it +might be a little super linear again + + align:start position:0% +might be a little super linear again + + + align:start position:0% +might be a little super linear again +where things get much much worse + + align:start position:0% +where things get much much worse + + + align:start position:0% +where things get much much worse +hopefully you don't have anyone exposed + + align:start position:0% +hopefully you don't have anyone exposed + + + align:start position:0% +hopefully you don't have anyone exposed +to let's say to gray of dose but the + + align:start position:0% +to let's say to gray of dose but the + + + align:start position:0% +to let's say to gray of dose but the +real controversies here in the small + + align:start position:0% +real controversies here in the small + + + align:start position:0% +real controversies here in the small +dose region we don't really know enough + + align:start position:0% +dose region we don't really know enough + + + align:start position:0% +dose region we don't really know enough +to say whether very small doses are + + align:start position:0% +to say whether very small doses are + + + align:start position:0% +to say whether very small doses are +hurtful or not or harmful or not in fact + + align:start position:0% +hurtful or not or harmful or not in fact + + + align:start position:0% +hurtful or not or harmful or not in fact +they might even be helpful so you guys I + + align:start position:0% +they might even be helpful so you guys I + + + align:start position:0% +they might even be helpful so you guys I +think with the first class that I know + + align:start position:0% +think with the first class that I know + + + align:start position:0% +think with the first class that I know +you had you last year no guys remember + + align:start position:0% +you had you last year no guys remember + + + align:start position:0% +you had you last year no guys remember +the answer to what is the idea that a + + align:start position:0% +the answer to what is the idea that a + + + align:start position:0% +the answer to what is the idea that a +little bit of radiation might be good + + align:start position:0% +little bit of radiation might be good + + + align:start position:0% +little bit of radiation might be good +for you from the cache class and you + + align:start position:0% +for you from the cache class and you + + + align:start position:0% +for you from the cache class and you +remember what that's called hormesis + + align:start position:0% +remember what that's called hormesis + + + align:start position:0% +remember what that's called hormesis +yeah this idea that a little bit of + + align:start position:0% +yeah this idea that a little bit of + + + align:start position:0% +yeah this idea that a little bit of +something bad could actually be good for + + align:start position:0% +something bad could actually be good for + + + align:start position:0% +something bad could actually be good for +you this is also a theory and to my + + align:start position:0% +you this is also a theory and to my + + + align:start position:0% +you this is also a theory and to my +knowledge has not been proven to be true + + align:start position:0% +knowledge has not been proven to be true + + + align:start position:0% +knowledge has not been proven to be true +but it is evident in some other studies + + align:start position:0% +but it is evident in some other studies + + + align:start position:0% +but it is evident in some other studies +along with different fields of research + + align:start position:0% +along with different fields of research + + + align:start position:0% +along with different fields of research +beyond radiation for example there had + + align:start position:0% +beyond radiation for example there had + + + align:start position:0% +beyond radiation for example there had +been an experiment where rats were kept + + align:start position:0% +been an experiment where rats were kept + + + align:start position:0% +been an experiment where rats were kept +in shielded lead boxes as opposed to + + align:start position:0% +in shielded lead boxes as opposed to + + + align:start position:0% +in shielded lead boxes as opposed to +just out on the bench where they got + + align:start position:0% +just out on the bench where they got + + + align:start position:0% +just out on the bench where they got +less radiation and the ward the rats + + align:start position:0% +less radiation and the ward the rats + + + align:start position:0% +less radiation and the ward the rats +that had less radiation had less + + align:start position:0% +that had less radiation had less + + + align:start position:0% +that had less radiation had less +incidence of cancer + + align:start position:0% +incidence of cancer + + + align:start position:0% +incidence of cancer +however it's extremely difficult to + + align:start position:0% +however it's extremely difficult to + + + align:start position:0% +however it's extremely difficult to +remove all other confounding variables + + align:start position:0% +remove all other confounding variables + + + align:start position:0% +remove all other confounding variables +from this data that's the trick there is + + align:start position:0% +from this data that's the trick there is + + + align:start position:0% +from this data that's the trick there is +when trying to tease out are small + + align:start position:0% +when trying to tease out are small + + + align:start position:0% +when trying to tease out are small +amounts of radiation bad for you you + + align:start position:0% +amounts of radiation bad for you you + + + align:start position:0% +amounts of radiation bad for you you +also have to tease out confounding + + align:start position:0% +also have to tease out confounding + + + align:start position:0% +also have to tease out confounding +variables or other things that might be + + align:start position:0% +variables or other things that might be + + + align:start position:0% +variables or other things that might be +obscuring your data why the harmonic + + align:start position:0% +obscuring your data why the harmonic + + + align:start position:0% +obscuring your data why the harmonic +effect so what are some of the ideas + + align:start position:0% +effect so what are some of the ideas + + + align:start position:0% +effect so what are some of the ideas +behind why hormesis might happen so + + align:start position:0% +behind why hormesis might happen so + + + align:start position:0% +behind why hormesis might happen so +there are some theories and some some + + align:start position:0% +there are some theories and some some + + + align:start position:0% +there are some theories and some some +controlled studies showing that if you'e + + align:start position:0% +controlled studies showing that if you'e + + + align:start position:0% +controlled studies showing that if you'e +radiate cells very lightly they mount an + + align:start position:0% +radiate cells very lightly they mount an + + + align:start position:0% +radiate cells very lightly they mount an +immune response there are proteins and + + align:start position:0% +immune response there are proteins and + + + align:start position:0% +immune response there are proteins and +things circulating throughout your cells + + align:start position:0% +things circulating throughout your cells + + + align:start position:0% +things circulating throughout your cells +that are there too + + align:start position:0% +that are there too + + + align:start position:0% +that are there too +our DNA and if you stimulate the + + align:start position:0% +our DNA and if you stimulate the + + + align:start position:0% +our DNA and if you stimulate the +production of those repair mechanisms + + align:start position:0% +production of those repair mechanisms + + + align:start position:0% +production of those repair mechanisms +then the repair will be more rapid given + + align:start position:0% +then the repair will be more rapid given + + + align:start position:0% +then the repair will be more rapid given +the same amount of stimulus so in this + + align:start position:0% +the same amount of stimulus so in this + + + align:start position:0% +the same amount of stimulus so in this +case there are let's see I'm just gonna + + align:start position:0% +case there are let's see I'm just gonna + + + align:start position:0% +case there are let's see I'm just gonna +say proteins I can't say anything more + + align:start position:0% +say proteins I can't say anything more + + + align:start position:0% +say proteins I can't say anything more +that will actually travel along DNA + + align:start position:0% +that will actually travel along DNA + + + align:start position:0% +that will actually travel along DNA +looking for certain types of kinks or + + align:start position:0% +looking for certain types of kinks or + + + align:start position:0% +looking for certain types of kinks or +breaks and repair them + + align:start position:0% +breaks and repair them + + + align:start position:0% +breaks and repair them +if those repairs happen before cell + + align:start position:0% +if those repairs happen before cell + + + align:start position:0% +if those repairs happen before cell +division than the mutations avoided if + + align:start position:0% +division than the mutations avoided if + + + align:start position:0% +division than the mutations avoided if +you have more of those repair mechanisms + + align:start position:0% +you have more of those repair mechanisms + + + align:start position:0% +you have more of those repair mechanisms +it takes a little bit more energy to + + align:start position:0% +it takes a little bit more energy to + + + align:start position:0% +it takes a little bit more energy to +make them but you also have less of a + + align:start position:0% +make them but you also have less of a + + + align:start position:0% +make them but you also have less of a +chance of a mutation manifesting itself + + align:start position:0% +chance of a mutation manifesting itself + + + align:start position:0% +chance of a mutation manifesting itself +past division number one so this is kind + + align:start position:0% +past division number one so this is kind + + + align:start position:0% +past division number one so this is kind +of the the cellular level idea why might + + align:start position:0% +of the the cellular level idea why might + + + align:start position:0% +of the the cellular level idea why might +hormesis be true because you stimulate + + align:start position:0% +hormesis be true because you stimulate + + + align:start position:0% +hormesis be true because you stimulate +your body's ability to defend against + + align:start position:0% +your body's ability to defend against + + + align:start position:0% +your body's ability to defend against +this kind of stuff and so there you go + + align:start position:0% +this kind of stuff and so there you go + + + align:start position:0% +this kind of stuff and so there you go +cells can actually signal each other so + + align:start position:0% +cells can actually signal each other so + + + align:start position:0% +cells can actually signal each other so +let's say a cell undergoes DNA damage + + align:start position:0% +let's say a cell undergoes DNA damage + + + align:start position:0% +let's say a cell undergoes DNA damage +and can't divide these cells can + + align:start position:0% +and can't divide these cells can + + + align:start position:0% +and can't divide these cells can +actually send what they call kill + + align:start position:0% +actually send what they call kill + + + align:start position:0% +actually send what they call kill +signals in the intercellular space to + + align:start position:0% +signals in the intercellular space to + + + align:start position:0% +signals in the intercellular space to +the nearby cells stimulating them to + + align:start position:0% +the nearby cells stimulating them to + + + align:start position:0% +the nearby cells stimulating them to +mount some sort of response either + + align:start position:0% +mount some sort of response either + + + align:start position:0% +mount some sort of response either +release something or divide more to make + + align:start position:0% +release something or divide more to make + + + align:start position:0% +release something or divide more to make +up for the dead cells which could be + + align:start position:0% +up for the dead cells which could be + + + align:start position:0% +up for the dead cells which could be +good or which could be bad if you make + + align:start position:0% +good or which could be bad if you make + + + align:start position:0% +good or which could be bad if you make +more of these DNA repair mechanisms + + align:start position:0% +more of these DNA repair mechanisms + + + align:start position:0% +more of these DNA repair mechanisms +that's probably a good thing + + align:start position:0% +that's probably a good thing + + + align:start position:0% +that's probably a good thing +if you stimulate the nearby cells to + + align:start position:0% +if you stimulate the nearby cells to + + + align:start position:0% +if you stimulate the nearby cells to +divide faster well what are the two + + align:start position:0% +divide faster well what are the two + + + align:start position:0% +divide faster well what are the two +things that could happen yeah more + + align:start position:0% +things that could happen yeah more + + + align:start position:0% +things that could happen yeah more +mutations + + align:start position:0% +mutations + + + align:start position:0% +mutations +why do you say more mutations + + align:start position:0% + + + + align:start position:0% + +exactly yeah if there are cells nearby + + align:start position:0% +exactly yeah if there are cells nearby + + + align:start position:0% +exactly yeah if there are cells nearby +that have been exposed or mutated and + + align:start position:0% +that have been exposed or mutated and + + + align:start position:0% +that have been exposed or mutated and +you induce faster division you may + + align:start position:0% +you induce faster division you may + + + align:start position:0% +you induce faster division you may +induce faster incidence of the what is + + align:start position:0% +induce faster incidence of the what is + + + align:start position:0% +induce faster incidence of the what is +it of manifestation of this mutation but + + align:start position:0% +it of manifestation of this mutation but + + + align:start position:0% +it of manifestation of this mutation but +also if let's say a few cells die and + + align:start position:0% +also if let's say a few cells die and + + + align:start position:0% +also if let's say a few cells die and +the other ones divide to make up take up + + align:start position:0% +the other ones divide to make up take up + + + align:start position:0% +the other ones divide to make up take up +the slack that might be a good thing + + align:start position:0% +the slack that might be a good thing + + + align:start position:0% +the slack that might be a good thing +this is a normal way that you repair + + align:start position:0% +this is a normal way that you repair + + + align:start position:0% +this is a normal way that you repair +injury is upon cell death the cells + + align:start position:0% +injury is upon cell death the cells + + + align:start position:0% +injury is upon cell death the cells +nearby divide faster fill in the gaps + + align:start position:0% +nearby divide faster fill in the gaps + + + align:start position:0% +nearby divide faster fill in the gaps +and try and repair the tissue so it's + + align:start position:0% +and try and repair the tissue so it's + + + align:start position:0% +and try and repair the tissue so it's +both a good thing and can be a bad thing + + align:start position:0% +both a good thing and can be a bad thing + + + align:start position:0% +both a good thing and can be a bad thing +depending on what the nearby cells have + + align:start position:0% +depending on what the nearby cells have + + + align:start position:0% +depending on what the nearby cells have +been exposed to and so there's also this + + align:start position:0% +been exposed to and so there's also this + + + align:start position:0% +been exposed to and so there's also this +they call that the bystander effect + + align:start position:0% +they call that the bystander effect + + + align:start position:0% +they call that the bystander effect +where interestingly you can have + + align:start position:0% +where interestingly you can have + + + align:start position:0% +where interestingly you can have +biological effects in cells that receive + + align:start position:0% +biological effects in cells that receive + + + align:start position:0% +biological effects in cells that receive +no radiation exposure if they're near + + align:start position:0% +no radiation exposure if they're near + + + align:start position:0% +no radiation exposure if they're near +cells that have received radiation + + align:start position:0% +cells that have received radiation + + + align:start position:0% +cells that have received radiation +exposure there are some awesome + + align:start position:0% +exposure there are some awesome + + + align:start position:0% +exposure there are some awesome +experiments showing this we had one here + + align:start position:0% +experiments showing this we had one here + + + align:start position:0% +experiments showing this we had one here +back when we had a professor that did + + align:start position:0% +back when we had a professor that did + + + align:start position:0% +back when we had a professor that did +medical physics she had created an + + align:start position:0% +medical physics she had created an + + + align:start position:0% +medical physics she had created an +accelerator with a micro beam like a + + align:start position:0% +accelerator with a micro beam like a + + + align:start position:0% +accelerator with a micro beam like a +micron wide proton beam when you could + + align:start position:0% +micron wide proton beam when you could + + + align:start position:0% +micron wide proton beam when you could +radiate single cells and watch what + + align:start position:0% +radiate single cells and watch what + + + align:start position:0% +radiate single cells and watch what +happens to the cells nearby so to study + + align:start position:0% +happens to the cells nearby so to study + + + align:start position:0% +happens to the cells nearby so to study +in a controlled way this bystander + + align:start position:0% +in a controlled way this bystander + + + align:start position:0% +in a controlled way this bystander +effect so if you were radiate one cell + + align:start position:0% +effect so if you were radiate one cell + + + align:start position:0% +effect so if you were radiate one cell +on a glass slide how did the other ones + + align:start position:0% +on a glass slide how did the other ones + + + align:start position:0% +on a glass slide how did the other ones +respond so you know which one was + + align:start position:0% +respond so you know which one was + + + align:start position:0% +respond so you know which one was +irradiated and you can watch what + + align:start position:0% +irradiated and you can watch what + + + align:start position:0% +irradiated and you can watch what +happens to the other ones + + align:start position:0% +happens to the other ones + + + align:start position:0% +happens to the other ones +pretty slick that accelerator actually + + align:start position:0% +pretty slick that accelerator actually + + + align:start position:0% +pretty slick that accelerator actually +parts of that live on on the Dante + + align:start position:0% +parts of that live on on the Dante + + + align:start position:0% +parts of that live on on the Dante +accelerator that we now use for physics + + align:start position:0% +accelerator that we now use for physics + + + align:start position:0% +accelerator that we now use for physics +and things but a lot of the parts from + + align:start position:0% +and things but a lot of the parts from + + + align:start position:0% +and things but a lot of the parts from +those machines are still here just the + + align:start position:0% +those machines are still here just the + + + align:start position:0% +those machines are still here just the +micro beams and the cell parts aren't + + align:start position:0% +micro beams and the cell parts aren't + + + align:start position:0% +micro beams and the cell parts aren't +and then I highlighted a few of these + + align:start position:0% +and then I highlighted a few of these + + + align:start position:0% +and then I highlighted a few of these +passages in sort of the the DNA damage + + align:start position:0% +passages in sort of the the DNA damage + + + align:start position:0% +passages in sort of the the DNA damage +bystander effect one of the reasons is + + align:start position:0% +bystander effect one of the reasons is + + + align:start position:0% +bystander effect one of the reasons is +when cells nearby divide they scale up + + align:start position:0% +when cells nearby divide they scale up + + + align:start position:0% +when cells nearby divide they scale up +their metabolism they have to burn more + + align:start position:0% +their metabolism they have to burn more + + + align:start position:0% +their metabolism they have to burn more +energy in order to go undergo division + + align:start position:0% +energy in order to go undergo division + + + align:start position:0% +energy in order to go undergo division +faster and that can undergo what's + + align:start position:0% +faster and that can undergo what's + + + align:start position:0% +faster and that can undergo what's +called oxidative metabolism cells can + + align:start position:0% +called oxidative metabolism cells can + + + align:start position:0% +called oxidative metabolism cells can +can produce energy aerobic Lior + + align:start position:0% +can produce energy aerobic Lior + + + align:start position:0% +can produce energy aerobic Lior +anaerobically when you're dividing very + + align:start position:0% +anaerobically when you're dividing very + + + align:start position:0% +anaerobically when you're dividing very +quickly all of a sudden you start + + align:start position:0% +quickly all of a sudden you start + + + align:start position:0% +quickly all of a sudden you start +burning more oxygen to divide faster to + + align:start position:0% +burning more oxygen to divide faster to + + + align:start position:0% +burning more oxygen to divide faster to +do whatever you have to do and that + + align:start position:0% +do whatever you have to do and that + + + align:start position:0% +do whatever you have to do and that +oxidative metabolism also creates free + + align:start position:0% +oxidative metabolism also creates free + + + align:start position:0% +oxidative metabolism also creates free +radicals just from normal wear and tear + + align:start position:0% +radicals just from normal wear and tear + + + align:start position:0% +radicals just from normal wear and tear +to your cells and those oxidative + + align:start position:0% +to your cells and those oxidative + + + align:start position:0% +to your cells and those oxidative +byproducts may also induce mutations in + + align:start position:0% +byproducts may also induce mutations in + + + align:start position:0% +byproducts may also induce mutations in +the same + + align:start position:0% +the same + + + align:start position:0% +the same +primary way that radiation does + + align:start position:0% +primary way that radiation does + + + align:start position:0% +primary way that radiation does +radiation does hydrolysis makes + + align:start position:0% +radiation does hydrolysis makes + + + align:start position:0% +radiation does hydrolysis makes +oxidative species that damage DNA + + align:start position:0% +oxidative species that damage DNA + + + align:start position:0% +oxidative species that damage DNA +chemical oxidative metabolism can + + align:start position:0% +chemical oxidative metabolism can + + + align:start position:0% +chemical oxidative metabolism can +produce the same sorts of things that + + align:start position:0% +produce the same sorts of things that + + + align:start position:0% +produce the same sorts of things that +can damage DNA in the same way just a + + align:start position:0% +can damage DNA in the same way just a + + + align:start position:0% +can damage DNA in the same way just a +different initial effect I'm gonna stop + + align:start position:0% +different initial effect I'm gonna stop + + + align:start position:0% +different initial effect I'm gonna stop +here even though we only have a few + + align:start position:0% +here even though we only have a few + + + align:start position:0% +here even though we only have a few +slides to go because it's exactly five + + align:start position:0% +slides to go because it's exactly five + + + align:start position:0% +slides to go because it's exactly five +of + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/z_QOKNpEVro.txt b/z_QOKNpEVro.txt new file mode 100644 index 0000000000000000000000000000000000000000..cf1bfaa618eba9f42ebfc49f4f4d3887070e8d06 --- /dev/null +++ b/z_QOKNpEVro.txt @@ -0,0 +1,763 @@ +align:start position:0% + +I mean there are a couple of different + + align:start position:0% +I mean there are a couple of different + + + align:start position:0% +I mean there are a couple of different +approaches to teaching this class. One + + align:start position:0% +approaches to teaching this class. One + + + align:start position:0% +approaches to teaching this class. One +is uh to make it fun. Uh I really like + + align:start position:0% +is uh to make it fun. Uh I really like + + + align:start position:0% +is uh to make it fun. Uh I really like +to make uh material uh as engaging and + + align:start position:0% +to make uh material uh as engaging and + + + align:start position:0% +to make uh material uh as engaging and +as accessible as possible especially if + + align:start position:0% +as accessible as possible especially if + + + align:start position:0% +as accessible as possible especially if +you have relatively little experience in + + align:start position:0% +you have relatively little experience in + + + align:start position:0% +you have relatively little experience in +algorithms. You've just taken 6006 + + align:start position:0% +algorithms. You've just taken 6006 + + + align:start position:0% +algorithms. You've just taken 6006 +uh and these some of these uh algorithms + + align:start position:0% +uh and these some of these uh algorithms + + + align:start position:0% +uh and these some of these uh algorithms +get really complicated and they're hard + + align:start position:0% +get really complicated and they're hard + + + align:start position:0% +get really complicated and they're hard +to understand. uh and uh you you makes + + align:start position:0% +to understand. uh and uh you you makes + + + align:start position:0% +to understand. uh and uh you you makes +you wonder how did they ever come up + + align:start position:0% +you wonder how did they ever come up + + + align:start position:0% +you wonder how did they ever come up +with that and so I like to talk about + + align:start position:0% +with that and so I like to talk about + + + align:start position:0% +with that and so I like to talk about +that um in some of the lectures uh I'll + + align:start position:0% +that um in some of the lectures uh I'll + + + align:start position:0% +that um in some of the lectures uh I'll +kind of give an idea of how they might + + align:start position:0% +kind of give an idea of how they might + + + align:start position:0% +kind of give an idea of how they might +have gotten there. It's like oh we could + + align:start position:0% +have gotten there. It's like oh we could + + + align:start position:0% +have gotten there. It's like oh we could +start with this really simple step. It's + + align:start position:0% +start with this really simple step. It's + + + align:start position:0% +start with this really simple step. It's +really inefficient but at least it + + align:start position:0% +really inefficient but at least it + + + align:start position:0% +really inefficient but at least it +solves a problem but then we add this + + align:start position:0% +solves a problem but then we add this + + + align:start position:0% +solves a problem but then we add this +extra thing and this extra thing and + + align:start position:0% +extra thing and this extra thing and + + + align:start position:0% +extra thing and this extra thing and +eventually you get to the really fast + + align:start position:0% +eventually you get to the really fast + + + align:start position:0% +eventually you get to the really fast +solution. So it's less of a mystery of + + align:start position:0% +solution. So it's less of a mystery of + + + align:start position:0% +solution. So it's less of a mystery of +how you got there or how the original + + align:start position:0% +how you got there or how the original + + + align:start position:0% +how you got there or how the original +researchers got there. And uh I also try + + align:start position:0% +researchers got there. And uh I also try + + + align:start position:0% +researchers got there. And uh I also try +to remind students when especially in + + align:start position:0% +to remind students when especially in + + + align:start position:0% +to remind students when especially in +the harder topics that this is not easy + + align:start position:0% +the harder topics that this is not easy + + + align:start position:0% +the harder topics that this is not easy +stuff and you should think about a + + align:start position:0% +stuff and you should think about a + + + align:start position:0% +stuff and you should think about a +little more you know do the problem sets + + align:start position:0% +little more you know do the problem sets + + + align:start position:0% +little more you know do the problem sets +and you'll uh learn it figure it out at + + align:start position:0% +and you'll uh learn it figure it out at + + + align:start position:0% +and you'll uh learn it figure it out at +a deeper level. But a lot of this + + align:start position:0% +a deeper level. But a lot of this + + + align:start position:0% +a deeper level. But a lot of this +material is hard and I think being + + align:start position:0% +material is hard and I think being + + + align:start position:0% +material is hard and I think being +honest about that makes it uh more + + align:start position:0% +honest about that makes it uh more + + + align:start position:0% +honest about that makes it uh more +reasonable. students don't feel bad for + + align:start position:0% +reasonable. students don't feel bad for + + + align:start position:0% +reasonable. students don't feel bad for +thinking that it's hard because the + + align:start position:0% +thinking that it's hard because the + + + align:start position:0% +thinking that it's hard because the +first time you learn it, it is hard. Um, + + align:start position:0% +first time you learn it, it is hard. Um, + + + align:start position:0% +first time you learn it, it is hard. Um, +but the whole algorithmic way of + + align:start position:0% +but the whole algorithmic way of + + + align:start position:0% +but the whole algorithmic way of +thinking of setting up a problem, what + + align:start position:0% +thinking of setting up a problem, what + + + align:start position:0% +thinking of setting up a problem, what +should the input and the output be? And + + align:start position:0% +should the input and the output be? And + + + align:start position:0% +should the input and the output be? And +then thinking about all different + + align:start position:0% +then thinking about all different + + + align:start position:0% +then thinking about all different +solutions for how to fill in the middle, + + align:start position:0% +solutions for how to fill in the middle, + + + align:start position:0% +solutions for how to fill in the middle, +um, I think is a really powerful + + align:start position:0% +um, I think is a really powerful + + + align:start position:0% +um, I think is a really powerful +perspective and it can shape pretty much + + align:start position:0% +perspective and it can shape pretty much + + + align:start position:0% +perspective and it can shape pretty much +your entire life, but especially if + + align:start position:0% +your entire life, but especially if + + + align:start position:0% +your entire life, but especially if +you're doing computer science, um, it's + + align:start position:0% +you're doing computer science, um, it's + + + align:start position:0% +you're doing computer science, um, it's +a really useful way of thinking. And + + align:start position:0% +a really useful way of thinking. And + + + align:start position:0% +a really useful way of thinking. And +I've gotten lots of letters later from + + align:start position:0% +I've gotten lots of letters later from + + + align:start position:0% +I've gotten lots of letters later from +students where uh you know they're doing + + align:start position:0% +students where uh you know they're doing + + + align:start position:0% +students where uh you know they're doing +some job some computer thing and they + + align:start position:0% +some job some computer thing and they + + + align:start position:0% +some job some computer thing and they +ran into this problem and then they + + align:start position:0% +ran into this problem and then they + + + align:start position:0% +ran into this problem and then they +discover and then they looked back at + + align:start position:0% +discover and then they looked back at + + + align:start position:0% +discover and then they looked back at +their notes and said oh this is the + + align:start position:0% +their notes and said oh this is the + + + align:start position:0% +their notes and said oh this is the +right data structure I should have you I + + align:start position:0% +right data structure I should have you I + + + align:start position:0% +right data structure I should have you I +should use now and they solve it and + + align:start position:0% +should use now and they solve it and + + + align:start position:0% +should use now and they solve it and +they tell me about it and it's kind of + + align:start position:0% +they tell me about it and it's kind of + + + align:start position:0% +they tell me about it and it's kind of +exciting to see uh years later that + + align:start position:0% +exciting to see uh years later that + + + align:start position:0% +exciting to see uh years later that +the diff the way of thinking and lots of + + align:start position:0% +the diff the way of thinking and lots of + + + align:start position:0% +the diff the way of thinking and lots of +the solutions and techniques you see in + + align:start position:0% +the solutions and techniques you see in + + + align:start position:0% +the solutions and techniques you see in +this class really are useful out there + + align:start position:0% +this class really are useful out there + + + align:start position:0% +this class really are useful out there +in the world. So, it's a it's a useful + + align:start position:0% +in the world. So, it's a it's a useful + + + align:start position:0% +in the world. So, it's a it's a useful +class to take you. It's it's a + + align:start position:0% +class to take you. It's it's a + + + align:start position:0% +class to take you. It's it's a +relatively hard class. The exams are are + + align:start position:0% +relatively hard class. The exams are are + + + align:start position:0% +relatively hard class. The exams are are +challenging and we try to make them not + + align:start position:0% +challenging and we try to make them not + + + align:start position:0% +challenging and we try to make them not +super challenging, but it's hard + + align:start position:0% +super challenging, but it's hard + + + align:start position:0% +super challenging, but it's hard +whenever especially whenever creativity + + align:start position:0% +whenever especially whenever creativity + + + align:start position:0% +whenever especially whenever creativity +is involved. Um it's hard to do that + + align:start position:0% +is involved. Um it's hard to do that + + + align:start position:0% +is involved. Um it's hard to do that +live in an exam. So uh students may not + + align:start position:0% +live in an exam. So uh students may not + + + align:start position:0% +live in an exam. So uh students may not +perform super well in the class but + + align:start position:0% +perform super well in the class but + + + align:start position:0% +perform super well in the class but +still they get the idea that this is a + + align:start position:0% +still they get the idea that this is a + + + align:start position:0% +still they get the idea that this is a +way to approach problems and they uh + + align:start position:0% +way to approach problems and they uh + + + align:start position:0% +way to approach problems and they uh +understand some of the techniques um and + + align:start position:0% +understand some of the techniques um and + + + align:start position:0% +understand some of the techniques um and +over time they can sort of fill in + + align:start position:0% +over time they can sort of fill in + + + align:start position:0% +over time they can sort of fill in +whatever holes they left behind and say + + align:start position:0% +whatever holes they left behind and say + + + align:start position:0% +whatever holes they left behind and say +you know this seems like a problem where + + align:start position:0% +you know this seems like a problem where + + + align:start position:0% +you know this seems like a problem where +dynamic programming would be really + + align:start position:0% +dynamic programming would be really + + + align:start position:0% +dynamic programming would be really +useful. It's time I really learn dynamic + + align:start position:0% +useful. It's time I really learn dynamic + + + align:start position:0% +useful. It's time I really learn dynamic +programming. Um, dynamic programming is + + align:start position:0% +programming. Um, dynamic programming is + + + align:start position:0% +programming. Um, dynamic programming is +one that we actually teach both in 006 + + align:start position:0% +one that we actually teach both in 006 + + + align:start position:0% +one that we actually teach both in 006 +and 046 because it's really it's + + align:start position:0% +and 046 because it's really it's + + + align:start position:0% +and 046 because it's really it's +conceptually weird. Um, + + align:start position:0% +conceptually weird. Um, + + + align:start position:0% +conceptually weird. Um, +it's actually really easy once you + + align:start position:0% +it's actually really easy once you + + + align:start position:0% +it's actually really easy once you +understand it, but getting to that point + + align:start position:0% +understand it, but getting to that point + + + align:start position:0% +understand it, but getting to that point +of understanding is really tough. So, we + + align:start position:0% +of understanding is really tough. So, we + + + align:start position:0% +of understanding is really tough. So, we +spend a lot of time on it. Uh, so the + + align:start position:0% +spend a lot of time on it. Uh, so the + + + align:start position:0% +spend a lot of time on it. Uh, so the +the idea is the more exposure you get to + + align:start position:0% +the idea is the more exposure you get to + + + align:start position:0% +the idea is the more exposure you get to +it, the clearer it will become. I think + + align:start position:0% +it, the clearer it will become. I think + + + align:start position:0% +it, the clearer it will become. I think +by the end of 6046 they have a pretty + + align:start position:0% +by the end of 6046 they have a pretty + + + align:start position:0% +by the end of 6046 they have a pretty +good idea, but if not years later if + + align:start position:0% +good idea, but if not years later if + + + align:start position:0% +good idea, but if not years later if +they come back to it, I'm sure it'll be + + align:start position:0% +they come back to it, I'm sure it'll be + + + align:start position:0% +they come back to it, I'm sure it'll be +a lot easier this this third time + + align:start position:0% +a lot easier this this third time + + + align:start position:0% +a lot easier this this third time +around. Um, so yeah, a lot of these + + align:start position:0% +around. Um, so yeah, a lot of these + + + align:start position:0% +around. Um, so yeah, a lot of these +concepts are I mean the ideas are + + align:start position:0% +concepts are I mean the ideas are + + + align:start position:0% +concepts are I mean the ideas are +actually really simple. They're just + + align:start position:0% +actually really simple. They're just + + + align:start position:0% +actually really simple. They're just +hard to + + align:start position:0% +hard to + + + align:start position:0% +hard to +shift your mind into that kind of + + align:start position:0% +shift your mind into that kind of + + + align:start position:0% +shift your mind into that kind of +mindset. Uh but once you do things + + align:start position:0% +mindset. Uh but once you do things + + + align:start position:0% +mindset. Uh but once you do things +become really clear and so hope is by + + align:start position:0% +become really clear and so hope is by + + + align:start position:0% +become really clear and so hope is by +the end of the semester they they get \ No newline at end of file